Formats: - HTML - YAML - JSON - 2026-01-29T12:05:30.066121 - next page
Query: /api/mf_newforms/?_offset=0
Show schema
  1. label: 23.1.b.a
    {'Nk2': 23, 'analytic_conductor': 0.011478495290559056, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [1, 0, -1, 1], 'artin_field_label': '3.1.23.1', 'artin_image': '6.1', 'char_conductor': 23, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [23, 2, [5], [1]], 'cm_discs': [-23], 'conrey_index': 22, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.23.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736253975, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 23, 2, -1, 2, -23]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '23.1.b.a', 'level': 23, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [23], 'level_radical': 23, 'minimal_twist': '23.1.b.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [1, 0, -1, 1], 'projective_field_label': '3.1.23.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\\cdots', 'related_objects': ['ArtinRepresentation/2.23.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-23], 'self_twist_type': 1, 'space_label': '23.1.b', 'trace_display': [-1, -1, 0, 0], 'trace_hash': 426797760822574538, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.020', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.962', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.919', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.841', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.678', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.359', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.508', 'prec': 17}, 'traces': [1, -1, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, -1, 1, 1, -1, 0, 0, 0, -1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 1, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -1, 0, 0, -2, 0, -1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 1, -2, 0, 0, 0, 2, 0, 0, 0, -1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, -1, 0, -1, 0, -1, 2, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, -1, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 2, -1, -1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 2, 0, 0, -1, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 2, 2, 0, -1, 0, -2, 0, 0, 0, 0, 1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 2, 0, 1, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, -2, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, -2, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0, 2, -1, 0, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1, 0, 1, -1, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -2, 1, 2, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, -1, 1, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, -2, 0, -2, -1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, -2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, -2, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, -2, 0, 0, 0, -1, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, -1, 0, 0, -2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, -1, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, -1, 0, -1, 2, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  2. label: 31.1.b.a
    {'Nk2': 31, 'analytic_conductor': 0.015471015391623074, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-1, 1, 0, 1], 'artin_field_label': '3.1.31.1', 'artin_image': '6.1', 'char_conductor': 31, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [31, 2, [3], [1]], 'cm_discs': [-31], 'conrey_index': 30, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.31.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736253983, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 31, 2, -1, 2, -31]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '31.1.b.a', 'level': 31, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [31], 'level_radical': 31, 'minimal_twist': '31.1.b.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [-1, 1, 0, 1], 'projective_field_label': '3.1.31.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\\cdots', 'related_objects': ['ArtinRepresentation/2.31.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-31], 'self_twist_type': 1, 'space_label': '31.1.b', 'trace_display': [-1, 0, -1, -1], 'trace_hash': 58047233262006326, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.013', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.972', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.945', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.886', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.773', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.544', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.507', 'prec': 17}, 'traces': [1, -1, 0, 0, -1, 0, -1, 1, 1, 1, 0, 0, 0, 1, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, -1, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, -1, 1, 0, 0, 2, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, -1, 0, 0, 2, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, -1, 0, 0, 1, 1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, -2, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -2, 2, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, -1, 0, 1, -2, -1, -1, 0, 0, 0, 0, 0, -1, 0, 1, 2, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, -2, 1, 0, 2, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, -1, -2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, -1, -2, -1, 0, 0, 0, 0, 0, 2, 0, 1, -1, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 1, 2, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, -1, 0, 1, 1, 0, 0, 0, -1, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, -2, 0, 2, -2, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, -1, 0, -2, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, -1, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, -1, -1, 0, 0, 0, 0, 0, -2, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 2, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 2, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, -1, 0, 1, 0, -2, -1, 0, 0, 0, -1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 2, 0, 0, 1, -2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, -2, 0, 0, -1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, -1], 'weight': 1, 'weight_parity': -1}
  3. label: 39.1.d.a
    {'Nk2': 39, 'analytic_conductor': 0.019463535492687093, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [1, 1, -1, -1, 1], 'artin_field_label': '4.0.117.1', 'artin_image': '8.3', 'char_conductor': 39, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [39, 2, [14, 28], [1, 1]], 'cm_discs': [-3, -39], 'conrey_index': 38, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.3_13.4t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207463, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 39, 4, -1, 2, -39], [1, 1, 13, 2, 1, 2, 13]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '39.1.d.a', 'level': 39, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 13], 'level_radical': 39, 'minimal_twist': '39.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [9, 3, 4, -1, 1], 'projective_field_label': '4.0.1521.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3_13.4t3.2'], 'relative_dim': 1, 'rm_discs': [13], 'self_twist_discs': [-3, -39, 13], 'self_twist_type': 3, 'space_label': '39.1.d', 'trace_display': [0, -1, 0, 0], 'trace_hash': 701519358932584307, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.021', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.951', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.080', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.800', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.313', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.193', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.761', 'prec': 17}, 'traces': [1, 0, -1, -1, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, -2, 0, 2, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0], 'weight': 1, 'weight_parity': -1}
  4. label: 44.1.d.a
    {'Nk2': 44, 'analytic_conductor': 0.021958860555852104, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [1, 1, -1, 1], 'artin_field_label': '3.1.44.1', 'artin_image': '6.1', 'char_conductor': 11, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [44, 2, [23, 13], [2, 1]], 'cm_discs': [-11], 'conrey_index': 21, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_11.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207468, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 2, -1, 2, -11]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '44.1.d.a', 'level': 44, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 11], 'level_radical': 22, 'minimal_twist': '44.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [1, 1, -1, 1], 'projective_field_label': '3.1.44.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_11.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-11], 'self_twist_type': 1, 'space_label': '44.1.d', 'trace_display': [0, -1, -1, 0], 'trace_hash': 912108308855815057, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.012', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.982', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.957', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.920', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.833', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.671', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.502', 'prec': 17}, 'traces': [1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, -1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, -1, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  5. label: 47.1.b.a
    {'Nk2': 47, 'analytic_conductor': 0.023456055593751114, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 10, 'artin_field': [1, 0, -1, 2, -2, 1], 'artin_field_label': '5.1.2209.1', 'artin_image': '10.1', 'char_conductor': 47, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [47, 2, [5], [1]], 'cm_discs': [-47], 'conrey_index': 46, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.47.5t2.1c1'], ['ArtinRepresentation/2.47.5t2.1c2']], 'field_disc': 5, 'field_disc_factorization': [[5, 1]], 'field_poly': [-1, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736253999, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 47, 2, -1, 2, -47]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '47.1.b.a', 'level': 47, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [47], 'level_radical': 47, 'minimal_twist': '47.1.b.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 2, 'projective_field': [1, 0, -1, 2, -2, 1], 'projective_field_label': '5.1.2209.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(-1+\\beta )q^{2}-\\beta q^{3}+(1-\\beta )q^{4}-q^{6}+\\cdots', 'related_objects': ['ArtinRepresentation/2.47.5t2.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-47], 'self_twist_type': 1, 'space_label': '47.1.b', 'trace_display': [-1, -1, 0, -1], 'trace_hash': 1614164790473007020, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.022', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.896', 'prec': 17}, {'__RealLiteral__': 0, 'data': '5.587', 'prec': 17}, {'__RealLiteral__': 0, 'data': '24.320', 'prec': 20}, {'__RealLiteral__': 0, 'data': '95.260', 'prec': 20}, {'__RealLiteral__': 0, 'data': '382.966', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.508', 'prec': 17}, 'traces': [2, -1, -1, 1, 0, -2, -1, -2, 1, 0, 0, 2, 0, 3, 0, 0, -1, 2, 0, 0, -2, 0, 0, 1, 2, 0, -2, -3, 0, 0, 0, 2, 0, -2, 0, -2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, -1, 3, 0, -1, 1, 0, 1, 0, 0, -1, 0, -1, 0, 2, -1, 0, 0, 0, 2, 0, 0, -1, -1, 0, -2, -1, 0, 0, 0, -1, 0, 0, 0, 4, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, -1, -3, 0, 1, -1, 1, -1, 0, 0, 3, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, -2, 0, 2, 3, 0, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 2, 2, -1, -2, 0, 0, -3, 0, 0, 0, -1, -2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0, -1, 0, -1, 0, -2, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 4, -2, 0, 3, 0, 3, 4, 0, 0, -2, 0, -2, 0, -1, 0, -2, 0, 0, 0, 0, 0, -3, 3, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 1, -1, 0, -1, -1, 2, -3, 0, 0, 0, 0, -2, 0, -1, 1, 0, 0, 0, -2, 0, 0, -2, 0, 0, 3, -1, 0, 0, 0, -2, 0, 4, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, -1, 2, 0, 0, 0, 1, 1, 0, -2, 0, 0, -1, 0, 1, 0, -2, 0, 2, 0, 0, 3, 0, 0, -1, -1, 0, 3, 0, 0, 0, 0, 3, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 2, -3, 0, 0, 0, -1, -1, 0, 0, 0, 0, -2, 0, 0, 3, -1, 0, 0, 3, 0, 0, -1, 1, 0, -3, 1, 0, 0, 0, 2, 0, -1, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, -3, -1, 0, 0, -2, -1, 2, 0, 0, 0, -3, 0, 0, 0, -1, -2, -2, 0, 0, -1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, 3, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, -1, 0, 0, 3, 3, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 1, 0, -1, 2, -2, -1, 0, 0, -2, 0, 1, 0, -1, 4, 1, 0, 0, -1, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, -2, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, -1, 0, 4, -3, -2, 3, 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, -2, 0, 0, -1, -2, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 1, 0, 0, -1, 0, -2, 0, 0, 2, 0, 2, 0, 0, -2, 1, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, -2, 0, 0, -1, 1, 4, 0, 0, 0, 3, 0, 2, 0, 0, -3, 3, 0, 0, 1, 0, 0, 0, -1, 0, 0, -3, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, -1, 0, -1, 3, 0, -4, 0, -1, 0, 0, 0, 0, 0, -2, 0, 3, -2, 1, 0, 0, 3, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 3, -2, -1, -1, 0, -3, 1, 0, 2, 0, 0, 3, 0, -1, 0, -2, -1, 3, 0, 0, -2, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 4, 0, 0, 2, 0, -2, 0, 1, -1, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 2, 2, -2, 0, 0, 0, 0, -2, 1, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0, -4, -1, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -1, 0, -2, -2, 0, -1, -1, -4, 0, 0, 0, 0, 0, 0, 0, 3, -1, -2, 0, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 1, -1, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 4, 0, -3, 0, -1, 0, 0, -2, 0, 0, 3, 2, 0, 0, 3, 0, 0, 0, -1, 0, -3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 4, -1, 0, 0, 0, 2, 0, -1, 0, 2, 0, 3, 0, 0, 2, 0, 0, 2, 0, 0, -1, -2, 0, 0, 0, 1, 0, -2, 0, 0, 4, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, -2, 1, 0, 4, 0, 0, 1, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -1, 0, -1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -2, 1, 0, 0, 3, 3, -2, 0, 0, -2, 0, 1, 0, 1, -1, -3, 0, 0, 0, 0, 0, -1, -2, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, -1, 2, 0, 0, -1, -2, 1, 0, 0, 0, -1, 0, 0, 0, -1, -1, 3, 0, 0, 0, 0, 0, 0, 1, 0, 2, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, -3, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 3, 0, 0, -2, -1, 0, 0, -2, 0, 0, 0, 0, 0, 6, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, -1, -4, -1, -1, 0, 0, -1, 0, 0, 0, 3, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 3, 0, 0, 0, 3, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 3, 1, 3, 0, 2, -1, 0, -1, 0, 0, -2, 0, -1, 0, -2, 1, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 3, 0, 4, -1, 0, 0, 1, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -2, -2, 4, 0, 0, -2, -1, -3, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -3, 0, 3, 1, 0, 0, 0, -3, 0, 1, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, 1, 0, 3, -1, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, 2, 1, 0, 2, 0, 3, 0, 0, 0, -1, 0, 0, 0, 0, -1, -2, 0, 0, 1, 0, 0, 1, 0, 0, -2, 3, 0, 0, 0, 1, 0, 1, 0, 1, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -1, 0, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, -1, 0, -2, 0, -1, 0, 0, 3, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, -1, 0, 1, 0, -1, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, -1, -1, -2, 0, 0, -3, 0, 0, 0, 0, 1, -2, 0, 0, -1, 0, 0, -4, 0, 0, -1, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 2, 0, -1, 0, 0, 0, -2, 0, 0, 0, -1, 1, -2, 0, 0, -1, 0, 0, 2, -4, 0, 1, 4, 0, 0, 0, -1, 0, 0, 0, -1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, -1, -1, -1, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -1, 0, 0, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, -2, 0, 0, 4, 0, 3, 0, 0, -1, 0, 1, 0, 0, 1, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 4, 3, 0, -1, 0, 1, -1, 2, -1, 0, 0, -3, 0, -2, 0, 4, 4, 0, 0, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, -3, 0, -2, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 4, 0, -4, 0, 0, -1, -1, 0, 0, 0, 3, 0, -1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, -2, 0, 0, 0, -1, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, -2, 0, 3, 1, 0, 0, 0, 0, -1, 0, 2, -2, 3, 0, 0, -1, 0, 0, -2, -2, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 3, -2, -1, 0, 0, -4, -1, -1, 0, 0, 0, 0, -2, 0, -3, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, -3, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -2, 0, -1, 0, -1, 3, 0, 0, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, 2, 0, 0, -1, -1, 0, -2, 0, 0, 0, 0, 3, 0, -2, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 3, 0, 0, 0, 3, 3, 3, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -1, 0], 'weight': 1, 'weight_parity': -1}
  6. label: 52.1.j.a
    {'Nk2': 52, 'analytic_conductor': 0.025951380656916125, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [1, 2, 0, -2, -1, 0, 1], 'artin_field_label': '6.0.10816.1', 'artin_image': '18.3', 'char_conductor': 52, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 10, 'char_orbit_label': 'j', 'char_order': 6, 'char_parity': -1, 'char_values': [52, 6, [27, 41], [3, 2]], 'cm_discs': [-4], 'conrey_index': 3, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_13.6t5.1c2'], ['ArtinRepresentation/2.2e2_13.6t5.1c1']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 618492067892, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 13, 3, 1, 3, 0], [1, 1, 52, 10, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '52.1.j.a', 'level': 52, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 13], 'level_radical': 26, 'minimal_twist': '52.1.j.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 10, 'projective_field': [12, -4, -1, 1], 'projective_field_label': '3.1.676.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{6}q^{2}+\\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\\zeta_{6}^{2}q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_13.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-4], 'self_twist_type': 1, 'space_label': '52.1.j', 'trace_display': [-1, 0, -2, 0], 'trace_hash': 1087237517701523738, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.007', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.941', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.832', 'prec': 17}, {'__RealLiteral__': 0, 'data': '17.174', 'prec': 20}, {'__RealLiteral__': 0, 'data': '47.007', 'prec': 20}, {'__RealLiteral__': 0, 'data': '229.392', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.504', 'prec': 17}, 'traces': [2, -1, 0, -1, -2, 0, 0, 2, -1, 1, 0, 0, -1, 0, 0, -1, 1, 2, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, -2, 0, -1, 1, 0, 0, -2, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 2, -2, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, -1, -2, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 4, 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, -1, -2, 0, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, -1, 1, 0, -2, 1, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, 0, -1, 2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 1, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 4, 0, 2, -2, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 1, 4, -1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, -2, -2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 1, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 2, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 1, -1, 1, 0, 0, 2, 0, 0, 0, -2, -1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, -2, 0, 0, -1, 0, -2, 0, 0, -2, 0, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, 1, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, -2, 0, -1, 2, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 1, -4, 0, 0, 1, 1, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 2, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, -2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, 4, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 2, -2, 0, 0, 4, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 1, 0, 0, 0, 0, 2, -1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, -1, 2, 0, 0, 4, 0, 0, 0, 0, -2, 4, 0, 0, -2, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 1, 0, 0, 0, 1, -1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 1, 0, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 1, -1, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, -2, 1, 0, 0, -2, -2, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, 0, 0, -2, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, -1, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 2, 0, 0, -2, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, -4, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 1, 0, 0, -1, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, -2, 0, 0, 0, -2, 0, -1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, -2, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 4, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -2, 1, -2, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, -2, 1, 0, 0, 1, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 0, -2, 1, 0, 0, 0, -2, -2, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -4, -2, 0, 0, -1, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 1, 0, 0, 4, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, -1, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 1, 0, 1, 0, -2, -2, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 4, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 1, 1, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, 0, 0, -2, 2, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, -2, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 1, 0, -2, 0, 0, 1, 0, 0, 4, -1, 0, 0, 0, 0, 0, 0, -1, -2, 1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, -2, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, -1, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, -2, 0, 0, -2, 0, 0, -1], 'weight': 1, 'weight_parity': -1}
  7. label: 55.1.d.a
    {'Nk2': 55, 'analytic_conductor': 0.027448575694815132, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [-1, 2, 0, -1, 1], 'artin_field_label': '4.2.275.1', 'artin_image': '8.3', 'char_conductor': 55, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [55, 2, [12, 46], [1, 1]], 'cm_discs': [-11, -55], 'conrey_index': 54, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.5_11.4t3.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207479, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 2, -1, 2, -11], [1, 1, 55, 4, -1, 2, -55], [1, 1, 5, 2, 1, 2, 5]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '55.1.d.a', 'level': 55, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [5, 11], 'level_radical': 55, 'minimal_twist': '55.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [16, 0, 3, 0, 1], 'projective_field_label': '4.0.3025.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\\cdots', 'related_objects': ['ArtinRepresentation/2.5_11.4t3.1'], 'relative_dim': 1, 'rm_discs': [5], 'self_twist_discs': [-11, -55, 5], 'self_twist_type': 3, 'space_label': '55.1.d', 'trace_display': [0, 0, -1, 0], 'trace_hash': 1163843973887440067, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.010', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.967', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.033', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.862', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.126', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.442', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.757', 'prec': 17}, 'traces': [1, 0, 0, -1, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, -1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, -1], 'weight': 1, 'weight_parity': -1}
  8. label: 56.1.h.a
    {'Nk2': 56, 'analytic_conductor': 0.027947640707448134, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [1, 1, 0, -1, 1], 'artin_field_label': '4.0.392.1', 'artin_image': '8.3', 'char_conductor': 56, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 8, 'char_orbit_label': 'h', 'char_order': 2, 'char_parity': -1, 'char_values': [56, 2, [15, 29, 17], [2, 1, 1]], 'cm_discs': [-7, -56], 'conrey_index': 13, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e3_7.4t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 481053114424, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7], [1, 1, 56, 8, -1, 2, -56], [1, 1, 8, 2, 1, 2, 8]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '56.1.h.a', 'level': 56, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 7], 'level_radical': 14, 'minimal_twist': '56.1.h.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 8, 'projective_field': [16, 0, 6, 0, 1], 'projective_field_label': '4.0.3136.3', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e3_7.4t3.2'], 'relative_dim': 1, 'rm_discs': [8], 'self_twist_discs': [-7, -56, 8], 'self_twist_type': 3, 'space_label': '56.1.h', 'trace_display': [-1, 0, 0, -1], 'trace_hash': 364671561088135787, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.021', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.975', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.080', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.893', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.313', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.566', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.755', 'prec': 17}, 'traces': [1, -1, 0, 1, 0, 0, -1, -1, -1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 2, -2, 0, 0, 0, 0, 0, -2, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, -2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0], 'weight': 1, 'weight_parity': -1}
  9. label: 57.1.h.a
    {'Nk2': 57, 'analytic_conductor': 0.028446705720081136, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [1, -3, 4, -2, 1, -1, 1], 'artin_field_label': '6.0.9747.1', 'artin_image': '18.3', 'char_conductor': 57, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 8, 'char_orbit_label': 'h', 'char_order': 6, 'char_parity': -1, 'char_values': [57, 6, [20, 40], [3, 4]], 'cm_discs': [-3], 'conrey_index': 11, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.3_19.6t5.1c2'], ['ArtinRepresentation/2.3_19.6t5.1c1']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 481053114425, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 19, 3, 1, 3, 0], [1, 1, 57, 8, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '57.1.h.a', 'level': 57, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 19], 'level_radical': 57, 'minimal_twist': '57.1.h.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 8, 'projective_field': [-12, -6, -1, 1], 'projective_field_label': '3.1.1083.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{6}^{2}q^{3}-\\zeta_{6}q^{4}-q^{7}-\\zeta_{6}q^{9}+q^{12}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3_19.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '57.1.h', 'trace_display': [0, -1, 0, -2], 'trace_hash': 1728791927144614380, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.010', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.975', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.047', 'prec': 17}, {'__RealLiteral__': 0, 'data': '17.885', 'prec': 20}, {'__RealLiteral__': 0, 'data': '50.117', 'prec': 20}, {'__RealLiteral__': 0, 'data': '241.216', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.508', 'prec': 17}, 'traces': [2, 0, -1, -1, 0, 0, -2, 0, -1, 0, 0, 2, 1, 0, 0, -1, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, 2, 1, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, -1, 0, 0, 1, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 2, 0, 0, 0, 4, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, -2, 0, 0, 0, -2, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, -1, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 1, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, -1, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, 0, 0, 1, 0, 2, 0, 0, 1, 4, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, -2, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, -1, 0, 4, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, 1, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 2, 0, -1, 0, 0, 0, -2, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, -2, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, -2, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, -1, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, -2, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 1, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, -2, 0, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 1, -2, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 4, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 0, 0, 0, -2, -2, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 4, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, -1, 0, -2, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, -2, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 2, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 4, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0], 'weight': 1, 'weight_parity': -1}
  10. label: 59.1.b.a
    {'Nk2': 59, 'analytic_conductor': 0.02944483574534714, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-1, 2, 0, 1], 'artin_field_label': '3.1.59.1', 'artin_image': '6.1', 'char_conductor': 59, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [59, 2, [2], [1]], 'cm_discs': [-59], 'conrey_index': 58, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.59.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254011, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 59, 2, -1, 2, -59]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '59.1.b.a', 'level': 59, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [59], 'level_radical': 59, 'minimal_twist': '59.1.b.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [-1, 2, 0, 1], 'projective_field_label': '3.1.59.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\\cdots', 'related_objects': ['ArtinRepresentation/2.59.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-59], 'self_twist_type': 1, 'space_label': '59.1.b', 'trace_display': [0, -1, -1, -1], 'trace_hash': 2204527099578963028, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.021', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.969', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.924', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.860', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.706', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.424', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.504', 'prec': 17}, 'traces': [1, 0, -1, 1, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 1, 2, 0, -1, -1, 1, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, -1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, -1, -1, -1, 0, 0, 1, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, -2, 0, 1, 0, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 1, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 2, -1, 0, 1, 0, 3, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 2, 0, 0, -1, 1, 0, -2, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, -1, 0, 0, 0, -1, 1, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, -1, 0, -2, 0, -1, 1, -2, 0, 0, 0, -2, 0, -1, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 1, 0, 1, 0, 0, 2, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 2, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 2, -1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -2, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, -1, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, 1, 0, 0, -2, 0, 2, 0, 0, -1, 0, 0, 1, 1, 1, 0, 0, -1, 1, 0, 0, 0, 2, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 2, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 2, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, -1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, -1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, -1, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, -1, 0, -1, 0, -1, -1, -2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 2, 0, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, -1, 0, -2, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 2, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -2, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 2, 0, -1, 0, 0, -1, 0, 0, 1, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -2, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -2, -1, 0, 2, 0, 0, 0, 0, 0, 2, 0, -2, 2, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 1, -1, 0, 0, 0, 1], 'weight': 1, 'weight_parity': -1}
  11. label: 63.1.d.a
    {'Nk2': 63, 'analytic_conductor': 0.03144109579587915, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [1, 2, 0, -1, 1], 'artin_field_label': '4.0.189.1', 'artin_image': '8.3', 'char_conductor': 7, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [63, 2, [29, 10], [2, 1]], 'cm_discs': [-3, -7], 'conrey_index': 55, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.3e2_7.4t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207487, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 7, 2, -1, 2, -7], [1, 1, 21, 3, 1, 2, 21]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '63.1.d.a', 'level': 63, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [3, 7], 'level_radical': 21, 'minimal_twist': '63.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [4, -2, -1, -1, 1], 'projective_field_label': '4.0.441.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3e2_7.4t3.2'], 'relative_dim': 1, 'rm_discs': [21], 'self_twist_discs': [-3, -7, 21], 'self_twist_type': 3, 'space_label': '63.1.d', 'trace_display': [0, 0, 0, -1], 'trace_hash': 1326877159012085197, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.015', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.946', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.055', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.783', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.219', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.129', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.763', 'prec': 17}, 'traces': [1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0], 'weight': 1, 'weight_parity': -1}
  12. label: 68.1.d.a
    {'Nk2': 68, 'analytic_conductor': 0.033936420859044164, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [1, -2, 1, 0, 1], 'artin_field_label': '4.0.272.1', 'artin_image': '8.3', 'char_conductor': 68, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [68, 2, [35, 37], [1, 1]], 'cm_discs': [-4, -68], 'conrey_index': 67, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_17.4t3.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207492, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 68, 4, -1, 2, -68], [1, 1, 17, 2, 1, 2, 17]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '68.1.d.a', 'level': 68, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 17], 'level_radical': 34, 'minimal_twist': '68.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [16, 0, 9, 0, 1], 'projective_field_label': '4.0.4624.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_17.4t3.1'], 'relative_dim': 1, 'rm_discs': [17], 'self_twist_discs': [-4, -68, 17], 'self_twist_type': 3, 'space_label': '68.1.d', 'trace_display': [-1, 0, 0, 0], 'trace_hash': 1116998248759082639, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.002', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.947', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.008', 'prec': 17}, {'__RealLiteral__': 0, 'data': '3.784', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.031', 'prec': 17}, {'__RealLiteral__': 0, 'data': '15.130', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.762', 'prec': 17}, 'traces': [1, -1, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, -2, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -2, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 1, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  13. label: 68.1.f.a
    {'Nk2': 68, 'analytic_conductor': 0.033936420859044164, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 32, 'artin_field': [1, -2, 3, 0, -4, 4, 0, -2, 1], 'artin_field_label': '8.0.1257728.1', 'artin_image': '32.11', 'char_conductor': 68, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 6, 'char_orbit_label': 'f', 'char_order': 4, 'char_parity': -1, 'char_values': [68, 4, [35, 37], [2, 1]], 'cm_discs': [-4], 'conrey_index': 47, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_17.8t17.1c1'], ['ArtinRepresentation/2.2e2_17.8t17.1c2']], 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 343614160964, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 17, 3, 1, 4, 0], [1, 1, 68, 6, -1, 4, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '68.1.f.a', 'level': 68, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 17], 'level_radical': 34, 'minimal_twist': '68.1.f.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 6, 'projective_field': [-17, 0, 0, 0, 1], 'projective_field_label': '4.2.19652.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q+i q^{2}-q^{4}+(-i-1)q^{5}-i q^{8}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_17.8t17.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-4], 'self_twist_type': 1, 'space_label': '68.1.f', 'trace_display': [0, 0, -2, 0], 'trace_hash': 1171692301803799012, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.012', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.000', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.047', 'prec': 17}, {'__RealLiteral__': 0, 'data': '19.580', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.681', 'prec': 17}, {'__RealLiteral__': 0, 'data': '263.595', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.681', 'prec': 17}, 'traces': [2, 0, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 4, 0, -2, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, -2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 4, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  14. label: 71.1.b.a
    {'Nk2': 71, 'analytic_conductor': 0.03543361589694317, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 14, 'artin_field': [1, 2, -1, -1, 1, -1, -1, 1], 'artin_field_label': '7.1.357911.1', 'artin_image': '14.1', 'char_conductor': 71, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [71, 2, [7], [1]], 'cm_discs': [-71], 'conrey_index': 70, 'dim': 3, 'embedded_related_objects': [['ArtinRepresentation/2.71.7t2.1c3'], ['ArtinRepresentation/2.71.7t2.1c1'], ['ArtinRepresentation/2.71.7t2.1c2']], 'field_disc': 49, 'field_disc_factorization': [[7, 2]], 'field_poly': [1, -2, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 14, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254023, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 71, 2, -1, 2, -71]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '71.1.b.a', 'level': 71, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [71], 'level_radical': 71, 'minimal_twist': '71.1.b.a', 'nf_label': '3.3.49.1', 'prim_orbit_index': 2, 'projective_field': [1, 2, -1, -1, 1, -1, -1, 1], 'projective_field_label': '7.1.357911.1', 'projective_image': 'D7', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\beta _{1}q^{2}+(-1+\\beta _{1}-\\beta _{2})q^{3}+(1+\\beta _{2})q^{4}+\\cdots', 'related_objects': ['ArtinRepresentation/2.71.7t2.1'], 'relative_dim': 3, 'rm_discs': [], 'self_twist_discs': [-71], 'self_twist_type': 1, 'space_label': '71.1.b', 'trace_display': [-1, -1, -1, 0], 'trace_hash': 1840246595524360083, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.022', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.812', 'prec': 17}, {'__RealLiteral__': 0, 'data': '13.892', 'prec': 20}, {'__RealLiteral__': 0, 'data': '86.229', 'prec': 20}, {'__RealLiteral__': 0, 'data': '514.180', 'prec': 24}, {'__RealLiteral__': 0, 'data': '3087.326', 'prec': 27}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.511', 'prec': 17}, 'traces': [3, -1, -1, 2, -1, -2, 0, -2, 2, -2, 0, -3, 0, 0, -2, 1, 0, 4, -1, 4, 0, 0, 0, 3, 2, 0, -2, 0, -1, 3, 0, -3, 0, 0, 0, -1, -1, 5, 0, -4, 0, 0, -1, 0, -3, 0, 0, 2, 3, -3, 0, 0, 0, -4, 0, 0, -2, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, -1, 5, 4, -3, 0, 0, -1, 2, 1, 0, -1, 0, 0, -2, 5, 0, -1, 1, 0, 0, 0, 0, -2, 1, 0, -1, 0, -1, -1, 0, -1, 0, 0, 0, 6, 1, -1, 0, -2, 0, 0, -4, 0, -3, 0, 0, 0, -1, 3, 0, 0, 0, -2, 0, 0, 3, -2, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, -4, -2, -2, -1, -3, 0, 1, -1, 3, 0, 0, 0, 0, -1, -2, 0, 1, 0, 2, 0, 0, 0, 5, -1, 0, 3, 0, 4, 4, 0, 3, 0, 0, 0, -2, -1, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2, 0, 0, -1, 1, 0, 5, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, -2, 5, -1, 0, -2, -2, 0, 0, -4, -1, 0, -1, 0, 0, 1, -1, 0, 0, 3, -1, 0, 0, 0, -2, 0, 0, -3, 0, -1, -3, 0, -1, 0, 0, 0, -2, 3, -1, 0, 0, 0, 0, -1, 0, 3, 0, 0, -3, -2, -1, 0, 0, 0, 5, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, -2, 3, 3, 0, 4, 6, -2, 0, 3, 0, 0, 0, -2, 0, -2, -2, -5, 0, 0, 0, 0, 5, 0, -1, 0, -1, -2, 0, 4, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 5, 0, 0, 0, 0, -3, 4, -2, 0, 0, 0, -1, 0, 0, 0, 1, 0, -4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -3, 0, -2, -1, 2, 2, 0, -1, 0, 5, 0, -1, 0, 0, 3, 0, 0, -1, 0, -4, 0, 0, 0, -1, -6, 0, -2, 0, -1, 0, 0, -3, 0, 0, 0, 0, -2, -2, 0, 5, 0, 0, 5, 0, 3, 0, 0, 0, -3, 2, 0, 0, 0, -1, 0, 0, -3, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, -4, -1, 4, 0, 0, -4, -3, 0, 3, 0, 0, 2, 0, 0, 1, -2, 5, 0, 0, 0, -2, 0, 0, 5, 0, 0, -1, 0, -2, 0, 0, 0, 0, -1, 2, 0, 5, 0, 0, 0, 0, 5, 0, 0, 3, -3, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, -1, 1, -2, 5, -1, 0, -2, 0, -1, 0, 6, 0, 0, 2, -4, 0, -2, 1, 0, 0, 0, 0, -1, -6, 0, 4, 0, -2, 0, 0, 3, 0, 0, 0, 0, 3, -2, 0, -2, 0, 0, 2, 0, -2, 0, 0, -2, 0, -1, 0, 0, 0, -2, 0, 0, 5, 3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, -1, -1, 0, 5, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, -4, 0, -2, -1, -3, 0, 0, 0, -5, -1, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -3, -1, -4, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 3, 0, 0, 0, 5, 0, 0, 1, 5, 0, -3, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, -1, -1, -4, 6, 0, 3, 0, 6, -3, 0, 0, 0, 0, 0, 3, 5, 0, -3, 0, -1, 0, 0, 0, 0, 3, 0, 1, 0, 4, -2, 0, 0, 0, 0, 0, 1, 2, -1, 0, 0, 0, 0, 0, 0, 5, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, -2, -3, 3, 0, 0, 0, 4, 0, -2, -1, -1, 0, -3, 0, 0, 4, -2, 0, 0, 0, -4, 0, 0, 0, -2, -2, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, -2, 4, 0, 0, -1, 0, 0, -2, 0, -2, 0, 0, -2, 0, 6, 0, 0, 0, -3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, -2, 3, -1, 0, -2, -4, 0, 0, 0, 0, 0, -3, -1, 0, 0, -2, -3, 0, 0, 0, 0, 0, 0, 3, 0, -3, -1, 0, 5, 0, 0, 0, -2, -2, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, -1, 3, -2, 0, 0, 0, 5, 0, 0, -2, -1, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -3, -1, 0, 1, -4, -1, 0, 0, 1, 0, 5, 0, 2, 0, 0, -1, 0, 0, -1, 0, 3, 0, 0, 0, 1, -1, 0, -2, 0, -1, 4, 0, 0, 0, 0, 0, -1, 0, 3, 0, -3, 0, 0, 5, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 3, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -3, 5, -3, 1, -1, 0, -1, -3, -2, 0, 0, 0, 0, 0, -2, 0, -1, 3, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, -2, 0, 0, 6, -2, 0, 0, 0, 0, -1, 0, 0, 4, -3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -1, -2, -4, -1, 0, 3, 0, -3, 0, -2, 0, 0, -1, 3, 0, 0, 6, -2, 0, 0, 0, -2, -1, 0, -1, 0, 0, -2, 0, -1, 0, 0, 0, 3, -1, -1, 0, 0, 0, 0, 0, 0, 6, 0, 0, -2, 0, -2, 0, 0, 0, -4, 0, 0, -1, 4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, -1, -4, 0, 0, -2, 3, -3, 0, -2, 0, 0, -2, 0, 0, -3, -3, 0, 0, 0, 0, 2, 3, 0, 0, 0, 5, 3, 0, -1, 0, 0, 0, -2, -4, -1, 0, 0, 0, 0, -3, 0, -1, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 6, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 5, -2, 0, 2, 0, 5, 0, 0, 5, 3, 0, 0, 0, 0, -1, 2, 0, -2, 0, 2, 0, 0, 0, -1, 3, 0, -1, 0, -2, 0, 0, 2, 0, 0, 0, 4, 0, -2, 0, 3, 0, 0, -3, 0, -1, 0, 0, 1, 3, -2, 0, 0, 0, 0, 0, 0, -1, -4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 1, -1, 0, 1, 0, 6, 0, 0, 0, 0, 0, -1, 0, 2, -2, 5, 0, 0, 0, -1, 0, 0, -2, 0, 1, -1, 0, 0, 0, 0, 0, 0, -3, 3, 0, -2, 0, 0, 2, 0, -3, 0, 0, -2, 3, 5, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, -2, 0, 5, -1, -6, 0, -2, 0, 0, 0, -1, 0, 0, -2, -2, 0, -2, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 1, 0, -4, 0, 0, 0, 1, 5, 0, 0, -2, 0, 0, -1, 0, -2, 0, 0, 0, -1, -5, 0, 0, 0, 5, 0, 0, -4, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, -2, 0, -2, -2, 0, 0, 0, -3, 0, 6, 0, 0, 0, 0, 0, 6, -5, 2, 0, 0, 0, 6, 3, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, -3, 0, 0, 0, 0, 0, -4, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 4, -1, 1, 6, 2, 1, 0, 0, 0, -1, 0, 0, -4, 0, 0, 0, 4, 0, 5, -1, 3, 0, 0, 0, 6, -1, 0, -1, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 4, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, 1, 0, 0, 5, 0, -1, 2, -2, 0, -3, 0, 0, -4, 0, 0, 5, 3, -1, 0, 0, 0, 3, -3, 0, 0, 0, -3, 2, 0, -1, 0, 0, 0, -2, 3, 0, 0, -1, 0, 0, 0, 0, -3, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, -2, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 6, -1, -3, 0, 3, -1, 1, 0, -2, 0, 0, 5, 3, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 3, 0, 5, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -4, 0, -1, 0, 0, 0, -3, 0, 0, 0, 0, -5, 0, 0, -1, -1, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, -4, -3, -1, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, -1, 5, 0, -6, 0, -4, 6, 0, 1, 0, 0, 0, -1, -4, 5, 0, 0, 0, 0, -3, 0, 5, 0, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 3, 0, -2, -2, 0, -1, -5, 0, 2, -2, -2, 0, 0, 0, 0, -3, -1, 0, 0, -1, -3, 0, 0, 0, 0, 0, 0, -2, 0, -1, -2, 0, 0, 0, 0, 0, 2, -1, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, -1, -1, -2, 0, 0, 0, -4, 0, 0, 5, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, -1, 0, 5, 1, 0, 0, -1, 3, 0, 0, -1, 0, 0, -4, 4, 0, 0, 0, 5, 0, 0, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 1, -1, 0, -2, 0, 0, 1, 0, 0, 0, 0, -1, 2, -3, 0, 0, 0, 0, 0, 0, -4, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 1, -2, -3, 0, -6, 0, 0, 0, 5, 0, 0, -1, 5, 0, 3, 5, -4, 0, 0, 0, 0, -1, 0, -1, 0, 2, 0, 0, -4, 0, 0, 0, 5, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, -2, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -2, 0, 5, -2, 0, -1, -2, 0, 0, 8, 0, 0, -2, 0, 0, 0, -1, 0, 1, 1, 0, 0, 0, 0, -2, -2, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -4, 0, -6, 0, 0, 3, 5, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, -1, -2, 0, -3, -1, -1, 0, -3], 'weight': 1, 'weight_parity': -1}
  15. label: 72.1.p.a
    {'Nk2': 72, 'analytic_conductor': 0.03593268090957617, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [1, 0, 2, -2, 3, -2, 1], 'artin_field_label': '6.0.41472.1', 'artin_image': '18.3', 'char_conductor': 72, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 16, 'char_orbit_label': 'p', 'char_order': 6, 'char_parity': -1, 'char_values': [72, 6, [55, 37, 65], [3, 3, 4]], 'cm_discs': [-8], 'conrey_index': 43, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e3_3e2.6t5.1c2'], ['ArtinRepresentation/2.2e3_3e2.6t5.1c1']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 1030808928328, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, -8], [1, 1, 9, 3, 1, 3, 0], [1, 1, 72, 16, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '72.1.p.a', 'level': 72, 'level_is_powerful': True, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 3], 'level_radical': 6, 'minimal_twist': '72.1.p.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 16, 'projective_field': [-10, -3, 0, 1], 'projective_field_label': '3.1.648.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{6}^{2}q^{2}+\\zeta_{6}^{2}q^{3}-\\zeta_{6}q^{4}-\\zeta_{6}q^{6}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e3_3e2.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-8], 'self_twist_type': 1, 'space_label': '72.1.p', 'trace_display': [-1, -1, 0, 0], 'trace_hash': 691516436078150477, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.026', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.904', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.620', 'prec': 17}, {'__RealLiteral__': 0, 'data': '16.472', 'prec': 20}, {'__RealLiteral__': 0, 'data': '43.923', 'prec': 20}, {'__RealLiteral__': 0, 'data': '217.624', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.506', 'prec': 17}, 'traces': [2, -1, -1, -1, 0, -1, 0, 2, -1, 0, 1, 2, 0, 0, 0, -1, -2, 2, -2, 0, 0, 1, 0, -1, -1, 0, 2, 0, 0, 0, 0, -1, 1, 1, 0, -1, 0, 1, 0, 0, 1, 0, 1, -2, 0, 0, 0, -1, -1, -1, 1, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, -2, 1, 1, 0, 0, 0, -1, -2, 0, -1, 1, 0, 0, 0, 0, -1, -2, -2, 0, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 2, 1, 2, -2, 2, 0, 1, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, -2, 1, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 1, 0, -2, 1, 0, -2, 0, -2, 1, 0, 1, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, 1, 0, -2, 0, 0, -1, 0, 1, -2, 0, 0, 0, 1, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, 1, 0, -1, 0, 1, 0, -1, -2, 0, 0, -2, 0, 0, 0, 0, -1, 0, -2, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 2, 4, 1, -2, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, -2, 0, -2, 0, 0, 0, 0, -1, 1, -2, 0, 0, 0, 4, 0, 1, 0, 0, -2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, 0, -2, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, -2, 0, 1, 0, 0, -2, 4, 0, 0, 0, 0, 1, -1, 4, 0, 0, -2, 0, 1, 0, 0, 1, 0, 0, 0, 0, -2, 1, 1, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, -2, -2, -2, 0, 0, 0, -1, 4, 0, 0, 1, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, -2, -1, -2, 0, 0, 4, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, -2, 0, 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, -1, 2, -2, 0, 1, 0, 1, 1, 0, -2, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, -2, 0, 1, 1, 0, 0, 0, 0, 0, 4, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, -2, -2, 0, 1, 0, 0, 0, 0, -2, 0, 4, -2, 0, 0, 0, -2, -1, 0, 1, 0, 0, -2, 0, 1, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, 1, -2, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -2, 1, 0, 0, 4, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, -2, 0, -2, 0, 0, -2, 0, -2, 0, 0, 1, -1, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, -1, 0, -1, 2, 0, 0, -2, 0, 0, 0, -2, 1, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -1, 2, 0, -2, 0, 0, 1, 0, -2, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0, -2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, 1, 0, 1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -1, 1, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, -1, -2, 0, 0, 0, -2, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 4, 0, 0, -1, 0, -2, -2, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, -2, -2, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 4, -1, -2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, -2, 0, 0, 1, -2, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 1, 0, 1, 0, 0, 4, 0, 1, 0, 0, 0, 0, -2, 0, 2, 1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -2, 0, 0, 0, 0, -1, 0, 4, -1, 0, 0, 0, 0, 1, -2, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 4, 0, -2, 0, 0, 2, 0, 0, -2, 0, 1, 0, 0, 0, 0, -1, -2, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, -2, 0, -2, -2, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 4, 0, 0, 0, -2, 0, -2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 1, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -2, 4, 0, -2, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, 1, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 1, 0, 2, -1, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, -2, 1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 1, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 1, 2, 1, -2, 0, 2, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, -2, 0, 0, 1, 0, 1, -1, 0, 0, 0, -1, -2, -1, 1, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -2, 0, 0, 1, 0, -1, 4, 0, 0, 0, -2, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, -1, 0, -1, -1, 0, 0, -2, 0, 0, 0, 0, 1, -2, 0, 0, 0, 1, 0, 1, 2, 0, 1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 1, 0, 1, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -1, -2, -2, 0, 1, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, -1, -2, 0, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -4, 0, 0, 1, 0, 0, 0, 0, 2, 4, 1, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, -1, 0, 4, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -2, 0, 1, -2, 0, 4, 0, 0, 2, 0, -2, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -2, 4, 0, 1, 0, -1, 0, -2, -2, 0, -2, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, -1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, -2, -2, 0, -4, 0, 0, 0, 0, 0, -2, -2, 1, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, -2, -2, 0, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 2, 2, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, -2, 0, 1, -1, 0, 0, 0, 4, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, -2, 1, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, -2, 0, -2, 0, 0, 1, 1, 0, 0, 0, 0, 4, -2, 2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, -1, 0, 1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, -1, 1, 0, 0, -2, 0, 1, -2, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  16. label: 76.1.c.a
    {'Nk2': 76, 'analytic_conductor': 0.03792894096010818, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-2, -2, 0, 1], 'artin_field_label': '3.1.76.1', 'artin_image': '6.1', 'char_conductor': 19, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 3, 'char_orbit_label': 'c', 'char_order': 2, 'char_parity': -1, 'char_values': [76, 2, [39, 21], [2, 1]], 'cm_discs': [-19], 'conrey_index': 37, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_19.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 137455730764, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 2, -1, 2, -19]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '76.1.c.a', 'level': 76, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 19], 'level_radical': 38, 'minimal_twist': '76.1.c.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [-2, -2, 0, 1], 'projective_field_label': '3.1.76.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_19.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-19], 'self_twist_type': 1, 'space_label': '76.1.c', 'trace_display': [0, 0, -1, -1], 'trace_hash': 80797675260605140, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.006', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.965', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.951', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.879', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.780', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.537', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.514', 'prec': 17}, 'traces': [1, 0, 0, 0, -1, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, -2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, -1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, -1, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0], 'weight': 1, 'weight_parity': -1}
  17. label: 77.1.j.a
    {'Nk2': 77, 'analytic_conductor': 0.03842800597274119, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 77, 'char_degree': 4, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 10, 'char_orbit_label': 'j', 'char_order': 10, 'char_parity': -1, 'char_values': [77, 10, [45, 57], [5, 6]], 'cm_discs': [-7], 'conrey_index': 20, 'dim': 4, 'field_disc': 125, 'field_disc_factorization': [[5, 3]], 'field_poly': [1, -1, 1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 618492067917, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7], [1, 1, 11, 3, 1, 5, 0], [1, 1, 77, 10, -1, 10, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '77.1.j.a', 'level': 77, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [7, 11], 'level_radical': 77, 'minimal_twist': '77.1.j.a', 'nf_label': '4.0.125.1', 'prim_orbit_index': 10, 'projective_field': [1, 4, -9, 6, -2, 1], 'projective_field_label': '5.1.717409.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(\\zeta_{10}^{2}+\\zeta_{10}^{4})q^{2}+(-\\zeta_{10}-\\zeta_{10}^{3}+\\cdots)q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-7], 'self_twist_type': 1, 'space_label': '77.1.j', 'trace_display': [-2, 0, 0, -1], 'trace_hash': 484288680974116680, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.014', 'prec': 17}, {'__RealLiteral__': 0, 'data': '3.901', 'prec': 17}, {'__RealLiteral__': 0, 'data': '11.383', 'prec': 20}, {'__RealLiteral__': 0, 'data': '93.924', 'prec': 20}, {'__RealLiteral__': 0, 'data': '635.383', 'prec': 24}, {'__RealLiteral__': 0, 'data': '4984.134', 'prec': 27}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.505', 'prec': 17}, 'traces': [4, -2, 0, -3, 0, 0, -1, 1, -1, 0, -1, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, -2, -2, 0, -1, 0, 0, 2, -2, 0, 0, 4, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, -2, 2, 0, 1, 0, 0, -1, -2, 0, 0, 3, 0, 0, -4, 0, 1, 0, 0, 0, 0, -1, -2, 0, 0, -2, 0, 0, 0, 3, 1, 0, -4, 0, 0, -1, 0, 3, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 4, 2, 0, 0, 0, 0, 0, 1, 3, 0, -2, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, -2, -3, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -1, -2, 0, 3, 0, 0, 3, 0, 0, 0, 1, 0, 0, 3, 3, -2, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 4, 0, 0, 0, 3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 2, -2, -2, 0, 1, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, -2, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 6, 0, 1, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 6, -1, 0, -2, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, -2, 1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 3, 0, 0, -4, 0, 2, 0, -4, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 3, 3, 0, 0, 0, 0, -1, 2, 0, 0, 3, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 1, 3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, -4, 3, 0, 3, 0, 0, 1, 0, 1, 0, -3, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 3, -4, 0, -3, 0, 0, 0, -6, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 3, -2, -2, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 6, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0, 1, 0, 6, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -2, -1, 0, 3, 0, 0, -2, -4, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, -1, 2, -2, 0, -2, 0, 0, 0, 3, 3, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 1, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, -3, 0, 1, 0, 0, 0, 1, -2, 0, -2, 0, 0, -1, 0, 0, 0, -4, 0, 0, 0, 4, 3, 0, 0, 0, 0, 0, 8, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 3, -4, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, -4, 0, 0, 0, 0, 0, -3, 3, 0, 0, -2, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0, -6, 0, -4, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 3, 0, 3, 0, 0, 1, 3, 0, 0, -4, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 3, 6, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 6, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 1, 0, 4, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, -2, 0, 0, -3, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 1, 0, 0, -2, 0, -1, 0, 0, 0, 0, 2, 0, -4, 0, 2, 0, 0, 0, -3, 0, 0, 3, 0, 0, 0, -2, 0, 0, 6, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 1, 0, -2, 0, 0, 0, -6, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 0, 3, 1, 0, 4, 0, 0, -2, 0, -1, 0, -2, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, -2, 6, 0, 0, 0, 0, 0, 0, -4, 0, 8, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, -3, 3, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, -2, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -2, -4, 0, -3, 0, 0, 0, 2, 0, 0, -2, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 3, 1, -2, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 3, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, -2, 0, -2, 0, 0, -1, 0, 1, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 3, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, -2, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 3, 0, -2, 0, 0, 0, -1, -6, 0, -3, 0, 0, 3, 0, 0, 0, 8, 0, 0, 0, 0, 1, 0, -1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, -2, 0, 2, 0, 0, -3, -2, 0, 0, -2, 0, 0, 3, 0, -2, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 3, 1, -2, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 3, 1, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -2, 1, 0, -4, 0, 0, 3, 1, 0, 0, 3, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, -6, -2, 0, 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, -2, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, -3, 0, 0, 3, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 6, -2, 0, -2, 0, 0, 2, 0, 0, 0, 4, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 6, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -1, 4, 0, -6, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 4, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, -3, 0, -4, 0, 0, 0, 0, -2, 4, -2, 0, -2, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, -2, 0, 0, -4, -2, 0, 0, 4, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 1, 0, 0, 0, 0, 6, 0, 0, 0, 0, -2, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 8, 0, 3, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -4, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0, -4, 0, -1, 0, 0, 0, -3, 8, 0, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, -1, 6, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 1, -4, 0, 4, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, -2, 0], 'weight': 1, 'weight_parity': -1}
  18. label: 79.1.b.a
    {'Nk2': 79, 'analytic_conductor': 0.03942613599800719, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 10, 'artin_field': [-1, 3, -2, 1, -1, 1], 'artin_field_label': '5.1.6241.1', 'artin_image': '10.1', 'char_conductor': 79, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [79, 2, [3], [1]], 'cm_discs': [-79], 'conrey_index': 78, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.79.5t2.1c1'], ['ArtinRepresentation/2.79.5t2.1c2']], 'field_disc': 5, 'field_disc_factorization': [[5, 1]], 'field_poly': [-1, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254031, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 79, 2, -1, 2, -79]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '79.1.b.a', 'level': 79, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [79], 'level_radical': 79, 'minimal_twist': '79.1.b.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 2, 'projective_field': [-1, 3, -2, 1, -1, 1], 'projective_field_label': '5.1.6241.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(-1+\\beta )q^{2}+(1-\\beta )q^{4}-\\beta q^{5}-q^{8}+\\cdots', 'related_objects': ['ArtinRepresentation/2.79.5t2.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-79], 'self_twist_type': 1, 'space_label': '79.1.b', 'trace_display': [-1, 0, -1, 0], 'trace_hash': 1478270469223400683, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.047', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.823', 'prec': 17}, {'__RealLiteral__': 0, 'data': '5.270', 'prec': 17}, {'__RealLiteral__': 0, 'data': '23.080', 'prec': 20}, {'__RealLiteral__': 0, 'data': '90.274', 'prec': 20}, {'__RealLiteral__': 0, 'data': '363.049', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.508', 'prec': 17}, 'traces': [2, -1, 0, 1, -1, 0, 0, -2, 2, -2, -1, 0, -1, 0, 0, 0, 0, -1, -1, 2, 0, 3, -1, 0, 1, 3, 0, 0, 0, 0, -1, 2, 0, 0, 0, 1, 0, -2, 0, 1, 0, 0, 0, -3, -1, -2, 0, 0, 2, 2, 0, -3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, 0, -1, -2, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 1, -1, -2, 0, 2, 0, 0, 3, 0, -1, -1, -1, -2, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 1, 0, 0, -3, -2, 0, 0, 1, 0, 1, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, -1, 1, 0, 0, -2, 0, 0, -1, 0, -1, 0, -1, -1, 0, 0, -2, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 3, 4, 2, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 1, 0, 3, 0, -1, 0, 3, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 4, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, -1, -3, 0, 0, -1, 0, -2, 1, 0, 1, 0, 0, -2, 0, 0, -2, -1, 0, 0, -1, 0, -2, -1, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, -4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 4, 0, 0, -2, 0, 0, 0, 1, 2, 3, 0, 0, 0, 0, 0, 2, 0, 3, 3, 0, -1, -3, 0, 0, 3, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -3, 0, -2, 0, 1, 1, 3, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 2, -1, 0, 0, -2, 0, 0, -1, -3, 4, 0, 0, 0, 0, 0, 3, -3, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 3, 0, -1, 2, 2, 0, 0, 0, -2, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, -2, 4, 0, 0, 3, 0, 3, 3, 0, -1, 0, 0, -2, 0, 0, 0, 1, -2, 0, 0, 0, -1, -1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, -1, 2, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -2, -1, 0, 4, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -2, 0, 0, -1, 3, 0, 0, 0, -2, 4, 0, 0, 3, 0, 0, -1, 0, -1, 4, 0, 0, -3, -1, 0, -1, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -1, 0, 0, 2, -1, 0, -1, 0, 0, 0, 0, -2, 0, -1, 0, -3, -1, 0, 3, 0, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -3, 0, 1, 0, 0, 0, -2, 0, 3, 4, 0, 0, 0, 0, -4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 1, -2, 0, 1, 2, 0, 0, -1, 0, 0, 2, 0, -3, 0, 0, 4, 0, 2, 1, 0, 0, -1, 3, 0, -1, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 4, 0, 0, 0, -1, 0, 0, 0, 3, 0, 4, 0, 0, -3, -1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 2, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 1, 0, -2, 0, 0, 0, 0, 0, 1, -1, 0, -2, 0, 0, -4, 0, 1, -1, -2, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 3, 0, 0, -2, -1, 0, 0, -1, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 0, -2, 4, 0, 0, -2, 0, 0, -1, 0, -2, 0, -1, 1, 0, 0, -1, -2, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, -1, 2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 4, 0, -1, 0, -1, 0, -2, 3, 0, 0, 0, 0, -1, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 3, 0, 1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, -1, 0, 0, 2, 0, -2, 0, 0, 1, 0, 0, -3, 0, 0, 4, -1, 0, 1, -1, 0, 0, 3, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, -1, -3, 0, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 1, -1, 0, 0, -3, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 3, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, -2, -2, -3, -1, 0, 0, 0, 0, 0, 0, 2, -2, -2, -1, 0, -1, 0, 0, -3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, -1, 0, 3, -1, 0, -2, 0, 0, -1, 0, 0, 0, -2, -2, 0, 1, 0, -1, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 3, 1, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 3, 3, 0, 0, 4, 0, 0, 1, 0, -2, -1, 0, -2, -2, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 3, 0, 0, 0, 1, 0, 0, 3, -2, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, -1, 0, -1, 0, 0, 4, 0, -2, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 3, 0, 3, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, -1, 0, 0, -3, 0, -4, 4, 0, 0, 0, 0, 3, 0, -1, -2, 0, 0, -2, -1, 0, -1, 1, 0, 0, 0, 0, -1, -2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -2, -1, -3, 0, 0, -1, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, 4, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, -1, 3, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -2, 0, 0, 0, 0, -1, 0, 1, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, -1, 0, 0, -2, 0, 0, 0, -1, 0, 0, 4, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -3, -2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 3, 0, 0, 0, 1, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 3, 0, 2, 0, -2, 0, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, -2, 0, -1, -3, 0, 0, -1, 0, -1, 1, 0, 2, 0, 0, -3, 0, 0, -2, 3, 0, 2, -1, 0, 2, 3, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -2, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, -1, 2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, -2, -1, -1, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, -1, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 3, -1, -4, 0, 0, -1, 0, -1, -4, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -3, 0, 0, 0, 0, 1, -1, 0, 0, -2, 0, 0, -1, 3, 0, 0, 0, -2, 0, 0, -3, 6, 0, -3, 0, 0, 0, 0, 0, 0, -2, 0, 3, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -1, -2, -1, 0, 0, 0, 4, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 3, -1, 0, -2, 0, 0, 1, 0, 0, -2, 2, 0, 0, -2, 0, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, -2, 0, 0, -3, 0, 0, -1, 0, 0, 0, 0, 0, 0, -4, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 4, -1, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 3, 0, 4, -2, 0, -3, 4, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  19. label: 80.1.h.a
    {'Nk2': 80, 'analytic_conductor': 0.03992520101064019, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [2, 0, 0, -2, 1], 'artin_field_label': '4.0.320.1', 'artin_image': '8.3', 'char_conductor': 20, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 8, 'char_orbit_label': 'h', 'char_order': 2, 'char_parity': -1, 'char_values': [80, 2, [31, 21, 17], [1, 2, 1]], 'cm_discs': [-4, -20], 'conrey_index': 79, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e4_5.4t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 481053114448, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 20, 4, -1, 2, -20], [1, 1, 5, 2, 1, 2, 5]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '80.1.h.a', 'level': 80, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 5], 'level_radical': 10, 'minimal_twist': '80.1.h.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [1, 0, 3, 0, 1], 'projective_field_label': '4.0.400.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e4_5.4t3.2'], 'relative_dim': 1, 'rm_discs': [5], 'self_twist_discs': [-4, -20, 5], 'self_twist_type': 3, 'space_label': '80.1.h', 'trace_display': [0, 0, -1, 0], 'trace_hash': 1107721117330381110, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.007', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.962', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.024', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.845', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.094', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.378', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.759', 'prec': 17}, 'traces': [1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  20. label: 83.1.b.a
    {'Nk2': 83, 'analytic_conductor': 0.0414223960485392, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-2, 1, -1, 1], 'artin_field_label': '3.1.83.1', 'artin_image': '6.1', 'char_conductor': 83, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [83, 2, [2], [1]], 'cm_discs': [-83], 'conrey_index': 82, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.83.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254035, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 83, 2, -1, 2, -83]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '83.1.b.a', 'level': 83, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [83], 'level_radical': 83, 'minimal_twist': '83.1.b.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [-2, 1, -1, 1], 'projective_field_label': '3.1.83.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\\cdots', 'related_objects': ['ArtinRepresentation/2.83.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-83], 'self_twist_type': 1, 'space_label': '83.1.b', 'trace_display': [0, -1, 0, -1], 'trace_hash': 1161792343161264227, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.021', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.969', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.924', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.860', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.706', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.424', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.504', 'prec': 17}, 'traces': [1, 0, -1, 1, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 1, -1, -1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, -2, -1, 0, 0, -1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, -1, -1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, -1, -1, 2, 0, 0, 0, -1, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, -2, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, -1, 2, 1, 0, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 1, 0, -1, 0, 1, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, -1, 0, 0, 0, 0, -2, 0, 0, -1, 2, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, 2, 0, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 2, 2, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, -1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, -1, 0, 2, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, -1, 0, -1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 4, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 2, 0, -1, 0, -1, 1, 2, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -1, -2, 0, -2, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 1, -2, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, -1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, -2, 0, 0, 1, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 1, -1, 0, 1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, -2, 0, 0, 0, 0, 1, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 2, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, -1, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, -1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, -1, 1, 0, 0, -1, 1, 0, -1, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0], 'weight': 1, 'weight_parity': -1}
  21. label: 84.1.p.a
    {'Nk2': 84, 'analytic_conductor': 0.0419214610611722, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [1, 1, -2, -1, 4, -3, 1], 'artin_field_label': '6.0.21168.1', 'artin_image': '18.3', 'char_conductor': 21, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 16, 'char_orbit_label': 'p', 'char_order': 6, 'char_parity': -1, 'char_values': [84, 6, [43, 29, 73], [6, 3, 4]], 'cm_discs': [-3], 'conrey_index': 53, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_3_7.6t5.1c2'], ['ArtinRepresentation/2.2e2_3_7.6t5.1c1']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 1030808928340, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 7, 3, 1, 3, 0], [1, 1, 21, 8, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '84.1.p.a', 'level': 84, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 3, 7], 'level_radical': 42, 'minimal_twist': '84.1.p.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 8, 'projective_field': [1, 5, -1, 1], 'projective_field_label': '3.1.588.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{6}^{2}q^{3}-\\zeta_{6}q^{7}-\\zeta_{6}q^{9}-q^{13}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_3_7.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '84.1.p', 'trace_display': [0, -1, 0, -1], 'trace_hash': 1909164154899339134, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.005', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.931', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.845', 'prec': 17}, {'__RealLiteral__': 0, 'data': '17.141', 'prec': 20}, {'__RealLiteral__': 0, 'data': '47.067', 'prec': 20}, {'__RealLiteral__': 0, 'data': '229.266', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.508', 'prec': 17}, 'traces': [2, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, -1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 4, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0], 'weight': 1, 'weight_parity': -1}
  22. label: 87.1.d.a
    {'Nk2': 87, 'analytic_conductor': 0.04341865609907121, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [1, 2, -1, 1], 'artin_field_label': '3.1.87.1', 'artin_image': '6.1', 'char_conductor': 87, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [87, 2, [59, 31], [1, 1]], 'cm_discs': [-87], 'conrey_index': 86, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.3_29.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207511, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 87, 4, -1, 2, -87]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '87.1.d.a', 'level': 87, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 29], 'level_radical': 87, 'minimal_twist': '87.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [1, 2, -1, 1], 'projective_field_label': '3.1.87.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3_29.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-87], 'self_twist_type': 1, 'space_label': '87.1.d', 'trace_display': [-1, 1, 0, -1], 'trace_hash': 453765226009714133, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.017', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.948', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.911', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.804', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.624', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.229', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.516', 'prec': 17}, 'traces': [1, -1, 1, 0, 0, -1, -1, 1, 1, 0, -1, 0, -1, 1, 0, -1, -1, -1, 0, 0, -1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 2, 1, 0, 0, 0, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, -1, 1, 0, 1, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, -2, 0, 0, 0, 0, 1, -1, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, -1, 1, 2, -1, 0, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, -1, 0, 0, -1, 0, 0, 1, 0, -1, 2, 0, -1, 0, -1, 0, 1, -1, 0, 0, 0, 0, 0, -1, 2, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, 1, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0, 1, 0, -1, 0, 2, 1, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, -1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, -1, 0, 0, -1, 0, -1, 0, 0, 1, 1, -2, -1, 0, -1, 1, 0, 0, 0, 1, 2, 0, 0, -1, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, 1, 0, 0, 2, 0, -1, -1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, -1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -1, 0, -1, -1, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 2, 1, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0, 0, 1, 0, -1, -1, -1, -2, 0, 2, 0, 0, 0, -1, 0, -1, 0, 2, -1, -1, -1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, -1, 2, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, -1, -2, 0, 1, 1, 0, 0, 0, -2, 1, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -2, -1, 0, -1, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 1, 2, -2, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0, -1, 1, 0, -2, 0, -1, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 1, -2, -2, 0, 0, 0, 1, 0, -1, 0, 0, 1, 0, 2, 0, 0, -1, 0, -1, 0, 0, 0, -2, 0, 0, -2, -1, -1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 2, 0, 1, -1, 0, -2, 0, 0, 2, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, -1, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 2, -1, 0, 2, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 2, 1, -1, 0, -1, 0, 2, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, -1, 0, -2, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 1, 1, -1, 0, 0, -2, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, -1, -2, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, -2, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, -2, -1, 0, 0, 0, 1, 0, -1, -2, 2, 2, 0, 1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, -1, 2, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, -1, 0, 1, -1, 0, -1, 0, 0, 0, -2, -1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, -1, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, -1, 0, -1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, -1, 0, -2, 1, 0, 0, 0, 1, 1, 0, 0, -2, 0, 1, 0, -2, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 2, 0, -1, -1, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 1, -1, 0, -1, 1, 0, 0, 0, -1, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, 1, -2, 0, 0, 0, 0, -1, 0, 1, -1, 0, 0, -1, 0, 0, -2, 1, 0, 0, 0, 0, 2, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 2, 0, 0, -1, 0, 0, -1, 0, 0, -1, 1, 2, 0, 0, 0, 0, -1, -1, 2, 0, 0, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, -1, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 0, 0, -1, 0, 2, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, -1, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 2, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 2, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, -2, -1, 0, 0, -1, -1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -1, -2, 1, 0, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, -2, 1, 0, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 3, -1, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, -1, 0, 0, 0, -2, 0, 2, -2, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, -1, 0, 0, 2, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, -1, 0, 0, 0, 1, -1, 0, -2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 1, -2, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 1, 0, 1, 1, 0, -1, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, -1, -1, 0, 1, 0, -2, -1, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, -1, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -2, 1, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  23. label: 87.1.d.b
    {'Nk2': 87, 'analytic_conductor': 0.04341865609907121, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 12, 'artin_field': [1, -3, 5, -4, 4, -1, 1], 'artin_field_label': '6.0.22707.1', 'artin_image': '12.4', 'char_conductor': 87, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [87, 2, [59, 31], [1, 1]], 'cm_discs': [-87], 'conrey_index': 86, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.3_29.6t3.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503805802578007, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 87, 4, -1, 2, -87]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '87.1.d.b', 'level': 87, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 29], 'level_radical': 87, 'minimal_twist': '87.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [1, 2, -1, 1], 'projective_field_label': '3.1.87.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3_29.6t3.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-87], 'self_twist_type': 1, 'space_label': '87.1.d', 'trace_display': [1, -1, 0, -1], 'trace_hash': 386922169675734460, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.009', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.948', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.038', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.804', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.155', 'prec': 20}, {'__RealLiteral__': 0, 'data': '10.229', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.516', 'prec': 17}, 'traces': [1, 1, -1, 0, 0, -1, -1, -1, 1, 0, 1, 0, -1, -1, 0, -1, 1, 1, 0, 0, 1, 1, 0, 1, 1, -1, -1, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, -2, 1, 0, 0, 0, 0, 1, 1, 0, 1, -1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 1, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, 1, 0, 0, 1, -2, 0, 0, 0, 0, 1, -1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, -1, 2, 1, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 2, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, -1, 0, -1, -2, 0, -1, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, -1, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, -1, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, 1, 0, -2, -1, 0, 0, 0, 0, 0, 1, -1, -1, 1, 1, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, 0, -1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, -1, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -2, 1, 0, 0, -1, 0, 1, 0, 0, -1, -1, -2, 1, 0, -1, -1, 0, 0, 0, -1, 2, 0, 0, -1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 2, -1, 0, 0, 1, 0, 0, -2, 0, 1, -1, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 2, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, -1, 1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 1, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 1, 0, -1, 1, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, -1, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, 0, 0, -1, 0, -1, 1, 1, -2, 0, -2, 0, 0, 0, -1, 0, -1, 0, -2, 1, -1, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, -1, 2, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, 1, -2, 0, 1, 1, 0, 0, 0, 2, -1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 2, -1, 0, 1, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 1, 1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, -1, 0, -1, 0, 0, 1, -2, -2, 0, 0, 0, 1, -1, -1, 1, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1, 1, 0, 2, 0, -1, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, -2, 2, 0, 0, 0, 1, 0, 1, 0, 0, -1, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, -2, 1, 1, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, 2, 0, 2, 0, -1, -1, 0, 2, 0, 0, -2, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, -1, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, -2, -1, 0, -2, 0, 0, 0, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, -1, -1, 0, 1, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, -1, 0, -2, 0, 0, 1, 0, 1, 0, 0, -1, 0, 0, -1, -1, -1, 0, 0, -2, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, -1, -2, 0, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, -2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 2, 1, 0, 0, 0, 1, 0, -1, -2, -2, -2, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, -2, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -2, -1, 0, 1, -1, 0, -1, 0, 0, 0, -2, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, -1, 0, -1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 1, 0, -1, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, -1, 0, 2, -1, 0, 0, 0, 1, -1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, -2, 0, 0, 1, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, -2, 0, -1, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 1, 1, 0, -1, -1, 0, 0, 0, 1, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 2, 1, -2, 0, 0, 0, 0, 1, 0, -1, -1, 0, 0, -1, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 2, 0, 0, -1, 0, 0, 1, 0, 0, -1, 1, -2, 0, 0, 0, 0, -1, 1, 2, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 1, -2, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 1, 0, -2, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, -2, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, -1, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, -1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 2, -1, 0, 0, 2, -1, 0, 0, -1, 1, -1, 0, 0, -1, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 1, -2, 1, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, -2, -1, 0, -1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 2, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 3, 1, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 1, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, -1, 0, 0, 0, 2, 0, 2, 2, 0, 0, -1, -1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, -2, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, -1, 0, 0, 0, -1, 1, 0, 2, 0, 0, 0, 0, 0, 0, -1, 1, 0, 2, 0, -1, 2, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 1, 1, 0, -1, -1, 0, 1, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, -1, 0, -1, 0, -2, 1, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -2, -1, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  24. label: 88.1.l.a
    {'Nk2': 88, 'analytic_conductor': 0.04391772111170421, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 88, 'char_degree': 4, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 12, 'char_orbit_label': 'l', 'char_order': 10, 'char_parity': -1, 'char_values': [88, 10, [23, 45, 57], [5, 5, 8]], 'cm_discs': [-8], 'conrey_index': 3, 'dim': 4, 'field_disc': 125, 'field_disc_factorization': [[5, 3]], 'field_poly': [1, -1, 1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 755931021400, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, -8], [1, 1, 11, 3, 1, 5, 0], [1, 1, 88, 12, -1, 10, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '88.1.l.a', 'level': 88, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 11], 'level_radical': 22, 'minimal_twist': '88.1.l.a', 'nf_label': '4.0.125.1', 'prim_orbit_index': 12, 'projective_field': [-23, 3, -8, -4, -1, 1], 'projective_field_label': '5.1.937024.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{10}q^{2}+(\\zeta_{10}^{2}+\\zeta_{10}^{4})q^{3}+\\zeta_{10}^{2}q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-8], 'self_twist_type': 1, 'space_label': '88.1.l', 'trace_display': [-1, -2, 0, 0], 'trace_hash': 1874476807280359954, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.011', 'prec': 17}, {'__RealLiteral__': 0, 'data': '3.843', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.919', 'prec': 20}, {'__RealLiteral__': 0, 'data': '90.003', 'prec': 20}, {'__RealLiteral__': 0, 'data': '603.775', 'prec': 24}, {'__RealLiteral__': 0, 'data': '4729.777', 'prec': 27}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.506', 'prec': 17}, 'traces': [4, -1, -2, -1, 0, 3, 0, -1, -3, 0, -1, -2, 0, 0, 0, -1, -2, 2, 3, 0, 0, -1, 0, 3, -1, 0, 1, 0, 0, 0, 0, 4, 3, -2, 0, 2, 0, -2, 0, 0, -2, 0, -2, 4, 0, 0, 0, -2, -1, -1, 1, 0, 0, -4, 0, 0, 1, 0, 3, 0, 0, 0, 0, -1, 0, -2, -2, -2, 0, 0, 0, -3, -2, 0, 3, -2, 0, 0, 0, 0, 0, 3, 3, 0, 0, 3, 0, -1, -2, 0, 0, 0, 0, 0, 0, -2, 3, 4, -3, 4, 0, 1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 3, 1, 0, 0, 0, 3, 0, 0, -1, 0, -4, 0, 0, 0, 0, -1, 1, 0, -2, -2, 0, -2, 0, 3, 3, 0, -2, 0, 0, 0, 0, 2, 0, -2, -2, 0, 0, -2, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, 0, -1, 0, -1, -2, 0, 0, 0, -1, -4, 3, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, -2, -2, 0, -1, 0, 2, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, -2, 0, 3, 0, 0, 3, 0, 1, 0, 0, 6, 0, 0, 0, 0, 0, -3, -2, 3, 1, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, -2, -1, 4, 0, 0, 1, 0, 0, 1, 0, -2, 0, 0, 0, 0, -1, -2, -4, 0, 0, 0, -2, 0, 3, 0, 0, 1, 3, 0, 0, 0, 3, 0, -2, -1, 0, 0, -2, 0, 0, 3, 0, -2, 0, 0, 0, 0, -3, -3, 0, -4, 3, 0, -2, 0, 0, 1, 0, 0, -2, 0, 0, 0, 3, 0, -1, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 3, 0, 3, 0, 0, -2, 3, 0, 0, 0, 0, 3, -1, 1, 0, 0, 4, 0, -2, 0, 0, -2, 0, 0, 0, 0, -1, -2, 1, 0, -2, 0, -2, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, 8, 4, -2, 0, 0, 0, -1, 1, 0, 0, -3, 0, 0, 0, -1, 3, 1, 0, 0, 0, 0, 0, -4, -2, 0, 1, 0, 0, 0, 0, 0, -4, 3, -2, 0, 0, -2, 0, 0, 3, 0, 0, -2, 0, 0, 0, 1, 3, 0, 0, 0, 0, -4, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -2, 2, 3, -2, 0, 3, 0, 1, 3, 0, -3, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, -1, 0, 0, 1, 0, -2, 1, 0, 0, 0, 0, 0, 1, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, -3, -2, 0, 6, 0, 0, 0, 0, 3, 0, -2, 3, 0, 0, 0, -2, 4, 0, -1, 0, 0, -4, 0, 3, 1, 0, -1, 0, 0, 0, 0, -2, 0, 0, 3, 3, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, -2, 3, 0, 0, -2, 0, 0, 3, 0, 8, 0, 0, 0, 0, 2, -2, 2, -4, 0, 0, 6, 0, -2, 0, 0, 3, 3, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 3, -2, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, -1, 0, 3, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, -1, -2, 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 1, 3, 0, 0, -4, 0, 0, -2, 0, 0, 3, 0, 0, 0, -2, -1, 0, -2, 0, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 1, -1, 0, 1, 0, 0, -4, 0, 8, -1, 0, 0, 0, 3, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, -4, 0, 0, 0, 0, -1, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -3, 1, 0, 0, -2, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 3, -6, -2, 0, 0, 0, 0, 0, 0, 0, -6, -2, 0, 0, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, 8, 0, 6, -2, 0, -1, 0, 3, 0, 0, 1, 0, 0, 0, 0, -1, 0, 1, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 4, -2, -2, -4, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, 1, 0, 0, 3, 0, -2, 0, 0, 0, 0, 0, 3, 6, 0, 3, 0, 3, 0, 0, -1, 0, 1, -2, 0, 0, 0, 0, 6, 3, 0, 0, 0, 0, 0, 3, -2, 0, -2, 0, 0, 0, 0, 1, 0, 3, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, -2, -3, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, -2, 0, -2, 0, 0, -2, -2, 0, 0, 0, -4, -2, -2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 3, -2, 0, 8, 0, 0, -2, 0, 1, 0, 0, 0, 0, -2, 0, 3, -2, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, 3, 0, 0, 0, -1, 2, 0, -2, -1, 0, 0, 0, 0, -2, -4, -2, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -4, 0, -2, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -2, 0, -4, 0, 0, 3, 0, 0, -1, 0, -2, 0, 0, 0, 0, 4, 3, -3, 0, 3, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, -2, 0, 3, -2, 0, 3, 0, 0, 0, 0, 3, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, 3, 6, 0, 0, 0, -2, 0, 1, -2, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 2, 0, -2, 0, 0, -2, 0, -2, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 6, 1, -2, 3, 0, -2, 0, 0, 3, 0, 0, 8, 0, 0, 0, 0, 1, -2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 2, 0, -4, 0, 0, -3, 0, 3, -4, 0, 0, 0, 3, 0, 0, -2, 0, 0, 3, 0, -2, 3, 0, -1, 0, 0, 0, 0, 0, 0, -2, 8, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 3, -2, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -1, -1, 0, 6, -2, 0, 0, 0, 0, -6, -2, 0, 0, 0, -2, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 3, -1, 4, -2, 0, -4, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 3, 3, 1, 0, -2, 0, 0, -2, 0, -2, 1, 0, 0, 0, 0, -2, -2, -4, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, -2, 0, 0, -2, 0, 1, -2, 0, 0, 0, -2, -4, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, -2, 0, 1, 0, 4, -4, 0, 0, 1, 0, 0, 0, 0, -2, 1, 0, 0, 0, -2, 0, -1, -1, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 8, 0, 1, 3, 0, 0, 0, 1, 0, 0, -4, 0, 0, 0, 0, 3, 1, 0, -2, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 1, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 3, -2, 0, 0, -4, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 6, -2, -2, 4, 0, 3, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, -2, 6, 0, -2, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 2, 3, -2, 0, 0, 0, 0, 0, 8, 0, 3, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -4, 0, -2, 0, 0, 0, -1, 0, 0, 0, -2, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -4, 0, 0, 0, 0, -1, 1, 0, 3, -4, 0, -2, 0, 0, 1, 0, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -2, -1, 0, 3, 0, 3, 0, 1, 3, 0, -1, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 1, 0, -2, 0, 0, 0, 0, 1, 0, 0, -4, 0, 0, 0, 0, -4, -2, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -4, 0, 0, 0, -2, 0, 0, 3, -2, 0, 0, 0, 0, -3, 4, -1, 0, 0, 1, 0, 3, -4, 0, 1, 0, 0, 0, 0, 0, -2, -4, 3, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, -4, 3, 0, 0, 0, -2, 0, 0, -2, 0, 3, 0, 0, 0, 0, -4, 0, 0, 1, -2, 0, -1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, -4, 3, 1, 2, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 2, 3, 0, 6, -2, 0, 0, 0, 3, 2, 0, -2, 0, 0, -2, 0, -2, 0, 0, 1, 0, 0, 0, 0, 1, -2, -2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, -2, 4, 0, 0, 3, 0, 3, 0, 0, 3, -2, 0, 0, 0, 0, 3, 3, 3, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, -1, -4, 0, 0, -6, 0, 3, 1, 0, -2, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, -2, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, -2, 0, -3, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 6, 3, 0, 0, 3, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  25. label: 93.1.l.a
    {'Nk2': 93, 'analytic_conductor': 0.04641304617486922, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 93, 'char_degree': 4, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 12, 'char_orbit_label': 'l', 'char_order': 10, 'char_parity': -1, 'char_values': [93, 10, [32, 34], [5, 8]], 'cm_discs': [-3], 'conrey_index': 2, 'dim': 4, 'field_disc': 125, 'field_disc_factorization': [[5, 3]], 'field_poly': [1, -1, 1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 755931021405, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 31, 4, 1, 5, 0], [1, 1, 93, 12, -1, 10, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '93.1.l.a', 'level': 93, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 31], 'level_radical': 93, 'minimal_twist': '93.1.l.a', 'nf_label': '4.0.125.1', 'prim_orbit_index': 12, 'projective_field': [-36, 63, 21, -12, -1, 1], 'projective_field_label': '5.1.8311689.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{10}q^{3}-\\zeta_{10}^{3}q^{4}+(\\zeta_{10}^{2}+\\zeta_{10}^{4}+\\cdots)q^{7}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '93.1.l', 'trace_display': [0, -1, 0, -2], 'trace_hash': 2182863326034639453, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.015', 'prec': 17}, {'__RealLiteral__': 0, 'data': '3.836', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.935', 'prec': 20}, {'__RealLiteral__': 0, 'data': '89.972', 'prec': 20}, {'__RealLiteral__': 0, 'data': '603.838', 'prec': 24}, {'__RealLiteral__': 0, 'data': '4729.653', 'prec': 27}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.508', 'prec': 17}, 'traces': [4, 0, -1, -1, 0, 0, -2, 0, -1, 0, 0, -1, -2, 0, 0, -1, 0, 0, -2, 0, 3, 0, 0, 0, 4, 0, -1, 3, 0, 0, -1, 0, 0, 0, 0, 4, -2, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, -1, -3, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, -1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -1, 3, 0, 0, 3, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 3, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, -1, 3, 0, 3, 3, 0, 0, 0, 0, 3, 0, 0, 0, -1, 0, 0, -1, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, 0, 2, -2, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 4, 3, 0, 0, -3, 0, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, -2, 0, -1, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 4, 3, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, -4, 0, 0, 0, -2, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, -2, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -1, 1, 0, 0, 8, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, -1, 0, 0, 3, 0, 0, 0, 0, 0, 8, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -2, 0, 0, 3, 0, 0, -2, 0, 2, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 1, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0, 0, -4, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, -4, 0, 0, 3, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -1, 3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 3, 3, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 3, 4, 0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -1, 2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, -2, 0, 0, -2, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -1, -2, 0, 0, -2, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 8, 0, -2, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 8, -2, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 3, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 1, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 0, -2, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -1, -4, 0, 3, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 8, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 4, 0, 0, -4, 0, -4, 0, 0, 0, -2, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 3, 0, -1, 0, 0, 1, 3, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 8, 0, 0, -1, 0, 0, 1, 0, -2, 0, 0, 3, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -1, -2, 0, 0, 6, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 3, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, -2, 0, 3, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, -3, -2, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -4, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, -2, 0, 0, 0, 0, 4, 3, 0, 0, -4, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 3, -2, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 3, 8, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 3, 0, 0, -4, 0, 0, 0, 0, 1, 3, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, -2, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -1, 0, 0, 3, 0, 0, 6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -1, -3, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 3, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 8, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, 3, 0, -1, 1, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 6, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 3, 0, 0, 3, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, -4, 0, -2, 4, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, -2, 0], 'weight': 1, 'weight_parity': -1}
  26. label: 95.1.d.a
    {'Nk2': 95, 'analytic_conductor': 0.04741117620013523, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [-1, -1, 2, -2, 1], 'artin_field_label': '4.2.475.1', 'artin_image': '8.3', 'char_conductor': 95, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [95, 2, [77, 21], [1, 1]], 'cm_discs': [-19, -95], 'conrey_index': 94, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.5_19.4t3.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [0, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207519, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 2, -1, 2, -19], [1, 1, 95, 4, -1, 2, -95], [1, 1, 5, 2, 1, 2, 5]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '95.1.d.a', 'level': 95, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [5, 19], 'level_radical': 95, 'minimal_twist': '95.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [36, 0, 7, 0, 1], 'projective_field_label': '4.0.9025.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\\cdots', 'related_objects': ['ArtinRepresentation/2.5_19.4t3.1'], 'relative_dim': 1, 'rm_discs': [5], 'self_twist_discs': [-19, -95, 5], 'self_twist_type': 3, 'space_label': '95.1.d', 'trace_display': [0, 0, 1, 0], 'trace_hash': 61361119298390834, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.019', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.955', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.084', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.815', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.340', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.255', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.760', 'prec': 17}, 'traces': [1, 0, 0, -1, 1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, -2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 1], 'weight': 1, 'weight_parity': -1}
  27. label: 95.1.d.b
    {'Nk2': 95, 'analytic_conductor': 0.04741117620013523, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 16, 'artin_field': [-1, 2, 2, -1, -2, 1, 0, -1, 1], 'artin_field_label': '8.2.4286875.1', 'artin_image': '16.7', 'char_conductor': 95, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [95, 2, [77, 21], [1, 1]], 'cm_discs': [-95], 'conrey_index': 94, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.5_19.8t6.1c1'], ['ArtinRepresentation/2.5_19.8t6.1c2']], 'field_disc': 8, 'field_disc_factorization': [[2, 3]], 'field_poly': [-2, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 8, 'has_non_self_twist': 1, 'hecke_cutters': [[2, [-2, 0, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503805802578015, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 95, 4, -1, 2, -95], [1, 1, 5, 2, 1, 2, 0], [1, 1, 19, 2, -1, 2, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '95.1.d.b', 'level': 95, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [5, 19], 'level_radical': 95, 'minimal_twist': '95.1.d.b', 'nf_label': '2.2.8.1', 'prim_orbit_index': 4, 'projective_field': [-1, -1, 2, -2, 1], 'projective_field_label': '4.2.475.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\beta q^{2}+\\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.5_19.8t6.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-95], 'self_twist_type': 1, 'space_label': '95.1.d', 'trace_display': [0, 0, -2, 0], 'trace_hash': 476004310623190306, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.031', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.829', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.451', 'prec': 20}, {'__RealLiteral__': 0, 'data': '29.167', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-7.035', 'prec': 20}, {'__RealLiteral__': 0, 'data': '466.304', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.884', 'prec': 17}, 'traces': [2, 0, 0, 2, -2, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -4, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 4, 2, 0, 0, -4, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, -4, 0, 0, -2, 0, 4, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, -4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 4, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -4, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, -4, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2], 'weight': 1, 'weight_parity': -1}
  28. label: 99.1.h.a
    {'Nk2': 99, 'analytic_conductor': 0.049407436250667236, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [1, 1, 3, -2, -1, 0, 1], 'artin_field_label': '6.0.107811.1', 'artin_image': '18.3', 'char_conductor': 99, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 8, 'char_orbit_label': 'h', 'char_order': 6, 'char_parity': -1, 'char_values': [99, 6, [56, 46], [4, 3]], 'cm_discs': [-11], 'conrey_index': 43, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.3e2_11.6t5.1c1'], ['ArtinRepresentation/2.3e2_11.6t5.1c2']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 481053114467, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 2, -1, 2, -11], [1, 1, 9, 3, 1, 3, 0], [1, 1, 99, 8, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '99.1.h.a', 'level': 99, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [3, 11], 'level_radical': 33, 'minimal_twist': '99.1.h.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 8, 'projective_field': [-1, 6, 0, 1], 'projective_field_label': '3.1.891.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{6}^{2}q^{3}+\\zeta_{6}^{2}q^{4}-\\zeta_{6}^{2}q^{5}-\\zeta_{6}q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3e2_11.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-11], 'self_twist_type': 1, 'space_label': '99.1.h', 'trace_display': [0, -1, 1, 0], 'trace_hash': 289227545479338818, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.014', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.951', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.807', 'prec': 17}, {'__RealLiteral__': 0, 'data': '17.220', 'prec': 20}, {'__RealLiteral__': 0, 'data': '46.912', 'prec': 20}, {'__RealLiteral__': 0, 'data': '229.578', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.502', 'prec': 17}, 'traces': [2, 0, -1, -1, 1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 1, 2, -1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, -2, 0, 0, 0, 2, 0, 0, 1, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0, -2, 1, -2, 0, 0, 0, -1, 0, 0, -2, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 1, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, -2, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, -2, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 1, 4, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 2, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 2, 0, -2, 0, 1, 0, 0, 0, 0, 0, 1, -2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, -3, 0, -2, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, -2, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 1, 0, -2, 0, -2, 0, 0, 0, 4, 0, -2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, -2, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, -1, 0, 0, 0, -2, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, -1, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, -2, 0, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, 4, 0, 0, 0, -1, 0, 1, -2, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, -4, 0, -1, 0, 0, 0, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -4, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 1, 0, 0, 0, 4, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 1, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, -2, 0, 0, 0, 0, -2, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, -1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, -2, 0, 1, 1, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 6, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -2, 2, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 1, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -2, 0, 0, 0, 0, -2, 0, -1, -1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, -2, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, -2, 0, 0, 0, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1], 'weight': 1, 'weight_parity': -1}
  29. label: 100.1.j.a
    {'Nk2': 100, 'analytic_conductor': 0.04990650126330024, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 100, 'char_degree': 4, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 10, 'char_orbit_label': 'j', 'char_order': 10, 'char_parity': -1, 'char_values': [100, 10, [51, 77], [5, 8]], 'cm_discs': [-4], 'conrey_index': 11, 'dim': 4, 'field_disc': 125, 'field_disc_factorization': [[5, 3]], 'field_poly': [1, -1, 1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 618492067940, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 25, 4, 1, 5, 0], [1, 1, 100, 10, -1, 10, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '100.1.j.a', 'level': 100, 'level_is_powerful': True, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': True, 'level_is_squarefree': False, 'level_primes': [2, 5], 'level_radical': 10, 'minimal_twist': '100.1.j.a', 'nf_label': '4.0.125.1', 'prim_orbit_index': 10, 'projective_field': [-18, -15, -10, 10, 0, 1], 'projective_field_label': '5.1.6250000.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{10}^{3}q^{2}-\\zeta_{10}q^{4}+\\zeta_{10}^{4}q^{5}+\\zeta_{10}^{4}q^{8}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-4], 'self_twist_type': 1, 'space_label': '100.1.j', 'trace_display': [-1, 0, -1, 0], 'trace_hash': 462255275374833578, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.002', 'prec': 17}, {'__RealLiteral__': 0, 'data': '3.846', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.870', 'prec': 20}, {'__RealLiteral__': 0, 'data': '89.971', 'prec': 20}, {'__RealLiteral__': 0, 'data': '603.446', 'prec': 24}, {'__RealLiteral__': 0, 'data': '4729.255', 'prec': 27}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.504', 'prec': 17}, 'traces': [4, -1, 0, -1, -1, 0, 0, -1, -1, -1, 0, 0, -2, 0, 0, -1, -2, 4, 0, 4, 0, 0, 0, 0, -1, -2, 0, 0, -2, 0, 0, 4, 0, 3, 0, -1, 3, 0, 0, -1, -2, 0, 0, 0, -1, 0, 0, 0, 4, -1, 0, -2, 3, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -1, 3, 0, 0, -2, 0, 0, 0, -1, -2, -2, 0, 0, 0, 0, 0, -1, -1, -2, 0, 0, 3, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0, -2, -1, 0, -1, -2, 0, 0, 3, 0, 3, 0, 0, -2, 0, 0, 0, 3, 0, 0, 3, 3, 0, 0, 0, -1, 3, 0, 0, -1, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, -1, -2, 3, 0, 3, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -1, 0, -1, 0, -2, 0, 0, 0, 0, -3, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, -1, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, -1, 3, 0, 0, -1, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 4, -2, 0, 0, 3, 0, 0, -2, 3, -2, 0, 0, 0, 0, 0, 0, 3, -1, 0, 3, -1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -1, -2, 0, 0, -2, 3, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, -2, 0, -2, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, -3, 3, 0, 3, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, -2, 0, 0, -1, 0, 0, 0, 4, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, -2, 2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 4, -1, 3, 0, 0, -2, 0, 0, 0, 3, -2, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 3, -2, 0, 0, -1, 0, 3, 0, 0, -2, 0, 0, 4, -2, 0, 0, -2, -1, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, -1, 1, 0, 0, 3, 0, 0, 0, -2, -1, 0, 3, 0, 0, 0, 0, 8, 3, 0, 0, 3, 0, 0, 3, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, -2, 0, -1, -2, 0, 0, -2, 0, -1, 0, 0, 6, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -2, 3, -2, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, -2, 3, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, -2, 2, 0, -2, 0, 0, 0, -2, -2, 3, 0, 0, 0, 0, 0, -2, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 3, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -1, 8, 0, -2, 1, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, -2, 0, 0, 3, -2, 0, 0, 0, -2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 8, 0, 2, -2, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, 3, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -2, -2, 0, 0, 0, -1, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 3, -2, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, -1, -2, 0, 0, -2, 0, 0, 0, 0, 6, -2, 0, 0, 3, 0, 0, -1, -2, -2, 0, 0, 0, 0, 0, -2, 3, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 3, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, -2, 0, 0, 0, -2, 4, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, -4, 0, 0, -2, 3, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, -2, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, -1, 1, 0, 3, 3, 0, 0, 4, 0, 3, 0, 0, 0, 0, 0, -2, -2, 0, 0, 4, 3, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, -2, 0, 0, 0, -2, -2, 0, 0, 3, 0, 0, 4, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, -2, 0, 3, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, 3, 3, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, -1, 3, 0, 0, -2, 0, 0, 3, -2, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, -2, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, -2, -2, 0, 2, -4, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 3, 0, 0, 1, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, 8, -2, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, -2, -1, -2, 0, 0, 3, 0, 0, 0, 3, -2, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, -2, 0, 0, 0, -2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, -1, 0, 8, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 3, 8, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, -2, 1, -2, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 3, 0, 0, 0, 3, -4, 0, 0, -2, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 3, 0, 0, 0, -4, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -3, 0, 0, 3, 0, 3, 0, 0, -2, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -4, -2, 0, 0, 1, 0, 0, 0, -3, 3, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, -2, 0, 0, 3, 3, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 3, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, -1, -2, 3, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 3, 0, -2, 0, -1, -2, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, -2, 3, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 2, 0, 3, -2, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 3, -2, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 3, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 3, -2, -2, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 8, 0, 0, -4, 1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, -2, 1, 0, 0, -1, 0, 0, -2, 0, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 4, 3, 0, 0, 1, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 3, -2, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -4, 0, 0, 0, -2, 0, -2, 0, 0, 3, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, -1, 1, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, -1], 'weight': 1, 'weight_parity': -1}
  30. label: 103.1.b.a
    {'Nk2': 103, 'analytic_conductor': 0.051403696301199245, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 10, 'artin_field': [1, 1, -3, 3, -2, 1], 'artin_field_label': '5.1.10609.1', 'artin_image': '10.1', 'char_conductor': 103, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [103, 2, [5], [1]], 'cm_discs': [-103], 'conrey_index': 102, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.103.5t2.1c2'], ['ArtinRepresentation/2.103.5t2.1c1']], 'field_disc': 5, 'field_disc_factorization': [[5, 1]], 'field_poly': [-1, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254055, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 103, 2, -1, 2, -103]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '103.1.b.a', 'level': 103, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [103], 'level_radical': 103, 'minimal_twist': '103.1.b.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 2, 'projective_field': [1, 1, -3, 3, -2, 1], 'projective_field_label': '5.1.10609.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(-1+\\beta )q^{2}+(1-\\beta )q^{4}-\\beta q^{7}-q^{8}+\\cdots', 'related_objects': ['ArtinRepresentation/2.103.5t2.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-103], 'self_twist_type': 1, 'space_label': '103.1.b', 'trace_display': [-1, 0, 0, -1], 'trace_hash': 1619066268445811528, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.005', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.995', 'prec': 17}, {'__RealLiteral__': 0, 'data': '5.954', 'prec': 17}, {'__RealLiteral__': 0, 'data': '25.820', 'prec': 20}, {'__RealLiteral__': 0, 'data': '101.231', 'prec': 24}, {'__RealLiteral__': 0, 'data': '406.878', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.496', 'prec': 17}, 'traces': [2, -1, 0, 1, 0, 0, -1, -2, 2, 0, 0, 0, -1, -2, 0, 0, -1, -1, -1, 0, 0, 0, -1, 0, 2, 3, 0, 2, -1, 0, 0, 2, 0, -2, 0, 1, 0, 3, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 1, -1, 0, -3, 0, 0, 0, 1, 0, -2, -1, 0, -1, 0, -1, -1, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -3, 0, 0, -1, 0, 2, 3, -1, 0, 0, 0, 0, 0, 0, 0, -2, -3, 0, 0, 0, 0, -1, 2, 0, 1, 0, 0, 2, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -2, 3, 0, 2, -2, 0, 0, 0, -2, 0, 1, 0, 0, -1, 0, -2, 0, 0, 1, -1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 3, 0, 0, -2, -1, -1, -3, 0, -2, 4, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 3, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, -1, -1, 2, 0, 0, 0, -1, 0, 0, 1, 0, 3, 0, 2, 0, 1, -1, 0, 0, -1, 0, 2, 0, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, -1, 3, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, -1, 0, 0, -3, -1, 0, 0, 0, 0, 1, -2, 1, -1, -2, 0, 1, 0, 0, 0, 2, 0, -2, 0, 0, -1, -3, 0, 0, 0, 3, -2, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 1, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 3, 3, 0, -1, 0, 0, -1, 0, 4, 0, 0, 0, -1, 0, 3, 2, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 1, 0, 0, 0, 3, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, -1, -3, 0, 0, 0, 1, 0, 0, -1, -1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, -3, 0, 0, 0, 0, 1, 0, -1, -1, 3, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, -1, 0, 0, -1, -3, -1, 0, -2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, -1, -1, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 2, 3, 0, 0, 0, 0, -1, 1, 0, -2, 0, 0, 2, 0, 0, 0, -1, 0, -1, -1, 0, 1, -1, -2, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, -1, 3, 0, 3, -1, 0, 3, 0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 2, 0, -2, 0, 0, -1, -3, 0, 0, -1, 0, 0, 2, 2, 0, 0, 0, 0, 3, 0, -1, 0, 3, -1, 0, 0, 0, 0, 0, 0, -2, -1, 0, -2, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, -2, 0, -1, 0, 0, -2, 0, 1, 0, -3, 0, 0, 0, 3, -3, 0, 0, 0, 0, 3, -1, 0, 1, -2, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 4, 1, 0, -4, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -4, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 0, 0, 4, 0, 0, 0, 0, -3, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, -1, -1, 0, 2, 0, 0, 3, 0, 1, 0, 0, 0, 0, 4, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, -3, -1, 0, 0, 2, 0, 0, -2, 0, 2, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, 1, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2, -1, 0, 3, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, -2, 2, 0, -2, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, -3, 0, 0, 0, -2, -1, 2, 0, -4, 0, 0, 0, 0, 3, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, -2, 2, 0, -1, 0, -1, -2, 0, 1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, -1, 0, 3, -1, 1, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, -1, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 1, -1, 0, 0, 4, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, -1, 4, -3, 3, 0, 0, 0, 0, 0, 4, 0, -2, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 2, 0, 0, -1, -1, 0, 3, 0, 0, -1, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, -1, 0, -1, 0, -2, 0, 0, 3, 0, -3, 0, 0, 0, -1, 0, 3, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 2, 0, 0, -1, 4, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 4, 1, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, -1, 0, 0, -2, 0, 3, 0, 0, 0, 0, -2, -2, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, -3, 0, 0, -1, 3, 0, 0, -1, -3, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -4, 0, 0, 3, 3, 4, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -4, -1, 0, -2, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, -1, 3, -1, 0, -2, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, -1, -1, 0, 3, 2, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, -1, -3, 0, -1, -1, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, -2, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 2, 0, 0, 3, 0, 0, -2, 0, -1, -1, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 4, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 3, 0, 2, 3, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 3, 0, -1, 1, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 3, 0, 0, 3, 0, -2, 0, 0, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, -2, 0, -2, 0, 0, -1, -1, -1, 0, 0, 0, 4, -3, 0, 0, -1, 0, 4, 0, 0, 0, -1, 0, -1, 0, 0, -2, -2, 0, 0, -4, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, -1, 0, 3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -1, -1, 0, -1, -3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  31. label: 104.1.h.a
    {'Nk2': 104, 'analytic_conductor': 0.05190276131383225, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 12, 'artin_field': [1, 0, 2, -2, 2, 0, 1], 'artin_field_label': '6.0.86528.1', 'artin_image': '12.4', 'char_conductor': 104, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 8, 'char_orbit_label': 'h', 'char_order': 2, 'char_parity': -1, 'char_values': [104, 2, [79, 53, 41], [1, 1, 1]], 'cm_discs': [-104], 'conrey_index': 51, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e3_13.6t3.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[5, [-1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 481053114472, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 104, 8, -1, 2, -104]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '104.1.h.a', 'level': 104, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 13], 'level_radical': 26, 'minimal_twist': '104.1.h.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 8, 'projective_field': [-2, -1, 0, 1], 'projective_field_label': '3.1.104.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e3_13.6t3.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-104], 'self_twist_type': 1, 'space_label': '104.1.h', 'trace_display': [-1, -1, 1, 1], 'trace_hash': 1021299277177204684, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.009', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.970', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.050', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.896', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.213', 'prec': 20}, {'__RealLiteral__': 0, 'data': '10.600', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.512', 'prec': 17}, 'traces': [1, -1, -1, 1, 1, 1, 1, -1, 0, -1, 0, -1, -1, -1, -1, 1, -1, 0, 0, 1, -1, 0, 0, 1, 0, 1, 1, 1, 0, 1, -2, -1, 0, 1, 1, 0, 1, 0, 1, -1, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 2, 0, 1, -1, 0, 0, -1, 0, -1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 1, -1, 0, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, 2, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, -1, 0, 2, 1, 1, 0, -1, 1, 2, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, -2, -1, 0, 0, -1, 1, 1, -1, 0, 0, 0, 1, 1, 0, 0, -1, 1, -1, -1, 0, 0, 0, 0, 0, 1, -2, 0, 1, 0, 0, 0, -2, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -2, 1, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, -2, 0, 1, 1, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, -1, 0, -1, -2, -1, -1, -2, -1, 0, 0, 1, 1, 1, -1, 0, -2, 0, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 1, 1, -1, 0, -1, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 1, 1, -1, -1, 1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, 0, 0, 0, 0, 1, 0, -1, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, -1, 0, 0, 0, -2, 0, 0, 1, -2, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 2, 0, -1, -1, -1, -2, -1, 0, 0, -1, 1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 1, -2, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, -1, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, -1, 2, 0, 1, 0, 0, 0, 0, 0, -1, -1, -1, 0, -1, 2, 1, 0, 0, 0, 2, -1, 0, -1, 0, 0, -1, -1, 0, 1, 0, -2, 0, 2, 1, 2, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 1, 1, -1, 0, 0, 1, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, -2, 1, 0, 0, -1, 2, -2, 0, 0, 0, 0, -1, 0, -2, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, -1, 0, 2, -1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 1, 1, -1, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 1, 1, 0, 0, -1, -1, 2, -2, -1, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, 0, 0, -1, -2, 0, 0, 0, 0, -1, 1, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, -1, 1, 0, 0, -1, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, -1, 2, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, -1, 0, 0, -1, 2, 0, -2, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, 1, -1, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, -2, -1, 0, 0, 0, -1, 0, -1, -1, 2, 0, 0, 0, -1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, -2, -2, 0, 0, 0, 2, -1, 0, 1, -2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -2, 0, -2, 1, -2, 1, 1, -1, 0, -1, 1, 0, 1, 0, -2, 0, 0, -1, 1, 0, 0, -2, 2, 0, 2, -1, 0, -1, 1, -1, 0, 1, 0, -2, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, -2, -1, -1, 0, 0, 0, 0, 0, 0, 1, -2, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, -1, -1, 0, 0, 2, 0, 0, 0, -2, 0, -1, 0, -2, 0, 0, 2, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, -1, 0, 0, 1, 0, -1, 0, -1, 3, 1, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 1, 1, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, -1, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 1, 1, -2, 0, 0, -2, -1, 1, -1, 0, 0, 0, 1, -2, -1, 0, 1, -1, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 2, 0, 0, -1, 0, -1, -1, 1, -2, 0, -2, -1, 0, -1, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, -1, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, -2, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, -2, 0, -1, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -2, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -1, 0, 0, -1, 0, 0, 1, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, -1, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, -1, -1, 0, 2, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, -1, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -2, 2, -2, -1, 0, 0, 0, 0, -1, -1, 0, -1, 0, 1, -1, 2, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -2, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 1, -2, 0, 0, 0, -1, -1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, -1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 2, 1, -2, 0, 0, 0, 0, 1, 0, -1, 1, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, -1, 2, 0, 1, 0, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 1, 0, -2, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, -1, 2, 0, 2, -1, 0, 0, 1, -1, 0, 0, -2, 0, -2, 0, 1, 0, 0, 0, -1, 0, 0, -1, -1, 0, -1, 0, 0, -1, 1, 2, 0, 2, -1, 0, 1, 0, 0, 0, 0, -2, 2, 1, 0, 0, 0, -1, -1, 2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, -1, 0, 1, 0, -2, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, -1, -2, 0, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, -2, 0, 1, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1, 1, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 1, 2, -1, 0, 1, 2, 0, -1, -1, 2, 0, -1, 1, -1, 0, 1, -1, 0, 0, 1, 1, -1, 0, 0, 0, -1, -2, 0, 0, 2, -1, 0, 0, 0, 1, 1, 0, -1, 1, 0, 1, 0, 0, 2, 1, -2, -1, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, -1, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, -2, -1, 1, 0, 0, 2, -2, 1, 0, 1, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 1, 0, 1, -1, 1, 2, 0, 0, -1, -1, 0, 1, -1, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1, 0, -1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, -1, -2, 1, 0, 1, -1, 1, -1, 0, -1, 0, 0, 0, 0, 1, 0, 2, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, -1, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, 1, 1, 1, 0, 0, 1, -2, -3, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -2, 0, -1, 0, 2, 0, 2, -2, -2, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, -1], 'weight': 1, 'weight_parity': -1}
  32. label: 104.1.h.b
    {'Nk2': 104, 'analytic_conductor': 0.05190276131383225, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-2, -1, 0, 1], 'artin_field_label': '3.1.104.1', 'artin_image': '6.1', 'char_conductor': 104, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 8, 'char_orbit_label': 'h', 'char_order': 2, 'char_parity': -1, 'char_values': [104, 2, [79, 53, 41], [1, 1, 1]], 'cm_discs': [-104], 'conrey_index': 51, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e3_13.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[5, [1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4504080680484968, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 104, 8, -1, 2, -104]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '104.1.h.b', 'level': 104, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 13], 'level_radical': 26, 'minimal_twist': '104.1.h.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 8, 'projective_field': [-2, -1, 0, 1], 'projective_field_label': '3.1.104.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e3_13.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-104], 'self_twist_type': 1, 'space_label': '104.1.h', 'trace_display': [1, -1, -1, -1], 'trace_hash': 1465355434445585020, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.003', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.970', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.960', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.896', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.812', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.600', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.512', 'prec': 17}, 'traces': [1, 1, -1, 1, -1, -1, -1, 1, 0, -1, 0, -1, 1, -1, 1, 1, -1, 0, 0, -1, 1, 0, 0, -1, 0, 1, 1, -1, 0, 1, 2, 1, 0, -1, 1, 0, -1, 0, -1, -1, 0, 1, -1, 0, 0, 0, -1, -1, 0, 0, 1, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 2, 0, 1, -1, 0, 0, -1, 0, 1, -1, 0, 0, -1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 1, 1, -1, 0, 0, 0, 0, -1, 0, -2, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, -1, 0, 2, 1, -1, 0, 1, -1, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 1, 0, 0, 1, 1, -1, -1, 0, 0, 0, -1, -1, 0, 0, -1, 1, 1, -1, 0, 0, 0, 0, 0, -1, 2, 0, -1, 0, 0, 0, -2, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 2, 1, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, -2, 0, -1, -1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, -1, 0, 1, 2, 1, 1, -2, -1, 0, 0, -1, 1, -1, -1, 0, 2, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 1, -1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, -1, 1, -1, 1, 1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 0, 0, 0, 0, -1, 0, 1, 0, 1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, -1, 0, 0, 0, 2, 0, 0, -1, -2, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 1, -1, 1, -2, 1, 0, 0, 1, -1, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, -1, 2, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, -1, -1, -1, 0, 0, 0, 1, 0, 2, 0, 1, -1, 1, -1, -2, 0, -1, 0, 0, 0, 0, 0, -1, -1, 1, 0, -1, -2, -1, 0, 0, 0, 2, 1, 0, 1, 0, 0, -1, -1, 0, -1, 0, 2, 0, 2, -1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, -1, 1, -1, 0, 0, 1, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 2, 1, 0, 0, 1, -2, 2, 0, 0, 0, 0, -1, 0, 2, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, -1, 0, 2, -1, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, -1, -1, -1, 0, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, -1, 1, 0, 0, -1, 1, -2, 2, 1, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, -1, 2, 0, 0, 0, 0, -1, 1, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, -1, -1, 0, 0, 1, 0, -1, 0, 1, 2, 0, 0, 0, 0, 0, -1, 2, -2, 0, 0, -1, 0, 0, -1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 1, 2, 0, 2, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, -1, -1, 0, 1, 0, -2, 0, 1, 0, 0, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 2, 1, 0, 0, 0, -1, 0, -1, 1, 2, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -2, -2, 0, 0, 0, -2, -1, 0, -1, -2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, 0, 2, -1, 2, -1, 1, -1, 0, -1, -1, 0, -1, 0, -2, 0, 0, 1, -1, 0, 0, 2, 2, 0, 2, 1, 0, -1, -1, 1, 0, -1, 0, -2, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, -1, 0, -1, 0, 1, 0, 0, 0, -1, 0, -2, 1, -1, 0, 0, 0, 0, 0, 0, -1, 2, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, -1, 0, 0, 2, 0, 0, 0, 2, 0, -1, 0, 2, 0, 0, 2, 0, 1, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 1, -1, 0, 0, -1, 0, -1, 0, 1, 3, -1, 0, 0, 0, 0, -1, 1, 0, 0, -1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, -1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, -1, 1, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 2, 0, -1, -1, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 1, -1, -2, 0, 0, 2, 1, -1, -1, 0, 0, 0, -1, -2, 1, 0, 1, 1, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, -2, 0, 0, -1, 0, -1, -1, -1, 2, 0, 2, -1, 0, 1, 2, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, -2, 0, 2, 0, 1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, -2, 0, 1, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -2, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, -1, -1, 0, 0, -1, 0, 0, -1, -2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 1, -1, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, -1, 1, 0, -2, 0, 1, 1, 0, 0, 0, -1, 1, 0, 0, 1, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 2, 2, -2, 1, 0, 0, 0, 0, -1, -1, 0, 1, 0, -1, -1, 2, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, -1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 1, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 1, -1, 1, 0, -1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, -2, 1, 2, 0, 0, 0, 0, -1, 0, 1, -1, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, -1, 2, 0, 1, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, -1, -1, 1, 0, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 1, 2, 0, -2, 1, 0, 0, 1, -1, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 1, -1, 0, -1, 0, 0, -1, -1, -2, 0, -2, -1, 0, -1, 0, 0, 0, 0, -2, 2, -1, 0, 0, 0, -1, -1, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, -1, 0, -2, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 0, 2, -2, 0, 0, -2, 0, -1, 2, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, 2, 0, -1, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, -1, -2, 1, 0, 1, 2, 0, -1, 1, 2, 0, -1, 1, 1, 0, -1, 1, 0, 0, -1, 1, -1, 0, 0, 0, -1, 2, 0, 0, -2, -1, 0, 0, 0, -1, 1, 0, -1, 1, 0, -1, 0, 0, 2, 1, 2, -1, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, -2, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, -1, 1, 0, 0, -2, 2, 1, 0, -1, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 2, 0, 0, -1, 1, 0, -1, 1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 0, -1, 0, 0, -2, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 2, 1, 0, -1, 1, -1, 1, 0, -1, 0, 0, 0, 0, -1, 0, 2, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 1, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 1, -1, -1, 0, 0, 1, -2, 3, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -2, 0, -1, 0, -2, 0, -2, 2, -2, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, 1], 'weight': 1, 'weight_parity': -1}
  33. label: 107.1.b.a
    {'Nk2': 107, 'analytic_conductor': 0.053399956351731254, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-2, 3, -1, 1], 'artin_field_label': '3.1.107.1', 'artin_image': '6.1', 'char_conductor': 107, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [107, 2, [2], [1]], 'cm_discs': [-107], 'conrey_index': 106, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.107.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254059, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 107, 2, -1, 2, -107]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '107.1.b.a', 'level': 107, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [107], 'level_radical': 107, 'minimal_twist': '107.1.b.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [-2, 3, -1, 1], 'projective_field_label': '3.1.107.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{3}+q^{4}-q^{11}-q^{12}-q^{13}+q^{16}+\\cdots', 'related_objects': ['ArtinRepresentation/2.107.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-107], 'self_twist_type': 1, 'space_label': '107.1.b', 'trace_display': [0, -1, 0, 0], 'trace_hash': 1621402541918698085, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.010', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.975', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.953', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.901', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.805', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.605', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.507', 'prec': 17}, 'traces': [1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, -1, 0, 0, 2, -1, 1, 0, 0, -1, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, -1, 0, 2, 0, 0, 0, -2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 1, 0, 0, 0, -1, -1, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, -1, -1, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, 2, 0, 0, -1, 0, 0, 1, 0, -2, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, -2, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 2, 1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, -1, 1, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 1, -1, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 2, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, -1, -2, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, -2, 0, 2, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, -2, 2, 0, -1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 1, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2, 0, -2, 0, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 2, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 2, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 2, 0, -1, 0, 1, 2, -1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 1, 0, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, -2, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, -2, 0, 0, 0, -1, -1, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 2, 1, -1, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, -1, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 1, 0, 0, -2, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  34. label: 108.1.c.a
    {'Nk2': 108, 'analytic_conductor': 0.05389902136436426, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-2, 0, 0, 1], 'artin_field_label': '3.1.108.1', 'artin_image': '6.1', 'char_conductor': 3, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 3, 'char_orbit_label': 'c', 'char_order': 2, 'char_parity': -1, 'char_values': [108, 2, [55, 29], [2, 1]], 'cm_discs': [-3], 'conrey_index': 53, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_3e3.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 137455730796, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '108.1.c.a', 'level': 108, 'level_is_powerful': True, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 3], 'level_radical': 6, 'minimal_twist': '108.1.c.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [-2, 0, 0, 1], 'projective_field_label': '3.1.108.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{7}-q^{13}-q^{19}+q^{25}+2q^{31}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_3e3.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '108.1.c', 'trace_display': [0, 0, 0, -1], 'trace_hash': 826169313317394634, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.016', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.967', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.936', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.870', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.741', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.481', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.509', 'prec': 17}, 'traces': [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0], 'weight': 1, 'weight_parity': -1}
  35. label: 111.1.d.a
    {'Nk2': 111, 'analytic_conductor': 0.05539621640226327, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [3, 0, -2, -1, 1], 'artin_field_label': '4.0.333.1', 'artin_image': '8.3', 'char_conductor': 111, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [111, 2, [38, 76], [1, 1]], 'cm_discs': [-3, -111], 'conrey_index': 110, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.3_37.4t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [0, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207535, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 111, 4, -1, 2, -111], [1, 1, 37, 2, 1, 2, 37]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '111.1.d.a', 'level': 111, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 37], 'level_radical': 111, 'minimal_twist': '111.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [81, 9, 10, -1, 1], 'projective_field_label': '4.0.12321.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3_37.4t3.2'], 'relative_dim': 1, 'rm_discs': [37], 'self_twist_discs': [-3, -111, 37], 'self_twist_type': 3, 'space_label': '111.1.d', 'trace_display': [0, 1, 0, -2], 'trace_hash': 84227207899207185, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.002', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.967', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.002', 'prec': 17}, {'__RealLiteral__': 0, 'data': '3.862', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.002', 'prec': 17}, {'__RealLiteral__': 0, 'data': '15.442', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.757', 'prec': 17}, 'traces': [1, 0, 1, -1, 0, 0, -2, 0, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 3, -1, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, -3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0], 'weight': 1, 'weight_parity': -1}
  36. label: 111.1.d.b
    {'Nk2': 111, 'analytic_conductor': 0.05539621640226327, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 16, 'artin_field': [1, -3, 6, -6, 5, -3, 3, -3, 1], 'artin_field_label': '8.0.4102893.1', 'artin_image': '16.7', 'char_conductor': 111, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [111, 2, [38, 76], [1, 1]], 'cm_discs': [-111], 'conrey_index': 110, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.3_37.8t6.1c2'], ['ArtinRepresentation/2.3_37.8t6.1c1']], 'field_disc': 8, 'field_disc_factorization': [[2, 3]], 'field_poly': [-2, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 8, 'has_non_self_twist': 1, 'hecke_cutters': [[2, [-2, 0, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503805802578031, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 111, 4, -1, 2, -111], [1, 1, 3, 2, -1, 2, 0], [1, 1, 37, 2, 1, 2, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '111.1.d.b', 'level': 111, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 37], 'level_radical': 111, 'minimal_twist': '111.1.d.b', 'nf_label': '2.2.8.1', 'prim_orbit_index': 4, 'projective_field': [-3, 0, 5, 0, 1], 'projective_field_label': '4.2.4107.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\beta q^{2}-q^{3}+q^{4}+\\beta q^{5}+\\beta q^{6}+q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3_37.8t6.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-111], 'self_twist_type': 1, 'space_label': '111.1.d', 'trace_display': [0, -2, 0, 0], 'trace_hash': 1982660780347013222, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.027', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.938', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.389', 'prec': 20}, {'__RealLiteral__': 0, 'data': '30.911', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-6.039', 'prec': 20}, {'__RealLiteral__': 0, 'data': '494.195', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.877', 'prec': 17}, 'traces': [2, 0, -2, 2, 0, 0, 0, 0, 2, -4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 4, 0, 0, 0, 4, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, -4, 0, 2, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 2, 0, -2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, -2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, -4, -4, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 4, 0, 0, 4, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 4, 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  37. label: 111.1.h.a
    {'Nk2': 111, 'analytic_conductor': 0.05539621640226327, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 111, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 8, 'char_orbit_label': 'h', 'char_order': 6, 'char_parity': -1, 'char_values': [111, 6, [38, 76], [3, 5]], 'cm_discs': [-3], 'conrey_index': 11, 'dim': 2, 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 481053114479, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 37, 5, 1, 6, 0], [1, 1, 111, 8, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '111.1.h.a', 'level': 111, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 37], 'level_radical': 111, 'minimal_twist': '111.1.h.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 8, 'projective_field': [-37, 0, 0, 0, 0, 0, 1], 'projective_field_label': '6.2.624095613.1', 'projective_image': 'D6', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{6}q^{3}+\\zeta_{6}q^{4}-\\zeta_{6}q^{7}+\\zeta_{6}^{2}q^{9}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '111.1.h', 'trace_display': [0, -1, 0, -1], 'trace_hash': 283288624854049103, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.022', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.939', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.308', 'prec': 20}, {'__RealLiteral__': 0, 'data': '17.266', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-4.487', 'prec': 20}, {'__RealLiteral__': 0, 'data': '191.336', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.646', 'prec': 17}, 'traces': [2, 0, -1, 1, 0, 0, -1, 0, -1, 0, 0, 1, -3, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -3, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, -3, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, -1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 3, 1, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -3, -1, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, -1, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -3, -1, 0, 0, -2, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 1, 0, 0, 3, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 3, 0, 0, -3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, -1, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 3, 0, -3, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, -2, 2, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 3, 0, 1, 0, 0, 0, -2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -3, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 3, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 3, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, -3, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, -3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, -3, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -3, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -2, 0, -3, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, -3, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -4, 0], 'weight': 1, 'weight_parity': -1}
  38. label: 111.1.i.a
    {'Nk2': 111, 'analytic_conductor': 0.05539621640226327, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [1, 2, -2, -2, 4, -3, 1], 'artin_field_label': '6.0.36963.1', 'artin_image': '18.3', 'char_conductor': 111, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 9, 'char_orbit_label': 'i', 'char_order': 6, 'char_parity': -1, 'char_values': [111, 6, [38, 76], [3, 2]], 'cm_discs': [-3], 'conrey_index': 26, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.3_37.6t5.1c1'], ['ArtinRepresentation/2.3_37.6t5.1c2']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 549772591215, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 37, 3, 1, 3, 0], [1, 1, 111, 9, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '111.1.i.a', 'level': 111, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 37], 'level_radical': 111, 'minimal_twist': '111.1.i.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 9, 'projective_field': [-37, 0, 0, 1], 'projective_field_label': '3.1.4107.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{6}q^{3}-\\zeta_{6}q^{4}+\\zeta_{6}q^{7}+\\zeta_{6}^{2}q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3_37.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '111.1.i', 'trace_display': [0, -1, 0, 1], 'trace_hash': 1343029396390960254, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.001', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.931', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.863', 'prec': 17}, {'__RealLiteral__': 0, 'data': '17.141', 'prec': 20}, {'__RealLiteral__': 0, 'data': '47.131', 'prec': 20}, {'__RealLiteral__': 0, 'data': '229.266', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.508', 'prec': 17}, 'traces': [2, 0, -1, -1, 0, 0, 1, 0, -1, 0, 0, -1, 1, 0, 0, -1, 0, 0, -2, 0, 1, 0, 0, 0, -1, 0, 2, 1, 0, 0, -2, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, 2, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 2, -2, 0, 0, 1, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, -1, 1, 0, -1, -2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -1, -2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -1, -2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 4, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -1, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 4, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, -1, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 4, 0, 0, 0, -1, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -2, 1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, -1, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 0, 0, 1, 0, 2, 0, 0, 4, 1, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, -2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -2, 1, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, -2, 0, 1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 1, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, -2, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 6, -2, 0, 0, 4, 0, -1, 0, 0, -1, -2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, -1, 0, 0, -4, 0, -2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, -2, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, -2, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, 0, 2, -2, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 4, 0, 4, -2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, -2, 0, -1, 2, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, 0, -2, -4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 1, -2, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 4, 0], 'weight': 1, 'weight_parity': -1}
  39. label: 112.1.l.a
    {'Nk2': 112, 'analytic_conductor': 0.05589528141489627, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 32, 'artin_field': [1, -2, 6, -9, 10, -8, 6, -3, 1], 'artin_field_label': '8.0.4917248.1', 'artin_image': '32.11', 'char_conductor': 112, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 12, 'char_orbit_label': 'l', 'char_order': 4, 'char_parity': -1, 'char_values': [112, 4, [15, 85, 17], [4, 3, 2]], 'cm_discs': [-7], 'conrey_index': 13, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e4_7.8t17.1c2'], ['ArtinRepresentation/2.2e4_7.8t17.1c1']], 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 755931021424, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7], [1, 1, 16, 5, 1, 4, 0], [1, 1, 112, 12, -1, 4, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '112.1.l.a', 'level': 112, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 7], 'level_radical': 14, 'minimal_twist': '112.1.l.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 12, 'projective_field': [-14, 0, -4, 0, 1], 'projective_field_label': '4.2.14336.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q+i q^{2}-q^{4}+i q^{7}-i q^{8}-i q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e4_7.8t17.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-7], 'self_twist_type': 1, 'space_label': '112.1.l', 'trace_display': [0, 0, 0, 0], 'trace_hash': 1969106827830686596, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.010', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.934', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.132', 'prec': 17}, {'__RealLiteral__': 0, 'data': '18.942', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.023', 'prec': 17}, {'__RealLiteral__': 0, 'data': '255.066', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.692', 'prec': 17}, 'traces': [2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -4, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, -2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -2, 0, 4, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  40. label: 116.1.d.a
    {'Nk2': 116, 'analytic_conductor': 0.05789154146542828, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 12, 'artin_field': [2, 2, 1, -2, 0, 0, 1], 'artin_field_label': '6.0.53824.1', 'artin_image': '12.4', 'char_conductor': 116, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [116, 2, [59, 89], [1, 1]], 'cm_discs': [-116], 'conrey_index': 115, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_29.6t3.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207540, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 116, 4, -1, 2, -116]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '116.1.d.a', 'level': 116, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 29], 'level_radical': 58, 'minimal_twist': '116.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [-2, 0, -1, 1], 'projective_field_label': '3.1.116.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_29.6t3.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-116], 'self_twist_type': 1, 'space_label': '116.1.d', 'trace_display': [-1, 1, -1, 0], 'trace_hash': 865784085630758838, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.010', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.959', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.039', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.839', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.156', 'prec': 20}, {'__RealLiteral__': 0, 'data': '10.356', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.511', 'prec': 17}, 'traces': [1, -1, 1, 1, -1, -1, 0, -1, 0, 1, 1, 1, -1, 0, -1, 1, 0, 0, -2, -1, 0, -1, 0, -1, 0, 1, -1, 0, 1, 1, 1, -1, 1, 0, 0, 0, 0, 2, -1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, -1, -1, 1, -1, 0, -2, -1, 0, -1, 0, -1, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 1, -1, -1, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 1, -1, 2, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, -1, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, -2, -1, 1, -1, -2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 0, 2, 0, 0, -1, -1, 0, -1, -1, 1, 0, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 2, -1, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, -2, -2, 1, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 1, -1, 0, 0, -1, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, -1, 0, -1, 0, 1, 0, 0, -1, -1, 0, 0, 0, -1, 0, 2, -1, 0, -1, 1, 0, 0, 2, 0, 1, -1, -1, 0, 1, 0, 2, 1, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, -1, 0, 0, 2, 1, 0, 0, 1, 1, 0, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 1, -2, 1, -1, 0, 0, 1, 0, 1, 1, -1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, -2, 0, 1, -1, 0, 1, -1, 2, 0, 0, 0, 0, 0, 1, 0, 3, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, -1, 0, 1, -1, -1, 0, -2, 2, -2, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, -2, -2, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, -1, -1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, -2, -1, 0, 0, -1, 2, 1, 0, 1, 1, 0, 2, -1, -1, 0, 0, -2, 0, -1, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 2, 0, -1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, -2, 0, -1, -2, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 1, -2, 0, 2, 0, -1, 1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 1, -1, 0, 2, 0, -1, -1, 1, -2, 0, 0, 0, 0, -1, 1, 0, 2, -1, -1, -1, 0, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, -1, 0, 1, -1, 0, -1, -1, 0, 1, -1, -2, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -3, -1, -1, 0, 0, -2, 0, 1, 0, 0, 0, 0, 2, -1, 0, 0, 0, 1, 0, 2, 0, -2, -1, 1, 1, 0, 0, 0, -1, -2, 1, 1, 1, 0, 0, 0, 2, 0, -2, 2, 2, 0, -2, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0, 2, 0, 2, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, -1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 0, -2, -1, 0, 1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, 1, -2, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, -1, 0, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 1, -2, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 2, 1, -2, -1, -2, -1, 0, 0, 2, 0, -1, -1, -1, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, -1, 0, 2, 0, 1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, -1, 1, 0, -2, 0, 0, 2, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 2, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, -1, 0, 1, 1, 0, -2, -1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -2, 0, 1, 0, 1, 0, 0, 2, 0, -1, 2, 2, 0, 0, 1, 1, 0, -1, -1, 0, -1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, 0, 3, 1, 0, 1, 1, 0, 0, -1, 1, 0, 2, 0, 0, 0, -1, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, -2, 0, 0, 0, 1, -1, 0, 0, 0, -2, -1, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 1, -1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -2, 0, 0, -1, 1, -2, -1, 0, 0, -1, 1, 2, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, -1, 0, -2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 1, 1, 0, 1, 0, -1, 0, 2, -1, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, -2, 0, 1, 0, 1, 0, 1, -1, 0, 1, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 1, -1, 0, 0, 1, -1, 0, -2, 0, 0, 0, 0, -1, 0, 0, -1, -2, 1, -1, -2, -1, 1, 0, 0, 0, 0, -2, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -2, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, -1, 0, 1, 0, 2, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, 1, 0, -2, 0, -2, 0, 0, 3, -1, 1, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, -2, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 1, 2, -2, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 2, 0, -1, 0, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, -2, 0, 0, 1, 2, 0, -2, 1, -2, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, -1, 0, 0, -1, 0, 1, 1, 0, -1, 0, 0, 0, -2, 0, 0, 0, -2, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -1, -1, 1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 0, -1, 0, 0, 1, -1, 0, 0, 2, 0, 0, 0, 0, 2, 0, -2, -1, -1, 0, -1, 0, 0, 0, 0, -2, -2, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 1, 0, 0, -1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, 0, -2, 0, 0, 0, 0, -1, 0, 2, 0, 0, -1, -1, 0, 0, 0, -1, 0, -1, -1, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, -2, 1, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 2, -2, -1, -1, 0, 0, 0, 1, 0, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, -1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, -1, 2, 2, 0, 1, 1, 2, -2, 1, 0, 0, -2, 0, 0, -2, -1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, -1, 2, -1, 0, 0, 0, 0, -1, 0, 2, 0, 2, 1, 0, 0, 0, -2, -1, 0, -1, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, -1, 0, 0, 0, 2, 0, 0, -1, 0, 0, -2, 1, 0, 0, 0, 0, 0, 2, 1, 1, -1, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -2, 1], 'weight': 1, 'weight_parity': -1}
  41. label: 116.1.d.b
    {'Nk2': 116, 'analytic_conductor': 0.05789154146542828, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-2, 0, -1, 1], 'artin_field_label': '3.1.116.1', 'artin_image': '6.1', 'char_conductor': 116, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [116, 2, [59, 89], [1, 1]], 'cm_discs': [-116], 'conrey_index': 115, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_29.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503805802578036, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 116, 4, -1, 2, -116]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '116.1.d.b', 'level': 116, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 29], 'level_radical': 58, 'minimal_twist': '116.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [-2, 0, -1, 1], 'projective_field_label': '3.1.116.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_29.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-116], 'self_twist_type': 1, 'space_label': '116.1.d', 'trace_display': [1, -1, -1, 0], 'trace_hash': 1387955392980470432, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.016', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.959', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.924', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.839', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.683', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.356', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.511', 'prec': 17}, 'traces': [1, 1, -1, 1, -1, -1, 0, 1, 0, -1, -1, -1, -1, 0, 1, 1, 0, 0, 2, -1, 0, -1, 0, -1, 0, -1, 1, 0, 1, 1, -1, 1, 1, 0, 0, 0, 0, 2, 1, -1, 0, 0, -1, -1, 0, 0, -1, -1, 1, 0, 0, -1, -1, 1, 1, 0, -2, 1, 0, 1, 0, -1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 1, -1, -2, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, -1, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 1, 0, 2, 1, 1, 1, 2, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 0, 2, 0, 0, 1, 1, 0, -1, 1, -1, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, -1, 0, -2, 2, -1, 0, 0, -1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, -1, -1, 0, 0, 1, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, -1, 0, 1, 0, 1, 0, 0, 1, -1, 0, 0, 0, -1, 0, -2, -1, 0, 1, -1, 0, 0, 2, 0, 1, -1, 1, 0, 1, 0, 2, -1, 1, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 1, 0, 0, 2, 1, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 1, 2, 1, -1, 0, 0, -1, 0, 1, -1, -1, 0, 0, 0, -1, 0, -1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, -1, -1, 0, -1, -1, 2, 0, 0, 0, 0, 0, -1, 0, 3, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, -1, 0, -1, -1, -1, 0, 2, -2, -2, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, -2, 2, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, -2, 0, -1, 0, 0, 0, 1, 0, -1, -1, 0, 0, 0, 0, 2, -1, 0, 0, 1, 2, -1, 0, 1, 1, 0, -2, 1, -1, 0, 0, 2, 0, -1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 2, 0, 1, -2, 0, 0, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, -2, 0, -2, 0, -1, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 1, 0, -1, -1, 0, 0, 0, 0, -1, 1, 0, 2, 0, 1, -1, -1, 2, 0, 0, 0, 0, -1, 1, 0, -2, 1, -1, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 1, -2, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 2, 0, 0, 0, -1, 0, -1, 1, 0, -1, -1, 0, -1, -1, 2, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 3, 1, -1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, -1, 0, 2, 0, 2, 1, 1, -1, 0, 0, 0, -1, 2, -1, 1, -1, 0, 0, 0, 2, 0, -2, 2, -2, 0, 2, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, -2, 0, 2, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, -2, 0, 0, 0, -1, 0, 2, 0, 0, 0, -1, 0, 0, 0, -2, -1, 0, 0, 0, -2, -1, 0, -1, 0, 1, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 0, 0, 0, 1, -2, 0, -1, 0, 1, 1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 1, 0, -2, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, -1, -2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, -1, 2, -1, -2, -1, 0, 0, 2, 0, 1, 1, -1, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, -1, 0, -2, 0, 1, -1, 0, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, -1, -1, 0, -2, 0, 0, -2, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, -2, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, -1, 0, -1, 1, 0, 2, 1, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 1, 0, -1, 0, 0, 2, 0, 1, 2, 2, 0, 0, -1, 1, 0, 1, 1, 0, 1, -2, 1, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, 0, -3, -1, 0, 1, -1, 0, 0, 1, -1, 0, 2, 0, 0, 0, -1, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 2, -1, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -1, -1, 0, -1, 0, 1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -2, 0, 0, -1, -1, 2, -1, 0, 0, 1, -1, 2, 0, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, -1, 0, 2, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, -1, 1, 0, -1, 0, -1, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 1, 0, 0, -1, -2, 0, 1, 0, -1, 0, -1, -1, 0, -1, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, -1, -1, 0, 0, -1, 1, 0, -2, 0, 0, 0, 0, 1, 0, 0, -1, 2, -1, -1, 2, 1, -1, 0, 0, 0, 0, -2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 1, 0, 0, 1, -1, 0, -1, 1, 0, 0, -1, 0, -1, 0, 2, 0, 0, 0, 0, 1, -1, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 1, 0, 2, 0, -2, 0, 0, 3, -1, 1, -1, -1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 1, 2, 2, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -2, 2, 0, -1, 0, 1, 0, -1, 1, 0, -1, 0, 0, 0, 0, 2, 0, 0, -1, -2, 0, 2, -1, -2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, -2, 0, 0, 0, 0, -1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, -1, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -1, 1, -1, 0, 0, 1, 0, 0, 0, -2, -1, 0, 2, 0, 1, 0, 0, -1, 1, 0, 0, 2, 0, 0, 0, 0, -2, 0, -2, -1, 1, 0, -1, 0, 0, 0, 0, -2, 2, -1, 0, 0, -1, 0, 2, 0, -2, -2, 0, -1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, -2, 0, 0, -1, -1, 0, 0, 0, 1, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, -1, -1, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, -2, 2, 1, -1, 0, 0, 0, 1, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, -1, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, -1, 2, 2, 0, -1, 1, -2, 2, -1, 0, 0, 2, 0, 0, 2, 1, 0, 0, 1, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, -1, -2, 1, 0, 0, 0, 0, -1, 0, -2, 0, 2, -1, 0, 0, 0, -2, 1, 0, -1, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 2, -1, 0, 0, 0, -2, 0, 0, -1, 0, 0, -2, 1, 0, 0, 0, 0, 0, -2, -1, 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 1], 'weight': 1, 'weight_parity': -1}
  42. label: 116.1.j.a
    {'Nk2': 116, 'analytic_conductor': 0.05789154146542828, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 116, 'char_degree': 6, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 10, 'char_orbit_label': 'j', 'char_order': 14, 'char_parity': -1, 'char_values': [116, 14, [59, 89], [7, 6]], 'cm_discs': [-4], 'conrey_index': 7, 'dim': 6, 'field_disc': -16807, 'field_disc_factorization': [[-1, 1], [7, 5]], 'field_poly': [1, -1, 1, -1, 1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 14, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 618492067956, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 29, 4, 1, 7, 0], [1, 1, 116, 10, -1, 14, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '116.1.j.a', 'level': 116, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 29], 'level_radical': 58, 'minimal_twist': '116.1.j.a', 'nf_label': '6.0.16807.1', 'prim_orbit_index': 10, 'projective_field': [162, -36, -9, 35, -14, 8, -3, 1], 'projective_field_label': '7.1.38068692544.1', 'projective_image': 'D7', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{14}q^{2}+\\zeta_{14}^{2}q^{4}+(\\zeta_{14}^{4}-\\zeta_{14}^{5}+\\cdots)q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-4], 'self_twist_type': 1, 'space_label': '116.1.j', 'trace_display': [-1, 0, -2, 0], 'trace_hash': 2284398938021220915, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.037', 'prec': 20}, {'__RealLiteral__': 0, 'data': '5.411', 'prec': 17}, {'__RealLiteral__': 0, 'data': '22.737', 'prec': 20}, {'__RealLiteral__': 0, 'data': '204.671', 'prec': 24}, {'__RealLiteral__': 0, 'data': '1829.788', 'prec': 27}, {'__RealLiteral__': 0, 'data': '19396.733', 'prec': 30}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.504', 'prec': 17}, 'traces': [6, -1, 0, -1, -2, 0, 0, -1, -1, -2, 0, 0, -2, 0, 0, -1, -2, -1, 0, 5, 0, 0, 0, 0, -3, 5, 0, 0, -1, 0, 0, -1, 0, 5, 0, -1, -2, 0, 0, 5, -2, 0, 0, 0, 5, 0, 0, 0, -1, -3, 0, -2, 5, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, -1, 3, 0, 0, -2, 0, 0, 0, -1, 5, -2, 0, 0, 0, 0, 0, -2, -1, -2, 0, 0, -4, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 5, -1, 0, -3, -2, 0, 0, -2, 0, -2, 0, 0, 5, 0, 0, 0, -2, 0, 0, -1, -2, 0, 0, 0, -1, 5, 0, 0, 3, 0, 0, 6, 0, 3, 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 0, 6, -2, -2, 0, 5, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 6, 0, 5, 0, 0, 0, 0, -3, 3, 0, 0, -2, 0, 0, 0, 0, -2, 0, -2, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, -1, -2, 0, 0, -3, 0, -2, 0, 0, 3, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, -3, -2, 0, 0, -2, 0, 0, 6, -2, -2, 0, 0, 0, 0, 0, 0, -2, -1, 0, -2, 5, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 5, 0, 0, -4, 6, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, -2, 0, 5, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 4, -2, 0, 5, 5, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 5, 0, 0, -2, 0, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, -3, 0, 3, 0, 0, 0, 0, 0, 5, 0, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, -2, -1, -2, 0, 0, -4, 0, 0, 0, -2, 3, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, -2, -2, 0, 0, -1, 0, -2, 0, 0, -2, 0, 0, 4, -2, 0, 0, -2, -2, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, -2, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -1, -4, 0, 0, -4, 0, 0, 0, 5, 4, 0, -2, 0, 0, 0, 0, -2, 5, 0, 0, -2, 0, 0, -1, 0, -2, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 10, -2, 0, -1, -4, 0, 0, 5, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 10, 0, 0, 0, -2, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 3, -2, -1, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, -2, 3, 0, 0, -2, 5, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 5, -3, 0, -2, 0, 0, 0, -2, 3, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, -2, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, -5, -2, 0, -2, 3, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -1, 0, -6, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 5, 0, 4, -2, 0, 0, 3, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, -4, 5, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, -2, 4, 0, 0, 0, -1, -4, 0, 0, -2, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 3, 5, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 5, -2, 0, 0, 5, 0, 5, 0, 0, 0, 0, 0, 6, 3, 0, 0, -2, 0, 0, 0, 0, -4, -2, 0, 0, -2, 0, 0, 4, 5, 5, 0, 0, 0, 0, 0, -2, 5, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, 12, 0, 0, -6, 0, 0, -2, 0, -6, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, -2, 0, 0, 0, -2, 6, 0, 3, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, -4, 0, 0, -2, 3, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, -1, -2, 0, 0, -2, 0, 0, 0, -2, 5, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 5, -2, 0, 0, 0, 0, 0, 0, -1, -4, 0, -2, -4, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, -2, 5, 0, 0, -2, -2, 0, 0, 0, 10, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, -2, 0, 0, 0, -2, 5, 0, 0, 5, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 3, 0, -2, 0, -1, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 3, -2, 0, 0, 0, 0, -4, 0, 0, 5, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 5, -1, -4, 0, 0, 5, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 5, 5, 0, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, -2, 10, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -1, -2, -2, 0, 4, 3, 0, 0, -2, 0, 0, 0, 0, 3, 0, 0, -2, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 5, -3, -2, 0, 0, 5, 0, 0, 0, -2, 5, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 5, 0, 0, 0, 5, 0, 3, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 1, -2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 5, -4, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -6, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, -2, 0, -2, 0, 0, 0, 4, 0, 5, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, -3, -4, 0, 0, -2, 0, 0, 0, 5, 3, 0, 0, 5, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, -2, 0, 0, -2, 5, 0, 0, 0, -4, -2, 0, 0, 6, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 1, 0, 0, -2, 0, 4, 0, 0, -2, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 3, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, -2, 0, 0, 3, 0, 0, 0, 4, -2, 0, 0, 8, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 5, 0, 0, -2, 0, 0, -2, 5, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, 0, -4, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 4, 5, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, -2, 0, -2, -2, 0, 0, 0, 6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, -4, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, 0, -2, 3, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 5, -2, 0, 0, -6, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 12, 0, 0, 5, -4, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 3, 0, 0, -4, -2, 0, 0, 0, -2, 0, 0, 0, 5, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 4, -2, 3, 0, 0, -2, 0, 0, -2, 0, 10, 0, 0, -2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -4, 0, 0, 0, -1, 1, 0, 0, -4, 0, 0, -1, 0, -2, 0, 0, -2, 0, 0, 5, -4, 0, 0, 0, 0, 0, 0, -2, -2, 5, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 5, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, -4, 0, 0, 0, 5, 0, -4, 0, 0, -2, 0, 0, -1, 3, 0, 0, 3, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, -2, 0, 5, 0, 0, 0, 0, 0, -2, 3, 5, 0, 0, 0, 0, 0, 0, 0, 3, 0, 5, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, -4], 'weight': 1, 'weight_parity': -1}
  43. label: 117.1.j.a
    {'Nk2': 117, 'analytic_conductor': 0.05839060647806128, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 32, 'artin_field': [1, 0, -2, 3, 3, -3, -2, 0, 1], 'artin_field_label': '8.0.1601613.1', 'artin_image': '32.11', 'char_conductor': 13, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 10, 'char_orbit_label': 'j', 'char_order': 4, 'char_parity': -1, 'char_values': [117, 4, [92, 28], [4, 1]], 'cm_discs': [-3], 'conrey_index': 73, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.3e2_13.8t17.1c2'], ['ArtinRepresentation/2.3e2_13.8t17.1c1']], 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 618492067957, 'hecke_ring_generator_nbound': 4, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 13, 4, -1, 4, 0], [1, 1, 39, 6, 1, 4, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '117.1.j.a', 'level': 117, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [3, 13], 'level_radical': 39, 'minimal_twist': '117.1.j.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 4, 'projective_field': [3, -9, 2, -1, 1], 'projective_field_label': '4.2.6591.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q+i q^{4}+(-i-1)q^{7}-i q^{13}-q^{16}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3e2_13.8t17.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '117.1.j', 'trace_display': [0, 0, 0, -2], 'trace_hash': 116221446893402629, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.008', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.883', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.218', 'prec': 17}, {'__RealLiteral__': 0, 'data': '17.992', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.860', 'prec': 17}, {'__RealLiteral__': 0, 'data': '239.315', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.693', 'prec': 17}, 'traces': [2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  44. label: 119.1.d.a
    {'Nk2': 119, 'analytic_conductor': 0.05938873650332729, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 10, 'artin_field': [-1, 3, -1, 0, -1, 1], 'artin_field_label': '5.1.14161.1', 'artin_image': '10.1', 'char_conductor': 119, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [119, 2, [52, 71], [1, 1]], 'cm_discs': [-119], 'conrey_index': 118, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.7_17.5t2.1c2'], ['ArtinRepresentation/2.7_17.5t2.1c1']], 'field_disc': 5, 'field_disc_factorization': [[5, 1]], 'field_poly': [-1, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-1, 1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207543, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 119, 4, -1, 2, -119]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '119.1.d.a', 'level': 119, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [7, 17], 'level_radical': 119, 'minimal_twist': '119.1.d.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 4, 'projective_field': [-1, 3, -1, 0, -1, 1], 'projective_field_label': '5.1.14161.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(-1+\\beta )q^{2}+(-1+\\beta )q^{3}+(1-\\beta )q^{4}+\\cdots', 'related_objects': ['ArtinRepresentation/2.7_17.5t2.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-119], 'self_twist_type': 1, 'space_label': '119.1.d', 'trace_display': [-1, -1, -1, 2], 'trace_hash': 1916917777867569182, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.040', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.861', 'prec': 17}, {'__RealLiteral__': 0, 'data': '5.400', 'prec': 17}, {'__RealLiteral__': 0, 'data': '23.596', 'prec': 20}, {'__RealLiteral__': 0, 'data': '92.295', 'prec': 20}, {'__RealLiteral__': 0, 'data': '371.083', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.502', 'prec': 17}, 'traces': [2, -1, -1, 1, -1, 3, 2, -2, 1, -2, 0, -3, 0, -1, -2, 0, 2, -3, 0, 2, -1, 0, 0, 1, 1, 0, -2, 1, 0, 1, -1, 2, 0, -1, -1, 3, 0, 0, 0, 1, -1, 3, -1, 0, 2, 0, 0, 0, 2, 2, -1, 0, -1, 1, 0, -2, 0, 0, 0, -1, -1, -2, 1, -1, 0, 0, -1, 1, 0, -2, 0, -1, -1, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, -3, -1, 3, 0, 0, 0, -1, 0, 0, -2, 0, 0, -1, -1, -1, 0, -2, 0, 3, 0, 0, -2, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 3, 3, 2, -2, -3, -1, 1, 3, 0, 4, 0, 0, -2, 1, -2, -1, 0, -1, 2, 0, 0, 0, 0, 0, 3, -1, 0, -1, -1, -1, 0, 1, 0, 3, 0, 0, 0, -2, -1, 0, 0, 0, -3, 0, 0, -1, 1, 2, -2, 0, -3, -1, 0, 1, 0, 0, 0, -1, 1, 4, 0, 3, 0, 0, 1, 0, 0, -2, 0, -1, 3, 0, -2, 0, 1, 0, 0, -1, -1, -2, 0, 0, -3, -2, 0, 0, 0, 0, 1, 0, 2, 0, 0, -2, 2, -1, 0, 3, 0, 0, 0, 0, 2, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, -1, 2, -3, -1, -4, 0, 1, 0, 1, 0, 3, 0, -2, -2, -2, 0, -4, 0, 0, 0, -2, 4, 0, 3, 0, 0, 2, 4, 2, 0, 0, 0, 3, 0, 0, 0, -2, 2, 1, -1, 0, -1, 0, 0, 0, -1, 1, 2, 0, -2, -3, 0, 3, 0, 0, 0, 3, 0, 1, -1, 3, 0, 0, -2, -3, 0, 0, 0, 1, -1, 0, -1, 0, 2, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 3, 3, 0, 0, -1, 0, 2, 0, 0, 2, 1, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 3, -1, -2, 2, -2, -1, 0, -2, -4, -1, 0, -3, 0, -1, -1, -1, 0, 1, 0, 0, 1, 0, 0, -2, -2, 0, -3, 0, 0, -3, 2, -1, 0, 0, -2, -2, 0, 0, 0, -1, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 3, 0, 0, 0, 0, 0, -2, 0, -1, -1, -1, 0, 0, 1, 1, 0, -1, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, -4, -1, 0, 1, 0, 4, 0, 0, 0, 3, -1, 0, 1, 0, 0, 3, -2, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 2, 3, -1, -2, 0, -2, 0, 1, 3, -1, 0, 1, 0, -2, -1, 4, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, -1, -1, 0, 0, -1, 2, 0, 1, -1, 0, 0, 0, 0, 4, 0, 0, 3, 0, -1, 0, 0, 2, 2, -2, -1, 0, 2, 1, 0, 0, 0, 0, 0, 1, 3, -2, 0, -2, 0, 0, -2, 2, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 2, 4, -1, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, -2, 3, 0, -3, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -1, -3, 3, 0, -1, -2, 4, 3, 2, -3, -1, 0, -1, 0, 0, 1, 0, 3, -1, 0, 1, 0, 0, 0, 4, -1, 0, -2, 0, 0, 0, -2, 0, 0, 0, -1, -1, 0, 0, 0, 3, -1, 0, 0, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -3, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, 1, 0, -1, 0, 0, -1, 1, 4, 0, -1, 1, -2, 0, 0, 0, -2, -1, 0, 0, 0, 0, -1, -3, 0, 0, 3, 0, -1, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 3, -2, -1, 0, 0, -1, -2, 2, 0, 3, 0, 0, -1, 1, -1, 4, 0, 3, -2, 0, 0, 4, -1, 0, 0, -2, 0, 2, -2, 3, 0, 0, 0, -3, 0, 0, 0, 0, -2, -1, -1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 4, -3, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 6, 4, 0, -2, 0, 0, 0, 0, -2, 1, -3, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, -2, 0, 1, -2, 4, 2, 2, 3, -2, 0, -1, 0, 2, 0, -2, 2, 0, 0, 4, 3, 0, 0, -1, 0, 0, -1, 3, 0, -1, -2, -2, 0, -1, 2, 0, 0, 0, 0, 2, 0, -2, 4, 0, 3, 0, 0, -1, -3, -1, 0, 0, -2, -1, 0, -1, 0, 0, 0, 0, -4, -2, 1, 0, 0, 0, -1, -1, 0, 3, 0, -2, -4, 0, 2, 0, 0, 0, 0, 0, -2, 1, 0, 4, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 2, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, -1, -1, 3, -3, 0, 3, -1, 1, 1, 0, 0, 2, 0, 0, -1, -2, 0, 1, 0, 1, -1, 0, 0, 0, -1, 0, 0, 2, 0, -2, -1, -3, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, -2, 0, -1, 0, 0, 2, 0, -4, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, -1, 3, 0, 1, 0, 0, 4, -1, 0, 3, 0, 2, 2, 0, 0, 0, -1, 0, 0, -3, -1, 0, 0, 0, -1, -4, 0, 0, 0, 3, -1, 0, 0, 0, 0, -4, -1, -1, 0, 2, 0, -2, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -4, 2, 2, -2, 0, 0, -1, 0, 0, -1, 0, 3, 6, 4, -1, 1, 0, -1, 0, 0, 0, 1, 1, 0, 4, 0, 0, 3, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, -2, -2, 0, 1, 0, 0, 3, -1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 3, -1, 0, 0, 0, 2, 0, 0, 1, 0, -3, 0, 0, 4, 3, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -2, 0, -1, 0, 4, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, -2, 1, -1, -4, -2, 0, 0, 3, 0, 0, 0, -2, 0, -3, 3, -1, 0, 1, 0, -2, -1, 0, 0, -2, -1, 0, -1, 0, 0, -1, 0, 0, 0, -1, 1, -2, 0, 0, 0, -3, -1, 0, -3, 0, 0, 0, 0, -2, 0, -3, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, -1, 0, 0, 0, -2, 0, 0, 1, 0, -2, 3, 0, 0, 0, 4, 0, 0, 1, -2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 3, 0, -1, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, 0, -1, 0, 4, -2, 0, 3, -2, -1, 0, -1, 0, -2, 2, -3, 0, 4, 0, -2, 0, 0, 0, -2, 0, 0, 1, -1, 0, 0, -1, -3, 0, 0, 3, -2, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, -2, -3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, -2, 1, -1, 0, 0, -1, 0, 0, 0, 0, -1, 3, 0, 1, 0, 0, 0, 0, 3, 1, 0, 0, -1, 3, -1, 0, 0, 0, -1, -1, 0, -2, 0, 0, 3, 0, -2, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -1, 0, 1, 1, 4, -4, -2, 2, 3, 3, 0, 2, 0, 0, 0, 1, -1, 1, 0, -4, 0, 0, 0, -3, -1, 0, 1, 0, 0, 3, 4, -1, 0, 3, 0, -3, 0, 0, 0, -3, 0, 1, 4, 0, -2, 0, 0, -4, 0, 3, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 4, 1, 0, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, -2, 0, 0, 0, -2, 1, 0, 2, 0, 3, 0, 0, 0, 0, -1, 0, 1, 0, 0, -1, 2, 0, 0, 1, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, -1, 0, 0, -1, 0, 3, 2, -3, 0, -1, 0, 0, 0, 3, 0, 3, 0, -1, 2, 0, 0, -1, -6, 0, -2, -2, 0, 0, 6, -1, 0, -2, 0, -1, 0, 0, 0, -1, 2, -1, 2, 0, 1, 0, 0, 0, 0, -1, 0, 0, 2, -1, 0, 0, 0, 0, 0, -1, 2, -1, 0, -3, 0, 0, 6, 0, 0, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, -1, 0, 2, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 3, 4, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, -2, 0, -1, 2, -3, 2, 0, -2, 0, 0, 1, -1, 0, -3, 0, 1, -1, 0, 0, -2, 0, 0, -1, -1, 0, -1, -1, 1, 0, -2, 2, 0, 0, 0, 0, -2, 3, -3, -1, 0, 0, 0, 0, -2, -1, 0, 0, 0, 2, 2, 0, -4, 0, 0, 0, -2, 0, 1, 0, 1, 0, 0, -1, 3, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 4, 0, 0, 1, 0, -3, 0, 0, 0, -3, 0, 0, -1, 0, 0, -2, 3, 3, 0, -2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, -1, 4, -1, 1, -3, -2, 0, 0, 3, 0, 3, 0, 0, 2, -1, -2, -2, 0, -1, -4, 0, 0, 1, -4, 0, 4, 0, 0, -2, 1, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 2, 0, -3, 0, 0, 0, -2, -2, -1, 0, 3, -2, 0, 4, 0, 0, 0, -1, 0, 4, 0, 1, 0, 0, -3, 0, 0, 3, 0, -2, -2, 0, -2, 0, 0, 0, 0, -2, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 3, 4, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -1, 1, 0, 1, 0, 1, 4, 0, 0, -3, 0, 3, 0, -1, 0, 2, 0, 0, 0, 0, 0, 1, 3, 0, -1, 0, 0, 3, -1, 0, 0, 0, 0, -1, 0, 0, 0, -2, 3, -2, 0, 0, -1, 0, 0, -1, 2, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, -4, -2, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -1, 0, -1, 0, 0, -2, 3, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 4, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  45. label: 119.1.d.b
    {'Nk2': 119, 'analytic_conductor': 0.05938873650332729, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 20, 'artin_field': [1, -1, -2, 4, 0, -4, 6, -7, 6, -3, 1], 'artin_field_label': '10.0.1403737447.1', 'artin_image': '20.4', 'char_conductor': 119, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [119, 2, [52, 71], [1, 1]], 'cm_discs': [-119], 'conrey_index': 118, 'dim': 2, 'field_disc': 5, 'field_disc_factorization': [[5, 1]], 'field_poly': [-1, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-1, -1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503805802578039, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 119, 4, -1, 2, -119]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '119.1.d.b', 'level': 119, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [7, 17], 'level_radical': 119, 'minimal_twist': '119.1.d.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 4, 'projective_field': [-1, 3, -1, 0, -1, 1], 'projective_field_label': '5.1.14161.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(-1+\\beta )q^{2}+(1-\\beta )q^{3}+(1-\\beta )q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-119], 'self_twist_type': 1, 'space_label': '119.1.d', 'trace_display': [-1, 1, 1, -2], 'trace_hash': 2187514003097039183, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.030', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.861', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.567', 'prec': 20}, {'__RealLiteral__': 0, 'data': '23.596', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-9.018', 'prec': 20}, {'__RealLiteral__': 0, 'data': '371.083', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.502', 'prec': 17}, 'traces': [2, -1, 1, 1, 1, -3, -2, -2, 1, 2, 0, 3, 0, 1, -2, 0, -2, -3, 0, -2, -1, 0, 0, -1, 1, 0, 2, -1, 0, 1, 1, 2, 0, 1, -1, 3, 0, 0, 0, -1, 1, 3, -1, 0, -2, 0, 0, 0, 2, 2, -1, 0, -1, -1, 0, 2, 0, 0, 0, -1, 1, 2, -1, -1, 0, 0, -1, -1, 0, -2, 0, -1, 1, 0, -2, 0, 0, 0, 0, 0, 0, -3, 0, -3, -1, 3, 0, 0, 0, 1, 0, 0, -2, 0, 0, 1, 1, -1, 0, -2, 0, 3, 0, 0, 2, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -3, 3, -2, 2, 3, -1, 1, -3, 0, -4, 0, 0, -2, 1, 2, -1, 0, 1, 2, 0, 0, 0, 0, 0, -3, 1, 0, -1, 1, -1, 0, -1, 0, 3, 0, 0, 0, 2, 1, 0, 0, 0, 3, 0, 0, 1, 1, 2, -2, 0, -3, 1, 0, -1, 0, 0, 0, -1, -1, -4, 0, 3, 0, 0, 1, 0, 0, -2, 0, -1, -3, 0, 2, 0, 1, 0, 0, 1, -1, 2, 0, 0, -3, -2, 0, 0, 0, 0, -1, 0, 2, 0, 0, 2, -2, -1, 0, 3, 0, 0, 0, 0, -2, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, -1, -2, 3, 1, -4, 0, -1, 0, -1, 0, -3, 0, -2, 2, -2, 0, 4, 0, 0, 0, 2, 4, 0, -3, 0, 0, 2, -4, 2, 0, 0, 0, 3, 0, 0, 0, 2, -2, 1, -1, 0, 1, 0, 0, 0, -1, 1, 2, 0, -2, 3, 0, -3, 0, 0, 0, 3, 0, -1, 1, 3, 0, 0, -2, 3, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -3, -3, 0, 0, -1, 0, 2, 0, 0, -2, 1, 0, -3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 3, -1, 2, 2, 2, 1, 0, -2, -4, 1, 0, 3, 0, 1, -1, -1, 0, 1, 0, 0, 1, 0, 0, 2, -2, 0, 3, 0, 0, -3, -2, -1, 0, 0, -2, -2, 0, 0, 0, 1, -3, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, -3, 0, 0, 0, 0, 0, -2, 0, 1, 1, -1, 0, 0, 1, -1, 0, -1, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, -4, 1, 0, 1, 0, 4, 0, 0, 0, -3, 1, 0, 1, 0, 0, -3, 2, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 1, -2, 0, 2, 0, 1, 3, 1, 0, -1, 0, 2, -1, 4, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 1, 1, 0, 0, 1, 2, 0, -1, -1, 0, 0, 0, 0, -4, 0, 0, 3, 0, 1, 0, 0, -2, 2, -2, -1, 0, 2, -1, 0, 0, 0, 0, 0, 1, -3, 2, 0, -2, 0, 0, -2, -2, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, -2, 4, 1, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 2, 3, 0, -3, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, -3, 3, 0, -1, 2, -4, -3, 2, -3, 1, 0, 1, 0, 0, 1, 0, -3, -1, 0, -1, 0, 0, 0, -4, -1, 0, 2, 0, 0, 0, 2, 0, 0, 0, -1, -1, 0, 0, 0, -3, 1, 0, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 3, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, -1, 0, -1, 0, 0, 1, 1, -4, 0, -1, 1, -2, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 3, 0, 0, 3, 0, -1, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, -3, -2, 1, 0, 0, -1, -2, -2, 0, -3, 0, 0, -1, 1, 1, 4, 0, -3, -2, 0, 0, -4, -1, 0, 0, 2, 0, 2, 2, 3, 0, 0, 0, -3, 0, 0, 0, 0, 2, -1, -1, 0, 0, 0, 0, -1, 0, 2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 4, 3, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 6, -4, 0, 2, 0, 0, 0, 0, 2, 1, 3, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -2, 0, 1, 2, -4, -2, 2, 3, 2, 0, 1, 0, -2, 0, -2, -2, 0, 0, -4, 3, 0, 0, 1, 0, 0, 1, -3, 0, -1, 2, -2, 0, 1, 2, 0, 0, 0, 0, -2, 0, -2, 4, 0, -3, 0, 0, 1, -3, -1, 0, 0, -2, 1, 0, 1, 0, 0, 0, 0, 4, 2, -1, 0, 0, 0, -1, 1, 0, 3, 0, -2, 4, 0, -2, 0, 0, 0, 0, 0, -2, -1, 0, 4, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, -2, 0, 0, -2, 0, 0, 0, 0, 2, -2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, -1, -1, -3, -3, 0, -3, 1, 1, 1, 0, 0, -2, 0, 0, -1, -2, 0, 1, 0, -1, -1, 0, 0, 0, -1, 0, 0, -2, 0, -2, 1, -3, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, -2, 0, 1, 0, 0, -2, 0, -4, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, -3, 0, 1, 0, 0, 4, 1, 0, 3, 0, 2, -2, 0, 0, 0, -1, 0, 0, 3, -1, 0, 0, 0, -1, -4, 0, 0, 0, -3, 1, 0, 0, 0, 0, 4, 1, -1, 0, 2, 0, -2, 0, 0, 1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 4, 2, -2, 2, 0, 0, -1, 0, 0, 1, 0, -3, 6, 4, 1, 1, 0, 1, 0, 0, 0, -1, 1, 0, -4, 0, 0, 3, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, -2, -2, 0, -1, 0, 0, -3, -1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 3, 1, 0, 0, 0, 2, 0, 0, -1, 0, -3, 0, 0, -4, 3, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 2, 0, -1, 0, 4, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, 1, 1, -4, 2, 0, 0, 3, 0, 0, 0, 2, 0, 3, 3, -1, 0, 1, 0, 2, -1, 0, 0, 2, -1, 0, 1, 0, 0, -1, 0, 0, 0, 1, 1, -2, 0, 0, 0, 3, 1, 0, -3, 0, 0, 0, 0, 2, 0, -3, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, -2, 0, 0, 1, 0, -2, -3, 0, 0, 0, 4, 0, 0, -1, -2, -2, 0, 0, 2, 0, 0, 0, 0, -1, -3, 0, -1, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 1, 0, -4, 2, 0, 3, -2, 1, 0, 1, 0, 2, 2, -3, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, -1, 1, 0, 0, 1, -3, 0, 0, 3, -2, 0, 0, 0, 0, 2, 0, -2, 0, 2, 0, 0, 0, -2, -3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, -1, 2, -1, -1, 0, 0, -1, 0, 0, 0, 0, -1, -3, 0, -1, 0, 0, 0, 0, -3, 1, 0, 0, -1, 3, -1, 0, 0, 0, 1, 1, 0, -2, 0, 0, -3, 0, -2, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, -1, 1, -4, 4, 2, 2, 3, -3, 0, -2, 0, 0, 0, 1, 1, 1, 0, 4, 0, 0, 0, 3, -1, 0, -1, 0, 0, 3, -4, -1, 0, -3, 0, -3, 0, 0, 0, 3, 0, 1, 4, 0, 2, 0, 0, 4, 0, 3, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, -4, -1, 0, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, -2, 0, 0, 0, -2, -1, 0, 2, 0, 3, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, -2, 0, 0, 1, 0, -1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, 1, 0, 0, 1, 0, 3, 2, 3, 0, 1, 0, 0, 0, 3, 0, 3, 0, 1, 2, 0, 0, 1, -6, 0, 2, 2, 0, 0, -6, -1, 0, 2, 0, -1, 0, 0, 0, 1, -2, -1, 2, 0, -1, 0, 0, 0, 0, -1, 0, 0, 2, 1, 0, 0, 0, 0, 0, -1, -2, 1, 0, -3, 0, 0, 6, 0, 0, 0, 0, -1, 0, 0, -3, 0, 0, 0, 0, 1, 0, -2, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, -3, -4, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 1, 2, 0, 1, 2, -3, -2, 0, 2, 0, 0, 1, -1, 0, -3, 0, -1, -1, 0, 0, 2, 0, 0, 1, 1, 0, -1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, -3, -3, -1, 0, 0, 0, 0, 2, -1, 0, 0, 0, 2, -2, 0, 4, 0, 0, 0, -2, 0, -1, 0, 1, 0, 0, -1, -3, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 4, 0, 0, 1, 0, -3, 0, 0, 0, 3, 0, 0, -1, 0, 0, 2, -3, 3, 0, -2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, -1, -4, -1, -1, 3, 2, 0, 0, -3, 0, -3, 0, 0, 2, -1, 2, -2, 0, 1, -4, 0, 0, -1, -4, 0, -4, 0, 0, -2, -1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 3, 0, 0, 0, -2, -2, -1, 0, 3, 2, 0, -4, 0, 0, 0, -1, 0, -4, 0, 1, 0, 0, -3, 0, 0, 3, 0, -2, 2, 0, 2, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 0, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 0, -1, 0, 1, 4, 0, 0, 3, 0, -3, 0, -1, 0, 2, 0, 0, 0, 0, 0, -1, 3, 0, 1, 0, 0, 3, 1, 0, 0, 0, 0, -1, 0, 0, 0, 2, -3, -2, 0, 0, 1, 0, 0, 1, 2, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 4, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, -1, 0, 0, 2, 3, -1, 0, 0, 0, 1, 0, 0, 0, -3, 0, 0, 4, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  46. label: 120.1.i.a
    {'Nk2': 120, 'analytic_conductor': 0.059887801515960286, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 16, 'artin_field': [1, -4, 7, -3, -2, 1, 3, -3, 1], 'artin_field_label': '8.0.3240000.1', 'artin_image': '16.13', 'char_conductor': 120, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 9, 'char_orbit_label': 'i', 'char_order': 2, 'char_parity': -1, 'char_values': [120, 2, [31, 61, 41, 97], [2, 1, 1, 1]], 'cm_discs': [-15, -24], 'conrey_index': 29, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e3_3_5.8t11.2c1'], ['ArtinRepresentation/2.2e3_3_5.8t11.2c2']], 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 549772591224, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 8, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 15, 4, -1, 2, -15], [1, 1, 24, 8, -1, 2, -24], [1, 1, 40, 6, 1, 2, 40], [1, 1, 3, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 8, 2, 1, 2, 0], [1, 1, 120, 9, -1, 2, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '120.1.i.a', 'level': 120, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 3, 5], 'level_radical': 30, 'minimal_twist': '120.1.i.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 9, 'projective_field': [16, 0, -2, 0, 1], 'projective_field_label': '4.0.14400.3', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q-i q^{2}-i q^{3}-q^{4}+i q^{5}-q^{6}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e3_3_5.8t11.2'], 'relative_dim': 2, 'rm_discs': [40], 'self_twist_discs': [-15, -24, 40], 'self_twist_type': 3, 'space_label': '120.1.i', 'trace_display': [0, 0, 0, 0], 'trace_hash': 809548404485571040, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.012', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.852', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.187', 'prec': 20}, {'__RealLiteral__': 0, 'data': '29.634', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-2.988', 'prec': 20}, {'__RealLiteral__': 0, 'data': '474.148', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.884', 'prec': 17}, 'traces': [2, 0, 0, -2, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, -2, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0], 'weight': 1, 'weight_parity': -1}
  47. label: 124.1.i.a
    {'Nk2': 124, 'analytic_conductor': 0.061884061566492295, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 48, 'artin_field': [1, 0, 2, 0, 1, 0, -6, 0, 12, 0, 6, 0, 1, 0, -2, 0, 1], 'artin_image': '48.33', 'char_conductor': 124, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 9, 'char_orbit_label': 'i', 'char_order': 6, 'char_parity': -1, 'char_values': [124, 6, [63, 65], [3, 4]], 'cm_discs': [], 'conrey_index': 67, 'dim': 4, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_31.16t60.1c3'], ['ArtinRepresentation/2.2e2_31.16t60.1c2'], ['ArtinRepresentation/2.2e2_31.16t60.1c4'], ['ArtinRepresentation/2.2e2_31.16t60.1c1']], 'field_disc': 144, 'field_disc_factorization': [[2, 4], [3, 2]], 'field_poly': [1, 0, -1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 12, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 549772591228, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 0], [1, 1, 31, 3, 1, 3, 0], [1, 1, 124, 9, -1, 6, 0]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '124.1.i.a', 'level': 124, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 31], 'level_radical': 62, 'minimal_twist': '124.1.i.a', 'nf_label': '4.0.144.1', 'prim_orbit_index': 9, 'projective_field': [14, -2, 7, 0, 1], 'projective_field_label': '4.0.15376.1', 'projective_image': 'A4', 'projective_image_type': 'A4', 'qexp_display': 'q-\\zeta_{12}^{3}q^{2}-\\zeta_{12}q^{3}-q^{4}-\\zeta_{12}^{2}q^{5}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_31.16t60.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '124.1.i', 'trace_display': [0, 0, -2, 0], 'trace_hash': 193505020699476273, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.008', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.852', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-1.432', 'prec': 20}, {'__RealLiteral__': 0, 'data': '168.560', 'prec': 24}, {'__RealLiteral__': 0, 'data': '-95.377', 'prec': 24}, {'__RealLiteral__': 0, 'data': '10475.953', 'prec': 30}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.635', 'prec': 17}, 'traces': [4, 0, 0, -4, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, -2, 0, 0, 2, -2, -2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 4, 0, -2, 2, 0, 0, 0, 0, 4, 0, -4, 2, 0, 0, 2, 0, -4, 0, 0, -2, 0, 0, 0, 4, -4, 0, -2, 2, 0, 0, 2, 4, -2, 0, 2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 4, -2, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, 4, 0, 0, 4, 0, 0, 0, -2, 4, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, -2, -2, 0, 2, -4, 0, 0, -2, 4, -2, 0, -4, -2, 0, 0, 0, -4, -2, 0, 2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, 4, 0, -4, 4, 0, 0, 0, 0, -2, 0, 4, 2, 0, 0, -2, 0, -2, 0, 0, 2, 0, 0, 0, 2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, -2, -8, 0, 0, 0, 0, 0, -4, -4, -2, 0, 4, -2, 0, 0, 0, 2, -4, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -8, 0, 0, -4, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -8, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, -2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -8, 0, 0, -2, -4, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 4, 0, 0, -2, -4, 0, 0, 0, 0, -2, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 2, 2, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -2, -2, 0, 0, 0, 4, -4, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, -2, 8, 0, 0, 2, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 2, 2, 0, -2, -2, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 0, -2, -4, 0, 0, -4, 0, 0, 0, -2, -4, 0, 0, -2, 0, 0, 2, 0, -2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 8, 2, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, -4, -4, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, -4, -2, 4, 0, 0, 4, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 2, -2, 2, 0, -4, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 2, -8, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 2, -2, 0, 0, 0, -2, -2, 0, 4, -2, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 4, -2, -2, 0, 2, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -4, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 2, -2, 0, 0, -2, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, -2, 4, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 2, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, -4, -2, -2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 8, -4, 0, -4, 0, 0, 0, -2, -2, -2, 0, 0, -2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, -2, 0, 0, 4, 0, 0, -2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 4, 0, 0, 2, 0, 0, 0, 0, 4, 4, 0, 2, 0, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 0, 0, -4, 0, -4, -2, 0, 0, -8, 0, 2, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, -2, 0, 0, -2, 0, 2, 0, -2, -4, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, -2, -2, 0, 0, -2, 0, -8, 0, 0, -4, 0, 0, 0, -2, -4, 0, 0, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -4, 0, 0, 8, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 4, 0, 0, 0, 4, -2, -8, 0, 2, 4, 0, 0, 0, -2, 0, 0, -4, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 4, 0, 4, -4, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 8, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 2, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 8, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, -2, 2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, -4, 0, -2, -2, 0, 0, 0, -2, -2, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, -2, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 8, 2, 0, 0, -4, 2, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 4, 0, -2, 0, 0, 0, 2, 0, -4, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, -2, 0, 4, 0, -2, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, -4, 0, 0, -2, 4, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 4, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 4, -4, 0, -2, 4, 0, 0, 0, -2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -8, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, -2, 0, -4, 2, 0, 0, 0, 2, 2, 0, -2, -4, 0, 0, 0, -4, -8, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, -4, 0, -2, -2, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, -2, 0, 0, 0, -2, -4, 0, -4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -4, 0, 0, 0, 4, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, -4, 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, -2, -2, 0, -4], 'weight': 1, 'weight_parity': -1}
  48. label: 127.1.b.a
    {'Nk2': 127, 'analytic_conductor': 0.06338125660439131, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 10, 'artin_field': [-1, 3, 1, -2, -1, 1], 'artin_field_label': '5.1.16129.1', 'artin_image': '10.1', 'char_conductor': 127, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [127, 2, [3], [1]], 'cm_discs': [-127], 'conrey_index': 126, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.127.5t2.1c2'], ['ArtinRepresentation/2.127.5t2.1c1']], 'field_disc': 5, 'field_disc_factorization': [[5, 1]], 'field_poly': [-1, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254079, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 127, 2, -1, 2, -127]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '127.1.b.a', 'level': 127, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [127], 'level_radical': 127, 'minimal_twist': '127.1.b.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 2, 'projective_field': [-1, 3, 1, -2, -1, 1], 'projective_field_label': '5.1.16129.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(-1+\\beta )q^{2}+(1-\\beta )q^{4}-q^{8}+q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.127.5t2.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-127], 'self_twist_type': 1, 'space_label': '127.1.b', 'trace_display': [-1, 0, 0, 0], 'trace_hash': 693041561428450192, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.031', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.866', 'prec': 17}, {'__RealLiteral__': 0, 'data': '5.461', 'prec': 17}, {'__RealLiteral__': 0, 'data': '23.823', 'prec': 20}, {'__RealLiteral__': 0, 'data': '93.267', 'prec': 20}, {'__RealLiteral__': 0, 'data': '374.998', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.509', 'prec': 17}, 'traces': [2, -1, 0, 1, 0, 0, 0, -2, 2, 0, -1, 0, -1, 0, 0, 0, -1, -1, -1, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, -1, 2, 0, 3, 0, 1, -1, 3, 0, 0, -1, 0, 0, 2, 0, 0, -1, 0, 2, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, -1, 0, 0, 0, -3, 0, 0, -1, -2, -1, 3, 0, -3, 0, 0, -1, 0, 2, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, -1, 1, 0, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 3, 0, -3, 0, 0, 2, 1, 0, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 3, 0, 0, -2, 0, -3, -1, 0, 0, 1, -1, 0, 0, 0, -1, -2, 0, 0, 0, -1, 4, 2, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 4, 0, 0, 0, 0, 1, -1, -2, -1, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, -2, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, -2, 1, 0, 0, -1, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -3, 0, 1, 0, 2, 1, 0, 0, 2, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 3, 1, -1, -2, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, -2, 0, 2, -1, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 1, -1, 0, 0, -2, -1, 0, -1, 0, 0, -3, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 1, -1, 0, 0, 0, 0, 0, -1, -1, 3, 2, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -2, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -1, 0, -1, 2, 0, 3, 3, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 3, -1, 0, 0, -2, 0, -1, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, -1, -1, -3, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 3, 0, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, -4, 0, -2, 0, -2, 0, 2, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, -1, 0, 0, -2, 4, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, -2, 0, 3, 0, 0, -1, 0, -1, 0, 0, 0, 0, -3, 0, 0, -1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 3, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, -2, -2, 0, -2, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 1, -2, 3, 0, 2, 4, 0, -2, 2, 0, 0, 3, 0, 0, 1, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, -1, 0, 3, 0, 0, 2, 0, 0, 2, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, -1, 0, 3, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, -2, 0, 1, 0, 1, 0, 1, 0, 0, -1, 2, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, -1, 3, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 1, 1, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -1, 0, 0, 0, -1, 0, 0, -2, -1, -2, 0, 0, 0, 0, 0, 2, -1, 0, 3, 0, 0, 0, -1, 0, -1, 1, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, -4, 0, 0, -1, -3, -1, -4, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, -1, 3, 1, 0, 0, 0, 0, 0, 0, 0, -1, 3, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, -3, 0, 0, 3, 0, 0, 0, 4, 1, 0, 3, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, -2, -4, 4, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 3, 0, 3, -1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 3, -1, 0, 0, 0, 4, 0, 0, -2, 3, 0, -1, 0, -1, 4, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, -4, 0, -2, -1, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, 0, 0, 0, 0, 0, 0, 3, 0, -1, 1, -2, 0, 0, 3, 0, 0, 3, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 1, 0, 0, -1, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, -3, -1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 4, 0, 0, 0, -1, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 3, -1, 0, -2, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, -1, 0, 0, 0, 0, 0, 0, -2, 4, -3, 3, 0, -1, 0, 0, 0, 0, 2, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 4, 0, 0, 3, 0, 0, -1, 3, 0, 0, 0, 0, 0, 2, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, -3, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 1, 0, -2, 0, 0, 4, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 4, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, -1, 0, -1, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, 1, -1, -2, 0, 0, 0, 0, 1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -1, 0, -1, 2, 0, 0, 3, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 2, 0, 0, 0, -3, -1, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, -1, 0, -1, 0, -1, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, -4, 0, 0, 3, 0, 0, -2, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 2, 3, 0, -3, 0, -2, 0, 0, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, -1, -3, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, -2, -3, 0, -1, 0, 3, 3, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -1, 0, -1, 2, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0], 'weight': 1, 'weight_parity': -1}
  49. label: 128.1.d.a
    {'Nk2': 128, 'analytic_conductor': 0.06388032161702431, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [2, 0, -2, 0, 1], 'artin_field_label': '4.0.512.1', 'artin_image': '8.3', 'char_conductor': 8, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [128, 2, [127, 5], [1, 1]], 'cm_discs': [-4, -8], 'conrey_index': 63, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e7.4t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207552, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 8, 4, -1, 2, -8], [1, 1, 8, 2, 1, 2, 8]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '128.1.d.a', 'level': 128, 'level_is_powerful': True, 'level_is_prime': False, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2], 'level_radical': 2, 'minimal_twist': '128.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [1, 0, 0, 0, 1], 'projective_field_label': '4.0.256.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e7.4t3.2'], 'relative_dim': 1, 'rm_discs': [8], 'self_twist_discs': [-4, -8, 8], 'self_twist_type': 3, 'space_label': '128.1.d', 'trace_display': [0, 0, 0, 0], 'trace_hash': 400650096766306013, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.016', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.965', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.062', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.860', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.249', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.440', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.759', 'prec': 17}, 'traces': [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  50. label: 129.1.l.a
    {'Nk2': 129, 'analytic_conductor': 0.06437938662965731, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 129, 'char_degree': 6, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 12, 'char_orbit_label': 'l', 'char_order': 14, 'char_parity': -1, 'char_values': [129, 14, [44, 46], [7, 10]], 'cm_discs': [-3], 'conrey_index': 11, 'dim': 6, 'field_disc': -16807, 'field_disc_factorization': [[-1, 1], [7, 5]], 'field_poly': [1, -1, 1, -1, 1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 14, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 755931021441, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 43, 5, 1, 7, 0], [1, 1, 129, 12, -1, 14, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '129.1.l.a', 'level': 129, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 43], 'level_radical': 129, 'minimal_twist': '129.1.l.a', 'nf_label': '6.0.16807.1', 'prim_orbit_index': 12, 'projective_field': [-6, 61, -146, 92, 22, 14, -2, 1], 'projective_field_label': '7.1.170676802323.1', 'projective_image': 'D7', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{14}^{5}q^{3}+\\zeta_{14}^{4}q^{4}+(-\\zeta_{14}+\\zeta_{14}^{6}+\\cdots)q^{7}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '129.1.l', 'trace_display': [0, -1, 0, -2], 'trace_hash': 2008563761355350952, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.005', 'prec': 17}, {'__RealLiteral__': 0, 'data': '5.783', 'prec': 17}, {'__RealLiteral__': 0, 'data': '27.705', 'prec': 20}, {'__RealLiteral__': 0, 'data': '264.483', 'prec': 24}, {'__RealLiteral__': 0, 'data': '2553.098', 'prec': 27}, {'__RealLiteral__': 0, 'data': '28095.122', 'prec': 30}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.508', 'prec': 17}, 'traces': [6, 0, -1, -1, 0, 0, -2, 0, -1, 0, 0, -1, -2, 0, 0, -1, 0, 0, -2, 0, -2, 0, 0, 0, -1, 0, -1, -2, 0, 0, 5, 0, 0, 0, 0, 6, -2, 0, 5, 0, 0, 0, -1, 0, 0, 0, 0, -1, 4, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, -2, -1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -1, -2, 0, 0, -2, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, -1, 5, 0, -2, 5, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, -2, 0, 0, 5, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 4, 5, 0, 0, 5, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -3, 0, -2, -1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, -1, -2, 0, 0, -3, 0, 0, 5, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -1, -2, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0, 3, 0, 0, 0, -2, 0, 5, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 5, -2, 0, 0, 0, 0, 0, 0, 0, 6, -2, 0, 0, 5, 0, 0, -2, 0, -2, 0, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 5, 0, -2, 0, 0, 0, 5, 0, 5, 0, 0, 5, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 5, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -1, 3, 0, 0, -2, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, -1, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -1, -2, 0, 0, -2, 0, 0, -2, 0, -3, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -4, 0, -2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0, 0, 3, 0, 5, 0, 0, 6, 0, 0, 0, 0, 0, 0, 12, 0, -2, 0, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 10, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, -2, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, -2, 5, 0, 0, 5, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -1, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, -1, -3, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, -2, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 5, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, -2, 0, 0, -2, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 6, 5, 0, 0, -2, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 5, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 5, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 5, 0, 0, 5, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 6, 3, 0, 0, 3, 0, 5, 0, 0, -2, 5, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 5, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, -1, -4, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, -4, 0, -4, 0, 0, 0, -2, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 5, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0, 0, -2, 0, -1, 0, 0, -4, -2, 0, 0, 0, 0, 0, 3, 0, 5, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 5, 0, 0, 0, 3, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0, 5, 0, 0, -1, 0, 0, 3, 0, -1, 0, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, -1, 5, 0, 0, -2, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 5, -2, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 5, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 5, 5, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 6, -2, 0, 5, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, -3, -2, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, -4, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 5, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -3, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 0, -4, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 5, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 1, 0, 4, 0, 0, -2, 5, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, -1, 5, 0, 0, -2, 0, 0, 0, 0, 3, 12, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 5, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 12, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 5, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 5, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -1, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, -1, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 10, 0, -2, 0, 0, -2, -6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 5, -2, 0, -1, -4, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 12, 0, 0, 0, -4, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 5, 0, 0, 6, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -4, 0, 0, -2, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, -2, 0, 0, -2, 0], 'weight': 1, 'weight_parity': -1}
  51. label: 131.1.b.a
    {'Nk2': 131, 'analytic_conductor': 0.06537751665492332, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 10, 'artin_field': [2, 1, -1, 2, -1, 1], 'artin_field_label': '5.1.17161.1', 'artin_image': '10.1', 'char_conductor': 131, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [131, 2, [2], [1]], 'cm_discs': [-131], 'conrey_index': 130, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.131.5t2.1c1'], ['ArtinRepresentation/2.131.5t2.1c2']], 'field_disc': 5, 'field_disc_factorization': [[5, 1]], 'field_poly': [-1, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254083, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 131, 2, -1, 2, -131]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '131.1.b.a', 'level': 131, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [131], 'level_radical': 131, 'minimal_twist': '131.1.b.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 2, 'projective_field': [2, 1, -1, 2, -1, 1], 'projective_field_label': '5.1.17161.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(-1+\\beta )q^{3}+q^{4}-\\beta q^{5}-\\beta q^{7}+\\cdots', 'related_objects': ['ArtinRepresentation/2.131.5t2.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-131], 'self_twist_type': 1, 'space_label': '131.1.b', 'trace_display': [0, -1, -1, -1], 'trace_hash': 1265214996053204109, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.053', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.770', 'prec': 17}, {'__RealLiteral__': 0, 'data': '5.089', 'prec': 17}, {'__RealLiteral__': 0, 'data': '22.327', 'prec': 20}, {'__RealLiteral__': 0, 'data': '87.292', 'prec': 20}, {'__RealLiteral__': 0, 'data': '351.089', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.517', 'prec': 17}, 'traces': [2, 0, -1, 2, -1, 0, -1, 0, 1, 0, -1, -1, -1, 0, -2, 2, 0, 0, 0, -1, -2, 0, 0, 0, 1, 0, -2, -1, 0, 0, 0, 0, 3, 0, 3, 1, 0, 0, 3, 0, -1, 0, -1, -1, 2, 0, 0, -1, 1, 0, 0, -1, 4, 0, -2, 0, 0, 0, -1, -2, -1, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, 1, -1, 0, 0, 0, 1, 0, -1, -2, -1, 0, 0, -1, -1, 0, 0, 0, -3, 0, 0, 0, 1, 0, 3, 0, -2, 0, 0, 0, -2, 0, 2, 3, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 3, 1, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, -1, 1, 0, 4, 0, 1, 0, 0, -1, 0, 0, -3, -1, -2, 0, -1, 2, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -1, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, -1, 4, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, 0, 0, -1, -2, 0, 0, 2, -1, -3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, -1, 0, -2, 0, -2, 0, -1, 0, -1, 0, 1, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 2, 3, 0, -2, 0, 3, 0, 4, -2, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, -1, -2, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 4, 0, 0, 0, 0, 2, 0, -3, -2, 0, 0, 4, 0, -3, 0, -2, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, -3, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 3, -1, -4, 0, -1, -2, 0, 0, 0, -1, 0, 0, -1, 0, -2, 0, 0, 0, -2, 0, 0, -1, 0, 0, 3, -1, 3, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -3, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 3, 2, 0, 2, 0, 3, 0, 3, 0, -2, 0, 2, 1, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 3, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 0, 3, 3, 0, 0, 1, -1, 0, -2, 0, 0, 0, -2, 0, -1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, -2, 2, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, -1, 0, -1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -1, -2, 0, -1, 0, -1, 0, 0, 0, 0, 0, -2, -3, -1, 0, 0, -1, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 1, -1, -2, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 1, 4, 0, 0, 0, 0, 0, -2, -1, 0, 0, -2, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 3, 0, -2, 0, -2, 0, -4, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, -1, -2, 4, 0, 0, 0, -1, 0, -1, 0, -1, 0, 3, -1, 0, 0, -2, 0, 0, 0, 4, 0, 2, 0, 0, -1, 2, 0, 2, 4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -2, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, -1, 0, 2, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 4, 0, 0, -1, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, -3, 0, 0, 0, 0, 0, 3, 0, -1, 0, -2, -1, 0, 0, 0, -2, 2, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, -1, -1, 0, -2, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, -1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, -1, 0, 0, -2, 0, -2, 0, 3, -2, -1, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, -3, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 3, 0, 4, 1, -1, 0, 0, 0, -1, 0, 0, 2, -2, 0, -1, 0, 0, 0, 1, -1, -1, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, -1, 0, 2, 2, -2, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -2, 0, 1, 3, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, 3, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, -1, 0, -1, 0, 0, 3, 0, 0, 4, 0, 3, 0, -2, 4, 0, 0, -1, -2, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, -1, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, 1, 0, 0, -2, 0, 0, 4, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, -1, 0, -1, 0, -1, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 4, 0, 0, 3, 0, -4, 0, -2, 3, 0, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 3, -2, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -2, 0, 3, 0, 1, 0, 0, 0, -1, 4, 0, 0, 4, 0, 0, 0, -4, 0, -1, 0, 1, 0, 0, 0, 4, 0, -1, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, -3, -1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 3, 0, 0, 0, 0, 0, -3, -3, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 2, -1, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -3, 0, 1, 0, 0, 0, 4, 0, 0, 0, -1, -3, -2, 0, -1, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -4, 1, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 4, 0, 0, 0, 3, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, -1, -2, 0, 0, 0, 3, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -2, 3, 0, 0, 0, -1, 0, 0, 1, -4, 0, 0, -3, 0, 0, 0, -1, -1, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 6, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 3, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, -1, 0, 0, 0, 4, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 3, -1, 0, 0, -1, 0, 0, 4, 3, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 3, 0, -2, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 6, 0, 0, 0, -3, 0, -1, 0, 0, 0, 0, 0, -1, -1, -4, 0, 0, -3, -1, 0, 0, 0, 4, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, -2, 3, 0, 3, 0, -2, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 3, 0, -2, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -2], 'weight': 1, 'weight_parity': -1}
  52. label: 133.1.m.a
    {'Nk2': 133, 'analytic_conductor': 0.06637564668018932, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 48, 'artin_field': [1, 1, 4, -1, 2, -2, -9, -3, 19, -23, 13, -1, 2, -3, 3, -3, 1], 'artin_image': '48.33', 'char_conductor': 133, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 13, 'char_orbit_label': 'm', 'char_order': 6, 'char_parity': -1, 'char_values': [133, 6, [115, 78], [3, 2]], 'cm_discs': [], 'conrey_index': 83, 'dim': 4, 'embedded_related_objects': [['ArtinRepresentation/2.7_19.16t60.1c4'], ['ArtinRepresentation/2.7_19.16t60.1c1'], ['ArtinRepresentation/2.7_19.16t60.1c3'], ['ArtinRepresentation/2.7_19.16t60.1c2']], 'field_disc': 144, 'field_disc_factorization': [[2, 4], [3, 2]], 'field_poly': [1, 0, -1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 12, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 824650498181, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0], [1, 1, 19, 3, 1, 3, 0], [1, 1, 133, 13, -1, 6, 0]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '133.1.m.a', 'level': 133, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [7, 19], 'level_radical': 133, 'minimal_twist': '133.1.m.a', 'nf_label': '4.0.144.1', 'prim_orbit_index': 13, 'projective_field': [4, -7, 3, 0, 1], 'projective_field_label': '4.0.17689.1', 'projective_image': 'A4', 'projective_image_type': 'A4', 'qexp_display': 'q-\\zeta_{12}^{2}q^{2}+\\zeta_{12}^{5}q^{3}-\\zeta_{12}^{5}q^{5}+\\cdots', 'related_objects': ['ArtinRepresentation/2.7_19.16t60.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '133.1.m', 'trace_display': [-2, 0, 0, 0], 'trace_hash': 1146412442866144201, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.018', 'prec': 17}, {'__RealLiteral__': 0, 'data': '3.817', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.070', 'prec': 17}, {'__RealLiteral__': 0, 'data': '164.685', 'prec': 24}, {'__RealLiteral__': 0, 'data': '0.280', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10221.385', 'prec': 30}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.629', 'prec': 17}, 'traces': [4, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 2, -2, 0, 0, 4, 0, 0, -4, 0, 2, 0, 2, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 4, 4, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, -4, 0, 2, 0, 0, 0, -2, -2, 0, -2, 0, 0, 4, 4, -2, 0, 2, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 8, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 4, 2, 0, 0, 0, 0, -4, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 4, 0, 0, 2, 0, -4, 0, 2, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 4, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, 2, -2, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 2, -2, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, -4, 4, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, -2, 0, 2, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 2, 2, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, -2, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 8, 2, 0, 0, 0, 0, 2, 2, 0, 0, -8, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, -4, 0, 2, 0, 0, 0, 2, -4, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, -4, 0, 0, 0, 0, -2, -4, -4, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, -4, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, -2, -2, 4, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, -4, 0, 0, -2, 0, 0, 4, 0, -2, 0, 8, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, -2, 0, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, -2, 0, -4, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 2, -8, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, -2, 0, 4, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 2, -2, 4, 0, 4, 0, 0, -2, 0, 0, 0, -8, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 4, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, -4, -4, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, -2, -4, 0, -2, 0, 0, 2, 0, -4, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, -4, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 2, -2, 0, -2, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 2, -4, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, -4, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, -4, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, -2, 0, 4, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -4, 4, 0, -2, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, -4, 0, 0, 0, 0, 2, 4, 8, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 0, 2, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 4, 2, 2, 0, -4, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, -4, 8, -2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, -8, 0, -2, 0, 0, 0, 2, 0, 0, -4, 0, 0, -2, 2, 0, 0, -4, 0, 0, 4, 4, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 2, 0, -2, 0, 0, 0, -2, 2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, -4, 2, 0, 2, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, -4, -2, 0, 2, 0, 0, 0, -4, 4, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, -2, 0, 0, 2, -4, 0, 0, 2, 0, 0, 0, -4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 4, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -4, -2, 0, 0, -2, 0, 0, 0, -2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 4, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0, -2, -2, 0, -4, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 4, 0, -2, 0, -2, 0, 0, 0, 2, 4, 0, -2, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, -2, -4, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 2, 0, -2, 0], 'weight': 1, 'weight_parity': -1}
  53. label: 133.1.r.a
    {'Nk2': 133, 'analytic_conductor': 0.06637564668018932, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [1, 4, 5, 0, 1, -1, 1], 'artin_field_label': '6.0.336091.1', 'artin_image': '18.3', 'char_conductor': 133, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 18, 'char_orbit_label': 'r', 'char_order': 6, 'char_parity': -1, 'char_values': [133, 6, [115, 78], [4, 3]], 'cm_discs': [-19], 'conrey_index': 18, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.7_19.6t5.1c2'], ['ArtinRepresentation/2.7_19.6t5.1c1']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 1168247881861, 'hecke_ring_generator_nbound': 4, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 2, -1, 2, -19], [1, 1, 7, 3, 1, 3, 0], [1, 1, 133, 18, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '133.1.r.a', 'level': 133, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [7, 19], 'level_radical': 133, 'minimal_twist': '133.1.r.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 18, 'projective_field': [-6, 5, -1, 1], 'projective_field_label': '3.1.931.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{6}q^{4}-\\zeta_{6}^{2}q^{5}+\\zeta_{6}^{2}q^{7}+\\zeta_{6}^{2}q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.7_19.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-19], 'self_twist_type': 1, 'space_label': '133.1.r', 'trace_display': [0, 0, 1, -1], 'trace_hash': 891415410863796260, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.017', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.791', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.402', 'prec': 17}, {'__RealLiteral__': 0, 'data': '15.063', 'prec': 20}, {'__RealLiteral__': 0, 'data': '39.293', 'prec': 20}, {'__RealLiteral__': 0, 'data': '197.024', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.514', 'prec': 17}, 'traces': [2, 0, 0, -1, 1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, -1, -2, 0, -1, -2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 2, -2, 0, 0, 1, -1, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 1, 0, -2, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, -1, 1, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 1, 0, 0, 0, 0, -1, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -1, 0, 0, 0, 4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, -1, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 1, 0, 0, -2, 0, 1, 0, -2, 0, 0, 0, 0, 1, 0, 0, 4, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, -2, 0, -4, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, 1, 0, 0, 0, 0, -2, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 1, 0, 0, -2, 0, 1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 1, -4, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -4, 0, 0, 0, -1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 4, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 4, 0, 0, -2, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 2, 0, -4, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 1, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 6, 0, 0, 1, 0, 0, 0, 4, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -2, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, -1, 0, 0, 0, 4, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 2, 1, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, -2, 0, 1, 0, -2, 0, 1, 0, 0, 0, 0, 0, 2, 0, -2, 1, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, -1, 3, 0, 0, 0, -2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 1, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 1, 0, 0, 0, 0, 2, -1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 2, -2, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, -4, 0, 0, 0, 0, 0, -1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, -2, 2, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 2, 4, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, -2, -2, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 1, -1], 'weight': 1, 'weight_parity': -1}
  54. label: 135.1.d.a
    {'Nk2': 135, 'analytic_conductor': 0.06737377670545533, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-1, 3, 0, 1], 'artin_field_label': '3.1.135.1', 'artin_image': '6.1', 'char_conductor': 15, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [135, 2, [56, 82], [1, 1]], 'cm_discs': [-15], 'conrey_index': 134, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.3e3_5.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207559, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 15, 4, -1, 2, -15]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '135.1.d.a', 'level': 135, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [3, 5], 'level_radical': 15, 'minimal_twist': '135.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [-1, 3, 0, 1], 'projective_field_label': '3.1.135.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}+q^{5}+q^{8}-q^{10}-q^{16}-q^{17}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3e3_5.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-15], 'self_twist_type': 1, 'space_label': '135.1.d', 'trace_display': [-1, 0, 1, 0], 'trace_hash': 1539615773950670867, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.019', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.967', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.926', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.858', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.708', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.422', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.506', 'prec': 17}, 'traces': [1, -1, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, -1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, -1, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, -1, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 2, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, -1, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, -1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 2, -1], 'weight': 1, 'weight_parity': -1}
  55. label: 135.1.d.b
    {'Nk2': 135, 'analytic_conductor': 0.06737377670545533, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 12, 'artin_field': [3, 0, -3, 0, 3, -3, 1], 'artin_field_label': '6.0.54675.1', 'artin_image': '12.4', 'char_conductor': 15, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [135, 2, [56, 82], [1, 1]], 'cm_discs': [-15], 'conrey_index': 134, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.3e3_5.6t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503805802578055, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 15, 4, -1, 2, -15]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '135.1.d.b', 'level': 135, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [3, 5], 'level_radical': 15, 'minimal_twist': '135.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [-1, 3, 0, 1], 'projective_field_label': '3.1.135.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{2}-q^{5}-q^{8}-q^{10}-q^{16}+q^{17}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3e3_5.6t3.2'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-15], 'self_twist_type': 1, 'space_label': '135.1.d', 'trace_display': [1, 0, -1, 0], 'trace_hash': 508665248374868190, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.010', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.967', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.056', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.858', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.243', 'prec': 20}, {'__RealLiteral__': 0, 'data': '10.422', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.506', 'prec': 17}, 'traces': [1, 1, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, -2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, -1, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -1, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, -2, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, -1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -1, -2, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 2, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1], 'weight': 1, 'weight_parity': -1}
  56. label: 136.1.e.a
    {'Nk2': 136, 'analytic_conductor': 0.06787284171808833, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [3, -2, 1, -2, 1], 'artin_field_label': '4.0.1088.1', 'artin_image': '8.3', 'char_conductor': 136, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 5, 'char_orbit_label': 'e', 'char_order': 2, 'char_parity': -1, 'char_values': [136, 2, [103, 69, 105], [1, 1, 1]], 'cm_discs': [-8, -136], 'conrey_index': 67, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e3_17.4t3.3c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 274894684296, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, -8], [1, 1, 136, 5, -1, 2, -136], [1, 1, 17, 2, 1, 2, 17]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '136.1.e.a', 'level': 136, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 17], 'level_radical': 34, 'minimal_twist': '136.1.e.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 5, 'projective_field': [38, 4, -3, -2, 1], 'projective_field_label': '4.0.18496.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{17}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e3_17.4t3.3'], 'relative_dim': 1, 'rm_discs': [17], 'self_twist_discs': [-8, -136, 17], 'self_twist_type': 3, 'space_label': '136.1.e', 'trace_display': [-1, 0, 0, 0], 'trace_hash': 1010523128567394446, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.006', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.967', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.018', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.862', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.064', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.442', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.757', 'prec': 17}, 'traces': [1, -1, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, -1, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, -2, -1, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 1, 0, -2, 2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  57. label: 136.1.j.a
    {'Nk2': 136, 'analytic_conductor': 0.06787284171808833, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 32, 'artin_field': [1, -4, 4, 2, -4, 0, 3, -2, 1], 'artin_field_label': '8.0.20123648.1', 'artin_image': '32.11', 'char_conductor': 136, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 10, 'char_orbit_label': 'j', 'char_order': 4, 'char_parity': -1, 'char_values': [136, 4, [103, 69, 105], [2, 2, 1]], 'cm_discs': [-8], 'conrey_index': 115, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e3_17.8t17.1c1'], ['ArtinRepresentation/2.2e3_17.8t17.1c2']], 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 618492067976, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, -8], [1, 1, 17, 3, 1, 4, 0], [1, 1, 136, 10, -1, 4, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '136.1.j.a', 'level': 136, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 17], 'level_radical': 34, 'minimal_twist': '136.1.j.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 10, 'projective_field': [50, 8, -7, -2, 1], 'projective_field_label': '4.0.314432.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q-i q^{2}+(-i-1)q^{3}-q^{4}+(i-1)q^{6}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e3_17.8t17.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-8], 'self_twist_type': 1, 'space_label': '136.1.j', 'trace_display': [0, -2, 0, 0], 'trace_hash': 274451553435631631, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.012', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.891', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.280', 'prec': 20}, {'__RealLiteral__': 0, 'data': '18.210', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-4.856', 'prec': 20}, {'__RealLiteral__': 0, 'data': '243.175', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.694', 'prec': 17}, 'traces': [2, 0, -2, -2, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 4, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 2, -4, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, -4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, 0, 4, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 2, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, -4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 4, 0, -4, 0, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 4, 0, -2, 0, 0, 2, 2, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, -2, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, -2, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, -8, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 2, 0, -4, -4, 0, 0, 0, 2, -2, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 6, 0, -4, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, -4, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  58. label: 136.1.p.a
    {'Nk2': 136, 'analytic_conductor': 0.06787284171808833, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 136, 'char_degree': 4, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 16, 'char_orbit_label': 'p', 'char_order': 8, 'char_parity': -1, 'char_values': [136, 8, [103, 69, 105], [4, 4, 7]], 'cm_discs': [-8], 'conrey_index': 19, 'dim': 4, 'field_disc': 256, 'field_disc_factorization': [[2, 8]], 'field_poly': [1, 0, 0, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 8, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 1030808928392, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, -8], [1, 1, 17, 4, 1, 8, 0], [1, 1, 136, 16, -1, 8, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '136.1.p.a', 'level': 136, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 17], 'level_radical': 34, 'minimal_twist': '136.1.p.a', 'nf_label': '4.0.256.1', 'prim_orbit_index': 16, 'projective_field': [425, 0, -272, 0, 102, 0, 0, 0, 1], 'projective_field_label': '8.0.1680747204608.3', 'projective_image': 'D8', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{8}^{3}q^{2}+(\\zeta_{8}^{2}-\\zeta_{8}^{3})q^{3}-\\zeta_{8}^{2}q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-8], 'self_twist_type': 1, 'space_label': '136.1.p', 'trace_display': [0, 0, 0, 0], 'trace_hash': 2292289000603608221, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.019', 'prec': 17}, {'__RealLiteral__': 0, 'data': '3.875', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.062', 'prec': 20}, {'__RealLiteral__': 0, 'data': '100.856', 'prec': 24}, {'__RealLiteral__': 0, 'data': '-24.903', 'prec': 24}, {'__RealLiteral__': 0, 'data': '4099.984', 'prec': 27}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.796', 'prec': 17}, 'traces': [4, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 4, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, -4, 0, -4, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, -4, -4, 0, 0, 4, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 8, 0, 8, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, -8, 0, -4, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, -4, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -8, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, -4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, -4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 8, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, -4, -4, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 4, 0, 0, 8, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, -4, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 4, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 8, -4, 0, 0, 0, 0, -8, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 0, 0, -8, 0, 0, -4, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  59. label: 139.1.b.a
    {'Nk2': 139, 'analytic_conductor': 0.06937003675598734, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [2, 1, -1, 1], 'artin_field_label': '3.1.139.1', 'artin_image': '6.1', 'char_conductor': 139, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [139, 2, [2], [1]], 'cm_discs': [-139], 'conrey_index': 138, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.139.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254091, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 139, 2, -1, 2, -139]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '139.1.b.a', 'level': 139, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [139], 'level_radical': 139, 'minimal_twist': '139.1.b.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [2, 1, -1, 1], 'projective_field_label': '3.1.139.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{4}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\\cdots', 'related_objects': ['ArtinRepresentation/2.139.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-139], 'self_twist_type': 1, 'space_label': '139.1.b', 'trace_display': [0, 0, -1, -1], 'trace_hash': 1884160477731627446, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.001', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.995', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.991', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.980', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.960', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.917', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.501', 'prec': 17}, 'traces': [1, 0, 0, 1, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 1, 1, 2, 0, 0, 0, 2, 0, 0, -1, -1, 0, 2, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, -1, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, -2, 0, 0, 2, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, -1, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, -1, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -2, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -2, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 2, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, -1, 0, 1, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, -1, -2, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 2, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -2, -2, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 1, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 2, 0, 3, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, -1, 0, 1, 0, 0, 1, -1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 1, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, 0, 2, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 1, 0, -1, 0, 4, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -2, -1, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 1, 0, 0, -1, -2, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, -1, 0, 0, -1, 1, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 1], 'weight': 1, 'weight_parity': -1}
  60. label: 140.1.h.a
    {'Nk2': 140, 'analytic_conductor': 0.06986910176862034, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-2, 2, 0, 1], 'artin_field_label': '3.1.140.1', 'artin_image': '6.1', 'char_conductor': 35, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 8, 'char_orbit_label': 'h', 'char_order': 2, 'char_parity': -1, 'char_values': [140, 2, [71, 57, 101], [2, 1, 1]], 'cm_discs': [-35], 'conrey_index': 69, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_5_7.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 481053114508, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 35, 3, -1, 2, -35]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '140.1.h.a', 'level': 140, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 5, 7], 'level_radical': 70, 'minimal_twist': '140.1.h.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 3, 'projective_field': [-2, 2, 0, 1], 'projective_field_label': '3.1.140.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{3}+q^{5}+q^{7}-q^{11}-q^{13}-q^{15}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_5_7.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-35], 'self_twist_type': 1, 'space_label': '140.1.h', 'trace_display': [0, -1, 1, 1], 'trace_hash': 251020376769984346, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.018', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.955', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.916', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.823', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.652', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.294', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.512', 'prec': 17}, 'traces': [1, 0, -1, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 2, 0, -1, 0, -1, 0, -1, 0, -1, 0, 2, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, -1, 0, 2, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -2, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 2, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -1, 0, 2, 0, 2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 2, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -1, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 2, 0, -2, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 2, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 2, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, -1, 0, 2, 0, 1, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 2, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 2, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -2, 0, 2, 0, -1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0], 'weight': 1, 'weight_parity': -1}
  61. label: 140.1.h.b
    {'Nk2': 140, 'analytic_conductor': 0.06986910176862034, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 12, 'artin_field': [1, -1, -2, 5, -2, -1, 1], 'artin_field_label': '6.2.98000.1', 'artin_image': '12.4', 'char_conductor': 35, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 8, 'char_orbit_label': 'h', 'char_order': 2, 'char_parity': -1, 'char_values': [140, 2, [71, 57, 101], [2, 1, 1]], 'cm_discs': [-35], 'conrey_index': 69, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_5_7.6t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4504080680485004, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 35, 3, -1, 2, -35]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '140.1.h.b', 'level': 140, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 5, 7], 'level_radical': 70, 'minimal_twist': '140.1.h.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 3, 'projective_field': [-2, 2, 0, 1], 'projective_field_label': '3.1.140.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{3}-q^{5}-q^{7}-q^{11}+q^{13}-q^{15}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_5_7.6t3.2'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-35], 'self_twist_type': 1, 'space_label': '140.1.h', 'trace_display': [0, 1, -1, -1], 'trace_hash': 404203854238850720, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.025', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.955', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.095', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.823', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.375', 'prec': 20}, {'__RealLiteral__': 0, 'data': '10.294', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.512', 'prec': 17}, 'traces': [1, 0, 1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -2, 0, 1, 0, 1, 0, -1, 0, -1, 0, -2, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 1, 0, 1, 0, 2, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, -2, 0, -1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 2, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -2, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 1, 0, 2, 0, 2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, -2, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, 1, 0, 1, 0, -1, 0, -2, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 2, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, -1, 0, 2, 0, -1, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, -1, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, -2, 0, 2, 0, 1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0], 'weight': 1, 'weight_parity': -1}
  62. label: 140.1.p.a
    {'Nk2': 140, 'analytic_conductor': 0.06986910176862034, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [1, 2, 4, 0, 3, -2, 1], 'artin_field_label': '6.0.392000.1', 'artin_image': '18.3', 'char_conductor': 140, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 16, 'char_orbit_label': 'p', 'char_order': 6, 'char_parity': -1, 'char_values': [140, 6, [71, 57, 101], [3, 3, 4]], 'cm_discs': [-20], 'conrey_index': 39, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_5_7.6t5.1c2'], ['ArtinRepresentation/2.2e2_5_7.6t5.1c1']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [[3, [1, -1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 1030808928396, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 20, 4, -1, 2, -20], [1, 1, 7, 3, 1, 3, 0], [1, 1, 140, 16, -1, 6, 0]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '140.1.p.a', 'level': 140, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 5, 7], 'level_radical': 70, 'minimal_twist': '140.1.p.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 16, 'projective_field': [-13, 5, -1, 1], 'projective_field_label': '3.1.980.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{6}q^{2}-\\zeta_{6}^{2}q^{3}+\\zeta_{6}^{2}q^{4}-\\zeta_{6}q^{5}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_5_7.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-20], 'self_twist_type': 1, 'space_label': '140.1.p', 'trace_display': [-1, 1, -1, -1], 'trace_hash': 1534173921203204599, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.004', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.924', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.872', 'prec': 17}, {'__RealLiteral__': 0, 'data': '17.099', 'prec': 20}, {'__RealLiteral__': 0, 'data': '47.163', 'prec': 20}, {'__RealLiteral__': 0, 'data': '229.084', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.506', 'prec': 17}, 'traces': [2, -1, 1, -1, -1, -2, -1, 2, 0, -1, 0, 1, 0, 2, -2, -1, 0, 0, 0, 2, 1, 0, 1, 1, -1, 0, 2, -1, -2, 1, 0, -1, 0, 0, 2, 0, 0, 0, 0, -1, -2, 1, -2, 0, 0, 1, -2, -2, -1, 2, 0, 0, 0, -1, 0, -1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 1, 1, -2, -2, 0, 1, -1, 0, 1, 0, 0, -2, 0, -2, 0, 1, 0, -1, 0, -1, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, -2, -1, 1, -1, 0, 2, 0, 4, -1, -1, 0, 0, 0, 0, -2, -1, 0, 0, -1, 0, -1, -4, 0, 0, 0, 1, 0, -2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, 1, 0, 1, -2, 1, 2, 0, 0, 1, 0, 2, -1, 0, 0, 1, 0, 0, -2, 0, 2, 1, 0, 0, 0, 4, -1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, -1, -1, -2, 1, 0, 1, 1, 0, 0, 0, -2, 0, 0, 0, 1, 1, 2, 0, -2, 0, 0, 0, 0, 4, -1, 0, 0, -2, 0, -2, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 1, -2, -1, 0, -2, -1, 2, 0, 0, -1, -1, 0, 0, 0, -2, 0, -1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 4, 2, -2, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -2, 1, 0, -1, 0, 1, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 1, 0, 1, 0, -2, -1, -2, 4, 0, 0, 1, 0, 1, -2, 1, 0, -1, 0, 0, 0, 0, 2, -2, -1, 0, 1, -1, -2, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 1, -2, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 1, -2, 0, 2, 0, 0, 2, 0, 1, -2, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 1, -1, 0, 1, -2, -2, 0, 0, 1, 1, 0, -2, 0, 0, 1, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -2, -2, 0, 1, 0, -1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, 2, -1, -2, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 1, 4, 0, -2, 1, 0, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, -1, 2, 0, 0, -2, 1, -4, 2, 0, -1, 0, 0, 0, 0, 0, 2, 0, -1, -1, 0, -2, 0, -2, 0, 1, -2, 1, 0, 0, 2, 0, 0, 1, -1, 0, 0, 0, 0, -2, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, -2, 0, 2, 1, 0, -1, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 1, 2, 0, 4, 1, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, -1, 0, -2, 1, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 4, -2, 0, 0, -1, -1, 1, 0, -1, -2, 0, 0, 0, 1, 2, 0, 0, -1, 0, 0, 1, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 1, -1, 4, 1, 2, 0, 1, 1, 0, 0, 0, 4, 0, -1, 0, 1, 0, -2, 0, 0, 1, 0, 0, -2, 0, 0, -1, 1, 2, 1, 0, -2, 0, 0, -1, -1, 0, 0, 0, 0, 2, 0, 1, 0, 0, -1, -4, 1, 0, -1, 0, 0, 0, -2, 0, -1, 0, 1, 0, 2, -2, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 1, 1, 1, -2, 0, 2, 0, 0, -1, 0, -2, 1, -2, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, -2, -4, 1, 0, 0, 1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 2, 1, 0, -1, 1, 1, 1, 0, 1, 0, 0, -2, 0, 0, -2, 0, -2, -2, 0, 1, 1, 0, 0, -2, 0, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, -1, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, -1, 0, 1, -1, 0, 0, -2, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 1, 1, 0, -2, -2, 0, -2, 0, -1, 0, 2, 0, 1, 0, 0, 0, 0, -1, 0, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 1, -1, -2, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -2, -2, 0, -1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, -2, 0, 2, -2, -1, 0, 0, 0, 0, 0, 4, 0, 1, 0, 2, 0, -1, 0, 0, 1, -1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 2, 0, 0, -1, 1, 0, 0, -2, 1, 0, 0, 0, -2, -2, 4, 0, 1, 0, 0, -2, 0, 0, -1, 1, 0, 0, 0, 1, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -2, 0, 0, -2, -1, 0, -2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -1, 1, -2, 0, -2, 0, 0, 1, 1, 0, 0, 0, -1, 2, 1, 1, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, -2, -1, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, -2, -2, 0, -2, 1, -4, 1, 0, 0, -2, 0, 1, 4, 0, 0, -2, 0, 0, 4, 0, 0, 0, -2, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, -2, -2, 4, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, -2, 4, -2, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 2, 1, 4, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, -2, 0, 2, 0, -1, 1, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -2, -2, -1, 0, -2, 0, -2, -2, -1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, -2, -2, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, -2, -2, 0, 0, 0, 0, -2, -2, -1, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, -1, -1, -2, 0, -4, 0, 1, 0, 0, 0, 1, -2, 0, -1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, -2, -2, 0, -1, 0, 0, -1, 0, 2, 0, 1, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 0, 1, -1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, -1, 2, 1, -1, 0, -2, 0, 2, 0, 1, 2, 0, 0, 0, 1, 4, 0, 0, 1, 0, 0, 1, 0, -2, 1, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, 2, 1, -2, 0, -2, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 1, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, -2, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, 1, 2, 0, 0, 0, 0, -2, 0, 0, 1, 1, 0, -2, 0, 0, 2, 0, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 1, -2, 2, -4, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 4, -2, -1, 0, 1, -1, -2, 1, 0, 0, 0, -1, 0, -2, 0, -2, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, -2, 0, 0, -2, -2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, -2, 0, 0, 1, 0, 0, 0, -2, 0, -2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, -4, -2, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 1, 4, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 4, -1, -2, 0, -1, 1, 0, 2, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -1, 1, 0, -1, -2, 1, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, -2, 0, 0, -1, 0, 0, -2, 0, 1, 0, 0, 0, 4, 0, 1, 0, 0, -2, 4, 0, 0, -2, -1, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, -1, 0, 0, 1, 1, 0, 0, 0, -2, 1, -2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 1, 2, 0, -2, 0, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, -2, 0, 2, 0, 0, 0, 1, -2, -1, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 4, 1, 0, 0, -1, 0, 0, 4, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, -1, -1, 0, 0, 0, 2, -2, 2, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, -1, 0, 4, 0, 0, -2, 1, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, -2, 0, -1, 0, 0, 0, 4, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1], 'weight': 1, 'weight_parity': -1}
  63. label: 140.1.p.b
    {'Nk2': 140, 'analytic_conductor': 0.06986910176862034, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 36, 'artin_field': [1, -6, 14, -16, 12, -12, 12, -6, 4, -4, 1, 0, 1], 'artin_field_label': '12.0.153664000000.1', 'artin_image': '36.12', 'char_conductor': 140, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 16, 'char_orbit_label': 'p', 'char_order': 6, 'char_parity': -1, 'char_values': [140, 6, [71, 57, 101], [3, 3, 4]], 'cm_discs': [-20], 'conrey_index': 39, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_5_7.12t18.1c2'], ['ArtinRepresentation/2.2e2_5_7.12t18.1c1']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [[3, [1, 1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4504630436298892, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 20, 4, -1, 2, -20], [1, 1, 7, 3, 1, 3, 0], [1, 1, 140, 16, -1, 6, 0]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '140.1.p.b', 'level': 140, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 5, 7], 'level_radical': 70, 'minimal_twist': '140.1.p.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 16, 'projective_field': [-13, 5, -1, 1], 'projective_field_label': '3.1.980.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{6}q^{2}+\\zeta_{6}^{2}q^{3}+\\zeta_{6}^{2}q^{4}-\\zeta_{6}q^{5}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_5_7.12t18.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-20], 'self_twist_type': 1, 'space_label': '140.1.p', 'trace_display': [1, -1, -1, 1], 'trace_hash': 461057434886582986, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.004', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.924', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.202', 'prec': 20}, {'__RealLiteral__': 0, 'data': '17.099', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-3.798', 'prec': 20}, {'__RealLiteral__': 0, 'data': '229.084', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.506', 'prec': 17}, 'traces': [2, 1, -1, -1, -1, -2, 1, -2, 0, 1, 0, -1, 0, 2, 2, -1, 0, 0, 0, 2, 1, 0, -1, 1, -1, 0, -2, 1, -2, 1, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, -2, -1, 2, 0, 0, 1, 2, 2, -1, -2, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 1, 0, 0, 2, 0, 0, -1, 0, 2, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, -1, 2, -2, 0, 1, 1, 0, 1, 0, 0, 2, 0, -2, 0, 1, 0, 1, 0, -1, 1, 0, -1, 0, 1, 0, -1, 1, 1, 0, 0, -2, 0, 0, -1, 1, 0, 0, 0, -2, -1, -1, 1, 0, 2, 0, -4, 1, -1, 0, 0, 0, 0, -2, 1, 0, 0, 1, 0, 1, -4, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 1, 0, 1, 2, -1, 2, 0, 0, -1, 0, 2, 1, 0, 0, -1, 0, 0, -2, 0, -2, 1, 0, 0, 0, -4, -1, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 1, -1, 2, -1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 1, -1, 2, 0, 2, 0, 0, 0, 0, -4, -1, 0, 0, 2, 0, -2, -2, 0, 2, 0, 0, 2, 0, 0, 0, 0, -1, -2, 1, 0, -2, -1, 2, 0, 0, -1, 1, 0, 0, 0, -2, 0, -1, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, -2, -1, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 4, -2, 2, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 2, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, 1, 0, -2, 1, 2, 4, 0, 0, -1, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, -2, -2, -1, 0, -1, 1, -2, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, -1, 2, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -2, 0, -2, 0, 0, 2, 0, -1, -2, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 1, -2, -2, 0, 0, 1, -1, 0, 2, 0, 0, -1, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 1, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, -2, -2, 1, -2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, -1, 4, 0, 2, 1, 0, 0, -1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 1, 2, 0, 0, 2, -1, -4, -2, 0, 1, 0, 0, 0, 0, 0, -2, 0, -1, -1, 0, 2, 0, -2, 0, -1, 2, 1, 0, 0, -2, 0, 0, -1, -1, 0, 0, 0, 0, -2, 0, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 2, 0, -2, 1, 0, 1, 0, -2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, -1, 2, 0, 4, -1, 0, -2, 0, 0, 0, 0, -2, 2, 0, 0, 1, 0, -2, 1, 0, 0, 0, 0, 0, -4, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 4, 2, 0, 0, -1, -1, -1, 0, -1, 2, 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, 1, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 1, -4, 1, 2, 0, -1, -1, 0, 0, 0, -4, 0, -1, 0, 1, 0, 2, 0, 0, 1, 0, 0, -2, 0, 0, 1, -1, 2, 1, 0, 2, 0, 0, 1, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0, -1, 4, -1, 0, 1, 0, 0, 0, -2, 0, -1, 0, -1, 0, -2, -2, 0, 0, 0, 2, 0, -1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, 1, 1, 2, 0, 2, 0, 0, 1, 0, -2, -1, -2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -2, -2, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, -2, 4, -1, 0, 0, 1, 0, -1, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 2, 1, 0, 1, -1, 1, -1, 0, -1, 0, 0, 2, 0, 0, 2, 0, -2, -2, 0, -1, 1, 0, 0, 2, 0, -2, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, -2, 0, -1, 0, -2, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, -1, 0, -1, -1, 0, 0, 2, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 1, -1, 0, -2, 2, 0, 2, 0, -1, 0, 2, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 1, -1, 2, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 2, -2, 0, 1, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, -2, 0, 2, 2, 1, 0, 0, 0, 0, 0, 4, 0, 1, 0, -2, 0, -1, 0, 0, -1, -1, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, -2, 0, 0, -1, 1, 0, 0, -2, -1, 0, 0, 0, -2, 2, 4, 0, -1, 0, 0, -2, 0, 0, -1, 1, 0, 0, 0, 1, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -4, 2, 0, 0, -2, 1, 0, -2, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 1, 1, -2, 0, 2, 0, 0, -1, 1, 0, 0, 0, -1, 2, -1, -1, 0, 0, 2, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 2, -1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 2, -2, 0, -2, -1, 4, 1, 0, 0, 2, 0, 1, -4, 0, 0, 2, 0, 0, 4, 0, 0, 0, -2, 0, 0, -1, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, -2, 2, -4, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, -2, -4, -2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 2, -2, 1, 4, 0, 0, 0, 0, -2, 0, -2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 1, -1, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 2, 1, -2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 2, 2, -1, 0, -2, 0, 2, -2, 1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, 2, -2, 0, 0, -1, -2, 0, 0, 0, -1, 0, 0, 2, -2, 0, 0, 0, 0, -2, 2, 1, 0, 0, 0, -1, -1, 2, 0, 0, 0, 0, -1, 1, -2, 0, 4, 0, -1, 0, 0, 0, 1, -2, 0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, 0, 0, -2, 2, 0, -1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 2, 1, 0, -2, 0, 0, 0, 0, -1, -1, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, -1, 2, -1, 1, 0, -2, 0, -2, 0, 1, -2, 0, 0, 0, 1, -4, 0, 0, -1, 0, 0, 1, 0, 2, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 2, -1, 2, 0, 2, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, -1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 4, -2, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, 1, -2, 0, 0, 0, 0, 2, 0, 0, -1, 1, 0, 2, 0, 0, 2, 0, 2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 1, 2, -2, -4, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -4, -2, -1, 0, -1, 1, -2, -1, 0, 0, 0, -1, 0, -2, 0, 2, 0, 1, 1, 0, -2, 1, 0, 0, -1, 0, 0, 4, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 2, 0, 0, -2, -2, -1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, 2, 0, 0, -1, 0, 0, 0, 2, 0, -2, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, -4, 2, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, 4, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 4, 1, 2, 0, -1, 1, 0, -2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 1, 0, 1, -2, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -2, 0, 0, -2, 0, 0, -1, 0, 0, 2, 0, 1, 0, 0, 0, -4, 0, 1, 0, 0, 2, 4, 0, 0, 2, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, -2, 0, 2, -1, 0, 0, 1, -1, 0, 0, 0, -2, -1, -2, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 1, -2, 0, -2, 0, 0, -4, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, -1, 0, 0, -2, 0, -2, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, -4, -1, 0, 0, -1, 0, 0, 4, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, -2, 2, 2, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 4, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 1, 0, 0, -2, 0, 1, 0, 0, 0, -4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1], 'weight': 1, 'weight_parity': -1}
  64. label: 143.1.d.a
    {'Nk2': 143, 'analytic_conductor': 0.07136629680651935, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 10, 'artin_field': [-1, 3, 0, -1, -1, 1], 'artin_field_label': '5.1.20449.1', 'artin_image': '10.1', 'char_conductor': 143, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [143, 2, [79, 67], [1, 1]], 'cm_discs': [-143], 'conrey_index': 142, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.11_13.5t2.1c1'], ['ArtinRepresentation/2.11_13.5t2.1c2']], 'field_disc': 5, 'field_disc_factorization': [[5, 1]], 'field_poly': [-1, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207567, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 143, 4, -1, 2, -143]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '143.1.d.a', 'level': 143, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [11, 13], 'level_radical': 143, 'minimal_twist': '143.1.d.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 4, 'projective_field': [-1, 3, 0, -1, -1, 1], 'projective_field_label': '5.1.20449.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(-1+\\beta )q^{2}+(-1+\\beta )q^{3}+(1-\\beta )q^{4}+\\cdots', 'related_objects': ['ArtinRepresentation/2.11_13.5t2.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-143], 'self_twist_type': 1, 'space_label': '143.1.d', 'trace_display': [-1, -1, 0, -1], 'trace_hash': 1166206444979241598, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.025', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.866', 'prec': 17}, {'__RealLiteral__': 0, 'data': '5.473', 'prec': 17}, {'__RealLiteral__': 0, 'data': '23.835', 'prec': 20}, {'__RealLiteral__': 0, 'data': '93.302', 'prec': 20}, {'__RealLiteral__': 0, 'data': '375.056', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.512', 'prec': 17}, 'traces': [2, -1, -1, 1, 0, 3, -1, -2, 1, 0, 2, -3, 2, -2, 0, 0, 0, -3, -1, 0, -2, -1, -1, 1, 2, -1, -2, 2, 0, 0, 0, 2, -1, 0, 0, 3, 0, 3, -1, 0, -1, 1, 0, 1, 0, -2, 0, 0, 1, -1, 0, 1, -1, 1, 0, 1, 3, 0, 0, 0, 0, 0, 2, -1, 0, 3, 0, 0, -2, 0, 0, -1, -1, 0, -1, -3, -1, 3, 0, 0, 0, -2, -1, -1, 0, 0, 0, -2, 0, 0, -1, 2, 0, 0, 0, -1, 0, 2, 1, 1, 0, 0, -1, -2, 0, 3, 0, -1, -1, 0, 0, 0, -1, -4, 0, 0, 1, 0, 0, 0, 2, 0, -2, 0, 0, -1, 0, 1, 0, 0, 0, -3, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 3, 2, 0, -1, 3, 4, 1, 0, -2, 0, -3, -1, 0, 3, 0, 3, 0, 0, 2, 0, -2, -1, 2, 2, 0, -3, 0, 0, 0, -1, 0, 0, 0, 4, 0, -1, -2, 0, 1, 0, 0, 0, 0, 1, 0, -1, 3, -1, 0, 0, -2, -1, -3, -1, -2, 0, 0, 0, 0, 0, -2, 2, 0, -1, 0, 0, -3, 0, 0, 0, 2, 0, 3, 3, 0, 0, 0, 0, -1, 1, 3, -1, 4, 0, 0, -2, 0, 0, -3, 0, 0, 0, 0, -1, 0, -1, -1, 2, 0, 0, 1, -1, 0, -2, 0, -1, 1, -1, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, -1, 0, -1, 0, -2, 0, 2, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 3, 1, 2, 0, 0, -3, 4, -1, 0, 0, -2, -2, -1, -3, 0, -2, 0, 0, 0, 0, 4, 2, -2, 0, -1, 1, -1, -2, 0, 0, 0, -4, 0, 0, 0, 1, 0, 0, 2, 0, 3, 1, 0, 0, 0, 2, 0, 3, 0, 0, 0, -1, 3, 0, 0, 4, -2, 0, 0, 0, 0, 0, -1, -2, -2, 2, 0, 0, 0, 0, 0, -2, -1, 0, 1, 3, -1, 2, 0, 0, -1, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, -3, 0, -2, 0, 0, -1, 0, 0, -1, 0, 3, 0, 3, 0, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, -1, 0, 2, 0, 3, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, -3, -2, -4, 0, 0, -2, 0, -1, 0, 0, 0, -2, -2, 0, -3, -1, -3, -2, 3, 0, -3, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 4, 3, 0, 0, -2, 0, 0, 0, -1, 0, -3, 3, 4, 0, 0, -2, 1, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 1, 0, 0, 3, -2, 0, -2, 0, -2, -1, 0, 0, 0, -2, 0, 1, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, -2, -2, 1, 0, -1, 3, 3, 0, 0, 1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 1, -1, -3, 0, -1, -2, 0, 3, 0, -1, 1, 0, -2, 0, 1, 0, 0, 3, 0, -1, 1, 0, 2, 3, -2, -1, 1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, -1, -2, 0, 1, 0, 1, 0, 0, 1, 3, 0, 0, 2, -2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 4, -4, 0, 0, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -3, 0, 0, 0, -2, 0, 0, -2, 1, 0, -4, 0, 0, 3, 0, 0, -4, 0, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 2, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, -2, 4, 0, 3, -3, -2, -3, 0, 3, -1, 1, -1, 0, 0, 0, -1, 3, 0, -1, 0, -1, -1, 0, 3, 1, 4, 0, 0, 0, 2, 0, 0, 0, -1, 0, -2, 0, 0, -2, -1, 0, -2, 0, -1, 0, -2, -3, 0, 0, 0, 1, -1, 0, -2, 2, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, -1, -3, 0, 0, -2, -1, 0, 0, 0, -3, 4, -3, 0, 2, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, -2, 2, 0, 4, 0, -1, 1, -1, 0, -1, 1, -1, 0, 0, -1, 0, 0, 0, -3, 0, -2, 0, 0, 2, 0, 3, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, -1, 0, 1, -2, 0, -2, 0, 3, -1, 0, 0, 0, 0, 1, 0, 1, 0, 4, -1, 0, -2, 0, -1, 1, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, -2, 0, 0, 3, 0, -2, 0, 1, 0, 6, -1, -3, 0, 0, -1, 0, -1, 3, 0, 0, 0, 0, 0, 0, -2, 3, 0, -1, 0, 0, 2, 0, 0, 0, 2, 0, 3, -2, 0, -1, 0, 0, -2, 0, -1, 1, 3, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 4, 0, -3, 0, -2, 0, 0, 2, 0, 0, 2, 0, 2, -1, -2, 0, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 2, 0, 0, 0, -3, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -4, 0, 2, 0, 0, 3, 0, -1, 0, 0, 2, 4, 3, 0, 0, -3, 0, -1, 0, 0, 1, 0, 2, -1, -3, 0, 2, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, -1, 0, 0, -2, 3, 0, 0, 0, -2, 0, -1, 1, -1, 0, 0, 0, 0, -1, -2, 2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, -2, 2, -1, 0, 0, -2, -3, -3, 0, -4, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, 4, 0, 3, 1, 3, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, -1, 0, -2, -1, 3, -1, 0, 0, 1, 0, 1, 0, 0, 0, 1, -1, 0, 0, 3, 3, 0, -2, 0, -1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, -1, 0, 0, -2, 0, -1, 0, 0, 0, 1, -1, -4, 0, 2, -1, 3, -1, 0, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -1, 0, 0, 3, 4, 0, -2, 0, 0, 0, 0, 0, 1, 3, -2, 2, 4, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, -1, -3, 0, 0, 0, -1, 0, -1, 0, 2, -2, -4, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -3, 0, 2, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, -3, -1, 0, 4, 0, -2, 3, 0, 0, 0, 0, 3, 1, 4, 0, 4, 0, 0, -2, 0, 4, 0, 0, 1, -1, 0, 4, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 1, -2, 0, -1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 3, -2, -2, 0, 0, 4, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 3, 2, 0, 3, -1, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 3, 0, 0, -1, 3, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 4, 1, -2, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, -4, -1, -4, 0, 2, -2, -2, 4, 0, 0, 1, 0, 3, 0, 1, 0, 1, -1, 0, -1, -3, -1, -2, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, -2, 0, -3, -1, 0, -1, -2, 0, 0, 0, 1, 0, -2, 0, 0, 0, -4, 4, -1, 0, -2, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 3, -3, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, -2, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -3, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, -2, 2, 1, -2, 0, -1, 0, 0, 1, 0, 0, 0, 0, 2, 0, -2, 0, 0, 1, 0, -2, 0, 3, 4, 0, -2, -1, -1, 0, 0, 0, 0, 3, 0, 0, -1, 0, 2, 0, 0, 1, 0, 0, 2, 0, -1, 0, -1, -2, -2, 0, 0, -4, -1, 0, -3, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, 3, 0, -2, -1, -2, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, -1, 0, -2, 1, -2, 0, 0, 2, 0, 0, -2, 0, 1, -1, 0, 0, 0, -4, 3, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, -3, 0, 0, 2, 4, 2, -2, 0, -1, 1, -2, 0, 0, -3, 0, 3, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 3, 0, 0, -3, 0, 3, 0, 0, 3, 6, 0, 0, 0, 3, 0, -1, 0, 3, 0, 0, 0, 0, 3, 2, -3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, -3, 1, 0, 1, 0, 0, 3, 0, 3, -1, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, -2, 0, 1, 0, 0, 0, 0, 0, -2, 0, 3, -1, -2, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 6, 0, -3, 0, 0, 0, 2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, -1, -1, 0, 0, 0, -4, -1, 2, 0, 0, -1, 0, -1, 0, -1, 0, -1, 1, 0, 0, -3, 3, 3, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, -3, -1, 0, 0, 0, 0, 0, 4, -4, 3, 0, 2, 1, -1, 0, 0, 2, 0, 0, 0, 0, 0, -1, -2, 0, -1, 0, 0, 1, 0, 0, -1, -2, 0, 3, 0, 0, -1, 0, 0, 0, 3, 3, 0, -2, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 4, 4, 0, 0, 0, -2, 0, 4, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, 0, 0, -1, 2, 0, 0, 0, 0, -1, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  65. label: 143.1.d.b
    {'Nk2': 143, 'analytic_conductor': 0.07136629680651935, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 20, 'artin_field': [-1, 6, -12, 13, -9, 3, 3, -6, 6, -3, 1], 'artin_field_label': '10.2.5436100813.1', 'artin_image': '20.4', 'char_conductor': 143, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [143, 2, [79, 67], [1, 1]], 'cm_discs': [-143], 'conrey_index': 142, 'dim': 2, 'field_disc': 5, 'field_disc_factorization': [[5, 1]], 'field_poly': [-1, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, -1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503805802578063, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 143, 4, -1, 2, -143]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '143.1.d.b', 'level': 143, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [11, 13], 'level_radical': 143, 'minimal_twist': '143.1.d.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 4, 'projective_field': [-1, 3, 0, -1, -1, 1], 'projective_field_label': '5.1.20449.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(1-\\beta )q^{2}+(-1+\\beta )q^{3}+(1-\\beta )q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-143], 'self_twist_type': 1, 'space_label': '143.1.d', 'trace_display': [1, -1, 0, 1], 'trace_hash': 1209999580595804389, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.023', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.866', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.385', 'prec': 20}, {'__RealLiteral__': 0, 'data': '23.835', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-6.035', 'prec': 20}, {'__RealLiteral__': 0, 'data': '375.056', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.512', 'prec': 17}, 'traces': [2, 1, -1, 1, 0, -3, 1, 2, 1, 0, -2, -3, -2, -2, 0, 0, 0, 3, 1, 0, 2, -1, -1, -1, 2, -1, -2, -2, 0, 0, 0, -2, 1, 0, 0, 3, 0, 3, 1, 0, 1, 1, 0, -1, 0, 2, 0, 0, 1, 1, 0, -1, -1, -1, 0, 1, -3, 0, 0, 0, 0, 0, -2, -1, 0, 3, 0, 0, -2, 0, 0, 1, 1, 0, -1, 3, -1, 3, 0, 0, 0, -2, 1, 1, 0, 0, 0, -2, 0, 0, -1, 2, 0, 0, 0, 1, 0, -2, -1, 1, 0, 0, -1, -2, 0, -3, 0, -1, 1, 0, 0, 0, -1, -4, 0, 0, -1, 0, 0, 0, 2, 0, 2, 0, 0, -1, 0, -1, 0, 0, 0, 3, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 3, 2, 0, 1, -3, -4, 1, 0, 2, 0, 3, -1, 0, 3, 0, -3, 0, 0, -2, 0, -2, 1, 2, 2, 0, 3, 0, 0, 0, 1, 0, 0, 0, 4, 0, -1, 2, 0, -1, 0, 0, 0, 0, -1, 0, -1, 3, 1, 0, 0, -2, 1, -3, -1, 2, 0, 0, 0, 0, 0, 2, 2, 0, -1, 0, 0, -3, 0, 0, 0, -2, 0, 3, -3, 0, 0, 0, 0, -1, 1, -3, 1, -4, 0, 0, -2, 0, 0, -3, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 0, 1, -1, 0, 2, 0, -1, -1, 1, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1, 0, -2, 0, -2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 3, -1, 2, 0, 0, 3, -4, 1, 0, 0, 2, -2, 1, -3, 0, -2, 0, 0, 0, 0, -4, 2, -2, 0, -1, 1, -1, 2, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, -2, 0, -3, 1, 0, 0, 0, -2, 0, 3, 0, 0, 0, 1, 3, 0, 0, 4, 2, 0, 0, 0, 0, 0, 1, -2, 2, 2, 0, 0, 0, 0, 0, 2, 1, 0, 1, -3, -1, 2, 0, 0, -1, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -3, 0, 3, 0, -2, 0, 0, -1, 0, 0, 1, 0, 3, 0, -3, 0, -3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 1, 0, 2, 0, -3, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 3, 2, -4, 0, 0, -2, 0, -1, 0, 0, 0, 2, 2, 0, 3, -1, -3, 2, 3, 0, -3, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 4, -3, 0, 0, -2, 0, 0, 0, 1, 0, -3, 3, -4, 0, 0, -2, -1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 1, 0, 0, -3, 2, 0, -2, 0, -2, -1, 0, 0, 0, -2, 0, -1, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, -2, 2, -1, 0, 1, 3, 3, 0, 0, -1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, -1, -1, -3, 0, 1, 2, 0, 3, 0, 1, 1, 0, -2, 0, 1, 0, 0, -3, 0, 1, 1, 0, -2, 3, -2, -1, -1, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 1, -2, 0, -1, 0, -1, 0, 0, 1, -3, 0, 0, 2, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 4, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 4, -4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, -2, 1, 0, 4, 0, 0, -3, 0, 0, 4, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, -2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -3, -2, 4, 0, -3, 3, 2, -3, 0, -3, -1, -1, -1, 0, 0, 0, 1, -3, 0, 1, 0, -1, 1, 0, 3, 1, -4, 0, 0, 0, -2, 0, 0, 0, -1, 0, -2, 0, 0, 2, -1, 0, 2, 0, 1, 0, -2, -3, 0, 0, 0, 1, 1, 0, -2, -2, 0, 0, 0, 0, 0, -3, -2, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 2, -1, 0, 0, 0, -3, 4, 3, 0, -2, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, -2, 2, 0, -4, 0, -1, -1, 1, 0, 1, 1, -1, 0, 0, 1, 0, 0, 0, -3, 0, 2, 0, 0, 2, 0, -3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -3, -1, 0, 1, -2, 0, 2, 0, -3, -1, 0, 0, 0, 0, 1, 0, 1, 0, -4, 1, 0, 2, 0, -1, -1, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 3, 0, 2, 0, -1, 0, 6, -1, 3, 0, 0, -1, 0, -1, 3, 0, 0, 0, 0, 0, 0, 2, 3, 0, -1, 0, 0, 2, 0, 0, 0, -2, 0, 3, 2, 0, -1, 0, 0, -2, 0, 1, -1, -3, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, -4, 0, 3, 0, -2, 0, 0, 2, 0, 0, -2, 0, 2, 1, 2, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, -3, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, -4, 0, 2, 0, 0, -3, 0, 1, 0, 0, -2, 4, -3, 0, 0, -3, 0, 1, 0, 0, -1, 0, 2, 1, -3, 0, 2, -1, 0, 0, 0, -4, 0, 0, 0, 0, 0, -1, 0, 0, 2, 3, 0, 0, 0, 2, 0, -1, 1, 1, 0, 0, 0, 0, -1, -2, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 2, 2, -1, 0, 0, -2, -3, 3, 0, 4, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, -4, 0, -3, -1, 3, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, -1, 0, 2, 1, -3, -1, 0, 0, 1, 0, 1, 0, 0, 0, -1, 1, 0, 0, 3, 3, 0, -2, 0, -1, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 1, 0, 0, -2, 0, 1, 0, 0, 0, 1, -1, 4, 0, -2, -1, -3, -1, 0, 1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -1, 0, 0, -3, -4, 0, -2, 0, 0, 0, 0, 0, 1, 3, 2, -2, -4, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 1, -3, 0, 0, 0, -1, 0, 1, 0, 2, 2, 4, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 2, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, -3, 1, 0, 4, 0, 2, -3, 0, 0, 0, 0, 3, -1, 4, 0, 4, 0, 0, 2, 0, -4, 0, 0, -1, -1, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, 2, 0, 1, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, -1, 3, 2, -2, 0, 0, 4, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 3, 2, 0, -3, 1, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, -3, 0, 0, 1, 3, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -4, 1, -2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 1, 4, -1, -4, 0, -2, 2, 2, 4, 0, 0, 1, 0, 3, 0, 1, 0, -1, 1, 0, 1, -3, -1, 2, 0, 0, 0, -3, 0, 0, 0, 0, 2, 0, 0, -2, 0, -3, 1, 0, 1, -2, 0, 0, 0, -1, 0, -2, 0, 0, 0, 4, 4, 1, 0, -2, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, -3, 3, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, 2, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, -2, -2, 1, -2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, -2, 0, 0, -1, 0, 2, 0, 3, -4, 0, -2, -1, 1, 0, 0, 0, 0, -3, 0, 0, -1, 0, 2, 0, 0, -1, 0, 0, -2, 0, 1, 0, -1, -2, 2, 0, 0, -4, 1, 0, -3, 0, 0, 0, 0, 0, 0, -2, -1, 1, -1, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 3, 0, 2, 1, 2, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, -1, -2, 0, 0, 2, 0, 0, 2, 0, 1, 1, 0, 0, 0, -4, 3, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, -3, 0, 0, -2, -4, -2, -2, 0, 1, 1, 2, 0, 0, -3, 0, -3, 0, 0, -2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 1, -3, 0, 0, -3, 0, 3, 0, 0, -3, 6, 0, 0, 0, -3, 0, -1, 0, -3, 0, 0, 0, 0, 3, 2, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -3, -1, 0, 1, 0, 0, 3, 0, -3, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 3, 1, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -3, 0, 0, 6, 0, 3, 0, 0, 0, -2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 1, -1, 0, 0, 0, 4, 1, 2, 0, 0, -1, 0, -1, 0, -1, 0, 1, -1, 0, 0, -3, 3, -3, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, 0, 3, -1, 0, 0, 0, 0, 0, 4, -4, -3, 0, -2, 1, 1, 0, 0, -2, 0, 0, 0, 0, 0, 1, -2, 0, -1, 0, 0, 1, 0, 0, 1, 2, 0, 3, 0, 0, -1, 0, 0, 0, 3, -3, 0, 2, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 4, 4, 0, 0, 0, -2, 0, -4, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  66. label: 144.1.g.a
    {'Nk2': 144, 'analytic_conductor': 0.07186536181915235, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [3, 0, -3, 0, 1], 'artin_field_label': '4.0.432.1', 'artin_image': '8.3', 'char_conductor': 4, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 7, 'char_orbit_label': 'g', 'char_order': 2, 'char_parity': -1, 'char_values': [144, 2, [127, 37, 65], [1, 2, 2]], 'cm_discs': [-3, -4], 'conrey_index': 127, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e4_3e2.4t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 412333637776, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 4, 2, -1, 2, -4], [1, 1, 12, 2, 1, 2, 12]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '144.1.g.a', 'level': 144, 'level_is_powerful': True, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': True, 'level_is_squarefree': False, 'level_primes': [2, 3], 'level_radical': 6, 'minimal_twist': '144.1.g.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [1, 0, -1, 0, 1], 'projective_field_label': '4.0.144.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q-2q^{13}-q^{25}+2q^{37}+q^{49}+2q^{61}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e4_3e2.4t3.2'], 'relative_dim': 1, 'rm_discs': [12], 'self_twist_discs': [-3, -4, 12], 'self_twist_type': 3, 'space_label': '144.1.g', 'trace_display': [0, 0, 0, 0], 'trace_hash': 1253703001154171466, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.019', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.965', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.078', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.860', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.311', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.440', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.759', 'prec': 17}, 'traces': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  67. label: 145.1.f.a
    {'Nk2': 145, 'analytic_conductor': 0.07236442683178534, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 32, 'artin_field': [1, 3, -2, -6, 3, 3, -3, -1, 1], 'artin_field_label': '8.4.15243125.1', 'artin_image': '32.11', 'char_conductor': 145, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 6, 'char_orbit_label': 'f', 'char_order': 4, 'char_parity': -1, 'char_values': [145, 4, [117, 31], [2, 1]], 'cm_discs': [], 'conrey_index': 99, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.5_29.8t17.2c2'], ['ArtinRepresentation/2.5_29.8t17.2c1']], 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 343614161041, 'hecke_ring_generator_nbound': 4, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 5], [1, 1, 29, 3, -1, 4, 0], [1, 1, 145, 6, -1, 4, 0]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '145.1.f.a', 'level': 145, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [5, 29], 'level_radical': 145, 'minimal_twist': '145.1.f.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 6, 'projective_field': [23, 9, 4, -1, 1], 'projective_field_label': '4.0.121945.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q+i q^{4}-i q^{5}+i q^{9}+(-i-1)q^{11}+\\cdots', 'related_objects': ['ArtinRepresentation/2.5_29.8t17.2'], 'relative_dim': 1, 'rm_discs': [5], 'self_twist_discs': [5], 'self_twist_type': 2, 'space_label': '145.1.f', 'trace_display': [0, 0, 0, 0], 'trace_hash': 136155829520816154, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.004', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.031', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.202', 'prec': 20}, {'__RealLiteral__': 0, 'data': '20.451', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-3.798', 'prec': 20}, {'__RealLiteral__': 0, 'data': '279.035', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.685', 'prec': 17}, 'traces': [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, -2, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 4, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0], 'weight': 1, 'weight_parity': -1}
  68. label: 145.1.h.a
    {'Nk2': 145, 'analytic_conductor': 0.07236442683178534, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 32, 'artin_field': [1, 1, -6, 11, -7, -1, 5, -4, 1], 'artin_field_label': '8.4.88410125.1', 'artin_image': '32.11', 'char_conductor': 145, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 8, 'char_orbit_label': 'h', 'char_order': 4, 'char_parity': -1, 'char_values': [145, 4, [117, 31], [3, 2]], 'cm_discs': [], 'conrey_index': 28, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.5_29.8t17.1c1'], ['ArtinRepresentation/2.5_29.8t17.1c2']], 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 481053114513, 'hecke_ring_generator_nbound': 4, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 29, 2, 1, 2, 29], [1, 1, 5, 3, -1, 4, 0], [1, 1, 145, 8, -1, 4, 0]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '145.1.h.a', 'level': 145, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [5, 29], 'level_radical': 145, 'minimal_twist': '145.1.h.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 8, 'projective_field': [11, -1, 6, -1, 1], 'projective_field_label': '4.0.3625.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q-i q^{4}-i q^{5}+(i-1)q^{7}+i q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.5_29.8t17.1'], 'relative_dim': 1, 'rm_discs': [29], 'self_twist_discs': [29], 'self_twist_type': 2, 'space_label': '145.1.h', 'trace_display': [0, 0, 0, -2], 'trace_hash': 841284807697068737, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.018', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.965', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.163', 'prec': 20}, {'__RealLiteral__': 0, 'data': '19.066', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-2.148', 'prec': 20}, {'__RealLiteral__': 0, 'data': '255.564', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.684', 'prec': 17}, 'traces': [2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, -2, -2, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, -2, 0, 0, -2, 2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, -2, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 4, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, -2, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  69. label: 147.1.l.a
    {'Nk2': 147, 'analytic_conductor': 0.07336255685705136, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 147, 'char_degree': 6, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 12, 'char_orbit_label': 'l', 'char_order': 14, 'char_parity': -1, 'char_values': [147, 14, [50, 52], [7, 12]], 'cm_discs': [-3], 'conrey_index': 8, 'dim': 6, 'field_disc': -16807, 'field_disc_factorization': [[-1, 1], [7, 5]], 'field_poly': [1, -1, 1, -1, 1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 14, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 755931021459, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 49, 5, 1, 7, 0], [1, 1, 147, 12, -1, 14, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '147.1.l.a', 'level': 147, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [3, 7], 'level_radical': 21, 'minimal_twist': '147.1.l.a', 'nf_label': '6.0.16807.1', 'prim_orbit_index': 12, 'projective_field': [900, 210, 273, 70, -21, 7, 0, 1], 'projective_field_label': '7.1.373714754427.1', 'projective_image': 'D7', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{14}^{2}q^{3}+\\zeta_{14}^{6}q^{4}-\\zeta_{14}^{3}q^{7}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '147.1.l', 'trace_display': [0, -1, 0, -1], 'trace_hash': 2142707220904427024, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.012', 'prec': 17}, {'__RealLiteral__': 0, 'data': '5.899', 'prec': 17}, {'__RealLiteral__': 0, 'data': '29.265', 'prec': 20}, {'__RealLiteral__': 0, 'data': '284.047', 'prec': 24}, {'__RealLiteral__': 0, 'data': '2792.113', 'prec': 27}, {'__RealLiteral__': 0, 'data': '30984.576', 'prec': 30}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.508', 'prec': 17}, 'traces': [6, 0, -1, -1, 0, 0, -1, 0, -1, 0, 0, -1, -2, 0, 0, -1, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, -1, -1, 0, 0, -2, 0, 0, 0, 0, -1, 5, 0, 5, 0, 0, 0, -2, 0, 0, 0, 0, 6, -1, 0, 0, 5, 0, 0, 0, 0, -2, 0, 0, 0, 5, 0, 6, -1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -1, -2, 0, 0, -2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, -2, -1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 5, 0, 0, -2, 0, -2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, -1, 0, 0, -1, -2, 0, 0, -2, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -3, 0, 5, 5, 0, 0, 6, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, -1, 5, 0, 0, -1, 0, 0, -2, 0, 5, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, 5, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -1, -2, 0, 0, -4, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -2, 0, 0, 5, 0, 5, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 6, -2, 0, 5, 0, 0, 0, -2, 0, -2, 0, 0, -1, 5, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -1, 5, 0, 0, -2, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -1, 0, 0, 3, 0, 0, 0, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 0, 5, 0, 0, -2, 0, -1, 0, 0, -2, 0, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 5, 0, 0, 0, 0, -1, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, -2, -2, 0, 0, 12, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, -2, -1, 0, 0, -2, 0, 0, -2, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, -1, -3, 0, 0, 5, 0, 0, 0, 0, 5, 0, 0, -2, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, 0, 0, -2, 0, -1, 0, 0, -2, 5, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 0, -2, 0, 0, -2, 0, 5, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, -2, -2, 0, 0, 0, 0, 5, 0, 0, 0, -1, 0, 0, -2, 0, 0, -1, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 3, 0, 5, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 5, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 5, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 5, 0, 0, 5, 0, 0, 0, 0, -1, 5, 0, 5, 5, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 5, 0, 5, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 5, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 3, 0, -1, 0, 0, 0, 5, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 5, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 5, 0, -1, 0, 0, -2, 5, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, -4, 0, 5, 0, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -1, -2, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 5, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, -1, 5, 0, 5, -2, 0, 0, 5, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, -1, -2, 0, 0, -2, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 4, 0, 0, 5, 0, 0, 0, 0, 6, 5, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 5, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 5, 0, 4, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 5, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 5, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 6, 5, 0, 0, -4, 0, 0, 0, 0, 5, -2, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, -4, 0, 0, 0, -1, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 3, 0, 5, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -4, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 5, 0, 0, -2, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 10, 0, 0, 0, 0, 0, -3, 0, 0, 5, 0, 0, 0, 0, -2, 0, 0, 0, 12, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 5, -2, 0, -1, 5, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 5, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -2, 0, -2, 0, 0, -2, -4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, -2, 0, 0, 5, 0], 'weight': 1, 'weight_parity': -1}
  70. label: 148.1.f.a
    {'Nk2': 148, 'analytic_conductor': 0.07386162186968435, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 37, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 6, 'char_orbit_label': 'f', 'char_order': 4, 'char_parity': -1, 'char_values': [148, 4, [75, 113], [4, 1]], 'cm_discs': [], 'conrey_index': 105, 'dim': 2, 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 343614161044, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 37, 4, -1, 4, 0]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '148.1.f.a', 'level': 148, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 37], 'level_radical': 74, 'minimal_twist': '148.1.f.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 4, 'projective_field': [12, -7, 5, -1, 1], 'projective_field_label': '4.0.202612.1', 'projective_image': 'S4', 'projective_image_type': 'S4', 'qexp_display': 'q+i q^{3}-q^{7}-i q^{11}+(-i-1)q^{17}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '148.1.f', 'trace_display': [0, 0, 0, -2], 'traces': [2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 2, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, -4, 0, -2, 0, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0], 'weight': 1, 'weight_parity': -1}
  71. label: 148.1.i.a
    {'Nk2': 148, 'analytic_conductor': 0.07386162186968435, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [1, -4, 3, 4, -2, -2, 1], 'artin_field_label': '6.0.87616.1', 'artin_image': '18.3', 'char_conductor': 148, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 9, 'char_orbit_label': 'i', 'char_order': 6, 'char_parity': -1, 'char_values': [148, 6, [75, 113], [3, 4]], 'cm_discs': [-4], 'conrey_index': 47, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_37.6t5.1c2'], ['ArtinRepresentation/2.2e2_37.6t5.1c1']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 549772591252, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 37, 3, 1, 3, 0], [1, 1, 148, 9, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '148.1.i.a', 'level': 148, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 37], 'level_radical': 74, 'minimal_twist': '148.1.i.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 9, 'projective_field': [26, -12, -1, 1], 'projective_field_label': '3.1.5476.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{6}^{2}q^{2}-\\zeta_{6}q^{4}+\\zeta_{6}q^{5}+q^{8}+\\zeta_{6}^{2}q^{9}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_37.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-4], 'self_twist_type': 1, 'space_label': '148.1.i', 'trace_display': [-1, 0, 1, 0], 'trace_hash': 1126512119171965331, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.004', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.973', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.946', 'prec': 17}, {'__RealLiteral__': 0, 'data': '17.685', 'prec': 20}, {'__RealLiteral__': 0, 'data': '48.965', 'prec': 20}, {'__RealLiteral__': 0, 'data': '237.420', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.504', 'prec': 17}, 'traces': [2, -1, 0, -1, 1, 0, 0, 2, -1, -2, 0, 0, -2, 0, 0, -1, 1, -1, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, -1, 0, 1, 0, 2, -1, 0, 0, 1, 1, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, -1, 4, 2, 0, 0, 0, 0, 0, -2, -1, -2, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 1, 0, 0, 0, -2, 0, 0, 1, 4, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, -1, -1, -2, 0, -1, -2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, -3, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -1, 0, 1, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, -4, 1, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, -3, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, -2, -1, -2, 0, 0, 2, 0, 0, 0, -2, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, -1, 0, 1, 0, 0, -2, 0, 0, 0, 4, 0, 0, 1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -1, 2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 1, -2, 0, 0, -2, 0, 0, 1, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 4, 0, -1, -1, 0, 0, 1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, -2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 2, 0, 0, 1, -2, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 0, 0, 4, 2, -2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -2, -2, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, -2, -2, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, -2, 0, 6, -2, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 8, 0, 0, -2, 0, 0, 0, 0, 2, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 2, -4, 0, 0, -2, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 4, 0, 0, 1, 1, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -1, 2, 0, 0, -2, 0, 0, 0, 0, 2, 1, 0, 0, -2, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -6, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, -2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, -2, -1, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 4, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, -1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 1, 1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 0, -2, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 1, 0, 0, -2, 1, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, -2, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, -2, -2, 0, 0, -4, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -2, 0, -4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 4, 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, -2, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1, 2, -2, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 4, 0, 1, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, -2, 0, 0, 0, -2, -4, 0, 0, -2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0, -4, -2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, -1, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, -3, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 1, 0, 0, 1, -2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, -1, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 1, 0, 4, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, -1, 0, 4, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 4, 1, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 4, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 2, 0, 0, -4, -1, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, -4, 0, 0, -2, 0, 0, -2, 0, -1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, -2, 0, -2, 0, 0, 4, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 4, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 4, 0, 0, 0, -2, 0, 2, 0, 0, 1, 0, 0, -1, 2, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 1, -2, 0, 0, 4, 0, 0, -1], 'weight': 1, 'weight_parity': -1}
  72. label: 148.1.p.a
    {'Nk2': 148, 'analytic_conductor': 0.07386162186968435, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 148, 'char_degree': 6, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 16, 'char_orbit_label': 'p', 'char_order': 18, 'char_parity': -1, 'char_values': [148, 18, [75, 113], [9, 16]], 'cm_discs': [-4], 'conrey_index': 7, 'dim': 6, 'field_disc': -19683, 'field_disc_factorization': [[-1, 1], [3, 9]], 'field_poly': [1, 0, 0, -1, 0, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 18, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 1030808928404, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 37, 6, 1, 9, 0], [1, 1, 148, 16, -1, 18, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '148.1.p.a', 'level': 148, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 37], 'level_radical': 74, 'minimal_twist': '148.1.p.a', 'nf_label': '6.0.19683.1', 'prim_orbit_index': 16, 'projective_field': [-216, 756, -1176, 952, -506, 205, -60, 10, -2, 1], 'projective_field_label': '9.1.899194740203776.1', 'projective_image': 'D9', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{18}q^{2}+\\zeta_{18}^{2}q^{4}+(\\zeta_{18}^{4}+\\zeta_{18}^{6}+\\cdots)q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-4], 'self_twist_type': 1, 'space_label': '148.1.p', 'trace_display': [0, 0, -3, 0], 'trace_hash': 1570775740450687245, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.015', 'prec': 20}, {'__RealLiteral__': 0, 'data': '5.542', 'prec': 17}, {'__RealLiteral__': 0, 'data': '12.791', 'prec': 20}, {'__RealLiteral__': 0, 'data': '203.052', 'prec': 24}, {'__RealLiteral__': 0, 'data': '1090.900', 'prec': 27}, {'__RealLiteral__': 0, 'data': '13468.771', 'prec': 30}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.726', 'prec': 17}, 'traces': [6, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 6, 0, 0, 0, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 6, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, -6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, -6, 0, 0, 0, -3, 0, 0, 0, 3, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 6, 0, -3, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 6, 0, -3, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, -3, 0, 0, -3, 0, 6, 0, 0, -3, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, -3, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, -3, -6, 0, 0, -3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 6, 0, 0, -3, 0, 0, 0, 0, 3, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 0, -3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, 6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, -6, 0, 0, -3, 6, 0, 0, 0, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -6, 0, 0, 0, 0, 6, 0, 3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -3, 0, 0, -3, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, -6, 0, 6, 0, 0, 0, 0, 0, 0, -3, -6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 6, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 6, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 12, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 12, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, -6, 0, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, 6, -3, 0, 0, 0, 0, 0, 0, 0, -3, 6, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 3, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, -3, 0, 0, -3, 0, 0, 0, 3, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -3, 0, 0, 0, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -6, 0, 0, 3, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, -6, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, -3, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, -6, 0, 0, 6, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 6, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -3, 6, -3, 0, 0, -6, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, -3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 3, 3, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 3, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -3, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -3, -3, 0, 0, 6, 0, 0, 0, 0, -3, 0, 0, -6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -3, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -6, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -6, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 6, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, -6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 6, -6, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, 6, -3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 3, 0, 0, 0, 0, 6, 0, 0, -6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, -6, 0, 0, 6, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, -6, 0, 0, 6], 'weight': 1, 'weight_parity': -1}
  73. label: 151.1.b.a
    {'Nk2': 151, 'analytic_conductor': 0.07535881690758336, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 14, 'artin_field': [1, 3, -1, 3, 0, 1, -1, 1], 'artin_field_label': '7.1.3442951.1', 'artin_image': '14.1', 'char_conductor': 151, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [151, 2, [6], [1]], 'cm_discs': [-151], 'conrey_index': 150, 'dim': 3, 'embedded_related_objects': [['ArtinRepresentation/2.151.7t2.1c2'], ['ArtinRepresentation/2.151.7t2.1c3'], ['ArtinRepresentation/2.151.7t2.1c1']], 'field_disc': 49, 'field_disc_factorization': [[7, 2]], 'field_poly': [1, -2, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 14, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254103, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 151, 2, -1, 2, -151]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '151.1.b.a', 'level': 151, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [151], 'level_radical': 151, 'minimal_twist': '151.1.b.a', 'nf_label': '3.3.49.1', 'prim_orbit_index': 2, 'projective_field': [1, 3, -1, 3, 0, 1, -1, 1], 'projective_field_label': '7.1.3442951.1', 'projective_image': 'D7', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\beta _{1}q^{2}+(1+\\beta _{2})q^{4}+(-1+\\beta _{1}-\\beta _{2})q^{5}+\\cdots', 'related_objects': ['ArtinRepresentation/2.151.7t2.1'], 'relative_dim': 3, 'rm_discs': [], 'self_twist_discs': [-151], 'self_twist_type': 1, 'space_label': '151.1.b', 'trace_display': [-1, 0, -1, 0], 'trace_hash': 173276719884675015, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.041', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.790', 'prec': 17}, {'__RealLiteral__': 0, 'data': '13.669', 'prec': 20}, {'__RealLiteral__': 0, 'data': '84.981', 'prec': 20}, {'__RealLiteral__': 0, 'data': '506.603', 'prec': 24}, {'__RealLiteral__': 0, 'data': '3041.953', 'prec': 27}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.499', 'prec': 17}, 'traces': [3, -1, 0, 2, -1, 0, 0, -2, 3, -2, -1, 0, 0, 0, 0, 1, -1, -1, -1, -3, 0, -2, 0, 0, 2, 0, 0, 0, -1, 0, -1, -3, 0, -2, 0, 2, -1, 5, 0, 3, 0, 0, -1, 4, -1, 0, -1, 0, 3, 4, 0, 0, 0, 0, -2, 0, 0, 5, -1, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, -2, 0, -3, 0, 0, 0, 2, 3, 0, 0, 0, -2, -2, 0, -4, 0, -2, 0, 0, 0, 5, -2, 0, -1, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 2, 0, 0, -3, -2, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, -4, -1, 0, -1, 0, 0, 0, 0, 1, -2, 0, 0, 4, 0, 0, 3, 3, -1, 0, 5, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 6, 0, 3, 3, -1, -3, -1, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, -2, 0, 5, -3, 0, -4, -1, 0, -1, 5, 0, 2, 0, -2, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, -1, 0, -1, 0, 0, 3, 0, 0, -2, -3, 0, 0, -1, 0, -1, -3, 0, 0, -1, 0, 0, 3, 0, -4, 6, 0, 0, -2, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, -2, -3, 0, 0, 5, -1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 2, -4, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, -1, 0, -5, 0, -2, -1, 0, 0, 3, -1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -1, 0, -1, -2, 0, 0, 0, -1, 0, 1, -2, 5, 0, 3, 0, 5, 6, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -4, 0, 3, 0, 0, 0, 1, 0, 5, -1, 0, 0, -2, -1, -3, 0, 0, 0, -2, 0, 0, 0, 4, -1, 0, 0, -4, -1, 0, 0, 0, -1, 0, 5, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, -3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 3, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, -1, 5, 0, 0, -1, 0, -1, -5, 0, 0, 0, 0, 0, -4, 0, 3, -2, 0, 4, 0, 0, -2, 0, 0, 0, -2, 0, -1, -2, 0, -1, 0, 0, -2, -1, 0, -2, 0, -2, 2, 0, 0, 0, 1, 0, -2, -1, 0, 0, 0, 0, -3, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, -1, 5, 0, 0, 0, 0, -2, 0, 3, 0, -1, 0, 0, 0, 0, 0, 0, -2, -1, 0, -1, 0, 0, 1, 0, 0, -1, -3, 0, 1, 5, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, -3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 4, 0, 0, 1, 0, 0, 0, 4, 6, -2, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 1, -2, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 3, 0, -1, -1, 0, -1, 0, 0, 3, -1, -2, -2, 0, 0, 0, 6, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, -1, 0, 3, 0, -3, 5, 0, 0, 2, 0, 0, 0, -3, 0, -2, -2, 0, 0, -2, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 4, 0, 6, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -5, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, -3, -2, -2, 0, 0, 0, 0, 0, -3, 6, -2, -3, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, -4, 0, 5, 0, 0, -1, 0, -2, -2, 0, 5, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, -1, -4, 0, 0, 6, 0, 6, 0, 0, 0, -1, 0, -2, -6, 0, 0, -1, 0, 2, 0, 0, 0, -1, 5, 0, 0, 0, 1, 0, 0, -1, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, -3, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 4, 5, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, -1, 0, 0, -2, 0, -3, 0, 0, 0, 0, 0, -2, 0, 0, -3, -2, -1, 1, 0, 0, -1, 0, 0, 0, 3, 0, -1, 0, 0, 1, 0, 0, 0, 2, 0, 3, 0, 0, 0, 1, 0, 0, -1, 0, -2, 4, 0, 0, 0, 0, 2, 0, 0, 4, 5, 0, 0, 1, 0, -4, 0, 0, 0, 5, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, 3, 0, 0, 0, 3, -1, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -2, 4, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, -1, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, -3, 3, 0, 0, 0, 0, 0, 6, 0, 0, 3, 0, 0, 0, -1, 0, 0, -1, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -3, 4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, -1, 5, 0, 3, -1, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, -3, 0, 0, 0, 0, -2, 0, 0, 0, -2, 5, 0, 0, -1, 0, 0, 0, 5, 0, -2, 0, 0, -2, 0, 0, 0, -2, -1, 0, -2, 0, -2, 0, 0, 0, -1, 3, 0, 5, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -1, -2, 0, 0, -2, 0, 0, -2, 0, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -4, 2, -2, 0, 4, 6, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -3, 0, 0, -2, 0, 0, 2, -1, -3, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -6, -1, 0, 0, -2, 0, -2, 0, 0, 0, 5, 0, 0, -1, 0, 0, -6, 0, -2, 0, 1, 0, 3, 0, 0, 0, 0, -1, 0, -2, -2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 4, 5, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, -3, -1, 0, 5, 1, 0, 0, -1, 3, 2, 3, 0, 0, 0, 0, 3, 1, -1, 0, 0, 0, -1, 0, 0, 3, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 5, 4, -2, 0, -1, 0, 0, -2, 0, 0, 0, 3, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 6, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 6, 4, 0, 6, 0, 0, 1, 0, 0, -1, -2, 0, 0, -2, -1, 6, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 6, 1, 0, 0, -2, 0, 0, -2, -1, 0, 0, -2, 0, 0, 0, 0, -1, 4, 3, 0, 0, 0, 0, 0, 0, 3, -2, 3, -1, -3, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, -2, 0, -3, -1, -6, 0, -5, -1, 0, 5, 0, -1, 0, -1, 0, 0, 0, 0, 0, 5, 0, 0, -3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, -3, 0, 0, -2, 0, 0, 5, 3, 0, 0, 3, 0, 0, -1, 0, 0, -3, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -4, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 2, -2, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, -1, 0, -1, 0, -2, -2, 0, 0, -1, -4, 0, 6, 0, 0, 0, 0, 0, 5, 0, 0, 3, -3, 5, 0, 0, 0, 0, 0, 0, -2, 0, -3, 6, 0, 0, 0, -1, 0, -1, -2, 0, 0, 0, 0, -4, -2, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, 0, -2, 0, -1, 0, -2, 0, -1, 0, 0, 0, -2, 5, -1, 0, 0, 0, 5, 0, 0, 0, 0, 4, 0, 0, 6, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, -4, 0, -4, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 1, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -1, 5, 0, -4, 0, 0, 0, 0, 0, 5, -1, 0, 0, 0, 0, -3, 5, 0, -1, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 5, 4, 0, 0, 0, 0, 2, 1, 0, 4, 0, -2, 0, 0, 0, 0, -1, 0, -1, 5, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0, 0, 5, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -2, 0, 0, 5, -1, 0, 0, -4, 0, -4, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 3, 0, 0, -1, 0, 5, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, -1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, -1, 1, 0, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, -1, 4], 'weight': 1, 'weight_parity': -1}
  74. label: 152.1.g.a
    {'Nk2': 152, 'analytic_conductor': 0.07585788192021636, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 12, 'artin_field': [-1, 0, -2, -2, 2, 0, 1], 'artin_field_label': '6.2.184832.1', 'artin_image': '12.4', 'char_conductor': 152, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 7, 'char_orbit_label': 'g', 'char_order': 2, 'char_parity': -1, 'char_values': [152, 2, [39, 77, 97], [2, 1, 1]], 'cm_discs': [-152], 'conrey_index': 37, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e3_19.6t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 412333637784, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 152, 7, -1, 2, -152]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '152.1.g.a', 'level': 152, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 19], 'level_radical': 38, 'minimal_twist': '152.1.g.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 7, 'projective_field': [-2, -2, -1, 1], 'projective_field_label': '3.1.152.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e3_19.6t3.2'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-152], 'self_twist_type': 1, 'space_label': '152.1.g', 'trace_display': [-1, 1, 0, -1], 'trace_hash': 2081472063324158583, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.018', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.973', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.088', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.864', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.368', 'prec': 20}, {'__RealLiteral__': 0, 'data': '10.428', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.500', 'prec': 17}, 'traces': [1, -1, 1, 1, 0, -1, -1, -1, 0, 0, 0, 1, 1, 1, 0, 1, -1, 0, -1, 0, -1, 0, -1, -1, 1, -1, -1, -1, 1, 0, 0, -1, 0, 1, 0, 0, -2, 1, 1, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, -1, -1, 1, 1, 1, 0, 1, -1, -1, 1, 0, 0, 0, 0, 1, 0, 0, 1, -1, -1, 0, 0, 0, -1, 2, 1, -1, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, -1, -1, 0, -2, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, -1, 1, -1, 1, 0, -2, -1, 0, 1, 0, 1, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 1, -1, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, -2, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, -1, -1, 0, 1, 0, -2, 0, -2, 1, 0, 1, 0, 0, 0, 2, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, -1, -1, 0, 0, 0, 1, 0, 0, 1, 1, 0, -1, 0, 1, 0, -1, -1, 0, -1, 2, 0, 1, 0, 0, 1, -1, 0, 0, 0, -1, 2, 0, 0, 1, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, -1, 0, 1, -2, 0, -1, -1, -1, 1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 2, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, -1, -1, -1, 0, 0, 0, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, 1, 0, -2, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 1, -1, 0, -1, -1, 0, 0, 1, 2, -1, 0, 1, 2, 1, -1, 0, 0, 2, -1, 0, 0, -1, 0, 1, 0, 0, -2, 1, -1, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, -1, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, -1, 0, 1, 0, 0, 0, 2, 1, 0, -2, 0, 0, -1, 0, 0, -1, 0, 0, -1, 1, 0, 1, 2, 0, -2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 1, -1, 1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 1, 0, -1, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -2, 2, 0, 0, 0, 1, -2, 1, 0, 1, -2, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 1, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, -1, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 2, 1, 0, 1, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, -1, 0, 0, 1, 0, 0, -2, 0, 0, 0, -1, 0, 0, 2, -1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, -2, -1, 1, -1, 0, 0, -1, 0, -2, 1, -1, -1, 1, 1, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 2, 0, -1, 0, 1, 0, -1, 0, 0, -1, 0, -1, -1, 0, 0, 1, 1, -1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, -1, 1, -1, -2, -1, 0, 0, 0, 1, 0, 0, -2, 0, -1, 0, 1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, -1, 1, 0, 1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, -1, 1, 0, 1, 0, 2, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, -1, 0, -2, 0, 0, 0, -2, -2, 0, -1, -1, 0, 0, 2, -1, 0, 0, 0, -1, 1, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, -1, 0, -2, 1, 0, 1, 2, 0, 0, 0, -1, 2, -1, 1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, -1, 0, 1, 0, -1, 0, 0, 1, 0, 2, 0, -1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 1, 0, 2, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 2, 0, -2, -1, 0, 0, 0, -2, 0, 1, -1, 0, 2, -1, -1, 0, 0, 1, -1, -2, 2, 0, 1, 0, 0, 0, 0, 2, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, -2, 0, 0, 2, 0, -2, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 1, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, -1, 1, -1, 0, 0, -2, -1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 1, 0, -1, 0, 1, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 1, 0, 0, -1, 2, 1, -2, 0, 0, -1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 1, 1, 0, 1, 0, -1, -1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 2, 0, 0, 2, 0, 0, 3, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 0, -2, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -1, 0, -2, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 1, 0, 0, -1, 2, 0, 1, 0, -1, 2, 1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 2, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 1, 0, -1, 0, -1, 0, 0, 1, 0, -1, 0, 0, -1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, -2, 0, 0, 1, -2, 1, 0, 0, 0, 0, 1, -1, 0, -1, 1, 1, 1, 0, -1, 0, -1, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 0, -2, 0, 1, -1, 0, 0, 0, -2, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, -1, 0, 1, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, 0, 1, -2, 0, 0, 0, -2, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 2, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, -1, -2, 0, 0, 0, 1, 1, 0, -1, 2, 0, 1, -1, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 1, -1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, -1, -1, 0, 0, 0, -1, -1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, -1, 0, -1, 0, 0, 2, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, -1, 0, 2, 0, 0, 1, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, -1, 0, 1, 2, 2, 2, -1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, -2, 0, 1, 0, 0, 0, 0, 2, 0, -1, 1, 1, -1, -2, 1, -1, 0, 0, -1, 2, 0, 0, 0, 2, -1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, -2, 1, -2, -2, 0, 1, 0, -1, 0, 0, -1, 2, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, -2, -1, 0], 'weight': 1, 'weight_parity': -1}
  75. label: 152.1.g.b
    {'Nk2': 152, 'analytic_conductor': 0.07585788192021636, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-2, -2, -1, 1], 'artin_field_label': '3.1.152.1', 'artin_image': '6.1', 'char_conductor': 152, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 7, 'char_orbit_label': 'g', 'char_order': 2, 'char_parity': -1, 'char_values': [152, 2, [39, 77, 97], [2, 1, 1]], 'cm_discs': [-152], 'conrey_index': 37, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e3_19.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4504011961008280, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 152, 7, -1, 2, -152]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '152.1.g.b', 'level': 152, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 19], 'level_radical': 38, 'minimal_twist': '152.1.g.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 7, 'projective_field': [-2, -2, -1, 1], 'projective_field_label': '3.1.152.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e3_19.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-152], 'self_twist_type': 1, 'space_label': '152.1.g', 'trace_display': [1, -1, 0, -1], 'trace_hash': 1405022168149094224, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.023', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.973', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.922', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.864', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.704', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.428', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.500', 'prec': 17}, 'traces': [1, 1, -1, 1, 0, -1, -1, 1, 0, 0, 0, -1, -1, -1, 0, 1, -1, 0, 1, 0, 1, 0, -1, -1, 1, -1, 1, -1, -1, 0, 0, 1, 0, -1, 0, 0, 2, 1, 1, 0, 0, 1, 0, 0, 0, -1, 2, -1, 0, 1, 1, -1, -1, 1, 0, -1, -1, -1, -1, 0, 0, 0, 0, 1, 0, 0, -1, -1, 1, 0, 0, 0, -1, 2, -1, 1, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, -1, 0, 2, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, -1, -1, 1, -1, 0, -2, -1, 0, -1, 0, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, -1, -1, 1, 0, 0, -2, 0, 0, 0, 0, -1, 0, 2, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, -1, 0, 1, 0, 2, 0, 2, 1, 0, -1, 0, 0, 0, 2, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 1, 1, 0, 0, 0, -1, 0, 0, -1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 1, -2, 0, -1, 0, 0, -1, -1, 0, 0, 0, -1, 2, 0, 0, -1, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 2, 0, 0, -1, 0, -1, 2, 0, -1, -1, -1, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 2, 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 1, 0, 0, 1, 1, -1, -1, -1, 0, 1, 0, -2, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, -1, -1, 0, -1, 1, 0, 0, -1, 2, -1, 0, 1, 2, -1, 1, 0, 0, 2, -1, 0, 0, 1, 0, -1, 0, 0, 2, 1, -1, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, -1, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0, -1, 0, 0, 0, 2, -1, 0, 2, 0, 0, 1, 0, 0, -1, 0, 0, 1, 1, 0, -1, 2, 0, -2, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 1, 1, 1, 0, 0, 0, 0, -2, -2, 0, 0, 0, -1, 0, 1, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 2, 0, 0, 0, -1, -2, -1, 0, -1, 2, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -2, 0, 0, 2, 0, 0, 2, 0, 0, 0, -1, -1, 0, 1, 1, -1, 0, 0, -2, 0, 2, 0, 1, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, -1, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -2, -1, 0, -1, -1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, -2, -1, 0, -1, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 2, 1, -1, -1, 0, 0, 1, 0, 2, -1, -1, -1, 1, 1, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 2, 0, 1, 0, -1, 0, -1, 0, 0, -1, 0, 1, -1, 0, 0, 1, -1, -1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, -1, -1, 1, -2, 1, 0, 0, 0, 1, 0, 0, -2, 0, -1, 0, -1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, -1, 0, -1, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, 1, -1, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, -1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, -1, 0, -2, 0, 0, 0, 2, 2, 0, -1, -1, 0, 0, 2, 1, 0, 0, 0, -1, 1, 1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, -1, 0, 2, 1, 0, 1, -2, 0, 0, 0, -1, 2, 1, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, -1, 1, 0, 1, 0, 1, 0, 0, -1, 0, 2, 0, -1, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 1, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -2, -2, 0, 2, 1, 0, 0, 0, -2, 0, -1, -1, 0, -2, -1, -1, 0, 0, -1, -1, 2, 2, 0, -1, 0, 0, 0, 0, -2, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, -1, 0, 2, 0, 0, 2, 0, -2, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, -1, -1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, -1, -1, 1, 0, 0, -2, -1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, -1, 0, -1, 0, 1, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, -2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 1, 0, 0, 1, -2, -1, 2, 0, 0, 1, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, -1, -1, 0, -1, 0, -1, -1, 0, 0, -1, 0, 0, 2, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, -2, 0, 0, 2, 0, 0, 3, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 0, 0, -1, 0, -2, 0, 1, 1, 1, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, 2, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, -1, 0, 0, -1, 2, 0, 1, 0, -1, -2, -1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, -1, 0, -1, 0, -1, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 1, 0, 1, 0, 0, -1, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 2, 0, 0, 1, -2, -1, 0, 0, 0, 0, -1, 1, 0, -1, 1, -1, -1, 0, 1, 0, -1, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, -1, 2, 0, 1, 0, 2, 0, -1, -1, 0, 0, 0, -2, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, -1, -1, 0, 1, 0, -2, 0, 1, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 2, 0, 0, 0, -2, 1, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 1, -1, 0, 0, 2, -1, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, 0, -1, -1, 0, -1, 2, 0, -1, -1, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, -1, 1, 0, -1, 0, 0, -1, -1, 0, 0, 0, 1, -1, -1, 0, 0, 0, 1, -1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 1, 0, -1, 0, 0, 2, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 0, -1, 0, 2, 0, 0, -1, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, -1, 0, 1, 2, -2, 2, 1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 1, 2, 0, 1, 0, 0, 0, 0, 2, 0, -1, -1, -1, 1, 2, 1, -1, 0, 0, -1, -2, 0, 0, 0, 2, -1, 0, 0, 0, 0, -2, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 2, -1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 2, 0, -1, 1, 0, -1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 2, -1, 0], 'weight': 1, 'weight_parity': -1}
  76. label: 152.1.k.a
    {'Nk2': 152, 'analytic_conductor': 0.07585788192021636, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [3, -4, 0, 2, 1, -2, 1], 'artin_field_label': '6.0.184832.1', 'artin_image': '18.3', 'char_conductor': 152, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 11, 'char_orbit_label': 'k', 'char_order': 6, 'char_parity': -1, 'char_values': [152, 6, [39, 77, 97], [3, 3, 4]], 'cm_discs': [-8], 'conrey_index': 11, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e3_19.6t5.1c1'], ['ArtinRepresentation/2.2e3_19.6t5.1c2']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 687211544728, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, -8], [1, 1, 19, 3, 1, 3, 0], [1, 1, 152, 11, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '152.1.k.a', 'level': 152, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 19], 'level_radical': 38, 'minimal_twist': '152.1.k.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 11, 'projective_field': [7, 13, -1, 1], 'projective_field_label': '3.1.2888.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{6}^{2}q^{2}-\\zeta_{6}^{2}q^{3}-\\zeta_{6}q^{4}+\\zeta_{6}q^{6}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e3_19.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-8], 'self_twist_type': 1, 'space_label': '152.1.k', 'trace_display': [-1, 1, 0, 0], 'trace_hash': 1619917964660319107, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.006', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.988', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.996', 'prec': 17}, {'__RealLiteral__': 0, 'data': '17.946', 'prec': 20}, {'__RealLiteral__': 0, 'data': '49.926', 'prec': 20}, {'__RealLiteral__': 0, 'data': '241.463', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.506', 'prec': 17}, 'traces': [2, -1, 1, -1, 0, 1, 0, 2, 0, 0, -2, -2, 0, 0, 0, -1, -2, 0, -1, 0, 0, 1, 0, 1, -1, 0, 2, 0, 0, 0, 0, -1, -1, -2, 0, 0, 0, 2, 0, 0, 1, 0, -2, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, -1, 0, 0, -2, 0, 1, 0, 0, 0, 0, 2, 0, -1, 1, 4, 0, 0, 0, 0, 1, 0, -2, -1, 0, 0, 0, 0, 1, 1, -2, 0, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, 1, -1, 0, -1, 0, -4, 0, 0, 0, 0, 4, -1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 2, 0, 1, 2, 0, -2, 0, -2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, 0, 1, 0, 0, -1, 0, 0, 4, 0, 0, 0, 1, -1, 4, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, -2, 1, 0, -1, 0, 0, 0, -1, 2, 0, 0, 2, 0, 0, 0, 0, 1, 0, -2, 0, 0, -2, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 1, -4, 0, 0, 0, 1, 0, -1, 0, 0, -4, 1, 0, 0, 0, -2, 0, -2, 1, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -3, 0, -1, -2, 0, 1, 0, 0, -2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, -2, 0, 1, 0, 1, 0, 0, -2, 1, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 1, -2, 2, 0, -2, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 1, 0, -2, 0, -2, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 2, 1, -1, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 0, 0, 2, -2, 4, 0, 0, -2, 0, 0, 4, 0, 0, -2, 0, 0, 0, -1, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -1, 1, 0, 1, 0, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1, 2, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, -2, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, -1, -2, 0, 2, 0, 0, 0, 0, -2, 0, -2, -2, 0, 0, 0, -1, -1, 0, 0, 0, 0, 2, 0, 1, -1, 0, -2, 0, 0, 0, 0, 4, 0, 0, -2, 1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, -2, -2, 0, 0, 1, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, -2, 6, 2, 0, 0, 2, 0, 1, 0, 0, -2, -2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, -1, -2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, -2, 0, 1, -1, 0, 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, -1, 2, 0, -1, 0, 0, -1, 0, 4, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 1, 0, 0, 2, 0, -1, 0, 0, 0, 0, -2, 0, 1, 0, -1, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 2, 4, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, -1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -1, -1, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -4, 4, -2, 0, 0, 0, -1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, -2, -1, 0, 1, 0, -2, 0, 0, -1, 0, 2, 4, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 4, 1, 0, 1, 0, 0, 0, 0, -1, 0, 4, -6, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 1, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -2, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, -2, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 2, -2, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, -2, -1, 2, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, -2, 0, -1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, -2, 2, 0, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 4, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, -2, 0, -1, 4, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 4, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 1, 0, 1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, -2, -4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -3, 0, -4, 0, 0, -2, 0, -2, -1, 0, 0, 0, 1, 0, 0, -2, 0, 0, -2, 0, 1, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, -1, 0, 1, 0, -1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, -4, 0, 1, 0, 0, 1, 0, -2, -2, 0, 0, 0, 1, 1, -1, -4, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 2, 1, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, -2, 0, 2, 0, -1, 1, 0, 0, 2, 0, 0, 0, 0, 4, -1, 0, 0, 0, -2, 0, 0, 2, 0, -1, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 4, 1, 0, 1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 1, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -1, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 8, 0, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 1, 0, 4, -2, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -4, 0, 1, -1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -2, 0, -1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -2, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, -2, 0, 1, 0, 0, 0, 0, -4, 0, 0, -1, 0, 0, 0, 0, 2, -1, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -1, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -2, -1, 0, -2, 0, 0, 0, 0, 0, 1, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, -1, 1, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, -1, -2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 2, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 0, -1, 2, 0, 0, 0, 1, 1, 0, -2, 0, 0, 1, 0, -2, 0, 0, -4, 0, 0, 0, 0, 1, -2, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -3, 0, 2, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 2, 0, 1, 0, 0, -2, 1, 0, 0, 0, 0, -2, -2, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 0, 0, 0, 0, 1, -1, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  77. label: 152.1.u.a
    {'Nk2': 152, 'analytic_conductor': 0.07585788192021636, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 152, 'char_degree': 6, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 21, 'char_orbit_label': 'u', 'char_order': 18, 'char_parity': -1, 'char_values': [152, 18, [39, 77, 97], [9, 9, 4]], 'cm_discs': [-8], 'conrey_index': 35, 'dim': 6, 'field_disc': -19683, 'field_disc_factorization': [[-1, 1], [3, 9]], 'field_poly': [1, 0, 0, -1, 0, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 18, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 1374406312088, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, -8], [1, 1, 19, 5, 1, 9, 0], [1, 1, 152, 21, -1, 18, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '152.1.u.a', 'level': 152, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 19], 'level_radical': 38, 'minimal_twist': '152.1.u.a', 'nf_label': '6.0.19683.1', 'prim_orbit_index': 21, 'projective_field': [-284, -84, 96, 164, -149, 67, -20, 4, -3, 1], 'projective_field_label': '9.1.69564674215936.1', 'projective_image': 'D9', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{18}^{5}q^{2}+(\\zeta_{18}^{6}-\\zeta_{18}^{7})q^{3}-\\zeta_{18}q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-8], 'self_twist_type': 1, 'space_label': '152.1.u', 'trace_display': [0, -3, 0, 0], 'trace_hash': 373065239775203077, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.035', 'prec': 20}, {'__RealLiteral__': 0, 'data': '5.936', 'prec': 17}, {'__RealLiteral__': 0, 'data': '17.650', 'prec': 20}, {'__RealLiteral__': 0, 'data': '278.457', 'prec': 24}, {'__RealLiteral__': 0, 'data': '1996.949', 'prec': 27}, {'__RealLiteral__': 0, 'data': '24903.718', 'prec': 30}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.729', 'prec': 17}, 'traces': [6, 0, -3, 0, 0, -3, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, -3, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, -3, 0, 0, -3, 0, 0, 6, 0, 0, 0, 6, -3, -3, 3, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, -3, -3, 3, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, -3, 0, 6, 0, 0, 0, 0, 0, 3, 0, 6, -6, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 0, -3, 0, 6, -3, 0, 0, 6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 6, 0, 0, 0, 0, -3, -6, 0, 0, 0, -3, 6, 3, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, -3, -3, 0, 6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, -3, -6, 0, 0, -6, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 6, 0, 0, 3, 0, 0, -3, 0, 0, 0, -3, 0, 3, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, 6, 0, -3, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 6, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 12, 0, 0, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0, -3, -3, 0, 0, 3, 0, 0, 0, 6, -3, -3, 0, 0, 0, 0, 0, -6, -3, 0, -6, 0, 0, 0, 0, 0, -6, 0, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -6, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, -3, 6, -3, 0, -3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 6, -3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -6, 0, 0, -6, 0, 6, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 3, 0, 0, 0, 0, -3, 0, 0, -6, 0, 0, 0, 0, 0, 0, -3, 0, 0, -6, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 6, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 3, -3, 0, 0, 0, 0, -6, -3, 0, 0, -3, 0, 0, 0, -3, 3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 6, 6, -3, 0, 6, 0, 0, -3, 0, -6, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 3, 0, 6, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 12, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 3, 0, -6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 6, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, -6, 3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -6, 6, 0, -3, 0, 0, 0, 0, 6, 0, -6, 0, 0, 0, 0, 0, 0, 12, 0, 0, -3, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, -3, 0, 0, 0, 0, -3, 6, 0, 0, 0, 6, -6, -3, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, -3, 0, -6, 0, 0, 0, 0, 6, 0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, -3, 0, 0, 0, 6, 3, 0, 6, 3, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 3, 0, -3, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 6, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 12, 0, -3, -3, 0, 6, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, -6, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 6, 3, 0, 0, -3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -9, 0, 3, 0, 0, 3, 0, -3, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, 0, 0, 0, 0, 0, 0, -6, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, -3, 6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -6, 0, -6, 0, 0, 0, 0, 0, -3, 0, 3, 6, 0, -3, 0, 0, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -6, 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 3, 6, 0, 0, 0, -3, 12, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, -3, 6, 0, -3, 0, 0, 0, 0, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 6, 0, -6, -3, 0, 0, 0, -3, 0, 0, -6, 0, 0, 0, 0, -6, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3, 0, -3, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, 0, 3, -3, 0, 0, 6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -6, 3, 0, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 3, -3, 0, -3, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, -6, 6, 0, 0, -3, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -3, 6, 0, 6, 0, 0, -3, 0, 6, 0, 0, 0, 0, 3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, 0, 3, 6, 0, 3, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 6, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0, 3, 6, -6, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 6, 0, 0, 0, 6, -3, 0, -3, -6, 0, 0, 0, 6, -9, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, -3, 6, 0, 0, -3, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, 6, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 3, 0, 6, -3, 0, 3, 0, 0, 0, 0, 6, 0, -6, 0, 0, 0, -3, 0, 3, 0, 0, 9, 0, 0, 0, 0, 0, 0, -3, 0, 12, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  78. label: 155.1.c.a
    {'Nk2': 155, 'analytic_conductor': 0.07735507695811537, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [-1, -3, 0, -1, 1], 'artin_field_label': '4.2.775.1', 'artin_image': '8.3', 'char_conductor': 155, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 3, 'char_orbit_label': 'c', 'char_order': 2, 'char_parity': -1, 'char_values': [155, 2, [32, 96], [1, 1]], 'cm_discs': [-31, -155], 'conrey_index': 154, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.5_31.4t3.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [0, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 137455730843, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 31, 2, -1, 2, -31], [1, 1, 155, 3, -1, 2, -155], [1, 1, 5, 2, 1, 2, 5]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '155.1.c.a', 'level': 155, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [5, 31], 'level_radical': 155, 'minimal_twist': '155.1.c.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 3, 'projective_field': [81, 0, 13, 0, 1], 'projective_field_label': '4.0.24025.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\\cdots', 'related_objects': ['ArtinRepresentation/2.5_31.4t3.1'], 'relative_dim': 1, 'rm_discs': [5], 'self_twist_discs': [-31, -155, 5], 'self_twist_type': 3, 'space_label': '155.1.c', 'trace_display': [0, 0, -1, 0], 'trace_hash': 1114836362764556570, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.004', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.955', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.010', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.815', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.033', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.255', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.760', 'prec': 17}, 'traces': [1, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -4, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], 'weight': 1, 'weight_parity': -1}
  79. label: 155.1.c.b
    {'Nk2': 155, 'analytic_conductor': 0.07735507695811537, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 155, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 3, 'char_orbit_label': 'c', 'char_order': 2, 'char_parity': -1, 'char_values': [155, 2, [32, 96], [1, 1]], 'cm_discs': [-31], 'conrey_index': 154, 'dim': 2, 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [[2, [3, 0, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503737083101339, 'hecke_ring_generator_nbound': 5, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 31, 2, -1, 2, -31], [1, 1, 5, 2, 1, 2, 0], [1, 1, 155, 3, -1, 2, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '155.1.c.b', 'level': 155, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [5, 31], 'level_radical': 155, 'minimal_twist': '155.1.c.b', 'nf_label': '2.0.3.1', 'prim_orbit_index': 3, 'projective_field': [-1, -1, 1, -4, 3, 0, 1], 'projective_field_label': '6.2.120125.1', 'projective_image': 'D6', 'projective_image_type': 'Dn', 'qexp_display': 'q+(\\zeta_{6}+\\zeta_{6}^{2})q^{2}+(-1-\\zeta_{6}+\\zeta_{6}^{2}+\\cdots)q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-31], 'self_twist_type': 1, 'space_label': '155.1.c', 'trace_display': [0, 0, 1, 0], 'trace_hash': 2268514883216856327, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.005', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.904', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.069', 'prec': 20}, {'__RealLiteral__': 0, 'data': '22.740', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-1.026', 'prec': 20}, {'__RealLiteral__': 0, 'data': '333.013', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.760', 'prec': 17}, 'traces': [2, 0, 0, -4, 1, 0, 0, 0, -2, -3, 0, 0, 0, 6, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 3, 4, 0, 0, 0, 3, -2, 0, 0, 0, -1, 0, 0, 0, -4, -3, 0, 0, 0, 0, 0, -6, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, -4, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, -2, -6, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0, 0, -6, 0, 8, 0, 0, 0, 3, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 2, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -3, 2, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, -2, 0, 0, 6, -3, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 1, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -4, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -6, 0, -4, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, -4, -3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3, 0, 0, 0, 0, 0, -4, 0, 0, 8, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, -8, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 6, 0, 0, 0, 0, 4, 0, -6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -6, -2, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 6, 0, 0, -2, 0, 0, 0, 0, -4, 3, 0, 0, 0, 0, 0, 6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, -4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -2, 0, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, -6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -2, -3, 0, 0, 0, 6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, -4, 2, -6, 0, 0, 0, -3, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 4, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, -6, 0, 0, -4, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -6, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -8, 0, 0, -2, 3, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -4, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0, -6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, -2, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 4, 1, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -1, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, -3, 0, 0, 0, 2, 0, -4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -4, 0, 0, 2, 2, 6, 0, 0, 0, -6, 0, 0, 0, -6, 0, 4, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 2, 0, 0, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -3, 4, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -2], 'weight': 1, 'weight_parity': -1}
  80. label: 156.1.o.a
    {'Nk2': 156, 'analytic_conductor': 0.07785414197074837, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [1, -5, 6, 3, -4, -1, 1], 'artin_field_label': '6.0.73008.1', 'artin_image': '18.3', 'char_conductor': 39, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 15, 'char_orbit_label': 'o', 'char_order': 6, 'char_parity': -1, 'char_values': [156, 6, [79, 53, 145], [6, 3, 2]], 'cm_discs': [-3], 'conrey_index': 29, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_3_13.6t5.1c1'], ['ArtinRepresentation/2.2e2_3_13.6t5.1c2']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 962089451676, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 13, 3, 1, 3, 0], [1, 1, 39, 9, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '156.1.o.a', 'level': 156, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 3, 13], 'level_radical': 78, 'minimal_twist': '156.1.o.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 9, 'projective_field': [-26, 0, 0, 1], 'projective_field_label': '3.1.2028.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{6}q^{3}-\\zeta_{6}^{2}q^{7}+\\zeta_{6}^{2}q^{9}+\\zeta_{6}^{2}q^{13}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_3_13.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '156.1.o', 'trace_display': [0, -1, 0, 1], 'trace_hash': 1220429655578111871, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.018', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.925', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.968', 'prec': 17}, {'__RealLiteral__': 0, 'data': '17.287', 'prec': 20}, {'__RealLiteral__': 0, 'data': '48.287', 'prec': 20}, {'__RealLiteral__': 0, 'data': '232.820', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.508', 'prec': 17}, 'traces': [2, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 4, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0], 'weight': 1, 'weight_parity': -1}
  81. label: 156.1.s.a
    {'Nk2': 156, 'analytic_conductor': 0.07785414197074837, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 39, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 19, 'char_orbit_label': 's', 'char_order': 6, 'char_parity': -1, 'char_values': [156, 6, [79, 53, 145], [6, 3, 1]], 'cm_discs': [-3], 'conrey_index': 17, 'dim': 2, 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 1236967358620, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 13, 5, 1, 6, 0], [1, 1, 39, 8, -1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '156.1.s.a', 'level': 156, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 3, 13], 'level_radical': 78, 'minimal_twist': '156.1.s.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 8, 'projective_field': [12, 12, -8, -9, 7, -3, 1], 'projective_field_label': '6.0.160398576.1', 'projective_image': 'D6', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{6}q^{3}+(-1-\\zeta_{6})q^{7}+\\zeta_{6}^{2}q^{9}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '156.1.s', 'trace_display': [0, 1, 0, -3], 'trace_hash': 885013910435053866, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.005', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.917', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.054', 'prec': 17}, {'__RealLiteral__': 0, 'data': '16.929', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.038', 'prec': 17}, {'__RealLiteral__': 0, 'data': '185.186', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.647', 'prec': 17}, 'traces': [2, 0, 1, 0, 0, 0, -3, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, -2, 0, -3, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, -1, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, -3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, -1, 0, -3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -2, 0, 0, 0, -1, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0], 'weight': 1, 'weight_parity': -1}
  82. label: 159.1.d.a
    {'Nk2': 159, 'analytic_conductor': 0.07935133700864738, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 10, 'artin_field': [-3, 1, -3, 1, 0, 1], 'artin_field_label': '5.1.25281.1', 'artin_image': '10.1', 'char_conductor': 159, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [159, 2, [107, 55], [1, 1]], 'cm_discs': [-159], 'conrey_index': 158, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.3_53.5t2.1c2'], ['ArtinRepresentation/2.3_53.5t2.1c1']], 'field_disc': 5, 'field_disc_factorization': [[5, 1]], 'field_poly': [-1, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207583, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 159, 4, -1, 2, -159]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '159.1.d.a', 'level': 159, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 53], 'level_radical': 159, 'minimal_twist': '159.1.d.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 4, 'projective_field': [-3, 1, -3, 1, 0, 1], 'projective_field_label': '5.1.25281.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(-1+\\beta )q^{2}+q^{3}+(1-\\beta )q^{4}-\\beta q^{5}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3_53.5t2.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-159], 'self_twist_type': 1, 'space_label': '159.1.d', 'trace_display': [-1, 2, -1, -1], 'trace_hash': 1382489676216534128, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.036', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.857', 'prec': 17}, {'__RealLiteral__': 0, 'data': '5.404', 'prec': 17}, {'__RealLiteral__': 0, 'data': '23.592', 'prec': 20}, {'__RealLiteral__': 0, 'data': '92.299', 'prec': 20}, {'__RealLiteral__': 0, 'data': '371.079', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.506', 'prec': 17}, 'traces': [2, -1, 2, 1, -1, -1, -1, -2, 2, -2, 0, 1, -1, 3, -1, 0, 0, -1, 0, 2, -1, 0, -1, -2, 1, -2, 2, -3, 0, -2, 0, 2, 0, 0, -2, 1, -1, 0, -1, 1, -1, 3, -1, 0, -1, 3, 0, 0, 1, 2, 0, 2, 2, -1, 0, 1, 0, 0, 0, 2, 0, 0, -1, -1, 3, 0, 0, 0, -1, 1, -1, -2, 0, 3, 1, 0, 0, -2, 0, 0, 2, 3, -1, -3, 0, -2, 0, 0, 0, -2, -2, -3, 0, 0, 0, 2, -1, -3, 0, -2, 4, 0, 0, 1, -2, -1, 0, 1, 0, 0, -1, 0, 0, 0, -2, 0, -1, 0, 0, 1, 2, 0, -1, 0, -2, 3, 0, 1, -1, 1, 0, 0, 0, 0, -1, 0, -1, 3, 0, -1, 0, -2, 0, 0, 0, 0, 1, -3, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, -1, 3, -1, 4, -3, 0, -2, -1, 1, 1, 0, 0, 2, -1, 0, 2, 0, 0, 0, -1, 2, 0, 1, 0, 1, -2, 0, 0, 0, -1, 0, -1, -1, 0, -2, 3, 3, 0, 0, -1, -1, 0, -2, 0, 0, -2, 0, -1, 0, 0, 1, -1, 1, -1, 0, 3, -2, 0, 0, 0, 0, 0, 3, 4, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, -2, 0, 0, 0, 0, 4, 0, -1, -1, 2, 0, 2, 3, 0, 0, -1, 1, -1, -3, 0, 0, 0, -2, -1, -2, 3, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, -2, -1, 0, -2, -2, 0, -3, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 3, 2, 2, 0, -1, 0, 0, -3, 0, 1, 0, 0, -2, -2, -2, 0, 4, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, -1, 0, -2, 0, -4, 0, 1, -3, -2, 0, 1, 0, 0, -1, 2, -1, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 1, -2, 3, 0, 0, 0, -1, -1, 0, 4, 0, 3, 0, 0, 3, 4, 1, 2, 0, 2, -1, 0, 0, -1, 0, -1, 1, -1, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 3, -1, 1, 0, 0, -1, 2, -1, 1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 2, -1, 0, 0, 0, -1, 1, -1, 0, 0, 3, 3, -1, 0, 0, -1, -1, 0, 3, 0, -2, 0, -2, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, -3, 0, -2, 0, 3, 0, 2, 0, 0, 0, 0, 1, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -1, -1, -2, 3, 3, 1, 3, -1, -1, 0, 4, -1, -1, -3, 0, 0, 0, 0, -2, -2, 0, -1, -1, 3, -1, 1, -2, 0, 1, 0, -1, 0, 0, 0, 0, 3, 0, 2, 0, -4, -1, -3, 0, 0, -1, 0, 2, -2, 0, 0, 1, -2, 0, 0, -2, 0, 0, 0, -1, 0, 0, 2, -1, -2, 0, 0, 0, 1, -1, 2, 0, 0, 0, 1, 0, 0, -2, 0, -1, 0, 3, 0, 0, 0, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, -4, 2, -1, -1, -1, 0, 0, -2, -2, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0, 1, 0, 0, -1, -2, -1, 0, 0, 0, 0, 0, 0, -2, -2, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 2, 0, -1, 2, 4, 0, 4, 4, 3, 0, 0, -2, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 4, 3, 0, 1, 0, 3, 0, 2, 4, 0, 0, -1, -1, 0, 1, -2, -1, 0, -2, 0, 0, 0, 0, 0, 3, 1, -1, 0, -1, 1, 0, -3, 0, 0, 0, 0, 0, 0, -1, 1, -1, -2, 0, 0, 0, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, -3, 4, -2, 4, 0, 0, -1, -1, 0, 0, -1, -1, 2, 2, 0, 0, 0, -1, 3, 2, -1, 0, 3, 0, -1, 0, 3, 0, 0, 0, 0, -1, 0, 0, 1, -1, 0, -1, 0, 0, -3, 4, 0, 0, 0, -1, 0, 0, -3, 0, -2, 0, -2, 0, 0, -1, 0, -1, -2, 0, 1, 3, 3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 1, 0, -2, 0, 0, 1, 0, 0, -4, -1, -2, -1, 0, -1, 0, -2, 0, 0, 3, -2, -1, 4, -2, -1, 0, 0, 0, -1, -3, 0, 1, 0, -2, 0, 0, 3, 0, 0, -2, 0, 2, 2, 0, 0, -3, -3, 0, -1, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, -1, -1, 3, 0, 0, 2, -2, 3, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 3, 0, 0, -1, -3, 0, 0, 0, -2, 4, 1, 0, 0, 0, 2, 0, 0, -2, -3, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, -1, 0, 4, 2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 2, -1, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 2, 0, 3, -2, -2, 2, 1, 0, -3, 0, -4, -1, -2, 0, 1, 0, 1, 0, -2, -3, 0, -1, -2, 0, 1, 0, -2, 0, 1, 0, 0, 0, 0, -2, 0, -1, 0, -1, 1, 3, 2, 4, 0, -1, 2, 0, -2, 0, -3, 0, 3, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, -2, -1, 0, 0, 0, 0, 2, 2, 0, 0, -3, -2, 0, 0, 1, 0, 0, -2, 4, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -1, -1, 2, -1, 0, -2, 0, 0, -3, 4, 2, 0, 0, 0, 0, 3, 1, 0, 0, -1, 0, 0, 0, 0, 3, -3, 0, 4, 0, 3, 1, 0, -2, 2, 2, 0, 0, 0, 0, 2, 0, 4, -1, 0, -2, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, -1, 3, -2, 0, -1, 1, 0, -2, 0, 0, -1, 0, -2, 3, -3, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 3, 0, 4, -1, -1, 0, 1, -1, 3, 0, 1, 0, 0, 0, 0, -1, 1, -1, 2, 3, 0, -1, 0, -2, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -2, -2, -1, 0, 0, 0, 0, 0, 0, -1, -1, -2, 0, 0, 0, 0, -2, 3, 2, -1, -2, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, -2, 0, -1, 2, 0, 1, 0, 0, -1, 3, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, 3, 0, -2, 0, -1, 0, 0, -1, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, -1, -2, -1, 1, 0, -2, 0, 0, -2, -2, 0, -3, 0, 1, 0, 0, 0, 0, 1, 0, -1, 0, -1, 1, 0, 0, 0, -4, 0, 0, -1, 0, 0, 0, 0, -1, -2, 0, 3, 0, -1, -2, 0, 0, -1, -2, 1, -3, 1, 0, 0, 0, -1, 0, 0, -3, 0, 0, 0, 1, 3, -2, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 2, 0, -1, 0, -2, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, -1, 4, 3, 0, -1, 0, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 2, 0, 0, 0, 0, -1, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 4, -2, 1, 2, -1, -2, -1, -1, 0, 0, -2, 1, -1, 3, 4, 0, 3, 0, -1, 1, 0, -2, 3, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 3, 4, -3, 0, -1, -1, 3, -1, 0, 0, -3, 3, 0, 0, 2, -1, 0, -1, -3, 0, 0, -1, 0, 0, 0, -2, 0, 0, -2, 1, 0, 0, 0, 0, -1, 0, -2, -1, 0, 1, 3, 0, 0, -1, 0, -1, 1, 0, -2, -2, 0, 3, 0, 0, 0, 1, 3, 4, 0, 0, 0, -1, 1, 0, 0, 4, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, -4, 0, -3, -1, 0, -1, -3, -2, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, -1, 0, 2, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, -2, 1, 0, 3, 0, 0, 4, 0, -2, 2, 0, 0, 3, 2, 0, 0, 0, 0, 0, -3, -1, 0, -1, 0, 0, 0, 0, 3, 0, 2, 0, 3, -1, 0, 1, -2, 4, 0, 0, -4, -2, 0, -2, 0, 0, -3, 0, 1, 0, 2, -1, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 0, 0, 0, -1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 1, -1, 0, -2, 0, 0, 2, 3, 0, 0, 0, 1, -1, 0, 0, 0, 0, 3, 1, -1, -1, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, -1, -4, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 3, -1, -3, 0, -4, 0, 0, 2, 0, 0, -1, 0, 1, -1, -3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -3, 0, 0, -1, -2, 3, -3, 3, 0, 4, 0, 0, 3, -2, 3, -2, 0, 0, 0, 0, 0, 0, 2, 0, -2, -3, 0, -1, 0, 0, 0, 3, 0, 0, -4, 0, 0, 0, 0, -1, 1, -1, 1, 0, 1, -2, 0, 0, 0, 3, -1, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -3, 3, -1, 0, 0, -2, 0, -2, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, 1, -1, 0, 1, -1, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 4, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 2, -4, 4, 0, 3, -3, -1, 1, 0, 2, 0, -1, 4, -1, 0, 0, 0, 1, 4, 0, 4, 4, -1, 3, 3, 0, 0, 0, 0, -1, 0, 0, 0, -2, -2, 0, 0, 2, -1, -1, -1, 0, 0, 3, 0, 2, 0, 0, 0, -2, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, -1, 0, 0, -2, 4, 0, 0, 3, 0, -1, 0, 1, 0, 1, 0, -2, 0, 0, 0, 3, -1, 0], 'weight': 1, 'weight_parity': -1}
  83. label: 159.1.d.b
    {'Nk2': 159, 'analytic_conductor': 0.07935133700864738, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 20, 'artin_field': [3, 6, 4, 6, 1, -2, 2, -4, 3, -1, 1], 'artin_field_label': '10.0.1917386883.1', 'artin_image': '20.4', 'char_conductor': 159, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [159, 2, [107, 55], [1, 1]], 'cm_discs': [-159], 'conrey_index': 158, 'dim': 2, 'field_disc': 5, 'field_disc_factorization': [[5, 1]], 'field_poly': [-1, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, -1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503805802578079, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 159, 4, -1, 2, -159]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '159.1.d.b', 'level': 159, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 53], 'level_radical': 159, 'minimal_twist': '159.1.d.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 4, 'projective_field': [-3, 1, -3, 1, 0, 1], 'projective_field_label': '5.1.25281.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q+(1-\\beta )q^{2}-q^{3}+(1-\\beta )q^{4}+\\beta q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-159], 'self_twist_type': 1, 'space_label': '159.1.d', 'trace_display': [1, -2, 1, -1], 'trace_hash': 1001297182202815987, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.001', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.857', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.071', 'prec': 20}, {'__RealLiteral__': 0, 'data': '23.592', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-1.052', 'prec': 20}, {'__RealLiteral__': 0, 'data': '371.079', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.506', 'prec': 17}, 'traces': [2, 1, -2, 1, 1, -1, -1, 2, 2, -2, 0, -1, -1, -3, -1, 0, 0, 1, 0, -2, 1, 0, 1, -2, 1, 2, -2, -3, 0, 2, 0, -2, 0, 0, 2, 1, -1, 0, 1, 1, 1, 3, -1, 0, 1, 3, 0, 0, 1, -2, 0, 2, -2, -1, 0, -1, 0, 0, 0, 2, 0, 0, -1, -1, -3, 0, 0, 0, -1, 1, 1, 2, 0, -3, -1, 0, 0, -2, 0, 0, 2, 3, 1, 3, 0, 2, 0, 0, 0, -2, -2, 3, 0, 0, 0, 2, -1, 3, 0, -2, -4, 0, 0, -1, -2, -1, 0, -1, 0, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, -1, 2, 0, -1, 0, 2, -3, 0, -1, 1, 1, 0, 0, 0, 0, -1, 0, 1, -3, 0, 1, 0, -2, 0, 0, 0, 0, -1, -3, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 2, -1, -3, 1, 4, 3, 0, -2, 1, 1, 1, 0, 0, 2, 1, 0, 2, 0, 0, 0, 1, -2, 0, -1, 0, 1, 2, 0, 0, 0, 1, 0, 1, 1, 0, 2, 3, 3, 0, 0, -1, 1, 0, -2, 0, 0, -2, 0, 1, 0, 0, -1, -1, -1, -1, 0, -3, -2, 0, 0, 0, 0, 0, 3, 4, 1, 1, 0, 0, 0, -1, -1, 0, 0, 1, 2, 0, 0, 0, 0, -4, 0, -1, 1, -2, 0, -2, -3, 0, 0, -1, 1, 1, -3, 0, 0, 0, -2, 1, -2, 3, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 2, -1, 0, 2, -2, 0, -3, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, -3, -2, 2, 0, 1, 0, 0, -3, 0, -1, 0, 0, 2, 2, -2, 0, 4, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, -4, 0, 1, -3, 2, 0, 1, 0, 0, -1, -2, -1, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, -1, 2, 3, 0, 0, 0, 1, 1, 0, -4, 0, 3, 0, 0, 3, -4, 1, 2, 0, -2, -1, 0, 0, -1, 0, 1, 1, 1, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 3, 1, 1, 0, 0, -1, 2, 1, -1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0, -1, -1, -1, 0, 0, 3, 3, 1, 0, 0, 1, -1, 0, -3, 0, -2, 0, 2, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 3, 0, 2, 0, 3, 0, -2, 0, 0, 0, 0, -1, 0, 0, -3, 0, -1, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, -2, -3, 3, 1, -3, -1, -1, 0, -4, -1, 1, -3, 0, 0, 0, 0, 2, 2, 0, 1, -1, 3, 1, -1, -2, 0, -1, 0, 1, 0, 0, 0, 0, 3, 0, -2, 0, 4, -1, -3, 0, 0, -1, 0, -2, -2, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, -1, 0, 0, 2, -1, 2, 0, 0, 0, 1, -1, -2, 0, 0, 0, -1, 0, 0, -2, 0, 1, 0, 3, 0, 0, 0, 1, 0, 0, 0, -1, 1, 1, 0, 0, 0, -1, -4, -2, -1, -1, 1, 0, 0, 2, -2, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, 0, -1, 0, 0, 1, 2, -1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 1, 2, -4, 0, 4, -4, 3, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 4, -3, 0, 1, 0, -3, 0, -2, -4, 0, 0, -1, -1, 0, -1, -2, 1, 0, -2, 0, 0, 0, 0, 0, 3, -1, 1, 0, 1, 1, 0, 3, 0, 0, 0, 0, 0, 0, -1, 1, 1, -2, 0, 0, 0, -2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 3, 4, -2, -4, 0, 0, 1, 1, 0, 0, -1, -1, -2, 2, 0, 0, 0, -1, -3, 2, -1, 0, 3, 0, 1, 0, 3, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, -1, 0, 0, 3, 4, 0, 0, 0, 1, 0, 0, 3, 0, -2, 0, 2, 0, 0, -1, 0, 1, 2, 0, -1, -3, 3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, -1, 0, -2, 0, 0, 1, 0, 0, -4, 1, -2, -1, 0, 1, 0, 2, 0, 0, -3, -2, -1, -4, 2, -1, 0, 0, 0, 1, 3, 0, -1, 0, -2, 0, 0, 3, 0, 0, -2, 0, -2, 2, 0, 0, -3, 3, 0, -1, 0, 0, 0, -3, 2, 0, 0, 0, 0, 0, 0, -1, 1, 3, 0, 0, 2, -2, -3, -2, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, -3, 0, 0, 1, 3, 0, 0, 0, -2, -4, 1, 0, 0, 0, 2, 0, 0, -2, 3, -2, 0, 0, -2, 0, 0, 2, 0, 0, 0, -1, 0, -4, 2, 0, 0, 0, 0, 0, -3, 0, 0, 0, -2, 1, 0, -3, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, -2, 0, 3, 2, -2, 2, -1, 0, -3, 0, 4, -1, 2, 0, 1, 0, -1, 0, 2, 3, 0, 1, -2, 0, -1, 0, -2, 0, -1, 0, 0, 0, 0, 2, 0, -1, 0, 1, 1, -3, 2, 4, 0, 1, 2, 0, 2, 0, 3, 0, 3, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, -2, 1, 0, 0, 0, 0, 2, -2, 0, 0, 3, 2, 0, 0, 1, 0, 0, -2, 4, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -1, -1, -2, -1, 0, 2, 0, 0, 3, 4, 2, 0, 0, 0, 0, -3, 1, 0, 0, -1, 0, 0, 0, 0, -3, -3, 0, 4, 0, -3, -1, 0, 2, -2, 2, 0, 0, 0, 0, 2, 0, -4, 1, 0, 2, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 3, 2, 0, -1, -1, 0, -2, 0, 0, -1, 0, 2, 3, 3, 0, -1, 0, 0, 0, 0, -3, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 2, -3, 0, -4, -1, -1, 0, -1, -1, -3, 0, 1, 0, 0, 0, 0, 1, 1, 1, -2, 3, 0, -1, 0, 2, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, -2, -2, 1, 0, 0, 0, 0, 0, 0, -1, -1, 2, 0, 0, 0, 0, -2, -3, 2, -1, 2, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 1, 2, 0, 1, 0, 0, 1, 3, 0, 0, 0, 2, 0, 0, 0, -3, 0, 0, -3, 0, 0, -1, 0, 0, 0, 0, -3, 0, -2, 0, -1, 0, 0, 1, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 1, -2, -1, -1, 0, -2, 0, 0, -2, 2, 0, -3, 0, -1, 0, 0, 0, 0, -1, 0, -1, 0, 1, 1, 0, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, -1, 2, 0, 3, 0, 1, -2, 0, 0, -1, 2, -1, -3, -1, 0, 0, 0, -1, 0, 0, -3, 0, 0, 0, 1, -3, -2, 0, 0, 0, 0, 0, -3, 0, 2, 0, 0, 0, 2, 0, 1, 0, -2, -3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, -1, 0, -1, -4, 3, 0, 1, 0, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 1, 0, 0, -2, 0, 6, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, -4, 2, 1, -2, -1, -2, 1, -1, 0, 0, 2, 1, 1, 3, 4, 0, -3, 0, 1, -1, 0, 2, 3, 0, 0, 1, -1, 0, 1, 0, 0, 0, 0, -3, 4, -3, 0, 1, -1, -3, -1, 0, 0, 3, 3, 0, 0, 2, 1, 0, -1, 3, 0, 0, 1, 0, 0, 0, -2, 0, 0, -2, 1, 0, 0, 0, 0, -1, 0, 2, 1, 0, -1, -3, 0, 0, -1, 0, 1, 1, 0, 2, 2, 0, -3, 0, 0, 0, 1, 3, -4, 0, 0, 0, -1, 1, 0, 0, 4, -2, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, -1, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, -4, 0, 3, 1, 0, 1, 3, -2, 0, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, -1, 0, 2, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, -2, -1, 0, 3, 0, 0, 4, 0, -2, 2, 0, 0, 3, -2, 0, 0, 0, 0, 0, 3, 1, 0, 1, 0, 0, 0, 0, 3, 0, -2, 0, -3, 1, 0, -1, -2, 4, 0, 0, -4, 2, 0, -2, 0, 0, -3, 0, -1, 0, -2, 1, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 1, 0, 0, 0, -1, 0, 0, 0, -2, 2, 0, 0, 0, 0, -1, -1, 0, 2, 0, 0, -2, -3, 0, 0, 0, 1, 1, 0, 0, 0, 0, 3, -1, -1, -1, 0, 0, 0, -3, 0, 2, 0, 0, 0, 0, 1, -4, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -3, 1, -3, 0, 4, 0, 0, 2, 0, 0, 1, 0, -1, 1, -3, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -3, 0, 0, -1, 2, 3, -3, -3, 0, 4, 0, 0, 3, 2, 3, -2, 0, 0, 0, 0, 0, 0, -2, 0, -2, 3, 0, -1, 0, 0, 0, -3, 0, 0, 4, 0, 0, 0, 0, -1, -1, -1, 1, 0, -1, -2, 0, 0, 0, -3, 1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -3, -3, -1, 0, 0, -2, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, -1, 0, 0, 2, 0, 0, 0, 0, 0, 2, -2, 0, 0, -2, 1, 1, 0, 1, 1, -1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 4, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 4, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, -1, -2, -4, -4, 0, 3, 3, -1, 1, 0, -2, 0, 1, 4, -1, 0, 0, 0, -1, -4, 0, -4, 4, -1, -3, -3, 0, 0, 0, 0, 1, 0, 0, 0, -2, -2, 0, 0, 2, 1, -1, -1, 0, 0, 3, 0, -2, 0, 0, 0, -2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 1, 1, 0, 0, 2, -4, 0, 0, 3, 0, 1, 0, 1, 0, -1, 0, 2, 0, 0, 0, 3, -1, 0], 'weight': 1, 'weight_parity': -1}
  84. label: 160.1.p.a
    {'Nk2': 160, 'analytic_conductor': 0.07985040202128038, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 32, 'artin_field': [5, 0, 0, 0, -2, 0, 0, 0, 1], 'artin_field_label': '8.0.8192000.1', 'artin_image': '32.11', 'char_conductor': 5, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 16, 'char_orbit_label': 'p', 'char_order': 4, 'char_parity': -1, 'char_values': [160, 4, [31, 101, 97], [4, 4, 3]], 'cm_discs': [-4], 'conrey_index': 33, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e5_5.8t17.2c2'], ['ArtinRepresentation/2.2e5_5.8t17.2c1']], 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 1030808928416, 'hecke_ring_generator_nbound': 5, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 5, 3, -1, 4, 0], [1, 1, 20, 5, 1, 4, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '160.1.p.a', 'level': 160, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 5], 'level_radical': 10, 'minimal_twist': '160.1.p.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 3, 'projective_field': [-5, 0, 0, 0, 1], 'projective_field_label': '4.2.2000.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q-i q^{5}+i q^{9}+(i-1)q^{13}+(-i-1)q^{17}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e5_5.8t17.2'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-4], 'self_twist_type': 1, 'space_label': '160.1.p', 'trace_display': [0, 0, 0, 0], 'trace_hash': 2033453905529301444, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.002', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.949', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.008', 'prec': 20}, {'__RealLiteral__': 0, 'data': '19.004', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-0.031', 'prec': 20}, {'__RealLiteral__': 0, 'data': '255.315', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.688', 'prec': 17}, 'traces': [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  85. label: 161.1.l.a
    {'Nk2': 161, 'analytic_conductor': 0.08034946703391338, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 161, 'char_degree': 10, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 12, 'char_orbit_label': 'l', 'char_order': 22, 'char_parity': -1, 'char_values': [161, 22, [24, 120], [11, 18]], 'cm_discs': [-7], 'conrey_index': 6, 'dim': 10, 'field_disc': -2357947691, 'field_disc_factorization': [[-1, 1], [11, 9]], 'field_poly': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 22, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 755931021473, 'hecke_ring_generator_nbound': 4, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7], [1, 1, 23, 3, 1, 11, 0], [1, 1, 161, 12, -1, 22, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '161.1.l.a', 'level': 161, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [7, 23], 'level_radical': 161, 'minimal_twist': '161.1.l.a', 'nf_label': '10.0.2357947691.1', 'prim_orbit_index': 12, 'projective_field': [-2025, 4891, 870, -2177, 181, 564, -330, 29, 21, 3, -5, 1], 'projective_image': 'D11', 'projective_image_type': 'Dn', 'qexp_display': 'q+(-\\zeta_{22}+\\zeta_{22}^{8})q^{2}+(\\zeta_{22}^{2}-\\zeta_{22}^{5}+\\cdots)q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-7], 'self_twist_type': 1, 'space_label': '161.1.l', 'trace_display': [-2, 0, 0, -1], 'trace_hash': 959068312353902186, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.007', 'prec': 17}, {'__RealLiteral__': 0, 'data': '9.176', 'prec': 17}, {'__RealLiteral__': 0, 'data': '69.083', 'prec': 20}, {'__RealLiteral__': 0, 'data': '742.892', 'prec': 24}, {'__RealLiteral__': 0, 'data': '8327.020', 'prec': 27}, {'__RealLiteral__': 0, 'data': '109326.550', 'prec': 34}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.505', 'prec': 17}, 'traces': [10, -2, 0, -3, 0, 0, -1, -4, -1, 0, -2, 0, 0, -2, 0, 6, 0, -2, 0, 0, 0, -4, -1, 0, -1, 0, 0, -3, -2, 0, 0, 5, 0, 0, 0, 8, -2, 0, 0, 0, 0, 0, -2, 5, 0, -2, 0, 0, -1, 9, 0, 0, -2, 0, 0, -4, 0, 7, 0, 0, 0, 0, -1, -7, 0, 0, -2, 0, 0, 0, -2, -4, 0, 7, 0, 0, 9, 0, -2, 0, -1, 0, 0, 0, 0, -4, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 9, -2, -3, 0, 0, 0, 0, 0, -4, -2, 0, 9, 0, 0, 6, -2, 0, 0, -6, 0, 0, 0, 0, -3, 0, 0, 0, 0, -2, -2, -8, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, -4, 0, -5, 0, 0, 0, 5, -2, 0, -2, 0, 0, -4, 0, 0, 0, 7, 0, 0, -1, -2, 9, 0, 0, 0, 0, 0, -1, 0, 0, 5, 0, 0, -1, 1, 0, 0, 9, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 9, 0, -2, 0, 0, -3, -2, 7, 0, -4, 0, 0, -2, 0, 0, 0, 10, 0, 0, 0, -2, 5, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 5, -1, -4, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, -2, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -2, -4, 0, 2, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -4, -2, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 5, -1, 0, 0, 0, 0, 0, 0, -8, 0, -4, 0, 0, -2, 7, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -6, -2, 0, -4, 0, 0, -2, 0, -3, 0, -4, 0, 0, 0, 0, 9, 0, -2, 0, 0, 0, 9, -2, 0, 0, 0, 0, -1, 14, 0, 0, -2, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 7, 9, 0, -1, 0, 0, 0, 0, 0, 0, -5, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 9, 0, 0, 7, 0, 0, 0, 7, -2, 0, -2, 0, 0, -4, 0, 7, 0, -6, 0, 0, 0, -5, 9, 0, 0, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -4, 0, 3, 0, 0, 0, -6, 0, 0, -2, 0, 0, 0, 0, -6, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 4, -2, -2, 0, -6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 1, 0, 7, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, -2, 7, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -4, 0, 7, 0, 5, 0, 0, 0, 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, -1, 0, 0, 0, 0, 0, 0, 14, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 16, 0, 7, 0, 0, -2, -4, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, -1, -8, -2, 0, -2, 0, 0, 0, -1, 4, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 5, 0, 0, -2, 0, 0, -4, -2, -6, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 9, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 3, 0, -4, 0, 0, 0, 3, -2, 0, -2, 0, 0, -3, 0, 0, 0, 7, 0, 0, 0, 5, -2, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 9, -4, 0, -3, 0, 0, 0, 0, 0, 0, 9, 0, 0, 9, 0, 1, 0, 0, 0, 0, 9, 7, 0, 0, 0, 0, 0, 8, -2, 0, 0, -3, 0, 0, 0, 0, -2, 0, 9, 0, 0, 0, 0, -6, 0, -4, 0, 0, 0, -2, 0, 0, 9, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -6, -4, 0, -2, 0, 0, -4, -2, 0, 0, -4, 0, 0, 9, 0, -2, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 9, -6, 0, 0, 0, 0, 0, 0, 0, 5, 0, 7, 0, 0, 0, -4, 0, 0, 18, 0, 0, -5, 0, 0, 0, 5, 0, 0, 9, -8, 0, 0, 0, 0, 0, 0, 0, 5, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -4, 0, 5, 0, 0, -3, 1, 0, 0, -2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, -4, 0, 0, -8, 0, 0, 0, 0, 9, 0, 0, 0, 0, -2, -2, 0, 0, 7, 0, 0, -2, 0, -2, 0, 0, 0, 0, -8, 0, -4, 0, -3, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -4, 0, -1, 0, 0, 0, -6, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -8, -2, 0, 0, 0, 0, 0, 9, 7, 0, 5, 0, 0, -2, 0, -1, 0, -2, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 7, 0, 0, -2, 0, 0, 0, -2, 7, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 7, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 5, 0, 0, 0, -8, 9, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 16, 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 0, -2, 16, 0, 0, 0, 0, -2, 9, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 7, 0, -2, 0, 0, -4, 0, 0, 0, 18, 0, 0, 0, 0, -2, 0, -3, 0, 0, 0, -2, -4, 0, 3, 0, 0, 0, -6, 0, 0, -2, 0, 0, 7, 0, -6, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 5, 0, 0, -1, 0, -2, 0, 0, 0, 0, -2, 0, 1, 0, -4, 0, 0, -2, -4, -2, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -1, -1, 0, 0, -2, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -4, -4, 0, -2, 0, 0, -6, 0, 7, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, -1, 7, 0, 0, -2, 0, 0, 1, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 7, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, -10, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, -12, 0, -4, 0, 0, 0, 18, -2, 0, 0, 0, 0, 7, -2, 0, 0, 0, 0, 0, 0, 6, -2, 0, 0, 0, 0, 0, -2, 3, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -6, -2, 0, -2, 0, 0, 0, 7, -6, 0, -4, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, -6, 0, 0, -2, 7, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 7, -2, 0, -3, 0, 0, -3, -2, 0, 0, -12, 0, 0, -2, 0, -2, 0, 0, 0, 0, -4, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, -4, 0, 18, 0, 0, 0, 0, 0, 6, 9, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, -4, 9, 0, 0, 0, 0, 0, -2, 0, 0, -8, 0, 0, 0, -6, 0, 0, 9, 0, 0, 0, 0, -3, 0, 0, 0, 0, -1, -4, -2, 0, 9, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 4, 0, 3, 0, 0, -2, -4, 0, 0, -2, 0, 0, 5, 0, -4, 0, 0, 0, 0, 0, 5, 9, 0, 0, 0, 0, -4, -2, 0, 0, -4, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, -4, 0, 5, 0, 0, 0, 0, -1, 0, 9, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, -2, 0, 0, -4, -2, 1, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, -6, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 7, -2, 0, -2, 0, 0, 3, 0, 0, 0, -1, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 9, 0, 0, 0, 0, 0, -1, -6, 0, 5, 0, 0, 0, 3, 0, 0, 0, 0, 0, 5, 0, -1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 12, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 9, -6, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 12, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 8, 0, -4, 0, 0, 0, 0, -2, -6, -2, 0, -2, 0, 0, 7, 0, 0, 0, 7, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, -4, 0, 0, -6, 0, 0, 0, 7, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, -4, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, -4, 0, -6, 0, 0, 0, -3, 0, 0, -2, 0, 0, 0, -1, -8, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -6, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, -4, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -4, 0, -6, 0, 0, 0, -8, -2, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, -2, 7, 0, 0, 0, 0, 0, 0, -2, 7, 0, 7, 0, 0, 9, 0, 0, 0, 7, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -4, 7, 0, 5, 0, 0, 9, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 7, 0, 0, 0, -4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, -2, 0], 'weight': 1, 'weight_parity': -1}
  86. label: 164.1.d.a
    {'Nk2': 164, 'analytic_conductor': 0.08184666207181239, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [2, 2, -1, -2, 1], 'artin_field_label': '4.0.656.1', 'artin_image': '8.3', 'char_conductor': 164, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [164, 2, [83, 129], [1, 1]], 'cm_discs': [-4, -164], 'conrey_index': 163, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_41.4t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [0, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207588, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 164, 4, -1, 2, -164], [1, 1, 41, 2, 1, 2, 41]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '164.1.d.a', 'level': 164, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 41], 'level_radical': 82, 'minimal_twist': '164.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 4, 'projective_field': [100, 0, 21, 0, 1], 'projective_field_label': '4.0.26896.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_41.4t3.2'], 'relative_dim': 1, 'rm_discs': [41], 'self_twist_discs': [-4, -164, 41], 'self_twist_type': 3, 'space_label': '164.1.d', 'trace_display': [1, 0, -2, 0], 'trace_hash': 340350220661267146, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.008', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.971', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.037', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.877', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.154', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.504', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.756', 'prec': 17}, 'traces': [1, 1, 0, 1, -2, 0, 0, 1, -1, -2, 0, 0, 0, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -2, 0, 0, -2, 1, 0, 0, 0, 2, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -2, -2, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, -4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 2, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 4, 0, 0, 0, -1, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, -2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, -3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 2, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -3, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, -2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 3, 2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 1, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4], 'weight': 1, 'weight_parity': -1}
  87. label: 164.1.d.b
    {'Nk2': 164, 'analytic_conductor': 0.08184666207181239, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 16, 'artin_field': [1, 2, -1, -2, 0, 0, 3, 0, 1], 'artin_field_label': '8.0.17643776.1', 'artin_image': '16.7', 'char_conductor': 164, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [164, 2, [83, 129], [1, 1]], 'cm_discs': [-164], 'conrey_index': 163, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_41.8t6.2c1'], ['ArtinRepresentation/2.2e2_41.8t6.2c2']], 'field_disc': 8, 'field_disc_factorization': [[2, 3]], 'field_poly': [-2, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 8, 'has_non_self_twist': 1, 'hecke_cutters': [[3, [-2, 0, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503805802578084, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 164, 4, -1, 2, -164], [1, 1, 4, 2, -1, 2, 0], [1, 1, 41, 2, 1, 2, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '164.1.d.b', 'level': 164, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 41], 'level_radical': 82, 'minimal_twist': '164.1.d.b', 'nf_label': '2.2.8.1', 'prim_orbit_index': 4, 'projective_field': [-4, 0, -5, 0, 1], 'projective_field_label': '4.2.6724.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}-\\beta q^{3}+q^{4}+\\beta q^{6}+\\beta q^{7}-q^{8}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_41.8t6.2'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-164], 'self_twist_type': 1, 'space_label': '164.1.d', 'trace_display': [-2, 0, 0, 0], 'trace_hash': 320379962415646211, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.016', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.907', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.249', 'prec': 20}, {'__RealLiteral__': 0, 'data': '30.412', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-3.984', 'prec': 20}, {'__RealLiteral__': 0, 'data': '486.226', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.879', 'prec': 17}, 'traces': [2, -2, 0, 2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, -2, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 2, 0, 0, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 2, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, -4, -2, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, -2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  88. label: 164.1.j.a
    {'Nk2': 164, 'analytic_conductor': 0.08184666207181239, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 164, 'char_degree': 4, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 10, 'char_orbit_label': 'j', 'char_order': 10, 'char_parity': -1, 'char_values': [164, 10, [83, 129], [5, 2]], 'cm_discs': [-4], 'conrey_index': 51, 'dim': 4, 'field_disc': 125, 'field_disc_factorization': [[5, 3]], 'field_poly': [1, -1, 1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 618492068004, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 41, 4, 1, 5, 0], [1, 1, 164, 10, -1, 10, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '164.1.j.a', 'level': 164, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 41], 'level_radical': 82, 'minimal_twist': '164.1.j.a', 'nf_label': '4.0.125.1', 'prim_orbit_index': 10, 'projective_field': [-32, 144, 36, -16, -1, 1], 'projective_field_label': '5.1.45212176.1', 'projective_image': 'D5', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{10}q^{2}+\\zeta_{10}^{2}q^{4}+(-\\zeta_{10}-\\zeta_{10}^{3}+\\cdots)q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-4], 'self_twist_type': 1, 'space_label': '164.1.j', 'trace_display': [-1, 0, -2, 0], 'trace_hash': 1030051467981990820, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.013', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.978', 'prec': 17}, {'__RealLiteral__': 0, 'data': '12.081', 'prec': 20}, {'__RealLiteral__': 0, 'data': '101.308', 'prec': 24}, {'__RealLiteral__': 0, 'data': '696.758', 'prec': 24}, {'__RealLiteral__': 0, 'data': '5488.258', 'prec': 27}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.504', 'prec': 17}, 'traces': [4, -1, 0, -1, -2, 0, 0, -1, 4, -2, 0, 0, -2, 0, 0, -1, -2, -1, 0, 3, 0, 0, 0, 0, -3, 3, 0, 0, -2, 0, 0, 4, 0, 3, 0, -1, 3, 0, 0, -2, -1, 0, 0, 0, -2, 0, 0, 0, -1, 2, 0, 3, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, -1, -2, 3, 0, 0, 0, 0, 0, 3, 4, -1, 0, 0, 6, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 3, -1, 0, -3, 3, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, 3, 0, 0, -2, -2, 0, 0, 0, -1, -2, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, -1, 6, -2, 0, -2, 3, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, -1, 0, -1, 0, 0, 0, 0, -3, -4, 0, 0, -2, 0, 0, 0, 0, 8, 0, 3, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 3, 0, 4, -2, 0, 0, 2, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, -3, -2, 0, 0, 3, 0, 0, 8, 3, 3, 0, 0, 0, 0, 0, 0, -2, -1, 0, -2, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, -2, 0, 0, -4, -2, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, -3, -4, 0, 3, 3, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 3, 0, 0, -2, 0, 0, 0, -1, 4, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, -2, -3, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, -2, -1, -2, 0, 0, 1, 0, 0, 0, -1, -4, 0, 0, 3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 3, 0, 0, -1, 0, 3, 0, 0, 3, 0, 0, 2, -2, 0, 0, 3, -2, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, -1, -4, 0, 0, 6, 0, 0, 0, 3, 2, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 3, 0, 0, -2, 0, -2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, -2, 0, -1, 1, 0, 0, 3, 0, 3, 0, 0, -4, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 1, 3, -2, 0, 0, 0, 0, 0, 0, -1, 6, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, -2, 1, 0, 0, 3, -2, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 3, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -1, -2, 2, 0, 6, 0, 0, 0, 3, 1, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, -2, -2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -4, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, -2, 0, 0, 4, -2, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 3, 0, 2, -2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 3, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, -2, -6, 0, 0, 0, 4, 1, 0, 0, 3, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 6, 0, 0, 0, 3, 0, 0, 3, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, 0, 6, -2, 0, 0, 3, 0, 0, -3, -2, 3, 0, 0, 0, 0, 0, -2, 3, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, -1, 0, 0, 3, 0, -1, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 3, 0, 0, 0, -2, -1, 0, 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, -3, 6, 0, 0, -2, -4, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -1, 1, 0, 3, -4, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, 3, -2, 0, 0, -2, -2, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 0, -2, 0, 0, 0, 3, 3, 0, 0, -2, 0, 0, 4, 2, 0, 0, 8, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 1, 0, 3, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, -4, -2, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, -4, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, -1, 1, 0, 0, -2, 0, 0, 3, 3, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, -2, 3, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -1, -2, 3, 0, 2, -4, 0, 0, -4, 0, 0, 0, 0, 1, 0, 0, -2, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, -2, 0, 0, -2, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, -4, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 3, 2, 3, 0, 0, -2, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 3, 0, 1, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, -1, -2, 0, 0, 0, 6, -2, 0, 0, 0, 0, 0, -1, -4, -2, 0, 0, 0, 0, 0, 0, 8, 3, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, -2, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 3, 0, 0, 0, -2, 1, 0, 0, -2, 0, 0, -2, 6, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, -2, 0, 0, 3, -2, 0, 0, 0, 1, -2, 0, 0, 8, 0, 0, -2, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, -1, 0, 0, -2, 0, 4, 0, 0, -2, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 1, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, -2, 0, 0, 3, 0, 0, 0, -3, -2, 0, 0, -1, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 6, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, -2, -2, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -1, 0, 1, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -4, 1, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 2, -2, 8, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 8, 0, 0, -2, 0, -2, 0, 3, -2, 0, 0, 0, -3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 3, 1, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 12, 0, -2, 1, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, -2, -2, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 3, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 3, -4, 3, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 4, -4, 0, 0, 1, -4, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -4, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, -2, -4, 0, 0, -2, 0, 0, 3, 0, 1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -1, -1, 0, 0, 1, 0, 0, -2, 0, -2, 0, 0, 3, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, -2, 3, -2, 0, 0, 8, 0, 0, 0, 0, 3, 0, 0, -8, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 6, 0, 0, 0, -2, 0, 6, 0, 0, -2, 0, 0, 4, -4, 0, 0, 1, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, -2, 0, 8, 0, 0, 0, 0, 0, -2, 1, 3, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, -4], 'weight': 1, 'weight_parity': -1}
  89. label: 164.1.l.a
    {'Nk2': 164, 'analytic_conductor': 0.08184666207181239, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 164, 'char_degree': 4, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 12, 'char_orbit_label': 'l', 'char_order': 10, 'char_parity': -1, 'char_values': [164, 10, [83, 129], [5, 9]], 'cm_discs': [-4], 'conrey_index': 23, 'dim': 4, 'field_disc': 125, 'field_disc_factorization': [[5, 3]], 'field_poly': [1, -1, 1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 10, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 755931021476, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 41, 6, 1, 10, 0], [1, 1, 164, 12, -1, 10, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '164.1.l.a', 'level': 164, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 41], 'level_radical': 82, 'minimal_twist': '164.1.l.a', 'nf_label': '4.0.125.1', 'prim_orbit_index': 12, 'projective_field': [1024, 6528, 1376, -416, 524, 136, 21, 22, 10, -2, 1], 'projective_field_label': '10.2.83809775204854016.1', 'projective_image': 'D10', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{10}^{2}q^{2}+\\zeta_{10}^{4}q^{4}+(\\zeta_{10}-\\zeta_{10}^{2}+\\cdots)q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-4], 'self_twist_type': 1, 'space_label': '164.1.l', 'trace_display': [-1, 0, 2, 0], 'trace_hash': 2034575049155665319, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.007', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.729', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-2.517', 'prec': 20}, {'__RealLiteral__': 0, 'data': '88.172', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-148.314', 'prec': 27}, {'__RealLiteral__': 0, 'data': '3292.989', 'prec': 27}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.680', 'prec': 17}, 'traces': [4, -1, 0, -1, 2, 0, 0, -1, -4, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, -3, 0, 0, 0, 0, -3, -5, 0, 0, 0, 0, 0, 4, 0, 5, 0, 1, -3, 0, 0, 2, -1, 0, 0, 0, -2, 0, 0, 0, 1, 2, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 5, 0, 0, 0, 0, 0, 0, 1, 2, -3, 0, 0, 0, 0, 0, -3, 4, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -5, 1, 0, -3, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, -1, 0, 0, -1, 0, -5, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 3, 5, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, -4, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, -5, 0, 0, 0, 3, 2, 0, 0, -5, 0, 0, 0, -5, 5, 0, 0, 0, 0, 0, 0, -2, 1, 0, -2, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, 0, 0, -3, 5, 0, 0, 2, 0, -5, 0, 0, 0, 0, 0, 0, -1, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 2, -1, 0, 5, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 1, 0, 0, 0, 1, -4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 3, 0, 0, 5, 0, 0, 2, 2, 0, 0, -5, 2, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, -5, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -5, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, -5, 0, 0, 5, 2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, -4, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, -3, -5, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 5, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, -3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -5, -3, 0, 4, 2, 0, 0, -5, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, 5, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, -4, 1, 0, 0, 3, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 5, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -5, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, -5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, -3, 0, 0, 0, 0, 0, 0, 5, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -5, 5, 0, 0, 0, 0, 0, 0, 0, -1, -5, 0, 0, 7, 0, 0, -5, 0, -5, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, -2, -1, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 3, -10, 0, 0, 2, 0, 0, 0, 0, -5, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 5, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 5, 0, 0, -5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 5, -1, 5, 0, 0, 0, 0, 0, -5, 3, 2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 5, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -5, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 2, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 4, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 5, -2, -3, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 5, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, -5, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 8, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, -3, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 5, 3, 0, 0, 5, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 1, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 0, 5, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -5, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 5, -1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 1, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0, 0, 2, 0, 0, 5, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -4, -5, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 4, -4, 0, 0, 5, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -3, 0, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -1, 1, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 5, -1, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -8, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 5, -5, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4], 'weight': 1, 'weight_parity': -1}
  90. label: 165.1.l.a
    {'Nk2': 165, 'analytic_conductor': 0.0823457270844454, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 32, 'artin_field': [1, 1, 1, -2, -3, 2, 1, -1, 1], 'artin_field_label': '8.0.16471125.2', 'artin_image': '32.11', 'char_conductor': 165, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 12, 'char_orbit_label': 'l', 'char_order': 4, 'char_parity': -1, 'char_values': [165, 4, [56, 67, 46], [2, 1, 2]], 'cm_discs': [-11], 'conrey_index': 32, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.3_5_11.8t17.3c2'], ['ArtinRepresentation/2.3_5_11.8t17.3c1']], 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [[23, [2, -2, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 755931021477, 'hecke_ring_generator_nbound': 4, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 2, -1, 2, -11], [1, 1, 15, 5, 1, 4, 0], [1, 1, 165, 12, -1, 4, 0]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '165.1.l.a', 'level': 165, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 5, 11], 'level_radical': 165, 'minimal_twist': '165.1.l.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 12, 'projective_field': [-29, -11, -4, -1, 1], 'projective_field_label': '4.2.12375.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{3}+i q^{4}+i q^{5}+q^{9}-i q^{11}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3_5_11.8t17.3'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-11], 'self_twist_type': 1, 'space_label': '165.1.l', 'trace_display': [0, -2, 0, 0], 'trace_hash': 158014309708095222, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.027', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.953', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.202', 'prec': 20}, {'__RealLiteral__': 0, 'data': '19.019', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-2.304', 'prec': 20}, {'__RealLiteral__': 0, 'data': '255.377', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.687', 'prec': 17}, 'traces': [2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  91. label: 165.1.l.b
    {'Nk2': 165, 'analytic_conductor': 0.0823457270844454, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 32, 'artin_field': [1, -1, 5, -2, 9, -2, 5, -1, 1], 'artin_field_label': '8.0.16471125.1', 'artin_image': '32.11', 'char_conductor': 165, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 12, 'char_orbit_label': 'l', 'char_order': 4, 'char_parity': -1, 'char_values': [165, 4, [56, 67, 46], [2, 1, 2]], 'cm_discs': [-11], 'conrey_index': 32, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.3_5_11.8t17.2c1'], ['ArtinRepresentation/2.3_5_11.8t17.2c2']], 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [[23, [2, 2, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4504355558391973, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 2, -1, 2, -11], [1, 1, 15, 5, 1, 4, 0], [1, 1, 165, 12, -1, 4, 0]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '165.1.l.b', 'level': 165, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [3, 5, 11], 'level_radical': 165, 'minimal_twist': '165.1.l.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 12, 'projective_field': [-29, -11, -4, -1, 1], 'projective_field_label': '4.2.12375.1', 'projective_image': 'D4', 'projective_image_type': 'Dn', 'qexp_display': 'q-i q^{3}+i q^{4}-i q^{5}-q^{9}+i q^{11}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3_5_11.8t17.2'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-11], 'self_twist_type': 1, 'space_label': '165.1.l', 'trace_display': [0, 0, 0, 0], 'trace_hash': 130510116874894442, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.006', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.949', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.163', 'prec': 20}, {'__RealLiteral__': 0, 'data': '19.004', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-3.642', 'prec': 20}, {'__RealLiteral__': 0, 'data': '255.315', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.688', 'prec': 17}, 'traces': [2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -2, -2, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 4, -2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'weight': 1, 'weight_parity': -1}
  92. label: 167.1.b.a
    {'Nk2': 167, 'analytic_conductor': 0.0833438571097114, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 167, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [167, 2, [5], [1]], 'cm_discs': [-167], 'conrey_index': 166, 'dim': 5, 'field_disc': 14641, 'field_disc_factorization': [[11, 4]], 'field_poly': [-1, 3, 3, -4, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 22, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254119, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 167, 2, -1, 2, -167]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '167.1.b.a', 'level': 167, 'level_is_powerful': False, 'level_is_prime': True, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': True, 'level_primes': [167], 'level_radical': 167, 'minimal_twist': '167.1.b.a', 'nf_label': '5.5.14641.1', 'prim_orbit_index': 2, 'projective_field': [1, 2, -4, 9, -7, 11, -6, 10, -4, 5, -1, 1], 'projective_field_label': '11.1.129891985607.1', 'projective_image': 'D11', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\beta _{4}q^{2}+(-1+\\beta _{1}-\\beta _{2}+\\beta _{3}-\\beta _{4})q^{3}+\\cdots', 'related_objects': [], 'relative_dim': 5, 'rm_discs': [], 'self_twist_discs': [-167], 'self_twist_type': 1, 'space_label': '167.1.b', 'trace_display': [-1, -1, 0, -1], 'trace_hash': 1545373863487011043, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.067', 'prec': 20}, {'__RealLiteral__': 0, 'data': '4.269', 'prec': 17}, {'__RealLiteral__': 0, 'data': '37.608', 'prec': 20}, {'__RealLiteral__': 0, 'data': '380.437', 'prec': 24}, {'__RealLiteral__': 0, 'data': '3796.363', 'prec': 27}, {'__RealLiteral__': 0, 'data': '37953.394', 'prec': 30}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.510', 'prec': 17}, 'traces': [5, -1, -1, 4, 0, -2, -1, -2, 4, 0, -1, -3, 0, -2, 0, 3, 0, -3, -1, 0, -2, -2, 0, -4, 5, 0, -2, -3, -1, 0, -1, -3, -2, 0, 0, 1, 0, -2, 0, 0, 0, 7, 0, 8, 0, 0, -1, 6, 4, -1, 0, 0, 0, 7, 0, -4, -2, -2, 0, 0, -1, 9, -3, 2, 0, -4, 0, 0, 0, 0, 0, 5, 0, 0, -1, -3, -2, 0, 0, 0, 3, 0, 0, 5, 0, 0, -2, -4, -1, 0, 0, 0, -2, -2, 0, -6, -1, 8, -3, 4, 0, 0, 0, 0, 0, 0, -1, -6, 0, 0, 0, -5, 0, 7, 0, -3, 0, 0, 0, 0, 4, -2, 0, -3, 0, -6, -1, -4, 0, 0, 0, 5, -2, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, -2, 0, 0, -3, 0, 0, -2, 0, 7, 0, -4, 0, 0, -1, 0, 0, 0, 0, -5, 0, 0, 0, 0, 5, 3, 5, 0, 8, 0, -1, 7, -1, 6, 0, -2, -1, 0, -1, 0, 9, 0, 0, -4, 0, -3, -4, 0, -1, 4, 0, -2, 0, 1, 0, 5, -1, -2, 0, 0, 9, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, -2, 0, 3, -2, 0, 0, 0, 0, 0, -1, 5, 4, 0, 0, -6, -1, 0, 7, -4, -1, 0, 0, 0, 0, 0, -1, 0, 0, -3, -3, -3, 0, 0, 0, 7, 0, 0, -1, 2, 0, -2, 0, 1, 0, 0, 0, 0, -3, 0, -1, -8, 0, -4, 9, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, -3, 0, -1, 7, -1, 0, 0, 0, 0, 2, 5, 0, -2, 0, -1, -6, 0, 0, -4, 0, 0, -3, 0, 0, 0, -5, 0, 0, 0, -6, 0, 0, 10, 0, 0, 9, 0, 0, -1, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 1, -1, -1, 0, 0, -2, -6, -2, 0, 0, -2, 0, 5, 0, -2, 0, -6, -1, 0, 0, -3, 0, -2, -1, 0, 4, -2, 8, 0, 0, -4, -1, 0, 0, 0, 0, -6, 0, 0, 0, 7, 0, 3, 0, 0, -2, 9, -1, 3, 0, 0, 0, 8, 0, 0, 0, 5, 0, 0, 0, 2, -1, -2, -4, 3, 0, 0, 0, 0, 0, 7, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 7, -1, 0, -1, 9, 8, 0, 0, 0, -2, -3, 0, 0, -1, 1, -1, -4, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 4, -1, -3, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, -1, 3, 0, -5, 0, 9, -1, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 5, 0, -4, 0, 0, 10, 0, 0, 0, 0, -5, 0, 0, 0, 0, -1, -2, -1, -1, 0, 0, -1, 8, -1, 0, 0, -5, -4, 0, 0, 0, -2, 0, -2, 0, 0, -6, -1, 0, -2, -2, 0, 1, 5, 0, 0, 5, 0, -4, 0, 0, -2, 0, -3, 0, 0, 0, -2, 0, 0, 0, 0, 8, -3, -2, -2, 0, 0, 0, 0, 0, -1, 5, 0, 0, 0, -2, -1, -6, 0, -2, 6, 0, 0, 0, 0, 0, -2, 0, 0, -5, -1, -1, 0, 0, 0, -4, 0, 0, 0, 9, 0, -9, -2, 0, 0, 0, 0, 3, 0, 0, -2, 0, -1, -4, -1, 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, -1, 0, 0, 3, -1, 0, 0, 0, 0, -2, -2, 0, 5, 0, -4, -3, 0, 0, -1, 0, -2, -2, 0, 0, 0, -4, 0, 0, 0, 7, 0, 0, 0, 0, 0, 1, 0, 0, 7, 0, -1, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 9, 0, -2, -1, 0, -2, -2, 4, 10, 0, -2, 0, 0, 7, 0, 2, 0, -4, -2, 0, 0, 0, 0, 8, 5, 0, 0, 3, 0, 0, -2, -3, -1, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -3, 9, 9, 0, 0, 0, -3, 0, -3, -1, -6, 0, 0, 2, 0, 0, 5, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 10, 3, 0, 0, 0, 0, 9, 0, 0, -5, -2, 0, 0, -1, -1, 0, 0, 0, -1, -4, 0, -3, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -1, -4, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 9, 0, 0, -1, 0, -2, 0, 8, 0, 3, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 5, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 7, 9, -1, 0, 4, -2, 9, -3, 0, -6, -3, 0, -2, 0, 0, 0, -1, 7, 0, -4, -1, 0, -1, 0, 0, -2, -1, -1, 0, -2, -1, -6, 0, 0, 0, 0, -3, 0, 0, 0, -1, 0, -2, 0, 0, 2, -1, 0, 0, 0, 0, 0, -2, 0, -5, -3, 9, 0, 0, 3, 0, -2, -2, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, -3, 0, 0, -1, 0, 0, -2, 0, -1, 0, 0, 0, 5, -1, 0, -3, -3, -2, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -1, 0, 0, -2, 9, 0, 0, 0, 0, -3, 7, 0, -2, 0, 4, 0, -3, 0, 0, 0, -1, -6, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 5, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, -3, 0, -2, 0, -4, -1, 0, -2, 0, -1, -2, 0, -4, 0, -2, 0, 0, -1, 0, -4, 0, 0, 3, 0, 0, 7, 0, -1, 0, -1, 7, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 9, 0, 0, -1, 7, -1, -3, 0, 0, 0, -1, 0, -1, -2, 0, 0, 0, -1, 3, 0, 0, 9, 5, 0, 0, 0, 0, 0, 7, 0, 0, -2, 5, 0, 0, 0, 0, -3, 0, 0, 7, -1, 0, 1, 0, -1, 0, 0, 0, 0, -4, 0, 5, -2, 8, -2, -4, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, -2, 0, 2, -1, 0, 0, 0, 0, 0, -1, -3, 0, -2, 0, 3, -1, 0, 0, 8, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -4, 0, 0, -2, 0, 0, -1, 0, 9, 0, 4, 0, 0, -2, 0, 0, 0, 0, 5, 0, 0, 0, 0, -1, 0, -1, -3, 0, 0, -1, -1, -2, -4, 0, 0, -1, 0, -1, 0, 0, 0, -1, -1, 0, 0, 9, 0, -1, -4, 0, 0, 5, -2, 0, 6, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, -7, -1, -8, 0, 0, 0, 0, -1, 0, 4, 9, -2, 0, 0, 0, -1, 1, -3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 7, 0, 0, 0, -1, 0, 0, -2, 3, 0, 7, -2, 0, 0, 0, 0, -2, -2, 0, 0, -4, -2, -3, -4, 0, 0, 0, 0, 0, 0, -6, -1, 0, 0, 0, -4, 0, -1, 5, 0, 0, 0, 0, 0, 0, -1, 0, 9, 0, 0, -7, -1, 0, -2, 0, -1, 3, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -1, 0, -1, 0, 5, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, -4, 0, 0, 0, -4, 0, -3, 0, 0, -2, -3, 0, 7, 0, -2, 0, -2, 0, 0, 0, -4, 0, 0, -1, 0, -2, -6, 0, 0, -1, -1, 5, 0, 0, -6, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, -1, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 9, -4, -1, -4, -2, -2, 0, 0, 0, 0, 0, -8, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, -1, 6, -2, 0, 0, 0, -1, 0, 0, 7, -1, -4, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 7, 0, -2, -1, 2, 0, 0, 0, 0, -2, -7, 0, 0, 0, 0, 7, 3, 0, -2, 0, -3, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, -10, 0, 0, 0, 0, -1, 0, 0, 0, 0, 7, 0, 0, 0, 0, 4, 5, 0, 7, 9, 0, 9, 0, -1, -5, 0, -2, 0, 0, 0, 0, 8, 0, 4, -2, 0, 5, -1, 0, -2, 7, 0, 0, -1, -3, 0, 0, 0, 1, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, -4, 6, -1, 0, 0, 0, -3, 0, -1, 0, -2, 0, 0, 0, 0, 3, 10, 2, -2, 0, 0, 0, 0, 0, -3, 0, 0, -4, -1, 0, 0, 0, 0, -4, 0, 0, -1, -3, 0, 0, 0, -4, 0, 0, 0, -1, -1, 0, 0, 2, -1, 5, 9, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -6, -2, -1, 0, 0, 0, 0, 3, 0, 0, -1, 0, 8, 0, -2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 7, 0, 0, -4, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, -2, -8, 0, -3, 0, -2, 0, 0, 5, 8, 0, -3, 0, -4, 0, 7, -2, 0, -2, 2, 0, 5, 0, 0, -1, -4, 10, 0, -6, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, -5, 0, -2, 0, 0, 0, -2, -3, 0, 0, 0, 0, -3, 0, -2, -2, -3, 0, 0, -2, -3, -1, -2, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 9, -4, 10, 0, 0, 0, 0, 3, 0, -2, 7, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, -4, 0, 0, 0, 1, 0, -4, 0, -4, 0, 0, 0, 0, -3, 2, 0, 0, 0, -3, -2, -4, 0, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 5, 0, 0, 0, 0, -4, 0, 0, 0, 0, -1, -2, -2, 0, -2, 0, -2, -3, 0, 0, 0, 6, 5, 0, -2, 0, 0, 0, 0, 4, 0, 9, -1, 0, -1, -6, 0, 7, 0, -4, 0, -3, -4, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -6, 0, 0, -6, 0, 0, 0, 0, 0, 0, -2, 0, 9, -2, 0, 0, 0, 0, -3, -3, -1, -4, 9, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, 3, 0, 0, 0, -4, 0, 0, 0, -3, 0, 0, -2, -6, 0, 0, 0, 0, 10, 0, -1, 9, 0, 9, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, -6, -6, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 8, 0, 0, -2, 0, -2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, -2, 0, 0, -7, 0, 0, 10, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, -1, 0], 'weight': 1, 'weight_parity': -1}
  93. label: 168.1.s.a
    {'Nk2': 168, 'analytic_conductor': 0.0838429221223444, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 18, 'artin_field': [1, -4, 8, -6, 3, -2, 1], 'artin_field_label': '6.0.677376.1', 'artin_image': '18.3', 'char_conductor': 168, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 19, 'char_orbit_label': 's', 'char_order': 6, 'char_parity': -1, 'char_values': [168, 6, [127, 85, 113, 73], [6, 3, 3, 4]], 'cm_discs': [-24], 'conrey_index': 53, 'dim': 2, 'embedded_related_objects': [['ArtinRepresentation/2.2e3_3_7.6t5.1c1'], ['ArtinRepresentation/2.2e3_3_7.6t5.1c2']], 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [[5, [1, -1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 1236967358632, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 24, 8, -1, 2, -24], [1, 1, 7, 3, 1, 3, 0], [1, 1, 168, 19, -1, 6, 0]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '168.1.s.a', 'level': 168, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 3, 7], 'level_radical': 42, 'minimal_twist': '168.1.s.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 19, 'projective_field': [-6, -2, -1, 1], 'projective_field_label': '3.1.1176.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+\\zeta_{6}^{2}q^{2}-\\zeta_{6}q^{3}-\\zeta_{6}q^{4}-\\zeta_{6}^{2}q^{5}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e3_3_7.6t5.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-24], 'self_twist_type': 1, 'space_label': '168.1.s', 'trace_display': [-1, -1, 1, -1], 'trace_hash': 161535324546610178, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.002', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.012', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.053', 'prec': 17}, {'__RealLiteral__': 0, 'data': '18.214', 'prec': 20}, {'__RealLiteral__': 0, 'data': '50.893', 'prec': 20}, {'__RealLiteral__': 0, 'data': '245.514', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.500', 'prec': 17}, 'traces': [2, -1, -1, -1, 1, 2, -1, 2, -1, 1, 1, -1, 0, 2, -2, -1, 0, -1, 0, -2, -1, -2, 0, -1, 0, 0, 2, -1, -2, 1, 1, -1, 1, 0, -2, 2, 0, 0, 0, 1, 0, -1, 0, 1, 1, 0, 0, 2, -1, 0, 0, 0, 1, -1, 2, -1, 0, 1, 1, 1, 0, -2, 2, 2, 0, 1, 0, 0, 0, 1, 0, -1, -2, 0, 0, 0, 1, 0, 1, 1, -1, 0, -2, 2, 0, 0, 1, 1, 0, -2, 0, 0, 1, 0, 0, -1, -2, -1, -2, 0, -2, 0, -2, 0, 1, -2, 1, -1, 0, -1, 0, 2, 0, 0, 0, 1, 0, -2, 0, -2, 0, 0, 0, 1, 2, -1, -2, -1, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, -1, 4, 2, 0, -2, 0, 1, 0, 0, 1, 2, 0, 0, 1, 1, -2, 0, 2, 0, 0, -1, 1, 0, -1, 2, 0, 0, 0, -2, -2, 0, -2, 1, 0, -2, 1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 1, 1, 0, 2, 4, 1, -2, 0, 0, 4, 1, 0, 0, -2, 0, 0, 0, -2, 0, 1, 0, 1, 0, 2, 1, 0, -2, -1, 0, 0, -2, -1, 0, 0, 1, 0, 0, 0, -2, -2, 0, 0, 0, 1, -2, 0, 0, 1, 1, 0, -1, 0, 1, 0, 0, 1, 1, -1, -2, -1, 0, 1, 0, -1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 1, -2, -2, -1, 2, 0, 1, -2, 0, 0, 0, -2, -2, 0, 0, 0, 0, -2, 4, -1, 0, 0, 1, 0, 1, -2, 1, 1, -1, 1, -2, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -1, -2, -1, 0, 0, -1, 0, 2, 0, 0, -2, -2, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 1, -1, 0, 0, 0, -4, 0, 1, 0, 0, 0, 1, -2, 0, 0, -1, 0, 0, 2, 0, 0, 1, 0, 0, 2, -1, -2, 0, 1, -2, 0, 0, -1, -2, -2, -1, 1, 0, 4, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 1, 0, 0, 4, 1, 0, -1, 0, 0, 0, 4, 1, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, -1, 4, 1, 2, 0, 0, -2, 1, 2, -1, 0, 1, 0, 0, 1, 4, -1, 0, 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 4, 1, 4, 1, -1, 0, -2, 0, 0, 0, 0, 1, 0, 1, 0, 0, -2, 0, 0, 1, 0, -2, 0, 0, -1, -1, 1, 0, 0, -2, -2, 0, 0, 0, -1, -2, 0, -2, 0, -1, 0, 1, 0, 2, -4, 0, -1, 1, 1, 0, -2, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 1, 0, -2, 0, 0, 0, 1, -1, -1, -2, 0, 0, 0, -1, 0, -2, -2, -2, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, 2, 1, -2, -1, -2, 0, 1, -2, -1, 0, -1, -2, 0, 0, -2, 0, 4, -2, 0, 0, 0, -2, 0, 0, 1, 0, -2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, -2, 1, 0, 1, -1, -2, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0, -2, 0, 1, 0, -1, 0, 4, 0, 4, -1, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 2, -2, 1, 0, -1, 1, 0, 1, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 4, 1, 4, 0, 1, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, -2, -2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, -2, 4, 2, 1, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 0, -2, 2, 1, 0, 1, 0, 2, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, -2, 2, 0, 1, -2, 0, 0, -2, 0, 4, 0, 0, 0, 0, -2, -1, 0, 1, 0, -2, 0, 2, 0, -2, 0, 0, -1, -2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, -2, 0, 1, 0, 1, -2, 0, 0, 0, 0, -2, 0, 0, 1, 0, -2, -2, 0, 1, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, -2, 0, 1, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 2, -2, 2, -2, 2, -1, 0, 0, 1, 0, -1, 4, 0, 1, 1, -1, 0, 2, 0, 0, -1, 1, 0, 0, 1, 0, 1, 1, 0, -2, -4, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 4, 0, 0, 0, -1, 1, 0, 0, -2, 0, -2, 0, 0, -2, 0, 1, 0, -2, -2, 1, 0, 2, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 1, 0, 0, -2, -2, 0, -2, 1, 0, 0, -2, 0, 0, 1, 0, 0, -1, 0, 0, -2, 0, 0, 1, 1, 2, 0, -2, 0, 0, -1, 1, 2, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, -1, 1, 1, 0, 0, -4, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, -1, -2, 2, 1, 0, 1, 2, 2, -2, 0, 1, 1, 0, 0, -2, 2, -1, 0, 0, 0, 0, -1, -4, 0, 0, 1, 0, 0, 0, 0, -2, 1, 0, -2, 0, 4, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 1, 2, 0, -1, 1, 1, 4, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, -2, 0, 1, 0, 1, 0, 1, 0, 0, -1, -2, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, -2, -2, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, -2, 0, 0, 1, 0, 0, 0, -4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -2, -1, 2, 0, 1, 0, -1, 0, -2, -2, 1, 0, -1, -2, 4, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 1, -1, -2, 4, -1, 0, -1, 0, 1, 1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 2, 0, 0, 1, 0, 0, 4, 4, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 4, 1, 0, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 1, 0, -2, -2, 0, -1, 0, -2, 0, 4, -2, 0, 1, 0, 1, 0, 0, 0, -2, 0, -1, 0, 1, 0, 0, 0, -1, 1, 0, -2, -2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -1, -2, 0, -2, 1, -2, 0, -1, 1, 1, 0, 0, 2, 0, 0, 0, -2, 0, 0, -2, -2, 0, -1, -2, 0, -1, 0, 0, 0, 1, 1, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -1, 2, 1, 0, 1, 0, 0, 1, 2, 0, 1, -1, 0, 0, -2, -2, 0, 0, 1, 0, 2, 0, -2, 0, 0, -1, 0, -2, -1, 4, 0, 1, 0, 0, 0, -2, 0, 0, 0, -2, -2, 0, -2, 0, -2, -2, 0, 0, -2, -2, 0, -1, 0, -1, 0, 4, 0, 4, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, -2, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 1, 2, -2, 0, -1, 1, 1, 1, 0, 0, 0, -2, 0, 0, 1, 2, 0, 0, -1, 0, 2, 1, 0, 0, 0, -1, 0, 0, 1, 0, 1, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 1, 1, -4, 0, 0, 1, 1, 0, 0, 0, 1, 4, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, -1, 0, -1, 0, 0, 2, 0, 0, 0, -2, 0, -1, 0, -2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, -1, -1, 1, 0, -1, 0, 0, 1, 1, 2, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, -2, 0, 0, 0, 1, 0, 0, 0, -1, 1, -2, 2, 0, 0, -2, 1, 0, 0, 0, 4, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, -1, 0, 1, 2, 0, -2, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 4, 0, 4, 0, 1, 1, 0, 4, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, -4, 0, 0, 1, -1, 0, 0, 4, 0, -2, 0, 0, 0, -2, 0, 1, 0, 0, 1, 0, 1, 2, -1, 0, -2, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, -2, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, -1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, -2, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 1, -2, 1, -1, -4, 1, -2, -1, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, -2, 1, 0, 0, -2, 1, -2, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0, -2, -2, 0, 0, 0, 1, -2, -2, 0, 0, 1, -2, 0, 2, 4, -1, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 1, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 1, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, -2, -2, -1, 0, 1, 0, 0, 1, 2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 2, 0, 0, -2, 0, 4, -1, -2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 1, 1, -2, 0, -2, 1, 1, 0, 0, -2, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, -2, 0, -2, -2, 0, 0, 0, -2, 1, -4, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 1, 0, -1, 4, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, -1, -4, 0, 2, 1, 1, 0, -2, 0, 1, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 1, -1, 0, 0, 0, 2, 2, -2, 0, 4, 0, 0, 0, -2, 0, -2, 2, 0, -2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, -2, 0, 0, 0, 1, 0, 1, -1], 'weight': 1, 'weight_parity': -1}
  94. label: 168.1.s.b
    {'Nk2': 168, 'analytic_conductor': 0.0838429221223444, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 36, 'artin_field': [1, -4, 8, -4, -6, 18, -20, 0, 24, -28, 17, -6, 1], 'artin_field_label': '12.0.458838245376.1', 'artin_image': '36.12', 'char_conductor': 168, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 19, 'char_orbit_label': 's', 'char_order': 6, 'char_parity': -1, 'char_values': [168, 6, [127, 85, 113, 73], [6, 3, 3, 4]], 'cm_discs': [-24], 'conrey_index': 53, 'dim': 2, 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [[5, [1, 1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4504836594729128, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 24, 8, -1, 2, -24], [1, 1, 7, 3, 1, 3, 0], [1, 1, 168, 19, -1, 6, 0]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '168.1.s.b', 'level': 168, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 3, 7], 'level_radical': 42, 'minimal_twist': '168.1.s.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 19, 'projective_field': [-6, -2, -1, 1], 'projective_field_label': '3.1.1176.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{6}^{2}q^{2}+\\zeta_{6}q^{3}-\\zeta_{6}q^{4}+\\zeta_{6}^{2}q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-24], 'self_twist_type': 1, 'space_label': '168.1.s', 'trace_display': [1, 1, -1, -1], 'trace_hash': 452921702502187155, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.019', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.012', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.346', 'prec': 20}, {'__RealLiteral__': 0, 'data': '18.214', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-5.856', 'prec': 20}, {'__RealLiteral__': 0, 'data': '245.514', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.500', 'prec': 17}, 'traces': [2, 1, 1, -1, -1, 2, -1, -2, -1, 1, -1, 1, 0, -2, -2, -1, 0, 1, 0, 2, 1, -2, 0, -1, 0, 0, -2, -1, 2, -1, 1, 1, 1, 0, 2, 2, 0, 0, 0, 1, 0, -1, 0, -1, -1, 0, 0, -2, -1, 0, 0, 0, -1, -1, 2, 1, 0, 1, -1, 1, 0, 2, 2, 2, 0, -1, 0, 0, 0, 1, 0, 1, -2, 0, 0, 0, -1, 0, 1, -1, -1, 0, 2, -2, 0, 0, 1, 1, 0, -2, 0, 0, -1, 0, 0, -1, -2, 1, 2, 0, 2, 0, -2, 0, 1, -2, -1, 1, 0, 1, 0, 2, 0, 0, 0, -1, 0, -2, 0, 2, 0, 0, 0, 1, -2, 1, -2, 1, 0, 0, -1, -2, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, -1, -4, -2, 0, 2, 0, 1, 0, 0, 1, -2, 0, 0, -1, 1, -2, 0, -2, 0, 0, 1, 1, 0, -1, 2, 0, 0, 0, 2, 2, 0, 2, 1, 0, 2, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, -1, 0, 2, -4, 1, -2, 0, 0, 4, -1, 0, 0, 2, 0, 0, 0, 2, 0, -1, 0, 1, 0, 2, 1, 0, 2, -1, 0, 0, -2, 1, 0, 0, -1, 0, 0, 0, -2, -2, 0, 0, 0, -1, 2, 0, 0, 1, 1, 0, 1, 0, -1, 0, 0, -1, 1, -1, 2, -1, 0, -1, 0, -1, 0, 0, 0, 0, -1, 1, 0, -1, 2, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, -1, 1, -1, -2, 2, -1, 2, 0, 1, -2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, -4, -1, 0, 0, 1, 0, -1, -2, -1, -1, -1, -1, -2, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 1, -2, 1, 0, 0, 1, 0, 2, 0, 0, -2, 2, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 4, 0, 1, -1, 0, 0, 0, 4, 0, 1, 0, 0, 0, -1, 2, 0, 0, -1, 0, 0, 2, 0, 0, -1, 0, 0, 2, -1, 2, 0, 1, 2, 0, 0, 1, -2, -2, 1, -1, 0, -4, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 1, 0, 0, 4, -1, 0, -1, 0, 0, 0, -4, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 4, -1, -2, 0, 0, -2, 1, -2, -1, 0, -1, 0, 0, -1, 4, -1, 0, 0, 0, 0, -1, -2, 0, 0, 1, 0, 0, 0, -4, -1, 4, -1, -1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, -1, 0, 2, 0, 0, 1, -1, 1, 0, 0, -2, 2, 0, 0, 0, -1, -2, 0, 2, 0, 1, 0, 1, 0, -2, -4, 0, 1, 1, -1, 0, -2, -2, 0, 0, -2, 0, 0, 0, 4, 0, 0, 1, 0, 2, 0, 0, 0, 1, -1, 1, 2, 0, 0, 0, -1, 0, -2, -2, 2, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, -1, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 2, -1, -2, -1, 2, 0, 1, 2, 1, 0, 1, -2, 0, 0, 2, 0, -4, 2, 0, 0, 0, -2, 0, 0, 1, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 1, -2, -1, 0, 1, 1, -2, 0, -2, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 2, 0, -1, 0, -1, 0, 4, 0, -4, 1, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 2, -2, -1, 0, -1, -1, 0, 1, 0, 1, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, -4, -1, 4, 0, -1, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 2, -2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, -2, -1, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, -1, 0, 2, -2, 1, 0, 1, 0, -2, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, -2, -2, 0, 1, 2, 0, 0, 2, 0, 4, 0, 0, 0, 0, -2, -1, 0, -1, 0, 2, 0, 2, 0, -2, 0, 0, 1, -2, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, -2, 0, 1, 0, -1, 2, 0, 0, 0, 0, 2, 0, 0, -1, 0, -2, 2, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -2, 0, -1, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, -2, -2, -2, -1, 0, 0, 1, 0, 1, -4, 0, -1, 1, -1, 0, -2, 0, 0, 1, 1, 0, 0, 1, 0, -1, 1, 0, 2, -4, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, -4, 0, 0, 0, -1, -1, 0, 0, 2, 0, -2, 0, 0, -2, 0, 1, 0, 2, -2, 1, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, -1, 0, 0, 2, -2, 0, 2, -1, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0, 0, -1, 1, -2, 0, -2, 0, 0, -1, -1, -2, 0, 2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 1, -1, 0, 0, 4, 1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, -1, -2, -2, -1, 0, -1, 2, 2, 2, 0, 1, -1, 0, 0, 2, 2, -1, 0, 0, 0, 0, 1, -4, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, -2, 0, -4, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, -2, 0, -1, -1, 1, 4, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 2, 0, -1, 0, 1, 0, -1, 0, 0, 1, -2, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 2, 0, -2, -2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 4, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 0, -2, 2, -1, 0, 1, -2, 4, 0, 0, 0, -1, 0, 1, 0, 2, 2, 0, -1, -1, 2, -4, -1, 0, -1, 0, -1, 1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, -1, 0, 0, -2, 0, 0, -1, 0, 0, -4, 4, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 4, -1, 0, 0, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, -2, -1, 0, -2, 2, 0, -1, 0, -2, 0, -4, 2, 0, -1, 0, 1, 0, 0, 0, 2, 0, -1, 0, -1, 0, 0, 0, -1, -1, 0, -2, 2, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 1, 2, 0, 2, 1, -2, 0, -1, 1, -1, 0, 0, -2, 0, 0, 0, 2, 0, 0, 2, -2, 0, -1, -2, 0, 1, 0, 0, 0, 1, -1, -2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 1, 2, -1, 0, 1, 0, 0, 1, -2, 0, 1, 1, 0, 0, 2, -2, 0, 0, -1, 0, -2, 0, -2, 0, 0, -1, 0, 2, -1, -4, 0, 1, 0, 0, 0, 2, 0, 0, 0, -2, -2, 0, -2, 0, 2, 2, 0, 0, -2, -2, 0, 1, 0, 1, 0, 4, 0, 4, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, -1, 2, 1, 0, 0, 0, 2, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, -1, -1, 1, 1, 0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 1, 0, -2, -1, 0, 0, 0, -1, 0, 0, 1, 0, -1, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, -1, 1, 4, 0, 0, -1, 1, 0, 0, 0, 1, -4, -1, 0, -1, 0, 0, 0, 2, 0, 0, 0, -1, 0, -1, 0, 0, -2, 0, 0, 0, -2, 0, -1, 0, 2, -1, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, -1, -1, -1, 0, -1, 0, 0, 1, -1, 2, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 1, -1, -2, -2, 0, 0, 2, 1, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 1, 0, -1, 2, 0, 2, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 4, 0, -4, 0, -1, -1, 0, -4, 1, 0, -1, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, -4, 0, 0, 1, 1, 0, 0, -4, 0, -2, 0, 0, 0, 2, 0, 1, 0, 0, 1, 0, -1, 2, 1, 0, -2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, -2, 0, 2, 0, 0, 0, -2, 2, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 2, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, -1, -2, -1, -1, -4, -1, -2, -1, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, -2, 2, 0, -2, 1, 0, 0, -2, -1, 2, 1, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, -2, 2, 0, 0, 0, 1, -2, 2, 0, 0, -1, -2, 0, -2, 4, -1, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 2, -2, 1, 0, 1, 0, 0, 1, -2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, -2, 0, -4, -1, 2, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 1, -1, 2, 0, 2, 1, 1, 0, 0, -2, -1, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, -2, 0, -2, -2, 0, 0, 0, 2, -1, -4, 0, 2, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, -1, 0, -1, -4, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 1, 0, -1, -4, 0, -2, 1, -1, 0, -2, 0, 1, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, -1, 1, 0, 0, 0, 2, -2, 2, 0, -4, 0, 0, 0, -2, 0, 2, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, -1, -2, 0, 0, 0, -1, 0, 1, 1], 'weight': 1, 'weight_parity': -1}
  95. label: 171.1.c.a
    {'Nk2': 171, 'analytic_conductor': 0.08534011716024341, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 8, 'artin_field': [4, 2, -3, -1, 1], 'artin_field_label': '4.0.513.1', 'artin_image': '8.3', 'char_conductor': 19, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 3, 'char_orbit_label': 'c', 'char_order': 2, 'char_parity': -1, 'char_values': [171, 2, [20, 154], [2, 1]], 'cm_discs': [-3, -19], 'conrey_index': 37, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.3e2_19.4t3.2c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 137455730859, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 19, 2, -1, 2, -19], [1, 1, 57, 4, 1, 2, 57]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': True, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '171.1.c.a', 'level': 171, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [3, 19], 'level_radical': 57, 'minimal_twist': '171.1.c.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [25, -5, -4, -1, 1], 'projective_field_label': '4.0.3249.1', 'projective_image': 'D2', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{4}-2q^{7}+q^{16}-q^{19}-q^{25}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3e2_19.4t3.2'], 'relative_dim': 1, 'rm_discs': [57], 'self_twist_discs': [-3, -19, 57], 'self_twist_type': 3, 'space_label': '171.1.c', 'trace_display': [0, 0, 0, -2], 'trace_hash': 659335172196934594, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.007', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.939', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.024', 'prec': 20}, {'__RealLiteral__': 0, 'data': '3.752', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.094', 'prec': 20}, {'__RealLiteral__': 0, 'data': '15.005', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.765', 'prec': 17}, 'traces': [1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 2, 0], 'weight': 1, 'weight_parity': -1}
  96. label: 171.1.o.a
    {'Nk2': 171, 'analytic_conductor': 0.08534011716024341, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 48, 'artin_field': [1, -1, 9, -23, 43, -57, 55, -23, -12, 32, -27, 15, -1, -4, 6, -3, 1], 'artin_image': '48.33', 'char_conductor': 171, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 15, 'char_orbit_label': 'o', 'char_order': 6, 'char_parity': -1, 'char_values': [171, 6, [20, 154], [2, 3]], 'cm_discs': [], 'conrey_index': 94, 'dim': 4, 'embedded_related_objects': [['ArtinRepresentation/2.3e2_19.16t60.1c4'], ['ArtinRepresentation/2.3e2_19.16t60.1c1'], ['ArtinRepresentation/2.3e2_19.16t60.1c3'], ['ArtinRepresentation/2.3e2_19.16t60.1c2']], 'field_disc': 144, 'field_disc_factorization': [[2, 4], [3, 2]], 'field_poly': [1, 0, -1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 12, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 962089451691, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0], [1, 1, 19, 2, -1, 2, 0], [1, 1, 171, 15, -1, 6, 0]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '171.1.o.a', 'level': 171, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [3, 19], 'level_radical': 57, 'minimal_twist': '171.1.o.a', 'nf_label': '4.0.144.1', 'prim_orbit_index': 15, 'projective_field': [20, 1, 3, -1, 1], 'projective_field_label': '4.0.29241.1', 'projective_image': 'A4', 'projective_image_type': 'A4', 'qexp_display': 'q+\\zeta_{12}^{5}q^{2}+\\zeta_{12}^{3}q^{3}+\\zeta_{12}^{4}q^{5}+\\cdots', 'related_objects': ['ArtinRepresentation/2.3e2_19.16t60.1'], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '171.1.o', 'trace_display': [0, 0, -2, -2], 'trace_hash': 1854558447297529876, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.000', 'prec': 17}, {'__RealLiteral__': 0, 'data': '3.463', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.467', 'prec': 20}, {'__RealLiteral__': 0, 'data': '144.591', 'prec': 24}, {'__RealLiteral__': 0, 'data': '-31.751', 'prec': 24}, {'__RealLiteral__': 0, 'data': '8945.681', 'prec': 27}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.645', 'prec': 17}, 'traces': [4, 0, 0, 0, -2, -2, -2, 0, -4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, -2, -2, 0, 0, -2, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 2, -4, 0, -4, -2, 0, 0, 2, 4, 2, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 4, -4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, -2, 0, 0, -2, 0, -4, 0, 0, 0, 0, 2, -2, 0, 0, 4, 0, 0, 2, -4, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, -2, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, -2, 0, 0, -2, 0, 0, 0, 0, 4, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, -2, 0, 4, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 2, 0, -2, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 2, -2, 0, 0, -4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -4, 0, 0, 0, -2, -2, 2, 0, 2, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 8, 2, -2, 2, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 2, -4, 0, 0, -2, 2, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 4, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, -2, 4, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 2, -2, 0, 0, -4, 2, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, -2, -4, -2, 0, 2, 0, -8, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 2, 2, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0, 8, -4, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, -2, 0, 2, 0, 0, 0, 0, -4, 2, 0, -2, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -4, 0, 0, 2, 0, 2, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, -4, -4, 0, 0, 0, -2, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, -2, 4, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 4, -2, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, -2, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, -2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 4, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -8, 0, -4, 2, 0, 0, 2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 4, -4, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2, -4, 0, -2, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 4, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, -2, 0, 0, 4, 0, 0, 2, 2, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 2, 0, 0, -8, 0, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 4, -4, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, -2, -2, -2, 0, 0, -4, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 2, -8, 0, 0, 0, 2, 0, 0, 0, 0, 4, -2, 0, -2, 0, 0, 0, -4, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -8, 0, -4, 0, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, -8, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, -2, 2, 0, -4, 0, -4, 0, 0, 0, 0, -2, -2, 0, -2, 4, 0, 0, 2, 0, 2, -2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 4, 0, 0, 0, -2, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, -2, 0, 0, 2, 0, -2, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 8, 0, -4, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, -4, 2, 4, -2, 0, 0, 0, 8, 0, 0, 0, 0, 0, -2, 0, 2, -4, 0, 0, -2, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 4, 0, -8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, -2, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 8, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -8, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, -2, -4, 2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 2, 0, 0, -2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 2, -4, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, -4, 0, 0, -2, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -4, 0, 4, -2, 0, 0, 2, 2, 2, 4, 0, -4, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, -2, -4, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 2, 0, -2, 2, 0, 0, 8, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, -2, 0, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 4, 0, -4, 0, 0, 0, 0, -2, -2, 0, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, -2, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 2, -2, 0, 0, 4, 0, 0, -2, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, -4, 4, -4, 0, 4, 0, -2, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, -4, -4, 0, 0, 2, 0, -4, 0, 0, 0, 0, -2, 4, 0, 0, -2, 0, 0, 0, 4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, 0, -4, 0, 0, 0, 0, -2], 'weight': 1, 'weight_parity': -1}
  97. label: 171.1.p.a
    {'Nk2': 171, 'analytic_conductor': 0.08534011716024341, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 19, 'char_degree': 2, 'char_is_minimal': True, 'char_is_real': False, 'char_orbit_index': 16, 'char_orbit_label': 'p', 'char_order': 6, 'char_parity': -1, 'char_values': [171, 6, [20, 154], [6, 1]], 'cm_discs': [-3], 'conrey_index': 46, 'dim': 2, 'field_disc': -3, 'field_disc_factorization': [[-1, 1], [3, 1]], 'field_poly': [1, -1, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 6, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 1030808928427, 'hecke_ring_generator_nbound': 4, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 19, 4, -1, 6, 0], [1, 1, 57, 6, 1, 6, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '171.1.p.a', 'level': 171, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [3, 19], 'level_radical': 57, 'minimal_twist': '171.1.p.a', 'nf_label': '2.0.3.1', 'prim_orbit_index': 4, 'projective_field': [19, 0, 0, 0, 0, 0, 1], 'projective_field_label': '6.0.22284891.1', 'projective_image': 'D6', 'projective_image_type': 'Dn', 'qexp_display': 'q-\\zeta_{6}q^{4}+q^{7}+(-1+\\zeta_{6}^{2})q^{13}+\\zeta_{6}^{2}q^{16}+\\cdots', 'related_objects': [], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '171.1.p', 'trace_display': [0, 0, 0, 2], 'trace_hash': 1937339919970153578, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.005', 'prec': 20}, {'__RealLiteral__': 0, 'data': '2.013', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.164', 'prec': 17}, {'__RealLiteral__': 0, 'data': '18.227', 'prec': 20}, {'__RealLiteral__': 0, 'data': '4.110', 'prec': 17}, {'__RealLiteral__': 0, 'data': '203.550', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.648', 'prec': 17}, 'traces': [2, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, -3, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -3, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -3, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, -3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0], 'weight': 1, 'weight_parity': -1}
  98. label: 172.1.b.a
    {'Nk2': 172, 'analytic_conductor': 0.08583918217287641, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [3, -1, -1, 1], 'artin_field_label': '3.1.172.1', 'artin_image': '6.1', 'char_conductor': 43, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 2, 'char_orbit_label': 'b', 'char_order': 2, 'char_parity': -1, 'char_values': [172, 2, [87, 89], [2, 1]], 'cm_discs': [-43], 'conrey_index': 85, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.2e2_43.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 68736254124, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 43, 2, -1, 2, -43]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '172.1.b.a', 'level': 172, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [2, 43], 'level_radical': 86, 'minimal_twist': '172.1.b.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [3, -1, -1, 1], 'projective_field_label': '3.1.172.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q+q^{9}-q^{11}-q^{13}-q^{17}-q^{23}+\\cdots', 'related_objects': ['ArtinRepresentation/2.2e2_43.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-43], 'self_twist_type': 1, 'space_label': '172.1.b', 'trace_display': [0, 0, 0, 0], 'trace_hash': 249568497317168116, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.011', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.958', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.935', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.849', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.717', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.413', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.515', 'prec': 17}, 'traces': [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, -2, 0, -1, 0, 0, 0, 0, 0, -1, 0], 'weight': 1, 'weight_parity': -1}
  99. label: 175.1.c.a
    {'Nk2': 175, 'analytic_conductor': 0.08733637721077542, 'analytic_rank': 0, 'analytic_rank_proved': True, 'char_conductor': 35, 'char_degree': 1, 'char_is_minimal': False, 'char_is_real': True, 'char_orbit_index': 3, 'char_orbit_label': 'c', 'char_order': 2, 'char_parity': -1, 'char_values': [175, 2, [127, 101], [1, 1]], 'cm_discs': [-7], 'conrey_index': 174, 'dim': 2, 'field_disc': -4, 'field_disc_factorization': [[-1, 1], [2, 2]], 'field_poly': [1, 0, 1], 'field_poly_is_cyclotomic': True, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 4, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 137455730863, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 4, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7], [1, 1, 5, 2, 1, 2, 0], [1, 1, 35, 3, -1, 2, 0]], 'is_cm': True, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': False, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '175.1.c.a', 'level': 175, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [5, 7], 'level_radical': 35, 'minimal_twist': '175.1.d.a', 'nf_label': '2.0.4.1', 'prim_orbit_index': 3, 'projective_field': [-3, 2, -1, 1], 'projective_field_label': '3.1.175.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-i q^{2}+i q^{7}-i q^{8}-q^{9}-q^{11}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'self_twist_discs': [-7], 'self_twist_type': 1, 'space_label': '175.1.c', 'trace_display': [0, 0, 0, 0], 'trace_hash': 1974909139053812612, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.004', 'prec': 20}, {'__RealLiteral__': 0, 'data': '1.837', 'prec': 17}, {'__RealLiteral__': 0, 'data': '-0.109', 'prec': 20}, {'__RealLiteral__': 0, 'data': '21.541', 'prec': 20}, {'__RealLiteral__': 0, 'data': '-1.930', 'prec': 20}, {'__RealLiteral__': 0, 'data': '313.276', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.763', 'prec': 17}, 'traces': [2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0], 'weight': 1, 'weight_parity': -1}
  100. label: 175.1.d.a
    {'Nk2': 175, 'analytic_conductor': 0.08733637721077542, 'analytic_rank': 0, 'analytic_rank_proved': True, 'artin_degree': 6, 'artin_field': [-3, 2, -1, 1], 'artin_field_label': '3.1.175.1', 'artin_image': '6.1', 'char_conductor': 7, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 4, 'char_orbit_label': 'd', 'char_order': 2, 'char_parity': -1, 'char_values': [175, 2, [127, 101], [2, 1]], 'cm_discs': [-7], 'conrey_index': 76, 'dim': 1, 'embedded_related_objects': [['ArtinRepresentation/2.5e2_7.3t2.1c1']], 'field_disc': 1, 'field_disc_factorization': [], 'field_poly': [0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 206175207599, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 2, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7]], 'is_cm': True, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '175.1.d.a', 'level': 175, 'level_is_powerful': False, 'level_is_prime': False, 'level_is_prime_power': False, 'level_is_prime_square': False, 'level_is_square': False, 'level_is_squarefree': False, 'level_primes': [5, 7], 'level_radical': 35, 'minimal_twist': '175.1.d.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 2, 'projective_field': [-3, 2, -1, 1], 'projective_field_label': '3.1.175.1', 'projective_image': 'D3', 'projective_image_type': 'Dn', 'qexp_display': 'q-q^{2}+q^{7}+q^{8}+q^{9}-q^{11}-q^{14}+\\cdots', 'related_objects': ['ArtinRepresentation/2.5e2_7.3t2.1'], 'relative_dim': 1, 'rm_discs': [], 'self_twist_discs': [-7], 'self_twist_type': 1, 'space_label': '175.1.d', 'trace_display': [-1, 0, 0, 1], 'trace_hash': 1991922227833151576, 'trace_moments': [{'__RealLiteral__': 0, 'data': '-0.009', 'prec': 20}, {'__RealLiteral__': 0, 'data': '0.980', 'prec': 17}, {'__RealLiteral__': 0, 'data': '0.960', 'prec': 17}, {'__RealLiteral__': 0, 'data': '2.917', 'prec': 17}, {'__RealLiteral__': 0, 'data': '4.836', 'prec': 17}, {'__RealLiteral__': 0, 'data': '10.668', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.505', 'prec': 17}, 'traces': [1, -1, 0, 0, 0, 0, 1, 1, 1, 0, -1, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, -1, 1, 0, 1, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -2, 2, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, -1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 2, -1, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 1, -1, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, -1, -1, 0, -1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -2, 2, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, 0, -2, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 2, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, -1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -1, 0, -1, 0, 0, 2, 1, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0], 'weight': 1, 'weight_parity': -1}