Formats: - HTML - YAML - JSON - 2026-09-11T19:39:56.417501 - next page
Query: /api/mf_newforms/?char_orbit_label=a&weight=2&_offset=0
Show schema
  1. label: 11.2.a.a
    {'Nk2': 44, 'analytic_conductor': 0.08783544222340842, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[11, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [11, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554443, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '11.2.a.a', 'level': 11, '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': [11], 'level_radical': 11, 'minimal_twist': '11.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/11/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '11.2.a', 'trace_display': [-2, -1, 1, -2], 'trace_hash': 1428752966040989219, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.006', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.989', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.019', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.947', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.053', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.782', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.012', 'prec': 7}, 'traces': [1, -2, -1, 2, 1, 2, -2, 0, -2, -2, 1, -2, 4, 4, -1, -4, -2, 4, 0, 2, 2, -2, -1, 0, -4, -8, 5, -4, 0, 2, 7, 8, -1, 4, -2, -4, 3, 0, -4, 0, -8, -4, -6, 2, -2, 2, 8, 4, -3, 8, 2, 8, -6, -10, 1, 0, 0, 0, 5, -2, 12, -14, 4, -8, 4, 2, -7, -4, 1, 4, -3, 0, 4, -6, 4, 0, -2, 8, -10, -4, 1, 16, -6, 4, -2, 12, 0, 0, 15, 4, -8, -2, -7, -16, 0, -8, -7, 6, -2, -8, 2, -4, -16, 0, 2, 12, 18, 10, 10, -2, -3, 8, 9, 0, -1, 0, -8, -10, 4, 0, 1, -24, 8, 14, -9, -8, 8, 0, 6, -8, -18, -2, 0, 14, 5, 0, -7, -2, 10, -4, -8, 6, 4, 8, 0, -8, 3, 6, -10, -8, 2, 0, 4, 4, 7, -8, -7, 20, 6, 8, 2, -2, 4, -16, -1, 12, -12, 0, 3, 4, 0, -12, -6, 0, 8, -4, -5, -30, -15, -4, 7, 16, -12, 0, 3, 14, -2, 16, -10, 0, 17, 8, 4, 14, -4, -6, -2, 4, 0, 0, 7, -4, 0, 4, -8, 32, 2, -16, 0, -4, 12, -12, 3, -36, -6, 0, -14, -20, -4, 2, -8, 6, 19, -16, 8, -18, 18, 0, 15, 2, 2, 0, 24, 16, 8, 10, 10, -8, -30, 4, -8, -2, -16, 24, -3, -16, 0, 0, 6, 18, -23, 8, -1, -16, 2, 16, -2, -12, -6, 8, 0, 36, 14, 0, -6, 0, -15, -14, 10, -10, -28, 8, 8, 14, -4, 2, -2, -20, -14, 0, -18, 16, 4, -6, 0, -8, 16, -16, -13, 0, 7, 8, 24, -6, 5, 0, 5, 20, -4, 8, 12, -4, -2, 0, 12, -8, 8, -4, 16, -14, 12, 0, -1, 14, 4, -20, 13, -12, 0, -8, -18, -4, 0, 2, -16, -8, -10, 0, -16, 2, 7, -12, -6, 24, -7, -8, -22, -6, -9, -4, 7, 0, 20, 0, 1, 12, 28, 0, 30, -16, 20, 8, -21, 10, -3, 30, -4, 30, -20, 0, -19, -14, -1, -16, 4, 24, -17, 4, 16, -6, 12, -14, -26, 4, 9, 0, 0, 20, -5, 0, -8, -34, -1, 0, -2, -8, 12, -14, -15, 8, 2, 0, 18, 4, -10, -4, -2, 0, 0, 16, 2, -14, 28, 4, 1, 0, 3, 0, -30, 16, 7, -32, -10, -4, -6, 32, -10, 0, 20, 4, 22, -24, -16, 0, 8, -6, -24, 36, -4, 12, -18, -20, -11, 28, 0, 20, 0, 8, 40, 0, 6, 16, -11, -6, 15, -38, 10, 16, 35, -16, -8, 18, -2, -36, -8, 0, -12, -30, -10, -2, 12, -4, -11, 0, -7, -48, -27, -16, 14, -16, 7, 0, -6, -20, 0, 8, 12, 60, 20, -8, 12, 16, -2, 2, -7, 32, 23, 0, -4, 6, -8, 16, 0, 0, -2, -28, 6, -12, 20, -18, 12, 46, -26, 0, 2, 2, -3, 16, 15, -4, -8, -32, 0, 4, -16, 12, 8, 12, 6, 0, -3, 0, -16, -36, -8, -28, -14, 4, -22, 12, -10, 0, -32, 30, 18, 0, 15, -20, -3, 10, -8, 56, -7, -16, 10, -16, 8, -14, -24, 8, 0, 0, 20, 4, -3, 20, -2, 28, -24, 8, 2, 36, 4, -16, 9, -8, -2, 0, 0, 0, -28, 8, -17, -32, 4, 16, 33, 26, -4, 0, 12, -14, -6, 0, -8, -48, 28, 6, 0, -10, 2, -12, 44, -10, 4, -20, 0, 8, 40, 0, 2, -24, 14, 4, 1, 4, -22, 0, 0, -24, 32, 8, -16, -16, 8, 0, 18, -32, -25, 14, -5, -24, -30, 16, 11, 2, 0, -14, -6, -8, 7, 0, -12, -26, 8, 12, -12, 0, 6, 0, -33, 36, 29, 4, 6, 0, -7, 0, 5, 32, 14, 8, -41, 20, -18, 32, -8, 32, 10, -2, 37, -14, 8, 0, 0, 12, 0, -24, -19, 14, 12, 16, 14, 44, -20, 6, -42, 18, 14, 0, -18, -14, -16, 0, -7, -40, -15, 24, -24, -2, 17, -12, 4, -56, 10, 0, 16, -60, -24, 16, 2, -40, 0, -8, -8, 42, -4, -10, -25, 6, 20, 0, -7, 8, 4, -30, 30, 40, 15, 8, 32, 38, 8, 14, 0, 2, 3, 0, 13, -8, 12, -24, -36, 34, 3, -8, -7, -32, 50, 6, 0, -24, 4, 0, -10, 52, 12, -4, -36, -18, -23, -32, 23, 0, 2, -20, -22, 10, 1, 0, 12, 16, -20, 34, 4, 2, 20, -16, 20, 4, 2, 8, -6, -24, -28, 0, 6, 30, 0, -8, -3, -4, 0, 12, -7, -36, -32, -4, -14, 20, -18, 0, 48, 4, 6, 0, 53, 0, -16, -32, -30, -4, 4, 14, 2, -56, -10, 0, 0, -2, -38, 0, 28, -6, 4, -8, 0, 60, 16, -16, 22, -14, 39, 0, 4, 20, -52, 4, 25, 12, 2, -32, 6, 20, -12, 0, 35, -40, -5, 0, -29, -44, 18, 24, 3, 32, -2, 24, -4, -16, -3, 6, 14, 48, 0, 0, 8, 8, -15, -12, -16, 36, 24, 40, -6, 22, 13, -28, -10, 0, -28, 0, 14, 0, 18, -8, -12, -80, -24, -4, -43, -12, 4, -16, -5, 22, -22, 0, -16, -30, 1, 38, 0, -20, -15, 0, 4, -70, 0, 16, 12, 16, -12, 0, 7, 4, -12, 36, -4, 16, 12, 0, -6, 24, -12, 30, 36, 20, 10, 0, -8, -24, -12, 4, -12, 22, 32, 0, -30, 14, 0, 48, -12, 54, -2, 0, 8, -28, 1, 16, 42, -14, 8, -20, -10, 12, -27, 20, 16, 0, -13, 0, 34, -24, 17, -60, 0, -40, 14, 8, 18, -24, -36, -16, 4, 4, -32, 0, 0, 14, 47, -32, -20, -46, 16, -48, -27, 8, 15, -6, -20, 16, 39, 0, -2, 0, 16, 0, 6, 4, -8, 56, -7, -12, 0, 12, 38, -40, 15, 0], 'weight': 2, 'weight_parity': 1}
  2. label: 14.2.a.a
    {'Nk2': 56, 'analytic_conductor': 0.11179056282979254, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [7, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [14, 1, [3], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554446, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '14.2.a.a', 'level': 14, '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': [2, 7], 'level_radical': 14, 'minimal_twist': '14.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\\cdots', 'related_objects': ['EllipticCurve/Q/14/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '14.2.a', 'trace_display': [-1, -2, 0, 1], 'trace_hash': 1459918945821948014, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.009', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.976', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.031', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.943', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.072', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.854', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.022', 'prec': 7}, 'traces': [1, -1, -2, 1, 0, 2, 1, -1, 1, 0, 0, -2, -4, -1, 0, 1, 6, -1, 2, 0, -2, 0, 0, 2, -5, 4, 4, 1, -6, 0, -4, -1, 0, -6, 0, 1, 2, -2, 8, 0, 6, 2, 8, 0, 0, 0, -12, -2, 1, 5, -12, -4, 6, -4, 0, -1, -4, 6, -6, 0, 8, 4, 1, 1, 0, 0, -4, 6, 0, 0, 0, -1, 2, -2, 10, 2, 0, -8, 8, 0, -11, -6, -6, -2, 0, -8, 12, 0, -6, 0, -4, 0, 8, 12, 0, 2, -10, -1, 0, -5, 0, 12, -4, 4, 0, -6, 12, 4, 2, 0, -4, 1, 6, 4, 0, -6, -4, 6, 6, 0, -11, -8, -12, -4, 0, -1, -16, -1, -16, 0, 18, 0, 2, 4, 0, -6, 18, 0, 14, 0, 24, 0, 0, 1, 0, -2, -2, 2, -18, -10, 8, -2, 6, 0, 0, 8, -4, -8, -12, 0, 0, 11, -16, 6, 0, 6, -12, 2, 3, 0, 2, 8, -12, -12, -5, 0, 12, 6, -12, 0, 20, 4, -16, 0, 0, -8, 0, -12, 4, 0, 24, -2, 14, 10, 0, 1, -18, 0, 20, 5, 8, 0, -6, -12, 0, 4, 0, -4, 0, 0, -4, 6, 0, -12, 0, -4, -4, -2, -4, 0, -24, 4, 8, -1, -5, -6, 18, -4, -4, 0, 0, 6, -6, 4, 0, -6, -16, -6, 24, 0, -10, 11, 10, 8, 0, 12, -8, 4, 12, 0, -18, 1, 0, 16, 0, 1, 18, 16, 2, 0, -6, -18, 0, 0, 0, -2, 12, -4, -12, 0, -16, 6, 8, -18, 0, 0, -10, -14, -4, 0, -6, -24, -22, 0, 0, 0, 6, -1, 19, 0, 20, 2, 24, 2, 0, -2, 0, 18, 0, 10, 8, -8, 0, 2, 0, -6, 2, 0, 8, 0, -24, -8, -10, 4, 0, 8, 6, 12, 0, 0, -24, 0, 12, -11, 20, 16, -4, -6, -12, 0, 8, -6, 2, 12, 0, -2, 14, -3, -12, 0, 0, -2, 1, -8, 0, 12, -24, 12, -28, 5, -16, 0, 18, -12, 0, -6, -12, 12, -24, 0, -15, -20, 22, -4, 0, 16, 8, 0, 6, 0, 6, 8, 14, 0, 0, 12, 24, -4, -16, 0, 32, -24, 36, 2, 0, -14, 8, -10, 18, 0, 0, -1, -36, 18, 0, 0, 20, -20, -4, -5, -18, -8, 16, 0, 0, 6, 0, 12, 14, 0, -36, -4, -6, 0, 0, 4, -28, 0, 6, 0, -10, 4, -12, -6, -30, 0, 8, 12, 0, 0, 24, 4, -34, 4, 0, 2, 0, 4, 8, 0, 1, 24, -12, -4, 0, -8, 36, 1, 18, 5, 0, 6, -16, -18, 0, 4, -10, 4, 24, 0, 12, 0, 32, -6, 0, 6, -6, -4, -4, 0, 8, 6, 0, 16, -10, 6, 6, -24, -36, 0, -8, 10, 0, -11, 0, -10, -16, -8, 32, 0, -12, -12, -36, 8, 0, -4, 0, -12, -4, 0, 24, 18, 0, -1, 0, 0, -6, -16, 36, 0, 2, -1, 8, -18, 0, -16, 0, -2, 24, 0, 6, 6, 2, 18, 10, 0, -24, 0, -23, 0, -6, 2, -24, -12, 0, 4, 24, 12, 0, 0, 38, 16, -40, -6, 0, -8, 8, 18, 8, 0, -12, 0, 8, 10, 0, 14, 6, 4, -32, 0, 0, 6, 30, 24, 0, 22, -11, 0, 6, 0, 32, 0, -48, -6, 0, 1, 2, -19, -28, 0, -6, -20, 0, -2, 0, -24, -42, -2, -8, 0, 36, 2, -6, 0, 0, -18, -40, 0, -24, -10, 26, -8, -4, 8, 0, 0, 32, -2, 12, 0, 48, 6, 2, -2, 0, 0, 6, -8, 26, 0, 0, 24, -6, 8, 25, 10, 0, -4, 12, 0, -16, -8, 8, -6, 0, -12, -4, 0, 0, 0, -18, 24, 14, 0, 0, -12, -12, 11, 0, -20, 8, -16, 18, 4, 0, 6, 2, 12, -24, 0, -40, -8, 48, 6, 0, -2, 0, -12, -16, 0, 0, 2, 26, -14, -20, 3, -12, 12, -10, 0, -36, 0, -12, 2, 0, -1, 8, 8, -24, 0, -46, -12, 0, 24, 0, -12, 36, 28, 12, -5, 18, 16, 4, 0, 0, -18, 0, 12, -46, 0, 8, 6, 0, 12, 0, -12, -48, 24, 12, 0, -4, 15, 20, 20, 30, -22, 44, 4, 13, 0, 48, -16, -40, -8, 0, 0, 0, -6, -16, 0, 16, -6, 24, -8, 0, -14, -6, 0, 12, 0, -40, -12, 36, -24, 0, 4, 2, 16, 0, 0, -18, -32, 2, 24, 0, -36, 24, -2, 14, 0, -36, 14, 24, -8, 20, 10, -4, -18, 12, 0, 0, 0, -24, 1, 0, 36, -22, -18, 0, 0, 6, 0, -32, -20, 0, 20, -12, 4, -72, 5, -6, 18, 0, 8, 0, -16, 24, 0, 6, 0, 2, -6, 32, 0, 0, -12, 16, -14, -4, 0, 6, 36, -40, 4, 0, 6, -36, 0, 56, 0, 20, -4, 6, 28, 0, 0, -16, -6, 12, 0, 7, 10, 12, -4, 0, 12, -11, 6, 44, 30, 0, 0, 44, -8, 0, -12, -18, 0, 14, 0, -12, -24, -24, -4, 0, 34, -38, -4, 0, 0, 16, -2, -10, 0, 0, -4, -22, -8, -48, 0, -54, -1, 20, -24, 0, 12, -36, 4, -16, 0, 0, 8, -24, -36, 0, -1, 0, -18, 24, -5, 36, 0, -16, -6, 0, 16, 44, 18, 0, 0, 48, -4, 0, 10, 0, -4, 18, -24, 56, 0, -4, -12, 0, 0, -10, -32, -4, 6, 6, 0, 2, -6, 48, 6, 0, 4, 2, 4, 20, 0, -24, -8, 0, -6, 0, 0, 24, -16, -8, 10, -12, -6, -54, -6, 0, 24, 0, 36, 18, 0, -15, 8, 12, -10, 0, 0, 32, 11, -24, 0, -6, 10, 14, 16, -40, 8, -6, -32, 0, 0, 2, 12, -36, 12, 0, 36, 24, -8, 0, 0, -16, 4, -16, 0, 0, 12, 8, 4, 8, 0], 'weight': 2, 'weight_parity': 1}
  3. label: 15.2.a.a
    {'Nk2': 60, 'analytic_conductor': 0.11977560303192057, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, 1], [5, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [15, 1, [11, 7], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554447, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '15.2.a.a', 'level': 15, '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], 'level_radical': 15, 'minimal_twist': '15.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\\cdots', 'related_objects': ['EllipticCurve/Q/15/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '15.2.a', 'trace_display': [-1, -1, 1, 0], 'trace_hash': 750292609497685491, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.011', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.977', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.038', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.926', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.780', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.015', 'prec': 7}, 'traces': [1, -1, -1, -1, 1, 1, 0, 3, 1, -1, -4, 1, -2, 0, -1, -1, 2, -1, 4, -1, 0, 4, 0, -3, 1, 2, -1, 0, -2, 1, 0, -5, 4, -2, 0, -1, -10, -4, 2, 3, 10, 0, 4, 4, 1, 0, 8, 1, -7, -1, -2, 2, -10, 1, -4, 0, -4, 2, -4, 1, -2, 0, 0, 7, -2, -4, 12, -2, 0, 0, -8, 3, 10, 10, -1, -4, 0, -2, 0, -1, 1, -10, 12, 0, 2, -4, 2, -12, -6, -1, 0, 0, 0, -8, 4, 5, 2, 7, -4, -1, 6, 2, -16, -6, 0, 10, -12, 1, 14, 4, 10, 0, 2, 4, 0, 2, -2, 4, 0, -3, 5, 2, -10, 0, 1, 0, -8, 3, -4, 2, -12, -4, 0, -12, -1, 6, -6, 0, -4, 0, -8, 8, 8, -1, -2, -10, 7, 10, 22, 1, -8, 12, 2, 0, 0, -2, 14, 0, 10, -5, 0, -1, -4, -10, 4, -12, 0, 0, -9, -2, 4, -4, -18, -2, 0, 4, 4, 6, 20, -1, -10, 0, 2, 0, -10, 0, -8, -8, 0, -4, 16, -7, 2, -2, 2, 7, 6, 4, -8, 3, -12, -6, 0, 2, 10, 16, 0, 2, -16, 0, 20, 10, 8, 12, 4, -3, 0, -14, -10, 4, -4, -10, 8, 0, 1, -2, -20, 4, 6, 0, 0, -6, -6, 2, 8, 4, 0, 0, -16, 1, -14, -5, -1, 2, -7, 10, -8, 0, -12, -1, 12, 0, 0, 8, -2, -17, 18, 4, 0, 2, -2, 12, 16, 12, -10, 0, 6, -12, 14, 1, 16, -2, 0, 6, -4, 0, 6, 4, 0, 0, -6, 8, -12, 8, -4, -8, 0, -5, -13, 2, -2, -10, 6, -7, -4, -30, 4, -22, 0, 1, 0, 8, -6, -4, -2, -2, 28, 0, 16, 0, -24, 6, 26, -14, 0, 0, -2, -10, 8, 7, 12, 0, 8, -1, -2, 4, -14, 30, 0, -4, 12, -12, -10, 0, 12, 0, -14, 9, -2, -2, 0, -4, 0, 12, 0, 18, -28, -2, -2, 0, 2, 20, 18, -4, -8, 6, 0, -20, -24, 3, -3, 10, -5, 0, 10, -2, -24, 0, 10, 10, 0, 0, -26, 8, -1, 24, 4, 0, -20, -4, 8, -16, -24, -3, 0, -2, 4, -2, 6, -2, 0, -21, 12, -6, 0, 4, -2, 8, 0, -1, 18, 12, 0, -6, 1, 0, 40, -6, 26, -10, 6, 16, 0, 0, 12, 10, 4, 16, 4, 0, -26, -20, 8, -30, 2, -8, 0, 12, -8, -4, 0, 1, -14, 0, 2, -14, 0, 10, 40, -12, -7, 4, -12, -10, -6, -8, -22, 0, 2, -1, -40, -2, 8, 20, 0, -12, 10, -6, -2, 0, -18, 0, 24, 2, 0, 6, 28, 2, 0, -8, -14, -12, -16, 0, 4, 0, -10, 16, 0, 5, 20, 14, 0, -5, 2, 1, 32, -6, 4, 7, 28, 10, -4, 8, -4, 0, 0, 12, 4, -1, 0, -12, -32, 0, 6, 0, 9, 8, -34, 2, 0, 11, -4, -18, -16, 4, -32, 0, 18, -6, 10, 2, 4, 12, 0, -16, 0, -4, -23, 10, -4, 0, -20, -6, -12, 36, -20, -14, 28, 1, 30, -16, 10, -10, 14, 0, -20, 6, -2, 4, -8, 0, 0, -6, 10, 4, -18, 0, -8, 0, 8, 6, 12, 8, 2, 12, 0, -24, -6, 4, -4, -8, -16, 0, 0, 7, 2, 13, -2, 2, 0, 2, 40, 30, -2, -6, -12, -7, 0, 4, -6, 10, 34, -4, 0, -22, 8, 0, -8, -3, 26, 0, 12, 8, 5, 6, -8, -20, 0, 2, -16, -2, 22, -28, -10, 0, -6, -16, -4, 0, 0, 24, 0, -2, 1, -26, 16, -14, -20, 0, -8, 0, -20, 2, -8, -10, 14, -8, -8, 3, -30, -12, -36, 0, -4, -8, 32, 3, 16, 2, 0, 4, 46, 14, -12, -10, 10, 0, 20, -4, 22, -12, 4, 36, 0, 10, 0, 0, -8, -12, 8, 0, -30, 14, -1, 9, 6, 2, 0, 6, 20, 0, 36, -4, -6, 0, -6, -4, 20, 0, -44, 18, 0, 28, -4, 6, 20, 2, 6, 0, -2, -2, -40, -28, -8, -18, 0, -4, -26, 8, 0, -18, 0, 0, 8, -20, 16, 24, -48, -1, 0, 3, 14, 10, -2, 5, -16, 0, 1, -10, 8, -2, 14, 24, 7, 0, -48, -10, -44, 10, 8, 0, -16, 0, 22, 26, 12, 8, 0, 1, 16, -8, -12, -4, -8, 0, -26, 20, 0, 12, -6, -8, 0, -16, 2, 24, 8, 17, 2, 0, -18, -2, 6, -4, 0, 6, 0, -6, 40, -2, 32, 0, 2, 7, 14, -12, 28, -6, -16, 0, 0, -12, 4, 2, 10, 8, -2, 0, 16, -5, -6, -18, -40, 12, 0, 0, -14, 18, 10, -1, 12, 0, -16, -40, -4, 2, 16, -26, 0, -10, 54, -6, 32, -48, 4, 0, -28, 0, 30, -12, -6, -14, -14, -4, 0, 16, 0, -4, 40, 0, -25, 26, 6, -20, -9, -8, 0, 10, 12, -2, 0, -8, 6, 0, 4, -36, -22, 8, -20, -4, 0, 0, -56, 5, -18, 14, 13, 0, 0, -2, -24, 42, 2, 0, 0, 10, 30, -40, -6, 4, -46, 7, 44, 4, 4, 12, 48, 30, 0, 6, -4, -8, 32, 22, 20, 0, 0, -2, 0, -1, -20, 40, 0, 6, -10, -8, -12, 20, 6, 0, 32, 4, -48, -10, 2, -6, 0, 2, 40, 0, -28, 18, 16, 0, -10, -24, -16, 10, 34, 0, -28, 6, 24, -28, -8, -6, -54, 0, -26, -8, -50, 14, 0, 4, 0, 16, -36, 0, -20, -4, 2, 0, -22, 10, 16, 16, -8, 0, 0, -7, -31, -20, -12, 14, 2, 0, 32, 15, -8, -2, 60, 1, 0, -32, 2, 2, 2, -4, 24, 7, 14, -28, 0, -30, 6, 4, 0, 8, 0, 4, 32, 0, -12, 0, -8, 12, 54, -4, 10, 3], 'weight': 2, 'weight_parity': 1}
  4. label: 17.2.a.a
    {'Nk2': 68, 'analytic_conductor': 0.13574568343617666, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[17, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [17, 1, [3], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554449, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '17.2.a.a', 'level': 17, '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': [17], 'level_radical': 17, 'minimal_twist': '17.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\\cdots', 'related_objects': ['EllipticCurve/Q/17/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '17.2.a', 'trace_display': [-1, 0, -2, 4], 'trace_hash': 256041048516234311, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.007', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.988', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.021', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.972', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.035', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.891', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.019', 'prec': 7}, 'traces': [1, -1, 0, -1, -2, 0, 4, 3, -3, 2, 0, 0, -2, -4, 0, -1, 1, 3, -4, 2, 0, 0, 4, 0, -1, 2, 0, -4, 6, 0, 4, -5, 0, -1, -8, 3, -2, 4, 0, -6, -6, 0, 4, 0, 6, -4, 0, 0, 9, 1, 0, 2, 6, 0, 0, 12, 0, -6, -12, 0, -10, -4, -12, 7, 4, 0, 4, -1, 0, 8, -4, -9, -6, 2, 0, 4, 0, 0, 12, 2, 9, 6, -4, 0, -2, -4, 0, 0, 10, -6, -8, -4, 0, 0, 8, 0, 2, -9, 0, 1, -10, 0, 8, -6, 0, -6, 8, 0, 6, 0, 0, -4, -14, 0, -8, -6, 6, 12, 4, 0, -11, 10, 0, -4, 12, 12, 8, 3, 0, -4, 16, 0, -16, -4, 0, 3, -6, 0, -8, 8, 0, 4, 0, 3, -12, 6, 0, 2, -10, 0, -16, -12, -3, 0, -8, 0, -2, -12, 0, 10, 16, -9, 24, 6, 0, 4, -4, 0, -9, 2, 12, -4, 22, 0, -4, 0, 0, -10, 12, -6, -2, 8, 0, 12, 4, 0, 0, 0, 0, -8, -16, 0, 2, -2, 0, -9, -18, 0, -20, -3, 0, 10, 24, 0, 12, -8, -12, 2, 0, 0, 8, -6, 0, -8, -8, 0, 16, -6, 0, 0, -2, 0, 24, -20, 3, 14, -24, 0, 6, 8, 0, 18, -6, -6, 0, 12, 0, -4, -16, 0, 18, 11, 0, 10, -18, 0, 8, 12, 0, -12, 12, 12, 0, -8, 0, -17, 18, 0, -8, -4, -18, -16, -16, 0, -12, 16, 0, -4, 22, 0, -16, -1, 0, 6, 0, 0, 14, 8, -12, -24, -6, 0, -16, 4, 0, 0, -24, 15, 1, 12, 0, 6, 6, 0, 24, -6, 0, 10, -8, 0, 16, 16, 0, 4, 20, 3, -12, 0, 0, 8, 28, 0, -22, 2, 24, -12, -10, 0, 0, -14, 0, -16, -4, -9, 2, -24, 0, -18, 0, 0, 4, 4, 6, 4, -8, 0, -14, 9, 0, 2, 0, -12, 8, 12, 0, -22, 32, 0, -18, 4, 0, 0, -30, 0, 8, -10, 0, -12, 0, 18, -3, 2, 0, 8, 12, 0, 28, -4, 18, -4, 24, 0, 6, 0, 0, 0, -12, 0, -8, -8, 0, 16, -24, 0, 0, -2, -12, -2, 6, 0, 4, 27, 0, 18, -24, 0, 6, 20, 0, 1, -14, 0, -8, 10, -18, -24, 0, 0, 26, -12, 0, -8, -48, 12, 8, 10, 0, 0, 8, 0, 22, -8, 0, 18, -1, 0, -40, -8, 0, 8, 12, 0, 2, -16, 0, -6, -16, 0, -20, 0, -27, 2, 28, 0, -20, -24, 0, 28, 34, -3, 0, 14, 0, 24, 16, 0, -6, -6, 0, 8, -2, 0, 32, -6, 0, 6, 12, -6, 16, 0, 0, -36, 0, 0, 4, -4, -18, 16, 36, 0, 4, -18, 0, 11, -4, 0, 20, -30, 0, 18, 20, 0, 6, -8, 0, -4, -16, 0, -40, -12, 0, -12, -12, -36, 20, 0, 0, -8, -2, 0, -24, 11, 0, -18, -16, 0, 0, 8, 0, 12, 26, 18, -36, -16, 0, 16, 4, 0, -7, 12, 36, 16, 12, 0, -16, 12, 0, -22, 0, 0, 6, 16, 0, -5, -12, 0, -32, 6, 30, 0, -24, 0, 48, -14, 0, 8, 30, 12, -8, 8, 0, 6, -4, 0, 28, 16, 36, -12, -38, 0, -32, 0, 0, 24, -4, -21, -14, -1, 0, 12, -16, 0, 0, -18, -12, -6, 4, 0, -16, -24, 0, 2, 18, 0, -8, 10, 0, 8, -24, 0, 10, -16, -12, 16, 22, 0, 20, 20, 0, -20, 0, 3, -26, 12, 0, 0, -6, 0, -48, 8, 0, -28, 40, 0, -19, 22, 0, 2, -2, -24, 16, 36, 0, 10, -16, 0, -18, 0, 12, -6, -30, 0, 32, -16, 0, 4, 8, 27, 0, -2, 0, -24, 6, 0, -32, 6, 18, 0, 4, 0, 38, -4, 0, -12, 32, -6, 24, 4, 0, 8, 0, 0, 2, 14, 0, 9, 30, 0, 8, -6, 0, 0, -40, -12, 12, -8, 0, -4, -12, 0, -8, -22, 0, -32, 16, 0, -6, 18, 0, 4, -18, 0, 8, 0, 0, 30, -40, 0, -34, -8, -36, 30, 16, 0, 0, -12, 0, 0, 4, -6, 32, 3, 0, 2, -6, 0, 40, -24, -27, -12, 4, 0, -50, -28, 0, -20, 0, -18, 28, -4, 0, -24, 12, 0, 20, -6, 12, 0, 32, 0, 20, 0, 0, 12, 32, 0, 22, 8, 0, 24, -22, 0, 24, 16, 6, 24, 24, 0, -14, 0, 0, -2, -26, 12, -4, 6, 0, -6, 24, 0, 0, -4, 0, -9, 4, 0, -32, 18, 0, 24, -56, 0, 20, -6, 0, 20, -50, 0, 0, 5, -30, 14, 0, 0, -32, 8, 0, -30, 26, 18, 40, -24, 0, 0, -48, 0, -16, -26, 24, -12, -18, 0, 20, 24, 0, 48, -48, 12, -34, -8, 0, -14, 9, 0, 8, 0, 0, -8, 20, 0, 7, -22, 0, -8, 18, 0, -44, -6, 0, 1, -8, 0, 14, 40, -24, 24, 10, 0, 52, 8, 0, -12, 16, 0, -44, -2, 0, -16, 0, 0, -8, 18, -6, 16, 48, 0, 6, 20, 0, 0, -46, 27, -12, 2, 0, -28, 12, 0, 32, 20, 0, -24, 0, 0, -24, 12, 0, -34, 24, -3, 6, 0, 0, -42, 4, 0, 32, 24, 30, -16, -4, 0, 0, 6, 0, -6, 64, 0, 24, -24, 0, 2, 8, 0, 2, -32, -24, -30, -30, 0, -36, 6, 0, -12, 0, 18, 10, -16, 0, 0, 6, 0, -24, 12, 0, 0, 32, 0, 12, -4, 0, 12, -22, 18, 32, 16, 0, -36, -24, 0, -15, -4, -24, -18, -4, 0, 0, -33, 0, 4, -12, 0, -32, -20, 0, 10, 18, 0, 0, 18, -18, -20, 12, 0, 36, -6, 0, -8, 16, 0, -12, -20, 0, 16, 40, 0, 46, 40, 0, 36], 'weight': 2, 'weight_parity': 1}
  5. label: 19.2.a.a
    {'Nk2': 76, 'analytic_conductor': 0.15171576384043273, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[19, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [19, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554451, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '19.2.a.a', 'level': 19, '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': [19], 'level_radical': 19, 'minimal_twist': '19.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\\cdots', 'related_objects': ['EllipticCurve/Q/19/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '19.2.a', 'trace_display': [0, -2, 3, -1], 'trace_hash': 409437620317032020, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.001', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.974', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.011', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.901', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.037', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.623', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.013', 'prec': 7}, 'traces': [1, 0, -2, -2, 3, 0, -1, 0, 1, 0, 3, 4, -4, 0, -6, 4, -3, 0, 1, -6, 2, 0, 0, 0, 4, 0, 4, 2, 6, 0, -4, 0, -6, 0, -3, -2, 2, 0, 8, 0, -6, 0, -1, -6, 3, 0, -3, -8, -6, 0, 6, 8, 12, 0, 9, 0, -2, 0, -6, 12, -1, 0, -1, -8, -12, 0, -4, 6, 0, 0, 6, 0, -7, 0, -8, -2, -3, 0, 8, 12, -11, 0, 12, -4, -9, 0, -12, 0, 12, 0, 4, 0, 8, 0, 3, 0, 8, 0, 3, -8, 6, 0, 14, 0, 6, 0, -18, -8, -16, 0, -4, -4, 6, 0, 0, -12, -4, 0, 3, 0, -2, 0, 12, 8, -3, 0, 2, 0, 2, 0, -15, 12, -1, 0, 12, 0, -3, 0, -13, 6, 6, 0, -12, 4, 18, 0, 12, -4, 21, 0, -10, 0, -3, 0, -12, -16, 14, 0, -24, 0, 0, 0, 20, 12, -18, 0, -18, 0, 3, 0, 1, 2, -18, 0, -4, 12, 12, 0, -18, -6, 2, 0, 2, 0, 6, 0, -9, 6, -4, 0, 3, 16, -4, 0, 24, 12, 18, 0, 11, 0, 8, 0, -6, -12, -18, 0, 0, -16, 3, 0, 14, -24, -12, 0, -3, 0, 4, 0, 14, -18, 12, 0, -10, 0, 4, 0, 12, 4, 5, 0, 6, 0, -21, 0, -9, 12, -16, 0, 15, -24, -10, 0, 10, 2, -18, 0, -4, 0, -24, 0, 21, 2, 0, 0, 18, 16, 0, 0, -2, 24, 6, 0, 9, 0, 36, 0, -24, 8, 24, 0, -16, -12, -8, 0, 12, 0, -19, 0, -4, 0, 6, 0, -13, -12, -6, 0, 6, 0, -8, 0, -16, 14, -12, 0, -18, 0, 12, 0, 0, 16, 1, 0, -12, 4, -3, 0, 20, 6, -28, 0, -3, 0, -10, 0, -3, -16, 6, 0, 18, -24, 36, 0, -3, 22, -16, 0, 32, 0, 3, 0, -28, -24, 2, 0, -12, 8, 32, 0, -12, 18, -12, 0, 13, 0, 0, 0, 21, 24, 17, 0, -16, 0, -6, 0, 18, -24, -6, 0, 15, 0, 1, 0, 4, -8, -21, 0, 8, 0, -6, 0, -12, -16, -4, 0, 6, 0, -24, 0, -34, -6, -4, 0, 12, 0, -9, 0, -1, -16, 15, 0, 0, 0, 30, 0, 24, -6, -7, 0, 2, 16, 12, 0, 16, -12, -33, 0, 6, 0, -4, 0, 6, -28, 6, 0, 36, 0, 26, 0, -12, -12, 8, 0, -3, 0, -12, 0, 1, 36, 24, 0, -24, 16, 2, 0, -36, 32, 0, 0, -10, 0, -6, 0, -3, 8, 36, 0, -42, 8, 0, 0, -18, -12, 20, 0, 12, 0, -37, 0, -12, 0, 9, 0, -31, 24, 24, 0, -27, 8, 4, 0, -28, 0, -3, 0, 4, -6, 12, 0, -12, 0, -8, 0, 0, 4, 24, 0, 2, 0, -40, 0, 12, -24, -18, 0, 9, -16, -6, 0, 5, 6, 36, 0, 12, 0, 18, 0, -6, -4, 0, 0, 7, 0, 4, 0, 42, -4, -9, 0, 36, 0, 0, 0, 38, 30, 8, 0, 12, -24, -23, 0, -6, 2, 24, 0, -54, 0, 36, 0, -18, -24, -25, 0, -4, 0, -48, 0, -28, 6, -1, 0, 6, 0, -8, 0, -12, 26, 21, 0, 4, -12, 18, 0, 6, -12, 18, 0, 11, 0, -24, 0, -4, 24, -6, 0, 0, -8, 11, 0, 8, -36, -12, 0, 36, 0, -12, 0, 45, -24, -4, 0, -36, 8, -42, 0, 9, -42, -22, 0, -36, 0, 26, 0, -4, 20, -6, 0, 32, 0, 12, 0, 12, 6, 29, 0, 36, 0, 9, 0, 44, 24, 0, 0, -12, 32, -29, 0, -6, -28, -6, 0, 11, 0, -28, 0, 6, 48, 24, 0, 6, 0, 0, 0, -13, 0, 6, 0, 27, 0, -18, 0, -8, -40, -39, 0, -45, -24, -7, 0, -30, 36, 32, 0, -24, 0, -3, 0, 0, 36, 20, 0, -3, 0, -10, 0, 16, -6, -42, 0, -8, 0, -24, 0, 36, -2, -9, 0, -10, -4, -48, 0, 17, 36, -3, 0, -39, 0, 18, 0, 42, 8, 6, 0, 2, -24, 18, 0, -6, -24, 26, 0, 8, 0, 0, 0, -36, 36, -30, 0, 15, 12, -14, 0, 20, -4, 24, 0, -19, 0, 13, 0, 3, -4, -22, 0, 36, 0, -12, 0, 11, -12, 8, 0, -24, 0, 63, 0, 12, 18, 18, 0, 32, -12, -42, 0, -30, 8, -25, 0, 0, 0, 33, 0, 16, -6, -9, 0, 24, -32, 23, 0, 0, 8, -6, 0, -16, 0, 4, 0, -6, -48, 18, 0, 24, -24, 42, 0, -4, -36, -18, 0, -6, 0, 4, 0, -72, -22, -12, 0, 9, 0, 12, 0, -21, -16, 0, 0, -48, 0, -9, 0, -16, 12, 32, 0, 60, 24, -1, 0, 4, 36, 33, 0, -49, 0, -24, 0, 12, 0, -16, 0, 38, 32, 18, 0, -54, -6, -16, 0, 18, 0, 7, 0, -12, -28, 9, 0, 2, 48, 26, 0, 0, 24, 26, 0, 3, 0, 18, 0, -49, 6, -12, 0, 18, 0, -54, 0, 16, -8, 24, 0, 16, 0, 8, 0, 3, -28, -22, 0, 24, 36, -27, 0, 47, -24, 36, 0, 18, 0, -2, 0, -33, 20, -3, 0, -54, 0, 0, 0, -24, -8, -36, 0, -2, 0, 6, 0, 8, -24, 6, 0, -6, -8, 36, 0, 6, -10, 15, 0, 20, 0, -40, 0, -24, -12, 8, 0, 14, 0, -18, 0, -6, 42, 6, 0, -27, 0, -7, 0, 20, 18, -18, 0, 0, -24, -12, 0, -36, 32, 28, 0, -12, 0, -48, 0, 9, -30, -36, 0, 3, 48, -15, 0, -18, 20, -12, 0, -40, 0, 6, 0, 60, -20, 13, 0, 32, -4, 24, 0, 36, 36, -16, 0, -36, 0, 54, 0, -6, 8, 0, 0, -34, 0, 56, 0, 33, 48, 17, 0, 8, 0], 'weight': 2, 'weight_parity': 1}
  6. label: 20.2.a.a
    {'Nk2': 80, 'analytic_conductor': 0.15970080404256076, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [5, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [20, 1, [11, 17], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554452, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '20.2.a.a', 'level': 20, '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': '20.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\\cdots', 'related_objects': ['EllipticCurve/Q/20/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '20.2.a', 'trace_display': [0, -2, -1, 2], 'trace_hash': 12896406231020588, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.009', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.977', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.017', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.926', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.064', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.779', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.013', 'prec': 7}, 'traces': [1, 0, -2, 0, -1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, -6, 0, -4, 0, -4, 0, 6, 0, 1, 0, 4, 0, 6, 0, -4, 0, 0, 0, -2, 0, 2, 0, -4, 0, 6, 0, -10, 0, -1, 0, -6, 0, -3, 0, 12, 0, -6, 0, 0, 0, 8, 0, 12, 0, 2, 0, 2, 0, -2, 0, 2, 0, -12, 0, -12, 0, 2, 0, -2, 0, 0, 0, 8, 0, -11, 0, 6, 0, 6, 0, -12, 0, -6, 0, 4, 0, 8, 0, 4, 0, 2, 0, 0, 0, 6, 0, 14, 0, 4, 0, -6, 0, 2, 0, -4, 0, -6, 0, -6, 0, 2, 0, -12, 0, -11, 0, -12, 0, -1, 0, 2, 0, 20, 0, 0, 0, -8, 0, -4, 0, 18, 0, -4, 0, 12, 0, 0, 0, -6, 0, 6, 0, -6, 0, 20, 0, -6, 0, 4, 0, -22, 0, 12, 0, 12, 0, -10, 0, 0, 0, 18, 0, -9, 0, -4, 0, -6, 0, 2, 0, -24, 0, -12, 0, -10, 0, -4, 0, -2, 0, 0, 0, 8, 0, -12, 0, 26, 0, 4, 0, 18, 0, 8, 0, -4, 0, 12, 0, -6, 0, 6, 0, 0, 0, -16, 0, 24, 0, 10, 0, -8, 0, -4, 0, -12, 0, -10, 0, 1, 0, -6, 0, 14, 0, 0, 0, -6, 0, 6, 0, -16, 0, -24, 0, 14, 0, 10, 0, 3, 0, -8, 0, -12, 0, 0, 0, 0, 0, -12, 0, -6, 0, 4, 0, 6, 0, -18, 0, 6, 0, 12, 0, 18, 0, 20, 0, -8, 0, 0, 0, 26, 0, -4, 0, 6, 0, 14, 0, -8, 0, 12, 0, 19, 0, -4, 0, -30, 0, -12, 0, 0, 0, 12, 0, -20, 0, -12, 0, -2, 0, 2, 0, -28, 0, 12, 0, -22, 0, -2, 0, -6, 0, 0, 0, 12, 0, 24, 0, 2, 0, -4, 0, -12, 0, 8, 0, 2, 0, -2, 0, 2, 0, 12, 0, 0, 0, -20, 0, 12, 0, -30, 0, -10, 0, 8, 0, 18, 0, 12, 0, 24, 0, 24, 0, -3, 0, 22, 0, -2, 0, -22, 0, 6, 0, -12, 0, 26, 0, 2, 0, 12, 0, -28, 0, -4, 0, 6, 0, 0, 0, -10, 0, -6, 0, -36, 0, 0, 0, -8, 0, 2, 0, 16, 0, -30, 0, -8, 0, 11, 0, 0, 0, -34, 0, -36, 0, 24, 0, -6, 0, 8, 0, 36, 0, 26, 0, -6, 0, -6, 0, 4, 0, 0, 0, 36, 0, 2, 0, 12, 0, -24, 0, 8, 0, -3, 0, 6, 0, 6, 0, 12, 0, 6, 0, 0, 0, -40, 0, -4, 0, 26, 0, -24, 0, 30, 0, 14, 0, -8, 0, -30, 0, 4, 0, 44, 0, 0, 0, -4, 0, -6, 0, -24, 0, 4, 0, -24, 0, -2, 0, 26, 0, 20, 0, 0, 0, -36, 0, 0, 0, -24, 0, -4, 0, -36, 0, -18, 0, -6, 0, 18, 0, 6, 0, 4, 0, -16, 0, -14, 0, 0, 0, 12, 0, -6, 0, 14, 0, -4, 0, 24, 0, 13, 0, 12, 0, 12, 0, 6, 0, 24, 0, 0, 0, 14, 0, 20, 0, -2, 0, 26, 0, 2, 0, -24, 0, 16, 0, 4, 0, -30, 0, -20, 0, 0, 0, -18, 0, 6, 0, -22, 0, 30, 0, 8, 0, 24, 0, 6, 0, -22, 0, -52, 0, 12, 0, 0, 0, -2, 0, -6, 0, 16, 0, -36, 0, 18, 0, 12, 0, -16, 0, 0, 0, -10, 0, 2, 0, 11, 0, -22, 0, -24, 0, -12, 0, 2, 0, 12, 0, -6, 0, 20, 0, 24, 0, -12, 0, 1, 0, 0, 0, -12, 0, -28, 0, 32, 0, -2, 0, -6, 0, -12, 0, -18, 0, 14, 0, -20, 0, 42, 0, 0, 0, 16, 0, 42, 0, 0, 0, 2, 0, 36, 0, -22, 0, 24, 0, 8, 0, 36, 0, 20, 0, 0, 0, -46, 0, 4, 0, 18, 0, 4, 0, 12, 0, -42, 0, -18, 0, -28, 0, -12, 0, 8, 0, 0, 0, 4, 0, -36, 0, 12, 0, -30, 0, -8, 0, -12, 0, 12, 0, -34, 0, 8, 0, -24, 0, 0, 0, 48, 0, -24, 0, 28, 0, -28, 0, 6, 0, -46, 0, 13, 0, 60, 0, -22, 0, -6, 0, 0, 0, 20, 0, 16, 0, 6, 0, 6, 0, 6, 0, -12, 0, -4, 0, 0, 0, -20, 0, -22, 0, 0, 0, 42, 0, 4, 0, 6, 0, 24, 0, 2, 0, 12, 0, -30, 0, -4, 0, -8, 0, -24, 0, 0, 0, 24, 0, 22, 0, 26, 0, 36, 0, -12, 0, 4, 0, -12, 0, 42, 0, 36, 0, -6, 0, 0, 0, -12, 0, -36, 0, -6, 0, -16, 0, -40, 0, 10, 0, 40, 0, 4, 0, -54, 0, 38, 0, 0, 0, -30, 0, 2, 0, -52, 0, 18, 0, -18, 0, -16, 0, -48, 0, 7, 0, -12, 0, 9, 0, -22, 0, -28, 0, 12, 0, 50, 0, 4, 0, 18, 0, -4, 0, -24, 0, 6, 0, 6, 0, -38, 0, 0, 0, 4, 0, 2, 0, -2, 0, 26, 0, 60, 0, -18, 0, 14, 0, 24, 0, 18, 0, 4, 0, 0, 0, 24, 0, 12, 0, -24, 0, -24, 0, 36, 0, 40, 0, 10, 0, -46, 0, 6, 0, 12, 0, 0, 0, 4, 0, 0, 0, -16, 0, -4, 0, -24, 0, 2, 0, 14, 0, -42, 0, 12, 0, -24, 0, 0, 0, -22, 0, 44, 0, -18, 0, 36, 0, -8, 0, 18, 0, 4, 0, 12, 0, -6, 0, 12, 0, 0, 0, 36, 0, -15, 0, -6, 0, -26, 0, -22, 0, -48, 0, -24, 0, -8, 0, -4, 0, 18, 0, 0, 0, 2, 0, -18, 0, -18, 0, 24, 0, -60, 0, -4, 0, -16, 0, -8, 0, 26, 0, 8, 0], 'weight': 2, 'weight_parity': 1}
  7. label: 21.2.a.a
    {'Nk2': 84, 'analytic_conductor': 0.1676858442446888, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1], [7, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [21, 1, [8, 10], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554453, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '21.2.a.a', 'level': 21, '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, 7], 'level_radical': 21, 'minimal_twist': '21.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/21/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '21.2.a', 'trace_display': [-1, 1, -2, -1], 'trace_hash': 1161919666425559947, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.019', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.978', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.032', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.908', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.050', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.694', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, 'traces': [1, -1, 1, -1, -2, -1, -1, 3, 1, 2, 4, -1, -2, 1, -2, -1, -6, -1, 4, 2, -1, -4, 0, 3, -1, 2, 1, 1, -2, 2, 0, -5, 4, 6, 2, -1, 6, -4, -2, -6, 2, 1, -4, -4, -2, 0, 0, -1, 1, 1, -6, 2, 6, -1, -8, -3, 4, 2, 12, 2, -2, 0, -1, 7, 4, -4, 4, 6, 0, -2, 0, 3, -6, -6, -1, -4, -4, 2, -16, 2, 1, -2, -12, 1, 12, 4, -2, 12, -14, 2, 2, 0, 0, 0, -8, -5, 18, -1, 4, 1, 14, 6, 8, -6, 2, -6, 4, -1, -18, 8, 6, 1, -14, -4, 0, 2, -2, -12, 6, -6, 5, 2, 2, 0, 12, 1, 0, 3, -4, -4, 4, -4, -4, -4, -2, -18, -6, 0, 12, -2, 0, 0, -8, -1, 4, 6, 1, -6, 6, 1, 8, 12, -6, 4, 0, 2, -2, 16, 6, 10, 0, -1, 4, -2, -8, 12, -8, -3, -9, -12, 4, 4, -10, 2, 1, -4, 12, 14, -4, 2, -26, -2, -2, 0, -12, 0, -24, 0, -1, 8, -8, 7, 2, -18, 4, -1, 22, -4, 24, -3, 4, -14, 2, 6, -4, -8, 0, 2, 16, -2, 4, -6, 0, -4, 8, 3, 0, 18, -6, 8, 12, -6, 16, 5, -1, 14, -12, -4, -10, 0, -4, -6, -6, 2, 0, -12, -16, -6, 24, 2, 2, -5, 1, 2, -2, -2, -8, 0, -12, -12, -20, 1, 0, 0, 12, -17, 26, 4, -6, -4, -2, -4, 16, 12, -12, 4, -14, -4, 6, 2, 16, 6, 2, 6, -4, 0, 22, -12, 0, 6, -22, 0, -20, 0, -8, 8, -2, -5, 19, -4, 18, 6, 14, -1, -24, 18, 4, -6, 0, 1, 4, -8, 14, -4, 4, 6, 4, 4, 8, 0, -24, -6, 26, 2, 2, 16, -18, -6, -8, -14, 4, 0, -24, -1, 2, -4, -18, 6, 0, 8, -4, 12, 6, 8, -8, 1, -14, 9, -14, -12, 0, -4, -1, -12, 0, 10, -28, 2, -2, -1, -2, -20, 10, -12, 0, 14, 6, 4, 32, -6, -3, 26, 5, -2, 12, 2, 0, 0, 2, 12, -6, 0, -10, 24, 12, 0, 4, 1, 12, 8, 0, 8, 0, 3, 8, -2, -4, -18, 6, -4, 0, 3, 4, -22, 32, -4, -18, -24, -4, 1, -30, -4, 0, -14, -2, -2, 24, -18, -22, 4, -6, -8, -12, 0, 24, 10, 12, -16, -12, -2, 38, -4, 0, 18, 6, 0, 2, -4, -8, -8, -24, -1, -14, 0, 4, 18, 0, 6, -24, -24, 1, -12, 36, -6, 28, -16, 6, -7, -30, 1, 8, 14, 8, 12, -4, 12, 10, 10, -6, 0, -10, 4, 16, 2, 0, 6, 36, 2, -4, 0, -2, 36, -16, 16, -4, -6, 6, -24, -16, 10, -12, -2, 0, -5, -36, -1, -8, -6, 4, 2, 20, -2, 12, 8, -8, 0, 0, 12, 4, -12, -8, 20, 24, -3, -28, 0, -9, 0, -10, -12, 6, 11, 4, -26, -16, 4, 0, 6, -10, 12, 18, 2, -20, -4, 1, -16, 0, -4, -23, 12, 12, 4, -4, 14, -8, 12, -4, -6, 4, 2, -34, -16, -26, 30, 36, -2, 4, 6, -2, 4, -8, 0, 16, -22, -12, -12, -2, 0, 8, -2, -24, 22, 4, 0, 28, 20, -1, 0, 10, 8, -4, 8, -8, 2, 0, 7, 34, -19, 2, -4, 12, -18, 24, -18, 4, -14, 28, -1, 0, 24, 22, -6, -6, -4, -12, -6, 24, 0, 48, -3, -6, -4, 4, -8, -10, -14, -16, -20, 2, -4, 0, 6, -26, -4, -4, -12, -6, -8, -20, 0, 0, 24, 14, 2, -19, -26, 16, 2, -36, -2, -40, -48, 4, 18, 0, -6, -2, 8, 0, -6, 18, -4, 20, 0, 8, 24, -40, 3, 48, -2, 0, -4, -18, 18, -8, -2, -6, 0, 12, 8, 22, 4, 12, -36, 8, -6, 0, 8, 16, 8, -8, 5, 34, 14, -1, 9, -18, 14, -18, 36, -12, 0, -12, -4, 12, 1, -10, 4, -12, 0, 20, 10, -4, 28, -24, -6, -12, 2, -6, -1, 30, 2, 24, 28, 0, -10, -14, -12, 6, 0, -16, -42, 0, -6, 16, 4, 24, -32, -48, 2, -8, 3, 2, 26, 2, -5, -40, 6, 1, -12, 24, 2, -18, 0, -2, 0, 16, -2, 36, 12, -8, 6, 0, 0, -12, 10, -12, 24, -4, -12, -32, 0, -20, -4, -16, 1, -10, -12, 0, -24, 18, 0, 18, 8, 12, 0, -24, -17, 2, -8, 26, -2, 14, 4, 0, 54, -6, -6, 8, -4, 0, 0, -2, -1, 4, -4, -44, -22, 16, -32, 14, 12, 4, 18, -12, -24, -26, 4, 0, 5, -14, 30, -24, -4, 0, 0, 6, 42, 42, 2, 44, -2, 16, -24, -8, 6, -16, 22, 2, 4, 38, 6, 24, 24, -4, 12, -12, 0, 14, -24, 22, -14, -6, -12, 16, -16, 0, 12, -8, 6, -25, -38, -22, -4, 18, 0, -5, -6, -20, -6, 0, 0, -10, -2, -8, 12, -14, 8, 44, -8, -2, 24, -24, -5, 20, 14, 19, 0, -64, -4, -8, -54, 18, 0, -12, 6, 46, 24, 14, 8, -6, -1, -28, -12, -24, -36, 8, 18, 0, -28, 4, -16, 0, -6, 8, -3, 0, 30, 0, 1, -36, -8, 4, -42, 52, -8, -4, 12, 14, 4, -24, -4, -48, -10, 4, 10, -4, 6, 8, 0, 4, 10, 0, 4, -6, -16, 8, 10, 26, 0, 4, 6, -24, -36, 48, -6, 42, 4, 26, 0, 38, 2, 0, -12, 2, 16, 44, 16, 12, 4, -18, 18, 26, -6, 16, -24, -8, 16, 6, -14, -31, 12, 4, -2, -4, 0, 40, 15, -24, 36, 12, -1, -12, 8, 2, 2, -30, -4, -56, 2, -18, -20, 24, 6, -44, -12, 0, 8, 0, 8, -16, 0, -4, 0, -48, 12, -26, -4, 6, 36], 'weight': 2, 'weight_parity': 1}
  8. label: 23.2.a.a
    {'Nk2': 92, 'analytic_conductor': 0.1836559246489449, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[23, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [23, 1, [5], [1]], 'cm_discs': [], 'conrey_index': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554455, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '23.2.a.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': '23.2.a.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 1, 'qexp_display': 'q-\\beta q^{2}+(-1+2\\beta )q^{3}+(-1+\\beta )q^{4}+\\cdots', 'related_objects': ['Genus2Curve/Q/529/a'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '23.2.a', 'trace_display': [-1, 0, -2, 2], 'trace_hash': 1804802565588895238, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.032', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.942', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.410', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.238', 'prec': 14}, {'__RealLiteral__': 0, 'data': '4.351', 'prec': 14}, {'__RealLiteral__': 0, 'data': '61.290', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.027', 'prec': 7}, 'traces': [2, -1, 0, -1, -2, -5, 2, 0, 4, 6, -6, 5, 6, 4, -10, -3, 6, -2, -4, -4, -10, -2, 2, 10, 2, -3, 0, -6, -6, 10, 0, 9, 10, -8, 8, -2, 2, 2, 0, -10, 2, 0, 0, 8, -4, -1, 0, -15, -2, -11, 10, -3, -8, 5, -4, -10, 0, 3, 4, 0, 4, 15, 4, 4, -6, 10, -10, 2, 0, -4, 20, 0, 22, -6, 20, 2, -16, -15, -4, 18, -22, -11, -22, 10, -16, 0, 0, 10, -12, 12, 6, -1, -30, -5, 4, -5, 22, 11, -12, 9, 0, -20, 14, 0, 0, 14, 0, -5, 0, -8, 10, 12, 22, 10, -2, 3, 12, 8, -4, -10, 6, -22, 20, -15, -12, 8, -28, -25, 0, 18, 24, -20, -4, 10, 10, 10, -8, -5, -8, -4, 10, -5, -18, -6, 6, -21, -20, 4, 12, -15, 4, 0, 12, -12, 30, 15, 4, -18, -20, -4, 2, 11, -16, 9, 20, 16, 12, 10, -8, 28, -8, 0, 28, 15, -18, -6, -20, -4, -12, -8, 2, 12, 40, 0, -12, 15, -8, 5, 10, -12, -30, 10, 2, 4, -30, -9, 6, -4, -38, 20, -10, 10, -6, 10, -22, -32, 4, -9, 12, -20, -20, -6, -10, 30, 0, -10, 30, 0, 20, 12, 18, -10, 8, 14, 4, -16, -2, -10, -24, 6, 40, 0, -22, -6, -10, -12, 40, 12, 32, 30, -6, 27, 0, 18, 22, -15, -12, -30, -10, -4, 18, -12, -6, 29, -40, 7, -6, 0, -8, -12, -12, 3, -12, -30, 28, -8, 20, 0, 2, -10, 16, -24, -30, -36, 14, 5, 22, -11, 0, 0, -22, -5, 42, -15, 20, -6, -18, 18, -6, -18, -30, -1, -12, 15, 16, 10, -10, 34, 6, -5, 0, 3, -20, 6, -44, -16, 28, 28, 50, -30, 4, 30, 4, -32, 16, 22, 24, 30, 18, -14, -60, 4, -12, 11, 6, 13, 0, 20, -10, 0, -8, 6, 4, -16, 20, 0, 20, 4, 10, -12, -30, 4, 4, 0, -10, 6, 16, -15, 22, 4, 0, -32, -26, 0, -10, 16, -20, 21, -4, -20, -30, 34, -60, -18, -42, -30, 14, -3, 4, 16, 12, 15, 2, 4, 20, 10, -18, 0, 4, 8, -30, -10, 32, -5, -24, 19, 0, -26, 60, 30, 6, -20, -30, -13, -36, 16, -22, 34, 20, -33, -6, 30, 0, -10, 22, -12, 4, 30, -2, 26, 80, 18, 24, -2, 32, 27, 30, 4, -36, 20, -34, -20, 0, -20, 26, -45, -36, -30, 30, 0, -44, 15, 58, 0, 30, 0, -4, -65, -24, 20, -4, -24, 36, 0, -8, -4, -80, -6, -12, -22, 14, -6, -10, -24, 24, -20, 30, 12, -10, -4, 6, 20, -40, 9, 30, 21, -44, -6, 0, 10, 60, -20, 0, -10, -4, -8, -16, -21, 14, -40, 6, -42, -10, -33, 8, 40, -16, 40, -10, -26, 48, -5, -18, 6, -8, 45, 30, 60, 52, 16, 20, -24, -36, -20, 20, -2, 0, -1, 6, 60, 2, 24, 0, -7, -64, 0, 10, 4, -40, -30, 36, 6, 42, -27, 10, 26, -30, 30, 2, -44, 8, 12, 6, 20, 60, -10, -30, -21, -14, 0, -42, -8, -70, 22, 0, 0, 8, 44, 8, 18, 12, 10, -44, -1, -20, 19, 12, 30, 0, -12, 0, 16, -48, -5, -32, -6, -22, -10, -22, -20, -42, 24, 50, 4, 2, 8, 10, -27, -40, 12, -12, -40, 4, 20, -12, 16, -36, 5, 0, -8, 20, -18, 12, -10, 24, -46, -30, -3, 32, 10, 58, 0, -20, -7, 54, 10, 44, -18, 30, 52, 0, 4, -2, -24, -30, 40, -24, -60, 12, 0, 0, 23, -32, -45, -18, 48, -20, 28, 16, -8, -20, 40, 60, 18, 58, -10, -6, 6, 40, 30, 28, 30, -10, -6, 0, 16, 0, 0, -32, -33, -30, 3, -14, 0, 6, -33, 44, 0, 10, -20, -28, -31, 30, -10, -16, -12, -6, 4, 0, -40, 28, -50, 6, 20, -20, 4, 36, -60, 52, -40, 50, -30, 4, 4, -72, -32, 0, 0, -24, 10, 32, -34, -32, -48, -22, -30, 26, 19, -20, 14, -30, 15, -4, -2, -10, 63, 20, 20, -26, 50, -8, 20, 0, 20, -12, -9, 10, -38, -24, 36, -36, 15, 90, -36, -6, 15, -42, -30, -14, 86, 0, -10, -58, -32, 30, 9, 20, -22, 76, -4, 0, -16, 42, 0, 68, 14, -44, 4, 60, 20, -44, -15, 30, 9, 6, -10, -46, 48, 10, 20, 30, 85, 0, 40, -32, -36, 12, 45, -6, -8, 20, -21, -20, 0, -60, -30, 0, -40, -4, 0, -70, -8, 0, 33, -64, -45, 76, 7, -40, 28, 12, 20, 12, -19, 60, 4, -24, 0, 10, -1, -24, -22, -46, -20, 8, 45, 40, -20, 60, -66, -80, 18, 0, 8, 26, -60, 0, 51, 12, -4, -60, -20, -12, 50, -50, 8, 12, -2, 0, -76, -20, 12, -26, 5, -32, -16, 30, 48, -42, 40, -40, 32, -10, 40, 8, -10, 66, 42, -30, -48, 2, 55, -48, 8, 8, -60, -6, 30, -20, 0, 10, 32, 24, 5, 12, -54, 60, -30, 52, -30, -30, 0, 44, 2, -32, 45, -64, -3, -20, -24, 66, 22, 8, 6, 0, 27, -12, 10, 2, -16, 66, -4, 0, 10, 42, -20, 0, -14, 0, 18, -44, 18, 0, 10, 68, -5, 0, 26, 0, -12, 0, 30, 56, -60, -60, 12, 54, 20, 42, -10, 20, -13, 60, -60, 22, 20, 28, -27, -66, -90, 4, 1, -50, 42, 8, 0, 46, -20, -100, 0, -18, -40, 2, 24, 0, 0, -44, -30, 66, 22, -60, -20, 32, 28, -20, -11, -30, 48, -88, -30, 28, -18, 0, 48, 38, 0, -12, -60, -20, 36, 24, -40, -38, -7, 60, -66, -78, 45, 56, 4, 0, -59, -72, 10, -26, 24, 10, 6, 0, -16, 48, 15, 70, 40, 68, -50, -20, -41, -10, 20], 'weight': 2, 'weight_parity': 1}
  9. label: 24.2.a.a
    {'Nk2': 96, 'analytic_conductor': 0.19164096485107293, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [3, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [24, 1, [7, 13, 17], [1, 1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554456, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '24.2.a.a', 'level': 24, '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], 'level_radical': 6, 'minimal_twist': '24.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\\cdots', 'related_objects': ['EllipticCurve/Q/24/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '24.2.a', 'trace_display': [0, -1, -2, 0], 'trace_hash': 906478665263567321, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.981', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.050', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.915', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.147', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.664', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.017', 'prec': 7}, 'traces': [1, 0, -1, 0, -2, 0, 0, 0, 1, 0, 4, 0, -2, 0, 2, 0, 2, 0, -4, 0, 0, 0, -8, 0, -1, 0, -1, 0, 6, 0, 8, 0, -4, 0, 0, 0, 6, 0, 2, 0, -6, 0, 4, 0, -2, 0, 0, 0, -7, 0, -2, 0, -2, 0, -8, 0, 4, 0, 4, 0, -2, 0, 0, 0, 4, 0, -4, 0, 8, 0, 8, 0, 10, 0, 1, 0, 0, 0, -8, 0, 1, 0, -4, 0, -4, 0, -6, 0, -6, 0, 0, 0, -8, 0, 8, 0, 2, 0, 4, 0, -18, 0, 16, 0, 0, 0, -12, 0, -2, 0, -6, 0, 18, 0, 16, 0, -2, 0, 0, 0, 5, 0, 6, 0, 12, 0, -8, 0, -4, 0, -4, 0, 0, 0, 2, 0, -6, 0, -12, 0, 0, 0, -8, 0, -12, 0, 7, 0, 14, 0, -16, 0, 2, 0, -16, 0, -2, 0, 2, 0, 0, 0, 12, 0, 8, 0, 24, 0, -9, 0, -4, 0, 6, 0, 0, 0, -4, 0, 12, 0, 6, 0, 2, 0, -12, 0, 8, 0, 0, 0, 0, 0, 2, 0, -4, 0, -18, 0, 16, 0, 4, 0, 0, 0, 12, 0, -8, 0, -16, 0, -20, 0, -8, 0, -8, 0, 0, 0, -10, 0, -4, 0, -8, 0, -1, 0, 12, 0, 22, 0, 0, 0, 10, 0, 0, 0, 8, 0, -16, 0, 18, 0, -1, 0, 14, 0, 8, 0, 4, 0, 20, 0, -32, 0, 4, 0, 2, 0, 0, 0, 6, 0, -8, 0, 4, 0, 6, 0, -10, 0, 8, 0, 0, 0, -4, 0, -26, 0, 8, 0, 26, 0, -28, 0, -8, 0, 0, 0, -13, 0, -2, 0, -18, 0, -8, 0, -4, 0, 16, 0, 0, 0, 18, 0, 4, 0, 12, 0, -16, 0, -24, 0, -6, 0, 0, 0, 6, 0, 24, 0, 12, 0, -8, 0, 2, 0, 2, 0, 0, 0, 20, 0, 6, 0, 8, 0, 18, 0, -18, 0, 32, 0, 0, 0, -16, 0, -12, 0, 30, 0, 2, 0, 2, 0, -16, 0, 0, 0, -24, 0, -3, 0, -5, 0, -20, 0, -8, 0, -6, 0, 0, 0, -10, 0, -12, 0, -12, 0, 20, 0, 8, 0, 0, 0, 0, 0, 4, 0, -2, 0, -16, 0, 4, 0, 16, 0, 14, 0, 0, 0, -30, 0, -16, 0, -2, 0, 24, 0, -6, 0, 6, 0, 0, 0, 8, 0, 12, 0, 12, 0, -10, 0, 0, 0, -2, 0, 0, 0, 8, 0, 32, 0, -14, 0, 12, 0, 32, 0, 0, 0, -7, 0, 20, 0, 12, 0, -14, 0, -14, 0, -24, 0, 16, 0, 0, 0, -22, 0, -2, 0, -26, 0, 8, 0, 16, 0, -36, 0, 0, 0, 2, 0, 16, 0, 4, 0, -2, 0, -16, 0, -12, 0, 0, 0, -4, 0, -32, 0, -12, 0, -12, 0, 12, 0, -8, 0, 0, 0, 12, 0, -24, 0, 24, 0, 36, 0, 9, 0, 6, 0, 0, 0, 4, 0, -32, 0, 0, 0, -6, 0, 26, 0, 4, 0, 0, 0, 16, 0, 41, 0, 4, 0, 12, 0, 24, 0, -12, 0, -28, 0, -18, 0, -6, 0, 4, 0, 44, 0, -2, 0, -24, 0, 0, 0, 12, 0, -26, 0, -8, 0, -8, 0, 28, 0, -36, 0, 0, 0, 10, 0, 36, 0, 0, 0, 8, 0, 2, 0, -2, 0, 0, 0, -8, 0, 4, 0, -44, 0, -32, 0, 18, 0, -14, 0, 0, 0, -16, 0, 24, 0, -38, 0, -4, 0, -10, 0, -40, 0, 0, 0, 0, 0, 38, 0, -12, 0, 42, 0, -44, 0, 8, 0, 0, 0, -19, 0, 16, 0, 12, 0, 16, 0, 20, 0, 16, 0, 14, 0, 8, 0, -14, 0, 12, 0, 8, 0, 8, 0, 16, 0, 0, 0, 6, 0, 8, 0, 10, 0, 12, 0, -10, 0, 4, 0, 0, 0, -48, 0, 8, 0, -8, 0, 34, 0, 1, 0, -2, 0, 0, 0, -12, 0, 4, 0, 12, 0, -22, 0, 4, 0, -4, 0, 0, 0, 24, 0, -12, 0, -10, 0, 6, 0, -24, 0, 0, 0, 0, 0, -10, 0, -8, 0, -64, 0, 16, 0, 16, 0, -32, 0, 0, 0, -18, 0, -6, 0, 48, 0, 1, 0, 8, 0, 14, 0, -14, 0, -16, 0, -4, 0, -8, 0, -8, 0, -28, 0, -4, 0, 0, 0, 24, 0, -20, 0, 32, 0, 38, 0, 32, 0, -22, 0, 0, 0, -4, 0, -8, 0, 2, 0, -2, 0, -18, 0, -8, 0, 0, 0, 24, 0, 32, 0, -6, 0, 4, 0, 28, 0, 8, 0, 0, 0, 4, 0, -4, 0, 22, 0, 0, 0, -6, 0, 40, 0, 0, 0, 10, 0, 26, 0, 4, 0, -8, 0, -24, 0, -16, 0, 0, 0, 30, 0, -16, 0, 4, 0, -28, 0, -50, 0, 26, 0, -14, 0, -48, 0, -8, 0, -24, 0, 7, 0, -26, 0, 18, 0, 0, 0, 28, 0, -48, 0, -10, 0, 8, 0, 42, 0, -12, 0, 0, 0, -32, 0, -12, 0, 13, 0, -32, 0, 8, 0, 2, 0, 0, 0, -18, 0, 18, 0, 50, 0, -4, 0, 8, 0, 8, 0, 0, 0, 4, 0, 0, 0, -24, 0, -16, 0, 48, 0, -4, 0, 0, 0, -12, 0, 4, 0, -18, 0, 16, 0, -16, 0, -4, 0, 0, 0, 16, 0, -12, 0, -16, 0, -6, 0, 16, 0, 50, 0, 28, 0, 24, 0, -16, 0, 42, 0, 6, 0, 6, 0, 48, 0, 0, 0, 12, 0, -20, 0, -6, 0, -54, 0, 0, 0, -24, 0, 0, 0, 33, 0, -12, 0, -4, 0, -16, 0, 8, 0, 36, 0, 0, 0, -2, 0, -30, 0, -24, 0, -2, 0, -24, 0, 36, 0, 0, 0, -32, 0, 40, 0, -20, 0, -32, 0, -26, 0, -6, 0], 'weight': 2, 'weight_parity': 1}
  10. label: 26.2.a.a
    {'Nk2': 104, 'analytic_conductor': 0.207611045255329, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [13, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [26, 1, [15], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554458, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '26.2.a.a', 'level': 26, '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': [2, 13], 'level_radical': 26, 'minimal_twist': '26.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/26/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '26.2.a', 'trace_display': [-1, 1, -3, -1], 'trace_hash': 2069639601307544454, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.985', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.026', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.942', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.108', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.762', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [1, -1, 1, 1, -3, -1, -1, -1, -2, 3, 6, 1, 1, 1, -3, 1, -3, 2, 2, -3, -1, -6, 0, -1, 4, -1, -5, -1, 6, 3, -4, -1, 6, 3, 3, -2, -7, -2, 1, 3, 0, 1, -1, 6, 6, 0, 3, 1, -6, -4, -3, 1, 0, 5, -18, 1, 2, -6, -6, -3, 8, 4, 2, 1, -3, -6, 14, -3, 0, -3, -3, 2, 2, 7, 4, 2, -6, -1, 8, -3, 1, 0, 12, -1, 9, 1, 6, -6, -6, -6, -1, 0, -4, -3, -6, -1, -10, 6, -12, 4, -12, 3, -4, -1, 3, 0, 12, -5, -7, 18, -7, -1, -6, -2, 0, 6, -2, 6, 3, 3, 25, -8, 0, -4, 3, -2, 20, -1, -1, 3, -21, 6, -2, -14, 15, 3, 0, 0, -13, 3, 3, 3, 6, -2, -18, -2, -6, -7, -6, -4, 17, -2, 6, 6, 12, 1, 14, -8, 0, 3, 0, -1, -16, 0, -18, -12, 0, 1, 1, -9, -4, -1, 0, -6, -4, 6, -6, 6, 3, 6, 20, 1, 8, 0, 21, 4, -18, 3, 5, 6, -18, 1, -4, 10, -3, -6, 3, 12, 2, -4, 14, 12, -6, -3, 0, 4, 0, 1, 12, -3, -13, 0, -3, -12, 3, 5, 4, 7, 2, -18, -3, 7, -19, 1, -8, 6, 0, 2, -13, 0, -6, -6, -27, 2, -9, -6, 8, -3, 15, -3, -10, -25, 16, 8, 18, 0, 2, 4, 12, -3, 24, 2, 0, -20, 9, 1, 9, 1, 7, -3, -12, 21, -12, -6, 0, 2, -6, 14, 24, -15, 11, -3, -1, 0, 24, 0, -28, 13, 8, -3, -6, -3, -4, -3, -6, -6, 0, 2, -8, 18, -10, 2, 21, 6, 18, 7, -30, 6, 0, 4, 1, -17, -12, 2, -24, -6, 2, -6, -4, -12, -30, -1, -1, -14, -6, 8, -6, 0, 36, -3, 12, 0, -6, 1, 4, 16, -7, 0, -3, 18, 8, 12, 14, 0, -42, -1, 23, -1, -6, 9, -24, 4, 13, 1, 0, 0, 3, 6, -19, 4, -5, -6, 24, 6, 9, -6, 3, -3, 0, -6, -15, -20, 25, -1, -6, -8, 26, 0, 0, -21, 0, -4, -4, 18, 3, -3, 6, -5, 20, -6, 20, 18, 21, -1, 18, 4, 2, -10, -6, 3, 0, 6, -21, -3, -24, -12, -34, -2, -2, 4, 36, -14, -4, -12, -3, 6, -42, 3, 32, 0, 0, -4, 6, 0, -36, -1, -13, -12, 9, 3, 17, 13, -6, 0, -12, 3, -8, 12, 6, -3, -33, -5, -25, -4, -18, -7, 0, -2, 26, 18, 12, 3, 21, -7, 18, 19, -6, -1, 6, 8, 0, -6, 17, 0, 3, -2, -10, 13, 15, 0, 9, 6, -40, 6, 12, 27, 36, -2, -14, 9, 14, 6, -6, -8, 8, 3, 0, -15, -21, 3, -7, 10, 0, 25, 30, -16, -16, -8, -16, -18, -9, 0, -18, -2, 36, -4, 3, -12, -40, 3, 0, -24, -30, -2, 36, 0, 1, 20, -18, -9, -2, -1, -10, -9, 12, -1, 18, -7, 0, 3, -9, 12, 20, -21, -4, 12, 12, 6, -23, 0, 12, -2, 0, 6, -36, -14, 3, -24, -36, 15, 11, -11, 20, 3, 21, 1, 17, 0, -16, -24, 12, 0, -8, 28, 21, -13, 3, -8, -1, 3, -18, 6, 39, 3, 18, 4, -1, 3, 15, 6, 5, 6, -18, 0, 0, -2, 38, 8, -4, -18, -12, 10, 0, -2, 6, -21, 24, -6, -8, -18, 3, -7, 18, 30, -9, -6, 2, 0, 6, -4, -19, -1, -28, 17, -75, 12, 14, -2, -6, 24, 3, 6, 38, -2, 0, 6, -24, 4, -28, 12, 0, 30, 6, 1, -29, 1, 12, 14, 21, 6, 29, -8, -13, 6, -60, 0, -6, -36, 6, 3, -18, -12, 14, 0, 3, 6, -6, -1, -36, -4, 4, -16, 0, 7, 63, 0, -4, 3, -36, -18, -22, -8, -3, -12, 6, -14, 0, 0, -19, 42, 48, 1, -19, -23, -20, 1, 48, 6, 10, -9, 0, 24, 24, -4, 0, -13, -13, -1, 0, 0, 8, 0, 12, -3, 39, -6, 0, 19, -27, -4, 0, 5, -14, 6, -9, -24, 12, -6, 26, -9, -16, 6, 0, -3, -18, 3, 15, 0, 6, 6, 4, 15, -10, 20, 24, -25, -10, 1, 13, 6, 3, 8, 23, -26, 18, 0, 84, 0, 20, 21, 2, 0, -9, 4, 18, 4, -24, -18, -12, -3, -40, 3, 24, -6, -51, 5, -16, -20, 0, 6, -6, -20, 7, -18, -18, -21, -6, 1, 32, -18, 9, -4, -39, -2, -16, 10, 7, 6, 0, -3, -18, 0, -30, -6, -42, 21, -40, 3, -12, 24, 6, 12, 8, 34, 0, 2, -42, 2, -9, -4, 12, -36, 12, 14, 0, 4, 24, 12, -33, 3, 20, -6, 11, 42, 48, -3, -2, -32, 2, 0, -3, 0, 14, 4, 24, -6, 18, 0, 38, 36, -28, 1, 18, 13, 0, 12, 20, -9, 0, -3, 7, -17, -6, -13, -3, 6, -25, 0, -4, 12, 0, -3, -37, 8, 12, -12, -42, -6, -4, 3, 0, 33, -45, 5, 0, 25, -8, 4, 48, 18, 14, 7, 20, 0, -3, 2, -13, -26, 21, -18, 21, -12, 29, -3, 18, -21, 0, 7, -20, -18, 6, -19, 6, 6, -9, 1, 0, -6, -24, -8, 0, 0, 1, 6, -60, -17, -37, 0, 24, -3, 30, 2, 72, 10, -24, -13, 21, -15, -16, 0, 2, -9, -3, -6, -28, 40, 8, -6, 36, -12, -12, -27, -30, -36, 54, 2, -34, 14, -1, -9, -21, -14, 0, -6, -15, 6, 6, 8, 2, -8, -6, -3, 15, 0, 54, 15, 36, 21, 0, -3, -15, 7, -24, -10, 12, 0, -31, -25, -6, -30, -3, 16, 13, 16, 4, 8, -54, 16, -36, 18, 14, 9, 39, 0, -9, 18, -3, 2, 0, -36, 2, 4, 8, -3, -6, 12, -46, 40, 35, -3], 'weight': 2, 'weight_parity': 1}
  11. label: 26.2.a.b
    {'Nk2': 104, 'analytic_conductor': 0.207611045255329, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [13, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [26, 1, [15], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [3, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924954, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '26.2.a.b', 'level': 26, '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': [2, 13], 'level_radical': 26, 'minimal_twist': '26.2.a.b', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/26/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '26.2.a', 'trace_display': [1, -3, -1, 1], 'trace_hash': 1458165707980378714, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.009', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.995', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.002', 'prec': 4}, {'__RealLiteral__': 0, 'data': '1.979', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.973', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.017', 'prec': 7}, 'traces': [1, 1, -3, 1, -1, -3, 1, 1, 6, -1, -2, -3, -1, 1, 3, 1, -3, 6, 6, -1, -3, -2, -4, -3, -4, -1, -9, 1, 2, 3, 4, 1, 6, -3, -1, 6, 3, 6, 3, -1, 0, -3, -5, -2, -6, -4, 13, -3, -6, -4, 9, -1, 12, -9, 2, 1, -18, 2, -10, 3, -8, 4, 6, 1, 1, 6, -2, -3, 12, -1, -5, 6, -10, 3, 12, 6, -2, 3, -4, -1, 9, 0, 0, -3, 3, -5, -6, -2, 6, -6, -1, -4, -12, 13, -6, -3, 14, -6, -12, -4, 4, 9, -8, -1, 3, 12, -4, -9, 19, 2, -9, 1, 2, -18, 4, 2, -6, -10, -3, 3, -7, -8, 0, 4, 9, 6, 16, 1, 15, 1, -1, 6, 6, -2, 9, -3, 12, 12, 7, -1, -39, -5, 2, 6, -2, -10, 18, 3, -18, 12, -9, 6, -18, -2, -4, 3, -10, -4, -36, -1, -4, 9, -4, 0, -6, 0, 0, -3, 1, 3, 36, -5, 20, -6, -4, -2, 30, 6, -9, -6, 0, -1, 24, -4, -3, -12, 6, 13, -9, -6, 10, -3, -16, 14, -3, -6, 9, -12, -10, -4, 6, 4, 2, 9, 0, -8, -24, -1, -12, 3, 23, 12, 15, -4, 5, -9, 4, 19, 30, 2, 3, -9, -21, 1, -24, 2, -24, -18, -15, 4, 6, 2, -11, -6, -13, -10, 12, -3, 9, 3, 18, -7, 0, -8, 6, 0, -6, 4, 0, 9, 0, 6, 8, 16, -9, 1, -15, 15, 3, 1, 12, -1, 12, 6, -12, 6, -18, -2, -24, 9, 13, -3, 3, 12, 8, 12, 12, 7, 24, -1, -26, -39, 4, -5, 18, 2, 0, 6, -8, -2, -42, -10, 7, 18, 10, 3, 18, -18, 4, 12, -5, -9, -12, 6, 8, -18, 14, -2, 24, -4, 18, 3, -1, -10, -6, -4, -18, -36, -4, -1, 12, -4, -18, 9, 4, -4, -57, 0, 13, -6, -4, 0, 18, 0, 2, -3, 23, 1, -6, 3, -8, 36, -13, -5, -12, 20, -9, -6, 7, -4, 9, -2, 4, 30, 5, 6, 9, -9, 24, -6, 17, 0, 21, -1, 10, 24, -10, -4, 0, -3, 12, -12, -4, 6, -27, 13, -2, -9, 16, -6, -48, 10, 27, -3, 2, -16, -30, 14, -30, -3, 12, -6, 3, 9, 4, -12, -22, -10, -18, -4, 24, 6, -4, 4, -9, 2, -6, 9, 4, 0, -36, -8, -10, -24, 0, -1, -21, -12, 21, 3, -5, 23, 78, 12, 12, 15, -8, -4, -6, 5, 33, -9, 7, 4, 6, 19, -24, 30, -22, 2, -36, 3, -39, -9, -6, -21, 54, 1, -26, -24, 0, 2, 27, -24, 1, -18, 10, -15, 27, 4, -21, 6, 16, 2, 12, -11, 20, -6, -2, -13, 30, -10, 10, 12, -24, -3, 72, 9, -3, 3, -3, 18, 12, -7, -14, 0, -16, -8, 12, 6, -5, 0, -6, -6, 12, 4, -5, 0, -32, 9, 0, 0, -14, 6, -4, 8, -3, 16, 34, -9, -10, 1, -54, -15, 8, 15, -26, 3, -60, 1, 39, 12, -36, -1, 12, 12, -12, 6, -7, -12, -60, 6, 0, -18, 4, -2, 27, -24, 12, 9, 17, 13, 0, -3, -19, 3, 37, 12, -48, 8, 12, 12, -4, 12, 9, 7, 33, 24, 5, -1, -18, -26, 11, -39, -2, 4, 9, -5, 31, 18, 33, 2, -30, 0, 16, 6, 18, -8, 48, -2, 0, -42, -24, -10, 6, 7, -28, 18, 24, 10, -27, 3, -22, 18, 3, -18, 30, 4, -2, 12, -35, -5, -12, -9, 7, -12, 6, 6, -6, 8, -13, -18, 26, 14, 0, -2, 16, 24, 4, -4, 36, 18, 6, 3, 11, -1, 36, -10, -9, -6, -5, -4, -69, -18, -16, -36, 6, -4, -30, -1, -2, 12, 14, -4, -15, -18, -38, 9, 20, 4, -12, -4, 24, -57, 1, 0, -60, 13, -12, -6, -10, -4, -9, 0, -6, 18, -8, 0, 63, 2, 16, -3, 37, 23, 36, 1, -36, -6, 14, 3, 72, -8, -44, 36, -12, -13, 45, -5, -12, -12, -8, 20, -12, -9, -7, -6, 0, 7, 33, -4, -12, 9, 18, -2, 39, 4, 4, 30, 38, 5, -24, 6, -16, 9, -2, -9, -27, 24, -22, -6, -8, 17, -54, 0, -8, 21, -14, -1, -27, 10, 15, 24, -43, -10, -18, -4, 4, 0, 12, -3, 18, 12, -47, -12, 18, -4, 0, 6, -4, -27, 24, 13, 0, -2, 9, -9, -12, 16, -24, -6, 6, -48, 19, 10, 18, 27, 10, -3, 0, 2, 45, -16, 11, -30, -16, 14, -9, -30, 0, -3, 10, 12, -18, -6, 10, 3, 32, 9, -36, 4, 2, -12, 8, -22, 36, -10, -42, -18, -39, -4, 36, 24, 20, 6, 4, -4, 72, 4, -9, -9, -28, 2, -39, -6, 4, 9, -30, 4, -6, 0, -25, -36, 54, -8, -24, -10, 30, -24, -38, 0, -36, -1, 18, -21, 0, -12, -36, 21, 56, 3, -25, -5, 78, 23, -1, 78, -7, 12, -12, 12, -12, 15, 49, -8, -36, -4, 46, -6, 20, 5, 0, 33, -11, -9, -20, 7, 24, 4, 8, 6, 2, 19, 84, -24, 9, 30, -39, -22, -21, 2, 21, -36, -47, 3, -30, -39, -8, -9, 16, -6, -18, -21, 78, 54, 9, 1, -12, -26, 8, -24, -36, 0, 15, 2, 0, 27, -9, -24, 24, 1, -54, -18, 0, 10, -24, -15, -1, 27, 24, 4, -42, -21, 5, 6, -12, 16, -48, 2, -36, 12, -36, -11, -54, 20, -6, -6, -42, -2, 3, -13, 25, 30, 0, -10, 9, 10, -18, 12, 10, -24, 54, -3, 23, 72, -10, 9, 12, -3, 12, 3, -15, -3, -24, 18, 16, 12, 23, -7, 54, -14, -15, 0, 7, -16, -12, -8, -30, 12, -12, 6, 114, -5, -31, 0, -9, -6, -39, -6, 20, 12, -30, 4, 12, -5, 10, 0, -10, -32, -27, 9], 'weight': 2, 'weight_parity': 1}
  12. label: 27.2.a.a
    {'Nk2': 108, 'analytic_conductor': 0.21559608545745704, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [27, 1, [2], [1]], 'cm_discs': [-3], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554459, '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': '27.2.a.a', 'level': 27, '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': [3], 'level_radical': 3, 'minimal_twist': '27.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-2q^{4}-q^{7}+5q^{13}+4q^{16}-7q^{19}+\\cdots', 'related_objects': ['EllipticCurve/Q/27/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.1.d1', 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '27.2.a', 'trace_display': [0, 0, 0, -1], 'trace_hash': 903291523394155081, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.019', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.967', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.070', 'prec': 7}, {'__RealLiteral__': 0, 'data': '2.870', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.239', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.481', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.509', 'prec': 10}, 'traces': [1, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 5, 0, 0, 4, 0, 0, -7, 0, 0, 0, 0, 0, -5, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -6, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -8, 0, 0, 5, 0, 0, 0, 0, 0, -7, 0, 0, 14, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -19, 0, 0, 10, 0, 0, -13, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 8, 0, 0, 20, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, -19, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, -25, 0, 0, 0, 0, 0, 12, 0, 0, -16, 0, 0, 5, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 12, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, -13, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 2, 0, 0, -35, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 29, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -17, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -28, 0, 0, -16, 0, 0, 0, 0, 0, 35, 0, 0, -34, 0, 0, 0, 0, 0, 0, 0, 0, -25, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, -37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 10, 0, 0, 35, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, -20, 0, 0, -20, 0, 0, 0, 0, 0, -31, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 55, 0, 0, 22, 0, 0, -25, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -43, 0, 0, 0, 0, 0, -23, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -17, 0, 0, -46, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 38, 0, 0, -49, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 25, 0, 0, -28, 0, 0, -43, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, -49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -37, 0, 0, -24, 0, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, -77, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 14, 0, 0, 44, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -49, 0, 0, -46, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -31, 0, 0, 0, 0, 0, -5, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -7, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, -29, 0, 0, 26, 0, 0, 11, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 25, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, -20, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, -52, 0, 0, 0, 0, 0, -55, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, -61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 0, 0, -34, 0, 0, 41, 0, 0, 0, 0, 0, -23, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, -61, 0, 0, 0, 0, 0, -10, 0, 0, 0], 'weight': 2, 'weight_parity': 1}
  13. label: 29.2.a.a
    {'Nk2': 116, 'analytic_conductor': 0.2315661658617131, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[29, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [29, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554461, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '29.2.a.a', 'level': 29, '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': [29], 'level_radical': 29, 'minimal_twist': '29.2.a.a', 'nf_label': '2.2.8.1', 'prim_orbit_index': 1, 'qexp_display': 'q+(-1+\\beta )q^{2}+(1-\\beta )q^{3}+(1-2\\beta )q^{4}+\\cdots', 'related_objects': ['Genus2Curve/Q/841/a'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '29.2.a', 'trace_display': [-2, 2, -2, 0], 'trace_hash': 1818542051159353914, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.950', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.178', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.154', 'prec': 14}, {'__RealLiteral__': 0, 'data': '1.946', 'prec': 14}, {'__RealLiteral__': 0, 'data': '60.016', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.019', 'prec': 7}, 'traces': [2, -2, 2, 2, -2, -6, 0, -6, 0, 2, 2, 10, -2, 8, -2, 6, -4, -8, 12, -2, -8, 2, -4, -10, -8, 10, 2, -16, 2, 6, 6, 6, -2, -4, 0, 16, -8, -12, -10, 6, 8, 16, 10, -6, 0, -12, 2, 6, 2, 8, 4, -18, 2, 2, -2, 8, 12, -2, 4, -10, -4, -26, -16, -14, 2, 2, 0, 12, 12, -8, -12, -8, 8, 8, -8, 12, 8, 22, -2, -6, -2, 16, 4, -24, 4, -6, 2, -2, -8, 8, 16, 28, 26, 10, -12, 2, -8, -2, -8, -8, -16, -4, -4, 14, 8, -26, -24, -6, 14, -2, -8, 0, -4, -36, 4, 2, -16, 12, -16, 10, -16, 12, -16, 46, 18, 16, -20, 10, 6, -10, 20, -2, 0, -16, -2, 4, 24, -20, 28, 16, -10, 20, 6, 0, -2, -8, 2, -8, -10, 24, 0, -36, 16, 0, -6, -34, 0, 6, 26, -6, -32, 26, 22, -40, 2, -20, -12, 32, -8, 4, 0, 2, 36, -6, 0, 6, -12, 32, 4, -16, -6, -24, -12, -4, 8, -58, -12, -22, 8, 12, 28, -22, -16, -16, 10, 2, 4, 0, 16, 24, 16, 0, 0, 4, -8, 12, 32, -6, 12, -16, -2, 50, -20, 32, -10, -2, -40, -30, 8, 6, -12, 24, -12, 8, 0, 36, 12, 60, -24, 12, 0, -6, 14, 24, -2, -28, -6, 0, -28, -6, -14, 24, -32, -20, -2, 24, -12, -38, 20, -18, 26, -16, -20, 4, -4, -26, -42, -22, 0, 18, 0, -52, 14, 6, -2, 48, -32, 32, 12, -2, 2, -12, 24, -24, -8, 28, -12, -28, 40, -8, 30, 18, 12, -28, -12, -2, 48, -8, -10, 2, 16, 8, 4, -6, -4, 24, 6, 18, -28, -40, 8, 40, 0, 36, 4, 0, -14, -8, -12, 26, 28, 42, 14, -24, 16, -10, -12, -54, 2, 14, -32, 16, -24, -50, 8, -2, 30, 0, 24, -2, -2, 36, 0, 4, 0, -24, 4, -8, -36, -12, -14, -48, 0, -26, -12, -20, -12, 10, 18, -32, 6, 10, 20, 20, 12, -56, 0, 20, 22, 8, 34, -26, -24, 32, -8, 28, 36, -12, -48, -8, -48, 90, -30, -4, 18, 6, -2, 0, 20, -12, -4, -60, -24, 54, -8, 8, -8, 40, 40, -22, 40, -6, 52, -4, 2, 8, 50, 8, -48, -24, -26, -32, -46, 16, 2, 8, -8, -12, -4, -16, 24, -20, 32, -16, -4, 2, 28, 12, -36, 24, 12, 54, -24, -30, 16, 52, 16, -40, 2, 6, 28, 6, 16, 64, -2, 46, -24, -24, -12, 2, 0, 4, -60, -40, 8, 4, -18, 16, -36, 32, 32, -68, -40, 28, -16, -60, 36, 0, -12, -28, 28, -8, -52, 6, -26, -46, -6, -32, -32, -10, 24, 4, 14, 14, -48, 16, 48, 44, -6, -2, 8, 46, -16, -32, 8, 48, -40, 20, 2, 2, -34, -32, -4, 60, 8, 18, 16, -44, 4, 18, -4, -46, 26, 48, 16, -4, 8, 12, -38, 4, 0, 54, 12, 34, 4, 38, 14, -32, 20, -14, -30, -8, 32, 84, 32, -2, 28, -6, 26, 26, -32, -96, 40, 72, 24, -16, -20, -84, 2, 6, -32, -46, 26, -20, -14, -64, 32, 24, -16, -8, 12, -44, 8, 44, 8, 28, -12, -64, -2, 0, 4, -78, -10, -26, 4, -28, 48, 44, -68, 36, -16, -2, 60, -16, 16, -16, -20, 42, -8, -2, -32, -24, -22, -24, 16, -20, 4, 10, 36, -12, 4, -24, -22, 2, 16, -26, -8, 28, -34, 40, -40, 32, 32, -80, 16, 16, 10, 36, -8, -12, 22, -16, -18, -14, 16, -16, 24, 28, 70, -46, -20, 4, 48, -30, 22, -22, -12, 48, 16, -16, -68, 10, -54, 84, 20, 82, -2, 2, -16, -10, -4, 88, 48, 0, -6, -24, 68, 30, 20, -40, -64, -18, -32, -74, -20, 24, 0, -16, 26, 2, 44, 6, -4, -28, 0, 32, -4, 4, -4, 16, 4, -16, 2, -60, -8, 24, -44, 76, -48, -4, -28, 6, 8, 96, -24, -48, 0, 30, -50, 20, 96, 4, -16, -12, -28, -10, -64, 22, 46, 64, -18, -2, -48, -6, 10, -68, -32, -28, 30, -20, -8, 48, 68, 16, -6, -44, -44, -2, -12, 0, 16, -34, -46, 58, -8, 64, -20, -56, -42, 8, -28, -44, 8, -36, -2, -28, -16, 16, -6, 8, -60, 56, 36, -110, 10, 62, 32, 20, 16, -54, 28, 6, 46, 10, 0, -8, 68, 28, 4, 36, 12, 28, -32, 92, -16, 0, 28, -74, -36, 0, -34, 0, -56, -32, -24, 0, 32, 8, 48, 34, -4, 8, 2, 6, 0, -124, -12, 4, 2, -6, 64, 16, 20, -34, -26, -32, -4, 96, -28, -24, -48, 42, 8, 48, 32, 90, 84, 32, 16, -26, 16, -16, 46, -8, -22, 12, 60, 52, 16, 40, 14, -72, -52, 20, 8, -16, 46, 0, -20, 20, -44, 30, -4, -84, 12, -36, -14, 12, -30, -32, 2, -100, 78, -106, 8, 16, 16, 6, 28, 16, 16, -84, -12, -32, 0, 80, -18, -10, 14, -2, 16, -44, -28, 10, -36, -80, -42, -88, 2, 6, -32, -58, 48, -72, 0, 40, -46, -4, 20, -6, 28, -8, -8, 4, 12, 44, 54, 40, -32, -32, 22, 4, 12, 46, -4, -88, -28, 84, 6, -64, 44, 8, -32, 44, 6, 80, -12, -68, 32, 24, -62, 36, -12, 12, 12, 24, -64, -4, -12, 4, 14, -28, 28, 16, 32, 52, -16, 6, 60, 58, 12, 78, -4, 106, 12, 56, 12, 32, 22, 22, -34, -48, -112, 12, -8, 10, 42, -22, -8, 48, -84, 32, -26, -56, -28, -60, -2, -22, 0, 22, 56, -40, -16, -78, 16, 64, -62, 56, 24, 16, -20, -64, 0, 16, 40, -12, 78, -26, 16, -2, 32, 46, 10, 56, -4, -4, 16, -108, -36, 0, -20, -2, -6, -64, -16, 68, 0, -52, -8, -54], 'weight': 2, 'weight_parity': 1}
  14. label: 30.2.a.a
    {'Nk2': 120, 'analytic_conductor': 0.23955120606384114, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [3, -1], [5, 1]], 'atkin_lehner_string': '+-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [30, 1, [11, 7], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554462, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '30.2.a.a', 'level': 30, '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': [2, 3, 5], 'level_radical': 30, 'minimal_twist': '30.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/30/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '30.2.a', 'trace_display': [-1, 1, -1, -4], 'trace_hash': 148452494971348580, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.008', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.999', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.965', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.757', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.032', 'prec': 7}, 'traces': [1, -1, 1, 1, -1, -1, -4, -1, 1, 1, 0, 1, 2, 4, -1, 1, 6, -1, -4, -1, -4, 0, 0, -1, 1, -2, 1, -4, -6, 1, 8, -1, 0, -6, 4, 1, 2, 4, 2, 1, -6, 4, -4, 0, -1, 0, 0, 1, 9, -1, 6, 2, -6, -1, 0, 4, -4, 6, 0, -1, -10, -8, -4, 1, -2, 0, -4, 6, 0, -4, 0, -1, 2, -2, 1, -4, 0, -2, 8, -1, 1, 6, 12, -4, -6, 4, -6, 0, 18, 1, -8, 0, 8, 0, 4, -1, 2, -9, 0, 1, 18, -6, -4, -2, 4, 6, -12, 1, -10, 0, 2, -4, -18, 4, 0, -6, 2, 0, -24, 1, -11, 10, -6, 8, -1, 4, 20, -1, -4, 2, 0, 0, 16, 4, -1, -6, 6, 0, -4, 4, 0, 0, 0, 1, 6, -2, 9, 2, -6, -1, 8, 4, 6, 0, -8, 2, 2, -8, -6, 1, 0, -1, -4, -6, 0, -12, 0, 4, -9, 6, -4, -4, 18, 6, -4, 0, 0, -18, 24, -1, 14, 8, -10, 0, -2, -8, 0, 0, -4, -4, -24, 1, -22, -2, -2, 9, -6, 0, 8, -1, -4, -18, 24, 6, 6, 4, 0, 2, 0, -4, 20, -6, 0, 12, 4, -1, -32, 10, 2, 0, 12, -2, 20, 4, 1, 18, -12, -4, -10, 0, 0, 6, -18, -2, 0, 0, 8, 24, 24, -1, 2, 11, 1, -10, -9, 6, -8, -8, 12, 1, -24, -4, 0, -20, -6, 1, -18, 4, -8, -2, -6, 0, 0, 0, 6, -16, 18, -4, -6, 1, -16, 6, -8, -6, 0, 0, 2, 4, 8, -4, 18, 0, -28, 0, 4, 0, 24, -1, 19, -6, 2, 2, -6, -9, 0, -2, 0, 6, 0, 1, 16, -8, 18, -4, 10, -6, 20, 0, -4, 8, 0, -2, 2, -2, 4, 8, 18, 6, 0, -1, -12, 0, -24, 1, 2, 4, -10, 6, 0, 0, -28, 12, 2, 0, 4, -4, 26, 9, -18, -6, 0, 4, -8, 4, 0, -18, 12, -6, -10, 4, 2, 0, 6, 0, 0, 18, -24, -24, -24, 1, -3, -14, -11, -8, -2, 10, -28, 0, -6, 2, 24, 8, 26, 0, -1, 0, -12, 4, -4, 4, 20, 24, 0, -1, 0, 22, -4, 2, -6, 2, 0, -9, 0, 6, -8, 0, -22, -8, 16, 1, -6, 4, 16, 18, -1, -24, 0, -6, 26, -6, 6, -4, 0, 0, -12, -2, -4, 0, 0, 4, -10, -20, 0, 6, 6, 0, 40, -12, 0, -4, 0, 1, 26, 32, 6, -10, 0, -2, 8, 0, 9, -12, 12, 2, -18, -20, -6, -4, -6, -1, 0, -18, 8, 12, 8, 4, 26, 10, 6, 0, -30, 0, -4, -6, -8, 18, -36, 2, 16, 0, 2, 0, 0, -8, -4, -24, -6, -24, -24, 1, 4, -2, 0, -11, -2, -1, -28, 10, -4, 9, 24, -6, -36, 8, 0, 8, 0, -12, -4, -1, 0, 24, 24, 4, -18, 0, -9, 20, -6, 6, -8, -1, -4, 18, 4, -4, 0, 8, 18, 2, 18, 6, 20, 0, -4, 0, 48, 0, -23, -6, 0, 16, -12, -18, 12, 4, 24, 6, 0, -1, -10, 16, 14, -6, 10, 8, -28, 6, -10, 0, 24, 0, -32, -2, -2, -4, 18, -8, -8, 4, 0, -18, -12, 0, 18, 28, -4, 0, 18, -4, 20, 0, -24, -24, 0, 1, 2, -19, -22, 6, -48, -2, 0, -2, -2, 6, -12, 9, -32, 0, -6, 2, 30, 0, 24, -6, 8, 0, -24, -1, -22, -16, -4, 8, 11, -18, -4, 4, 24, -10, 0, 6, 2, -20, 6, 0, 30, 4, 44, -8, 0, 0, -72, 2, 1, -2, 0, 2, 12, -4, 32, -8, 20, -18, -20, -6, 18, 0, 0, 1, -30, 12, -4, 0, 4, 24, 24, -1, 0, -2, -32, -4, 18, 10, 0, -6, 2, 0, 48, 0, 14, 28, 12, -12, -16, -2, 0, 0, 20, -4, 0, 4, 26, -26, 1, -9, -6, 18, -8, 6, -12, 0, -12, -4, -6, 8, -10, -4, -12, 0, 44, 18, 0, -12, 4, 6, -36, 10, -18, -4, -6, -2, -8, 0, 0, -6, -72, 0, 38, 0, 8, -18, 0, 24, 0, 24, 24, 24, 0, -1, 16, 3, 2, 14, -6, 11, -28, 8, 1, 2, -24, -10, -22, 28, -9, 0, 0, 6, -52, -2, -8, -24, -24, -8, 6, -26, 12, 0, 48, 1, -40, 0, -24, 12, -8, -4, 2, 4, 0, -4, 18, -20, 40, -24, -6, 0, 0, 1, 2, 0, -18, -22, 42, 4, 8, -2, -8, 6, 24, -2, 0, 0, -6, 9, -2, 0, -4, -6, 0, 8, 72, 0, -20, 22, 6, 8, -30, -16, 0, -1, 18, 6, 0, -4, 0, -16, -6, -18, -54, 1, -4, 24, -16, 0, 4, 6, 16, -26, -8, 6, 18, -6, 20, 4, 0, 0, 12, 0, 38, 12, 2, 2, 54, 4, 0, 0, 8, 0, 24, -4, 7, 10, 18, 20, 9, 0, 44, -6, -28, -6, 0, 0, -46, -40, 4, 12, -18, 0, -4, 4, 24, 0, 24, -1, -18, -26, 19, -32, 0, -6, -8, 10, 2, 0, 4, 2, 2, -8, -6, 0, -54, -9, -4, 12, 0, -12, 0, -2, -80, 18, 0, 20, 0, 6, -24, 4, 0, 6, -48, 1, -36, 0, 16, 18, -14, -8, 44, -12, 18, -8, -48, -4, 0, -26, 10, -10, 0, -6, -16, 0, 20, 30, 0, 0, 2, 4, -4, 6, -6, 8, -36, -18, 0, 36, 0, -2, 26, -16, 2, 0, 18, -2, 0, 0, 4, 0, 36, 8, 4, 4, 18, 24, 6, 6, 24, 24, 0, 24, -24, -1, 33, -4, -12, 2, 22, 0, -4, 11, -24, 2, 24, 1, 16, 28, 2, -10, -42, 4, 0, -9, -10, -24, -24, 6, 6, 36, 0, -8, 0, 0, -16, -8, -28, 0, -8, 12, 26, 4, 2, 1], 'weight': 2, 'weight_parity': 1}
  15. label: 31.2.a.a
    {'Nk2': 124, 'analytic_conductor': 0.24753624626596918, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[31, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [31, 1, [3], [1]], 'cm_discs': [], 'conrey_index': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554463, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '31.2.a.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': '31.2.a.a', 'nf_label': '2.2.5.1', 'prim_orbit_index': 1, 'qexp_display': 'q+\\beta q^{2}-2\\beta q^{3}+(-1+\\beta )q^{4}+q^{5}+\\cdots', 'related_objects': ['Genus2Curve/Q/961/a'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '31.2.a', 'trace_display': [1, -2, 2, -4], 'trace_hash': 1527705443971435305, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.031', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.967', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.084', 'prec': 7}, {'__RealLiteral__': 0, 'data': '9.383', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.154', 'prec': 10}, {'__RealLiteral__': 0, 'data': '63.569', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [2, 1, -2, -1, 2, -6, -4, 0, 6, 1, 4, -4, -2, 3, -2, -3, 6, 13, 0, -1, -6, 2, -2, 10, -8, -6, -20, 7, 10, -6, 2, -9, -4, -2, -4, 7, -4, -5, 12, 0, 14, 2, -2, -2, 6, 14, -4, 18, 4, -4, 4, -4, -12, -20, 4, -10, 10, 0, 0, -4, -6, 1, 8, 4, -2, -12, 16, -8, -28, 3, 4, -20, 8, -2, 8, -5, -8, 16, -10, -3, 22, 7, -12, 8, 6, 4, 0, 0, 10, 13, -6, 16, -2, 8, 0, 4, -14, -18, 12, 4, -6, -8, 8, 10, -6, -16, 16, 0, -10, 2, 4, -9, -2, 10, -2, -10, -26, 5, -22, 10, -14, 22, -14, -1, -18, -1, 16, 25, -8, -6, 24, -8, -10, 8, -20, 10, 26, -24, 0, 7, -16, -23, -4, -39, 10, 14, 36, 2, 20, 24, -6, 10, -2, 6, 2, 4, 6, -20, 32, -9, 34, 41, 8, -7, -4, -26, -4, -10, -14, -2, -20, 6, -12, -20, 16, -6, -10, 20, -10, 7, 14, 2, -44, -30, -4, -6, 12, 12, 20, -5, -16, -14, -2, -27, 12, -22, -4, 26, -20, 0, -16, -3, -30, -12, 14, 9, 54, 18, 0, 2, 24, -4, 46, 3, -2, 20, -4, -25, -28, -2, 4, 12, 8, 23, -24, 9, -4, 0, 0, 14, -12, 10, 18, -38, -4, 5, 40, 14, -10, 18, -16, -7, -22, 28, 4, -42, 10, 0, 52, -9, -26, -9, -4, 18, 4, 7, -14, -4, 8, -4, 10, 12, -42, 20, -12, 5, -40, -8, -40, -20, -6, 6, -4, -2, -16, 4, 6, 30, 6, -10, 34, -8, 8, -27, 10, -12, -28, -17, -6, 0, 54, 6, 8, 28, 0, 0, -40, 10, -28, 16, 14, -28, 6, 15, -6, 14, -44, 14, -18, 1, -36, -20, 38, 43, 8, -10, 26, 56, 20, 4, -6, -18, 10, 19, 8, 19, 50, 0, 28, -12, 4, -14, -12, -12, 16, -6, -34, 3, -18, -8, 4, -25, -20, -10, -28, 14, 26, -20, 20, -12, 40, -18, -12, -10, 4, 10, -28, 10, 40, -20, -28, -18, 14, 8, 8, -32, 36, -42, 42, -2, 4, -4, 38, -4, 18, -20, 0, -20, -40, -5, -36, -33, -12, -30, -8, 9, 14, -13, 0, 16, -36, 40, -24, 28, -10, 14, -14, -30, -10, 12, 54, -48, -2, 3, 22, 20, -8, 20, -30, 7, 4, 1, 10, 62, -12, 4, -60, -10, 20, 8, 14, 37, 28, 20, -24, 38, 62, -13, 24, 4, 24, 60, -2, 3, 0, -15, -30, -44, 20, 0, -68, -8, 48, 8, 10, 4, -20, 2, 0, -52, 28, 11, 56, -12, -6, -10, -24, -30, -40, 16, 24, 4, -32, 0, -2, 29, -4, -12, -32, 8, -86, -10, -4, 60, 0, 36, -76, -20, 60, 4, 4, 42, 36, 7, -14, -66, -34, -50, -38, -18, -36, -28, 40, 10, 12, -3, -58, 76, -40, 9, 24, 12, 28, 10, -6, 28, -6, 2, 10, -8, 4, -24, 20, 13, 8, 4, -8, -6, -28, 10, 4, 40, -22, -12, 24, -26, 6, 36, 46, -16, 20, 15, -14, -60, 16, 0, -20, 0, 8, 0, -6, -28, 36, -32, -10, 8, 16, -28, 82, -8, 10, 20, -10, -32, 4, 30, -24, 13, -8, -9, 8, 17, -12, 8, -2, -36, 16, 50, 20, 10, 34, -8, 66, 21, 8, 32, -4, -33, -18, -10, -16, 82, -24, -20, -26, -6, -4, -8, 0, 5, -56, 6, -22, -40, -22, -10, 60, -24, 20, -40, -6, -8, 48, -22, -14, 18, 36, -5, -40, 22, -16, 16, -52, -37, -14, -20, 56, -34, -10, -1, -40, -43, 10, -48, 22, 14, 20, 37, -12, -1, 24, 30, -74, -7, 16, 24, 36, 0, -88, 25, 24, -38, 48, -52, -8, -10, 16, -60, 0, 24, -6, 11, -32, 70, 24, -21, 64, -16, 20, -8, -46, 2, 16, 40, -10, -26, -40, -8, -8, 8, -12, 32, 18, -12, 80, 17, -4, -14, -12, 10, 24, 2, -12, -5, 26, 5, 60, -12, 32, -24, -16, 26, 16, 38, 0, 40, 42, -30, -58, -28, 14, 80, 0, 8, -16, 24, 12, 0, 60, -23, -90, -30, -2, 16, -4, 20, 40, 25, -50, -39, -6, -14, -84, -32, -40, 42, -84, -10, 66, 14, -16, 12, -2, 18, 36, 24, 32, 91, -10, 2, -20, -8, 78, 10, 20, 19, -116, -16, -42, 54, 24, -24, -24, -20, -6, -40, -14, 20, -56, 10, 4, -68, -20, -17, -2, -46, -10, -52, -50, 6, -26, 11, 18, 12, -8, 40, 12, -40, 0, 4, 8, 32, -80, 54, 6, -72, 46, 32, 52, -20, 24, -40, -44, -7, 32, -10, -84, 10, -32, 36, 90, 52, 16, -32, 34, -6, 0, 0, 20, 41, -56, 50, 56, -4, 8, 24, -10, 10, 2, -7, -6, -48, -42, -10, 16, -5, 66, 8, -20, -26, 64, -14, 52, -60, -4, -10, -20, -35, 40, -10, 2, 57, -34, 13, -14, 24, 28, 48, 72, 8, 4, -8, 48, -34, -20, 10, -4, 32, 40, 6, -42, 12, -42, 80, -12, 24, 66, 7, -20, -20, -16, 40, -122, -10, 36, -16, -54, -15, 12, -6, 4, -74, 8, -12, -10, 39, -4, -20, -12, 20, 44, -4, -20, -60, -10, -45, 48, -70, 10, -28, -16, 14, 16, -20, 14, 68, -44, -8, -18, 2, 14, -30, -24, 8, -44, -30, -48, 0, -20, -30, 74, 62, 46, 16, 16, 14, 44, -50, -40, -6, 40, 11, 86, 13, 12, 50, 36, 24, -28, 12, -76, -98, -14, -15, 20, 8, -44, 20, -28, 20, 14, -50, 78, -128, -16, -10, 0, 15, -82, -14, 2, 12, 28, 58, -2, -32, 76, 0, 20, -27, -56, -44, 60, -22, -48, -66, -14, -54, 20, -22, -110, 32, 88, 70, -4, -20, 32, 0, 32, 26, 34, -9, -4, 31, -20, 24, -14, 10, 40, 0], 'weight': 2, 'weight_parity': 1}
  16. label: 32.2.a.a
    {'Nk2': 128, 'analytic_conductor': 0.25552128646809724, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [32, 1, [31, 5], [1, 1]], 'cm_discs': [-4], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554464, '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, 4, 2, -1, 2, -4]], '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': '32.2.a.a', 'level': 32, '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': '32.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-2q^{5}-3q^{9}+6q^{13}+2q^{17}-q^{25}+\\cdots', 'related_objects': ['EllipticCurve/Q/32/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.1.d1', 'self_twist_discs': [-4], 'self_twist_type': 1, 'space_label': '32.2.a', 'trace_display': [0, 0, -2, 0], 'trace_hash': 1485208795141819780, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.974', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.046', 'prec': 7}, {'__RealLiteral__': 0, 'data': '2.892', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.149', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.568', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.505', 'prec': 10}, 'traces': [1, 0, 0, 0, -2, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 10, 0, 0, 0, 6, 0, 0, 0, -7, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, -4, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -14, 0, 0, 0, -18, 0, 0, 0, -11, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 14, 0, 0, 0, -6, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 3, 0, 0, 0, 30, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 30, 0, 0, 0, -28, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -13, 0, 0, 0, -34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0, 12, 0, 0, 0, -30, 0, 0, 0, 14, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 2, 0, 0, 0, -18, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, -20, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -42, 0, 0, 0, -12, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, -23, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, -42, 0, 0, 0, -12, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, -38, 0, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -42, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, 0, 18, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -46, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -27, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, -38, 0, 0, 0, 12, 0, 0, 0, 50, 0, 0, 0, -34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 22, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 71, 0, 0, 0, -46, 0, 0, 0, 0, 0, 0, 0, 46, 0, 0, 0, 58, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, -54, 0, 0, 0, -58, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 36, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -46, 0, 0, 0, 0, 0, 0, 0, -38, 0, 0, 0, -58, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, -31, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -62, 0, 0, 0, -18, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62, 0, 0, 0], 'weight': 2, 'weight_parity': 1}
  17. label: 33.2.a.a
    {'Nk2': 132, 'analytic_conductor': 0.2635063266702253, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, 1], [11, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [33, 1, [23, 13], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554465, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '33.2.a.a', 'level': 33, '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, 11], 'level_radical': 33, 'minimal_twist': '33.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}+4q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/33/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '33.2.a', 'trace_display': [1, -1, -2, 4], 'trace_hash': 2215180138185436427, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.022', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.965', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.037', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.878', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.052', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.596', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.021', 'prec': 7}, 'traces': [1, 1, -1, -1, -2, -1, 4, -3, 1, -2, 1, 1, -2, 4, 2, -1, -2, 1, 0, 2, -4, 1, 8, 3, -1, -2, -1, -4, -6, 2, -8, 5, -1, -2, -8, -1, 6, 0, 2, 6, -2, -4, 0, -1, -2, 8, 8, 1, 9, -1, 2, 2, 6, -1, -2, -12, 0, -6, -4, -2, 6, -8, 4, 7, 4, -1, -4, 2, -8, -8, 0, -3, -14, 6, 1, 0, 4, 2, -4, 2, 1, -2, 12, 4, 4, 0, 6, -3, -6, -2, -8, -8, 8, 8, 0, -5, 2, 9, 1, 1, 2, 2, 8, 6, 8, 6, -12, 1, -2, -2, -6, -4, -6, 0, -16, 6, -2, -4, -8, -6, 1, 6, 2, 8, 12, 4, -4, -3, 0, 4, -12, 1, 0, -4, 2, 6, 2, -8, -8, 8, -8, 0, -2, -1, 12, -14, -9, -6, -22, 1, 20, 0, -2, 4, 16, -2, 14, -4, -6, -10, 32, 1, 4, 2, 2, 12, 0, 12, -9, 4, 0, 0, -6, 6, -4, -1, 4, -6, 12, 2, 22, -8, -6, -24, -12, 8, -2, -8, -4, 0, 8, -7, -14, 2, -4, -9, -14, 1, 0, 3, 4, 2, -24, -2, 4, 8, 8, 2, 0, 8, 0, -6, 0, -12, 0, 3, -32, -2, 14, 2, 4, -6, 16, 20, -1, -6, 12, 0, 6, -16, -4, 18, 30, -2, -16, 4, 4, -8, 24, -2, 10, 1, -1, -6, -18, 2, 0, 24, -12, 12, 4, -4, 8, -4, -4, -17, -14, 0, 24, -4, -6, -12, -16, 3, -12, 0, 6, 4, -2, 2, 20, 2, 8, 2, -1, 8, -26, -8, -8, 24, -18, -8, 16, 0, 0, -2, -8, 5, -13, 12, -2, 14, -6, -9, 8, -18, -1, -22, -16, -1, 0, 20, -2, 0, -12, -2, 32, -4, -8, 16, -24, -6, -22, 14, -8, 4, 22, -6, -6, -14, 12, 32, 0, -1, 2, 4, 2, 6, 32, 2, -20, -12, 6, 0, 8, 4, -22, -9, 6, -4, -8, 0, 8, 0, 16, -6, 4, -6, 6, -4, 2, 5, 18, 4, 0, 6, 8, 12, -8, 6, -19, 22, -1, 8, 28, -6, -32, -8, -2, -12, 24, -8, -2, -2, -12, -24, 12, -4, 28, 0, 4, 8, -16, 3, -8, -14, 0, -2, -18, -4, -16, -27, 12, -14, 8, -1, -2, 0, 0, 1, 26, 4, 16, -2, -2, -24, 6, -6, 18, 4, -2, -8, -16, 8, -24, -10, 8, 0, -4, -8, -26, 0, 8, -18, 2, 0, 24, 12, 2, 0, -24, 1, 34, -32, -12, 2, 0, 14, -20, 6, 9, 4, 28, 6, 12, 16, 22, 28, 2, -1, -2, 6, -20, 12, 16, 0, 18, 6, 2, 16, -30, -4, 16, 6, -16, 30, -12, 2, -16, -16, -14, 12, 0, 4, 0, 8, 6, 24, 8, 10, -12, 10, -32, -1, -4, -1, -16, -18, -4, -18, 4, -2, 12, 0, -2, 8, 0, -12, -4, -12, 0, 4, -32, -12, -4, 8, 9, 4, 30, -4, -56, -11, 0, -14, -16, 0, 8, 24, 6, -12, -30, -6, -16, 12, 4, -16, 16, 1, 41, -12, -4, 0, 4, 6, 24, 12, -12, -2, 9, -2, 46, 20, -22, -10, 4, 8, 8, -2, 6, -1, 0, 24, -16, -26, 12, 8, -14, -8, 0, 8, 2, -18, -44, 8, 12, 16, 4, 0, -42, 0, -16, 2, -8, -8, -8, 7, -30, -13, 14, -12, 48, -2, 6, 42, 4, -6, 28, 9, 0, 8, 14, -6, 38, -1, 16, 22, 0, -16, -8, -3, 26, 0, -4, -20, -2, -2, -4, 0, 24, -12, -16, 2, 14, 32, -4, -12, -30, -8, 44, -16, -8, -24, -24, -2, -19, -22, 0, -14, -12, -8, 16, 12, 0, 22, 8, 6, -18, -6, 0, 6, 18, 12, 20, -32, 0, 0, 8, -3, -4, 2, 32, -4, -2, 2, 24, 2, -14, 32, 4, -2, -26, -20, -4, -36, 0, 6, -48, 0, -16, 8, 6, -20, -46, -22, 1, 9, 18, 6, 8, -12, -12, -8, 20, 0, -4, 8, -6, 0, -12, 16, -28, 6, 4, 4, 16, -18, 4, 6, -30, 4, 50, 2, 0, 7, 16, 18, 8, -4, 38, 0, -4, 18, -64, 8, 4, -12, -24, -8, 24, 2, 32, -19, -10, -22, 6, -1, 0, 24, 1, 28, 0, 6, 30, -32, 18, 40, -4, -2, 8, 12, 0, 24, 40, -24, 44, -2, 12, 2, -48, -12, -8, -8, -4, 12, -40, 4, -10, 28, -8, 0, 6, 4, -8, -8, 4, -16, 8, 17, 2, -8, 14, 14, 6, 0, 8, -6, -24, -18, 0, 4, 0, -16, 6, -9, -28, 12, -8, 14, 16, 8, -24, -3, -12, -2, 12, 0, -10, 0, -16, -5, -6, 26, -14, -4, -64, 16, 2, -6, 54, -2, -56, 24, -20, 6, -8, -2, 0, 18, -8, -4, -14, -2, 24, -24, 1, -16, 20, -8, -2, -24, 26, -14, -18, 8, 0, 0, 8, -4, -56, -24, 7, -26, 18, 0, 18, 8, 4, -6, -16, 2, 48, 0, -34, 24, 0, 36, -10, 2, -36, 0, 8, -24, 48, -5, 12, 34, 13, 32, -4, -12, 8, 6, 2, 0, 48, -14, 6, -20, 6, 2, 26, 9, -20, -4, -8, 28, 8, 18, -16, 12, 1, -16, 0, 22, -24, -12, 16, 2, 48, 1, -12, -2, 0, 18, -44, -20, 12, -12, 2, 16, 24, 0, 12, 18, 12, -6, -48, 2, -20, 48, -32, -30, 0, 4, -6, 16, 8, -30, -6, -16, 0, -30, 24, -12, 4, 6, 26, -16, 22, 16, -54, -14, -16, 4, 8, 0, 12, -4, 28, 0, -22, 24, 22, 6, -16, -24, 6, 8, 8, 14, 33, -12, -12, -10, 28, -32, 4, -3, 0, -4, -52, 1, -32, -16, -2, -6, -6, -4, -6, 18, -2, 4, 24, -6, 28, 12, -32, 0, 0, -2, 40, -40, 20, 0, 0, 12, 14, -4, -6, -36], 'weight': 2, 'weight_parity': 1}
  18. label: 34.2.a.a
    {'Nk2': 136, 'analytic_conductor': 0.2714913668723533, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [17, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [34, 1, [3], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554466, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '34.2.a.a', 'level': 34, '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': [2, 17], 'level_radical': 34, 'minimal_twist': '34.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-2q^{3}+q^{4}-2q^{6}-4q^{7}+q^{8}+\\cdots', 'related_objects': ['EllipticCurve/Q/34/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '34.2.a', 'trace_display': [1, -2, 0, -4], 'trace_hash': 2246807206681965941, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.011', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.966', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.039', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.872', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.083', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.577', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.021', 'prec': 7}, 'traces': [1, 1, -2, 1, 0, -2, -4, 1, 1, 0, 6, -2, 2, -4, 0, 1, -1, 1, -4, 0, 8, 6, 0, -2, -5, 2, 4, -4, 0, 0, -4, 1, -12, -1, 0, 1, -4, -4, -4, 0, 6, 8, 8, 6, 0, 0, 0, -2, 9, -5, 2, 2, -6, 4, 0, -4, 8, 0, 0, 0, -4, -4, -4, 1, 0, -12, 8, -1, 0, 0, 0, 1, 2, -4, 10, -4, -24, -4, 8, 0, -11, 6, 0, 8, 0, 8, 0, 6, -6, 0, -8, 0, 8, 0, 0, -2, 14, 9, 6, -5, 18, 2, -16, 2, 0, -6, -6, 4, -16, 0, 8, -4, -6, 8, 0, 0, 2, 0, 4, 0, 25, -4, -12, -4, 0, -4, -16, 1, -16, 0, -6, -12, 16, 8, 0, -1, 6, 0, 2, 0, 0, 0, 12, 1, 0, 2, -18, -4, 6, 10, -16, -4, -1, -24, 0, -4, 14, 8, 12, 0, 0, -11, 2, 6, 0, 0, 12, 8, -9, 0, -4, 8, 24, 0, 20, 6, 0, -6, 12, 0, -4, -8, 8, 0, 0, 8, -6, 0, -16, 0, -24, -2, -10, 14, 0, 9, -12, 6, -16, -5, -16, 18, 0, 2, 0, -16, 0, 2, -24, 0, -10, -6, 0, -6, 0, 4, 16, -16, -4, 0, -2, 8, 8, -4, -5, -6, -6, 8, 14, 0, 48, 0, 18, 2, 0, 0, -16, 4, 24, 0, -10, 25, 10, -4, 0, -12, -8, -4, 0, 0, -24, -4, 0, -16, 0, 1, 6, -16, 16, 0, 0, -6, 24, -12, 0, 16, 12, 8, -24, 0, 8, -1, 16, 6, -30, 0, 8, 2, -4, 0, 6, 0, 14, 0, 0, 12, -24, 1, 1, 0, -28, 2, 6, -18, 0, -4, 24, 6, 0, 10, -32, -16, -36, -4, 0, -1, 20, -24, 32, 0, 12, -4, -34, 14, 0, 8, -12, 12, 0, 0, 12, 0, 4, -11, -10, 2, 32, 6, 0, 0, -16, 0, -4, 12, 0, 8, -22, -9, 12, 0, -24, -4, -8, 8, 0, 24, 18, 0, 26, 20, 8, 6, 6, 0, 0, -6, -8, 12, 24, 0, -3, -4, -50, -8, 0, 8, -16, 0, 6, 0, 24, 8, -22, -6, 0, 0, 0, -16, 14, 0, 32, -24, -24, -2, 0, -10, 8, 14, 30, 0, 0, 9, 12, -12, 0, 6, 20, -16, -32, -5, 30, -16, -8, 18, 0, 0, -24, 2, -10, 0, -12, -16, 0, 0, 0, 2, -4, -24, -30, 0, 2, -10, 0, -6, 5, 0, 16, -6, -24, 0, 24, 4, 2, 16, 0, -16, 0, -4, 8, 0, 9, -2, -24, 8, 0, 8, -12, -4, -18, -5, 36, -6, 32, -6, 0, 8, 26, 14, -4, 0, -6, 48, -16, 0, 0, 18, 12, 2, -32, 0, -28, 0, 48, -16, 20, 4, -6, 24, 24, 0, -8, -10, 0, 25, 0, 10, 8, -4, -4, 0, -12, -12, 0, -8, 0, -4, 0, 0, 14, 0, -24, -24, -24, -4, 0, 0, 18, -16, 30, 0, -8, 1, -16, 6, 0, -16, 0, 16, -48, 0, -18, 0, -16, -6, -40, 24, 4, -12, -23, 0, 0, 16, 12, 12, 0, 8, -24, -24, 54, 0, 20, 8, 8, -1, 0, 16, 2, 6, -4, -30, 0, 0, -32, 8, 0, 2, -30, -4, 16, 0, 12, 6, -24, 0, 0, 14, 44, 0, -30, 0, 26, 12, 48, -24, 0, 1, 14, 1, 20, 0, 0, -28, -36, 2, 0, 6, 12, -18, 16, 0, 24, -4, -30, 24, 0, 6, 32, 0, -24, 10, -46, -32, 8, -16, 0, -36, 20, -4, 0, 0, 0, -1, 14, 20, 0, -24, -30, 32, 26, 0, 0, 12, 24, -4, 25, -34, 48, 14, 4, 0, 8, 8, 20, -12, 0, 12, 18, 0, 0, 0, -18, 12, 14, 0, 0, 4, -48, -11, 0, -10, -32, 2, 24, 32, 0, 6, 2, 0, -12, 0, -46, -16, 4, 0, 0, -4, 0, 12, -16, 0, -24, 8, 38, -22, -20, -9, -12, 12, -56, 0, 12, -24, 30, -4, 0, -8, -28, 8, -12, 0, -10, 24, -24, 18, 0, 0, -6, 26, -36, 20, 18, 8, 16, 6, 0, 6, -72, 0, -16, 0, 8, -6, 0, -8, 0, 12, -48, 24, 48, 0, 64, -3, 20, -4, 0, -50, 8, -8, 13, 0, -8, 8, -22, -16, 0, 0, 48, 6, 20, 0, 16, 24, -36, 8, 0, -22, 0, -6, 24, 0, 8, 0, 48, 0, 0, -16, -10, 14, 0, 0, 6, 32, 64, -24, 0, -24, 0, -2, 14, 0, -12, -10, -42, 8, 20, 14, -32, 30, -24, 0, 0, 0, 0, 9, 0, 12, -46, -12, -48, 0, 24, 6, -8, 20, 0, -16, 42, -32, 0, -5, -6, 30, 12, -16, 0, -8, 48, 18, 30, 0, 38, 0, -16, -24, 0, 2, -32, -10, -8, 0, 36, -12, -16, -16, 60, 0, 6, 0, -10, 0, -16, 2, -9, -4, 0, -24, -16, -30, -36, 0, -29, 2, -12, -10, 0, 0, -100, -6, -28, 5, 0, 0, -40, 16, 0, -6, -18, -24, -16, 0, 48, 24, 48, 4, 0, 2, -2, 16, 48, 0, 16, -16, 14, 0, 0, -4, 32, 8, -12, 0, 18, 9, -16, -2, 0, -24, 24, 8, 64, 0, -66, 8, 0, -12, 0, -4, 0, -18, 0, -5, 6, 36, 64, -6, 0, 32, -58, -6, 18, 0, 12, 8, 0, 26, 0, 14, 24, -4, 56, 0, -40, -6, 0, 48, 20, -16, -16, 0, -18, 0, -36, 18, -24, 12, 0, 2, -58, -32, 68, 0, -36, -28, 0, 0, 0, 48, 18, -16, 4, 20, 24, 4, -30, -6, 0, 24, 0, 24, -24, 0, -15, -8, -6, -10, 0, 0, -40, 25, -8, 0, -24, 10, -8, 8, 20, -4, 42, -4, -36, 0, -16, -12, 0, -12, 0, 0, 0, -8, 0, 0, -16, -4, 32, 0, 0, 0, -28, 14, -16, 0], 'weight': 2, 'weight_parity': 1}
  19. label: 35.2.a.a
    {'Nk2': 140, 'analytic_conductor': 0.27947640707448135, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[5, 1], [7, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [35, 1, [22, 31], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [0, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554467, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '35.2.a.a', 'level': 35, '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, 7], 'level_radical': 35, 'minimal_twist': '35.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{3}-2q^{4}-q^{5}+q^{7}-2q^{9}-3q^{11}+\\cdots', 'related_objects': ['EllipticCurve/Q/35/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '35.2.a', 'trace_display': [0, 1, -1, 1], 'trace_hash': 2198604108451929950, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.010', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.990', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.055', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.965', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.206', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.922', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, 'traces': [1, 0, 1, -2, -1, 0, 1, 0, -2, 0, -3, -2, 5, 0, -1, 4, 3, 0, 2, 2, 1, 0, -6, 0, 1, 0, -5, -2, 3, 0, -4, 0, -3, 0, -1, 4, 2, 0, 5, 0, -12, 0, -10, 6, 2, 0, 9, 4, 1, 0, 3, -10, 12, 0, 3, 0, 2, 0, 0, 2, 8, 0, -2, -8, -5, 0, -4, -6, -6, 0, 0, 0, 2, 0, 1, -4, -3, 0, -1, -4, 1, 0, 12, -2, -3, 0, 3, 0, -12, 0, 5, 12, -4, 0, -2, 0, -1, 0, 6, -2, 6, 0, 5, 0, -1, 0, 6, 10, -7, 0, 2, 4, 6, 0, 6, -6, -10, 0, 3, 0, -2, 0, -12, 8, -1, 0, -16, 0, -10, 0, -6, 6, 2, 0, 5, 0, -12, 0, 14, 2, 9, 0, -15, -8, -3, 0, 1, -4, -6, 0, -1, 0, -6, 0, 4, -10, 14, 0, 12, 0, -6, 0, 2, 24, 3, 0, -3, 0, 12, 0, -4, 20, -9, 0, 1, -12, 0, 0, 12, -4, 20, 0, 8, 0, -2, 0, -9, -18, -5, 0, 9, -8, -4, 0, -5, -2, 0, 0, -16, 0, -4, 0, 3, -6, 12, 0, 12, 20, -6, 0, -13, -24, 0, 0, 10, 0, -4, 0, 2, -6, 15, 0, -19, 0, -2, 0, -3, -4, -4, 0, -3, 0, 24, 0, -9, 0, -1, 0, -21, -4, -10, 0, 16, -16, -1, 0, 10, 0, 12, 0, 18, 4, 18, 0, -3, 16, 30, 0, 2, 10, -6, 0, 6, 0, -12, 0, -12, 8, -6, 0, -16, 12, 5, 0, -3, 12, -10, 0, 8, 0, 3, 0, -13, 0, -2, 0, -12, 0, -8, 0, -1, -4, -21, 0, 0, 0, 15, 0, -30, -2, -10, 0, 6, 8, -8, 0, 11, 6, 5, 0, 18, 0, -19, 0, 2, 2, -18, 0, -9, 8, 6, 0, 6, -2, 5, 0, -7, 0, 9, 0, -28, -24, -4, 0, 4, 4, 14, 0, 6, 6, 12, 0, 1, 0, 6, 0, -18, -6, 26, 0, -25, 0, 15, 0, 0, 24, 3, 0, 24, 0, -15, 0, -2, -10, -2, 0, 17, -24, 24, 0, 12, 8, -4, 0, -1, 0, 15, 0, 20, 4, -16, 0, 12, 0, 3, 0, 20, 2, -3, 0, -18, 0, -6, 0, 1, -12, -25, 0, 2, 4, -15, 0, -20, -12, -1, 0, -6, 0, 14, 0, -12, -10, 0, 0, -12, 0, 14, 0, -12, 2, 17, 0, -18, 0, 3, 0, 8, -12, -15, 0, 21, -20, 2, 0, -3, 14, -12, 0, 26, 0, -2, 0, -18, -4, 12, 0, -6, -8, -9, 0, 36, -12, -1, 0, -5, 0, 8, 0, -15, -12, -24, 0, 32, 12, 4, 0, 15, 20, -4, 0, 14, 0, 30, 0, 2, -6, -24, 0, -30, 0, 10, 0, -6, 4, 1, 0, 38, 0, 2, 0, 15, 24, 9, 0, -6, -16, 0, 0, -31, 2, -3, 0, 27, 0, -6, 0, 12, 32, -6, 0, 2, 0, -10, 0, -5, 20, -27, 0, -9, 0, -42, 0, 20, 12, 1, 0, -12, -12, 13, 0, 0, -4, -60, 0, -6, 0, 12, 0, -3, -10, 11, 0, 20, 0, 7, 0, 8, 24, -16, 0, 6, 0, -1, 0, -2, -28, -24, 0, -50, -4, -9, 0, 36, -18, -6, 0, 1, 0, 18, 0, -4, 30, 9, 0, -6, 16, -7, 0, -4, 6, 12, 0, -36, 0, 10, 0, -24, -2, -8, 0, 0, 8, -39, 0, -3, 12, -16, 0, 45, 0, -10, 0, 8, 2, 2, 0, -13, 0, 3, 0, 45, 12, 2, 0, 12, 0, 42, 0, 26, -8, 30, 0, -12, 20, 1, 0, -6, -28, 6, 0, 29, 0, -13, 0, 16, -24, 5, 0, 0, 0, -30, 0, 41, 12, 10, 0, -24, 0, 0, 0, -4, -4, -6, 0, 6, -48, -4, 0, -15, -6, 32, 0, 15, 0, -2, 0, -18, 6, -19, 0, -24, 0, -28, 0, -5, -24, 45, 0, -1, 0, -3, 0, -24, 8, 12, 0, -4, -40, 60, 0, -28, 18, 6, 0, -14, 0, -36, 0, 24, -2, -9, 0, 4, 24, -9, 0, 6, 0, 35, 0, 2, 0, 24, 0, 15, -24, -21, 0, -30, 8, 5, 0, -10, -40, 3, 0, 8, 0, 13, 0, -30, -16, -31, 0, -1, 0, 12, 0, -43, 4, 10, 0, -12, 0, 6, 0, -24, 18, 6, 0, 23, 36, 18, 0, 1, 10, -16, 0, 18, 0, 30, 0, -7, -18, 6, 0, 0, 16, 14, 0, 30, 8, 21, 0, -4, 0, 2, 0, -24, 10, 0, 0, -15, 4, -14, 0, 5, 0, 6, 0, 6, 0, 40, 0, -12, 32, 15, 0, 27, 0, 24, 0, -6, 8, 6, 0, -6, 0, -15, 0, 2, -6, -16, 0, -2, 12, -20, 0, -10, -24, -27, 0, -4, 0, -3, 0, 54, -24, -52, 0, -10, -40, 3, 0, 3, 12, 20, 0, -42, 0, -20, 0, 3, 26, -12, 0, -2, 48, -13, 0, -12, 0, -10, 0, 4, 0, -30, 0, -4, -20, -12, 0, 24, 0, 9, 0, -8, 8, 3, 0, -20, 0, 2, 0, -1, -4, 50, 0, -21, 12, 0, 0, 20, -30, 0, 0, -24, 0, -16, 0, -3, 38, 18, 0, -12, 0, -30, 0, -12, 4, 36, 0, -10, 0, -20, 0, 26, 6, -12, 0, -24, 8, -36, 0, -8, 8, -6, 0, 11, 0, 11, 0, 0, 6, 2, 0, -10, 0, 36, 0, 2, -48, 18, 0, 9, 0, 47, 0, -19, 18, 0, 0, 72, 0, 5, 0, 0, 2, 10, 0, -18, 0, 0, 0, -9, 42, -9, 0, -12, 8, -15, 0, -12, 20, 4, 0, -22, 0, 6, 0, -48, -32, 14, 0, 5, 32, 54, 0, 36, 2, 14, 0, -21, 0, 0, 0, 9, -20, 60, 0, 56, 0, -28, 0, 16, -24, -37, 0, -10, 0], 'weight': 2, 'weight_parity': 1}
  20. label: 35.2.a.b
    {'Nk2': 140, 'analytic_conductor': 0.27947640707448135, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[5, -1], [7, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [35, 1, [22, 31], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, 'field_disc': 17, 'field_disc_factorization': [[17, 1]], 'field_poly': [-4, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-4, 1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924963, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '35.2.a.b', 'level': 35, '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, 7], 'level_radical': 35, 'minimal_twist': '35.2.a.b', 'nf_label': '2.2.17.1', 'prim_orbit_index': 1, 'qexp_display': 'q-\\beta q^{2}+(-1+\\beta )q^{3}+(2+\\beta )q^{4}+q^{5}+\\cdots', 'related_objects': ['Genus2Curve/Q/1225/a'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '35.2.a', 'trace_display': [-1, -1, 2, -2], 'trace_hash': 1488746108957299258, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.947', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.290', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.723', 'prec': 14}, {'__RealLiteral__': 0, 'data': '2.753', 'prec': 14}, {'__RealLiteral__': 0, 'data': '68.273', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.021', 'prec': 7}, 'traces': [2, -1, -1, 5, 2, -8, -2, -9, 3, -1, 1, 6, 5, 1, -1, 3, -5, 7, -6, 5, 1, 8, -2, -4, 2, 6, -7, -5, 1, -8, 0, -9, -9, -6, -2, -1, 12, 20, -11, -9, 2, 8, 10, -6, 3, -16, -5, 24, 2, -1, 11, 4, -2, 12, 1, 9, -14, -26, -8, 6, 6, 0, -3, 7, 5, -4, 4, -4, 18, 1, 16, -5, -8, -6, -1, -32, -1, -20, -9, 3, -14, -18, 8, -6, -5, 12, 25, 4, 6, 7, -5, 12, 0, 28, -6, -4, -9, -1, 10, 5, -16, 20, 7, -14, 1, 18, 2, -26, 23, 8, -6, -3, -28, 24, -2, 28, 16, 4, 5, -4, -13, -54, 16, 0, 2, -7, 4, 23, -22, 6, -10, -14, 6, -36, -7, 14, -26, 8, -22, -5, -23, -8, 11, -21, 1, 38, -1, 30, 8, -8, 15, 44, -16, -8, 0, -2, 24, -4, -16, -9, 2, 7, -6, 22, -9, -4, 15, 4, -5, -6, 8, 8, -13, -4, -2, -24, 4, 14, 40, -1, 6, -6, 48, -8, 12, 0, -11, -38, 7, 20, -23, -12, 14, -38, -11, 5, -6, 12, -20, -9, 32, 42, -1, 2, 2, -12, -20, -18, 14, 8, -9, -22, -8, -52, 10, 40, 0, 14, -30, -6, -21, -48, -9, 9, 3, 14, 35, -52, 30, -16, 9, -30, 2, 26, -5, -20, 13, 6, 19, 24, 8, 15, 28, 66, 2, -8, 2, 0, -4, -1, -26, 1, -18, 32, 11, -17, 12, -40, -12, 4, -24, -12, -34, 32, -2, -20, -20, 44, 8, 12, -32, 18, 11, 30, 1, 28, 16, 28, 0, 9, 29, 20, -35, 40, -14, 20, -2, -5, -13, -26, 47, -54, 7, -8, -8, -54, 5, -38, -22, 6, -10, 52, -26, -60, 6, -26, -51, 6, 5, 0, 22, 24, 9, -46, -3, -14, -12, 8, -25, 7, 50, 16, -2, -35, 5, 20, -37, -26, 5, -4, 24, 20, 18, 52, 4, -24, -36, 45, 14, -4, 0, -4, -2, -28, 18, -2, 6, 54, -12, 1, -9, 4, -9, 32, 16, -2, -11, -20, 16, -5, 14, 82, -2, -4, -8, -24, -5, 48, -14, -6, 2, 0, 34, -20, -1, 48, -23, -12, 0, -32, -36, 20, -4, -20, -1, -58, 32, 20, -21, -20, 22, -9, 22, -14, -9, 8, 51, -24, 14, 3, 59, -16, 0, -74, -14, 26, 6, -24, -20, -18, -4, 26, 8, -24, 8, -14, -6, -24, 36, -6, 7, -72, 18, 26, -5, -64, -6, 56, -31, 12, -19, -36, 0, 0, 25, 32, -28, 32, -6, 4, 3, -32, -30, 36, 6, -4, 30, -7, 17, 7, -16, -70, -67, 8, -5, 80, -26, 2, 9, 12, -18, 4, -8, 78, 0, -18, 49, 6, -4, 28, 22, 36, 22, 36, -6, 4, 14, -52, 18, -4, 30, 30, -18, -41, -9, 20, 2, -78, -14, -1, -37, 40, 23, 16, 10, 0, -16, -32, 37, 5, -67, -4, 49, 5, -16, -8, -40, -24, -40, 20, 8, 39, 38, 62, 7, -4, 23, 6, 15, -14, 20, -22, 48, -8, 1, 0, 0, 12, -10, 18, -12, 32, -12, -24, 2, -52, -20, 98, 1, -26, -55, 16, -88, 14, 23, 20, 12, -82, -42, 8, -54, -64, 9, 26, -6, -72, -18, 0, 42, -3, 31, -6, -56, -66, -28, -8, 14, -72, 4, 24, 48, 2, 3, 18, -2, 19, -11, 49, 44, 28, -8, 36, 16, 70, 16, 22, -36, 6, 0, 4, 20, 18, -51, -28, 5, 54, 44, -40, -3, -4, -20, -12, -28, -22, -13, 64, -47, 44, -25, -54, 13, -6, 32, 0, 16, -4, 48, -28, -10, 0, -10, -96, -6, 60, 2, 106, 10, 94, -30, -7, -3, 32, 81, -62, 4, -40, 5, 4, 24, 23, 4, -8, -1, -12, -22, -16, 40, 63, -4, 6, 0, -32, 16, -92, -10, 54, 22, -28, -27, -14, -2, -12, 53, -36, 6, 42, 50, -22, 13, -36, -48, 4, 6, -50, -7, -55, -19, 112, 9, 14, -43, 0, 36, 20, -26, 1, -32, -36, 12, 8, -16, -24, -10, -20, -22, -104, 12, -62, 16, -5, 29, -4, -36, 12, -23, -38, 16, -24, 9, -8, -22, -10, 0, -20, 11, 100, 33, -8, 58, -21, -7, -109, -38, -70, 1, 52, 72, 14, -6, 38, -42, 120, 1, 28, -1, -8, -32, -10, 41, 30, -18, -18, 0, 0, 8, 34, 12, -2, -2, -8, 63, -84, 30, -48, 15, 26, 54, 68, 26, 44, 80, -16, -23, -66, -16, -32, -20, -68, -52, -8, -74, 86, 45, 52, 0, -2, 6, 70, -40, -2, 8, 40, -29, 3, 24, 40, -53, 2, 34, -4, 28, -28, -36, -34, -16, -16, 11, -24, -13, -9, 26, -38, 30, 80, 2, 0, -106, 106, -37, 7, -2, -28, 16, 48, -6, -60, 4, -58, -16, 22, 19, 104, -40, -40, -9, -4, 14, -16, 78, -4, -42, 26, -5, 88, 15, 52, 0, -52, -66, 4, 19, 22, -23, 54, -5, 8, 13, -54, 43, -6, -12, 48, -64, 54, 8, -60, -48, -44, 0, 8, -16, 52, -68, 40, -13, -34, -36, 0, -13, -4, -24, -78, -56, 48, -2, -92, -64, -48, -29, -24, 34, 7, 16, -10, 4, -36, 8, -24, -4, 14, -7, -14, 66, -32, 40, -23, 62, 34, 0, -1, -12, 8, 22, 126, 6, -60, 26, 62, 10, -6, -24, -72, 4, 30, 48, 58, 10, 4, 27, -8, 51, 26, 40, 14, 12, -64, 2, -30, -30, 0, -6, 22, 74, -16, -11, -38, -33, 36, -115, -38, 30, -96, 32, -12, 7, 40, 8, -10, 14, 20, 74, -14, -58, 10, -23, 90, 21, 8, 26, -12, -62, 36, -48, -14, 14, -8, -62, 67, 18, -38, 0, 36, 22, 16, -11, 162, -16, 24, 20, 5, 60, 112, 41, -72, -6, 48, 23, -12, -44, 12, -8, 0, -12, 8, -20, 24, 7, -112, -42, -9], 'weight': 2, 'weight_parity': 1}
  21. label: 36.2.a.a
    {'Nk2': 144, 'analytic_conductor': 0.2874614472766094, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [3, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [36, 1, [19, 29], [1, 1]], 'cm_discs': [-3], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554468, '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': '36.2.a.a', 'level': 36, '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': '36.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-4q^{7}+2q^{13}+8q^{19}-5q^{25}-4q^{31}+\\cdots', 'related_objects': ['EllipticCurve/Q/36/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.1.d1', 'self_twist_discs': [-3], 'self_twist_type': 1, 'space_label': '36.2.a', 'trace_display': [0, 0, 0, -4], 'trace_hash': 1143229866697692889, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.004', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.958', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.025', 'prec': 7}, {'__RealLiteral__': 0, 'data': '2.839', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.103', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.383', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.509', 'prec': 10}, 'traces': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, -58, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, -10, 0, 0, 0], 'weight': 2, 'weight_parity': 1}
  22. label: 37.2.a.a
    {'Nk2': 148, 'analytic_conductor': 0.2954464874787374, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[37, 1]], 'atkin_lehner_string': '+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [37, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [2, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554469, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '37.2.a.a', 'level': 37, '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': [37], 'level_radical': 37, 'minimal_twist': '37.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-2q^{2}-3q^{3}+2q^{4}-2q^{5}+6q^{6}+\\cdots', 'related_objects': ['EllipticCurve/Q/37/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '37.2.a', 'trace_display': [-2, -3, -2, -1], 'trace_hash': 1127515239490717889, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.992', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.946', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.828', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.009', 'prec': 4}, 'traces': [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 10, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2, -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6, -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0, -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2, 3, 0, 18, 0, -6, -2, -12, -18, -16, -20, 3, 4, -18, 0, -4, 12, -12, -16, 0, 0, 14, 16, 27, -8, 12, 12, 1, 0, -6, -8, -12, 30, 0, -16, 18, 0, -6, 12, 4, 4, 27, -18, 10, -24, -12, 2, 18, -2, -5, -6, 16, 0, 0, -10, 8, 12, 23, -8, -3, -16, -2, -18, -18, -18, -30, 30, -12, 0, -9, 0, 0, 4, 9, 36, 1, 20, -24, -8, 18, -24, 5, -4, 24, 0, 2, -24, 0, -18, 9, 0, -4, 24, -26, -8, -12, -12, 3, 60, 2, 0, -24, -6, -6, 0, 18, -36, 12, 8, 0, 12, -13, 2, -27, 24, -4, 0, 4, 32, 3, 20, 0, -6, -17, -8, -6, 36, -16, 0, 7, 8, -15, 0, 6, 24, 18, 16, -12, 0, -6, -24, 14, -28, 0, -16, 12, -54, 0, 0, 45, -24, -2, -12, -10, -2, 0, 16, 0, 12, 1, 8, 36, 24, 19, 0, -2, 0, -12, 16, -6, -36, -31, 0, -6, 12, 5, -12, 12, -8, -24, 0, 12, -54, 4, 18, 0, -20, 9, 48, -17, 24, -12, -2, -2, -36, -16, 0, 45, 10, -4, 6, -2, -32, -9, 0, 16, 0, -17, 10, -54, -16, 0, 0, 22, -46, 12, 8, 22, 6, -30, 16, 36, 4, 0, 18, 2, 36, 48, 0, 9, 60, -2, -30, -6, 24, -16, -12, -25, 18, 54, 0, 20, 0, 13, 0, 12, -18, -10, -36, 6, -2, 18, -40, 8, 48, -18, 8, 0, -36, -15, 0, -19, -10, -42, 4, 2, -48, 8, -8, -54, -4, -1, 24, -19, 0, -36, 0, -12, -18, 15, 0, -3, 8, 20, 0, -10, 52, 12, 8, 4, 24, 0, 0, 36, -6, -8, -60, -5, -4, 0, 4, 18, 48, 8, 6, -18, 12, 5, 0, 20, -36, 18, 36, -8, -24, 30, -16, -12, 0, 7, -12, -24, 26, -54, 0, 0, 54, 8, -24, -30, 8, -30, 36, 9, -8, 36, -32, 0, -6, 28, 0, -36, 0, 1, 6, -8, 34, 15, 8, 36, 12, 45, -36, -48, 32, -4, 0, 18, -14, 0, -8, 30, 30, -22, -24, -24, -12, -2, -24, -8, -36, -69, 0, -10, 24, 0, 0, 6, 12, 14, 48, 2, -28, 6, 28, -8, 0, -24, 0, 54, -24, -28, 54, 0, 0, 60, 16, -9, -90, 12, 24, 36, 4, 16, 0, -6, 20, 27, 2, -31, 0, 1, -32, 0, 0, -36, -12, 45, -2, -27, 0, -33, -72, -22, -24, -3, -38, 0, -60, -19, 4, 48, 0, 18, 24, 24, 0, -54, 12, 30, 36, 20, 62, -15, 0, 32, 12, 8, -12, -48, -10, 0, 0, -4, -24, -6, 8, -18, 48, -4, -8, 0, -24, -30, 54, 36, -8, -9, 0, -24, 0, 7, 20, 12, -18, -2, -48, 0, 34, 78, -24, 15, 24, -5, 0, 24, 4, -32, 36, 0, 32, -9, 4, -5, -90, 0, -10, -6, 8, 1, 0, -22, 4, 48, 32, -28, 18, -32, 0, 18, -32, 18, 0, 15, 34, -54, 0, 17, 108, -1, 16, -18, 0, -4, -24, -19, -44, 0, 46, 0, -24, -28, 0, 39, -44, -2, -6, 12, 60, 54, 0, -1, -72, 14, -4, 12, 0, -8, 0, -40, -4, -12, -36, -24, -96, 24, 36, -6, -18, -15, -60, -28, 4, 0, 0, 0, 12, 12, -24, 51, 32, 40, 24, 27, 50, 9, -18, -11, -108, -4, 0, 48, -40, 18, 0, 12, -26, -21, -8, -2, -24, -20, 18, 30, 20, -8, 0, 0, -12, -18, 2, -12, -36, 0, 40, -54, -16, -3, -48, 40, 36, 24, 0, -8, 0, -20, 36, 18, 30, 39, 48, -18, 38, -42, 10, -6, 84, 16, 0, -27, -4, 0, 48, 7, -16, -36, 16, -40, 108, -9, 4, 0, 2, 21, 0, 10, 38, -90, 0, 12, 72, 25, 36, 6, 24, -32, 18, -50, -30, 30, 0, -35, 6, 16, -8, 0, -40, -16, -48, 26, 20, 0, -52, -9, -24, 4, 0, -3, -8, 0, -24, -45, 0, -54, 24, -46, -72, -5, 6, -57, 16, 18, 0, 16, 10, 6, 4, 52, 0, 0, -8, 24, -36, 5, -48, 4, -16, 18, 0, 2, 36, 47, -12, 93, -10, 36, 0, 0, -40, 12, 36, -47, -36, -16, 0, -15, 16, 22, 24, -4, -60, -36, 16, 0, 24, 24, 0, 36, -14, 44, 0, 7, 48, -36, -26, 18, 108, -14, -4, -12, 0, -2, -54, 26, -16, 0, 0, -48, 60, -20, -8, -27, 60, -24, -72, -18, -18, 51, 8, -20, -72, -16, 0, 24, 0, -12, 6, 50, -56, 6, -40, -14, 72, 48, 0, 48, -2, 25, 0, -1, 16, -45, -34, 0, -30, -36, 0, 12, -72, -24, -12, 0, -90, 6, 0, -10, 96, 52, -32, 18, 8, 26, 0, 75, -36, -48, 14, 12, 0, -58, 0, 51, -60, -18, -30, 1, 44, 108, 48, 18, 48, 0, 12, 0, 4, 0, 0, 37, 16, -66, 36, -10, 138, -18, -32, -18, 20, 12, -24, 2, 0, -66, 0, 61, -12, 8, -12, 90, -28, 6, -48, -15, -4, -72, 28, 52, -12, -14, 0, 0, 16, -8, 0, -4, 48, -6, 32, 28, -108, -20, 24, -96, 56, 9, 0, -6, 0, -27, 0, 4, -120, -18, -32, 6, 18, -4, 90, -42, -24, 9, 0], 'weight': 2, 'weight_parity': 1}
  23. label: 37.2.a.b
    {'Nk2': 148, 'analytic_conductor': 0.2954464874787374, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[37, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [37, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [0, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924965, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '37.2.a.b', 'level': 37, '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': [37], 'level_radical': 37, 'minimal_twist': '37.2.a.b', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{3}-2q^{4}-q^{7}-2q^{9}+3q^{11}+\\cdots', 'related_objects': ['EllipticCurve/Q/37/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '37.2.a', 'trace_display': [0, 1, 0, -1], 'trace_hash': 683917573311474685, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.011', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.995', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.040', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.979', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.128', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.964', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.015', 'prec': 7}, 'traces': [1, 0, 1, -2, 0, 0, -1, 0, -2, 0, 3, -2, -4, 0, 0, 4, 6, 0, 2, 0, -1, 0, 6, 0, -5, 0, -5, 2, -6, 0, -4, 0, 3, 0, 0, 4, 1, 0, -4, 0, -9, 0, 8, -6, 0, 0, 3, 4, -6, 0, 6, 8, -3, 0, 0, 0, 2, 0, 12, 0, 8, 0, 2, -8, 0, 0, -4, -12, 6, 0, -15, 0, 11, 0, -5, -4, -3, 0, -10, 0, 1, 0, 9, 2, 0, 0, -6, 0, 6, 0, 4, -12, -4, 0, 0, 0, 8, 0, -6, 10, 3, 0, -4, 0, 0, 0, 12, 10, 2, 0, 1, -4, -6, 0, 0, 12, 8, 0, -6, 0, -2, 0, -9, 8, 0, 0, -7, 0, 8, 0, -6, -6, -2, 0, 0, 0, -6, 0, -4, 0, 3, 0, -12, -8, 0, 0, -6, -2, 15, 0, 8, 0, -12, 0, 0, 8, -13, 0, -3, 0, -6, 0, -16, 18, 0, 0, 18, 0, 3, 0, -4, -16, 9, 0, 5, 12, 12, 0, 18, 0, -7, 0, 8, 0, 0, 0, 18, -6, 5, 0, -24, -8, -4, 0, 0, 12, 15, 0, 2, 0, -4, 0, 6, -12, 0, 0, -12, -16, 6, 0, -13, 6, -15, 0, 0, 0, 4, 0, 11, 0, -24, 0, -1, 0, 10, 0, 24, -4, 23, 0, -3, 0, -18, 0, 0, -24, -10, 0, -6, 0, -10, 0, 16, -16, 0, 0, -8, 0, 9, 0, 0, -4, 18, 0, 0, 16, -24, 0, -1, 0, 12, 0, 15, 0, 0, 0, 6, 8, -18, 0, 29, 24, 4, 0, -15, -12, 8, 0, 8, 0, 0, 0, -4, 30, 0, 0, 9, 0, 19, 0, 8, -22, -18, 0, 0, 0, -15, 0, -24, 10, -8, 0, 3, 8, 0, 0, -25, 6, -4, 0, -6, 0, -28, 0, 0, 20, -18, 0, -18, 0, 12, 0, 12, -2, 20, 0, 2, 0, -3, 0, -10, -18, -2, 0, 0, -4, 23, 0, -6, 0, -12, 0, 13, 0, 0, 0, 6, 12, -10, 0, 20, 0, -18, 0, 0, -12, -6, 0, -27, 0, -15, 0, -2, -8, 0, 0, 8, 24, 18, 0, 3, 8, 5, 0, 0, 0, 24, 0, 11, 0, -7, 0, 36, 0, 0, 0, -16, -16, -12, 0, 36, 0, -6, 0, 0, 12, 11, 0, -2, -20, 24, 0, 16, -6, 0, 0, 3, 0, -4, 0, -6, 8, -12, 0, 0, 0, -4, 0, 3, 0, -10, 0, -6, 0, -30, 0, -8, -24, -12, 0, 12, -20, 29, 0, 0, -4, 12, 0, -28, 0, 12, 0, -15, -2, 0, 0, 15, 8, -6, 0, -27, 12, 8, 0, 0, 0, -28, 0, -30, 0, 36, 0, 14, -24, 0, 0, 18, -16, 4, 0, -13, 0, 24, 0, -10, 12, 6, 0, 18, 0, -4, 0, -6, 4, 0, 0, 2, 0, -16, 0, -12, 18, -36, 0, 0, -16, 15, 0, 32, 0, 18, 0, 42, 0, 0, 0, 3, 14, 21, 0, -11, 0, -10, 0, 0, -16, 9, 0, 9, 0, 3, 0, -16, 12, 5, 0, -24, 12, 13, 0, -24, 4, 36, 0, 0, 0, 18, 0, -18, 0, 20, 0, -7, 0, 0, 0, -28, 12, -16, 0, -12, 0, 10, 0, 0, 8, -30, 0, -32, 0, 18, 0, -12, -6, 0, 0, -1, 0, 12, 0, 23, 24, -24, 0, -30, 16, -34, 0, -4, 0, -9, 0, -9, 0, 0, 0, 6, 12, -8, 0, 15, 4, 27, 0, 0, -30, 2, 0, -27, 0, -10, 0, 8, -16, 0, 0, 14, 0, 6, 0, -12, 24, -25, 0, 0, 0, -15, 0, -37, 0, -30, 0, -6, -16, 25, 0, 6, 26, 6, 0, 38, 0, -13, 0, 0, 6, 24, 0, 30, 0, -9, 0, 14, 12, 0, 0, -6, 0, 36, 0, 4, 32, 36, 0, 0, -36, -22, 0, -3, 0, 50, 0, -24, 0, 0, 0, -36, -36, -1, 0, 24, 0, -1, 0, 25, -6, 21, 0, -8, 0, 24, 0, 24, 8, 0, 0, 23, 32, 12, 0, -28, -18, 6, 0, 0, 0, -54, 0, -18, -10, -48, 0, 2, -24, 0, 0, -3, -24, 26, 0, 20, 0, -24, 0, 0, -36, -6, 0, 15, 0, 4, 0, -10, 14, 30, 0, -10, 0, 13, 0, 48, -16, -13, 0, 0, 0, -12, 0, 11, 0, -8, 0, -27, 0, 0, 0, -18, -36, -12, 0, 41, 12, 0, 0, 0, -10, 2, 0, 18, 0, -15, 0, -2, 48, 0, 0, -48, 16, -22, 0, -24, 8, 3, 0, 20, 0, -1, 0, -18, 0, -45, 0, 30, -24, 0, 0, 23, -30, 15, 0, 6, 0, -32, 0, 0, -4, 12, 0, 18, 0, -12, 0, 33, 8, 0, 0, -18, 0, 30, 0, 11, -12, 29, 0, 0, 24, 16, 0, -8, 0, -3, 0, 32, 0, -15, 0, 30, 24, 20, 0, 8, 32, -36, 0, 0, -12, 20, 0, 0, 0, 7, 0, 0, 26, 0, 0, 2, -12, -4, 0, 6, 30, -46, 0, 0, 0, -6, 0, 14, 0, 9, 0, -48, 0, 0, 0, 19, -8, -30, 0, 16, 0, -16, 0, 0, -22, -22, 0, -18, 0, -6, 0, -52, 48, 0, 0, -3, 0, 7, 0, 3, 2, 6, 0, 0, 0, -24, 0, 24, -20, -18, 0, -8, 0, 0, 0, 8, -48, -6, 0, -24, 8, 27, 0, 0, -46, 6, 0, 20, 0, -25, 0, 60, 6, -5, 0, 8, 0, 6, 0, -12, 36, -6, 0, 0, 0, -7, 0, -28, 0, 30, 0, -54, 48, 0, 0, 18, 20, -44, 0, -18, 0, -3, 0, 0, 12, -18, 0, 6, 0, -15, 0, -24, 20, 0, 0, -22, 0, 12, 0, -12, -32, 4, 0, 20, 32, 12, 0, 18, 0, -4, 0, -27, 0, 0, 0, -3, 16, 48, 0, 20, 0, -10, 0, 0, -18, -10, 0, -5, 0], 'weight': 2, 'weight_parity': 1}
  24. label: 38.2.a.a
    {'Nk2': 152, 'analytic_conductor': 0.30343152768086545, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [19, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [38, 1, [21], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554470, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '38.2.a.a', 'level': 38, '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': [2, 19], 'level_radical': 38, 'minimal_twist': '38.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\\cdots', 'related_objects': ['EllipticCurve/Q/38/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '38.2.a', 'trace_display': [-1, 1, 0, -1], 'trace_hash': 1328635374754788503, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.999', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.037', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.973', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.147', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.869', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [1, -1, 1, 1, 0, -1, -1, -1, -2, 0, -6, 1, 5, 1, 0, 1, 3, 2, 1, 0, -1, 6, 3, -1, -5, -5, -5, -1, 9, 0, -4, -1, -6, -3, 0, -2, 2, -1, 5, 0, 0, 1, 8, -6, 0, -3, 0, 1, -6, 5, 3, 5, -3, 5, 0, 1, 1, -9, 9, 0, -10, 4, 2, 1, 0, 6, 5, 3, 3, 0, -6, 2, -7, -2, -5, 1, 6, -5, -10, 0, 1, 0, -6, -1, 0, -8, 9, 6, -12, 0, -5, 3, -4, 0, 0, -1, -10, 6, 12, -5, 18, -3, 14, -5, 0, 3, -9, -5, 11, 0, 2, -1, 6, -1, 0, 9, -10, -9, -3, 0, 25, 10, 0, -4, 0, -2, 2, -1, 8, 0, 0, -6, -1, -5, 0, -3, -9, -3, -4, 0, 0, 6, -30, -2, 0, 7, -6, 2, 0, 5, -10, -1, -6, -6, 0, 5, -22, 10, -3, 0, -3, -1, 20, 0, 0, 6, 12, 1, 12, 0, -2, 8, 6, -9, 5, -6, 9, 12, 0, 0, 2, 5, -10, -3, 0, 4, -18, 0, 5, 0, 3, 1, 14, 10, 0, -6, 0, -12, 11, 5, 5, -18, -9, 3, 0, -14, -6, 5, -6, 0, 5, -3, -6, 9, 0, 5, 4, -11, -7, 0, 15, -2, 26, 1, 10, -6, -15, 1, -22, 0, 6, -9, -6, 10, 0, 9, -10, 3, -21, 0, 8, -25, 16, -10, 0, 0, 5, 4, -6, 0, 6, 2, -18, -2, 0, 1, 12, -8, -2, 0, -18, 0, 24, 6, 0, 1, -12, 5, -6, 0, 11, 3, -5, 9, 30, 3, 8, 4, 8, 0, 0, 0, -22, -6, 0, 30, 0, 2, -8, 0, -10, -7, -21, 6, 0, -2, 30, 0, 15, -5, -8, 10, 18, 1, 0, 6, 20, 6, 14, 0, -21, -5, -19, 22, 0, -10, -9, 3, -54, 0, -9, 3, 3, 1, -25, -20, 11, 0, 0, 0, -1, -6, -4, -12, 0, -1, -4, -12, 6, 0, 24, 2, 13, -8, 0, -6, 18, 9, -10, -5, -25, 6, -15, -9, 0, -12, -3, 0, 21, 0, 1, -2, 25, -5, 0, 10, -28, 3, 0, 0, 3, -4, 23, 18, 0, 0, 45, -5, -7, 0, 2, -3, 18, -1, 0, -14, -16, -10, 18, 0, 9, 6, 0, 0, 0, 12, 20, -11, -1, -5, 0, -5, -20, 18, 0, 9, -12, -3, 32, 0, -9, 14, -9, 6, 0, -5, -4, 6, -12, 0, 17, -5, 0, 3, -15, 6, 10, -9, -30, 0, 6, -5, 2, -4, 0, 11, 3, 7, -28, 0, 12, -15, -18, 2, 0, -26, 0, -1, -18, -10, 0, 6, -10, 15, 0, -1, 17, 22, -15, 0, -12, -6, -4, 9, 0, 6, 18, -10, -5, 0, -22, -9, -48, 10, -5, -3, 6, 21, 36, 0, 10, -8, -3, 25, 0, -16, 2, 10, 20, 0, -36, 0, 27, -5, 0, -4, 6, 6, -4, 0, 12, -6, -21, -2, 0, 18, 12, 2, 30, 0, 7, -1, -5, -12, 0, 8, 0, 2, 6, 0, -36, 18, 11, 0, 5, -24, -12, -6, -14, 0, -18, -1, 0, 12, 0, -5, 0, 6, 36, 0, 2, -11, 2, -3, 0, 5, 44, -9, 20, -30, 9, -3, 10, -8, 0, -4, 24, -8, 40, 0, -18, 0, -12, 0, 0, 22, -1, 6, -24, 0, -4, -30, 3, 0, -15, -2, 11, 8, 14, 0, 6, 10, 18, 7, 0, 21, -12, -6, -4, 0, 0, 2, -30, -30, 0, 0, 11, -15, -24, 5, -28, 8, -10, -10, 0, -18, -22, -1, -9, 0, 0, -6, 2, -20, 0, -6, -6, -14, -10, 0, -15, 21, 12, 5, 25, 19, -6, -22, 6, 0, -16, 10, 5, 9, 0, -3, -30, 54, 12, 0, 6, 9, -22, -3, 0, -3, 27, -1, -54, 25, 4, 20, 24, -11, 0, 0, 14, 0, -45, 0, -13, 1, 15, 6, 0, 4, 27, 12, 26, 0, 60, 1, 44, 4, 25, 12, -33, -6, 10, 0, -15, -24, 36, -2, 0, -13, -22, 8, -15, 0, -10, 6, -12, -18, 0, -9, 0, 10, -6, 5, 12, 25, 2, -6, 0, 15, -18, 9, -10, 0, 20, 12, -12, 3, 0, 0, -21, -21, 39, 0, -14, -1, 8, 2, -45, -25, -37, 5, 13, 0, 24, -10, 32, 28, 0, -3, -30, 0, -16, 0, 5, -3, -36, 4, 0, -23, 12, -18, 9, 0, -40, 0, 6, -45, 0, 5, 2, 7, -18, 0, -21, -2, -11, 3, 0, -18, 45, 1, 5, 0, 12, 14, 51, 16, 20, 10, -2, -18, 0, 0, 36, -9, -45, -6, 0, 0, -31, 0, 24, 0, -6, -12, -50, -20, 0, 11, -39, 1, 0, 5, 24, 0, 42, 5, 0, 20, -6, -18, 9, 0, 11, -9, 11, 12, 0, 3, 8, -32, 10, 0, 0, 9, 41, -14, 30, 9, 33, -6, 11, 0, 8, 5, -18, 4, 0, -6, 20, 12, -48, 0, 52, -17, 0, 5, 0, 0, -25, -3, -22, 15, 6, -6, -46, -10, 0, 9, -12, 30, 14, 0, 0, -6, -18, 5, 0, -2, -8, 4, 60, 0, 25, -11, 20, -3, 0, -7, 23, 28, -21, 0, -18, -12, -34, 15, 0, 18, -42, -2, -2, 0, -6, 26, 0, 0, 0, 1, 15, 18, -36, 10, -9, 0, -8, -6, 0, 10, -37, -15, -36, 0, 48, 1, 36, -17, 0, -22, 0, 15, -7, 0, 20, 12, -30, 6, -10, 4, -28, -9, 33, 0, -6, -6, -21, -18, 0, 10, -7, 5, -19, 0, 21, 22, 0, 9, 0, 48, -48, -10, -35, 5, -9, 3, 30, -6, 0, -21, -54, -36, 9, 0, -15, -10, 18, 8, 0, 3, 32, -25, 3, 0, 12, 16, 4, -2, -25, -10, -12, -20, 72, 0, -22, 36, -30, 0, 0, -27, 0, 5, 24, 0, 20, 4, -1, -6, 0, -6, 8, 4, -10, 0], 'weight': 2, 'weight_parity': 1}
  25. label: 38.2.a.b
    {'Nk2': 152, 'analytic_conductor': 0.30343152768086545, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [19, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [38, 1, [21], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924966, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '38.2.a.b', 'level': 38, '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': [2, 19], 'level_radical': 38, 'minimal_twist': '38.2.a.b', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/38/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '38.2.a', 'trace_display': [1, -1, -4, 3], 'trace_hash': 51301870551309226, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.026', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.978', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.086', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.919', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.256', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.703', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.015', 'prec': 7}, 'traces': [1, 1, -1, 1, -4, -1, 3, 1, -2, -4, 2, -1, -1, 3, 4, 1, 3, -2, -1, -4, -3, 2, -1, -1, 11, -1, 5, 3, -5, 4, -8, 1, -2, 3, -12, -2, -2, -1, 1, -4, -8, -3, 4, 2, 8, -1, 8, -1, 2, 11, -3, -1, -1, 5, -8, 3, 1, -5, 15, 4, 2, -8, -6, 1, 4, -2, 3, 3, 1, -12, 2, -2, 9, -2, -11, -1, 6, 1, -10, -4, 1, -8, -6, -3, -12, 4, 5, 2, 0, 8, -3, -1, 8, 8, 4, -1, -2, 2, -4, 11, 2, -3, -6, -1, 12, -1, -7, 5, -15, -8, 2, 3, 14, 1, 4, -5, 2, 15, 9, 4, -7, 2, 8, -8, -24, -6, 18, 1, -4, 4, 12, -2, -3, 3, -20, 3, -17, 1, 0, -12, -8, 2, -2, -2, 20, 9, -2, -2, 0, -11, 2, -1, -6, 6, 32, 1, -2, -10, 1, -4, -3, 1, -16, -8, 8, -6, -12, -3, -12, -12, 2, 4, -6, 5, 33, 2, -15, 0, 0, 8, 22, -3, -2, -1, 8, 8, 6, 8, 15, 4, 7, -1, -6, -2, -4, 2, 8, -4, -25, 11, -3, 2, -15, -3, 32, -6, 2, -1, -2, 12, 27, -1, -2, -7, -16, 5, -24, -15, -9, -8, -3, 2, 14, 3, -22, 14, -17, 1, -10, 4, -6, -5, -6, 2, -32, 15, 10, 9, 15, 4, -8, -7, -16, 2, -8, 8, 1, -8, 6, -24, 2, -6, -2, 18, 12, 1, 8, -4, -6, 4, 10, 12, 24, -2, 4, -3, 0, 3, 30, -20, 7, 3, 3, -17, 22, 1, 28, 0, 16, -12, -8, -8, -6, 2, -4, -2, -24, -2, -8, 20, 2, 9, 9, -2, -60, -2, 10, 0, 1, -11, 12, 2, -2, -1, -8, -6, -12, 6, 6, 32, 7, 1, 29, -2, 24, -10, -27, 1, -10, -4, 7, -3, -3, 1, -11, -16, 15, -8, 24, 8, 17, -6, 4, -12, -12, -3, -32, -12, -14, -12, -16, 2, -15, 4, -4, -6, -2, 5, 10, 33, -5, 2, 9, -15, -8, 0, -9, 0, -15, 8, 1, 22, 7, -3, -36, -2, 28, -1, 16, 8, -3, 8, 29, 6, 24, 8, 5, 15, 15, 4, -18, 7, -26, -1, -24, -6, -8, -2, -30, -4, -3, 2, -12, 8, 40, -4, 8, -25, 3, 11, -8, -3, 8, 2, -4, -15, -4, -3, -20, 32, 17, -6, 45, 2, 24, -1, 0, -2, 0, 12, -13, 27, -16, -1, 33, -2, 6, -7, 2, -16, -18, 5, 14, -24, -20, -15, 1, -9, 20, -8, -4, -3, -26, 2, 0, 14, 0, 3, 10, -22, -16, 14, -2, -17, 12, 1, -7, -10, 15, 4, -28, -6, 4, -5, -32, -6, -2, 2, 9, -32, 2, 15, 8, 10, -11, 9, 2, 15, -20, 4, 2, -8, 3, -7, 8, -16, -2, 2, 16, -8, -28, 8, -15, 1, 16, -8, 6, 6, 40, -24, 12, 2, 39, -6, -8, -2, 12, 18, -30, 12, 27, 1, -5, 8, 24, -4, 16, -6, 6, 4, -28, 10, 29, 12, -33, 24, -24, -2, -22, 4, -30, -3, 8, 0, 28, 3, 0, 30, 4, -20, 2, 7, -22, 3, 60, 3, 28, -17, -4, 22, 5, 1, -30, 28, -8, 0, 28, 16, -4, -12, -6, -8, -36, -8, -56, -6, 3, 2, 40, -4, -28, -2, -7, -24, -11, -2, -37, -8, 6, 20, -18, 2, -2, 9, -8, 9, -12, -2, 8, -60, -8, -2, 34, 10, -36, 0, 25, 1, 0, -11, -8, 12, -6, 2, 28, -2, -22, -1, 15, -8, -8, -6, 34, -12, -32, 6, 18, 6, 10, 32, -5, 7, 0, 1, 41, 29, 2, -2, -6, 24, 32, -10, -27, -27, -72, 1, -2, -10, -4, -4, 42, 7, -26, -3, 16, -3, 23, 1, 30, -11, 24, -16, -36, 15, -48, -8, -18, 24, 5, 8, -23, 17, 3, -6, 12, 4, 5, -12, -14, -12, 4, -3, 44, -32, 55, -12, 13, -14, -6, -12, 17, -16, 4, 2, 68, -15, 10, 4, 1, -4, 42, -6, -12, -2, 0, 5, -24, 10, 6, 33, -28, -5, 2, 2, 32, 9, 6, -15, -30, -8, 20, 0, 8, -9, 8, 0, -15, -15, -5, 8, -18, 1, 8, 22, -55, 7, -17, -3, 13, -36, 12, -2, -36, 28, 8, -1, 6, 16, -40, 8, -1, -3, -16, 8, 0, 29, 12, 6, -21, 24, 32, 8, -2, 5, -8, 15, -2, 15, 2, 4, 27, -18, -45, 7, 24, -26, -15, -1, -35, -24, -8, -6, 9, -8, -88, -2, 6, -30, 8, -4, 4, -3, -25, 2, 8, -12, -17, 8, -24, 40, 42, -4, -2, 8, -4, -25, 3, 3, 24, 11, 0, -8, 18, -3, 12, 8, -30, 2, -15, -4, -3, -15, -7, -4, 64, -3, -4, -20, 6, 32, 12, 17, 29, -6, -22, 45, 23, 2, -15, 24, -28, -1, 6, 0, 48, -2, -40, 0, 20, 12, -4, -13, 8, 27, 48, -16, -21, -1, 6, 33, 2, -2, -6, 6, -8, -7, -12, 2, -50, -16, 24, -18, 54, 5, 24, 14, 8, -24, -20, -20, -3, -15, 4, 1, -72, -9, 13, 20, -9, -8, -18, -4, 34, -3, 60, -26, -2, 2, 54, 0, 2, 14, -8, 0, 0, 3, -1, 10, 40, -22, -3, -16, -12, 14, -88, -2, 53, -17, -4, 12, 12, 1, -12, -7, 8, -10, 36, 15, 5, 4, 12, -28, -2, -6, -22, 4, 12, -5, -55, -32, -2, -6, -7, -2, -24, 2, -7, 9, -29, -32, 7, 2, 8, 15, -60, 8, -12, 10, -9, -11, 27, 9, -46, 2, -28, 15, 10, -20, -51, 4, 33, 2, 14, -8, 24, 3, 48, -7, 3, 8, -28, -16, 0, -2, 11, 2, 8, 16, 0, -8, 30, -28, -6, 8, -32, -15, -24, 1, -4, 16, -8, -8, -17, 6, 100, 6, 28, 40, -10, -24], 'weight': 2, 'weight_parity': 1}
  26. label: 39.2.a.a
    {'Nk2': 156, 'analytic_conductor': 0.3114165678829935, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, 1], [13, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [39, 1, [14, 28], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554471, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '39.2.a.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': '39.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{3}-q^{4}+2q^{5}-q^{6}-4q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/39/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '39.2.a', 'trace_display': [1, -1, 2, -4], 'trace_hash': 1907566206816012334, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.978', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.925', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.763', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [1, 1, -1, -1, 2, -1, -4, -3, 1, 2, 4, 1, 1, -4, -2, -1, 2, 1, 0, -2, 4, 4, 0, 3, -1, 1, -1, 4, -10, -2, 4, 5, -4, 2, -8, -1, -2, 0, -1, -6, 6, 4, -12, -4, 2, 0, 0, 1, 9, -1, -2, -1, 6, -1, 8, 12, 0, -10, 12, 2, -2, 4, -4, 7, 2, -4, -8, -2, 0, -8, 0, -3, 2, -2, 1, 0, -16, -1, 8, -2, 1, 6, 4, -4, 4, -12, 10, -12, -2, 2, -4, 0, -4, 0, 0, -5, 10, 9, 4, 1, -18, -2, 0, -3, 8, 6, 12, 1, -2, 8, 2, 4, -6, 0, 0, 10, 1, 12, -8, 6, 5, -2, -6, -4, -12, -4, -16, -3, 12, 2, 4, 4, 0, -8, -2, -6, 6, 0, 12, 8, 0, 0, 4, -1, -20, 2, -9, 2, -6, 1, 4, 0, 2, -16, 8, 1, -18, 8, -6, 10, 0, 1, 8, -6, -8, 4, -8, -12, 1, 4, 0, 12, 6, 10, 4, -4, -12, -2, 4, -2, -10, -4, 2, 0, -4, -4, 8, 0, 4, 0, 8, -7, 18, 10, -2, -9, 18, 4, 8, 3, 8, -18, 40, 2, 12, 0, 0, -1, 0, 8, -20, -6, 0, 12, -24, 3, -16, -2, -2, -8, 2, 2, 4, -20, -1, -6, -20, 0, -10, 0, 16, 30, -14, 1, 0, -12, -8, -8, -24, 2, 10, 5, -1, 2, 18, -6, 0, -12, -4, -12, -12, 4, 0, -16, -4, -17, 26, 12, 8, -2, -10, 4, 24, 12, 12, 0, 2, 8, 22, -2, -12, -2, 4, 6, -4, 0, -10, 12, 4, 24, -10, 0, 12, 0, 0, 4, -24, 5, -13, -20, -10, -2, -6, -9, 24, 6, -4, -6, 0, -1, 48, 4, 18, 0, -4, 2, -16, 16, 0, 8, 0, 3, -6, -18, -8, -8, 26, -6, -40, 14, -12, 0, 0, -1, -1, 8, 2, -18, 0, -8, -16, -4, -2, -8, -16, -4, 18, 1, 6, -4, 16, 0, -8, 36, 0, 6, -12, -10, -26, 4, -1, 20, -2, -12, 0, 2, 8, 4, 24, -6, -19, -10, -5, 4, 4, 2, 16, 0, 6, -4, -24, 4, -26, 8, 12, 0, -10, 4, -24, 0, 16, 8, -16, 3, -32, 18, -12, -10, 22, -2, 0, -27, -4, 18, 16, -4, 38, 8, 0, 1, 22, 8, 4, 18, 2, 40, -8, 6, 34, 12, -6, 0, -48, 0, 8, 5, -12, 0, 4, -8, -10, -20, 0, -18, -2, 0, 8, -12, -4, -24, 0, 1, 34, -16, 20, 2, 0, -2, 32, -24, 9, 2, -4, -2, -4, 4, 6, -28, 22, -1, 24, 6, -4, -20, -8, 0, 2, -10, -2, 0, -38, 16, 4, 10, -8, -14, 12, -1, 32, 0, 18, -36, -48, -8, 0, 8, 6, -24, -24, -10, -2, 10, 0, -5, 20, -1, 12, 6, -8, 18, -12, 6, -20, 0, 8, -4, 0, -4, -24, 12, 8, -12, -8, 12, -36, 0, -1, 16, 10, -4, -8, -11, 0, 26, 0, -12, 0, 8, -6, -6, 18, -10, 44, -4, -4, 24, 8, 4, -23, 12, 12, 0, 6, 2, 24, 24, -4, 22, 36, 2, 30, -12, 10, 10, -4, 4, 4, -6, -2, -4, 0, 0, -32, -10, 4, -12, 18, 4, -12, 8, -8, -10, -12, 0, -12, 12, -4, 0, 34, 0, -4, -4, -8, -24, 0, 7, -46, -13, -18, 20, -16, -10, 24, -6, 2, -6, 28, 9, 0, 24, -18, 2, -26, -4, -16, 6, -8, 0, -40, -3, -38, 48, -8, -4, 10, 18, -16, 0, -40, -4, 0, -2, -2, -16, -12, 48, 22, 0, 24, -8, 0, 0, 8, 1, -19, -6, 0, 18, -4, -8, 20, -24, 20, 26, -32, 6, 9, -40, 0, -6, 2, -12, -40, 0, 24, 0, -8, -3, 48, -1, 16, -8, 6, 2, 8, -6, 2, 0, 28, 8, 30, -16, -2, -12, 0, -2, 0, 8, -4, -16, -8, 20, -14, 18, 1, -1, 22, 6, -40, -12, 20, 16, -12, 0, 12, -8, 10, 12, 6, 0, -24, -6, -16, -12, 24, -30, 12, -26, 14, -4, -34, -1, 0, 28, 0, -2, 72, 12, -26, 0, 8, 6, 0, 8, 8, -4, 24, 24, -24, -2, 0, -19, -10, 10, 10, -5, 8, 12, 1, 4, -24, -2, 30, 16, -18, 0, -32, 6, 32, 4, 0, -24, 48, 12, -12, -26, 4, -8, -48, 12, 8, 0, 12, -10, 8, -4, 22, -24, 0, 0, -10, 16, 8, -8, 4, -16, 12, 17, -30, -32, -26, -18, 10, -12, -4, -30, -8, 22, 0, 2, 0, 0, 10, -9, -36, -4, -32, -18, -24, 16, 24, -12, -2, 38, -12, -8, 46, 0, 0, -5, -2, 22, 8, -8, 0, 4, -22, 54, -30, 2, 8, -40, 12, -8, 16, 2, 0, 34, -4, -12, -22, -6, 0, 0, 4, -48, 4, 0, -34, 8, 10, 7, 18, -12, -16, 0, -4, 4, 48, -24, 71, -10, 10, 20, 2, 0, -20, -6, -12, -2, 0, 0, 30, 8, 0, -36, -46, -4, -44, 24, 24, 0, 16, -5, 12, 34, 13, 16, 32, 20, -8, 6, 10, 0, 48, 2, -10, 32, 6, -8, 58, 9, -44, -2, -24, -4, -48, -6, 64, -4, 4, -4, 0, 6, 8, 12, 0, 22, -40, 1, 12, 24, -48, 18, -20, -4, 12, 20, -18, -8, -40, 0, 16, 2, 4, 10, -16, -2, -48, 0, 16, -38, 0, -16, 2, 4, 0, -50, 30, -8, 0, 14, 0, 12, 16, -3, 26, 32, 6, 0, -14, 18, 0, -12, 8, -48, -60, 8, 2, 0, -26, 24, -30, 6, 16, 24, 40, -24, -24, -14, -15, -2, 12, -10, 36, 0, -52, -15, 0, 20, -60, 1, -48, 12, 1, 2, -42, -8, -8, -18, -2, -12, 16, 18, 36, -20, 0, 0, 0, 8, 16, 20, 16, 0, 16, 4, -26, -24, 2, 36], 'weight': 2, 'weight_parity': 1}
  27. label: 39.2.a.b
    {'Nk2': 156, 'analytic_conductor': 0.3114165678829935, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1], [13, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [39, 1, [14, 28], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 2, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924967, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '39.2.a.b', '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': '39.2.a.b', 'nf_label': '2.2.8.1', 'prim_orbit_index': 1, 'qexp_display': 'q+(-1+\\beta )q^{2}+q^{3}+(1-2\\beta )q^{4}-2\\beta q^{5}+\\cdots', 'related_objects': ['Genus2Curve/Q/1521/a'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '39.2.a', 'trace_display': [-2, 2, 0, 0], 'trace_hash': 1437883122427244167, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.007', 'prec': 4}, {'__RealLiteral__': 0, 'data': '1.887', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.090', 'prec': 7}, {'__RealLiteral__': 0, 'data': '8.929', 'prec': 14}, {'__RealLiteral__': 0, 'data': '1.541', 'prec': 14}, {'__RealLiteral__': 0, 'data': '58.986', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.025', 'prec': 7}, 'traces': [2, -2, 2, 2, 0, -2, 0, -6, 2, -8, -4, 2, -2, 8, 0, 6, 4, -2, 0, 16, 0, 4, -8, -6, 6, 2, 2, -16, 4, -8, -8, 6, -4, 12, -16, 2, -4, -8, -2, -8, 16, 8, 8, -4, 0, 8, -12, 6, 2, -6, 4, -2, -4, -2, 0, 8, 0, -4, 4, 16, 4, 16, 0, -14, 0, 4, 8, -28, -8, 16, 4, -6, 12, -12, 6, 16, 0, 2, 0, 0, 2, -24, -4, -16, -32, -24, 4, 12, 24, -8, 0, -8, -8, -4, 16, 6, -4, -2, -4, 6, 4, 12, 16, 6, -16, 4, 0, 2, -12, 16, -4, 0, 12, -8, 0, 4, -2, 12, 32, -8, -14, 28, 16, -24, 0, 8, 0, 10, 8, 8, -16, -4, -16, 0, 0, 4, -16, 8, 8, -16, -12, -4, 4, 6, 0, -28, 2, 28, -24, -6, -24, -8, 4, -16, -16, -2, -20, -32, -4, -8, 0, -2, 32, 32, 0, 20, 4, 8, 2, 16, 0, 40, -12, -4, 0, -12, 4, -16, -24, 16, 28, -8, 4, 24, 32, 16, -8, 20, 0, -16, -16, -14, -12, 20, 0, 2, -16, 4, 32, -18, 8, 12, 0, -28, 16, -32, -8, -6, 0, 16, -24, -4, 4, -32, 32, -6, 16, 44, 12, -32, -4, -12, -8, 8, 6, -44, -12, 16, 20, 32, 0, -12, -20, 2, 32, -28, 0, -16, 4, 0, 12, 14, 2, -60, 0, -24, 0, 32, -4, 16, 0, -16, 16, 16, -32, -26, -20, -24, -32, -16, 4, 16, 24, 12, 0, 16, 24, -8, 36, -8, -16, 12, 0, 8, -12, -8, -4, -40, -8, 48, 48, -4, 24, 4, 16, -4, -16, 6, 38, -16, -4, 44, -24, -2, -32, -4, -4, 32, 8, 6, -32, 48, 4, 0, -64, 12, -40, 32, 16, 48, 24, 6, 12, 20, -16, 64, 0, 4, -8, -16, 0, -32, -32, 2, -6, -24, -12, -56, -32, 16, 24, -36, -4, -20, -16, 0, -4, -2, 12, 0, 16, -8, 0, -40, 0, -4, -40, 4, -4, 24, -2, -12, -16, 12, 0, 8, 32, -8, 36, -8, -22, -28, -14, 16, 32, 28, -48, -24, 16, -16, 0, -24, 20, -24, 0, 20, -4, 8, -16, 16, 0, 48, 28, 10, 32, 44, 8, -36, -20, 8, -16, -6, -16, 40, 64, -4, 28, -16, -16, 18, 24, 0, 8, -28, 0, 16, 8, 4, -36, -80, -16, 48, 32, 8, -32, -6, 8, 16, -16, -16, 52, 24, -12, 12, 12, -4, 64, 64, 4, -64, 28, 6, -20, -48, 0, -76, 0, -28, 0, 16, 2, -12, 16, 28, -16, -16, -24, 16, -24, -6, -32, 76, -24, -20, 16, -8, -4, -52, 4, -64, 16, -16, -32, 12, -16, 68, -16, -2, 16, 16, -20, 4, -16, -32, 0, 0, -4, -4, 28, -8, 4, -28, 0, -14, -32, -2, 24, 20, 32, -8, 16, 32, 8, 8, 0, -24, 0, 20, 24, -32, 4, 0, 8, 8, -32, -16, 2, -32, -16, 16, -32, 54, 0, 36, 32, 40, 24, 16, -12, 8, 28, -4, -8, -16, 0, -24, 16, -12, -14, 16, 4, -16, -16, -16, 64, -16, -24, -36, -4, 16, 20, -40, 28, 28, -64, -8, 24, 0, 4, 12, 0, 24, -64, 4, 32, 72, 24, 16, -8, -48, -8, -56, 8, 20, 64, 24, 0, -12, -52, -16, 8, 4, -16, 80, -24, -14, 4, 26, -12, 32, 32, 20, 8, -52, 0, 64, 12, 2, -16, 16, -16, -12, -24, 4, -32, -40, 32, -8, -24, -18, 44, 64, 8, -72, 0, 12, 16, -8, 0, 48, 12, -28, -84, 32, 16, -16, -64, -32, 8, -80, -8, -88, 16, -6, -62, -12, 0, -20, -72, 16, 24, -32, -24, 24, -32, -4, -2, 8, 4, 88, 4, -32, 40, 64, 32, 16, 0, -6, -8, 6, 16, 16, -28, 44, 0, 48, 12, -16, -72, -32, -36, 16, -4, 28, 0, -12, -16, 36, -8, -16, -8, 8, -12, 36, 6, 2, 76, -44, 32, 80, -12, -32, 28, 16, 16, -48, 20, 24, 4, 32, -40, 20, 0, 72, 64, -12, 0, 20, -20, -48, 44, 2, 32, 28, 32, -56, 32, -28, 36, -16, 0, -64, 32, -16, 0, 40, 4, 12, 8, 0, -32, 22, 12, 28, 12, 14, -32, -8, 2, -80, -48, -60, -28, 48, 0, -24, -16, -24, -8, 0, 0, -16, 4, 32, -16, -20, -4, 56, -64, 16, 32, -36, 0, 4, -48, -16, 36, 40, 16, -48, 48, 16, 64, -80, -32, 20, -4, -26, 84, -32, -20, -76, 40, -24, -24, 28, -32, -28, 16, -16, -8, -48, 4, 6, 0, 16, -8, -64, 24, -64, -64, 12, -4, 20, 0, 0, 60, 16, -88, 18, 24, 16, -24, -8, 64, -16, 36, 4, 60, -8, -32, -32, -16, 24, -16, 12, 32, -12, 0, 144, -8, 8, 64, -64, -12, -16, -52, -8, -12, 48, -4, 14, 4, -40, 32, -32, -8, 80, -4, 48, -50, -20, 48, -24, 0, -4, 0, -12, 24, 36, 16, 4, -4, -48, 16, -32, -20, -4, -24, 96, -16, -44, -68, 6, 32, -12, 38, 80, 0, -16, -8, 68, -4, 32, 32, 44, 28, 48, -24, 0, 28, -2, -24, 28, -32, -112, -16, -4, 32, -80, -4, 40, 32, 32, 64, -88, 8, -32, -16, 6, -8, 48, -32, -68, 0, 48, 8, 52, 4, -16, -80, 0, 8, -12, -64, 84, 0, 12, -16, 32, -40, -24, -4, 32, -12, 8, 16, 12, -16, 48, 0, -116, 24, 16, 64, 6, -20, 16, 12, -64, 40, 20, -64, 12, -16, 48, -76, 64, -12, -24, 0, -80, 92, 4, -64, 4, -8, 4, -16, -16, -14, 12, 0, 44, -64, -32, 8, 42, -32, 48, -8, 2, -64, -80, -6, 12, 56, -24, -48, 16, -12, 48, 28, -56, -48, 24, -32, -16, -32, 16, 32, -16, 24, 16, -32, -36, 12, 16, -4, 16], 'weight': 2, 'weight_parity': 1}
  28. label: 40.2.a.a
    {'Nk2': 160, 'analytic_conductor': 0.3194016080851215, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [5, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [40, 1, [31, 21, 17], [1, 1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554472, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '40.2.a.a', 'level': 40, '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': '40.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{5}-4q^{7}-3q^{9}+4q^{11}-2q^{13}+\\cdots', 'related_objects': ['EllipticCurve/Q/40/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '40.2.a', 'trace_display': [0, 0, 1, -4], 'trace_hash': 716883178609633242, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.010', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.974', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.902', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.660', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [1, 0, 0, 0, 1, 0, -4, 0, -3, 0, 4, 0, -2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 1, 0, 0, 0, -2, 0, -8, 0, 0, 0, -4, 0, 6, 0, 0, 0, -6, 0, -8, 0, -3, 0, 4, 0, 9, 0, 0, 0, 6, 0, 4, 0, 0, 0, -4, 0, -2, 0, 12, 0, -2, 0, 8, 0, 0, 0, 0, 0, -6, 0, 0, 0, -16, 0, 0, 0, 9, 0, -16, 0, 2, 0, 0, 0, -6, 0, 8, 0, 0, 0, 4, 0, -14, 0, -12, 0, 6, 0, 4, 0, 0, 0, 0, 0, 14, 0, 0, 0, 18, 0, 4, 0, 6, 0, -8, 0, 5, 0, 0, 0, 1, 0, -12, 0, 0, 0, 12, 0, -16, 0, 0, 0, 10, 0, 12, 0, 0, 0, -8, 0, -2, 0, 0, 0, -10, 0, -16, 0, -6, 0, -8, 0, -2, 0, 0, 0, -16, 0, 16, 0, 0, 0, 12, 0, -9, 0, -12, 0, 14, 0, -4, 0, 0, 0, 20, 0, -10, 0, 0, 0, 6, 0, 8, 0, 0, 0, 8, 0, -14, 0, 0, 0, 22, 0, 8, 0, 0, 0, 8, 0, -6, 0, -12, 0, 16, 0, -4, 0, 0, 0, -8, 0, 32, 0, 0, 0, -4, 0, -4, 0, -3, 0, -24, 0, -26, 0, 0, 0, -6, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 9, 0, -8, 0, 0, 0, -12, 0, 16, 0, 0, 0, -30, 0, -24, 0, 6, 0, -12, 0, 6, 0, 0, 0, 14, 0, 24, 0, 0, 0, 4, 0, -10, 0, 24, 0, 10, 0, 8, 0, 0, 0, 24, 0, -13, 0, 0, 0, -26, 0, -4, 0, 0, 0, -8, 0, 32, 0, 0, 0, -2, 0, -8, 0, 0, 0, 32, 0, 26, 0, 12, 0, -18, 0, -8, 0, 0, 0, 8, 0, -2, 0, 0, 0, -16, 0, -12, 0, -18, 0, 8, 0, -14, 0, 0, 0, -32, 0, -8, 0, 0, 0, -16, 0, 30, 0, 0, 0, 2, 0, 0, 0, 0, 0, -24, 0, -3, 0, 0, 0, -6, 0, 20, 0, 18, 0, -24, 0, 22, 0, 0, 0, 4, 0, -20, 0, 0, 0, -36, 0, -16, 0, 24, 0, 6, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, 0, 18, 0, 16, 0, 9, 0, 24, 0, 10, 0, 0, 0, 16, 0, -16, 0, 0, 0, 36, 0, 6, 0, -12, 0, 2, 0, 8, 0, 0, 0, -40, 0, 2, 0, 0, 0, 16, 0, -8, 0, -27, 0, 24, 0, -6, 0, 0, 0, 18, 0, -24, 0, 0, 0, 8, 0, 10, 0, 0, 0, -18, 0, 12, 0, 0, 0, 8, 0, -32, 0, 0, 0, -32, 0, 4, 0, -18, 0, 16, 0, -12, 0, 0, 0, -14, 0, -20, 0, 0, 0, 36, 0, -4, 0, -12, 0, 0, 0, -28, 0, 0, 0, -12, 0, 6, 0, 0, 0, -2, 0, 24, 0, 0, 0, 4, 0, 16, 0, 0, 0, 10, 0, -8, 0, 0, 0, -16, 0, -7, 0, 12, 0, 12, 0, 0, 0, 0, 0, 36, 0, -2, 0, 0, 0, 14, 0, 8, 0, 6, 0, -8, 0, 0, 0, 0, 0, 14, 0, 16, 0, 0, 0, 16, 0, 18, 0, -36, 0, -22, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 64, 0, 24, 0, 6, 0, -48, 0, -32, 0, 0, 0, 18, 0, -8, 0, 0, 0, -24, 0, 10, 0, -24, 0, 5, 0, -12, 0, 0, 0, -8, 0, -42, 0, 0, 0, -6, 0, -4, 0, 0, 0, 24, 0, 1, 0, 0, 0, 12, 0, 16, 0, 0, 0, -12, 0, -18, 0, 0, 0, 18, 0, -48, 0, 0, 0, 12, 0, -16, 0, 0, 0, -34, 0, 12, 0, 18, 0, -12, 0, -42, 0, 0, 0, -16, 0, -8, 0, 0, 0, -8, 0, 18, 0, 0, 0, 22, 0, 56, 0, 0, 0, 24, 0, 10, 0, 0, 0, -12, 0, 44, 0, 48, 0, 12, 0, -12, 0, 0, 0, -34, 0, 24, 0, 0, 0, -24, 0, 38, 0, 0, 0, -32, 0, -8, 0, 0, 0, -32, 0, -16, 0, 0, 0, -2, 0, 44, 0, -27, 0, -16, 0, 30, 0, 0, 0, 32, 0, 36, 0, 0, 0, 36, 0, -10, 0, 48, 0, 0, 0, -24, 0, 0, 0, -16, 0, -10, 0, 0, 0, -6, 0, -56, 0, -6, 0, 8, 0, 34, 0, 0, 0, -42, 0, -8, 0, 0, 0, -24, 0, 0, 0, 0, 0, -2, 0, 8, 0, 0, 0, -72, 0, 4, 0, 0, 0, -18, 0, 8, 0, 18, 0, -24, 0, -16, 0, 0, 0, 42, 0, -28, 0, 0, 0, 16, 0, -32, 0, -24, 0, 22, 0, 4, 0, 0, 0, 48, 0, -2, 0, 0, 0, 18, 0, 12, 0, 0, 0, -40, 0, -25, 0, 0, 0, -9, 0, -20, 0, 0, 0, 24, 0, 38, 0, -12, 0, -6, 0, -4, 0, 0, 0, 12, 0, 14, 0, 0, 0, 0, 0, -16, 0, 42, 0, -4, 0, 46, 0, 0, 0, -30, 0, -16, 0, 0, 0, -20, 0, 48, 0, 36, 0, 16, 0, 20, 0, 0, 0, 16, 0, 12, 0, 0, 0, -10, 0, 48, 0, -18, 0, 40, 0, -64, 0, 0, 0, -48, 0, 8, 0, 0, 0, 0, 0, 6, 0, -12, 0, -14, 0, 36, 0, 0, 0, 8, 0, -38, 0, 0, 0, 46, 0, -24, 0, 0, 0, -8, 0, 12, 0, 0, 0, -6, 0, 8, 0, 0, 0, -40, 0, 33, 0, 0, 0, -14, 0, -36, 0, 0, 0, 20, 0, -48, 0, 0, 0, 2, 0, -24, 0, -42, 0, 36, 0, 22, 0, 0, 0, -32, 0, -40, 0, 0, 0, 8, 0, -42, 0, 0, 0], 'weight': 2, 'weight_parity': 1}
  29. label: 41.2.a.a
    {'Nk2': 164, 'analytic_conductor': 0.32738664828724956, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[41, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [41, 1, [6], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 3, 'field_disc': 148, 'field_disc_factorization': [[2, 2], [37, 1]], 'field_poly': [1, -3, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554473, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '41.2.a.a', 'level': 41, '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': [41], 'level_radical': 41, 'minimal_twist': '41.2.a.a', 'nf_label': '3.3.148.1', 'prim_orbit_index': 1, 'qexp_display': 'q+(-\\beta _{1}-\\beta _{2})q^{2}+\\beta _{2}q^{3}+(1+2\\beta _{1}+\\cdots)q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 3, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '41.2.a', 'trace_display': [-1, 0, -2, 6], 'trace_hash': 1843874081841428676, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.029', 'prec': 7}, {'__RealLiteral__': 0, 'data': '2.851', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.427', 'prec': 10}, {'__RealLiteral__': 0, 'data': '21.355', 'prec': 17}, {'__RealLiteral__': 0, 'data': '5.686', 'prec': 14}, {'__RealLiteral__': 0, 'data': '245.964', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.006', 'prec': 4}, 'traces': [3, -1, 0, 5, -2, -6, 6, -9, -1, -10, 2, -4, -2, 4, 6, 13, -6, 11, 4, 6, -8, -4, 4, -2, -3, 10, -6, 14, -6, 10, 16, -29, -12, 2, -10, -11, -6, 2, 4, -14, 3, -20, -4, 34, -10, -4, 0, 24, -1, 13, 0, -30, 6, 14, 2, -16, 12, 14, -8, 18, 2, 16, 4, 13, -8, -16, -2, -10, 20, -30, 20, 23, -2, -30, -16, -24, 16, 8, 32, 34, -13, -1, 0, -12, 4, -8, -16, -40, -6, 2, -8, -28, -12, -46, -6, 2, 6, 35, -4, 3, 18, 12, -4, 42, 28, 10, -16, -2, -6, -34, 18, 2, 6, 4, 0, -2, 10, 0, -12, -14, 11, 30, 0, 8, 0, 26, 16, -17, -4, 24, -20, 16, -4, 4, -8, 18, 18, 12, -12, -6, 12, 18, -32, -47, -8, -26, -38, 18, 10, -10, 28, 22, 2, 8, -32, -20, -14, -26, -16, -10, -12, -37, -16, 5, 28, 24, -14, 0, -11, 20, 2, 20, -30, -4, 10, 22, 20, 18, 2, -34, -34, 12, -8, 20, 36, -44, -4, 68, 4, 14, 14, 12, -26, -26, -12, 5, 50, 38, 46, 13, 12, -34, 4, 8, -2, -72, -4, -46, -40, 48, 10, 18, 0, 48, 12, 22, 44, -50, -22, 14, 4, 30, -8, -60, 13, -18, 8, -24, -6, 24, -26, 22, 26, -34, 46, -48, 4, -8, 16, -22, 6, -17, 32, -42, -34, -6, 28, -8, -32, 40, -28, -8, -52, -8, -12, 61, 10, 4, -30, -32, 14, -24, 20, -20, -16, 0, 28, -34, 10, 0, -4, -26, 4, -54, 22, -20, -2, 92, 16, -14, 38, 12, -4, -16, -16, 44, 6, 39, -39, 0, 32, 94, 42, -36, 8, -42, 20, 14, 32, -4, -4, -46, -12, 4, -32, -22, -40, 52, 32, -56, 10, 24, -34, 62, -30, 76, -42, -28, 20, 62, -24, -20, -8, 33, -6, 24, 20, -9, -12, 24, 6, 16, -30, 32, -2, 56, -38, -39, 46, -12, 4, -16, -6, -24, -32, 34, 12, 0, -50, 36, -4, -84, -22, 36, -38, -98, 16, -80, -24, 46, -9, -6, 26, -40, 28, -12, -16, 28, -1, 24, 28, -52, -54, 8, -4, -114, -4, 32, 48, -2, 20, 96, -22, -18, -24, 6, -8, -6, 2, 4, -8, 31, 8, 14, -6, -48, 22, 24, 10, -61, -6, 16, 8, 110, 50, 32, 6, 4, 6, -10, 64, 76, -36, -20, -24, 82, -68, 20, -4, 52, 22, -64, -46, -14, 6, -40, 12, -64, -28, -4, -12, -74, 30, 76, 20, 54, 60, -18, 50, -50, 35, -20, 80, 54, -12, -40, -56, 14, 22, -3, 2, -50, 16, 22, -4, 16, 10, 78, 12, 16, -38, -58, -4, -74, 56, -22, -56, 62, -16, -22, -60, 56, 28, -60, -28, -28, 10, -26, -2, -62, -24, -62, 32, -7, 20, -2, 8, 70, 8, -38, -8, -4, 12, -24, -34, -16, 40, -32, 48, -72, -20, 40, -40, 30, 16, 4, 24, -8, -50, -20, 18, -5, -32, -62, 76, 28, 56, -90, -32, 64, -42, -14, 20, 12, -36, 22, -32, 28, 11, -40, 0, -24, -2, 40, -32, 40, 40, 22, 44, -48, 30, -20, 56, 58, 56, 20, -68, -2, 30, 36, -32, 12, 60, -2, -48, -60, -50, 40, -24, 90, 24, 6, 58, 80, 12, 52, -40, 14, 2, -4, -6, -64, -52, 4, -44, -75, -46, 13, 20, -48, 32, 20, 28, -118, 24, 54, -18, -30, 28, 64, -8, 102, -38, 40, 20, 94, -36, -16, -40, 10, 26, -20, 4, 88, 6, -48, -52, 26, -28, 8, -68, 22, 46, 44, 6, -60, 94, 40, 44, -32, -48, 4, -40, -20, -25, 70, -50, -18, 12, -26, 52, -134, 48, -38, -8, -16, -6, 40, 18, -70, -2, 8, -34, -36, 0, -4, -64, -57, -60, -26, -88, -80, -6, 32, 44, 13, -26, -104, 44, 36, 26, -40, -8, 8, 4, 6, -48, -38, 24, 34, -36, 52, 26, 90, 38, 19, 50, 34, -20, 28, 0, 52, -28, 26, 36, 78, -52, 20, -12, -32, 4, -34, 8, -14, -80, 12, -6, 6, -48, 10, -78, -36, -18, 114, -24, 10, 48, -4, 34, -42, -26, 122, 16, 40, -12, 82, 44, -72, 0, -38, -40, 3, 80, -134, 38, 4, 24, 60, 11, -64, 8, -56, 66, 44, 74, 28, -44, 11, 72, 84, 36, 48, -68, 20, -24, -30, 24, -68, -8, -4, 50, 184, -8, -36, 18, -4, 2, -56, -48, 22, 22, -12, -32, -74, 20, 68, 40, -8, 54, -92, -4, -78, -18, 12, 8, -26, 84, -110, 4, -20, -36, 8, 44, -143, -48, 48, -52, 38, -104, -114, -34, 90, 44, -22, 44, 70, 10, 18, 0, 25, 18, 122, 118, -16, 32, -8, 32, -162, -102, 30, -36, -4, 12, -102, -8, -48, -36, 78, 12, 6, -38, 28, 24, -144, 8, -36, 86, 12, -18, -40, -54, -126, 2, -44, -18, 20, -8, -160, 42, -32, -43, 66, 8, 42, 50, 68, -4, -22, -84, -26, 0, -76, -22, 72, 14, 128, 50, 36, 8, 20, -8, -16, 32, 54, -4, 6, 0, 68, 40, 36, 32, -98, -26, -12, 4, 78, 34, -128, 8, 142, 30, 3, -32, 60, -56, -20, -34, -42, 12, 92, 32, 24, -56, -76, 78, -16, 40, -14, -8, 39, -12, -4, 12, 26, 40, -40, 8, -36, -34, 44, 72, 20, 48, 2, 20, -58, -48, -28, 90, 8, -8, -14, 36, -22, -30, -102, -72, 54, -54, 120, -46, 166, 56, 40, -4, -106, 6, -8, 4, 138, 26, -32, 4, -24, -36, -36, -24, -16, -96, -10, 20, 32, -82, 30, -110, -20, 20, 12, -28, 2, 35, 72, 48, -30, 20, 56, 46, -21, -24, 20, -72, 92, 44, 180, -12, -114, -6, 40, -120, -106, -50, 72, 100, -2, -64, -28, 70, 4, -40, 18, 76, -96, -48, 76, -70, -16, 30, -22, -24, 112], 'weight': 2, 'weight_parity': 1}
  30. label: 42.2.a.a
    {'Nk2': 168, 'analytic_conductor': 0.3353716884893776, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [3, 1], [7, 1]], 'atkin_lehner_string': '-++', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [42, 1, [29, 31], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554474, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '42.2.a.a', 'level': 42, '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': [2, 3, 7], 'level_radical': 42, 'minimal_twist': '42.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/42/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '42.2.a', 'trace_display': [1, -1, -2, -1], 'trace_hash': 1611795495172191507, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.004', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.976', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.039', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.927', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.133', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.761', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.015', 'prec': 7}, 'traces': [1, 1, -1, 1, -2, -1, -1, 1, 1, -2, -4, -1, 6, -1, 2, 1, 2, 1, -4, -2, 1, -4, 8, -1, -1, 6, -1, -1, -2, 2, 0, 1, 4, 2, 2, 1, -10, -4, -6, -2, -6, 1, -4, -4, -2, 8, 0, -1, 1, -1, -2, 6, 6, -1, 8, -1, 4, -2, 4, 2, 6, 0, -1, 1, -12, 4, 4, 2, -8, 2, 8, 1, 10, -10, 1, -4, 4, -6, 0, -2, 1, -6, -4, 1, -4, -4, 2, -4, -6, -2, -6, 8, 0, 0, 8, -1, -14, 1, -4, -1, -2, -2, 8, 6, -2, 6, 12, -1, -2, 8, 10, -1, -14, 4, -16, -2, 6, 4, -2, 2, 5, 6, 6, 0, 12, -1, 0, 1, 4, -12, -20, 4, 4, 4, 2, 2, 10, -8, 4, 2, 0, 8, -24, 1, 4, 10, -1, -10, 6, 1, -8, -4, 2, 4, 0, -6, -10, 0, -6, -2, -8, 1, 20, -6, -8, -4, -8, 1, 23, -4, -4, -4, 22, 2, 1, -4, -4, -6, -12, -2, -18, -6, -6, 8, 20, 0, -8, 0, 1, 8, 0, -1, 2, -14, 12, 1, -10, -4, 8, -1, -4, -2, 2, -2, 12, 8, 8, 6, 16, -2, 20, 6, -8, 12, 8, -1, 0, -2, -10, 8, 12, 10, -16, -1, -1, -14, 12, 4, -2, -16, -4, -2, -22, 6, 0, 4, 0, -2, 0, 2, 2, 5, -1, 6, -2, 6, -24, 0, 4, 12, -12, -1, -32, 0, 4, 1, -30, 4, 10, -12, -2, -20, -24, 4, -12, 4, 6, 4, 22, 2, 0, 2, 6, 10, 4, -8, -10, 4, 0, 2, 26, 0, 4, 8, -8, -24, 6, 1, -13, 4, 14, 10, 30, -1, -8, -10, 4, 6, 48, 1, 4, -8, 2, -4, -12, 2, 28, 4, -8, 0, -8, -6, 10, -10, 2, 0, -18, -6, 8, -2, -12, -8, -8, 1, -6, 20, 2, -6, 0, -8, -4, -4, -10, -8, -8, 1, 18, 23, 14, -4, 0, -4, -1, -4, 16, 22, 12, 2, 22, 1, -6, -4, -30, -4, -16, -6, 2, -12, -8, -2, -3, -18, -5, -6, -20, -6, 32, 8, -6, 20, -6, 0, 22, -8, -12, 0, -12, 1, -20, 8, 0, 0, -16, -1, -8, 2, -4, -14, -26, 12, 16, 1, 20, -10, 0, -4, 6, 8, -4, -1, 18, -4, 0, -2, -2, 2, 40, -2, -22, 12, -10, 8, -4, 8, 8, 6, -4, 16, -36, -2, 6, 20, 0, 6, -2, -8, -6, 12, 24, 8, 0, -1, 2, 0, -4, -2, -32, -10, -24, 8, 1, 12, -4, 10, 12, -16, -6, -1, 34, -1, 24, -14, 8, 12, 12, 4, 10, -2, -2, -16, 22, -4, -32, -2, 0, -22, 28, 6, -4, 0, 10, 4, 16, 0, 4, -2, 6, 0, -16, 2, -60, 2, 8, 5, 28, -1, 8, 6, -20, -2, 12, 6, -4, -24, 8, 0, -8, 4, -44, 12, 8, -12, 24, -1, 4, -32, -23, 0, 6, 4, -10, 1, 4, -30, -16, 4, 0, 10, -22, -12, -6, -2, 20, -20, -1, -24, 0, 4, 41, -12, 4, 4, -36, 6, -24, 4, 12, 22, -4, 2, 30, 0, 18, 2, 4, 6, -12, 10, 6, 4, 8, -8, 0, -10, -20, 4, -2, 0, -24, 2, 8, 26, 44, 0, 28, 4, -1, 8, -6, -8, 12, -24, 0, 6, -8, 1, 34, -13, -2, 4, 4, 14, -24, 10, -12, 30, -28, -1, 0, -8, 10, -10, 18, 4, 4, 6, -8, 48, 24, 1, 26, 4, 4, -8, -10, 2, 48, -4, -2, -12, 0, 2, -42, 28, -12, 4, -22, -8, -44, 0, -8, -8, 6, -6, -19, 10, -16, -10, -20, 2, 8, 0, -20, -18, 0, -6, 6, 8, 8, -2, 2, -12, -4, -8, -8, -8, 24, 1, -16, -6, 0, 20, -18, 2, 40, -6, 10, 0, -28, -8, -2, -4, -12, -4, -8, -10, -16, -8, 16, -8, -24, 1, 2, 18, 1, 23, -18, 14, 14, -4, -12, 0, 12, -4, -20, -1, 2, -4, 36, 16, -4, 22, 4, 12, -8, 2, -12, 22, 22, 1, -2, -6, 40, -4, 0, -30, 2, -4, -10, -16, 0, -6, 0, 2, 48, -12, 0, -8, 0, -2, -8, -3, -2, -18, 2, -5, -8, -6, 1, -20, -8, -6, 6, 32, 2, 8, -16, -6, -12, 20, 24, -6, 24, 0, -12, 22, -4, -8, -12, -12, 48, 0, 12, -12, 16, 1, 6, -20, 32, 8, -22, 0, 2, 0, -4, -16, 24, -1, -14, -8, 30, 2, -2, -4, 0, -14, -10, -26, 24, 12, -32, 16, 2, 1, 20, 20, -36, -10, 24, 0, 14, -4, 36, 6, 12, 8, 6, -4, 0, -1, -6, 18, -40, -4, 16, 0, -22, -2, 10, -2, -44, 2, 0, 40, -40, -2, 16, -22, -6, 12, 38, -10, -56, 8, -4, -4, -36, 8, -26, 8, 10, 6, 2, -4, 16, 16, 0, -36, 56, -2, -25, 6, -26, 20, -46, 0, -5, 6, -4, -2, -80, -8, 14, -6, 8, 12, 42, 24, 20, 8, -6, 0, -32, -1, -44, 2, 13, 0, 0, -4, 24, -2, -14, -32, -12, -10, -2, -24, -30, 8, 18, 1, 20, 12, 8, -4, -24, 10, 0, 12, -4, -16, 0, -6, 24, -1, -48, 34, 0, -1, 12, 24, -4, -14, 36, 8, 12, 12, -2, 12, 0, 4, 16, 10, 12, -2, 20, -2, 40, -16, -28, 22, 48, -4, 10, -32, 8, -2, 18, 0, -4, -22, 8, 28, 16, 6, -22, -4, -10, 0, -26, 10, -48, 4, -2, 16, 4, 0, 60, 4, 18, -2, 26, 6, 0, 0, -8, -16, -10, 2, -31, -60, 12, 2, -4, 8, 8, 5, 8, 28, -12, -1, -4, 8, 6, 6, 18, -20, 24, -2, -2, 12, -24, 6, 20, -4, 0, -24, -32, 8, -16, 0, 4, -8, -16, 4, 14, -44, 10, 12], 'weight': 2, 'weight_parity': 1}
  31. label: 43.2.a.a
    {'Nk2': 172, 'analytic_conductor': 0.34335672869150563, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[43, 1]], 'atkin_lehner_string': '+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [43, 1, [3], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [2, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554475, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '43.2.a.a', 'level': 43, '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': [43], 'level_radical': 43, 'minimal_twist': '43.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-2q^{2}-2q^{3}+2q^{4}-4q^{5}+4q^{6}+\\cdots', 'related_objects': ['EllipticCurve/Q/43/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '43.2.a', 'trace_display': [-2, -2, -4, 0], 'trace_hash': 1979952357373928000, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.982', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.915', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.669', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.012', 'prec': 7}, 'traces': [1, -2, -2, 2, -4, 4, 0, 0, 1, 8, 3, -4, -5, 0, 8, -4, -3, -2, -2, -8, 0, -6, -1, 0, 11, 10, 4, 0, -6, -16, -1, 8, -6, 6, 0, 2, 0, 4, 10, 0, 5, 0, -1, 6, -4, 2, 4, 8, -7, -22, 6, -10, -5, -8, -12, 0, 4, 12, -12, 16, 2, 2, 0, -8, 20, 12, -3, -6, 2, 0, 2, 0, 2, 0, -22, -4, 0, -20, -8, 16, -11, -10, 15, 0, 12, 2, 12, 0, -4, 8, 0, -2, 2, -8, 8, -16, 7, 14, 3, 22, -9, -12, 1, 0, 0, 10, -12, 8, 7, 24, 0, 0, -20, -8, 4, -12, -5, 24, 0, 0, -2, -4, -10, -2, -24, 0, 1, 0, 2, -40, 8, -12, 0, 6, -16, 0, 6, -4, 19, 0, -8, -4, -15, -4, 24, -4, 14, 0, 12, 44, -20, 0, -3, 0, 4, 20, -10, 16, 10, -32, 0, 22, 14, 10, 24, -30, -9, 0, 12, -24, -2, -2, 6, -24, 0, -12, 24, 8, 20, -8, 10, 0, -4, 0, 0, -4, -9, 8, 0, -16, -16, 16, 3, -14, -40, -14, 2, -6, 14, 0, 6, 18, 0, 12, -20, -2, -1, 20, -6, 0, 2, -10, -4, 24, 4, 0, 0, -14, -4, -24, 15, 0, -28, 0, 11, 40, -4, 8, -15, -8, 0, 0, 6, 10, -16, -24, 16, 0, 16, -32, -12, 4, 10, 4, 28, 20, 10, 0, -30, 48, -23, 0, -3, -2, -24, 16, -24, -4, 0, 40, -6, -16, -18, 0, 20, 0, 8, -6, -25, 32, 23, 12, 0, -12, 33, 4, -32, -38, -1, 0, 19, 16, 21, 4, -16, 30, 0, 8, -8, -48, -14, 4, -26, -28, 48, 0, 12, -24, 5, -44, 0, 40, 18, 8, -8, 6, -7, 0, -2, -8, 15, 0, 22, 20, 0, -16, 9, -20, -18, 32, 24, 0, 6, -22, -55, -28, -14, 0, 0, -48, -26, 30, 0, 18, 12, 0, -3, -24, 40, 24, -3, 4, 0, 0, -8, -12, 28, 24, 14, 0, -20, 24, -31, -48, -8, -8, 0, -40, 19, 0, -15, -20, 4, 0, -8, 8, -32, 4, 5, 0, 0, 4, 32, 18, 48, 0, 30, 0, 11, 16, -2, 32, 32, 0, 0, -6, -1, 14, 6, 80, 3, 0, -16, -4, 32, 6, -6, -28, 0, -44, 5, -12, 5, -18, 44, 0, 0, 0, -24, 40, -12, 2, 0, 2, -60, -40, -38, 12, -28, 0, -10, -4, 4, 0, -33, 8, 0, -24, 30, -8, -21, -16, -12, 0, -48, 14, 2, 8, 17, 0, -7, -30, -4, 0, 16, 56, -24, 0, 30, -22, 15, -40, 40, 8, 0, 0, -18, 30, -12, 8, 30, 0, 4, 24, -8, -12, 6, -10, 0, 32, 20, 0, -3, -32, -22, 0, -5, -32, 21, 64, 0, 24, 0, -4, -28, -20, 36, 0, -28, -56, -6, -20, 18, -20, -12, 4, 0, 60, -8, -48, 18, 46, 6, 0, 36, 6, -24, 2, -15, 48, 0, -32, -8, 48, -4, 4, 12, 0, -12, 0, 14, 12, 12, 16, 0, 36, 3, 24, -22, -40, -12, 0, -25, -16, 48, 0, -40, 50, -21, -32, 1, -46, -20, -24, -28, 0, -29, 12, 2, -66, 12, 0, 0, 64, 0, 38, -3, 2, 5, 0, 18, -38, 37, -16, 80, -42, 0, 0, 7, 32, -14, -30, 32, 0, -11, -8, -20, 16, -6, 48, 0, 28, -15, 0, 20, 52, 2, 28, 2, -96, -4, 0, -16, -24, 0, 24, -28, -10, -1, 0, -4, 0, -3, -40, 8, -36, -4, -16, 0, 16, -20, -6, -18, 14, 40, 0, -21, 4, 36, 8, -4, -30, 0, -40, 41, -44, 12, -20, 0, 0, -6, 0, -4, -18, -4, 20, 35, 36, 2, 0, 12, -48, -36, 0, -8, -12, -12, 0, -36, 110, 0, 28, -14, 28, -32, -20, 2, 0, -19, 48, 31, 52, -30, 0, 0, 0, 6, -18, 56, -24, 6, 0, 14, 6, 44, 24, 34, -80, 0, 0, 8, 6, -9, -4, -24, 0, 30, 4, 25, 16, -40, 12, 0, -56, -76, 0, -15, -28, -12, 0, -2, 40, 0, -24, 32, 62, 0, 48, -1, 16, -8, 0, 1, 0, 60, 40, -32, -38, 8, 16, 0, 30, 24, 20, -66, -8, 16, 0, 13, 16, 3, -8, 32, 64, -56, -8, -9, -10, -10, 0, -20, 0, -24, 0, -48, -64, 15, -18, 0, -96, -6, -16, 46, -60, 80, 0, 28, -22, 6, 0, 20, 4, 0, -32, 12, -64, 60, -32, -42, 0, 48, 6, -4, 2, -11, 0, 0, -12, -10, -80, 6, -6, -24, 28, 40, 32, 4, 4, 36, -64, 0, 0, -10, 12, -40, 28, -42, 0, -12, 88, -4, -10, 6, 12, 0, -10, 50, 0, 26, -88, -14, 0, -46, 0, -56, -24, 2, 48, 0, -40, 49, 24, -1, 0, -66, 0, -36, -2, 44, 120, 64, 40, 21, 76, 36, -12, -4, 56, -40, 0, 7, 20, -38, 4, -48, -8, 0, 20, -42, 66, 0, -8, -29, 0, 8, 0, -10, -60, -32, 8, 0, 42, -6, 32, -24, 24, 16, 0, -24, 96, 15, 0, 7, -4, 0, -8, 41, -34, 52, 48, 37, 14, 31, 30, -96, 8, -22, 0, 0, -32, -33, -56, -8, 48, -80, 0, -10, -60, 6, 22, 15, -30, 0, 0, -40, -80, 47, -8, -9, 0, -22, -16, 45, 36, 16, -30, 0, 24, -49, 0, 14, -60, -10, 0, 0, -8, 1, -48, -6, 16, 14, 12, -30, -12, 36, 0, 32, 0, -44, -32, 33, -40, -5, 48, 0, 6, -33, 32, -10, 44, -18, 0, 22, 10, 64, 32, 36, -42, 0, -64, -30, 0, -12, -24, -12, 0, 37, 0, -12, 56, -13, 20, 0, -72, 110, -8, 34, 56, -12, 56, 7, 12, -24, 0, -8, -36, 0, 20, 1, 24, 2, -8, 52, 0, -56, -60, 4, 16, 0, 0], 'weight': 2, 'weight_parity': 1}
  32. label: 43.2.a.b
    {'Nk2': 172, 'analytic_conductor': 0.34335672869150563, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[43, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [43, 1, [3], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-2, 0, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924971, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '43.2.a.b', 'level': 43, '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': [43], 'level_radical': 43, 'minimal_twist': '43.2.a.b', 'nf_label': '2.2.8.1', 'prim_orbit_index': 1, 'qexp_display': 'q+\\beta q^{2}-\\beta q^{3}+(2-\\beta )q^{5}-2q^{6}+(-2+\\cdots)q^{7}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '43.2.a', 'trace_display': [0, 0, 4, -4], 'trace_hash': 1110757377874853645, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.032', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.931', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.260', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.451', 'prec': 14}, {'__RealLiteral__': 0, 'data': '1.974', 'prec': 14}, {'__RealLiteral__': 0, 'data': '63.698', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.026', 'prec': 7}, 'traces': [2, 0, 0, 0, 4, -4, -4, 0, -2, -4, -2, 0, 2, 4, 4, -8, 10, 0, -4, 0, -4, 8, 2, 8, 2, 8, 0, 0, 0, -8, -6, 0, -8, 8, -12, 0, 0, -8, -8, 8, -2, 8, 2, 0, -4, -16, 12, 0, -2, -16, -8, 0, 22, 16, -12, -8, 8, 12, -4, 0, 8, 0, 4, 16, -4, 4, 2, 0, 16, 16, -12, 0, -24, -24, 16, 0, 12, -4, 4, -16, -10, -8, 18, 0, 12, 0, -12, -16, -12, 4, 4, 0, 0, 0, 0, 0, -2, -16, 2, 0, 6, -20, 18, -16, -16, -8, -12, 0, -6, 20, 24, 16, -8, 8, 20, 0, -2, 8, -12, 16, -4, 12, 8, 0, 0, -4, 2, 0, 0, 12, 8, 0, 0, 24, -16, -16, -12, -4, -6, 0, 0, -8, 14, 8, -12, 12, 16, 0, 0, -4, 28, 16, -10, -20, -12, 0, -20, -8, 8, 0, -20, 0, -32, 0, -20, 16, -6, -16, -8, -4, 4, 0, 36, 0, -20, 8, -8, -12, -12, 0, -8, -12, -12, 32, 24, 12, 6, 0, 16, -8, 16, 0, -2, -8, -12, 0, 0, -8, 4, 32, -24, -8, 12, 0, 4, 24, -2, -8, -12, 24, 28, 0, 8, -16, 4, -32, 12, 48, -12, 0, 26, 0, 28, 0, -2, 8, -24, 0, -18, -36, 20, -24, 4, -8, 24, 0, 8, 4, 12, -16, 8, -16, 0, 0, 12, 4, -20, 0, -16, -16, 18, 0, -34, -8, 4, 0, -12, -4, -24, 0, 0, -16, -28, -8, 52, 8, 12, 0, -6, 32, -18, -40, 12, 24, -34, 0, -4, -24, 6, -32, -6, -24, 14, 0, 8, 0, -4, 0, 32, 24, 8, 0, 32, 4, -16, 48, 32, -24, -30, 0, -4, -12, 8, 16, 4, -8, 14, 0, -24, 12, 6, 8, -8, 0, 12, 0, 46, -44, 24, 32, 16, 36, -36, 0, -30, -12, -48, 16, -24, 24, 40, 0, 0, 32, -20, 16, -10, 16, -8, 0, 6, 8, 16, 0, 36, -16, -12, 0, -32, 36, 32, 0, 6, 8, -16, 0, -4, -4, -54, -8, -14, -32, 16, 0, -60, -16, -20, -8, 2, -48, -52, 0, 0, 32, 16, 0, 24, -32, 38, 0, 8, 40, -24, -32, 44, -48, -2, 0, 12, 8, -22, 32, 16, 40, 16, 0, 8, -16, -8, -8, -42, -4, -6, 0, -20, -24, -48, 40, 20, -12, -24, 0, 16, 16, 20, 0, 24, -8, -28, 0, -20, 40, -12, 16, -22, 24, -4, 0, 0, -4, -10, 0, 52, -12, -24, 0, 28, 48, 6, -40, 2, 48, 44, 0, -12, 28, 24, -32, 24, 16, -14, 0, 12, -16, 20, -16, -24, 48, 32, 0, 40, -24, -36, 0, -12, -8, 36, 0, 20, -24, 0, -16, -2, -8, 28, 0, -22, -24, -2, 0, -48, 0, -36, 0, 4, -28, 56, -24, 12, -28, 24, 0, 24, -24, 12, 24, 16, -36, -60, 0, -32, -40, 12, 8, 20, 24, -16, 0, 18, -24, 60, 0, -32, -12, 12, 0, -12, 48, 16, -24, 48, -12, -36, 0, -36, -40, -30, 32, 20, -60, 4, 0, -18, 24, -8, -48, 4, 0, -30, 0, -22, 48, 32, 0, -60, -8, 18, 0, -8, 24, -24, 8, -16, -28, 48, 0, -18, 0, 2, 48, -32, 16, 34, 0, -24, -32, 20, 16, 38, 0, 8, 0, -40, 12, 66, -16, 52, 80, 48, 0, -20, 4, -38, -24, 4, 16, 28, 0, 12, 24, -40, 0, -4, -16, -28, 0, 16, -8, 62, 8, -16, 4, -2, 0, 8, -12, -32, 0, 24, 8, 12, 0, 8, -56, 12, 40, 6, -36, 24, 0, -64, 48, 12, 32, 6, 60, 8, 0, -48, -16, 20, 16, -40, -8, 12, 0, -34, -12, 12, -32, -28, 24, -36, 0, 4, -56, -8, 0, 20, -8, 12, 0, 36, 12, 32, 8, 24, 24, 10, 0, -34, -4, -48, -32, -8, 24, -48, 0, -28, 44, 16, 0, -8, 0, -64, 0, 28, 16, -4, 8, 16, -24, -42, 0, -48, 0, -48, -8, 6, -40, -28, 0, -12, -4, 12, 0, -26, 12, 8, 0, -48, 16, 48, -16, 24, -8, -20, 0, -14, 8, -4, 24, -6, 24, 28, 0, 24, -16, 0, 16, -12, 32, 0, 0, -48, 8, -16, 24, 58, 72, 10, 0, 0, -56, 28, 0, 46, 8, -28, 0, 24, 60, -32, -24, 24, -24, -18, 0, 8, 0, -32, -48, 40, 12, 68, 0, 24, -32, -24, 16, -24, -4, 60, 0, -12, 24, 12, 0, 16, -64, 12, 0, 36, 0, -6, 16, -48, 64, 20, 0, -4, -72, 48, 8, -40, -16, -20, 0, 40, -24, 24, 16, 32, -72, 60, 0, 48, 0, 60, 0, 12, -24, 48, 0, -76, -24, 0, 16, 0, 20, 72, 0, -48, 24, -52, 32, -4, 76, -4, 0, -42, 24, -98, -48, -24, -24, 8, 0, 8, -4, 28, 16, -42, 12, -44, 0, 0, 28, -44, -48, -22, 16, -16, 0, -32, 0, -8, -88, 32, -72, 96, 0, 14, -8, 0, 32, 4, -28, 0, 0, -12, -80, -4, 0, 88, 12, -80, 0, -20, 24, 50, -96, 2, 24, -16, 0, 34, -24, -16, 48, -18, 16, -50, 0, -24, 40, 84, 0, -12, 0, 10, 0, -24, 0, -20, 32, 8, -60, 0, 0, 94, 0, -4, -16, 16, -56, -6, 0, -6, -32, 0, -32, 14, -36, -8, 0, -32, 80, -42, 72, 56, -64, -28, 0, 96, 36, -18, 0, 84, 24, 36, 0, -48, -16, -20, 16, -20, -44, -60, 0, -18, 40, 30, 16, 64, 8, -6, 0, 0, 24, 8, -8, 0, 8, -8, 0, 12, 16, 48, 32, -44, -24, 12, 0, 44, 40, -14, 32, 56, -12, 22, 0, -12, 16, 8, -32, -24, 64, -12, 0, 6, -4, -60, -8, -40, 60, -24, 0, 2, -20, -8, 0, 4, -8, 24, 0, 20, -12, -96, 32], 'weight': 2, 'weight_parity': 1}
  33. label: 44.2.a.a
    {'Nk2': 176, 'analytic_conductor': 0.35134176889363367, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [11, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [44, 1, [23, 13], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554476, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '44.2.a.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': '44.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{3}-3q^{5}+2q^{7}-2q^{9}-q^{11}+\\cdots', 'related_objects': ['EllipticCurve/Q/44/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '44.2.a', 'trace_display': [0, 1, -3, 2], 'trace_hash': 685433102328794143, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.009', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.978', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.900', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.034', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.664', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, 'traces': [1, 0, 1, 0, -3, 0, 2, 0, -2, 0, -1, 0, -4, 0, -3, 0, 6, 0, 8, 0, 2, 0, -3, 0, 4, 0, -5, 0, 0, 0, 5, 0, -1, 0, -6, 0, -1, 0, -4, 0, 0, 0, -10, 0, 6, 0, 0, 0, -3, 0, 6, 0, -6, 0, 3, 0, 8, 0, 3, 0, -4, 0, -4, 0, 12, 0, -1, 0, -3, 0, 15, 0, -4, 0, 4, 0, -2, 0, 2, 0, 1, 0, 6, 0, -18, 0, 0, 0, -9, 0, -8, 0, 5, 0, -24, 0, -7, 0, 2, 0, 18, 0, 8, 0, -6, 0, 6, 0, 2, 0, -1, 0, -15, 0, 9, 0, 8, 0, 12, 0, 1, 0, 0, 0, 3, 0, -16, 0, -10, 0, -6, 0, 16, 0, 15, 0, 9, 0, 14, 0, 0, 0, 4, 0, 0, 0, -3, 0, 6, 0, -10, 0, -12, 0, -15, 0, 5, 0, -6, 0, -6, 0, -4, 0, 3, 0, -12, 0, 3, 0, -16, 0, 18, 0, 8, 0, 3, 0, -9, 0, -13, 0, -4, 0, 3, 0, -6, 0, -10, 0, -21, 0, 20, 0, 12, 0, 6, 0, 8, 0, -1, 0, 0, 0, 0, 0, 6, 0, -8, 0, 20, 0, 15, 0, 30, 0, 10, 0, -4, 0, -24, 0, 17, 0, -8, 0, 6, 0, -13, 0, -2, 0, -24, 0, 0, 0, 2, 0, 6, 0, 8, 0, 16, 0, 9, 0, -32, 0, 6, 0, -9, 0, 3, 0, -18, 0, -18, 0, -2, 0, 0, 0, 18, 0, 18, 0, -9, 0, -6, 0, 20, 0, -8, 0, -4, 0, -10, 0, -10, 0, -18, 0, -4, 0, -24, 0, 0, 0, 19, 0, -7, 0, 0, 0, -9, 0, 5, 0, 12, 0, -20, 0, 18, 0, 12, 0, -16, 0, 8, 0, 12, 0, -1, 0, 12, 0, 33, 0, 0, 0, 6, 0, 48, 0, -16, 0, 2, 0, 0, 0, -7, 0, 2, 0, 3, 0, 2, 0, -15, 0, -5, 0, -20, 0, 9, 0, 12, 0, 14, 0, 20, 0, -21, 0, -45, 0, 12, 0, -36, 0, 45, 0, 1, 0, 12, 0, -19, 0, 0, 0, -12, 0, -10, 0, 3, 0, 0, 0, 29, 0, -16, 0, -27, 0, 6, 0, 20, 0, -27, 0, -18, 0, -6, 0, -6, 0, -34, 0, 16, 0, 18, 0, -20, 0, -3, 0, 1, 0, 2, 0, 9, 0, 6, 0, -18, 0, 14, 0, 12, 0, -10, 0, 0, 0, 24, 0, -8, 0, 4, 0, 18, 0, 29, 0, 0, 0, -24, 0, 8, 0, 6, 0, -21, 0, 27, 0, 6, 0, 3, 0, 0, 0, -10, 0, 24, 0, -28, 0, -30, 0, 12, 0, 23, 0, -15, 0, 3, 0, -2, 0, 5, 0, 10, 0, 32, 0, 12, 0, -12, 0, 4, 0, -6, 0, 21, 0, 29, 0, -4, 0, 24, 0, 0, 0, -6, 0, 30, 0, -4, 0, -12, 0, -30, 0, -54, 0, 3, 0, -21, 0, -8, 0, -40, 0, -24, 0, 0, 0, 18, 0, -27, 0, 8, 0, 8, 0, 30, 0, -14, 0, -6, 0, 0, 0, -18, 0, -9, 0, 3, 0, -16, 0, -13, 0, -6, 0, 8, 0, 8, 0, 0, 0, 4, 0, 3, 0, -18, 0, 40, 0, -6, 0, -36, 0, 45, 0, 2, 0, 0, 0, 44, 0, -21, 0, -12, 0, 17, 0, 20, 0, 12, 0, 6, 0, -24, 0, -12, 0, 40, 0, 6, 0, -36, 0, -36, 0, 8, 0, 0, 0, 26, 0, 2, 0, -3, 0, 14, 0, 0, 0, 0, 0, 32, 0, 0, 0, 18, 0, 17, 0, 15, 0, -18, 0, -29, 0, -8, 0, -6, 0, -43, 0, 20, 0, 48, 0, 12, 0, -30, 0, 39, 0, -13, 0, 30, 0, 3, 0, -3, 0, 10, 0, 3, 0, 18, 0, 8, 0, -42, 0, 17, 0, -24, 0, -48, 0, 0, 0, 17, 0, 4, 0, -34, 0, -20, 0, -42, 0, -14, 0, 6, 0, 48, 0, -27, 0, -13, 0, 24, 0, -1, 0, 4, 0, -42, 0, 0, 0, -24, 0, 18, 0, -8, 0, 0, 0, 36, 0, -37, 0, -4, 0, -15, 0, -12, 0, 6, 0, 45, 0, 16, 0, 8, 0, 0, 0, 17, 0, 13, 0, -60, 0, -4, 0, 9, 0, 1, 0, -34, 0, -32, 0, 12, 0, -18, 0, -12, 0, 12, 0, 35, 0, -9, 0, 30, 0, -22, 0, 3, 0, 36, 0, 4, 0, 36, 0, -12, 0, 44, 0, -18, 0, 42, 0, 20, 0, -2, 0, 0, 0, -15, 0, 0, 0, -15, 0, 32, 0, 18, 0, -30, 0, 16, 0, 18, 0, 9, 0, 0, 0, 18, 0, 4, 0, 18, 0, -6, 0, -24, 0, 38, 0, 20, 0, 12, 0, -80, 0, 16, 0, 30, 0, -43, 0, -4, 0, -36, 0, -19, 0, -10, 0, -18, 0, 36, 0, -25, 0, -39, 0, -29, 0, -18, 0, -9, 0, 2, 0, -4, 0, 3, 0, 38, 0, 48, 0, 24, 0, -25, 0, 0, 0, 48, 0, -54, 0, 19, 0, -2, 0, 4, 0, 14, 0, 6, 0, -52, 0, 0, 0, -27, 0, -4, 0, -9, 0, 30, 0, -32, 0, -1, 0, 0, 0, 27, 0, 12, 0, 0, 0, -36, 0, -20, 0, 39, 0, -4, 0, -36, 0, 12, 0, -6, 0, 12, 0, -12, 0, -34, 0, -16, 0, -60, 0, -4, 0, -16, 0, 18, 0, -24, 0, 12, 0, 18, 0, 32, 0, -1, 0, -30, 0, 0, 0, 30, 0, 27, 0, 16, 0, 33, 0, 42, 0, 63, 0, 0, 0, 18, 0, -6, 0, -12, 0, -60, 0, -16, 0, 48, 0, -15, 0, 28, 0, -16, 0, 45, 0, 9, 0, -4, 0, 45, 0, -18, 0, 0, 0, 30, 0, -16, 0, -7, 0, -24, 0, -10, 0, 5, 0], 'weight': 2, 'weight_parity': 1}
  34. label: 45.2.a.a
    {'Nk2': 180, 'analytic_conductor': 0.3593268090957617, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1], [5, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [45, 1, [11, 37], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554477, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': False, 'label': '45.2.a.a', 'level': 45, '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': '15.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+4q^{11}+\\cdots', 'related_objects': ['EllipticCurve/Q/45/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '45.2.a', 'trace_display': [1, 0, -1, 0], 'trace_hash': 804981580358494444, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.011', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.977', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.925', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.780', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, 'traces': [1, 1, 0, -1, -1, 0, 0, -3, 0, -1, 4, 0, -2, 0, 0, -1, -2, 0, 4, 1, 0, 4, 0, 0, 1, -2, 0, 0, 2, 0, 0, 5, 0, -2, 0, 0, -10, 4, 0, 3, -10, 0, 4, -4, 0, 0, -8, 0, -7, 1, 0, 2, 10, 0, -4, 0, 0, 2, 4, 0, -2, 0, 0, 7, 2, 0, 12, 2, 0, 0, 8, 0, 10, -10, 0, -4, 0, 0, 0, 1, 0, -10, -12, 0, 2, 4, 0, -12, 6, 0, 0, 0, 0, -8, -4, 0, 2, -7, 0, -1, -6, 0, -16, 6, 0, 10, 12, 0, 14, -4, 0, 0, -2, 0, 0, -2, 0, 4, 0, 0, 5, -2, 0, 0, -1, 0, -8, -3, 0, 2, 12, 0, 0, 12, 0, 6, 6, 0, -4, 0, 0, 8, -8, 0, -2, 10, 0, 10, -22, 0, -8, -12, 0, 0, 0, 0, 14, 0, 0, -5, 0, 0, -4, 10, 0, -12, 0, 0, -9, 2, 0, -4, 18, 0, 0, -4, 0, 6, -20, 0, -10, 0, 0, 0, 10, 0, -8, 8, 0, -4, -16, 0, 2, 2, 0, 7, -6, 0, -8, -3, 0, -6, 0, 0, 10, -16, 0, 2, 16, 0, 20, -10, 0, 12, -4, 0, 0, 14, 0, 4, 4, 0, 8, 0, 0, -2, 20, 0, 6, 0, 0, -6, 6, 0, 8, -4, 0, 0, 16, 0, -14, 5, 0, 2, 7, 0, -8, 0, 0, -1, -12, 0, 0, -8, 0, -17, -18, 0, 0, -2, 0, 12, -16, 0, -10, 0, 0, -12, -14, 0, 16, 2, 0, 6, 4, 0, 6, -4, 0, 0, 6, 0, -12, -8, 0, -8, 0, 0, -13, -2, 0, -10, -6, 0, -4, 30, 0, -22, 0, 0, 0, -8, 0, -4, 2, 0, 28, 0, 0, 0, 24, 0, 26, 14, 0, 0, 2, 0, 8, -7, 0, 0, -8, 0, -2, -4, 0, 30, 0, 0, 12, 12, 0, 0, -12, 0, -14, -9, 0, -2, 0, 0, 0, -12, 0, 18, 28, 0, -2, 0, 0, 20, -18, 0, -8, -6, 0, -20, 24, 0, -3, -10, 0, 0, -10, 0, -24, 0, 0, 10, 0, 0, -26, -8, 0, 24, -4, 0, -20, 4, 0, -16, 24, 0, 0, 2, 0, -2, -6, 0, 0, 21, 0, -6, 0, 0, -2, -8, 0, -1, -18, 0, 0, 6, 0, 0, -40, 0, 26, 10, 0, 16, 0, 0, 12, -10, 0, 16, -4, 0, -26, 20, 0, -30, -2, 0, 0, -12, 0, -4, 0, 0, -14, 0, 0, -14, 0, 0, 40, 12, 0, 4, 12, 0, -6, 8, 0, 0, -2, 0, -40, 2, 0, 20, 0, 0, 10, 6, 0, 0, 18, 0, 24, -2, 0, 6, -28, 0, 0, 8, 0, -12, 16, 0, 4, 0, 0, 16, 0, 0, 20, -14, 0, -5, -2, 0, 32, 6, 0, 7, -28, 0, -4, -8, 0, 0, 0, 0, 4, 1, 0, -12, 32, 0, 6, 0, 0, 8, 34, 0, 0, -11, 0, -18, 16, 0, -32, 0, 0, -6, -10, 0, 4, -12, 0, -16, 0, 0, -23, -10, 0, 0, 20, 0, -12, -36, 0, -14, -28, 0, 30, 16, 0, -10, -14, 0, -20, -6, 0, 4, 8, 0, 0, 6, 0, 4, 18, 0, -8, 0, 0, 6, -12, 0, 2, -12, 0, -24, 6, 0, -4, 8, 0, 0, 0, 0, 2, -13, 0, 2, 0, 0, 40, -30, 0, -6, 12, 0, 0, -4, 0, 10, -34, 0, 0, 22, 0, 0, 8, 0, 26, 0, 0, 8, -5, 0, -8, 20, 0, 2, 16, 0, 22, 28, 0, 0, 6, 0, -4, 0, 0, 24, 0, 0, 1, 26, 0, -14, 20, 0, -8, 0, 0, 2, 8, 0, 14, 8, 0, 3, 30, 0, -36, 0, 0, -8, -32, 0, 16, -2, 0, 4, -46, 0, -12, 10, 0, 0, -20, 0, 22, 12, 0, 36, 0, 0, 0, 0, 0, -12, -8, 0, -30, -14, 0, 9, -6, 0, 0, -6, 0, 0, -36, 0, -6, 0, 0, -4, -20, 0, -44, -18, 0, 28, 4, 0, 20, -2, 0, 0, 2, 0, -40, 28, 0, -18, 0, 0, -26, -8, 0, -18, 0, 0, 8, 20, 0, 24, 48, 0, 0, -3, 0, 10, 2, 0, -16, 0, 0, -10, -8, 0, 14, -24, 0, 0, 48, 0, -44, -10, 0, 0, 16, 0, 22, -26, 0, 8, 0, 0, 16, 8, 0, -4, 8, 0, -26, -20, 0, 12, 6, 0, 0, 16, 0, 24, -8, 0, 2, 0, 0, -2, -6, 0, 0, -6, 0, -6, -40, 0, 32, 0, 0, 7, -14, 0, 28, 6, 0, 0, 0, 0, 4, -2, 0, 8, 2, 0, 16, 5, 0, -18, 40, 0, 0, 0, 0, 18, -10, 0, 12, 0, 0, -40, 4, 0, 16, 26, 0, -10, -54, 0, 32, 48, 0, 0, 28, 0, 30, 12, 0, -14, 14, 0, 0, -16, 0, -4, -40, 0, -25, -26, 0, -20, 9, 0, 0, -10, 0, -2, 0, 0, 6, 0, 0, -36, 22, 0, -20, 4, 0, 0, 56, 0, -18, -14, 0, 0, 0, 0, -24, -42, 0, 0, 0, 0, 30, 40, 0, 4, 46, 0, 44, -4, 0, 12, -48, 0, 0, -6, 0, -8, -32, 0, 20, 0, 0, -2, 0, 0, -20, -40, 0, 6, 10, 0, -12, -20, 0, 0, -32, 0, -48, 10, 0, -6, 0, 0, 40, 0, 0, 18, -16, 0, -10, 24, 0, 10, -34, 0, -28, -6, 0, -28, 8, 0, -54, 0, 0, -8, 50, 0, 0, -4, 0, 16, 36, 0, -20, 4, 0, 0, 22, 0, 16, -16, 0, 0, 0, 0, -31, 20, 0, 14, -2, 0, 32, -15, 0, -2, -60, 0, 0, 32, 0, 2, -2, 0, 24, -7, 0, -28, 0, 0, 6, -4, 0, 8, 0, 0, 32, 0, 0, 0, 8, 0, 54, 4, 0, 3], 'weight': 2, 'weight_parity': 1}
  35. label: 46.2.a.a
    {'Nk2': 184, 'analytic_conductor': 0.3673118492978898, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [23, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [46, 1, [5], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554478, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '46.2.a.a', 'level': 46, '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': [2, 23], 'level_radical': 46, 'minimal_twist': '46.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}+q^{4}+4q^{5}-4q^{7}-q^{8}-3q^{9}+\\cdots', 'related_objects': ['EllipticCurve/Q/46/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '46.2.a', 'trace_display': [-1, 0, 4, -4], 'trace_hash': 753733786167000906, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.017', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.970', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.041', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.926', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.133', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.822', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [1, -1, 0, 1, 4, 0, -4, -1, -3, -4, 2, 0, -2, 4, 0, 1, -2, 3, -2, 4, 0, -2, 1, 0, 11, 2, 0, -4, 2, 0, 0, -1, 0, 2, -16, -3, -4, 2, 0, -4, 6, 0, 10, 2, -12, -1, 0, 0, 9, -11, 0, -2, -4, 0, 8, 4, 0, -2, 12, 0, -8, 0, 12, 1, -8, 0, -10, -2, 0, 16, 0, 3, 6, 4, 0, -2, -8, 0, -12, 4, 9, -6, 14, 0, -8, -10, 0, -2, -6, 12, 8, 1, 0, 0, -8, 0, 6, -9, -6, 11, -10, 0, -8, 2, 0, 4, -10, 0, 0, -8, 0, -4, -14, 0, 4, 2, 6, -12, 8, 0, -7, 8, 0, 0, 24, -12, 16, -1, 0, 8, 12, 0, 8, 10, 0, 2, 6, 0, -4, -16, 0, 0, -4, -3, 8, -6, 0, -4, -4, 0, -8, 2, 6, 8, 0, 0, 12, 12, 0, -4, -4, -9, -8, 6, 0, -14, 16, 0, -9, 8, 6, 10, -6, 0, -44, 2, 0, 6, -16, -12, -24, -8, 0, -1, -16, 0, -4, 0, 0, 8, 20, 0, 26, -6, 0, 9, 18, 6, -4, -11, 0, 10, -8, 0, 24, 8, -3, -2, -4, 0, -20, -4, 0, 10, 40, 0, 0, 0, 0, 8, 4, 0, -16, 4, -33, 14, -6, 0, 8, -4, 0, -2, -6, -6, 0, 12, 0, -8, -24, 0, 22, 7, 0, -8, 36, 0, 4, 0, 0, -24, 14, 12, 2, -16, 0, 1, 22, 0, 16, -8, -6, -12, -16, 0, -16, -8, 0, -10, -14, 0, 8, -2, 0, -6, 22, 0, -14, 4, 0, 16, -6, 0, -14, 0, 0, 4, -24, 3, -13, -8, 0, 6, 4, 0, 48, 4, 0, 4, -2, 0, -40, 8, 0, -2, -32, -6, -16, -8, 0, 0, 32, 0, 22, -12, 48, -12, 2, 0, 4, 4, 0, 4, 4, 9, -22, 8, 0, -6, 0, 0, -4, 14, 12, -16, -40, 0, 10, 9, 0, -8, 0, -6, -8, -10, 0, 6, 8, 0, 26, 44, 0, -2, 2, 0, 0, -6, 0, 16, -12, 12, -15, 24, 0, 8, 24, 0, 12, 1, -18, 16, 16, 0, -4, 4, 0, 0, -4, 0, 22, -8, 0, -20, -24, 0, -32, -26, -30, 6, 0, 0, -2, -9, 0, -18, -48, -6, 14, 4, 0, 11, -18, 0, 0, -10, 36, 8, -8, 0, 34, -24, 0, -8, -48, 3, 56, 2, 0, 4, -18, 0, 28, 20, 0, 4, -22, 0, 32, -10, 0, -40, -12, 0, -26, 0, 0, 0, -2, 0, 8, -8, -27, -4, 8, 0, -24, 16, 0, -4, 14, 33, 12, -14, 0, 6, 32, 0, -10, -8, 0, 4, 18, 0, 40, 2, 0, 6, -2, 6, 40, 0, 0, -12, 20, 0, -22, 8, 12, 24, -8, 0, 8, -22, 0, -7, 24, 0, -8, 8, 0, -36, 24, 0, -4, -4, -24, 0, 0, 0, 16, 24, 0, -14, 12, -12, -40, -2, 0, 16, 18, 0, -24, -1, 0, -22, -32, 0, 0, -16, 0, 8, 38, 6, -34, 12, 0, 16, 0, 0, 1, 16, -36, 8, -12, 0, -40, 10, 0, 14, 18, 0, -6, -8, 0, 2, 0, 0, -36, 6, 24, -22, -4, 0, 48, 14, 0, -4, 16, 0, -20, -16, 0, 6, -14, 0, -56, 14, -36, 0, 14, 0, 14, -4, 0, 24, 11, -3, 30, 13, 0, 8, -56, 0, -8, -6, 24, -4, -28, 0, 0, -48, 0, -4, 6, 0, 32, -4, 0, 2, 16, 0, -26, 40, 30, -8, -28, 0, 32, 2, 0, 32, 0, 6, -16, 16, 0, 8, 18, 0, -14, 0, 0, -32, 24, 0, 41, -22, 0, 12, 8, -48, -40, 12, 0, -2, 64, 0, -18, -4, 0, -4, 14, 0, 10, -4, 0, -4, -40, -9, 24, 22, 0, -8, -42, 0, 48, 6, -18, 0, 30, 0, -24, 4, 0, -14, 32, -12, 2, 16, 0, 40, -16, 0, -2, -10, 0, -9, -12, 0, -24, 8, 0, 0, 12, 6, 24, 8, 0, 10, 8, 0, -4, -6, 24, -8, -16, 0, -12, -26, 0, -44, 0, 0, 8, 2, 0, -2, 40, 0, -28, 0, 36, 6, 0, 0, -16, -16, 0, 12, 48, -12, 32, 15, 0, -24, 22, 0, -36, -8, -27, -24, -20, 0, -44, -12, 0, -1, -20, 18, -32, -16, 0, -16, -24, 0, -16, 4, -42, -4, 40, 0, 48, 0, 0, 4, -32, 0, -48, -22, 0, 8, -30, 0, 0, 20, 24, 24, -24, 0, 22, 32, 0, 26, -40, 30, 0, -6, 0, 0, -12, 0, 0, 2, 0, 9, 48, 0, 18, 18, 0, 48, 56, 6, 16, -14, 0, -4, 8, 0, 0, -11, 18, 18, 12, 0, -16, 0, 0, 10, -30, -36, 20, -8, 0, 8, -32, 0, -20, -34, -24, 24, 30, 0, 24, 8, 0, 48, 6, -3, -30, -56, 0, -2, -18, 0, 64, -4, 0, 18, 24, 0, -25, -28, 0, -20, -36, 0, 28, -4, 0, 22, -4, 0, 46, -32, 24, 10, 42, 0, 40, 40, 0, 12, -8, 0, -24, 26, 0, 0, -24, 0, 20, 0, -18, 2, -96, 0, 18, -8, 0, 8, 18, 27, -36, 4, 0, -8, 24, 0, -64, 24, 18, -16, 0, 0, -64, 4, 0, -14, 0, -33, 8, -12, 0, 14, -96, 0, 10, -6, 30, -32, 20, 0, 28, 10, 0, 8, -48, 0, -4, -4, 0, -18, 0, 0, -44, -40, 24, -2, -18, 0, -18, -6, 0, 2, -16, -6, 58, -40, 0, 0, 36, 0, 6, 12, 0, -20, 48, 0, -12, 22, 0, -8, 46, -12, 80, -24, 0, 8, -24, 0, -31, -8, 30, 22, 104, 0, -16, 7, 0, -24, -38, 0, 16, 8, 0, -8, 6, 0, -12, 36, 0, -24, -36, 0, 72, 4, 0, 4, 10, 24, -56, 0, 0, 0, -16, 0, 10, -16, 0, -24], 'weight': 2, 'weight_parity': 1}
  36. label: 47.2.a.a
    {'Nk2': 188, 'analytic_conductor': 0.3752968895000178, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[47, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [47, 1, [5], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 4, 'field_disc': 1957, 'field_disc_factorization': [[19, 1], [103, 1]], 'field_poly': [1, -1, -4, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554479, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '47.2.a.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': '47.2.a.a', 'nf_label': '4.4.1957.1', 'prim_orbit_index': 1, 'qexp_display': 'q+\\beta _{3}q^{2}+(-\\beta _{2}-\\beta _{3})q^{3}+(1-\\beta _{1}+\\cdots)q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 4, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '47.2.a', 'trace_display': [1, 0, -2, 4], 'trace_hash': 519028922956201300, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.058', 'prec': 7}, {'__RealLiteral__': 0, 'data': '3.732', 'prec': 14}, {'__RealLiteral__': 0, 'data': '1.169', 'prec': 14}, {'__RealLiteral__': 0, 'data': '39.016', 'prec': 17}, {'__RealLiteral__': 0, 'data': '25.740', 'prec': 17}, {'__RealLiteral__': 0, 'data': '603.660', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.009', 'prec': 4}, 'traces': [4, 1, 0, 3, -2, -8, 4, -3, 2, -8, -6, -11, 8, -5, -2, 5, 6, 16, 0, 0, 4, 4, -6, -13, 16, 16, -12, 16, -10, 10, -8, 10, 12, -10, -20, 11, 10, -2, -18, -14, 6, -15, 2, -30, -34, 18, 4, 6, 2, 15, -8, 4, -6, -5, -16, 2, 10, -8, 4, 46, -6, -16, 16, -31, 16, 32, 10, 43, -6, -30, -12, 27, 22, 18, 24, -24, -10, -28, 20, -12, 4, -20, 20, -19, -2, 38, -12, 2, -6, -30, -22, -32, 18, 1, 16, 26, 30, -15, 4, -39, -22, -39, -20, 2, -6, -45, 12, -33, -6, 28, -12, 3, -4, 26, 4, 18, 2, -1, 36, 30, 0, 15, 16, -4, -36, 45, 22, -21, -44, -4, 28, 4, -22, -20, 22, 3, 36, 20, -28, 38, 0, 20, -20, 6, 24, -34, 12, 17, -6, 8, 0, -18, 10, 28, -16, -34, -2, 28, 48, 26, -40, 2, 6, 8, -56, 20, 6, -29, 12, -50, -26, 20, -42, 0, 8, 10, -16, -9, 28, -22, -36, 8, -44, 10, -38, 28, -48, 3, -34, 32, 20, 12, 48, -3, 40, -8, -12, -60, -2, -17, -6, 18, -6, -12, 12, -28, 2, 6, 16, 12, 2, -10, -10, 26, -12, -9, 22, 46, 54, 32, -10, -45, -2, 0, 22, -20, -14, 28, 10, 40, 18, 10, 2, 32, -2, 64, -10, -31, 8, -32, 18, -39, 4, 30, 32, 6, 12, -2, 4, 40, -4, -19, 36, -50, 52, -31, -24, -60, 24, -84, -12, 9, -16, 30, -4, -12, -28, 12, 32, 56, -44, -12, -28, 54, 46, -8, -14, -90, -2, 12, 26, -8, -52, -1, -36, -48, 18, -52, 10, 4, -40, -26, 6, 21, -52, 21, 34, -34, 28, -69, -18, -44, 0, 8, 44, 89, 48, -86, 10, 4, -26, -28, -6, -1, -22, 23, 20, 61, -20, 40, 16, 46, -38, 28, 16, 12, 12, -28, 4, -44, -56, 12, 50, -34, 100, 17, 90, 55, 70, 6, 20, -58, -40, 48, -12, -41, -16, 40, 18, 21, -12, -10, -30, -67, -62, 82, -10, 78, 0, 2, -44, -34, 12, 54, 16, -39, -4, 6, -28, -46, 40, 34, 24, 52, -116, -3, -12, 3, -24, 8, 82, -12, 16, 53, -32, 32, 56, 86, -42, 72, -70, -30, 16, -70, -78, -36, -74, -12, 20, 55, -42, -2, -64, -81, 72, -8, -8, -46, 0, -8, -42, -23, 74, -60, -80, 4, 22, 8, -8, 92, 2, 38, 2, -40, -54, -7, -36, -68, 32, -28, -12, -7, 18, -8, 64, -62, 28, 38, 20, 64, -44, 40, -6, -88, -28, 124, 72, -81, -26, -8, -20, -74, 10, 64, -72, 34, 62, 84, -56, -52, 56, 68, 22, -30, -40, 42, 24, 118, -44, -8, 16, 38, -16, -71, 32, 83, -44, -8, 0, -62, 18, -70, -18, 55, 60, -19, 20, 28, -40, 22, -12, 36, 24, -20, 40, -6, 20, -52, 36, 64, 34, 56, -40, 17, 46, -84, -52, -48, -16, 46, 20, 25, 32, 94, 78, -98, -6, 35, 8, -84, 58, -4, 20, -40, 64, -13, 10, 30, -16, 14, 68, -16, -16, -67, -8, -54, -68, -18, -10, 8, -26, -112, -6, 0, -120, -40, -26, 44, 0, -28, -16, 28, 52, 18, 12, 42, 6, -32, 68, -56, -6, 56, 16, -11, -60, 7, -40, 53, -20, -56, 32, -8, 60, -58, 30, -52, -26, -90, -48, -32, 56, -113, 18, -84, -96, -4, 84, 55, -12, -94, 48, 16, 14, -4, 70, -61, 72, -12, -40, -31, 6, 78, -94, 8, -2, 85, -14, 36, -34, -2, 8, 6, 66, -28, -24, 8, -34, 71, -8, 84, 46, 54, 68, -20, 24, 12, -20, -14, 22, -8, 10, 29, -98, -26, 12, 101, 6, 12, 72, 72, -40, 30, 8, -64, 100, -18, -12, -8, -42, 16, 28, 52, -70, 22, 36, 2, -70, -5, 68, -36, 38, 27, -42, 16, -44, 91, -12, 10, -86, 28, -46, 62, 134, 11, -16, -47, -20, 98, 16, -38, -90, 48, -32, -36, -64, -15, -2, -4, -106, 8, 50, -38, 14, 60, 132, 22, 32, 76, -64, -60, 146, -68, -26, 84, -2, -57, -104, -75, -50, -18, 88, 48, -28, -88, 40, 10, -30, 22, -56, -48, -52, 17, 72, 26, -110, -16, -2, 86, -70, 12, -4, -3, 26, -36, -18, -26, -72, 2, -24, -22, 36, -76, -40, 28, -42, -64, 76, -144, -48, -68, -56, 5, -130, -16, 120, -64, 44, 31, 20, 4, -28, 76, 10, -32, -28, 56, -46, 67, -22, 80, -82, 106, 90, 88, -16, -20, -14, 16, 4, 68, 44, 112, 14, -1, -36, 3, 24, 50, -60, -82, 26, -94, 62, -18, -102, -74, -16, 50, 6, 50, 56, 30, -4, 94, -64, -68, -28, -1, -46, 4, 24, 22, 34, -52, 20, -19, -24, 52, 100, 60, 38, -134, 28, -29, 108, 16, -56, 60, -22, -72, 64, -24, -4, 76, -8, 60, 12, -132, 102, 46, -56, 2, 2, 46, 106, 16, 68, -3, 32, 34, -10, -68, -74, 20, 4, -24, -16, 76, 72, -152, 38, 67, 56, 6, 124, -16, 4, -54, -4, 4, 80, 54, -20, -8, -104, 60, -66, 0, 94, -44, -42, -43, -56, 58, 66, -124, -92, -74, 28, -90, -68, 2, 0, 101, -4, 40, 16, -92, 12, 5, 28, 92, -86, -36, 36, 36, 16, 28, -46, -68, -12, 10, 8, 62, 146, -152, -42, 12, -52, 8, 70, -108, -46, -22, 54, -50, -88, -30, 62, -72, 26, 68, -80, 50, 8, 112, 32, -110, 24, 0, 38, 17, -48, -13, 16, -148, 84, -156, -8, 2, -82, -61, 122, -75, -88, -3, -60, 55, 34, -46, -60, 64, -8, -11, -52, 58, -20, -11, 30, -86, 40, 129, -2, 56, -62, -35, 96, -70, -62, 22, 108, -59, -128, 6, -36, -12, 4, -84, 48, 52, 28, -4, -48, 95, -96, -136, -24, 12, -56, 100], 'weight': 2, 'weight_parity': 1}
  37. label: 48.2.a.a
    {'Nk2': 192, 'analytic_conductor': 0.38328192970214586, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [3, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': False, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [48, 1, [31, 37, 17], [1, 1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554480, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': False, 'label': '48.2.a.a', 'level': 48, '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], 'level_radical': 6, 'minimal_twist': '24.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\\cdots', 'related_objects': ['EllipticCurve/Q/48/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '48.2.a', 'trace_display': [0, 1, -2, 0], 'trace_hash': 1588924079463638771, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.011', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.981', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.019', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.915', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.052', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.664', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.017', 'prec': 7}, 'traces': [1, 0, 1, 0, -2, 0, 0, 0, 1, 0, -4, 0, -2, 0, -2, 0, 2, 0, 4, 0, 0, 0, 8, 0, -1, 0, 1, 0, 6, 0, -8, 0, -4, 0, 0, 0, 6, 0, -2, 0, -6, 0, -4, 0, -2, 0, 0, 0, -7, 0, 2, 0, -2, 0, 8, 0, 4, 0, -4, 0, -2, 0, 0, 0, 4, 0, 4, 0, 8, 0, -8, 0, 10, 0, -1, 0, 0, 0, 8, 0, 1, 0, 4, 0, -4, 0, 6, 0, -6, 0, 0, 0, -8, 0, -8, 0, 2, 0, -4, 0, -18, 0, -16, 0, 0, 0, 12, 0, -2, 0, 6, 0, 18, 0, -16, 0, -2, 0, 0, 0, 5, 0, -6, 0, 12, 0, 8, 0, -4, 0, 4, 0, 0, 0, -2, 0, -6, 0, 12, 0, 0, 0, 8, 0, -12, 0, -7, 0, 14, 0, 16, 0, 2, 0, 16, 0, -2, 0, -2, 0, 0, 0, -12, 0, 8, 0, -24, 0, -9, 0, 4, 0, 6, 0, 0, 0, -4, 0, -12, 0, 6, 0, -2, 0, -12, 0, -8, 0, 0, 0, 0, 0, 2, 0, 4, 0, -18, 0, -16, 0, 4, 0, 0, 0, 12, 0, 8, 0, -16, 0, 20, 0, -8, 0, 8, 0, 0, 0, 10, 0, -4, 0, 8, 0, -1, 0, -12, 0, 22, 0, 0, 0, 10, 0, 0, 0, 8, 0, 16, 0, 18, 0, 1, 0, 14, 0, -8, 0, 4, 0, -20, 0, -32, 0, -4, 0, 2, 0, 0, 0, 6, 0, 8, 0, 4, 0, -6, 0, -10, 0, -8, 0, 0, 0, 4, 0, -26, 0, -8, 0, 26, 0, 28, 0, -8, 0, 0, 0, -13, 0, 2, 0, -18, 0, 8, 0, -4, 0, -16, 0, 0, 0, -18, 0, 4, 0, -12, 0, -16, 0, 24, 0, -6, 0, 0, 0, 6, 0, -24, 0, 12, 0, 8, 0, 2, 0, -2, 0, 0, 0, -20, 0, 6, 0, -8, 0, 18, 0, 18, 0, 32, 0, 0, 0, -16, 0, 12, 0, 30, 0, -2, 0, 2, 0, 16, 0, 0, 0, 24, 0, -3, 0, 5, 0, -20, 0, 8, 0, -6, 0, 0, 0, -10, 0, 12, 0, -12, 0, -20, 0, 8, 0, 0, 0, 0, 0, -4, 0, -2, 0, 16, 0, 4, 0, -16, 0, 14, 0, 0, 0, -30, 0, 16, 0, -2, 0, -24, 0, -6, 0, -6, 0, 0, 0, -8, 0, 12, 0, -12, 0, -10, 0, 0, 0, -2, 0, 0, 0, 8, 0, -32, 0, -14, 0, -12, 0, 32, 0, 0, 0, -7, 0, -20, 0, 12, 0, 14, 0, -14, 0, 24, 0, 16, 0, 0, 0, -22, 0, 2, 0, -26, 0, -8, 0, 16, 0, 36, 0, 0, 0, -2, 0, 16, 0, -4, 0, -2, 0, 16, 0, -12, 0, 0, 0, -4, 0, 32, 0, -12, 0, 12, 0, 12, 0, 8, 0, 0, 0, -12, 0, -24, 0, -24, 0, 36, 0, -9, 0, 6, 0, 0, 0, 4, 0, 32, 0, 0, 0, 6, 0, 26, 0, -4, 0, 0, 0, -16, 0, 41, 0, -4, 0, 12, 0, -24, 0, -12, 0, 28, 0, -18, 0, 6, 0, 4, 0, -44, 0, -2, 0, 24, 0, 0, 0, -12, 0, -26, 0, 8, 0, -8, 0, -28, 0, -36, 0, 0, 0, 10, 0, -36, 0, 0, 0, -8, 0, 2, 0, 2, 0, 0, 0, 8, 0, 4, 0, 44, 0, -32, 0, -18, 0, -14, 0, 0, 0, -16, 0, -24, 0, -38, 0, 4, 0, -10, 0, 40, 0, 0, 0, 0, 0, 38, 0, 12, 0, 42, 0, 44, 0, 8, 0, 0, 0, -19, 0, -16, 0, 12, 0, -16, 0, 20, 0, -16, 0, 14, 0, -8, 0, -14, 0, -12, 0, 8, 0, -8, 0, 16, 0, 0, 0, 6, 0, -8, 0, 10, 0, -12, 0, -10, 0, -4, 0, 0, 0, 48, 0, 8, 0, 8, 0, 34, 0, -1, 0, -2, 0, 0, 0, -12, 0, -4, 0, 12, 0, 22, 0, 4, 0, 4, 0, 0, 0, -24, 0, -12, 0, 10, 0, 6, 0, 24, 0, 0, 0, 0, 0, -10, 0, 8, 0, -64, 0, -16, 0, 16, 0, 32, 0, 0, 0, 18, 0, -6, 0, -48, 0, 1, 0, -8, 0, 14, 0, 14, 0, -16, 0, 4, 0, -8, 0, 8, 0, -28, 0, 4, 0, 0, 0, -24, 0, -20, 0, -32, 0, 38, 0, -32, 0, -22, 0, 0, 0, -4, 0, 8, 0, 2, 0, 2, 0, -18, 0, 8, 0, 0, 0, -24, 0, 32, 0, 6, 0, 4, 0, -28, 0, 8, 0, 0, 0, 4, 0, 4, 0, 22, 0, 0, 0, -6, 0, -40, 0, 0, 0, -10, 0, 26, 0, -4, 0, -8, 0, 24, 0, -16, 0, 0, 0, 30, 0, 16, 0, 4, 0, 28, 0, -50, 0, -26, 0, -14, 0, 48, 0, -8, 0, 24, 0, 7, 0, 26, 0, 18, 0, 0, 0, 28, 0, 48, 0, -10, 0, -8, 0, 42, 0, 12, 0, 0, 0, 32, 0, -12, 0, -13, 0, -32, 0, -8, 0, 2, 0, 0, 0, -18, 0, -18, 0, 50, 0, 4, 0, 8, 0, -8, 0, 0, 0, -4, 0, 0, 0, 24, 0, -16, 0, -48, 0, -4, 0, 0, 0, -12, 0, -4, 0, -18, 0, -16, 0, -16, 0, 4, 0, 0, 0, -16, 0, -12, 0, 16, 0, -6, 0, -16, 0, 50, 0, -28, 0, 24, 0, 16, 0, 42, 0, -6, 0, 6, 0, -48, 0, 0, 0, -12, 0, -20, 0, 6, 0, -54, 0, 0, 0, -24, 0, 0, 0, 33, 0, 12, 0, -4, 0, 16, 0, 8, 0, -36, 0, 0, 0, 2, 0, -30, 0, 24, 0, -2, 0, 24, 0, 36, 0, 0, 0, -32, 0, -40, 0, -20, 0, 32, 0, -26, 0, 6, 0], 'weight': 2, 'weight_parity': 1}
  38. label: 49.2.a.a
    {'Nk2': 196, 'analytic_conductor': 0.3912669699042739, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[7, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [49, 1, [3], [1]], 'cm_discs': [-7], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554481, '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': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': True, 'is_twist_minimal': True, 'label': '49.2.a.a', 'level': 49, 'level_is_powerful': True, 'level_is_prime': False, 'level_is_prime_power': True, 'level_is_prime_square': True, 'level_is_square': True, 'level_is_squarefree': False, 'level_primes': [7], 'level_radical': 7, 'minimal_twist': '49.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{4}-3q^{8}-3q^{9}+4q^{11}+\\cdots', 'related_objects': ['EllipticCurve/Q/49/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.1.d1', 'self_twist_discs': [-7], 'self_twist_type': 1, 'space_label': '49.2.a', 'trace_display': [1, 0, 0, 0], 'trace_hash': 1094831497817794886, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.004', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.964', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.002', 'prec': 4}, {'__RealLiteral__': 0, 'data': '2.862', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.004', 'prec': 4}, {'__RealLiteral__': 0, 'data': '9.475', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.506', 'prec': 10}, 'traces': [1, 1, 0, -1, 0, 0, 0, -3, -3, 0, 4, 0, 0, 0, 0, -1, 0, -3, 0, 0, 0, 4, 8, 0, -5, 0, 0, 0, 2, 0, 0, 5, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, -12, -4, 0, 8, 0, 0, 0, -5, 0, 0, -10, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 7, 0, 0, 4, 0, 0, 0, 16, 9, 0, -6, 0, 0, 0, 0, 8, 0, 9, 0, 0, 0, 0, -12, 0, -12, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -12, 5, 0, 0, 0, 0, 0, -10, -20, 0, 18, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 16, -3, 0, 0, 0, 0, 0, 4, 0, 0, -10, 0, 0, 0, 0, 16, 0, 3, 0, 0, 0, 6, 22, 0, -24, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 9, -20, 0, 0, 0, 0, 0, -13, 0, 0, 12, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 8, 0, 18, 0, 0, 0, -26, -12, 0, 15, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, -12, 10, 0, -20, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 15, 2, 0, 0, 0, 0, 0, -6, 22, 0, 0, 0, 0, 0, 16, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 16, 0, -17, 0, 0, 0, 0, -6, 0, 32, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -10, -20, 0, -10, 0, 0, 0, -26, 0, 0, -16, 0, 0, 0, -15, -17, 0, 0, 0, 0, 0, 0, 18, 0, 22, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -34, 0, 8, 0, 0, 0, 0, -9, 0, -20, 0, 0, 0, 0, 36, 0, 18, 0, 0, 0, 30, -13, 0, 0, 0, 0, 0, 36, 0, 0, 4, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 4, 8, 0, -19, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, -12, 0, 0, 8, 0, 0, 0, 18, 36, 0, -38, 0, 0, 0, 0, -26, 0, 12, 0, 0, 0, 5, -34, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, -26, -12, 0, 30, 0, 0, 0, 20, 0, 0, 32, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 2, 15, 0, -2, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -40, -2, 0, 22, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 30, 16, 0, 0, 0, 0, 0, -5, 0, 0, -24, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 32, 0, -16, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 32, 0, 0, 41, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 44, 10, 0, -20, 0, 0, 0, -10, 0, 0, 46, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, -48, 22, 0, 4, 0, 0, 0, -40, -21, 0, -17, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -22, 0, 0, 32, 0, 0, 0, -12, 24, 0, 0, 0, 0, 0, 0, 0, 0, -38, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 16, -24, 0, -34, 0, 0, 0, 8, -48, 0, 46, 0, 0, 0, 0, 0, 0, -27, 0, 0, 0, 20, 50, 0, 0, 0, 0, 0, 44, 0, 0, 36, 0, 0, 0, 18, 16, 0, 0, 0, 0, 0, 30, 30, 0, 13, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 28, 0, 0, 0, 0, -6, 0, -24, 0, 0, 0, 0, -4, 0, 8, 0, 0, 0, -19, 0, 0, -10, 0, 0, 0, -27, 0, 0, 0, 0, 0, 0, 40, 16, 0, -52, 0, 0, 0, -40, 0, 0, 22, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -54, -12, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -18, 0, 36, 0, 0, 0, -38, 0, 0, 64, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, -25, 0, -34, 0, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 22, 0, 32, 0, 0, 0, 44, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25, -26, 0, 12, 0, 0, 0, 10, 0, 0, -48, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 32, 8, 0, 0, 0, 0, 0, 32, 0, 0, -54, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, -12, 0, 0, -20, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 2, 0, -15, 0, 0, 0, -6, 0, 0, 60, 0, 0, 0, 16, 0, 0, -6, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 30, -40, 0, 10, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, -20, 0, 0, 0, 0, 0, 58, 30, 0, -16, 0, 0, 0, 0, -31, 0, 60, 0, 0, 0, -40, -15, 0, 0, 0, 0, 0, -24, 0, 0, 46, 0, 0, 0, -54, 44, 0, 0, 0, 0, 0, 0, -96, 0, -24, 0, 0, 0, 0, 0, 0, 36, 0, 0], 'weight': 2, 'weight_parity': 1}
  39. label: 50.2.a.a
    {'Nk2': 200, 'analytic_conductor': 0.39925201010640193, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [5, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [50, 1, [27], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554482, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '50.2.a.a', 'level': 50, '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': '50.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\\cdots', 'related_objects': ['EllipticCurve/Q/50/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '50.2.a', 'trace_display': [-1, 1, 0, 2], 'trace_hash': 1291586430715429255, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.995', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.045', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.955', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.144', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.760', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, 'traces': [1, -1, 1, 1, 0, -1, 2, -1, -2, 0, -3, 1, -4, -2, 0, 1, -3, 2, 5, 0, 2, 3, 6, -1, 0, 4, -5, 2, 0, 0, 2, -1, -3, 3, 0, -2, 2, -5, -4, 0, -3, -2, -4, -3, 0, -6, 12, 1, -3, 0, -3, -4, 6, 5, 0, -2, 5, 0, 0, 0, 2, -2, -4, 1, 0, 3, -13, -3, 6, 0, 12, 2, 11, -2, 0, 5, -6, 4, -10, 0, 1, 3, -9, 2, 0, 4, 0, 3, 15, 0, -8, 6, 2, -12, 0, -1, 2, 3, 6, 0, -18, 3, -4, 4, 0, -6, -3, -5, -10, 0, 2, 2, -9, -5, 0, 0, 8, 0, -6, 0, -2, -2, -3, 2, 0, 4, 2, -1, -4, 0, 12, -3, 10, 13, 0, 3, -3, -6, 5, 0, 12, -12, 12, -2, 0, -11, -3, 2, 0, 0, 2, -5, 6, 6, 0, -4, 2, 10, 6, 0, 12, -1, 11, -3, 0, 9, 12, -2, 3, 0, -10, -4, -24, 0, 0, -3, 0, -15, -15, 0, 2, 8, 2, -6, 0, -2, 9, 12, -10, 0, -18, 1, -19, -2, 0, -3, -18, -6, 20, 0, -13, 18, 0, -3, 0, 4, -12, -4, -15, 0, -13, 6, 12, 3, 0, 5, 4, 10, 11, 0, 12, -2, -4, -2, 0, 9, 12, 5, 20, 0, -6, 0, 6, -8, 0, 0, -10, 6, 0, 0, 17, 2, 16, 2, 0, 3, -20, -2, -9, 0, 27, -4, -18, -2, 0, 1, -18, 4, 4, 0, 0, -12, 6, 3, 0, -10, 15, -13, 0, 0, 2, -3, -8, 3, 0, 6, 32, -5, -4, 0, -18, -12, 11, 12, 0, -12, -6, 2, -8, 0, 2, 11, 6, 3, 0, -2, 15, 0, -24, 0, -8, -2, -18, 5, 0, -6, 17, -6, -4, 0, -18, 4, 26, -2, 0, -10, 12, -6, 0, 0, -3, -12, -15, 1, 0, -11, -10, 3, 24, 0, 17, -9, -4, -12, 0, 2, -13, -3, -9, 0, -6, 10, -20, 4, 0, 24, -3, 0, -10, 0, 20, 3, 6, 0, 0, 15, -6, 15, 30, 0, 6, -2, -2, -8, 0, -2, -28, 6, 6, 0, 12, 2, 26, -9, 0, -12, 0, 10, -25, 0, 2, 18, 6, -1, 0, 19, 8, 2, 30, 0, -18, 3, 12, 18, 0, 6, -28, -20, 10, 0, -3, 13, -8, -18, 0, 0, -6, 3, 5, 0, -3, -4, 0, 12, 0, 4, 5, 15, -15, 0, -28, 13, -24, -6, 0, -12, 4, -3, 12, 0, -18, -5, -19, -4, 0, -10, 30, -11, -40, 0, 6, -12, -9, 2, 0, 4, 0, 2, -15, 0, 9, -9, 2, -12, 0, -5, 17, -20, 15, 0, 12, 6, -4, 0, 0, -6, 12, 8, -26, 0, 2, 0, 12, 10, 0, -6, -12, 0, 30, 0, -8, -17, 12, -2, 0, -16, 2, -2, 11, 0, 12, -3, 0, 20, 0, 2, 24, 9, 20, 0, 12, -27, 36, 4, 0, 18, 3, 2, -30, 0, 22, -1, -25, 18, 0, -4, -36, -4, -24, 0, -3, 0, 41, 12, 0, -6, -6, -3, 13, 0, 0, 10, 12, -15, 0, 13, -15, 0, 9, 0, 32, -2, 2, 3, 0, 8, 17, -3, -4, 0, 0, -6, -20, -32, 0, 5, 12, 4, 16, 0, 9, 18, -24, 12, 0, -11, 2, -12, -15, 0, -28, 12, -18, 6, 0, -2, -13, 8, -19, 0, -18, -2, -18, -11, 0, -6, -33, -3, 10, 0, -18, 2, -9, -15, 0, 0, 20, 24, 30, 0, -13, 8, 26, 2, 0, 18, 32, -5, 0, 0, -48, 6, -34, -17, 0, 6, -18, 4, 20, 0, -30, 18, 30, -4, 0, -26, -15, 2, -6, 0, 2, 10, -13, -12, 0, 6, 12, 0, -24, 0, 42, 3, -4, 12, 0, 15, 12, -1, 0, 0, 4, 11, 6, 10, 0, -3, -22, -24, 15, 0, 32, -17, 12, 9, 0, 4, 0, 12, -4, 0, -6, -2, 26, 13, 0, 3, -48, 9, 4, 0, 12, 6, -39, -10, 0, 20, 20, -4, -24, 0, 17, -24, 12, 3, 0, 0, 9, 10, 6, 0, 12, -20, 10, -3, 0, -6, -36, 0, 20, 0, 20, -15, 12, 6, 0, -15, 0, -30, -30, 0, -8, -6, 17, 2, 0, 2, 32, 8, 13, 0, 12, 2, -4, 28, 0, -6, 39, -6, 20, 0, -20, -12, 6, -2, 0, -26, 18, 9, -6, 0, 32, 12, 27, 0, 0, -10, 32, 25, -18, 0, -3, -2, -20, -18, 0, -6, 0, 1, 5, 0, -18, -19, -24, -8, 0, -2, 4, -30, -15, 0, -36, 18, 0, -3, 0, -12, -28, -18, 6, 0, -18, -6, -8, 28, 0, 20, 42, -10, -36, 0, -30, 3, -33, -13, 0, 8, 0, 18, -30, 0, -28, 0, 2, 6, 0, -3, -20, -5, 16, 0, 42, 3, -4, 4, 0, 0, -33, -12, 20, 0, 32, -4, 9, -5, 0, -15, -10, 15, 0, 0, -29, 28, -18, -13, 0, 24, -4, 6, 11, 0, 12, 12, 26, -4, 0, 3, -3, -12, 5, 0, -6, 18, -24, 5, 0, 19, -8, 4, 30, 0, 52, 10, -4, -30, 0, 11, -28, 40, 6, 0, -18, -6, 41, 12, 0, 9, 12, -2, 4, 0, -3, -4, 60, 0, 0, -2, -24, 15, 0, 0, -18, -9, -8, 9, 0, -2, -28, 12, 36, 0, 12, 5, 27, -17, 0, 20, 24, -15, -10, 0, 17, -12, -48, -6, 0, 4, 8, 0, 30, 0, -15, 6, -18, -12, 0, -8, -13, 26, 26, 0, 12, -2, -18, 0, 0, -12, -48, -10, -44, 0, 12, 6, -39, 12, 0, 0, 0, -30, -6, 0, -27, 8, 6, 17, 0, -12, 32, 2, -15, 0, -3, 16, 10, -2, 0, 2, 57, -11, -45, 0, 20, -12, 6, 3, 0, 0, 24, -20, -24, 0, -58, -2, 17, -24, 0, -9, -28, -20, -10, 0], 'weight': 2, 'weight_parity': 1}
  40. label: 50.2.a.b
    {'Nk2': 200, 'analytic_conductor': 0.39925201010640193, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [5, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [50, 1, [27], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924978, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '50.2.a.b', 'level': 50, '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': '50.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\\cdots', 'related_objects': ['EllipticCurve/Q/50/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '50.2.a', 'trace_display': [1, -1, 0, -2], 'trace_hash': 977379866071001924, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.021', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.995', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.071', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.955', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.197', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.760', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, 'traces': [1, 1, -1, 1, 0, -1, -2, 1, -2, 0, -3, -1, 4, -2, 0, 1, 3, -2, 5, 0, 2, -3, -6, -1, 0, 4, 5, -2, 0, 0, 2, 1, 3, 3, 0, -2, -2, 5, -4, 0, -3, 2, 4, -3, 0, -6, -12, -1, -3, 0, -3, 4, -6, 5, 0, -2, -5, 0, 0, 0, 2, 2, 4, 1, 0, 3, 13, 3, 6, 0, 12, -2, -11, -2, 0, 5, 6, -4, -10, 0, 1, -3, 9, 2, 0, 4, 0, -3, 15, 0, -8, -6, -2, -12, 0, -1, -2, -3, 6, 0, -18, -3, 4, 4, 0, -6, 3, 5, -10, 0, 2, -2, 9, -5, 0, 0, -8, 0, -6, 0, -2, 2, 3, 2, 0, 4, -2, 1, -4, 0, 12, 3, -10, 13, 0, 3, 3, 6, 5, 0, 12, 12, -12, -2, 0, -11, 3, -2, 0, 0, 2, 5, -6, 6, 0, -4, -2, -10, 6, 0, 12, 1, -11, -3, 0, 9, -12, 2, 3, 0, -10, 4, 24, 0, 0, -3, 0, 15, -15, 0, 2, -8, -2, -6, 0, -2, -9, -12, -10, 0, -18, -1, 19, -2, 0, -3, 18, 6, 20, 0, -13, -18, 0, -3, 0, 4, 12, 4, -15, 0, -13, -6, -12, 3, 0, 5, -4, -10, 11, 0, 12, 2, 4, -2, 0, 9, -12, -5, 20, 0, -6, 0, -6, -8, 0, 0, 10, -6, 0, 0, 17, -2, -16, 2, 0, 3, 20, 2, -9, 0, 27, 4, 18, -2, 0, 1, 18, -4, 4, 0, 0, 12, -6, 3, 0, -10, -15, 13, 0, 0, 2, 3, 8, 3, 0, 6, -32, 5, -4, 0, -18, 12, -11, 12, 0, -12, 6, -2, -8, 0, 2, -11, -6, 3, 0, -2, -15, 0, -24, 0, -8, 2, 18, 5, 0, -6, -17, 6, -4, 0, -18, -4, -26, -2, 0, -10, -12, 6, 0, 0, -3, 12, 15, 1, 0, -11, 10, -3, 24, 0, 17, 9, 4, -12, 0, 2, 13, 3, -9, 0, -6, -10, 20, 4, 0, 24, 3, 0, -10, 0, 20, -3, -6, 0, 0, 15, 6, -15, 30, 0, 6, 2, 2, -8, 0, -2, 28, -6, 6, 0, 12, -2, -26, -9, 0, -12, 0, -10, -25, 0, 2, -18, -6, -1, 0, 19, -8, -2, 30, 0, -18, -3, -12, 18, 0, 6, 28, 20, 10, 0, -3, -13, 8, -18, 0, 0, 6, -3, 5, 0, -3, 4, 0, 12, 0, 4, -5, -15, -15, 0, -28, -13, 24, -6, 0, -12, -4, 3, 12, 0, -18, 5, 19, -4, 0, -10, -30, 11, -40, 0, 6, 12, 9, 2, 0, 4, 0, -2, -15, 0, 9, 9, -2, -12, 0, -5, -17, 20, 15, 0, 12, -6, 4, 0, 0, -6, -12, -8, -26, 0, 2, 0, -12, 10, 0, -6, 12, 0, 30, 0, -8, 17, -12, -2, 0, -16, -2, 2, 11, 0, 12, 3, 0, 20, 0, 2, -24, -9, 20, 0, 12, 27, -36, 4, 0, 18, -3, -2, -30, 0, 22, 1, 25, 18, 0, -4, 36, 4, -24, 0, -3, 0, -41, 12, 0, -6, 6, 3, 13, 0, 0, -10, -12, -15, 0, 13, 15, 0, 9, 0, 32, 2, -2, 3, 0, 8, -17, 3, -4, 0, 0, 6, 20, -32, 0, 5, -12, -4, 16, 0, 9, -18, 24, 12, 0, -11, -2, 12, -15, 0, -28, -12, 18, 6, 0, -2, 13, -8, -19, 0, -18, 2, 18, -11, 0, -6, 33, 3, 10, 0, -18, -2, 9, -15, 0, 0, -20, -24, 30, 0, -13, -8, -26, 2, 0, 18, -32, 5, 0, 0, -48, -6, 34, -17, 0, 6, 18, -4, 20, 0, -30, -18, -30, -4, 0, -26, 15, -2, -6, 0, 2, -10, 13, -12, 0, 6, -12, 0, -24, 0, 42, -3, 4, 12, 0, 15, -12, 1, 0, 0, 4, -11, -6, 10, 0, -3, 22, 24, 15, 0, 32, 17, -12, 9, 0, 4, 0, -12, -4, 0, -6, 2, -26, 13, 0, 3, 48, -9, 4, 0, 12, -6, 39, -10, 0, 20, -20, 4, -24, 0, 17, 24, -12, 3, 0, 0, -9, -10, 6, 0, 12, 20, -10, -3, 0, -6, 36, 0, 20, 0, 20, 15, -12, 6, 0, -15, 0, 30, -30, 0, -8, 6, -17, 2, 0, 2, -32, -8, 13, 0, 12, -2, 4, 28, 0, -6, -39, 6, 20, 0, -20, 12, -6, -2, 0, -26, -18, -9, -6, 0, 32, -12, -27, 0, 0, -10, -32, -25, -18, 0, -3, 2, 20, -18, 0, -6, 0, -1, 5, 0, -18, 19, 24, -8, 0, -2, -4, 30, -15, 0, -36, -18, 0, -3, 0, -12, 28, 18, 6, 0, -18, 6, 8, 28, 0, 20, -42, 10, -36, 0, -30, -3, 33, -13, 0, 8, 0, -18, -30, 0, -28, 0, -2, 6, 0, -3, 20, 5, 16, 0, 42, -3, 4, 4, 0, 0, 33, 12, 20, 0, 32, 4, -9, -5, 0, -15, 10, -15, 0, 0, -29, -28, 18, -13, 0, 24, 4, -6, 11, 0, 12, -12, -26, -4, 0, 3, 3, 12, 5, 0, -6, -18, 24, 5, 0, 19, 8, -4, 30, 0, 52, -10, 4, -30, 0, 11, 28, -40, 6, 0, -18, 6, -41, 12, 0, 9, -12, 2, 4, 0, -3, 4, -60, 0, 0, -2, 24, -15, 0, 0, -18, 9, 8, 9, 0, -2, 28, -12, 36, 0, 12, -5, -27, -17, 0, 20, -24, 15, -10, 0, 17, 12, 48, -6, 0, 4, -8, 0, 30, 0, -15, -6, 18, -12, 0, -8, 13, -26, 26, 0, 12, 2, 18, 0, 0, -12, 48, 10, -44, 0, 12, -6, 39, 12, 0, 0, 0, 30, -6, 0, -27, -8, -6, 17, 0, -12, -32, -2, -15, 0, -3, -16, -10, -2, 0, 2, -57, 11, -45, 0, 20, 12, -6, 3, 0, 0, -24, 20, -24, 0, -58, 2, -17, -24, 0, -9, 28, 20, -10, 0], 'weight': 2, 'weight_parity': 1}
  41. label: 51.2.a.a
    {'Nk2': 204, 'analytic_conductor': 0.40723705030852997, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1], [17, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [51, 1, [35, 37], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [0, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554483, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '51.2.a.a', 'level': 51, '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, 17], 'level_radical': 51, 'minimal_twist': '51.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{3}-2q^{4}+3q^{5}-4q^{7}+q^{9}-3q^{11}+\\cdots', 'related_objects': ['EllipticCurve/Q/51/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '51.2.a', 'trace_display': [0, 1, 3, -4], 'trace_hash': 2233362678190722081, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.007', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.961', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.021', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.850', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.058', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.516', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.015', 'prec': 7}, 'traces': [1, 0, 1, -2, 3, 0, -4, 0, 1, 0, -3, -2, -1, 0, 3, 4, -1, 0, -1, -6, -4, 0, 9, 0, 4, 0, 1, 8, 6, 0, 2, 0, -3, 0, -12, -2, -4, 0, -1, 0, -3, 0, -7, 6, 3, 0, -6, 4, 9, 0, -1, 2, -6, 0, -9, 0, -1, 0, 6, -6, 8, 0, -4, -8, -3, 0, -4, 2, 9, 0, 12, 0, 2, 0, 4, 2, 12, 0, -10, 12, 1, 0, -6, 8, -3, 0, 6, 0, 0, 0, 4, -18, 2, 0, -3, 0, -16, 0, -3, -8, 0, 0, 5, 0, -12, 0, 9, -2, 20, 0, -4, -16, -9, 0, 27, -12, -1, 0, 4, 0, -2, 0, -3, -4, -3, 0, -13, 0, -7, 0, 3, 6, 4, 0, 3, 0, -6, 0, 2, 24, -6, 0, 3, 4, 18, 0, 9, 8, -18, 0, 8, 0, -1, 0, 6, 2, 11, 0, -6, 0, -36, 0, 2, 6, -9, 0, 21, 0, -12, 0, -1, 14, 15, 0, -16, -12, 6, 0, -6, -6, 14, 0, 8, 0, -12, 0, 3, 12, -4, 0, 18, -8, -22, 0, -3, -18, 3, 0, -16, 0, -4, 0, -24, 2, -9, 0, 9, -4, 3, 0, 2, 12, 12, 0, -21, 0, -8, 0, 2, 18, 1, 0, -1, 0, 4, 0, 3, 2, 14, 0, 12, 0, 21, 0, -18, -12, -10, 0, -12, 12, 8, 0, 1, -16, 27, 0, 1, 0, -6, 0, 24, 8, -27, 0, -3, 16, 12, 0, 16, 6, 6, 0, 12, 0, -18, 0, 0, 8, -15, 0, 11, -4, 4, 0, -12, -18, 2, 0, 2, 0, 12, 0, -10, -24, -3, 0, 12, 0, 1, 0, -16, -4, -24, 0, 18, 0, -3, 0, -9, -8, 28, 0, 0, -4, 24, 0, 20, -24, 5, 0, -24, 0, -16, 0, -12, 20, -6, 0, -18, -24, 9, 0, 1, -2, -4, 0, 20, 0, 24, 0, -13, 12, -4, 0, -12, -16, 14, 0, -9, 6, -6, 0, -8, 0, 27, 0, -12, -12, -19, 0, -1, 0, 6, 0, 36, 0, 4, 0, 0, 0, -18, 0, -2, -8, 6, 0, 8, 36, -3, 0, 24, -4, -22, 0, -3, 0, -6, 0, 32, 6, -13, 0, -12, 0, 36, 0, -7, 32, 36, 0, -9, 0, 3, 0, -30, 6, 20, 0, 4, 16, -15, 0, -2, 0, 3, 0, 12, 0, -19, 0, -6, -10, -24, 0, -18, 0, 2, 0, 12, 24, -25, 0, -6, 0, -4, 0, -32, -18, 3, 0, -24, 4, -1, 0, 18, -40, -9, 0, -28, 0, 9, 0, 6, 8, 0, 0, -18, 32, -6, 0, 9, 18, 8, 0, 12, 0, -19, 0, -1, -54, 30, 0, 8, 24, 6, 0, 42, 2, 16, 0, 11, 0, 21, 0, -4, -8, -6, 0, -27, 0, 4, 0, -36, 4, -48, 0, -22, 0, 2, 0, -6, 6, -6, 0, -9, 8, -48, 0, -22, 6, 21, 0, 15, 0, 0, 0, -12, 26, 36, 0, -8, 0, -1, 0, 15, 14, 18, 0, 15, 0, 21, 0, 20, -6, -16, 0, -2, -12, 58, 0, 6, -8, 3, 0, 27, 0, -6, 0, -27, -6, -16, 0, 14, 0, 60, 0, 8, 12, 8, 0, -6, 0, 40, 0, -12, -4, -30, 0, 7, -48, 3, 0, -30, 12, -27, 0, -4, 0, -24, 0, 8, -6, 18, 0, 36, -8, -7, 0, -22, -36, 24, 0, 18, 0, -3, 0, -36, -18, -2, 0, 3, -16, -18, 0, 12, 36, -16, 0, -6, 0, 38, 0, -4, -16, -6, 0, 38, 0, -24, 0, 6, 2, 11, 0, -9, 0, -6, 0, -10, -12, 9, 0, 0, -4, -29, 0, 3, -22, 4, 0, -37, 0, 2, 0, -39, 12, -9, 0, 12, 0, -33, 0, 32, 72, -21, 0, 18, 0, -18, 0, -8, -4, 27, 0, 9, -12, 2, 0, 6, 18, -31, 0, 1, 0, 12, 0, 54, -42, -1, 0, -24, 0, -22, 0, 4, 24, -27, 0, 64, 0, 3, 0, 3, 2, -18, 0, 14, -28, 6, 0, 20, -30, 12, 0, 6, 0, 3, 0, 21, 32, 24, 0, 4, 24, -18, 0, 0, -12, 14, 0, -10, 0, 18, 0, 9, 12, -12, 0, 3, 12, -20, 0, 8, -28, 24, 0, 8, 0, 1, 0, 7, -16, 2, 0, 27, 0, 12, 0, -1, 24, 1, 0, 24, 0, -54, 0, -6, -6, -36, 0, -46, -24, 24, 0, 24, 8, -43, 0, -27, 0, 30, 0, -80, -36, -3, 0, -6, 16, 41, 0, 12, 44, 24, 0, 8, 0, 16, 0, 3, 6, -36, 0, 6, 36, 33, 0, -40, -6, 12, 0, 36, 0, -8, 0, -18, 32, -48, 0, 6, 0, 0, 0, -6, 8, -108, 0, -15, 0, -51, 0, -10, 48, 11, 0, 6, -4, 7, 0, 4, 18, -21, 0, -28, 0, -12, 0, -21, -18, 14, 0, 2, 8, -9, 0, 63, -6, 2, 0, -57, 0, 7, 0, 12, -4, -36, 0, 8, -24, -10, 0, -36, -24, 26, 0, -3, 0, -18, 0, 20, 42, 12, 0, 24, 0, 45, 0, 1, 16, 30, 0, 4, 0, -16, 0, 12, -4, 14, 0, -24, -36, 18, 0, 11, -2, 18, 0, 39, 0, 52, 0, -3, 2, 6, 0, -18, 0, -9, 0, 12, -8, 6, 0, 28, 0, 42, 0, 2, -6, 0, 0, -27, -4, 18, 0, 24, -28, -12, 0, 11, 0, 20, 0, -12, -24, -16, 0, 5, 0, 15, 0, -9, -42, -24, 0, 9, 0, -22, 0, -16, 36, 18, 0, -27, 24, -12, 0, 36, 20, -2, 0, -6, 0, 36, 0, 54, 24, -18, 0, 24, -24, -27, 0, 9, -16, -66, 0, 41, 0, 1, 0, 6, -2, -8, 0, -4, 32, -30, 0, 0, -54, 20, 0, -9, 0, 9, 0, 24, -2, -63, 0, -52, 0, -13, 0, -48, 12, 62, 0, -4, 0], 'weight': 2, 'weight_parity': 1}
  42. label: 51.2.a.b
    {'Nk2': 204, 'analytic_conductor': 0.40723705030852997, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, 1], [17, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [51, 1, [35, 37], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, 'field_disc': 17, 'field_disc_factorization': [[17, 1]], 'field_poly': [-4, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-4, 1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924979, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '51.2.a.b', 'level': 51, '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, 17], 'level_radical': 51, 'minimal_twist': '51.2.a.b', 'nf_label': '2.2.17.1', 'prim_orbit_index': 1, 'qexp_display': 'q-\\beta q^{2}-q^{3}+(2+\\beta )q^{4}+(1+\\beta )q^{5}+\\cdots', 'related_objects': ['Genus2Curve/Q/2601/a'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '51.2.a', 'trace_display': [-1, -2, 3, 0], 'trace_hash': 923891408700471813, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.025', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.950', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.048', 'prec': 7}, {'__RealLiteral__': 0, 'data': '9.372', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '63.460', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.013', 'prec': 7}, 'traces': [2, -1, -2, 5, 3, 1, 0, -9, 2, -10, -1, -5, 5, 0, -3, 3, 2, -1, 3, 16, 0, -8, -9, 9, 3, 6, -2, 0, 0, 10, -2, -9, 1, -1, 0, 5, -2, 24, -5, -22, -3, 0, -3, 6, 3, -4, -14, -3, -14, -27, -2, 4, 8, 1, 7, 0, -3, 34, 6, -16, 10, -16, 0, 7, -1, 8, 8, 5, 9, 0, 4, -9, -8, 18, -3, -18, 0, -6, 6, 30, 2, 10, -10, 0, 3, -24, 0, -4, 6, -10, 0, -14, 2, 24, -21, 9, -14, 7, -1, 33, 30, 1, 21, -14, 0, -38, 3, -5, -22, -12, 2, 0, -5, -24, -5, -34, 5, -20, 0, 22, -13, -22, 3, 12, 15, 0, 19, 23, 3, -8, 33, -6, 0, -4, -3, -9, -16, 4, -10, 0, 14, 32, -11, 3, -34, 38, 14, -22, 8, 27, 16, 12, 2, 0, 14, -4, 1, 48, -8, -22, 0, -1, -22, -16, -7, -12, 19, 0, -5, -10, 3, 18, -17, -34, 0, 24, -6, 14, -10, 16, 12, 0, -10, 32, -20, 16, -1, -52, 0, 36, -18, -7, -32, -10, 1, -35, 11, -8, 32, -39, -8, 2, 0, -5, -13, -36, -9, -18, -27, 0, 2, 54, -4, 24, 21, 9, 0, -6, 8, 26, 5, -18, -1, 0, 3, -6, 9, 18, 12, 28, 0, 34, -3, 6, -38, 32, -6, 0, 4, -30, -18, 15, -2, 42, -21, -10, 33, -8, 10, -16, -16, 0, 13, -52, -3, -17, -6, 24, 0, 6, 0, -8, -8, 4, 46, 0, -6, 20, 37, 10, 19, 3, 0, -26, 24, 14, 12, -12, -2, 0, -30, -24, 18, -24, 21, -20, 0, -9, 2, 68, 14, -54, -6, -7, 26, 26, 1, -38, -31, -33, 0, -8, -30, -72, 32, -1, 32, 0, -21, -24, 0, 14, 26, -26, 0, -36, -36, 38, -34, 2, -3, 0, 3, 5, -18, 28, 22, 22, 0, 12, -41, -8, -2, -52, 12, 0, 16, 45, 5, 16, 18, 24, 0, -12, 5, -34, 16, 34, 19, 0, -5, -4, 12, 20, -28, -2, 0, -12, 12, -22, 43, -6, 13, 0, -46, 22, -20, 12, -3, 44, 0, -12, 16, -8, -15, 80, 34, 0, -24, -78, -19, -8, -4, -23, 0, -18, -3, -18, 14, 8, -9, 63, -33, 54, -42, 6, -14, -16, 0, 81, 33, 4, -22, 58, 3, 0, -16, 9, -17, 32, 16, 78, 0, -4, 2, -14, 10, -12, 32, 0, 53, -52, -14, -70, 3, -32, 0, -18, 11, -36, -48, -3, 41, 0, 34, -38, -39, -38, -28, -40, -14, 6, -54, 22, -8, 60, -8, 0, 24, -27, -7, -4, -16, 72, 0, -12, 7, -6, -2, -38, 0, 0, -16, -102, -14, 10, 18, 4, 0, 104, -1, -44, 27, -48, -72, 0, 8, 32, -5, 22, 12, -42, 0, -41, -4, 1, 10, -62, 22, 70, -18, 16, 0, 60, 7, 48, 0, 12, 2, 46, -19, -60, -55, 0, 28, 36, 5, 90, 42, 10, 0, 39, -3, 54, 57, -18, -10, 0, 17, -4, -67, 34, -40, 74, 0, 72, -2, -24, 3, -108, 6, 0, 1, -14, -21, -36, 10, -10, 7, -16, -6, -52, -12, -9, -16, 0, 56, -6, 10, -12, 102, -32, 0, -6, 20, -8, 20, -16, -33, 0, 1, -2, 54, 52, 1, -60, 0, 16, 34, -36, -12, -2, 18, 0, 12, 7, -45, -1, 32, -136, 0, 10, 30, 70, -1, -14, 8, 35, -54, -64, -11, -54, 72, 8, 0, 54, -32, -44, -42, 39, 4, 0, 8, 40, -28, -2, 6, 12, 0, -84, -18, 5, 17, -84, 13, 0, -72, 36, -14, 52, 9, 0, 0, 18, 16, -98, 27, 28, -2, 0, 11, 24, -2, 18, 71, -54, -35, 0, 4, 26, -29, -24, -44, 0, -21, 24, 6, -9, 14, -42, 0, -72, -37, 6, 41, -30, -8, 0, 38, -26, 39, 80, -5, 28, 0, 18, -34, 90, 1, -40, 12, 0, 48, 94, -3, -55, -15, 6, 0, -22, -9, 8, -15, -18, 10, 0, -12, 72, -14, -28, 8, 0, 0, 60, 2, -34, -3, -18, 3, 0, 6, -6, 48, -12, 38, 62, 0, -32, -40, 48, 6, -10, 26, 0, 9, -8, -4, -40, -3, 30, 0, 55, 18, 30, -102, -15, -16, 0, 2, 108, -3, -42, -40, -24, 21, 32, -4, 10, -29, -84, -33, 0, 24, 8, 46, 26, -10, 6, 0, 16, -26, -72, 16, 68, 24, 0, -5, 12, -13, 120, -48, 52, 0, -28, 3, -32, -2, 17, 11, 0, 6, -46, -42, -24, 48, 46, 0, -126, 21, -6, -36, -4, 0, -21, 27, 8, -4, -32, 8, 72, 0, -4, 8, 58, -46, 80, 22, 0, -14, -39, 6, -110, -30, -20, 0, -40, -37, -118, 69, -10, -66, 0, -19, 8, -50, -3, -81, 34, 0, -58, -29, 26, 40, -120, -24, 0, 33, -14, 68, 16, -12, 26, -14, 12, 71, -42, 2, 52, -15, 0, 78, -18, 30, 56, -50, 24, 0, 114, -18, -27, -8, 24, -8, 0, -21, 12, -12, 20, 24, 78, 0, 24, -36, 9, 17, -46, -2, 0, -54, -68, 20, 82, -14, -108, 0, 54, -68, 48, 6, 36, 64, 7, 15, 4, -26, 44, 41, -26, 0, 4, -1, -62, 30, 38, 2, 0, 31, -114, -68, 33, 8, 12, 0, 14, 18, 8, 38, -54, 30, 0, -5, 72, 22, -46, -32, 30, 0, 1, -21, 48, -32, 34, 44, 0, -54, 144, 21, 34, 35, 24, -21, -16, 0, -60, 7, -14, -44, 0, -26, -180, 60, 26, 5, 60, 0, 12, 24, 36, 14, 36, 36, 0, -18, -38, -10, -24, 34, -108, 0, -2, -26, 28, 3, 6, -14, 0, 89, 67, -3, 36, -46, -5, 0, -56, 18, 66, 0, -28, -20, -112, -22, 60, 33, -22, -43, 34, 0, 6, 39, -12, 36, -8, 41, 0, 48, 8, -20, -52, 2, -76], 'weight': 2, 'weight_parity': 1}
  43. label: 52.2.a.a
    {'Nk2': 208, 'analytic_conductor': 0.415222090510658, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [13, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [52, 1, [27, 41], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554484, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '52.2.a.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': '52.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+2q^{5}-2q^{7}-3q^{9}-2q^{11}-q^{13}+\\cdots', 'related_objects': ['EllipticCurve/Q/52/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '52.2.a', 'trace_display': [0, 0, 2, -2], 'trace_hash': 1178087633165594685, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.005', 'prec': 4}, {'__RealLiteral__': 0, 'data': '1.005', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '2.036', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '5.164', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.011', 'prec': 7}, 'traces': [1, 0, 0, 0, 2, 0, -2, 0, -3, 0, -2, 0, -1, 0, 0, 0, 6, 0, -6, 0, 0, 0, 8, 0, -1, 0, 0, 0, 2, 0, 10, 0, 0, 0, -4, 0, -6, 0, 0, 0, -6, 0, 4, 0, -6, 0, -2, 0, -3, 0, 0, 0, 6, 0, -4, 0, 0, 0, -10, 0, -2, 0, 6, 0, -2, 0, 10, 0, 0, 0, 10, 0, 2, 0, 0, 0, 4, 0, -4, 0, 9, 0, -6, 0, 12, 0, 0, 0, -6, 0, 2, 0, 0, 0, -12, 0, 2, 0, 6, 0, -2, 0, -8, 0, 0, 0, -16, 0, -14, 0, 0, 0, 14, 0, 16, 0, 3, 0, -12, 0, -7, 0, 0, 0, -12, 0, -8, 0, 0, 0, -16, 0, 12, 0, 0, 0, 18, 0, 16, 0, 0, 0, 2, 0, 4, 0, 0, 0, 18, 0, 6, 0, -18, 0, 20, 0, 2, 0, 0, 0, -16, 0, -10, 0, 0, 0, 6, 0, 1, 0, 18, 0, -10, 0, 2, 0, 0, 0, 12, 0, -6, 0, 0, 0, -12, 0, -12, 0, 0, 0, 4, 0, 2, 0, 0, 0, -6, 0, -16, 0, 0, 0, -4, 0, -12, 0, -24, 0, 12, 0, 8, 0, 0, 0, 8, 0, -20, 0, 0, 0, -6, 0, -6, 0, 3, 0, 18, 0, 18, 0, 0, 0, 10, 0, -4, 0, 0, 0, 18, 0, -6, 0, 0, 0, -6, 0, 6, 0, 0, 0, 12, 0, -16, 0, 0, 0, 18, 0, 12, 0, -6, 0, -12, 0, 12, 0, 0, 0, 18, 0, -2, 0, 0, 0, 2, 0, 30, 0, -30, 0, -14, 0, 4, 0, 0, 0, 12, 0, 19, 0, 0, 0, -14, 0, -20, 0, 0, 0, -8, 0, -8, 0, 0, 0, -4, 0, -34, 0, 0, 0, 0, 0, -10, 0, 12, 0, 18, 0, -4, 0, 0, 0, -36, 0, 1, 0, 0, 0, 4, 0, -22, 0, 18, 0, 20, 0, -10, 0, 0, 0, -20, 0, 20, 0, 0, 0, -24, 0, 10, 0, 0, 0, -14, 0, 20, 0, 0, 0, 30, 0, 17, 0, 0, 0, 4, 0, -4, 0, 18, 0, -12, 0, -22, 0, 0, 0, -2, 0, 10, 0, 0, 0, 18, 0, 8, 0, -12, 0, -6, 0, 48, 0, 0, 0, -8, 0, 2, 0, 0, 0, -6, 0, -10, 0, 18, 0, 12, 0, -14, 0, 0, 0, 20, 0, -12, 0, 0, 0, 24, 0, 10, 0, 6, 0, -6, 0, 4, 0, 0, 0, -30, 0, -14, 0, 0, 0, -48, 0, -16, 0, 9, 0, -24, 0, -12, 0, 0, 0, -38, 0, 12, 0, 0, 0, 4, 0, 34, 0, 0, 0, -6, 0, 22, 0, 0, 0, 20, 0, -20, 0, 0, 0, -8, 0, 6, 0, -18, 0, -18, 0, 6, 0, 0, 0, 4, 0, 2, 0, 0, 0, -20, 0, 12, 0, 12, 0, -20, 0, -14, 0, 0, 0, 28, 0, -4, 0, 0, 0, -14, 0, -4, 0, 0, 0, -16, 0, 4, 0, 0, 0, 6, 0, 24, 0, 0, 0, 60, 0, 41, 0, 30, 0, 6, 0, -32, 0, 0, 0, 6, 0, 26, 0, 0, 0, -28, 0, -32, 0, 6, 0, -12, 0, 8, 0, 0, 0, 42, 0, -4, 0, 0, 0, -4, 0, 28, 0, -18, 0, 10, 0, -12, 0, 0, 0, -8, 0, -6, 0, 0, 0, 12, 0, -12, 0, 6, 0, 26, 0, -60, 0, 0, 0, 26, 0, -24, 0, 0, 0, 4, 0, -26, 0, -30, 0, -14, 0, -12, 0, 0, 0, 2, 0, 26, 0, 0, 0, 34, 0, -2, 0, 0, 0, 12, 0, -19, 0, 0, 0, -36, 0, 22, 0, 0, 0, -16, 0, 3, 0, -30, 0, -26, 0, 2, 0, 0, 0, -32, 0, 20, 0, 0, 0, 18, 0, -32, 0, -6, 0, 0, 0, 2, 0, 0, 0, 24, 0, 16, 0, 0, 0, 4, 0, -26, 0, 0, 0, 6, 0, -4, 0, 0, 0, -2, 0, 36, 0, 0, 0, -6, 0, 34, 0, -12, 0, 32, 0, -36, 0, 0, 0, 18, 0, 36, 0, 0, 0, 4, 0, -22, 0, 12, 0, 80, 0, 4, 0, 0, 0, -40, 0, 16, 0, 0, 0, -2, 0, -32, 0, -27, 0, 24, 0, 26, 0, 0, 0, -20, 0, 6, 0, 0, 0, -14, 0, 36, 0, 18, 0, 32, 0, 0, 0, 0, 0, 12, 0, -42, 0, 0, 0, 18, 0, 28, 0, -36, 0, 10, 0, -54, 0, 0, 0, -46, 0, -10, 0, 0, 0, 36, 0, -20, 0, 0, 0, 4, 0, 38, 0, 0, 0, -28, 0, 2, 0, 0, 0, 18, 0, -12, 0, 18, 0, -4, 0, -32, 0, 0, 0, 6, 0, -22, 0, 0, 0, -20, 0, -24, 0, -6, 0, 2, 0, -24, 0, 0, 0, 6, 0, 22, 0, 0, 0, -18, 0, 12, 0, 0, 0, -10, 0, -25, 0, 0, 0, 2, 0, 14, 0, 0, 0, -48, 0, -38, 0, 36, 0, -38, 0, 8, 0, 0, 0, 34, 0, -20, 0, 0, 0, 8, 0, -10, 0, -6, 0, 24, 0, 18, 0, 0, 0, 18, 0, 28, 0, 0, 0, 4, 0, 16, 0, -18, 0, 12, 0, 24, 0, 0, 0, 20, 0, 36, 0, 0, 0, -12, 0, 36, 0, 6, 0, -36, 0, 12, 0, 0, 0, 32, 0, -12, 0, 0, 0, -10, 0, 6, 0, 24, 0, -54, 0, 18, 0, 0, 0, -24, 0, 42, 0, 0, 0, 10, 0, -48, 0, 0, 0, -42, 0, -2, 0, 0, 0, 26, 0, 8, 0, 0, 0, -36, 0, 69, 0, 48, 0, 4, 0, 50, 0, 0, 0, -48, 0, -32, 0, 0, 0, 18, 0, 12, 0, 42, 0, 14, 0, -12, 0, 0, 0, 32, 0, 12, 0, 0, 0, -32, 0, -58, 0, 0, 0], 'weight': 2, 'weight_parity': 1}
  44. label: 53.2.a.a
    {'Nk2': 212, 'analytic_conductor': 0.42320713071278604, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[53, 1]], 'atkin_lehner_string': '+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [53, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554485, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '53.2.a.a', 'level': 53, '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': [53], 'level_radical': 53, 'minimal_twist': '53.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}-3q^{3}-q^{4}+3q^{6}-4q^{7}+3q^{8}+\\cdots', 'related_objects': ['EllipticCurve/Q/53/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '53.2.a', 'trace_display': [-1, -3, 0, -4], 'trace_hash': 59218195339168879, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.985', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.919', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.660', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, 'traces': [1, -1, -3, -1, 0, 3, -4, 3, 6, 0, 0, 3, -3, 4, 0, -1, -3, -6, -5, 0, 12, 0, 7, -9, -5, 3, -9, 4, -7, 0, 4, -5, 0, 3, 0, -6, 5, 5, 9, 0, 6, -12, -2, 0, 0, -7, -2, 3, 9, 5, 9, 3, -1, 9, 0, -12, 15, 7, -2, 0, -8, -4, -24, 7, 0, 0, -12, 3, -21, 0, 1, 18, -4, -5, 15, 5, 0, -9, -1, 0, 9, -6, -1, -12, 0, 2, 21, 0, -14, 0, 12, -7, -12, 2, 0, 15, 1, -9, 0, 5, -2, -9, -1, -9, 0, 1, 6, 9, 16, 0, -15, 4, 15, -15, 0, 7, -18, 2, 12, 0, -11, 8, -18, -4, 0, 24, 13, 3, 6, 0, -2, 0, 20, 12, 0, -9, 12, 21, -20, 0, 6, -1, 0, -6, 0, 4, -27, -5, -5, -15, -3, -15, -18, 0, 0, -9, -4, 1, 3, 0, -28, -9, -6, -6, 0, 1, 21, 36, -4, 0, -30, 2, 10, -21, 20, 0, 6, 14, 11, 0, -2, -12, 24, 21, 0, 12, 0, 2, 36, 0, -21, -21, -16, -1, 0, -9, -18, 0, 4, -15, 36, 2, 28, -9, 0, 1, 42, 3, 0, 0, -2, 1, -3, -6, 0, -27, -16, -16, 12, 0, 9, 15, -14, 20, -30, -15, 6, -15, 21, 0, 0, -21, -8, 18, 0, 2, 3, -12, 0, 0, -11, 11, 0, 8, 0, 18, 15, 12, 3, 0, 20, 24, 0, -13, 0, -17, -28, -6, -20, 0, -42, 2, -28, 0, 0, -20, 42, 12, 9, 0, -14, 3, -36, -12, 0, 21, -8, 20, 24, 0, 17, -6, -9, -1, 0, 0, -24, -30, -8, 0, -3, 4, 26, 27, 0, 15, 0, 5, -21, -15, 8, 3, 6, 5, 0, 18, -16, 0, 3, 0, 16, 27, -6, 4, 0, 1, 3, -3, 0, 0, -18, 28, 15, -9, 15, 6, -48, 18, 8, 0, 28, 1, 30, -21, 0, -12, 10, 4, -45, 0, 0, 30, -8, -6, 0, -10, -30, -21, 24, -20, 27, 0, -18, -6, 0, 14, -36, -11, 9, 0, 6, 2, 33, -12, 0, -24, 22, -7, 36, 0, 4, 12, -10, 0, 0, -6, 21, -36, 11, 0, -39, 21, 16, -9, 0, 16, -12, -1, 12, 0, -21, 27, 6, 18, 0, 0, 18, -4, -60, 5, -32, -36, -12, 2, 0, -28, 0, 27, 19, 0, -36, 1, 8, -42, 0, 15, 60, 0, -12, 0, 14, 2, -12, -3, 15, 3, 32, -6, 0, 0, -36, 9, -7, 16, 0, -16, -35, -12, -34, 0, 54, -9, -33, 15, 0, 14, 15, -28, -11, 30, 0, -15, 9, -6, 0, 45, 38, -21, 27, 0, -9, 0, -23, 7, 0, 8, -28, 18, 48, 0, 12, -6, 0, -3, 25, -12, -6, 0, 3, 0, -15, 11, 84, 11, 0, 0, 20, -24, 18, 0, 27, 18, 21, -15, 0, -4, -4, -3, -23, 0, -63, -20, 16, -72, 0, 0, 12, -13, 2, 0, 16, 11, 45, 28, 0, -6, 0, 20, -30, 0, -45, 42, -42, 2, -60, 28, -12, 0, 26, 0, -12, -20, -18, -42, 0, -36, -33, -9, 0, 0, 22, 14, 6, 15, 0, 36, -38, -12, -48, 0, 35, -63, 4, 8, 0, 20, 14, -24, 6, 0, 0, -17, -1, -6, 0, 9, -36, 3, 24, 0, -4, 0, 63, 24, -35, 42, 10, 8, 48, 0, 4, 3, 0, -12, 0, -26, 28, 27, -20, 0, 54, -5, 25, 0, 0, 5, -12, 21, -30, 45, 22, -8, -72, 3, 0, -6, -8, 25, -84, 0, 6, 18, -16, 16, 0, 0, -42, -3, 16, 0, -63, -16, 56, -9, 25, 6, 0, 4, -15, 0, 7, -3, 6, -3, 0, -3, -27, 0, 6, 0, 46, 18, -8, 28, 0, -15, 38, 27, 0, -15, 48, 6, -38, 48, 0, -6, -24, -8, 12, 0, -1, -28, -27, -3, 0, -30, -49, -21, 42, 0, 0, -60, -10, -10, 45, 4, 40, 45, -4, 0, -18, 0, 2, 30, 0, 8, -63, 2, 3, 0, 41, -10, 0, 30, 0, 63, -18, -24, 24, -20, 12, -27, -25, 0, 0, 18, 8, -6, 6, 0, -6, -42, 28, 36, 0, -11, 0, -9, 24, 0, 4, -6, 33, 2, 35, -33, -30, 36, -27, 0, 6, -24, 14, -22, 0, -35, 0, -36, 15, 0, -45, -4, -26, -36, 0, 10, -6, 0, -24, 0, 0, 2, -60, -21, 0, -36, -43, -11, 0, 0, -28, 39, -64, 21, 0, -16, 6, 51, -2, 0, 84, 16, 40, 12, -20, 3, 60, -12, -30, 0, 0, 21, 63, -9, 0, -6, -4, 18, 84, 0, -60, 0, 24, -18, 0, -4, 16, 60, 6, 25, -84, 32, 0, -36, 0, 12, -27, -6, -16, 0, 42, -28, 42, 0, 0, -9, 10, -19, 72, 0, -24, 36, 26, -3, 0, -8, 47, -42, -30, 0, 24, -21, -27, -60, 0, 0, -36, 12, -30, 0, 20, -14, -51, 2, 0, 12, 44, 1, 27, -15, 35, 3, -56, -32, 0, 18, 42, 0, -58, 0, 72, 36, -30, 45, 0, 7, 24, 16, 0, 0, 36, 48, 6, 35, 0, -12, -2, 34, -78, 0, 16, -54, -36, -9, 0, 33, -7, -45, -52, 0, 0, 14, 10, -15, 0, -12, 63, 11, -28, 30, 3, 0, -24, 45, 0, -9, 46, -6, -12, 0, -32, -15, 0, -38, 0, -21, 8, -27, 15, 0, 48, 9, -3, 0, -25, 23, -6, 35, 38, 0, -45, 8, -48, 28, 0, -54, -55, -48, 18, 0, 10, -12, 42, 2, 0, 0, -12, -3, 12, -25, -9, 36, -42, 6, 0, 0, 0, -3, -48, 0, -15, 15, 36, 11, 0, -84, 52, -33, -45, 0, 42, 0, 80, -20, -45, 8, -20, -18, 0, 0, 96, -27, 46, -54, 0, -21, -24, -15, -14, 0, 34, -20, -84, 4, 0, -3, -13, 23, -45, 0], 'weight': 2, 'weight_parity': 1}
  45. label: 53.2.a.b
    {'Nk2': 212, 'analytic_conductor': 0.42320713071278604, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[53, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [53, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 3, 'field_disc': 148, 'field_disc_factorization': [[2, 2], [37, 1]], 'field_poly': [1, -3, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, -3, 1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924981, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '53.2.a.b', 'level': 53, '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': [53], 'level_radical': 53, 'minimal_twist': '53.2.a.b', 'nf_label': '3.3.148.1', 'prim_orbit_index': 1, 'qexp_display': 'q-\\beta _{1}q^{2}+(1-\\beta _{2})q^{3}+(\\beta _{1}+\\beta _{2})q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 3, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '53.2.a', 'trace_display': [-1, 3, -2, 4], 'trace_hash': 1640490373351194081, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.024', 'prec': 7}, {'__RealLiteral__': 0, 'data': '2.851', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.158', 'prec': 10}, {'__RealLiteral__': 0, 'data': '20.784', 'prec': 17}, 0, {'__RealLiteral__': 0, 'data': '215.098', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.006', 'prec': 4}, 'traces': [3, -1, 3, 1, -2, -3, 4, -3, 2, -4, -4, -5, 3, -6, -8, -3, -5, 0, 11, 10, -2, 10, 3, 5, -3, -1, 15, 12, -5, 2, -2, 3, -14, 15, 8, -22, -5, 3, 3, -4, -10, -4, 18, 0, -24, -17, -10, 13, -5, -3, -9, 1, 3, 7, 4, -10, 9, -11, 2, 20, -10, 32, -20, -11, -2, 4, 6, -11, -7, -16, -5, 20, 6, 37, 13, -1, -4, -3, -7, -10, 35, -10, 27, 10, -6, -32, 21, -6, -2, 20, 4, 27, -4, -14, -12, -7, -1, -21, -24, -13, 32, 5, 11, -3, 12, -1, 14, -33, -20, 4, -23, -16, -11, -11, 24, -15, 2, -6, -16, -14, -9, -24, -6, -30, 0, 20, 7, 33, 48, -4, -14, 18, 10, 24, -48, 1, 18, -3, 14, 12, 10, -31, -4, 42, -10, 20, -13, -19, 1, 3, 5, -13, -2, 24, -28, -5, 26, -1, 3, 24, 30, -15, 18, 6, 32, 11, -9, -4, -36, 16, 8, 2, 22, 5, -16, -16, -26, 46, -13, 28, 18, -6, -24, -13, -14, 2, 24, -6, -18, -10, -19, -29, 18, -23, -8, 29, -10, -16, -44, 19, -24, -2, -20, 3, 16, -1, -44, -3, -6, -8, 10, 1, 27, -4, -16, 11, -32, -20, -8, -32, -5, 5, -6, 30, 42, 3, 10, -21, 15, -30, 4, 31, -4, 0, 4, 34, -43, 46, -6, -36, -17, -1, 28, 38, 34, 10, 11, 0, 21, 36, 30, -16, -10, 1, 12, 13, -12, -18, -24, 10, 62, 0, -26, -8, -2, -4, 14, 6, 7, 18, 30, -3, -2, -8, -16, 31, -48, -44, 24, -4, -21, 10, 61, -1, -30, 10, -4, -44, -16, 20, -31, -6, 6, 5, 32, -13, -34, -23, 3, -23, 20, -15, 22, -15, 48, -36, 48, -32, 25, 32, 4, 5, -8, -40, 4, 37, -35, -3, -32, -10, 36, -64, -5, -23, -3, 28, -12, 14, -16, -4, -4, -5, -22, 29, 0, -10, -32, 12, -33, -34, 36, -18, -4, 12, 38, -50, -10, -31, -10, 10, 15, -10, 48, -2, 4, -62, -6, 39, 37, -24, -10, -2, 7, 12, -12, 10, 22, -23, -8, 24, 4, -24, -8, -26, 4, 30, -5, 32, -7, 28, 43, 31, 38, 25, -28, 44, 76, 53, -24, 2, -37, -3, -20, -46, 44, 68, -42, -26, -12, 35, 60, -6, -2, 12, -58, -2, 60, 1, -75, 4, -48, -13, 36, 58, -32, 3, 48, 32, -6, -8, -22, -22, 36, -3, -3, 5, 28, -18, -14, -20, -32, 37, -37, 96, -52, 12, -5, -6, -14, 24, -50, 15, -45, 9, -60, -28, -7, -32, -9, -4, -4, 19, 83, -68, 8, 23, 22, -79, -1, 16, -99, 4, -7, 57, -20, 0, -36, -22, 12, 16, 28, -30, -80, 7, -15, -56, 2, -4, -3, 38, -5, 59, 24, -15, 54, -56, -36, -4, -44, -24, 45, 22, -17, 3, 92, -2, -6, -27, -23, -40, 35, 56, 6, 16, -20, 36, -36, -37, -18, 6, 0, -61, 67, -16, -24, -64, -24, 98, 94, -4, 69, 12, 26, 6, -10, 36, 66, -30, 2, -4, -88, 26, -10, 2, -32, -36, 21, 1, -8, 64, -18, 42, 2, -37, 32, -4, 50, 74, -76, -22, -31, -21, 30, 64, 32, 10, -24, -92, 18, 0, 22, 49, 41, -6, 30, -41, 12, 37, 24, 12, 18, 0, -19, -16, -23, -26, 74, -40, 40, 22, 22, 1, -4, -20, -24, 66, 12, 47, 24, -36, -10, -31, -1, 12, -40, 31, -54, -17, 98, 7, -20, -84, -60, -63, -6, -32, 44, -5, -10, -28, -10, 62, 32, -56, 28, 12, -28, -11, -8, -40, -73, -36, -64, 13, -25, -90, -52, 38, 79, 36, -15, -29, -14, 45, -44, -5, -5, -30, 60, -16, 42, -14, -28, 70, -112, 39, 18, 3, 20, -3, -28, 34, 22, 20, 20, 18, -16, -12, -70, -68, 17, 4, -9, -33, 16, -88, -19, -73, 40, -12, 0, 24, 26, -14, 37, -12, 24, 11, 52, 24, 96, -36, -74, -68, 56, -24, 89, 42, 3, -24, 79, -22, 44, 30, -4, 5, -10, 64, -48, -16, 26, 7, 17, 68, -16, 2, 44, 58, -22, 6, -116, 18, -92, 16, 4, -73, -56, 89, 30, -72, -2, 52, -33, 18, 57, 9, 18, -10, 11, 0, -82, 72, 26, -24, 60, 71, 48, 36, -11, -70, 9, -6, -30, 26, 30, -42, 20, 28, -4, 0, -20, 50, -12, -11, -68, -2, 11, 7, 32, -6, -94, -7, -8, -31, 64, -36, 2, 25, 74, 36, -80, -66, 62, 48, -2, -29, -14, 56, -50, 20, -58, 83, 41, -11, 12, 14, 50, 46, -12, -30, 8, -28, -10, 18, -8, 36, -42, -10, -18, -23, 92, -32, 28, 24, 40, 32, -31, -42, -10, -12, 30, -8, -30, -34, 16, -7, 40, 3, -20, -16, -52, -18, -86, 3, -30, -48, -85, -8, -14, -22, -92, -11, -37, -14, -64, 14, 76, 52, -10, 4, 12, 34, -115, 46, 24, 32, -24, -3, 45, -35, -75, -23, 48, -76, -76, 8, -18, 4, 22, 116, 16, -26, 2, -73, -44, -17, -32, -100, 42, 10, 6, 28, -114, -35, -40, -4, 26, 110, 30, 52, 50, 76, 46, -11, 84, 3, 101, 9, -30, 64, -88, -18, -54, -1, -60, 50, -7, 23, -34, -30, -5, -24, -16, -11, 0, -5, 38, -18, 0, -16, 0, 55, -10, 22, 96, 5, -8, -13, -25, -10, 60, 41, -5, -32, -31, 21, 52, -19, 30, 28, -41, 44, 44, -32, 4, 20, 55, 36, 42, 4, 110, -26, 22, -58, 16, 56, -96, 87, 6, -31, 29, 26, -2, 0, -12, 54, -42, -9, 92, 48, 63, 37, 76, -43, -84, -30, 64, 25, -31, -52, -6, -32, 24, 44, 13, -18, 36, -18, 32, -2, -16, -21, -110, -26, 56, -39, 4, -1, 36, -44, -18, -92, -64, -56, 80, -53, -43, 17, 9, 4], 'weight': 2, 'weight_parity': 1}
  46. label: 54.2.a.a
    {'Nk2': 216, 'analytic_conductor': 0.4311921709149141, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [3, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [54, 1, [29], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[5, [-3, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554486, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '54.2.a.a', 'level': 54, '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], 'level_radical': 6, 'minimal_twist': '54.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\\cdots', 'related_objects': ['EllipticCurve/Q/54/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '54.2.a', 'trace_display': [-1, 0, 3, -1], 'trace_hash': 1215354540506513513, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.995', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.013', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.985', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.931', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.011', 'prec': 7}, 'traces': [1, -1, 0, 1, 3, 0, -1, -1, 0, -3, -3, 0, -4, 1, 0, 1, 0, 0, 2, 3, 0, 3, -6, 0, 4, 4, 0, -1, 6, 0, 5, -1, 0, 0, -3, 0, 2, -2, 0, -3, -6, 0, -10, -3, 0, 6, 6, 0, -6, -4, 0, -4, 9, 0, -9, 1, 0, -6, 12, 0, 8, -5, 0, 1, -12, 0, 14, 0, 0, 3, 0, 0, -7, -2, 0, 2, 3, 0, 8, 3, 0, 6, -3, 0, 0, 10, 0, 3, -18, 0, 4, -6, 0, -6, 6, 0, -1, 6, 0, 4, -3, 0, -4, 4, 0, -9, 9, 0, 2, 9, 0, -1, -6, 0, -18, 6, 0, -12, 0, 0, -2, -8, 0, 5, -3, 0, -7, -1, 0, 12, -15, 0, -2, -14, 0, 0, 6, 0, -4, -3, 0, 0, 12, 0, 18, 7, 0, 2, 3, 0, 17, -2, 0, -3, 15, 0, -4, -8, 0, -3, 6, 0, 20, -6, 0, 3, -6, 0, 3, 0, 0, -10, 15, 0, -4, -3, 0, 18, -9, 0, -16, -4, 0, 6, 6, 0, 0, 6, 0, -6, -12, 0, 5, 1, 0, -6, 9, 0, -7, -4, 0, 3, -6, 0, -18, 4, 0, -4, -6, 0, -22, 9, 0, -9, -30, 0, -5, -2, 0, -9, 0, 0, 8, 1, 0, 6, -12, 0, 14, 18, 0, -6, 18, 0, 18, 12, 0, 0, 30, 0, -10, 2, 0, 8, -18, 0, -8, -5, 0, 3, 0, 0, 18, 7, 0, 1, 12, 0, -2, -12, 0, 15, -30, 0, 27, 2, 0, 14, -18, 0, -25, 0, 0, -6, -12, 0, 8, 4, 0, 3, 24, 0, 14, 0, 0, -12, 6, 0, -17, -18, 0, -7, -6, 0, 36, -2, 0, -3, 24, 0, 10, -17, 0, 2, 24, 0, -16, 3, 0, -15, -6, 0, -19, 4, 0, 8, -3, 0, -18, 3, 0, -6, 0, 0, -16, -20, 0, 6, -6, 0, -10, -3, 0, 6, 42, 0, -22, -3, 0, 0, -15, 0, 13, 10, 0, -15, 3, 0, -10, 4, 0, 3, 6, 0, 0, -18, 0, 9, 18, 0, -15, 16, 0, 4, -21, 0, 17, -6, 0, -6, -9, 0, 32, 0, 0, -6, -24, 0, 20, 6, 0, 12, -24, 0, 9, -5, 0, -1, -21, 0, 0, 6, 0, -9, 24, 0, 20, 7, 0, 4, 12, 0, -20, -3, 0, 6, -6, 0, 23, 18, 0, -4, -12, 0, -9, 4, 0, 6, 12, 0, 8, 22, 0, -9, 0, 0, -8, 9, 0, 30, 18, 0, 29, 5, 0, 2, -12, 0, -19, 9, 0, 0, -12, 0, -54, -8, 0, -1, -18, 0, 18, -6, 0, 12, 12, 0, -1, -14, 0, -18, -21, 0, -13, 6, 0, -18, -27, 0, -14, -18, 0, -12, 30, 0, 8, 0, 0, -30, 6, 0, -8, 10, 0, -2, -3, 0, -16, -8, 0, 18, 39, 0, 0, 8, 0, 5, 0, 0, 14, -3, 0, 0, -18, 0, -9, -18, 0, -7, -15, 0, 7, -1, 0, -12, -12, 0, -18, 2, 0, 12, 36, 0, -16, -15, 0, 30, 0, 0, 13, -27, 0, -2, 24, 0, 27, -14, 0, 18, 18, 0, 20, 25, 0, 0, 6, 0, 8, 6, 0, 12, 12, 0, -8, -8, 0, -4, 27, 0, 40, -3, 0, -24, 3, 0, -18, -14, 0, 0, -12, 0, -4, 12, 0, -6, -24, 0, 38, 17, 0, 18, 3, 0, -27, 7, 0, 6, -3, 0, 10, -36, 0, 2, 18, 0, 0, 3, 0, -24, -42, 0, 35, -10, 0, 17, -6, 0, 32, -2, 0, -24, -24, 0, -34, 16, 0, -3, -42, 0, -28, 15, 0, 6, 18, 0, -29, 19, 0, -4, 0, 0, -25, -8, 0, 3, -21, 0, 24, 18, 0, -3, 42, 0, -4, 6, 0, 0, 0, 0, -36, 16, 0, 20, 39, 0, -45, -6, 0, 6, -21, 0, 14, 10, 0, 3, -6, 0, -36, -6, 0, -42, -24, 0, -19, 22, 0, 3, 42, 0, 1, 0, 0, 15, -36, 0, 18, -13, 0, -10, -36, 0, 44, 15, 0, -3, -12, 0, 0, 10, 0, -4, 9, 0, 4, -3, 0, -6, 3, 0, 44, 0, 0, 18, -30, 0, 36, -9, 0, -18, 36, 0, 4, 15, 0, -16, 24, 0, -1, -4, 0, 21, 0, 0, -22, -17, 0, 6, -42, 0, -16, 6, 0, 9, 12, 0, 9, -32, 0, 0, -9, 0, 41, 6, 0, 24, 51, 0, 2, -20, 0, -6, 48, 0, -2, -12, 0, 24, -48, 0, -31, -9, 0, 5, -18, 0, 20, 1, 0, 21, -12, 0, 0, 0, 0, -6, -12, 0, 32, 9, 0, -24, 6, 0, -32, -20, 0, -7, 39, 0, 0, -4, 0, -12, 21, 0, 18, 20, 0, 3, 18, 0, 2, -6, 0, 6, 60, 0, -20, -23, 0, -18, 6, 0, -31, 4, 0, 12, 0, 0, 2, 9, 0, -4, 0, 0, -18, -6, 0, -12, 24, 0, 7, -8, 0, -22, 9, 0, 2, 9, 0, 0, -12, 0, -10, 8, 0, -9, -48, 0, -40, -30, 0, -18, -36, 0, 45, -29, 0, -5, -24, 0, -56, -2, 0, 12, 3, 0, -22, 19, 0, -9, -36, 0, 2, 0, 0, 12, 12, 0, 7, 54, 0, 8, 12, 0, -27, 1, 0, 18, 30, 0, 0, -18, 0, 6, -48, 0, 26, -12, 0, -12, 6, 0, 9, 1, 0, 14, 15, 0, 29, 18, 0, 21, 0, 0, 8, 13, 0, -6, -12, 0, -12, 18, 0, 27, 0, 0, 11, 14, 0, 18, -33, 0, 36, 12, 0, -30, 51, 0, 28, -8, 0, 0, -36, 0, -36, 30, 0, -6, -6, 0, -6, 8, 0, -10, 15, 0, 23, 2, 0, 3, -27, 0, 4, 16, 0, 8, -42, 0, 54, -18, 0, -39, 6, 0, 27, 0, 0, -8, 60, 0, 47, -5, 0, 0, -21, 0, -28, -14, 0, 3], 'weight': 2, 'weight_parity': 1}
  47. label: 54.2.a.b
    {'Nk2': 216, 'analytic_conductor': 0.4311921709149141, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [3, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [54, 1, [29], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[5, [3, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924982, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '54.2.a.b', 'level': 54, '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], 'level_radical': 6, 'minimal_twist': '54.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\\cdots', 'related_objects': ['EllipticCurve/Q/54/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '54.2.a', 'trace_display': [1, 0, -3, -1], 'trace_hash': 689246320802081722, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.995', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.045', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.985', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.138', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.931', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.011', 'prec': 7}, 'traces': [1, 1, 0, 1, -3, 0, -1, 1, 0, -3, 3, 0, -4, -1, 0, 1, 0, 0, 2, -3, 0, 3, 6, 0, 4, -4, 0, -1, -6, 0, 5, 1, 0, 0, 3, 0, 2, 2, 0, -3, 6, 0, -10, 3, 0, 6, -6, 0, -6, 4, 0, -4, -9, 0, -9, -1, 0, -6, -12, 0, 8, 5, 0, 1, 12, 0, 14, 0, 0, 3, 0, 0, -7, 2, 0, 2, -3, 0, 8, -3, 0, 6, 3, 0, 0, -10, 0, 3, 18, 0, 4, 6, 0, -6, -6, 0, -1, -6, 0, 4, 3, 0, -4, -4, 0, -9, -9, 0, 2, -9, 0, -1, 6, 0, -18, -6, 0, -12, 0, 0, -2, 8, 0, 5, 3, 0, -7, 1, 0, 12, 15, 0, -2, 14, 0, 0, -6, 0, -4, 3, 0, 0, -12, 0, 18, -7, 0, 2, -3, 0, 17, 2, 0, -3, -15, 0, -4, 8, 0, -3, -6, 0, 20, 6, 0, 3, 6, 0, 3, 0, 0, -10, -15, 0, -4, 3, 0, 18, 9, 0, -16, 4, 0, 6, -6, 0, 0, -6, 0, -6, 12, 0, 5, -1, 0, -6, -9, 0, -7, 4, 0, 3, 6, 0, -18, -4, 0, -4, 6, 0, -22, -9, 0, -9, 30, 0, -5, 2, 0, -9, 0, 0, 8, -1, 0, 6, 12, 0, 14, -18, 0, -6, -18, 0, 18, -12, 0, 0, -30, 0, -10, -2, 0, 8, 18, 0, -8, 5, 0, 3, 0, 0, 18, -7, 0, 1, -12, 0, -2, 12, 0, 15, 30, 0, 27, -2, 0, 14, 18, 0, -25, 0, 0, -6, 12, 0, 8, -4, 0, 3, -24, 0, 14, 0, 0, -12, -6, 0, -17, 18, 0, -7, 6, 0, 36, 2, 0, -3, -24, 0, 10, 17, 0, 2, -24, 0, -16, -3, 0, -15, 6, 0, -19, -4, 0, 8, 3, 0, -18, -3, 0, -6, 0, 0, -16, 20, 0, 6, 6, 0, -10, 3, 0, 6, -42, 0, -22, 3, 0, 0, 15, 0, 13, -10, 0, -15, -3, 0, -10, -4, 0, 3, -6, 0, 0, 18, 0, 9, -18, 0, -15, -16, 0, 4, 21, 0, 17, 6, 0, -6, 9, 0, 32, 0, 0, -6, 24, 0, 20, -6, 0, 12, 24, 0, 9, 5, 0, -1, 21, 0, 0, -6, 0, -9, -24, 0, 20, -7, 0, 4, -12, 0, -20, 3, 0, 6, 6, 0, 23, -18, 0, -4, 12, 0, -9, -4, 0, 6, -12, 0, 8, -22, 0, -9, 0, 0, -8, -9, 0, 30, -18, 0, 29, -5, 0, 2, 12, 0, -19, -9, 0, 0, 12, 0, -54, 8, 0, -1, 18, 0, 18, 6, 0, 12, -12, 0, -1, 14, 0, -18, 21, 0, -13, -6, 0, -18, 27, 0, -14, 18, 0, -12, -30, 0, 8, 0, 0, -30, -6, 0, -8, -10, 0, -2, 3, 0, -16, 8, 0, 18, -39, 0, 0, -8, 0, 5, 0, 0, 14, 3, 0, 0, 18, 0, -9, 18, 0, -7, 15, 0, 7, 1, 0, -12, 12, 0, -18, -2, 0, 12, -36, 0, -16, 15, 0, 30, 0, 0, 13, 27, 0, -2, -24, 0, 27, 14, 0, 18, -18, 0, 20, -25, 0, 0, -6, 0, 8, -6, 0, 12, -12, 0, -8, 8, 0, -4, -27, 0, 40, 3, 0, -24, -3, 0, -18, 14, 0, 0, 12, 0, -4, -12, 0, -6, 24, 0, 38, -17, 0, 18, -3, 0, -27, -7, 0, 6, 3, 0, 10, 36, 0, 2, -18, 0, 0, -3, 0, -24, 42, 0, 35, 10, 0, 17, 6, 0, 32, 2, 0, -24, 24, 0, -34, -16, 0, -3, 42, 0, -28, -15, 0, 6, -18, 0, -29, -19, 0, -4, 0, 0, -25, 8, 0, 3, 21, 0, 24, -18, 0, -3, -42, 0, -4, -6, 0, 0, 0, 0, -36, -16, 0, 20, -39, 0, -45, 6, 0, 6, 21, 0, 14, -10, 0, 3, 6, 0, -36, 6, 0, -42, 24, 0, -19, -22, 0, 3, -42, 0, 1, 0, 0, 15, 36, 0, 18, 13, 0, -10, 36, 0, 44, -15, 0, -3, 12, 0, 0, -10, 0, -4, -9, 0, 4, 3, 0, -6, -3, 0, 44, 0, 0, 18, 30, 0, 36, 9, 0, -18, -36, 0, 4, -15, 0, -16, -24, 0, -1, 4, 0, 21, 0, 0, -22, 17, 0, 6, 42, 0, -16, -6, 0, 9, -12, 0, 9, 32, 0, 0, 9, 0, 41, -6, 0, 24, -51, 0, 2, 20, 0, -6, -48, 0, -2, 12, 0, 24, 48, 0, -31, 9, 0, 5, 18, 0, 20, -1, 0, 21, 12, 0, 0, 0, 0, -6, 12, 0, 32, -9, 0, -24, -6, 0, -32, 20, 0, -7, -39, 0, 0, 4, 0, -12, -21, 0, 18, -20, 0, 3, -18, 0, 2, 6, 0, 6, -60, 0, -20, 23, 0, -18, -6, 0, -31, -4, 0, 12, 0, 0, 2, -9, 0, -4, 0, 0, -18, 6, 0, -12, -24, 0, 7, 8, 0, -22, -9, 0, 2, -9, 0, 0, 12, 0, -10, -8, 0, -9, 48, 0, -40, 30, 0, -18, 36, 0, 45, 29, 0, -5, 24, 0, -56, 2, 0, 12, -3, 0, -22, -19, 0, -9, 36, 0, 2, 0, 0, 12, -12, 0, 7, -54, 0, 8, -12, 0, -27, -1, 0, 18, -30, 0, 0, 18, 0, 6, 48, 0, 26, 12, 0, -12, -6, 0, 9, -1, 0, 14, -15, 0, 29, -18, 0, 21, 0, 0, 8, -13, 0, -6, 12, 0, -12, -18, 0, 27, 0, 0, 11, -14, 0, 18, 33, 0, 36, -12, 0, -30, -51, 0, 28, 8, 0, 0, 36, 0, -36, -30, 0, -6, 6, 0, -6, -8, 0, -10, -15, 0, 23, -2, 0, 3, 27, 0, 4, -16, 0, 8, 42, 0, 54, 18, 0, -39, -6, 0, 27, 0, 0, -8, -60, 0, 47, 5, 0, 0, 21, 0, -28, 14, 0, 3], 'weight': 2, 'weight_parity': 1}
  48. label: 55.2.a.a
    {'Nk2': 220, 'analytic_conductor': 0.4391772111170421, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[5, -1], [11, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [55, 1, [12, 46], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554487, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '55.2.a.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': '55.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\\cdots', 'related_objects': ['EllipticCurve/Q/55/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '55.2.a', 'trace_display': [1, 0, 1, 0], 'trace_hash': 467045135390574132, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.973', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.883', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.610', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.017', 'prec': 7}, 'traces': [1, 1, 0, -1, 1, 0, 0, -3, -3, 1, -1, 0, 2, 0, 0, -1, 6, -3, -4, -1, 0, -1, 4, 0, 1, 2, 0, 0, 6, 0, -8, 5, 0, 6, 0, 3, -2, -4, 0, -3, 2, 0, 4, 1, -3, 4, -12, 0, -7, 1, 0, -2, -2, 0, -1, 0, 0, 6, 4, 0, -10, -8, 0, 7, 2, 0, -16, -6, 0, 0, 8, 9, 14, -2, 0, 4, 0, 0, 8, -1, 9, 2, -4, 0, 6, 4, 0, 3, 10, -3, 0, -4, 0, -12, -4, 0, 10, -7, 3, -1, -10, 0, -4, -6, 0, -2, 12, 0, -18, -1, 0, 0, -6, 0, 4, -6, -6, 4, 0, 0, 1, -10, 0, 8, 1, 0, 16, -3, 0, 2, -12, 0, 0, -16, 0, -18, 18, 0, 12, 0, 0, 8, -2, 3, 6, 14, 0, 2, -10, 0, 8, 12, -18, 0, -8, 0, -2, 8, 0, 5, 0, 9, 16, -2, 0, -4, -8, 0, -9, 6, 12, -4, -6, 0, 0, 1, 0, 10, 4, 3, -10, 0, 0, -12, -2, 0, -6, 12, 0, -4, 8, 0, -26, 10, 0, 7, 2, 3, 0, -3, 0, -10, 0, 0, 2, -4, -12, -2, 4, 0, 4, 2, 0, 12, 4, 0, 0, -18, 0, 1, 12, 0, -4, 0, -3, -6, -20, 0, -10, 4, 0, -18, 6, -6, -12, -4, 0, 0, 8, 0, 10, 1, 0, 10, -7, 0, -8, 24, 0, 1, 12, 0, -4, 16, 0, -17, 18, 0, 0, -2, -18, -12, 24, 0, -2, 0, 0, 16, -18, 0, 0, -6, 0, 18, -1, 0, 10, 12, 24, 0, 18, 0, 4, -8, 0, -2, 0, -15, 19, 6, 0, -14, 10, 0, 4, 6, 0, -10, 8, 0, 0, 8, 0, 4, -10, -18, 20, 0, 0, -8, -24, 0, -22, -2, 0, -8, -18, 0, -6, 7, 0, 0, -24, -9, 2, 16, 0, -6, 0, 0, 4, 4, 6, -8, -16, 0, 6, -9, 0, -6, 8, 12, 0, -12, 0, -6, -4, 0, -10, 0, 0, -5, 18, 0, 8, -10, 0, 4, -32, 9, -3, -10, 0, 0, 14, 0, 4, -4, -6, -2, 0, 0, 18, -6, 0, 36, 12, 0, 20, 4, 0, 8, -12, 0, 0, -26, -12, -10, 6, 0, 24, 21, 0, 2, 8, -3, 30, 0, 0, -1, 2, 0, -16, 10, 9, 0, 2, 0, -6, 2, 0, 4, 0, -12, -4, 10, 0, 4, -28, 0, 6, 4, 36, 6, 6, 0, 0, -12, 0, 4, -24, 0, -22, 0, 0, 18, -16, 0, -8, 3, 21, 12, 8, 0, 10, -4, 0, 0, 2, -3, -2, 6, 0, -20, 0, 0, -26, -10, 0, -4, -34, 0, -36, -6, 0, 6, 0, 6, 0, -12, 0, -12, -4, 0, -4, 0, 6, 8, 24, 0, -4, 10, 0, -1, 10, 0, 28, 30, 0, -7, -28, 0, 36, -8, 3, 8, 0, 0, -36, -1, 0, 12, -16, 0, -10, -4, 0, -16, 14, 0, 0, -11, 0, 18, -4, 0, 12, 0, 0, -6, -6, -18, -20, 12, 0, 24, -48, 0, -7, -2, -12, 0, 4, 0, 12, 48, 0, -18, 7, 0, -34, 0, 0, 30, -18, 0, 12, -18, 30, -1, -24, 0, 0, 10, 0, -12, 10, 24, 8, 0, 0, 18, 36, 0, -6, 4, 0, -24, 26, 0, 36, 2, 0, 0, 4, -21, -22, 19, 0, -6, 0, 0, 2, -42, -6, 10, -24, 0, 32, 4, 0, 2, 22, 0, 0, 10, 0, 8, 24, 0, 2, 0, 48, -8, 1, 0, -32, -20, 0, -10, -24, 18, 34, 20, 0, 0, 2, 0, -20, 8, 0, -24, 0, 0, 1, -22, 0, 2, -12, 0, 40, -24, 0, -18, 16, 0, -14, -6, -24, -3, 34, 0, -16, 0, 0, -24, 20, -27, -4, 2, 0, -16, -10, 0, -12, -2, -42, 0, 36, 0, -10, 4, 0, 12, 0, 6, 24, 8, 0, -16, 10, 0, -26, 6, 0, 9, -38, 0, 0, -18, 0, 8, -16, -12, 18, 0, 0, -4, -4, 0, -28, 6, 0, -4, 12, 0, 12, -10, 0, 0, 22, 0, 8, -7, 0, 18, 0, 0, -10, 8, -24, -30, -32, 0, -2, -4, 0, -32, 0, 3, 0, -3, 0, 10, 6, 0, 52, 0, -27, 14, 24, 0, 42, 4, 0, 20, 16, -6, 4, 2, 0, 0, 40, 0, -10, 18, 12, 6, 0, 0, 16, 12, 0, 12, 8, 0, 6, 20, 0, 12, 10, 0, 0, -8, -18, -12, 8, 0, -22, 0, 0, 26, 14, -12, -8, -30, 0, 6, -8, 0, -8, 24, 0, 7, -2, 0, 52, -2, 0, 8, 0, -9, -20, 30, 0, 0, -2, 0, -72, 5, -30, 2, -14, 0, 0, -16, 0, 30, 18, 9, -12, 0, 0, 2, 16, 0, -16, -6, 0, -2, -18, 0, -36, 12, 0, 0, 12, 12, -2, -4, 0, 14, -42, 0, -8, -4, 0, -28, -32, 0, 7, 6, 0, -4, -9, 36, 0, 2, 0, 6, -8, 0, 2, 0, 12, -36, -18, 0, 28, -4, 0, -24, 4, 0, -6, -22, 0, 0, -8, 0, -32, 54, -30, -16, 0, 0, -22, -8, 0, 1, 18, 21, -16, -12, 0, 8, 56, 0, 0, 10, -9, 4, 48, 0, 4, 0, 0, 2, -48, 3, -12, -2, 0, 18, -10, 0, -40, 20, 30, 0, 8, 0, 4, -26, 0, 10, 0, 0, 24, -12, 0, -34, 16, 0, -2, -36, 12, 30, -14, 0, 28, -6, 0, 0, -6, 18, 6, 0, 0, 12, -2, 0, 8, -4, 0, -4, 0, 0, 28, -4, 0, 0, -42, 6, 8, -8, 0, 24, 0, 0, 33, -4, -36, -10, -26, 0, 8, -3, 0, 10, 36, 0, 0, 28, 0, 10, 10, 0, -10, 7, 54, -28, -4, 0, 2, 36, 0, 8, 16, 3, 8, -40, 0, 0, 0, 0, -46, -36, 0, -3], 'weight': 2, 'weight_parity': 1}
  49. label: 55.2.a.b
    {'Nk2': 220, 'analytic_conductor': 0.4391772111170421, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[5, 1], [11, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [55, 1, [12, 46], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, -2, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924983, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '55.2.a.b', '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': '55.2.a.b', 'nf_label': '2.2.8.1', 'prim_orbit_index': 1, 'qexp_display': 'q+(1+\\beta )q^{2}-2\\beta q^{3}+(1+2\\beta )q^{4}-q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '55.2.a', 'trace_display': [2, 0, -2, -4], 'trace_hash': 518603272395225706, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '1.935', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.139', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.046', 'prec': 14}, {'__RealLiteral__': 0, 'data': '1.990', 'prec': 14}, {'__RealLiteral__': 0, 'data': '59.136', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.026', 'prec': 7}, 'traces': [2, 2, 0, 2, -2, -8, -4, 6, 10, -2, 2, -16, -8, -4, 0, 6, 8, 10, 0, -2, 0, 2, 0, -8, 2, 0, 0, -4, 4, 8, 0, -6, 0, 16, 4, 10, -4, 0, -16, -6, 12, 16, -12, 2, -10, -8, 0, 0, -6, 2, -16, 8, 12, -16, -2, -12, 0, -12, -8, 16, 4, 0, -20, -14, 8, -8, 8, 24, 16, 4, 0, 30, -8, -20, 0, 0, -4, 16, 8, -6, 2, 12, -12, 32, -8, -12, 32, 6, -4, -10, 16, -16, 0, 8, 0, -8, -4, -6, 10, 2, -4, -48, 8, -16, 0, 28, 4, -32, -4, -2, 32, -12, 28, 0, 0, -28, -40, 8, -16, 8, 2, -28, 0, 0, -2, -20, 20, -10, 0, 0, 0, -16, 0, 32, 0, 32, 12, 16, -8, 4, -16, 32, -8, 30, -4, 0, 0, -36, 12, -8, -24, 0, 40, -4, 0, 48, -28, 8, -32, 6, 0, 2, 16, 12, 0, -12, -12, 16, 22, -16, 0, -12, -16, 16, -4, 6, -32, -36, 8, -10, 20, 0, 64, -8, 4, 0, 8, 16, 0, 0, -16, 16, -8, 12, 16, -6, -16, 10, 32, 6, -48, 28, -8, -80, -12, 16, 0, -24, 0, -16, -32, 44, -64, 20, 12, -16, 0, -20, -16, -2, -16, 48, -16, 12, 10, 44, 28, 0, -20, 8, 0, -4, 16, 0, 0, 24, 0, -32, -24, 0, 12, 2, 0, -60, 6, -48, 0, 0, 0, -2, 24, -20, 0, 4, 16, -26, 4, 48, 8, -8, 20, -32, 12, -8, -12, 0, 64, 56, 12, 16, -8, 24, 32, -36, 2, 16, 8, -8, 0, 12, 12, -16, 20, 64, 0, 0, -24, -30, 14, 12, -32, 8, -24, 24, 8, -28, 0, -4, -16, -16, 24, -24, -64, 0, -4, 80, -44, -4, -16, 0, 32, -16, 20, -28, 20, 8, 20, -80, 4, 14, -32, 16, 0, 2, -8, 40, 32, 36, 0, 8, 8, -12, -20, -60, -8, 0, -24, -42, -32, -24, 0, 0, 40, -36, -16, -56, -12, 0, 20, -4, -32, -6, 20, 0, 0, -68, 32, 24, 24, -30, -38, 52, 0, -16, 8, 48, 0, 0, 60, 20, -24, 0, 32, 16, 0, 8, -48, 32, 56, 0, 32, 16, -40, 88, 4, 0, -60, 28, -4, -16, -16, -18, 64, -24, -8, 10, 4, 16, 0, 6, 12, -80, 0, 60, -2, 24, -4, -80, 36, -12, 96, 24, 16, -40, 12, 32, 0, 0, -40, -32, -12, -32, 0, 52, 8, -64, -8, 36, -16, 12, 0, 0, -4, 0, -32, -36, 0, 16, -32, -6, -30, -16, -48, 64, 4, -24, 32, 28, 12, 10, 12, 60, 0, 60, -16, 0, -16, 12, -32, 16, -20, 16, 16, 12, 0, -24, -24, 40, -16, -8, 0, -8, -12, -32, 0, -48, 60, -56, -72, 8, -16, 12, -32, 2, 4, 40, -32, -20, -48, 6, -24, -96, -16, 0, -10, 0, 0, 48, 8, -2, 96, 24, -12, -60, 4, -8, 128, -12, -4, 48, 16, -54, 0, -28, -8, 96, 0, 40, 80, 16, 28, -60, -4, -64, 0, -36, 0, 0, -30, -28, -40, 0, -48, 80, -4, 48, -32, 44, -6, 32, 12, 24, -64, -16, 4, -32, -68, -84, 20, 2, 0, 48, -16, 16, -32, -8, 48, 0, 48, 12, -16, 44, 12, -16, -28, 84, -4, 32, 52, 0, 24, 8, -64, -24, 0, -70, -20, 78, -16, 28, 24, -16, 12, -16, 40, -16, 24, 48, 0, -8, 16, -12, 24, -16, 16, -20, 32, 16, 0, -8, -20, 24, 40, -24, -2, -48, 20, 0, -64, 28, 16, 120, 0, -28, 0, -12, 12, -48, -40, 0, 32, 0, 8, -48, 2, -12, 0, -28, -48, 20, 0, 24, 0, -12, -20, -128, 24, -12, 0, 10, 60, -48, 48, 32, 0, 0, -8, 6, -8, 0, 0, 64, 12, 48, 0, 36, -40, -16, 24, 16, 44, -24, 0, -36, 0, -100, 32, -108, 16, -32, 4, 16, -8, -48, 0, -106, 40, -144, 8, -32, -64, 0, 24, 0, -12, 40, -64, -36, -16, -16, -56, -96, -20, 36, 8, 80, 48, 68, 80, -4, 20, 32, 0, -14, 16, 52, 8, 32, 4, -32, 40, -44, 0, 96, 8, 40, 64, -8, 48, -30, -16, -38, 0, 84, 4, -8, -56, 32, -86, 0, -48, 32, 16, -24, 0, -8, 8, 60, -8, 36, 0, -56, -20, 0, -12, 88, -60, 24, -8, 8, -32, 0, 0, 32, 24, 64, 4, 72, 16, 0, -60, -48, 8, 48, -40, 0, 64, 96, -4, 4, 64, 8, -4, -60, 0, 4, -64, 60, 0, -48, 0, -48, 64, -18, 28, 64, 4, -32, 96, -8, -56, 30, -80, -28, 32, 0, 20, 0, 16, -6, -20, -20, -8, -112, 0, 0, -64, 20, 12, -2, 40, 56, -64, -20, -16, -48, 0, -12, 80, -12, -60, 48, 56, 32, 0, -16, -12, -80, 36, 12, -16, 40, -24, 32, 12, 0, 0, -56, 64, -16, 14, -12, -64, -32, -22, 40, -4, 36, -128, 16, 32, -64, -48, 56, 0, 28, -24, 16, -8, 12, 0, -32, -24, -16, 16, -20, -128, 0, 8, -16, 16, -28, -20, 0, 4, 48, -48, -32, -16, -6, -60, -30, 80, -16, 32, -56, 20, 112, -40, 36, 2, -32, 0, -16, -8, 20, -64, 76, 0, 10, 80, 12, 0, 100, -20, 96, -72, 92, -20, 0, 48, 0, -12, 8, -64, 44, 0, -96, -64, 8, -32, 44, 64, 32, -4, -24, 40, -28, -12, 0, 0, -64, 64, -32, -8, -80, 48, -64, 64, -16, -36, 112, 0, -24, 0, -12, 88, -64, 48, 0, 64, -64, 112, 140, 16, -88, 32, -72, -24, -16, -62, 32, 20, 12, 8, -32, 4, 6, 0, -12, -40, 80, 16, -56, -16, 12, 76, -112, -4, 6, -20, 8, -72, -48, 16, -64, 32, 0, 0, -10, -48, 0, 64, -64, -32, 96, -32, 24, 64, -6], 'weight': 2, 'weight_parity': 1}
  50. label: 56.2.a.a
    {'Nk2': 224, 'analytic_conductor': 0.44716225131917015, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [7, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [56, 1, [15, 29, 17], [1, 1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [0, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554488, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '56.2.a.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': '56.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+2q^{5}-q^{7}-3q^{9}-4q^{11}+2q^{13}+\\cdots', 'related_objects': ['EllipticCurve/Q/56/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '56.2.a', 'trace_display': [0, 0, 2, -1], 'trace_hash': 1158293942075606764, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.004', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.997', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.989', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.004', 'prec': 4}, {'__RealLiteral__': 0, 'data': '4.938', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.020', 'prec': 7}, 'traces': [1, 0, 0, 0, 2, 0, -1, 0, -3, 0, -4, 0, 2, 0, 0, 0, -6, 0, 8, 0, 0, 0, 0, 0, -1, 0, 0, 0, 6, 0, 8, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, -4, 0, -6, 0, -8, 0, 1, 0, 0, 0, 6, 0, -8, 0, 0, 0, 0, 0, -6, 0, 3, 0, 4, 0, -4, 0, 0, 0, -8, 0, 10, 0, 0, 0, 4, 0, 16, 0, 9, 0, 8, 0, -12, 0, 0, 0, -6, 0, -2, 0, 0, 0, 16, 0, -6, 0, 12, 0, 2, 0, -16, 0, 0, 0, -12, 0, -10, 0, 0, 0, 2, 0, 0, 0, -6, 0, 6, 0, 5, 0, 0, 0, -12, 0, -8, 0, 0, 0, 8, 0, -8, 0, 0, 0, -6, 0, -8, 0, 0, 0, -8, 0, 12, 0, 0, 0, 6, 0, 0, 0, 18, 0, 16, 0, 18, 0, 0, 0, 0, 0, -12, 0, 0, 0, 16, 0, -9, 0, -24, 0, 18, 0, 1, 0, 0, 0, -4, 0, 10, 0, 0, 0, -4, 0, 24, 0, 0, 0, -16, 0, -14, 0, 0, 0, 6, 0, 0, 0, 0, 0, -6, 0, 4, 0, 0, 0, -32, 0, 12, 0, 0, 0, -8, 0, -8, 0, 0, 0, -12, 0, 0, 0, 3, 0, -8, 0, 10, 0, 0, 0, -22, 0, -16, 0, 0, 0, 8, 0, 10, 0, 0, 0, 2, 0, 16, 0, 0, 0, 24, 0, 0, 0, 0, 0, 2, 0, 2, 0, -18, 0, 24, 0, 12, 0, 0, 0, -14, 0, 0, 0, 0, 0, 4, 0, 22, 0, -24, 0, -6, 0, 16, 0, 0, 0, -2, 0, 19, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -12, 0, -8, 0, 0, 0, 8, 0, -14, 0, 6, 0, 30, 0, -24, 0, 0, 0, -48, 0, -2, 0, 0, 0, 8, 0, -4, 0, 6, 0, -8, 0, 2, 0, 0, 0, -32, 0, -1, 0, 0, 0, 12, 0, -30, 0, 0, 0, -14, 0, -16, 0, 0, 0, 0, 0, 45, 0, 0, 0, 20, 0, 16, 0, -6, 0, -6, 0, -26, 0, 0, 0, 12, 0, -4, 0, 0, 0, -24, 0, 8, 0, 12, 0, -2, 0, 0, 0, 0, 0, 32, 0, -14, 0, 0, 0, 18, 0, 16, 0, 18, 0, 8, 0, -14, 0, 0, 0, 0, 0, 16, 0, 0, 0, -16, 0, -26, 0, 24, 0, 6, 0, 6, 0, 0, 0, -8, 0, 10, 0, 0, 0, 0, 0, 24, 0, -3, 0, 36, 0, -12, 0, 0, 0, 34, 0, -8, 0, 0, 0, -4, 0, -38, 0, 0, 0, -30, 0, -16, 0, 0, 0, -8, 0, 4, 0, 0, 0, 16, 0, -8, 0, -18, 0, -24, 0, -4, 0, 0, 0, -12, 0, -16, 0, 0, 0, -12, 0, -36, 0, 24, 0, 8, 0, -4, 0, 0, 0, 40, 0, 4, 0, 0, 0, 34, 0, -10, 0, 0, 0, -32, 0, 32, 0, 0, 0, 18, 0, -32, 0, 0, 0, -48, 0, -23, 0, 0, 0, 4, 0, -24, 0, 0, 0, -4, 0, 14, 0, 0, 0, -20, 0, 36, 0, 18, 0, 48, 0, -16, 0, 0, 0, 14, 0, -8, 0, 0, 0, 32, 0, 4, 0, -9, 0, 26, 0, 28, 0, 0, 0, 0, 0, -14, 0, 0, 0, -8, 0, -24, 0, -12, 0, -24, 0, 64, 0, 0, 0, 34, 0, 12, 0, 0, 0, -24, 0, 26, 0, 12, 0, 10, 0, 32, 0, 0, 0, -16, 0, -18, 0, 0, 0, -38, 0, -32, 0, 0, 0, 6, 0, -19, 0, 0, 0, 12, 0, 24, 0, 0, 0, -16, 0, 2, 0, 24, 0, -30, 0, 16, 0, 0, 0, -32, 0, 0, 0, 0, 0, -26, 0, 16, 0, -30, 0, -12, 0, 2, 0, 0, 0, -16, 0, 0, 0, 0, 0, 24, 0, -14, 0, 0, 0, -6, 0, 6, 0, 0, 0, 36, 0, -12, 0, 0, 0, 12, 0, -8, 0, -12, 0, -16, 0, -12, 0, 0, 0, -42, 0, -16, 0, 0, 0, -2, 0, 30, 0, -48, 0, 0, 0, -16, 0, 0, 0, 8, 0, 16, 0, 0, 0, -6, 0, 16, 0, -27, 0, 24, 0, 26, 0, 0, 0, 16, 0, 52, 0, 0, 0, 32, 0, 12, 0, -24, 0, 12, 0, -8, 0, 0, 0, 0, 0, -2, 0, 0, 0, -30, 0, 10, 0, 36, 0, 0, 0, -22, 0, 0, 0, 50, 0, -8, 0, 0, 0, 16, 0, 32, 0, 0, 0, 36, 0, -40, 0, 0, 0, -2, 0, -12, 0, 0, 0, -30, 0, 48, 0, 18, 0, -40, 0, 0, 0, 0, 0, 26, 0, 16, 0, 0, 0, -24, 0, -32, 0, 6, 0, -10, 0, 24, 0, 0, 0, -28, 0, 26, 0, 0, 0, -6, 0, 32, 0, 0, 0, -48, 0, 7, 0, 0, 0, -18, 0, -5, 0, 0, 0, 0, 0, 26, 0, -48, 0, 18, 0, -40, 0, 0, 0, 16, 0, 36, 0, 0, 0, -64, 0, -8, 0, 18, 0, 12, 0, 6, 0, 0, 0, 18, 0, -20, 0, 0, 0, -16, 0, 8, 0, -36, 0, -64, 0, -8, 0, 0, 0, 48, 0, -36, 0, 0, 0, 20, 0, -28, 0, -6, 0, 24, 0, -32, 0, 0, 0, -8, 0, -40, 0, 0, 0, -16, 0, 2, 0, 48, 0, 10, 0, 8, 0, 0, 0, 48, 0, 10, 0, 0, 0, -54, 0, 0, 0, 0, 0, 52, 0, 20, 0, 0, 0, -6, 0, -32, 0, 0, 0, 6, 0, 33, 0, 36, 0, -28, 0, -16, 0, 0, 0, 48, 0, 8, 0, 0, 0, 2, 0, 24, 0, 30, 0, 0, 0, 12, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -14, 0, 0, 0], 'weight': 2, 'weight_parity': 1}
  51. label: 56.2.a.b
    {'Nk2': 224, 'analytic_conductor': 0.44716225131917015, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [7, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [56, 1, [15, 29, 17], [1, 1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-2, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924984, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '56.2.a.b', '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': '56.2.a.b', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+2q^{3}-4q^{5}+q^{7}+q^{9}-8q^{15}+\\cdots', 'related_objects': ['EllipticCurve/Q/56/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '56.2.a', 'trace_display': [0, 2, -4, 1], 'trace_hash': 537829933984420021, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.982', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.025', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.936', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.035', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.806', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [1, 0, 2, 0, -4, 0, 1, 0, 1, 0, 0, 0, 0, 0, -8, 0, -2, 0, -2, 0, 2, 0, 8, 0, 11, 0, -4, 0, 2, 0, 4, 0, 0, 0, -4, 0, -6, 0, 0, 0, -2, 0, 8, 0, -4, 0, -4, 0, 1, 0, -4, 0, -10, 0, 0, 0, -4, 0, 6, 0, 4, 0, 1, 0, 0, 0, -12, 0, 16, 0, 0, 0, -14, 0, 22, 0, 0, 0, -8, 0, -11, 0, 6, 0, 8, 0, 4, 0, 10, 0, 0, 0, 8, 0, 8, 0, -2, 0, 0, 0, 12, 0, -12, 0, -8, 0, -12, 0, 10, 0, -12, 0, 6, 0, -32, 0, 0, 0, -2, 0, -11, 0, -4, 0, -24, 0, 8, 0, 16, 0, 14, 0, -2, 0, 16, 0, 2, 0, 18, 0, -8, 0, 0, 0, -8, 0, 2, 0, -2, 0, 16, 0, -2, 0, -16, 0, 0, 0, -20, 0, 8, 0, 16, 0, 0, 0, 12, 0, -13, 0, -2, 0, 8, 0, 11, 0, 12, 0, -4, 0, 8, 0, 8, 0, 24, 0, 0, 0, -4, 0, -8, 0, -18, 0, 0, 0, -18, 0, -4, 0, -24, 0, 2, 0, 8, 0, 8, 0, 0, 0, 20, 0, 0, 0, -32, 0, 4, 0, -28, 0, 0, 0, -24, 0, 11, 0, 14, 0, -16, 0, 0, 0, 26, 0, 16, 0, -16, 0, -16, 0, -2, 0, -10, 0, -4, 0, 0, 0, 12, 0, -14, 0, 0, 0, 16, 0, 18, 0, -6, 0, 2, 0, 0, 0, 40, 0, 20, 0, -24, 0, 32, 0, 0, 0, 0, 0, 22, 0, 4, 0, -6, 0, -10, 0, 16, 0, -2, 0, -13, 0, -4, 0, -12, 0, -24, 0, 0, 0, 0, 0, 8, 0, 24, 0, -16, 0, -2, 0, -24, 0, -24, 0, 14, 0, -4, 0, 6, 0, 0, 0, -24, 0, 4, 0, 0, 0, 20, 0, -4, 0, 8, 0, -6, 0, 48, 0, 14, 0, 12, 0, 0, 0, 1, 0, -64, 0, -24, 0, 8, 0, 0, 0, -30, 0, 0, 0, -4, 0, 0, 0, -15, 0, -22, 0, 56, 0, 8, 0, -2, 0, -10, 0, -34, 0, -48, 0, 0, 0, 0, 0, 16, 0, 12, 0, 0, 0, 8, 0, 10, 0, -16, 0, 28, 0, 32, 0, -8, 0, -4, 0, 30, 0, 0, 0, 44, 0, 0, 0, 6, 0, 4, 0, 6, 0, -24, 0, 36, 0, 26, 0, 22, 0, -4, 0, -22, 0, 4, 0, 0, 0, 0, 0, -26, 0, -16, 0, -16, 0, 24, 0, 1, 0, -4, 0, -40, 0, -4, 0, -14, 0, 0, 0, 32, 0, 0, 0, 22, 0, 8, 0, 0, 0, -16, 0, -32, 0, 6, 0, -12, 0, 0, 0, 0, 0, -22, 0, -10, 0, 4, 0, 0, 0, 16, 0, 8, 0, -8, 0, 32, 0, -36, 0, -4, 0, 0, 0, 0, 0, 4, 0, 24, 0, -32, 0, -48, 0, -26, 0, -24, 0, -14, 0, 8, 0, 48, 0, 0, 0, 16, 0, -18, 0, -34, 0, 22, 0, -8, 0, 41, 0, 6, 0, 0, 0, 48, 0, -8, 0, 0, 0, 22, 0, 16, 0, -40, 0, -8, 0, 4, 0, -4, 0, -8, 0, 48, 0, -26, 0, 0, 0, 0, 0, 34, 0, -24, 0, -11, 0, -42, 0, -16, 0, -16, 0, 88, 0, 18, 0, -36, 0, 6, 0, 0, 0, 0, 0, 10, 0, -8, 0, -36, 0, 42, 0, 8, 0, -8, 0, 40, 0, 10, 0, -12, 0, 44, 0, -32, 0, 4, 0, 0, 0, 10, 0, 16, 0, 6, 0, 6, 0, -32, 0, 10, 0, 41, 0, 0, 0, 12, 0, 32, 0, 40, 0, -32, 0, 0, 0, 0, 0, -2, 0, -14, 0, -64, 0, -36, 0, 0, 0, 8, 0, -22, 0, -56, 0, -14, 0, -40, 0, 20, 0, 0, 0, 8, 0, 16, 0, -48, 0, 0, 0, 10, 0, -44, 0, -24, 0, -2, 0, 28, 0, 12, 0, -8, 0, -32, 0, 0, 0, 14, 0, 0, 0, -72, 0, 4, 0, 52, 0, 10, 0, 12, 0, 32, 0, 12, 0, 10, 0, -8, 0, 32, 0, 0, 0, -32, 0, 36, 0, -12, 0, -4, 0, 22, 0, 20, 0, 13, 0, -16, 0, 52, 0, -8, 0, 0, 0, 16, 0, 0, 0, -16, 0, 8, 0, 6, 0, -12, 0, 32, 0, -28, 0, -64, 0, 10, 0, 0, 0, -42, 0, 10, 0, 8, 0, 0, 0, -26, 0, 36, 0, 4, 0, 44, 0, -12, 0, 4, 0, 0, 0, -8, 0, 0, 0, 22, 0, 0, 0, 6, 0, 0, 0, 80, 0, -24, 0, 8, 0, 10, 0, 0, 0, -32, 0, -48, 0, 6, 0, 30, 0, 64, 0, -64, 0, -16, 0, 0, 0, 6, 0, 8, 0, 0, 0, 36, 0, 20, 0, 44, 0, -2, 0, -48, 0, -16, 0, 36, 0, -25, 0, -12, 0, 52, 0, -11, 0, -20, 0, -48, 0, -32, 0, 8, 0, 6, 0, -14, 0, -4, 0, 8, 0, -32, 0, -26, 0, 0, 0, 0, 0, -2, 0, -24, 0, 2, 0, -24, 0, 10, 0, -20, 0, -48, 0, 36, 0, 8, 0, 0, 0, 8, 0, 16, 0, 0, 0, 8, 0, 20, 0, 16, 0, -32, 0, -28, 0, 12, 0, -8, 0, 0, 0, -32, 0, 14, 0, 40, 0, -4, 0, 0, 0, -66, 0, -12, 0, -2, 0, -2, 0, -48, 0, 0, 0, 18, 0, 28, 0, -12, 0, -16, 0, 16, 0, 40, 0, 0, 0, 12, 0, 10, 0, 32, 0, 0, 0, 2, 0, -15, 0, -12, 0, 72, 0, -24, 0, 8, 0, -26, 0, 18, 0, 0, 0, -54, 0, 0, 0, 10, 0, -12, 0, 72, 0, -8, 0, 64, 0, -48, 0, 16, 0, 16, 0, 52, 0, 24, 0], 'weight': 2, 'weight_parity': 1}
  52. label: 57.2.a.a
    {'Nk2': 228, 'analytic_conductor': 0.4551472915212982, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, 1], [19, 1]], 'atkin_lehner_string': '++', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [57, 1, [20, 40], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [2, 1]], [5, [3, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554489, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '57.2.a.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': '57.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\\cdots', 'related_objects': ['EllipticCurve/Q/57/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '57.2.a', 'trace_display': [-2, -1, -3, -5], 'trace_hash': 1883722513434514463, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.989', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.917', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.622', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.015', 'prec': 7}, 'traces': [1, -2, -1, 2, -3, 2, -5, 0, 1, 6, 1, -2, 2, 10, 3, -4, -1, -2, -1, -6, 5, -2, -4, 0, 4, -4, -1, -10, -2, -6, -6, 8, -1, 2, 15, 2, 0, 2, -2, 0, 0, -10, -1, 2, -3, 8, -9, 4, 18, -8, 1, 4, 10, 2, -3, 0, 1, 4, -8, 6, -1, 12, -5, -8, -6, 2, 8, -2, 4, -30, -12, 0, -11, 0, -4, -2, -5, 4, 16, 12, 1, 0, 12, 10, 3, 2, 2, 0, -6, 6, -10, -8, 6, 18, 3, -8, -10, -36, 1, 8, 2, -2, -2, 0, -15, -20, 6, -2, 4, 6, 0, 20, 2, -2, 12, -4, 2, 16, 5, 0, -10, 2, 0, -12, 3, 10, -2, 0, 1, 12, 7, -2, 5, -16, 3, 0, -9, -8, -13, 30, 9, 24, 2, -4, 6, 22, -18, 0, -21, 8, 0, 0, -1, 10, 18, -4, -18, -32, -10, -24, 20, -2, 0, 0, 3, -24, 10, 0, -9, -6, -1, -2, 6, -4, -20, -4, 8, 12, -18, -6, -14, 20, 1, 0, 0, -12, -1, -18, 5, -6, 9, 8, 4, 20, 6, 36, -2, -2, -21, 0, -8, -4, 10, 2, 0, 4, -4, -8, -1, 30, 12, 20, 12, -12, 3, 0, 30, -8, 11, -6, -2, 0, 12, -40, 4, -4, 18, 2, 25, -24, 5, 0, 9, -4, 27, -16, -16, -10, -3, -12, 20, 20, -1, -2, -54, 0, -2, 0, -12, -6, 7, -10, -4, 4, -3, 16, -8, -2, 0, -12, -2, -14, 23, 0, -30, -10, 6, 16, -14, -6, 12, 4, 10, 18, 4, 8, -11, 26, -6, 0, 10, -18, -13, -24, -3, -4, 0, 8, -16, -12, 10, -22, -28, 36, 24, 0, -1, 42, -8, -8, 5, 0, -2, 4, 3, 2, -12, -10, 2, -36, -21, 0, -2, 36, 15, 32, -4, 20, -2, 24, -6, -40, 1, 2, 8, 0, -4, 0, 45, -6, -4, 24, 0, -20, -24, -20, -14, 18, -2, 6, -6, 2, -55, 0, -12, -12, -25, 4, 9, 40, -2, 8, -2, -16, 36, -12, -5, 36, 37, 0, 1, 28, 10, -20, 33, -2, -8, 16, 0, 0, -50, 12, 16, 2, -3, 0, -4, -10, 34, 6, 2, -18, -34, 0, 15, -8, -1, -20, -27, -12, 4, 0, -7, 4, -48, 2, 25, 42, -5, -16, 36, 16, -12, 4, -3, -20, 0, 0, -14, 0, 9, -4, 40, 8, -36, 16, 13, 2, 28, -30, 26, -24, -9, 0, -4, -24, 5, 12, -2, -6, -34, 4, 6, -60, -6, 8, 4, -22, 26, 0, 18, 4, -5, 0, 18, -24, 21, 40, -36, -8, 0, 4, 0, -36, 30, 0, -29, -50, 1, 24, 27, -10, 17, 8, -18, -18, -5, 4, -40, -54, 18, 0, -1, 32, -4, 10, 10, 6, -16, 24, 0, -40, -20, -20, 30, 2, -16, 0, 0, 108, 0, 0, 2, 4, -3, 24, 60, 24, 5, 6, -10, -14, 16, 0, -6, 8, 9, -4, 6, 6, 55, -32, 1, 16, 6, 2, -9, 0, -6, 0, 36, 4, -34, 14, 20, -46, 6, 4, -7, 60, -8, 10, 0, -12, -18, 0, 18, 28, 18, 6, 3, -24, 14, -8, -12, -20, -26, -18, -1, -8, 2, 0, -80, 22, 0, -26, -41, 12, -2, -60, 1, -20, -12, 18, -6, 26, -5, 0, -18, 6, 0, 4, -9, 0, -16, -8, 27, 32, -4, 12, -60, -20, 10, 0, -6, 56, 7, -36, 6, -48, 2, 0, -6, 2, -15, -42, 21, 16, 0, 0, 0, -10, 8, 0, 30, 4, 26, -8, -10, -6, -18, -2, 33, 24, 0, 0, 27, -4, 4, 36, 4, 42, 30, 8, -29, 4, 1, -36, 0, -30, 15, 0, -12, 8, 6, -20, 36, 4, -12, 0, 18, 12, -1, 40, -3, -2, -39, 0, -8, -16, -30, 0, 3, 8, -21, 0, -11, -90, -14, 6, 12, 8, 2, 0, -15, 0, 8, 20, -12, 48, -1, 40, -24, 28, -4, -18, 34, 4, 50, 0, -18, 12, -6, -2, 27, 110, -25, 4, 20, 24, -31, 12, -5, 50, 39, 0, 0, -18, -9, -40, -22, 4, 0, -8, -27, 4, -10, 16, -42, -72, 16, 0, 24, 10, -6, -36, 3, -74, 33, 12, 10, -2, -20, -28, -8, -20, -23, 0, 1, -66, 1, 2, -14, 16, 54, -32, 8, 0, -5, 0, 2, 100, -8, 0, 63, -32, 12, -2, -30, 6, 24, 36, -7, 8, 0, 10, -17, -68, 4, 0, 15, -4, -20, 18, 3, 68, -16, -16, 11, -30, 8, 8, 20, 2, -24, 0, 0, 54, 0, 12, -12, -8, 2, -72, 54, 14, 40, -4, -23, 96, -10, 0, -2, -50, 30, -42, -44, 10, 9, 32, -6, -72, -11, -16, -60, 24, 14, 0, -55, 6, -38, 20, -12, 0, 0, -4, 1, 28, -10, 0, -45, -18, 43, 0, -4, -80, 12, -8, 52, 72, 11, -16, -18, -26, -30, -2, 6, -56, 54, 0, -25, -52, -10, 24, 27, 18, 50, -40, 13, 8, 0, 24, -14, -10, 3, 0, -8, 4, 27, 6, 0, 68, -44, -8, -18, -12, 16, 60, 16, 12, 16, 0, -10, -8, -15, 22, -6, -52, 28, 12, -37, -36, 35, -4, -24, 10, -12, 0, 10, -36, 1, 24, 9, -42, 54, 0, 8, 72, 12, 8, -10, 0, -5, 0, 42, 0, -26, 36, 2, -60, -6, -4, 12, 58, -3, 50, -35, -2, 8, 0, 12, -54, -24, 10, 0, -34, -2, -16, -2, 36, -18, 18, 21, 10, 3, 0, 21, 80, 2, 54, 42, -36, 0, 32, -15, 2, -28, -32, -22, 8, 4, 0, -32, -20, -27, -6, 2, 32, 45, -24, 5, 0, 6, 40, -12, 40, -32, 0, -1, -60, 12, -2, 65, 32, -8, 4, 54, 0, -6, -108, 4, 0, -44, 0, 6, -4, -45, -4, 4, 6, -16, -48, 4, -120, 63, -24, -47, -10, 0, 0], 'weight': 2, 'weight_parity': 1}
  53. label: 57.2.a.b
    {'Nk2': 228, 'analytic_conductor': 0.4551472915212982, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1], [19, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [57, 1, [20, 40], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [2, 1]], [5, [-1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924985, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '57.2.a.b', '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': '57.2.a.b', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/57/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '57.2.a', 'trace_display': [-2, 1, 1, 3], 'trace_hash': 27661726142936421, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.008', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.989', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.024', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.982', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.072', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.961', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.017', 'prec': 7}, 'traces': [1, -2, 1, 2, 1, -2, 3, 0, 1, -2, -3, 2, -6, -6, 1, -4, 3, -2, -1, 2, 3, 6, 4, 0, -4, 12, 1, 6, -10, -2, 2, 8, -3, -6, 3, 2, 8, 2, -6, 0, -8, -6, -1, -6, 1, -8, 3, -4, 2, 8, 3, -12, -6, -2, -3, 0, -1, 20, 0, 2, 7, -4, 3, -8, -6, 6, 8, 6, 4, -6, 12, 0, -11, -16, -4, -2, -9, 12, 0, -4, 1, 16, 4, 6, 3, 2, -10, 0, 10, -2, -18, 8, 2, -6, -1, 8, -2, -4, -3, -8, 2, -6, 14, 0, 3, 12, -2, 2, 20, 6, 8, -12, -6, 2, 4, -20, -6, 0, 9, 0, -2, -14, -8, 4, -9, -6, -2, 0, -1, 12, -13, -6, -3, -16, 1, 0, 3, -8, -5, 6, 3, -24, 18, -4, -10, 22, 2, 16, 15, 8, -8, 0, 3, 18, 2, -12, -2, 0, -6, 8, 12, -2, -16, -16, -3, -8, 18, 0, 23, -6, -1, -2, 14, 20, -12, 12, 0, -20, -10, 2, 2, 36, 7, 0, 8, -4, -9, 6, 3, 2, -3, -8, 4, 4, -6, 4, -2, 6, -5, 0, 8, -4, -30, 6, -8, -28, 4, 24, 3, -6, -28, -12, 12, 4, -1, 0, 6, -40, -11, -6, -18, -16, 4, 24, -4, 12, 18, -2, -15, -8, -9, 0, -11, 12, 3, 0, 0, -18, -15, -4, 12, 4, 1, 14, 2, 16, 6, 0, 4, 18, 27, 6, -12, 4, 3, 16, 8, 2, 24, -12, -10, 26, -21, 0, -6, 6, 10, 16, -30, -2, 12, -12, -18, -6, 12, 8, 13, 10, 2, 0, 2, -6, 19, 24, -1, -36, -24, 8, -8, 20, -2, -22, 4, -4, 0, 0, -3, -30, -24, -8, -3, 16, 2, 4, 7, -6, -12, -18, 14, -4, 7, 0, 14, 4, 3, 0, -12, 12, 30, -8, -2, -24, -3, 2, 24, 32, 20, 0, 9, 6, 12, 8, 8, -36, 8, -12, -22, -46, -6, 6, -6, 2, -15, 0, 4, -28, 3, -20, 25, 24, -6, -24, 14, 0, 12, 20, 9, 20, 25, 0, 1, -4, -2, -36, -11, -14, 8, -16, -8, -16, -18, 4, -16, 18, -9, 0, 60, -6, -30, -2, -2, 6, 14, 0, -9, -8, -1, -4, -15, 12, 12, 0, -13, 4, 0, -6, -7, 10, -3, 16, -28, -16, -12, 4, 1, 60, -24, 0, 10, 16, 3, 28, 0, -8, 4, -48, -5, -6, 20, 6, 2, 56, 3, 0, -12, -24, 21, -4, 18, 2, -18, -4, -26, -12, -10, 40, -4, 22, 10, 0, 2, 36, 39, 16, 10, -8, 15, -24, -20, 8, 24, -12, -8, -36, -18, 0, 3, 30, 3, 8, -33, 18, -31, 40, 2, 22, -17, -12, 24, -6, -2, 0, 3, 0, 4, 18, -6, 30, -40, 8, -48, -24, 12, -4, -2, -2, 8, 0, -16, -4, -8, -16, -30, -12, -3, -8, 36, -8, -35, -18, 18, -54, 24, 0, 2, 24, 23, -4, -10, -6, -33, -32, -1, -16, 14, -2, -9, -48, 14, 0, -28, 20, 14, -26, -12, 42, 6, 12, -7, 12, 0, -6, 48, -20, -2, 0, -10, 60, -6, 2, -13, -24, 2, 24, 20, 36, -2, 6, 7, -24, 10, 0, 0, -26, 8, -10, 3, -4, 6, -12, -9, -4, 44, 6, -6, -38, 3, 0, 30, 2, 32, 36, -3, 48, -16, -8, 3, 16, 4, -20, 12, 4, 18, 0, -6, -8, -37, 4, -2, 0, -2, -32, -6, 6, 9, 30, -5, 48, 0, 0, -8, 6, 8, -16, -2, -4, 18, -8, -30, -14, -18, 6, 9, 24, -8, 0, 23, -28, 20, 4, 4, -14, 30, 24, 11, -28, 3, -4, 24, -6, 7, 0, -28, 24, -2, -12, -12, -60, 12, 0, 2, 4, -1, 24, -1, 6, -27, 0, 0, -48, 6, -32, -1, -40, -13, 32, -11, -18, 10, -6, 12, -24, -18, 0, -3, -16, -40, 36, 4, -16, -21, 24, -16, 44, -4, 46, -22, 12, -6, 0, 18, 12, -6, -2, 3, 30, -15, 4, 36, -8, 17, 28, -9, -6, -5, 0, -24, -50, -11, -24, 42, 12, -8, 24, 3, -28, 6, 0, -10, -24, 0, 0, 8, -18, 18, -20, -15, -50, -35, -4, 42, -2, 12, 4, 40, 4, -7, 0, 1, 22, -3, 14, 34, -16, 2, 32, -24, 16, -45, 16, 6, 36, 24, 0, 15, 32, 4, -18, -6, 18, -8, -12, 27, -120, -8, 6, 23, 60, -12, 0, -13, 4, 60, -6, 3, -28, 0, 16, -45, 18, 8, 8, -36, 2, -8, 0, 24, 30, 8, -12, -36, -24, -10, -8, -2, 26, 8, -4, -21, 0, -18, 0, -42, 14, -6, -10, -12, 6, 9, -32, 10, 56, 33, 16, 12, 24, -30, 0, 5, -2, 2, -60, 12, 48, -16, -12, 1, -20, -18, -16, -33, -6, 19, 0, 12, 0, -52, 8, 20, -8, 13, 48, 6, 10, 18, 6, 2, -40, 30, 0, 71, -4, 2, -56, 23, -6, -6, 24, 19, 24, 32, 24, 34, -42, -1, 0, 48, -36, 35, -2, -24, 36, 44, 8, 14, 52, -8, 12, 0, 20, -48, 0, -2, 8, -27, -22, -22, -20, 4, 12, 7, -4, -21, -36, 0, -78, -52, 0, -6, -20, -3, 8, -3, -30, -10, 0, -24, 40, -20, -8, -18, -48, -3, 0, 2, 16, -2, 36, 2, 36, 2, 4, -12, -6, 7, -30, -39, -6, -40, 0, -12, 66, -72, -18, -32, 62, 14, -80, -50, -4, -2, -22, 7, 34, -9, 0, 53, -48, 14, 6, 2, 4, -32, 0, 3, -6, 28, 0, 66, -8, -12, 0, -16, 12, -3, -30, 30, 80, 9, -8, -27, 96, -2, 24, 4, -24, -32, 0, -3, 4, 12, 2, -15, -16, 24, -28, -42, 32, -30, 4, 20, 16, 4, 0, -2, 60, 9, 12, -4, 6, -8, 16, 12, -72, -5, 8, -7, 70, 8, 0], 'weight': 2, 'weight_parity': 1}
  54. label: 57.2.a.c
    {'Nk2': 228, 'analytic_conductor': 0.4551472915212982, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1], [19, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [57, 1, [20, 40], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1]], [5, [2, 1]]], 'hecke_orbit': 3, 'hecke_orbit_code': 9007199288295481, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '57.2.a.c', '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': '57.2.a.c', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\\cdots', 'related_objects': ['EllipticCurve/Q/57/c'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '57.2.a', 'trace_display': [1, 1, -2, 0], 'trace_hash': 75089547396961172, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.009', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.997', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.962', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.817', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.019', 'prec': 7}, 'traces': [1, 1, 1, -1, -2, 1, 0, -3, 1, -2, 0, -1, 6, 0, -2, -1, -6, 1, -1, 2, 0, 0, 4, -3, -1, 6, 1, 0, 2, -2, 8, 5, 0, -6, 0, -1, -10, -1, 6, 6, -2, 0, -4, 0, -2, 4, 12, -1, -7, -1, -6, -6, -6, 1, 0, 0, -1, 2, -12, 2, -2, 8, 0, 7, -12, 0, -4, 6, 4, 0, 0, -3, 10, -10, -1, 1, 0, 6, 0, 2, 1, -2, 16, 0, 12, -4, 2, 0, -2, -2, 0, -4, 8, 12, 2, 5, 10, -7, 0, 1, -10, -6, 8, -18, 0, -6, 4, -1, -10, 0, -10, 0, 6, -1, -8, -2, 6, -12, 0, 6, -11, -2, -2, -8, 12, 0, -8, -3, -4, -12, 8, 0, 0, -4, -2, 18, 18, 4, 4, 0, 12, 0, 0, -1, -4, 10, -7, 10, 6, -1, -8, 3, -6, 0, -16, -6, -2, 0, -6, -10, 0, 1, -4, 2, 0, 16, 24, 0, 23, 12, -1, 4, -22, 2, 0, 0, -12, -2, -4, 2, 14, 0, -2, -12, 20, 8, 0, -12, 0, 2, -12, 7, -14, 10, -12, 7, -2, 0, -8, 3, -4, -10, 0, 6, 4, 8, 4, -6, 0, 0, -4, 6, 0, 4, 8, -3, 0, -10, 10, 0, -36, -10, 16, 0, -1, 6, -12, 1, 6, -8, 0, -6, 10, 6, -24, 12, 0, 0, -12, 2, -6, -11, 1, 2, 14, -2, -6, -24, 16, 12, -24, 0, 0, -8, 12, -17, 14, -4, 0, 12, 2, 8, 12, 0, 12, 0, -2, 4, -6, -2, 0, 6, 0, 18, 0, -4, 22, 4, 8, 0, -10, 12, -20, 0, 2, 0, 0, 5, 19, -4, 10, -10, -14, -7, 24, 30, 0, 6, 24, 1, 0, -8, -10, 1, 4, -6, -12, 0, 8, -16, 4, -18, -22, -2, 0, 0, -6, -6, 0, -14, 4, 0, 6, -1, -6, -4, -10, 6, 0, 0, 12, -16, -10, 24, 8, 0, -22, 23, 6, -12, 0, -1, 0, 12, -8, -22, 0, -2, -2, 0, 6, 0, -22, -12, 0, 2, 0, -4, -20, 6, 1, 14, -11, 0, -20, -2, 32, -4, -2, 20, 0, -8, -10, 0, 12, -36, 12, 0, 12, -2, -8, -12, 8, -3, 0, -14, -4, -10, 30, -12, -24, 21, 8, -2, 0, 0, 14, -8, 0, 1, 38, -4, 48, 10, -2, 0, 0, 18, -14, 4, 18, -8, 0, 4, -32, 30, 4, 0, 8, 0, 14, -4, 12, 18, 6, 0, 0, -4, 0, 8, -24, -1, -14, 0, -4, 10, -4, 10, -8, 0, -7, -36, 0, 10, 4, 16, 6, 0, -2, -1, 0, -6, -8, -12, 0, 3, -6, 6, -6, 8, -18, 0, 32, -2, -16, 10, -32, -6, 0, -24, -2, 36, 0, 0, 1, 0, -6, -12, 20, -10, -60, -6, 0, 11, -20, 1, 32, 6, -4, 14, -32, 2, -12, -6, 0, -8, 0, 16, 28, -12, 24, -24, 12, 0, 20, 0, 23, 8, -22, 12, 0, -11, -1, 14, -16, 4, 0, 0, -22, 36, 14, 2, -28, -8, 0, 12, -48, 0, -7, 12, -12, 0, -12, -2, -8, 12, -4, -6, 0, 2, 14, 0, 14, -30, 20, 0, 4, -18, -2, 0, -2, -12, 0, 22, 20, -4, 30, 8, -24, 0, 0, -10, 20, -12, -12, -20, 0, 0, 6, 2, 44, 0, -12, 0, -4, 7, 18, 19, -14, 4, 0, 10, 0, -30, -12, -14, 8, 7, -8, 24, -2, 10, -30, 0, 0, -6, -8, 24, -24, 3, 10, 0, -4, 8, 22, -10, 24, -5, 0, 4, 72, 6, 6, -12, 4, 0, 2, 8, -28, 16, 4, 4, 0, -6, -19, -22, 0, 2, 60, 0, -32, 0, -4, -6, 16, 6, -42, 0, 0, 6, 38, 4, 20, 0, 8, 6, 36, -3, 0, -6, 0, 4, 14, -10, -16, 2, 10, 0, -44, 0, 6, 12, -36, -48, 0, -10, 8, -24, 16, 8, 0, 0, -46, -22, -1, -23, -22, 6, 0, -36, -12, 0, 36, 1, -36, 0, 6, 4, -36, -8, 20, 22, 0, 0, -8, -6, 12, -2, 10, 0, -18, 6, 10, 0, -24, -22, 0, 12, 38, 0, 0, 6, 32, 0, 0, 4, -12, -20, -20, 2, 0, 1, -6, -14, -2, -11, 8, 0, 1, -20, 24, 2, 46, 32, 14, 20, 0, -2, -36, -20, -6, 0, 0, -24, -12, -10, 16, 0, 0, 12, 16, -12, -24, 12, 16, 0, 38, 12, 0, -6, 50, -8, 0, 12, 12, 8, -72, -17, 18, 0, 14, 14, 18, -4, -8, -30, 0, 30, 2, 12, 0, -24, 2, 7, 4, 8, 44, 2, 12, 0, 0, 0, -12, 14, 12, 8, -6, 0, -72, -5, -2, 38, 0, 4, 0, 48, -6, 30, 26, -2, 44, 0, 0, 0, 8, 6, 4, -14, 0, -4, -42, 18, -32, -24, 0, 0, -28, -4, -10, -32, 22, 42, 42, 4, -48, 0, 8, 8, 0, 0, -25, 14, -10, 4, -46, 12, 0, 6, -20, 6, -40, 0, 22, 0, 2, -12, 30, 0, -28, -8, 0, -24, -40, 5, 44, -14, 19, 0, 0, -4, -24, 30, 10, -4, 0, -10, -34, -8, -14, 0, -38, -7, -36, 36, 24, 0, -40, 30, 0, 4, 0, -16, -12, 6, 8, 0, 24, -2, 16, 1, 36, 0, 0, -18, -28, -8, 4, 12, -10, 0, -16, 1, 0, -6, 4, -6, 0, -6, -16, 24, -12, -18, 0, 0, 10, 32, 8, 10, 34, -16, 7, -10, 4, -32, 0, -18, -22, 0, -22, 24, -22, -2, -8, 12, 0, 0, -8, 0, 60, 1, -6, 0, 38, -6, 24, 12, 0, 20, 0, -14, 33, -60, 4, 6, 28, 0, -32, 33, 6, -20, -36, -1, 0, 32, -6, 2, -42, -4, 0, -14, -10, -32, -8, 6, 4, -12, 0, 6, -16, 0, 40, 40, 12, 0, 16, -16, -58, 28, -10, -36], 'weight': 2, 'weight_parity': 1}
  55. label: 58.2.a.a
    {'Nk2': 232, 'analytic_conductor': 0.4631323317234262, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [29, 1]], 'atkin_lehner_string': '++', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [58, 1, [31], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [3, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554490, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '58.2.a.a', 'level': 58, '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': [2, 29], 'level_radical': 58, 'minimal_twist': '58.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}-3q^{3}+q^{4}-3q^{5}+3q^{6}-2q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/58/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '58.2.a', 'trace_display': [-1, -3, -3, -2], 'trace_hash': 465711061579246240, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.991', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '2.010', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '5.161', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, 'traces': [1, -1, -3, 1, -3, 3, -2, -1, 6, 3, -1, -3, 3, 2, 9, 1, -4, -6, -8, -3, 6, 1, 0, 3, 4, -3, -9, -2, -1, -9, 3, -1, 3, 4, 6, 6, -8, 8, -9, 3, -2, -6, 7, -1, -18, 0, 11, -3, -3, -4, 12, 3, 1, 9, 3, 2, 24, 1, -4, 9, 4, -3, -12, 1, -9, -3, -4, -4, 0, -6, -2, -6, -12, 8, -12, -8, 2, 9, -7, -3, 9, 2, 0, 6, 12, -7, 3, 1, -6, 18, -6, 0, -9, -11, 24, 3, -6, 3, -6, 4, 8, -12, -6, -3, -18, -1, -2, -9, 1, -3, 24, -2, 18, -24, 0, -1, 18, 4, 8, -9, -10, -4, 6, 3, 3, 12, -8, -1, -21, 9, 12, 3, 16, 4, 27, 4, -20, 0, 0, 6, -33, 2, -3, 6, 3, 12, 9, -8, 3, 12, 10, 8, -24, -2, -9, -9, 22, 7, -3, 3, 0, -9, 19, -2, -9, 0, -22, -6, -4, -12, -48, 7, -14, -3, -8, -1, 12, 6, -14, -18, -13, 6, -12, 0, 24, 9, 4, 11, 18, -24, 0, -3, 10, 6, 27, -3, 2, 6, -2, -4, 12, -8, 2, 12, 6, 6, 0, 3, 8, 18, -25, 1, 6, 2, -21, 9, -6, -1, 36, 3, -12, -24, 26, 2, 24, -18, -18, 24, 14, 0, -6, 1, -25, -18, -33, -4, 21, -8, 20, 9, 17, 10, 0, 4, 9, -6, -24, -3, 0, -3, -7, -12, 0, 8, -36, 1, 21, 21, 16, -9, -6, -12, -17, -3, -3, -16, 18, -4, 20, -27, 13, -4, 18, 20, -4, 0, 14, 0, 18, -6, -13, 33, 0, -2, -72, 3, 4, -6, -1, -3, 18, -12, -34, -9, 12, 8, 9, -3, 0, -12, -14, -10, -24, -8, -12, 24, -29, 2, 18, 9, 0, 9, 25, -22, 36, -7, 0, 3, 1, -3, 6, 0, 32, 9, 12, -19, -3, 2, -22, 9, 3, 0, -48, 22, 12, 6, 4, 4, -54, 12, -3, 48, 20, -7, 0, 14, 18, 3, -19, 8, -27, 1, -2, -12, 6, -6, -24, 14, 9, 18, 45, 13, 30, -6, 36, 12, -16, 0, -12, -24, -2, -9, -1, -4, -9, -11, -3, -18, -28, 24, 24, 0, -34, 3, -6, -10, 42, -6, 16, -27, 0, 3, -36, -2, 21, -6, 19, 2, -48, 4, -5, -12, 9, 8, -27, -2, 8, -12, 22, -6, 60, -6, 8, 0, 0, -3, 0, -8, -14, -18, -28, 25, 66, -1, -16, -6, -8, -2, 9, 21, -20, -9, -16, 6, -9, 1, 0, -36, -8, -3, -18, 12, 12, 24, 18, -26, -9, -2, 22, -24, 2, 18, -30, 18, 18, -24, -10, -14, 36, 0, -30, 6, -16, -1, 27, 25, 23, 18, 8, 33, -66, 4, -7, -21, -32, 8, 6, -20, -11, -9, -24, -17, 0, -10, 18, 0, 2, -4, -57, -9, 5, 6, 4, 24, 18, 3, 4, 0, -8, 3, 66, 7, -19, 12, -24, 0, 12, -8, 21, 36, 24, -1, 72, -21, 18, -21, -11, -16, 42, 9, 27, 6, 16, 12, 24, 17, -12, 3, -23, 3, -24, 16, -6, -18, 6, 4, 42, -20, 3, 27, -8, -13, 39, 4, -3, -18, -2, -20, 24, 4, 8, 0, 14, -14, -72, 0, -18, -18, 21, 6, -12, 13, -9, -33, -54, 0, -18, 2, -30, 72, -36, -3, 0, -4, 0, 6, -44, 1, -30, 3, 0, -18, -1, 12, -54, 34, 0, 9, -24, -12, -6, -8, -17, -9, -24, 3, 6, 0, 13, 12, -10, 14, -24, 10, 30, 24, 29, 8, -6, 12, 33, -24, -27, 29, -18, -2, 12, -18, 31, -9, 0, 0, 12, -9, -29, -25, -24, 22, 32, -36, 22, 7, 75, 0, 24, -3, -9, -1, -12, 3, 36, -6, 2, 0, 63, -32, -20, -9, 4, -12, 18, 19, -14, 3, -36, -2, -72, 22, 21, -9, 46, -3, 36, 0, -48, 48, 0, -22, -78, -12, -4, -6, 1, -4, -36, -4, -18, 54, 12, -12, 54, 3, -16, -48, 60, -20, -42, 7, 3, 0, 4, -14, 12, -18, 0, -3, 8, 19, 75, -8, 31, 27, 64, -1, 99, 2, -16, 12, 35, -6, -42, 6, 0, 24, 9, -14, -60, -9, -6, -18, 12, -45, -51, -13, -4, -30, 32, 6, -27, -36, -28, -12, -48, 16, -27, 0, 4, 12, 1, 24, 72, 2, -28, 9, -9, 1, 0, 4, 4, 9, 32, 11, 21, 3, -30, 18, -28, 28, 0, -24, 34, -24, -2, 0, 72, 34, -12, -3, 48, 6, -63, 10, -6, -42, 12, 6, -48, -16, 16, 27, 2, 0, 9, -3, -66, 36, 46, 2, 51, -21, -36, 6, 12, -19, 9, -2, 12, 48, -44, -4, -36, 5, 12, 12, 0, -9, -60, -8, 24, 27, 6, 2, -39, -8, -57, 12, -56, -22, -36, 6, -37, -60, -16, 6, 12, -8, 23, 0, -28, 0, -42, 3, 12, 0, 66, 8, -27, 14, -45, 18, 1, 28, 39, -25, 12, -66, 20, 1, 0, 16, 0, 6, 30, 8, 144, 2, -11, -9, -51, -21, -12, 20, 6, 9, 42, 16, 3, -6, 7, 9, -12, -1, -36, 0, -6, 36, -23, 8, 102, 3, 42, 18, -42, -12, -36, -12, -1, -24, 16, -18, -9, 26, -88, 9, 42, 2, 0, -22, -3, 24, -4, -2, 42, -18, 39, 30, -28, -18, 48, -18, -3, 24, 0, 10, 36, 14, -24, -36, -6, 0, 87, 30, -6, -6, -32, 16, -36, 1, 18, -27, 24, -25, 0, -23, -12, -18, 14, -8, -75, -33, -15, 66, 0, -4, -54, 7, 51, 21, -36, 32, 0, -8, 15, -6, 0, 20, -3, 11, 40, 9, -22, 24, -12, 17, -30, 0, 59, 10, -96, -18, -52, 0, 0, -2, -36, 4, 37, 57, 6, 9, 6, -5, 39, -6, -6, -4, 66, -24, 0, -18, 26, -3, -9, -4, 6, 0, 16, 8, 72, -3], 'weight': 2, 'weight_parity': 1}
  56. label: 58.2.a.b
    {'Nk2': 232, 'analytic_conductor': 0.4631323317234262, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [29, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [58, 1, [31], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924986, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '58.2.a.b', 'level': 58, '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': [2, 29], 'level_radical': 58, 'minimal_twist': '58.2.a.b', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/58/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '58.2.a', 'trace_display': [1, -1, 1, -2], 'trace_hash': 708012337630994629, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.006', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.966', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.005', 'prec': 4}, {'__RealLiteral__': 0, 'data': '1.894', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.650', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.017', 'prec': 7}, 'traces': [1, 1, -1, 1, 1, -1, -2, 1, -2, 1, -3, -1, -1, -2, -1, 1, 8, -2, 0, 1, 2, -3, 4, -1, -4, -1, 5, -2, -1, -1, -3, 1, 3, 8, -2, -2, 8, 0, 1, 1, 2, 2, -11, -3, -2, 4, 13, -1, -3, -4, -8, -1, -11, 5, -3, -2, 0, -1, 0, -1, -8, -3, 4, 1, -1, 3, -12, 8, -4, -2, 2, -2, 4, 8, 4, 0, 6, 1, 15, 1, 1, 2, 4, 2, 8, -11, 1, -3, -10, -2, 2, 4, 3, 13, 0, -1, -2, -3, 6, -4, -8, -8, 14, -1, 2, -11, -2, 5, 5, -3, -8, -2, -6, 0, 4, -1, 2, 0, -16, -1, -2, -8, -2, -3, -9, 4, 8, 1, 11, -1, 12, 3, 0, -12, 5, 8, -12, -4, -20, -2, -13, 2, 3, -2, -1, 4, 3, 8, 15, 4, 2, 0, -16, 6, -3, 1, 18, 15, 11, 1, -8, 1, 9, 2, 3, 4, -2, 2, -12, 8, 0, -11, -6, 1, 8, -3, 0, -10, -10, -2, 7, 2, 8, 4, 8, 3, -24, 13, -10, 0, -8, -1, 14, -2, 1, -3, 18, 6, -10, -4, 12, -8, 2, -8, 2, 14, -8, -1, 0, 2, -3, -11, -2, -2, -11, 5, 6, 5, -4, -3, -8, -8, -26, -2, 8, -6, 18, 0, 10, 4, -6, -1, -1, 2, 13, 0, -15, -16, 0, -1, 17, -2, -16, -8, -3, -2, 0, -3, -4, -9, 27, 4, -12, 8, -8, 1, 13, 11, -16, -1, 2, 12, 9, 3, -11, 0, 10, -12, 0, 5, -13, 8, -2, -12, 12, -4, -2, -20, 6, -2, 27, -13, 4, 2, 0, 3, -4, -2, 47, -1, 2, 4, 14, 3, 0, 8, -15, 15, -4, 4, 22, 2, 8, 0, -8, -16, -7, 6, -14, -3, -8, 1, 9, 18, 4, 15, -12, 11, 3, 1, 2, -8, 0, 1, 4, 9, -5, 2, -26, 3, -23, 4, -16, -2, -12, 2, -32, -12, 6, 8, 9, 0, 20, -11, -4, -6, -2, 1, -15, 8, -5, -3, -26, 0, 2, -10, 16, -10, -25, -2, -19, 7, 2, 2, 4, 8, -32, 4, -4, 8, 22, 3, -21, -24, 9, 13, 1, -10, 20, 0, -8, -8, 14, -1, 6, 14, 22, -2, 0, 1, 32, -3, -12, 18, 15, 6, -17, -10, 0, -4, 27, 12, 3, -8, 1, 2, -24, -8, 30, 2, 12, 14, 0, -8, 4, -1, 20, 0, -10, 2, 32, -3, -26, -11, -32, -2, 16, -2, -3, -11, 32, 5, -16, 6, 1, 5, 0, -4, 20, -3, 6, -8, 4, -8, -10, -26, -15, -2, -10, 8, -6, -6, -2, 18, 2, 0, -2, 10, 40, 4, 2, -6, 4, -1, 3, -1, -27, 2, 24, 13, -18, 0, 33, -15, 0, -16, 22, 0, -5, -1, -8, 17, 8, -2, -2, -16, -22, -8, -9, -3, -33, -2, -8, 0, 6, -3, -4, -4, -20, -9, 2, 27, 19, 4, -8, -12, 12, 8, -15, -8, -8, 1, 0, 13, 14, 11, -39, -16, 6, -1, -13, 2, 24, 12, -8, 9, -24, 3, -7, -11, 0, 0, -2, 10, -2, -12, 10, 0, 9, 5, -8, -13, -7, 8, 5, -2, 38, -12, 16, 12, 0, -4, -30, -2, -8, -20, -2, 6, 11, -2, 24, 27, -11, -13, -6, 4, -2, 2, -30, 0, -28, 3, 8, -4, -16, -2, 8, 47, -14, -1, -8, 2, 33, 4, 2, 14, 28, 3, 0, 0, -18, 8, 39, -15, -16, 15, 10, -4, -5, 4, 2, 22, 24, 2, -2, 8, 3, 0, -2, -8, -13, -16, -31, -7, -2, 6, -12, -14, -35, -3, 20, -8, 20, 1, 11, 9, 0, 18, 64, 4, -38, 15, 3, -12, 8, 11, 3, 3, -4, 1, -8, 2, 34, -8, 11, 0, -32, 1, 0, 4, -6, 9, -26, -5, 12, 2, -8, -26, 15, 3, -18, -23, 8, 4, 0, -16, -4, -2, 26, -12, 24, 2, 9, -32, -20, -12, 38, 6, 4, 8, -18, 9, 24, 0, -12, 20, -10, -11, 11, -4, -28, -6, -12, -2, -20, 1, 16, -15, 1, 8, 27, -5, 0, -3, -13, -26, 16, 0, 15, 2, -30, -10, -12, 16, 3, -10, 0, -25, -50, -2, -28, -19, -17, 7, 4, 2, 8, 2, 13, 4, -88, 8, 24, -32, 3, 4, 36, -4, -5, 8, 0, 22, 44, 3, 15, -21, -8, -24, 4, 9, 32, 13, -27, 1, 2, -10, 8, 20, 12, 0, 42, -8, -10, -8, -16, 14, 0, -1, -20, 6, -13, 14, 14, 22, 12, -2, 16, 0, 0, 1, -6, 32, -5, -3, 18, -12, -22, 18, -9, 15, 12, 6, 8, -17, 11, -10, -32, 0, 104, -4, 20, 27, -12, 12, -8, 3, 0, -8, 0, 1, -18, 2, 13, -24, 9, -8, 0, 30, -4, 2, -33, 12, -16, 14, -12, 0, 13, -8, 40, 4, 2, -1, -24, 20, -2, 0, -15, -10, 45, 2, 1, 32, -27, -3, -12, -26, 4, -11, -4, -32, 32, -2, 14, 16, 0, -2, -27, -3, -25, -11, 4, 32, -46, 5, -6, -16, -47, 6, -45, 1, 12, 5, 4, 0, 18, -4, 13, 20, -14, -3, 42, 6, -26, -8, 0, 4, 33, -8, -16, -10, -3, -26, 0, -15, -10, -2, 4, -10, 3, 8, -88, -6, -22, -6, 7, -2, 28, 18, 16, 2, -13, 0, -12, -2, 8, 10, -24, 40, 30, 4, 7, 2, -2, -6, -32, 4, -28, -1, -30, 3, 0, -1, 8, -27, -24, 2, -2, 24, -9, 13, 37, -18, 8, 0, -10, 33, 33, -15, -4, 0, 12, -16, -1, 22, -8, 0, -3, -5, 24, -1, -22, -8, 4, 17, 14, 8, 13, -2, 0, -2, -28, -16, 40, -22, -4, -8, 13, -9, 30, -3, -10, -33, 49, -2, 18, -8, 26, 0, -44, 6, 22, -3, 23, -4, -10, -4, 8, -20, 40, -9], 'weight': 2, 'weight_parity': 1}
  57. label: 59.2.a.a
    {'Nk2': 236, 'analytic_conductor': 0.47111737192555425, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[59, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [59, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 5, 'field_disc': 138136, 'field_disc_factorization': [[2, 3], [31, 1], [557, 1]], 'field_poly': [-2, 4, 3, -6, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554491, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '59.2.a.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': '59.2.a.a', 'nf_label': '5.5.138136.1', 'prim_orbit_index': 1, 'qexp_display': 'q+(\\beta _{1}-\\beta _{3})q^{2}+(-1-\\beta _{2}+\\beta _{4})q^{3}+\\cdots', 'related_objects': [], 'relative_dim': 5, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '59.2.a', 'trace_display': [0, -2, 2, 2], 'trace_hash': 125457122493961900, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.044', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.656', 'prec': 14}, {'__RealLiteral__': 0, 'data': '1.749', 'prec': 14}, {'__RealLiteral__': 0, 'data': '58.743', 'prec': 17}, {'__RealLiteral__': 0, 'data': '57.064', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1161.442', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.007', 'prec': 4}, 'traces': [5, 0, -2, 8, 2, -4, 2, -6, 5, -8, -2, -22, 8, -18, -9, 10, -1, -2, 6, 6, 15, 8, -8, 6, 7, 8, -11, -2, 14, 14, 0, -2, -14, -2, -9, 42, 18, 0, -18, -18, -10, 34, -4, 12, 1, 16, -20, -54, 1, 8, -12, 28, -10, -26, -20, -38, -3, -38, 5, -28, 22, 48, -12, 18, -16, 28, 0, -14, -4, -24, 3, 28, -8, 8, 8, 14, 2, 20, 10, 50, -3, -48, 6, 28, 40, -8, 11, -24, 10, -8, 6, 4, 6, -36, 26, 42, -22, 24, -4, -38, -4, 54, -2, -36, -23, 24, -22, -20, 62, -40, 24, -18, 2, -66, -30, 46, 6, 0, -12, 50, -3, 64, 46, -56, 3, -86, -14, -46, -6, -56, 4, -36, -25, -12, 17, -52, -30, -44, 13, 36, 16, -14, 48, 40, -15, 24, -23, 8, 28, 66, 18, 54, -39, 20, 14, -80, 10, -4, 30, -22, -18, 66, 9, -38, -14, -4, -38, 110, -1, 2, 41, -8, -20, 26, 15, 24, -2, -8, 40, 42, 2, -16, -10, 60, -36, -80, -2, -20, 21, 44, -18, -2, 18, -4, -32, 38, 3, 12, -14, -80, -60, 20, 62, -8, 23, 80, 26, 44, -56, 28, -28, -62, -4, 32, 6, -38, -60, -44, -20, 48, -4, -72, -5, -26, -82, 48, -18, -32, 26, 12, -24, -54, -50, 8, 8, 8, -32, 28, 70, -46, 6, -16, 25, -4, -22, 30, -44, 80, -10, 18, -46, -64, 20, -48, 1, -26, -2, 80, 24, 60, 38, -4, 18, -8, -9, -84, 58, 80, -58, 8, 22, 64, 6, -18, 16, 4, 22, 38, -40, -10, 18, 68, -36, 14, 16, 0, 45, -36, 6, -64, -20, 28, 6, -86, 2, 36, -12, 32, 4, 40, 16, -8, 94, 10, -4, -30, -26, -12, 16, 84, 26, 4, 32, -8, 43, 42, -14, -74, -2, -2, 41, -4, -12, -60, 30, -122, -2, -10, 28, 0, -30, 64, 22, 6, -6, -42, 4, 16, -46, -12, -36, 60, -53, -72, 22, -48, 34, -52, 84, 84, -34, -56, 48, -4, -24, -44, -83, 4, -22, -52, -3, -112, 78, -16, -2, -148, -40, -36, -19, -8, -27, 68, 61, -80, 31, -28, 26, 54, -2, -42, -43, -24, 48, 54, 0, 8, -40, 24, 5, 28, -52, 84, -50, 102, 67, 8, 0, -12, 83, 4, 2, 112, -36, -116, -1, -56, -20, 60, -30, 50, 29, -48, 2, 84, 12, -60, 28, 16, 2, -64, 54, 36, -16, 94, 87, 98, -66, -42, 28, -36, 30, 2, 34, 28, -65, 96, -2, -140, -45, 40, 68, -84, 66, 4, -48, 66, -94, 90, -18, -88, -78, 76, -20, -4, -18, -54, 46, 28, 31, -8, 42, 100, 18, 14, 66, -16, -50, 92, 10, 12, -60, -6, 36, -50, -61, 72, -27, 46, -31, 70, 16, -30, 52, -80, -58, 26, -98, 104, 44, 8, -62, 150, -64, 16, 88, -64, 48, -176, -50, -68, 59, -42, -10, -132, -86, 24, 18, -10, 42, 28, -70, -26, -17, 90, -76, 4, -8, -44, -44, 4, 1, -114, -2, 4, -81, -16, 48, -8, -51, 90, 5, -68, -98, 4, -110, -112, 60, 4, 14, 20, 108, 56, 66, -28, 60, 168, -56, -62, 16, -28, -3, -124, -49, -88, -18, -94, 70, 116, 28, 86, 50, 0, -58, 92, -44, 44, -69, -104, 72, 18, 74, 32, -68, 46, -72, -12, 6, -22, 47, 120, -46, 72, -46, 156, 90, 50, 24, -86, 46, -8, -44, -84, -62, -44, 5, 128, 16, 56, 22, 48, 10, 60, 30, 120, -34, -44, 6, 50, 7, 48, -48, -10, 40, 158, 11, -104, 2, -160, -10, -188, -24, 96, 70, -116, 17, -36, -78, 68, -82, 12, 64, 30, 2, -8, 158, 142, 16, 60, -31, -90, 75, -106, 54, -112, -18, 50, 6, 58, -2, -12, 78, -38, -46, -24, 118, -70, 94, 68, -24, -36, 78, -124, 26, 164, 21, -4, -18, -154, -4, -128, -28, 114, -52, -128, 7, -16, 38, -172, 18, -108, 6, 8, 38, 114, -69, 40, -26, 40, -66, -56, -32, 60, -74, -124, -4, 206, -4, -116, 26, 94, -34, -96, 28, 48, 8, -44, 60, -22, 102, -90, 59, -24, -4, 12, -52, -40, -41, -68, -18, 16, -56, 56, -65, -2, -45, -12, 0, -180, -100, 76, 52, -60, 41, -112, 15, 20, 116, -150, 28, -28, -84, 54, 77, -272, -30, 170, 148, 76, 3, -96, -88, -12, -41, -16, -68, 136, 42, -42, 20, -70, 50, 166, 58, 104, -67, 16, 8, 130, 8, -68, 15, -10, -120, -68, 74, -28, 130, 114, 41, -92, 70, -28, 5, 8, 130, 84, 28, 2, -69, 38, -78, -32, 16, 128, 67, -34, -46, 52, 8, 24, -52, -76, -36, -200, 14, 104, 6, 52, -28, 56, -46, 122, -135, 128, 168, 44, -66, -12, -98, -20, 34, 182, -6, 164, 76, -18, -87, -4, -42, 76, -61, 84, -67, 78, 35, 8, -46, 40, -18, 106, 31, -124, 38, -48, -110, -96, 62, -126, 136, 0, 8, -28, -58, -84, -99, 150, 32, 0, 60, 44, -80, -64, -48, -42, 2, 14, 82, -168, -62, 120, 116, -100, 12, 28, -45, -52, -10, 42, 163, 48, 34, 154, 70, 48, -9, 0, 18, -68, -37, -16, 16, -114, -24, 64, -6, 50, 12, 104, -160, -64, -12, 12, -106, 168, 5, -112, -2, -76, -100, -116, -58, -78, -92, 40, 34, 28, -56, 36, -46, 116, -65, -72, 76, -40, -14, 52, -6, -90, -14, -156, 40, -88, -137, -12, -68, 24, 128, -32, -56, 44, -44, -92, -40, 10, 44, -56, -34, -126, -52, -54, -52, 12, -70, 58, 4, 174, -116, 46, 78, -110, 77, 144, 17, 14, -48, 56, 144, 18, -17, -72, 46, 110, 20, -140, 92, -40, -80, 198, -12, 4, 68, -180, -80, 202, -44, 24, -128, 36, -28, 28, -22, 192, 44, 56, 41, -96, -38, -22, -66, 90], 'weight': 2, 'weight_parity': 1}
  58. label: 61.2.a.a
    {'Nk2': 244, 'analytic_conductor': 0.4870874523298103, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[61, 1]], 'atkin_lehner_string': '+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [61, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554493, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '61.2.a.a', 'level': 61, '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': [61], 'level_radical': 61, 'minimal_twist': '61.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}-2q^{3}-q^{4}-3q^{5}+2q^{6}+q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/61/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '61.2.a', 'trace_display': [-1, -2, -3, 1], 'trace_hash': 1741252524209688521, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.999', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.993', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.981', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.012', 'prec': 7}, 'traces': [1, -1, -2, -1, -3, 2, 1, 3, 1, 3, -5, 2, 1, -1, 6, -1, 4, -1, -4, 3, -2, 5, -9, -6, 4, -1, 4, -1, -6, -6, 0, -5, 10, -4, -3, -1, 8, 4, -2, -9, 5, 2, -8, 5, -3, 9, 4, 2, -6, -4, -8, -1, 6, -4, 15, 3, 8, 6, 9, -6, -1, 0, 1, 7, -3, -10, -7, -4, 18, 3, -8, 3, -11, -8, -8, 4, -5, 2, 3, 3, -11, -5, 4, 2, -12, 8, 12, -15, -4, 3, 1, 9, 0, -4, 12, 10, -14, 6, -5, -4, 0, 8, 4, 3, 6, -6, -2, -4, -17, -15, -16, -1, 1, -8, 27, 6, 1, -9, 4, 18, 14, 1, -10, 0, 3, -1, 6, 3, 16, 3, -16, -10, -4, 7, -12, 12, 9, -18, -11, 3, -8, 8, -5, -1, 18, 11, 12, -8, 19, 8, 11, -12, 4, 5, 0, 2, -4, -3, -12, 15, -9, 11, 18, -5, -30, -4, -12, -6, -12, 12, -4, 8, 10, -12, 4, 5, -18, 4, -18, 3, 8, -1, 2, -27, -24, 0, -20, -4, 4, -12, 3, -14, -8, 14, 6, 6, -3, 5, 6, 12, 14, 0, -6, 8, -15, -4, -9, -1, 20, -6, 4, -6, 16, 2, 24, 12, 0, 17, 22, -15, 4, 16, 23, -5, 4, -1, 21, -8, 9, -27, 10, -18, -14, -1, -12, -9, -6, -4, 2, -6, -3, -14, 10, 1, 18, 10, -4, 0, -8, -3, -12, -1, 45, -6, 24, -17, -22, -16, 8, 3, -6, 16, -16, 30, -18, 4, 8, 7, -18, 12, 14, -4, -2, -9, -20, -18, 10, 11, 0, -9, 0, 8, 6, 8, -24, 5, 5, -5, -1, -18, 28, 11, 18, -12, -27, 24, -20, -19, -9, 8, -8, -11, 0, 4, 3, -4, -19, 5, -8, 0, -15, -6, -6, 4, -3, -3, -30, 12, 30, -21, 4, 9, -16, 11, 4, -18, 34, 15, 4, 30, -17, -4, 8, 12, 21, 2, -2, 12, -2, 12, 0, 4, -13, -24, -54, -10, 8, -12, -24, -4, 4, 25, 19, 18, 24, 4, -8, 18, 12, -9, -3, -8, -28, -1, 33, -2, 14, 9, 5, 24, 6, 0, -10, 20, -6, 12, -6, -4, -14, -12, -12, -3, 5, -6, 15, 8, -8, 14, -14, -6, -36, -18, 32, 3, -9, 5, 8, -6, 8, -4, 16, -14, 0, 0, 33, 6, -40, -24, 30, 15, -18, -4, 9, 9, -12, -5, 22, -20, 4, -6, 8, -4, 4, 18, 16, -16, -1, 2, 10, -24, 6, -4, -8, 0, -36, 17, 36, -22, 0, 45, -6, -4, 12, 16, 12, -23, -38, 7, -35, -4, -25, -1, -22, -21, -3, 24, -20, -9, 16, -27, -18, -10, -4, 6, 0, 14, 11, -1, -7, 12, 8, 27, 40, 6, -16, -4, 6, -2, 14, -30, 8, 3, 18, -14, 42, -10, -12, -3, -36, -18, -28, 10, -24, 4, 15, 0, -8, 8, 13, -3, 24, 12, 10, 3, 0, -45, 24, -6, 28, -24, -11, 11, -16, 22, -12, -16, -20, -8, -20, -9, -20, 6, -9, 16, -8, 16, 0, -10, 58, 18, 9, 4, 5, -8, 6, -21, 36, 18, 30, 12, 28, -14, -16, -20, 51, 2, -29, -9, -1, 20, 24, 54, 3, -10, 48, 11, -28, 0, -8, 3, 40, 0, -10, 8, -3, -6, -11, -24, -15, 24, 38, 5, -6, -5, -36, 7, 10, 1, 16, -18, 4, -28, -30, -33, -3, -18, 32, -12, 0, 27, 6, -8, -6, 20, -12, -19, -12, 9, -35, -24, -43, 8, -7, -11, -42, 0, -26, 20, 12, -3, 4, -4, -6, 19, 30, -15, 10, 8, -28, 0, -36, 15, -4, 2, -29, 6, -40, 4, 32, 3, 25, 9, -8, 30, -18, 12, -6, -30, -8, -9, 46, -4, -4, 9, -48, 16, 39, -33, -45, -4, 0, -18, 46, -34, 48, -5, -11, -4, -34, 30, 34, 17, -8, 12, 12, -8, 54, 12, -46, -21, 5, 10, 32, 2, 16, 12, -32, 2, -14, -36, -42, 0, 26, 4, -27, 13, -18, 8, 6, 54, 16, -10, -5, -8, 33, 36, 20, 24, 28, -4, 18, -4, -32, -35, 24, -19, 0, 18, -34, -24, 3, -12, 0, 8, 15, 18, -4, -12, -46, 3, 4, 3, 6, -8, -24, 28, 8, 3, 13, -33, -32, -2, 49, -14, -36, 45, 35, -5, 45, 24, 8, -6, 27, 0, -57, 10, 4, 20, -2, 6, -10, -4, 24, 6, -33, -4, 27, 14, -90, 36, -26, 12, -17, -3, -12, -5, 9, 34, -52, -15, 44, 8, -46, 8, 0, -42, -16, 14, -20, -6, 40, 36, -24, 6, 12, -32, 48, 3, 32, 9, 1, -15, -1, -8, 36, -6, -23, -8, 16, -20, -4, -16, 55, -14, 27, 0, 36, 0, -15, -33, 7, 6, -28, 40, -54, 8, 32, -30, 1, 15, -36, 18, -12, 12, 40, -9, 8, 9, 3, 12, -20, 7, -24, -22, 36, -20, 0, -4, -30, 18, 7, -8, 0, -4, 36, -4, 14, -6, -12, -16, -72, -16, -43, 1, 12, -6, 37, -10, 6, -24, -10, -6, 16, -20, -30, 8, 2, 0, -15, 36, -7, -51, -14, -36, 3, -22, -12, 0, -36, -15, -29, 6, 9, -4, 54, -12, 16, -48, 6, -12, 55, -23, -16, 38, 54, 3, 18, 35, 0, -4, 24, 25, 16, 3, -24, 22, 12, -21, 0, 3, 2, -8, -20, 20, -6, -9, -16, -16, -56, 81, 38, 18, -8, -10, 32, 4, 4, 30, -3, 0, 24, 14, 30, -11, 60, 3, -21, 7, 12, 12, -6, -8, -45, -9, -12, -40, -41, 6, -11, 16, 60, 12, 14, -6, -9, -2, -60, -14, 9, 42, -31, -8, -2, 3, 24, -18, 14, 42, 32, -42, -6, -10, -11, 12, -8, 1, -18, 36, 20, -18, -17, 28, -36, -30, 9, 24, -8, 4, 72, -15, -48, 0, 34, 8, -18, 8, -56, -13, 32, 9], 'weight': 2, 'weight_parity': 1}
  59. label: 61.2.a.b
    {'Nk2': 244, 'analytic_conductor': 0.4870874523298103, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[61, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [61, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 3, 'field_disc': 148, 'field_disc_factorization': [[2, 2], [37, 1]], 'field_poly': [1, -3, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [1, -3, -1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924989, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '61.2.a.b', 'level': 61, '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': [61], 'level_radical': 61, 'minimal_twist': '61.2.a.b', 'nf_label': '3.3.148.1', 'prim_orbit_index': 1, 'qexp_display': 'q+\\beta _{1}q^{2}+(1-\\beta _{1}-\\beta _{2})q^{3}+(\\beta _{1}+\\beta _{2})q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 3, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '61.2.a', 'trace_display': [1, 2, -1, -3], 'trace_hash': 303522873075009981, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.023', 'prec': 7}, {'__RealLiteral__': 0, 'data': '2.965', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.495', 'prec': 10}, {'__RealLiteral__': 0, 'data': '23.858', 'prec': 17}, {'__RealLiteral__': 0, 'data': '8.271', 'prec': 14}, {'__RealLiteral__': 0, 'data': '281.807', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.003', 'prec': 4}, 'traces': [3, 1, 2, 1, -1, -4, -3, 3, 3, -9, 13, -10, -9, -3, -2, -3, -2, 5, 0, 1, -8, 11, 5, -4, 4, 1, 8, 5, 4, 0, -2, -3, 4, 8, 11, -11, -6, 14, 6, 9, 3, -2, -14, 9, -21, -5, -4, 10, -10, -12, 0, -15, -2, 20, -13, 5, -32, 10, 29, 22, 3, -32, -19, -11, -17, -22, 9, -2, 8, 1, 14, -13, -1, 12, 12, 32, -15, 24, 13, -19, -1, -7, -8, 20, -18, 4, 4, 11, -4, 7, -7, -3, 28, 20, 4, 24, 10, -4, 17, -8, -10, 4, 12, -25, 24, -14, 26, 0, 13, -37, -36, -13, -9, -32, 7, 0, 23, -15, -8, 20, 30, 1, -22, -30, 21, -3, -18, -33, -8, 43, 8, -52, 18, -35, -40, -12, 3, -2, -3, -13, 12, 36, -35, 29, -20, -13, 16, 30, 9, 4, 3, 18, 18, -13, 34, 10, -10, -21, 8, 7, -3, -23, 10, 25, -8, 16, -32, 14, 20, 16, -36, -6, -10, -4, 0, -9, 44, 4, 42, 25, -20, 9, 2, 7, 6, 32, 0, -16, -28, -18, 31, 10, -20, 38, -38, -26, -29, 15, -50, 8, 40, -4, -14, -12, 39, 18, 1, 41, 14, 2, 22, -10, -20, 10, -14, -12, 4, 31, -14, -5, 26, -24, -11, -7, -4, -47, 11, 4, -9, -17, -34, -6, -40, -19, -56, -15, 56, 2, -38, -42, 7, 68, 6, 1, -18, -28, -36, 0, -48, 29, 38, 33, 15, 16, -20, 13, 2, 20, 24, 21, 24, -10, -28, -26, 18, 0, -36, -31, -10, -4, -2, 22, -20, -57, 4, -8, 4, 1, -6, -3, 28, 20, 34, 34, 68, -29, 29, 17, -31, -2, 12, 13, -2, 36, 15, 12, 52, 7, -19, 4, 4, 51, 16, -36, -1, -12, 7, 19, -24, 4, 15, -8, -30, -60, 39, -43, 58, 12, 26, 57, -28, -5, -4, -31, -20, -12, -10, 35, -32, 18, -13, 40, -42, 26, 39, -36, 26, -36, 10, 2, -40, -14, 9, -24, -4, 14, 32, -32, 14, -4, 16, -29, -15, -14, -38, 32, -16, -22, 14, -3, 39, -60, -28, 13, 39, -4, -38, -9, -61, 0, 6, 40, 24, 26, 6, -40, 8, -8, 18, -64, -20, 11, -37, -16, 45, 20, 6, -2, -34, -4, -12, -32, -8, -41, -1, -47, 6, -26, 68, -12, -28, 22, 2, -26, 15, -4, -12, -16, -2, -41, 50, 36, -29, 15, 8, 29, 4, 88, 50, -48, 2, 28, 68, 2, -20, -48, -3, 54, 48, 52, 2, 32, -44, 2, -24, 23, -14, -12, -44, 19, 34, -44, -4, 24, 24, 31, 18, 29, -29, 20, 5, -19, 4, -75, -5, 4, 90, 27, 32, 11, 6, -4, 36, 16, -24, -10, -21, -11, -5, 48, -4, 29, -52, 30, -28, 8, -10, -44, 22, -44, -18, 31, -14, 58, -78, -28, 20, 3, 84, 52, 8, 30, 16, -70, -77, -2, -16, -32, 45, 15, -84, 20, -22, 17, -18, -13, -16, 2, -58, 16, 27, 61, -8, 18, 0, 28, 4, 6, -4, -39, -58, -2, -19, 16, -12, -62, -32, 56, -54, 2, 29, -50, -73, -28, 34, 13, 68, 26, -44, 8, -8, -52, 24, -4, -39, -6, -31, -47, 3, -48, -4, 2, -35, 34, 72, -7, -40, 28, 62, 17, 4, 40, -22, -44, 75, 56, -7, 12, -1, 60, -46, -83, 72, -3, 20, -47, 8, -41, -32, 4, 32, -8, -22, 25, 27, 42, -22, 12, -88, -87, 10, -30, 12, 96, 4, -9, -12, 35, 45, 12, 15, 14, 1, -1, -78, 36, -46, -78, -32, -9, 84, -14, -2, 33, 86, 17, 46, -48, 0, 58, -4, 33, 32, 22, -63, 26, -160, -6, 0, 21, 23, -9, 52, 42, -30, 24, 74, 48, 18, 1, 46, -80, -6, 11, -12, 4, -1, -9, 101, 68, -20, -74, 54, -36, 36, -67, -53, 4, 62, 108, 12, 11, 32, 16, -50, -24, -2, 52, -76, -31, 13, -38, -10, -10, -24, 36, 40, 28, -50, -32, 92, -162, 106, 68, 67, 31, 10, 34, -2, -18, -68, -6, -79, 42, -9, -24, -42, -44, 8, 12, 34, -84, 96, -83, -84, 9, -12, -72, -40, -40, 57, 24, 28, 0, -25, -26, 4, 12, 38, -15, 6, 105, -82, -44, -12, -88, 52, -3, -9, -23, 28, -10, -17, 14, -60, 11, 1, 13, -13, -66, 24, 2, 63, 36, -23, -90, -56, -4, 18, -36, -38, 76, 72, -42, -103, 36, 1, -76, 30, -42, -88, 16, -21, -41, 10, -31, -87, 30, -62, 13, 4, 12, 34, -32, 60, -30, 84, -6, 72, -14, 92, 22, 48, 54, 114, -24, -38, -39, -4, -17, 37, -45, -9, 76, 0, -38, -17, 32, 60, 28, -60, -32, -17, 12, 21, 156, 32, -32, 55, 11, -45, 18, -32, 66, -50, 32, -4, -50, -15, -47, -52, 44, -38, 30, 52, -29, 60, -19, 49, 0, -72, -3, 28, 10, 0, 174, -72, 108, -6, -26, -63, -8, 12, -30, 108, -28, -40, -6, -16, 28, -24, -80, -5, -3, 96, 70, 67, 118, -50, -2, 80, -70, -64, -20, -34, -20, -14, 24, 31, 16, -35, 5, 90, -4, -35, 42, 48, 34, -120, -51, -19, -16, 93, -6, -44, 40, -18, 12, 4, -16, -27, 65, -44, 0, 18, 25, -12, -37, -36, -16, -16, 3, 16, 19, 76, -2, -30, -81, 34, 17, 50, -40, -16, 12, -2, -19, 18, -16, 64, 35, -76, -54, -38, 90, -36, 92, -24, -10, 3, -92, -68, -48, 20, 31, -56, 31, 5, -9, -60, 28, -20, 16, 13, -29, 52, -18, -77, -40, -49, -36, 8, -2, -8, 10, -63, -42, 12, 10, 7, 26, 63, -72, -62, 89, -28, -8, -58, 20, -36, 10, 2, 18, -5, 18, -36, -3, -6, 64, -12, 42, 29, 10, -70, 36, 43, -8, -76, -60, -32, 11, -88, 92, -12, -14, 14, 32, 6, -15, -24, 7], 'weight': 2, 'weight_parity': 1}
  60. label: 62.2.a.a
    {'Nk2': 248, 'analytic_conductor': 0.49507249253193836, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [31, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [62, 1, [3], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [0, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554494, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '62.2.a.a', 'level': 62, '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': [2, 31], 'level_radical': 62, 'minimal_twist': '62.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\\cdots', 'related_objects': ['EllipticCurve/Q/62/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '62.2.a', 'trace_display': [1, 0, -2, 0], 'trace_hash': 1208802814391652580, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.979', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.068', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.910', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.234', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.647', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.027', 'prec': 7}, 'traces': [1, 1, 0, 1, -2, 0, 0, 1, -3, -2, 0, 0, 2, 0, 0, 1, -6, -3, 4, -2, 0, 0, 8, 0, -1, 2, 0, 0, 2, 0, -1, 1, 0, -6, 0, -3, 10, 4, 0, -2, -6, 0, 8, 0, 6, 8, -8, 0, -7, -1, 0, 2, -6, 0, 0, 0, 0, 2, -12, 0, -6, -1, 0, 1, -4, 0, -12, -6, 0, 0, 8, -3, 10, 10, 0, 4, 0, 0, -8, -2, 9, -6, 8, 0, 12, 8, 0, 0, -6, 6, 0, 8, 0, -8, -8, 0, 2, -7, 0, -1, 14, 0, 8, 2, 0, -6, 20, 0, -2, 0, 0, 0, 2, 0, -16, 2, -6, -12, 0, 0, -11, -6, 0, -1, 12, 0, -8, 1, 0, -4, -12, 0, 0, -12, 0, -6, 2, 0, 0, 0, 0, 8, 0, -3, -4, 10, 0, 10, -2, 0, -16, 4, 18, 0, 2, 0, 14, -8, 0, -2, 0, 9, -4, -6, 0, 8, 8, 0, -9, 12, -12, 8, -2, 0, 0, 0, 0, -6, 16, 6, 2, 0, 0, 8, -20, 0, 0, -8, 0, -8, 24, 0, -14, 2, 0, -7, -6, 0, 24, -1, 0, 14, 0, 0, 12, 8, -24, 2, 0, 0, -4, -6, 0, 20, -16, 0, 0, -2, 0, 0, -12, 0, 8, 0, 3, 2, 12, 0, -22, -16, 0, 2, -6, -6, 16, -12, 0, 0, 8, 0, -22, -11, 0, -6, 14, 0, 8, -1, 0, 12, 8, 0, 0, -8, 0, 1, 2, 0, 0, -4, -6, -12, -16, 0, 12, 0, 0, -12, -6, 0, -8, -6, 0, 2, 0, 0, 10, 0, 3, 0, -6, 0, 4, 8, 0, 0, 0, -3, 19, -4, 0, 10, -10, 0, 24, 10, 0, -2, 16, 0, 0, -16, 0, 4, 12, 18, -20, 0, 0, 2, 8, 0, 34, 14, 0, -8, -10, 0, 0, -2, 0, 0, -24, 9, -2, -4, 0, -6, 0, 0, 32, 8, -30, 8, 24, 0, 18, -9, 0, 12, 0, -12, 0, 8, 0, -2, -24, 0, -26, 0, 0, 0, -14, 0, -16, -6, 0, 16, 16, 6, -3, 2, 0, 0, -20, 0, -32, 8, 18, -20, 0, 0, -26, 0, 0, -8, 4, 0, 20, -8, 0, 24, -24, 0, 0, -14, -24, 2, 10, 0, -48, -7, 0, -6, 16, 0, 6, 24, 0, -1, -6, 0, -2, 14, -18, 0, 0, 0, 34, 12, 0, 8, 0, -24, -16, 2, 0, 0, -4, 0, -18, -4, 24, -6, 6, 0, 0, 20, 0, -16, 8, 0, 26, 0, 0, -2, 32, 0, 32, 0, 21, -12, 28, 0, 12, 8, 0, 0, -6, 3, 0, 2, 0, 12, 0, 0, -14, -22, 0, -16, 42, 0, -32, 2, 0, -6, -20, -6, 0, 16, 0, -12, 0, 0, -4, 0, 18, 8, -32, 0, 20, -22, 0, -11, -4, 0, 32, -6, 0, 14, 0, 0, -12, 8, 0, -1, 0, 0, -24, 12, 0, 8, 24, 0, -28, 0, 0, -8, 10, 0, 0, 1, 0, 2, -16, 0, 0, 0, 0, -4, 10, -6, -16, -12, 0, -16, 6, 0, 41, 12, 36, 0, -12, 0, -40, -12, 0, -6, 0, 0, -34, -8, 0, -6, 4, 0, -20, 2, 18, 0, 8, 0, 0, 10, 0, 0, -14, 3, 16, 0, 0, -6, -12, 0, -4, 4, 0, 8, -46, 0, -8, 0, 0, 0, -8, -3, 18, 19, 0, -4, 0, 0, 0, 10, 12, -10, -16, 0, -4, 24, 0, 10, -30, 0, 0, -2, 0, 16, -32, 0, -6, 0, 36, -16, 22, 0, 16, 4, 0, 12, -16, 18, 2, -20, 0, 0, 42, 0, 40, 2, 0, 8, 0, 0, -19, 34, 0, 14, -60, 0, 0, -8, 0, -10, 16, 0, -14, 0, -24, -2, -22, 0, -8, 0, 0, -24, 16, 9, 0, -2, 0, -4, 6, 0, 24, -6, -30, 0, 36, 0, 22, 32, 0, 8, 0, -30, 16, 8, 0, 24, 0, 0, -6, 18, 0, -9, 42, 0, 0, 12, 0, 0, -28, -12, -4, 0, 0, 8, -12, 0, 36, -2, 0, -24, 0, 0, 36, -26, 0, 0, 30, 0, 40, 0, 0, -14, 0, 0, -46, -16, 24, -6, -8, 0, 0, 16, 0, 16, -16, 6, 0, -3, 0, 2, -2, 0, -8, 0, -27, -20, -48, 0, -26, -32, 0, 8, 0, 18, -8, -20, 0, 0, -16, 0, 4, -26, -24, 0, 0, 0, 8, -8, 0, 4, 32, 0, 2, 20, 0, -8, 34, 0, 0, 24, -36, -24, -24, 0, -30, 0, 0, -14, 34, -24, 1, 2, 0, 10, -24, 0, 0, -48, 0, -7, -28, 0, 40, -6, 0, 16, 0, 0, -12, 6, 0, 24, 18, 0, 48, -1, 18, -6, 0, 0, 0, -2, 0, 14, -30, -18, -28, 0, 0, 0, 8, 0, 32, 34, 0, 12, 26, 0, 48, 8, 0, 0, 8, -24, 10, -16, 0, 2, 42, 0, -16, 0, 0, -4, 0, 0, -25, -18, 0, -4, 18, 24, 0, -6, 0, 6, 80, 0, -34, 0, 24, 20, -54, 0, -32, -16, 0, 8, -24, 0, 4, 26, 0, 0, 0, 0, -24, -2, -6, 32, 0, 0, 22, 32, 0, 0, -14, 21, 56, -12, 0, 28, 0, 0, 0, 12, 0, 8, -32, 0, -32, 0, 0, -6, -2, 3, 36, 0, 0, 2, -4, 0, 36, 12, -42, 0, 0, 0, 0, -14, 0, -22, 0, 0, 8, -16, 0, 42, 16, 0, -10, -32, -24, 2, -38, 0, -28, -6, 0, -20, 0, -6, -22, 0, 0, 16, 18, 0, -48, -12, 0, 0, -16, 0, 20, -4, 0, 0, 34, 18, -48, 8, 0, -32, 0, 0, 1, 20, -60, -22, 28, 0, -32, -11, 0, -4, -20, 0, 0, 32, 0, -6, 18, 0, 0, 14, 6, 0, -16, 0, 12, -12, 0, 8, 64, 0, 32, -1, 0, 0, -48, 0, -26, -24, 0, 12], 'weight': 2, 'weight_parity': 1}
  61. label: 62.2.a.b
    {'Nk2': 248, 'analytic_conductor': 0.49507249253193836, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [31, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [62, 1, [3], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, 'field_disc': 12, 'field_disc_factorization': [[2, 2], [3, 1]], 'field_poly': [-3, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 12, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-2, -2, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924990, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '62.2.a.b', 'level': 62, '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': [2, 31], 'level_radical': 62, 'minimal_twist': '62.2.a.b', 'nf_label': '2.2.12.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}+(1+\\beta )q^{3}+q^{4}-2\\beta q^{5}+(-1+\\cdots)q^{6}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '62.2.a', 'trace_display': [-2, 2, 0, 4], 'trace_hash': 548104537926377346, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.028', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.945', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.327', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.250', 'prec': 14}, {'__RealLiteral__': 0, 'data': '3.642', 'prec': 14}, {'__RealLiteral__': 0, 'data': '61.789', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.027', 'prec': 7}, 'traces': [2, -2, 2, 2, 0, -2, 4, -2, 2, 0, -6, 2, -2, -4, -12, 2, 0, -2, -8, 0, 4, 6, 0, -2, 14, 2, 8, 4, -6, 12, 2, -2, 0, 0, 0, 2, 10, 8, -20, 0, 12, -4, -2, -6, -24, 0, 12, 2, -6, -14, 12, -2, 6, -8, -12, -4, -8, 6, -12, -12, -2, -2, 4, 2, 36, 0, 16, 0, 0, 0, 0, -2, -20, -10, 14, -8, -12, 20, 4, 0, 2, -12, 6, 4, -24, 2, 12, 6, 12, 24, -4, 0, 2, -12, 0, -2, 4, 6, 6, 14, 0, -12, 16, 2, -24, -6, -12, 8, -20, 12, 28, 4, 12, 8, 0, -6, -38, 12, 0, 12, 2, 2, 0, 2, 0, -4, 4, -2, 16, -36, -24, 0, -16, -16, 0, 0, 0, 0, -26, 0, 12, 0, -12, 2, -36, 20, -6, 10, 0, -14, 4, 8, 24, 12, 0, -20, 4, -4, 12, 0, 0, -2, 4, 12, 24, -6, -24, -4, 30, 24, -8, -2, 12, -12, 28, -6, 0, -12, 18, -24, 10, 4, -20, 0, -36, -2, 12, 12, 16, 0, 36, 2, 4, -4, 48, -6, 18, -6, -8, -14, 16, 0, -12, 12, 24, -16, 0, -2, 24, 24, 4, 6, -48, 12, -36, -8, 4, 20, -20, -12, -36, -28, -20, -4, 14, -12, 12, -8, 10, 0, 0, 6, 12, 38, 0, -12, -32, 0, -36, -12, -8, -2, -34, -2, 0, 0, 8, -2, -24, 0, -42, 4, 0, -4, -24, 2, -12, -16, 20, 36, 30, 24, -12, 0, -12, 16, 12, 16, 42, 0, 4, 0, -40, 0, -42, 0, 46, 26, 2, 0, 12, -12, 4, 0, 48, 12, 24, -2, -10, 36, 40, -20, -12, 6, -24, -10, -24, 0, 0, 14, -4, -4, 36, -8, 36, -24, 4, -12, 16, 0, 24, 20, -8, -4, -48, 4, -48, -12, 36, 0, 0, 0, 0, 2, -14, -4, -20, -12, 24, -24, -26, 6, 46, 24, 0, 4, 28, -30, 0, -24, -6, 8, -40, 2, 0, -12, -6, 12, 16, -28, -8, 6, -12, 0, 96, 12, 24, -18, -36, 24, -6, -10, -34, -4, 0, 20, -8, 0, -12, 36, 12, 2, 28, -12, -24, -12, -48, -16, 52, 0, -32, -36, -12, -2, -24, -4, 34, 4, 6, -48, 0, 6, -48, -18, 72, 6, -8, 8, -16, 14, 0, -16, -2, 0, 24, 12, -12, -12, 16, -24, -12, 16, -24, 0, 60, 2, -8, -24, -36, -24, -32, -4, 12, -6, 0, 48, -4, -12, 36, 36, -12, 8, -56, -4, 0, -20, 0, 20, -20, 12, -6, 36, 0, 28, 0, 20, 12, 4, 48, -14, -48, 12, 40, -12, 72, 8, -8, -10, 0, 0, 18, 0, 16, -6, -12, -12, 36, -38, 32, 0, 4, 12, 24, 32, -56, 0, 18, 36, 0, 12, -64, 8, 0, 2, -72, 34, 52, 2, -32, 0, 6, 0, 36, -8, 60, 2, 0, 24, -38, 0, -48, 42, 48, -4, -72, 0, 66, 4, -6, 24, -40, -2, -32, 12, 0, 16, -36, -20, -36, -36, 12, -30, -14, -24, 28, 12, 0, 0, -46, 12, 12, -16, 24, -12, -24, -16, -24, -42, 18, 0, -20, -4, 28, 0, 0, 40, 4, 0, -38, 42, 24, 0, 8, -46, -96, -26, -54, -2, -52, 0, -24, -12, 24, 12, 24, -4, 4, 0, 24, -48, -2, -12, 60, -24, 0, 2, 28, 10, 76, -36, 12, -40, -12, 20, 60, 12, -78, -6, -8, 24, 60, 10, 12, 24, -48, 0, -8, 0, 12, -14, 4, 4, 16, 4, 72, -36, 40, 8, 24, -36, -12, 24, 46, -4, -48, 12, 12, -16, -2, 0, 0, -24, 24, -20, -22, 8, 0, 4, 36, 48, -44, -4, 40, 48, 72, 12, 6, -36, -96, 0, 24, 0, 22, 0, -24, 0, -12, -2, 48, 14, 4, 4, 48, 20, 48, 12, -20, -24, 0, 24, -20, 26, -48, -6, 0, -46, 0, -24, -56, 0, -12, -4, 40, -28, 56, 30, -42, 0, 8, 24, 72, 6, 12, -8, 24, 40, 28, -2, -24, 0, -32, 12, 12, 6, -36, -12, -24, -16, 48, 28, -12, 8, -40, -6, -72, 12, 0, 0, 58, -96, -68, -12, 0, -24, -96, 18, -48, 36, -24, -24, 32, 6, -44, 10, -42, 34, 16, 4, -46, 0, 36, -20, 64, 8, 36, 0, -48, 12, 22, -36, 80, -12, 12, -2, -24, -28, -54, 12, -24, 24, 4, 12, -48, 48, -72, 16, -26, -52, 0, 0, 72, 32, -40, 36, -24, 12, -24, 2, 52, 24, -60, 4, -30, -34, 14, -4, 56, -6, -48, 48, -48, 0, -24, -6, 0, 48, 70, 18, -48, -72, 24, -6, 56, 8, -48, -8, 18, 16, 0, -14, 12, 0, 60, 16, 0, 2, 12, 0, 24, -24, 4, -12, 40, 12, 72, 12, 8, -16, -76, 24, -6, 12, 52, -16, 0, 24, 6, 0, -86, -60, 28, -2, 0, 8, 48, 24, 8, 36, -60, 24, 14, 32, 12, 4, -72, -12, 4, 6, -32, 0, 0, -48, 40, 4, 96, 12, -60, -36, -14, -36, 0, 12, -60, -8, 96, 56, -10, 4, -48, 0, -16, 20, 76, 0, 0, -20, 40, 20, -36, -12, 60, 6, -50, -36, 48, 0, -36, -28, 8, 0, -18, -20, -48, -12, 84, -4, 0, -48, -6, 14, 12, 48, 32, -12, -36, -40, 52, 12, 72, -72, -48, -8, -48, 8, 48, 10, -48, 0, 40, 0, 40, -18, 144, 0, 70, -16, 16, 6, 0, 12, 24, 12, 96, -36, 72, 38, -20, -32, 28, 0, -42, -4, 0, -12, 0, -24, -30, -32, 20, 56, -36, 0, -24, -18, -48, -36, -36, 0, 0, -12, 2, 64, 12, -8, -144, 0, -92, -2, -48, 72, 48, -34, -52, -52, -140, -2, 84, 32, -36, 0, -20, -6, 60, 0, -84, -36, 24, 8, 0, -60, -8, -2, -8, 0, 0, -24, 4, 38, 40, 0], 'weight': 2, 'weight_parity': 1}
  62. label: 63.2.a.a
    {'Nk2': 252, 'analytic_conductor': 0.5030575327340664, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1], [7, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [63, 1, [29, 10], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554495, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': False, 'label': '63.2.a.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': '21.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{4}+2q^{5}-q^{7}-3q^{8}+2q^{10}+\\cdots', 'related_objects': ['EllipticCurve/Q/63/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '63.2.a', 'trace_display': [1, 0, 2, -1], 'trace_hash': 2278490076300767204, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.010', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.978', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.037', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.908', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.095', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.694', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.015', 'prec': 7}, 'traces': [1, 1, 0, -1, 2, 0, -1, -3, 0, 2, -4, 0, -2, -1, 0, -1, 6, 0, 4, -2, 0, -4, 0, 0, -1, -2, 0, 1, 2, 0, 0, 5, 0, 6, -2, 0, 6, 4, 0, -6, -2, 0, -4, 4, 0, 0, 0, 0, 1, -1, 0, 2, -6, 0, -8, 3, 0, 2, -12, 0, -2, 0, 0, 7, -4, 0, 4, -6, 0, -2, 0, 0, -6, 6, 0, -4, 4, 0, -16, -2, 0, -2, 12, 0, 12, -4, 0, 12, 14, 0, 2, 0, 0, 0, 8, 0, 18, 1, 0, 1, -14, 0, 8, 6, 0, -6, -4, 0, -18, -8, 0, 1, 14, 0, 0, -2, 0, -12, -6, 0, 5, -2, 0, 0, -12, 0, 0, -3, 0, -4, -4, 0, -4, 4, 0, -18, 6, 0, 12, 2, 0, 0, 8, 0, 4, -6, 0, -6, -6, 0, 8, -12, 0, 4, 0, 0, -2, -16, 0, 10, 0, 0, 4, 2, 0, 12, 8, 0, -9, 12, 0, 4, 10, 0, 1, 4, 0, 14, 4, 0, -26, 2, 0, 0, 12, 0, -24, 0, 0, 8, 8, 0, 2, 18, 0, -1, -22, 0, 24, 3, 0, -14, -2, 0, -4, 8, 0, 2, -16, 0, 4, 6, 0, -4, -8, 0, 0, -18, 0, 8, -12, 0, 16, -5, 0, 14, 12, 0, -10, 0, 0, -6, 6, 0, 0, 12, 0, -6, -24, 0, 2, 5, 0, 2, 2, 0, -8, 0, 0, -12, 20, 0, 0, 0, 0, -17, -26, 0, -6, 4, 0, -4, -16, 0, -12, -4, 0, -4, -6, 0, 16, -6, 0, 6, 4, 0, 22, 12, 0, 6, 22, 0, -20, 0, 0, 8, 2, 0, 19, 4, 0, 6, -14, 0, -24, -18, 0, -6, 0, 0, 4, 8, 0, -4, -4, 0, 4, -4, 0, 0, 24, 0, 26, -2, 0, 16, 18, 0, -8, 14, 0, 0, 24, 0, 2, 4, 0, 6, 0, 0, -4, -12, 0, 8, 8, 0, -14, -9, 0, -12, 0, 0, -1, 12, 0, 10, 28, 0, -2, 1, 0, -20, -10, 0, 0, -14, 0, 4, -32, 0, -3, -26, 0, -2, -12, 0, 0, 0, 0, 12, 6, 0, -10, -24, 0, 0, -4, 0, 12, -8, 0, 8, 0, 0, 8, 2, 0, -18, -6, 0, 0, -3, 0, -22, -32, 0, -18, 24, 0, 1, 30, 0, 0, 14, 0, -2, -24, 0, -22, -4, 0, -8, 12, 0, 24, -10, 0, -16, 12, 0, 38, 4, 0, 18, -6, 0, 2, 4, 0, -8, 24, 0, -14, 0, 0, 18, 0, 0, -24, 24, 0, -12, -36, 0, 28, 16, 0, -7, 30, 0, 8, -14, 0, 12, 4, 0, 10, -10, 0, 0, 10, 0, 16, -2, 0, 6, -36, 0, -4, 0, 0, 36, 16, 0, -4, 6, 0, -24, 16, 0, -12, 2, 0, -5, 36, 0, -8, 6, 0, 2, -20, 0, 12, -8, 0, 0, 0, 0, 4, 12, 0, 20, -24, 0, -28, 0, 0, 0, 10, 0, 6, -11, 0, -26, 16, 0, 0, -6, 0, 12, -18, 0, -20, 4, 0, -16, 0, 0, -23, -12, 0, 4, 4, 0, -8, -12, 0, -6, -4, 0, -34, 16, 0, 30, -36, 0, 4, -6, 0, 4, 8, 0, 16, 22, 0, -12, 2, 0, 8, 2, 0, 22, -4, 0, 28, -20, 0, 0, -10, 0, -4, -8, 0, 2, 0, 0, 34, 19, 0, -4, -12, 0, 24, 18, 0, -14, -28, 0, 0, -24, 0, -6, 6, 0, -12, 6, 0, 0, -48, 0, -6, 4, 0, -8, 10, 0, -16, 20, 0, -4, 0, 0, -26, 4, 0, -12, 6, 0, -20, 0, 0, 24, -14, 0, -19, 26, 0, 2, 36, 0, -40, 48, 0, 18, 0, 0, -2, -8, 0, -6, -18, 0, 20, 0, 0, 24, 40, 0, 48, 2, 0, -4, 18, 0, -8, 2, 0, 0, -12, 0, 22, -4, 0, -36, -8, 0, 0, -8, 0, 8, 8, 0, 34, -14, 0, 9, 18, 0, -18, -36, 0, 0, 12, 0, 12, -1, 0, 4, 12, 0, 20, -10, 0, 28, 24, 0, -12, -2, 0, -1, -30, 0, 24, -28, 0, -10, 14, 0, 6, 0, 0, -42, 0, 0, 16, -4, 0, -32, 48, 0, -8, -3, 0, 26, -2, 0, -40, -6, 0, -12, -24, 0, -18, 0, 0, 0, -16, 0, 36, -12, 0, 6, 0, 0, -12, -10, 0, 24, 4, 0, -32, 0, 0, -4, 16, 0, -10, 12, 0, -24, -18, 0, 18, -8, 0, 0, 24, 0, 2, 8, 0, -2, -14, 0, 0, -54, 0, -6, -8, 0, 0, 0, 0, -1, -4, 0, -44, 22, 0, -32, -14, 0, 4, -18, 0, -24, 26, 0, 0, -5, 0, 30, 24, 0, 0, 0, 0, 42, -42, 0, 44, 2, 0, -24, 8, 0, -16, -22, 0, 4, -38, 0, 24, -24, 0, 12, 12, 0, 14, 24, 0, -14, 6, 0, 16, 16, 0, 12, 8, 0, -25, 38, 0, -4, -18, 0, -5, 6, 0, -6, 0, 0, -10, 2, 0, 12, 14, 0, 44, 8, 0, 24, 24, 0, 20, -14, 0, 0, 64, 0, -8, 54, 0, 0, 12, 0, 46, -24, 0, 8, 6, 0, -28, 12, 0, -36, -8, 0, 0, 28, 0, -16, 0, 0, 8, 3, 0, 30, 0, 0, -36, 8, 0, -42, -52, 0, -4, -12, 0, 4, 24, 0, -48, 10, 0, 10, 4, 0, 8, 0, 0, 10, 0, 0, -6, 16, 0, 10, -26, 0, 4, -6, 0, -36, -48, 0, 42, -4, 0, 0, -38, 0, 0, 12, 0, 16, -44, 0, 12, -4, 0, 18, -26, 0, 16, 24, 0, 16, -6, 0, -31, -12, 0, -2, 4, 0, 40, -15, 0, 36, -12, 0, -12, -8, 0, 2, 30, 0, -56, -2, 0, -20, -24, 0, -44, 12, 0, 8, 0, 0, -16, 0, 0, 0, 48, 0, -26, 4, 0, 36], 'weight': 2, 'weight_parity': 1}
  63. label: 63.2.a.b
    {'Nk2': 252, 'analytic_conductor': 0.5030575327340664, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, 1], [7, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [63, 1, [29, 10], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, 'field_disc': 12, 'field_disc_factorization': [[2, 2], [3, 1]], 'field_poly': [-3, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 12, 'fricke_eigenval': -1, 'has_non_self_twist': 1, 'hecke_cutters': [[2, [-3, 0, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924991, '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, 3, 2, -1, 2, 0]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '63.2.a.b', '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': '63.2.a.b', 'nf_label': '2.2.12.1', 'prim_orbit_index': 1, 'qexp_display': 'q+\\beta q^{2}+q^{4}-2\\beta q^{5}+q^{7}-\\beta q^{8}+\\cdots', 'related_objects': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/441.2/a', 'EllipticCurve/2.0.3.1/441.2/a', 'Genus2Curve/Q/3969/d', 'EllipticCurve/2.0.3.1/441.2/a'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '63.2.a', 'trace_display': [0, 0, 0, 2], 'trace_hash': 2292748438181998889, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.027', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.906', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.295', 'prec': 10}, {'__RealLiteral__': 0, 'data': '15.011', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.879', 'prec': 14}, {'__RealLiteral__': 0, 'data': '148.875', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.509', 'prec': 10}, 'traces': [2, 0, 0, 2, 0, 0, 2, 0, 0, -12, 0, 0, 4, 0, 0, -10, 0, 0, -8, 0, 0, 12, 0, 0, 14, 0, 0, 2, 0, 0, -8, 0, 0, 12, 0, 0, 4, 0, 0, 12, 0, 0, -8, 0, 0, -12, 0, 0, 2, 0, 0, 4, 0, 0, -24, 0, 0, 0, 0, 0, -20, 0, 0, 2, 0, 0, -8, 0, 0, -12, 0, 0, 28, 0, 0, -8, 0, 0, 16, 0, 0, 36, 0, 0, -24, 0, 0, -12, 0, 0, 4, 0, 0, 24, 0, 0, 28, 0, 0, 14, 0, 0, -8, 0, 0, -24, 0, 0, 4, 0, 0, -10, 0, 0, 24, 0, 0, -24, 0, 0, 2, 0, 0, -8, 0, 0, 16, 0, 0, -24, 0, 0, -8, 0, 0, -12, 0, 0, -32, 0, 0, -36, 0, 0, 0, 0, 0, 4, 0, 0, 16, 0, 0, 12, 0, 0, -20, 0, 0, 36, 0, 0, 40, 0, 0, 0, 0, 0, -18, 0, 0, -8, 0, 0, 14, 0, 0, -12, 0, 0, 4, 0, 0, 12, 0, 0, 24, 0, 0, 48, 0, 0, 28, 0, 0, 2, 0, 0, -32, 0, 0, 12, 0, 0, -72, 0, 0, -20, 0, 0, 40, 0, 0, 60, 0, 0, -8, 0, 0, -24, 0, 0, 16, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, -48, 0, 0, 12, 0, 0, -20, 0, 0, -20, 0, 0, -16, 0, 0, -24, 0, 0, -24, 0, 0, 38, 0, 0, 4, 0, 0, -48, 0, 0, 48, 0, 0, -8, 0, 0, 40, 0, 0, -24, 0, 0, -20, 0, 0, 12, 0, 0, -8, 0, 0, 24, 0, 0, -10, 0, 0, 28, 0, 0, 48, 0, 0, 24, 0, 0, -8, 0, 0, 40, 0, 0, -56, 0, 0, 48, 0, 0, 4, 0, 0, 16, 0, 0, 0, 0, 0, -12, 0, 0, 28, 0, 0, -36, 0, 0, 40, 0, 0, -72, 0, 0, 28, 0, 0, -24, 0, 0, 2, 0, 0, 60, 0, 0, 28, 0, 0, -36, 0, 0, 72, 0, 0, -60, 0, 0, -6, 0, 0, 4, 0, 0, -32, 0, 0, -24, 0, 0, -20, 0, 0, -24, 0, 0, -56, 0, 0, -84, 0, 0, -24, 0, 0, 28, 0, 0, -24, 0, 0, 72, 0, 0, 76, 0, 0, -70, 0, 0, -16, 0, 0, 0, 0, 0, 28, 0, 0, -8, 0, 0, 0, 0, 0, -48, 0, 0, -20, 0, 0, 24, 0, 0, -20, 0, 0, 48, 0, 0, 52, 0, 0, 4, 0, 0, -32, 0, 0, 24, 0, 0, 24, 0, 0, 2, 0, 0, 72, 0, 0, -24, 0, 0, -20, 0, 0, 24, 0, 0, 64, 0, 0, 24, 0, 0, -8, 0, 0, 24, 0, 0, -56, 0, 0, 36, 0, 0, 8, 0, 0, 2, 0, 0, -80, 0, 0, -12, 0, 0, 0, 0, 0, 40, 0, 0, -8, 0, 0, 72, 0, 0, -24, 0, 0, 16, 0, 0, 28, 0, 0, -12, 0, 0, 48, 0, 0, 24, 0, 0, -32, 0, 0, -60, 0, 0, -22, 0, 0, -8, 0, 0, -120, 0, 0, -60, 0, 0, 28, 0, 0, -36, 0, 0, -8, 0, 0, 84, 0, 0, 16, 0, 0, -32, 0, 0, -16, 0, 0, -72, 0, 0, 0, 0, 0, 36, 0, 0, -56, 0, 0, 36, 0, 0, 4, 0, 0, 0, 0, 0, -48, 0, 0, -36, 0, 0, 32, 0, 0, -20, 0, 0, -24, 0, 0, -24, 0, 0, -44, 0, 0, 16, 0, 0, 16, 0, 0, 120, 0, 0, 76, 0, 0, -12, 0, 0, 16, 0, 0, 120, 0, 0, -22, 0, 0, -20, 0, 0, 16, 0, 0, 24, 0, 0, 4, 0, 0, -84, 0, 0, 40, 0, 0, -48, 0, 0, -48, 0, 0, 40, 0, 0, 96, 0, 0, 24, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, -20, 0, 0, -18, 0, 0, 28, 0, 0, -48, 0, 0, 48, 0, 0, 40, 0, 0, 16, 0, 0, -60, 0, 0, 72, 0, 0, 14, 0, 0, -16, 0, 0, 12, 0, 0, 52, 0, 0, 12, 0, 0, -48, 0, 0, -84, 0, 0, -8, 0, 0, 4, 0, 0, -8, 0, 0, -168, 0, 0, -44, 0, 0, 36, 0, 0, 40, 0, 0, -24, 0, 0, -48, 0, 0, 24, 0, 0, 16, 0, 0, 0, 0, 0, 52, 0, 0, -48, 0, 0, 4, 0, 0, -48, 0, 0, -44, 0, 0, 28, 0, 0, -56, 0, 0, 48, 0, 0, -72, 0, 0, -10, 0, 0, 64, 0, 0, -96, 0, 0, -40, 0, 0, -32, 0, 0, 48, 0, 0, 24, 0, 0, 24, 0, 0, -12, 0, 0, -32, 0, 0, 24, 0, 0, 32, 0, 0, -72, 0, 0, 64, 0, 0, -24, 0, 0, 100, 0, 0, 4, 0, 0, 144, 0, 0, 72, 0, 0, -58, 0, 0, 40, 0, 0, 2, 0, 0, 84, 0, 0, -20, 0, 0, -60, 0, 0, -8, 0, 0, 12, 0, 0, -120, 0, 0, -8, 0, 0, -16, 0, 0, 48, 0, 0, 28, 0, 0, 120, 0, 0, -104, 0, 0, -12, 0, 0, 16, 0, 0, 16, 0, 0, 120, 0, 0, 144, 0, 0, -48, 0, 0, 0, 0, 0, -56, 0, 0, -24, 0, 0, 0, 0, 0, -44, 0, 0, -32, 0, 0, 108, 0, 0, 28, 0, 0, 0, 0, 0, -8, 0, 0, 24, 0, 0, -92, 0, 0, -48, 0, 0, -72, 0, 0, -48, 0, 0, 56, 0, 0, -12, 0, 0, 168, 0, 0, -24, 0, 0, -30, 0, 0, -20, 0, 0, -32, 0, 0, -168, 0, 0, -32, 0, 0, 100, 0, 0, -24, 0, 0, 36, 0, 0, -144, 0, 0, -16, 0, 0, 112, 0, 0, -36, 0, 0, -20, 0, 0, 24], 'weight': 2, 'weight_parity': 1}
  64. label: 64.2.a.a
    {'Nk2': 256, 'analytic_conductor': 0.5110425729361945, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': False, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [64, 1, [63, 5], [1, 1]], 'cm_discs': [-4], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554496, '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, 4, 2, -1, 2, -4]], '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': False, 'label': '64.2.a.a', 'level': 64, 'level_is_powerful': True, 'level_is_prime': False, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': True, 'level_is_squarefree': False, 'level_primes': [2], 'level_radical': 2, 'minimal_twist': '32.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+2q^{5}-3q^{9}-6q^{13}+2q^{17}-q^{25}+\\cdots', 'related_objects': ['EllipticCurve/Q/64/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.1.d1', 'self_twist_discs': [-4], 'self_twist_type': 1, 'space_label': '64.2.a', 'trace_display': [0, 0, 2, 0], 'trace_hash': 439256381361310617, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.019', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.974', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.055', 'prec': 7}, {'__RealLiteral__': 0, 'data': '2.892', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.204', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.568', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.505', 'prec': 10}, 'traces': [1, 0, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, -6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 10, 0, 0, 0, -6, 0, 0, 0, -7, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 4, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -14, 0, 0, 0, 18, 0, 0, 0, -11, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, -14, 0, 0, 0, -6, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 3, 0, 0, 0, -30, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -30, 0, 0, 0, -28, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -13, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0, -12, 0, 0, 0, -30, 0, 0, 0, -14, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, -38, 0, 0, 0, 2, 0, 0, 0, 18, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 20, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, -38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, -12, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, -23, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, -12, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, -38, 0, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 18, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -46, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -27, 0, 0, 0, -54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, -38, 0, 0, 0, -12, 0, 0, 0, 50, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, -22, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, -54, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 71, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, -46, 0, 0, 0, 58, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, -54, 0, 0, 0, 58, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 36, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -46, 0, 0, 0, 0, 0, 0, 0, -38, 0, 0, 0, 58, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, -31, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -62, 0, 0, 0, 18, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -62, 0, 0, 0], 'weight': 2, 'weight_parity': 1}
  65. label: 65.2.a.a
    {'Nk2': 260, 'analytic_conductor': 0.5190276131383225, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[5, 1], [13, 1]], 'atkin_lehner_string': '++', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [65, 1, [27, 41], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554497, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '65.2.a.a', 'level': 65, '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, 13], 'level_radical': 65, 'minimal_twist': '65.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}-4q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/65/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '65.2.a', 'trace_display': [-1, -2, -1, -4], 'trace_hash': 1364169308829084149, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.996', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.965', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.794', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.005', 'prec': 4}, 'traces': [1, -1, -2, -1, -1, 2, -4, 3, 1, 1, 2, 2, -1, 4, 2, -1, 2, -1, -6, 1, 8, -2, -6, -6, 1, 1, 4, 4, 2, -2, -10, -5, -4, -2, 4, -1, -2, 6, 2, -3, -6, -8, 10, -2, -1, 6, 4, 2, 9, -1, -4, 1, 2, -4, -2, -12, 12, -2, 6, -2, 2, 10, -4, 7, 1, 4, -4, -2, 12, -4, 6, 3, -6, 2, -2, 6, -8, -2, -12, 1, -11, 6, -16, -8, -2, -10, -4, 6, 2, 1, 4, 6, 20, -4, 6, 10, -2, -9, 2, -1, -18, 4, 2, -3, -8, -2, 10, -4, 10, 2, 4, 4, -14, -12, 6, -2, -1, -6, -8, 6, -7, -2, 12, 10, -1, 4, -2, 3, -20, -1, 20, 4, 24, 4, -4, 6, -2, -12, 0, -4, -8, -6, -2, -1, -2, 6, -18, 2, 18, 2, 10, -18, 2, 8, 10, -2, -6, 12, -4, 5, 24, 11, -12, 6, 4, 16, -12, 24, 1, 2, -6, -10, -6, 4, -4, -2, -12, -2, 12, 1, -22, -4, -4, -18, 2, -20, 4, -4, -16, -6, 0, -14, -2, 2, -2, -9, -6, -2, -16, 3, 8, 18, -8, 4, 6, -2, -6, 1, -12, 8, 12, -2, -12, -10, -10, 12, 40, -10, 12, 2, -2, -4, 4, 20, 1, 14, 4, -12, -22, -6, 16, 6, 10, 1, -4, -6, 24, 8, -6, -2, 10, 7, 10, -2, -9, -12, 6, -30, 32, 1, 24, 4, -12, 2, 4, -17, 2, 20, 8, -1, 2, -20, 14, -12, -2, -24, -4, 4, 6, 4, 2, -2, -8, 2, 2, -12, -14, 0, -10, 12, -6, 8, 2, -6, -12, 2, 24, -5, -13, 2, 4, 6, 22, 18, -6, -6, 8, -18, 6, 2, -40, -10, 36, 6, -2, -2, 8, 8, -4, -10, -4, 6, -22, 6, 4, 12, -18, 4, 4, -7, -20, -24, -12, 11, -1, 12, -20, -18, -16, -4, -18, 16, -2, 12, 4, -8, 26, -1, 28, 2, -20, 6, -8, 30, -12, 6, -22, 4, -30, 4, -4, -10, 18, 12, -6, -2, 16, -12, -10, -3, 17, 22, 14, -4, 6, 4, -14, 6, -6, -2, -8, -20, 34, -4, 2, 12, -2, 16, 10, -6, 4, 0, 12, -6, 8, 2, 10, 2, -10, 2, -12, 27, -40, 6, 12, -2, 6, 16, -48, -1, 10, -8, 10, 18, 11, 8, -4, -12, 18, -6, 4, -2, -24, 6, 16, 5, 0, 12, -40, 8, 10, -12, 4, 6, 2, 12, -8, -10, 4, 10, 14, -4, 10, -40, 4, -10, 36, -12, 0, -6, 9, 2, 14, -4, -2, -4, -36, -28, -6, -1, -12, 14, -20, -4, -4, 36, 38, 22, 8, -6, 10, -16, -24, -2, -20, -10, -10, 1, 16, 4, 12, 18, 20, -24, -6, 8, 2, 6, 30, -10, 2, -10, -48, 7, 2, -10, -40, 6, 24, 9, -24, -12, 4, -6, -2, 10, -24, -32, 10, 1, 24, -24, -18, -12, 18, 12, -2, 2, -6, -4, 24, 11, -24, -2, -2, 20, 8, -8, 12, 3, 6, -2, 6, -20, 8, -14, -20, 4, 13, 2, 6, -24, 6, 4, -10, -12, -24, -6, 18, 4, -22, -2, 44, -10, -10, 8, -6, 2, 2, -2, -12, 36, 48, 14, -4, 0, -26, 10, -10, -4, -8, 6, -22, 8, 14, -2, 44, 18, -26, 12, 24, 2, 0, -24, -6, 7, 2, 13, 4, 2, 64, -4, 4, -18, 1, -22, -44, 18, 60, 6, 12, 2, 14, -8, 8, -18, 32, -6, -4, -6, 10, 40, -4, -10, 7, -36, 34, 30, 16, 2, -4, -2, -6, -8, -12, -24, -42, 4, -2, -10, -24, 4, -8, -2, 1, 22, 24, 6, -4, -4, -14, -36, -24, 18, 2, 4, -9, -4, 6, -3, -46, 20, -16, -24, 20, 12, 38, -33, 12, 1, -80, 12, -6, 20, -20, 6, -6, 16, 0, -4, 2, 18, 4, -48, -24, 2, -12, 12, -8, -4, 4, -40, -30, -26, 4, -1, -6, -28, 8, -6, -8, 20, -20, 6, 2, 8, 44, -10, -2, 12, 22, 6, -8, 22, 0, -12, -12, 30, -20, 4, -26, 4, 12, 14, 8, -18, 72, 12, 10, 6, -12, 6, 60, -16, 2, -12, 12, 10, -32, 1, -8, -17, -20, 22, 2, -14, -18, 12, 13, -6, 20, 4, 34, 14, 18, 30, -8, 6, 6, -2, -12, 8, -12, 60, -18, -34, -16, -4, -40, -2, -28, -4, -48, 2, -10, 16, 2, -10, 24, 18, 18, -4, -40, 0, -2, -12, -6, 34, 26, -8, -4, 2, -2, -10, -10, -6, -16, 10, 36, 2, 12, 12, 8, -9, 6, 40, 8, 6, -28, -12, 56, 6, -2, -6, 4, 16, 42, 48, 8, -5, 2, -10, -12, -8, -24, -10, -12, -54, -2, -11, -42, 8, -4, 4, 12, 4, -60, -18, 4, -6, 50, -4, -46, 6, -4, 24, -32, 6, 34, -16, 28, -7, 18, 0, 12, 12, -40, 40, 38, -24, -25, -10, 12, -12, -1, -4, 28, -2, -4, -2, 12, 12, 6, 8, 6, 30, 18, -4, 40, 10, -48, -14, 12, -20, 6, -10, 26, -40, -24, -4, 4, 30, -2, -36, 4, -12, 18, 0, -44, 2, 38, -9, -22, 2, 12, -14, 58, 12, 8, 2, -22, -4, -24, 36, -12, -12, -12, 6, -20, -1, 4, 12, 80, -42, 22, 20, -34, -4, -18, 4, -48, -12, -32, -38, 4, 22, -80, -8, -52, 18, -16, -10, -6, -16, -2, 24, 2, -10, -38, 20, -54, -10, 8, 10, -4, -3, -30, -16, 44, 4, 18, -12, 36, -6, 16, -20, 24, -24, 6, 6, 36, -24, 18, -2, 0, 6, -8, -30, 8, 14, 69, -2, 10, -10, 2, 48, -8, -21, 24, -2, -28, -10, 0, 40, 2, -2, 18, -24, 4, 9, 10, 24, 56, 36, 6, -4, 32, -6, -60, 2, 48, 50, 36, 24, 16, -32, -22, -10, -8, -3], 'weight': 2, 'weight_parity': 1}
  66. label: 65.2.a.b
    {'Nk2': 260, 'analytic_conductor': 0.5190276131383225, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[5, -1], [13, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [65, 1, [27, 41], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 2, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924993, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '65.2.a.b', 'level': 65, '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, 13], 'level_radical': 65, 'minimal_twist': '65.2.a.b', 'nf_label': '2.2.8.1', 'prim_orbit_index': 1, 'qexp_display': 'q+(-1+\\beta )q^{2}+\\beta q^{3}+(1-2\\beta )q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '65.2.a', 'trace_display': [-2, 0, 2, 4], 'trace_hash': 1916806337191425823, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.905', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.020', 'prec': 7}, {'__RealLiteral__': 0, 'data': '9.086', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.142', 'prec': 10}, {'__RealLiteral__': 0, 'data': '60.780', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.026', 'prec': 7}, 'traces': [2, -2, 0, 2, 2, 4, 4, -6, -2, -2, 4, -8, -2, -12, 0, 6, -4, 2, 4, 2, -8, -8, 0, 4, 2, 2, 0, 20, 0, 4, 12, 6, -4, -4, 4, -2, 0, 0, 0, -6, -12, 16, -8, 12, -2, -4, -4, 0, 10, -2, -8, -2, -12, -16, 4, -20, 4, 16, 12, -8, -16, 0, -4, -14, -2, 12, -4, 12, -4, -12, 4, 6, 0, 24, 0, -4, 16, -4, 0, 6, -10, 4, -12, -24, -4, 28, 16, -16, 12, 2, -4, 8, 12, 12, 4, 4, -4, -42, -4, 2, 4, 0, 32, 6, -8, -12, -16, 32, -4, -8, 24, 12, -12, 4, 0, -32, 2, 0, 8, 4, -10, 16, -8, -12, 2, 12, -16, 10, 20, 2, 0, -20, 0, 4, 0, 4, -12, 4, -8, 20, 8, -32, -4, -6, 0, -24, -32, -48, -12, 4, 28, -8, 4, -40, 12, 8, 36, 24, -24, 6, 8, 10, 4, 4, -4, 4, -12, 32, 2, -4, -4, -48, 28, -16, 4, 12, 12, -12, 0, -2, 0, 12, 0, -4, 0, 12, 0, -20, 32, 0, 16, 8, 20, 20, 0, 74, -12, 8, 8, -6, 0, 12, -32, 8, -12, -28, 0, -6, 4, 16, -16, 36, -28, 20, -8, -16, 0, 4, -24, 12, 4, -24, 36, 4, -2, 20, -44, -12, -4, -4, -24, 16, 4, -2, -4, -12, 24, -8, -4, 0, -12, -6, 0, -16, 10, -16, -4, -24, -8, -2, 0, -20, 4, 12, -8, -26, 44, -36, -48, -2, 0, 48, -24, 20, -12, -8, 0, -4, -28, -16, 28, -12, 8, 44, 4, -4, -20, -16, -12, -20, 4, -16, -8, 60, 4, 8, -8, -6, -10, 16, 16, 48, 24, 52, 12, 24, 16, 28, 0, -8, -56, -16, 16, 12, -16, 4, 44, 64, 4, 0, 0, -4, -4, -36, -4, -48, 24, 0, -16, -14, 4, -16, -16, -10, -2, -52, 0, 28, -24, 12, -4, 4, 0, 4, -4, -24, 20, -2, 8, 12, 12, 0, 56, 44, -4, -36, 0, 16, 20, -12, 0, 8, 24, 12, 4, 12, 0, -16, -36, 6, -26, 0, -16, -20, 0, -32, 40, 0, 12, 24, 24, -36, -28, -8, 0, 20, 0, -64, 44, -4, -4, 0, 4, -44, 16, -4, 8, -36, 12, -4, 8, -62, 48, -36, 0, -12, -16, -8, -8, 6, 12, -8, -12, -28, -10, 64, -24, 16, 20, 4, 32, 24, 0, 4, -12, -6, -24, -4, 16, -24, -36, -16, 4, 12, -4, 36, -32, -24, 4, 28, 44, 0, 4, -24, 16, -4, -4, 24, -32, -16, -10, 4, -16, 24, 12, -12, 16, -44, -4, 2, -16, -28, 12, 28, -4, -4, -36, 12, 32, 8, 36, 56, -20, 0, 12, 60, -24, 2, -8, 12, 0, -24, -36, -24, 4, 8, 12, 8, -36, 4, 0, 36, -8, 22, -4, 28, 12, 48, -48, -42, 16, 40, -32, 0, -4, 36, 64, -16, 52, 2, -8, -56, 56, 20, 4, -12, 0, -8, 20, 0, 48, 54, -16, -60, 32, 52, -16, 96, -8, 6, -24, -16, -48, -96, -8, 20, -48, -12, -42, -12, -12, 16, 12, 24, -16, 12, -16, 60, 52, 32, -20, -64, 0, -20, -4, -16, -16, -76, 16, -8, 16, 12, -48, 28, 24, 40, -32, 0, 8, 12, -8, -60, -24, 24, -12, 44, -20, -40, -32, 4, -40, -12, 16, 40, 0, 14, -64, 42, 16, -32, -8, -24, 0, -24, 2, -64, 52, -72, 36, 0, -48, 0, -4, -48, 8, -44, 0, 4, 0, 4, -44, 128, 4, 4, -10, -8, 72, 16, 32, 16, 4, -12, -52, -52, -8, -72, -12, 60, 12, -12, 16, -24, 24, 0, 2, 12, 0, 36, -48, 12, -28, 24, -32, 16, -16, 24, -10, 48, -4, 10, 84, -36, 36, 24, 20, -8, 16, 30, 12, 2, -24, 100, 60, -8, 0, -36, 0, 56, 64, -20, -20, 72, 8, 28, 0, -24, -16, 4, 24, 4, -32, -16, -4, -28, 0, 2, -12, -32, -40, 4, -16, -12, 44, 4, -12, -104, 8, -24, 12, 4, 28, 44, -16, 12, -8, -48, 40, -44, 64, 20, 52, 16, 24, -36, 8, -32, -24, -36, 28, -32, 0, -36, -12, 16, -4, 32, 4, 8, 24, -6, 56, 42, 24, 0, 0, -4, -32, 20, 58, -24, -24, 64, 20, -84, -32, -4, -8, -4, 36, -48, -4, -24, -60, -12, -12, -4, 12, 16, -40, 4, -72, -12, -56, -16, 28, 96, -20, -64, -8, -8, -28, -28, -8, -16, 4, 84, -12, 48, -12, -40, -16, -12, -16, -28, 12, 28, 48, -76, -32, 8, 36, 0, -64, 30, 36, -48, 28, 84, -4, 24, -40, 16, 16, -40, -24, 8, -12, 8, -8, 6, -12, 20, 24, 16, 8, 0, 32, 4, 0, 10, -20, -96, -36, 72, 4, -24, 4, -12, 4, 4, -12, -56, 32, -92, -4, -24, 84, -8, 48, 4, 8, 14, 44, 8, -12, 4, -48, -24, -12, 32, 6, 84, -56, 48, 2, -12, 12, -36, 36, -4, -24, -44, 24, 96, -4, 52, 12, -12, -16, -48, 32, -96, -12, -16, 28, -20, 32, 48, -24, -16, 4, 12, 4, -4, 4, -24, 28, -16, -40, 12, 72, 42, -56, -12, 12, 20, -8, -72, -24, -12, -20, -12, 0, -40, 0, 108, 4, 92, 48, -2, 72, 24, 72, 44, 0, 44, -24, -12, -4, 12, -24, 12, -16, 36, 0, -20, -96, 0, -16, -4, -8, -12, -4, -88, 0, 4, -32, 16, 28, 12, -12, -124, -24, 28, 0, -6, -12, 24, 8, -20, -36, 72, 8, 36, 32, 92, -28, 24, 0, 0, 40, -24, -20, 12, 16, -12, 32, 72, -88, 8, 46, -24, 16, -60, 20, 24, 28, 14, -24, 20, 32, -56, 32, 36, 0, -48, -96, 56, 24, 74, 4, -8, -36, 0, -12, 0, 32, 4, -20, 8, 64, 48, 68, -136, 8, 40, 52, -96, -96, -6], 'weight': 2, 'weight_parity': 1}
  67. label: 65.2.a.c
    {'Nk2': 260, 'analytic_conductor': 0.5190276131383225, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[5, 1], [13, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [65, 1, [27, 41], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, 'field_disc': 12, 'field_disc_factorization': [[2, 2], [3, 1]], 'field_poly': [-3, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 12, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-3, 0, 1]]], 'hecke_orbit': 3, 'hecke_orbit_code': 9007199288295489, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '65.2.a.c', 'level': 65, '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, 13], 'level_radical': 65, 'minimal_twist': '65.2.a.c', 'nf_label': '2.2.12.1', 'prim_orbit_index': 1, 'qexp_display': 'q+\\beta q^{2}+(1-\\beta )q^{3}+q^{4}-q^{5}+(-3+\\cdots)q^{6}+\\cdots', 'related_objects': ['Genus2Curve/Q/4225/a'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '65.2.a', 'trace_display': [0, 2, -2, 4], 'trace_hash': 1811255940982796660, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.021', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.879', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.276', 'prec': 10}, {'__RealLiteral__': 0, 'data': '8.740', 'prec': 14}, {'__RealLiteral__': 0, 'data': '2.619', 'prec': 14}, {'__RealLiteral__': 0, 'data': '56.486', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.025', 'prec': 7}, 'traces': [2, 0, 2, 2, -2, -6, 4, 0, 2, 0, -6, 2, 2, 0, -2, -10, 0, -12, -2, -2, 4, 6, 6, 6, 2, 0, 8, 4, -12, 6, 10, 0, -12, 12, -4, 2, -8, 18, 2, 0, 0, -12, 10, -6, -2, 6, 12, -10, -6, 0, -12, 2, 0, 0, 6, 0, -20, -12, -6, -2, 4, -18, 4, 2, -2, 24, -8, 0, 0, 0, 6, 12, -8, 0, 2, -2, -12, -6, 4, 10, 2, -12, -12, 4, 0, 18, 0, -6, -12, 12, 4, 6, 28, 0, 2, 18, 4, 0, -18, 2, 12, 12, 10, 0, -4, -36, 18, 8, 4, -6, -8, -20, 24, 24, -6, -12, 2, -42, 0, -6, 2, 36, 12, 10, -2, -24, 22, 0, -8, 0, 0, -12, -4, -36, -8, -12, -12, -12, 4, -4, 12, -6, -6, -10, 12, 0, -6, -8, 12, -6, -14, -18, -24, 12, -10, 2, -20, 36, 36, 0, 12, 12, -8, 0, 12, 0, 12, 12, 2, -12, -38, 10, 24, 24, 4, 30, 36, 24, -24, -2, -20, 0, -32, -6, 8, -48, 12, 12, 16, -18, -24, 2, -20, 0, -2, -6, -12, 42, 40, 0, 28, 24, -24, -12, 0, 18, -6, -10, 24, 12, 16, 0, 12, -30, -10, 0, 20, 0, -8, 6, 0, 24, 4, 0, 2, 12, 0, -20, -8, -6, -24, 12, -12, -12, -12, -6, -32, 24, -18, 10, 16, -36, -34, 4, 6, -12, -2, 18, -12, 0, -36, 4, -12, -18, 12, 38, 12, -12, -16, -2, 12, 0, 6, -24, 0, 36, -36, -8, -12, 0, 10, 0, 4, -24, -6, 0, -32, -36, 46, 0, 24, -36, 34, 6, 20, 6, 0, 36, -10, 12, 4, -8, -24, 18, 6, 0, -24, 48, 6, 2, 20, -18, -12, 10, -4, 12, 4, -12, -8, 18, -12, 6, -8, 0, -4, 4, 48, -36, 24, -2, 48, 12, 36, 2, 2, 36, 4, 12, 24, -24, -26, -12, -8, 24, 8, -20, -32, 0, 12, 0, -48, 30, -40, -18, 0, 12, 6, 0, -8, 0, 8, -18, 0, -24, -6, -12, -24, 24, 6, -12, 18, -36, 38, 4, 8, 24, 34, -30, 24, 0, 0, 28, -20, -36, -2, 0, -12, 0, -14, 2, 40, -24, 12, -42, 12, 0, -26, 4, 12, 6, 12, 0, 0, 24, -4, -18, 16, 0, -40, -10, -60, -12, 10, 12, -2, -24, 24, -12, -56, 12, 12, 10, -12, -30, 12, 0, 40, -60, -12, -4, -20, 0, 12, 36, 0, -24, 8, 18, -12, -18, -6, -40, 28, -36, 0, 4, 12, 24, 64, 6, -6, 12, 18, -8, 12, 0, -36, 4, 48, -12, -12, 24, 4, 12, -4, -24, -20, -36, 0, -6, 0, 48, 16, 60, -28, 0, 66, 2, -16, 0, -20, 42, -12, 24, -2, 0, 72, 18, 54, -18, -8, 36, 0, 2, -4, 6, -32, -36, -44, 0, -12, 12, -24, 18, 18, -50, 12, 36, -26, -2, -12, 12, -6, 24, -12, 0, 2, 22, 72, -12, -16, 0, -8, -48, -10, -8, -36, 0, 12, 0, -36, 60, -38, 0, 4, 6, -36, 60, -22, 36, 78, -4, 0, 60, -18, 36, -48, 48, 18, -8, -32, -90, 16, -36, -4, -12, -14, -12, -68, 6, -24, 12, 8, 36, 8, 4, -24, -78, 10, 20, 48, -36, -6, 12, -24, -54, 4, 6, -12, -24, 52, -6, 0, -24, 6, 2, -8, 0, -20, 12, -24, -12, -36, 0, -2, -24, -24, -6, -64, 42, -36, 40, 12, 24, 0, 12, 40, 6, -36, 6, 4, 36, 64, -14, -2, -12, -2, -54, 0, -36, 12, -24, 52, 72, -12, -12, 12, -12, -38, -10, 24, 36, -24, -10, 2, 36, 84, -20, 0, 24, 22, -36, 16, 0, -22, 36, -6, 0, 18, 0, 12, -84, 28, 12, 8, -12, 6, -12, -24, 0, 56, -8, -12, -12, 0, 0, -8, 0, -36, 12, -20, -54, -12, 0, 4, 48, -48, 12, 4, 36, 24, 36, -8, 36, 8, 2, 0, -60, 8, 12, -12, 84, 72, -38, 12, 0, 28, -50, 0, 12, -2, 24, -36, 30, -4, -24, -24, 36, -12, 4, 84, 0, 8, -6, -12, 96, 24, 36, 40, 6, -68, -24, 12, 24, 6, -24, -36, 18, -24, 10, 20, -36, -20, -20, -12, -42, 58, 0, -46, 0, 36, -32, 76, 18, 6, -18, -12, -12, -26, 8, -20, -72, -60, 48, -12, 0, -12, 12, 36, 6, 52, -60, -48, -12, 14, 16, 16, -90, -12, 18, -12, -84, 8, -24, 24, -24, -6, 38, 28, -12, 60, -20, 0, -42, 10, 0, -16, 0, -36, -2, -24, 36, -48, 30, 20, 0, -20, -12, 0, -36, 48, -42, 4, -72, -36, 40, -12, 48, 0, 0, -60, 24, 24, 28, -12, -18, -60, -24, -12, -12, 46, -24, 100, -24, 8, 60, 44, -36, 4, 0, -12, 12, -62, -18, -12, -84, 36, -6, -20, 0, -68, 2, 0, -48, -12, 24, 40, -12, 18, -12, 38, 72, 60, 16, -2, -72, 4, 0, 88, 12, -24, 12, 16, 72, 38, 30, 12, 24, 28, -10, 24, 78, -36, 0, -24, -72, -10, 20, 24, -24, -8, 0, 4, 48, -4, -8, 4, 0, 0, -30, -60, 36, 58, 0, -36, 90, -30, -24, 44, -24, 6, 4, -12, 12, 24, 0, 0, 12, -24, 2, -72, 36, -16, -12, 20, 24, -14, 0, -36, 0, -72, 100, 36, -72, 32, -8, 0, 48, -44, 6, -68, 12, 6, -24, -8, 36, -26, 36, 96, 48, 6, -12, -48, 18, -12, 12, 28, -72, -44, -12, 0, 60, -12, 30, -16, -24, 12, -32, -8, 18, 48, -24, -12, -36, 24, -18, 24, -30, -24, -2, 42, 0, 78, 16, 20, -24, -80, 36, 48, 0, 24, -34, 8, 36, 2, -20, 24, 60, 60, 6, 4, -12, -48, 12, 12, -72, 24, -2, 48, -42, 16, 54, 28, -12, -40, -12, 88, 90, -32, 0], 'weight': 2, 'weight_parity': 1}
  68. label: 66.2.a.a
    {'Nk2': 264, 'analytic_conductor': 0.5270126533404506, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [3, -1], [11, 1]], 'atkin_lehner_string': '+-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [66, 1, [23, 13], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[5, [0, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554498, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '66.2.a.a', 'level': 66, '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': [2, 3, 11], 'level_radical': 66, 'minimal_twist': '66.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\\cdots', 'related_objects': ['EllipticCurve/Q/66/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '66.2.a', 'trace_display': [-1, 1, 0, 2], 'trace_hash': 1360131026130408405, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.994', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.071', 'prec': 7}, {'__RealLiteral__': 0, 'data': '2.004', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.281', 'prec': 10}, {'__RealLiteral__': 0, 'data': '5.089', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [1, -1, 1, 1, 0, -1, 2, -1, 1, 0, -1, 1, -4, -2, 0, 1, -6, -1, -4, 0, 2, 1, 6, -1, -5, 4, 1, 2, 6, 0, 8, -1, -1, 6, 0, 1, -10, 4, -4, 0, 6, -2, 8, -1, 0, -6, -6, 1, -3, 5, -6, -4, 0, -1, 0, -2, -4, -6, 0, 0, 8, -8, 2, 1, 0, 1, -4, -6, 6, 0, 6, -1, 2, 10, -5, -4, -2, 4, 14, 0, 1, -6, -12, 2, 0, -8, 6, 1, -6, 0, -8, 6, 8, 6, 0, -1, 14, 3, -1, -5, 6, 6, -4, 4, 0, 0, -12, 1, -4, 0, -10, 2, 18, 4, 0, 6, -4, 0, -12, 0, 1, -8, 6, 8, 0, -2, 14, -1, 8, 0, -12, -1, -8, 4, 0, 6, -18, -6, -4, 0, -6, -6, 4, 1, 0, -2, -3, -10, -6, 5, -10, 4, -6, 2, 0, -4, 2, -14, 0, 0, 12, -1, -4, 6, 0, 12, 12, -2, 3, 0, -4, 8, 6, -6, -10, -1, 0, 6, 24, 0, -22, 8, 8, -6, 0, -8, 6, -6, 2, 0, 18, 1, 14, -14, 0, -3, 6, 1, -4, 5, -4, -6, 12, -6, 0, 4, 6, -4, 4, 0, 8, 0, 6, 12, 0, -1, 16, 4, 2, 0, 24, 10, -16, -2, -5, -18, -12, -4, -22, 0, -2, -6, -18, 4, 0, 0, 14, 12, -12, 0, -10, -1, 1, 8, 0, -6, 16, -8, -12, 0, 0, 2, -6, -14, 0, 1, -30, -8, -20, 0, 6, 12, 0, 1, 0, 8, -6, -4, -24, 0, 2, -6, -8, 18, 5, 6, -16, 4, 8, 0, -6, 6, 8, 6, 0, -4, 12, -1, 19, 0, 14, 2, -6, 3, 0, 10, -1, 6, -24, -5, 16, 10, 6, -4, 0, 6, 20, -2, -4, 0, -18, 4, 26, -2, 0, 14, 12, 0, -6, 0, -12, -12, 24, 1, 20, 4, -4, -6, -12, 0, -4, -12, -10, -12, 0, 2, 2, -3, 18, 0, -8, 4, -20, -8, 0, -6, 36, 6, -4, 10, -4, 1, -6, 0, 0, -6, -12, -24, -12, 0, -3, 22, 1, -8, 0, -8, 8, 6, 6, 0, 0, 8, 20, -6, 0, 6, -24, -2, 20, 0, 14, -18, 6, -1, 0, -14, 8, 14, 0, 0, -36, 3, -12, -6, 0, -1, 26, 4, -8, -5, 30, 4, -32, 6, 0, -12, 10, 6, -34, 0, -18, -4, 0, -6, 0, 4, -4, -4, 24, 0, -10, -8, -6, 0, 30, -6, 16, -12, 4, 0, 0, 1, 26, -16, 0, -4, -24, -2, -10, 0, -3, -24, -24, -10, 0, 16, -6, 2, 6, 5, -6, 18, -10, 12, 0, 4, -10, 22, -6, 0, 42, 2, -4, 6, 0, 18, -12, -4, -8, 0, 2, 0, -8, -14, 20, -12, 0, 12, -24, 0, 40, 10, 12, 1, 0, -1, 20, -8, -4, 0, 12, 6, -36, -16, 0, 8, 12, 12, -4, 0, 12, 0, 12, -2, 0, 6, 3, 14, 24, 0, 4, -1, -4, 30, 0, 8, 6, 20, 6, 0, -18, -6, -16, -12, -10, 0, -48, -1, 13, 0, 0, -8, -24, 6, 0, 4, 24, 24, 3, 0, 20, -2, -22, 6, 0, 8, -28, -18, 8, -5, -24, -6, 28, 16, 0, -4, 18, -8, -32, 0, 6, 6, -12, -6, 0, -8, 2, -6, 18, 0, -28, 4, 18, -12, -30, 1, -34, -19, 14, 0, -24, -14, 0, -2, 0, 6, 24, -3, -32, 0, 6, -10, -30, 1, 0, -6, -4, 24, 30, 5, -22, -16, -4, -10, 0, -6, 14, 4, 12, 0, 24, -6, -16, -20, 0, 2, -30, 4, 44, 0, 6, 18, -12, -4, 25, -26, 4, 2, 60, 0, -16, -14, 8, -12, 0, 0, 12, 6, 6, 0, 6, 12, -4, 12, 0, -24, 6, -1, 0, -20, 16, -4, -36, 4, 0, 6, 2, 12, 36, 0, -22, 4, 24, 12, 0, 10, 36, 12, -16, 0, -8, -2, 14, -2, -5, 3, 30, -18, 28, 0, -12, 8, -24, -4, 0, 20, -22, 8, 0, 0, 20, 6, -2, -36, 0, -6, -36, 4, -18, -10, -6, 4, 40, -1, 0, 6, 12, 0, 26, 0, 14, 6, 48, 12, 0, 24, -12, 12, 30, 0, -8, 3, -10, -22, -30, -1, -28, 8, 1, 0, -48, 8, -4, -8, 0, -6, 4, -6, 8, 0, 16, 0, 36, -8, 0, -20, -12, 6, -24, 0, 8, -6, 0, 24, 0, 2, -34, -20, -6, 0, 18, -14, -8, 18, 0, -6, 0, 1, -34, 0, -30, 14, 0, -8, -40, -14, -20, 0, -24, 0, -6, 36, 6, -3, 0, 12, 32, 6, 0, 0, 36, 1, -32, -26, 0, -4, 0, 8, 36, 5, -6, -30, -2, -4, 0, 32, -24, -6, -42, 0, 8, 12, 2, -10, 0, -6, -32, 34, -8, 0, -18, 18, 8, 4, 5, 0, -12, 6, 14, 0, -16, -4, 18, 4, 0, 4, 8, -24, 18, 0, 7, 10, -6, 8, 0, 6, 2, 0, 8, -30, -60, 6, 8, -16, 0, 12, 54, -4, 20, 0, 12, 0, 42, -1, 0, -26, 19, 16, -14, 0, 16, 4, 14, 24, 0, 2, -52, 10, -6, 0, -30, 3, -28, 24, 0, 24, -36, 10, 28, 0, -1, -16, 24, 6, 0, -2, -24, -6, 48, -5, 0, 6, 16, -18, 0, 10, 20, -12, 6, 0, -42, -4, 12, 10, 0, -22, -24, 6, 2, 0, 20, -42, -24, -2, 50, 4, -4, -6, 30, 0, 12, -18, -18, 12, 0, 4, -22, 8, 26, 0, -18, -2, 36, 0, 0, 8, 12, 14, -8, -20, 12, 12, -42, 0, 0, -12, -6, 24, -36, 0, 33, -40, -12, -10, 0, -12, 14, -1, 24, 0, 0, 1, -8, -20, 20, 8, 54, 4, 6, 0, -4, -12, 30, -6, 0, 36, -12, 16, 48, 0, 56, -8, -4, -12, 0, -12, 44, 4, -10, 0], 'weight': 2, 'weight_parity': 1}
  69. label: 66.2.a.b
    {'Nk2': 264, 'analytic_conductor': 0.5270126533404506, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [3, 1], [11, 1]], 'atkin_lehner_string': '-++', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [66, 1, [23, 13], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[5, [-2, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924994, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '66.2.a.b', 'level': 66, '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': [2, 3, 11], 'level_radical': 66, 'minimal_twist': '66.2.a.b', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-4q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/66/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '66.2.a', 'trace_display': [1, -1, 2, -4], 'trace_hash': 1085673562421270116, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.972', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.953', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.887', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.012', 'prec': 7}, 'traces': [1, 1, -1, 1, 2, -1, -4, 1, 1, 2, -1, -1, -6, -4, -2, 1, 2, 1, 4, 2, 4, -1, 4, -1, -1, -6, -1, -4, 6, -2, 0, 1, 1, 2, -8, 1, 6, 4, 6, 2, -6, 4, 4, -1, 2, 4, -12, -1, 9, -1, -2, -6, 2, -1, -2, -4, -4, 6, 12, -2, -14, 0, -4, 1, -12, 1, 4, 2, -4, -8, -12, 1, -6, 6, 1, 4, 4, 6, -4, 2, 1, -6, 4, 4, 4, 4, -6, -1, 10, 2, 24, 4, 0, -12, 8, -1, -14, 9, -1, -1, 14, -2, 0, -6, 8, 2, 4, -1, -6, -2, -6, -4, 2, -4, 8, 6, -6, 12, -8, -2, 1, -14, 6, 0, -12, -4, 12, 1, -4, -12, 4, 1, -16, 4, -2, 2, 2, -4, -4, -8, 12, -12, 6, 1, 12, -6, -9, 6, -10, 1, 4, 4, 2, 4, 0, 6, -10, -4, -2, 2, -16, 1, -20, -6, 2, 4, 0, 4, 23, 4, 4, 4, -10, -6, 4, -1, -12, 10, 20, 2, -2, 24, 14, 4, 12, 0, -2, -12, 4, 8, -12, -1, 10, -14, 12, 9, -2, -1, -16, -1, -4, 14, -24, -2, -12, 0, 4, -6, -4, 8, -4, 2, 12, 4, 8, -1, 0, -6, 6, -2, -12, -6, 0, -4, -1, 2, 12, -4, 14, 8, -4, 6, 10, -6, -24, 12, 4, -8, 8, -2, 10, 1, -1, -14, 18, 6, -24, 0, -4, -12, -4, -4, -4, 12, -4, 1, 2, -4, -24, -12, 6, 4, -24, 1, 4, -16, -10, 4, 26, -2, 20, 2, -24, 2, 1, -4, 26, -4, 0, -8, -22, 12, 4, -12, -8, 6, 24, 1, -13, 12, 14, -6, 22, -9, 24, 6, 1, -10, -24, 1, -16, 4, -14, 4, -28, 2, 4, 4, 0, 0, 4, 6, 26, -10, -8, -4, 18, -2, -6, 2, -4, -16, 8, 1, 6, -20, 6, -6, 48, 2, 20, 4, 6, 0, 8, 4, 18, 23, -2, 4, 0, 4, -8, 4, -8, -10, -4, -6, -6, 4, 6, -1, 18, -12, -24, 10, 8, 20, 0, 2, -3, -2, -1, 24, -12, 14, -16, 4, -6, 12, -8, 0, -14, -2, 12, -12, -36, 4, -28, 8, -12, -12, -4, -1, 8, 10, 4, -14, -30, 12, 8, 9, -4, -2, -8, -1, 22, -16, 16, -1, -38, -4, 0, 14, 2, -24, -6, -2, -14, -12, -2, 0, -48, 4, 8, -6, 4, -4, -12, 8, -10, -4, -12, 2, -2, 12, 56, 4, -6, 8, 0, -1, 2, 0, -12, -6, 16, 6, 4, -2, 9, -12, 28, -6, 20, 0, 10, -4, -22, -1, 6, 2, -4, 12, 48, -4, 34, 14, -2, 8, 14, -4, -24, 6, 0, 10, 12, -6, -16, -24, 10, 12, -4, 4, -4, -8, 2, 8, 0, -2, -36, 10, 16, 1, -28, -1, -16, -14, 20, 18, -28, 6, 12, -24, -2, 0, 48, -4, -4, -12, 0, -4, 32, -4, 28, -4, -23, 12, -22, -4, 24, 1, -4, 2, 0, -4, 12, -24, 10, -12, 18, 6, 20, 4, -4, -24, 0, 1, -7, 4, 12, -16, 36, -10, 8, 4, -20, 26, -9, -2, -38, 20, 2, 2, -12, -24, -28, 2, -14, 1, 24, -4, 16, 26, -12, -4, 30, 0, -24, -8, 2, -22, -20, 12, 4, 4, -4, -12, 10, -8, -20, 6, 12, 24, -4, 1, -46, -13, -10, 12, -16, 14, -2, -6, -12, 22, -36, -9, 0, 24, 2, 6, -30, 1, -16, -10, 16, -24, 36, 1, 10, -16, 4, 4, 2, -14, 28, 4, 24, -28, 72, 2, -6, 4, 12, 4, -22, 0, -4, 0, -4, 4, -40, 6, -19, 26, 4, -10, 12, -8, -8, -4, 4, 18, 24, -2, -54, -6, -12, 2, 42, -4, -28, -16, -8, 8, -28, 1, -12, 6, 0, -20, 18, 6, 8, -6, -6, 48, -36, 2, -18, 20, 12, 4, -32, 6, 24, 0, 0, 8, 14, 4, 26, 18, 1, 23, 46, -2, 56, 4, -12, 0, 12, 4, 4, -8, -14, 4, -12, -8, -12, -10, 4, -4, -8, -6, -12, -6, -10, 4, 30, 6, 24, -1, 24, 18, -56, -12, -18, -24, -4, 10, 0, 8, 12, 20, -8, 0, 12, 2, 0, -3, -10, -2, -6, -1, 0, 24, 1, -12, 8, 14, -22, -16, -18, 4, -4, -6, 44, 12, 24, -8, -32, 0, -20, -14, 4, -2, -16, 12, 32, -12, 4, -36, 8, 4, 38, -28, 4, 8, 42, -12, 24, -12, 4, -4, -72, -1, 10, 8, -2, 10, 18, 4, 0, -14, 24, -30, -24, 12, 12, 8, -6, 9, -20, -4, -20, -2, 24, -8, -8, -1, 84, 22, -4, -16, -54, 16, -24, -1, 10, -38, 6, -4, -32, 0, -26, 14, 10, 2, -28, -24, -20, -6, -40, -2, 16, -14, 24, -12, -2, -2, -40, 0, -1, -48, -52, 4, 46, 8, -26, -6, 18, 4, 0, -4, 0, -12, 12, 8, 7, -10, 22, -4, 46, -12, -4, 2, -4, -2, 24, 12, -6, 56, 8, 4, 26, -6, 4, 8, -24, 0, 20, -1, -20, 2, 13, 0, 4, -12, -24, -6, -14, 16, 48, 6, 42, 4, -22, -2, -14, 9, 4, -12, -24, 28, 0, -6, -48, 20, -1, 0, -48, 10, 40, -4, 24, -22, 0, -1, 4, 6, 16, 2, -4, -4, 28, 12, 14, 48, 12, -4, -4, 34, 28, 14, -16, -2, -4, 8, -4, 14, 72, -4, -6, -24, 0, 6, 42, 0, 36, 10, -4, 12, -4, -6, -38, -16, -26, -24, -42, 10, -24, 12, 8, -4, 12, 4, 36, -4, -18, -8, -6, 2, -24, 8, 6, 0, -8, -2, -31, -36, 4, 10, 20, 16, -44, 1, -8, -28, 12, -1, 16, -16, -6, -14, 26, 20, -10, 18, -6, -28, 36, 6, -4, 12, -48, -24, 16, -2, 32, 0, -20, 48, -32, -4, -14, -4, -6, -12], 'weight': 2, 'weight_parity': 1}
  70. label: 66.2.a.c
    {'Nk2': 264, 'analytic_conductor': 0.5270126533404506, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [3, -1], [11, -1]], 'atkin_lehner_string': '---', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [66, 1, [23, 13], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[5, [4, 1]]], 'hecke_orbit': 3, 'hecke_orbit_code': 9007199288295490, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '66.2.a.c', 'level': 66, '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': [2, 3, 11], 'level_radical': 66, 'minimal_twist': '66.2.a.c', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/66/c'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '66.2.a', 'trace_display': [1, 1, -4, -2], 'trace_hash': 603621058800683965, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.005', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.976', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.025', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.934', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.115', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.871', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.015', 'prec': 7}, 'traces': [1, 1, 1, 1, -4, 1, -2, 1, 1, -4, 1, 1, 4, -2, -4, 1, -2, 1, 0, -4, -2, 1, -6, 1, 11, 4, 1, -2, 10, -4, -8, 1, 1, -2, 8, 1, -2, 0, 4, -4, 2, -2, 4, 1, -4, -6, -2, 1, -3, 11, -2, 4, 4, 1, -4, -2, 0, 10, 0, -4, -8, -8, -2, 1, -16, 1, -12, -2, -6, 8, 2, 1, -6, -2, 11, 0, -2, 4, 10, -4, 1, 2, 4, -2, 8, 4, 10, 1, 10, -4, -8, -6, -8, -2, 0, 1, -2, -3, 1, 11, 2, -2, 4, 4, 8, 4, -12, 1, 20, -4, -2, -2, -6, 0, 24, 10, 4, 0, 4, -4, 1, -8, 2, -8, -24, -2, -22, 1, 4, -16, 12, 1, 0, -12, -4, -2, -2, -6, 0, 8, -2, 2, 4, 1, -40, -6, -3, -2, -10, 11, 2, 0, -2, -2, 32, 4, 18, 10, 4, -4, 12, 1, 4, 2, -4, 4, -12, -2, 3, 8, 0, 4, -6, 10, -22, 1, 0, 10, 0, -4, 2, -8, -8, -6, 8, -8, -2, -2, -2, 0, 22, 1, 14, -2, -16, -3, 18, 1, 20, 11, -12, 2, -20, -2, -8, 4, -6, 4, 0, 8, 12, 4, 2, -12, -16, 1, 16, 20, -6, -4, -8, -2, -16, -2, 11, -6, -12, 0, 10, 24, -2, 10, -6, 4, 8, 0, 10, 4, -20, -4, -18, 1, 1, -8, 12, 2, 0, -8, 4, -24, -8, -2, -6, -22, 8, 1, 18, 4, 4, -16, 10, 12, -16, 1, -16, 0, 10, -12, -20, -4, 22, -2, -8, -2, 11, -6, 8, 0, -8, 8, 22, -2, 4, 2, 0, 4, -4, 1, -13, -40, -2, -6, 14, -3, 0, -2, 1, -10, -24, 11, -8, 2, 2, 0, 32, -2, 8, -2, 4, 32, 2, 4, -6, 18, 8, 10, -32, 4, 10, -4, -12, 12, 0, 1, 44, 4, 20, 2, 4, -4, -28, 4, -2, -12, 48, -2, -22, 3, -6, 8, -8, 0, 20, 4, 24, -6, -12, 10, -20, -22, 4, 1, -6, 0, -8, 10, 4, 0, -20, -4, -19, 2, 1, -8, 24, -8, 8, -6, 2, 8, -8, -8, 4, -2, -24, -2, 40, -2, -20, 0, -22, 22, -6, 1, 8, 14, 4, -2, -20, -16, 12, -3, 12, 18, -40, 1, 18, 20, 0, 11, -18, -12, -32, 2, -4, -20, -2, -2, -10, -8, -2, 4, 0, -6, -16, 4, 0, 0, 0, 8, -18, 12, -2, 4, -22, 2, 16, -12, 4, -16, 32, 1, -6, 16, -40, 20, 0, -6, 10, -4, -3, -8, 24, -2, -40, -16, -10, -2, 30, 11, 2, -6, 2, -12, 32, 0, -2, 10, -2, 24, -18, -2, 4, 10, 32, -6, 28, 4, 24, 8, 18, 0, 4, 10, 0, 4, 4, -20, 40, -4, -8, -18, 12, 1, 8, 1, 28, -8, 4, 12, 12, 2, -20, 0, -4, -8, -4, 4, -20, -24, -12, -8, 4, -2, -8, -6, 3, -22, -20, 8, 12, 1, 0, 18, -16, 4, -2, 4, -6, -16, -18, 10, 44, 12, -22, -16, 16, 1, 13, -16, 0, 0, 8, 10, 48, -12, 0, -20, -3, -4, 12, 22, 2, -2, -80, -8, -32, -2, -8, 11, 0, -6, -20, 8, 8, 0, 38, -8, 16, 8, -2, 22, -36, -2, 24, 4, -2, 2, -10, 0, 32, 4, 22, -4, -66, 1, -2, -13, 14, -40, -8, -2, 4, -6, -16, 14, 8, -3, 0, 0, 18, -2, 14, 1, -16, -10, 20, -24, -30, 11, 42, -8, -12, 2, -4, 2, -22, 0, -20, 32, -8, -2, -16, 8, -8, -2, -22, 4, -20, 32, -6, 2, -20, 4, 41, -6, 0, 18, 4, 8, -48, 10, 12, -32, 88, 4, -12, 10, 2, -4, -18, -12, 44, 12, -16, 0, -22, 1, 0, 44, 16, 4, 24, 20, -48, 2, -6, 4, -20, -4, 42, -28, -8, 4, 0, -2, -60, -12, -16, 48, -8, -2, 14, -22, 11, 3, -22, -6, 4, 8, -12, -8, -16, 0, 8, 20, 10, 4, 16, 24, 52, -6, -2, -12, 0, 10, -4, -20, -6, -22, -18, 4, 0, 1, 8, -6, -4, 0, 10, -8, 10, 10, 48, 4, -16, 0, -20, -20, 10, -4, -8, -19, -18, 2, 110, 1, 28, -8, 1, 24, -8, -8, 4, 8, 12, -6, -12, 2, 20, 8, 0, -8, 44, -8, 40, 4, 4, -2, 24, -24, -8, -2, -8, 40, -8, -2, -42, -20, -6, 0, 22, -22, -40, 22, 8, -6, 0, 1, -50, 8, 18, 14, 4, 4, -88, -2, 4, -20, 0, -16, 2, 12, 10, -3, -72, 12, -52, 18, -16, -40, 12, 1, -32, 18, -16, 20, 28, 0, 4, 11, 10, -18, -6, -12, -48, -32, -20, 2, 10, -4, 12, -20, 22, -2, -16, -2, 0, -10, -8, -8, -38, -2, 24, 4, 11, 0, -12, -6, 30, -16, 8, 4, 6, 0, 48, 0, -8, 0, 30, 8, 71, -18, 22, 12, -12, -2, -2, 4, 4, -22, 12, 2, 24, 16, 0, -12, -22, 4, -20, -16, -4, 32, 54, 1, 24, -6, -13, 16, 10, -40, -48, 20, -2, 0, 48, -6, 28, 10, 14, -4, -38, -3, 44, -8, 0, 24, -12, -2, 44, -40, 1, -16, 0, -10, 0, -2, -24, 30, -80, 11, -8, 2, -8, -6, -8, 2, -12, -12, 2, 32, 2, 0, 4, -2, 32, 10, -24, -2, -10, 24, 8, -18, 8, -2, -22, 4, 4, 10, 30, 32, 0, -6, 2, 28, 8, 4, 58, 24, -6, 8, 42, 18, -12, 0, 8, 4, 28, 10, -24, 0, -32, 4, -6, 4, -88, -20, 10, 40, 4, -4, 33, -8, -12, -18, -56, 12, -22, 1, 0, 8, 32, 1, 0, 28, 44, -8, 38, 4, 10, 12, 20, 12, -46, 2, -72, -20, 4, 0, -24, -4, -8, -8, -28, -4, -80, 4, -52, -20, -2, -24], 'weight': 2, 'weight_parity': 1}
  71. label: 67.2.a.a
    {'Nk2': 268, 'analytic_conductor': 0.5349976935425785, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[67, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [67, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-2, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554499, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '67.2.a.a', 'level': 67, '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': [67], 'level_radical': 67, 'minimal_twist': '67.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+2q^{2}-2q^{3}+2q^{4}+2q^{5}-4q^{6}+\\cdots', 'related_objects': ['EllipticCurve/Q/67/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '67.2.a', 'trace_display': [2, -2, 2, -2], 'trace_hash': 1356389227688008752, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.015', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.978', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.901', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.627', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.010', 'prec': 7}, 'traces': [1, 2, -2, 2, 2, -4, -2, 0, 1, 4, -4, -4, 2, -4, -4, -4, 3, 2, 7, 4, 4, -8, 9, 0, -1, 4, 4, -4, -5, -8, -10, -8, 8, 6, -4, 2, -1, 14, -4, 0, 0, 8, -2, -8, 2, 18, -1, 8, -3, -2, -6, 4, 10, 8, -8, 0, -14, -10, 9, -8, -2, -20, -2, -8, 4, 16, 1, 6, -18, -8, 0, 0, -7, -2, 2, 14, 8, -8, -8, -8, -11, 0, 4, 8, 6, -4, 10, 0, 7, 4, -4, 18, 20, -2, 14, 16, 0, -6, -4, -2, 2, -12, -16, 0, 8, 20, -7, 8, 2, -16, 2, 8, -12, -28, 18, -10, 2, 18, -6, 0, 5, -4, 0, -20, -12, -4, 7, 0, 4, 8, -12, 16, -14, 2, 8, 0, 12, -36, 22, -8, 2, 0, -8, -4, -10, -14, 6, -2, 21, 4, 3, 0, 3, 16, -20, -8, 9, -16, -20, -16, -18, -22, 19, 0, 16, 8, 24, 0, -9, 12, 7, -4, 11, 20, 2, 16, -18, 14, -12, 4, 7, -8, 4, 0, -2, 40, -12, -2, -8, 28, -6, 16, -23, 0, -8, -6, -2, -8, 7, 0, -2, 4, 10, -12, 0, -32, 9, -8, -28, 16, -12, 20, 0, -14, -4, 0, 20, 4, 14, -16, 6, 4, 11, 16, -1, -24, 3, -28, 4, 36, -16, 0, 10, 4, -2, 18, 16, -12, -20, 16, -19, 10, 10, -4, -6, 0, 14, 0, -8, -24, -2, -4, -36, 14, -12, 16, -1, 8, 2, 8, -5, -24, 16, 0, 20, -28, -14, 2, 2, 16, 8, -12, 8, 24, 4, -36, -2, 44, -10, 0, -18, 4, -3, 0, -28, -16, 0, -8, -8, -20, 0, -14, 18, 12, 18, 0, -16, 42, 18, 4, 4, 6, -4, -28, -4, 6, -25, 16, 32, -40, 18, 0, -16, 18, -4, -16, -18, -40, 20, -16, 14, -36, 21, -22, -2, 38, -4, 0, 2, 32, -6, 8, -1, 48, 2, -16, 22, -18, 24, 12, 40, 14, 20, 0, -36, 22, -30, 20, 6, 4, 8, 32, 0, -36, 0, 14, 12, -24, 19, 0, 30, 14, -10, -8, -14, 8, -8, -36, 0, -4, -20, 40, 0, -24, 24, 0, -10, -16, -18, 28, -14, -12, -16, 0, 16, -46, -2, 0, -10, -16, 27, 0, 24, -4, -16, -8, -31, 14, 28, 4, -20, -4, -20, 4, -22, 20, 4, 0, 8, 0, -24, -32, -18, 18, 8, -16, -44, -56, -9, 16, -21, -24, -1, 0, -3, 0, 4, -14, 16, -8, -9, -16, -18, 40, 20, 4, 63, 28, 23, 0, -3, 12, 2, 4, 14, 22, -42, 16, 39, -2, 0, -24, -6, 6, -8, 0, 29, 8, 12, 36, 37, -32, -8, 20, 40, 20, -12, 4, -2, -4, -18, 0, 8, 32, -7, -12, 10, -40, -29, 32, -2, -38, 36, 10, 0, 20, 2, 0, -38, -12, -9, 0, -15, 28, -8, 40, 0, -16, 24, -24, -48, -4, -2, 0, 4, -72, 18, 14, 9, -24, 14, 32, 28, -2, -32, 8, 4, 4, -22, 0, 4, -10, -19, -24, -4, 32, -30, -32, 58, 40, 9, -28, 0, -28, -14, 0, 24, 4, 12, 16, 14, 16, -14, -24, 4, 16, 38, 24, -2, 8, -35, 0, 16, -4, 4, 44, -2, -20, -4, 16, 24, -36, -24, 4, -24, -6, 22, 0, 9, -56, -23, -16, 12, 0, -9, -8, -24, -16, 46, -20, -8, 0, -40, 0, 4, 36, 12, 12, -70, 36, 4, 4, 18, -32, -12, 42, -14, 36, -32, 0, -5, 8, 1, 6, 10, -8, 8, -56, -20, -8, -2, 6, 39, -50, 0, 0, -1, 64, 20, -40, 36, 36, -14, 16, -19, -32, 56, 18, -3, -8, -50, 0, 24, -36, 14, -40, -6, 40, 0, 0, 20, 28, 12, -36, 8, 42, 6, 0, -36, -4, -40, 38, -18, -8, -24, 0, -7, 4, -9, 32, -18, -12, -12, 0, -28, -2, -45, 48, -22, 4, 8, -32, -14, 44, -4, -18, 12, 48, 0, 0, -6, 80, -30, 14, 24, 40, -8, 8, 20, -72, 15, 22, 8, -60, 44, 0, 0, 12, -20, 4, 20, 16, -7, 32, 4, 0, -4, -36, -10, 0, -8, 0, -90, 24, -16, -24, 40, 38, 25, -8, 32, 60, 38, 14, 5, -20, -2, 0, 13, -28, -6, 8, 0, -16, 12, -72, -4, 0, -20, -4, -28, -40, -24, 0, 42, 0, 4, -24, 14, 48, 35, 4, 4, -20, 6, -16, 40, -36, 72, 0, 47, -28, -4, -12, 6, -32, 18, -32, -18, 32, 2, -46, 9, -4, 10, 0, -4, -20, 0, -16, 0, 54, -20, 12, 18, 48, 52, -4, -32, -32, 24, 0, -4, -62, -40, 14, -6, 56, -3, 8, 7, -40, 28, -4, -36, -40, -4, 0, -6, -44, 38, 20, -16, 8, 38, 24, -14, 16, -4, 0, -25, -48, 51, 0, -8, -36, -15, 18, -55, 16, 4, -16, -9, -88, 48, -56, -40, -18, -23, 0, -4, -42, 36, -24, -18, -2, -10, -40, 6, -6, -9, 0, 29, 8, 14, 0, -6, 32, -8, -8, 0, -18, 1, -32, 22, -36, 16, 40, 32, 40, 2, 0, 0, 126, 24, 28, 41, 46, -36, 32, -57, -6, -44, 12, -36, 4, -31, 0, -14, 28, 44, 22, -7, -84, -24, 0, -36, 78, 50, -2, 30, 0, -8, 0, 14, -12, -43, 6, 2, -16, -15, 56, -16, 58, 8, 8, 24, 24, 12, 0, 50, 74, 0, -32, 1, -16, -16, 40, 50, 80, -21, 20, -36, -24, -24, 0, 30, -4, 32, -4, 8, -36, 0, -36, -16, 16, 9, 32, -14, -14, 36, 0, -7, 20, -12, -40, -40, -58, -24, 32, 69, -4, -7, -38, -46, 72, 0, 0, -42, 0, -15, 20, -44, 4, 4, 8, -13, -76, -28, -12, 2, -18, 16, 0, -4, -30, -4, 28, -18, -16, 44, 80, 12, 0, 14, -16, 6, 48, -4, 0], 'weight': 2, 'weight_parity': 1}
  72. label: 67.2.a.b
    {'Nk2': 268, 'analytic_conductor': 0.5349976935425785, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[67, 1]], 'atkin_lehner_string': '+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [67, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [1, 3, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924995, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '67.2.a.b', 'level': 67, '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': [67], 'level_radical': 67, 'minimal_twist': '67.2.a.b', 'nf_label': '2.2.5.1', 'prim_orbit_index': 1, 'qexp_display': 'q+(-1-\\beta )q^{2}+(-2+\\beta )q^{3}+3\\beta q^{4}+\\cdots', 'related_objects': ['Genus2Curve/Q/4489/a'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '67.2.a', 'trace_display': [-3, -3, -6, -1], 'trace_hash': 1733840430896082901, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '1.943', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '9.408', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '62.334', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [2, -3, -3, 3, -6, 2, -1, -6, 1, 9, 0, 3, -7, 9, 9, 13, -6, 6, 1, -9, -6, -5, 6, -1, 8, 3, 0, -24, -6, -6, -2, -15, 5, 4, 3, -21, -1, 6, 18, 18, -3, -1, 3, 15, -3, -19, -15, -12, 9, -12, 14, 12, -18, -5, 0, 33, -9, 19, 12, -9, -7, 3, 22, 4, 21, 0, -2, 6, 1, -27, 12, 27, -8, 9, -12, -21, -15, -7, -7, -39, 2, 2, -15, 21, 18, -12, -1, -20, 0, -18, -19, 39, 3, 25, -3, 15, 2, -21, -15, 12, -9, -6, -5, -9, 18, 27, 24, 15, -3, 15, -6, -29, 33, 1, -18, -39, -26, -18, -12, 3, -12, 33, 7, -3, 6, -33, -5, 9, 3, -9, -6, -15, 22, 3, 0, -2, -12, 6, -6, 72, 20, -13, 15, -16, 18, 12, -6, -24, 9, 8, -2, 27, -18, 25, 6, -33, 13, -12, 27, 45, -33, -18, -7, 3, -15, 40, 12, -22, 21, -12, 23, 27, -39, -6, -4, 15, -18, 5, -18, 63, -7, 6, -12, -58, 3, -2, 10, -30, -15, -18, -6, 9, 27, -33, -54, 36, -18, 20, -13, -24, 3, 26, 33, -24, 9, -15, -27, -23, -15, 3, -11, -27, -23, -21, -9, -20, 1, 12, 12, -45, 36, -1, 18, 30, 4, -47, -3, 24, -31, 57, 20, 58, 12, 9, 45, 18, 33, -2, -27, 36, 45, 18, 12, -78, -27, -3, -26, 6, 5, -9, 18, 33, 20, 15, -42, -9, -18, 3, 23, -36, 27, 9, -3, 15, 54, -33, -5, -3, 9, 15, 36, -24, 51, 3, 0, -21, 12, 9, -1, -99, 15, -15, -18, 3, 27, -5, -6, 15, -6, -57, 27, -12, -18, 9, -36, 33, 10, -46, 9, 12, -24, 3, 1, -16, 21, 2, 8, -30, 30, -9, 0, 26, -21, 3, -66, 57, -12, -18, -20, -12, -51, 77, -18, 48, -28, 18, -3, -1, 15, 0, 20, -75, 22, 22, 6, -9, 17, 21, -52, -18, 0, -27, -20, -39, -3, 46, 0, 21, -12, 36, 15, -15, 3, 12, -36, -15, 38, 22, -36, -81, -15, -12, 18, 39, 24, -7, 2, 69, -9, -27, 9, -3, -17, 0, -9, 55, -9, 25, 8, 63, 0, -1, -39, -26, 45, -48, -21, 93, -6, 21, 2, -57, 9, 17, 21, -15, -51, -18, -33, 52, 9, -2, 7, -51, -6, -77, -15, 18, -14, -6, 33, 60, -6, 58, 45, 30, 9, 20, 0, -63, -55, 9, 0, 54, -24, 12, 71, -9, -40, 36, 60, 15, -7, -9, 3, -27, -27, -8, -17, 60, -18, -14, -30, 21, 0, -42, 19, -47, 33, 24, 5, 42, 3, 47, 57, -23, -46, 54, 10, -117, -21, -15, -35, -69, -9, -8, 24, 51, 1, -75, -42, -36, 15, -7, 4, 42, -9, 53, 30, -45, -19, -75, 22, -18, -6, 17, 26, 111, 3, 63, 30, -12, -2, 9, 45, -13, 9, -15, -50, 9, -58, -32, 66, -66, 27, -45, -84, -30, -12, 18, 4, 18, -15, 67, 15, -18, -5, -42, 71, 27, -36, -58, 17, -9, -24, -18, 6, 10, 12, -81, 6, 33, 18, 0, -72, 6, 32, -41, 15, -45, 36, -69, 33, 30, 9, -19, 31, 27, 64, -20, 27, 27, -64, -78, 18, -9, -63, -6, 12, 87, -30, -25, -6, -15, -99, 57, -46, -16, 18, -3, 5, -30, 19, -1, 24, -43, 32, 39, -33, 117, 60, 2, 0, 24, 78, -3, 57, -9, -1, 54, 37, -29, -60, -15, 36, 111, 57, -1, 12, -4, 26, 51, -1, -3, 36, -9, 67, 15, -22, -99, 45, 48, -2, -42, -21, 55, -45, -5, -82, 9, 20, 60, 15, 57, -58, 39, 25, -48, -12, 99, -29, -69, 24, -37, 15, -27, -9, 45, 21, -27, 24, 24, -21, -132, -9, 2, -54, -66, 0, 12, 6, -33, 0, -3, 18, -12, -4, -80, -42, 45, 60, 0, -94, 115, -66, -33, -58, -102, -12, -9, -45, 15, -11, 12, 0, -126, 0, 33, -91, 6, -38, 5, 21, 12, 36, 15, 39, 42, 63, -18, 16, -21, 0, 25, 18, -27, 14, 18, -28, -96, 36, -5, 22, 30, -60, 38, 42, 18, 16, 39, -71, 20, -6, -12, -45, -12, 28, 54, 90, 48, -65, 30, -60, 57, -24, -12, 56, -33, -59, -36, 6, 57, 8, 42, 18, -75, 0, 1, 11, 72, 69, -81, 0, 1, -27, 48, 45, -30, 33, 6, 48, -105, -22, 1, 6, -30, 50, -12, -15, -81, -24, -5, 24, 21, 54, 31, -42, -9, -8, -75, -13, 63, -6, 39, -8, -126, -27, 44, -9, 99, -10, 12, -20, 81, -39, -6, -14, 3, 27, 36, -9, 35, -43, 99, -81, 93, 9, 22, 40, -60, 15, -21, 0, -3, 99, -3, 14, 77, -15, 54, -56, 132, -39, 25, 21, 46, -21, -24, -77, -9, -36, -12, -7, -75, 20, 54, 30, -93, 32, -120, 42, 31, -12, -6, -36, -15, 0, -50, 24, 66, 0, 90, -20, 6, -63, -55, 6, -117, -3, 16, -33, 33, 19, -144, -69, -12, -18, 15, 43, -81, 19, -85, 51, -15, 117, 93, -21, 24, 45, 18, 7, 39, -89, 58, -3, -12, 16, 93, 57, -45, -48, 57, 28, -66, 54, 35, -12, -22, 25, -15, 30, 72, 0, 9, 54, 33, -26, -32, 6, -84, 54, 0, 21, -89, 21, -2, -49, -132, 33, -18, -93, -21, -35, 39, 36, -69, 3, 0, -74, 174, 18, 39, -57, -15, -4, 75, -70, 75, 18, 6, -18, -12, -60, -61, -30, -42, 36, -9, 24, 90, -54, 13, 1, 78, 45, -30, -39, -78, 28, 24, 73, -44, 18, -54, 18, -78, 15, -80, -39, -27, -60, 6, 57, 90, -81, -33, -62, 36, 52, 99, 30, -87, 3, -99, 72, -113, -24, -7, -10, -108, 21, -75, -6, 9, 54, -12, 35, 51, 39, -60, 81, 15, -60, 29, 39, 30, -12, 75, -15, -18], 'weight': 2, 'weight_parity': 1}
  73. label: 67.2.a.c
    {'Nk2': 268, 'analytic_conductor': 0.5349976935425785, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[67, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [67, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1, 1]]], 'hecke_orbit': 3, 'hecke_orbit_code': 9007199288295491, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '67.2.a.c', 'level': 67, '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': [67], 'level_radical': 67, 'minimal_twist': '67.2.a.c', 'nf_label': '2.2.5.1', 'prim_orbit_index': 1, 'qexp_display': 'q-\\beta q^{2}+(1-\\beta )q^{3}+(-1+\\beta )q^{4}+(1+\\cdots)q^{5}+\\cdots', 'related_objects': ['Genus2Curve/Q/4489/c'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '67.2.a', 'trace_display': [-1, 1, 4, 1], 'trace_hash': 2156498262764654527, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.019', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.958', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.206', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.076', 'prec': 14}, {'__RealLiteral__': 0, 'data': '1.617', 'prec': 14}, {'__RealLiteral__': 0, 'data': '58.103', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.009', 'prec': 4}, 'traces': [2, -1, 1, -1, 4, 2, 1, 0, -3, -7, 2, -3, -1, -3, -3, -3, 6, 4, -11, 3, -2, -1, -2, -5, 8, 3, -2, 2, 10, 4, 0, 9, 1, -8, 7, -1, 3, 8, 2, 10, 5, 1, -9, -1, -11, 11, -7, 6, -11, -24, -2, -2, 0, -9, 4, 5, -3, 5, -12, -1, -9, 15, -4, 4, -7, 2, 2, 2, 9, -11, 0, -5, 16, 1, -16, 3, 1, -1, -11, -21, -2, 10, 13, 1, 22, -8, 15, 0, -16, 18, -3, -9, 15, 1, -27, 7, 0, 3, -3, 16, 19, 6, 3, -5, -4, 15, 16, 11, 9, -7, 4, -9, 11, -11, -24, -15, 4, 6, 8, -5, -20, -3, 15, -15, 36, 7, -21, -25, -17, 11, 6, -3, -8, -1, 16, 10, -26, -2, 24, 4, -6, -35, -1, 12, 0, -8, -8, -4, -3, 8, 6, -5, -14, -3, -30, -1, 13, -12, 15, 13, -11, -14, 13, -15, -3, -14, 28, 0, -23, -36, 19, 17, 17, 10, 24, -3, -6, 23, 6, -7, -11, 4, -12, -20, 1, 0, 6, 6, 9, 46, -32, -3, -1, 15, 4, 8, 36, 4, 39, 40, 1, -22, -5, -4, -15, 1, 13, 9, -11, 7, 1, -15, -35, -23, 7, 20, -15, 8, 8, 3, -8, 3, 2, 2, -32, 17, 21, 14, -7, 37, -2, -20, -20, -7, -9, 6, -23, -14, 15, 12, 17, 10, -10, 12, -17, 5, 8, -30, -1, -53, -14, -3, -2, 23, -14, 7, -2, -9, -1, -4, -5, -13, -23, -5, -30, 19, 7, -1, 29, -23, -34, -24, 1, 3, 8, -7, -4, -7, 15, 15, -11, -7, 14, 35, 19, 3, -10, -11, -6, -5, 15, -8, 26, -11, -24, -5, -2, -16, 11, 8, 8, 17, -3, 24, -3, 22, 20, 2, 4, 45, -24, 0, -7, 31, -18, 23, 44, 0, 10, 18, -7, 13, -38, 16, -24, -4, 17, -25, -1, 4, -12, 1, -2, -14, 4, 3, -11, 9, 28, 14, 0, -27, -10, 25, 13, -16, -10, -25, -28, -32, -9, 9, 55, -12, 70, -7, -6, -18, 28, -25, 25, -2, -10, -1, 32, -9, -6, 33, 5, -3, -15, -15, -5, -8, -17, 5, 5, -7, 24, -19, 2, 31, -17, -10, 7, -2, 1, -15, -10, -7, -26, 5, -7, -23, 13, -1, -7, -32, 11, -72, -45, 2, 15, 3, 26, -5, 3, -10, 6, 20, -23, -4, -6, -24, 41, -2, 17, 8, -28, -3, 13, 17, 8, -30, 64, 0, 3, 7, 2, -6, -8, -27, -21, 15, -5, -17, 21, 16, 31, 10, 14, 14, -56, -7, -62, -46, -19, 7, -27, 56, 5, -28, 23, 27, -11, 25, 18, -34, 14, -13, -21, 1, -21, 15, 15, -20, 36, 3, 1, 17, 44, 0, -9, -11, -64, 6, 15, 25, 2, -11, 1, 9, 2, 10, -30, 25, -16, 15, 9, 31, 2, -20, 10, -19, -11, 45, 35, 13, 28, 17, 14, -28, 16, -10, 63, 11, -14, -2, 8, 22, 8, 24, 1, 21, 1, 26, -7, -2, 1, -15, -72, 0, -3, 7, -8, 4, -30, 6, -4, 45, 18, -11, 10, -16, 62, 0, -12, 3, -11, 7, -12, 27, -13, 22, -7, -3, -29, 23, 6, -24, -45, -5, 12, -18, -2, -17, 1, -30, -8, -33, -2, -17, -58, 13, -23, -37, 14, 70, -2, -27, -31, -2, -1, 5, -88, -11, 2, -27, -3, 5, 14, 0, 0, 0, 18, 7, -41, 19, 15, 42, 13, 3, 36, -9, 36, 19, 7, -13, -24, 0, 10, 1, -3, -23, -40, 19, 11, -47, -10, 9, 1, -8, -42, 30, 5, 5, 3, 3, -30, -15, -38, -8, -23, -3, 102, -29, -3, -44, 4, 29, 45, 35, 18, -7, -67, -15, 3, 5, -35, -55, -10, 16, -21, -2, 1, 54, -38, 30, -12, 32, 0, -9, 44, 9, 32, 30, -24, 8, -18, -1, 14, -4, 6, 15, -46, 1, 30, -14, -44, -7, -9, -9, 77, -32, 72, 14, 34, 11, -15, 50, 48, 15, 35, 8, -32, 35, -41, -24, 15, -24, 40, -1, -4, 45, 38, -35, -10, 54, -40, 8, 20, 7, -14, 4, 8, -30, 22, 18, 0, -105, -1, -30, 60, 8, -7, 12, 40, -34, 50, 54, -1, -40, 26, 13, -40, -20, -4, -5, 21, -56, -2, 21, 40, -62, 14, 1, 2, -15, 25, 2, -11, 15, 72, -15, 29, 20, -27, 2, 23, 36, 20, 3, -42, 5, -28, -2, -60, -32, 9, -65, 24, -21, -8, 1, -58, -49, 6, -19, -46, -11, 19, 3, 58, 7, -120, -30, -3, 20, -15, 3, 0, 48, -50, 9, -49, 6, 44, -13, -19, -14, -17, -5, -3, 31, 15, -7, 93, -8, -16, 16, 39, 35, 16, -3, -37, -15, 32, 25, -87, -38, -34, 10, -7, 1, 21, 18, 37, 52, 7, -5, -20, -26, 37, -5, -16, 18, -30, 11, -40, -68, -22, -7, -28, 24, 56, 3, -60, -6, 4, -10, 32, -24, -28, -18, -41, -9, -10, 45, -23, -112, 7, 35, 63, 6, 73, 30, -12, -1, -1, -1, -5, 9, 27, -19, 49, 53, -33, 0, -11, 0, -1, -25, 15, -68, 53, -24, -88, -3, 33, -21, 16, -17, -38, -6, 18, 43, 68, -10, -23, 101, -2, 44, 36, -3, 42, -15, -2, 46, 60, -24, -30, 10, 9, -45, -7, 6, 19, -48, -41, 18, 35, -33, 13, 21, 6, 41, 13, -32, 4, -50, 50, -37, -35, 1, -8, 43, -2, 55, 0, -30, 58, 40, -32, -3, 22, 10, -110, -3, -36, -8, -4, 13, 45, 18, 23, -8, 33, 34, -8, 152, 37, 20, 26, -30, -94, -40, 15, -36, -3, -11, 28, 2, -39, -26, 3, -11, -50, 0, 16, 45, 10, -15, 7, -7, 8, -9, -36, 13, -16, -14, -1, 59, -8, -25, 82, 0, 7, 11, -41, 18, -67, 15, -16, -35, 103, -12, -8, 11, -13, 70], 'weight': 2, 'weight_parity': 1}
  74. label: 68.2.a.a
    {'Nk2': 272, 'analytic_conductor': 0.5429827337447066, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [17, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [68, 1, [35, 37], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, 'field_disc': 12, 'field_disc_factorization': [[2, 2], [3, 1]], 'field_poly': [-3, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 12, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554500, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '68.2.a.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': '68.2.a.a', 'nf_label': '2.2.12.1', 'prim_orbit_index': 1, 'qexp_display': 'q+(1+\\beta )q^{3}-2\\beta q^{5}+(-1-\\beta )q^{7}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '68.2.a', 'trace_display': [0, 2, 0, -2], 'trace_hash': 1709142697651164148, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.025', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.991', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.348', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.777', 'prec': 14}, {'__RealLiteral__': 0, 'data': '3.438', 'prec': 14}, {'__RealLiteral__': 0, 'data': '66.651', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.026', 'prec': 7}, 'traces': [2, 0, 2, 0, 0, 0, -2, 0, 2, 0, -6, 0, 4, 0, -12, 0, -2, 0, 4, 0, -8, 0, -6, 0, 14, 0, 8, 0, 0, 0, -2, 0, 0, 0, 12, 0, 16, 0, 16, 0, -12, 0, 4, 0, -24, 0, 0, 0, -6, 0, -2, 0, 12, 0, -12, 0, -8, 0, 12, 0, -8, 0, -14, 0, -24, 0, 16, 0, 0, 0, -6, 0, 4, 0, 14, 0, 0, 0, -14, 0, 2, 0, -12, 0, 0, 0, 12, 0, 12, 0, -16, 0, 16, 0, 24, 0, 4, 0, 6, 0, -12, 0, -8, 0, 24, 0, 18, 0, -8, 0, 4, 0, 12, 0, -12, 0, 28, 0, 2, 0, 2, 0, -12, 0, 0, 0, -20, 0, -32, 0, -6, 0, 8, 0, 0, 0, 12, 0, -26, 0, -24, 0, 0, 0, -24, 0, 6, 0, 12, 0, -20, 0, -2, 0, -36, 0, 4, 0, 36, 0, 0, 0, 10, 0, 24, 0, -6, 0, 6, 0, -20, 0, -24, 0, -14, 0, 0, 0, 36, 0, 16, 0, 4, 0, 24, 0, 6, 0, -8, 0, 24, 0, 28, 0, -48, 0, 0, 0, -2, 0, 40, 0, -12, 0, 0, 0, 6, 0, -24, 0, 22, 0, -24, 0, 72, 0, -16, 0, 4, 0, -4, 0, 4, 0, 14, 0, -30, 0, -20, 0, 12, 0, 12, 0, 48, 0, -32, 0, 0, 0, 4, 0, -34, 0, -24, 0, -16, 0, 0, 0, 0, 0, 24, 0, 12, 0, -36, 0, -4, 0, 24, 0, -12, 0, -48, 0, 0, 0, -48, 0, 16, 0, -40, 0, -42, 0, -8, 0, 34, 0, -12, 0, 10, 0, 0, 0, 12, 0, 2, 0, -20, 0, 60, 0, 24, 0, -24, 0, 0, 0, 32, 0, 0, 0, -24, 0, -8, 0, -32, 0, 18, 0, 28, 0, 36, 0, 24, 0, 12, 0, 24, 0, -4, 0, 28, 0, -44, 0, 24, 0, 4, 0, -8, 0, -48, 0, 28, 0, 60, 0, 24, 0, 8, 0, 24, 0, -30, 0, -20, 0, 16, 0, -12, 0, 36, 0, 8, 0, -12, 0, -6, 0, -34, 0, 0, 0, 22, 0, -12, 0, -36, 0, 4, 0, -24, 0, 24, 0, -14, 0, 16, 0, -12, 0, -24, 0, -68, 0, 12, 0, 6, 0, 24, 0, 36, 0, -32, 0, 8, 0, 36, 0, 32, 0, 24, 0, -60, 0, -20, 0, 0, 0, 0, 0, -24, 0, -32, 0, -18, 0, 4, 0, -48, 0, -14, 0, -4, 0, -24, 0, 18, 0, 28, 0, -24, 0, -24, 0, -38, 0, 18, 0, 0, 0, 24, 0, 12, 0, 12, 0, 36, 0, -32, 0, 48, 0, -20, 0, -8, 0, 12, 0, -32, 0, -24, 0, 36, 0, -40, 0, 4, 0, -48, 0, 28, 0, 60, 0, -18, 0, 8, 0, 12, 0, 48, 0, -26, 0, 64, 0, -12, 0, 0, 0, 60, 0, 24, 0, -2, 0, 24, 0, 30, 0, -24, 0, 54, 0, 12, 0, -4, 0, 16, 0, 48, 0, -24, 0, -36, 0, -12, 0, 16, 0, -56, 0, 2, 0, -22, 0, -12, 0, -24, 0, -12, 0, 24, 0, 30, 0, 16, 0, 4, 0, 72, 0, 82, 0, 16, 0, -24, 0, 32, 0, -72, 0, -60, 0, -64, 0, 0, 0, -36, 0, -96, 0, 10, 0, 12, 0, -2, 0, 24, 0, -42, 0, -20, 0, 52, 0, 0, 0, -12, 0, -72, 0, 36, 0, -40, 0, 12, 0, -36, 0, -12, 0, 16, 0, 0, 0, -20, 0, 64, 0, 72, 0, -74, 0, -24, 0, -48, 0, -68, 0, 72, 0, 12, 0, 34, 0, -24, 0, 0, 0, -22, 0, 24, 0, -16, 0, 76, 0, -8, 0, -72, 0, 12, 0, -42, 0, -12, 0, 34, 0, 48, 0, 48, 0, -48, 0, -28, 0, 0, 0, -60, 0, 4, 0, 72, 0, -44, 0, -16, 0, 0, 0, 12, 0, 40, 0, 36, 0, 28, 0, 56, 0, 0, 0, 20, 0, -48, 0, -54, 0, 24, 0, -56, 0, 72, 0, -62, 0, 24, 0, 12, 0, 12, 0, 12, 0, -12, 0, 56, 0, 48, 0, 0, 0, 16, 0, -50, 0, 24, 0, 48, 0, 72, 0, 42, 0, 32, 0, 4, 0, 0, 0, -32, 0, -46, 0, -4, 0, 4, 0, 12, 0, -24, 0, 4, 0, -16, 0, -18, 0, 0, 0, 12, 0, -24, 0, 34, 0, 24, 0, 24, 0, 28, 0, -12, 0, 12, 0, 44, 0, 24, 0, 0, 0, -20, 0, -72, 0, -36, 0, -14, 0, -40, 0, -24, 0, 0, 0, 0, 0, 0, 0, 22, 0, 48, 0, -60, 0, 8, 0, -120, 0, 36, 0, 0, 0, -12, 0, -12, 0, -24, 0, -60, 0, 12, 0, -2, 0, -8, 0, -108, 0, 80, 0, -64, 0, 0, 0, -14, 0, 0, 0, 6, 0, 52, 0, 28, 0, 6, 0, -60, 0, -8, 0, 54, 0, -34, 0, -60, 0, -96, 0, 34, 0, 64, 0, -60, 0, -32, 0, -24, 0, -36, 0, -20, 0, 48, 0, 48, 0, 24, 0, 2, 0, 24, 0, 80, 0, -44, 0, 24, 0, 40, 0, 60, 0, -36, 0, 40, 0, -48, 0, 54, 0, -16, 0, -18, 0, 48, 0, 24, 0, -24, 0, 36, 0, -12, 0, 56, 0, 24, 0, 10, 0, 12, 0, -42, 0, 48, 0, 24, 0, -24, 0, -104, 0, -80, 0, -48, 0, 112, 0, -56, 0, 36, 0, -36, 0, -24, 0, 12, 0, 28, 0, 52, 0, 48, 0, 36, 0, 48, 0, 102, 0, 8, 0, 12, 0, -36, 0, 0, 0, -24, 0, 0, 0, -6, 0, 30, 0, -48, 0, 76, 0, 8, 0, -36, 0, 32, 0, 112, 0, -84, 0, -48, 0, -80, 0, -6, 0, -24, 0, 48, 0, -48, 0, 10, 0, 64, 0, -36, 0, 64, 0, 64, 0], 'weight': 2, 'weight_parity': 1}
  75. label: 69.2.a.a
    {'Nk2': 276, 'analytic_conductor': 0.5509677739468346, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1], [23, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [69, 1, [47, 28], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554501, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '69.2.a.a', 'level': 69, '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, 23], 'level_radical': 69, 'minimal_twist': '69.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\\cdots', 'related_objects': ['EllipticCurve/Q/69/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '69.2.a', 'trace_display': [1, 1, 0, -2], 'trace_hash': 538245996156256486, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.006', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.982', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.969', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.889', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.020', 'prec': 7}, 'traces': [1, 1, 1, -1, 0, 1, -2, -3, 1, 0, 4, -1, -6, -2, 0, -1, 4, 1, 2, 0, -2, 4, -1, -3, -5, -6, 1, 2, 2, 0, 4, 5, 4, 4, 0, -1, 2, 2, -6, 0, 2, -2, 10, -4, 0, -1, 0, -1, -3, -5, 4, 6, -12, 1, 0, 6, 2, 2, -12, 0, -6, 4, -2, 7, 0, 4, -10, -4, -1, 0, 8, -3, -14, 2, -5, -2, -8, -6, 10, 0, 1, 2, 12, 2, 0, 10, 2, -12, -16, 0, 12, 1, 4, 0, 0, 5, -10, -3, 4, 5, 14, 4, -6, 18, 0, -12, 12, -1, 14, 0, 2, 2, 16, 2, 0, -2, -6, -12, -8, 0, 5, -6, 2, -4, 0, -2, -12, -3, 10, 0, -4, -4, -4, -10, 0, -12, 8, -1, 4, 0, 0, 8, -24, -1, 0, -14, -3, -2, 0, -5, 8, -6, 4, -8, 0, 6, 10, 10, -12, 0, 2, 1, 8, -2, 0, 12, -16, 6, 23, 0, 2, -10, 2, 2, 10, -4, -12, -16, 12, 0, -2, 12, -6, 3, 0, 4, 16, 0, -2, 0, -12, 7, -18, -10, 0, 3, 18, 4, -6, 15, -10, 14, -4, -4, 0, -6, -1, 6, 8, 0, 8, 12, 8, 12, 0, -3, -8, 14, -14, 0, -24, 2, 0, -10, -5, 16, -24, -2, 6, 0, -8, -6, 10, -6, 0, 12, 10, -8, 8, 0, -2, 5, 1, 6, 0, 2, -12, -12, 12, 0, 24, 2, -4, -12, 0, -17, 18, 10, -4, 0, 2, -4, -12, -12, 0, -4, -16, 10, 10, 0, -20, -4, 12, 8, -20, 1, -10, 4, 4, 0, -24, 0, 6, -8, 0, -24, -4, 5, -1, 0, -10, 14, 20, -3, 0, -6, 4, 0, 6, 5, -20, 8, 14, -2, 0, 4, -16, 8, -6, 0, 0, 18, 2, 10, 0, -10, -30, -12, 8, 0, 12, 2, 8, -1, 30, 8, 14, -6, 0, 0, 0, -12, 2, -16, 0, 2, -2, 23, 16, 0, 16, 2, 20, -30, 0, 2, 12, -2, 2, 10, -6, 20, 6, -12, 0, 16, -8, 12, 20, 0, -15, -2, 5, -12, 0, -6, -38, 1, 2, 0, 24, -4, 34, 16, 0, 0, -12, -2, 10, 0, -12, -12, -28, -3, 0, -18, 10, 10, -20, 0, -4, 9, -4, 18, 0, -4, -18, -6, -4, 5, -4, -10, -24, -14, 0, -4, 8, -12, -26, 0, 8, 6, 24, -1, 0, -30, 4, 8, -4, 0, 38, 8, 0, 36, -20, 8, 12, -12, -24, 0, 0, -1, 2, -8, 0, -14, -2, -14, 8, 0, -3, -24, -12, -2, 0, 0, 0, -14, 10, -5, 8, -16, 8, -24, 0, -6, -18, 6, 4, 0, 2, -8, -8, -2, 0, 10, 8, 6, 20, 0, 10, 36, 40, 10, -10, 8, -12, 8, 16, 0, -12, -2, 2, -5, 0, 1, 24, 18, 8, 0, -20, -2, 8, -12, 0, -4, -16, 12, -8, 0, -16, 24, 16, 6, 0, -4, 23, 12, -38, 0, 28, -11, 2, 18, 0, -10, 0, -4, 2, 0, 0, 2, 38, 4, 10, -12, 16, -4, 1, 0, -12, 4, -12, -16, 0, 30, 12, 10, -12, 0, 2, -20, -2, 20, 0, 12, 8, -8, -6, -20, 4, 3, -20, -10, 0, -4, -4, 4, -60, 0, 16, -24, 24, 0, 0, 6, -2, -24, -12, 0, -34, 24, -12, -4, 5, 7, -2, -1, -18, 0, -24, -10, -48, 42, 0, 20, -12, 3, 8, 0, 18, -2, 34, 4, 0, 0, -6, 6, 16, 15, -26, -20, -10, -8, 0, 14, -8, 10, -4, 0, 0, -4, -6, -16, 0, 24, -24, -6, -10, 0, -1, 0, 32, 6, 25, 2, 8, -10, 8, 0, 26, -30, 8, -30, 0, 12, 18, 8, 8, 0, 4, 12, -14, -2, 0, 8, 8, -3, -48, 30, -8, -8, -42, 14, 0, -2, -14, 0, 40, 0, 2, 0, -24, -36, 0, 2, -2, 16, 0, 0, -24, -10, -10, -2, -5, -23, 0, 16, 20, 0, -24, 16, -52, -2, 0, 20, 6, -10, 72, 0, 16, -2, -8, 12, 0, -6, 8, 2, 10, -10, -8, -6, 4, 28, 0, 6, -28, 12, 6, 0, 10, 48, -4, -8, 0, -12, 8, 20, 48, 0, 12, -15, -2, 2, -10, 5, 6, -36, 1, 0, 40, 6, 6, -38, 0, -5, -40, 2, 12, 0, -12, 24, -20, -12, 0, 34, 12, -16, -24, 0, 30, 0, 24, -12, 0, 2, 46, 10, -4, 0, -18, -12, -28, 12, 0, -28, 72, -17, 42, 0, 18, 18, -32, 10, -20, 30, -4, -20, 4, 0, 32, -4, 2, 3, 0, -4, 2, -18, -12, 0, -32, -12, 36, -18, 0, 6, 44, -4, 0, -25, -16, -4, -56, 10, 0, -24, 10, -42, -2, 0, -40, 4, -20, 8, 0, -4, 20, -26, 12, 0, -26, 8, 52, 18, -20, 24, -16, 1, -14, 0, -10, -42, -12, 4, 0, -8, 4, -4, -36, 0, -25, 38, -24, -8, 0, 0, -10, 12, 6, -20, -2, -8, 22, 12, 0, -36, 2, -24, 20, 0, -4, 0, -32, 5, 0, 2, -1, 8, 40, 0, 60, -42, -10, -2, 0, 14, -42, 8, 20, 0, 0, -3, 16, 24, 0, -12, 48, -6, 24, 0, 4, 0, 0, 0, 0, 6, 6, 10, 8, 5, -48, 8, -20, -48, 0, 8, -34, 24, 14, 0, 40, -2, 48, -18, 0, -6, 8, 4, -14, 0, -16, 2, -48, 8, -10, -8, -6, 10, -6, 0, -6, -10, 0, 8, 0, 18, 34, 20, 2, 0, 40, 10, -2, 12, 0, 40, 28, -10, 84, -10, -30, 24, 12, -12, 0, -8, 8, 16, -16, 0, -15, -12, 12, 2, 0, 2, 4, -15, 8, 0, 40, -1, -8, 24, 30, 6, 16, 8, -64, 0, 14, -20, -16, -6, 0, 8, 0, 12, -10, 0, -4, 20, 0, -16, 0, -12, -38, -8, 2, 0], 'weight': 2, 'weight_parity': 1}
  76. label: 69.2.a.b
    {'Nk2': 276, 'analytic_conductor': 0.5509677739468346, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, 1], [23, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [69, 1, [47, 28], [1, 1]], 'cm_discs': [], 'conrey_index': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-5, 0, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924997, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 2, 'hecke_ring_index_factorization': [[2, 1]], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '69.2.a.b', 'level': 69, '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, 23], 'level_radical': 69, 'minimal_twist': '69.2.a.b', 'nf_label': '2.2.5.1', 'prim_orbit_index': 1, 'qexp_display': 'q-\\beta q^{2}-q^{3}+3q^{4}+(-1+\\beta )q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '69.2.a', 'trace_display': [0, -2, -2, 2], 'trace_hash': 2262196210867976799, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '1.896', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.131', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.214', 'prec': 14}, {'__RealLiteral__': 0, 'data': '2.144', 'prec': 14}, {'__RealLiteral__': 0, 'data': '63.157', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.019', 'prec': 7}, 'traces': [2, 0, -2, 6, -2, 0, 2, 0, 2, -10, 8, -6, 0, -10, 2, -2, -10, 0, 10, -6, -2, 0, 2, 0, 2, 20, -2, 6, 0, 10, -4, 0, -8, -10, 8, 6, 0, -10, 0, -10, -4, 10, 2, 24, -2, 0, -8, 2, -2, 20, 10, 0, -6, 0, -8, -10, -10, -20, 8, 6, 0, 20, 2, -26, -20, 0, 6, -30, -2, 0, -16, 0, -4, -20, -2, 30, 8, -20, 6, 2, 2, 40, 8, -6, 20, 30, 0, 0, 2, -10, -20, 6, 4, 0, 0, 0, 8, -20, 8, 6, 4, 10, -18, 20, -8, 10, 16, -6, -12, -40, 0, -2, 10, 10, -2, 0, 0, 40, 0, 10, 10, -20, 4, -12, -12, -10, 12, 0, -2, -20, 16, -24, 20, 10, 2, -10, 2, 0, 0, 24, 8, 0, 0, -2, 20, -40, 2, 0, -10, -20, -32, -10, -10, -40, -16, 0, -16, -30, 6, 30, 2, 0, -12, -12, 8, 0, 8, 10, 14, 60, 10, 6, 0, 20, -18, -8, -8, 10, 24, -6, 12, 20, 0, 0, 20, -20, -40, -24, -2, -40, 12, 26, 8, -20, 20, -6, 8, 0, 6, 20, -6, 40, 20, 30, -36, 10, 2, 0, 40, 0, 36, -18, 16, -40, -32, 0, -24, 40, 4, -24, -20, 20, -16, 30, 2, 50, -36, -30, -12, -10, -8, -20, -28, 20, 8, 24, -6, 40, -8, -2, 48, 0, -2, 0, 22, -40, -20, 20, -8, 20, -12, 6, 8, 20, -20, -18, -44, -30, 20, -60, 0, -40, 4, 0, -4, -60, -2, 18, 8, 10, -44, 10, 20, 10, 8, -6, -4, 40, -4, 0, 18, 0, -2, -48, 0, 80, -44, 0, 26, 20, -8, -12, 2, 20, -48, -20, -8, 30, 0, -6, -28, 0, -4, -10, 20, -10, -4, 24, 18, 0, 32, -20, 28, -20, 8, 18, 32, -10, 0, 26, -16, -10, -40, 6, 40, -60, 12, 40, -8, 40, 20, 24, 0, -40, -16, 2, 16, 0, -10, 60, -16, -10, 4, 30, 2, -20, 16, 0, -56, 10, 0, 0, -8, -40, 16, 6, 0, -40, 4, -10, 22, 80, -10, -60, 44, 20, 38, -2, -4, 20, -16, 12, 32, -40, 12, 0, -40, 10, 2, 0, -12, 20, 60, 0, 32, -60, 2, 24, 10, 20, -10, -20, -16, -60, 24, 24, -4, -30, -20, -2, -18, -10, 40, 12, -2, -20, 0, 10, 8, -20, -2, -54, -32, 0, -8, -60, 0, -40, -8, -24, -44, 20, -8, 10, -30, 0, 20, 48, 0, -40, 16, 2, 20, 40, -20, -36, 10, 40, 16, -40, -2, -100, -16, 0, -12, 80, 10, -26, 12, 20, -16, 30, 32, -20, 0, 10, 8, -40, 10, -6, 16, 40, -8, 0, 16, 0, -4, 0, -4, 40, 16, 40, 8, 30, -10, 0, -6, -40, -32, -30, -40, 20, -2, 30, 12, 0, 48, -20, 12, 30, 80, 12, 20, 100, -8, 4, -16, 0, 20, -36, -8, 20, -56, -10, -44, 0, -14, 36, -24, -60, 36, 0, -10, 0, 8, -6, -32, -20, 0, -20, -62, -20, -18, 48, 18, -20, 0, 8, 2, 20, 8, 60, 80, -10, 24, 10, -24, 20, -8, 6, -40, -20, -12, 30, -28, -20, 36, 6, 0, 80, 20, 0, 36, -80, -20, 0, -62, 20, 60, -8, 40, -70, 12, 24, -60, -30, 2, 0, -26, 40, 46, 0, -12, 60, 2, -26, 24, 100, -8, 60, 8, 20, -24, -40, -20, -30, 16, 6, -40, -80, -8, 0, 68, 0, -40, -30, -6, 20, -24, -20, -40, 20, 6, -96, -10, -40, 24, 30, -20, 20, 0, -30, -72, -20, 36, -40, -54, -10, 22, -48, -2, 40, -8, 0, -18, 40, -40, -48, 20, 0, -10, -30, -36, 60, -32, 18, -40, -80, -16, 70, 22, 40, 18, 6, 32, 0, 24, 0, 32, 20, 24, -36, -28, -40, 24, 4, -4, 40, 28, 24, -32, -60, 20, 0, 40, -20, 0, 24, 16, -40, 0, -30, 32, 100, -2, 42, -10, -50, 28, 60, 36, 80, -40, 30, -12, 60, 12, -2, 20, 10, -36, 0, 8, 80, -40, 20, -20, -20, 28, -54, 46, -20, 20, -104, -8, 60, -36, -24, -12, 80, 6, 10, -4, -40, -80, 72, 8, -20, 8, 2, -28, -100, -48, 36, -40, 0, 34, 20, 2, 60, -40, 0, 44, -30, -22, 0, 24, 40, 0, 60, 20, 40, -4, -20, -20, -20, 8, -120, 56, -20, 42, 8, 12, 0, 32, -6, 44, -130, -8, -40, 40, -20, -52, 36, 20, 20, 80, 18, -20, 0, 44, 24, 86, 30, 36, -20, -20, -70, -60, 60, -64, -10, 0, 2, 36, 40, -14, 24, -4, 0, -40, 0, -40, 0, 4, 18, -6, 60, 40, -60, 2, -130, -16, -18, 8, -40, -8, 40, -24, -10, -20, 60, 44, -80, 72, -10, -20, -60, -20, -108, 60, -10, -60, 10, -8, 0, 44, 6, -24, -40, 4, 0, 30, -40, 32, 120, 4, -80, -52, 0, -18, 40, -18, 108, -14, 0, 10, 6, 2, -110, 0, 48, 44, -20, 0, -40, -68, -80, -32, -96, 44, 0, -8, 0, 20, -80, -26, -72, 24, -20, 20, 40, 8, -10, -32, 12, 84, 80, -2, 8, -14, -20, 12, -60, 48, 120, 80, 20, -8, -20, 8, -48, -40, -30, 16, 70, 0, -40, -40, 6, 20, 160, 28, 50, -92, 0, 38, -108, 4, 80, 8, 10, 32, -20, -20, -36, 56, 10, 30, -10, 4, 60, 0, -24, -40, 40, -18, 60, -4, 0, 10, -84, -32, -100, 80, 20, 28, -20, -28, 24, -18, 20, -4, -8, -8, 120, -56, -18, -80, 90, -32, 40, -34, 10, -32, -24, 0, 80, -8, -26, -14, 0, 16, 144, 52, 10, -60, 0, 40, -20, -28, -6, -40, 0, -40, 0, -6, 60, 8, 66, -12, 0, -8, -40, 52, 100, 8, -60, 2, -40, -12, -60, -20, 80, 24, -24, 40, 100, 0, 20], 'weight': 2, 'weight_parity': 1}
  77. label: 70.2.a.a
    {'Nk2': 280, 'analytic_conductor': 0.5589528141489627, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [5, 1], [7, 1]], 'atkin_lehner_string': '-++', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [70, 1, [57, 31], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554502, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '70.2.a.a', 'level': 70, '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': [2, 5, 7], 'level_radical': 70, 'minimal_twist': '70.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-3q^{9}+\\cdots', 'related_objects': ['EllipticCurve/Q/70/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '70.2.a', 'trace_display': [1, 0, -1, -1], 'trace_hash': 1338735293501548123, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.985', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.934', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.680', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.023', 'prec': 7}, 'traces': [1, 1, 0, 1, -1, 0, -1, 1, -3, -1, 4, 0, -6, -1, 0, 1, 2, -3, 0, -1, 0, 4, 0, 0, 1, -6, 0, -1, 6, 0, 8, 1, 0, 2, 1, -3, -10, 0, 0, -1, 2, 0, 4, 4, 3, 0, 8, 0, 1, 1, 0, -6, -2, 0, -4, -1, 0, 6, -8, 0, -14, 8, 3, 1, 6, 0, -12, 2, 0, 1, -16, -3, 2, -10, 0, 0, -4, 0, -8, -1, 9, 2, 8, 0, -2, 4, 0, 4, 10, 3, 6, 0, 0, 8, 0, 0, 2, 1, -12, 1, -6, 0, 16, -6, 0, -2, 12, 0, 6, -4, 0, -1, 2, 0, 0, 6, 18, -8, -2, 0, 5, -14, 0, 8, -1, 3, -8, 1, 0, 6, -16, 0, 0, -12, 0, 2, -6, 0, 16, 1, 0, -16, -24, -3, -6, 2, 0, -10, 6, 0, 8, 0, -6, -4, -8, 0, 10, -8, 0, -1, 0, 9, -4, 2, 0, 8, 0, 0, 23, -2, 0, 4, -22, 0, -1, 4, 0, 10, -12, 3, -14, 6, 0, 0, 10, 0, 8, 8, 0, 0, 24, 0, 2, 2, 0, 1, 14, -12, -16, 1, 0, -6, -6, 0, -2, 16, 0, -6, 0, 0, 4, -2, 0, 12, -4, 0, -8, 6, 0, -4, -12, 0, 16, -1, -3, 2, 8, 0, -14, 0, 0, 6, -6, 18, -8, -8, 0, -2, 16, 0, 10, 5, 0, -14, -1, 0, 0, 8, 0, -1, 0, 3, 0, -8, 0, 1, -22, 0, 10, 6, -18, -16, 8, 0, 2, 0, 0, -12, -6, 0, 0, 2, 0, -6, 4, 0, -18, 16, -24, 1, 26, 0, 32, -16, 0, -24, -2, -3, -13, -6, 0, 2, 10, 0, 8, -10, 0, 6, 0, 0, -4, 8, 0, 0, 14, -6, -8, -4, 0, -8, -24, 0, -22, 10, -3, -8, 22, 0, 24, -1, 0, 0, 0, 9, -6, -4, 0, 2, -8, 0, 4, 8, 30, 0, 12, 0, -14, 23, 0, -2, 32, 0, -1, 4, 0, -22, 4, 0, 10, -1, 0, 4, -6, 0, 16, 10, 0, -12, 8, 3, -19, -14, 0, 6, -2, 0, 16, 0, -6, 10, 2, 0, 14, 8, 0, 8, -36, 0, -12, 0, 0, 24, 24, 0, 4, 2, -12, 2, 14, 0, 0, 1, 0, 14, 8, -12, 10, -16, 0, 1, -14, 0, -48, -6, -9, -6, -40, 0, -30, -2, 0, 16, 8, 0, -8, -6, 0, 0, 24, 0, -10, 4, -24, -2, 2, 0, 14, 12, 0, -4, 0, 0, 2, -8, 0, 6, 0, 0, -8, -4, -3, -12, -20, 0, -10, 16, 0, -1, -30, -3, 8, 2, 0, 8, -6, 0, 10, -14, 0, 0, 10, 0, -16, 6, 0, -6, -40, 18, 12, -8, 0, -8, 16, 0, 0, -2, 6, 16, 24, 0, 60, 10, 0, 5, -2, 0, 32, -14, 0, -1, 12, 0, 12, 0, 12, 8, 16, 0, -12, -1, 0, 0, -24, 3, 6, 0, 0, -8, 10, 0, -2, 1, 0, -22, -16, 0, 32, 10, 0, 6, 2, -18, 16, -16, 0, 8, 16, 0, -23, 2, 24, 0, -12, 0, -12, -12, 0, -6, 4, 0, -18, 0, 0, 2, -6, 0, 12, -6, 42, 4, 0, 0, 8, -18, 0, 16, 22, -24, -24, 1, 0, 26, -16, 0, -2, 32, -9, -16, -6, 0, -12, -24, 0, -2, 0, -3, 10, -13, 0, -6, -8, 0, -8, 2, -18, 10, 8, 0, 0, 8, 0, -10, -6, 0, 2, 6, 0, 0, 0, 0, 42, -4, 36, 8, -5, 0, -32, 0, 0, 14, -48, -6, 6, -8, 0, -4, -22, 0, 8, -8, 0, -24, -10, 0, 1, -22, 0, 10, -20, -3, -16, -8, 0, 22, 8, 0, -6, 24, 48, -1, 2, 0, -32, 0, 0, 0, 16, 9, -32, -6, 0, -4, 14, 0, 16, 2, -6, -8, 28, 0, -38, 4, 0, 8, 0, 30, 0, 0, 0, 12, -56, 0, -14, -14, 0, 23, 18, 0, -2, -2, 0, 32, -4, 0, 6, -1, 0, 4, 12, 0, -32, -22, 12, 4, -16, 0, 4, 10, 0, -1, 22, 0, 0, 4, 0, -6, 6, 0, -2, 16, 24, 10, 0, 0, 24, -12, 0, 8, 24, 3, -16, -19, 0, -14, 6, 0, 0, 6, -27, -2, 8, 0, -14, 16, 0, 0, -48, -6, 28, 10, 0, 2, 48, 0, -6, 14, -24, 8, -12, 0, -16, 8, 0, -36, -8, 0, 22, -12, 0, 0, 18, 0, -6, 24, 6, 24, 48, 0, 10, 4, 0, 2, 42, -12, 8, 2, 0, 14, 0, 0, -64, 0, 0, 1, -10, 0, -8, 14, 0, 8, -2, -12, 84, 10, 0, -16, -6, 0, 16, 1, -30, -14, 8, 0, 0, -48, 0, -6, -6, -9, 8, -6, 0, -40, 4, 0, 0, -30, -18, -2, 6, 0, -8, 16, 0, 8, 44, 0, -46, -8, 0, -6, 2, 0, 0, 0, 0, 24, -16, 0, 7, -10, 0, 4, -23, -24, -5, -2, 0, 2, 0, 0, -46, 14, 0, 12, -54, 0, -48, -4, 0, 0, -32, 0, 22, 2, 0, -8, -32, 0, 72, 6, -6, 0, 1, 0, 14, -8, 0, -4, 2, -3, -12, -12, 0, -20, -16, 0, 8, -10, 36, 16, 0, 0, 12, -1, 0, -30, 48, -3, -4, 8, 0, 2, 14, 0, -52, 8, 18, -6, 0, 0, 32, 10, 0, -14, 16, 0, -16, 0, 0, 10, 96, 0, -10, -16, -48, 6, 58, 0, 0, -6, 0, -40, -8, 18, 50, 12, 0, -8, 2, 0, 0, -8, 0, 16, 44, 0, -12, 0, 0, -2, -54, 6, -24, 16, 0, 24, 6, 0, 33, 60, -36, 10, -2, 0, 16, 5, 0, -2, -24, 0, -16, 32, 0, -14, -30, 0, 40, -1, -18, 12, -16, 0, -14, 12, 0, 0, 0, 12, 40, 8, 0, 16, 16, 0, -22, -12, 0, -1], 'weight': 2, 'weight_parity': 1}
  78. label: 71.2.a.a
    {'Nk2': 284, 'analytic_conductor': 0.5669378543510907, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[71, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [71, 1, [7], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 3, 'field_disc': 257, 'field_disc_factorization': [[257, 1]], 'field_poly': [3, -4, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-3, -4, 1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554503, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '71.2.a.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': '71.2.a.a', 'nf_label': '3.3.257.1', 'prim_orbit_index': 1, 'qexp_display': 'q-\\beta _{1}q^{2}+\\beta _{1}q^{3}+(1+\\beta _{2})q^{4}+(2-\\beta _{1}+\\cdots)q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 3, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '71.2.a', 'trace_display': [-1, 1, 5, 2], 'trace_hash': 325099449762415536, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.029', 'prec': 7}, {'__RealLiteral__': 0, 'data': '2.922', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.592', 'prec': 10}, {'__RealLiteral__': 0, 'data': '23.911', 'prec': 17}, {'__RealLiteral__': 0, 'data': '7.760', 'prec': 14}, {'__RealLiteral__': 0, 'data': '286.051', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.008', 'prec': 4}, 'traces': [3, -1, 1, 3, 5, -9, 2, 0, 0, 8, 0, 2, -6, -18, -8, -5, -2, -1, 1, -6, 18, -2, -12, -1, 14, 4, -2, 4, 11, -4, 12, -6, 2, 16, -16, 10, -15, 16, -4, 11, -2, -8, 13, 20, -11, 4, 4, 6, 15, 6, -16, -26, -18, 17, -22, -2, -16, 7, -4, -27, 16, -4, 2, -16, 12, -20, -12, 16, -4, -8, 3, -10, 27, 6, -6, 9, 4, 38, -3, -7, -17, -34, -19, 38, -6, -12, -7, -20, 1, 19, -8, -12, 4, 14, 10, 26, 22, -9, 20, -7, 9, -12, -7, 20, 8, 10, 28, 6, -1, 38, -6, 12, -8, -11, -20, -10, -20, -18, -32, 19, 7, -40, 34, 12, 30, -20, 10, 29, 12, -54, 9, 24, -32, 6, 5, -18, 8, 36, 8, -54, -14, -1, -40, -9, 50, 16, 9, -25, -4, -21, 47, -8, 18, -40, 20, -28, -23, 28, -10, -61, -8, 1, -42, 2, -38, -12, 9, -20, 13, 46, 8, 4, -22, -12, -12, -18, 18, -7, -1, 7, -6, 76, 40, 0, -14, -36, 36, 22, -34, 35, 15, -17, 12, 10, 54, 55, -20, -22, 37, 21, -6, -2, -14, -14, -42, -37, 0, 28, 16, 86, -38, -58, 1, -44, 23, -8, 8, 11, -16, 14, -32, 55, -5, 52, -21, 18, 0, -24, 11, -32, 40, 21, 7, 24, 4, 18, -28, -24, 4, 39, 36, -33, 5, 20, -19, 2, -18, 0, 12, -34, 37, 24, 0, -40, -46, 5, -38, -30, -12, -2, -21, 16, 39, -22, 14, -22, 7, -32, -34, 27, -15, -30, -76, 28, -42, -8, -7, -16, 0, 38, -10, -30, -6, 3, -35, 48, 68, 23, 17, -2, -10, 34, -54, -85, -48, 10, 16, -12, 24, -33, 24, -7, 2, -26, -12, -2, 22, 48, 37, 32, 3, 24, 13, -7, -38, -16, -16, 94, -42, 16, 44, 72, 48, -56, 14, 10, -11, -4, -28, 30, 4, -7, -10, 24, 2, -48, -8, -43, -18, 68, 0, 8, 4, 9, 32, 42, -16, -35, 36, -42, -12, 46, 20, -10, 5, -18, 24, 4, 5, -18, -16, 50, 33, -56, 63, -52, 53, 20, 4, -59, -20, 8, 3, -4, 34, -18, 20, -4, -65, 55, 40, -23, -34, 27, -76, -10, -9, 20, 18, -22, 8, -40, -16, 26, 35, 2, 0, 4, 22, -13, 6, 56, -24, -1, 6, -24, -20, -2, 39, -32, -28, -42, 36, 4, -62, -34, 16, 16, -41, -22, -6, 24, 18, 40, -30, -9, 80, 32, -48, 9, 47, -21, 14, -72, 2, -22, -4, -88, -8, -36, 40, -28, -30, -22, 14, -92, 12, -34, -68, 27, 8, 10, 7, -42, 108, 8, 80, -56, 50, 24, -20, -56, -21, -8, -32, 62, 18, -22, -12, 62, 7, -22, -18, 22, 5, -28, -40, 24, -72, -2, 50, 40, -72, -29, 56, 39, 2, -4, -10, 116, 30, 72, -28, -48, 36, -20, 2, 45, 9, 13, -24, 0, -27, -22, 26, 8, 43, 34, -14, -56, -32, -3, 40, -18, -16, 15, 36, 110, -42, 14, -25, 28, -80, 76, 42, -44, -8, -6, -21, -124, 22, -48, -4, 16, 8, 20, -4, -12, 80, 61, 38, 39, -50, -6, 30, 72, -95, 44, 4, 54, 4, 4, -56, 38, 59, -30, 79, -4, -8, 78, 4, -16, -18, -10, -16, 54, -2, 0, -3, -75, 7, -44, 23, 4, -56, -31, 3, 37, 10, -11, 24, -64, -80, -7, -14, 22, 47, 58, 4, 14, -26, 34, -7, 18, -92, -42, -4, -16, 8, 27, 36, -60, -20, 46, 17, -17, -100, -35, 24, 16, -44, -22, -13, 10, 32, -44, -61, 56, -20, -24, 8, -44, 14, -6, -27, -38, -16, 38, -8, 30, -58, 13, -24, -18, -44, -60, -110, 56, 0, 29, -61, -88, -8, -16, -9, 38, 96, 39, 44, -66, 72, -2, 118, 24, -33, 34, 7, -60, -21, -40, 18, 78, 28, -12, -70, 16, -44, -4, 92, -70, 8, 10, 14, 124, -9, 57, -35, 6, -20, -74, 42, -8, 0, -13, 8, -44, 56, -5, 116, 16, 48, -26, 44, 44, 38, 28, -60, -70, -62, -66, -60, -52, -13, -62, -62, -34, 4, 58, 10, 8, -13, 19, -48, 92, -28, 48, -24, -48, -7, -15, 74, 65, -40, 28, 104, 15, 76, 48, 12, 111, -42, 84, 12, 48, -116, 24, -40, -38, -44, 23, 48, 188, 52, -4, 18, 24, 12, -44, 88, -73, -18, -40, 0, -70, 88, -52, -28, 65, -8, -45, -4, -54, -22, -62, 74, 50, -36, -55, 84, 60, 18, 72, 60, -3, 56, 2, -110, -46, -66, 94, 0, -64, -7, -61, -114, -94, 43, -42, 44, -7, -36, 18, -40, 6, 124, 45, 31, 112, 64, -102, -19, -54, 14, -32, 64, 16, 12, 10, 86, -128, 11, -70, -39, 32, -114, 42, -20, -137, -48, -96, -73, -60, 26, 35, -54, -20, 112, -40, -21, -45, -38, 94, 62, 14, 55, -26, -8, 61, 21, 30, 6, -40, 16, 20, -61, -4, 66, 66, -54, 96, 60, 2, -25, -104, 45, -4, -21, 124, -44, -58, -4, -136, -56, -29, 2, 72, -37, 16, -26, -89, 64, 21, -2, -64, 68, -25, -103, 8, -22, -30, -15, -49, 30, 12, -14, -44, -48, 16, 80, -42, -78, 75, 50, 50, -47, 54, 16, -16, 44, 36, -60, -76, 60, -18, 4, -140, 24, -94, -10, -44, 12, 51, 24, -40, -16, 106, -32, 22, 12, -44, -10, 84, -6, 124, -49, -44, -35, -96, 5, -16, 37, 49, 44, 86, 148, 2, 18, 112, 38, 56, 89, 8, 8, 4, -54, -6, -111, -69, -68, 75, 18, -4, 59, 50, 84, -78, -56, 24, -56, 93, -45, -44, 4, 30, -46, 32, 20, 36, -38, 72, -8, -59, 32, 32, 66, 4, -51, 86, -38, -2, -21, 42, 67, -38, 8, 80, 60, 8, -52, 2, -14, -24, -78, -18, 70, 36, 67, 27, 2, 17], 'weight': 2, 'weight_parity': 1}
  79. label: 71.2.a.b
    {'Nk2': 284, 'analytic_conductor': 0.5669378543510907, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[71, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [71, 1, [7], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 3, 'field_disc': 257, 'field_disc_factorization': [[257, 1]], 'field_poly': [3, -4, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [3, -5, 0, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660924999, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '71.2.a.b', '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': '71.2.a.b', 'nf_label': '3.3.257.1', 'prim_orbit_index': 1, 'qexp_display': 'q+\\beta _{2}q^{2}+(-\\beta _{1}+\\beta _{2})q^{3}+(1+\\beta _{1}+\\cdots)q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 3, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '71.2.a', 'trace_display': [0, -1, -3, 2], 'trace_hash': 492302141750762433, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.070', 'prec': 7}, {'__RealLiteral__': 0, 'data': '2.844', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.925', 'prec': 10}, {'__RealLiteral__': 0, 'data': '21.058', 'prec': 17}, {'__RealLiteral__': 0, 'data': '13.367', 'prec': 17}, {'__RealLiteral__': 0, 'data': '223.196', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.008', 'prec': 4}, 'traces': [3, 0, -1, 4, -3, 9, 2, -9, 8, -10, -2, -18, 12, 2, -8, 2, 2, -21, 11, 5, -16, -2, 8, 12, -2, 0, -10, 18, -5, 11, -6, -3, 16, 2, -4, 21, 9, -1, -4, -1, 14, 2, -17, -18, 13, -18, -10, -11, 15, 11, -16, 16, 0, 39, 4, -4, 4, 11, -22, -12, 8, -20, -16, -7, -12, -2, -12, 18, -36, -24, 3, -45, 3, 17, 2, 7, -36, 36, 7, 19, 23, 2, 23, -6, -4, -12, 3, 4, 13, -16, 8, 44, -16, -18, -10, 24, 4, 40, 16, -4, -3, 2, -9, -36, 14, -20, -12, -57, 19, 24, 38, -20, 0, 35, 10, -8, 32, 2, 36, 35, 3, -24, -20, 10, 6, -58, -26, 15, 12, -40, -13, 6, -10, 40, -29, -4, -22, 60, 26, -18, -30, 0, -8, 58, -6, 10, 31, -29, -10, -28, -27, -34, -16, -40, 26, -72, -7, -52, -18, 6, 36, -45, 10, 34, -14, -1, 55, 50, 9, -24, 40, -29, -6, -37, 18, 20, -8, 25, -3, 66, 38, 8, 10, -42, -26, 22, -36, 20, -16, -28, -23, 19, -2, -22, -32, -16, 0, 58, -25, 17, 40, -23, 16, -6, -16, -27, 42, 8, 10, 36, 14, 18, -1, 40, 29, 69, -8, 51, 8, 18, 8, -7, 5, -54, -37, 46, 4, -69, 23, -42, -24, 26, -21, -84, 28, -14, -32, 40, -46, -37, 62, 40, -61, -2, -55, 38, 44, -2, 0, 47, 7, 48, -36, 44, 14, -20, -12, -27, -42, 20, -45, 32, -15, -50, 20, -12, 61, -52, -24, 38, 23, -20, -64, 62, -18, -102, -3, -18, 26, -12, 20, 6, -54, 4, -39, -8, 44, 24, -15, 7, -4, -5, -10, -35, 20, -10, 16, -44, 32, 45, -48, -13, 6, 18, 16, -58, -20, -12, -47, 22, -23, 48, 9, 29, 74, 39, -18, 40, -16, -2, 40, 0, -10, 114, -8, -42, 31, -40, 24, -36, 18, 23, 14, -12, -28, -32, 56, 0, -10, -18, 8, -55, 4, 39, -24, 54, 14, 63, 10, 40, -40, 54, -32, -70, -3, -48, 24, -64, -21, -55, -8, 42, 35, 72, -13, 72, -29, 26, 16, -6, -4, -24, 7, -40, 66, 12, -20, 62, 13, 29, 14, 71, -10, -87, 76, -96, -3, 8, -40, 44, 36, -5, 16, -40, 45, -48, -6, 39, -76, -33, -6, -116, -24, -9, 22, 38, 42, 50, 75, -64, 46, 38, 20, -174, -22, -12, -42, 12, -3, -48, -10, 36, -6, -20, 18, 9, -68, -52, 64, 75, 17, -80, -8, -48, 34, -12, 14, -11, -50, 12, -44, 8, 24, -3, -38, -47, -2, -20, -16, 29, -44, 10, 23, 10, -16, 23, -38, 18, -16, 34, 4, -28, -67, -35, -6, -29, 42, 84, 0, 18, 37, 68, 48, 125, -17, 12, 42, -38, 30, -21, 36, -18, -12, -32, 18, 42, 10, -48, -24, -54, -18, -78, 16, -4, -74, 38, 2, 71, -17, -60, -12, -45, 11, -10, 26, 0, -3, -40, 90, 36, 4, 84, -32, 74, 36, 66, -24, -8, 102, -4, 23, 50, 14, -29, 30, -36, -8, 32, 19, 2, -80, 66, 56, -11, -28, 76, -108, -6, -18, -90, 4, 9, 8, -54, -70, 8, -17, -68, 106, -40, -28, 168, -40, 29, -31, 68, 19, -32, -68, 82, -24, -4, 16, 6, -46, -60, 92, -9, -35, 26, 65, -72, 63, 48, -8, -29, 39, 40, -120, -40, -2, 56, 4, 1, 52, -32, 45, 30, -20, 56, -36, -4, 17, -62, -76, -8, 52, -72, 8, -34, 50, -72, -116, -50, -43, 37, -30, 15, 46, 10, -40, 48, 7, 72, -18, 68, 27, 27, -12, 32, -114, -11, -72, -44, -43, 69, 76, -44, -42, 42, -26, -73, 62, -20, -18, -60, 60, -38, 8, 19, 3, -116, -64, 48, 15, -12, -16, -114, -20, 44, 28, 34, 38, -45, -19, -12, -13, -12, -19, 48, -32, -12, -64, -70, 22, 77, -16, 67, 16, 36, 68, -36, -34, -24, 41, 12, -31, -92, -36, -12, -78, 48, 94, 60, -40, 84, -60, 31, 0, 114, -52, -108, -12, -12, -8, -46, 44, 78, 58, -12, 6, 156, 57, 20, 24, 4, -58, 138, 94, -10, 145, -14, 20, 28, 16, 105, -36, -44, -29, 8, 40, 2, -54, 30, 24, -71, 4, -16, -28, -11, -48, -120, -42, 80, 4, -54, 0, -142, 52, 5, 16, -44, -74, 70, 54, -38, 72, -12, 0, -76, 16, 14, 0, 44, 40, -60, -30, -9, 12, 2, -40, -166, 40, -86, 74, 102, -88, 75, 0, 124, 122, 118, -14, 126, -18, -34, -96, 22, 34, -48, -2, 0, 51, -74, -22, -103, -27, 36, 24, -1, 112, 10, 32, -66, -22, -77, 95, -6, 24, -27, 25, 112, -4, 192, -36, -80, 54, -14, -24, -115, 33, -30, 9, 8, 32, -32, -44, -33, -64, 2, 95, -190, 4, 0, -30, 24, -42, 264, -53, -68, -50, -28, 18, 114, -43, -66, -58, -13, -29, -6, -58, -138, 24, -48, -9, -48, 10, 42, -36, 40, -58, -18, -5, -116, 15, 76, -109, -8, 56, 14, -40, 33, 84, 24, -48, -156, 41, -36, 40, -32, -48, -6, 74, -72, -38, 12, 121, 12, -94, -82, 25, 43, 48, 72, 78, 86, 20, -121, 60, -3, -92, -11, -52, 58, 67, 106, -144, -38, -12, -84, -4, -48, 54, 46, -80, -55, 92, 82, 66, -96, 2, -28, 2, 90, -82, 83, 32, 62, -30, -72, 140, 58, 12, 96, -13, -35, 7, -24, -19, 34, 51, -79, 92, 14, 76, -180, 34, 80, -18, 4, 121, -79, 68, -36, -46, 72, 39, -198, 12, 24, -12, -68, -85, -74, -48, -10, -46, -66, 32, 20, -41, 68, -116, 116, 98, 108, -74, 31, -76, 6, 76, -102, 48, 104, 8, 90, -87, 114, 72, -59, -65, 60, -11, 98, 40, 38, 84, 28, -58, -42, -82, 12, 86, 2, -14, -141, -41, 57, 62, 29], 'weight': 2, 'weight_parity': 1}
  80. label: 72.2.a.a
    {'Nk2': 288, 'analytic_conductor': 0.5749228945532188, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [3, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [72, 1, [55, 37, 65], [1, 1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554504, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': False, 'label': '72.2.a.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': '24.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+2q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{19}+\\cdots', 'related_objects': ['EllipticCurve/Q/72/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '72.2.a', 'trace_display': [0, 0, 2, 0], 'trace_hash': 1436269620903515173, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.015', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.980', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.065', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.915', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.177', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.664', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, -4, 0, 0, 0, 8, 0, -1, 0, 0, 0, -6, 0, 8, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, -7, 0, 0, 0, 2, 0, -8, 0, 0, 0, -4, 0, -2, 0, 0, 0, -4, 0, -4, 0, 0, 0, -8, 0, 10, 0, 0, 0, 0, 0, -8, 0, 0, 0, 4, 0, -4, 0, 0, 0, 6, 0, 0, 0, 0, 0, -8, 0, 2, 0, 0, 0, 18, 0, 16, 0, 0, 0, 12, 0, -2, 0, 0, 0, -18, 0, 16, 0, 0, 0, 0, 0, 5, 0, 0, 0, -12, 0, -8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, -12, 0, 0, 0, 8, 0, -12, 0, 0, 0, -14, 0, -16, 0, 0, 0, 16, 0, -2, 0, 0, 0, 0, 0, 12, 0, 0, 0, -24, 0, -9, 0, 0, 0, -6, 0, 0, 0, 0, 0, -12, 0, 6, 0, 0, 0, 12, 0, 8, 0, 0, 0, 0, 0, 2, 0, 0, 0, 18, 0, 16, 0, 0, 0, 0, 0, 12, 0, 0, 0, 16, 0, -20, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, -8, 0, 0, 0, -12, 0, 22, 0, 0, 0, -10, 0, 0, 0, 0, 0, 16, 0, 18, 0, 0, 0, -14, 0, 8, 0, 0, 0, -20, 0, -32, 0, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 10, 0, 8, 0, 0, 0, 4, 0, -26, 0, 0, 0, -26, 0, -28, 0, 0, 0, 0, 0, -13, 0, 0, 0, 18, 0, -8, 0, 0, 0, -16, 0, 0, 0, 0, 0, -4, 0, 12, 0, 0, 0, 24, 0, -6, 0, 0, 0, -6, 0, 24, 0, 0, 0, 8, 0, 2, 0, 0, 0, 0, 0, 20, 0, 0, 0, -8, 0, 18, 0, 0, 0, -32, 0, 0, 0, 0, 0, 12, 0, 30, 0, 0, 0, -2, 0, -16, 0, 0, 0, 24, 0, -3, 0, 0, 0, 20, 0, -8, 0, 0, 0, 0, 0, -10, 0, 0, 0, 12, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -16, 0, 0, 0, -16, 0, 14, 0, 0, 0, 30, 0, -16, 0, 0, 0, -24, 0, -6, 0, 0, 0, 0, 0, 8, 0, 0, 0, -12, 0, -10, 0, 0, 0, 2, 0, 0, 0, 0, 0, -32, 0, -14, 0, 0, 0, -32, 0, 0, 0, 0, 0, -20, 0, 12, 0, 0, 0, 14, 0, -24, 0, 0, 0, 0, 0, -22, 0, 0, 0, 26, 0, 8, 0, 0, 0, 36, 0, 0, 0, 0, 0, -16, 0, 4, 0, 0, 0, 16, 0, -12, 0, 0, 0, 4, 0, -32, 0, 0, 0, 12, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, -24, 0, 36, 0, 0, 0, -6, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -26, 0, 4, 0, 0, 0, -16, 0, 41, 0, 0, 0, -12, 0, 24, 0, 0, 0, 28, 0, -18, 0, 0, 0, -4, 0, 44, 0, 0, 0, 24, 0, 0, 0, 0, 0, 26, 0, -8, 0, 0, 0, -28, 0, -36, 0, 0, 0, -10, 0, 36, 0, 0, 0, -8, 0, 2, 0, 0, 0, 0, 0, -8, 0, 0, 0, 44, 0, -32, 0, 0, 0, 14, 0, 0, 0, 0, 0, -24, 0, -38, 0, 0, 0, 10, 0, -40, 0, 0, 0, 0, 0, 38, 0, 0, 0, -42, 0, -44, 0, 0, 0, 0, 0, -19, 0, 0, 0, -12, 0, 16, 0, 0, 0, -16, 0, 14, 0, 0, 0, 14, 0, 12, 0, 0, 0, -8, 0, 16, 0, 0, 0, -6, 0, 8, 0, 0, 0, -12, 0, -10, 0, 0, 0, 0, 0, -48, 0, 0, 0, 8, 0, 34, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 12, 0, 0, 0, -4, 0, -4, 0, 0, 0, -24, 0, -12, 0, 0, 0, -6, 0, -24, 0, 0, 0, 0, 0, -10, 0, 0, 0, 64, 0, 16, 0, 0, 0, 32, 0, 0, 0, 0, 0, 6, 0, 48, 0, 0, 0, -8, 0, 14, 0, 0, 0, 16, 0, -4, 0, 0, 0, 8, 0, -28, 0, 0, 0, 0, 0, 24, 0, 0, 0, -32, 0, 38, 0, 0, 0, 22, 0, 0, 0, 0, 0, 8, 0, 2, 0, 0, 0, 18, 0, -8, 0, 0, 0, -24, 0, 32, 0, 0, 0, -4, 0, 28, 0, 0, 0, 0, 0, 4, 0, 0, 0, -22, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -26, 0, 4, 0, 0, 0, 24, 0, -16, 0, 0, 0, -30, 0, -16, 0, 0, 0, 28, 0, -50, 0, 0, 0, 14, 0, -48, 0, 0, 0, 24, 0, 7, 0, 0, 0, -18, 0, 0, 0, 0, 0, 48, 0, -10, 0, 0, 0, -42, 0, -12, 0, 0, 0, 32, 0, -12, 0, 0, 0, 32, 0, 8, 0, 0, 0, 0, 0, -18, 0, 0, 0, -50, 0, -4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, -48, 0, -4, 0, 0, 0, 12, 0, 4, 0, 0, 0, -16, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 16, 0, -6, 0, 0, 0, -50, 0, 28, 0, 0, 0, 16, 0, 42, 0, 0, 0, -6, 0, 48, 0, 0, 0, -12, 0, -20, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 33, 0, 0, 0, 4, 0, -16, 0, 0, 0, -36, 0, 0, 0, 0, 0, 30, 0, -24, 0, 0, 0, 24, 0, 36, 0, 0, 0, 32, 0, 40, 0, 0, 0, 32, 0, -26, 0, 0, 0], 'weight': 2, 'weight_parity': 1}
  81. label: 73.2.a.a
    {'Nk2': 292, 'analytic_conductor': 0.5829079347553469, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[73, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [73, 1, [5], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554505, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '73.2.a.a', 'level': 73, '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': [73], 'level_radical': 73, 'minimal_twist': '73.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-q^{4}+2q^{5}+2q^{7}-3q^{8}-3q^{9}+\\cdots', 'related_objects': ['EllipticCurve/Q/73/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '73.2.a', 'trace_display': [1, 0, 2, 2], 'trace_hash': 86513668210316004, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.980', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.922', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.727', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.011', 'prec': 7}, 'traces': [1, 1, 0, -1, 2, 0, 2, -3, -3, 2, -2, 0, -6, 2, 0, -1, 2, -3, 8, -2, 0, -2, 4, 0, -1, -6, 0, -2, 2, 0, -2, 5, 0, 2, 4, 3, -6, 8, 0, -6, 6, 0, -2, 2, -6, 4, 6, 0, -3, -1, 0, 6, 10, 0, -4, -6, 0, 2, -6, 0, -14, -2, -6, 7, -12, 0, 8, -2, 0, 4, 0, 9, 1, -6, 0, -8, -4, 0, -4, -2, 9, 6, -14, 0, 4, -2, 0, 6, -6, -6, -12, -4, 0, 6, 16, 0, -10, -3, 6, 1, 10, 0, 6, 18, 0, 10, 18, 0, -2, -4, 0, -2, 2, 0, 8, -2, 18, -6, 4, 0, -7, -14, 0, 2, -12, -6, 12, -3, 0, -12, -18, 0, 16, 8, 0, -6, -6, 0, -14, -4, 0, 0, 12, 3, 4, 1, 0, 6, -22, 0, 10, -24, -6, -4, -4, 0, 2, -4, 0, 10, 8, 9, -14, -6, 0, -14, 14, 0, 23, 4, -24, 2, 6, 0, -2, 2, 0, -6, -6, 6, 10, -12, 0, -12, -12, 0, -4, -6, 0, 16, 26, 0, 10, -10, 0, 3, 18, 6, 10, 3, 0, 10, 4, 0, 12, 6, -12, 6, -16, 0, -28, -10, 0, 18, -4, 0, -4, -2, 0, 4, -12, 0, 8, 10, 3, 2, -12, 0, 2, 8, 0, -6, 18, 18, 12, 6, 0, 4, -22, 0, 10, -7, 0, 14, -6, 0, -48, 6, 0, -12, -12, 6, -8, 12, 0, -17, 22, 0, -12, 12, -6, -18, 6, 0, 20, 16, 0, -8, 6, 0, -10, -2, 0, -6, 2, 0, -6, -14, 6, -12, 18, 0, 28, 0, 0, 12, 12, -15, -13, 4, 0, -1, -26, 0, -12, 18, 0, -22, -24, 0, -4, 10, 0, -8, -28, -6, -2, 4, 0, -4, 12, 0, -6, 2, -12, 4, 6, 0, -4, 14, 0, 8, 16, -9, 6, -14, 0, -18, 12, 0, 18, 14, 18, 14, 16, 0, -22, 23, 0, -4, 4, -24, -20, 6, 0, 6, -12, 0, 2, -2, 0, -10, -10, 0, 0, 6, 0, -6, 20, 18, 45, 10, 0, 12, 2, 0, 16, -4, -18, -12, 20, 0, -10, -4, 0, -18, -12, 0, 18, -16, 0, 26, 8, 0, -8, 10, 6, 10, -22, 0, 8, 9, 0, 18, -8, -6, 14, 10, 0, 1, 14, 0, 12, -10, 18, 4, 12, 0, -14, 12, 0, -6, -12, -12, -28, -30, 0, -16, -32, 0, 34, -28, -18, -30, -2, 0, -28, -18, 0, -4, 10, 0, -6, -4, 0, 2, 32, 0, 0, 12, 9, -12, 18, 0, -12, 8, 0, 14, 2, 3, -12, -2, 0, -12, -24, 0, -34, 2, 0, -8, 6, 0, -4, -2, 0, 18, 6, -18, 16, 12, 0, 18, 4, 0, -8, -4, -30, -22, -24, 0, 36, 10, 0, 7, -20, 0, 20, 42, 0, -6, 2, 0, 4, -48, 12, 2, 0, 0, 32, 12, 0, -12, 24, 18, 20, -8, 0, -12, -30, 0, 2, -11, 0, 22, 12, 0, -12, -12, 0, 36, -14, -6, 16, 18, 0, 6, -4, 0, -7, 20, 18, -16, -36, 0, 36, -24, 0, 6, 6, 0, 26, -10, 0, 10, -4, 0, -28, 6, 42, 2, 16, 0, -8, -6, 0, 14, -42, 6, 12, -4, 0, 18, -10, 0, 4, 28, 18, 0, 18, 0, -10, -12, 0, 12, -4, -21, 2, -13, 0, -4, -28, 0, -20, -3, 36, -26, 32, 0, -16, -12, 0, 6, -18, 0, 8, 22, 0, -24, 30, 0, -46, -4, -24, -10, -14, 0, -20, 40, 0, -28, -36, 6, 26, -2, 0, 12, -6, 0, 0, 4, 0, 12, -12, 0, -19, -6, 0, -2, -12, -12, -2, 12, 0, 6, 24, 0, 18, -4, 0, -6, -18, 0, 34, -8, 0, 16, -30, -27, 12, 6, 0, 14, 14, 0, -36, -6, -3, 12, -12, 0, -26, 18, 0, 42, 32, 18, 8, -14, 0, 16, 28, 0, -14, -22, 0, -23, 26, 0, -20, -12, 0, 4, 30, 24, -12, -20, 0, 2, -60, 0, -6, -6, 12, -12, -28, 0, 12, 2, 0, 2, -46, 0, -48, -14, 0, -10, 20, 0, 18, 0, 12, 18, -8, 0, 24, 6, 0, 20, -42, 6, 12, 45, 0, -10, -2, 0, 4, 36, -27, 2, -4, 0, -10, 16, 0, 20, -16, -18, 20, 12, 0, 20, 6, 0, -44, -10, 42, 4, 36, 0, 38, -6, 0, -12, 20, 0, -2, 18, 0, -48, -22, 0, -4, -26, -12, 8, 36, 0, -14, -8, 0, -10, 18, 6, 2, 30, 0, -22, 48, 0, 0, 8, 0, 3, 4, 0, 4, -18, 0, -8, 4, -18, 84, 14, 0, -10, -30, 0, 12, -5, 18, 14, -2, 0, 16, 12, 0, -30, 30, 18, -44, -4, 0, 12, -28, 0, -16, -14, 36, -12, 22, 0, 34, -18, 0, -12, -48, 12, 2, -28, 0, -42, -6, 0, 28, 16, 0, -32, 0, 0, -25, 34, 0, 28, 46, -18, -14, -10, 0, -2, -24, 0, -34, -28, -48, -54, -6, 0, 26, 4, 0, 10, 30, 0, 12, -6, 0, 4, 8, 0, -48, 6, 30, 32, -24, 0, -14, 0, 0, 4, -6, 9, -6, 12, 0, 18, -18, 0, 24, -12, -18, -8, 48, 0, -12, -6, 0, 2, -4, -3, 20, -12, 0, -6, 20, 0, -2, 12, -30, -24, -36, 0, 28, -34, 0, -2, -36, 0, -34, -24, 0, 6, 0, 0, 6, -4, -18, 10, 26, 0, -24, -18, 0, 6, -8, -54, 14, 16, 0, -12, 18, 0, 24, 6, 0, 4, 28, 0, -6, -8, 0, -12, 22, -30, 52, 22, 0, -24, -12, 0, -27, 36, -54, -10, 20, 0, 56, 21, 0, -20, 30, 0, -28, 20, 0, 14, 2, 0, 12, 6, 6, 2, -6, 0, 36, 4, 0, 48, -8, 12, -58, -10, 0, 0, 20, 0, 58, 32, 0, 36], 'weight': 2, 'weight_parity': 1}
  82. label: 73.2.a.b
    {'Nk2': 292, 'analytic_conductor': 0.5829079347553469, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[73, 1]], 'atkin_lehner_string': '+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [73, 1, [5], [1]], 'cm_discs': [], 'conrey_index': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [1, 3, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660925001, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '73.2.a.b', 'level': 73, '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': [73], 'level_radical': 73, 'minimal_twist': '73.2.a.b', 'nf_label': '2.2.5.1', 'prim_orbit_index': 1, 'qexp_display': 'q+(-1-\\beta )q^{2}+(-2+\\beta )q^{3}+3\\beta q^{4}+\\cdots', 'related_objects': ['Genus2Curve/Q/5329/b'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '73.2.a', 'trace_display': [-3, -3, -3, -6], 'trace_hash': 391968563378657010, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '1.962', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '9.900', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '73.086', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [2, -3, -3, 3, -3, 2, -6, -6, 1, 7, -3, 3, 1, 9, 2, 13, 0, 6, 2, -12, 9, 2, -15, -1, -3, 6, 0, -9, 6, -3, 2, -15, 7, -15, 9, -21, -4, -3, -9, 19, 0, -6, -2, 3, 6, 25, -6, -12, 4, -3, 15, -21, 6, -5, 2, 18, -3, -19, -12, 3, 7, 12, -3, 4, 6, -3, 16, 45, 20, -21, -21, 27, -2, -9, 12, 3, 9, 1, -19, -27, 2, 10, -3, -9, -15, 3, 1, -1, 12, -19, -3, -30, -18, -1, -3, 15, -9, -6, -9, 18, -6, 0, 18, 27, -6, 11, -15, 15, -17, -3, 21, -39, -21, 2, 25, 39, 23, 28, 0, -6, -15, -3, -10, -42, 12, -18, -7, 9, 3, -19, 15, -12, -6, -9, -5, -60, 6, -15, 21, 36, 19, 34, -9, -16, -19, 3, -6, 39, 0, -3, 5, -6, -45, -6, 12, 24, 17, 36, -29, 30, 45, -18, 3, -30, -3, -3, 15, 3, -3, 45, 1, -3, -21, 6, 9, -12, 8, -23, 9, 39, -10, -18, -18, 55, -9, 2, 15, 21, 0, 7, -24, 9, 14, 6, 1, 6, -6, 1, -5, -21, -39, -16, -18, -45, 10, -27, 0, -16, -3, 9, -6, -51, 29, 25, 3, -20, -6, 18, 3, 3, -45, -4, -4, 45, -24, 14, 9, 3, 3, -60, -21, -58, 0, -27, -1, -48, 21, 45, 3, 13, -12, 30, 12, -12, -6, 0, 1, 54, 12, -23, 15, 63, 20, 3, 0, -9, 33, -2, 12, 39, -27, -20, -18, 9, 11, 9, -13, -21, -9, 15, -18, 45, 27, 21, 12, -15, 13, -39, 46, -57, 24, -6, 36, -39, 2, 1, 0, 15, 56, 51, 21, -3, -36, 4, 28, -48, 5, -10, 0, -27, 6, -15, 34, 13, -3, 60, 28, -9, -27, -38, 15, -23, -27, -33, -18, -51, -36, 6, 1, -21, 20, -75, 0, 48, -24, -12, 33, 40, 18, 2, -20, 18, -47, -15, -9, 36, -7, 12, 49, -90, -18, 6, 30, 6, -15, 39, 6, -21, -7, 9, -15, 15, 21, -12, 34, 33, -45, 4, -21, -58, -36, 45, 15, 63, 3, 7, -34, -105, 30, 31, -18, 48, -12, 0, -13, -22, -27, 15, -8, -12, 18, 61, -60, -26, -6, -6, -1, 9, -27, 6, -15, -12, -25, -21, 36, 24, -22, 0, 9, 3, -6, 16, 46, 66, -18, 57, 21, 45, 10, -30, -39, 27, 36, -55, -3, 15, -24, 2, -27, -9, 18, -21, -33, 62, 45, -21, -21, -30, 26, -7, 36, 15, -13, -36, 6, -3, -15, -2, -24, -6, 2, 60, -18, -51, -23, 6, 10, -12, 9, 21, -10, 21, 0, 9, -18, -1, 19, -42, 30, 105, 18, 9, -4, 69, 2, 55, 24, 12, -48, 9, -18, 76, 3, -19, -3, -135, 63, -17, -30, -15, -47, 33, -60, -45, 6, 17, -32, 9, 3, 14, 45, 30, 60, 6, 1, -32, 63, -3, -50, 33, -30, -55, 3, -81, -16, -15, -3, 12, 48, -15, 6, 18, 0, -62, -27, -3, 19, 27, 24, -58, 0, 58, -58, 15, -36, 37, -90, 23, 69, -39, 24, -9, 30, 12, 25, 12, -31, 61, -6, -30, 51, 42, -15, -45, 18, -3, -31, -81, 26, -3, 6, 0, 57, -57, -4, 54, 48, -54, -1, 81, -45, -41, -18, -39, 14, -84, -6, 73, 36, -3, -40, 24, 11, -30, 15, -43, -30, -84, -36, -96, 9, -9, -29, 6, -27, 24, 36, 6, 2, -72, 39, 19, 9, 0, 45, 30, 15, -55, 27, 24, -7, -9, 53, 30, 30, -6, -16, -15, -3, 2, -33, -45, -65, -12, 0, 3, -54, 18, -8, 78, -5, -55, -36, -21, -8, 3, 7, 48, 90, 57, 61, 87, 39, 64, 3, 69, 2, 6, -3, -1, 12, -15, -44, 90, -2, -15, 39, -66, 8, 21, 54, 27, 15, -17, -20, -30, -1, 3, 18, 3, -53, 0, 75, -21, 9, 48, -55, 0, 6, 11, -18, -45, 80, 63, 15, -27, 12, -21, 27, 135, -36, 2, -6, -21, 21, -45, 33, -13, 63, 25, -32, -54, 27, 56, -39, 27, -60, -12, -55, -54, -42, 20, -4, 9, -6, -79, 18, 12, -39, -81, 13, -56, 0, 0, 1, -39, 8, -16, 18, 69, -54, 54, 3, -105, 21, -15, -15, -81, -59, -7, 0, 33, -12, 6, 4, 120, -39, -40, -93, -66, -9, -33, -24, -46, -10, 33, -24, -45, 45, 12, 6, -9, 10, 58, -15, -45, 40, 12, -45, 19, 15, -7, 51, -111, 60, 95, 24, -9, -17, 9, -37, -24, -18, -6, -48, -3, -63, 48, 0, -21, 29, 135, 20, 26, -33, 15, 40, 81, 17, -89, 63, -23, 26, 78, 6, 15, 21, -6, 60, 0, -9, 14, 3, 69, -75, -54, -34, -82, -18, 52, 68, -117, 12, -4, -12, 30, -2, -15, -69, 60, 66, 6, 47, -54, -33, -84, -69, 165, -14, 12, 18, -43, 0, 21, -15, 3, -30, 28, -27, 18, 0, -27, -31, 81, 12, 22, 45, -21, -24, -45, 15, -24, -44, 9, 6, 55, -45, -9, -10, 12, 30, -84, 3, -15, 39, 57, -84, 126, 21, -19, 53, 21, -27, 25, -36, -3, 42, 81, 84, 13, -39, 12, 39, -45, -12, 82, -9, 47, 21, 57, 12, -6, -6, 0, 4, -27, 55, -16, -54, 9, -120, 0, -9, -7, 45, 5, -20, -54, -78, 57, -60, -12, 12, -51, 7, 117, -45, -45, 66, -165, -72, -17, -3, 36, 51, 21, 9, -75, 54, 12, 4, -165, 10, -31, 0, -39, 26, 27, 78, -24, -27, 17, 10, -108, 15, -2, -9, -6, -1, -3, 44, 180, 66, -62, 61, 42, -9, 80, -18, 4, 30, 48, 0, -63, -6, 45, -49, 75, 15, -9, 84, -87, -63, 48, 51, 23, -9, 3, -13, -24, -31, -25, -60, -30, -21, -135, -57, -21, 15, 6, -4, 30, 60, -102, 0, -27, 41, 75, 30, -56], 'weight': 2, 'weight_parity': 1}
  83. label: 73.2.a.c
    {'Nk2': 292, 'analytic_conductor': 0.5829079347553469, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[73, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [73, 1, [5], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, 'field_disc': 13, 'field_disc_factorization': [[13, 1]], 'field_poly': [-3, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-3, -1, 1]]], 'hecke_orbit': 3, 'hecke_orbit_code': 9007199288295497, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '73.2.a.c', 'level': 73, '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': [73], 'level_radical': 73, 'minimal_twist': '73.2.a.c', 'nf_label': '2.2.13.1', 'prim_orbit_index': 1, 'qexp_display': 'q+\\beta q^{2}+(1-\\beta )q^{3}+(1+\\beta )q^{4}-\\beta q^{5}+\\cdots', 'related_objects': ['Genus2Curve/Q/5329/a'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '73.2.a', 'trace_display': [1, 1, -1, -2], 'trace_hash': 1838212080306629382, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.030', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.969', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.345', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.321', 'prec': 14}, {'__RealLiteral__': 0, 'data': '3.183', 'prec': 14}, {'__RealLiteral__': 0, 'data': '59.415', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, 'traces': [2, 1, 1, 3, -1, -6, -2, 6, 1, -7, 7, -5, -1, -1, 6, -3, -4, -6, -14, -8, -1, 10, 13, 3, -3, 6, 4, -3, 2, 3, 6, -7, -3, 11, 1, -5, 8, -7, -7, -3, -12, 6, 6, 17, 6, 13, 18, -8, -12, 5, -15, 5, -2, 15, -10, -6, -7, -25, 0, 9, -9, 16, -1, -4, -6, -21, 4, 7, 0, 7, 3, 3, 2, -9, -8, -21, -7, 3, 1, -5, -14, -6, 7, 5, -11, -23, 27, 21, 12, 3, 1, 26, -10, 9, 7, 3, -5, -6, -3, 2, -14, 12, 2, -3, -6, 25, -9, 19, 3, -31, 17, 3, 17, 42, -13, -23, -7, 0, 4, 18, 9, -11, -6, 22, 0, 6, -7, -27, 29, -3, 9, -24, 14, -37, -15, -12, 42, -39, 3, 8, 9, -18, 3, -8, 25, 1, -6, -1, -16, 9, 27, -42, -15, -10, -16, -4, -5, 20, -27, 10, -13, 6, -3, -18, 21, -29, 17, -3, -19, 1, -7, -17, -9, -6, 3, -4, 0, 45, -9, 9, 30, -6, 2, 39, 9, -18, -1, 27, -4, 49, -16, 37, -30, -22, -3, -18, 18, -21, 9, -9, 41, -20, -2, -3, 6, 27, 0, 8, -49, -3, -26, 23, 21, 15, 23, 12, -6, 34, 1, -41, 15, -24, -20, 7, -8, 2, -3, 35, 1, -52, 3, 6, 0, 3, -9, 0, -19, -11, 17, -9, 0, 50, -32, -20, 6, 36, 7, 18, 36, 39, -21, 5, 52, 3, -12, -25, 1, -18, -8, -9, 27, 24, 18, -9, -25, 7, -33, -33, -21, -27, -26, 19, 7, 21, -4, -39, -25, -5, -10, 3, -24, -54, -24, -15, -42, 21, 12, 3, 0, 19, 17, 3, 4, 36, 0, 24, 27, -34, 0, 1, -6, 7, 6, 21, 11, 12, 12, -17, -25, -34, -9, -21, 35, 17, -6, 21, -24, 6, -19, 41, -24, -13, 28, -8, 8, -8, -31, -36, -18, 30, -28, -22, 17, -37, 37, 8, 7, -16, 15, -10, 34, 42, 26, 18, 39, 15, -42, 21, 1, -5, 11, -31, 5, 0, 18, 57, 15, -24, 23, 18, 60, -11, -41, -5, -1, 27, -6, -13, -6, -15, 2, -28, 40, 32, -39, 54, -27, -15, 8, 56, -10, -73, -4, 6, 10, -2, 29, -27, -7, 18, -13, -36, -15, 9, -20, -24, -26, 76, 7, 11, 2, -12, 10, -34, -6, 25, 15, -45, 18, 42, 21, 29, 0, -39, 29, -3, 8, -70, 1, -9, -18, -13, 9, -6, 19, -9, 9, 6, -18, 5, 28, 7, -19, -16, 6, 37, -91, -6, 8, -30, -6, -12, 6, -7, -45, -10, 18, 4, -37, 9, -42, 19, 20, 57, 6, -21, -5, -58, 18, -65, 54, 21, -8, -29, 18, -39, 48, -4, -4, -63, -22, 0, -5, -3, 21, -7, -27, 41, -18, -21, -17, -65, 0, 59, 22, -3, 40, -27, 5, 42, 47, 30, -56, -42, 21, 4, -3, -21, -14, 39, 54, 9, -9, -3, 20, 91, -3, -4, 0, 33, -2, 22, -28, 46, -27, 11, 63, 9, -24, -18, 16, -6, 18, 33, 8, -69, 14, -15, 45, -19, 0, 21, 6, -36, -15, 12, 15, 9, -42, -42, -23, 26, 41, 1, -34, -3, 25, 63, 2, 11, -14, 0, -1, 33, 24, -2, 24, -18, -29, 5, -33, -51, -22, -45, -2, 40, 14, 9, -36, -21, 28, 24, 57, 6, -13, 37, -38, -52, -28, 44, -7, 15, 19, 6, -3, 28, -16, 30, -42, 0, 9, -25, -51, 72, 11, -50, -67, 39, -15, -24, 43, 23, 41, 34, -50, 42, 12, 49, -27, 38, -9, -3, 37, -20, -36, -21, -66, -6, 32, -50, 39, -63, -12, 17, -24, -15, 21, 12, -42, -3, -9, 3, -13, -12, -3, -21, 6, -94, 21, 33, 0, 27, -24, -26, 18, -77, 9, -42, 0, -9, 10, -11, -49, -9, -24, 18, 1, -9, 6, 51, 63, 12, 27, 21, -7, -24, -13, -20, -10, 25, -38, -3, 12, 101, 7, -35, -28, -51, 5, -33, -60, 82, 42, 35, -21, 13, 59, -35, 27, 39, -28, 6, 3, -60, 5, 81, 24, 20, 39, -2, -34, 12, -56, -53, 54, -43, 14, 0, -49, 9, -19, 36, 52, -12, -21, -33, -24, 44, 6, -9, -2, 30, 65, 19, -29, -27, -27, 3, 13, -7, -64, 29, 4, 10, -36, -52, -25, 36, -5, -6, 49, -25, 84, -30, 34, -19, 36, 31, 9, 0, -14, -27, -30, 6, -7, -19, 0, 108, -39, 21, 17, 21, -3, -89, -12, 11, 0, 7, 57, 31, -45, -32, 54, -18, 4, -15, -17, 68, 84, 15, -9, 65, -48, 18, -17, -27, 36, 27, 87, -23, -17, -9, -2, 26, -6, 85, -15, -42, -36, 4, -33, 14, 7, 29, 13, 18, -30, -42, -30, 36, -24, 23, -52, -12, 8, 42, -42, -17, 7, 48, 46, -126, 45, 6, -15, 0, 51, -39, 10, 8, -58, -37, 24, -9, 37, -119, 38, -32, 33, -18, 48, 43, 27, -39, 16, -54, -9, 29, -64, -23, 39, 12, -56, 11, -42, -27, 3, -9, 82, 28, 6, 40, 93, -27, -15, -81, 52, -22, 23, -75, -41, 9, 17, -91, 0, -5, 30, -87, -24, -11, 15, 36, -19, 3, 0, 42, 45, 51, 7, -81, -36, -30, -126, 48, 24, 27, -39, -64, -46, 1, 56, -60, -29, 51, 11, -81, -72, 54, 6, 3, 12, 56, -8, -139, -27, -57, -9, 9, -26, -39, 32, 27, -21, 24, -25, 113, -25, 19, 38, 48, 84, -39, 54, 63, -32, -21, -26, 37, 50, -72, 57, 15, -78, 0, 15, -74, 43, -22, -1, -35, -12, 12, -14, 6, 73, 58, 75, 108, -42, -12, -18, 24, -24, -65, 2, 39, -29, 27, 105, 37, -24, -35, -3, 20, 17, 7, 77, 9, 81, 48, -31, 17, 0, -18, -9, 37, -9, -35, 13, 30, 52, -34, -40, 18, -76, 15, -63, 71, -10, 0], 'weight': 2, 'weight_parity': 1}
  84. label: 74.2.a.a
    {'Nk2': 296, 'analytic_conductor': 0.5908929749574748, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [37, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [74, 1, [39], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, 'field_disc': 13, 'field_disc_factorization': [[13, 1]], 'field_poly': [-3, -1, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-1, -3, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554506, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '74.2.a.a', 'level': 74, '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': [2, 37], 'level_radical': 74, 'minimal_twist': '74.2.a.a', 'nf_label': '2.2.13.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}+(1+\\beta )q^{3}+q^{4}-\\beta q^{5}+(-1+\\cdots)q^{6}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '74.2.a', 'trace_display': [-2, 3, -1, 2], 'trace_hash': 1243543212558769297, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.022', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.966', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.367', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.305', 'prec': 14}, {'__RealLiteral__': 0, 'data': '3.919', 'prec': 14}, {'__RealLiteral__': 0, 'data': '62.818', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.008', 'prec': 4}, 'traces': [2, -2, 3, 2, -1, -3, 2, -2, 5, 1, -1, 3, -1, -2, -8, 2, -12, -5, 4, -1, -10, 1, -3, -3, -3, 1, 18, 2, 3, 8, 3, -2, -8, 12, 12, 5, 2, -4, 5, 1, 9, 10, -6, -1, -22, 3, 2, 3, 14, 3, -18, -1, -12, -18, 7, -2, 6, -3, 14, -8, -3, -3, -34, 2, -6, 8, 11, -12, 15, -12, 12, -5, -21, -2, 2, 4, 12, -5, -7, -1, 38, -9, 20, -10, 6, 6, -15, 1, -4, 22, -14, -3, -2, -2, -2, -3, -4, -14, -22, -3, 4, 18, 3, 1, 18, 12, 5, 18, 4, -7, 3, 2, 8, -6, -18, 3, 17, -14, -12, 8, -15, 3, 33, 3, 0, 34, -24, -2, 4, 6, 14, -8, 4, -11, -35, 12, -9, -15, 7, 12, 16, -12, -6, 5, 18, 21, -5, 2, 18, -2, -34, -4, -30, -12, 5, 5, 0, 7, -18, 1, -42, -38, -12, 9, 17, -20, 7, 10, -19, -6, 10, -6, -32, 15, -16, -1, 34, 4, -6, -22, 40, 14, 28, 3, -1, 2, 6, 2, -34, 2, 7, 3, -8, 4, -9, 14, -12, 22, 24, 3, -16, -4, 42, -18, -24, -3, 51, -1, -2, -18, 17, -12, 18, -5, -10, -18, 16, -4, -38, 7, 6, -3, 10, -2, 12, -8, 6, 6, 42, 18, 18, -3, -1, -17, -14, 14, 35, 12, -17, -8, 16, 15, 42, -3, 19, -33, -2, -3, 4, 0, -28, -34, -18, 24, 48, 2, -8, -4, 2, -6, -51, -14, 6, 8, 6, -4, -32, 11, -28, 35, -16, -12, -8, 9, -5, 15, -25, -7, -12, -12, -24, -16, 42, 12, -16, 6, -30, -5, 38, -18, -58, -21, -14, 5, -20, -2, -35, -18, 21, 2, -32, 34, -46, 4, -31, 30, 25, 12, -2, -5, 21, -5, 18, 0, 30, -7, 4, 18, 18, -1, 1, 42, -24, 38, 8, 12, 6, -9, -24, -17, -12, 20, 5, -7, 27, -10, -13, 19, -14, 6, 5, -10, 52, 6, -27, 32, 42, -15, 6, 16, 17, 1, 42, -34, -6, -4, 60, 6, -8, 22, -30, -40, -16, -14, 17, -28, -14, -3, 81, 1, -12, -2, -14, -6, 39, -2, -21, 34, 9, -2, -62, -7, -16, -3, -6, 8, 24, -4, -49, 9, 18, -14, 34, 12, -42, -22, 34, -24, -20, -3, 6, 16, -8, 4, -58, -42, -1, 18, 26, 24, 6, 3, -12, -51, 16, 1, -9, 2, 11, 18, 25, -17, 44, 12, 18, -18, -68, 5, -9, 10, 4, 18, 23, -16, 27, 4, -6, 38, 21, -7, -43, -6, 33, 3, 28, -10, 66, 2, -16, -12, -24, 8, -64, -6, -6, -6, 2, -42, -108, -18, -4, -18, 57, 3, 1, 1, 0, 17, 76, 14, -26, -14, -10, -35, -6, -12, -30, 17, -1, 8, -1, -16, -24, -15, 54, -42, -60, 3, 34, -19, 3, 33, -18, 2, 37, 3, 12, -4, -34, 0, -22, 28, -31, 34, 50, 18, -35, -24, -30, -48, -8, -2, 36, 8, 5, 4, -14, -2, -22, 6, 24, 51, 14, 14, 2, -6, -18, -8, 17, -6, 74, 4, 15, 32, 4, -11, -48, 28, 19, -35, 5, 16, 60, 12, -2, 8, -34, -9, 90, 5, 6, -15, -98, 25, -8, 7, 5, 12, 16, 12, 48, 24, 16, 16, 22, -42, -40, -12, 8, 16, -37, -6, -22, 30, 24, 5, -6, -38, -12, 18, 72, 58, 6, 21, -15, 14, -48, -5, 6, 20, -18, 2, 55, 35, -72, 18, 88, -21, -56, -2, -45, 32, -70, -34, 1, 46, -45, -4, 24, 31, 12, -30, -38, -25, -75, -12, 5, 2, -9, 5, 51, -21, 48, 5, -24, -18, -16, 0, -12, -30, 33, 7, 32, -4, 38, -18, -33, -18, 30, 1, -23, -1, -38, -42, -2, 24, -5, -38, -20, -8, -2, -12, 3, -6, -20, 9, -72, 24, -59, 17, -43, 12, -30, -20, 24, -5, -63, 7, -24, -27, -31, 10, 45, 13, -1, -19, -22, 14, 100, -6, 48, -5, 24, 10, -15, -52, 76, -6, 6, 27, 16, -32, 30, -42, 16, 15, -54, -6, 31, -16, 55, -17, 4, -1, -34, -42, 108, 34, -43, 6, 119, 4, -24, -60, 3, -6, -58, 8, -60, -22, 16, 30, 24, 40, -24, 16, 49, 14, 53, -17, 36, 28, 16, 14, -4, 3, 27, -81, -45, -1, 10, 12, 6, 2, -48, 14, -28, 6, 18, -39, 28, 2, -68, 21, 30, -34, 15, -9, -27, 2, 59, 62, 4, 7, 132, 16, 6, 3, -44, 6, 14, -8, -28, -24, -11, 4, -10, 49, 18, -9, -6, -18, -51, 14, 26, -34, 36, -12, 48, 42, 60, 22, 34, -34, 48, 24, 5, 20, -12, 3, -88, -6, 17, -16, -18, 8, -68, -4, -6, 58, 47, 42, -76, 1, -46, -18, -12, -26, 4, -24, 8, -6, 32, -3, -1, 12, 62, 51, -23, -16, 8, -1, -84, 9, 29, -2, 1, -11, -62, -18, 5, -25, -36, 17, 16, -44, -28, -12, 76, -18, -3, 18, 31, 68, -44, -5, 28, 9, 24, -10, -84, -4, 24, -18, -10, -23, 57, 16, -42, -27, -38, -4, -166, 6, -78, -38, 0, -21, 44, 7, -3, 43, 24, 6, -82, -33, 28, -3, 28, -28, -58, 10, 4, -66, 42, -2, 12, 16, 24, 12, 72, 24, 4, -8, -20, 64, 52, 6, -146, 6, -64, 6, 16, -2, -53, 42, -12, 108, -48, 18, 57, 4, -6, 18, -3, -57, -12, -3, -55, -1, 28, -1, 51, 0, -42, -17, -47, -76, -38, -14, 6, 26, 45, 14, 108, 10, 36, 35, 4, 6, 32, 12, 31, 30, 29, -17, 27, 1, -48, -8, -51, 1, -7, 16, 4, 24, 19, 15, -36, -54, 9, 42, 46, 60, -1, -3, 36, -34, 28, 19, 10, -3, -24, -33, 6, 18, -36, -2, 48, -37, 105, -3, -44, -12, -64, 4, -76, 34, 18, 0], 'weight': 2, 'weight_parity': 1}
  85. label: 74.2.a.b
    {'Nk2': 296, 'analytic_conductor': 0.5908929749574748, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [37, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [74, 1, [39], [1]], 'cm_discs': [], 'conrey_index': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-1, 1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660925002, 'hecke_ring_generator_nbound': 3, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '74.2.a.b', 'level': 74, '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': [2, 37], 'level_radical': 74, 'minimal_twist': '74.2.a.b', 'nf_label': '2.2.5.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}-\\beta q^{3}+q^{4}+(-1+3\\beta )q^{5}+\\cdots', 'related_objects': [], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '74.2.a', 'trace_display': [2, -1, 1, -2], 'trace_hash': 380605827047653105, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.939', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.195', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.342', 'prec': 14}, {'__RealLiteral__': 0, 'data': '2.038', 'prec': 14}, {'__RealLiteral__': 0, 'data': '61.706', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.011', 'prec': 7}, 'traces': [2, 2, -1, 2, 1, -1, -2, 2, -3, 1, -5, -1, 1, -2, -8, 2, 0, -3, 0, 1, 6, -5, -1, -1, 13, 1, 2, -2, -3, -8, 17, 2, 0, 0, -16, -3, -2, 0, 7, 1, 17, 6, -6, -5, 6, -1, 2, -1, -2, 13, 10, 1, -8, 2, 5, -2, -10, -3, -14, -8, 19, 17, -2, 2, -22, 0, -9, 0, -7, -16, -12, -3, 3, -2, -14, 0, 0, 7, 3, 1, -2, 17, -20, 6, -30, -6, 19, -5, -12, 6, 14, -1, -6, 2, 30, -1, 8, -2, 10, 13, 16, 10, 1, 1, 18, -8, 1, 2, -12, 5, 1, -2, 4, -10, 22, -3, -9, -14, 20, -8, -7, 19, -11, 17, 24, -2, -8, 2, 8, -22, -14, 0, -20, -9, 31, 0, 23, -7, 3, -16, 4, -12, -10, -3, -54, 3, -9, -2, 10, -14, 22, 0, -10, 0, 1, 7, -24, 3, -6, 1, -14, -2, -16, 17, 15, -20, 21, 6, -3, -30, 10, -6, 8, 19, -28, -5, 2, -12, 6, 6, 20, 14, -12, -1, -1, -6, -10, 2, -22, 30, -3, -1, 8, 8, 11, -2, -24, 10, 24, 13, -8, 16, 38, 10, 16, 1, 9, 1, 10, 18, -11, -8, -14, 1, -18, 2, -12, -12, -14, 5, 30, 1, 6, -2, -12, 4, -22, -10, -6, 22, -10, -3, 7, -9, -14, -14, 21, 20, 13, -8, -12, -7, 10, 19, 29, -11, -30, 17, 20, 24, -24, -2, 10, -8, 20, 2, -20, 8, 2, -22, -13, -14, -22, 0, 26, -20, -4, -9, 8, 31, 8, 0, -12, 23, -25, -7, 9, 3, -28, -16, 24, 4, 18, -12, -20, -10, -22, -3, 6, -54, 6, 3, 6, -9, 8, -2, 5, 10, -23, -14, 16, 22, 2, 0, 17, -10, -19, 0, -38, 1, -25, 7, 34, -24, 14, 3, 24, -6, -10, 1, 17, -14, -40, -2, -16, -16, -14, 17, 8, 15, 56, -20, 3, 21, 33, 6, -5, -3, 18, -30, -45, 10, -4, -6, -11, 8, 30, 19, 2, -28, -29, -5, 46, 2, 54, -12, -20, 6, 0, 6, 2, 20, 16, 14, 39, -12, -14, -1, -23, -1, -12, -6, 42, -10, -27, 2, 51, -22, 45, 30, 14, -3, 0, -1, 30, 8, 4, 8, -7, 11, -30, -2, 42, -24, -66, 10, 10, 24, 20, 13, -14, -8, 16, 16, -46, 38, 5, 10, -30, 16, 6, 1, 4, 9, -40, 1, -9, 10, -1, 18, -33, -11, -8, -8, -30, -14, -24, 1, -15, -18, -20, 2, -57, -12, 47, -12, 30, -14, -9, 5, 13, 30, -3, 1, 24, 6, -30, -2, -48, -12, -40, 4, 4, -22, 22, -10, -54, -6, -40, 22, -60, -10, 11, -3, -63, 7, -4, -9, -16, -14, 22, -14, 10, 21, 30, 20, 22, 13, 53, -8, -1, -12, 12, -7, -26, 10, 12, 19, -2, 29, -1, -11, 70, -30, -25, 17, -28, 20, 34, 24, -18, -24, 27, -2, -22, 10, 9, -8, -22, 20, -28, 2, 40, -20, 113, 8, -10, 2, 6, -22, 24, -13, 46, -14, 54, -22, 10, 0, -23, 26, 26, -20, 1, -4, -52, -9, 32, 8, 15, 31, -5, 8, -20, 0, 54, -12, 26, 23, -26, -25, -70, -7, 42, 9, 8, 3, 19, -28, 12, -16, -20, 24, -20, 4, -58, 18, 32, -12, -8, -20, -1, -10, 14, -22, 16, -3, -10, 6, -4, -54, 40, 6, 30, 3, 33, 6, -44, -9, -10, 8, 2, -2, 15, 5, 40, 10, 8, -23, 32, -14, 11, 16, 26, 22, -41, 2, 41, 0, -44, 17, 16, -10, -50, -19, -73, 0, -11, -38, 3, 1, 29, -25, -8, 7, -8, 34, 20, -24, 0, 14, -21, 3, -32, 24, -34, -6, -31, -10, 38, 1, -7, 17, -62, -14, 34, -40, 49, -2, 40, -16, 46, -16, -43, -14, -112, 17, 8, 8, 25, 15, 19, 56, -10, -20, -40, 3, -51, 21, -28, 33, -45, 6, 29, -5, 43, -3, 38, 18, 12, -30, -4, -45, -44, 10, -41, -4, 48, -6, -34, -11, 0, 8, 10, 30, 24, 19, -10, 2, 19, -28, -39, -29, 0, -5, 2, 46, 4, 2, 35, 54, -27, -12, -16, -20, 55, 6, -14, 0, 28, 6, -76, 2, -4, 20, -72, 16, -53, 14, 21, 39, 20, -12, 64, -14, -12, -1, 35, -23, -33, -1, 10, -12, -38, -6, 80, 42, 20, -10, 34, -27, -20, 2, 32, 51, -34, -22, -15, 45, 15, 30, -45, 14, -28, -3, 40, 0, -22, -1, 12, 30, -10, 8, -48, 4, 103, 8, -6, -7, 10, 11, 50, -30, -73, -2, -42, 42, -60, -24, 16, -66, 36, 10, 2, 10, 12, 24, 59, 20, 20, 13, 28, -14, 5, -8, -22, 16, -4, 16, 14, -46, 19, 38, -24, 5, 22, 10, -20, -30, -16, 16, 16, 6, -32, 1, 15, 4, 54, 9, 87, -40, -32, 1, -40, -9, 33, 10, 7, -1, -42, 18, 69, -33, -52, -11, -24, -8, 32, -8, -4, -30, 1, -14, 17, -24, -40, 1, -36, -15, 80, -18, 56, -20, 12, 2, -26, -57, -3, -12, -30, 47, -42, -12, -22, 30, -54, -14, 20, -9, 32, 5, -3, 13, -4, 30, 46, -3, 20, 1, 28, 24, -10, 6, -20, -30, -102, -2, 4, -48, -8, -12, -40, -40, -28, 4, 40, 4, -76, -22, -34, 22, -8, -10, 40, -54, -81, -6, 84, -40, 24, 22, 17, -60, -66, -10, -13, 11, 36, -3, 1, -63, 40, 7, 45, -4, 70, -9, 9, -16, -42, -14, -30, 22, -1, -14, -56, 10, -16, 21, -36, 30, -32, 20, -33, 22, -39, 13, -35, 53, 12, -8, 85, -1, -19, -12, 4, 12, 57, -7, 20, -26, 69, 10, -18, 12, 53, 19, 96, -2, 40, 29, 38, -1, 8, -11, 18, 70, -4, -30, -12, -25, -21, 17, -28, -28, -48, 20, 36, 34, -2, 24], 'weight': 2, 'weight_parity': 1}
  86. label: 75.2.a.a
    {'Nk2': 300, 'analytic_conductor': 0.5988780151596029, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1], [5, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [75, 1, [26, 52], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [2, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554507, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '75.2.a.a', 'level': 75, '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': '75.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-2q^{2}+q^{3}+2q^{4}-2q^{6}+3q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/75/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '75.2.a', 'trace_display': [-2, 1, 0, 3], 'trace_hash': 2059292129865388632, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.021', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.962', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.048', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.867', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.128', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.543', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, 'traces': [1, -2, 1, 2, 0, -2, 3, 0, 1, 0, 2, 2, -1, -6, 0, -4, -2, -2, -5, 0, 3, -4, -6, 0, 0, 2, 1, 6, 10, 0, -3, 8, 2, 4, 0, 2, -2, 10, -1, 0, -8, -6, -1, 4, 0, 12, -2, -4, 2, 0, -2, -2, 4, -2, 0, 0, -5, -20, -10, 0, 7, 6, 3, -8, 0, -4, 3, -4, -6, 0, -8, 0, 14, 4, 0, -10, 6, 2, 0, 0, 1, 16, -6, 6, 0, 2, 10, 0, 0, 0, -3, -12, -3, 4, 0, 8, -17, -4, 2, 0, 12, 4, 4, 0, 0, -8, -12, 2, 5, 0, -2, -12, 4, 10, 0, 20, -1, 20, -6, 0, -7, -14, -8, -6, 0, -6, 8, 0, -1, 0, 12, 4, -15, -6, 0, 0, 18, 12, 20, 0, -2, 16, -2, -4, 0, -28, 2, -4, 10, 0, 7, 0, -2, -12, 0, -2, 13, 0, 4, 0, -18, -2, -11, -16, 0, 12, -12, 0, -12, 0, -5, -2, -6, -20, 0, -8, -10, 0, -10, 0, 17, 6, 7, 0, 0, 6, -4, -4, 3, 0, 22, -8, -11, 34, 0, 4, 18, -4, -5, 0, 3, -24, 30, -4, 0, -8, -6, 4, -10, 0, -13, 8, -8, 24, 0, 0, -9, -10, 14, 0, 2, 4, 19, 24, 0, -8, 8, -10, -15, 0, 6, 0, 24, 2, 0, -20, 0, 12, 20, 0, -23, 14, 1, 14, 0, 16, 5, 0, -6, 0, 12, 6, -12, -16, 0, 16, -12, 2, -6, 0, 10, -24, -16, 0, 0, 30, 0, 6, -10, 0, -8, 8, -3, -36, 0, -12, 3, -40, -3, 0, -18, 4, 9, -16, 0, 4, -24, 8, -13, 0, -17, 28, -6, -4, 0, 0, 2, -20, 6, 0, -3, -14, 12, 20, 0, 4, -7, 12, 4, 0, -18, 0, -11, -26, 0, 0, 8, -8, 20, 0, -12, 36, 10, 2, 0, 22, 5, 0, -6, 0, 12, -12, -2, 24, 0, -12, 23, 24, 4, 0, -6, 10, -15, 0, 0, 12, -2, 20, 10, 0, -1, 16, -6, 20, 0, 0, -6, 20, 0, 0, 6, -34, -7, -6, 0, -14, -27, 24, -8, 0, 12, -6, 29, 8, 0, 0, -10, -6, 25, 0, 8, -44, -36, 0, 0, 22, -1, -34, 0, 0, 12, 0, 12, -36, 0, 4, -7, 10, -15, 0, 12, -6, 3, 24, 0, -60, -4, 0, 5, 0, 18, 8, -30, 12, 0, -8, 20, 20, -20, 0, 22, 26, -2, 0, 0, 16, 21, -24, -2, 0, -18, -4, 29, 18, 0, 10, 30, -28, -35, 0, 2, -4, 24, -4, 0, -38, 10, -24, 20, 0, -16, 8, 7, -16, 0, 0, -22, 30, -2, 0, 12, -12, 24, -40, 0, -48, 38, -2, 9, 0, 13, 0, -2, 0, 0, -12, 4, -40, 30, 0, 2, 46, -18, -14, 0, -2, 13, 0, -11, 0, -8, -16, -20, -10, 0, 12, -24, 12, -5, 0, -12, -24, -16, 0, 0, 24, -12, 16, -10, 0, 42, -32, -5, 24, 0, -2, -4, 12, -6, 0, 22, -20, -31, 24, 0, 32, 6, -8, 13, 0, -10, -30, 8, 0, 0, 0, -10, 20, 4, 0, -3, 16, 17, -16, 0, 6, 8, 36, 7, 0, -50, 0, 0, -6, 0, 40, -42, 6, 1, 0, -4, 36, -6, -4, 0, -18, 3, 0, 30, 0, -13, -4, 22, 48, 0, -8, 13, 26, -11, 0, -18, 34, 8, 0, 0, 12, -12, 4, 15, 0, 18, 8, -16, -4, 0, 20, -5, -12, -20, 0, -13, 6, 3, 14, 0, -24, 8, -40, 30, 0, 2, -4, 14, 14, 0, 0, -12, -8, -25, 0, -6, 36, 0, 4, 0, 22, -10, 26, 4, 0, -23, 0, -13, -16, 0, 8, -2, -40, -8, 0, 12, 24, -36, -36, 0, -20, 28, 0, -20, 0, -9, -22, 14, -10, 0, 32, 14, 12, -40, 0, -38, -24, 2, 0, 0, 4, -60, -24, 19, 0, 14, 24, -6, -46, 0, -24, -42, -8, -51, 0, 8, 12, 24, -10, 0, 30, -15, 4, -4, 0, -8, -12, 6, 4, 0, 0, 16, -20, 24, 0, 22, 2, 10, -16, 0, 12, 36, -20, 25, 0, 0, 0, 18, 12, 0, -20, 20, 0, 30, 0, 12, -12, -23, 34, 0, 14, 43, 0, 1, 0, 2, 14, 34, 54, 0, -48, 6, 16, -20, 0, 5, -24, 4, 0, 0, -58, -6, -8, -36, 0, -8, 8, 12, 20, 0, 6, 23, -50, -12, 0, 12, -16, 15, 44, 0, 72, 10, 16, 35, 0, -12, -22, 24, 2, 0, 0, -6, 0, 40, 0, -16, -24, 10, -8, 0, -24, -7, 36, -16, 0, 12, 0, -7, 14, 0, -10, -52, 30, 4, 0, 0, -24, 28, 6, 0, -6, -10, 0, -20, 0, 27, 60, -8, 8, 0, 8, 5, -10, -3, 0, -18, -36, -41, 0, 0, 60, 28, -12, -30, 0, 3, 8, -4, -40, 0, -20, -3, 40, 10, 0, 71, -44, -18, -26, 0, 4, -21, -16, 9, 0, 12, -16, -51, -42, 0, 0, 28, 4, 40, 0, -24, 36, -16, 8, 0, -58, -13, -18, 0, 0, -3, 0, -17, -60, 0, 28, -27, 70, -6, 0, 32, -4, -41, 4, 0, -48, 18, 0, 24, 0, 2, 38, 10, -20, 0, 0, 6, -40, -30, 0, -8, 32, -3, 0, 0, -14, -12, 16, 12, 0, -58, 20, -12, 44, 0, -30, 36, 4, 55, 0, -7, -24, 8, 12, 0, -48, 4, 80, -50, 0, -10, 48, -18, -76, 0, 0, 33, -18, -11, 0, 22, -26, 48, 40, 0, 4, 18, 0, -14, 0, 8, 0, -56, -8, 0, 40, 20, -60, 54, 0, -22, -4, -12, -46, 0, 36, -32, 0, 10, 0, 42, 2, 60, -26, 0, -28, -2, 22, 0, 0, 5, 16, -36, 0, 0, 40, -6, 10, 6, 0, 17, -24, 12, 48, 0, -12, -42, 10, -2, 0], 'weight': 2, 'weight_parity': 1}
  87. label: 75.2.a.b
    {'Nk2': 300, 'analytic_conductor': 0.5988780151596029, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1], [5, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [75, 1, [26, 52], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660925003, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': False, 'label': '75.2.a.b', 'level': 75, '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': '15.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\\cdots', 'related_objects': ['EllipticCurve/Q/75/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '75.2.a', 'trace_display': [1, 1, 0, 0], 'trace_hash': 1988189362737059693, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.003', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.977', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.926', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.780', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, 'traces': [1, 1, 1, -1, 0, 1, 0, -3, 1, 0, -4, -1, 2, 0, 0, -1, -2, 1, 4, 0, 0, -4, 0, -3, 0, 2, 1, 0, -2, 0, 0, 5, -4, -2, 0, -1, 10, 4, 2, 0, 10, 0, -4, 4, 0, 0, -8, -1, -7, 0, -2, -2, 10, 1, 0, 0, 4, -2, -4, 0, -2, 0, 0, 7, 0, -4, -12, 2, 0, 0, -8, -3, -10, 10, 0, -4, 0, 2, 0, 0, 1, 10, -12, 0, 0, -4, -2, 12, -6, 0, 0, 0, 0, -8, 0, 5, -2, -7, -4, 0, 6, -2, 16, -6, 0, 10, 12, -1, 14, 0, 10, 0, -2, 4, 0, 2, 2, -4, 0, 0, 5, -2, 10, 0, 0, 0, 8, -3, -4, 0, -12, 4, 0, -12, 0, 6, 6, 0, -4, 0, -8, -8, -8, -1, 0, -10, -7, -10, 22, 0, -8, -12, -2, 0, 0, -2, -14, 0, 10, 0, 0, 1, 4, -10, 0, -12, 0, 0, -9, 0, 4, 4, 18, -2, 0, 4, -4, -6, 20, 0, -10, 0, -2, 0, 0, 0, 8, 8, 0, 0, 16, 7, -2, -2, 0, 7, -6, -4, -8, 0, -12, 6, 0, 2, 0, 16, 0, -2, -16, 0, 20, -10, -8, 12, 0, -3, 0, 14, -10, 0, -4, 10, -8, 0, 0, -2, 20, -4, 6, 0, 0, 6, 6, 2, 0, 4, 0, 0, -16, 0, -14, 5, 1, 2, 0, 10, 8, 0, -12, 0, 12, 0, 0, 8, 0, -17, -18, -4, 0, 0, -2, -12, -16, 12, 0, 0, -6, 12, 14, 0, 16, 2, 0, 6, 0, 0, -6, -4, 0, 0, -6, -8, 12, 8, 0, -8, 0, 5, -13, 0, -2, 10, -6, -7, 0, -30, -4, 22, 0, 0, 0, -8, 6, -4, 0, -2, -28, 0, 16, 0, -24, -6, -26, -14, 0, 0, 2, 10, 8, 0, 12, 0, -8, -1, 0, 4, 14, -30, 0, 0, 12, 12, 10, 0, 0, 0, 14, -9, -2, 0, 0, 4, 0, 12, 0, 18, 28, 2, -2, 0, 2, -20, -18, -4, 0, 6, 0, 20, -24, 0, -3, -10, 5, 0, 0, -2, 24, 0, 10, 0, 0, 0, 26, 8, 0, 24, -4, 0, -20, 0, 8, 16, 24, -3, 0, -2, -4, 2, 6, 0, 0, 21, -12, -6, 0, 4, 2, -8, 0, 0, 18, -12, 0, -6, 0, 0, -40, 6, 26, 0, 6, -16, 0, 0, 0, 10, -4, -16, 4, 0, -26, 20, -8, -30, 0, -8, 0, -12, -8, 0, 0, -1, 14, 0, 0, -14, 0, -10, 40, 0, -7, -4, 12, -10, 0, -8, 22, 0, 2, 0, -40, 2, -8, 20, 0, -12, -10, 6, -2, 0, -18, 0, -24, 2, 0, 6, -28, -2, 0, 0, -14, 12, 16, 0, 0, 0, 10, -16, 0, 0, 20, -14, 0, -5, 0, 1, -32, 6, 4, 0, 28, -10, 4, 8, 0, 0, 0, -12, 4, 0, 0, 12, 32, 0, 0, 0, -9, -8, -34, 0, 0, -11, 4, -18, 0, 4, 32, 0, 18, 0, 10, -2, -4, 12, 0, -16, 0, 4, -23, 0, -4, 0, 20, -6, 0, 36, 20, 14, 28, 0, 30, 16, -10, -10, 0, 0, 20, -6, -2, 0, -8, 0, 0, -6, 0, 4, 18, 0, -8, 0, 8, -6, -12, 8, 0, 12, 0, 24, -6, 0, -4, 8, 16, 0, 0, 7, -2, -13, -2, 0, 0, -2, -40, 30, 0, -6, 12, 7, 0, 0, -6, -10, -34, -4, 0, -22, -8, 0, -8, 0, 26, 0, -12, 8, 0, 6, 8, 20, 0, 0, -16, 2, -22, -28, 0, 0, 6, 16, -4, 0, 0, -24, 0, -2, 0, -26, -16, 14, -20, 0, -8, 0, 20, 2, 0, -10, -14, 8, -8, 0, -30, 12, 36, 0, 0, -8, -32, -3, 16, 0, 0, -4, -46, 14, 0, -10, -10, 0, 20, 0, 22, 12, -4, 36, 0, 10, 0, 0, -8, 0, 8, 0, 30, 14, 0, 9, -6, -2, 0, 0, 20, 0, -36, -4, 0, 0, 6, 4, 20, 0, -44, -18, 0, 28, 0, 6, -20, -2, 6, 0, -2, 2, 40, -28, 0, -18, 0, 4, -26, 0, 0, 18, 0, 0, 0, -20, -16, -24, -48, 0, 0, -3, -14, 10, 0, 5, 16, 0, 1, 0, 8, 2, -14, 24, 0, 0, 48, 10, -44, 0, 8, 0, 16, 0, 0, 26, -12, -8, 0, 0, 16, 8, 12, -4, 0, 0, 26, -20, 0, 0, -6, 8, 0, -16, 0, 24, -8, -17, 2, 0, -18, 2, -6, -4, 0, 6, 0, 6, 40, 0, 32, 0, -2, 7, 0, -12, -28, 6, -16, 0, 0, 12, -4, 2, 0, 8, 2, 0, 16, 0, -6, 18, 40, 12, 0, 0, 14, -18, 10, 0, 12, 0, 16, -40, 0, 2, -16, 26, 0, 0, 54, 6, -32, -48, 0, 0, 28, 0, 30, 0, -6, 14, 14, -4, 0, 16, 0, 4, 40, 0, -25, -26, -6, -20, 0, -8, 0, -10, 12, 0, 0, 8, -6, 0, 0, -36, 22, -8, -20, 0, 0, 0, 56, 5, 0, 14, -13, 0, 0, 0, -24, -42, -2, 0, 0, 10, -30, 40, -6, 0, -46, -7, -44, 4, 0, 12, -48, -30, 0, 0, -4, 8, -32, 22, 0, 0, 0, 2, 0, 0, -20, -40, 0, 6, 0, -8, 12, -20, 6, 0, 32, -4, 48, -10, 0, -6, 0, -2, 40, 0, -28, -18, -16, 0, 0, -24, 16, -10, 34, 0, -28, -6, -24, -28, 0, -6, 54, 0, -26, 0, -50, -14, 0, 4, 0, 16, 36, 0, -20, 0, 2, 0, 22, 10, 0, 16, 8, 0, 0, 0, -31, 20, 12, 14, 0, 0, -32, -15, -8, 0, 60, -1, 0, -32, 0, 2, -2, 4, 24, 0, 14, 28, 0, -30, 0, 4, 0, -8, 0, 0, 32, 0, 12, 0, 0, 12, -54, 4, 10, 0], 'weight': 2, 'weight_parity': 1}
  88. label: 75.2.a.c
    {'Nk2': 300, 'analytic_conductor': 0.5988780151596029, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, 1], [5, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [75, 1, [26, 52], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-2, 1]]], 'hecke_orbit': 3, 'hecke_orbit_code': 9007199288295499, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '75.2.a.c', 'level': 75, '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': '75.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/75/c'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '75.2.a', 'trace_display': [2, -1, 0, -3], 'trace_hash': 270043000761900717, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.031', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.962', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.079', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.867', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.215', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.543', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, 'traces': [1, 2, -1, 2, 0, -2, -3, 0, 1, 0, 2, -2, 1, -6, 0, -4, 2, 2, -5, 0, 3, 4, 6, 0, 0, 2, -1, -6, 10, 0, -3, -8, -2, 4, 0, 2, 2, -10, -1, 0, -8, 6, 1, 4, 0, 12, 2, 4, 2, 0, -2, 2, -4, -2, 0, 0, 5, 20, -10, 0, 7, -6, -3, -8, 0, -4, -3, 4, -6, 0, -8, 0, -14, 4, 0, -10, -6, -2, 0, 0, 1, -16, 6, 6, 0, 2, -10, 0, 0, 0, -3, 12, 3, 4, 0, 8, 17, 4, 2, 0, 12, -4, -4, 0, 0, -8, 12, -2, 5, 0, -2, 12, -4, 10, 0, 20, 1, -20, -6, 0, -7, 14, 8, -6, 0, -6, -8, 0, -1, 0, 12, -4, 15, -6, 0, 0, -18, -12, 20, 0, -2, -16, 2, -4, 0, -28, -2, 4, 10, 0, 7, 0, 2, -12, 0, -2, -13, 0, 4, 0, -18, 2, 11, -16, 0, 12, 12, 0, -12, 0, -5, 2, 6, -20, 0, -8, 10, 0, -10, 0, 17, -6, -7, 0, 0, 6, 4, 4, 3, 0, 22, 8, 11, 34, 0, 4, -18, 4, -5, 0, 3, 24, -30, -4, 0, -8, 6, -4, -10, 0, -13, -8, 8, 24, 0, 0, 9, 10, 14, 0, 2, -4, -19, 24, 0, -8, -8, 10, -15, 0, 6, 0, -24, 2, 0, -20, 0, -12, 20, 0, -23, -14, -1, 14, 0, 16, -5, 0, -6, 0, 12, -6, 12, -16, 0, 16, 12, -2, -6, 0, 10, 24, 16, 0, 0, 30, 0, -6, -10, 0, -8, -8, 3, -36, 0, -12, -3, 40, -3, 0, -18, -4, -9, -16, 0, 4, 24, -8, -13, 0, -17, -28, 6, -4, 0, 0, -2, 20, 6, 0, -3, 14, -12, 20, 0, 4, 7, -12, 4, 0, -18, 0, 11, -26, 0, 0, -8, 8, 20, 0, -12, -36, -10, 2, 0, 22, -5, 0, -6, 0, 12, 12, 2, 24, 0, -12, -23, -24, 4, 0, -6, -10, 15, 0, 0, 12, 2, -20, 10, 0, -1, -16, 6, 20, 0, 0, 6, -20, 0, 0, 6, 34, 7, -6, 0, -14, 27, -24, -8, 0, 12, 6, -29, 8, 0, 0, 10, 6, 25, 0, 8, 44, 36, 0, 0, 22, 1, 34, 0, 0, 12, 0, -12, -36, 0, 4, 7, -10, -15, 0, 12, 6, -3, 24, 0, -60, 4, 0, 5, 0, 18, -8, 30, 12, 0, -8, -20, -20, -20, 0, 22, -26, 2, 0, 0, 16, -21, 24, -2, 0, -18, 4, -29, 18, 0, 10, -30, 28, -35, 0, 2, 4, -24, -4, 0, -38, -10, 24, 20, 0, -16, -8, -7, -16, 0, 0, 22, -30, -2, 0, 12, 12, -24, -40, 0, -48, -38, 2, 9, 0, 13, 0, 2, 0, 0, -12, -4, 40, 30, 0, 2, -46, 18, -14, 0, -2, -13, 0, -11, 0, -8, 16, 20, -10, 0, 12, 24, -12, -5, 0, -12, 24, 16, 0, 0, 24, 12, -16, -10, 0, 42, 32, 5, 24, 0, -2, 4, -12, -6, 0, 22, 20, 31, 24, 0, 32, -6, 8, 13, 0, -10, 30, -8, 0, 0, 0, 10, -20, 4, 0, -3, -16, -17, -16, 0, 6, -8, -36, 7, 0, -50, 0, 0, -6, 0, 40, 42, -6, 1, 0, -4, -36, 6, -4, 0, -18, -3, 0, 30, 0, -13, 4, -22, 48, 0, -8, -13, -26, -11, 0, -18, -34, -8, 0, 0, 12, 12, -4, 15, 0, 18, -8, 16, -4, 0, 20, 5, 12, -20, 0, -13, -6, -3, 14, 0, -24, -8, 40, 30, 0, 2, 4, -14, 14, 0, 0, 12, 8, -25, 0, -6, -36, 0, 4, 0, 22, 10, -26, 4, 0, -23, 0, 13, -16, 0, 8, 2, 40, -8, 0, 12, -24, 36, -36, 0, -20, -28, 0, -20, 0, -9, 22, -14, -10, 0, 32, -14, -12, -40, 0, -38, 24, -2, 0, 0, 4, 60, 24, 19, 0, 14, -24, 6, -46, 0, -24, 42, 8, -51, 0, 8, -12, -24, -10, 0, 30, 15, -4, -4, 0, -8, 12, -6, 4, 0, 0, -16, 20, 24, 0, 22, -2, -10, -16, 0, 12, -36, 20, 25, 0, 0, 0, -18, 12, 0, -20, -20, 0, 30, 0, 12, 12, 23, 34, 0, 14, -43, 0, 1, 0, 2, -14, -34, 54, 0, -48, -6, -16, -20, 0, 5, 24, -4, 0, 0, -58, 6, 8, -36, 0, -8, -8, -12, 20, 0, 6, -23, 50, -12, 0, 12, 16, -15, 44, 0, 72, -10, -16, 35, 0, -12, 22, -24, 2, 0, 0, 6, 0, 40, 0, -16, 24, -10, -8, 0, -24, 7, -36, -16, 0, 12, 0, 7, 14, 0, -10, 52, -30, 4, 0, 0, 24, -28, 6, 0, -6, 10, 0, -20, 0, 27, -60, 8, 8, 0, 8, -5, 10, -3, 0, -18, 36, 41, 0, 0, 60, -28, 12, -30, 0, 3, -8, 4, -40, 0, -20, 3, -40, 10, 0, 71, 44, 18, -26, 0, 4, 21, 16, 9, 0, 12, 16, 51, -42, 0, 0, -28, -4, 40, 0, -24, -36, 16, 8, 0, -58, 13, 18, 0, 0, -3, 0, 17, -60, 0, 28, 27, -70, -6, 0, 32, 4, 41, 4, 0, -48, -18, 0, 24, 0, 2, -38, -10, -20, 0, 0, -6, 40, -30, 0, -8, -32, 3, 0, 0, -14, 12, -16, 12, 0, -58, -20, 12, 44, 0, -30, -36, -4, 55, 0, -7, 24, -8, 12, 0, -48, -4, -80, -50, 0, -10, -48, 18, -76, 0, 0, -33, 18, -11, 0, 22, 26, -48, 40, 0, 4, -18, 0, -14, 0, 8, 0, 56, -8, 0, 40, -20, 60, 54, 0, -22, 4, 12, -46, 0, 36, 32, 0, 10, 0, 42, -2, -60, -26, 0, -28, 2, -22, 0, 0, 5, -16, 36, 0, 0, 40, 6, -10, 6, 0, 17, 24, -12, 48, 0, -12, 42, -10, -2, 0], 'weight': 2, 'weight_parity': 1}
  89. label: 76.2.a.a
    {'Nk2': 304, 'analytic_conductor': 0.6068630553617309, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [19, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [76, 1, [39, 21], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554508, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '76.2.a.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': '76.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\\cdots', 'related_objects': ['EllipticCurve/Q/76/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '76.2.a', 'trace_display': [0, 2, -1, -3], 'trace_hash': 1354001870116862942, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.010', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.987', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.048', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.973', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.117', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.946', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, 'traces': [1, 0, 2, 0, -1, 0, -3, 0, 1, 0, 5, 0, -4, 0, -2, 0, -3, 0, -1, 0, -6, 0, 8, 0, -4, 0, -4, 0, -2, 0, 4, 0, 10, 0, 3, 0, 10, 0, -8, 0, 10, 0, 1, 0, -1, 0, -1, 0, 2, 0, -6, 0, -4, 0, -5, 0, -2, 0, 6, 0, -13, 0, -3, 0, 4, 0, -12, 0, 16, 0, 2, 0, 9, 0, -8, 0, -15, 0, 8, 0, -11, 0, -12, 0, 3, 0, -4, 0, 12, 0, 12, 0, 8, 0, 1, 0, -8, 0, 5, 0, -10, 0, -6, 0, 6, 0, 2, 0, 0, 0, 20, 0, -10, 0, -8, 0, -4, 0, 9, 0, 14, 0, 20, 0, 9, 0, 6, 0, 2, 0, -9, 0, 3, 0, 4, 0, -11, 0, -3, 0, -2, 0, -20, 0, 2, 0, 4, 0, -15, 0, 2, 0, -3, 0, -4, 0, -2, 0, -8, 0, -24, 0, -4, 0, -10, 0, -6, 0, 3, 0, -1, 0, 6, 0, 12, 0, 12, 0, 18, 0, 10, 0, -26, 0, -10, 0, -15, 0, 12, 0, 25, 0, 12, 0, 8, 0, 2, 0, -7, 0, -24, 0, 6, 0, -10, 0, 8, 0, -5, 0, 18, 0, 4, 0, -1, 0, -12, 0, 18, 0, 12, 0, 2, 0, -4, 0, 4, 0, 17, 0, -30, 0, 3, 0, 1, 0, 16, 0, 21, 0, -26, 0, -10, 0, -2, 0, 4, 0, -24, 0, 11, 0, 40, 0, 6, 0, 32, 0, -30, 0, -2, 0, -21, 0, 4, 0, 24, 0, -24, 0, -8, 0, 24, 0, -20, 0, 1, 0, 4, 0, 22, 0, -3, 0, 2, 0, -30, 0, -8, 0, -16, 0, -12, 0, -6, 0, -20, 0, -32, 0, -3, 0, -20, 0, 13, 0, 12, 0, -12, 0, 7, 0, -10, 0, 3, 0, 30, 0, -10, 0, 4, 0, 3, 0, 16, 0, 0, 0, 3, 0, -4, 0, 10, 0, 12, 0, -32, 0, -20, 0, 20, 0, 15, 0, -16, 0, 19, 0, -11, 0, 16, 0, -6, 0, -2, 0, 18, 0, 21, 0, 1, 0, 28, 0, -9, 0, 16, 0, 10, 0, 12, 0, -4, 0, 18, 0, 8, 0, -30, 0, 12, 0, 4, 0, 15, 0, 1, 0, -21, 0, -24, 0, -18, 0, -8, 0, 5, 0, 6, 0, 28, 0, -16, 0, 11, 0, 50, 0, -20, 0, -22, 0, -18, 0, 12, 0, -6, 0, -36, 0, -40, 0, -1, 0, 12, 0, 39, 0, -40, 0, 24, 0, 2, 0, 4, 0, -8, 0, 2, 0, 2, 0, -5, 0, -12, 0, -30, 0, 16, 0, 50, 0, 4, 0, -12, 0, -13, 0, 12, 0, -19, 0, 19, 0, -8, 0, -5, 0, 36, 0, -4, 0, 5, 0, 4, 0, -4, 0, 4, 0, -40, 0, -48, 0, 8, 0, -26, 0, -8, 0, -28, 0, 6, 0, -5, 0, -6, 0, 19, 0, -12, 0, -36, 0, 10, 0, 6, 0, 0, 0, -27, 0, 4, 0, 6, 0, -5, 0, 12, 0, 32, 0, 26, 0, 24, 0, -12, 0, 41, 0, 6, 0, -40, 0, -2, 0, 36, 0, 10, 0, 11, 0, 20, 0, 0, 0, 28, 0, -13, 0, 2, 0, -24, 0, -20, 0, 1, 0, -4, 0, -30, 0, 42, 0, 10, 0, 33, 0, -8, 0, 20, 0, 50, 0, -32, 0, -13, 0, 24, 0, 36, 0, -20, 0, 4, 0, 3, 0, -4, 0, 4, 0, 22, 0, -9, 0, -14, 0, -12, 0, 10, 0, -12, 0, -14, 0, 32, 0, 12, 0, 4, 0, -47, 0, -20, 0, 9, 0, 4, 0, -32, 0, -36, 0, 11, 0, -10, 0, -30, 0, -7, 0, 36, 0, -6, 0, -8, 0, 2, 0, 0, 0, -11, 0, -2, 0, -7, 0, 30, 0, -24, 0, -27, 0, 9, 0, 9, 0, -34, 0, 16, 0, 24, 0, -3, 0, -16, 0, 4, 0, -65, 0, -10, 0, 16, 0, -2, 0, 24, 0, 8, 0, -20, 0, 11, 0, 34, 0, 16, 0, -33, 0, -15, 0, 3, 0, -30, 0, 6, 0, -10, 0, -10, 0, 2, 0, 30, 0, -6, 0, 8, 0, 32, 0, 20, 0, 42, 0, 13, 0, 18, 0, -52, 0, 8, 0, 7, 0, 13, 0, -3, 0, -6, 0, -4, 0, -60, 0, -43, 0, 8, 0, -40, 0, 15, 0, -12, 0, -6, 0, -16, 0, 22, 0, -2, 0, -5, 0, 80, 0, 9, 0, 0, 0, 3, 0, -24, 0, 31, 0, 64, 0, 18, 0, -16, 0, -60, 0, -10, 0, 10, 0, 8, 0, 2, 0, 4, 0, -42, 0, 30, 0, 52, 0, 8, 0, -12, 0, 3, 0, 12, 0, 45, 0, 24, 0, -48, 0, 39, 0, 0, 0, -16, 0, 4, 0, -1, 0, 12, 0, 45, 0, 53, 0, -40, 0, -28, 0, -48, 0, 2, 0, -6, 0, 6, 0, -16, 0, -10, 0, -25, 0, 44, 0, -3, 0, -42, 0, -6, 0, 80, 0, 42, 0, 1, 0, 18, 0, 1, 0, -60, 0, 6, 0, -6, 0, -16, 0, 40, 0, 48, 0, -8, 0, -27, 0, 34, 0, -24, 0, -51, 0, 1, 0, -12, 0, 22, 0, -18, 0, -55, 0, 1, 0, -18, 0, -64, 0, -8, 0, 12, 0, -6, 0, -10, 0, -40, 0, -10, 0, -18, 0, -60, 0, 26, 0, 27, 0, -28, 0, 24, 0, -8, 0, -40, 0, -6, 0, 14, 0, -2, 0, 14, 0, 15, 0, -31, 0, -20, 0, -26, 0, 80, 0, -12, 0, -12, 0, -36, 0, 60, 0, -16, 0, -25, 0, -20, 0, 33, 0, -15, 0, 2, 0, -12, 0, 48, 0, 6, 0, 20, 0, 9, 0, 32, 0, 56, 0, 60, 0, 0, 0, -12, 0, -2, 0, 6, 0, 8, 0, -38, 0, -8, 0, 7, 0, 37, 0, -40, 0], 'weight': 2, 'weight_parity': 1}
  90. label: 77.2.a.a
    {'Nk2': 308, 'analytic_conductor': 0.614848095563859, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[7, 1], [11, 1]], 'atkin_lehner_string': '++', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [77, 1, [45, 57], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [0, 1]], [3, [3, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554509, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '77.2.a.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': '77.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-3q^{3}-2q^{4}-q^{5}-q^{7}+6q^{9}-q^{11}+\\cdots', 'related_objects': ['EllipticCurve/Q/77/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '77.2.a', 'trace_display': [0, -3, -1, -1], 'trace_hash': 199318774382275402, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '1.000', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '1.960', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.816', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.014', 'prec': 7}, 'traces': [1, 0, -3, -2, -1, 0, -1, 0, 6, 0, -1, 6, -4, 0, 3, 4, 2, 0, -6, 2, 3, 0, -5, 0, -4, 0, -9, 2, 10, 0, 1, 0, 3, 0, 1, -12, -5, 0, 12, 0, -2, 0, -8, 2, -6, 0, 8, -12, 1, 0, -6, 8, -6, 0, 1, 0, 18, 0, 3, -6, -2, 0, -6, -8, 4, 0, -3, -4, 15, 0, 1, 0, 10, 0, 12, 12, 1, 0, 6, -4, 9, 0, 12, -6, -2, 0, -30, 0, -15, 0, 4, 10, -3, 0, 6, 0, -5, 0, -6, 8, -12, 0, -12, 0, -3, 0, -10, 18, 4, 0, 15, -4, -19, 0, 5, -20, -24, 0, -2, 0, 1, 0, 6, -2, 9, 0, 2, 0, 24, 0, 18, -6, 6, 0, 9, 0, -3, 0, -10, -2, -24, 0, 4, 24, -10, 0, -3, 10, -22, 0, 6, 0, 12, 0, -1, -24, 7, 0, 18, 0, 5, 0, 4, 4, -3, 0, -2, 0, 3, 0, -36, 16, 16, 0, 4, -4, -9, 0, 1, 12, 5, 0, 6, 0, 5, 0, -2, -16, 9, 0, 5, 24, 14, 0, -12, -2, 18, 0, -8, 0, 9, 0, -10, 12, 2, 0, -30, -16, 6, 0, -2, 12, -3, 0, 8, 0, -1, 0, -30, -2, -8, 0, 1, 0, -24, 0, 4, -36, -7, 0, -3, 0, 6, 0, -8, -6, -18, 0, 4, 12, -12, 0, 0, 4, -1, 0, 24, 0, -36, 0, -21, 12, 5, 0, 6, 16, -6, 0, 5, -8, 60, 0, 18, 0, 6, 0, 45, 6, -18, 0, 16, 8, -12, 0, 4, -30, 24, 0, 6, 0, -4, 0, 0, -2, -18, 0, 2, 0, -13, 0, 15, -20, -6, 0, -3, 0, 9, 0, 20, -24, 8, 0, 36, -24, 2, 0, -28, -2, 36, 0, 8, 0, -23, 0, 6, -12, 9, 0, -10, 8, 30, 0, -12, -18, 16, 0, -12, 0, -8, 0, -17, -24, -30, 0, 3, 12, -18, 0, 57, 4, -1, 0, -1, 0, -15, 0, 14, 60, -34, 0, 36, 0, 9, 0, -1, 30, 6, 0, 8, 0, 17, 0, -3, -8, -10, 0, -11, -20, -12, 0, 6, 6, -4, 0, -27, 0, -40, 0, -29, -12, -6, 0, 17, 0, -1, 0, -48, 10, 9, 0, -10, 0, -54, 0, -6, 12, 18, 0, -18, -16, -6, 0, -4, 24, -9, 0, 5, 0, -26, 0, 9, 24, -3, 0, -12, 0, 30, 0, 16, 6, 22, 0, 48, 0, -8, 0, 2, 20, -12, 0, -20, -36, -25, 0, 30, -8, 30, 0, -14, 0, 6, 0, -39, -30, 15, 0, 66, 8, 15, 0, 2, 38, -18, 0, -4, 0, 8, 0, -18, -10, 18, 0, 13, 40, 3, 0, 3, 48, 3, 0, -21, 0, 8, 0, 24, 4, -36, 0, -28, 0, 20, 0, -15, -2, 5, 0, -13, 0, -12, 0, -30, -12, 20, 0, 6, 4, -1, 0, 44, -18, 6, 0, 0, 0, 12, 0, -9, -4, -31, 0, -10, 0, 54, 0, 12, -48, -8, 0, -48, 0, 7, 0, 32, -36, -12, 0, 2, 12, 2, 0, 18, -12, 8, 0, 10, 0, -3, 0, -1, -18, 32, 0, -15, 0, -4, 0, -24, 6, -12, 0, -60, 0, -6, 0, -15, 20, 14, 0, 32, 4, 6, 0, 20, 48, 19, 0, -9, 0, -18, 0, -20, -8, -15, 0, 20, -48, -25, 0, -42, 20, -12, 0, 6, 0, 24, 0, 36, 6, -6, 0, -54, -20, 30, 0, 2, 44, 24, 0, -48, 0, 8, 0, -18, -12, -1, 0, -10, 0, 30, 0, -32, -24, 16, 0, -6, 0, -30, 0, 17, 2, 45, 0, 15, 48, 11, 0, -18, -14, -10, 0, 27, 0, 6, 0, -2, -36, -4, 0, 6, 0, 15, 0, -29, -10, -24, 0, -21, 0, -3, 0, 3, -8, -17, 0, -18, -8, 60, 0, -2, 6, 35, 0, 24, 0, -6, 0, -50, 4, -3, 0, 2, 0, 4, 0, 36, -6, 38, 0, 5, 0, -12, 0, 12, 72, 3, 0, 21, -32, 24, 0, 15, -32, 6, 0, 10, 0, -4, 0, -18, -8, 0, 0, 30, 8, 24, 0, 12, 18, 39, 0, 36, 0, -5, 0, -4, -2, -12, 0, -11, -24, 12, 0, 36, -10, -40, 0, -19, 0, -27, 0, -16, -12, -4, 0, 3, 0, 3, 0, -18, -10, -72, 0, -24, 0, 22, 0, 72, 4, 10, 0, -23, 32, 63, 0, -6, -18, 38, 0, -15, 0, -48, 0, -4, -10, -12, 0, -12, -48, 40, 0, 18, -28, -6, 0, -4, 0, -15, 0, 12, 24, -1, 0, -90, 4, -7, 0, -22, -36, -54, 0, 19, 0, 8, 0, -18, 16, 23, 0, 16, 0, -90, 0, -10, -18, -5, 0, 54, 0, 30, 0, -22, 20, -48, 0, -4, -24, 48, 0, 24, -4, 18, 0, -25, 0, -12, 0, 20, 60, -29, 0, -72, 32, 2, 0, 2, -12, -9, 0, 45, 0, 71, 0, 12, 4, -3, 0, -1, -24, 0, 0, 25, 6, -34, 0, 36, 0, -28, 0, 55, -16, -6, 0, 52, 0, -16, 0, 39, 2, -6, 0, 12, 0, -30, 0, -9, 60, -38, 0, 18, 4, 27, 0, -44, 16, 9, 0, -2, 0, -2, 0, -9, -2, -48, 0, -1, 0, -60, 0, 10, 48, -12, 0, -24, 0, -5, 0, -40, -8, -72, 0, 0, 72, -12, 0, -6, 14, -18, 0, 48, 0, 84, 0, -4, 6, 20, 0, -72, 0, -30, 0, -6, -12, -24, 0, 2, 0, 36, 0, 69, 16, 58, 0, 10, 12, -9, 0, 5, 36, -40, 0, -27, 0, 44, 0, -5, -8, 30, 0, 3, -24, -30, 0, -60, 24, -14, 0, -34, 0, 36, 0, 29, 0, 10, 0, -48, -8, -31, 0, 15, 2, 24, 0, -27, 0, -18, 0, 24, -48, 40, 0, -32, 0, 51, 0, 8, 72, -12, 0, 45, 0], 'weight': 2, 'weight_parity': 1}
  91. label: 77.2.a.b
    {'Nk2': 308, 'analytic_conductor': 0.614848095563859, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[7, -1], [11, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [77, 1, [45, 57], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [0, 1]], [3, [-1, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660925005, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': False, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '77.2.a.b', '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': '77.2.a.b', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{3}-2q^{4}+3q^{5}+q^{7}-2q^{9}-q^{11}+\\cdots', 'related_objects': ['EllipticCurve/Q/77/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '77.2.a', 'trace_display': [0, 1, 3, 1], 'trace_hash': 874065559975919228, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.022', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.015', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.069', 'prec': 7}, {'__RealLiteral__': 0, 'data': '2.043', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.200', 'prec': 10}, {'__RealLiteral__': 0, 'data': '5.112', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, 'traces': [1, 0, 1, -2, 3, 0, 1, 0, -2, 0, -1, -2, -4, 0, 3, 4, -6, 0, 2, -6, 1, 0, 3, 0, 4, 0, -5, -2, -6, 0, 5, 0, -1, 0, 3, 4, 11, 0, -4, 0, 6, 0, 8, 2, -6, 0, 0, 4, 1, 0, -6, 8, -6, 0, -3, 0, 2, 0, -9, -6, -10, 0, -2, -8, -12, 0, 5, 12, 3, 0, 9, 0, 2, 0, 4, -4, -1, 0, -10, 12, 1, 0, 12, -2, -18, 0, -6, 0, -3, 0, -4, -6, 5, 0, 6, 0, -1, 0, 2, -8, -12, 0, -4, 0, 3, 0, 6, 10, 20, 0, 11, 4, -3, 0, 9, 12, 8, 0, -6, 0, 1, 0, 6, -10, -3, 0, 2, 0, 8, 0, -6, 2, 2, 0, -15, 0, -3, 0, 14, -6, 0, 0, 4, -8, -18, 0, 1, -22, -6, 0, -10, 0, 12, 0, 15, 8, -13, 0, -6, 0, 3, 0, 20, -12, -3, 0, 6, 0, 3, 0, -4, -16, 0, 0, 4, -4, -9, 0, -15, 12, -7, 0, -10, 0, 33, 0, 6, 0, -5, 0, -27, -8, 14, 0, -12, -2, 18, 0, -16, 0, 5, 0, -6, 12, 18, 0, -6, -16, -2, 0, 14, 12, 9, 0, 24, 0, 5, 0, 2, 6, 24, 0, -19, 0, -8, 0, -12, -4, 5, 0, -1, 0, 6, 0, 0, 18, -10, 0, -12, 12, -28, 0, 16, 20, 3, 0, -8, 0, 12, 0, -9, 4, -3, 0, -18, 16, -6, 0, 11, 24, 12, 0, -30, 0, -18, 0, -3, -10, 30, 0, -16, -24, -4, 0, -4, -6, 8, 0, -10, 0, 12, 0, 32, -18, 6, 0, 6, 0, 19, 0, -1, -4, -30, 0, -27, 0, 5, 0, -12, -8, 8, 0, -12, 8, -30, 0, 20, 2, -4, 0, 0, 0, -19, 0, -6, 20, 9, 0, 6, -24, 6, 0, -12, -2, -16, 0, 20, 0, 0, 0, -1, -24, -22, 0, 15, 4, 14, 0, -3, 36, -5, 0, 1, 0, 9, 0, -18, 12, -10, 0, 20, 0, -3, 0, 27, 6, -6, 0, 24, 0, -15, 0, 1, 8, 6, 0, 17, 12, -12, 0, -6, -10, -4, 0, -3, 0, 24, 0, 11, -12, 2, 0, 21, 0, -3, 0, -16, 2, 33, 0, -18, 0, -6, 0, -30, -4, 2, 0, 2, 16, -6, 0, -20, 24, 3, 0, -11, 0, 14, 0, -3, 8, -9, 0, 36, 0, 14, 0, 24, -6, -10, 0, 0, 0, -24, 0, -10, -12, 4, 0, 12, -20, 11, 0, -18, -40, 6, 0, 26, 0, -2, 0, 9, -22, -9, 0, -6, -8, -9, 0, -6, 6, -10, 0, -12, 0, 8, 0, 30, -18, -6, 0, 5, -24, 15, 0, 15, -16, 5, 0, -13, 0, -8, 0, 8, 12, 12, 0, -12, 0, -44, 0, 3, -2, -3, 0, 11, 0, 20, 0, -30, -12, 36, 0, 6, 20, 9, 0, -4, 6, 6, 0, 0, 0, -36, 0, 3, -4, 21, 0, 2, 0, -10, 0, -12, -16, 0, 0, 0, 0, 3, 0, -16, 12, 4, 0, -30, -4, -14, 0, 18, -4, -24, 0, 18, 0, -15, 0, -1, 30, -16, 0, -7, 0, 60, 0, 8, 6, 20, 0, -12, 0, -10, 0, 33, -28, 30, 0, -32, 12, 6, 0, 36, 0, -9, 0, 1, 0, -18, 0, -4, -8, -27, 0, 12, 16, 11, 0, 14, 36, 12, 0, 6, 0, 24, 0, 12, -2, 10, 0, 18, 44, 6, 0, -18, 12, -16, 0, 0, 0, 8, 0, -10, 20, 3, 0, 14, 0, -6, 0, 0, -24, -16, 0, 18, 0, -30, 0, -19, -30, -15, 0, -3, -16, -29, 0, -2, 26, -66, 0, 11, 0, 14, 0, 6, 12, -4, 0, -18, 0, 15, 0, -49, -6, 24, 0, -33, 0, 9, 0, 5, -40, 39, 0, -18, 24, -4, 0, 30, 6, -49, 0, 24, 0, 6, 0, -18, -12, -19, 0, 10, 0, -28, 0, -20, -6, -18, 0, -1, 0, -12, 0, 12, 8, -9, 0, 5, 32, 24, 0, 35, 0, 2, 0, 42, 0, -36, 0, 6, -8, 0, 0, 22, 8, 0, 0, -12, 18, -1, 0, 20, 0, 15, 0, 12, 30, -12, 0, -39, -24, -4, 0, -28, 14, -24, 0, 17, 0, 13, 0, -48, 20, -4, 0, 3, 0, -5, 0, -34, -66, -8, 0, 24, 0, -18, 0, -24, -12, 6, 0, -31, 0, -9, 0, -30, 10, 38, 0, -3, 0, 48, 0, 20, 54, 36, 0, 36, 16, -40, 0, -6, -28, -6, 0, 20, 0, 11, 0, 12, 24, -9, 0, 30, 4, -39, 0, 50, -36, -30, 0, -3, 0, 40, 0, -18, 32, -21, 0, 0, 0, 6, 0, -2, -10, 9, 0, 30, 0, 30, 0, 2, 12, -16, 0, 60, -24, 16, 0, 8, -36, 18, 0, 23, 0, -4, 0, 36, 12, -25, 0, 8, 32, -6, 0, 18, 4, -25, 0, -15, 0, 7, 0, 12, -28, 9, 0, 1, -24, 32, 0, 33, -18, -10, 0, -12, 0, -12, 0, -13, -48, 6, 0, -12, 0, 0, 0, 19, -10, 10, 0, -20, 0, 2, 0, -3, -4, -22, 0, -30, -12, -9, 0, 20, -48, -27, 0, -42, 0, 2, 0, -1, 38, 0, 0, -45, 0, -12, 0, -30, 16, 36, 0, 8, 0, -21, 0, 8, 24, 24, 0, 48, 8, -12, 0, -30, -10, -6, 0, -16, 0, 20, 0, -36, 2, 44, 0, 8, 0, 18, 0, 2, -12, 0, 0, 18, 0, 20, 0, -19, 0, 18, 0, 18, -36, -15, 0, -27, 20, -8, 0, 9, 0, -36, 0, -81, 24, 6, 0, -3, -24, -6, 0, -12, 56, 42, 0, 14, 0, -12, 0, -39, -32, 14, 0, -16, -40, 9, 0, 3, -6, -40, 0, 33, 0, 54, 0, 0, 16, 24, 0, -16, 0, -1, 0, -48, -24, -28, 0, -55, 0], 'weight': 2, 'weight_parity': 1}
  92. label: 77.2.a.c
    {'Nk2': 308, 'analytic_conductor': 0.614848095563859, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[7, 1], [11, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [77, 1, [45, 57], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 1]], [3, [-2, 1]]], 'hecke_orbit': 3, 'hecke_orbit_code': 9007199288295501, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '77.2.a.c', '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': '77.2.a.c', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{2}+2q^{3}-q^{4}-2q^{5}+2q^{6}-q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/77/c'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '77.2.a', 'trace_display': [1, 2, -2, -1], 'trace_hash': 1452091175035734793, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.023', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.963', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.075', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.850', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.221', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.445', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.022', 'prec': 7}, 'traces': [1, 1, 2, -1, -2, 2, -1, -3, 1, -2, 1, -2, 4, -1, -4, -1, 4, 1, 0, 2, -2, 1, -4, -6, -1, 4, -4, 1, -6, -4, 10, 5, 2, 4, 2, -1, -6, 0, 8, 6, 4, -2, 12, -1, -2, -4, -10, -2, 1, -1, 8, -4, -6, -4, -2, 3, 0, -6, 2, 4, 0, 10, -1, 7, -8, 2, 8, -4, -8, 2, -12, -3, -8, -6, -2, 0, -1, 8, 8, 2, -11, 4, 0, 2, -8, 12, -12, -3, -6, -2, -4, 4, 20, -10, 0, 10, -10, 1, 1, 1, -4, 8, 14, -12, 4, -6, 12, 4, -14, -2, -12, 1, 18, 0, 8, 6, 4, 2, -4, 12, 1, 0, 8, -10, 12, -1, 8, -3, 24, -8, 12, -2, 0, 8, 8, -12, -10, -8, -8, -2, -20, -12, 4, -1, 12, -8, 2, 6, -10, -2, -16, 0, 4, -1, -20, -8, 14, 8, -12, -10, 4, -11, -8, -4, -4, 0, 0, 6, 3, -8, 0, -12, 12, -12, 1, -1, 4, -6, 12, 2, 10, -4, 0, 12, 12, 20, 4, 10, 4, 0, 8, 14, -14, -10, -16, -1, 22, 1, -18, 3, 16, -4, 6, -8, -8, 14, -4, -4, 0, 4, -12, 6, -24, 12, -24, 12, -10, -14, -16, 2, 16, -12, 22, -5, -1, 18, 12, 0, 18, 8, -2, 18, -18, 4, 20, -2, 16, -4, 0, 4, -20, 1, -10, 0, -2, 8, 0, -30, 0, 12, -2, 1, -4, 8, -16, -17, -14, 24, 6, 8, -6, 12, 8, -6, 12, 0, -12, -8, 10, 8, -4, -4, -8, -10, -1, 8, 22, -8, 10, -6, 6, -20, 4, 12, 0, 4, -4, 5, -1, 12, -20, 8, -24, 2, -4, 18, -4, -10, -16, 2, -12, -16, -8, 0, 0, 4, 20, 1, 28, -20, -18, -24, 2, 14, 2, -8, -2, -12, -6, -14, 24, 4, 0, 11, -4, -8, -28, -12, 10, -4, -20, 0, -6, 0, -16, 2, 14, 3, 36, 8, 10, 0, -1, -36, 16, 12, 4, 12, 0, 1, -16, 5, -30, 4, 24, 6, -8, 12, 16, 6, -19, 10, 2, 4, 16, 0, 22, 4, 4, 12, 6, -20, -26, 4, 24, 30, -24, 4, -8, 0, 16, 8, 2, -6, 2, -14, 12, 10, 6, -16, -16, -3, 24, 22, -16, -1, 22, -18, 0, 1, -22, 16, 40, 4, 22, 6, -6, -24, 24, -8, -20, -14, -2, -4, 0, 20, -16, 0, 2, -4, -14, -12, -10, 18, -4, -24, 0, -12, 8, -24, 0, 4, -26, -10, 24, 14, 0, -16, -20, 6, 1, 16, 4, 12, 12, 22, -20, -7, -10, -1, 4, -18, -32, 12, 8, 0, 18, 18, -16, -8, 0, -2, 4, 6, -40, -18, 30, -4, -8, 20, 28, -6, 12, 16, 0, 4, -6, 0, -4, -20, -24, -20, 8, -1, 20, -10, -28, 0, -16, -2, 28, -8, -24, 0, -2, -10, 12, 0, -16, -12, 0, -2, 4, 3, 8, -4, 6, -8, 18, -16, 8, -11, 0, -14, -28, -24, -10, 6, 24, 24, 6, -6, 20, -12, 2, 8, 40, -2, -7, 12, 2, 0, 16, -12, -24, -24, 24, 10, 1, -8, -26, -4, 20, 20, 28, -8, -28, 10, 0, -1, 0, 24, -8, 22, 24, 8, 22, 10, 48, -2, 8, 6, -32, 20, -36, 4, 11, 36, 30, 0, 20, -4, 16, -4, 4, 7, -18, -1, -28, -12, 0, -20, -6, 24, -8, -24, -2, -2, 0, -4, 44, 6, 32, -4, 8, 10, -36, -16, -20, 6, -28, -12, 8, 16, -2, -8, -40, 0, 12, 0, -40, -4, 26, 20, -16, 3, 6, 28, 14, 20, 16, -18, 6, -8, -19, 2, 0, -14, -24, 2, -8, -24, -24, -2, -16, 12, 4, -6, -12, 6, -18, 24, 14, -4, -48, 0, -22, 33, 2, -4, -20, 8, -26, -28, -24, -4, -8, 10, 4, 4, 22, -20, 32, 0, 0, -6, 24, 0, 44, -16, 0, -10, -34, 14, 4, -3, -12, 36, 10, 24, 24, 10, -4, 0, 20, -1, 36, -12, -24, 16, -46, -12, -1, 4, 16, 36, 16, 0, -36, -1, -22, -16, 0, 7, 40, -30, 4, -4, -34, 24, 8, 18, -40, -8, -8, -12, 0, 16, -6, 2, -14, -19, -40, -10, 6, 2, 18, 12, 13, 16, 48, 0, 0, 22, -4, -20, 8, 4, -4, -12, 0, 6, -8, -60, 20, -26, 0, -4, -12, 24, -20, 10, -4, -24, 32, -4, -10, -8, -8, 0, 48, 16, 14, -8, -8, 2, 8, -34, 32, 2, -28, 14, -30, 12, -10, 30, 12, 6, 0, 16, -12, -16, 24, -1, -28, 24, 16, -22, 16, -16, -18, -3, 0, 22, 24, 18, 14, 0, -40, -5, -6, -22, -8, -16, -8, 40, 20, 12, -30, 22, 28, -6, -8, -6, 16, -8, 0, 24, -4, 8, 46, -20, 24, -42, -2, -2, -28, 4, -2, 0, 44, 28, 4, -16, 0, 0, -40, 2, 34, -12, 7, -14, 12, 12, -6, -10, -1, 6, 8, -4, 24, 24, 44, 0, 0, -36, 56, 8, 6, 24, -8, 0, 24, -20, -24, -26, -2, 10, 8, 24, 32, 42, -10, 0, -12, 16, 42, -20, -48, 2, -34, 1, 28, -16, -8, 4, -28, 36, -8, 12, -11, -22, 0, -20, -24, 3, -32, -10, -60, 1, -24, 4, -24, -54, -20, -32, 0, -12, -4, 8, 36, 0, 0, 18, 0, -18, -12, -16, 40, -24, 40, 0, -48, 2, 6, 4, 14, -30, 6, -40, 0, 18, -36, 30, -8, -12, -16, -8, 4, -20, -24, 28, -16, -2, -8, 12, -36, -16, -32, 0, -4, 12, 34, -6, -16, 0, -12, -4, 10, -28, 69, -24, 12, 20, 28, 8, 40, -3, 0, 20, 14, 10, 8, -28, -8, 0, 42, -16, -6, 2, -14, 28, 54, -24, -44, -24, 20, 0, -48, -2, 52, 50, -40, 12, 36, 0, 20, -16, 24, -36], 'weight': 2, 'weight_parity': 1}
  93. label: 77.2.a.d
    {'Nk2': 308, 'analytic_conductor': 0.614848095563859, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[7, -1], [11, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [77, 1, [45, 57], [1, 1]], 'cm_discs': [], 'conrey_index': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-5, 0, 1]], [3, [-4, -2, 1]]], 'hecke_orbit': 4, 'hecke_orbit_code': 13510798915665997, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 2, 'hecke_ring_index_factorization': [[2, 1]], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': False, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '77.2.a.d', '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': '77.2.a.d', 'nf_label': '2.2.5.1', 'prim_orbit_index': 1, 'qexp_display': 'q-\\beta q^{2}+(1+\\beta )q^{3}+3q^{4}-2q^{5}+(-5+\\cdots)q^{6}+\\cdots', 'related_objects': ['Genus2Curve/Q/5929/b'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '77.2.a', 'trace_display': [0, 2, -4, 2], 'trace_hash': 961614922517298413, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.012', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.966', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.298', 'prec': 10}, {'__RealLiteral__': 0, 'data': '9.835', 'prec': 14}, {'__RealLiteral__': 0, 'data': '3.647', 'prec': 14}, {'__RealLiteral__': 0, 'data': '69.269', 'prec': 17}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.028', 'prec': 7}, 'traces': [2, 0, 2, 6, -4, -10, 2, 0, 6, 0, -2, 6, 2, 0, -4, -2, -2, -20, 4, -12, 2, 0, -4, -10, -2, 10, 20, 6, 8, 20, -10, 0, -2, -10, -4, 18, -8, 20, -8, 0, -18, -10, 16, -6, -12, 20, 10, -2, 2, 0, 8, 6, 8, -20, 4, 0, -16, 20, 2, -12, -10, 10, 6, -26, -4, 10, 20, -6, -24, 0, -12, -20, -6, -20, -2, 12, -2, 0, 0, 4, 22, -10, 4, 6, 4, 0, -12, 0, 4, 40, 2, -12, -20, -10, -8, 30, 8, 0, -6, -6, -14, 0, 2, 10, -4, -20, -8, 60, 0, 0, 12, -2, 4, 0, 8, 24, -14, -10, -2, 20, 2, -10, -8, -30, 24, -20, 24, 0, 16, -20, 8, -6, 4, 20, -40, -10, 24, 40, -12, -12, 20, -20, -2, -6, -16, 10, 2, -24, 28, 10, 0, 20, 14, 0, 20, -24, 4, -40, 28, 0, -4, -60, 20, -54, 4, -60, -8, -10, -14, 20, -28, 48, -30, -20, -2, 2, 12, 0, 0, -36, -24, 10, 0, 20, 16, 60, 2, 30, 20, -40, -24, -26, -12, 60, 16, 6, -4, 20, 18, 0, 0, 10, 8, 24, 36, 30, -52, -2, -4, 20, 8, 24, 8, 0, -32, -20, -10, -20, -16, 12, -12, 20, 2, 0, -6, 0, -24, -48, 0, -40, -2, 20, -8, 10, -20, 6, 40, -10, 16, 4, 14, 0, 22, -30, -4, 80, 24, 10, 64, 0, 22, 18, 4, -40, -16, -18, -12, -80, -8, -12, -16, 80, 0, 10, -16, 20, 4, 60, 0, 40, -12, 2, -8, 20, 2, -72, -4, 20, -50, 0, -16, -60, 24, -36, 32, -10, -18, 60, -22, -40, -52, -18, -10, -10, -4, -20, -20, 0, 16, -6, 16, 40, -24, -4, 20, -10, 0, -6, -28, -20, -30, 0, 12, 40, -12, 0, 28, -60, -8, 52, -8, 20, -24, 66, -2, -60, 20, -10, 10, -20, 8, 12, 16, 40, -40, -2, -32, 20, 4, 12, 10, 20, 2, 0, 48, 10, 24, -36, -10, 0, 0, 0, 4, -20, 24, 12, 8, -40, -32, 40, 10, -60, 2, 6, 12, 40, -6, 4, -34, 40, 8, -60, 12, 10, 24, -10, 28, -20, 12, -24, 64, 40, 22, 70, 4, 80, 48, 24, -4, 0, -16, 0, -72, 0, 0, -18, -36, -50, -16, 2, 28, -80, 0, -42, -44, 20, 8, 0, -22, 20, 4, 6, 2, 100, -8, -30, -32, -20, 18, -12, 0, -80, 50, -20, 2, 40, -10, -24, 8, 0, 24, -20, -8, 10, 24, 0, 32, 40, 12, 0, 6, -20, -32, 36, -8, -50, 28, -26, -48, 20, 18, 12, -40, 80, -4, 0, -4, -20, 0, 24, -2, 10, -20, -8, 40, 60, -10, -42, 20, 20, -36, -10, -16, -40, -4, -6, 64, -80, 36, -60, -28, -90, -24, 6, -16, -110, -28, -10, 80, 0, 0, -24, -28, 40, 12, 10, -12, -80, 12, 72, -48, -30, 20, -20, 28, -20, -34, 72, 72, 0, -6, 0, 0, 0, -4, 48, -10, -20, -40, -20, 16, -20, 88, 24, -2, 0, 0, 2, 2, 40, 26, 12, -28, -20, 16, 20, 40, 60, -2, -120, -12, -20, 36, 30, 0, 0, 56, 72, -10, 0, 56, 40, 0, -80, -24, -36, -60, 130, 16, 4, -8, 20, 52, 60, -8, 80, 22, -20, 24, 0, -48, -6, -64, -10, 4, -78, -48, 20, -92, -48, 4, 20, -8, 10, 28, -90, 14, 6, 0, 20, -4, 8, -78, 20, 4, 84, 68, 0, -20, 10, -34, 0, 20, 0, -4, 80, 8, -60, -12, 20, 0, 42, -32, -40, 16, 0, 40, 20, -18, 60, -80, 30, 4, 8, -38, 40, 16, 12, 28, 40, -48, -40, 88, 0, -48, 84, 2, -20, 4, 0, -40, 40, -18, -12, -32, -40, 14, -60, -2, -10, -20, 60, 68, -20, -16, 18, -38, -10, 0, 12, -28, -80, 8, -60, -8, 20, 24, -24, 52, -40, 10, 30, -16, 20, -20, -42, -6, -20, 8, 20, -104, -10, 24, -84, -48, 0, 20, -16, -12, -80, -30, -90, -6, 40, 24, -20, 28, -10, -68, -6, -40, 80, -56, 26, -40, 80, -14, 36, -12, 40, 80, 0, 40, 0, 4, 0, 96, -40, -18, 12, 2, 80, 104, -72, -8, -10, -26, 10, 66, -20, -16, 0, 22, -90, -4, -60, -20, 150, 32, 48, -16, -20, -32, 60, -56, 0, 132, 6, -8, -120, 68, -10, 52, 60, 0, 60, -4, 140, 24, -40, -14, -160, 0, -72, -28, -70, -8, -18, 50, 0, -12, -36, -32, -160, 10, 60, 12, 80, -56, 48, 12, 0, 40, -2, -8, 40, -60, -12, 0, 80, 4, 20, -20, -80, -56, 54, -12, 0, 0, 0, 12, 40, 6, 0, 8, -40, -60, 10, 60, 120, -16, 24, 8, 20, -40, -8, 32, 90, -14, 108, 36, -100, -64, 30, 2, -10, -8, -156, 20, 120, 76, -26, -2, 80, 16, -12, -120, 70, 30, 20, 14, 100, -36, 24, 28, -130, 2, -8, -56, 10, -24, 24, -30, -10, 56, 0, 26, 0, 14, -96, -8, 0, -24, 60, 60, -20, -42, -30, 0, 40, 40, -20, -96, 0, 24, -48, 56, 20, 80, -4, 32, -20, 0, -36, -24, -40, 36, 20, 24, 0, -22, 6, 0, -140, 0, 0, 16, -20, -20, -18, 12, 10, 16, 0, 48, 40, 36, -72, -62, -20, 76, 16, -4, -120, 0, 0, 8, -80, 48, -40, 40, -50, -32, -6, 8, 20, -54, -60, -24, -120, 4, -24, -60, 130, -4, 10, 10, 20, -28, -60, -34, 20, 16, -2, -40, 0, -64, 120, 4, -20, 28, -10, 28, -140, 48, 48, 12, -20, 24, 52, -2, -60, -24, 42, 24, 40, 8, 0, 16, -120, -18, 66, -12, -100, 8, 10, 28, -160, -4, -12, 40, 0, 66, 80, 8, -60, 20, 72, -32, -40, 28, -30, 88, -20, -36, 192, 34, -20, -40, 0], 'weight': 2, 'weight_parity': 1}
  94. label: 78.2.a.a
    {'Nk2': 312, 'analytic_conductor': 0.622833135765987, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [3, 1], [13, -1]], 'atkin_lehner_string': '++-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [78, 1, [53, 67], [1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554510, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '78.2.a.a', 'level': 78, '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': [2, 3, 13], 'level_radical': 78, 'minimal_twist': '78.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/78/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '78.2.a', 'trace_display': [-1, -1, 2, 4], 'trace_hash': 124393021660496081, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.022', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.997', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.055', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.999', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.186', 'prec': 10}, {'__RealLiteral__': 0, 'data': '4.959', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.022', 'prec': 7}, 'traces': [1, -1, -1, 1, 2, 1, 4, -1, 1, -2, -4, -1, 1, -4, -2, 1, 2, -1, -8, 2, -4, 4, 0, 1, -1, -1, -1, 4, 6, 2, -4, -1, 4, -2, 8, 1, -2, 8, -1, -2, -10, 4, 4, -4, 2, 0, 8, -1, 9, 1, -2, 1, -10, 1, -8, -4, 8, -6, 4, -2, -2, 4, 4, 1, 2, -4, -16, 2, 0, -8, -8, -1, 2, 2, 1, -8, -16, 1, 8, 2, 1, 10, 12, -4, 4, -4, -6, 4, 14, -2, 4, 0, 4, -8, -16, 1, 10, -9, -4, -1, -2, 2, 16, -1, -8, 10, 12, -1, -2, 8, 2, 4, -6, -8, 0, 6, 1, -4, 8, 2, 5, 2, 10, -4, -12, -4, 0, -1, -4, -2, 4, 4, -32, 16, -2, -2, -10, 0, 12, 8, -8, 8, -4, 1, 12, -2, -9, -2, -6, -1, 12, 8, 2, 16, -8, -1, 14, -8, 10, -2, 0, -1, -16, -10, 8, -12, 0, 4, 1, -4, -8, 4, -10, 6, -4, -4, -4, -14, -12, 2, -10, -4, 2, 0, -4, -4, -8, 8, -4, 16, -8, -1, -14, -10, -2, 9, 18, 4, -8, 1, 16, 2, 24, -2, -20, -16, 0, 1, 32, 8, 12, -10, 8, -12, 8, 1, -16, 2, -2, -8, 2, -2, -4, -4, -1, 6, 20, 8, 22, 0, 16, -6, 18, -1, 16, 4, -8, -8, 0, -2, 10, -5, -1, -2, 18, -10, -8, 4, -12, 12, 4, 4, 0, 0, -4, 1, -6, 4, -8, 2, 6, -4, 8, -4, -20, 32, -14, -16, -26, 2, -4, 2, -4, 10, 4, 0, 22, -12, -4, -8, -26, 8, -4, -8, 16, 4, -40, -1, -13, -12, -10, 2, 26, 9, 8, 2, 4, 6, 0, 1, 16, -12, 2, -8, -4, -2, -8, -16, -16, 8, 0, 1, -6, -14, 8, 8, -6, -10, -24, 2, -12, 0, -16, 1, -1, 16, 2, 10, 32, -8, 8, 12, -2, 0, -32, -4, 18, -1, 6, 4, 16, 8, 8, -4, 0, 10, -12, -6, 6, 4, -1, 4, 14, 4, -16, 14, -8, 12, 0, -2, 45, 10, -5, 4, 4, -2, 16, 0, -10, 4, -40, 4, 6, 8, 12, -8, 6, 4, 0, -16, 0, 8, -24, 1, -32, 14, 4, 10, -26, 2, 0, -9, -4, -18, 16, -4, 6, 8, 32, -1, 6, -16, -4, -2, 2, -24, 8, 2, 2, 20, 10, 16, 16, 0, 24, -1, -12, -32, 4, -8, 22, -12, 8, 10, -2, -8, -8, 12, 4, -8, -8, -1, -30, 16, -12, -2, 0, 2, 16, 8, 9, -2, -4, 2, 28, 4, 6, 4, 6, 1, 40, -6, -12, -20, 8, -8, -30, -22, -2, 0, -6, -16, -20, 6, 8, -18, -4, 1, -64, -16, -14, -4, -16, 8, 8, 8, -10, 0, -16, 2, -2, -10, 0, 5, 20, 1, 4, 2, 16, -18, 36, 10, 12, 8, -8, -4, -32, 12, 0, -12, 0, -4, 40, -4, -4, 0, -1, 0, 42, 4, 8, -1, 8, 6, 32, -4, -32, 8, 10, -2, -14, -6, -20, 4, 4, -8, -8, 4, -23, 20, 4, -32, -10, 14, 24, 16, 12, 26, -36, -2, -34, 4, 10, -2, -4, 4, -28, -10, -2, -4, -48, 0, 32, -22, 4, 12, 18, 4, 4, 8, 8, 26, 4, -8, -12, 4, 4, 8, -30, -16, -20, -4, 8, 40, 0, 1, 18, 13, 14, 12, 48, 10, 40, -2, 2, -26, 4, -9, 32, -8, -18, -2, -42, -4, 16, -6, 8, 0, -24, -1, 26, -16, -16, 12, 10, -2, -16, 8, -24, 4, 8, 2, -2, 8, 20, 16, 6, 16, 32, -8, 0, 0, 56, -1, -19, 6, -32, 14, -4, -8, -36, -8, -12, 6, 0, 10, 9, 24, -8, -2, 2, 12, -16, 0, -8, 16, 24, -1, -16, 1, 16, -16, -10, -2, 8, -10, 2, -32, -36, 8, -2, -8, -2, -12, -64, 2, 0, 0, 4, 32, 8, 4, -14, -18, 1, 1, 38, -6, 40, -4, -20, -16, 44, -8, -20, -8, -22, 4, -10, 0, -32, -10, -16, 12, 24, 6, -20, -6, -18, -4, -50, 1, 16, -4, -16, -14, -8, -4, 6, 16, 8, -14, 0, 8, -8, -12, 0, 0, -24, 2, 64, -45, -10, -10, -6, 5, -40, -4, 1, -4, 8, 2, -2, -16, -18, 0, 64, 10, 40, -4, 8, 40, -24, -4, -12, -6, 12, -8, 48, -12, -40, 8, -4, -6, 24, -4, 54, 0, 0, 16, -26, 0, -8, -8, 4, 24, 4, -1, 2, 32, 6, -14, -54, -4, 4, -10, 8, 26, 80, -2, 32, 0, -6, 9, 28, 4, 40, 18, -8, -16, -24, 4, -2, -6, 20, -8, -2, -32, 16, 1, 14, -6, -8, 16, 0, 4, 26, 2, 2, -2, 0, 24, 4, -8, -32, -2, -32, -2, 4, -20, 42, -10, -16, -16, -4, -16, 28, 0, -2, -24, -22, 1, 18, 12, 0, 32, 4, -4, -40, 8, 7, -22, 26, 12, 2, -8, 20, -10, 4, 2, 0, 8, -2, 8, -16, -12, 18, -4, -44, 8, 40, 8, 40, 1, -20, 30, 13, -16, -32, 12, -16, 2, 10, 0, -48, -2, 22, -16, -26, -8, 26, -9, 4, 2, -8, 4, 0, -2, 0, -28, -4, -4, -64, -6, -24, -4, 0, -6, -24, -1, -20, -40, -16, 6, -20, 12, 28, 20, -2, -8, 40, 8, -48, 30, 4, 22, 16, 2, -16, 0, 8, 6, -8, 16, 2, 20, 16, -6, 46, -8, -72, 18, 0, 4, -16, -1, 26, 64, 6, 16, -46, 14, 0, 4, -8, 16, -4, -8, 2, -8, 6, -8, -30, 10, -16, 0, 24, 16, -40, -2, -15, 2, 12, 10, -28, 0, 4, -5, 16, -20, -28, -1, 48, -4, 1, -2, 6, -16, -56, 18, -2, -36, 24, -10, 36, -12, -32, -8, 0, 8, -48, 4, -8, 32, -16, -12, -26, 0, 2, 12], 'weight': 2, 'weight_parity': 1}
  95. label: 79.2.a.a
    {'Nk2': 316, 'analytic_conductor': 0.6308181759681151, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[79, 1]], 'atkin_lehner_string': '+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [79, 1, [3], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [1, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554511, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '79.2.a.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': '79.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/79/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '79.2.a', 'trace_display': [-1, -1, -3, -1], 'trace_hash': 1030334534842869988, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.952', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.873', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.680', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.016', 'prec': 7}, 'traces': [1, -1, -1, -1, -3, 1, -1, 3, -2, 3, -2, 1, 3, 1, 3, -1, -6, 2, 4, 3, 1, 2, 2, -3, 4, -3, 5, 1, -6, -3, -10, -5, 2, 6, 3, 2, -2, -4, -3, -9, -10, -1, 4, 2, 6, -2, 7, 1, -6, -4, 6, -3, 8, -5, 6, -3, -4, 6, -3, -3, -4, 10, 2, 7, -9, -2, 8, 6, -2, -3, 15, -6, 2, 2, -4, -4, 2, 3, -1, 3, 1, 10, -6, -1, 18, -4, 6, -6, -7, -6, -3, -2, 10, -7, -12, 5, -19, 6, 4, -4, 11, -6, -9, 9, -3, -8, -11, -5, 10, -6, 2, 1, 0, 4, -6, 6, -6, 3, 6, 9, -7, 4, 10, 10, 3, -2, -11, 3, -4, 9, 6, -2, -4, -8, -15, -18, 12, 2, -21, -3, -7, -15, -6, 2, 18, -2, 6, 2, -6, 4, 6, 12, 12, -2, 30, 3, -18, 1, -8, 15, -2, -1, 4, 10, -6, 6, 18, 3, -4, -18, -8, -4, -8, -6, -4, 2, 3, 7, -16, -6, 22, 3, 4, 6, 6, -10, 12, -7, -5, 12, -15, -7, 14, 19, 9, 6, -6, -4, 11, 12, -8, -11, 6, -6, 30, 9, -4, -3, -8, 3, -12, -8, -15, 11, -12, 15, 10, -10, -2, -6, -18, -2, -26, 5, -8, 0, -8, 4, 16, 6, -2, -18, -18, 6, -21, 3, 1, -6, 12, -3, -15, 7, -16, 4, 18, -10, 12, -30, 6, -3, -5, -2, -4, 11, -18, -17, -2, 4, 2, 9, 12, -6, 26, 6, -24, 4, 7, -8, -19, 15, 0, 6, 3, -12, -8, 2, 11, 21, 20, 9, 23, 7, 24, -15, 12, 6, 10, 10, 19, -18, 19, -2, -12, -6, 9, -6, -10, 6, 6, 4, -4, -6, -11, -4, 12, -12, 12, -2, 9, -30, 4, -9, -26, 18, -6, 1, 31, 8, 12, -21, 11, 2, -24, -1, 12, -4, -10, -30, -7, 6, 20, 6, 4, -18, -24, -1, 31, 4, 0, -18, 20, 8, 13, 12, 6, 8, -14, -6, 12, 4, 15, 10, -4, -3, -45, 7, -6, 16, -35, 18, -3, -22, 7, 3, -6, -4, -2, -2, 20, -6, -8, -10, -2, -12, -3, 21, -18, 5, -23, 12, 11, 15, 2, -3, -6, -14, -8, 19, -9, -9, -12, -18, -6, 6, 3, -4, -1, -11, 4, -4, 10, 8, -30, -11, -3, -6, 4, 18, 0, -30, -12, 9, 3, 4, 18, -15, 21, 8, 9, 3, -13, 12, -14, 24, -24, 15, 4, 11, 6, 12, 20, -5, -3, -10, -18, -10, 8, 2, -20, 18, 12, 18, -4, -2, 21, 26, 6, -7, -22, 8, 20, 0, -6, 8, 9, -12, 7, -16, -30, 6, -10, 2, -19, 6, -30, 18, 6, 6, -8, 21, 18, -9, -8, -1, 16, -6, -16, -12, 0, -15, -6, 15, 2, 7, 57, 16, 18, -12, -4, -18, 13, -10, 36, -12, -12, 10, -15, -6, 10, -3, -18, 5, -13, 6, -33, 4, 4, 11, -20, 18, -2, 11, 20, 2, 27, 4, -14, -2, 8, -27, 0, -12, -6, -6, 4, -26, 60, -2, -19, 24, 6, 4, -30, -7, 33, 24, 16, 19, 12, 15, -29, 0, -22, 30, -30, -3, -18, -12, 8, 8, -24, -6, 1, -11, -6, 21, -11, -20, 12, -3, -12, -23, 18, 7, 0, -24, -1, 45, -30, -12, 26, 6, 15, -10, 8, -14, -16, -19, -14, -18, 6, -19, -16, 6, 18, 12, 25, -6, -40, -9, 6, 2, 27, 10, -18, 6, -11, -6, 12, -12, -44, 4, -16, -6, 21, 11, 13, -20, -6, -12, 21, -12, 6, -12, -30, 6, 37, -9, 37, -30, 10, -4, 7, 3, -29, 26, 8, 18, 12, 6, -7, -3, 12, -31, 33, 8, -18, -12, -30, -9, -9, -11, 16, 2, 12, 24, -32, 3, 6, -12, -10, -4, -7, 10, -18, 10, -4, 7, 15, 6, 14, -20, 18, -18, 12, -4, -12, -18, 26, 24, 8, -5, -30, -31, 20, 4, -15, 0, 19, 54, 8, -20, 24, 8, -36, -13, -16, -4, 24, -6, -23, 8, -4, 14, 63, 18, 60, -12, 18, 4, 2, -15, -8, -14, 21, 4, -11, -3, 38, 45, 2, -21, -20, 6, 18, 16, -12, 35, 6, -6, 9, 3, 15, -22, -24, -7, 30, -9, 13, 6, -24, -4, 34, 2, -18, -10, -16, -20, -13, -6, -12, 8, 20, 30, 18, 2, 12, -12, 11, 3, 10, -7, 5, 18, -18, 5, -9, 23, 4, -36, -10, -11, -10, 15, -36, -2, -9, 17, -36, 6, 2, -14, -6, 8, -40, -57, -2, 9, -40, -9, -30, 12, -30, 6, 54, 6, -26, 6, -26, -3, 0, 12, -12, 1, 24, -11, -10, -4, -42, -20, 14, -10, -4, 8, 6, 30, 19, 33, -9, 3, 50, -6, 0, -4, -12, -6, 16, 0, 6, -30, 2, 12, -48, -27, 8, -3, -1, 4, -4, -18, -11, 21, 36, -21, -54, 8, -50, -9, 12, -9, 7, 13, -23, 12, 12, 14, 7, -8, -24, 24, -4, 15, -4, -4, 24, -33, 41, -6, 45, 12, -10, -20, 14, -25, 24, 3, -19, -10, 2, 18, 24, 30, 38, -8, -3, 2, -30, 20, 12, -6, -32, -12, -49, 18, -9, 4, 38, 6, 11, -21, -2, 26, 28, -6, 48, -3, -6, 22, 60, 8, -48, -20, 4, 0, -66, 6, -32, 8, -22, -9, -48, 4, 12, -7, -12, -16, -6, 30, 56, -18, -12, 10, 45, 2, -8, 19, 18, 30, 12, 30, -24, 18, -4, -6, -36, -18, 28, 8, 26, 21, -6, -18, -20, 3, 15, 8, 0, -1, 6, -16, -31, 18, 9, 16, 45, -12, -12, 0, -12, 21, 69, 6, 22, 15, -42, -2, -32, -21, 24, -57, -18, 16, 21, -18, -12, 4, -6, 4, 14, -18, -20, -13, -40, 30, 18, -36, 7, -12, 8, 12, -57, 50, -20, 15, -33, -6, 2, -10, -10, 9], 'weight': 2, 'weight_parity': 1}
  96. label: 79.2.a.b
    {'Nk2': 316, 'analytic_conductor': 0.6308181759681151, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[79, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [79, 1, [3], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 5, 'field_disc': 81589, 'field_disc_factorization': [[83, 1], [983, 1]], 'field_poly': [-1, 8, 0, -6, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': False, 'field_poly_root_of_unity': 0, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[2, [-1, 8, 0, -6, 0, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660925007, 'hecke_ring_generator_nbound': 2, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '79.2.a.b', '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': '79.2.a.b', 'nf_label': '5.5.81589.1', 'prim_orbit_index': 1, 'qexp_display': 'q+\\beta _{1}q^{2}+(1-\\beta _{2}-\\beta _{4})q^{3}+\\beta _{2}q^{4}+\\cdots', 'related_objects': [], 'relative_dim': 5, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '79.2.a', 'trace_display': [0, 1, 7, -5], 'trace_hash': 355892447832279626, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.064', 'prec': 7}, {'__RealLiteral__': 0, 'data': '4.632', 'prec': 14}, {'__RealLiteral__': 0, 'data': '2.283', 'prec': 14}, {'__RealLiteral__': 0, 'data': '62.619', 'prec': 17}, {'__RealLiteral__': 0, 'data': '78.301', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1320.168', 'prec': 24}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.005', 'prec': 4}, 'traces': [5, 0, 1, 2, 7, -1, -5, 0, 10, -7, 2, -9, -3, 1, -13, -12, 10, -25, -4, 6, -7, -1, 2, 1, 6, 16, 7, -15, 6, 7, 2, 5, -4, -8, 1, 17, 0, 0, -11, 10, 30, 27, -14, 10, 20, 2, 5, 1, 2, -14, 2, 15, 2, -11, -18, -11, -30, 32, 5, -27, -6, 15, -44, -8, -5, 38, -16, -6, -20, 1, 3, 27, -12, -22, -38, 17, -16, -31, 5, -9, 29, 8, -30, 3, 8, -2, 18, -16, 47, -48, -19, 1, -4, 9, -12, 3, -1, -9, 20, 5, 41, 46, -3, 5, 13, 4, -31, 17, -16, -47, -10, 47, 18, 64, 38, -10, -16, -39, 10, 7, 19, -18, 6, 30, 3, 60, 1, -18, 28, 46, 30, -8, -4, -48, -1, -16, 16, -14, -33, -35, -7, 9, -10, -69, -6, -16, 46, -26, -28, 80, -10, -17, 16, -2, -6, -5, -2, 0, 60, 15, 18, -84, -8, 22, -62, 18, -14, -29, -10, -60, 0, -2, -24, -62, 28, -45, -1, -2, 12, 49, -20, -43, 88, 15, 30, -58, 38, -31, -93, -47, 7, 59, 44, -7, 7, -11, -50, -27, -5, -7, 30, 60, 2, -18, 48, 51, -20, -10, 76, 27, 10, -12, -43, -7, -42, 61, -56, 26, 8, 47, -48, 66, 42, 13, 6, 16, -22, -22, 26, 33, -10, -10, 0, 41, -11, -1, 1, 18, 24, 67, -13, 32, 92, -56, 8, -54, 4, 16, -18, -32, -11, 0, -68, 5, -54, 48, 52, -48, 62, 24, -60, 18, -18, -36, -68, -30, 11, -25, 35, 65, 34, -18, 35, 16, 20, -24, -47, 59, 28, -21, -3, 107, 4, 43, -90, -14, -50, 56, -17, 80, -73, -21, -30, -106, 49, -6, -58, -66, 18, -50, -24, -82, 93, -34, -30, -54, -58, 42, -79, 45, 40, -1, 48, 10, -58, 2, -25, -20, -52, -75, -29, -24, 26, -6, -36, 65, -34, 16, 69, 54, -32, -18, -18, -53, 12, 55, -7, 59, 60, 6, 6, 12, 11, 12, 8, -54, -42, 6, -2, -10, 49, 38, 22, 5, 31, 41, -10, 60, -45, 25, 15, -13, 27, -11, -16, -80, 42, 32, 64, -52, -36, -8, -6, 20, -37, -59, 38, 81, 7, 68, 35, 71, 14, -17, -32, 18, 14, 40, 33, -79, -30, 39, -56, -26, 7, 4, 7, 115, 56, -4, 52, -32, 74, -5, 51, -46, -26, -30, 12, 4, -120, 27, 3, 16, -14, -77, 53, -5, 41, 11, 29, 46, -82, -24, 54, -25, 24, 17, 36, 34, -8, -67, -65, -34, 70, 20, -50, 34, -16, 51, 44, -26, 22, -10, 37, -62, 50, -27, 18, -38, -22, -40, 64, -4, -55, -64, -31, -30, -86, -14, -36, -50, 67, 28, -6, -2, -14, -48, 20, -65, -50, 37, 4, -1, 52, -2, 30, -16, 36, -55, -76, 26, 62, -61, 7, -112, -30, 14, -22, 60, -61, -54, -32, 1, 108, -57, -43, -38, 34, 6, 96, -39, 1, -84, -29, -71, -70, -3, 2, 94, 34, 0, -124, -87, 11, 56, 54, 34, -88, -10, 88, 74, 22, 17, 76, 51, -58, 4, -25, -26, 80, 54, 24, 3, -3, 49, 60, -63, -88, 1, 55, -20, 72, 74, 18, 37, -42, 2, 6, -63, -76, 10, -5, 51, -14, -33, -45, -19, 20, 71, -12, 3, 14, -17, 18, -9, -101, 25, -36, 116, -26, -61, 39, -10, 24, 35, 16, 16, 118, -52, 54, 135, 86, -5, -42, 94, -59, 42, 8, -47, 6, 60, 61, 6, 42, -20, -27, 61, -24, -52, -2, 32, 60, -29, -39, -167, 35, 30, 30, 36, -77, 60, 16, 16, -50, 32, 47, 47, -65, 59, 6, -50, -93, 19, -37, 11, 16, 28, 56, 56, -11, 0, -36, 127, -55, 56, 8, 40, 28, -62, 65, -51, -52, -60, 80, -18, -116, 100, -42, 19, -18, 0, -21, -90, 38, -78, -14, -25, -35, -26, -42, -52, 42, 10, -46, -4, 40, -34, 42, -5, -80, -57, 2, -13, -160, 38, -31, -96, -7, 40, -64, -12, -84, -3, 118, 57, 12, 2, -30, 22, 97, 44, 62, -10, -179, -2, 12, -56, -86, -10, -28, 79, -16, 83, -55, -48, -83, -11, 4, 31, 10, -5, 0, -46, 22, 32, -62, 9, 58, -150, 25, -69, 19, -24, -68, 131, 6, 7, 121, -25, -48, 100, 8, 109, 124, -36, -80, -146, -29, -50, 72, 52, -16, 28, -20, -110, -120, 52, -5, 189, -38, 45, -23, 34, 6, -35, 119, -133, -68, 34, 12, 5, -6, -29, 86, 89, -47, -47, -46, 32, 4, 6, -20, 26, -64, -24, 38, -72, -58, 17, -10, -74, 58, 15, 32, 142, 18, 36, -36, -7, 20, 2, -72, -33, 40, -21, 78, -140, 110, 76, 144, 114, 4, 62, 20, 102, 3, -23, 129, -75, 74, -70, -128, -34, -32, 22, -10, 176, 80, 42, 28, 152, -96, -35, -92, 77, -23, 23, -24, 122, 21, -40, -56, 15, -70, -41, 142, -37, 64, -29, -5, -53, 21, -54, 20, 76, 95, -46, -106, -74, 36, -49, 34, 124, 128, 47, 119, -42, 3, -16, -46, -32, 78, -71, 30, 41, -45, -14, 2, -214, -56, 36, 20, -59, 25, 32, 20, -32, -48, -57, 126, -59, 87, -38, -13, -28, 58, -22, -29, -104, -66, -14, 56, -50, -44, 49, -22, -12, 36, 85, 44, -28, -84, 2, -106, -22, 60, 4, 4, -85, -44, 108, -108, 38, 204, -78, 22, -18, 20, -48, -68, -52, 83, 22, 96, -65, -130, -102, 144, -106, -136, 78, -116, 33, -44, -42, 116, 126, 0, -43, -58, 2, 46, -3, -113, 44, 82, -9, -46, -129, -53, 10, -21, -32, -53, 53, 88, -148, 116, 59, -25, -72, -12, 49, -26, 14, -72, -111, -60, -108, -30, 4, 13, -17, 96, 82, -106, -32, 106, -63, -62, 47, -2, 38, -40, 44, 101, -71, -46, -101, 33, -90, -156, -61, -27, 42, -52, -15, -150, -44], 'weight': 2, 'weight_parity': 1}
  97. label: 80.2.a.a
    {'Nk2': 320, 'analytic_conductor': 0.638803216170243, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [5, -1]], 'atkin_lehner_string': '+-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': False, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [80, 1, [31, 21, 17], [1, 1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [0, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554512, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': False, 'label': '80.2.a.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': '40.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+q^{5}+4q^{7}-3q^{9}-4q^{11}-2q^{13}+\\cdots', 'related_objects': ['EllipticCurve/Q/80/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '80.2.a', 'trace_display': [0, 0, 1, 4], 'trace_hash': 1816714693887773720, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.004', 'prec': 4}, {'__RealLiteral__': 0, 'data': '0.974', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.902', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.660', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.018', 'prec': 7}, 'traces': [1, 0, 0, 0, 1, 0, 4, 0, -3, 0, -4, 0, -2, 0, 0, 0, 2, 0, -4, 0, 0, 0, -4, 0, 1, 0, 0, 0, -2, 0, 8, 0, 0, 0, 4, 0, 6, 0, 0, 0, -6, 0, 8, 0, -3, 0, -4, 0, 9, 0, 0, 0, 6, 0, -4, 0, 0, 0, 4, 0, -2, 0, -12, 0, -2, 0, -8, 0, 0, 0, 0, 0, -6, 0, 0, 0, -16, 0, 0, 0, 9, 0, 16, 0, 2, 0, 0, 0, -6, 0, -8, 0, 0, 0, -4, 0, -14, 0, 12, 0, 6, 0, -4, 0, 0, 0, 0, 0, 14, 0, 0, 0, 18, 0, -4, 0, 6, 0, 8, 0, 5, 0, 0, 0, 1, 0, 12, 0, 0, 0, -12, 0, -16, 0, 0, 0, 10, 0, -12, 0, 0, 0, 8, 0, -2, 0, 0, 0, -10, 0, 16, 0, -6, 0, 8, 0, -2, 0, 0, 0, -16, 0, -16, 0, 0, 0, -12, 0, -9, 0, 12, 0, 14, 0, 4, 0, 0, 0, -20, 0, -10, 0, 0, 0, 6, 0, -8, 0, 0, 0, -8, 0, -14, 0, 0, 0, 22, 0, -8, 0, 0, 0, -8, 0, -6, 0, 12, 0, 16, 0, 4, 0, 0, 0, 8, 0, 32, 0, 0, 0, -4, 0, 4, 0, -3, 0, 24, 0, -26, 0, 0, 0, -6, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 9, 0, 8, 0, 0, 0, 12, 0, 16, 0, 0, 0, -30, 0, 24, 0, 6, 0, 12, 0, 6, 0, 0, 0, 14, 0, -24, 0, 0, 0, -4, 0, -10, 0, -24, 0, 10, 0, -8, 0, 0, 0, -24, 0, -13, 0, 0, 0, -26, 0, 4, 0, 0, 0, 8, 0, 32, 0, 0, 0, -2, 0, 8, 0, 0, 0, -32, 0, 26, 0, -12, 0, -18, 0, 8, 0, 0, 0, -8, 0, -2, 0, 0, 0, -16, 0, 12, 0, -18, 0, -8, 0, -14, 0, 0, 0, -32, 0, 8, 0, 0, 0, 16, 0, 30, 0, 0, 0, 2, 0, 0, 0, 0, 0, 24, 0, -3, 0, 0, 0, -6, 0, -20, 0, 18, 0, 24, 0, 22, 0, 0, 0, 4, 0, 20, 0, 0, 0, 36, 0, -16, 0, -24, 0, 6, 0, -8, 0, 0, 0, 0, 0, -2, 0, 0, 0, 18, 0, -16, 0, 9, 0, -24, 0, 10, 0, 0, 0, 16, 0, 16, 0, 0, 0, -36, 0, 6, 0, 12, 0, 2, 0, -8, 0, 0, 0, 40, 0, 2, 0, 0, 0, 16, 0, 8, 0, -27, 0, -24, 0, -6, 0, 0, 0, 18, 0, 24, 0, 0, 0, -8, 0, 10, 0, 0, 0, -18, 0, -12, 0, 0, 0, -8, 0, -32, 0, 0, 0, -32, 0, -4, 0, -18, 0, -16, 0, -12, 0, 0, 0, -14, 0, 20, 0, 0, 0, -36, 0, -4, 0, 12, 0, 0, 0, 28, 0, 0, 0, 12, 0, 6, 0, 0, 0, -2, 0, -24, 0, 0, 0, -4, 0, 16, 0, 0, 0, 10, 0, 8, 0, 0, 0, 16, 0, -7, 0, -12, 0, 12, 0, 0, 0, 0, 0, -36, 0, -2, 0, 0, 0, 14, 0, -8, 0, 6, 0, 8, 0, 0, 0, 0, 0, 14, 0, -16, 0, 0, 0, -16, 0, 18, 0, 36, 0, -22, 0, -4, 0, 0, 0, -4, 0, 2, 0, 0, 0, 64, 0, -24, 0, 6, 0, 48, 0, -32, 0, 0, 0, 18, 0, 8, 0, 0, 0, 24, 0, 10, 0, 24, 0, 5, 0, 12, 0, 0, 0, 8, 0, -42, 0, 0, 0, -6, 0, 4, 0, 0, 0, -24, 0, 1, 0, 0, 0, 12, 0, -16, 0, 0, 0, 12, 0, -18, 0, 0, 0, 18, 0, 48, 0, 0, 0, -12, 0, -16, 0, 0, 0, -34, 0, -12, 0, 18, 0, 12, 0, -42, 0, 0, 0, -16, 0, 8, 0, 0, 0, 8, 0, 18, 0, 0, 0, 22, 0, -56, 0, 0, 0, -24, 0, 10, 0, 0, 0, -12, 0, -44, 0, 48, 0, -12, 0, -12, 0, 0, 0, -34, 0, -24, 0, 0, 0, 24, 0, 38, 0, 0, 0, -32, 0, 8, 0, 0, 0, 32, 0, -16, 0, 0, 0, -2, 0, -44, 0, -27, 0, 16, 0, 30, 0, 0, 0, 32, 0, -36, 0, 0, 0, -36, 0, -10, 0, -48, 0, 0, 0, 24, 0, 0, 0, 16, 0, -10, 0, 0, 0, -6, 0, 56, 0, -6, 0, -8, 0, 34, 0, 0, 0, -42, 0, 8, 0, 0, 0, 24, 0, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0, 72, 0, 4, 0, 0, 0, -18, 0, -8, 0, 18, 0, 24, 0, -16, 0, 0, 0, 42, 0, 28, 0, 0, 0, -16, 0, -32, 0, 24, 0, 22, 0, -4, 0, 0, 0, -48, 0, -2, 0, 0, 0, 18, 0, -12, 0, 0, 0, 40, 0, -25, 0, 0, 0, -9, 0, 20, 0, 0, 0, -24, 0, 38, 0, 12, 0, -6, 0, 4, 0, 0, 0, -12, 0, 14, 0, 0, 0, 0, 0, 16, 0, 42, 0, 4, 0, 46, 0, 0, 0, -30, 0, 16, 0, 0, 0, 20, 0, 48, 0, -36, 0, 16, 0, -20, 0, 0, 0, -16, 0, 12, 0, 0, 0, -10, 0, -48, 0, -18, 0, -40, 0, -64, 0, 0, 0, -48, 0, -8, 0, 0, 0, 0, 0, 6, 0, 12, 0, -14, 0, -36, 0, 0, 0, -8, 0, -38, 0, 0, 0, 46, 0, 24, 0, 0, 0, 8, 0, 12, 0, 0, 0, -6, 0, -8, 0, 0, 0, 40, 0, 33, 0, 0, 0, -14, 0, 36, 0, 0, 0, -20, 0, -48, 0, 0, 0, 2, 0, 24, 0, -42, 0, -36, 0, 22, 0, 0, 0, -32, 0, 40, 0, 0, 0, -8, 0, -42, 0, 0, 0], 'weight': 2, 'weight_parity': 1}
  98. label: 80.2.a.b
    {'Nk2': 320, 'analytic_conductor': 0.638803216170243, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, -1], [5, 1]], 'atkin_lehner_string': '-+', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': False, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [80, 1, [31, 21, 17], [1, 1, 1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': -1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [-2, 1]]], 'hecke_orbit': 2, 'hecke_orbit_code': 4503599660925008, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': False, 'label': '80.2.a.b', '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': '20.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q+2q^{3}-q^{5}-2q^{7}+q^{9}+2q^{13}+\\cdots', 'related_objects': ['EllipticCurve/Q/80/b'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '80.2.a', 'trace_display': [0, 2, -1, -2], 'trace_hash': 203926327671425217, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.013', 'prec': 7}, {'__RealLiteral__': 0, 'data': '0.977', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.926', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.779', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.013', 'prec': 7}, 'traces': [1, 0, 2, 0, -1, 0, -2, 0, 1, 0, 0, 0, 2, 0, -2, 0, -6, 0, 4, 0, -4, 0, -6, 0, 1, 0, -4, 0, 6, 0, 4, 0, 0, 0, 2, 0, 2, 0, 4, 0, 6, 0, 10, 0, -1, 0, 6, 0, -3, 0, -12, 0, -6, 0, 0, 0, 8, 0, -12, 0, 2, 0, -2, 0, -2, 0, -2, 0, -12, 0, 12, 0, 2, 0, 2, 0, 0, 0, -8, 0, -11, 0, -6, 0, 6, 0, 12, 0, -6, 0, -4, 0, 8, 0, -4, 0, 2, 0, 0, 0, 6, 0, -14, 0, 4, 0, 6, 0, 2, 0, 4, 0, -6, 0, 6, 0, 2, 0, 12, 0, -11, 0, 12, 0, -1, 0, -2, 0, 20, 0, 0, 0, -8, 0, 4, 0, 18, 0, 4, 0, 12, 0, 0, 0, -6, 0, -6, 0, -6, 0, -20, 0, -6, 0, -4, 0, -22, 0, -12, 0, 12, 0, 10, 0, 0, 0, -18, 0, -9, 0, 4, 0, -6, 0, -2, 0, -24, 0, 12, 0, -10, 0, 4, 0, -2, 0, 0, 0, 8, 0, 12, 0, 26, 0, -4, 0, 18, 0, -8, 0, -4, 0, -12, 0, -6, 0, -6, 0, 0, 0, 16, 0, 24, 0, -10, 0, -8, 0, 4, 0, -12, 0, 10, 0, 1, 0, 6, 0, 14, 0, 0, 0, -6, 0, -6, 0, -16, 0, 24, 0, 14, 0, -10, 0, 3, 0, 8, 0, -12, 0, 0, 0, 0, 0, 12, 0, -6, 0, -4, 0, 6, 0, 18, 0, 6, 0, -12, 0, 18, 0, -20, 0, -8, 0, 0, 0, 26, 0, 4, 0, 6, 0, -14, 0, -8, 0, -12, 0, 19, 0, 4, 0, -30, 0, 12, 0, 0, 0, -12, 0, -20, 0, 12, 0, -2, 0, -2, 0, -28, 0, -12, 0, -22, 0, 2, 0, -6, 0, 0, 0, 12, 0, -24, 0, 2, 0, 4, 0, -12, 0, -8, 0, 2, 0, 2, 0, 2, 0, -12, 0, 0, 0, 20, 0, 12, 0, 30, 0, -10, 0, -8, 0, 18, 0, -12, 0, 24, 0, -24, 0, -3, 0, -22, 0, -2, 0, 22, 0, 6, 0, 12, 0, 26, 0, -2, 0, 12, 0, 28, 0, -4, 0, -6, 0, 0, 0, 10, 0, -6, 0, 36, 0, 0, 0, 8, 0, 2, 0, -16, 0, -30, 0, 8, 0, 11, 0, 0, 0, -34, 0, 36, 0, 24, 0, 6, 0, 8, 0, -36, 0, 26, 0, 6, 0, -6, 0, -4, 0, 0, 0, -36, 0, 2, 0, -12, 0, -24, 0, -8, 0, -3, 0, -6, 0, 6, 0, -12, 0, 6, 0, 0, 0, -40, 0, 4, 0, 26, 0, 24, 0, 30, 0, -14, 0, -8, 0, 30, 0, 4, 0, -44, 0, 0, 0, 4, 0, -6, 0, 24, 0, 4, 0, 24, 0, -2, 0, -26, 0, 20, 0, 0, 0, -36, 0, 0, 0, -24, 0, 4, 0, -36, 0, 18, 0, -6, 0, -18, 0, 6, 0, -4, 0, -16, 0, 14, 0, 0, 0, -12, 0, -6, 0, -14, 0, -4, 0, -24, 0, 13, 0, -12, 0, 12, 0, -6, 0, 24, 0, 0, 0, 14, 0, -20, 0, -2, 0, -26, 0, 2, 0, 24, 0, 16, 0, -4, 0, -30, 0, 20, 0, 0, 0, 18, 0, 6, 0, 22, 0, 30, 0, -8, 0, 24, 0, -6, 0, -22, 0, 52, 0, 12, 0, 0, 0, -2, 0, 6, 0, 16, 0, 36, 0, 18, 0, -12, 0, -16, 0, 0, 0, -10, 0, -2, 0, 11, 0, 22, 0, -24, 0, 12, 0, 2, 0, -12, 0, -6, 0, -20, 0, 24, 0, 12, 0, 1, 0, 0, 0, -12, 0, 28, 0, 32, 0, 2, 0, -6, 0, 12, 0, -18, 0, -14, 0, -20, 0, -42, 0, 0, 0, -16, 0, 42, 0, 0, 0, 2, 0, -36, 0, -22, 0, -24, 0, 8, 0, -36, 0, 20, 0, 0, 0, -46, 0, -4, 0, 18, 0, -4, 0, 12, 0, 42, 0, -18, 0, 28, 0, -12, 0, -8, 0, 0, 0, -4, 0, -36, 0, -12, 0, -30, 0, 8, 0, -12, 0, -12, 0, -34, 0, -8, 0, -24, 0, 0, 0, 48, 0, 24, 0, 28, 0, 28, 0, 6, 0, 46, 0, 13, 0, -60, 0, -22, 0, 6, 0, 0, 0, -20, 0, 16, 0, -6, 0, 6, 0, -6, 0, -12, 0, 4, 0, 0, 0, 20, 0, -22, 0, 0, 0, 42, 0, -4, 0, 6, 0, -24, 0, 2, 0, -12, 0, -30, 0, 4, 0, -8, 0, 24, 0, 0, 0, -24, 0, 22, 0, -26, 0, 36, 0, 12, 0, 4, 0, 12, 0, 42, 0, -36, 0, -6, 0, 0, 0, -12, 0, 36, 0, -6, 0, 16, 0, -40, 0, -10, 0, 40, 0, -4, 0, -54, 0, -38, 0, 0, 0, 30, 0, 2, 0, 52, 0, 18, 0, 18, 0, -16, 0, 48, 0, 7, 0, 12, 0, 9, 0, 22, 0, -28, 0, -12, 0, 50, 0, -4, 0, 18, 0, 4, 0, -24, 0, -6, 0, 6, 0, 38, 0, 0, 0, -4, 0, 2, 0, 2, 0, 26, 0, -60, 0, -18, 0, -14, 0, 24, 0, -18, 0, 4, 0, 0, 0, 24, 0, -12, 0, -24, 0, 24, 0, 36, 0, -40, 0, 10, 0, 46, 0, 6, 0, -12, 0, 0, 0, -4, 0, 0, 0, 16, 0, -4, 0, 24, 0, 2, 0, -14, 0, -42, 0, -12, 0, -24, 0, 0, 0, -22, 0, -44, 0, -18, 0, -36, 0, -8, 0, -18, 0, 4, 0, -12, 0, -6, 0, -12, 0, 0, 0, -36, 0, -15, 0, 6, 0, -26, 0, 22, 0, -48, 0, 24, 0, -8, 0, 4, 0, 18, 0, 0, 0, 2, 0, 18, 0, -18, 0, -24, 0, -60, 0, 4, 0, -16, 0, 8, 0, 26, 0, -8, 0], 'weight': 2, 'weight_parity': 1}
  99. label: 81.2.a.a
    {'Nk2': 324, 'analytic_conductor': 0.6467882563723711, 'analytic_rank': 0, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[3, -1]], 'atkin_lehner_string': '-', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [81, 1, [2], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 2, 'field_disc': 12, 'field_disc_factorization': [[2, 2], [3, 1]], 'field_poly': [-3, 0, 1], 'field_poly_is_cyclotomic': False, 'field_poly_is_real_cyclotomic': True, 'field_poly_root_of_unity': 12, 'fricke_eigenval': -1, 'has_non_self_twist': 1, 'hecke_cutters': [], 'hecke_orbit': 1, 'hecke_orbit_code': 33554513, '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, 3, 2, -1, 2, 0]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '81.2.a.a', 'level': 81, 'level_is_powerful': True, 'level_is_prime': False, 'level_is_prime_power': True, 'level_is_prime_square': False, 'level_is_square': True, 'level_is_squarefree': False, 'level_primes': [3], 'level_radical': 3, 'minimal_twist': '81.2.a.a', 'nf_label': '2.2.12.1', 'prim_orbit_index': 1, 'qexp_display': 'q+\\beta q^{2}+q^{4}-\\beta q^{5}+2q^{7}-\\beta q^{8}+\\cdots', 'related_objects': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/729.1/a', 'EllipticCurve/2.0.3.1/729.1/a'], 'relative_dim': 2, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '81.2.a', 'trace_display': [0, 0, 0, 4], 'trace_hash': 1843164376072571325, 'trace_moments': [{'__RealLiteral__': 0, 'data': '0.025', 'prec': 7}, {'__RealLiteral__': 0, 'data': '1.943', 'prec': 14}, {'__RealLiteral__': 0, 'data': '0.195', 'prec': 10}, {'__RealLiteral__': 0, 'data': '15.274', 'prec': 17}, {'__RealLiteral__': 0, 'data': '1.901', 'prec': 14}, {'__RealLiteral__': 0, 'data': '148.952', 'prec': 20}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.509', 'prec': 10}, 'traces': [2, 0, 0, 2, 0, 0, 4, 0, 0, -6, 0, 0, -2, 0, 0, -10, 0, 0, 4, 0, 0, -12, 0, 0, -4, 0, 0, 4, 0, 0, 16, 0, 0, 18, 0, 0, -14, 0, 0, 6, 0, 0, 4, 0, 0, 12, 0, 0, -6, 0, 0, -2, 0, 0, 12, 0, 0, 6, 0, 0, -14, 0, 0, 2, 0, 0, -20, 0, 0, -12, 0, 0, -14, 0, 0, 4, 0, 0, 4, 0, 0, -24, 0, 0, -18, 0, 0, 12, 0, 0, -4, 0, 0, 24, 0, 0, 4, 0, 0, -4, 0, 0, 16, 0, 0, 0, 0, 0, 22, 0, 0, -20, 0, 0, -12, 0, 0, 48, 0, 0, 2, 0, 0, 16, 0, 0, 4, 0, 0, 6, 0, 0, 8, 0, 0, -18, 0, 0, 16, 0, 0, -36, 0, 0, -6, 0, 0, -14, 0, 0, 40, 0, 0, -24, 0, 0, 34, 0, 0, 18, 0, 0, -32, 0, 0, -48, 0, 0, -24, 0, 0, 4, 0, 0, -8, 0, 0, -18, 0, 0, 4, 0, 0, -12, 0, 0, -36, 0, 0, -12, 0, 0, -2, 0, 0, -6, 0, 0, 40, 0, 0, 24, 0, 0, 24, 0, 0, 10, 0, 0, -20, 0, 0, 0, 0, 0, 32, 0, 0, 12, 0, 0, 4, 0, 0, -6, 0, 0, -2, 0, 0, -6, 0, 0, -24, 0, 0, 36, 0, 0, 58, 0, 0, -14, 0, 0, -4, 0, 0, 42, 0, 0, -24, 0, 0, 38, 0, 0, -28, 0, 0, 12, 0, 0, 0, 0, 0, -20, 0, 0, 4, 0, 0, 6, 0, 0, 4, 0, 0, 12, 0, 0, -56, 0, 0, 12, 0, 0, 20, 0, 0, -14, 0, 0, -48, 0, 0, 30, 0, 0, 8, 0, 0, -20, 0, 0, -32, 0, 0, -48, 0, 0, -50, 0, 0, 4, 0, 0, -12, 0, 0, 24, 0, 0, 4, 0, 0, 24, 0, 0, 4, 0, 0, -60, 0, 0, 52, 0, 0, -18, 0, 0, -40, 0, 0, -66, 0, 0, 4, 0, 0, 36, 0, 0, 36, 0, 0, 72, 0, 0, -30, 0, 0, -4, 0, 0, 40, 0, 0, 42, 0, 0, -20, 0, 0, -24, 0, 0, -32, 0, 0, 60, 0, 0, 24, 0, 0, 4, 0, 0, 36, 0, 0, -18, 0, 0, 58, 0, 0, 20, 0, 0, -16, 0, 0, 12, 0, 0, -38, 0, 0, 16, 0, 0, 48, 0, 0, -24, 0, 0, -50, 0, 0, 0, 0, 0, -28, 0, 0, -12, 0, 0, 22, 0, 0, 22, 0, 0, 40, 0, 0, -18, 0, 0, 18, 0, 0, 4, 0, 0, 48, 0, 0, -12, 0, 0, 58, 0, 0, -12, 0, 0, 16, 0, 0, -90, 0, 0, -40, 0, 0, -48, 0, 0, -8, 0, 0, -96, 0, 0, 14, 0, 0, 2, 0, 0, -32, 0, 0, 18, 0, 0, 18, 0, 0, -80, 0, 0, -20, 0, 0, 36, 0, 0, -24, 0, 0, 4, 0, 0, -28, 0, 0, 30, 0, 0, -48, 0, 0, -6, 0, 0, 76, 0, 0, 24, 0, 0, -22, 0, 0, 8, 0, 0, 0, 0, 0, -54, 0, 0, 22, 0, 0, -54, 0, 0, 40, 0, 0, 24, 0, 0, 8, 0, 0, 16, 0, 0, -4, 0, 0, 42, 0, 0, 6, 0, 0, 36, 0, 0, 16, 0, 0, -48, 0, 0, 22, 0, 0, -6, 0, 0, 0, 0, 0, 66, 0, 0, 32, 0, 0, 70, 0, 0, -36, 0, 0, -12, 0, 0, -50, 0, 0, 40, 0, 0, 52, 0, 0, 42, 0, 0, -68, 0, 0, 24, 0, 0, 40, 0, 0, -24, 0, 0, -22, 0, 0, 34, 0, 0, 40, 0, 0, -30, 0, 0, 6, 0, 0, -42, 0, 0, 16, 0, 0, 36, 0, 0, -96, 0, 0, -32, 0, 0, -12, 0, 0, 48, 0, 0, 34, 0, 0, 48, 0, 0, 12, 0, 0, 60, 0, 0, -50, 0, 0, -24, 0, 0, 8, 0, 0, -96, 0, 0, -6, 0, 0, -20, 0, 0, 4, 0, 0, 12, 0, 0, -72, 0, 0, -8, 0, 0, -28, 0, 0, -48, 0, 0, -50, 0, 0, 18, 0, 0, -12, 0, 0, 36, 0, 0, 32, 0, 0, 4, 0, 0, -68, 0, 0, 42, 0, 0, -92, 0, 0, -36, 0, 0, 40, 0, 0, 0, 0, 0, -30, 0, 0, -36, 0, 0, -20, 0, 0, -6, 0, 0, 4, 0, 0, 12, 0, 0, 44, 0, 0, -60, 0, 0, -2, 0, 0, -2, 0, 0, -32, 0, 0, 96, 0, 0, 72, 0, 0, 30, 0, 0, 52, 0, 0, -12, 0, 0, 14, 0, 0, 40, 0, 0, 72, 0, 0, -42, 0, 0, -24, 0, 0, -24, 0, 0, -32, 0, 0, 84, 0, 0, 8, 0, 0, 24, 0, 0, -56, 0, 0, 96, 0, 0, 4, 0, 0, -2, 0, 0, 60, 0, 0, -24, 0, 0, -52, 0, 0, -20, 0, 0, 4, 0, 0, -36, 0, 0, -68, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 66, 0, 0, 32, 0, 0, 20, 0, 0, 24, 0, 0, 106, 0, 0, -60, 0, 0, 112, 0, 0, -120, 0, 0, 8, 0, 0, 4, 0, 0, -72, 0, 0, 72, 0, 0, 0, 0, 0, 6, 0, 0, -104, 0, 0, 12, 0, 0, 96, 0, 0, -2, 0, 0, 4, 0, 0, -48, 0, 0, 28, 0, 0, -18, 0, 0, -12, 0, 0, -72, 0, 0, -50, 0, 0, -24, 0, 0, -48, 0, 0, -24, 0, 0, 14, 0, 0, -36, 0, 0, -60, 0, 0, -84, 0, 0, 66, 0, 0, 58, 0, 0, -92, 0, 0, -12, 0, 0, 32, 0, 0, 70, 0, 0, 36, 0, 0, -60, 0, 0, 18, 0, 0, -4, 0, 0, -68, 0, 0, -72, 0, 0, -14, 0, 0, -42], 'weight': 2, 'weight_parity': 1}
  100. label: 82.2.a.a
    {'Nk2': 328, 'analytic_conductor': 0.6547732965744991, 'analytic_rank': 1, 'analytic_rank_proved': True, 'atkin_lehner_eigenvals': [[2, 1], [41, 1]], 'atkin_lehner_string': '++', 'char_conductor': 1, 'char_degree': 1, 'char_is_minimal': True, 'char_is_real': True, 'char_orbit_index': 1, 'char_orbit_label': 'a', 'char_order': 1, 'char_parity': 1, 'char_values': [82, 1, [47], [1]], 'cm_discs': [], 'conrey_index': 1, 'dim': 1, '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, 'fricke_eigenval': 1, 'has_non_self_twist': 0, 'hecke_cutters': [[3, [2, 1]]], 'hecke_orbit': 1, 'hecke_orbit_code': 33554514, 'hecke_ring_generator_nbound': 1, 'hecke_ring_index': 1, 'hecke_ring_index_factorization': [], 'hecke_ring_index_proved': True, 'inner_twist_count': 1, 'inner_twists': [[1, 1, 1, 1, 1, 1, 1]], 'is_cm': False, 'is_largest': True, 'is_maximal': True, 'is_polredabs': True, 'is_rm': False, 'is_self_dual': True, 'is_self_twist': False, 'is_twist_minimal': True, 'label': '82.2.a.a', 'level': 82, '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': [2, 41], 'level_radical': 82, 'minimal_twist': '82.2.a.a', 'nf_label': '1.1.1.1', 'prim_orbit_index': 1, 'qexp_display': 'q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-4q^{7}+\\cdots', 'related_objects': ['EllipticCurve/Q/82/a'], 'relative_dim': 1, 'rm_discs': [], 'sato_tate_group': '1.2.3.c1', 'self_twist_discs': [], 'self_twist_type': 0, 'space_label': '82.2.a', 'trace_display': [-1, -2, -2, -4], 'trace_hash': 1061891762443100711, 'trace_moments': [0, {'__RealLiteral__': 0, 'data': '0.991', 'prec': 10}, 0, {'__RealLiteral__': 0, 'data': '1.937', 'prec': 14}, 0, {'__RealLiteral__': 0, 'data': '4.813', 'prec': 14}], 'trace_zratio': {'__RealLiteral__': 0, 'data': '0.024', 'prec': 7}, 'traces': [1, -1, -2, 1, -2, 2, -4, -1, 1, 2, -2, -2, 4, 4, 4, 1, -2, -1, 6, -2, 8, 2, -8, 2, -1, -4, 4, -4, 0, -4, -8, -1, 4, 2, 8, 1, 2, -6, -8, 2, -1, -8, -12, -2, -2, 8, 4, -2, 9, 1, 4, 4, -4, -4, 4, 4, -12, 0, 8, 4, -14, 8, -4, 1, -8, -4, -2, -2, 16, -8, 8, -1, 10, -2, 2, 6, 8, 8, 4, -2, -11, 1, 12, 8, 4, 12, 0, 2, -14, 2, -16, -8, 16, -4, -12, 2, 6, -9, -2, -1, -12, -4, 0, -4, -16, 4, -4, 4, -12, -4, -4, -4, 2, 12, 16, 0, 4, -8, 8, -4, -7, 14, 2, -8, 12, 4, -8, -1, 24, 8, 0, 4, -24, 2, -8, 2, 6, -16, 8, 8, -8, -8, -8, 1, 0, -10, -18, 2, 12, -2, -8, -6, -2, -8, 16, -8, 4, -4, 8, 2, 32, 11, 12, -1, -8, -12, 8, -8, 3, -4, 6, -12, -6, 0, 4, -2, -16, 14, 18, -2, -16, 16, 28, 8, -4, -16, 4, 4, -16, 12, 0, -2, 6, -6, 16, 9, -22, 2, -4, 1, 4, 12, 0, 4, 2, 0, -8, 4, -12, 16, 14, -4, -16, 4, 24, -4, 32, 12, -20, 4, -8, 4, -24, 4, -1, -2, -18, -12, -8, -16, -16, 0, 10, -4, -8, 8, -8, -8, -24, 4, -2, 7, 10, -14, -18, -2, 24, 8, -24, -12, 0, -4, 16, 8, -8, 1, -22, -24, -8, -8, 0, 0, -28, -4, 8, 24, 28, -2, 30, 8, -16, -2, 32, -6, 2, 16, 18, -8, -8, -8, -14, 8, -16, 8, 24, 8, 4, -1, -13, 0, -12, 10, 8, 18, -16, -2, -8, -12, -32, 2, 48, 8, 24, 6, 28, 2, -8, 8, 0, -16, 8, 8, 14, -4, 8, 4, 4, -8, 0, -2, 8, -32, -12, -11, -4, -12, 24, 1, -16, 8, 18, 12, 2, -8, 4, 8, 6, -3, -4, 4, 16, -6, -8, 12, -32, 6, -10, 0, -10, -4, 16, 2, 14, 16, -16, -14, -16, -18, -24, 2, 17, 16, 14, -16, -20, -28, 8, -8, -1, 4, 16, 16, 14, -4, -24, -4, 0, 16, -8, -12, 16, 0, 8, 2, -16, -6, -12, 6, 18, -16, 16, -9, 0, 22, -8, -2, 8, 4, 48, -1, 2, -4, -32, -12, 22, 0, -4, -4, -26, -2, -12, 0, -32, 8, -24, -4, -16, 12, -12, -16, 0, -14, 4, 4, 2, 16, 56, -4, 16, -24, -24, 4, 14, -32, 0, -12, -48, 20, 8, -4, 9, 8, 0, -4, 28, 24, -24, -4, -6, 1, 2, 2, 16, 18, 32, 12, -34, 8, -8, 16, 2, 16, 4, 0, -32, -10, 8, 4, 8, 8, -8, -8, 24, 8, -6, 8, -4, 24, 36, -4, 8, 2, -64, -7, -12, -10, 8, 14, -24, 18, -8, 2, 0, -24, 4, -8, -32, 24, 26, 12, -16, 0, 36, 4, 24, -16, -6, -8, 32, 8, -40, -1, 24, 22, 0, 24, -8, 8, 12, 8, -10, 0, -4, 0, -8, 28, 16, 4, 41, -8, 8, -24, -4, -28, 8, 2, -36, -30, -18, -8, -10, 16, 32, 2, 24, -32, -6, 6, -14, -2, 0, -16, -16, -18, 8, 8, 24, 8, -48, 8, -8, 14, 2, -8, -4, 16, 44, -8, -6, -24, -6, -8, 0, -4, 8, 1, 34, 13, -12, 0, -48, 12, 8, -10, -8, -8, -10, -18, -48, 16, 44, 2, -6, 8, -16, 12, 8, 32, 0, -2, 34, -48, -2, -8, 14, -24, 16, -6, 0, -28, 16, -2, 22, 8, -4, -8, -38, 0, 48, 16, -32, -8, 56, -8, -19, -14, 24, 4, -4, -8, -32, -4, -28, -4, 16, 8, 36, 0, 8, 2, 30, -8, -38, 32, -48, 12, -32, 11, -16, 4, -64, 12, -24, -24, 0, -1, 10, 16, -30, -8, 14, -18, 16, -12, 48, -2, 0, 8, 48, -4, 28, -8, -50, -6, -4, 3, -18, 4, -24, -4, 36, -16, -38, 6, -12, 8, 16, -12, -16, 32, -14, -6, 8, 10, -16, 0, 2, 10, -20, 4, 2, -16, 12, -2, 16, -14, 48, -16, 16, 16, 4, 14, 64, 16, 16, 18, 48, 24, -16, -2, 0, -17, 4, -16, 0, -14, -8, 16, 13, 20, 24, 28, -22, -8, 36, 8, 4, 1, 52, -4, -48, -16, -32, -16, -24, -14, 12, 4, 16, 24, -8, 4, 0, 0, 16, -16, -24, 8, -32, 12, 50, -16, 48, 0, 4, -8, 32, -2, -14, 16, 44, 6, 24, 12, 8, -6, 16, -18, -6, 16, -16, -16, 0, 9, -8, 0, -48, -22, 56, 8, -8, 2, -56, -8, -16, -4, -10, -48, -8, 1, -14, -2, -20, 4, -64, 32, -60, 12, -26, -22, 0, 0, 32, 4, -24, 4, -72, 26, -16, 2, 18, 12, -16, 0, -4, 32, -14, -8, -18, 24, -36, 4, -18, 16, -16, -12, -32, 12, 12, 16, -29, 0, 28, 14, -6, -4, 28, -4, 32, -2, -16, -16, -14, -56, -12, 4, -42, -16, 0, 24, -8, 24, 56, -4, 12, -14, 26, 32, -8, 0, -8, 12, 6, 48, -48, -20, 22, -8, -16, 4, 30, -9, -22, -8, 32, 0, 52, 4, 32, -28, 22, -24, 24, 24, -36, 4, 64, 6, 0, -1, 8, -2, -96, -2, 32, -16, 48, -18, -12, -32, 40, -12, -24, 34, -56, -8, 0, 8, 40, -16, 16, -2, 32, -16, -2, -4, 0, 0, 14, 32, 54, 10, -16, -8, -8, -4, -46, -8, -28, -8, -46, 8, 8, 8, 32, -24, -24, -8, 40, 6, -8, -8, -58, 4, 0, -24, 0, -36, -24, 4, 33, -8, -4, -2, -12, 64, 44, 7, 24, 12, -18, 10, -32, -8, 8, -14, 30, 24, 28, -18, -12, 8, 0, -2, 44, 0, 32, 24, 96, -4, 32, 8, -36, 32, 8, -24, 28, -26, 8, -12], 'weight': 2, 'weight_parity': 1}