# Stored data for newform 256.8.a.f, downloaded from the LMFDB on 12 June 2024.
{"Nk2": 16384, "analytic_conductor": 79.97056652393518, "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": [256, 1, [255, 5], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 184, "field_disc_factorization": [[2, 3], [23, 1]], "field_poly": [-46, 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": 1, "hecke_cutters": [[3, [-2944, 0, 1]], [5, [180, 1]], [7, [-47104, 0, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998271070464, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 8, "hecke_ring_index_factorization": [[2, 3]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 0]], "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": "256.8.a.f", "level": 256, "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": "128.8.b.e", "nf_label": "2.2.184.1", "prim_orbit_index": 1, "qexp_display": "q+\\beta q^{3}-180q^{5}+4\\beta q^{7}+757q^{9}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "256.8.a", "trace_display": [0, 0, -360, 0], "trace_hash": 848120203139695527, "trace_moments": [{"__RealLiteral__": 0, "data": "0.029", "prec": 17}, {"__RealLiteral__": 0, "data": "1.974", "prec": 17}, {"__RealLiteral__": 0, "data": "0.217", "prec": 17}, {"__RealLiteral__": 0, "data": "15.845", "prec": 20}, {"__RealLiteral__": 0, "data": "1.356", "prec": 17}, {"__RealLiteral__": 0, "data": "161.721", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.505", "prec": 17}, "traces": [0, 2, 0, 0, 0, -360, 0, 0, 0, 1514, 0, 0, 0, 7640, 0, 0, 0, -31684, 0, 0, 0, 23552, 0, 0, 0, -91450, 0, 0, 0, -195496, 0, 0, 0, -288512, 0, 0, 0, 477496, 0, 0, 0, 911244, 0, 0, 0, -272520, 0, 0, 0, -1552878, 0, 0, 0, 2568728, 0, 0, 0, 3891968, 0, 0, 0, -3205128, 0, 0, 0, -1375200, 0, 0, 0, 11281408, 0, 0, 0, 5485524, 0, 0, 0, -1154048, 0, 0, 0, -11730958, 0, 0, 0, 5703120, 0, 0, 0, 692916, 0, 0, 0, 13377536, 0, 0, 0, -13682596, 0, 0, 0, 36388856, 0, 0, 0, -4239360, 0, 0, 0, 41708600, 0, 0, 0, 37253924, 0, 0, 0, 5783480, 0, 0, 0, -24837254, 0, 0, 0, 44586000, 0, 0, 0, 43588864, 0, 0, 0, 15567872, 0, 0, 0, -20640948, 0, 0, 0, 146728960, 0, 0, 0, 35189280, 0, 0, 0, 4874616, 0, 0, 0, -23984788, 0, 0, 0, 151020280, 0, 0, 0, 45125632, 0, 0, 0, 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