# Stored data for newform 500.3.b.a, downloaded from the LMFDB on 10 June 2024.
{"Nk2": 4500, "analytic_conductor": 13.624013218014845, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 4, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 2, "char_orbit_label": "b", "char_order": 2, "char_parity": -1, "char_values": [500, 2, [251, 377], [1, 2]], "cm_discs": [-20], "conrey_index": 251, "dim": 8, "field_disc": 4000000, "field_disc_factorization": [[2, 8], [5, 6]], "field_poly": [1, 0, -1, 0, 1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 20, "has_non_self_twist": 1, "hecke_cutters": [[3, [3481, 0, 10034, 0, 1651, 0, 74, 0, 1]], [13, [0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 68769808884, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 160000, "hecke_ring_index_factorization": [[2, 8], [5, 4]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 20, 4, -1, 2, -20], [1, 1, 5, 2, 1, 2, 0], [1, 1, 4, 2, -1, 2, 0]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": true, "is_twist_minimal": true, "label": "500.3.b.a", "level": 500, "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, 5], "level_radical": 10, "minimal_twist": "500.3.b.a", "nf_label": "8.0.4000000.1", "prim_orbit_index": 2, "qexp_display": "q+\\zeta_{20}q^{2}+(-\\zeta_{20}-\\zeta_{20}^{3})q^{3}-4q^{4}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "2.2.1.d2", "self_twist_discs": [-20], "self_twist_type": 1, "space_label": "500.3.b", "trace_display": [0, 0, 0, 0], "trace_hash": 1183275954880103382, "trace_moments": [{"__RealLiteral__": 0, "data": "0.058", "prec": 17}, {"__RealLiteral__": 0, "data": "6.738", "prec": 17}, {"__RealLiteral__": 0, "data": "8.108", "prec": 17}, {"__RealLiteral__": 0, "data": "984.755", "prec": 24}, {"__RealLiteral__": 0, "data": "2316.845", "prec": 27}, {"__RealLiteral__": 0, "data": "202299.514", "prec": 34}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.760", "prec": 17}, "traces": [0, 8, 0, 0, -32, 0, 16, 0, 0, -76, 0, 0, 0, 0, 16, 0, 128, 0, 0, 0, 0, 32, 0, 0, -64, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 304, 0, 0, 0, 0, -124, 0, 0, 0, 0, 176, 0, 0, -556, 0, 0, 0, 0, 32, 0, -64, 0, 0, 0, 0, 116, 0, 0, -512, 0, 0, 0, 0, 352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000, 0, 0, -128, 0, -304, 0, 0, -284, 0, 0, 0, 0, 16, 0, 256, 0, 0, 0, 0, -244, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 968, 0, 0, 0, 0, -2592, 0, 0, 1812, 0, 0, 0, 0, 1856, 0, 0, 0, 0, 0, 0, -2148, 0, 0, -1216, 0, 0, 0, 0, 556, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1428, 0, 0, 496, 0, -304, 0, 0, -1352, 0, 0, 0, 0, 1872, 0, 0, 0, 0, 0, 0, 716, 0, 0, -704, 0, 0, 0, 0, 1284, 0, 0, 0, 0, 0, 0, 2224, 0, 0, 0, 0, -928, 0, 0, 0, 0, -704, 0, 0, 0, 0, 0, 0, 0, 496, 0, -128, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, -524, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -604, 0, 0, -464, 0, 912, 0, 0, -608, 0, 0, 0, 0, -944, 0, 2048, 0, 0, 0, 0, 308, 0, 0, 0, 0, 0, 0, 0, -304, 0, 0, 0, 0, 0, 0, -1408, 0, 0, 0, 0, 836, 0, 0, 0, 0, 0, 0, 0, -2312, 0, 0, 0, 0, -352, 0, 0, 0, 0, 0, 0, -608, 0, 0, 0, 0, 0, 0, 0, 352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2412, 0, 0, -4000, 0, 656, 0, 0, 32, 0, 0, 0, 0, 976, 0, 512, 0, 0, 0, 0, 0, 0, 0, 1216, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 1136, 0, 0, 0, 0, 2888, 0, 0, 0, 0, -928, 0, 0, 868, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 732, 0, 0, -1024, 0, 0, 0, 0, -404, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 956, 0, 0, 976, 0, 352, 0, 0, -1604, 0, 0, 0, 0, -4512, 0, 0, 0, 0, 0, 0, 1556, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -304, 0, 0, 0, 0, 4872, 0, 0, 0, 0, -1744, 0, 0, -3184, 0, 0, 0, 0, -1424, 0, 0, 0, 0, 0, 0, -1684, 0, 0, -704, 0, 0, 0, 0, -928, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3872, 0, 3488, 0, 0, 1312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8028, 0, 0, 10368, 0, 0, 0, 0, 7856, 0, 0, 0, 0, 0, 0, -7248, 0, 0, 0, 0, -1444, 0, 0, 0, 0, 1136, 0, 0, -2476, 0, 0, 0, 0, 2272, 0, -7424, 0, 0, 0, 0, -724, 0, 0, 0, 0, 0, 0, 0, 8208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8592, 0, 5056, 0, 0, 316, 0, 0, 0, 0, 992, 0, 4864, 0, 0, 0, 0, -8988, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2224, 0, 0, 0, 0, 836, 0, 0, 0, 0, 1952, 0, 0, -6476, 0, 0, 0, 0, -2384, 0, 0, 0, 0, 0, 0, -6876, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2276, 0, 0, 5712, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8688, 0, -1984, 0, 0, 0, 0, 596, 0, 0, 1216, 0, 0, 0, 0, 3132, 0, 0, 0, 0, 0, 0, 5408, 0, 0, 0, 0, -2848, 0, 0, 0, 0, 1312, 0, 0, 0, 0, 0, 0, 0, -464, 0, -7488, 0, 0, 0, 0, 7216, 0, 0, 0, 0, 0, 0, 0, 1396, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 352, 0, 0, -2864, 0, 1936, 0, 0, -8044, 0, 0, 0, 0, 2896, 0, 2816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 992, 0, 0, 0, 0, 0, 0, -5136, 0, 0, 0, 0, -484, 0, 0, 0, 0, 176, 0, 0, -2684, 0, 0, 0, 0, 2128, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8896, 0, 0, 0, 0, 6492, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13008, 0, 0, 3712, 0, 0, 0, 0, 2596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1324, 0, 0, 2816, 0, 0, 0, 0, 2956, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9124, 0, 0, 0, 0, -112, 0, 0, -2528, 0, 0, 0, 0, -13008, 0, -1984, 0, 0, 0, 0, -796, 0, 0, 512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3236, 0, 0, 0, 0, -3184, 0, 0, -1888, 0, 0, 0, 0, -4448, 0, -1024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11472, 0, 0, 0, 0, 0, 0, 2096, 0, 0, 0, 0, -4768, 0, 0, 0, 0, 3056, 0, 0, -1124, 0, 0, 0, 0, 496, 0, 0, 0, 0, 0, 0, -944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7688, 0, 0, 2416, 0, 11504, 0, 0, 0, 0, 0, 0, 0, 1936, 0, 1856, 0, 0, 0, 0, -532, 0, 0, -3648, 0, 0, 0, 0, -6688, 0, 0, 0, 0, 0, 0, 2432, 0, 0, 0, 0], "weight": 3, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, 0, 0, 0], [-4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, -1, 1, 0], [0, 1, 0, 1, -2, 0, 0, -1], [0, -4, 0, 0, 0, 0, 0, 0], [-10, 0, 2, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -3, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [16, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -6, 0, 2, -5, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 2, 0, 0, 6, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 5, -4, 0, 0, 1], [-4, 0, 0, 0, 0, 4, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 12, 2, 0, 0, 5], [0, -4, 0, -4, 8, 0, 0, 4], [-8, 0, 0, 0, 0, 1, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 16, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [40, 0, -8, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-16, 0, 0, 0, 0, 5, 6, 0], [0, -5, 0, -20, -2, 0, 0, -6], [0, 17, 0, 13, -2, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [27, 0, -3, 0, 0, 10, 0, 0], [0, -5, 0, -13, -4, 0, 0, 4], [0, -16, 0, -16, 0, 0, 0, 0], [-69, 0, 0, 0, 0, 7, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [16, 0, 7, 0, 0, 15, -9, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-12, 0, 12, 0, 0, -8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 10, 7, 0, 0, -7], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [15, 0, 12, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 74, 0, -4, 10, 0, 0, 17], [-64, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -58, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [57, 0, -8, 0, 0, 12, -14, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 24, 0, -8, 20, 0, 0, 12], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [124, 0, -18, 0, 0, -6, -4, 0], [0, -20, 0, 2, 11, 0, 0, -11], [0, 17, 0, -1, -16, 0, 0, -17], [-36, 0, -8, 0, 0, -24, 16, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-25, 0, 0, 0, 0, 17, -9, 0], [0, -41, 0, 19, -16, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-45, 0, 12, 0, 0, -19, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, -20, 16, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [-11, 0, 0, 0, 0, -5, 21, 0], [0, 0, 0, 0, 0, 0, 0, 0], [16, 0, 0, 0, 0, -16, 16, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -77, 0, -2, 13, 0, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}