# Stored data for newform 1200.3.c.c, downloaded from the LMFDB on 15 April 2021. {"level_primes": [2, 3, 5], "is_polredabs": true, "sato_tate_group": "2.2.1.d2", "rm_discs": [], "conrey_indexes": [449], "cm_discs": [-3], "trace_hash": 1611025293497560488, "level_radical": 30, "hecke_ring_index_proved": true, "self_twist_type": 1, "related_objects": [], "prim_orbit_index": 4, "is_cm": true, "hecke_orbit": 3, "analytic_conductor": 32.69763172323563, "inner_twist_count": 4, "field_disc_factorization": [[-1, 1], [2, 2]], "is_rm": false, "char_order": 2, "level_is_square": false, "weight_parity": -1, "label": "1200.3.c.c", "field_poly_is_real_cyclotomic": false, "is_self_twist": true, "is_twist_minimal": false, "minimal_twist": "12.3.c.a", "field_poly_is_cyclotomic": true, "dim": 2, "trace_zratio": {"__RealLiteral__": 0, "data": "0.761", "prec": 17}, "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -284, 0, 162, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 428, 0, 156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 242, 0, 0, 0, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -630, 0, -468, 0, 0, 0, 0, 0, 0, 0, 0, 0, 628, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 772, 0, -732, 0, 0, 0, 0, 0, 0, 0, 0, 0, 332, 0, 0, 0, 0, 0, 0, 0, 276, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -572, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -484, 0, 0, 0, 0, 0, 0, 0, -828, 0, 0, 0, 0, 0, 0, 0, 0, 0, -578, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 1164, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -724, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1004, 0, -1188, 0, 0, 0, 0, 0, 0, 0, 0, 0, 630, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1388, 0, -876, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -312, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -716, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -188, 0, -810, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -488, 0, -708, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1144, 0, 0, 0, 0, 0, 0, 0, -1572, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1058, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2068, 0, 0, 0, 0, 0, 0, 0, -1332, 0, 0, 0, 0, 0, 0, 0, 0, 0, 968, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1772, 0, 0, 0, 0, 0, 0, 0, 2292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1052, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -428, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1348, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 244, 0, 0, 0, 0, 0, 0, 0, 2028, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2636, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1868, 0, 2556, 0, 0, 0, 0, 0, 0, 0, 0, 0, 776, 0, 0, 0, 0, 0, 0, 0, -1458, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2444, 0, 3432, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2404, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3068, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3028, 0, 0, 0, 0, 0, 0, 0, -792, 0, 0, 0, 0, 0, 0, 0, 0, 0, -916, 0, 732, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1682, 0, 0, 0, 0, 0, 0, 0, 2748, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2836, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5368, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1732, 0, 2148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2340, 0, 0, 0, 0, 0, 0, 0, 852, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2310, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3852, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, -1404, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3652, 0, 2892, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3692, 0, 0, 0, 0, 0, 0, 0, -1128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3988, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2178, 0, 0, 0, 0, 0, 0, 0, 0, 0, -472, 0, 4308, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4188, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1628, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1048, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3848, 0, 1188, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3508, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2172, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4796, 0, 0, 0, 0, 0, 0, 0, 6072, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4324, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4604, 0, 396, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3548, 0, -888, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1108, 0, 0, 0, 0, 0, 0, 0, 5172, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4316, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1528, 0, 0, 0, 0, 0, 0, 0, -5148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1386, 0, -4884, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5428, 0, 0, 0, 0, 0, 0, 0, -3156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3652, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1012, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 436, 0, -5772, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3644, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4140, 0, 5670, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2068, 0, 0, 0, 0, 0, 0, 0, 4212, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1492, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1352, 0, 0, 0, 0, 0, 0, 0, -5892, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4268, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5132, 0, 0, 0, 0, 0, 0, 0, -5652, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3036, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6424, 0, 0, 0, 0, 0, 0, 0, 1704, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4276, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3362, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1396, 0, -972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2288, 0, 5772, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4652, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1628, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6292, 0, -6948, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3748, 0, 0, 0, 0, 0, 0, 0, 6588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4884, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1924, 0, 0, 0, 0, 0, 0, 0, 6756, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2730, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7348, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7484, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6808, 0, 0, 0, 0, 0, 0, 0, -2988, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5940, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1884, 0, 0, 0, 0, 0, 0, 0, 0, 0, 488, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3748, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2484, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1832, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2588, 0], "hecke_ring_index_factorization": [], "nf_label": "2.0.4.1", "field_poly": [1, 0, 1], "has_non_self_twist": 1, "char_values": [1200, 2, [751, 901, 401, 577], [2, 2, 1, 1]], "Nk2": 10800, "field_poly_root_of_unity": 4, "analytic_rank": 0, "char_orbit_label": "c", "weight": 3, "trace_display": [0, 0, 0, 0], "analytic_rank_proved": true, "char_parity": -1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q+3iq^{3}+2iq^{7}-9q^{9}-22iq^{13}+\\cdots", "self_twist_discs": [-3], "char_is_real": true, "field_disc": -4, "level_is_prime_power": false, "relative_dim": 2, "hecke_cutters": [[7, [4, 0, 1]], [11, [0, 1]]], "space_label": "1200.3.c", "level": 1200, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 15, 4, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0]], "char_degree": 1, "char_conductor": 15, "char_orbit_index": 3, "hecke_ring_generator_nbound": 7, "hecke_orbit_code": 9007336744027312, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.828", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21.700", "prec": 20}, {"__RealLiteral__": 0, "data": "0.956", "prec": 17}, {"__RealLiteral__": 0, "data": "287.547", "prec": 24}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 3], [0, 0], [0, 0], [0, 0], [0, 2], [0, 0], [-9, 0], [0, 0], [0, 0], [0, 0], [0, -22], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [26, 0], [0, 0], [-6, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -27], [0, 0], [0, 0], [0, 0], [46, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -26], [0, 0], [66, 0], [0, 0], [0, 0], [0, 0], [0, 22], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [45, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 78], [0, 0], [0, 0], [0, 0], [74, 0], [0, 0], [0, -18], [0, 0], [0, 0], [0, 0], [0, 122], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -46], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-142, 0], [0, 0], [81, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [44, 0], [0, 0], [0, 138], [0, 0], [0, 0], [0, 0], [0, -2], [0, 0], [0, 0], [0, 0]]}