# Stored data for newform 400.4.c.g, downloaded from the LMFDB on 09 October 2024. {"Nk2": 6400, "analytic_conductor": 23.600764002296245, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": 1, "char_values": [400, 2, [351, 101, 177], [2, 2, 1]], "cm_discs": [], "conrey_index": 49, "dim": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[3, [25, 0, 1]], [7, [4, 0, 1]], [11, [39, 1]]], "hecke_orbit": 7, "hecke_orbit_code": 27021735270285712, "hecke_ring_generator_nbound": 7, "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, 5, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "400.4.c.g", "level": 400, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2, 5], "level_radical": 10, "minimal_twist": "200.4.a.c", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q+5iq^{3}-2iq^{7}+2q^{9}-39q^{11}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "400.4.c", "trace_display": [0, 0, 0, 0], "trace_hash": 1375388628773101778, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.894", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.733", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "145.857", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, -78, 0, 0, 0, 0, 0, 0, 0, 302, 0, 20, 0, 0, 0, 0, 0, 0, 0, -384, 0, 36, 0, 0, 0, 0, 0, 0, 0, 840, 0, 458, 0, 0, 0, 0, 0, 0, 0, 678, 0, 610, 0, 0, 0, 0, 0, 0, 0, -672, 0, 1716, 0, 0, 0, 0, 0, 0, 0, 580, 0, 1560, 0, 0, 0, 0, 0, 0, 0, -460, 0, -1342, 0, 0, 0, 0, 0, 0, 0, 2738, 0, -336, 0, 0, 0, 0, 0, 0, 0, -156, 0, -1588, 0, 0, 0, 0, 0, 0, 0, -892, 0, 1380, 0, 0, 0, 0, 0, 0, 0, -244, 0, 380, 0, 0, 0, 0, 0, 0, 0, 1640, 0, -4904, 0, 0, 0, 0, 0, 0, 0, -2754, 0, -2120, 0, 0, 0, 0, 0, 0, 0, -3840, 0, -3708, 0, 0, 0, 0, 0, 0, 0, 5780, 0, -232, 0, 0, 0, 0, 0, 0, 0, -9718, 0, 604, 0, 0, 0, 0, 0, 0, 0, -4490, 0, 6100, 0, 0, 0, 0, 0, 0, 0, 580, 0, 8444, 0, 0, 0, 0, 0, 0, 0, 6744, 0, -2090, 0, 0, 0, 0, 0, 0, 0, -11778, 0, -11202, 0, 0, 0, 0, 0, 0, 0, -4030, 0, -10248, 0, 0, 0, 0, 0, 0, 0, 5688, 0, -780, 0, 0, 0, 0, 0, 0, 0, -8640, 0, 7714, 0, 0, 0, 0, 0, 0, 0, 12930, 0, 574, 0, 0, 0, 0, 0, 0, 0, -552, 0, -768, 0, 0, 0, 0, 0, 0, 0, 7488, 0, 6692, 0, 0, 0, 0, 0, 0, 0, 72, 0, -6020, 0, 0, 0, 0, 0, 0, 0, 2384, 0, -3820, 0, 0, 0, 0, 0, 0, 0, -9744, 0, -656, 0, 0, 0, 0, 0, 0, 0, 13480, 0, 1756, 0, 0, 0, 0, 0, 0, 0, 14976, 0, -7750, 0, 0, 0, 0, 0, 0, 0, 848, 0, 5434, 0, 0, 0, 0, 0, 0, 0, -2310, 0, -1404, 0, 0, 0, 0, 0, 0, 0, -8060, 0, 24360, 0, 0, 0, 0, 0, 0, 0, 14788, 0, 31884, 0, 0, 0, 0, 0, 0, 0, 916, 0, -2312, 0, 0, 0, 0, 0, 0, 0, 2570, 0, 23860, 0, 0, 0, 0, 0, 0, 0, -3948, 0, -7076, 0, 0, 0, 0, 0, 0, 0, 3020, 0, -11334, 0, 0, 0, 0, 0, 0, 0, 9670, 0, 11250, 0, 0, 0, 0, 0, 0, 0, 9238, 0, 14952, 0, 0, 0, 0, 0, 0, 0, -32760, 0, -15620, 0, 0, 0, 0, 0, 0, 0, 6416, 0, 1356, 0, 0, 0, 0, 0, 0, 0, -7234, 0, -17862, 0, 0, 0, 0, 0, 0, 0, 17690, 0, -14216, 0, 0, 0, 0, 0, 0, 0, 836, 0, 6340, 0, 0, 0, 0, 0, 0, 0, -21852, 0, -23184, 0, 0, 0, 0, 0, 0, 0, -1030, 0, 2648, 0, 0, 0, 0, 0, 0, 0, 18136, 0, 440, 0, 0, 0, 0, 0, 0, 0, -5364, 0, 1612, 0, 0, 0, 0, 0, 0, 0, -11280, 0, -6070, 0, 0, 0, 0, 0, 0, 0, 17606, 0, -1344, 0, 0, 0, 0, 0, 0, 0, -26442, 0, -36224, 0, 0, 0, 0, 0, 0, 0, 3432, 0, -57984, 0, 0, 0, 0, 0, 0, 0, -27552, 0, -23790, 0, 0, 0, 0, 0, 0, 0, 19246, 0, -1208, 0, 0, 0, 0, 0, 0, 0, -33570, 0, -5172, 0, 0, 0, 0, 0, 0, 0, 5436, 0, 1660, 0, 0, 0, 0, 0, 0, 0, -34172, 0, 18070, 0, 0, 0, 0, 0, 0, 0, -3840, 0, 35616, 0, 0, 0, 0, 0, 0, 0, -19112, 0, 16820, 0, 0, 0, 0, 0, 0, 0, -16836, 0, 38788, 0, 0, 0, 0, 0, 0, 0, 3120, 0, 24276, 0, 0, 0, 0, 0, 0, 0, 26208, 0, 360, 0, 0, 0, 0, 0, 0, 0, 21034, 0, 2816, 0, 0, 0, 0, 0, 0, 0, -8280, 0, -66924, 0, 0, 0, 0, 0, 0, 0, 1528, 0, -23880, 0, 0, 0, 0, 0, 0, 0, -97104, 0, 63562, 0, 0, 0, 0, 0, 0, 0, 59620, 0, -56008, 0, 0, 0, 0, 0, 0, 0, 70456, 0, -920, 0, 0, 0, 0, 0, 0, 0, -17316, 0, -5392, 0, 0, 0, 0, 0, 0, 0, -41834, 0, -20008, 0, 0, 0, 0, 0, 0, 0, 58328, 0, 126840, 0, 0, 0, 0, 0, 0, 0, 3100, 0, -1152, 0, 0, 0, 0, 0, 0, 0, -22620, 0, 41578, 0, 0, 0, 0, 0, 0, 0, -52842, 0, -21300, 0, 0, 0, 0, 0, 0, 0, 69158, 0, -60840, 0, 0, 0, 0, 0, 0, 0, 30660, 0, 924, 0, 0, 0, 0, 0, 0, 0, 25864, 0, 5476, 0, 0, 0, 0, 0, 0, 0, 73884, 0, 23496, 0, 0, 0, 0, 0, 0, 0, -672, 0, -2396, 0, 0, 0, 0, 0, 0, 0, -35464, 0, -70400, 0, 0, 0, 0, 0, 0, 0, 16960, 0, 24950, 0, 0, 0, 0, 0, 0, 0, 60010, 0, -16008, 0, 0, 0, 0, 0, 0, 0, 5598, 0, 4580, 0, 0, 0, 0, 0, 0, 0, 17940, 0, 35112, 0, 0, 0, 0, 0, 0, 0, 48020, 0, 8860, 0, 0, 0, 0, 0, 0, 0, -9544, 0, 52338, 0, 0, 0, 0, 0, 0, 0, -6912, 0, -70516, 0, 0, 0, 0, 0, 0, 0, -3176, 0, 59800, 0, 0, 0, 0, 0, 0, 0, -69676, 0, 61490, 0, 0, 0, 0, 0, 0, 0, -52668, 0, 102378, 0, 0, 0, 0, 0, 0, 0, -40420, 0, 50552, 0, 0, 0, 0, 0, 0, 0, 67704, 0, -38440, 0, 0, 0, 0, 0, 0, 0, -4500, 0, -58934, 0, 0, 0, 0, 0, 0, 0, 92110, 0, 4210, 0, 0, 0, 0, 0, 0, 0, -106782, 0, -1784, 0, 0, 0, 0, 0, 0, 0, -19024, 0, 4460, 0, 0, 0, 0, 0, 0, 0, 40020, 0], "weight": 4, "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], [1, 0], [0, 0], [0, 5], [0, 0], [0, 0], [0, 0], [0, -2], [0, 0], [2, 0], [0, 0], [-39, 0], [0, 0], [0, -84], [0, 0], [0, 0], [0, 0], [0, -61], [0, 0], [151, 0], [0, 0], [10, 0], [0, 0], [0, -58], [0, 0], [0, 0], [0, 0], [0, 145], [0, 0], [-192, 0], [0, 0], [18, 0], [0, 0], [0, -195], [0, 0], [0, 0], [0, 0], [0, -138], [0, 0], [420, 0], [0, 0], [229, 0], [0, 0], [0, -164], [0, 0], [0, 0], [0, 0], [0, 212], [0, 0], [339, 0], [0, 0], [305, 0], [0, 0], [0, -578], [0, 0], [0, 0], [0, 0], [0, 755], [0, 0], [-336, 0], [0, 0], [858, 0], [0, 0], [0, -4], [0, 0], [0, 0], [0, 0], [0, 209], [0, 0], [290, 0], [0, 0], [780, 0], [0, 0], [0, 403], [0, 0], [0, 0], [0, 0], [0, 78], [0, 0], [-230, 0], [0, 0], [-671, 0], [0, 0], [0, -1293], [0, 0], [0, 0], [0, 0], [0, -960], [0, 0], [1369, 0], [0, 0], [-168, 0], [0, 0], [0, 90], [0, 0], [0, 0], [0, 0], [0, 382], [0, 0], [-78, 0], [0, 0]]}