# Stored data for newform 400.9.h.b, downloaded from the LMFDB on 17 May 2025. {"Nk2": 32400, "analytic_conductor": 162.9514440244509, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 20, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 8, "char_orbit_label": "h", "char_order": 2, "char_parity": -1, "char_values": [400, 2, [351, 101, 177], [1, 2, 1]], "cm_discs": [], "conrey_index": 399, "dim": 4, "field_disc": 19600, "field_disc_factorization": [[2, 4], [5, 2], [7, 2]], "field_poly": [81, 0, -17, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [-20160, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504080814702992, "hecke_ring_generator_nbound": 13, "hecke_ring_index": 115200, "hecke_ring_index_factorization": [[2, 9], [3, 2], [5, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0], [1, 1, 20, 4, -1, 2, 0], [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": false, "is_self_twist": false, "is_twist_minimal": false, "label": "400.9.h.b", "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": "16.9.c.a", "nf_label": "4.0.19600.2", "prim_orbit_index": 4, "qexp_display": "q-\\beta _{2}q^{3}-18\\beta _{2}q^{7}+13599q^{9}-3^{3}\\beta _{3}q^{11}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "8.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "400.9.h", "trace_display": [0, 0, 0, 0], "trace_hash": 740602641318653100, "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "3.527", "prec": 17}, {"__RealLiteral__": 0, "data": "1.425", "prec": 17}, {"__RealLiteral__": 0, "data": "108.601", "prec": 24}, {"__RealLiteral__": 0, "data": "89.804", "prec": 20}, {"__RealLiteral__": 0, "data": "4289.233", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.760", "prec": 17}, "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 54396, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1451520, 0, 0, 0, 0, 0, 0, 0, -219912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -302328, 0, 0, 0, 0, 0, 0, 0, 3068156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -95306488, 0, 0, 0, 0, 0, 0, 0, 100154880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 210652164, 0, 0, 0, 0, 0, 0, 0, -347183112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 263964168, 0, 0, 0, 0, 0, 0, 0, 624474872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -612228476, 0, 0, 0, 0, 0, 0, 0, 283772160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1628605440, 0, 0, 0, 0, 0, 0, 0, 1816394232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1802787840, 0, 0, 0, 0, 0, 0, 0, 191546484, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2508377608, 0, 0, 0, 0, 0, 0, 0, 10215797760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4256582400, 0, 0, 0, 0, 0, 0, 0, 8328096000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5583010800, 0, 0, 0, 0, 0, 0, 0, -6777872392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6485913848, 0, 0, 0, 0, 0, 0, 0, 41714507520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2990583288, 0, 0, 0, 0, 0, 0, 0, -1385800968, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41702308872, 0, 0, 0, 0, 0, 0, 0, 17754482164, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5107898880, 0, 0, 0, 0, 0, 0, 0, 93644812800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72314000640, 0, 0, 0, 0, 0, 0, 0, -29314897920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -90139392000, 0, 0, 0, 0, 0, 0, 0, 2557522168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20741708164, 0, 0, 0, 0, 0, 0, 0, -4111358472, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 208856309760, 0, 0, 0, 0, 0, 0, 0, 109382935032, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -85106935032, 0, 0, 0, 0, 0, 0, 0, -45713373448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 91506351112, 0, 0, 0, 0, 0, 0, 0, -301662144000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41723853444, 0, 0, 0, 0, 0, 0, 0, -100794707208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -155238398712, 0, 0, 0, 0, 0, 0, 0, -76618483200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -87977033200, 0, 0, 0, 0, 0, 0, 0, 138615079680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -381289628160, 0, 0, 0, 0, 0, 0, 0, -42370971912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 499830849288, 0, 0, 0, 0, 0, 0, 0, -188851580164, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 578634993928, 0, 0, 0, 0, 0, 0, 0, -1296072930312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -548347968000, 0, 0, 0, 0, 0, 0, 0, -51128915208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 750861135360, 0, 0, 0, 0, 0, 0, 0, 510789888000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -771769337848, 0, 0, 0, 0, 0, 0, 0, -79801666560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 704890045440, 0, 0, 0, 0, 0, 0, 0, -159920720400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -455613575928, 0, 0, 0, 0, 0, 0, 0, -1673947296000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1078195109368, 0, 0, 0, 0, 0, 0, 0, 1293902346240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 845457419520, 0, 0, 0, 0, 0, 0, 0, 1237662716400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1094410754808, 0, 0, 0, 0, 0, 0, 0, 706646227448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1685606630400, 0, 0, 0, 0, 0, 0, 0, -858999505284, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1709418816000, 0, 0, 0, 0, 0, 0, 0, -1301652011520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1709674545912, 0, 0, 0, 0, 0, 0, 0, 2039877532408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 773043264000, 0, 0, 0, 0, 0, 0, 0, 4195657751040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4721343140088, 0, 0, 0, 0, 0, 0, 0, 2337263488248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1809879798792, 0, 0, 0, 0, 0, 0, 0, -1342127694088, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1988895329908, 0, 0, 0, 0, 0, 0, 0, 727207891200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -109708784640, 0, 0, 0, 0, 0, 0, 0, -3740784768000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4163384779272, 0, 0, 0, 0, 0, 0, 0, 3759413575680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2249767990800, 0, 0, 0, 0, 0, 0, 0, 3589648720632, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3096089982720, 0, 0, 0, 0, 0, 0, 0, -1179890080008, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 507565876488, 0, 0, 0, 0, 0, 0, 0, 722301052400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2116985226236, 0, 0, 0, 0, 0, 0, 0, 3107305152000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8492233784328, 0, 0, 0, 0, 0, 0, 0, 352445022720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight": 9, "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], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -18, 0], [0, 0, 0, 0], [13599, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -27], [0, 0, 0, 0], [0, 2771, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 5037, 0, 0], [0, 0, 0, 0], [0, 0, 0, 153], [0, 0, 0, 0], [362880, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1242, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -7038, 0], [0, 0, 0, 0], [-54978, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1656], [0, 0, 0, 0], [0, 272160, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 79373, 0, 0], [0, 0, 0, 0], [0, 0, 0, -5542], [0, 0, 0, 0], [-75582, 0, 0, 0], [0, 0, 0, 0], [0, 0, -3519, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 20196, 0], [0, 0, 0, 0], [767039, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -10074], [0, 0, 0, 0], [0, -1116621, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1542240, 0, 0], [0, 0, 0, 0], [0, 0, 0, -30753], [0, 0, 0, 0], [-23826622, 0, 0, 0], [0, 0, 0, 0], [0, 0, -244782, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 52785, 0], [0, 0, 0, 0], [25038720, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 14202], [0, 0, 0, 0], [0, -651661, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4898880, 0, 0], [0, 0, 0, 0], [0, 0, 0, -68724], [0, 0, 0, 0], [52663041, 0, 0, 0], [0, 0, 0, 0], [0, 0, -517293, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 54978, 0], [0, 0, 0, 0], [-86795778, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -99756], [0, 0, 0, 0], [0, 16692480, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4667027, 0, 0], [0, 0, 0, 0], [0, 0, 0, -367173], [0, 0, 0, 0]]}