# Stored data for newform 400.5.p.c, downloaded from the LMFDB on 29 April 2026.
{"Nk2": 10000, "analytic_conductor": 41.34798523353773, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 16, "char_orbit_label": "p", "char_order": 4, "char_parity": -1, "char_values": [400, 4, [351, 101, 177], [4, 4, 3]], "cm_discs": [], "conrey_index": 193, "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, [162, -18, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9008230130778512, "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, 3, -1, 4, 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": "400.5.p.c", "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": "10.5.c.a", "nf_label": "2.0.4.1", "prim_orbit_index": 3, "qexp_display": "q+(-9 i+9)q^{3}+(29 i+29)q^{7}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "4.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "400.5.p", "trace_display": [0, 18, 0, 58], "trace_hash": 1817357992333909535, "trace_moments": [{"__RealLiteral__": 0, "data": "0.033", "prec": 17}, {"__RealLiteral__": 0, "data": "1.955", "prec": 17}, {"__RealLiteral__": 0, "data": "0.142", "prec": 17}, {"__RealLiteral__": 0, "data": "11.509", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "93.935", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.248", "prec": 17}, "traces": [0, 2, 0, 18, 0, 0, 0, 58, 0, 0, 0, 236, 0, -138, 0, 0, 0, 542, 0, 0, 0, 1044, 0, 538, 0, 0, 0, 0, 0, 0, 0, -404, 0, 2124, 0, 0, 0, 1302, 0, 0, 0, 3364, 0, 2178, 0, 0, 0, 2538, 0, 0, 0, 9756, 0, 1222, 0, 0, 0, -5040, 0, 0, 0, -11196, 0, 4698, 0, 0, 0, -1502, 0, 0, 0, -12884, 0, 5902, 0, 0, 0, 6844, 0, 0, 0, 13122, 0, -12462, 0, 0, 0, 12240, 0, 0, 0, -8004, 0, -3636, 0, 0, 0, 14622, 0, 0, 0, -1756, 0, 20858, 0, 0, 0, -9422, 0, 0, 0, 23436, 0, 4222, 0, 0, 0, 11178, 0, 0, 0, -1434, 0, 30276, 0, 0, 0, 11818, 0, 0, 0, 12716, 0, 16240, 0, 0, 0, -40818, 0, 0, 0, 45684, 0, -16284, 0, 0, 0, -12942, 0, 0, 0, 37996, 0, 43902, 0, 0, 0, 32742, 0, 0, 0, 31204, 0, 40018, 0, 0, 0, 3098, 0, 0, 0, -45360, 0, -5578, 0, 0, 0, -20880, 0, 0, 0, -88796, 0, -100764, 0, 0, 0, 63956, 0, 0, 0, 29356, 0, -85698, 0, 0, 0, 21942, 0, 0, 0, -27036, 0, -39440, 0, 0, 0, -43578, 0, 0, 0, -145684, 0, -115956, 0, 0, 0, -11716, 0, 0, 0, -74796, 0, -61782, 0, 0, 0, -109822, 0, 0, 0, 123192, 0, 4782, 0, 0, 0, -190080, 0, 0, 0, -56476, 0, 118098, 0, 0, 0, 38640, 0, 0, 0, -242004, 0, 63484, 0, 0, 0, 144862, 0, 0, 0, 110160, 0, -29542, 0, 0, 0, -260640, 0, 0, 0, -136404, 0, -72036, 0, 0, 0, -37098, 0, 0, 0, 4644, 0, -183422, 0, 0, 0, 97556, 0, 0, 0, 263196, 0, 9702, 0, 0, 0, 0, 0, 0, 0, 126324, 0, -15804, 0, 0, 0, 85698, 0, 0, 0, 144556, 0, -36498, 0, 0, 0, -50298, 0, 0, 0, -169596, 0, 151760, 0, 0, 0, 396720, 0, 0, 0, 108076, 0, 105462, 0, 0, 0, -17058, 0, 0, 0, -47672, 0, 180960, 0, 0, 0, -113102, 0, 0, 0, 0, 0, 89022, 0, 0, 0, 282924, 0, 0, 0, 103842, 0, -12906, 0, 0, 0, -29942, 0, 0, 0, 70876, 0, 27622, 0, 0, 0, -93840, 0, 0, 0, 212724, 0, -172182, 0, 0, 0, -176418, 0, 0, 0, 291596, 0, 114444, 0, 0, 0, -58298, 0, 0, 0, -91836, 0, 27876, 0, 0, 0, 153636, 0, 0, 0, -734724, 0, 67280, 0, 0, 0, 169200, 0, 0, 0, 442564, 0, 205578, 0, 0, 0, -324684, 0, 0, 0, -425044, 0, -290818, 0, 0, 0, -150640, 0, 0, 0, -116478, 0, 481218, 0, 0, 0, 248400, 0, 0, 0, 396952, 0, 341964, 0, 0, 0, 376302, 0, 0, 0, -652316, 0, -437462, 0, 0, 0, 118498, 0, 0, 0, 589356, 0, 257004, 0, 0, 0, -98982, 0, 0, 0, -179676, 0, 280836, 0, 0, 0, -247302, 0, 0, 0, -396884, 0, -368560, 0, 0, 0, -373636, 0, 0, 0, 55764, 0, 219738, 0, 0, 0, 342702, 0, 0, 0, 342316, 0, 0, 0, 0, 0, 299484, 0, 0, 0, 594564, 0, -50142, 0, 0, 0, -109484, 0, 0, 0, -187920, 0, -232116, 0, 0, 0, 46800, 0, 0, 0, -284956, 0, -799164, 0, 0, 0, 582018, 0, 0, 0, 380800, 0, 612480, 0, 0, 0, 166182, 0, 0, 0, 1151208, 0, 86898, 0, 0, 0, 380538, 0, 0, 0, -114964, 0, 264204, 0, 0, 0, -391778, 0, 0, 0, -722796, 0, 144196, 0, 0, 0, -809262, 0, 0, 0, 394956, 0, 421982, 0, 0, 0, 686880, 0, 0, 0, 734884, 0, -121662, 0, 0, 0, 292938, 0, 0, 0, -350244, 0, -321978, 0, 0, 0, -640818, 0, 0, 0, 0, 0, 839840, 0, 0, 0, -594720, 0, 0, 0, 781996, 0, -1311156, 0, 0, 0, 99222, 0, 0, 0, -1170076, 0, -63822, 0, 0, 0, -561862, 0, 0, 0, -210888, 0, -1047978, 0, 0, 0, -478062, 0, 0, 0, -10556, 0, -673164, 0, 0, 0, 365840, 0, 0, 0, -1321128, 0, 664222, 0, 0, 0, -1156618, 0, 0, 0, -1976796, 0, -698622, 0, 0, 0, -905040, 0, 0, 0, -565524, 0, 554364, 0, 0, 0, 911644, 0, 0, 0, 540484, 0, 364560, 0, 0, 0, -50924, 0, 0, 0, -1710720, 0, -108676, 0, 0, 0, 319680, 0, 0, 0, 1209764, 0, -508284, 0, 0, 0, -835302, 0, 0, 0, 1180476, 0, -789098, 0, 0, 0, -177236, 0, 0, 0, 695520, 0, -932902, 0, 0, 0, 1009422, 0, 0, 0, -2021844, 0, -2178036, 0, 0, 0, -626538, 0, 0, 0, 284164, 0, -1278320, 0, 0, 0, 160080, 0, 0, 0, 2607516, 0, 1564422, 0, 0, 0, 679644, 0, 0, 0, -1520312, 0, 0, 0, 0, 0, 402818, 0, 0, 0, 244876, 0, 772524, 0, 0, 0, 72582, 0, 0, 0, -2345760, 0, 696436, 0, 0, 0, 1614960, 0, 0, 0, 206636, 0, -1227636, 0, 0, 0, -609840, 0, 0, 0, -314876, 0, 1582618, 0, 0, 0, -1779342, 0, 0, 0, -667764, 0, 389698, 0, 0, 0, 0, 0, 0, 0, 489762, 0, 41796, 0, 0, 0, -41586, 0, 0, 0, 700476, 0, 1396582, 0, 0, 0, -288978, 0, 0, 0, 1756008, 0, 876298, 0, 0, 0, 1140498, 0, 0, 0, 207276, 0, 1184382, 0, 0, 0, -562938, 0, 0, 0, 1753444, 0, -654862, 0, 0, 0, -954342, 0, 0, 0, 1548396, 0, 710640, 0, 0, 0, 668196, 0, 0, 0, 662324, 0, 1136916, 0, 0, 0, 2224178, 0, 0, 0, 1767916, 0, -1470516, 0, 0, 0, 368764, 0, 0, 0, 1542564, 0, 888996, 0, 0, 0, -1689498, 0, 0, 0, -402640, 0, 1301004, 0, 0, 0, 2140942, 0, 0, 0, 1117284, 0, 904916, 0, 0, 0, -383422, 0, 0, 0, -905364, 0, 1260462, 0, 0, 0, 1444320, 0, 0, 0, -1765434, 0, -763182, 0, 0, 0, -690982, 0, 0, 0, -2166164, 0, -545200, 0, 0, 0, 293502, 0, 0, 0, 3570480, 0, 933818, 0, 0, 0, 1324836, 0, 0, 0, 1802476, 0, 972684, 0, 0, 0, -304298, 0, 0, 0], "weight": 5, "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], [9, -9], [0, 0], [0, 0], [0, 0], [29, 29], [0, 0], [0, -81], [0, 0], [118, 0], [0, 0], [-69, 69], [0, 0], [0, 0], [0, 0], [271, 271], [0, 0], [0, -280], [0, 0], [522, 0], [0, 0], [269, -269], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 680], [0, 0], [-202, 0], [0, 0], [1062, -1062], [0, 0], [0, 0], [0, 0], [651, 651], [0, 0], [0, 1242], [0, 0], [1682, 0], [0, 0], [1089, -1089], [0, 0], [0, 0], [0, 0], [1269, 1269], [0, 0], [0, -719], [0, 0], [4878, 0], [0, 0], [611, -611], [0, 0], [0, 0], [0, 0], [-2520, -2520], [0, 0], [0, -1160], [0, 0], [-5598, 0], [0, 0], [2349, -2349], [0, 0], [0, 0], [0, 0], [-751, -751], [0, 0], [0, -4842], [0, 0], [-6442, 0], [0, 0], [2951, -2951], [0, 0], [0, 0], [0, 0], [3422, 3422], [0, 0], [0, -10560], [0, 0], [6561, 0], [0, 0], [-6231, 6231], [0, 0], [0, 0], [0, 0], [6120, 6120], [0, 0], [0, -14480], [0, 0], [-4002, 0], [0, 0], [-1818, 1818], [0, 0], [0, 0], [0, 0], [7311, 7311], [0, 0], [0, -9558], [0, 0]]}