# Stored data for newform 2205.4.a.bk, downloaded from the LMFDB on 07 May 2024.
{"label": "2205.4.a.bk", "space_label": "2205.4.a", "level": 2205, "weight": 4, "hecke_orbit": 37, "hecke_orbit_code": 162129586652448925, "dim": 3, "is_polredabs": true, "nf_label": "3.3.22952.1", "trace_hash": 248951824782594256, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [-4, -17, 2, 1]], [11, [32160, -2212, -20, 1]], [13, [17328, -1748, 0, 1]], [17, [-282328, 15612, -234, 1]]], "qexp_display": "q+(-1+\\beta _{1})q^{2}+(5-2\\beta _{1}+\\beta _{2})q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 35280, "fricke_eigenval": 1, "atkin_lehner_string": "+--", "analytic_conductor": 130.09921156265804, "hecke_ring_index": 1, "level_radical": 105, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [2205, 1, [1226, 442, 1081], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5, 7], "conrey_indexes": [1], "field_disc": 22952, "field_disc_factorization": [[2, 3], [19, 1], [151, 1]], "field_poly": [14, -18, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.872", "prec": 17}, {"__RealLiteral__": 0, "data": "0.197", "prec": 17}, {"__RealLiteral__": 0, "data": "22.177", "prec": 20}, {"__RealLiteral__": 0, "data": "7.652", "prec": 17}, {"__RealLiteral__": 0, "data": "250.990", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [5, -1], [7, -1]], "trace_display": [-2, 0, 15, 0], "traces": [0, 3, -2, 0, 14, 15, 0, 0, -66, 0, -10, 20, 0, 0, 0, 0, 114, 234, 0, 82, 70, 0, -236, -30, 0, 75, 76, 0, 0, 32, 0, 362, -430, 0, -596, 0, 0, 302, 160, 0, -330, 626, 0, -68, -300, 0, -412, 936, 0, 0, -50, 0, 684, -298, 0, 100, 0, 0, -1184, 428, 0, -1050, -608, 0, -154, 0, 0, -52, 1964, 0, 0, -416, 0, 312, -1668, 0, -1712, 0, 0, -488, 570, 0, 1476, 948, 0, 1170, 1928, 0, 124, -142, 0, 0, 3220, 0, -328, 410, 0, 3052, 0, 0, 350, 822, 0, 2308, -1292, 0, 2192, -382, 0, -166, -1180, 0, 0, 794, 0, -150, 5792, 0, -824, 0, 0, 831, -3700, 0, 2416, 375, 0, -464, 3054, 0, 380, 972, 0, 0, 7672, 0, -7332, -182, 0, 1206, 0, 0, -2140, -3800, 0, 160, 628, 0, 4316, -1264, 0, 3960, 2600, 0, 0, 1810, 0, -456, 4944, 0, -2150, 0, 0, 1964, -5004, 0, -5376, 1644, 0, -3095, -2980, 0, -11560, 7722, 0, 0, 8620, 0, 3300, -2944, 0, -3042, 0, 0, -6492, 1510, 0, 4232, 4616, 0, 800, -4380, 0, -394, -9596, 0, 0, 2810, 0, 3774, -1650, 0, 2572, 0, 0, 3130, -10088, 0, -4332, 5920, 0, 240, -1168, 0, -10196, -340, 0, 0, 5964, 0, -1500, -912, 0, -4780, 0, 0, 17272, 1944, 0, -3910, -2060, 0, -13152, -10034, 0, 4680, 18088, 0, 0, 6380, 0, -13486, 7902, 0, 3820, 0, 0, -6232, -9784, 0, -250, 9964, 0, -7592, -21248, 0, 1906, 3338, 0, 0, 3420, 0, 2512, 7598, 0, -1490, 0, 0, -12040, 8746, 0, -18, 19476, 0, -1952, 500, 0, 4822, 17064, 0, 0, 2128, 0, 9916, 3684, 0, -5624, 0, 0, 8793, -5920, 0, 8980, 16694, 0, 2140, -13924, 0, 2040, 9120, 0, 0, 18032, 0, 2960, -5250, 0, 2784, 0, 0, -3040, -11840, 0, 4272, 19492, 0, 11104, -12114, 0, -6080, -770, 0, 0, 3820, 0, 0, -14728, 0, 3972, 0, 0, 5768, -2032, 0, -4520, -260, 0, -10082, 7586, 0, 9820, 4640, 0, 0, 25864, 0, -12964, 17954, 0, -482, 0, 0, 948, -3242, 0, -2080, -13692, 0, 23788, 8828, 0, -3725, 15156, 0, 0, 1560, 0, 4796, 1740, 0, -8340, 0, 0, -12670, -14840, 0, -20792, 10944, 0, 26260, -8560, 0, 13252, -6032, 0, 0, 12996, 0, 26724, 6308, 0, 2844, 0, 0, -20512, -2440, 0, 24316, -8312, 0, 2850, 2404, 0, -760, 10172, 0, 0, 10920, 0, -9722, 7380, 0, 14360, 0, 0, 4740, -5700, 0, 1824, -21996, 0, -7134, 5400, 0, 8104, 5850, 0, 0, 53148, 0, 9640, 25952, 0, 2744, 0, 0, -16548, -23380, 0, -5050, 620, 0, -2888, 1810, 0, -710, 20224, 0, 0, 10456, 0, 9368, -37416, 0, 8408, 0, 0, 20498, -1068, 0, 16100, 16822, 0, 18504, 19168, 0, -768, -12280, 0, 0, -1640, 0, -42136, 18160, 0, 2050, 0, 0, 18988, -4160, 0, -3040, 5692, 0, -28738, 15260, 0, -3208, 1260, 0, 0, 43792, 0, 16448, 3040, 0, 22576, 0, 0, 14548, 1750, 0, 15208, -3096, 0, 4110, -9160, 0, 41392, 19106, 0, 0, 22402, 0, 41572, 11540, 0, 1104, 0, 0, -6460, 28366, 0, 6148, 23312, 0, -42076, 32636, 0, -1065, 10960, 0, 0, -12768, 0, -1910, 32376, 0, -46812, 0, 0, -7422, -704, 0, -39196, -830, 0, -20916, -25952, 0, -5900, -32640, 0, 0, -20124, 0, -14760, 4494, 0, -26144, 0, 0, 43480, -228, 0, 3970, -20744, 0, -4516, 524, 0, -36008, 15960, 0, 0, -750, 0, -15208, -77926, 0, 28960, 0, 0, -30784, -21076, 0, -9972, -33500, 0, 7748, -4120, 0, 46756, -29226, 0, 0, -46664, 0, -4408, 20596, 0, -4458, 0, 0, -24992, 4155, 0, -27884, 4360, 0, -18500, 3952, 0, -27818, 73016, 0, 0, -5346, 0, -28594, 12080, 0, 1400, 0, 0, 1875, 14092, 0, -71036, 41156, 0, -21112, -11408, 0, -37856, -2320, 0, 0, -13120, 0, 15270, -16192, 0, 24368, 0, 0, 23872, 13844, 0, -53968, 1900, 0, 13224, -14218, 0, 4860, -9236, 0, 0, 800, 0, 41590, -67016, 0, -12688, 0, 0, 53440, 44504, 0, 38360, 19720, 0, -382, -8044, 0, -41246, 6470, 0, 0, -36660, 0, -25504, 19210, 0, -910, 0, 0, -25336, 20824, 0, 70834, 38172, 0, 34852, 6030, 0, 26108, -11940, 0, 0, -67968, 0, -332, -28940, 0, 50492, 0, 0, -25882, -10700, 0, 32388, 700, 0, -19000, -42804, 0, 2212, -22048, 0, 0, 2518, 0, -16844, 800, 0, -17224, 0, 0, 3140, -27896, 0, 12688, -40944, 0, -21284, -60080, 0, 21896, 21580, 0, 0, 7826, 0, -6320, -25660, 0, 168, 0, 0, -24748, 25944, 0, -15808, 19800, 0, 20898, -30648, 0, 13000, -35870, 0, 0, -43420, 0, 6752, 58976, 0, -74674, 0, 0, 56388, 20266, 0, 9050, -99668, 0, 45088, 61580, 0, 8568, -64600, 0, 0, -2280, 0, -16884, -22560, 0, 24720, 0, 0, -9120, -6476, 0, 74168, 23674, 0, 69456, -10750, 0, 86280, -39720, 0, 0, 1824, 0, -27636, 68340, 0, 54606, 0, 0, -11864, 9820, 0, 69256, -22660, 0, -25020, 36052, 0, -53272, -66504, 0, 0, -65942, 0, -4426, -26880, 0, 29868, 0, 0, 8220, -59760, 0, 136, -7960, 0, 17457, 54388, 0, -105880, -15475, 0, 0, -71792, 0, -14900, 14260, 0, -3252, 0, 0, -111908, 48998, 0, -89266, -57800, 0, -19500, 59482, 0, 38610, -5220, 0, 0, -121440, 0, 29184, 41052, 0, 24608, 0, 0, -19474, -38264, 0, 43100, -2258, 0, -33900, 56088, 0, 5748, -82392, 0, 0, 16500, 0, -94464, 20640, 0, -14720, 0, 0, 20880, 15488, 0, -47164, -39560, 0, 82576, -15210, 0, 40084, -94456, 0, 0, 18252, 0, 98560, -90476, 0, -59372, 0, 0, 27020, -32460, 0, 127420, -1672, 0, 7550, -41264, 0, -46240, -58614, 0, 0, -47904, 0, 109384, 21160, 0, -11308, 0, 0, 23080, 118146, 0, -78644, -15848, 0, 35152, 86558, 0, 38456, 4000, 0, 0, -81958, 0, -21900, -63860, 0, -114328, 0, 0, -42025, -21736, 0, -124836, -1970, 0, -17848, 55406, 0, -47980, -11116, 0, 0, 70336, 0, 65940, 9094, 0, 6296, 0, 0, 31148, 31812, 0, 14050, -155456, 0, 37392, -111640, 0, -67700, -56600, 0, 0, 18870, 0, -31236, 7800, 0, -8250, 0, 0, 39848, 48264, 0, -69808, -29860, 0, 32386, 12860, 0, 86232, 74054, 0, 0, -98464, 0, -89196, 40820, 0, -43750, 0, 0, -138362, 15650, 0, 99712, -134652, 0, -50440, 42656, 0, -30242, -81040, 0, 0, -29100, 0, 35386, -21660, 0, -71796, 0, 0, 29600, -71824, 0, -55776, 19014, 0, -19876, 92948, 0, -106304, 1200, 0, 0, -33466, 0, -5840, 5676, 0, 161248, 0, 0, 45448, 76280, 0, -61742, -50980, 0, -195704, 49728, 0, -1700, 102836, 0, 0, -73264, 0, -2832, -105020, 0, 29712, 0, 0, 69832, -6148, 0, 29820, 41836, 0, -30854, 96440, 0, 52136, 44138, 0, 0, -7500, 0, 51840, -3362, 0, -4560, 0, 0, -49148, 52190, 0, -63544, 32112, 0, -99024, -23900, 0, 61662, 20976, 0, 0, -111640, 0, -6628, -119112, 0, -75224, 0, 0, 2746, 86360, 0, 241208, 120720, 0, 9720, 39836, 0, -61336, -95704, 0, 0, -7176, 0, 8056, -19550, 0, 51108, 0, 0, -10300, 54368, 0, -1764, -129620, 0, 213898, -20064, 0, -54460, -65760, 0, 0, -59838, 0, -50170, -17760, 0, -35796, 0, 0, 34716, 70604, 0, 26088, 23400, 0, -75960, 28800, 0, 90440, -56586, 0, 0, -62140, 0, 6236, 7902, 0, -120128, 0, 0, 110536, 95934, 0, 31900, -34200, 0, -33644, -19960, 0, 45830, 108644, 0, 0, -67430, 0, -3440, 20496, 0, 39510, 0, 0, 13154, 70624, 0, -68832, 59914, 0, 29572, 19100, 0, 31312, 13860, 0, 0, -132748, 0, -158760, -62468, 0, -7778, 0, 0, -131936, -31160, 0, 201868, -6600, 0, -48920, 14304, 0, -79440, -9000, 0, 0, -180608, 0, 100074, -1250, 0, 124076, 0, 0, 49820, 167036, 0, -197544, 10468, 0, -25688, -88464, 0, -197248, -37960, 0, 0, 3616, 0, -106240, 56604, 0, 16584, 0, 0, 139200, 7882, 0, -164638, 9530, 0, -9192, 91266, 0, 16690, -34856, 0, 0, 123924, 0, -7634, -166400, 0, 81448, 0, 0, -102646, -119440, 0, 17100, 67970, 0, 90200, -64744, 0, 62792, -17988, 0, 0, 12560, 0, -32004, 56544, 0, 37990, 0, 0, -71468, 109168, 0, 24646, -142260, 0, 211368, -7450, 0, 28200, 197712, 0, 0, -9000, 0, -27032, -130240, 0, -113256, 0, 0, -71136, -60200, 0, 118280, -93488, 0, 43730, 4484, 0, -2764, -32200, 0, 0, 127218, 0, 86236, -90, 0, 182344, 0, 0, 97380, -62426, 0, 13952, -16560, 0, 101204, -51666, 0, -62891, -9760, 0, 0, -60546, 0, 2500, 94040, 0, 40736, 0, 0, -45994, -156280, 0, -181972, 24110, 0, -60024, 1844, 0, 85320, 115216, 0, 0, 103272, 0, 40412, 124480, 0, -73478, 0, 0, 104896, 62340, 0, 10640, 54080, 0, -37828, -24388, 0, 130872, -132612, 0, 0, 49580, 0, -4560, -134500, 0, 18420, 0, 0, -158664, -62468, 0, -76768, -13504, 0, -14134, -28120, 0, 144724, -131118, 0, 0, 149508, 0, -1472, 106424, 0, -112864, 0, 0, -190218, 43965, 0, 97580, 85348, 0, -29600, 147992, 0, -134014, 48200, 0, 0, 109984, 0, -138774, 44900, 0, 280208, 0, 0, 83470, -239972, 0, -11312, 13528, 0, 24136, 99940, 0, -77872, 10700, 0, 0, 44568, 0, -69620, 197852, 0, -110328, 0, 0, -5988, 22028, 0, -50866, 10200, 0, -108380, -91982, 0, 45600, -65960, 0, 0, 17128, 0, -166576, -26912, 0, -137032, 0, 0, 128224, -25536, 0, 90160, 114952, 0, -49540, -70868, 0, 121048, -12716, 0, 0, 14800, 0, 165076, 196998, 0, -26250, 0, 0, 152652, -160560, 0, 126302, -96992, 0, 30096, 13920, 0, 384, 36580, 0, 0, -49400, 0, 76760, -95052, 0, 69212, 0, 0, -18198, -15200, 0, 305372, -60290, 0, -59200, -201792, 0, -40672, -53808, 0, 0, 47320, 0, 342856, 21360, 0, -97560, 0, 0, 97460, 123756, 0, -45904, -41328, 0, -9112, 125000, 0, 48652, 55520, 0, 0, 42794, 0, -60570, -114760, 0, 88340, 0, 0, -82152, -201936, 0, -316660, -30400, 0, -223594, -168208, 0, -3850, -229658, 0, 0, -16056, 0, -86408, -41802, 0, 105118, 0, 0, 84816, -116878, 0, 19100, -81372, 0, -19888, -34404, 0, 99190, 195432, 0, 0, 0, 0, -88900, 48360, 0, -73640, 0, 0, 42656, -97440, 0, -202948, 266154, 0, 137872, 19860, 0, 106184, -55892, 0, 0, 195408, 0, 333416, 328792, 0, -41344, 0, 0, -148180, 28840, 0, 157640, 108212, 0, -10160, -89120, 0, -10960, 47348, 0, 0, 67906, 0, 14930, -22600, 0, 50304, 0, 0, -1300, -30456, 0, -206616, 97200, 0, 105089, -237430, 0, -21484, -50410, 0, 0, 214280, 0, 37930, 68300, 0, -28696, 0, 0, 34952, -124586, 0, -54646, 49100, 0, -149688, 106704, 0, 23200, 169844, 0, 0, 16028, 0, 262016, 134212, 0, -243996, 0, 0, 26676, -129424, 0, 129320, -47938, 0, -90716, 102932, 0, -169292, 3960, 0, 0, -64820, 0, -146564, -8314, 0, 89770, 0, 0, -134272, 82384, 0, -107518, 158384, 0, -134588, -2410, 0, 214572, 80000, 0, 0, 282616, 0, -28028, 120740, 0, 88984, 0, 0, -125076, 4740, 0, 183196, 233256, 0, -16210, 14456, 0, -104120, 128320, 0, 0, 13860, 0, 66968, -10400, 0, -14380, 0, 0, -68460, -121144, 0, -53584, 266512, 0, 47264, 14178, 0, -277530, 118940, 0, 0, 184720, 0, 44140, -195024, 0, -195456, 0, 0, 43986, 196064, 0, -264168, -18625, 0, 97128, -380504, 0, 75780, 202324, 0, 0, 155208, 0, 173992, 220880, 0, 95612, 0, 0, 17892, 54108, 0, 7800, 59040, 0, 169428, 57032, 0, -98528, 164596, 0, 0, 23980, 0, -88432, -262256, 0, 8700, 0, 0, 59184, -323108, 0, -57304, -33660, 0, 130103, -41700, 0, 224640, -83188, 0, 0, 137376, 0, -109484, 9260, 0, -111454, 0, 0, 215448, -63350, 0, 232116, -75080, 0, -74200, -147468, 0, 13250, 396604, 0, 0, 133766, 0, 123002, -103960, 0, -108012, 0, 0, 54720, 103800, 0, -188456, 84946, 0, -82700, -274320, 0, -5972, 131300, 0, 0, 43016, 0, -42800, -109348, 0, 152360, 0, 0, 35752, 68796, 0, -143880, 66260, 0, 70148, 111086, 0, -30160, 147560, 0, 0, -59420, 0, -151684, -62850, 0, 77976, 0, 0, 193904, 417196, 0, 64980, -66324, 0, 298706, -328032, 0, -124254, -151088, 0, 0, 133620, 0, -359200, -189312, 0, 31540, 0, 0, -242768, 29974, 0, -750, 93940, 0, 217472, 14220, 0, 119864, 25240, 0, 0, -109732, 0, 32832, 35532, 0, 208768, 0, 0, -208920, -102560, 0, 676928, 77498, 0, -12200, 3040, 0, 238384, 217636, 0, 0, 119104, 0, -13696, 121580, 0, -72436, 0, 0, -41560, -193480, 0, -145436, 29812, 0, -44408, -180394, 0, -106628, 14250, 0, 0, -2754, 0, 12020, -315824, 0, -200888, 0, 0, -255072, -57296, 0, -42464, -3800, 0, -327578, 43372, 0, 50860, -36064, 0, 0, -90520, 0, 5116, 75502, 0, 165362, 0, 0, 498416, -345380, 0, 54600, 410116, 0, -75292, 415672, 0, -83752, -33188, 0, 0, -48610, 0, -116468, 135390, 0, 36900, 0, 0, -93510, 125248, 0, 270820, -36654, 0, 85568, 71800, 0, 211428, 101052, 0, 0, 382988, 0, -89424, 83976, 0, 63116, 0, 0, -204040, 23700, 0, -82648, -143512, 0, -28500, 884, 0, 125500, 439996, 0, 0, -80774, 0, -73062, 9120, 0, 127856, 0, 0, -109980, -114192, 0, 244108, 4100, 0, -81928, 463256, 0, -319148, -35670, 0, 0, 344896, 0, 27000, 15736, 0, 191036, 0, 0, -167594, 123712, 0, -117952, 40520, 0, -182016, -413800, 0, 29250, -47704, 0, 0, 328092, 0, -39226, 181032, 0, -163752, 0, 0, 169434, 63692, 0, 265740, 111006, 0, 239664, 78920, 0, -329536, 172660, 0, 0, 48200, 0, -357436, 223718, 0, 129760, 0, 0, -102752, 222496, 0, 73530, -116720, 0, 376932, 13720, 0, 422368, -59912, 0, 0, 113088, 0, -42716, 137408, 0, 205692, 0, 0, 257296, -82740, 0, -225264, 64632, 0, -116900, 3460, 0, -514824, -119920, 0, 0, 130592, 0, -237460, -25250, 0, -51984, 0, 0, 3100, -26024, 0, -247500, 21760, 0, -236956, 80734, 0, -13709, -14440, 0, 0, 198394, 0, 9050, 20308, 0, -169284, 0, 0, 159874, -165080, 0, -429048, -3550, 0, 37896, 567664, 0, 101120, 28520, 0, 0, -95988, 0, 62928, 32070, 0, -234058, 0, 0, 126912, 40236, 0, 52280, -56896, 0, 256168, -69616, 0, -361916, 335272, 0, 0, 46840, 0, 70300, 22348, 0, -187080, 0, 0, 29288, -622152, 0, -32112, 27596, 0, -38214, 42040, 0, 21876, -209398, 0, 0, 223464, 0, 686512, -41128, 0, -135990, 0, 0, -41976, 102490, 0, -144232, -760, 0, -5340, 208896, 0, 29930, -257472, 0, 0, 275462, 0, 199082, 80500, 0, 133968, 0, 0, 84110, 97220, 0, 233548, -130230, 0, -341512, -611238, 0, 47272, 92520, 0, 0, 57920, 0, 95840, 351760, 0, 105252, 0, 0, -104804, 101992, 0, 10684, -3840, 0, 23184, -334522, 0, -61400, -107420, 0, 0, 70592, 0, -100710, -111672, 0, -351508, 0, 0, -129956, -457560, 0, -8200, 1480, 0, 120688, -90520, 0, -233968, 9062, 0, 0, -210680, 0, -219348, -120348, 0, 90800, 0, 0, 4044, -82600, 0, 35154, -584196, 0, 60844, 10250, 0, -166062, 158016, 0, 0, -205812, 0, -20672, 38344, 0, 315084, 0, 0, -400570, 94940, 0, -45448, -41506, 0, -20800, 306676, 0, -9368, 125784, 0, 0, 114180, 0, -253596, -15200, 0, -93184, 0, 0, 28460, 129092, 0, -145568, -154072, 0, -339264, 190354, 0, -238968, -143690, 0, 0, -146342, 0, 76300, 253492, 0, -426880, 0, 0, -198512, 15880, 0, -607068, -16040, 0, 44370, 137920, 0, 6300, -174758, 0, 0, 201552, 0, -107800, -403550, 0, -105072, 0, 0, 328596, 18240, 0, 218960, 357128, 0, -304296, 49192, 0, 537580, -100472, 0, 0, 82240, 0, -340748, 89184, 0, 15200, 0, 0, 123674, -154580, 0, 171144, 346178, 0, -310728, 112880, 0, -93752, 11400, 0, 0, -171760, 0, 161480, -155240, 0, -60192, 0, 0, 537216, 72740, 0, 291216, -333348, 0, 8750, -446300, 0, -94968, -285324, 0, 0, -117380, 0, 360240, 76040, 0, -386244, 0, 0, -15480, 629336, 0, 169232, 189880, 0, -82670, -79192, 0, 190656, 20550, 0, 0, -50960, 0, -45800, -137880, 0, -112960, 0, 0, 100280, -578192, 0, -208250, 206960, 0, 168224, 414474, 0, 95530, -180480, 0, 0, -193736, 0, 131854, -218560, 0, 61404, 0, 0, -8330, -55848, 0, 112010, -329080, 0, 41824, -277992, 0, -279380, 60816, 0, 0, 207860, 0, 155608, 161832, 0, 57700, 0, 0, -451840, 241332, 0, -209984, -2896, 0, 310832, 5520, 0, 168264, -103416, 0, 0, -396064, 0, 239824, 99788, 0, 346608, 0, 0, -287780, -32300, 0, 409236, 216580, 0, 141830, 335120, 0, 465016, -43194, 0, 0, -401528, 0, -186528, 30740, 0, 167328, 0, 0, 116560, -121490, 0, -202120, -211772, 0, 108376, 54816, 0, 91688, -210380, 0, 0, -356782, 0, 163180, 183540, 0, 75608, 0, 0, 17388, -345756, 0, 379340, -5325, 0, 152536, -558968, 0, 54800, 203880, 0, 0, -135136, 0, -70000, 185910, 0, -215562, 0, 0, 275320, 230408, 0, -63840, 340832, 0, 203200, -265824, 0, 5804, 54696, 0, 0, -9550, 0, 206256, -139536, 0, 161880, 0, 0, 135564, 340680, 0, 259680, -136936, 0, -68366, -234060, 0, 28228, 225278, 0, 0, 118468, 0, 45408, -577112, 0, -2032, 0, 0, -202882, -37110, 0, -78992, 5980, 0, -3520, -172000, 0, -84450, -278800, 0, 0, -291840, 0, -59102, -195980, 0, 306108, 0, 0, -4150, -353664, 0, -48064, -139906, 0, -91128, 154980, 0, -159596, -104580, 0, 0, -291406, 0, -129760, -94296, 0, -372400, 0, 0, 291448, 316744, 0, 212714, -29500, 0, -299528, -235278, 0, -163200, -130416, 0, 0, -49188, 0, -246544, 497980, 0, 359736, 0, 0, 15528, 521508, 0, -100620, 314216, 0, 189280, 50080, 0, -184284, -342418, 0, 0, -73800, 0, -150632, -298230, 0, 22470, 0, 0, -539640, 92634, 0, 345482, -86980, 0, 206304, -130720, 0, -269322, 136496, 0, 0, -3008, 0, -255152, -239968, 0, -180440, 0, 0, -225203, 217400, 0, -281888, 232256, 0, -1140, -93300, 0, 526000, 264092, 0, 0, -442944, 0, 354620, 19850, 0, 10008, 0, 0, -103720, 279600, 0, -206668, 104728, 0, 607292, -463374, 0, 169320, -22580, 0, 0, -316222, 0, 2620, 70128, 0, 114972, 0, 0, -258656, 464960, 0, -175888, -180040, 0, 34422, 441948, 0, 79800, 8354, 0, 0, -679436, 0, 342004, -363120, 0, 249296, 0, 0, -402740, -307682, 0, -3750, -82528, 0, -102516, -239020, 0, 273136, -252320, 0, 0, -76040, 0, -400424, 427654, 0, -389630, 0, 0, 338840, 636376, 0, -501492, -244990, 0, -118256, 144800, 0, -214788, 321872, 0, 0, -352164, 0, 424, -104116, 0, -228320, 0, 0, -158432, -153920, 0, 302100, 387552, 0, -105380, 268640, 0, -233872, -1304656, 0, 0, 62946, 0, 110144, -49860, 0, 472124, 0, 0, -167500, -75872, 0, 365104, -446524, 0, 696108, -202128, 0, 62724, 38740, 0, 0, -323760, 0, -20600, -317072, 0, 619304, 0, 0, 324616, 123102, 0, 383960, 233780, 0, -146096, 633446, 0, -146130, 21064, 0, 0, 29748, 0, -244318, 164076, 0, -247344, 0, 0, -201248, -155780, 0, -233320, -109280, 0, 346920, 343140, 0, 29152, 82048, 0, 0, -22040, 0, 580120, -75344, 0, 102980, 0, 0, -535028, 454016, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "315.4.a.n", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0], [1, 0, 0], [-1, 1, 0], [0, 0, 0], [5, -2, 1], [5, 0, 0], [0, 0, 0], [0, 0, 0], [-23, 5, -2], [0, 0, 0], [-5, 5, 0], [10, -6, -4], [0, 0, 0], [-2, 2, 4], [0, 0, 0], [0, 0, 0], [47, -24, -3], [82, -12, 0], [0, 0, 0], [28, 6, -8], [25, -10, 5], [0, 0, 0], [-74, -8, -6], [-10, -12, 12], [0, 0, 0], [25, 0, 0], [18, 20, 2], [0, 0, 0], [0, 0, 0], [16, -32, 16], [0, 0, 0], [124, -10, 0], [-145, 13, -8], [0, 0, 0], [-226, 94, -12], [0, 0, 0], [0, 0, 0], [114, -40, 0], [60, -26, 6], [0, 0, 0], [-115, 25, -10], [198, 52, -20], [0, 0, 0], [-28, 52, -36], [-90, -54, 24], [0, 0, 0], [-158, 74, -12], [308, 8, 4], [0, 0, 0], [0, 0, 0], [-25, 25, 0], [0, 0, 0], [234, -6, -12], [-124, 54, 20], [0, 0, 0], [50, -30, -20], [0, 0, 0], [0, 0, 0], [-432, 144, -32], [124, -16, 72], [0, 0, 0], [-310, -120, 0], [-244, 134, -10], [0, 0, 0], [-59, -14, 37], [-10, 10, 20], [0, 0, 0], [-92, 208, 16], [722, -296, 94], [0, 0, 0], [0, 0, 0], [-118, -66, 4], [0, 0, 0], [82, 22, 44], [-594, 154, -40], [0, 0, 0], [-608, 74, 38], [0, 0, 0], [0, 0, 0], [-240, 124, 108], [235, -120, -15], [0, 0, 0], [466, 26, 52], [384, -128, -76], [0, 0, 0], [410, -60, 0], [724, -296, 52], [0, 0, 0], [-14, 172, -6], [-66, 88, -32], [0, 0, 0], [0, 0, 0], [1150, -208, -22], [0, 0, 0], [-220, 324, 8], [140, 30, -40], [0, 0, 0], [1090, -206, -12], [0, 0, 0], [0, 0, 0], [125, -50, 25]]}