# Stored data for newform 1225.4.a.m, downloaded from the LMFDB on 23 April 2024.
{"label": "1225.4.a.m", "space_label": "1225.4.a", "level": 1225, "weight": 4, "hecke_orbit": 13, "hecke_orbit_code": 54043195595556041, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 669151089535630140, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [14, 8, 1]], [3, [-31, -2, 1]], [19, [-3548, 36, 1]]], "qexp_display": "q+(-4+\\beta )q^{2}+(1+4\\beta )q^{3}+(10-8\\beta )q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 19600, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 72.27733975703225, "hecke_ring_index": 1, "level_radical": 35, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "field_poly_is_real_cyclotomic": true, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [1225, 1, [1177, 101], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [5, 7], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.936", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.177", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "59.992", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [7, -1]], "trace_display": [-8, 2, 0, 0], "traces": [0, 2, -8, 2, 20, 0, 8, 0, -48, 12, 0, -14, -108, 50, 0, 0, 168, -50, -16, -36, 0, 0, 184, -244, 496, 0, -216, 86, 0, -26, 0, 120, -672, 498, 24, 0, -136, -564, 320, -14, 0, 328, 0, 260, -1164, 0, 704, -350, -1368, 0, 0, -754, 628, 56, -648, 0, 0, 668, 8, 1232, 0, -336, -1200, 0, 2128, 0, -1976, 152, 908, -1332, 0, -1904, 800, 676, 2016, 0, -1768, 0, 440, 1014, 0, -1454, -816, -376, 0, 0, -768, -410, 4688, 216, 0, 0, -264, -2760, 1928, 0, 2464, 2742, 0, 940, 0, 676, 2440, -1334, -1744, 0, 288, -1724, 3292, 482, 0, -1524, 0, 484, -2784, 0, 508, 172, -4928, 0, 0, 1532, 912, 2312, 6960, 0, 0, -2608, -4544, 1348, 0, 220, 4852, 0, -864, 0, -4784, -1288, 3104, -332, 0, 1762, 7616, -862, -2064, 0, -1328, 0, -3720, 452, 0, -1290, 6848, -1708, 0, 0, -3212, 1548, -5048, 2104, 0, 0, 5336, 348, -688, 0, -896, -1590, 0, -3080, 0, 1192, 424, 806, 1336, 0, -13464, 1232, -688, 4600, 0, -4056, 0, -2064, -3392, 0, 11280, -5282, -7724, 0, 0, -2198, -3504, 808, -11848, 0, 0, 1392, -3216, -6160, 0, -872, -2976, 0, -2932, 0, 2472, -3640, 5736, 5884, 0, 9726, -3536, -1904, 5072, 0, -12400, 0, -6152, 6180, 0, -546, 1344, -5622, 0, 0, -6496, 650, 7576, 2520, 0, 0, -2640, -176, 16, 0, 12320, -2954, 0, 526, 0, 6292, -7920, -5696, 96, 0, -6128, -1604, -27360, -9976, 0, 236, 0, -6996, 10688, 0, 4768, -9636, -3040, 0, 0, -924, 4416, -4028, -11408, 0, 0, 920, 3568, -4532, 0, -3808, 12696, 0, 720, 0, 4472, -8572, 304, -5040, 0, -3706, -9320, -410, -19040, 0, 6760, 0, 2240, -832, 0, -778, -4248, 7726, 0, 0, 5376, -10330, -3376, -5012, 0, 0, 9896, -412, -19920, 0, 4976, 1158, 0, -12790, 0, -8932, 13392, 7122, -6896, 0, 18076, 1284, -7456, -2890, 0, -9020, 0, -6844, -10700, 0, -4720, -16414, 8992, 0, 0, -14616, 15440, -5304, 7592, 0, 0, 7092, 11520, -17756, 0, -23880, -4288, 0, 3008, 0, 4952, -1692, -1668, 8988, 0, 3366, 29792, 8598, 4928, 0, 752, 0, -16480, -896, 0, -5326, 17824, -5636, 0, 0, 5136, -4190, 5616, 5936, 0, 0, -29520, -3832, 19160, 0, 26352, -266, 0, -4920, 0, -1584, 10840, -5512, 9920, 0, -6448, 3736, 34460, -7494, 0, 18068, 0, 21404, -1616, 0, 5048, 2262, 25248, 0, 0, -13006, 4448, 5880, 8936, 0, 0, -3732, -1488, 12020, 0, -19016, 9572, 0, 9024, 0, -19936, -4428, -27072, 10056, 0, 6802, -36696, 2124, 16064, 0, -7616, 0, -2648, 12386, 0, -11614, 36408, 3780, 0, 0, 38612, -7576, -17936, 11004, 0, 0, -1816, 16980, 22776, 0, 12424, -5820, 0, -24082, 0, 13576, 41320, 17654, -6392, 0, -19840, -12448, -25264, 11226, 0, -20112, 0, 27584, 7032, 0, -768, 238, -3912, 0, 0, -1268, -29568, 6884, 18936, 0, 0, 4432, -17144, -20532, 0, -13140, -34080, 0, 29656, 0, 18880, -22124, -6624, -12964, 0, 758, -1840, 4874, 11104, 0, 79200, 0, 34496, 6538, 0, 3338, 272, -7178, 0, 0, 14272, -6280, -28128, -15860, 0, 0, 4992, -14924, 47152, 0, -5336, 19346, 0, 33510, 0, -14780, 2704, -24456, -40168, 0, 25200, 28680, 40296, 23930, 0, 7392, 0, 6216, -1776, 0, -12352, 12280, 15344, 0, 0, 30950, 23152, 2344, -17696, 0, 0, -18384, 22576, -5472, 0, -3756, -43648, 0, 47504, 0, 4872, -17424, 17760, 5412, 0, -13154, 10632, 37432, 35796, 0, 17528, 0, 45696, -22364, 0, -17352, -35116, 5994, 0, 0, 1504, 4138, 12128, -12056, 0, 0, 24168, 15992, 30560, 0, -41032, -24192, 0, -33840, 0, 17200, -24336, 18522, 48952, 0, 17064, -3728, 15200, 2658, 0, 31940, 0, -1136, -50788, 0, 6784, -11834, 46592, 0, 0, -10862, -2232, 3964, -840, 0, 0, 4764, 37624, -1220, 0, 10180, 44928, 0, -38040, 0, -42616, -8260, 21112, 24660, 0, 19362, -58064, 18558, -25328, 0, 13360, 0, 10568, -11424, 0, -35516, 20464, -19198, 0, 0, 26144, 16720, 18576, -8624, 0, 0, 30104, -628, 65288, 0, -20064, 15064, 0, 21402, 0, 8192, 51744, -16546, -72576, 0, 10752, 9700, -25756, -45878, 0, -11472, 0, -1128, -38480, 0, -24400, -26638, 70336, 0, 0, -14518, 108240, -18768, 8080, 0, 0, -58216, -4272, -648, 0, 24856, -57348, 0, 31360, 0, -496, -30024, -19616, -6064, 0, -17266, -21752, -408, -59952, 0, -38632, 0, -66528, 33606, 0, -1852, 800, 34320, 0, 0, 30640, -59634, -4096, 19148, 0, 0, 14968, -29356, -53360, 0, 33008, 27984, 0, 17946, 0, -18468, 4320, 1978, 31688, 0, 28672, -9256, -15520, -5086, 0, 17148, 0, -41880, 74400, 0, 28144, -21456, -37076, 0, 0, 11478, -80088, 5100, -1128, 0, 0, -3648, 24736, -61844, 0, 26980, -14272, 0, -38364, 0, 33152, 30800, -44384, 628, 0, 24796, 33808, -15870, -9152, 0, -95728, 0, 37400, 15920, 0, 13328, -44000, 6178, 0, 0, -78560, -58166, -17696, 32324, 0, 0, -4064, -6672, -17864, 0, -66464, -16858, 0, -14482, 0, 2704, 58616, 39300, -16400, 0, -42480, -15668, -25472, -20158, 0, 36812, 0, 27872, -19488, 0, -8040, 7288, -31984, 0, 0, 4234, 61328, 7480, -65360, 0, 0, -50348, 7888, -53352, 0, 44292, 58832, 0, 14032, 0, 87128, 59880, -62176, 30564, 0, -46136, 1496, -20474, 79596, 0, -10928, 0, -44448, 63142, 0, 85128, 102816, 22748, 0, 0, -20640, -9276, -53128, -24600, 0, 0, 44696, -33376, -88480, 0, 2224, 34368, 0, -38842, 0, 4824, -155184, 9412, 13728, 0, 7528, 49948, -43824, -32786, 0, -30784, 0, -8008, 26540, 0, -76416, 40496, -124992, 0, 0, -5182, 24292, 29532, 25328, 0, 0, -24404, 109928, 15720, 0, -23928, -36784, 0, -166656, 0, -76200, -42932, 36836, 1880, 0, 20736, 66864, -74168, 75600, 0, 146672, 0, -44872, 40158, 0, 16326, 91712, -47600, 0, 0, -95824, -30916, -10080, -36120, 0, 0, 10016, 27868, -20456, 0, 19808, 64854, 0, -49390, 0, -12960, 16752, -73744, 103488, 0, -12800, 36304, -86500, 11396, 0, -79484, 0, -13616, -13760, 0, 125580, -6858, 104384, 0, 0, 77218, 51072, -24936, 134216, 0, 0, 43964, -97696, -11772, 0, -44400, -25728, 0, 103984, 0, 13248, -28748, 51312, 4120, 0, -30900, -2584, 42278, 50592, 0, -14808, 0, -53544, -50216, 0, -10688, -181440, -41496, 0, 0, -56496, -101426, -33704, -6012, 0, 0, -24840, -30800, -7368, 0, 51384, 21520, 0, -8710, 0, -33356, 39736, 12100, -320, 0, 71296, -33576, 35728, -82480, 0, -25300, 0, 27000, -28352, 0, 72736, 29318, -165224, 0, 0, 20138, 47616, 4140, -103480, 0, 0, 27408, -119416, 19068, 0, 96676, 55520, 0, -1304, 0, 110432, 74332, 174784, -77608, 0, -36662, -112984, -34430, -107280, 0, -164192, 0, -29352, -8362, 0, 67562, -9856, 56152, 0, 0, -15088, -47354, -6032, -45424, 0, 0, 37344, 13092, -10400, 0, -23048, -31616, 0, 200, 0, 6796, -106360, -30670, -101440, 0, -40224, 59064, 8752, -5144, 0, 1000, 0, -1340, 78352, 0, -119776, 38924, 13920, 0, 0, 55522, 14464, 78664, 101616, 0, 0, -23592, -191448, 60204, 0, -13436, -26848, 0, 22784, 0, -31200, 11728, -16928, 47432, 0, -22176, 8392, -6286, -3524, 0, -158368, 0, -119536, 42498, 0, -9034, -131204, -82310, 0, 0, -159936, 15304, 92848, 7464, 0, 0, 61184, -13600, 133296, 0, -39512, 9360, 0, 38904, 0, -50304, 1664, 123940, -24088, 0, -78720, 4696, 51472, -12960, 0, -9492, 0, 70836, -176228, 0, -63968, 22202, -75312, 0, 0, 91062, 158284, 131156, 86432, 0, 0, -46300, 158880, 43688, 0, 132944, -53712, 0, 142464, 0, -101464, -34536, -164356, -16168, 0, -33002, -64160, 80442, -33760, 0, -11336, 0, -70952, -138542, 0, 33198, -127696, 13362, 0, 0, 5440, 47600, 191984, -69960, 0, 0, -45208, 14648, 104120, 0, -100256, 5838, 0, -41648, 0, -141396, 59448, 50890, -22112, 0, -8368, 76404, -18756, 30124, 0, 47180, 0, -43184, 39728, 0, -19612, 69044, -28384, 0, 0, -77444, -15328, -149308, -162920, 0, 0, -9908, 79968, -154804, 0, -10184, 184244, 0, 76576, 0, -61088, -77752, -43008, 34836, 0, 72070, -65288, 121618, 180408, 0, 5784, 0, 174376, -55178, 0, -69600, -17856, -14000, 0, 0, -20964, 58574, 15232, -24340, 0, 0, 146864, -70216, 34728, 0, 91208, 21324, 0, 85260, 0, 109792, -58584, -18654, -7328, 0, -76056, 83832, 113344, 73156, 0, -2884, 0, -23032, -121504, 0, -33408, -28870, -161196, 0, 0, -73880, -12992, 17988, -41184, 0, 0, 11772, -49480, 35516, 0, 82488, -18144, 0, -92400, 0, 57816, 88444, 198816, -17004, 0, -49434, 30672, -33360, -23552, 0, 80048, 0, 128472, -21894, 0, -9832, 27408, 18298, 0, 0, 77008, 30318, 151816, 34272, 0, 0, 46720, 83656, 80840, 0, -172056, -150304, 0, 30148, 0, 63256, 59480, -8122, -340560, 0, 126384, -23844, -12288, 72142, 0, 90784, 0, -37820, 237840, 0, -34048, 57470, 14944, 0, 0, -31740, -158528, 24944, 258640, 0, 0, 48376, -213656, 85632, 0, -35804, -5256, 0, 78832, 0, -40808, 26448, 21376, -88276, 0, -77778, 138728, 70368, 99964, 0, -43680, 0, 147520, 19946, 0, 115000, 119900, 3656, 0, 0, 305536, 28946, -125656, 65828, 0, 0, 17680, -5012, 1248, 0, -65760, 46362, 0, 53820, 0, -36504, -45120, -36074, 227704, 0, 52480, 68492, -72352, -141822, 0, 167932, 0, -19092, -2572, 0, 158848, 38938, 151744, 0, 0, -63704, -140072, -96776, -61984, 0, 0, -116040, -108296, 17972, 0, 39828, 44192, 0, -56544, 0, 37256, -24536, -161324, 30340, 0, -28064, -163872, 2550, 48544, 0, -6432, 0, -5320, 23626, 0, -21598, -76736, -151542, 0, 0, 181696, -34870, -254880, 10064, 0, 0, -140848, 34624, 65408, 0, 59856, -23670, 0, -35018, 0, -61900, 10184, 316, 221088, 0, -17296, -132808, 14876, 83510, 0, -69124, 0, -13144, 2208, 0, -89648, -122256, 177696, 0, 0, -24880, -63488, -92208, 149024, 0, 0, -126708, 122384, -30444, 0, -87248, -143952, 0, -133056, 0, 124032, -13016, -65168, 5052, 0, -1136, -167664, -34254, -128736, 0, 13672, 0, -8976, -28452, 0, -85038, 314808, 83546, 0, 0, -134332, 70244, -43744, 31540, 0, 0, -175168, -29180, -45496, 0, -24888, 23888, 0, 25976, 0, -9700, 157592, 45468, 209640, 0, 100960, -98832, -152432, 65278, 0, 58440, 0, -17580, 26736, 0, 18576, 289402, 93148, 0, 0, -89640, 168512, 52976, -22952, 0, 0, 64124, 75528, 45320, 0, 163772, -6304, 0, -182796, 0, -123568, 8280, 53568, 161360, 0, 42960, 210480, 32636, 23632, 0, 82896, 0, 103608, 17098, 0, 133308, -102288, 100710, 0, 0, -134032, -69960, 238008, -11536, 0, 0, 140448, 232288, -11168, 0, -8568, 129954, 0, -53340, 0, 880, -61576, -88800, -72272, 0, 20368, 18384, 162888, -29830, 0, -66224, 0, -5996, 172976, 0, -100864, -168950, 200144, 0, 0, 160582, -232528, -177820, -128064, 0, 0, 162460, -14840, -95688, 0, -205072, -261440, 0, -288720, 0, 276176, 24292, -85472, -176040, 0, -22546, 187040, -47436, -161612, 0, 48056, 0, -158352, 2872, 0, 3856, 40696, -64774, 0, 0, 81536, 122596, -239960, -196596, 0, 0, -234528, -15684, -472192, 0, -96560, -8796, 0, 76730, 0, -16016, 30288, -50248, -28880, 0, 152532, -4932, 115424, 3196, 0, 96828, 0, 117368, -102060, 0, 194160, -33364, 198512, 0, 0, -26006, -100952, 155100, -135328, 0, 0, -20880, 227208, 67020, 0, -98144, -26912, 0, 445992, 0, 944, 2744, 56848, 15992, 0, 159366, 82336, -211082, -184896, 0, 108504, 0, 182824, 33192, 0, -65536, 39744, 76368, 0, 0, 29520, 60240, -122896, 14736, 0, 0, 237768, 39968, -214272, 0, 328176, -116596, 0, -90982, 0, -14472, -68968, -146766, -207248, 0, -158432, -145048, -74584, 1748, 0, -32096, 0, -108932, 52672, 0, -349620, -238622, -59280, 0, 0, -167214, 77984, 32196, -4400, 0, 0, -4204, 478416, 25992, 0, -145188, 221212, 0, 165440, 0, -144528, -56252, 1664, 123356, 0, 215302, -151520, -255462, -246400, 0, 289408, 0, -330944, 73920, 0, -144026, -576736, 53138, 0, 0, 112004, 50554, -176888, 33916, 0, 0, -52248, -88076, -291232, 0, 205632, -15776, 0, -106718, 0, 239900, 159744, 173806, 85136, 0, 6128, -134276, 148416, -4040, 0, -163884, 0, 210028, -45824, 0, -173728, 83002, 158412, 0, 0, 80338, -53136, 53940, -265192, 0, 0, 88684, 240408, -119800, 0, 7016, 73552, 0, -106120, 0, 189856, 247188, -413952, -84104, 0, 57600, -49048, 68002, -201616, 0, 312976, 0, -16592, 76020, 0, -64726, 308016, 255990, 0, 0, 49456, 103854, 12576, 209072, 0, 0, -523984, -77376, 3320, 0, -383368, -81872, 0, -24136, 0, 188540, -395272, -16316, -119496, 0, 61216, 8072, -454016, 38466, 0, -191256, 0, -168244, -81168, 0, 300720, 17572, -8896, 0, 0, 254928, 178032, 4168, 3968, 0, 0, 306768, -345144, 132432, 0, 10204, 28224, 0, 114912, 0, -125288, -102004, -3888, -144308, 0, -46512, 105968, -51194, 3996, 0, -206792, 0, -105312, 29240, 0, -75508, 11236, 78818, 0, 0, 197888, 165914, 132320, -72216, 0, 0, 127168, 66688, 381120, 0, 42336, -174830, 0, -35276, 0, 79592, 55552, -2402, 405752, 0, 125796, -53068, 99456, -157062, 0, 70692, 0, 154784, 125284, 0, 14784, -114244, 35680, 0, 0, 3766, -253156, -85392, -90368, 0, 0, 158124, -80968, 288856, 0, -9596, 180048, 0, -298304, 0, 4880, 38500, 140720, 32384, 0, -129486, -243648, -49224, 114688, 0, 63096, 0, 352832, -36816, 0, 41516, 17328, -26436, 0, 0, -286320, -38320, 62720, 186480, 0, 0, -253560, 51088, -150184, 0, 523936, 40548, 0, 24752, 0, -106352, -16584, -164272, -112560, 0, -92688, 48760, 402228, 106222, 0, -194532, 0, -211560, -69264, 0, 218108, 55200, -17888, 0, 0, 90076, -375648, -151804, -119000, 0, 0, 123876, -11552, 69752, 0, -195080, -345424, 0, -209088, 0, -489936, -12832, 309856, 132380, 0, 80922, 206392, 261390, 405664, 0, 137352, 0, 227280, -181656, 0, -211758, 524240, -25058, 0, 0, -291644, -41812, 97992, 22012, 0, 0, -337448, -108568, -83776, 0, -246976, 68678, 0, 191482, 0, 252804, -16048, 118994, 371064, 0, 42656, -17200, 112752, 320400, 0, -40052, 0, -12152, -101248, 0, -22176, -209352, -186960, 0, 0, -117164, 14112, -82460, 111616, 0, 0, 36108, -57792, 53936, 0, 33896, -44000, 0, 169980, 0, 73736, 116720, 360672, -33544, 0, -44678, 270224, 72672, -135504, 0, -45504, 0, 34336, 100502, 0, 227792, 14832, -347424, 0, 0, 30208, 25690, -222368, 62576, 0, 0, 317280, -137188, -127920, 0, 9024, -183650, 0, 182650, 0, -114240, -240680, -84088, -33080, 0, -325872, -60384, 11648, -76700, 0, 36824, 0, -128296, 65840, 0, 655072, -107742, -178560, 0, 0, -99652, 98912, 27880, 70416, 0, 0, -238524, 201056, 14824, 0, -274684, 39360, 0, -64864, 0, 16360, 43464, -207568, -88460, 0, 166232, 197120, -44650, 222252, 0, 111176, 0, -53584, -12554, 0, -142776, 443440, 235862, 0, 0, 366120, 120672, -229320, 11144, 0, 0, 31816, -207120, 550032, 0, 263912, -203230, 0, -30366, 0, -53184, 639744, 213572, -95520, 0, -250776, -151672, -36832, 42096, 0, 153396, 0, 204708, -107728, 0, 14208, 209106, -390360, 0, 0, 10626, 184228, -138948, 151200, 0, 0, 86832, -188608, -106424, 0, -8624, 259824, 0, -69696, 0, -455632, -249996, 101668, -147028, 0, 131706, 319168, 11048, -16112, 0, -146544, 0, 30048, -215102, 0, 2574, 10144, -63976, 0, 0, -186464, 107320, 734576, 227208, 0, 0, 159920, -38092, -141336, 0, 42560, 95664, 0, 166504, 0, -184972, -328888, -474096, -529776, 0, -351808, -91128, -159232, 30422, 0, -18964, 0, -107800, 87632, 0, -526560, -252218, -139456, 0, 0, -150262, -550480, 53356, 51296, 0, 0, 48536, -515616, 357500, 0, -93296, 404228, 0, 162176, 0, 507408, 18528, 42480, -39120, 0, -38390, 141288, 11202, 188496, 0, -334872, 0, 352096, -37238, 0, -378394, -44544, -72836, 0, 0, 509140, 55918, 614584, 219284, 0, 0, -166296, -4088, 318888, 0, -150904, 62488, 0, 173828, 0, 117156, -18528, 58208, -22848, 0, -563016, -355188, 307920, 202048, 0, -49464, 0, 21388, 184512, 0, -118896, 71746, -572612, 0, 0, -124178, 240896, 216652, 62808, 0, 0, -149376, 96512, 40512, 0, 284016, 501312, 0, -236620, 0, -89048, 62896, 34704, 239400, 0, 79224, -20264, -282694, -193360, 0, 101136, 0, -137072, -27718, 0, 334360, -94320, -174326, 0, 0, 125536, 102184, -422632, 208632, 0, 0, -153264, 320124, -212784, 0, 253912, 17526, 0, -27504, 0, -164012, 215888, -63142, -101336, 0, 660128, -106408, 527168, 229064, 0, 57784, 0, 54296, 23616, 0, -150064, -125894, 612896, 0, 0, -108672, 29280, 248252, -651280, 0, 0, 228428, -430888, 33064, 0, -840, 197616, 0, 369504, 0, -198456, 177700, -132320, -503528, 0, -192838, -332216, -36152, 96340, 0, -403352, 0, -535136, -55772, 0, 14394, -454548, 57692, 0, 0, -717344, 160160, 296616, -13856, 0, 0, 190080, 19856, 84576, 0, 73984, 124644, 0, 203182, 0, -1612, 35632, 509064, -132968, 0, 129472, -8612, 35152, 476, 0, 18992, 0, -45872, -393560, 0, 319760, -176134, -314464, 0, 0, -273212, -307308, 409440, -79216, 0, 0, 43496, -245616, 86864, 0, -7032, -473104, 0, 122368, 0, -20056, -156432, -309216, 209248, 0, 225450, 394464, 79786, -324752, 0, -717024, 0, -245040, 251032, 0, 65408, -79088, -171824, 0, 0, 226032, 248518, 348720, -119500, 0, 0, 281080, -25640, -78456, 0, 381424, -121166, 0, 184786, 0, 15620, 218336, -73056, 174400, 0, -84160, 536928, -1936, -484962, 0, 109532, 0, 5716, 41136, 0, -75004, -34668, -227664, 0, 0, -39080, -327152, -364352, -35072, 0, 0, -107688, 122304, -18056, 0, -329228, -98516, 0, -312896, 0, -344064, -162828, 195360, 88640, 0, -168656, 137960, 266250, -228480, 0, 56160, 0, -24984, -7724, 0, 123538, -251832, -85056, 0, 0, -18460, 235794, 26648, -131684, 0, 0, 37152, 57656, 33120, 0, -137624, -50594, 0, -127022, 0, -68856, -591248, -51954, -300328, 0, -514016, 30120, -304640, 325262, 0, -273192, 0, -94840, -181920, 0, -208496, 314824, -60684, 0, 0, -273566, 402752, -133904, 433664, 0, 0, 161244, -112816, -209064, 0, -68084, -443088, 0, -156444, 0, 42424, 49740, 1005600, -76480, 0, 105410, -598176, -253568, 58816, 0, 54048, 0, -153208, -103224, 0, -114604, -436912, 234318, 0, 0, 35056, -6816, -621968, -315896, 0, 0, 180896, 40408, -89928, 0, -105296, -24866, 0, -18720, 0, 37260, 342160, 37284, 721392, 0, -249408, -408612, -717192, 13328, 0, 137732, 0, -215600, -158784, 0, 876736, 361062, -107344, 0, 0, 160302, 111408, -65048, 78176, 0, 0, -20376, 29872, -104376, 0, 213036, 339712, 0, -274496, 0, -37600, -212324, 337552, 20008, 0, -308066, 293512, -214888, -729972, 0, -183072, 0, -362576, -230650, 0, 41750, 358416, -14526, 0, 0, -426592, -70292, 91896, -317592, 0, 0, -366912, 73888, -350512, 0, 5920, 342908, 0, -494224, 0, -77128, -842688, 82646, -225240, 0, 265916, 73156, -193504, -14458, 0, -189296, 0, 164772, -100696, 0, -53008, 127364, -38080, 0, 0, -32408, -228960, -153832, -217528, 0, 0, 147652, -197008, -33648, 0, 204912, 159520, 0, 202080, 0, 53144, 1776, -509684, 231604, 0, -25276, -239616, 112200, -415968, 0, 157560, 0, 562136, -103358, 0, 2352, -694720, -268382, 0, 0, -30240, 73000, -87600, 64492, 0, 0, -624952, 319012, -260632, 0, -494304, 69044, 0, -100294, 0, 422716, 309952, -289926, 491040, 0, 429424, -50920, -119776, 155682, 0, -312256, 0, -42672, 621840, 0, 471556, -9412, -8944, 0, 0, 300768, -320816, -226428, 52760, 0, 0, 53388, 126144, -2260, 0, -29068, -341564, 0, 83744, 0, 608112, 54488, -239232, 159768, 0, -379894, 92704, 341750, 308480, 0, -3688, 0, -184720, -108442, 0, 31418, 137152, 309490, 0, 0, 154452, 230982, -50824, -57364, 0, 0, 9048, -341408, 236632, 0, 542280, -324392, 0, -182892, 0, 94960, -532208, 326976, 59592, 0, 974400, 123736, 54512, -141456, 0, 280096, 0, -58840, 527712, 0, -104864, 86078, -51232, 0, 0, -101234, -254760, 281488, 139432, 0, 0, 438828, -16312, -221344, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "35.4.a.b", "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], [1, 0], [-4, 1], [1, 4], [10, -8], [0, 0], [4, -15], [0, 0], [-24, 34], [6, 8], [0, 0], [-7, 32], [-54, 32], [25, -4], [0, 0], [0, 0], [84, -96], [-25, -44], [-8, -26], [-18, 44], [0, 0], [0, 0], [92, -135], [-122, -68], [248, -62], [0, 0], [-108, 41], [43, -76], [0, 0], [-13, -24], [0, 0], [60, -180], [-336, 196], [249, 4], [12, 151], [0, 0], [-68, 32], [-282, -60], [160, -194], [-7, 96], [0, 0], [164, 124], [0, 0], [130, 68], [-582, 376], [0, 0], [352, 150], [-175, 132], [-684, 240], [0, 0], [0, 0], [-377, -144], [314, -240], [28, 128], [-324, 347], [0, 0], [0, 0], [334, -28], [4, 83], [616, 0], [0, 0], [-168, -108], [-600, 780], [0, 0], [1064, -352], [0, 0], [-988, 233], [76, -64], [454, -240], [-666, -556], [0, 0], [-952, 0], [400, 12], [338, 344], [1008, -42], [0, 0], [-884, 584], [0, 0], [220, -391], [507, -248], [0, 0], [-727, -120], [-408, -332], [-188, -600], [0, 0], [0, 0], [-384, -142], [-205, -76], [2344, -1006], [108, 44], [0, 0], [0, 0], [-132, 296], [-1380, 60], [964, -703], [0, 0], [1232, -1148], [1371, -220], [0, 0], [470, 136], [0, 0]]}