# Stored data for newform 432.4.a.r, downloaded from the LMFDB on 25 April 2024.
{"label": "432.4.a.r", "space_label": "432.4.a", "level": 432, "weight": 4, "hecke_orbit": 18, "hecke_orbit_code": 76561193732407728, "dim": 2, "is_polredabs": true, "nf_label": "2.2.5.1", "trace_hash": 1402328218231623280, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-176, -4, 1]], [7, [-711, -6, 1]]], "qexp_display": "q+(2+\\beta )q^{5}+(3-2\\beta )q^{7}+(-26+3\\beta )q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 6912, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 25.488825122479945, "hecke_ring_index": 12, "level_radical": 6, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 10, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [432, 1, [271, 325, 353], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "hecke_ring_index_factorization": [[2, 2], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "1.971", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.064", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "71.190", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, 1]], "trace_display": [0, 0, 4, 6], "traces": [0, 2, 0, 0, 0, 4, 0, 6, 0, 0, 0, -52, 0, 26, 0, 0, 0, 188, 0, 74, 0, 0, 0, -148, 0, 118, 0, 0, 0, 288, 0, 248, 0, 0, 0, -708, 0, 342, 0, 0, 0, 0, 0, 256, 0, 0, 0, -132, 0, 772, 0, 0, 0, 952, 0, 976, 0, 0, 0, 1004, 0, -34, 0, 0, 0, -668, 0, 866, 0, 0, 0, -776, 0, 1874, 0, 0, 0, -2316, 0, -182, 0, 0, 0, 1336, 0, 16, 0, 0, 0, 876, 0, 1518, 0, 0, 0, 3028, 0, -38, 0, 0, 0, -1440, 0, 190, 0, 0, 0, -732, 0, 260, 0, 0, 0, -2868, 0, -2096, 0, 0, 0, 1284, 0, 1930, 0, 0, 0, 1176, 0, 2008, 0, 0, 0, 880, 0, -5538, 0, 0, 0, -588, 0, 342, 0, 0, 0, -2836, 0, 3456, 0, 0, 0, 1448, 0, -5422, 0, 0, 0, -2384, 0, -4228, 0, 0, 0, 3156, 0, -906, 0, 0, 0, -708, 0, -2616, 0, 0, 0, 2304, 0, -2526, 0, 0, 0, -1752, 0, -3630, 0, 0, 0, 4284, 0, -5968, 0, 0, 0, -3612, 0, 2686, 0, 0, 0, -588, 0, 1966, 0, 0, 0, -4896, 0, -11520, 0, 0, 0, 6716, 0, -482, 0, 0, 0, 1952, 0, 6504, 0, 0, 0, 3164, 0, -4376, 0, 0, 0, 2904, 0, -7228, 0, 0, 0, -5648, 0, -624, 0, 0, 0, -8936, 0, 114, 0, 0, 0, -2776, 0, -4798, 0, 0, 0, 6160, 0, -1552, 0, 0, 0, -1720, 0, -6174, 0, 0, 0, -1624, 0, 6944, 0, 0, 0, -7300, 0, 11714, 0, 0, 0, 1252, 0, -7276, 0, 0, 0, -6784, 0, 8912, 0, 0, 0, 23040, 0, 8206, 0, 0, 0, 7788, 0, -5552, 0, 0, 0, 1676, 0, -2112, 0, 0, 0, -12308, 0, -4176, 0, 0, 0, 420, 0, 9222, 0, 0, 0, -312, 0, 1152, 0, 0, 0, 4076, 0, -1346, 0, 0, 0, 324, 0, 13190, 0, 0, 0, 7492, 0, 8202, 0, 0, 0, -15088, 0, 8898, 0, 0, 0, 312, 0, -1866, 0, 0, 0, -760, 0, 9248, 0, 0, 0, -8508, 0, 12060, 0, 0, 0, -572, 0, 10798, 0, 0, 0, -7224, 0, 7462, 0, 0, 0, -2016, 0, -4270, 0, 0, 0, 2592, 0, 17328, 0, 0, 0, 5668, 0, -12112, 0, 0, 0, 8996, 0, -4580, 0, 0, 0, 21336, 0, 8984, 0, 0, 0, 1908, 0, 3666, 0, 0, 0, 18132, 0, 19232, 0, 0, 0, -15972, 0, 7546, 0, 0, 0, 9652, 0, 24378, 0, 0, 0, -22484, 0, 980, 0, 0, 0, -19876, 0, 72, 0, 0, 0, -11624, 0, -5808, 0, 0, 0, 14212, 0, -34560, 0, 0, 0, -8484, 0, 4636, 0, 0, 0, 2236, 0, -730, 0, 0, 0, -3588, 0, -8922, 0, 0, 0, -2336, 0, 15886, 0, 0, 0, -24248, 0, -2754, 0, 0, 0, 31604, 0, 742, 0, 0, 0, 14244, 0, 24192, 0, 0, 0, -23928, 0, -14688, 0, 0, 0, -11412, 0, -28800, 0, 0, 0, 12660, 0, 14262, 0, 0, 0, 18380, 0, 2352, 0, 0, 0, 24068, 0, -13262, 0, 0, 0, 26192, 0, -4382, 0, 0, 0, 23040, 0, -38544, 0, 0, 0, -33032, 0, -5958, 0, 0, 0, -35480, 0, 3734, 0, 0, 0, 33696, 0, -19266, 0, 0, 0, -40484, 0, 448, 0, 0, 0, 6944, 0, 6864, 0, 0, 0, 18364, 0, 28218, 0, 0, 0, -15932, 0, -25082, 0, 0, 0, -29112, 0, -9632, 0, 0, 0, 1364, 0, -13864, 0, 0, 0, 15112, 0, -66192, 0, 0, 0, 30816, 0, -3676, 0, 0, 0, -52300, 0, -27706, 0, 0, 0, -996, 0, -5906, 0, 0, 0, -25884, 0, 5098, 0, 0, 0, 17748, 0, -33278, 0, 0, 0, 28548, 0, -2174, 0, 0, 0, 37136, 0, 18676, 0, 0, 0, -2936, 0, 7104, 0, 0, 0, 34336, 0, -48784, 0, 0, 0, -8904, 0, 34880, 0, 0, 0, -264, 0, 3118, 0, 0, 0, -29076, 0, -35712, 0, 0, 0, -35836, 0, -5098, 0, 0, 0, -41036, 0, -63474, 0, 0, 0, -13936, 0, 9264, 0, 0, 0, 2296, 0, -3616, 0, 0, 0, -35316, 0, 11520, 0, 0, 0, 37404, 0, 41454, 0, 0, 0, 47520, 0, 22618, 0, 0, 0, -3952, 0, 27088, 0, 0, 0, 19784, 0, -35430, 0, 0, 0, 28512, 0, -36744, 0, 0, 0, 22624, 0, 31300, 0, 0, 0, -5236, 0, -51760, 0, 0, 0, -24052, 0, -39584, 0, 0, 0, 71964, 0, 30954, 0, 0, 0, -15884, 0, 21322, 0, 0, 0, -9796, 0, 72780, 0, 0, 0, 28172, 0, -67682, 0, 0, 0, -31416, 0, 3112, 0, 0, 0, -92160, 0, 52576, 0, 0, 0, 13144, 0, 22138, 0, 0, 0, -33804, 0, 24038, 0, 0, 0, 22768, 0, -12048, 0, 0, 0, -61684, 0, 54192, 0, 0, 0, 9656, 0, 13024, 0, 0, 0, 15468, 0, 20992, 0, 0, 0, 13524, 0, -41902, 0, 0, 0, 76540, 0, -3166, 0, 0, 0, 76888, 0, -30576, 0, 0, 0, -67704, 0, 15734, 0, 0, 0, -23952, 0, 118110, 0, 0, 0, -43308, 0, 15862, 0, 0, 0, 17592, 0, 63054, 0, 0, 0, -47716, 0, 16128, 0, 0, 0, 32812, 0, -262, 0, 0, 0, 45288, 0, 9510, 0, 0, 0, -10492, 0, -42250, 0, 0, 0, 2248, 0, -60216, 0, 0, 0, -7764, 0, 96, 0, 0, 0, 12672, 0, 84448, 0, 0, 0, 58260, 0, 33442, 0, 0, 0, -11728, 0, 14944, 0, 0, 0, -63600, 0, 12280, 0, 0, 0, -31688, 0, 34578, 0, 0, 0, -4840, 0, -5996, 0, 0, 0, 98944, 0, -7962, 0, 0, 0, 15852, 0, 57600, 0, 0, 0, -26892, 0, 33002, 0, 0, 0, -16164, 0, 36336, 0, 0, 0, -22644, 0, -5790, 0, 0, 0, 15452, 0, 3578, 0, 0, 0, 6756, 0, 73026, 0, 0, 0, -78648, 0, -45456, 0, 0, 0, 40740, 0, 3504, 0, 0, 0, -26144, 0, 81742, 0, 0, 0, -41428, 0, -73876, 0, 0, 0, -74028, 0, 101936, 0, 0, 0, 75544, 0, 18202, 0, 0, 0, -36020, 0, -104832, 0, 0, 0, -9768, 0, 21084, 0, 0, 0, -46080, 0, -21086, 0, 0, 0, -11396, 0, 34970, 0, 0, 0, 9044, 0, -55426, 0, 0, 0, 89304, 0, -21488, 0, 0, 0, 78008, 0, -12304, 0, 0, 0, 69596, 0, -6186, 0, 0, 0, 21084, 0, 62266, 0, 0, 0, 96028, 0, -60308, 0, 0, 0, 78048, 0, 20864, 0, 0, 0, -15752, 0, 11568, 0, 0, 0, -84912, 0, -13126, 0, 0, 0, 95176, 0, -2604, 0, 0, 0, -117228, 0, -55884, 0, 0, 0, -25680, 0, -66032, 0, 0, 0, -35736, 0, -40320, 0, 0, 0, -100912, 0, 57890, 0, 0, 0, -23332, 0, -80226, 0, 0, 0, -35528, 0, 11930, 0, 0, 0, 49060, 0, 59808, 0, 0, 0, 75644, 0, -37278, 0, 0, 0, -80696, 0, 13608, 0, 0, 0, 5052, 0, 33314, 0, 0, 0, 26508, 0, -99178, 0, 0, 0, -57288, 0, -70336, 0, 0, 0, 56196, 0, 7582, 0, 0, 0, -9228, 0, -92208, 0, 0, 0, -34916, 0, 29592, 0, 0, 0, -492, 0, -92160, 0, 0, 0, -9772, 0, 30368, 0, 0, 0, -114760, 0, -45946, 0, 0, 0, 18948, 0, -83744, 0, 0, 0, -16128, 0, -27214, 0, 0, 0, 46172, 0, -95648, 0, 0, 0, -20424, 0, 28268, 0, 0, 0, 16988, 0, -6334, 0, 0, 0, 1204, 0, 61666, 0, 0, 0, 180476, 0, 112368, 0, 0, 0, 48384, 0, 29642, 0, 0, 0, -12456, 0, -112960, 0, 0, 0, -86064, 0, -63854, 0, 0, 0, -36224, 0, -141930, 0, 0, 0, 92160, 0, 78122, 0, 0, 0, -7464, 0, 5474, 0, 0, 0, -10212, 0, -112160, 0, 0, 0, 106340, 0, 36274, 0, 0, 0, -124668, 0, 74958, 0, 0, 0, 80580, 0, -5126, 0, 0, 0, -13508, 0, -239664, 0, 0, 0, 33120, 0, -126368, 0, 0, 0, 7792, 0, -49538, 0, 0, 0, 76328, 0, 128120, 0, 0, 0, -149448, 0, 20224, 0, 0, 0, -97956, 0, -33530, 0, 0, 0, -26468, 0, -3440, 0, 0, 0, 57688, 0, -12102, 0, 0, 0, 32788, 0, -36496, 0, 0, 0, -108980, 0, -21888, 0, 0, 0, -121560, 0, -6824, 0, 0, 0, -12408, 0, -93216, 0, 0, 0, -11124, 0, 64546, 0, 0, 0, 110728, 0, 34778, 0, 0, 0, 64644, 0, 96618, 0, 0, 0, 47152, 0, -86616, 0, 0, 0, 63716, 0, -25088, 0, 0, 0, -29136, 0, 109024, 0, 0, 0, 16384, 0, 75380, 0, 0, 0, 76608, 0, 89384, 0, 0, 0, -71580, 0, -153170, 0, 0, 0, 5196, 0, 11520, 0, 0, 0, 87996, 0, 76480, 0, 0, 0, -51268, 0, 11502, 0, 0, 0, -38068, 0, -54, 0, 0, 0, -13488, 0, -44048, 0, 0, 0, 89988, 0, 71376, 0, 0, 0, -62484, 0, -51016, 0, 0, 0, 28996, 0, -142566, 0, 0, 0, -83564, 0, 46926, 0, 0, 0, 36916, 0, -11318, 0, 0, 0, 86812, 0, 33232, 0, 0, 0, 30232, 0, 68146, 0, 0, 0, -92064, 0, 46608, 0, 0, 0, -119656, 0, 89904, 0, 0, 0, -115200, 0, 130288, 0, 0, 0, 24456, 0, -50966, 0, 0, 0, -116892, 0, 10826, 0, 0, 0, 53568, 0, 177408, 0, 0, 0, -92884, 0, 70354, 0, 0, 0, 154212, 0, -16906, 0, 0, 0, 48348, 0, -30480, 0, 0, 0, 52516, 0, 171192, 0, 0, 0, -54996, 0, -108422, 0, 0, 0, 81504, 0, 137410, 0, 0, 0, 181912, 0, -48128, 0, 0, 0, -20048, 0, -74784, 0, 0, 0, -99288, 0, 58176, 0, 0, 0, 82944, 0, -67740, 0, 0, 0, -36588, 0, 110796, 0, 0, 0, -45428, 0, -24934, 0, 0, 0, -132732, 0, 265552, 0, 0, 0, 40212, 0, 78466, 0, 0, 0, 57048, 0, 121840, 0, 0, 0, 101136, 0, 3424, 0, 0, 0, -137088, 0, -165088, 0, 0, 0, 77728, 0, 47088, 0, 0, 0, -35252, 0, -40136, 0, 0, 0, 27820, 0, 70148, 0, 0, 0, 125852, 0, 113398, 0, 0, 0, -40764, 0, -35446, 0, 0, 0, -123288, 0, 74134, 0, 0, 0, -117076, 0, 230798, 0, 0, 0, 10644, 0, -37098, 0, 0, 0, -28068, 0, -94146, 0, 0, 0, 89032, 0, 13040, 0, 0, 0, -54800, 0, 178624, 0, 0, 0, -93652, 0, 84096, 0, 0, 0, -26124, 0, -109440, 0, 0, 0, -113416, 0, -4912, 0, 0, 0, 174728, 0, -35994, 0, 0, 0, -49540, 0, 109344, 0, 0, 0, -26172, 0, -64066, 0, 0, 0, 102108, 0, 26366, 0, 0, 0, -140, 0, 2636, 0, 0, 0, 269040, 0, -96902, 0, 0, 0, -46080, 0, -58400, 0, 0, 0, -102816, 0, 61584, 0, 0, 0, -2584, 0, 65900, 0, 0, 0, -28524, 0, -147490, 0, 0, 0, -216708, 0, 231292, 0, 0, 0, 75396, 0, -126096, 0, 0, 0, 212280, 0, -52060, 0, 0, 0, 237240, 0, 76446, 0, 0, 0, 56336, 0, 88812, 0, 0, 0, -33332, 0, -31728, 0, 0, 0, -122500, 0, 93286, 0, 0, 0, 184976, 0, 253720, 0, 0, 0, -3604, 0, -69072, 0, 0, 0, 241368, 0, 252034, 0, 0, 0, -229120, 0, -120486, 0, 0, 0, 60440, 0, -342048, 0, 0, 0, 11856, 0, -46826, 0, 0, 0, -116836, 0, 63230, 0, 0, 0, -67276, 0, 161362, 0, 0, 0, 62280, 0, -57754, 0, 0, 0, -44220, 0, -70272, 0, 0, 0, -120220, 0, 93704, 0, 0, 0, -177020, 0, 16422, 0, 0, 0, -217244, 0, -25344, 0, 0, 0, -4560, 0, -181664, 0, 0, 0, 36904, 0, -72576, 0, 0, 0, -260640, 0, -282192, 0, 0, 0, -48804, 0, 11520, 0, 0, 0, -196416, 0, 102444, 0, 0, 0, 103784, 0, -272388, 0, 0, 0, 170784, 0, -204304, 0, 0, 0, -20192, 0, 18614, 0, 0, 0, -166784, 0, 151030, 0, 0, 0, 213192, 0, -60406, 0, 0, 0, 2688, 0, 56352, 0, 0, 0, 46404, 0, 26702, 0, 0, 0, 148272, 0, 29616, 0, 0, 0, 167960, 0, -165478, 0, 0, 0, 290940, 0, 152950, 0, 0, 0, -4192, 0, -76648, 0, 0, 0, -19264, 0, -76128, 0, 0, 0, 138240, 0, -176994, 0, 0, 0, -108752, 0, -187892, 0, 0, 0, -18336, 0, 159978, 0, 0, 0, -127164, 0, -259142, 0, 0, 0, -323724, 0, 94896, 0, 0, 0, 57280, 0, -98164, 0, 0, 0, 13092, 0, -27024, 0, 0, 0, -88236, 0, -11834, 0, 0, 0, 237580, 0, -25344, 0, 0, 0, 139836, 0, -347856, 0, 0, 0, -78384, 0, -278380, 0, 0, 0, 145064, 0, 61304, 0, 0, 0, -48592, 0, 11590, 0, 0, 0, -61516, 0, -132644, 0, 0, 0, -54732, 0, 22416, 0, 0, 0, 299964, 0, 224592, 0, 0, 0, -77788, 0, 81536, 0, 0, 0, -61284, 0, 72652, 0, 0, 0, 235296, 0, -46338, 0, 0, 0, -39596, 0, 131424, 0, 0, 0, -302940, 0, -140846, 0, 0, 0, 24276, 0, 173126, 0, 0, 0, -83656, 0, -261656, 0, 0, 0, -5316, 0, -136368, 0, 0, 0, -201944, 0, -202288, 0, 0, 0, 155632, 0, -82326, 0, 0, 0, 58120, 0, 29328, 0, 0, 0, 49116, 0, -161280, 0, 0, 0, 63900, 0, -11712, 0, 0, 0, 96084, 0, -319472, 0, 0, 0, -187196, 0, 174546, 0, 0, 0, 181584, 0, -53690, 0, 0, 0, -182624, 0, 1296, 0, 0, 0, -296092, 0, -198574, 0, 0, 0, -59268, 0, -147808, 0, 0, 0, 147384, 0, 261482, 0, 0, 0, 21444, 0, 49600, 0, 0, 0, -155588, 0, -157824, 0, 0, 0, -96240, 0, -163374, 0, 0, 0, 98544, 0, 299504, 0, 0, 0, 6912, 0, 193440, 0, 0, 0, 230400, 0, -128214, 0, 0, 0, -502572, 0, 266936, 0, 0, 0, 120696, 0, -51082, 0, 0, 0, -276444, 0, 43482, 0, 0, 0, 142016, 0, -106340, 0, 0, 0, 370712, 0, 3960, 0, 0, 0, 48672, 0, 50006, 0, 0, 0, 131028, 0, -377870, 0, 0, 0, -46632, 0, 113552, 0, 0, 0, 127848, 0, -28230, 0, 0, 0, 164860, 0, 36690, 0, 0, 0, 224212, 0, 236160, 0, 0, 0, -29976, 0, -65712, 0, 0, 0, 227440, 0, -128496, 0, 0, 0, -10012, 0, 155460, 0, 0, 0, -312324, 0, -230864, 0, 0, 0, 255480, 0, -178230, 0, 0, 0, -988, 0, 36126, 0, 0, 0, 68148, 0, 96128, 0, 0, 0, -104060, 0, 128634, 0, 0, 0, -123528, 0, 109762, 0, 0, 0, -72800, 0, 45480, 0, 0, 0, -462864, 0, -8570, 0, 0, 0, 61556, 0, 15584, 0, 0, 0, 286856, 0, -150262, 0, 0, 0, -81828, 0, 324864, 0, 0, 0, -183152, 0, 339256, 0, 0, 0, -27152, 0, 241920, 0, 0, 0, -63960, 0, 124478, 0, 0, 0, -216504, 0, -299344, 0, 0, 0, -369316, 0, -152498, 0, 0, 0, 103728, 0, -217278, 0, 0, 0, -223176, 0, -97448, 0, 0, 0, -162704, 0, 25968, 0, 0, 0, 27196, 0, 239568, 0, 0, 0, 267264, 0, 211966, 0, 0, 0, 111480, 0, -98898, 0, 0, 0, -23364, 0, 205686, 0, 0, 0, -134076, 0, 263904, 0, 0, 0, 297520, 0, -67872, 0, 0, 0, 123264, 0, 86496, 0, 0, 0, 391680, 0, 484150, 0, 0, 0, 160760, 0, 14758, 0, 0, 0, 192636, 0, 79056, 0, 0, 0, -10792, 0, -80674, 0, 0, 0, -188640, 0, -390060, 0, 0, 0, 344260, 0, 178592, 0, 0, 0, 98272, 0, 316590, 0, 0, 0, -12128, 0, 93360, 0, 0, 0, 110800, 0, 11158, 0, 0, 0, -659076, 0, 116650, 0, 0, 0, -17004, 0, -30272, 0, 0, 0, -504628, 0, 82794, 0, 0, 0, 33184, 0, 83210, 0, 0, 0, 147276, 0, 65664, 0, 0, 0, -57216, 0, 116278, 0, 0, 0, -72960, 0, 94910, 0, 0, 0, 306992, 0, 149232, 0, 0, 0, 61764, 0, -26384, 0, 0, 0, -72888, 0, 285906, 0, 0, 0, -213724, 0, -305078, 0, 0, 0, 177348, 0, -53312, 0, 0, 0, -24696, 0, 377056, 0, 0, 0, 212192, 0, -262976, 0, 0, 0, 126432, 0, -275346, 0, 0, 0, 257636, 0, -198366, 0, 0, 0, 53196, 0, 324150, 0, 0, 0, 77976, 0, 15898, 0, 0, 0, -29448, 0, -103680, 0, 0, 0, -419032, 0, 326184, 0, 0, 0, -191508, 0, 303538, 0, 0, 0, 163296, 0, 207622, 0, 0, 0, -251484, 0, 136124, 0, 0, 0, -112640, 0, 463136, 0, 0, 0, 49068, 0, 277254, 0, 0, 0, 55044, 0, 52506, 0, 0, 0, -174036, 0, 103778, 0, 0, 0, 157148, 0, -343326, 0, 0, 0, 448284, 0, -128660, 0, 0, 0, -206412, 0, -118336, 0, 0, 0, 83788, 0, 248784, 0, 0, 0, 100240, 0, -147386, 0, 0, 0, -184320, 0, -54884, 0, 0, 0, -36624, 0, 588672, 0, 0, 0, 169104, 0, -536000, 0, 0, 0, 55068, 0, 283528, 0, 0, 0, -102444, 0, -58704, 0, 0, 0, 106880, 0, -367980, 0, 0, 0, 137980, 0, -118768, 0, 0, 0, -307736, 0, 256600, 0, 0, 0, -72544, 0, -146638, 0, 0, 0, -311976, 0, -195322, 0, 0, 0, 301608, 0, 225958, 0, 0, 0, 247968, 0, -455552, 0, 0, 0, -383532, 0, 280392, 0, 0, 0, -118812, 0, -281440, 0, 0, 0, -286264, 0, 220180, 0, 0, 0, 266920, 0, -37392, 0, 0, 0, 277660, 0, -78832, 0, 0, 0, -176436, 0, 96214, 0, 0, 0, 374676, 0, 451026, 0, 0, 0, -114260, 0, -522, 0, 0, 0, 14484, 0, -240934, 0, 0, 0, -227184, 0, 17376, 0, 0, 0, -150852, 0, 133888, 0, 0, 0, -333844, 0, 139250, 0, 0, 0, 478264, 0, -327136, 0, 0, 0, -108000, 0, 127432, 0, 0, 0, 65560, 0, -489504, 0, 0, 0, 33812, 0, -345600, 0, 0, 0, 363776, 0, -279284, 0, 0, 0, -314192, 0, 62478, 0, 0, 0, -249428, 0, -414720, 0, 0, 0, -156636, 0, 131248, 0, 0, 0, -148880, 0, 205056, 0, 0, 0, 222832, 0, 208398, 0, 0, 0, -70248, 0, -91804, 0, 0, 0, 87488, 0, 223280, 0, 0, 0, 264860, 0, 434144, 0, 0, 0, -410472, 0, 28704, 0, 0, 0, -199284, 0, 38516, 0, 0, 0, -276484, 0, 16364, 0, 0, 0, 171360, 0, 133756, 0, 0, 0, 138240, 0, -252288, 0, 0, 0, 273968, 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": "216.4.a.f", "char_is_minimal": false, "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], [0, 0], [0, 0], [0, 0], [2, 1], [0, 0], [3, -2], [0, 0], [0, 0], [0, 0], [-26, 3], [0, 0], [13, -2], [0, 0], [0, 0], [0, 0], [94, -1], [0, 0], [37, 8], [0, 0], [0, 0], [0, 0], [-74, -5], [0, 0], [59, 4], [0, 0], [0, 0], [0, 0], [144, 8], [0, 0], [124, -8], [0, 0], [0, 0], [0, 0], [-354, -1], [0, 0], [171, 10], [0, 0], [0, 0], [0, 0], [0, -32], [0, 0], [128, 4], [0, 0], [0, 0], [0, 0], [-66, -1], [0, 0], [386, -12], [0, 0], [0, 0], [0, 0], [476, 14], [0, 0], [488, -20], [0, 0], [0, 0], [0, 0], [502, -21], [0, 0], [-17, -34], [0, 0], [0, 0], [0, 0], [-334, 9], [0, 0], [433, 16], [0, 0], [0, 0], [0, 0], [-388, 30], [0, 0], [937, -12], [0, 0], [0, 0], [0, 0], [-1158, 61], [0, 0], [-91, 26], [0, 0], [0, 0], [0, 0], [668, 46], [0, 0], [8, 92], [0, 0], [0, 0], [0, 0], [438, -21], [0, 0], [759, -32], [0, 0], [0, 0], [0, 0], [1514, 53], [0, 0], [-19, 88], [0, 0], [0, 0], [0, 0]]}