# Stored data for newform 400.4.a.x, downloaded from the LMFDB on 13 June 2025.
{"Nk2": 6400, "analytic_conductor": 23.600764002296245, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [5, -1]], "atkin_lehner_string": "+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [400, 1, [351, 101, 177], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 24, "field_disc_factorization": [[2, 3], [3, 1]], "field_poly": [-6, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[3, [-20, -4, 1]], [7, [-212, -4, 1]]], "hecke_orbit": 24, "hecke_orbit_code": 103582791496630672, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "400.4.a.x", "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": "40.4.c.a", "nf_label": "2.2.24.1", "prim_orbit_index": 1, "qexp_display": "q+(2+\\beta )q^{3}+(2-3\\beta )q^{7}+(1+4\\beta )q^{9}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "400.4.a", "trace_display": [0, 4, 0, 4], "trace_hash": 798087815089207542, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.946", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.206", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "60.277", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "traces": [0, 2, 0, 4, 0, 0, 0, 4, 0, 2, 0, -40, 0, -104, 0, 0, 0, -96, 0, -40, 0, -136, 0, 284, 0, 0, 0, 88, 0, -140, 0, -192, 0, -464, 0, 0, 0, -200, 0, -112, 0, -524, 0, 372, 0, 0, 0, 84, 0, -246, 0, -960, 0, 296, 0, 0, 0, 304, 0, -696, 0, -692, 0, -572, 0, 0, 0, 316, 0, -56, 0, -688, 0, 656, 0, 0, 0, 1072, 0, 736, 0, -742, 0, -1628, 0, 0, 0, -1048, 0, -660, 0, -496, 0, 1920, 0, 0, 0, -896, 0, -1576, 0, -708, 0, -644, 0, 0, 0, -1460, 0, -108, 0, 1232, 0, 352, 0, 0, 0, 280, 0, 2112, 0, 1210, 0, -472, 0, 0, 0, 1716, 0, 1752, 0, -120, 0, -1232, 0, 0, 0, 176, 0, -2264, 0, 3288, 0, 1312, 0, 0, 0, -1068, 0, -348, 0, 3184, 0, -3168, 0, 0, 0, -3832, 0, 5872, 0, 2440, 0, 5956, 0, 0, 0, 900, 0, 1206, 0, 1496, 0, -2664, 0, 0, 0, 2832, 0, -5224, 0, 1052, 0, -40, 0, 0, 0, 8064, 0, 2768, 0, 4992, 0, -1600, 0, 0, 0, 3000, 0, 7600, 0, 968, 0, 2024, 0, 0, 0, -2212, 0, -2272, 0, 1960, 0, -2912, 0, 0, 0, -7296, 0, -3104, 0, 3456, 0, 3084, 0, 0, 0, -7108, 0, 3012, 0, 4256, 0, 8400, 0, 0, 0, 704, 0, 1184, 0, 4900, 0, -8660, 0, 0, 0, 2848, 0, -904, 0, -8648, 0, -688, 0, 0, 0, 7680, 0, -5296, 0, -3212, 0, -3204, 0, 0, 0, -3624, 0, -4908, 0, -1888, 0, 6688, 0, 0, 0, -3624, 0, 9024, 0, -10092, 0, -7596, 0, 0, 0, -2776, 0, 7070, 0, -3712, 0, 8776, 0, 0, 0, 5152, 0, -16016, 0, -2280, 0, -5256, 0, 0, 0, 3740, 0, -5368, 0, -336, 0, -4048, 0, 0, 0, -1272, 0, 8944, 0, -1240, 0, -4224, 0, 0, 0, -14616, 0, -9192, 0, -6056, 0, 6328, 0, 0, 0, -7840, 0, -448, 0, -14592, 0, -136, 0, 0, 0, 3308, 0, 2548, 0, -6304, 0, -7104, 0, 0, 0, 9600, 0, -9872, 0, -9846, 0, 17780, 0, 0, 0, 21140, 0, 1780, 0, -15248, 0, -8984, 0, 0, 0, 5744, 0, 200, 0, 4248, 0, -180, 0, 0, 0, 4404, 0, -10236, 0, -3648, 0, 2448, 0, 0, 0, -3096, 0, 1184, 0, 1124, 0, 14592, 0, 0, 0, -9056, 0, -4244, 0, 4384, 0, -14064, 0, 0, 0, -19504, 0, -13512, 0, -5956, 0, 12564, 0, 0, 0, -5416, 0, 20672, 0, -2336, 0, -6624, 0, 0, 0, -10672, 0, 7248, 0, -2550, 0, -1644, 0, 0, 0, 14088, 0, -12804, 0, 5872, 0, -6688, 0, 0, 0, 8112, 0, 9600, 0, 12204, 0, 15212, 0, 0, 0, 2460, 0, -376, 0, 688, 0, -15504, 0, 0, 0, 21416, 0, -2752, 0, 13664, 0, -16816, 0, 0, 0, 9796, 0, 13496, 0, 9368, 0, 19008, 0, 0, 0, 3232, 0, 15128, 0, -11784, 0, -4772, 0, 0, 0, -7572, 0, -18892, 0, 14560, 0, -8672, 0, 0, 0, -26640, 0, -6384, 0, -13900, 0, -12556, 0, 0, 0, -27648, 0, 24106, 0, 16200, 0, 28400, 0, 0, 0, -9296, 0, 9528, 0, 40076, 0, -18632, 0, 0, 0, -25028, 0, 4684, 0, -3344, 0, 3776, 0, 0, 0, 3432, 0, -17328, 0, 49920, 0, 14628, 0, 0, 0, 12916, 0, -9300, 0, 26296, 0, 11520, 0, 0, 0, 32768, 0, 34048, 0, -10312, 0, -48160, 0, 0, 0, 38860, 0, 22272, 0, 12624, 0, 40736, 0, 0, 0, 19808, 0, -30704, 0, -15852, 0, 1660, 0, 0, 0, -38476, 0, 12592, 0, 1872, 0, -10616, 0, 0, 0, -16208, 0, 37480, 0, 23728, 0, 5592, 0, 0, 0, -4544, 0, -16512, 0, -12496, 0, 23504, 0, 0, 0, 11640, 0, -6832, 0, 30852, 0, -11580, 0, 0, 0, 16132, 0, -19872, 0, 3840, 0, -35304, 0, 0, 0, -17008, 0, -13608, 0, -10148, 0, 42240, 0, 0, 0, -9896, 0, 22248, 0, 3088, 0, 10496, 0, 0, 0, 15480, 0, 3968, 0, -37304, 0, -30988, 0, 0, 0, 25224, 0, -4832, 0, 34920, 0, 9520, 0, 0, 0, 15936, 0, 20832, 0, -13492, 0, 17056, 0, 0, 0, 10104, 0, 2180, 0, -2336, 0, -57216, 0, 0, 0, -50624, 0, -44576, 0, 10952, 0, 15752, 0, 0, 0, -15324, 0, -1366, 0, -33984, 0, -1032, 0, 0, 0, -9008, 0, 49848, 0, -16192, 0, 14652, 0, 0, 0, 7780, 0, -7960, 0, -53920, 0, -48400, 0, 0, 0, 35224, 0, -43424, 0, -30124, 0, 42984, 0, 0, 0, 44640, 0, 18428, 0, 0, 0, -25016, 0, 0, 0, 7072, 0, 15088, 0, 26048, 0, 7664, 0, 0, 0, 7388, 0, -42360, 0, 4160, 0, 38672, 0, 0, 0, -65592, 0, -53952, 0, -9876, 0, 22208, 0, 0, 0, -28056, 0, -31860, 0, -3816, 0, -38336, 0, 0, 0, 624, 0, 30224, 0, -62436, 0, 14684, 0, 0, 0, -60372, 0, 23732, 0, -68976, 0, 21024, 0, 0, 0, -49920, 0, -15696, 0, -26690, 0, -8088, 0, 0, 0, -43660, 0, -1128, 0, -49616, 0, -15512, 0, 0, 0, -2288, 0, -34808, 0, 33328, 0, -13620, 0, 0, 0, 87868, 0, -8576, 0, -15760, 0, -8576, 0, 0, 0, 82280, 0, 36656, 0, 7460, 0, -44252, 0, 0, 0, 40164, 0, 984, 0, 53240, 0, 23280, 0, 0, 0, 14048, 0, -23424, 0, -98688, 0, -29328, 0, 0, 0, -34420, 0, -16068, 0, 35232, 0, 13744, 0, 0, 0, -8304, 0, -11376, 0, -51704, 0, 32704, 0, 0, 0, -16964, 0, 25276, 0, 312, 0, 50784, 0, 0, 0, -14416, 0, 26656, 0, 65260, 0, -81896, 0, 0, 0, -17124, 0, -42944, 0, -45264, 0, 58800, 0, 0, 0, 60128, 0, -11744, 0, 69442, 0, 5260, 0, 0, 0, -5948, 0, -11520, 0, -47784, 0, 40400, 0, 0, 0, -352, 0, 31632, 0, -57708, 0, 1244, 0, 0, 0, -18192, 0, 39720, 0, 2752, 0, -10192, 0, 0, 0, 16632, 0, -38176, 0, -51520, 0, -34176, 0, 0, 0, 36320, 0, -25508, 0, 39232, 0, -16344, 0, 0, 0, -4256, 0, 10184, 0, 40908, 0, -38400, 0, 0, 0, -39808, 0, 65680, 0, 39120, 0, 8848, 0, 0, 0, 11712, 0, 27488, 0, 82024, 0, -45048, 0, 0, 0, 33512, 0, -32788, 0, -5256, 0, 28984, 0, 0, 0, 45536, 0, -40320, 0, 58300, 0, 53500, 0, 0, 0, 33280, 0, 14100, 0, 23616, 0, -12112, 0, 0, 0, -51232, 0, 89360, 0, -28632, 0, -35052, 0, 0, 0, -41548, 0, 62650, 0, 24840, 0, 17736, 0, 0, 0, 29424, 0, -32720, 0, 55000, 0, 95724, 0, 0, 0, -33424, 0, -42460, 0, 44880, 0, -41248, 0, 0, 0, -74104, 0, -6160, 0, 47712, 0, 30980, 0, 0, 0, -27444, 0, 32396, 0, 44704, 0, 45520, 0, 0, 0, -82160, 0, -20544, 0, 7160, 0, 4980, 0, 0, 0, 97536, 0, -41112, 0, 69888, 0, -70528, 0, 0, 0, 29712, 0, 24592, 0, -1776, 0, 20724, 0, 0, 0, -47160, 0, 42552, 0, 8488, 0, -86400, 0, 0, 0, 15760, 0, 10632, 0, 18060, 0, 32364, 0, 0, 0, 7932, 0, 27464, 0, 12912, 0, -90928, 0, 0, 0, 13360, 0, 117360, 0, 17060, 0, 92104, 0, 0, 0, 57600, 0, -99840, 0, -2160, 0, -52616, 0, 0, 0, -64384, 0, -26608, 0, -12352, 0, -84676, 0, 0, 0, -42856, 0, 124500, 0, 20512, 0, 16304, 0, 0, 0, -2152, 0, 30432, 0, 39168, 0, 2176, 0, 0, 0, -42168, 0, 17852, 0, -62168, 0, -13904, 0, 0, 0, -56592, 0, -72344, 0, 42752, 0, 47032, 0, 0, 0, 64312, 0, -52464, 0, 77952, 0, -3632, 0, 0, 0, 17096, 0, 13312, 0, 41680, 0, 61252, 0, 0, 0, 73504, 0, 56908, 0, 61912, 0, -11584, 0, 0, 0, 23584, 0, -96960, 0, -81828, 0, 56156, 0, 0, 0, -17044, 0, -85248, 0, 45664, 0, 29136, 0, 0, 0, 138144, 0, 112112, 0, -11788, 0, -456, 0, 0, 0, 85396, 0, 43032, 0, -93840, 0, 12672, 0, 0, 0, 5376, 0, 25328, 0, 58788, 0, -23040, 0, 0, 0, -30024, 0, 1472, 0, -114944, 0, 100832, 0, 0, 0, -153744, 0, -49040, 0, 42724, 0, -55800, 0, 0, 0, -96796, 0, -25818, 0, -80352, 0, -16072, 0, 0, 0, 112416, 0, -13872, 0, -68036, 0, -86952, 0, 0, 0, -48448, 0, 89512, 0, 79280, 0, 1376, 0, 0, 0, -40848, 0, -28976, 0, -136056, 0, -115736, 0, 0, 0, -22832, 0, -28164, 0, 40512, 0, 29576, 0, 0, 0, -23184, 0, -122592, 0, 26436, 0, 19116, 0, 0, 0, 78812, 0, -92252, 0, -82016, 0, 16176, 0, 0, 0, 74368, 0, 155072, 0, -19104, 0, -67136, 0, 0, 0, -61820, 0, -84344, 0, -121320, 0, 39256, 0, 0, 0, 141696, 0, -110184, 0, -86536, 0, -4544, 0, 0, 0, 12292, 0, -20608, 0, -94848, 0, 89776, 0, 0, 0, -54832, 0, 128640, 0, -81740, 0, 90676, 0, 0, 0, -3756, 0, -64100, 0, 52928, 0, 164328, 0, 0, 0, -28496, 0, -115960, 0, -20864, 0, -53436, 0, 0, 0, -35776, 0, 18248, 0, 182160, 0, 68544, 0, 0, 0, 71984, 0, -4032, 0, -38730, 0, -46364, 0, 0, 0, -13976, 0, 165088, 0, -64456, 0, -26944, 0, 0, 0, -105200, 0, -23560, 0, 40504, 0, 1660, 0, 0, 0, -99072, 0, -11564, 0, -131808, 0, -29664, 0, 0, 0, -6888, 0, -11120, 0, -42072, 0, -119960, 0, 0, 0, 149492, 0, -92840, 0, -153144, 0, -32200, 0, 0, 0, 51376, 0, -43800, 0, -92160, 0, -115156, 0, 0, 0, -129004, 0, 55048, 0, -2928, 0, -106656, 0, 0, 0, -55032, 0, 1696, 0, -59772, 0, -51576, 0, 0, 0, 516, 0, -134068, 0, -616, 0, -84392, 0, 0, 0, 77808, 0, 90456, 0, -80420, 0, 99352, 0, 0, 0, 146284, 0, -81892, 0, 4704, 0, -77728, 0, 0, 0, 5560, 0, -111312, 0, 70472, 0, 225024, 0, 0, 0, -54640, 0, 73728, 0, -87600, 0, -18208, 0, 0, 0, -139824, 0, -46976, 0, 40768, 0, -46708, 0, 0, 0, -73220, 0, 99332, 0, -75024, 0, 161344, 0, 0, 0, -69216, 0, 150560, 0, 6358, 0, 143232, 0, 0, 0, -8056, 0, 27384, 0, -5232, 0, -153736, 0, 0, 0, -100224, 0, -144072, 0, -5080, 0, 11616, 0, 0, 0, 85272, 0, -23276, 0, -18864, 0, 155120, 0, 0, 0, 95424, 0, 11136, 0, 89044, 0, 98196, 0, 0, 0, 9824, 0, 71360, 0, 153856, 0, -214776, 0, 0, 0, 147392, 0, 97680, 0, 26540, 0, 101296, 0, 0, 0, 133276, 0, -258752, 0, 96192, 0, -141008, 0, 0, 0, 76016, 0, -16064, 0, 63656, 0, -85368, 0, 0, 0, -38400, 0, 26936, 0, 124768, 0, 29496, 0, 0, 0, -240096, 0, 27328, 0, -1088, 0, 89372, 0, 0, 0, -4244, 0, 77364, 0, 26032, 0, -131792, 0, 0, 0, -156640, 0, 61440, 0, -111564, 0, 18792, 0, 0, 0, 87776, 0, 7856, 0, -37336, 0, 5016, 0, 0, 0, 114496, 0, 43200, 0, -80360, 0, 75724, 0, 0, 0, 36200, 0, 269568, 0, -19952, 0, -154464, 0, 0, 0, 90672, 0, -206800, 0, 101448, 0, 2560, 0, 0, 0, 22436, 0, -68654, 0, 34976, 0, 235584, 0, 0, 0, 13136, 0, 55752, 0, 256124, 0, -42964, 0, 0, 0, -67252, 0, 54096, 0, 184608, 0, -35488, 0, 0, 0, -120936, 0, 115216, 0, -2272, 0, 44904, 0, 0, 0, -34560, 0, -32452, 0, 130944, 0, 97120, 0, 0, 0, 99904, 0, 80296, 0, 18284, 0, 61728, 0, 0, 0, -6628, 0, -261752, 0, 41424, 0, -27664, 0, 0, 0, -2624, 0, -16560, 0, 1536, 0, -39864, 0, 0, 0, 15432, 0, 118584, 0, -108840, 0, 96984, 0, 0, 0, 47664, 0, 177936, 0, 176504, 0, -27496, 0, 0, 0, 9408, 0, -8076, 0, -54208, 0, 66432, 0, 0, 0, -19760, 0, -160368, 0, 149920, 0, -191680, 0, 0, 0, -56472, 0, 95264, 0, 108352, 0, -81432, 0, 0, 0, 58416, 0, -30136, 0, -57384, 0, 62456, 0, 0, 0, -14212, 0, 144768, 0, 144848, 0, 18896, 0, 0, 0, 140072, 0, -77344, 0, -85168, 0, -148188, 0, 0, 0, 67404, 0, 57540, 0, 116984, 0, 112160, 0, 0, 0, 88320, 0, 185728, 0, 81144, 0, -207044, 0, 0, 0, 136140, 0, 123284, 0, -169776, 0, 42640, 0, 0, 0, 68608, 0, 50640, 0, 215968, 0, -99460, 0, 0, 0, -63768, 0, -150824, 0, -39760, 0, 99208, 0, 0, 0, -303840, 0, 72736, 0, 79812, 0, -101460, 0, 0, 0, -270016, 0, 32676, 0, -113040, 0, 54096, 0, 0, 0, -14208, 0, 9152, 0, -316, 0, 154180, 0, 0, 0, -234748, 0, -18804, 0, 205440, 0, -170272, 0, 0, 0, 24528, 0, -72552, 0, -112128, 0, -140072, 0, 0, 0, -57852, 0, -36928, 0, 270464, 0, 273792, 0, 0, 0, 24736, 0, -306544, 0, 63504, 0, -265984, 0, 0, 0, 111112, 0, -117860, 0, 162472, 0, 46208, 0, 0, 0, 12688, 0, 272640, 0, -160244, 0, 40140, 0, 0, 0, -16256, 0, 185032, 0, -210784, 0, 220816, 0, 0, 0, -37696, 0, -95424, 0, -161756, 0, 60112, 0, 0, 0, -112992, 0, 28708, 0, -73968, 0, -14192, 0, 0, 0, -155040, 0, 127096, 0, 56376, 0, 213216, 0, 0, 0, 144688, 0, -188864, 0, -112352, 0, -259200, 0, 0, 0, 145808, 0, -170928, 0, -7680, 0, 149460, 0, 0, 0, 129332, 0, -1318, 0, -85408, 0, 261896, 0, 0, 0, 108528, 0, 125616, 0, 3308, 0, -84704, 0, 0, 0, -37248, 0, -155640, 0, -102272, 0, -108832, 0, 0, 0, 18760, 0, -62336, 0, -113968, 0, 186308, 0, 0, 0, 92560, 0, 136416, 0, -30888, 0, -132416, 0, 0, 0, 114896, 0, -133064, 0, 768, 0, -274944, 0, 0, 0, -98644, 0, -240652, 0, 33296, 0, -221632, 0, 0, 0, -168880, 0, 165936, 0, 61812, 0, 75688, 0, 0, 0, -165036, 0, 64944, 0, -39232, 0, -22936, 0, 0, 0, -1072, 0, 98680, 0, -163776, 0, -47772, 0, 0, 0, 239608, 0, 216068, 0, -75056, 0, -53760, 0, 0, 0, -17872, 0, -197200, 0, -195872, 0, -50616, 0, 0, 0, 273952, 0, -72960, 0, 65360, 0, -64776, 0, 0, 0, -81952, 0, 28728, 0, 48572, 0, 214912, 0, 0, 0, -20340, 0, 128740, 0, -44064, 0, -96176, 0, 0, 0, 53848, 0, -180416, 0, 76936, 0, 348288, 0, 0, 0, -147012, 0, -38408, 0, -135416, 0, -19328, 0, 0, 0, -68560, 0, -25760, 0, -93780, 0, 194988, 0, 0, 0, -1536, 0, -160220, 0, -212304, 0, -8144, 0, 0, 0, -289920, 0, -171968, 0, -113750, 0, 12432, 0, 0, 0, 76328, 0, 6784, 0, -241768, 0, -27792, 0, 0, 0, 164960, 0, 233040, 0, -77868, 0, 274588, 0, 0, 0, 71448, 0, -219608, 0, -351744, 0, -46416, 0, 0, 0, 246712, 0, -140128, 0, -62028, 0, -80152, 0, 0, 0, 272212, 0, -107520, 0, 52512, 0, -190320, 0, 0, 0, -160064, 0, -66168, 0, -229160, 0, -98952, 0, 0, 0, -122756, 0, 113224, 0, 64128, 0, -26672, 0, 0, 0, -212184, 0, -20176, 0, -165144, 0, -256512, 0, 0, 0, -76760, 0, 23904, 0, 355632, 0, -250536, 0, 0, 0, 326864, 0, 164160, 0, 197432, 0, 37372, 0, 0, 0, 171864, 0, 157696, 0, -159168, 0, 74720, 0, 0, 0, 53856, 0, -213840, 0, -51692, 0, 54140, 0, 0, 0, 26388, 0, 38292, 0, -91320, 0, -219840, 0, 0, 0, -40752, 0, 73576, 0, -143720, 0, 238380, 0, 0, 0, 48660, 0, -244892, 0, -9680, 0, 194912, 0, 0, 0, 60808, 0, 131696, 0, -142752, 0, -200256, 0, 0, 0, 56064, 0, 4120, 0, -10144, 0, 269184, 0, 0, 0, -225136, 0, -36904, 0, 83064, 0, 152744, 0, 0, 0, -385984, 0, -18456, 0, -133824, 0, 308032, 0, 0, 0, -99768, 0, 64960, 0, 301982, 0, 28736, 0, 0, 0, -143104, 0, -395428, 0, -53392, 0, -33824, 0, 0, 0, 55888, 0, -4864, 0, -227508, 0, -100488, 0, 0, 0, 16576, 0, 400256, 0, 140272, 0, -365488, 0, 0, 0, 85192, 0, -88160, 0, -74528, 0, 182920, 0, 0, 0, -216476, 0, -15880, 0, -145616, 0, 248080, 0, 0, 0, -231616, 0, -96328, 0, 257976, 0, -477060, 0, 0, 0, -119952, 0, 50304, 0, 304224, 0, 205840, 0, 0, 0, -57064, 0, 288, 0, 121896, 0, 23188, 0, 0, 0, 7284, 0, 157308, 0, 168304, 0, -73848, 0, 0, 0, -134400, 0, -42200, 0, -215744, 0, -564480, 0, 0, 0, 41884, 0, -101352, 0, 337520, 0, 353264, 0, 0, 0, 118144, 0, -24128, 0, -203096, 0, 59592, 0, 0, 0, 37968, 0, -12660, 0, 67608, 0, -88512, 0, 0, 0, 230016, 0, 293024, 0, 196124, 0, -62752, 0, 0, 0, -78760, 0, -258636, 0, -2592, 0, 156224, 0, 0, 0, 170784, 0, -47232, 0, 421792, 0, -232996, 0, 0, 0, -91308, 0, 112256, 0, -311232, 0, 245328, 0, 0, 0, 203152, 0, -63504, 0, 45104, 0, -27860, 0, 0, 0, 433208, 0, 267204, 0, -454768, 0, -35088, 0, 0, 0, 101032, 0, 205488, 0, -145244, 0, 10340, 0, 0, 0, -267320, 0, 326854, 0, -80480, 0, 93440, 0, 0, 0, 134960, 0, -197768, 0, 416256, 0, 220376, 0, 0, 0, -30720, 0, 81488, 0, 125232, 0, -175072, 0, 0, 0, -175656, 0, 174144, 0, 113160, 0, -191916, 0, 0, 0, 175232, 0, -35392, 0, 541640, 0, -172152, 0, 0, 0, 36656, 0, 110112, 0, -154132, 0, 94616, 0, 0, 0, 58296, 0, -168128, 0, 177904, 0, 101856, 0, 0, 0, -28096, 0, -8832, 0, 65832, 0, -303484, 0, 0, 0, -138812, 0, -94480, 0, 34920, 0, 351696, 0, 0, 0, 42272, 0, -128208, 0, 47480, 0, -89636, 0, 0, 0, -16512, 0, -326924, 0, 161824, 0, 24624, 0, 0, 0, -232712, 0, 213856, 0, 233064, 0, -99712, 0, 0, 0, -166572, 0, 111000, 0, 375616, 0, 61680, 0, 0, 0, 236064, 0, -180024, 0, 144768, 0, 254448, 0, 0, 0, -188744, 0, 528328, 0, 323440, 0, -183600, 0, 0, 0, -194904, 0, 244080, 0, -8424, 0, 332708, 0, 0, 0, 106512, 0, 30316, 0, -109960, 0, -141952, 0, 0, 0, -118224, 0, 1624, 0, 314240, 0, 143456, 0, 0, 0, 110360, 0, 68988, 0, -81456, 0, -224864, 0, 0, 0, -89000, 0, 182864, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 0], [2, 1], [0, 0], [0, 0], [0, 0], [2, -3], [0, 0], [1, 4], [0, 0], [-20, -8], [0, 0], [-52, 2], [0, 0], [0, 0], [0, 0], [-48, -16], [0, 0], [-20, 8], [0, 0], [-68, -4], [0, 0], [142, -13], [0, 0], [0, 0], [0, 0], [44, -18], [0, 0], [-70, -16], [0, 0], [-96, 48], [0, 0], [-232, -36], [0, 0], [0, 0], [0, 0], [-100, 34], [0, 0], [-56, -48], [0, 0], [-262, 12], [0, 0], [186, 21], [0, 0], [0, 0], [0, 0], [42, 65], [0, 0], [-123, -12], [0, 0], [-480, -80], [0, 0], [148, 110], [0, 0], [0, 0], [0, 0], [152, -4], [0, 0], [-348, 88], [0, 0], [-346, 28], [0, 0], [-286, 5], [0, 0], [0, 0], [0, 0], [158, 7], [0, 0], [-28, 116], [0, 0], [-344, -32], [0, 0], [328, -92], [0, 0], [0, 0], [0, 0], [536, 44], [0, 0], [368, -16], [0, 0], [-371, -100], [0, 0], [-814, 49], [0, 0], [0, 0], [0, 0], [-524, -102], [0, 0], [-330, -48], [0, 0], [-248, 160], [0, 0], [960, 0], [0, 0], [0, 0], [0, 0], [-448, -40], [0, 0], [-788, -88], [0, 0]]}