# Stored data for newform 2352.4.a.r, downloaded from the LMFDB on 18 April 2024.
{"label": "2352.4.a.r", "space_label": "2352.4.a", "level": 2352, "weight": 4, "hecke_orbit": 18, "hecke_orbit_code": 76561193732409648, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 426911541161278103, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-18, 1]], [11, [-36, 1]]], "qexp_display": "q-3q^{3}+18q^{5}+9q^{9}+6^{2}q^{11}+34q^{13}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 37632, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 138.77249233350193, "hecke_ring_index": 1, "level_radical": 42, "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": [2352, 1, [1471, 1765, 785, 2257], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "0.986", "prec": 17}, {"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "1.982", "prec": 17}, {"__RealLiteral__": 0, "data": "0.037", "prec": 17}, {"__RealLiteral__": 0, "data": "4.967", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, 1], [7, -1]], "trace_display": [0, -3, 18, 0], "traces": [0, 1, 0, -3, 0, 18, 0, 0, 0, 9, 0, 36, 0, 34, 0, -54, 0, -42, 0, -124, 0, 0, 0, 0, 0, 199, 0, -27, 0, 102, 0, -160, 0, -108, 0, 0, 0, 398, 0, -102, 0, 318, 0, 268, 0, 162, 0, 240, 0, 0, 0, 126, 0, -498, 0, 648, 0, 372, 0, -132, 0, -398, 0, 0, 0, 612, 0, -92, 0, 0, 0, 720, 0, 502, 0, -597, 0, 0, 0, 1024, 0, 81, 0, -204, 0, -756, 0, -306, 0, -354, 0, 0, 0, 480, 0, -2232, 0, 286, 0, 324, 0, -414, 0, 56, 0, 0, 0, -12, 0, 1478, 0, -1194, 0, 402, 0, 0, 0, 306, 0, 0, 0, -35, 0, -954, 0, 1332, 0, -1280, 0, -804, 0, 1764, 0, 0, 0, -486, 0, -2358, 0, -52, 0, -720, 0, 1224, 0, 1836, 0, 0, 0, -1746, 0, 232, 0, -378, 0, -2880, 0, -1694, 0, 1494, 0, 0, 0, 2932, 0, -1944, 0, 1176, 0, -1041, 0, -1116, 0, -870, 0, 0, 0, 396, 0, 2316, 0, 106, 0, 1194, 0, 7164, 0, -1512, 0, 0, 0, 1128, 0, 4034, 0, -1836, 0, -1314, 0, 5096, 0, 276, 0, 0, 0, 5724, 0, 0, 0, -4464, 0, 3076, 0, -2160, 0, 4824, 0, 0, 0, -1506, 0, -1428, 0, -1888, 0, 1791, 0, -4716, 0, 1690, 0, 0, 0, 138, 0, 4320, 0, -3072, 0, -1896, 0, 3598, 0, -243, 0, 0, 0, -4216, 0, 612, 0, -3060, 0, 0, 0, 2268, 0, 6822, 0, 0, 0, 918, 0, -2592, 0, -8964, 0, 1062, 0, -8214, 0, -5344, 0, 0, 0, 7164, 0, -6514, 0, -1440, 0, 6618, 0, 3260, 0, 6696, 0, 0, 0, -3149, 0, -858, 0, -5118, 0, -2376, 0, -972, 0, 0, 0, 0, 0, 1242, 0, -7164, 0, 452, 0, -168, 0, 5016, 0, -5402, 0, 0, 0, 10086, 0, 3672, 0, 36, 0, 5208, 0, 6766, 0, -4434, 0, 0, 0, 8044, 0, 3582, 0, -1656, 0, 4178, 0, -1206, 0, -5760, 0, 0, 0, 0, 0, -156, 0, 12418, 0, -918, 0, 7830, 0, 12960, 0, 0, 0, 9312, 0, 8517, 0, 105, 0, 9036, 0, -3760, 0, 2862, 0, 0, 0, 5870, 0, -3996, 0, 3468, 0, 1852, 0, 3840, 0, 2160, 0, 0, 0, 2412, 0, -6786, 0, 0, 0, -5292, 0, 18432, 0, 6514, 0, 0, 0, 3330, 0, -5440, 0, 1458, 0, 14328, 0, 5398, 0, 7074, 0, 0, 0, -3672, 0, 156, 0, 13092, 0, -322, 0, 2160, 0, -8358, 0, 0, 0, -3672, 0, -2616, 0, -4322, 0, -5508, 0, 0, 0, -9016, 0, 0, 0, 5268, 0, -6372, 0, 5238, 0, -5310, 0, 11448, 0, -696, 0, 0, 0, 15770, 0, 1134, 0, 5370, 0, 3328, 0, 8640, 0, 4548, 0, 0, 0, 5082, 0, 9648, 0, -24676, 0, -4482, 0, -8064, 0, 13532, 0, 0, 0, 5148, 0, -16616, 0, -8796, 0, 7140, 0, -4284, 0, 5832, 0, 0, 0, 9124, 0, -3528, 0, -6552, 0, -7452, 0, 3123, 0, -2790, 0, 0, 0, 3348, 0, 1008, 0, 8640, 0, 2610, 0, 14862, 0, 17660, 0, 0, 0, 6720, 0, -12167, 0, -1188, 0, 10812, 0, -216, 0, -6948, 0, 0, 0, -19834, 0, -318, 0, 26604, 0, -20972, 0, -3582, 0, -12648, 0, 0, 0, -21492, 0, 21174, 0, 9112, 0, 4536, 0, -17772, 0, 7236, 0, 0, 0, 8250, 0, -20756, 0, -3384, 0, 0, 0, -2, 0, -12102, 0, 0, 0, -17928, 0, 5508, 0, 26364, 0, 19840, 0, 3942, 0, -2298, 0, 0, 0, -15288, 0, -3072, 0, -24554, 0, -828, 0, -630, 0, 16832, 0, 0, 0, 8160, 0, -2482, 0, -17172, 0, -15798, 0, -15460, 0, 0, 0, 0, 0, -899, 0, 13392, 0, -16716, 0, 7720, 0, -9228, 0, -23040, 0, 0, 0, 6480, 0, -17262, 0, -12220, 0, -14472, 0, 13560, 0, -4752, 0, 0, 0, 23094, 0, 31752, 0, 4518, 0, -22548, 0, -17462, 0, 4284, 0, 0, 0, 0, 0, 5664, 0, -14328, 0, -22462, 0, -5373, 0, 25554, 0, 0, 0, 14148, 0, -9276, 0, -42444, 0, -5070, 0, -16932, 0, 27380, 0, 0, 0, -936, 0, -13356, 0, -414, 0, 25830, 0, -49352, 0, -12960, 0, 0, 0, -6226, 0, 9216, 0, 0, 0, 22032, 0, 5688, 0, -15072, 0, 0, 0, -10794, 0, 20298, 0, -32920, 0, 729, 0, -11256, 0, 6946, 0, 0, 0, -3312, 0, 2356, 0, 12648, 0, 23520, 0, -31428, 0, -1836, 0, 0, 0, -3008, 0, 9180, 0, 4176, 0, -20770, 0, 0, 0, -11538, 0, 0, 0, -6804, 0, -4488, 0, -8498, 0, -20466, 0, 32322, 0, -31840, 0, 0, 0, -39432, 0, 25920, 0, -2754, 0, -30492, 0, 26228, 0, 7776, 0, 0, 0, -13532, 0, 26892, 0, 43338, 0, -10080, 0, -3186, 0, 18072, 0, 0, 0, 24642, 0, -28902, 0, 27164, 0, 16032, 0, 52776, 0, -33232, 0, 0, 0, -17202, 0, 5992, 0, -21492, 0, -25884, 0, 1474, 0, 19542, 0, 0, 0, 21168, 0, 4320, 0, 33528, 0, -13985, 0, -19854, 0, -18738, 0, 0, 0, -9780, 0, 0, 0, -1190, 0, -20088, 0, -34578, 0, -44404, 0, 0, 0, 38328, 0, -15660, 0, 9447, 0, 36864, 0, -3128, 0, 2574, 0, 0, 0, -38842, 0, 15354, 0, 35046, 0, -14204, 0, 7128, 0, -26136, 0, 0, 0, 2916, 0, -29760, 0, 41688, 0, 0, 0, -16320, 0, 20916, 0, 0, 0, 1908, 0, 9052, 0, -3726, 0, -5016, 0, -7344, 0, 21492, 0, 0, 0, -44552, 0, -1356, 0, 24480, 0, 79202, 0, 504, 0, -24234, 0, 0, 0, -15048, 0, -27216, 0, 13894, 0, 16206, 0, -46758, 0, 0, 0, 0, 0, -13812, 0, 17068, 0, -30258, 0, -58518, 0, 20304, 0, -11016, 0, 0, 0, -4191, 0, -108, 0, 72612, 0, -19640, 0, -15624, 0, -58308, 0, 0, 0, -20298, 0, -23550, 0, -12744, 0, 13302, 0, 15768, 0, -23652, 0, 0, 0, 0, 0, -35264, 0, -24132, 0, 91728, 0, 29338, 0, -10746, 0, 0, 0, 5544, 0, 4968, 0, 61752, 0, -18286, 0, -12534, 0, 64098, 0, 0, 0, 3618, 0, -13212, 0, 33730, 0, 17280, 0, 63282, 0, 34816, 0, 0, 0, -29520, 0, 17786, 0, 0, 0, 16716, 0, -34432, 0, 468, 0, 0, 0, -80352, 0, -37254, 0, -978, 0, 32092, 0, 2754, 0, 55368, 0, 0, 0, -23490, 0, 14334, 0, 20072, 0, -38880, 0, 10296, 0, -7454, 0, 0, 0, 40596, 0, 53332, 0, -27936, 0, -6936, 0, 0, 0, -25551, 0, 0, 0, -55136, 0, -315, 0, 22260, 0, -33874, 0, -27108, 0, 10878, 0, 0, 0, 11280, 0, 49272, 0, -25704, 0, -8586, 0, -4734, 0, -14904, 0, 0, 0, -33984, 0, -2266, 0, -17610, 0, 16368, 0, 3908, 0, 11988, 0, 0, 0, 43130, 0, -10404, 0, 2016, 0, -84888, 0, -5556, 0, 3864, 0, 0, 0, -11520, 0, 30420, 0, -63680, 0, -6480, 0, -3792, 0, -46802, 0, 0, 0, -12036, 0, 49352, 0, -7236, 0, -8940, 0, 2484, 0, 20358, 0, 0, 0, 17188, 0, 0, 0, 47760, 0, -432, 0, 15876, 0, -71286, 0, 0, 0, -55296, 0, -25044, 0, 32436, 0, -19542, 0, 14334, 0, -34128, 0, 0, 0, 53208, 0, 2450, 0, -9990, 0, 64764, 0, -30240, 0, 16320, 0, 0, 0, 52310, 0, -4374, 0, 6918, 0, 0, 0, -42984, 0, -312, 0, 0, 0, -16194, 0, 42294, 0, -1888, 0, -21222, 0, -75888, 0, -10118, 0, 0, 0, -21084, 0, 14472, 0, 11016, 0, 27336, 0, 19726, 0, -468, 0, 0, 0, -55080, 0, -39276, 0, -49284, 0, 9724, 0, 966, 0, 0, 0, 0, 0, -6480, 0, -50880, 0, 11408, 0, 25074, 0, 2874, 0, 2288, 0, 0, 0, 30492, 0, 122796, 0, 11016, 0, 39738, 0, 39548, 0, 7848, 0, 0, 0, 24914, 0, 12966, 0, 24258, 0, 59272, 0, 16524, 0, -70356, 0, 0, 0, 0, 0, -14076, 0, -46656, 0, 27048, 0, -55320, 0, 5110, 0, 0, 0, -99102, 0, 79792, 0, -15804, 0, -49176, 0, -42880, 0, 19116, 0, 0, 0, 1904, 0, -15714, 0, -43008, 0, -147852, 0, 15930, 0, -89280, 0, 0, 0, -34344, 0, -96192, 0, 0, 0, 2088, 0, -20682, 0, 24480, 0, 0, 0, -76944, 0, 107751, 0, -47310, 0, 33990, 0, 47952, 0, -3402, 0, 0, 0, -22642, 0, -16110, 0, -117252, 0, -62248, 0, -9984, 0, -408, 0, 0, 0, -25920, 0, -46080, 0, -34792, 0, -13644, 0, 0, 0, 119124, 0, 0, 0, 6498, 0, 8568, 0, -15246, 0, 58680, 0, 50252, 0, -28944, 0, 0, 0, -15104, 0, 74028, 0, 40020, 0, -35170, 0, 13446, 0, -104802, 0, 0, 0, 24192, 0, 76008, 0, 63504, 0, -40596, 0, -56682, 0, 3944, 0, 0, 0, 108372, 0, -23578, 0, -15444, 0, -38400, 0, -45484, 0, 49848, 0, 0, 0, -92124, 0, 26388, 0, 13668, 0, -64064, 0, -21420, 0, -26268, 0, 0, 0, 12852, 0, -23910, 0, 83468, 0, -17496, 0, 8784, 0, -46802, 0, 0, 0, 43086, 0, 0, 0, -27372, 0, 21396, 0, -126976, 0, 10584, 0, 0, 0, -84888, 0, 19656, 0, -56232, 0, 14868, 0, 22356, 0, 126564, 0, 0, 0, -9369, 0, 85500, 0, -79202, 0, 8370, 0, -1872, 0, 30764, 0, 0, 0, 8136, 0, -50796, 0, -10044, 0, 0, 0, 11576, 0, -3024, 0, 0, 0, 25814, 0, -25920, 0, -8682, 0, 90288, 0, -7830, 0, 93480, 0, 0, 0, -44586, 0, -97236, 0, 67664, 0, -52980, 0, -61260, 0, -1190, 0, 0, 0, 25296, 0, -92900, 0, -20160, 0, -21528, 0, 181548, 0, 36501, 0, 0, 0, 106664, 0, 3564, 0, 66096, 0, 47558, 0, -32436, 0, -51402, 0, 0, 0, 648, 0, -84432, 0, -27722, 0, 20844, 0, -5814, 0, 93744, 0, 0, 0, 81564, 0, -97090, 0, 59502, 0, 45288, 0, -58804, 0, 954, 0, 0, 0, 0, 0, -79812, 0, 74754, 0, -62856, 0, 62916, 0, 79680, 0, 0, 0, 10746, 0, -12012, 0, -43520, 0, 37944, 0, 144792, 0, 54502, 0, 0, 0, 8352, 0, -25184, 0, 64476, 0, -10164, 0, -99830, 0, -63522, 0, 0, 0, -18308, 0, -27336, 0, 0, 0, 32203, 0, -13608, 0, 75204, 0, 0, 0, 53316, 0, 43896, 0, 99538, 0, -21708, 0, 105126, 0, -81772, 0, 0, 0, 59976, 0, -103680, 0, -24750, 0, -124074, 0, -13464, 0, 62268, 0, 0, 0, 17388, 0, 10152, 0, -14898, 0, -22916, 0, 0, 0, -60984, 0, 0, 0, 6, 0, -54690, 0, -2808, 0, 36306, 0, 95520, 0, -31790, 0, 0, 0, 223524, 0, -26444, 0, 53784, 0, -2352, 0, -84890, 0, -16524, 0, 0, 0, 115504, 0, -79092, 0, 85224, 0, 140940, 0, -59520, 0, -40596, 0, 0, 0, -11826, 0, 143280, 0, -109154, 0, 6894, 0, -80172, 0, -130408, 0, 0, 0, -78156, 0, 22790, 0, 45864, 0, 105552, 0, 167616, 0, 9216, 0, 0, 0, -21670, 0, 73662, 0, 153306, 0, -1768, 0, 2484, 0, -15132, 0, 0, 0, 1890, 0, 0, 0, 504, 0, -50496, 0, -32928, 0, 99898, 0, 0, 0, 21120, 0, -105896, 0, -24480, 0, -67680, 0, 42336, 0, 7446, 0, 0, 0, -35464, 0, 51516, 0, 24600, 0, -7683, 0, 47394, 0, -62076, 0, 0, 0, 46380, 0, -37476, 0, -77510, 0, 0, 0, 105660, 0, -143908, 0, 0, 0, 81384, 0, -11086, 0, 2697, 0, 92238, 0, -81016, 0, -40176, 0, 0, 0, 62424, 0, 50148, 0, -23706, 0, 63680, 0, -23160, 0, 33336, 0, 0, 0, 27684, 0, 55638, 0, -31320, 0, 69120, 0, 14676, 0, 0, 0, 0, 0, -28998, 0, 38880, 0, -19440, 0, 51336, 0, -16884, 0, 51786, 0, 0, 0, 76320, 0, 36660, 0, 136140, 0, -28330, 0, 43416, 0, -59364, 0, 0, 0, -40680, 0, -9384, 0, -122148, 0, 14256, 0, 65994, 0, -160, 0, 0, 0, 0, 0, -6944, 0, -69282, 0, -198204, 0, 7888, 0, -95256, 0, 0, 0, 83376, 0, -13554, 0, 7602, 0, 203776, 0, 67644, 0, 47532, 0, 0, 0, 52386, 0, 117252, 0, 28244, 0, -12852, 0, 3816, 0, 106198, 0, 0, 0, 65046, 0, -156800, 0, 0, 0, -35700, 0, 59940, 0, -16992, 0, 0, 0, -99380, 0, 42984, 0, -97920, 0, -98782, 0, 67386, 0, 64320, 0, 0, 0, 16119, 0, -77004, 0, 61810, 0, -76662, 0, 1488, 0, 257904, 0, 0, 0, -12240, 0, -57596, 0, -42444, 0, 97164, 0, 0, 0, 27828, 0, 0, 0, 52958, 0, 127332, 0, 1470, 0, 73440, 0, 15210, 0, 28464, 0, 0, 0, 50796, 0, -121170, 0, -183272, 0, -82140, 0, -40596, 0, 14720, 0, 0, 0, -140142, 0, -51356, 0, 2808, 0, -68832, 0, 148246, 0, 40068, 0, 0, 0, 235656, 0, 1242, 0, -115548, 0, 40608, 0, -77490, 0, -5796, 0, 0, 0, 148056, 0, 125304, 0, -140402, 0, 38880, 0, 51204, 0, 99688, 0, 0, 0, 145224, 0, -55944, 0, 18678, 0, 105954, 0, -27628, 0, -27648, 0, 0, 0, 5546, 0, 0, 0, -108486, 0, 93472, 0, -66096, 0, -49848, 0, 0, 0, -17064, 0, 42714, 0, -47088, 0, 45216, 0, 53760, 0, -189074, 0, 0, 0, -77796, 0, -47304, 0, 32382, 0, 39984, 0, -158364, 0, -60894, 0, 0, 0, 11284, 0, 98760, 0, -52536, 0, 0, 0, -2187, 0, 183456, 0, 0, 0, 33768, 0, -162288, 0, -110092, 0, -20838, 0, -115200, 0, 143228, 0, 0, 0, -145608, 0, -46223, 0, 9936, 0, 702, 0, 94824, 0, -7068, 0, 0, 0, -41290, 0, -37944, 0, -70446, 0, -74088, 0, -70560, 0, 0, 0, 0, 0, 94284, 0, 57990, 0, -15712, 0, 5508, 0, -43164, 0, -95580, 0, 0, 0, -29580, 0, 132460, 0, 9024, 0, 206064, 0, -158404, 0, -27540, 0, 0, 0, -80320, 0, -12528, 0, -166500, 0, 145334, 0, 62310, 0, 179622, 0, 0, 0, 0, 0, -133464, 0, 147670, 0, 34614, 0, 283860, 0, 81488, 0, 0, 0, 104448, 0, 31502, 0, 20412, 0, -174246, 0, 4340, 0, 13464, 0, 0, 0, 96660, 0, 25494, 0, -121470, 0, -81272, 0, 61398, 0, 59904, 0, 0, 0, -96966, 0, 110736, 0, 0, 0, 95520, 0, 78744, 0, 99036, 0, 0, 0, 76902, 0, 81864, 0, 118296, 0, -177732, 0, 189754, 0, -77760, 0, 0, 0, 84076, 0, 8262, 0, -28752, 0, 3604, 0, 91476, 0, 158802, 0, 0, 0, -78684, 0, 2184, 0, 173664, 0, -23328, 0, 0, 0, -65788, 0, 0, 0, -165168, 0, 141338, 0, 40596, 0, -2442, 0, -50848, 0, -80676, 0, 0, 0, 27758, 0, -130014, 0, 97326, 0, -145152, 0, 30240, 0, 42480, 0, 0, 0, 9558, 0, 243576, 0, -20808, 0, -54216, 0, 48732, 0, 158720, 0, 0, 0, 25362, 0, -41976, 0, -73926, 0, -52464, 0, 56914, 0, 86706, 0, 0, 0, -51408, 0, -81492, 0, -299088, 0, -137122, 0, -48096, 0, 33582, 0, 0, 0, -158328, 0, -110328, 0, -163840, 0, 99696, 0, -67968, 0, 128520, 0, 0, 0, -223836, 0, 0, 0, 51606, 0, -77112, 0, -177244, 0, -17976, 0, 0, 0, -4102, 0, 64476, 0, -30486, 0, -36616, 0, 77652, 0, 38352, 0, 0, 0, -4422, 0, -218736, 0, -119520, 0, -58626, 0, 164232, 0, -169776, 0, 0, 0, -126564, 0, 45160, 0, -63504, 0, 0, 0, 137156, 0, -12960, 0, 0, 0, -117936, 0, -100584, 0, 60840, 0, 49610, 0, 41955, 0, -82386, 0, 0, 0, 59562, 0, 2268, 0, 73332, 0, 56214, 0, -35376, 0, -217924, 0, 0, 0, -185544, 0, -50220, 0, 29340, 0, -143250, 0, 59096, 0, 0, 0, 0, 0, -212506, 0, 3570, 0, -44676, 0, 4968, 0, 60264, 0, -9744, 0, 0, 0, 103734, 0, 32640, 0, 11144, 0, 133212, 0, -122892, 0, -36108, 0, 0, 0, 155520, 0, 173264, 0, -114984, 0, 92520, 0, 7486, 0, 46980, 0, 0, 0, 0, 0, -28341, 0, 292392, 0, 267516, 0, -110592, 0, -71850, 0, 0, 0, 9384, 0, 317880, 0, 14902, 0, -7722, 0, 37962, 0, -106664, 0, 0, 0, 286560, 0, -68256, 0, 116526, 0, -68358, 0, 120960, 0, -46062, 0, 0, 0, 6448, 0, -105138, 0, -219006, 0, 27160, 0, 42612, 0, 129528, 0, 0, 0, -21384, 0, -226494, 0, 243380, 0, 78408, 0, -29064, 0, 194616, 0, 0, 0, 71148, 0, -53552, 0, -8748, 0, -2388, 0, 30490, 0, 89280, 0, 0, 0, 143548, 0, -125064, 0, 220416, 0, -94174, 0, 0, 0, -18798, 0, 0, 0, 48960, 0, 107796, 0, 199796, 0, -62748, 0, -357012, 0, -49804, 0, 0, 0, -43440, 0, -59254, 0, -5724, 0, -151776, 0, 64784, 0, -27156, 0, 0, 0, 294122, 0, 11178, 0, -40242, 0, 168748, 0, 15048, 0, -377496, 0, 0, 0, 22032, 0, 242958, 0, 104584, 0, -64476, 0, -29256, 0, 23506, 0, 0, 0, 43842, 0, -227664, 0, 133656, 0, 56640, 0, -110160, 0, 4068, 0, 0, 0, 37600, 0, -73440, 0, -123144, 0, -31680, 0, -237606, 0, -168786, 0, 0, 0, -1512, 0, 0, 0, 381132, 0, 72702, 0, -137310, 0, 188552, 0, 0, 0, 164016, 0, 110486, 0, 45144, 0, 157170, 0, 67268, 0, 81648, 0, 0, 0, 99127, 0, -41682, 0, 29172, 0, -319896, 0, -48618, 0, -227964, 0, 0, 0, 140274, 0, 79998, 0, 245592, 0, 0, 0, 216504, 0, -129170, 0, 0, 0, 13038, 0, -49392, 0, 41436, 0, -197244, 0, 148500, 0, -51204, 0, 0, 0, -275852, 0, 90774, 0, -373608, 0, 112538, 0, 175554, 0, -98166, 0, 0, 0, -60912, 0, -95520, 0, -28768, 0, 33048, 0, 43722, 0, 0, 0, 0, 0, -44904, 0, -24656, 0, 12573, 0, -36, 0, -44584, 0, 324, 0, 0, 0, -93312, 0, -217836, 0, -41130, 0, -64192, 0, 58920, 0, 7704, 0, 0, 0, 46872, 0, -245754, 0, 228960, 0, 174924, 0, -322704, 0, -19910, 0, 0, 0, 0, 0, 407552, 0, 60894, 0, 48696, 0, -42228, 0, 70650, 0, 0, 0, 474552, 0, 38232, 0, -119460, 0, 36540, 0, -39906, 0, 357120, 0, 0, 0, -47304, 0, -160344, 0, 183382, 0, 70956, 0, -141654, 0, -295704, 0, 0, 0, -130596, 0, -41364, 0, 0, 0, 23994, 0, -157156, 0, 105792, 0, 0, 0, 57460, 0, 72396, 0, -192384, 0, 210056, 0, -275184, 0, 5712, 0, 0, 0, -88014, 0, 159636, 0, -55296, 0, 32238, 0, 81864, 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": "21.4.a.a", "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], [1], [0], [-3], [0], [18], [0], [0], [0], [9], [0], [36], [0], [34], [0], [-54], [0], [-42], [0], [-124], [0], [0], [0], [0], [0], [199], [0], [-27], [0], [102], [0], [-160], [0], [-108], [0], [0], [0], [398], [0], [-102], [0], [318], [0], [268], [0], [162], [0], [240], [0], [0], [0], [126], [0], [-498], [0], [648], [0], [372], [0], [-132], [0], [-398], [0], [0], [0], [612], [0], [-92], [0], [0], [0], [720], [0], [502], [0], [-597], [0], [0], [0], [1024], [0], [81], [0], [-204], [0], [-756], [0], [-306], [0], [-354], [0], [0], [0], [480], [0], [-2232], [0], [286], [0], [324], [0]]}