# Stored data for newform 2352.4.a.m, downloaded from the LMFDB on 23 April 2024.
{"label": "2352.4.a.m", "space_label": "2352.4.a", "level": 2352, "weight": 4, "hecke_orbit": 13, "hecke_orbit_code": 54043195595557168, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2303874499501799621, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-8, 1]], [11, [40, 1]]], "qexp_display": "q-3q^{3}+8q^{5}+9q^{9}-40q^{11}+4q^{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": "0.002", "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": "0.066", "prec": 17}, {"__RealLiteral__": 0, "data": "0.982", "prec": 17}, {"__RealLiteral__": 0, "data": "0.106", "prec": 17}, {"__RealLiteral__": 0, "data": "1.940", "prec": 17}, {"__RealLiteral__": 0, "data": "0.257", "prec": 17}, {"__RealLiteral__": 0, "data": "4.831", "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, 8, 0], "traces": [0, 1, 0, -3, 0, 8, 0, 0, 0, 9, 0, -40, 0, 4, 0, -24, 0, -84, 0, -148, 0, 0, 0, -84, 0, -61, 0, -27, 0, 58, 0, 136, 0, 120, 0, 0, 0, -222, 0, -12, 0, 420, 0, 164, 0, 72, 0, -488, 0, 0, 0, 252, 0, 478, 0, -320, 0, 444, 0, -548, 0, 692, 0, 0, 0, 32, 0, 908, 0, 252, 0, 524, 0, 440, 0, 183, 0, 0, 0, -1216, 0, 81, 0, 684, 0, -672, 0, -174, 0, 604, 0, 0, 0, -408, 0, -1184, 0, -832, 0, -360, 0, 464, 0, 632, 0, 0, 0, 160, 0, -2198, 0, 666, 0, 770, 0, -672, 0, 36, 0, 0, 0, 269, 0, -1260, 0, -1488, 0, 184, 0, -492, 0, 1452, 0, 0, 0, -216, 0, 646, 0, 3012, 0, 1464, 0, -160, 0, 464, 0, 0, 0, -3170, 0, 1880, 0, -756, 0, 1088, 0, 604, 0, -1434, 0, 0, 0, -1116, 0, 960, 0, 1784, 0, -2181, 0, -1332, 0, -344, 0, 0, 0, 1644, 0, -1392, 0, 4052, 0, -2076, 0, -1776, 0, 3360, 0, 0, 0, 3108, 0, 50, 0, -96, 0, -162, 0, -1544, 0, -2724, 0, 0, 0, 3360, 0, -756, 0, 5920, 0, 1204, 0, -1572, 0, 1312, 0, 0, 0, -1320, 0, -336, 0, -2000, 0, -549, 0, -388, 0, 4180, 0, 0, 0, -1322, 0, -3904, 0, 3648, 0, -2412, 0, -4336, 0, -243, 0, 0, 0, -592, 0, -2052, 0, -764, 0, 3360, 0, 2016, 0, 4300, 0, 0, 0, 522, 0, 3860, 0, 3824, 0, -1812, 0, -2800, 0, 4880, 0, 0, 0, 2440, 0, -6674, 0, 1224, 0, -9402, 0, 9100, 0, 3552, 0, 0, 0, 2143, 0, 2496, 0, 5952, 0, -4384, 0, 1080, 0, -336, 0, 0, 0, -1392, 0, 5536, 0, 3004, 0, -1896, 0, -688, 0, 5592, 0, 0, 0, -2922, 0, -2320, 0, -480, 0, 12432, 0, -244, 0, 6594, 0, 0, 0, 7492, 0, -1998, 0, 7264, 0, 10766, 0, -2310, 0, -5440, 0, 0, 0, 2016, 0, 3984, 0, -180, 0, -108, 0, -10428, 0, 4192, 0, 0, 0, -8684, 0, 15045, 0, -807, 0, 3520, 0, -5648, 0, 3780, 0, 0, 0, -2546, 0, 4464, 0, 232, 0, -8268, 0, -552, 0, 10872, 0, 0, 0, 1476, 0, 10434, 0, 7056, 0, -4356, 0, -9728, 0, -3044, 0, 0, 0, 8910, 0, 544, 0, 648, 0, 8880, 0, 5616, 0, -1938, 0, 0, 0, 5472, 0, -9036, 0, 8932, 0, -5538, 0, -4392, 0, 5124, 0, 0, 0, 480, 0, 6700, 0, -5048, 0, -1392, 0, 12432, 0, 1344, 0, 0, 0, 4392, 0, 4832, 0, 9510, 0, 3666, 0, -16800, 0, -5640, 0, 0, 0, 26, 0, 2268, 0, 7656, 0, -12608, 0, -3264, 0, 3068, 0, 0, 0, -1812, 0, -6560, 0, 9028, 0, 4302, 0, -6456, 0, -888, 0, 0, 0, -6656, 0, -11896, 0, 3348, 0, 264, 0, -4872, 0, -2880, 0, 0, 0, 2628, 0, -5352, 0, 13568, 0, 3712, 0, 6543, 0, 20656, 0, 0, 0, 3996, 0, 5056, 0, 19520, 0, 1032, 0, 3628, 0, -4852, 0, 0, 0, -11424, 0, -5111, 0, -4932, 0, 1680, 0, 1280, 0, 4176, 0, 0, 0, -7130, 0, -12156, 0, -17584, 0, 12788, 0, 6228, 0, -8584, 0, 0, 0, 5328, 0, 2406, 0, 656, 0, -10080, 0, 25412, 0, 6160, 0, 0, 0, -9690, 0, -5604, 0, -9324, 0, 5124, 0, -21568, 0, -150, 0, 0, 0, -19120, 0, 288, 0, -20300, 0, -20128, 0, 486, 0, 13812, 0, 0, 0, 4632, 0, 21996, 0, 8368, 0, 8172, 0, 2152, 0, -21504, 0, 0, 0, -1952, 0, -10270, 0, -10080, 0, 28358, 0, -16292, 0, 2268, 0, 0, 0, -4279, 0, -17760, 0, 18648, 0, -11256, 0, -3612, 0, 1472, 0, 0, 0, 4716, 0, 15518, 0, 10452, 0, -3936, 0, -72, 0, 21920, 0, 0, 0, 11962, 0, 11616, 0, 3960, 0, 6016, 0, 26068, 0, 1008, 0, 0, 0, -4872, 0, 6000, 0, -27680, 0, -20530, 0, 1647, 0, -10056, 0, 0, 0, 1164, 0, -6152, 0, 5168, 0, -12540, 0, 1912, 0, 14716, 0, 0, 0, 24096, 0, -35280, 0, 3966, 0, 28202, 0, 32856, 0, 11712, 0, 0, 0, 22114, 0, -10944, 0, -11424, 0, -1280, 0, 7236, 0, 9288, 0, 0, 0, 13008, 0, -3538, 0, -23848, 0, 729, 0, -13776, 0, -34756, 0, 0, 0, -36320, 0, -26044, 0, 1776, 0, -36204, 0, -25360, 0, 6156, 0, 0, 0, 11424, 0, 2292, 0, 15040, 0, -16622, 0, -10080, 0, -38524, 0, 0, 0, -6048, 0, -2192, 0, -18440, 0, -12900, 0, -13968, 0, -8296, 0, 0, 0, -62160, 0, -20960, 0, -1566, 0, 4832, 0, -10916, 0, -11580, 0, 0, 0, 2768, 0, -11472, 0, 12360, 0, 40992, 0, 5436, 0, -17600, 0, 0, 0, 8400, 0, 3402, 0, -292, 0, -14640, 0, -8928, 0, -24272, 0, 0, 0, 6910, 0, -568, 0, -7320, 0, 12144, 0, 14828, 0, 20022, 0, 0, 0, 14272, 0, -3672, 0, 22824, 0, -21025, 0, 28206, 0, -17448, 0, 0, 0, -27300, 0, 18648, 0, -41780, 0, -10656, 0, -21420, 0, 18132, 0, 0, 0, -24036, 0, -2752, 0, -6429, 0, 48640, 0, 3632, 0, -7488, 0, 0, 0, -4374, 0, -17856, 0, -46348, 0, 20660, 0, 13152, 0, 1800, 0, 0, 0, -3240, 0, 72224, 0, -11136, 0, 1008, 0, 7888, 0, -40152, 0, 0, 0, 32416, 0, 41996, 0, 4176, 0, 41308, 0, -27360, 0, -16608, 0, 0, 0, -3936, 0, -9012, 0, 2096, 0, 13542, 0, 5688, 0, -7212, 0, 0, 0, 2064, 0, 26880, 0, -38976, 0, -16776, 0, 53544, 0, -35280, 0, 0, 0, 21392, 0, 1760, 0, 8766, 0, 21162, 0, 24864, 0, 6960, 0, 0, 0, -11295, 0, 1440, 0, 400, 0, -8224, 0, -37296, 0, 8140, 0, 0, 0, 732, 0, 32158, 0, -24160, 0, -19782, 0, 41416, 0, -1296, 0, 0, 0, -13776, 0, -12296, 0, -22476, 0, -12352, 0, 57652, 0, 5994, 0, 0, 0, 46032, 0, -21792, 0, -70744, 0, -8414, 0, -32298, 0, -3336, 0, 0, 0, 6930, 0, 44880, 0, 47532, 0, 16320, 0, -25620, 0, -4864, 0, 0, 0, -54900, 0, -43338, 0, -6048, 0, -58128, 0, 7864, 0, -11952, 0, 0, 0, 47360, 0, 540, 0, -7580, 0, -55820, 0, 324, 0, 9632, 0, 0, 0, 31284, 0, -8046, 0, -37312, 0, -12576, 0, 33280, 0, 13220, 0, 0, 0, -12876, 0, -10004, 0, 26052, 0, 2736, 0, 40992, 0, -45135, 0, 0, 0, 24696, 0, 2421, 0, -50908, 0, 31074, 0, -10560, 0, 46068, 0, 0, 0, 16944, 0, 43700, 0, -2688, 0, -11340, 0, 64696, 0, -18560, 0, 0, 0, -16000, 0, 66854, 0, 7638, 0, 81104, 0, 21612, 0, -13392, 0, 0, 0, 7030, 0, -696, 0, -25280, 0, -3104, 0, 24804, 0, -76272, 0, 0, 0, 1656, 0, 33440, 0, -30192, 0, -32616, 0, -28456, 0, 37288, 0, 0, 0, 2416, 0, -102416, 0, -4428, 0, 64528, 0, -10576, 0, -31302, 0, 0, 0, -30476, 0, -21168, 0, 29768, 0, -6400, 0, 13068, 0, -51480, 0, 0, 0, 29184, 0, 1336, 0, 24360, 0, 9132, 0, -59788, 0, -19296, 0, 0, 0, 87920, 0, 11230, 0, -26730, 0, -34688, 0, -44016, 0, -1632, 0, 0, 0, -44774, 0, -1944, 0, -9844, 0, -40152, 0, -26640, 0, -62160, 0, 0, 0, -16848, 0, -22442, 0, 24200, 0, 5814, 0, -4736, 0, 64204, 0, 0, 0, -36960, 0, -30800, 0, -16416, 0, 9512, 0, -48152, 0, 27108, 0, 0, 0, -6112, 0, -26796, 0, -70260, 0, -3328, 0, 16614, 0, 26880, 0, 0, 0, 13176, 0, 57120, 0, -134384, 0, -15372, 0, 46656, 0, 24328, 0, 0, 0, -36864, 0, 34400, 0, -1440, 0, -24070, 0, -6028, 0, -20100, 0, 0, 0, 30414, 0, 15144, 0, 3768, 0, -52408, 0, 4176, 0, -16116, 0, 0, 0, -37296, 0, 1856, 0, 30880, 0, -4032, 0, -19184, 0, -31448, 0, 0, 0, -29158, 0, 24536, 0, -13176, 0, 42480, 0, 22304, 0, -14496, 0, 0, 0, 2528, 0, -28530, 0, 102144, 0, -22400, 0, -10998, 0, -77552, 0, 0, 0, 50400, 0, 39040, 0, 46032, 0, 16920, 0, 7980, 0, -28304, 0, 0, 0, 65316, 0, -1369, 0, -78, 0, 100858, 0, 59520, 0, -6804, 0, 0, 0, -74462, 0, -22968, 0, -53392, 0, -65120, 0, 37824, 0, 640, 0, 0, 0, 9792, 0, -7360, 0, -43344, 0, -9204, 0, -58128, 0, -75216, 0, 0, 0, 38706, 0, -57456, 0, 5436, 0, 72800, 0, -8792, 0, 19680, 0, 0, 0, 38464, 0, -27084, 0, 51708, 0, -10606, 0, -12906, 0, 30044, 0, 0, 0, 19368, 0, -2012, 0, -58080, 0, 2664, 0, 17144, 0, 31488, 0, 0, 0, -42432, 0, -62550, 0, 19968, 0, -66368, 0, 3268, 0, 35688, 0, 0, 0, 47616, 0, -10044, 0, 3080, 0, -48328, 0, -792, 0, 33428, 0, 0, 0, 14616, 0, 8746, 0, 62172, 0, 8640, 0, -3008, 0, 24752, 0, 0, 0, 12014, 0, -2688, 0, -7884, 0, -47240, 0, 179968, 0, 16056, 0, 0, 0, -25840, 0, -40704, 0, -30368, 0, -50736, 0, -11136, 0, -93240, 0, 0, 0, -19629, 0, -69656, 0, -42212, 0, -61968, 0, -120480, 0, 33292, 0, 0, 0, 24032, 0, 27724, 0, -11988, 0, -76272, 0, -9808, 0, -15168, 0, 0, 0, 84854, 0, -58560, 0, 67356, 0, -5504, 0, -3096, 0, 60024, 0, 0, 0, -10884, 0, 44736, 0, -67568, 0, 14556, 0, -23700, 0, 1076, 0, 0, 0, -101232, 0, 59708, 0, 34272, 0, 102988, 0, -23376, 0, 15333, 0, 0, 0, -36408, 0, 14796, 0, -18560, 0, 77478, 0, -5040, 0, 17636, 0, 0, 0, -3840, 0, 11724, 0, 53240, 0, -12528, 0, 24000, 0, 99456, 0, 0, 0, -66280, 0, -100174, 0, 21390, 0, -5952, 0, 66292, 0, 36468, 0, 0, 0, -44016, 0, 52752, 0, 82176, 0, 126800, 0, -38364, 0, 65008, 0, 0, 0, -18684, 0, 69888, 0, 736, 0, 25752, 0, 59936, 0, 71608, 0, 0, 0, -75200, 0, -11528, 0, -15984, 0, 83512, 0, -102308, 0, -7218, 0, 0, 0, -55388, 0, -1968, 0, -36960, 0, 107479, 0, 30240, 0, 86128, 0, 0, 0, -76236, 0, -89392, 0, 130212, 0, -18480, 0, 8172, 0, -52108, 0, 0, 0, 5808, 0, -43520, 0, 29070, 0, 113718, 0, -31784, 0, 16812, 0, 0, 0, -38976, 0, 27972, 0, -94572, 0, 5380, 0, -15372, 0, -24160, 0, 0, 0, 64704, 0, 28562, 0, 31872, 0, 450, 0, 108336, 0, -74532, 0, 0, 0, -1440, 0, 58124, 0, 57360, 0, -53088, 0, -138008, 0, -864, 0, 0, 0, -9904, 0, 60900, 0, 68880, 0, -83424, 0, 60384, 0, 40136, 0, 0, 0, -1458, 0, -31964, 0, 50248, 0, -41436, 0, 2584, 0, -133984, 0, 0, 0, -66088, 0, -17018, 0, -13896, 0, 44640, 0, -69472, 0, -65988, 0, 0, 0, 60010, 0, -25104, 0, 120360, 0, 12048, 0, -24516, 0, 45708, 0, 0, 0, -6456, 0, 102144, 0, -13440, 0, 64512, 0, 88880, 0, -26840, 0, 0, 0, -74528, 0, 58360, 0, 5856, 0, -45184, 0, -71360, 0, 30810, 0, 0, 0, 123136, 0, 30240, 0, -74104, 0, -52611, 0, -85074, 0, 184632, 0, 0, 0, 48876, 0, 87240, 0, 49540, 0, -6804, 0, -20368, 0, 51676, 0, 0, 0, 7692, 0, -76078, 0, 12837, 0, -62610, 0, -79688, 0, 53280, 0, 0, 0, 1856, 0, -55944, 0, -12084, 0, 94112, 0, 33768, 0, -66144, 0, 0, 0, 10836, 0, 33366, 0, 13760, 0, -4416, 0, -76484, 0, -57456, 0, 0, 0, 132438, 0, 86976, 0, -14148, 0, -68672, 0, -64680, 0, -46554, 0, 0, 0, -204960, 0, -31356, 0, 104380, 0, 5526, 0, 11808, 0, -12680, 0, 0, 0, 216, 0, 52664, 0, 83472, 0, -65760, 0, -13208, 0, 47200, 0, 0, 0, 56448, 0, -93536, 0, -35886, 0, -106116, 0, 7520, 0, -34848, 0, 0, 0, 55680, 0, -11880, 0, 98000, 0, 74176, 0, -18048, 0, 142452, 0, 0, 0, -78204, 0, -24352, 0, 28612, 0, -3024, 0, -162080, 0, 74120, 0, 0, 0, 35946, 0, -142912, 0, 14616, 0, 4032, 0, 71280, 0, -18000, 0, 0, 0, 119052, 0, 83040, 0, 4352, 0, 16766, 0, 61590, 0, -80032, 0, 0, 0, -4941, 0, -135088, 0, 32524, 0, 30168, 0, -23680, 0, 71040, 0, 0, 0, 129684, 0, 2416, 0, -3492, 0, 44928, 0, -50736, 0, 18456, 0, 0, 0, 35518, 0, -15504, 0, -22596, 0, 30392, 0, 37620, 0, 149616, 0, 0, 0, -5736, 0, -41502, 0, 325304, 0, -44148, 0, -41724, 0, 123488, 0, 0, 0, -59058, 0, 96220, 0, -72288, 0, -54284, 0, 9592, 0, 105840, 0, 0, 0, 71456, 0, -11898, 0, -2828, 0, -124320, 0, -84606, 0, -44304, 0, 0, 0, -98568, 0, 68492, 0, -52168, 0, -35136, 0, 25520, 0, -4464, 0, 0, 0, -2000, 0, 124992, 0, -66342, 0, 112046, 0, -58300, 0, 32832, 0, 0, 0, -55546, 0, 34272, 0, -27312, 0, 53048, 0, 3840, 0, -113960, 0, 0, 0, -21708, 0, -159254, 0, 53600, 0, -27864, 0, -15456, 0, 95232, 0, 0, 0, -40384, 0, 6480, 0, -39024, 0, 7136, 0, 200760, 0, 10614, 0, 0, 0, -167004, 0, 71544, 0, 121656, 0, 99456, 0, -2187, 0, 61760, 0, 0, 0, 41328, 0, 10752, 0, -17512, 0, 104268, 0, 71264, 0, 81324, 0, 0, 0, -23892, 0, 134321, 0, 108960, 0, 76018, 0, 35136, 0, 78132, 0, 0, 0, 23510, 0, -5328, 0, -36844, 0, -121968, 0, 108612, 0, 69888, 0, 0, 0, 76080, 0, -90582, 0, 33912, 0, -18468, 0, -6172, 0, 29328, 0, 0, 0, -1376, 0, 28852, 0, -34272, 0, -134400, 0, -153624, 0, -6876, 0, 0, 0, 59840, 0, -45120, 0, 126716, 0, -99590, 0, 49866, 0, 844, 0, 0, 0, 30240, 0, 78392, 0, 38872, 0, 115572, 0, 208, 0, 66168, 0, 0, 0, -70528, 0, -15154, 0, 18144, 0, -40986, 0, -39812, 0, 6576, 0, 0, 0, 61248, 0, 55320, 0, 2320, 0, -93072, 0, 38700, 0, -100864, 0, 0, 0, 41904, 0, -48160, 0, -38976, 0, 24888, 0, -5568, 0, -54264, 0, 0, 0, 106138, 0, 24544, 0, 186480, 0, -8304, 0, -124140, 0, 62880, 0, 0, 0, 102740, 0, 4698, 0, 183408, 0, 16208, 0, -14496, 0, 118848, 0, 0, 0, 32748, 0, -253008, 0, -52480, 0, 34740, 0, -53088, 0, -168204, 0, 0, 0, 220224, 0, 199082, 0, -8304, 0, -215978, 0, -34072, 0, 34416, 0, 0, 0, 25166, 0, -37080, 0, 48356, 0, -51648, 0, -122976, 0, -57432, 0, 0, 0, -16308, 0, -7104, 0, 39672, 0, 52800, 0, 37564, 0, -27232, 0, 0, 0, 106466, 0, -230160, 0, -25200, 0, -207052, 0, 50752, 0, -10206, 0, 0, 0, 13440, 0, 876, 0, -95168, 0, 93278, 0, 43920, 0, 83868, 0, 0, 0, 26784, 0, 120156, 0, -165376, 0, 72816, 0, 80000, 0, 2112, 0, 0, 0, -170096, 0, -13440, 0, -20730, 0, -38976, 0, -36596, 0, 1704, 0, 0, 0, -179466, 0, 21960, 0, 177408, 0, -201576, 0, -36432, 0, 12432, 0, 0, 0, -44484, 0, -214896, 0, -233264, 0, -60066, 0, 21024, 0, 15520, 0, 0, 0, 290640, 0, -6944, 0, -42816, 0, 184632, 0, 200, 0, 11016, 0, 0, 0, 108544, 0, -68472, 0, -167200, 0, -25606, 0, 63075, 0, -28304, 0, 0, 0, -84618, 0, -35328, 0, 266280, 0, 52344, 0, -89872, 0, -118204, 0, 0, 0, 31268, 0, 165248, 0, 81900, 0, 68014, 0, 150064, 0, -55944, 0, 0, 0, -89786, 0, 125340, 0, -648, 0, 52880, 0, 31968, 0, -157920, 0, 0, 0, 64260, 0, 93024, 0, -38552, 0, -54396, 0, -144356, 0, 35032, 0, 0, 0, 156160, 0, -6176, 0, 72108, 0, -159500, 0, 141328, 0, 8256, 0, 0, 0, -64680, 0, 19287, 0, -95608, 0, 29024, 0, -145920, 0, 31004, 0, 0, 0, -10896, 0, -38816, 0, 186992, 0, 22464, 0, -129672, 0, 113488, 0, 0, 0, -116328, 0, 96480, 0, 13122, 0, -57846, 0, -91392, 0, 53568, 0, 0, 0, -445776, 0, 139044, 0, -40888, 0, 138000, 0, -61980, 0, 173440, 0, 0, 0, -39456, 0, -183806, 0, -93820, 0, -5400, 0, -239568, 0, 13440, 0, 0, 0, -50736, 0, 123912, 0, 9720, 0, -9760, 0, -30084, 0, -216672, 0, 0, 0, 221572, 0, 33408, 0, -88296, 0, -74962, 0, -3024, 0, -118232, 0, 0, 0, -23664, 0, 146000, 0, -97680, 0, 120456, 0, -57040, 0, -174332, 0, 0, 0, -144860, 0, -152522, 0, -97248, 0, 23680, 0, 48600, 0, -125988, 0, 0, 0, 134078, 0, -12528, 0, 66780, 0, 57124, 0, -123924, 0, 102304, 0, 0, 0, 82080, 0, 76434, 0, 4816, 0, 49824, 0, 381360, 0, -55820, 0, 0, 0, -71374, 0, -68672, 0, 11808, 0, 82144, 0, 30560, 0, 27036, 0, 0, 0, -259664, 0, -6288, 0, 93744, 0, 267424, 0, -40626, 0, 125284, 0, 0, 0, -17064, 0, -22596, 0, 19248, 0, 21636, 0, -21168, 0, 146792, 0, 0, 0, 5248, 0, 116854, 0, -6192, 0, 55026, 0, 152564, 0, -80640, 0, 0, 0, 79607, 0, 116928, 0, -48256, 0, 203296, 0, 50328, 0, 9540, 0, 0, 0, -160632, 0, -46970, 0, -172000, 0, 105840, 0, 469160, 0, -84656, 0, 0, 0, 85554, 0, -149856, 0, -64176, 0, -32272, 0, -77520, 0, -5280, 0, 0, 0, -22732, 0, -26298, 0, -44832, 0, 219030, 0, -63486, 0, -111696, 0, 0, 0, -74592, 0, -337696, 0, -278240, 0, -20880, 0, 183204, 0, 124992, 0, 0, 0, 90972, 0, 148912, 0, 33885, 0, -172544, 0, -15176, 0, -4320, 0, 0, 0, -154400, 0, -1200, 0, -75476, 0, -8000, 0, 24672, 0, 118848, 0, 0, 0, 111888, 0, -308678, 0, 220080, 0, -24420, 0, -152960, 0, -46492, 0, 0, 0, -15456, 0, 269952, 0, -2196, 0, -123276, 0, 26912, 0, -96474, 0, 0, 0, -162400, 0, 72480, 0, 94740, 0, 28896, 0, 59346, 0, -161024, 0, 0, 0, -124248, 0, -1552, 0, 73640, 0, 3888, 0, -4400, 0, 112000, 0, 0, 0, -180840, 0, 110496, 0, 41328, 0, -83994, 0, 164932, 0, 36888, 0, 0, 0, 16720, 0, 67428, 0, -195200, 0, -89392, 0, 37056, 0, 36656, 0, 0, 0, -172956, 0, 184800, 0, 175968, 0, -17982, 0, -239336, 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": "294.4.a.b", "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], [8], [0], [0], [0], [9], [0], [-40], [0], [4], [0], [-24], [0], [-84], [0], [-148], [0], [0], [0], [-84], [0], [-61], [0], [-27], [0], [58], [0], [136], [0], [120], [0], [0], [0], [-222], [0], [-12], [0], [420], [0], [164], [0], [72], [0], [-488], [0], [0], [0], [252], [0], [478], [0], [-320], [0], [444], [0], [-548], [0], [692], [0], [0], [0], [32], [0], [908], [0], [252], [0], [524], [0], [440], [0], [183], [0], [0], [0], [-1216], [0], [81], [0], [684], [0], [-672], [0], [-174], [0], [604], [0], [0], [0], [-408], [0], [-1184], [0], [-832], [0], [-360], [0]]}