# Stored data for newform 1800.4.a.f, downloaded from the LMFDB on 25 April 2024.
{"label": "1800.4.a.f", "space_label": "1800.4.a", "level": 1800, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22517998203963144, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1467563051338596638, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [20, 1]], [11, [-56, 1]], [17, [106, 1]]], "qexp_display": "q-20q^{7}+56q^{11}+86q^{13}-106q^{17}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 28800, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 106.2034380103331, "hecke_ring_index": 1, "level_radical": 30, "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": [1800, 1, [1351, 901, 1001, 577], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "0.975", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.918", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.705", "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], [5, 1]], "trace_display": [0, 0, 0, -20], "traces": [0, 1, 0, 0, 0, 0, 0, -20, 0, 0, 0, 56, 0, 86, 0, 0, 0, -106, 0, 4, 0, 0, 0, 136, 0, 0, 0, 0, 0, 206, 0, -152, 0, 0, 0, 0, 0, -282, 0, 0, 0, 246, 0, -412, 0, 0, 0, 40, 0, 57, 0, 0, 0, -126, 0, 0, 0, 0, 0, -56, 0, -2, 0, 0, 0, 0, 0, 388, 0, 0, 0, 672, 0, -1170, 0, 0, 0, -1120, 0, 408, 0, 0, 0, 668, 0, 0, 0, 0, 0, -66, 0, -1720, 0, 0, 0, 0, 0, 926, 0, 0, 0, 198, 0, 1532, 0, 0, 0, -444, 0, 62, 0, 0, 0, 414, 0, 0, 0, 0, 0, 2120, 0, 1805, 0, 0, 0, 0, 0, 996, 0, 0, 0, 264, 0, -80, 0, 0, 0, 2278, 0, 1812, 0, 0, 0, 4816, 0, 0, 0, 0, 0, 1534, 0, -3016, 0, 0, 0, 0, 0, 1814, 0, 0, 0, -2720, 0, 1844, 0, 0, 0, 3768, 0, 5199, 0, 0, 0, 938, 0, 0, 0, 0, 0, -3968, 0, -3514, 0, 0, 0, 0, 0, -5936, 0, 0, 0, 1480, 0, 2774, 0, 0, 0, -3806, 0, -856, 0, 0, 0, -4120, 0, 0, 0, 0, 0, 224, 0, 3020, 0, 0, 0, 0, 0, 3040, 0, 0, 0, -9116, 0, 1684, 0, 0, 0, 2004, 0, -5042, 0, 0, 0, -3090, 0, 0, 0, 0, 0, -2136, 0, 98, 0, 0, 0, 0, 0, 344, 0, 0, 0, 5040, 0, 7616, 0, 0, 0, -1986, 0, 5640, 0, 0, 0, 1416, 0, 0, 0, 0, 0, 6670, 0, 48, 0, 0, 0, 0, 0, -6938, 0, 0, 0, 1694, 0, 6364, 0, 0, 0, -4920, 0, 6323, 0, 0, 0, -3134, 0, 0, 0, 0, 0, 11696, 0, 8240, 0, 0, 0, 0, 0, 236, 0, 0, 0, -3776, 0, 7918, 0, 0, 0, 4362, 0, 11536, 0, 0, 0, -424, 0, 0, 0, 0, 0, -800, 0, 7980, 0, 0, 0, 0, 0, 8294, 0, 0, 0, -8512, 0, 5720, 0, 0, 0, -964, 0, 8670, 0, 0, 0, -2314, 0, 0, 0, 0, 0, 1896, 0, -6843, 0, 0, 0, 0, 0, -1484, 0, 0, 0, 2520, 0, -12370, 0, 0, 0, 17716, 0, 5620, 0, 0, 0, 5880, 0, 0, 0, 0, 0, -2082, 0, -14416, 0, 0, 0, 0, 0, 1742, 0, 0, 0, 3270, 0, -13072, 0, 0, 0, -15792, 0, -6134, 0, 0, 0, 1120, 0, 0, 0, 0, 0, 10392, 0, -12690, 0, 0, 0, 0, 0, 40, 0, 0, 0, 7408, 0, 5062, 0, 0, 0, 544, 0, -7160, 0, 0, 0, 17100, 0, 0, 0, 0, 0, -8634, 0, 13776, 0, 0, 0, 0, 0, -2986, 0, 0, 0, 2406, 0, 14316, 0, 0, 0, -292, 0, -7760, 0, 0, 0, -23072, 0, 0, 0, 0, 0, -14056, 0, -24252, 0, 0, 0, 0, 0, 11204, 0, 0, 0, -4608, 0, -21836, 0, 0, 0, -13440, 0, 2468, 0, 0, 0, 12192, 0, 0, 0, 0, 0, -1714, 0, 23400, 0, 0, 0, 0, 0, 2240, 0, 0, 0, 18014, 0, 16748, 0, 0, 0, 16112, 0, 6329, 0, 0, 0, 21156, 0, 0, 0, 0, 0, 3192, 0, -14018, 0, 0, 0, 0, 0, 412, 0, 0, 0, 824, 0, -8160, 0, 0, 0, 18218, 0, -35432, 0, 0, 0, 23524, 0, 0, 0, 0, 0, -23330, 0, -13124, 0, 0, 0, 0, 0, -11714, 0, 0, 0, -13360, 0, -7056, 0, 0, 0, -17628, 0, -608, 0, 0, 0, -2802, 0, 0, 0, 0, 0, 2664, 0, 23962, 0, 0, 0, 0, 0, -11940, 0, 0, 0, 3440, 0, -16794, 0, 0, 0, -20706, 0, 10724, 0, 0, 0, 1320, 0, 0, 0, 0, 0, 29892, 0, -5744, 0, 0, 0, 0, 0, 4902, 0, 0, 0, -27906, 0, -20556, 0, 0, 0, -10224, 0, -3136, 0, 0, 0, -12982, 0, 0, 0, 0, 0, 1512, 0, 16710, 0, 0, 0, 0, 0, 28016, 0, 0, 0, -112, 0, -7962, 0, 0, 0, 12226, 0, -18520, 0, 0, 0, -8748, 0, 0, 0, 0, 0, -10836, 0, -7324, 0, 0, 0, 0, 0, -26076, 0, 0, 0, 21934, 0, -1128, 0, 0, 0, -3960, 0, -10690, 0, 0, 0, -20672, 0, 0, 0, 0, 0, -13792, 0, -30640, 0, 0, 0, 0, 0, 24004, 0, 0, 0, 43672, 0, -8562, 0, 0, 0, 21728, 0, -13836, 0, 0, 0, -22224, 0, 0, 0, 0, 0, 8880, 0, 11544, 0, 0, 0, 0, 0, 3814, 0, 0, 0, 25662, 0, -1240, 0, 0, 0, -4816, 0, 30658, 0, 0, 0, -30894, 0, 0, 0, 0, 0, 984, 0, 37632, 0, 0, 0, 0, 0, -21596, 0, 0, 0, -8280, 0, -172, 0, 0, 0, -8646, 0, -4240, 0, 0, 0, -65520, 0, 0, 0, 0, 0, -24954, 0, 40004, 0, 0, 0, 0, 0, -1648, 0, 0, 0, -16570, 0, 4388, 0, 0, 0, 14364, 0, -21170, 0, 0, 0, -6042, 0, 0, 0, 0, 0, -10664, 0, 18047, 0, 0, 0, 0, 0, -36100, 0, 0, 0, -38352, 0, 3190, 0, 0, 0, 20814, 0, -18988, 0, 0, 0, 11664, 0, 0, 0, 0, 0, 22848, 0, 33368, 0, 0, 0, 0, 0, 8246, 0, 0, 0, -22890, 0, -33548, 0, 0, 0, -32264, 0, -19920, 0, 0, 0, 160, 0, 0, 0, 0, 0, -31312, 0, 13356, 0, 0, 0, 0, 0, -51228, 0, 0, 0, 2144, 0, 37408, 0, 0, 0, -5280, 0, 33584, 0, 0, 0, 57792, 0, 0, 0, 0, 0, 3590, 0, 228, 0, 0, 0, 0, 0, 21686, 0, 0, 0, 5174, 0, 33456, 0, 0, 0, 35524, 0, -100620, 0, 0, 0, -16122, 0, 0, 0, 0, 0, -45560, 0, -6687, 0, 0, 0, 0, 0, -19188, 0, 0, 0, 38464, 0, -36240, 0, 0, 0, -43930, 0, -3696, 0, 0, 0, 17328, 0, 0, 0, 0, 0, -56032, 0, -18160, 0, 0, 0, 0, 0, 9102, 0, 0, 0, -96320, 0, 5936, 0, 0, 0, -504, 0, 14306, 0, 0, 0, -5710, 0, 0, 0, 0, 0, 56056, 0, -12170, 0, 0, 0, 0, 0, 35088, 0, 0, 0, 4360, 0, -8450, 0, 0, 0, 212, 0, 31400, 0, 0, 0, -30680, 0, 0, 0, 0, 0, 31806, 0, -60428, 0, 0, 0, 0, 0, 60320, 0, 0, 0, -21170, 0, -2668, 0, 0, 0, 51856, 0, -62474, 0, 0, 0, -58092, 0, 0, 0, 0, 0, 57448, 0, 5440, 0, 0, 0, 0, 0, -8756, 0, 0, 0, 8952, 0, 25558, 0, 0, 0, -5018, 0, -36280, 0, 0, 0, 23864, 0, 0, 0, 0, 0, -33698, 0, 11088, 0, 0, 0, 0, 0, -36170, 0, 0, 0, -224, 0, 2308, 0, 0, 0, 7752, 0, 64490, 0, 0, 0, 85792, 0, 0, 0, 0, 0, -41128, 0, -36880, 0, 0, 0, 0, 0, 42864, 0, 0, 0, 63080, 0, -18314, 0, 0, 0, -5676, 0, -8, 0, 0, 0, -36276, 0, 0, 0, 0, 0, -75360, 0, 380, 0, 0, 0, 0, 0, -24864, 0, 0, 0, 49318, 0, -103980, 0, 0, 0, 46108, 0, 50676, 0, 0, 0, 76454, 0, 0, 0, 0, 0, 3472, 0, 51666, 0, 0, 0, 0, 0, -71232, 0, 0, 0, -18760, 0, -7578, 0, 0, 0, -10066, 0, -17136, 0, 0, 0, 29552, 0, 0, 0, 0, 0, 77238, 0, -63992, 0, 0, 0, 0, 0, 29374, 0, 0, 0, 124020, 0, 23184, 0, 0, 0, -84872, 0, -59694, 0, 0, 0, 79360, 0, 0, 0, 0, 0, -23160, 0, 79636, 0, 0, 0, 0, 0, 70280, 0, 0, 0, -37392, 0, 1552, 0, 0, 0, -37318, 0, 20104, 0, 0, 0, -29084, 0, 0, 0, 0, 0, 40398, 0, -2356, 0, 0, 0, 0, 0, 47414, 0, 0, 0, -22322, 0, -31604, 0, 0, 0, 40044, 0, 118720, 0, 0, 0, 17028, 0, 0, 0, 0, 0, -16672, 0, -74262, 0, 0, 0, 0, 0, -58780, 0, 0, 0, 26544, 0, 62624, 0, 0, 0, -29600, 0, 131752, 0, 0, 0, -43248, 0, 0, 0, 0, 0, 2688, 0, -55480, 0, 0, 0, 0, 0, -7616, 0, 0, 0, 37702, 0, 8240, 0, 0, 0, 12432, 0, 28871, 0, 0, 0, -62438, 0, 0, 0, 0, 0, 76120, 0, -13330, 0, 0, 0, 0, 0, -4680, 0, 0, 0, -38184, 0, 17120, 0, 0, 0, 55776, 0, -84680, 0, 0, 0, -272, 0, 0, 0, 0, 0, 92318, 0, -70808, 0, 0, 0, 0, 0, 5332, 0, 0, 0, 11742, 0, -25284, 0, 0, 0, -67380, 0, 28990, 0, 0, 0, 6662, 0, 0, 0, 0, 0, 4768, 0, 14784, 0, 0, 0, 0, 0, 101524, 0, 0, 0, -105272, 0, -54442, 0, 0, 0, -6080, 0, 21852, 0, 0, 0, -4480, 0, 0, 0, 0, 0, 35604, 0, -12400, 0, 0, 0, 0, 0, -60400, 0, 0, 0, 68030, 0, 26940, 0, 0, 0, -94608, 0, -41070, 0, 0, 0, 52530, 0, 0, 0, 0, 0, 94040, 0, 1632, 0, 0, 0, 0, 0, 127568, 0, 0, 0, -38160, 0, 6996, 0, 0, 0, -69372, 0, -8664, 0, 0, 0, 66772, 0, 0, 0, 0, 0, 101472, 0, 52252, 0, 0, 0, 0, 0, -25956, 0, 0, 0, 52768, 0, 41588, 0, 0, 0, 182320, 0, 42094, 0, 0, 0, 56534, 0, 0, 0, 0, 0, -96800, 0, -33680, 0, 0, 0, 0, 0, -94828, 0, 0, 0, -80240, 0, 155230, 0, 0, 0, 2672, 0, 23548, 0, 0, 0, -106528, 0, 0, 0, 0, 0, -40080, 0, 116184, 0, 0, 0, 0, 0, -94386, 0, 0, 0, -21250, 0, 100840, 0, 0, 0, -48024, 0, 56810, 0, 0, 0, 8762, 0, 0, 0, 0, 0, -10968, 0, -35242, 0, 0, 0, 0, 0, 2412, 0, 0, 0, 61800, 0, 91392, 0, 0, 0, 82866, 0, 85904, 0, 0, 0, 19152, 0, 0, 0, 0, 0, -98156, 0, 85656, 0, 0, 0, 0, 0, -117906, 0, 0, 0, -168896, 0, 110324, 0, 0, 0, -83020, 0, 31518, 0, 0, 0, 42720, 0, 0, 0, 0, 0, -159120, 0, -8405, 0, 0, 0, 0, 0, -1960, 0, 0, 0, -264, 0, -54722, 0, 0, 0, 82622, 0, -93836, 0, 0, 0, 22704, 0, 0, 0, 0, 0, -56602, 0, -11536, 0, 0, 0, 0, 0, -20988, 0, 0, 0, -28026, 0, 45708, 0, 0, 0, 101584, 0, -6880, 0, 0, 0, -99614, 0, 0, 0, 0, 0, -11280, 0, -29530, 0, 0, 0, 0, 0, 9164, 0, 0, 0, -162392, 0, 2814, 0, 0, 0, -100800, 0, -30040, 0, 0, 0, -101352, 0, 0, 0, 0, 0, -412, 0, -152320, 0, 0, 0, 0, 0, -31322, 0, 0, 0, 195908, 0, 17932, 0, 0, 0, 134956, 0, 111758, 0, 0, 0, 103264, 0, 0, 0, 0, 0, 39720, 0, 133370, 0, 0, 0, 0, 0, 155832, 0, 0, 0, -120216, 0, -16074, 0, 0, 0, 55488, 0, 47064, 0, 0, 0, -50400, 0, 0, 0, 0, 0, 8512, 0, 31656, 0, 0, 0, 0, 0, 211008, 0, 0, 0, -28320, 0, 3704, 0, 0, 0, -101776, 0, 90237, 0, 0, 0, -6572, 0, 0, 0, 0, 0, 291144, 0, -63698, 0, 0, 0, 0, 0, -57004, 0, 0, 0, 127064, 0, 29230, 0, 0, 0, 22674, 0, -67704, 0, 0, 0, -133400, 0, 0, 0, 0, 0, 4062, 0, 304, 0, 0, 0, 0, 0, -960, 0, 0, 0, 38726, 0, 52528, 0, 0, 0, 121884, 0, 90848, 0, 0, 0, 69726, 0, 0, 0, 0, 0, 792, 0, -43884, 0, 0, 0, 0, 0, 9840, 0, 0, 0, -125928, 0, 159134, 0, 0, 0, 131924, 0, 138760, 0, 0, 0, 79928, 0, 0, 0, 0, 0, 31926, 0, 66680, 0, 0, 0, 0, 0, 6128, 0, 0, 0, 35532, 0, -259376, 0, 0, 0, -33880, 0, -222208, 0, 0, 0, 139602, 0, 0, 0, 0, 0, 27848, 0, -127280, 0, 0, 0, 0, 0, 25212, 0, 0, 0, -196784, 0, 52638, 0, 0, 0, 90954, 0, -69280, 0, 0, 0, -139300, 0, 0, 0, 0, 0, 14022, 0, -102996, 0, 0, 0, 0, 0, 40526, 0, 0, 0, -16480, 0, -126460, 0, 0, 0, -121788, 0, -83786, 0, 0, 0, -1776, 0, 0, 0, 0, 0, 5376, 0, 156004, 0, 0, 0, 0, 0, -8976, 0, 0, 0, 62680, 0, 88414, 0, 0, 0, -191330, 0, 138432, 0, 0, 0, 107584, 0, 0, 0, 0, 0, -65610, 0, 248, 0, 0, 0, 0, 0, -58976, 0, 0, 0, 105366, 0, -14260, 0, 0, 0, -154096, 0, -11798, 0, 0, 0, -233920, 0, 0, 0, 0, 0, 55616, 0, 82880, 0, 0, 0, 0, 0, -23484, 0, 0, 0, -75048, 0, -104986, 0, 0, 0, -241020, 0, 158584, 0, 0, 0, 155344, 0, 0, 0, 0, 0, -89698, 0, 169220, 0, 0, 0, 0, 0, -125714, 0, 0, 0, 92958, 0, -22612, 0, 0, 0, 1656, 0, -4720, 0, 0, 0, 6334, 0, 0, 0, 0, 0, -105576, 0, 66018, 0, 0, 0, 0, 0, -213136, 0, 0, 0, 324048, 0, -30996, 0, 0, 0, 75520, 0, -163652, 0, 0, 0, 15792, 0, 0, 0, 0, 0, -47936, 0, -158360, 0, 0, 0, 0, 0, 258172, 0, 0, 0, -102144, 0, -123212, 0, 0, 0, 143576, 0, -102223, 0, 0, 0, -510, 0, 0, 0, 0, 0, -87240, 0, 29318, 0, 0, 0, 0, 0, -27984, 0, 0, 0, 125936, 0, -230720, 0, 0, 0, -40454, 0, -86984, 0, 0, 0, -37748, 0, 0, 0, 0, 0, 80668, 0, -28172, 0, 0, 0, 0, 0, 564, 0, 0, 0, 8480, 0, 177840, 0, 0, 0, 135348, 0, 26342, 0, 0, 0, 172038, 0, 0, 0, 0, 0, 51912, 0, -129062, 0, 0, 0, 0, 0, -201564, 0, 0, 0, 84048, 0, 42814, 0, 0, 0, -109458, 0, 7220, 0, 0, 0, 2280, 0, 0, 0, 0, 0, -73402, 0, 181832, 0, 0, 0, 0, 0, -159600, 0, 0, 0, 169120, 0, 26928, 0, 0, 0, -341248, 0, -241468, 0, 0, 0, -127958, 0, 0, 0, 0, 0, -221920, 0, -60002, 0, 0, 0, 0, 0, 119636, 0, 0, 0, 3480, 0, -302204, 0, 0, 0, 97842, 0, -165880, 0, 0, 0, -192072, 0, 0, 0, 0, 0, 208352, 0, 153676, 0, 0, 0, 0, 0, 111414, 0, 0, 0, -110242, 0, -196028, 0, 0, 0, 170240, 0, -112090, 0, 0, 0, -482, 0, 0, 0, 0, 0, 179664, 0, -133951, 0, 0, 0, 0, 0, 137608, 0, 0, 0, 198056, 0, 3984, 0, 0, 0, -82322, 0, -13776, 0, 0, 0, 64088, 0, 0, 0, 0, 0, 19280, 0, -510496, 0, 0, 0, 0, 0, 16174, 0, 0, 0, -156442, 0, -173400, 0, 0, 0, -81304, 0, -62016, 0, 0, 0, 94304, 0, 0, 0, 0, 0, -79320, 0, -60384, 0, 0, 0, 0, 0, 24516, 0, 0, 0, 46280, 0, -48346, 0, 0, 0, 87546, 0, -109416, 0, 0, 0, 127280, 0, 0, 0, 0, 0, 1056, 0, -5040, 0, 0, 0, 0, 0, 112224, 0, 0, 0, -492, 0, 135916, 0, 0, 0, 8432, 0, 238564, 0, 0, 0, -37920, 0, 0, 0, 0, 0, -282352, 0, 166922, 0, 0, 0, 0, 0, 136860, 0, 0, 0, 167232, 0, -162604, 0, 0, 0, 23072, 0, -10876, 0, 0, 0, 5480, 0, 0, 0, 0, 0, 71718, 0, 35976, 0, 0, 0, 0, 0, -210866, 0, 0, 0, -327316, 0, -173040, 0, 0, 0, 319696, 0, 29680, 0, 0, 0, -101536, 0, 0, 0, 0, 0, 79680, 0, -13596, 0, 0, 0, 0, 0, -73616, 0, 0, 0, 71776, 0, 201838, 0, 0, 0, -7182, 0, 56304, 0, 0, 0, 9112, 0, 0, 0, 0, 0, -67914, 0, 247400, 0, 0, 0, 0, 0, -45962, 0, 0, 0, -101738, 0, 824, 0, 0, 0, -189504, 0, -119616, 0, 0, 0, 5350, 0, 0, 0, 0, 0, -354320, 0, 7248, 0, 0, 0, 0, 0, -68436, 0, 0, 0, 5488, 0, -112400, 0, 0, 0, 81990, 0, -33300, 0, 0, 0, 12952, 0, 0, 0, 0, 0, -192284, 0, -101336, 0, 0, 0, 0, 0, 216006, 0, 0, 0, -117600, 0, 105828, 0, 0, 0, 134224, 0, 187522, 0, 0, 0, -19614, 0, 0, 0, 0, 0, 157848, 0, 329940, 0, 0, 0, 0, 0, 37460, 0, 0, 0, -194552, 0, 131686, 0, 0, 0, 19264, 0, -117904, 0, 0, 0, 41640, 0, 0, 0, 0, 0, 85734, 0, -165028, 0, 0, 0, 0, 0, 288320, 0, 0, 0, -41106, 0, 259720, 0, 0, 0, 95448, 0, -168042, 0, 0, 0, -138066, 0, 0, 0, 0, 0, 10032, 0, 282240, 0, 0, 0, 0, 0, -203500, 0, 0, 0, -195464, 0, -2240, 0, 0, 0, -31434, 0, -34840, 0, 0, 0, 245480, 0, 0, 0, 0, 0, -244074, 0, 131904, 0, 0, 0, 0, 0, -263986, 0, 0, 0, 9414, 0, -129100, 0, 0, 0, -65400, 0, -133001, 0, 0, 0, 190756, 0, 0, 0, 0, 0, 230472, 0, 261440, 0, 0, 0, 0, 0, -111216, 0, 0, 0, 6136, 0, -96802, 0, 0, 0, -250158, 0, -399408, 0, 0, 0, 38852, 0, 0, 0, 0, 0, 315840, 0, 110116, 0, 0, 0, 0, 0, 106286, 0, 0, 0, 226158, 0, 122680, 0, 0, 0, -80, 0, -12064, 0, 0, 0, -551094, 0, 0, 0, 0, 0, -159520, 0, -159856, 0, 0, 0, 0, 0, 97196, 0, 0, 0, -3192, 0, 79296, 0, 0, 0, 248190, 0, 144824, 0, 0, 0, -153720, 0, 0, 0, 0, 0, 24150, 0, 165312, 0, 0, 0, 0, 0, 8846, 0, 0, 0, 135456, 0, -115056, 0, 0, 0, -5672, 0, 40788, 0, 0, 0, -207840, 0, 0, 0, 0, 0, -102736, 0, -99428, 0, 0, 0, 0, 0, 253800, 0, 0, 0, 172344, 0, -209010, 0, 0, 0, -27030, 0, 373520, 0, 0, 0, -153636, 0, 0, 0, 0, 0, -131946, 0, -191332, 0, 0, 0, 0, 0, -433612, 0, 0, 0, 2688, 0, 7256, 0, 0, 0, 315592, 0, -114, 0, 0, 0, -287820, 0, 0, 0, 0, 0, -45752, 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": "120.4.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], [1], [0], [0], [0], [0], [0], [-20], [0], [0], [0], [56], [0], [86], [0], [0], [0], [-106], [0], [4], [0], [0], [0], [136], [0], [0], [0], [0], [0], [206], [0], [-152], [0], [0], [0], [0], [0], [-282], [0], [0], [0], [246], [0], [-412], [0], [0], [0], [40], [0], [57], [0], [0], [0], [-126], [0], [0], [0], [0], [0], [-56], [0], [-2], [0], [0], [0], [0], [0], [388], [0], [0], [0], [672], [0], [-1170], [0], [0], [0], [-1120], [0], [408], [0], [0], [0], [668], [0], [0], [0], [0], [0], [-66], [0], [-1720], [0], [0], [0], [0], [0], [926], [0], [0], [0]]}