# Stored data for newform 1344.4.a.h, downloaded from the LMFDB on 25 April 2024.
{"label": "1344.4.a.h", "space_label": "1344.4.a", "level": 1344, "weight": 4, "hecke_orbit": 8, "hecke_orbit_code": 31525197458703680, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2177459489433885039, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [-2, 1]], [11, [-12, 1]]], "qexp_display": "q-3q^{3}+2q^{5}-7q^{7}+9q^{9}+12q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 21504, "fricke_eigenval": -1, "atkin_lehner_string": "-++", "analytic_conductor": 79.29856704771538, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [1344, 1, [127, 1093, 449, 577], [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": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.991", "prec": 17}, {"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "2.008", "prec": 17}, {"__RealLiteral__": 0, "data": "0.120", "prec": 17}, {"__RealLiteral__": 0, "data": "5.061", "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, 2, -7], "traces": [0, 1, 0, -3, 0, 2, 0, -7, 0, 9, 0, 12, 0, 66, 0, -6, 0, -70, 0, -92, 0, 21, 0, -16, 0, -121, 0, -27, 0, 122, 0, -64, 0, -36, 0, -14, 0, 306, 0, -198, 0, 50, 0, 20, 0, 18, 0, 176, 0, 49, 0, 210, 0, -526, 0, 24, 0, 276, 0, 540, 0, 818, 0, -63, 0, 132, 0, -228, 0, 48, 0, -864, 0, 106, 0, 363, 0, -84, 0, -736, 0, 81, 0, -588, 0, -140, 0, -366, 0, 146, 0, -462, 0, 192, 0, -184, 0, -1214, 0, 108, 0, -846, 0, 168, 0, 42, 0, -708, 0, -646, 0, -918, 0, 1938, 0, -32, 0, 594, 0, 490, 0, -1187, 0, -150, 0, -492, 0, -224, 0, -60, 0, -2588, 0, 644, 0, -54, 0, 490, 0, -1716, 0, -528, 0, 792, 0, 244, 0, -147, 0, 2386, 0, 104, 0, -630, 0, -128, 0, -1566, 0, 1578, 0, 112, 0, -1076, 0, -72, 0, 2760, 0, 2159, 0, -828, 0, -1558, 0, 847, 0, -1620, 0, -3452, 0, 1162, 0, -2454, 0, 612, 0, -840, 0, 189, 0, -1928, 0, -318, 0, -396, 0, -4062, 0, -5480, 0, 684, 0, -854, 0, 100, 0, -144, 0, -1104, 0, 4892, 0, 2592, 0, 40, 0, 448, 0, -318, 0, -4620, 0, -4320, 0, -1089, 0, -5516, 0, -1670, 0, 252, 0, -3926, 0, 352, 0, 2208, 0, -3640, 0, 5650, 0, -243, 0, 98, 0, -6072, 0, 1764, 0, 4652, 0, -192, 0, 420, 0, -6006, 0, -2142, 0, 1098, 0, -5040, 0, -1052, 0, -438, 0, -5478, 0, 2176, 0, 1386, 0, -1452, 0, 4658, 0, -576, 0, -4614, 0, 1244, 0, 552, 0, -350, 0, -13, 0, 3642, 0, 6354, 0, 1080, 0, -324, 0, -1056, 0, -140, 0, 2538, 0, 1636, 0, -3740, 0, -504, 0, 2184, 0, 4442, 0, -126, 0, 4314, 0, 1464, 0, 2124, 0, 6440, 0, -7986, 0, 1938, 0, -1232, 0, 7988, 0, 2754, 0, -456, 0, -10606, 0, -5814, 0, -768, 0, -343, 0, 96, 0, -8340, 0, 10498, 0, -1782, 0, -7878, 0, -1728, 0, -1470, 0, -11856, 0, 1605, 0, 3561, 0, 212, 0, 5488, 0, 450, 0, 3682, 0, 7570, 0, 1476, 0, 8052, 0, -13596, 0, 672, 0, 8592, 0, -168, 0, 180, 0, 610, 0, 1120, 0, 7764, 0, -1472, 0, -910, 0, -1932, 0, -8094, 0, -4224, 0, 162, 0, 3672, 0, 10122, 0, -1470, 0, -3780, 0, -1176, 0, 5148, 0, 4228, 0, 9218, 0, 1584, 0, 8470, 0, -5726, 0, -2376, 0, -9192, 0, -3614, 0, -732, 0, 1472, 0, 4344, 0, 441, 0, 10876, 0, 292, 0, -7158, 0, -15550, 0, 600, 0, -312, 0, -924, 0, 7834, 0, 1890, 0, -15990, 0, 12448, 0, 384, 0, 13860, 0, 1596, 0, 4698, 0, 240, 0, 11132, 0, -4734, 0, 14368, 0, 20196, 0, -336, 0, -2428, 0, 17240, 0, 3228, 0, 18156, 0, -8540, 0, 216, 0, 6048, 0, 1084, 0, -8280, 0, 1048, 0, -1692, 0, -6477, 0, -5046, 0, -742, 0, 2484, 0, 336, 0, 2112, 0, 4674, 0, -3390, 0, 13052, 0, -2541, 0, 4480, 0, -11911, 0, 4860, 0, 3300, 0, -1416, 0, 10356, 0, 588, 0, -16966, 0, -3486, 0, -1292, 0, -11348, 0, 7362, 0, -11224, 0, 5152, 0, -1836, 0, -16118, 0, 1320, 0, 2520, 0, -15244, 0, 3876, 0, -567, 0, -18918, 0, -19372, 0, 5784, 0, 1936, 0, -7230, 0, 954, 0, 4116, 0, -6312, 0, 1188, 0, -7396, 0, 5888, 0, 12186, 0, 714, 0, 980, 0, 16440, 0, 11536, 0, 4138, 0, -2052, 0, -2374, 0, 6848, 0, 2562, 0, 11616, 0, 12722, 0, -300, 0, -24726, 0, 23964, 0, 432, 0, -1022, 0, 14141, 0, 3312, 0, -21420, 0, 17224, 0, -14676, 0, -448, 0, 3234, 0, -7776, 0, -18190, 0, 14116, 0, -120, 0, -4056, 0, 6480, 0, -1344, 0, 16490, 0, -5176, 0, 954, 0, -4988, 0, -4982, 0, 13860, 0, 1288, 0, -1952, 0, 12960, 0, 9816, 0, -16190, 0, 3267, 0, 23202, 0, 8498, 0, 16548, 0, 13452, 0, 980, 0, 5010, 0, -34716, 0, 31220, 0, -756, 0, -3432, 0, -3500, 0, 11778, 0, -33542, 0, -28152, 0, -1056, 0, 5922, 0, 28562, 0, -6624, 0, 1024, 0, 1584, 0, 10920, 0, -1248, 0, -1176, 0, -16950, 0, -14762, 0, 4216, 0, 729, 0, -1400, 0, -12670, 0, -294, 0, -2736, 0, 25996, 0, 18216, 0, 24368, 0, 4772, 0, -5292, 0, 4956, 0, -17600, 0, -13956, 0, 208, 0, -17182, 0, 576, 0, -7038, 0, 4522, 0, -1260, 0, 35640, 0, -18254, 0, 18018, 0, -2990, 0, 7744, 0, 6426, 0, -4600, 0, -10368, 0, -3294, 0, -3132, 0, 10804, 0, 15120, 0, -13566, 0, 53988, 0, 3156, 0, -11238, 0, -12320, 0, 1314, 0, 1272, 0, 224, 0, 16434, 0, 35034, 0, -9252, 0, -6528, 0, -2152, 0, -1840, 0, -4158, 0, -18318, 0, -30200, 0, 4356, 0, 9612, 0, -3806, 0, -13974, 0, -3430, 0, 5520, 0, 1728, 0, 19176, 0, -9505, 0, 13842, 0, 4318, 0, 8309, 0, -3732, 0, -4896, 0, 38234, 0, -1656, 0, 34818, 0, -15764, 0, 1050, 0, 1832, 0, -3116, 0, 39, 0, -8832, 0, -15048, 0, -10926, 0, 3444, 0, -18374, 0, -19062, 0, 40490, 0, -548, 0, -3240, 0, 1272, 0, 1568, 0, 972, 0, -16192, 0, -6904, 0, 3168, 0, -7808, 0, 36820, 0, 420, 0, 2324, 0, -15100, 0, -7614, 0, -53192, 0, -7056, 0, -4908, 0, 18116, 0, 53624, 0, 11220, 0, -57024, 0, -37026, 0, 1512, 0, -28966, 0, -4508, 0, -6552, 0, -1680, 0, 50874, 0, -13326, 0, -16566, 0, -800, 0, 378, 0, -38428, 0, 6996, 0, -12942, 0, 746, 0, -3856, 0, -4392, 0, -3430, 0, -25695, 0, -6372, 0, -636, 0, -9432, 0, -19320, 0, 3452, 0, 12012, 0, 23958, 0, -18078, 0, 1752, 0, -5814, 0, -792, 0, -8124, 0, 3696, 0, -320, 0, 14976, 0, -23964, 0, -10960, 0, 17114, 0, -8262, 0, -5544, 0, -37800, 0, 1368, 0, 48392, 0, 1170, 0, 31818, 0, 26866, 0, -1708, 0, 17442, 0, 29324, 0, 53442, 0, 2304, 0, -6050, 0, -48576, 0, 1029, 0, 1728, 0, -46406, 0, -288, 0, -57260, 0, 8640, 0, 25020, 0, -16702, 0, -2208, 0, -31494, 0, 52258, 0, -17308, 0, 5346, 0, 9784, 0, -728, 0, 23634, 0, -10782, 0, 15032, 0, 5184, 0, -14568, 0, 29090, 0, 4410, 0, 37332, 0, -2420, 0, 35568, 0, -38808, 0, -2816, 0, -4815, 0, 896, 0, 27584, 0, -10683, 0, -70604, 0, -57262, 0, -636, 0, 26642, 0, 10962, 0, -16464, 0, 14568, 0, -9240, 0, -1350, 0, -11310, 0, -10152, 0, -11046, 0, -8640, 0, 26074, 0, -22710, 0, -49680, 0, 46340, 0, -4428, 0, -784, 0, -22086, 0, -24156, 0, 2016, 0, -11032, 0, 40788, 0, 15960, 0, 7532, 0, -2016, 0, -3340, 0, -19584, 0, -25776, 0, -69360, 0, 45746, 0, 504, 0, 9636, 0, -75256, 0, -540, 0, 66780, 0, -7852, 0, -1830, 0, -19320, 0, -67012, 0, -3360, 0, -21296, 0, -8496, 0, -23292, 0, 13338, 0, -15113, 0, 4416, 0, -700, 0, 6100, 0, 2730, 0, -13998, 0, -7280, 0, 5796, 0, -7752, 0, 27154, 0, 24282, 0, 11300, 0, 60480, 0, 12672, 0, 10906, 0, -40790, 0, -486, 0, 24170, 0, 8416, 0, -11016, 0, -48872, 0, -5929, 0, -30366, 0, -1270, 0, -40608, 0, 4410, 0, -12144, 0, 56602, 0, 11340, 0, -7420, 0, 23256, 0, 3528, 0, 2440, 0, -78062, 0, -15444, 0, 24164, 0, 9304, 0, -12684, 0, 57276, 0, -80124, 0, -27654, 0, -384, 0, -8134, 0, -4752, 0, -3200, 0, 20976, 0, -25410, 0, -65334, 0, -80240, 0, 17178, 0, 40404, 0, -12012, 0, 7128, 0, -70406, 0, -29732, 0, 27576, 0, -4284, 0, 50514, 0, 10842, 0, -19086, 0, -68152, 0, 2196, 0, -6612, 0, 5880, 0, -4416, 0, -55836, 0, -10080, 0, -13032, 0, -60424, 0, -37302, 0, -1323, 0, 63646, 0, -2832, 0, -32628, 0, -30216, 0, -1280, 0, -876, 0, 13496, 0, 11088, 0, 21474, 0, 51520, 0, -10956, 0, 46650, 0, 79488, 0, 2226, 0, -1800, 0, 4352, 0, -8640, 0, 936, 0, -58982, 0, 21472, 0, 2772, 0, -3360, 0, 42983, 0, -23502, 0, 34330, 0, -5904, 0, -5670, 0, 28434, 0, -10446, 0, 47970, 0, 9316, 0, -9752, 0, -37344, 0, -46728, 0, 38360, 0, -1152, 0, -2688, 0, -51064, 0, -41580, 0, -13088, 0, -9228, 0, -4788, 0, 57250, 0, 41160, 0, -14094, 0, 2488, 0, -42636, 0, -720, 0, 5978, 0, 10368, 0, -33396, 0, -31852, 0, 10786, 0, 14202, 0, 51474, 0, -700, 0, -43104, 0, 70616, 0, -31056, 0, -60588, 0, -26, 0, 45560, 0, 1008, 0, 35388, 0, -67750, 0, 7284, 0, -11264, 0, -33100, 0, -51720, 0, 7728, 0, 12708, 0, -9684, 0, 127908, 0, 82304, 0, -54468, 0, -65340, 0, -34244, 0, 25620, 0, 9626, 0, 41452, 0, -648, 0, -27984, 0, 21170, 0, -18144, 0, 100338, 0, -2112, 0, -3252, 0, -9028, 0, 67712, 0, 24840, 0, -280, 0, 5880, 0, -3144, 0, 12840, 0, -10220, 0, 5076, 0, 15300, 0, -3136, 0, 19431, 0, -25772, 0, -98978, 0, 15138, 0, -20592, 0, -90772, 0, 2226, 0, -7480, 0, -64172, 0, -7452, 0, 3648, 0, 82504, 0, -1008, 0, 32340, 0, 56810, 0, -6336, 0, 47706, 0, 4368, 0, -14022, 0, -69128, 0, 30240, 0, 10170, 0, 8884, 0, -49264, 0, -39156, 0, -24812, 0, -78342, 0, 7623, 0, 54096, 0, 33060, 0, -13440, 0, 122648, 0, 8628, 0, 35733, 0, 38612, 0, 6120, 0, -14580, 0, 2928, 0, -77894, 0, -9900, 0, -28646, 0, 11690, 0, 4248, 0, -18560, 0, 73770, 0, -31068, 0, -1190, 0, 12880, 0, -1764, 0, 25620, 0, -29630, 0, 50898, 0, -32472, 0, 11564, 0, 10458, 0, 27482, 0, 13824, 0, 3876, 0, -81390, 0, 28632, 0, 34044, 0, 33664, 0, -2464, 0, -22086, 0, 84980, 0, -14784, 0, 33672, 0, 15976, 0, 104922, 0, -15456, 0, 1248, 0, 6784, 0, 5508, 0, -69180, 0, -62166, 0, 48354, 0, 25480, 0, 27588, 0, -3960, 0, -1696, 0, -66421, 0, -7560, 0, -21212, 0, -39550, 0, 45732, 0, -13432, 0, -7918, 0, -11628, 0, 115242, 0, 31892, 0, 1701, 0, -170808, 0, -1536, 0, 56754, 0, 79210, 0, 65880, 0, 58116, 0, -686, 0, 59220, 0, -17352, 0, 27458, 0, 39108, 0, -5808, 0, -18792, 0, 42504, 0, 21690, 0, 49410, 0, -16680, 0, -2862, 0, 53856, 0, 46226, 0, -12348, 0, 20996, 0, -62228, 0, 18936, 0, -11760, 0, -123142, 0, -3564, 0, -32564, 0, 20976, 0, 22188, 0, 1000, 0, -15756, 0, -17664, 0, 99796, 0, 1344, 0, -36558, 0, 104544, 0, 11010, 0, -2142, 0, 32340, 0, 36232, 0, -2940, 0, 30844, 0, -21190, 0, -49320, 0, -12912, 0, -23712, 0, -34608, 0, 42042, 0, -75814, 0, -12414, 0, 3210, 0, -113256, 0, 6156, 0, 119748, 0, 14994, 0, 7122, 0, 11776, 0, 49560, 0, -20544, 0, 71712, 0, -12826, 0, -7686, 0, -34560, 0, 110584, 0, -34848, 0, 10976, 0, 33120, 0, -38166, 0, 35280, 0, 111688, 0, 900, 0, -792, 0, -79107, 0, 74178, 0, 45220, 0, 7364, 0, -71892, 0, 25908, 0, 99450, 0, -1296, 0, 15140, 0, 61532, 0, 3066, 0, 81720, 0, 109362, 0, -42423, 0, -96590, 0, 114840, 0, -9936, 0, 38346, 0, 16104, 0, 64260, 0, 19530, 0, -52352, 0, -51672, 0, -27192, 0, -15232, 0, 44028, 0, 75882, 0, -18696, 0, 1344, 0, -69676, 0, 9408, 0, -9702, 0, -131366, 0, 17184, 0, 23328, 0, 77832, 0, -135660, 0, 54570, 0, 10164, 0, 8800, 0, -42348, 0, 127532, 0, -34262, 0, 360, 0, 157476, 0, -32606, 0, 12168, 0, -27816, 0, 1220, 0, -19440, 0, -73190, 0, 62496, 0, 4032, 0, 2240, 0, -15456, 0, -49470, 0, -160956, 0, 6864, 0, 15528, 0, 32298, 0, -41424, 0, -2862, 0, 43682, 0, 89056, 0, 14964, 0, -97140, 0, -8708, 0, 14946, 0, -1820, 0, 69140, 0, -41580, 0, 13944, 0, -46678, 0, -3864, 0, 18570, 0, -20064, 0, 5856, 0, 160164, 0, -16188, 0, -38880, 0, 2450, 0, -82188, 0, -29448, 0, -8448, 0, -48286, 0, 48570, 0, 3520, 0, 91, 0, -9801, 0, -119652, 0, 108434, 0, -69606, 0, 65136, 0, 7344, 0, -25494, 0, -68864, 0, -103356, 0, -49644, 0, 20244, 0, -2336, 0, -40356, 0, -44478, 0, 93922, 0, -2940, 0, 83090, 0, -105408, 0, -15030, 0, 177488, 0, -7560, 0, 104148, 0, -102862, 0, 59432, 0, -93660, 0, 71148, 0, 14592, 0, 2268, 0, 41522, 0, 167356, 0, 10296, 0, 46736, 0, -45110, 0, 10500, 0, 7392, 0, 8456, 0, -35334, 0, -7516, 0, -23136, 0, 100626, 0, 18436, 0, 980, 0, 84456, 0, -70424, 0, -2606, 0, 3168, 0, 12932, 0, -71016, 0, -17766, 0, -3816, 0, 34440, 0, -85686, 0, 92994, 0, -132940, 0, 19872, 0, -11452, 0, -54742, 0, -3072, 0, 166794, 0, -161056, 0, -4752, 0, -178296, 0, 26180, 0, -32760, 0, -75878, 0, -18384, 0, 3744, 0, 15680, 0, 37874, 0, 3528, 0, -7228, 0, -48744, 0, 50850, 0, 182160, 0, -26300, 0, 44286, 0, -15288, 0, 175852, 0, -12648, 0, 165240, 0, 2944, 0, -2187, 0, -65760, 0, -31094, 0, 4200, 0, 8688, 0, -2508, 0, 38010, 0, 55296, 0, 3292, 0, 882, 0, -88824, 0, -72847, 0, 8208, 0, 7650, 0, 21752, 0, -77988, 0, -30198, 0, 39882, 0, -54648, 0, -17666, 0, 181160, 0, -73104, 0, 19424, 0, -10248, 0, -14316, 0, -30822, 0, -9280, 0, 15876, 0, -138172, 0, -31100, 0, -14868, 0, -102828, 0, -127084, 0, 52800, 0, 1200, 0, 250308, 0, 41868, 0, -45080, 0, -6784, 0, -624, 0, 166780, 0, -7990, 0, 51546, 0, 55562, 0, 55902, 0, -1728, 0, -10520, 0, -72502, 0, 21114, 0, 15668, 0, 154640, 0, -13566, 0, -89792, 0, -176526, 0, 3780, 0, 115578, 0, 109204, 0, -106920, 0, 8624, 0, -31980, 0, 54762, 0, 63474, 0, -76472, 0, -54054, 0, 24896, 0, -55916, 0, 8970, 0, 58704, 0, 13536, 0, -23232, 0, -227832, 0, -34300, 0, -19278, 0, -73414, 0, 27720, 0, 13800, 0, -51084, 0, -204262, 0, 31104, 0, 3192, 0, -14924, 0, 9882, 0, 45712, 0, 76692, 0, 9396, 0, 44066, 0, 74242, 0, -32412, 0, 120120, 0, 480, 0, -45360, 0, -2688, 0, -37852, 0, 40698, 0, 45264, 0, 74266, 0, -161964, 0, -93366, 0, -200544, 0, -9468, 0, 5376, 0, -144366, 0, 33714, 0, 5538, 0, 28736, 0, 36960, 0, 27216, 0, 2401, 0, -3942, 0, 40392, 0, -71736, 0, -3816, 0, -130532, 0, 20608, 0, -672, 0, 161682, 0, 27000, 0, -49302, 0, 53472, 0, 146894, 0, -105102, 0, 58380, 0, -55440, 0, 27756, 0, 34480, 0, 23458, 0, 19584, 0, -101310, 0, -73486, 0, 6456, 0, 137304, 0, 47104, 0, 5520, 0, -51840, 0, 36312, 0, 12474, 0, -153396, 0, 11328, 0, 54954, 0, -17080, 0, 25380, 0, 90600, 0, 55146, 0, -14470, 0, -13068, 0, 102234, 0, -69768, 0, -28836, 0, -127248, 0, 12096, 0, 11418, 0, 238096, 0, -92576, 0, 41922, 0, 2168, 0, -66192, 0, 10290, 0, 40900, 0, -91512, 0, -16560, 0, 10336, 0, -20988, 0, -5184, 0, 82992, 0, 2096, 0, -57528, 0, -20040, 0, -8630, 0, 28515, 0, 102366, 0, -11235, 0, -41526, 0, 92980, 0, -167020, 0, -12954, 0, 10800, 0, -44836, 0, -24927, 0, 45576, 0, -10092, 0, 11196, 0, -170414, 0, 31496, 0, 14688, 0, -1484, 0, 144474, 0, -114702, 0, -268092, 0, -47112, 0, 4968, 0, -7280, 0, -38416, 0, -104454, 0, 37632, 0, -20328, 0, 47292, 0, -229516, 0, 17812, 0, -3150, 0, 4224, 0, -361680, 0, -5496, 0, 98904, 0, 24962, 0, 9348, 0, -25774, 0, -31008, 0, -117, 0, -45080, 0, -6780, 0, 26496, 0, 28474, 0, -52990, 0, 45144, 0, 26104, 0, -70934, 0, 32778, 0, 37978, 0, 16360, 0, -10332, 0, -264384, 0, -43680, 0, 55122, 0, 11962, 0, 8960, 0, 57186, 0, -56364, 0, 157872, 0, -121470, 0, -23822, 0, -15784, 0, 1644, 0, 67800, 0, 95172, 0, 9720, 0, -184446, 0, -198220, 0, -3816, 0, -122808, 0, 6600, 0, -4704, 0, 109620, 0, -77360, 0, -2916, 0, 85668, 0, 50554, 0, 48576, 0, -60144, 0, 212996, 0, 20712, 0, -209120, 0, 108002, 0, -9504, 0, -57470, 0, 1176, 0, 23424, 0, 159132, 0, 32436, 0, -110460, 0, -33932, 0, 177108, 0, -1260, 0, -220832, 0, 52298, 0, -6972, 0, -72864, 0, 72752, 0, 45300, 0, -4270, 0, 78166, 0, 22842, 0, -236350, 0, 77716, 0, 159576, 0, -22696, 0, -7840, 0, 21168, 0, 68754, 0, 322872, 0, 14724, 0, -11400, 0, -28974, 0, -54348, 0, -125630, 0, -22448, 0, -160872, 0, -9344, 0, 55824, 0, -33660, 0, 10304, 0, 123072, 0, 171072, 0, 75320, 0, 95040, 0, 111078, 0, -231486, 0, 6370, 0, -4536, 0, 18992, 0, -32236, 0, 86898, 0, -25390, 0, 6712, 0, 13524, 0, 2640, 0, 170794, 0, 19656, 0, 146738, 0, 190596, 0, 5040, 0, 56658, 0, 127799, 0, -152622, 0, -148108, 0, -30488, 0, 39978, 0, -924, 0, 29568, 0, 49698, 0, -234498, 0, -72072, 0, 2400, 0, -219512, 0, 273618, 0, -1134, 0, 53490, 0, -193200, 0, 115284, 0, -42548, 0, -37836, 0, -20988, 0, -25704, 0, -53204, 0, 38826, 0, -38744, 0, -228006, 0, -2238, 0, 38010, 0, -70854, 0, 11568, 0, 143968, 0, -9568, 0, 13176, 0, -151130, 0, 7872, 0, 10290, 0, 28360, 0, -4560, 0, 77085, 0, -14460, 0, -169528, 0, 19116, 0, 26460, 0, -60480, 0, 1908, 0, 152826, 0, -285120, 0, 28296, 0, -5048, 0, 8232, 0, 57960, 0, -60774, 0, -43200, 0, -10356, 0, -12624, 0, 133690, 0, -36036, 0, 3584, 0, -225216, 0, -71874, 0, -161016, 0, -103212, 0, 54234, 0, -29596, 0, -14792, 0, -5256, 0, 159324, 0, 109060, 0, 17442, 0, 11776, 0, -64526, 0, 2376, 0, -364056, 0, -103254, 0, 24372, 0, 298938, 0, -65736, 0, -11088, 0, -99724, 0, 1428, 0, 960, 0, 240666, 0, 193628, 0, -44928, 0, -59290, 0, -110220, 0, 71892, 0, 26112, 0, 144072, 0, 32880, 0, 20496, 0, 40082, 0, -51342, 0, 5300, 0, 23072, 0, 24786, 0, -159080, 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": "168.4.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], [2], [0], [-7], [0], [9], [0], [12], [0], [66], [0], [-6], [0], [-70], [0], [-92], [0], [21], [0], [-16], [0], [-121], [0], [-27], [0], [122], [0], [-64], [0], [-36], [0], [-14], [0], [306], [0], [-198], [0], [50], [0], [20], [0], [18], [0], [176], [0], [49], [0], [210], [0], [-526], [0], [24], [0], [276], [0], [540], [0], [818], [0], [-63], [0], [132], [0], [-228], [0], [48], [0], [-864], [0], [106], [0], [363], [0], [-84], [0], [-736], [0], [81], [0], [-588], [0], [-140], [0], [-366], [0], [146], [0], [-462], [0], [192], [0], [-184], [0], [-1214], [0], [108], [0]]}