# Stored data for newform 1856.4.a.i, downloaded from the LMFDB on 28 March 2024. {"label": "1856.4.a.i", "space_label": "1856.4.a", "level": 1856, "weight": 4, "hecke_orbit": 9, "hecke_orbit_code": 36028797086074688, "dim": 2, "is_polredabs": true, "nf_label": "2.2.24.1", "trace_hash": 365154722276258136, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [-5, 2, 1]], [5, [-191, -10, 1]], [7, [-320, -16, 1]]], "qexp_display": "q+(-1+\\beta )q^{3}+(5+6\\beta )q^{5}+(8-8\\beta )q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 29696, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 109.50754497065458, "hecke_ring_index": 1, "level_radical": 58, "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": [1856, 1, [639, 581, 321], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 29], "conrey_indexes": [1], "field_disc": 24, "field_disc_factorization": [[2, 3], [3, 1]], "field_poly": [-6, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.949", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.512", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "64.222", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [29, 1]], "trace_display": [0, -2, 10, 16], "traces": [0, 2, 0, -2, 0, 10, 0, 16, 0, -40, 0, -90, 0, 50, 0, 62, 0, -44, 0, 108, 0, -112, 0, 28, 0, 232, 0, 70, 0, -58, 0, -66, 0, 126, 0, -496, 0, -40, 0, 46, 0, 304, 0, -130, 0, -344, 0, 514, 0, 210, 0, -148, 0, 958, 0, -234, 0, -60, 0, -180, 0, -1028, 0, -128, 0, 826, 0, -912, 0, -964, 0, -796, 0, -856, 0, 488, 0, -1008, 0, 318, 0, 470, 0, -1828, 0, -1372, 0, 58, 0, -944, 0, -368, 0, 1374, 0, 828, 0, 368, 0, 1728, 0, 112, 0, -1780, 0, 592, 0, -1000, 0, 1994, 0, 88, 0, -84, 0, -5476, 0, -1192, 0, 1184, 0, 1496, 0, 656, 0, 4230, 0, 548, 0, -506, 0, 1092, 0, 480, 0, -2890, 0, 504, 0, -4780, 0, -1702, 0, -1962, 0, -290, 0, -1746, 0, 1722, 0, -304, 0, 1264, 0, 7518, 0, -1896, 0, -334, 0, 7712, 0, -390, 0, -2826, 0, -1916, 0, -2376, 0, -2256, 0, 3228, 0, -3904, 0, -2820, 0, 5884, 0, -5474, 0, 884, 0, 88, 0, 1404, 0, 4880, 0, -8924, 0, -2504, 0, 1454, 0, 4140, 0, 5216, 0, 1152, 0, -464, 0, 7280, 0, 1312, 0, -4716, 0, 4386, 0, 1204, 0, -4466, 0, -10992, 0, -1256, 0, -2636, 0, -4364, 0, -6080, 0, -9468, 0, 4000, 0, 5616, 0, -6098, 0, -4558, 0, -4650, 0, -6636, 0, -5006, 0, -752, 0, -8166, 0, 3084, 0, 2284, 0, -2826, 0, -4068, 0, -1172, 0, 5966, 0, -704, 0, 1160, 0, -4506, 0, 8534, 0, 80, 0, 1548, 0, -6262, 0, -1264, 0, -8280, 0, -13220, 0, -1296, 0, 414, 0, -12892, 0, 3300, 0, -5248, 0, -5786, 0, -1568, 0, -1780, 0, -18900, 0, -4770, 0, -6788, 0, 4048, 0, -5776, 0, -6004, 0, 310, 0, 2476, 0, -9212, 0, 8934, 0, 9728, 0, 4068, 0, 2610, 0, 4312, 0, -3144, 0, 11560, 0, -7730, 0, 13616, 0, -9454, 0, 704, 0, -3120, 0, 6380, 0, -8076, 0, 6894, 0, 8480, 0, 1804, 0, -2932, 0, -3762, 0, -2570, 0, 11348, 0, -1532, 0, -608, 0, 10646, 0, -7694, 0, -4736, 0, -16952, 0, 10060, 0, -8000, 0, 2672, 0, -10650, 0, -1278, 0, -1450, 0, -7388, 0, 2428, 0, 6632, 0, 22608, 0, 3872, 0, 168, 0, 14360, 0, 6156, 0, -24402, 0, -7898, 0, -5280, 0, 4662, 0, 8814, 0, 11998, 0, 1944, 0, 60, 0, 6072, 0, 22560, 0, -6404, 0, 2500, 0, 4132, 0, -23284, 0, -7904, 0, -16624, 0, -7072, 0, -1458, 0, 5900, 0, 1168, 0, -1798, 0, -2232, 0, -4300, 0, -1128, 0, -4924, 0, -9904, 0, -5850, 0, 3388, 0, -10800, 0, 4864, 0, -11632, 0, 10148, 0, 7100, 0, 12884, 0, -3044, 0, -3354, 0, 6654, 0, -9216, 0, 9048, 0, 3942, 0, 15408, 0, -20408, 0, 36466, 0, -616, 0, -16544, 0, -5360, 0, 3032, 0, -5766, 0, -3750, 0, 1276, 0, 10800, 0, -9632, 0, -3364, 0, 3668, 0, 4258, 0, -33424, 0, 7176, 0, 25350, 0, 10048, 0, 1620, 0, -4724, 0, -26694, 0, 1476, 0, -30326, 0, -13104, 0, -1472, 0, -19476, 0, 49066, 0, 9600, 0, 15280, 0, 14872, 0, -1540, 0, -14058, 0, 12160, 0, 8714, 0, -24446, 0, 15136, 0, 20848, 0, -3132, 0, 37200, 0, -1288, 0, -11060, 0, -8338, 0, 6444, 0, 21386, 0, -49380, 0, -9104, 0, -9876, 0, 5488, 0, 10844, 0, -52912, 0, 13156, 0, 20264, 0, -18272, 0, -41238, 0, -21080, 0, 23180, 0, 1668, 0, 948, 0, -15630, 0, 9376, 0, 1840, 0, 2542, 0, 9280, 0, 17760, 0, -11960, 0, 26178, 0, 3248, 0, 3346, 0, 29738, 0, 8464, 0, -15144, 0, 13178, 0, 43100, 0, -640, 0, 9862, 0, 4500, 0, 112, 0, -7364, 0, 2466, 0, 20596, 0, -7038, 0, 15104, 0, 20372, 0, -47920, 0, -3394, 0, -13820, 0, -900, 0, 24624, 0, 4264, 0, 48948, 0, 21344, 0, 3366, 0, 27828, 0, -4276, 0, -26400, 0, -812, 0, 18836, 0, 45828, 0, -8430, 0, -24280, 0, 14396, 0, 12544, 0, 10932, 0, 4872, 0, 41976, 0, -24640, 0, 28942, 0, -28208, 0, 10944, 0, -37580, 0, -22048, 0, 6434, 0, -510, 0, -1968, 0, 17122, 0, 46208, 0, 5586, 0, 2304, 0, -102948, 0, -30330, 0, 25620, 0, -17996, 0, -19808, 0, -3154, 0, -6728, 0, 12500, 0, 3854, 0, 13036, 0, -8664, 0, 8046, 0, 41760, 0, 27398, 0, 3300, 0, 51356, 0, -16158, 0, 35648, 0, -34496, 0, -8620, 0, -25194, 0, 25840, 0, -40156, 0, 46692, 0, 6252, 0, 61840, 0, 32528, 0, -28500, 0, -21820, 0, 6682, 0, -12784, 0, 70824, 0, 3008, 0, 20256, 0, 37044, 0, -2030, 0, 33432, 0, 2236, 0, -19674, 0, 64608, 0, -26852, 0, 29074, 0, -36068, 0, 7700, 0, 20608, 0, 32184, 0, -14432, 0, -20940, 0, 33456, 0, -31200, 0, 13114, 0, -38886, 0, -9564, 0, 10624, 0, -49326, 0, -63676, 0, -19944, 0, 3122, 0, -1844, 0, 15908, 0, 19956, 0, 932, 0, -61170, 0, -26862, 0, 1682, 0, 28866, 0, 16920, 0, 37888, 0, 4, 0, -4304, 0, 7196, 0, -24816, 0, -15018, 0, -47366, 0, -1664, 0, -8764, 0, 44364, 0, 14234, 0, -27306, 0, -20880, 0, -4960, 0, 10224, 0, 37534, 0, 23956, 0, -2100, 0, -36280, 0, -2580, 0, 13662, 0, -19424, 0, -16326, 0, 23004, 0, 55484, 0, -15268, 0, 1914, 0, -31060, 0, -2896, 0, -7930, 0, -12460, 0, 9088, 0, 45770, 0, 83628, 0, -31724, 0, -49248, 0, 42852, 0, -23698, 0, -16636, 0, -1760, 0, 34208, 0, 10428, 0, 5196, 0, -7876, 0, 54108, 0, -44932, 0, 2994, 0, 10810, 0, -70624, 0, -21680, 0, -4050, 0, -38296, 0, 15948, 0, 8998, 0, -33100, 0, -3654, 0, -48576, 0, 85168, 0, 13376, 0, 94040, 0, 86194, 0, -8280, 0, -24692, 0, -20000, 0, 17576, 0, -87994, 0, 39888, 0, -28408, 0, 33610, 0, 51228, 0, -47792, 0, 47788, 0, 13900, 0, 33586, 0, 68416, 0, -28096, 0, -3560, 0, 11664, 0, 51960, 0, -28512, 0, 54228, 0, -7586, 0, -11708, 0, -31736, 0, 14384, 0, 18000, 0, -23832, 0, -9590, 0, -66942, 0, 92864, 0, -26706, 0, 2080, 0, 88684, 0, -8972, 0, 116864, 0, 24920, 0, 45132, 0, 42172, 0, 46800, 0, -24876, 0, 9090, 0, 7764, 0, 7760, 0, 24614, 0, 63042, 0, -38912, 0, -2996, 0, 4404, 0, -81106, 0, -25084, 0, -20160, 0, -64364, 0, -24832, 0, 1160, 0, -53240, 0, -1730, 0, -42052, 0, 99860, 0, 12878, 0, 26832, 0, 91702, 0, -23440, 0, -16638, 0, 38852, 0, -24424, 0, 31486, 0, -72384, 0, -25852, 0, 3800, 0, -54652, 0, -32560, 0, 32254, 0, -22032, 0, -43664, 0, 65012, 0, 71844, 0, -9294, 0, -21720, 0, 51124, 0, -90504, 0, 122748, 0, -22356, 0, -1334, 0, 82188, 0, -38556, 0, 23420, 0, 16224, 0, 46128, 0, -16912, 0, -103840, 0, 6552, 0, -38504, 0, -43560, 0, -56678, 0, -35856, 0, -30512, 0, -56088, 0, 24070, 0, -55482, 0, -28474, 0, 19560, 0, -29344, 0, 37470, 0, 3544, 0, -11656, 0, 54936, 0, -36336, 0, -12280, 0, -57408, 0, 14190, 0, 22188, 0, -8816, 0, 31298, 0, -76860, 0, 80724, 0, 0, 0, -106938, 0, -37464, 0, -12774, 0, -73990, 0, 10984, 0, 20718, 0, -11808, 0, 21540, 0, 90992, 0, -13110, 0, -35260, 0, -4824, 0, -55296, 0, -67800, 0, 3540, 0, 18832, 0, -6444, 0, -23232, 0, 53724, 0, -37848, 0, -37920, 0, 52624, 0, -20700, 0, -57124, 0, 3770, 0, 29472, 0, 100160, 0, 12320, 0, -182250, 0, -26860, 0, 55804, 0, -400, 0, 10324, 0, 235404, 0, -69712, 0, 71450, 0, 94608, 0, -48288, 0, -21488, 0, 26062, 0, -58818, 0, 55264, 0, 28668, 0, 105718, 0, 46080, 0, -55254, 0, 69898, 0, 34924, 0, 10304, 0, 123864, 0, 35504, 0, -39708, 0, -14710, 0, 9976, 0, -40666, 0, -51552, 0, -47640, 0, -42512, 0, -167610, 0, 53140, 0, 119028, 0, 60654, 0, 76470, 0, 148568, 0, 11392, 0, -32756, 0, 42750, 0, -65034, 0, -28400, 0, -86752, 0, -38932, 0, -26184, 0, 62316, 0, -108612, 0, 54980, 0, -41352, 0, -162112, 0, -26928, 0, 9802, 0, 231480, 0, -3040, 0, 117352, 0, -14906, 0, -9776, 0, -20960, 0, -100314, 0, -44228, 0, -95476, 0, -181494, 0, -36068, 0, -7584, 0, -103636, 0, 23884, 0, -49972, 0, -54672, 0, 71516, 0, 1496, 0, -14720, 0, -158688, 0, -15732, 0, -59480, 0, -55098, 0, -3160, 0, 177750, 0, 54912, 0, 131260, 0, 32920, 0, 23616, 0, -141788, 0, 3962, 0, 22338, 0, -6090, 0, 81126, 0, 29040, 0, -4152, 0, 63644, 0, 5450, 0, -15744, 0, -67712, 0, -40510, 0, -10308, 0, -27396, 0, -104, 0, 21758, 0, -19118, 0, -136576, 0, -12112, 0, 78216, 0, 12608, 0, -146454, 0, -124016, 0, 2008, 0, -36000, 0, 124156, 0, 20112, 0, -67380, 0, 55844, 0, 26226, 0, -200880, 0, -19728, 0, 4292, 0, -28576, 0, -53604, 0, 129510, 0, 43308, 0, -91388, 0, 51104, 0, 22720, 0, -166276, 0, 34060, 0, 132472, 0, -156, 0, 34816, 0, 27152, 0, -2952, 0, -5134, 0, -12858, 0, 34592, 0, 9136, 0, -2240, 0, -174354, 0, 37920, 0, -68822, 0, -127888, 0, -44070, 0, 208260, 0, 22972, 0, 14144, 0, -138778, 0, -27782, 0, 31812, 0, -31488, 0, -111076, 0, -55876, 0, 34208, 0, -67928, 0, 89406, 0, -41396, 0, -148588, 0, -73968, 0, -75972, 0, -150688, 0, 6926, 0, 116238, 0, -72708, 0, -14496, 0, -12428, 0, 11480, 0, 88832, 0, -96888, 0, 63028, 0, -2964, 0, 51926, 0, 140436, 0, -75274, 0, -87456, 0, 56, 0, 128700, 0, 6786, 0, -268, 0, 23312, 0, 54218, 0, 197120, 0, -34312, 0, -193278, 0, 140192, 0, -126368, 0, -90744, 0, -84264, 0, 86958, 0, -154224, 0, -64888, 0, -45376, 0, 129366, 0, -115050, 0, 103000, 0, -51472, 0, -42968, 0, 67550, 0, -67380, 0, -89874, 0, 32, 0, 36402, 0, -136976, 0, -29500, 0, 11104, 0, 37508, 0, 1740, 0, 97522, 0, 44850, 0, -87120, 0, 27360, 0, -53684, 0, 640, 0, -139098, 0, -154732, 0, -3052, 0, -204960, 0, -91392, 0, -13802, 0, 152752, 0, -14834, 0, -43776, 0, -68, 0, 25232, 0, -30806, 0, -54432, 0, -16220, 0, 5556, 0, 39468, 0, 82078, 0, -132352, 0, 85284, 0, -325818, 0, -17340, 0, -135200, 0, 5220, 0, -31264, 0, 105760, 0, 88160, 0, 174640, 0, 15660, 0, 18724, 0, -45584, 0, 106776, 0, -26400, 0, -38548, 0, 145914, 0, 220780, 0, 14560, 0, -15032, 0, -143074, 0, 109664, 0, 13158, 0, 27188, 0, 30402, 0, 28024, 0, 35530, 0, -73690, 0, 201552, 0, 40340, 0, 39532, 0, -70640, 0, 106852, 0, 67380, 0, 29812, 0, -373536, 0, -92976, 0, -67856, 0, 48344, 0, -24906, 0, 65208, 0, -122570, 0, 36128, 0, 47292, 0, 146422, 0, -118432, 0, -918, 0, 106726, 0, 85430, 0, -53456, 0, -2424, 0, -43504, 0, -7366, 0, -137740, 0, -42720, 0, -74916, 0, -10344, 0, 49616, 0, 342348, 0, -30992, 0, -67662, 0, 50532, 0, -226016, 0, 3712, 0, -321060, 0, 121956, 0, -8374, 0, -44452, 0, 91476, 0, -51314, 0, 157392, 0, 15072, 0, -177088, 0, 13304, 0, -116856, 0, -5928, 0, 47908, 0, -232592, 0, 18730, 0, 121320, 0, 16060, 0, -118844, 0, -172914, 0, 85740, 0, 39040, 0, 137964, 0, 98828, 0, 67178, 0, -83992, 0, 125632, 0, 94752, 0, 167520, 0, -23954, 0, 2672, 0, -23326, 0, 18228, 0, -34756, 0, 59252, 0, -104912, 0, -101424, 0, 7838, 0, -131148, 0, 14012, 0, 49924, 0, -61160, 0, -21282, 0, -85350, 0, -158072, 0, -46220, 0, -16608, 0, 132408, 0, 13276, 0, 159552, 0, -16912, 0, 63904, 0, -194298, 0, 80468, 0, 105040, 0, 10026, 0, -127264, 0, 99668, 0, 26448, 0, 119208, 0, 132660, 0, -19006, 0, 62378, 0, 192576, 0, 179224, 0, -93336, 0, 34376, 0, -16664, 0, 28880, 0, 26604, 0, -230928, 0, -251748, 0, 65080, 0, 21174, 0, -223032, 0, 150, 0, -91040, 0, -32, 0, -71316, 0, 100910, 0, 93620, 0, 66544, 0, 256050, 0, -111740, 0, 19680, 0, -52828, 0, 47180, 0, 27956, 0, -71994, 0, -25362, 0, 58336, 0, -90960, 0, -166524, 0, -57852, 0, 221262, 0, 112470, 0, -73026, 0, 29554, 0, -113872, 0, 151000, 0, -23022, 0, -158534, 0, 64948, 0, -40752, 0, -7560, 0, -39808, 0, 36536, 0, 9816, 0, 186432, 0, 21900, 0, 54176, 0, -58776, 0, -191648, 0, 32798, 0, 9048, 0, 18928, 0, 23084, 0, -38720, 0, 109420, 0, 20640, 0, 32642, 0, 44456, 0, 84732, 0, 38576, 0, -184688, 0, 56256, 0, -242640, 0, -57348, 0, -90684, 0, -145900, 0, -174000, 0, 128110, 0, -28256, 0, 122144, 0, -115708, 0, 121288, 0, 215468, 0, 407340, 0, -93426, 0, -194180, 0, 67758, 0, 3600, 0, -183612, 0, 140702, 0, 66032, 0, 24824, 0, -58998, 0, -96896, 0, 165960, 0, -140292, 0, -15330, 0, 78972, 0, -42866, 0, 206070, 0, 253792, 0, -442, 0, 152148, 0, -156300, 0, -33182, 0, -57402, 0, -37176, 0, 189584, 0, 94752, 0, -201042, 0, 274444, 0, 37700, 0, -59672, 0, -30472, 0, 110816, 0, 225872, 0, -171036, 0, 116440, 0, -33884, 0, 195536, 0, -14152, 0, 63008, 0, -245020, 0, -24692, 0, -8400, 0, -310392, 0, -47270, 0, -213552, 0, -23952, 0, 13436, 0, 271540, 0, -130850, 0, -75144, 0, 70740, 0, 210592, 0, 163560, 0, 136462, 0, 42064, 0, -68976, 0, -93054, 0, -250700, 0, 13270, 0, -127584, 0, 136424, 0, -74448, 0, -161344, 0, -139992, 0, -111644, 0, 98752, 0, 29232, 0, 57510, 0, -216150, 0, -167504, 0, -84500, 0, 63364, 0, 367148, 0, 108992, 0, 118332, 0, -33598, 0, 116764, 0, -280368, 0, 19984, 0, 112560, 0, 66240, 0, -201960, 0, -13984, 0, -55368, 0, 167844, 0, -24452, 0, -211716, 0, -140608, 0, -3888, 0, -95342, 0, -55980, 0, -145644, 0, -153740, 0, 241816, 0, -203440, 0, -9222, 0, -39148, 0, 66460, 0, 90836, 0, 67824, 0, -55140, 0, 206034, 0, 285028, 0, 28300, 0, -87900, 0, 98856, 0, -144616, 0, 395612, 0, -268688, 0, 30256, 0, -176814, 0, 443360, 0, 57144, 0, 181852, 0, -116304, 0, 9472, 0, 27820, 0, -257394, 0, 38880, 0, -278154, 0, -108612, 0, -69732, 0, 228096, 0, -129404, 0, -13630, 0, -218298, 0, -110930, 0, -65928, 0, -17604, 0, 93664, 0, 2732, 0, 141640, 0, 177390, 0, 138480, 0, -79208, 0, -341756, 0, -125856, 0, 240228, 0, -76332, 0, -26092, 0, -195396, 0, 202220, 0, -245896, 0, 535536, 0, 88948, 0, 97748, 0, -49276, 0, 158066, 0, -30908, 0, 51542, 0, -88670, 0, 5840, 0, -7400, 0, 53012, 0, 47448, 0, -160264, 0, 41496, 0, 247904, 0, -128652, 0, -267360, 0, 7824, 0, 36900, 0, -29312, 0, 86400, 0, -337376, 0, 97884, 0, 18336, 0, 45400, 0, 156726, 0, 111536, 0, 26418, 0, -72720, 0, -5934, 0, 262566, 0, -482682, 0, -27900, 0, 239796, 0, 116106, 0, 60560, 0, 62276, 0, -272336, 0, -55506, 0, 39788, 0, 68430, 0, 22876, 0, 23968, 0, -46080, 0, 222048, 0, 355976, 0, 19200, 0, -128318, 0, -207740, 0, 200672, 0, 72740, 0, 87960, 0, 184430, 0, 259024, 0, 167356, 0, 430452, 0, -6324, 0, -167776, 0, -435124, 0, -61148, 0, 475324, 0, 79480, 0, 159762, 0, 13840, 0, 16034, 0, -77670, 0, -241920, 0, -120988, 0, -1682, 0, -326848, 0, -103024, 0, -66840, 0, 93762, 0, 28164, 0, -78456, 0, 170700, 0, -337204, 0, -135616, 0, 206304, 0, 14430, 0, 283616, 0, 155308, 0, -83748, 0, 23696, 0, 195392, 0, -130254, 0, -47804, 0, 144204, 0, 275418, 0, -156780, 0, -66272, 0, 206816, 0, -18558, 0, 110028, 0, -164720, 0, 170210, 0, -64220, 0, 27376, 0, 118784, 0, 242802, 0, 186848, 0, -63644, 0, -208950, 0, -125604, 0, 95364, 0, 20718, 0, 635304, 0, 98824, 0, 53520, 0, -292030, 0, 227970, 0, 320042, 0, 74352, 0, -16896, 0, -231120, 0, 349102, 0, 66880, 0, 107880, 0, 74452, 0, -189648, 0, 17552, 0, 355572, 0, -97582, 0, 257958, 0, -232020, 0, -8752, 0, 10672, 0, -267240, 0, 4356, 0, 88082, 0, 26090, 0, 106024, 0, 200790, 0, -187360, 0, 420960, 0, 126420, 0, 218248, 0, 71118, 0, 365112, 0, 307952, 0, 16928, 0, -72720, 0, 25844, 0, 81216, 0, 82720, 0, -109262, 0, -74820, 0, 308032, 0, 102098, 0, 178060, 0, 156404, 0, -49084, 0, 179872, 0, 108774, 0, 367110, 0, -39846, 0, 209006, 0, 8672, 0, -74636, 0, -138496, 0, -202910, 0, -83264, 0, -58722, 0, 210742, 0, -172934, 0, -119628, 0, -136064, 0, 151612, 0, -156480, 0, -112856, 0, 258800, 0, -278320, 0, -210916, 0, 72154, 0, 166688, 0, -28352, 0, -137052, 0, -52052, 0, 164466, 0, 195536, 0, -119424, 0, 186884, 0, 54816, 0, -11684, 0, -24012, 0, 34260, 0, -63024, 0, 43110, 0, 40576, 0, -113520, 0, -293588, 0, -11372, 0, 107076, 0, 250740, 0, -7072, 0, 117898, 0, -250384, 0, -93620, 0, 273664, 0, -139972, 0, 108900, 0, 149930, 0, -51812, 0, -83100, 0, -174530, 0, 249514, 0, 218416, 0, -139868, 0, -269066, 0, 35676, 0, 102192, 0, 193576, 0, 197572, 0, -10672, 0, 50410, 0, -202536, 0, -7736, 0, -165744, 0, -23266, 0, -499344, 0, -230526, 0, -58208, 0, 76476, 0, -286868, 0, -103696, 0, -39378, 0, 14120, 0, 195222, 0, 58896, 0, -212676, 0, -55592, 0, 38592, 0, 167420, 0, -121392, 0, -127216, 0, -195160, 0, 71834, 0, -111404, 0, -28320, 0, -278564, 0, -249940, 0, 1824, 0, -50112, 0, -24528, 0, -171036, 0, 76992, 0, 182850, 0, 46560, 0, -171496, 0, -86572, 0, -199956, 0, -184040, 0, 365100, 0, 130230, 0, -95384, 0, -122496, 0, 6676, 0, -146422, 0, -274658, 0, 456992, 0, 85728, 0, 316476, 0, -88352, 0, 81476, 0, -271206, 0, 8068, 0, 231200, 0, -224456, 0, -23688, 0, -289472, 0, 114378, 0, -3248, 0, 87922, 0, 214880, 0, 492172, 0, -18000, 0, 105810, 0, -146280, 0, 327910, 0, 422628, 0, -82592, 0, 62066, 0, -224988, 0, 148862, 0, 123252, 0, 113898, 0, -127836, 0, -203968, 0, -76476, 0, -321366, 0, 4148, 0, 33320, 0, 101940, 0, -96196, 0, 171904, 0, -65120, 0, 140816, 0, 302346, 0, -73776, 0, 154640, 0, 51620, 0, -89508, 0, 80368, 0, -299072, 0, 540542, 0, -2968, 0, -38374, 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": "58.4.a.c", "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, 0], [1, 0], [0, 0], [-1, 1], [0, 0], [5, 6], [0, 0], [8, -8], [0, 0], [-20, -2], [0, 0], [-45, 3], [0, 0], [25, 8], [0, 0], [31, -1], [0, 0], [-22, -16], [0, 0], [54, 4], [0, 0], [-56, 16], [0, 0], [14, -78], [0, 0], [116, 60], [0, 0], [35, -45], [0, 0], [-29, 0], [0, 0], [-33, 109], [0, 0], [63, -48], [0, 0], [-248, 8], [0, 0], [-20, 4], [0, 0], [23, 17], [0, 0], [152, 80], [0, 0], [-65, -53], [0, 0], [-172, -130], [0, 0], [257, -99], [0, 0], [105, -128], [0, 0], [-74, -6], [0, 0], [479, 52], [0, 0], [-117, -255], [0, 0], [-30, 50], [0, 0], [-90, -250], [0, 0], [-514, -12], [0, 0], [-64, 144], [0, 0], [413, 190], [0, 0], [-456, 20], [0, 0], [-482, 92], [0, 0], [-398, 34], [0, 0], [-428, -176], [0, 0], [244, 56], [0, 0], [-504, 384], [0, 0], [159, -361], [0, 0], [235, 134], [0, 0], [-914, 38], [0, 0], [-686, -212], [0, 0], [29, -29], [0, 0], [-472, -72], [0, 0], [-184, -136], [0, 0], [687, -142], [0, 0], [414, 344], [0, 0], [184, -100], [0, 0], [864, 30], [0, 0]]}