# Stored data for newform 648.4.a.k, downloaded from the LMFDB on 20 April 2024.
{"label": "648.4.a.k", "space_label": "648.4.a", "level": 648, "weight": 4, "hecke_orbit": 11, "hecke_orbit_code": 45035996340814472, "dim": 5, "is_polredabs": true, "trace_hash": 1121449443121109587, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-86528, 36176, -1097, -461, 5, 1]]], "qexp_display": "q+(-1-\\beta _{2})q^{5}+(1+\\beta _{1})q^{7}+(5-2\\beta _{2}+\\cdots)q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 10368, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 38.23323768371992, "hecke_ring_index": 1296, "level_radical": 6, "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": [648, 1, [487, 325, 569], [1, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 248610177, "field_disc_factorization": [[3, 2], [27623353, 1]], "field_poly": [12, 81, 4, -19, -1, 1], "hecke_ring_index_factorization": [[2, 4], [3, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "4.632", "prec": 17}, {"__RealLiteral__": 0, "data": "0.149", "prec": 17}, {"__RealLiteral__": 0, "data": "56.482", "prec": 20}, {"__RealLiteral__": 0, "data": "7.445", "prec": 17}, {"__RealLiteral__": 0, "data": "1089.911", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1]], "trace_display": [0, 0, -5, 3], "traces": [0, 5, 0, 0, 0, -5, 0, 3, 0, 0, 0, 25, 0, 29, 0, 0, 0, -28, 0, 64, 0, 0, 0, -89, 0, 322, 0, 0, 0, -129, 0, 241, 0, 0, 0, 243, 0, 366, 0, 0, 0, -171, 0, 803, 0, 0, 0, 477, 0, 1072, 0, 0, 0, -374, 0, 1469, 0, 0, 0, 607, 0, 1349, 0, 0, 0, -527, 0, 1549, 0, 0, 0, 812, 0, 1928, 0, 0, 0, -903, 0, 1727, 0, 0, 0, 1025, 0, 2902, 0, 0, 0, -2310, 0, 2985, 0, 0, 0, 2012, 0, 2875, 0, 0, 0, -3081, 0, 3221, 0, 0, 0, 3192, 0, 2678, 0, 0, 0, -2289, 0, 3143, 0, 0, 0, 3078, 0, 1750, 0, 0, 0, -2499, 0, 2072, 0, 0, 0, 3251, 0, 1512, 0, 0, 0, -3699, 0, 2793, 0, 0, 0, 703, 0, 2499, 0, 0, 0, -3157, 0, 535, 0, 0, 0, 5801, 0, 917, 0, 0, 0, -3777, 0, 444, 0, 0, 0, 2451, 0, 666, 0, 0, 0, -2013, 0, -1836, 0, 0, 0, 9516, 0, -1710, 0, 0, 0, -10170, 0, 454, 0, 0, 0, -603, 0, -3797, 0, 0, 0, -6738, 0, -4876, 0, 0, 0, 14523, 0, -3153, 0, 0, 0, -4954, 0, -4231, 0, 0, 0, 4735, 0, -5415, 0, 0, 0, -6706, 0, -2821, 0, 0, 0, 15057, 0, -3439, 0, 0, 0, -2396, 0, -9507, 0, 0, 0, -4153, 0, -9273, 0, 0, 0, -12250, 0, -10196, 0, 0, 0, 824, 0, -6043, 0, 0, 0, 1157, 0, -15234, 0, 0, 0, -3983, 0, -12574, 0, 0, 0, -1822, 0, -8456, 0, 0, 0, 7568, 0, -11419, 0, 0, 0, 7355, 0, -9035, 0, 0, 0, 2127, 0, -5927, 0, 0, 0, -7497, 0, -11677, 0, 0, 0, 4453, 0, -6957, 0, 0, 0, -20147, 0, -4632, 0, 0, 0, 6063, 0, -4641, 0, 0, 0, -10521, 0, -771, 0, 0, 0, 17308, 0, -17552, 0, 0, 0, 1821, 0, -8453, 0, 0, 0, 2657, 0, -8781, 0, 0, 0, 12167, 0, -9375, 0, 0, 0, -4509, 0, -8847, 0, 0, 0, -12391, 0, -11828, 0, 0, 0, -30216, 0, -9933, 0, 0, 0, 21562, 0, -2377, 0, 0, 0, 7194, 0, -9011, 0, 0, 0, 21609, 0, 6748, 0, 0, 0, -21069, 0, -6219, 0, 0, 0, 31651, 0, -5810, 0, 0, 0, 24055, 0, 8830, 0, 0, 0, -15555, 0, 7483, 0, 0, 0, -41262, 0, 17679, 0, 0, 0, -24033, 0, 2785, 0, 0, 0, 31935, 0, 10645, 0, 0, 0, 7954, 0, 12645, 0, 0, 0, -22336, 0, 2588, 0, 0, 0, 4928, 0, 10287, 0, 0, 0, 36053, 0, 12390, 0, 0, 0, 20212, 0, -4779, 0, 0, 0, -69519, 0, 17251, 0, 0, 0, -13097, 0, 2473, 0, 0, 0, -19680, 0, 11541, 0, 0, 0, 46315, 0, 7148, 0, 0, 0, -40759, 0, -6990, 0, 0, 0, 39953, 0, 40760, 0, 0, 0, 7887, 0, 12306, 0, 0, 0, 49476, 0, 19641, 0, 0, 0, -18348, 0, 33087, 0, 0, 0, -17889, 0, 22026, 0, 0, 0, -29243, 0, 34119, 0, 0, 0, -12280, 0, 3056, 0, 0, 0, -6470, 0, 43816, 0, 0, 0, 11985, 0, 43092, 0, 0, 0, 25862, 0, -390, 0, 0, 0, 11878, 0, 38743, 0, 0, 0, -2172, 0, 32487, 0, 0, 0, 41686, 0, 13493, 0, 0, 0, -23837, 0, 10563, 0, 0, 0, -19679, 0, -315, 0, 0, 0, -110044, 0, 35440, 0, 0, 0, 72585, 0, -7738, 0, 0, 0, -4355, 0, -1396, 0, 0, 0, 32794, 0, 38910, 0, 0, 0, -52989, 0, -15337, 0, 0, 0, 71186, 0, 25909, 0, 0, 0, 50055, 0, 54478, 0, 0, 0, -17751, 0, 33767, 0, 0, 0, -88002, 0, 28123, 0, 0, 0, -43452, 0, 3488, 0, 0, 0, 76720, 0, 55030, 0, 0, 0, -4223, 0, 50013, 0, 0, 0, -25144, 0, -16405, 0, 0, 0, -3417, 0, 22387, 0, 0, 0, 84669, 0, 6085, 0, 0, 0, 63708, 0, -1521, 0, 0, 0, -87557, 0, -27859, 0, 0, 0, -8849, 0, -14175, 0, 0, 0, -51416, 0, 18687, 0, 0, 0, 70822, 0, -63305, 0, 0, 0, -89835, 0, -14208, 0, 0, 0, 38886, 0, 12024, 0, 0, 0, 12015, 0, -17927, 0, 0, 0, 87581, 0, -35089, 0, 0, 0, -16304, 0, -13611, 0, 0, 0, -41448, 0, 48351, 0, 0, 0, -17134, 0, 16861, 0, 0, 0, -54715, 0, 244, 0, 0, 0, 16411, 0, 31447, 0, 0, 0, -22344, 0, -13347, 0, 0, 0, 79991, 0, -43490, 0, 0, 0, -1429, 0, 27342, 0, 0, 0, 9169, 0, 13537, 0, 0, 0, 59526, 0, -76876, 0, 0, 0, -18984, 0, -56636, 0, 0, 0, -83051, 0, -27475, 0, 0, 0, -111693, 0, -24337, 0, 0, 0, 48919, 0, -64950, 0, 0, 0, 48322, 0, -104433, 0, 0, 0, 13412, 0, 8912, 0, 0, 0, -65244, 0, -31682, 0, 0, 0, 84567, 0, -24239, 0, 0, 0, 84020, 0, 8258, 0, 0, 0, -95150, 0, -49557, 0, 0, 0, -82899, 0, -33118, 0, 0, 0, -124116, 0, -9750, 0, 0, 0, 119238, 0, 21217, 0, 0, 0, -9501, 0, 30717, 0, 0, 0, 24088, 0, -106209, 0, 0, 0, 11929, 0, -54101, 0, 0, 0, 170421, 0, -28383, 0, 0, 0, 17858, 0, -79136, 0, 0, 0, -124057, 0, -48360, 0, 0, 0, -98472, 0, -110844, 0, 0, 0, -10287, 0, -81956, 0, 0, 0, 102342, 0, -70621, 0, 0, 0, -18599, 0, -70097, 0, 0, 0, 50235, 0, 33176, 0, 0, 0, 65924, 0, -77616, 0, 0, 0, 2723, 0, -98116, 0, 0, 0, 45506, 0, 81006, 0, 0, 0, -136845, 0, -1149, 0, 0, 0, -23199, 0, 38618, 0, 0, 0, -88716, 0, -76875, 0, 0, 0, 95631, 0, -23544, 0, 0, 0, -24943, 0, 57169, 0, 0, 0, 102936, 0, -105855, 0, 0, 0, -55479, 0, 53322, 0, 0, 0, 83409, 0, -33738, 0, 0, 0, -32921, 0, -159688, 0, 0, 0, 26332, 0, -25903, 0, 0, 0, -68001, 0, -79982, 0, 0, 0, -103336, 0, -16178, 0, 0, 0, 67399, 0, -136077, 0, 0, 0, 47709, 0, -99951, 0, 0, 0, -22026, 0, 115589, 0, 0, 0, 8375, 0, -56593, 0, 0, 0, 10682, 0, -18227, 0, 0, 0, 126639, 0, 34612, 0, 0, 0, -77953, 0, -44237, 0, 0, 0, -70151, 0, 108255, 0, 0, 0, -119850, 0, 46232, 0, 0, 0, 136307, 0, 102097, 0, 0, 0, -99978, 0, 68944, 0, 0, 0, 71747, 0, -121695, 0, 0, 0, -103263, 0, 68059, 0, 0, 0, 144365, 0, 16041, 0, 0, 0, 63264, 0, -47355, 0, 0, 0, -57021, 0, -32318, 0, 0, 0, -50757, 0, -122703, 0, 0, 0, -10853, 0, 98450, 0, 0, 0, -36046, 0, -69177, 0, 0, 0, -37042, 0, -86209, 0, 0, 0, -66353, 0, 76509, 0, 0, 0, 84046, 0, -132444, 0, 0, 0, 102397, 0, 57210, 0, 0, 0, -3504, 0, 100640, 0, 0, 0, -12246, 0, 99172, 0, 0, 0, 37065, 0, 106370, 0, 0, 0, -187965, 0, -94648, 0, 0, 0, 95100, 0, 174234, 0, 0, 0, -125321, 0, 189060, 0, 0, 0, 108768, 0, 19659, 0, 0, 0, -6355, 0, 111079, 0, 0, 0, 127762, 0, -8617, 0, 0, 0, 66069, 0, 10184, 0, 0, 0, 20175, 0, -25687, 0, 0, 0, -133171, 0, 28850, 0, 0, 0, -66480, 0, 47174, 0, 0, 0, -61921, 0, -39629, 0, 0, 0, 45188, 0, -26291, 0, 0, 0, 50486, 0, 167061, 0, 0, 0, -30561, 0, 66539, 0, 0, 0, 39444, 0, -5036, 0, 0, 0, 155760, 0, 28399, 0, 0, 0, -177911, 0, 191022, 0, 0, 0, -20283, 0, 168602, 0, 0, 0, -48138, 0, 87016, 0, 0, 0, 78111, 0, 221347, 0, 0, 0, 3245, 0, 72137, 0, 0, 0, 25278, 0, 540, 0, 0, 0, 17355, 0, 90395, 0, 0, 0, 60245, 0, 123534, 0, 0, 0, -71499, 0, -9247, 0, 0, 0, -10861, 0, -88145, 0, 0, 0, -126688, 0, 30337, 0, 0, 0, 8379, 0, 104677, 0, 0, 0, 156309, 0, -100609, 0, 0, 0, -778, 0, -129662, 0, 0, 0, 25816, 0, 55809, 0, 0, 0, 9704, 0, 110771, 0, 0, 0, 25597, 0, 23061, 0, 0, 0, -7656, 0, 207739, 0, 0, 0, -120153, 0, 113451, 0, 0, 0, -36042, 0, 14581, 0, 0, 0, 19393, 0, 49900, 0, 0, 0, 32052, 0, 185628, 0, 0, 0, 162604, 0, 340053, 0, 0, 0, -70511, 0, -138497, 0, 0, 0, -132051, 0, 80018, 0, 0, 0, 17429, 0, 217058, 0, 0, 0, -37158, 0, -34112, 0, 0, 0, -93225, 0, -899, 0, 0, 0, 70119, 0, -75585, 0, 0, 0, 48984, 0, 51589, 0, 0, 0, 146513, 0, -6921, 0, 0, 0, -64835, 0, -17439, 0, 0, 0, -26745, 0, 246620, 0, 0, 0, 66060, 0, -131829, 0, 0, 0, -73575, 0, -159863, 0, 0, 0, -63736, 0, 263673, 0, 0, 0, 110509, 0, 203811, 0, 0, 0, 6629, 0, 157621, 0, 0, 0, 130798, 0, 39581, 0, 0, 0, -8593, 0, 22036, 0, 0, 0, -39633, 0, 145845, 0, 0, 0, 68512, 0, -141288, 0, 0, 0, 7782, 0, 74714, 0, 0, 0, -69075, 0, 153700, 0, 0, 0, 36897, 0, -229700, 0, 0, 0, 9396, 0, 86418, 0, 0, 0, 13409, 0, -200059, 0, 0, 0, -201750, 0, 8882, 0, 0, 0, -100095, 0, -330513, 0, 0, 0, 66677, 0, -337845, 0, 0, 0, -15123, 0, 247232, 0, 0, 0, -138501, 0, -96050, 0, 0, 0, 105940, 0, 94673, 0, 0, 0, 35792, 0, 99483, 0, 0, 0, 86265, 0, -125082, 0, 0, 0, -85587, 0, 192957, 0, 0, 0, -63480, 0, -105651, 0, 0, 0, -134593, 0, 251225, 0, 0, 0, -99237, 0, 114536, 0, 0, 0, -127884, 0, -308114, 0, 0, 0, 202983, 0, 216923, 0, 0, 0, -102294, 0, -74156, 0, 0, 0, 143478, 0, -195335, 0, 0, 0, -7570, 0, -193683, 0, 0, 0, 26032, 0, -150016, 0, 0, 0, 63131, 0, -25924, 0, 0, 0, 64037, 0, -62497, 0, 0, 0, -184683, 0, -160891, 0, 0, 0, 229839, 0, 111248, 0, 0, 0, 52546, 0, -315808, 0, 0, 0, 186957, 0, 48909, 0, 0, 0, -151968, 0, 150570, 0, 0, 0, 171451, 0, -74057, 0, 0, 0, 23513, 0, 33415, 0, 0, 0, -98758, 0, -129741, 0, 0, 0, -313911, 0, 158622, 0, 0, 0, 216725, 0, -87659, 0, 0, 0, -107285, 0, -193620, 0, 0, 0, 144923, 0, -40521, 0, 0, 0, -158718, 0, -298711, 0, 0, 0, 9369, 0, -10220, 0, 0, 0, 18122, 0, -85597, 0, 0, 0, 196608, 0, -268507, 0, 0, 0, -35241, 0, -218633, 0, 0, 0, -57219, 0, -504687, 0, 0, 0, 1792, 0, -2233, 0, 0, 0, 121809, 0, -11960, 0, 0, 0, -248805, 0, -107615, 0, 0, 0, -210756, 0, -182976, 0, 0, 0, -11109, 0, -96448, 0, 0, 0, 115959, 0, 73431, 0, 0, 0, 27553, 0, 90516, 0, 0, 0, 387811, 0, 12636, 0, 0, 0, 59227, 0, -11006, 0, 0, 0, 111953, 0, 46493, 0, 0, 0, -195905, 0, -68259, 0, 0, 0, 11193, 0, 15728, 0, 0, 0, -141959, 0, -38898, 0, 0, 0, -135940, 0, -447270, 0, 0, 0, -57456, 0, -215579, 0, 0, 0, 312473, 0, -28295, 0, 0, 0, 103276, 0, 11446, 0, 0, 0, 29427, 0, -32021, 0, 0, 0, -37110, 0, -424167, 0, 0, 0, -188548, 0, -170081, 0, 0, 0, -5776, 0, -66744, 0, 0, 0, -230693, 0, -38487, 0, 0, 0, -335004, 0, 25789, 0, 0, 0, 209893, 0, 43371, 0, 0, 0, 225372, 0, -130974, 0, 0, 0, 490392, 0, 58065, 0, 0, 0, -322749, 0, 57129, 0, 0, 0, 21557, 0, -16575, 0, 0, 0, -52191, 0, -211393, 0, 0, 0, -88673, 0, -260057, 0, 0, 0, -487642, 0, 149368, 0, 0, 0, 58884, 0, -144971, 0, 0, 0, 97719, 0, -178644, 0, 0, 0, 251871, 0, -444356, 0, 0, 0, 212652, 0, -279027, 0, 0, 0, -143866, 0, 19495, 0, 0, 0, 71658, 0, -218777, 0, 0, 0, -69706, 0, 198016, 0, 0, 0, -30341, 0, -211353, 0, 0, 0, 45684, 0, -332763, 0, 0, 0, -60109, 0, 178198, 0, 0, 0, 288525, 0, 58401, 0, 0, 0, -360699, 0, 209557, 0, 0, 0, -16362, 0, -310446, 0, 0, 0, -4309, 0, 34007, 0, 0, 0, 104853, 0, 522438, 0, 0, 0, -316821, 0, -242522, 0, 0, 0, 220672, 0, 214188, 0, 0, 0, -14547, 0, -65853, 0, 0, 0, 91098, 0, -212216, 0, 0, 0, -115796, 0, -9277, 0, 0, 0, 105551, 0, 160025, 0, 0, 0, 251776, 0, 134032, 0, 0, 0, -493659, 0, -357921, 0, 0, 0, -50775, 0, -347481, 0, 0, 0, -18763, 0, 352642, 0, 0, 0, 169551, 0, 10939, 0, 0, 0, 108150, 0, -85380, 0, 0, 0, -361021, 0, 272106, 0, 0, 0, 51099, 0, -36241, 0, 0, 0, 381405, 0, 195047, 0, 0, 0, 121586, 0, 148448, 0, 0, 0, -233004, 0, 301992, 0, 0, 0, 110155, 0, 236872, 0, 0, 0, 208808, 0, -327840, 0, 0, 0, 330466, 0, 142026, 0, 0, 0, -248415, 0, 124626, 0, 0, 0, -205209, 0, 252, 0, 0, 0, 432174, 0, -247892, 0, 0, 0, -293552, 0, -466155, 0, 0, 0, -121689, 0, 497503, 0, 0, 0, -141956, 0, -286281, 0, 0, 0, 184093, 0, 78104, 0, 0, 0, -3234, 0, 142585, 0, 0, 0, -170205, 0, -283831, 0, 0, 0, -544620, 0, 124982, 0, 0, 0, 164333, 0, 86205, 0, 0, 0, 128619, 0, 379707, 0, 0, 0, 109389, 0, 72398, 0, 0, 0, 463245, 0, -381168, 0, 0, 0, -130335, 0, 483066, 0, 0, 0, 170220, 0, 257158, 0, 0, 0, -420516, 0, 31910, 0, 0, 0, -221271, 0, 391236, 0, 0, 0, -18302, 0, 220663, 0, 0, 0, -555367, 0, -38220, 0, 0, 0, 238383, 0, 145469, 0, 0, 0, 471015, 0, 303704, 0, 0, 0, 582858, 0, -46285, 0, 0, 0, -44949, 0, -247557, 0, 0, 0, -161215, 0, 35931, 0, 0, 0, -204737, 0, 616179, 0, 0, 0, 169980, 0, 103128, 0, 0, 0, -349457, 0, 213492, 0, 0, 0, -44876, 0, 57006, 0, 0, 0, 466041, 0, 165083, 0, 0, 0, 367977, 0, 218298, 0, 0, 0, 315266, 0, 334869, 0, 0, 0, -462018, 0, 480281, 0, 0, 0, -314855, 0, -153255, 0, 0, 0, -5868, 0, 258436, 0, 0, 0, -440381, 0, 69255, 0, 0, 0, -566769, 0, 80353, 0, 0, 0, 46742, 0, -17207, 0, 0, 0, 611671, 0, -189607, 0, 0, 0, 554178, 0, 334857, 0, 0, 0, 354572, 0, 223084, 0, 0, 0, -400529, 0, 18099, 0, 0, 0, 423489, 0, -26182, 0, 0, 0, -603501, 0, -202946, 0, 0, 0, -67232, 0, 154033, 0, 0, 0, -291771, 0, -31959, 0, 0, 0, -173508, 0, 508381, 0, 0, 0, 249649, 0, 259923, 0, 0, 0, 306665, 0, 122208, 0, 0, 0, 39366, 0, 180632, 0, 0, 0, 76407, 0, 98871, 0, 0, 0, -273501, 0, 325914, 0, 0, 0, 190191, 0, -216540, 0, 0, 0, 126820, 0, 370470, 0, 0, 0, 28989, 0, 264141, 0, 0, 0, -21903, 0, 23852, 0, 0, 0, 108502, 0, 314191, 0, 0, 0, -300456, 0, -81756, 0, 0, 0, 516091, 0, -165436, 0, 0, 0, -719988, 0, 261255, 0, 0, 0, 276749, 0, 291458, 0, 0, 0, 65797, 0, 433992, 0, 0, 0, 178691, 0, 163095, 0, 0, 0, -504821, 0, -79219, 0, 0, 0, -178974, 0, 95170, 0, 0, 0, -338238, 0, -45334, 0, 0, 0, 521998, 0, 240927, 0, 0, 0, -57005, 0, 599788, 0, 0, 0, -299229, 0, -265554, 0, 0, 0, 221547, 0, 342980, 0, 0, 0, 58932, 0, 17318, 0, 0, 0, 398060, 0, 25623, 0, 0, 0, -212136, 0, -3470, 0, 0, 0, -917988, 0, -63039, 0, 0, 0, 624952, 0, 348757, 0, 0, 0, 53187, 0, -291895, 0, 0, 0, 63672, 0, 267181, 0, 0, 0, -137071, 0, -234118, 0, 0, 0, 221001, 0, -413070, 0, 0, 0, 53342, 0, -80016, 0, 0, 0, 294231, 0, -35580, 0, 0, 0, -141111, 0, 255785, 0, 0, 0, 158616, 0, -70659, 0, 0, 0, -293902, 0, 39579, 0, 0, 0, 37260, 0, 397333, 0, 0, 0, 257715, 0, -398980, 0, 0, 0, -346125, 0, 141143, 0, 0, 0, 319315, 0, 197986, 0, 0, 0, -62532, 0, -172020, 0, 0, 0, -442014, 0, 447723, 0, 0, 0, -340323, 0, 30869, 0, 0, 0, -95008, 0, -33252, 0, 0, 0, -59841, 0, -210968, 0, 0, 0, 71061, 0, -255623, 0, 0, 0, 892187, 0, 145878, 0, 0, 0, -234641, 0, 557387, 0, 0, 0, -128679, 0, -170639, 0, 0, 0, -580332, 0, 265932, 0, 0, 0, 499722, 0, -192890, 0, 0, 0, -854625, 0, 56945, 0, 0, 0, -309552, 0, 84033, 0, 0, 0, 684659, 0, -245298, 0, 0, 0, 542402, 0, 207578, 0, 0, 0, 447346, 0, -15916, 0, 0, 0, -226091, 0, 278045, 0, 0, 0, -527775, 0, 107269, 0, 0, 0, 52263, 0, -118613, 0, 0, 0, -40395, 0, -590977, 0, 0, 0, 244569, 0, -462501, 0, 0, 0, 38328, 0, 519649, 0, 0, 0, 312676, 0, -60113, 0, 0, 0, 421939, 0, -224178, 0, 0, 0, 232652, 0, -233149, 0, 0, 0, -714054, 0, -737449, 0, 0, 0, 527937, 0, -12243, 0, 0, 0, -685298, 0, -284163, 0, 0, 0, -240981, 0, 443072, 0, 0, 0, -430662, 0, -153951, 0, 0, 0, 437184, 0, -152045, 0, 0, 0, 332954, 0, 100375, 0, 0, 0, 381986, 0, -280213, 0, 0, 0, 278580, 0, -690463, 0, 0, 0, 77603, 0, -305295, 0, 0, 0, -216049, 0, 66492, 0, 0, 0, -496202, 0, -69242, 0, 0, 0, 239560, 0, 219846, 0, 0, 0, -213547, 0, 141327, 0, 0, 0, -439185, 0, -702415, 0, 0, 0, 722639, 0, -637326, 0, 0, 0, -65996, 0, 178413, 0, 0, 0, 321903, 0, 137774, 0, 0, 0, -177385, 0, 38806, 0, 0, 0, -161843, 0, -342682, 0, 0, 0, -22350, 0, -66012, 0, 0, 0, 323760, 0, -470377, 0, 0, 0, 112160, 0, -199388, 0, 0, 0, -316611, 0, -56630, 0, 0, 0, -108972, 0, -46773, 0, 0, 0, 145921, 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": "72.4.i.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "nf_label": 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, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-1, 0, -1, 0, 0], [0, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [5, 0, -2, 0, 1], [0, 0, 0, 0, 0], [7, 2, 1, -1, 1], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-6, 0, -3, 1, -1], [0, 0, 0, 0, 0], [12, -1, -2, 1, -2], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-17, -1, -2, -3, -1], [0, 0, 0, 0, 0], [62, -2, 1, 4, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-23, 6, -1, -1, 1], [0, 0, 0, 0, 0], [49, -1, -6, -3, 1], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [41, -11, -2, 8, -6], [0, 0, 0, 0, 0], [72, -6, 12, -3, -5], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-33, 2, 4, -1, 1], [0, 0, 0, 0, 0], [161, 0, -8, -1, 6], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [99, 7, 8, -2, 10], [0, 0, 0, 0, 0], [218, 4, 11, -5, 9], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-68, 10, 16, -7, 7], [0, 0, 0, 0, 0], [289, -5, -18, 7, 3], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [121, -6, 12, -5, 0], [0, 0, 0, 0, 0], [267, -2, 23, 5, -13], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-121, -32, 9, 7, -11], [0, 0, 0, 0, 0], [305, -6, -2, 6, -15], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [170, 18, 18, -1, -3], [0, 0, 0, 0, 0], [390, 8, -23, -3, 3], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-187, 4, 3, 20, -4], [0, 0, 0, 0, 0], [359, 17, -18, -17, 3], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [215, 23, 6, -2, -8], [0, 0, 0, 0, 0], [576, 6, -12, 17, -1], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [-464, -22, -14, -17, 9], [0, 0, 0, 0, 0], [613, 37, 76, -3, 13], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [408, 20, -16, 6, 2], [0, 0, 0, 0, 0], [577, -2, -48, -7, 11], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]}