# Stored data for newform 588.4.a.f, downloaded from the LMFDB on 24 April 2024.
{"label": "588.4.a.f", "space_label": "588.4.a", "level": 588, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22517998203961932, "dim": 2, "is_polredabs": true, "nf_label": "2.2.193.1", "trace_hash": 1865345827185970785, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-18, 11, 1]]], "qexp_display": "q-3q^{3}+(-5-\\beta )q^{5}+9q^{9}+(1-7\\beta )q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 9408, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 34.69312308337548, "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": [588, 1, [295, 197, 493], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 193, "field_disc_factorization": [[193, 1]], "field_poly": [-48, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.024", "prec": 17}, {"__RealLiteral__": 0, "data": "1.902", "prec": 17}, {"__RealLiteral__": 0, "data": "0.170", "prec": 17}, {"__RealLiteral__": 0, "data": "9.432", "prec": 17}, {"__RealLiteral__": 0, "data": "1.952", "prec": 17}, {"__RealLiteral__": 0, "data": "65.774", "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], [3, 1], [7, -1]], "trace_display": [0, -6, -11, 0], "traces": [0, 2, 0, -6, 0, -11, 0, 0, 0, 18, 0, -5, 0, -5, 0, 33, 0, -100, 0, -67, 0, 0, 0, 76, 0, -93, 0, -54, 0, 275, 0, -362, 0, 15, 0, 0, 0, -5, 0, 15, 0, 162, 0, 721, 0, -99, 0, 216, 0, 0, 0, 300, 0, 495, 0, 703, 0, 201, 0, -173, 0, 532, 0, 0, 0, 510, 0, 111, 0, -228, 0, 1600, 0, -1215, 0, 279, 0, 0, 0, 1460, 0, 162, 0, 1409, 0, 164, 0, -825, 0, 1974, 0, 0, 0, 1086, 0, 658, 0, -561, 0, -45, 0, -188, 0, 1025, 0, 0, 0, 351, 0, 123, 0, 15, 0, 1634, 0, -2348, 0, -45, 0, 0, 0, 2079, 0, -486, 0, 825, 0, 2360, 0, -2163, 0, -347, 0, 0, 0, 297, 0, 554, 0, 183, 0, -648, 0, 3390, 0, -451, 0, 0, 0, -4614, 0, 1203, 0, -900, 0, 3921, 0, -1702, 0, -1485, 0, 0, 0, 2872, 0, -2109, 0, 4744, 0, -1969, 0, -603, 0, -134, 0, 0, 0, 519, 0, 1506, 0, -5537, 0, -1596, 0, 4370, 0, -2452, 0, 0, 0, -6786, 0, -4784, 0, -1530, 0, -2870, 0, 1124, 0, -333, 0, 0, 0, -2628, 0, 684, 0, 2194, 0, -3746, 0, -4800, 0, -3676, 0, 0, 0, 3645, 0, -1680, 0, -2305, 0, -837, 0, 11643, 0, -2493, 0, 0, 0, -6566, 0, 2286, 0, -4380, 0, -1794, 0, 203, 0, -486, 0, 0, 0, 1615, 0, -4227, 0, 759, 0, -13700, 0, -492, 0, 8412, 0, 0, 0, 2475, 0, 11502, 0, -3591, 0, -5922, 0, 11743, 0, -3479, 0, 0, 0, -7198, 0, -10583, 0, -3258, 0, -6458, 0, 1287, 0, -1974, 0, 0, 0, -3282, 0, 1683, 0, 1473, 0, -4163, 0, 135, 0, -9840, 0, 0, 0, 564, 0, -6786, 0, -9, 0, -3075, 0, 16498, 0, 5376, 0, 0, 0, -7761, 0, 6743, 0, -1053, 0, 2192, 0, -5075, 0, -369, 0, 0, 0, -71, 0, -45, 0, 6820, 0, -5578, 0, -4902, 0, 14415, 0, 0, 0, 7044, 0, 6252, 0, -1884, 0, 135, 0, 13206, 0, -13046, 0, 0, 0, -13666, 0, -10605, 0, -6237, 0, 1568, 0, 1094, 0, 1458, 0, 0, 0, -477, 0, -2475, 0, 4620, 0, 5337, 0, -7080, 0, -13834, 0, 0, 0, 6489, 0, 1304, 0, 3920, 0, 1041, 0, -14013, 0, 1465, 0, 0, 0, 7668, 0, 10555, 0, -891, 0, 30410, 0, -11164, 0, -1662, 0, 0, 0, 1997, 0, -549, 0, -3210, 0, 6323, 0, 1944, 0, 8896, 0, 0, 0, -10170, 0, -714, 0, -12013, 0, 1353, 0, -8336, 0, -959, 0, 0, 0, 8881, 0, -14910, 0, 13842, 0, -6418, 0, -12564, 0, -3609, 0, 0, 0, 19716, 0, 2700, 0, 8146, 0, 14553, 0, -11763, 0, -3566, 0, 0, 0, 5106, 0, 224, 0, -69, 0, 4455, 0, -13762, 0, 21725, 0, 0, 0, 287, 0, 15190, 0, -8616, 0, 13425, 0, -17996, 0, 6327, 0, 0, 0, 25137, 0, -14232, 0, 7950, 0, 18790, 0, 5907, 0, 17907, 0, 0, 0, 1809, 0, 5074, 0, 23778, 0, 402, 0, -5994, 0, 6131, 0, 0, 0, 10380, 0, 17154, 0, -1557, 0, -9090, 0, 18045, 0, -4518, 0, 0, 0, -4969, 0, 16611, 0, -3668, 0, 11744, 0, 4788, 0, -6028, 0, 0, 0, -13110, 0, -10501, 0, -355, 0, 7356, 0, -26119, 0, 1628, 0, 0, 0, 25734, 0, 737, 0, 20358, 0, 17696, 0, 5202, 0, 14352, 0, 0, 0, -7317, 0, 4590, 0, 12809, 0, 17917, 0, 8610, 0, 19938, 0, 0, 0, -3372, 0, 7998, 0, -6778, 0, 999, 0, -14812, 0, 33970, 0, 0, 0, 16830, 0, 16214, 0, 7884, 0, -11948, 0, 18261, 0, -2052, 0, 0, 0, -3624, 0, -6582, 0, -17120, 0, -28955, 0, 11238, 0, -2751, 0, 0, 0, 14400, 0, 16978, 0, 18779, 0, 11028, 0, -17796, 0, -35369, 0, 0, 0, 1407, 0, -30419, 0, -10935, 0, 2788, 0, -11949, 0, 5040, 0, 0, 0, -10780, 0, 6915, 0, -28350, 0, 13972, 0, 2511, 0, -15621, 0, 0, 0, -34929, 0, -44697, 0, -2854, 0, 7479, 0, -5580, 0, 10607, 0, 0, 0, 16460, 0, -1152, 0, 19698, 0, -43633, 0, 13195, 0, -6858, 0, 0, 0, -40748, 0, 13140, 0, -52356, 0, -21540, 0, 5382, 0, -35436, 0, 0, 0, -609, 0, -24464, 0, 38892, 0, 1458, 0, -37208, 0, -34007, 0, 0, 0, 51736, 0, 32045, 0, -4845, 0, -14436, 0, 17850, 0, 12681, 0, 0, 0, -29440, 0, -2277, 0, -35663, 0, 18284, 0, 41100, 0, -5512, 0, 0, 0, 1476, 0, -25140, 0, -7980, 0, -25236, 0, 280, 0, -4397, 0, 0, 0, -10638, 0, -33722, 0, -7425, 0, -29432, 0, 35050, 0, -34506, 0, 0, 0, -20630, 0, 10773, 0, 30519, 0, -24696, 0, 17766, 0, -32764, 0, 0, 0, -35229, 0, 65270, 0, -34674, 0, 10437, 0, -25060, 0, -23285, 0, 0, 0, -29987, 0, -35256, 0, 21594, 0, -23973, 0, 24411, 0, 31749, 0, 0, 0, -25706, 0, 9774, 0, -45400, 0, 711, 0, 19374, 0, 8417, 0, 0, 0, -3861, 0, -87040, 0, 41291, 0, 5922, 0, 48954, 0, 19202, 0, 0, 0, -13264, 0, 48022, 0, 9846, 0, -45531, 0, 36875, 0, -5049, 0, 0, 0, -35502, 0, -4419, 0, -46998, 0, -45623, 0, 12489, 0, -29910, 0, 0, 0, -405, 0, 3186, 0, 15456, 0, 29520, 0, -28545, 0, -21276, 0, 0, 0, 50622, 0, 30533, 0, -1692, 0, -52722, 0, 64703, 0, 20358, 0, 0, 0, -40359, 0, 27, 0, -25230, 0, -47535, 0, 9225, 0, 19128, 0, 0, 0, -49494, 0, -19324, 0, -39874, 0, -16128, 0, -8237, 0, 40896, 0, 0, 0, 12626, 0, -22535, 0, 23283, 0, -16514, 0, 39060, 0, -20229, 0, 0, 0, 44540, 0, 3159, 0, 62789, 0, 15760, 0, -6576, 0, 19617, 0, 0, 0, 15225, 0, 67920, 0, -33306, 0, 1107, 0, -56040, 0, 35278, 0, 0, 0, 21608, 0, -17666, 0, 213, 0, 6556, 0, 7475, 0, 135, 0, 0, 0, 29108, 0, -20460, 0, -19188, 0, 21460, 0, 16734, 0, -10761, 0, 0, 0, 14706, 0, -37657, 0, 76176, 0, -43245, 0, 11574, 0, -33565, 0, 0, 0, -5820, 0, 70658, 0, -21132, 0, -11160, 0, -46016, 0, -18756, 0, 0, 0, -35420, 0, 5652, 0, -188, 0, 10559, 0, -405, 0, -15874, 0, 0, 0, -39618, 0, -28853, 0, -74032, 0, 39138, 0, -18187, 0, -50425, 0, 0, 0, 47080, 0, -36711, 0, 40998, 0, 45210, 0, -61272, 0, 31815, 0, 0, 0, 86246, 0, 18711, 0, -18175, 0, 103323, 0, -4704, 0, 12946, 0, 0, 0, -3282, 0, 9908, 0, -13920, 0, -4374, 0, -9465, 0, 124762, 0, 0, 0, -46091, 0, 41168, 0, 1431, 0, -9548, 0, -37567, 0, 7425, 0, 0, 0, 93932, 0, -13860, 0, 72418, 0, -69537, 0, -16011, 0, -35272, 0, 0, 0, 21240, 0, 3386, 0, 87755, 0, 41502, 0, -64662, 0, -57954, 0, 0, 0, -25200, 0, -29402, 0, -19467, 0, 97845, 0, -5768, 0, -3912, 0, 0, 0, -50256, 0, -11760, 0, -48258, 0, 138951, 0, -3123, 0, 104606, 0, 0, 0, 42039, 0, 3825, 0, 3168, 0, -4395, 0, 33074, 0, 69504, 0, 0, 0, -21248, 0, -32327, 0, -23004, 0, 86023, 0, -63016, 0, -31665, 0, 0, 0, -58368, 0, 2673, 0, 35016, 0, 36180, 0, -91230, 0, -82470, 0, 0, 0, 33492, 0, 74979, 0, -8561, 0, 4986, 0, -25770, 0, -78844, 0, 0, 0, 81208, 0, 70220, 0, -5991, 0, 102322, 0, 8956, 0, 1647, 0, 0, 0, 27381, 0, 9630, 0, 110958, 0, -12590, 0, -18969, 0, 105844, 0, 0, 0, -5832, 0, -64062, 0, 18573, 0, -26688, 0, 49719, 0, -5584, 0, 0, 0, 21009, 0, -78690, 0, 30510, 0, 85512, 0, -39802, 0, 2142, 0, 0, 0, 47545, 0, 36039, 0, 35911, 0, -12625, 0, -4059, 0, 40453, 0, 0, 0, 25008, 0, 89250, 0, -58050, 0, 2877, 0, 1404, 0, 2207, 0, 0, 0, -13464, 0, -14343, 0, -26643, 0, -22185, 0, -124711, 0, 44730, 0, 0, 0, 50995, 0, -41526, 0, -49068, 0, -28013, 0, 19254, 0, -66338, 0, 0, 0, 37692, 0, 13827, 0, 95716, 0, 10827, 0, 67304, 0, 67914, 0, 0, 0, -69806, 0, 94119, 0, -59148, 0, 24916, 0, -77043, 0, -8100, 0, 0, 0, 20673, 0, -24438, 0, 20282, 0, 25359, 0, -43659, 0, 99000, 0, 0, 0, 35289, 0, 65703, 0, 70629, 0, 10698, 0, 97416, 0, -34154, 0, 0, 0, -2532, 0, -109436, 0, -15318, 0, -100780, 0, -15265, 0, -672, 0, 0, 0, 90279, 0, 207, 0, 68415, 0, -18278, 0, -13365, 0, 10418, 0, 0, 0, 41286, 0, 42818, 0, -225425, 0, -65175, 0, 56651, 0, -15680, 0, 0, 0, -81678, 0, -84145, 0, -861, 0, 30384, 0, 14508, 0, -45570, 0, 0, 0, 8979, 0, 25848, 0, 48990, 0, -13620, 0, -40275, 0, 64304, 0, 0, 0, 53988, 0, -39408, 0, 39071, 0, -18981, 0, 45978, 0, 110232, 0, 0, 0, -121569, 0, 77280, 0, -75411, 0, 67872, 0, -66859, 0, 42696, 0, 0, 0, -34, 0, -23850, 0, 27118, 0, -82488, 0, -56370, 0, -78570, 0, 0, 0, -17721, 0, -33074, 0, 17722, 0, -53721, 0, 121808, 0, -65011, 0, 0, 0, -13750, 0, 58509, 0, -5427, 0, -144392, 0, 124556, 0, -15222, 0, 0, 0, -147544, 0, -71334, 0, 33872, 0, -109460, 0, -1206, 0, -71088, 0, 0, 0, 17982, 0, 21191, 0, -149792, 0, -18393, 0, 116798, 0, -22085, 0, 0, 0, -17962, 0, -51368, 0, -31140, 0, 94584, 0, 113613, 0, -51462, 0, 0, 0, 11225, 0, 4671, 0, 53141, 0, -26805, 0, 27270, 0, 158118, 0, 0, 0, -54135, 0, 130272, 0, 16833, 0, 13554, 0, 27029, 0, -13600, 0, 0, 0, -105815, 0, -41453, 0, 14907, 0, -55620, 0, 41431, 0, -49833, 0, 0, 0, 145720, 0, 11004, 0, 37459, 0, -41154, 0, -35232, 0, -106965, 0, 0, 0, -14364, 0, 39244, 0, 45245, 0, 18084, 0, 52790, 0, -224275, 0, 0, 0, -206333, 0, -10299, 0, 39330, 0, 102509, 0, -99351, 0, 31503, 0, 0, 0, -86897, 0, 1065, 0, 56120, 0, -93454, 0, -22068, 0, 14853, 0, 0, 0, 78357, 0, -78288, 0, -181731, 0, -4884, 0, 215496, 0, -66525, 0, 0, 0, -160770, 0, -206373, 0, -77202, 0, -110589, 0, -80047, 0, -2211, 0, 0, 0, -61624, 0, -61074, 0, -151250, 0, -2352, 0, -53088, 0, -267296, 0, 0, 0, -15606, 0, -149937, 0, -70284, 0, -43056, 0, 155790, 0, 104929, 0, 0, 0, -8938, 0, 260866, 0, 21951, 0, -94096, 0, 47998, 0, -13770, 0, 0, 0, 97246, 0, -38427, 0, 53190, 0, -128796, 0, -53751, 0, 30690, 0, 0, 0, -25830, 0, -27694, 0, 57177, 0, -59814, 0, -420, 0, -53372, 0, 0, 0, 29101, 0, -12361, 0, 10116, 0, -72028, 0, 106622, 0, -23994, 0, 0, 0, -55959, 0, 20334, 0, 38931, 0, 86875, 0, -2997, 0, 93240, 0, 0, 0, 44436, 0, 175140, 0, -97452, 0, -101910, 0, -109458, 0, 112757, 0, 0, 0, -70977, 0, -244168, 0, -50490, 0, 75043, 0, -9158, 0, -48642, 0, 0, 0, 10398, 0, -23652, 0, -9534, 0, 101775, 0, 35844, 0, 5816, 0, 0, 0, -54783, 0, -11965, 0, -151351, 0, 6156, 0, -82586, 0, -48134, 0, 0, 0, 2254, 0, 140864, 0, 10872, 0, -35057, 0, 95144, 0, 19746, 0, 0, 0, 38280, 0, 51360, 0, -127782, 0, -173492, 0, 86865, 0, -45662, 0, 0, 0, -33714, 0, -212622, 0, 331330, 0, 8253, 0, 27933, 0, -141388, 0, 0, 0, -31302, 0, 49646, 0, -43200, 0, 59566, 0, -124160, 0, -50934, 0, 0, 0, -45036, 0, -56337, 0, 74032, 0, -56297, 0, -33084, 0, -26100, 0, 0, 0, 53388, 0, 96998, 0, -153466, 0, 106107, 0, 42945, 0, 81545, 0, 0, 0, 60272, 0, -2203, 0, -4221, 0, -40320, 0, -148240, 0, 91257, 0, 0, 0, 162408, 0, 32805, 0, 151566, 0, -2077, 0, -8364, 0, 110898, 0, 0, 0, 35847, 0, -45210, 0, -85979, 0, -15120, 0, 155022, 0, 228828, 0, 0, 0, 70971, 0, 166617, 0, 32340, 0, 63489, 0, 9936, 0, -20745, 0, 0, 0, -47675, 0, 85050, 0, -150210, 0, -28169, 0, -41916, 0, 88290, 0, 0, 0, -7533, 0, 245555, 0, 271445, 0, 46863, 0, 48168, 0, -179800, 0, 0, 0, 56530, 0, -189710, 0, 104787, 0, 17977, 0, 156072, 0, 134091, 0, 0, 0, -137987, 0, 8562, 0, -90440, 0, 173294, 0, -22437, 0, 3810, 0, 0, 0, 16740, 0, -81220, 0, -13095, 0, -31821, 0, -172730, 0, 128519, 0, 0, 0, 151610, 0, -35024, 0, -49380, 0, -72100, 0, 20201, 0, 3456, 0, 0, 0, -52404, 0, -59094, 0, 208617, 0, 29124, 0, 130899, 0, 83436, 0, 0, 0, -39585, 0, 143900, 0, 176210, 0, 20574, 0, -223322, 0, -53500, 0, 0, 0, 267299, 0, 1596, 0, 122244, 0, 56994, 0, 4721, 0, -39420, 0, 0, 0, 49209, 0, 157068, 0, -58413, 0, 137817, 0, 64620, 0, -22894, 0, 0, 0, -16146, 0, -89578, 0, -12864, 0, 106308, 0, -158916, 0, 174044, 0, 0, 0, -65072, 0, 143626, 0, 1827, 0, -9930, 0, 55728, 0, 73392, 0, 0, 0, -91073, 0, -116676, 0, -229720, 0, 121504, 0, -4374, 0, 86356, 0, 0, 0, 111624, 0, -136677, 0, 3845, 0, 102021, 0, -374520, 0, -4977, 0, 0, 0, 144658, 0, -59254, 0, -155208, 0, 155179, 0, -125177, 0, -96135, 0, 0, 0, -22421, 0, 14535, 0, -47208, 0, 146660, 0, 43308, 0, 34652, 0, 0, 0, -53550, 0, 12823, 0, 292489, 0, -38043, 0, -109150, 0, 95708, 0, 0, 0, 236760, 0, 86895, 0, 88320, 0, 128160, 0, -175030, 0, 6831, 0, 0, 0, 117625, 0, 106989, 0, 216214, 0, 103826, 0, -54852, 0, -65642, 0, 0, 0, -123300, 0, 175842, 0, 33194, 0, 16536, 0, -166145, 0, -192060, 0, 0, 0, 134937, 0, -141539, 0, -4428, 0, 180936, 0, -79779, 0, 75420, 0, 0, 0, -11414, 0, 23940, 0, -31815, 0, 85940, 0, 75708, 0, -184358, 0, 0, 0, -840, 0, -245974, 0, -362264, 0, 13191, 0, 114930, 0, -28472, 0, 0, 0, -20835, 0, 58792, 0, 31914, 0, -41763, 0, -111475, 0, 101166, 0, 0, 0, 127582, 0, 22275, 0, -237456, 0, 114685, 0, 88296, 0, -57753, 0, 0, 0, -105150, 0, -79016, 0, 241562, 0, 103518, 0, -175280, 0, 309596, 0, 0, 0, -59772, 0, 256477, 0, 61890, 0, -233796, 0, -10325, 0, -32319, 0, 0, 0, 203829, 0, -91557, 0, -21532, 0, 28406, 0, 74088, 0, 26524, 0, 0, 0, -53298, 0, -131550, 0, 300949, 0, 98292, 0, -264549, 0, -48373, 0, 0, 0, 126268, 0, 78048, 0, 105687, 0, -83468, 0, 56870, 0, -195810, 0, 0, 0, -157920, 0, 104022, 0, -38383, 0, 186192, 0, -31311, 0, 40514, 0, 0, 0, 75180, 0, 184040, 0, -383920, 0, 69855, 0, -405617, 0, -49809, 0, 0, 0, 298978, 0, -386172, 0, 89961, 0, -7172, 0, 160065, 0, 105768, 0, 0, 0, -207863, 0, -64782, 0, -211290, 0, 334095, 0, 71919, 0, 25650, 0, 0, 0, -73233, 0, -85358, 0, 22194, 0, -95247, 0, -176564, 0, -67611, 0, 0, 0, 112572, 0, 134663, 0, 77118, 0, 64504, 0, 194345, 0, -29322, 0, 0, 0, -9564, 0, 136200, 0, -66046, 0, -269337, 0, -2133, 0, -186574, 0, 0, 0, -58122, 0, -146477, 0, 260808, 0, -25251, 0, -77710, 0, -196215, 0, 0, 0, 151128, 0, 62763, 0, 11583, 0, 107813, 0, 151023, 0, 261120, 0, 0, 0, -155799, 0, -123873, 0, 104640, 0, -276752, 0, -17766, 0, 56036, 0, 0, 0, -146862, 0, -60099, 0, -165489, 0, -57606, 0, 326640, 0, 226842, 0, 0, 0, -66510, 0, 60880, 0, 39792, 0, -330272, 0, 225879, 0, -144066, 0, 0, 0, -150208, 0, -29538, 0, -17980, 0, -191106, 0, 136593, 0, -196690, 0, 0, 0, -110625, 0, -34010, 0, 5441, 0, 15147, 0, 180138, 0, 180206, 0, 0, 0, -195070, 0, 421944, 0, 106506, 0, 80762, 0, -83724, 0, 13257, 0, 0, 0, 46269, 0, 140994, 0, -241027, 0, -85080, 0, 136869, 0, 609469, 0, 0, 0, -37467, 0, 200100, 0, 323310, 0, 89730, 0, -84950, 0, 93420, 0, 0, 0, 240272, 0, -260879, 0, 1215, 0, -236052, 0, 323286, 0, -9558, 0, 0, 0, 50313, 0, -46368, 0, -23770, 0, -81494, 0, -88560, 0, -396852, 0, 0, 0, 85635, 0, -262175, 0, -227115, 0, 63828, 0, -20052, 0, -329047, 0, 0, 0, -94696, 0, -631, 0, -151866, 0, -122250, 0, 224247, 0, -91599, 0, 0, 0, 27187, 0, 5076, 0, 31424, 0, 161081, 0, 158166, 0, 8748, 0, 0, 0, -194109, 0, -149369, 0, -173020, 0, -61074, 0, -124758, 0, 260330, 0, 0, 0, -418512, 0, 37400, 0, 121077, 0, -438354, 0, 218991, 0, -81, 0, 0, 0, -45084, 0, 75690, 0, -106544, 0, -202806, 0, 142605, 0, -211160, 0, 0, 0, -27675, 0, 146552, 0, 154931, 0, -57384, 0, -36117, 0, -236152, 0, 0, 0, 175170, 0, 236676, 0, 148482, 0, -310434, 0, 43211, 0, 57972, 0, 0, 0, -167425, 0, 119622, 0, -107921, 0, 164981, 0, 48384, 0, -190993, 0, 0, 0, 24711, 0, -192746, 0, -247998, 0, -122688, 0, 131988, 0, 65511, 0, 0, 0, 200881, 0, -238744, 0, -37878, 0, -46181, 0, -281076, 0, 67605, 0, 0, 0, -56998, 0, -69849, 0, -80964, 0, -140933, 0, 49542, 0, 334691, 0, 0, 0, -117180, 0, -81504, 0, -127440, 0, 60687, 0, 108100, 0, 245580, 0, 0, 0, -115934, 0, 62307, 0, -133620, 0, 139685, 0, 9825, 0, -9477, 0, 0, 0, 7722, 0, -188367, 0, -152496, 0, -288080, 0, -47280, 0, -346298, 0, 0, 0, 19728, 0, 209965, 0, 206028, 0, -58851, 0, 209601, 0, -429457, 0, 0, 0, -114900, 0, -272885, 0, -45675, 0, -189686, 0, 169466, 0, -203760, 0, 0, 0, -298093, 0, 99918, 0, -30387, 0, -182440, 0, -3321, 0, -215598, 0, 0, 0, 168120, 0, -56610, 0, 187424, 0, -105834, 0, 54964, 0, 226657, 0, 0, 0, 191045, 0, -224880, 0, -64824, 0, -27468, 0, -203282, 0, 52998, 0, 0, 0, -45395, 0, -639, 0, -28455, 0, -59362, 0, -19668, 0, 258764, 0, 0, 0, -22425, 0, -6354, 0, -85098, 0, -405, 0, -87172, 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": "84.4.i.a", "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, 0], [1, 0], [0, 0], [-3, 0], [0, 0], [-5, -1], [0, 0], [0, 0], [0, 0], [9, 0], [0, 0], [1, -7], [0, 0], [0, -5], [0, 0], [15, 3], [0, 0], [-52, 4], [0, 0], [-32, -3], [0, 0], [0, 0], [0, 0], [28, 20], [0, 0], [-52, 11], [0, 0], [-27, 0], [0, 0], [143, -11], [0, 0], [-171, -20], [0, 0], [-3, 21], [0, 0], [0, 0], [0, 0], [20, -45], [0, 0], [0, 15], [0, 0], [72, 18], [0, 0], [362, -3], [0, 0], [-45, -9], [0, 0], [126, -36], [0, 0], [0, 0], [0, 0], [156, -12], [0, 0], [243, 9], [0, 0], [331, 41], [0, 0], [96, 9], [0, 0], [-113, 53], [0, 0], [246, 40], [0, 0], [0, 0], [0, 0], [240, 30], [0, 0], [94, -77], [0, 0], [-84, -60], [0, 0], [778, 44], [0, 0], [-634, 53], [0, 0], [156, -33], [0, 0], [0, 0], [0, 0], [699, 62], [0, 0], [81, 0], [0, 0], [755, -101], [0, 0], [68, 28], [0, 0], [-429, 33], [0, 0], [966, 42], [0, 0], [0, 0], [0, 0], [513, 60], [0, 0], [304, 50], [0, 0], [-295, 29], [0, 0], [9, -63], [0, 0]]}