# Stored data for newform 350.4.a.m, downloaded from the LMFDB on 19 April 2024.
{"label": "350.4.a.m", "space_label": "350.4.a", "level": 350, "weight": 4, "hecke_orbit": 13, "hecke_orbit_code": 54043195595555166, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 116757738345845750, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [7, 1]], [11, [37, 1]]], "qexp_display": "q+2q^{2}-7q^{3}+4q^{4}-14q^{6}+7q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 5600, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 20.650668502009214, "hecke_ring_index": 1, "level_radical": 70, "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": [350, 1, [127, 101], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 5, 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": "0.976", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.913", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.732", "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], [5, -1], [7, -1]], "trace_display": [2, -7, 0, 7], "traces": [0, 1, 2, -7, 4, 0, -14, 7, 8, 22, 0, -37, -28, 51, 14, 0, 16, 41, 44, -108, 0, -49, -74, -70, -56, 0, 102, 35, 28, -249, 0, -134, 32, 259, 82, 0, 88, -334, -216, -357, 0, 206, -98, -376, -148, 0, -140, -287, -112, 49, 0, -287, 204, -6, 70, 0, 56, 756, -498, -2, 0, -940, -268, 154, 64, 0, 518, 106, 164, 490, 0, 456, 176, 650, -668, 0, -432, -259, -714, -1239, 0, -839, 412, 428, -196, 0, -752, 1743, -296, -220, 0, 357, -280, 938, -574, 0, -224, -1055, 98, -814, 0, 1960, -574, 1825, 408, 0, -12, -144, 140, 1681, 0, 2338, 112, 798, 1512, 0, -996, 1122, -4, 287, 0, 38, -1880, -1442, -536, 0, 308, 434, 128, 2632, 0, -1290, 1036, -756, 212, 0, 328, 192, 980, 1402, 0, 2009, 912, -1887, 352, 0, 1300, -343, -1336, -302, 0, -3167, -864, 902, -518, 0, -1428, -470, -2478, 42, 0, -490, -1678, -2390, 824, 0, 856, -2631, -392, 404, 0, -2376, -1504, -2243, 3486, 0, -592, 14, -440, 52, 0, 2462, 714, 6580, -560, 0, 1876, -1517, -1148, 245, 0, 3159, -448, 2060, -2110, 0, 196, 1738, -1628, -894, 0, -742, 3920, -1743, -1148, 0, 3650, -1540, 816, 3996, 0, -4083, -24, -3192, -288, 0, 280, -938, 3362, -4550, 0, 2091, 4676, 377, 224, 0, 1596, -2551, 3024, 74, 0, 1813, -1992, 1888, 2244, 0, -8, 8673, 574, 4997, 0, -3830, 76, 4928, -3760, 0, -2884, -5508, -1072, -2996, 0, -3390, 616, 2590, 868, 0, 256, 7170, 5264, -2338, 0, -5478, -2580, -7672, 2072, 0, -1512, 1540, 424, -54, 0, 2932, 656, -2499, 384, 0, 1960, 3254, 2804, -2948, 0, 3327, 4018, 4627, 1824, 0, -3774, 1442, 704, -3232, 0, 7385, 2600, -4083, -686, 0, -2672, -1295, -604, -3570, 0, -2632, -6334, -13720, -1728, 0, 1804, -4089, -1036, -12775, 0, -4008, -2856, 7355, -940, 0, -4956, -1684, 84, 9213, 0, 1008, -980, -4428, -3356, 0, -4780, -11767, 1648, -2009, 0, -1460, 1712, -7348, -5262, 0, -784, 7514, 808, -5586, 0, 4958, -4752, 343, -3008, 0, -4486, -2862, 6972, -6368, 0, 1785, -1184, -3635, 28, 0, -880, -2009, 104, 7116, 0, 4805, 4924, -266, 1428, 0, 13160, -319, -1120, 4532, 0, -42, 3752, -11652, -3034, 0, -2296, -12699, 490, 7748, 0, -3038, 6318, 8680, -896, 0, 4120, -8272, -4220, -1711, 0, -2870, 392, 9030, 3476, 0, -3256, 1589, -1788, 5292, 0, -5147, -1484, -6834, 7840, 0, -3486, 12358, -2296, -9100, 0, -1344, 7300, -14, -3080, 0, 1632, -9814, 7992, 2618, 0, -3695, -8166, -6314, -48, 0, -6384, -6580, -576, 13209, 0, 15779, 560, 7238, -1876, 0, 6724, 7560, -9100, -2646, 0, 1078, 4182, 5688, 9352, 0, 754, 2114, 448, -3285, 0, -7622, 3192, 22169, -5102, 0, 6048, 14834, 148, 1435, 0, -9972, 3626, -9096, -3984, 0, 3776, 15867, 4488, 742, 0, 3290, -16, 13912, 17346, 0, 1148, -132, 9994, 242, 0, -17034, -7660, 3430, 152, 0, 9856, -3558, -7520, 16730, 0, 1473, -5768, -10209, -11016, 0, -2144, 3192, -5992, 603, 0, 18417, -6780, 18387, 1232, 0, 5180, -2828, 1736, 9018, 0, 4550, 512, -3780, 14340, 0, 10528, 10619, -4676, 15701, 0, 4624, -10956, -5876, -5160, 0, -15344, -5494, 4144, -7267, 0, -44, -3024, 10506, 3080, 0, 848, -364, -108, -1813, 0, -8537, 5864, -17234, 1312, 0, -4998, -13060, 768, -20680, 0, 26892, 3920, -8673, 6508, 0, 5608, 21372, -5896, -19176, 0, 10619, 6654, -12704, 8036, 0, 9254, -5873, 3648, 8762, 0, -24764, -7548, -22113, 2884, 0, 1408, 1811, -6464, -14420, 0, 2996, 14770, 222, 5200, 0, -8166, 10548, -1372, 14472, 0, -12166, -5344, 17439, -2590, 0, -1208, 6258, -7140, 2451, 0, -7792, -5264, 2332, -12668, 0, -27440, -1937, -3456, 12201, 0, -14637, 3608, 5036, -8178, 0, -2072, -27286, -25550, 28538, 0, -2450, -8016, -1540, -5712, 0, 14710, -27972, -1880, -13694, 0, 25007, -9912, 28581, -3368, 0, 168, 2499, 18426, 10032, 0, -12130, 2016, 14385, -1960, 0, -8856, -2208, -6712, 74, 0, 6566, -9560, 22448, -23534, 0, 3296, 14300, -4018, 8791, 0, -13180, -2920, -14637, 3424, 0, -14696, 17430, -10524, -2639, 0, 34780, -1568, -7164, 15028, 0, 1616, 12335, -11172, -7385, 0, 17857, 9916, -15436, -9504, 0, 686, -518, -6016, -306, 0, -19184, -8972, -5698, -5724, 0, 13944, 8446, -12736, -13216, 0, 32975, 3570, 36072, -2368, 0, -7270, 13720, 56, -31497, 0, -27258, -1760, 9380, -4018, 0, 208, -34979, 14232, -18610, 0, 12775, 9610, 26810, 9848, 0, -532, -17508, 2856, -11843, 0, -15416, 26320, -4685, -638, 0, -2240, -3922, 9064, -25925, 0, 38556, -84, 25578, 7504, 0, -23304, 9416, -6068, -1008, 0, -4291, -4592, 23730, -25398, 0, 980, -31528, 15496, -18130, 0, -23154, -6076, 11767, 12636, 0, 17360, -102, -1792, 13992, 0, -50190, 8240, -21681, -16544, 0, -8440, 16366, -3422, -22248, 0, -16872, -5740, -8715, 784, 0, 18060, -16903, 6952, 53704, 0, 5586, -6512, -47940, 3178, 0, -3576, 18905, 10584, -11767, 0, -4840, -10294, -24050, -2968, 0, -13668, 378, 15680, -5571, 0, 10894, -6972, -20524, 24716, 0, -4592, 40608, -18200, 7854, 0, -30731, -2688, 1038, 14600, 0, -28, 7958, -6160, -30666, 0, -22778, 3264, 2009, -19628, 0, 15984, -4690, 5236, -5354, 0, 37612, -7390, -23289, -16332, 0, -12628, 266, -96, -32389, 0, 23380, -12768, -42890, -13160, 0, -1152, 22950, 26418, -2824, 0, -10094, 31558, -4866, 1120, 0, 14476, 22624, -3752, 45843, 0, 5406, 13448, -23210, 15120, 0, -18200, -10676, -5292, 28581, 0, -29856, 2156, -1944, 8364, 0, 11376, -14628, 18704, 3038, 0, 31043, 1508, 30996, 4228, 0, 896, 24990, -6570, 33366, 0, -246, -15244, 18424, 6384, 0, 44338, -12858, -10204, 43120, 0, -18324, 12096, -15836, 29668, 0, 296, -9030, 2870, -14751, 0, 28623, -19944, 23256, 7252, 0, -18192, 40150, -7968, -47922, 0, -5292, 7552, 28056, 31734, 0, 8976, -44987, 1484, -51485, 0, -20356, 6580, -14420, -32, 0, 27824, -27786, 34692, 33150, 0, 11788, 2296, -48674, -264, 0, 19988, -64491, 484, 1344, 0, -11835, -34068, -3168, -15320, 0, 6860, -11168, 304, 30996, 0, 20094, 19712, 9814, -7116, 0, -15040, 49104, 33460, 8140, 0, 36982, 2946, 27751, -11536, 0, -20418, 14063, -22032, 26320, 0, 37600, -4288, 10220, 6384, 0, -11984, -10911, 1206, -11690, 0, -13209, 36834, -82, -13560, 0, 36774, 648, 2464, -6103, 0, -52598, 10360, -8718, -5656, 0, 3472, 17556, 18036, 11748, 0, 8172, 9100, -34706, 1024, 0, -7560, -63189, 28680, -2401, 0, -22585, 21056, 53302, 21238, 0, -9352, -38540, 31402, 2032, 0, 20034, 9248, -2114, -21912, 0, -11752, 44576, -10320, 16128, 0, -673, -30688, -42789, -10988, 0, 8288, -22169, -14534, 25445, 0, -18783, -88, 20540, -6048, 0, 21012, 39035, 6160, 28496, 0, 6314, 1696, 83166, -728, 0, -216, -49812, -3626, 21828, 0, 20090, -17074, -33635, 11728, 0, -34468, 8324, 2624, 836, 0, 8548, -9996, -32348, -26120, 0, 1536, 24534, -41360, -3290, 0, 2233, 53784, -61232, 7840, 0, -17346, 7210, 13016, -19206, 0, -72520, 11216, 294, 42744, 0, -11792, -50110, -38352, 81564, 0, 216, 21238, 43885, 13308, 0, -25408, -3430, 16072, 16841, 0, 88893, 18508, -67525, -11746, 0, 7296, -54236, 17524, 4346, 0, -16730, -49528, 9548, -15096, 0, -44226, 44756, 5768, -60760, 0, 31480, 2816, -41838, 3622, 0, -12928, -11220, -28840, 101520, 0, -13160, 5992, -39160, 29540, 0, 444, 11977, 10400, -18417, 0, 37633, -16332, 20090, 21096, 0, -2744, 5328, 28944, -28380, 0, 64014, -24332, 2828, -10688, 0, 34878, 22404, -5180, -51294, 0, -11123, -2416, 7107, 12516, 0, -14280, -16632, 4902, -62197, 0, 52995, -15584, 36029, -10528, 0, 4664, 18696, -25336, 47838, 0, -15701, -54880, 36270, -3874, 0, -6912, -20091, 24402, 420, 0, -86506, -29274, -40187, 7216, 0, 10072, 63700, -16356, -55986, 0, 2628, -4144, 4224, -54572, 0, -51100, -5754, 57076, 98, 0, 26650, -4900, -29526, -16032, 0, -3080, 93624, -11424, -32768, 0, 30844, 29420, 364, -55944, 0, -3760, -18326, -27388, -41704, 0, -53805, 50014, 25865, -19824, 0, 57162, 17234, -6736, -10045, 0, -27604, 336, -11448, 4998, 0, 36852, -12267, 20064, -21486, 0, 46060, -24260, -62884, 4032, 0, 28770, -41514, -3920, 21970, 0, 52768, -17712, -110453, -4416, 0, -13424, -8378, 148, -50666, 0, -48210, 13132, 30598, -19120, 0, 44896, -36159, -47068, -10619, 0, -52920, 6592, 99960, 28600, 0, -8036, 18522, 17582, -52916, 0, 9496, -26360, 1715, -5840, 0, -29274, 59758, 6848, -39816, 0, 47841, -29392, 50384, 34860, 0, -21048, 22113, -5278, 93075, 0, -6644, 69560, -50799, -3136, 0, -14328, 22995, 30056, -49248, 0, 14420, 3232, 53354, 24670, 0, -22344, 140, -14770, -69674, 0, -88730, 35714, 71463, 19832, 0, -30872, 30736, -19008, 60903, 0, -103838, 1372, 61982, -1036, 0, -12032, -34399, -612, 12166, 0, -57714, -38368, 69804, -17944, 0, -11396, -70200, -11448, 63672, 0, -7344, 27888, -6258, 16892, 0, -25472, -16058, -26432, -32816, 0, -111069, 65950, 65800, 7140, 0, 72144, -5194, -4736, -86475, 0, 17548, -14540, -10340, 27440, 0, 112, 85731, -62994, -97384, 0, -12201, -54516, 20284, -3520, 0, 18760, 51729, -8036, 39186, 0, -210, 416, 48713, -69958, 0, 28464, -1694, -37220, -14201, 0, 47730, 25550, 119238, 19220, 0, 53620, 36001, 19696, -10780, 0, -77068, -1064, -50948, -35016, 0, 5712, 38458, -23686, 84304, 0, 24906, -30832, 27972, 52640, 0, -9370, -52580, -1276, 40698, 0, 49712, -4480, -10311, -7844, 0, 18128, -28581, -51850, 71463, 0, -55491, 77112, -33367, -168, 0, 51156, -39043, 15008, -47334, 0, -22344, -46608, -103388, 18832, 0, -12136, -4221, -2016, 96201, 0, 133812, -8582, -57882, -9184, 0, 47460, -7104, -50796, -128709, 0, 2382, 1960, -9020, -63056, 0, 30992, -68804, -36260, -6566, 0, 8888, -46308, 71940, -12152, 0, 23534, -63126, 25272, -51874, 0, 54452, 34720, -31850, -204, 0, -3584, 1494, 27984, 90612, 0, -7420, -100380, 45557, 16480, 0, -43362, 14637, -33088, -31970, 0, -74333, -16880, -35521, 32732, 0, -6844, -49346, -44496, 79476, 0, 2639, -33744, -32368, -11480, 0, -17430, 3336, 1568, 41132, 0, 24372, 36120, 1938, -33806, 0, 13904, -46224, 107408, -27259, 0, 38458, 11172, 69044, -13024, 0, -95880, 50869, 6356, -17857, 0, 125584, -7152, -70, 37810, 0, 21168, -21852, -23534, -73542, 0, 4688, -9680, 518, -20588, 0, -48100, -116642, -5936, -35996, 0, 1144, -27336, -55238, 756, 0, 31360, 12691, -11142, 61923, 0, -56162, 21788, 59759, -13944, 0, -41048, 121216, 49432, 54164, 0, 13216, -9184, -31920, 81216, 0, -36400, 38875, 15708, 11174, 0, 91420, -61462, 804, -5376, 0, 2076, -32900, 29200, -43255, 0, 22134, -56, -188244, 15916, 0, -12320, -15461, -61332, 60711, 0, 117179, -45556, -63744, 6528, 0, 4018, 91286, -39256, 2614, 0, -149604, 31968, 34979, -9380, 0, 10472, 134232, -10708, -45500, 0, -26485, 75224, -33374, -14780, 0, -46578, -26810, -32664, 88928, 0, 23760, -25256, 70279, 532, 0, -192, -2370, -64778, -1906, 0, 34496, 46760, -65790, -25536, 0, -85780, -61334, -26320, 112209, 0, 498, -2304, 173348, 45900, 0, 52836, 80360, -5648, 69498, 0, 92468, -20188, -49726, 63116, 0, -9732, 17390, 2240, -38556, 0, -12677, 28952, -38328, 45248, 0, -7504, 45320, 91686, 95858, 0, -11614, 10812, -20972, 26896, 0, -46420, 41254, 30240, -1554, 0, 74825, -36400, 43933, -21352, 0, -10584, -23730, 57162, 7624, 0, -73836, -59712, -77456, 4312, 0, -3888, -101304, 16728, 234060, 0, 18130, 22752, 38236, -29256, 0, 37408, -56710, 6076, -122073, 0, 9792, 62086, -67283, 3016, 0, 61992, -23540, 8456, 11750, 0, -19668, 1792, 88430, 49980, 0, -13140, -17157, 66732, 50190, 0, -76663, -492, 54544, -30488, 0, 36848, 71502, 12768, 3710, 0, -37500, 88676, -16366, -25716, 0, -20408, 86730, 86240, -5904, 0, 13559, -36648, 6981, 24192, 0, -31672, -38346, 59336, 268, 0, -91195, 592, 102459, -18060, 0, 5740, 97347, -29502, -35252, 0, -53704, 57246, 113940, -39888, 0, 46512, 22504, 14504, 61869, 0, 191002, -36384, 68921, 80300, 0, -15936, -199766, -95844, -14948, 0, 109114, -10584, 58730, 15104, 0, 56112, 87025, 63468, 10780, 0, -131257, 17952, -93984, -89974, 0, 2968, 130468, -102970, -84226, 0, 87912, -40712, -378, 13160, 0, -28840, 95858, -64, -15730, 0, 125960, 55648, -175049, -55572, 0, 69384, 20524, 66300, -89826, 0, -116695, 23576, 82991, 4592, 0, -97348, -149781, -528, -29960, 0, -17493, 39976, -71034, -128982, 0, 968, 15960, 2688, -211680, 0, 32718, -23670, 84910, -68136, 0, -6336, -59122, -30640, -100695, 0, -64374, 13720, 7256, -22336, 0, 608, -15402, 61992, 22778, 0, 15456, 40188, -26394, 39424, 0, 19628, -518, -14232, 143778, 0, -28194, -30080, -20636, 98208, 0, 66920, -197100, 16280, -157136, 0, 2004, 73964, -161517, 5892, 0, 55502, 23289, -23072, -1924, 0, 22750, -40836, 76491, 28126, 0, -44064, -61537, 52640, -131764, 0, 32389, 75200, 92260, -8576, 0, 20440, -98859, 12768, 46002, 0, -91094, -23968, 151549, -21822, 0, 2412, 169986, -23380, 95795, 0, -122010, -26418, -114612, 73668, 0, -164, 8294, -27120, 10094, 0, 133373, 73548, -243460, 1296, 0, 4928, -130138, -12206, 50148, 0, 107912, -105196, -22624, 20720, 0, -17436, -71744, -11312, 90140, 0, -86345, 6944, 15552, 35112, 0, 36072, 51695, 23496, 115888, 0, -23970, 16344, -56122, 18200, 0, -69412, 15400, 2048, 108052, 0, -28581, -15120, -84750, -126378, 0, 57360, 1558, -4802, -113544, 0, 1628, -45170, 10512, 42112, 0, 106604, 2142, 42476, -61497, 0, -181548, -18704, 134288, -77080, 0, 62804, -14204, 4064, -9065, 0, 48522, 40068, -118020, 18496, 0, -4228, -119116, -43824, 118892, 0, -59122, -23504, -24990, 89152, 0, -20640, 41536, 32256, -59036, 0, -116883, -1346, -230825, -61376, 0, -85578, -18424, -21976, -252504, 0, -45533, 16576, -84619, -44338, 0, -29068, -161850, 50890, -121890, 0, -96040, -37566, -76220, -176, 0, 41080, 220479, -12096, 7005, 0, -134116, 42024, -43365, 78070, 0, 12320, -62822, 56992, -65660, 0, -54966, 12628, -68590, 3392, 0, 166332, -86184, -1456, -28623, 0, 109934, -432, 38040, -99624, 0, -7252, 130270, 43656, 17794, 0, -134578, 40180, -89425, -34148, 0, -67270, -64306, 23456, -84260, 0, -134181, -68936, -1236, 16648, 0, 5248, -28056, 1672, 97977, 0, 122556, 17096, 668, -19992, 0, -64696, -50155, -52240, 33078, 0, 51485, 3072, 107912, 49068, 0, -82720, -91443, -6580, 32795, 0, -61104, 4466, -18876, 107568, 0, -122464, -28234, 15680, -21454, 0, 27454, -34692, -58654, 14420, 0, 26032, 181475, -38412, -11788, 0, 17902, -145040, -121176, 22432, 0, 588, -52890, 85488, -179046, 0, 73850, -23584, 64491, -100220, 0, -76704, -131830, 163128, -148834, 0, 14980, 432, 190087, 42476, 0, 87770, 7056, 26616, -114393, 0, 133572, -50816, 30037, -6860, 0, 32144, 313960, 33682, -74580, 0, -30996, 177786, -87100, 37016, 0, -135050, 64173, -23492, 6037, 0, 220696, 14592, 109458, -108472, 0, 35048, 56980, 8692, 2256, 0, 9220, -33460, 162078, -99056, 0, 19096, 216317, -30192, -82369, 0, 308511, -88452, 157386, 89512, 0, 11536, -145622, -121520, -4104, 0, 714, 62960, -14063, 5632, 0, -83676, -97944, 7244, -70726, 0, -94585, -25856, 157740, -22440, 0, -57680, -10220, 203040, 151767, 0, 151071, -26320, -137200, 11984, 0, -78320, 2652, 59080, 7872, 0, -51436, 888, -181042, 23954, 0, 20800, 155736, -36834, -55584, 0, -97218, 75266, 118104, -32664, 0, 40180, -56492, 42192, 208911, 0, 3814, -5488, 125562, 10656, 0, 57888, 161529, -56760, 52598, 0, 118321, 128028, 57482, -48664, 0, 5656, -168784, -21376, -127750, 0, 45266, 69756, -39102, 44808, 0, -10360, 23424, -102588, 335580, 0, 56949, -22246, 112533, -4832, 0, 14214, 34706, 25032, 37877, 0, -132335, -28560, 150726, -33264, 0, 9804, 82369, -124394, 134640, 0, 2401, 105990, -7700, -31168, 0, 72058, -106572, -21056, 168350, 0, 35610, 9328, -46872, 37392, 0, -50672, -21904, 95676, -412, 0, -1188, -31402, -1678, -109760, 0, 72540, 38997, -7748, -20034, 0, -77367, -13824, -76258, -40182, 0, 48804, -159244, 840, 64504, 0, 167310, -173012, -44576, -58548, 0, -80374, -40686, 14432, 166026, 0, -284256, 20144, -13949, 127400, 0, -32712, 12495, -111972, -125173, 0, 10080, 5256, 215117, -8288, 0, 8448, 18708, -109144, -7266, 0, -25445, -102200, -70252, -11508, 0, 114152, 34977, 196, -35404, 0, -55706, 53300, 161109, -9800, 0, -59052, 214662, -32064, 139320, 0, 1722, -6160, 71588, 187248, 0, -22848, 94387, -65536, -14063, 0, -193640, 61688, 26028, 58840, 0, 728, -117670, -111888, 105060, 0, 112426, -7520, 49812, -36652, 0, -54776, 37478, -83408, -2738, 0, -82659, -107610, -263284, 100028, 0, 51730, 33635, -39648, 73194, 0, 176791, 114324, -12382, 34468, 0, -13472, 752, -20090, 43400, 0, -1862, -55208, -110638, 672, 0, -22896, 101794, 9996, -101637, 0, 244776, 73704, -163660, -24534, 0, 40128, 170076, -42972, 300230, 0, 88638, 92120, -69856, -48520, 0, -125768, -129847, 8064, -2233, 0, -160650, 57540, -57352, -83028, 0, -7840, 19768, 43940, 200420, 0, 54780, 105536, 31724, -35424, 0, -220906, -45594, -8832, 34062, 0, 192679, -26848, 72075, -16756, 0, 296, -294, -101332, -55860, 0, -71104, -96420, -20736, 26264, 0, 61196, -320901, -38240, 61062, 0, -81564, 89792, -37842, -72318, 0, -94136, 204007, -21238, -36925, 0, 112200, -105840, 353440, 13184, 0, 199920, -152304, 57200, -184889, 0, 74732, -16072, 73462, 37044, 0, 35164, -89826, -105832, -88893, 0, -151416, 18992, 208992, -52720, 0, 3430, -152666, -11680, 13608, 0, 141710, -58548, 54236, 119516, 0, 13696, 165934, -79632, 4506, 0, 102396, 95682, -193839, -58784, 0, 100768, -21266, 69720, -19270, 0, -115305, -42096, -182336, 44226, 0, -10556, -256709, 186150, -216972, 0, 60760, -13288, 76932, 139120, 0, -101598, -233389, -6272, -165235, 0, -78540, -28656, 55713, 45990, 0, 60112, -233562, -98496, 48045, 0, -217100, 28840, 1722, 6464, 0, 106708, 81124, 49340, -57904, 0, 62215, -44688, -240136, 280, 0, -29540, 203796, -139348, 136604, 0, 90006, -177460, -11977, 71428, 0, 142926, 68600, 39664, -87122, 0, -200797, -61744, 128268, 61472, 0, -38016, -20090, 121806, 110852, 0, -157278, -207676, -208233, 2744, 0, 123964, 21836, -2072, 150268, 0, 63210, -24064, 2150, -68798, 0, -1224, 103257, 24332, 29480, 0, 125430, -115428, -89958, -76736, 0, 139608, 173374, -35888, -162792, 0, -97990, -22792, 574, -140400, 0, -22896, 149145, 127344, 11123, 0, 63875, -14688, -2660, 55776, 0, -12516, 335454, 33784, -269952, 0, -234604, -50944, 37044, -32116, 0, -52864, -219366, -65632, -88176, 0, -128925, -222138, 164404, 131900, 0, 131600, -36029, 14280, -148841, 0, 314909, 144288, 262695, -10388, 0, -9472, 161810, -172950, -65700, 0, -47838, 35096, 142492, -29080, 0, -20680, -265290, 54880, 100940, 0, 32616, 224, 71317, 171462, 0, -125988, 174300, -194768, -107871, 0, 194502, -24402, -161826, -109032, 0, 40568, -232050, -7040, 86506, 0, -159188, 37520, -37048, 103458, 0, -16072, 160670, 78372, 340718, 0, -90232, -420, -63700, 832, 0, 97426, 269780, -139916, 342036, 0, 202686, 56928, 16564, -3388, 0, -74440, -9408, -28402, 297527, 0, -39856, 95460, 82845, 51100, 0, 238476, 269256, 38440, -5040, 0, -98, 107240, 283864, 72002, 0, 39392, 102806, -21560, 19227, 0, 78176, -154136, -166479, -2128, 0, -101896, -97416, -70032, -185763, 0, 93936, 11424, -140658, 76916, 0, -47372, 7246, 168608, -68698, 0, -30380, 49812, 413826, -61664, 0, 55944, 1436, 105280, -488040, 0, -343728, -18740, 18326, -105160, 0, -2552, -56980, 81396, 243348, 0, -91963, 99424, 58835, -8960, 0, -20622, -25865, -15688, -194257, 0, -130101, 36256, 60847, -57162, 0, -103700, -301635, 142926, 1998, 0, -44198, -110982, -37646, 154224, 0, -66734, -184240, -336, 1978, 0, -198042, 102312, -263200, -78086, 0, 30016, 3774, -94668, -32120, 0, -108484, -44688, 50760, -93216, 0, -206776, -454425, 37664, -46060, 0, 76377, -24272, 133900, -8442, 0, -4032, 280226, 192402, -127144, 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": "70.4.c.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], [1], [2], [-7], [4], [0], [-14], [7], [8], [22], [0], [-37], [-28], [51], [14], [0], [16], [41], [44], [-108], [0], [-49], [-74], [-70], [-56], [0], [102], [35], [28], [-249], [0], [-134], [32], [259], [82], [0], [88], [-334], [-216], [-357], [0], [206], [-98], [-376], [-148], [0], [-140], [-287], [-112], [49], [0], [-287], [204], [-6], [70], [0], [56], [756], [-498], [-2], [0], [-940], [-268], [154], [64], [0], [518], [106], [164], [490], [0], [456], [176], [650], [-668], [0], [-432], [-259], [-714], [-1239], [0], [-839], [412], [428], [-196], [0], [-752], [1743], [-296], [-220], [0], [357], [-280], [938], [-574], [0], [-224], [-1055], [98], [-814], [0]]}