# Stored data for newform 966.4.a.e, downloaded from the LMFDB on 25 April 2024.
{"label": "966.4.a.e", "space_label": "966.4.a", "level": 966, "weight": 4, "hecke_orbit": 5, "hecke_orbit_code": 18014398576591814, "dim": 3, "is_polredabs": true, "nf_label": "3.3.65101.1", "trace_hash": 1937191818899834136, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [878, -191, -5, 1]]], "qexp_display": "q+2q^{2}-3q^{3}+4q^{4}+(2+\\beta _{2})q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 15456, "fricke_eigenval": -1, "atkin_lehner_string": "-+++", "analytic_conductor": 56.99584506554543, "hecke_ring_index": 1, "level_radical": 966, "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": 0, "analytic_rank_proved": true, "char_values": [966, 1, [323, 829, 925], [1, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [2, 3, 7, 23], "conrey_indexes": [1], "field_disc": 65101, "field_disc_factorization": [[65101, 1]], "field_poly": [-29, -28, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.887", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21.486", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "237.158", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, 1], [7, 1], [23, 1]], "trace_display": [6, -9, 5, -21], "traces": [0, 3, 6, -9, 12, 5, -18, -21, 24, 27, 10, -56, -36, 29, -42, -15, 48, 28, 54, -18, 20, 63, -112, -69, -72, 32, 58, -81, -84, -242, -30, -86, 96, 168, 56, -35, 108, -70, -36, -87, 40, -402, 126, -553, -224, 45, -138, -368, -144, 147, 64, -84, 116, 23, -162, -467, -168, 54, -484, -861, -60, -311, -172, -189, 192, -624, 336, -215, 112, 207, -70, 121, 216, -588, -140, -96, -72, 392, -174, -1418, 80, 243, -804, -352, 252, -827, -1106, 726, -448, 1275, 90, -203, -276, 258, -736, -3593, -288, -602, 294, -504, 128, 1417, -168, -1368, 232, 105, 46, -3821, -324, -2121, -934, 210, -336, -1499, 108, -115, -968, 261, -1722, -196, -120, -2543, -622, 1206, -344, -894, -378, -1075, 384, 1659, -1248, -676, 672, 126, -430, -135, 224, 1174, 414, 377, -140, 1104, 242, 361, 432, 665, -1176, -441, -280, 540, -192, -3102, -144, 252, 784, -2059, -348, 5512, -2836, -69, 160, 483, 486, -2899, -1608, 1401, -704, -4222, 504, -3816, -1654, -162, -2212, -5604, 1452, -224, -896, 2583, 2550, 2689, 180, 4304, -406, 933, -552, -2085, 516, -738, -1472, 567, -7186, -4974, -576, 3292, -1204, 1872, 588, -2795, -1008, 5729, 256, 645, 2834, 1694, -336, 3793, -2736, -621, 464, 3730, 210, -11184, 92, -363, -7642, 198, -648, 602, -4242, 1764, -1868, -3427, 420, 1291, -672, 288, -2998, -371, 216, -253, -230, -1176, -1936, -8589, 522, 4868, -3444, 4254, -392, -1649, -240, 2190, -5086, -729, -1244, 245, 2412, 6107, -688, 1056, -1788, 9440, -756, 1288, -2150, 2481, 768, 3784, 3318, 490, -2496, -2178, -1352, 3394, 1344, -1255, 252, -3825, -860, 11919, -270, 3736, 448, 609, 2348, 739, 828, 3709, 754, -774, -280, 60, 2208, 9395, 484, 10779, 722, 2814, 864, 7087, 1330, 1806, -2352, 3770, -882, -3831, -560, 1512, 1080, -667, -384, 3871, -6204, -4251, -288, 15506, 504, 1324, 1568, 4104, -4118, -2869, -696, 19040, 11024, -315, -5672, 9909, -138, 1502, 320, 11463, 966, 6606, 972, 6024, -5798, 6363, -3216, 2576, 2802, -40, -1408, -630, -8444, 11011, 1008, -8769, -7632, 4497, -3308, 5306, -324, -1029, -4424, 345, -11208, -6870, 2904, 10349, -448, -783, -1792, 6502, 5166, 3966, 5100, 588, 5378, -1241, 360, 11429, 8608, 7629, -812, -2067, 1866, 23547, -1104, -3618, -4170, -161, 1032, 2042, -1476, 2682, -2944, -14211, 1134, 6280, -14372, 3225, -9948, -10562, -1152, 3269, 6584, -4977, -2408, -2260, 3744, -644, 1176, 2028, -5590, -11413, -2016, -13510, 11458, -378, 512, -10184, 1290, 11925, 5668, 405, 3388, 3206, -672, 14834, 7586, -3522, -5472, 6027, -1242, -8573, 928, -1131, 7460, 9099, 420, 6401, -22368, -3312, 184, -18645, -726, 2177, -15284, -1083, 396, -18991, -1296, 24022, 1204, -1995, -8484, 414, 3528, -5618, -3736, 1323, -6854, -23984, 840, -12960, 2582, -1620, -1344, -2759, 576, 5226, -5996, 9306, -742, 4368, 432, 3393, -506, -756, -460, -16623, -2352, 4094, -3872, 6177, -17178, -23460, 1044, 1505, 9736, -16536, -6888, 8239, 8508, 3723, -784, 207, -3298, -7380, -480, 2915, 4380, -1449, -10172, -26773, -1458, 6134, -2488, 8697, 490, -8503, 4824, 33666, 12214, -4203, -1376, -847, 2112, 21273, -3576, 12666, 18880, 115, -1512, 27041, 2576, 11448, -4300, -11158, 4962, 4116, 1536, 486, 7568, -10348, 6636, 1514, 980, 16812, -4992, -3940, -4356, 9826, -2704, 672, 6788, -32802, 2688, 1587, -2510, -7749, 504, -1887, -7650, 9098, -1720, -8067, 23838, -2744, -540, 5352, 7472, -12912, 896, 7929, 1218, 37661, 4696, -2799, 1478, -10110, 1656, 9926, 7418, 6255, 1508, 10048, -1548, -12405, -560, 2214, 120, 8065, 4416, 42409, 18790, -1701, 968, -33262, 21558, -7694, 1444, 14922, 5628, -736, 1728, -30, 14174, -9876, 2660, 2464, 3612, 2307, -4704, -5616, 7540, -16287, -1764, 19542, -7662, 8385, -1120, -5236, 3024, 5789, 2160, -17187, -1334, -40419, -768, 10265, 7742, -1935, -12408, 6548, -8502, -20475, -576, -5082, 31012, -13890, 1008, 11228, 2648, -11379, 3136, 13075, 8208, 40621, -8236, 1863, -5738, -8925, -1392, -30623, 38080, -11190, 22048, 2626, -630, 43812, -11344, 33552, 19818, -72766, -276, 1421, 3004, 1089, 640, 17775, 22926, -1079, 1932, -594, 13212, 5305, 1944, 15705, 12048, -1806, -11596, 4535, 12726, -9837, -6432, -5292, 5152, -2896, 5604, 968, -80, 10281, -2816, 25151, -1260, 5566, -16888, -3873, 22022, -7309, 2016, 23256, -17538, -864, -15264, -37189, 8994, 4214, -6616, 1113, 10612, -23954, -648, 24777, -2058, 759, -8848, 10024, 690, -37355, -22416, 3528, -13740, -5923, 5808, -49730, 20698, 25767, -896, 15537, -1566, 18066, -3584, -14604, 13004, -9919, 10332, 7983, 7932, -12762, 10200, 1978, 1176, 1466, 10756, 4947, -2482, -53672, 720, 9576, 22858, -6570, 17216, -41711, 15258, 2460, -1624, 2187, -4134, 12035, 3732, 26920, 47094, -735, -2208, -1853, -7236, -30816, -8340, -18321, -322, -25209, 2064, 38296, 4084, -3168, -2952, 26747, 5364, -63617, -5888, -28320, -28422, -9804, 2268, 29590, 12560, -3864, -28744, -28970, 6450, 14847, -19896, -7443, -21124, -17346, -2304, -7182, 6538, -11352, 13168, -7984, -9954, 36829, -4816, -1470, -4520, -35570, 7488, -4535, -1288, 6534, 2352, 36446, 4056, 24779, -11180, -10182, -22826, 10493, -4032, -20505, -27020, 3765, 22916, 49588, -756, -11310, 1024, 11475, -20368, 1816, 2580, 805, 23850, -35757, 11336, -39913, 810, -21982, 6776, -11208, 6412, 55583, -1344, -7723, 29668, -1827, 15172, -2508, -7044, -5817, -10944, -2217, 12054, 15571, -2484, 7756, -17146, -11127, 1856, 1372, -2262, -18163, 14920, 2322, 18198, -68709, 840, 23735, 12802, -180, -44736, -35860, -6624, 17801, 368, -28185, -37290, 1610, -1452, -51138, 4354, -32337, -30568, 52572, -2166, -77280, 792, -8442, -37982, -12994, -2592, -79621, 48044, -21261, 2408, 31740, -3990, 2698, -16968, -5418, 828, 6258, 7056, 82146, -11236, -11310, -7472, -51226, 2646, -7577, -13708, 11493, -47968, -40733, 1680, 7525, -25920, -4536, 5164, -46998, -3240, -29821, -2688, 2001, -5518, -68686, 1152, -25909, 10452, -11613, -11992, -22765, 18612, -10761, -1484, 12753, 8736, -28410, 864, 21840, 6786, -46518, -1012, 4732, -1512, -56400, -920, -3972, -33246, 1081, -4704, 1879, 8188, -12312, -7744, -68271, 12354, -882, -34356, 8607, -46920, 20067, 2088, -34564, 3010, -57120, 19472, 28730, -33072, 9246, -13776, 945, 16478, -14792, 17016, -54745, 7446, -29727, -1568, 5351, 414, 2828, -6596, -4506, -14760, -8218, -960, -11023, 5830, -34389, 8760, 27078, -2898, -19904, -20344, -19818, -53546, 16087, -2916, -2639, 12268, -18072, -4976, -28313, 17394, -16465, 980, -19089, -17006, -49798, 9648, -63168, 67332, -7728, 24428, 12719, -8406, -71933, -2752, 120, -1694, 64853, 4224, -4176, 42546, 1890, -7152, -2527, 25332, 46857, 37760, -33033, 230, 12945, -3024, 41497, 54082, 26307, 5152, -9345, 22896, -4655, -8600, -13491, -22316, -105459, 9924, -59640, 8232, -15918, 3072, 28301, 972, -14503, 15136, 3087, -20696, 44405, 13272, -41878, 3028, -1035, 1960, -74217, 33624, -65974, -9984, 20610, -7880, -3780, -8712, 51149, 19652, -31047, -5408, 39878, 1344, 56659, 13576, 2349, -65604, -51091, 5376, 21714, 3174, -19506, -5020, 2645, -15498, 47227, 1008, -11898, -3774, 47856, -15300, -75201, 18196, -1764, -3440, -1642, -16134, -26454, 47676, 3723, -5488, 48985, -1080, 8464, 10704, -34287, 14944, 14413, -25824, 12117, 1792, -22887, 15858, -11335, 2436, 52699, 75322, 6201, 9392, -17101, -5598, -38584, 2956, -70641, -20220, 37972, 3312, -26146, 19852, 10854, 14836, 77591, 12510, -41853, 3016, 483, 20096, -37167, -3096, -43026, -24810, -6126, -1120, 23967, 4428, 33332, 240, -8046, 16130, -3381, 8832, -120841, 84818, 42633, 37580, 36364, -3402, 58709, 1936, -18840, -66524, -117933, 43116, 20293, -15388, -9675, 2888, 53913, 29844, 13370, 11256, 31686, -1472, -19234, 3456, 34663, -60, -9807, 28348, 3745, -19752, -139443, 5320, 14931, 4928, 33963, 7224, 37973, 4614, 6780, -9408, 29554, -11232, 53138, 15080, 1932, -32574, -12494, -3528, 52311, 39084, -6084, -15324, -42956, 16770, 26712, -2240, 34239, -10472, 34765, 6048, -26102, 11578, 40530, 4320, 102907, -34374, 10923, -2668, 1134, -80838, 30371, -1536, -44379, 20530, 30552, 15484, 112753, -3870, -30907, -24816, -35775, 13096, 39228, -17004, 74320, -40950, -1215, -1152, 75116, -10164, -529, 62024, -9618, -27780, -30147, 2016, 1568, 22456, -44502, 5296, 105434, -22758, 54650, 6272, 10566, 26150, -91950, 16416, 116927, 81242, -18081, -16472, 190292, 3726, -9211, -11476, 25719, -17850, 85875, -2784, -56033, -61246, 3393, 76160, -18823, -22380, -3858, 44096, -27297, 5252, 63906, -1260, 99965, 87624, -19203, -22688, 10741, 67104, -30128, 39636, 9936, -145532, 56758, -552, -95531, 2842, 55935, 6008, 5028, 2178, 810, 1280, -6531, 35550, 90035, 45852, -20088, -2158, 3249, 3864, -11505, -1188, 80038, 26424, 56973, 10610, 14595, 3888, 83556, 31410, -72066, 24096, 52029, -3612, 124138, -23192, 5985, 9070, 15210, 25452, 5166, -19674, -1242, -12864, 10724, -10584, -46607, 10304, 16854, -5792, 42457, 11208, 84601, 1936, -3969, -160, 30249, 20562, -40056, -5632, 71952, 50302, 110208, -2520, -25725, 11132, 38880, -33776, 34818, -7746, 16712, 44044, 4860, -14618, 67616, 4032, 9780, 46512, 8277, -35076, -33117, -1728, -23044, -30528, -15678, -74378, 224793, 17988, 19803, 8428, -27918, -13232, 155667, 2226, 52430, 21224, -13104, -47908, -48322, -1296, -140553, 49554, -10179, -4116, 25920, 1518, 45416, -17696, 2268, 20048, 19565, 1380, 13701, -74710, 49869, -44832, 127022, 7056, 3064, -27480, -12282, -11846, -85609, 11616, -40103, -99460, -18531, 41396, 95245, 51534, -63964, -1792, 70380, 31074, 7153, -3132, 67962, 36132, -4515, -7168, 138991, -29208, -133676, 26008, 49608, -19838, -12329, 20664, -32216, 15966, -24717, 15864, -11858, -25524, 47828, 20400, -11169, 3956, 97982, 2352, 71347, 2932, -621, 21512, -184366, 9894, -26551, -4964, 22140, -107344, -76052, 1440, 11366, 19152, -8745, 45716, 155086, -13140, 115883, 34432, 4347, -83422, -16318, 30516, -26668, 4920, 80319, -3248, -23410, 4374, 130631, -8268, -18402, 24070, -26110, 7464, 82544, 53840, -26091, 94188, -65730, -1470, -6319, -4416, 25509, -3706, -56889, -14472, 78288, -61632, -100998, -16680, 146878, -36642, -143273, -644, 12609, -50418, 54985, 4128, -67698, 76592, 2541, 8168, 10478, -6336, 14352, -5904, -63819, 53494, 5338, 10728, 86176, -127234, -37998, -11776, -1386, -56640, -29206, -56844, -345, -19608, 103178, 4536, 174235, 59180, -81123, 25120, -10750, -7728, -4214, -57488, -34344, -57940, 33868, 12900, 19924, 29694, 33474, -39792, -16029, -14886, -34755, -42248, -12348, -34692, 100823, -4608, -61713, -14364, -1458, 13076, 4945, -22704, -191024, 26336, 31044, -15968, 23989, -19908, -103386, 73658, -4542, -9632, 102314, -2940, 102574, -9040, -50436, -71140, -197405, 14976, -9037, -9070, 11820, -2576, 46628, 13068, -48478, 4704, -29478, 72892, 3926, 8112, -51210, 49558, -2016, -22360, 81272, -20364, -99048, -45652, 98406, 20986, -39254, -8064, 94615, -41010, -4761, -54040, 2597, 7530, 6341, 45832, 23247, 99176, 47147, -1512, 123994, -22620, 5661, 2048, 49568, 22950, 1771, -40736, -27294, 3632, -93904, 5160, -31920, 1610, 24201, 47700, -59654, -71514, 119725, 22672, 8232, -79826, -23518, 1620, -140178, -43964, -16056, 13552, 59599, -22416, 19374, 12824, 38736, 111166, 60123, -2688, -2783, -15446, -23787, 59336, -27589, -3654, -31414, 30344, -112983, -5016, 58899, -14088, -34076, -11634, 8397, -21888, -185980, -4434, 152577, 24108, 30330, 31142, -11082, -4968, -17782, 15512, -29778, -34292, 62574, -22254, -62639, 3712, -18765, 2744, -89012, -4524, -164579, -36326, -30144, 29840, 11543, 4644, 79525, 36396, 37215, -137418, 13524, 1680, -36253, 47470, -6642, 25604, -75668, -360, -15330, -89472, -24195, -71720, 120365, -13248, 119982, 35602, -127227, 736, 88153, -56370, 9964, -74580, 5103, 3220, -38929, -2904, 16871, -102276, 99786, 8708, 84774, -64674, 159705, -61136, 23082, 105144, -1715, -4332, -187717, -154560, -44766, 1584, 116870, -16884, 195266, -75964, 2208, -25988, -128114, -5184, -42749, -159242, 90, 96088, 88967, -42522, 102999, 4816, 29628, 63480, -18694, -7980, -11976, 5396, -7392, -33936, 65965, -10836, -27792, 1656, -6921, 12516, -57140, 14112, 142633, 164292, 16848, -22472, -66080, -22620, -195266, -14944, 48861, -102452, 50439, 5292, 130957, -15154, -58626, -27416, -2461, 22986, -9016, -95936, -25155, -81466, 22034, 3360, -474, 15050, 15708, -51840, 43353, -9072, -40974, 10328, -17367, -93996, -80554, -6480, 18990, -59642, 51561, -5376, 8375, 4002, -112081, -11036, 121257, -137372, -26488, 2304, 184438, -51818, -30795, 20904, -88348, -23226, -60968, -23984, 5805, -45530, 22808, 37224, -3430, -21522, -19644, -2968, 32614, 25506, 16283, 17472, 61425, -56820, -40748, 1728, -198791, 43680, 15246, 13572, -55251, -93036, 133487, -2024, 41670, 9464, -638, -3024, 64146, -112800, -33684, -1840, -23758, -7944, 246388, -66492, 34137, 2162, 60046, -9408, -113790, 3758, -39225, 16376, -73877, -24624, 8785, -15488, -121863, -136542, 99753, 24708, -50880, -1764, -5589, -68712, -177621, 17214, 37783, -93840, 26775, 40134, -177838, 4176, 14138, -69128, 91869, 6020, 7522, -114240, -57465, 38944, 33570, 57460, -83433, -66144, 85022, 18492, -7878, -27552, -101410, 1890, -1405, 32956, -131436, -29584, -154704, 34032, -26152, -109490, -100656, 14892, 68121, -59454, 176306, -3136, 218298, 10702, 213569, 828, 8096, 5656, -4263, -13192, -5905, -9012, -72587, -29520, -3267, -16436, -221339, -1920, -205483, -22046, -53325, 11660, -5173, -68778, 103054, 17520, 3237, 54156, 72866, -5796, 52450, -39808, 1782, -40688, 10738, -39636, -25963, -107092, -15915, 32174, -129421, -5832, -244171, -5278, -47115, 24536, 39256, -36144, 101816, -9952, 5418, -56626, 19021, 34788, 83580, -32930, -13605, 1960, 7373, -38178, -20538, -34012, 29511, -99596, -420, 19296, -29365, -126336, 15876, 134664, 269723, -15456, -68827, 48856, 8688, 25438, -157282, -16812, -65765, -143866, -2904, -5504, -83044, 240, -181488, -3388, -30843, 129706, -61044, 8448, 50185, -8352, -75453, 85092, 296730, 3780, -27174, -14304, -16698, -5054, -241259, 50664, 9639, 93714, 11619, 75520, -19698, -66066, -19032, 460, 21927, 25890, -39190, -6048, 43146, 82994, -69768, 108164, 87366, 52614, -49609, 10304, 2592, -18690, -45525, 45792, -70034, -9310, 111567, -17200, -119819, -26982, 37313, -44632, -12642, -210918, -105122, 19848, 8944, -119280, -3339, 16464, 337899, -31836, -29325, 6144, 71862, 56602, -26390, 1944, 114823, -29006, -74331, 30272, -15312, 6174, -45995, -41392, -2277, 88810, -225032, 26544, 26817, -83756, -30072, 6056, -244818, -2070, -88207, 3920, 112065, -148434, 150595, 67248, 119183, -131948, -10584, -19968, -351407, 41220, -42906, -15760, 17769, -7560, 206390, -17424, -110448, 102298, 149190, 39304, 4669, -62094, -114677, -10816, -77301, 79756, 89114, 2688, 85802, 113318, -46611, 27152, -206114, 4698, -27097, -131208, -54198, -102182, 237626, 10752, -86320, 43428, 43812, 6348, 421136, -39012, -75478, -10040, 29757, 5290, -72870, -30996, -51516, 94454, -23949, 2016, 32804, -23796, -119278, -7548, 38286, 95712, -108542, -30600, -64965, -150402, -5934, 36392, -362183, -3528, 232350, -6880, -4398, -3284, -387457, -32268, -9268, -52908, -14841, 95352, -36144, 7446, -91606, -10976, 161016, 97970, -18935, -2160, -157317, 16928, -28728, 21408, 34734, -68574, 87255, 29888, 19710, 28826, -147515, -51648, 35783, 24234, 125133, 3584, 20083, -45774, -1026, 31716, -7380, -22670, 29307, 4872, 82639, 105398, -6561, 150644, -132977, 12402, -133280, 18784, -36105, -34202, 151893, -11196, -46496, -77168, -80760, 5912, 22261, -141282, 278285, -40440, 2205, 75944, -339342, 6624, -190093, -52292, 5559, 39704, -247696, 21708, 141120, 29672, 92448, 155182, -69363, 25020, -161018, -83706, 54963, 6032, -103480, 966, 191698, 40192, 75627, -74334, 13846, -6192, -10514, -86052, -114888, -49620, 44920, -12252, -151353, -2240, 9504, 47934, 89827, 8856, -247173, 66664, -80241, 480, 93475, -16092, 312606, 32260, 190851, -6762, -21661, 17664, -69955, -241682, 84960, 169636, -46242, 85266, -334180, 75160, 29412, 72728, -123752, -6804, 300, 117418, -88770, 3872, -206574, -37680, -42168, -133048, 11592, -235866, -36830, 86232, -217123, 40586, 86910, -30776, 137491, -19350, 157675, 5776, -44541, 107826, 208960, 59688, 18684, 26740, 22329, 22512, -173726, 63372, -82830, -2944, 52038, -38468, -18032, 6912, -88023, 69326, 21546, -120, 79653, -19614, -20228, 56696, 34056, 7490, -141811, -39504, 280, -278886, 23952, 10640, 249254, 29862, -32591, 9856, -110487, 67926, 27234, 14448, -306914, 75946, 4410, 9228, 55818, 13560, 39921, -18816, 106710, 59108, -263261, -22464, 186379, 106276, 13605, 30160, -77077, 3864, -125209, -65148, -19602, -24988, -351363, -7056, 48277, 104622, -109338, 78168, 81722, -12168, 61383, -30648, -74337, -85912, 305387, 33540, 83096, 53424, 30546, -4480, 31464, 68478, 51977, -20944, -31479, 69530, 235156, 12096, -158952, -52204, 61515, 23156, 4704, 81060, -120171, 8640, -11295, 205814, -37142, -68748, -103420, 21846, -148764, -5336, -236086, 2268, 523441, -161676, 33930, 60742, -138126, -3072, 7203, -88758, -34425, 41060, -38378, 61104, -281008, 30968, -5448, 225506, 101094, -7740, 649423, -61814, -2415, -49632, -118578, -71550, -2895, 26192, 107271, 78456, -115594, -34008, 251249, 148640, 119739, -81900, 48090, -2430, 97657, -2304, 65946, 150232, -146937, -20328, -87656, -1058, 33624, 124048, -366674, -19236, -72443, -55560, -166749, -60294, 156474, 4032, -28268, 3136, 23169, 44912, -19905, -89004, 311212, 10592, 5481, 210868, 40684, -45516, 87883, 109300, 7524, 12544, 335947, 21132, 326954, 52300, 17451, -183900, -45514, 32832, -253098, 233854, 6651, 162484, -559305, -36162, -46327, -32944, -46713, 380584, -49958, 7452, -27762, -18422, -23268, -22952, 72486, 51438, -26700, -35700, 33381, 171750, -218131, -5568, -64467, -112066, -4116, -122492, 287743, 6786, 321066, 152320, 54489, -37646, 48783, -44760, 39500, -7716, -6966, 88192, 8687, -54594, -44083, 10504, 206127, 127812, -100637, -2520, 12439, 199930, -71205, 175248, 142019, -38406, -80003, -45376, 540, 21482, 225261, 134208, -337534, -60256, 107580, 79272, 201624, 19872, -82820, -291064, -53403, 113516, -100072, -1104, -271256, -191062, 84555, 5684, -124384, 111870, 413728, 12016, -4830, 10056, 14469, 4356, 72600, 1620, 153414, 2560, -27139, -13062, 87151, 71100, 97011, 180070, -25002, 91704, -164829, -40176, -157716, -4316, 320900, 6498, 53984, 7728, 231840, -23010, -86403, -2376, 108475, 160076, 25326, 52848, -15484, 113946, 91116, 21220, 38982, 29190, -372781, 7776, -382, 167112, 238863, 62820, 1127, -144132, 34477, 48192, 63783, 104058, -196898, -7224, -123646, 248276, -95220, -46384, -263852, 11970, -14294, 18140, -8094, 30420, 257666, 50904, -57386, 10332, 16254, -39348, 23554, -2484, 66135, -25728, -18774, 21448, -20157, -21168, -3479, -93214, -246438, 20608, -26345, 33708, -199721, -11584, 33930, 84914, 99477, 22416, 41157, 169202, 153678, 3872, 2645, -7938, -277458, -320, 22731, 60498, -147768, 41124, -43960, -80112, -34479, -11264, 112859, 143904, -204479, 100604, 122199, 220416, -170695, -5040, 197562, -51450, -22575, 22264, -14498, 77760, 62541, -67552, 13608, 69636, -139102, -15492, -266296, 33424, 140994, 88088, 73934, 9720, -156408, -29236, 89463, 135232, 195446, 8064, 167120, 19560, -6003, 93024, -132819, 16554, -22883, -70152, 206058, -66234, 212224, -3456, 8908, -46088, 77727, -61056, 188960, -31356, 289418, -148756, 34839, 449586, 200883, 35976, -300349, 39606, 68295, 16856, -14953, -55836, 203748, -26464, 32283, 311334, 15820, 4452, -2935, 104860, -38259, 42448, -489128, -26208, -119899, -95816, 85230, -96644, 294101, -2592, 4508, -281106, -65520, 99108, 401168, -20358, -3035, -8232, 139554, 51840, 323739, 3036, -154116, 90832, -14196, -35392, 3323, 4536, 640125, 40096, 169200, 39130, -202205, 2760, -162314, 27402, 11916, -149420, 79891, 99738, -60906, -89664, -3243, 254044, -366297, 14112, 83124, 6128, -5637, -54960, 252901, -24564, 94570, -23692, 36936, -171218, 58489, 23232, -402810, -80206, 204813, -198920, 49909, -37062, 388543, 82792, 2646, 190490, 148147, 103068, 51342, -127928, -25821, -3584, 190456, 140760, -181470, 62148, -60201, 14306, 71288, -6264, -399584, 135924, 103692, 72264, -481700, -9030, -287612, -14336, 171360, 277982, 163149, -58416, -83475, -267352, -86190, 52016, 40781, 99216, 30310, -39676, -27738, -24658, -323742, 41328, -230989, -64432, -2835, 31932, -13356, -49434, 461750, 31728, 44376, -23716, -207476, -51048, -163548, 95656, 164235, 40800, -22442, -22338, -302703, 7912, 89181, 195964, -566563, 4704, 89345, 142694, -16053, 5864, 84528, -1242, -103838, 43024, -8484, -368732, 250850, 19788, 60354, -53102, 13518, -9928, 12485, 44280, 20562, -214688, 24654, -152104, 128284, 2880, -19448, 22732, 33069, 38304, -24618, -17490, -54906, 91432, 103167, 310172, -42189, -26280, -23132, 231766, -81234, 68864, -251510, 8694, -84508, -166844, 59712, -32636, -46226, 61032, 60011, -53336, 59454, 9840, 94734, 160638, 69745, -6496, -48261, -46820, -4083, 8748, 259952, 261262, 7917, -16536, 24725, -36804, 74556, 48140, 54216, -52220, -34457, 14928, -334157, 165088, 84939, 107680, -63693, -52182, 255480, 188376, 49395, -131460, -278015, -2940, -8946, -12638, 57267, -8832, -245295, 51018, -44807, -7412, 149394, -113778, -182566, -28944, -332519, 156576, 189504, -123264, 385018, -201996, -208953, -33360, 23184, 293756, -322457, -73284, 81474, -286546, -38157, -1288, -226420, 25218, 67917, -100836, 215799, 109970, 130515, 8256, -366240, -135396, -360, 153184, -292616, 5082, -276370, 16336, -194559, 20956, -32108, -12672, -15239, 28704, 12528, -11808, -289636, -127638, 30352, 106988, -5670, 10676, -223037, 21456], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "966.4.a.e", "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, 0], [1, 0, 0], [2, 0, 0], [-3, 0, 0], [4, 0, 0], [2, 0, 1], [-6, 0, 0], [-7, 0, 0], [8, 0, 0], [9, 0, 0], [4, 0, 2], [-19, -1, -1], [-12, 0, 0], [9, -5, -2], [-14, 0, 0], [-6, 0, -3], [16, 0, 0], [9, 19, -1], [18, 0, 0], [-9, -1, -9], [8, 0, 4], [21, 0, 0], [-38, -2, -2], [-23, 0, 0], [-24, 0, 0], [10, -19, -2], [18, -10, -4], [-27, 0, 0], [-28, 0, 0], [-79, 37, 5], [-12, 0, -6], [-31, -35, -7], [32, 0, 0], [57, 3, 3], [18, 38, -2], [-14, 0, -7], [36, 0, 0], [-25, -1, -5], [-18, -2, -18], [-27, 15, 6], [16, 0, 8], [-131, -35, 9], [42, 0, 0], [-183, 19, 4], [-76, -4, -4], [18, 0, 9], [-46, 0, 0], [-118, 4, 14], [-48, 0, 0], [49, 0, 0], [20, -38, -4], [-27, -57, 3], [36, -20, -8], [6, -28, -5], [-54, 0, 0], [-160, 12, -13], [-56, 0, 0], [27, 3, 27], [-158, 74, 10], [-288, 48, -3], [-24, 0, -12], [-91, -35, 38], [-62, -70, -14], [-63, 0, 0], [64, 0, 0], [-199, 3, 27], [114, 6, 6], [-64, -88, 23], [36, 76, -4], [69, 0, 0], [-28, 0, -14], [43, -23, 8], [72, 0, 0], [-193, 187, 9], [-50, -2, -10], [-30, 57, 6], [-36, -4, -36], [133, 7, 7], [-54, 30, 12], [-479, 59, -19], [32, 0, 16], [81, 0, 0], [-262, -70, 18], [-127, -143, -29], [84, 0, 0], [-284, 152, -25], [-366, 38, 8], [237, -111, -15], [-152, -8, -8], [415, 125, -30], [36, 0, 18], [-63, 35, 14], [-92, 0, 0], [93, 105, 21], [-236, 8, 28], [-1188, 164, 29], [-96, 0, 0], [-227, -229, -79], [98, 0, 0], [-171, -9, -9], [40, -76, -8]]}