# Stored data for newform 1386.4.a.be, downloaded from the LMFDB on 30 April 2024.
{"label": "1386.4.a.be", "space_label": "1386.4.a", "level": 1386, "weight": 4, "hecke_orbit": 31, "hecke_orbit_code": 135107988888225130, "dim": 3, "is_polredabs": true, "nf_label": "3.3.21324.1", "trace_hash": 570871187929439329, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [-14, -139, 8, 1]], [13, [32068, -2307, -30, 1]]], "qexp_display": "q-2q^{2}+4q^{4}+(-3+\\beta _{2})q^{5}-7q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 22176, "fricke_eigenval": -1, "atkin_lehner_string": "+++-", "analytic_conductor": 81.77664726795649, "hecke_ring_index": 2, "level_radical": 462, "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": [1386, 1, [155, 199, 1135], [1, 1, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 1, "level_primes": [2, 3, 7, 11], "conrey_indexes": [1], "field_disc": 21324, "field_disc_factorization": [[2, 2], [3, 1], [1777, 1]], "field_poly": [-84, -44, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.846", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.721", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "280.545", "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], [11, -1]], "trace_display": [-6, 0, -8, -21], "traces": [0, 3, -6, 0, 12, -8, 0, -21, -24, 0, 16, 33, 0, 30, 42, 0, 48, 38, 0, -184, -32, 0, -66, 98, 0, -33, -60, 0, -84, 180, 0, -244, -96, 0, -76, 56, 0, 64, 368, 0, 64, 574, 0, 26, 132, 0, -196, 264, 0, 147, 66, 0, 120, 418, 0, -88, 168, 0, -360, -650, 0, -1008, 488, 0, 192, 1202, 0, -1022, 152, 0, -112, -258, 0, -636, -128, 0, -736, -231, 0, 824, -128, 0, -1148, -788, 0, -1700, -52, 0, -264, 1840, 0, -210, 392, 0, -528, 494, 0, -1682, -294, 0, -132, 882, 0, -656, -240, 0, -836, 1310, 0, -2028, 176, 0, -336, -252, 0, -2520, 720, 0, 1300, -266, 0, 363, 2016, 0, -976, -1806, 0, 0, -384, 0, -2404, -1048, 0, 1288, 2044, 0, -304, -672, 0, -858, 224, 0, 516, 330, 0, -482, 1272, 0, 256, 4224, 0, 908, 1472, 0, 462, 2268, 0, -2598, -1648, 0, 256, -686, 0, -2798, 2296, 0, 1576, -556, 0, -1077, 3400, 0, 104, 3446, 0, 231, 528, 0, -3680, -5864, 0, -990, 420, 0, -784, -1114, 0, 418, 1056, 0, -988, -6398, 0, -4930, 3364, 0, 588, -2862, 0, 1200, 264, 0, -1764, -1260, 0, -9208, 1312, 0, 480, -2024, 0, -1954, 1672, 0, -2620, 2124, 0, 1708, 4056, 0, -352, -6632, 0, -17904, 672, 0, 504, -4248, 0, -4614, 5040, 0, -1440, -5286, 0, 1586, -2600, 0, 532, -9862, 0, -10412, -726, 0, -4032, -392, 0, -2270, 1952, 0, 3612, 622, 0, 1078, 0, 0, 768, -274, 0, -448, 4808, 0, 2096, -1230, 0, -5948, -2576, 0, -4088, -9850, 0, -3922, 608, 0, 1344, -363, 0, -684, 1716, 0, -448, 2240, 0, -7872, -1032, 0, -660, -4018, 0, -1943, 964, 0, -2544, 402, 0, -2450, -512, 0, -8448, -6188, 0, -182, -1816, 0, -2944, -8204, 0, 286, -924, 0, -4536, -10030, 0, -11378, 5196, 0, 3296, -4050, 0, 1980, -512, 0, 1372, 756, 0, -10836, 5596, 0, -4592, -1848, 0, -10728, -3152, 0, 1112, -14894, 0, 5794, 2154, 0, -6800, -2684, 0, -1029, -208, 0, -6892, -3172, 0, -9774, -462, 0, -1056, 6338, 0, 6448, 7360, 0, 11728, -424, 0, -7075, 1980, 0, -840, 3634, 0, -5372, 1568, 0, 2228, -2926, 0, 19608, -836, 0, -2112, 2058, 0, 1094, 1976, 0, 12796, -1886, 0, 616, 9860, 0, -6728, -10062, 0, -532, -1176, 0, 5724, -16396, 0, 14406, -2400, 0, -528, -24992, 0, 2164, 3528, 0, 2520, 704, 0, -3682, 18416, 0, -2624, 4550, 0, 25552, -960, 0, 4048, -3362, 0, 852, 3908, 0, -3344, 6562, 0, 7056, 5240, 0, -4248, -27990, 0, 20634, -3416, 0, -8112, -15344, 0, 8066, 704, 0, 13264, -14792, 0, 7228, 35808, 0, -1344, -5820, 0, 6314, -1008, 0, 8496, -8414, 0, 4654, 9228, 0, -10080, 6698, 0, 18010, 2880, 0, 10572, 9290, 0, 7154, -3172, 0, 5200, 286, 0, -3326, -1064, 0, 19724, -6232, 0, -5614, 20824, 0, 1452, -2140, 0, 17504, 8064, 0, 784, 15542, 0, 428, 4540, 0, -3904, 1806, 0, 13914, -7224, 0, -1244, 17436, 0, 31272, -2156, 0, 0, 3310, 0, 4452, -1536, 0, 548, -41192, 0, 2904, 896, 0, -9616, 7966, 0, -16004, -4192, 0, 2460, 1880, 0, 21711, 11896, 0, 5152, -27436, 0, -20126, 8176, 0, 19700, 1617, 0, -11300, 7844, 0, -1216, 21076, 0, 25454, -2688, 0, 726, -12370, 0, -5768, 1368, 0, -3432, 18188, 0, 15856, 896, 0, -4480, -20488, 0, 34040, 15744, 0, 2064, -9058, 0, 24086, 1320, 0, 8036, 41650, 0, -30334, 3886, 0, -1928, 5516, 0, 4598, 5088, 0, -804, -8862, 0, 24292, 4900, 0, 1024, 64698, 0, 11900, 16896, 0, 12376, -22710, 0, 16376, 364, 0, 3632, -968, 0, 4046, 5888, 0, 16408, 5766, 0, 25304, -572, 0, 1848, 53144, 0, -12800, 9072, 0, 20060, -12880, 0, -3501, 22756, 0, -10392, 22892, 0, 28720, -6592, 0, 8100, 33068, 0, 1470, -3960, 0, 1024, -27288, 0, -13728, -2744, 0, -1512, -27444, 0, -7150, 21672, 0, -11192, -37522, 0, 8108, 9184, 0, 3696, 6750, 0, -21074, 21456, 0, 6304, -3458, 0, 11480, -2224, 0, 29788, -11088, 0, 45290, -11588, 0, -4308, 51734, 0, 11774, 13600, 0, 5368, 36444, 0, 40032, 2058, 0, 416, -12040, 0, -6108, 13784, 0, 6344, 15500, 0, 62924, 19548, 0, 924, 43998, 0, 8478, 2112, 0, -12676, -6174, 0, -46640, -12896, 0, -14720, -58464, 0, 13222, -23456, 0, 848, 14680, 0, 4592, 14150, 0, -3960, 1230, 0, -5804, 1680, 0, -7268, -58396, 0, 50344, 10744, 0, -3136, -11242, 0, -21746, -4456, 0, 5852, 6634, 0, -33874, -39216, 0, 1672, -9170, 0, -17110, 4224, 0, -4116, -54664, 0, 19688, -2188, 0, -3952, 27378, 0, 14196, -25592, 0, 3772, -21274, 0, 47664, -1232, 0, -19720, 44180, 0, -34256, 13456, 0, 20124, -22872, 0, -2838, 1064, 0, 2352, 496, 0, -20292, -11448, 0, 32792, 1764, 0, -55044, -28812, 0, 4800, 16492, 0, 34132, 1056, 0, 49984, -6996, 0, 17640, -4328, 0, -7056, -6748, 0, 23184, -5040, 0, -1408, 34106, 0, -35708, 7364, 0, -36832, -11180, 0, 106962, 5248, 0, -9100, 20814, 0, -11982, -51104, 0, 1920, 1862, 0, -41412, -8096, 0, 6724, 84, 0, -61569, -1704, 0, -7816, 18426, 0, -2541, 6688, 0, -13124, -43400, 0, -11288, -14112, 0, -10480, 11486, 0, 34664, 8496, 0, 55980, 494, 0, 25872, -41268, 0, 6832, 9064, 0, -82966, 16224, 0, 30688, 12642, 0, 11324, -16132, 0, -1408, -41598, 0, 27902, -26528, 0, 29584, 18420, 0, 0, -14456, 0, -71616, 13978, 0, 98804, 2688, 0, 11640, -20236, 0, 7668, -12628, 0, 2016, -38248, 0, -25900, -16992, 0, 16828, -80998, 0, -8668, -9308, 0, -18456, 7336, 0, -79252, 20160, 0, -13396, 22044, 0, -21982, -36020, 0, -5760, 19634, 0, -9016, -21144, 0, -18580, -18700, 0, 55990, -14308, 0, 6344, -1214, 0, 20692, -10400, 0, -572, -8956, 0, -474, 6652, 0, 2128, 76188, 0, -55008, -39448, 0, 12464, 4704, 0, -22269, 11228, 0, -41648, -23660, 0, 40988, -2904, 0, 4280, 34970, 0, 6006, -35008, 0, -16128, -64388, 0, 20240, -1568, 0, -31084, -2326, 0, -75696, -856, 0, -9080, 128772, 0, -57742, 7808, 0, -3612, -58400, 0, -87516, -27828, 0, 14448, -2310, 0, -1032, 2488, 0, -34872, -41204, 0, -4642, -62544, 0, 4312, 94448, 0, 3374, 0, 0, -6620, -25250, 0, 1518, -8904, 0, 3072, 33182, 0, -36644, -1096, 0, 82384, -85064, 0, 65722, -5808, 0, -1792, 51464, 0, -80456, 19232, 0, -15932, -29568, 0, 5434, 32008, 0, 8384, 12, 0, -42070, -4920, 0, -3760, 35460, 0, -6356, -43422, 0, -23792, 35442, 0, 5630, -10304, 0, 54872, -18502, 0, -63322, 40252, 0, -16352, -3602, 0, 61846, -39400, 0, -3234, 80288, 0, -134120, 22600, 0, -15688, -15876, 0, -61726, 2432, 0, -42152, 13264, 0, 58890, -50908, 0, 5376, -9938, 0, 18186, -1452, 0, 24740, -14966, 0, 4160, 11536, 0, -2736, -13864, 0, 9702, 6864, 0, -36376, 48376, 0, 67836, -31712, 0, -1792, 30070, 0, -155348, 8960, 0, 40976, 4802, 0, -11702, -68080, 0, -31488, -7216, 0, 12436, -4128, 0, 18116, 91032, 0, 19586, -48172, 0, -2640, 5432, 0, 42172, -16072, 0, -83300, -34876, 0, -20314, 60668, 0, -7772, 73652, 0, 68804, 3856, 0, -11032, -178766, 0, 17880, -9196, 0, -10176, 3892, 0, -120938, 1608, 0, 17724, -95922, 0, 14410, -48584, 0, -9800, 123148, 0, 7539, -2048, 0, -129396, -8954, 0, 27040, -23800, 0, -33792, 7074, 0, -75018, -24752, 0, 45420, -22308, 0, 61090, -32752, 0, -728, 89254, 0, -43156, -7264, 0, 1936, -24122, 0, -95578, -8092, 0, -11776, 31370, 0, 112868, -32816, 0, -11532, 32936, 0, -1617, -50608, 0, 1144, -19902, 0, -30026, -3696, 0, -106288, -95486, 0, -102166, 25600, 0, -18144, -4684, 0, -2772, -40120, 0, 25760, 22028, 0, -187692, 7002, 0, -45512, 41048, 0, -58574, 20784, 0, -45784, -22972, 0, -57760, -57440, 0, 13184, -27720, 0, 6930, -16200, 0, -66136, -33272, 0, 74026, -2940, 0, 7920, 122414, 0, -137196, -2048, 0, 54576, -27622, 0, -12670, 27456, 0, 5488, 126006, 0, 11348, 3024, 0, 54888, 7798, 0, -8050, 14300, 0, -43344, 97444, 0, -42, 22384, 0, 75044, -78220, 0, -2926, -16216, 0, -18368, 149364, 0, -74838, -7392, 0, -13500, 143724, 0, -99894, 42148, 0, -42912, 76262, 0, 37228, -12608, 0, 6916, 3993, 0, -134424, -22960, 0, 4448, 44786, 0, -181960, -59576, 0, 22176, -1944, 0, 40952, -90580, 0, 23176, 7904, 0, 34510, 8616, 0, -103468, 57738, 0, 49196, -23548, 0, -27200, -7914, 0, -2262, -10736, 0, -72888, -13618, 0, -78305, -80064, 0, -4116, 65222, 0, -19866, -832, 0, 24080, 20034, 0, -85108, 12216, 0, -27568, 187896, 0, 48338, -12688, 0, -31000, -58982, 0, -8400, -125848, 0, -39096, 0, 0, 810, -1848, 0, -87996, 14000, 0, -76106, -16956, 0, -4224, 236616, 0, -87792, 25352, 0, 12348, 24390, 0, 48300, 93280, 0, 25792, 8820, 0, -43306, 29440, 0, 116928, -175440, 0, 121140, -26444, 0, 46912, -87146, 0, 64456, -1696, 0, -29360, -149838, 0, -11528, -9184, 0, -28300, 25560, 0, -117202, 7920, 0, -2460, 56018, 0, 52546, 11608, 0, -3360, 116692, 0, -143192, 14536, 0, 116792, 14168, 0, 86604, -100688, 0, -21488, 128400, 0, 24212, 6272, 0, 22484, 68312, 0, 13678, 43492, 0, 8912, -62012, 0, -19432, -11704, 0, -13268, 44160, 0, 28466, 67748, 0, 78432, 98540, 0, 157836, -3344, 0, 18340, -5588, 0, -110092, 34220, 0, -8448, -14868, 0, -7392, 8232, 0, 109328, -26988, 0, -84360, -39376, 0, 4376, 104344, 0, -11956, 7904, 0, -54756, -92432, 0, 92364, -28392, 0, 51184, -9438, 0, 33574, -7544, 0, 42548, 80460, 0, 34420, -95328, 0, 2464, 42308, 0, -210232, 39440, 0, -88360, 46424, 0, -108594, 68512, 0, -26912, 98794, 0, -20924, -40248, 0, 45744, -64872, 0, 125328, 5676, 0, -2128, 14684, 0, -50248, -4704, 0, -992, -214386, 0, 3630, 40584, 0, 22896, 76504, 0, 151050, -65584, 0, -3528, 141242, 0, 24552, 110088, 0, 57624, 29736, 0, -197060, -9600, 0, -32984, -5302, 0, 227576, -68264, 0, -2112, 158586, 0, 32298, -99968, 0, 13992, 87434, 0, -49062, -35280, 0, 8656, 15126, 0, 134040, 14112, 0, 13496, 169564, 0, 54928, -46368, 0, 10080, -76314, 0, -27304, 2816, 0, -68212, 37002, 0, -15484, 71416, 0, -14728, -188384, 0, 46464, 73664, 0, 22360, -123544, 0, -11102, -213924, 0, -10496, 112892, 0, 126972, 18200, 0, -41628, 146464, 0, 24436, 23964, 0, 102208, 9988, 0, -14264, -3840, 0, -3724, -4172, 0, 44408, 82824, 0, 16192, 69034, 0, 142592, -13448, 0, -168, -73528, 0, 156385, 123138, 0, 3408, 27592, 0, 72884, 15632, 0, -36852, -146420, 0, 12326, 5082, 0, -13376, -95570, 0, -86052, 26248, 0, 86800, -13532, 0, 24948, 22576, 0, 28224, 39770, 0, -33122, 20960, 0, -22972, 2744, 0, -199284, -69328, 0, -16992, -269078, 0, 124614, -111960, 0, -988, -28578, 0, 15890, -51744, 0, 82536, 107830, 0, 226072, -13664, 0, -18128, 167714, 0, 132550, 165932, 0, -32448, 138578, 0, 157310, -61376, 0, -25284, 231840, 0, -177670, -22648, 0, 32264, -4354, 0, 34848, 2816, 0, 83196, -238700, 0, -32746, -55804, 0, 53056, -64668, 0, -7546, -59168, 0, -36840, -29994, 0, 213828, 0, 0, 28912, 135432, 0, 34064, 143232, 0, -27956, -110988, 0, -127176, -197608, 0, -5376, -30778, 0, -944, -23280, 0, 40472, 1918, 0, 189434, -15336, 0, 25256, 26530, 0, 78288, -4032, 0, 76496, -44752, 0, 3136, 51800, 0, 33984, 376432, 0, 138616, -33656, 0, 161996, -336300, 0, -32838, 17336, 0, 18616, -9196, 0, 130216, 36912, 0, -14672, -240676, 0, -6116, 158504, 0, -40320, 8610, 0, 175356, 26792, 0, -44088, -47784, 0, 302403, 43964, 0, 72040, -145384, 0, 41636, 11520, 0, -39268, -11847, 0, 115158, 18032, 0, 42288, -60148, 0, 151012, 37160, 0, 37400, 32022, 0, 118500, -111980, 0, 28616, 58038, 0, -105460, -12688, 0, 2428, 68950, 0, 85178, -41384, 0, 20800, -181746, 0, 56840, 1144, 0, 17912, -228858, 0, 27454, 948, 0, -13304, -180958, 0, 37906, -4256, 0, -152376, -93296, 0, -308224, 110016, 0, 78896, 189720, 0, -8556, -24928, 0, -9408, -84336, 0, -152168, 44538, 0, -22456, 2541, 0, 164504, 83296, 0, 47320, -218992, 0, 150888, -81976, 0, 5808, -26430, 0, 4788, -8560, 0, -69940, -68126, 0, 22152, -12012, 0, 70016, -80498, 0, 171308, 32256, 0, 128776, -228032, 0, 58408, -40480, 0, 3136, -63756, 0, -203240, 62168, 0, 4652, -15680, 0, -64504, 151392, 0, 1712, -68954, 0, 261652, 18160, 0, -257544, 58588, 0, 55104, 115484, 0, -15616, -87588, 0, -291044, 7224, 0, 116800, -10890, 0, -61568, 175032, 0, 55656, 96928, 0, 22644, -28896, 0, 4620, -209912, 0, -213680, 2064, 0, -4976, 28126, 0, 178258, 69744, 0, 82408, -208572, 0, 86368, 9284, 0, 125088, -446300, 0, 13601, -8624, 0, -188896, -181580, 0, 39326, -6748, 0, 0, -52590, 0, -12254, 13240, 0, 50500, 42502, 0, -49212, -3036, 0, 17808, 223920, 0, 116144, -6144, 0, -66364, -2814, 0, -81572, 73288, 0, 2192, 4598, 0, -10728, -164768, 0, 170128, -82920, 0, 17150, -131444, 0, 11616, -48166, 0, 94844, 3584, 0, -102928, -270004, 0, 42668, 160912, 0, -38464, 203624, 0, 148292, 31864, 0, 59136, -86208, 0, -128790, -10868, 0, -64016, 43316, 0, -136294, -16768, 0, -24, -224716, 0, -70378, 84140, 0, 9840, 203314, 0, 1274, 7520, 0, -70920, 30756, 0, -86430, 12712, 0, 86844, -43758, 0, 74642, 47584, 0, -70884, -54230, 0, 98736, -11260, 0, 20608, 267486, 0, -156048, -109744, 0, 37004, 57428, 0, 90300, 126644, 0, -80504, -171754, 0, 98880, 32704, 0, 7204, 28216, 0, -2002, -123692, 0, 78800, -184292, 0, 17914, 6468, 0, -160576, -128240, 0, 32062, 268240, 0, -45200, -199408, 0, -31482, 31376, 0, 31752, -144332, 0, 108804, 123452, 0, -4864, 70210, 0, -142560, 84304, 0, -26528, -56178, 0, 182980, -117780, 0, 101816, 13200, 0, 79646, -10752, 0, 19876, 242562, 0, 6606, -36372, 0, 2904, 16520, 0, 127500, -49480, 0, 29932, 214170, 0, 138105, -8320, 0, -23072, 11484, 0, 140080, 5472, 0, 27728, 28350, 0, -26596, -19404, 0, -13728, -48892, 0, 130296, 72752, 0, -96752, -311780, 0, -13860, -135672, 0, 63424, 26042, 0, 53010, 3584, 0, -60140, 333688, 0, 192432, 310696, 0, -17920, 202828, 0, -107478, -81952, 0, -9604, -101288, 0, 50260, 23404, 0, 136160, -5292, 0, 100604, 62976, 0, 14432, -79446, 0, -127640, -24872, 0, 8256, 64502, 0, 75852, -36232, 0, -182064, 209516, 0, 74834, -39172, 0, 96344, -335760, 0, -82852, 5280, 0, -10864, 85172, 0, 49702, -84344, 0, 32144, -237564, 0, -22264, 166600, 0, 69752, 12936, 0, -244, 40628, 0, -121336, -80818, 0, -120418, 15544, 0, -147304, -192070, 0, 75096, -137608, 0, -7712, -21494, 0, -79548, 22064, 0, 357532, 301340, 0, -124056, -35760, 0, 18392, 455654, 0, -46258, 20352, 0, -7784, -239394, 0, 24054, 241876, 0, -3216, 104258, 0, -32064, -35448, 0, 191844, -580416, 0, -151644, -28820, 0, 97168, 96678, 0, -40558, 19600, 0, -246296, -315068, 0, 23364, -15078, 0, 4096, 202832, 0, 52450, 258792, 0, 17908, 153198, 0, 264144, -54080, 0, 47600, -78730, 0, 326, 67584, 0, -14148, 18788, 0, 143608, 150036, 0, 49504, 58206, 0, -177524, -90840, 0, 44616, 13812, 0, 7203, -122180, 0, 65504, -84590, 0, -64184, 1456, 0, -178508, -107752, 0, 26500, 86312, 0, 14528, -62588, 0, -78828, -3872, 0, 48244, 180318, 0, -95134, 191156, 0, 16184, 22204, 0, -72952, 23552, 0, -62740, -193832, 0, 180292, -225736, 0, 65632, 66678, 0, 68418, 23064, 0, -65872, -172742, 0, -388136, 3234, 0, 101216, -196944, 0, 120962, -2288, 0, 39804, 96414, 0, 42644, 60052, 0, 7392, -119864, 0, 196928, 212576, 0, 190972, -44366, 0, 145360, 204332, 0, -51200, 127498, 0, 94578, 36288, 0, 9368, -362836, 0, -45136, 5544, 0, 80240, 185804, 0, -208756, -51520, 0, -44056, 241166, 0, -46728, 375384, 0, -14004, 107632, 0, 117936, 91024, 0, -82096, -51856, 0, -205760, 117148, 0, -41568, 2968, 0, -233316, 91568, 0, 45944, -50754, 0, 158206, 115520, 0, 114880, -239742, 0, 49525, -26368, 0, 55440, -179836, 0, 14164, -13860, 0, 32400, 115952, 0, -174148, 132272, 0, 66544, -81366, 0, -2688, -148052, 0, 5880, 24236, 0, -55816, -15840, 0, -244828, -25438, 0, 21604, 274392, 0, 4096, -367788, 0, -58146, -109152, 0, 55244, 296160, 0, 37604, 25340, 0, -54912, 299672, 0, 350072, -10976, 0, -252012, 107922, 0, 130540, -22696, 0, -6048, 17446, 0, -245304, -109776, 0, -15596, 427058, 0, 71360, 16100, 0, -28600, 20482, 0, -295400, 86688, 0, -194888, 95256, 0, 396170, 84, 0, -44768, 35730, 0, -137256, -150088, 0, 156440, 62802, 0, -289210, 5852, 0, 32432, -220868, 0, -192472, 36736, 0, -298728, -67136, 0, -108482, 149676, 0, 14784, 200300, 0, 297208, 27000, 0, -287448, -14406, 0, -117476, 199788, 0, -84296, -434608, 0, 95972, 85824, 0, -152524, -114532, 0, -7658, -74456, 0, 25216, 123452, 0, -139122, -13832, 0, -7986, 360800, 0, 201244, 268848, 0, 45920, -18220, 0, -268278, -8896, 0, -89572, 68668, 0, -189890, 363920, 0, 119152, 13202, 0, -222290, -44352, 0, 3888, -22372, 0, -293568, -81904, 0, 181160, -273174, 0, -4312, -46352, 0, -15808, -339888, 0, 32866, -69020, 0, -17232, 161964, 0, 416200, 206936, 0, -115476, -201218, 0, -302938, -98392, 0, 47096, -24970, 0, -263126, 54400, 0, 15828, 70434, 0, -47808, 4524, 0, 21472, 213086, 0, -108720, 145776, 0, 27236, 130028, 0, 3724, 156610, 0, 160128, 262012, 0, 87208, 8232, 0, -130444, 290844, 0, -176346, 39732, 0, 1664, -131172, 0, 28466, -48160, 0, -40068, -229960, 0, 6842, 170216, 0, -24432, 114772, 0, -67916, 55136, 0, -375792, -140968, 0, -219718, -96676, 0, 25376, 49476, 0, -100842, 62000, 0, 117964, 11858, 0, -363218, 16800, 0, 251696, 285226, 0, -423618, 78192, 0, 0, 318408, 0, -198756, -1620, 0, 3696, -179670, 0, 70872, 175992, 0, -28000, 174944, 0, -206923, 152212, 0, 33912, -144236, 0, -412412, 8448, 0, -473232, 467200, 0, -15148, 175584, 0, -50704, -328164, 0, -3014, -24696, 0, -48780, -367922, 0, -193770, -96600, 0, -186560, 496994, 0, -22216, -51584, 0, -17640, -261688, 0, -197056, 86612, 0, -58880, -4928, 0, 72058, -233856, 0, 350880, -182532, 0, -62182, -242280, 0, 52888, 139484, 0, 25774, -93824, 0, 174292, -70020, 0, -38944, -128912, 0, 3392, -238902, 0, -150108, 58720, 0, 299676, 168390, 0, -306880, 23056, 0, 18368, 151360, 0, 86584, 56600, 0, -51120, -31850, 0, -13530, 234404, 0, -15840, -35948, 0, -175272, 4920, 0, -112036, 89020, 0, -178864, -105092, 0, -23216, -152922, 0, -231956, 6720, 0, -233384, -65428, 0, -8850, 286384, 0, -29072, -342776, 0, -273324, -233584, 0, -28336, 220638, 0, 71064, -173208, 0, 201376, 23534, 0, -81222, 42976, 0, -256800, -62688, 0, -328516, -48424, 0, -12544, -157004, 0, -5964, -44968, 0, -136624, -100116, 0, 149218, -27356, 0, -86984, -462652, 0, -108350, -17824, 0, 124024, 205144, 0, -276924, 38864, 0, 23408, 319392, 0, 415608, 26536, 0, -88320, -45934, 0, -55260, -56932, 0, -135496, -43142, 0, 146864, -156864, 0, -197080, -50264, 0, -49392, -315672, 0, 6688, -115952, 0, -20688, -36680, 0, 11176, 174028, 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": "1386.4.a.be", "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], [0, 0, 0], [4, 0, 0], [-3, 0, 1], [0, 0, 0], [-7, 0, 0], [-8, 0, 0], [0, 0, 0], [6, 0, -2], [11, 0, 0], [0, 0, 0], [9, -1, 4], [14, 0, 0], [0, 0, 0], [16, 0, 0], [12, 7, -5], [0, 0, 0], [-63, 5, 0], [-12, 0, 4], [0, 0, 0], [-22, 0, 0], [42, -21, -7], [0, 0, 0], [-4, -12, -9], [-18, 2, -8], [0, 0, 0], [-28, 0, 0], [61, -3, 0], [0, 0, 0], [-90, 21, 5], [-32, 0, 0], [0, 0, 0], [-24, -14, 10], [21, 0, -7], [0, 0, 0], [13, 28, -3], [126, -10, 0], [0, 0, 0], [24, 0, -8], [190, 28, -24], [0, 0, 0], [32, -77, 7], [44, 0, 0], [0, 0, 0], [-84, 42, 14], [63, 68, 7], [0, 0, 0], [49, 0, 0], [8, 24, 18], [0, 0, 0], [36, -4, 16], [156, -35, -15], [0, 0, 0], [-33, 0, 11], [56, 0, 0], [0, 0, 0], [-122, 6, 0], [-205, -22, -13], [0, 0, 0], [-330, 16, -34], [180, -42, -10], [0, 0, 0], [64, 0, 0], [421, -49, -12], [0, 0, 0], [-331, 26, -55], [48, 28, -20], [0, 0, 0], [-42, 0, 14], [-86, -18, 18], [0, 0, 0], [-221, 21, 6], [-26, -56, 6], [0, 0, 0], [-252, 20, 0], [-77, 0, 0], [0, 0, 0], [334, -134, -44], [-48, 0, 16], [0, 0, 0], [-380, -56, 48], [-308, 63, 73], [0, 0, 0], [-596, 67, 21], [-64, 154, -14], [0, 0, 0], [-88, 0, 0], [626, -76, 38], [0, 0, 0], [-63, 7, -28], [168, -84, -28], [0, 0, 0], [-126, -136, -14], [189, 5, -78], [0, 0, 0], [-608, 163, -21], [-98, 0, 0], [0, 0, 0], [-16, -48, -36]]}