# Stored data for newform 1216.4.a.m, downloaded from the LMFDB on 23 April 2024.
{"label": "1216.4.a.m", "space_label": "1216.4.a", "level": 1216, "weight": 4, "hecke_orbit": 13, "hecke_orbit_code": 54043195595556032, "dim": 2, "is_polredabs": true, "nf_label": "2.2.57.1", "trace_hash": 1404398739272075287, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [-14, -1, 1]], [5, [-8, -5, 1]]], "qexp_display": "q+\\beta q^{3}+(3-\\beta )q^{5}+(-5+4\\beta )q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 19456, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 71.74632256698058, "hecke_ring_index": 1, "level_radical": 38, "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": [1216, 1, [191, 837, 705], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 19], "conrey_indexes": [1], "field_disc": 57, "field_disc_factorization": [[3, 1], [19, 1]], "field_poly": [-14, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.906", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8.634", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "55.389", "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], [19, -1]], "trace_display": [0, 1, 5, -6], "traces": [0, 2, 0, 1, 0, 5, 0, -6, 0, -25, 0, 15, 0, 59, 0, -26, 0, -104, 0, 38, 0, 111, 0, -21, 0, -209, 0, -11, 0, 137, 0, 4, 0, -192, 0, -129, 0, 152, 0, 229, 0, -210, 0, -67, 0, -91, 0, 273, 0, -212, 0, -337, 0, -209, 0, 237, 0, 19, 0, -799, 0, -149, 0, 189, 0, -52, 0, -201, 0, -951, 0, 792, 0, -246, 0, -247, 0, -843, 0, -254, 0, -442, 0, -374, 0, 25, 0, 325, 0, -564, 0, 621, 0, -796, 0, 95, 0, -178, 0, -387, 0, -192, 0, -1420, 0, 306, 0, 151, 0, -675, 0, -722, 0, -944, 0, 888, 0, -538, 0, -828, 0, -1153, 0, 2460, 0, -1005, 0, -3336, 0, 622, 0, 723, 0, -114, 0, 1084, 0, -1380, 0, 4157, 0, -1146, 0, -954, 0, 86, 0, -790, 0, -2629, 0, -3452, 0, 1015, 0, 808, 0, 1904, 0, -19, 0, -3699, 0, 2080, 0, -594, 0, 2822, 0, -1257, 0, -475, 0, -3524, 0, 57, 0, -2195, 0, -3402, 0, -2644, 0, 1436, 0, 1178, 0, 1215, 0, -4413, 0, 4266, 0, -4602, 0, -368, 0, -4098, 0, 162, 0, -243, 0, 615, 0, -3090, 0, -678, 0, 285, 0, -5895, 0, -2454, 0, -823, 0, -3204, 0, -2175, 0, -5063, 0, 1484, 0, 2470, 0, -2537, 0, -3935, 0, 1032, 0, -9467, 0, 1965, 0, 3122, 0, 7350, 0, -7470, 0, -1406, 0, 154, 0, 1121, 0, 4202, 0, -7351, 0, 6426, 0, 782, 0, -804, 0, -3648, 0, -1456, 0, 1805, 0, -608, 0, -5868, 0, 3610, 0, -9181, 0, 3075, 0, -570, 0, 4947, 0, -848, 0, -3626, 0, 8503, 0, -494, 0, 10890, 0, -1568, 0, 10570, 0, 4661, 0, -202, 0, 7698, 0, -7203, 0, 2823, 0, -13890, 0, -1883, 0, 5356, 0, 8182, 0, 5348, 0, -12701, 0, 1983, 0, 12903, 0, -768, 0, -2461, 0, -1976, 0, -7163, 0, 6075, 0, -5949, 0, 6373, 0, -2698, 0, -360, 0, 2820, 0, -7882, 0, 5616, 0, -42, 0, -1608, 0, 7677, 0, -11383, 0, -8105, 0, -5405, 0, 4830, 0, -5487, 0, 1448, 0, 722, 0, -3569, 0, 1437, 0, -18268, 0, 5190, 0, 969, 0, -14591, 0, 5682, 0, 5837, 0, 5205, 0, -5430, 0, -10342, 0, -3561, 0, 1493, 0, 14431, 0, 10497, 0, -4854, 0, -3884, 0, -965, 0, 2109, 0, 5928, 0, -5468, 0, 377, 0, 6726, 0, 26312, 0, 10083, 0, -4785, 0, -5324, 0, 9346, 0, -26232, 0, 6767, 0, -4695, 0, 12293, 0, 6489, 0, -4866, 0, -14298, 0, 23072, 0, -1268, 0, -399, 0, 29246, 0, 1966, 0, 28105, 0, 4176, 0, -7670, 0, 25254, 0, -19530, 0, -2410, 0, -1212, 0, 17780, 0, 11687, 0, 22515, 0, -12983, 0, -1648, 0, -6763, 0, 33, 0, 2206, 0, -5091, 0, -3971, 0, 2698, 0, 19024, 0, -1102, 0, -225, 0, -11104, 0, 3740, 0, 18140, 0, -5984, 0, -9689, 0, -3675, 0, -13776, 0, -2813, 0, 3976, 0, -7593, 0, 13314, 0, 11142, 0, -9662, 0, -7470, 0, -209, 0, -12442, 0, 11025, 0, -8830, 0, -17416, 0, 31811, 0, -11457, 0, 7772, 0, 6923, 0, 8192, 0, 11760, 0, 2914, 0, -18060, 0, 3198, 0, 26623, 0, -20474, 0, -8100, 0, -9680, 0, 3373, 0, 2603, 0, 13758, 0, -3572, 0, 30467, 0, 2612, 0, 8844, 0, 5042, 0, 5050, 0, -4602, 0, -8216, 0, -8176, 0, 17067, 0, 6897, 0, 19750, 0, 1290, 0, 18678, 0, -2166, 0, 308, 0, 10699, 0, 76, 0, 19212, 0, -29328, 0, 3003, 0, 23451, 0, 2656, 0, 26302, 0, 2370, 0, 110, 0, -20238, 0, 7347, 0, -924, 0, 37265, 0, 7860, 0, -24957, 0, -22274, 0, 36795, 0, -20652, 0, 17428, 0, -3648, 0, 76, 0, 38951, 0, 729, 0, -4578, 0, -11042, 0, -12750, 0, -30426, 0, -13321, 0, 2182, 0, 26690, 0, 6576, 0, 1020, 0, -16449, 0, 7023, 0, 1023, 0, -19473, 0, 3305, 0, -21313, 0, -2451, 0, -9903, 0, 23314, 0, -11691, 0, 1002, 0, 6707, 0, -14693, 0, 43170, 0, 3377, 0, 40352, 0, -14223, 0, 10316, 0, -5567, 0, 501, 0, 11991, 0, 3125, 0, -14730, 0, 1280, 0, 4638, 0, 2888, 0, -6114, 0, -54600, 0, -22896, 0, 6424, 0, 26292, 0, 2004, 0, 11883, 0, -13118, 0, 39828, 0, -4932, 0, -15599, 0, 28412, 0, 34202, 0, -3071, 0, 5182, 0, 1388, 0, -510, 0, -7703, 0, 4351, 0, 40800, 0, -217, 0, 9064, 0, -10599, 0, -7592, 0, 13624, 0, -7946, 0, 8567, 0, -1746, 0, -9692, 0, 27675, 0, 457, 0, -36139, 0, 20212, 0, -32436, 0, -26081, 0, 3572, 0, 9234, 0, -3990, 0, 25890, 0, -10757, 0, 3506, 0, -36433, 0, -22154, 0, -26808, 0, 6178, 0, 2888, 0, -48381, 0, -1371, 0, 1464, 0, 12519, 0, -10872, 0, 31730, 0, -33336, 0, -18063, 0, -21719, 0, -11900, 0, -1273, 0, -4998, 0, 32479, 0, -27220, 0, 19494, 0, 50507, 0, -35487, 0, -25542, 0, 17864, 0, 4490, 0, 31100, 0, 30762, 0, -37085, 0, 44756, 0, -14913, 0, -8511, 0, -280, 0, 24738, 0, -32316, 0, -1729, 0, -36994, 0, -2377, 0, -14220, 0, -38052, 0, -1742, 0, 28856, 0, -24648, 0, -6927, 0, 12884, 0, 27753, 0, 26611, 0, 10339, 0, 6323, 0, -17425, 0, 6796, 0, -23552, 0, -5040, 0, 7059, 0, 5187, 0, 7854, 0, -33441, 0, -6908, 0, 10013, 0, -4374, 0, 12542, 0, 28837, 0, -11394, 0, -34198, 0, -33528, 0, 4958, 0, -23031, 0, -71011, 0, -50332, 0, 3414, 0, -11894, 0, 26642, 0, -31209, 0, -4028, 0, 25303, 0, -5199, 0, 41026, 0, -29749, 0, -58591, 0, -82440, 0, -13740, 0, 8636, 0, -21621, 0, -1557, 0, 7082, 0, -4269, 0, -12126, 0, 47232, 0, -37230, 0, -4424, 0, -15096, 0, 29856, 0, -6403, 0, 41912, 0, 16599, 0, -28633, 0, -6040, 0, 34872, 0, 14850, 0, -52706, 0, -31506, 0, 16434, 0, -20928, 0, -3194, 0, 48815, 0, -22965, 0, 10063, 0, 30286, 0, -14694, 0, 59503, 0, 2328, 0, -3971, 0, -84596, 0, -68244, 0, -118617, 0, -5502, 0, 4390, 0, 77075, 0, 12611, 0, -3576, 0, 9120, 0, 15250, 0, -49155, 0, 106288, 0, -29503, 0, -13152, 0, -7357, 0, 43092, 0, -30276, 0, -17535, 0, 4503, 0, 9784, 0, -38903, 0, -67804, 0, -23413, 0, -18414, 0, 7620, 0, -41833, 0, -10743, 0, 3344, 0, -15996, 0, -75948, 0, 26033, 0, 5277, 0, 3230, 0, 3724, 0, -26351, 0, 19690, 0, 39456, 0, 361, 0, -10632, 0, 15118, 0, 11420, 0, -24347, 0, 6472, 0, -906, 0, -40506, 0, -696, 0, -14036, 0, -21554, 0, 6124, 0, -98880, 0, -52379, 0, 95118, 0, -11685, 0, -18862, 0, 51059, 0, -1681, 0, -15181, 0, 8918, 0, 18747, 0, 24798, 0, -60548, 0, 24151, 0, -72894, 0, -10988, 0, -219, 0, 11877, 0, 62160, 0, 37938, 0, -22121, 0, 22648, 0, -5570, 0, 52583, 0, 44144, 0, 13866, 0, -55740, 0, -2831, 0, -25196, 0, -29567, 0, -29681, 0, 10664, 0, 1794, 0, 28972, 0, 57147, 0, -22116, 0, 18888, 0, -14253, 0, -13785, 0, 50853, 0, 9800, 0, -28788, 0, 8700, 0, 105566, 0, 13944, 0, 10167, 0, 3591, 0, -49950, 0, -98386, 0, -68400, 0, -17478, 0, -12684, 0, -25876, 0, -17700, 0, 20890, 0, -26486, 0, -44279, 0, -627, 0, -17784, 0, -28266, 0, 25574, 0, 24784, 0, -60858, 0, 13090, 0, 28023, 0, -988, 0, 108451, 0, -42549, 0, 33312, 0, 44790, 0, 13640, 0, 1310, 0, -69218, 0, -44695, 0, -55230, 0, -35677, 0, 14244, 0, -37918, 0, 69362, 0, 76201, 0, 21024, 0, -68676, 0, 48516, 0, -72240, 0, -3819, 0, 43339, 0, 22315, 0, 11404, 0, -9780, 0, 112611, 0, 30024, 0, 7536, 0, -56706, 0, -82567, 0, 6018, 0, -20178, 0, 32207, 0, 50866, 0, -92914, 0, -3321, 0, -2386, 0, 85309, 0, 29301, 0, -18069, 0, -102222, 0, 27569, 0, 5560, 0, 58286, 0, -37428, 0, 27842, 0, 21413, 0, -153969, 0, 14024, 0, -7665, 0, -18488, 0, -3840, 0, 46938, 0, 20354, 0, 26507, 0, -19282, 0, -20900, 0, -8406, 0, 15048, 0, 28170, 0, 30420, 0, -5824, 0, 67641, 0, 42466, 0, -104686, 0, 7158, 0, -2544, 0, -55518, 0, -67410, 0, -24683, 0, -117617, 0, -50829, 0, 37804, 0, 97338, 0, -12900, 0, 19038, 0, 40383, 0, -4674, 0, 78866, 0, -13301, 0, 92994, 0, -12152, 0, 1314, 0, -95872, 0, -52316, 0, -48282, 0, -55634, 0, -11013, 0, 28584, 0, -24442, 0, -22546, 0, 25789, 0, 24975, 0, 9054, 0, -20678, 0, -56800, 0, -4693, 0, 93243, 0, 47739, 0, -2185, 0, 43236, 0, 46890, 0, 33908, 0, -77566, 0, 41931, 0, -8930, 0, -33560, 0, 15124, 0, 47862, 0, 5023, 0, -39321, 0, 23632, 0, 36456, 0, 121519, 0, -43958, 0, -16017, 0, 3644, 0, -8900, 0, -79718, 0, 34656, 0, 104852, 0, 92473, 0, 32391, 0, -37705, 0, -30444, 0, -12199, 0, 26484, 0, 73584, 0, -24369, 0, 46806, 0, -47051, 0, 11832, 0, 100766, 0, -138154, 0, -4826, 0, -32710, 0, 12843, 0, -85761, 0, 9513, 0, 16524, 0, 85188, 0, -25092, 0, -87780, 0, 18728, 0, 27483, 0, -6510, 0, 8018, 0, 41966, 0, -19695, 0, 569, 0, -11601, 0, 66400, 0, -13547, 0, -8398, 0, 6813, 0, 66433, 0, 36244, 0, -59937, 0, -7023, 0, -31338, 0, 86610, 0, -9259, 0, 36982, 0, -206835, 0, 85836, 0, -15548, 0, -8354, 0, 106841, 0, -42377, 0, -79928, 0, -54961, 0, -12198, 0, -7106, 0, 60932, 0, 44812, 0, 49872, 0, 40266, 0, 23212, 0, 26193, 0, -23446, 0, 74419, 0, 9822, 0, 130832, 0, 60600, 0, 52078, 0, 60939, 0, -7036, 0, 22947, 0, 91930, 0, 26166, 0, 54405, 0, 475, 0, 17616, 0, 65162, 0, 2065, 0, -73072, 0, 13644, 0, -116978, 0, 13898, 0, 52455, 0, 85734, 0, 21600, 0, -66792, 0, 24771, 0, 1316, 0, -2812, 0, -34281, 0, -58090, 0, -97334, 0, -124746, 0, 6175, 0, -29696, 0, 76456, 0, -17346, 0, -21102, 0, 94810, 0, -18886, 0, 63450, 0, 203725, 0, 19138, 0, 10782, 0, 21717, 0, 13960, 0, 70299, 0, 115058, 0, -6951, 0, 76704, 0, 17622, 0, -11672, 0, -10716, 0, -85575, 0, -2548, 0, 101073, 0, 34223, 0, 96102, 0, -15180, 0, 20424, 0, -111952, 0, 144561, 0, -70891, 0, 16204, 0, 49029, 0, 147924, 0, -38391, 0, -72014, 0, -136393, 0, 103227, 0, 5502, 0, 11799, 0, 112475, 0, -85797, 0, 53307, 0, 61116, 0, 56658, 0, 14571, 0, -25146, 0, -43933, 0, -86333, 0, 20406, 0, -15080, 0, -30662, 0, 13624, 0, 91251, 0, 85160, 0, -24946, 0, 66030, 0, 25618, 0, -15124, 0, 3388, 0, -39114, 0, 72486, 0, -68514, 0, -15982, 0, -16374, 0, 34701, 0, -200451, 0, 618, 0, -134117, 0, 159895, 0, 21345, 0, -104100, 0, 30695, 0, 162296, 0, -125724, 0, 52978, 0, -18712, 0, 1805, 0, 173504, 0, 6663, 0, 117885, 0, 3040, 0, 9004, 0, -104550, 0, 17513, 0, 23910, 0, 96360, 0, 35967, 0, -648, 0, 48676, 0, 85923, 0, -11064, 0, -40768, 0, 3210, 0, 364, 0, -97641, 0, -3382, 0, 48030, 0, -124504, 0, -141693, 0, -118812, 0, -29025, 0, 14592, 0, 66782, 0, -91821, 0, -73323, 0, 53547, 0, -42092, 0, 186305, 0, -25716, 0, -497, 0, 114792, 0, 56309, 0, 58330, 0, -75832, 0, -7353, 0, 108870, 0, -6640, 0, 19874, 0, -86162, 0, -42592, 0, 93034, 0, 15834, 0, -40971, 0, 77364, 0, 24136, 0, 23046, 0, 35844, 0, 5749, 0, -140910, 0, -46846, 0, 15642, 0, -25456, 0, 106794, 0, -3648, 0, 123188, 0, 63162, 0, 80826, 0, -144090, 0, -147080, 0, -132374, 0, 37684, 0, 12881, 0, -122044, 0, -126903, 0, -4325, 0, -15051, 0, 32629, 0, 69522, 0, -12542, 0, 73930, 0, 42672, 0, -25656, 0, -26980, 0, 15858, 0, -18278, 0, -106622, 0, -19830, 0, 197154, 0, 88998, 0, 81381, 0, -26389, 0, 10298, 0, 101727, 0, -47459, 0, -43635, 0, 201523, 0, -108461, 0, 120189, 0, 44506, 0, 114234, 0, 109175, 0, 5814, 0, -26329, 0, -93262, 0, -72069, 0, -182269, 0, 86184, 0, 4022, 0, -39300, 0, -134517, 0, 20346, 0, 9472, 0, -62938, 0, 116496, 0, -38643, 0, 123264, 0, 53599, 0, -23073, 0, -38797, 0, -72013, 0, 2869, 0, 37962, 0, -20538, 0, -139033, 0, 64946, 0, 36358, 0, 54152, 0, 190260, 0, 95644, 0, 18051, 0, -134622, 0, 39486, 0, 89881, 0, 28602, 0, 61471, 0, -100209, 0, 28194, 0, -21109, 0, 9824, 0, -12825, 0, 105672, 0, 17138, 0, 3588, 0, -52050, 0, -25758, 0, -225118, 0, -39506, 0, 5208, 0, 45228, 0, -110820, 0, -97749, 0, -92940, 0, 124351, 0, 269149, 0, -72543, 0, -205560, 0, -55900, 0, -8630, 0, -13718, 0, 299306, 0, 216682, 0, -31659, 0, -35319, 0, 181060, 0, 3138, 0, -59652, 0, -9585, 0, -184614, 0, 21587, 0, 183823, 0, -125314, 0, 29247, 0, 151056, 0, 19644, 0, 11465, 0, 124414, 0, 3624, 0, -17936, 0, -228108, 0, -83667, 0, -226843, 0, -48912, 0, 76319, 0, 211092, 0, 149138, 0, -87702, 0, 18350, 0, -179562, 0, 92178, 0, 101204, 0, 29640, 0, -44365, 0, 74472, 0, 160327, 0, -86969, 0, -10450, 0, 16872, 0, 86527, 0, -162375, 0, -55491, 0, -26074, 0, 82178, 0, -84311, 0, -4420, 0, 81384, 0, -275273, 0, -614, 0, 12958, 0, -112669, 0, 18726, 0, 179115, 0, 70291, 0, 1478, 0, -70743, 0, -229903, 0, -10222, 0, 86868, 0, 14559, 0, 134172, 0, -349878, 0, -44664, 0, 21466, 0, -235853, 0, -273785, 0, -169114, 0, -160285, 0, 84168, 0, 10917, 0, -153434, 0, 180735, 0, -201472, 0, -89010, 0, -53618, 0, 109187, 0, -15732, 0, 56964, 0, 43508, 0, 38799, 0, 517, 0, 227752, 0, -152586, 0, -78717, 0, -85284, 0, 8968, 0, 66770, 0, 99863, 0, 78023, 0, -94547, 0, -43875, 0, 11842, 0, 34417, 0, -30148, 0, -194236, 0, -21907, 0, -150737, 0, 1842, 0, 48507, 0, -72031, 0, -47359, 0, 216986, 0, -21984, 0, -117815, 0, 163395, 0, -63913, 0, -69948, 0, 457218, 0, 84892, 0, -214872, 0, -35970, 0, 56658, 0, 9585, 0, 32027, 0, 46740, 0, 179356, 0, -183452, 0, -87432, 0, 11112, 0, 87723, 0, -43615, 0, -161010, 0, -212062, 0, -22244, 0, -280761, 0, -287076, 0, -124607, 0, -288839, 0, -24327, 0, -45619, 0, -278526, 0, 145370, 0, -44982, 0, -19095, 0, 203718, 0, 32786, 0, 160317, 0, -314586, 0, 10792, 0, -42384, 0, -122630, 0, -145743, 0, -269808, 0, 23164, 0, 27102, 0, 214759, 0, -123694, 0, 220956, 0, 5624, 0, 13882, 0, 15408, 0, -212004, 0, -63384, 0, 51336, 0, 80824, 0, -77700, 0, -15200, 0, 301788, 0, -34694, 0, -16155, 0, -159489, 0, 93498, 0, -13221, 0, 55178, 0, 239015, 0, 97634, 0, -135648, 0, 96051, 0, 7160, 0, 355596, 0, -91480, 0, 11818, 0, -146874, 0, -122804, 0, -111231, 0, -182945, 0, 82119, 0, 145658, 0, 8638, 0, 27161, 0, 59293, 0, -140307, 0, -233590, 0, 26904, 0, 103624, 0, -11286, 0, 86785, 0, 230385, 0, -88134, 0, -197949, 0, 13737, 0, -32376, 0, -89853, 0, -109205, 0, -51546, 0, 74710, 0, 151590, 0, 81900, 0, -31556, 0, -204525, 0, -110622, 0, 40612, 0, -112644, 0, -32292, 0, -18876, 0, -115497, 0, -2126, 0, 16598, 0, 89034, 0, -2166, 0, 91894, 0, 132570, 0, 200263, 0, 39882, 0, -14530, 0, -268149, 0, -60999, 0, 3396, 0, -70952, 0, -110819, 0, -24155, 0, -234829, 0, -50730, 0, -10809, 0, -15977, 0, 3678, 0, 27936, 0, -113097, 0, 20596, 0, 186344, 0, 35196, 0, 94648, 0, -123640, 0, 103930, 0, 45124, 0, -94827, 0, -88908, 0, -155790, 0, 64413, 0, 168369, 0, -169506, 0, 389104, 0, -82399, 0, 31676, 0, 20102, 0, 254442, 0, 49240, 0, -26220, 0, -36700, 0, 37380, 0, -265568, 0, 66231, 0, -27717, 0, 137810, 0, 127740, 0, -414722, 0, 198036, 0, 39733, 0, -61962, 0, 139992, 0, -2331, 0, -91261, 0, -153819, 0, -21496, 0, -50254, 0, 67419, 0, 78983, 0, -169976, 0, -2443, 0, -325630, 0, 149548, 0, -47646, 0, -26901, 0, 9422, 0, 211569, 0, -362447, 0, -87586, 0, 190374, 0, -25320, 0, -181386, 0, -111548, 0, 214921, 0, -171342, 0, -3097, 0, 341530, 0, -21774, 0, 29430, 0, 2741, 0, 11508, 0, 73842, 0, -284968, 0, 60198, 0, -259725, 0, -8022, 0, -57604, 0, -266370, 0, 38760, 0, 30343, 0, 152941, 0, 201413, 0, -41073, 0, -317874, 0, -195928, 0, -3932, 0, -18126, 0, 185866, 0, 174275, 0, -29499, 0, 38475, 0, 539022, 0, -109598, 0, -230066, 0, 119188, 0, -30356, 0, 176103, 0, 53460, 0, -18098, 0, -148167, 0, 29437, 0, 8280, 0, -151838, 0, 45342, 0, -243487, 0, 1634, 0, -87005, 0, 155280, 0, -176229, 0, -119960, 0, 58620, 0, 192378, 0, -3366, 0, -279160, 0, -28266, 0, 66614, 0, 35802, 0, 427089, 0, -338978, 0, 110859, 0, 72263, 0, -105009, 0, -196010, 0, -71156, 0, -15010, 0, -6124, 0, -262675, 0, -44221, 0, -168558, 0, 222947, 0, 678, 0, -303240, 0, -275657, 0, -16879, 0, 83738, 0, 26798, 0, 135364, 0, -266921, 0, -76164, 0, 58057, 0, 135698, 0, 218208, 0, 30600, 0, -49951, 0, 5996, 0, 9243, 0, 64191, 0, -172394, 0, -23840, 0, -176795, 0, 87304, 0, -95883, 0, -104766, 0, -33943, 0, -169296, 0, -40732, 0, -428393, 0, 193066, 0, -234738, 0, -32424, 0, -25590, 0, -88311, 0, -65588, 0, -2142, 0, -52341, 0, -193536, 0, -87363, 0, 423126, 0, 3456, 0, -21807, 0, -53225, 0, 56020, 0, 98093, 0, 127786, 0, 174933, 0, 67008, 0, 18805, 0, 201782, 0, 238368, 0, 173634, 0, 81180, 0, 19285, 0, -135038, 0, -339660, 0, -274988, 0, -26904, 0, 139307, 0, 223446, 0, 159174, 0, -110276, 0, 64486, 0, -148962, 0, -137298, 0, 196708, 0, 188136, 0, 57043, 0, 31800, 0, 244467, 0, 253928, 0, -246375, 0, 15352, 0, 270969, 0, -276754, 0, -42323, 0, -98026, 0, 95796, 0, 57597, 0, -182400, 0, 93771, 0, 66021, 0, -71610, 0, 14160, 0, 1550, 0, 276521, 0, 74384, 0, 111891, 0, -30098, 0, -34034, 0, 51042, 0, 36176, 0, 44634, 0, -17242, 0, -20458, 0, -240382, 0, -158850, 0, -154328, 0, 7904, 0, -342036, 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": "152.4.a.a", "char_is_minimal": false, "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], [0, 1], [0, 0], [3, -1], [0, 0], [-5, 4], [0, 0], [-13, 1], [0, 0], [11, -7], [0, 0], [26, 7], [0, 0], [-14, 2], [0, 0], [-47, -10], [0, 0], [19, 0], [0, 0], [56, -1], [0, 0], [6, -33], [0, 0], [-102, -5], [0, 0], [14, -39], [0, 0], [64, 9], [0, 0], [16, -28], [0, 0], [-98, 4], [0, 0], [-71, 13], [0, 0], [90, -28], [0, 0], [98, 33], [0, 0], [-150, 90], [0, 0], [-45, 23], [0, 0], [-53, 15], [0, 0], [159, -45], [0, 0], [-94, -24], [0, 0], [-140, -57], [0, 0], [-106, 3], [0, 0], [131, -25], [0, 0], [0, 19], [0, 0], [-368, -63], [0, 0], [-101, 53], [0, 0], [121, -53], [0, 0], [-20, -12], [0, 0], [-98, -5], [0, 0], [-462, -27], [0, 0], [446, -100], [0, 0], [-87, -72], [0, 0], [-70, -107], [0, 0], [-447, 51], [0, 0], [-184, 114], [0, 0], [-195, -52], [0, 0], [-264, 154], [0, 0], [-1, 27], [0, 0], [126, 73], [0, 0], [-184, -196], [0, 0], [262, 97], [0, 0], [-392, -12], [0, 0], [57, -19], [0, 0], [-276, 374], [0, 0], [-241, 95], [0, 0]]}