# Stored data for newform 882.4.a.u, downloaded from the LMFDB on 16 April 2024.
{"label": "882.4.a.u", "space_label": "882.4.a", "level": 882, "weight": 4, "hecke_orbit": 21, "hecke_orbit_code": 90071992614519666, "dim": 2, "is_polredabs": true, "nf_label": "2.2.193.1", "trace_hash": 1235749988841411127, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [-36, 7, 1]], [11, [-2208, 25, 1]], [13, [-606, -49, 1]]], "qexp_display": "q-2q^{2}+4q^{4}+(-3-\\beta )q^{5}-8q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 14112, "fricke_eigenval": -1, "atkin_lehner_string": "++-", "analytic_conductor": 52.039684625063224, "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": [882, 1, [785, 199], [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": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.934", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.318", "prec": 17}, {"__RealLiteral__": 0, "data": "1.047", "prec": 17}, {"__RealLiteral__": 0, "data": "63.537", "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": [-4, 0, -7, 0], "traces": [0, 2, -4, 0, 8, -7, 0, 0, -16, 0, 14, -25, 0, 49, 0, 0, 32, -98, 0, 119, -28, 0, 50, 122, 0, -129, -98, 0, 0, 73, 0, -98, -64, 0, 196, 0, 0, 289, -238, 0, 56, -336, 0, 307, -100, 0, -244, -672, 0, 0, 258, 0, 196, -375, 0, 763, 0, 0, -146, -763, 0, 406, 196, 0, 128, -654, 0, -1041, -392, 0, 0, 1652, 0, 189, -578, 0, 476, 0, 0, 524, -112, 0, 672, -287, 0, -622, -614, 0, 200, -2394, 0, 0, 488, 0, 1344, -706, 0, 63, 0, 0, -516, -910, 0, 161, -392, 0, 750, -1419, 0, -717, -1526, 0, 0, 3052, 0, -1778, 292, 0, 1526, 0, 0, 2379, -812, 0, -392, 651, 0, -688, -256, 0, 1308, -4459, 0, 0, 2082, 0, 784, -2666, 0, -3465, 0, 0, -3304, -3990, 0, -931, -378, 0, 1156, -2958, 0, 243, -952, 0, 0, 3045, 0, -4018, -1048, 0, 224, 0, 0, 226, -1344, 0, 574, -2086, 0, -781, 1244, 0, 1228, -4774, 0, 0, -400, 0, 4788, -3768, 0, -3689, 0, 0, -976, -3038, 0, -5530, -2688, 0, 1412, 1632, 0, 3640, -126, 0, 0, 1058, 0, -4396, 1032, 0, 1820, 0, 0, 1176, -322, 0, 784, -3514, 0, -3560, -1500, 0, 2838, 952, 0, 0, 1434, 0, 3052, 2424, 0, -8785, 0, 0, -6104, -3549, 0, -105, 3556, 0, -584, 1718, 0, 36, -3052, 0, 0, 1014, 0, -5005, -4758, 0, 1624, 0, 0, 4363, 784, 0, -1302, 4977, 0, -10982, 1376, 0, 512, -462, 0, 0, -2616, 0, 8918, 2496, 0, -4767, 0, 0, -4164, 6755, 0, 301, -1568, 0, 5332, -3116, 0, -5807, 6930, 0, 0, -8854, 0, -5607, 6608, 0, 7980, 0, 0, 4626, 1862, 0, 756, 1239, 0, 8557, -2312, 0, 5916, 9744, 0, 0, -486, 0, 1904, 1860, 0, 2121, 0, 0, -6090, 17108, 0, -924, 8036, 0, 2096, 5061, 0, -5641, -448, 0, 0, -2936, 0, 217, -452, 0, 2688, 0, 0, 5989, -1148, 0, 4172, 266, 0, -3070, 1562, 0, -2488, 20139, 0, 0, -2456, 0, 9548, 13872, 0, 5292, 0, 0, 800, 2604, 0, -3080, -9576, 0, 7536, 9106, 0, -5769, 7378, 0, 0, -10022, 0, -19222, 1952, 0, 6076, 0, 0, 11331, 11060, 0, 5376, 5166, 0, 2037, -2824, 0, -3264, 13762, 0, 0, -7280, 0, 252, -698, 0, 7532, 0, 0, -2116, 7623, 0, 25249, 8792, 0, -2064, -2844, 0, -15911, -3640, 0, 0, -17798, 0, 11564, -2352, 0, 644, 0, 0, 9593, -1568, 0, 7028, 6972, 0, 3425, 7120, 0, 3000, 13076, 0, 0, -5676, 0, -1904, 4596, 0, 7091, 0, 0, -2868, 11312, 0, -21035, -6104, 0, -4848, 13703, 0, 13590, 17570, 0, 0, -7778, 0, 4200, 12208, 0, 7098, 0, 0, 4092, 210, 0, -7112, -8218, 0, 2589, 1168, 0, -3436, -2632, 0, 0, -72, 0, 6104, 10348, 0, -5649, 0, 0, -2028, -15764, 0, 17213, 10010, 0, 9516, 14737, 0, -5246, -3248, 0, 0, -12933, 0, 3178, -8726, 0, -1568, 0, 0, -26511, 2604, 0, -9954, -8862, 0, -16694, 21964, 0, -2752, 8715, 0, 0, -1024, 0, 924, -8380, 0, -7812, 0, 0, 5232, 3696, 0, -5215, -17836, 0, -4992, -22218, 0, 2022, 9534, 0, 0, -8232, 0, -9219, 8328, 0, -13510, 0, 0, 4745, -602, 0, 3136, 23450, 0, 12866, -10664, 0, 6232, 6370, 0, 0, 11614, 0, -13860, 3583, 0, -2611, 0, 0, 17708, 24157, 0, -13384, 11214, 0, -13216, 2022, 0, 2027, -15960, 0, 0, 1588, 0, 17094, -9252, 0, -3724, 0, 0, -37869, -1512, 0, -2478, -11753, 0, -13937, -17114, 0, 4624, -21294, 0, 0, -11832, 0, -19488, -17946, 0, -12670, 0, 0, 972, -25214, 0, -32858, -3808, 0, -3720, -4884, 0, 40640, -4242, 0, 0, 54668, 0, -5481, 12180, 0, -34216, 0, 0, -2076, 1848, 0, -16072, 6104, 0, 19309, -4192, 0, -10122, -4347, 0, 0, 11282, 0, 896, -3712, 0, -1477, 0, 0, 5872, -20244, 0, 50743, -434, 0, 904, -30417, 0, 19177, -5376, 0, 0, 23480, 0, 28413, -11978, 0, 2296, 0, 0, 13910, -8344, 0, -532, 17892, 0, -4964, 6140, 0, -3124, -40551, 0, 0, 4976, 0, -40278, 6501, 0, 26894, 0, 0, 4912, 21210, 0, -37597, -19096, 0, -27744, 10294, 0, 16464, -10584, 0, 0, 14437, 0, 23275, -1600, 0, -5208, 0, 0, -32984, 6160, 0, 19152, -43806, 0, 36546, -15072, 0, -18212, -40362, 0, 0, 11538, 0, -14756, 20, 0, -24612, 0, 0, 20044, -35308, 0, 22183, 38444, 0, -3904, -10630, 0, -2515, -12152, 0, 0, 19974, 0, 30618, -22662, 0, -22120, 0, 0, -31324, -10752, 0, -10332, -24493, 0, -35602, -4074, 0, 5648, -8330, 0, 0, 6528, 0, -27524, -48126, 0, 25956, 0, 0, 14560, -51814, 0, -12593, -504, 0, 1396, -19992, 0, -1736, -15064, 0, 0, -5044, 0, -33824, 4232, 0, -15246, 0, 0, -6458, -50498, 0, -17584, 19257, 0, 56088, 4128, 0, 5688, -67886, 0, 0, 31822, 0, 7280, -39776, 0, 38514, 0, 0, 35596, 19474, 0, 12187, -23128, 0, 4704, 31973, 0, -26532, -1288, 0, 0, 24279, 0, 76041, -19186, 0, 3136, 0, 0, -12578, -14056, 0, -13944, -14126, 0, -41385, -6850, 0, -14240, -20909, 0, 0, -6000, 0, -26152, 46000, 0, 61103, 0, 0, 11352, -84924, 0, 728, 3808, 0, -9192, -34178, 0, -7802, -14182, 0, 0, 59649, 0, -8617, 5736, 0, -22624, 0, 0, 9870, 42070, 0, 12208, -38514, 0, 60457, 9696, 0, -27406, -10878, 0, 0, -27180, 0, -35140, -33036, 0, -19236, 0, 0, 15556, -22491, 0, 79170, -8400, 0, -24416, -10152, 0, -51169, -14196, 0, 0, -3948, 0, 63707, -8184, 0, -420, 0, 0, -32235, 14224, 0, 16436, 26964, 0, -4455, -5178, 0, -2336, 1428, 0, 0, 6872, 0, 5264, -1682, 0, 34370, 0, 0, 144, 68621, 0, -20496, -12208, 0, -20696, 47356, 0, 51433, 11298, 0, 0, -29440, 0, 10500, 4056, 0, 31528, 0, 0, 20876, -34426, 0, -20020, -8687, 0, -3764, -19032, 0, -29474, 6615, 0, 0, 10492, 0, 6496, -3180, 0, 66402, 0, 0, 25866, -37884, 0, 43582, -6356, 0, 17452, -9644, 0, -6074, 3136, 0, 0, 53600, 0, -5509, 53022, 0, -5208, 0, 0, -21478, 19908, 0, 17724, -4074, 0, 7528, 33388, 0, -43928, 14721, 0, 0, 5504, 0, -17430, -20315, 0, -3150, 0, 0, 2048, 21672, 0, -34447, -1848, 0, 16760, -73038, 0, 43346, 15624, 0, 0, -52704, 0, 14224, -10464, 0, -7392, 0, 0, 56110, 10430, 0, 35672, 117656, 0, 81533, 9984, 0, 44436, 61096, 0, 0, -4044, 0, -19068, 39131, 0, 11648, 0, 0, 16464, 103915, 0, 74837, 18438, 0, -16656, 24734, 0, -33987, 27020, 0, 0, -49974, 0, -8568, -9490, 0, 1204, 0, 0, -25906, -6272, 0, -46900, -7973, 0, -27849, -25732, 0, 21328, 14210, 0, 0, -12464, 0, -12740, 31726, 0, -8484, 0, 0, -23228, 10857, 0, -127778, 27720, 0, -7166, 25247, 0, -58378, 5222, 0, 0, -63058, 0, -50995, -35416, 0, -48314, 0, 0, 5720, 26768, 0, -22428, -56728, 0, -19713, 26432, 0, -4044, 84784, 0, 0, -4054, 0, 31920, 57592, 0, -70903, 0, 0, -3176, 15834, 0, 54138, -34188, 0, 18504, -84708, 0, 14314, 7448, 0, 0, -78195, 0, -15470, 75738, 0, 3024, 0, 0, -47874, 4956, 0, 23506, 59556, 0, -81561, 27874, 0, 34228, 18130, 0, 0, -9248, 0, 42588, 14919, 0, -12264, 0, 0, 23664, 99106, 0, -40026, 38976, 0, 35892, 155546, 0, 86233, 25340, 0, 0, 18965, 0, -107968, -1944, 0, 50428, 0, 0, 37410, 65716, 0, 7616, -58044, 0, 62238, 7440, 0, 9768, 63336, 0, 0, -81280, 0, 8484, 14127, 0, -104825, 0, 0, -109336, -51072, 0, -17248, 10962, 0, -24360, 84344, 0, -57064, 68432, 0, 0, -2980, 0, 110320, 4152, 0, -3696, 0, 0, -30447, 32144, 0, -12208, 64260, 0, -73244, -38618, 0, 8384, 96530, 0, 0, 20244, 0, 8694, 16464, 0, -51807, 0, 0, -22564, 24591, 0, -92428, -1792, 0, 7424, -49947, 0, 79782, 2954, 0, 0, -39882, 0, -33586, -11744, 0, 40488, 0, 0, 51397, -101486, 0, 868, 15869, 0, -67489, -1808, 0, 60834, 32207, 0, 0, -38354, 0, 10752, 77100, 0, 23688, 0, 0, -46960, 66654, 0, 9779, -56826, 0, 23956, 66744, 0, 67809, -4592, 0, 0, -114675, 0, 41699, -27820, 0, 16688, 0, 0, 43027, 1064, 0, -35784, -120246, 0, -54233, 9928, 0, -12280, 90188, 0, 0, 6248, 0, 81102, -6747, 0, -128954, 0, 0, -9952, -9254, 0, -8316, 80556, 0, -13002, 52370, 0, -16989, -53788, 0, 0, -76390, 0, -119595, -9824, 0, -42420, 0, 0, -34011, 75194, 0, 38192, 42616, 0, 39327, 55488, 0, -20588, 36162, 0, 0, -32928, 0, 21168, -38685, 0, -87759, 0, 0, -28874, -21168, 0, 29638, -46550, 0, 3200, -53748, 0, -71822, 10416, 0, 0, -31424, 0, -122269, 65968, 0, -12320, 0, 0, 40611, -38304, 0, 87612, -693, 0, -88838, -73092, 0, 30144, -18578, 0, 0, 36424, 0, 80724, -28100, 0, 80731, 0, 0, -23076, 78379, 0, -67592, 29512, 0, -40, -4524, 0, -17539, 49224, 0, 0, -31920, 0, -73248, -40088, 0, 70616, 0, 0, 27219, -44366, 0, -76888, 88284, 0, 79896, 7808, 0, 21260, 8008, 0, 0, 5030, 0, 24304, 19398, 0, 50435, 0, 0, -39948, -25578, 0, -16716, -61236, 0, 45324, 59751, 0, -96636, 44240, 0, 0, 143664, 0, 2807, 62648, 0, 21504, 0, 0, 156266, 20664, 0, 48986, -46270, 0, 65196, 71204, 0, 8148, -48552, 0, 0, -11296, 0, 16660, 87476, 0, -49154, 0, 0, -13056, 30478, 0, -20587, 55048, 0, 96252, 21430, 0, 28869, -51912, 0, 0, -16216, 0, -14812, -29120, 0, 103628, 0, 0, -25828, 25186, 0, 1008, -33614, 0, -68756, -2792, 0, 39984, -24948, 0, 0, 3472, 0, 30128, -96161, 0, -54992, 0, 0, 10088, 32368, 0, 142723, 67648, 0, -8464, -42842, 0, 25048, 30492, 0, 0, 67368, 0, -80535, 12916, 0, 100996, 0, 0, 1805, 35168, 0, -38514, 52843, 0, -73029, -112176, 0, -8256, -27804, 0, 0, -11376, 0, 135772, 145950, 0, 57729, 0, 0, -63644, -141281, 0, -32956, -14560, 0, 79552, -65617, 0, -139067, -77028, 0, 0, 95562, 0, -50309, -71192, 0, -38948, 0, 0, 62944, -24374, 0, 46256, -20713, 0, 178830, -9408, 0, -63946, -151851, 0, 0, 53064, 0, 2576, -152662, 0, 16919, 0, 0, -48558, -22988, 0, 62741, -152082, 0, 38372, -168535, 0, 46857, -6272, 0, 0, -8633, 0, 3465, 25156, 0, 28112, 0, 0, 90787, 27888, 0, 28252, 142576, 0, -81394, 82770, 0, 13700, -48699, 0, 0, 28480, 0, 41818, -158076, 0, 147525, 0, 0, 12000, 4452, 0, 116655, 52304, 0, -92000, -127098, 0, -137361, -122206, 0, 0, 94959, 0, -69055, -22704, 0, 169848, 0, 0, 243380, -1456, 0, -7616, -135814, 0, -120516, 18384, 0, 68356, -83524, 0, 0, 15604, 0, 28364, 157563, 0, -97188, 0, 0, -119298, -48468, 0, -19355, 17234, 0, -11472, -13118, 0, -241154, 45248, 0, 0, 70276, 0, 91042, -19740, 0, -84140, 0, 0, -160910, -24416, 0, 77028, -51576, 0, 87000, -120914, 0, -19392, -8148, 0, 0, 54812, 0, 21756, -125468, 0, -121275, 0, 0, 54360, -153132, 0, -51548, 70280, 0, 66072, 18341, 0, 28433, 38472, 0, 0, 139030, 0, 42434, -31112, 0, 44982, 0, 0, 68529, -158340, 0, 16800, -14259, 0, -75725, 48832, 0, 20304, -160944, 0, 0, 102338, 0, 28392, -100434, 0, 211386, 0, 0, 7896, 8232, 0, 53333, -127414, 0, 16368, 202209, 0, 149372, 840, 0, 0, 47591, 0, -113078, 64470, 0, -28448, 0, 0, -41124, -32872, 0, -53928, -100674, 0, -69333, 8910, 0, 10356, -174272, 0, 0, 4672, 0, -2856, -155735, 0, 53753, 0, 0, -13744, -156520, 0, -83258, -10528, 0, 3364, -70966, 0, 128384, -68740, 0, 0, 47723, 0, 82124, -288, 0, -137242, 0, 0, -52242, 40992, 0, 24416, 111636, 0, 71974, 41392, 0, -94712, -79408, 0, 0, -102866, 0, -22596, 65694, 0, -111902, 0, 0, 58880, -80577, 0, -137746, -21000, 0, -8112, -161328, 0, -101242, -63056, 0, 0, 5492, 0, -122528, -41752, 0, 68852, 0, 0, 112896, 40040, 0, 17374, -122668, 0, 85729, 7528, 0, 38064, -173796, 0, 0, 58948, 0, -13230, -14354, 0, -61054, 0, 0, -20984, -38787, 0, -49819, -12992, 0, 6360, -19028, 0, 33029, -132804, 0, 0, 73482, 0, 124166, -51732, 0, 75768, 0, 0, -179868, -87164, 0, 12712, -133014, 0, -99997, -34904, 0, 19288, 116256, 0, 0, 12148, 0, -6272, -80748, 0, 5887, 0, 0, -107200, -115332, 0, -19236, 11018, 0, -106044, -5325, 0, -23355, 10416, 0, 0, -18141, 0, 66696, 42956, 0, -39816, 0, 0, -27605, -35448, 0, 8148, 145530, 0, 37447, -15056, 0, -66776, -151788, 0, 0, 87856, 0, -29442, 73159, 0, -97363, 0, 0, -11008, -41874, 0, 185234, 34860, 0, 40630, 71210, 0, -2906, 6300, 0, 0, 59693, 0, -218988, -4096, 0, -43344, 0, 0, -54551, 68894, 0, 3696, 52304, 0, 41384, -33520, 0, 146076, -100338, 0, 0, -86692, 0, -31248, -137522, 0, -105483, 0, 0, 105408, -41608, 0, -43561, -28448, 0, 20928, 142018, 0, 94864, 14784, 0, 0, 96886, 0, 112637, -112220, 0, -20860, 0, 0, 27708, -71344, 0, -235312, 31857, 0, 93084, -163066, 0, -19968, 15708, 0, 0, -88872, 0, -122192, 10678, 0, 1106, 0, 0, 8088, 72422, 0, -95788, 38136, 0, -78262, -17129, 0, 127326, -23296, 0, 0, 9216, 0, 75677, -32928, 0, -207830, 0, 0, 24909, -149674, 0, -36876, -42189, 0, -123555, 33312, 0, -49468, 189700, 0, 0, 67974, 0, -54040, 163012, 0, 40656, 0, 0, 99948, 101262, 0, -46984, 17136, 0, 18980, 27002, 0, 317770, -2408, 0, 0, 48288, 0, 63000, 51812, 0, 12544, 0, 0, -81827, 93800, 0, 15946, -233870, 0, -137636, 55698, 0, 51464, 322448, 0, 0, -42656, 0, -28420, 84141, 0, -8575, 0, 0, 24928, -5292, 0, 182175, 25480, 0, -63452, -127306, 0, 73730, 16968, 0, 0, -147661, 0, -63497, 46456, 0, -21714, 0, 0, -95051, 255556, 0, -55440, 117936, 0, 182786, 14332, 0, -50494, -205562, 0, 0, 116756, 0, -10444, -25885, 0, -71771, 0, 0, 126116, 167020, 0, -149758, 101990, 0, 70832, 5592, 0, -205629, 96628, 0, 0, -128184, 0, -10234, -11440, 0, -53536, 0, 0, -271355, 44856, 0, 113456, -69328, 0, 41072, 39426, 0, -52864, -47656, 0, 0, 8088, 0, -169568, -185232, 0, -58198, 0, 0, 8108, 195083, 0, 40068, -63840, 0, -115184, -47073, 0, -21101, 141806, 0, 0, -55842, 0, 192213, 6352, 0, -31668, 0, 0, -10802, -108276, 0, 68376, 198639, 0, -132496, -37008, 0, 169416, 64568, 0, 0, -28628, 0, -14896, 384952, 0, 222796, 0, 0, 156390, 69804, 0, -44996, 30940, 0, -151476, -198243, 0, 228460, -6048, 0, 0, -117951, 0, 87689, 95748, 0, -9912, 0, 0, -57170, -47012, 0, -119112, 101430, 0, 24937, 163122, 0, -55748, 287427, 0, 0, -68456, 0, -36260, 188120, 0, 42140, 0, 0, 18496, 119252, 0, 22778, -85176, 0, -29838, 86502, 0, -232835, 24528, 0, 0, 91482, 0, 228739, -47328, 0, -198212, 0, 0, -127545, 80052, 0, -77952, -169148, 0, 108056, -71784, 0, -311092, 298256, 0, 0, -172466, 0, -50680, -179616, 0, -70595, 0, 0, -37930, 1029, 0, -20671, 215936, 0, 3888, 257900, 0, 128184, -100856, 0, 0, -224902, 0, -108766, -74820, 0, -131432, 0, 0, -30300, -15232, 0, 116088, 115633, 0, 142542, -124476, 0, -14880, 43036, 0, 0, -19536, 0, -126672, 207250, 0, 239120, 0, 0, 162560, 71309, 0, 43239, -16968, 0, -28254, 255452, 0, 112038, 209650, 0, 0, -13246, 0, 239463, 218672, 0, 102144, 0, 0, -179315, 34496, 0, -21924, 174174, 0, -79497, 48720, 0, -168688, -41076, 0, 0, 114128, 0, -136864, -276022, 0, 271908, 0, 0, 5960, 117782, 0, -180579, -220640, 0, -8304, -68208, 0, 163715, 7392, 0, 0, -336904, 0, 68915, 60894, 0, -64288, 0, 0, 199506, 24416, 0, -128520, 401884, 0, 424887, 146488, 0, 77236, 197848, 0, 0, -16768, 0, -193060, 38045, 0, -57708, 0, 0, -40488, 6496, 0, 400953, -17388, 0, -32928, 59994, 0, -155277, 103614, 0, 0, -139715, 0, 365967, 45128, 0, -49182, 0, 0, -100413, 184856, 0, 3584, -210504, 0, -87674, -14848, 0, 99894, 224518, 0, 0, -159564, 0, -5908, 254541, 0, 44331, 0, 0, 79764, 30240, 0, -123858, 67172, 0, 23488, -170676, 0, -298772, -80976, 0, 0, 50402, 0, 42399, -102794, 0, 202972, 0, 0, 224000, -1736, 0, -31738, -211316, 0, -87048, 134978, 0, 3616, 320194, 0, 0, -121668, 0, -64414, 115814, 0, 134813, 0, 0, 76708, 102186, 0, 131222, -21504, 0, -154200, 181972, 0, -268014, -47376, 0, 0, -490292, 0, -7350, 93920, 0, -133308, 0, 0, -200667, -19558, 0, 113652, -171899, 0, -214380, -47912, 0, -133488, 72695, 0, 0, -135618, 0, 9184, 68778, 0, 397236, 0, 0, 229350, -76132, 0, 109872, -83398, 0, 55640, 387952, 0, 70837, -33376, 0, 0, 190824, 0, -252042, -86054, 0, -2128, 0, 0, 277407, 71568, 0, 240492, -22190, 0, 391210, 108466, 0, -19856, -74466, 0, 0, 24560, 0, -180376, -337969, 0, 223881, 0, 0, -12496, -199668, 0, 257999, -162204, 0, 13494, 18010, 0, 158429, 257908, 0, 0, -305148, 0, 211575, 19904, 0, 18508, 0, 0, -100337, 16632, 0, -161112, 420910, 0, -27937, 26004, 0, -104740, 126546, 0, 0, 33978, 0, 107576, 112811, 0, -330400, 0, 0, 152780, 174888, 0, -7336, 239190, 0, 19648, -42306, 0, -73054, 84840, 0, 0, 263214, 0, -153405, 68022, 0, -150388, 0, 0, -511680, -76384, 0, -85232, -213724, 0, 115092, -78654, 0, -110976, -116326, 0, 0, 41176, 0, -72324, 381544, 0, -17269, 0, 0, 65856, 274407, 0, 165452, -42336, 0, 77370, -15276, 0, -99696, 175518, 0, 0, -48240, 0, 285173, 57748, 0, 42336, 0, 0, 155567, -59276, 0, 93100, -102403, 0, -19219, -6400, 0, 107496, 337729, 0, 0, 143644, 0, -20832, -177940, 0, 552930, 0, 0, 62848, -236796, 0, -179529, 244538, 0, -131936, -321385, 0, 301004, 24640, 0, 0, -133663, 0, 183414, -81222, 0, 76608, 0, 0, 200876, -175224, 0, 1386, 113820, 0, 87571, 177676, 0, 146184, -350105, 0, 0, -60288, 0, 37156, -215160, 0, 85386, 0, 0, -72848, 274694, 0, 262626, -161448, 0, 56200, -152056, 0, -230721, -161462, 0, 0, 101905, 0, -71631, 46152, 0, -156758, 0, 0, 195768, 135184, 0, -59024, -110250, 0, -187730, 80, 0, 9048, -253624, 0, 0, 35078, 0, -98448, 68759, 0, -277536, 0, 0, 63840, 81879, 0, -78169, 146496, 0, 80176, 52602, 0, -122879, -141232, 0, 0, -162724, 0, 105938, -54438, 0, 88732, 0, 0, -178981, 153776, 0, -176568, 317457, 0, 479036, -159792, 0, -15616, 223734, 0, 0, -42520, 0, -16016, 73722, 0, 121520, 0, 0, -10060, -304066, 0, -298571, -48608, 0, -38796, -123227, 0, -48798, -100870, 0, 0, 341778, 0, -87374, 79896, 0, 51156, 0, 0, -288695, 33432, 0, 122472, -43617, 0, -181750, -90648, 0, -119502, 60592, 0, 0, 193272, 0, -88480, -31752, 0, 26334, 0, 0, -287328, 274708, 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": "126.4.g.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], [1, 0], [-2, 0], [0, 0], [4, 0], [-3, -1], [0, 0], [0, 0], [-8, 0], [0, 0], [6, 2], [-9, -7], [0, 0], [22, 5], [0, 0], [0, 0], [16, 0], [-54, 10], [0, 0], [58, 3], [-12, -4], [0, 0], [18, 14], [54, 14], [0, 0], [-68, 7], [-44, -10], [0, 0], [0, 0], [33, 7], [0, 0], [-35, -28], [-32, 0], [0, 0], [108, -20], [0, 0], [0, 0], [134, 21], [-116, -6], [0, 0], [24, 8], [-168, 0], [0, 0], [164, -21], [-36, -28], [0, 0], [-108, -28], [-348, 24], [0, 0], [0, 0], [136, -14], [0, 0], [88, 20], [-219, 63], [0, 0], [363, 37], [0, 0], [0, 0], [-66, -14], [-351, -61], [0, 0], [220, -34], [70, 56], [0, 0], [64, 0], [-306, -42], [0, 0], [-538, 35], [-216, 40], [0, 0], [0, 0], [840, -28], [0, 0], [46, 97], [-268, -42], [0, 0], [232, 12], [0, 0], [0, 0], [311, -98], [-48, -16], [0, 0], [336, 0], [-99, -89], [0, 0], [-318, 14], [-328, 42], [0, 0], [72, 56], [-1170, -54], [0, 0], [0, 0], [216, 56], [0, 0], [696, -48], [-318, -70], [0, 0], [109, -155], [0, 0], [0, 0], [-272, 28]]}