# Stored data for newform 294.6.a.m, downloaded from the LMFDB on 16 April 2024.
{"label": "294.6.a.m", "space_label": "294.6.a", "level": 294, "weight": 6, "hecke_orbit": 13, "hecke_orbit_code": 54043195629109542, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1314886411679184494, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-66, 1]], [11, [60, 1]]], "qexp_display": "q+4q^{2}+9q^{3}+2^{4}q^{4}+66q^{5}+6^{2}q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 10584, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 47.1528430250163, "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": 0, "analytic_rank_proved": true, "char_values": [294, 1, [197, 199], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.029", "prec": 17}, {"__RealLiteral__": 0, "data": "0.969", "prec": 17}, {"__RealLiteral__": 0, "data": "0.083", "prec": 17}, {"__RealLiteral__": 0, "data": "1.929", "prec": 17}, {"__RealLiteral__": 0, "data": "0.253", "prec": 17}, {"__RealLiteral__": 0, "data": "4.841", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1], [7, -1]], "trace_display": [4, 9, 66, 0], "traces": [0, 1, 4, 9, 16, 66, 36, 0, 64, 81, 264, -60, 144, 658, 0, 594, 256, 414, 324, -956, 1056, 0, -240, 600, 576, 1231, 2632, 729, 0, 5574, 2376, 3592, 1024, -540, 1656, 0, 1296, -8458, -3824, 5922, 4224, -19194, 0, 13316, -960, 5346, 2400, 19680, 2304, 0, 4924, 3726, 10528, -31266, 2916, -3960, 0, -8604, 22296, -26340, 9504, 31090, 14368, 0, 4096, 43428, -2160, -16804, 6624, 5400, 0, 6120, 5184, 25558, -33832, 11079, -15296, 0, 23688, 74408, 16896, 6561, -76776, 6468, 0, 27324, 53264, 50166, -3840, 32742, 21384, 0, 9600, 32328, 78720, -63096, 9216, -166082, 0, -4860, 19696, 22002, 14904, 79264, 42112, 0, -125064, 227988, 11664, -8530, -15840, -76122, 0, -195438, -34416, 39600, 89184, 53298, -105360, 0, 38016, -157451, 124360, -172746, 57472, -125004, 0, 173000, 16384, 119844, 173712, -151260, -8640, 0, -67216, 48114, 26496, -128454, 21600, -154196, 0, 177120, 24480, -39480, 20736, 367884, 102232, 0, -135328, 29454, 44316, -203872, -61184, 33534, 0, 237072, 94752, -136142, 297632, -281394, 67584, 0, 26244, -171124, -307104, -35640, 25872, 676200, 0, 61671, 109296, -77436, 213056, -133158, 200664, 0, -15360, -237060, 130968, -693396, 85536, -377174, 0, 279810, 38400, -558228, 129312, -24840, 314880, 0, -252384, -265344, 36864, 295298, -664328, 390852, 0, 201294, -19440, -652448, 78784, -151236, 88008, 0, 59616, -1266804, 317056, 48600, 168448, 57360, 0, -1147060, -500256, 55080, 911952, 878856, 46656, 0, -34120, 230022, -63360, 272412, -304488, -701960, 0, 99711, -781752, -1236108, -137664, -105830, 158400, 0, 356736, -438678, 213192, 1298880, -421440, 669672, 0, 28464, 152064, -892562, -629804, 59049, 497440, 0, -690984, -629048, 229888, 58212, -500016, 110124, 0, -36000, 692000, 245916, 65536, -140802, 479376, 0, 694848, 451494, -605040, -938760, -34560, -2063556, 0, 294678, -268864, 1114506, 192456, -567704, 105984, 0, -513816, -73860, 86400, -1213258, -616784, 290952, 0, 687738, 708480, 830908, 97920, -567864, -157920, 0, 82944, -1248461, 1471536, -1494738, 408928, 1312626, 0, -1738440, -541312, -43740, 117816, 394800, 177264, 0, -815488, 198018, -244736, 2051940, 134136, -1690220, 0, 713376, 948288, 1502040, 379008, -810842, -544568, 0, 1190528, 903558, -1125576, -334440, 270336, 2051892, 0, -395784, 104976, 809998, -684496, -76770, -1228416, 0, -142560, 1121972, 103488, -685098, 2704800, -1109064, 0, -2752174, 246684, -1758942, 437184, -215520, -309744, 0, 852224, 356400, -532632, 1917492, 802656, -1836590, 0, 479682, -61440, 622014, -948240, 403920, 523872, 0, -2773584, 3740616, 342144, -1562163, -1508696, -1417059, 0, 1686828, 1119240, -16232, 153600, -1554714, -2232912, 0, 517248, 293606, -99360, -1125036, 1259520, 3667692, 0, 3180116, -1009536, 1557000, -1061376, 2979840, 147456, 0, 1181192, 1078596, -2657312, 3459774, 1563408, 248400, 0, -1361340, 805176, 4910928, -77760, 3904162, -2609792, 0, 315136, 5441154, -604944, 2363536, 352032, 433026, 0, 507480, 238464, -1969946, -5067216, -1156086, 1268224, 0, 194400, 426888, 673792, -1387764, 229440, -139020, 0, 4327430, -4588240, 1594080, -2001024, 509634, 220320, 0, 3647808, -355320, 3515424, -2799360, 186624, 5902414, 0, 3310956, -136480, -573600, 920088, 446512, -253440, 0, 1089648, 3495252, -1217952, 2160972, -2807840, 265086, 0, -1206126, 398844, 1151640, -3127008, -1834848, -4944432, 0, -550656, 233546, -423320, 301806, 633600, 1744890, 0, -2917864, 1426944, 2133648, -1754712, 5310756, 852768, 0, 5195520, -1225278, -1685760, -798960, 2678688, -1176836, 0, -2532546, 113856, -2344656, 608256, -5565364, -3570248, 0, -2519216, -10961412, 236196, 9815312, 1989760, -1540116, 0, -5945196, -2763936, 2307636, -2516192, -320760, 919552, 0, 232848, 6478316, -2000064, 6085800, 440496, -4717944, 0, 1452132, -144000, 555039, 2768000, 1907706, 983664, 0, 262144, -696924, -563208, 5231424, 1917504, -1180800, 0, -1198422, 2779392, -8019738, 1805976, -1911620, -2420160, 0, -3755040, 1487088, -138240, -6076343, -8254224, -2133540, 0, -12629652, 1178712, 15047208, -1075456, -6240564, 4458024, 0, 769824, -11990050, -2270816, -3394566, 423936, -562980, 0, 4458092, -2055264, 2518290, -295440, -5328744, 345600, 0, -4853032, -5024052, -2467136, 9026118, 1163808, 8761928, 0, -223560, 2750952, -6848988, 2833920, -12898908, 3323632, 0, 391680, -5463222, -2271456, -10232380, -631680, -2388096, 0, 738600, 331776, -15943682, -4993844, 2657682, 5886144, 0, -5978952, 1875960, 1635712, 3517668, 5250504, 9477132, 0, -3433952, -6953760, 1811646, -2165248, -2453490, -174960, 0, 471264, -5872032, 1579200, -9299784, 709056, 11461702, 0, -1361124, -3261952, -10391766, 792072, -11278376, -978944, 0, 8207760, 12949440, 536544, 93782, -6760880, -11401236, 0, -14964150, 2853504, 5068876, 3793152, 437400, 6008160, 0, 1516032, -12097139, -3243368, 516240, -2178272, -3501612, 0, 15591872, 4762112, -10323540, 3614232, 11418000, -4502304, 0, -1337760, 495720, 1081344, 10970130, 8207568, 2837044, 0, 7909704, -1583136, 6056856, 419904, 1580400, 3239992, 0, -2737984, -1088922, -307080, -9983160, -4913664, 2070198, 0, 7418028, -570240, -767654, 4487888, 2451708, 413952, 0, -2740392, 3344400, 10819200, -6317640, -4436256, -1865400, 0, 1422626, -11008696, 897399, 986736, 6162306, -7035768, 0, 1748736, -11124972, -862080, 15062148, -1238976, -8477964, 0, -952470, 3408896, -20573028, 1425600, 5876356, -2130528, 0, 7669968, -10176936, 3210624, -7946316, -7346360, -3948102, 0, 3600774, 1918728, 8085848, -245760, 11689920, 2488056, 0, -3792960, 9225158, 1615680, 6027048, 2095488, 2155200, 0, -2605680, -11094336, 256176, 14962464, 26392320, 1368576, 0, -6248652, -8033058, -6034784, 6861594, -5668236, 9794848, 0, 531441, 6747312, 5512824, 4476960, -4075838, -64928, 0, 614400, 1008240, -6218856, -16570852, -8931648, -5661432, 0, 14414136, 2068992, 1943964, 1174424, 523908, -397440, 0, -4500144, 16794440, 5038080, 991116, 14670768, -13455552, 0, 13294262, 12720464, -324000, -4038144, 2147862, 6228000, 0, -4245504, 2213244, 11919360, -17331720, 589824, 13105918, 0, -1267218, 4724768, 23715378, 4314384, 4421752, -10629248, 0, 13839096, 18349464, 6253632, -367200, 993600, 4063446, 0, -8985372, -5445360, 8400484, 3220704, -8448840, 19643712, 0, -311040, 20457220, 15616648, -18572004, -10439168, -5410230, 0, 8147520, 1260544, 2652102, 21764616, -1533480, -2419776, 0, 9454144, 10030554, 1408128, -26077734, 1732104, -19002116, 0, -5109336, 2029920, -11294184, 953856, -12730096, -7879784, 0, -20268864, -31017282, -4624344, -15628960, 5072896, -664740, 0, 15842052, 777600, -2061758, 1707552, -10919322, 2695168, 0, -5551056, 44629200, 917760, 2618568, -556080, -30390024, 0, 10558327, 17309720, 6189642, -18352960, 4070286, 6376320, 0, -8004096, 7478172, 2038536, -5074800, 881280, 29773786, 0, -5110776, 14591232, -8641002, -1421280, 33566284, 14061696, 0, -11197440, 39019104, 746496, -8788428, 23609656, -11236149, 0, -4464480, 13243824, -11057032, -545920, -13452642, -2294400, 0, 3680352, -18138178, 1786048, 11813634, -1013760, -30531186, 0, -43553284, 4358592, -15645960, 13981008, 13415160, -4871808, 0, 8643888, -393660, -11231360, -18814080, 1060344, -45764136, 0, 3553200, -4824504, 20021808, 1595376, -12944124, 4606560, 0, -12508032, -24893484, -7339392, 3108164, -19777728, 1782162, 0, 1190352, -2202624, -388080, 934184, 18467460, -1693280, 0, 1207224, -47199616, 2534400, -15211980, 6979560, 4026960, 0, -10411798, -11671456, 6420384, 5707776, -1335954, 8534592, 0, -7018848, 13518360, 21243024, -1639440, 3411072, -14723786, 0, -7297578, 20782080, 26919642, -4901112, -11516400, -6743040, 0, -3195840, -3731604, 10714752, 16817164, -4707344, 8132022, 0, 21873546, -10130184, -17512704, 455424, -3009960, -9378624, 0, 2433024, -15726687, -22261456, 18467028, -14280992, 19489668, 0, 17602496, -10076864, -3562056, -43845648, -16731684, 944784, 0, 39261248, 7289982, 7959040, 55538178, -6160464, -1964520, 0, -690930, -23780784, 38678424, -11055744, 13285404, 9230544, 0, -10064768, 7989600, -1283040, 9584984, 3678208, 10097748, 0, -43061568, 931392, 10365034, 25913264, -6165882, -8000256, 0, 24343200, -10904760, 1761984, -9981576, -18871776, 29890296, 0, -15326638, 5808528, -24769566, -576000, 2400114, 2220156, 0, 11072000, -15830478, 7630824, 6185028, 3934656, 49247506, 0, -1939680, 1048576, -23627814, -2787696, 48960464, -2252832, 0, 20925696, 31599384, 7670016, 44534570, -4723200, 3207600, 0, 12871260, -4793688, -58310216, 11117568, 17257428, -32078952, 0, 7223904, 3785760, -7646480, -16529310, -9680640, 41260422, 0, 69004868, -15020160, 4317138, 5948352, -75705960, -552960, 0, -24305372, 5598126, -33016896, 1073502, -8534160, -42406112, 0, 3635280, -50518608, 9964920, 4714848, -10636574, 60188832, 0, -4301824, -47144892, -24962256, 16391996, 17832096, 33665544, 0, 4255944, 3079296, 11808000, -47960200, -14059467, -9083264, 0, -13578264, -30311752, 1695744, -12753531, -2251920, 72877812, 0, -17593210, 17832368, 15181452, -8221056, 4900374, 10073160, 0, -1181760, -146088, -21314976, 32915760, 1382400, 17979192, 0, -13992426, -19412128, -54190254, -20096208, -1320120, -9868544, 0, 36104472, -46329360, 4655232, 49039742, 35047712, 2642454, 0, 25181040, -894240, -712508, 11003808, -10125324, -27395952, 0, 11335680, -73548694, -51595632, 33009228, 13294528, -4755840, 0, -81583128, 1566720, 28621044, -21852888, -6956856, -9085824, 0, -40929520, 14013000, -2526720, -6984780, -9552384, -30381136, 0, 26818560, 2954400, -12093696, 1327104, -36530498, -63774728, 0, -19975376, 21544236, 10630728, -29722040, 23544576, 9707364, 0, -15155628, -23915808, -28952748, 7503840, 31137966, 6542848, 0, 14070672, -10480948, 21002016, 2235600, 37908528, 24226080, 0, -13679280, -13735808, -12252060, -27815040, -71216310, 7246584, 0, -8660992, 44198352, -9813960, -46421316, -699840, -106987356, 0, 35137458, 1885056, 15499254, -23488128, 1878624, 6316800, 0, -37199136, 511800, 2836224, 80400050, 45846808, 48970386, 0, -58909092, -5444496, 2533680, -13047808, 21271824, -41567064, 0, 3168288, 15166814, -45113504, 3897234, -3915776, -35567490, 0, -18759600, 32831040, 4567320, 51797760, -101093976, 2146176, 0, 375128, -17729514, -27043520, -53886522, -45604944, 71197672, 0, -10404774, -59856600, -41517168, 11414016, -2354678, 20275504, 0, 15172608, 10581012, 1749600, 11726280, 24032640, 3841992, 0, 74223384, 6064128, 46040926, -48388556, -12489876, -12973472, 0, 2064960, 7268184, -8713088, -1251180, -14006448, 62451900, 0, -109281956, 62367488, 38946870, 19048448, -2376000, -41294160, 0, 14456928, 14346720, 45672000, -68944848, -18009216, 16064624, 0, 4586706, -5351040, 11026170, 1982880, -15583880, 4325376, 0, 43880520, 95301708, 32830272, -9292932, 11348176, -3197880, 0, 87798090, 31638816, 83244988, -6332544, -25194240, 24227424, 0, 1679616, 38354258, 6321600, 53121726, 12959968, -75785262, 0, -54179536, -10951936, 29798604, -4355688, -7896900, -1228320, 0, -39932640, -5162400, -19654656, 14477316, 8280792, -61958160, 0, 4018608, 29672112, 68570328, -2280960, 96508534, -3070616, 0, 17951552, -38488446, 9806832, 89079560, 1655808, 31457268, 0, 19110120, -10961568, 47831072, 13377600, 19448748, 43276800, 0, -25270560, 52155712, -17745024, 2385774, -7461600, 30804912, 0, 73557396, 5690504, -10855134, -44034784, -5850720, 3589596, 0, 3946944, 10364760, 24649224, -37468464, -28143072, -15804000, 0, -16513632, 6994944, 52890846, -44499888, 109696320, -3448320, 0, 60248592, 46727784, -4955904, 2193807, -33911856, 2101914, 0, -132937194, -3809880, 7500240, 13635584, 2716254, -82292112, 0, 5702400, 80891270, 23505424, 15704010, -8522112, -80075028, 0, -24433448, 30679872, -26260776, -40707744, 150016104, 12842496, 0, -31785264, 19202832, -29385440, -10380000, -15792408, -63682640, 0, 47796804, 14403096, 18654000, 7674912, 45390708, 32343392, 0, -983040, -6919950, 46759680, 2677752, 9952224, -11027502, 0, 54839928, -15171840, -5612740, 36900632, -7190640, 6462720, 0, 24108192, -66683752, 8381952, -10591524, 8620800, 50614788, 0, 4946342, -10422720, -22792914, -44377344, -66766746, 1024704, 0, 59849856, -21101904, 105569280, -92859120, 5474304, 9075600, 0, -50088276, -24994608, -82398426, -32132232, -62179520, -24139136, 0, 27446376, -52396332, -22672944, -89568658, 39179392, -98652708, 0, 70690560, 2125764, -94457180, 26989248, 88337808, 22051296, 0, 17907840, 86633316, -16303352, -13861044, -259712, -128598204, 0, 50557544, 2457600, -53506764, 4032960, -32424540, -24875424, 0, -66283408, 20768724, -35726592, 108395178, -22645728, -72794372, 0, -2886840, 57656544, 84509664, 8275968, 60806350, 7775856, 0, 4697696, 57180366, 2095632, 26056800, -1589760, 58304844, 0, 84863508, -18000576, -71134048, 67177760, 54772200, 20152320, 0, 3964464, 7707240, 58683072, -42461496, -53822208, 57666168, 0, 13555188, 53177048, 13069188, 50881856, 162342852, -1296000, 0, -16152576, 4995351, 8591448, 43822236, 24912000, 38271790, 0, 17169354, -16982016, 9251760, 8852976, -55033220, 47677440, 0, -69326880, -111554520, 2359296, -174276684, 52423672, -6272316, 0, -10082400, -5068872, -89499248, 18899072, 47082816, 94861512, 0, 17257536, 87949118, 17687008, -10627200, -42516992, -39559506, 0, 99134640, 55356384, -10785798, 73397856, -160722552, 25014528, 0, -1468800, -72177642, 3974400, -53515572, 16253784, 82349512, 0, -17204580, -35941488, -78933084, -21781440, -103602758, 33601936, 0, 12882816, -6183408, -33795360, -34183468, 78574848, 13383792, 0, -51019344, -1244160, 59634828, 81828880, -54687087, 62466592, 0, -74288016, -112626728, -41756672, -19201860, -21640920, -22073040, 0, 78276158, 32590080, -113666868, 5042176, 104437854, 10608408, 0, 87058464, 135424872, -6133920, 104077032, -9679104, 180401494, 0, -56165076, 37816576, 183988554, 40122216, -26121744, 5632512, 0, -104310936, -135176148, 6928416, -111151114, -76008464, -107910450, 0, -82252632, -20437344, 35388508, 8119680, -30551094, -45176736, 0, 3815424, 3672000, -50920384, -5066820, -31519136, 24678738, 0, -1767240, -81075456, 40122828, -124069128, -112307472, -18497376, 0, -62515840, 22664610, 20291584, -68757948, -2658960, 113834000, 0, -47958696, 63368208, 74050152, 3110400, 102038758, -8247032, 0, 6830208, 12232320, -43677288, -16592440, 10780672, -45216468, 0, 90300828, -22204224, -58884902, 178516800, 81235062, 3671040, 0, 10474272, -20685724, -2224320, 78857352, -121560096, 15334800, 0, 252553435, 42233308, -2012040, 69238880, -181643484, 24758568, 0, -73411840, -61640892, 16281144, -31301352, 25505280, 31358194, 0, -116090172, -32016384, -50403282, 29912688, 17135716, 8154144, 0, -20299200, -99529080, 3525120, -14224320, 119095144, -49168998, 0, -109142010, -20443104, -146819160, 58364928, -92091420, -34564008, 0, -5685120, 9108828, 134265136, -21492864, 56246784, -145435962, 0, -217276876, -44789760, 6647400, 156076416, 8168520, 2985984, 0, -35153712, -143493138, 94438624, -34810626, -44944596, 126554472, 0, 23919138, -17857920, -166453440, 52975296, -88169246, -44228128, 0, -2183680, -121214940, -53810568, 104448620, -9177600, 16883640, 0, 32815296, 14721408, 18036166, -72552712, 31659012, 7144192, 0, 47254536, -127777960, -4055040, 85294188, -122124744, -255587304, 0, 41052924, -174213136, -30905568, 17434368, 173295660, -62583840, 0, 55924032, 16304814, 53660640, 7533720, -19487232, -86618546, 0, -22081410, 34575552, -84522732, -1574640, -129914768, -44925440, 0, -75256320, -124533516, 4241376, -158124082, -183056544, -52848288, 0, 10267440, 14212800, 246880656, -19298016, -83698056, 80087232, 0, 6381504, 59282858, -51776496, 103155318, 18426240, -103102758, 0, -101460968, -50032128, -12250116, -99573936, 74600340, -29357568, 0, 12432656, -93525894, -79110912, 44644800, 7128648, 94387032, 0, -101505384, 4761408, -140748432, -8810496, 31461898, -1552320, 0, 3736736, -94613280, 73869840, 35859680, -6773120, 116544960, 0, -1071312, 4828896, -40572000, -188798464, 844038, 10137600, 0, -60847920, 158774392, 27918240, -102611124, 16107840, 112601832, 0, 30307413, -41647192, -134677350, -46685824, -3531420, 25681536, 0, 22831104, 45619884, -5343816, -3700260, 34138368, 194050570, 0, 3936600, -28075392, 19377996, 54073440, -157434596, 84972096, 0, -6557760, 184801104, 13644288, -47957326, -58895144, -108874251, 0, -86917458, -29190312, -79612448, 83128320, 4646160, 107678568, 0, -19604448, 242067672, -46065600, -31514508, -26972160, 26687934, 0, 111675280, -12783360, 140326848, -14926416, 209887656, 42859008, 0, 67268656, -92911860, -18829376, 37892550, 32528088, 7989480, 0, 102762000, 87494184, -55124460, -40520736, 3880800, -70050816, 0, 1821696, 230903034, -12039840, 196669440, -37514496, 4461480, 0, -21033912, 9732096, -80911332, -62906748, 98731170, -89045824, 0, 73868112, -377737920, -57123968, 25533396, 77958672, 237963180, 0, -198699394, 70409984, 71187336, -40307456, 19380732, -14248224, 0, -175382592, 54511704, -66926736, -93665496, 3779136, 228345084, 0, 14223600, 157044992, 120638442, 29159928, 280168024, 31836160, 0, 222152712, 16394400, -24641856, -75776384, -7858080, -9800298, 0, 264447828, -2763720, -134147776, -95123136, -89848440, 154713696, 0, -44222976, 41603760, 53141616, 18631782, 36922176, -271671582, 0, 91596248, -40259072, 66762252, 31958400, -314239860, -5132160, 0, 38339936, -6908886, 14712832, 257674692, 40390992, -50615852, 0, 22065372, -172246272, 22630440, 3725568, -169836650, 41460136, 0, 103653056, -121845978, -24663528, 165519560, -32001024, 30099600, 0, -280374708, 97372800, 359116164, -43619040, -56858760, 7047936, 0, -39926304, 106271828, -75487104, -16788600, 119561184, 155993376, 0, 314137154, -61306552, 12803634, 23234112, 262058880, -99078264, 0, -2304000, 8076591, 9600456, -282596892, 8880624, -269653454, 0, 55460754, 44288000, -217956528, -63321912, 33493680, 30523296, 0, 24740112, 245242968, 15738624, -89581436, 196990024, -100124748, 0, -130016436, -7758720, 19645200, 4194304, 135559332, -94511256, 0, -11150784, 267256694, 195841856, -76301676, -9011328, -65184714, 0, 34112880, 83702784, -8572230, 126397536, -224602032, 30680064, 0, 178138280, -185157252, -18892800, 274803966, 12830400, 8154680, 0, 52887204, 51485040, 7962108, -19174752, -60359968, -233240864, 0, 44470272, -129917454, 69029712, -119094868, -128315808, -91592424, 0, -96145992, 28895616, 10248694, 15143040, -71516844, -30585920, 0, -66117240, -9175320, -38722560, -35532918, 165041688, 268974132, 0, 15920640, 276019472, 32406966, -60080640, 285610380, 17268552, 0, 23793408, 72772632, -302823840, 380189904, -2211840, -338688770, 0, 105209280, -97221488, 142460292, 22392504, -112599592, -132067584, 0, 4294008, -17717880, -34136640, -51751656, -169624448, 83026422, 0, -256543950, 14541120, 67703476, -202074432, 54243432, 39859680, 0, 18859392, -228632518, -42546296, 19396800, 240755328, 81075834, 0, -253261384, -17207296, -23451120, -188579568, 186838728, -99849024, 0, 65567984, 2305584, 71328384, -181632966, 134662176, -184757760, 0, 237530880, 17023776, 71622000, 12317184, 328443118, 47232000, 0, -191840800, 389559324, -56237868, -12077640, -36333056, -72297522, 0, 444939600, -54313056, 600119604, -121247008, 61754346, 6782976, 0, -51014124, 59611340, -9007680, 88153632, 291511248, 222783720, 0, -37857600, -70372840, 4782969, 71329472, 39146880, 60725808, 0, -32884224, 49615416, 19601496, 29469792, 40292640, -203731276, 0, -36682542, -4727040, 21983040, -584352, -327209684, -85259904, 0, 131663040, 344787168, 5529600, 157957393, 71916768, 9074160, 0, -177756066, -55969704, 230686632, -77648512, -149137668, -216761016, 0, -80384832, 29330222, -5280480, -50952888, -39474176, 40305402, 0, -62621640, 144417888, 129727224, -185317440, -99649200, 18620928, 0, 196158968, 17495676, 140190848, 402617526, 10569816, -68534312, 0, 4715172, 100724160, 173703300, -3576960, -79604316, -2850032, 0, 44015232, -87617964, -40501296, -359802412, -109583808, 151149960, 0, 76008240, 45342720, -262959220, -294194776, 8920044, -206382528, 0, 132036912, 91804336, 53178112, -121099968, -19023360, 260819244, 0, 93198926, -326332512, 119648358, 6266880, 218038782, 114484176, 0, -87411552, -2916000, -27827424, -416338056, -36343296, 117341686, 0, 19330758, -163718080, 15414036, 56052000, -16163480, -10106880, 0, -27939120, 414750192, -38209536, 171839174, -121524544, 19919196, 0, -9740022, 107274240, 150523156, 11817600, -155985480, -48374784, 0, 5308416, 115162740, -146121992, 117953262, -255098912, -56169582, 0, -225865120, -79901504, -11404962, 86176944, -192579024, 42522912, 0, -118888160, 213438402, 94178304, 68823600, 38829456, 13201200, 0, 39795768, -60622512, -456254568, -95663232, -53179956, -115810992, 0, 30015360, 105100518, 124551864, 350509896, 26171392, 165145176, 0, -60300756, 56282688, -214202918, -41923792, -3304800, 84008064, 0, 8942400, -335148844, 151634112, 36571014, 96904320, -205006368, 0, -248180492, -54717120, -80868348, -54943232, -262532862, -49008240, 0, -111260160, 75604356, -284865240, -63837144, 28986336, -52731360, 0, -76039560, -34643968, 47558400, 176793408, 114689620, -39255840, 0, -185685264, 119503824, -2799360, 82573130, -427949424, 184114980, 0, -344564778, 140549832, -214957112, 7540224, -167148036, 61997016, 0, -93952512, -280015066, 7514496, -48692070, 25267200, -64262394, 0, -154747296, -148796544, 73327680, 2047200, 536671488, 11344896, 0, 321600200, 23868918, 183387232, -367314024, 195881544, 36052632, 0, -13801320, -235636368, -34643412, -21777984, -165388000, 10134720, 0, -52191232, -133340286, 85087296, 505569960, -166268256, 90274986, 0, 13732392, 12673152, -204446942, 60667256, -234699606, -180454016, 0, 15588936, -16344720, -15663104, -171019044, -142269960, 647810592, 0, -109198570, -75038400, -45984024, 131324160, 289362678, 18269280, 0, 207191040, -101647656, -404375904, 255576240, 8584704, 267273536, 0, -114570864, 1500512, 42117600, -70918056, -392382936, -108174080, 0, -215546088, -129080940, -182419776, 136792800, 284790688, -279155538, 0, 152303976, -41619096, -279872732, -239426400, -140660640, -166068672, 0, 45656064, -389435062, -9418712, -5982660, 81102016, -435560790, 0, 142128232, 60690432, 142578468, 42324048, -174596352, 6998400, 0, 46905120, -18555822, 96130560, 144604560, 15367968, -615314880, 0, -98273898, 296893536, 427568856, 24256512, 74166480, 184163704, 0, -193554224, -596741460, -49959504, -156936112, -51893888, 401662800, 0, -5118000, 8259840, 194306084, 29072736, 23567112, -34852352, 0, -5004720, -311384304, -56025792, -273510216, 249807600, 6349800, 0, 475554746, -437127824, 95024943, 249469952, 27084462, 155787480, 0, 76193792, 55706778, -9504000, 34835916, -165176640, 12193956, 0, 36632574, 57827712, -350743440, 57386880, 483381916, 182688000, 0, -275779392, 45054672, -72036864, 125908596, 64258496, 67303548, 0, -3584418, 18346824, -531304640, -21404160, -45673200, 44104680, 0, 7931520, -480935842, -62335520, 267964074, 17301504, 132451452, 0, 26320680, 175522080, -45996984, 381206832, -84403008, 131321088, 0, -37171728, -77769018, 45392704, 23233056, -12791520, 97573984, 0, 302096556, 351192360, -244960764, 126555264, 182503908, 332979952, 0, -25330176, -77932800, -100776960, -429310784, 96909696, 351171936, 0, 473633568, 6718464, -406618274, 153417032, -79095852, 25286400, 0, 212486904, -117262800, 51839872, -101125341, -303141048, 122802024, 0, -529302708, -216718144, -40180320, -43807744, -297322722, 119194416, 0, -17422752, -99513288, -31587600, -126166920, -4913280, 373236934, 0, -121073778, -159730560, -30900918, -20649600, 413994440, -78618624, 0, 57909264, -51762960, 33123168, -1707840, -247832640, -163243602, 0, 19103226, 16074432, 98147808, 118688448, 106322706, 274281312, 0, -9123840, 147411376, 386034136, -274780674, -12282464, -401038638, 0, 118841312, 71806208, -391979556, -153953784, 53553720, 39227328, 0, 356318240, -140813640, 6623232, 359587938, 125829072, -650502188, 0, 120736440, 76440480, 622609128, -43846272, -833557032, 191324288, 0, 53510400, -56362788, 77794992, 16848968, 173107200, -3542940, 0, 280653228, -101082240, 194291434, 208622848, -169326720, -70980096, 0, 9543096, -4410268, -29846400, -411877224, 123219648, 542804304, 0, 159539522, 294229584, 31978800, 22762016, -640721694, -43420536, 0, -176139136, 180196272, -23402880, 116268372, 14358384, -216169564, 0, -116497116, 15787776, -791343300, 41459040, 605144452, 98596896, 0, -149873856, -284134776, -112572288, -183521062, -63216000, -224041356, 0, 37742880, -66054528, -193659752, 27979776, 27973476, 211563384, 0, -177999552, -10500430, 438785280, 16039458, -13793280, 632961798, 0, 564867620, 240994368, 10713168, 186911136, 294234072, -19823616, 0, 8775228, -3492720, -135647424, 59527086, 8407656, -754765480, 0, 166207140, -531748776, 322535976, -15239520, 118691506, 30000960, 0, 54542336, -394865550, 10865016, -351697104, -329168448, -424796544, 0, 117609264, 22809600, -6607440, 323565080, -136907820, 94021696, 0, 62816040, -224410888, -34088448, 36242640, -320300112, -70845336, 0, -518371200, -97733792, -93706182, 122719488, 644836566, -105043104, 0, -162830976, 57783456, 600064416, -94470600, 51369984, 595723788, 0, -12023586, -127141056, 635837490, 76811328, 17110096, -117541760, 0, -41520000, 578287248, -63169632, 168228014, -254730560, 121665240, 0, 371278434, 191187216, 69505444, 57612384, -14754960, 74616000, 0, 30699648, 559367263, 181562832, -132514074, 129373568, -925741068, 0, -452033208, -3932160, -65678202, -27679800, -604745292, 187038720, 0, 10711008, 242276778, 39808896, -240584178, -44110008, 8448120, 0, -103647600, 219359712, -28158024, -60687360, 720944878, -22450960, 0, 147602528, 142904046, -28762560, 279946800, 25850880, -33584436, 0, -661129740, 96432768, -360572652, -266735008, 151354476, 33527808, 0, -42366096, -265467316, 34483200, 73188198, 202459152, -675337080, 0, 450993482, 19785368, 196861914, -41690880, 431408106, -91171656, 0, -177509376, -157614336, -267066984, 611851200, 4098816, 194901632, 0, -27089640, 239399424, 25531794, -84407616, -75002400, 422277120, 0, -371436480, 261454464, 21897216, -223762064, 36302400, -141540183, 0, -1052283012, -200353104, -198750992, -99978432, 166203252, -329593704, 0, -128528928, 56325600, -248718080, 175407012, -96556544, 189979902, 0, -461889680, 109785504, 158422464, -209585328, 673839624, -90691776, 0, -358274632, -32058504, 156717568, -85286058, -394610832, -117467280, 0, -150585156, 282762240, 123813360, 8503056, -870776246, -377828720, 0, 107956992, 103800000, 353351232, -629342864, 88205184, 65609838, 0, 112161072, 71631360, 122639148, 346533264, 499843602, -65213408, 0, -55444176, 625490712, -1038848, -17680680, -514392816, -274409268, 0, -55127412, 202230176, -6218370, 9830400, -226640832, -214027056, 0, 16131840, 348105816, -129698160, -813359064, -99501696, 214654678, 0, 119568636, -265133632, -609534582, 83074896, -66870360, -142906368, 0, 433580712, 369797916, -90582912, -161930340, -291177488, 71906400, 0, 395106714, -11547360, 812417740, 230626176, 86264856, 338038656, 0, 33103872, -69636140, 243225400, 90879732, 31103424, 34062240, 0, 130151752, 18790784, -387554112, 228721464, 441817536, 8382528, 0, 104227200, 93285306, -6359040, -490560252, 233219376, -613785744, 0, -55492938, 339454032, 120774984, -72002304], "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": "6.6.a.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], [4], [9], [16], [66], [36], [0], [64], [81], [264], [-60], [144], [658], [0], [594], [256], [414], [324], [-956], [1056], [0], [-240], [600], [576], [1231], [2632], [729], [0], [5574], [2376], [3592], [1024], [-540], [1656], [0], [1296], [-8458], [-3824], [5922], [4224], [-19194], [0], [13316], [-960], [5346], [2400], [19680], [2304], [0], [4924], [3726], [10528], [-31266], [2916], [-3960], [0], [-8604], [22296], [-26340], [9504], [31090], [14368], [0], [4096], [43428], [-2160], [-16804], [6624], [5400], [0], [6120], [5184], [25558], [-33832], [11079], [-15296], [0], [23688], [74408], [16896], [6561], [-76776], [6468], [0], [27324], [53264], [50166], [-3840], [32742], [21384], [0], [9600], [32328], [78720], [-63096], [9216], [-166082], [0], [-4860], [19696]]}