# Stored data for newform 546.8.a.e, downloaded from the LMFDB on 20 April 2024.
{"label": "546.8.a.e", "space_label": "546.8.a", "level": 546, "weight": 8, "hecke_orbit": 5, "hecke_orbit_code": 18014398643700258, "dim": 3, "is_polredabs": true, "trace_hash": 1528037388070688425, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [2461550, -66705, 378, 1]]], "qexp_display": "q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-126+\\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": 34944, "fricke_eigenval": -1, "atkin_lehner_string": "--+-", "analytic_conductor": 170.56222391433047, "hecke_ring_index": 3, "level_radical": 546, "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": [546, 1, [365, 157, 379], [1, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [2, 3, 7, 13], "conrey_indexes": [1], "field_disc": 11562538233, "field_disc_factorization": [[3, 1], [14783, 1], [260717, 1]], "field_poly": [97248, -33506, -1, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.944", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "24.445", "prec": 20}, {"__RealLiteral__": 0, "data": "7.927", "prec": 17}, {"__RealLiteral__": 0, "data": "319.081", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "7.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1], [7, 1], [13, -1]], "trace_display": [24, 81, -378, -1029], "traces": [0, 3, 24, 81, 192, -378, 648, -1029, 1536, 2187, -3024, -6069, 5184, 6591, -8232, -10206, 12288, -12231, 17496, -4836, -24192, -27783, -48552, 111606, 41472, 41919, 52728, 59049, -65856, 105414, -81648, -263061, 98304, -163863, -97848, 129654, 139968, -585969, -38688, 177957, -193536, -649608, -222264, -76182, -388416, -275562, 892848, -1269219, 331776, 352947, 335352, -330237, 421824, 326511, 472392, 475311, -526848, -130572, 843312, -3434316, -653184, -1450497, -2104488, -750141, 786432, -830466, -1310904, -1302372, -782784, 3013362, 1037232, -5186076, 1119744, -3662940, -4687752, 1131813, -309504, 2081667, 1423656, -2950251, -1548288, 1594323, -5196864, -13650225, -1778112, -9353769, -609456, 2846178, -3107328, 6379533, -2204496, -2260713, 7142784, -7102647, -10153752, -10607646, 2654208, -18032235, 2823576, -4424301, 2682816, -7404864, -2641896, 15983115, 3374592, 3500658, 2612088, -3540570, 3779136, -32239305, 3802488, -15821163, -4214784, -16313175, -1044576, -30349920, 6746496, 4804839, -27474528, 4195233, -5225472, -20181156, -11603976, -17539416, -16835904, -77975772, -6001128, -19739166, 6291456, -2056914, -6643728, -25815765, -10487232, 1658748, -10418976, -7440174, -6262272, -18239847, 24106896, 50319474, 8297856, -34268913, -41488608, -13333593, 8957952, -11234874, -29303520, 9529569, -37502016, 2643180, 9054504, -42645183, -2476032, -8916399, 16653336, 53909841, 11389248, 26801385, -23602008, 8815797, -12386304, -38280858, 12754584, 28869006, -41574912, 12833397, -109201800, -11795784, -14224896, 14480427, -74830152, -3525444, -4875648, 40178184, 22769424, -14378217, -24858624, -92726532, 51036264, 93735267, -17635968, -18948474, -18085704, -39163419, 57142272, -111787479, -56821176, 56279451, -81230016, -20253807, -84861168, -67288245, 21233664, 117379116, -144257880, -22422582, 22588608, -172456008, -35394408, 210410313, 21462528, -35164044, -59238912, -36157002, -21135168, 240166518, 127864920, 81360774, 26996736, -267883617, 28005264, -186270060, 20896704, -140024052, -28324560, 128809248, 30233088, 90229923, -257914440, -98899380, 30419904, -26871507, -126569304, -114985689, -33718272, 30558951, -130505400, 158253138, -8356608, 183307974, -242799360, 56205009, 53971968, -264088635, 38438712, 240447207, -219796224, -79656777, 33561864, -56136264, -41803776, -190794819, -161449248, 43046721, -92831808, -44471322, -140315328, -10624692, -134687232, -368556075, -623806176, -541956039, -48009024, -272216019, -157913328, -252551763, 50331648, -332512134, -16455312, 200987367, -53149824, 76846806, -206526120, 334136493, -83897856, 119062227, 13269984, 172247391, -83351808, 230961756, -59521392, -448098150, -50098176, -61039251, -145918776, 64287072, 192855168, -494679651, 402555792, -191771469, 66382848, 806729682, -274151304, -185917440, -331908864, -286406442, -106668744, 222815544, 71663616, -649772598, -89878992, -486870345, -234428160, -1294322229, 76236552, 805085880, -300016128, -119456127, 21145440, 245198382, 72436032, 26130426, -341161464, -199931328, -19808256, 71512845, -71331192, 369665925, 133226688, 431544105, 431278728, 423035208, 91113984, 162648444, 214411080, 94517766, -188816064, -29173626, 70526376, 115459659, -99090432, -95595390, -306246864, 352095099, 102036672, 92096043, 230952048, -870461235, -332599296, 435342117, 102667176, -1980065664, -873614400, -427171401, -94366272, 398018556, -113799168, -128034474, 115843416, -440455725, -598641216, -982997022, -28203552, -121060821, -39005184, -819447840, 321425472, -277069824, 182155392, -1205757699, -115025736, 129730653, -198868992, -492744006, -741812256, -2306053932, 408290112, 113271291, 749882136, 815527488, -141087744, 1199157585, -151587792, -544891212, -144685632, 2852298588, -313307352, -3352574118, 457138176, -473564232, -894299832, -111993273, -454569408, 702914772, 450235608, -2105345844, -649840128, 231594558, -162030456, 324391182, -678889344, -532957482, -538305960, -3333030843, 169869312, -163031673, 939032928, -55536678, -1154063040, 1943328018, -179380656, 274590429, 180708864, -697025655, -1379648064, 2679154923, -283155264, 2578195113, 1683282504, 44786196, 171700224, -1413602484, -281312352, -577945017, -473911296, -200884698, -289256016, 1165928433, -169081344, 804776382, 1921332144, -492475869, 1022919360, 1177970388, 650886192, -511697331, 215973888, 1358625798, -2143068936, 1605861483, 224042112, 1739906328, -1490160480, -925260651, 167173632, 4713307122, -1120192416, 497520471, -226596480, -360007011, 1030473984, 1253462220, 241864704, -1222364298, 721839384, -303341598, -2063315520, 1382393304, -791195040, 1786772745, 243359232, 257298363, -214972056, -3517983243, -1012554432, 3073031505, -919885512, 71365860, -269746176, 7040811621, 244471608, 352595652, -1044043200, -1151419941, 1266025104, 284849838, -66852864, 431591190, 1466463792, -240742773, -1942394880, -4482333309, 449640072, -1449119865, 431775744, 1455565707, -2112709080, -1024799223, 307509696, 446713596, 1923577656, 723637395, -1758369792, 30860901, -637254216, 4722473508, 268494912, 238026519, -449090112, 416836170, -334430208, -1287373893, -1526358552, -1033583166, -1291593984, -4781374815, 344373768, -412211778, -742654464, 779463162, -355770576, 3319126422, -1122522624, -297953085, -84997536, 346501719, -1077497856, 1778824068, -2948448600, -145781964, -4990449408, -318486168, -4335648312, -517644288, -384072192, 2677675482, -2177728152, 390971529, -1263306624, 3958282752, -2020414104, 1256388420, 402653184, -95186988, -2660097072, -4621426953, -131642496, 5926656678, 1607898936, 1084810968, -425198592, 800922483, 614774448, 489572838, -1652208960, -388211859, 2673091944, -947587308, -671182848, -4727009139, 952497816, -2503616364, 106159872, -1427188776, 1377979128, 3015166506, -666814464, 2530852209, 1847694048, -714011781, -476171136, -1454020923, -3584785200, -511608798, -400785408, 3594246861, -488314008, 5738890533, -1167350208, -1057412313, 514296576, -4042113294, 1542841344, 1011936093, -3957437208, -3018261933, 3220446336, -12552058314, -1534171752, -167371854, 531062784, 1519545177, 6453837456, 962862831, -2193210432, 4373210157, -1487339520, -546852789, -2655270912, -898175265, -2291251536, 5591529927, -853349952, -1816782615, 1782524352, 8789256240, 573308928, 11920211598, -5198180784, 3169236132, -719031936, 4682027175, -3894962760, 10249185048, -1875425280, -605409714, -10354577832, 9696681747, 609892416, 16355950257, 6440687040, -4656312216, -2400129024, 11884539699, -955649016, 3208342767, 169163520, 5681078451, 1961587056, -734664552, 579488256, 2184489684, 209043408, -949429188, -2729291712, 8592743151, -1599450624, 7988279469, -158466048, -976239054, 572102760, -2788474143, -570649536, 4355648637, 2957327400, 6484495986, 1065813504, 6578965377, 3452352840, 9836075613, 3450229824, 2196740898, 3384281664, -2188179819, 728911872, 24715264611, 1301187552, -7232857659, 1715288640, 11056789359, 756142128, 5484667263, -1510528512, -5029291620, -233389008, 5017288962, 564211008, 775424559, 923677272, -3780649404, -792723456, 10666145013, -764763120, 4653714111, -2449974912, 3477849696, 2816760792, 12404229750, 816293376, 15705544296, 736768344, 2436207921, 1847616384, 11185739007, -6963689880, 10624627083, -2660794368, -2670283260, 3482736936, 3422797659, 821337408, 17650190613, -15840525312, -725530689, -6988915200, 3638422578, -3417371208, 2909301000, -754930176, -3104613603, 3184148448, -6581945397, -910393344, 25626300546, -1024275792, 825091677, 926747328, -18710076954, -3523645800, 6185056605, -4789129728, 4272834726, -7863976176, 11743573923, -225628416, 19492032519, -968486568, 4949315298, -312041472, 717344667, -6555582720, -2167262331, 2571403776, 1517535243, -2216558592, -19531735086, 1457243136, -5421557820, -9646061592, -7130393145, -920205888, 16086166785, 1037845224, 12946136037, -1590951936, 6492074589, -3941952048, 2539868352, -5934498048, 39795355902, -18448431456, -2150732979, 3266320896, -7371372687, 906170328, 1044258267, 5999057088, -1515679128, 6524219904, -5698355592, -1128701952, -5482208445, 9593260680, -5151460113, -1212702336, 812556522, -4359129696, 11518902081, -1157485056, 1162261467, 22818388704, -5350111347, -2506458816, -5149125537, -26820592944, -1200725694, 3657105408, 21049402830, -3788513856, 18699473052, -7154398656, -286866684, -895946184, 22001858166, -3636555264, 10843009590, 5623318176, -9951014025, 3601884864, 1214415510, -16842766752, 47946209991, -5198721024, -14632813053, 1852756464, -7249460571, -1296243648, -4873388679, 2595129456, -7349832513, -5431114752, -4775334459, -4263659856, 11058081615, -4306447680, -6818897601, -26664246744, -7545192252, 1358954496, 6150607500, -1304253384, -8977827618, 7512263424, -12523607913, -444293424, -14103676668, -9232504320, 5426658909, 15546624144, 1947202818, -1435045248, 12067511952, 2196723432, 2074863762, 1445670912, -20493897789, -5576205240, -2670501732, -11037184512, 9021685311, 21433239384, 5595419025, -2265242112, -3186741909, 20625560904, 3214680129, 13466260032, -30164686044, 358289568, 3733964868, 1373601792, 4650679557, -11308819872, -14819200545, -2250498816, 10410022560, -4623560136, 6235967412, -3791290368, -4825386351, -1607077584, -11261232447, -2314048128, -12098650050, 9327427464, -10280087358, -1352650752, -6039250656, 6438211056, -1648059777, 15370657152, -26265151548, -3939806952, -1728209916, 8183354880, 1735750944, 9423763104, -19683425835, 5207089536, 10000129071, -4093578648, -13356350577, 1727791104, -1438964919, 10869006384, 28884221586, -17144551488, -5177829663, 12846891864, -42359825364, 1792336896, -43745806809, 13919250624, 21781701414, -11921283840, -1824533802, -7402085208, 6922136508, 1337389056, -5019770880, 37706456976, -7912455717, -8961539328, -11784185391, 3980163768, -7732973934, -1812771840, -36427806546, -2880056088, 12474120954, 8243791872, 6016019688, 10027697760, -19338079650, 1934917632, -44863716426, -9778914384, -17543860146, 5774715072, 10011532104, -2426732784, -2861311284, -16506524160, -13145499315, 11059146432, 26745689796, -6329560320, 21480760116, 14294181960, -34946700183, 1946873856, -4250209209, 2058386904, -4082891925, -1719776448, 21737318760, -28143865944, -12771896064, -8100435456, 6770533938, 24584252040, -3225315429, -7359084096, -41305524633, 570926880, -9582186003, -2157969408, 6620356314, 56326492968, -28298595603, 1955772864, -1270857462, 2820765216, 705521502, -8352345600, -21343472784, -9211359528, 10303872843, 10128200832, -5398145856, 2278798704, 21566661558, -534822912, 52787741484, 3452729520, 1930846815, 11731710336, 8854807395, -1925942184, 6977961174, -15539159040, 9980979975, -35858666472, -11393808972, 3597120576, 74597873262, -11592958920, 11651690835, 3454205952, -79021952307, 11644525656, -568950564, -16901672640, 11421950616, -8198393784, 15944592063, 2460077568, -18347141676, 3573708768, 4391507988, 15388621248, -40293995931, 5789099160, -33452488470, -14066958336, 2551979682, 246887208, -27733196085, -5098033728, -8047479180, 37779788064, -787687902, 2147959296, -64524071049, 1904212152, 8304517191, -3592720896, 3117410793, 3334689360, 6256267521, -2675441664, 28884945324, -10298991144, -2581075530, -12210868416, -101719577766, -8268665328, 40476099969, -10332751872, 9506567673, -38250998520, -33614332914, 2754990144, -17259579582, -3297694224, 2486593161, -5941235712, -6055027527, 6235705296, -44109239148, -2846164608, -23502453345, 26553011376, 4826112078, -8980180992, 100387165314, -2383624680, 11754237159, -679980288, -11397516342, 2772013752, -26110520334, -8619982848, -53461772928, 14230592544, -69256580067, -23587588800, 4842405516, -1166255712, -11533627827, -39923595264, 4573422399, -2547889344, 2649796512, -34685186496, 10746501012, -4141154304, -134895969753, -3072577536, -48150844038, 21421403856, -3456930798, -17421825216, -77656060998, 3127772232, 3853561782, -10106452992, -11892304575, 31666262016, -33193361889, -16163312832, -48094560306, 10051107360, -26540919594, 3221225472, -80437709154, -761495904, -6481701447, -21280776576, -3268642167, -36971415624, -26057961471, -1053139968, -31043705124, 47413253424, -22125091680, 12863191488, 4528534497, 8678487744, 19157073537, -3401588736, -7480885248, 6407379864, -906610740, 4918195584, -3468132393, 3916582704, -32555457873, -13217671680, -36408551568, -3105694872, -43006428006, 21384735552, 3502727631, -7580698464, -47741952030, -5369462784, 14627297769, -37816073112, -13304088162, 7619982528, -99828418716, -20028930912, 20172049938, 849278976, -62263456164, -11417510208, 7307643372, 11023833024, -43473512571, 24121332048, 3058324857, -5334515712, -25539211875, 20246817672, -54336273804, 14781552384, 22019242176, -5712094248, -29989544325, -3809369088, -62004887145, -11632167384, 32377254795, -28678281600, -18491075463, -4092870384, -10075574361, -3206283264, -14712062724, 28753974888, -174512706402, -3906512064, 78478975578, 45911124264, 77012061876, -9338801664, -107957297949, -8459298504, -9192875055, 4114372608, -90519501186, -32336906352, -6060692442, 12342730752, -20550230493, 8095488744, -12786234264, -31659497664, 68867271540, -24146095464, 36503677476, 25763570688, -3023818371, -100416466512, 49533181569, -12273374016, 46137238977, -1338974832, 18978698844, 4248502272, -117800137296, 12156361416, -75801399876, 51630699648, -56844337788, 7702902648, 13130334294, -17545683456, 42694052214, 34985681256, 6253053066, -11898716160, -100656510009, -4374822312, 3544487070, -21242167296, 8758561914, -7185402120, 7118168382, -18330012288, -9902069058, 44732239416, -14389852014, -6826799616, -31702238856, -14534260920, 49300953768, 14260194816, -89991832761, 70314049920, -62762558976, 4586471424, -37691255370, 95361692784, -4401855171, -41585446272, 14015834001, 25353889056, 117737707977, -5752255488, -1499490306, 37456217400, -25896522873, -31159702080, 151812127389, 81993480384, 52469856486, -15003402240, 4045953912, -4843277712, -10367796309, -82836622656, 7413941583, 77573453976, -51071548116, 4879139328, 54707226798, 130847602056, -18819692685, 51525496320, -210258695550, -37250497728, -4966786461, -19201032192, 72337182921, 95076317592, 159272401263, -7645192128, -31245646626, 25666742136, 69611268051, 1353308160, 118128849729, 45448627608, -82523944248, 15692696448, 1209227292, -5877316416, 110820179223, 4635906048, -55076511960, 17475917472, -38167267068, 1672347264, -19573397463, -7595433504, 160648279752, -21834333696, -15604515459, 68741945208, -13781117112, -12795604992, 39099451377, 63906235752, -5423886846, -1267728384, -45851995539, -7809912432, -28327499565, 4576822080, 31480067691, -22307793144, -27357307566, -4565196288, 4931728431, 34845189096, 21728962314, 23658619200, 15451722150, 51875967888, -78782424633, 8526508032, -13296848463, 52631723016, -23304998262, 27618822720, 26381501337, 78688604904, 31805200476, 27601838592, -112270115733, 17573927184, 137672857764, 27074253312, -13815827937, -17505438552, -1252782648, 5831294976, 247040332224, 197722116888, 36682896546, 10409500416, -32151196581, -57862861272, 185659512597, 13722309120, 43358260041, 88454314872, -19284868323, 6049137024, -39616820295, 43877338104, 46977470856, -12084228096, 38045480205, -40234332960, 6499326582, -1867112064, -24982037577, 40138311696, 115546783266, 4513688064, -222389804940, 6203396472, 127259292294, 7389418176, -58068248568, -30245195232, 68674672755, -6341787648, 13433052717, 85329160104, 147788607015, -6118104960, 192112371864, 37229712888, -9720189297, -19599799296, 53553858315, 27822797568, -141978940398, 22534086336, 33843479940, 99233838000, 38343105297, 6530347008, 191582579454, 125644354368, -33003836046, 5894146752, 89140713834, 19489663368, 196229712882, 14780931072, -8190223146, 89485912056, 137109863130, -55709519040, -19303851693, 84997016664, 37324619208, -21286354944, -16268486208, -21362266080, -249507029865, 27861895488, 48242864115, 27382381272, -8064867894, 6570699264, -30604912824, 141201524904, 6947055801, -126724202496, -58508260626, -5804245512, 127366824597, -55911321600, -94985547561, 29107380624, 32876639055, -27338969664, 15901714209, 23274408000, 82971850635, -6039441408, 23079868035, -24836908824, 35114903655, 25473187584, 1926878220, -52655563176, -93089118642, -7283146752, 99629870826, 205010404368, 190101913767, -8194206336, 178231279428, 6600733416, -40261036788, 7413978624, 9520082604, -149680615632, 275012354466, -28189166400, -178424056368, 49480452840, -31088338407, -38313037824, -77864401203, 34182677808, 849059883, -62911809408, 7690945626, 93948591384, 83416426812, -1805027328, -17141396994, 155936260152, 11652962130, -7747892544, 197321142162, 39594522384, 127302066489, -2496331776, -6500054871, 5738757336, 59152410744, -52444661760, 251564112951, -17338098648, -121022999343, 20571230208, 12324071133, 12140281944, 107255185920, -17732468736, -39126236355, -156253880688, -7778632290, 11657945088, -72170737359, -43372462560, 39300274089, -77168492736, 48605992374, -57043145160, -77135555784, -7361647104, -27669579021, 128689334280, -20780215389, 8302761792, -292045447536, 103569088296, 12061267092, -12727615488, -139739084283, 51936596712, 177451078158, -31535616384, 19538209665, 20318946816, 262126084788, -47475984384, -70829753085, 318362847216, 833244327, -147587451648, 12401851686, -17205863832, 228815165550, 26130567168, 127506784716, -58970981496, -225250420389, 7249362624, 21205352187, 8354066136, 6426716013, 47992456704, -269783520867, -12125433024, -82377115674, 52193759232, 11254576590, -45586844736, 35066243781, -9029615616, -52903806717, -43857667560, -34759095111, 76746085440, 70555070127, -41211680904, 91878444621, -9701618688, -27906745482, 6500452176, 158792202597, -34873037568, -149593353210, 92151216648, -129097120005, -9259880448, -82394212857, 9298091736, 56290413738, 182547109632, -11129718006, -42800890776, 91884080631, -20051670528, 334497960399, -41193004296, 21045505374, -214564743552, -35840045475, -9605805552, -206490527865, 29256843264, 89616413394, 168395222640, -207352957380, -30308110848, 63890630580, 149595784416, -8044733295, -57235189248, -156324758892, -2294933472, -178900602480, -7167569472, 9355546413, 176014865328, -7722532902, -29092442112, -286814016789, 86744076720, 48028249836, 44986545408, 229404658266, -79608112200, -66678774240, 28815078912, -3936113028, 9715324080, -138902167029, -134742134016, -187706812389, 383569679928, -8599126536, -41589768192, -44181572064, -117062504424, -264130772385, 14822051712, -13976395776, -57995684568, 153340819674, -10369949184, -228929157126, -38987109432, 72297238014, 20761035648, 5924008020, -58798660104, -30948863589, -43448918016, 10556231283, -38202675672, 65884053360, -34109278848, 22037932230, 88464652920, 106873634304, -34451581440, 110070892044, -54551180808, -409112676438, -213313973952, 33922487340, -60361538016, 287082938787, 10871635968, 156514411383, 49204860000, -2570048676, -10434027072, -114048390768, -71822620944, 123434614083, 60098107392, -124778527731, -100188863304, 9216926901, -3554347392, -161094875070, -112829413344, 160019730306, -73860034560, -294334566003, 43413271272, 214352536212, 124372993152, 29289896136, 15577622544, -120560753316, -11480361984, 39440091327, 96540095616, 21624907041, 17573787456, 161441668698, 16598910096, 241726279875, 11565367296, 13218466626, -163951182312, 185671801203, -44609641920, -44337999732, -21364013856, -10481720193, -88297476096, -122962190139, 72173482488, 402426907998, 171465915072, -25584857316, 44763352200, -57628322454, -18121936896, -273706607460, -25493935272, -127629246753, 165004487232, -54280826334, 25717441032, -82162812021, 107730080256, -67597641828, -241317488352, 36122275083, 2866316544, -36426043929, 29871718944, -38534096952, 10988814336, 100151911140, 37205436456, -62874635082, -90470558976, 81409495662, -118553604360, 447785317578, -18003990528, 235373528154, 83280180480, 68333009643, -36988481088, -534289867572, 49887739296, -114696469593, -30330322944, -19278318087, -38603090808, 364788620679, -12856620672, 141215117229, -90089859576, -39258564921, -18512385024, -171312771084, -96789200400, -129118632564, 74619419712, -13813437546, -82240698864, 90582401805, -10821206016, 23542084980, -48314005248, 97044665247, 51505688448, -209797405788, -13184478216, 47254992072, 122965257216, 154950044391, -210121212384, -659460815967, -31518455616, -82473392001, -13825679328, -28550132451, 65466839040, 383205517026, 13886007552, -43366947702, 75390104832, -109137058938, -157467406680, 289443948840, 41656716288, -610546675632, 80001032568, 27322274511, -32748629184, 149549016045, -106850804616, -137425757889, 13822328832, -81493072191, -11511719352, 161030640225, 86952051072, -255702608103, 231073772688, -338905574478, -137156411904, 19254738552, -41422637304, -108379059708, 102775134912, -4519040058, -338878602912, -256334630634, 14338695168, -311387942211, -349966454472, 41027719779, 111354004992, -319649419122, 174253611312, 65442622917, -95370270720, 25997296437, -14596270416, 98924365773, -59216681664, 550758851367, 55377092064, 118076674239, 10699112448, -131641208736, -40158167040, -861649541208, 301651655808, -14765025303, -63299645736, -56717235705, -71692314624, -174816496842, -94273483128, -24250732155, 31841310144, -888682612086, -61863791472, 1927941912, -14502174720, 150971308029, -291422452368, 15253663446, -23040448704, -36505918188, 99792967632, -49053130605, 65950334976, 5310914409, 48128157504, 18890683218, 80221582080, 237309918480, -154704637200, 61952847147, 15479341056, 3644269356, -358909731408, 321845713146, -78231315072, 511817275434, -140350881168, 722982032292, 46197720576, 85569375564, 80092256832, 148197900768, -19413862272, -751509660858, -22890490272, 126414733725, -132052193280, 168662092245, -105163994520, -49899556638, 88473171456, 276727996296, 213965518368, 9489847701, -50636482560, 448983680013, 171846080928, -16346062278, 114353455680, 185890921377, -279573601464, -130767588807, 15574990848, 261810407169, -34001673672, 98211126306, 16467095232, -508950873936, -32663135400, 441610656939, -13758211584, -176762926335, 173898550080, 93370094517, -225150927552, -125720429832, -102175168512, 1248911763816, -64803483648, 63292965294, 54164271504, 320882571873, 196674016320, -40072943859, -25802523432, -243391585788, -58872672768, 86625254709, -330444197064, 134749491447, 4567415040, 284798450007, -76657488024, 153389118177, -17263755264, -331480971678, 52962850512, -485846681952, 450611943744, -19835942904, -226388764824, 114051661962, 15646182912, 103945537470, -10166859696, 58981221468, 22566121728, 447873404790, 5644172016, 110551884378, -66818764800, -25634588076, -170747782272, -61966394616, -73690876224, -68938666881, 82430982744, 232004065077, 81025606656, -292321476321, -43185166848, -72802278102, 18230389632, 215683545663, 172533292464, 244965952554, -4278583296, -1134748243074, 422301931872, -26358454458, 27621836160, -201043626888, 15446774520, -735438947715, 93853682688, -75288801861, 70838459160, 54069962478, -15407537472, -238927926501, 55823689392, 117602513199, -124313272320, -114608817099, 79847839800, 808796972013, -286869331776, 175081391622, -91150471776, -523821689004, 28776964608, -751343688903, 596782986096, 177632065179, -92743671360, 184892505933, 93213526680, -40838343861, 27633647616, 265574041551, -632175618456, -29293903821, 93156205248, -236615895105, -4551604512, 59312004246, -135213381120, -578409258714, 91375604928, -689195014815, -65587150272, -59080855113, 127556736504, 44542674867, 19680620544, -731050538964, -146777133408, 667312144497, 28589670144, -752578310784, 35132063904, 899015444292, 123108969984, -195287156793, -322351967448, -79219882308, 46312793280, -24683018178, -267619907760, 298533312693, -112535666688, -554717538081, 20415837456, 677941724694, 1975097664, 148086016101, -221865568680, 108002267742, -40784269824, 153697665450, -64379833440, -135790873740, 302238304512, 920698832820, -6301503216, 384941527182, 17183674368, 135466801974, -516192568392, -469508876451, 15233697216, -407311681959, 66436137528, 20936463093, -28741767168, -264795688749, 24939286344, 637613447601, 26677514880, -102077533908, 50050140168, -343820668866, -21403533312, 30574174290, 231079562592, 287985915351, -82391929152, -22050465696, -20648604240, 227820046494, -97686947328, 125650280997, -813756622128, 420384979659, -66149322624, -185844021255, 323808799752, 93901941792, -82662014976, 5807066460, 76052541384, 169675120293, -306007988160, 334914203250, -268914663312, 198131859900, 22039921152, 114529849308, -138076636656, 424049695992, -26381553792, 1065657796758, 19892745288, -65010311766, -47529885696, 65777613867, -48440220216, -532438591095, 49885642368, 917541937839, -352873913184, 302014953189, -22769316864, -304089313302, -188019626760, -93691467051, 212424091008, 286864931241, 38608896624, -276708280926, -71841447936, 401266252482, 803097322512, -72097648020, -19068997440, -41496704184, 94033897272, -1067402007684, -5439842304, 92415536793, -91180130736, 164775577221, 22176110016, 63769681920, -208884162672, 476555146551, -68959862784, -814005739167, -427694183424, 68911747110, 113844740352, -19589328603, -554052640536, -137855432298, -188700710400, -828458474808, 38739244128, 98237409606, -9330045696, -247125264846, -92269022616, 442326646425, -319388762112, 78551127000, 36587379192, -524765097765, -20383114752, 1320581320134, 21198372096, -83824567281, -277481491968, -76425731592, 85972008096, 690048269382, -33129234432, -177712525719, -1079167758024, 118439920677, -24580620288, -1293680563452, -385206752304, 691910114742, 171371230848, 77938079079, -27655446384, 222872001114, -139374601728, 22277475279, -621248487984, 852530292492, 25022177856, 575735377623, 30828494256, -505172077758, -80851623936, -698606359758, -95138436600, 173926001613, 253330096128, 166996528335, -265546895112, -77107819764, -129306502656, 58882642845, -384756482448, 115366537602, 80408858880, -1002397667730, -212327356752, 29965760649, 25769803776, 317076495921, -643501673232, 443952524547, -6091967232, -735474626733, -51853611576, 526284878013, -170246212608, -288052746984, -26149137336, -236758635708, -295771324992, 133631513046, -208463691768, -632776629084, -8425119744, -276144456840, -248349640992, 19368306009, 379306027392, 430612740144, -177000733440, -437475436983, 102905531904, -58516082937, 36228275976, 824106228168, 69427901952, -951219660126, 153256588296, 40973451561, -27212709888, -145445660976, -59847081984, -425536389036, 51259038912, -527356847322, -7252885920, 502994301570, 39345564672, 634364595606, -27745059144, -146382061140, 31332661632, -84103045026, -260443662984, 251488472055, -105741373440, -192520614915, -291268412544, 692851127367, -24845558976, 106323672651, -344051424048, 434326503195, 171077884416, 370544273214, 28021821048, -8962736118, -60645587712, 349545672999, -381935616240, -222232139058, -42955702272, 396533872716, 117018382152, 175286013903, -302528584896, -355474878876, -106432705296, 63425206182, 60959860224, 68576445504, -798627349728, 112547656068, -160231447296, -552742910211, 161376399504, 1074474609354, 6794231808, -1034724685419, -498107649312, 102084644802, -91340081664, -58069790433, 58461146976, -24528905835, 88190664192, -1314111364974, -347788100568, -199027062549, 192970656384, -24504247788, 24466598856, -811915117455, -42676125696, 28194973209, -204313695000, -1312433695719, 161974541376, -126795412275, -434690190432, -40923336456, 118252419072, -1031641877379, 176153937408, 487216940976, -45696753984, -153855600984, -239916354600, -31851937446, -30474952704, -871000544292, -496039097160, -148019628015, -93057339072, 1444880166912, 259018038360, -634057009500, -229426252800, -139089423051, -147928603704, -25915337448, -32742963072, -289740312306, -80604594888, 21939026094, -25650266112, -145101076344, -117696501792, 666675710364, 230031799104, 311010356187, -1396101651216, 276954446496, -31252096512, -553649875530, 627831804624, 31381059609, 367288994112, -1402117022739, 616096495008, -55788416292, -74710413312, -144453006369, -863658383592, -180797245479, -67674388032, 31813498119, -73543000440, -139026389499, 32914980864, 311995450572, -724156009488, 808917483282, -258695250816, -32419593738, -48485539536, 97360281039, 98741846016, -487313579268, -164401843944, 568333876410, 64763909952, 70315077363, -102289874112, 1428540453159, -253275981312, 504885772404, 550938172320, 10006553718, -193168763712, 749625691809, 292029419808, -7745400468, 206108565504, -1664235941670, -24190546968, -312306128799, -803331732096, 594050170482, 396265452552, -68788036551, -98186992128, -39602663037, 369097911816, 292761258930, -10711798656, 465290958972, 151829590752, -42912797814, 33988018176, -268677378675, -942401098368, 1680369290031, 97250891328, -1475707825989, -606411199008, 32789218770, 413045597184, 88271470248, -454754702304, 1012079924838, 61623221184, 1294547669757, 105042674352, -397038966156, -140365467648, 469450457619, 341552417712, -395085952431, 279885450048, -120768618957, 50024424528, 1653581881155, -95189729280, -195735435417, -805252080072, -876278874411, -34998578496, 1060923357519, 28355896560, -131581494333, -169937338368, -1718387000460, 70068495312, -31588942749, -57483216960, -198445477851, 56945347056, 87194178939, -146640098304, 1224835328862, -79216552464, -128934030393, 357857915328, 1138396233768, -115118816112, 1151965535769, -54614396928, 298568203605, -253617910848, 6979892079, -116274087360, 204813222432, 394407630144, -184110235227, 114081558528, -2125559081304, -719934662088, 1085532420069, 562512399360, -203720190804, -502100471808, -149322346131, 36691771392, -3379232967, -301530042960, 166066402500, 762893542272, 82013520333, -35214841368, 624687239058, -332683570176, -242401345686, 112126672008, 529194237567, 202831112448, 679162522752, 941901663816, -338137413651, -46018043904, 1232578549083, -11995922448, -461812808634, 299649739200, -380799270036, -207172182984, 205936381599, -249277616640, -938182868271, 1214497019112, 146519790543, 655947843072, -655012232220, 419758851888, 2386339848429, -120027217920, 52574476086, 32367631296, 350502837498, -38746221696, 375261165165, -82942370472, 325822822704, -662692981248, -136520364708, 59311532664, 261518907702, 620587631808, 56021321574, -408572384928, -452383682925, 39033114624, -41629797378, 437657814384, -553335240303, 1046780816448, -1629911072082, -150557541480, 43915824582, 412203970560, -72103546764, -1682069564400, 558480224472, -298003981824, -192637264491, -39734291688, 243585503397, -153608257536, 967656998001, 578697463368, -1092397883949, 760610540736, 151076313675, 1274179210104, -680516144154, -61161537024, -152848099284, -249965173008, -86042031543, 205333937088, -1240159974030, 556890144408, 2255327687910, 10826465280, 86796363483, 945030797832, 337167978546, 363589020864, -498012617334, -660191553984, -814446523188, 125541571584, 918218352807, 9673818336, 1442198208372, -47018531328, 100817051436, 886561433784, 438151216068, 37087248384, 41523861603, -440612095680, 125568348039, 139807339776, -245597091363, -305338136544, -210801940599, 13378778112, -400118414715, -156587179704, 275560282335, -60763468032, -227494210734, 1285186238016, 281070609120, -174674669568, 1142739741474, -124836123672, 727421326296, 549935561664, 168371120124, -110248936896, -2084480462514, -102364839936, 2871971130210, 312795611016, -130285431477, 511249886016, 95034949632, -43391094768, 123645953847, -10141827072, -304053276069, -366815964312, -1985055031422, -62479299456, -165420423705, -226619996520, -326663551350, 36614576640, 1069024915719, 251840541528, 413574890757, -178462345152, -277562358666, -218858460528, 721396554546, -36521570304, 63819707277, 39453827448, -163059767712, 278761512768, 149221211364, 173831698512, -2146362968550, 189268953600, -44497613979, 123613777200, 1215091437480, 415007743104, -447557224842, -630259397064, -709159091796, 68212064256, -301885496637, -106374787704, 466231200696, 421053784128, -46661667732, -186439986096, 169011194058, 220950581760, 350479197183, 211052010696, 46865275488, 629508839232, -1287070852728, 254441603808, -121169115774, 220814708736, -531452497545, -898160925864, -147832274265, 140591417472, 790976498676, 1101382862112, 270003484917, 216594026496, 770641022907, -110526623496, 1418459746431, -140043508416, -360621465579, -10022261184, 2759357899872, 46650359808, 102997485666, 1976322657792, -38852052813, 1581776935104, 523802819760, 293463172368, 1714979993781, 83276003328, 779873982822, -257209572648, -1283751372357, -462902890176, 257881917852, 1485276100776, -139801400901, 109778472960, -279725928384, 346866080328, 441317889516, 707634518976, -1143715284828, -154278946584, -100002801702, 48393096192, 952267225662, -316934562360, -1181136783843, 351018704832, -865165252806, 375819766848, -411311051655, -96673824768, 588105938178, 304363841640, -1940362674, -321874663680, -497054649264, 51994612656, -49262412654, -14936896512, 291273416448, -199856300616, -694906428390, 321106493568, 186897685716, 924374266128, 1574558200164, 36109504512, -1269946218960, -1779118439520, -135533813760, 49627171776, -828122742942, 1018074338352, 2616167981301, 59115345408, -213636304359, -464545988544, -978338415684, -241961561856, -1101199104663, 549397382040, -318173005557, -50734301184, -378885849576, 107464421736, -1020657050046, 682633280832, -208790296218, 1182308856120, 808028603703, -48944839680, 1149932922474, 1536898974912, -983550776742, 297837703104, -303666927465, -77761514376, 1333946038764, -156798394368, 336801265758, 428430866520, -46373388672, 222582380544, -80966280771, -1135831523184, 162432531576, 180272690688, -88722814734, 270747839520, 462271457661, 793870704000, -522128150550, 306744842376, 527816973837, 52242776064, 267619961439, 1532660635632, -1211320343502, 1005154834944, 38413692639, -264030688368, -1053399983643, 47153174016, -473684223942, 713125710672, 2365367458875, 155917306944, -762015128007, 1569837703056, 270311366808, 118247448576, -260334533415, -65521785168, -241099766796, 715887296448, -77255404668, 1096878905040, 1497453769254, -445676152320, -1209202586262, -154430813544, -354928481505, 679976133312, 643262565003, 298596953664, -31563805821, -170290839552, 722133624492, -130147889664, 3436858567272, -170898128640, -118724095488, -1996056238920, 579980523132, 222895163904, -1718105436471, 385942912920, 1037801564268, 219059050176, -943560904941, -64518943152, -79436933394, 52565594112, -1655989737654, -244839302592, -114755648643, 1129612199232, -800991186594, 55576446408, -471574920129, -1013793619968, -110238081975, -468066085008, 1257347039964, -46433964096, -111266175426, 1018934596776, 586907606520, -447290572800, 1091377794240, -759884380488, 1146203381865, 232859044992, -344841193728, 263013112440, -658341156150, -218711757312, 527645840046, 127213713672, 182804416326, 186195264000, 771702891405, 663774805080, 808855785387, -48315531264, -87083516583, 184638944280, -1158895583628, -198695270592, 190087134573, 280919229240, -1115249165091, 203785500672, 1143229579149, 15415025760, 236234596548, -421244505408, -258719022081, -744712949136, -2993215013958, -58265174016, -25658386074, 797038966608, 178749620478, 1640083234944, 2118608159037, 1520815310136, 55919863839, -65553650688, -764062081281, 1425850235424, -207451456188, 52805867328, -1034688811971, -322088294304, -34313151474, 59311828992, 937749950535, 76160660832, 1440783838764, -1197444925056, 19049080554, 2200098835728, 3765591845772, -225513331200, -3539947946283, -1427392450944, -576273765168, 395843622720, -588540306549, -248706707256, 726138975150, -306504302592, 278204566761, -622915209624, -666561510174, 273461422464, -206680959018, 6792479064, -145749938112, -503294475264, -669828586569, 61527565008, -596797589940, 751588731072, 582299862066, 667331414496, -517358695317, -14440218624, -94184517147, -137131175952, 1425269020068, 1247490081216, -814759549236, 93223697040, -409235321820, -61983140352, 52132864005, 1578569137296, -111601230420, 316756179072, -1290983112735, 1018416531912, 239079799665, -19970654208, -136306520373, -52000438968, -618742167288, 45910058688, 188404951698, 473219285952, 1319897273319, -419557294080, 2654283843651, 2012512903608, 269486459325, -138704789184, -918950138589, -968183994744, -1322449471209, 164569841664, -307632842244, 98592569064, 3915335550, 97122255552, 2830031341320, 858041487360, 2014142578074, -141859749888, -151734421065, -313009890840, -884320923759, -1250031045504, 314595652545, -62229058320, -871623651771, 93263560704, 2274658671468, -577365898872, -2133592712289, -346979700480, -256286473257, 314402192712, 147439651923, -617347941888, -15361665228, 388847938992, 282993917856, -456345161280, -2010580842252, -617084446272, 308392666632, -58893176832, -1248447436887, -221356632168, 2055529475502, 1029514674240, 430503985701, -166241723112, 484865652012, 66422094336, 1440463397130, -2336363580288, -495372825252, 828552706368, -1189109289843, 96490136736, 2273332005255, -101820923904, 118570715676, -1117912674264, -2333610119427, 415492773696, 198235140831, 1419608625264, -1087937890137, -252284931072, -1181322442206, 156305677320, -23890025898, 162551574528, -903217188690, 2097008678304, -1312365341862, -379807875072, 580806245172, -566638024680, 68903451414, 2546902777728, 1521362170812, 6665954616, -1415221856433, -1180699613184, -748796294295, 99214813488, -2011208176251, -137646910656, -1038458730753, 1830521324400, -217281937860, 209044537344, -399913452519, 1020054277728, 598322819757, -471767851968, -21267573354, -1802003363112, -3733284829983, 57994900992, -1930909539150, 169642817496, -1742149918323, 66832529088, 186880365594, 51413728104, -276038299026, 383939653632, 224221964157, -2158268166936, -729218127870, -97003464192, 149409861165, -659016925392, 84170091411, 417550073856, -59036700879, 90036612720, -4175243709120, -364694757888, 168919223067, 280529950248, -902810888178, -72236924928, 175171674000, -423230453736, 779893523748, -350861340480, -1236421735332, -278072760888, 356459416725, 613968683520, -69689039310, 564440561016, -404043843084, -329693447232, 387079929882, 735027556968, -2746428599682, -77612949504, -1286606101866, -223253963856, -252623558733, 52003617408, 1092854699163, 1270337620776, 1455805710072, -278984300544, 175512184533, -1196746825680, 256677327171, 737209733184, 463292114280, -1032776960040, -861614521944, -74079043584, -907586988678, -659153702856, 563049508476, 74384733888, -319710690462, 450323309904, -466008648714, 1460376877056, -945615199338, -89037744048, -1365895626954, -342407126208, 67138015347, 735072645048, -2585711705232, -160413364224, 62112897906, 2675983683192, -163485743229, -329544034368, -550810488669, 168364042992, -1057238040423, -1716517948416, -1190949456996, -286720363800, 3366383806128, -76846444416, 2020437175206, -1651924222920, -634566240315, 234054746112, 2429922589587, 716931307152, -596787870504, 1347161781120, 130305026106, -1658823659040, 347682144186, -242464886784, -2779804806963, 511125044640, 2710453463478, 1196766275328, -3285675268761, -64357866360, 61782174186, -457881513984, 317364403293, -1250598071136, 416487303981, -18359467776, 240108829467, -1431204819840, -307732941234, -57340555776, -2416658693928, 74844371304, 528961210314, 1408118922624, -704984049018, -61780263216, -1616664342846, -232739536896, 402727618878, -2294512134312, -1443467869056, 693952613760, 728864356410, 384225998688, -279511643937, 359892363264, -1869927661809, 1835237266128, -387315590013, -636864897600, -170649521553, -533430193920, 130744948932, 230520631296, 3018599848722, -31488904224, -35114162502, 77722592640, -311407951329, -1111217336232, 1787526633654, -1077937072128], "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": "546.8.a.e", "char_is_minimal": true, "conrey_index": 1, "id": null, "nf_label": 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], [8, 0, 0], [27, 0, 0], [64, 0, 0], [-126, 0, 1], [216, 0, 0], [-343, 0, 0], [512, 0, 0], [729, 0, 0], [-1008, 0, 8], [-2023, -13, 4], [1728, 0, 0], [2197, 0, 0], [-2744, 0, 0], [-3402, 0, 27], [4096, 0, 0], [-4077, -9, -44], [5832, 0, 0], [-1612, 148, -109], [-8064, 0, 64], [-9261, 0, 0], [-16184, -104, 32], [37202, 34, -85], [13824, 0, 0], [13973, -10, -443], [17576, 0, 0], [19683, 0, 0], [-21952, 0, 0], [35138, -168, 77], [-27216, 0, 216], [-87687, 755, -215], [32768, 0, 0], [-54621, -351, 108], [-32616, -72, -352], [43218, 0, -343], [46656, 0, 0], [-195323, 129, -864], [-12896, 1184, -872], [59319, 0, 0], [-64512, 0, 512], [-216536, 386, 536], [-74088, 0, 0], [-25394, -14, 527], [-129472, -832, 256], [-91854, 0, 729], [297616, 272, -680], [-423073, -1755, 1063], [110592, 0, 0], [117649, 0, 0], [111784, -80, -3544], [-110079, -243, -1188], [140608, 0, 0], [108837, -5635, 2983], [157464, 0, 0], [158437, -885, -1172], [-175616, 0, 0], [-43524, 3996, -2943], [281104, -1344, 616], [-1144772, -4680, 3524], [-217728, 0, 1728], [-483499, 4897, -2470], [-701496, 6040, -1720], [-250047, 0, 0], [262144, 0, 0], [-276822, 0, 2197], [-436968, -2808, 864], [-434124, -9488, 4866], [-260928, -576, -2816], [1004454, 918, -2295], [345744, 0, -2744], [-1728692, 1100, -13388], [373248, 0, 0], [-1220980, 9738, 6511], [-1562584, 1032, -6912], [377271, -270, -11961], [-103168, 9472, -6976], [693889, 4459, -1372], [474552, 0, 0], [-983417, -3531, 11521], [-516096, 0, 4096], [531441, 0, 0], [-1732288, 3088, 4288], [-4550075, -11333, -5169], [-592704, 0, 0], [-3117923, -145, 11338], [-203152, -112, 4216], [948726, -4536, 2079], [-1035776, -6656, 2048], [2126511, 13335, 11553], [-734832, 0, 5832], [-753571, 0, 0], [2380928, 2176, -5440], [-2367549, 20385, -5805], [-3384584, -14040, 8504], [-3535882, 10710, 8817], [884736, 0, 0], [-6010745, 19319, -38671], [941192, 0, 0], [-1474767, -9477, 2916], [894272, -640, -28352]]}