# Stored data for newform 363.8.a.f, downloaded from the LMFDB on 25 September 2025.
{"Nk2": 23232, "analytic_conductor": 113.39576425073619, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [11, -1]], "atkin_lehner_string": "--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [363, 1, [122, 244], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 4, "field_disc": 95577305912, "field_disc_factorization": [[2, 3], [11, 1], [2141, 1], [507289, 1]], "field_poly": [28880, -1544, -510, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [14736, -5416, -426, 15, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998271070571, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 36, "hecke_ring_index_factorization": [[2, 2], [3, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "363.8.a.f", "level": 363, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 11], "level_radical": 33, "minimal_twist": "33.8.a.e", "prim_orbit_index": 1, "qexp_display": "q+(-4+\\beta _{1})q^{2}+3^{3}q^{3}+(142-2\\beta _{1}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "363.8.a", "trace_display": [-15, 108, 306, -890], "trace_hash": 51892825235351259, "trace_moments": [{"__RealLiteral__": 0, "data": "0.064", "prec": 17}, {"__RealLiteral__": 0, "data": "3.725", "prec": 17}, {"__RealLiteral__": 0, "data": "1.061", "prec": 17}, {"__RealLiteral__": 0, "data": "39.408", "prec": 20}, {"__RealLiteral__": 0, "data": "21.199", "prec": 20}, {"__RealLiteral__": 0, "data": "632.430", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 4, -15, 108, 565, 306, -405, -890, -2457, 2916, 8946, 0, 15255, 1822, 35340, 8262, 65041, -32856, -10935, 12784, -4002, -24030, 0, 114858, -66339, 72856, -221466, 78732, -10112, 104952, 241542, -24976, -337761, 0, -741690, 722856, 411885, -498856, -897156, 49194, 2676930, -734556, 954180, 201916, 0, 223074, 3068508, 1995894, 1756107, -771024, -1632129, -887112, 4412266, 929970, -295245, 0, 7224888, 345168, 2864322, 1353156, -108054, -3998774, 3783264, -648810, 1480129, -6612108, 0, 1722008, -1596906, 3101166, -2751024, 5571858, -1791153, -5600528, 10907838, 1967112, 19634884, 0, -5979582, 7710226, -24073794, 2125764, -11230842, -3431856, -273024, -5909484, -25687140, 2833704, 0, 4611528, 6521634, -9032696, 13608576, -674352, 3497436, -21828000, -9119547, 1401692, 7230081, 0, 43725043, -21577560, -20025630, 19101020, -59519562, 19517112, -78776334, 40247616, 11120895, 23831038, 0, -13469112, -59353544, -4856136, -24223212, 4030608, 11919234, 1328238, -57741732, -7231932, 72277110, 0, 82266750, -19833012, 62928224, -10953804, 25762860, 57767458, -135311745, 5451732, 128035572, -4553472, 0, -26385560, -44108292, 6022998, -58591806, -41600676, 82849716, 69477112, 200131728, 53889138, 42655836, 0, 47414889, 128992140, 118606374, -20817648, -118257658, 68708388, -44067483, 78767218, -216867396, -23952024, 0, 155510112, 119131182, -10694140, -12343476, 25109190, 304926786, 15689412, -7971615, 256472, -146193570, 0, 209526132, -154911156, 195071976, -32554344, -181283364, 9319536, -245681876, 207510360, 77336694, 43673026, 0, 36535212, 95433066, 198102300, -2917458, -307589908, 287101104, -107966898, 127477848, -99643956, 102148128, 0, 620705112, -17517870, 492153960, 73561182, 39963483, 273430180, -280231302, -178526916, -21476115, 88704792, 0, 391131140, -120882975, 46494216, 327166698, 264890604, -43116462, 200411028, -269777952, 83731482, 741875914, 0, -74277648, 40567732, -210466674, 150440166, -206574036, -192211008, -48361131, 512344544, -793783386, -151214256, 0, 121206204, 294511626, -204660928, 531119400, 53112024, 523157346, -464641704, 530141868, -307005700, 1145968368, 0, 872723430, 200285004, -161448714, 615549984, -1117360140, 208176102, -318931944, -236598228, -649992438, 327930460, 0, 57395628, -746580662, -379741422, -303232734, 847128784, 1129544736, -92660112, -310316364, 407254572, -7371648, 0, -513916356, -159556068, 469656961, 109605960, -693552780, 37038068, -1856603604, 76510008, 714672180, 554224704, 0, -82443492, 1197740256, 124511256, 109164572, 1085401362, 176084118, -335132258, -587876946, -243882792, -1080831342, 0, 367431552, -726299798, 56327844, -18207504, -1031562960, 583474992, 94430772, -160944980, 1308004080, -589356000, 0, 368005932, -246227769, -514517852, -702392940, 37845684, -2184945986, 439340892, 195212187, 32625960, 563703906, 0, 1088439426, 50434992, 1180576161, -1407525776, 892487700, -582594120, 2753553028, 637769508, -540692010, -1223365880, 0, 515727540, -8227008, -625413726, -1607028174, -1141305808, -497493714, 526962024, 2319021112, 750592758, -2126961018, 0, -3591818562, 1086685632, 1950429096, 535271928, 300264165, 858657202, -224194068, 643438026, 1138198602, 1334924556, 0, -683894368, -2774616012, -363666024, -2515085040, 771163704, -1602545688, 2612866840, -2918699673, -131115672, -2279999772, 0, -654026724, 507271844, -2691287004, 108826416, -2460479694, 67016808, 321819318, 951516766, 1942411716, 35862426, 0, -751774080, -1559026764, -1032301488, -1920586446, -195262164, 1062901716, -935004564, 1951481970, -198800532, -1143019578, 0, -5084622416, 2357700732, 2221202250, 1946623880, 4302123672, -535491324, 1048446204, -2402363736, 1699062048, -884543330, 0, -295752708, 1915272048, -1847990652, 695597220, 40645064, -6686391240, 1559721366, -1942899204, -1796100462, -3653417115, 0, -2158288170, 147196764, -1424305222, 3576284850, 3456960444, -4663138764, -1260698625, -122943744, -166561590, 482570520, 0, 2152193564, -5644797408, -712410120, 1589201671, -1397502060, -1190923884, -511917856, -9102237462, 162620946, -233287704, 0, -1581978762, 1628070220, -9580405812, -1123218252, 6753857576, -3902523360, 2236942332, -2209328328, -9905905866, 1875882024, 0, -3866537124, 5403556656, 643264256, 2501171556, 1455006726, -5969418894, 1416129936, 1151707572, 3489912544, 10844486988, 0, -8357747688, 1084365960, 1280202003, 1152746456, 1904459904, 3482787780, 11817771658, -205810128, 3202372098, -3113995214, 0, -562076496, 164917812, -6795746916, -3192956766, 3647397780, 5196895536, 1855126476, -7475986280, -2913213444, -1189822041, 0, -3569200422, 2126714886, 1100935572, 4291404432, -5855419692, -3964245548, -6052241370, -646704648, 5280343824, -901628508, 0, 4910446340, -7338889302, 4198773024, -8803868586, 3179654616, 3216541914, 25163096, 7504930944, -288741780, -3318738900, 0, -333273852, 4302194800, -8722687008, 677948130, 307177752, -1425105648, 8233023222, -643245772, -6817739226, 423614124, 0, 4893123924, -215233605, 8164033052, 12605421318, 6924744, 5599523778, 3384926040, -3947226390, -1698600888, -14559892680, 0, -8513192992, -2098072524, 5657205564, 3075228392, -2436395412, -4182601212, 5238402060, -1421316180, 5266943352, -3420979812, 0, -878967288, 3743249320, 414175794, -4894650828, 5592327220, -7720313601, 251627472, 7477517538, -7709696832, -6633410652, 0, -3419959992, 5602779720, 20632464660, 7290738876, 2088090738, -8359428428, -11441865468, 1179171702, 6407306520, 663219840, 0, 7600238440, -21428650692, 986450724, -19469154464, -5371909668, 2576692782, 4446464136, 503257428, 5348762100, -10445668230, 0, -78771366, 10437246838, -4607897772, -8304927516, -1418545998, -2810722860, 7751729808, 5069910232, 2167272018, -2915106246, 0, -5649065736, 3441901896, 794972500, -10964601882, -2690386812, 37291567420, -12822360660, 2757999456, -4470833840, 24620703696, 0, 2467246062, 19524757512, 16759038024, -1519346412, 1299899148, -472982490, -8627565240, -8811708024, 13288156920, 17009990272, 0, 1986151914, -16886934264, -5302984962, 1079014041, -9838140412, 17739017283, 7382614860, 28515249900, -4563220680, -7566245154, 0, 27797523690, -4820226732, -4237399998, -6398277588, -579855105, 1052280608, -35317917720, 2395029384, 264407918, 8443874736, 0, -6228152064, -22857606390, 10560540780, -9839743920, -14840237982, -3263840325, 8139875800, -16830453552, 1255343832, -14457577184, 0, 8833500846, 16412775826, -37952943108, 7152046308, -8971957932, 3452150688, -1164144474, 3526860394, 1246032684, 5411097756, 0, 22971832752, -7284004704, -3698633008, 32790993216, 2260750014, 3623996076, 2222857980, 20030649678, -16243513664, 34482564042, 0, 15013260638, -7116646272, -2005496496, 14753605664, -5549056848, 1095328764, -38180741598, -10553355624, -5682600198, 6908238558, 0, 4061884482, 3215230530, -5350006020, -5577498972, -7320945208, 26598418896, -5189697216, -2060634072, 857624778, -1305750537, 0, -11224354518, 13833302688, 21344140604, 30468525510, -21432151422, -13985501112, -46072437306, -4082784912, 31663155576, 41121071640, 0, 16486790852, -26712228012, 3272567508, 5303162844, 18156714480, 7951813902, 1010139660, -19309277448, -5525845056, -17194822056, 0, 14340223800, 4125081220, -24023480514, 1434024648, 19440425403, -16973263680, 14125248342, 1615724756, -12137242980, -12545326008, 0, 2399671476, 14313830436, -14053917276, -24821722008, -8289153900, -9014008388, -6843703932, 30941145936, -6611977504, 59880721554, 0, 20894286924, 3191786160, 23563532610, 25149290544, -7681442010, 5407695108, -20163047072, 850582020, -4359115278, -6129468112, 0, 16619849568, 2022260562, -6908386500, -30168723780, -31138348516, 59188299792, 5620754754, 26721511974, -5193027456, -8611162488, 0, -4028462340, -6388152156, 53813547456, 23455536114, -17549795826, -17650535704, -41692622715, 8854122420, -49236451258, 8186350800, 0, 9516792812, 55458145296, 1549681956, -55007886228, 15670091520, -20157677874, 20792643070, 38754349872, -10253018394, -18956726328, 0, -8187283818, -211855868, 7235646372, 22872477168, -29317521168, -14436568068, 30497707872, 43938815340, 43508754270, -2501823024, 0, 3208643304, -8378541828, 28196319104, 16871652576, 10995873444, 38500994844, 44000482728, -199034496, -35973795304, 11840798676, 0, 85094889480, -11223992520, -13875741612, -8937397304, -48583578456, -4308013836, 17416346916, -34958096232, 12680737947, 14065304308, 0, 2959360920, 3637391590, 7300338258, -18725925060, 28345689872, 11878274574, 1000027836, -27049126350, -16938631896, -50128297308, 0, -45626385768, 2065770216, 23987417625, 34357980204, 19296148860, -9785959556, 1240933386, 14964067008, 47487086880, 1097393196, 0, -21065684708, -29183212770, -2225974284, 32166035912, 32848632618, 32338986912, -13176743604, -34024808439, 3361803912, -42983077926, 0, 2947443444, 33826470528, 36411638976, 29305836774, 24446698782, -36417930108, 4754271186, -22083729908, 61545116640, -9048570966, 0, 7613806248, -15872677542, -21783882584, -71198452242, -6584835384, 26484106164, -11171520480, -29182446234, 68072668688, -83495733336, 0, -72632139648, 32073275208, 9920651904, -19613056000, 22946573832, -19610094546, 98688881098, -3621565104, 1520851788, -2184861984, 0, -491602608, -31548530076, -5553883506, -27852199920, -24401281004, 32200845630, 15753824784, 13903205812, -70649283378, 2549630844, 0, -36917710002, -4345514460, -25257341574, 38797774524, 35316110160, 37283145010, -41003081472, -15912612000, -25237790748, 14029557828, 0, -839742760, -69408237624, 9936160164, -141582985104, 35569027134, -6648149763, 14178596172, -72876047358, -13891982004, 52036574720, 0, -18964609380, -12561010360, -95975323818, 1021833468, -23533111488, -24390755184, -58993541622, 31247516830, -21515150364, 11862204084, 0, -12043209144, 5270729049, 3384786896, 699298188, 880900920, -65911822452, -4537901004, 15220005462, -56387814188, -59068661580, 0, -141498860224, 27756940944, 29387864502, 93283609080, 36744513768, 1361744784, -38676784662, 61535666112, 31875556347, 61446248388, 0, -38003195952, 31295638206, -9800017188, 24097167900, 28138041752, -28359503868, -15730041240, -102823262688, -4668172614, 74345931756, 0, 75821387694, 17219776716, -83444946058, -36697002024, -14598684270, -52468225754, 87294228720, -33030878760, 16234458618, 39003626544, 0, -44890933936, -58617877656, 13924643580, 87618257910, 7162142484, -222129216, 21789355296, 21888321918, -16886170602, -80183331060, 0, -43389760698, 9343910968, -13024787856, -30815256816, 87410691072, -46188427944, -13432330278, -128755922676, -78644444268, 14227974648, 0, -93327377112, 62613570024, -83371556732, -45808009500, 20266004466, -44053372848, 145293565044, -57427947486, 65641362912, -149182073376, 0, -90585603216, -16189387740, -96979101174, 23296673028, 13495472724, 29340512064, -17996079530, 57484755132, 52661585592, 6954726394, 0, 14452342056, -165057262236, -25039195020, 8107132455, 40320639688, -123050843952, 23183744454, -118872698150, -25133024196, -6053239836, 0, -56266477746, 17372826702, 15706850844, 31490363202, 30731362254, -115771035204, -68153090292, 36042963012, 207450216040, -89406351672, 0, 95844707504, 50783853600, -18465147936, 118872403656, -58251830640, -74914632324, 78704348614, 48320474220, -9818982648, -73153651500, 0, -67907296080, 23008983240, 83197258836, 20821420008, -42078549216, -23856566256, -43268733576, 112922673316, -82999492572, 70547404680, 0, 61251395694, -78804891171, 1426364640, -139929110784, -3540123144, 133840337034, 125663716344, -61559993844, -49639175740, -141413122104, 0, -35082921599, 26552722308, -17658721548, 39559581784, -40258948758, 13696339788, 202691867568, -74763758100, -72664749108, -1408785488, 0, 2938313232, 70456228928, -18767293788, -66432951738, 75096007592, -232123706388, 1809453816, 74566104114, 18489832692, 8689121586, 0, 12094335084, 25690952682, -23581119060, -62027352, 52445116332, -26263252520, 185221654728, 968285502, -97907061312, -70219861632, 0, 26262817924, 200671676721, -20297900160, -145221939036, -6497067546, -42093722628, -97868580314, 223323625248, -27872140176, 161739250692, 0, -51855834042, -41611446914, 160147347576, -5272078428, -60383233396, -39947978784, 28698346332, -51233987948, 257372546646, -25245123228, 0, -36477598104, 52690013190, 46529255148, -67477977306, -5367614364, -73378232216, 25244187072, -30861528606, 176757259928, 108402222606, 0, 111099780660, 128928831456, -137284805232, 61516524440, -38174730516, 63657919764, -126876313770, 37890794724, 59972460750, 97177677980, 0, 52558844760, 149340553272, 210442107258, 116157339144, -32679711288, 140992409496, -14458265748, -50837284574, -43299039930, 28308047508, 0, -62614029948, -64863820872, -218571382326, -26486172912, 45874675296, -4658102822, 18363622728, -23882669910, -237733857744, -150755767776, 0, 24186144440, 31845609342, -7985323116, -122975324844, 48083874114, 51712345296, 34044882796, 73780464708, -49895747604, 21224244508, 0, 18781124940, -53343779784, 290711978088, 1097416728, 87328009614, 35960871696, -180532563480, 54175418360, 71362327956, 42112476882, 0, -72291424980, -52458278508, -65152206752, -18037979136, -48494712474, 106711096308, -87030761784, -98642262105, 33125583644, -154196572230, 0, -116164439057, -119333701044, -58273780590, -84869853248, -64416604140, 3974312628, -66580761072, -106407253632, -38456240994, -79569986988, 0, 96559690950, -361145050010, 9407231784, 93337931988, -143435145088, 186102731130, -125904746628, 91596352668, 160948243074, -34038862875, 0, 151435024896, -3319481088, -41951189160, 83098217946, -4497162930, -129649413006, 22859947698, 13029404040, 8895942822, -52719109608, 0, 65837349792, -177261940704, 58109226228, 308604417198, 87696739440, -152409530016, -202850850000, 110711408304, -19235073240, 190405060332, 0, 42908445117, 187389526672, 115294556694, -37732555620, -161872761728, 35481127308, -32154944868, -134178565596, 281072771496, -13821782112, 0, -15340234932, -245760411474, 4775106164, -102925722852, 4390765542, 377166193924, -14610049068, -6298768008, -325537860672, 308897071884, 0, -54637505664, 166362995520, -42713426574, -31199285412, 70830335910, 43957895940, -229737546236, 23029070220, -258670956924, 196069200382, 0, -30326892804, -251632359558, -215393670720, 182354154552, -85031320612, 570033665748, -105368130720, 17436120000, -14949398544, 60397442964, 0, 450242179008, -59651864856, -118617381576, -96938021040, -267459458382, 151125269560, 133371618501, 50648814648, -176201386990, 77051545536, 0, 185199632712, 166695367770, -104396502348, 65361195444, -236106606708, 145896029712, -116574184660, 15492910440, 17368134912, 215338048672, 0, 67531632012, 47577514844, 316188460662, 39285181602, 176162666496, 109526668608, -161174310138, -34065360160, -110384958378, 38235508272, 0, -50968729554, 31096104444, 67397007524, -224106624834, 94227638688, -264952952982, -42955844040, 292801148676, 31552817124, 262930446540, 0, 290330793312, 42048418848, -225659187576, -101015493712, -31132489992, 29277880920, -370131764628, -76894600176, 34565454081, -159141016628, 0, 31124154312, 173025510406, 170528828982, 51420417408, -74211323728, 9812797908, 94035270060, 3544788738, 70067043984, 319079834766, 0, 139161820968, -5556873456, 356049114330, -152797530636, 86464046646, 262672013472, 99492095280, -84077870778, -120622787628, -80850928356, 0, 15742030124, 139191941430, -15176065392, 318575894612, 37455900318, 4452780924, -95597251430, 110026512324, -183485166732, -381609523200, 0, -86209832682, -315741265312, 407443048488, 98479740060, -47566817064, -40960405188, 140316179472, 259827865568, 58928100072, 50088414852, 0, -65332518276, -201851629560, -99333964020, 10011250230, -78656762988, 154272005830, 138034181520, -32125195107, -75799564916, -607605298695, 0, 540027754938, 241617025608, -96368411394, -225828974928, -230437088376, 57421301922, -240912143004, 13459340688, 29725260444, 250998481908, 0, 115867919664, -106164544692, 265967556762, -158096331684, -135369614916, -89180513196, -107034629796, -79514508640, 361892975718, -163410516990, 0, 173386948356, -17461025496, 57233587860, -284770654692, 142569283248, 120568934674, 183719548332, -24343969716, -275877014058, -241334628444, 0, -325824515408, 388210070652, 132582051180, 813885802200, 142286280792, -198150011154, -376384769704, 216230436420, 113366871648, 60074934298, 0, -237704451822, 132694016242, 306749881800, 85850674632, 274134632874, 73901676312, 86846631678, 196671542388, 96550127880, 679403592, 0, 71626082124, 202633135488, -246127914096, 398030131050, -7796028060, -418823240568, 234452260992, -89605950300, 317007847948, 547244555718, 0, -193982208144, -122626706832, -8998394004, -82005233128, -298693425654, 116159259600, 530207436288, 21968757120, -235512549216, -190247419802, 0, 18304599510, 494669035044, -124998889224, 8293799304, -281833005792, 194029387032, -38477852496, -339860464332, 5335740150, 222291626994, 0, 477836938224, -17367635844, 283410944985, 96397398438, -184078959102, 372784788586, 130135311474, 11437581348, 124700284350, 121690704168, 0, 344122795136, 342733751616, 132114345948, -656400637712, 485837438208, -5811307335, -7564124732, 770875163316, 220428892404, 367586128008, 0, 340346375586, -318291839028, -93667781994, 186968088, 187304202128, -65725783764, 151187142006, 117615097030, -239776225800, 91393003080, 0, -256551547140, -106575112530, -96874070480, 190021541700, -45862223976, -374365825380, 291194759472, -393117102360, 244841586944, -518671072944, 0, -459654683424, -261346704744, -229856210784, 37533810584, -702619775100, -56647958148, 190191103762, -132898161636, 152744550228, 83315192736, 0, 83031166584, 596406343344, 139919374212, -65782676124, 182107107688, -638218270704, -112930232724, -185314832064, -228516856368, 141436855620, 0, -570386212764, -38375536860, -570186927312, -115376161698, 142207470504, -120131391312, -273708618402, -92366454924, -633688889788, -246386915256, 0, -100780345296, -934937005320, -23732116776, -401168245938, -121325402616, 101067731640, -142092688682, 539613144048, 11182746438, 267181868928, 0, -132155572356, 107850916444, -245474745192, 150992834940, 365706262776, -380802738624, -208448467227, -65597149764, -181827674538, 6793941744, 0, -232980268824, 201892973526, -62946071344, 13927011762, -208161814464, 58796969250, -133803451200, -179102087604, 189680036060, 209497813152, 0, -669793985278, -654911553696, -92338919784, -504190764528, 364223540574, 151275052440, 537421285320, -222511051596, 557076545820, -130432502752, 0, 196849949652, -523694519904, -11615046012, 56378449926, -165312957628, -309887524137, -225704567556, -320305617396, 123050135736, -308930367636, 0, 968769426660, 31837635954, -767910802434, -240951398352, 172997276040, 77377709080, -60213904320, 17906935680, -35820179784, -785209198620, 0, -340216700676, 588883801884, 205206437880, 484663747886, 132064140840, -578573568684, -149714679400, -1013606802744, 26634169548, -141246087606, 0, -525667170528, -279982145150, -761215993416, -145041561036, 363084112663, -345015345828, 69570705114, -224719195396, -154839541494, 120054531672, 0, -144382274370, 13587950556, 302553547148, 568284029568, 144416576700, -664164520000, -86803841508, -282033042210, -144909027600, -384940520526, 0, -543631853706, -275644860000, -2126826882, -24277580704, 46603071948, 281805664626, -251221639824, 115818855432, -124413239844, -382912097876, 0, -224233042932, 264605197848, -375995659908, -38300741946, 696744506964, -62959362576, -75889517220, 153979256542, 207078798006, 209296704816, 0, -963321300660, 136887576264, -247973013846, -341832342240, 58516344486, 560556310464, -426557453640, -78707868642, 1245093530360, 347852523048, 0, 127242254104, 13931227296, -152524774872, 352607948268, -171287713128, 92931351192, 212887612972, -538363156170, 21464257500, 98045859576, 0, -296044250814, -169241199362, -586049842890, -72640443924, 122883716550, -38272125000, 1006872320340, 640971130054, -1204342582704, -346203737820, 0, -557665262376, 74465985312, 127870248344, 210661125516, -120712513680, -954892187340, -111683391972, 664758999792, 153502107268, 103541307519, 0, 155703732806, -224682007284, 66615643674, -270216147140, -303220266564, 527168452824, 601996388622, -465426567360, 452494026648, -248064496658, 0, -41022353124, 350310657330, -817597229532, 35097276996, -283704938200, -286476210342, -12770527230, -409509553560, -99879950280, -232944261480, 0, 128931623430, -237916116648, 874516552528, -925891819170, 358780236840, -132328266696, 791173888764, 459269737344, -32610912762, -574029274320, 0, -196860715992, -308469631500, 53626101678, -545233399560, 357209143536, -455947225128, -315171002552, 398336806704, -143180593974, -132122753892, 0, 29133379107, -755428205072, 678658872372, -265629791124, 139468769114, 367706611944, 478953466641, 7078932456, -133228442880, 199330601220, 0, -499953689724, 769911747300, -14923058860, 217672123080, -123206958360, 852362861482, 784739580420, -204288619158, -112717376128, 544539001632, 0, -89871742944, -89798755320, 750533139630, 266286114716, -191802335658, -130146121764, 501220890016, 377069982000, -114409799946, -216481340438, 0, -172753494876, 737894332002, 463982132832, -15656087835, -216251216892, -217657101060, 28411576416, -270097519116, 203353730364, -953583778440, 0, -108218228844, 64665793368, 508472301312, -19094708298, 7139013786, -1379453360, 426426248280, 227984617872, 941770472940, 369337165596, 0, -29222344468, 456808499232, -168160105728, -178373851680, 979996340760, -617155372530, 676130976610, -839509078920, 285134601060, -1031144377832, 0, -265673085840, 341071684560, -763568440038, -400686425514, 112939698240, 36683653260, -88123688775, -353791306592, 650788437852, 219776646600, 0, -1149550605654, -454422245904, 832876927936, 171045487218, 33894283464, -1570061348388, 25241077104, -390354583968, 321084499776, 893368290180, 0, 100288760940, 333793035084, 238504522842, -172661841456, 1581849334176, 443144947302, 1542521158212, -572824127016, -1024729463916, -368744784968, 0, 193105250316, 380374900078, -1019681946432, -242242864164, -405118927252, -525199107102, 93208068576, -205651839888, 435900162864, -31431900798, 0, 1527174893100, 95225230638, 746718148368, 666877867728, 33642882468, -370525932112, -2163141643806, 146099639412, -1076844333648, -464229315660, 0, 453970825308, 587252042274, 620239484304, 702956812544, 546588038172, -196668127008, -363781467792, -1084733893302, -99863091216, -1031991400470, 0, 885356816832, -686792732498, -352896518052, 61040250378, -1201353056118, 1008866519892, 97847894052, 120149357968, -225519552084, 60017165460, 0, -342687152814, 540827541306, 560253532076, 2023779709062, -438574868928, -66099455296, 302454992016, 931029229134, -378323958052, 1868209071360, 0, -259751189358, -500123540904, 405358037226, 249251596920, -398912257080, -192149449344, 1406422074348, 78921518304, -54148405392, 391778974496, 0, 398347352928, 967482198444, 159996770520, -149824534896, 463160312716, 1749572009508, 29573876628, 700657001500, -494285203638, -1030880023146, 0, -258986095728, -284940601848, -950402370618, -158832648924, -153430205346, 1133173564536, -2271918572448, 186522441066, -884537676720, 111925296912, 0, 587671239648, 160372034688, 109670881014, -112991167128, -787214538120, 86811224310, -541647948096, 1033804331793, -144450162540, -475675896244, 0, -150592472244, -106288349292, -432380345406, -197665520616, -883339926948, -1542191197656, 718157310192, 701647097758, -585135234636, -140121824832, 0, -1460697337596, -55637119944, -325450176944, 495504557052, 23155869006, 424352355468, 254197963824, -35255264499, 25644722700, 2222233625952, 0, 493308701000, -618416738988, -303057571986, -160009082764, 1169291005158, 373499172576, 367740276234, -1085501221152, 576291796308, 991795368368, 0, 822650188770, 128803851090, -957936788244, -578668088394, -1250079898808, 737719262508, -377608530024, 136475193708, 147592195236, -1243955807262, 0, 1729933567716, -110235192624, -913985651844, -148559646822, 854905200552, 444287808070, -3017858490408, 1110268934280, -1371348280080, 435164977368, 0, 628396495408, -1044552843936, 445143353004, -852664005664, 19790786364, -721230156324, -1098229659548, -121981104240, 88359322716, 603053214000, 0, 143185396788, 14781878932, 533262833502, 490231290960, 451341629132, 170665409916, 214698975354, 522002158174, 428978056236, 27273770820, 0, 166558191288, -521350491096, 140890684212, 978169324680, -149197816512, 1081438105452, -485062013508, -464260195512, 610928831048, 1888984838856, 0, -160585879320, 156471428544, 387186042600, 168200080616, -1268406096714, 111377192940, 424894460124, -1231333960296, -648633973878, 551971870786, 0, 38718665496, -516945048342, -390884072712, 524891485881, 429675793520, 1528755959520, -458278119360, 1851979581136, 727048991376, 381381705234, 0, 507296242854, 43624568412, 197382112284, 181827329406, -327705560460, -69845787916, 26120769918, -338723802216, 2070859885312, 143640306780, 0, 166171562820, 591984073215, 64791129852, -271743626022, -594902469180, 386473421772, -187471934858, -882887057376, -379455766452, 632289649614, 0, -670186494216, -306548159652, -2294778833136, -223807155300, 37507311840, -1027012025676, -243378226476, -970171855200, -849822675354, -184780006164, 0, -380656103466, 835410940272, 1430488985200, -776331612528, -178523392608, 137625264996, -1256146028928, 1616779481958, 229677211840, 650805649200, 0, 2599929045012, 9886494372, 564145746948, 525576905624, -518186337582, 86178226320, -1385283923112, -366507838728, 636215380470, 580689299344, 0, 679030844688, -1920283681748, 200457174144, -207398934270, -663140627880, 967498204596, 146007767916, 1516103943834, -397272883056, -544402270944, 0, 831347076132, 22965714540, 1417354548216, 339418246332, -117696112506, -374652587364, -1960140717504, -165495639024, 1944041247528, -913353061896, 0, 1757519015144, -953465077512, 448735938336, 722689993597, 670529073648, 54601035174, 482825621048, -508501969380, -186526435500, -898506700374, 0, -814555542060, 233365595976, 129014247660, -840735409932, -2465252396192, -581107497948, 1598084094384, -704490179072, -2204379349380, 151760378358, 0, -816137163792, 721480823298, 1057223669732, -418152613482, -140211741312, -139085294712, -292660061220, -232501387176, -1335117392860, 625350158388, 0, 409253230908, -394087942032, -108768483180, -469571250536, -1247303287068, -172480108212, -2272996839990, 1366082264736, 1452965781312, -1057669809072, 0, 633299475078, 62426146776, -546332137284, -473844487302, 587593266884, 3426930521976, -476564464008, 1779958627162, 683579451828, -1125700813305, 0, 1460086450992, 239061305340, 1890957103872, -143535799872, -1329384183966, 1891117293444, -903554373072, 221031471600, 1080555408498, 324084174324, 0, 55940175248, -2557352625300, 256953405924, -1566791483820, -390779651304, 1497369922992, 313287700800, 1624752252174, 41841412812, -463926524012, 0, -1485212928156, 858589031852, -1423211910, 423092471040, 1681604565846, -1696871997480, -544257302598, 1566311181068, 81232922424, 561401362890, 0, -423130071552, 1046367446544, -551232515992, -2041150420248, -276831496638, 799974956580, 1501942734612, -511831610856, 926312474344, 684844184472, 0, -344272594448, -525532396800, -221056663086, -1959492207192, -1596305546322, -5720108436, 718571900058, -1107802814880, 195362452044, -166741433342, 0, 617556883536, 3082236197692, -485324763120, -791573071536, -1114498757088, 775797452130, -389787337836, -1450565417472, -2047393512180, 823438112544, 0, 1662572442414, 1186348014180, 578680627096, 1867641780210, 1174736365290, 1343174675734, 1624710744528, -67549221648, 970993200624, -367938889560, 0, -1782373246140, -1752990688116, 86633369208, 902322698490, 975916894212, -226220629356, -822004960820, 2832402677556, 761300615808, -1019158770804, 0, 455534619552, 936399880604, -62705643906, 296888582988, 821932378524, -705145793280, 1039526860788, 480156448736, 1580056793076, 1188013033656, 0, 302961244008, -5373931392, 206330354156, -204934487064, -971292473208, -2415730327176, 886872874944, 319701564252, -1148519822408, -1493524394082, 0, -80813802456, 3246031915632, 2297562015960, -342061693384, 967541867088, -303047798040, 3043422014380, 326338631676, -374645023524, 1606501237330, 0, -241309727208, -2605827407940, 299896120308, -1311756618312, 1386083811428, 357603888192, -116316373572, -3008383953456, -1017126236652, 470241366732, 0, 1372800192864, -943868598264, -806516262336, -615282116226, 342379924569, 595174150428, -3085900485942, 379763216316, -515210442982, -1168241231916, 0, 377060153504, 2185892289381, 79902744840, 1751805796284, -1314756214512, 98209572930, 276149546840, 2491864143096, 197109132966, 1962959075820, 0, -505599976620, 785056621308, 1766568486336, 765333626544, 2970630722124, -1977987691320, 320713413498, 1492532210952, -364816184628, 27000751572, 0, 933130596114, -730326411450, -766546640616, 4119145857210, -457343061192, -2269866202512, 364142507136, -1353464027316, -589919576332, -841107669828, 0, -2671071262434, -93612601056, -1231912415736, 2502595064024, -1890556565436, 55775795832, -210994118316, 504577754364, 647660275875, -508168913788, 0, 927665465508, -2467945024384, -872395303758, 520996019220, -2087690061452, -3145990117080, -264220908012, -2679014733366, -555053336472, 33505201422, 0, 1231352977956, 404029809216, -911984634994, 987135207384, 1282151345760, -329660174876, 621110433174, 29629616292, 1660591621572, 315622392000, 0, 1075376960288, -3192301708884, -568773487116, -1283639536032, 3607211518098, -787946744790, 1647916171474, -3391097473662, -60101305668, -1840131695190, 0, 868482969624, 1488780359986, -402904613280, 886913080686, -275464877232, -628448009628, 873152646624, -3125388483600, -3962808420384, -355772077308, 0, -1321003201902, -918669827853, -1372612262728, -1924715887554, 90768705624, 428442350542, 1694921566968, -1160543104002, -1024507022256, -1312369566816, 0, -2095430926212, 437832471336, 79580972988, 310031134984, -1538155072680, 913314704256, -2863488259736, -458749387116, 983114252352, 1579368690792, 0, 791257592898, 3030120534120, 533052051486, 660060867114, 562548777164, 1611149522958, -983284112916, 4315776777544, 1084810545816, 128365322022, 0, -2479361081604, -596260707516, -799082076786, 184796810544, 1661718149280, 700767880330, -1932549947568, -244311416082, -4051420323660, 177935558064, 0, 997718931208, 841574968320, 205572768696, -462828383736, -1561248437478, -428562293634, 809878144736, 450565987983, -588164829768, -1765877270702, 0, -1922358210534, 3423026968968, -1128763604772, -177790555368, -1751885841174, -3234331911216, 715070866428, 739622693352, 2814135789828, -301631052960, 0, -554614974360, -787926048318, 1695731588936, 3678165588450, 1837962054576, 4727465414160, 845474897148, -2254384800072, 112045650104, 2059316608902, 0, -3444748901164, -1563590822028, -1961067770496, -1086132453680, 2195017177152, 865978430616, 563232962148, -2517976540512, 267857601408, 2008778066112, 0, -529552512000, -2810664718920, -878081998368, 619557493464, -1097818094736, 2717096319360, -529472552742, -3158568964584, 885546969720, 2664599789646, 0, -2073368262930, -97782257808, -5805223540367, 234152677524, 41062998276, -2446030567166, 3103178828742, -58991273568, -711934361664, -1995215160048, 0, -1403532145820, 959052325992, -13273270416, -2729039302378, 2490351631752, -851810312052, -2590360717248, -328324718604, -149954854662, 675053222748, 0, -752009397840, -1807744237556, 2463205657548, -658834587108, 4862335675112, -2709300587712, 869422832010, -2280478566642, -2148285735552, 425353269168, 0, -436881759948, 375386556924, -1586315111088, -3906666729864, -1907530651206, -5320466315526, 5311055950464, 68840032788, -2067303075400, -3175046137632, 0, -3612044306496, 2911902739896, -996778170054, 4902137705580, 569347785936, -117328890420, 1135477483962, -1404501148752, -681948222498, -103432114214, 0, 1047539912148, -1122647820654, -2360852960688, 953534974320, 1594334177672, 1258132010616, 1006644915270, -1881526056894, 1562677992084, -1107083199744, 0, -2510205331494, -429640524000, 297682797828, -1424065103172, -681420350196, 702397247696, 778101432804, 378798061356, -367731590404, -2717925052032, 0, 860165186708, -53749620864, -22673054520, -4988678453682, 651078686184, -1874022415848, 986098470480, 4272071877828, 268276324428, -1340610430392, 0, -3822740597808, 854486023856, 3501065121168, 960363732618, 1683253039584, -377030376348, -179500043601, 147938266456, 3162259683510, 382822096644, 0, -1563242189742, -1967653278666, 2485367185284, -3890087475750, -375083514108, -4386287326182, 1506296300304, 1404987517440, 2025439779012, 190130306952, 0, 397733544908, 667107898068, -512044453260, 3623212226968, 2999665079046, -339147279720, -2284701584076, 306948448512, -2591333743086, 76047601300, 0, 27589503636, -791525927016, -799581096966, -635394010176, -1785317386544, -1198564359066, -658550389968, 2332569326412, 899977829868, -1592825623794, 0, 2415850615632, 843682954410, 4366519931616, 882900435300, -580909059828, -1410085532928, 5773275240084, 320279510268, 1717351061952, 1078845095712, 0, 3735006621304, -2058977194062, -325166646888, 953300294726, 4351279043682, 142309684323, -643928992574, -2582629863492, 91389246192, -3765807410562, 0, 18881051076, -782237207992, 4089950400204, 23784324840, 753820808316, -1171947481968, -1779619206204, -2187832006556, 6540326059200, -122523327108, 0, -1127451423978, 410940147474, 732705212616, -4989609748992, -1522470983076, 2487833567136, 1608371757672, -1594853862660, -1561007974264, -5149357379640, 0, -3971685833832, 2420626539696, -3820469226048, -227778170320, -5710624983792, 749437405488, -118629254760, 2037122615844, 793472341554, -2481945996860, 0, 2518657445160, -2294822563656, 2284007536470, 992101871736, 4430938981844, 5467979305740, 36767109168, -3464295661562, 1098856483374, -1044273185874, 0, -4847970655710, 1661462985024, -3705928250112, -1538943659484, 860640021369, 880557222656, -382508002152, 1659048706476, 5102044950447, 1395615407508, 0, 3758395965104, -1617381636918, -1026086290704, -6478065252192, -1523415725298, 844982231562, 1553758664140, -2804337109824, -264600464076, -199397140384, 0, 650623533300, 3444409538038, 2001782860956, 759727127304, -5758948250394, -1791667835352, -765706604436, 3549108435730, 2808964023624, -424711113480, 0, -1774630009956, -2776228092576, 178958498432, -1534122735036, -126040660578, -3598384815204, 1395911693136, 2007340157412, -1159856673528, -2207691810297, 0, -4581210047988, 327503703072, 2047177467738, 1347172381552, -5304283461840, 464933971332, -1264741132302, 1761342718656, -2253013543566, 1323027203146, 0, -990819054648, 1349000021116, -1960040500740, -394164475290, 1457166259440, 1311963860556, -1416642095358, 2182531942536, -189600521760, 2356944175440, 0, 2948877756102, -891833726520, -1915637979988, 2444086839120, 438330382686, -2984457704810, 4232982287034, 1053097916688, -1410557076924, 684271916160, 0, -4021904419152, 6753536467368, -1212055216272, 945122256084, 1600242175956, -1582682696712, -745034087092, -1284886200120, 375965376660, -3363367566936, 0, 2365692963570, -5199226237764, 2425106685360, 193377847068, 2073392314500, 301179624516, -5997488832, 279875536294, 3498300657510, 588312592992, 0, -959460855936, 590984691786, -2720154118552, -927967810668, -455926606254, -2080096004984, 3401793240660, -2164949938620, -663427288840, 971875708050, 0, 93749896032, 120079270500, -1171523538846, 4170006064984, -671143402452, 252285596136, -2071281063880, 1533002005752, -351669272112, -319942577688, 0, -832011934032, -1255700006118, 2803981731504, 2360088658944, -126673081408, 946050532536, -1247087554488, -1045885093074, -1906144344672, -362672917506, 0, 3547004183136, -3476409912252, -2761413848328, -5718957022584, -2123399995236, 1204512975832, -5331746908356, 384155315496, -6732690403306, -1887210340356, 0, 4681735752552, 7193626212240, -2519839182024, 1803178524546, -769086970272, 1690566390648, 1838123446020, 2453241366000, -2251032031764, 4956677431254, 0, -1236816256500, 172187023048, 6637039912704, 547182120582, 296270317572, -150952435392, -1189441066896, 5180653945216, -1290508468338, 3922926256188, 0, -2269055142786, -1550554582122, -1517522100788, -4522627284324, 1772316798624, 3791132225658, -917392650792, -4027915981152, -4756736942744, -114262644192, 0, 5943490915800, 2286364301328, -2445811286832, -609531165792, 1040100278856, -437113468980, 4439546310156, -4315586241756, -2618435731698, 1497746647760, 0, 629010171756, -5671724652256, -3393453792156, 364377763548, 1700115516884, -9711472464525, 792193825728, 31286611638, -1855268672604, -485894147310, 0, 706680251556, 1552088388564, -7981870993666, 4262587546764, 1421862810984, -3083312989936, -734514256050, 187777612638, 2756061365916, 359812093476, 0, -1164104317248, -3076459912314, 390213235512, 1023025359704, 2167073043990, -4456546080372, -5181440682084, 8563625172240, -676058265540, 5218931301120, 0, 218892576285, 2996540546314, 3644236294788, 1088657271576, -10760624998260, 2371642002732, -3322372786704, -1110542070532, 7986999538152, 625961100258, 0, 773551261386, -3209562850050, -1853910283896, 7742654436132, -678591653292, 5794729786810, 902453714208, -163437475572, 3029426374344, 3561311441904, 0, 414100749420, 2229544500432, -1519194899142, 410564818344, 3584225940036, 469066320954, -5296814939256, 1163982047040, 424084972788, 1120785463268, 0, 850239806454, -2999394252540, 1098927876264, 829746780858, 424639359188, 2731775297904, -3125817950508, -5698809859676, 323254365762, -1840133437884, 0, 6871836598884, 973160001324, 656710573422, 1165413082368, 5601155833080, 5624129391012, -8060980853628, -2413971495144, -1877903383248, -972162579300, 0, 1412613418400, -5433349566120, 2587807102608, -636299718624, -2280541270644, 1371164047200, -530009708524, -3354623048814, -498558994272, 11200852565820, 0, 3209554898712, 604062185888, 9259672273230, -1572799427280, 3962530032786, -2250167592936, -2022695072748, 666904108890, -1340502823584, 2125017412578, 0, 2745959346552, 1304652803940, 2601528978480, -1912671758400, -265112531496, 2506897086108, 1875915812640, -1975148590500], "weight": 8, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [-4, 1, 0, 0], [27, 0, 0, 0], [142, -2, 1, 0], [74, 10, 0, 1], [-108, 27, 0, 0], [-230, 32, 2, 2], [-646, 126, -1, 6], [729, 0, 0, 0], [2224, 70, 20, -14], [0, 0, 0, 0], [3834, -54, 27, 0], [514, -206, 28, -15], [8844, 18, 54, -16], [1998, 270, 0, 27], [16374, -398, 57, -90], [-8000, -842, 14, 21], [-2916, 729, 0, 0], [3430, -810, 126, -43], [-1948, 3740, -50, 188], [-6210, 864, 54, 54], [0, 0, 0, 0], [27864, 3414, 12, -149], [-17442, 3402, -27, 162], [18599, -1260, 280, 106], [-56376, 3710, -328, 378], [19683, 0, 0, 0], [-5472, 11432, -344, 292], [25452, 3254, 110, 349], [60048, 1890, 540, -378], [-7016, 3832, 744, 532], [-86774, 8222, -1113, 834], [0, 0, 0, 0], [-183436, -8564, -618, -210], [180884, 100, 780, -234], [103518, -1458, 729, 0], [-126982, 8708, -364, -610], [-228932, 17458, -1114, 1358], [13878, -5562, 756, -405], [673420, -13740, 3010, -1140], [-180316, -13602, -310, 1477], [238788, 486, 1458, -432], [56034, -25034, -2814, -119], [0, 0, 0, 0], [53946, 7290, 0, 729], [757696, 39660, 1936, 2158], [496912, 11674, 3428, 1677], [442098, -10746, 1539, -2430], [-193675, 4216, 540, -1336], [-419516, 46015, 80, 196], [-216000, -22734, 378, 567], [1121388, -69708, 3578, -5340], [250110, -74378, -3908, 1883], [-78732, 19683, 0, 0], [0, 0, 0, 0], [1815952, -31824, 7096, -4104], [92610, -21870, 3402, -1161], [708708, 36344, 6854, -4226], [348820, -54068, -11944, 582], [-52596, 100980, -1350, 5076], [-1016210, 66010, -56, 1057], [929744, 74184, 9896, -2984], [-167670, 23328, 1458, 1458], [414198, -168510, 8153, -6834], [-1679452, 100100, -5600, 1322], [0, 0, 0, 0], [439412, -36688, -1048, 3760], [-362636, -159436, -13074, -3456], [752328, 92178, 324, -4023], [-757416, 277180, -1460, 7956], [1378400, 62262, 4004, -7581], [-470934, 91854, -729, 4374], [-1425918, 94460, -8684, 6122], [2761808, -137150, 2244, 6356], [502173, -34020, 7560, 2862], [4975208, -252152, 13796, -20192], [0, 0, 0, 0], [-1522152, 100170, -8856, 10206], [1925610, 18508, 10722, -16], [-6158316, 543740, -15730, 9956], [531441, 0, 0, 0], [-2737764, -278928, 858, -22538], [-909448, 186716, -19220, -16670], [-147744, 308664, -9288, 7884], [-1430656, -202160, -15300, 3556], [-6349644, -317602, -29038, -15218], [687204, 87858, 2970, 9423], [0, 0, 0, 0], [1121490, 107288, -18280, 6580], [1621296, 51030, 14580, -10206], [-2325516, 243332, -26036, 6982], [3274352, 572808, 61640, 476], [-189432, 103464, 20088, 14364], [662912, 877660, 31872, -2910], [-5561860, 398540, -20900, 9130], [-2342898, 221994, -30051, 22518], [414422, -269112, -13116, 27384], [1828004, -90539, -8604, 21944], [0, 0, 0, 0], [10974722, -161630, 12215, -15832]]}