{"label":"60.8.a","level":60,"weight":8,"dims":{"new":4,"cusp":78,"eisenstein":12,"modsym":168},"old":[[2,1,8],[3,1,6],[5,3,6],[6,1,4],[10,1,4],[12,2,2],[15,4,3],[20,3,2],[30,6,2]],"T":[[7,1],[11,1]],"status":"proven","checks":["dim M^+ at levels [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]: [1, 3, 3, 5, 5, 9, 13, 17, 16, 24, 46, 90] (certified at ell = 2147483629)","T = [(7, 1), (11, 1)]; h of degree 4 = 1 x 4 (phi(ord eps) x dim S_k^new); 2 primes, 0 rejected"],"newforms":[{"label":"60.8.a.a","letter":"a","dim":1,"charpoly":["-4124","1"],"traces":["1","0","-27","0","-125","0","1028","0","729","0","3096","0","-13030","0","3375","0","1878","0","-31180","0","-27756","0","-33288","0","15625","0","-19683","0","-213054","0","-172696","0","-83592","0","-128500","0","27434","0","351810","0","532650","0","-911908","0","-91125","0","-732648","0","233241","0","-50706","0","409074","0","-387000","0","841860","0","1508136","0","-302578","0","749412","0","1628750","0","1254332","0","898776","0","4781280","0","-502414","0","-421875","0","3182688","0","-1991368","0","531441","0","-8099268","0","-234750","0","5752458","0","7487970","0","-13394840","0","4662792","0","3897500","0","-17172574","0","2256984","0","-9744342","0","-16985452","0","3469500","0","-12038556","0","11825102","0","-740718","0","17386206","0","4161000","0","-9498870","0","1930584","0","-9901955","0","-14381550","0","-1953125","0","-14389972","0","24621516","0","-18058968","0","-32053040","0","2460375","0","45130374","0","13477604","0","19781496","0","-40340880","0","26631750","0","-6297507","0","73174002","0","-3515560","0","1369062","0","21587000","0","48402266","0","-11044998","0","-34220064","0","7465580","0","10449000","0","11290824","0","107032383","0","-22730220","0","-98920902","0","16062500","0","-40719672","0","77014416","0","106545590","0","8169606","0","-3429250","0","5814288","0","-20234124","0","-29853096","0","-79635862","0","-43976250","0","-88220718","0","113662952","0","-33866964","0","-219019512","0","-66581250","0","-24266952","0","-96533280","0","-75445540","0","-129094560","0","113988500","0","-177531488","0","13565178","0","-24470340","0","169317980","0","11390625","0","13250580","0","144713534","0","-85932576","0","213204750","0","91581000","0","53766936","0","-336644328","0","-240329182","0","-14348907","0","-29155125","0","406275400","0","218680236","0","87523488","0","-103059648","0","6338250","0","105874494","0","28202152","0","-155316366","0","28154232","0","-51134250","0","-202175190","0","-380407806","0","613367984","0","361660680","0","48375000","0","-286406614","0","-125895384","0","438704706","0","485746916","0","-105232500","0","547564200","0","-406811789","0","463659498","0","376441266","0","-188517000","0","-60938568","0","433742640","0","-937441424","0","263097234","0","37822250","0","-822473836","0","458607204","0","-461865216","0","299153138","0","-93676500","0","625970778","0","-659615184","0","325041012","0","-58556040","0","-203593750","0","-319277754","0","-753162144","0","1121890652","0","19999386","0","-156791500","0","-206060326","0","-469427562","0","-534666816","0","-606830456","0","-112347000","0","520291164","0","-1253626066","0","256469490","0","-354823434","0","-597660000","0","-52125768","0","-1649046984","0","78320661","0","267352785","0","62801750","0","-396700132","0","388301850","0","420528072","0","-220144798","0","52734375","0","2776093620","0","605423492","0","388529244","0","-1188024","0","-397836000","0","-664780932","0","-2160646446","0","-62514864","0","487592136","0","248921000","0","-1307621086","0","865432080","0","1233182586","0","2250228880","0","-66430125","0","84935664","0","2743385834","0","-1218520098","0","1550363808","0","1012408500","0","-363895308","0","-1575475272","0","-515395810","0","-534100392","0","29343750","0","-311050184","0","1089203760","0","920460528","0","901254458","0","-719057250","0","1037919840","0","757868552","0","170032689","0","-2212697652","0","-935996250","0","-1975698054","0","2655059322","0","1649084400","0","94920120","0","1674355000","0","3388120010","0","-36964674","0","-2551761174","0","940848836","0","-582849000","0","-2811975396","0","1289453296","0","-1306861182","0","-2823267168","0","-487187500","0","298214946","0","-4411400664","0","-357465020","0","923941728","0","2146571750","0","-1584819604","0","-201570660","0","-2252658096","0","-400115412","0","-282123000","0","4915155840","0","3213768596","0","-304852248","0","-1466726832","0","1218042750","0","-2889874341","0","-622222782","0","-516481592","0","613715940","0","2123181500","0","-2268278208","0","2670864354","0","-3800295678","0","-3048892204","0","-433687500","0","-324323088","0","-2296734503","0","1099431144","0","-6940429500","0","1504819500","0","-2079389232","0","722114136","0","-4906207282","0","-2876730930","0","-1478137750","0","-4243620124","0","-220579362","0","6643023720","0","-2047126304","0","92589750","0","6833967546","0","11882161240","0","-156985776","0","-5195749500","0","-2173275750","0","546321348","0","4990968834","0","5636238380","0","806033592","0","-520125000","0","234583106","0","2150168274","0","-8326047504","0","1266493104","0","1187358750","0","6816900228","0","5384661280","0","2381959386","0","7447609422","0","-241323000","0","-3068899704","0","-4833391176","0","3346450298","0","914408028","0","1237744375","0","-8463265996","0","5913526824","0","9546403440","0","-6103814614","0","1797693750","0","1775213502","0","-8842197004","0","655207704","0","7697633160","0","244140625","0","2606398560","0","51521052","0","-5569940368","0","2037029580","0","1798746500","0","-3039130230","0","3485553120","0","-11710261566","0","-6053687572","0","-3077689500","0","11677492704","0","4669189056","0","4793350176","0","-8812482918","0","2257371000","0","-366259806","0","1839405672","0","-5814265162","0","660699180","0","4006630000","0","7092141552","0","-4571585460","0","-936781488","0","8531290970","0","-307546875","0","-10339924302","0","-17653406072","0","-357765660","0","-7041123372","0","-5641296750","0","-3907265418","0","-5330234220","0","4872290228","0","2320179552","0","-1684700500","0","1000316700","0","-5756528250","0","14454695586","0","-855392120","0","-2472687000","0","-10017183576","0","-4764423634","0","-1451707272","0","5748704448","0","5042610000","0","9089396856","0","3592961952","0","-17461044656","0","6488887914","0","-3328968750","0","-13451704084","0","387420489","0","-1712563224","0","12139217762","0","787188375","0","3883411872","0","-3591244060","0","-10969435800","0","13084668768","0","-9146750250","0","-5904366372","0","-12375635568","0","8097432152","0","-2363134176","0","439445000","0","16583690282","0","2782610496","0","-2341970718","0","12156204856","0","-171132750","0","-19651012080","0","1384318658","0","-2858611338","0","12389640834","0","-2698375000","0","-761458104","0","-16608027000","0","14802842880","0","4193541882","0","-6050283250","0","3447757916","0","-760164264","0","17873019768","0","3942591340","0","1380624750","0","-1581774774","0","-1375912944","0","5458730130","0","-1555473744","0","4277508000","0","10271010762","0","6062803674","0","10924117940","0","-16560935568","0","-933197500","0","28433291440","0","-9764838360","0","9108303786","0","-2134105684","0","-1306125000","0","17465729916","0","21679664798","0","7732978578","0","438026598","0","-1411353000","0","3399175368","0","-15195644664","0","28142130607","0","-11845027062","0","-13379047875","0","-10179209740","0","-13115166732","0","-913222992","0","18879044954","0","2841277500","0","-2491050834","0","-16151967580","0","-14784233400","0","19187602464","0","12365112750","0","10983918303","0","-6165275328","0","-16343945960","0","-12518806446","0","-2007812500","0","20495942522","0","-10163914182","0","-20716780950","0","-5289801556","0","5089959000","0","-26747889912","0","-14792891216","0","1645341336","0","22843964640","0","-9626802000","0","-11711051280","0","36793573584","0","768240972","0","25310918448","0","-13318198750","0","316031804","0","-7103625318","0","-18274703232","0","-25075333728","0","-1021200750","0","-18564619104","0","-40701820048","0","22206793572","0","-62300078400","0","428656250","0","-12382394508","0","39374315322","0","-7272454380","0","12470360832","0","-726786000","0","-24096867286","0","-8077134726","0","-15722861670","0","-17730853200","0","2529265500","0","-11179511676","0","6546454420","0","-16901211006","0","7023714918","0","3731637000","0","17809609968","0","46394024472","0","2311294305","0","-8776107324","0","9954482750","0","8098202660","0","1581013080","0","35185046928","0","13854976912","0","5497031250","0","-35851786074","0","23182755120","0","8620499358","0","-18681400224","0","11027589750","0","20335377888","0","30355593504","0","-6864955312","0","-30291047604","0","-14207869000","0","4820856002","0","-539983422","0"],"derived":{"al":[[2,null],[3,1],[5,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"60.8.a.b","letter":"b","dim":1,"charpoly":["-2324","1"],"traces":["1","0","-27","0","125","0","-832","0","729","0","3156","0","-7690","0","-3375","0","258","0","45740","0","22464","0","104832","0","15625","0","-19683","0","38646","0","192224","0","-85212","0","-104000","0","403454","0","207630","0","86010","0","-127348","0","91125","0","601272","0","-131319","0","-6966","0","-1628226","0","394500","0","-1234980","0","198996","0","1209782","0","-606528","0","-961250","0","-699388","0","-2830464","0","-4939320","0","-1275334","0","-421875","0","-2625792","0","6559712","0","531441","0","-3108348","0","32250","0","-1043442","0","5542410","0","6398080","0","-5190048","0","5717500","0","4513346","0","2300724","0","-10958802","0","16018448","0","2808000","0","7601244","0","20953382","0","-10893258","0","-9605694","0","13104000","0","-5606010","0","-214656","0","-9526835","0","-2322270","0","1953125","0","15012488","0","3438396","0","32631132","0","-38055680","0","-2460375","0","-40021686","0","46742324","0","-16234344","0","-24269640","0","4830750","0","3545613","0","39385182","0","-63991960","0","188082","0","24028000","0","-43934554","0","43962102","0","-87220224","0","-91916140","0","-10651500","0","-12538176","0","-3612417","0","33344460","0","-104411322","0","-13000000","0","-5372892","0","71078076","0","48692030","0","-32664114","0","50431750","0","814248","0","16376256","0","102523824","0","-22960702","0","25953750","0","170675502","0","-18512728","0","18883476","0","-32153472","0","10751250","0","76422528","0","144355440","0","-126039460","0","133361640","0","-15918500","0","-159930368","0","34434018","0","-1984020","0","-167908360","0","11390625","0","256474020","0","328302254","0","70896384","0","114740490","0","75159000","0","-177112224","0","-252620208","0","-8471662","0","-14348907","0","-16414875","0","-351740600","0","83925396","0","-312793212","0","330849792","0","-870750","0","-71277006","0","-335673728","0","28172934","0","139551792","0","-203528250","0","-149645070","0","-285983706","0","164573264","0","-172748160","0","49312500","0","486667886","0","140131296","0","-86677494","0","52594076","0","-154372500","0","-71560320","0","-410272109","0","-121860342","0","-147536274","0","24874500","0","-62119548","0","-806158080","0","105953536","0","295887654","0","151222750","0","-303686476","0","-432498096","0","327473304","0","765611498","0","-75816000","0","526544118","0","121966776","0","-205233588","0","11800920","0","-120156250","0","-565741314","0","-500258304","0","439450532","0","294117966","0","-87423500","0","1122390674","0","259353738","0","606658944","0","794445184","0","-353808000","0","1238637804","0","1550594294","0","151362270","0","-945768654","0","-617415000","0","5795712","0","-1634654184","0","1198275861","0","257224545","0","-159416750","0","-1123264552","0","62701290","0","1354684032","0","1428674702","0","-52734375","0","-297187740","0","-777825148","0","-405337176","0","1462985496","0","-328224000","0","-92836692","0","-1583321106","0","27046656","0","-881040564","0","819964000","0","-1127252746","0","1027503360","0","-2489084814","0","-1478202560","0","66430125","0","1273300824","0","-1452321046","0","1080585522","0","-165564672","0","-388543500","0","-1262042748","0","-276421812","0","-1738777330","0","438327288","0","4031250","0","-1006538624","0","655280280","0","-326210112","0","-745470382","0","-130430250","0","4795015680","0","1751919992","0","-95731551","0","-1660101732","0","692801250","0","-1063399914","0","-2950351998","0","271447560","0","1727782920","0","799760000","0","-1996000390","0","-5078214","0","-1965763194","0","-425970904","0","-648756000","0","-350650956","0","581890816","0","1186232958","0","-401910288","0","714687500","0","-1186976754","0","3460747776","0","-3102561260","0","2354946048","0","564168250","0","-3286790944","0","2481735780","0","3802262964","0","9970668","0","287590500","0","4109514240","0","-821368084","0","338530752","0","-2594270112","0","-1369850250","0","97535259","0","3761353878","0","1061077888","0","-900300420","0","2002306000","0","1897614432","0","2819105694","0","-5558861958","0","1412922956","0","351000000","0","49593792","0","7584922777","0","145068084","0","-661416900","0","950155500","0","-1919108052","0","-414442764","0","1546868438","0","-1314684810","0","2619172750","0","-5265078364","0","881931078","0","1767668040","0","-5457680384","0","-1361657250","0","5299646406","0","979306120","0","-21984696","0","-4826567100","0","-1200711750","0","-442158912","0","-6049190646","0","1563328820","0","-2768143248","0","1638000000","0","5788470146","0","619938954","0","2586145536","0","-5138681256","0","-700751250","0","-99822372","0","8792325760","0","-4608238554","0","-5190677598","0","-26832000","0","499843656","0","-9964012536","0","-6853111702","0","-509853852","0","-1190854375","0","-5510385976","0","868143744","0","-4623781680","0","3783844766","0","-290283750","0","-1543291638","0","3539133236","0","-2063408256","0","-4611285120","0","244140625","0","-3897596880","0","104091132","0","-1806253528","0","3403065420","0","1876561000","0","1009843110","0","-3600764280","0","2739036834","0","6586464308","0","429799500","0","-3908697696","0","628031376","0","4318119936","0","4432524102","0","4078891500","0","-929718486","0","4088985852","0","11551942238","0","53568540","0","-4756960000","0","4051337472","0","4533525720","0","3818071992","0","1258209890","0","-307546875","0","2844924078","0","-3755103872","0","-6924798540","0","-11254163412","0","-5002710750","0","-8864160858","0","12521057940","0","11601917468","0","-1914202368","0","5842790500","0","22190580","0","-3097993230","0","-14797615434","0","18453985960","0","-2029293000","0","9117723264","0","-5609116594","0","4782030048","0","20151226368","0","-3033705000","0","6820745616","0","-17757867408","0","-13327348736","0","228734874","0","603843750","0","11268824336","0","387420489","0","-32855784","0","4404440102","0","443201625","0","-2207268528","0","-11136387940","0","9496996200","0","20912394768","0","4923147750","0","-2265985692","0","-6324235008","0","11885816912","0","8445416724","0","-7998995000","0","-3688964338","0","-8932944384","0","5449582602","0","-17433213824","0","23510250","0","-1530279240","0","-13599901822","0","1924479162","0","2479482414","0","3003500000","0","9063190656","0","3934097400","0","-15588493920","0","-760669218","0","-5491819250","0","-19064531404","0","-3767898384","0","7991937408","0","-9303223580","0","5495262750","0","14137315446","0","155128176","0","4040416890","0","-4024954104","0","-10902528000","0","7721560062","0","-12259987206","0","10144329380","0","-4443478128","0","-11489517500","0","-5824897520","0","4664200320","0","-10964608194","0","7729406816","0","-1331437500","0","-28037902164","0","-22930857322","0","-13140032922","0","-33880302","0","-1567272000","0","-3783544992","0","-3416182824","0","-15756362993","0","2340292338","0","-451552125","0","7926326720","0","-1420040052","0","42294889728","0","5732912174","0","4168057500","0","-11748388134","0","-6751913980","0","1932128640","0","-5997173256","0","-13051415250","0","11077346943","0","20702451072","0","5378293720","0","3290229234","0","-1625000000","0","-8044751338","0","3983479398","0","18045281970","0","-5336619676","0","-671611500","0","8241372048","0","-12490390016","0","1677227796","0","27502181280","0","8884759500","0","21766268160","0","7428688704","0","-420082308","0","-2860745472","0","6086503750","0","30111522524","0","-7988966658","0","-8871978912","0","-9809946288","0","-4083014250","0","-27149101824","0","-1755428488","0","8199534852","0","37983370800","0","6303968750","0","11677448592","0","41219920482","0","-6006531060","0","-8841779208","0","101781000","0","34168841594","0","-20671510446","0","-25399386330","0","9016600320","0","2047032000","0","-23608600716","0","9807318460","0","-14216691186","0","-44609682342","0","12815478000","0","-3293102952","0","33298042752","0","9437452065","0","5541306876","0","-2870087750","0","41242540640","0","-318624840","0","-274033452","0","-38889613568","0","3244218750","0","-24296882814","0","17491845960","0","15275015478","0","-1316402304","0","21334437750","0","13506974208","0","-13350145536","0","73758848","0","-11865164364","0","-2314091000","0","-3661968898","0","-7941185082","0"],"derived":{"al":[[2,null],[3,1],[5,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"60.8.a.c","letter":"c","dim":1,"charpoly":["-3548","1"],"traces":["1","0","27","0","-125","0","92","0","729","0","3456","0","4610","0","-3375","0","17502","0","-1300","0","2484","0","14088","0","15625","0","19683","0","174306","0","189824","0","93312","0","-11500","0","279506","0","124470","0","357690","0","-283852","0","-91125","0","101688","0","-815079","0","472554","0","-392574","0","-432000","0","-35100","0","-539904","0","-1946338","0","67068","0","-576250","0","-1855852","0","380376","0","1683840","0","-4110046","0","421875","0","317952","0","-4565008","0","531441","0","5444868","0","-2187750","0","4706262","0","-5461230","0","424120","0","5125248","0","162500","0","-12074686","0","2519424","0","4871658","0","18036572","0","-310500","0","17989836","0","-14603218","0","7546662","0","23766054","0","-1761000","0","3360690","0","1610184","0","-7543235","0","9657630","0","-1953125","0","15929732","0","-7664004","0","10040112","0","-119600","0","-2460375","0","-26927874","0","-50811556","0","2745576","0","15932160","0","-21788250","0","-22007133","0","-74708238","0","16549760","0","12758958","0","-23728000","0","-8176846","0","-10599498","0","1296096","0","55190420","0","-11664000","0","35492616","0","-41496417","0","-947700","0","-1528518","0","1437500","0","-14577408","0","-118498344","0","99982070","0","-52551126","0","-34938250","0","60486912","0","1810836","0","24292344","0","77243642","0","-15558750","0","45913698","0","94614272","0","-50108004","0","16036152","0","-44711250","0","10270152","0","-4492800","0","147535940","0","45463680","0","35481500","0","17463808","0","-110971242","0","80684220","0","198780020","0","11390625","0","99239100","0","108136814","0","8584704","0","99408390","0","-12711000","0","-123255216","0","-272892648","0","-37744222","0","14348907","0","101884875","0","-5993000","0","147011436","0","-305522712","0","48688128","0","-59069250","0","-23613114","0","25714552","0","127069074","0","-515452392","0","49071750","0","-147453210","0","221615874","0","-530499976","0","11451240","0","54000000","0","-472381246","0","138381696","0","17620626","0","-444980596","0","4387500","0","32907480","0","-104018669","0","-326016522","0","88638114","0","67488000","0","68024448","0","64945680","0","-26114384","0","131534766","0","243292250","0","-10457044","0","486987444","0","-326497296","0","-771915838","0","-8383500","0","1068567882","0","602401536","0","485725572","0","-22752600","0","72031250","0","-394286886","0","9355296","0","251333972","0","203759874","0","231981500","0","-1107524374","0","641683458","0","656031744","0","-150753224","0","-47547000","0","893011476","0","877237694","0","90738630","0","-1387801746","0","-210480000","0","43474968","0","594438456","0","-892181739","0","-203667345","0","513755750","0","255831332","0","260756010","0","-36116808","0","-441416422","0","-52734375","0","803550660","0","1875047372","0","430102764","0","-1114756296","0","-39744000","0","-206928108","0","-799670766","0","246568176","0","271083024","0","570626000","0","-1333290454","0","-3229200","0","-926018214","0","875088640","0","-66430125","0","965972736","0","-1271982166","0","-727052598","0","-49671168","0","-680608500","0","-1371912012","0","-1444700592","0","75120110","0","74130552","0","273468750","0","-179063096","0","430168320","0","-2055680352","0","-832011478","0","-588282750","0","-18314400","0","1295938592","0","-594192591","0","-714205788","0","682653750","0","-2017122426","0","-3424907238","0","1236176640","0","446843520","0","-53015000","0","-1332620470","0","344491866","0","1637783466","0","4000880444","0","-640656000","0","3260732196","0","-170738384","0","-220774842","0","-980992512","0","-20312500","0","-286186446","0","-2378498664","0","1288522660","0","34994592","0","1509335750","0","2668250564","0","1490141340","0","-1875601656","0","3050703612","0","-314928000","0","154913280","0","3138850076","0","958300632","0","4234456512","0","-608957250","0","-1120403259","0","-3736074462","0","-378124232","0","-25587900","0","-2254571500","0","351433728","0","-41269986","0","3942228642","0","2982336044","0","38812500","0","3322299648","0","-3206353703","0","-393590016","0","1648950900","0","-2248729500","0","-3199455288","0","-2816913024","0","5878721678","0","2699515890","0","1825402250","0","-579084436","0","-1418880402","0","-226597800","0","-419980736","0","-943332750","0","6351576474","0","-1308557720","0","1633146624","0","-6240225780","0","-2970756750","0","48892572","0","-6398904126","0","-3801697660","0","655893288","0","220125000","0","-6840110686","0","2085578334","0","500927856","0","-1356735744","0","-420086250","0","4759439532","0","-246771200","0","1239669846","0","810892278","0","-201273000","0","2554585344","0","-4613140296","0","3053983418","0","-1352916108","0","942904375","0","-5880835444","0","432976104","0","468781680","0","1300450034","0","-1207203750","0","-4881625482","0","-5895074644","0","277294104","0","-502433160","0","244140625","0","-121305600","0","4891914012","0","-9716849128","0","3983470380","0","-1991216500","0","-3757514190","0","1227519360","0","-548066286","0","-5141878348","0","958000500","0","9081115536","0","-1865908224","0","471522816","0","1121099898","0","-1255014000","0","-2996223534","0","-1510108848","0","6309186278","0","2178473940","0","14950000","0","2455622928","0","5367060540","0","-6726544128","0","-1085627350","0","307546875","0","-169724718","0","-1110871112","0","2679455700","0","7272078252","0","3365984250","0","2919693978","0","-1809766140","0","-7067497492","0","231787008","0","6351444500","0","6260290380","0","2684026530","0","15397156866","0","-363357800","0","-343197000","0","448192536","0","14953059326","0","-3327890832","0","2674240512","0","-1991520000","0","-7368101496","0","18530806992","0","1659364624","0","-1019093994","0","2723531250","0","3154914404","0","387420489","0","-4967977704","0","-112401382","0","2750891625","0","-6413824512","0","8310631340","0","-161811000","0","-10025222208","0","9338529750","0","3969308772","0","1655064912","0","-16241036368","0","-8249113224","0","-2068720000","0","-10338847582","0","1314579456","0","-12913089918","0","-1343496056","0","-1594869750","0","-2488957440","0","1768160738","0","-637554078","0","-11174400654","0","2966000000","0","694292904","0","-464997000","0","5819351040","0","3430864998","0","1022105750","0","13832705924","0","-13917214584","0","2186476968","0","-8972618180","0","1324937250","0","-26708360406","0","1779743376","0","-3981236670","0","-14204318976","0","-162012000","0","5983628598","0","15378060714","0","15770896220","0","-14323499352","0","-6898802500","0","369007600","0","309183480","0","-25993621494","0","-7212352156","0","1458000000","0","13695508164","0","11016103358","0","-12754293642","0","-14265512658","0","-4436577000","0","3736305792","0","17469296616","0","13132705327","0","475756902","0","5187052125","0","-693977620","0","-12014476092","0","3937680528","0","-2437734334","0","118462500","0","-21549877866","0","16672868780","0","888501960","0","8904774576","0","191064750","0","-2808504063","0","-15776667648","0","-8555477720","0","-8802446094","0","-179687500","0","1580474258","0","2393229078","0","25020275130","0","-9575008204","0","1822176000","0","-11074364568","0","1465535344","0","1836660096","0","-132194400","0","14812293000","0","1753533360","0","33087462144","0","-6870830148","0","-705088368","0","-12497758750","0","27785844116","0","3551438682","0","2920663968","0","18817463808","0","6568890750","0","923690304","0","-25183599208","0","-282340188","0","7762502400","0","4367281250","0","13148660988","0","20718285882","0","1059602700","0","-8815426992","0","-7560864000","0","46104316106","0","-20841727626","0","-1375473510","0","5039136720","0","-226354500","0","-32820585444","0","-18947312060","0","28851332814","0","51312303582","0","-3036543000","0","16264841472","0","-2477364408","0","8520536865","0","13114590444","0","-9655455250","0","-20948126260","0","-614320200","0","24962537688","0","-4674663152","0","1944843750","0","-16520321106","0","-18874010880","0","-10645745922","0","44010535104","0","-5739212250","0","252592992","0","-3998906976","0","-18142132792","0","6786017244","0","-11826784000","0","2649641498","0","5501516598","0"],"derived":{"al":[[2,null],[3,-1],[5,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"60.8.a.d","letter":"d","dim":1,"charpoly":["5452","1"],"traces":["1","0","27","0","125","0","-1408","0","729","0","-4044","0","-5890","0","3375","0","31002","0","-40300","0","-38016","0","-78912","0","15625","0","19683","0","-157194","0","114824","0","-109188","0","-176000","0","-471994","0","-159030","0","-404310","0","-253852","0","91125","0","437688","0","1158921","0","837054","0","334926","0","-505500","0","-1088100","0","562596","0","3246662","0","-1026432","0","-736250","0","3895148","0","-2130624","0","-2345160","0","5726954","0","421875","0","5693952","0","-5222008","0","531441","0","-2928132","0","3875250","0","-4244238","0","-3160230","0","8293120","0","3100248","0","-5037500","0","-1898686","0","-2948076","0","-9829842","0","5891072","0","-4752000","0","-22537164","0","3291782","0","-12743838","0","23374554","0","-9864000","0","-4293810","0","-43650816","0","-3133235","0","-10916370","0","1953125","0","16564232","0","-6854004","0","34005612","0","56742400","0","2460375","0","1408626","0","-29949556","0","11817576","0","23819160","0","-19649250","0","31290867","0","-39372738","0","-12628240","0","22600458","0","14353000","0","31610654","0","9043002","0","111108096","0","-1746580","0","-13648500","0","74141616","0","-28056417","0","-29378700","0","-32805018","0","-22000000","0","15190092","0","-83747844","0","93211070","0","87659874","0","-58999250","0","-125372088","0","-27713664","0","-48070656","0","17222642","0","-19878750","0","-30728802","0","-181385728","0","105168996","0","221329152","0","-50538750","0","-57526848","0","162973200","0","-108304060","0","-63319320","0","-31731500","0","-161672192","0","154627758","0","-182601780","0","-225721480","0","11390625","0","271001100","0","-276697186","0","153736704","0","-215356110","0","54711000","0","-140994216","0","-412011648","0","-42490222","0","14348907","0","144865125","0","237367000","0","-79059564","0","57304788","0","319120128","0","104631750","0","176317386","0","664567552","0","-114594426","0","237052608","0","41865750","0","-85326210","0","100666374","0","28976024","0","223914240","0","-63187500","0","-338054746","0","83706696","0","-336322374","0","33132404","0","-136012500","0","569268480","0","550785331","0","-51264522","0","-502960386","0","70324500","0","-79598052","0","464791680","0","357423616","0","-265405734","0","405832750","0","-619829044","0","159058944","0","327307704","0","75755162","0","-128304000","0","-889914618","0","635692536","0","-608503428","0","-1249380600","0","-92031250","0","88878114","0","-616264704","0","-475587028","0","-344083626","0","486893500","0","778710626","0","631112958","0","-464348256","0","-472212224","0","-266328000","0","299149476","0","1281922694","0","-115932870","0","-1065894246","0","-293145000","0","-1178572032","0","-778277544","0","730218261","0","-84597345","0","715869250","0","766621832","0","-294741990","0","-471575808","0","-765360922","0","52734375","0","925872660","0","-808440628","0","447234264","0","-242686296","0","711744000","0","-185058108","0","-1223989266","0","-2446429824","0","918151524","0","-652751000","0","-114697954","0","1532044800","0","2388216786","0","-676313360","0","66430125","0","1908743736","0","2734265834","0","38032902","0","-792135168","0","-366016500","0","-808638012","0","2138728908","0","1462254110","0","319074552","0","484406250","0","-4571300096","0","643117320","0","-2297834352","0","2511707522","0","-530529750","0","3180153600","0","885268592","0","844853409","0","2547652212","0","-395028750","0","-1063063926","0","-1478846238","0","1635029640","0","-340962480","0","1036640000","0","-2493746470","0","610212366","0","-2780243034","0","2439501944","0","387531000","0","3092021196","0","-5484368384","0","853487658","0","1026577488","0","-629687500","0","244161054","0","-4537517664","0","2780044660","0","2999918592","0","-237335750","0","-1009249936","0","-47157660","0","-2812986156","0","-4873328388","0","-368509500","0","3301985280","0","-2572288924","0","2001823632","0","-3112573488","0","-1228730250","0","-757523259","0","-3299845962","0","-8063551232","0","-793224900","0","736384000","0","-1770010272","0","-885735486","0","4623183642","0","2141781044","0","-594000000","0","3559773648","0","2822278297","0","410132484","0","2381385900","0","-2817145500","0","-2261191788","0","-4686676524","0","222350678","0","2516698890","0","411472750","0","3099215564","0","2366816598","0","6334918200","0","7352587264","0","-1592979750","0","-5673748026","0","1495188280","0","-3385046376","0","-2920893780","0","2921819250","0","-748268928","0","-8372187126","0","5150749340","0","-1297907712","0","-1233000000","0","-1049474686","0","465011334","0","4122809856","0","-1354440744","0","-536726250","0","5340260532","0","-4627407200","0","-829677654","0","1571402778","0","-5456352000","0","-4897414656","0","6493273704","0","6405325418","0","2839562892","0","-391654375","0","7677300056","0","5975887104","0","-2577982320","0","7850222534","0","-1364546250","0","218100018","0","9023037356","0","-1553224896","0","4449603840","0","244140625","0","4400276400","0","-14632757988","0","5587035872","0","-2924209620","0","2070529000","0","-6826044690","0","-1709621640","0","3298461714","0","-1924387348","0","-856750500","0","-572440464","0","-2275138224","0","-4365149184","0","-1547632602","0","4250701500","0","4174949466","0","3707828652","0","-2935244722","0","-4930248060","0","7092800000","0","12404492928","0","-6094479960","0","-13129501128","0","-7090598350","0","307546875","0","369688782","0","2673349888","0","7317029700","0","-14101472748","0","176078250","0","-7470824022","0","-1972714140","0","-8612158492","0","4150891008","0","-3743694500","0","-12534418620","0","-5814614970","0","-10074350634","0","19021358200","0","1477197000","0","13840417536","0","18191391326","0","-3806843832","0","-9060991488","0","2977395000","0","-11124314496","0","-630763008","0","-8294629376","0","-1147235994","0","-2456156250","0","-12094384096","0","387420489","0","-7869919704","0","-17893066882","0","3911358375","0","-15751978512","0","-12375535660","0","6408909000","0","13074243792","0","-4921592250","0","-2134608228","0","31732326912","0","5290320632","0","1547229276","0","-1578530000","0","-8944797082","0","8616243456","0","22577543082","0","-4634829056","0","2825057250","0","-3313690440","0","-786783262","0","4760569422","0","2857662846","0","1794125000","0","17943323904","0","16293693000","0","9483827040","0","-3094049502","0","3951331750","0","10917722924","0","6400420416","0","-32911372032","0","-19122839180","0","1130375250","0","14416991094","0","13569203376","0","-2303807670","0","-23159801976","0","13888512000","0","2717992098","0","10953612714","0","-16187629780","0","782352648","0","-218322500","0","10230235600","0","6045684480","0","3296331006","0","-5473508656","0","-1706062500","0","-2648041836","0","-9412933642","0","-9127478142","0","35928868842","0","9267702000","0","2260080792","0","645230616","0","7460077327","0","-9080704098","0","-3507052125","0","4411594880","0","894574908","0","37245990528","0","-22445197834","0","-3672337500","0","-13743960366","0","-3199095220","0","15370248960","0","-8086868424","0","-4100627250","0","14871203937","0","21117800352","0","-22942421720","0","-1384142094","0","-2750000000","0","12536703758","0","-13579930422","0","-5176443870","0","-28571851204","0","1898761500","0","-14675621568","0","-23322438656","0","-2149147404","0","-17638826400","0","-10468480500","0","12549375360","0","-18049643856","0","10383375852","0","9650437632","0","11651383750","0","-2659211884","0","-7165954818","0","35046691968","0","11841365808","0","10957484250","0","-47879901696","0","23954123792","0","-16735384188","0","13812992400","0","-7374906250","0","4294591488","0","25592910882","0","-46704516300","0","8837308008","0","-15671511000","0","-4512553894","0","2045389374","0","5615805990","0","31904910720","0","-3464208000","0","-35215191444","0","-33731759060","0","-24027694686","0","-23657169918","0","-6008832000","0","17163698472","0","-1983345408","0","-14328063135","0","-16429592556","0","2152830250","0","12786344240","0","-33733276200","0","-8301430812","0","42168974848","0","-2484843750","0","-48233805606","0","12779970120","0","2399709078","0","19164355104","0","-3841100250","0","-16639147008","0","20031969024","0","54456853208","0","-12840849756","0","-22673216000","0","22388058998","0","-9290257902","0"],"derived":{"al":[[2,null],[3,-1],[5,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.362,"computed":"atlas","estimate":{"seconds":0.881,"low":0.537,"high":1.524,"bytes":2079109},"url":"https://sagebrush.space/atlas/mf/60.8.a"}