{"label":"51.6.a","level":51,"weight":6,"dims":{"new":14,"cusp":28,"eisenstein":4,"modsym":60},"old":[[3,1,2],[17,6,2]],"T":[[2,1],[5,1]],"status":"proven","checks":["dim M^+ at levels [1, 3, 17, 51]: [1, 3, 8, 32] (certified at ell = 2147483489)","T = [(2, 1), (5, 1)]; h of degree 14 = 1 x 14 (phi(ord eps) x dim S_k^new); 4 primes, 0 rejected"],"newforms":[{"label":"51.6.a.a","letter":"a","dim":2,"charpoly":["2295","120","1"],"traces":["2","-7","18","33","-113","-63","0","-399","162","758","297","297","-1479","-2320","-1017","993","578","-567","-2147","-4402","0","-1692","-6395","-3591","1947","8294","1458","16240","-4584","6822","-1110","8785","2673","-2023","-11600","2673","14790","18172","-13311","25806","-15435","-20880","3723","9468","-9153","38840","5286","8937","40626","-47777","5202","-46226","-21120","-5103","-20043","-20880","-19323","22134","10002","-39618","-56654","47240","0","-45631","99151","-15228","-25776","9537","-57555","171680","-145996","-32319","28760","15950","17523","-110028","20880","74646","-28990","-58642","13122","35970","-82606","146160","-32657","73172","-41256","-65124","37558","61398","-99760","-220720","-9990","-50256","174593","79065","85714","-142191","24057","318863","30062","-18207","14023","323118","-104400","-64410","159821","24057","-122302","160848","133110","16240","30739","163548","443605","-118266","-119799","-490452","0","232254","-272125","27334","-138915","-321800","38307","-187920","301009","154161","33507","-791236","-43889","85212","-341040","409796","-82377","-115311","95568","349560","88842","-1108960","47574","419056","-247689","80433","289446","-24390","365634","-229970","-283936","-429993","298984","524244","46818","-417600","279490","-416034","-848547","140760","-190080","-411890","-526640","-45927","586502","-128310","-180387","-213884","324305","-187920","485187","219062","-173907","-541988","130579","199206","1310800","152028","90018","718682","-451710","-356562","34140","2064800","-509886","1423920","-497060","425160","85833","309504","0","-1602368","-485878","-410679","1813504","-852014","892359","670329","1041567","-137052","264384","-757089","-231984","1568518","-194880","85833","781815","-1946768","-517995","-756146","-414747","1545120","1477150","619830","-1313964","882724","220663","-290871","-1387360","-857658","258840","-965592","-427431","143550","233021","-540560","157707","-1601014","923415","-990252","-1275268","-3641560","187920","969318","-675027","671814","-457434","3353148","-260910","-670480","-853252","-527778","-1246738","758645","118098","261894","-2295369","323730","2045979","611640","-743454","1400388","-984216","1315440","-1097775","-1464824","-293913","-2238559","-1908774","658548","-2166880","4745444","-371304","1581644","1082792","-586116","501630","3684160","338022","-2662364","-1411487","552582","1711057","286977","-897840","-3630918","657792","-1986480","1178092","4157228","-89910","3493920","2465538","-452304","1153726","-1765424","1571337","1812384","577680","711585","167042","-2187996","771426","-59350","-2857638","-1279719","-2842338","-2341170","216513","-2940074","5436775","2869767","-2758480","-1055144","270558","-1140588","2346176","-163863","-1136584","2756160","126207","-3628960","-3501128","2908062","-2216438","4800902","-939600","-753400","-3067804","-579690","-735534","3956014","1438389","9261440","-620483","216513","-3201194","1291668","-1100718","2916810","1016160","1447632","3251529","2158036","1197990","142600","3054244","146160","-137088","-6308937","276651","-1272178","-555030","1471932","0","33084","3992445","-3511234","-2219296","-1064394","-2765929","-6846320","-1078191","1152540","-945444","-4414068","7789124","-5331238","0","2287860","-15228","2090286","-1080741","3483470","-2449125","-13655520","-1243590","246006","-1850508","-3290320","-1250235","594500","4426560","-2896200","243968","-488988","344763","-1340352","3651738","-1691280","2277960","9819832","2709081","1977088","-67788","1387449","-2902320","-6643934","301563","5278386","-2883858","-7121124","-1848155","-8104887","-395001","-7680762","1834410","766908","3278186","158096","-3069360","1253423","-2190959","3688164","2685110","-11220122","-741393","5999520","1586880","-1037799","1393807","-4513980","860112","13515192","14574240","3146040","2152214","-5770130","799578","3734712","-4076512","-9980640","5613513","-10745420","428166","2968470","562683","3771504","5470560","-7457636","-2229201","-4967968","2041560","723897","660457","6143360","2605014","6982022","9284285","-219510","-4903140","4814856","3290706","2396966","-3475634","-2069730","2128648","-807816","-2555424","-8818320","5063224","-3869937","-2129625","10961186","2690856","6457020","14214640","4718196","-6728185","11269158","421362","21942080","2532424","-3758400","-7501832","-2318586","2515410","7799442","-3992394","-3744306","-10226560","4353264","-7636923","-6094404","-222957","1266840","-8111592","4693360","-1710720","-11538848","56265","-3707010","-8025460","-4264062","-4739760","-3133515","-7602916","-413343","4556014","9763878","5278518","15397254","-6045574","-1154790","-1324776","-18388784","-1623483","-854600","2941760","-1924956","-6999122","-10109172","2918745","9614796","-4549149","-1691280","6670172","8372520","4366683","7845696","-17653718","1971558","-2440640","10728977","-1565163","632034","-10280737","-4877892","1070766","-9572320","1175211","-23778492","-4056835","1792854","-15629632","-10720396","11797200","11894008","-320790","1368252","11311179","2231940","810162","-23060800","10637925","6468138","-1819399","8018532","-4065390","-8166418","6032961","-3209058","-12117070","-12963272","307260","2538865","481488","18583200","21322200","24651882","-4588974","-9020412","5816154","12815280","-1257440","9967198","-4473540","-29811332","3622524","3826440","953549","-6676960","772497","861882","-24470446","2785536","-9203891","-14913476","0","28298832","-7979342","-14421312","4808892","-10705176","-4372902","15882720","-15524020","-3696111","-15461301","-584647","16321536","13000404","16096160","-7668126","-1891350","-5051190","8031231","6707478","9425056","6032961","7564770","37493688","9374103","6869230","11046168","-1233468","-3352400","22852006","2379456","-41167240","12607554","-6813801","-16004508","5336000","-2087856","4994136","14406100","14116662","-4081166","-6947500","-1753920","-8821196","-5274462","772497","-771891","27856644","7036335","-7266240","23113128","-17520912","30879902","23166800","-4661955","30037328","-27204320","-6805314","-576408","-16115702","-3732723","-26817938","4274310","13906080","-4991511","6137160","13294350","29817574","-19063471","5578470","-30042927","4974264","-11825676","-24506034","-9322245","7944516","11222908","-60616960","1985967","5251708","-22261726","-2617839","5584302","44530834","-12486240","-13733692","-11504313","-7718922","9619891","-7537110","2329560","-9688320","-11031950","-8690328","-11113421","-8376604","-3846879","11952852","31721360","1291950","16039770","-3592640","2097189","-33418024","-6874524","-4865040","34105600","-758782","1419363","40281063","-2364363","-14409126","17664480","7457934","8310735","8742960","-10131793","-8912268","-21881742","-8133920","-11477412","1245052","9670050","-32774040","-19514328","23534006","1691280","-15695204","17321302","8723862","-4460715","-617946","-6075243","37437840","20634726","6046326","-5922960","-9256356","-4116906","-17447406","-53559520","30178332","-8155592","-48529664","-2348190","158394","13390810","-6034320","18721791","-12401340","-7679268","4237128","-6448841","-4750002","60726000","-19099059","-11220642","-24657410","-7903374","6827805","30384408","35342880","1062882","5256060","1075947","2357046","-5389032","26920328","-20658321","-24255440","-6703956","2913570","-6735483","-185020","18413811","9006240","41825088","5504760","-3626866","-40153818","-6691086","2736252","-46147120","12603492","3501682","2846784","-8857944","-24429948","-16936096","11838960","6865503","-49098340","-9879975","-43752936","25774928","-13183416","41142880","-9952592","-2645217","-11204112","-26980614","-20147031","-3184101","33408000","-17178966","31999506","-5852138","5926932","-25576160","-22068078","-19501920","27735798","13915755","42708996","-20853036","11224760","-3341736","20170809","57097843","14234796","8694036","45432798","9745128","-13895040","47789680","-5275044","34544568","-5623626","4514670","-3221744","-867674","33157440","1527654","-992065","3042198","36187754","3584430","-23961276","66846160","-43189120","-12703383","9066246","61884725","4973238","-25864206","-40437600","15399513","-323640","-16415238","2582793","8675127","-6514142","-8080560","25343340","-7480017","-32678262","17198584","-19876776","5920128","-62612160","-17185041","-17878320","2589460","5914696","10602828","45593742","11740914","37415052","-11934895","-22825008","-809190","-5217308","21542435","31445280","-30004210","24238622","22189842","63400740","-50466978","-4070736","6201360","-9517770","10383534","-13807553","-31919720","-15888816","-48127448","46571680","14142033","-18905412","9958996","16311456","24996240","33010472","5199120","-26763960","-6248492","6404265","-22648751","29648938","1503378","-31904640","-4658670","-19691964","32803292","12827814","6942834","-84239480","-49102800","-534150","-29945380","45474560","-25718742","-10586232","-5018032","-11517471","-53366527","-13359314","-25581042","-4906276","-36209229","-21070530","13161360","-48675508","1948617","3790544","-10342506","-26460666","29055990","101094000","48930975","-3728494","6185940","25827903","-6103680","9808560","-24826320","-19573278","16085890","-9496296","15713146","-52586460","2435022","-164766400","30120209","-10265292","-7739946","41450130","21115584","-68681962","-45697040","-1474767","45927665","-107299680","-10229256","-67597474","104011052","24805440","-23860910","51582112","1135863","-18716250","-10643277","-32660640","-43612011","-49195878","-31510152","47288724","-5792427","26172558","16720692","65693120","-19947942","-26813376","-23981580","43208118","45255495","8154108","-8456400","12366792","1247048","-6780600","-17988410","82738892","-27610236","-6034320","-21255394","-5217210","28834682","87597952","-6619806","56910960","105485760","35604126","-30715962","1067780","12945501","39822338","-103946326","83352960","36956339","52544805","-5584347","73334716","18889830","1948617","-142981600","26194576","-28810746","-26932026","-47695296","11625012","-2073852","-89417826","-9906462","-22942676","-28774485","26251290","-79024923","6396726","9145440","112353656","7663675","13028688","3369644","5226040","29263761","159059200","-9520496","19422324","-25703892","76860052","10781910","6167916"],"derived":{"al":[[3,-1],[17,-1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"51.6.a.b","letter":"b","dim":3,"charpoly":["65634","-4031","32","1"],"traces":["3","5","-27","37","-37","-45","-176","-153","243","-860","-197","-333","-1041","-1610","333","-2959","-867","405","-55","-2148","1584","256","1799","1377","1298","3394","-2187","-2410","-4446","7740","-4438","2639","1773","-1445","12644","2997","-17824","20180","9369","1412","-5631","14490","5935","23040","-2997","-7106","29270","26631","-25373","47975","7803","-3246","25510","-3645","-65627","20946","495","-29852","-94374","19332","-137364","-28126","-14256","5249","-49611","-2304","-37452","-10693","-16191","86840","25104","-12393","2662","-81356","-11682","-71228","-20340","-30546","-27738","54076","19683","70990","95750","21690","10693","55132","40014","131552","-9220","-69660","-4940","-110178","39942","263604","25015","-23751","-49164","80081","-15957","144967","-144812","13005","83759","49766","-113796","477430","259879","-26973","-60520","-466944","160416","159230","66187","-181620","384509","120796","-84321","-118148","50864","-12708","342888","-211212","50679","-328222","-566367","-130410","28353","-42737","-53415","-16536","159197","-207360","-149212","-635932","26973","44217","126574","63954","-247074","399880","-263430","-162558","465425","-239679","-215926","-540182","228357","-55076","-332086","-431775","-129984","-552660","-70227","-331008","893922","29214","23699","-592110","-229590","1040004","137972","32805","-291994","-410546","590643","724228","722979","-188514","-369926","248540","-4455","320828","1095679","268668","-709036","-230496","849366","-747146","-55922","-173988","-945302","148732","1236276","-652534","195316","253134","56933","594292","128304","940240","1375582","-47241","-1345554","1170318","446499","-119951","504643","20736","-153876","120477","337068","-1137498","332064","96237","319379","-22540","145719","935498","-1843677","-781560","1359070","-67194","-225936","-275648","-1031575","111537","761872","-850488","-23958","-1096480","300849","732204","-309019","1024898","105138","-548326","-1897611","641052","-1658214","2374104","183060","1329316","-1920303","274914","-2555390","-2024756","249642","465290","2724900","-486684","763452","3782137","-177147","-2071076","-1087293","-638910","-40981","-933802","-861750","-1363240","-1618064","-195210","-4474583","-3336792","-96237","1715873","-789264","-496188","1449064","-702536","-360126","5184912","-967188","-1183968","-2621930","144728","82980","289396","-3061703","626940","23817","855151","44460","3063106","4824468","991602","-309298","-2577272","-359478","-82824","479352","-2372436","-775990","2735810","-225135","2666368","-212676","213759","250563","-1699472","442476","2388522","3315564","-720729","3022406","2249284","143613","402962","-3023511","-1304703","-1093460","6192712","1303308","1537396","2503496","-117045","4858820","-2487360","-753831","7239464","3754940","-447894","-67580","-5968818","1024164","-1758990","-2809706","-4296870","5409122","2715324","-2338911","1657604","15895","242757","3595544","-224740","544680","-2222054","-4313496","4202496","-3588787","1607092","-1443744","-967818","2884988","-1433070","1664450","-3349917","-595683","620772","-8706894","1634580","2907536","483060","-3460581","-3236444","3090852","-1087164","-2092115","-5050510","758889","-6555808","-575118","1063332","-4842116","-1258794","-457776","-4677804","1480608","114372","524392","-3089468","-3085992","-1416868","-1837418","1900908","891164","334342","-456111","3054064","-5898816","2953998","755926","-73984","5097303","-2474500","3023402","1173690","1014184","-910768","-255177","-2728180","4434436","384633","8070420","3544910","480735","-3222530","-6587288","148824","-519911","1035243","-1432773","-8043984","7978422","1866240","-5282888","-2672602","1342908","-2831189","2017037","5723388","-3410214","-5149034","-242757","698040","5404660","-397953","731385","6507160","-1139166","-82124","5966856","-575586","-6481190","-7511882","2223666","-8204928","-131380","-3598920","2056743","4057992","2370870","-7559230","-375122","1463022","8240600","6767648","-4188825","-7739728","9900","2157111","10835707","7793980","1943334","3048352","8652115","4861638","-1211544","5487232","-2055213","-980866","-6220558","495684","8464760","11812428","2988774","540382","-2655418","3885975","-8887849","10448522","1169856","-14183148","2273540","4973940","7908889","-7595706","632043","6556872","-2355910","2979072","-4628456","1085340","-8045298","-484430","12542910","-262926","7754512","-18212336","-213291","117604","8247549","5328990","-3827540","696490","2066310","-3650148","-17562037","-9360036","6120508","27057174","-1241748","-4938759","-2245144","-295245","2299458","4943684","2627946","477076","-10781906","3694914","1284894","-14325880","-5315787","8736410","-1650584","-6518052","-11465882","-9053368","-6506811","-8969364","-1009487","1696626","16914648","-25244544","3329334","-65624","5515256","-2236860","3478944","-2973137","40095","-30744870","2970889","-2887452","9400922","9511960","-9861111","1415336","-16192207","-2418012","-10716100","319472","6381324","4968388","1282582","2074464","5502140","-10114440","-7644294","1768504","825863","6724314","-6795511","11401692","503298","5221180","10008947","1565892","-8081580","-5100912","8507718","-762671","-3118340","-1338588","-14399208","-669630","-11126484","32336256","-16084794","5872806","9048864","16893968","-1757844","6140328","-11263538","-2278206","3680101","-15697400","-512397","5918758","-20334050","-5348628","-19957063","21959168","-1154736","12894646","2175052","-8462160","10750144","-2878048","-12380238","4460772","-27900056","425169","26285653","417605","12109986","-55984","-12254600","-10532862","-5656506","17088878","-4018491","26381146","-9990516","1079559","18045158","43330672","-4541787","14056508","1232370","-186624","-3654116","-20066638","1384884","-10958772","237342","-1084293","27515786","-9409208","-3033612","-3325816","-5389602","10237482","-15805498","-1063412","-2988576","46490608","3430074","-866133","19252659","-16179564","-2874411","-7174080","13287174","202860","-32372126","19356888","-1311471","21226646","9735560","-8419482","11244093","-14488178","16593093","-4235058","5151136","7034040","-5269887","-211002","-12231630","3089368","26068943","604746","17415223","25863552","2033424","-11357692","36905315","2480832","-5295624","14113348","9284175","-5832020","-9908738","-1003833","-20194162","3841334","-6856848","-151236","-30793997","7654392","-34750413","12477942","215622","-30181992","-4982646","9868320","-23095","-23046988","-2707641","-8398820","-10132292","-6589836","-28616854","16098038","2781171","9474448","-2524776","-9224082","20803022","-32317566","-946242","-7649437","10516197","4934934","-8274376","-408068","17078499","-52824064","15629077","-5769468","-17375426","31469924","14923926","-9430228","6270062","-21366936","23159244","11753980","-1647540","19392748","-3680574","-11963844","1627359","-59925462","17282727","-25408430","-24566964","-2474226","-18800692","-37878624","22998510","12501446","21716248","18222804","-29287958","-50814808","-2246778","2062610","46350378","-4187610","1625535","-7489036","-24524100","-62803648","8361245","4380156","-2015188","-14796031","-6871068","-13406548","20086044","-34039233","-27640992","-8097420","1594323","-34806072","-1715215","18639684","20607918","26814226","9785637","40788090","15515452","5750190","2927681","15842704","368829","-29326956","60461436","8404218","36849714","19047898","7755750","-6658560","-11012132","12269160","-20427918","-29828508","14562576","22464104","-42160304","1756890","-20576779","26101900","40271247","-16357680","-40097966","30031128","8001576","27713868","866133","6795052","22125278","-15442857","23585949","57691392","7103376","-10516866","-33288580","4465692","-61107868","-23096086","-13041576","30809226","36264621","6322824","70995252","2053634","3241134","23458701","56088449","-46664208","-26794728","-9657448","8704692","49390440","-6270172","10655712","43042048","11223692","23597370","27776230","-36921980","-1302552","-8459030","-67770731","-746820","10320054","63954006","-2604564","-43438268","-31910668","27555327","-468238","41039017","-5642460","25529650","-7894968","-214353","16732544","-6988174","-7696359","-12946225","7042078","-400140","2965064","-7699741","-27567954","-5431440","-8226084","-43420212","62463240","9090501","-8924418","-11154230","-49523312","2783682","-17813910","7332797","23195448","-10574111","11124000","3235302","3316292","29720905","745416","-17249363","26052010","-4314168","-3096600","32780264","21351924","-46265612","-12581682","6983910","-13864775","-30304820","-24622290","-49294266","78863000","2026215","11646336","-61035574","-23997312","-6884828","-24193232","1914084","-55828122","-7049464","-1923831","28854429","-47871066","-2255067","35673596","-52909290","15295248","-3352068","29556560","-3982284","54668536","39907284","-21496698","-57010790","-95389970","-29840076","64604544","13250382","6486561","8394525","938094","-27201654","43221388","-11377919","-20243556","35976452","43107384","-1292517","-9387956","9668862","-3626658","52072538","-17887230","27211599","8072702","-47054308","11742327","-7372390","-43795584","9841140","51371918","27383018","-55734408","-29433026","-7704012","-11729772","24767792","-11682141","-13836564","17582866","-13129970","-22531464","4463142","-61811020","1053405","451809","-27869544","-43729380","-17946834","16759820","22386240","-757444","-41258644","6784479","-25316060","27346123","-65155176","1741809","-55605758","-33794460","19421916","18966203","4031046","-39735562","36753976","608220","-74186448","-84136770","53719362","41339087","108265980","-9217476","53499264","40114732","15830910","7364414","-67412900","25287354","-6053394","32214016","38671830","-6180278","44046332","-48682098","-52333230","-36568608","-24437916","21896143","14377224","21050199","-7401018","-42006834","-14918436","-30652213","-95432413","-143055","36362968","21710122","-2184813","29127736","102224290","-32359896","142142524","-18071610","2022660","-49002512","-14798036","-4902120","-50245844","27986961","19998486","100117433","8627228","38821464","35941000","-44908579","-37822464","-33612768","76974310","32299083","-42071684","-54166216","-14463828","-74457334","17814816","12993696","22736792"],"derived":{"al":[[3,1],[17,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"51.6.a.c","letter":"c","dim":4,"charpoly":["672282","123177","3991","-151","1"],"traces":["4","5","36","113","146","45","60","-153","324","-536","1114","1017","-166","1738","1314","2745","-1156","405","3454","5748","540","-6368","998","-1377","3150","2890","2916","-13382","3048","-4824","-7808","-8881","10026","-1445","-14080","9153","-1700","-26836","-1494","-55648","-1386","15642","-27654","35196","11826","-43646","38156","24705","-17012","-42601","-10404","-79378","52648","3645","38782","78510","31086","-75320","50028","51732","13076","83438","4860","-32847","59250","-57312","7880","-32657","8982","132272","106836","-12393","52488","-164192","28350","178608","-8520","26010","37688","17368","26244","104254","9812","-120438","-42194","-145316","27432","-162784","20876","-43416","65984","-302994","-70272","-125700","81658","-79929","-1996","-321967","90234","264551","113668","-13005","-247838","-230242","-126720","-3746","-140126","82377","-279812","-624192","-15300","-78302","-9494","-241524","-26242","391000","-13446","743044","-17340","-500832","4870","154944","-12474","579430","402498","140778","161846","249871","-248886","1076208","-369226","316764","-125976","871244","106434","44217","81352","-392814","-288028","-915248","343404","1217502","-422026","222345","-139372","499786","-153108","1065480","-358528","-383409","-605728","-438540","-93636","881760","-1112460","-714402","-592526","1483470","473832","-659520","553664","32805","-1182884","116410","349038","12508","-34530","706590","260278","154904","279774","-1567160","844954","-677880","-1215380","1806984","450252","588742","-563348","465588","-476352","-880652","117684","-733642","2119288","750942","-321946","506644","43740","-3054464","-1067828","-295623","296360","-1735242","533250","-1104227","399058","-515808","-835948","-3608403","70920","-1018338","-428856","-293913","-408010","-1749748","80838","-2831222","2470278","1190448","-1946364","2522406","961524","3394336","-1331818","-111537","-371416","1417260","472392","3782996","47974","-1477728","-739898","309182","255150","1403378","-118002","1607472","3268808","-328560","-76680","-319232","3072198","234090","-397748","265948","339192","-502282","2395200","156312","1614164","-4761671","236196","5065944","-774318","938286","-2850414","5422394","88308","551888","-3285272","-1083942","2248138","-1429080","-379746","-2721087","1613244","-1307844","-4860952","-1212452","246888","-127104","1685664","-1465056","4712836","3721976","187884","-2863380","1250254","-390744","-2673130","-793305","593856","633250","544344","-2726946","1660072","764392","-632448","4690560","-757308","-1131300","2368108","5337038","734922","1347040","382416","-719361","334084","-8385248","-17964","-6956350","-38220","-2897703","1506644","-10258088","812106","-1643278","1447734","2380959","1045352","-3421592","1023012","8228196","-1270144","-117045","-5844032","-8817840","-2230542","-3692368","3329396","-2072178","-1569708","-2727234","-1140480","677078","-4855376","-33714","5168156","2394576","-1261134","-1041820","-998206","741393","4082476","-3875644","-2518308","3256138","3114912","-5617728","3673774","-559196","-137700","9823578","-2990440","-704718","83680","7802307","-85446","-1661172","-3129132","-2173716","-786360","-6540","-236178","3685672","-533568","3519000","5743542","6696398","-121014","-4186144","-5779992","6687396","1367920","9384966","-156060","3612564","6276960","-4507488","626614","1187296","43830","2699172","500068","1394496","-58916","2481346","-112266","-7991456","-4337256","5214870","-477840","1840352","3622482","2097140","-9707284","1267002","-1351848","14192156","1456614","-15679036","7694080","2248839","-8889720","18184598","-2239974","6364518","-2018996","9685872","-288422","-4128021","-3323034","3059676","-4453524","2850876","8041164","-10975894","-1133784","-3584197","-5271538","7841196","-14650268","9331246","957906","7755984","-92456","397953","6059270","3340528","732168","-19374168","4959696","-3535326","-5869460","-1395410","-2592252","-14795232","-2431408","-8237232","5141978","-3813624","3090636","-13142470","-910350","10957518","-5842104","-3288340","-3798234","2233856","-738348","2001105","-3847686","-857252","-1254348","-3325692","6338638","4498074","-3122932","-21061760","-1377972","-835210","-9610348","9589320","5037992","21658644","-3226752","-4408158","-5117536","-3450681","-3687262","-18468874","-5451552","-4220580","7135496","-3946860","-3539898","14044758","-842724","7191012","-10355008","7935840","-3502680","21037968","-10012140","-9609350","4704636","-6429618","11543744","-18331712","-5332734","9997372","-2286678","13351230","-741816","3867398","4264488","-5177628","8166758","-5935680","4220528","-4485378","4982976","2438881","21367208","295245","-4890736","11020376","-10645956","-10421816","-6763988","1047690","-880872","-2333416","3141342","10661734","3183448","112572","4144212","15493148","-310770","-16342740","3682930","6359310","-6230040","-7391424","2342502","-5343636","-2625172","1394136","18521080","-6113489","2517966","9952122","-5732834","-14104440","23539940","22332352","7604586","7539584","-12486202","-6100920","16443112","-28170556","-10938420","6122620","2256512","16262856","3277230","-6733680","4052268","-32007640","-1501426","5298678","849638","24724500","-5070132","26825248","8309162","4190292","25675604","-21435120","-4287168","2566609","-28848776","-7925868","18002480","52128378","1059156","-32790912","25612452","-6602778","11561512","-1875820","19073592","-3492352","-19039208","6758478","2601998","-25985888","-2897514","17855350","12714532","4559796","11434370","-32491120","393660","24831562","-19172252","-27490176","7895544","-27357532","-9610452","-4558884","-7888556","-2660607","-973194","417605","2667240","27074840","8554288","-15617178","9096420","5888558","4799250","6555370","8739312","-9938043","1431324","39263392","3591522","-6034328","-28904112","-4642272","4069120","-56946982","-7523532","17828772","26171124","-32475627","-19535216","-15629288","638280","-31276088","8772144","-9165042","-38910392","-12739436","-3859704","-38761280","-21358980","-2645217","1946354","10466484","-3672090","42842880","-7896096","-15747732","22539876","-38082456","727542","-39078214","-18573544","-25480998","7821928","-4254314","22232502","16402178","491300","10714032","-3141010","44303610","-17517276","-44839916","29075714","22701654","-5525606","-27944640","8653716","42120128","-11827270","30549024","6023864","-33701996","-11986362","7755604","1798156","-1003833","-14583076","68479982","-3342744","-75933316","18626434","12755340","-25556670","-4901970","4251528","15521016","23405916","34046964","14487550","6581876","431766","22690564","-36179144","-13299552","12483140","14653046","-6659082","57245152","5446032","2782638","-16952552","13499922","2296350","17916275","31856070","12630402","-39887832","16082272","-1062018","37885568","46517710","14467248","-3233708","-29355748","29419272","-10916108","13314692","-2957040","-5453224","87192292","-690120","-52768316","9195660","-2873088","400554","-1699422","27649782","-37741362","17838180","2106810","269016","-21029232","-3579732","28482278","-737528","2393532","-19891632","17201648","3052728","-2688670","-50012964","-4520538","-32054526","5509100","21556800","-18610048","29761826","1406808","10757160","-61972735","14527476","-32514752","-15586044","-42855039","-7957312","-35969988","2125764","77708400","7992006","45593496","-4750288","21013006","-6968862","-17063802","-25367144","8444574","-54716978","99604144","-25653726","41894652","23982660","48801546","1513932","-60748910","794772","-10171644","-401672","4966992","-21062200","72831804","-29567448","-28343344","-10900112","-9755478","1607926","36583732","20233242","-75843648","-31646288","-12861720","13080712","23526204","-3417714","119820868","35399156","-24489783","-12425194","80950560","14519196","-35840098","-60954268","-11770596","-56880668","-106231390","-43748568","20587386","-12040554","-10912068","-7307016","12613694","2221992","18892821","6857834","-1143936","-35670592","-54008968","15170976","53015280","22898432","-13185504","-70578856","25249256","42415524","46388202","24012004","33497784","-11027084","-28956251","1690956","21461478","-3095820","-25770420","-11048744","-137391460","11252286","18921146","-42253370","-3516696","-36297660","-62499072","-24058170","-96017152","-82369828","-7139745","-6806226","370270","5344704","-35032684","11370194","5699250","-38041516","-33909852","4899096","-22571064","-45105162","-24542514","81571704","-22381184","14940648","41561666","4916468","6879528","-11447930","95421828","-5692032","-15916276","101299450","42215040","-7299292","-3793934","-6815772","17123648","33465452","-10181700","-26281500","7236006","21312972","12311689","-46842464","48033342","-49922344","45159872","6614298","42692160","66743096","12123360","3300720","-27958844","3441744","49507626","-11636272","-6474249","95220906","1804614","3006756","85549692","-32178084","-75467232","35101960","113098412","-161676","-32645864","-4466520","-62607150","74958000","-5110142","-343980","99541176","9221856","-26079327","-44761354","22940242","13559796","68235772","43885162","-92322792","-10037208","-21481584","7308954","41956200","92015628","-14789502","-43993300","-18440514","13029606","39682718","39964544","21428631","-15215272","34638912","9408168","-30666538","-34509148","-30794328","46211028","-136200672","9207108","-48677248","45247062","74053764","22417252","-148642898","-11431296","58385630","40313192","-1053405","-61875034","14882112","-52596288","-47887530","-16750000","-79360560","162063148","59473316","-20074878","-15381536","-3093302","-33231312","36069870","3585670","29964564","77713260","-11207998","-18649602","8436448","-74833640","-14127372","61838184","65685888","-24545106","-30119374","-60066540","-10264320","31867872","122711080","6093702","100885236","-167231324","-43698384","-22689390","-91915244","-303426","34025980","12387092","46513404","-79211586","-79056936","21551184","98491156","163969536","-11350206","18389582","-60386556","-9376380","28530058","-110838109","-8983854","-52708592","6988540","6672537","-31477264","20938702","36742284","94383240","-50169528","-34880796","-28061600","45723220","-22664772","-38482628","19296282","29305242","-39799150","21767480","28034208","-133050172","65597426","-50559552","-47810788","68134186","33063966","15554812","-29250952","-5032764","90101344","155920896","-1239300","-23529472"],"derived":{"al":[[3,-1],[17,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"51.6.a.d","letter":"d","dim":5,"charpoly":["-623316384","24597432","135327","-10079","-5","1"],"traces":["5","1","-45","117","4","-9","-40","-15","405","1234","-46","-1053","1912","4544","-36","7465","1445","81","-774","-4350","360","3184","-3914","135","1813","2690","-3645","-10128","3510","-11106","7308","-16199","414","289","4144","9477","5754","-32000","-17208","36830","-3228","-40896","12662","-114264","324","-29204","3172","-67185","78781","-54749","-13005","46738","13574","-729","95254","116112","6966","-93602","-23304","39150","78346","-992","-3240","241729","78594","-28656","156628","33813","35226","-40864","-37488","-1215","52442","926","-16317","-272776","172032","-24210","-85220","-169234","32805","-101810","12784","91152","1156","170912","-31590","-114100","92230","99954","-293328","-178524","-65772","122136","-190690","145791","7606","-204455","-3726","-314649","89954","-2601","-146094","424390","-37296","-68810","-225430","-85293","126762","-417324","-51786","-1090032","-247048","288000","-91690","520262","154872","-570572","-11560","-331470","687035","818790","29052","-211200","-112182","368064","-30458","64985","-113958","155760","-510050","1028376","-70400","206164","-2916","-4335","291050","262836","377824","1868000","-28548","-487296","-230414","604665","-13456","1591610","-709029","40118","324310","492741","-903896","-871092","117045","-518688","-5220","-420642","779280","-717696","-122166","2032134","-600032","6561","720672","527822","-857286","589804","-1316850","-1045008","113821","356626","-62694","426504","843620","842418","-1137912","-4601556","209736","-102494","-561088","-352350","1123622","964256","-705114","-574216","-1676260","8928","-13294","955592","29160","-315260","-372340","-2175561","-733550","2313690","-707346","1110445","-1656028","257904","260296","-929625","-1409652","-1615938","-2650416","-304317","1447826","-876356","-317034","4552470","1313466","367776","2286416","-3440754","337392","-1607408","-487550","10935","1984512","-221610","-471978","542108","552568","-8334","2840142","6907408","146853","-4423762","-1825938","2454984","2365774","-1014516","-1548288","-5742242","3092820","217890","343924","419156","766980","1313216","1066248","1523106","3083518","3424697","-295245","-1267810","2681700","916290","-1599350","-3272408","-115056","-4182376","2613932","-820368","-63014","-1394628","-10404","4248193","-769194","-1538208","3966288","-2453080","284310","4653984","-1212840","1026900","30352","-2738336","-830070","8179076","2950544","-899586","-611930","2157385","2639952","-4999622","1377900","1606716","345366","1392476","591948","-11621472","5424126","-1099224","-906888","-5040080","1716210","-5402420","-8965296","-1312119","417605","3198092","-68454","-2590142","3691338","1840095","-8701252","998678","33534","635606","-846174","2831841","-1933056","-7725112","-809586","-7906324","3779956","23409","-2095644","10330368","1314846","2173352","-1573880","-3819510","794846","-7923102","335664","-13784480","-4528546","619290","-1895404","-7786986","2028870","-4391200","-223686","767637","2020014","2522644","-1140858","-961838","-4433856","3755916","1540362","10116236","466074","11197788","1554256","9810288","-3299406","3759867","2223432","-1257150","6785700","-2592000","-53456","24522228","825210","-2820182","-8353308","-4682358","3496100","-2110496","-1393848","1912676","6917178","5135148","-1964264","-3193158","104040","6391020","-3087312","2983230","-2128637","-967066","-6183315","6622432","2527856","-7369110","-2589240","-5075272","-261468","4687924","3454992","1900800","1161494","920176","1009638","17155040","3267352","-3312576","1062884","-181556","274122","-4065640","-5387944","-584865","-7537824","4023826","1025622","15520658","-4506670","-1401840","-1131146","-35666487","4590450","20333106","7613100","-9255384","-2773750","6031600","633600","-1598673","-1114412","-1855476","-4636396","12045830","26244","16686336","-4242856","39015","283384","-3366040","-2619450","-3713164","3936","-2365524","-1217348","3001790","-3400416","14924004","-3435572","-16812000","-821648","6837636","256932","1262918","523957","4385664","9262096","-20757656","2073726","-3227332","-232752","-5441985","-12947644","10706624","121104","19527566","5233970","-14324490","-4966688","-29652880","6381261","777410","-7462496","-361062","-6910180","-8194932","-2918790","-11383792","-13014926","-4434669","-5530678","-82562","8135064","-8792688","-17017856","7839828","-16958632","-20286858","-1053405","-2618508","10895182","4668192","-2604352","25717422","46980","7362478","4099992","3785778","-5487264","-3385816","-7013520","-11861300","-22021626","6459264","12112268","-2926992","1099494","-5648064","8278054","-18289206","-12275844","8984730","5400288","32446037","6531700","-59049","8304796","53596270","-6486048","23184130","699176","-4750398","1014390","-19654436","7715574","-13937112","-799360","-5308236","13809008","2841712","11851650","-6624756","14632442","9405072","-19597524","3607956","-1024389","35086724","22193794","-3209634","30384368","-33465847","564246","10875258","11735474","-3838536","-20532148","-927808","-7592580","25653740","12002788","-7581762","13343292","-24691928","10241208","-22925480","2112012","41414004","-24731345","-6568260","-1887624","-11125248","24248686","922446","23255966","-1430988","5049792","-33170654","41112322","3171150","-9277142","24948828","-10112598","-4681511","-24909772","-8678304","-5963780","2589378","6346026","14025804","-4524828","5167944","-29192704","-1501754","15086340","-28968068","-17211178","-80352","25924758","33007328","119646","-3257198","9228656","-8600328","-39972898","629740","-262440","-17241728","8956862","2837340","2236364","-65615804","3351060","2924448","8345888","19580049","4045256","83521","6601950","-55156180","-401248","-20823210","28262100","97415242","6366114","-20343026","-1730724","-9994005","9197332","15571472","14904252","-8150874","-25781022","-2321136","1197616","-34309490","-2342664","-12690108","6706020","8366625","-25111038","-39151456","12686868","-14983896","28590462","14543442","26927484","-51194044","23853744","-9257420","26062428","2738853","13951192","-28485180","-13030434","-140923008","-209430","7887204","-1690600","-4482216","2853306","-7779808","-13092176","-40972230","-29834995","-28215982","-11821194","9935218","1662906","-3309984","9263134","5175528","-20577744","24790318","7498846","30966786","12413368","49249296","-3036528","58748150","13234504","14466672","-3667964","-4103104","4387950","-9248000","4375076","-98415","-41171764","-25808630","-17860608","85724596","-31357252","1994490","-2054358","53812482","4247802","-23827392","-51388128","-4878972","13273764","-32374808","-4973112","24766372","-19741984","75006","3710924","66183988","-25561278","47852776","12257424","-62166672","-28810350","-33215454","-1321677","-31718305","13587792","39813858","62276848","10643870","16433442","58067240","-25177450","-22094856","-5761184","67462528","-21291966","59358420","-4195592","9130644","55645852","76098266","13934592","27095716","9719004","51680178","-932892","-57106710","-27835380","-9640624","25638858","-1961010","22961944","-113640732","-3095316","10373954","-28169776","-3772404","25035902","-12407504","-6902820","82819370","-10110540","-11818944","32983506","-37892276","-9596232","4287368","11330458","-13707954","-47618912","51515377","-27751662","61263342","8199678","-30822273","37135960","47731872","2657205","-23684700","3659318","11410290","-29121458","35108888","-24135300","-30167376","-28746232","-8246610","36031914","50204324","14394150","-28923648","20133480","29451672","29465328","15496022","1035504","-33022296","-75887872","37641384","-21072452","69021600","-23525388","-33114676","-94191232","7383312","-16334052","60168788","567126","-57457008","-17317510","12551652","5185424","-154223832","93636","-48745952","-47560892","-38233737","-24153224","123319008","6922746","32276986","25737730","13843872","-951696","-12564494","-35696592","25708638","-27882174","22077720","29721528","-8439956","-2558790","51670593","-70412966","-41885856","-8012684","391426","10915560","-74703864","-38577584","-9242100","59058852","-11801834","-273168","-26518432","-633046","24645024","916708","-87734329","7470630","32006406","3141228","-73611684","-27128672","-34947944","-26554896","-36656890","-3850828","8096274","25662368","-126851040","5507370","19956728","15676516","-19416465","-14295698","27241478","-23759568","-90847168","62628772","44996598","-27633656","-43790352","-12401100","-23779392","22639686","-14460444","16162934","24839456","-3108294","58294606","22767709","-12532284","21035854","140437692","-5327532","13038668","-984406","104593248","-24724269","134400698","-48817134","-16650044","111373006","9893016","62653592","-101273898","8161992","-15822461","-9146560","45360720","-29110034","-43784384","-15445890","-50130756","-17841950","48621780","-35110228","105041972","80687664","-134270520","-64515752","11809071","-88471530","-46761114","-3758445","-40883456","84476436","-28782828","76642976","32071006","616086","53482084","-83414592","23311278","101154830","-12706192","-33222042","97990128","-35728830","-16560855","20761666","13507282","78311268","-50983052","59947514","-8988102","-109385312","-6611556","-301806","122233364","-36803172","-5720454","82440764","206561424","7615566","22581074","-5612456","-25486569","3922886","-48412500","17397504","-154853494","81330664","69526008","17172176","-23579592","7286274","-10567456","-84045402","71156916","-89934308","4655510","-34019604","76977646","188424832","-210681","62404990","-14398824","18860796","-33816402","-34177880","-92973312","-7276938","-128752304","-11833614","-192383186","-32110168","-19560168","-7468566","74652110","14164920","-112746276","27528406","34375590","52134642","196895744","-7153614","40828536","100211214","71307918","24587114","14349036","-3020976","-283398756","48877676","124060320","29146504","59705900","40756914","33556368","-14878858","-5573610","13070092","224076832","17058636","-29877228","-82582032","70082874","-65597075","14428644","-18259830","-45351566","-11237568","39520800","16456554","-58829459","2013174","49636060","28925792","-6908733","54329760","-85505560","-18180126","18460286","657426","-22703796","-68107616","-273946702","10267722","180450148","-95562486","8656542","23410670","-27050978","39904704","-165019308","49870","-33803244","-94866200","-74546536","-13863258","-56186240","36755440","-91046124","170074230","-100676892","-4194666","-122202220"],"derived":{"al":[[3,1],[17,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.238,"computed":"atlas","estimate":{"seconds":0.389,"low":0.237,"high":0.673,"bytes":1936433},"url":"https://sagebrush.space/atlas/mf/51.6.a"}