{"label":"111.6.a","level":111,"weight":6,"dims":{"new":30,"cusp":62,"eisenstein":4,"modsym":128},"old":[[3,1,2],[37,15,2]],"T":[[2,1],[5,1]],"status":"proven","checks":["dim M^+ at levels [1, 3, 37, 111]: [1, 3, 17, 66] (certified at ell = 2147483629)","T = [(2, 1), (5, 1)]; h of degree 30 = 1 x 30 (phi(ord eps) x dim S_k^new); 7 primes, 0 rejected"],"newforms":[{"label":"111.6.a.a","letter":"a","dim":5,"charpoly":["279930168","3998052","-275284","-3980","67","1"],"traces":["5","-3","45","49","-64","-27","-216","-495","405","-1020","-598","441","-1984","-739","-576","673","-556","-243","-3628","1776","-1944","-1187","-448","-4455","-1345","11213","3645","-10829","-8704","-9180","-8416","-14063","-5382","-21013","-2856","3969","6845","1435","-17856","-21440","-29574","-6651","-44336","-17161","-5184","6037","14212","6057","-17305","9727","-5004","-67973","-33138","-2187","-26620","57799","-32652","111348","41034","15984","-88610","79686","-17496","35009","11964","-10683","-3060","229241","-4032","163376","15708","-40095","-13844","-4107","-12105","6701","152172","100917","21880","304944","32805","1026","4782","-97461","34460","168916","-78336","165235","89236","-82620","-49400","93191","-75744","-266582","7288","-126567","-164398","235548","-48438","67179","348558","-189117","104000","459455","-25704","-265841","261194","35721","-79356","361272","61605","-139249","-10252","12915","-132400","-382544","-160704","-70128","-185834","-192960","-391237","272142","-266166","96186","125556","-59859","-725748","153521","-399024","505632","-598610","-154449","-187022","-268938","-46656","-687131","-329746","54333","-212324","140496","127908","846284","-127042","54513","-532952","318215","-155745","67081","522058","87543","-714044","881801","-45036","174831","-166876","-611757","409010","-680898","-298242","42160","-367860","-19683","-1131136","-1049574","-239580","573445","-522068","520191","151493","-1137880","-293868","-566628","456314","1002132","-277776","-751829","369306","170003","-16666","143856","364698","-1085485","-797490","363451","-87616","717174","29648","1195070","-157464","692848","-68640","315081","-1185538","2210082","107676","522030","828686","-96147","-147364","115995","-27540","107902","-150788","2063169","663888","-1027678","-36288","-1227289","-28616","1470384","180172","733749","141372","2519847","-62356","-360855","690280","-179161","-124596","328000","-1672764","-36963","508152","2161391","-108945","2936770","914002","60309","1310322","-491304","1369548","2615680","365334","908253","2845568","-1373784","196920","964325","926174","2744496","965174","396832","295245","-2199162","-1450572","9234","2839676","-3509566","43038","2696720","700286","-877149","-251874","-3406353","310140","-835679","-2757732","1520244","-295704","-5285152","-705024","-129130","1733080","1487115","-748236","-2654543","803124","-825414","145086","-743580","594412","2212173","-444600","-2245328","-244458","838719","-1610156","-7721334","-681696","1140624","-3500276","-2399238","-638172","-5327220","65592","-2252061","5302764","-1139103","1587029","1828144","-1479582","-6623551","1035070","2119932","3261204","-677655","-435942","-3473634","1040918","604611","2008856","-4273089","3137022","-1731359","-1943344","-1702053","637448","2153953","936000","-3264184","4342614","4135095","-4616458","-4270292","-231336","4034714","-1870738","-2392569","403488","-3063824","2350746","-3768537","2646414","321489","1126936","-4987183","-714204","1191738","-4935156","3251448","-4819988","-9013513","554445","1651679","9566276","-1253241","-2045432","-8982922","-92268","9450768","1470012","116235","-890700","1732860","-1191600","-2489967","7558082","-3442896","-827910","-2234049","-1446336","3844267","1095496","-631152","-9230952","-7236535","-1672506","8058060","2055588","-1736640","-2830029","-5950080","-3521133","7935685","2777272","2449278","6516148","-3060845","-2395494","-1396380","10560214","865674","-4973786","3457669","1130004","-5337322","9521312","-538731","1750896","-5092752","-6531732","10311337","12970328","1381689","-3567188","2651114","-3591216","-9734766","4368064","4550688","4436600","3457330","-5387490","-4700435","10032388","-1390041","4773738","11686164","-1683198","-2107477","2719884","-2420442","-2968020","7324438","-419904","-11009880","-818662","-6184179","-5172050","11234712","-2967714","17369446","-704136","488997","-123076","6218823","-1910916","-4927783","16825770","1264464","-5073062","-4713372","1151172","-3523383","3201584","7616556","6808408","14503861","-1143378","5081096","16318652","490617","2859048","9943002","-4796568","-9867607","6992968","2863935","-4495892","2436400","-1401705","23938393","6086868","603729","-6059188","10628320","4698522","10263135","-4372392","787887","9681048","760162","-6426396","-2333488","10897220","7936209","-9022870","-9012140","-405324","-2823968","-16090312","1573479","4100520","-18962960","-1501884","-4041946","7475234","-5505813","-8391704","-8117744","3681090","-7841520","5312656","-6128082","4606052","-19872433","-2684178","-25266496","-12831724","379440","-2716096","9003440","-3310740","-6180782","-10407520","-177147","9721452","19747974","-10180224","-6297428","-1940490","-9446166","-9036936","899573","-2156220","-3942894","1321856","5161005","-8703648","-7735504","-4698612","19700494","-5461182","4681719","-10850312","-6607457","1363437","-9151279","-21104830","-10240920","16730996","20952721","-2644812","-12187205","8604660","-5099652","-14301760","-1011691","4106826","24191760","-4552906","9019188","-18828584","-18105086","-2499984","-9648790","2055156","-6766461","-23907997","9421280","3323754","2488539","938172","1530027","-14908988","-12117998","-149994","-15859223","-5065672","1294704","-5121752","23300984","3282282","-22743891","-5408372","-9769365","11054840","-15406420","-7177410","-3538417","11286276","3271059","-25622652","5255867","-788544","25190278","6795628","6454566","16317040","-25284464","266832","14560311","-11223242","10755630","-13766888","-28824243","-1417176","46832748","-39751124","6235632","-11164952","22142801","-617760","30537594","5280732","2835729","10240062","-28898510","-10669842","-34176880","11037996","19890738","28209572","-1358259","969084","25303711","2800362","4698270","-24658672","-1677888","7458174","921337","-12155550","-865323","6002516","26796942","-1326276","7825539","8556804","1043955","12972280","7148812","-247860","14814017","7955876","971118","-3632564","-9121599","-1357092","29151000","936896","18568521","10933254","-4789552","5974992","-9088035","-14476426","-9249102","-1768640","13138096","-326592","4029576","7435174","-11045601","-40537595","-31882946","-257544","59877712","-761164","13233456","12439100","-8707422","1621548","-17064946","4874956","6603741","22993098","-23173504","1272348","1437936","10987242","22678623","-38032436","-11273543","-561204","32101955","-10506428","-3247695","-14605668","1163423","6212520","11169751","-8880160","-1612449","34293652","3401178","-1121364","12388166","-4062140","2952000","-18209436","4132548","-15054876","29036451","24186748","-332667","8901060","388397","4573368","-5105480","21358388","19452519","9866716","-35022977","-980505","49276184","-20929582","26430930","5589268","-52388816","8226018","21802186","2288218","542781","37654448","-29823033","11792898","-19838404","-40992548","-4421736","15116508","53556731","12325932","-28741582","8015772","23541120","-26610804","36001170","3288006","-6958639","-37115924","8174277","-4966732","28709019","25610112","-40432758","-23045164","-12364056","2999728","38370304","1772280","53994965","-18082680","8678925","23636372","-9895324","8335566","28784234","1726904","24700464","-36816356","40238752","8686566","14518060","9262516","3571488","20454060","-42789695","2657205","34079128","-4567476","-19792458","9972058","-65253131","-13055148","-21831053","-39901100","83106","29514844","2431344","25557084","54902009","1544976","-31586094","34999416","37936728","387342","-61686957","-52026020","24270480","-238188","70809094","6302574","-80024264","44218828","-7894341","21511972","-35781000","-2266866","-2347024","3873866","-30657177","11024192","-25642181","2791260","-18395173","-4733040","-7521111","-89218226","-40907784","-24819588","-55847014","-46804546","13682196","-1452576","51644114","-2661336","-58758230","-35052996","-47566368","13917736","16585093","-6345216","-42652374","-12631572","-1162170","-30367808","1365631","15597720","-29526024","-39201040","13384035","41890056","31981244","-6734124","-10709516","-15089104","-23890887","26021668","-11096453","7228116","-28832261","14920934","-7428726","33607660","-67377070","1305774","-35775306","-82885192","-6692220","-37989964","32059488","5349708","-1625003","81399912","19909557","5168888","-41477358","-4001400","12749280","-20419810","-20207952","-41033940","-94244962","-2200122","40974480","67178106","7548471","46574076","54930296","-14491404","-71791433","28612484","-69492006","4891520","3424383","-6135264","-14173705","-26752044","10265616","-27940121","72613534","-31502484","-15790940","38830964","-21593142","2887252","-5569999","-5743548","12668977","-613312","-47944980","72413988","-23968834","590328","-121045223","86248940","-20268549","-35640096","-23960848","47724876","17329343","67295568","-10251927","-23462236","25003221","14283261","-3219082","-66065336","16453296","40159836","115391365","-13316238","32225921","36384784","-59611959","18477122","-63959350","9315630","-60385136","-62320334","19079388","-32808244","-139454113","29350836","-117719852","106392388","-6098895","99727422","63394536","-3923478","-84727984","30630764","-31262706","-1091356","-36262993","9368262","25064806","25380412","5441499","56134678","48950538","18079704","-956198","60719916","-38457801","77682536","19028688","28233198","-45899800","41792682","-15582231","6902674","70139924","-17490096","34340136","27552828","-15318477","-45831360","-10421744","5737032","-93155990","68738480","19385577","-1841305","28340474","8424000","37932144","-63045794","-29377656","67912348","182394158","39083526","-76352510","23747916","37215855","60015114","70357546","-41548122","40193952","33197954","-38432628","-58020372","77975472","-2082024","12805660","-6317474","36312426","-929394","18584105","-16836642","93487355","104436094","-21533121","-12705560","61311728","3631392","-58757785","16839336","-27574416","93717725","15350597","21156714","53193196","-36985184","-33916833","-64221108","62821206","23817726","50655896","-23825256","2893401","71556824","36688882","10142424","-88316442","4476524","-44884647","16737928","-65275984","-6427836","7388057","-25368820","10725642","64424164","160554912","-44416404","49673307","-11363636","29263032","-32659920","79516626","-43379892","-180357860","-89545068","-81121617","34886104","93575529","4990005","72007200"],"derived":{"al":[[3,-1],[37,-1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"111.6.a.b","letter":"b","dim":6,"charpoly":["1938558872","-319365284","15676940","-147812","-5984","67","1"],"traces":["6","-9","-54","53","-58","81","176","-327","486","1168","-390","-477","234","-479","522","177","-910","-729","632","-5960","-1584","-2809","-2192","2943","-4874","-10249","-4374","-7321","-9766","-10512","-14152","-21903","3510","-28897","-17420","4293","-8214","-32703","-2106","24688","-26220","4311","15332","-21203","-4698","-25799","-5172","-1593","14192","-59219","8190","8941","4180","6561","22828","-28469","-5688","77396","-37118","53640","5652","51950","14256","104321","-73368","25281","28464","152513","19728","82144","-2412","-26487","-28754","12321","43866","223759","-143932","92241","-25392","-153712","39366","123674","-144826","65889","-58568","-4948","87894","299793","-302474","94608","172744","301859","127368","325574","-181184","197127","182332","261630","-31590","171783","-49196","260073","53000","10897","156780","90077","-241550","-38637","7822","-199368","73926","137139","-366546","294327","-223760","-296236","18954","379928","-569214","-222192","-238032","-528498","235980","-679982","-411228","-38799","-471788","-92815","-137988","213832","-305490","190827","-403850","-157594","42282","-541451","-888240","232191","-277080","-139008","46548","309512","-387850","14337","-175980","236779","-127728","-72557","-928824","532971","-438204","-668237","-73710","-591615","212148","-80469","-1109576","540882","-37620","864304","-685712","-59049","95876","-22130","-205452","668551","425632","256221","-861524","793912","51192","905692","335792","-696564","492616","79641","334062","1259575","667522","-482760","-496704","974873","-50868","-1214537","79402","-467550","1258608","596866","-128304","1189920","485852","-938889","-36448","11874","660312","-1113350","857508","-227529","99028","-195597","-256176","-1933594","1403920","-1372617","298740","1819490","-177552","-79559","-689848","-739296","1076048","2304795","21708","530933","711868","238383","149032","-908035","258786","838368","-481816","-110889","1234712","1221715","-394794","1600510","2434030","-2013831","-838104","2116000","1295388","1412012","-1841048","-830169","1998296","72696","228528","-798655","520742","1383408","-3524424","3368778","-354294","378554","78026","-1113066","2578892","5680346","1303434","-1038872","2732202","-593001","1133042","1432379","527112","-106847","41286","44532","-240944","-824368","-791046","-2166746","1053888","-2698137","-1598976","1233215","2722266","-1953910","-1745540","-851472","6516","6887597","-1554696","-2520908","951190","-2716731","-2643930","3050066","-1146312","-2943664","-3021826","-2930166","1090064","2309520","1630656","-1168897","-1842436","-1774143","172384","-1394112","-1640988","-5148511","1354556","-2354670","-1387292","447663","284310","-2598218","-1567654","-1546047","135048","603763","442764","1932379","-4263548","-2340657","3123636","451103","-477000","-6250600","-1332170","-98073","-5085592","306620","-1411020","-7774154","-2744012","-810693","-2160744","-6256592","2173950","-4811513","4860570","347733","2831654","-1028821","-70398","-397530","-4791468","1794312","1895512","-2636139","-665334","-4917285","-3165856","-1234251","6211914","4953324","3298914","-10828288","2052004","-2648943","2132860","-12350036","2013840","4856219","-3477262","2666124","-4439872","-4365509","-170586","-548583","-2771170","-3419352","5434512","-13216031","5122926","-1650776","-1446676","1999728","-1446112","12874492","2142288","3021743","4220152","4756482","10788796","9204911","-2123820","-1598992","1250554","6119838","3764436","10902663","3701052","-5963030","170164","349191","6722676","-8989648","4246092","7133389","63132","835335","-1359060","1372650","1241892","13245758","-8783010","-1924488","10769320","5639970","2749410","-9843969","14687476","-1717443","15918416","-11445032","3634650","8704027","-902054","1418346","3284100","11054514","-380538","-4864076","533910","4873059","7553840","-629456","7994160","1274294","-9848900","-2089719","11486508","2646969","2493720","3944737","-5565598","1251072","-2950808","-7484984","-418932","-16885297","6797870","-2785608","13136328","-5243641","3490650","2888184","-12994348","-129033","3574946","301418","1583820","20359823","5523328","-2131011","3928388","-5490672","1149552","-4927057","-13801856","653013","11675912","-11848768","8359416","9811907","-11580658","-4796739","9700624","-6026926","3943836","6729788","-7130964","6014133","-8668692","21884032","663390","-14261792","-10233938","5324535","-113224","-13760212","-1909332","2167310","2148098","724221","-673024","-8645040","9986184","23645168","-13308560","-4867938","6264552","7773059","338580","-5775688","-3681120","-7778736","-320346","5971536","6171408","-13700738","-10127004","531441","583676","-12579518","-862884","-5951192","-17568866","199170","-18017580","-7630839","1849068","-27621334","-8859416","-6016959","5709468","9488240","-3830688","9951914","-16930706","-2305989","-18297012","18272329","7753716","-1748299","-22950992","-7145208","-4605012","20504401","-460728","8232695","3084956","-8151228","-15343880","655751","-3022128","2265872","-1593360","6269076","2783492","4251114","-4433544","17386374","-15516020","-716769","-17939276","15087000","-3006558","10295221","-23493144","-11336175","4396268","36677810","-6007698","-10879453","-17347012","4344840","-11700054","19740168","4470336","-25159315","-11076360","-8773857","25791452","-8816812","457812","17362541","-13923300","10930833","-8727340","-8298951","-714618","-16328962","-7619314","4207950","393832","16253648","-11327472","8948323","6255226","-5371794","-8285908","-23729249","1154736","-30733952","-2389506","-10709280","-3947988","4206469","-4372668","-29581218","15474608","8450001","-18049648","-4809176","328032","33290176","-21922548","-106866","-27649628","44728213","-5942808","13932829","15754774","10020150","-6421632","-3673000","-7717572","-242313","-18411212","2047761","6934764","8471674","-891252","-12276367","5958156","1760373","-17810518","32149164","2305584","-35475283","14988026","17402346","24298308","-21831685","-12635280","34973712","-8035048","12353553","-36207692","13092636","-2688660","27953763","24248912","-16375410","14015908","58010288","1597968","20016592","9095554","716031","-4747254","52355418","6208632","-48064596","1245790","6653664","-31771044","26925614","-9684432","26055366","28521380","-20743155","14715648","-9665420","-195372","14490800","-22088524","-4778397","43431336","6796841","-6406812","-38763119","22593232","-2145447","16362012","1161901","-1341288","25890533","4879626","8172315","-12278012","21104374","-2329074","19149362","26296464","-7545312","29696926","53697692","4336344","-3891031","-13413804","998001","-8484692","1503233","-11112408","8517256","24277740","-10995435","-67224442","19536515","3553146","-16082636","37302608","-14404590","9500988","83774544","-21906270","-14208298","3822930","18124479","-28572548","17997011","7542936","40874252","8600736","-19044000","29666704","4890533","-11658492","3326426","22545344","-12708108","19891912","11564006","16569432","17455309","10138318","7471521","-865208","-37791575","-17984664","24596918","50179524","-654264","-35345190","-21784320","-2056752","58124709","-22136408","7187895","-4370276","-11728816","-4686678","-46237366","15847160","-12450672","-19963996","-38283878","31719816","-40099012","14773494","-30319002","-1313148","-15898589","3188646","-54360544","10749524","-3406986","2001048","-27305231","-702234","-46013809","47767636","10017594","-39881616","8159240","-23210028","2123107","1408616","-51123114","9467700","-28370516","-11730906","-43640847","3566028","9349848","38480268","-39817670","-24589818","19208500","25322324","5337009","-4339146","-21910004","-10197378","80349648","-61183060","-12891411","-1688064","-33049929","-4744008","39517119","-11634664","961623","9274352","-675976","-371574","-466138","34411604","-400788","9960408","-96640618","2168496","-10978862","-51410780","7419312","-54835008","-22201375","7119414","-88947326","66901460","19500714","84327436","66787105","-9484992","-100589752","27256460","24283233","-24906868","-86741164","14390784","39503440","-5069810","-11098935","-21011748","-16687973","-24500394","44382423","14874018","17585190","1818596","22973750","15709860","-116280230","43444026","7663248","36498032","-7484812","-58644","3845521","-21204360","-61988373","23271624","-50695370","13992264","10643760","-50779356","22688172","66877052","-437874","-8560710","-106305728","15083134","24450579","-32450386","-55734536","23795370","84595785","-93411110","-27450594","-61297520","-9241481","10316808","-27909659","2606036","26492976","-38246506","-16565162","27196434","-9474280","24941302","26371494","84768900","12795767","-9810576","17372733","3000848","-20785680","-37204466","-60439518","-14675904","21180195","9288590","10520073","77784084","-90453456","16581924","15867523","-142988192","15967287","33941888","-9838719","-1551456","8968742","11780744","12547008","-7493252","-156366053","14768892","-43887513","20272160","46336599","57921488","-52323474","-12191004","52688624","8610212","21192030","57225296","47332017","12485628","109830388","-63044012","-4028967","-116158978","-140127288","-2558790","144193520","28662340","23383962","-58128828","3937811","14108886","-15309214","62869332","13914423","-13590714","62155346","-1215432","42872002","32884484","-5433867","-25324532","-69184756","-3984876","63069352","-25588306","-17391411","65540530","-66472028","38371932","-128753904","91154704","21065913","-58638152","102025808","-28112724","73687522","18398664","-4059927","6672506","-77815614","4293000","71240844","23148760","56255400","-10949032","-129760382","11989530","-56260170","44627164","882657","-109206524","-128556174","45770328","31676192","76150144","-2759580","65340756","-175974032","12699180","-25065116","78830162","69967386","37195982","-12625813","24696108","25111343","76686392","7296237","40784600","95474984","19446696","183182563","27351240","56309328","-46551874","14030881","-19565550","-154431672","74292372","43303617","105437900","-64201258","-43745130","122171632","62030604","-3129597","87913200","-213676642","-25484886","218539698","104506058","9259389","7587128","115648248","633582","64375403","4012260","3577770","6328656","107130388","43123212","-3142265","-7126988","-16148808","18270744","128125034","-17059608","155717808","28361988","23725251","95516522","-17708389","5988006","-55471232"],"derived":{"al":[[3,1],[37,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"111.6.a.c","letter":"c","dim":9,"charpoly":["-1140432891935112","74276944596324","2010156194988","-154228330600","-1214042481","85744671","437466","-15980","-45","1"],"traces":["9","3","-81","133","42","-27","-20","249","729","-468","-498","-1197","44","543","-378","3085","3354","243","704","7962","180","4049","6222","-2241","6375","16695","-6561","20631","20118","4212","6872","49671","4482","21139","29100","10773","12321","44697","-396","27152","9366","-4887","-32904","5337","3402","12413","-22296","-27765","6859","-27435","-30186","-36069","36462","-2187","-34964","56433","-6336","-52788","-840","-71658","12630","-3846","-1620","-2343","98016","-36441","-11984","1377","-55998","-189176","115800","20169","-81744","4107","-57375","-22423","86436","-150255","-27756","-20538","59049","-319914","-58098","-185679","69736","-47904","-181062","-523609","301650","-37908","-81704","349311","-61848","-519238","118452","-447039","-10","-345468","-40338","-702577","389970","-190251","-232588","-12519","-261900","-236905","25314","-96957","-146168","-132372","-110889","-139393","856890","-402273","226540","421986","3564","-829524","1021086","-244368","731055","436698","-84294","-122018","699348","43983","908140","535233","296136","-116772","893592","-48033","369106","403902","-30618","423173","1007934","-111717","415392","519288","200664","242128","747570","249885","932900","61365","-61731","182077","1548378","246915","149868","433287","271674","-392013","189552","324621","-465346","-961170","-328158","1312796","707664","19683","-1637488","-487902","314676","557885","-1094454","-507897","1556929","-1347600","57024","-776132","31734","475092","296116","-1470075","7560","253927","458832","644922","-926642","-825027","-113670","1234547","57498","34614","-1146848","-2972790","14580","1113200","-1626978","21087","1742606","-1930806","-882144","-1734390","1679334","327969","-1633876","-1921269","107856","-351790","-598632","-12393","617364","-1896846","503982","-2156185","642912","1702584","-1362780","438903","-1042200","4204995","-1342176","-181521","-568256","-3968547","735696","-1067260","-576288","-36963","-1331600","1152501","516375","948686","-1829928","201807","1489162","-834324","-777924","-548416","-1408782","1352295","-483320","-5971854","249804","-2242091","-2771544","184842","-1738894","-4650000","-531441","2623462","-1626114","2879226","-1795788","-5846814","522882","-2417732","-1395840","1671111","-458970","-1690035","-627624","5749669","2944554","431136","-27380","-2163480","1629558","-4326842","3169944","4712481","183216","-453429","-2714850","2464750","347214","341172","403944","-744495","735336","4735340","-4892550","-3143799","4087272","-6837558","556632","4552800","3751602","4673142","-5696960","4542600","-1066068","11678391","-3205092","4023351","5091453","758268","90","3596081","4838574","3109212","-2883264","340881","363042","8634366","-293850","6323193","1167504","-859611","-3509730","10412817","2707788","1712259","-8740744","354915","2093292","5724796","-4123728","112671","-2736226","4789500","2357100","1546814","-2732094","2132145","130560","3409974","-227826","6825699","6936846","872613","5924748","3740979","1315512","-5541918","3374700","1191348","4338888","-3998067","998001","4689403","6603744","1254537","1674936","-621630","-7712010","8013900","9600132","3620457","-4666828","-10697652","-2038860","-482595","-6471240","-3797874","-2453018","-13592811","-32076","-13238617","-3200574","7465716","-9815184","2750337","-9189774","11170212","6734736","2199312","-7205817","14618112","-6579495","3779125","1201584","-3930282","-6833268","9863619","758646","-640692","-1422246","1098162","-9332838","11228331","-6294132","-18547538","-522276","-395847","-5587316","-297624","-8173260","2192885","5740266","-4817097","-14883988","-2731758","-2665224","-1899134","-773994","1050948","-14087636","-7211976","-8042328","3110297","3233040","432297","3671758","1125744","-3321954","-7219245","14176050","-3635118","-12734836","19111374","275562","-7835460","-681762","-3808557","-6239910","-6640800","-9071406","13035378","-580068","1005453","-5556308","-13821699","-3738528","-20474999","469842","-4673592","-5902866","-10368804","-1805976","-2721555","12607158","-2179152","-20073152","8982087","-6728130","-13328252","9031650","-2248965","-1223804","13184946","-8396100","157577","-4387836","-552285","4882380","-5351100","555579","-1062043","-10971516","-1638693","-2519720","-5216856","-13935402","21182227","13460226","-2222235","-13914264","11374344","-1348812","-860120","11980308","-3899583","2032598","8164476","-2445066","305060","15310878","3528117","-10786304","-3023874","-1705968","12381310","-13384800","-2921589","27506344","-14634648","4188114","-43157172","41802120","8650530","8718128","11497761","2953422","36330412","8433930","-11815164","60236","-22735140","-6368976","14623414","21940740","-177147","-9969656","13611678","14737392","-19954000","7214886","4391118","13803012","-2298609","-2832084","-11343374","11145840","-5020965","2183848","-34310904","9850086","-15534622","5497416","4571073","3250940","-7904019","-14012361","13567253","22709214","12128400","9219372","19992507","-513216","20449799","29347584","6985188","-24048320","743367","-285606","6788940","7043202","-4275828","21379392","-35414664","-2665044","-10711886","-1550784","13230675","40774899","-10306596","-68040","19574543","26228604","-2285343","-27263452","12096030","-4129488","38471501","-8350992","-5804298","20111460","-25401360","8339778","-22429119","14597112","7425243","-15038032","47050044","1023030","29422867","7651032","-11110923","24385844","-24939639","-517482","-13066734","9458286","-311526","30336520","-1169712","10321632","-41190453","14156520","26755110","35841764","-9482649","-131220","4777392","27700266","-10018800","-14767524","-33636261","14642802","2296194","14179290","-189783","-7264994","-19439550","-15683454","4915432","-1340652","17377254","18817612","11617047","7939296","-2549953","23843868","15609510","28691448","-46910304","-15114006","4223365","17511354","-2951721","4797988","27343578","14704884","-60560997","-4767408","17291421","48866676","-53901876","-970704","5519669","-12685578","3166110","-57165816","14264667","5387688","60359304","-39978840","111537","7105246","-41127516","-5556276","-41993511","-4698966","17071614","-21582696","-51369948","-4535838","10544604","13600998","19405665","3435541","-13998450","-5786208","-30032076","4591626","-15323256","-4608136","-27280290","12265020","-17711834","-39938028","-3950127","35260374","-3854760","9379800","-408540","-27199158","-37844955","-9294456","-7034661","12079584","-12440585","-31057674","1633689","41816916","-63446979","5114304","-60179913","1927170","35716923","-9712984","-112978110","-6621264","16435570","-32214948","9605340","9651700","-15567864","5186592","16206123","-54590676","332667","-76843536","-73951815","11984400","-42865204","-1454628","-10372509","12429768","-23316471","-4647375","281692","-17078346","-8538174","-35838260","24335556","16469352","-31334242","-31580376","-1816263","-11961908","-34147299","-13402458","-47578744","-47413068","7508916","32358400","-17299227","7001316","-10598606","17008320","4935744","-11303256","97603866","12679038","27997493","21103518","-12170655","963776","-68862339","4349880","21880386","-53844300","53746686","41428572","-59439264","-2248236","48601249","-4073700","20178819","-108672308","-24791118","24943896","73420798","-22197588","-1663578","81740428","-37215864","15650046","8824584","3068970","41850000","-15240668","51246663","4782969","33280736","-9207216","-23611158","-23153334","92583567","14635026","217059911","20012700","-25913034","-51629892","10899978","16162092","-61834559","54441912","52621326","50119452","5486844","-4705938","82717299","-25580532","21759588","57825808","-162649254","12562560","144650216","-39556044","-15039999","16268736","87646944","4130730","-14395928","-16147050","15210315","-4659840","155428203","5648616","-19068953","-36161292","-51747021","40344006","59690988","-26500986","102188606","-4435794","-3880224","-14874152","-28669314","246420","-61775290","-100833204","19471320","57426920","6560175","-14666022","-65310066","28446756","38941578","-64507416","91787829","-28529496","-28607004","95339676","-42412329","44557808","95881236","-1648944","-101101596","-20567382","4080861","41458436","10530921","24433650","-35941717","1833714","-22182750","-33722308","127616490","-3124926","67657134","95398938","-3070548","16693352","66462948","-3635496","5543081","-99400692","6700455","-17622336","135911622","-6618024","-45202044","-31060530","-42618060","14799292","74491722","44032950","-139090248","-21934452","28294191","38961880","-9362772","-36785448","-26401497","-71514966","61538022","-47267180","49973169","-5009688","611647","76655364","-40975200","213919","59351418","-33764418","43237380","-70207974","-42058278","48709632","149916675","51272640","-160860427","8517918","-40883400","-97754492","137454978","9594612","43448405","-3290550","-105105519","-35826080","42009444","28845828","31167391","-41138940","-36210159","96333352","-6463305","-45823077","-72915654","8171088","-6824412","98746868","-204575829","-810","155545657","-46096440","-32364729","-17376418","-20533758","-43547166","54627836","50556486","-27982908","14739056","241960473","25949376","9007580","-48489708","-3067929","29140238","-83653152","-3267378","-109723552","-44079540","-77709294","-162408080","93944673","2644650","156794030","79663944","-56908737","-88830262","283290942","-10507536","-14146690","30468516","7736499","-74814664","27094746","31587570","-7414436","22134216","-93715353","-18111118","-21119316","-24370092","-17620760","-18361032","-15410331","-35638676","159118920","78666696","-66652210","107114376","-3194235","8727375","33254406","-18839628","-33981660","-8168526","-51523164","-123318664","-34326774","37113552","90158114","-9904548","-1014039","-170405246","-94029678","24626034","-132092832","-56527518","-43105500","-41814984","-92304870","-21213900","-74174452","-9158424","-13921326","-137287114","-2713677","24588846","-31536461","-97715550","-19189305","-25312564","31578210","-1175040","98259787","119887512","-30689766","65080417","22855455","2050434","-227890020","-119228508","-61431291","-12343268","17590908","-62431614","10337248","-33383556","-7853517","40018440","-97371258","-53322732","130522582","-73964982","-33668811","-61953832","38565990","-11839608","-41370623","-137237436","49877262","-38359576","74510748","-30372300","14753759","-185786328","-10722132","18133096","-71445978","-39049992","19974188","79464600","35982603","-61410552","-172340085","-8982009","-127691388"],"derived":{"al":[[3,1],[37,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"111.6.a.d","letter":"d","dim":10,"charpoly":["-91888937281465720","-3981043549079628","486689462409316","12404835142572","-466754022884","-6396565335","166248617","980598","-22504","-45","1"],"traces":["10","9","90","225","36","81","372","81","810","1416","1446","2025","910","591","324","5957","960","729","3520","-4146","3348","-301","-2514","729","12406","-2211","7290","10283","9072","12744","13452","11151","13014","42895","17844","18225","-13690","3579","8190","48152","34560","5319","38496","20787","2916","10177","48744","53613","73444","-56061","8640","-6443","-35988","6561","-14988","-80139","31680","-55148","23868","-37314","-44852","-146118","30132","-66103","-99972","-2709","93020","-209727","-22626","-139184","-11280","6561","81850","-12321","111654","-208189","-124980","-19899","-10952","-370206","65610","-213962","-253770","92547","88268","-331320","81648","103845","-251112","114696","225856","-555849","121068","-215042","-332796","100359","-28536","-938622","117126","248395","43488","386055","56056","-799329","160596","-16123","-113742","164025","347794","-784476","-123210","415411","-458904","32211","854356","-142986","73710","143412","164910","433368","332132","341898","311040","453150","54504","47871","1048068","-7131","346464","198276","-108852","187083","-216610","-954702","26244","1049141","31200","91593","822484","80100","438696","-38228","495738","482517","621480","220197","660996","-308025","-168312","-504549","1121860","658485","77760","-493339","1128648","-57987","1076476","7722","-323892","-721796","1872000","59049","977824","199566","-134892","-505969","1363698","-721251","449672","-1281852","285120","770172","1079148","-496332","-275988","907359","214812","-1516077","966156","-335826","1202636","-1212681","-403668","-2395129","-49284","-1315062","438000","1966998","271188","-1330944","1459998","-594927","-641080","2397786","-899748","-843346","-839940","-24381","34408","-536493","837180","-5096822","10656","-1887543","-771912","1005930","-203634","-2215463","-1334016","-1252656","-766728","193017","-101520","-2272319","-2204496","59049","-169824","-1903329","736650","-4690948","-2139300","-110889","-1329760","-1089915","1004886","2206658","-3605052","-1873701","-1058048","-2645544","-1124820","-5581412","1049340","-179091","-513944","2208882","-98568","-3331031","-2133360","-3331854","2394932","6812694","590490","-6835614","-4281360","-1925658","-1262660","-954750","-2283930","364820","-2191476","832923","2442234","5766105","794412","-2434875","-385320","-2981880","-509268","4723224","734832","4887998","1417920","934605","-2595332","15966693","-2260008","7470062","163308","1032264","3369872","9572361","2032704","573032","-3635982","-5002641","-181686","8508174","1089612","1494568","371016","-1935378","567776","12160668","-2995164","-1475605","-1881612","903231","4760496","16850664","-256824","4212329","1169148","-8447598","-9244376","-110889","1054134","4925718","1056570","2235555","4650064","9201033","391392","-5285317","1989096","3474495","-2761796","14024109","504504","6395316","-11969640","-7193961","-3831256","5460720","1445364","7220386","-1531872","-145107","-7982376","1654566","-1023678","-9809469","-7351230","1476225","2364570","10286145","3130146","-811602","-2681988","-7060284","-7630872","-4883169","-1108890","26871","-11202792","3738699","478634","7144668","-4130136","11061148","-3414948","289899","-1301892","-2424828","7689204","10514911","-3915924","-1286874","2561956","6435933","663390","7549493","-1912320","1290708","-5946864","-11913963","1484190","3581696","-6519000","3900312","13760580","-2439528","2989188","17859311","-7758948","3077082","-8062844","-9144573","2799360","-1938504","-13601802","4078350","13172864","5749401","490536","-1301542","-2565288","430839","-4529424","-7715928","9432612","7851049","-6238926","-64179","-2824324","-5475534","3118176","-46002","2411520","1784484","8079860","-31282128","-979668","-7975989","-12679080","1683747","10076444","3143820","-1949490","-8087901","5836200","-8592318","-8429236","-1977390","236196","-11793976","-1979574","9442269","22436364","3454056","280800","-20163902","-11984028","824337","-17949276","-16585557","7402356","7367297","-6528654","720900","-5536828","-14512440","3948264","-16294997","-12013056","-344052","-3037120","-10273251","4461642","-22040380","-29395614","4342653","7165654","-6627774","5593320","6207863","-11402292","1981773","-13995976","-30123252","5948964","-22174589","-14620344","-2772225","17627804","247800","-1514808","6024471","561744","-4540941","-4641184","-28793436","10096740","5999220","-33743628","5926365","17322624","1323792","699840","-2791644","-2033520","-4440051","20269884","9162138","10157832","-23413418","-24753924","-521883","19468496","6871272","9688284","16570036","28489608","69498","10485696","3294225","-2915028","-6279668","-6201174","-6496164","-1245790","-3267180","16848000","5901642","31203192","531441","-7528172","32105394","8800416","27950228","-24555786","1796094","22896984","43243539","-1214028","-4666486","17765568","-4553721","23206680","30155508","12273282","-6707818","-25096488","-6491259","6046632","9653139","4047048","55479201","41301492","-11536668","-19268348","11074035","2566080","-10300997","3228600","6931548","18954680","-809079","9712332","19934980","20156220","-4466988","5259768","39782184","-2483892","7420894","-25167048","8166231","17250652","38242716","1933308","-79947535","27962664","-13644693","-11157044","-10036794","8695404","1424311","2195316","-3022434","14689526","13431972","10823724","28107961","10756788","-10914129","-20619552","16668660","-3633012","-38310447","-37810896","-21556161","42506940","37228083","-443556","5337594","14347824","-11835558","-7996904","-20789820","3942000","9895199","-24482460","17702982","16498768","-42873819","2440692","-5481196","20007648","-11978496","10902112","-19666257","13139982","1143270","-59661510","-5354343","2257960","-16799592","-5769720","19306496","15624540","21580074","10765980","33207663","-8097732","-44241627","-40079016","-7590114","16931160","13749372","-7559460","-8155133","43670700","-219429","-39916260","-10616634","309672","17945073","24577632","-4828437","-6569058","-44607156","7534620","60337641","55580256","-45871398","1787812","18766761","95904","-76255304","36895056","-16987887","20661404","38963568","-6947208","-15201441","-14576868","9053370","5730244","6338052","-1832706","-19874308","-34448490","-19939167","-5431294","5504418","-12006144","3559360","-1314240","-11273904","-14236228","-38821422","-6900552","15195694","29583756","1737153","-21951852","-68065812","-913680","-79967348","47809548","-20450871","4583936","67455663","-19840464","-10685323","-34700322","531441","-10723612","17272983","-1528416","11994829","29404620","-17129961","-21358672","-16650978","6629850","-69617690","31142976","-42218532","-20055146","-114416328","-19253700","-69998279","94124988","-998001","13633616","51877365","-11967840","-11710244","-19601532","-9809235","-13599014","41865285","9043974","-64007008","-12020748","19859922","58846172","-83900028","-32445468","-122812494","-3593652","-16863309","-14163424","-51840639","-9522432","85645112","26448024","-23809896","-54515700","-8270517","-10123380","-53635134","11657928","-50232708","-40067428","-49987446","9444060","-139260287","-4495632","-1611819","-4818880","100538703","-4625496","-3882282","-9276516","19879938","14899078","100942512","-887112","-50567343","16590252","-29979279","77038500","100755162","-19200240","-47961002","23392596","-29986686","-16806164","-61864770","21554388","146843480","58331424","61314246","-63870320","-71064483","5314410","37503888","45452880","-61520526","-426968","91656219","-38532240","-78788221","15497388","-17330922","80254152","5675874","-11363940","89135827","-25071072","-8592750","-14630504","107273820","-20555370","27685041","-24586524","3283380","-14518640","45891006","-19723284","-25944940","24445548","7496307","2447890","22487784","21980106","13823352","43160760","51894945","-9381272","163813071","7149708","63537515","-51076260","-21913875","1313136","10423116","-3467880","-133333494","-46739292","-26836920","-26481260","168166386","-4583412","186133062","64968108","42509016","-97622496","-177672993","6613488","122494574","26630784","43991982","52251108","-61853373","12761280","10581596","-77560932","8411445","20230244","93973392","-23357988","231089592","-63440388","143700237","27479844","84996549","-20340072","-57352881","-29795322","67230558","-20054956","-1890642","1469772","-69649486","33003816","9290376","31669140","-53716260","30328848","412069","-1388196","86151249","-43741872","-72656454","18294336","139181436","67334748","5157288","-56275860","-53833638","-32723838","137002176","-6873240","-45023769","14233842","-12983244","-1635174","-12232199","36569712","76573566","33656348","17687097","9806508","43387581","-52406340","13451112","39627542","41537010","3339144","-5526376","-81902568","-17418402","-103983008","-101990787","5109984","243033897","3441666","109446012","9952294","-3722874","-26956476","49622055","59368752","-13280445","50017696","-197976756","-16934508","-37491805","27913716","8129079","-166674572","11977359","42844464","162389586","-7959312","151655976","-84149828","-102043707","-2311416","218461095","30521784","37910961","45419316","-27529266","10522332","-232881636","-75892320","-76028382","-50766152","-107013225","-83199384","81612588","-67496700","-998001","54105438","29398572","9487206","-187746576","-152932236","44331462","9245832","-139494507","9509130","8019010","11214192","20119995","-107502318","-242045994","41850576","181189958","98451840","82809297","-3780600","-245868726","3522528","78296668","1672512","-47567853","-31585966","-38448396","17901864","61878272","-150027528","31270455","-99275600","-192863328","-24856164","-160978786","-53772960","126216981","-16983814","127313502","4540536","-51523176","-48578556","57557844","80086912","63389214","-107726760","4601038","-149773044","-64745649","74569068","5392674","-34481304","107677072","47662320","49146480","-138280776","141933546","13008276","186967684","-75706140","64983474","-689298","-341897463","-13786848","-140194385","197731620","-1305963","-86344044","-40493466","-71841384","24633511","-108493272","14891094","75695794","3026859","-9213102","164601328","32983464","-88285221","-8275120","244182876","-66161070","-310662696","-60832320","13286025","-114383776","60448050","21281130","-64159870","119527920","92575305","-29914792","-299940342","28171314","5161683","-93341004","-7304418","-6948396","140165988","-24137892","-41441965","-45157128","-63542556","-127818660","-246928938","-68677848","-162661032","-190777152","-43948521","-200901134","71187177","-9980010","188729300"],"derived":{"al":[[3,-1],[37,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.28,"computed":"atlas","estimate":{"seconds":0.635,"low":0.387,"high":1.099,"bytes":2127457},"url":"https://sagebrush.space/atlas/mf/111.6.a"}