{"label":"42.8.a","level":42,"weight":8,"dims":{"new":6,"cusp":52,"eisenstein":8,"modsym":112},"old":[[2,1,4],[3,1,4],[6,1,2],[7,3,4],[14,4,2],[21,8,2]],"T":[[5,1],[11,3]],"status":"proven","checks":["dim M^+ at levels [1, 2, 3, 6, 7, 14, 21, 42]: [1, 3, 3, 9, 5, 16, 20, 60] (certified at ell = 2147483647)","T = [(5, 1), (11, 3)]; h of degree 6 = 1 x 6 (phi(ord eps) x dim S_k^new); 3 primes, 0 rejected"],"newforms":[{"label":"42.8.a.a","letter":"a","dim":1,"charpoly":["17054","1"],"traces":["1","-8","-27","64","-410","216","-343","-512","729","3280","-5548","-1728","-1698","2744","11070","4096","9506","-5832","57620","-26240","9261","44384","59192","13824","89975","13584","-19683","-21952","27190","-88560","-252288","-32768","149796","-76048","140630","46656","524126","-460960","45846","209920","-463638","-74088","96212","-355072","-298890","-473536","-1068864","-110592","117649","-719800","-256662","-108672","125262","157464","2274680","175616","-1555740","-217520","932620","708480","546942","2018304","-250047","262144","696180","-1198368","3472396","608384","-1598184","-1125040","-33928","-373248","-3640838","-4193008","-2429325","3687680","1902964","-366768","4272960","-1679360","531441","3709104","9841172","592704","-3897460","-769696","-734130","2840576","-1681590","2391120","582414","3788288","6811776","8550912","-23624200","884736","-10813454","-941192","-4044492","5758400","-5573978","2053296","10879352","869376","-3797010","-1002096","19339716","-1259712","-20003690","-18197440","-14151402","-1404928","10290322","12445920","-24268720","1740160","-1237842","-7460960","-3260558","-5667840","11293133","-4375536","12518226","-16146432","-4858500","2000376","-1972224","-2097152","-2597724","-5569440","-12754268","9586944","-19763660","-27779168","8070030","-4867072","54174586","12785472","45196300","9000320","28859328","271424","9420504","2985984","-11147900","29126704","-3176523","33544064","46032270","19434600","-16516088","-29501440","6929874","-15223712","103438080","2934144","-44785234","-34183680","-3382074","13434880","-20302856","-4251528","41523452","-29672832","-61416360","-78729376","78627016","-4741632","-59865313","31179680","42004980","6157568","-42827858","5873040","-30861425","-22724608","-25180740","13452720","130278300","-19128960","-11875338","-4659312","-14767434","-30306304","-214891660","-54494208","-52739288","-68407296","6751269","188993600","-31291008","-7077888","-103367038","86507632","-18796860","7529536","108237086","32355936","54385400","-46067200","-93754692","44591824","-9326170","-16426368","190091580","-87034816","43150968","-6955008","-319675760","30376080","-133396228","8016768","916056","-154717728","-39446920","10077696","86534784","160029520","98302626","145579520","-16141188","113211216","238563152","11239424","65591775","-82322576","-277633404","-99567360","-19333850","194149760","-51380028","-13921280","130217882","9902736","438234240","59687680","-115369920","26084464","-350612160","45342720","331686242","-90345064","-14348907","35004288","-48236090","-100145808","-97838760","129171456","-265711644","38868000","127770012","-16003008","-328397216","15777792","105231420","16777216","327088866","20781792","-179775218","44555520","19821510","102034144","301675032","-76695552","-51357420","158109280","45402930","222233344","-12353810","-64560240","411177792","38936576","-15725178","-433396688","-499181300","-102283776","415998206","-361570400","-183917952","-72002560","-7478038","-230874624","-401957108","-2171392","637853400","-75364032","159027834","-23887872","-319974637","89183200","291963258","-233013632","53361222","25412184","-382374200","-268352512","109201284","-368258160","-100508016","-155476800","-33000716","132128704","150497406","236011520","-224246220","-55438992","338364916","121789696","-293742504","-827504640","170827912","-23473152","60533722","358281872","102519270","273469440","-201069594","27056592","-150850120","-107479040","-522172332","162422848","547735720","34012224","-152777550","-332187616","540099630","237382656","366620352","491330880","-960929068","629835008","382087854","-629016128","-1423682360","37933056","-293359374","478922504","-277838694","-249437440","1399693824","-336039840","-40353607","-49260544","655255440","342622864","-357308604","-46984320","-1206314930","246891400","33421734","181796864","175730082","201445920","13910480","-107621760","88035066","-1042226400","-512890040","153031680","2426192661","95002704","-304914591","37274496","1492743580","118139472","1264763936","242450432","-337992102","1719133280","-42964866","435953664","-253450658","421914304","131179500","547258368","-46168620","-54010152","1354596580","-1511948800","53250048","250328064","-686967088","56623104","-780215240","826936304","70138548","-692061056","-96799730","150374880","562679152","-60236288","344365236","-865896688","-1751913600","-258847488","-1439404194","-435083200","533618820","368537600","710919282","750037536","428385024","-356734592","-217890810","74609360","-2907851048","131410944","-41284870","-1520732640","-1462713822","696278528","-319888660","-345207744","-4034880520","55640064","-1220300100","2557406080","-1820808780","-243008640","-2571613458","1067169824","-779201856","-64134144","855302350","-7328448","-187601106","1237741824","-254353608","315575360","2370576192","-80621568","1860810722","-692278272","300993300","-1280236160","3410643040","-786421008","-1020496680","-1164636160","85766121","129129504","3491282132","-905689728","689451900","-1908505216","-1242871290","-89915392","-839034590","-524734200","2572263624","658580608","445934376","2221067232","-238789740","796538880","1718182906","154670800","-187106598","-1553198080","-899058578","411040224","481400032","111370240","-2792828160","-1041743056","3811180276","-79221888","-1191031828","-3505873920","1209201318","-477501440","-533784176","922959360","5184359500","-208675712","91315998","2804897280","-4510114480","-362741760","-889965948","-2653489936","548177112","722760512","4433516140","114791256","-1362521224","-280034304","-1121133204","385888720","2118496452","801166464","258468140","782710080","1658241720","-1033371648","11637304","2125693152","4165623100","-310944000","-2122929432","-1022160096","-1777503768","128024064","2285330980","2627177728","1616363451","-126222336","-702617730","-841851360","1248807434","-134217728","-1134134460","-2616710928","-4460534320","-166254336","5930057472","1438201744","1156352166","-356444160","1695868842","-158572080","-3553866628","-816273152","833258475","-2413400256","-2398249728","613564416","98867417","410859360","679879980","-1264874240","787257324","-363223440","-7929283560","-1777866752","-3517514100","98830480","-652716652","516481920","-3387962538","-3289422336","320634126","-311492608","8201512900","125801424","-2663587044","3467173504","398720718","3993450400","1566687800","818270208","-1465625280","-3327985648","5802074820","2892563200","-5948587754","1471343616","-163367976","576020480","1423960776","59824304","2353267172","1846996992","-4219032020","3215656864","-182284263","17371136","-2659407990","-5102827200","655894212","602912256","844857216","-1272222672","5325800200","191102976","-5273069534","2559797096","2790910026","-713465600","-3375521996","-2335706064","-694953576","1864109056","507515220","-426889776","-4504339924","-203297472","-14536834560","3058993600","-2922401322","2146820096","414190962","-873610272","1336828780","2946065280","-1468405800","804064128","-8238491160","1243814400","6064120682","264005728","2531376684","-1057029632","-4630184530","-1203979248","-3087201264","-1888092160","251806590","1793969760","1814931072","443511936","3798302142","-2706919328","-5132472660","-974317568","2824667546","2349940032","5292465340","6620037120","-1165076136","-1366623296","576785370","187785216","-5037311875","-484269776","8631245520","-2866254976","4982341756","-820154160","5345711672","-2187755520","3601698156","1608556752","808611840","-216452736","-199768002","1206800960","-24733512","859832320","-8359576318","4177378656","8246877332","-1299382784","1065066840","-4381885760","7084021416","-272097792","-5174175760","1222220400","-2336439168","2657500928","8620351302","-4320797040","5229249880","-1899061248","-2654170902","-2932962816","4216565420","-3930647040","5676381382","7687432544","435812076","-5038680064","8103100600","-3056702832","1609430480","5032129024","-6441205104","11389458880","-3034434216","-303464448","3366880322","2346874992","-1770977925","-3831380032","-10416862314","2222709552","3709014722","1995499520","7496101908","-11197550592","-592758588","2688318720","-22211580260","322828856","522013950","394084352","-212694876","-5242043520","8291834132","-2740982912","1387260756","2858468832","-18530483000","375874560","-4407342828","9650519440","-3515882814","-1975131200","10200672502","-267373872","30200140120","-1454374912","-11832324480","-1405840656","1911874454","-1611567360","15249693470","-111283840","3114987840","860974080","-14933431296","-704280528","-3862406640","8337811200","9466528320","4103120320","-3707367360","-1224253440","-3731617736","-19409541288","-8955528534","-760021632","2446420250","2439316728","4152958216","-298195968","387420489","-11941948640","914591272","-945115776","19795106622","-10118111488","1302374430","-1939603456","-19264853008","2703936816","-11214469860","-13753066240","2641646520","343718928","-15454204248","-3487629312","-18873230700","2027605264","7174214388","-3375314432","-6633522588","-1049436000","-3911840688","-4378066944","-3449790324","369348960","6771596080","432081216","12585045966","-10836772640","8866724832","12095590400","18246824762","-426000384","6861265670","-2002624512","-2841248340","5495736704","-1583588760","-452984832","13078857010","6241721920","-8831399382","-6615490432","-7977224858","-561108384","-22699612800","5536488448","4853930886","774397840","-26714821560","-1202999040","188232544","-4501433216","-535180770","481890304","18361945940","-2754921888","17223993396","6927173504","-8145225864","14015308800","-3529580446","2070779904","-928707516","11515233552","1386650340","3480665600","13862266686","-4268950560","-10160621184","-2948300800","-1225879110","-5687354256","20199369224","-6000300288","8324170960","-3427080192","333552870","2853876736","28571674810","1743126480","-4060197188","-596874880","-11101800384","23262808384","-17024615320","-1051287552","5543735440","330278960","424579806","12165861120","11254282862","11701710576","-28797582728","-5570228224","13477895100","2559109280","2472000756","2761661952","6931389790","32279044160","-11231951562","-445120512","1118371394","9762400800","-32237076560","-20459248640","4965784704","14566470240","12275027720","1944069120","-16510580209","20572907664","201907026","-8537358592","24544778330","6233614848","-3873544619","513073152","10852841916","-6842418800","31024066192","58627584","-25298588458","1500808848","-17222041800","-9901934592","-12212246214","2034828864","12973006460","-2524602880","-4293751518","-18964609536","-10329704288","644972544","17559421780","-14886485776","8639315199","5538226176","-23706382080","-2407946400","-5896128408","10241889280","-7883007966","-27285144320","1666465500","6291368064","12592155286","8163973440","-1440752994","9317089280","15674845362","-686128968","9772075772","-1033036032","10324103400","-27930257056","21098285016","7245517824","676472832","-5515615200","-2948434668","15268041728","-61587943680","9942970320","-53414103000","719323136","2713716432","6712276720","-6859710720","4197873600","1190740572","-20578108992","891019332","-5268644864","4868888580","-3567475008","10115807556","-17768537856","-4063429962","1910317920","-7542988608","-6372311040","-54598822256","-13745463248","6054647940","-1237366400","4374713924","1496852784","12245917720","12425584640","-9135852732","7192468624","57609744","-3288321792","47158236850","-3851200256","7931047608","-890961920","-22405957230","22342625280","6778935380","8333944448","-4612353624","-30489442208","21623108080","633775104","-28361852134","9528254624","-1634410494","28046991360","16305496702","-9673610544","-27443660496","3820011520","-2768020290","4270273408","18908857996","-7383674880","6182142924","-41474876000","5428879038","1669405696","34219815722","-730527984","12829313280","-22439178240","4072953240","36080915840","-18581882998","2901934080","36136620833","7119727584","14098652964","21227919488","42380485580","-4385416896","-36813007624","-5782084096","-14788864440","-35468129120","24315446172","-918330048","-15502330900","10900169792","4124993850","2240274432","-7505344014","8969065632","9329461320","-3087109760","-14582690010","-16947971616","14773954392","-6409331712","-44377205260","-2067745120","-9898749504","-6261680640","5694980704","-13265933760","-6572648368","8266973184","25945084836","-93098432","-22298014000","-17005545216","39023061686","-33324984800","-10316372058","2487552000"],"derived":{"al":[[2,1],[3,1],[7,1]],"fricke":1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"42.8.a.b","letter":"b","dim":1,"charpoly":["-24498","1"],"traces":["1","-8","-27","64","-18","216","343","-512","729","144","8172","-1728","-14242","-2744","486","4096","-21462","-5832","-5884","-1152","-9261","-65376","-98784","13824","-77801","113936","-19683","21952","165174","-3888","-241312","-32768","-220644","171696","-6174","46656","185438","47072","384534","9216","59682","74088","-809308","523008","-13122","790272","942096","-110592","117649","622408","579474","-911488","226398","157464","-147096","-175616","158868","-1321392","-2205732","31104","-1156690","1930496","250047","262144","256356","1765152","-3740404","-1373568","2667168","49392","-2593296","-373248","-1038742","-1483504","2100627","-376576","2802996","-3076272","2280032","-73728","531441","-477456","-283404","-592704","386316","6474464","-4459698","-4184064","-5227230","104976","-4885006","-6322176","6515424","-7536768","105912","884736","6168770","-941192","5957388","-4979264","1512990","-4635792","16585304","7291904","166698","-1811184","16438524","-1259712","-9007306","1176768","-5006826","1404928","9007698","-1270944","1778112","10571136","-10382418","17645856","-7361466","-248832","47294413","9253520","-1611414","-15443968","2806668","-2000376","-9068992","-2097152","21851316","-2050848","-34452252","-14121216","-2018212","29923232","354294","10988544","-23282262","-21337344","-8228596","-395136","-25436592","20746368","-116385624","2985984","-2973132","8309936","-3176523","11868032","2343870","-16805016","35506232","3012608","-15645798","-22423968","4343616","24610176","-38987554","-18240256","-6112746","589824","-33882912","-4251528","-8437732","3819648","3971592","2267232","-490344","4741632","140086047","-3090528","-4289436","-51795712","-47613786","35677584","-26685743","33472512","59554764","41817840","-3015420","-839808","116277302","39080048","31230630","50577408","-3337884","-52123392","-175387464","60294144","-6751269","-847296","93511992","-7077888","31007426","-49350160","-6921612","7529536","127599534","-47659104","34692104","39834112","100990908","-12103920","56654682","37086336","-1074276","-132682432","-72013536","-58335232","-48084048","-1333584","-195279700","14489472","70018992","-131508192","14567544","10077696","-82770016","72058448","28046034","-9414144","305661804","40054608","-34369984","-11239424","-56716929","-72061584","-118922796","10167552","240588806","-14224896","-75680892","-84569088","94684650","83059344","-16957728","-141166848","-61560864","58891728","-48146136","1990656","-217362286","-378355304","-14348907","-74028160","-2117682","12891312","83799928","123551744","7651908","-22453344","246331980","16003008","-807262848","72551936","-10430532","16777216","284387130","-174810528","63605234","16406784","120411846","275618016","169646688","112969728","-4075164","16145696","141135210","-239385856","-219211818","-2834352","-330288640","-87908352","131895162","186258096","-635789772","170698752","292800446","65828768","-175916448","3161088","85172730","203492736","554395100","-165970944","-2859624","931084992","20470926","-23887872","50278771","23785056","-166556790","-66479488","-720948930","25412184","39703176","-94944256","-160849476","-18750960","1406881728","134440128","-277592644","-284049856","-40850730","-24100864","20820420","125166384","-546390844","179391744","-447803208","-34748928","-433853256","-196881408","593612954","311900432","-4500846","145922048","-345799914","48901968","1349801928","-4718592","-443840148","271063296","126282408","34012224","1108041842","67501856","243197262","-30557184","323138928","-31772736","-1230691708","-18137856","135184302","3922752","67327272","-37933056","-70011886","-1120688376","-243207846","24724224","-1972001664","34315488","40353607","414365696","-48009024","380910288","434128812","-285420672","860825726","213485944","280325286","-267780096","361753290","-476438112","46679328","-334542720","198759582","24123360","1481420544","6718464","-859250283","-930218416","-1276949151","-312640384","18697356","-249845040","-1356175504","-404619264","43508178","26703072","77654514","416987136","-1846033762","1403099712","-75780036","-482353152","-2352408108","54010152","-467995660","6778368","244862784","-748095936","1576685520","56623104","-50453928","-248059408","-589985532","394801280","564725358","55372896","2120102208","-60236288","930210804","-1020796272","-41040576","381272832","1063292366","-277536832","54491724","-318672896","200881026","-807927264","3436765504","96831360","-9565938","-453237456","1515399336","-296690688","242312234","8594208","628621074","1061459456","-756566076","576108288","5101272","466681856","222172092","384672384","-1747108860","10668672","-84461266","1562237600","686787984","-115915776","1669765062","-560151936","-396744670","1052065536","3142411848","-116540352","-345601608","-80621568","-46825918","662160128","80274564","-576467584","581245056","-224368272","-3282001912","75313152","85766121","-2445294432","-553577316","-320436864","94090140","274959872","-63284490","89915392","-2207323134","453735432","487721304","576492672","-958668264","951382368","87930108","-81340416","86914106","-1924710448","422436546","113799168","911932422","605447136","-1271119072","676552704","-117277632","-757477200","-134559228","-664474752","-1282958572","135661824","1052663958","1129334784","-6613664976","492486912","457781084","-471133824","165044142","385169088","2044684512","-15925248","-2641007996","1738898288","914838624","3026842432","-111037860","114791256","-1873189816","592225280","227818764","16941456","-874890420","-103130496","-3544964388","-670399424","-107232984","-988413952","-889500528","-61215264","-584889268","179626752","13239288","-1970655840","-291025656","-128024064","-27233820","6458102784","-3782323269","-580415488","1633406310","83444256","-356288506","-134217728","115814772","-2275097040","-298535472","1398484224","7698808512","-508841872","1285572222","-131254272","-4760551086","-963294768","-2827846564","-2204944128","720515061","-1357173504","5179038144","-903757824","6353453209","32601312","-1607978628","-129165568","-849991044","-1129081680","-295893432","1915086848","81416340","1753694544","961427628","22674816","1429607702","2642309120","-3139487154","703266816","162131508","-1055161296","-5867837380","-1490064768","-843227010","5086318176","-971883816","-1365590016","782050976","-2342403568","90122868","-526630144","-2924758554","1407331584","11526164536","-25288704","4735461528","-681381840","-982630092","-1627941888","-162138564","-4435160800","182284263","1327767552","7249904346","22876992","-7554461116","-7448679936","-2524823784","-163767408","7685493984","191102976","7097461058","-402230168","-837200502","-190280448","-97207572","1332454320","1850124456","531835904","186883524","5767591440","6078738876","-203297472","1419879808","-317625408","-3445187418","759554048","-859606374","1286795808","132506388","150007680","-936686808","-11255053824","-661964160","-1075521024","1139639498","2220741152","-2726754516","2272398848","-851299434","326805840","2871641696","192806912","-1529676414","-166563360","-13417331232","-1001331072","4433701214","4371126752","29005452","-1435133952","2462799018","3582425664","1822299452","277991424","1944365472","3470826048","-1792939890","1575051264","6027683101","-4748903632","1298269296","-2495203456","-3979870356","36006768","3897825176","-1167376384","5272551900","2766399312","163241856","-391215744","-1675557058","-10798415424","-1890512784","37748736","-3869504046","3550721184","-12766109404","-2168506368","-393323688","-1010259264","2731652472","-272097792","-18025241904","-8864334736","2234790432","-540014848","8992531782","-1945578096","620140536","244457472","-757242918","-2585111424","7941648516","254181888","6145479158","9845533664","-8252868708","145102848","36327816","-1081474416","-16316548416","-31382016","927989568","-538618176","-9452470680","303464448","-4110946174","560095088","1531357083","8965507008","8699710350","1945662768","2115888110","-197793792","3210915492","15776013312","-10645800468","-274523904","419080716","-322828856","-6495897762","-3314925568","-3224360316","384072192","499888628","-3047282304","2043384084","-3473030496","148114728","2283365376","-1280895084","-6886605808","-2556485550","-1707887552","3675892086","-2242602288","-1091117192","2142240768","457858656","-2894026320","518955570","3811504896","-3134295874","-373434624","1662143328","2676341760","23837764608","-1590076656","2094941232","-192986880","1299945672","-11851364352","16316977344","-53747712","5688759272","6874002264","5868781722","7441747328","-12850702374","10215593208","-7535424952","2501123072","387420489","-149578848","17369368296","1998760320","-3916989058","10849404032","57177414","3236954112","-30566581488","-348065424","-4748683876","-213624576","-2262598056","-621236112","3968481216","-3335897088","-42189660","14768270096","-206601516","-11224797696","5638413732","606240288","-13748385280","3858825216","-6650963460","18819264864","-639112176","-432081216","3182824046","3743965280","21796096896","-54226944","142850034","-1958902272","-3089505958","5984767488","281624364","-12613484160","31414035144","-452984832","160316690","403631424","-7678452510","1984475264","-2462718210","4719884256","18774314912","-3158410240","-1717341318","-4517802864","-351168888","-442983168","-21192414912","-16960817664","-3251119842","481890304","701775972","-7441686432","-888648844","8166370176","-4580460576","328324608","3089640414","-3050182656","16473578980","-8506338928","110029428","2220294656","-16025193546","-435933792","-20219264352","2549383168","-3810650670","-1607048208","-8488599624","6463418112","609892416","-27494124032","5918719086","-774650880","11664009210","76527504","-1328854084","3625899648","8917793280","-12123194688","151879176","2373525504","4761968272","-1938497872","-3561169374","-68753664","-24657703458","-5028968592","19462859096","-8491675648","17166323844","6052528608","-20940267060","-4608866304","-16368488098","-40810176","-7905612042","-3733454848","-2524982838","-1777376736","8826192","-3077379072","4749744096","13976870880","-305165640","-85349376","10032573967","675690128","-2299663710","-12497900800","-2521548846","-5494303872","16221983659","927326208","-14968667700","-13358120496","-18318307392","4481215488","-10115297146","3173957360","77209848","-8416524288","-24562648782","-25139294784","16439043020","932322816","-552715002","2764812864","-18686886744","644972544","857048148","374607344","-1357526817","-5297281024","18632421504","-642196512","53270833768","4611740672","4497033330","-4649960448","962687124","1794946176","27846538934","26256015296","19465621110","-602505216","30048579450","-686128968","26527171052","19562355456","-1071985752","4428618528","29105591400","2563494912","-3110664256","-752721120","4342935852","-2199678976","-5543292864","506275920","54277560","-719323136","-37985806656","17658585072","-39858468288","-3629883456","-4858953876","-3901770432","7495001388","-4611941376","-2092991436","7669346112","8974447028","-7611058944","1102969710","-703440864","-27335481384","650723328","-2315977488","-695312848","-562151340","15397683584","-11817122436","-3379492368","14885375240","-910393344","14752552788","-7295459376","36933721632","-4843577088","-14427261838","10168952576","12090686616","-5412421632","3066937770","938221056","-692246716","6059817600","11714037912","1076473824","3156974352","5315798016","-46396734118","10263668576","-16027549758","-1085294592","-24392880570","-8421311664","-5895626688","-9034678272","121522842","52909319808","-20696942364","-3939895296","14793763564","-3662248672","9336597678","3769070592","20326192650","-1320353136","-1683215856","-3081352704","-36444652056","-16357476096","-7985815866","127401984","30718867233","21128063968","11983683996","-13911186304","-558133668","-7318708992","7092147992","-24214739456","-3409625016","888302880","10826189916","-918330048","-2822408428","14985518528","-29917129734","-4737802240","-6886911486","-1822550112","-42716923560","-135531648","-6566326074","6999123360","21395728152","825043968","-2296791612","28359715104","-8724751056","5363195392","79946681472","857863872","-50776863136","7907311616","33228676116","7116004224","-624457872","489722112","-28379836954","4679114144","-3649976154","-1437014016"],"derived":{"al":[[2,1],[3,1],[7,-1]],"fricke":-1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"42.8.a.c","letter":"c","dim":1,"charpoly":["3158","1"],"traces":["1","-8","27","64","-122","-216","-343","-512","729","976","-1012","1728","3126","2744","-3294","4096","-28294","-5832","-22228","-7808","-9261","8096","-108640","-13824","-63241","-25008","19683","-21952","-41354","26352","46656","-32768","-27324","226352","41846","46656","-85714","177824","84402","62464","-155694","74088","926804","-64768","-88938","869120","-529152","110592","117649","505928","-763938","200064","-294066","-157464","123464","175616","-600156","330832","-667292","-210816","833430","-373248","-250047","262144","-381372","218592","1153996","-1810816","-2933280","-334768","3842336","-373248","1483690","685712","-1707507","-1422592","347116","-675216","-3763824","-499712","531441","1245552","-5393092","-592704","3451868","-7414432","-1116558","518144","2502690","711504","-1072218","-6952960","1259712","4233216","2711816","-884736","-4597550","-941192","-737748","-4047424","20528470","6111504","14233400","-1600512","1129842","2352528","-9320244","1259712","4306246","-987712","-2314278","-1404928","6935698","4801248","13254080","-2646656","2278854","5338336","9704842","1686528","-18463027","-6667440","-4203738","2985984","17246652","2000376","-31450176","-2097152","25023708","3050976","-4488020","-1748736","7624204","-9231968","-2401326","14486528","15625642","23466240","-54243548","2678144","-14287104","-30738688","-3163512","2985984","5045188","-11869520","3176523","-5485696","-32494962","13660056","-76333832","11380736","-20626326","-2776928","-5692032","5401728","-29242090","30110592","-7939782","3997696","37263520","-4251528","-95089780","-9964416","3333528","43144736","-22994936","4741632","-52976641","-27614944","-16204212","59315456","119486062","8932464","21691663","-4145152","-18016884","-20021520","93825492","-5692032","148834062","8577744","22502610","55623680","10457108","-10077696","28633528","-33865728","-6751269","-21694528","-101405976","7077888","70589570","36780400","-10297044","7529536","50230718","5901984","208897256","32379392","31157892","-164227760","14184422","-48892032","18994668","-113867200","-79198560","12804096","22494736","-9038736","-84493108","-18820224","103743072","74561952","-113070088","-10077696","-16003008","-34449968","40059630","7901696","-88447044","18514224","150174512","11239424","-46102689","-55485584","-302873796","-38409984","-53137346","-106032640","9372132","21173248","-136350742","-18230832","64556544","-42706688","-101623248","-77638736","226801992","-13492224","405053090","147704216","14348907","53339520","-14353178","33629904","-69484728","-23887872","-145613484","-137973216","-30806460","-16003008","109943680","251601408","93200436","16777216","-275131590","-200189664","29399902","-24407808","-30147066","35904160","-483995952","13989888","35876052","-60993632","67572630","73855744","247374526","19210608","-228286608","-115892224","-28949886","-125005136","63999892","-187729920","-355115746","433948384","34012224","-21425152","228167162","114296832","-213791228","245909504","73219032","25308096","53403042","-23887872","390211763","-40361504","-124133850","94956160","378816342","-25412184","81409624","43885568","-19919196","259959696","-339608640","-109280448","-317893772","610670656","554268690","-91045888","-101678460","165010608","633813676","22215424","384301800","45536256","-390195368","-43213824","-1004441750","233936720","30505734","-240884736","242974566","63518256","41850248","-31981568","-251646588","-298108160","628919032","34012224","-197691366","760718240","116268642","79715328","181499136","-26668224","-28351660","-345157888","-62485506","183959488","-140787512","-37933056","-1016754606","423813128","187263846","220919552","-47215872","129633696","-40353607","-474523648","357860160","-955888496","-970493652","-71459712","884144662","-173533304","61529058","33161216","-1090461270","144135072","-468764992","160172160","262030734","-750603936","1033729216","45536256","-399787755","-1190672496","-498501729","-68621952","-181010180","-180020880","-242183104","-444989440","-113500926","-83656864","100864638","80621568","-1437687362","-229068224","465659604","270925824","-129272604","54010152","1201689028","173556224","-849154752","811247808","630858560","-56623104","-42348152","-564716560","675640116","-294243200","-1421858066","82376352","3073860160","-60236288","-121176540","-401845744","459186528","-47215872","70496934","-1671178048","205853508","-259035136","2023221378","-249263136","145846656","1313822080","-64835802","-113475376","86742568","391136256","1437263930","-151957344","421892334","910937600","228881156","633588480","657957224","-102432768","-1464575796","-179957888","86209788","72309888","-1182543090","675944864","-385751808","150561792","1789340854","-829944576","-285866490","-596495616","-85414824","904560704","604657464","80621568","71639378","128024064","136220076","275599744","2414849920","-320477040","194917464","-63213568","85766121","707576352","-2080181332","-148113792","-305328180","-1201396096","-877363974","-89915392","1786059490","368821512","157562328","443884672","-2061013464","2422990368","130810596","307279872","-2243079686","425098768","-556910802","848261120","-2602543442","-74977056","-712556816","-169385984","-153684864","1090805936","-633468788","145846656","-395820628","-516452352","-789536430","341653504","-937925648","812985984","1405720948","621109888","-214374114","-1814415936","-220552048","107937792","-267941964","-3240424720","1006115040","-1181633728","560901100","-114791256","3929324552","-426716160","-2567424060","114825424","-3289035972","-269039232","1170070076","555877824","90005256","191102976","-1317921248","1164907872","-4306303412","1103785728","-620863272","246451680","-2563922328","128024064","-2504473340","-879549440","-1430369307","-2012811264","4203859278","-745603488","-508905670","-134217728","-437513724","2201052720","-1736474800","1601517312","535501824","-235199216","3226123674","195262464","4507695714","241176528","-5463516796","-287233280","585674901","3871967616","-1320084864","-111919104","8397824153","-287008416","-486455868","487949056","-486699444","-540581040","1137069768","-590845952","2533288284","-1978996208","-119060788","-153684864","-6586294122","1826292864","4018519674","927137792","-525362012","231599088","-1717485300","1000041088","607570470","-511999136","919216712","1501839360","1290991632","2840925968","282341916","-3471587072","4942642582","-272097792","2897189304","171401216","773105256","-1825337296","-3383078164","-914374656","-846155156","1710329824","-182284263","-1967276032","-2246350758","-585752256","-681093804","-202464768","-2737961352","-427224336","6870502240","191102976","-748295774","-3121694104","1905918390","322892032","1849830556","993070800","297594792","-759649280","-278020188","-3030530736","-6172941292","203297472","-1037069568","-651276992","1356229386","-351084544","10042491834","159353568","-1183990724","-2079677568","5640225912","2716869120","-1322442384","874243584","-448599862","2543150176","841263084","-4885365248","2252489294","-4434149520","891499728","728367104","382979394","813427680","-1654129152","-1320084864","3514170126","-5070509408","512856036","-177723392","3780665834","-3074414400","2689663108","-364290048","-2138361120","3121562944","-858422670","345710592","2836611581","8035534000","607357872","-1871493760","2425191916","-244045872","-6918236248","1927077888","-2281313916","-1943796528","3836921472","-508146048","367770774","-334801984","2801062944","255852544","-5499586990","2013172704","-1359307300","2384865280","-3052892376","-5031352256","-7291846488","-272097792","675299504","1581530928","-432081216","-6085745920","-996883962","-930149136","547538440","-637722624","1081610010","-1451993088","-13511781244","213345792","-7799360450","226813280","-2388070188","2761263104","-930152888","499884048","4492698560","-1471675904","4054711824","1126300096","-843431160","303464448","-6852306334","8134036848","-1244772603","-3390505024","-7657038090","-1498110768","1576959650","-1767356416","-8177592492","377726976","-5526750756","-1037069568","-1906328324","322828856","-1434708342","3796189184","-919250316","-2862881280","1519270556","7647107968","253047564","7763949216","6617712856","571677696","4405206036","-7073157296","-3681470034","1388266432","6819665110","-492232464","1905250792","-265289728","1743026688","8723690160","-7041265210","-1153080576","12169941998","3750119936","-2743827696","-1281377280","-5068707840","-2096245872","385948464","6004831488","6123653784","-8269833728","2000250480","-364290048","-4882056200","3198302040","10936433430","9525379968","2615268314","3988013832","12119316712","548975616","387420489","1448081440","-26222992376","1440167040","13045326150","1937464832","-387535806","3559915520","-1167843952","908007408","2275871340","669254912","-1876087656","-806917104","2134110048","-644972544","3964385364","11501498896","-3931564068","1832545792","3196843692","-3725276832","20417709984","-2167406592","-831774420","1034180832","9312727504","-432081216","8047591422","-9613512224","2968479360","-1388449792","5617343426","6793238016","-1477042378","-6489982464","2516411772","-5046868480","-2085954792","452984832","-8926527038","338785216","-7428552930","4517732480","-17986566506","-5405120928","-2950572096","2353945600","793797354","11374864528","3460766232","-659010816","-3888444032","-24590881280","-813970782","481890304","3567534980","969412320","-13158819108","3214765952","-13067890704","-3673492224","-2378944414","377726976","2605302180","-563975472","968653404","13369424384","2500988670","-1646828064","14971826688","2072281088","1824461010","-16185771024","-1501494280","1994105088","-4546149440","-1166773248","6679112202","-10510576640","11211856474","518686416","-23819361596","907803008","-6163738416","-693940544","11600953160","-3129090048","-20600999312","-11498111440","-781646922","1215658752","-20292141586","-3375138672","-5559294872","-7287500800","1727997084","-1831049248","20219455068","-5068707840","3747994534","-5263657792","-9588125142","819462144","-3328760806","11716606368","2805382192","1439663104","918330048","-689678304","20322373256","-578479104","-15539722993","9460344720","6160513374","-5407558912","6463150202","3086014464","6332818261","-1204494336","-5772363156","-14314726832","9311968960","6639556608","386409950","2286931920","1976913864","4771964928","-4642442910","683318592","-27330733564","-7236485632","1441882134","-4837259712","18433380664","-644972544","-14577299564","-573115024","10535717601","-1024192512","3808989888","-1089760608","3607391496","-2204797952","-3351613950","-19318799360","-5915601636","2563816320","-13028744186","-1559339712","10228041234","505708544","34634824314","-686128968","34034588396","-5660610816","2198059848","16641450656","-4781482248","1184910336","10787410368","2442625440","-537818292","9611168768","11761990656","7018911792","-11446710024","719323136","-9169433280","-14288475920","-1929412224","-2950572096","8320303404","-1260498624","-8583131844","-3551077376","-18157755564","16488107712","-27863911788","-19383922944","14965254630","-1046484768","32105038776","-2458238976","5457809104","17944637488","-2745318420","-3400790144","1539390860","4455286416","28245375544","-6786088960","17112969252","20820347536","12011142336","599816448","5420639074","5700454528","10376148600","1355087872","10297418298","1229478912","-2615101972","-8726447488","-10535274936","5067750304","-3493290416","-1166773248","-39664794022","3166565024","-27119927250","4131618816","2862940894","6316291440","16914596160","-2733228032","823654818","7503405184","6842471524","-6503887872","4638014940","-11245767584","6560313282","-4968879104","-25028279254","1714992912","12371529072","14515327488","1129956696","1764416384","-5359595206","-863502336","-25335831775","2143535712","-6794457876","25923397760","-8611927540","-8048920320","-51329233768","9453069824","16980813864","-4487208800","36253196004","918330048","18605536964","-31434596416","-5337666882","3413729280","-35797372926","20539392480","-2532722280","-918603392","3139253334","26312287776","48901986216","2152313856","-6128147596","-9360560608","4900476672","-4447022592","-100687986560","-720042048","-6898821040","-1528823808","-765494820","10543369984","-25485465232","-9319262976","-5530307986","34450427296","-1687108662","-8830285824"],"derived":{"al":[[2,1],[3,-1],[7,1]],"fricke":-1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"42.8.a.d","letter":"d","dim":1,"charpoly":["3942","1"],"traces":["1","-8","27","64","270","-216","343","-512","729","-2160","-1404","1728","-2362","-2744","7290","4096","18354","-5832","27164","17280","9261","11232","86184","-13824","-5225","18896","19683","21952","251862","-58320","-27040","-32768","-37908","-146832","92610","46656","-410290","-217312","-63774","-138240","-246246","-74088","49508","-89856","196830","-689472","-409200","110592","117649","41800","495558","-151168","1486398","-157464","-379080","-175616","733428","-2014896","427956","466560","-2048554","216320","250047","262144","-637740","303264","940748","1174656","2326968","-740880","789048","-373248","374330","3282320","-141075","1738496","-481572","510192","-4260880","1105920","531441","1969968","-8772132","592704","4955580","-396064","6800274","718848","2703786","-1574640","-810166","5515776","-730080","3273600","7334280","-884736","-13666078","-941192","-1023516","-334400","-3501522","-3964464","7746584","1209344","2500470","-11891184","-12574236","1259712","-22926778","3032640","-11077830","1404928","-17744622","-5867424","23269680","16119168","-1721898","-3423648","6295422","-3732480","-17515955","16388432","-6648642","-1730560","-22504500","-2000376","22586240","-2097152","1336716","5101920","11944620","-2426112","9317252","-7525984","5314410","-9397248","-8868870","-18615744","54337316","5927040","-11048400","-6312384","3316248","2985984","68002740","-2994640","3176523","-26258560","-64145826","1128600","74500712","-13907968","13380066","3852576","-7300800","-4081536","90121910","34087040","40132746","-8847360","29561112","-4251528","-62467540","-15759744","-10235160","70177056","70477464","-4741632","-57169473","-39644640","19802556","3168512","-21678234","-54402192","-1792175","-5750784","11554812","-21630288","-34881828","12597120","-110916898","6481328","-55310958","-44126208","-110778300","5840640","-25769016","-26188800","6751269","-58674240","-89033280","7077888","-15804094","109328624","-17218980","7529536","50499630","8188128","-31140808","2675200","25400196","28012176","86388666","31715712","-66486420","-61972672","62828136","-9674752","-38138256","-20003760","-41524420","95129472","21304296","100593888","13367160","-10077696","-9274720","183414224","10106910","-24261120","-43352148","88622640","17486432","-11239424","-3809025","141956976","249364044","46939392","-325117138","-186157440","-13002444","-128953344","-25415526","13775184","-110484000","27389184","-115043760","-50363376","182917200","29859840","310975442","140127640","14348907","-131107456","31765230","53189136","-64161368","13844480","-236847564","180036000","425737908","16003008","-121002336","-180689920","133800660","16777216","11477250","-10693728","-140729470","-40815360","183607398","-95556960","30968568","19408896","401327460","-74538016","73002222","60207872","-187321722","-42515280","-511959760","75177984","-21874482","70950960","7335900","148925952","-177473890","-434698528","-19712160","-47416320","517017066","88387200","273421652","50499072","198025560","-26529984","-84462378","-23887872","-73469357","-544021920","-368984106","23957120","-323734290","-25412184","115548120","210068480","-27634932","513166608","-203566608","-9028800","16981244","-596005696","-94541094","111263744","-553109580","-107040528","787418876","-30820608","209157768","58406400","-955165368","32652288","32139530","-720975280","67512690","-272696320","983617014","-321061968","-353614248","70778880","-339504372","-236488896","498568056","34012224","12341450","499740320","-619023006","126077952","-140355600","81881280","317705156","-561416448","-299101410","-563819712","254001960","37933056","677938226","457355784","-479104794","317157120","37964160","-158420448","40353607","-25348096","628281360","173425872","290097204","435217536","1192894838","14337400","-46491246","46006272","419246370","-92438496","213042960","173042304","169976394","279054624","478834008","-100776960","-155988843","887335184","-472930785","-51850624","101069100","442487664","-1017922096","353009664","-179513334","886226400","509834514","-46725120","723888446","206152128","-607621500","209510400","-594898044","-54010152","-2054597740","469393920","609828480","712266240","-175243968","-56623104","-130024440","126432752","36091332","-874628992","-1766702034","137751840","1581821136","-60236288","322504740","-403997040","-1150437600","-65505024","-658715578","249126464","251565804","-21401600","-414473742","-203201568","63868480","-224097408","143489070","-691109328","576047160","-253725696","296028842","531891360","-239459490","495781376","146788908","-502625088","-2368475640","77398016","1467107532","305106048","-1012458804","160030080","-2308316914","332195360","-298306800","-761035776","-95899650","-170434368","-702654022","-804751104","89538696","-106937280","-3067424880","80621568","2925095186","74197760","1836073980","-1467313792","2341102176","-80855280","-2440047736","194088960","85766121","346817184","2186207508","-708981120","730022220","-139891456","-1731937302","89915392","-2388823614","30472200","345729384","-1135655808","2011519224","-1994912352","-218744820","-375515136","-1223155270","2600937104","361261782","1489259520","-16916538","104019552","601489904","1031626752","-197121600","203324208","961078236","-110201472","322676564","883872000","2433291570","-219113472","-69509232","920350080","-141931900","402907008","1083584142","-1463337600","4425542496","-238878720","969104980","-2487803536","798150024","-1121021120","-3689841060","-114791256","3616195736","1048859648","-1686623580","-254121840","3339322212","-425513088","4622675148","513290944","-276349320","-110755840","270643464","1894780512","-3674470756","-1440288000","1902891528","-3405903264","-3119111928","-128024064","-945410940","968018688","-1543575771","1445519360","1877885334","-1070405280","128395190","-134217728","534669012","-91818000","2091577680","85549824","574516800","1125835760","-585312318","326522880","-2806712646","-1468859184","3481275620","764455680","-48388725","-247748544","-496292160","-155271168","4022856409","-3210619680","311979924","596304128","581633052","-584017776","-3395043720","-481662976","-941809356","1498573776","-165179196","340122240","-3888120490","4095678080","-2994756246","-601423872","-6190230060","174995856","-146009044","-567607680","-1493395866","-58687200","6841579368","-1191407616","-1461481840","1419791120","-2991014100","3477588224","-2173607034","157697280","-116937896","379330560","-695763432","-4136136528","2622604092","-707097600","-4791047940","-2187373216","182284263","-403992576","-5860723254","-1584204480","8155451732","212239872","-2403898560","675699024","-450311400","191102976","2638253378","587754856","-426710538","4352175360","-3008841276","2951872848","-2086902792","-191656960","-464912460","2589874320","4101620964","203297472","-734514560","-924384960","1363490010","-1680547840","2006372274","221079456","1699763940","-4105332864","-840801816","1628532864","-2065715544","72230400","6036132266","-135849952","685805292","4768045568","-4729307850","756328752","-7241702944","-890109952","2332493982","4424876640","966530400","856324224","516336014","-6299351008","-1795133340","246564864","-8427591654","-1673262144","-347095036","-467251200","1696359672","7641322944","927398598","-261218304","-5668011875","-257116240","-1029732912","5767802240","-7530462660","-540101520","-5427637432","2181570560","-1121159340","-7868936112","6098284800","2568495744","-277886938","2828913984","575215992","-566231040","7579542402","2716034976","-1866259732","1891911168","360913320","-3988544448","-8941344072","-272097792","-600850224","-98731600","-250417440","-3997922560","8637552486","4952184048","3225047400","-1008623616","272886570","1122844800","10263391548","-655050240","10240285118","-2541641248","-1170507996","4491331584","2515658040","2392811280","21706474608","4510557696","472133664","-2032015680","2876169816","-303464448","-1469330974","-5423505808","-102843675","-3658846272","14367594414","3832838352","-4687464754","-2537256960","6732829188","-303713280","2380563876","1267363584","-2394594900","-322828856","-8778162726","202784768","-3510872076","-5026250880","1244674556","-1387406976","-351065988","-2320777632","14671075320","-3481740288","-4519599084","-9543158704","-686219202","-114699200","-2768167242","371929968","-11145117560","-368050176","-2983068000","-3353970960","-1201022046","739507968","-5710347730","-1704343680","-3106181520","-1384338432","-2330415360","-1359811152","895386960","-2232436992","4938764400","-3830672064","-5333097360","806215680","2657078312","1247910744","8396336934","-7098681472","-1315978950","3783446280","-14990095576","414804992","387420489","-808552800","908669832","-3539901312","-2079031882","8143376768","857661210","-2824077312","-1320810192","1436106672","-8229377428","-7089811200","-1732356936","-4078676112","-2216068008","373800960","-17319373020","-5791107568","-6394884228","-1649217024","-4312962948","4860972000","8832660368","-1676083200","11494923516","4759184352","20115192240","432081216","-6913982338","16436781920","-3267063072","-3755151360","-500427702","-4878627840","-7863884854","-5698129920","3612617820","1401951744","-1010832072","452984832","-8464054846","1040195520","309885750","-1011462016","-12836276466","-288730656","141284000","6997031936","-3799695690","14133616272","-6689026344","-1102014720","-1107823392","-12654569088","4957399746","481890304","24332915700","-2580037920","6273627548","3231976320","836151336","9203500800","-6086405346","524040192","4838684548","5269724624","10835841420","-1993011712","18814127862","-2012526432","-7510456800","171212800","1971059994","3315789936","-525559320","1625612544","7981500240","-510947840","-5057686494","1792779264","8418702810","-1147912560","14400895556","5528874624","-13822913520","-4608377280","-16866235800","2029805568","1344835312","-2368230736","-590611014","-4255130880","-18627442242","1915675920","7231622792","-3966251008","198069300","-1174311264","17039039508","4021000704","3868074326","18947805120","-4791795030","-619184128","2159329746","-11736860256","19028915280","-2440848384","-532228320","8099670432","4866634104","-1280240640","46184590735","18466535312","13959460782","-2657562880","-15435757710","2386454400","-6007972565","6088286208","7382384604","767197200","-35360433360","1363474944","-15577493698","5621232176","5346690120","6438008832","-9819031446","-716309568","-7029193900","855498240","-2280484206","24539399040","-25228878816","-644972544","-5853123180","-23400761488","-1983672639","-593582080","5982275520","-14688591840","-2222046776","11738510336","-9962570862","-18728817408","-7719043500","646842240","29267858246","19520381888","-8740825830","-1552711680","-6811027182","-686128968","-16958048740","-2774537472","3119799240","-17489660064","-26592577848","5671848960","7747080320","-5840177760","-746143164","1119131648","-11115508800","13855498416","-9418093560","-719323136","-5496298416","19110588912","-6810348480","-243777600","27281348892","-2765835072","458493588","9085246464","-29947562460","-16092153792","4706461124","15959298816","-2552609538","1749958560","-29951271120","3004121088","12316073328","9785242160","-14933958660","-20807496832","4097004660","-2890094256","12577730600","-11914076160","21260309652","135332304","-1863731376","-832156416","2143765250","-4811919232","5647259736","-8253014016","36915847842","1576972800","3195817436","-1626593664","-25789464936","-7688625888","-6957634320","881611776","-2271324454","-2581412512","867767310","-7070976000","35752095654","-19466332560","-21222465264","1752907776","1822842630","556073856","933685788","-7362800640","-884167460","1135455200","26557659378","-3223256064","11129156298","-8668673136","-24038985600","11706700800","-9547584696","-35404339968","-3042022410","1911029760","-26781452511","-7752839840","-9166618044","19902428288","-4267105380","-6385200192","20628376376","8968168960","13461337512","29518728480","23799196068","918330048","18637699388","-28929565888","333219150","-8390877184","26069919666","13492988640","-3796115544","2032974720","-16713621162","-26714577696","2452422888","3404104704","13634900100","-36981401184","-3789601200","-4106327552","4266797472","2210794560","-31873234336","886046720","8578039212","-2165147712","-8408018160","-15158244096","49808375918","29395766048","-8075738070","11522304000"],"derived":{"al":[[2,1],[3,-1],[7,-1]],"fricke":1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"42.8.a.e","letter":"e","dim":1,"charpoly":["-5394","1"],"traces":["1","8","-27","64","30","-216","343","512","729","240","1788","-1728","9374","2744","-810","4096","23994","5832","30692","1920","-9261","14304","-7440","-13824","-77225","74992","-19683","21952","41046","-6480","21056","32768","-48276","191952","10290","46656","160094","245536","-253098","15360","-223854","-74088","-694684","114432","21870","-59520","-548688","-110592","117649","-617800","-647838","599936","-1616994","-157464","53640","175616","-828684","328368","-1180932","-51840","2701070","168448","250047","262144","281220","-386208","3059564","1535616","200880","82320","-3451104","373248","4548170","1280752","2085075","1964288","613284","-2024784","2594816","122880","531441","-1790832","-1797708","-592704","719820","-5557472","-1108242","915456","9366930","174960","3215282","-476160","-568512","-4389504","920760","-884736","-3443230","941192","1303452","-4942400","-8378130","-5182704","2043320","4799488","-277830","-12935952","-18435636","-1259712","4011446","429120","-4322538","1404928","3733842","-6629472","-223200","2626944","6833646","-9447456","8229942","-414720","-16290227","21608560","6044058","1347584","-4660500","2000376","-19779424","2097152","18756468","2249760","-8313180","-3089664","10527356","24476512","-590490","12284928","31051338","1607040","-47026228","658560","14814576","-27608832","16760712","2985984","1231380","36385360","-3176523","10246016","-70597122","16680600","-5325832","15714304","17491626","4906272","631680","-16198272","74974910","20758528","43658838","983040","-2551920","4251528","-43346500","-14326656","-1448280","-14381664","-92280264","-4741632","25123359","5758560","22374468","-44459776","50550198","-8865936","-26488175","7323648","31885164","74935440","41591412","1399680","-98625418","25722256","-72928890","-3809280","4802820","-4548096","42901272","-35116032","-6751269","7366080","-164170776","-7077888","149677250","-27545840","-7592940","7529536","-49518738","10427616","-31670584","-39539200","-82608228","-67025040","14078778","-41461632","-6715620","16346560","-5423760","38395904","54877296","-2222640","-38465428","-103487616","93179808","-147485088","-20840520","-10077696","7222208","32091568","-122800590","3432960","224919756","-34580304","4845248","11239424","-56297025","29870736","-206180364","-53035776","338951174","-1785600","-16558668","21015552","265899402","54669168","-16460640","-75579648","-70060032","65839536","202879992","-3317760","155726450","-130321816","-14348907","172868480","3529470","48352464","287706808","10780672","48538116","-37284000","391298220","16003008","-13302720","-158235392","-19435140","16777216","-47021910","150051744","54912242","17998080","29922534","-66505440","290276592","-24717312","-48509820","84218848","-252907110","195812096","-604141434","-4723920","-17126368","98279424","-86812614","248410704","-138078300","12856320","-505048834","-376209824","15349824","5268480","-593473638","118516608","-622637572","-220870656","-24860520","134085696","-76781922","23887872","165373363","9851040","92967210","291082880","141063438","-25412184","-35427960","81968128","-35193204","-564776976","-69742560","133444800","-238276612","-42606656","226209510","125714432","81032100","139933008","-963630556","39250176","-55169640","5053440","96278232","-129586176","-193764070","599799280","7501410","166068224","248339094","349270704","73390248","7864320","497762172","-20415360","736423848","34012224","-723907150","-346772000","-108309042","-114613248","-188199984","-11586240","1137395780","-115053312","116708526","-738242112","91786920","-37933056","176606546","200986872","-100813734","46068480","37648128","178995744","40353607","-355678208","6026400","404401584","1074281052","-70927488","-1458868258","-211905400","-184508442","58589184","55490010","255081312","-103533120","599483520","-222208434","332731296","1406828016","11197440","48127125","-789003344","439836129","205778048","136445100","-583431120","-222366736","-30474240","-163189566","38422560","-554628942","-36384768","1925103902","343210176","125833500","-280928256","384765204","-54010152","355375028","58928640","534044448","-1313366208","894395280","-56623104","18398520","1197418000","-506424636","-220366720","-1500421746","-60743520","-178515360","60236288","224455860","-396149904","77844480","83420928","374204846","-253364672","-284238612","-316313600","-1711857822","-660865824","197378944","-536200320","15943230","112630224","286248072","-331693056","-269536630","-53724960","-838386126","130772480","-405059676","-43390080","-53931240","307167232","1269708156","439018368","92632548","-17781120","1779302510","-307723424","-399993552","-827900928","-1852936650","745438464","926467010","-1179880704","-452539224","-166724160","871461864","-80621568","-1260662398","57777664","-33247260","256732544","-228348480","-982404720","218091464","27463680","85766121","1799358048","-2775140148","-276642432","281007900","38761984","1906122294","89915392","-3454700670","-450376200","-400250952","238965888","143797464","-1649442912","96458460","-424286208","1723318586","2711609392","-472273902","-14284800","-1718862762","-132469344","3025213376","168124416","-17055360","2127195216","1803261348","437353344","1049430452","-131685120","-2024322570","-604637184","-1242094992","-560480256","-2370189700","526716288","-1178788626","1623039936","-465293568","-26542080","1500721156","1245811600","68901840","-1042574528","-103296900","-114791256","1906161608","1382947840","1170355500","28235760","-2800227012","386819712","984857724","2301654464","39103560","86245376","-1183728672","388304928","-3742777012","-298272000","2491567128","3130385760","4521707208","128024064","-251343900","-106421760","-678330693","-1265883136","549374358","-155481120","1560022310","134217728","-604110636","-376175280","61299600","1200413952","-981054144","439297936","-1364855346","143984640","5308163874","239380272","3422611676","-532043520","715180725","2322212736","505217664","-197738496","-3349471847","-388078560","-860899428","673750784","-2098407396","-2023256880","-553069080","1566496768","-1122968124","-4833131472","210356412","-37791360","1207756118","-137010944","2662886286","786235392","120343380","-694500912","-5595733540","1987285632","1969080030","-1104626400","1259783832","102850560","890021888","-4040390672","-129676140","-3009678592","369344358","122798592","-6511967816","42147840","-1158334344","-4747789104","5084303124","948132864","112015260","-4981100576","182284263","-1766965248","-7465198278","-198884160","-7354140124","1072685568","4432610952","-614255376","574554000","191102976","94015874","1322986904","-4041285750","78808320","-616613844","743737680","-2891185272","2328663040","205009380","1128507504","1489397532","-203297472","646250752","-283423680","1337005926","655745024","6978267306","-281545632","246898260","-4518215808","855105768","-557940480","-1589239824","1067558400","2293508618","-1906212896","2230422156","-340853248","-488706810","1809676080","-1182366688","1005715456","-380127006","648256800","-5143401312","1119464064","2509679774","-7709044448","181321740","314001408","10319491146","-441357120","-849236932","40427520","146441520","770225856","3212856990","-1036689408","5893388125","-1550112560","-1481686992","4798394240","3841295436","60011280","7587182072","1328545792","1038566556","1986712752","-593382720","2794165632","1102841726","587121984","-2515854816","62914560","-5286826830","3982097376","-5577052540","-163322880","562694040","5891390784","10451302488","272097792","-2111506416","-5791257200","-194999616","-2774176000","5656518822","-866472336","-249395400","-916905984","3315615930","-1505599872","-2930036844","-92689920","3104244950","9099166240","-6072833412","-920426496","315820680","933668208","-305382240","-5905936896","-130821696","734295360","4829513160","-303464448","10766781314","1412852368","1520019675","1607894976","-9477859170","-806509872","-1181027890","368547840","5566869828","301185024","-2983448484","1431965952","931540140","322828856","-9151681698","-2845425664","-15157701756","48211200","-15080909644","3235212672","447084036","8594248416","-1410786840","-567419904","-5371152876","-11670946064","-7179283854","-1695243200","6045502230","-1476067536","4913605048","468713472","444437280","443920080","-2873698590","2040650496","-4104733762","-828264960","1891620864","4795868160","-156656640","-1777667472","502821360","2661850368","-5477759784","11254624128","12572763840","89579520","700858760","385017000","-4204614150","-6312026752","-3169777350","3518689032","4999065128","1646224384","387420489","1091560800","-16668247896","-4667448960","-2749469890","-1778933888","-95295690","-243793920","5470500432","-1305516528","-4024479940","307380480","-7768083816","-4437031536","17340205872","-291078144","-2117913660","15400831216","-1310529132","2745681408","-6323423148","1006668000","14908302464","-2247426048","-10565051940","3078121632","-159774960","-432081216","-9064369042","2843000224","359173440","471429120","-7471536414","4272355584","1375925978","-10506929664","524748780","7155162240","-11070056568","-452984832","8574188882","147188160","1269591570","9579344000","-9464067954","-4051397088","-1626049600","-1762933760","-1482630534","-12003373968","-6870526968","-485948160","-6170573952","-1428122880","-807908418","481890304","2249247300","1795646880","942951668","-3169199232","-7837467984","622755840","1280707806","667367424","25319830180","2993638768","1309765140","-2026917376","17321596230","-2273908896","-13165219872","-2530508800","6828491970","-13694862576","8132127960","-5286926592","-76557600","1579031552","16311818718","-4289602560","-7502992326","127545840","13377257084","901041792","462411936","2289984576","-1300395000","-2653544448","-21321241328","-2156293040","2343940578","-429799680","8365710174","-6707089008","27362850872","1046179840","3728114100","-3240477408","10756061532","-347120640","1036438814","-431449920","13636318518","2457337856","2822870106","10157665248","-2768407920","3512146944","-414445248","741060384","6872968536","-142248960","-15565102193","14234420080","16023788226","-2461787392","753700770","-3199948416","-5587547861","-6623207424","16811214444","-14823493200","-1191099360","5963507712","19519202150","7411736080","671234040","-9439045632","-19698690270","-3620313792","21821422316","-1333793280","2073111894","6971694912","-339285384","-644972544","1516505940","-10085299184","-4465080801","462221312","4639531008","-265978080","28680352936","2053860352","-2510114670","-1826787840","-1598551500","-7859237760","-9072712714","1744731712","-3808712826","219709440","-4512846006","686128968","-21702874516","14394864384","956554920","-22201121184","21770078088","-2213139456","-6784342432","2248063200","950216508","310095872","-16840332096","15248978352","1247742360","719323136","1883049120","-27637605360","864264576","-3603009600","-38798154036","-3202007616","6433468524","1911727104","-2958762540","1150379712","-17664979852","-13195543296","-6107656770","771667680","-16359007224","-3394289664","-3214301904","13786548688","-2187866700","21692875136","-2851420740","-3778191216","-25979927416","-114278400","26018025012","-13750902096","-32350648896","-1059754752","-12363259150","24201707008","1489580280","1344995328","25923038298","-136442880","3610883108","17017561728","-2599512264","14426090784","1287038160","3498826752","-11085249958","8395443616","5231629890","-1053480960","-41339417226","-16194580560","1665473760","-4837097472","-202538070","-9936759936","-26860413324","-4483842048","42634545580","-18961517600","-6705155538","4213730304","1441700874","-9430309008","-4925123280","12984319488","-1981536696","-3722348544","10650608934","-212336640","-27069258975","12005769248","-13439578644","9966492800","4490317500","551214720","-3762005512","-8340596224","-19883443896","-826375200","6351514524","-918330048","-16129996204","15249292864","19545493050","11063582720","1336229346","9362844000","16748070840","225886080","2924344134","-22401816096","36604471704","3094557696","-1485562140","7878861792","5081399568","18413235712","5168448960","312828480","35991140960","689963008","-30709686060","-9469829376","-950117520","3106439424","-43320886714","-29942216096","-3151130202","-2386176000"],"derived":{"al":[[2,-1],[3,1],[7,-1]],"fricke":1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"42.8.a.f","letter":"f","dim":1,"charpoly":["21334","1"],"traces":["1","8","27","64","470","216","-343","512","729","3760","-7268","1728","11382","-2744","12690","4096","20842","5832","-13684","30080","-9261","-58144","-46736","13824","142775","91056","19683","-21952","2774","101520","-11232","32768","-196236","166736","-161210","46656","-239698","-109472","307314","240640","52962","-74088","-874732","-465152","342630","-373888","-451296","110592","117649","1142200","562734","728448","-1943538","157464","-3415960","-175616","-369468","22192","1563908","812160","-3183690","-89856","-250047","262144","5349540","-1569888","2128684","1333888","-1261872","-1289680","5694544","373248","-2253878","-1917584","3854925","-875776","2492924","2458512","132912","1925120","531441","423696","6950524","-592704","9795740","-6997856","74898","-3721216","-10626510","2741040","-3904026","-2991104","-303264","-3610368","-6431480","884736","2407090","941192","-5298372","9137600","7775750","4501872","-13234024","5827584","-4352670","-15548304","-7209444","1259712","3890374","-27327680","-6471846","-1404928","14664722","-2955744","-21965920","177536","8297478","12511264","-7148806","6497280","33336653","-25469520","1429974","-718848","30385500","-2000376","3873312","2097152","-23617764","42796320","22747628","-12559104","4693612","17029472","9251010","10671104","-42238198","-10094976","-2023196","-10317440","-12184992","45556352","-82724376","2985984","1303780","-18031024","3176523","-15340672","63301710","30839400","-53962568","-7006208","15193818","19943392","-5279040","19668096","58336694","1063296","-52475526","15400960","16030448","4251528","60584492","3389568","-92230920","55604192","59419304","-4741632","66801407","78365920","-9975636","-55982848","55856606","599184","-48971825","-29769728","42225516","-85012080","80225220","21928320","-71863218","-31232208","-85959630","-23928832","-112658060","-2426112","-151479656","-28882944","-6751269","-51451840","-16743528","7077888","-134702206","19256720","144437580","7529536","-58941314","-42386976","131373224","73100800","57474468","62206000","-951482","36014976","24892140","-105872192","-34070544","46620672","99455312","-34821360","-29660020","-124386432","153752688","-57675552","-411124040","10077696","3852576","31122992","-60854706","-218621440","237223644","-51774768","316036784","-11239424","104082975","117317776","47605596","-23645952","-104288834","-175727360","67308948","1420288","235058890","66379824","-212109120","100090112","3588624","-57190448","37436184","51978240","9876674","266693224","14348907","-203756160","55295030","11439792","-155751288","-5750784","187664148","243084000","132438180","-16003008","339677248","30986496","264484980","16777216","332667210","-188942112","82216414","342370560","2022246","181981024","-95122848","-100472832","-913462860","37548896","-286915770","136235776","-268854898","74008080","452883600","85368832","-105408702","-337905584","-1037688700","-80759808","-16470946","-16185568","-8188128","-82539520","508113370","-97479936","-257495900","364450816","-173649960","-661795008","-18165966","23887872","24050291","10430240","64991430","-144248192","73384710","25412184","735036760","-122725376","-143056044","506413680","-531949152","246715200","300033076","-431700544","209945250","-56049664","-1496334300","121550544","-93162356","159547136","-357318648","-42232320","610934264","157344768","-212230934","466693552","-117522090","8506368","-1103944986","-419804208","-20161432","123207680","-194654988","128243584","-285201928","34012224","1625065050","484675936","105040098","27116544","154794528","-737847360","-670587628","444833536","-174739842","475354432","1000481480","-37933056","-684122094","534411256","395947494","626927360","81634176","-79805088","-40353607","-447862784","-593079840","446852848","437552988","4793472","9398326","-391774600","224031906","-238157824","1414718490","337804128","2676435680","-680096640","-193017762","641801760","-307583056","175426560","-706619883","-574905744","900089631","-249857664","-1059322660","-687677040","-1231272256","-191430656","38609298","-901264480","666633534","-19408896","1835916862","-1211837248","820408500","-231063552","31573668","-54010152","-648933500","-411614720","104579424","-133948224","-680320640","56623104","1171674280","-1077617648","-637679628","154053760","273705038","1155500640","-974071712","60236288","614185956","-471530512","62468640","-339095808","-1210341306","1050985792","126727524","584806400","-597102174","459795744","-127842624","497648000","249777270","-7611856","1742125064","288119808","-1197671206","199137120","-1140431346","-846977536","-536420444","-272564352","3266746280","372965376","-54626292","795642496","-1686801060","-278570880","-960355506","-237280160","-328994784","-995091456","2975716550","1230021504","1092005670","-461404416","-2233558152","-3288992320","-103165848","80621568","-2332775662","30820608","35202060","248983936","639535424","-486837648","-1561587432","-1748971520","85766121","1897789152","1624807516","-414198144","-4994459700","2528294272","1709146170","-89915392","-818477854","832663800","-384927816","938542208","-1456989336","380844768","-1834892220","-189167616","-1533255686","-834310672","410233086","-1405818880","3435073502","538471584","1732004752","11362304","-142534080","1880471120","-481487572","531038592","-730138612","-1696872960","1575090738","800720896","6357552176","28708992","-1953733100","-457523584","-1416839202","299489472","-1659393488","415825920","-2728242636","79013392","432822096","2133545792","1131332300","114791256","1720165256","-1630049280","1635781284","442360240","-667097940","91518336","57815708","-1246010304","-2490234840","-46006272","-1953228592","1501313184","-545977268","1944672000","1604321208","1059505440","4132843176","-128024064","3654602500","2717417984","1803637989","247891968","-1912129890","2115879840","773080154","134217728","-269342172","2661337680","-6219991280","-1511536896","3280019328","657731312","1508128362","2738964480","62117394","16177968","682074884","1455848192","-1322239275","-760982784","-234097344","-803782656","-1220571751","-7307702880","1140088932","300391168","602813484","-2295326160","-3388438680","1089886208","2166080940","-2150839184","-855072932","592064640","220541142","3623068800","-1940306886","682950656","1828475780","-843269616","5394610860","-2703244672","-2320910010","-8301509600","-37959416","-646078464","-45588816","-131767568","-3041767620","-129484544","-1223867626","-65505024","-9956199624","-660316160","-4089950712","4064906960","-3670938548","-779839488","6892419340","-2059967200","-182284263","2915606528","5003697786","-1389199680","1511658804","-5294360064","-452075256","-145327728","-6672732400","191102976","-4391197598","192402328","-3636959562","83441920","-2384029732","519931440","14125634184","-1153985536","3899814660","587077680","-6476284556","203297472","153698688","5880294080","-1591415478","-981803008","528183594","-1144448352","-3359938820","4051309440","3547077048","-4255593216","-9034225440","1973721600","5039916938","2400264608","1551810636","-3453604352","15668226910","1679562000","5965616784","-448397312","-25690014","-11970674400","-5136651072","972404352","5423503566","-745298848","672087780","1276377088","2180730442","-2858549184","-5357350268","-337858560","-919904688","4887474112","3644892930","1258758144","3126888125","-1697847472","2685293424","3733548416","-4995785716","-940176720","11455930376","68050944","-800820540","-8831559888","1820456640","-3358433664","1339080918","-161291456","4151322576","985661440","10128747634","-1557239904","-4991522116","1025948672","-11100349080","-2281615424","-5542367352","272097792","-11366483344","13000520400","104019552","3877407488","-7425891162","840320784","10691385160","216932352","-1643077062","1238356224","868126996","-5902778880","3369201118","-5364701024","6405038388","3558668288","2205997640","-1397918736","-129645664","3802835456","8532993168","8003851840","23139058920","-303464448","-3434060446","-5472976752","2810240325","4275290048","12889920870","3167579952","-825631870","5015418880","1285351092","653073408","-6520121652","-638440704","-19851953060","-322828856","-2815798518","-3582902272","-22121349516","-4744638720","-15126445732","3574822784","1817341596","3500423904","-950902120","38347776","1103834004","75186608","6346590030","-3134196800","-8527038154","1792255248","3280027432","-1905262592","-5726946240","11317747920","-2667082250","2702433024","-9845790994","21411485440","96892848","-5440773120","524938752","-1544142096","-38880456720","5134414080","1010776968","-2460664448","4027955184","1403412480","4539270232","-5652959064","266670198","-4599245952","396057850","7200717048","-5954629688","-1998861312","387420489","-8474581280","-18231164344","-5501416320","16554477318","-9850178048","1492965810","-1531445248","-15471275312","308874384","11444627724","-7210115840","-4205284776","5333068272","-425895216","-155271168","29751803700","14687334896","5066931996","-9694697984","2472839292","6563268000","-295035360","-1848508416","3575830860","252589344","-25362406960","-432081216","18737743614","-5191468000","9171285696","-3292917760","4074961234","836635392","-1334398282","-1071585792","7141094460","-5442565120","17800400856","452984832","11960386690","9373394240","8982014670","-8620941184","467302790","-5101437024","-1603648800","1232430080","2219843178","2189640304","-724732008","9244005120","-41387945792","-7792573696","54600642","481890304","27418246180","4913487648","-8079868836","-3772244096","-2568316896","499749120","-5029999646","-2712766464","-36236759580","-9682730448","-24663497220","8407886336","-14879936274","1013820192","-9405911232","4678451200","-7746725790","-4776817392","16381185304","3678365952","7534310560","-1022740992","-7259082246","3981184000","7151324570","1998218160","2130582916","-60894848","12227857200","13937000512","28474711240","2304958464","11969832688","-9581369648","-2846034954","1593096960","2040519022","-9123450768","29913862984","-6775820288","-28017594900","-4291363552","10510325100","-2180514816","19114593382","26133970240","-444715542","2983723008","2452040458","-437010336","27927072880","6365139968","-221079456","-13494408480","2316345640","-2228567040","-17242181233","-7682844048","13719060990","-1898241280","31396661290","-2631958272","-11434471979","-7960731648","-6952389300","23805732400","11202525728","9840172032","-857597314","8736045360","-4688548920","-3691235328","-27386516238","-17868465216","-10191561820","-26311938560","-490481082","-825326784","3706745864","644972544","26252604820","-18662205296","649357857","246564864","-966004416","281616480","24228681288","1991871488","1754768610","5116283392","-10422226500","-3894701184","2186810566","-12492699456","1981387170","-13991772160","-9105315030","686128968","19939128428","15182313216","19845992520","12998460128","-7244250600","-3313585152","-1328546016","-39955677600","-3862513188","20226354176","6175534464","13673169360","37705853400","-719323136","-14362627104","-6547822832","-31157568","6661310400","-40507218996","-3079422528","8100893052","7508337664","-33775712460","-11655914688","8753338452","3046758144","5668521750","-14679137760","19986904296","-1513340928","-50516408432","-12266045488","-40401026100","-6674485376","-7802436404","3281864688","-9930749000","-11246551040","-2515383612","27480588016","64815299808","4307772672","-34222881950","13856038016","-9647603496","90898432","19590755850","-1140272640","-1609908916","15043768960","16495225128","-3851900576","-71195438320","4248308736","42028579418","-5841108896","-5730235218","-13574983680","-9954304210","12600725904","-2475232032","6405767168","-3173096430","50860417408","-24344965516","229671936","-25653639396","-15629864800","-29806514622","-3660188672","17119787050","-11334713616","-7869458160","2395915776","-544358664","-13275147904","14487701914","3326607360","-27386456287","-21825941088","-5255684676","632107136","-63310036820","3462576768","-52944293512","17068366336","-7700452056","9050658400","-24472250844","918330048","693956228","13761322048","43876756350","-13040394240","-32167834974","13086250272","77233474680","3538881920","2836082646","-5336783520","18556375848","732146688","-27702417580","462525664","4179452256","-9968082432","40881474752","-19921878720","16014872144","-368050176","-18105865956","-15625828736","61745415280","12010505472","32096476814","-4367818144","-4717975734","15557376000"],"derived":{"al":[[2,-1],[3,-1],[7,1]],"fricke":1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.326,"computed":"atlas","estimate":{"seconds":0.6,"low":0.366,"high":1.038,"bytes":1961200},"url":"https://sagebrush.space/atlas/mf/42.8.a"}