Properties

Label 1.94.a
Level 1
Weight 94
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 7
Newform subspaces 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 94 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{94}(\Gamma_0(1))\).

Total New Old
Modular forms 8 8 0
Cusp forms 7 7 0
Eisenstein series 1 1 0

Trace form

\( 7q + 43735426713792q^{2} - 3678766354327579216884q^{3} + 37433779444352805880587218944q^{4} - 242501922056818695041616562179750q^{5} - 3422349689703076907975614807426150656q^{6} - 921137753903839555947108372394316103208q^{7} + 628568314501252186502498490389635108700160q^{8} + 362824653360866901561998689210341299050559211q^{9} + O(q^{10}) \) \( 7q + 43735426713792q^{2} - 3678766354327579216884q^{3} + 37433779444352805880587218944q^{4} - 242501922056818695041616562179750q^{5} - 3422349689703076907975614807426150656q^{6} - 921137753903839555947108372394316103208q^{7} + 628568314501252186502498490389635108700160q^{8} + 362824653360866901561998689210341299050559211q^{9} + 56663128890275718532856219951648854919834448000q^{10} + 1081566396126190174166498109003279139923369012324q^{11} - 163904625261310040243241458042755377696324875010048q^{12} + 1923851638471797431690458036346871401286646408469426q^{13} - 827492161115181455891429526236298470299001717526508032q^{14} - 16711611501720521025854082681912174509227777477242411000q^{15} - 183863117199568288307852091185855957272115704336744448q^{16} + 809325537307953309871783611300921224816172571619454935742q^{17} + 79483944128603792717921302063558947044650774054000109708736q^{18} - 491316328040151561437984621759105514680907320256463264658500q^{19} - 5819101371751539891329503686613738398860076574931824253952000q^{20} + 54451750333719895476183963426175615210898459319681281516277984q^{21} + 341061341496448817039487179432626029859991533289656810924326144q^{22} - 2595697104202345855126053487687658963668179272707633091075699064q^{23} - 29432689846399066174371175818785662556182882963620634526849433600q^{24} + 184388886386678531186865888507627315189418933935123407708899515625q^{25} + 793059166145746283698718389909557916534745558035448772312212840064q^{26} - 10506923232698637098067136941837198924358450251426727402321208664840q^{27} + 1916814131388145595393790805747801246689773266225672358812878209024q^{28} + 115585291038420509795092429775705167101645550654624527668945364036450q^{29} - 646359246874848354315998274237243944693324584248820365706098812352000q^{30} - 1163635467946810748613893942791764663199899897323284701513531956983456q^{31} - 7066990866795922437106429389517828098400874624281122281464920526553088q^{32} + 66569296470254314915045188377632673804554883301553196046747543676316112q^{33} + 80911624156374405155780927188384543491071504244617539921495324380294528q^{34} - 1672188852118103650980495790489284130570309869892526153633308501275462000q^{35} + 5276416924359744904633666070671763693285317535397001093231145577416896512q^{36} + 11072759435314078994932599484815080247923078570346623467670584315337670842q^{37} - 42692186143014046654789275667852179938472092905944200699148410427788924160q^{38} - 205635087839752927920079557406846610376307390801963146422737416149757222168q^{39} + 760187696799287916151508882607919116749295190931669242261910585944965120000q^{40} - 509603803596826806676973650829096820638503322986104149790656476262528674746q^{41} - 542653738615875619591084295077236547022836265832353730045755853854336280576q^{42} - 7275658116979055674748970912580687053338617746072325435955591393683798211644q^{43} + 9423347779397833928027118997217234224491886242773059800183027480258516369408q^{44} + 164505351109492760826482356226220602919737242087979463171032783958351054923250q^{45} - 639778771092842366359510076082228574613573083413403803040568658686807125218816q^{46} - 371149830895115606730684780470708713676568637183334957675426341554516993409008q^{47} - 416843258596979693775599022471376378646238618283847940753742770006189894795264q^{48} + 2561975156227711495237514871966779964501558283497058708235084248829398599957999q^{49} - 31492320141514234591073138519794385457712593727985587891779934655429621403000000q^{50} - 55702073279983479511744597938778959921377812834972727705529236388320801422608936q^{51} - 55278983045853834535146427408736596689073596604984335518990233309047240924848128q^{52} - 363766241548602923075270727552075967170433033161760056492510229436384310833635734q^{53} - 1988318954489765046302005332528558912554496159988340641069330680002958019070937600q^{54} - 3520855393890604949232827617669938515471701214675853816941159595183623184386577000q^{55} - 12936956692485908268365121199611114191360014164491088694387999166431300696512921600q^{56} - 13862265625178226892264597068584427924864963571452022505627535112981742091059296080q^{57} - 73663001170657752665346575473371223431752845037418753763472734766611572171441325440q^{58} - 119839908140624573484226478891501296275544385047787439213910489726968365086286210700q^{59} - 468107546718994029022024884762568911834725078620349067042941227204209206458724352000q^{60} - 328281166748320542242523532793984772143143166398612931227281116669834617338050603326q^{61} - 999402477792071119370831029463209574610493980381087626216590758004912070795081435136q^{62} - 2240117215552784969170617635914585450026055291898885166701984645532069514866650525064q^{63} - 4748321960274080197621802735261780227229800262185345649692550833454877416714840047616q^{64} + 2401958293154067008332922023669433962969772004736123854920087208208149417890196631500q^{65} + 12481418287827593167181900965724458478832175604254852160085986797561206241884769502208q^{66} + 9715050085721519766982024893817705652242604355912950898916137527198529527932523084492q^{67} + 51110178162381015351883898716980001063480395685110983605059672645927223406195391258624q^{68} + 125665844363573358610510037253282595268580727449546920119880250916295279742987985413792q^{69} + 437770522317274261347763126091338009235407849188339858200284725822565513739255154816000q^{70} + 420099768445021912291978352393445519280746916987347799091649913407485898651223357176984q^{71} + 1153857576733974210773243583317262094473717150308417455216249971043377175999426453831680q^{72} + 249990884773795871360906735022065792056914028590737521750721031757996649920054698123686q^{73} + 988848152146322932205109547460090361956964236264222955609677033303897103570301064734848q^{74} + 944080624555199942138536838755965622984512203073943882229003778583589699488457416312500q^{75} - 9872924363930092749183448370538218854882826462181838927155554514487863834399954370969600q^{76} - 16552736755381232703525388842736711985373990693881749218915711388952768140257306836693856q^{77} - 73115054525877473148472082243219461137606249175371809547554984327725748004401082971708928q^{78} - 43369884997252312790262999909905208728154246791055779943371432494520439561399960810221200q^{79} - 88894687813962777903012798348655018553862729556819104796394604135123942915181092274176000q^{80} - 70612572309757383558801217018071484518377724651384007545224773102476238636837549694743953q^{81} - 236357995159599133663604843384379044643064499685381579522884048932961281765779447211829376q^{82} - 206459225650342475045148123542600401116221913586781003327705338223920418727874732010864004q^{83} + 1649840105905513745515070352659141454913812021851911846045941535531840033929951137654243328q^{84} + 1637661121678145282281696006564110640734919603287375198985971859556394144920752854974380500q^{85} + 3239900597437756786176903087412721547247433713557247371056571790561416975430434191434708224q^{86} + 6559051070263618632233284423714108103382010904819072234989172243851503736785525745425626280q^{87} + 6336674026069399594730100443279513731166873520796702455565229756349453295686310223539077120q^{88} + 5580799156439265704685765323272125687903700231557911629488221982292995723510480958101067350q^{89} + 19840068851074490675120863444780810644229753682905466429373855007108663777299926218608144000q^{90} - 18025272478314007503227783954648499409552734863956310123113904904033321293148703549329112496q^{91} - 81750027044574246291550532241925751638073881610946649428268147310600744342795416362583031808q^{92} - 125975338781791055721238628453160089358246167768072651306884109747935024714536192316708787328q^{93} - 306478475429892162274969547511367839192733042761577860914963828391848832364650578690812603392q^{94} - 216711696129933523762297615654778954621414663971673687874218846402427636558070586043601335000q^{95} - 229425406959806321843310706398725653116223652026933598684053060220054993118393316925679599616q^{96} + 43971291171253027759915173352741872464098193495293359649108047104658615767375645954946743342q^{97} - 690328280759812206538864038068682435013428219472201721649324072601042235191425205897720616256q^{98} + 306809773352993420176583539450272713060724644284625495060244639714128125893072287559839588052q^{99} + O(q^{100}) \)

Decomposition of \(S_{94}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.94.a.a \(7\) \(54.773\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(43\!\cdots\!92\) \(-3\!\cdots\!84\) \(-2\!\cdots\!50\) \(-9\!\cdots\!08\) \(+\) \(q+(6247918101970+\beta _{1})q^{2}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 43735426713792 T + \)\(16\!\cdots\!32\)\( T^{2} - \)\(77\!\cdots\!80\)\( T^{3} + \)\(23\!\cdots\!72\)\( T^{4} - \)\(82\!\cdots\!64\)\( T^{5} + \)\(30\!\cdots\!84\)\( T^{6} - \)\(10\!\cdots\!40\)\( T^{7} + \)\(30\!\cdots\!28\)\( T^{8} - \)\(81\!\cdots\!96\)\( T^{9} + \)\(23\!\cdots\!36\)\( T^{10} - \)\(74\!\cdots\!80\)\( T^{11} + \)\(16\!\cdots\!24\)\( T^{12} - \)\(41\!\cdots\!48\)\( T^{13} + \)\(93\!\cdots\!48\)\( T^{14} \)
$3$ \( 1 + \)\(36\!\cdots\!84\)\( T + \)\(65\!\cdots\!53\)\( T^{2} + \)\(55\!\cdots\!20\)\( T^{3} + \)\(26\!\cdots\!77\)\( T^{4} + \)\(27\!\cdots\!08\)\( T^{5} + \)\(74\!\cdots\!41\)\( T^{6} + \)\(84\!\cdots\!60\)\( T^{7} + \)\(17\!\cdots\!43\)\( T^{8} + \)\(15\!\cdots\!32\)\( T^{9} + \)\(34\!\cdots\!59\)\( T^{10} + \)\(17\!\cdots\!20\)\( T^{11} + \)\(47\!\cdots\!79\)\( T^{12} + \)\(63\!\cdots\!76\)\( T^{13} + \)\(40\!\cdots\!47\)\( T^{14} \)
$5$ \( 1 + \)\(24\!\cdots\!50\)\( T + \)\(29\!\cdots\!75\)\( T^{2} + \)\(10\!\cdots\!00\)\( T^{3} + \)\(62\!\cdots\!25\)\( T^{4} + \)\(18\!\cdots\!50\)\( T^{5} + \)\(86\!\cdots\!75\)\( T^{6} + \)\(24\!\cdots\!00\)\( T^{7} + \)\(87\!\cdots\!75\)\( T^{8} + \)\(19\!\cdots\!50\)\( T^{9} + \)\(64\!\cdots\!25\)\( T^{10} + \)\(10\!\cdots\!00\)\( T^{11} + \)\(30\!\cdots\!75\)\( T^{12} + \)\(25\!\cdots\!50\)\( T^{13} + \)\(10\!\cdots\!25\)\( T^{14} \)
$7$ \( 1 + \)\(92\!\cdots\!08\)\( T + \)\(12\!\cdots\!57\)\( T^{2} - \)\(33\!\cdots\!00\)\( T^{3} + \)\(76\!\cdots\!97\)\( T^{4} - \)\(67\!\cdots\!24\)\( T^{5} + \)\(40\!\cdots\!29\)\( T^{6} - \)\(30\!\cdots\!00\)\( T^{7} + \)\(15\!\cdots\!03\)\( T^{8} - \)\(10\!\cdots\!76\)\( T^{9} + \)\(46\!\cdots\!71\)\( T^{10} - \)\(78\!\cdots\!00\)\( T^{11} + \)\(12\!\cdots\!99\)\( T^{12} + \)\(33\!\cdots\!92\)\( T^{13} + \)\(14\!\cdots\!43\)\( T^{14} \)
$11$ \( 1 - \)\(10\!\cdots\!24\)\( T + \)\(32\!\cdots\!21\)\( T^{2} - \)\(41\!\cdots\!44\)\( T^{3} + \)\(48\!\cdots\!61\)\( T^{4} - \)\(65\!\cdots\!52\)\( T^{5} + \)\(47\!\cdots\!73\)\( T^{6} - \)\(59\!\cdots\!92\)\( T^{7} + \)\(33\!\cdots\!63\)\( T^{8} - \)\(32\!\cdots\!72\)\( T^{9} + \)\(17\!\cdots\!51\)\( T^{10} - \)\(10\!\cdots\!24\)\( T^{11} + \)\(56\!\cdots\!71\)\( T^{12} - \)\(13\!\cdots\!44\)\( T^{13} + \)\(88\!\cdots\!11\)\( T^{14} \)
$13$ \( 1 - \)\(19\!\cdots\!26\)\( T + \)\(17\!\cdots\!63\)\( T^{2} - \)\(37\!\cdots\!60\)\( T^{3} + \)\(15\!\cdots\!57\)\( T^{4} - \)\(33\!\cdots\!02\)\( T^{5} + \)\(85\!\cdots\!11\)\( T^{6} - \)\(17\!\cdots\!80\)\( T^{7} + \)\(33\!\cdots\!83\)\( T^{8} - \)\(52\!\cdots\!18\)\( T^{9} + \)\(93\!\cdots\!89\)\( T^{10} - \)\(91\!\cdots\!60\)\( T^{11} + \)\(16\!\cdots\!59\)\( T^{12} - \)\(73\!\cdots\!54\)\( T^{13} + \)\(15\!\cdots\!37\)\( T^{14} \)
$17$ \( 1 - \)\(80\!\cdots\!42\)\( T + \)\(11\!\cdots\!07\)\( T^{2} - \)\(11\!\cdots\!40\)\( T^{3} + \)\(63\!\cdots\!97\)\( T^{4} - \)\(75\!\cdots\!94\)\( T^{5} + \)\(23\!\cdots\!19\)\( T^{6} - \)\(26\!\cdots\!20\)\( T^{7} + \)\(62\!\cdots\!03\)\( T^{8} - \)\(54\!\cdots\!86\)\( T^{9} + \)\(12\!\cdots\!41\)\( T^{10} - \)\(62\!\cdots\!40\)\( T^{11} + \)\(16\!\cdots\!99\)\( T^{12} - \)\(31\!\cdots\!78\)\( T^{13} + \)\(10\!\cdots\!33\)\( T^{14} \)
$19$ \( 1 + \)\(49\!\cdots\!00\)\( T + \)\(40\!\cdots\!13\)\( T^{2} + \)\(12\!\cdots\!00\)\( T^{3} + \)\(53\!\cdots\!01\)\( T^{4} + \)\(97\!\cdots\!00\)\( T^{5} + \)\(34\!\cdots\!65\)\( T^{6} + \)\(47\!\cdots\!00\)\( T^{7} + \)\(28\!\cdots\!35\)\( T^{8} + \)\(68\!\cdots\!00\)\( T^{9} + \)\(31\!\cdots\!79\)\( T^{10} + \)\(61\!\cdots\!00\)\( T^{11} + \)\(16\!\cdots\!87\)\( T^{12} + \)\(17\!\cdots\!00\)\( T^{13} + \)\(29\!\cdots\!19\)\( T^{14} \)
$23$ \( 1 + \)\(25\!\cdots\!64\)\( T + \)\(15\!\cdots\!73\)\( T^{2} + \)\(32\!\cdots\!60\)\( T^{3} + \)\(13\!\cdots\!37\)\( T^{4} + \)\(26\!\cdots\!88\)\( T^{5} + \)\(83\!\cdots\!81\)\( T^{6} + \)\(13\!\cdots\!80\)\( T^{7} + \)\(36\!\cdots\!23\)\( T^{8} + \)\(51\!\cdots\!32\)\( T^{9} + \)\(11\!\cdots\!19\)\( T^{10} + \)\(11\!\cdots\!60\)\( T^{11} + \)\(25\!\cdots\!39\)\( T^{12} + \)\(18\!\cdots\!16\)\( T^{13} + \)\(30\!\cdots\!27\)\( T^{14} \)
$29$ \( 1 - \)\(11\!\cdots\!50\)\( T + \)\(20\!\cdots\!23\)\( T^{2} - \)\(31\!\cdots\!00\)\( T^{3} + \)\(44\!\cdots\!41\)\( T^{4} - \)\(51\!\cdots\!50\)\( T^{5} + \)\(57\!\cdots\!15\)\( T^{6} - \)\(61\!\cdots\!00\)\( T^{7} + \)\(58\!\cdots\!35\)\( T^{8} - \)\(52\!\cdots\!50\)\( T^{9} + \)\(45\!\cdots\!29\)\( T^{10} - \)\(32\!\cdots\!00\)\( T^{11} + \)\(21\!\cdots\!27\)\( T^{12} - \)\(12\!\cdots\!50\)\( T^{13} + \)\(10\!\cdots\!29\)\( T^{14} \)
$31$ \( 1 + \)\(11\!\cdots\!56\)\( T + \)\(11\!\cdots\!81\)\( T^{2} + \)\(32\!\cdots\!96\)\( T^{3} + \)\(77\!\cdots\!81\)\( T^{4} + \)\(22\!\cdots\!48\)\( T^{5} + \)\(64\!\cdots\!13\)\( T^{6} + \)\(90\!\cdots\!88\)\( T^{7} + \)\(32\!\cdots\!83\)\( T^{8} + \)\(55\!\cdots\!88\)\( T^{9} + \)\(95\!\cdots\!51\)\( T^{10} + \)\(20\!\cdots\!56\)\( T^{11} + \)\(35\!\cdots\!31\)\( T^{12} + \)\(17\!\cdots\!96\)\( T^{13} + \)\(75\!\cdots\!31\)\( T^{14} \)
$37$ \( 1 - \)\(11\!\cdots\!42\)\( T + \)\(42\!\cdots\!07\)\( T^{2} - \)\(37\!\cdots\!20\)\( T^{3} + \)\(80\!\cdots\!97\)\( T^{4} - \)\(56\!\cdots\!34\)\( T^{5} + \)\(87\!\cdots\!99\)\( T^{6} - \)\(49\!\cdots\!60\)\( T^{7} + \)\(60\!\cdots\!03\)\( T^{8} - \)\(27\!\cdots\!06\)\( T^{9} + \)\(27\!\cdots\!81\)\( T^{10} - \)\(87\!\cdots\!20\)\( T^{11} + \)\(70\!\cdots\!99\)\( T^{12} - \)\(12\!\cdots\!18\)\( T^{13} + \)\(79\!\cdots\!13\)\( T^{14} \)
$41$ \( 1 + \)\(50\!\cdots\!46\)\( T + \)\(28\!\cdots\!11\)\( T^{2} + \)\(30\!\cdots\!16\)\( T^{3} + \)\(51\!\cdots\!41\)\( T^{4} + \)\(54\!\cdots\!98\)\( T^{5} + \)\(79\!\cdots\!83\)\( T^{6} + \)\(57\!\cdots\!28\)\( T^{7} + \)\(77\!\cdots\!43\)\( T^{8} + \)\(51\!\cdots\!18\)\( T^{9} + \)\(47\!\cdots\!01\)\( T^{10} + \)\(27\!\cdots\!96\)\( T^{11} + \)\(25\!\cdots\!11\)\( T^{12} + \)\(43\!\cdots\!66\)\( T^{13} + \)\(83\!\cdots\!41\)\( T^{14} \)
$43$ \( 1 + \)\(72\!\cdots\!44\)\( T + \)\(39\!\cdots\!93\)\( T^{2} + \)\(29\!\cdots\!00\)\( T^{3} + \)\(73\!\cdots\!97\)\( T^{4} + \)\(55\!\cdots\!68\)\( T^{5} + \)\(87\!\cdots\!21\)\( T^{6} + \)\(58\!\cdots\!00\)\( T^{7} + \)\(71\!\cdots\!03\)\( T^{8} + \)\(36\!\cdots\!32\)\( T^{9} + \)\(40\!\cdots\!79\)\( T^{10} + \)\(13\!\cdots\!00\)\( T^{11} + \)\(14\!\cdots\!99\)\( T^{12} + \)\(21\!\cdots\!56\)\( T^{13} + \)\(24\!\cdots\!07\)\( T^{14} \)
$47$ \( 1 + \)\(37\!\cdots\!08\)\( T + \)\(11\!\cdots\!57\)\( T^{2} + \)\(50\!\cdots\!40\)\( T^{3} + \)\(66\!\cdots\!97\)\( T^{4} + \)\(30\!\cdots\!96\)\( T^{5} + \)\(29\!\cdots\!89\)\( T^{6} + \)\(11\!\cdots\!20\)\( T^{7} + \)\(94\!\cdots\!03\)\( T^{8} + \)\(30\!\cdots\!84\)\( T^{9} + \)\(21\!\cdots\!51\)\( T^{10} + \)\(52\!\cdots\!40\)\( T^{11} + \)\(37\!\cdots\!99\)\( T^{12} + \)\(39\!\cdots\!12\)\( T^{13} + \)\(34\!\cdots\!03\)\( T^{14} \)
$53$ \( 1 + \)\(36\!\cdots\!34\)\( T + \)\(10\!\cdots\!03\)\( T^{2} + \)\(19\!\cdots\!20\)\( T^{3} + \)\(39\!\cdots\!77\)\( T^{4} + \)\(66\!\cdots\!58\)\( T^{5} + \)\(13\!\cdots\!91\)\( T^{6} + \)\(19\!\cdots\!60\)\( T^{7} + \)\(29\!\cdots\!43\)\( T^{8} + \)\(34\!\cdots\!82\)\( T^{9} + \)\(46\!\cdots\!09\)\( T^{10} + \)\(52\!\cdots\!20\)\( T^{11} + \)\(65\!\cdots\!79\)\( T^{12} + \)\(50\!\cdots\!26\)\( T^{13} + \)\(31\!\cdots\!97\)\( T^{14} \)
$59$ \( 1 + \)\(11\!\cdots\!00\)\( T + \)\(87\!\cdots\!53\)\( T^{2} + \)\(45\!\cdots\!00\)\( T^{3} + \)\(18\!\cdots\!61\)\( T^{4} + \)\(64\!\cdots\!00\)\( T^{5} + \)\(18\!\cdots\!65\)\( T^{6} + \)\(43\!\cdots\!00\)\( T^{7} + \)\(88\!\cdots\!35\)\( T^{8} + \)\(15\!\cdots\!00\)\( T^{9} + \)\(22\!\cdots\!79\)\( T^{10} + \)\(26\!\cdots\!00\)\( T^{11} + \)\(24\!\cdots\!47\)\( T^{12} + \)\(16\!\cdots\!00\)\( T^{13} + \)\(66\!\cdots\!59\)\( T^{14} \)
$61$ \( 1 + \)\(32\!\cdots\!26\)\( T + \)\(80\!\cdots\!71\)\( T^{2} + \)\(14\!\cdots\!56\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} + \)\(27\!\cdots\!98\)\( T^{5} + \)\(31\!\cdots\!23\)\( T^{6} + \)\(33\!\cdots\!08\)\( T^{7} + \)\(34\!\cdots\!63\)\( T^{8} + \)\(31\!\cdots\!78\)\( T^{9} + \)\(27\!\cdots\!01\)\( T^{10} + \)\(19\!\cdots\!76\)\( T^{11} + \)\(12\!\cdots\!71\)\( T^{12} + \)\(53\!\cdots\!06\)\( T^{13} + \)\(17\!\cdots\!61\)\( T^{14} \)
$67$ \( 1 - \)\(97\!\cdots\!92\)\( T + \)\(34\!\cdots\!57\)\( T^{2} - \)\(28\!\cdots\!40\)\( T^{3} + \)\(54\!\cdots\!97\)\( T^{4} - \)\(39\!\cdots\!44\)\( T^{5} + \)\(53\!\cdots\!69\)\( T^{6} - \)\(33\!\cdots\!20\)\( T^{7} + \)\(36\!\cdots\!03\)\( T^{8} - \)\(17\!\cdots\!36\)\( T^{9} + \)\(16\!\cdots\!91\)\( T^{10} - \)\(56\!\cdots\!40\)\( T^{11} + \)\(45\!\cdots\!99\)\( T^{12} - \)\(86\!\cdots\!28\)\( T^{13} + \)\(59\!\cdots\!83\)\( T^{14} \)
$71$ \( 1 - \)\(42\!\cdots\!84\)\( T + \)\(12\!\cdots\!01\)\( T^{2} - \)\(26\!\cdots\!24\)\( T^{3} + \)\(46\!\cdots\!21\)\( T^{4} - \)\(67\!\cdots\!52\)\( T^{5} + \)\(90\!\cdots\!93\)\( T^{6} - \)\(10\!\cdots\!52\)\( T^{7} + \)\(13\!\cdots\!23\)\( T^{8} - \)\(14\!\cdots\!92\)\( T^{9} + \)\(14\!\cdots\!51\)\( T^{10} - \)\(12\!\cdots\!84\)\( T^{11} + \)\(87\!\cdots\!51\)\( T^{12} - \)\(42\!\cdots\!24\)\( T^{13} + \)\(14\!\cdots\!71\)\( T^{14} \)
$73$ \( 1 - \)\(24\!\cdots\!86\)\( T + \)\(71\!\cdots\!23\)\( T^{2} - \)\(23\!\cdots\!40\)\( T^{3} + \)\(29\!\cdots\!37\)\( T^{4} - \)\(91\!\cdots\!62\)\( T^{5} + \)\(81\!\cdots\!31\)\( T^{6} - \)\(22\!\cdots\!20\)\( T^{7} + \)\(15\!\cdots\!23\)\( T^{8} - \)\(34\!\cdots\!18\)\( T^{9} + \)\(21\!\cdots\!69\)\( T^{10} - \)\(33\!\cdots\!40\)\( T^{11} + \)\(19\!\cdots\!39\)\( T^{12} - \)\(13\!\cdots\!34\)\( T^{13} + \)\(10\!\cdots\!77\)\( T^{14} \)
$79$ \( 1 + \)\(43\!\cdots\!00\)\( T + \)\(15\!\cdots\!73\)\( T^{2} + \)\(36\!\cdots\!00\)\( T^{3} + \)\(71\!\cdots\!41\)\( T^{4} + \)\(11\!\cdots\!00\)\( T^{5} + \)\(16\!\cdots\!65\)\( T^{6} + \)\(25\!\cdots\!00\)\( T^{7} + \)\(48\!\cdots\!35\)\( T^{8} + \)\(10\!\cdots\!00\)\( T^{9} + \)\(19\!\cdots\!79\)\( T^{10} + \)\(30\!\cdots\!00\)\( T^{11} + \)\(38\!\cdots\!27\)\( T^{12} + \)\(32\!\cdots\!00\)\( T^{13} + \)\(22\!\cdots\!79\)\( T^{14} \)
$83$ \( 1 + \)\(20\!\cdots\!04\)\( T + \)\(15\!\cdots\!33\)\( T^{2} + \)\(29\!\cdots\!80\)\( T^{3} + \)\(11\!\cdots\!17\)\( T^{4} + \)\(19\!\cdots\!28\)\( T^{5} + \)\(53\!\cdots\!01\)\( T^{6} + \)\(71\!\cdots\!40\)\( T^{7} + \)\(15\!\cdots\!63\)\( T^{8} + \)\(16\!\cdots\!32\)\( T^{9} + \)\(30\!\cdots\!99\)\( T^{10} + \)\(23\!\cdots\!80\)\( T^{11} + \)\(36\!\cdots\!19\)\( T^{12} + \)\(14\!\cdots\!36\)\( T^{13} + \)\(20\!\cdots\!67\)\( T^{14} \)
$89$ \( 1 - \)\(55\!\cdots\!50\)\( T + \)\(12\!\cdots\!83\)\( T^{2} - \)\(62\!\cdots\!00\)\( T^{3} + \)\(72\!\cdots\!81\)\( T^{4} - \)\(29\!\cdots\!50\)\( T^{5} + \)\(23\!\cdots\!15\)\( T^{6} - \)\(77\!\cdots\!00\)\( T^{7} + \)\(46\!\cdots\!35\)\( T^{8} - \)\(11\!\cdots\!50\)\( T^{9} + \)\(55\!\cdots\!29\)\( T^{10} - \)\(93\!\cdots\!00\)\( T^{11} + \)\(37\!\cdots\!67\)\( T^{12} - \)\(32\!\cdots\!50\)\( T^{13} + \)\(11\!\cdots\!89\)\( T^{14} \)
$97$ \( 1 - \)\(43\!\cdots\!42\)\( T + \)\(20\!\cdots\!07\)\( T^{2} - \)\(46\!\cdots\!60\)\( T^{3} + \)\(22\!\cdots\!97\)\( T^{4} + \)\(91\!\cdots\!46\)\( T^{5} + \)\(16\!\cdots\!39\)\( T^{6} + \)\(19\!\cdots\!20\)\( T^{7} + \)\(96\!\cdots\!03\)\( T^{8} + \)\(31\!\cdots\!34\)\( T^{9} + \)\(45\!\cdots\!01\)\( T^{10} - \)\(55\!\cdots\!60\)\( T^{11} + \)\(14\!\cdots\!99\)\( T^{12} - \)\(18\!\cdots\!38\)\( T^{13} + \)\(24\!\cdots\!53\)\( T^{14} \)
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