Properties

Label 1.98.a
Level 1
Weight 98
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 7
Newform subspaces 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 98 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{98}(\Gamma_0(1))\).

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

Trace form

\( 7q - 16697241085008q^{2} + 100515854497394358147996q^{3} + 163057083940695061811962902784q^{4} - 3658387999529088680958306590731350q^{5} - 30592714388364079315260992082788233536q^{6} - 184642311743115370607493500489904481438408q^{7} + 36028528195426625427479134330455698506199040q^{8} + 34775775472129528349857305774273773877811641051q^{9} + O(q^{10}) \) \( 7q - 16697241085008q^{2} + 100515854497394358147996q^{3} + 163057083940695061811962902784q^{4} - 3658387999529088680958306590731350q^{5} - 30592714388364079315260992082788233536q^{6} - 184642311743115370607493500489904481438408q^{7} + 36028528195426625427479134330455698506199040q^{8} + 34775775472129528349857305774273773877811641051q^{9} + 2369114123959441270700616822719459966510786272800q^{10} - 211379321299339211995860033669883746379479318698796q^{11} + 29500590587146562092031430274877546417191966208812032q^{12} - 883667637845783834437332163606692334928033653755299614q^{13} + 24884922778173528138085777326574033504771595080747613568q^{14} - 1421739776861319561135033238174867421082029896683725376600q^{15} - 31468671341370205538262999960370611414173356196203424841728q^{16} + 163250436637003263661570089512096377905088225334685131721342q^{17} - 7054606772048003028382413409749231596837718873737440667537424q^{18} + 133084372359310898958448501523235681541051727436663191570359820q^{19} - 1318696260534044061297364386263469065025874939722479973417331200q^{20} - 8226961344750528298533572507576209983448935264598913374247505696q^{21} - 193421584410477868290586506488587370358898549812529751083484246976q^{22} + 925260914184001305416523826357059292226482310773339215111132964776q^{23} + 1719359518493251306391725804700467921422689016189510541760687554560q^{24} - 15111829774373494694703308579556617230149980669179989285410298974375q^{25} + 252570839996871764139482603418038366978372757286009959646749464447904q^{26} - 16291464003153760806194022590188439733978909915063668620863256233960q^{27} + 2270023864280230580582797832096861251181573169347509612847861972977664q^{28} - 119228645746988213289933973286594685848645193803889692652451844737975470q^{29} + 350448354156350400480979435069989695492221249186335731168327070817564800q^{30} + 1783283666881858864849681148885200501497581294973934227348751364131906784q^{31} - 5665372498136527985720301619489703024215195383428523596691479514791804928q^{32} + 31524650657546522511070078635079454480923539002999356172307109465073458512q^{33} - 360491523041063125717708388027762293189396999595568175085448186659598970272q^{34} + 1278268341035082746531666145800358760269267683649420892787253371588938750800q^{35} - 216561481226385812264597126278375191173372906326221899147967914271513631488q^{36} - 4532061622841943284542390241171859851726205146853788500539269747469617514358q^{37} - 2979582210919721773595405461863152858097797783237497905501709239616681227840q^{38} + 43268347489134056222423767530379619668087154910038087692852374564634305176712q^{39} - 252514831298472678734291758335102132215188475493571956673272319739362987008000q^{40} + 123663386655433999860484853403953500874113711440208020678841289201379470695974q^{41} + 3296122851141924824443574220618174749418258893075867148421980920155200276985344q^{42} - 6595249409358954185694714287710218939626711013706300289026511229489118746183244q^{43} + 31427981619155317050453798326367420934595218826815326227502736274099059309390848q^{44} - 252057107931731391251960224707597558538839631727412739243273361199825466582835550q^{45} + 333743461536679365083903174537100831945624746347277312419032904840551699600111744q^{46} + 1582413179705462665936960636748613012540566075462612818643843634715630112826042192q^{47} - 5861556434117332280930374286873664455351210291383528056190272983552191849213722624q^{48} + 4345635008055985505106601346877321132027699788278385269907095782368403364891488399q^{49} - 26742593205970009143775889336520990050133941492259748319418427757724876722706030000q^{50} + 7043565089506559965061572069632281800522096763383079376468682406398600422146676984q^{51} + 45800222007571685487736059984048709986270205428489770979037497696929384027946163712q^{52} - 653999931744204429821742741003701830521617657540517458768483866216741544701292475654q^{53} - 1692275654206728716605786947196644220317392594111136065941704729626944069981837438080q^{54} - 2797264930804680667438884831689324464716285797264284803651188210713133784740241832200q^{55} - 13571511538900847480549793700693331801076437559096966169392506220987757777557857402880q^{56} - 32156245276763940566100505959698139630384956043693169857398532690693294678041975751120q^{57} - 110275012470967940484400158535846043036245771061355495516009955997986614502808104491360q^{58} - 289716843512018767811919727809674339112407721830489506743846640027004030301179845118940q^{59} - 910863091257112962110410128770927709732237428874631129572443550789630933691032398899200q^{60} - 1779644273771380099149369471014727845406783738447834645166296866716596067825339549188046q^{61} - 4893410323209515393605311670149478112622973098189152140516775294151722525768562137565696q^{62} - 12773855755538157144284595252262546905649007916763284311597736303148976241726684562602024q^{63} - 24329532034212074257236420324752039539459926287390018025638252399891746834835822530789376q^{64} - 40979880706222898178317998710539228015340375450212825952623031288613904725454054500850100q^{65} - 142841613731497146561089386918878946227924637814625892149907766833242924230825872606056192q^{66} - 183094181851902905703789039636502649221241410347877100016575616698548103898875205122783908q^{67} - 250132580738896836682574414547500843555901286243235420681429272583107380144497499057716736q^{68} - 372244836961332226973480986215431578494847115740354696097669790201492502675456308855459168q^{69} - 587389541033882485666068522391834191601610745639266949076956170254929472707526921059782400q^{70} - 36618527208607574135274147674246343687098099724640001025727994874106062220116534447931656q^{71} + 2495502705800463241319297965149724088435827677064467496346161624547668625438549984339128320q^{72} + 5937141741627411574629383951784847225959103237898806939243808260531064318159784943464907526q^{73} + 25603418812897773069861990064614106209712057876935905208225093500026599325689360114519970848q^{74} + 43416229043729585532262686371625117245611844558141193068941674421259839404159894884059222500q^{75} + 64491781461168277038374423376126180174707623388661413952117963143585395013082375272839869440q^{76} + 122801524700573133455664123216977109508839271312008866744292206338517188364407357732160152224q^{77} + 256518622739178273010532892375526005382856863147760611859324715551823107217212845963281985152q^{78} + 155279975164311735091235448536513906273532801204307686975280157544842456609207922540776901680q^{79} + 343037548751841740038666995050634479050946344382038763901789904170114217394648666813900390400q^{80} - 799336653019442009471583631583081099983526554777301855450568718504605547656753900698628831153q^{81} - 2054599455199243418451530458808296516745297582440826399667363552358055209069956455679452833056q^{82} - 2745080838526935126539434486643898932954125805020264508203796620734019354440308801326974021684q^{83} - 12055830667015300843296227009204563031159870111997209215974794552386444770918151507927520305152q^{84} - 16156906986132970771716277890961343081101351325821342812927748903601690598916612215092853170700q^{85} - 16073101085057033129856695763368798351047883803740227513388827997968391823543719379002604387776q^{86} - 44931373084677669249994770736329381356923858000626008622029156778901658182110994195783000791480q^{87} - 20900444501134905678673788524771632932447417317035512416151379720801969394444956958395302789120q^{88} + 8652425236627243255051028260917634407304730072980172181544783646255542601500269383337979350390q^{89} + 169914380219009102880054256907856294069041898142575788262717672760376053145875718225670932330400q^{90} + 235279610532724372901602846332263408075886672274330172793822218199845308058643167074949650230544q^{91} + 622950794384614085632156625042963081233986358617743991991586248417198315809579918444522808891392q^{92} + 1619655729334717431421579797164299646702152339363664709672746834797775058100318492643375449441152q^{93} + 1784387548746436753701888750274366538460858609156963702431495773056050960861585984793528939671808q^{94} + 1109691419127482658877926123378178695834970817464791602098716148821958373905367930889408748989000q^{95} + 2773817117979873680694700349927475687549477810523157816910439588411515192104026991177258420404224q^{96} - 462826972284038426621245345324758076530452205891330025493894671876723283114629445572915788984658q^{97} - 10100804559243313775965110405631054964918520327952856127425837778067309219959758215138751854831056q^{98} - 13792894935722775136702660269810636953813664741795563019740674282913700184659028566406972539495228q^{99} + O(q^{100}) \)

Decomposition of \(S_{98}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.98.a.a \(7\) \(59.585\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\!\cdots\!08\) \(10\!\cdots\!96\) \(-3\!\cdots\!50\) \(-1\!\cdots\!08\) \(+\) \(q+(-2385320155001+\beta _{1})q^{2}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 16697241085008 T + \)\(47\!\cdots\!92\)\( T^{2} - \)\(49\!\cdots\!40\)\( T^{3} + \)\(12\!\cdots\!92\)\( T^{4} - \)\(17\!\cdots\!84\)\( T^{5} + \)\(27\!\cdots\!04\)\( T^{6} - \)\(16\!\cdots\!20\)\( T^{7} + \)\(43\!\cdots\!88\)\( T^{8} - \)\(43\!\cdots\!56\)\( T^{9} + \)\(50\!\cdots\!16\)\( T^{10} - \)\(31\!\cdots\!40\)\( T^{11} + \)\(47\!\cdots\!44\)\( T^{12} + \)\(26\!\cdots\!32\)\( T^{13} + \)\(25\!\cdots\!88\)\( T^{14} \)
$3$ \( 1 - \)\(10\!\cdots\!96\)\( T + \)\(54\!\cdots\!53\)\( T^{2} - \)\(44\!\cdots\!40\)\( T^{3} + \)\(17\!\cdots\!77\)\( T^{4} - \)\(11\!\cdots\!72\)\( T^{5} + \)\(40\!\cdots\!61\)\( T^{6} - \)\(23\!\cdots\!20\)\( T^{7} + \)\(77\!\cdots\!43\)\( T^{8} - \)\(40\!\cdots\!68\)\( T^{9} + \)\(12\!\cdots\!19\)\( T^{10} - \)\(59\!\cdots\!40\)\( T^{11} + \)\(13\!\cdots\!79\)\( T^{12} - \)\(48\!\cdots\!64\)\( T^{13} + \)\(92\!\cdots\!67\)\( T^{14} \)
$5$ \( 1 + \)\(36\!\cdots\!50\)\( T + \)\(23\!\cdots\!75\)\( T^{2} + \)\(24\!\cdots\!00\)\( T^{3} + \)\(25\!\cdots\!25\)\( T^{4} - \)\(35\!\cdots\!50\)\( T^{5} + \)\(17\!\cdots\!75\)\( T^{6} - \)\(48\!\cdots\!00\)\( T^{7} + \)\(11\!\cdots\!75\)\( T^{8} - \)\(14\!\cdots\!50\)\( T^{9} + \)\(63\!\cdots\!25\)\( T^{10} + \)\(39\!\cdots\!00\)\( T^{11} + \)\(23\!\cdots\!75\)\( T^{12} + \)\(23\!\cdots\!50\)\( T^{13} + \)\(39\!\cdots\!25\)\( T^{14} \)
$7$ \( 1 + \)\(18\!\cdots\!08\)\( T + \)\(47\!\cdots\!57\)\( T^{2} + \)\(72\!\cdots\!00\)\( T^{3} + \)\(11\!\cdots\!97\)\( T^{4} + \)\(13\!\cdots\!76\)\( T^{5} + \)\(15\!\cdots\!29\)\( T^{6} + \)\(15\!\cdots\!00\)\( T^{7} + \)\(15\!\cdots\!03\)\( T^{8} + \)\(12\!\cdots\!24\)\( T^{9} + \)\(93\!\cdots\!71\)\( T^{10} + \)\(56\!\cdots\!00\)\( T^{11} + \)\(35\!\cdots\!99\)\( T^{12} + \)\(12\!\cdots\!92\)\( T^{13} + \)\(66\!\cdots\!43\)\( T^{14} \)
$11$ \( 1 + \)\(21\!\cdots\!96\)\( T + \)\(24\!\cdots\!61\)\( T^{2} + \)\(84\!\cdots\!16\)\( T^{3} + \)\(47\!\cdots\!41\)\( T^{4} + \)\(15\!\cdots\!48\)\( T^{5} + \)\(70\!\cdots\!33\)\( T^{6} + \)\(17\!\cdots\!28\)\( T^{7} + \)\(73\!\cdots\!43\)\( T^{8} + \)\(16\!\cdots\!68\)\( T^{9} + \)\(52\!\cdots\!51\)\( T^{10} + \)\(97\!\cdots\!96\)\( T^{11} + \)\(29\!\cdots\!11\)\( T^{12} + \)\(26\!\cdots\!16\)\( T^{13} + \)\(12\!\cdots\!91\)\( T^{14} \)
$13$ \( 1 + \)\(88\!\cdots\!14\)\( T + \)\(40\!\cdots\!63\)\( T^{2} + \)\(26\!\cdots\!20\)\( T^{3} + \)\(79\!\cdots\!57\)\( T^{4} + \)\(44\!\cdots\!38\)\( T^{5} + \)\(11\!\cdots\!51\)\( T^{6} + \)\(57\!\cdots\!60\)\( T^{7} + \)\(13\!\cdots\!83\)\( T^{8} + \)\(57\!\cdots\!82\)\( T^{9} + \)\(11\!\cdots\!09\)\( T^{10} + \)\(43\!\cdots\!20\)\( T^{11} + \)\(73\!\cdots\!59\)\( T^{12} + \)\(18\!\cdots\!66\)\( T^{13} + \)\(23\!\cdots\!77\)\( T^{14} \)
$17$ \( 1 - \)\(16\!\cdots\!42\)\( T + \)\(70\!\cdots\!87\)\( T^{2} - \)\(14\!\cdots\!20\)\( T^{3} + \)\(30\!\cdots\!57\)\( T^{4} - \)\(55\!\cdots\!54\)\( T^{5} + \)\(90\!\cdots\!79\)\( T^{6} - \)\(15\!\cdots\!60\)\( T^{7} + \)\(20\!\cdots\!83\)\( T^{8} - \)\(28\!\cdots\!66\)\( T^{9} + \)\(35\!\cdots\!81\)\( T^{10} - \)\(36\!\cdots\!20\)\( T^{11} + \)\(41\!\cdots\!59\)\( T^{12} - \)\(21\!\cdots\!38\)\( T^{13} + \)\(29\!\cdots\!53\)\( T^{14} \)
$19$ \( 1 - \)\(13\!\cdots\!20\)\( T + \)\(52\!\cdots\!73\)\( T^{2} - \)\(49\!\cdots\!80\)\( T^{3} + \)\(11\!\cdots\!41\)\( T^{4} - \)\(81\!\cdots\!00\)\( T^{5} + \)\(14\!\cdots\!65\)\( T^{6} - \)\(93\!\cdots\!00\)\( T^{7} + \)\(16\!\cdots\!35\)\( T^{8} - \)\(97\!\cdots\!00\)\( T^{9} + \)\(14\!\cdots\!79\)\( T^{10} - \)\(71\!\cdots\!80\)\( T^{11} + \)\(82\!\cdots\!27\)\( T^{12} - \)\(22\!\cdots\!20\)\( T^{13} + \)\(18\!\cdots\!79\)\( T^{14} \)
$23$ \( 1 - \)\(92\!\cdots\!76\)\( T + \)\(50\!\cdots\!73\)\( T^{2} - \)\(24\!\cdots\!20\)\( T^{3} + \)\(10\!\cdots\!37\)\( T^{4} - \)\(73\!\cdots\!52\)\( T^{5} + \)\(12\!\cdots\!41\)\( T^{6} + \)\(21\!\cdots\!40\)\( T^{7} + \)\(14\!\cdots\!23\)\( T^{8} - \)\(11\!\cdots\!68\)\( T^{9} + \)\(18\!\cdots\!99\)\( T^{10} - \)\(55\!\cdots\!20\)\( T^{11} + \)\(13\!\cdots\!39\)\( T^{12} - \)\(31\!\cdots\!04\)\( T^{13} + \)\(41\!\cdots\!87\)\( T^{14} \)
$29$ \( 1 + \)\(11\!\cdots\!70\)\( T + \)\(34\!\cdots\!63\)\( T^{2} + \)\(33\!\cdots\!80\)\( T^{3} + \)\(60\!\cdots\!01\)\( T^{4} + \)\(48\!\cdots\!50\)\( T^{5} + \)\(64\!\cdots\!15\)\( T^{6} + \)\(42\!\cdots\!00\)\( T^{7} + \)\(45\!\cdots\!35\)\( T^{8} + \)\(24\!\cdots\!50\)\( T^{9} + \)\(21\!\cdots\!29\)\( T^{10} + \)\(86\!\cdots\!80\)\( T^{11} + \)\(64\!\cdots\!87\)\( T^{12} + \)\(15\!\cdots\!70\)\( T^{13} + \)\(92\!\cdots\!69\)\( T^{14} \)
$31$ \( 1 - \)\(17\!\cdots\!84\)\( T + \)\(94\!\cdots\!01\)\( T^{2} - \)\(16\!\cdots\!24\)\( T^{3} + \)\(76\!\cdots\!21\)\( T^{4} - \)\(15\!\cdots\!52\)\( T^{5} + \)\(42\!\cdots\!93\)\( T^{6} - \)\(74\!\cdots\!52\)\( T^{7} + \)\(19\!\cdots\!23\)\( T^{8} - \)\(32\!\cdots\!92\)\( T^{9} + \)\(73\!\cdots\!51\)\( T^{10} - \)\(74\!\cdots\!84\)\( T^{11} + \)\(19\!\cdots\!51\)\( T^{12} - \)\(16\!\cdots\!24\)\( T^{13} + \)\(43\!\cdots\!71\)\( T^{14} \)
$37$ \( 1 + \)\(45\!\cdots\!58\)\( T + \)\(35\!\cdots\!47\)\( T^{2} + \)\(21\!\cdots\!40\)\( T^{3} + \)\(68\!\cdots\!77\)\( T^{4} + \)\(49\!\cdots\!86\)\( T^{5} + \)\(10\!\cdots\!79\)\( T^{6} + \)\(79\!\cdots\!20\)\( T^{7} + \)\(13\!\cdots\!43\)\( T^{8} + \)\(84\!\cdots\!54\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} + \)\(61\!\cdots\!40\)\( T^{11} + \)\(13\!\cdots\!79\)\( T^{12} + \)\(22\!\cdots\!02\)\( T^{13} + \)\(64\!\cdots\!73\)\( T^{14} \)
$41$ \( 1 - \)\(12\!\cdots\!74\)\( T + \)\(12\!\cdots\!71\)\( T^{2} - \)\(31\!\cdots\!44\)\( T^{3} + \)\(70\!\cdots\!61\)\( T^{4} - \)\(24\!\cdots\!02\)\( T^{5} + \)\(25\!\cdots\!23\)\( T^{6} - \)\(94\!\cdots\!92\)\( T^{7} + \)\(69\!\cdots\!63\)\( T^{8} - \)\(18\!\cdots\!22\)\( T^{9} + \)\(14\!\cdots\!01\)\( T^{10} - \)\(17\!\cdots\!24\)\( T^{11} + \)\(19\!\cdots\!71\)\( T^{12} - \)\(54\!\cdots\!94\)\( T^{13} + \)\(12\!\cdots\!61\)\( T^{14} \)
$43$ \( 1 + \)\(65\!\cdots\!44\)\( T + \)\(67\!\cdots\!93\)\( T^{2} - \)\(11\!\cdots\!00\)\( T^{3} + \)\(19\!\cdots\!97\)\( T^{4} - \)\(34\!\cdots\!32\)\( T^{5} + \)\(30\!\cdots\!21\)\( T^{6} - \)\(14\!\cdots\!00\)\( T^{7} + \)\(85\!\cdots\!03\)\( T^{8} - \)\(27\!\cdots\!68\)\( T^{9} + \)\(42\!\cdots\!79\)\( T^{10} - \)\(67\!\cdots\!00\)\( T^{11} + \)\(11\!\cdots\!99\)\( T^{12} + \)\(31\!\cdots\!56\)\( T^{13} + \)\(13\!\cdots\!07\)\( T^{14} \)
$47$ \( 1 - \)\(15\!\cdots\!92\)\( T + \)\(71\!\cdots\!77\)\( T^{2} - \)\(11\!\cdots\!80\)\( T^{3} + \)\(26\!\cdots\!37\)\( T^{4} - \)\(38\!\cdots\!44\)\( T^{5} + \)\(63\!\cdots\!29\)\( T^{6} - \)\(76\!\cdots\!40\)\( T^{7} + \)\(99\!\cdots\!23\)\( T^{8} - \)\(94\!\cdots\!36\)\( T^{9} + \)\(10\!\cdots\!11\)\( T^{10} - \)\(69\!\cdots\!80\)\( T^{11} + \)\(66\!\cdots\!39\)\( T^{12} - \)\(22\!\cdots\!28\)\( T^{13} + \)\(22\!\cdots\!83\)\( T^{14} \)
$53$ \( 1 + \)\(65\!\cdots\!54\)\( T + \)\(10\!\cdots\!03\)\( T^{2} + \)\(46\!\cdots\!60\)\( T^{3} + \)\(43\!\cdots\!77\)\( T^{4} + \)\(14\!\cdots\!78\)\( T^{5} + \)\(10\!\cdots\!11\)\( T^{6} + \)\(28\!\cdots\!80\)\( T^{7} + \)\(19\!\cdots\!43\)\( T^{8} + \)\(45\!\cdots\!82\)\( T^{9} + \)\(25\!\cdots\!69\)\( T^{10} + \)\(48\!\cdots\!60\)\( T^{11} + \)\(19\!\cdots\!79\)\( T^{12} + \)\(22\!\cdots\!86\)\( T^{13} + \)\(60\!\cdots\!17\)\( T^{14} \)
$59$ \( 1 + \)\(28\!\cdots\!40\)\( T + \)\(60\!\cdots\!33\)\( T^{2} + \)\(91\!\cdots\!60\)\( T^{3} + \)\(11\!\cdots\!81\)\( T^{4} + \)\(12\!\cdots\!00\)\( T^{5} + \)\(11\!\cdots\!65\)\( T^{6} + \)\(90\!\cdots\!00\)\( T^{7} + \)\(65\!\cdots\!35\)\( T^{8} + \)\(42\!\cdots\!00\)\( T^{9} + \)\(23\!\cdots\!79\)\( T^{10} + \)\(11\!\cdots\!60\)\( T^{11} + \)\(44\!\cdots\!67\)\( T^{12} + \)\(12\!\cdots\!40\)\( T^{13} + \)\(25\!\cdots\!39\)\( T^{14} \)
$61$ \( 1 + \)\(17\!\cdots\!46\)\( T + \)\(20\!\cdots\!11\)\( T^{2} + \)\(16\!\cdots\!16\)\( T^{3} + \)\(11\!\cdots\!41\)\( T^{4} + \)\(60\!\cdots\!98\)\( T^{5} + \)\(28\!\cdots\!83\)\( T^{6} + \)\(11\!\cdots\!28\)\( T^{7} + \)\(43\!\cdots\!43\)\( T^{8} + \)\(13\!\cdots\!18\)\( T^{9} + \)\(37\!\cdots\!01\)\( T^{10} + \)\(86\!\cdots\!96\)\( T^{11} + \)\(15\!\cdots\!11\)\( T^{12} + \)\(20\!\cdots\!66\)\( T^{13} + \)\(17\!\cdots\!41\)\( T^{14} \)
$67$ \( 1 + \)\(18\!\cdots\!08\)\( T + \)\(22\!\cdots\!37\)\( T^{2} + \)\(19\!\cdots\!80\)\( T^{3} + \)\(13\!\cdots\!57\)\( T^{4} + \)\(78\!\cdots\!96\)\( T^{5} + \)\(37\!\cdots\!29\)\( T^{6} + \)\(14\!\cdots\!40\)\( T^{7} + \)\(50\!\cdots\!83\)\( T^{8} + \)\(14\!\cdots\!84\)\( T^{9} + \)\(33\!\cdots\!31\)\( T^{10} + \)\(65\!\cdots\!80\)\( T^{11} + \)\(10\!\cdots\!59\)\( T^{12} + \)\(10\!\cdots\!12\)\( T^{13} + \)\(80\!\cdots\!03\)\( T^{14} \)
$71$ \( 1 + \)\(36\!\cdots\!56\)\( T + \)\(16\!\cdots\!81\)\( T^{2} + \)\(12\!\cdots\!96\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} + \)\(37\!\cdots\!48\)\( T^{5} + \)\(72\!\cdots\!13\)\( T^{6} + \)\(13\!\cdots\!88\)\( T^{7} + \)\(27\!\cdots\!83\)\( T^{8} + \)\(52\!\cdots\!88\)\( T^{9} + \)\(69\!\cdots\!51\)\( T^{10} + \)\(23\!\cdots\!56\)\( T^{11} + \)\(11\!\cdots\!31\)\( T^{12} + \)\(99\!\cdots\!96\)\( T^{13} + \)\(10\!\cdots\!31\)\( T^{14} \)
$73$ \( 1 - \)\(59\!\cdots\!26\)\( T + \)\(46\!\cdots\!23\)\( T^{2} - \)\(18\!\cdots\!20\)\( T^{3} + \)\(83\!\cdots\!37\)\( T^{4} - \)\(25\!\cdots\!02\)\( T^{5} + \)\(79\!\cdots\!91\)\( T^{6} - \)\(18\!\cdots\!60\)\( T^{7} + \)\(44\!\cdots\!23\)\( T^{8} - \)\(76\!\cdots\!18\)\( T^{9} + \)\(14\!\cdots\!49\)\( T^{10} - \)\(17\!\cdots\!20\)\( T^{11} + \)\(23\!\cdots\!39\)\( T^{12} - \)\(16\!\cdots\!54\)\( T^{13} + \)\(15\!\cdots\!37\)\( T^{14} \)
$79$ \( 1 - \)\(15\!\cdots\!80\)\( T + \)\(80\!\cdots\!13\)\( T^{2} - \)\(99\!\cdots\!20\)\( T^{3} + \)\(27\!\cdots\!01\)\( T^{4} - \)\(27\!\cdots\!00\)\( T^{5} + \)\(53\!\cdots\!65\)\( T^{6} - \)\(41\!\cdots\!00\)\( T^{7} + \)\(62\!\cdots\!35\)\( T^{8} - \)\(37\!\cdots\!00\)\( T^{9} + \)\(44\!\cdots\!79\)\( T^{10} - \)\(18\!\cdots\!20\)\( T^{11} + \)\(18\!\cdots\!87\)\( T^{12} - \)\(40\!\cdots\!80\)\( T^{13} + \)\(30\!\cdots\!19\)\( T^{14} \)
$83$ \( 1 + \)\(27\!\cdots\!84\)\( T + \)\(55\!\cdots\!33\)\( T^{2} + \)\(10\!\cdots\!40\)\( T^{3} + \)\(19\!\cdots\!17\)\( T^{4} + \)\(26\!\cdots\!08\)\( T^{5} + \)\(37\!\cdots\!81\)\( T^{6} + \)\(47\!\cdots\!20\)\( T^{7} + \)\(52\!\cdots\!63\)\( T^{8} + \)\(53\!\cdots\!32\)\( T^{9} + \)\(54\!\cdots\!39\)\( T^{10} + \)\(43\!\cdots\!40\)\( T^{11} + \)\(31\!\cdots\!19\)\( T^{12} + \)\(21\!\cdots\!76\)\( T^{13} + \)\(11\!\cdots\!47\)\( T^{14} \)
$89$ \( 1 - \)\(86\!\cdots\!90\)\( T + \)\(19\!\cdots\!03\)\( T^{2} - \)\(78\!\cdots\!60\)\( T^{3} + \)\(13\!\cdots\!61\)\( T^{4} - \)\(84\!\cdots\!50\)\( T^{5} + \)\(32\!\cdots\!15\)\( T^{6} - \)\(74\!\cdots\!00\)\( T^{7} + \)\(40\!\cdots\!35\)\( T^{8} - \)\(12\!\cdots\!50\)\( T^{9} + \)\(25\!\cdots\!29\)\( T^{10} - \)\(18\!\cdots\!60\)\( T^{11} + \)\(56\!\cdots\!47\)\( T^{12} - \)\(30\!\cdots\!90\)\( T^{13} + \)\(43\!\cdots\!09\)\( T^{14} \)
$97$ \( 1 + \)\(46\!\cdots\!58\)\( T + \)\(19\!\cdots\!27\)\( T^{2} + \)\(26\!\cdots\!20\)\( T^{3} + \)\(18\!\cdots\!37\)\( T^{4} + \)\(40\!\cdots\!06\)\( T^{5} + \)\(11\!\cdots\!79\)\( T^{6} + \)\(29\!\cdots\!60\)\( T^{7} + \)\(59\!\cdots\!23\)\( T^{8} + \)\(10\!\cdots\!14\)\( T^{9} + \)\(26\!\cdots\!61\)\( T^{10} + \)\(19\!\cdots\!20\)\( T^{11} + \)\(76\!\cdots\!39\)\( T^{12} + \)\(92\!\cdots\!22\)\( T^{13} + \)\(10\!\cdots\!33\)\( T^{14} \)
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