Properties

Label 1.92.a
Level 1
Weight 92
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: \( k \) \(=\) \( 92 \)
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 \(M_{92}(\Gamma_0(1))\).

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

Trace form

\( 7q + 3841716838056q^{2} + 6226865993447967511332q^{3} + 5671662926176418572725837376q^{4} + 23504964778584408375486754830930q^{5} + 451174906579592943363587112684473184q^{6} - 171085178649369081126501604564827872344q^{7} - 10385570201002723586914837423420014159360q^{8} + 38080901154162874719072934775718033448005459q^{9} + O(q^{10}) \) \( 7q + 3841716838056q^{2} + 6226865993447967511332q^{3} + 5671662926176418572725837376q^{4} + 23504964778584408375486754830930q^{5} + 451174906579592943363587112684473184q^{6} - 171085178649369081126501604564827872344q^{7} - 10385570201002723586914837423420014159360q^{8} + 38080901154162874719072934775718033448005459q^{9} + 4697789292978379445837627874024155681811061680q^{10} - 240582832892068760628122732280591830839146659316q^{11} + 15234465137330235186821811325942149339051634358016q^{12} + 712268684544237976989939315593627958143865337752122q^{13} + 17766212926078897376844163559794320416860400218986432q^{14} + 818092333276881407770547708857297926161740517153634360q^{15} - 5543121629719415776419174196841312964977690510556459008q^{16} - 116788563921119361626790446343979264424208809345044156194q^{17} + 2532221674884609223972217344567154578664327889292374599112q^{18} + 24914430965691713272160835064548829827762713320225549023860q^{19} + 213622308691313951002559876190359340784045827397766986247040q^{20} - 2997932825643989744485469587195205163128865044067155102498976q^{21} + 2770354076929612113872013355190927517116944942304065995485472q^{22} + 28060217473226028795108958325793316282935533444516172471797112q^{23} - 676645515624503740032420639044230674317241134651601877083678720q^{24} + 3263569264491109562693810546136813966434457662326151208223443025q^{25} + 14647231349517882504358224484901087010163561052132416579801164144q^{26} + 88534490857595263563477937784200716693877558838426769810977256360q^{27} - 1267961512722154560010156489449223630509765593702989988702255606272q^{28} - 1998207010601468906936357688217559269263973686319086789407593851510q^{29} + 46684773092381185628041557878825569520483461165868165669687502423360q^{30} - 59925208170796133190382607870079728441723654705660441096474565882976q^{31} - 349236116256080438032682462092197690284580228848172295706337753268224q^{32} + 48956964959741209887245659130472098420831296585540373363667238885584q^{33} + 4422724362741906584267050702673869603971959112955389299199109971390672q^{34} - 13368721150607890395306302586915792313883425318712829768566063087971920q^{35} + 48271193532350417136817688340793844028122089698778111115225583548795712q^{36} - 193385642725694230212647842547384176779300890377457537180445039472551694q^{37} + 648885030040198126856514202904430175712235671732708835862375911231617760q^{38} - 1888050736392299353100554804844814233146715239003942457135725287045138792q^{39} + 612437306889339293021693643280174203404468934648721750255585003111910400q^{40} + 27467963396808209903058935820529109024708043852794661490538346949004391894q^{41} + 2490746600045939910899268282231591851463383036227202908840686832900714752q^{42} - 305936680392367608196854535263961824203961856383604167638158912234512481108q^{43} + 205463536657254300042685770932278214832998693823974867822888457185152941312q^{44} + 4760687647415457141753353234910279174019798332678698076640623508070611166010q^{45} - 1366266407223913965782607380535324534407310537728351887747959292074575330496q^{46} + 6016385666666683617266527127107702489089132053603324831460234388201640236656q^{47} + 34119609737617524136090987754275812795178080643639536100065326182318914650112q^{48} + 147622366871958729066285529870014845360644877218444002326443275466876372382751q^{49} + 987686706148773430200902630527966650567454297252982416951455545242325575637400q^{50} + 742769239785716829162529676417470760468992847219971127251563531253033686474504q^{51} + 4318717132385281312358095915519383012120671308396466785048290702799702098686336q^{52} + 13308120064559469621843967381370895719631000840255977547855692839275328956239682q^{53} + 49855304363851366001446865238806860151072717129384273575810932439561849626548160q^{54} + 71294075726222567616681402637553088151526343199773263267028104308906720840973160q^{55} + 221193813355805774602587289215941353561793271848452643887988504737893638457815040q^{56} + 528504764627515846582196025944068103123296527378022647769732650016063847427593520q^{57} + 1238229446269131105368662021237658933365297194812595452448484778585094416520960240q^{58} + 1315161090691534242045211041321797641427216505845115765078938874240054573263728380q^{59} + 4823153254365391976824193526392851616116082049689724166967862952927612944155374080q^{60} + 5062201896875711919454365982321524134556244374094873318866473906778984033476168234q^{61} + 5944009317613068040880423794674923373270855087786172352031955991395153732464744192q^{62} - 3636043453736261219929075304472074905914693023981615502769720183430994506848383288q^{63} - 51461933507510968227229909173673546488880558907251327588128558485838721977163710464q^{64} - 77004978625744224526600511688707953799859895672813324064129546096894713766789516340q^{65} - 308541964188130582740963794759741868505184177678097911786772179394411954828298046592q^{66} - 375865111304983135837477510931607479316175718244865448118159181323617876690058988444q^{67} - 1534213067668968494728693973596412463295117507399423353249302546218581933051381708672q^{68} - 2173315533882618835358431426746324715455060324131802571545777868624263537306736200672q^{69} - 2678915571128698388724922631831368101885281292954514535801987008907571514431164929920q^{70} + 965663858399224787677892593054987300813257337626219343051035389437608903566853136104q^{71} + 4759225550598725097796726774244526164682601876181738961172151381039656425240893268480q^{72} + 9530120766269923537811918138494095655717782977571711295781136472585782479177982847862q^{73} + 19110889051618327071497328002063508382221976511726809975089825510120232325728977189552q^{74} + 125021668038726866132333086418803849235968631984043287433627055625310081344612351442300q^{75} + 201417481997189328603388340686282158978023686930352491852420967420198850453092214874880q^{76} + 203838117981454989170200594078013407199331583446926407393231313568448855161412400016672q^{77} + 348422592585817152583346169273764440235290509078131053609004533439300203952600764751424q^{78} - 5875385290546216656185911308903463222289330212802402962421344496345859662855253387760q^{79} - 704730665751803958915921202265388401277484106681191434954636540435925847481999762923520q^{80} - 645876221088024404019866830164659790161069128158743050337018784266949283332298558348353q^{81} - 5377119810649520829232661929626958820402325732939303335851648698643252753720266284836848q^{82} - 7188939673179725085045886441204184334512306517239973817301478804674514872311469770345548q^{83} - 17037797188065238374634346038194001797920522141104843305926325070074414892172026480416768q^{84} - 18949626274852488910142757348951127712395103983201418376580212098044613619651779587066620q^{85} - 13930550649009692825744367374854352346751992408208092118301786049776748630048877827166176q^{86} + 14997220283992832178383660427617039138145206474606482931148662045188858037160846958683480q^{87} + 35205946317573638735966560050796709996519491901124319190557129002743085716478822258247680q^{88} + 58910603928414585742462774445274283779895728554450265497847918725594089228346625287686470q^{89} + 596817611113547745433166439395807555701671900247626319346669516201533941956589878026043760q^{90} + 431556051755722691175733360455273666621786312136528121760420810812400911428233396155619184q^{91} + 649582018326251344367774515135408104477035917640264872918599325106081734967368208117408256q^{92} + 176140526645345381525949017432055243763067046580068760248910898954659817267839614775511424q^{93} + 528728237301347142597743478920778358077668394817645608650770473672424789094546213047704192q^{94} + 460150241832447303916160340674008161933312298406246509746195633852627501820464219531336600q^{95} - 5308520687978816513495454896751155260796827272022533467944875093089923121365143311537012736q^{96} - 7025964934206676021621272614488614108607978598995771668040441707563730547939229623877790994q^{97} - 20729666350145773779493369529709111649648862211758783582357755821769845548186544170995584792q^{98} - 23913014682919445875702212438204672119308558146529134638425833150071457007907375951005388292q^{99} + O(q^{100}) \)

Decomposition of \(S_{92}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.92.a.a \(7\) \(52.442\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(38\!\cdots\!56\) \(62\!\cdots\!32\) \(23\!\cdots\!30\) \(-1\!\cdots\!44\) \(+\) \(q+(548816691151+\beta _{1})q^{2}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 3841716838056 T + \)\(58\!\cdots\!48\)\( T^{2} - \)\(15\!\cdots\!00\)\( T^{3} + \)\(21\!\cdots\!12\)\( T^{4} + \)\(19\!\cdots\!28\)\( T^{5} + \)\(67\!\cdots\!76\)\( T^{6} + \)\(35\!\cdots\!00\)\( T^{7} + \)\(16\!\cdots\!48\)\( T^{8} + \)\(11\!\cdots\!12\)\( T^{9} + \)\(33\!\cdots\!04\)\( T^{10} - \)\(59\!\cdots\!00\)\( T^{11} + \)\(54\!\cdots\!64\)\( T^{12} - \)\(88\!\cdots\!84\)\( T^{13} + \)\(57\!\cdots\!72\)\( T^{14} \)
$3$ \( 1 - \)\(62\!\cdots\!32\)\( T + \)\(91\!\cdots\!97\)\( T^{2} - \)\(46\!\cdots\!00\)\( T^{3} + \)\(43\!\cdots\!77\)\( T^{4} - \)\(20\!\cdots\!64\)\( T^{5} + \)\(14\!\cdots\!69\)\( T^{6} - \)\(62\!\cdots\!00\)\( T^{7} + \)\(37\!\cdots\!43\)\( T^{8} - \)\(14\!\cdots\!76\)\( T^{9} + \)\(78\!\cdots\!71\)\( T^{10} - \)\(21\!\cdots\!00\)\( T^{11} + \)\(11\!\cdots\!79\)\( T^{12} - \)\(20\!\cdots\!28\)\( T^{13} + \)\(84\!\cdots\!63\)\( T^{14} \)
$5$ \( 1 - \)\(23\!\cdots\!30\)\( T + \)\(12\!\cdots\!75\)\( T^{2} - \)\(28\!\cdots\!00\)\( T^{3} + \)\(79\!\cdots\!25\)\( T^{4} - \)\(16\!\cdots\!50\)\( T^{5} + \)\(33\!\cdots\!75\)\( T^{6} - \)\(72\!\cdots\!00\)\( T^{7} + \)\(13\!\cdots\!75\)\( T^{8} - \)\(27\!\cdots\!50\)\( T^{9} + \)\(52\!\cdots\!25\)\( T^{10} - \)\(75\!\cdots\!00\)\( T^{11} + \)\(13\!\cdots\!75\)\( T^{12} - \)\(10\!\cdots\!50\)\( T^{13} + \)\(17\!\cdots\!25\)\( T^{14} \)
$7$ \( 1 + \)\(17\!\cdots\!44\)\( T + \)\(22\!\cdots\!93\)\( T^{2} + \)\(32\!\cdots\!00\)\( T^{3} + \)\(27\!\cdots\!97\)\( T^{4} + \)\(46\!\cdots\!68\)\( T^{5} + \)\(25\!\cdots\!21\)\( T^{6} + \)\(40\!\cdots\!00\)\( T^{7} + \)\(20\!\cdots\!03\)\( T^{8} + \)\(29\!\cdots\!32\)\( T^{9} + \)\(14\!\cdots\!79\)\( T^{10} + \)\(13\!\cdots\!00\)\( T^{11} + \)\(73\!\cdots\!99\)\( T^{12} + \)\(45\!\cdots\!56\)\( T^{13} + \)\(21\!\cdots\!07\)\( T^{14} \)
$11$ \( 1 + \)\(24\!\cdots\!16\)\( T + \)\(18\!\cdots\!01\)\( T^{2} + \)\(44\!\cdots\!76\)\( T^{3} + \)\(15\!\cdots\!21\)\( T^{4} + \)\(32\!\cdots\!48\)\( T^{5} + \)\(90\!\cdots\!93\)\( T^{6} + \)\(17\!\cdots\!48\)\( T^{7} + \)\(53\!\cdots\!23\)\( T^{8} + \)\(11\!\cdots\!08\)\( T^{9} + \)\(31\!\cdots\!51\)\( T^{10} + \)\(51\!\cdots\!16\)\( T^{11} + \)\(12\!\cdots\!51\)\( T^{12} + \)\(95\!\cdots\!76\)\( T^{13} + \)\(23\!\cdots\!71\)\( T^{14} \)
$13$ \( 1 - \)\(71\!\cdots\!22\)\( T + \)\(12\!\cdots\!87\)\( T^{2} - \)\(65\!\cdots\!00\)\( T^{3} + \)\(63\!\cdots\!57\)\( T^{4} - \)\(26\!\cdots\!54\)\( T^{5} + \)\(20\!\cdots\!59\)\( T^{6} - \)\(69\!\cdots\!00\)\( T^{7} + \)\(47\!\cdots\!83\)\( T^{8} - \)\(14\!\cdots\!26\)\( T^{9} + \)\(81\!\cdots\!21\)\( T^{10} - \)\(19\!\cdots\!00\)\( T^{11} + \)\(85\!\cdots\!59\)\( T^{12} - \)\(11\!\cdots\!98\)\( T^{13} + \)\(38\!\cdots\!33\)\( T^{14} \)
$17$ \( 1 + \)\(11\!\cdots\!94\)\( T + \)\(35\!\cdots\!83\)\( T^{2} + \)\(27\!\cdots\!00\)\( T^{3} + \)\(47\!\cdots\!17\)\( T^{4} + \)\(32\!\cdots\!98\)\( T^{5} + \)\(45\!\cdots\!11\)\( T^{6} + \)\(32\!\cdots\!00\)\( T^{7} + \)\(42\!\cdots\!63\)\( T^{8} + \)\(28\!\cdots\!22\)\( T^{9} + \)\(38\!\cdots\!29\)\( T^{10} + \)\(21\!\cdots\!00\)\( T^{11} + \)\(25\!\cdots\!19\)\( T^{12} + \)\(78\!\cdots\!86\)\( T^{13} + \)\(62\!\cdots\!77\)\( T^{14} \)
$19$ \( 1 - \)\(24\!\cdots\!60\)\( T + \)\(70\!\cdots\!33\)\( T^{2} - \)\(45\!\cdots\!40\)\( T^{3} + \)\(10\!\cdots\!81\)\( T^{4} - \)\(73\!\cdots\!00\)\( T^{5} + \)\(62\!\cdots\!65\)\( T^{6} - \)\(75\!\cdots\!00\)\( T^{7} + \)\(14\!\cdots\!35\)\( T^{8} - \)\(39\!\cdots\!00\)\( T^{9} + \)\(13\!\cdots\!79\)\( T^{10} - \)\(13\!\cdots\!40\)\( T^{11} + \)\(48\!\cdots\!67\)\( T^{12} - \)\(39\!\cdots\!60\)\( T^{13} + \)\(36\!\cdots\!39\)\( T^{14} \)
$23$ \( 1 - \)\(28\!\cdots\!12\)\( T + \)\(39\!\cdots\!77\)\( T^{2} - \)\(13\!\cdots\!00\)\( T^{3} + \)\(78\!\cdots\!37\)\( T^{4} - \)\(25\!\cdots\!44\)\( T^{5} + \)\(96\!\cdots\!49\)\( T^{6} - \)\(26\!\cdots\!00\)\( T^{7} + \)\(79\!\cdots\!23\)\( T^{8} - \)\(17\!\cdots\!76\)\( T^{9} + \)\(44\!\cdots\!71\)\( T^{10} - \)\(61\!\cdots\!00\)\( T^{11} + \)\(15\!\cdots\!39\)\( T^{12} - \)\(89\!\cdots\!68\)\( T^{13} + \)\(26\!\cdots\!03\)\( T^{14} \)
$29$ \( 1 + \)\(19\!\cdots\!10\)\( T + \)\(41\!\cdots\!03\)\( T^{2} + \)\(70\!\cdots\!40\)\( T^{3} + \)\(80\!\cdots\!61\)\( T^{4} + \)\(95\!\cdots\!50\)\( T^{5} + \)\(10\!\cdots\!15\)\( T^{6} + \)\(98\!\cdots\!00\)\( T^{7} + \)\(12\!\cdots\!35\)\( T^{8} + \)\(13\!\cdots\!50\)\( T^{9} + \)\(13\!\cdots\!29\)\( T^{10} + \)\(14\!\cdots\!40\)\( T^{11} + \)\(10\!\cdots\!47\)\( T^{12} + \)\(58\!\cdots\!10\)\( T^{13} + \)\(35\!\cdots\!09\)\( T^{14} \)
$31$ \( 1 + \)\(59\!\cdots\!76\)\( T + \)\(28\!\cdots\!21\)\( T^{2} + \)\(13\!\cdots\!56\)\( T^{3} + \)\(37\!\cdots\!61\)\( T^{4} + \)\(15\!\cdots\!48\)\( T^{5} + \)\(29\!\cdots\!73\)\( T^{6} + \)\(10\!\cdots\!08\)\( T^{7} + \)\(15\!\cdots\!63\)\( T^{8} + \)\(41\!\cdots\!28\)\( T^{9} + \)\(51\!\cdots\!51\)\( T^{10} + \)\(98\!\cdots\!76\)\( T^{11} + \)\(10\!\cdots\!71\)\( T^{12} + \)\(11\!\cdots\!56\)\( T^{13} + \)\(99\!\cdots\!11\)\( T^{14} \)
$37$ \( 1 + \)\(19\!\cdots\!94\)\( T + \)\(77\!\cdots\!63\)\( T^{2} + \)\(25\!\cdots\!00\)\( T^{3} + \)\(48\!\cdots\!57\)\( T^{4} + \)\(54\!\cdots\!58\)\( T^{5} + \)\(15\!\cdots\!91\)\( T^{6} - \)\(40\!\cdots\!00\)\( T^{7} + \)\(77\!\cdots\!83\)\( T^{8} + \)\(14\!\cdots\!02\)\( T^{9} + \)\(63\!\cdots\!29\)\( T^{10} + \)\(16\!\cdots\!00\)\( T^{11} + \)\(26\!\cdots\!59\)\( T^{12} + \)\(33\!\cdots\!46\)\( T^{13} + \)\(88\!\cdots\!17\)\( T^{14} \)
$41$ \( 1 - \)\(27\!\cdots\!94\)\( T + \)\(33\!\cdots\!31\)\( T^{2} - \)\(78\!\cdots\!04\)\( T^{3} + \)\(50\!\cdots\!81\)\( T^{4} - \)\(10\!\cdots\!02\)\( T^{5} + \)\(45\!\cdots\!63\)\( T^{6} - \)\(74\!\cdots\!12\)\( T^{7} + \)\(26\!\cdots\!83\)\( T^{8} - \)\(33\!\cdots\!62\)\( T^{9} + \)\(97\!\cdots\!01\)\( T^{10} - \)\(89\!\cdots\!44\)\( T^{11} + \)\(21\!\cdots\!31\)\( T^{12} - \)\(10\!\cdots\!54\)\( T^{13} + \)\(22\!\cdots\!81\)\( T^{14} \)
$43$ \( 1 + \)\(30\!\cdots\!08\)\( T + \)\(19\!\cdots\!57\)\( T^{2} + \)\(39\!\cdots\!00\)\( T^{3} + \)\(16\!\cdots\!97\)\( T^{4} + \)\(26\!\cdots\!76\)\( T^{5} + \)\(92\!\cdots\!29\)\( T^{6} + \)\(12\!\cdots\!00\)\( T^{7} + \)\(40\!\cdots\!03\)\( T^{8} + \)\(51\!\cdots\!24\)\( T^{9} + \)\(14\!\cdots\!71\)\( T^{10} + \)\(15\!\cdots\!00\)\( T^{11} + \)\(32\!\cdots\!99\)\( T^{12} + \)\(22\!\cdots\!92\)\( T^{13} + \)\(33\!\cdots\!43\)\( T^{14} \)
$47$ \( 1 - \)\(60\!\cdots\!56\)\( T + \)\(61\!\cdots\!53\)\( T^{2} - \)\(38\!\cdots\!00\)\( T^{3} + \)\(20\!\cdots\!77\)\( T^{4} - \)\(11\!\cdots\!12\)\( T^{5} + \)\(41\!\cdots\!81\)\( T^{6} - \)\(21\!\cdots\!00\)\( T^{7} + \)\(60\!\cdots\!43\)\( T^{8} - \)\(24\!\cdots\!08\)\( T^{9} + \)\(60\!\cdots\!79\)\( T^{10} - \)\(17\!\cdots\!00\)\( T^{11} + \)\(39\!\cdots\!79\)\( T^{12} - \)\(55\!\cdots\!24\)\( T^{13} + \)\(13\!\cdots\!87\)\( T^{14} \)
$53$ \( 1 - \)\(13\!\cdots\!82\)\( T + \)\(12\!\cdots\!47\)\( T^{2} - \)\(79\!\cdots\!00\)\( T^{3} + \)\(41\!\cdots\!77\)\( T^{4} - \)\(17\!\cdots\!14\)\( T^{5} + \)\(64\!\cdots\!19\)\( T^{6} - \)\(19\!\cdots\!00\)\( T^{7} + \)\(52\!\cdots\!43\)\( T^{8} - \)\(11\!\cdots\!26\)\( T^{9} + \)\(22\!\cdots\!21\)\( T^{10} - \)\(34\!\cdots\!00\)\( T^{11} + \)\(43\!\cdots\!79\)\( T^{12} - \)\(37\!\cdots\!78\)\( T^{13} + \)\(23\!\cdots\!13\)\( T^{14} \)
$59$ \( 1 - \)\(13\!\cdots\!80\)\( T + \)\(13\!\cdots\!13\)\( T^{2} - \)\(93\!\cdots\!20\)\( T^{3} + \)\(58\!\cdots\!01\)\( T^{4} - \)\(29\!\cdots\!00\)\( T^{5} + \)\(13\!\cdots\!65\)\( T^{6} - \)\(54\!\cdots\!00\)\( T^{7} + \)\(19\!\cdots\!35\)\( T^{8} - \)\(59\!\cdots\!00\)\( T^{9} + \)\(16\!\cdots\!79\)\( T^{10} - \)\(36\!\cdots\!20\)\( T^{11} + \)\(71\!\cdots\!87\)\( T^{12} - \)\(10\!\cdots\!80\)\( T^{13} + \)\(10\!\cdots\!19\)\( T^{14} \)
$61$ \( 1 - \)\(50\!\cdots\!34\)\( T + \)\(22\!\cdots\!51\)\( T^{2} - \)\(73\!\cdots\!24\)\( T^{3} + \)\(20\!\cdots\!21\)\( T^{4} - \)\(48\!\cdots\!02\)\( T^{5} + \)\(10\!\cdots\!43\)\( T^{6} - \)\(18\!\cdots\!52\)\( T^{7} + \)\(29\!\cdots\!23\)\( T^{8} - \)\(41\!\cdots\!42\)\( T^{9} + \)\(51\!\cdots\!01\)\( T^{10} - \)\(53\!\cdots\!84\)\( T^{11} + \)\(48\!\cdots\!51\)\( T^{12} - \)\(31\!\cdots\!74\)\( T^{13} + \)\(17\!\cdots\!21\)\( T^{14} \)
$67$ \( 1 + \)\(37\!\cdots\!44\)\( T + \)\(11\!\cdots\!33\)\( T^{2} + \)\(25\!\cdots\!00\)\( T^{3} + \)\(47\!\cdots\!17\)\( T^{4} + \)\(77\!\cdots\!48\)\( T^{5} + \)\(11\!\cdots\!61\)\( T^{6} + \)\(14\!\cdots\!00\)\( T^{7} + \)\(17\!\cdots\!63\)\( T^{8} + \)\(17\!\cdots\!72\)\( T^{9} + \)\(15\!\cdots\!79\)\( T^{10} + \)\(12\!\cdots\!00\)\( T^{11} + \)\(83\!\cdots\!19\)\( T^{12} + \)\(40\!\cdots\!36\)\( T^{13} + \)\(16\!\cdots\!27\)\( T^{14} \)
$71$ \( 1 - \)\(96\!\cdots\!04\)\( T + \)\(10\!\cdots\!61\)\( T^{2} + \)\(86\!\cdots\!16\)\( T^{3} + \)\(31\!\cdots\!41\)\( T^{4} + \)\(69\!\cdots\!48\)\( T^{5} + \)\(80\!\cdots\!33\)\( T^{6} + \)\(35\!\cdots\!28\)\( T^{7} + \)\(23\!\cdots\!43\)\( T^{8} + \)\(58\!\cdots\!68\)\( T^{9} + \)\(78\!\cdots\!51\)\( T^{10} + \)\(62\!\cdots\!96\)\( T^{11} + \)\(21\!\cdots\!11\)\( T^{12} - \)\(59\!\cdots\!84\)\( T^{13} + \)\(17\!\cdots\!91\)\( T^{14} \)
$73$ \( 1 - \)\(95\!\cdots\!62\)\( T + \)\(17\!\cdots\!27\)\( T^{2} - \)\(11\!\cdots\!00\)\( T^{3} + \)\(12\!\cdots\!37\)\( T^{4} - \)\(73\!\cdots\!94\)\( T^{5} + \)\(64\!\cdots\!99\)\( T^{6} - \)\(32\!\cdots\!00\)\( T^{7} + \)\(23\!\cdots\!23\)\( T^{8} - \)\(98\!\cdots\!26\)\( T^{9} + \)\(62\!\cdots\!21\)\( T^{10} - \)\(20\!\cdots\!00\)\( T^{11} + \)\(11\!\cdots\!39\)\( T^{12} - \)\(22\!\cdots\!18\)\( T^{13} + \)\(86\!\cdots\!53\)\( T^{14} \)
$79$ \( 1 + \)\(58\!\cdots\!60\)\( T + \)\(17\!\cdots\!53\)\( T^{2} + \)\(78\!\cdots\!40\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} + \)\(14\!\cdots\!00\)\( T^{5} + \)\(80\!\cdots\!65\)\( T^{6} + \)\(10\!\cdots\!00\)\( T^{7} + \)\(38\!\cdots\!35\)\( T^{8} + \)\(33\!\cdots\!00\)\( T^{9} + \)\(16\!\cdots\!79\)\( T^{10} + \)\(42\!\cdots\!40\)\( T^{11} + \)\(46\!\cdots\!47\)\( T^{12} + \)\(74\!\cdots\!60\)\( T^{13} + \)\(61\!\cdots\!59\)\( T^{14} \)
$83$ \( 1 + \)\(71\!\cdots\!48\)\( T + \)\(41\!\cdots\!17\)\( T^{2} + \)\(16\!\cdots\!00\)\( T^{3} + \)\(58\!\cdots\!17\)\( T^{4} + \)\(16\!\cdots\!16\)\( T^{5} + \)\(43\!\cdots\!89\)\( T^{6} + \)\(95\!\cdots\!00\)\( T^{7} + \)\(18\!\cdots\!63\)\( T^{8} + \)\(31\!\cdots\!24\)\( T^{9} + \)\(47\!\cdots\!71\)\( T^{10} + \)\(58\!\cdots\!00\)\( T^{11} + \)\(62\!\cdots\!19\)\( T^{12} + \)\(47\!\cdots\!12\)\( T^{13} + \)\(28\!\cdots\!23\)\( T^{14} \)
$89$ \( 1 - \)\(58\!\cdots\!70\)\( T + \)\(99\!\cdots\!23\)\( T^{2} - \)\(33\!\cdots\!80\)\( T^{3} + \)\(43\!\cdots\!41\)\( T^{4} - \)\(10\!\cdots\!50\)\( T^{5} + \)\(14\!\cdots\!15\)\( T^{6} - \)\(32\!\cdots\!00\)\( T^{7} + \)\(35\!\cdots\!35\)\( T^{8} - \)\(67\!\cdots\!50\)\( T^{9} + \)\(65\!\cdots\!29\)\( T^{10} - \)\(12\!\cdots\!80\)\( T^{11} + \)\(93\!\cdots\!27\)\( T^{12} - \)\(13\!\cdots\!70\)\( T^{13} + \)\(57\!\cdots\!29\)\( T^{14} \)
$97$ \( 1 + \)\(70\!\cdots\!94\)\( T + \)\(54\!\cdots\!03\)\( T^{2} + \)\(25\!\cdots\!00\)\( T^{3} + \)\(11\!\cdots\!77\)\( T^{4} + \)\(37\!\cdots\!38\)\( T^{5} + \)\(12\!\cdots\!31\)\( T^{6} + \)\(31\!\cdots\!00\)\( T^{7} + \)\(76\!\cdots\!43\)\( T^{8} + \)\(14\!\cdots\!42\)\( T^{9} + \)\(27\!\cdots\!29\)\( T^{10} + \)\(38\!\cdots\!00\)\( T^{11} + \)\(52\!\cdots\!79\)\( T^{12} + \)\(42\!\cdots\!26\)\( T^{13} + \)\(37\!\cdots\!37\)\( T^{14} \)
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