# Properties

 Label 605.2.s.b Level $605$ Weight $2$ Character orbit 605.s Analytic conductor $4.831$ Analytic rank $0$ Dimension $880$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$605 = 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 605.s (of order $$55$$, degree $$40$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.83094932229$$ Analytic rank: $$0$$ Dimension: $$880$$ Relative dimension: $$22$$ over $$\Q(\zeta_{55})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{55}]$

## $q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $$q$$-expansion, but we have computed the trace expansion.

 $$\operatorname{Tr}(f)(q) =$$ $$880q + 4q^{2} - q^{3} + 24q^{4} + 22q^{5} - 13q^{6} + 3q^{7} + 2q^{8} - 217q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$880q + 4q^{2} - q^{3} + 24q^{4} + 22q^{5} - 13q^{6} + 3q^{7} + 2q^{8} - 217q^{9} - 6q^{10} + 5q^{11} - 5q^{12} - 26q^{13} - 108q^{14} - 12q^{15} + 34q^{16} - q^{17} - 14q^{18} + q^{19} + 19q^{20} - 10q^{21} + 275q^{22} - 51q^{23} + 283q^{24} + 22q^{25} - 16q^{27} - 4q^{28} - 19q^{29} + q^{30} - 34q^{31} - 122q^{32} + 19q^{33} + 52q^{34} + 8q^{35} - 21q^{36} - 109q^{37} - 10q^{38} - 9q^{39} - 64q^{40} + 4q^{41} - 49q^{42} - 97q^{43} + 17q^{44} - 80q^{45} - 91q^{46} + 166q^{47} - 159q^{48} + 175q^{49} + 4q^{50} - 112q^{51} - 128q^{52} - 141q^{53} - 37q^{54} - 5q^{55} + 79q^{56} - 204q^{57} - 190q^{58} + 9q^{59} - 22q^{60} + 2q^{61} - 105q^{62} - q^{63} - 176q^{64} - 14q^{65} - 112q^{66} - 13q^{67} - 35q^{68} - 53q^{69} + 24q^{70} - 50q^{71} + 705q^{72} + q^{73} + 40q^{74} - q^{75} - 148q^{76} - 104q^{77} - 187q^{78} - 83q^{79} - q^{80} - 238q^{81} - 54q^{82} - 151q^{83} + 4q^{84} - 29q^{85} - 39q^{86} - 74q^{87} - 143q^{88} - 52q^{89} - 28q^{90} - 188q^{91} - 253q^{92} + 122q^{93} - 187q^{94} + 122q^{95} - 155q^{96} + 283q^{97} - 92q^{98} + 172q^{99} + O(q^{100})$$

## Embeddings

For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.

For more information on an embedded modular form you can click on its label.

Label $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
16.1 −2.61070 0.299550i −0.194849 0.141566i 4.77802 + 1.11108i −0.564443 + 0.825472i 0.466287 + 0.427954i 3.66250 + 3.76862i −7.19116 2.56580i −0.909126 2.79800i 1.72086 1.98598i
16.2 −2.40958 0.276474i −1.30445 0.947741i 3.78161 + 0.879377i −0.564443 + 0.825472i 2.88116 + 2.64430i −2.42714 2.49747i −4.30030 1.53434i −0.123665 0.380602i 1.58829 1.83299i
16.3 −2.03821 0.233862i 0.653999 + 0.475158i 2.15157 + 0.500325i −0.564443 + 0.825472i −1.22186 1.12142i −0.0770600 0.0792929i −0.403791 0.144072i −0.725112 2.23166i 1.34350 1.55048i
16.4 −1.80070 0.206611i −1.29126 0.938155i 1.25182 + 0.291098i −0.564443 + 0.825472i 2.13134 + 1.95613i −0.0685099 0.0704951i 1.22021 + 0.435369i −0.139834 0.430365i 1.18695 1.36981i
16.5 −1.72317 0.197715i −2.49016 1.80921i 0.982201 + 0.228401i −0.564443 + 0.825472i 3.93327 + 3.60992i −0.450743 0.463803i 1.61987 + 0.577969i 2.00063 + 6.15729i 1.13584 1.31083i
16.6 −1.56544 0.179618i 1.90128 + 1.38136i 0.470322 + 0.109369i −0.564443 + 0.825472i −2.72823 2.50395i −2.64879 2.72554i 2.25154 + 0.803346i 0.779664 + 2.39956i 1.03187 1.19084i
16.7 −1.42148 0.163100i 1.67703 + 1.21843i 0.0459846 + 0.0106933i −0.564443 + 0.825472i −2.18514 2.00550i 2.67320 + 2.75065i 2.63157 + 0.938944i 0.400791 + 1.23351i 0.936980 1.08133i
16.8 −0.756073 0.0867513i −0.251034 0.182387i −1.38390 0.321813i −0.564443 + 0.825472i 0.173978 + 0.159675i −2.99384 3.08059i 2.45196 + 0.874859i −0.897298 2.76160i 0.498371 0.575151i
16.9 −0.457329 0.0524736i −2.01066 1.46083i −1.74163 0.404998i −0.564443 + 0.825472i 0.842877 + 0.773585i 1.60972 + 1.65636i 1.64236 + 0.585993i 0.981676 + 3.02129i 0.301451 0.347893i
16.10 −0.325381 0.0373340i 1.10628 + 0.803759i −1.84355 0.428698i −0.564443 + 0.825472i −0.329954 0.302829i 0.602100 + 0.619546i 1.20079 + 0.428440i −0.349226 1.07481i 0.214477 0.247520i
16.11 0.00892359 + 0.00102389i −0.467498 0.339657i −1.94795 0.452975i −0.564443 + 0.825472i −0.00382399 0.00350963i 1.06012 + 1.09083i −0.0338384 0.0120735i −0.823864 2.53559i −0.00588205 + 0.00678825i
16.12 0.252480 + 0.0289694i 2.55133 + 1.85365i −1.88512 0.438365i −0.564443 + 0.825472i 0.590461 + 0.541921i −0.840226 0.864572i −0.941970 0.336094i 2.14622 + 6.60538i −0.166424 + 0.192064i
16.13 0.742152 + 0.0851540i 0.230756 + 0.167654i −1.40448 0.326599i −0.564443 + 0.825472i 0.156980 + 0.144075i 0.473372 + 0.487088i −2.42169 0.864056i −0.901911 2.77580i −0.489195 + 0.564561i
16.14 1.25197 + 0.143650i 0.302448 + 0.219741i −0.401226 0.0933012i −0.564443 + 0.825472i 0.347090 + 0.318557i −2.98838 3.07497i −2.86272 1.02142i −0.883862 2.72025i −0.825246 + 0.952385i
16.15 1.27289 + 0.146051i −1.27498 0.926331i −0.349093 0.0811782i −0.564443 + 0.825472i −1.48763 1.36533i 1.90619 + 1.96142i −2.84597 1.01544i −0.159553 0.491055i −0.839038 + 0.968301i
16.16 1.46553 + 0.168154i −2.14433 1.55794i 0.171477 + 0.0398753i −0.564443 + 0.825472i −2.88060 2.64379i 0.537054 + 0.552615i −2.53411 0.904170i 1.24390 + 3.82832i −0.966014 + 1.11484i
16.17 1.82551 + 0.209458i 2.66801 + 1.93842i 1.34058 + 0.311739i −0.564443 + 0.825472i 4.46445 + 4.09744i 0.0611421 + 0.0629137i −1.07930 0.385094i 2.43374 + 7.49028i −1.20330 + 1.38868i
16.18 2.04825 + 0.235014i 1.13699 + 0.826074i 2.19205 + 0.509740i −0.564443 + 0.825472i 2.13470 + 1.95921i 3.19973 + 3.29244i 0.486498 + 0.173582i −0.316695 0.974688i −1.35012 + 1.55812i
16.19 2.13889 + 0.245415i −1.59867 1.16150i 2.56661 + 0.596840i −0.564443 + 0.825472i −3.13432 2.87666i −2.87657 2.95992i 1.28779 + 0.459482i 0.279601 + 0.860523i −1.40987 + 1.62707i
16.20 2.28990 + 0.262741i 1.65951 + 1.20570i 3.22657 + 0.750306i −0.564443 + 0.825472i 3.48331 + 3.19696i −1.38442 1.42453i 2.84961 + 1.01674i 0.373196 + 1.14858i −1.50940 + 1.74194i
See next 80 embeddings (of 880 total)
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 586.22 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
121.g even 55 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 605.2.s.b 880
121.g even 55 1 inner 605.2.s.b 880

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
605.2.s.b 880 1.a even 1 1 trivial
605.2.s.b 880 121.g even 55 1 inner

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$23\!\cdots\!99$$$$T_{2}^{854} +$$$$62\!\cdots\!67$$$$T_{2}^{853} +$$$$34\!\cdots\!64$$$$T_{2}^{852} + 492665180714 T_{2}^{851} -$$$$23\!\cdots\!56$$$$T_{2}^{850} -$$$$68\!\cdots\!42$$$$T_{2}^{849} +$$$$11\!\cdots\!40$$$$T_{2}^{848} +$$$$81\!\cdots\!91$$$$T_{2}^{847} +$$$$60\!\cdots\!64$$$$T_{2}^{846} -$$$$55\!\cdots\!88$$$$T_{2}^{845} -$$$$94\!\cdots\!06$$$$T_{2}^{844} +$$$$22\!\cdots\!79$$$$T_{2}^{843} +$$$$11\!\cdots\!17$$$$T_{2}^{842} +$$$$61\!\cdots\!71$$$$T_{2}^{841} -$$$$93\!\cdots\!50$$$$T_{2}^{840} -$$$$19\!\cdots\!67$$$$T_{2}^{839} +$$$$47\!\cdots\!25$$$$T_{2}^{838} +$$$$17\!\cdots\!73$$$$T_{2}^{837} +$$$$14\!\cdots\!39$$$$T_{2}^{836} -$$$$12\!\cdots\!23$$$$T_{2}^{835} -$$$$27\!\cdots\!73$$$$T_{2}^{834} +$$$$65\!\cdots\!34$$$$T_{2}^{833} +$$$$26\!\cdots\!96$$$$T_{2}^{832} -$$$$80\!\cdots\!96$$$$T_{2}^{831} -$$$$16\!\cdots\!26$$$$T_{2}^{830} -$$$$27\!\cdots\!70$$$$T_{2}^{829} +$$$$69\!\cdots\!81$$$$T_{2}^{828} +$$$$30\!\cdots\!94$$$$T_{2}^{827} +$$$$18\!\cdots\!05$$$$T_{2}^{826} -$$$$21\!\cdots\!04$$$$T_{2}^{825} -$$$$34\!\cdots\!11$$$$T_{2}^{824} +$$$$11\!\cdots\!79$$$$T_{2}^{823} +$$$$32\!\cdots\!68$$$$T_{2}^{822} -$$$$22\!\cdots\!81$$$$T_{2}^{821} -$$$$21\!\cdots\!54$$$$T_{2}^{820} -$$$$34\!\cdots\!70$$$$T_{2}^{819} +$$$$12\!\cdots\!79$$$$T_{2}^{818} +$$$$44\!\cdots\!00$$$$T_{2}^{817} -$$$$51\!\cdots\!92$$$$T_{2}^{816} -$$$$35\!\cdots\!06$$$$T_{2}^{815} +$$$$39\!\cdots\!86$$$$T_{2}^{814} +$$$$21\!\cdots\!34$$$$T_{2}^{813} +$$$$20\!\cdots\!02$$$$T_{2}^{812} -$$$$52\!\cdots\!95$$$$T_{2}^{811} -$$$$36\!\cdots\!61$$$$T_{2}^{810} -$$$$47\!\cdots\!06$$$$T_{2}^{809} +$$$$36\!\cdots\!20$$$$T_{2}^{808} +$$$$76\!\cdots\!78$$$$T_{2}^{807} -$$$$21\!\cdots\!84$$$$T_{2}^{806} -$$$$83\!\cdots\!93$$$$T_{2}^{805} +$$$$56\!\cdots\!99$$$$T_{2}^{804} +$$$$70\!\cdots\!51$$$$T_{2}^{803} +$$$$33\!\cdots\!47$$$$T_{2}^{802} -$$$$33\!\cdots\!86$$$$T_{2}^{801} -$$$$82\!\cdots\!42$$$$T_{2}^{800} +$$$$16\!\cdots\!99$$$$T_{2}^{799} +$$$$92\!\cdots\!76$$$$T_{2}^{798} +$$$$11\!\cdots\!73$$$$T_{2}^{797} -$$$$63\!\cdots\!56$$$$T_{2}^{796} -$$$$13\!\cdots\!87$$$$T_{2}^{795} +$$$$22\!\cdots\!22$$$$T_{2}^{794} +$$$$10\!\cdots\!34$$$$T_{2}^{793} +$$$$60\!\cdots\!42$$$$T_{2}^{792} -$$$$52\!\cdots\!29$$$$T_{2}^{791} -$$$$18\!\cdots\!36$$$$T_{2}^{790} +$$$$15\!\cdots\!08$$$$T_{2}^{789} +$$$$17\!\cdots\!33$$$$T_{2}^{788} +$$$$56\!\cdots\!72$$$$T_{2}^{787} -$$$$10\!\cdots\!43$$$$T_{2}^{786} -$$$$76\!\cdots\!53$$$$T_{2}^{785} +$$$$34\!\cdots\!15$$$$T_{2}^{784} +$$$$78\!\cdots\!17$$$$T_{2}^{783} +$$$$17\!\cdots\!97$$$$T_{2}^{782} -$$$$42\!\cdots\!85$$$$T_{2}^{781} -$$$$12\!\cdots\!78$$$$T_{2}^{780} +$$$$20\!\cdots\!85$$$$T_{2}^{779} +$$$$12\!\cdots\!02$$$$T_{2}^{778} -$$$$12\!\cdots\!79$$$$T_{2}^{777} -$$$$60\!\cdots\!57$$$$T_{2}^{776} +$$$$42\!\cdots\!57$$$$T_{2}^{775} +$$$$15\!\cdots\!76$$$$T_{2}^{774} +$$$$21\!\cdots\!65$$$$T_{2}^{773} -$$$$32\!\cdots\!26$$$$T_{2}^{772} -$$$$32\!\cdots\!38$$$$T_{2}^{771} +$$$$25\!\cdots\!36$$$$T_{2}^{770} +$$$$28\!\cdots\!75$$$$T_{2}^{769} -$$$$26\!\cdots\!98$$$$T_{2}^{768} -$$$$19\!\cdots\!85$$$$T_{2}^{767} +$$$$23\!\cdots\!41$$$$T_{2}^{766} +$$$$53\!\cdots\!59$$$$T_{2}^{765} -$$$$10\!\cdots\!89$$$$T_{2}^{764} +$$$$28\!\cdots\!43$$$$T_{2}^{763} -$$$$21\!\cdots\!99$$$$T_{2}^{762} -$$$$35\!\cdots\!45$$$$T_{2}^{761} +$$$$45\!\cdots\!74$$$$T_{2}^{760} +$$$$21\!\cdots\!74$$$$T_{2}^{759} -$$$$99\!\cdots\!35$$$$T_{2}^{758} -$$$$42\!\cdots\!48$$$$T_{2}^{757} -$$$$18\!\cdots\!22$$$$T_{2}^{756} -$$$$98\!\cdots\!22$$$$T_{2}^{755} +$$$$29\!\cdots\!58$$$$T_{2}^{754} +$$$$96\!\cdots\!06$$$$T_{2}^{753} -$$$$19\!\cdots\!69$$$$T_{2}^{752} -$$$$25\!\cdots\!75$$$$T_{2}^{751} -$$$$34\!\cdots\!47$$$$T_{2}^{750} -$$$$13\!\cdots\!63$$$$T_{2}^{749} +$$$$17\!\cdots\!19$$$$T_{2}^{748} +$$$$20\!\cdots\!87$$$$T_{2}^{747} -$$$$15\!\cdots\!63$$$$T_{2}^{746} -$$$$18\!\cdots\!03$$$$T_{2}^{745} +$$$$80\!\cdots\!54$$$$T_{2}^{744} +$$$$10\!\cdots\!34$$$$T_{2}^{743} -$$$$13\!\cdots\!18$$$$T_{2}^{742} -$$$$34\!\cdots\!93$$$$T_{2}^{741} -$$$$21\!\cdots\!15$$$$T_{2}^{740} +$$$$15\!\cdots\!53$$$$T_{2}^{739} +$$$$26\!\cdots\!56$$$$T_{2}^{738} +$$$$82\!\cdots\!35$$$$T_{2}^{737} -$$$$16\!\cdots\!78$$$$T_{2}^{736} -$$$$10\!\cdots\!35$$$$T_{2}^{735} +$$$$47\!\cdots\!19$$$$T_{2}^{734} +$$$$60\!\cdots\!33$$$$T_{2}^{733} +$$$$17\!\cdots\!53$$$$T_{2}^{732} -$$$$24\!\cdots\!67$$$$T_{2}^{731} -$$$$36\!\cdots\!98$$$$T_{2}^{730} +$$$$18\!\cdots\!09$$$$T_{2}^{729} +$$$$25\!\cdots\!83$$$$T_{2}^{728} -$$$$14\!\cdots\!83$$$$T_{2}^{727} -$$$$76\!\cdots\!18$$$$T_{2}^{726} +$$$$48\!\cdots\!70$$$$T_{2}^{725} -$$$$21\!\cdots\!02$$$$T_{2}^{724} +$$$$35\!\cdots\!56$$$$T_{2}^{723} +$$$$42\!\cdots\!62$$$$T_{2}^{722} -$$$$13\!\cdots\!37$$$$T_{2}^{721} -$$$$31\!\cdots\!54$$$$T_{2}^{720} +$$$$13\!\cdots\!50$$$$T_{2}^{719} +$$$$12\!\cdots\!41$$$$T_{2}^{718} -$$$$84\!\cdots\!62$$$$T_{2}^{717} +$$$$61\!\cdots\!96$$$$T_{2}^{716} +$$$$23\!\cdots\!61$$$$T_{2}^{715} -$$$$45\!\cdots\!30$$$$T_{2}^{714} -$$$$25\!\cdots\!91$$$$T_{2}^{713} +$$$$37\!\cdots\!77$$$$T_{2}^{712} -$$$$32\!\cdots\!95$$$$T_{2}^{711} -$$$$18\!\cdots\!24$$$$T_{2}^{710} +$$$$43\!\cdots\!83$$$$T_{2}^{709} +$$$$25\!\cdots\!48$$$$T_{2}^{708} -$$$$77\!\cdots\!06$$$$T_{2}^{707} +$$$$41\!\cdots\!61$$$$T_{2}^{706} -$$$$29\!\cdots\!65$$$$T_{2}^{705} -$$$$40\!\cdots\!83$$$$T_{2}^{704} +$$$$25\!\cdots\!41$$$$T_{2}^{703} +$$$$20\!\cdots\!78$$$$T_{2}^{702} -$$$$80\!\cdots\!58$$$$T_{2}^{701} -$$$$58\!\cdots\!33$$$$T_{2}^{700} +$$$$35\!\cdots\!21$$$$T_{2}^{699} -$$$$11\!\cdots\!73$$$$T_{2}^{698} +$$$$17\!\cdots\!30$$$$T_{2}^{697} +$$$$30\!\cdots\!87$$$$T_{2}^{696} -$$$$22\!\cdots\!44$$$$T_{2}^{695} -$$$$21\!\cdots\!59$$$$T_{2}^{694} +$$$$15\!\cdots\!03$$$$T_{2}^{693} +$$$$87\!\cdots\!41$$$$T_{2}^{692} -$$$$59\!\cdots\!45$$$$T_{2}^{691} -$$$$14\!\cdots\!38$$$$T_{2}^{690} +$$$$17\!\cdots\!61$$$$T_{2}^{689} -$$$$13\!\cdots\!29$$$$T_{2}^{688} +$$$$33\!\cdots\!88$$$$T_{2}^{687} +$$$$14\!\cdots\!23$$$$T_{2}^{686} -$$$$56\!\cdots\!94$$$$T_{2}^{685} -$$$$70\!\cdots\!29$$$$T_{2}^{684} +$$$$14\!\cdots\!70$$$$T_{2}^{683} +$$$$16\!\cdots\!50$$$$T_{2}^{682} +$$$$16\!\cdots\!92$$$$T_{2}^{681} +$$$$83\!\cdots\!60$$$$T_{2}^{680} -$$$$90\!\cdots\!12$$$$T_{2}^{679} -$$$$50\!\cdots\!37$$$$T_{2}^{678} -$$$$48\!\cdots\!00$$$$T_{2}^{677} +$$$$42\!\cdots\!44$$$$T_{2}^{676} +$$$$16\!\cdots\!89$$$$T_{2}^{675} -$$$$14\!\cdots\!40$$$$T_{2}^{674} -$$$$20\!\cdots\!66$$$$T_{2}^{673} -$$$$23\!\cdots\!91$$$$T_{2}^{672} +$$$$21\!\cdots\!01$$$$T_{2}^{671} +$$$$49\!\cdots\!68$$$$T_{2}^{670} -$$$$11\!\cdots\!07$$$$T_{2}^{669} -$$$$31\!\cdots\!24$$$$T_{2}^{668} +$$$$36\!\cdots\!55$$$$T_{2}^{667} +$$$$14\!\cdots\!56$$$$T_{2}^{666} -$$$$39\!\cdots\!49$$$$T_{2}^{665} -$$$$28\!\cdots\!56$$$$T_{2}^{664} -$$$$55\!\cdots\!68$$$$T_{2}^{663} -$$$$18\!\cdots\!85$$$$T_{2}^{662} +$$$$56\!\cdots\!08$$$$T_{2}^{661} +$$$$20\!\cdots\!19$$$$T_{2}^{660} -$$$$18\!\cdots\!27$$$$T_{2}^{659} -$$$$14\!\cdots\!03$$$$T_{2}^{658} +$$$$49\!\cdots\!97$$$$T_{2}^{657} +$$$$88\!\cdots\!97$$$$T_{2}^{656} -$$$$96\!\cdots\!22$$$$T_{2}^{655} -$$$$33\!\cdots\!53$$$$T_{2}^{654} +$$$$17\!\cdots\!02$$$$T_{2}^{653} +$$$$33\!\cdots\!59$$$$T_{2}^{652} -$$$$79\!\cdots\!71$$$$T_{2}^{651} +$$$$28\!\cdots\!67$$$$T_{2}^{650} +$$$$68\!\cdots\!01$$$$T_{2}^{649} -$$$$26\!\cdots\!31$$$$T_{2}^{648} -$$$$65\!\cdots\!81$$$$T_{2}^{647} +$$$$20\!\cdots\!94$$$$T_{2}^{646} +$$$$31\!\cdots\!13$$$$T_{2}^{645} -$$$$10\!\cdots\!54$$$$T_{2}^{644} -$$$$60\!\cdots\!21$$$$T_{2}^{643} +$$$$30\!\cdots\!67$$$$T_{2}^{642} -$$$$15\!\cdots\!87$$$$T_{2}^{641} -$$$$35\!\cdots\!92$$$$T_{2}^{640} +$$$$29\!\cdots\!59$$$$T_{2}^{639} -$$$$25\!\cdots\!08$$$$T_{2}^{638} -$$$$24\!\cdots\!67$$$$T_{2}^{637} +$$$$32\!\cdots\!26$$$$T_{2}^{636} +$$$$11\!\cdots\!84$$$$T_{2}^{635} -$$$$16\!\cdots\!94$$$$T_{2}^{634} -$$$$43\!\cdots\!15$$$$T_{2}^{633} +$$$$41\!\cdots\!27$$$$T_{2}^{632} +$$$$16\!\cdots\!10$$$$T_{2}^{631} -$$$$10\!\cdots\!84$$$$T_{2}^{630} -$$$$32\!\cdots\!80$$$$T_{2}^{629} +$$$$43\!\cdots\!90$$$$T_{2}^{628} -$$$$21\!\cdots\!70$$$$T_{2}^{627} +$$$$19\!\cdots\!34$$$$T_{2}^{626} +$$$$17\!\cdots\!14$$$$T_{2}^{625} -$$$$22\!\cdots\!15$$$$T_{2}^{624} -$$$$66\!\cdots\!67$$$$T_{2}^{623} +$$$$32\!\cdots\!74$$$$T_{2}^{622} +$$$$35\!\cdots\!09$$$$T_{2}^{621} +$$$$71\!\cdots\!63$$$$T_{2}^{620} -$$$$21\!\cdots\!47$$$$T_{2}^{619} +$$$$10\!\cdots\!90$$$$T_{2}^{618} +$$$$66\!\cdots\!61$$$$T_{2}^{617} -$$$$75\!\cdots\!41$$$$T_{2}^{616} -$$$$80\!\cdots\!31$$$$T_{2}^{615} +$$$$58\!\cdots\!31$$$$T_{2}^{614} +$$$$43\!\cdots\!08$$$$T_{2}^{613} -$$$$86\!\cdots\!21$$$$T_{2}^{612} -$$$$37\!\cdots\!38$$$$T_{2}^{611} +$$$$59\!\cdots\!90$$$$T_{2}^{610} +$$$$99\!\cdots\!78$$$$T_{2}^{609} -$$$$27\!\cdots\!46$$$$T_{2}^{608} -$$$$88\!\cdots\!37$$$$T_{2}^{607} +$$$$51\!\cdots\!73$$$$T_{2}^{606} +$$$$15\!\cdots\!21$$$$T_{2}^{605} +$$$$22\!\cdots\!11$$$$T_{2}^{604} -$$$$13\!\cdots\!00$$$$T_{2}^{603} -$$$$23\!\cdots\!84$$$$T_{2}^{602} +$$$$37\!\cdots\!90$$$$T_{2}^{601} -$$$$21\!\cdots\!64$$$$T_{2}^{600} +$$$$50\!\cdots\!91$$$$T_{2}^{599} -$$$$28\!\cdots\!51$$$$T_{2}^{598} -$$$$71\!\cdots\!36$$$$T_{2}^{597} +$$$$27\!\cdots\!47$$$$T_{2}^{596} +$$$$24\!\cdots\!38$$$$T_{2}^{595} -$$$$12\!\cdots\!01$$$$T_{2}^{594} -$$$$88\!\cdots\!48$$$$T_{2}^{593} +$$$$35\!\cdots\!69$$$$T_{2}^{592} +$$$$66\!\cdots\!71$$$$T_{2}^{591} -$$$$15\!\cdots\!39$$$$T_{2}^{590} -$$$$33\!\cdots\!98$$$$T_{2}^{589} +$$$$85\!\cdots\!17$$$$T_{2}^{588} +$$$$61\!\cdots\!14$$$$T_{2}^{587} -$$$$23\!\cdots\!56$$$$T_{2}^{586} +$$$$17\!\cdots\!47$$$$T_{2}^{585} +$$$$14\!\cdots\!27$$$$T_{2}^{584} +$$$$60\!\cdots\!68$$$$T_{2}^{583} +$$$$13\!\cdots\!43$$$$T_{2}^{582} -$$$$65\!\cdots\!67$$$$T_{2}^{581} -$$$$30\!\cdots\!41$$$$T_{2}^{580} +$$$$23\!\cdots\!96$$$$T_{2}^{579} +$$$$12\!\cdots\!98$$$$T_{2}^{578} -$$$$69\!\cdots\!62$$$$T_{2}^{577} -$$$$73\!\cdots\!27$$$$T_{2}^{576} +$$$$27\!\cdots\!92$$$$T_{2}^{575} +$$$$44\!\cdots\!32$$$$T_{2}^{574} -$$$$86\!\cdots\!81$$$$T_{2}^{573} -$$$$27\!\cdots\!09$$$$T_{2}^{572} +$$$$11\!\cdots\!86$$$$T_{2}^{571} +$$$$12\!\cdots\!01$$$$T_{2}^{570} +$$$$28\!\cdots\!73$$$$T_{2}^{569} -$$$$50\!\cdots\!43$$$$T_{2}^{568} -$$$$47\!\cdots\!71$$$$T_{2}^{567} +$$$$25\!\cdots\!05$$$$T_{2}^{566} +$$$$33\!\cdots\!03$$$$T_{2}^{565} -$$$$96\!\cdots\!65$$$$T_{2}^{564} -$$$$14\!\cdots\!31$$$$T_{2}^{563} +$$$$20\!\cdots\!13$$$$T_{2}^{562} +$$$$68\!\cdots\!79$$$$T_{2}^{561} -$$$$65\!\cdots\!51$$$$T_{2}^{560} -$$$$33\!\cdots\!67$$$$T_{2}^{559} +$$$$44\!\cdots\!22$$$$T_{2}^{558} +$$$$83\!\cdots\!71$$$$T_{2}^{557} -$$$$17\!\cdots\!38$$$$T_{2}^{556} +$$$$16\!\cdots\!69$$$$T_{2}^{555} +$$$$24\!\cdots\!04$$$$T_{2}^{554} -$$$$20\!\cdots\!51$$$$T_{2}^{553} +$$$$16\!\cdots\!61$$$$T_{2}^{552} +$$$$76\!\cdots\!08$$$$T_{2}^{551} -$$$$18\!\cdots\!65$$$$T_{2}^{550} -$$$$16\!\cdots\!36$$$$T_{2}^{549} +$$$$90\!\cdots\!48$$$$T_{2}^{548} -$$$$55\!\cdots\!79$$$$T_{2}^{547} -$$$$25\!\cdots\!57$$$$T_{2}^{546} +$$$$28\!\cdots\!29$$$$T_{2}^{545} +$$$$59\!\cdots\!30$$$$T_{2}^{544} -$$$$13\!\cdots\!03$$$$T_{2}^{543} -$$$$14\!\cdots\!73$$$$T_{2}^{542} +$$$$36\!\cdots\!10$$$$T_{2}^{541} +$$$$61\!\cdots\!14$$$$T_{2}^{540} -$$$$93\!\cdots\!64$$$$T_{2}^{539} +$$$$70\!\cdots\!91$$$$T_{2}^{538} +$$$$26\!\cdots\!40$$$$T_{2}^{537} +$$$$65\!\cdots\!09$$$$T_{2}^{536} -$$$$28\!\cdots\!12$$$$T_{2}^{535} +$$$$38\!\cdots\!53$$$$T_{2}^{534} -$$$$35\!\cdots\!18$$$$T_{2}^{533} -$$$$12\!\cdots\!48$$$$T_{2}^{532} +$$$$45\!\cdots\!59$$$$T_{2}^{531} +$$$$61\!\cdots\!97$$$$T_{2}^{530} -$$$$86\!\cdots\!50$$$$T_{2}^{529} -$$$$16\!\cdots\!58$$$$T_{2}^{528} +$$$$58\!\cdots\!49$$$$T_{2}^{527} +$$$$35\!\cdots\!10$$$$T_{2}^{526} -$$$$18\!\cdots\!85$$$$T_{2}^{525} +$$$$30\!\cdots\!03$$$$T_{2}^{524} +$$$$30\!\cdots\!90$$$$T_{2}^{523} -$$$$64\!\cdots\!28$$$$T_{2}^{522} +$$$$20\!\cdots\!46$$$$T_{2}^{521} +$$$$14\!\cdots\!24$$$$T_{2}^{520} -$$$$48\!\cdots\!66$$$$T_{2}^{519} +$$$$33\!\cdots\!99$$$$T_{2}^{518} +$$$$22\!\cdots\!71$$$$T_{2}^{517} -$$$$28\!\cdots\!11$$$$T_{2}^{516} -$$$$46\!\cdots\!41$$$$T_{2}^{515} +$$$$12\!\cdots\!95$$$$T_{2}^{514} -$$$$35\!\cdots\!70$$$$T_{2}^{513} -$$$$35\!\cdots\!94$$$$T_{2}^{512} +$$$$62\!\cdots\!49$$$$T_{2}^{511} -$$$$10\!\cdots\!96$$$$T_{2}^{510} -$$$$25\!\cdots\!97$$$$T_{2}^{509} +$$$$49\!\cdots\!03$$$$T_{2}^{508} +$$$$48\!\cdots\!99$$$$T_{2}^{507} -$$$$21\!\cdots\!13$$$$T_{2}^{506} +$$$$78\!\cdots\!60$$$$T_{2}^{505} +$$$$64\!\cdots\!54$$$$T_{2}^{504} -$$$$83\!\cdots\!93$$$$T_{2}^{503} -$$$$13\!\cdots\!06$$$$T_{2}^{502} +$$$$31\!\cdots\!50$$$$T_{2}^{501} -$$$$36\!\cdots\!43$$$$T_{2}^{500} -$$$$77\!\cdots\!64$$$$T_{2}^{499} +$$$$11\!\cdots\!00$$$$T_{2}^{498} +$$$$28\!\cdots\!94$$$$T_{2}^{497} -$$$$38\!\cdots\!66$$$$T_{2}^{496} +$$$$87\!\cdots\!95$$$$T_{2}^{495} +$$$$69\!\cdots\!14$$$$T_{2}^{494} -$$$$49\!\cdots\!59$$$$T_{2}^{493} +$$$$67\!\cdots\!93$$$$T_{2}^{492} +$$$$16\!\cdots\!96$$$$T_{2}^{491} -$$$$10\!\cdots\!89$$$$T_{2}^{490} -$$$$35\!\cdots\!39$$$$T_{2}^{489} +$$$$33\!\cdots\!86$$$$T_{2}^{488} +$$$$30\!\cdots\!43$$$$T_{2}^{487} -$$$$92\!\cdots\!72$$$$T_{2}^{486} +$$$$14\!\cdots\!86$$$$T_{2}^{485} -$$$$34\!\cdots\!38$$$$T_{2}^{484} -$$$$88\!\cdots\!91$$$$T_{2}^{483} +$$$$22\!\cdots\!46$$$$T_{2}^{482} +$$$$27\!\cdots\!49$$$$T_{2}^{481} -$$$$86\!\cdots\!99$$$$T_{2}^{480} -$$$$53\!\cdots\!32$$$$T_{2}^{479} +$$$$21\!\cdots\!82$$$$T_{2}^{478} +$$$$34\!\cdots\!35$$$$T_{2}^{477} -$$$$23\!\cdots\!80$$$$T_{2}^{476} +$$$$17\!\cdots\!78$$$$T_{2}^{475} -$$$$68\!\cdots\!13$$$$T_{2}^{474} -$$$$63\!\cdots\!73$$$$T_{2}^{473} +$$$$54\!\cdots\!32$$$$T_{2}^{472} +$$$$48\!\cdots\!53$$$$T_{2}^{471} -$$$$21\!\cdots\!99$$$$T_{2}^{470} +$$$$47\!\cdots\!73$$$$T_{2}^{469} +$$$$58\!\cdots\!85$$$$T_{2}^{468} -$$$$25\!\cdots\!89$$$$T_{2}^{467} -$$$$12\!\cdots\!16$$$$T_{2}^{466} +$$$$66\!\cdots\!08$$$$T_{2}^{465} +$$$$15\!\cdots\!48$$$$T_{2}^{464} -$$$$52\!\cdots\!47$$$$T_{2}^{463} +$$$$63\!\cdots\!51$$$$T_{2}^{462} -$$$$38\!\cdots\!50$$$$T_{2}^{461} -$$$$99\!\cdots\!07$$$$T_{2}^{460} +$$$$22\!\cdots\!54$$$$T_{2}^{459} +$$$$27\!\cdots\!40$$$$T_{2}^{458} -$$$$70\!\cdots\!01$$$$T_{2}^{457} -$$$$41\!\cdots\!31$$$$T_{2}^{456} +$$$$14\!\cdots\!16$$$$T_{2}^{455} -$$$$64\!\cdots\!00$$$$T_{2}^{454} -$$$$94\!\cdots\!92$$$$T_{2}^{453} +$$$$30\!\cdots\!05$$$$T_{2}^{452} -$$$$65\!\cdots\!71$$$$T_{2}^{451} -$$$$11\!\cdots\!33$$$$T_{2}^{450} +$$$$34\!\cdots\!93$$$$T_{2}^{449} +$$$$23\!\cdots\!52$$$$T_{2}^{448} -$$$$98\!\cdots\!57$$$$T_{2}^{447} -$$$$27\!\cdots\!70$$$$T_{2}^{446} +$$$$17\!\cdots\!22$$$$T_{2}^{445} -$$$$33\!\cdots\!29$$$$T_{2}^{444} -$$$$11\!\cdots\!56$$$$T_{2}^{443} +$$$$30\!\cdots\!51$$$$T_{2}^{442} -$$$$51\!\cdots\!56$$$$T_{2}^{441} -$$$$90\!\cdots\!84$$$$T_{2}^{440} +$$$$23\!\cdots\!73$$$$T_{2}^{439} +$$$$16\!\cdots\!87$$$$T_{2}^{438} -$$$$50\!\cdots\!45$$$$T_{2}^{437} -$$$$28\!\cdots\!36$$$$T_{2}^{436} +$$$$53\!\cdots\!97$$$$T_{2}^{435} +$$$$45\!\cdots\!83$$$$T_{2}^{434} +$$$$82\!\cdots\!07$$$$T_{2}^{433} -$$$$39\!\cdots\!48$$$$T_{2}^{432} -$$$$60\!\cdots\!61$$$$T_{2}^{431} +$$$$36\!\cdots\!27$$$$T_{2}^{430} +$$$$15\!\cdots\!03$$$$T_{2}^{429} +$$$$32\!\cdots\!48$$$$T_{2}^{428} -$$$$18\!\cdots\!01$$$$T_{2}^{427} -$$$$15\!\cdots\!45$$$$T_{2}^{426} -$$$$21\!\cdots\!96$$$$T_{2}^{425} +$$$$73\!\cdots\!39$$$$T_{2}^{424} +$$$$17\!\cdots\!58$$$$T_{2}^{423} -$$$$21\!\cdots\!82$$$$T_{2}^{422} -$$$$53\!\cdots\!70$$$$T_{2}^{421} +$$$$54\!\cdots\!67$$$$T_{2}^{420} +$$$$10\!\cdots\!06$$$$T_{2}^{419} -$$$$89\!\cdots\!41$$$$T_{2}^{418} -$$$$14\!\cdots\!30$$$$T_{2}^{417} +$$$$73\!\cdots\!06$$$$T_{2}^{416} +$$$$16\!\cdots\!37$$$$T_{2}^{415} +$$$$31\!\cdots\!96$$$$T_{2}^{414} -$$$$24\!\cdots\!00$$$$T_{2}^{413} -$$$$81\!\cdots\!29$$$$T_{2}^{412} +$$$$89\!\cdots\!83$$$$T_{2}^{411} +$$$$13\!\cdots\!47$$$$T_{2}^{410} +$$$$11\!\cdots\!05$$$$T_{2}^{409} -$$$$14\!\cdots\!20$$$$T_{2}^{408} -$$$$55\!\cdots\!33$$$$T_{2}^{407} +$$$$56\!\cdots\!01$$$$T_{2}^{406} +$$$$21\!\cdots\!97$$$$T_{2}^{405} -$$$$79\!\cdots\!76$$$$T_{2}^{404} -$$$$51\!\cdots\!19$$$$T_{2}^{403} +$$$$45\!\cdots\!41$$$$T_{2}^{402} +$$$$49\!\cdots\!70$$$$T_{2}^{401} -$$$$97\!\cdots\!27$$$$T_{2}^{400} +$$$$73\!\cdots\!24$$$$T_{2}^{399} +$$$$95\!\cdots\!88$$$$T_{2}^{398} -$$$$39\!\cdots\!46$$$$T_{2}^{397} +$$$$57\!\cdots\!46$$$$T_{2}^{396} +$$$$89\!\cdots\!26$$$$T_{2}^{395} -$$$$77\!\cdots\!91$$$$T_{2}^{394} -$$$$59\!\cdots\!30$$$$T_{2}^{393} +$$$$24\!\cdots\!87$$$$T_{2}^{392} -$$$$37\!\cdots\!16$$$$T_{2}^{391} -$$$$42\!\cdots\!26$$$$T_{2}^{390} +$$$$14\!\cdots\!38$$$$T_{2}^{389} +$$$$80\!\cdots\!87$$$$T_{2}^{388} -$$$$26\!\cdots\!81$$$$T_{2}^{387} -$$$$27\!\cdots\!45$$$$T_{2}^{386} +$$$$21\!\cdots\!86$$$$T_{2}^{385} +$$$$73\!\cdots\!63$$$$T_{2}^{384} +$$$$79\!\cdots\!26$$$$T_{2}^{383} -$$$$13\!\cdots\!62$$$$T_{2}^{382} -$$$$45\!\cdots\!08$$$$T_{2}^{381} +$$$$13\!\cdots\!61$$$$T_{2}^{380} +$$$$12\!\cdots\!76$$$$T_{2}^{379} +$$$$33\!\cdots\!23$$$$T_{2}^{378} -$$$$20\!\cdots\!49$$$$T_{2}^{377} -$$$$23\!\cdots\!31$$$$T_{2}^{376} +$$$$21\!\cdots\!15$$$$T_{2}^{375} +$$$$65\!\cdots\!31$$$$T_{2}^{374} +$$$$21\!\cdots\!49$$$$T_{2}^{373} -$$$$12\!\cdots\!46$$$$T_{2}^{372} -$$$$16\!\cdots\!87$$$$T_{2}^{371} +$$$$14\!\cdots\!62$$$$T_{2}^{370} +$$$$44\!\cdots\!86$$$$T_{2}^{369} +$$$$75\!\cdots\!83$$$$T_{2}^{368} -$$$$74\!\cdots\!23$$$$T_{2}^{367} -$$$$62\!\cdots\!64$$$$T_{2}^{366} +$$$$86\!\cdots\!59$$$$T_{2}^{365} +$$$$17\!\cdots\!19$$$$T_{2}^{364} -$$$$81\!\cdots\!55$$$$T_{2}^{363} -$$$$29\!\cdots\!93$$$$T_{2}^{362} -$$$$25\!\cdots\!69$$$$T_{2}^{361} +$$$$37\!\cdots\!94$$$$T_{2}^{360} +$$$$67\!\cdots\!27$$$$T_{2}^{359} -$$$$18\!\cdots\!99$$$$T_{2}^{358} -$$$$11\!\cdots\!99$$$$T_{2}^{357} -$$$$53\!\cdots\!19$$$$T_{2}^{356} +$$$$13\!\cdots\!86$$$$T_{2}^{355} +$$$$16\!\cdots\!03$$$$T_{2}^{354} -$$$$87\!\cdots\!41$$$$T_{2}^{353} -$$$$29\!\cdots\!57$$$$T_{2}^{352} -$$$$79\!\cdots\!46$$$$T_{2}^{351} +$$$$45\!\cdots\!47$$$$T_{2}^{350} +$$$$25\!\cdots\!95$$$$T_{2}^{349} -$$$$44\!\cdots\!05$$$$T_{2}^{348} -$$$$55\!\cdots\!87$$$$T_{2}^{347} +$$$$24\!\cdots\!77$$$$T_{2}^{346} +$$$$12\!\cdots\!73$$$$T_{2}^{345} -$$$$17\!\cdots\!42$$$$T_{2}^{344} -$$$$16\!\cdots\!60$$$$T_{2}^{343} -$$$$73\!\cdots\!12$$$$T_{2}^{342} +$$$$18\!\cdots\!10$$$$T_{2}^{341} +$$$$34\!\cdots\!88$$$$T_{2}^{340} -$$$$27\!\cdots\!54$$$$T_{2}^{339} -$$$$56\!\cdots\!08$$$$T_{2}^{338} -$$$$95\!\cdots\!26$$$$T_{2}^{337} +$$$$76\!\cdots\!73$$$$T_{2}^{336} +$$$$89\!\cdots\!59$$$$T_{2}^{335} -$$$$94\!\cdots\!36$$$$T_{2}^{334} -$$$$15\!\cdots\!76$$$$T_{2}^{333} -$$$$37\!\cdots\!80$$$$T_{2}^{332} +$$$$23\!\cdots\!70$$$$T_{2}^{331} +$$$$29\!\cdots\!31$$$$T_{2}^{330} -$$$$23\!\cdots\!87$$$$T_{2}^{329} -$$$$42\!\cdots\!77$$$$T_{2}^{328} -$$$$28\!\cdots\!22$$$$T_{2}^{327} +$$$$62\!\cdots\!16$$$$T_{2}^{326} +$$$$91\!\cdots\!24$$$$T_{2}^{325} -$$$$46\!\cdots\!87$$$$T_{2}^{324} -$$$$93\!\cdots\!18$$$$T_{2}^{323} -$$$$12\!\cdots\!36$$$$T_{2}^{322} +$$$$13\!\cdots\!05$$$$T_{2}^{321} +$$$$27\!\cdots\!81$$$$T_{2}^{320} -$$$$82\!\cdots\!92$$$$T_{2}^{319} -$$$$21\!\cdots\!37$$$$T_{2}^{318} -$$$$39\!\cdots\!81$$$$T_{2}^{317} +$$$$31\!\cdots\!56$$$$T_{2}^{316} +$$$$69\!\cdots\!91$$$$T_{2}^{315} -$$$$23\!\cdots\!10$$$$T_{2}^{314} -$$$$39\!\cdots\!36$$$$T_{2}^{313} -$$$$82\!\cdots\!28$$$$T_{2}^{312} +$$$$53\!\cdots\!95$$$$T_{2}^{311} +$$$$14\!\cdots\!59$$$$T_{2}^{310} -$$$$51\!\cdots\!04$$$$T_{2}^{309} -$$$$69\!\cdots\!38$$$$T_{2}^{308} -$$$$15\!\cdots\!69$$$$T_{2}^{307} +$$$$98\!\cdots\!43$$$$T_{2}^{306} +$$$$27\!\cdots\!94$$$$T_{2}^{305} -$$$$12\!\cdots\!35$$$$T_{2}^{304} -$$$$12\!\cdots\!51$$$$T_{2}^{303} -$$$$20\!\cdots\!85$$$$T_{2}^{302} +$$$$10\!\cdots\!14$$$$T_{2}^{301} +$$$$46\!\cdots\!53$$$$T_{2}^{300} -$$$$18\!\cdots\!70$$$$T_{2}^{299} -$$$$19\!\cdots\!30$$$$T_{2}^{298} -$$$$25\!\cdots\!28$$$$T_{2}^{297} +$$$$47\!\cdots\!10$$$$T_{2}^{296} +$$$$68\!\cdots\!17$$$$T_{2}^{295} -$$$$22\!\cdots\!39$$$$T_{2}^{294} -$$$$14\!\cdots\!70$$$$T_{2}^{293} -$$$$31\!\cdots\!08$$$$T_{2}^{292} -$$$$23\!\cdots\!15$$$$T_{2}^{291} +$$$$84\!\cdots\!67$$$$T_{2}^{290} -$$$$34\!\cdots\!98$$$$T_{2}^{289} -$$$$13\!\cdots\!40$$$$T_{2}^{288} -$$$$34\!\cdots\!73$$$$T_{2}^{287} -$$$$57\!\cdots\!12$$$$T_{2}^{286} +$$$$10\!\cdots\!30$$$$T_{2}^{285} +$$$$19\!\cdots\!54$$$$T_{2}^{284} -$$$$91\!\cdots\!51$$$$T_{2}^{283} -$$$$57\!\cdots\!15$$$$T_{2}^{282} -$$$$14\!\cdots\!53$$$$T_{2}^{281} +$$$$13\!\cdots\!58$$$$T_{2}^{280} +$$$$96\!\cdots\!53$$$$T_{2}^{279} +$$$$61\!\cdots\!92$$$$T_{2}^{278} -$$$$53\!\cdots\!49$$$$T_{2}^{277} -$$$$23\!\cdots\!45$$$$T_{2}^{276} +$$$$50\!\cdots\!23$$$$T_{2}^{275} +$$$$66\!\cdots\!22$$$$T_{2}^{274} +$$$$49\!\cdots\!11$$$$T_{2}^{273} +$$$$71\!\cdots\!41$$$$T_{2}^{272} -$$$$14\!\cdots\!79$$$$T_{2}^{271} +$$$$11\!\cdots\!29$$$$T_{2}^{270} +$$$$65\!\cdots\!71$$$$T_{2}^{269} -$$$$12\!\cdots\!82$$$$T_{2}^{268} -$$$$76\!\cdots\!05$$$$T_{2}^{267} -$$$$23\!\cdots\!47$$$$T_{2}^{266} +$$$$22\!\cdots\!57$$$$T_{2}^{265} +$$$$31\!\cdots\!12$$$$T_{2}^{264} +$$$$29\!\cdots\!11$$$$T_{2}^{263} -$$$$70\!\cdots\!15$$$$T_{2}^{262} -$$$$37\!\cdots\!68$$$$T_{2}^{261} -$$$$13\!\cdots\!14$$$$T_{2}^{260} +$$$$24\!\cdots\!30$$$$T_{2}^{259} +$$$$13\!\cdots\!73$$$$T_{2}^{258} +$$$$17\!\cdots\!60$$$$T_{2}^{257} -$$$$12\!\cdots\!11$$$$T_{2}^{256} -$$$$19\!\cdots\!74$$$$T_{2}^{255} +$$$$43\!\cdots\!15$$$$T_{2}^{254} -$$$$40\!\cdots\!27$$$$T_{2}^{253} +$$$$11\!\cdots\!05$$$$T_{2}^{252} +$$$$25\!\cdots\!33$$$$T_{2}^{251} -$$$$59\!\cdots\!29$$$$T_{2}^{250} +$$$$45\!\cdots\!79$$$$T_{2}^{249} -$$$$61\!\cdots\!93$$$$T_{2}^{248} -$$$$99\!\cdots\!37$$$$T_{2}^{247} +$$$$85\!\cdots\!21$$$$T_{2}^{246} -$$$$48\!\cdots\!09$$$$T_{2}^{245} +$$$$13\!\cdots\!13$$$$T_{2}^{244} +$$$$33\!\cdots\!52$$$$T_{2}^{243} +$$$$14\!\cdots\!39$$$$T_{2}^{242} -$$$$99\!\cdots\!28$$$$T_{2}^{241} -$$$$23\!\cdots\!97$$$$T_{2}^{240} -$$$$57\!\cdots\!69$$$$T_{2}^{239} -$$$$69\!\cdots\!21$$$$T_{2}^{238} +$$$$32\!\cdots\!30$$$$T_{2}^{237} -$$$$38\!\cdots\!04$$$$T_{2}^{236} +$$$$24\!\cdots\!64$$$$T_{2}^{235} -$$$$11\!\cdots\!15$$$$T_{2}^{234} -$$$$52\!\cdots\!41$$$$T_{2}^{233} +$$$$41\!\cdots\!49$$$$T_{2}^{232} +$$$$99\!\cdots\!92$$$$T_{2}^{231} +$$$$35\!\cdots\!51$$$$T_{2}^{230} +$$$$87\!\cdots\!70$$$$T_{2}^{229} -$$$$21\!\cdots\!28$$$$T_{2}^{228} -$$$$11\!\cdots\!23$$$$T_{2}^{227} -$$$$10\!\cdots\!10$$$$T_{2}^{226} -$$$$63\!\cdots\!52$$$$T_{2}^{225} +$$$$13\!\cdots\!99$$$$T_{2}^{224} -$$$$11\!\cdots\!56$$$$T_{2}^{223} +$$$$17\!\cdots\!98$$$$T_{2}^{222} -$$$$22\!\cdots\!30$$$$T_{2}^{221} +$$$$18\!\cdots\!61$$$$T_{2}^{220} -$$$$12\!\cdots\!28$$$$T_{2}^{219} +$$$$45\!\cdots\!10$$$$T_{2}^{218} +$$$$15\!\cdots\!45$$$$T_{2}^{217} -$$$$26\!\cdots\!99$$$$T_{2}^{216} -$$$$10\!\cdots\!97$$$$T_{2}^{215} +$$$$20\!\cdots\!70$$$$T_{2}^{214} -$$$$25\!\cdots\!41$$$$T_{2}^{213} +$$$$27\!\cdots\!73$$$$T_{2}^{212} -$$$$25\!\cdots\!29$$$$T_{2}^{211} +$$$$17\!\cdots\!96$$$$T_{2}^{210} -$$$$79\!\cdots\!89$$$$T_{2}^{209} -$$$$46\!\cdots\!84$$$$T_{2}^{208} +$$$$14\!\cdots\!18$$$$T_{2}^{207} -$$$$14\!\cdots\!41$$$$T_{2}^{206} +$$$$67\!\cdots\!41$$$$T_{2}^{205} +$$$$64\!\cdots\!86$$$$T_{2}^{204} -$$$$37\!\cdots\!27$$$$T_{2}^{203} +$$$$42\!\cdots\!64$$$$T_{2}^{202} -$$$$27\!\cdots\!53$$$$T_{2}^{201} +$$$$10\!\cdots\!72$$$$T_{2}^{200} +$$$$13\!\cdots\!08$$$$T_{2}^{199} -$$$$80\!\cdots\!85$$$$T_{2}^{198} +$$$$77\!\cdots\!70$$$$T_{2}^{197} -$$$$10\!\cdots\!47$$$$T_{2}^{196} -$$$$51\!\cdots\!89$$$$T_{2}^{195} +$$$$65\!\cdots\!62$$$$T_{2}^{194} -$$$$43\!\cdots\!55$$$$T_{2}^{193} +$$$$12\!\cdots\!05$$$$T_{2}^{192} +$$$$79\!\cdots\!61$$$$T_{2}^{191} -$$$$12\!\cdots\!66$$$$T_{2}^{190} +$$$$73\!\cdots\!57$$$$T_{2}^{189} -$$$$32\!\cdots\!62$$$$T_{2}^{188} +$$$$22\!\cdots\!74$$$$T_{2}^{187} -$$$$17\!\cdots\!47$$$$T_{2}^{186} +$$$$72\!\cdots\!73$$$$T_{2}^{185} +$$$$27\!\cdots\!67$$$$T_{2}^{184} -$$$$87\!\cdots\!37$$$$T_{2}^{183} +$$$$10\!\cdots\!64$$$$T_{2}^{182} -$$$$92\!\cdots\!15$$$$T_{2}^{181} +$$$$82\!\cdots\!59$$$$T_{2}^{180} -$$$$62\!\cdots\!46$$$$T_{2}^{179} +$$$$24\!\cdots\!33$$$$T_{2}^{178} +$$$$11\!\cdots\!27$$$$T_{2}^{177} -$$$$22\!\cdots\!86$$$$T_{2}^{176} +$$$$13\!\cdots\!49$$$$T_{2}^{175} -$$$$22\!\cdots\!11$$$$T_{2}^{174} -$$$$23\!\cdots\!42$$$$T_{2}^{173} +$$$$17\!\cdots\!51$$$$T_{2}^{172} -$$$$59\!\cdots\!54$$$$T_{2}^{171} +$$$$40\!\cdots\!61$$$$T_{2}^{170} -$$$$47\!\cdots\!71$$$$T_{2}^{169} +$$$$49\!\cdots\!60$$$$T_{2}^{168} +$$$$49\!\cdots\!65$$$$T_{2}^{167} -$$$$61\!\cdots\!50$$$$T_{2}^{166} +$$$$37\!\cdots\!89$$$$T_{2}^{165} -$$$$11\!\cdots\!91$$$$T_{2}^{164} -$$$$18\!\cdots\!97$$$$T_{2}^{163} +$$$$79\!\cdots\!69$$$$T_{2}^{162} -$$$$12\!\cdots\!61$$$$T_{2}^{161} +$$$$13\!\cdots\!86$$$$T_{2}^{160} -$$$$96\!\cdots\!48$$$$T_{2}^{159} +$$$$35\!\cdots\!27$$$$T_{2}^{158} +$$$$12\!\cdots\!23$$$$T_{2}^{157} -$$$$28\!\cdots\!30$$$$T_{2}^{156} +$$$$22\!\cdots\!65$$$$T_{2}^{155} -$$$$12\!\cdots\!91$$$$T_{2}^{154} +$$$$42\!\cdots\!51$$$$T_{2}^{153} +$$$$13\!\cdots\!93$$$$T_{2}^{152} -$$$$19\!\cdots\!75$$$$T_{2}^{151} +$$$$18\!\cdots\!09$$$$T_{2}^{150} -$$$$99\!\cdots\!49$$$$T_{2}^{149} +$$$$24\!\cdots\!66$$$$T_{2}^{148} +$$$$37\!\cdots\!88$$$$T_{2}^{147} -$$$$50\!\cdots\!15$$$$T_{2}^{146} +$$$$37\!\cdots\!29$$$$T_{2}^{145} -$$$$44\!\cdots\!05$$$$T_{2}^{144} +$$$$35\!\cdots\!92$$$$T_{2}^{143} -$$$$90\!\cdots\!99$$$$T_{2}^{142} -$$$$93\!\cdots\!48$$$$T_{2}^{141} +$$$$98\!\cdots\!00$$$$T_{2}^{140} -$$$$25\!\cdots\!16$$$$T_{2}^{139} -$$$$20\!\cdots\!55$$$$T_{2}^{138} +$$$$20\!\cdots\!48$$$$T_{2}^{137} -$$$$40\!\cdots\!62$$$$T_{2}^{136} -$$$$46\!\cdots\!83$$$$T_{2}^{135} +$$$$40\!\cdots\!63$$$$T_{2}^{134} -$$$$65\!\cdots\!26$$$$T_{2}^{133} -$$$$96\!\cdots\!45$$$$T_{2}^{132} +$$$$73\!\cdots\!62$$$$T_{2}^{131} -$$$$82\!\cdots\!67$$$$T_{2}^{130} -$$$$18\!\cdots\!08$$$$T_{2}^{129} +$$$$11\!\cdots\!40$$$$T_{2}^{128} -$$$$64\!\cdots\!80$$$$T_{2}^{127} -$$$$29\!\cdots\!63$$$$T_{2}^{126} +$$$$15\!\cdots\!03$$$$T_{2}^{125} +$$$$75\!\cdots\!59$$$$T_{2}^{124} -$$$$38\!\cdots\!02$$$$T_{2}^{123} +$$$$12\!\cdots\!28$$$$T_{2}^{122} +$$$$36\!\cdots\!51$$$$T_{2}^{121} -$$$$39\!\cdots\!60$$$$T_{2}^{120} +$$$$46\!\cdots\!18$$$$T_{2}^{119} +$$$$69\!\cdots\!63$$$$T_{2}^{118} -$$$$30\!\cdots\!96$$$$T_{2}^{117} -$$$$57\!\cdots\!32$$$$T_{2}^{116} +$$$$81\!\cdots\!20$$$$T_{2}^{115} -$$$$12\!\cdots\!41$$$$T_{2}^{114} -$$$$13\!\cdots\!84$$$$T_{2}^{113} +$$$$66\!\cdots\!30$$$$T_{2}^{112} +$$$$68\!\cdots\!89$$$$T_{2}^{111} -$$$$15\!\cdots\!18$$$$T_{2}^{110} +$$$$33\!\cdots\!81$$$$T_{2}^{109} +$$$$20\!\cdots\!23$$$$T_{2}^{108} -$$$$13\!\cdots\!16$$$$T_{2}^{107} +$$$$85\!\cdots\!54$$$$T_{2}^{106} +$$$$21\!\cdots\!72$$$$T_{2}^{105} -$$$$92\!\cdots\!47$$$$T_{2}^{104} +$$$$17\!\cdots\!94$$$$T_{2}^{103} +$$$$11\!\cdots\!02$$$$T_{2}^{102} -$$$$40\!\cdots\!11$$$$T_{2}^{101} +$$$$48\!\cdots\!71$$$$T_{2}^{100} -$$$$38\!\cdots\!50$$$$T_{2}^{99} +$$$$68\!\cdots\!47$$$$T_{2}^{98} +$$$$64\!\cdots\!92$$$$T_{2}^{97} -$$$$61\!\cdots\!31$$$$T_{2}^{96} +$$$$18\!\cdots\!83$$$$T_{2}^{95} +$$$$46\!\cdots\!05$$$$T_{2}^{94} -$$$$63\!\cdots\!75$$$$T_{2}^{93} +$$$$22\!\cdots\!31$$$$T_{2}^{92} +$$$$24\!\cdots\!11$$$$T_{2}^{91} -$$$$34\!\cdots\!82$$$$T_{2}^{90} +$$$$14\!\cdots\!16$$$$T_{2}^{89} -$$$$12\!\cdots\!51$$$$T_{2}^{88} -$$$$12\!\cdots\!06$$$$T_{2}^{87} +$$$$68\!\cdots\!38$$$$T_{2}^{86} -$$$$12\!\cdots\!32$$$$T_{2}^{85} -$$$$24\!\cdots\!03$$$$T_{2}^{84} +$$$$23\!\cdots\!06$$$$T_{2}^{83} -$$$$62\!\cdots\!50$$$$T_{2}^{82} +$$$$12\!\cdots\!97$$$$T_{2}^{81} +$$$$55\!\cdots\!40$$$$T_{2}^{80} -$$$$18\!\cdots\!63$$$$T_{2}^{79} +$$$$10\!\cdots\!84$$$$T_{2}^{78} +$$$$11\!\cdots\!08$$$$T_{2}^{77} -$$$$37\!\cdots\!74$$$$T_{2}^{76} +$$$$10\!\cdots\!05$$$$T_{2}^{75} +$$$$25\!\cdots\!07$$$$T_{2}^{74} -$$$$67\!\cdots\!39$$$$T_{2}^{73} -$$$$33\!\cdots\!72$$$$T_{2}^{72} +$$$$59\!\cdots\!86$$$$T_{2}^{71} -$$$$12\!\cdots\!88$$$$T_{2}^{70} -$$$$11\!\cdots\!63$$$$T_{2}^{69} +$$$$11\!\cdots\!83$$$$T_{2}^{68} -$$$$22\!\cdots\!80$$$$T_{2}^{67} +$$$$52\!\cdots\!22$$$$T_{2}^{66} +$$$$37\!\cdots\!28$$$$T_{2}^{65} +$$$$12\!\cdots\!32$$$$T_{2}^{64} -$$$$10\!\cdots\!30$$$$T_{2}^{63} +$$$$28\!\cdots\!05$$$$T_{2}^{62} -$$$$41\!\cdots\!93$$$$T_{2}^{61} +$$$$31\!\cdots\!79$$$$T_{2}^{60} -$$$$59\!\cdots\!68$$$$T_{2}^{59} +$$$$32\!\cdots\!66$$$$T_{2}^{58} -$$$$10\!\cdots\!25$$$$T_{2}^{57} +$$$$20\!\cdots\!33$$$$T_{2}^{56} -$$$$29\!\cdots\!02$$$$T_{2}^{55} +$$$$33\!\cdots\!54$$$$T_{2}^{54} -$$$$31\!\cdots\!86$$$$T_{2}^{53} -$$$$19\!\cdots\!14$$$$T_{2}^{52} +$$$$21\!\cdots\!28$$$$T_{2}^{51} -$$$$54\!\cdots\!86$$$$T_{2}^{50} +$$$$56\!\cdots\!72$$$$T_{2}^{49} +$$$$68\!\cdots\!15$$$$T_{2}^{48} -$$$$37\!\cdots\!54$$$$T_{2}^{47} +$$$$68\!\cdots\!74$$$$T_{2}^{46} -$$$$52\!\cdots\!46$$$$T_{2}^{45} -$$$$28\!\cdots\!10$$$$T_{2}^{44} +$$$$86\!\cdots\!35$$$$T_{2}^{43} -$$$$31\!\cdots\!53$$$$T_{2}^{42} -$$$$10\!\cdots\!12$$$$T_{2}^{41} +$$$$72\!\cdots\!86$$$$T_{2}^{40} +$$$$50\!\cdots\!46$$$$T_{2}^{39} -$$$$16\!\cdots\!26$$$$T_{2}^{38} +$$$$22\!\cdots\!23$$$$T_{2}^{37} +$$$$15\!\cdots\!87$$$$T_{2}^{36} -$$$$97\!\cdots\!23$$$$T_{2}^{35} +$$$$17\!\cdots\!92$$$$T_{2}^{34} -$$$$23\!\cdots\!50$$$$T_{2}^{33} +$$$$13\!\cdots\!79$$$$T_{2}^{32} +$$$$15\!\cdots\!12$$$$T_{2}^{31} -$$$$40\!\cdots\!71$$$$T_{2}^{30} +$$$$62\!\cdots\!97$$$$T_{2}^{29} -$$$$54\!\cdots\!21$$$$T_{2}^{28} +$$$$10\!\cdots\!61$$$$T_{2}^{27} +$$$$54\!\cdots\!77$$$$T_{2}^{26} -$$$$12\!\cdots\!32$$$$T_{2}^{25} +$$$$18\!\cdots\!40$$$$T_{2}^{24} -$$$$21\!\cdots\!15$$$$T_{2}^{23} +$$$$21\!\cdots\!51$$$$T_{2}^{22} -$$$$17\!\cdots\!29$$$$T_{2}^{21} +$$$$14\!\cdots\!44$$$$T_{2}^{20} -$$$$82\!\cdots\!51$$$$T_{2}^{19} +$$$$49\!\cdots\!72$$$$T_{2}^{18} -$$$$21\!\cdots\!02$$$$T_{2}^{17} +$$$$92\!\cdots\!82$$$$T_{2}^{16} -$$$$24\!\cdots\!31$$$$T_{2}^{15} +$$$$39\!\cdots\!91$$$$T_{2}^{14} -$$$$70\!\cdots\!43$$$$T_{2}^{13} +$$$$10\!\cdots\!81$$$$T_{2}^{12} +$$$$12\!\cdots\!23$$$$T_{2}^{11} -$$$$59\!\cdots\!13$$$$T_{2}^{10} -$$$$95\!\cdots\!08$$$$T_{2}^{9} +$$$$66\!\cdots\!24$$$$T_{2}^{8} -$$$$11\!\cdots\!98$$$$T_{2}^{7} +$$$$89\!\cdots\!09$$$$T_{2}^{6} -$$$$36\!\cdots\!66$$$$T_{2}^{5} +$$$$23\!\cdots\!58$$$$T_{2}^{4} -$$$$22\!\cdots\!66$$$$T_{2}^{3} +$$$$82\!\cdots\!03$$$$T_{2}^{2} -$$$$34\!\cdots\!32$$$$T_{2} +$$$$43\!\cdots\!21$$">$$T_{2}^{880} - \cdots$$ acting on $$S_{2}^{\mathrm{new}}(605, [\chi])$$.