Properties

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

Related objects

Downloads

Learn more about

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.

\(\operatorname{Tr}(f)(q) = \) \( 880q + 2q^{2} + 5q^{3} + 24q^{4} - 22q^{5} + 7q^{6} + q^{7} - 4q^{8} - 217q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 880q + 2q^{2} + 5q^{3} + 24q^{4} - 22q^{5} + 7q^{6} + q^{7} - 4q^{8} - 217q^{9} - 2q^{10} - 3q^{11} - 49q^{12} + 2q^{13} + 60q^{14} - 16q^{15} + 18q^{16} + 13q^{17} - 15q^{19} - 19q^{20} + 42q^{21} - 301q^{22} + 31q^{23} - 409q^{24} + 22q^{25} - 4q^{26} - 4q^{27} + 6q^{28} + 9q^{29} + 19q^{30} - 10q^{31} + 94q^{32} - 5q^{33} + 12q^{34} + 4q^{35} + 35q^{36} + 73q^{37} - 8q^{38} - 21q^{39} + 4q^{40} - 8q^{41} - 17q^{42} + 93q^{43} + q^{44} + 80q^{45} + 129q^{46} - 178q^{47} + 153q^{48} - 177q^{49} + 2q^{50} - 12q^{51} - 126q^{52} - 99q^{53} - 93q^{54} - 7q^{55} - 25q^{56} + 100q^{57} - 26q^{58} + 25q^{59} - 4q^{60} - 6q^{61} + 63q^{62} - 25q^{63} + 8q^{64} - 2q^{65} + 64q^{66} + 47q^{67} - 11q^{68} + 67q^{69} - 60q^{70} + 18q^{71} - 641q^{72} - 35q^{73} - 108q^{74} - 5q^{75} - 132q^{76} - 166q^{77} + 115q^{78} - 103q^{79} - 23q^{80} - 230q^{81} - 72q^{82} + 149q^{83} - 28q^{84} - 21q^{85} + 49q^{86} + 6q^{87} - 85q^{88} + 44q^{89} - 34q^{90} - 135q^{92} - 172q^{93} + 49q^{94} - 106q^{95} - 115q^{96} - 421q^{97} - 192q^{98} - 156q^{99} + O(q^{100}) \)

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 −2.64787 0.303815i 1.98682 + 1.44351i 4.97089 + 1.15593i 0.564443 0.825472i −4.82227 4.42584i 0.0313353 + 0.0322433i −7.79061 2.77968i 0.936675 + 2.88279i −1.74536 + 2.01426i
16.2 −2.40732 0.276215i −0.917619 0.666690i 3.77088 + 0.876881i 0.564443 0.825472i 2.02486 + 1.85840i 0.271254 + 0.279114i −4.27113 1.52393i −0.529500 1.62963i −1.58680 + 1.83127i
16.3 −2.25925 0.259225i 0.692604 + 0.503206i 3.08898 + 0.718312i 0.564443 0.825472i −1.43432 1.31641i −1.93384 1.98987i −2.50894 0.895186i −0.700567 2.15612i −1.48920 + 1.71863i
16.4 −2.03514 0.233510i 2.04797 + 1.48794i 2.13922 + 0.497455i 0.564443 0.825472i −3.82045 3.50637i 2.83652 + 2.91871i −0.378738 0.135133i 1.05317 + 3.24133i −1.34147 + 1.54814i
16.5 −1.96587 0.225563i −1.14488 0.831801i 1.86575 + 0.433862i 0.564443 0.825472i 2.06306 + 1.89346i 2.64315 + 2.71973i 0.157420 + 0.0561672i −0.308203 0.948551i −1.29582 + 1.49546i
16.6 −1.41473 0.162326i −2.46787 1.79301i 0.0270973 + 0.00630121i 0.564443 0.825472i 3.20032 + 2.93723i −2.76991 2.85017i 2.64509 + 0.943766i 1.94843 + 5.99666i −0.932532 + 1.07620i
16.7 −1.18251 0.135680i 0.544716 + 0.395759i −0.568105 0.132107i 0.564443 0.825472i −0.590435 0.541896i 2.13190 + 2.19368i 2.89596 + 1.03328i −0.786961 2.42202i −0.779459 + 0.899544i
16.8 −1.07976 0.123891i 0.718084 + 0.521719i −0.797485 0.185447i 0.564443 0.825472i −0.710724 0.652297i −0.657495 0.676547i 2.88540 + 1.02951i −0.683596 2.10389i −0.711734 + 0.821384i
16.9 −0.949888 0.108989i −1.30238 0.946237i −1.05762 0.245938i 0.564443 0.825472i 1.13399 + 1.04077i −0.316454 0.325624i 2.77884 + 0.991490i −0.126212 0.388441i −0.626126 + 0.722587i
16.10 0.144844 + 0.0166193i −2.68544 1.95109i −1.92732 0.448179i 0.564443 0.825472i −0.356545 0.327234i 2.53859 + 2.61215i −0.546344 0.194935i 2.47780 + 7.62590i 0.0954751 0.110184i
16.11 0.217809 + 0.0249913i 1.53233 + 1.11330i −1.90121 0.442107i 0.564443 0.825472i 0.305933 + 0.280782i −1.17803 1.21217i −0.816028 0.291158i 0.181542 + 0.558728i 0.143570 0.165689i
16.12 0.229050 + 0.0262811i −1.48776 1.08092i −1.89625 0.440954i 0.564443 0.825472i −0.312365 0.286686i −1.06136 1.09211i −0.857039 0.305791i 0.117995 + 0.363151i 0.150980 0.174240i
16.13 0.329324 + 0.0377864i 1.61702 + 1.17484i −1.84100 0.428106i 0.564443 0.825472i 0.488132 + 0.448003i −2.98313 3.06957i −1.21452 0.433340i 0.307474 + 0.946309i 0.217076 0.250519i
16.14 0.710733 + 0.0815490i 2.35793 + 1.71314i −1.44953 0.337074i 0.564443 0.825472i 1.53616 + 1.40987i 2.60666 + 2.68219i −2.35033 0.838595i 1.69796 + 5.22577i 0.468485 0.540661i
16.15 1.06134 + 0.121777i −0.605637 0.440021i −0.836420 0.194501i 0.564443 0.825472i −0.589199 0.540762i −1.40253 1.44317i −2.87638 1.02629i −0.753874 2.32018i 0.699587 0.807367i
16.16 1.50155 + 0.172287i −0.190847 0.138659i 0.276953 + 0.0644028i 0.564443 0.825472i −0.262678 0.241084i −0.620747 0.638734i −2.44225 0.871393i −0.909855 2.80024i 0.989759 1.14224i
16.17 1.66802 + 0.191388i −1.24319 0.903228i 0.797652 + 0.185486i 0.564443 0.825472i −1.90080 1.74454i 3.32658 + 3.42297i −1.86765 0.666376i −0.197358 0.607406i 1.09949 1.26888i
16.18 1.90115 + 0.218137i 1.85412 + 1.34710i 1.61876 + 0.376427i 0.564443 0.825472i 3.23112 + 2.96549i 0.529131 + 0.544463i −0.609275 0.217389i 0.696047 + 2.14221i 1.25316 1.44622i
16.19 1.92192 + 0.220520i −2.15448 1.56532i 1.69713 + 0.394651i 0.564443 0.825472i −3.79556 3.48353i −0.812019 0.835548i −0.469333 0.167458i 1.26451 + 3.89175i 1.26685 1.46202i
16.20 2.46804 + 0.283181i 2.06854 + 1.50288i 4.06299 + 0.944807i 0.564443 0.825472i 4.67964 + 4.29494i −3.42528 3.52452i 5.08053 + 1.81273i 1.09315 + 3.36437i 1.62682 1.87745i
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:

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(10\!\cdots\!85\)\( T_{2}^{855} + \)\(28\!\cdots\!51\)\( T_{2}^{854} + \)\(10\!\cdots\!91\)\( T_{2}^{853} + \)\(11\!\cdots\!68\)\( T_{2}^{852} + \)\(26\!\cdots\!48\)\( T_{2}^{851} - \)\(17\!\cdots\!58\)\( T_{2}^{850} - \)\(13\!\cdots\!12\)\( T_{2}^{849} + \)\(12\!\cdots\!96\)\( T_{2}^{848} - \)\(63\!\cdots\!47\)\( T_{2}^{847} - \)\(59\!\cdots\!60\)\( T_{2}^{846} + \)\(12\!\cdots\!42\)\( T_{2}^{845} - \)\(44\!\cdots\!48\)\( T_{2}^{844} - \)\(12\!\cdots\!09\)\( T_{2}^{843} + \)\(32\!\cdots\!67\)\( T_{2}^{842} + \)\(13\!\cdots\!19\)\( T_{2}^{841} - \)\(12\!\cdots\!66\)\( T_{2}^{840} - \)\(10\!\cdots\!79\)\( T_{2}^{839} - \)\(13\!\cdots\!65\)\( T_{2}^{838} + \)\(28\!\cdots\!23\)\( T_{2}^{837} + \)\(36\!\cdots\!95\)\( T_{2}^{836} + \)\(11\!\cdots\!43\)\( T_{2}^{835} - \)\(38\!\cdots\!93\)\( T_{2}^{834} - \)\(14\!\cdots\!12\)\( T_{2}^{833} + \)\(20\!\cdots\!34\)\( T_{2}^{832} + \)\(19\!\cdots\!60\)\( T_{2}^{831} - \)\(22\!\cdots\!00\)\( T_{2}^{830} - \)\(32\!\cdots\!30\)\( T_{2}^{829} - \)\(72\!\cdots\!39\)\( T_{2}^{828} + \)\(33\!\cdots\!34\)\( T_{2}^{827} + \)\(75\!\cdots\!77\)\( T_{2}^{826} - \)\(19\!\cdots\!20\)\( T_{2}^{825} - \)\(43\!\cdots\!43\)\( T_{2}^{824} + \)\(32\!\cdots\!19\)\( T_{2}^{823} + \)\(21\!\cdots\!42\)\( T_{2}^{822} + \)\(55\!\cdots\!65\)\( T_{2}^{821} - \)\(78\!\cdots\!50\)\( T_{2}^{820} - \)\(70\!\cdots\!60\)\( T_{2}^{819} - \)\(44\!\cdots\!27\)\( T_{2}^{818} + \)\(61\!\cdots\!34\)\( T_{2}^{817} + \)\(68\!\cdots\!66\)\( T_{2}^{816} - \)\(41\!\cdots\!60\)\( T_{2}^{815} - \)\(48\!\cdots\!58\)\( T_{2}^{814} + \)\(85\!\cdots\!44\)\( T_{2}^{813} - \)\(25\!\cdots\!96\)\( T_{2}^{812} + \)\(16\!\cdots\!55\)\( T_{2}^{811} + \)\(11\!\cdots\!59\)\( T_{2}^{810} - \)\(18\!\cdots\!96\)\( T_{2}^{809} + \)\(15\!\cdots\!52\)\( T_{2}^{808} + \)\(86\!\cdots\!38\)\( T_{2}^{807} - \)\(94\!\cdots\!82\)\( T_{2}^{806} - \)\(11\!\cdots\!19\)\( T_{2}^{805} + \)\(23\!\cdots\!13\)\( T_{2}^{804} - \)\(21\!\cdots\!01\)\( T_{2}^{803} + \)\(14\!\cdots\!95\)\( T_{2}^{802} + \)\(31\!\cdots\!46\)\( T_{2}^{801} - \)\(40\!\cdots\!18\)\( T_{2}^{800} - \)\(23\!\cdots\!95\)\( T_{2}^{799} + \)\(39\!\cdots\!72\)\( T_{2}^{798} + \)\(85\!\cdots\!21\)\( T_{2}^{797} - \)\(19\!\cdots\!66\)\( T_{2}^{796} + \)\(15\!\cdots\!63\)\( T_{2}^{795} + \)\(11\!\cdots\!68\)\( T_{2}^{794} - \)\(52\!\cdots\!18\)\( T_{2}^{793} + \)\(13\!\cdots\!32\)\( T_{2}^{792} + \)\(46\!\cdots\!33\)\( T_{2}^{791} - \)\(17\!\cdots\!42\)\( T_{2}^{790} - \)\(18\!\cdots\!28\)\( T_{2}^{789} + \)\(10\!\cdots\!69\)\( T_{2}^{788} - \)\(19\!\cdots\!76\)\( T_{2}^{787} - \)\(29\!\cdots\!05\)\( T_{2}^{786} + \)\(58\!\cdots\!19\)\( T_{2}^{785} - \)\(15\!\cdots\!21\)\( T_{2}^{784} - \)\(36\!\cdots\!79\)\( T_{2}^{783} + \)\(29\!\cdots\!11\)\( T_{2}^{782} + \)\(69\!\cdots\!41\)\( T_{2}^{781} - \)\(26\!\cdots\!48\)\( T_{2}^{780} + \)\(17\!\cdots\!91\)\( T_{2}^{779} + \)\(12\!\cdots\!94\)\( T_{2}^{778} - \)\(19\!\cdots\!77\)\( T_{2}^{777} - \)\(14\!\cdots\!69\)\( T_{2}^{776} + \)\(74\!\cdots\!49\)\( T_{2}^{775} - \)\(26\!\cdots\!68\)\( T_{2}^{774} + \)\(97\!\cdots\!27\)\( T_{2}^{773} + \)\(33\!\cdots\!74\)\( T_{2}^{772} - \)\(47\!\cdots\!90\)\( T_{2}^{771} - \)\(23\!\cdots\!62\)\( T_{2}^{770} + \)\(61\!\cdots\!13\)\( T_{2}^{769} + \)\(45\!\cdots\!18\)\( T_{2}^{768} - \)\(38\!\cdots\!71\)\( T_{2}^{767} + \)\(56\!\cdots\!23\)\( T_{2}^{766} + \)\(62\!\cdots\!61\)\( T_{2}^{765} - \)\(48\!\cdots\!31\)\( T_{2}^{764} + \)\(57\!\cdots\!13\)\( T_{2}^{763} + \)\(24\!\cdots\!05\)\( T_{2}^{762} - \)\(62\!\cdots\!41\)\( T_{2}^{761} - \)\(11\!\cdots\!26\)\( T_{2}^{760} + \)\(62\!\cdots\!88\)\( T_{2}^{759} - \)\(49\!\cdots\!85\)\( T_{2}^{758} - \)\(35\!\cdots\!84\)\( T_{2}^{757} + \)\(11\!\cdots\!60\)\( T_{2}^{756} - \)\(23\!\cdots\!26\)\( T_{2}^{755} - \)\(65\!\cdots\!46\)\( T_{2}^{754} + \)\(11\!\cdots\!86\)\( T_{2}^{753} + \)\(12\!\cdots\!49\)\( T_{2}^{752} - \)\(55\!\cdots\!97\)\( T_{2}^{751} + \)\(27\!\cdots\!03\)\( T_{2}^{750} + \)\(22\!\cdots\!29\)\( T_{2}^{749} - \)\(95\!\cdots\!61\)\( T_{2}^{748} - \)\(13\!\cdots\!45\)\( T_{2}^{747} + \)\(10\!\cdots\!09\)\( T_{2}^{746} - \)\(18\!\cdots\!83\)\( T_{2}^{745} - \)\(39\!\cdots\!70\)\( T_{2}^{744} + \)\(15\!\cdots\!94\)\( T_{2}^{743} - \)\(10\!\cdots\!78\)\( T_{2}^{742} - \)\(46\!\cdots\!35\)\( T_{2}^{741} + \)\(45\!\cdots\!45\)\( T_{2}^{740} + \)\(97\!\cdots\!31\)\( T_{2}^{739} - \)\(61\!\cdots\!74\)\( T_{2}^{738} + \)\(64\!\cdots\!21\)\( T_{2}^{737} + \)\(63\!\cdots\!06\)\( T_{2}^{736} - \)\(21\!\cdots\!19\)\( T_{2}^{735} - \)\(12\!\cdots\!35\)\( T_{2}^{734} + \)\(16\!\cdots\!35\)\( T_{2}^{733} - \)\(14\!\cdots\!93\)\( T_{2}^{732} - \)\(41\!\cdots\!43\)\( T_{2}^{731} + \)\(71\!\cdots\!50\)\( T_{2}^{730} + \)\(22\!\cdots\!51\)\( T_{2}^{729} - \)\(16\!\cdots\!91\)\( T_{2}^{728} + \)\(50\!\cdots\!01\)\( T_{2}^{727} + \)\(12\!\cdots\!58\)\( T_{2}^{726} - \)\(11\!\cdots\!94\)\( T_{2}^{725} + \)\(54\!\cdots\!38\)\( T_{2}^{724} + \)\(80\!\cdots\!06\)\( T_{2}^{723} - \)\(11\!\cdots\!36\)\( T_{2}^{722} - \)\(15\!\cdots\!71\)\( T_{2}^{721} + \)\(33\!\cdots\!36\)\( T_{2}^{720} + \)\(43\!\cdots\!96\)\( T_{2}^{719} - \)\(34\!\cdots\!95\)\( T_{2}^{718} + \)\(13\!\cdots\!32\)\( T_{2}^{717} + \)\(89\!\cdots\!28\)\( T_{2}^{716} - \)\(58\!\cdots\!33\)\( T_{2}^{715} - \)\(25\!\cdots\!44\)\( T_{2}^{714} + \)\(37\!\cdots\!89\)\( T_{2}^{713} - \)\(32\!\cdots\!13\)\( T_{2}^{712} - \)\(28\!\cdots\!45\)\( T_{2}^{711} - \)\(69\!\cdots\!68\)\( T_{2}^{710} - \)\(19\!\cdots\!19\)\( T_{2}^{709} + \)\(72\!\cdots\!14\)\( T_{2}^{708} + \)\(16\!\cdots\!88\)\( T_{2}^{707} + \)\(81\!\cdots\!41\)\( T_{2}^{706} - \)\(47\!\cdots\!91\)\( T_{2}^{705} - \)\(57\!\cdots\!43\)\( T_{2}^{704} + \)\(39\!\cdots\!93\)\( T_{2}^{703} + \)\(64\!\cdots\!60\)\( T_{2}^{702} - \)\(15\!\cdots\!02\)\( T_{2}^{701} + \)\(58\!\cdots\!51\)\( T_{2}^{700} + \)\(48\!\cdots\!31\)\( T_{2}^{699} - \)\(58\!\cdots\!25\)\( T_{2}^{698} + \)\(50\!\cdots\!40\)\( T_{2}^{697} + \)\(91\!\cdots\!01\)\( T_{2}^{696} - \)\(29\!\cdots\!92\)\( T_{2}^{695} - \)\(42\!\cdots\!01\)\( T_{2}^{694} + \)\(25\!\cdots\!41\)\( T_{2}^{693} + \)\(31\!\cdots\!11\)\( T_{2}^{692} - \)\(12\!\cdots\!89\)\( T_{2}^{691} + \)\(49\!\cdots\!76\)\( T_{2}^{690} + \)\(64\!\cdots\!81\)\( T_{2}^{689} - \)\(69\!\cdots\!11\)\( T_{2}^{688} - \)\(25\!\cdots\!66\)\( T_{2}^{687} + \)\(61\!\cdots\!63\)\( T_{2}^{686} - \)\(57\!\cdots\!60\)\( T_{2}^{685} - \)\(20\!\cdots\!93\)\( T_{2}^{684} + \)\(62\!\cdots\!44\)\( T_{2}^{683} - \)\(38\!\cdots\!28\)\( T_{2}^{682} - \)\(36\!\cdots\!78\)\( T_{2}^{681} + \)\(58\!\cdots\!84\)\( T_{2}^{680} + \)\(15\!\cdots\!62\)\( T_{2}^{679} - \)\(32\!\cdots\!95\)\( T_{2}^{678} - \)\(19\!\cdots\!72\)\( T_{2}^{677} + \)\(14\!\cdots\!36\)\( T_{2}^{676} - \)\(60\!\cdots\!33\)\( T_{2}^{675} - \)\(23\!\cdots\!98\)\( T_{2}^{674} + \)\(63\!\cdots\!92\)\( T_{2}^{673} - \)\(15\!\cdots\!83\)\( T_{2}^{672} - \)\(36\!\cdots\!41\)\( T_{2}^{671} + \)\(29\!\cdots\!04\)\( T_{2}^{670} + \)\(14\!\cdots\!35\)\( T_{2}^{669} + \)\(37\!\cdots\!48\)\( T_{2}^{668} - \)\(81\!\cdots\!17\)\( T_{2}^{667} - \)\(97\!\cdots\!86\)\( T_{2}^{666} - \)\(41\!\cdots\!93\)\( T_{2}^{665} - \)\(12\!\cdots\!36\)\( T_{2}^{664} + \)\(36\!\cdots\!96\)\( T_{2}^{663} + \)\(22\!\cdots\!11\)\( T_{2}^{662} - \)\(19\!\cdots\!20\)\( T_{2}^{661} - \)\(21\!\cdots\!43\)\( T_{2}^{660} + \)\(78\!\cdots\!75\)\( T_{2}^{659} + \)\(96\!\cdots\!59\)\( T_{2}^{658} - \)\(18\!\cdots\!37\)\( T_{2}^{657} + \)\(90\!\cdots\!81\)\( T_{2}^{656} - \)\(29\!\cdots\!00\)\( T_{2}^{655} - \)\(42\!\cdots\!25\)\( T_{2}^{654} + \)\(53\!\cdots\!42\)\( T_{2}^{653} + \)\(35\!\cdots\!53\)\( T_{2}^{652} - \)\(29\!\cdots\!43\)\( T_{2}^{651} - \)\(18\!\cdots\!89\)\( T_{2}^{650} + \)\(10\!\cdots\!87\)\( T_{2}^{649} + \)\(59\!\cdots\!91\)\( T_{2}^{648} - \)\(22\!\cdots\!63\)\( T_{2}^{647} + \)\(38\!\cdots\!60\)\( T_{2}^{646} + \)\(81\!\cdots\!79\)\( T_{2}^{645} - \)\(17\!\cdots\!24\)\( T_{2}^{644} - \)\(46\!\cdots\!97\)\( T_{2}^{643} + \)\(12\!\cdots\!71\)\( T_{2}^{642} + \)\(18\!\cdots\!03\)\( T_{2}^{641} - \)\(52\!\cdots\!96\)\( T_{2}^{640} - \)\(20\!\cdots\!71\)\( T_{2}^{639} + \)\(10\!\cdots\!30\)\( T_{2}^{638} + \)\(17\!\cdots\!73\)\( T_{2}^{637} + \)\(36\!\cdots\!56\)\( T_{2}^{636} - \)\(10\!\cdots\!72\)\( T_{2}^{635} - \)\(41\!\cdots\!14\)\( T_{2}^{634} + \)\(45\!\cdots\!43\)\( T_{2}^{633} + \)\(19\!\cdots\!49\)\( T_{2}^{632} - \)\(10\!\cdots\!22\)\( T_{2}^{631} - \)\(48\!\cdots\!70\)\( T_{2}^{630} - \)\(52\!\cdots\!30\)\( T_{2}^{629} - \)\(80\!\cdots\!92\)\( T_{2}^{628} + \)\(82\!\cdots\!88\)\( T_{2}^{627} + \)\(14\!\cdots\!62\)\( T_{2}^{626} - \)\(63\!\cdots\!88\)\( T_{2}^{625} - \)\(66\!\cdots\!07\)\( T_{2}^{624} + \)\(36\!\cdots\!05\)\( T_{2}^{623} + \)\(10\!\cdots\!92\)\( T_{2}^{622} - \)\(15\!\cdots\!13\)\( T_{2}^{621} + \)\(75\!\cdots\!85\)\( T_{2}^{620} + \)\(41\!\cdots\!85\)\( T_{2}^{619} - \)\(91\!\cdots\!66\)\( T_{2}^{618} + \)\(14\!\cdots\!31\)\( T_{2}^{617} + \)\(54\!\cdots\!17\)\( T_{2}^{616} - \)\(10\!\cdots\!91\)\( T_{2}^{615} - \)\(21\!\cdots\!65\)\( T_{2}^{614} + \)\(87\!\cdots\!24\)\( T_{2}^{613} + \)\(68\!\cdots\!43\)\( T_{2}^{612} - \)\(46\!\cdots\!86\)\( T_{2}^{611} - \)\(97\!\cdots\!72\)\( T_{2}^{610} + \)\(18\!\cdots\!32\)\( T_{2}^{609} - \)\(93\!\cdots\!20\)\( T_{2}^{608} - \)\(54\!\cdots\!23\)\( T_{2}^{607} + \)\(99\!\cdots\!05\)\( T_{2}^{606} + \)\(36\!\cdots\!39\)\( T_{2}^{605} - \)\(63\!\cdots\!95\)\( T_{2}^{604} + \)\(83\!\cdots\!36\)\( T_{2}^{603} + \)\(33\!\cdots\!88\)\( T_{2}^{602} - \)\(69\!\cdots\!60\)\( T_{2}^{601} - \)\(13\!\cdots\!92\)\( T_{2}^{600} + \)\(38\!\cdots\!89\)\( T_{2}^{599} + \)\(29\!\cdots\!73\)\( T_{2}^{598} - \)\(17\!\cdots\!08\)\( T_{2}^{597} + \)\(57\!\cdots\!69\)\( T_{2}^{596} + \)\(52\!\cdots\!30\)\( T_{2}^{595} - \)\(11\!\cdots\!15\)\( T_{2}^{594} - \)\(74\!\cdots\!26\)\( T_{2}^{593} + \)\(79\!\cdots\!67\)\( T_{2}^{592} - \)\(36\!\cdots\!91\)\( T_{2}^{591} - \)\(35\!\cdots\!45\)\( T_{2}^{590} + \)\(42\!\cdots\!24\)\( T_{2}^{589} + \)\(11\!\cdots\!17\)\( T_{2}^{588} - \)\(24\!\cdots\!46\)\( T_{2}^{587} - \)\(14\!\cdots\!40\)\( T_{2}^{586} + \)\(99\!\cdots\!41\)\( T_{2}^{585} - \)\(10\!\cdots\!89\)\( T_{2}^{584} - \)\(28\!\cdots\!90\)\( T_{2}^{583} + \)\(10\!\cdots\!39\)\( T_{2}^{582} + \)\(37\!\cdots\!67\)\( T_{2}^{581} - \)\(50\!\cdots\!89\)\( T_{2}^{580} + \)\(25\!\cdots\!54\)\( T_{2}^{579} + \)\(16\!\cdots\!36\)\( T_{2}^{578} - \)\(23\!\cdots\!28\)\( T_{2}^{577} - \)\(31\!\cdots\!81\)\( T_{2}^{576} + \)\(10\!\cdots\!96\)\( T_{2}^{575} - \)\(73\!\cdots\!68\)\( T_{2}^{574} - \)\(36\!\cdots\!65\)\( T_{2}^{573} + \)\(91\!\cdots\!47\)\( T_{2}^{572} + \)\(72\!\cdots\!60\)\( T_{2}^{571} - \)\(42\!\cdots\!09\)\( T_{2}^{570} + \)\(13\!\cdots\!67\)\( T_{2}^{569} + \)\(13\!\cdots\!37\)\( T_{2}^{568} - \)\(16\!\cdots\!35\)\( T_{2}^{567} - \)\(16\!\cdots\!17\)\( T_{2}^{566} + \)\(73\!\cdots\!47\)\( T_{2}^{565} - \)\(94\!\cdots\!75\)\( T_{2}^{564} - \)\(22\!\cdots\!85\)\( T_{2}^{563} + \)\(71\!\cdots\!13\)\( T_{2}^{562} + \)\(27\!\cdots\!43\)\( T_{2}^{561} - \)\(26\!\cdots\!79\)\( T_{2}^{560} + \)\(18\!\cdots\!69\)\( T_{2}^{559} + \)\(61\!\cdots\!96\)\( T_{2}^{558} - \)\(12\!\cdots\!53\)\( T_{2}^{557} + \)\(23\!\cdots\!36\)\( T_{2}^{556} + \)\(48\!\cdots\!03\)\( T_{2}^{555} - \)\(98\!\cdots\!08\)\( T_{2}^{554} - \)\(14\!\cdots\!83\)\( T_{2}^{553} + \)\(51\!\cdots\!85\)\( T_{2}^{552} + \)\(15\!\cdots\!46\)\( T_{2}^{551} - \)\(17\!\cdots\!13\)\( T_{2}^{550} + \)\(12\!\cdots\!52\)\( T_{2}^{549} + \)\(32\!\cdots\!24\)\( T_{2}^{548} - \)\(82\!\cdots\!99\)\( T_{2}^{547} + \)\(50\!\cdots\!81\)\( T_{2}^{546} + \)\(32\!\cdots\!77\)\( T_{2}^{545} - \)\(64\!\cdots\!88\)\( T_{2}^{544} - \)\(10\!\cdots\!07\)\( T_{2}^{543} + \)\(28\!\cdots\!27\)\( T_{2}^{542} + \)\(17\!\cdots\!30\)\( T_{2}^{541} - \)\(95\!\cdots\!80\)\( T_{2}^{540} + \)\(15\!\cdots\!94\)\( T_{2}^{539} + \)\(23\!\cdots\!55\)\( T_{2}^{538} - \)\(19\!\cdots\!98\)\( T_{2}^{537} - \)\(45\!\cdots\!31\)\( T_{2}^{536} + \)\(10\!\cdots\!68\)\( T_{2}^{535} + \)\(13\!\cdots\!81\)\( T_{2}^{534} - \)\(49\!\cdots\!64\)\( T_{2}^{533} - \)\(68\!\cdots\!22\)\( T_{2}^{532} + \)\(17\!\cdots\!21\)\( T_{2}^{531} + \)\(34\!\cdots\!01\)\( T_{2}^{530} - \)\(61\!\cdots\!50\)\( T_{2}^{529} - \)\(14\!\cdots\!28\)\( T_{2}^{528} + \)\(25\!\cdots\!83\)\( T_{2}^{527} + \)\(44\!\cdots\!88\)\( T_{2}^{526} - \)\(84\!\cdots\!29\)\( T_{2}^{525} - \)\(80\!\cdots\!89\)\( T_{2}^{524} + \)\(22\!\cdots\!76\)\( T_{2}^{523} + \)\(12\!\cdots\!78\)\( T_{2}^{522} - \)\(78\!\cdots\!04\)\( T_{2}^{521} + \)\(85\!\cdots\!80\)\( T_{2}^{520} + \)\(28\!\cdots\!96\)\( T_{2}^{519} - \)\(57\!\cdots\!77\)\( T_{2}^{518} - \)\(68\!\cdots\!05\)\( T_{2}^{517} + \)\(22\!\cdots\!11\)\( T_{2}^{516} + \)\(17\!\cdots\!63\)\( T_{2}^{515} - \)\(66\!\cdots\!85\)\( T_{2}^{514} - \)\(52\!\cdots\!62\)\( T_{2}^{513} + \)\(23\!\cdots\!98\)\( T_{2}^{512} - \)\(52\!\cdots\!53\)\( T_{2}^{511} - \)\(67\!\cdots\!24\)\( T_{2}^{510} + \)\(98\!\cdots\!59\)\( T_{2}^{509} + \)\(14\!\cdots\!43\)\( T_{2}^{508} - \)\(33\!\cdots\!03\)\( T_{2}^{507} - \)\(58\!\cdots\!23\)\( T_{2}^{506} + \)\(14\!\cdots\!46\)\( T_{2}^{505} + \)\(25\!\cdots\!56\)\( T_{2}^{504} - \)\(73\!\cdots\!21\)\( T_{2}^{503} - \)\(31\!\cdots\!70\)\( T_{2}^{502} + \)\(16\!\cdots\!58\)\( T_{2}^{501} - \)\(44\!\cdots\!27\)\( T_{2}^{500} - \)\(19\!\cdots\!40\)\( T_{2}^{499} - \)\(48\!\cdots\!88\)\( T_{2}^{498} + \)\(22\!\cdots\!30\)\( T_{2}^{497} + \)\(13\!\cdots\!16\)\( T_{2}^{496} - \)\(22\!\cdots\!73\)\( T_{2}^{495} + \)\(40\!\cdots\!82\)\( T_{2}^{494} - \)\(59\!\cdots\!83\)\( T_{2}^{493} - \)\(97\!\cdots\!05\)\( T_{2}^{492} + \)\(32\!\cdots\!26\)\( T_{2}^{491} - \)\(28\!\cdots\!93\)\( T_{2}^{490} + \)\(53\!\cdots\!85\)\( T_{2}^{489} - \)\(90\!\cdots\!80\)\( T_{2}^{488} - \)\(16\!\cdots\!39\)\( T_{2}^{487} + \)\(78\!\cdots\!68\)\( T_{2}^{486} - \)\(97\!\cdots\!58\)\( T_{2}^{485} - \)\(11\!\cdots\!30\)\( T_{2}^{484} + \)\(16\!\cdots\!77\)\( T_{2}^{483} - \)\(19\!\cdots\!68\)\( T_{2}^{482} + \)\(14\!\cdots\!11\)\( T_{2}^{481} - \)\(12\!\cdots\!91\)\( T_{2}^{480} + \)\(39\!\cdots\!50\)\( T_{2}^{479} - \)\(21\!\cdots\!92\)\( T_{2}^{478} - \)\(15\!\cdots\!71\)\( T_{2}^{477} + \)\(21\!\cdots\!46\)\( T_{2}^{476} - \)\(16\!\cdots\!20\)\( T_{2}^{475} - \)\(22\!\cdots\!19\)\( T_{2}^{474} + \)\(11\!\cdots\!27\)\( T_{2}^{473} - \)\(15\!\cdots\!98\)\( T_{2}^{472} + \)\(32\!\cdots\!25\)\( T_{2}^{471} - \)\(13\!\cdots\!61\)\( T_{2}^{470} + \)\(98\!\cdots\!61\)\( T_{2}^{469} + \)\(24\!\cdots\!95\)\( T_{2}^{468} - \)\(40\!\cdots\!95\)\( T_{2}^{467} + \)\(72\!\cdots\!44\)\( T_{2}^{466} + \)\(24\!\cdots\!90\)\( T_{2}^{465} - \)\(14\!\cdots\!76\)\( T_{2}^{464} + \)\(81\!\cdots\!71\)\( T_{2}^{463} - \)\(27\!\cdots\!19\)\( T_{2}^{462} + \)\(81\!\cdots\!54\)\( T_{2}^{461} + \)\(24\!\cdots\!23\)\( T_{2}^{460} - \)\(26\!\cdots\!44\)\( T_{2}^{459} + \)\(19\!\cdots\!16\)\( T_{2}^{458} - \)\(17\!\cdots\!55\)\( T_{2}^{457} + \)\(69\!\cdots\!91\)\( T_{2}^{456} + \)\(54\!\cdots\!80\)\( T_{2}^{455} - \)\(40\!\cdots\!12\)\( T_{2}^{454} + \)\(27\!\cdots\!04\)\( T_{2}^{453} + \)\(22\!\cdots\!45\)\( T_{2}^{452} + \)\(12\!\cdots\!67\)\( T_{2}^{451} + \)\(35\!\cdots\!37\)\( T_{2}^{450} - \)\(35\!\cdots\!87\)\( T_{2}^{449} + \)\(26\!\cdots\!56\)\( T_{2}^{448} + \)\(42\!\cdots\!47\)\( T_{2}^{447} - \)\(22\!\cdots\!54\)\( T_{2}^{446} - \)\(71\!\cdots\!92\)\( T_{2}^{445} - \)\(23\!\cdots\!15\)\( T_{2}^{444} + \)\(27\!\cdots\!20\)\( T_{2}^{443} + \)\(37\!\cdots\!97\)\( T_{2}^{442} - \)\(43\!\cdots\!18\)\( T_{2}^{441} - \)\(30\!\cdots\!96\)\( T_{2}^{440} - \)\(86\!\cdots\!37\)\( T_{2}^{439} + \)\(24\!\cdots\!01\)\( T_{2}^{438} + \)\(38\!\cdots\!97\)\( T_{2}^{437} - \)\(20\!\cdots\!12\)\( T_{2}^{436} - \)\(18\!\cdots\!07\)\( T_{2}^{435} - \)\(70\!\cdots\!73\)\( T_{2}^{434} + \)\(29\!\cdots\!01\)\( T_{2}^{433} - \)\(18\!\cdots\!86\)\( T_{2}^{432} - \)\(18\!\cdots\!35\)\( T_{2}^{431} + \)\(28\!\cdots\!97\)\( T_{2}^{430} - \)\(91\!\cdots\!85\)\( T_{2}^{429} + \)\(25\!\cdots\!04\)\( T_{2}^{428} - \)\(23\!\cdots\!85\)\( T_{2}^{427} - \)\(21\!\cdots\!51\)\( T_{2}^{426} + \)\(74\!\cdots\!22\)\( T_{2}^{425} - \)\(10\!\cdots\!25\)\( T_{2}^{424} + \)\(15\!\cdots\!38\)\( T_{2}^{423} - \)\(11\!\cdots\!54\)\( T_{2}^{422} - \)\(22\!\cdots\!68\)\( T_{2}^{421} + \)\(73\!\cdots\!15\)\( T_{2}^{420} - \)\(90\!\cdots\!52\)\( T_{2}^{419} + \)\(62\!\cdots\!95\)\( T_{2}^{418} + \)\(68\!\cdots\!54\)\( T_{2}^{417} - \)\(18\!\cdots\!44\)\( T_{2}^{416} + \)\(44\!\cdots\!03\)\( T_{2}^{415} - \)\(50\!\cdots\!66\)\( T_{2}^{414} + \)\(17\!\cdots\!32\)\( T_{2}^{413} + \)\(28\!\cdots\!97\)\( T_{2}^{412} - \)\(92\!\cdots\!01\)\( T_{2}^{411} + \)\(20\!\cdots\!77\)\( T_{2}^{410} - \)\(24\!\cdots\!93\)\( T_{2}^{409} + \)\(99\!\cdots\!82\)\( T_{2}^{408} + \)\(10\!\cdots\!71\)\( T_{2}^{407} - \)\(23\!\cdots\!73\)\( T_{2}^{406} + \)\(71\!\cdots\!51\)\( T_{2}^{405} - \)\(18\!\cdots\!74\)\( T_{2}^{404} + \)\(18\!\cdots\!59\)\( T_{2}^{403} + \)\(28\!\cdots\!23\)\( T_{2}^{402} - \)\(19\!\cdots\!28\)\( T_{2}^{401} + \)\(24\!\cdots\!17\)\( T_{2}^{400} - \)\(74\!\cdots\!12\)\( T_{2}^{399} + \)\(14\!\cdots\!30\)\( T_{2}^{398} - \)\(12\!\cdots\!00\)\( T_{2}^{397} - \)\(63\!\cdots\!36\)\( T_{2}^{396} + \)\(23\!\cdots\!96\)\( T_{2}^{395} - \)\(73\!\cdots\!67\)\( T_{2}^{394} + \)\(11\!\cdots\!24\)\( T_{2}^{393} - \)\(36\!\cdots\!23\)\( T_{2}^{392} - \)\(83\!\cdots\!46\)\( T_{2}^{391} + \)\(12\!\cdots\!32\)\( T_{2}^{390} - \)\(29\!\cdots\!58\)\( T_{2}^{389} + \)\(56\!\cdots\!61\)\( T_{2}^{388} - \)\(20\!\cdots\!97\)\( T_{2}^{387} - \)\(59\!\cdots\!57\)\( T_{2}^{386} + \)\(95\!\cdots\!16\)\( T_{2}^{385} - \)\(12\!\cdots\!53\)\( T_{2}^{384} + \)\(97\!\cdots\!80\)\( T_{2}^{383} + \)\(69\!\cdots\!54\)\( T_{2}^{382} - \)\(81\!\cdots\!02\)\( T_{2}^{381} + \)\(43\!\cdots\!65\)\( T_{2}^{380} - \)\(42\!\cdots\!24\)\( T_{2}^{379} + \)\(54\!\cdots\!07\)\( T_{2}^{378} + \)\(14\!\cdots\!33\)\( T_{2}^{377} - \)\(90\!\cdots\!03\)\( T_{2}^{376} + \)\(10\!\cdots\!81\)\( T_{2}^{375} + \)\(68\!\cdots\!07\)\( T_{2}^{374} - \)\(31\!\cdots\!15\)\( T_{2}^{373} + \)\(48\!\cdots\!16\)\( T_{2}^{372} + \)\(60\!\cdots\!19\)\( T_{2}^{371} - \)\(63\!\cdots\!68\)\( T_{2}^{370} - \)\(72\!\cdots\!04\)\( T_{2}^{369} + \)\(86\!\cdots\!39\)\( T_{2}^{368} - \)\(11\!\cdots\!93\)\( T_{2}^{367} + \)\(67\!\cdots\!88\)\( T_{2}^{366} + \)\(10\!\cdots\!21\)\( T_{2}^{365} + \)\(28\!\cdots\!69\)\( T_{2}^{364} + \)\(66\!\cdots\!49\)\( T_{2}^{363} - \)\(63\!\cdots\!61\)\( T_{2}^{362} + \)\(87\!\cdots\!81\)\( T_{2}^{361} + \)\(39\!\cdots\!72\)\( T_{2}^{360} - \)\(20\!\cdots\!11\)\( T_{2}^{359} + \)\(16\!\cdots\!61\)\( T_{2}^{358} + \)\(58\!\cdots\!53\)\( T_{2}^{357} - \)\(23\!\cdots\!95\)\( T_{2}^{356} + \)\(10\!\cdots\!72\)\( T_{2}^{355} + \)\(34\!\cdots\!67\)\( T_{2}^{354} + \)\(36\!\cdots\!49\)\( T_{2}^{353} - \)\(56\!\cdots\!15\)\( T_{2}^{352} - \)\(46\!\cdots\!76\)\( T_{2}^{351} + \)\(19\!\cdots\!19\)\( T_{2}^{350} - \)\(23\!\cdots\!35\)\( T_{2}^{349} - \)\(83\!\cdots\!25\)\( T_{2}^{348} + \)\(77\!\cdots\!53\)\( T_{2}^{347} - \)\(62\!\cdots\!97\)\( T_{2}^{346} - \)\(94\!\cdots\!97\)\( T_{2}^{345} + \)\(16\!\cdots\!02\)\( T_{2}^{344} - \)\(19\!\cdots\!02\)\( T_{2}^{343} - \)\(12\!\cdots\!74\)\( T_{2}^{342} + \)\(19\!\cdots\!22\)\( T_{2}^{341} - \)\(11\!\cdots\!88\)\( T_{2}^{340} - \)\(25\!\cdots\!62\)\( T_{2}^{339} + \)\(24\!\cdots\!04\)\( T_{2}^{338} + \)\(45\!\cdots\!74\)\( T_{2}^{337} - \)\(22\!\cdots\!89\)\( T_{2}^{336} - \)\(11\!\cdots\!27\)\( T_{2}^{335} + \)\(10\!\cdots\!88\)\( T_{2}^{334} + \)\(10\!\cdots\!04\)\( T_{2}^{333} - \)\(26\!\cdots\!72\)\( T_{2}^{332} + \)\(23\!\cdots\!28\)\( T_{2}^{331} + \)\(16\!\cdots\!71\)\( T_{2}^{330} - \)\(75\!\cdots\!97\)\( T_{2}^{329} + \)\(47\!\cdots\!23\)\( T_{2}^{328} + \)\(79\!\cdots\!84\)\( T_{2}^{327} - \)\(11\!\cdots\!60\)\( T_{2}^{326} - \)\(10\!\cdots\!86\)\( T_{2}^{325} + \)\(11\!\cdots\!69\)\( T_{2}^{324} - \)\(79\!\cdots\!88\)\( T_{2}^{323} - \)\(63\!\cdots\!64\)\( T_{2}^{322} + \)\(18\!\cdots\!97\)\( T_{2}^{321} - \)\(58\!\cdots\!23\)\( T_{2}^{320} - \)\(36\!\cdots\!82\)\( T_{2}^{319} + \)\(17\!\cdots\!33\)\( T_{2}^{318} + \)\(57\!\cdots\!59\)\( T_{2}^{317} - \)\(64\!\cdots\!00\)\( T_{2}^{316} - \)\(38\!\cdots\!53\)\( T_{2}^{315} + \)\(12\!\cdots\!98\)\( T_{2}^{314} - \)\(66\!\cdots\!90\)\( T_{2}^{313} - \)\(10\!\cdots\!60\)\( T_{2}^{312} + \)\(22\!\cdots\!61\)\( T_{2}^{311} - \)\(42\!\cdots\!49\)\( T_{2}^{310} - \)\(31\!\cdots\!38\)\( T_{2}^{309} + \)\(29\!\cdots\!32\)\( T_{2}^{308} + \)\(19\!\cdots\!55\)\( T_{2}^{307} - \)\(47\!\cdots\!51\)\( T_{2}^{306} + \)\(12\!\cdots\!50\)\( T_{2}^{305} + \)\(42\!\cdots\!45\)\( T_{2}^{304} - \)\(51\!\cdots\!61\)\( T_{2}^{303} - \)\(10\!\cdots\!75\)\( T_{2}^{302} + \)\(79\!\cdots\!64\)\( T_{2}^{301} - \)\(39\!\cdots\!81\)\( T_{2}^{300} - \)\(83\!\cdots\!70\)\( T_{2}^{299} + \)\(94\!\cdots\!62\)\( T_{2}^{298} + \)\(51\!\cdots\!78\)\( T_{2}^{297} - \)\(13\!\cdots\!56\)\( T_{2}^{296} + \)\(31\!\cdots\!65\)\( T_{2}^{295} + \)\(13\!\cdots\!07\)\( T_{2}^{294} - \)\(15\!\cdots\!90\)\( T_{2}^{293} - \)\(33\!\cdots\!68\)\( T_{2}^{292} + \)\(25\!\cdots\!91\)\( T_{2}^{291} - \)\(16\!\cdots\!71\)\( T_{2}^{290} - \)\(23\!\cdots\!18\)\( T_{2}^{289} + \)\(36\!\cdots\!98\)\( T_{2}^{288} + \)\(26\!\cdots\!47\)\( T_{2}^{287} - \)\(42\!\cdots\!06\)\( T_{2}^{286} + \)\(31\!\cdots\!72\)\( T_{2}^{285} + \)\(20\!\cdots\!34\)\( T_{2}^{284} - \)\(58\!\cdots\!01\)\( T_{2}^{283} + \)\(25\!\cdots\!43\)\( T_{2}^{282} + \)\(56\!\cdots\!47\)\( T_{2}^{281} - \)\(72\!\cdots\!22\)\( T_{2}^{280} - \)\(19\!\cdots\!85\)\( T_{2}^{279} + \)\(91\!\cdots\!76\)\( T_{2}^{278} - \)\(35\!\cdots\!09\)\( T_{2}^{277} - \)\(65\!\cdots\!27\)\( T_{2}^{276} + \)\(80\!\cdots\!49\)\( T_{2}^{275} + \)\(45\!\cdots\!92\)\( T_{2}^{274} - \)\(90\!\cdots\!59\)\( T_{2}^{273} + \)\(59\!\cdots\!39\)\( T_{2}^{272} + \)\(62\!\cdots\!07\)\( T_{2}^{271} - \)\(95\!\cdots\!65\)\( T_{2}^{270} - \)\(18\!\cdots\!39\)\( T_{2}^{269} + \)\(89\!\cdots\!78\)\( T_{2}^{268} - \)\(16\!\cdots\!95\)\( T_{2}^{267} - \)\(50\!\cdots\!81\)\( T_{2}^{266} + \)\(27\!\cdots\!63\)\( T_{2}^{265} + \)\(56\!\cdots\!16\)\( T_{2}^{264} - \)\(19\!\cdots\!27\)\( T_{2}^{263} + \)\(24\!\cdots\!13\)\( T_{2}^{262} + \)\(74\!\cdots\!86\)\( T_{2}^{261} - \)\(31\!\cdots\!62\)\( T_{2}^{260} - \)\(61\!\cdots\!70\)\( T_{2}^{259} + \)\(20\!\cdots\!33\)\( T_{2}^{258} + \)\(18\!\cdots\!32\)\( T_{2}^{257} - \)\(12\!\cdots\!93\)\( T_{2}^{256} - \)\(36\!\cdots\!02\)\( T_{2}^{255} - \)\(17\!\cdots\!55\)\( T_{2}^{254} + \)\(49\!\cdots\!49\)\( T_{2}^{253} + \)\(33\!\cdots\!67\)\( T_{2}^{252} - \)\(48\!\cdots\!53\)\( T_{2}^{251} - \)\(45\!\cdots\!05\)\( T_{2}^{250} + \)\(35\!\cdots\!07\)\( T_{2}^{249} + \)\(54\!\cdots\!77\)\( T_{2}^{248} - \)\(13\!\cdots\!41\)\( T_{2}^{247} - \)\(57\!\cdots\!95\)\( T_{2}^{246} - \)\(10\!\cdots\!15\)\( T_{2}^{245} + \)\(55\!\cdots\!63\)\( T_{2}^{244} + \)\(29\!\cdots\!78\)\( T_{2}^{243} - \)\(47\!\cdots\!81\)\( T_{2}^{242} - \)\(40\!\cdots\!16\)\( T_{2}^{241} + \)\(35\!\cdots\!33\)\( T_{2}^{240} + \)\(44\!\cdots\!27\)\( T_{2}^{239} - \)\(21\!\cdots\!93\)\( T_{2}^{238} - \)\(42\!\cdots\!16\)\( T_{2}^{237} + \)\(94\!\cdots\!04\)\( T_{2}^{236} + \)\(36\!\cdots\!88\)\( T_{2}^{235} - \)\(35\!\cdots\!63\)\( T_{2}^{234} - \)\(28\!\cdots\!65\)\( T_{2}^{233} - \)\(49\!\cdots\!37\)\( T_{2}^{232} + \)\(20\!\cdots\!12\)\( T_{2}^{231} + \)\(70\!\cdots\!85\)\( T_{2}^{230} - \)\(13\!\cdots\!36\)\( T_{2}^{229} - \)\(70\!\cdots\!18\)\( T_{2}^{228} + \)\(87\!\cdots\!69\)\( T_{2}^{227} + \)\(59\!\cdots\!32\)\( T_{2}^{226} - \)\(52\!\cdots\!08\)\( T_{2}^{225} - \)\(44\!\cdots\!89\)\( T_{2}^{224} + \)\(29\!\cdots\!66\)\( T_{2}^{223} + \)\(31\!\cdots\!72\)\( T_{2}^{222} - \)\(15\!\cdots\!86\)\( T_{2}^{221} - \)\(20\!\cdots\!85\)\( T_{2}^{220} + \)\(80\!\cdots\!48\)\( T_{2}^{219} + \)\(13\!\cdots\!80\)\( T_{2}^{218} - \)\(39\!\cdots\!63\)\( T_{2}^{217} - \)\(82\!\cdots\!43\)\( T_{2}^{216} + \)\(18\!\cdots\!87\)\( T_{2}^{215} + \)\(49\!\cdots\!66\)\( T_{2}^{214} - \)\(80\!\cdots\!69\)\( T_{2}^{213} - \)\(28\!\cdots\!91\)\( T_{2}^{212} + \)\(33\!\cdots\!07\)\( T_{2}^{211} + \)\(15\!\cdots\!54\)\( T_{2}^{210} - \)\(13\!\cdots\!01\)\( T_{2}^{209} - \)\(82\!\cdots\!74\)\( T_{2}^{208} + \)\(60\!\cdots\!06\)\( T_{2}^{207} + \)\(42\!\cdots\!89\)\( T_{2}^{206} - \)\(28\!\cdots\!33\)\( T_{2}^{205} - \)\(21\!\cdots\!88\)\( T_{2}^{204} + \)\(13\!\cdots\!49\)\( T_{2}^{203} + \)\(10\!\cdots\!16\)\( T_{2}^{202} - \)\(57\!\cdots\!05\)\( T_{2}^{201} - \)\(49\!\cdots\!34\)\( T_{2}^{200} + \)\(28\!\cdots\!98\)\( T_{2}^{199} + \)\(21\!\cdots\!17\)\( T_{2}^{198} - \)\(14\!\cdots\!42\)\( T_{2}^{197} - \)\(90\!\cdots\!93\)\( T_{2}^{196} + \)\(79\!\cdots\!33\)\( T_{2}^{195} + \)\(34\!\cdots\!86\)\( T_{2}^{194} - \)\(51\!\cdots\!69\)\( T_{2}^{193} - \)\(11\!\cdots\!69\)\( T_{2}^{192} + \)\(36\!\cdots\!39\)\( T_{2}^{191} + \)\(37\!\cdots\!18\)\( T_{2}^{190} - \)\(23\!\cdots\!95\)\( T_{2}^{189} - \)\(12\!\cdots\!94\)\( T_{2}^{188} + \)\(12\!\cdots\!78\)\( T_{2}^{187} + \)\(51\!\cdots\!23\)\( T_{2}^{186} - \)\(55\!\cdots\!21\)\( T_{2}^{185} - \)\(18\!\cdots\!41\)\( T_{2}^{184} + \)\(21\!\cdots\!29\)\( T_{2}^{183} + \)\(37\!\cdots\!42\)\( T_{2}^{182} - \)\(87\!\cdots\!67\)\( T_{2}^{181} + \)\(27\!\cdots\!07\)\( T_{2}^{180} + \)\(42\!\cdots\!88\)\( T_{2}^{179} + \)\(42\!\cdots\!67\)\( T_{2}^{178} - \)\(11\!\cdots\!59\)\( T_{2}^{177} + \)\(14\!\cdots\!60\)\( T_{2}^{176} + \)\(35\!\cdots\!65\)\( T_{2}^{175} - \)\(28\!\cdots\!67\)\( T_{2}^{174} - \)\(31\!\cdots\!86\)\( T_{2}^{173} + \)\(18\!\cdots\!99\)\( T_{2}^{172} + \)\(11\!\cdots\!72\)\( T_{2}^{171} + \)\(25\!\cdots\!71\)\( T_{2}^{170} - \)\(84\!\cdots\!49\)\( T_{2}^{169} + \)\(57\!\cdots\!80\)\( T_{2}^{168} + \)\(48\!\cdots\!79\)\( T_{2}^{167} - \)\(43\!\cdots\!88\)\( T_{2}^{166} - \)\(36\!\cdots\!77\)\( T_{2}^{165} + \)\(43\!\cdots\!87\)\( T_{2}^{164} + \)\(12\!\cdots\!37\)\( T_{2}^{163} + \)\(69\!\cdots\!25\)\( T_{2}^{162} + \)\(40\!\cdots\!61\)\( T_{2}^{161} + \)\(20\!\cdots\!70\)\( T_{2}^{160} + \)\(40\!\cdots\!04\)\( T_{2}^{159} - \)\(45\!\cdots\!07\)\( T_{2}^{158} - \)\(38\!\cdots\!23\)\( T_{2}^{157} - \)\(53\!\cdots\!52\)\( T_{2}^{156} + \)\(16\!\cdots\!53\)\( T_{2}^{155} + \)\(99\!\cdots\!57\)\( T_{2}^{154} + \)\(82\!\cdots\!55\)\( T_{2}^{153} + \)\(25\!\cdots\!57\)\( T_{2}^{152} - \)\(13\!\cdots\!67\)\( T_{2}^{151} - \)\(23\!\cdots\!89\)\( T_{2}^{150} - \)\(89\!\cdots\!59\)\( T_{2}^{149} + \)\(98\!\cdots\!20\)\( T_{2}^{148} + \)\(17\!\cdots\!20\)\( T_{2}^{147} + \)\(41\!\cdots\!73\)\( T_{2}^{146} + \)\(36\!\cdots\!21\)\( T_{2}^{145} + \)\(14\!\cdots\!39\)\( T_{2}^{144} + \)\(22\!\cdots\!54\)\( T_{2}^{143} - \)\(18\!\cdots\!13\)\( T_{2}^{142} - \)\(71\!\cdots\!40\)\( T_{2}^{141} + \)\(53\!\cdots\!96\)\( T_{2}^{140} + \)\(21\!\cdots\!04\)\( T_{2}^{139} + \)\(80\!\cdots\!69\)\( T_{2}^{138} + \)\(22\!\cdots\!66\)\( T_{2}^{137} + \)\(50\!\cdots\!10\)\( T_{2}^{136} + \)\(32\!\cdots\!49\)\( T_{2}^{135} + \)\(77\!\cdots\!33\)\( T_{2}^{134} - \)\(11\!\cdots\!48\)\( T_{2}^{133} - \)\(99\!\cdots\!01\)\( T_{2}^{132} - \)\(97\!\cdots\!48\)\( T_{2}^{131} + \)\(58\!\cdots\!67\)\( T_{2}^{130} - \)\(50\!\cdots\!38\)\( T_{2}^{129} - \)\(30\!\cdots\!44\)\( T_{2}^{128} + \)\(12\!\cdots\!54\)\( T_{2}^{127} + \)\(15\!\cdots\!77\)\( T_{2}^{126} + \)\(34\!\cdots\!95\)\( T_{2}^{125} - \)\(18\!\cdots\!97\)\( T_{2}^{124} - \)\(17\!\cdots\!32\)\( T_{2}^{123} - \)\(10\!\cdots\!64\)\( T_{2}^{122} - \)\(67\!\cdots\!91\)\( T_{2}^{121} - \)\(33\!\cdots\!68\)\( T_{2}^{120} - \)\(40\!\cdots\!96\)\( T_{2}^{119} + \)\(75\!\cdots\!55\)\( T_{2}^{118} + \)\(62\!\cdots\!58\)\( T_{2}^{117} + \)\(21\!\cdots\!72\)\( T_{2}^{116} - \)\(72\!\cdots\!78\)\( T_{2}^{115} - \)\(40\!\cdots\!45\)\( T_{2}^{114} - \)\(18\!\cdots\!42\)\( T_{2}^{113} - \)\(23\!\cdots\!00\)\( T_{2}^{112} + \)\(11\!\cdots\!91\)\( T_{2}^{111} + \)\(60\!\cdots\!66\)\( T_{2}^{110} + \)\(10\!\cdots\!31\)\( T_{2}^{109} - \)\(11\!\cdots\!27\)\( T_{2}^{108} + \)\(70\!\cdots\!20\)\( T_{2}^{107} + \)\(78\!\cdots\!42\)\( T_{2}^{106} + \)\(89\!\cdots\!84\)\( T_{2}^{105} - \)\(16\!\cdots\!43\)\( T_{2}^{104} - \)\(10\!\cdots\!00\)\( T_{2}^{103} - \)\(22\!\cdots\!40\)\( T_{2}^{102} + \)\(53\!\cdots\!87\)\( T_{2}^{101} + \)\(55\!\cdots\!65\)\( T_{2}^{100} + \)\(18\!\cdots\!58\)\( T_{2}^{99} + \)\(13\!\cdots\!19\)\( T_{2}^{98} - \)\(17\!\cdots\!46\)\( T_{2}^{97} - \)\(66\!\cdots\!61\)\( T_{2}^{96} - \)\(89\!\cdots\!37\)\( T_{2}^{95} + \)\(39\!\cdots\!29\)\( T_{2}^{94} + \)\(15\!\cdots\!93\)\( T_{2}^{93} + \)\(65\!\cdots\!35\)\( T_{2}^{92} - \)\(16\!\cdots\!33\)\( T_{2}^{91} - \)\(28\!\cdots\!84\)\( T_{2}^{90} - \)\(93\!\cdots\!84\)\( T_{2}^{89} - \)\(25\!\cdots\!65\)\( T_{2}^{88} + \)\(63\!\cdots\!66\)\( T_{2}^{87} + \)\(14\!\cdots\!38\)\( T_{2}^{86} - \)\(61\!\cdots\!02\)\( T_{2}^{85} + \)\(25\!\cdots\!39\)\( T_{2}^{84} - \)\(10\!\cdots\!08\)\( T_{2}^{83} + \)\(32\!\cdots\!04\)\( T_{2}^{82} - \)\(14\!\cdots\!73\)\( T_{2}^{81} + \)\(64\!\cdots\!96\)\( T_{2}^{80} - \)\(21\!\cdots\!17\)\( T_{2}^{79} + \)\(56\!\cdots\!86\)\( T_{2}^{78} - \)\(60\!\cdots\!22\)\( T_{2}^{77} - \)\(18\!\cdots\!24\)\( T_{2}^{76} + \)\(10\!\cdots\!09\)\( T_{2}^{75} - \)\(20\!\cdots\!63\)\( T_{2}^{74} - \)\(33\!\cdots\!41\)\( T_{2}^{73} + \)\(33\!\cdots\!96\)\( T_{2}^{72} - \)\(96\!\cdots\!94\)\( T_{2}^{71} + \)\(88\!\cdots\!04\)\( T_{2}^{70} + \)\(43\!\cdots\!67\)\( T_{2}^{69} - \)\(20\!\cdots\!85\)\( T_{2}^{68} + \)\(20\!\cdots\!64\)\( T_{2}^{67} + \)\(14\!\cdots\!98\)\( T_{2}^{66} - \)\(90\!\cdots\!26\)\( T_{2}^{65} + \)\(29\!\cdots\!26\)\( T_{2}^{64} - \)\(69\!\cdots\!04\)\( T_{2}^{63} + \)\(13\!\cdots\!65\)\( T_{2}^{62} - \)\(28\!\cdots\!63\)\( T_{2}^{61} + \)\(85\!\cdots\!09\)\( T_{2}^{60} - \)\(27\!\cdots\!64\)\( T_{2}^{59} + \)\(74\!\cdots\!50\)\( T_{2}^{58} - \)\(15\!\cdots\!21\)\( T_{2}^{57} + \)\(25\!\cdots\!47\)\( T_{2}^{56} - \)\(32\!\cdots\!38\)\( T_{2}^{55} + \)\(45\!\cdots\!14\)\( T_{2}^{54} - \)\(12\!\cdots\!18\)\( T_{2}^{53} + \)\(39\!\cdots\!04\)\( T_{2}^{52} - \)\(97\!\cdots\!02\)\( T_{2}^{51} + \)\(16\!\cdots\!10\)\( T_{2}^{50} - \)\(10\!\cdots\!08\)\( T_{2}^{49} - \)\(41\!\cdots\!69\)\( T_{2}^{48} + \)\(19\!\cdots\!30\)\( T_{2}^{47} - \)\(52\!\cdots\!36\)\( T_{2}^{46} + \)\(10\!\cdots\!12\)\( T_{2}^{45} - \)\(13\!\cdots\!34\)\( T_{2}^{44} + \)\(84\!\cdots\!87\)\( T_{2}^{43} + \)\(17\!\cdots\!91\)\( T_{2}^{42} - \)\(75\!\cdots\!30\)\( T_{2}^{41} + \)\(16\!\cdots\!74\)\( T_{2}^{40} - \)\(23\!\cdots\!28\)\( T_{2}^{39} + \)\(23\!\cdots\!50\)\( T_{2}^{38} - \)\(73\!\cdots\!87\)\( T_{2}^{37} - \)\(31\!\cdots\!81\)\( T_{2}^{36} + \)\(90\!\cdots\!75\)\( T_{2}^{35} - \)\(15\!\cdots\!22\)\( T_{2}^{34} + \)\(19\!\cdots\!84\)\( T_{2}^{33} - \)\(17\!\cdots\!89\)\( T_{2}^{32} + \)\(79\!\cdots\!72\)\( T_{2}^{31} + \)\(89\!\cdots\!51\)\( T_{2}^{30} - \)\(29\!\cdots\!11\)\( T_{2}^{29} + \)\(47\!\cdots\!69\)\( T_{2}^{28} - \)\(58\!\cdots\!73\)\( T_{2}^{27} + \)\(62\!\cdots\!29\)\( T_{2}^{26} - \)\(60\!\cdots\!40\)\( T_{2}^{25} + \)\(53\!\cdots\!74\)\( T_{2}^{24} - \)\(43\!\cdots\!39\)\( T_{2}^{23} + \)\(32\!\cdots\!75\)\( T_{2}^{22} - \)\(22\!\cdots\!01\)\( T_{2}^{21} + \)\(14\!\cdots\!46\)\( T_{2}^{20} - \)\(92\!\cdots\!33\)\( T_{2}^{19} + \)\(55\!\cdots\!62\)\( T_{2}^{18} - \)\(31\!\cdots\!60\)\( T_{2}^{17} + \)\(16\!\cdots\!28\)\( T_{2}^{16} - \)\(81\!\cdots\!19\)\( T_{2}^{15} + \)\(37\!\cdots\!77\)\( T_{2}^{14} - \)\(16\!\cdots\!07\)\( T_{2}^{13} + \)\(62\!\cdots\!17\)\( T_{2}^{12} - \)\(20\!\cdots\!85\)\( T_{2}^{11} + \)\(55\!\cdots\!55\)\( T_{2}^{10} - \)\(11\!\cdots\!40\)\( T_{2}^{9} + \)\(15\!\cdots\!16\)\( T_{2}^{8} - \)\(13\!\cdots\!78\)\( T_{2}^{7} + \)\(76\!\cdots\!01\)\( T_{2}^{6} - \)\(87\!\cdots\!32\)\( T_{2}^{5} - \)\(12\!\cdots\!72\)\( T_{2}^{4} + \)\(21\!\cdots\!62\)\( T_{2}^{3} + \)\(76\!\cdots\!93\)\( T_{2}^{2} - \)\(40\!\cdots\!36\)\( T_{2} + \)\(61\!\cdots\!61\)\( \)">\(T_{2}^{880} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(605, [\chi])\).