Properties

Label 648.2.bb.b
Level $648$
Weight $2$
Character orbit 648.bb
Analytic conductor $5.174$
Analytic rank $0$
Dimension $1872$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 648.bb (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.17430605098\)
Analytic rank: \(0\)
Dimension: \(1872\)
Relative dimension: \(104\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1872q - 18q^{2} - 36q^{3} - 18q^{4} - 18q^{6} - 18q^{8} - 36q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 1872q - 18q^{2} - 36q^{3} - 18q^{4} - 18q^{6} - 18q^{8} - 36q^{9} - 18q^{10} - 36q^{11} - 18q^{12} - 18q^{14} - 18q^{16} - 36q^{17} - 90q^{18} - 36q^{19} - 18q^{20} - 18q^{22} - 18q^{24} - 36q^{25} - 27q^{26} - 36q^{27} - 9q^{28} - 18q^{30} - 18q^{32} - 36q^{33} - 18q^{34} - 36q^{35} - 18q^{36} + 90q^{38} - 18q^{40} - 36q^{41} - 63q^{42} - 36q^{43} + 54q^{44} - 18q^{46} + 81q^{48} - 36q^{49} - 135q^{50} - 54q^{51} - 18q^{52} - 144q^{54} + 108q^{56} - 36q^{57} - 18q^{58} + 18q^{59} + 99q^{60} - 117q^{62} - 18q^{64} - 36q^{65} - 90q^{66} - 36q^{67} + 243q^{68} - 18q^{70} - 18q^{72} - 36q^{73} - 18q^{74} - 36q^{75} - 54q^{76} - 45q^{78} - 36q^{81} - 36q^{82} - 36q^{83} + 9q^{84} - 18q^{86} + 54q^{88} - 198q^{89} - 81q^{90} - 36q^{91} - 108q^{92} - 18q^{94} - 423q^{96} - 36q^{97} - 189q^{98} - 36q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
11.1 −1.41419 + 0.00803184i 0.351152 1.69608i 1.99987 0.0227171i −0.912599 0.106667i −0.482973 + 2.40140i 1.19613 + 2.38169i −2.82802 + 0.0481890i −2.75338 1.19116i 1.29145 + 0.143518i
11.2 −1.41418 0.00999629i −1.69825 + 0.340513i 1.99980 + 0.0282731i −2.95291 0.345146i 2.40503 0.464570i 2.31141 + 4.60240i −2.82779 0.0599737i 2.76810 1.15655i 4.17249 + 0.517616i
11.3 −1.41387 + 0.0309486i −1.73010 0.0822491i 1.99808 0.0875149i −1.34302 0.156976i 2.44869 + 0.0627459i −1.24958 2.48811i −2.82233 + 0.185573i 2.98647 + 0.284598i 1.90372 + 0.180380i
11.4 −1.41020 0.106512i 0.964587 1.43860i 1.97731 + 0.300407i 3.91821 + 0.457974i −1.51349 + 1.92597i 0.785018 + 1.56310i −2.75640 0.634241i −1.13914 2.77531i −5.47667 1.06317i
11.5 −1.40370 + 0.172115i 1.49726 0.870756i 1.94075 0.483196i −1.56914 0.183407i −1.95183 + 1.47998i −1.80991 3.60382i −2.64107 + 1.01229i 1.48357 2.60749i 2.23418 0.0126250i
11.6 −1.40154 0.188885i 0.0948694 + 1.72945i 1.92864 + 0.529461i 3.02884 + 0.354021i 0.193704 2.44182i −0.170146 0.338788i −2.60307 1.10635i −2.98200 + 0.328144i −4.17818 1.06828i
11.7 −1.40007 + 0.199536i −1.10877 1.33065i 1.92037 0.558728i −0.0676767 0.00791027i 1.81786 + 1.64176i −0.717020 1.42770i −2.57716 + 1.16544i −0.541275 + 2.95077i 0.0963302 0.00242905i
11.8 −1.37861 0.315321i 1.21519 + 1.23422i 1.80115 + 0.869410i −1.24512 0.145534i −1.28611 2.08469i −0.829597 1.65186i −2.20894 1.76652i −0.0466089 + 2.99964i 1.67065 + 0.593247i
11.9 −1.36258 + 0.378650i 1.53556 + 0.801277i 1.71325 1.03188i 3.32079 + 0.388144i −2.39573 0.510362i −1.72247 3.42973i −1.94371 + 2.05474i 1.71591 + 2.46082i −4.67181 + 0.728539i
11.10 −1.33712 0.460544i −1.22030 + 1.22918i 1.57580 + 1.23161i −0.472160 0.0551875i 2.19778 1.08156i −0.456285 0.908537i −1.53983 2.37254i −0.0217478 2.99992i 0.605919 + 0.291243i
11.11 −1.33569 0.464682i 1.72890 + 0.104486i 1.56814 + 1.24134i 1.18213 + 0.138172i −2.26072 0.942948i 0.848159 + 1.68882i −1.51772 2.38674i 2.97817 + 0.361290i −1.51476 0.733871i
11.12 −1.33082 + 0.478461i 0.282526 + 1.70885i 1.54215 1.27349i 0.145311 + 0.0169844i −1.19361 2.13899i 1.23352 + 2.45614i −1.44301 + 2.43264i −2.84036 + 0.965591i −0.201508 + 0.0469224i
11.13 −1.32861 + 0.484545i −1.07834 + 1.35543i 1.53043 1.28755i 1.48986 + 0.174139i 0.775925 2.32335i −0.383526 0.763663i −1.40948 + 2.45222i −0.674386 2.92322i −2.06382 + 0.490538i
11.14 −1.29903 + 0.559026i −1.63070 0.583786i 1.37498 1.45239i 3.63522 + 0.424896i 2.44469 0.153247i 1.12021 + 2.23051i −0.974225 + 2.65535i 2.31839 + 1.90396i −4.95980 + 1.48022i
11.15 −1.29842 0.560449i −0.296891 1.70642i 1.37179 + 1.45540i −4.17186 0.487621i −0.570870 + 2.38204i −1.01368 2.01841i −0.965487 2.65854i −2.82371 + 1.01324i 5.14354 + 2.97125i
11.16 −1.29246 + 0.574065i 1.53515 0.802073i 1.34090 1.48391i −2.80026 0.327303i −1.52367 + 1.91792i 1.45058 + 2.88834i −0.881195 + 2.68766i 1.71336 2.46260i 3.80711 1.18450i
11.17 −1.27199 + 0.618090i −0.696679 + 1.58576i 1.23593 1.57241i −4.31632 0.504506i −0.0939720 2.44769i −1.58862 3.16321i −0.600204 + 2.76401i −2.02928 2.20953i 5.80216 2.02615i
11.18 −1.24556 0.669769i −1.70483 0.305889i 1.10282 + 1.66847i 2.63396 + 0.307866i 1.91858 + 1.52284i −0.382909 0.762434i −0.256135 2.81681i 2.81286 + 1.04297i −3.07455 2.14761i
11.19 −1.23855 0.682644i −0.996621 1.41660i 1.06799 + 1.69097i 0.173565 + 0.0202869i 0.267330 + 2.43486i 1.54089 + 3.06816i −0.168429 2.82341i −1.01349 + 2.82362i −0.201120 0.143610i
11.20 −1.19669 + 0.753613i −0.126707 1.72741i 0.864134 1.80368i 1.63478 + 0.191079i 1.45343 + 1.97169i −1.16083 2.31140i 0.325179 + 2.80967i −2.96789 + 0.437751i −2.10033 + 1.00333i
See next 80 embeddings (of 1872 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 635.104
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.d odd 2 1 inner
81.h odd 54 1 inner
648.bb even 54 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 648.2.bb.b 1872
8.d odd 2 1 inner 648.2.bb.b 1872
81.h odd 54 1 inner 648.2.bb.b 1872
648.bb even 54 1 inner 648.2.bb.b 1872
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
648.2.bb.b 1872 1.a even 1 1 trivial
648.2.bb.b 1872 8.d odd 2 1 inner
648.2.bb.b 1872 81.h odd 54 1 inner
648.2.bb.b 1872 648.bb even 54 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(13\!\cdots\!17\)\( T_{5}^{1852} + \)\(13\!\cdots\!30\)\( T_{5}^{1850} + \)\(11\!\cdots\!83\)\( T_{5}^{1848} + \)\(25\!\cdots\!99\)\( T_{5}^{1846} + \)\(20\!\cdots\!96\)\( T_{5}^{1844} + \)\(34\!\cdots\!98\)\( T_{5}^{1842} - \)\(13\!\cdots\!56\)\( T_{5}^{1840} - \)\(14\!\cdots\!57\)\( T_{5}^{1838} + \)\(33\!\cdots\!81\)\( T_{5}^{1836} + \)\(63\!\cdots\!84\)\( T_{5}^{1834} + \)\(55\!\cdots\!37\)\( T_{5}^{1832} + \)\(46\!\cdots\!62\)\( T_{5}^{1830} + \)\(22\!\cdots\!75\)\( T_{5}^{1828} + \)\(68\!\cdots\!80\)\( T_{5}^{1826} + \)\(10\!\cdots\!40\)\( T_{5}^{1824} - \)\(44\!\cdots\!29\)\( T_{5}^{1822} - \)\(28\!\cdots\!09\)\( T_{5}^{1820} + \)\(10\!\cdots\!61\)\( T_{5}^{1818} + \)\(17\!\cdots\!87\)\( T_{5}^{1816} + \)\(13\!\cdots\!74\)\( T_{5}^{1814} + \)\(13\!\cdots\!42\)\( T_{5}^{1812} + \)\(12\!\cdots\!24\)\( T_{5}^{1810} + \)\(47\!\cdots\!30\)\( T_{5}^{1808} + \)\(18\!\cdots\!81\)\( T_{5}^{1806} - \)\(53\!\cdots\!21\)\( T_{5}^{1804} - \)\(29\!\cdots\!23\)\( T_{5}^{1802} + \)\(20\!\cdots\!25\)\( T_{5}^{1800} + \)\(37\!\cdots\!30\)\( T_{5}^{1798} + \)\(22\!\cdots\!48\)\( T_{5}^{1796} + \)\(23\!\cdots\!99\)\( T_{5}^{1794} + \)\(36\!\cdots\!39\)\( T_{5}^{1792} - \)\(44\!\cdots\!14\)\( T_{5}^{1790} + \)\(75\!\cdots\!94\)\( T_{5}^{1788} + \)\(50\!\cdots\!05\)\( T_{5}^{1786} + \)\(23\!\cdots\!44\)\( T_{5}^{1784} + \)\(29\!\cdots\!87\)\( T_{5}^{1782} + \)\(57\!\cdots\!28\)\( T_{5}^{1780} + \)\(28\!\cdots\!15\)\( T_{5}^{1778} + \)\(25\!\cdots\!31\)\( T_{5}^{1776} + \)\(69\!\cdots\!30\)\( T_{5}^{1774} - \)\(20\!\cdots\!76\)\( T_{5}^{1772} - \)\(39\!\cdots\!95\)\( T_{5}^{1770} + \)\(15\!\cdots\!38\)\( T_{5}^{1768} + \)\(12\!\cdots\!32\)\( T_{5}^{1766} + \)\(29\!\cdots\!18\)\( T_{5}^{1764} + \)\(66\!\cdots\!92\)\( T_{5}^{1762} + \)\(32\!\cdots\!58\)\( T_{5}^{1760} + \)\(68\!\cdots\!50\)\( T_{5}^{1758} + \)\(88\!\cdots\!86\)\( T_{5}^{1756} + \)\(59\!\cdots\!91\)\( T_{5}^{1754} - \)\(12\!\cdots\!73\)\( T_{5}^{1752} + \)\(22\!\cdots\!60\)\( T_{5}^{1750} + \)\(35\!\cdots\!88\)\( T_{5}^{1748} + \)\(20\!\cdots\!52\)\( T_{5}^{1746} + \)\(52\!\cdots\!30\)\( T_{5}^{1744} + \)\(33\!\cdots\!40\)\( T_{5}^{1742} - \)\(62\!\cdots\!05\)\( T_{5}^{1740} + \)\(59\!\cdots\!49\)\( T_{5}^{1738} + \)\(40\!\cdots\!90\)\( T_{5}^{1736} - \)\(11\!\cdots\!74\)\( T_{5}^{1734} + \)\(12\!\cdots\!17\)\( T_{5}^{1732} + \)\(37\!\cdots\!76\)\( T_{5}^{1730} + \)\(12\!\cdots\!47\)\( T_{5}^{1728} + \)\(30\!\cdots\!40\)\( T_{5}^{1726} + \)\(24\!\cdots\!95\)\( T_{5}^{1724} - \)\(40\!\cdots\!42\)\( T_{5}^{1722} + \)\(26\!\cdots\!84\)\( T_{5}^{1720} + \)\(34\!\cdots\!09\)\( T_{5}^{1718} - \)\(59\!\cdots\!39\)\( T_{5}^{1716} + \)\(42\!\cdots\!18\)\( T_{5}^{1714} + \)\(22\!\cdots\!38\)\( T_{5}^{1712} + \)\(55\!\cdots\!13\)\( T_{5}^{1710} + \)\(12\!\cdots\!04\)\( T_{5}^{1708} + \)\(12\!\cdots\!94\)\( T_{5}^{1706} - \)\(12\!\cdots\!70\)\( T_{5}^{1704} + \)\(85\!\cdots\!81\)\( T_{5}^{1702} + \)\(17\!\cdots\!86\)\( T_{5}^{1700} - \)\(22\!\cdots\!48\)\( T_{5}^{1698} + \)\(83\!\cdots\!02\)\( T_{5}^{1696} + \)\(89\!\cdots\!27\)\( T_{5}^{1694} + \)\(20\!\cdots\!17\)\( T_{5}^{1692} + \)\(42\!\cdots\!15\)\( T_{5}^{1690} + \)\(45\!\cdots\!90\)\( T_{5}^{1688} - \)\(17\!\cdots\!24\)\( T_{5}^{1686} + \)\(19\!\cdots\!61\)\( T_{5}^{1684} + \)\(57\!\cdots\!75\)\( T_{5}^{1682} - \)\(68\!\cdots\!74\)\( T_{5}^{1680} + \)\(22\!\cdots\!46\)\( T_{5}^{1678} + \)\(25\!\cdots\!66\)\( T_{5}^{1676} + \)\(55\!\cdots\!41\)\( T_{5}^{1674} + \)\(10\!\cdots\!55\)\( T_{5}^{1672} + \)\(12\!\cdots\!71\)\( T_{5}^{1670} - \)\(46\!\cdots\!50\)\( T_{5}^{1668} + \)\(28\!\cdots\!99\)\( T_{5}^{1666} + \)\(13\!\cdots\!77\)\( T_{5}^{1664} - \)\(18\!\cdots\!23\)\( T_{5}^{1662} - \)\(48\!\cdots\!99\)\( T_{5}^{1660} + \)\(51\!\cdots\!82\)\( T_{5}^{1658} + \)\(11\!\cdots\!61\)\( T_{5}^{1656} + \)\(21\!\cdots\!15\)\( T_{5}^{1654} + \)\(26\!\cdots\!56\)\( T_{5}^{1652} - \)\(17\!\cdots\!80\)\( T_{5}^{1650} + \)\(17\!\cdots\!06\)\( T_{5}^{1648} + \)\(21\!\cdots\!71\)\( T_{5}^{1646} - \)\(40\!\cdots\!24\)\( T_{5}^{1644} - \)\(16\!\cdots\!38\)\( T_{5}^{1642} + \)\(79\!\cdots\!01\)\( T_{5}^{1640} + \)\(19\!\cdots\!36\)\( T_{5}^{1638} + \)\(35\!\cdots\!29\)\( T_{5}^{1636} + \)\(45\!\cdots\!45\)\( T_{5}^{1634} - \)\(57\!\cdots\!32\)\( T_{5}^{1632} - \)\(26\!\cdots\!44\)\( T_{5}^{1630} + \)\(26\!\cdots\!82\)\( T_{5}^{1628} - \)\(74\!\cdots\!57\)\( T_{5}^{1626} - \)\(31\!\cdots\!10\)\( T_{5}^{1624} + \)\(92\!\cdots\!72\)\( T_{5}^{1622} + \)\(24\!\cdots\!67\)\( T_{5}^{1620} + \)\(44\!\cdots\!92\)\( T_{5}^{1618} + \)\(62\!\cdots\!68\)\( T_{5}^{1616} - \)\(12\!\cdots\!78\)\( T_{5}^{1614} - \)\(81\!\cdots\!57\)\( T_{5}^{1612} + \)\(23\!\cdots\!89\)\( T_{5}^{1610} - \)\(11\!\cdots\!67\)\( T_{5}^{1608} - \)\(37\!\cdots\!43\)\( T_{5}^{1606} + \)\(79\!\cdots\!59\)\( T_{5}^{1604} + \)\(26\!\cdots\!88\)\( T_{5}^{1602} + \)\(46\!\cdots\!25\)\( T_{5}^{1600} + \)\(69\!\cdots\!67\)\( T_{5}^{1598} - \)\(20\!\cdots\!01\)\( T_{5}^{1596} - \)\(99\!\cdots\!11\)\( T_{5}^{1594} + \)\(12\!\cdots\!89\)\( T_{5}^{1592} - \)\(13\!\cdots\!10\)\( T_{5}^{1590} - \)\(27\!\cdots\!80\)\( T_{5}^{1588} + \)\(43\!\cdots\!99\)\( T_{5}^{1586} + \)\(23\!\cdots\!04\)\( T_{5}^{1584} + \)\(37\!\cdots\!84\)\( T_{5}^{1582} + \)\(63\!\cdots\!85\)\( T_{5}^{1580} - \)\(25\!\cdots\!66\)\( T_{5}^{1578} - \)\(55\!\cdots\!55\)\( T_{5}^{1576} - \)\(10\!\cdots\!67\)\( T_{5}^{1574} - \)\(12\!\cdots\!77\)\( T_{5}^{1572} - \)\(48\!\cdots\!99\)\( T_{5}^{1570} + \)\(15\!\cdots\!02\)\( T_{5}^{1568} + \)\(18\!\cdots\!46\)\( T_{5}^{1566} + \)\(24\!\cdots\!25\)\( T_{5}^{1564} + \)\(48\!\cdots\!34\)\( T_{5}^{1562} - \)\(25\!\cdots\!14\)\( T_{5}^{1560} + \)\(19\!\cdots\!47\)\( T_{5}^{1558} - \)\(80\!\cdots\!25\)\( T_{5}^{1556} - \)\(96\!\cdots\!54\)\( T_{5}^{1554} + \)\(15\!\cdots\!17\)\( T_{5}^{1552} - \)\(28\!\cdots\!64\)\( T_{5}^{1550} + \)\(13\!\cdots\!46\)\( T_{5}^{1548} + \)\(11\!\cdots\!42\)\( T_{5}^{1546} + \)\(32\!\cdots\!28\)\( T_{5}^{1544} - \)\(20\!\cdots\!24\)\( T_{5}^{1542} + \)\(72\!\cdots\!80\)\( T_{5}^{1540} - \)\(10\!\cdots\!03\)\( T_{5}^{1538} - \)\(58\!\cdots\!18\)\( T_{5}^{1536} + \)\(23\!\cdots\!93\)\( T_{5}^{1534} - \)\(38\!\cdots\!58\)\( T_{5}^{1532} + \)\(90\!\cdots\!58\)\( T_{5}^{1530} + \)\(26\!\cdots\!90\)\( T_{5}^{1528} + \)\(18\!\cdots\!75\)\( T_{5}^{1526} - \)\(13\!\cdots\!98\)\( T_{5}^{1524} + \)\(80\!\cdots\!49\)\( T_{5}^{1522} - \)\(83\!\cdots\!21\)\( T_{5}^{1520} - \)\(28\!\cdots\!61\)\( T_{5}^{1518} + \)\(19\!\cdots\!29\)\( T_{5}^{1516} - \)\(32\!\cdots\!16\)\( T_{5}^{1514} + \)\(55\!\cdots\!90\)\( T_{5}^{1512} - \)\(10\!\cdots\!70\)\( T_{5}^{1510} + \)\(90\!\cdots\!75\)\( T_{5}^{1508} - \)\(79\!\cdots\!48\)\( T_{5}^{1506} + \)\(57\!\cdots\!61\)\( T_{5}^{1504} - \)\(51\!\cdots\!72\)\( T_{5}^{1502} - \)\(10\!\cdots\!14\)\( T_{5}^{1500} + \)\(11\!\cdots\!47\)\( T_{5}^{1498} - \)\(19\!\cdots\!66\)\( T_{5}^{1496} + \)\(29\!\cdots\!12\)\( T_{5}^{1494} - \)\(16\!\cdots\!71\)\( T_{5}^{1492} + \)\(40\!\cdots\!15\)\( T_{5}^{1490} - \)\(38\!\cdots\!30\)\( T_{5}^{1488} + \)\(30\!\cdots\!97\)\( T_{5}^{1486} - \)\(24\!\cdots\!52\)\( T_{5}^{1484} - \)\(33\!\cdots\!91\)\( T_{5}^{1482} + \)\(54\!\cdots\!31\)\( T_{5}^{1480} - \)\(93\!\cdots\!40\)\( T_{5}^{1478} + \)\(13\!\cdots\!68\)\( T_{5}^{1476} - \)\(10\!\cdots\!36\)\( T_{5}^{1474} + \)\(16\!\cdots\!74\)\( T_{5}^{1472} - \)\(15\!\cdots\!96\)\( T_{5}^{1470} + \)\(12\!\cdots\!62\)\( T_{5}^{1468} - \)\(89\!\cdots\!18\)\( T_{5}^{1466} - \)\(82\!\cdots\!58\)\( T_{5}^{1464} + \)\(19\!\cdots\!95\)\( T_{5}^{1462} - \)\(34\!\cdots\!52\)\( T_{5}^{1460} + \)\(49\!\cdots\!31\)\( T_{5}^{1458} - \)\(46\!\cdots\!60\)\( T_{5}^{1456} + \)\(56\!\cdots\!07\)\( T_{5}^{1454} - \)\(52\!\cdots\!19\)\( T_{5}^{1452} + \)\(40\!\cdots\!73\)\( T_{5}^{1450} - \)\(24\!\cdots\!53\)\( T_{5}^{1448} - \)\(19\!\cdots\!63\)\( T_{5}^{1446} + \)\(57\!\cdots\!77\)\( T_{5}^{1444} - \)\(10\!\cdots\!78\)\( T_{5}^{1442} + \)\(14\!\cdots\!44\)\( T_{5}^{1440} - \)\(14\!\cdots\!99\)\( T_{5}^{1438} + \)\(16\!\cdots\!75\)\( T_{5}^{1436} - \)\(14\!\cdots\!91\)\( T_{5}^{1434} + \)\(10\!\cdots\!93\)\( T_{5}^{1432} - \)\(52\!\cdots\!42\)\( T_{5}^{1430} - \)\(45\!\cdots\!00\)\( T_{5}^{1428} + \)\(13\!\cdots\!08\)\( T_{5}^{1426} - \)\(24\!\cdots\!32\)\( T_{5}^{1424} + \)\(32\!\cdots\!68\)\( T_{5}^{1422} - \)\(34\!\cdots\!63\)\( T_{5}^{1420} + \)\(35\!\cdots\!49\)\( T_{5}^{1418} - \)\(29\!\cdots\!93\)\( T_{5}^{1416} + \)\(19\!\cdots\!62\)\( T_{5}^{1414} - \)\(73\!\cdots\!71\)\( T_{5}^{1412} - \)\(10\!\cdots\!42\)\( T_{5}^{1410} + \)\(27\!\cdots\!76\)\( T_{5}^{1408} - \)\(43\!\cdots\!91\)\( T_{5}^{1406} + \)\(56\!\cdots\!78\)\( T_{5}^{1404} - \)\(58\!\cdots\!05\)\( T_{5}^{1402} + \)\(56\!\cdots\!21\)\( T_{5}^{1400} - \)\(44\!\cdots\!37\)\( T_{5}^{1398} + \)\(26\!\cdots\!57\)\( T_{5}^{1396} - \)\(53\!\cdots\!22\)\( T_{5}^{1394} - \)\(18\!\cdots\!24\)\( T_{5}^{1392} + \)\(40\!\cdots\!20\)\( T_{5}^{1390} - \)\(58\!\cdots\!12\)\( T_{5}^{1388} + \)\(68\!\cdots\!19\)\( T_{5}^{1386} - \)\(67\!\cdots\!50\)\( T_{5}^{1384} + \)\(58\!\cdots\!13\)\( T_{5}^{1382} - \)\(41\!\cdots\!34\)\( T_{5}^{1380} + \)\(18\!\cdots\!84\)\( T_{5}^{1378} + \)\(33\!\cdots\!89\)\( T_{5}^{1376} - \)\(24\!\cdots\!71\)\( T_{5}^{1374} + \)\(41\!\cdots\!28\)\( T_{5}^{1372} - \)\(51\!\cdots\!37\)\( T_{5}^{1370} + \)\(55\!\cdots\!65\)\( T_{5}^{1368} - \)\(49\!\cdots\!51\)\( T_{5}^{1366} + \)\(39\!\cdots\!61\)\( T_{5}^{1364} - \)\(25\!\cdots\!88\)\( T_{5}^{1362} + \)\(89\!\cdots\!56\)\( T_{5}^{1360} + \)\(53\!\cdots\!99\)\( T_{5}^{1358} - \)\(17\!\cdots\!62\)\( T_{5}^{1356} + \)\(24\!\cdots\!99\)\( T_{5}^{1354} - \)\(28\!\cdots\!48\)\( T_{5}^{1352} + \)\(28\!\cdots\!41\)\( T_{5}^{1350} - \)\(24\!\cdots\!53\)\( T_{5}^{1348} + \)\(18\!\cdots\!28\)\( T_{5}^{1346} - \)\(10\!\cdots\!84\)\( T_{5}^{1344} + \)\(30\!\cdots\!76\)\( T_{5}^{1342} + \)\(32\!\cdots\!03\)\( T_{5}^{1340} - \)\(78\!\cdots\!61\)\( T_{5}^{1338} + \)\(10\!\cdots\!24\)\( T_{5}^{1336} - \)\(11\!\cdots\!59\)\( T_{5}^{1334} + \)\(10\!\cdots\!42\)\( T_{5}^{1332} - \)\(86\!\cdots\!47\)\( T_{5}^{1330} + \)\(62\!\cdots\!23\)\( T_{5}^{1328} - \)\(35\!\cdots\!42\)\( T_{5}^{1326} + \)\(87\!\cdots\!34\)\( T_{5}^{1324} + \)\(10\!\cdots\!71\)\( T_{5}^{1322} - \)\(23\!\cdots\!42\)\( T_{5}^{1320} + \)\(29\!\cdots\!70\)\( T_{5}^{1318} - \)\(30\!\cdots\!13\)\( T_{5}^{1316} + \)\(27\!\cdots\!77\)\( T_{5}^{1314} - \)\(21\!\cdots\!75\)\( T_{5}^{1312} + \)\(15\!\cdots\!45\)\( T_{5}^{1310} - \)\(85\!\cdots\!03\)\( T_{5}^{1308} + \)\(20\!\cdots\!93\)\( T_{5}^{1306} + \)\(22\!\cdots\!41\)\( T_{5}^{1304} - \)\(47\!\cdots\!64\)\( T_{5}^{1302} + \)\(59\!\cdots\!28\)\( T_{5}^{1300} - \)\(60\!\cdots\!81\)\( T_{5}^{1298} + \)\(52\!\cdots\!88\)\( T_{5}^{1296} - \)\(39\!\cdots\!31\)\( T_{5}^{1294} + \)\(28\!\cdots\!13\)\( T_{5}^{1292} - \)\(16\!\cdots\!90\)\( T_{5}^{1290} + \)\(45\!\cdots\!87\)\( T_{5}^{1288} + \)\(26\!\cdots\!31\)\( T_{5}^{1286} - \)\(61\!\cdots\!41\)\( T_{5}^{1284} + \)\(80\!\cdots\!73\)\( T_{5}^{1282} - \)\(82\!\cdots\!22\)\( T_{5}^{1280} + \)\(68\!\cdots\!25\)\( T_{5}^{1278} - \)\(50\!\cdots\!00\)\( T_{5}^{1276} + \)\(37\!\cdots\!42\)\( T_{5}^{1274} - \)\(21\!\cdots\!43\)\( T_{5}^{1272} + \)\(63\!\cdots\!77\)\( T_{5}^{1270} + \)\(17\!\cdots\!42\)\( T_{5}^{1268} - \)\(51\!\cdots\!36\)\( T_{5}^{1266} + \)\(78\!\cdots\!56\)\( T_{5}^{1264} - \)\(79\!\cdots\!05\)\( T_{5}^{1262} + \)\(61\!\cdots\!17\)\( T_{5}^{1260} - \)\(44\!\cdots\!88\)\( T_{5}^{1258} + \)\(38\!\cdots\!97\)\( T_{5}^{1256} - \)\(22\!\cdots\!55\)\( T_{5}^{1254} + \)\(67\!\cdots\!86\)\( T_{5}^{1252} - \)\(28\!\cdots\!79\)\( T_{5}^{1250} - \)\(19\!\cdots\!42\)\( T_{5}^{1248} + \)\(52\!\cdots\!91\)\( T_{5}^{1246} - \)\(54\!\cdots\!02\)\( T_{5}^{1244} + \)\(34\!\cdots\!10\)\( T_{5}^{1242} - \)\(24\!\cdots\!70\)\( T_{5}^{1240} + \)\(28\!\cdots\!27\)\( T_{5}^{1238} - \)\(16\!\cdots\!26\)\( T_{5}^{1236} + \)\(39\!\cdots\!35\)\( T_{5}^{1234} - \)\(53\!\cdots\!37\)\( T_{5}^{1232} + \)\(55\!\cdots\!53\)\( T_{5}^{1230} + \)\(30\!\cdots\!52\)\( T_{5}^{1228} - \)\(29\!\cdots\!84\)\( T_{5}^{1226} + \)\(11\!\cdots\!92\)\( T_{5}^{1224} - \)\(71\!\cdots\!50\)\( T_{5}^{1222} + \)\(16\!\cdots\!97\)\( T_{5}^{1220} - \)\(98\!\cdots\!97\)\( T_{5}^{1218} + \)\(13\!\cdots\!75\)\( T_{5}^{1216} - \)\(11\!\cdots\!07\)\( T_{5}^{1214} + \)\(60\!\cdots\!08\)\( T_{5}^{1212} + \)\(15\!\cdots\!53\)\( T_{5}^{1210} - \)\(13\!\cdots\!46\)\( T_{5}^{1208} - \)\(14\!\cdots\!58\)\( T_{5}^{1206} + \)\(14\!\cdots\!49\)\( T_{5}^{1204} + \)\(77\!\cdots\!17\)\( T_{5}^{1202} - \)\(47\!\cdots\!50\)\( T_{5}^{1200} + \)\(27\!\cdots\!42\)\( T_{5}^{1198} + \)\(28\!\cdots\!30\)\( T_{5}^{1196} + \)\(34\!\cdots\!70\)\( T_{5}^{1194} + \)\(83\!\cdots\!51\)\( T_{5}^{1192} - \)\(51\!\cdots\!51\)\( T_{5}^{1190} - \)\(22\!\cdots\!44\)\( T_{5}^{1188} + \)\(28\!\cdots\!08\)\( T_{5}^{1186} + \)\(30\!\cdots\!46\)\( T_{5}^{1184} - \)\(20\!\cdots\!68\)\( T_{5}^{1182} + \)\(12\!\cdots\!52\)\( T_{5}^{1180} + \)\(26\!\cdots\!44\)\( T_{5}^{1178} + \)\(11\!\cdots\!11\)\( T_{5}^{1176} + \)\(38\!\cdots\!78\)\( T_{5}^{1174} - \)\(18\!\cdots\!82\)\( T_{5}^{1172} - \)\(13\!\cdots\!49\)\( T_{5}^{1170} + \)\(17\!\cdots\!46\)\( T_{5}^{1168} + \)\(97\!\cdots\!16\)\( T_{5}^{1166} - \)\(73\!\cdots\!98\)\( T_{5}^{1164} + \)\(11\!\cdots\!40\)\( T_{5}^{1162} + \)\(14\!\cdots\!40\)\( T_{5}^{1160} + \)\(22\!\cdots\!31\)\( T_{5}^{1158} + \)\(13\!\cdots\!91\)\( T_{5}^{1156} - \)\(48\!\cdots\!24\)\( T_{5}^{1154} - \)\(45\!\cdots\!67\)\( T_{5}^{1152} + \)\(67\!\cdots\!01\)\( T_{5}^{1150} + \)\(25\!\cdots\!75\)\( T_{5}^{1148} - \)\(21\!\cdots\!45\)\( T_{5}^{1146} + \)\(62\!\cdots\!59\)\( T_{5}^{1144} + \)\(51\!\cdots\!72\)\( T_{5}^{1142} + \)\(24\!\cdots\!21\)\( T_{5}^{1140} + \)\(39\!\cdots\!01\)\( T_{5}^{1138} - \)\(93\!\cdots\!48\)\( T_{5}^{1136} - \)\(10\!\cdots\!95\)\( T_{5}^{1134} + \)\(18\!\cdots\!86\)\( T_{5}^{1132} + \)\(53\!\cdots\!67\)\( T_{5}^{1130} - \)\(45\!\cdots\!04\)\( T_{5}^{1128} + \)\(21\!\cdots\!94\)\( T_{5}^{1126} + \)\(14\!\cdots\!29\)\( T_{5}^{1124} - \)\(56\!\cdots\!23\)\( T_{5}^{1122} + \)\(81\!\cdots\!31\)\( T_{5}^{1120} - \)\(70\!\cdots\!34\)\( T_{5}^{1118} - \)\(14\!\cdots\!41\)\( T_{5}^{1116} + \)\(35\!\cdots\!76\)\( T_{5}^{1114} + \)\(96\!\cdots\!85\)\( T_{5}^{1112} - \)\(70\!\cdots\!87\)\( T_{5}^{1110} + \)\(48\!\cdots\!23\)\( T_{5}^{1108} + \)\(30\!\cdots\!48\)\( T_{5}^{1106} - \)\(42\!\cdots\!19\)\( T_{5}^{1104} + \)\(12\!\cdots\!28\)\( T_{5}^{1102} + \)\(13\!\cdots\!37\)\( T_{5}^{1100} - \)\(12\!\cdots\!11\)\( T_{5}^{1098} + \)\(50\!\cdots\!82\)\( T_{5}^{1096} + \)\(14\!\cdots\!21\)\( T_{5}^{1094} - \)\(72\!\cdots\!55\)\( T_{5}^{1092} + \)\(77\!\cdots\!43\)\( T_{5}^{1090} + \)\(47\!\cdots\!46\)\( T_{5}^{1088} - \)\(90\!\cdots\!50\)\( T_{5}^{1086} + \)\(15\!\cdots\!47\)\( T_{5}^{1084} + \)\(57\!\cdots\!16\)\( T_{5}^{1082} - \)\(31\!\cdots\!52\)\( T_{5}^{1080} + \)\(48\!\cdots\!93\)\( T_{5}^{1078} + \)\(19\!\cdots\!96\)\( T_{5}^{1076} - \)\(32\!\cdots\!99\)\( T_{5}^{1074} + \)\(82\!\cdots\!75\)\( T_{5}^{1072} + \)\(52\!\cdots\!35\)\( T_{5}^{1070} + \)\(25\!\cdots\!03\)\( T_{5}^{1068} + \)\(15\!\cdots\!50\)\( T_{5}^{1066} + \)\(84\!\cdots\!18\)\( T_{5}^{1064} + \)\(76\!\cdots\!54\)\( T_{5}^{1062} + \)\(37\!\cdots\!47\)\( T_{5}^{1060} + \)\(20\!\cdots\!06\)\( T_{5}^{1058} + \)\(95\!\cdots\!29\)\( T_{5}^{1056} + \)\(63\!\cdots\!39\)\( T_{5}^{1054} + \)\(46\!\cdots\!84\)\( T_{5}^{1052} + \)\(69\!\cdots\!66\)\( T_{5}^{1050} + \)\(10\!\cdots\!10\)\( T_{5}^{1048} + \)\(78\!\cdots\!45\)\( T_{5}^{1046} + \)\(17\!\cdots\!99\)\( T_{5}^{1044} + \)\(21\!\cdots\!32\)\( T_{5}^{1042} + \)\(15\!\cdots\!60\)\( T_{5}^{1040} + \)\(35\!\cdots\!38\)\( T_{5}^{1038} + \)\(36\!\cdots\!57\)\( T_{5}^{1036} + \)\(29\!\cdots\!15\)\( T_{5}^{1034} + \)\(85\!\cdots\!60\)\( T_{5}^{1032} + \)\(59\!\cdots\!97\)\( T_{5}^{1030} + \)\(47\!\cdots\!46\)\( T_{5}^{1028} + \)\(16\!\cdots\!04\)\( T_{5}^{1026} + \)\(11\!\cdots\!37\)\( T_{5}^{1024} + \)\(81\!\cdots\!14\)\( T_{5}^{1022} + \)\(30\!\cdots\!11\)\( T_{5}^{1020} + \)\(18\!\cdots\!40\)\( T_{5}^{1018} + \)\(13\!\cdots\!73\)\( T_{5}^{1016} + \)\(55\!\cdots\!48\)\( T_{5}^{1014} + \)\(29\!\cdots\!44\)\( T_{5}^{1012} + \)\(20\!\cdots\!53\)\( T_{5}^{1010} + \)\(92\!\cdots\!75\)\( T_{5}^{1008} + \)\(49\!\cdots\!72\)\( T_{5}^{1006} + \)\(32\!\cdots\!65\)\( T_{5}^{1004} + \)\(14\!\cdots\!19\)\( T_{5}^{1002} + \)\(76\!\cdots\!09\)\( T_{5}^{1000} + \)\(49\!\cdots\!16\)\( T_{5}^{998} + \)\(23\!\cdots\!71\)\( T_{5}^{996} + \)\(11\!\cdots\!47\)\( T_{5}^{994} + \)\(68\!\cdots\!17\)\( T_{5}^{992} + \)\(34\!\cdots\!20\)\( T_{5}^{990} + \)\(16\!\cdots\!40\)\( T_{5}^{988} + \)\(98\!\cdots\!04\)\( T_{5}^{986} + \)\(49\!\cdots\!42\)\( T_{5}^{984} + \)\(23\!\cdots\!33\)\( T_{5}^{982} + \)\(13\!\cdots\!86\)\( T_{5}^{980} + \)\(67\!\cdots\!11\)\( T_{5}^{978} + \)\(31\!\cdots\!94\)\( T_{5}^{976} + \)\(17\!\cdots\!39\)\( T_{5}^{974} + \)\(87\!\cdots\!07\)\( T_{5}^{972} + \)\(41\!\cdots\!69\)\( T_{5}^{970} + \)\(21\!\cdots\!89\)\( T_{5}^{968} + \)\(11\!\cdots\!41\)\( T_{5}^{966} + \)\(52\!\cdots\!74\)\( T_{5}^{964} + \)\(26\!\cdots\!90\)\( T_{5}^{962} + \)\(13\!\cdots\!02\)\( T_{5}^{960} + \)\(61\!\cdots\!57\)\( T_{5}^{958} + \)\(30\!\cdots\!26\)\( T_{5}^{956} + \)\(14\!\cdots\!79\)\( T_{5}^{954} + \)\(70\!\cdots\!24\)\( T_{5}^{952} + \)\(33\!\cdots\!92\)\( T_{5}^{950} + \)\(16\!\cdots\!23\)\( T_{5}^{948} + \)\(75\!\cdots\!11\)\( T_{5}^{946} + \)\(35\!\cdots\!97\)\( T_{5}^{944} + \)\(16\!\cdots\!61\)\( T_{5}^{942} + \)\(76\!\cdots\!34\)\( T_{5}^{940} + \)\(35\!\cdots\!17\)\( T_{5}^{938} + \)\(16\!\cdots\!29\)\( T_{5}^{936} + \)\(74\!\cdots\!61\)\( T_{5}^{934} + \)\(33\!\cdots\!13\)\( T_{5}^{932} + \)\(15\!\cdots\!13\)\( T_{5}^{930} + \)\(68\!\cdots\!75\)\( T_{5}^{928} + \)\(30\!\cdots\!76\)\( T_{5}^{926} + \)\(13\!\cdots\!22\)\( T_{5}^{924} + \)\(59\!\cdots\!71\)\( T_{5}^{922} + \)\(25\!\cdots\!80\)\( T_{5}^{920} + \)\(11\!\cdots\!48\)\( T_{5}^{918} + \)\(50\!\cdots\!41\)\( T_{5}^{916} + \)\(21\!\cdots\!42\)\( T_{5}^{914} + \)\(95\!\cdots\!90\)\( T_{5}^{912} + \)\(40\!\cdots\!53\)\( T_{5}^{910} + \)\(17\!\cdots\!99\)\( T_{5}^{908} + \)\(72\!\cdots\!21\)\( T_{5}^{906} + \)\(30\!\cdots\!92\)\( T_{5}^{904} + \)\(12\!\cdots\!01\)\( T_{5}^{902} + \)\(53\!\cdots\!97\)\( T_{5}^{900} + \)\(22\!\cdots\!67\)\( T_{5}^{898} + \)\(95\!\cdots\!43\)\( T_{5}^{896} + \)\(39\!\cdots\!21\)\( T_{5}^{894} + \)\(16\!\cdots\!55\)\( T_{5}^{892} + \)\(65\!\cdots\!82\)\( T_{5}^{890} + \)\(26\!\cdots\!03\)\( T_{5}^{888} + \)\(10\!\cdots\!12\)\( T_{5}^{886} + \)\(42\!\cdots\!97\)\( T_{5}^{884} + \)\(17\!\cdots\!57\)\( T_{5}^{882} + \)\(71\!\cdots\!61\)\( T_{5}^{880} + \)\(28\!\cdots\!12\)\( T_{5}^{878} + \)\(11\!\cdots\!21\)\( T_{5}^{876} + \)\(44\!\cdots\!89\)\( T_{5}^{874} + \)\(16\!\cdots\!11\)\( T_{5}^{872} + \)\(62\!\cdots\!74\)\( T_{5}^{870} + \)\(23\!\cdots\!60\)\( T_{5}^{868} + \)\(92\!\cdots\!76\)\( T_{5}^{866} + \)\(37\!\cdots\!19\)\( T_{5}^{864} + \)\(15\!\cdots\!77\)\( T_{5}^{862} + \)\(59\!\cdots\!59\)\( T_{5}^{860} + \)\(22\!\cdots\!14\)\( T_{5}^{858} + \)\(80\!\cdots\!04\)\( T_{5}^{856} + \)\(27\!\cdots\!41\)\( T_{5}^{854} + \)\(96\!\cdots\!13\)\( T_{5}^{852} + \)\(34\!\cdots\!09\)\( T_{5}^{850} + \)\(13\!\cdots\!54\)\( T_{5}^{848} + \)\(54\!\cdots\!24\)\( T_{5}^{846} + \)\(22\!\cdots\!40\)\( T_{5}^{844} + \)\(88\!\cdots\!18\)\( T_{5}^{842} + \)\(31\!\cdots\!57\)\( T_{5}^{840} + \)\(10\!\cdots\!68\)\( T_{5}^{838} + \)\(31\!\cdots\!47\)\( T_{5}^{836} + \)\(92\!\cdots\!78\)\( T_{5}^{834} + \)\(29\!\cdots\!57\)\( T_{5}^{832} + \)\(11\!\cdots\!29\)\( T_{5}^{830} + \)\(50\!\cdots\!98\)\( T_{5}^{828} + \)\(22\!\cdots\!33\)\( T_{5}^{826} + \)\(87\!\cdots\!68\)\( T_{5}^{824} + \)\(29\!\cdots\!27\)\( T_{5}^{822} + \)\(85\!\cdots\!25\)\( T_{5}^{820} + \)\(19\!\cdots\!93\)\( T_{5}^{818} + \)\(35\!\cdots\!23\)\( T_{5}^{816} + \)\(57\!\cdots\!65\)\( T_{5}^{814} + \)\(27\!\cdots\!91\)\( T_{5}^{812} + \)\(22\!\cdots\!40\)\( T_{5}^{810} + \)\(14\!\cdots\!39\)\( T_{5}^{808} + \)\(67\!\cdots\!46\)\( T_{5}^{806} + \)\(25\!\cdots\!28\)\( T_{5}^{804} + \)\(74\!\cdots\!25\)\( T_{5}^{802} + \)\(16\!\cdots\!96\)\( T_{5}^{800} + \)\(18\!\cdots\!57\)\( T_{5}^{798} - \)\(36\!\cdots\!34\)\( T_{5}^{796} - \)\(24\!\cdots\!83\)\( T_{5}^{794} - \)\(33\!\cdots\!20\)\( T_{5}^{792} + \)\(27\!\cdots\!46\)\( T_{5}^{790} + \)\(23\!\cdots\!87\)\( T_{5}^{788} + \)\(10\!\cdots\!83\)\( T_{5}^{786} + \)\(35\!\cdots\!88\)\( T_{5}^{784} + \)\(86\!\cdots\!77\)\( T_{5}^{782} + \)\(11\!\cdots\!50\)\( T_{5}^{780} - \)\(17\!\cdots\!26\)\( T_{5}^{778} - \)\(16\!\cdots\!81\)\( T_{5}^{776} - \)\(51\!\cdots\!16\)\( T_{5}^{774} - \)\(35\!\cdots\!68\)\( T_{5}^{772} + \)\(48\!\cdots\!52\)\( T_{5}^{770} + \)\(31\!\cdots\!96\)\( T_{5}^{768} + \)\(12\!\cdots\!79\)\( T_{5}^{766} + \)\(33\!\cdots\!26\)\( T_{5}^{764} + \)\(58\!\cdots\!96\)\( T_{5}^{762} - \)\(16\!\cdots\!37\)\( T_{5}^{760} - \)\(60\!\cdots\!38\)\( T_{5}^{758} - \)\(26\!\cdots\!49\)\( T_{5}^{756} - \)\(67\!\cdots\!00\)\( T_{5}^{754} - \)\(77\!\cdots\!64\)\( T_{5}^{752} + \)\(21\!\cdots\!36\)\( T_{5}^{750} + \)\(17\!\cdots\!94\)\( T_{5}^{748} + \)\(69\!\cdots\!82\)\( T_{5}^{746} + \)\(18\!\cdots\!52\)\( T_{5}^{744} + \)\(29\!\cdots\!52\)\( T_{5}^{742} - \)\(18\!\cdots\!26\)\( T_{5}^{740} - \)\(29\!\cdots\!17\)\( T_{5}^{738} - \)\(10\!\cdots\!83\)\( T_{5}^{736} - \)\(23\!\cdots\!68\)\( T_{5}^{734} - \)\(27\!\cdots\!16\)\( T_{5}^{732} + \)\(56\!\cdots\!97\)\( T_{5}^{730} + \)\(49\!\cdots\!52\)\( T_{5}^{728} + \)\(17\!\cdots\!08\)\( T_{5}^{726} + \)\(38\!\cdots\!02\)\( T_{5}^{724} + \)\(29\!\cdots\!03\)\( T_{5}^{722} - \)\(11\!\cdots\!17\)\( T_{5}^{720} - \)\(59\!\cdots\!31\)\( T_{5}^{718} - \)\(15\!\cdots\!72\)\( T_{5}^{716} - \)\(29\!\cdots\!43\)\( T_{5}^{714} - \)\(12\!\cdots\!15\)\( T_{5}^{712} + \)\(18\!\cdots\!34\)\( T_{5}^{710} + \)\(87\!\cdots\!09\)\( T_{5}^{708} + \)\(19\!\cdots\!53\)\( T_{5}^{706} + \)\(18\!\cdots\!98\)\( T_{5}^{704} - \)\(35\!\cdots\!67\)\( T_{5}^{702} - \)\(20\!\cdots\!33\)\( T_{5}^{700} - \)\(60\!\cdots\!79\)\( T_{5}^{698} - \)\(13\!\cdots\!08\)\( T_{5}^{696} - \)\(10\!\cdots\!24\)\( T_{5}^{694} + \)\(60\!\cdots\!01\)\( T_{5}^{692} + \)\(29\!\cdots\!84\)\( T_{5}^{690} + \)\(61\!\cdots\!77\)\( T_{5}^{688} + \)\(45\!\cdots\!28\)\( T_{5}^{686} - \)\(10\!\cdots\!22\)\( T_{5}^{684} - \)\(49\!\cdots\!34\)\( T_{5}^{682} - \)\(14\!\cdots\!17\)\( T_{5}^{680} - \)\(33\!\cdots\!47\)\( T_{5}^{678} - \)\(26\!\cdots\!77\)\( T_{5}^{676} + \)\(14\!\cdots\!20\)\( T_{5}^{674} + \)\(65\!\cdots\!18\)\( T_{5}^{672} + \)\(11\!\cdots\!33\)\( T_{5}^{670} + \)\(42\!\cdots\!05\)\( T_{5}^{668} - \)\(24\!\cdots\!98\)\( T_{5}^{666} - \)\(79\!\cdots\!12\)\( T_{5}^{664} - \)\(23\!\cdots\!88\)\( T_{5}^{662} - \)\(55\!\cdots\!27\)\( T_{5}^{660} - \)\(35\!\cdots\!47\)\( T_{5}^{658} + \)\(28\!\cdots\!39\)\( T_{5}^{656} + \)\(10\!\cdots\!48\)\( T_{5}^{654} + \)\(13\!\cdots\!27\)\( T_{5}^{652} - \)\(37\!\cdots\!72\)\( T_{5}^{650} - \)\(42\!\cdots\!01\)\( T_{5}^{648} - \)\(89\!\cdots\!34\)\( T_{5}^{646} - \)\(25\!\cdots\!00\)\( T_{5}^{644} - \)\(55\!\cdots\!95\)\( T_{5}^{642} - \)\(82\!\cdots\!20\)\( T_{5}^{640} + \)\(36\!\cdots\!74\)\( T_{5}^{638} + \)\(99\!\cdots\!61\)\( T_{5}^{636} + \)\(79\!\cdots\!35\)\( T_{5}^{634} - \)\(12\!\cdots\!46\)\( T_{5}^{632} - \)\(39\!\cdots\!46\)\( T_{5}^{630} - \)\(50\!\cdots\!52\)\( T_{5}^{628} - \)\(17\!\cdots\!46\)\( T_{5}^{626} - \)\(32\!\cdots\!86\)\( T_{5}^{624} + \)\(52\!\cdots\!17\)\( T_{5}^{622} + \)\(27\!\cdots\!92\)\( T_{5}^{620} + \)\(56\!\cdots\!13\)\( T_{5}^{618} + \)\(33\!\cdots\!93\)\( T_{5}^{616} - \)\(82\!\cdots\!77\)\( T_{5}^{614} - \)\(21\!\cdots\!86\)\( T_{5}^{612} - \)\(22\!\cdots\!78\)\( T_{5}^{610} - \)\(10\!\cdots\!36\)\( T_{5}^{608} - \)\(10\!\cdots\!21\)\( T_{5}^{606} + \)\(14\!\cdots\!60\)\( T_{5}^{604} + \)\(13\!\cdots\!36\)\( T_{5}^{602} + \)\(20\!\cdots\!97\)\( T_{5}^{600} + \)\(14\!\cdots\!35\)\( T_{5}^{598} - \)\(32\!\cdots\!91\)\( T_{5}^{596} - \)\(99\!\cdots\!44\)\( T_{5}^{594} - \)\(30\!\cdots\!03\)\( T_{5}^{592} - \)\(49\!\cdots\!15\)\( T_{5}^{590} + \)\(15\!\cdots\!27\)\( T_{5}^{588} - \)\(79\!\cdots\!36\)\( T_{5}^{586} + \)\(53\!\cdots\!24\)\( T_{5}^{584} + \)\(27\!\cdots\!88\)\( T_{5}^{582} + \)\(89\!\cdots\!32\)\( T_{5}^{580} - \)\(90\!\cdots\!69\)\( T_{5}^{578} - \)\(26\!\cdots\!31\)\( T_{5}^{576} + \)\(72\!\cdots\!21\)\( T_{5}^{574} - \)\(18\!\cdots\!26\)\( T_{5}^{572} + \)\(17\!\cdots\!54\)\( T_{5}^{570} - \)\(46\!\cdots\!46\)\( T_{5}^{568} + \)\(14\!\cdots\!30\)\( T_{5}^{566} + \)\(12\!\cdots\!59\)\( T_{5}^{564} + \)\(23\!\cdots\!26\)\( T_{5}^{562} - \)\(37\!\cdots\!78\)\( T_{5}^{560} - \)\(68\!\cdots\!30\)\( T_{5}^{558} + \)\(88\!\cdots\!13\)\( T_{5}^{556} - \)\(44\!\cdots\!99\)\( T_{5}^{554} + \)\(54\!\cdots\!94\)\( T_{5}^{552} - \)\(12\!\cdots\!07\)\( T_{5}^{550} + \)\(24\!\cdots\!52\)\( T_{5}^{548} - \)\(11\!\cdots\!71\)\( T_{5}^{546} + \)\(51\!\cdots\!77\)\( T_{5}^{544} - \)\(29\!\cdots\!78\)\( T_{5}^{542} + \)\(48\!\cdots\!53\)\( T_{5}^{540} - \)\(53\!\cdots\!50\)\( T_{5}^{538} - \)\(15\!\cdots\!67\)\( T_{5}^{536} + \)\(89\!\cdots\!35\)\( T_{5}^{534} - \)\(29\!\cdots\!71\)\( T_{5}^{532} + \)\(79\!\cdots\!29\)\( T_{5}^{530} + \)\(68\!\cdots\!08\)\( T_{5}^{528} + \)\(22\!\cdots\!91\)\( T_{5}^{526} + \)\(41\!\cdots\!08\)\( T_{5}^{524} - \)\(25\!\cdots\!42\)\( T_{5}^{522} - \)\(40\!\cdots\!85\)\( T_{5}^{520} - \)\(81\!\cdots\!47\)\( T_{5}^{518} - \)\(80\!\cdots\!66\)\( T_{5}^{516} - \)\(10\!\cdots\!67\)\( T_{5}^{514} + \)\(26\!\cdots\!59\)\( T_{5}^{512} + \)\(50\!\cdots\!90\)\( T_{5}^{510} + \)\(11\!\cdots\!58\)\( T_{5}^{508} + \)\(60\!\cdots\!52\)\( T_{5}^{506} + \)\(28\!\cdots\!07\)\( T_{5}^{504} - \)\(18\!\cdots\!31\)\( T_{5}^{502} - \)\(27\!\cdots\!18\)\( T_{5}^{500} - \)\(51\!\cdots\!67\)\( T_{5}^{498} - \)\(25\!\cdots\!00\)\( T_{5}^{496} + \)\(47\!\cdots\!73\)\( T_{5}^{494} + \)\(21\!\cdots\!14\)\( T_{5}^{492} + \)\(33\!\cdots\!74\)\( T_{5}^{490} + \)\(34\!\cdots\!03\)\( T_{5}^{488} + \)\(91\!\cdots\!59\)\( T_{5}^{486} - \)\(36\!\cdots\!47\)\( T_{5}^{484} - \)\(97\!\cdots\!66\)\( T_{5}^{482} - \)\(14\!\cdots\!42\)\( T_{5}^{480} - \)\(12\!\cdots\!95\)\( T_{5}^{478} + \)\(61\!\cdots\!74\)\( T_{5}^{476} + \)\(42\!\cdots\!40\)\( T_{5}^{474} + \)\(79\!\cdots\!86\)\( T_{5}^{472} + \)\(89\!\cdots\!73\)\( T_{5}^{470} + \)\(52\!\cdots\!30\)\( T_{5}^{468} - \)\(32\!\cdots\!53\)\( T_{5}^{466} - \)\(14\!\cdots\!65\)\( T_{5}^{464} - \)\(25\!\cdots\!01\)\( T_{5}^{462} - \)\(24\!\cdots\!13\)\( T_{5}^{460} - \)\(16\!\cdots\!91\)\( T_{5}^{458} + \)\(44\!\cdots\!10\)\( T_{5}^{456} + \)\(91\!\cdots\!59\)\( T_{5}^{454} + \)\(11\!\cdots\!64\)\( T_{5}^{452} + \)\(77\!\cdots\!58\)\( T_{5}^{450} - \)\(10\!\cdots\!99\)\( T_{5}^{448} - \)\(13\!\cdots\!95\)\( T_{5}^{446} - \)\(23\!\cdots\!60\)\( T_{5}^{444} - \)\(23\!\cdots\!68\)\( T_{5}^{442} - \)\(40\!\cdots\!78\)\( T_{5}^{440} + \)\(33\!\cdots\!98\)\( T_{5}^{438} + \)\(73\!\cdots\!48\)\( T_{5}^{436} + \)\(89\!\cdots\!87\)\( T_{5}^{434} + \)\(64\!\cdots\!44\)\( T_{5}^{432} + \)\(10\!\cdots\!51\)\( T_{5}^{430} - \)\(75\!\cdots\!19\)\( T_{5}^{428} - \)\(12\!\cdots\!25\)\( T_{5}^{426} - \)\(13\!\cdots\!75\)\( T_{5}^{424} - \)\(66\!\cdots\!19\)\( T_{5}^{422} + \)\(36\!\cdots\!72\)\( T_{5}^{420} + \)\(12\!\cdots\!24\)\( T_{5}^{418} + \)\(16\!\cdots\!27\)\( T_{5}^{416} + \)\(11\!\cdots\!23\)\( T_{5}^{414} + \)\(26\!\cdots\!04\)\( T_{5}^{412} - \)\(57\!\cdots\!04\)\( T_{5}^{410} - \)\(10\!\cdots\!51\)\( T_{5}^{408} - \)\(10\!\cdots\!36\)\( T_{5}^{406} - \)\(67\!\cdots\!13\)\( T_{5}^{404} - \)\(12\!\cdots\!06\)\( T_{5}^{402} + \)\(46\!\cdots\!30\)\( T_{5}^{400} + \)\(84\!\cdots\!85\)\( T_{5}^{398} + \)\(76\!\cdots\!38\)\( T_{5}^{396} + \)\(27\!\cdots\!15\)\( T_{5}^{394} - \)\(31\!\cdots\!74\)\( T_{5}^{392} - \)\(61\!\cdots\!79\)\( T_{5}^{390} - \)\(47\!\cdots\!05\)\( T_{5}^{388} - \)\(76\!\cdots\!17\)\( T_{5}^{386} + \)\(25\!\cdots\!31\)\( T_{5}^{384} + \)\(31\!\cdots\!57\)\( T_{5}^{382} + \)\(16\!\cdots\!26\)\( T_{5}^{380} - \)\(31\!\cdots\!47\)\( T_{5}^{378} - \)\(12\!\cdots\!39\)\( T_{5}^{376} - \)\(10\!\cdots\!25\)\( T_{5}^{374} - \)\(27\!\cdots\!22\)\( T_{5}^{372} + \)\(27\!\cdots\!38\)\( T_{5}^{370} + \)\(39\!\cdots\!91\)\( T_{5}^{368} + \)\(22\!\cdots\!93\)\( T_{5}^{366} + \)\(10\!\cdots\!30\)\( T_{5}^{364} - \)\(98\!\cdots\!14\)\( T_{5}^{362} - \)\(93\!\cdots\!31\)\( T_{5}^{360} - \)\(37\!\cdots\!26\)\( T_{5}^{358} + \)\(94\!\cdots\!37\)\( T_{5}^{356} + \)\(25\!\cdots\!70\)\( T_{5}^{354} + \)\(17\!\cdots\!42\)\( T_{5}^{352} + \)\(38\!\cdots\!86\)\( T_{5}^{350} - \)\(41\!\cdots\!80\)\( T_{5}^{348} - \)\(49\!\cdots\!35\)\( T_{5}^{346} - \)\(22\!\cdots\!98\)\( T_{5}^{344} + \)\(11\!\cdots\!77\)\( T_{5}^{342} + \)\(91\!\cdots\!71\)\( T_{5}^{340} + \)\(64\!\cdots\!55\)\( T_{5}^{338} + \)\(16\!\cdots\!77\)\( T_{5}^{336} - \)\(83\!\cdots\!81\)\( T_{5}^{334} - \)\(11\!\cdots\!77\)\( T_{5}^{332} - \)\(59\!\cdots\!34\)\( T_{5}^{330} - \)\(99\!\cdots\!67\)\( T_{5}^{328} + \)\(10\!\cdots\!16\)\( T_{5}^{326} + \)\(11\!\cdots\!90\)\( T_{5}^{324} + \)\(55\!\cdots\!65\)\( T_{5}^{322} + \)\(45\!\cdots\!96\)\( T_{5}^{320} - \)\(13\!\cdots\!33\)\( T_{5}^{318} - \)\(10\!\cdots\!46\)\( T_{5}^{316} - \)\(32\!\cdots\!90\)\( T_{5}^{314} + \)\(47\!\cdots\!66\)\( T_{5}^{312} + \)\(92\!\cdots\!33\)\( T_{5}^{310} + \)\(43\!\cdots\!17\)\( T_{5}^{308} + \)\(15\!\cdots\!46\)\( T_{5}^{306} + \)\(76\!\cdots\!86\)\( T_{5}^{304} + \)\(15\!\cdots\!46\)\( T_{5}^{302} - \)\(33\!\cdots\!88\)\( T_{5}^{300} - \)\(38\!\cdots\!21\)\( T_{5}^{298} - \)\(16\!\cdots\!62\)\( T_{5}^{296} + \)\(20\!\cdots\!98\)\( T_{5}^{294} + \)\(61\!\cdots\!26\)\( T_{5}^{292} + \)\(32\!\cdots\!95\)\( T_{5}^{290} + \)\(45\!\cdots\!74\)\( T_{5}^{288} - \)\(41\!\cdots\!21\)\( T_{5}^{286} - \)\(34\!\cdots\!19\)\( T_{5}^{284} - \)\(15\!\cdots\!78\)\( T_{5}^{282} - \)\(32\!\cdots\!68\)\( T_{5}^{280} + \)\(19\!\cdots\!04\)\( T_{5}^{278} + \)\(25\!\cdots\!84\)\( T_{5}^{276} + \)\(12\!\cdots\!26\)\( T_{5}^{274} + \)\(70\!\cdots\!98\)\( T_{5}^{272} - \)\(25\!\cdots\!79\)\( T_{5}^{270} - \)\(15\!\cdots\!35\)\( T_{5}^{268} - \)\(26\!\cdots\!72\)\( T_{5}^{266} + \)\(14\!\cdots\!27\)\( T_{5}^{264} + \)\(11\!\cdots\!83\)\( T_{5}^{262} + \)\(34\!\cdots\!59\)\( T_{5}^{260} + \)\(34\!\cdots\!70\)\( T_{5}^{258} - \)\(29\!\cdots\!01\)\( T_{5}^{256} - \)\(27\!\cdots\!52\)\( T_{5}^{254} - \)\(12\!\cdots\!18\)\( T_{5}^{252} - \)\(16\!\cdots\!32\)\( T_{5}^{250} + \)\(18\!\cdots\!72\)\( T_{5}^{248} + \)\(12\!\cdots\!01\)\( T_{5}^{246} + \)\(31\!\cdots\!14\)\( T_{5}^{244} - \)\(21\!\cdots\!95\)\( T_{5}^{242} - \)\(36\!\cdots\!21\)\( T_{5}^{240} - \)\(11\!\cdots\!87\)\( T_{5}^{238} - \)\(16\!\cdots\!96\)\( T_{5}^{236} + \)\(19\!\cdots\!55\)\( T_{5}^{234} + \)\(53\!\cdots\!62\)\( T_{5}^{232} + \)\(39\!\cdots\!53\)\( T_{5}^{230} + \)\(16\!\cdots\!92\)\( T_{5}^{228} + \)\(33\!\cdots\!10\)\( T_{5}^{226} + \)\(21\!\cdots\!19\)\( T_{5}^{224} - \)\(17\!\cdots\!69\)\( T_{5}^{222} - \)\(36\!\cdots\!00\)\( T_{5}^{220} + \)\(79\!\cdots\!90\)\( T_{5}^{218} + \)\(13\!\cdots\!79\)\( T_{5}^{216} + \)\(10\!\cdots\!02\)\( T_{5}^{214} + \)\(56\!\cdots\!79\)\( T_{5}^{212} + \)\(22\!\cdots\!33\)\( T_{5}^{210} + \)\(71\!\cdots\!25\)\( T_{5}^{208} + \)\(20\!\cdots\!39\)\( T_{5}^{206} + \)\(64\!\cdots\!15\)\( T_{5}^{204} + \)\(22\!\cdots\!70\)\( T_{5}^{202} + \)\(89\!\cdots\!02\)\( T_{5}^{200} + \)\(36\!\cdots\!81\)\( T_{5}^{198} + \)\(14\!\cdots\!22\)\( T_{5}^{196} + \)\(53\!\cdots\!17\)\( T_{5}^{194} + \)\(17\!\cdots\!25\)\( T_{5}^{192} + \)\(54\!\cdots\!77\)\( T_{5}^{190} + \)\(14\!\cdots\!41\)\( T_{5}^{188} + \)\(36\!\cdots\!44\)\( T_{5}^{186} + \)\(82\!\cdots\!39\)\( T_{5}^{184} + \)\(16\!\cdots\!99\)\( T_{5}^{182} + \)\(30\!\cdots\!08\)\( T_{5}^{180} + \)\(57\!\cdots\!42\)\( T_{5}^{178} + \)\(12\!\cdots\!49\)\( T_{5}^{176} + \)\(33\!\cdots\!77\)\( T_{5}^{174} + \)\(95\!\cdots\!72\)\( T_{5}^{172} + \)\(25\!\cdots\!25\)\( T_{5}^{170} + \)\(61\!\cdots\!00\)\( T_{5}^{168} + \)\(12\!\cdots\!83\)\( T_{5}^{166} + \)\(24\!\cdots\!03\)\( T_{5}^{164} + \)\(42\!\cdots\!62\)\( T_{5}^{162} + \)\(80\!\cdots\!05\)\( T_{5}^{160} + \)\(19\!\cdots\!92\)\( T_{5}^{158} + \)\(54\!\cdots\!30\)\( T_{5}^{156} + \)\(15\!\cdots\!83\)\( T_{5}^{154} + \)\(38\!\cdots\!48\)\( T_{5}^{152} + \)\(88\!\cdots\!48\)\( T_{5}^{150} + \)\(18\!\cdots\!75\)\( T_{5}^{148} + \)\(33\!\cdots\!25\)\( T_{5}^{146} + \)\(57\!\cdots\!18\)\( T_{5}^{144} + \)\(89\!\cdots\!70\)\( T_{5}^{142} + \)\(12\!\cdots\!17\)\( T_{5}^{140} + \)\(17\!\cdots\!90\)\( T_{5}^{138} + \)\(21\!\cdots\!34\)\( T_{5}^{136} + \)\(24\!\cdots\!03\)\( T_{5}^{134} + \)\(26\!\cdots\!04\)\( T_{5}^{132} + \)\(26\!\cdots\!36\)\( T_{5}^{130} + \)\(24\!\cdots\!08\)\( T_{5}^{128} + \)\(21\!\cdots\!94\)\( T_{5}^{126} + \)\(17\!\cdots\!37\)\( T_{5}^{124} + \)\(13\!\cdots\!28\)\( T_{5}^{122} + \)\(10\!\cdots\!65\)\( T_{5}^{120} + \)\(80\!\cdots\!31\)\( T_{5}^{118} + \)\(60\!\cdots\!99\)\( T_{5}^{116} + \)\(44\!\cdots\!28\)\( T_{5}^{114} + \)\(32\!\cdots\!08\)\( T_{5}^{112} + \)\(22\!\cdots\!33\)\( T_{5}^{110} + \)\(15\!\cdots\!29\)\( T_{5}^{108} + \)\(90\!\cdots\!61\)\( T_{5}^{106} + \)\(59\!\cdots\!29\)\( T_{5}^{104} + \)\(25\!\cdots\!77\)\( T_{5}^{102} + \)\(19\!\cdots\!12\)\( T_{5}^{100} + \)\(13\!\cdots\!02\)\( T_{5}^{98} + \)\(10\!\cdots\!08\)\( T_{5}^{96} - \)\(65\!\cdots\!10\)\( T_{5}^{94} + \)\(64\!\cdots\!54\)\( T_{5}^{92} - \)\(42\!\cdots\!33\)\( T_{5}^{90} + \)\(30\!\cdots\!85\)\( T_{5}^{88} - \)\(20\!\cdots\!09\)\( T_{5}^{86} + \)\(98\!\cdots\!56\)\( T_{5}^{84} + \)\(41\!\cdots\!02\)\( T_{5}^{82} - \)\(15\!\cdots\!75\)\( T_{5}^{80} + \)\(19\!\cdots\!07\)\( T_{5}^{78} - \)\(14\!\cdots\!79\)\( T_{5}^{76} + \)\(71\!\cdots\!78\)\( T_{5}^{74} - \)\(88\!\cdots\!47\)\( T_{5}^{72} - \)\(20\!\cdots\!59\)\( T_{5}^{70} + \)\(24\!\cdots\!83\)\( T_{5}^{68} - \)\(17\!\cdots\!27\)\( T_{5}^{66} + \)\(96\!\cdots\!48\)\( T_{5}^{64} - \)\(43\!\cdots\!84\)\( T_{5}^{62} + \)\(16\!\cdots\!76\)\( T_{5}^{60} - \)\(57\!\cdots\!77\)\( T_{5}^{58} + \)\(16\!\cdots\!33\)\( T_{5}^{56} - \)\(43\!\cdots\!17\)\( T_{5}^{54} + \)\(97\!\cdots\!65\)\( T_{5}^{52} - \)\(19\!\cdots\!34\)\( T_{5}^{50} + \)\(33\!\cdots\!65\)\( T_{5}^{48} - \)\(49\!\cdots\!41\)\( T_{5}^{46} + \)\(63\!\cdots\!44\)\( T_{5}^{44} - \)\(69\!\cdots\!85\)\( T_{5}^{42} + \)\(65\!\cdots\!46\)\( T_{5}^{40} - \)\(51\!\cdots\!77\)\( T_{5}^{38} + \)\(34\!\cdots\!49\)\( T_{5}^{36} - \)\(18\!\cdots\!92\)\( T_{5}^{34} + \)\(76\!\cdots\!72\)\( T_{5}^{32} - \)\(25\!\cdots\!56\)\( T_{5}^{30} + \)\(69\!\cdots\!28\)\( T_{5}^{28} - \)\(18\!\cdots\!56\)\( T_{5}^{26} + \)\(57\!\cdots\!88\)\( T_{5}^{24} - \)\(20\!\cdots\!24\)\( T_{5}^{22} + \)\(71\!\cdots\!92\)\( T_{5}^{20} - \)\(19\!\cdots\!00\)\( T_{5}^{18} + \)\(41\!\cdots\!36\)\( T_{5}^{16} - \)\(58\!\cdots\!56\)\( T_{5}^{14} + \)\(39\!\cdots\!76\)\( T_{5}^{12} + \)\(92\!\cdots\!92\)\( T_{5}^{10} + \)\(10\!\cdots\!72\)\( T_{5}^{8} - \)\(38\!\cdots\!80\)\( T_{5}^{6} + \)\(11\!\cdots\!12\)\( T_{5}^{4} + \)\(74\!\cdots\!76\)\( T_{5}^{2} + \)\(77\!\cdots\!44\)\( \)">\(T_{5}^{1872} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(648, [\chi])\).