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: Complex embeddings Normalized embeddings Satake parameters Satake angles

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 $$S_{2}^{\mathrm{new}}(648, [\chi])$$.