# Properties

 Label 1050.2.u Level 1050 Weight 2 Character orbit u Rep. character $$\chi_{1050}(299,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 96 Newform subspaces 10 Sturm bound 480 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ = $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1050.u (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$105$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$10$$ Sturm bound: $$480$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$11$$, $$13$$, $$17$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1050, [\chi])$$.

Total New Old
Modular forms 528 96 432
Cusp forms 432 96 336
Eisenstein series 96 0 96

## Trace form

 $$96q - 48q^{4} - 12q^{9} + O(q^{10})$$ $$96q - 48q^{4} - 12q^{9} - 48q^{16} - 12q^{19} - 8q^{21} + 12q^{24} + 12q^{31} + 24q^{36} + 12q^{39} + 16q^{46} - 32q^{49} - 4q^{51} + 60q^{61} + 96q^{64} - 48q^{66} + 56q^{79} - 20q^{81} - 20q^{84} + 20q^{91} - 144q^{94} - 12q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1050, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1050.2.u.a $$4$$ $$8.384$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$-6$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}+(-1-\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots$$
1050.2.u.b $$4$$ $$8.384$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots$$
1050.2.u.c $$4$$ $$8.384$$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots$$
1050.2.u.d $$4$$ $$8.384$$ $$\Q(\zeta_{12})$$ None $$2$$ $$6$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{2}+(1+\zeta_{12}^{2})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{4}+\cdots$$
1050.2.u.e $$12$$ $$8.384$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-6$$ $$2$$ $$0$$ $$-6$$ $$q-\beta _{5}q^{2}-\beta _{8}q^{3}+(-1+\beta _{5})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$$
1050.2.u.f $$12$$ $$8.384$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-6$$ $$4$$ $$0$$ $$6$$ $$q-\beta _{5}q^{2}+\beta _{1}q^{3}+(-1+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$$
1050.2.u.g $$12$$ $$8.384$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$6$$ $$-4$$ $$0$$ $$-6$$ $$q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-1+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$$
1050.2.u.h $$12$$ $$8.384$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$6$$ $$-2$$ $$0$$ $$6$$ $$q+\beta _{5}q^{2}+\beta _{8}q^{3}+(-1+\beta _{5})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$$
1050.2.u.i $$16$$ $$8.384$$ 16.0.$$\cdots$$.8 None $$-8$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{12}q^{2}-\beta _{14}q^{3}+(-1-\beta _{12})q^{4}+\cdots$$
1050.2.u.j $$16$$ $$8.384$$ 16.0.$$\cdots$$.8 None $$8$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{12}q^{2}+\beta _{14}q^{3}+(-1-\beta _{12})q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1050, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1050, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$( 1 + T + T^{2} )^{2}$$)($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 + T + T^{2} )^{6}$$)($$( 1 + T + T^{2} )^{6}$$)($$( 1 - T + T^{2} )^{6}$$)($$( 1 - T + T^{2} )^{6}$$)($$( 1 + T + T^{2} )^{8}$$)($$( 1 - T + T^{2} )^{8}$$)
$3$ ($$( 1 + 3 T + 3 T^{2} )^{2}$$)($$1 + 3 T^{2} + 9 T^{4}$$)($$1 + 3 T^{2} + 9 T^{4}$$)($$( 1 - 3 T + 3 T^{2} )^{2}$$)($$1 - 2 T + 2 T^{2} + 8 T^{3} - 8 T^{4} - 6 T^{5} + 66 T^{6} - 18 T^{7} - 72 T^{8} + 216 T^{9} + 162 T^{10} - 486 T^{11} + 729 T^{12}$$)($$1 - 4 T + 11 T^{2} - 32 T^{3} + 64 T^{4} - 120 T^{5} + 237 T^{6} - 360 T^{7} + 576 T^{8} - 864 T^{9} + 891 T^{10} - 972 T^{11} + 729 T^{12}$$)($$1 + 4 T + 11 T^{2} + 32 T^{3} + 64 T^{4} + 120 T^{5} + 237 T^{6} + 360 T^{7} + 576 T^{8} + 864 T^{9} + 891 T^{10} + 972 T^{11} + 729 T^{12}$$)($$1 + 2 T + 2 T^{2} - 8 T^{3} - 8 T^{4} + 6 T^{5} + 66 T^{6} + 18 T^{7} - 72 T^{8} - 216 T^{9} + 162 T^{10} + 486 T^{11} + 729 T^{12}$$)($$1 - 6 T + 18 T^{2} - 36 T^{3} + 50 T^{4} - 18 T^{5} - 144 T^{6} + 498 T^{7} - 1013 T^{8} + 1494 T^{9} - 1296 T^{10} - 486 T^{11} + 4050 T^{12} - 8748 T^{13} + 13122 T^{14} - 13122 T^{15} + 6561 T^{16}$$)($$1 + 6 T + 18 T^{2} + 36 T^{3} + 50 T^{4} + 18 T^{5} - 144 T^{6} - 498 T^{7} - 1013 T^{8} - 1494 T^{9} - 1296 T^{10} + 486 T^{11} + 4050 T^{12} + 8748 T^{13} + 13122 T^{14} + 13122 T^{15} + 6561 T^{16}$$)
$5$ 1
$7$ ($$1 + 11 T^{2} + 49 T^{4}$$)($$1 + 11 T^{2} + 49 T^{4}$$)($$1 + 11 T^{2} + 49 T^{4}$$)($$1 + 11 T^{2} + 49 T^{4}$$)($$1 + 6 T + 11 T^{2} - 6 T^{3} - 69 T^{4} - 252 T^{5} - 782 T^{6} - 1764 T^{7} - 3381 T^{8} - 2058 T^{9} + 26411 T^{10} + 100842 T^{11} + 117649 T^{12}$$)($$1 - 6 T + 11 T^{2} + 6 T^{3} - 69 T^{4} + 252 T^{5} - 782 T^{6} + 1764 T^{7} - 3381 T^{8} + 2058 T^{9} + 26411 T^{10} - 100842 T^{11} + 117649 T^{12}$$)($$1 + 6 T + 11 T^{2} - 6 T^{3} - 69 T^{4} - 252 T^{5} - 782 T^{6} - 1764 T^{7} - 3381 T^{8} - 2058 T^{9} + 26411 T^{10} + 100842 T^{11} + 117649 T^{12}$$)($$1 - 6 T + 11 T^{2} + 6 T^{3} - 69 T^{4} + 252 T^{5} - 782 T^{6} + 1764 T^{7} - 3381 T^{8} + 2058 T^{9} + 26411 T^{10} - 100842 T^{11} + 117649 T^{12}$$)($$( 1 + 77 T^{4} + 2401 T^{8} )^{2}$$)($$( 1 + 77 T^{4} + 2401 T^{8} )^{2}$$)
$11$ ($$1 + 13 T^{2} + 48 T^{4} + 1573 T^{6} + 14641 T^{8}$$)($$1 - 14 T^{2} + 75 T^{4} - 1694 T^{6} + 14641 T^{8}$$)($$1 - 14 T^{2} + 75 T^{4} - 1694 T^{6} + 14641 T^{8}$$)($$1 + 13 T^{2} + 48 T^{4} + 1573 T^{6} + 14641 T^{8}$$)($$1 - 12 T + 104 T^{2} - 672 T^{3} + 3656 T^{4} - 16524 T^{5} + 63276 T^{6} - 198252 T^{7} + 468664 T^{8} - 516768 T^{9} - 2129576 T^{10} + 16995156 T^{11} - 68897930 T^{12} + 186946716 T^{13} - 257678696 T^{14} - 687818208 T^{15} + 6861709624 T^{16} - 31928682852 T^{17} + 112097293836 T^{18} - 322006013604 T^{19} + 783696068936 T^{20} - 1584540848352 T^{21} + 2697492158504 T^{22} - 3423740047332 T^{23} + 3138428376721 T^{24}$$)($$1 + 12 T + 104 T^{2} + 672 T^{3} + 3656 T^{4} + 16524 T^{5} + 63276 T^{6} + 198252 T^{7} + 468664 T^{8} + 516768 T^{9} - 2129576 T^{10} - 16995156 T^{11} - 68897930 T^{12} - 186946716 T^{13} - 257678696 T^{14} + 687818208 T^{15} + 6861709624 T^{16} + 31928682852 T^{17} + 112097293836 T^{18} + 322006013604 T^{19} + 783696068936 T^{20} + 1584540848352 T^{21} + 2697492158504 T^{22} + 3423740047332 T^{23} + 3138428376721 T^{24}$$)($$1 + 12 T + 104 T^{2} + 672 T^{3} + 3656 T^{4} + 16524 T^{5} + 63276 T^{6} + 198252 T^{7} + 468664 T^{8} + 516768 T^{9} - 2129576 T^{10} - 16995156 T^{11} - 68897930 T^{12} - 186946716 T^{13} - 257678696 T^{14} + 687818208 T^{15} + 6861709624 T^{16} + 31928682852 T^{17} + 112097293836 T^{18} + 322006013604 T^{19} + 783696068936 T^{20} + 1584540848352 T^{21} + 2697492158504 T^{22} + 3423740047332 T^{23} + 3138428376721 T^{24}$$)($$1 - 12 T + 104 T^{2} - 672 T^{3} + 3656 T^{4} - 16524 T^{5} + 63276 T^{6} - 198252 T^{7} + 468664 T^{8} - 516768 T^{9} - 2129576 T^{10} + 16995156 T^{11} - 68897930 T^{12} + 186946716 T^{13} - 257678696 T^{14} - 687818208 T^{15} + 6861709624 T^{16} - 31928682852 T^{17} + 112097293836 T^{18} - 322006013604 T^{19} + 783696068936 T^{20} - 1584540848352 T^{21} + 2697492158504 T^{22} - 3423740047332 T^{23} + 3138428376721 T^{24}$$)($$1 + 44 T^{2} + 852 T^{4} + 11656 T^{6} + 155594 T^{8} + 1774884 T^{10} + 14908720 T^{12} + 132122900 T^{14} + 1489364739 T^{16} + 15986870900 T^{18} + 218278569520 T^{20} + 3144315273924 T^{22} + 33352955730314 T^{24} + 302326621149256 T^{26} + 2673940976966292 T^{28} + 16708992677662604 T^{30} + 45949729863572161 T^{32}$$)($$1 + 44 T^{2} + 852 T^{4} + 11656 T^{6} + 155594 T^{8} + 1774884 T^{10} + 14908720 T^{12} + 132122900 T^{14} + 1489364739 T^{16} + 15986870900 T^{18} + 218278569520 T^{20} + 3144315273924 T^{22} + 33352955730314 T^{24} + 302326621149256 T^{26} + 2673940976966292 T^{28} + 16708992677662604 T^{30} + 45949729863572161 T^{32}$$)
$13$ ($$( 1 + 14 T^{2} + 169 T^{4} )^{2}$$)($$( 1 + 23 T^{2} + 169 T^{4} )^{2}$$)($$( 1 + 23 T^{2} + 169 T^{4} )^{2}$$)($$( 1 + 14 T^{2} + 169 T^{4} )^{2}$$)($$( 1 + 4 T + 20 T^{2} + 28 T^{3} + 228 T^{4} + 1012 T^{5} + 6466 T^{6} + 13156 T^{7} + 38532 T^{8} + 61516 T^{9} + 571220 T^{10} + 1485172 T^{11} + 4826809 T^{12} )^{2}$$)($$( 1 - 4 T + 20 T^{2} - 28 T^{3} + 228 T^{4} - 1012 T^{5} + 6466 T^{6} - 13156 T^{7} + 38532 T^{8} - 61516 T^{9} + 571220 T^{10} - 1485172 T^{11} + 4826809 T^{12} )^{2}$$)($$( 1 + 4 T + 20 T^{2} + 28 T^{3} + 228 T^{4} + 1012 T^{5} + 6466 T^{6} + 13156 T^{7} + 38532 T^{8} + 61516 T^{9} + 571220 T^{10} + 1485172 T^{11} + 4826809 T^{12} )^{2}$$)($$( 1 - 4 T + 20 T^{2} - 28 T^{3} + 228 T^{4} - 1012 T^{5} + 6466 T^{6} - 13156 T^{7} + 38532 T^{8} - 61516 T^{9} + 571220 T^{10} - 1485172 T^{11} + 4826809 T^{12} )^{2}$$)($$( 1 + 56 T^{2} + 1320 T^{4} + 18088 T^{6} + 213086 T^{8} + 3056872 T^{10} + 37700520 T^{12} + 270301304 T^{14} + 815730721 T^{16} )^{2}$$)($$( 1 + 56 T^{2} + 1320 T^{4} + 18088 T^{6} + 213086 T^{8} + 3056872 T^{10} + 37700520 T^{12} + 270301304 T^{14} + 815730721 T^{16} )^{2}$$)
$17$ ($$( 1 + 6 T + 29 T^{2} + 102 T^{3} + 289 T^{4} )^{2}$$)($$( 1 + 17 T^{2} + 289 T^{4} )^{2}$$)($$( 1 + 17 T^{2} + 289 T^{4} )^{2}$$)($$( 1 - 6 T + 29 T^{2} - 102 T^{3} + 289 T^{4} )^{2}$$)($$1 - 12 T + 134 T^{2} - 1032 T^{3} + 7265 T^{4} - 43632 T^{5} + 246714 T^{6} - 1285884 T^{7} + 6436174 T^{8} - 30674004 T^{9} + 140508886 T^{10} - 618034944 T^{11} + 2599619125 T^{12} - 10506594048 T^{13} + 40607068054 T^{14} - 150701381652 T^{15} + 537555688654 T^{16} - 1825771398588 T^{17} + 5955076198266 T^{18} - 17903896980336 T^{19} + 50678877808865 T^{20} - 122382688544904 T^{21} + 270143182660166 T^{22} - 411262755691596 T^{23} + 582622237229761 T^{24}$$)($$1 - 12 T + 134 T^{2} - 1032 T^{3} + 7265 T^{4} - 43632 T^{5} + 246714 T^{6} - 1285884 T^{7} + 6436174 T^{8} - 30674004 T^{9} + 140508886 T^{10} - 618034944 T^{11} + 2599619125 T^{12} - 10506594048 T^{13} + 40607068054 T^{14} - 150701381652 T^{15} + 537555688654 T^{16} - 1825771398588 T^{17} + 5955076198266 T^{18} - 17903896980336 T^{19} + 50678877808865 T^{20} - 122382688544904 T^{21} + 270143182660166 T^{22} - 411262755691596 T^{23} + 582622237229761 T^{24}$$)($$1 + 12 T + 134 T^{2} + 1032 T^{3} + 7265 T^{4} + 43632 T^{5} + 246714 T^{6} + 1285884 T^{7} + 6436174 T^{8} + 30674004 T^{9} + 140508886 T^{10} + 618034944 T^{11} + 2599619125 T^{12} + 10506594048 T^{13} + 40607068054 T^{14} + 150701381652 T^{15} + 537555688654 T^{16} + 1825771398588 T^{17} + 5955076198266 T^{18} + 17903896980336 T^{19} + 50678877808865 T^{20} + 122382688544904 T^{21} + 270143182660166 T^{22} + 411262755691596 T^{23} + 582622237229761 T^{24}$$)($$1 + 12 T + 134 T^{2} + 1032 T^{3} + 7265 T^{4} + 43632 T^{5} + 246714 T^{6} + 1285884 T^{7} + 6436174 T^{8} + 30674004 T^{9} + 140508886 T^{10} + 618034944 T^{11} + 2599619125 T^{12} + 10506594048 T^{13} + 40607068054 T^{14} + 150701381652 T^{15} + 537555688654 T^{16} + 1825771398588 T^{17} + 5955076198266 T^{18} + 17903896980336 T^{19} + 50678877808865 T^{20} + 122382688544904 T^{21} + 270143182660166 T^{22} + 411262755691596 T^{23} + 582622237229761 T^{24}$$)($$( 1 + 6 T + 46 T^{2} + 204 T^{3} + 757 T^{4} + 2244 T^{5} + 4210 T^{6} - 918 T^{7} + 2788 T^{8} - 15606 T^{9} + 1216690 T^{10} + 11024772 T^{11} + 63225397 T^{12} + 289650828 T^{13} + 1110328174 T^{14} + 2462032038 T^{15} + 6975757441 T^{16} )^{2}$$)($$( 1 - 6 T + 46 T^{2} - 204 T^{3} + 757 T^{4} - 2244 T^{5} + 4210 T^{6} + 918 T^{7} + 2788 T^{8} + 15606 T^{9} + 1216690 T^{10} - 11024772 T^{11} + 63225397 T^{12} - 289650828 T^{13} + 1110328174 T^{14} - 2462032038 T^{15} + 6975757441 T^{16} )^{2}$$)
$19$ ($$( 1 - T + 19 T^{2} )^{2}( 1 + 7 T + 19 T^{2} )^{2}$$)($$( 1 - 3 T + 22 T^{2} - 57 T^{3} + 361 T^{4} )^{2}$$)($$( 1 - 3 T + 22 T^{2} - 57 T^{3} + 361 T^{4} )^{2}$$)($$( 1 - T + 19 T^{2} )^{2}( 1 + 7 T + 19 T^{2} )^{2}$$)($$1 + 24 T^{2} - 316 T^{4} - 144 T^{5} - 5636 T^{6} + 33888 T^{7} + 181380 T^{8} + 941760 T^{9} + 1187824 T^{10} - 9129072 T^{11} - 54892570 T^{12} - 173452368 T^{13} + 428804464 T^{14} + 6459531840 T^{15} + 23637622980 T^{16} + 83910042912 T^{17} - 265150585316 T^{18} - 128717530416 T^{19} - 5366805920956 T^{20} + 147145590187224 T^{22} + 2213314919066161 T^{24}$$)($$1 + 24 T^{2} - 316 T^{4} - 144 T^{5} - 5636 T^{6} + 33888 T^{7} + 181380 T^{8} + 941760 T^{9} + 1187824 T^{10} - 9129072 T^{11} - 54892570 T^{12} - 173452368 T^{13} + 428804464 T^{14} + 6459531840 T^{15} + 23637622980 T^{16} + 83910042912 T^{17} - 265150585316 T^{18} - 128717530416 T^{19} - 5366805920956 T^{20} + 147145590187224 T^{22} + 2213314919066161 T^{24}$$)($$1 + 24 T^{2} - 316 T^{4} - 144 T^{5} - 5636 T^{6} + 33888 T^{7} + 181380 T^{8} + 941760 T^{9} + 1187824 T^{10} - 9129072 T^{11} - 54892570 T^{12} - 173452368 T^{13} + 428804464 T^{14} + 6459531840 T^{15} + 23637622980 T^{16} + 83910042912 T^{17} - 265150585316 T^{18} - 128717530416 T^{19} - 5366805920956 T^{20} + 147145590187224 T^{22} + 2213314919066161 T^{24}$$)($$1 + 24 T^{2} - 316 T^{4} - 144 T^{5} - 5636 T^{6} + 33888 T^{7} + 181380 T^{8} + 941760 T^{9} + 1187824 T^{10} - 9129072 T^{11} - 54892570 T^{12} - 173452368 T^{13} + 428804464 T^{14} + 6459531840 T^{15} + 23637622980 T^{16} + 83910042912 T^{17} - 265150585316 T^{18} - 128717530416 T^{19} - 5366805920956 T^{20} + 147145590187224 T^{22} + 2213314919066161 T^{24}$$)($$( 1 + 34 T^{2} + 558 T^{4} + 1260 T^{5} - 1864 T^{6} + 50232 T^{7} - 145345 T^{8} + 954408 T^{9} - 672904 T^{10} + 8642340 T^{11} + 72719118 T^{12} + 1599559954 T^{14} + 16983563041 T^{16} )^{2}$$)($$( 1 + 34 T^{2} + 558 T^{4} + 1260 T^{5} - 1864 T^{6} + 50232 T^{7} - 145345 T^{8} + 954408 T^{9} - 672904 T^{10} + 8642340 T^{11} + 72719118 T^{12} + 1599559954 T^{14} + 16983563041 T^{16} )^{2}$$)
$23$ ($$( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} )^{2}$$)($$( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} )^{2}$$)($$( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} )^{2}$$)($$( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} )^{2}$$)($$1 - 2 T - 77 T^{2} + 98 T^{3} + 2919 T^{4} - 1252 T^{5} - 81644 T^{6} - 32808 T^{7} + 2039477 T^{8} + 1200754 T^{9} - 41616423 T^{10} - 12505102 T^{11} + 834053510 T^{12} - 287617346 T^{13} - 22015087767 T^{14} + 14609573918 T^{15} + 570729283157 T^{16} - 211163541144 T^{17} - 12086242121516 T^{18} - 4262841459644 T^{19} + 228589766035239 T^{20} + 176512960823374 T^{21} - 3189841363450973 T^{22} - 1905619515827854 T^{23} + 21914624432020321 T^{24}$$)($$1 - 2 T - 77 T^{2} + 98 T^{3} + 2919 T^{4} - 1252 T^{5} - 81644 T^{6} - 32808 T^{7} + 2039477 T^{8} + 1200754 T^{9} - 41616423 T^{10} - 12505102 T^{11} + 834053510 T^{12} - 287617346 T^{13} - 22015087767 T^{14} + 14609573918 T^{15} + 570729283157 T^{16} - 211163541144 T^{17} - 12086242121516 T^{18} - 4262841459644 T^{19} + 228589766035239 T^{20} + 176512960823374 T^{21} - 3189841363450973 T^{22} - 1905619515827854 T^{23} + 21914624432020321 T^{24}$$)($$1 + 2 T - 77 T^{2} - 98 T^{3} + 2919 T^{4} + 1252 T^{5} - 81644 T^{6} + 32808 T^{7} + 2039477 T^{8} - 1200754 T^{9} - 41616423 T^{10} + 12505102 T^{11} + 834053510 T^{12} + 287617346 T^{13} - 22015087767 T^{14} - 14609573918 T^{15} + 570729283157 T^{16} + 211163541144 T^{17} - 12086242121516 T^{18} + 4262841459644 T^{19} + 228589766035239 T^{20} - 176512960823374 T^{21} - 3189841363450973 T^{22} + 1905619515827854 T^{23} + 21914624432020321 T^{24}$$)($$1 + 2 T - 77 T^{2} - 98 T^{3} + 2919 T^{4} + 1252 T^{5} - 81644 T^{6} + 32808 T^{7} + 2039477 T^{8} - 1200754 T^{9} - 41616423 T^{10} + 12505102 T^{11} + 834053510 T^{12} + 287617346 T^{13} - 22015087767 T^{14} - 14609573918 T^{15} + 570729283157 T^{16} + 211163541144 T^{17} - 12086242121516 T^{18} + 4262841459644 T^{19} + 228589766035239 T^{20} - 176512960823374 T^{21} - 3189841363450973 T^{22} + 1905619515827854 T^{23} + 21914624432020321 T^{24}$$)($$( 1 - 2 T - 16 T^{2} - 288 T^{3} + 635 T^{4} + 5384 T^{5} + 41980 T^{6} - 157962 T^{7} - 747584 T^{8} - 3633126 T^{9} + 22207420 T^{10} + 65507128 T^{11} + 177699035 T^{12} - 1853666784 T^{13} - 2368574224 T^{14} - 6809650894 T^{15} + 78310985281 T^{16} )^{2}$$)($$( 1 + 2 T - 16 T^{2} + 288 T^{3} + 635 T^{4} - 5384 T^{5} + 41980 T^{6} + 157962 T^{7} - 747584 T^{8} + 3633126 T^{9} + 22207420 T^{10} - 65507128 T^{11} + 177699035 T^{12} + 1853666784 T^{13} - 2368574224 T^{14} + 6809650894 T^{15} + 78310985281 T^{16} )^{2}$$)
$29$ ($$( 1 - 49 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 49 T^{2} + 841 T^{4} )^{2}$$)($$1 - 158 T^{2} + 12415 T^{4} - 625726 T^{6} + 22774147 T^{8} - 673287380 T^{10} + 19008498890 T^{12} - 566234686580 T^{14} + 16107721464307 T^{16} - 372196417356046 T^{18} + 6210559216910815 T^{20} - 66471742861431758 T^{22} + 353814783205469041 T^{24}$$)($$1 - 158 T^{2} + 12415 T^{4} - 625726 T^{6} + 22774147 T^{8} - 673287380 T^{10} + 19008498890 T^{12} - 566234686580 T^{14} + 16107721464307 T^{16} - 372196417356046 T^{18} + 6210559216910815 T^{20} - 66471742861431758 T^{22} + 353814783205469041 T^{24}$$)($$1 - 158 T^{2} + 12415 T^{4} - 625726 T^{6} + 22774147 T^{8} - 673287380 T^{10} + 19008498890 T^{12} - 566234686580 T^{14} + 16107721464307 T^{16} - 372196417356046 T^{18} + 6210559216910815 T^{20} - 66471742861431758 T^{22} + 353814783205469041 T^{24}$$)($$1 - 158 T^{2} + 12415 T^{4} - 625726 T^{6} + 22774147 T^{8} - 673287380 T^{10} + 19008498890 T^{12} - 566234686580 T^{14} + 16107721464307 T^{16} - 372196417356046 T^{18} + 6210559216910815 T^{20} - 66471742861431758 T^{22} + 353814783205469041 T^{24}$$)($$( 1 - 60 T^{2} + 4000 T^{4} - 140436 T^{6} + 5155470 T^{8} - 118106676 T^{10} + 2829124000 T^{12} - 35689399260 T^{14} + 500246412961 T^{16} )^{2}$$)($$( 1 - 60 T^{2} + 4000 T^{4} - 140436 T^{6} + 5155470 T^{8} - 118106676 T^{10} + 2829124000 T^{12} - 35689399260 T^{14} + 500246412961 T^{16} )^{2}$$)
$31$ ($$( 1 - 4 T + 31 T^{2} )^{2}( 1 + 7 T + 31 T^{2} )^{2}$$)($$( 1 + 6 T + 43 T^{2} + 186 T^{3} + 961 T^{4} )^{2}$$)($$( 1 + 6 T + 43 T^{2} + 186 T^{3} + 961 T^{4} )^{2}$$)($$( 1 - 4 T + 31 T^{2} )^{2}( 1 + 7 T + 31 T^{2} )^{2}$$)($$1 - 12 T + 162 T^{2} - 1368 T^{3} + 10769 T^{4} - 77664 T^{5} + 554878 T^{6} - 3968772 T^{7} + 27631230 T^{8} - 178188132 T^{9} + 1059815698 T^{10} - 6109630032 T^{11} + 33269854325 T^{12} - 189398530992 T^{13} + 1018482885778 T^{14} - 5308402640412 T^{15} + 25518021160830 T^{16} - 113622572872572 T^{17} + 492456267505918 T^{18} - 2136739662316704 T^{19} + 9184783582202129 T^{20} - 36169403115797928 T^{21} + 132779782490889762 T^{22} - 304901722756857972 T^{23} + 787662783788549761 T^{24}$$)($$1 - 12 T + 162 T^{2} - 1368 T^{3} + 10769 T^{4} - 77664 T^{5} + 554878 T^{6} - 3968772 T^{7} + 27631230 T^{8} - 178188132 T^{9} + 1059815698 T^{10} - 6109630032 T^{11} + 33269854325 T^{12} - 189398530992 T^{13} + 1018482885778 T^{14} - 5308402640412 T^{15} + 25518021160830 T^{16} - 113622572872572 T^{17} + 492456267505918 T^{18} - 2136739662316704 T^{19} + 9184783582202129 T^{20} - 36169403115797928 T^{21} + 132779782490889762 T^{22} - 304901722756857972 T^{23} + 787662783788549761 T^{24}$$)($$1 - 12 T + 162 T^{2} - 1368 T^{3} + 10769 T^{4} - 77664 T^{5} + 554878 T^{6} - 3968772 T^{7} + 27631230 T^{8} - 178188132 T^{9} + 1059815698 T^{10} - 6109630032 T^{11} + 33269854325 T^{12} - 189398530992 T^{13} + 1018482885778 T^{14} - 5308402640412 T^{15} + 25518021160830 T^{16} - 113622572872572 T^{17} + 492456267505918 T^{18} - 2136739662316704 T^{19} + 9184783582202129 T^{20} - 36169403115797928 T^{21} + 132779782490889762 T^{22} - 304901722756857972 T^{23} + 787662783788549761 T^{24}$$)($$1 - 12 T + 162 T^{2} - 1368 T^{3} + 10769 T^{4} - 77664 T^{5} + 554878 T^{6} - 3968772 T^{7} + 27631230 T^{8} - 178188132 T^{9} + 1059815698 T^{10} - 6109630032 T^{11} + 33269854325 T^{12} - 189398530992 T^{13} + 1018482885778 T^{14} - 5308402640412 T^{15} + 25518021160830 T^{16} - 113622572872572 T^{17} + 492456267505918 T^{18} - 2136739662316704 T^{19} + 9184783582202129 T^{20} - 36169403115797928 T^{21} + 132779782490889762 T^{22} - 304901722756857972 T^{23} + 787662783788549761 T^{24}$$)($$( 1 + 40 T^{2} + 1035 T^{4} + 4536 T^{5} + 30392 T^{6} + 284760 T^{7} + 482936 T^{8} + 8827560 T^{9} + 29206712 T^{10} + 135131976 T^{11} + 955844235 T^{12} + 35500147240 T^{14} + 852891037441 T^{16} )^{2}$$)($$( 1 + 40 T^{2} + 1035 T^{4} + 4536 T^{5} + 30392 T^{6} + 284760 T^{7} + 482936 T^{8} + 8827560 T^{9} + 29206712 T^{10} + 135131976 T^{11} + 955844235 T^{12} + 35500147240 T^{14} + 852891037441 T^{16} )^{2}$$)
$37$ ($$( 1 - 12 T + 107 T^{2} - 444 T^{3} + 1369 T^{4} )( 1 + 12 T + 107 T^{2} + 444 T^{3} + 1369 T^{4} )$$)($$1 + 25 T^{2} - 744 T^{4} + 34225 T^{6} + 1874161 T^{8}$$)($$1 + 25 T^{2} - 744 T^{4} + 34225 T^{6} + 1874161 T^{8}$$)($$( 1 - 12 T + 107 T^{2} - 444 T^{3} + 1369 T^{4} )( 1 + 12 T + 107 T^{2} + 444 T^{3} + 1369 T^{4} )$$)($$1 + 136 T^{2} + 9604 T^{4} + 1584 T^{5} + 442460 T^{6} + 614448 T^{7} + 15142564 T^{8} + 69480000 T^{9} + 459976384 T^{10} + 4218954336 T^{11} + 15196793798 T^{12} + 156101310432 T^{13} + 629707669696 T^{14} + 3519370440000 T^{15} + 28379602888804 T^{16} + 42608255690736 T^{17} + 1135231306926140 T^{18} + 150372093378672 T^{19} + 33733852675457284 T^{20} + 653967474648827464 T^{22} + 6582952005840035281 T^{24}$$)($$1 + 136 T^{2} + 9604 T^{4} - 1584 T^{5} + 442460 T^{6} - 614448 T^{7} + 15142564 T^{8} - 69480000 T^{9} + 459976384 T^{10} - 4218954336 T^{11} + 15196793798 T^{12} - 156101310432 T^{13} + 629707669696 T^{14} - 3519370440000 T^{15} + 28379602888804 T^{16} - 42608255690736 T^{17} + 1135231306926140 T^{18} - 150372093378672 T^{19} + 33733852675457284 T^{20} + 653967474648827464 T^{22} + 6582952005840035281 T^{24}$$)($$1 + 136 T^{2} + 9604 T^{4} + 1584 T^{5} + 442460 T^{6} + 614448 T^{7} + 15142564 T^{8} + 69480000 T^{9} + 459976384 T^{10} + 4218954336 T^{11} + 15196793798 T^{12} + 156101310432 T^{13} + 629707669696 T^{14} + 3519370440000 T^{15} + 28379602888804 T^{16} + 42608255690736 T^{17} + 1135231306926140 T^{18} + 150372093378672 T^{19} + 33733852675457284 T^{20} + 653967474648827464 T^{22} + 6582952005840035281 T^{24}$$)($$1 + 136 T^{2} + 9604 T^{4} - 1584 T^{5} + 442460 T^{6} - 614448 T^{7} + 15142564 T^{8} - 69480000 T^{9} + 459976384 T^{10} - 4218954336 T^{11} + 15196793798 T^{12} - 156101310432 T^{13} + 629707669696 T^{14} - 3519370440000 T^{15} + 28379602888804 T^{16} - 42608255690736 T^{17} + 1135231306926140 T^{18} - 150372093378672 T^{19} + 33733852675457284 T^{20} + 653967474648827464 T^{22} + 6582952005840035281 T^{24}$$)($$1 + 204 T^{2} + 21584 T^{4} + 1569912 T^{6} + 89400898 T^{8} + 4413449556 T^{10} + 201538374752 T^{12} + 8607122519268 T^{14} + 335798367364723 T^{16} + 11783150728877892 T^{18} + 377715361963583072 T^{20} + 11323704080618524404 T^{22} +$$$$31\!\cdots\!58$$$$T^{24} +$$$$75\!\cdots\!88$$$$T^{26} +$$$$14\!\cdots\!04$$$$T^{28} +$$$$18\!\cdots\!56$$$$T^{30} +$$$$12\!\cdots\!41$$$$T^{32}$$)($$1 + 204 T^{2} + 21584 T^{4} + 1569912 T^{6} + 89400898 T^{8} + 4413449556 T^{10} + 201538374752 T^{12} + 8607122519268 T^{14} + 335798367364723 T^{16} + 11783150728877892 T^{18} + 377715361963583072 T^{20} + 11323704080618524404 T^{22} +$$$$31\!\cdots\!58$$$$T^{24} +$$$$75\!\cdots\!88$$$$T^{26} +$$$$14\!\cdots\!04$$$$T^{28} +$$$$18\!\cdots\!56$$$$T^{30} +$$$$12\!\cdots\!41$$$$T^{32}$$)
$41$ ($$( 1 + 34 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 26 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 26 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 + 34 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 2 T + 101 T^{2} - 150 T^{3} + 6062 T^{4} - 7442 T^{5} + 295913 T^{6} - 305122 T^{7} + 10190222 T^{8} - 10338150 T^{9} + 285401861 T^{10} - 231712402 T^{11} + 4750104241 T^{12} )^{2}$$)($$( 1 + 2 T + 101 T^{2} + 150 T^{3} + 6062 T^{4} + 7442 T^{5} + 295913 T^{6} + 305122 T^{7} + 10190222 T^{8} + 10338150 T^{9} + 285401861 T^{10} + 231712402 T^{11} + 4750104241 T^{12} )^{2}$$)($$( 1 + 2 T + 101 T^{2} + 150 T^{3} + 6062 T^{4} + 7442 T^{5} + 295913 T^{6} + 305122 T^{7} + 10190222 T^{8} + 10338150 T^{9} + 285401861 T^{10} + 231712402 T^{11} + 4750104241 T^{12} )^{2}$$)($$( 1 - 2 T + 101 T^{2} - 150 T^{3} + 6062 T^{4} - 7442 T^{5} + 295913 T^{6} - 305122 T^{7} + 10190222 T^{8} - 10338150 T^{9} + 285401861 T^{10} - 231712402 T^{11} + 4750104241 T^{12} )^{2}$$)($$( 1 + 280 T^{2} + 35970 T^{4} + 2762144 T^{6} + 138512387 T^{8} + 4643164064 T^{10} + 101642623170 T^{12} + 1330029187480 T^{14} + 7984925229121 T^{16} )^{2}$$)($$( 1 + 280 T^{2} + 35970 T^{4} + 2762144 T^{6} + 138512387 T^{8} + 4643164064 T^{10} + 101642623170 T^{12} + 1330029187480 T^{14} + 7984925229121 T^{16} )^{2}$$)
$43$ ($$( 1 - 22 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 70 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 70 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 1849 T^{4} )^{2}$$)($$1 - 262 T^{2} + 32119 T^{4} - 2550678 T^{6} + 156312195 T^{8} - 8188394932 T^{10} + 376534570714 T^{12} - 15140342229268 T^{14} + 534400288578195 T^{16} - 16123761659097222 T^{18} + 375413304716266519 T^{20} - 5662208366080473238 T^{22} + 39959630797262576401 T^{24}$$)($$1 - 262 T^{2} + 32119 T^{4} - 2550678 T^{6} + 156312195 T^{8} - 8188394932 T^{10} + 376534570714 T^{12} - 15140342229268 T^{14} + 534400288578195 T^{16} - 16123761659097222 T^{18} + 375413304716266519 T^{20} - 5662208366080473238 T^{22} + 39959630797262576401 T^{24}$$)($$1 - 262 T^{2} + 32119 T^{4} - 2550678 T^{6} + 156312195 T^{8} - 8188394932 T^{10} + 376534570714 T^{12} - 15140342229268 T^{14} + 534400288578195 T^{16} - 16123761659097222 T^{18} + 375413304716266519 T^{20} - 5662208366080473238 T^{22} + 39959630797262576401 T^{24}$$)($$1 - 262 T^{2} + 32119 T^{4} - 2550678 T^{6} + 156312195 T^{8} - 8188394932 T^{10} + 376534570714 T^{12} - 15140342229268 T^{14} + 534400288578195 T^{16} - 16123761659097222 T^{18} + 375413304716266519 T^{20} - 5662208366080473238 T^{22} + 39959630797262576401 T^{24}$$)($$( 1 - 116 T^{2} + 9516 T^{4} - 572476 T^{6} + 26987126 T^{8} - 1058508124 T^{10} + 32533310316 T^{12} - 733278113684 T^{14} + 11688200277601 T^{16} )^{2}$$)($$( 1 - 116 T^{2} + 9516 T^{4} - 572476 T^{6} + 26987126 T^{8} - 1058508124 T^{10} + 32533310316 T^{12} - 733278113684 T^{14} + 11688200277601 T^{16} )^{2}$$)
$47$ ($$( 1 + 12 T + 95 T^{2} + 564 T^{3} + 2209 T^{4} )^{2}$$)($$( 1 + 18 T + 155 T^{2} + 846 T^{3} + 2209 T^{4} )^{2}$$)($$( 1 - 18 T + 155 T^{2} - 846 T^{3} + 2209 T^{4} )^{2}$$)($$( 1 - 12 T + 95 T^{2} - 564 T^{3} + 2209 T^{4} )^{2}$$)($$1 - 24 T + 384 T^{2} - 4608 T^{3} + 46508 T^{4} - 414696 T^{5} + 3156140 T^{6} - 20858712 T^{7} + 113610684 T^{8} - 488950272 T^{9} + 1199435048 T^{10} + 4264227672 T^{11} - 58297583722 T^{12} + 200418700584 T^{13} + 2649552021032 T^{14} - 50764284089856 T^{15} + 554383896111804 T^{16} - 4783841449650984 T^{17} + 34020712668470060 T^{18} - 210094581563524248 T^{19} + 1107415320065180588 T^{20} - 5156953220057550336 T^{21} + 20198066778558738816 T^{22} - 59331821162016295272 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 - 24 T + 384 T^{2} - 4608 T^{3} + 46508 T^{4} - 414696 T^{5} + 3156140 T^{6} - 20858712 T^{7} + 113610684 T^{8} - 488950272 T^{9} + 1199435048 T^{10} + 4264227672 T^{11} - 58297583722 T^{12} + 200418700584 T^{13} + 2649552021032 T^{14} - 50764284089856 T^{15} + 554383896111804 T^{16} - 4783841449650984 T^{17} + 34020712668470060 T^{18} - 210094581563524248 T^{19} + 1107415320065180588 T^{20} - 5156953220057550336 T^{21} + 20198066778558738816 T^{22} - 59331821162016295272 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 + 24 T + 384 T^{2} + 4608 T^{3} + 46508 T^{4} + 414696 T^{5} + 3156140 T^{6} + 20858712 T^{7} + 113610684 T^{8} + 488950272 T^{9} + 1199435048 T^{10} - 4264227672 T^{11} - 58297583722 T^{12} - 200418700584 T^{13} + 2649552021032 T^{14} + 50764284089856 T^{15} + 554383896111804 T^{16} + 4783841449650984 T^{17} + 34020712668470060 T^{18} + 210094581563524248 T^{19} + 1107415320065180588 T^{20} + 5156953220057550336 T^{21} + 20198066778558738816 T^{22} + 59331821162016295272 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 + 24 T + 384 T^{2} + 4608 T^{3} + 46508 T^{4} + 414696 T^{5} + 3156140 T^{6} + 20858712 T^{7} + 113610684 T^{8} + 488950272 T^{9} + 1199435048 T^{10} - 4264227672 T^{11} - 58297583722 T^{12} - 200418700584 T^{13} + 2649552021032 T^{14} + 50764284089856 T^{15} + 554383896111804 T^{16} + 4783841449650984 T^{17} + 34020712668470060 T^{18} + 210094581563524248 T^{19} + 1107415320065180588 T^{20} + 5156953220057550336 T^{21} + 20198066778558738816 T^{22} + 59331821162016295272 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$( 1 - 42 T + 944 T^{2} - 14952 T^{3} + 185547 T^{4} - 1920744 T^{5} + 17260444 T^{6} - 137982474 T^{7} + 994376960 T^{8} - 6485176278 T^{9} + 38128320796 T^{10} - 199417404312 T^{11} + 905410170507 T^{12} - 3429166544664 T^{13} + 10175579270576 T^{14} - 21278171059446 T^{15} + 23811286661761 T^{16} )^{2}$$)($$( 1 + 42 T + 944 T^{2} + 14952 T^{3} + 185547 T^{4} + 1920744 T^{5} + 17260444 T^{6} + 137982474 T^{7} + 994376960 T^{8} + 6485176278 T^{9} + 38128320796 T^{10} + 199417404312 T^{11} + 905410170507 T^{12} + 3429166544664 T^{13} + 10175579270576 T^{14} + 21278171059446 T^{15} + 23811286661761 T^{16} )^{2}$$)
$53$ ($$( 1 + 9 T + 28 T^{2} + 477 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 - 53 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 - 53 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 - 9 T + 28 T^{2} - 477 T^{3} + 2809 T^{4} )^{2}$$)($$1 - 8 T - 88 T^{2} + 488 T^{3} + 12104 T^{4} - 83832 T^{5} - 305812 T^{6} + 2676792 T^{7} + 22811384 T^{8} - 292893064 T^{9} + 1322605656 T^{10} - 1616113592 T^{11} - 9032303562 T^{12} - 85654020376 T^{13} + 3715199287704 T^{14} - 43605040689128 T^{15} + 179992792035704 T^{16} + 1119422350098456 T^{17} - 6778127605581748 T^{18} - 98478384274815384 T^{19} + 753591292739113544 T^{20} + 1610284632799440904 T^{21} - 15390097392165148312 T^{22} - 74152287434977532776 T^{23} +$$$$49\!\cdots\!41$$$$T^{24}$$)($$1 - 8 T - 88 T^{2} + 488 T^{3} + 12104 T^{4} - 83832 T^{5} - 305812 T^{6} + 2676792 T^{7} + 22811384 T^{8} - 292893064 T^{9} + 1322605656 T^{10} - 1616113592 T^{11} - 9032303562 T^{12} - 85654020376 T^{13} + 3715199287704 T^{14} - 43605040689128 T^{15} + 179992792035704 T^{16} + 1119422350098456 T^{17} - 6778127605581748 T^{18} - 98478384274815384 T^{19} + 753591292739113544 T^{20} + 1610284632799440904 T^{21} - 15390097392165148312 T^{22} - 74152287434977532776 T^{23} +$$$$49\!\cdots\!41$$$$T^{24}$$)($$1 + 8 T - 88 T^{2} - 488 T^{3} + 12104 T^{4} + 83832 T^{5} - 305812 T^{6} - 2676792 T^{7} + 22811384 T^{8} + 292893064 T^{9} + 1322605656 T^{10} + 1616113592 T^{11} - 9032303562 T^{12} + 85654020376 T^{13} + 3715199287704 T^{14} + 43605040689128 T^{15} + 179992792035704 T^{16} - 1119422350098456 T^{17} - 6778127605581748 T^{18} + 98478384274815384 T^{19} + 753591292739113544 T^{20} - 1610284632799440904 T^{21} - 15390097392165148312 T^{22} + 74152287434977532776 T^{23} +$$$$49\!\cdots\!41$$$$T^{24}$$)($$1 + 8 T - 88 T^{2} - 488 T^{3} + 12104 T^{4} + 83832 T^{5} - 305812 T^{6} - 2676792 T^{7} + 22811384 T^{8} + 292893064 T^{9} + 1322605656 T^{10} + 1616113592 T^{11} - 9032303562 T^{12} + 85654020376 T^{13} + 3715199287704 T^{14} + 43605040689128 T^{15} + 179992792035704 T^{16} - 1119422350098456 T^{17} - 6778127605581748 T^{18} + 98478384274815384 T^{19} + 753591292739113544 T^{20} - 1610284632799440904 T^{21} - 15390097392165148312 T^{22} + 74152287434977532776 T^{23} +$$$$49\!\cdots\!41$$$$T^{24}$$)($$( 1 - 14 T + 12 T^{2} + 924 T^{3} - 5230 T^{4} - 6342 T^{5} + 113888 T^{6} - 713762 T^{7} + 5806695 T^{8} - 37829386 T^{9} + 319911392 T^{10} - 944177934 T^{11} - 41267215630 T^{12} + 386412635532 T^{13} + 265972333548 T^{14} - 16445955957718 T^{15} + 62259690411361 T^{16} )^{2}$$)($$( 1 + 14 T + 12 T^{2} - 924 T^{3} - 5230 T^{4} + 6342 T^{5} + 113888 T^{6} + 713762 T^{7} + 5806695 T^{8} + 37829386 T^{9} + 319911392 T^{10} + 944177934 T^{11} - 41267215630 T^{12} - 386412635532 T^{13} + 265972333548 T^{14} + 16445955957718 T^{15} + 62259690411361 T^{16} )^{2}$$)
$59$ ($$1 - 115 T^{2} + 9744 T^{4} - 400315 T^{6} + 12117361 T^{8}$$)($$1 - 10 T^{2} - 3381 T^{4} - 34810 T^{6} + 12117361 T^{8}$$)($$1 - 10 T^{2} - 3381 T^{4} - 34810 T^{6} + 12117361 T^{8}$$)($$1 - 115 T^{2} + 9744 T^{4} - 400315 T^{6} + 12117361 T^{8}$$)($$1 - 12 T - 62 T^{2} + 192 T^{3} + 13661 T^{4} - 4488 T^{5} - 291210 T^{6} - 10035204 T^{7} + 17708314 T^{8} + 439140108 T^{9} + 4538367434 T^{10} - 27175198584 T^{11} - 197381258843 T^{12} - 1603336716456 T^{13} + 15798057037754 T^{14} + 90190156240932 T^{15} + 214578033439354 T^{16} - 7174411185021996 T^{17} - 12283393201595610 T^{18} - 11169067863867672 T^{19} + 2005850608112629181 T^{20} + 1663295197181748288 T^{21} - 31689238704639766862 T^{22} -$$$$36\!\cdots\!08$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 + 12 T - 62 T^{2} - 192 T^{3} + 13661 T^{4} + 4488 T^{5} - 291210 T^{6} + 10035204 T^{7} + 17708314 T^{8} - 439140108 T^{9} + 4538367434 T^{10} + 27175198584 T^{11} - 197381258843 T^{12} + 1603336716456 T^{13} + 15798057037754 T^{14} - 90190156240932 T^{15} + 214578033439354 T^{16} + 7174411185021996 T^{17} - 12283393201595610 T^{18} + 11169067863867672 T^{19} + 2005850608112629181 T^{20} - 1663295197181748288 T^{21} - 31689238704639766862 T^{22} +$$$$36\!\cdots\!08$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 + 12 T - 62 T^{2} - 192 T^{3} + 13661 T^{4} + 4488 T^{5} - 291210 T^{6} + 10035204 T^{7} + 17708314 T^{8} - 439140108 T^{9} + 4538367434 T^{10} + 27175198584 T^{11} - 197381258843 T^{12} + 1603336716456 T^{13} + 15798057037754 T^{14} - 90190156240932 T^{15} + 214578033439354 T^{16} + 7174411185021996 T^{17} - 12283393201595610 T^{18} + 11169067863867672 T^{19} + 2005850608112629181 T^{20} - 1663295197181748288 T^{21} - 31689238704639766862 T^{22} +$$$$36\!\cdots\!08$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 - 12 T - 62 T^{2} + 192 T^{3} + 13661 T^{4} - 4488 T^{5} - 291210 T^{6} - 10035204 T^{7} + 17708314 T^{8} + 439140108 T^{9} + 4538367434 T^{10} - 27175198584 T^{11} - 197381258843 T^{12} - 1603336716456 T^{13} + 15798057037754 T^{14} + 90190156240932 T^{15} + 214578033439354 T^{16} - 7174411185021996 T^{17} - 12283393201595610 T^{18} - 11169067863867672 T^{19} + 2005850608112629181 T^{20} + 1663295197181748288 T^{21} - 31689238704639766862 T^{22} -$$$$36\!\cdots\!08$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 - 392 T^{2} + 82872 T^{4} - 12348112 T^{6} + 1439957090 T^{8} - 138681126360 T^{10} + 11389108537504 T^{12} - 813599166279704 T^{14} + 51103980716496291 T^{16} - 2832138697819649624 T^{18} +$$$$13\!\cdots\!44$$$$T^{20} -$$$$58\!\cdots\!60$$$$T^{22} +$$$$21\!\cdots\!90$$$$T^{24} -$$$$63\!\cdots\!12$$$$T^{26} +$$$$14\!\cdots\!32$$$$T^{28} -$$$$24\!\cdots\!12$$$$T^{30} +$$$$21\!\cdots\!41$$$$T^{32}$$)($$1 - 392 T^{2} + 82872 T^{4} - 12348112 T^{6} + 1439957090 T^{8} - 138681126360 T^{10} + 11389108537504 T^{12} - 813599166279704 T^{14} + 51103980716496291 T^{16} - 2832138697819649624 T^{18} +$$$$13\!\cdots\!44$$$$T^{20} -$$$$58\!\cdots\!60$$$$T^{22} +$$$$21\!\cdots\!90$$$$T^{24} -$$$$63\!\cdots\!12$$$$T^{26} +$$$$14\!\cdots\!32$$$$T^{28} -$$$$24\!\cdots\!12$$$$T^{30} +$$$$21\!\cdots\!41$$$$T^{32}$$)
$61$ ($$( 1 + 61 T^{2} + 3721 T^{4} )^{2}$$)($$( 1 + 9 T + 88 T^{2} + 549 T^{3} + 3721 T^{4} )^{2}$$)($$( 1 + 9 T + 88 T^{2} + 549 T^{3} + 3721 T^{4} )^{2}$$)($$( 1 + 61 T^{2} + 3721 T^{4} )^{2}$$)($$1 + 30 T + 633 T^{2} + 9990 T^{3} + 134066 T^{4} + 1612650 T^{5} + 18045535 T^{6} + 190552410 T^{7} + 1899056448 T^{8} + 17814782910 T^{9} + 157346567941 T^{10} + 1317498445782 T^{11} + 10515537066752 T^{12} + 80367405192702 T^{13} + 585486579308461 T^{14} + 4043617239694710 T^{15} + 26294033629032768 T^{16} + 160939860632635410 T^{17} + 929712718744528135 T^{18} + 5068144234509265650 T^{19} + 25701432624293474546 T^{20} +$$$$11\!\cdots\!90$$$$T^{21} +$$$$45\!\cdots\!33$$$$T^{22} +$$$$13\!\cdots\!30$$$$T^{23} +$$$$26\!\cdots\!21$$$$T^{24}$$)($$1 + 30 T + 633 T^{2} + 9990 T^{3} + 134066 T^{4} + 1612650 T^{5} + 18045535 T^{6} + 190552410 T^{7} + 1899056448 T^{8} + 17814782910 T^{9} + 157346567941 T^{10} + 1317498445782 T^{11} + 10515537066752 T^{12} + 80367405192702 T^{13} + 585486579308461 T^{14} + 4043617239694710 T^{15} + 26294033629032768 T^{16} + 160939860632635410 T^{17} + 929712718744528135 T^{18} + 5068144234509265650 T^{19} + 25701432624293474546 T^{20} +$$$$11\!\cdots\!90$$$$T^{21} +$$$$45\!\cdots\!33$$$$T^{22} +$$$$13\!\cdots\!30$$$$T^{23} +$$$$26\!\cdots\!21$$$$T^{24}$$)($$1 + 30 T + 633 T^{2} + 9990 T^{3} + 134066 T^{4} + 1612650 T^{5} + 18045535 T^{6} + 190552410 T^{7} + 1899056448 T^{8} + 17814782910 T^{9} + 157346567941 T^{10} + 1317498445782 T^{11} + 10515537066752 T^{12} + 80367405192702 T^{13} + 585486579308461 T^{14} + 4043617239694710 T^{15} + 26294033629032768 T^{16} + 160939860632635410 T^{17} + 929712718744528135 T^{18} + 5068144234509265650 T^{19} + 25701432624293474546 T^{20} +$$$$11\!\cdots\!90$$$$T^{21} +$$$$45\!\cdots\!33$$$$T^{22} +$$$$13\!\cdots\!30$$$$T^{23} +$$$$26\!\cdots\!21$$$$T^{24}$$)($$1 + 30 T + 633 T^{2} + 9990 T^{3} + 134066 T^{4} + 1612650 T^{5} + 18045535 T^{6} + 190552410 T^{7} + 1899056448 T^{8} + 17814782910 T^{9} + 157346567941 T^{10} + 1317498445782 T^{11} + 10515537066752 T^{12} + 80367405192702 T^{13} + 585486579308461 T^{14} + 4043617239694710 T^{15} + 26294033629032768 T^{16} + 160939860632635410 T^{17} + 929712718744528135 T^{18} + 5068144234509265650 T^{19} + 25701432624293474546 T^{20} +$$$$11\!\cdots\!90$$$$T^{21} +$$$$45\!\cdots\!33$$$$T^{22} +$$$$13\!\cdots\!30$$$$T^{23} +$$$$26\!\cdots\!21$$$$T^{24}$$)($$( 1 - 54 T + 1528 T^{2} - 30024 T^{3} + 457410 T^{4} - 5741010 T^{5} + 61597952 T^{6} - 577586742 T^{7} + 4788758087 T^{8} - 35232791262 T^{9} + 229205979392 T^{10} - 1303100190810 T^{11} + 6333226131810 T^{12} - 25358159341224 T^{13} + 78723132023608 T^{14} - 169708113145134 T^{15} + 191707312997281 T^{16} )^{2}$$)($$( 1 - 54 T + 1528 T^{2} - 30024 T^{3} + 457410 T^{4} - 5741010 T^{5} + 61597952 T^{6} - 577586742 T^{7} + 4788758087 T^{8} - 35232791262 T^{9} + 229205979392 T^{10} - 1303100190810 T^{11} + 6333226131810 T^{12} - 25358159341224 T^{13} + 78723132023608 T^{14} - 169708113145134 T^{15} + 191707312997281 T^{16} )^{2}$$)
$67$ ($$1 + 130 T^{2} + 12411 T^{4} + 583570 T^{6} + 20151121 T^{8}$$)($$( 1 - 109 T^{2} + 4489 T^{4} )( 1 + 122 T^{2} + 4489 T^{4} )$$)($$( 1 - 109 T^{2} + 4489 T^{4} )( 1 + 122 T^{2} + 4489 T^{4} )$$)($$1 + 130 T^{2} + 12411 T^{4} + 583570 T^{6} + 20151121 T^{8}$$)($$1 + 6 T + 365 T^{2} + 2118 T^{3} + 73802 T^{4} + 425022 T^{5} + 10500435 T^{6} + 59263014 T^{7} + 1154715592 T^{8} + 6293670990 T^{9} + 102704273449 T^{10} + 526619905806 T^{11} + 7543905009712 T^{12} + 35283533689002 T^{13} + 461039483512561 T^{14} + 1892903367965370 T^{15} + 23268813614978632 T^{16} + 80012483117892498 T^{17} + 949852362170743515 T^{18} + 2575935767917592106 T^{19} + 29968606739035219082 T^{20} + 57623439851352697746 T^{21} +$$$$66\!\cdots\!85$$$$T^{22} +$$$$73\!\cdots\!98$$$$T^{23} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 - 6 T + 365 T^{2} - 2118 T^{3} + 73802 T^{4} - 425022 T^{5} + 10500435 T^{6} - 59263014 T^{7} + 1154715592 T^{8} - 6293670990 T^{9} + 102704273449 T^{10} - 526619905806 T^{11} + 7543905009712 T^{12} - 35283533689002 T^{13} + 461039483512561 T^{14} - 1892903367965370 T^{15} + 23268813614978632 T^{16} - 80012483117892498 T^{17} + 949852362170743515 T^{18} - 2575935767917592106 T^{19} + 29968606739035219082 T^{20} - 57623439851352697746 T^{21} +$$$$66\!\cdots\!85$$$$T^{22} -$$$$73\!\cdots\!98$$$$T^{23} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 + 6 T + 365 T^{2} + 2118 T^{3} + 73802 T^{4} + 425022 T^{5} + 10500435 T^{6} + 59263014 T^{7} + 1154715592 T^{8} + 6293670990 T^{9} + 102704273449 T^{10} + 526619905806 T^{11} + 7543905009712 T^{12} + 35283533689002 T^{13} + 461039483512561 T^{14} + 1892903367965370 T^{15} + 23268813614978632 T^{16} + 80012483117892498 T^{17} + 949852362170743515 T^{18} + 2575935767917592106 T^{19} + 29968606739035219082 T^{20} + 57623439851352697746 T^{21} +$$$$66\!\cdots\!85$$$$T^{22} +$$$$73\!\cdots\!98$$$$T^{23} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 - 6 T + 365 T^{2} - 2118 T^{3} + 73802 T^{4} - 425022 T^{5} + 10500435 T^{6} - 59263014 T^{7} + 1154715592 T^{8} - 6293670990 T^{9} + 102704273449 T^{10} - 526619905806 T^{11} + 7543905009712 T^{12} - 35283533689002 T^{13} + 461039483512561 T^{14} - 1892903367965370 T^{15} + 23268813614978632 T^{16} - 80012483117892498 T^{17} + 949852362170743515 T^{18} - 2575935767917592106 T^{19} + 29968606739035219082 T^{20} - 57623439851352697746 T^{21} +$$$$66\!\cdots\!85$$$$T^{22} -$$$$73\!\cdots\!98$$$$T^{23} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 + 128 T^{2} + 600 T^{4} - 951488 T^{6} - 43249054 T^{8} + 3964452960 T^{10} + 377388054688 T^{12} - 6436691415616 T^{14} - 1931826199679325 T^{16} - 28894307764700224 T^{18} + 7604792353972505248 T^{20} +$$$$35\!\cdots\!40$$$$T^{22} -$$$$17\!\cdots\!14$$$$T^{24} -$$$$17\!\cdots\!12$$$$T^{26} +$$$$49\!\cdots\!00$$$$T^{28} +$$$$47\!\cdots\!12$$$$T^{30} +$$$$16\!\cdots\!81$$$$T^{32}$$)($$1 + 128 T^{2} + 600 T^{4} - 951488 T^{6} - 43249054 T^{8} + 3964452960 T^{10} + 377388054688 T^{12} - 6436691415616 T^{14} - 1931826199679325 T^{16} - 28894307764700224 T^{18} + 7604792353972505248 T^{20} +$$$$35\!\cdots\!40$$$$T^{22} -$$$$17\!\cdots\!14$$$$T^{24} -$$$$17\!\cdots\!12$$$$T^{26} +$$$$49\!\cdots\!00$$$$T^{28} +$$$$47\!\cdots\!12$$$$T^{30} +$$$$16\!\cdots\!81$$$$T^{32}$$)
$71$ ($$( 1 + 2 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 106 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 106 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 5041 T^{4} )^{2}$$)($$1 - 300 T^{2} + 49610 T^{4} - 6300412 T^{6} + 667955583 T^{8} - 59469293656 T^{10} + 4533955360172 T^{12} - 299784709319896 T^{14} + 16973874197365023 T^{16} - 807084566019275452 T^{18} + 32035832685102203210 T^{20} -$$$$97\!\cdots\!00$$$$T^{22} +$$$$16\!\cdots\!41$$$$T^{24}$$)($$1 - 300 T^{2} + 49610 T^{4} - 6300412 T^{6} + 667955583 T^{8} - 59469293656 T^{10} + 4533955360172 T^{12} - 299784709319896 T^{14} + 16973874197365023 T^{16} - 807084566019275452 T^{18} + 32035832685102203210 T^{20} -$$$$97\!\cdots\!00$$$$T^{22} +$$$$16\!\cdots\!41$$$$T^{24}$$)($$1 - 300 T^{2} + 49610 T^{4} - 6300412 T^{6} + 667955583 T^{8} - 59469293656 T^{10} + 4533955360172 T^{12} - 299784709319896 T^{14} + 16973874197365023 T^{16} - 807084566019275452 T^{18} + 32035832685102203210 T^{20} -$$$$97\!\cdots\!00$$$$T^{22} +$$$$16\!\cdots\!41$$$$T^{24}$$)($$1 - 300 T^{2} + 49610 T^{4} - 6300412 T^{6} + 667955583 T^{8} - 59469293656 T^{10} + 4533955360172 T^{12} - 299784709319896 T^{14} + 16973874197365023 T^{16} - 807084566019275452 T^{18} + 32035832685102203210 T^{20} -$$$$97\!\cdots\!00$$$$T^{22} +$$$$16\!\cdots\!41$$$$T^{24}$$)($$( 1 - 172 T^{2} + 12162 T^{4} - 750752 T^{6} + 58967291 T^{8} - 3784540832 T^{10} + 309056864322 T^{12} - 22033248834412 T^{14} + 645753531245761 T^{16} )^{2}$$)($$( 1 - 172 T^{2} + 12162 T^{4} - 750752 T^{6} + 58967291 T^{8} - 3784540832 T^{10} + 309056864322 T^{12} - 22033248834412 T^{14} + 645753531245761 T^{16} )^{2}$$)
$73$ ($$1 - 98 T^{2} + 4275 T^{4} - 522242 T^{6} + 28398241 T^{8}$$)($$( 1 - 97 T^{2} + 5329 T^{4} )( 1 - 46 T^{2} + 5329 T^{4} )$$)($$( 1 - 97 T^{2} + 5329 T^{4} )( 1 - 46 T^{2} + 5329 T^{4} )$$)($$1 - 98 T^{2} + 4275 T^{4} - 522242 T^{6} + 28398241 T^{8}$$)($$1 - 158 T^{2} + 1008 T^{3} + 8161 T^{4} - 157032 T^{5} + 94142 T^{6} + 10339488 T^{7} - 43316978 T^{8} - 543674664 T^{9} + 5990041714 T^{10} + 17216153208 T^{11} - 594295552363 T^{12} + 1256779184184 T^{13} + 31920932293906 T^{14} - 211498686765288 T^{15} - 1230125980635698 T^{16} + 21434498858964384 T^{17} + 14246906731299038 T^{18} - 1734795084250840104 T^{19} + 6581520809947595041 T^{20} + 59342559401934056304 T^{21} -$$$$67\!\cdots\!42$$$$T^{22} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$1 - 158 T^{2} - 1008 T^{3} + 8161 T^{4} + 157032 T^{5} + 94142 T^{6} - 10339488 T^{7} - 43316978 T^{8} + 543674664 T^{9} + 5990041714 T^{10} - 17216153208 T^{11} - 594295552363 T^{12} - 1256779184184 T^{13} + 31920932293906 T^{14} + 211498686765288 T^{15} - 1230125980635698 T^{16} - 21434498858964384 T^{17} + 14246906731299038 T^{18} + 1734795084250840104 T^{19} + 6581520809947595041 T^{20} - 59342559401934056304 T^{21} -$$$$67\!\cdots\!42$$$$T^{22} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$1 - 158 T^{2} + 1008 T^{3} + 8161 T^{4} - 157032 T^{5} + 94142 T^{6} + 10339488 T^{7} - 43316978 T^{8} - 543674664 T^{9} + 5990041714 T^{10} + 17216153208 T^{11} - 594295552363 T^{12} + 1256779184184 T^{13} + 31920932293906 T^{14} - 211498686765288 T^{15} - 1230125980635698 T^{16} + 21434498858964384 T^{17} + 14246906731299038 T^{18} - 1734795084250840104 T^{19} + 6581520809947595041 T^{20} + 59342559401934056304 T^{21} -$$$$67\!\cdots\!42$$$$T^{22} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$1 - 158 T^{2} - 1008 T^{3} + 8161 T^{4} + 157032 T^{5} + 94142 T^{6} - 10339488 T^{7} - 43316978 T^{8} + 543674664 T^{9} + 5990041714 T^{10} - 17216153208 T^{11} - 594295552363 T^{12} - 1256779184184 T^{13} + 31920932293906 T^{14} + 211498686765288 T^{15} - 1230125980635698 T^{16} - 21434498858964384 T^{17} + 14246906731299038 T^{18} + 1734795084250840104 T^{19} + 6581520809947595041 T^{20} - 59342559401934056304 T^{21} -$$$$67\!\cdots\!42$$$$T^{22} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$( 1 - 180 T^{2} + 16666 T^{4} - 913680 T^{6} + 46500915 T^{8} - 4869000720 T^{10} + 473285084506 T^{12} - 27240160732020 T^{14} + 806460091894081 T^{16} )^{2}$$)($$( 1 - 180 T^{2} + 16666 T^{4} - 913680 T^{6} + 46500915 T^{8} - 4869000720 T^{10} + 473285084506 T^{12} - 27240160732020 T^{14} + 806460091894081 T^{16} )^{2}$$)
$79$ ($$( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} )^{2}$$)($$1 - 4 T - 254 T^{2} - 1984 T^{3} + 51521 T^{4} + 543784 T^{5} - 2546434 T^{6} - 103559324 T^{7} - 209408530 T^{8} + 8333233172 T^{9} + 86160957682 T^{10} - 365142325960 T^{11} - 8321189358475 T^{12} - 28846243750840 T^{13} + 537730536893362 T^{14} + 4108608949889708 T^{15} - 8156479205590930 T^{16} - 318657880590314276 T^{17} - 619006161712162114 T^{18} + 10442778444129485656 T^{19} + 78162962995195929281 T^{20} -$$$$23\!\cdots\!96$$$$T^{21} -$$$$24\!\cdots\!54$$$$T^{22} -$$$$29\!\cdots\!16$$$$T^{23} +$$$$59\!\cdots\!41$$$$T^{24}$$)($$1 - 4 T - 254 T^{2} - 1984 T^{3} + 51521 T^{4} + 543784 T^{5} - 2546434 T^{6} - 103559324 T^{7} - 209408530 T^{8} + 8333233172 T^{9} + 86160957682 T^{10} - 365142325960 T^{11} - 8321189358475 T^{12} - 28846243750840 T^{13} + 537730536893362 T^{14} + 4108608949889708 T^{15} - 8156479205590930 T^{16} - 318657880590314276 T^{17} - 619006161712162114 T^{18} + 10442778444129485656 T^{19} + 78162962995195929281 T^{20} -$$$$23\!\cdots\!96$$$$T^{21} -$$$$24\!\cdots\!54$$$$T^{22} -$$$$29\!\cdots\!16$$$$T^{23} +$$$$59\!\cdots\!41$$$$T^{24}$$)($$1 - 4 T - 254 T^{2} - 1984 T^{3} + 51521 T^{4} + 543784 T^{5} - 2546434 T^{6} - 103559324 T^{7} - 209408530 T^{8} + 8333233172 T^{9} + 86160957682 T^{10} - 365142325960 T^{11} - 8321189358475 T^{12} - 28846243750840 T^{13} + 537730536893362 T^{14} + 4108608949889708 T^{15} - 8156479205590930 T^{16} - 318657880590314276 T^{17} - 619006161712162114 T^{18} + 10442778444129485656 T^{19} + 78162962995195929281 T^{20} -$$$$23\!\cdots\!96$$$$T^{21} -$$$$24\!\cdots\!54$$$$T^{22} -$$$$29\!\cdots\!16$$$$T^{23} +$$$$59\!\cdots\!41$$$$T^{24}$$)($$1 - 4 T - 254 T^{2} - 1984 T^{3} + 51521 T^{4} + 543784 T^{5} - 2546434 T^{6} - 103559324 T^{7} - 209408530 T^{8} + 8333233172 T^{9} + 86160957682 T^{10} - 365142325960 T^{11} - 8321189358475 T^{12} - 28846243750840 T^{13} + 537730536893362 T^{14} + 4108608949889708 T^{15} - 8156479205590930 T^{16} - 318657880590314276 T^{17} - 619006161712162114 T^{18} + 10442778444129485656 T^{19} + 78162962995195929281 T^{20} -$$$$23\!\cdots\!96$$$$T^{21} -$$$$24\!\cdots\!54$$$$T^{22} -$$$$29\!\cdots\!16$$$$T^{23} +$$$$59\!\cdots\!41$$$$T^{24}$$)($$( 1 - 12 T - 156 T^{2} + 1632 T^{3} + 23959 T^{4} - 159888 T^{5} - 2286612 T^{6} + 4972548 T^{7} + 201275328 T^{8} + 392831292 T^{9} - 14270745492 T^{10} - 78831019632 T^{11} + 933204990679 T^{12} + 5021756043168 T^{13} - 37921643061276 T^{14} - 230446907833908 T^{15} + 1517108809906561 T^{16} )^{2}$$)($$( 1 - 12 T - 156 T^{2} + 1632 T^{3} + 23959 T^{4} - 159888 T^{5} - 2286612 T^{6} + 4972548 T^{7} + 201275328 T^{8} + 392831292 T^{9} - 14270745492 T^{10} - 78831019632 T^{11} + 933204990679 T^{12} + 5021756043168 T^{13} - 37921643061276 T^{14} - 230446907833908 T^{15} + 1517108809906561 T^{16} )^{2}$$)
$83$ ($$( 1 - 91 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 58 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 58 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 91 T^{2} + 6889 T^{4} )^{2}$$)($$1 - 870 T^{2} + 355487 T^{4} - 90222262 T^{6} + 15841880811 T^{8} - 2027424957268 T^{10} + 193917361121450 T^{12} - 13966930530619252 T^{14} + 751829064772178331 T^{16} - 29497300024475740678 T^{18} +$$$$80\!\cdots\!67$$$$T^{20} -$$$$13\!\cdots\!30$$$$T^{22} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 - 870 T^{2} + 355487 T^{4} - 90222262 T^{6} + 15841880811 T^{8} - 2027424957268 T^{10} + 193917361121450 T^{12} - 13966930530619252 T^{14} + 751829064772178331 T^{16} - 29497300024475740678 T^{18} +$$$$80\!\cdots\!67$$$$T^{20} -$$$$13\!\cdots\!30$$$$T^{22} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 - 870 T^{2} + 355487 T^{4} - 90222262 T^{6} + 15841880811 T^{8} - 2027424957268 T^{10} + 193917361121450 T^{12} - 13966930530619252 T^{14} + 751829064772178331 T^{16} - 29497300024475740678 T^{18} +$$$$80\!\cdots\!67$$$$T^{20} -$$$$13\!\cdots\!30$$$$T^{22} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 - 870 T^{2} + 355487 T^{4} - 90222262 T^{6} + 15841880811 T^{8} - 2027424957268 T^{10} + 193917361121450 T^{12} - 13966930530619252 T^{14} + 751829064772178331 T^{16} - 29497300024475740678 T^{18} +$$$$80\!\cdots\!67$$$$T^{20} -$$$$13\!\cdots\!30$$$$T^{22} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$( 1 - 244 T^{2} + 29232 T^{4} - 2582300 T^{6} + 210508718 T^{8} - 17789464700 T^{10} + 1387301639472 T^{12} - 79773451102036 T^{14} + 2252292232139041 T^{16} )^{2}$$)($$( 1 - 244 T^{2} + 29232 T^{4} - 2582300 T^{6} + 210508718 T^{8} - 17789464700 T^{10} + 1387301639472 T^{12} - 79773451102036 T^{14} + 2252292232139041 T^{16} )^{2}$$)
$89$ ($$1 - 70 T^{2} - 3021 T^{4} - 554470 T^{6} + 62742241 T^{8}$$)($$1 - 70 T^{2} - 3021 T^{4} - 554470 T^{6} + 62742241 T^{8}$$)($$1 - 70 T^{2} - 3021 T^{4} - 554470 T^{6} + 62742241 T^{8}$$)($$1 - 70 T^{2} - 3021 T^{4} - 554470 T^{6} + 62742241 T^{8}$$)($$1 - 26 T + 101 T^{2} + 1838 T^{3} + 1058 T^{4} - 234822 T^{5} - 191269 T^{6} + 17352042 T^{7} - 36283792 T^{8} - 94067578 T^{9} - 6641487 T^{10} - 7507089026 T^{11} - 13384168368 T^{12} - 668130923314 T^{13} - 52607218527 T^{14} - 66314726395082 T^{15} - 2276526422057872 T^{16} + 96894834089544858 T^{17} - 95057114540819509 T^{18} - 10386490522837910838 T^{19} + 4164910956432801698 T^{20} +$$$$64\!\cdots\!42$$$$T^{21} +$$$$31\!\cdots\!01$$$$T^{22} -$$$$72\!\cdots\!14$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$1 + 26 T + 101 T^{2} - 1838 T^{3} + 1058 T^{4} + 234822 T^{5} - 191269 T^{6} - 17352042 T^{7} - 36283792 T^{8} + 94067578 T^{9} - 6641487 T^{10} + 7507089026 T^{11} - 13384168368 T^{12} + 668130923314 T^{13} - 52607218527 T^{14} + 66314726395082 T^{15} - 2276526422057872 T^{16} - 96894834089544858 T^{17} - 95057114540819509 T^{18} + 10386490522837910838 T^{19} + 4164910956432801698 T^{20} -$$$$64\!\cdots\!42$$$$T^{21} +$$$$31\!\cdots\!01$$$$T^{22} +$$$$72\!\cdots\!14$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$1 + 26 T + 101 T^{2} - 1838 T^{3} + 1058 T^{4} + 234822 T^{5} - 191269 T^{6} - 17352042 T^{7} - 36283792 T^{8} + 94067578 T^{9} - 6641487 T^{10} + 7507089026 T^{11} - 13384168368 T^{12} + 668130923314 T^{13} - 52607218527 T^{14} + 66314726395082 T^{15} - 2276526422057872 T^{16} - 96894834089544858 T^{17} - 95057114540819509 T^{18} + 10386490522837910838 T^{19} + 4164910956432801698 T^{20} -$$$$64\!\cdots\!42$$$$T^{21} +$$$$31\!\cdots\!01$$$$T^{22} +$$$$72\!\cdots\!14$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$1 - 26 T + 101 T^{2} + 1838 T^{3} + 1058 T^{4} - 234822 T^{5} - 191269 T^{6} + 17352042 T^{7} - 36283792 T^{8} - 94067578 T^{9} - 6641487 T^{10} - 7507089026 T^{11} - 13384168368 T^{12} - 668130923314 T^{13} - 52607218527 T^{14} - 66314726395082 T^{15} - 2276526422057872 T^{16} + 96894834089544858 T^{17} - 95057114540819509 T^{18} - 10386490522837910838 T^{19} + 4164910956432801698 T^{20} +$$$$64\!\cdots\!42$$$$T^{21} +$$$$31\!\cdots\!01$$$$T^{22} -$$$$72\!\cdots\!14$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$1 - 280 T^{2} + 33934 T^{4} - 2359280 T^{6} + 86826641 T^{8} + 3149241200 T^{10} - 1390981471378 T^{12} + 224015580284440 T^{14} - 23587997383426652 T^{16} + 1774427411433049240 T^{18} - 87273294703733078098 T^{20} +$$$$15\!\cdots\!00$$$$T^{22} +$$$$34\!\cdots\!21$$$$T^{24} -$$$$73\!\cdots\!80$$$$T^{26} +$$$$83\!\cdots\!14$$$$T^{28} -$$$$54\!\cdots\!80$$$$T^{30} +$$$$15\!\cdots\!61$$$$T^{32}$$)($$1 - 280 T^{2} + 33934 T^{4} - 2359280 T^{6} + 86826641 T^{8} + 3149241200 T^{10} - 1390981471378 T^{12} + 224015580284440 T^{14} - 23587997383426652 T^{16} + 1774427411433049240 T^{18} - 87273294703733078098 T^{20} +$$$$15\!\cdots\!00$$$$T^{22} +$$$$34\!\cdots\!21$$$$T^{24} -$$$$73\!\cdots\!80$$$$T^{26} +$$$$83\!\cdots\!14$$$$T^{28} -$$$$54\!\cdots\!80$$$$T^{30} +$$$$15\!\cdots\!61$$$$T^{32}$$)
$97$ ($$( 1 + 167 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 49 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 49 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 + 167 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 36 T + 890 T^{2} - 15900 T^{3} + 234435 T^{4} - 2872320 T^{5} + 30607204 T^{6} - 278615040 T^{7} + 2205798915 T^{8} - 14511500700 T^{9} + 78791060090 T^{10} - 309144249252 T^{11} + 832972004929 T^{12} )^{2}$$)($$( 1 + 36 T + 890 T^{2} + 15900 T^{3} + 234435 T^{4} + 2872320 T^{5} + 30607204 T^{6} + 278615040 T^{7} + 2205798915 T^{8} + 14511500700 T^{9} + 78791060090 T^{10} + 309144249252 T^{11} + 832972004929 T^{12} )^{2}$$)($$( 1 - 36 T + 890 T^{2} - 15900 T^{3} + 234435 T^{4} - 2872320 T^{5} + 30607204 T^{6} - 278615040 T^{7} + 2205798915 T^{8} - 14511500700 T^{9} + 78791060090 T^{10} - 309144249252 T^{11} + 832972004929 T^{12} )^{2}$$)($$( 1 + 36 T + 890 T^{2} + 15900 T^{3} + 234435 T^{4} + 2872320 T^{5} + 30607204 T^{6} + 278615040 T^{7} + 2205798915 T^{8} + 14511500700 T^{9} + 78791060090 T^{10} + 309144249252 T^{11} + 832972004929 T^{12} )^{2}$$)($$( 1 + 468 T^{2} + 112546 T^{4} + 17841600 T^{6} + 2025951627 T^{8} + 167871614400 T^{10} + 9963616459426 T^{12} + 389830898306772 T^{14} + 7837433594376961 T^{16} )^{2}$$)($$( 1 + 468 T^{2} + 112546 T^{4} + 17841600 T^{6} + 2025951627 T^{8} + 167871614400 T^{10} + 9963616459426 T^{12} + 389830898306772 T^{14} + 7837433594376961 T^{16} )^{2}$$)