# Properties

 Label 392.3.k Level 392 Weight 3 Character orbit k Rep. character $$\chi_{392}(67,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 152 Newform subspaces 16 Sturm bound 168 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$392 = 2^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 392.k (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$56$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$16$$ Sturm bound: $$168$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(392, [\chi])$$.

Total New Old
Modular forms 240 168 72
Cusp forms 208 152 56
Eisenstein series 32 16 16

## Trace form

 $$152q - q^{2} + 2q^{3} + 7q^{4} - 4q^{6} - 34q^{8} - 202q^{9} + O(q^{10})$$ $$152q - q^{2} + 2q^{3} + 7q^{4} - 4q^{6} - 34q^{8} - 202q^{9} + 18q^{10} + 34q^{11} - 22q^{12} + 3q^{16} + 2q^{17} - 29q^{18} + 2q^{19} + 80q^{20} + 60q^{22} + 98q^{24} + 302q^{25} + 58q^{26} - 28q^{27} + 4q^{30} - 61q^{32} - 34q^{33} - 164q^{34} - 18q^{36} - 140q^{38} + 98q^{40} + 8q^{41} + 176q^{43} - 24q^{44} + 142q^{46} - 328q^{48} + 314q^{50} + 154q^{51} - 248q^{52} - 80q^{54} + 44q^{57} + 242q^{58} - 62q^{59} + 166q^{60} + 392q^{62} + 226q^{64} - 48q^{65} + 380q^{66} - 302q^{67} + 649q^{72} + 82q^{73} - 216q^{74} - 84q^{75} + 284q^{76} - 284q^{78} + 412q^{80} - 392q^{81} + 22q^{82} + 488q^{83} - 702q^{86} - 252q^{88} - 46q^{89} - 884q^{90} - 1332q^{92} - 420q^{94} - 80q^{96} + 424q^{97} - 1336q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(392, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
392.3.k.a $$2$$ $$10.681$$ $$\Q(\sqrt{-3})$$ None $$-4$$ $$1$$ $$9$$ $$0$$ $$q-2q^{2}+\zeta_{6}q^{3}+4q^{4}+(3+3\zeta_{6})q^{5}+\cdots$$
392.3.k.b $$2$$ $$10.681$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-2})$$ $$2$$ $$-2$$ $$0$$ $$0$$ $$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots$$
392.3.k.c $$2$$ $$10.681$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$1$$ $$-9$$ $$0$$ $$q+2\zeta_{6}q^{2}+\zeta_{6}q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$$
392.3.k.d $$2$$ $$10.681$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-2})$$ $$2$$ $$2$$ $$0$$ $$0$$ $$q+(2-2\zeta_{6})q^{2}+2\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots$$
392.3.k.e $$4$$ $$10.681$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ $$-4$$ $$-8$$ $$0$$ $$0$$ $$q+(-2-2\beta _{2})q^{2}+(-\beta _{1}+4\beta _{2}-\beta _{3})q^{3}+\cdots$$
392.3.k.f $$4$$ $$10.681$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ $$-4$$ $$8$$ $$0$$ $$0$$ $$q+(-2-2\beta _{2})q^{2}+(-\beta _{1}-4\beta _{2}-\beta _{3})q^{3}+\cdots$$
392.3.k.g $$4$$ $$10.681$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ $$\Q(\sqrt{-7})$$ $$3$$ $$0$$ $$0$$ $$0$$ $$q+(2-\beta _{1}-2\beta _{2})q^{2}+(\beta _{2}-3\beta _{3})q^{4}+\cdots$$
392.3.k.h $$4$$ $$10.681$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-2})$$ $$4$$ $$0$$ $$0$$ $$0$$ $$q-2\beta _{2}q^{2}+\beta _{1}q^{3}+(-4-4\beta _{2})q^{4}+\cdots$$
392.3.k.i $$8$$ $$10.681$$ 8.0.796594176.2 None $$0$$ $$-8$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{3}+\beta _{4}-\beta _{6})q^{2}+(-2-2\beta _{1}+\cdots)q^{3}+\cdots$$
392.3.k.j $$8$$ $$10.681$$ 8.0.796594176.2 None $$0$$ $$8$$ $$0$$ $$0$$ $$q+(-\beta _{2}-\beta _{3}-\beta _{4})q^{2}+(2+2\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots$$
392.3.k.k $$12$$ $$10.681$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{3}+\beta _{4}+\beta _{7}+\beta _{8})q^{3}+\cdots$$
392.3.k.l $$12$$ $$10.681$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$2$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{10}q^{2}+(-\beta _{3}+\beta _{5}+\beta _{6}-\beta _{9}+\cdots)q^{3}+\cdots$$
392.3.k.m $$16$$ $$10.681$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-8$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}+\beta _{8})q^{2}-\beta _{7}q^{3}+(1-2\beta _{3}+\cdots)q^{4}+\cdots$$
392.3.k.n $$16$$ $$10.681$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-1$$ $$-8$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{6}+\beta _{9})q^{3}+\cdots$$
392.3.k.o $$16$$ $$10.681$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-1$$ $$8$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{8}-\beta _{10}+\cdots)q^{3}+\cdots$$
392.3.k.p $$40$$ $$10.681$$ None $$6$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(392, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(392, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$( 1 + 2 T )^{2}$$)($$1 - 2 T + 4 T^{2}$$)($$1 - 2 T + 4 T^{2}$$)($$1 - 2 T + 4 T^{2}$$)($$( 1 + 2 T + 4 T^{2} )^{2}$$)($$( 1 + 2 T + 4 T^{2} )^{2}$$)($$1 - 3 T + 5 T^{2} - 12 T^{3} + 16 T^{4}$$)($$( 1 - 2 T + 4 T^{2} )^{2}$$)($$1 - 6 T^{2} + 20 T^{4} - 96 T^{6} + 256 T^{8}$$)($$1 - 6 T^{2} + 20 T^{4} - 96 T^{6} + 256 T^{8}$$)($$1 + 2 T^{2} - 12 T^{3} + 12 T^{4} - 12 T^{5} + 148 T^{6} - 48 T^{7} + 192 T^{8} - 768 T^{9} + 512 T^{10} + 4096 T^{12}$$)($$1 - 2 T + 4 T^{2} - 8 T^{3} + 8 T^{4} - 32 T^{5} + 80 T^{6} - 128 T^{7} + 128 T^{8} - 512 T^{9} + 1024 T^{10} - 2048 T^{11} + 4096 T^{12}$$)($$( 1 + 4 T + 6 T^{2} + 8 T^{3} + 20 T^{4} + 32 T^{5} + 96 T^{6} + 256 T^{7} + 256 T^{8} )^{2}$$)($$1 + T + 3 T^{2} - 6 T^{3} - 22 T^{4} - 44 T^{5} - 20 T^{6} + 112 T^{7} + 368 T^{8} + 448 T^{9} - 320 T^{10} - 2816 T^{11} - 5632 T^{12} - 6144 T^{13} + 12288 T^{14} + 16384 T^{15} + 65536 T^{16}$$)($$1 + T + 3 T^{2} - 6 T^{3} - 22 T^{4} - 44 T^{5} - 20 T^{6} + 112 T^{7} + 368 T^{8} + 448 T^{9} - 320 T^{10} - 2816 T^{11} - 5632 T^{12} - 6144 T^{13} + 12288 T^{14} + 16384 T^{15} + 65536 T^{16}$$)
$3$ ($$1 - T - 8 T^{2} - 9 T^{3} + 81 T^{4}$$)($$1 + 2 T - 5 T^{2} + 18 T^{3} + 81 T^{4}$$)($$1 - T - 8 T^{2} - 9 T^{3} + 81 T^{4}$$)($$1 - 2 T - 5 T^{2} - 18 T^{3} + 81 T^{4}$$)($$1 + 8 T + 32 T^{2} + 112 T^{3} + 367 T^{4} + 1008 T^{5} + 2592 T^{6} + 5832 T^{7} + 6561 T^{8}$$)($$1 - 8 T + 32 T^{2} - 112 T^{3} + 367 T^{4} - 1008 T^{5} + 2592 T^{6} - 5832 T^{7} + 6561 T^{8}$$)($$( 1 - 9 T^{2} + 81 T^{4} )^{2}$$)($$1 + 14 T^{2} + 115 T^{4} + 1134 T^{6} + 6561 T^{8}$$)($$( 1 + 4 T - 4 T^{2} + 8 T^{3} + 175 T^{4} + 72 T^{5} - 324 T^{6} + 2916 T^{7} + 6561 T^{8} )^{2}$$)($$( 1 - 4 T - 4 T^{2} - 8 T^{3} + 175 T^{4} - 72 T^{5} - 324 T^{6} - 2916 T^{7} + 6561 T^{8} )^{2}$$)($$( 1 + 3 T - 7 T^{2} - 22 T^{3} + 7 T^{4} - 61 T^{5} - 350 T^{6} - 549 T^{7} + 567 T^{8} - 16038 T^{9} - 45927 T^{10} + 177147 T^{11} + 531441 T^{12} )^{2}$$)($$( 1 - 3 T + T^{2} + 14 T^{3} - 65 T^{4} + 37 T^{5} + 514 T^{6} + 333 T^{7} - 5265 T^{8} + 10206 T^{9} + 6561 T^{10} - 177147 T^{11} + 531441 T^{12} )^{2}$$)($$( 1 - 16 T^{2} + 38 T^{4} - 896 T^{6} + 20227 T^{8} - 72576 T^{10} + 249318 T^{12} - 8503056 T^{14} + 43046721 T^{16} )^{2}$$)($$( 1 + 4 T + 2 T^{2} - 14 T^{4} - 140 T^{5} + 672 T^{6} + 3140 T^{7} + 3439 T^{8} + 28260 T^{9} + 54432 T^{10} - 102060 T^{11} - 91854 T^{12} + 1062882 T^{14} + 19131876 T^{15} + 43046721 T^{16} )^{2}$$)($$( 1 - 4 T + 2 T^{2} - 14 T^{4} + 140 T^{5} + 672 T^{6} - 3140 T^{7} + 3439 T^{8} - 28260 T^{9} + 54432 T^{10} + 102060 T^{11} - 91854 T^{12} + 1062882 T^{14} - 19131876 T^{15} + 43046721 T^{16} )^{2}$$)
$5$ ($$1 - 9 T + 52 T^{2} - 225 T^{3} + 625 T^{4}$$)($$( 1 - 5 T + 25 T^{2} )( 1 + 5 T + 25 T^{2} )$$)($$1 + 9 T + 52 T^{2} + 225 T^{3} + 625 T^{4}$$)($$( 1 - 5 T + 25 T^{2} )( 1 + 5 T + 25 T^{2} )$$)($$( 1 - 5 T + 25 T^{2} )^{2}( 1 + 5 T + 25 T^{2} )^{2}$$)($$( 1 - 5 T + 25 T^{2} )^{2}( 1 + 5 T + 25 T^{2} )^{2}$$)($$( 1 - 5 T + 25 T^{2} )^{2}( 1 + 5 T + 25 T^{2} )^{2}$$)($$( 1 - 5 T + 25 T^{2} )^{2}( 1 + 5 T + 25 T^{2} )^{2}$$)($$1 + 16 T^{2} + 510 T^{4} - 24064 T^{6} - 486109 T^{8} - 15040000 T^{10} + 199218750 T^{12} + 3906250000 T^{14} + 152587890625 T^{16}$$)($$1 + 16 T^{2} + 510 T^{4} - 24064 T^{6} - 486109 T^{8} - 15040000 T^{10} + 199218750 T^{12} + 3906250000 T^{14} + 152587890625 T^{16}$$)($$1 + 17 T^{2} - 437 T^{4} - 28164 T^{6} - 270975 T^{8} + 5916803 T^{10} + 456152134 T^{12} + 3698001875 T^{14} - 105849609375 T^{16} - 6875976562500 T^{18} - 66680908203125 T^{20} + 1621246337890625 T^{22} + 59604644775390625 T^{24}$$)($$1 + 121 T^{2} + 7979 T^{4} + 380588 T^{6} + 14474897 T^{8} + 457025259 T^{10} + 12295779174 T^{12} + 285640786875 T^{14} + 5654256640625 T^{16} + 92916992187500 T^{18} + 1217498779296875 T^{20} + 11539459228515625 T^{22} + 59604644775390625 T^{24}$$)($$( 1 + 16 T^{2} - 858 T^{4} - 2176 T^{6} + 690371 T^{8} - 1360000 T^{10} - 335156250 T^{12} + 3906250000 T^{14} + 152587890625 T^{16} )^{2}$$)($$1 + 92 T^{2} + 3000 T^{4} + 78776 T^{6} + 4124130 T^{8} + 144056708 T^{10} + 2959272640 T^{12} + 91907152084 T^{14} + 3067686313171 T^{16} + 57441970052500 T^{18} + 1155965875000000 T^{20} + 35170094726562500 T^{22} + 629292297363281250 T^{24} + 7512664794921875000 T^{26} +$$$$17\!\cdots\!00$$$$T^{28} +$$$$34\!\cdots\!00$$$$T^{30} +$$$$23\!\cdots\!25$$$$T^{32}$$)($$1 + 92 T^{2} + 3000 T^{4} + 78776 T^{6} + 4124130 T^{8} + 144056708 T^{10} + 2959272640 T^{12} + 91907152084 T^{14} + 3067686313171 T^{16} + 57441970052500 T^{18} + 1155965875000000 T^{20} + 35170094726562500 T^{22} + 629292297363281250 T^{24} + 7512664794921875000 T^{26} +$$$$17\!\cdots\!00$$$$T^{28} +$$$$34\!\cdots\!00$$$$T^{30} +$$$$23\!\cdots\!25$$$$T^{32}$$)
$7$ 1
$11$ ($$1 + 17 T + 168 T^{2} + 2057 T^{3} + 14641 T^{4}$$)($$1 + 14 T + 75 T^{2} + 1694 T^{3} + 14641 T^{4}$$)($$1 + 17 T + 168 T^{2} + 2057 T^{3} + 14641 T^{4}$$)($$1 + 14 T + 75 T^{2} + 1694 T^{3} + 14641 T^{4}$$)($$1 + 46 T^{2} - 12525 T^{4} + 673486 T^{6} + 214358881 T^{8}$$)($$1 + 46 T^{2} - 12525 T^{4} + 673486 T^{6} + 214358881 T^{8}$$)($$( 1 + 6 T - 85 T^{2} + 726 T^{3} + 14641 T^{4} )^{2}$$)($$( 1 - 14 T + 75 T^{2} - 1694 T^{3} + 14641 T^{4} )^{2}$$)($$( 1 + 8 T - 122 T^{2} - 448 T^{3} + 12211 T^{4} - 54208 T^{5} - 1786202 T^{6} + 14172488 T^{7} + 214358881 T^{8} )^{2}$$)($$( 1 + 8 T - 122 T^{2} - 448 T^{3} + 12211 T^{4} - 54208 T^{5} - 1786202 T^{6} + 14172488 T^{7} + 214358881 T^{8} )^{2}$$)($$( 1 + 7 T - 193 T^{2} - 2268 T^{3} + 15415 T^{4} + 171941 T^{5} - 336170 T^{6} + 20804861 T^{7} + 225691015 T^{8} - 4017900348 T^{9} - 41371264033 T^{10} + 181561972207 T^{11} + 3138428376721 T^{12} )^{2}$$)($$( 1 - 15 T - 129 T^{2} + 924 T^{3} + 35727 T^{4} - 38013 T^{5} - 5198650 T^{6} - 4599573 T^{7} + 523079007 T^{8} + 1636922364 T^{9} - 27652295649 T^{10} - 389061369015 T^{11} + 3138428376721 T^{12} )^{2}$$)($$( 1 - 114 T^{2} - 1645 T^{4} - 1669074 T^{6} + 214358881 T^{8} )^{4}$$)($$( 1 - 16 T - 72 T^{2} + 4640 T^{3} - 20750 T^{4} - 644496 T^{5} + 8328608 T^{6} + 43860880 T^{7} - 1416483549 T^{8} + 5307166480 T^{9} + 121939149728 T^{10} - 1141763978256 T^{11} - 4447946780750 T^{12} + 120349650148640 T^{13} - 225966843123912 T^{14} - 6075997337331856 T^{15} + 45949729863572161 T^{16} )^{2}$$)($$( 1 - 16 T - 72 T^{2} + 4640 T^{3} - 20750 T^{4} - 644496 T^{5} + 8328608 T^{6} + 43860880 T^{7} - 1416483549 T^{8} + 5307166480 T^{9} + 121939149728 T^{10} - 1141763978256 T^{11} - 4447946780750 T^{12} + 120349650148640 T^{13} - 225966843123912 T^{14} - 6075997337331856 T^{15} + 45949729863572161 T^{16} )^{2}$$)
$13$ ($$( 1 - 22 T + 169 T^{2} )( 1 + 22 T + 169 T^{2} )$$)($$( 1 - 13 T )^{2}( 1 + 13 T )^{2}$$)($$( 1 - 22 T + 169 T^{2} )( 1 + 22 T + 169 T^{2} )$$)($$( 1 - 13 T )^{2}( 1 + 13 T )^{2}$$)($$( 1 - 13 T )^{4}( 1 + 13 T )^{4}$$)($$( 1 - 13 T )^{4}( 1 + 13 T )^{4}$$)($$( 1 - 13 T )^{4}( 1 + 13 T )^{4}$$)($$( 1 - 13 T )^{4}( 1 + 13 T )^{4}$$)($$( 1 - 592 T^{2} + 143170 T^{4} - 16908112 T^{6} + 815730721 T^{8} )^{2}$$)($$( 1 - 592 T^{2} + 143170 T^{4} - 16908112 T^{6} + 815730721 T^{8} )^{2}$$)($$( 1 - 950 T^{2} + 386271 T^{4} - 85941828 T^{6} + 11032286031 T^{8} - 774944184950 T^{10} + 23298085122481 T^{12} )^{2}$$)($$( 1 - 86 T^{2} + 60895 T^{4} - 4902788 T^{6} + 1739222095 T^{8} - 70152842006 T^{10} + 23298085122481 T^{12} )^{2}$$)($$( 1 - 80 T^{2} + 46554 T^{4} - 2284880 T^{6} + 815730721 T^{8} )^{4}$$)($$( 1 - 444 T^{2} + 142936 T^{4} - 35361044 T^{6} + 6575436334 T^{8} - 1009946777684 T^{10} + 116597286336856 T^{12} - 10344349794381564 T^{14} + 665416609183179841 T^{16} )^{2}$$)($$( 1 - 444 T^{2} + 142936 T^{4} - 35361044 T^{6} + 6575436334 T^{8} - 1009946777684 T^{10} + 116597286336856 T^{12} - 10344349794381564 T^{14} + 665416609183179841 T^{16} )^{2}$$)
$17$ ($$1 + 25 T + 336 T^{2} + 7225 T^{3} + 83521 T^{4}$$)($$1 - 2 T - 285 T^{2} - 578 T^{3} + 83521 T^{4}$$)($$1 + 25 T + 336 T^{2} + 7225 T^{3} + 83521 T^{4}$$)($$1 + 2 T - 285 T^{2} + 578 T^{3} + 83521 T^{4}$$)($$1 - 48 T + 1152 T^{2} - 27552 T^{3} + 577727 T^{4} - 7962528 T^{5} + 96216192 T^{6} - 1158603312 T^{7} + 6975757441 T^{8}$$)($$1 + 48 T + 1152 T^{2} + 27552 T^{3} + 577727 T^{4} + 7962528 T^{5} + 96216192 T^{6} + 1158603312 T^{7} + 6975757441 T^{8}$$)($$( 1 - 289 T^{2} + 83521 T^{4} )^{2}$$)($$1 + 574 T^{2} + 245955 T^{4} + 47941054 T^{6} + 6975757441 T^{8}$$)($$( 1 + 36 T + 426 T^{2} + 10512 T^{3} + 298835 T^{4} + 3037968 T^{5} + 35579946 T^{6} + 868952484 T^{7} + 6975757441 T^{8} )^{2}$$)($$( 1 - 36 T + 426 T^{2} - 10512 T^{3} + 298835 T^{4} - 3037968 T^{5} + 35579946 T^{6} - 868952484 T^{7} + 6975757441 T^{8} )^{2}$$)($$( 1 - 41 T + 471 T^{2} - 5456 T^{3} + 209253 T^{4} - 1462951 T^{5} - 27854634 T^{6} - 422792839 T^{7} + 17477019813 T^{8} - 131694576464 T^{9} + 3285581754711 T^{10} - 82655749918409 T^{11} + 582622237229761 T^{12} )^{2}$$)($$( 1 + 15 T - 665 T^{2} - 3920 T^{3} + 405365 T^{4} + 1221665 T^{5} - 124870762 T^{6} + 353061185 T^{7} + 33856490165 T^{8} - 94619270480 T^{9} - 4638878698265 T^{10} + 30239908506735 T^{11} + 582622237229761 T^{12} )^{2}$$)($$( 1 - 452 T^{2} + 86538 T^{4} + 22272752 T^{6} - 10170601069 T^{8} + 1860242519792 T^{10} + 603668097429258 T^{12} - 263345251227851972 T^{14} + 48661191875666868481 T^{16} )^{2}$$)($$( 1 + 40 T + 292 T^{2} - 10704 T^{3} - 137846 T^{4} + 3266264 T^{5} + 77813520 T^{6} + 47796952 T^{7} - 13592851501 T^{8} + 13813319128 T^{9} + 6499063003920 T^{10} + 78839672672216 T^{11} - 961580260212086 T^{12} - 21579198710406096 T^{13} + 170125693271090212 T^{14} + 6735113062376037160 T^{15} + 48661191875666868481 T^{16} )^{2}$$)($$( 1 - 40 T + 292 T^{2} + 10704 T^{3} - 137846 T^{4} - 3266264 T^{5} + 77813520 T^{6} - 47796952 T^{7} - 13592851501 T^{8} - 13813319128 T^{9} + 6499063003920 T^{10} - 78839672672216 T^{11} - 961580260212086 T^{12} + 21579198710406096 T^{13} + 170125693271090212 T^{14} - 6735113062376037160 T^{15} + 48661191875666868481 T^{16} )^{2}$$)
$19$ ($$1 + 7 T - 312 T^{2} + 2527 T^{3} + 130321 T^{4}$$)($$1 + 34 T + 795 T^{2} + 12274 T^{3} + 130321 T^{4}$$)($$1 + 7 T - 312 T^{2} + 2527 T^{3} + 130321 T^{4}$$)($$1 - 34 T + 795 T^{2} - 12274 T^{3} + 130321 T^{4}$$)($$1 - 24 T + 288 T^{2} + 10416 T^{3} - 255313 T^{4} + 3760176 T^{5} + 37532448 T^{6} - 1129101144 T^{7} + 16983563041 T^{8}$$)($$1 + 24 T + 288 T^{2} - 10416 T^{3} - 255313 T^{4} - 3760176 T^{5} + 37532448 T^{6} + 1129101144 T^{7} + 16983563041 T^{8}$$)($$( 1 - 361 T^{2} + 130321 T^{4} )^{2}$$)($$1 - 434 T^{2} + 58035 T^{4} - 56559314 T^{6} + 16983563041 T^{8}$$)($$( 1 + 4 T + 12 T^{2} - 2872 T^{3} - 136081 T^{4} - 1036792 T^{5} + 1563852 T^{6} + 188183524 T^{7} + 16983563041 T^{8} )^{2}$$)($$( 1 - 4 T + 12 T^{2} + 2872 T^{3} - 136081 T^{4} + 1036792 T^{5} + 1563852 T^{6} - 188183524 T^{7} + 16983563041 T^{8} )^{2}$$)($$( 1 - 47 T + 487 T^{2} - 8532 T^{3} + 642195 T^{4} - 10028861 T^{5} + 46257550 T^{6} - 3620418821 T^{7} + 83691494595 T^{8} - 401395456692 T^{9} + 8270995200967 T^{10} - 288160114116647 T^{11} + 2213314919066161 T^{12} )^{2}$$)($$( 1 + 39 T + 151 T^{2} - 3964 T^{3} + 263147 T^{4} + 5820949 T^{5} + 41830430 T^{6} + 2101362589 T^{7} + 34293580187 T^{8} - 186489872284 T^{9} + 2564518019191 T^{10} + 239111584054239 T^{11} + 2213314919066161 T^{12} )^{2}$$)($$( 1 - 80 T^{2} - 254490 T^{4} - 19840 T^{6} + 50245974659 T^{8} - 2585568640 T^{10} - 4322146958304090 T^{12} - 177065193525292880 T^{14} +$$$$28\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 28 T - 926 T^{2} + 14784 T^{3} + 1071538 T^{4} - 10273676 T^{5} - 557016672 T^{6} + 569025380 T^{7} + 272464898159 T^{8} + 205418162180 T^{9} - 72590969711712 T^{10} - 483334138528556 T^{11} + 18198533173827058 T^{12} + 90641683555329984 T^{13} - 2049529615055265086 T^{14} - 22372187201920755388 T^{15} +$$$$28\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 + 28 T - 926 T^{2} - 14784 T^{3} + 1071538 T^{4} + 10273676 T^{5} - 557016672 T^{6} - 569025380 T^{7} + 272464898159 T^{8} - 205418162180 T^{9} - 72590969711712 T^{10} + 483334138528556 T^{11} + 18198533173827058 T^{12} - 90641683555329984 T^{13} - 2049529615055265086 T^{14} + 22372187201920755388 T^{15} +$$$$28\!\cdots\!81$$$$T^{16} )^{2}$$)
$23$ ($$1 - 9 T + 556 T^{2} - 4761 T^{3} + 279841 T^{4}$$)($$( 1 - 23 T + 529 T^{2} )( 1 + 23 T + 529 T^{2} )$$)($$1 + 9 T + 556 T^{2} + 4761 T^{3} + 279841 T^{4}$$)($$( 1 - 23 T + 529 T^{2} )( 1 + 23 T + 529 T^{2} )$$)($$( 1 - 23 T + 529 T^{2} )^{2}( 1 + 23 T + 529 T^{2} )^{2}$$)($$( 1 - 23 T + 529 T^{2} )^{2}( 1 + 23 T + 529 T^{2} )^{2}$$)($$( 1 - 18 T - 205 T^{2} - 9522 T^{3} + 279841 T^{4} )( 1 + 18 T - 205 T^{2} + 9522 T^{3} + 279841 T^{4} )$$)($$( 1 - 23 T + 529 T^{2} )^{2}( 1 + 23 T + 529 T^{2} )^{2}$$)($$1 + 268 T^{2} - 405462 T^{4} - 22082128 T^{6} + 129391640531 T^{8} - 6179484781648 T^{10} - 31752128714004822 T^{12} + 5873119347781446028 T^{14} +$$$$61\!\cdots\!61$$$$T^{16}$$)($$1 + 268 T^{2} - 405462 T^{4} - 22082128 T^{6} + 129391640531 T^{8} - 6179484781648 T^{10} - 31752128714004822 T^{12} + 5873119347781446028 T^{14} +$$$$61\!\cdots\!61$$$$T^{16}$$)($$1 + 2381 T^{2} + 2947123 T^{4} + 2827993812 T^{6} + 2298643835613 T^{8} + 1531108455942719 T^{10} + 862820921151363886 T^{12} +$$$$42\!\cdots\!79$$$$T^{14} +$$$$18\!\cdots\!53$$$$T^{16} +$$$$61\!\cdots\!52$$$$T^{18} +$$$$18\!\cdots\!03$$$$T^{20} +$$$$40\!\cdots\!81$$$$T^{22} +$$$$48\!\cdots\!41$$$$T^{24}$$)($$1 + 693 T^{2} - 15581 T^{4} - 315659500 T^{6} - 121343121715 T^{8} + 25399919636503 T^{10} + 46081428374834798 T^{12} + 7107938910998636023 T^{14} -$$$$95\!\cdots\!15$$$$T^{16} -$$$$69\!\cdots\!00$$$$T^{18} -$$$$95\!\cdots\!41$$$$T^{20} +$$$$11\!\cdots\!93$$$$T^{22} +$$$$48\!\cdots\!41$$$$T^{24}$$)($$( 1 + 1932 T^{2} + 2247978 T^{4} + 1787030448 T^{6} + 1081321527251 T^{8} + 500084387598768 T^{10} + 176041372070011818 T^{12} + 42339054402663260172 T^{14} +$$$$61\!\cdots\!61$$$$T^{16} )^{2}$$)($$1 + 1744 T^{2} + 1769380 T^{4} + 1394487904 T^{6} + 800412311114 T^{8} + 293154906699184 T^{10} + 41608418133156240 T^{12} - 40513926748661757392 T^{14} -$$$$37\!\cdots\!61$$$$T^{16} -$$$$11\!\cdots\!72$$$$T^{18} +$$$$32\!\cdots\!40$$$$T^{20} +$$$$64\!\cdots\!64$$$$T^{22} +$$$$49\!\cdots\!54$$$$T^{24} +$$$$23\!\cdots\!04$$$$T^{26} +$$$$84\!\cdots\!80$$$$T^{28} +$$$$23\!\cdots\!64$$$$T^{30} +$$$$37\!\cdots\!21$$$$T^{32}$$)($$1 + 1744 T^{2} + 1769380 T^{4} + 1394487904 T^{6} + 800412311114 T^{8} + 293154906699184 T^{10} + 41608418133156240 T^{12} - 40513926748661757392 T^{14} -$$$$37\!\cdots\!61$$$$T^{16} -$$$$11\!\cdots\!72$$$$T^{18} +$$$$32\!\cdots\!40$$$$T^{20} +$$$$64\!\cdots\!64$$$$T^{22} +$$$$49\!\cdots\!54$$$$T^{24} +$$$$23\!\cdots\!04$$$$T^{26} +$$$$84\!\cdots\!80$$$$T^{28} +$$$$23\!\cdots\!64$$$$T^{30} +$$$$37\!\cdots\!21$$$$T^{32}$$)
$29$ ($$1 - 1490 T^{2} + 707281 T^{4}$$)($$( 1 - 29 T )^{2}( 1 + 29 T )^{2}$$)($$1 - 1490 T^{2} + 707281 T^{4}$$)($$( 1 - 29 T )^{2}( 1 + 29 T )^{2}$$)($$( 1 - 29 T )^{4}( 1 + 29 T )^{4}$$)($$( 1 - 29 T )^{4}( 1 + 29 T )^{4}$$)($$( 1 - 54 T + 841 T^{2} )^{2}( 1 + 54 T + 841 T^{2} )^{2}$$)($$( 1 - 29 T )^{4}( 1 + 29 T )^{4}$$)($$( 1 - 1178 T^{2} + 707281 T^{4} )^{4}$$)($$( 1 - 1178 T^{2} + 707281 T^{4} )^{4}$$)($$( 1 - 1838 T^{2} + 2723567 T^{4} - 2423469812 T^{6} + 1926327191327 T^{8} - 919452907022318 T^{10} + 353814783205469041 T^{12} )^{2}$$)($$( 1 - 3662 T^{2} + 6471151 T^{4} - 6858243380 T^{6} + 4576922150431 T^{8} - 1831902364263182 T^{10} + 353814783205469041 T^{12} )^{2}$$)($$( 1 - 324 T^{2} - 656346 T^{4} - 229159044 T^{6} + 500246412961 T^{8} )^{4}$$)($$( 1 - 3384 T^{2} + 6555580 T^{4} - 8754768776 T^{6} + 8490907402822 T^{8} - 6192081614658056 T^{10} + 3279405379878872380 T^{12} -$$$$11\!\cdots\!44$$$$T^{14} +$$$$25\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 3384 T^{2} + 6555580 T^{4} - 8754768776 T^{6} + 8490907402822 T^{8} - 6192081614658056 T^{10} + 3279405379878872380 T^{12} -$$$$11\!\cdots\!44$$$$T^{14} +$$$$25\!\cdots\!21$$$$T^{16} )^{2}$$)
$31$ ($$1 + 57 T + 2044 T^{2} + 54777 T^{3} + 923521 T^{4}$$)($$( 1 - 31 T + 961 T^{2} )( 1 + 31 T + 961 T^{2} )$$)($$1 - 57 T + 2044 T^{2} - 54777 T^{3} + 923521 T^{4}$$)($$( 1 - 31 T + 961 T^{2} )( 1 + 31 T + 961 T^{2} )$$)($$( 1 - 31 T + 961 T^{2} )^{2}( 1 + 31 T + 961 T^{2} )^{2}$$)($$( 1 - 31 T + 961 T^{2} )^{2}( 1 + 31 T + 961 T^{2} )^{2}$$)($$( 1 - 31 T + 961 T^{2} )^{2}( 1 + 31 T + 961 T^{2} )^{2}$$)($$( 1 - 31 T + 961 T^{2} )^{2}( 1 + 31 T + 961 T^{2} )^{2}$$)($$1 + 1380 T^{2} + 484426 T^{4} - 589353840 T^{6} - 595318269165 T^{8} - 544280647670640 T^{10} + 413162593703393866 T^{12} +$$$$10\!\cdots\!80$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16}$$)($$1 + 1380 T^{2} + 484426 T^{4} - 589353840 T^{6} - 595318269165 T^{8} - 544280647670640 T^{10} + 413162593703393866 T^{12} +$$$$10\!\cdots\!80$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16}$$)($$1 + 3329 T^{2} + 4631887 T^{4} + 6475839496 T^{6} + 10686875408317 T^{8} + 11546553377441207 T^{10} + 9928800654054771830 T^{12} +$$$$10\!\cdots\!47$$$$T^{14} +$$$$91\!\cdots\!97$$$$T^{16} +$$$$51\!\cdots\!56$$$$T^{18} +$$$$33\!\cdots\!47$$$$T^{20} +$$$$22\!\cdots\!29$$$$T^{22} +$$$$62\!\cdots\!21$$$$T^{24}$$)($$1 + 3561 T^{2} + 5838879 T^{4} + 8280992264 T^{6} + 11856779149293 T^{8} + 13054196823637455 T^{10} + 12193464685853753718 T^{12} +$$$$12\!\cdots\!55$$$$T^{14} +$$$$10\!\cdots\!13$$$$T^{16} +$$$$65\!\cdots\!04$$$$T^{18} +$$$$42\!\cdots\!99$$$$T^{20} +$$$$23\!\cdots\!61$$$$T^{22} +$$$$62\!\cdots\!21$$$$T^{24}$$)($$( 1 + 1092 T^{2} + 540298 T^{4} - 1304804592 T^{6} - 1528836091629 T^{8} - 1205014441608432 T^{10} + 460815321747297418 T^{12} +$$$$86\!\cdots\!12$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16} )^{2}$$)($$1 + 3944 T^{2} + 7116516 T^{4} + 8387060656 T^{6} + 8423414263178 T^{8} + 8514445544397720 T^{10} + 8434364772846028816 T^{12} +$$$$79\!\cdots\!12$$$$T^{14} +$$$$74\!\cdots\!23$$$$T^{16} +$$$$73\!\cdots\!52$$$$T^{18} +$$$$71\!\cdots\!56$$$$T^{20} +$$$$67\!\cdots\!20$$$$T^{22} +$$$$61\!\cdots\!18$$$$T^{24} +$$$$56\!\cdots\!56$$$$T^{26} +$$$$44\!\cdots\!36$$$$T^{28} +$$$$22\!\cdots\!04$$$$T^{30} +$$$$52\!\cdots\!61$$$$T^{32}$$)($$1 + 3944 T^{2} + 7116516 T^{4} + 8387060656 T^{6} + 8423414263178 T^{8} + 8514445544397720 T^{10} + 8434364772846028816 T^{12} +$$$$79\!\cdots\!12$$$$T^{14} +$$$$74\!\cdots\!23$$$$T^{16} +$$$$73\!\cdots\!52$$$$T^{18} +$$$$71\!\cdots\!56$$$$T^{20} +$$$$67\!\cdots\!20$$$$T^{22} +$$$$61\!\cdots\!18$$$$T^{24} +$$$$56\!\cdots\!56$$$$T^{26} +$$$$44\!\cdots\!36$$$$T^{28} +$$$$22\!\cdots\!04$$$$T^{30} +$$$$52\!\cdots\!61$$$$T^{32}$$)
$37$ ($$1 - 15 T + 1444 T^{2} - 20535 T^{3} + 1874161 T^{4}$$)($$( 1 - 37 T + 1369 T^{2} )( 1 + 37 T + 1369 T^{2} )$$)($$1 + 15 T + 1444 T^{2} + 20535 T^{3} + 1874161 T^{4}$$)($$( 1 - 37 T + 1369 T^{2} )( 1 + 37 T + 1369 T^{2} )$$)($$( 1 - 37 T + 1369 T^{2} )^{2}( 1 + 37 T + 1369 T^{2} )^{2}$$)($$( 1 - 37 T + 1369 T^{2} )^{2}( 1 + 37 T + 1369 T^{2} )^{2}$$)($$( 1 - 38 T + 75 T^{2} - 52022 T^{3} + 1874161 T^{4} )( 1 + 38 T + 75 T^{2} + 52022 T^{3} + 1874161 T^{4} )$$)($$( 1 - 37 T + 1369 T^{2} )^{2}( 1 + 37 T + 1369 T^{2} )^{2}$$)($$1 + 1780 T^{2} + 1136778 T^{4} - 3055726000 T^{6} - 5323083215437 T^{8} - 5726922495886000 T^{10} + 3992909368669406538 T^{12} +$$$$11\!\cdots\!80$$$$T^{14} +$$$$12\!\cdots\!41$$$$T^{16}$$)($$1 + 1780 T^{2} + 1136778 T^{4} - 3055726000 T^{6} - 5323083215437 T^{8} - 5726922495886000 T^{10} + 3992909368669406538 T^{12} +$$$$11\!\cdots\!80$$$$T^{14} +$$$$12\!\cdots\!41$$$$T^{16}$$)($$1 + 6401 T^{2} + 22091395 T^{4} + 55331146644 T^{6} + 111395987301489 T^{8} + 188098942339055675 T^{10} +$$$$27\!\cdots\!06$$$$T^{12} +$$$$35\!\cdots\!75$$$$T^{14} +$$$$39\!\cdots\!69$$$$T^{16} +$$$$36\!\cdots\!64$$$$T^{18} +$$$$27\!\cdots\!95$$$$T^{20} +$$$$14\!\cdots\!01$$$$T^{22} +$$$$43\!\cdots\!61$$$$T^{24}$$)($$1 + 5785 T^{2} + 17889827 T^{4} + 38047414052 T^{6} + 62842022068961 T^{8} + 88030006321881747 T^{10} +$$$$11\!\cdots\!14$$$$T^{12} +$$$$16\!\cdots\!67$$$$T^{14} +$$$$22\!\cdots\!81$$$$T^{16} +$$$$25\!\cdots\!12$$$$T^{18} +$$$$22\!\cdots\!07$$$$T^{20} +$$$$13\!\cdots\!85$$$$T^{22} +$$$$43\!\cdots\!61$$$$T^{24}$$)($$( 1 + 1668 T^{2} + 705834 T^{4} - 2788782576 T^{6} - 4415419735885 T^{8} - 5226627541418736 T^{10} + 2479227422878875114 T^{12} +$$$$10\!\cdots\!08$$$$T^{14} +$$$$12\!\cdots\!41$$$$T^{16} )^{2}$$)($$1 + 3512 T^{2} + 3145476 T^{4} - 4974960880 T^{6} - 8515936106358 T^{8} + 12549151402549448 T^{10} + 35685999046008816016 T^{12} +$$$$80\!\cdots\!88$$$$T^{14} -$$$$37\!\cdots\!25$$$$T^{16} +$$$$15\!\cdots\!68$$$$T^{18} +$$$$12\!\cdots\!36$$$$T^{20} +$$$$82\!\cdots\!88$$$$T^{22} -$$$$10\!\cdots\!78$$$$T^{24} -$$$$11\!\cdots\!80$$$$T^{26} +$$$$13\!\cdots\!36$$$$T^{28} +$$$$28\!\cdots\!52$$$$T^{30} +$$$$15\!\cdots\!81$$$$T^{32}$$)($$1 + 3512 T^{2} + 3145476 T^{4} - 4974960880 T^{6} - 8515936106358 T^{8} + 12549151402549448 T^{10} + 35685999046008816016 T^{12} +$$$$80\!\cdots\!88$$$$T^{14} -$$$$37\!\cdots\!25$$$$T^{16} +$$$$15\!\cdots\!68$$$$T^{18} +$$$$12\!\cdots\!36$$$$T^{20} +$$$$82\!\cdots\!88$$$$T^{22} -$$$$10\!\cdots\!78$$$$T^{24} -$$$$11\!\cdots\!80$$$$T^{26} +$$$$13\!\cdots\!36$$$$T^{28} +$$$$28\!\cdots\!52$$$$T^{30} +$$$$15\!\cdots\!81$$$$T^{32}$$)
$41$ ($$( 1 + 26 T + 1681 T^{2} )^{2}$$)($$( 1 - 46 T + 1681 T^{2} )^{2}$$)($$( 1 + 26 T + 1681 T^{2} )^{2}$$)($$( 1 + 46 T + 1681 T^{2} )^{2}$$)($$( 1 + 96 T + 4608 T^{2} + 161376 T^{3} + 2825761 T^{4} )^{2}$$)($$( 1 - 96 T + 4608 T^{2} - 161376 T^{3} + 2825761 T^{4} )^{2}$$)($$( 1 + 1681 T^{2} )^{4}$$)($$( 1 - 1246 T^{2} + 2825761 T^{4} )^{2}$$)($$( 1 + 20 T + 3174 T^{2} + 33620 T^{3} + 2825761 T^{4} )^{4}$$)($$( 1 - 20 T + 3174 T^{2} - 33620 T^{3} + 2825761 T^{4} )^{4}$$)($$( 1 + 30 T + 4755 T^{2} + 100496 T^{3} + 7993155 T^{4} + 84772830 T^{5} + 4750104241 T^{6} )^{4}$$)($$( 1 - 58 T + 3139 T^{2} - 88960 T^{3} + 5276659 T^{4} - 163894138 T^{5} + 4750104241 T^{6} )^{4}$$)($$( 1 + 2436 T^{2} + 3692358 T^{4} + 6883553796 T^{6} + 7984925229121 T^{8} )^{4}$$)($$( 1 + 64 T + 4956 T^{2} + 221760 T^{3} + 11848326 T^{4} + 372778560 T^{5} + 14004471516 T^{6} + 304006671424 T^{7} + 7984925229121 T^{8} )^{4}$$)($$( 1 - 64 T + 4956 T^{2} - 221760 T^{3} + 11848326 T^{4} - 372778560 T^{5} + 14004471516 T^{6} - 304006671424 T^{7} + 7984925229121 T^{8} )^{4}$$)
$43$ ($$( 1 - 14 T + 1849 T^{2} )^{2}$$)($$( 1 - 14 T + 1849 T^{2} )^{2}$$)($$( 1 - 14 T + 1849 T^{2} )^{2}$$)($$( 1 - 14 T + 1849 T^{2} )^{2}$$)($$( 1 - 3502 T^{2} + 3418801 T^{4} )^{2}$$)($$( 1 - 3502 T^{2} + 3418801 T^{4} )^{2}$$)($$( 1 + 58 T + 1849 T^{2} )^{4}$$)($$( 1 + 14 T + 1849 T^{2} )^{4}$$)($$( 1 + 40 T + 4090 T^{2} + 73960 T^{3} + 3418801 T^{4} )^{4}$$)($$( 1 + 40 T + 4090 T^{2} + 73960 T^{3} + 3418801 T^{4} )^{4}$$)($$( 1 - 10 T + 3855 T^{2} - 53388 T^{3} + 7127895 T^{4} - 34188010 T^{5} + 6321363049 T^{6} )^{4}$$)($$( 1 + 50 T + 4047 T^{2} + 107900 T^{3} + 7482903 T^{4} + 170940050 T^{5} + 6321363049 T^{6} )^{4}$$)($$( 1 - 80 T + 5170 T^{2} - 147920 T^{3} + 3418801 T^{4} )^{8}$$)($$( 1 + 4680 T^{2} - 58016 T^{3} + 10251086 T^{4} - 107271584 T^{5} + 15999988680 T^{6} + 11688200277601 T^{8} )^{4}$$)($$( 1 + 4680 T^{2} - 58016 T^{3} + 10251086 T^{4} - 107271584 T^{5} + 15999988680 T^{6} + 11688200277601 T^{8} )^{4}$$)
$47$ ($$1 - 87 T + 4732 T^{2} - 192183 T^{3} + 4879681 T^{4}$$)($$( 1 - 47 T + 2209 T^{2} )( 1 + 47 T + 2209 T^{2} )$$)($$1 + 87 T + 4732 T^{2} + 192183 T^{3} + 4879681 T^{4}$$)($$( 1 - 47 T + 2209 T^{2} )( 1 + 47 T + 2209 T^{2} )$$)($$( 1 - 47 T + 2209 T^{2} )^{2}( 1 + 47 T + 2209 T^{2} )^{2}$$)($$( 1 - 47 T + 2209 T^{2} )^{2}( 1 + 47 T + 2209 T^{2} )^{2}$$)($$( 1 - 47 T + 2209 T^{2} )^{2}( 1 + 47 T + 2209 T^{2} )^{2}$$)($$( 1 - 47 T + 2209 T^{2} )^{2}( 1 + 47 T + 2209 T^{2} )^{2}$$)($$1 + 7492 T^{2} + 32739594 T^{4} + 102124261136 T^{6} + 249405993329555 T^{8} + 498333816704377616 T^{10} +$$$$77\!\cdots\!34$$$$T^{12} +$$$$87\!\cdots\!72$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16}$$)($$1 + 7492 T^{2} + 32739594 T^{4} + 102124261136 T^{6} + 249405993329555 T^{8} + 498333816704377616 T^{10} +$$$$77\!\cdots\!34$$$$T^{12} +$$$$87\!\cdots\!72$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16}$$)($$1 + 8313 T^{2} + 34702703 T^{4} + 101154992824 T^{6} + 247422958854189 T^{8} + 586359622432093519 T^{10} +$$$$13\!\cdots\!26$$$$T^{12} +$$$$28\!\cdots\!39$$$$T^{14} +$$$$58\!\cdots\!29$$$$T^{16} +$$$$11\!\cdots\!84$$$$T^{18} +$$$$19\!\cdots\!63$$$$T^{20} +$$$$22\!\cdots\!13$$$$T^{22} +$$$$13\!\cdots\!81$$$$T^{24}$$)($$1 + 3905 T^{2} + 6537087 T^{4} + 2079696952 T^{6} - 28977286497379 T^{8} - 99900087904130553 T^{10} -$$$$24\!\cdots\!46$$$$T^{12} -$$$$48\!\cdots\!93$$$$T^{14} -$$$$68\!\cdots\!19$$$$T^{16} +$$$$24\!\cdots\!32$$$$T^{18} +$$$$37\!\cdots\!27$$$$T^{20} +$$$$10\!\cdots\!05$$$$T^{22} +$$$$13\!\cdots\!81$$$$T^{24}$$)($$( 1 + 3524 T^{2} + 6208522 T^{4} - 12507761392 T^{6} - 45845205333101 T^{8} - 61033885617075952 T^{10} +$$$$14\!\cdots\!42$$$$T^{12} +$$$$40\!\cdots\!84$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16} )^{2}$$)($$1 + 8392 T^{2} + 30858916 T^{4} + 77629558512 T^{6} + 181309996781322 T^{8} + 338519134932094776 T^{10} +$$$$32\!\cdots\!52$$$$T^{12} +$$$$46\!\cdots\!92$$$$T^{14} -$$$$14\!\cdots\!37$$$$T^{16} +$$$$22\!\cdots\!52$$$$T^{18} +$$$$77\!\cdots\!72$$$$T^{20} +$$$$39\!\cdots\!16$$$$T^{22} +$$$$10\!\cdots\!62$$$$T^{24} +$$$$21\!\cdots\!12$$$$T^{26} +$$$$41\!\cdots\!96$$$$T^{28} +$$$$55\!\cdots\!12$$$$T^{30} +$$$$32\!\cdots\!41$$$$T^{32}$$)($$1 + 8392 T^{2} + 30858916 T^{4} + 77629558512 T^{6} + 181309996781322 T^{8} + 338519134932094776 T^{10} +$$$$32\!\cdots\!52$$$$T^{12} +$$$$46\!\cdots\!92$$$$T^{14} -$$$$14\!\cdots\!37$$$$T^{16} +$$$$22\!\cdots\!52$$$$T^{18} +$$$$77\!\cdots\!72$$$$T^{20} +$$$$39\!\cdots\!16$$$$T^{22} +$$$$10\!\cdots\!62$$$$T^{24} +$$$$21\!\cdots\!12$$$$T^{26} +$$$$41\!\cdots\!96$$$$T^{28} +$$$$55\!\cdots\!12$$$$T^{30} +$$$$32\!\cdots\!41$$$$T^{32}$$)
$53$ ($$( 1 - 53 T )^{2}( 1 - 53 T + 2809 T^{2} )$$)($$( 1 - 53 T + 2809 T^{2} )( 1 + 53 T + 2809 T^{2} )$$)($$( 1 + 53 T )^{2}( 1 + 53 T + 2809 T^{2} )$$)($$( 1 - 53 T + 2809 T^{2} )( 1 + 53 T + 2809 T^{2} )$$)($$( 1 - 53 T + 2809 T^{2} )^{2}( 1 + 53 T + 2809 T^{2} )^{2}$$)($$( 1 - 53 T + 2809 T^{2} )^{2}( 1 + 53 T + 2809 T^{2} )^{2}$$)($$( 1 - 6 T - 2773 T^{2} - 16854 T^{3} + 7890481 T^{4} )( 1 + 6 T - 2773 T^{2} + 16854 T^{3} + 7890481 T^{4} )$$)($$( 1 - 53 T + 2809 T^{2} )^{2}( 1 + 53 T + 2809 T^{2} )^{2}$$)($$1 + 1604 T^{2} + 8727850 T^{4} - 35185337584 T^{6} - 44676002634701 T^{8} - 277629237685137904 T^{10} +$$$$54\!\cdots\!50$$$$T^{12} +$$$$78\!\cdots\!64$$$$T^{14} +$$$$38\!\cdots\!21$$$$T^{16}$$)($$1 + 1604 T^{2} + 8727850 T^{4} - 35185337584 T^{6} - 44676002634701 T^{8} - 277629237685137904 T^{10} +$$$$54\!\cdots\!50$$$$T^{12} +$$$$78\!\cdots\!64$$$$T^{14} +$$$$38\!\cdots\!21$$$$T^{16}$$)($$1 + 9273 T^{2} + 34839939 T^{4} + 130830291652 T^{6} + 620089921398753 T^{8} + 1876428047292173523 T^{10} +$$$$44\!\cdots\!94$$$$T^{12} +$$$$14\!\cdots\!63$$$$T^{14} +$$$$38\!\cdots\!33$$$$T^{16} +$$$$64\!\cdots\!32$$$$T^{18} +$$$$13\!\cdots\!19$$$$T^{20} +$$$$28\!\cdots\!73$$$$T^{22} +$$$$24\!\cdots\!81$$$$T^{24}$$)($$1 + 10561 T^{2} + 59733731 T^{4} + 209884512884 T^{6} + 494098524300977 T^{8} + 757507316642438811 T^{10} +$$$$12\!\cdots\!10$$$$T^{12} +$$$$59\!\cdots\!91$$$$T^{14} +$$$$30\!\cdots\!97$$$$T^{16} +$$$$10\!\cdots\!44$$$$T^{18} +$$$$23\!\cdots\!51$$$$T^{20} +$$$$32\!\cdots\!61$$$$T^{22} +$$$$24\!\cdots\!81$$$$T^{24}$$)($$( 1 + 260 T^{2} - 12772950 T^{4} - 764507120 T^{6} + 102086637375539 T^{8} - 6032328904724720 T^{10} -$$$$79\!\cdots\!50$$$$T^{12} +$$$$12\!\cdots\!60$$$$T^{14} +$$$$38\!\cdots\!21$$$$T^{16} )^{2}$$)($$1 + 18920 T^{2} + 195169572 T^{4} + 1399932528560 T^{6} + 7743546865787466 T^{8} + 34991808675085792280 T^{10} +$$$$13\!\cdots\!12$$$$T^{12} +$$$$44\!\cdots\!80$$$$T^{14} +$$$$13\!\cdots\!79$$$$T^{16} +$$$$35\!\cdots\!80$$$$T^{18} +$$$$83\!\cdots\!32$$$$T^{20} +$$$$17\!\cdots\!80$$$$T^{22} +$$$$30\!\cdots\!86$$$$T^{24} +$$$$42\!\cdots\!60$$$$T^{26} +$$$$47\!\cdots\!32$$$$T^{28} +$$$$36\!\cdots\!20$$$$T^{30} +$$$$15\!\cdots\!41$$$$T^{32}$$)($$1 + 18920 T^{2} + 195169572 T^{4} + 1399932528560 T^{6} + 7743546865787466 T^{8} + 34991808675085792280 T^{10} +$$$$13\!\cdots\!12$$$$T^{12} +$$$$44\!\cdots\!80$$$$T^{14} +$$$$13\!\cdots\!79$$$$T^{16} +$$$$35\!\cdots\!80$$$$T^{18} +$$$$83\!\cdots\!32$$$$T^{20} +$$$$17\!\cdots\!80$$$$T^{22} +$$$$30\!\cdots\!86$$$$T^{24} +$$$$42\!\cdots\!60$$$$T^{26} +$$$$47\!\cdots\!32$$$$T^{28} +$$$$36\!\cdots\!20$$$$T^{30} +$$$$15\!\cdots\!41$$$$T^{32}$$)
$59$ ($$1 + 55 T - 456 T^{2} + 191455 T^{3} + 12117361 T^{4}$$)($$1 + 82 T + 3243 T^{2} + 285442 T^{3} + 12117361 T^{4}$$)($$1 + 55 T - 456 T^{2} + 191455 T^{3} + 12117361 T^{4}$$)($$1 - 82 T + 3243 T^{2} - 285442 T^{3} + 12117361 T^{4}$$)($$1 + 120 T + 7200 T^{2} + 28560 T^{3} - 10403761 T^{4} + 99417360 T^{5} + 87244999200 T^{6} + 5061664036920 T^{7} + 146830437604321 T^{8}$$)($$1 - 120 T + 7200 T^{2} - 28560 T^{3} - 10403761 T^{4} - 99417360 T^{5} + 87244999200 T^{6} - 5061664036920 T^{7} + 146830437604321 T^{8}$$)($$( 1 - 3481 T^{2} + 12117361 T^{4} )^{2}$$)($$1 + 238 T^{2} - 12060717 T^{4} + 2883931918 T^{6} + 146830437604321 T^{8}$$)($$( 1 + 92 T - 372 T^{2} + 172408 T^{3} + 36494351 T^{4} + 600152248 T^{5} - 4507658292 T^{6} + 3880609094972 T^{7} + 146830437604321 T^{8} )^{2}$$)($$( 1 - 92 T - 372 T^{2} - 172408 T^{3} + 36494351 T^{4} - 600152248 T^{5} - 4507658292 T^{6} - 3880609094972 T^{7} + 146830437604321 T^{8} )^{2}$$)($$( 1 + 31 T - 7567 T^{2} - 176030 T^{3} + 36214647 T^{4} + 412965247 T^{5} - 131958052142 T^{6} + 1437532024807 T^{7} + 438825951186567 T^{8} - 7425039336825230 T^{9} - 1111065921351897007 T^{10} + 15844619352319883431 T^{11} +$$$$17\!\cdots\!81$$$$T^{12} )^{2}$$)($$( 1 - 55 T - 7367 T^{2} + 181142 T^{3} + 51119807 T^{4} - 598293727 T^{5} - 186579818926 T^{6} - 2082660463687 T^{7} + 619437155669327 T^{8} + 7640666224798022 T^{9} - 1081699833831032807 T^{10} - 28111421431535277055 T^{11} +$$$$17\!\cdots\!81$$$$T^{12} )^{2}$$)($$( 1 - 13008 T^{2} + 102726438 T^{4} - 549547727232 T^{6} + 2222620962400451 T^{8} - 6659068197599674752 T^{10} +$$$$15\!\cdots\!98$$$$T^{12} -$$$$23\!\cdots\!48$$$$T^{14} +$$$$21\!\cdots\!41$$$$T^{16} )^{2}$$)($$( 1 - 52 T + 450 T^{2} - 532224 T^{3} + 35666162 T^{4} - 868645540 T^{5} + 179864519968 T^{6} - 10977595733044 T^{7} + 261680209248047 T^{8} - 38213010746726164 T^{9} + 2179483319543964448 T^{10} - 36639932422074611140 T^{11} +$$$$52\!\cdots\!02$$$$T^{12} -$$$$27\!\cdots\!24$$$$T^{13} +$$$$80\!\cdots\!50$$$$T^{14} -$$$$32\!\cdots\!72$$$$T^{15} +$$$$21\!\cdots\!41$$$$T^{16} )^{2}$$)($$( 1 + 52 T + 450 T^{2} + 532224 T^{3} + 35666162 T^{4} + 868645540 T^{5} + 179864519968 T^{6} + 10977595733044 T^{7} + 261680209248047 T^{8} + 38213010746726164 T^{9} + 2179483319543964448 T^{10} + 36639932422074611140 T^{11} +$$$$52\!\cdots\!02$$$$T^{12} +$$$$27\!\cdots\!24$$$$T^{13} +$$$$80\!\cdots\!50$$$$T^{14} +$$$$32\!\cdots\!72$$$$T^{15} +$$$$21\!\cdots\!41$$$$T^{16} )^{2}$$)
$61$ ($$1 + 39 T + 4228 T^{2} + 145119 T^{3} + 13845841 T^{4}$$)($$( 1 - 61 T + 3721 T^{2} )( 1 + 61 T + 3721 T^{2} )$$)($$1 - 39 T + 4228 T^{2} - 145119 T^{3} + 13845841 T^{4}$$)($$( 1 - 61 T + 3721 T^{2} )( 1 + 61 T + 3721 T^{2} )$$)($$( 1 - 61 T + 3721 T^{2} )^{2}( 1 + 61 T + 3721 T^{2} )^{2}$$)($$( 1 - 61 T + 3721 T^{2} )^{2}( 1 + 61 T + 3721 T^{2} )^{2}$$)($$( 1 - 61 T + 3721 T^{2} )^{2}( 1 + 61 T + 3721 T^{2} )^{2}$$)($$( 1 - 61 T + 3721 T^{2} )^{2}( 1 + 61 T + 3721 T^{2} )^{2}$$)($$1 + 13232 T^{2} + 103975486 T^{4} + 574515656192 T^{6} + 2440762377018979 T^{8} + 7954652427645097472 T^{10} +$$$$19\!\cdots\!66$$$$T^{12} +$$$$35\!\cdots\!72$$$$T^{14} +$$$$36\!\cdots\!61$$$$T^{16}$$)($$1 + 13232 T^{2} + 103975486 T^{4} + 574515656192 T^{6} + 2440762377018979 T^{8} + 7954652427645097472 T^{10} +$$$$19\!\cdots\!66$$$$T^{12} +$$$$35\!\cdots\!72$$$$T^{14} +$$$$36\!\cdots\!61$$$$T^{16}$$)($$1 - 503 T^{2} - 13520125 T^{4} - 91919186268 T^{6} + 20373908662561 T^{8} + 680714329682975843 T^{10} +$$$$44\!\cdots\!06$$$$T^{12} +$$$$94\!\cdots\!63$$$$T^{14} +$$$$39\!\cdots\!41$$$$T^{16} -$$$$24\!\cdots\!28$$$$T^{18} -$$$$49\!\cdots\!25$$$$T^{20} -$$$$25\!\cdots\!03$$$$T^{22} +$$$$70\!\cdots\!41$$$$T^{24}$$)($$1 + 9201 T^{2} + 56941411 T^{4} + 154999649300 T^{6} - 75695642240335 T^{8} - 3911957905117164149 T^{10} -$$$$19\!\cdots\!14$$$$T^{12} -$$$$54\!\cdots\!09$$$$T^{14} -$$$$14\!\cdots\!35$$$$T^{16} +$$$$41\!\cdots\!00$$$$T^{18} +$$$$20\!\cdots\!71$$$$T^{20} +$$$$46\!\cdots\!01$$$$T^{22} +$$$$70\!\cdots\!41$$$$T^{24}$$)($$( 1 + 12432 T^{2} + 88224358 T^{4} + 480354876288 T^{6} + 2068058124914691 T^{8} + 6650917240658318208 T^{10} +$$$$16\!\cdots\!98$$$$T^{12} +$$$$32\!\cdots\!72$$$$T^{14} +$$$$36\!\cdots\!61$$$$T^{16} )^{2}$$)($$1 + 16316 T^{2} + 126039736 T^{4} + 653164234872 T^{6} + 2819894062793314 T^{8} + 11641021751267899300 T^{10} +$$$$46\!\cdots\!32$$$$T^{12} +$$$$16\!\cdots\!44$$$$T^{14} +$$$$61\!\cdots\!79$$$$T^{16} +$$$$23\!\cdots\!04$$$$T^{18} +$$$$88\!\cdots\!92$$$$T^{20} +$$$$30\!\cdots\!00$$$$T^{22} +$$$$10\!\cdots\!54$$$$T^{24} +$$$$33\!\cdots\!72$$$$T^{26} +$$$$88\!\cdots\!76$$$$T^{28} +$$$$15\!\cdots\!96$$$$T^{30} +$$$$13\!\cdots\!21$$$$T^{32}$$)($$1 + 16316 T^{2} + 126039736 T^{4} + 653164234872 T^{6} + 2819894062793314 T^{8} + 11641021751267899300 T^{10} +$$$$46\!\cdots\!32$$$$T^{12} +$$$$16\!\cdots\!44$$$$T^{14} +$$$$61\!\cdots\!79$$$$T^{16} +$$$$23\!\cdots\!04$$$$T^{18} +$$$$88\!\cdots\!92$$$$T^{20} +$$$$30\!\cdots\!00$$$$T^{22} +$$$$10\!\cdots\!54$$$$T^{24} +$$$$33\!\cdots\!72$$$$T^{26} +$$$$88\!\cdots\!76$$$$T^{28} +$$$$15\!\cdots\!96$$$$T^{30} +$$$$13\!\cdots\!21$$$$T^{32}$$)
$67$ ($$1 + 17 T - 4200 T^{2} + 76313 T^{3} + 20151121 T^{4}$$)($$1 + 62 T - 645 T^{2} + 278318 T^{3} + 20151121 T^{4}$$)($$1 + 17 T - 4200 T^{2} + 76313 T^{3} + 20151121 T^{4}$$)($$1 + 62 T - 645 T^{2} + 278318 T^{3} + 20151121 T^{4}$$)($$( 1 - 62 T - 645 T^{2} - 278318 T^{3} + 20151121 T^{4} )^{2}$$)($$( 1 - 62 T - 645 T^{2} - 278318 T^{3} + 20151121 T^{4} )^{2}$$)($$( 1 - 118 T + 9435 T^{2} - 529702 T^{3} + 20151121 T^{4} )^{2}$$)($$( 1 + 62 T - 645 T^{2} + 278318 T^{3} + 20151121 T^{4} )^{2}$$)($$( 1 - 112 T + 942 T^{2} - 293888 T^{3} + 58145267 T^{4} - 1319263232 T^{5} + 18982355982 T^{6} - 10131338802928 T^{7} + 406067677556641 T^{8} )^{2}$$)($$( 1 - 112 T + 942 T^{2} - 293888 T^{3} + 58145267 T^{4} - 1319263232 T^{5} + 18982355982 T^{6} - 10131338802928 T^{7} + 406067677556641 T^{8} )^{2}$$)($$( 1 + 89 T - 19 T^{2} - 251662 T^{3} - 15244389 T^{4} - 746405371 T^{5} - 32107721582 T^{6} - 3350613710419 T^{7} - 307191527310069 T^{8} - 22764937373414878 T^{9} - 7715285873576179 T^{10} +$$$$16\!\cdots\!61$$$$T^{11} +$$$$81\!\cdots\!61$$$$T^{12} )^{2}$$)($$( 1 - 217 T + 18053 T^{2} - 1666970 T^{3} + 209974835 T^{4} - 15078221277 T^{5} + 815515698066 T^{6} - 67686135312453 T^{7} + 4231228307040035 T^{8} - 150791409324257930 T^{9} + 7330739782930039973 T^{10} -$$$$39\!\cdots\!33$$$$T^{11} +$$$$81\!\cdots\!61$$$$T^{12} )^{2}$$)($$( 1 + 48 T - 978 T^{2} - 273408 T^{3} - 19722253 T^{4} - 1227328512 T^{5} - 19707796338 T^{6} + 4342002344112 T^{7} + 406067677556641 T^{8} )^{4}$$)($$( 1 + 152 T + 880 T^{2} - 696592 T^{3} + 25800514 T^{4} + 6259290472 T^{5} + 135213846720 T^{6} - 1900601864504 T^{7} + 289722470344099 T^{8} - 8531801769758456 T^{9} + 2724710586130173120 T^{10} +$$$$56\!\cdots\!68$$$$T^{11} +$$$$10\!\cdots\!74$$$$T^{12} -$$$$12\!\cdots\!08$$$$T^{13} +$$$$72\!\cdots\!80$$$$T^{14} +$$$$55\!\cdots\!08$$$$T^{15} +$$$$16\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 + 152 T + 880 T^{2} - 696592 T^{3} + 25800514 T^{4} + 6259290472 T^{5} + 135213846720 T^{6} - 1900601864504 T^{7} + 289722470344099 T^{8} - 8531801769758456 T^{9} + 2724710586130173120 T^{10} +$$$$56\!\cdots\!68$$$$T^{11} +$$$$10\!\cdots\!74$$$$T^{12} -$$$$12\!\cdots\!08$$$$T^{13} +$$$$72\!\cdots\!80$$$$T^{14} +$$$$55\!\cdots\!08$$$$T^{15} +$$$$16\!\cdots\!81$$$$T^{16} )^{2}$$)
$71$ ($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{4}( 1 + 71 T )^{4}$$)($$( 1 - 71 T )^{4}( 1 + 71 T )^{4}$$)($$( 1 - 114 T + 5041 T^{2} )^{2}( 1 + 114 T + 5041 T^{2} )^{2}$$)($$( 1 - 71 T )^{4}( 1 + 71 T )^{4}$$)($$( 1 - 9412 T^{2} + 47279686 T^{4} - 239174741572 T^{6} + 645753531245761 T^{8} )^{2}$$)($$( 1 - 9412 T^{2} + 47279686 T^{4} - 239174741572 T^{6} + 645753531245761 T^{8} )^{2}$$)($$( 1 - 7830 T^{2} + 72414895 T^{4} - 385201987444 T^{6} + 1840184211388495 T^{8} - 5056250149654308630 T^{10} +$$$$16\!\cdots\!41$$$$T^{12} )^{2}$$)($$( 1 - 23062 T^{2} + 245626031 T^{4} - 1559141837940 T^{6} + 6241770345068111 T^{8} - 14892367937589740182 T^{10} +$$$$16\!\cdots\!41$$$$T^{12} )^{2}$$)($$( 1 - 15108 T^{2} + 102348486 T^{4} - 383919676548 T^{6} + 645753531245761 T^{8} )^{4}$$)($$( 1 - 9864 T^{2} + 51888284 T^{4} - 294531431096 T^{6} + 1789421441990854 T^{8} - 7484538771485032376 T^{10} +$$$$33\!\cdots\!24$$$$T^{12} -$$$$16\!\cdots\!24$$$$T^{14} +$$$$41\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 9864 T^{2} + 51888284 T^{4} - 294531431096 T^{6} + 1789421441990854 T^{8} - 7484538771485032376 T^{10} +$$$$33\!\cdots\!24$$$$T^{12} -$$$$16\!\cdots\!24$$$$T^{14} +$$$$41\!\cdots\!21$$$$T^{16} )^{2}$$)
$73$ ($$1 - 119 T + 8832 T^{2} - 634151 T^{3} + 28398241 T^{4}$$)($$1 + 142 T + 14835 T^{2} + 756718 T^{3} + 28398241 T^{4}$$)($$1 - 119 T + 8832 T^{2} - 634151 T^{3} + 28398241 T^{4}$$)($$1 - 142 T + 14835 T^{2} - 756718 T^{3} + 28398241 T^{4}$$)($$1 - 48 T + 1152 T^{2} + 456288 T^{3} - 39349153 T^{4} + 2431558752 T^{5} + 32714773632 T^{6} - 7264042861872 T^{7} + 806460091894081 T^{8}$$)($$1 + 48 T + 1152 T^{2} - 456288 T^{3} - 39349153 T^{4} - 2431558752 T^{5} + 32714773632 T^{6} + 7264042861872 T^{7} + 806460091894081 T^{8}$$)($$( 1 - 5329 T^{2} + 28398241 T^{4} )^{2}$$)($$1 - 9506 T^{2} + 61965795 T^{4} - 269953678946 T^{6} + 806460091894081 T^{8}$$)($$( 1 + 116 T - 438 T^{2} + 375376 T^{3} + 92937971 T^{4} + 2000378704 T^{5} - 12438429558 T^{6} + 17554770249524 T^{7} + 806460091894081 T^{8} )^{2}$$)($$( 1 - 116 T - 438 T^{2} - 375376 T^{3} + 92937971 T^{4} - 2000378704 T^{5} - 12438429558 T^{6} - 17554770249524 T^{7} + 806460091894081 T^{8} )^{2}$$)($$( 1 + 27 T - 12877 T^{2} - 216188 T^{3} + 104738937 T^{4} + 821298961 T^{5} - 619422939130 T^{6} + 4376702163169 T^{7} + 2974401575009817 T^{8} - 32716643712966332 T^{9} - 10384786603320081037 T^{10} +$$$$11\!\cdots\!23$$$$T^{11} +$$$$22\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 + 51 T - 9165 T^{2} - 579660 T^{3} + 45654729 T^{4} + 1993134921 T^{5} - 160997144218 T^{6} + 10621415994009 T^{7} + 1296513996931689 T^{8} - 87722397610681740 T^{9} - 7391206742209252365 T^{10} +$$$$21\!\cdots\!99$$$$T^{11} +$$$$22\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 - 11076 T^{2} + 37309002 T^{4} - 316466706192 T^{6} + 2997534434176979 T^{8} - 8987097790916608272 T^{10} +$$$$30\!\cdots\!62$$$$T^{12} -$$$$25\!\cdots\!96$$$$T^{14} +$$$$65\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 + 56 T - 15324 T^{2} - 438256 T^{3} + 161331658 T^{4} + 2027862984 T^{5} - 1181077316848 T^{6} - 5241850793144 T^{7} + 6684367707557907 T^{8} - 27933822876664376 T^{9} - 33540518283482864368 T^{10} +$$$$30\!\cdots\!76$$$$T^{11} +$$$$13\!\cdots\!98$$$$T^{12} -$$$$18\!\cdots\!44$$$$T^{13} -$$$$35\!\cdots\!04$$$$T^{14} +$$$$68\!\cdots\!04$$$$T^{15} +$$$$65\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 - 56 T - 15324 T^{2} + 438256 T^{3} + 161331658 T^{4} - 2027862984 T^{5} - 1181077316848 T^{6} + 5241850793144 T^{7} + 6684367707557907 T^{8} + 27933822876664376 T^{9} - 33540518283482864368 T^{10} -$$$$30\!\cdots\!76$$$$T^{11} +$$$$13\!\cdots\!98$$$$T^{12} +$$$$18\!\cdots\!44$$$$T^{13} -$$$$35\!\cdots\!04$$$$T^{14} -$$$$68\!\cdots\!04$$$$T^{15} +$$$$65\!\cdots\!61$$$$T^{16} )^{2}$$)
$79$ ($$1 - 129 T + 11788 T^{2} - 805089 T^{3} + 38950081 T^{4}$$)($$( 1 - 79 T + 6241 T^{2} )( 1 + 79 T + 6241 T^{2} )$$)($$1 + 129 T + 11788 T^{2} + 805089 T^{3} + 38950081 T^{4}$$)($$( 1 - 79 T + 6241 T^{2} )( 1 + 79 T + 6241 T^{2} )$$)($$( 1 - 79 T + 6241 T^{2} )^{2}( 1 + 79 T + 6241 T^{2} )^{2}$$)($$( 1 - 79 T + 6241 T^{2} )^{2}( 1 + 79 T + 6241 T^{2} )^{2}$$)($$( 1 - 94 T + 2595 T^{2} - 586654 T^{3} + 38950081 T^{4} )( 1 + 94 T + 2595 T^{2} + 586654 T^{3} + 38950081 T^{4} )$$)($$( 1 - 79 T + 6241 T^{2} )^{2}( 1 + 79 T + 6241 T^{2} )^{2}$$)($$1 + 16900 T^{2} + 142729866 T^{4} + 1098161526800 T^{6} + 7773091247541395 T^{8} + 42773480419943670800 T^{10} +$$$$21\!\cdots\!26$$$$T^{12} +$$$$99\!\cdots\!00$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16}$$)($$1 + 16900 T^{2} + 142729866 T^{4} + 1098161526800 T^{6} + 7773091247541395 T^{8} + 42773480419943670800 T^{10} +$$$$21\!\cdots\!26$$$$T^{12} +$$$$99\!\cdots\!00$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16}$$)($$1 + 27485 T^{2} + 389982499 T^{4} + 4285373244996 T^{6} + 40173777270526125 T^{8} +$$$$31\!\cdots\!47$$$$T^{10} +$$$$20\!\cdots\!50$$$$T^{12} +$$$$12\!\cdots\!07$$$$T^{14} +$$$$60\!\cdots\!25$$$$T^{16} +$$$$25\!\cdots\!36$$$$T^{18} +$$$$89\!\cdots\!79$$$$T^{20} +$$$$24\!\cdots\!85$$$$T^{22} +$$$$34\!\cdots\!81$$$$T^{24}$$)($$1 + 16693 T^{2} + 149251283 T^{4} + 640487711012 T^{6} - 978609215845699 T^{8} - 44625107831251066425 T^{10} -$$$$37\!\cdots\!74$$$$T^{12} -$$$$17\!\cdots\!25$$$$T^{14} -$$$$14\!\cdots\!39$$$$T^{16} +$$$$37\!\cdots\!92$$$$T^{18} +$$$$34\!\cdots\!43$$$$T^{20} +$$$$14\!\cdots\!93$$$$T^{22} +$$$$34\!\cdots\!81$$$$T^{24}$$)($$( 1 + 20932 T^{2} + 253365514 T^{4} + 2237273867536 T^{6} + 15561764536526995 T^{8} + 87141998359710470416 T^{10} +$$$$38\!\cdots\!54$$$$T^{12} +$$$$12\!\cdots\!12$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16} )^{2}$$)($$1 + 24968 T^{2} + 292531236 T^{4} + 2048900954480 T^{6} + 9731167232364042 T^{8} + 40635655541936341112 T^{10} +$$$$28\!\cdots\!16$$$$T^{12} +$$$$28\!\cdots\!32$$$$T^{14} +$$$$21\!\cdots\!95$$$$T^{16} +$$$$11\!\cdots\!92$$$$T^{18} +$$$$43\!\cdots\!76$$$$T^{20} +$$$$24\!\cdots\!92$$$$T^{22} +$$$$22\!\cdots\!82$$$$T^{24} +$$$$18\!\cdots\!80$$$$T^{26} +$$$$10\!\cdots\!16$$$$T^{28} +$$$$33\!\cdots\!48$$$$T^{30} +$$$$52\!\cdots\!41$$$$T^{32}$$)($$1 + 24968 T^{2} + 292531236 T^{4} + 2048900954480 T^{6} + 9731167232364042 T^{8} + 40635655541936341112 T^{10} +$$$$28\!\cdots\!16$$$$T^{12} +$$$$28\!\cdots\!32$$$$T^{14} +$$$$21\!\cdots\!95$$$$T^{16} +$$$$11\!\cdots\!92$$$$T^{18} +$$$$43\!\cdots\!76$$$$T^{20} +$$$$24\!\cdots\!92$$$$T^{22} +$$$$22\!\cdots\!82$$$$T^{24} +$$$$18\!\cdots\!80$$$$T^{26} +$$$$10\!\cdots\!16$$$$T^{28} +$$$$33\!\cdots\!48$$$$T^{30} +$$$$52\!\cdots\!41$$$$T^{32}$$)
$83$ ($$( 1 + 110 T + 6889 T^{2} )^{2}$$)($$( 1 + 158 T + 6889 T^{2} )^{2}$$)($$( 1 + 110 T + 6889 T^{2} )^{2}$$)($$( 1 - 158 T + 6889 T^{2} )^{2}$$)($$( 1 - 72 T + 2592 T^{2} - 496008 T^{3} + 47458321 T^{4} )^{2}$$)($$( 1 + 72 T + 2592 T^{2} + 496008 T^{3} + 47458321 T^{4} )^{2}$$)($$( 1 + 6889 T^{2} )^{4}$$)($$( 1 + 11186 T^{2} + 47458321 T^{4} )^{2}$$)($$( 1 - 44 T + 13924 T^{2} - 303116 T^{3} + 47458321 T^{4} )^{4}$$)($$( 1 + 44 T + 13924 T^{2} + 303116 T^{3} + 47458321 T^{4} )^{4}$$)($$( 1 - 98 T + 12183 T^{2} - 526716 T^{3} + 83928687 T^{4} - 4650915458 T^{5} + 326940373369 T^{6} )^{4}$$)($$( 1 - 134 T + 22583 T^{2} - 1661172 T^{3} + 155574287 T^{4} - 6359415014 T^{5} + 326940373369 T^{6} )^{4}$$)($$( 1 + 12816 T^{2} + 133550298 T^{4} + 608225841936 T^{6} + 2252292232139041 T^{8} )^{4}$$)($$( 1 + 36 T + 16478 T^{2} + 177884 T^{3} + 135298114 T^{4} + 1225442876 T^{5} + 782018213438 T^{6} + 11769853441284 T^{7} + 2252292232139041 T^{8} )^{4}$$)($$( 1 - 36 T + 16478 T^{2} - 177884 T^{3} + 135298114 T^{4} - 1225442876 T^{5} + 782018213438 T^{6} - 11769853441284 T^{7} + 2252292232139041 T^{8} )^{4}$$)
$89$ ($$1 - 71 T - 2880 T^{2} - 562391 T^{3} + 62742241 T^{4}$$)($$1 - 146 T + 13395 T^{2} - 1156466 T^{3} + 62742241 T^{4}$$)($$1 - 71 T - 2880 T^{2} - 562391 T^{3} + 62742241 T^{4}$$)($$1 + 146 T + 13395 T^{2} + 1156466 T^{3} + 62742241 T^{4}$$)($$1 + 144 T + 10368 T^{2} - 788256 T^{3} - 119496673 T^{4} - 6243775776 T^{5} + 650511554688 T^{6} + 71565305898384 T^{7} + 3936588805702081 T^{8}$$)($$1 - 144 T + 10368 T^{2} + 788256 T^{3} - 119496673 T^{4} + 6243775776 T^{5} + 650511554688 T^{6} - 71565305898384 T^{7} + 3936588805702081 T^{8}$$)($$( 1 - 7921 T^{2} + 62742241 T^{4} )^{2}$$)($$1 - 5474 T^{2} - 32777565 T^{4} - 343451027234 T^{6} + 3936588805702081 T^{8}$$)($$( 1 + 156 T + 3562 T^{2} + 769392 T^{3} + 176051379 T^{4} + 6094354032 T^{5} + 223487862442 T^{6} + 77529081389916 T^{7} + 3936588805702081 T^{8} )^{2}$$)($$( 1 - 156 T + 3562 T^{2} - 769392 T^{3} + 176051379 T^{4} - 6094354032 T^{5} + 223487862442 T^{6} - 77529081389916 T^{7} + 3936588805702081 T^{8} )^{2}$$)($$( 1 - 13 T - 19181 T^{2} + 141748 T^{3} + 218594713 T^{4} - 635752183 T^{5} - 1943770650106 T^{6} - 5035793041543 T^{7} + 13715122164371833 T^{8} + 70446104031139828 T^{9} - 75507709882171615661 T^{10} -$$$$40\!\cdots\!13$$$$T^{11} +$$$$24\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 + 107 T + 1395 T^{2} - 497084 T^{3} - 62702935 T^{4} - 2422278015 T^{5} + 93422604838 T^{6} - 19186864156815 T^{7} - 3934122659177335 T^{8} - 247041448036057724 T^{9} + 5491541383954402995 T^{10} +$$$$33\!\cdots\!07$$$$T^{11} +$$$$24\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 - 16068 T^{2} + 128739018 T^{4} - 63583068432 T^{6} - 3380290374381229 T^{8} - 3989344203080036112 T^{10} +$$$$50\!\cdots\!58$$$$T^{12} -$$$$39\!\cdots\!28$$$$T^{14} +$$$$15\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 + 256 T + 17284 T^{2} - 187392 T^{3} + 84842826 T^{4} + 25389871104 T^{5} + 1853625901584 T^{6} + 111590371439872 T^{7} + 11164291531924819 T^{8} + 883907332175226112 T^{9} +$$$$11\!\cdots\!44$$$$T^{10} +$$$$12\!\cdots\!44$$$$T^{11} +$$$$33\!\cdots\!06$$$$T^{12} -$$$$58\!\cdots\!92$$$$T^{13} +$$$$42\!\cdots\!64$$$$T^{14} +$$$$50\!\cdots\!96$$$$T^{15} +$$$$15\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 - 256 T + 17284 T^{2} + 187392 T^{3} + 84842826 T^{4} - 25389871104 T^{5} + 1853625901584 T^{6} - 111590371439872 T^{7} + 11164291531924819 T^{8} - 883907332175226112 T^{9} +$$$$11\!\cdots\!44$$$$T^{10} -$$$$12\!\cdots\!44$$$$T^{11} +$$$$33\!\cdots\!06$$$$T^{12} +$$$$58\!\cdots\!92$$$$T^{13} +$$$$42\!\cdots\!64$$$$T^{14} -$$$$50\!\cdots\!96$$$$T^{15} +$$$$15\!\cdots\!61$$$$T^{16} )^{2}$$)
$97$ ($$( 1 - 22 T + 9409 T^{2} )^{2}$$)($$( 1 - 94 T + 9409 T^{2} )^{2}$$)($$( 1 - 22 T + 9409 T^{2} )^{2}$$)($$( 1 + 94 T + 9409 T^{2} )^{2}$$)($$( 1 - 240 T + 28800 T^{2} - 2258160 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 + 240 T + 28800 T^{2} + 2258160 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 + 9409 T^{2} )^{4}$$)($$( 1 - 9982 T^{2} + 88529281 T^{4} )^{2}$$)($$( 1 + 68 T + 3046 T^{2} + 639812 T^{3} + 88529281 T^{4} )^{4}$$)($$( 1 - 68 T + 3046 T^{2} - 639812 T^{3} + 88529281 T^{4} )^{4}$$)($$( 1 - 46 T + 18423 T^{2} - 458352 T^{3} + 173342007 T^{4} - 4072346926 T^{5} + 832972004929 T^{6} )^{4}$$)($$( 1 - 38 T + 25191 T^{2} - 597344 T^{3} + 237022119 T^{4} - 3364112678 T^{5} + 832972004929 T^{6} )^{4}$$)($$( 1 + 27716 T^{2} + 356960134 T^{4} + 2453677552196 T^{6} + 7837433594376961 T^{8} )^{4}$$)($$( 1 + 32 T + 19484 T^{2} + 1437536 T^{3} + 199130566 T^{4} + 13525776224 T^{5} + 1724904511004 T^{6} + 26655104157728 T^{7} + 7837433594376961 T^{8} )^{4}$$)($$( 1 - 32 T + 19484 T^{2} - 1437536 T^{3} + 199130566 T^{4} - 13525776224 T^{5} + 1724904511004 T^{6} - 26655104157728 T^{7} + 7837433594376961 T^{8} )^{4}$$)