# Properties

 Label 1849.2.a Level 1849 Weight 2 Character orbit a Rep. character $$\chi_{1849}(1,\cdot)$$ Character field $$\Q$$ Dimension 130 Newform subspaces 18 Sturm bound 315 Trace bound 4

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1849 = 43^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1849.a (trivial) Character field: $$\Q$$ Newform subspaces: $$18$$ Sturm bound: $$315$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(1849))$$.

Total New Old
Modular forms 179 171 8
Cusp forms 136 130 6
Eisenstein series 43 41 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$43$$Dim.
$$+$$$$60$$
$$-$$$$70$$

## Trace form

 $$130q + 2q^{2} + 2q^{3} + 110q^{4} + 4q^{7} + 92q^{9} + O(q^{10})$$ $$130q + 2q^{2} + 2q^{3} + 110q^{4} + 4q^{7} + 92q^{9} - 4q^{10} + 4q^{12} + 4q^{13} - 4q^{14} - 12q^{15} + 82q^{16} - 6q^{17} + 2q^{18} + 6q^{19} + 8q^{20} + 4q^{21} - 2q^{22} - 8q^{24} + 36q^{25} - 18q^{26} - 4q^{27} + 6q^{29} + 24q^{30} + 8q^{31} - 8q^{32} + 14q^{33} - 14q^{34} + 12q^{35} + 26q^{36} + 4q^{38} - 2q^{39} - 8q^{40} - 2q^{41} - 8q^{42} - 44q^{44} + 8q^{45} + 14q^{46} - 12q^{47} - 8q^{48} + 16q^{49} + 38q^{50} + 2q^{51} + 14q^{52} - 16q^{53} + 6q^{54} + 24q^{55} + 22q^{56} - 12q^{57} - 24q^{58} + 20q^{59} - 2q^{60} - 10q^{61} - 2q^{62} - 4q^{63} - 22q^{64} - 16q^{65} - 2q^{66} + 2q^{67} + 10q^{68} - 18q^{69} - 16q^{70} + 10q^{71} + 22q^{73} + 38q^{74} + 6q^{75} + 4q^{76} - 12q^{77} + 24q^{78} + 8q^{79} - 14q^{81} + 18q^{82} - 32q^{83} + 14q^{84} - 24q^{85} - 32q^{87} + 16q^{88} + 16q^{89} - 86q^{90} - 4q^{91} + 6q^{92} - 2q^{93} + 8q^{94} + 2q^{95} + 30q^{96} + 2q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(1849))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 43
1849.2.a.a $$1$$ $$14.764$$ $$\Q$$ None $$-1$$ $$-1$$ $$1$$ $$-3$$ $$-$$ $$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-3q^{7}+\cdots$$
1849.2.a.b $$1$$ $$14.764$$ $$\Q$$ $$\Q(\sqrt{-43})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q-2q^{4}-3q^{9}-q^{11}+3q^{13}+4q^{16}+\cdots$$
1849.2.a.c $$1$$ $$14.764$$ $$\Q$$ None $$1$$ $$1$$ $$-1$$ $$3$$ $$+$$ $$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+3q^{7}+\cdots$$
1849.2.a.d $$1$$ $$14.764$$ $$\Q$$ None $$2$$ $$2$$ $$4$$ $$0$$ $$-$$ $$q+2q^{2}+2q^{3}+2q^{4}+4q^{5}+4q^{6}+\cdots$$
1849.2.a.e $$2$$ $$14.764$$ $$\Q(\sqrt{5})$$ None $$-3$$ $$-3$$ $$-2$$ $$-4$$ $$+$$ $$q+(-1-\beta )q^{2}+(-2+\beta )q^{3}+3\beta q^{4}+\cdots$$
1849.2.a.f $$2$$ $$14.764$$ $$\Q(\sqrt{2})$$ None $$0$$ $$0$$ $$-4$$ $$4$$ $$-$$ $$q+\beta q^{2}-\beta q^{3}+(-2-\beta )q^{5}-2q^{6}+\cdots$$
1849.2.a.g $$2$$ $$14.764$$ $$\Q(\sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q+\beta q^{2}-\beta q^{3}+4q^{4}-\beta q^{5}-6q^{6}+\cdots$$
1849.2.a.h $$2$$ $$14.764$$ $$\Q(\sqrt{5})$$ None $$3$$ $$3$$ $$2$$ $$4$$ $$-$$ $$q+(1+\beta )q^{2}+(2-\beta )q^{3}+3\beta q^{4}+2\beta q^{5}+\cdots$$
1849.2.a.i $$3$$ $$14.764$$ $$\Q(\zeta_{14})^+$$ None $$-2$$ $$-5$$ $$-6$$ $$-8$$ $$+$$ $$q+(-1-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\cdots$$
1849.2.a.j $$3$$ $$14.764$$ $$\Q(\zeta_{14})^+$$ None $$-1$$ $$-1$$ $$-2$$ $$0$$ $$-$$ $$q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2})q^{5}+\cdots$$
1849.2.a.k $$3$$ $$14.764$$ $$\Q(\zeta_{14})^+$$ None $$1$$ $$1$$ $$2$$ $$0$$ $$+$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{2})q^{5}+\cdots$$
1849.2.a.l $$3$$ $$14.764$$ $$\Q(\zeta_{14})^+$$ None $$2$$ $$5$$ $$6$$ $$8$$ $$-$$ $$q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$$
1849.2.a.m $$10$$ $$14.764$$ $$\Q(\zeta_{44})^+$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
1849.2.a.n $$18$$ $$14.764$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$-5$$ $$-5$$ $$-11$$ $$-6$$ $$+$$ $$q-\beta _{1}q^{2}-\beta _{14}q^{3}+(1+\beta _{3}-\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots$$
1849.2.a.o $$18$$ $$14.764$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$5$$ $$5$$ $$11$$ $$6$$ $$-$$ $$q+\beta _{1}q^{2}+\beta _{14}q^{3}+(1+\beta _{3}-\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots$$
1849.2.a.p $$20$$ $$14.764$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-5$$ $$1$$ $$3$$ $$2$$ $$-$$ $$q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots$$
1849.2.a.q $$20$$ $$14.764$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$+$$ $$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{19})q^{3}+(1+\beta _{6}+\cdots)q^{4}+\cdots$$
1849.2.a.r $$20$$ $$14.764$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$5$$ $$-1$$ $$-3$$ $$-2$$ $$-$$ $$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(1849))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(1849)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(43))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + T + 2 T^{2}$$)($$1 + 2 T^{2}$$)($$1 - T + 2 T^{2}$$)($$1 - 2 T + 2 T^{2}$$)($$1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$$)($$1 + 2 T^{2} + 4 T^{4}$$)($$1 - 2 T^{2} + 4 T^{4}$$)($$1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4}$$)($$1 + 2 T + 5 T^{2} + 7 T^{3} + 10 T^{4} + 8 T^{5} + 8 T^{6}$$)($$1 + T + 4 T^{2} + 3 T^{3} + 8 T^{4} + 4 T^{5} + 8 T^{6}$$)($$1 - T + 4 T^{2} - 3 T^{3} + 8 T^{4} - 4 T^{5} + 8 T^{6}$$)($$1 - 2 T + 5 T^{2} - 7 T^{3} + 10 T^{4} - 8 T^{5} + 8 T^{6}$$)($$1 + 9 T^{2} + 48 T^{4} + 179 T^{6} + 511 T^{8} + 1145 T^{10} + 2044 T^{12} + 2864 T^{14} + 3072 T^{16} + 2304 T^{18} + 1024 T^{20}$$)($$1 + 5 T + 21 T^{2} + 64 T^{3} + 179 T^{4} + 437 T^{5} + 1008 T^{6} + 2147 T^{7} + 4381 T^{8} + 8465 T^{9} + 15785 T^{10} + 28194 T^{11} + 48769 T^{12} + 81286 T^{13} + 131557 T^{14} + 205927 T^{15} + 313527 T^{16} + 462513 T^{17} + 664265 T^{18} + 925026 T^{19} + 1254108 T^{20} + 1647416 T^{21} + 2104912 T^{22} + 2601152 T^{23} + 3121216 T^{24} + 3608832 T^{25} + 4040960 T^{26} + 4334080 T^{27} + 4486144 T^{28} + 4397056 T^{29} + 4128768 T^{30} + 3579904 T^{31} + 2932736 T^{32} + 2097152 T^{33} + 1376256 T^{34} + 655360 T^{35} + 262144 T^{36}$$)($$1 - 5 T + 21 T^{2} - 64 T^{3} + 179 T^{4} - 437 T^{5} + 1008 T^{6} - 2147 T^{7} + 4381 T^{8} - 8465 T^{9} + 15785 T^{10} - 28194 T^{11} + 48769 T^{12} - 81286 T^{13} + 131557 T^{14} - 205927 T^{15} + 313527 T^{16} - 462513 T^{17} + 664265 T^{18} - 925026 T^{19} + 1254108 T^{20} - 1647416 T^{21} + 2104912 T^{22} - 2601152 T^{23} + 3121216 T^{24} - 3608832 T^{25} + 4040960 T^{26} - 4334080 T^{27} + 4486144 T^{28} - 4397056 T^{29} + 4128768 T^{30} - 3579904 T^{31} + 2932736 T^{32} - 2097152 T^{33} + 1376256 T^{34} - 655360 T^{35} + 262144 T^{36}$$)($$1 + 5 T + 21 T^{2} + 63 T^{3} + 171 T^{4} + 395 T^{5} + 861 T^{6} + 1697 T^{7} + 3232 T^{8} + 5730 T^{9} + 9969 T^{10} + 16462 T^{11} + 27043 T^{12} + 42784 T^{13} + 67961 T^{14} + 104635 T^{15} + 161930 T^{16} + 242650 T^{17} + 363878 T^{18} + 526409 T^{19} + 758669 T^{20} + 1052818 T^{21} + 1455512 T^{22} + 1941200 T^{23} + 2590880 T^{24} + 3348320 T^{25} + 4349504 T^{26} + 5476352 T^{27} + 6923008 T^{28} + 8428544 T^{29} + 10208256 T^{30} + 11735040 T^{31} + 13238272 T^{32} + 13901824 T^{33} + 14106624 T^{34} + 12943360 T^{35} + 11206656 T^{36} + 8257536 T^{37} + 5505024 T^{38} + 2621440 T^{39} + 1048576 T^{40}$$)($$1 + 13 T^{2} + 88 T^{4} + 421 T^{6} + 1601 T^{8} + 5137 T^{10} + 14485 T^{12} + 36989 T^{14} + 87208 T^{16} + 191889 T^{18} + 396021 T^{20} + 767556 T^{22} + 1395328 T^{24} + 2367296 T^{26} + 3708160 T^{28} + 5260288 T^{30} + 6557696 T^{32} + 6897664 T^{34} + 5767168 T^{36} + 3407872 T^{38} + 1048576 T^{40}$$)($$1 - 5 T + 21 T^{2} - 63 T^{3} + 171 T^{4} - 395 T^{5} + 861 T^{6} - 1697 T^{7} + 3232 T^{8} - 5730 T^{9} + 9969 T^{10} - 16462 T^{11} + 27043 T^{12} - 42784 T^{13} + 67961 T^{14} - 104635 T^{15} + 161930 T^{16} - 242650 T^{17} + 363878 T^{18} - 526409 T^{19} + 758669 T^{20} - 1052818 T^{21} + 1455512 T^{22} - 1941200 T^{23} + 2590880 T^{24} - 3348320 T^{25} + 4349504 T^{26} - 5476352 T^{27} + 6923008 T^{28} - 8428544 T^{29} + 10208256 T^{30} - 11735040 T^{31} + 13238272 T^{32} - 13901824 T^{33} + 14106624 T^{34} - 12943360 T^{35} + 11206656 T^{36} - 8257536 T^{37} + 5505024 T^{38} - 2621440 T^{39} + 1048576 T^{40}$$)
$3$ ($$1 + T + 3 T^{2}$$)($$1 + 3 T^{2}$$)($$1 - T + 3 T^{2}$$)($$1 - 2 T + 3 T^{2}$$)($$1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4}$$)($$1 + 4 T^{2} + 9 T^{4}$$)($$1 + 9 T^{4}$$)($$1 - 3 T + 7 T^{2} - 9 T^{3} + 9 T^{4}$$)($$1 + 5 T + 15 T^{2} + 31 T^{3} + 45 T^{4} + 45 T^{5} + 27 T^{6}$$)($$1 + T + 7 T^{2} + 5 T^{3} + 21 T^{4} + 9 T^{5} + 27 T^{6}$$)($$1 - T + 7 T^{2} - 5 T^{3} + 21 T^{4} - 9 T^{5} + 27 T^{6}$$)($$1 - 5 T + 15 T^{2} - 31 T^{3} + 45 T^{4} - 45 T^{5} + 27 T^{6}$$)($$1 + 8 T^{2} + 42 T^{4} + 182 T^{6} + 653 T^{8} + 2089 T^{10} + 5877 T^{12} + 14742 T^{14} + 30618 T^{16} + 52488 T^{18} + 59049 T^{20}$$)($$1 + 5 T + 32 T^{2} + 121 T^{3} + 487 T^{4} + 1519 T^{5} + 4810 T^{6} + 12993 T^{7} + 35099 T^{8} + 84694 T^{9} + 203425 T^{10} + 447800 T^{11} + 980330 T^{12} + 1997474 T^{13} + 4049010 T^{14} + 7709756 T^{15} + 14612100 T^{16} + 26142572 T^{17} + 46568083 T^{18} + 78427716 T^{19} + 131508900 T^{20} + 208163412 T^{21} + 327969810 T^{22} + 485386182 T^{23} + 714660570 T^{24} + 979338600 T^{25} + 1334671425 T^{26} + 1667032002 T^{27} + 2072560851 T^{28} + 2301670971 T^{29} + 2556231210 T^{30} + 2421776637 T^{31} + 2329305903 T^{32} + 1736217747 T^{33} + 1377495072 T^{34} + 645700815 T^{35} + 387420489 T^{36}$$)($$1 - 5 T + 32 T^{2} - 121 T^{3} + 487 T^{4} - 1519 T^{5} + 4810 T^{6} - 12993 T^{7} + 35099 T^{8} - 84694 T^{9} + 203425 T^{10} - 447800 T^{11} + 980330 T^{12} - 1997474 T^{13} + 4049010 T^{14} - 7709756 T^{15} + 14612100 T^{16} - 26142572 T^{17} + 46568083 T^{18} - 78427716 T^{19} + 131508900 T^{20} - 208163412 T^{21} + 327969810 T^{22} - 485386182 T^{23} + 714660570 T^{24} - 979338600 T^{25} + 1334671425 T^{26} - 1667032002 T^{27} + 2072560851 T^{28} - 2301670971 T^{29} + 2556231210 T^{30} - 2421776637 T^{31} + 2329305903 T^{32} - 1736217747 T^{33} + 1377495072 T^{34} - 645700815 T^{35} + 387420489 T^{36}$$)($$1 - T + 17 T^{2} - 23 T^{3} + 167 T^{4} - 232 T^{5} + 1222 T^{6} - 1630 T^{7} + 7167 T^{8} - 9204 T^{9} + 35773 T^{10} - 43758 T^{11} + 157158 T^{12} - 182474 T^{13} + 618648 T^{14} - 684729 T^{15} + 2226544 T^{16} - 2352876 T^{17} + 7416388 T^{18} - 7539203 T^{19} + 23008870 T^{20} - 22617609 T^{21} + 66747492 T^{22} - 63527652 T^{23} + 180350064 T^{24} - 166389147 T^{25} + 450994392 T^{26} - 399070638 T^{27} + 1031113638 T^{28} - 861288714 T^{29} + 2112359877 T^{30} - 1630460988 T^{31} + 3808837647 T^{32} - 2598746490 T^{33} + 5844788118 T^{34} - 3328946424 T^{35} + 7188802407 T^{36} - 2970223749 T^{37} + 6586148313 T^{38} - 1162261467 T^{39} + 3486784401 T^{40}$$)($$1 + 33 T^{2} + 552 T^{4} + 6226 T^{6} + 53068 T^{8} + 363000 T^{10} + 2065709 T^{12} + 10006931 T^{14} + 41887653 T^{16} + 152934639 T^{18} + 489574513 T^{20} + 1376411751 T^{22} + 3392899893 T^{24} + 7295052699 T^{26} + 13553116749 T^{28} + 21434787000 T^{30} + 28202510988 T^{32} + 29778764994 T^{34} + 23761789992 T^{36} + 12784876137 T^{38} + 3486784401 T^{40}$$)($$1 + T + 17 T^{2} + 23 T^{3} + 167 T^{4} + 232 T^{5} + 1222 T^{6} + 1630 T^{7} + 7167 T^{8} + 9204 T^{9} + 35773 T^{10} + 43758 T^{11} + 157158 T^{12} + 182474 T^{13} + 618648 T^{14} + 684729 T^{15} + 2226544 T^{16} + 2352876 T^{17} + 7416388 T^{18} + 7539203 T^{19} + 23008870 T^{20} + 22617609 T^{21} + 66747492 T^{22} + 63527652 T^{23} + 180350064 T^{24} + 166389147 T^{25} + 450994392 T^{26} + 399070638 T^{27} + 1031113638 T^{28} + 861288714 T^{29} + 2112359877 T^{30} + 1630460988 T^{31} + 3808837647 T^{32} + 2598746490 T^{33} + 5844788118 T^{34} + 3328946424 T^{35} + 7188802407 T^{36} + 2970223749 T^{37} + 6586148313 T^{38} + 1162261467 T^{39} + 3486784401 T^{40}$$)
$5$ ($$1 - T + 5 T^{2}$$)($$1 + 5 T^{2}$$)($$1 + T + 5 T^{2}$$)($$1 - 4 T + 5 T^{2}$$)($$1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4}$$)($$1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4}$$)($$1 + 4 T^{2} + 25 T^{4}$$)($$1 - 2 T + 6 T^{2} - 10 T^{3} + 25 T^{4}$$)($$( 1 + 2 T + 5 T^{2} )^{3}$$)($$1 + 2 T + 14 T^{2} + 19 T^{3} + 70 T^{4} + 50 T^{5} + 125 T^{6}$$)($$1 - 2 T + 14 T^{2} - 19 T^{3} + 70 T^{4} - 50 T^{5} + 125 T^{6}$$)($$( 1 - 2 T + 5 T^{2} )^{3}$$)($$1 + 28 T^{2} + 410 T^{4} + 4066 T^{6} + 29885 T^{8} + 169289 T^{10} + 747125 T^{12} + 2541250 T^{14} + 6406250 T^{16} + 10937500 T^{18} + 9765625 T^{20}$$)($$1 + 11 T + 101 T^{2} + 669 T^{3} + 3903 T^{4} + 19466 T^{5} + 88477 T^{6} + 363160 T^{7} + 1386460 T^{8} + 4905936 T^{9} + 16359692 T^{10} + 51316565 T^{11} + 153036579 T^{12} + 433243564 T^{13} + 1172911578 T^{14} + 3031457583 T^{15} + 7519728391 T^{16} + 17863052655 T^{17} + 40796547233 T^{18} + 89315263275 T^{19} + 187993209775 T^{20} + 378932197875 T^{21} + 733069736250 T^{22} + 1353886137500 T^{23} + 2391196546875 T^{24} + 4009106640625 T^{25} + 6390504687500 T^{26} + 9581906250000 T^{27} + 13539648437500 T^{28} + 17732421875000 T^{29} + 21600830078125 T^{30} + 23762207031250 T^{31} + 23822021484375 T^{32} + 20416259765625 T^{33} + 15411376953125 T^{34} + 8392333984375 T^{35} + 3814697265625 T^{36}$$)($$1 - 11 T + 101 T^{2} - 669 T^{3} + 3903 T^{4} - 19466 T^{5} + 88477 T^{6} - 363160 T^{7} + 1386460 T^{8} - 4905936 T^{9} + 16359692 T^{10} - 51316565 T^{11} + 153036579 T^{12} - 433243564 T^{13} + 1172911578 T^{14} - 3031457583 T^{15} + 7519728391 T^{16} - 17863052655 T^{17} + 40796547233 T^{18} - 89315263275 T^{19} + 187993209775 T^{20} - 378932197875 T^{21} + 733069736250 T^{22} - 1353886137500 T^{23} + 2391196546875 T^{24} - 4009106640625 T^{25} + 6390504687500 T^{26} - 9581906250000 T^{27} + 13539648437500 T^{28} - 17732421875000 T^{29} + 21600830078125 T^{30} - 23762207031250 T^{31} + 23822021484375 T^{32} - 20416259765625 T^{33} + 15411376953125 T^{34} - 8392333984375 T^{35} + 3814697265625 T^{36}$$)($$1 - 3 T + 49 T^{2} - 144 T^{3} + 1263 T^{4} - 3607 T^{5} + 22534 T^{6} - 61984 T^{7} + 309298 T^{8} - 813710 T^{9} + 3448115 T^{10} - 8635650 T^{11} + 32236817 T^{12} - 76617151 T^{13} + 257923006 T^{14} - 580352696 T^{15} + 1789501390 T^{16} - 3803096299 T^{17} + 10857165918 T^{18} - 21729721248 T^{19} + 57872565353 T^{20} - 108648606240 T^{21} + 271429147950 T^{22} - 475387037375 T^{23} + 1118438368750 T^{24} - 1813602175000 T^{25} + 4030046968750 T^{26} - 5985714921875 T^{27} + 12592506640625 T^{28} - 16866503906250 T^{29} + 33672998046875 T^{30} - 39731933593750 T^{31} + 75512207031250 T^{32} - 75664062500000 T^{33} + 137536621093750 T^{34} - 110076904296875 T^{35} + 192718505859375 T^{36} - 109863281250000 T^{37} + 186920166015625 T^{38} - 57220458984375 T^{39} + 95367431640625 T^{40}$$)($$1 + 40 T^{2} + 816 T^{4} + 11301 T^{6} + 120252 T^{8} + 1058397 T^{10} + 8091780 T^{12} + 55414621 T^{14} + 345351343 T^{16} + 1969780626 T^{18} + 10291287491 T^{20} + 49244515650 T^{22} + 215844589375 T^{24} + 865853453125 T^{26} + 3160851562500 T^{28} + 10335908203125 T^{30} + 29358398437500 T^{32} + 68975830078125 T^{34} + 124511718750000 T^{36} + 152587890625000 T^{38} + 95367431640625 T^{40}$$)($$1 + 3 T + 49 T^{2} + 144 T^{3} + 1263 T^{4} + 3607 T^{5} + 22534 T^{6} + 61984 T^{7} + 309298 T^{8} + 813710 T^{9} + 3448115 T^{10} + 8635650 T^{11} + 32236817 T^{12} + 76617151 T^{13} + 257923006 T^{14} + 580352696 T^{15} + 1789501390 T^{16} + 3803096299 T^{17} + 10857165918 T^{18} + 21729721248 T^{19} + 57872565353 T^{20} + 108648606240 T^{21} + 271429147950 T^{22} + 475387037375 T^{23} + 1118438368750 T^{24} + 1813602175000 T^{25} + 4030046968750 T^{26} + 5985714921875 T^{27} + 12592506640625 T^{28} + 16866503906250 T^{29} + 33672998046875 T^{30} + 39731933593750 T^{31} + 75512207031250 T^{32} + 75664062500000 T^{33} + 137536621093750 T^{34} + 110076904296875 T^{35} + 192718505859375 T^{36} + 109863281250000 T^{37} + 186920166015625 T^{38} + 57220458984375 T^{39} + 95367431640625 T^{40}$$)
$7$ ($$1 + 3 T + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 - 3 T + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 + 4 T + 13 T^{2} + 28 T^{3} + 49 T^{4}$$)($$1 - 4 T + 16 T^{2} - 28 T^{3} + 49 T^{4}$$)($$1 + 8 T^{2} + 49 T^{4}$$)($$1 - 4 T + 13 T^{2} - 28 T^{3} + 49 T^{4}$$)($$1 + 8 T + 40 T^{2} + 125 T^{3} + 280 T^{4} + 392 T^{5} + 343 T^{6}$$)($$1 + 14 T^{2} - 7 T^{3} + 98 T^{4} + 343 T^{6}$$)($$1 + 14 T^{2} + 7 T^{3} + 98 T^{4} + 343 T^{6}$$)($$1 - 8 T + 40 T^{2} - 125 T^{3} + 280 T^{4} - 392 T^{5} + 343 T^{6}$$)($$1 + 26 T^{2} + 401 T^{4} + 4541 T^{6} + 42232 T^{8} + 324259 T^{10} + 2069368 T^{12} + 10902941 T^{14} + 47177249 T^{16} + 149884826 T^{18} + 282475249 T^{20}$$)($$1 + 6 T + 84 T^{2} + 404 T^{3} + 3274 T^{4} + 13241 T^{5} + 80350 T^{6} + 281196 T^{7} + 1411311 T^{8} + 4354137 T^{9} + 19080222 T^{10} + 52630458 T^{11} + 208882075 T^{12} + 522279147 T^{13} + 1931335668 T^{14} + 4450614354 T^{15} + 15661259403 T^{16} + 33919735838 T^{17} + 114695007659 T^{18} + 237438150866 T^{19} + 767401710747 T^{20} + 1526560723422 T^{21} + 4637136938868 T^{22} + 8777945623629 T^{23} + 24574767241675 T^{24} + 43343445272694 T^{25} + 109993682865822 T^{26} + 175705133322159 T^{27} + 398660426141439 T^{28} + 556016370824628 T^{29} + 1112147426600350 T^{30} + 1282907386799087 T^{31} + 2220502340507626 T^{32} + 1918014850016972 T^{33} + 2791566167846484 T^{34} + 1395783083923242 T^{35} + 1628413597910449 T^{36}$$)($$1 - 6 T + 84 T^{2} - 404 T^{3} + 3274 T^{4} - 13241 T^{5} + 80350 T^{6} - 281196 T^{7} + 1411311 T^{8} - 4354137 T^{9} + 19080222 T^{10} - 52630458 T^{11} + 208882075 T^{12} - 522279147 T^{13} + 1931335668 T^{14} - 4450614354 T^{15} + 15661259403 T^{16} - 33919735838 T^{17} + 114695007659 T^{18} - 237438150866 T^{19} + 767401710747 T^{20} - 1526560723422 T^{21} + 4637136938868 T^{22} - 8777945623629 T^{23} + 24574767241675 T^{24} - 43343445272694 T^{25} + 109993682865822 T^{26} - 175705133322159 T^{27} + 398660426141439 T^{28} - 556016370824628 T^{29} + 1112147426600350 T^{30} - 1282907386799087 T^{31} + 2220502340507626 T^{32} - 1918014850016972 T^{33} + 2791566167846484 T^{34} - 1395783083923242 T^{35} + 1628413597910449 T^{36}$$)($$1 - 2 T + 62 T^{2} - 65 T^{3} + 1889 T^{4} - 519 T^{5} + 39331 T^{6} + 15569 T^{7} + 639716 T^{8} + 616487 T^{9} + 8694547 T^{10} + 12252311 T^{11} + 102295606 T^{12} + 176127090 T^{13} + 1061310639 T^{14} + 2021411595 T^{15} + 9802789013 T^{16} + 19335318101 T^{17} + 80959704741 T^{18} + 157473424267 T^{19} + 598780926318 T^{20} + 1102313969869 T^{21} + 3967025532309 T^{22} + 6632014108643 T^{23} + 23536496420213 T^{24} + 33973864677165 T^{25} + 124862135367711 T^{26} + 145048232079870 T^{27} + 589713811764406 T^{28} + 494424942935777 T^{29} + 2455994328767203 T^{30} + 1218996231811841 T^{31} + 8854492883074916 T^{32} + 1508465003026583 T^{33} + 26675191678224019 T^{34} - 2463984423660417 T^{35} + 62777005845976289 T^{36} - 15120983409168455 T^{37} + 100961643070447838 T^{38} - 22797790370746286 T^{39} + 79792266297612001 T^{40}$$)($$1 + 80 T^{2} + 3128 T^{4} + 80110 T^{6} + 1519434 T^{8} + 22863527 T^{10} + 285235077 T^{12} + 3041104389 T^{14} + 28315900111 T^{16} + 233769578782 T^{18} + 1727104571291 T^{20} + 11454709360318 T^{22} + 67986476166511 T^{24} + 357782890261461 T^{26} + 1644323457124677 T^{28} + 6458380482343223 T^{30} + 21030922376964234 T^{32} + 54332450365933390 T^{34} + 103952606821711928 T^{36} + 130273087832835920 T^{38} + 79792266297612001 T^{40}$$)($$1 + 2 T + 62 T^{2} + 65 T^{3} + 1889 T^{4} + 519 T^{5} + 39331 T^{6} - 15569 T^{7} + 639716 T^{8} - 616487 T^{9} + 8694547 T^{10} - 12252311 T^{11} + 102295606 T^{12} - 176127090 T^{13} + 1061310639 T^{14} - 2021411595 T^{15} + 9802789013 T^{16} - 19335318101 T^{17} + 80959704741 T^{18} - 157473424267 T^{19} + 598780926318 T^{20} - 1102313969869 T^{21} + 3967025532309 T^{22} - 6632014108643 T^{23} + 23536496420213 T^{24} - 33973864677165 T^{25} + 124862135367711 T^{26} - 145048232079870 T^{27} + 589713811764406 T^{28} - 494424942935777 T^{29} + 2455994328767203 T^{30} - 1218996231811841 T^{31} + 8854492883074916 T^{32} - 1508465003026583 T^{33} + 26675191678224019 T^{34} + 2463984423660417 T^{35} + 62777005845976289 T^{36} + 15120983409168455 T^{37} + 100961643070447838 T^{38} + 22797790370746286 T^{39} + 79792266297612001 T^{40}$$)
$11$ ($$1 + 11 T^{2}$$)($$1 + T + 11 T^{2}$$)($$1 + 11 T^{2}$$)($$1 - 3 T + 11 T^{2}$$)($$1 + 5 T + 27 T^{2} + 55 T^{3} + 121 T^{4}$$)($$1 + 2 T + 15 T^{2} + 22 T^{3} + 121 T^{4}$$)($$( 1 + T + 11 T^{2} )^{2}$$)($$1 + 5 T + 27 T^{2} + 55 T^{3} + 121 T^{4}$$)($$1 + 12 T^{2} - 7 T^{3} + 132 T^{4} + 1331 T^{6}$$)($$1 - 2 T + 18 T^{2} - 57 T^{3} + 198 T^{4} - 242 T^{5} + 1331 T^{6}$$)($$1 - 2 T + 18 T^{2} - 57 T^{3} + 198 T^{4} - 242 T^{5} + 1331 T^{6}$$)($$1 + 12 T^{2} - 7 T^{3} + 132 T^{4} + 1331 T^{6}$$)($$( 1 + 5 T + 54 T^{2} + 208 T^{3} + 1182 T^{4} + 3367 T^{5} + 13002 T^{6} + 25168 T^{7} + 71874 T^{8} + 73205 T^{9} + 161051 T^{10} )^{2}$$)($$1 + 2 T + 106 T^{2} + 229 T^{3} + 5690 T^{4} + 12747 T^{5} + 204282 T^{6} + 465265 T^{7} + 5488286 T^{8} + 12572724 T^{9} + 117435749 T^{10} + 268589062 T^{11} + 2084590259 T^{12} + 4722228468 T^{13} + 31603117559 T^{14} + 70103709703 T^{15} + 417787467273 T^{16} + 892536995699 T^{17} + 4878827245269 T^{18} + 9817906952689 T^{19} + 50552283540033 T^{20} + 93308037614693 T^{21} + 462701244181319 T^{22} + 760519616999868 T^{23} + 3692978803824299 T^{24} + 5234040979923602 T^{25} + 25173395745036869 T^{26} + 29645825525380284 T^{27} + 142352004313723886 T^{28} + 132745534426826915 T^{29} + 641124425653319322 T^{30} + 440061011698688457 T^{31} + 2160776553088641290 T^{32} + 956589830796184079 T^{33} + 4870671365538649066 T^{34} + 1010894056998587542 T^{35} + 5559917313492231481 T^{36}$$)($$1 + 2 T + 106 T^{2} + 229 T^{3} + 5690 T^{4} + 12747 T^{5} + 204282 T^{6} + 465265 T^{7} + 5488286 T^{8} + 12572724 T^{9} + 117435749 T^{10} + 268589062 T^{11} + 2084590259 T^{12} + 4722228468 T^{13} + 31603117559 T^{14} + 70103709703 T^{15} + 417787467273 T^{16} + 892536995699 T^{17} + 4878827245269 T^{18} + 9817906952689 T^{19} + 50552283540033 T^{20} + 93308037614693 T^{21} + 462701244181319 T^{22} + 760519616999868 T^{23} + 3692978803824299 T^{24} + 5234040979923602 T^{25} + 25173395745036869 T^{26} + 29645825525380284 T^{27} + 142352004313723886 T^{28} + 132745534426826915 T^{29} + 641124425653319322 T^{30} + 440061011698688457 T^{31} + 2160776553088641290 T^{32} + 956589830796184079 T^{33} + 4870671365538649066 T^{34} + 1010894056998587542 T^{35} + 5559917313492231481 T^{36}$$)($$1 - 21 T + 332 T^{2} - 3830 T^{3} + 37841 T^{4} - 320137 T^{5} + 2436666 T^{6} - 16742723 T^{7} + 106159161 T^{8} - 623189861 T^{9} + 3426949878 T^{10} - 17699462467 T^{11} + 86459926113 T^{12} - 400240623516 T^{13} + 1763631303304 T^{14} - 7407316029817 T^{15} + 29739414733198 T^{16} - 114225849306908 T^{17} + 420481686442108 T^{18} - 1483819660190874 T^{19} + 5024676407893132 T^{20} - 16322016262099614 T^{21} + 50878284059495068 T^{22} - 152034605427494548 T^{23} + 435414771108751918 T^{24} - 1192955653918057667 T^{25} + 3124380435312537544 T^{26} - 7799557471602913236 T^{27} + 18533453012925359553 T^{28} - 41734406656003813697 T^{29} + 88886254072031148678 T^{30} -$$$$17\!\cdots\!71$$$$T^{31} +$$$$33\!\cdots\!81$$$$T^{32} -$$$$57\!\cdots\!13$$$$T^{33} +$$$$92\!\cdots\!06$$$$T^{34} -$$$$13\!\cdots\!87$$$$T^{35} +$$$$17\!\cdots\!01$$$$T^{36} -$$$$19\!\cdots\!30$$$$T^{37} +$$$$18\!\cdots\!92$$$$T^{38} -$$$$12\!\cdots\!11$$$$T^{39} +$$$$67\!\cdots\!01$$$$T^{40}$$)($$( 1 + 10 T + 89 T^{2} + 560 T^{3} + 3312 T^{4} + 16609 T^{5} + 78717 T^{6} + 333233 T^{7} + 1335269 T^{8} + 4868709 T^{9} + 16857633 T^{10} + 53555799 T^{11} + 161567549 T^{12} + 443533123 T^{13} + 1152495597 T^{14} + 2674896059 T^{15} + 5867410032 T^{16} + 10912815760 T^{17} + 19077940409 T^{18} + 23579476910 T^{19} + 25937424601 T^{20} )^{2}$$)($$1 - 21 T + 332 T^{2} - 3830 T^{3} + 37841 T^{4} - 320137 T^{5} + 2436666 T^{6} - 16742723 T^{7} + 106159161 T^{8} - 623189861 T^{9} + 3426949878 T^{10} - 17699462467 T^{11} + 86459926113 T^{12} - 400240623516 T^{13} + 1763631303304 T^{14} - 7407316029817 T^{15} + 29739414733198 T^{16} - 114225849306908 T^{17} + 420481686442108 T^{18} - 1483819660190874 T^{19} + 5024676407893132 T^{20} - 16322016262099614 T^{21} + 50878284059495068 T^{22} - 152034605427494548 T^{23} + 435414771108751918 T^{24} - 1192955653918057667 T^{25} + 3124380435312537544 T^{26} - 7799557471602913236 T^{27} + 18533453012925359553 T^{28} - 41734406656003813697 T^{29} + 88886254072031148678 T^{30} -$$$$17\!\cdots\!71$$$$T^{31} +$$$$33\!\cdots\!81$$$$T^{32} -$$$$57\!\cdots\!13$$$$T^{33} +$$$$92\!\cdots\!06$$$$T^{34} -$$$$13\!\cdots\!87$$$$T^{35} +$$$$17\!\cdots\!01$$$$T^{36} -$$$$19\!\cdots\!30$$$$T^{37} +$$$$18\!\cdots\!92$$$$T^{38} -$$$$12\!\cdots\!11$$$$T^{39} +$$$$67\!\cdots\!01$$$$T^{40}$$)
$13$ ($$1 + 5 T + 13 T^{2}$$)($$1 - 3 T + 13 T^{2}$$)($$1 + 5 T + 13 T^{2}$$)($$1 + 5 T + 13 T^{2}$$)($$1 - 5 T + 31 T^{2} - 65 T^{3} + 169 T^{4}$$)($$1 - 2 T + 19 T^{2} - 26 T^{3} + 169 T^{4}$$)($$( 1 + 3 T + 13 T^{2} )^{2}$$)($$1 - 5 T + 31 T^{2} - 65 T^{3} + 169 T^{4}$$)($$1 - 6 T + 44 T^{2} - 157 T^{3} + 572 T^{4} - 1014 T^{5} + 2197 T^{6}$$)($$1 + T + 9 T^{2} + 67 T^{3} + 117 T^{4} + 169 T^{5} + 2197 T^{6}$$)($$1 + T + 9 T^{2} + 67 T^{3} + 117 T^{4} + 169 T^{5} + 2197 T^{6}$$)($$1 - 6 T + 44 T^{2} - 157 T^{3} + 572 T^{4} - 1014 T^{5} + 2197 T^{6}$$)($$( 1 + 7 T + 56 T^{2} + 292 T^{3} + 1458 T^{4} + 5203 T^{5} + 18954 T^{6} + 49348 T^{7} + 123032 T^{8} + 199927 T^{9} + 371293 T^{10} )^{2}$$)($$1 + 7 T + 177 T^{2} + 1018 T^{3} + 14604 T^{4} + 71860 T^{5} + 763549 T^{6} + 3294581 T^{7} + 28732485 T^{8} + 110474722 T^{9} + 834095319 T^{10} + 2891021534 T^{11} + 19507460320 T^{12} + 61516713994 T^{13} + 378392228455 T^{14} + 1094212986566 T^{15} + 6206713401763 T^{16} + 16564106110855 T^{17} + 87079098238593 T^{18} + 215333379441115 T^{19} + 1048934564897947 T^{20} + 2403985931485502 T^{21} + 10807260436903255 T^{22} + 22840725288974242 T^{23} + 94158785039718880 T^{24} + 181407313873565078 T^{25} + 680397175950594999 T^{26} + 1171529120181349306 T^{27} + 3961017049174014765 T^{28} + 5904417583146813497 T^{29} + 17789229597185245069 T^{30} + 21764605159719300580 T^{31} + 57501444736752416556 T^{32} + 52107239088344390626 T^{33} +$$$$11\!\cdots\!57$$$$T^{34} + 60552911435669365531 T^{35} +$$$$11\!\cdots\!29$$$$T^{36}$$)($$1 + 7 T + 177 T^{2} + 1018 T^{3} + 14604 T^{4} + 71860 T^{5} + 763549 T^{6} + 3294581 T^{7} + 28732485 T^{8} + 110474722 T^{9} + 834095319 T^{10} + 2891021534 T^{11} + 19507460320 T^{12} + 61516713994 T^{13} + 378392228455 T^{14} + 1094212986566 T^{15} + 6206713401763 T^{16} + 16564106110855 T^{17} + 87079098238593 T^{18} + 215333379441115 T^{19} + 1048934564897947 T^{20} + 2403985931485502 T^{21} + 10807260436903255 T^{22} + 22840725288974242 T^{23} + 94158785039718880 T^{24} + 181407313873565078 T^{25} + 680397175950594999 T^{26} + 1171529120181349306 T^{27} + 3961017049174014765 T^{28} + 5904417583146813497 T^{29} + 17789229597185245069 T^{30} + 21764605159719300580 T^{31} + 57501444736752416556 T^{32} + 52107239088344390626 T^{33} +$$$$11\!\cdots\!57$$$$T^{34} + 60552911435669365531 T^{35} +$$$$11\!\cdots\!29$$$$T^{36}$$)($$1 - 11 T + 196 T^{2} - 1713 T^{3} + 18160 T^{4} - 133662 T^{5} + 1079881 T^{6} - 6932011 T^{7} + 46713697 T^{8} - 267489078 T^{9} + 1571773670 T^{10} - 8150101646 T^{11} + 42825515208 T^{12} - 203146993039 T^{13} + 969462848845 T^{14} - 4235770049611 T^{15} + 18539666968204 T^{16} - 74930665858929 T^{17} + 302660024363703 T^{18} - 1134071638747758 T^{19} + 4242290418159309 T^{20} - 14742931303720854 T^{21} + 51149544117465807 T^{22} - 164622672892067013 T^{23} + 529511428278874444 T^{24} - 1572711769030217023 T^{25} + 4679412003970685605 T^{26} - 12747172546206573163 T^{27} + 34934088397818304968 T^{28} - 86427747794893267958 T^{29} +$$$$21\!\cdots\!30$$$$T^{30} -$$$$47\!\cdots\!86$$$$T^{31} +$$$$10\!\cdots\!57$$$$T^{32} -$$$$20\!\cdots\!83$$$$T^{33} +$$$$42\!\cdots\!09$$$$T^{34} -$$$$68\!\cdots\!34$$$$T^{35} +$$$$12\!\cdots\!60$$$$T^{36} -$$$$14\!\cdots\!29$$$$T^{37} +$$$$22\!\cdots\!84$$$$T^{38} -$$$$16\!\cdots\!47$$$$T^{39} +$$$$19\!\cdots\!01$$$$T^{40}$$)($$( 1 - 3 T + 62 T^{2} - 191 T^{3} + 1868 T^{4} - 5937 T^{5} + 40013 T^{6} - 126293 T^{7} + 713982 T^{8} - 2075216 T^{9} + 10448043 T^{10} - 26977808 T^{11} + 120662958 T^{12} - 277465721 T^{13} + 1142811293 T^{14} - 2204366541 T^{15} + 9016479212 T^{16} - 11984966747 T^{17} + 50575304702 T^{18} - 31813498119 T^{19} + 137858491849 T^{20} )^{2}$$)($$1 - 11 T + 196 T^{2} - 1713 T^{3} + 18160 T^{4} - 133662 T^{5} + 1079881 T^{6} - 6932011 T^{7} + 46713697 T^{8} - 267489078 T^{9} + 1571773670 T^{10} - 8150101646 T^{11} + 42825515208 T^{12} - 203146993039 T^{13} + 969462848845 T^{14} - 4235770049611 T^{15} + 18539666968204 T^{16} - 74930665858929 T^{17} + 302660024363703 T^{18} - 1134071638747758 T^{19} + 4242290418159309 T^{20} - 14742931303720854 T^{21} + 51149544117465807 T^{22} - 164622672892067013 T^{23} + 529511428278874444 T^{24} - 1572711769030217023 T^{25} + 4679412003970685605 T^{26} - 12747172546206573163 T^{27} + 34934088397818304968 T^{28} - 86427747794893267958 T^{29} +$$$$21\!\cdots\!30$$$$T^{30} -$$$$47\!\cdots\!86$$$$T^{31} +$$$$10\!\cdots\!57$$$$T^{32} -$$$$20\!\cdots\!83$$$$T^{33} +$$$$42\!\cdots\!09$$$$T^{34} -$$$$68\!\cdots\!34$$$$T^{35} +$$$$12\!\cdots\!60$$$$T^{36} -$$$$14\!\cdots\!29$$$$T^{37} +$$$$22\!\cdots\!84$$$$T^{38} -$$$$16\!\cdots\!47$$$$T^{39} +$$$$19\!\cdots\!01$$$$T^{40}$$)
$17$ ($$1 - 3 T + 17 T^{2}$$)($$1 - 5 T + 17 T^{2}$$)($$1 - 3 T + 17 T^{2}$$)($$1 + 3 T + 17 T^{2}$$)($$1 - T + 3 T^{2} - 17 T^{3} + 289 T^{4}$$)($$1 - 10 T + 51 T^{2} - 170 T^{3} + 289 T^{4}$$)($$( 1 + 7 T + 17 T^{2} )^{2}$$)($$1 - T + 3 T^{2} - 17 T^{3} + 289 T^{4}$$)($$1 - 4 T + 47 T^{2} - 128 T^{3} + 799 T^{4} - 1156 T^{5} + 4913 T^{6}$$)($$1 + 2 T + 43 T^{2} + 60 T^{3} + 731 T^{4} + 578 T^{5} + 4913 T^{6}$$)($$1 + 2 T + 43 T^{2} + 60 T^{3} + 731 T^{4} + 578 T^{5} + 4913 T^{6}$$)($$1 - 4 T + 47 T^{2} - 128 T^{3} + 799 T^{4} - 1156 T^{5} + 4913 T^{6}$$)($$( 1 + 8 T + 60 T^{2} + 273 T^{3} + 1594 T^{4} + 6285 T^{5} + 27098 T^{6} + 78897 T^{7} + 294780 T^{8} + 668168 T^{9} + 1419857 T^{10} )^{2}$$)($$1 + 11 T + 231 T^{2} + 2107 T^{3} + 25583 T^{4} + 199091 T^{5} + 1812738 T^{6} + 12335903 T^{7} + 92694466 T^{8} + 562106618 T^{9} + 3654967661 T^{10} + 20022851568 T^{11} + 115745414311 T^{12} + 578272697713 T^{13} + 3021053869261 T^{14} + 13847422994218 T^{15} + 66040420965504 T^{16} + 278550252870720 T^{17} + 1219711875918623 T^{18} + 4735354298802240 T^{19} + 19085681659030656 T^{20} + 68032389170593034 T^{21} + 252321440214547981 T^{22} + 821064537756687041 T^{23} + 2793812924365349959 T^{24} + 8216150342089089264 T^{25} + 25496167857835115501 T^{26} + 66659030193530357146 T^{27} +$$$$18\!\cdots\!34$$$$T^{28} +$$$$42\!\cdots\!99$$$$T^{29} +$$$$10\!\cdots\!18$$$$T^{30} +$$$$19\!\cdots\!67$$$$T^{31} +$$$$43\!\cdots\!07$$$$T^{32} +$$$$60\!\cdots\!51$$$$T^{33} +$$$$11\!\cdots\!11$$$$T^{34} +$$$$90\!\cdots\!47$$$$T^{35} +$$$$14\!\cdots\!09$$$$T^{36}$$)($$1 + 11 T + 231 T^{2} + 2107 T^{3} + 25583 T^{4} + 199091 T^{5} + 1812738 T^{6} + 12335903 T^{7} + 92694466 T^{8} + 562106618 T^{9} + 3654967661 T^{10} + 20022851568 T^{11} + 115745414311 T^{12} + 578272697713 T^{13} + 3021053869261 T^{14} + 13847422994218 T^{15} + 66040420965504 T^{16} + 278550252870720 T^{17} + 1219711875918623 T^{18} + 4735354298802240 T^{19} + 19085681659030656 T^{20} + 68032389170593034 T^{21} + 252321440214547981 T^{22} + 821064537756687041 T^{23} + 2793812924365349959 T^{24} + 8216150342089089264 T^{25} + 25496167857835115501 T^{26} + 66659030193530357146 T^{27} +$$$$18\!\cdots\!34$$$$T^{28} +$$$$42\!\cdots\!99$$$$T^{29} +$$$$10\!\cdots\!18$$$$T^{30} +$$$$19\!\cdots\!67$$$$T^{31} +$$$$43\!\cdots\!07$$$$T^{32} +$$$$60\!\cdots\!51$$$$T^{33} +$$$$11\!\cdots\!11$$$$T^{34} +$$$$90\!\cdots\!47$$$$T^{35} +$$$$14\!\cdots\!09$$$$T^{36}$$)($$1 - 15 T + 313 T^{2} - 3573 T^{3} + 44424 T^{4} - 414231 T^{5} + 3917027 T^{6} - 31128563 T^{7} + 244617241 T^{8} - 1703384965 T^{9} + 11619991396 T^{10} - 72257120664 T^{11} + 438711655391 T^{12} - 2468350927685 T^{13} + 13546454355779 T^{14} - 69584613261749 T^{15} + 348603683348992 T^{16} - 1644463538759774 T^{17} + 7566533178075647 T^{18} - 32888168110340244 T^{19} + 139446945683457267 T^{20} - 559098857875784148 T^{21} + 2186728088463861983 T^{22} - 8079249365926769662 T^{23} + 29115728236991160832 T^{24} - 98800200231987149893 T^{25} +$$$$32\!\cdots\!51$$$$T^{26} -$$$$10\!\cdots\!05$$$$T^{27} +$$$$30\!\cdots\!31$$$$T^{28} -$$$$85\!\cdots\!08$$$$T^{29} +$$$$23\!\cdots\!04$$$$T^{30} -$$$$58\!\cdots\!45$$$$T^{31} +$$$$14\!\cdots\!01$$$$T^{32} -$$$$30\!\cdots\!31$$$$T^{33} +$$$$65\!\cdots\!83$$$$T^{34} -$$$$11\!\cdots\!83$$$$T^{35} +$$$$21\!\cdots\!44$$$$T^{36} -$$$$29\!\cdots\!21$$$$T^{37} +$$$$44\!\cdots\!17$$$$T^{38} -$$$$35\!\cdots\!95$$$$T^{39} +$$$$40\!\cdots\!01$$$$T^{40}$$)($$( 1 + 4 T + 120 T^{2} + 423 T^{3} + 6791 T^{4} + 21150 T^{5} + 244131 T^{6} + 671314 T^{7} + 6280349 T^{8} + 15217026 T^{9} + 121947849 T^{10} + 258689442 T^{11} + 1815020861 T^{12} + 3298165682 T^{13} + 20390065251 T^{14} + 30029975550 T^{15} + 163918231079 T^{16} + 173573258679 T^{17} + 837090892920 T^{18} + 474351505988 T^{19} + 2015993900449 T^{20} )^{2}$$)($$1 - 15 T + 313 T^{2} - 3573 T^{3} + 44424 T^{4} - 414231 T^{5} + 3917027 T^{6} - 31128563 T^{7} + 244617241 T^{8} - 1703384965 T^{9} + 11619991396 T^{10} - 72257120664 T^{11} + 438711655391 T^{12} - 2468350927685 T^{13} + 13546454355779 T^{14} - 69584613261749 T^{15} + 348603683348992 T^{16} - 1644463538759774 T^{17} + 7566533178075647 T^{18} - 32888168110340244 T^{19} + 139446945683457267 T^{20} - 559098857875784148 T^{21} + 2186728088463861983 T^{22} - 8079249365926769662 T^{23} + 29115728236991160832 T^{24} - 98800200231987149893 T^{25} +$$$$32\!\cdots\!51$$$$T^{26} -$$$$10\!\cdots\!05$$$$T^{27} +$$$$30\!\cdots\!31$$$$T^{28} -$$$$85\!\cdots\!08$$$$T^{29} +$$$$23\!\cdots\!04$$$$T^{30} -$$$$58\!\cdots\!45$$$$T^{31} +$$$$14\!\cdots\!01$$$$T^{32} -$$$$30\!\cdots\!31$$$$T^{33} +$$$$65\!\cdots\!83$$$$T^{34} -$$$$11\!\cdots\!83$$$$T^{35} +$$$$21\!\cdots\!44$$$$T^{36} -$$$$29\!\cdots\!21$$$$T^{37} +$$$$44\!\cdots\!17$$$$T^{38} -$$$$35\!\cdots\!95$$$$T^{39} +$$$$40\!\cdots\!01$$$$T^{40}$$)
$19$ ($$1 + T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$1 - T + 19 T^{2}$$)($$1 - 2 T + 19 T^{2}$$)($$1 - 2 T + 34 T^{2} - 38 T^{3} + 361 T^{4}$$)($$1 - 4 T + 34 T^{2} - 76 T^{3} + 361 T^{4}$$)($$1 + 14 T^{2} + 361 T^{4}$$)($$1 + 2 T + 34 T^{2} + 38 T^{3} + 361 T^{4}$$)($$1 - 12 T + 98 T^{2} - 485 T^{3} + 1862 T^{4} - 4332 T^{5} + 6859 T^{6}$$)($$1 - 13 T + 111 T^{2} - 565 T^{3} + 2109 T^{4} - 4693 T^{5} + 6859 T^{6}$$)($$1 + 13 T + 111 T^{2} + 565 T^{3} + 2109 T^{4} + 4693 T^{5} + 6859 T^{6}$$)($$1 + 12 T + 98 T^{2} + 485 T^{3} + 1862 T^{4} + 4332 T^{5} + 6859 T^{6}$$)($$1 + 146 T^{2} + 10261 T^{4} + 453469 T^{6} + 13907084 T^{8} + 308703099 T^{10} + 5020457324 T^{12} + 59096533549 T^{14} + 482737784941 T^{16} + 2479600203986 T^{18} + 6131066257801 T^{20}$$)($$1 + 31 T + 675 T^{2} + 10622 T^{3} + 138940 T^{4} + 1530782 T^{5} + 14850476 T^{6} + 127843653 T^{7} + 997668299 T^{8} + 7093671340 T^{9} + 46564190903 T^{10} + 283329671122 T^{11} + 1614507118332 T^{12} + 8652670079090 T^{13} + 44043302083234 T^{14} + 213996678807527 T^{15} + 1002183404208665 T^{16} + 4542498121139650 T^{17} + 20064380211625821 T^{18} + 86307464301653350 T^{19} + 361788208919328065 T^{20} + 1467803219940827693 T^{21} + 5739767170789138114 T^{22} + 21424867730164669910 T^{23} + 75955909762700190492 T^{24} +$$$$25\!\cdots\!58$$$$T^{25} +$$$$79\!\cdots\!23$$$$T^{26} +$$$$22\!\cdots\!60$$$$T^{27} +$$$$61\!\cdots\!99$$$$T^{28} +$$$$14\!\cdots\!07$$$$T^{29} +$$$$32\!\cdots\!36$$$$T^{30} +$$$$64\!\cdots\!38$$$$T^{31} +$$$$11\!\cdots\!40$$$$T^{32} +$$$$16\!\cdots\!78$$$$T^{33} +$$$$19\!\cdots\!75$$$$T^{34} +$$$$16\!\cdots\!09$$$$T^{35} +$$$$10\!\cdots\!41$$$$T^{36}$$)($$1 - 31 T + 675 T^{2} - 10622 T^{3} + 138940 T^{4} - 1530782 T^{5} + 14850476 T^{6} - 127843653 T^{7} + 997668299 T^{8} - 7093671340 T^{9} + 46564190903 T^{10} - 283329671122 T^{11} + 1614507118332 T^{12} - 8652670079090 T^{13} + 44043302083234 T^{14} - 213996678807527 T^{15} + 1002183404208665 T^{16} - 4542498121139650 T^{17} + 20064380211625821 T^{18} - 86307464301653350 T^{19} + 361788208919328065 T^{20} - 1467803219940827693 T^{21} + 5739767170789138114 T^{22} - 21424867730164669910 T^{23} + 75955909762700190492 T^{24} -$$$$25\!\cdots\!58$$$$T^{25} +$$$$79\!\cdots\!23$$$$T^{26} -$$$$22\!\cdots\!60$$$$T^{27} +$$$$61\!\cdots\!99$$$$T^{28} -$$$$14\!\cdots\!07$$$$T^{29} +$$$$32\!\cdots\!36$$$$T^{30} -$$$$64\!\cdots\!38$$$$T^{31} +$$$$11\!\cdots\!40$$$$T^{32} -$$$$16\!\cdots\!78$$$$T^{33} +$$$$19\!\cdots\!75$$$$T^{34} -$$$$16\!\cdots\!09$$$$T^{35} +$$$$10\!\cdots\!41$$$$T^{36}$$)($$1 - 7 T + 231 T^{2} - 1374 T^{3} + 25024 T^{4} - 130485 T^{5} + 1715592 T^{6} - 8012436 T^{7} + 84195440 T^{8} - 357387230 T^{9} + 3159874579 T^{10} - 12319711684 T^{11} + 94598235142 T^{12} - 342087763955 T^{13} + 2339303113735 T^{14} - 7951572377870 T^{15} + 49783554013471 T^{16} - 162524198764971 T^{17} + 966128590282455 T^{18} - 3115875295016196 T^{19} + 18283539240533924 T^{20} - 59201630605307724 T^{21} + 348772421091966255 T^{22} - 1114753479328936089 T^{23} + 6487842542589554191 T^{24} - 19688880413271529130 T^{25} +$$$$11\!\cdots\!35$$$$T^{26} -$$$$30\!\cdots\!45$$$$T^{27} +$$$$16\!\cdots\!22$$$$T^{28} -$$$$39\!\cdots\!36$$$$T^{29} +$$$$19\!\cdots\!79$$$$T^{30} -$$$$41\!\cdots\!70$$$$T^{31} +$$$$18\!\cdots\!40$$$$T^{32} -$$$$33\!\cdots\!24$$$$T^{33} +$$$$13\!\cdots\!32$$$$T^{34} -$$$$19\!\cdots\!15$$$$T^{35} +$$$$72\!\cdots\!44$$$$T^{36} -$$$$75\!\cdots\!86$$$$T^{37} +$$$$24\!\cdots\!71$$$$T^{38} -$$$$13\!\cdots\!53$$$$T^{39} +$$$$37\!\cdots\!01$$$$T^{40}$$)($$1 + 107 T^{2} + 7227 T^{4} + 360211 T^{6} + 14713794 T^{8} + 510883835 T^{10} + 15543473190 T^{12} + 420092793969 T^{14} + 10206899333785 T^{16} + 224136189553522 T^{18} + 4468613587347447 T^{20} + 80913164428821442 T^{22} + 1330173328078194985 T^{24} + 19763635594023091689 T^{26} +$$$$26\!\cdots\!90$$$$T^{28} +$$$$31\!\cdots\!35$$$$T^{30} +$$$$32\!\cdots\!34$$$$T^{32} +$$$$28\!\cdots\!31$$$$T^{34} +$$$$20\!\cdots\!87$$$$T^{36} +$$$$11\!\cdots\!87$$$$T^{38} +$$$$37\!\cdots\!01$$$$T^{40}$$)($$1 + 7 T + 231 T^{2} + 1374 T^{3} + 25024 T^{4} + 130485 T^{5} + 1715592 T^{6} + 8012436 T^{7} + 84195440 T^{8} + 357387230 T^{9} + 3159874579 T^{10} + 12319711684 T^{11} + 94598235142 T^{12} + 342087763955 T^{13} + 2339303113735 T^{14} + 7951572377870 T^{15} + 49783554013471 T^{16} + 162524198764971 T^{17} + 966128590282455 T^{18} + 3115875295016196 T^{19} + 18283539240533924 T^{20} + 59201630605307724 T^{21} + 348772421091966255 T^{22} + 1114753479328936089 T^{23} + 6487842542589554191 T^{24} + 19688880413271529130 T^{25} +$$$$11\!\cdots\!35$$$$T^{26} +$$$$30\!\cdots\!45$$$$T^{27} +$$$$16\!\cdots\!22$$$$T^{28} +$$$$39\!\cdots\!36$$$$T^{29} +$$$$19\!\cdots\!79$$$$T^{30} +$$$$41\!\cdots\!70$$$$T^{31} +$$$$18\!\cdots\!40$$$$T^{32} +$$$$33\!\cdots\!24$$$$T^{33} +$$$$13\!\cdots\!32$$$$T^{34} +$$$$19\!\cdots\!15$$$$T^{35} +$$$$72\!\cdots\!44$$$$T^{36} +$$$$75\!\cdots\!86$$$$T^{37} +$$$$24\!\cdots\!71$$$$T^{38} +$$$$13\!\cdots\!53$$$$T^{39} +$$$$37\!\cdots\!01$$$$T^{40}$$)
$23$ ($$1 + 7 T + 23 T^{2}$$)($$1 - 7 T + 23 T^{2}$$)($$1 + 7 T + 23 T^{2}$$)($$1 + T + 23 T^{2}$$)($$1 - 11 T + 75 T^{2} - 253 T^{3} + 529 T^{4}$$)($$1 - 2 T + 15 T^{2} - 46 T^{3} + 529 T^{4}$$)($$( 1 - T + 23 T^{2} )^{2}$$)($$1 - 11 T + 75 T^{2} - 253 T^{3} + 529 T^{4}$$)($$1 - 11 T + 107 T^{2} - 547 T^{3} + 2461 T^{4} - 5819 T^{5} + 12167 T^{6}$$)($$1 + 3 T + 44 T^{2} + 55 T^{3} + 1012 T^{4} + 1587 T^{5} + 12167 T^{6}$$)($$1 + 3 T + 44 T^{2} + 55 T^{3} + 1012 T^{4} + 1587 T^{5} + 12167 T^{6}$$)($$1 - 11 T + 107 T^{2} - 547 T^{3} + 2461 T^{4} - 5819 T^{5} + 12167 T^{6}$$)($$( 1 + 9 T + 55 T^{2} + 27 T^{3} - 1431 T^{4} - 10897 T^{5} - 32913 T^{6} + 14283 T^{7} + 669185 T^{8} + 2518569 T^{9} + 6436343 T^{10} )^{2}$$)($$1 + 11 T + 345 T^{2} + 3132 T^{3} + 54949 T^{4} + 426589 T^{5} + 5467252 T^{6} + 37174733 T^{7} + 385954917 T^{8} + 2338057961 T^{9} + 20753234723 T^{10} + 113433389569 T^{11} + 889059106742 T^{12} + 4426383841877 T^{13} + 31268375908075 T^{14} + 142781111925693 T^{15} + 920860147265066 T^{16} + 3872880455307088 T^{17} + 22970106119407687 T^{18} + 89076250472063024 T^{19} + 487135017903219914 T^{20} + 1737217788799906731 T^{21} + 8750173582491616075 T^{22} + 28489724655978135811 T^{23} +$$$$13\!\cdots\!38$$$$T^{24} +$$$$38\!\cdots\!43$$$$T^{25} +$$$$16\!\cdots\!63$$$$T^{26} +$$$$42\!\cdots\!43$$$$T^{27} +$$$$15\!\cdots\!33$$$$T^{28} +$$$$35\!\cdots\!91$$$$T^{29} +$$$$11\!\cdots\!92$$$$T^{30} +$$$$21\!\cdots\!87$$$$T^{31} +$$$$63\!\cdots\!41$$$$T^{32} +$$$$83\!\cdots\!24$$$$T^{33} +$$$$21\!\cdots\!45$$$$T^{34} +$$$$15\!\cdots\!33$$$$T^{35} +$$$$32\!\cdots\!69$$$$T^{36}$$)($$1 + 11 T + 345 T^{2} + 3132 T^{3} + 54949 T^{4} + 426589 T^{5} + 5467252 T^{6} + 37174733 T^{7} + 385954917 T^{8} + 2338057961 T^{9} + 20753234723 T^{10} + 113433389569 T^{11} + 889059106742 T^{12} + 4426383841877 T^{13} + 31268375908075 T^{14} + 142781111925693 T^{15} + 920860147265066 T^{16} + 3872880455307088 T^{17} + 22970106119407687 T^{18} + 89076250472063024 T^{19} + 487135017903219914 T^{20} + 1737217788799906731 T^{21} + 8750173582491616075 T^{22} + 28489724655978135811 T^{23} +$$$$13\!\cdots\!38$$$$T^{24} +$$$$38\!\cdots\!43$$$$T^{25} +$$$$16\!\cdots\!63$$$$T^{26} +$$$$42\!\cdots\!43$$$$T^{27} +$$$$15\!\cdots\!33$$$$T^{28} +$$$$35\!\cdots\!91$$$$T^{29} +$$$$11\!\cdots\!92$$$$T^{30} +$$$$21\!\cdots\!87$$$$T^{31} +$$$$63\!\cdots\!41$$$$T^{32} +$$$$83\!\cdots\!24$$$$T^{33} +$$$$21\!\cdots\!45$$$$T^{34} +$$$$15\!\cdots\!33$$$$T^{35} +$$$$32\!\cdots\!69$$$$T^{36}$$)($$1 - 26 T + 593 T^{2} - 9245 T^{3} + 129577 T^{4} - 1511139 T^{5} + 16221238 T^{6} - 154957328 T^{7} + 1384484378 T^{8} - 11370338208 T^{9} + 88282943166 T^{10} - 641718697525 T^{11} + 4442215536019 T^{12} - 29114088050089 T^{13} + 182617431976691 T^{14} - 1092252819275905 T^{15} + 6272762653585341 T^{16} - 34502594610117177 T^{17} + 182584167899486144 T^{18} - 927641876546830932 T^{19} + 4538624829212785064 T^{20} - 21335763160577111436 T^{21} + 96587024818828170176 T^{22} -$$$$41\!\cdots\!59$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24} -$$$$70\!\cdots\!15$$$$T^{25} +$$$$27\!\cdots\!99$$$$T^{26} -$$$$99\!\cdots\!83$$$$T^{27} +$$$$34\!\cdots\!39$$$$T^{28} -$$$$11\!\cdots\!75$$$$T^{29} +$$$$36\!\cdots\!34$$$$T^{30} -$$$$10\!\cdots\!16$$$$T^{31} +$$$$30\!\cdots\!38$$$$T^{32} -$$$$78\!\cdots\!24$$$$T^{33} +$$$$18\!\cdots\!42$$$$T^{34} -$$$$40\!\cdots\!73$$$$T^{35} +$$$$79\!\cdots\!97$$$$T^{36} -$$$$13\!\cdots\!35$$$$T^{37} +$$$$19\!\cdots\!17$$$$T^{38} -$$$$19\!\cdots\!62$$$$T^{39} +$$$$17\!\cdots\!01$$$$T^{40}$$)($$( 1 + 23 T + 396 T^{2} + 4883 T^{3} + 50830 T^{4} + 443047 T^{5} + 3415281 T^{6} + 23180741 T^{7} + 142307418 T^{8} + 785568948 T^{9} + 3960909963 T^{10} + 18068085804 T^{11} + 75280624122 T^{12} + 282040075747 T^{13} + 955735650321 T^{14} + 2851602457121 T^{15} + 7524664237870 T^{16} + 16625762657701 T^{17} + 31011150171276 T^{18} + 41426511213649 T^{19} + 41426511213649 T^{20} )^{2}$$)($$1 - 26 T + 593 T^{2} - 9245 T^{3} + 129577 T^{4} - 1511139 T^{5} + 16221238 T^{6} - 154957328 T^{7} + 1384484378 T^{8} - 11370338208 T^{9} + 88282943166 T^{10} - 641718697525 T^{11} + 4442215536019 T^{12} - 29114088050089 T^{13} + 182617431976691 T^{14} - 1092252819275905 T^{15} + 6272762653585341 T^{16} - 34502594610117177 T^{17} + 182584167899486144 T^{18} - 927641876546830932 T^{19} + 4538624829212785064 T^{20} - 21335763160577111436 T^{21} + 96587024818828170176 T^{22} -$$$$41\!\cdots\!59$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24} -$$$$70\!\cdots\!15$$$$T^{25} +$$$$27\!\cdots\!99$$$$T^{26} -$$$$99\!\cdots\!83$$$$T^{27} +$$$$34\!\cdots\!39$$$$T^{28} -$$$$11\!\cdots\!75$$$$T^{29} +$$$$36\!\cdots\!34$$$$T^{30} -$$$$10\!\cdots\!16$$$$T^{31} +$$$$30\!\cdots\!38$$$$T^{32} -$$$$78\!\cdots\!24$$$$T^{33} +$$$$18\!\cdots\!42$$$$T^{34} -$$$$40\!\cdots\!73$$$$T^{35} +$$$$79\!\cdots\!97$$$$T^{36} -$$$$13\!\cdots\!35$$$$T^{37} +$$$$19\!\cdots\!17$$$$T^{38} -$$$$19\!\cdots\!62$$$$T^{39} +$$$$17\!\cdots\!01$$$$T^{40}$$)
$29$ ($$1 + 3 T + 29 T^{2}$$)($$1 + 29 T^{2}$$)($$1 - 3 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$( 1 - 3 T + 29 T^{2} )^{2}$$)($$1 + 40 T^{2} + 841 T^{4}$$)($$1 + 52 T^{2} + 841 T^{4}$$)($$( 1 + 3 T + 29 T^{2} )^{2}$$)($$1 - T + 71 T^{2} - 71 T^{3} + 2059 T^{4} - 841 T^{5} + 24389 T^{6}$$)($$( 1 - 6 T + 29 T^{2} )^{3}$$)($$( 1 + 6 T + 29 T^{2} )^{3}$$)($$1 + T + 71 T^{2} + 71 T^{3} + 2059 T^{4} + 841 T^{5} + 24389 T^{6}$$)($$1 + 92 T^{2} + 4944 T^{4} + 212793 T^{6} + 8043434 T^{8} + 260511681 T^{10} + 6764527994 T^{12} + 150504445833 T^{14} + 2940806499024 T^{16} + 46022669992412 T^{18} + 420707233300201 T^{20}$$)($$1 + 37 T + 947 T^{2} + 17923 T^{3} + 283912 T^{4} + 3855141 T^{5} + 46586206 T^{6} + 507248339 T^{7} + 5061572456 T^{8} + 46624628122 T^{9} + 400155735430 T^{10} + 3214306403195 T^{11} + 24300142007900 T^{12} + 173384015282340 T^{13} + 1171644165735371 T^{14} + 7510398411648064 T^{15} + 45763756699519426 T^{16} + 265249439219992246 T^{17} + 1463952283209284935 T^{18} + 7692233737379775134 T^{19} + 38487319384295837266 T^{20} +$$$$18\!\cdots\!96$$$$T^{21} +$$$$82\!\cdots\!51$$$$T^{22} +$$$$35\!\cdots\!60$$$$T^{23} +$$$$14\!\cdots\!00$$$$T^{24} +$$$$55\!\cdots\!55$$$$T^{25} +$$$$20\!\cdots\!30$$$$T^{26} +$$$$67\!\cdots\!18$$$$T^{27} +$$$$21\!\cdots\!56$$$$T^{28} +$$$$61\!\cdots\!31$$$$T^{29} +$$$$16\!\cdots\!46$$$$T^{30} +$$$$39\!\cdots\!49$$$$T^{31} +$$$$84\!\cdots\!72$$$$T^{32} +$$$$15\!\cdots\!27$$$$T^{33} +$$$$23\!\cdots\!87$$$$T^{34} +$$$$26\!\cdots\!33$$$$T^{35} +$$$$21\!\cdots\!61$$$$T^{36}$$)($$1 - 37 T + 947 T^{2} - 17923 T^{3} + 283912 T^{4} - 3855141 T^{5} + 46586206 T^{6} - 507248339 T^{7} + 5061572456 T^{8} - 46624628122 T^{9} + 400155735430 T^{10} - 3214306403195 T^{11} + 24300142007900 T^{12} - 173384015282340 T^{13} + 1171644165735371 T^{14} - 7510398411648064 T^{15} + 45763756699519426 T^{16} - 265249439219992246 T^{17} + 1463952283209284935 T^{18} - 7692233737379775134 T^{19} + 38487319384295837266 T^{20} -$$$$18\!\cdots\!96$$$$T^{21} +$$$$82\!\cdots\!51$$$$T^{22} -$$$$35\!\cdots\!60$$$$T^{23} +$$$$14\!\cdots\!00$$$$T^{24} -$$$$55\!\cdots\!55$$$$T^{25} +$$$$20\!\cdots\!30$$$$T^{26} -$$$$67\!\cdots\!18$$$$T^{27} +$$$$21\!\cdots\!56$$$$T^{28} -$$$$61\!\cdots\!31$$$$T^{29} +$$$$16\!\cdots\!46$$$$T^{30} -$$$$39\!\cdots\!49$$$$T^{31} +$$$$84\!\cdots\!72$$$$T^{32} -$$$$15\!\cdots\!27$$$$T^{33} +$$$$23\!\cdots\!87$$$$T^{34} -$$$$26\!\cdots\!33$$$$T^{35} +$$$$21\!\cdots\!61$$$$T^{36}$$)($$1 - 12 T + 389 T^{2} - 3720 T^{3} + 68933 T^{4} - 541228 T^{5} + 7485382 T^{6} - 48633620 T^{7} + 560017432 T^{8} - 2961118542 T^{9} + 30502328697 T^{10} - 123368346582 T^{11} + 1233796038955 T^{12} - 3114560706046 T^{13} + 36613152683904 T^{14} - 7331957410626 T^{15} + 751283965485840 T^{16} + 3447445803430502 T^{17} + 9273961941957196 T^{18} + 180596486019813978 T^{19} + 99640287316737551 T^{20} + 5237298094574605362 T^{21} + 7799401993186001836 T^{22} + 84079755699866513278 T^{23} +$$$$53\!\cdots\!40$$$$T^{24} -$$$$15\!\cdots\!74$$$$T^{25} +$$$$21\!\cdots\!84$$$$T^{26} -$$$$53\!\cdots\!14$$$$T^{27} +$$$$61\!\cdots\!55$$$$T^{28} -$$$$17\!\cdots\!58$$$$T^{29} +$$$$12\!\cdots\!97$$$$T^{30} -$$$$36\!\cdots\!18$$$$T^{31} +$$$$19\!\cdots\!12$$$$T^{32} -$$$$49\!\cdots\!80$$$$T^{33} +$$$$22\!\cdots\!42$$$$T^{34} -$$$$46\!\cdots\!72$$$$T^{35} +$$$$17\!\cdots\!93$$$$T^{36} -$$$$26\!\cdots\!80$$$$T^{37} +$$$$81\!\cdots\!29$$$$T^{38} -$$$$73\!\cdots\!28$$$$T^{39} +$$$$17\!\cdots\!01$$$$T^{40}$$)($$1 + 355 T^{2} + 61637 T^{4} + 7010484 T^{6} + 590034042 T^{8} + 39313078799 T^{10} + 2162612821331 T^{12} + 100939658183434 T^{14} + 4068834289792210 T^{16} + 143205948796309798 T^{18} + 4427082547596807219 T^{20} +$$$$12\!\cdots\!18$$$$T^{22} +$$$$28\!\cdots\!10$$$$T^{24} +$$$$60\!\cdots\!14$$$$T^{26} +$$$$10\!\cdots\!91$$$$T^{28} +$$$$16\!\cdots\!99$$$$T^{30} +$$$$20\!\cdots\!22$$$$T^{32} +$$$$20\!\cdots\!04$$$$T^{34} +$$$$15\!\cdots\!77$$$$T^{36} +$$$$74\!\cdots\!55$$$$T^{38} +$$$$17\!\cdots\!01$$$$T^{40}$$)($$1 + 12 T + 389 T^{2} + 3720 T^{3} + 68933 T^{4} + 541228 T^{5} + 7485382 T^{6} + 48633620 T^{7} + 560017432 T^{8} + 2961118542 T^{9} + 30502328697 T^{10} + 123368346582 T^{11} + 1233796038955 T^{12} + 3114560706046 T^{13} + 36613152683904 T^{14} + 7331957410626 T^{15} + 751283965485840 T^{16} - 3447445803430502 T^{17} + 9273961941957196 T^{18} - 180596486019813978 T^{19} + 99640287316737551 T^{20} - 5237298094574605362 T^{21} + 7799401993186001836 T^{22} - 84079755699866513278 T^{23} +$$$$53\!\cdots\!40$$$$T^{24} +$$$$15\!\cdots\!74$$$$T^{25} +$$$$21\!\cdots\!84$$$$T^{26} +$$$$53\!\cdots\!14$$$$T^{27} +$$$$61\!\cdots\!55$$$$T^{28} +$$$$17\!\cdots\!58$$$$T^{29} +$$$$12\!\cdots\!97$$$$T^{30} +$$$$36\!\cdots\!18$$$$T^{31} +$$$$19\!\cdots\!12$$$$T^{32} +$$$$49\!\cdots\!80$$$$T^{33} +$$$$22\!\cdots\!42$$$$T^{34} +$$$$46\!\cdots\!72$$$$T^{35} +$$$$17\!\cdots\!93$$$$T^{36} +$$$$26\!\cdots\!80$$$$T^{37} +$$$$81\!\cdots\!29$$$$T^{38} +$$$$73\!\cdots\!28$$$$T^{39} +$$$$17\!\cdots\!01$$$$T^{40}$$)
$31$ ($$1 - 5 T + 31 T^{2}$$)($$1 + 9 T + 31 T^{2}$$)($$1 - 5 T + 31 T^{2}$$)($$1 + T + 31 T^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 3 T + 31 T^{2} )^{2}$$)($$( 1 + 3 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$1 - 5 T + 71 T^{2} - 213 T^{3} + 2201 T^{4} - 4805 T^{5} + 29791 T^{6}$$)($$1 - 11 T + 47 T^{2} - 135 T^{3} + 1457 T^{4} - 10571 T^{5} + 29791 T^{6}$$)($$1 - 11 T + 47 T^{2} - 135 T^{3} + 1457 T^{4} - 10571 T^{5} + 29791 T^{6}$$)($$1 - 5 T + 71 T^{2} - 213 T^{3} + 2201 T^{4} - 4805 T^{5} + 29791 T^{6}$$)($$( 1 + T + 74 T^{2} - 11 T^{3} + 3015 T^{4} - 2141 T^{5} + 93465 T^{6} - 10571 T^{7} + 2204534 T^{8} + 923521 T^{9} + 28629151 T^{10} )^{2}$$)($$1 + 12 T + 394 T^{2} + 4062 T^{3} + 73790 T^{4} + 667459 T^{5} + 8810142 T^{6} + 71153719 T^{7} + 759179657 T^{8} + 5555787033 T^{9} + 50683565295 T^{10} + 340153856696 T^{11} + 2745099275027 T^{12} + 17046603704779 T^{13} + 124394247414918 T^{14} + 718550937993414 T^{15} + 4809074473741562 T^{16} + 25882288865469751 T^{17} + 160293089661061235 T^{18} + 802350954829562281 T^{19} + 4621520569265641082 T^{20} + 21406350993761796474 T^{21} +$$$$11\!\cdots\!78$$$$T^{22} +$$$$48\!\cdots\!29$$$$T^{23} +$$$$24\!\cdots\!87$$$$T^{24} +$$$$93\!\cdots\!56$$$$T^{25} +$$$$43\!\cdots\!95$$$$T^{26} +$$$$14\!\cdots\!43$$$$T^{27} +$$$$62\!\cdots\!57$$$$T^{28} +$$$$18\!\cdots\!89$$$$T^{29} +$$$$69\!\cdots\!62$$$$T^{30} +$$$$16\!\cdots\!69$$$$T^{31} +$$$$55\!\cdots\!90$$$$T^{32} +$$$$95\!\cdots\!62$$$$T^{33} +$$$$28\!\cdots\!14$$$$T^{34} +$$$$27\!\cdots\!32$$$$T^{35} +$$$$69\!\cdots\!41$$$$T^{36}$$)($$1 + 12 T + 394 T^{2} + 4062 T^{3} + 73790 T^{4} + 667459 T^{5} + 8810142 T^{6} + 71153719 T^{7} + 759179657 T^{8} + 5555787033 T^{9} + 50683565295 T^{10} + 340153856696 T^{11} + 2745099275027 T^{12} + 17046603704779 T^{13} + 124394247414918 T^{14} + 718550937993414 T^{15} + 4809074473741562 T^{16} + 25882288865469751 T^{17} + 160293089661061235 T^{18} + 802350954829562281 T^{19} + 4621520569265641082 T^{20} + 21406350993761796474 T^{21} +$$$$11\!\cdots\!78$$$$T^{22} +$$$$48\!\cdots\!29$$$$T^{23} +$$$$24\!\cdots\!87$$$$T^{24} +$$$$93\!\cdots\!56$$$$T^{25} +$$$$43\!\cdots\!95$$$$T^{26} +$$$$14\!\cdots\!43$$$$T^{27} +$$$$62\!\cdots\!57$$$$T^{28} +$$$$18\!\cdots\!89$$$$T^{29} +$$$$69\!\cdots\!62$$$$T^{30} +$$$$16\!\cdots\!69$$$$T^{31} +$$$$55\!\cdots\!90$$$$T^{32} +$$$$95\!\cdots\!62$$$$T^{33} +$$$$28\!\cdots\!14$$$$T^{34} +$$$$27\!\cdots\!32$$$$T^{35} +$$$$69\!\cdots\!41$$$$T^{36}$$)($$1 - 26 T + 699 T^{2} - 11988 T^{3} + 197159 T^{4} - 2606034 T^{5} + 32787948 T^{6} - 358975262 T^{7} + 3752975389 T^{8} - 35462352562 T^{9} + 321545092610 T^{10} - 2692085875236 T^{11} + 21727037022202 T^{12} - 164069990196176 T^{13} + 1198764838137908 T^{14} - 8264662661616974 T^{15} + 55280859892476778 T^{16} - 350744272756180416 T^{17} + 2162834271239151139 T^{18} - 12687257023224161930 T^{19} + 72392713215803297198 T^{20} -$$$$39\!\cdots\!30$$$$T^{21} +$$$$20\!\cdots\!79$$$$T^{22} -$$$$10\!\cdots\!56$$$$T^{23} +$$$$51\!\cdots\!38$$$$T^{24} -$$$$23\!\cdots\!74$$$$T^{25} +$$$$10\!\cdots\!48$$$$T^{26} -$$$$45\!\cdots\!36$$$$T^{27} +$$$$18\!\cdots\!82$$$$T^{28} -$$$$71\!\cdots\!56$$$$T^{29} +$$$$26\!\cdots\!10$$$$T^{30} -$$$$90\!\cdots\!22$$$$T^{31} +$$$$29\!\cdots\!29$$$$T^{32} -$$$$87\!\cdots\!42$$$$T^{33} +$$$$24\!\cdots\!08$$$$T^{34} -$$$$61\!\cdots\!34$$$$T^{35} +$$$$14\!\cdots\!79$$$$T^{36} -$$$$27\!\cdots\!68$$$$T^{37} +$$$$48\!\cdots\!59$$$$T^{38} -$$$$56\!\cdots\!46$$$$T^{39} +$$$$67\!\cdots\!01$$$$T^{40}$$)($$( 1 + 19 T + 341 T^{2} + 3954 T^{3} + 42555 T^{4} + 364364 T^{5} + 2954570 T^{6} + 20513682 T^{7} + 137929044 T^{8} + 823585701 T^{9} + 4835787010 T^{10} + 25531156731 T^{11} + 132549811284 T^{12} + 611123100462 T^{13} + 2728607440970 T^{14} + 10431431974964 T^{15} + 37767719144955 T^{16} + 108784876194894 T^{17} + 290835843767381 T^{18} + 502352821052749 T^{19} + 819628286980801 T^{20} )^{2}$$)($$1 - 26 T + 699 T^{2} - 11988 T^{3} + 197159 T^{4} - 2606034 T^{5} + 32787948 T^{6} - 358975262 T^{7} + 3752975389 T^{8} - 35462352562 T^{9} + 321545092610 T^{10} - 2692085875236 T^{11} + 21727037022202 T^{12} - 164069990196176 T^{13} + 1198764838137908 T^{14} - 8264662661616974 T^{15} + 55280859892476778 T^{16} - 350744272756180416 T^{17} + 2162834271239151139 T^{18} - 12687257023224161930 T^{19} + 72392713215803297198 T^{20} -$$$$39\!\cdots\!30$$$$T^{21} +$$$$20\!\cdots\!79$$$$T^{22} -$$$$10\!\cdots\!56$$$$T^{23} +$$$$51\!\cdots\!38$$$$T^{24} -$$$$23\!\cdots\!74$$$$T^{25} +$$$$10\!\cdots\!48$$$$T^{26} -$$$$45\!\cdots\!36$$$$T^{27} +$$$$18\!\cdots\!82$$$$T^{28} -$$$$71\!\cdots\!56$$$$T^{29} +$$$$26\!\cdots\!10$$$$T^{30} -$$$$90\!\cdots\!22$$$$T^{31} +$$$$29\!\cdots\!29$$$$T^{32} -$$$$87\!\cdots\!42$$$$T^{33} +$$$$24\!\cdots\!08$$$$T^{34} -$$$$61\!\cdots\!34$$$$T^{35} +$$$$14\!\cdots\!79$$$$T^{36} -$$$$27\!\cdots\!68$$$$T^{37} +$$$$48\!\cdots\!59$$$$T^{38} -$$$$56\!\cdots\!46$$$$T^{39} +$$$$67\!\cdots\!01$$$$T^{40}$$)
$37$ ($$1 - 9 T + 37 T^{2}$$)($$1 + 37 T^{2}$$)($$1 + 9 T + 37 T^{2}$$)($$1 + 37 T^{2}$$)($$1 + 3 T + 65 T^{2} + 111 T^{3} + 1369 T^{4}$$)($$1 + 2 T^{2} + 1369 T^{4}$$)($$1 + 50 T^{2} + 1369 T^{4}$$)($$1 - 3 T + 65 T^{2} - 111 T^{3} + 1369 T^{4}$$)($$1 + 2 T + 26 T^{2} + 399 T^{3} + 962 T^{4} + 2738 T^{5} + 50653 T^{6}$$)($$1 - 7 T + 97 T^{2} - 427 T^{3} + 3589 T^{4} - 9583 T^{5} + 50653 T^{6}$$)($$1 + 7 T + 97 T^{2} + 427 T^{3} + 3589 T^{4} + 9583 T^{5} + 50653 T^{6}$$)($$1 - 2 T + 26 T^{2} - 399 T^{3} + 962 T^{4} - 2738 T^{5} + 50653 T^{6}$$)($$1 - 70 T^{2} + 5461 T^{4} - 259752 T^{6} + 13400962 T^{8} - 494954340 T^{10} + 18345916978 T^{12} - 486817068072 T^{14} + 14011431919549 T^{16} - 245873561774470 T^{18} + 4808584372417849 T^{20}$$)($$1 - 19 T + 589 T^{2} - 8420 T^{3} + 151063 T^{4} - 1759614 T^{5} + 23459736 T^{6} - 233272537 T^{7} + 2542189646 T^{8} - 22257059122 T^{9} + 208488795367 T^{10} - 1643111338752 T^{11} + 13649989650958 T^{12} - 98401118005386 T^{13} + 740427345007403 T^{14} - 4935637642077440 T^{15} + 34126021579140508 T^{16} - 211580817085833068 T^{17} + 1356370300983331895 T^{18} - 7828490232175823516 T^{19} + 46718523541843355452 T^{20} -$$$$25\!\cdots\!20$$$$T^{21} +$$$$13\!\cdots\!83$$$$T^{22} -$$$$68\!\cdots\!02$$$$T^{23} +$$$$35\!\cdots\!22$$$$T^{24} -$$$$15\!\cdots\!16$$$$T^{25} +$$$$73\!\cdots\!07$$$$T^{26} -$$$$28\!\cdots\!94$$$$T^{27} +$$$$12\!\cdots\!54$$$$T^{28} -$$$$41\!\cdots\!81$$$$T^{29} +$$$$15\!\cdots\!16$$$$T^{30} -$$$$42\!\cdots\!58$$$$T^{31} +$$$$13\!\cdots\!07$$$$T^{32} -$$$$28\!\cdots\!60$$$$T^{33} +$$$$72\!\cdots\!49$$$$T^{34} -$$$$86\!\cdots\!23$$$$T^{35} +$$$$16\!\cdots\!29$$$$T^{36}$$)($$1 + 19 T + 589 T^{2} + 8420 T^{3} + 151063 T^{4} + 1759614 T^{5} + 23459736 T^{6} + 233272537 T^{7} + 2542189646 T^{8} + 22257059122 T^{9} + 208488795367 T^{10} + 1643111338752 T^{11} + 13649989650958 T^{12} + 98401118005386 T^{13} + 740427345007403 T^{14} + 4935637642077440 T^{15} + 34126021579140508 T^{16} + 211580817085833068 T^{17} + 1356370300983331895 T^{18} + 7828490232175823516 T^{19} + 46718523541843355452 T^{20} +$$$$25\!\cdots\!20$$$$T^{21} +$$$$13\!\cdots\!83$$$$T^{22} +$$$$68\!\cdots\!02$$$$T^{23} +$$$$35\!\cdots\!22$$$$T^{24} +$$$$15\!\cdots\!16$$$$T^{25} +$$$$73\!\cdots\!07$$$$T^{26} +$$$$28\!\cdots\!94$$$$T^{27} +$$$$12\!\cdots\!54$$$$T^{28} +$$$$41\!\cdots\!81$$$$T^{29} +$$$$15\!\cdots\!16$$$$T^{30} +$$$$42\!\cdots\!58$$$$T^{31} +$$$$13\!\cdots\!07$$$$T^{32} +$$$$28\!\cdots\!60$$$$T^{33} +$$$$72\!\cdots\!49$$$$T^{34} +$$$$86\!\cdots\!23$$$$T^{35} +$$$$16\!\cdots\!29$$$$T^{36}$$)($$1 - 19 T + 674 T^{2} - 10602 T^{3} + 214944 T^{4} - 2880765 T^{5} + 43380980 T^{6} - 506355490 T^{7} + 6241509967 T^{8} - 64506815954 T^{9} + 682665477543 T^{10} - 6324666556184 T^{11} + 59031781806262 T^{12} - 494695786144745 T^{13} + 4139373674392274 T^{14} - 31576171482499992 T^{15} + 239318805423602520 T^{16} - 1668642371011655963 T^{17} + 11528995954659392273 T^{18} - 73635723896403709878 T^{19} +$$$$46\!\cdots\!96$$$$T^{20} -$$$$27\!\cdots\!86$$$$T^{21} +$$$$15\!\cdots\!37$$$$T^{22} -$$$$84\!\cdots\!39$$$$T^{23} +$$$$44\!\cdots\!20$$$$T^{24} -$$$$21\!\cdots\!44$$$$T^{25} +$$$$10\!\cdots\!66$$$$T^{26} -$$$$46\!\cdots\!85$$$$T^{27} +$$$$20\!\cdots\!02$$$$T^{28} -$$$$82\!\cdots\!68$$$$T^{29} +$$$$32\!\cdots\!07$$$$T^{30} -$$$$11\!\cdots\!02$$$$T^{31} +$$$$41\!\cdots\!27$$$$T^{32} -$$$$12\!\cdots\!30$$$$T^{33} +$$$$39\!\cdots\!20$$$$T^{34} -$$$$96\!\cdots\!45$$$$T^{35} +$$$$26\!\cdots\!04$$$$T^{36} -$$$$48\!\cdots\!34$$$$T^{37} +$$$$11\!\cdots\!46$$$$T^{38} -$$$$11\!\cdots\!87$$$$T^{39} +$$$$23\!\cdots\!01$$$$T^{40}$$)($$1 + 544 T^{2} + 145924 T^{4} + 25610022 T^{6} + 3292942466 T^{8} + 329356598647 T^{10} + 26564739745913 T^{12} + 1768153360037473 T^{14} + 98591681997173059 T^{16} + 4649349777875033374 T^{18} +$$$$18\!\cdots\!27$$$$T^{20} +$$$$63\!\cdots\!06$$$$T^{22} +$$$$18\!\cdots\!99$$$$T^{24} +$$$$45\!\cdots\!57$$$$T^{26} +$$$$93\!\cdots\!73$$$$T^{28} +$$$$15\!\cdots\!03$$$$T^{30} +$$$$21\!\cdots\!46$$$$T^{32} +$$$$23\!\cdots\!58$$$$T^{34} +$$$$18\!\cdots\!84$$$$T^{36} +$$$$91\!\cdots\!76$$$$T^{38} +$$$$23\!\cdots\!01$$$$T^{40}$$)($$1 + 19 T + 674 T^{2} + 10602 T^{3} + 214944 T^{4} + 2880765 T^{5} + 43380980 T^{6} + 506355490 T^{7} + 6241509967 T^{8} + 64506815954 T^{9} + 682665477543 T^{10} + 6324666556184 T^{11} + 59031781806262 T^{12} + 494695786144745 T^{13} + 4139373674392274 T^{14} + 31576171482499992 T^{15} + 239318805423602520 T^{16} + 1668642371011655963 T^{17} + 11528995954659392273 T^{18} + 73635723896403709878 T^{19} +$$$$46\!\cdots\!96$$$$T^{20} +$$$$27\!\cdots\!86$$$$T^{21} +$$$$15\!\cdots\!37$$$$T^{22} +$$$$84\!\cdots\!39$$$$T^{23} +$$$$44\!\cdots\!20$$$$T^{24} +$$$$21\!\cdots\!44$$$$T^{25} +$$$$10\!\cdots\!66$$$$T^{26} +$$$$46\!\cdots\!85$$$$T^{27} +$$$$20\!\cdots\!02$$$$T^{28} +$$$$82\!\cdots\!68$$$$T^{29} +$$$$32\!\cdots\!07$$$$T^{30} +$$$$11\!\cdots\!02$$$$T^{31} +$$$$41\!\cdots\!27$$$$T^{32} +$$$$12\!\cdots\!30$$$$T^{33} +$$$$39\!\cdots\!20$$$$T^{34} +$$$$96\!\cdots\!45$$$$T^{35} +$$$$26\!\cdots\!04$$$$T^{36} +$$$$48\!\cdots\!34$$$$T^{37} +$$$$11\!\cdots\!46$$$$T^{38} +$$$$11\!\cdots\!87$$$$T^{39} +$$$$23\!\cdots\!01$$$$T^{40}$$)
$41$ ($$1 + 10 T + 41 T^{2}$$)($$1 + 11 T + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$1 - 5 T + 41 T^{2}$$)($$1 - 10 T + 87 T^{2} - 410 T^{3} + 1681 T^{4}$$)($$1 + 2 T + 75 T^{2} + 82 T^{3} + 1681 T^{4}$$)($$( 1 + 5 T + 41 T^{2} )^{2}$$)($$1 - 10 T + 87 T^{2} - 410 T^{3} + 1681 T^{4}$$)($$1 + 6 T + 86 T^{2} + 311 T^{3} + 3526 T^{4} + 10086 T^{5} + 68921 T^{6}$$)($$1 - 22 T + 275 T^{2} - 2132 T^{3} + 11275 T^{4} - 36982 T^{5} + 68921 T^{6}$$)($$1 - 22 T + 275 T^{2} - 2132 T^{3} + 11275 T^{4} - 36982 T^{5} + 68921 T^{6}$$)($$1 + 6 T + 86 T^{2} + 311 T^{3} + 3526 T^{4} + 10086 T^{5} + 68921 T^{6}$$)($$( 1 + 128 T^{2} - 66 T^{3} + 8549 T^{4} - 3223 T^{5} + 350509 T^{6} - 110946 T^{7} + 8821888 T^{8} + 115856201 T^{10} )^{2}$$)($$1 + 7 T + 420 T^{2} + 3240 T^{3} + 90202 T^{4} + 716786 T^{5} + 13103701 T^{6} + 102786964 T^{7} + 1433407248 T^{8} + 10828886149 T^{9} + 124839503390 T^{10} + 895792488941 T^{11} + 8953259514722 T^{12} + 60526589311090 T^{13} + 540233339209753 T^{14} + 3422358652721154 T^{15} + 27793767354912440 T^{16} + 164244156889528625 T^{17} + 1228158616200818539 T^{18} + 6734010432470673625 T^{19} + 46721322923607811640 T^{20} +$$$$23\!\cdots\!34$$$$T^{21} +$$$$15\!\cdots\!33$$$$T^{22} +$$$$70\!\cdots\!90$$$$T^{23} +$$$$42\!\cdots\!02$$$$T^{24} +$$$$17\!\cdots\!21$$$$T^{25} +$$$$99\!\cdots\!90$$$$T^{26} +$$$$35\!\cdots\!89$$$$T^{27} +$$$$19\!\cdots\!48$$$$T^{28} +$$$$56\!\cdots\!24$$$$T^{29} +$$$$29\!\cdots\!81$$$$T^{30} +$$$$66\!\cdots\!06$$$$T^{31} +$$$$34\!\cdots\!22$$$$T^{32} +$$$$50\!\cdots\!40$$$$T^{33} +$$$$26\!\cdots\!20$$$$T^{34} +$$$$18\!\cdots\!67$$$$T^{35} +$$$$10\!\cdots\!21$$$$T^{36}$$)($$1 + 7 T + 420 T^{2} + 3240 T^{3} + 90202 T^{4} + 716786 T^{5} + 13103701 T^{6} + 102786964 T^{7} + 1433407248 T^{8} + 10828886149 T^{9} + 124839503390 T^{10} + 895792488941 T^{11} + 8953259514722 T^{12} + 60526589311090 T^{13} + 540233339209753 T^{14} + 3422358652721154 T^{15} + 27793767354912440 T^{16} + 164244156889528625 T^{17} + 1228158616200818539 T^{18} + 6734010432470673625 T^{19} + 46721322923607811640 T^{20} +$$$$23\!\cdots\!34$$$$T^{21} +$$$$15\!\cdots\!33$$$$T^{22} +$$$$70\!\cdots\!90$$$$T^{23} +$$$$42\!\cdots\!02$$$$T^{24} +$$$$17\!\cdots\!21$$$$T^{25} +$$$$99\!\cdots\!90$$$$T^{26} +$$$$35\!\cdots\!89$$$$T^{27} +$$$$19\!\cdots\!48$$$$T^{28} +$$$$56\!\cdots\!24$$$$T^{29} +$$$$29\!\cdots\!81$$$$T^{30} +$$$$66\!\cdots\!06$$$$T^{31} +$$$$34\!\cdots\!22$$$$T^{32} +$$$$50\!\cdots\!40$$$$T^{33} +$$$$26\!\cdots\!20$$$$T^{34} +$$$$18\!\cdots\!67$$$$T^{35} +$$$$10\!\cdots\!21$$$$T^{36}$$)($$1 - 27 T + 869 T^{2} - 16530 T^{3} + 319061 T^{4} - 4759485 T^{5} + 69410492 T^{6} - 858796296 T^{7} + 10290120942 T^{8} - 109274591678 T^{9} + 1122948542213 T^{10} - 10479929878806 T^{11} + 94920152010059 T^{12} - 793170034277493 T^{13} + 6465307666310432 T^{14} - 49195805087779524 T^{15} + 367588572508585940 T^{16} - 2588560044156107325 T^{17} + 18023329911574085292 T^{18} -$$$$11\!\cdots\!60$$$$T^{19} +$$$$78\!\cdots\!59$$$$T^{20} -$$$$48\!\cdots\!60$$$$T^{21} +$$$$30\!\cdots\!52$$$$T^{22} -$$$$17\!\cdots\!25$$$$T^{23} +$$$$10\!\cdots\!40$$$$T^{24} -$$$$56\!\cdots\!24$$$$T^{25} +$$$$30\!\cdots\!12$$$$T^{26} -$$$$15\!\cdots\!33$$$$T^{27} +$$$$75\!\cdots\!39$$$$T^{28} -$$$$34\!\cdots\!66$$$$T^{29} +$$$$15\!\cdots\!13$$$$T^{30} -$$$$60\!\cdots\!98$$$$T^{31} +$$$$23\!\cdots\!02$$$$T^{32} -$$$$79\!\cdots\!16$$$$T^{33} +$$$$26\!\cdots\!12$$$$T^{34} -$$$$74\!\cdots\!85$$$$T^{35} +$$$$20\!\cdots\!01$$$$T^{36} -$$$$43\!\cdots\!30$$$$T^{37} +$$$$93\!\cdots\!49$$$$T^{38} -$$$$11\!\cdots\!47$$$$T^{39} +$$$$18\!\cdots\!01$$$$T^{40}$$)($$( 1 + 28 T + 644 T^{2} + 10141 T^{3} + 139888 T^{4} + 1586005 T^{5} + 16258560 T^{6} + 145249239 T^{7} + 1191564631 T^{8} + 8716554418 T^{9} + 58920438831 T^{10} + 357378731138 T^{11} + 2003020144711 T^{12} + 10010722801119 T^{13} + 45942804764160 T^{14} + 183748514067005 T^{15} + 664482582065008 T^{16} + 1975003091427221 T^{17} + 5142291847553924 T^{18} + 9166694163030908 T^{19} + 13422659310152401 T^{20} )^{2}$$)($$1 - 27 T + 869 T^{2} - 16530 T^{3} + 319061 T^{4} - 4759485 T^{5} + 69410492 T^{6} - 858796296 T^{7} + 10290120942 T^{8} - 109274591678 T^{9} + 1122948542213 T^{10} - 10479929878806 T^{11} + 94920152010059 T^{12} - 793170034277493 T^{13} + 6465307666310432 T^{14} - 49195805087779524 T^{15} + 367588572508585940 T^{16} - 2588560044156107325 T^{17} + 18023329911574085292 T^{18} -$$$$11\!\cdots\!60$$$$T^{19} +$$$$78\!\cdots\!59$$$$T^{20} -$$$$48\!\cdots\!60$$$$T^{21} +$$$$30\!\cdots\!52$$$$T^{22} -$$$$17\!\cdots\!25$$$$T^{23} +$$$$10\!\cdots\!40$$$$T^{24} -$$$$56\!\cdots\!24$$$$T^{25} +$$$$30\!\cdots\!12$$$$T^{26} -$$$$15\!\cdots\!33$$$$T^{27} +$$$$75\!\cdots\!39$$$$T^{28} -$$$$34\!\cdots\!66$$$$T^{29} +$$$$15\!\cdots\!13$$$$T^{30} -$$$$60\!\cdots\!98$$$$T^{31} +$$$$23\!\cdots\!02$$$$T^{32} -$$$$79\!\cdots\!16$$$$T^{33} +$$$$26\!\cdots\!12$$$$T^{34} -$$$$74\!\cdots\!85$$$$T^{35} +$$$$20\!\cdots\!01$$$$T^{36} -$$$$43\!\cdots\!30$$$$T^{37} +$$$$93\!\cdots\!49$$$$T^{38} -$$$$11\!\cdots\!47$$$$T^{39} +$$$$18\!\cdots\!01$$$$T^{40}$$)
$43$ 1
$47$ ($$1 + 8 T + 47 T^{2}$$)($$1 + 4 T + 47 T^{2}$$)($$1 + 8 T + 47 T^{2}$$)($$1 - 4 T + 47 T^{2}$$)($$1 - 9 T + 103 T^{2} - 423 T^{3} + 2209 T^{4}$$)($$( 1 - 6 T + 47 T^{2} )^{2}$$)($$( 1 + 10 T + 47 T^{2} )^{2}$$)($$1 - 9 T + 103 T^{2} - 423 T^{3} + 2209 T^{4}$$)($$( 1 + T + 47 T^{2} )^{3}$$)($$1 + 23 T + 301 T^{2} + 2469 T^{3} + 14147 T^{4} + 50807 T^{5} + 103823 T^{6}$$)($$1 + 23 T + 301 T^{2} + 2469 T^{3} + 14147 T^{4} + 50807 T^{5} + 103823 T^{6}$$)($$( 1 + T + 47 T^{2} )^{3}$$)($$( 1 + 9 T + 219 T^{2} + 1639 T^{3} + 19871 T^{4} + 114327 T^{5} + 933937 T^{6} + 3620551 T^{7} + 22737237 T^{8} + 43917129 T^{9} + 229345007 T^{10} )^{2}$$)($$1 + T + 441 T^{2} + 378 T^{3} + 100243 T^{4} + 64059 T^{5} + 15507867 T^{6} + 6421735 T^{7} + 1823396570 T^{8} + 389880529 T^{9} + 172695386616 T^{10} + 9060656475 T^{11} + 13634569947126 T^{12} - 876954772658 T^{13} + 916565401866601 T^{14} - 124355291786094 T^{15} + 53146338562582634 T^{16} - 8694613538868321 T^{17} + 2676993076546814875 T^{18} - 408646836326811087 T^{19} +$$$$11\!\cdots\!06$$$$T^{20} - 12910939459107637362 T^{21} +$$$$44\!\cdots\!81$$$$T^{22} -$$$$20\!\cdots\!06$$$$T^{23} +$$$$14\!\cdots\!54$$$$T^{24} +$$$$45\!\cdots\!25$$$$T^{25} +$$$$41\!\cdots\!76$$$$T^{26} +$$$$43\!\cdots\!43$$$$T^{27} +$$$$95\!\cdots\!30$$$$T^{28} +$$$$15\!\cdots\!05$$$$T^{29} +$$$$18\!\cdots\!47$$$$T^{30} +$$$$34\!\cdots\!93$$$$T^{31} +$$$$25\!\cdots\!67$$$$T^{32} +$$$$45\!\cdots\!54$$$$T^{33} +$$$$25\!\cdots\!61$$$$T^{34} +$$$$26\!\cdots\!87$$$$T^{35} +$$$$12\!\cdots\!89$$$$T^{36}$$)($$1 + T + 441 T^{2} + 378 T^{3} + 100243 T^{4} + 64059 T^{5} + 15507867 T^{6} + 6421735 T^{7} + 1823396570 T^{8} + 389880529 T^{9} + 172695386616 T^{10} + 9060656475 T^{11} + 13634569947126 T^{12} - 876954772658 T^{13} + 916565401866601 T^{14} - 124355291786094 T^{15} + 53146338562582634 T^{16} - 8694613538868321 T^{17} + 2676993076546814875 T^{18} - 408646836326811087 T^{19} +$$$$11\!\cdots\!06$$$$T^{20} - 12910939459107637362 T^{21} +$$$$44\!\cdots\!81$$$$T^{22} -$$$$20\!\cdots\!06$$$$T^{23} +$$$$14\!\cdots\!54$$$$T^{24} +$$$$45\!\cdots\!25$$$$T^{25} +$$$$41\!\cdots\!76$$$$T^{26} +$$$$43\!\cdots\!43$$$$T^{27} +$$$$95\!\cdots\!30$$$$T^{28} +$$$$15\!\cdots\!05$$$$T^{29} +$$$$18\!\cdots\!47$$$$T^{30} +$$$$34\!\cdots\!93$$$$T^{31} +$$$$25\!\cdots\!67$$$$T^{32} +$$$$45\!\cdots\!54$$$$T^{33} +$$$$25\!\cdots\!61$$$$T^{34} +$$$$26\!\cdots\!87$$$$T^{35} +$$$$12\!\cdots\!89$$$$T^{36}$$)($$1 - 45 T + 1511 T^{2} - 36937 T^{3} + 770808 T^{4} - 13736882 T^{5} + 219798824 T^{6} - 3167477674 T^{7} + 42058010785 T^{8} - 516011995467 T^{9} + 5923697054548 T^{10} - 63764307510743 T^{11} + 648591155045327 T^{12} - 6243318059242073 T^{13} + 57164463799000625 T^{14} - 498296134307400984 T^{15} + 4149644163892787994 T^{16} - 33024657601896825176 T^{17} +$$$$25\!\cdots\!32$$$$T^{18} -$$$$18\!\cdots\!69$$$$T^{19} +$$$$12\!\cdots\!66$$$$T^{20} -$$$$86\!\cdots\!43$$$$T^{21} +$$$$55\!\cdots\!88$$$$T^{22} -$$$$34\!\cdots\!48$$$$T^{23} +$$$$20\!\cdots\!14$$$$T^{24} -$$$$11\!\cdots\!88$$$$T^{25} +$$$$61\!\cdots\!25$$$$T^{26} -$$$$31\!\cdots\!99$$$$T^{27} +$$$$15\!\cdots\!47$$$$T^{28} -$$$$71\!\cdots\!81$$$$T^{29} +$$$$31\!\cdots\!52$$$$T^{30} -$$$$12\!\cdots\!01$$$$T^{31} +$$$$48\!\cdots\!85$$$$T^{32} -$$$$17\!\cdots\!98$$$$T^{33} +$$$$56\!\cdots\!56$$$$T^{34} -$$$$16\!\cdots\!26$$$$T^{35} +$$$$43\!\cdots\!68$$$$T^{36} -$$$$98\!\cdots\!19$$$$T^{37} +$$$$18\!\cdots\!79$$$$T^{38} -$$$$26\!\cdots\!35$$$$T^{39} +$$$$27\!\cdots\!01$$$$T^{40}$$)($$( 1 + 12 T + 339 T^{2} + 3526 T^{3} + 56816 T^{4} + 511010 T^{5} + 6080868 T^{6} + 47412308 T^{7} + 456152128 T^{8} + 3078600974 T^{9} + 24961460139 T^{10} + 144694245778 T^{11} + 1007640050752 T^{12} + 4922488053484 T^{13} + 29672696043108 T^{14} + 117197592027070 T^{15} + 612431898132464 T^{16} + 1786353122752538 T^{17} + 8072026178336979 T^{18} + 13429565677233204 T^{19} + 52599132235830049 T^{20} )^{2}$$)($$1 - 45 T + 1511 T^{2} - 36937 T^{3} + 770808 T^{4} - 13736882 T^{5} + 219798824 T^{6} - 3167477674 T^{7} + 42058010785 T^{8} - 516011995467 T^{9} + 5923697054548 T^{10} - 63764307510743 T^{11} + 648591155045327 T^{12} - 6243318059242073 T^{13} + 57164463799000625 T^{14} - 498296134307400984 T^{15} + 4149644163892787994 T^{16} - 33024657601896825176 T^{17} +$$$$25\!\cdots\!32$$$$T^{18} -$$$$18\!\cdots\!69$$$$T^{19} +$$$$12\!\cdots\!66$$$$T^{20} -$$$$86\!\cdots\!43$$$$T^{21} +$$$$55\!\cdots\!88$$$$T^{22} -$$$$34\!\cdots\!48$$$$T^{23} +$$$$20\!\cdots\!14$$$$T^{24} -$$$$11\!\cdots\!88$$$$T^{25} +$$$$61\!\cdots\!25$$$$T^{26} -$$$$31\!\cdots\!99$$$$T^{27} +$$$$15\!\cdots\!47$$$$T^{28} -$$$$71\!\cdots\!81$$$$T^{29} +$$$$31\!\cdots\!52$$$$T^{30} -$$$$12\!\cdots\!01$$$$T^{31} +$$$$48\!\cdots\!85$$$$T^{32} -$$$$17\!\cdots\!98$$$$T^{33} +$$$$56\!\cdots\!56$$$$T^{34} -$$$$16\!\cdots\!26$$$$T^{35} +$$$$43\!\cdots\!68$$$$T^{36} -$$$$98\!\cdots\!19$$$$T^{37} +$$$$18\!\cdots\!79$$$$T^{38} -$$$$26\!\cdots\!35$$$$T^{39} +$$$$27\!\cdots\!01$$$$T^{40}$$)
$53$ ($$1 + 5 T + 53 T^{2}$$)($$1 + 13 T + 53 T^{2}$$)($$1 + 5 T + 53 T^{2}$$)($$1 + 5 T + 53 T^{2}$$)($$1 + 5 T + 111 T^{2} + 265 T^{3} + 2809 T^{4}$$)($$1 - 22 T + 219 T^{2} - 1166 T^{3} + 2809 T^{4}$$)($$( 1 + T + 53 T^{2} )^{2}$$)($$1 + 5 T + 111 T^{2} + 265 T^{3} + 2809 T^{4}$$)($$1 - 9 T + 165 T^{2} - 925 T^{3} + 8745 T^{4} - 25281 T^{5} + 148877 T^{6}$$)($$1 - 6 T + 108 T^{2} - 707 T^{3} + 5724 T^{4} - 16854 T^{5} + 148877 T^{6}$$)($$1 - 6 T + 108 T^{2} - 707 T^{3} + 5724 T^{4} - 16854 T^{5} + 148877 T^{6}$$)($$1 - 9 T + 165 T^{2} - 925 T^{3} + 8745 T^{4} - 25281 T^{5} + 148877 T^{6}$$)($$( 1 - T + 217 T^{2} - 165 T^{3} + 20879 T^{4} - 12533 T^{5} + 1106587 T^{6} - 463485 T^{7} + 32306309 T^{8} - 7890481 T^{9} + 418195493 T^{10} )^{2}$$)($$1 - 3 T + 471 T^{2} - 1056 T^{3} + 113523 T^{4} - 153549 T^{5} + 18344467 T^{6} - 6960585 T^{7} + 2222494860 T^{8} + 1426226391 T^{9} + 215187452214 T^{10} + 355484655993 T^{11} + 17400446510730 T^{12} + 44440317183162 T^{13} + 1215028415653965 T^{14} + 3904928969645238 T^{15} + 75147380191168470 T^{16} + 262691650979577669 T^{17} + 4185046851497965019 T^{18} + 13922657501917616457 T^{19} +$$$$21\!\cdots\!30$$$$T^{20} +$$$$58\!\cdots\!26$$$$T^{21} +$$$$95\!\cdots\!65$$$$T^{22} +$$$$18\!\cdots\!66$$$$T^{23} +$$$$38\!\cdots\!70$$$$T^{24} +$$$$41\!\cdots\!41$$$$T^{25} +$$$$13\!\cdots\!54$$$$T^{26} +$$$$47\!\cdots\!03$$$$T^{27} +$$$$38\!\cdots\!40$$$$T^{28} -$$$$64\!\cdots\!45$$$$T^{29} +$$$$90\!\cdots\!47$$$$T^{30} -$$$$39\!\cdots\!77$$$$T^{31} +$$$$15\!\cdots\!87$$$$T^{32} -$$$$77\!\cdots\!92$$$$T^{33} +$$$$18\!\cdots\!91$$$$T^{34} -$$$$61\!\cdots\!39$$$$T^{35} +$$$$10\!\cdots\!89$$$$T^{36}$$)($$1 - 3 T + 471 T^{2} - 1056 T^{3} + 113523 T^{4} - 153549 T^{5} + 18344467 T^{6} - 6960585 T^{7} + 2222494860 T^{8} + 1426226391 T^{9} + 215187452214 T^{10} + 355484655993 T^{11} + 17400446510730 T^{12} + 44440317183162 T^{13} + 1215028415653965 T^{14} + 3904928969645238 T^{15} + 75147380191168470 T^{16} + 262691650979577669 T^{17} + 4185046851497965019 T^{18} + 13922657501917616457 T^{19} +$$$$21\!\cdots\!30$$$$T^{20} +$$$$58\!\cdots\!26$$$$T^{21} +$$$$95\!\cdots\!65$$$$T^{22} +$$$$18\!\cdots\!66$$$$T^{23} +$$$$38\!\cdots\!70$$$$T^{24} +$$$$41\!\cdots\!41$$$$T^{25} +$$$$13\!\cdots\!54$$$$T^{26} +$$$$47\!\cdots\!03$$$$T^{27} +$$$$38\!\cdots\!40$$$$T^{28} -$$$$64\!\cdots\!45$$$$T^{29} +$$$$90\!\cdots\!47$$$$T^{30} -$$$$39\!\cdots\!77$$$$T^{31} +$$$$15\!\cdots\!87$$$$T^{32} -$$$$77\!\cdots\!92$$$$T^{33} +$$$$18\!\cdots\!91$$$$T^{34} -$$$$61\!\cdots\!39$$$$T^{35} +$$$$10\!\cdots\!89$$$$T^{36}$$)($$1 - 3 T + 613 T^{2} - 1912 T^{3} + 186977 T^{4} - 607031 T^{5} + 37799602 T^{6} - 127535552 T^{7} + 5694013788 T^{8} - 19875117064 T^{9} + 681406942949 T^{10} - 2441370740336 T^{11} + 67442970127123 T^{12} - 245242274964199 T^{13} + 5672683623486178 T^{14} - 20630924101460484 T^{15} + 413096049704419240 T^{16} - 1476192887327507123 T^{17} + 26367839384243376638 T^{18} - 90699112484413664918 T^{19} +$$$$14\!\cdots\!27$$$$T^{20} -$$$$48\!\cdots\!54$$$$T^{21} +$$$$74\!\cdots\!42$$$$T^{22} -$$$$21\!\cdots\!71$$$$T^{23} +$$$$32\!\cdots\!40$$$$T^{24} -$$$$86\!\cdots\!12$$$$T^{25} +$$$$12\!\cdots\!62$$$$T^{26} -$$$$28\!\cdots\!63$$$$T^{27} +$$$$41\!\cdots\!03$$$$T^{28} -$$$$80\!\cdots\!88$$$$T^{29} +$$$$11\!\cdots\!01$$$$T^{30} -$$$$18\!\cdots\!08$$$$T^{31} +$$$$27\!\cdots\!08$$$$T^{32} -$$$$33\!\cdots\!96$$$$T^{33} +$$$$52\!\cdots\!38$$$$T^{34} -$$$$44\!\cdots\!67$$$$T^{35} +$$$$72\!\cdots\!17$$$$T^{36} -$$$$39\!\cdots\!56$$$$T^{37} +$$$$66\!\cdots\!57$$$$T^{38} -$$$$17\!\cdots\!51$$$$T^{39} +$$$$30\!\cdots\!01$$$$T^{40}$$)($$( 1 + 21 T + 498 T^{2} + 6309 T^{3} + 87582 T^{4} + 825969 T^{5} + 8991377 T^{6} + 72779787 T^{7} + 699192874 T^{8} + 5071930248 T^{9} + 42659895983 T^{10} + 268812303144 T^{11} + 1964032783066 T^{12} + 10835236349199 T^{13} + 70946289382337 T^{14} + 345416513157717 T^{15} + 1941199076400078 T^{16} + 7411252581231633 T^{17} + 31005325824857778 T^{18} + 69295035427844793 T^{19} + 174887470365513049 T^{20} )^{2}$$)($$1 - 3 T + 613 T^{2} - 1912 T^{3} + 186977 T^{4} - 607031 T^{5} + 37799602 T^{6} - 127535552 T^{7} + 5694013788 T^{8} - 19875117064 T^{9} + 681406942949 T^{10} - 2441370740336 T^{11} + 67442970127123 T^{12} - 245242274964199 T^{13} + 5672683623486178 T^{14} - 20630924101460484 T^{15} + 413096049704419240 T^{16} - 1476192887327507123 T^{17} + 26367839384243376638 T^{18} - 90699112484413664918 T^{19} +$$$$14\!\cdots\!27$$$$T^{20} -$$$$48\!\cdots\!54$$$$T^{21} +$$$$74\!\cdots\!42$$$$T^{22} -$$$$21\!\cdots\!71$$$$T^{23} +$$$$32\!\cdots\!40$$$$T^{24} -$$$$86\!\cdots\!12$$$$T^{25} +$$$$12\!\cdots\!62$$$$T^{26} -$$$$28\!\cdots\!63$$$$T^{27} +$$$$41\!\cdots\!03$$$$T^{28} -$$$$80\!\cdots\!88$$$$T^{29} +$$$$11\!\cdots\!01$$$$T^{30} -$$$$18\!\cdots\!08$$$$T^{31} +$$$$27\!\cdots\!08$$$$T^{32} -$$$$33\!\cdots\!96$$$$T^{33} +$$$$52\!\cdots\!38$$$$T^{34} -$$$$44\!\cdots\!67$$$$T^{35} +$$$$72\!\cdots\!17$$$$T^{36} -$$$$39\!\cdots\!56$$$$T^{37} +$$$$66\!\cdots\!57$$$$T^{38} -$$$$17\!\cdots\!51$$$$T^{39} +$$$$30\!\cdots\!01$$$$T^{40}$$)
$59$ ($$1 - 12 T + 59 T^{2}$$)($$1 - 8 T + 59 T^{2}$$)($$1 - 12 T + 59 T^{2}$$)($$1 + 12 T + 59 T^{2}$$)($$1 + T + 87 T^{2} + 59 T^{3} + 3481 T^{4}$$)($$1 + 4 T + 114 T^{2} + 236 T^{3} + 3481 T^{4}$$)($$( 1 + 10 T + 59 T^{2} )^{2}$$)($$1 + T + 87 T^{2} + 59 T^{3} + 3481 T^{4}$$)($$1 + 24 T + 348 T^{2} + 3169 T^{3} + 20532 T^{4} + 83544 T^{5} + 205379 T^{6}$$)($$1 + 8 T + 182 T^{2} + 943 T^{3} + 10738 T^{4} + 27848 T^{5} + 205379 T^{6}$$)($$1 + 8 T + 182 T^{2} + 943 T^{3} + 10738 T^{4} + 27848 T^{5} + 205379 T^{6}$$)($$1 + 24 T + 348 T^{2} + 3169 T^{3} + 20532 T^{4} + 83544 T^{5} + 205379 T^{6}$$)($$( 1 - 7 T + 198 T^{2} - 1030 T^{3} + 16660 T^{4} - 72387 T^{5} + 982940 T^{6} - 3585430 T^{7} + 40665042 T^{8} - 84821527 T^{9} + 714924299 T^{10} )^{2}$$)($$1 - 17 T + 890 T^{2} - 12969 T^{3} + 371964 T^{4} - 4775447 T^{5} + 98199544 T^{6} - 1131507793 T^{7} + 18510827194 T^{8} - 193828091271 T^{9} + 2662524759788 T^{10} - 25536895733756 T^{11} + 304262792505393 T^{12} - 2684476478739574 T^{13} + 28341034676025816 T^{14} - 230279921162601801 T^{15} + 2186359093053923584 T^{16} - 16332723780371798493 T^{17} +$$$$14\!\cdots\!85$$$$T^{18} -$$$$96\!\cdots\!87$$$$T^{19} +$$$$76\!\cdots\!04$$$$T^{20} -$$$$47\!\cdots\!79$$$$T^{21} +$$$$34\!\cdots\!76$$$$T^{22} -$$$$19\!\cdots\!26$$$$T^{23} +$$$$12\!\cdots\!13$$$$T^{24} -$$$$63\!\cdots\!64$$$$T^{25} +$$$$39\!\cdots\!48$$$$T^{26} -$$$$16\!\cdots\!69$$$$T^{27} +$$$$94\!\cdots\!94$$$$T^{28} -$$$$34\!\cdots\!87$$$$T^{29} +$$$$17\!\cdots\!64$$$$T^{30} -$$$$50\!\cdots\!13$$$$T^{31} +$$$$23\!\cdots\!04$$$$T^{32} -$$$$47\!\cdots\!31$$$$T^{33} +$$$$19\!\cdots\!90$$$$T^{34} -$$$$21\!\cdots\!23$$$$T^{35} +$$$$75\!\cdots\!21$$$$T^{36}$$)($$1 - 17 T + 890 T^{2} - 12969 T^{3} + 371964 T^{4} - 4775447 T^{5} + 98199544 T^{6} - 1131507793 T^{7} + 18510827194 T^{8} - 193828091271 T^{9} + 2662524759788 T^{10} - 25536895733756 T^{11} + 304262792505393 T^{12} - 2684476478739574 T^{13} + 28341034676025816 T^{14} - 230279921162601801 T^{15} + 2186359093053923584 T^{16} - 16332723780371798493 T^{17} +$$$$14\!\cdots\!85$$$$T^{18} -$$$$96\!\cdots\!87$$$$T^{19} +$$$$76\!\cdots\!04$$$$T^{20} -$$$$47\!\cdots\!79$$$$T^{21} +$$$$34\!\cdots\!76$$$$T^{22} -$$$$19\!\cdots\!26$$$$T^{23} +$$$$12\!\cdots\!13$$$$T^{24} -$$$$63\!\cdots\!64$$$$T^{25} +$$$$39\!\cdots\!48$$$$T^{26} -$$$$16\!\cdots\!69$$$$T^{27} +$$$$94\!\cdots\!94$$$$T^{28} -$$$$34\!\cdots\!87$$$$T^{29} +$$$$17\!\cdots\!64$$$$T^{30} -$$$$50\!\cdots\!13$$$$T^{31} +$$$$23\!\cdots\!04$$$$T^{32} -$$$$47\!\cdots\!31$$$$T^{33} +$$$$19\!\cdots\!90$$$$T^{34} -$$$$21\!\cdots\!23$$$$T^{35} +$$$$75\!\cdots\!21$$$$T^{36}$$)($$1 - 66 T + 2815 T^{2} - 88361 T^{3} + 2275828 T^{4} - 49883249 T^{5} + 962488724 T^{6} - 16630945847 T^{7} + 261502441352 T^{8} - 3778845268886 T^{9} + 50649777859055 T^{10} - 633662617235908 T^{11} + 7443048277471240 T^{12} - 82425509095651651 T^{13} + 863910544933685903 T^{14} - 8593161165219341990 T^{15} + 81320010966712563121 T^{16} -$$$$73\!\cdots\!79$$$$T^{17} +$$$$63\!\cdots\!87$$$$T^{18} -$$$$51\!\cdots\!89$$$$T^{19} +$$$$40\!\cdots\!16$$$$T^{20} -$$$$30\!\cdots\!51$$$$T^{21} +$$$$21\!\cdots\!47$$$$T^{22} -$$$$15\!\cdots\!41$$$$T^{23} +$$$$98\!\cdots\!81$$$$T^{24} -$$$$61\!\cdots\!10$$$$T^{25} +$$$$36\!\cdots\!23$$$$T^{26} -$$$$20\!\cdots\!69$$$$T^{27} +$$$$10\!\cdots\!40$$$$T^{28} -$$$$54\!\cdots\!12$$$$T^{29} +$$$$25\!\cdots\!55$$$$T^{30} -$$$$11\!\cdots\!74$$$$T^{31} +$$$$46\!\cdots\!12$$$$T^{32} -$$$$17\!\cdots\!13$$$$T^{33} +$$$$59\!\cdots\!64$$$$T^{34} -$$$$18\!\cdots\!51$$$$T^{35} +$$$$49\!\cdots\!48$$$$T^{36} -$$$$11\!\cdots\!59$$$$T^{37} +$$$$21\!\cdots\!15$$$$T^{38} -$$$$29\!\cdots\!74$$$$T^{39} +$$$$26\!\cdots\!01$$$$T^{40}$$)($$( 1 + 45 T + 1251 T^{2} + 25722 T^{3} + 430204 T^{4} + 6101381 T^{5} + 75494762 T^{6} + 828309220 T^{7} + 8153878001 T^{8} + 72482217211 T^{9} + 584374584815 T^{10} + 4276450815449 T^{11} + 28383649321481 T^{12} + 170117319294380 T^{13} + 914797284763082 T^{14} + 4362025534356919 T^{15} + 18146234294492764 T^{16} + 64013093492514318 T^{17} + 183684877443005571 T^{18} + 389834811839472255 T^{19} + 511116753300641401 T^{20} )^{2}$$)($$1 - 66 T + 2815 T^{2} - 88361 T^{3} + 2275828 T^{4} - 49883249 T^{5} + 962488724 T^{6} - 16630945847 T^{7} + 261502441352 T^{8} - 3778845268886 T^{9} + 50649777859055 T^{10} - 633662617235908 T^{11} + 7443048277471240 T^{12} - 82425509095651651 T^{13} + 863910544933685903 T^{14} - 8593161165219341990 T^{15} + 81320010966712563121 T^{16} -$$$$73\!\cdots\!79$$$$T^{17} +$$$$63\!\cdots\!87$$$$T^{18} -$$$$51\!\cdots\!89$$$$T^{19} +$$$$40\!\cdots\!16$$$$T^{20} -$$$$30\!\cdots\!51$$$$T^{21} +$$$$21\!\cdots\!47$$$$T^{22} -$$$$15\!\cdots\!41$$$$T^{23} +$$$$98\!\cdots\!81$$$$T^{24} -$$$$61\!\cdots\!10$$$$T^{25} +$$$$36\!\cdots\!23$$$$T^{26} -$$$$20\!\cdots\!69$$$$T^{27} +$$$$10\!\cdots\!40$$$$T^{28} -$$$$54\!\cdots\!12$$$$T^{29} +$$$$25\!\cdots\!55$$$$T^{30} -$$$$11\!\cdots\!74$$$$T^{31} +$$$$46\!\cdots\!12$$$$T^{32} -$$$$17\!\cdots\!13$$$$T^{33} +$$$$59\!\cdots\!64$$$$T^{34} -$$$$18\!\cdots\!51$$$$T^{35} +$$$$49\!\cdots\!48$$$$T^{36} -$$$$11\!\cdots\!59$$$$T^{37} +$$$$21\!\cdots\!15$$$$T^{38} -$$$$29\!\cdots\!74$$$$T^{39} +$$$$26\!\cdots\!01$$$$T^{40}$$)
$61$ ($$1 - 13 T + 61 T^{2}$$)($$1 + 61 T^{2}$$)($$1 + 13 T + 61 T^{2}$$)($$1 + 2 T + 61 T^{2}$$)($$1 + T + 111 T^{2} + 61 T^{3} + 3721 T^{4}$$)($$1 + 8 T + 120 T^{2} + 488 T^{3} + 3721 T^{4}$$)($$1 + 68 T^{2} + 3721 T^{4}$$)($$1 - T + 111 T^{2} - 61 T^{3} + 3721 T^{4}$$)($$1 + T + 139 T^{2} + 205 T^{3} + 8479 T^{4} + 3721 T^{5} + 226981 T^{6}$$)($$1 + 6 T + 167 T^{2} + 740 T^{3} + 10187 T^{4} + 22326 T^{5} + 226981 T^{6}$$)($$1 - 6 T + 167 T^{2} - 740 T^{3} + 10187 T^{4} - 22326 T^{5} + 226981 T^{6}$$)($$1 - T + 139 T^{2} - 205 T^{3} + 8479 T^{4} - 3721 T^{5} + 226981 T^{6}$$)($$1 + 379 T^{2} + 71239 T^{4} + 8701202 T^{6} + 774928669 T^{8} + 53283270877 T^{10} + 2883509577349 T^{12} + 120475459400882 T^{14} + 3670259949103279 T^{16} + 72657071625969499 T^{18} + 713342911662882601 T^{20}$$)($$1 + 28 T + 1019 T^{2} + 20072 T^{3} + 437347 T^{4} + 6824646 T^{5} + 112590320 T^{6} + 1473831616 T^{7} + 20079161609 T^{8} + 228034178555 T^{9} + 2684926553124 T^{10} + 27078104395535 T^{11} + 283831171459274 T^{12} + 2590252054230334 T^{13} + 24721592527244465 T^{14} + 207570410437628343 T^{15} + 1836081624449708055 T^{16} + 14378049045728950908 T^{17} +$$$$11\!\cdots\!89$$$$T^{18} +$$$$87\!\cdots\!88$$$$T^{19} +$$$$68\!\cdots\!55$$$$T^{20} +$$$$47\!\cdots\!83$$$$T^{21} +$$$$34\!\cdots\!65$$$$T^{22} +$$$$21\!\cdots\!34$$$$T^{23} +$$$$14\!\cdots\!14$$$$T^{24} +$$$$85\!\cdots\!35$$$$T^{25} +$$$$51\!\cdots\!44$$$$T^{26} +$$$$26\!\cdots\!55$$$$T^{27} +$$$$14\!\cdots\!09$$$$T^{28} +$$$$64\!\cdots\!76$$$$T^{29} +$$$$29\!\cdots\!20$$$$T^{30} +$$$$11\!\cdots\!26$$$$T^{31} +$$$$43\!\cdots\!27$$$$T^{32} +$$$$12\!\cdots\!72$$$$T^{33} +$$$$37\!\cdots\!59$$$$T^{34} +$$$$62\!\cdots\!88$$$$T^{35} +$$$$13\!\cdots\!81$$$$T^{36}$$)($$1 - 28 T + 1019 T^{2} - 20072 T^{3} + 437347 T^{4} - 6824646 T^{5} + 112590320 T^{6} - 1473831616 T^{7} + 20079161609 T^{8} - 228034178555 T^{9} + 2684926553124 T^{10} - 27078104395535 T^{11} + 283831171459274 T^{12} - 2590252054230334 T^{13} + 24721592527244465 T^{14} - 207570410437628343 T^{15} + 1836081624449708055 T^{16} - 14378049045728950908 T^{17} +$$$$11\!\cdots\!89$$$$T^{18} -$$$$87\!\cdots\!88$$$$T^{19} +$$$$68\!\cdots\!55$$$$T^{20} -$$$$47\!\cdots\!83$$$$T^{21} +$$$$34\!\cdots\!65$$$$T^{22} -$$$$21\!\cdots\!34$$$$T^{23} +$$$$14\!\cdots\!14$$$$T^{24} -$$$$85\!\cdots\!35$$$$T^{25} +$$$$51\!\cdots\!44$$$$T^{26} -$$$$26\!\cdots\!55$$$$T^{27} +$$$$14\!\cdots\!09$$$$T^{28} -$$$$64\!\cdots\!76$$$$T^{29} +$$$$29\!\cdots\!20$$$$T^{30} -$$$$11\!\cdots\!26$$$$T^{31} +$$$$43\!\cdots\!27$$$$T^{32} -$$$$12\!\cdots\!72$$$$T^{33} +$$$$37\!\cdots\!59$$$$T^{34} -$$$$62\!\cdots\!88$$$$T^{35} +$$$$13\!\cdots\!81$$$$T^{36}$$)($$1 + 30 T + 922 T^{2} + 17978 T^{3} + 345594 T^{4} + 5305743 T^{5} + 80142022 T^{6} + 1050374877 T^{7} + 13559425579 T^{8} + 158226315366 T^{9} + 1819771079659 T^{10} + 19368804087758 T^{11} + 203166699504050 T^{12} + 2001054980174280 T^{13} + 19412282312992375 T^{14} + 178471358955453852 T^{15} + 1615021614573728110 T^{16} + 13931247955336092241 T^{17} +$$$$11\!\cdots\!07$$$$T^{18} +$$$$95\!\cdots\!05$$$$T^{19} +$$$$76\!\cdots\!03$$$$T^{20} +$$$$58\!\cdots\!05$$$$T^{21} +$$$$43\!\cdots\!47$$$$T^{22} +$$$$31\!\cdots\!21$$$$T^{23} +$$$$22\!\cdots\!10$$$$T^{24} +$$$$15\!\cdots\!52$$$$T^{25} +$$$$10\!\cdots\!75$$$$T^{26} +$$$$62\!\cdots\!80$$$$T^{27} +$$$$38\!\cdots\!50$$$$T^{28} +$$$$22\!\cdots\!78$$$$T^{29} +$$$$12\!\cdots\!59$$$$T^{30} +$$$$68\!\cdots\!26$$$$T^{31} +$$$$35\!\cdots\!59$$$$T^{32} +$$$$17\!\cdots\!37$$$$T^{33} +$$$$79\!\cdots\!02$$$$T^{34} +$$$$31\!\cdots\!43$$$$T^{35} +$$$$12\!\cdots\!34$$$$T^{36} +$$$$40\!\cdots\!38$$$$T^{37} +$$$$12\!\cdots\!82$$$$T^{38} +$$$$25\!\cdots\!30$$$$T^{39} +$$$$50\!\cdots\!01$$$$T^{40}$$)($$1 + 790 T^{2} + 309299 T^{4} + 80006711 T^{6} + 15356484539 T^{8} + 2325961684078 T^{10} + 288434648480662 T^{12} + 29976458677407681 T^{14} + 2650762140208233663 T^{16} +$$$$20\!\cdots\!90$$$$T^{18} +$$$$13\!\cdots\!81$$$$T^{20} +$$$$74\!\cdots\!90$$$$T^{22} +$$$$36\!\cdots\!83$$$$T^{24} +$$$$15\!\cdots\!41$$$$T^{26} +$$$$55\!\cdots\!22$$$$T^{28} +$$$$16\!\cdots\!78$$$$T^{30} +$$$$40\!\cdots\!19$$$$T^{32} +$$$$79\!\cdots\!51$$$$T^{34} +$$$$11\!\cdots\!39$$$$T^{36} +$$$$10\!\cdots\!90$$$$T^{38} +$$$$50\!\cdots\!01$$$$T^{40}$$)($$1 - 30 T + 922 T^{2} - 17978 T^{3} + 345594 T^{4} - 5305743 T^{5} + 80142022 T^{6} - 1050374877 T^{7} + 13559425579 T^{8} - 158226315366 T^{9} + 1819771079659 T^{10} - 19368804087758 T^{11} + 203166699504050 T^{12} - 2001054980174280 T^{13} + 19412282312992375 T^{14} - 178471358955453852 T^{15} + 1615021614573728110 T^{16} - 13931247955336092241 T^{17} +$$$$11\!\cdots\!07$$$$T^{18} -$$$$95\!\cdots\!05$$$$T^{19} +$$$$76\!\cdots\!03$$$$T^{20} -$$$$58\!\cdots\!05$$$$T^{21} +$$$$43\!\cdots\!47$$$$T^{22} -$$$$31\!\cdots\!21$$$$T^{23} +$$$$22\!\cdots\!10$$$$T^{24} -$$$$15\!\cdots\!52$$$$T^{25} +$$$$10\!\cdots\!75$$$$T^{26} -$$$$62\!\cdots\!80$$$$T^{27} +$$$$38\!\cdots\!50$$$$T^{28} -$$$$22\!\cdots\!78$$$$T^{29} +$$$$12\!\cdots\!59$$$$T^{30} -$$$$68\!\cdots\!26$$$$T^{31} +$$$$35\!\cdots\!59$$$$T^{32} -$$$$17\!\cdots\!37$$$$T^{33} +$$$$79\!\cdots\!02$$$$T^{34} -$$$$31\!\cdots\!43$$$$T^{35} +$$$$12\!\cdots\!34$$$$T^{36} -$$$$40\!\cdots\!38$$$$T^{37} +$$$$12\!\cdots\!82$$$$T^{38} -$$$$25\!\cdots\!30$$$$T^{39} +$$$$50\!\cdots\!01$$$$T^{40}$$)
$67$ ($$1 + 3 T + 67 T^{2}$$)($$1 + 15 T + 67 T^{2}$$)($$1 + 3 T + 67 T^{2}$$)($$1 + 3 T + 67 T^{2}$$)($$1 + T + 123 T^{2} + 67 T^{3} + 4489 T^{4}$$)($$1 - 2 T + 63 T^{2} - 134 T^{3} + 4489 T^{4}$$)($$( 1 - 9 T + 67 T^{2} )^{2}$$)($$1 + T + 123 T^{2} + 67 T^{3} + 4489 T^{4}$$)($$1 + 2 T + 172 T^{2} + 281 T^{3} + 11524 T^{4} + 8978 T^{5} + 300763 T^{6}$$)($$1 - 12 T + 221 T^{2} - 1504 T^{3} + 14807 T^{4} - 53868 T^{5} + 300763 T^{6}$$)($$1 - 12 T + 221 T^{2} - 1504 T^{3} + 14807 T^{4} - 53868 T^{5} + 300763 T^{6}$$)($$1 + 2 T + 172 T^{2} + 281 T^{3} + 11524 T^{4} + 8978 T^{5} + 300763 T^{6}$$)($$( 1 - 13 T + 308 T^{2} - 3053 T^{3} + 39181 T^{4} - 293685 T^{5} + 2625127 T^{6} - 13704917 T^{7} + 92635004 T^{8} - 261964573 T^{9} + 1350125107 T^{10} )^{2}$$)($$1 - 18 T + 747 T^{2} - 11021 T^{3} + 266098 T^{4} - 3386261 T^{5} + 61776616 T^{6} - 700286712 T^{7} + 10647673611 T^{8} - 109744348215 T^{9} + 1459937506974 T^{10} - 13858055653902 T^{11} + 165766321224565 T^{12} - 1460245745643108 T^{13} + 15966332829424392 T^{14} - 131058934756843494 T^{15} + 1323312512220230094 T^{16} - 10136102287940402999 T^{17} + 95100333637183309469 T^{18} -$$$$67\!\cdots\!33$$$$T^{19} +$$$$59\!\cdots\!66$$$$T^{20} -$$$$39\!\cdots\!22$$$$T^{21} +$$$$32\!\cdots\!32$$$$T^{22} -$$$$19\!\cdots\!56$$$$T^{23} +$$$$14\!\cdots\!85$$$$T^{24} -$$$$83\!\cdots\!46$$$$T^{25} +$$$$59\!\cdots\!34$$$$T^{26} -$$$$29\!\cdots\!05$$$$T^{27} +$$$$19\!\cdots\!39$$$$T^{28} -$$$$85\!\cdots\!96$$$$T^{29} +$$$$50\!\cdots\!76$$$$T^{30} -$$$$18\!\cdots\!07$$$$T^{31} +$$$$97\!\cdots\!42$$$$T^{32} -$$$$27\!\cdots\!03$$$$T^{33} +$$$$12\!\cdots\!07$$$$T^{34} -$$$$19\!\cdots\!86$$$$T^{35} +$$$$74\!\cdots\!09$$$$T^{36}$$)($$1 - 18 T + 747 T^{2} - 11021 T^{3} + 266098 T^{4} - 3386261 T^{5} + 61776616 T^{6} - 700286712 T^{7} + 10647673611 T^{8} - 109744348215 T^{9} + 1459937506974 T^{10} - 13858055653902 T^{11} + 165766321224565 T^{12} - 1460245745643108 T^{13} + 15966332829424392 T^{14} - 131058934756843494 T^{15} + 1323312512220230094 T^{16} - 10136102287940402999 T^{17} + 95100333637183309469 T^{18} -$$$$67\!\cdots\!33$$$$T^{19} +$$$$59\!\cdots\!66$$$$T^{20} -$$$$39\!\cdots\!22$$$$T^{21} +$$$$32\!\cdots\!32$$$$T^{22} -$$$$19\!\cdots\!56$$$$T^{23} +$$$$14\!\cdots\!85$$$$T^{24} -$$$$83\!\cdots\!46$$$$T^{25} +$$$$59\!\cdots\!34$$$$T^{26} -$$$$29\!\cdots\!05$$$$T^{27} +$$$$19\!\cdots\!39$$$$T^{28} -$$$$85\!\cdots\!96$$$$T^{29} +$$$$50\!\cdots\!76$$$$T^{30} -$$$$18\!\cdots\!07$$$$T^{31} +$$$$97\!\cdots\!42$$$$T^{32} -$$$$27\!\cdots\!03$$$$T^{33} +$$$$12\!\cdots\!07$$$$T^{34} -$$$$19\!\cdots\!86$$$$T^{35} +$$$$74\!\cdots\!09$$$$T^{36}$$)($$1 + 6 T + 713 T^{2} + 4865 T^{3} + 256067 T^{4} + 1917283 T^{5} + 61955432 T^{6} + 492179942 T^{7} + 11362573071 T^{8} + 93015796636 T^{9} + 1680301496756 T^{10} + 13848234931211 T^{11} + 207778921318378 T^{12} + 1693635064497520 T^{13} + 21986354136885960 T^{14} + 174788972094032572 T^{15} + 2021682240803889472 T^{16} + 15486466214090967294 T^{17} +$$$$16\!\cdots\!83$$$$T^{18} +$$$$11\!\cdots\!21$$$$T^{19} +$$$$11\!\cdots\!62$$$$T^{20} +$$$$79\!\cdots\!07$$$$T^{21} +$$$$73\!\cdots\!87$$$$T^{22} +$$$$46\!\cdots\!22$$$$T^{23} +$$$$40\!\cdots\!12$$$$T^{24} +$$$$23\!\cdots\!04$$$$T^{25} +$$$$19\!\cdots\!40$$$$T^{26} +$$$$10\!\cdots\!60$$$$T^{27} +$$$$84\!\cdots\!98$$$$T^{28} +$$$$37\!\cdots\!17$$$$T^{29} +$$$$30\!\cdots\!44$$$$T^{30} +$$$$11\!\cdots\!88$$$$T^{31} +$$$$92\!\cdots\!31$$$$T^{32} +$$$$26\!\cdots\!54$$$$T^{33} +$$$$22\!\cdots\!28$$$$T^{34} +$$$$47\!\cdots\!69$$$$T^{35} +$$$$42\!\cdots\!27$$$$T^{36} +$$$$53\!\cdots\!55$$$$T^{37} +$$$$52\!\cdots\!17$$$$T^{38} +$$$$29\!\cdots\!18$$$$T^{39} +$$$$33\!\cdots\!01$$$$T^{40}$$)($$( 1 + 31 T + 839 T^{2} + 14659 T^{3} + 233414 T^{4} + 2954891 T^{5} + 35492860 T^{6} + 366766920 T^{7} + 3681988473 T^{8} + 32750116631 T^{9} + 284096631401 T^{10} + 2194257814277 T^{11} + 16528446255297 T^{12} + 110309919159960 T^{13} + 715220916496060 T^{14} + 3989472527548337 T^{15} + 21114252815594966 T^{16} + 88843971422429857 T^{17} + 340690781470021799 T^{18} + 843402566285143357 T^{19} + 1822837804551761449 T^{20} )^{2}$$)($$1 + 6 T + 713 T^{2} + 4865 T^{3} + 256067 T^{4} + 1917283 T^{5} + 61955432 T^{6} + 492179942 T^{7} + 11362573071 T^{8} + 93015796636 T^{9} + 1680301496756 T^{10} + 13848234931211 T^{11} + 207778921318378 T^{12} + 1693635064497520 T^{13} + 21986354136885960 T^{14} + 174788972094032572 T^{15} + 2021682240803889472 T^{16} + 15486466214090967294 T^{17} +$$$$16\!\cdots\!83$$$$T^{18} +$$$$11\!\cdots\!21$$$$T^{19} +$$$$11\!\cdots\!62$$$$T^{20} +$$$$79\!\cdots\!07$$$$T^{21} +$$$$73\!\cdots\!87$$$$T^{22} +$$$$46\!\cdots\!22$$$$T^{23} +$$$$40\!\cdots\!12$$$$T^{24} +$$$$23\!\cdots\!04$$$$T^{25} +$$$$19\!\cdots\!40$$$$T^{26} +$$$$10\!\cdots\!60$$$$T^{27} +$$$$84\!\cdots\!98$$$$T^{28} +$$$$37\!\cdots\!17$$$$T^{29} +$$$$30\!\cdots\!44$$$$T^{30} +$$$$11\!\cdots\!88$$$$T^{31} +$$$$92\!\cdots\!31$$$$T^{32} +$$$$26\!\cdots\!54$$$$T^{33} +$$$$22\!\cdots\!28$$$$T^{34} +$$$$47\!\cdots\!69$$$$T^{35} +$$$$42\!\cdots\!27$$$$T^{36} +$$$$53\!\cdots\!55$$$$T^{37} +$$$$52\!\cdots\!17$$$$T^{38} +$$$$29\!\cdots\!18$$$$T^{39} +$$$$33\!\cdots\!01$$$$T^{40}$$)
$71$ ($$1 - T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + T + 71 T^{2}$$)($$1 + 2 T + 71 T^{2}$$)($$1 - 3 T - 7 T^{2} - 213 T^{3} + 5041 T^{4}$$)($$1 - 12 T + 170 T^{2} - 852 T^{3} + 5041 T^{4}$$)($$1 + 118 T^{2} + 5041 T^{4}$$)($$1 + 3 T - 7 T^{2} + 213 T^{3} + 5041 T^{4}$$)($$1 + 129 T^{2} - 56 T^{3} + 9159 T^{4} + 357911 T^{6}$$)($$1 - 22 T + 309 T^{2} - 3228 T^{3} + 21939 T^{4} - 110902 T^{5} + 357911 T^{6}$$)($$1 + 22 T + 309 T^{2} + 3228 T^{3} + 21939 T^{4} + 110902 T^{5} + 357911 T^{6}$$)($$1 + 129 T^{2} + 56 T^{3} + 9159 T^{4} + 357911 T^{6}$$)($$1 + 336 T^{2} + 58644 T^{4} + 7325325 T^{6} + 719409326 T^{8} + 56796003109 T^{10} + 3626542412366 T^{12} + 186148822121325 T^{14} + 7512313050263124 T^{16} + 216973186498575696 T^{18} + 3255243551009881201 T^{20}$$)($$1 + 86 T + 4381 T^{2} + 161393 T^{3} + 4751593 T^{4} + 117237598 T^{5} + 2504196342 T^{6} + 47287231405 T^{7} + 802182116929 T^{8} + 12371512985841 T^{9} + 175156069890510 T^{10} + 2294291010191878 T^{11} + 27986288362685489 T^{12} + 319629084849093298 T^{13} + 3433341088218201345 T^{14} + 34811199581426803904 T^{15} +$$$$33\!\cdots\!95$$$$T^{16} +$$$$30\!\cdots\!98$$$$T^{17} +$$$$26\!\cdots\!75$$$$T^{18} +$$$$21\!\cdots\!58$$$$T^{19} +$$$$16\!\cdots\!95$$$$T^{20} +$$$$12\!\cdots\!44$$$$T^{21} +$$$$87\!\cdots\!45$$$$T^{22} +$$$$57\!\cdots\!98$$$$T^{23} +$$$$35\!\cdots\!69$$$$T^{24} +$$$$20\!\cdots\!98$$$$T^{25} +$$$$11\!\cdots\!10$$$$T^{26} +$$$$56\!\cdots\!71$$$$T^{27} +$$$$26\!\cdots\!29$$$$T^{28} +$$$$10\!\cdots\!55$$$$T^{29} +$$$$41\!\cdots\!22$$$$T^{30} +$$$$13\!\cdots\!78$$$$T^{31} +$$$$39\!\cdots\!33$$$$T^{32} +$$$$94\!\cdots\!43$$$$T^{33} +$$$$18\!\cdots\!01$$$$T^{34} +$$$$25\!\cdots\!26$$$$T^{35} +$$$$21\!\cdots\!61$$$$T^{36}$$)($$1 - 86 T + 4381 T^{2} - 161393 T^{3} + 4751593 T^{4} - 117237598 T^{5} + 2504196342 T^{6} - 47287231405 T^{7} + 802182116929 T^{8} - 12371512985841 T^{9} + 175156069890510 T^{10} - 2294291010191878 T^{11} + 27986288362685489 T^{12} - 319629084849093298 T^{13} + 3433341088218201345 T^{14} - 34811199581426803904 T^{15} +$$$$33\!\cdots\!95$$$$T^{16} -$$$$30\!\cdots\!98$$$$T^{17} +$$$$26\!\cdots\!75$$$$T^{18} -$$$$21\!\cdots\!58$$$$T^{19} +$$$$16\!\cdots\!95$$$$T^{20} -$$$$12\!\cdots\!44$$$$T^{21} +$$$$87\!\cdots\!45$$$$T^{22} -$$$$57\!\cdots\!98$$$$T^{23} +$$$$35\!\cdots\!69$$$$T^{24} -$$$$20\!\cdots\!98$$$$T^{25} +$$$$11\!\cdots\!10$$$$T^{26} -$$$$56\!\cdots\!71$$$$T^{27} +$$$$26\!\cdots\!29$$$$T^{28} -$$$$10\!\cdots\!55$$$$T^{29} +$$$$41\!\cdots\!22$$$$T^{30} -$$$$13\!\cdots\!78$$$$T^{31} +$$$$39\!\cdots\!33$$$$T^{32} -$$$$94\!\cdots\!43$$$$T^{33} +$$$$18\!\cdots\!01$$$$T^{34} -$$$$25\!\cdots\!26$$$$T^{35} +$$$$21\!\cdots\!61$$$$T^{36}$$)($$1 - 31 T + 1322 T^{2} - 31320 T^{3} + 798364 T^{4} - 15452678 T^{5} + 299944301 T^{6} - 4942514823 T^{7} + 79706547295 T^{8} - 1148868791647 T^{9} + 16066350850621 T^{10} - 206368868523456 T^{11} + 2564945996247701 T^{12} - 29747128248307392 T^{13} + 333708285975141834 T^{14} - 3526768418326305726 T^{15} + 36069118289707342370 T^{16} -$$$$34\!\cdots\!13$$$$T^{17} +$$$$32\!\cdots\!14$$$$T^{18} -$$$$29\!\cdots\!04$$$$T^{19} +$$$$25\!\cdots\!70$$$$T^{20} -$$$$20\!\cdots\!84$$$$T^{21} +$$$$16\!\cdots\!74$$$$T^{22} -$$$$12\!\cdots\!43$$$$T^{23} +$$$$91\!\cdots\!70$$$$T^{24} -$$$$63\!\cdots\!26$$$$T^{25} +$$$$42\!\cdots\!14$$$$T^{26} -$$$$27\!\cdots\!72$$$$T^{27} +$$$$16\!\cdots\!61$$$$T^{28} -$$$$94\!\cdots\!36$$$$T^{29} +$$$$52\!\cdots\!21$$$$T^{30} -$$$$26\!\cdots\!37$$$$T^{31} +$$$$13\!\cdots\!95$$$$T^{32} -$$$$57\!\cdots\!53$$$$T^{33} +$$$$24\!\cdots\!81$$$$T^{34} -$$$$90\!\cdots\!78$$$$T^{35} +$$$$33\!\cdots\!44$$$$T^{36} -$$$$92\!\cdots\!20$$$$T^{37} +$$$$27\!\cdots\!42$$$$T^{38} -$$$$46\!\cdots\!61$$$$T^{39} +$$$$10\!\cdots\!01$$$$T^{40}$$)($$1 + 883 T^{2} + 375953 T^{4} + 102911488 T^{6} + 20417028278 T^{8} + 3145772941707 T^{10} + 394935886833835 T^{12} + 41937626625065310 T^{14} + 3880901102881147810 T^{16} +$$$$32\!\cdots\!10$$$$T^{18} +$$$$23\!\cdots\!51$$$$T^{20} +$$$$16\!\cdots\!10$$$$T^{22} +$$$$98\!\cdots\!10$$$$T^{24} +$$$$53\!\cdots\!10$$$$T^{26} +$$$$25\!\cdots\!35$$$$T^{28} +$$$$10\!\cdots\!07$$$$T^{30} +$$$$33\!\cdots\!98$$$$T^{32} +$$$$85\!\cdots\!28$$$$T^{34} +$$$$15\!\cdots\!13$$$$T^{36} +$$$$18\!\cdots\!63$$$$T^{38} +$$$$10\!\cdots\!01$$$$T^{40}$$)($$1 + 31 T + 1322 T^{2} + 31320 T^{3} + 798364 T^{4} + 15452678 T^{5} + 299944301 T^{6} + 4942514823 T^{7} + 79706547295 T^{8} + 1148868791647 T^{9} + 16066350850621 T^{10} + 206368868523456 T^{11} + 2564945996247701 T^{12} + 29747128248307392 T^{13} + 333708285975141834 T^{14} + 3526768418326305726 T^{15} + 36069118289707342370 T^{16} +$$$$34\!\cdots\!13$$$$T^{17} +$$$$32\!\cdots\!14$$$$T^{18} +$$$$29\!\cdots\!04$$$$T^{19} +$$$$25\!\cdots\!70$$$$T^{20} +$$$$20\!\cdots\!84$$$$T^{21} +$$$$16\!\cdots\!74$$$$T^{22} +$$$$12\!\cdots\!43$$$$T^{23} +$$$$91\!\cdots\!70$$$$T^{24} +$$$$63\!\cdots\!26$$$$T^{25} +$$$$42\!\cdots\!14$$$$T^{26} +$$$$27\!\cdots\!72$$$$T^{27} +$$$$16\!\cdots\!61$$$$T^{28} +$$$$94\!\cdots\!36$$$$T^{29} +$$$$52\!\cdots\!21$$$$T^{30} +$$$$26\!\cdots\!37$$$$T^{31} +$$$$13\!\cdots\!95$$$$T^{32} +$$$$57\!\cdots\!53$$$$T^{33} +$$$$24\!\cdots\!81$$$$T^{34} +$$$$90\!\cdots\!78$$$$T^{35} +$$$$33\!\cdots\!44$$$$T^{36} +$$$$92\!\cdots\!20$$$$T^{37} +$$$$27\!\cdots\!42$$$$T^{38} +$$$$46\!\cdots\!61$$$$T^{39} +$$$$10\!\cdots\!01$$$$T^{40}$$)
$73$ ($$1 + 11 T + 73 T^{2}$$)($$1 + 73 T^{2}$$)($$1 - 11 T + 73 T^{2}$$)($$1 + 2 T + 73 T^{2}$$)($$1 + 3 T + 137 T^{2} + 219 T^{3} + 5329 T^{4}$$)($$1 - 24 T + 272 T^{2} - 1752 T^{3} + 5329 T^{4}$$)($$1 - 4 T^{2} + 5329 T^{4}$$)($$1 - 3 T + 137 T^{2} - 219 T^{3} + 5329 T^{4}$$)($$1 + 14 T + 212 T^{2} + 1743 T^{3} + 15476 T^{4} + 74606 T^{5} + 389017 T^{6}$$)($$1 - 15 T + 245 T^{2} - 2119 T^{3} + 17885 T^{4} - 79935 T^{5} + 389017 T^{6}$$)($$1 + 15 T + 245 T^{2} + 2119 T^{3} + 17885 T^{4} + 79935 T^{5} + 389017 T^{6}$$)($$1 - 14 T + 212 T^{2} - 1743 T^{3} + 15476 T^{4} - 74606 T^{5} + 389017 T^{6}$$)($$1 + 609 T^{2} + 173420 T^{4} + 30452178 T^{6} + 3655326744 T^{8} + 313602113089 T^{10} + 19479236218776 T^{12} + 864788289818898 T^{14} + 26244381523038380 T^{16} + 491134195963495329 T^{18} + 4297625829703557649 T^{20}$$)($$1 - 27 T + 1007 T^{2} - 19815 T^{3} + 447765 T^{4} - 7156446 T^{5} + 124212868 T^{6} - 1702517030 T^{7} + 24770220974 T^{8} - 300583815481 T^{9} + 3832197589506 T^{10} - 42031917749538 T^{11} + 482153954860024 T^{12} - 4847925257622480 T^{13} + 50891805726542784 T^{14} - 473582143472657046 T^{15} + 4599037907896224962 T^{16} - 39832962881131374483 T^{17} +$$$$36\!\cdots\!59$$$$T^{18} -$$$$29\!\cdots\!59$$$$T^{19} +$$$$24\!\cdots\!98$$$$T^{20} -$$$$18\!\cdots\!82$$$$T^{21} +$$$$14\!\cdots\!44$$$$T^{22} -$$$$10\!\cdots\!40$$$$T^{23} +$$$$72\!\cdots\!36$$$$T^{24} -$$$$46\!\cdots\!86$$$$T^{25} +$$$$30\!\cdots\!86$$$$T^{26} -$$$$17\!\cdots\!53$$$$T^{27} +$$$$10\!\cdots\!26$$$$T^{28} -$$$$53\!\cdots\!10$$$$T^{29} +$$$$28\!\cdots\!28$$$$T^{30} -$$$$11\!\cdots\!18$$$$T^{31} +$$$$54\!\cdots\!85$$$$T^{32} -$$$$17\!\cdots\!55$$$$T^{33} +$$$$65\!\cdots\!27$$$$T^{34} -$$$$12\!\cdots\!31$$$$T^{35} +$$$$34\!\cdots\!69$$$$T^{36}$$)($$1 + 27 T + 1007 T^{2} + 19815 T^{3} + 447765 T^{4} + 7156446 T^{5} + 124212868 T^{6} + 1702517030 T^{7} + 24770220974 T^{8} + 300583815481 T^{9} + 3832197589506 T^{10} + 42031917749538 T^{11} + 482153954860024 T^{12} + 4847925257622480 T^{13} + 50891805726542784 T^{14} + 473582143472657046 T^{15} + 4599037907896224962 T^{16} + 39832962881131374483 T^{17} +$$$$36\!\cdots\!59$$$$T^{18} +$$$$29\!\cdots\!59$$$$T^{19} +$$$$24\!\cdots\!98$$$$T^{20} +$$$$18\!\cdots\!82$$$$T^{21} +$$$$14\!\cdots\!44$$$$T^{22} +$$$$10\!\cdots\!40$$$$T^{23} +$$$$72\!\cdots\!36$$$$T^{24} +$$$$46\!\cdots\!86$$$$T^{25} +$$$$30\!\cdots\!86$$$$T^{26} +$$$$17\!\cdots\!53$$$$T^{27} +$$$$10\!\cdots\!26$$$$T^{28} +$$$$53\!\cdots\!10$$$$T^{29} +$$$$28\!\cdots\!28$$$$T^{30} +$$$$11\!\cdots\!18$$$$T^{31} +$$$$54\!\cdots\!85$$$$T^{32} +$$$$17\!\cdots\!55$$$$T^{33} +$$$$65\!\cdots\!27$$$$T^{34} +$$$$12\!\cdots\!31$$$$T^{35} +$$$$34\!\cdots\!69$$$$T^{36}$$)($$1 - 26 T + 1291 T^{2} - 27722 T^{3} + 783640 T^{4} - 14380525 T^{5} + 300791939 T^{6} - 4827381656 T^{7} + 82453306014 T^{8} - 1176453930867 T^{9} + 17238057078813 T^{10} - 221303711720328 T^{11} + 2861428005828764 T^{12} - 33345380649687651 T^{13} + 387137229185140814 T^{14} - 4120923032974543647 T^{15} + 43437310660293055700 T^{16} -$$$$42\!\cdots\!70$$$$T^{17} +$$$$40\!\cdots\!62$$$$T^{18} -$$$$36\!\cdots\!52$$$$T^{19} +$$$$32\!\cdots\!57$$$$T^{20} -$$$$26\!\cdots\!96$$$$T^{21} +$$$$21\!\cdots\!98$$$$T^{22} -$$$$16\!\cdots\!90$$$$T^{23} +$$$$12\!\cdots\!00$$$$T^{24} -$$$$85\!\cdots\!71$$$$T^{25} +$$$$58\!\cdots\!46$$$$T^{26} -$$$$36\!\cdots\!47$$$$T^{27} +$$$$23\!\cdots\!84$$$$T^{28} -$$$$13\!\cdots\!64$$$$T^{29} +$$$$74\!\cdots\!37$$$$T^{30} -$$$$36\!\cdots\!59$$$$T^{31} +$$$$18\!\cdots\!94$$$$T^{32} -$$$$80\!\cdots\!48$$$$T^{33} +$$$$36\!\cdots\!51$$$$T^{34} -$$$$12\!\cdots\!25$$$$T^{35} +$$$$50\!\cdots\!40$$$$T^{36} -$$$$13\!\cdots\!66$$$$T^{37} +$$$$44\!\cdots\!79$$$$T^{38} -$$$$65\!\cdots\!62$$$$T^{39} +$$$$18\!\cdots\!01$$$$T^{40}$$)($$1 + 686 T^{2} + 236929 T^{4} + 55292228 T^{6} + 9832089880 T^{8} + 1421510767666 T^{10} + 173988005462946 T^{12} + 18523591874249588 T^{14} + 1747963825372995868 T^{16} +$$$$14\!\cdots\!98$$$$T^{18} +$$$$11\!\cdots\!53$$$$T^{20} +$$$$78\!\cdots\!42$$$$T^{22} +$$$$49\!\cdots\!88$$$$T^{24} +$$$$28\!\cdots\!32$$$$T^{26} +$$$$14\!\cdots\!26$$$$T^{28} +$$$$61\!\cdots\!34$$$$T^{30} +$$$$22\!\cdots\!80$$$$T^{32} +$$$$67\!\cdots\!52$$$$T^{34} +$$$$15\!\cdots\!69$$$$T^{36} +$$$$23\!\cdots\!34$$$$T^{38} +$$$$18\!\cdots\!01$$$$T^{40}$$)($$1 + 26 T + 1291 T^{2} + 27722 T^{3} + 783640 T^{4} + 14380525 T^{5} + 300791939 T^{6} + 4827381656 T^{7} + 82453306014 T^{8} + 1176453930867 T^{9} + 17238057078813 T^{10} + 221303711720328 T^{11} + 2861428005828764 T^{12} + 33345380649687651 T^{13} + 387137229185140814 T^{14} + 4120923032974543647 T^{15} + 43437310660293055700 T^{16} +$$$$42\!\cdots\!70$$$$T^{17} +$$$$40\!\cdots\!62$$$$T^{18} +$$$$36\!\cdots\!52$$$$T^{19} +$$$$32\!\cdots\!57$$$$T^{20} +$$$$26\!\cdots\!96$$$$T^{21} +$$$$21\!\cdots\!98$$$$T^{22} +$$$$16\!\cdots\!90$$$$T^{23} +$$$$12\!\cdots\!00$$$$T^{24} +$$$$85\!\cdots\!71$$$$T^{25} +$$$$58\!\cdots\!46$$$$T^{26} +$$$$36\!\cdots\!47$$$$T^{27} +$$$$23\!\cdots\!84$$$$T^{28} +$$$$13\!\cdots\!64$$$$T^{29} +$$$$74\!\cdots\!37$$$$T^{30} +$$$$36\!\cdots\!59$$$$T^{31} +$$$$18\!\cdots\!94$$$$T^{32} +$$$$80\!\cdots\!48$$$$T^{33} +$$$$36\!\cdots\!51$$$$T^{34} +$$$$12\!\cdots\!25$$$$T^{35} +$$$$50\!\cdots\!40$$$$T^{36} +$$$$13\!\cdots\!66$$$$T^{37} +$$$$44\!\cdots\!79$$$$T^{38} +$$$$65\!\cdots\!62$$$$T^{39} +$$$$18\!\cdots\!01$$$$T^{40}$$)
$79$ ($$1 + 5 T + 79 T^{2}$$)($$1 - 12 T + 79 T^{2}$$)($$1 + 5 T + 79 T^{2}$$)($$1 + 8 T + 79 T^{2}$$)($$1 + 5 T + 163 T^{2} + 395 T^{3} + 6241 T^{4}$$)($$1 - 4 T + 154 T^{2} - 316 T^{3} + 6241 T^{4}$$)($$( 1 + 6 T + 79 T^{2} )^{2}$$)($$1 + 5 T + 163 T^{2} + 395 T^{3} + 6241 T^{4}$$)($$1 - 3 T + 212 T^{2} - 391 T^{3} + 16748 T^{4} - 18723 T^{5} + 493039 T^{6}$$)($$1 + 10 T + 254 T^{2} + 1581 T^{3} + 20066 T^{4} + 62410 T^{5} + 493039 T^{6}$$)($$1 + 10 T + 254 T^{2} + 1581 T^{3} + 20066 T^{4} + 62410 T^{5} + 493039 T^{6}$$)($$1 - 3 T + 212 T^{2} - 391 T^{3} + 16748 T^{4} - 18723 T^{5} + 493039 T^{6}$$)($$( 1 + 28 T + 449 T^{2} + 5527 T^{3} + 64884 T^{4} + 640171 T^{5} + 5125836 T^{6} + 34494007 T^{7} + 221374511 T^{8} + 1090602268 T^{9} + 3077056399 T^{10} )^{2}$$)($$1 - 17 T + 946 T^{2} - 13939 T^{3} + 432350 T^{4} - 5643790 T^{5} + 128080842 T^{6} - 1504658537 T^{7} + 27779437033 T^{8} - 297208185691 T^{9} + 4716645703113 T^{10} - 46373717355855 T^{11} + 653486932362430 T^{12} - 5942510278530939 T^{13} + 75878465997252205 T^{14} - 640670189666756761 T^{15} + 7507412874523164847 T^{16} - 58935399487024227850 T^{17} +$$$$63\!\cdots\!79$$$$T^{18} -$$$$46\!\cdots\!50$$$$T^{19} +$$$$46\!\cdots\!27$$$$T^{20} -$$$$31\!\cdots\!79$$$$T^{21} +$$$$29\!\cdots\!05$$$$T^{22} -$$$$18\!\cdots\!61$$$$T^{23} +$$$$15\!\cdots\!30$$$$T^{24} -$$$$89\!\cdots\!45$$$$T^{25} +$$$$71\!\cdots\!93$$$$T^{26} -$$$$35\!\cdots\!29$$$$T^{27} +$$$$26\!\cdots\!33$$$$T^{28} -$$$$11\!\cdots\!23$$$$T^{29} +$$$$75\!\cdots\!22$$$$T^{30} -$$$$26\!\cdots\!10$$$$T^{31} +$$$$15\!\cdots\!50$$$$T^{32} -$$$$40\!\cdots\!61$$$$T^{33} +$$$$21\!\cdots\!66$$$$T^{34} -$$$$30\!\cdots\!03$$$$T^{35} +$$$$14\!\cdots\!61$$$$T^{36}$$)($$1 - 17 T + 946 T^{2} - 13939 T^{3} + 432350 T^{4} - 5643790 T^{5} + 128080842 T^{6} - 1504658537 T^{7} + 27779437033 T^{8} - 297208185691 T^{9} + 4716645703113 T^{10} - 46373717355855 T^{11} + 653486932362430 T^{12} - 5942510278530939 T^{13} + 75878465997252205 T^{14} - 640670189666756761 T^{15} + 7507412874523164847 T^{16} - 58935399487024227850 T^{17} +$$$$63\!\cdots\!79$$$$T^{18} -$$$$46\!\cdots\!50$$$$T^{19} +$$$$46\!\cdots\!27$$$$T^{20} -$$$$31\!\cdots\!79$$$$T^{21} +$$$$29\!\cdots\!05$$$$T^{22} -$$$$18\!\cdots\!61$$$$T^{23} +$$$$15\!\cdots\!30$$$$T^{24} -$$$$89\!\cdots\!45$$$$T^{25} +$$$$71\!\cdots\!93$$$$T^{26} -$$$$35\!\cdots\!29$$$$T^{27} +$$$$26\!\cdots\!33$$$$T^{28} -$$$$11\!\cdots\!23$$$$T^{29} +$$$$75\!\cdots\!22$$$$T^{30} -$$$$26\!\cdots\!10$$$$T^{31} +$$$$15\!\cdots\!50$$$$T^{32} -$$$$40\!\cdots\!61$$$$T^{33} +$$$$21\!\cdots\!66$$$$T^{34} -$$$$30\!\cdots\!03$$$$T^{35} +$$$$14\!\cdots\!61$$$$T^{36}$$)($$1 - 39 T + 1449 T^{2} - 35558 T^{3} + 812562 T^{4} - 15192159 T^{5} + 267563164 T^{6} - 4155506201 T^{7} + 61579924350 T^{8} - 834905764293 T^{9} + 10910568449802 T^{10} - 133193600438580 T^{11} + 1578428678113741 T^{12} - 17695120582970783 T^{13} + 193525885871052352 T^{14} - 2018288570921152211 T^{15} + 20606670235364380219 T^{16} -$$$$20\!\cdots\!02$$$$T^{17} +$$$$19\!\cdots\!13$$$$T^{18} -$$$$17\!\cdots\!42$$$$T^{19} +$$$$16\!\cdots\!26$$$$T^{20} -$$$$14\!\cdots\!18$$$$T^{21} +$$$$12\!\cdots\!33$$$$T^{22} -$$$$99\!\cdots\!78$$$$T^{23} +$$$$80\!\cdots\!39$$$$T^{24} -$$$$62\!\cdots\!89$$$$T^{25} +$$$$47\!\cdots\!92$$$$T^{26} -$$$$33\!\cdots\!97$$$$T^{27} +$$$$23\!\cdots\!01$$$$T^{28} -$$$$15\!\cdots\!20$$$$T^{29} +$$$$10\!\cdots\!02$$$$T^{30} -$$$$62\!\cdots\!47$$$$T^{31} +$$$$36\!\cdots\!50$$$$T^{32} -$$$$19\!\cdots\!39$$$$T^{33} +$$$$98\!\cdots\!84$$$$T^{34} -$$$$44\!\cdots\!41$$$$T^{35} +$$$$18\!\cdots\!02$$$$T^{36} -$$$$64\!\cdots\!22$$$$T^{37} +$$$$20\!\cdots\!89$$$$T^{38} -$$$$44\!\cdots\!41$$$$T^{39} +$$$$89\!\cdots\!01$$$$T^{40}$$)($$( 1 + 5 T + 507 T^{2} + 1337 T^{3} + 119796 T^{4} + 92825 T^{5} + 18138748 T^{6} - 10048960 T^{7} + 2022931171 T^{8} - 2401078215 T^{9} + 178030821825 T^{10} - 189685178985 T^{11} + 12625113438211 T^{12} - 4954529189440 T^{13} + 706505703838588 T^{14} + 285627760237175 T^{15} + 29120904821593716 T^{16} + 25675626314494583 T^{17} + 769174166622626427 T^{18} + 599257979913091595 T^{19} + 9468276082626847201 T^{20} )^{2}$$)($$1 - 39 T + 1449 T^{2} - 35558 T^{3} + 812562 T^{4} - 15192159 T^{5} + 267563164 T^{6} - 4155506201 T^{7} + 61579924350 T^{8} - 834905764293 T^{9} + 10910568449802 T^{10} - 133193600438580 T^{11} + 1578428678113741 T^{12} - 17695120582970783 T^{13} + 193525885871052352 T^{14} - 2018288570921152211 T^{15} + 20606670235364380219 T^{16} -$$$$20\!\cdots\!02$$$$T^{17} +$$$$19\!\cdots\!13$$$$T^{18} -$$$$17\!\cdots\!42$$$$T^{19} +$$$$16\!\cdots\!26$$$$T^{20} -$$$$14\!\cdots\!18$$$$T^{21} +$$$$12\!\cdots\!33$$$$T^{22} -$$$$99\!\cdots\!78$$$$T^{23} +$$$$80\!\cdots\!39$$$$T^{24} -$$$$62\!\cdots\!89$$$$T^{25} +$$$$47\!\cdots\!92$$$$T^{26} -$$$$33\!\cdots\!97$$$$T^{27} +$$$$23\!\cdots\!01$$$$T^{28} -$$$$15\!\cdots\!20$$$$T^{29} +$$$$10\!\cdots\!02$$$$T^{30} -$$$$62\!\cdots\!47$$$$T^{31} +$$$$36\!\cdots\!50$$$$T^{32} -$$$$19\!\cdots\!39$$$$T^{33} +$$$$98\!\cdots\!84$$$$T^{34} -$$$$44\!\cdots\!41$$$$T^{35} +$$$$18\!\cdots\!02$$$$T^{36} -$$$$64\!\cdots\!22$$$$T^{37} +$$$$20\!\cdots\!89$$$$T^{38} -$$$$44\!\cdots\!41$$$$T^{39} +$$$$89\!\cdots\!01$$$$T^{40}$$)
$83$ ($$1 - 9 T + 83 T^{2}$$)($$1 + 17 T + 83 T^{2}$$)($$1 - 9 T + 83 T^{2}$$)($$1 - 15 T + 83 T^{2}$$)($$1 - 3 T - 43 T^{2} - 249 T^{3} + 6889 T^{4}$$)($$1 - 18 T + 215 T^{2} - 1494 T^{3} + 6889 T^{4}$$)($$( 1 - T + 83 T^{2} )^{2}$$)($$1 - 3 T - 43 T^{2} - 249 T^{3} + 6889 T^{4}$$)($$1 - 19 T + 248 T^{2} - 2231 T^{3} + 20584 T^{4} - 130891 T^{5} + 571787 T^{6}$$)($$1 + 4 T + 154 T^{2} + 747 T^{3} + 12782 T^{4} + 27556 T^{5} + 571787 T^{6}$$)($$1 + 4 T + 154 T^{2} + 747 T^{3} + 12782 T^{4} + 27556 T^{5} + 571787 T^{6}$$)($$1 - 19 T + 248 T^{2} - 2231 T^{3} + 20584 T^{4} - 130891 T^{5} + 571787 T^{6}$$)($$( 1 + 19 T + 500 T^{2} + 6136 T^{3} + 88868 T^{4} + 757387 T^{5} + 7376044 T^{6} + 42270904 T^{7} + 285893500 T^{8} + 901708099 T^{9} + 3939040643 T^{10} )^{2}$$)($$1 + 12 T + 1078 T^{2} + 11305 T^{3} + 561490 T^{4} + 5215328 T^{5} + 188751070 T^{6} + 1566682212 T^{7} + 46085293241 T^{8} + 344087059159 T^{9} + 8713394246075 T^{10} + 58850822346822 T^{11} + 1327322439513751 T^{12} + 8154166109275604 T^{13} + 167189447742982401 T^{14} + 939442501420537189 T^{15} + 17709135064744613010 T^{16} + 91493035467322566291 T^{17} +$$$$15\!\cdots\!39$$$$T^{18} +$$$$75\!\cdots\!53$$$$T^{19} +$$$$12\!\cdots\!90$$$$T^{20} +$$$$53\!\cdots\!43$$$$T^{21} +$$$$79\!\cdots\!21$$$$T^{22} +$$$$32\!\cdots\!72$$$$T^{23} +$$$$43\!\cdots\!19$$$$T^{24} +$$$$15\!\cdots\!94$$$$T^{25} +$$$$19\!\cdots\!75$$$$T^{26} +$$$$64\!\cdots\!77$$$$T^{27} +$$$$71\!\cdots\!09$$$$T^{28} +$$$$20\!\cdots\!04$$$$T^{29} +$$$$20\!\cdots\!70$$$$T^{30} +$$$$46\!\cdots\!64$$$$T^{31} +$$$$41\!\cdots\!10$$$$T^{32} +$$$$69\!\cdots\!35$$$$T^{33} +$$$$54\!\cdots\!18$$$$T^{34} +$$$$50\!\cdots\!76$$$$T^{35} +$$$$34\!\cdots\!09$$$$T^{36}$$)($$1 + 12 T + 1078 T^{2} + 11305 T^{3} + 561490 T^{4} + 5215328 T^{5} + 188751070 T^{6} + 1566682212 T^{7} + 46085293241 T^{8} + 344087059159 T^{9} + 8713394246075 T^{10} + 58850822346822 T^{11} + 1327322439513751 T^{12} + 8154166109275604 T^{13} + 167189447742982401 T^{14} + 939442501420537189 T^{15} + 17709135064744613010 T^{16} + 91493035467322566291 T^{17} +$$$$15\!\cdots\!39$$$$T^{18} +$$$$75\!\cdots\!53$$$$T^{19} +$$$$12\!\cdots\!90$$$$T^{20} +$$$$53\!\cdots\!43$$$$T^{21} +$$$$79\!\cdots\!21$$$$T^{22} +$$$$32\!\cdots\!72$$$$T^{23} +$$$$43\!\cdots\!19$$$$T^{24} +$$$$15\!\cdots\!94$$$$T^{25} +$$$$19\!\cdots\!75$$$$T^{26} +$$$$64\!\cdots\!77$$$$T^{27} +$$$$71\!\cdots\!09$$$$T^{28} +$$$$20\!\cdots\!04$$$$T^{29} +$$$$20\!\cdots\!70$$$$T^{30} +$$$$46\!\cdots\!64$$$$T^{31} +$$$$41\!\cdots\!10$$$$T^{32} +$$$$69\!\cdots\!35$$$$T^{33} +$$$$54\!\cdots\!18$$$$T^{34} +$$$$50\!\cdots\!76$$$$T^{35} +$$$$34\!\cdots\!09$$$$T^{36}$$)($$1 - 13 T + 940 T^{2} - 11084 T^{3} + 440421 T^{4} - 4812065 T^{5} + 137986658 T^{6} - 1414251517 T^{7} + 32565902809 T^{8} - 315087302047 T^{9} + 6164011043080 T^{10} - 56448298149495 T^{11} + 970896449158067 T^{12} - 8418999649219894 T^{13} + 130224284451608500 T^{14} - 1068214850843374843 T^{15} + 15093540496126075108 T^{16} -$$$$11\!\cdots\!18$$$$T^{17} +$$$$15\!\cdots\!46$$$$T^{18} -$$$$11\!\cdots\!02$$$$T^{19} +$$$$13\!\cdots\!36$$$$T^{20} -$$$$92\!\cdots\!66$$$$T^{21} +$$$$10\!\cdots\!94$$$$T^{22} -$$$$66\!\cdots\!66$$$$T^{23} +$$$$71\!\cdots\!68$$$$T^{24} -$$$$42\!\cdots\!49$$$$T^{25} +$$$$42\!\cdots\!00$$$$T^{26} -$$$$22\!\cdots\!38$$$$T^{27} +$$$$21\!\cdots\!47$$$$T^{28} -$$$$10\!\cdots\!85$$$$T^{29} +$$$$95\!\cdots\!20$$$$T^{30} -$$$$40\!\cdots\!49$$$$T^{31} +$$$$34\!\cdots\!49$$$$T^{32} -$$$$12\!\cdots\!71$$$$T^{33} +$$$$10\!\cdots\!82$$$$T^{34} -$$$$29\!\cdots\!55$$$$T^{35} +$$$$22\!\cdots\!01$$$$T^{36} -$$$$46\!\cdots\!32$$$$T^{37} +$$$$32\!\cdots\!60$$$$T^{38} -$$$$37\!\cdots\!11$$$$T^{39} +$$$$24\!\cdots\!01$$$$T^{40}$$)($$( 1 + 34 T + 1205 T^{2} + 26070 T^{3} + 543584 T^{4} + 8719411 T^{5} + 133183791 T^{6} + 1688637709 T^{7} + 20356364785 T^{8} + 209959755927 T^{9} + 2059284856595 T^{10} + 17426659741941 T^{11} + 140234997003865 T^{12} + 965541089715983 T^{13} + 6320679105274911 T^{14} + 34346114312021273 T^{15} + 177719555917414496 T^{16} + 707436849299575890 T^{17} + 2714012139727544405 T^{18} + 6355968679096373702 T^{19} + 15516041187205853449 T^{20} )^{2}$$)($$1 - 13 T + 940 T^{2} - 11084 T^{3} + 440421 T^{4} - 4812065 T^{5} + 137986658 T^{6} - 1414251517 T^{7} + 32565902809 T^{8} - 315087302047 T^{9} + 6164011043080 T^{10} - 56448298149495 T^{11} + 970896449158067 T^{12} - 8418999649219894 T^{13} + 130224284451608500 T^{14} - 1068214850843374843 T^{15} + 15093540496126075108 T^{16} -$$$$11\!\cdots\!18$$$$T^{17} +$$$$15\!\cdots\!46$$$$T^{18} -$$$$11\!\cdots\!02$$$$T^{19} +$$$$13\!\cdots\!36$$$$T^{20} -$$$$92\!\cdots\!66$$$$T^{21} +$$$$10\!\cdots\!94$$$$T^{22} -$$$$66\!\cdots\!66$$$$T^{23} +$$$$71\!\cdots\!68$$$$T^{24} -$$$$42\!\cdots\!49$$$$T^{25} +$$$$42\!\cdots\!00$$$$T^{26} -$$$$22\!\cdots\!38$$$$T^{27} +$$$$21\!\cdots\!47$$$$T^{28} -$$$$10\!\cdots\!85$$$$T^{29} +$$$$95\!\cdots\!20$$$$T^{30} -$$$$40\!\cdots\!49$$$$T^{31} +$$$$34\!\cdots\!49$$$$T^{32} -$$$$12\!\cdots\!71$$$$T^{33} +$$$$10\!\cdots\!82$$$$T^{34} -$$$$29\!\cdots\!55$$$$T^{35} +$$$$22\!\cdots\!01$$$$T^{36} -$$$$46\!\cdots\!32$$$$T^{37} +$$$$32\!\cdots\!60$$$$T^{38} -$$$$37\!\cdots\!11$$$$T^{39} +$$$$24\!\cdots\!01$$$$T^{40}$$)
$89$ ($$1 - T + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 + T + 89 T^{2}$$)($$1 - 4 T + 89 T^{2}$$)($$1 - 3 T + 169 T^{2} - 267 T^{3} + 7921 T^{4}$$)($$1 - 12 T + 196 T^{2} - 1068 T^{3} + 7921 T^{4}$$)($$1 - 116 T^{2} + 7921 T^{4}$$)($$1 + 3 T + 169 T^{2} + 267 T^{3} + 7921 T^{4}$$)($$1 + 26 T + 350 T^{2} + 3439 T^{3} + 31150 T^{4} + 205946 T^{5} + 704969 T^{6}$$)($$1 + 2 T + 112 T^{2} + 579 T^{3} + 9968 T^{4} + 15842 T^{5} + 704969 T^{6}$$)($$1 - 2 T + 112 T^{2} - 579 T^{3} + 9968 T^{4} - 15842 T^{5} + 704969 T^{6}$$)($$1 - 26 T + 350 T^{2} - 3439 T^{3} + 31150 T^{4} - 205946 T^{5} + 704969 T^{6}$$)($$1 + 769 T^{2} + 274572 T^{4} + 59995506 T^{6} + 8889881144 T^{8} + 933750066017 T^{10} + 70416748541624 T^{12} + 3764252496368946 T^{14} + 136457147021743692 T^{16} + 3027236791584900289 T^{18} + 31181719929966183601 T^{20}$$)($$1 + 51 T + 2269 T^{2} + 69808 T^{3} + 1913596 T^{4} + 43812335 T^{5} + 915214729 T^{6} + 16990491798 T^{7} + 292605997565 T^{8} + 4611751813072 T^{9} + 68223773399243 T^{10} + 939340780074915 T^{11} + 12244142926058626 T^{12} + 150150675566213465 T^{13} + 1754271192106775274 T^{14} + 19419208919876480401 T^{15} +$$$$20\!\cdots\!07$$$$T^{16} +$$$$20\!\cdots\!40$$$$T^{17} +$$$$20\!\cdots\!57$$$$T^{18} +$$$$18\!\cdots\!60$$$$T^{19} +$$$$16\!\cdots\!47$$$$T^{20} +$$$$13\!\cdots\!69$$$$T^{21} +$$$$11\!\cdots\!34$$$$T^{22} +$$$$83\!\cdots\!85$$$$T^{23} +$$$$60\!\cdots\!86$$$$T^{24} +$$$$41\!\cdots\!35$$$$T^{25} +$$$$26\!\cdots\!83$$$$T^{26} +$$$$16\!\cdots\!48$$$$T^{27} +$$$$91\!\cdots\!65$$$$T^{28} +$$$$47\!\cdots\!22$$$$T^{29} +$$$$22\!\cdots\!09$$$$T^{30} +$$$$96\!\cdots\!15$$$$T^{31} +$$$$37\!\cdots\!36$$$$T^{32} +$$$$12\!\cdots\!92$$$$T^{33} +$$$$35\!\cdots\!09$$$$T^{34} +$$$$70\!\cdots\!79$$$$T^{35} +$$$$12\!\cdots\!81$$$$T^{36}$$)($$1 - 51 T + 2269 T^{2} - 69808 T^{3} + 1913596 T^{4} - 43812335 T^{5} + 915214729 T^{6} - 16990491798 T^{7} + 292605997565 T^{8} - 4611751813072 T^{9} + 68223773399243 T^{10} - 939340780074915 T^{11} + 12244142926058626 T^{12} - 150150675566213465 T^{13} + 1754271192106775274 T^{14} - 19419208919876480401 T^{15} +$$$$20\!\cdots\!07$$$$T^{16} -$$$$20\!\cdots\!40$$$$T^{17} +$$$$20\!\cdots\!57$$$$T^{18} -$$$$18\!\cdots\!60$$$$T^{19} +$$$$16\!\cdots\!47$$$$T^{20} -$$$$13\!\cdots\!69$$$$T^{21} +$$$$11\!\cdots\!34$$$$T^{22} -$$$$83\!\cdots\!85$$$$T^{23} +$$$$60\!\cdots\!86$$$$T^{24} -$$$$41\!\cdots\!35$$$$T^{25} +$$$$26\!\cdots\!83$$$$T^{26} -$$$$16\!\cdots\!48$$$$T^{27} +$$$$91\!\cdots\!65$$$$T^{28} -$$$$47\!\cdots\!22$$$$T^{29} +$$$$22\!\cdots\!09$$$$T^{30} -$$$$96\!\cdots\!15$$$$T^{31} +$$$$37\!\cdots\!36$$$$T^{32} -$$$$12\!\cdots\!92$$$$T^{33} +$$$$35\!\cdots\!09$$$$T^{34} -$$$$70\!\cdots\!79$$$$T^{35} +$$$$12\!\cdots\!81$$$$T^{36}$$)($$1 - 4 T + 1028 T^{2} - 4088 T^{3} + 523306 T^{4} - 2066896 T^{5} + 176115864 T^{6} - 687204558 T^{7} + 44130361600 T^{8} - 168664694084 T^{9} + 8788135497517 T^{10} - 32564477960810 T^{11} + 1448948480228385 T^{12} - 5153430855025836 T^{13} + 203304254976165983 T^{14} - 688359262903258760 T^{15} + 24738386446626412881 T^{16} - 79304421418613845292 T^{17} +$$$$26\!\cdots\!32$$$$T^{18} -$$$$79\!\cdots\!92$$$$T^{19} +$$$$24\!\cdots\!25$$$$T^{20} -$$$$71\!\cdots\!88$$$$T^{21} +$$$$20\!\cdots\!72$$$$T^{22} -$$$$55\!\cdots\!48$$$$T^{23} +$$$$15\!\cdots\!21$$$$T^{24} -$$$$38\!\cdots\!40$$$$T^{25} +$$$$10\!\cdots\!63$$$$T^{26} -$$$$22\!\cdots\!44$$$$T^{27} +$$$$57\!\cdots\!85$$$$T^{28} -$$$$11\!\cdots\!90$$$$T^{29} +$$$$27\!\cdots\!17$$$$T^{30} -$$$$46\!\cdots\!76$$$$T^{31} +$$$$10\!\cdots\!00$$$$T^{32} -$$$$15\!\cdots\!02$$$$T^{33} +$$$$34\!\cdots\!24$$$$T^{34} -$$$$35\!\cdots\!04$$$$T^{35} +$$$$81\!\cdots\!66$$$$T^{36} -$$$$56\!\cdots\!52$$$$T^{37} +$$$$12\!\cdots\!68$$$$T^{38} -$$$$43\!\cdots\!36$$$$T^{39} +$$$$97\!\cdots\!01$$$$T^{40}$$)($$1 + 732 T^{2} + 290380 T^{4} + 81076078 T^{6} + 17694037714 T^{8} + 3187529936855 T^{10} + 489734789644473 T^{12} + 65519895614350941 T^{14} + 7737018844136455179 T^{16} +$$$$81\!\cdots\!50$$$$T^{18} +$$$$76\!\cdots\!55$$$$T^{20} +$$$$64\!\cdots\!50$$$$T^{22} +$$$$48\!\cdots\!39$$$$T^{24} +$$$$32\!\cdots\!01$$$$T^{26} +$$$$19\!\cdots\!13$$$$T^{28} +$$$$99\!\cdots\!55$$$$T^{30} +$$$$43\!\cdots\!94$$$$T^{32} +$$$$15\!\cdots\!98$$$$T^{34} +$$$$44\!\cdots\!80$$$$T^{36} +$$$$89\!\cdots\!92$$$$T^{38} +$$$$97\!\cdots\!01$$$$T^{40}$$)($$1 + 4 T + 1028 T^{2} + 4088 T^{3} + 523306 T^{4} + 2066896 T^{5} + 176115864 T^{6} + 687204558 T^{7} + 44130361600 T^{8} + 168664694084 T^{9} + 8788135497517 T^{10} + 32564477960810 T^{11} + 1448948480228385 T^{12} + 5153430855025836 T^{13} + 203304254976165983 T^{14} + 688359262903258760 T^{15} + 24738386446626412881 T^{16} + 79304421418613845292 T^{17} +$$$$26\!\cdots\!32$$$$T^{18} +$$$$79\!\cdots\!92$$$$T^{19} +$$$$24\!\cdots\!25$$$$T^{20} +$$$$71\!\cdots\!88$$$$T^{21} +$$$$20\!\cdots\!72$$$$T^{22} +$$$$55\!\cdots\!48$$$$T^{23} +$$$$15\!\cdots\!21$$$$T^{24} +$$$$38\!\cdots\!40$$$$T^{25} +$$$$10\!\cdots\!63$$$$T^{26} +$$$$22\!\cdots\!44$$$$T^{27} +$$$$57\!\cdots\!85$$$$T^{28} +$$$$11\!\cdots\!90$$$$T^{29} +$$$$27\!\cdots\!17$$$$T^{30} +$$$$46\!\cdots\!76$$$$T^{31} +$$$$10\!\cdots\!00$$$$T^{32} +$$$$15\!\cdots\!02$$$$T^{33} +$$$$34\!\cdots\!24$$$$T^{34} +$$$$35\!\cdots\!04$$$$T^{35} +$$$$81\!\cdots\!66$$$$T^{36} +$$$$56\!\cdots\!52$$$$T^{37} +$$$$12\!\cdots\!68$$$$T^{38} +$$$$43\!\cdots\!36$$$$T^{39} +$$$$97\!\cdots\!01$$$$T^{40}$$)
$97$ ($$1 + 2 T + 97 T^{2}$$)($$1 + T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 - 7 T + 97 T^{2}$$)($$1 + 14 T + 238 T^{2} + 1358 T^{3} + 9409 T^{4}$$)($$1 + 2 T + 187 T^{2} + 194 T^{3} + 9409 T^{4}$$)($$( 1 - 11 T + 97 T^{2} )^{2}$$)($$1 + 14 T + 238 T^{2} + 1358 T^{3} + 9409 T^{4}$$)($$1 - 50 T + 1122 T^{2} - 14291 T^{3} + 108834 T^{4} - 470450 T^{5} + 912673 T^{6}$$)($$1 + 21 T + 347 T^{2} + 3577 T^{3} + 33659 T^{4} + 197589 T^{5} + 912673 T^{6}$$)($$1 + 21 T + 347 T^{2} + 3577 T^{3} + 33659 T^{4} + 197589 T^{5} + 912673 T^{6}$$)($$1 - 50 T + 1122 T^{2} - 14291 T^{3} + 108834 T^{4} - 470450 T^{5} + 912673 T^{6}$$)($$( 1 - 17 T + 264 T^{2} - 2439 T^{3} + 23811 T^{4} - 156801 T^{5} + 2309667 T^{6} - 22948551 T^{7} + 240945672 T^{8} - 1504997777 T^{9} + 8587340257 T^{10} )^{2}$$)($$1 + 19 T + 1209 T^{2} + 19154 T^{3} + 675661 T^{4} + 9241955 T^{5} + 237136112 T^{6} + 2876020341 T^{7} + 59712863582 T^{8} + 655928587660 T^{9} + 11654954223677 T^{10} + 117944609895823 T^{11} + 1856060149182267 T^{12} + 17528861806014983 T^{13} + 250072895629370224 T^{14} + 2222533021348576604 T^{15} + 29240177165801608601 T^{16} +$$$$24\!\cdots\!45$$$$T^{17} +$$$$30\!\cdots\!63$$$$T^{18} +$$$$23\!\cdots\!65$$$$T^{19} +$$$$27\!\cdots\!09$$$$T^{20} +$$$$20\!\cdots\!92$$$$T^{21} +$$$$22\!\cdots\!44$$$$T^{22} +$$$$15\!\cdots\!31$$$$T^{23} +$$$$15\!\cdots\!43$$$$T^{24} +$$$$95\!\cdots\!99$$$$T^{25} +$$$$91\!\cdots\!97$$$$T^{26} +$$$$49\!\cdots\!20$$$$T^{27} +$$$$44\!\cdots\!18$$$$T^{28} +$$$$20\!\cdots\!73$$$$T^{29} +$$$$16\!\cdots\!92$$$$T^{30} +$$$$62\!\cdots\!35$$$$T^{31} +$$$$44\!\cdots\!09$$$$T^{32} +$$$$12\!\cdots\!22$$$$T^{33} +$$$$74\!\cdots\!89$$$$T^{34} +$$$$11\!\cdots\!03$$$$T^{35} +$$$$57\!\cdots\!89$$$$T^{36}$$)($$1 + 19 T + 1209 T^{2} + 19154 T^{3} + 675661 T^{4} + 9241955 T^{5} + 237136112 T^{6} + 2876020341 T^{7} + 59712863582 T^{8} + 655928587660 T^{9} + 11654954223677 T^{10} + 117944609895823 T^{11} + 1856060149182267 T^{12} + 17528861806014983 T^{13} + 250072895629370224 T^{14} + 2222533021348576604 T^{15} + 29240177165801608601 T^{16} +$$$$24\!\cdots\!45$$$$T^{17} +$$$$30\!\cdots\!63$$$$T^{18} +$$$$23\!\cdots\!65$$$$T^{19} +$$$$27\!\cdots\!09$$$$T^{20} +$$$$20\!\cdots\!92$$$$T^{21} +$$$$22\!\cdots\!44$$$$T^{22} +$$$$15\!\cdots\!31$$$$T^{23} +$$$$15\!\cdots\!43$$$$T^{24} +$$$$95\!\cdots\!99$$$$T^{25} +$$$$91\!\cdots\!97$$$$T^{26} +$$$$49\!\cdots\!20$$$$T^{27} +$$$$44\!\cdots\!18$$$$T^{28} +$$$$20\!\cdots\!73$$$$T^{29} +$$$$16\!\cdots\!92$$$$T^{30} +$$$$62\!\cdots\!35$$$$T^{31} +$$$$44\!\cdots\!09$$$$T^{32} +$$$$12\!\cdots\!22$$$$T^{33} +$$$$74\!\cdots\!89$$$$T^{34} +$$$$11\!\cdots\!03$$$$T^{35} +$$$$57\!\cdots\!89$$$$T^{36}$$)($$1 + 2 T + 1189 T^{2} + 3583 T^{3} + 696112 T^{4} + 2780155 T^{5} + 268164947 T^{6} + 1317002885 T^{7} + 76580507893 T^{8} + 438837705949 T^{9} + 17300229878303 T^{10} + 110945920301791 T^{11} + 3218716322383712 T^{12} + 22271189365451886 T^{13} + 506456339637067704 T^{14} + 3652951957138677156 T^{15} + 68610447555198868641 T^{16} +$$$$49\!\cdots\!58$$$$T^{17} +$$$$80\!\cdots\!66$$$$T^{18} +$$$$57\!\cdots\!15$$$$T^{19} +$$$$83\!\cdots\!29$$$$T^{20} +$$$$55\!\cdots\!55$$$$T^{21} +$$$$76\!\cdots\!94$$$$T^{22} +$$$$45\!\cdots\!34$$$$T^{23} +$$$$60\!\cdots\!21$$$$T^{24} +$$$$31\!\cdots\!92$$$$T^{25} +$$$$42\!\cdots\!16$$$$T^{26} +$$$$17\!\cdots\!18$$$$T^{27} +$$$$25\!\cdots\!32$$$$T^{28} +$$$$84\!\cdots\!47$$$$T^{29} +$$$$12\!\cdots\!47$$$$T^{30} +$$$$31\!\cdots\!97$$$$T^{31} +$$$$53\!\cdots\!13$$$$T^{32} +$$$$88\!\cdots\!45$$$$T^{33} +$$$$17\!\cdots\!43$$$$T^{34} +$$$$17\!\cdots\!15$$$$T^{35} +$$$$42\!\cdots\!52$$$$T^{36} +$$$$21\!\cdots\!71$$$$T^{37} +$$$$68\!\cdots\!21$$$$T^{38} +$$$$11\!\cdots\!66$$$$T^{39} +$$$$54\!\cdots\!01$$$$T^{40}$$)($$( 1 + 22 T + 937 T^{2} + 16324 T^{3} + 392836 T^{4} + 5615225 T^{5} + 98111241 T^{6} + 1173560157 T^{7} + 16271043365 T^{8} + 164104753461 T^{9} + 1878652272815 T^{10} + 15918161085717 T^{11} + 153094247021285 T^{12} + 1071076669169661 T^{13} + 8685717623747721 T^{14} + 48219847694612825 T^{15} + 327221390528288644 T^{16} + 1318951195820716612 T^{17} + 7343675277931212457 T^{18} + 16725083290400434774 T^{19} + 73742412689492826049 T^{20} )^{2}$$)($$1 + 2 T + 1189 T^{2} + 3583 T^{3} + 696112 T^{4} + 2780155 T^{5} + 268164947 T^{6} + 1317002885 T^{7} + 76580507893 T^{8} + 438837705949 T^{9} + 17300229878303 T^{10} + 110945920301791 T^{11} + 3218716322383712 T^{12} + 22271189365451886 T^{13} + 506456339637067704 T^{14} + 3652951957138677156 T^{15} + 68610447555198868641 T^{16} +$$$$49\!\cdots\!58$$$$T^{17} +$$$$80\!\cdots\!66$$$$T^{18} +$$$$57\!\cdots\!15$$$$T^{19} +$$$$83\!\cdots\!29$$$$T^{20} +$$$$55\!\cdots\!55$$$$T^{21} +$$$$76\!\cdots\!94$$$$T^{22} +$$$$45\!\cdots\!34$$$$T^{23} +$$$$60\!\cdots\!21$$$$T^{24} +$$$$31\!\cdots\!92$$$$T^{25} +$$$$42\!\cdots\!16$$$$T^{26} +$$$$17\!\cdots\!18$$$$T^{27} +$$$$25\!\cdots\!32$$$$T^{28} +$$$$84\!\cdots\!47$$$$T^{29} +$$$$12\!\cdots\!47$$$$T^{30} +$$$$31\!\cdots\!97$$$$T^{31} +$$$$53\!\cdots\!13$$$$T^{32} +$$$$88\!\cdots\!45$$$$T^{33} +$$$$17\!\cdots\!43$$$$T^{34} +$$$$17\!\cdots\!15$$$$T^{35} +$$$$42\!\cdots\!52$$$$T^{36} +$$$$21\!\cdots\!71$$$$T^{37} +$$$$68\!\cdots\!21$$$$T^{38} +$$$$11\!\cdots\!66$$$$T^{39} +$$$$54\!\cdots\!01$$$$T^{40}$$)