Properties

Label 2009.2.a
Level 2009
Weight 2
Character orbit a
Rep. character \(\chi_{2009}(1,\cdot)\)
Character field \(\Q\)
Dimension 136
Newform subspaces 21
Sturm bound 392
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2009.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 21 \)
Sturm bound: \(392\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2009))\).

Total New Old
Modular forms 204 136 68
Cusp forms 189 136 53
Eisenstein series 15 0 15

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

\(7\)\(41\)FrickeDim.
\(+\)\(+\)\(+\)\(29\)
\(+\)\(-\)\(-\)\(37\)
\(-\)\(+\)\(-\)\(41\)
\(-\)\(-\)\(+\)\(29\)
Plus space\(+\)\(58\)
Minus space\(-\)\(78\)

Trace form

\( 136q - 2q^{2} + 136q^{4} + 2q^{6} - 6q^{8} + 132q^{9} + O(q^{10}) \) \( 136q - 2q^{2} + 136q^{4} + 2q^{6} - 6q^{8} + 132q^{9} - 6q^{11} - 8q^{12} - 12q^{13} - 2q^{15} + 120q^{16} - 8q^{17} - 22q^{18} - 4q^{19} + 16q^{20} - 8q^{22} - 12q^{23} + 26q^{24} + 124q^{25} + 8q^{26} - 6q^{27} - 8q^{29} + 10q^{30} + 8q^{31} - 14q^{32} - 4q^{33} + 140q^{36} + 16q^{37} + 26q^{38} - 16q^{39} + 20q^{40} - 4q^{41} - 8q^{43} - 38q^{44} + 32q^{45} + 20q^{46} + 4q^{48} - 6q^{50} - 32q^{51} - 36q^{52} + 4q^{53} + 30q^{54} - 18q^{55} - 4q^{57} - 32q^{58} - 16q^{59} + 34q^{60} - 4q^{61} + 80q^{64} + 4q^{65} + 96q^{66} + 6q^{67} + 32q^{68} + 32q^{69} - 12q^{71} - 50q^{72} - 52q^{73} - 16q^{74} + 24q^{75} + 24q^{76} - 24q^{78} - 24q^{79} + 36q^{80} + 96q^{81} - 2q^{82} + 4q^{83} - 44q^{85} + 36q^{86} - 4q^{87} + 28q^{88} + 44q^{89} - 32q^{90} + 20q^{92} + 8q^{93} + 42q^{94} - 18q^{95} + 46q^{96} - 36q^{97} - 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2009))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 41
2009.2.a.a \(2\) \(16.042\) \(\Q(\sqrt{5}) \) None \(-1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(q-\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{5}+\cdots\)
2009.2.a.b \(2\) \(16.042\) \(\Q(\sqrt{5}) \) None \(-1\) \(3\) \(1\) \(0\) \(-\) \(+\) \(q-\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
2009.2.a.c \(2\) \(16.042\) \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(q-\beta q^{3}-2q^{4}+(1-\beta )q^{5}+\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
2009.2.a.d \(2\) \(16.042\) \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(-1\) \(0\) \(+\) \(+\) \(q+\beta q^{3}-2q^{4}+(-1+\beta )q^{5}+\beta q^{9}+\cdots\)
2009.2.a.e \(2\) \(16.042\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2009.2.a.f \(2\) \(16.042\) \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(-2\) \(0\) \(+\) \(+\) \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots\)
2009.2.a.g \(3\) \(16.042\) 3.3.148.1 None \(-1\) \(0\) \(2\) \(0\) \(-\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
2009.2.a.h \(3\) \(16.042\) 3.3.257.1 None \(0\) \(-3\) \(0\) \(0\) \(-\) \(+\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
2009.2.a.i \(3\) \(16.042\) 3.3.257.1 None \(0\) \(3\) \(0\) \(0\) \(-\) \(-\) \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
2009.2.a.j \(3\) \(16.042\) 3.3.257.1 None \(1\) \(1\) \(-6\) \(0\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2009.2.a.k \(3\) \(16.042\) \(\Q(\zeta_{14})^+\) None \(4\) \(-5\) \(-2\) \(0\) \(-\) \(+\) \(q+(1+\beta _{1})q^{2}+(-2+\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
2009.2.a.l \(5\) \(16.042\) 5.5.233489.1 None \(-2\) \(-2\) \(2\) \(0\) \(+\) \(+\) \(q-\beta _{2}q^{2}-\beta _{3}q^{3}+(1+\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\)
2009.2.a.m \(5\) \(16.042\) 5.5.233489.1 None \(-2\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(q-\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1})q^{4}-\beta _{3}q^{5}+\cdots\)
2009.2.a.n \(5\) \(16.042\) 5.5.633117.1 None \(-1\) \(-4\) \(5\) \(0\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2009.2.a.o \(6\) \(16.042\) 6.6.185257757.1 None \(-1\) \(4\) \(1\) \(0\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
2009.2.a.p \(7\) \(16.042\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(-7\) \(-4\) \(0\) \(-\) \(-\) \(q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
2009.2.a.q \(7\) \(16.042\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(7\) \(4\) \(0\) \(-\) \(+\) \(q+\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
2009.2.a.r \(17\) \(16.042\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(3\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots\)
2009.2.a.s \(17\) \(16.042\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(3\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots\)
2009.2.a.t \(20\) \(16.042\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(-8\) \(-8\) \(0\) \(+\) \(+\) \(q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{18}q^{5}+\cdots\)
2009.2.a.u \(20\) \(16.042\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(8\) \(8\) \(0\) \(+\) \(-\) \(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{18}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2009))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2009)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} \))(\( 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} \))(\( ( 1 + 2 T^{2} )^{2} \))(\( ( 1 + 2 T^{2} )^{2} \))(\( 1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4} \))(\( 1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4} \))(\( 1 + T + T^{2} + 3 T^{3} + 2 T^{4} + 4 T^{5} + 8 T^{6} \))(\( 1 + T^{2} - 3 T^{3} + 2 T^{4} + 8 T^{6} \))(\( 1 + T^{2} - 3 T^{3} + 2 T^{4} + 8 T^{6} \))(\( 1 - T + 2 T^{2} - T^{3} + 4 T^{4} - 4 T^{5} + 8 T^{6} \))(\( 1 - 4 T + 9 T^{2} - 15 T^{3} + 18 T^{4} - 16 T^{5} + 8 T^{6} \))(\( 1 + 2 T + 4 T^{2} + 5 T^{3} + 12 T^{4} + 17 T^{5} + 24 T^{6} + 20 T^{7} + 32 T^{8} + 32 T^{9} + 32 T^{10} \))(\( 1 + 2 T + 4 T^{2} + 5 T^{3} + 12 T^{4} + 17 T^{5} + 24 T^{6} + 20 T^{7} + 32 T^{8} + 32 T^{9} + 32 T^{10} \))(\( 1 + T + 4 T^{2} + 4 T^{3} + 10 T^{4} + 11 T^{5} + 20 T^{6} + 16 T^{7} + 32 T^{8} + 16 T^{9} + 32 T^{10} \))(\( 1 + T + 2 T^{2} + 3 T^{4} + 4 T^{5} + 17 T^{6} + 8 T^{7} + 12 T^{8} + 32 T^{10} + 32 T^{11} + 64 T^{12} \))(\( 1 + T + 3 T^{2} + 6 T^{3} + 11 T^{4} + 16 T^{5} + 28 T^{6} + 43 T^{7} + 56 T^{8} + 64 T^{9} + 88 T^{10} + 96 T^{11} + 96 T^{12} + 64 T^{13} + 128 T^{14} \))(\( 1 + T + 3 T^{2} + 6 T^{3} + 11 T^{4} + 16 T^{5} + 28 T^{6} + 43 T^{7} + 56 T^{8} + 64 T^{9} + 88 T^{10} + 96 T^{11} + 96 T^{12} + 64 T^{13} + 128 T^{14} \))(\( 1 - 3 T + 9 T^{2} - 19 T^{3} + 41 T^{4} - 74 T^{5} + 131 T^{6} - 199 T^{7} + 313 T^{8} - 419 T^{9} + 591 T^{10} - 717 T^{11} + 971 T^{12} - 1156 T^{13} + 1617 T^{14} - 1933 T^{15} + 2922 T^{16} - 3604 T^{17} + 5844 T^{18} - 7732 T^{19} + 12936 T^{20} - 18496 T^{21} + 31072 T^{22} - 45888 T^{23} + 75648 T^{24} - 107264 T^{25} + 160256 T^{26} - 203776 T^{27} + 268288 T^{28} - 303104 T^{29} + 335872 T^{30} - 311296 T^{31} + 294912 T^{32} - 196608 T^{33} + 131072 T^{34} \))(\( 1 - 3 T + 9 T^{2} - 19 T^{3} + 41 T^{4} - 74 T^{5} + 131 T^{6} - 199 T^{7} + 313 T^{8} - 419 T^{9} + 591 T^{10} - 717 T^{11} + 971 T^{12} - 1156 T^{13} + 1617 T^{14} - 1933 T^{15} + 2922 T^{16} - 3604 T^{17} + 5844 T^{18} - 7732 T^{19} + 12936 T^{20} - 18496 T^{21} + 31072 T^{22} - 45888 T^{23} + 75648 T^{24} - 107264 T^{25} + 160256 T^{26} - 203776 T^{27} + 268288 T^{28} - 303104 T^{29} + 335872 T^{30} - 311296 T^{31} + 294912 T^{32} - 196608 T^{33} + 131072 T^{34} \))(\( 1 + 2 T + 13 T^{2} + 24 T^{3} + 90 T^{4} + 152 T^{5} + 440 T^{6} + 686 T^{7} + 1713 T^{8} + 2504 T^{9} + 5667 T^{10} + 7896 T^{11} + 16605 T^{12} + 22270 T^{13} + 44164 T^{14} + 57232 T^{15} + 107898 T^{16} + 135172 T^{17} + 243189 T^{18} + 293950 T^{19} + 506133 T^{20} + 587900 T^{21} + 972756 T^{22} + 1081376 T^{23} + 1726368 T^{24} + 1831424 T^{25} + 2826496 T^{26} + 2850560 T^{27} + 4250880 T^{28} + 4042752 T^{29} + 5803008 T^{30} + 5128192 T^{31} + 7016448 T^{32} + 5619712 T^{33} + 7208960 T^{34} + 4980736 T^{35} + 5898240 T^{36} + 3145728 T^{37} + 3407872 T^{38} + 1048576 T^{39} + 1048576 T^{40} \))(\( 1 + 2 T + 13 T^{2} + 24 T^{3} + 90 T^{4} + 152 T^{5} + 440 T^{6} + 686 T^{7} + 1713 T^{8} + 2504 T^{9} + 5667 T^{10} + 7896 T^{11} + 16605 T^{12} + 22270 T^{13} + 44164 T^{14} + 57232 T^{15} + 107898 T^{16} + 135172 T^{17} + 243189 T^{18} + 293950 T^{19} + 506133 T^{20} + 587900 T^{21} + 972756 T^{22} + 1081376 T^{23} + 1726368 T^{24} + 1831424 T^{25} + 2826496 T^{26} + 2850560 T^{27} + 4250880 T^{28} + 4042752 T^{29} + 5803008 T^{30} + 5128192 T^{31} + 7016448 T^{32} + 5619712 T^{33} + 7208960 T^{34} + 4980736 T^{35} + 5898240 T^{36} + 3145728 T^{37} + 3407872 T^{38} + 1048576 T^{39} + 1048576 T^{40} \))
$3$ (\( 1 - T + 5 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - 3 T + 7 T^{2} - 9 T^{3} + 9 T^{4} \))(\( 1 + T + 3 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 - T + 3 T^{2} - 3 T^{3} + 9 T^{4} \))(\( ( 1 + T + 3 T^{2} )^{2} \))(\( ( 1 - T + 3 T^{2} )^{2} \))(\( 1 + 5 T^{2} - 2 T^{3} + 15 T^{4} + 27 T^{6} \))(\( 1 + 3 T + 7 T^{2} + 11 T^{3} + 21 T^{4} + 27 T^{5} + 27 T^{6} \))(\( 1 - 3 T + 7 T^{2} - 11 T^{3} + 21 T^{4} - 27 T^{5} + 27 T^{6} \))(\( 1 - T + T^{2} - 3 T^{3} + 3 T^{4} - 9 T^{5} + 27 T^{6} \))(\( 1 + 5 T + 15 T^{2} + 31 T^{3} + 45 T^{4} + 45 T^{5} + 27 T^{6} \))(\( 1 + 2 T + 7 T^{2} + 5 T^{3} + 16 T^{4} + T^{5} + 48 T^{6} + 45 T^{7} + 189 T^{8} + 162 T^{9} + 243 T^{10} \))(\( 1 - 2 T + 7 T^{2} - 5 T^{3} + 16 T^{4} - T^{5} + 48 T^{6} - 45 T^{7} + 189 T^{8} - 162 T^{9} + 243 T^{10} \))(\( 1 + 4 T + 15 T^{2} + 38 T^{3} + 87 T^{4} + 157 T^{5} + 261 T^{6} + 342 T^{7} + 405 T^{8} + 324 T^{9} + 243 T^{10} \))(\( 1 - 4 T + 10 T^{2} - 14 T^{3} + 26 T^{4} - 57 T^{5} + 130 T^{6} - 171 T^{7} + 234 T^{8} - 378 T^{9} + 810 T^{10} - 972 T^{11} + 729 T^{12} \))(\( 1 + 7 T + 32 T^{2} + 110 T^{3} + 315 T^{4} + 765 T^{5} + 1616 T^{6} + 2979 T^{7} + 4848 T^{8} + 6885 T^{9} + 8505 T^{10} + 8910 T^{11} + 7776 T^{12} + 5103 T^{13} + 2187 T^{14} \))(\( 1 - 7 T + 32 T^{2} - 110 T^{3} + 315 T^{4} - 765 T^{5} + 1616 T^{6} - 2979 T^{7} + 4848 T^{8} - 6885 T^{9} + 8505 T^{10} - 8910 T^{11} + 7776 T^{12} - 5103 T^{13} + 2187 T^{14} \))(\( 1 + T + 13 T^{2} + 8 T^{3} + 86 T^{4} + 31 T^{5} + 442 T^{6} + 103 T^{7} + 2012 T^{8} + 262 T^{9} + 7968 T^{10} - 15 T^{11} + 27710 T^{12} - 3718 T^{13} + 90192 T^{14} - 18363 T^{15} + 285619 T^{16} - 59651 T^{17} + 856857 T^{18} - 165267 T^{19} + 2435184 T^{20} - 301158 T^{21} + 6733530 T^{22} - 10935 T^{23} + 17426016 T^{24} + 1718982 T^{25} + 39602196 T^{26} + 6082047 T^{27} + 78298974 T^{28} + 16474671 T^{29} + 137111778 T^{30} + 38263752 T^{31} + 186535791 T^{32} + 43046721 T^{33} + 129140163 T^{34} \))(\( 1 - T + 13 T^{2} - 8 T^{3} + 86 T^{4} - 31 T^{5} + 442 T^{6} - 103 T^{7} + 2012 T^{8} - 262 T^{9} + 7968 T^{10} + 15 T^{11} + 27710 T^{12} + 3718 T^{13} + 90192 T^{14} + 18363 T^{15} + 285619 T^{16} + 59651 T^{17} + 856857 T^{18} + 165267 T^{19} + 2435184 T^{20} + 301158 T^{21} + 6733530 T^{22} + 10935 T^{23} + 17426016 T^{24} - 1718982 T^{25} + 39602196 T^{26} - 6082047 T^{27} + 78298974 T^{28} - 16474671 T^{29} + 137111778 T^{30} - 38263752 T^{31} + 186535791 T^{32} - 43046721 T^{33} + 129140163 T^{34} \))(\( 1 + 8 T + 54 T^{2} + 264 T^{3} + 1150 T^{4} + 4324 T^{5} + 14960 T^{6} + 47228 T^{7} + 139797 T^{8} + 387252 T^{9} + 1017570 T^{10} + 2536820 T^{11} + 6044272 T^{12} + 13775228 T^{13} + 30152662 T^{14} + 63452032 T^{15} + 128655747 T^{16} + 251559792 T^{17} + 474850744 T^{18} + 865817032 T^{19} + 1525440191 T^{20} + 2597451096 T^{21} + 4273656696 T^{22} + 6792114384 T^{23} + 10421115507 T^{24} + 15418843776 T^{25} + 21981290598 T^{26} + 30126423636 T^{27} + 39656468592 T^{28} + 49932228060 T^{29} + 60086490930 T^{30} + 68600530044 T^{31} + 74293857477 T^{32} + 75296686644 T^{33} + 71553216240 T^{34} + 62044673868 T^{35} + 49503729150 T^{36} + 34093003032 T^{37} + 20920706406 T^{38} + 9298091736 T^{39} + 3486784401 T^{40} \))(\( 1 - 8 T + 54 T^{2} - 264 T^{3} + 1150 T^{4} - 4324 T^{5} + 14960 T^{6} - 47228 T^{7} + 139797 T^{8} - 387252 T^{9} + 1017570 T^{10} - 2536820 T^{11} + 6044272 T^{12} - 13775228 T^{13} + 30152662 T^{14} - 63452032 T^{15} + 128655747 T^{16} - 251559792 T^{17} + 474850744 T^{18} - 865817032 T^{19} + 1525440191 T^{20} - 2597451096 T^{21} + 4273656696 T^{22} - 6792114384 T^{23} + 10421115507 T^{24} - 15418843776 T^{25} + 21981290598 T^{26} - 30126423636 T^{27} + 39656468592 T^{28} - 49932228060 T^{29} + 60086490930 T^{30} - 68600530044 T^{31} + 74293857477 T^{32} - 75296686644 T^{33} + 71553216240 T^{34} - 62044673868 T^{35} + 49503729150 T^{36} - 34093003032 T^{37} + 20920706406 T^{38} - 9298091736 T^{39} + 3486784401 T^{40} \))
$5$ (\( 1 + T + 9 T^{2} + 5 T^{3} + 25 T^{4} \))(\( 1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4} \))(\( 1 - T + 7 T^{2} - 5 T^{3} + 25 T^{4} \))(\( 1 + T + 7 T^{2} + 5 T^{3} + 25 T^{4} \))(\( ( 1 - T + 5 T^{2} )^{2} \))(\( ( 1 + T + 5 T^{2} )^{2} \))(\( 1 - 2 T + 11 T^{2} - 16 T^{3} + 55 T^{4} - 50 T^{5} + 125 T^{6} \))(\( ( 1 + 5 T^{2} )^{3} \))(\( ( 1 + 5 T^{2} )^{3} \))(\( ( 1 + 2 T + 5 T^{2} )^{3} \))(\( 1 + 2 T + 7 T^{2} + 12 T^{3} + 35 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 - 2 T + 17 T^{2} - 21 T^{3} + 128 T^{4} - 117 T^{5} + 640 T^{6} - 525 T^{7} + 2125 T^{8} - 1250 T^{9} + 3125 T^{10} \))(\( 1 + 2 T + 17 T^{2} + 21 T^{3} + 128 T^{4} + 117 T^{5} + 640 T^{6} + 525 T^{7} + 2125 T^{8} + 1250 T^{9} + 3125 T^{10} \))(\( 1 - 5 T + 14 T^{2} - 14 T^{3} - 11 T^{4} + 86 T^{5} - 55 T^{6} - 350 T^{7} + 1750 T^{8} - 3125 T^{9} + 3125 T^{10} \))(\( 1 - T + T^{2} - 9 T^{3} - 5 T^{4} + 6 T^{5} + 134 T^{6} + 30 T^{7} - 125 T^{8} - 1125 T^{9} + 625 T^{10} - 3125 T^{11} + 15625 T^{12} \))(\( 1 + 4 T + 10 T^{2} + 28 T^{3} + 109 T^{4} + 334 T^{5} + 700 T^{6} + 1332 T^{7} + 3500 T^{8} + 8350 T^{9} + 13625 T^{10} + 17500 T^{11} + 31250 T^{12} + 62500 T^{13} + 78125 T^{14} \))(\( 1 - 4 T + 10 T^{2} - 28 T^{3} + 109 T^{4} - 334 T^{5} + 700 T^{6} - 1332 T^{7} + 3500 T^{8} - 8350 T^{9} + 13625 T^{10} - 17500 T^{11} + 31250 T^{12} - 62500 T^{13} + 78125 T^{14} \))(\( 1 - T + 31 T^{2} - 22 T^{3} + 530 T^{4} - 307 T^{5} + 6506 T^{6} - 3323 T^{7} + 63192 T^{8} - 30588 T^{9} + 511922 T^{10} - 245463 T^{11} + 3576628 T^{12} - 1728104 T^{13} + 22057028 T^{14} - 10627417 T^{15} + 121990067 T^{16} - 56999971 T^{17} + 609950335 T^{18} - 265685425 T^{19} + 2757128500 T^{20} - 1080065000 T^{21} + 11176962500 T^{22} - 3835359375 T^{23} + 39993906250 T^{24} - 11948437500 T^{25} + 123421875000 T^{26} - 32451171875 T^{27} + 317675781250 T^{28} - 74951171875 T^{29} + 646972656250 T^{30} - 134277343750 T^{31} + 946044921875 T^{32} - 152587890625 T^{33} + 762939453125 T^{34} \))(\( 1 + T + 31 T^{2} + 22 T^{3} + 530 T^{4} + 307 T^{5} + 6506 T^{6} + 3323 T^{7} + 63192 T^{8} + 30588 T^{9} + 511922 T^{10} + 245463 T^{11} + 3576628 T^{12} + 1728104 T^{13} + 22057028 T^{14} + 10627417 T^{15} + 121990067 T^{16} + 56999971 T^{17} + 609950335 T^{18} + 265685425 T^{19} + 2757128500 T^{20} + 1080065000 T^{21} + 11176962500 T^{22} + 3835359375 T^{23} + 39993906250 T^{24} + 11948437500 T^{25} + 123421875000 T^{26} + 32451171875 T^{27} + 317675781250 T^{28} + 74951171875 T^{29} + 646972656250 T^{30} + 134277343750 T^{31} + 946044921875 T^{32} + 152587890625 T^{33} + 762939453125 T^{34} \))(\( 1 + 8 T + 72 T^{2} + 384 T^{3} + 2125 T^{4} + 9004 T^{5} + 39052 T^{6} + 142704 T^{7} + 530750 T^{8} + 1742364 T^{9} + 5790782 T^{10} + 17432080 T^{11} + 52894486 T^{12} + 147702968 T^{13} + 414505318 T^{14} + 1081511548 T^{15} + 2830571057 T^{16} + 6931611904 T^{17} + 17006679256 T^{18} + 39174910428 T^{19} + 90356308826 T^{20} + 195874552140 T^{21} + 425166981400 T^{22} + 866451488000 T^{23} + 1769106910625 T^{24} + 3379723587500 T^{25} + 6476645593750 T^{26} + 11539294375000 T^{27} + 20661908593750 T^{28} + 34047031250000 T^{29} + 56550605468750 T^{30} + 85076367187500 T^{31} + 129577636718750 T^{32} + 174199218750000 T^{33} + 238354492187500 T^{34} + 274780273437500 T^{35} + 324249267578125 T^{36} + 292968750000000 T^{37} + 274658203125000 T^{38} + 152587890625000 T^{39} + 95367431640625 T^{40} \))(\( 1 - 8 T + 72 T^{2} - 384 T^{3} + 2125 T^{4} - 9004 T^{5} + 39052 T^{6} - 142704 T^{7} + 530750 T^{8} - 1742364 T^{9} + 5790782 T^{10} - 17432080 T^{11} + 52894486 T^{12} - 147702968 T^{13} + 414505318 T^{14} - 1081511548 T^{15} + 2830571057 T^{16} - 6931611904 T^{17} + 17006679256 T^{18} - 39174910428 T^{19} + 90356308826 T^{20} - 195874552140 T^{21} + 425166981400 T^{22} - 866451488000 T^{23} + 1769106910625 T^{24} - 3379723587500 T^{25} + 6476645593750 T^{26} - 11539294375000 T^{27} + 20661908593750 T^{28} - 34047031250000 T^{29} + 56550605468750 T^{30} - 85076367187500 T^{31} + 129577636718750 T^{32} - 174199218750000 T^{33} + 238354492187500 T^{34} - 274780273437500 T^{35} + 324249267578125 T^{36} - 292968750000000 T^{37} + 274658203125000 T^{38} - 152587890625000 T^{39} + 95367431640625 T^{40} \))
$7$ 1
$11$ (\( ( 1 + T + 11 T^{2} )^{2} \))(\( 1 + 17 T^{2} + 121 T^{4} \))(\( 1 + 5 T + 25 T^{2} + 55 T^{3} + 121 T^{4} \))(\( 1 + 5 T + 25 T^{2} + 55 T^{3} + 121 T^{4} \))(\( ( 1 - T + 11 T^{2} )^{2} \))(\( ( 1 - T + 11 T^{2} )^{2} \))(\( 1 - 2 T + 13 T^{2} + 6 T^{3} + 143 T^{4} - 242 T^{5} + 1331 T^{6} \))(\( 1 + 8 T + 37 T^{2} + 136 T^{3} + 407 T^{4} + 968 T^{5} + 1331 T^{6} \))(\( 1 + 8 T + 37 T^{2} + 136 T^{3} + 407 T^{4} + 968 T^{5} + 1331 T^{6} \))(\( ( 1 + 2 T + 11 T^{2} )^{3} \))(\( 1 + 4 T + 29 T^{2} + 80 T^{3} + 319 T^{4} + 484 T^{5} + 1331 T^{6} \))(\( 1 + 6 T + 52 T^{2} + 219 T^{3} + 1118 T^{4} + 3419 T^{5} + 12298 T^{6} + 26499 T^{7} + 69212 T^{8} + 87846 T^{9} + 161051 T^{10} \))(\( 1 + 6 T + 52 T^{2} + 219 T^{3} + 1118 T^{4} + 3419 T^{5} + 12298 T^{6} + 26499 T^{7} + 69212 T^{8} + 87846 T^{9} + 161051 T^{10} \))(\( 1 - 2 T - 8 T^{2} + 52 T^{3} + 103 T^{4} - 844 T^{5} + 1133 T^{6} + 6292 T^{7} - 10648 T^{8} - 29282 T^{9} + 161051 T^{10} \))(\( 1 - 6 T + 37 T^{2} - 112 T^{3} + 567 T^{4} - 1994 T^{5} + 8902 T^{6} - 21934 T^{7} + 68607 T^{8} - 149072 T^{9} + 541717 T^{10} - 966306 T^{11} + 1771561 T^{12} \))(\( 1 + 35 T^{2} + 32 T^{3} + 512 T^{4} + 1448 T^{5} + 4674 T^{6} + 23960 T^{7} + 51414 T^{8} + 175208 T^{9} + 681472 T^{10} + 468512 T^{11} + 5636785 T^{12} + 19487171 T^{14} \))(\( 1 + 35 T^{2} + 32 T^{3} + 512 T^{4} + 1448 T^{5} + 4674 T^{6} + 23960 T^{7} + 51414 T^{8} + 175208 T^{9} + 681472 T^{10} + 468512 T^{11} + 5636785 T^{12} + 19487171 T^{14} \))(\( 1 - 15 T + 190 T^{2} - 1703 T^{3} + 13752 T^{4} - 94013 T^{5} + 595117 T^{6} - 3382487 T^{7} + 18091657 T^{8} - 89333962 T^{9} + 419455284 T^{10} - 1846870802 T^{11} + 7788551201 T^{12} - 31097507282 T^{13} + 119511159637 T^{14} - 437373695104 T^{15} + 1545278692727 T^{16} - 5213529235339 T^{17} + 16998065619997 T^{18} - 52922217107584 T^{19} + 159069353476847 T^{20} - 455298604115762 T^{21} + 1254353959472251 T^{22} - 3271844284861922 T^{23} + 8173996846161564 T^{24} - 19149528129616522 T^{25} + 42659180849513987 T^{26} - 87733001526362687 T^{27} + 169793825479006487 T^{28} - 295053066980671373 T^{29} + 474756337403339112 T^{30} - 646713966592259423 T^{31} + 793677152188973690 T^{32} - 689245947953582415 T^{33} + 505447028499293771 T^{34} \))(\( 1 - 15 T + 190 T^{2} - 1703 T^{3} + 13752 T^{4} - 94013 T^{5} + 595117 T^{6} - 3382487 T^{7} + 18091657 T^{8} - 89333962 T^{9} + 419455284 T^{10} - 1846870802 T^{11} + 7788551201 T^{12} - 31097507282 T^{13} + 119511159637 T^{14} - 437373695104 T^{15} + 1545278692727 T^{16} - 5213529235339 T^{17} + 16998065619997 T^{18} - 52922217107584 T^{19} + 159069353476847 T^{20} - 455298604115762 T^{21} + 1254353959472251 T^{22} - 3271844284861922 T^{23} + 8173996846161564 T^{24} - 19149528129616522 T^{25} + 42659180849513987 T^{26} - 87733001526362687 T^{27} + 169793825479006487 T^{28} - 295053066980671373 T^{29} + 474756337403339112 T^{30} - 646713966592259423 T^{31} + 793677152188973690 T^{32} - 689245947953582415 T^{33} + 505447028499293771 T^{34} \))(\( 1 + 118 T^{2} - 48 T^{3} + 6940 T^{4} - 4968 T^{5} + 274334 T^{6} - 253504 T^{7} + 8230854 T^{8} - 8623240 T^{9} + 199488002 T^{10} - 221588984 T^{11} + 4048815422 T^{12} - 4586283352 T^{13} + 70400158082 T^{14} - 79217170200 T^{15} + 1064372283529 T^{16} - 1165843530480 T^{17} + 14122131561000 T^{18} - 14793883394904 T^{19} + 165270460487788 T^{20} - 162732717343944 T^{21} + 1708777918881000 T^{22} - 1551737739068880 T^{23} + 15583474603148089 T^{24} - 12758004477880200 T^{25} + 124718174451906002 T^{26} - 89373687934877192 T^{27} + 867899543235462782 T^{28} - 522495233173835944 T^{29} + 5174205010679137202 T^{30} - 2460311010479599640 T^{31} + 25831945758247549734 T^{32} - 8751645619335084224 T^{33} + \)\(10\!\cdots\!94\)\( T^{34} - 20752568905656954168 T^{35} + \)\(31\!\cdots\!40\)\( T^{36} - 24261457367966101008 T^{37} + \)\(65\!\cdots\!58\)\( T^{38} + \)\(67\!\cdots\!01\)\( T^{40} \))(\( 1 + 118 T^{2} - 48 T^{3} + 6940 T^{4} - 4968 T^{5} + 274334 T^{6} - 253504 T^{7} + 8230854 T^{8} - 8623240 T^{9} + 199488002 T^{10} - 221588984 T^{11} + 4048815422 T^{12} - 4586283352 T^{13} + 70400158082 T^{14} - 79217170200 T^{15} + 1064372283529 T^{16} - 1165843530480 T^{17} + 14122131561000 T^{18} - 14793883394904 T^{19} + 165270460487788 T^{20} - 162732717343944 T^{21} + 1708777918881000 T^{22} - 1551737739068880 T^{23} + 15583474603148089 T^{24} - 12758004477880200 T^{25} + 124718174451906002 T^{26} - 89373687934877192 T^{27} + 867899543235462782 T^{28} - 522495233173835944 T^{29} + 5174205010679137202 T^{30} - 2460311010479599640 T^{31} + 25831945758247549734 T^{32} - 8751645619335084224 T^{33} + \)\(10\!\cdots\!94\)\( T^{34} - 20752568905656954168 T^{35} + \)\(31\!\cdots\!40\)\( T^{36} - 24261457367966101008 T^{37} + \)\(65\!\cdots\!58\)\( T^{38} + \)\(67\!\cdots\!01\)\( T^{40} \))
$13$ (\( 1 - 8 T + 37 T^{2} - 104 T^{3} + 169 T^{4} \))(\( ( 1 - 3 T + 13 T^{2} )^{2} \))(\( 1 - T + 23 T^{2} - 13 T^{3} + 169 T^{4} \))(\( 1 + T + 23 T^{2} + 13 T^{3} + 169 T^{4} \))(\( 1 + 6 T^{2} + 169 T^{4} \))(\( 1 + 6 T^{2} + 169 T^{4} \))(\( 1 - 2 T + 27 T^{2} - 44 T^{3} + 351 T^{4} - 338 T^{5} + 2197 T^{6} \))(\( 1 - 5 T + 21 T^{2} - 67 T^{3} + 273 T^{4} - 845 T^{5} + 2197 T^{6} \))(\( 1 + 5 T + 21 T^{2} + 67 T^{3} + 273 T^{4} + 845 T^{5} + 2197 T^{6} \))(\( 1 + 9 T + 61 T^{2} + 249 T^{3} + 793 T^{4} + 1521 T^{5} + 2197 T^{6} \))(\( 1 + 7 T + 39 T^{2} + 133 T^{3} + 507 T^{4} + 1183 T^{5} + 2197 T^{6} \))(\( 1 - 2 T + 57 T^{2} - 85 T^{3} + 1376 T^{4} - 1541 T^{5} + 17888 T^{6} - 14365 T^{7} + 125229 T^{8} - 57122 T^{9} + 371293 T^{10} \))(\( 1 + 2 T + 57 T^{2} + 85 T^{3} + 1376 T^{4} + 1541 T^{5} + 17888 T^{6} + 14365 T^{7} + 125229 T^{8} + 57122 T^{9} + 371293 T^{10} \))(\( 1 + 5 T + 56 T^{2} + 180 T^{3} + 1219 T^{4} + 2941 T^{5} + 15847 T^{6} + 30420 T^{7} + 123032 T^{8} + 142805 T^{9} + 371293 T^{10} \))(\( 1 + 7 T + 29 T^{2} + 125 T^{3} + 387 T^{4} + 877 T^{5} + 3108 T^{6} + 11401 T^{7} + 65403 T^{8} + 274625 T^{9} + 828269 T^{10} + 2599051 T^{11} + 4826809 T^{12} \))(\( 1 + T + 59 T^{2} + 31 T^{3} + 1698 T^{4} + 434 T^{5} + 31576 T^{6} + 5143 T^{7} + 410488 T^{8} + 73346 T^{9} + 3730506 T^{10} + 885391 T^{11} + 21906287 T^{12} + 4826809 T^{13} + 62748517 T^{14} \))(\( 1 - T + 59 T^{2} - 31 T^{3} + 1698 T^{4} - 434 T^{5} + 31576 T^{6} - 5143 T^{7} + 410488 T^{8} - 73346 T^{9} + 3730506 T^{10} - 885391 T^{11} + 21906287 T^{12} - 4826809 T^{13} + 62748517 T^{14} \))(\( 1 - 5 T + 118 T^{2} - 391 T^{3} + 6048 T^{4} - 11546 T^{5} + 185403 T^{6} - 86690 T^{7} + 4012572 T^{8} + 4434458 T^{9} + 72641222 T^{10} + 175315312 T^{11} + 1303121483 T^{12} + 3464313554 T^{13} + 23515148950 T^{14} + 49279593825 T^{15} + 376615333127 T^{16} + 633534601766 T^{17} + 4895999330651 T^{18} + 8328251356425 T^{19} + 51662782243150 T^{20} + 98944259415794 T^{21} + 483839884787519 T^{22} + 846213525799408 T^{23} + 4558128953567774 T^{24} + 3617323621584218 T^{25} + 42551317258117356 T^{26} - 11950952658389810 T^{27} + 332271913535641911 T^{28} - 268999690824165626 T^{29} + 1831788644669946144 T^{30} - 1539514166808421999 T^{31} + 6039935375662709326 T^{32} - 3327083045915899205 T^{33} + 8650415919381337933 T^{34} \))(\( 1 + 5 T + 118 T^{2} + 391 T^{3} + 6048 T^{4} + 11546 T^{5} + 185403 T^{6} + 86690 T^{7} + 4012572 T^{8} - 4434458 T^{9} + 72641222 T^{10} - 175315312 T^{11} + 1303121483 T^{12} - 3464313554 T^{13} + 23515148950 T^{14} - 49279593825 T^{15} + 376615333127 T^{16} - 633534601766 T^{17} + 4895999330651 T^{18} - 8328251356425 T^{19} + 51662782243150 T^{20} - 98944259415794 T^{21} + 483839884787519 T^{22} - 846213525799408 T^{23} + 4558128953567774 T^{24} - 3617323621584218 T^{25} + 42551317258117356 T^{26} + 11950952658389810 T^{27} + 332271913535641911 T^{28} + 268999690824165626 T^{29} + 1831788644669946144 T^{30} + 1539514166808421999 T^{31} + 6039935375662709326 T^{32} + 3327083045915899205 T^{33} + 8650415919381337933 T^{34} \))(\( 1 + 12 T + 162 T^{2} + 1348 T^{3} + 11391 T^{4} + 76244 T^{5} + 503238 T^{6} + 2860300 T^{7} + 15861222 T^{8} + 78595288 T^{9} + 378798880 T^{10} + 1660181216 T^{11} + 7078847534 T^{12} + 27663926544 T^{13} + 105678763228 T^{14} + 371720204456 T^{15} + 1298297800421 T^{16} + 4225917320468 T^{17} + 14249311356054 T^{18} + 46462289478260 T^{19} + 167577058110571 T^{20} + 604009763217380 T^{21} + 2408133619173126 T^{22} + 9284340353068196 T^{23} + 37080683477824181 T^{24} + 138017109873081608 T^{25} + 510091205457779452 T^{26} + 1735870365032935248 T^{27} + 5774433402758892014 T^{28} + 17605390664138377568 T^{29} + 52220642310890329120 T^{30} + \)\(14\!\cdots\!56\)\( T^{31} + \)\(36\!\cdots\!82\)\( T^{32} + \)\(86\!\cdots\!00\)\( T^{33} + \)\(19\!\cdots\!82\)\( T^{34} + \)\(39\!\cdots\!08\)\( T^{35} + \)\(75\!\cdots\!31\)\( T^{36} + \)\(11\!\cdots\!84\)\( T^{37} + \)\(18\!\cdots\!98\)\( T^{38} + \)\(17\!\cdots\!24\)\( T^{39} + \)\(19\!\cdots\!01\)\( T^{40} \))(\( 1 - 12 T + 162 T^{2} - 1348 T^{3} + 11391 T^{4} - 76244 T^{5} + 503238 T^{6} - 2860300 T^{7} + 15861222 T^{8} - 78595288 T^{9} + 378798880 T^{10} - 1660181216 T^{11} + 7078847534 T^{12} - 27663926544 T^{13} + 105678763228 T^{14} - 371720204456 T^{15} + 1298297800421 T^{16} - 4225917320468 T^{17} + 14249311356054 T^{18} - 46462289478260 T^{19} + 167577058110571 T^{20} - 604009763217380 T^{21} + 2408133619173126 T^{22} - 9284340353068196 T^{23} + 37080683477824181 T^{24} - 138017109873081608 T^{25} + 510091205457779452 T^{26} - 1735870365032935248 T^{27} + 5774433402758892014 T^{28} - 17605390664138377568 T^{29} + 52220642310890329120 T^{30} - \)\(14\!\cdots\!56\)\( T^{31} + \)\(36\!\cdots\!82\)\( T^{32} - \)\(86\!\cdots\!00\)\( T^{33} + \)\(19\!\cdots\!82\)\( T^{34} - \)\(39\!\cdots\!08\)\( T^{35} + \)\(75\!\cdots\!31\)\( T^{36} - \)\(11\!\cdots\!84\)\( T^{37} + \)\(18\!\cdots\!98\)\( T^{38} - \)\(17\!\cdots\!24\)\( T^{39} + \)\(19\!\cdots\!01\)\( T^{40} \))
$17$ (\( 1 - 4 T + 33 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 23 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 + 3 T + 7 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 - 3 T + 7 T^{2} - 51 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 33 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 33 T^{2} - 68 T^{3} + 289 T^{4} \))(\( ( 1 - 2 T + 17 T^{2} )^{3} \))(\( 1 - 7 T + 59 T^{2} - 231 T^{3} + 1003 T^{4} - 2023 T^{5} + 4913 T^{6} \))(\( 1 + 7 T + 59 T^{2} + 231 T^{3} + 1003 T^{4} + 2023 T^{5} + 4913 T^{6} \))(\( 1 + T + 29 T^{2} + 61 T^{3} + 493 T^{4} + 289 T^{5} + 4913 T^{6} \))(\( 1 + 3 T + 5 T^{2} + 5 T^{3} + 85 T^{4} + 867 T^{5} + 4913 T^{6} \))(\( 1 + 3 T + 60 T^{2} + 153 T^{3} + 1723 T^{4} + 3629 T^{5} + 29291 T^{6} + 44217 T^{7} + 294780 T^{8} + 250563 T^{9} + 1419857 T^{10} \))(\( 1 - 3 T + 60 T^{2} - 153 T^{3} + 1723 T^{4} - 3629 T^{5} + 29291 T^{6} - 44217 T^{7} + 294780 T^{8} - 250563 T^{9} + 1419857 T^{10} \))(\( 1 + 13 T + 110 T^{2} + 580 T^{3} + 2611 T^{4} + 10157 T^{5} + 44387 T^{6} + 167620 T^{7} + 540430 T^{8} + 1085773 T^{9} + 1419857 T^{10} \))(\( 1 + 7 T + 105 T^{2} + 569 T^{3} + 4539 T^{4} + 18913 T^{5} + 103464 T^{6} + 321521 T^{7} + 1311771 T^{8} + 2795497 T^{9} + 8769705 T^{10} + 9938999 T^{11} + 24137569 T^{12} \))(\( 1 - 11 T + 123 T^{2} - 861 T^{3} + 5850 T^{4} - 30762 T^{5} + 157516 T^{6} - 657593 T^{7} + 2677772 T^{8} - 8890218 T^{9} + 28741050 T^{10} - 71911581 T^{11} + 174642411 T^{12} - 265513259 T^{13} + 410338673 T^{14} \))(\( 1 + 11 T + 123 T^{2} + 861 T^{3} + 5850 T^{4} + 30762 T^{5} + 157516 T^{6} + 657593 T^{7} + 2677772 T^{8} + 8890218 T^{9} + 28741050 T^{10} + 71911581 T^{11} + 174642411 T^{12} + 265513259 T^{13} + 410338673 T^{14} \))(\( 1 + 4 T + 103 T^{2} + 289 T^{3} + 5293 T^{4} + 12123 T^{5} + 202094 T^{6} + 438464 T^{7} + 6390066 T^{8} + 13419659 T^{9} + 170586050 T^{10} + 348340234 T^{11} + 4000040556 T^{12} + 8048611729 T^{13} + 84016416289 T^{14} + 163472204469 T^{15} + 1578369366460 T^{16} + 2928191129994 T^{17} + 26832279229820 T^{18} + 47243467091541 T^{19} + 412772653227857 T^{20} + 672228100217809 T^{21} + 5679485583720492 T^{22} + 8408086433651146 T^{23} + 69998053389311650 T^{24} + 93612286124932619 T^{25} + 757784357615678802 T^{26} + 883940749566470336 T^{27} + 6926144612394783502 T^{28} + 7063129381936392603 T^{29} + 52424931528171124541 T^{30} + 48661191875666868481 T^{31} + \)\(29\!\cdots\!79\)\( T^{32} + \)\(19\!\cdots\!24\)\( T^{33} + \)\(82\!\cdots\!77\)\( T^{34} \))(\( 1 - 4 T + 103 T^{2} - 289 T^{3} + 5293 T^{4} - 12123 T^{5} + 202094 T^{6} - 438464 T^{7} + 6390066 T^{8} - 13419659 T^{9} + 170586050 T^{10} - 348340234 T^{11} + 4000040556 T^{12} - 8048611729 T^{13} + 84016416289 T^{14} - 163472204469 T^{15} + 1578369366460 T^{16} - 2928191129994 T^{17} + 26832279229820 T^{18} - 47243467091541 T^{19} + 412772653227857 T^{20} - 672228100217809 T^{21} + 5679485583720492 T^{22} - 8408086433651146 T^{23} + 69998053389311650 T^{24} - 93612286124932619 T^{25} + 757784357615678802 T^{26} - 883940749566470336 T^{27} + 6926144612394783502 T^{28} - 7063129381936392603 T^{29} + 52424931528171124541 T^{30} - 48661191875666868481 T^{31} + \)\(29\!\cdots\!79\)\( T^{32} - \)\(19\!\cdots\!24\)\( T^{33} + \)\(82\!\cdots\!77\)\( T^{34} \))(\( 1 + 8 T + 188 T^{2} + 1404 T^{3} + 18085 T^{4} + 124924 T^{5} + 1175044 T^{6} + 7503260 T^{7} + 57635920 T^{8} + 341058196 T^{9} + 2264483658 T^{10} + 12456956532 T^{11} + 73852475484 T^{12} + 378800564684 T^{13} + 2045377570258 T^{14} + 9805660532232 T^{15} + 48824768187985 T^{16} + 219128934197240 T^{17} + 1014001283185446 T^{18} + 4262772348868168 T^{19} + 18417422467269295 T^{20} + 72467129930758856 T^{21} + 293046370840593894 T^{22} + 1076580453711040120 T^{23} + 4077893463828695185 T^{24} + 13922635746313330824 T^{25} + 49370442233154822802 T^{26} + \)\(15\!\cdots\!32\)\( T^{27} + \)\(51\!\cdots\!44\)\( T^{28} + \)\(14\!\cdots\!04\)\( T^{29} + \)\(45\!\cdots\!42\)\( T^{30} + \)\(11\!\cdots\!68\)\( T^{31} + \)\(33\!\cdots\!20\)\( T^{32} + \)\(74\!\cdots\!20\)\( T^{33} + \)\(19\!\cdots\!76\)\( T^{34} + \)\(35\!\cdots\!32\)\( T^{35} + \)\(88\!\cdots\!85\)\( T^{36} + \)\(11\!\cdots\!08\)\( T^{37} + \)\(26\!\cdots\!92\)\( T^{38} + \)\(19\!\cdots\!24\)\( T^{39} + \)\(40\!\cdots\!01\)\( T^{40} \))(\( 1 - 8 T + 188 T^{2} - 1404 T^{3} + 18085 T^{4} - 124924 T^{5} + 1175044 T^{6} - 7503260 T^{7} + 57635920 T^{8} - 341058196 T^{9} + 2264483658 T^{10} - 12456956532 T^{11} + 73852475484 T^{12} - 378800564684 T^{13} + 2045377570258 T^{14} - 9805660532232 T^{15} + 48824768187985 T^{16} - 219128934197240 T^{17} + 1014001283185446 T^{18} - 4262772348868168 T^{19} + 18417422467269295 T^{20} - 72467129930758856 T^{21} + 293046370840593894 T^{22} - 1076580453711040120 T^{23} + 4077893463828695185 T^{24} - 13922635746313330824 T^{25} + 49370442233154822802 T^{26} - \)\(15\!\cdots\!32\)\( T^{27} + \)\(51\!\cdots\!44\)\( T^{28} - \)\(14\!\cdots\!04\)\( T^{29} + \)\(45\!\cdots\!42\)\( T^{30} - \)\(11\!\cdots\!68\)\( T^{31} + \)\(33\!\cdots\!20\)\( T^{32} - \)\(74\!\cdots\!20\)\( T^{33} + \)\(19\!\cdots\!76\)\( T^{34} - \)\(35\!\cdots\!32\)\( T^{35} + \)\(88\!\cdots\!85\)\( T^{36} - \)\(11\!\cdots\!08\)\( T^{37} + \)\(26\!\cdots\!92\)\( T^{38} - \)\(19\!\cdots\!24\)\( T^{39} + \)\(40\!\cdots\!01\)\( T^{40} \))
$19$ (\( 1 - T + 27 T^{2} - 19 T^{3} + 361 T^{4} \))(\( 1 - 3 T + 29 T^{2} - 57 T^{3} + 361 T^{4} \))(\( 1 + 25 T^{2} + 361 T^{4} \))(\( 1 + 25 T^{2} + 361 T^{4} \))(\( 1 - 6 T + 27 T^{2} - 114 T^{3} + 361 T^{4} \))(\( 1 + 6 T + 27 T^{2} + 114 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 41 T^{2} + 162 T^{3} + 779 T^{4} + 1444 T^{5} + 6859 T^{6} \))(\( 1 - 13 T + 103 T^{2} - 543 T^{3} + 1957 T^{4} - 4693 T^{5} + 6859 T^{6} \))(\( 1 + 13 T + 103 T^{2} + 543 T^{3} + 1957 T^{4} + 4693 T^{5} + 6859 T^{6} \))(\( 1 + 13 T + 109 T^{2} + 555 T^{3} + 2071 T^{4} + 4693 T^{5} + 6859 T^{6} \))(\( 1 - 11 T + 81 T^{2} - 431 T^{3} + 1539 T^{4} - 3971 T^{5} + 6859 T^{6} \))(\( 1 - 7 T + 79 T^{2} - 391 T^{3} + 2739 T^{4} - 10441 T^{5} + 52041 T^{6} - 141151 T^{7} + 541861 T^{8} - 912247 T^{9} + 2476099 T^{10} \))(\( 1 + 7 T + 79 T^{2} + 391 T^{3} + 2739 T^{4} + 10441 T^{5} + 52041 T^{6} + 141151 T^{7} + 541861 T^{8} + 912247 T^{9} + 2476099 T^{10} \))(\( 1 + 47 T^{2} + 132 T^{3} + 851 T^{4} + 5017 T^{5} + 16169 T^{6} + 47652 T^{7} + 322373 T^{8} + 2476099 T^{10} \))(\( 1 + 2 T + 46 T^{2} + 42 T^{3} + 1172 T^{4} - 383 T^{5} + 21830 T^{6} - 7277 T^{7} + 423092 T^{8} + 288078 T^{9} + 5994766 T^{10} + 4952198 T^{11} + 47045881 T^{12} \))(\( 1 + 9 T + 72 T^{2} + 358 T^{3} + 2255 T^{4} + 10619 T^{5} + 60588 T^{6} + 249857 T^{7} + 1151172 T^{8} + 3833459 T^{9} + 15467045 T^{10} + 46654918 T^{11} + 178279128 T^{12} + 423412929 T^{13} + 893871739 T^{14} \))(\( 1 - 9 T + 72 T^{2} - 358 T^{3} + 2255 T^{4} - 10619 T^{5} + 60588 T^{6} - 249857 T^{7} + 1151172 T^{8} - 3833459 T^{9} + 15467045 T^{10} - 46654918 T^{11} + 178279128 T^{12} - 423412929 T^{13} + 893871739 T^{14} \))(\( 1 + 5 T + 163 T^{2} + 787 T^{3} + 13026 T^{4} + 63832 T^{5} + 695766 T^{6} + 3514392 T^{7} + 28400960 T^{8} + 145663624 T^{9} + 954747570 T^{10} + 4806528997 T^{11} + 27529531216 T^{12} + 131264750268 T^{13} + 691369674246 T^{14} + 3057167436295 T^{15} + 15126874241747 T^{16} + 62004032178313 T^{17} + 287410610593193 T^{18} + 1103637444502495 T^{19} + 4742104595653314 T^{20} + 17106553519676028 T^{21} + 68165844714406384 T^{22} + 226127391215911357 T^{23} + 853421870701924230 T^{24} + 2473887340984520584 T^{25} + 9164640397113467840 T^{26} + 21546970207885771992 T^{27} + 81049961472578240754 T^{28} + \)\(14\!\cdots\!52\)\( T^{29} + \)\(54\!\cdots\!34\)\( T^{30} + \)\(62\!\cdots\!27\)\( T^{31} + \)\(24\!\cdots\!37\)\( T^{32} + \)\(14\!\cdots\!05\)\( T^{33} + \)\(54\!\cdots\!39\)\( T^{34} \))(\( 1 - 5 T + 163 T^{2} - 787 T^{3} + 13026 T^{4} - 63832 T^{5} + 695766 T^{6} - 3514392 T^{7} + 28400960 T^{8} - 145663624 T^{9} + 954747570 T^{10} - 4806528997 T^{11} + 27529531216 T^{12} - 131264750268 T^{13} + 691369674246 T^{14} - 3057167436295 T^{15} + 15126874241747 T^{16} - 62004032178313 T^{17} + 287410610593193 T^{18} - 1103637444502495 T^{19} + 4742104595653314 T^{20} - 17106553519676028 T^{21} + 68165844714406384 T^{22} - 226127391215911357 T^{23} + 853421870701924230 T^{24} - 2473887340984520584 T^{25} + 9164640397113467840 T^{26} - 21546970207885771992 T^{27} + 81049961472578240754 T^{28} - \)\(14\!\cdots\!52\)\( T^{29} + \)\(54\!\cdots\!34\)\( T^{30} - \)\(62\!\cdots\!27\)\( T^{31} + \)\(24\!\cdots\!37\)\( T^{32} - \)\(14\!\cdots\!05\)\( T^{33} + \)\(54\!\cdots\!39\)\( T^{34} \))(\( 1 + 36 T + 850 T^{2} + 14832 T^{3} + 213196 T^{4} + 2615244 T^{5} + 28297470 T^{6} + 274680524 T^{7} + 2429084823 T^{8} + 19761847584 T^{9} + 149213238548 T^{10} + 1052186135312 T^{11} + 6968334560366 T^{12} + 43526384683348 T^{13} + 257403895691492 T^{14} + 1445357420049560 T^{15} + 7725859686222233 T^{16} + 39386485891561008 T^{17} + 191806819405103800 T^{18} + 893159691307611332 T^{19} + 3979674328886919883 T^{20} + 16970034134844615308 T^{21} + 69242261805242471800 T^{22} + \)\(27\!\cdots\!72\)\( T^{23} + \)\(10\!\cdots\!93\)\( T^{24} + \)\(35\!\cdots\!40\)\( T^{25} + \)\(12\!\cdots\!52\)\( T^{26} + \)\(38\!\cdots\!72\)\( T^{27} + \)\(11\!\cdots\!06\)\( T^{28} + \)\(33\!\cdots\!48\)\( T^{29} + \)\(91\!\cdots\!48\)\( T^{30} + \)\(23\!\cdots\!96\)\( T^{31} + \)\(53\!\cdots\!03\)\( T^{32} + \)\(11\!\cdots\!16\)\( T^{33} + \)\(22\!\cdots\!70\)\( T^{34} + \)\(39\!\cdots\!56\)\( T^{35} + \)\(61\!\cdots\!76\)\( T^{36} + \)\(81\!\cdots\!48\)\( T^{37} + \)\(88\!\cdots\!50\)\( T^{38} + \)\(71\!\cdots\!44\)\( T^{39} + \)\(37\!\cdots\!01\)\( T^{40} \))(\( 1 - 36 T + 850 T^{2} - 14832 T^{3} + 213196 T^{4} - 2615244 T^{5} + 28297470 T^{6} - 274680524 T^{7} + 2429084823 T^{8} - 19761847584 T^{9} + 149213238548 T^{10} - 1052186135312 T^{11} + 6968334560366 T^{12} - 43526384683348 T^{13} + 257403895691492 T^{14} - 1445357420049560 T^{15} + 7725859686222233 T^{16} - 39386485891561008 T^{17} + 191806819405103800 T^{18} - 893159691307611332 T^{19} + 3979674328886919883 T^{20} - 16970034134844615308 T^{21} + 69242261805242471800 T^{22} - \)\(27\!\cdots\!72\)\( T^{23} + \)\(10\!\cdots\!93\)\( T^{24} - \)\(35\!\cdots\!40\)\( T^{25} + \)\(12\!\cdots\!52\)\( T^{26} - \)\(38\!\cdots\!72\)\( T^{27} + \)\(11\!\cdots\!06\)\( T^{28} - \)\(33\!\cdots\!48\)\( T^{29} + \)\(91\!\cdots\!48\)\( T^{30} - \)\(23\!\cdots\!96\)\( T^{31} + \)\(53\!\cdots\!03\)\( T^{32} - \)\(11\!\cdots\!16\)\( T^{33} + \)\(22\!\cdots\!70\)\( T^{34} - \)\(39\!\cdots\!56\)\( T^{35} + \)\(61\!\cdots\!76\)\( T^{36} - \)\(81\!\cdots\!48\)\( T^{37} + \)\(88\!\cdots\!50\)\( T^{38} - \)\(71\!\cdots\!44\)\( T^{39} + \)\(37\!\cdots\!01\)\( T^{40} \))
$23$ (\( 1 + 5 T + 51 T^{2} + 115 T^{3} + 529 T^{4} \))(\( 1 - 3 T + 47 T^{2} - 69 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 37 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 37 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 5 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 5 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 37 T^{2} - 216 T^{3} + 851 T^{4} - 2116 T^{5} + 12167 T^{6} \))(\( 1 + T + 49 T^{2} + 71 T^{3} + 1127 T^{4} + 529 T^{5} + 12167 T^{6} \))(\( 1 + T + 49 T^{2} + 71 T^{3} + 1127 T^{4} + 529 T^{5} + 12167 T^{6} \))(\( 1 + 11 T + 101 T^{2} + 525 T^{3} + 2323 T^{4} + 5819 T^{5} + 12167 T^{6} \))(\( 1 + 13 T + 109 T^{2} + 627 T^{3} + 2507 T^{4} + 6877 T^{5} + 12167 T^{6} \))(\( 1 + 77 T^{2} + 19 T^{3} + 2870 T^{4} + 683 T^{5} + 66010 T^{6} + 10051 T^{7} + 936859 T^{8} + 6436343 T^{10} \))(\( 1 + 77 T^{2} + 19 T^{3} + 2870 T^{4} + 683 T^{5} + 66010 T^{6} + 10051 T^{7} + 936859 T^{8} + 6436343 T^{10} \))(\( 1 - 2 T + 49 T^{2} - 158 T^{3} + 1885 T^{4} - 3835 T^{5} + 43355 T^{6} - 83582 T^{7} + 596183 T^{8} - 559682 T^{9} + 6436343 T^{10} \))(\( 1 - 20 T + 290 T^{2} - 2858 T^{3} + 22970 T^{4} - 145271 T^{5} + 774478 T^{6} - 3341233 T^{7} + 12151130 T^{8} - 34773286 T^{9} + 81153890 T^{10} - 128726860 T^{11} + 148035889 T^{12} \))(\( 1 - 3 T + 106 T^{2} - 236 T^{3} + 5717 T^{4} - 10577 T^{5} + 194242 T^{6} - 292425 T^{7} + 4467566 T^{8} - 5595233 T^{9} + 69558739 T^{10} - 66042476 T^{11} + 682252358 T^{12} - 444107667 T^{13} + 3404825447 T^{14} \))(\( 1 - 3 T + 106 T^{2} - 236 T^{3} + 5717 T^{4} - 10577 T^{5} + 194242 T^{6} - 292425 T^{7} + 4467566 T^{8} - 5595233 T^{9} + 69558739 T^{10} - 66042476 T^{11} + 682252358 T^{12} - 444107667 T^{13} + 3404825447 T^{14} \))(\( 1 - 12 T + 239 T^{2} - 2133 T^{3} + 24739 T^{4} - 179111 T^{5} + 1572283 T^{6} - 9780962 T^{7} + 72560030 T^{8} - 405378699 T^{9} + 2708038262 T^{10} - 14052708460 T^{11} + 87562240915 T^{12} - 430213729605 T^{13} + 2530157859979 T^{14} - 11807208498605 T^{15} + 65455351872286 T^{16} - 288563966305146 T^{17} + 1505473093062578 T^{18} - 6246013295762045 T^{19} + 30784430682364493 T^{20} - 120391440306392805 T^{21} + 563580616377573845 T^{22} - 2080305189733920940 T^{23} + 9220397585907253114 T^{24} - 31745605330619929419 T^{25} + \)\(13\!\cdots\!90\)\( T^{26} - \)\(40\!\cdots\!38\)\( T^{27} + \)\(14\!\cdots\!41\)\( T^{28} - \)\(39\!\cdots\!31\)\( T^{29} + \)\(12\!\cdots\!37\)\( T^{30} - \)\(24\!\cdots\!97\)\( T^{31} + \)\(63\!\cdots\!73\)\( T^{32} - \)\(73\!\cdots\!32\)\( T^{33} + \)\(14\!\cdots\!03\)\( T^{34} \))(\( 1 - 12 T + 239 T^{2} - 2133 T^{3} + 24739 T^{4} - 179111 T^{5} + 1572283 T^{6} - 9780962 T^{7} + 72560030 T^{8} - 405378699 T^{9} + 2708038262 T^{10} - 14052708460 T^{11} + 87562240915 T^{12} - 430213729605 T^{13} + 2530157859979 T^{14} - 11807208498605 T^{15} + 65455351872286 T^{16} - 288563966305146 T^{17} + 1505473093062578 T^{18} - 6246013295762045 T^{19} + 30784430682364493 T^{20} - 120391440306392805 T^{21} + 563580616377573845 T^{22} - 2080305189733920940 T^{23} + 9220397585907253114 T^{24} - 31745605330619929419 T^{25} + \)\(13\!\cdots\!90\)\( T^{26} - \)\(40\!\cdots\!38\)\( T^{27} + \)\(14\!\cdots\!41\)\( T^{28} - \)\(39\!\cdots\!31\)\( T^{29} + \)\(12\!\cdots\!37\)\( T^{30} - \)\(24\!\cdots\!97\)\( T^{31} + \)\(63\!\cdots\!73\)\( T^{32} - \)\(73\!\cdots\!32\)\( T^{33} + \)\(14\!\cdots\!03\)\( T^{34} \))(\( 1 + 12 T + 264 T^{2} + 2536 T^{3} + 33322 T^{4} + 269640 T^{5} + 2694120 T^{6} + 18910876 T^{7} + 157274667 T^{8} + 975374992 T^{9} + 7077829886 T^{10} + 39272677016 T^{11} + 256551997944 T^{12} + 1286998279004 T^{13} + 7771548029638 T^{14} + 35698353619756 T^{15} + 204851440961633 T^{16} + 879534542310616 T^{17} + 4938010042319026 T^{18} + 20433799859147148 T^{19} + 114483924767861047 T^{20} + 469977396760384404 T^{21} + 2612207312386764754 T^{22} + 10701296776293264872 T^{23} + 57325832090144340353 T^{24} + \)\(22\!\cdots\!08\)\( T^{25} + \)\(11\!\cdots\!82\)\( T^{26} + \)\(43\!\cdots\!88\)\( T^{27} + \)\(20\!\cdots\!64\)\( T^{28} + \)\(70\!\cdots\!08\)\( T^{29} + \)\(29\!\cdots\!14\)\( T^{30} + \)\(92\!\cdots\!84\)\( T^{31} + \)\(34\!\cdots\!07\)\( T^{32} + \)\(95\!\cdots\!08\)\( T^{33} + \)\(31\!\cdots\!80\)\( T^{34} + \)\(71\!\cdots\!80\)\( T^{35} + \)\(20\!\cdots\!42\)\( T^{36} + \)\(35\!\cdots\!08\)\( T^{37} + \)\(85\!\cdots\!16\)\( T^{38} + \)\(89\!\cdots\!44\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))(\( 1 + 12 T + 264 T^{2} + 2536 T^{3} + 33322 T^{4} + 269640 T^{5} + 2694120 T^{6} + 18910876 T^{7} + 157274667 T^{8} + 975374992 T^{9} + 7077829886 T^{10} + 39272677016 T^{11} + 256551997944 T^{12} + 1286998279004 T^{13} + 7771548029638 T^{14} + 35698353619756 T^{15} + 204851440961633 T^{16} + 879534542310616 T^{17} + 4938010042319026 T^{18} + 20433799859147148 T^{19} + 114483924767861047 T^{20} + 469977396760384404 T^{21} + 2612207312386764754 T^{22} + 10701296776293264872 T^{23} + 57325832090144340353 T^{24} + \)\(22\!\cdots\!08\)\( T^{25} + \)\(11\!\cdots\!82\)\( T^{26} + \)\(43\!\cdots\!88\)\( T^{27} + \)\(20\!\cdots\!64\)\( T^{28} + \)\(70\!\cdots\!08\)\( T^{29} + \)\(29\!\cdots\!14\)\( T^{30} + \)\(92\!\cdots\!84\)\( T^{31} + \)\(34\!\cdots\!07\)\( T^{32} + \)\(95\!\cdots\!08\)\( T^{33} + \)\(31\!\cdots\!80\)\( T^{34} + \)\(71\!\cdots\!80\)\( T^{35} + \)\(20\!\cdots\!42\)\( T^{36} + \)\(35\!\cdots\!08\)\( T^{37} + \)\(85\!\cdots\!16\)\( T^{38} + \)\(89\!\cdots\!44\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))
$29$ (\( 1 + 5 T + 53 T^{2} + 145 T^{3} + 841 T^{4} \))(\( 1 - 9 T + 67 T^{2} - 261 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 49 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 49 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 + 38 T^{2} + 841 T^{4} \))(\( 1 + 38 T^{2} + 841 T^{4} \))(\( 1 + 6 T + 83 T^{2} + 308 T^{3} + 2407 T^{4} + 5046 T^{5} + 24389 T^{6} \))(\( 1 + 67 T^{2} - 24 T^{3} + 1943 T^{4} + 24389 T^{6} \))(\( 1 + 67 T^{2} - 24 T^{3} + 1943 T^{4} + 24389 T^{6} \))(\( 1 - 10 T + 103 T^{2} - 572 T^{3} + 2987 T^{4} - 8410 T^{5} + 24389 T^{6} \))(\( 1 - 2 T + 51 T^{2} - 108 T^{3} + 1479 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( 1 + 10 T + 154 T^{2} + 1024 T^{3} + 8899 T^{4} + 42621 T^{5} + 258071 T^{6} + 861184 T^{7} + 3755906 T^{8} + 7072810 T^{9} + 20511149 T^{10} \))(\( 1 + 10 T + 154 T^{2} + 1024 T^{3} + 8899 T^{4} + 42621 T^{5} + 258071 T^{6} + 861184 T^{7} + 3755906 T^{8} + 7072810 T^{9} + 20511149 T^{10} \))(\( 1 + 5 T + 74 T^{2} + 230 T^{3} + 2629 T^{4} + 6442 T^{5} + 76241 T^{6} + 193430 T^{7} + 1804786 T^{8} + 3536405 T^{9} + 20511149 T^{10} \))(\( 1 + 9 T + 95 T^{2} + 533 T^{3} + 3647 T^{4} + 18534 T^{5} + 110962 T^{6} + 537486 T^{7} + 3067127 T^{8} + 12999337 T^{9} + 67191695 T^{10} + 184600341 T^{11} + 594823321 T^{12} \))(\( 1 + 14 T + 162 T^{2} + 1246 T^{3} + 9813 T^{4} + 61032 T^{5} + 384012 T^{6} + 2001928 T^{7} + 11136348 T^{8} + 51327912 T^{9} + 239329257 T^{10} + 881272126 T^{11} + 3322806138 T^{12} + 8327526494 T^{13} + 17249876309 T^{14} \))(\( 1 + 14 T + 162 T^{2} + 1246 T^{3} + 9813 T^{4} + 61032 T^{5} + 384012 T^{6} + 2001928 T^{7} + 11136348 T^{8} + 51327912 T^{9} + 239329257 T^{10} + 881272126 T^{11} + 3322806138 T^{12} + 8327526494 T^{13} + 17249876309 T^{14} \))(\( 1 - 14 T + 355 T^{2} - 3740 T^{3} + 56093 T^{4} - 485019 T^{5} + 5537717 T^{6} - 41259601 T^{7} + 394776748 T^{8} - 2612080276 T^{9} + 21996183568 T^{10} - 131841485053 T^{11} + 1005289757439 T^{12} - 5533937998669 T^{13} + 38868388142751 T^{14} - 198363811397758 T^{15} + 1295632977449316 T^{16} - 6163616090425740 T^{17} + 37573356346030164 T^{18} - 166823965385514478 T^{19} + 947961118413554139 T^{20} - 3914049201636608989 T^{21} + 20619648003005187411 T^{22} - 78422389984797321013 T^{23} + \)\(37\!\cdots\!12\)\( T^{24} - \)\(13\!\cdots\!36\)\( T^{25} + \)\(57\!\cdots\!12\)\( T^{26} - \)\(17\!\cdots\!01\)\( T^{27} + \)\(67\!\cdots\!93\)\( T^{28} - \)\(17\!\cdots\!79\)\( T^{29} + \)\(57\!\cdots\!77\)\( T^{30} - \)\(11\!\cdots\!40\)\( T^{31} + \)\(30\!\cdots\!95\)\( T^{32} - \)\(35\!\cdots\!94\)\( T^{33} + \)\(72\!\cdots\!09\)\( T^{34} \))(\( 1 - 14 T + 355 T^{2} - 3740 T^{3} + 56093 T^{4} - 485019 T^{5} + 5537717 T^{6} - 41259601 T^{7} + 394776748 T^{8} - 2612080276 T^{9} + 21996183568 T^{10} - 131841485053 T^{11} + 1005289757439 T^{12} - 5533937998669 T^{13} + 38868388142751 T^{14} - 198363811397758 T^{15} + 1295632977449316 T^{16} - 6163616090425740 T^{17} + 37573356346030164 T^{18} - 166823965385514478 T^{19} + 947961118413554139 T^{20} - 3914049201636608989 T^{21} + 20619648003005187411 T^{22} - 78422389984797321013 T^{23} + \)\(37\!\cdots\!12\)\( T^{24} - \)\(13\!\cdots\!36\)\( T^{25} + \)\(57\!\cdots\!12\)\( T^{26} - \)\(17\!\cdots\!01\)\( T^{27} + \)\(67\!\cdots\!93\)\( T^{28} - \)\(17\!\cdots\!79\)\( T^{29} + \)\(57\!\cdots\!77\)\( T^{30} - \)\(11\!\cdots\!40\)\( T^{31} + \)\(30\!\cdots\!95\)\( T^{32} - \)\(35\!\cdots\!94\)\( T^{33} + \)\(72\!\cdots\!09\)\( T^{34} \))(\( 1 - 4 T + 220 T^{2} - 244 T^{3} + 22487 T^{4} + 32268 T^{5} + 1632064 T^{6} + 5509328 T^{7} + 102545570 T^{8} + 438777020 T^{9} + 5759544558 T^{10} + 25922431552 T^{11} + 281410604106 T^{12} + 1289331313248 T^{13} + 11973920371798 T^{14} + 55252548869188 T^{15} + 453676297490541 T^{16} + 2046976880657540 T^{17} + 15492456976010384 T^{18} + 66546147792227480 T^{19} + 475112880598256414 T^{20} + 1929838285974596920 T^{21} + 13029156316824732944 T^{22} + 49923719142356743060 T^{23} + \)\(32\!\cdots\!21\)\( T^{24} + \)\(11\!\cdots\!12\)\( T^{25} + \)\(71\!\cdots\!58\)\( T^{26} + \)\(22\!\cdots\!32\)\( T^{27} + \)\(14\!\cdots\!66\)\( T^{28} + \)\(37\!\cdots\!88\)\( T^{29} + \)\(24\!\cdots\!58\)\( T^{30} + \)\(53\!\cdots\!80\)\( T^{31} + \)\(36\!\cdots\!70\)\( T^{32} + \)\(56\!\cdots\!92\)\( T^{33} + \)\(48\!\cdots\!84\)\( T^{34} + \)\(27\!\cdots\!32\)\( T^{35} + \)\(56\!\cdots\!27\)\( T^{36} - \)\(17\!\cdots\!96\)\( T^{37} + \)\(46\!\cdots\!20\)\( T^{38} - \)\(24\!\cdots\!76\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))(\( 1 - 4 T + 220 T^{2} - 244 T^{3} + 22487 T^{4} + 32268 T^{5} + 1632064 T^{6} + 5509328 T^{7} + 102545570 T^{8} + 438777020 T^{9} + 5759544558 T^{10} + 25922431552 T^{11} + 281410604106 T^{12} + 1289331313248 T^{13} + 11973920371798 T^{14} + 55252548869188 T^{15} + 453676297490541 T^{16} + 2046976880657540 T^{17} + 15492456976010384 T^{18} + 66546147792227480 T^{19} + 475112880598256414 T^{20} + 1929838285974596920 T^{21} + 13029156316824732944 T^{22} + 49923719142356743060 T^{23} + \)\(32\!\cdots\!21\)\( T^{24} + \)\(11\!\cdots\!12\)\( T^{25} + \)\(71\!\cdots\!58\)\( T^{26} + \)\(22\!\cdots\!32\)\( T^{27} + \)\(14\!\cdots\!66\)\( T^{28} + \)\(37\!\cdots\!88\)\( T^{29} + \)\(24\!\cdots\!58\)\( T^{30} + \)\(53\!\cdots\!80\)\( T^{31} + \)\(36\!\cdots\!70\)\( T^{32} + \)\(56\!\cdots\!92\)\( T^{33} + \)\(48\!\cdots\!84\)\( T^{34} + \)\(27\!\cdots\!32\)\( T^{35} + \)\(56\!\cdots\!27\)\( T^{36} - \)\(17\!\cdots\!96\)\( T^{37} + \)\(46\!\cdots\!20\)\( T^{38} - \)\(24\!\cdots\!76\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))
$31$ (\( 1 + 5 T + 37 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 - 17 T + 133 T^{2} - 527 T^{3} + 961 T^{4} \))(\( 1 - T + 59 T^{2} - 31 T^{3} + 961 T^{4} \))(\( 1 + T + 59 T^{2} + 31 T^{3} + 961 T^{4} \))(\( 1 + 4 T + 61 T^{2} + 124 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 61 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 + 16 T + 157 T^{2} + 1024 T^{3} + 4867 T^{4} + 15376 T^{5} + 29791 T^{6} \))(\( 1 + 2 T + 25 T^{2} + 180 T^{3} + 775 T^{4} + 1922 T^{5} + 29791 T^{6} \))(\( 1 - 2 T + 25 T^{2} - 180 T^{3} + 775 T^{4} - 1922 T^{5} + 29791 T^{6} \))(\( 1 - 2 T + 77 T^{2} - 100 T^{3} + 2387 T^{4} - 1922 T^{5} + 29791 T^{6} \))(\( 1 + 9 T^{2} + 56 T^{3} + 279 T^{4} + 29791 T^{6} \))(\( 1 + 6 T + 93 T^{2} + 515 T^{3} + 4802 T^{4} + 20097 T^{5} + 148862 T^{6} + 494915 T^{7} + 2770563 T^{8} + 5541126 T^{9} + 28629151 T^{10} \))(\( 1 - 6 T + 93 T^{2} - 515 T^{3} + 4802 T^{4} - 20097 T^{5} + 148862 T^{6} - 494915 T^{7} + 2770563 T^{8} - 5541126 T^{9} + 28629151 T^{10} \))(\( 1 + 17 T + 226 T^{2} + 2084 T^{3} + 16065 T^{4} + 96590 T^{5} + 498015 T^{6} + 2002724 T^{7} + 6732766 T^{8} + 15699857 T^{9} + 28629151 T^{10} \))(\( 1 - 27 T + 443 T^{2} - 5167 T^{3} + 47219 T^{4} - 349172 T^{5} + 2134434 T^{6} - 10824332 T^{7} + 45377459 T^{8} - 153930097 T^{9} + 409119803 T^{10} - 772987077 T^{11} + 887503681 T^{12} \))(\( 1 + 34 T + 608 T^{2} + 7498 T^{3} + 72199 T^{4} + 579438 T^{5} + 3996968 T^{6} + 23893956 T^{7} + 123906008 T^{8} + 556839918 T^{9} + 2150880409 T^{10} + 6924560458 T^{11} + 17406523808 T^{12} + 30175125154 T^{13} + 27512614111 T^{14} \))(\( 1 - 34 T + 608 T^{2} - 7498 T^{3} + 72199 T^{4} - 579438 T^{5} + 3996968 T^{6} - 23893956 T^{7} + 123906008 T^{8} - 556839918 T^{9} + 2150880409 T^{10} - 6924560458 T^{11} + 17406523808 T^{12} - 30175125154 T^{13} + 27512614111 T^{14} \))(\( 1 - 3 T + 347 T^{2} - 1300 T^{3} + 59126 T^{4} - 256653 T^{5} + 6622408 T^{6} - 31452855 T^{7} + 548340437 T^{8} - 2723127577 T^{9} + 35654760419 T^{10} - 178563886691 T^{11} + 1883992694832 T^{12} - 9237468719559 T^{13} + 82547595645174 T^{14} - 386125535886930 T^{15} + 3034111157193856 T^{16} - 13206622392649632 T^{17} + 94057445873009536 T^{18} - 371066639987339730 T^{19} + 2459175421865378634 T^{20} - 8530996349355847239 T^{21} + 53937111343242247632 T^{22} - \)\(15\!\cdots\!71\)\( T^{23} + \)\(98\!\cdots\!09\)\( T^{24} - \)\(23\!\cdots\!57\)\( T^{25} + \)\(14\!\cdots\!27\)\( T^{26} - \)\(25\!\cdots\!55\)\( T^{27} + \)\(16\!\cdots\!48\)\( T^{28} - \)\(20\!\cdots\!33\)\( T^{29} + \)\(14\!\cdots\!66\)\( T^{30} - \)\(98\!\cdots\!00\)\( T^{31} + \)\(81\!\cdots\!97\)\( T^{32} - \)\(21\!\cdots\!43\)\( T^{33} + \)\(22\!\cdots\!11\)\( T^{34} \))(\( 1 + 3 T + 347 T^{2} + 1300 T^{3} + 59126 T^{4} + 256653 T^{5} + 6622408 T^{6} + 31452855 T^{7} + 548340437 T^{8} + 2723127577 T^{9} + 35654760419 T^{10} + 178563886691 T^{11} + 1883992694832 T^{12} + 9237468719559 T^{13} + 82547595645174 T^{14} + 386125535886930 T^{15} + 3034111157193856 T^{16} + 13206622392649632 T^{17} + 94057445873009536 T^{18} + 371066639987339730 T^{19} + 2459175421865378634 T^{20} + 8530996349355847239 T^{21} + 53937111343242247632 T^{22} + \)\(15\!\cdots\!71\)\( T^{23} + \)\(98\!\cdots\!09\)\( T^{24} + \)\(23\!\cdots\!57\)\( T^{25} + \)\(14\!\cdots\!27\)\( T^{26} + \)\(25\!\cdots\!55\)\( T^{27} + \)\(16\!\cdots\!48\)\( T^{28} + \)\(20\!\cdots\!33\)\( T^{29} + \)\(14\!\cdots\!66\)\( T^{30} + \)\(98\!\cdots\!00\)\( T^{31} + \)\(81\!\cdots\!97\)\( T^{32} + \)\(21\!\cdots\!43\)\( T^{33} + \)\(22\!\cdots\!11\)\( T^{34} \))(\( 1 + 80 T + 3462 T^{2} + 105312 T^{3} + 2503157 T^{4} + 49192900 T^{5} + 827980240 T^{6} + 12224645744 T^{7} + 161090092794 T^{8} + 1919482258212 T^{9} + 20892465795374 T^{10} + 209404899706928 T^{11} + 1945347509950614 T^{12} + 16838784245902600 T^{13} + 136391722177006866 T^{14} + 1037364865659009948 T^{15} + 7429138295090538405 T^{16} + 50204137294293347096 T^{17} + \)\(32\!\cdots\!46\)\( T^{18} + \)\(19\!\cdots\!32\)\( T^{19} + \)\(11\!\cdots\!02\)\( T^{20} + \)\(60\!\cdots\!92\)\( T^{21} + \)\(30\!\cdots\!06\)\( T^{22} + \)\(14\!\cdots\!36\)\( T^{23} + \)\(68\!\cdots\!05\)\( T^{24} + \)\(29\!\cdots\!48\)\( T^{25} + \)\(12\!\cdots\!46\)\( T^{26} + \)\(46\!\cdots\!00\)\( T^{27} + \)\(16\!\cdots\!74\)\( T^{28} + \)\(55\!\cdots\!88\)\( T^{29} + \)\(17\!\cdots\!74\)\( T^{30} + \)\(48\!\cdots\!72\)\( T^{31} + \)\(12\!\cdots\!34\)\( T^{32} + \)\(29\!\cdots\!04\)\( T^{33} + \)\(62\!\cdots\!40\)\( T^{34} + \)\(11\!\cdots\!00\)\( T^{35} + \)\(18\!\cdots\!17\)\( T^{36} + \)\(23\!\cdots\!32\)\( T^{37} + \)\(24\!\cdots\!42\)\( T^{38} + \)\(17\!\cdots\!80\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))(\( 1 - 80 T + 3462 T^{2} - 105312 T^{3} + 2503157 T^{4} - 49192900 T^{5} + 827980240 T^{6} - 12224645744 T^{7} + 161090092794 T^{8} - 1919482258212 T^{9} + 20892465795374 T^{10} - 209404899706928 T^{11} + 1945347509950614 T^{12} - 16838784245902600 T^{13} + 136391722177006866 T^{14} - 1037364865659009948 T^{15} + 7429138295090538405 T^{16} - 50204137294293347096 T^{17} + \)\(32\!\cdots\!46\)\( T^{18} - \)\(19\!\cdots\!32\)\( T^{19} + \)\(11\!\cdots\!02\)\( T^{20} - \)\(60\!\cdots\!92\)\( T^{21} + \)\(30\!\cdots\!06\)\( T^{22} - \)\(14\!\cdots\!36\)\( T^{23} + \)\(68\!\cdots\!05\)\( T^{24} - \)\(29\!\cdots\!48\)\( T^{25} + \)\(12\!\cdots\!46\)\( T^{26} - \)\(46\!\cdots\!00\)\( T^{27} + \)\(16\!\cdots\!74\)\( T^{28} - \)\(55\!\cdots\!88\)\( T^{29} + \)\(17\!\cdots\!74\)\( T^{30} - \)\(48\!\cdots\!72\)\( T^{31} + \)\(12\!\cdots\!34\)\( T^{32} - \)\(29\!\cdots\!04\)\( T^{33} + \)\(62\!\cdots\!40\)\( T^{34} - \)\(11\!\cdots\!00\)\( T^{35} + \)\(18\!\cdots\!17\)\( T^{36} - \)\(23\!\cdots\!32\)\( T^{37} + \)\(24\!\cdots\!42\)\( T^{38} - \)\(17\!\cdots\!80\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))
$37$ (\( 1 + 10 T + 94 T^{2} + 370 T^{3} + 1369 T^{4} \))(\( 1 - 2 T + 30 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 + 22 T^{2} + 1369 T^{4} \))(\( 1 + 22 T^{2} + 1369 T^{4} \))(\( 1 - 2 T + 55 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 - 2 T + 55 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 + 6 T + 75 T^{2} + 336 T^{3} + 2775 T^{4} + 8214 T^{5} + 50653 T^{6} \))(\( 1 + 13 T + 141 T^{2} + 953 T^{3} + 5217 T^{4} + 17797 T^{5} + 50653 T^{6} \))(\( 1 + 13 T + 141 T^{2} + 953 T^{3} + 5217 T^{4} + 17797 T^{5} + 50653 T^{6} \))(\( 1 - 3 T - 11 T^{2} + 277 T^{3} - 407 T^{4} - 4107 T^{5} + 50653 T^{6} \))(\( 1 - 3 T + 93 T^{2} - 195 T^{3} + 3441 T^{4} - 4107 T^{5} + 50653 T^{6} \))(\( 1 + 18 T + 250 T^{2} + 2442 T^{3} + 20191 T^{4} + 131177 T^{5} + 747067 T^{6} + 3343098 T^{7} + 12663250 T^{8} + 33734898 T^{9} + 69343957 T^{10} \))(\( 1 + 18 T + 250 T^{2} + 2442 T^{3} + 20191 T^{4} + 131177 T^{5} + 747067 T^{6} + 3343098 T^{7} + 12663250 T^{8} + 33734898 T^{9} + 69343957 T^{10} \))(\( 1 + 7 T + 149 T^{2} + 879 T^{3} + 9772 T^{4} + 45884 T^{5} + 361564 T^{6} + 1203351 T^{7} + 7547297 T^{8} + 13119127 T^{9} + 69343957 T^{10} \))(\( 1 - 19 T + 276 T^{2} - 3096 T^{3} + 28095 T^{4} - 214681 T^{5} + 1424272 T^{6} - 7943197 T^{7} + 38462055 T^{8} - 156821688 T^{9} + 517268436 T^{10} - 1317535183 T^{11} + 2565726409 T^{12} \))(\( 1 - 7 T + 121 T^{2} - 651 T^{3} + 7671 T^{4} - 38793 T^{5} + 395023 T^{6} - 1773722 T^{7} + 14615851 T^{8} - 53107617 T^{9} + 388559163 T^{10} - 1220078811 T^{11} + 8390618797 T^{12} - 17960084863 T^{13} + 94931877133 T^{14} \))(\( 1 - 7 T + 121 T^{2} - 651 T^{3} + 7671 T^{4} - 38793 T^{5} + 395023 T^{6} - 1773722 T^{7} + 14615851 T^{8} - 53107617 T^{9} + 388559163 T^{10} - 1220078811 T^{11} + 8390618797 T^{12} - 17960084863 T^{13} + 94931877133 T^{14} \))(\( 1 - 24 T + 635 T^{2} - 10550 T^{3} + 172557 T^{4} - 2265053 T^{5} + 28602825 T^{6} - 315182397 T^{7} + 3324477148 T^{8} - 31793967732 T^{9} + 290992183272 T^{10} - 2463971058773 T^{11} + 19986593517171 T^{12} - 151691430047243 T^{13} + 1104063428511095 T^{14} - 7565479281788688 T^{15} + 49751467190780188 T^{16} - 308878786314680280 T^{17} + 1840804286058866956 T^{18} - 10357141136768713872 T^{19} + 55924124844372495035 T^{20} - \)\(28\!\cdots\!23\)\( T^{21} + \)\(13\!\cdots\!47\)\( T^{22} - \)\(63\!\cdots\!57\)\( T^{23} + \)\(27\!\cdots\!76\)\( T^{24} - \)\(11\!\cdots\!72\)\( T^{25} + \)\(43\!\cdots\!96\)\( T^{26} - \)\(15\!\cdots\!53\)\( T^{27} + \)\(50\!\cdots\!25\)\( T^{28} - \)\(14\!\cdots\!93\)\( T^{29} + \)\(42\!\cdots\!29\)\( T^{30} - \)\(95\!\cdots\!50\)\( T^{31} + \)\(21\!\cdots\!55\)\( T^{32} - \)\(29\!\cdots\!84\)\( T^{33} + \)\(45\!\cdots\!17\)\( T^{34} \))(\( 1 - 24 T + 635 T^{2} - 10550 T^{3} + 172557 T^{4} - 2265053 T^{5} + 28602825 T^{6} - 315182397 T^{7} + 3324477148 T^{8} - 31793967732 T^{9} + 290992183272 T^{10} - 2463971058773 T^{11} + 19986593517171 T^{12} - 151691430047243 T^{13} + 1104063428511095 T^{14} - 7565479281788688 T^{15} + 49751467190780188 T^{16} - 308878786314680280 T^{17} + 1840804286058866956 T^{18} - 10357141136768713872 T^{19} + 55924124844372495035 T^{20} - \)\(28\!\cdots\!23\)\( T^{21} + \)\(13\!\cdots\!47\)\( T^{22} - \)\(63\!\cdots\!57\)\( T^{23} + \)\(27\!\cdots\!76\)\( T^{24} - \)\(11\!\cdots\!72\)\( T^{25} + \)\(43\!\cdots\!96\)\( T^{26} - \)\(15\!\cdots\!53\)\( T^{27} + \)\(50\!\cdots\!25\)\( T^{28} - \)\(14\!\cdots\!93\)\( T^{29} + \)\(42\!\cdots\!29\)\( T^{30} - \)\(95\!\cdots\!50\)\( T^{31} + \)\(21\!\cdots\!55\)\( T^{32} - \)\(29\!\cdots\!84\)\( T^{33} + \)\(45\!\cdots\!17\)\( T^{34} \))(\( 1 - 4 T + 374 T^{2} - 1660 T^{3} + 70523 T^{4} - 338700 T^{5} + 8965224 T^{6} - 45621500 T^{7} + 865632083 T^{8} - 4582276244 T^{9} + 67710044698 T^{10} - 366407864592 T^{11} + 4461496150465 T^{12} - 24259552100896 T^{13} + 253783168848574 T^{14} - 1363596231230644 T^{15} + 12654287455652152 T^{16} - 66128635855706968 T^{17} + 558189785908848346 T^{18} - 2794489891421497944 T^{19} + 21888197222810126128 T^{20} - \)\(10\!\cdots\!28\)\( T^{21} + \)\(76\!\cdots\!74\)\( T^{22} - \)\(33\!\cdots\!04\)\( T^{23} + \)\(23\!\cdots\!72\)\( T^{24} - \)\(94\!\cdots\!08\)\( T^{25} + \)\(65\!\cdots\!66\)\( T^{26} - \)\(23\!\cdots\!68\)\( T^{27} + \)\(15\!\cdots\!65\)\( T^{28} - \)\(47\!\cdots\!84\)\( T^{29} + \)\(32\!\cdots\!02\)\( T^{30} - \)\(81\!\cdots\!72\)\( T^{31} + \)\(56\!\cdots\!23\)\( T^{32} - \)\(11\!\cdots\!00\)\( T^{33} + \)\(80\!\cdots\!36\)\( T^{34} - \)\(11\!\cdots\!00\)\( T^{35} + \)\(87\!\cdots\!43\)\( T^{36} - \)\(75\!\cdots\!20\)\( T^{37} + \)\(63\!\cdots\!46\)\( T^{38} - \)\(24\!\cdots\!92\)\( T^{39} + \)\(23\!\cdots\!01\)\( T^{40} \))(\( 1 - 4 T + 374 T^{2} - 1660 T^{3} + 70523 T^{4} - 338700 T^{5} + 8965224 T^{6} - 45621500 T^{7} + 865632083 T^{8} - 4582276244 T^{9} + 67710044698 T^{10} - 366407864592 T^{11} + 4461496150465 T^{12} - 24259552100896 T^{13} + 253783168848574 T^{14} - 1363596231230644 T^{15} + 12654287455652152 T^{16} - 66128635855706968 T^{17} + 558189785908848346 T^{18} - 2794489891421497944 T^{19} + 21888197222810126128 T^{20} - \)\(10\!\cdots\!28\)\( T^{21} + \)\(76\!\cdots\!74\)\( T^{22} - \)\(33\!\cdots\!04\)\( T^{23} + \)\(23\!\cdots\!72\)\( T^{24} - \)\(94\!\cdots\!08\)\( T^{25} + \)\(65\!\cdots\!66\)\( T^{26} - \)\(23\!\cdots\!68\)\( T^{27} + \)\(15\!\cdots\!65\)\( T^{28} - \)\(47\!\cdots\!84\)\( T^{29} + \)\(32\!\cdots\!02\)\( T^{30} - \)\(81\!\cdots\!72\)\( T^{31} + \)\(56\!\cdots\!23\)\( T^{32} - \)\(11\!\cdots\!00\)\( T^{33} + \)\(80\!\cdots\!36\)\( T^{34} - \)\(11\!\cdots\!00\)\( T^{35} + \)\(87\!\cdots\!43\)\( T^{36} - \)\(75\!\cdots\!20\)\( T^{37} + \)\(63\!\cdots\!46\)\( T^{38} - \)\(24\!\cdots\!92\)\( T^{39} + \)\(23\!\cdots\!01\)\( T^{40} \))
$41$ (\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{7} \))(\( ( 1 + T )^{17} \))(\( ( 1 - T )^{17} \))(\( ( 1 + T )^{20} \))(\( ( 1 - T )^{20} \))
$43$ (\( ( 1 + T + 43 T^{2} )^{2} \))(\( 1 + 2 T + 7 T^{2} + 86 T^{3} + 1849 T^{4} \))(\( 1 + 12 T + 109 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 + 12 T + 109 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 + 4 T + 70 T^{2} + 172 T^{3} + 1849 T^{4} \))(\( 1 + 4 T + 70 T^{2} + 172 T^{3} + 1849 T^{4} \))(\( 1 + 4 T + 121 T^{2} + 328 T^{3} + 5203 T^{4} + 7396 T^{5} + 79507 T^{6} \))(\( 1 + T + 121 T^{2} + 83 T^{3} + 5203 T^{4} + 1849 T^{5} + 79507 T^{6} \))(\( 1 + T + 121 T^{2} + 83 T^{3} + 5203 T^{4} + 1849 T^{5} + 79507 T^{6} \))(\( 1 - 9 T + 25 T^{2} + 61 T^{3} + 1075 T^{4} - 16641 T^{5} + 79507 T^{6} \))(\( 1 - 11 T + 125 T^{2} - 945 T^{3} + 5375 T^{4} - 20339 T^{5} + 79507 T^{6} \))(\( 1 + 14 T + 162 T^{2} + 1230 T^{3} + 7725 T^{4} + 51435 T^{5} + 332175 T^{6} + 2274270 T^{7} + 12880134 T^{8} + 47863214 T^{9} + 147008443 T^{10} \))(\( 1 + 14 T + 162 T^{2} + 1230 T^{3} + 7725 T^{4} + 51435 T^{5} + 332175 T^{6} + 2274270 T^{7} + 12880134 T^{8} + 47863214 T^{9} + 147008443 T^{10} \))(\( 1 - T + 102 T^{2} - 198 T^{3} + 6135 T^{4} - 15081 T^{5} + 263805 T^{6} - 366102 T^{7} + 8109714 T^{8} - 3418801 T^{9} + 147008443 T^{10} \))(\( 1 - 19 T + 285 T^{2} - 3095 T^{3} + 29793 T^{4} - 236989 T^{5} + 1697038 T^{6} - 10190527 T^{7} + 55087257 T^{8} - 246074165 T^{9} + 974358285 T^{10} - 2793160417 T^{11} + 6321363049 T^{12} \))(\( 1 + 3 T + 91 T^{2} + 111 T^{3} + 6288 T^{4} - 1242 T^{5} + 282726 T^{6} - 294681 T^{7} + 12157218 T^{8} - 2296458 T^{9} + 499940016 T^{10} + 379486911 T^{11} + 13377768313 T^{12} + 18964089147 T^{13} + 271818611107 T^{14} \))(\( 1 + 3 T + 91 T^{2} + 111 T^{3} + 6288 T^{4} - 1242 T^{5} + 282726 T^{6} - 294681 T^{7} + 12157218 T^{8} - 2296458 T^{9} + 499940016 T^{10} + 379486911 T^{11} + 13377768313 T^{12} + 18964089147 T^{13} + 271818611107 T^{14} \))(\( 1 - 14 T + 501 T^{2} - 5620 T^{3} + 115543 T^{4} - 1085639 T^{5} + 16701801 T^{6} - 134788067 T^{7} + 1720763284 T^{8} - 12108396512 T^{9} + 135918356264 T^{10} - 843646315319 T^{11} + 8674070184701 T^{12} - 48173565945585 T^{13} + 468181132007451 T^{14} - 2377958296010682 T^{15} + 22259636743436564 T^{16} - 106350257816075028 T^{17} + 957164379967772252 T^{18} - 4396844889323751018 T^{19} + 37223677262516406657 T^{20} - \)\(16\!\cdots\!85\)\( T^{21} + \)\(12\!\cdots\!43\)\( T^{22} - \)\(53\!\cdots\!31\)\( T^{23} + \)\(36\!\cdots\!48\)\( T^{24} - \)\(14\!\cdots\!12\)\( T^{25} + \)\(86\!\cdots\!12\)\( T^{26} - \)\(29\!\cdots\!83\)\( T^{27} + \)\(15\!\cdots\!07\)\( T^{28} - \)\(43\!\cdots\!39\)\( T^{29} + \)\(19\!\cdots\!49\)\( T^{30} - \)\(41\!\cdots\!80\)\( T^{31} + \)\(15\!\cdots\!07\)\( T^{32} - \)\(19\!\cdots\!14\)\( T^{33} + \)\(58\!\cdots\!43\)\( T^{34} \))(\( 1 - 14 T + 501 T^{2} - 5620 T^{3} + 115543 T^{4} - 1085639 T^{5} + 16701801 T^{6} - 134788067 T^{7} + 1720763284 T^{8} - 12108396512 T^{9} + 135918356264 T^{10} - 843646315319 T^{11} + 8674070184701 T^{12} - 48173565945585 T^{13} + 468181132007451 T^{14} - 2377958296010682 T^{15} + 22259636743436564 T^{16} - 106350257816075028 T^{17} + 957164379967772252 T^{18} - 4396844889323751018 T^{19} + 37223677262516406657 T^{20} - \)\(16\!\cdots\!85\)\( T^{21} + \)\(12\!\cdots\!43\)\( T^{22} - \)\(53\!\cdots\!31\)\( T^{23} + \)\(36\!\cdots\!48\)\( T^{24} - \)\(14\!\cdots\!12\)\( T^{25} + \)\(86\!\cdots\!12\)\( T^{26} - \)\(29\!\cdots\!83\)\( T^{27} + \)\(15\!\cdots\!07\)\( T^{28} - \)\(43\!\cdots\!39\)\( T^{29} + \)\(19\!\cdots\!49\)\( T^{30} - \)\(41\!\cdots\!80\)\( T^{31} + \)\(15\!\cdots\!07\)\( T^{32} - \)\(19\!\cdots\!14\)\( T^{33} + \)\(58\!\cdots\!43\)\( T^{34} \))(\( 1 + 506 T^{2} - 260 T^{3} + 123969 T^{4} - 108184 T^{5} + 19695068 T^{6} - 20707044 T^{7} + 2291957422 T^{8} - 2384282952 T^{9} + 209137290724 T^{10} - 179028757692 T^{11} + 15642979002248 T^{12} - 8541669931816 T^{13} + 991388610021174 T^{14} - 184064643392124 T^{15} + 54749735683103433 T^{16} + 7151756916697124 T^{17} + 2700979966466963536 T^{18} + 835585910411141060 T^{19} + \)\(12\!\cdots\!59\)\( T^{20} + 35930194147679065580 T^{21} + \)\(49\!\cdots\!64\)\( T^{22} + \)\(56\!\cdots\!68\)\( T^{23} + \)\(18\!\cdots\!33\)\( T^{24} - \)\(27\!\cdots\!32\)\( T^{25} + \)\(62\!\cdots\!26\)\( T^{26} - \)\(23\!\cdots\!12\)\( T^{27} + \)\(18\!\cdots\!48\)\( T^{28} - \)\(89\!\cdots\!56\)\( T^{29} + \)\(45\!\cdots\!76\)\( T^{30} - \)\(22\!\cdots\!64\)\( T^{31} + \)\(91\!\cdots\!22\)\( T^{32} - \)\(35\!\cdots\!92\)\( T^{33} + \)\(14\!\cdots\!32\)\( T^{34} - \)\(34\!\cdots\!88\)\( T^{35} + \)\(16\!\cdots\!69\)\( T^{36} - \)\(15\!\cdots\!80\)\( T^{37} + \)\(12\!\cdots\!94\)\( T^{38} + \)\(46\!\cdots\!01\)\( T^{40} \))(\( 1 + 506 T^{2} - 260 T^{3} + 123969 T^{4} - 108184 T^{5} + 19695068 T^{6} - 20707044 T^{7} + 2291957422 T^{8} - 2384282952 T^{9} + 209137290724 T^{10} - 179028757692 T^{11} + 15642979002248 T^{12} - 8541669931816 T^{13} + 991388610021174 T^{14} - 184064643392124 T^{15} + 54749735683103433 T^{16} + 7151756916697124 T^{17} + 2700979966466963536 T^{18} + 835585910411141060 T^{19} + \)\(12\!\cdots\!59\)\( T^{20} + 35930194147679065580 T^{21} + \)\(49\!\cdots\!64\)\( T^{22} + \)\(56\!\cdots\!68\)\( T^{23} + \)\(18\!\cdots\!33\)\( T^{24} - \)\(27\!\cdots\!32\)\( T^{25} + \)\(62\!\cdots\!26\)\( T^{26} - \)\(23\!\cdots\!12\)\( T^{27} + \)\(18\!\cdots\!48\)\( T^{28} - \)\(89\!\cdots\!56\)\( T^{29} + \)\(45\!\cdots\!76\)\( T^{30} - \)\(22\!\cdots\!64\)\( T^{31} + \)\(91\!\cdots\!22\)\( T^{32} - \)\(35\!\cdots\!92\)\( T^{33} + \)\(14\!\cdots\!32\)\( T^{34} - \)\(34\!\cdots\!88\)\( T^{35} + \)\(16\!\cdots\!69\)\( T^{36} - \)\(15\!\cdots\!80\)\( T^{37} + \)\(12\!\cdots\!94\)\( T^{38} + \)\(46\!\cdots\!01\)\( T^{40} \))
$47$ (\( 1 + 6 T + 58 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 2 T + 90 T^{2} - 94 T^{3} + 2209 T^{4} \))(\( ( 1 - 9 T + 47 T^{2} )^{2} \))(\( ( 1 + 9 T + 47 T^{2} )^{2} \))(\( 1 + 2 T + 75 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( 1 - 2 T + 75 T^{2} - 94 T^{3} + 2209 T^{4} \))(\( 1 + 21 T^{2} + 502 T^{3} + 987 T^{4} + 103823 T^{6} \))(\( 1 + 9 T + 129 T^{2} + 713 T^{3} + 6063 T^{4} + 19881 T^{5} + 103823 T^{6} \))(\( 1 - 9 T + 129 T^{2} - 713 T^{3} + 6063 T^{4} - 19881 T^{5} + 103823 T^{6} \))(\( 1 - 7 T + 101 T^{2} - 445 T^{3} + 4747 T^{4} - 15463 T^{5} + 103823 T^{6} \))(\( 1 + 13 T + 195 T^{2} + 1293 T^{3} + 9165 T^{4} + 28717 T^{5} + 103823 T^{6} \))(\( 1 - 3 T + 148 T^{2} - 509 T^{3} + 10681 T^{4} - 35789 T^{5} + 502007 T^{6} - 1124381 T^{7} + 15365804 T^{8} - 14639043 T^{9} + 229345007 T^{10} \))(\( 1 + 3 T + 148 T^{2} + 509 T^{3} + 10681 T^{4} + 35789 T^{5} + 502007 T^{6} + 1124381 T^{7} + 15365804 T^{8} + 14639043 T^{9} + 229345007 T^{10} \))(\( 1 + 9 T + 115 T^{2} + 653 T^{3} + 5488 T^{4} + 31712 T^{5} + 257936 T^{6} + 1442477 T^{7} + 11939645 T^{8} + 43917129 T^{9} + 229345007 T^{10} \))(\( 1 - 19 T + 376 T^{2} - 4402 T^{3} + 50057 T^{4} - 412039 T^{5} + 3251324 T^{6} - 19365833 T^{7} + 110575913 T^{8} - 457028846 T^{9} + 1834760056 T^{10} - 4357555133 T^{11} + 10779215329 T^{12} \))(\( 1 + 17 T + 289 T^{2} + 3311 T^{3} + 36705 T^{4} + 325523 T^{5} + 2728049 T^{6} + 19146138 T^{7} + 128218303 T^{8} + 719080307 T^{9} + 3810823215 T^{10} + 16156623791 T^{11} + 66280707023 T^{12} + 183246660593 T^{13} + 506623120463 T^{14} \))(\( 1 - 17 T + 289 T^{2} - 3311 T^{3} + 36705 T^{4} - 325523 T^{5} + 2728049 T^{6} - 19146138 T^{7} + 128218303 T^{8} - 719080307 T^{9} + 3810823215 T^{10} - 16156623791 T^{11} + 66280707023 T^{12} - 183246660593 T^{13} + 506623120463 T^{14} \))(\( 1 + 19 T + 564 T^{2} + 7453 T^{3} + 132748 T^{4} + 1402530 T^{5} + 19412149 T^{6} + 176443224 T^{7} + 2084935814 T^{8} + 16917367649 T^{9} + 178088363476 T^{10} + 1317287494422 T^{11} + 12664555786511 T^{12} + 86665702079342 T^{13} + 772816680328506 T^{14} + 4938564140525389 T^{15} + 41201413204769941 T^{16} + 247105881695558708 T^{17} + 1936466420624187227 T^{18} + 10909288186420584301 T^{19} + 80236146201746478438 T^{20} + \)\(42\!\cdots\!02\)\( T^{21} + \)\(29\!\cdots\!77\)\( T^{22} + \)\(14\!\cdots\!38\)\( T^{23} + \)\(90\!\cdots\!88\)\( T^{24} + \)\(40\!\cdots\!89\)\( T^{25} + \)\(23\!\cdots\!38\)\( T^{26} + \)\(92\!\cdots\!76\)\( T^{27} + \)\(47\!\cdots\!47\)\( T^{28} + \)\(16\!\cdots\!30\)\( T^{29} + \)\(72\!\cdots\!96\)\( T^{30} + \)\(19\!\cdots\!57\)\( T^{31} + \)\(68\!\cdots\!52\)\( T^{32} + \)\(10\!\cdots\!99\)\( T^{33} + \)\(26\!\cdots\!87\)\( T^{34} \))(\( 1 - 19 T + 564 T^{2} - 7453 T^{3} + 132748 T^{4} - 1402530 T^{5} + 19412149 T^{6} - 176443224 T^{7} + 2084935814 T^{8} - 16917367649 T^{9} + 178088363476 T^{10} - 1317287494422 T^{11} + 12664555786511 T^{12} - 86665702079342 T^{13} + 772816680328506 T^{14} - 4938564140525389 T^{15} + 41201413204769941 T^{16} - 247105881695558708 T^{17} + 1936466420624187227 T^{18} - 10909288186420584301 T^{19} + 80236146201746478438 T^{20} - \)\(42\!\cdots\!02\)\( T^{21} + \)\(29\!\cdots\!77\)\( T^{22} - \)\(14\!\cdots\!38\)\( T^{23} + \)\(90\!\cdots\!88\)\( T^{24} - \)\(40\!\cdots\!89\)\( T^{25} + \)\(23\!\cdots\!38\)\( T^{26} - \)\(92\!\cdots\!76\)\( T^{27} + \)\(47\!\cdots\!47\)\( T^{28} - \)\(16\!\cdots\!30\)\( T^{29} + \)\(72\!\cdots\!96\)\( T^{30} - \)\(19\!\cdots\!57\)\( T^{31} + \)\(68\!\cdots\!52\)\( T^{32} - \)\(10\!\cdots\!99\)\( T^{33} + \)\(26\!\cdots\!87\)\( T^{34} \))(\( 1 + 32 T + 1054 T^{2} + 22228 T^{3} + 446949 T^{4} + 7249148 T^{5} + 111313470 T^{6} + 1492042972 T^{7} + 19005714531 T^{8} + 219398395704 T^{9} + 2420133399230 T^{10} + 24711993291428 T^{11} + 242401505158173 T^{12} + 2230767047947508 T^{13} + 19813104531813714 T^{14} + 166592131922405944 T^{15} + 1357040640856503412 T^{16} + 10528006969596451932 T^{17} + 79348272356280509140 T^{18} + \)\(57\!\cdots\!80\)\( T^{19} + \)\(40\!\cdots\!48\)\( T^{20} + \)\(26\!\cdots\!60\)\( T^{21} + \)\(17\!\cdots\!60\)\( T^{22} + \)\(10\!\cdots\!36\)\( T^{23} + \)\(66\!\cdots\!72\)\( T^{24} + \)\(38\!\cdots\!08\)\( T^{25} + \)\(21\!\cdots\!06\)\( T^{26} + \)\(11\!\cdots\!04\)\( T^{27} + \)\(57\!\cdots\!53\)\( T^{28} + \)\(27\!\cdots\!76\)\( T^{29} + \)\(12\!\cdots\!70\)\( T^{30} + \)\(54\!\cdots\!12\)\( T^{31} + \)\(22\!\cdots\!71\)\( T^{32} + \)\(81\!\cdots\!44\)\( T^{33} + \)\(28\!\cdots\!30\)\( T^{34} + \)\(87\!\cdots\!64\)\( T^{35} + \)\(25\!\cdots\!29\)\( T^{36} + \)\(59\!\cdots\!36\)\( T^{37} + \)\(13\!\cdots\!06\)\( T^{38} + \)\(18\!\cdots\!56\)\( T^{39} + \)\(27\!\cdots\!01\)\( T^{40} \))(\( 1 - 32 T + 1054 T^{2} - 22228 T^{3} + 446949 T^{4} - 7249148 T^{5} + 111313470 T^{6} - 1492042972 T^{7} + 19005714531 T^{8} - 219398395704 T^{9} + 2420133399230 T^{10} - 24711993291428 T^{11} + 242401505158173 T^{12} - 2230767047947508 T^{13} + 19813104531813714 T^{14} - 166592131922405944 T^{15} + 1357040640856503412 T^{16} - 10528006969596451932 T^{17} + 79348272356280509140 T^{18} - \)\(57\!\cdots\!80\)\( T^{19} + \)\(40\!\cdots\!48\)\( T^{20} - \)\(26\!\cdots\!60\)\( T^{21} + \)\(17\!\cdots\!60\)\( T^{22} - \)\(10\!\cdots\!36\)\( T^{23} + \)\(66\!\cdots\!72\)\( T^{24} - \)\(38\!\cdots\!08\)\( T^{25} + \)\(21\!\cdots\!06\)\( T^{26} - \)\(11\!\cdots\!04\)\( T^{27} + \)\(57\!\cdots\!53\)\( T^{28} - \)\(27\!\cdots\!76\)\( T^{29} + \)\(12\!\cdots\!70\)\( T^{30} - \)\(54\!\cdots\!12\)\( T^{31} + \)\(22\!\cdots\!71\)\( T^{32} - \)\(81\!\cdots\!44\)\( T^{33} + \)\(28\!\cdots\!30\)\( T^{34} - \)\(87\!\cdots\!64\)\( T^{35} + \)\(25\!\cdots\!29\)\( T^{36} - \)\(59\!\cdots\!36\)\( T^{37} + \)\(13\!\cdots\!06\)\( T^{38} - \)\(18\!\cdots\!56\)\( T^{39} + \)\(27\!\cdots\!01\)\( T^{40} \))
$53$ (\( 1 - 7 T + 117 T^{2} - 371 T^{3} + 2809 T^{4} \))(\( 1 + 17 T + 147 T^{2} + 901 T^{3} + 2809 T^{4} \))(\( 1 - 9 T + 97 T^{2} - 477 T^{3} + 2809 T^{4} \))(\( 1 - 9 T + 97 T^{2} - 477 T^{3} + 2809 T^{4} \))(\( 1 + 16 T + 165 T^{2} + 848 T^{3} + 2809 T^{4} \))(\( 1 + 16 T + 165 T^{2} + 848 T^{3} + 2809 T^{4} \))(\( 1 - 6 T + 155 T^{2} - 628 T^{3} + 8215 T^{4} - 16854 T^{5} + 148877 T^{6} \))(\( 1 + 8 T + 163 T^{2} + 808 T^{3} + 8639 T^{4} + 22472 T^{5} + 148877 T^{6} \))(\( 1 + 8 T + 163 T^{2} + 808 T^{3} + 8639 T^{4} + 22472 T^{5} + 148877 T^{6} \))(\( 1 - 2 T + 119 T^{2} - 284 T^{3} + 6307 T^{4} - 5618 T^{5} + 148877 T^{6} \))(\( 1 + 20 T + 283 T^{2} + 2352 T^{3} + 14999 T^{4} + 56180 T^{5} + 148877 T^{6} \))(\( 1 + 9 T + 145 T^{2} + 535 T^{3} + 6097 T^{4} + 4521 T^{5} + 323141 T^{6} + 1502815 T^{7} + 21587165 T^{8} + 71014329 T^{9} + 418195493 T^{10} \))(\( 1 + 9 T + 145 T^{2} + 535 T^{3} + 6097 T^{4} + 4521 T^{5} + 323141 T^{6} + 1502815 T^{7} + 21587165 T^{8} + 71014329 T^{9} + 418195493 T^{10} \))(\( 1 - 5 T + 156 T^{2} - 36 T^{3} + 7939 T^{4} + 26602 T^{5} + 420767 T^{6} - 101124 T^{7} + 23224812 T^{8} - 39452405 T^{9} + 418195493 T^{10} \))(\( 1 - 5 T + 191 T^{2} - 861 T^{3} + 19247 T^{4} - 75162 T^{5} + 1236466 T^{6} - 3983586 T^{7} + 54064823 T^{8} - 128183097 T^{9} + 1507081871 T^{10} - 2090977465 T^{11} + 22164361129 T^{12} \))(\( 1 - 24 T + 558 T^{2} - 8100 T^{3} + 108225 T^{4} - 1107964 T^{5} + 10410464 T^{6} - 79084328 T^{7} + 551754592 T^{8} - 3112270876 T^{9} + 16112213325 T^{10} - 63912896100 T^{11} + 233353085094 T^{12} - 531944667096 T^{13} + 1174711139837 T^{14} \))(\( 1 - 24 T + 558 T^{2} - 8100 T^{3} + 108225 T^{4} - 1107964 T^{5} + 10410464 T^{6} - 79084328 T^{7} + 551754592 T^{8} - 3112270876 T^{9} + 16112213325 T^{10} - 63912896100 T^{11} + 233353085094 T^{12} - 531944667096 T^{13} + 1174711139837 T^{14} \))(\( 1 - 4 T + 396 T^{2} - 878 T^{3} + 75201 T^{4} - 33051 T^{5} + 9386549 T^{6} + 12571486 T^{7} + 899147447 T^{8} + 2625685509 T^{9} + 73339077909 T^{10} + 290043535074 T^{11} + 5398154896079 T^{12} + 23098013958351 T^{13} + 361855448785051 T^{14} + 1494527926036494 T^{15} + 21725315334045739 T^{16} + 83995816250399126 T^{17} + 1151441712704424167 T^{18} + 4198128944236511646 T^{19} + 53871953648772037727 T^{20} + \)\(18\!\cdots\!31\)\( T^{21} + \)\(22\!\cdots\!47\)\( T^{22} + \)\(64\!\cdots\!46\)\( T^{23} + \)\(86\!\cdots\!33\)\( T^{24} + \)\(16\!\cdots\!49\)\( T^{25} + \)\(29\!\cdots\!51\)\( T^{26} + \)\(21\!\cdots\!14\)\( T^{27} + \)\(87\!\cdots\!53\)\( T^{28} - \)\(16\!\cdots\!91\)\( T^{29} + \)\(19\!\cdots\!73\)\( T^{30} - \)\(12\!\cdots\!82\)\( T^{31} + \)\(28\!\cdots\!72\)\( T^{32} - \)\(15\!\cdots\!84\)\( T^{33} + \)\(20\!\cdots\!13\)\( T^{34} \))(\( 1 - 4 T + 396 T^{2} - 878 T^{3} + 75201 T^{4} - 33051 T^{5} + 9386549 T^{6} + 12571486 T^{7} + 899147447 T^{8} + 2625685509 T^{9} + 73339077909 T^{10} + 290043535074 T^{11} + 5398154896079 T^{12} + 23098013958351 T^{13} + 361855448785051 T^{14} + 1494527926036494 T^{15} + 21725315334045739 T^{16} + 83995816250399126 T^{17} + 1151441712704424167 T^{18} + 4198128944236511646 T^{19} + 53871953648772037727 T^{20} + \)\(18\!\cdots\!31\)\( T^{21} + \)\(22\!\cdots\!47\)\( T^{22} + \)\(64\!\cdots\!46\)\( T^{23} + \)\(86\!\cdots\!33\)\( T^{24} + \)\(16\!\cdots\!49\)\( T^{25} + \)\(29\!\cdots\!51\)\( T^{26} + \)\(21\!\cdots\!14\)\( T^{27} + \)\(87\!\cdots\!53\)\( T^{28} - \)\(16\!\cdots\!91\)\( T^{29} + \)\(19\!\cdots\!73\)\( T^{30} - \)\(12\!\cdots\!82\)\( T^{31} + \)\(28\!\cdots\!72\)\( T^{32} - \)\(15\!\cdots\!84\)\( T^{33} + \)\(20\!\cdots\!13\)\( T^{34} \))(\( 1 - 4 T + 584 T^{2} - 1300 T^{3} + 169427 T^{4} - 155500 T^{5} + 33254640 T^{6} + 990320 T^{7} + 4979714798 T^{8} + 3500809188 T^{9} + 602915899774 T^{10} + 702863596368 T^{11} + 60989810945046 T^{12} + 89141676459680 T^{13} + 5259984505732254 T^{14} + 8541232596335756 T^{15} + 391701482247910545 T^{16} + 657449612733733044 T^{17} + 25386378216055146108 T^{18} + 41761549760320485088 T^{19} + \)\(14\!\cdots\!86\)\( T^{20} + \)\(22\!\cdots\!64\)\( T^{21} + \)\(71\!\cdots\!72\)\( T^{22} + \)\(97\!\cdots\!88\)\( T^{23} + \)\(30\!\cdots\!45\)\( T^{24} + \)\(35\!\cdots\!08\)\( T^{25} + \)\(11\!\cdots\!66\)\( T^{26} + \)\(10\!\cdots\!60\)\( T^{27} + \)\(37\!\cdots\!06\)\( T^{28} + \)\(23\!\cdots\!44\)\( T^{29} + \)\(10\!\cdots\!26\)\( T^{30} + \)\(32\!\cdots\!36\)\( T^{31} + \)\(24\!\cdots\!18\)\( T^{32} + \)\(25\!\cdots\!60\)\( T^{33} + \)\(45\!\cdots\!60\)\( T^{34} - \)\(11\!\cdots\!00\)\( T^{35} + \)\(65\!\cdots\!67\)\( T^{36} - \)\(26\!\cdots\!00\)\( T^{37} + \)\(63\!\cdots\!76\)\( T^{38} - \)\(23\!\cdots\!68\)\( T^{39} + \)\(30\!\cdots\!01\)\( T^{40} \))(\( 1 - 4 T + 584 T^{2} - 1300 T^{3} + 169427 T^{4} - 155500 T^{5} + 33254640 T^{6} + 990320 T^{7} + 4979714798 T^{8} + 3500809188 T^{9} + 602915899774 T^{10} + 702863596368 T^{11} + 60989810945046 T^{12} + 89141676459680 T^{13} + 5259984505732254 T^{14} + 8541232596335756 T^{15} + 391701482247910545 T^{16} + 657449612733733044 T^{17} + 25386378216055146108 T^{18} + 41761549760320485088 T^{19} + \)\(14\!\cdots\!86\)\( T^{20} + \)\(22\!\cdots\!64\)\( T^{21} + \)\(71\!\cdots\!72\)\( T^{22} + \)\(97\!\cdots\!88\)\( T^{23} + \)\(30\!\cdots\!45\)\( T^{24} + \)\(35\!\cdots\!08\)\( T^{25} + \)\(11\!\cdots\!66\)\( T^{26} + \)\(10\!\cdots\!60\)\( T^{27} + \)\(37\!\cdots\!06\)\( T^{28} + \)\(23\!\cdots\!44\)\( T^{29} + \)\(10\!\cdots\!26\)\( T^{30} + \)\(32\!\cdots\!36\)\( T^{31} + \)\(24\!\cdots\!18\)\( T^{32} + \)\(25\!\cdots\!60\)\( T^{33} + \)\(45\!\cdots\!60\)\( T^{34} - \)\(11\!\cdots\!00\)\( T^{35} + \)\(65\!\cdots\!67\)\( T^{36} - \)\(26\!\cdots\!00\)\( T^{37} + \)\(63\!\cdots\!76\)\( T^{38} - \)\(23\!\cdots\!68\)\( T^{39} + \)\(30\!\cdots\!01\)\( T^{40} \))
$59$ (\( 1 + 19 T + 207 T^{2} + 1121 T^{3} + 3481 T^{4} \))(\( 1 + 13 T + 159 T^{2} + 767 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 121 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 121 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 4 T + 77 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 4 T + 77 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 161 T^{2} - 784 T^{3} + 9499 T^{4} - 27848 T^{5} + 205379 T^{6} \))(\( 1 + 4 T + 85 T^{2} + 640 T^{3} + 5015 T^{4} + 13924 T^{5} + 205379 T^{6} \))(\( 1 - 4 T + 85 T^{2} - 640 T^{3} + 5015 T^{4} - 13924 T^{5} + 205379 T^{6} \))(\( ( 1 - 4 T + 59 T^{2} )^{3} \))(\( 1 + 4 T + 61 T^{2} + 576 T^{3} + 3599 T^{4} + 13924 T^{5} + 205379 T^{6} \))(\( 1 + 19 T + 292 T^{2} + 3271 T^{3} + 33435 T^{4} + 271711 T^{5} + 1972665 T^{6} + 11386351 T^{7} + 59970668 T^{8} + 230229859 T^{9} + 714924299 T^{10} \))(\( 1 - 19 T + 292 T^{2} - 3271 T^{3} + 33435 T^{4} - 271711 T^{5} + 1972665 T^{6} - 11386351 T^{7} + 59970668 T^{8} - 230229859 T^{9} + 714924299 T^{10} \))(\( 1 + 7 T + 124 T^{2} + 772 T^{3} + 12043 T^{4} + 63362 T^{5} + 710537 T^{6} + 2687332 T^{7} + 25466996 T^{8} + 84821527 T^{9} + 714924299 T^{10} \))(\( 1 - 7 T + 171 T^{2} - 589 T^{3} + 9235 T^{4} + 15790 T^{5} + 310242 T^{6} + 931610 T^{7} + 32147035 T^{8} - 120968231 T^{9} + 2072068731 T^{10} - 5004470093 T^{11} + 42180533641 T^{12} \))(\( 1 + 4 T + 320 T^{2} + 1216 T^{3} + 47827 T^{4} + 165810 T^{5} + 4320864 T^{6} + 12717596 T^{7} + 254930976 T^{8} + 577184610 T^{9} + 9822661433 T^{10} + 14734710976 T^{11} + 228775775680 T^{12} + 168722134564 T^{13} + 2488651484819 T^{14} \))(\( 1 - 4 T + 320 T^{2} - 1216 T^{3} + 47827 T^{4} - 165810 T^{5} + 4320864 T^{6} - 12717596 T^{7} + 254930976 T^{8} - 577184610 T^{9} + 9822661433 T^{10} - 14734710976 T^{11} + 228775775680 T^{12} - 168722134564 T^{13} + 2488651484819 T^{14} \))(\( 1 - 27 T + 790 T^{2} - 14273 T^{3} + 254314 T^{4} - 3508798 T^{5} + 46825069 T^{6} - 517772828 T^{7} + 5489749622 T^{8} - 48746836501 T^{9} + 408142642896 T^{10} - 2694251996406 T^{11} + 15237077106519 T^{12} - 30876487133150 T^{13} - 387432455729864 T^{14} + 8685525217754091 T^{15} - 89925393528327001 T^{16} + 807078885733891640 T^{17} - 5305598218171293059 T^{18} + 30234313283001990771 T^{19} - 79570490325343738456 T^{20} - \)\(37\!\cdots\!50\)\( T^{21} + \)\(10\!\cdots\!81\)\( T^{22} - \)\(11\!\cdots\!46\)\( T^{23} + \)\(10\!\cdots\!24\)\( T^{24} - \)\(71\!\cdots\!21\)\( T^{25} + \)\(47\!\cdots\!58\)\( T^{26} - \)\(26\!\cdots\!28\)\( T^{27} + \)\(14\!\cdots\!71\)\( T^{28} - \)\(62\!\cdots\!38\)\( T^{29} + \)\(26\!\cdots\!06\)\( T^{30} - \)\(88\!\cdots\!53\)\( T^{31} + \)\(28\!\cdots\!10\)\( T^{32} - \)\(58\!\cdots\!07\)\( T^{33} + \)\(12\!\cdots\!19\)\( T^{34} \))(\( 1 + 27 T + 790 T^{2} + 14273 T^{3} + 254314 T^{4} + 3508798 T^{5} + 46825069 T^{6} + 517772828 T^{7} + 5489749622 T^{8} + 48746836501 T^{9} + 408142642896 T^{10} + 2694251996406 T^{11} + 15237077106519 T^{12} + 30876487133150 T^{13} - 387432455729864 T^{14} - 8685525217754091 T^{15} - 89925393528327001 T^{16} - 807078885733891640 T^{17} - 5305598218171293059 T^{18} - 30234313283001990771 T^{19} - 79570490325343738456 T^{20} + \)\(37\!\cdots\!50\)\( T^{21} + \)\(10\!\cdots\!81\)\( T^{22} + \)\(11\!\cdots\!46\)\( T^{23} + \)\(10\!\cdots\!24\)\( T^{24} + \)\(71\!\cdots\!21\)\( T^{25} + \)\(47\!\cdots\!58\)\( T^{26} + \)\(26\!\cdots\!28\)\( T^{27} + \)\(14\!\cdots\!71\)\( T^{28} + \)\(62\!\cdots\!38\)\( T^{29} + \)\(26\!\cdots\!06\)\( T^{30} + \)\(88\!\cdots\!53\)\( T^{31} + \)\(28\!\cdots\!10\)\( T^{32} + \)\(58\!\cdots\!07\)\( T^{33} + \)\(12\!\cdots\!19\)\( T^{34} \))(\( 1 + 32 T + 1152 T^{2} + 25224 T^{3} + 554909 T^{4} + 9586340 T^{5} + 162283028 T^{6} + 2365075960 T^{7} + 33525032782 T^{8} + 427758810284 T^{9} + 5295067780982 T^{10} + 60491889842272 T^{11} + 669839688701614 T^{12} + 6949954494440600 T^{13} + 69873828708462014 T^{14} + 664531361577479268 T^{15} + 6123656874409519873 T^{16} + 53692784608363601920 T^{17} + \)\(45\!\cdots\!08\)\( T^{18} + \)\(36\!\cdots\!52\)\( T^{19} + \)\(29\!\cdots\!98\)\( T^{20} + \)\(21\!\cdots\!68\)\( T^{21} + \)\(15\!\cdots\!48\)\( T^{22} + \)\(11\!\cdots\!80\)\( T^{23} + \)\(74\!\cdots\!53\)\( T^{24} + \)\(47\!\cdots\!32\)\( T^{25} + \)\(29\!\cdots\!74\)\( T^{26} + \)\(17\!\cdots\!00\)\( T^{27} + \)\(98\!\cdots\!94\)\( T^{28} + \)\(52\!\cdots\!08\)\( T^{29} + \)\(27\!\cdots\!82\)\( T^{30} + \)\(12\!\cdots\!56\)\( T^{31} + \)\(59\!\cdots\!42\)\( T^{32} + \)\(24\!\cdots\!40\)\( T^{33} + \)\(10\!\cdots\!08\)\( T^{34} + \)\(35\!\cdots\!60\)\( T^{35} + \)\(11\!\cdots\!69\)\( T^{36} + \)\(32\!\cdots\!56\)\( T^{37} + \)\(86\!\cdots\!92\)\( T^{38} + \)\(14\!\cdots\!48\)\( T^{39} + \)\(26\!\cdots\!01\)\( T^{40} \))(\( 1 - 32 T + 1152 T^{2} - 25224 T^{3} + 554909 T^{4} - 9586340 T^{5} + 162283028 T^{6} - 2365075960 T^{7} + 33525032782 T^{8} - 427758810284 T^{9} + 5295067780982 T^{10} - 60491889842272 T^{11} + 669839688701614 T^{12} - 6949954494440600 T^{13} + 69873828708462014 T^{14} - 664531361577479268 T^{15} + 6123656874409519873 T^{16} - 53692784608363601920 T^{17} + \)\(45\!\cdots\!08\)\( T^{18} - \)\(36\!\cdots\!52\)\( T^{19} + \)\(29\!\cdots\!98\)\( T^{20} - \)\(21\!\cdots\!68\)\( T^{21} + \)\(15\!\cdots\!48\)\( T^{22} - \)\(11\!\cdots\!80\)\( T^{23} + \)\(74\!\cdots\!53\)\( T^{24} - \)\(47\!\cdots\!32\)\( T^{25} + \)\(29\!\cdots\!74\)\( T^{26} - \)\(17\!\cdots\!00\)\( T^{27} + \)\(98\!\cdots\!94\)\( T^{28} - \)\(52\!\cdots\!08\)\( T^{29} + \)\(27\!\cdots\!82\)\( T^{30} - \)\(12\!\cdots\!56\)\( T^{31} + \)\(59\!\cdots\!42\)\( T^{32} - \)\(24\!\cdots\!40\)\( T^{33} + \)\(10\!\cdots\!08\)\( T^{34} - \)\(35\!\cdots\!60\)\( T^{35} + \)\(11\!\cdots\!69\)\( T^{36} - \)\(32\!\cdots\!56\)\( T^{37} + \)\(86\!\cdots\!92\)\( T^{38} - \)\(14\!\cdots\!48\)\( T^{39} + \)\(26\!\cdots\!01\)\( T^{40} \))
$61$ (\( 1 + 10 T + 127 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( ( 1 - 11 T + 61 T^{2} )^{2} \))(\( 1 + 70 T^{2} + 3721 T^{4} \))(\( 1 + 70 T^{2} + 3721 T^{4} \))(\( 1 + 10 T + 127 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 127 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 + 2 T + 131 T^{2} + 60 T^{3} + 7991 T^{4} + 7442 T^{5} + 226981 T^{6} \))(\( 1 + 6 T - 17 T^{2} - 444 T^{3} - 1037 T^{4} + 22326 T^{5} + 226981 T^{6} \))(\( 1 - 6 T - 17 T^{2} + 444 T^{3} - 1037 T^{4} - 22326 T^{5} + 226981 T^{6} \))(\( 1 - 4 T + 147 T^{2} - 336 T^{3} + 8967 T^{4} - 14884 T^{5} + 226981 T^{6} \))(\( 1 + 8 T + 139 T^{2} + 632 T^{3} + 8479 T^{4} + 29768 T^{5} + 226981 T^{6} \))(\( 1 + 23 T + 321 T^{2} + 4061 T^{3} + 41031 T^{4} + 336925 T^{5} + 2502891 T^{6} + 15110981 T^{7} + 72860901 T^{8} + 318454343 T^{9} + 844596301 T^{10} \))(\( 1 - 23 T + 321 T^{2} - 4061 T^{3} + 41031 T^{4} - 336925 T^{5} + 2502891 T^{6} - 15110981 T^{7} + 72860901 T^{8} - 318454343 T^{9} + 844596301 T^{10} \))(\( 1 + 22 T + 458 T^{2} + 5620 T^{3} + 64261 T^{4} + 519412 T^{5} + 3919921 T^{6} + 20912020 T^{7} + 103957298 T^{8} + 304608502 T^{9} + 844596301 T^{10} \))(\( 1 - 12 T + 183 T^{2} - 1050 T^{3} + 10135 T^{4} - 11674 T^{5} + 272594 T^{6} - 712114 T^{7} + 37712335 T^{8} - 238330050 T^{9} + 2533788903 T^{10} - 10135155612 T^{11} + 51520374361 T^{12} \))(\( 1 + 16 T + 437 T^{2} + 4848 T^{3} + 75368 T^{4} + 637128 T^{5} + 7247662 T^{6} + 48913976 T^{7} + 442107382 T^{8} + 2370753288 T^{9} + 17107104008 T^{10} + 67124637168 T^{11} + 369088583537 T^{12} + 824325989776 T^{13} + 3142742836021 T^{14} \))(\( 1 - 16 T + 437 T^{2} - 4848 T^{3} + 75368 T^{4} - 637128 T^{5} + 7247662 T^{6} - 48913976 T^{7} + 442107382 T^{8} - 2370753288 T^{9} + 17107104008 T^{10} - 67124637168 T^{11} + 369088583537 T^{12} - 824325989776 T^{13} + 3142742836021 T^{14} \))(\( 1 - T + 560 T^{2} + 324 T^{3} + 153994 T^{4} + 291106 T^{5} + 28293893 T^{6} + 82014011 T^{7} + 3947642817 T^{8} + 14174537221 T^{9} + 446283326496 T^{10} + 1783064608833 T^{11} + 42328790366983 T^{12} + 176139656013474 T^{13} + 3434627111823547 T^{14} + 14185239745648499 T^{15} + 241035083860586949 T^{16} + 947656364864180242 T^{17} + 14703140115495803889 T^{18} + 52783277093558064779 T^{19} + \)\(77\!\cdots\!07\)\( T^{20} + \)\(24\!\cdots\!34\)\( T^{21} + \)\(35\!\cdots\!83\)\( T^{22} + \)\(91\!\cdots\!13\)\( T^{23} + \)\(14\!\cdots\!16\)\( T^{24} + \)\(27\!\cdots\!01\)\( T^{25} + \)\(46\!\cdots\!97\)\( T^{26} + \)\(58\!\cdots\!11\)\( T^{27} + \)\(12\!\cdots\!73\)\( T^{28} + \)\(77\!\cdots\!26\)\( T^{29} + \)\(24\!\cdots\!14\)\( T^{30} + \)\(32\!\cdots\!84\)\( T^{31} + \)\(33\!\cdots\!60\)\( T^{32} - \)\(36\!\cdots\!61\)\( T^{33} + \)\(22\!\cdots\!21\)\( T^{34} \))(\( 1 + T + 560 T^{2} - 324 T^{3} + 153994 T^{4} - 291106 T^{5} + 28293893 T^{6} - 82014011 T^{7} + 3947642817 T^{8} - 14174537221 T^{9} + 446283326496 T^{10} - 1783064608833 T^{11} + 42328790366983 T^{12} - 176139656013474 T^{13} + 3434627111823547 T^{14} - 14185239745648499 T^{15} + 241035083860586949 T^{16} - 947656364864180242 T^{17} + 14703140115495803889 T^{18} - 52783277093558064779 T^{19} + \)\(77\!\cdots\!07\)\( T^{20} - \)\(24\!\cdots\!34\)\( T^{21} + \)\(35\!\cdots\!83\)\( T^{22} - \)\(91\!\cdots\!13\)\( T^{23} + \)\(14\!\cdots\!16\)\( T^{24} - \)\(27\!\cdots\!01\)\( T^{25} + \)\(46\!\cdots\!97\)\( T^{26} - \)\(58\!\cdots\!11\)\( T^{27} + \)\(12\!\cdots\!73\)\( T^{28} - \)\(77\!\cdots\!26\)\( T^{29} + \)\(24\!\cdots\!14\)\( T^{30} - \)\(32\!\cdots\!84\)\( T^{31} + \)\(33\!\cdots\!60\)\( T^{32} + \)\(36\!\cdots\!61\)\( T^{33} + \)\(22\!\cdots\!21\)\( T^{34} \))(\( 1 + 44 T + 1650 T^{2} + 43108 T^{3} + 1001356 T^{4} + 19510876 T^{5} + 347743822 T^{6} + 5531538940 T^{7} + 81951261982 T^{8} + 1116220971516 T^{9} + 14331179981302 T^{10} + 172041573544228 T^{11} + 1962985818315698 T^{12} + 21163810901955204 T^{13} + 218124016507465870 T^{14} + 2138725833819101548 T^{15} + 20124979775029100817 T^{16} + \)\(18\!\cdots\!44\)\( T^{17} + \)\(15\!\cdots\!08\)\( T^{18} + \)\(12\!\cdots\!40\)\( T^{19} + \)\(10\!\cdots\!48\)\( T^{20} + \)\(79\!\cdots\!40\)\( T^{21} + \)\(58\!\cdots\!68\)\( T^{22} + \)\(41\!\cdots\!64\)\( T^{23} + \)\(27\!\cdots\!97\)\( T^{24} + \)\(18\!\cdots\!48\)\( T^{25} + \)\(11\!\cdots\!70\)\( T^{26} + \)\(66\!\cdots\!84\)\( T^{27} + \)\(37\!\cdots\!38\)\( T^{28} + \)\(20\!\cdots\!48\)\( T^{29} + \)\(10\!\cdots\!02\)\( T^{30} + \)\(48\!\cdots\!76\)\( T^{31} + \)\(21\!\cdots\!22\)\( T^{32} + \)\(89\!\cdots\!40\)\( T^{33} + \)\(34\!\cdots\!02\)\( T^{34} + \)\(11\!\cdots\!76\)\( T^{35} + \)\(36\!\cdots\!16\)\( T^{36} + \)\(96\!\cdots\!68\)\( T^{37} + \)\(22\!\cdots\!50\)\( T^{38} + \)\(36\!\cdots\!04\)\( T^{39} + \)\(50\!\cdots\!01\)\( T^{40} \))(\( 1 - 44 T + 1650 T^{2} - 43108 T^{3} + 1001356 T^{4} - 19510876 T^{5} + 347743822 T^{6} - 5531538940 T^{7} + 81951261982 T^{8} - 1116220971516 T^{9} + 14331179981302 T^{10} - 172041573544228 T^{11} + 1962985818315698 T^{12} - 21163810901955204 T^{13} + 218124016507465870 T^{14} - 2138725833819101548 T^{15} + 20124979775029100817 T^{16} - \)\(18\!\cdots\!44\)\( T^{17} + \)\(15\!\cdots\!08\)\( T^{18} - \)\(12\!\cdots\!40\)\( T^{19} + \)\(10\!\cdots\!48\)\( T^{20} - \)\(79\!\cdots\!40\)\( T^{21} + \)\(58\!\cdots\!68\)\( T^{22} - \)\(41\!\cdots\!64\)\( T^{23} + \)\(27\!\cdots\!97\)\( T^{24} - \)\(18\!\cdots\!48\)\( T^{25} + \)\(11\!\cdots\!70\)\( T^{26} - \)\(66\!\cdots\!84\)\( T^{27} + \)\(37\!\cdots\!38\)\( T^{28} - \)\(20\!\cdots\!48\)\( T^{29} + \)\(10\!\cdots\!02\)\( T^{30} - \)\(48\!\cdots\!76\)\( T^{31} + \)\(21\!\cdots\!22\)\( T^{32} - \)\(89\!\cdots\!40\)\( T^{33} + \)\(34\!\cdots\!02\)\( T^{34} - \)\(11\!\cdots\!76\)\( T^{35} + \)\(36\!\cdots\!16\)\( T^{36} - \)\(96\!\cdots\!68\)\( T^{37} + \)\(22\!\cdots\!50\)\( T^{38} - \)\(36\!\cdots\!04\)\( T^{39} + \)\(50\!\cdots\!01\)\( T^{40} \))
$67$ (\( 1 + 13 T + 145 T^{2} + 871 T^{3} + 4489 T^{4} \))(\( 1 - 11 T + 163 T^{2} - 737 T^{3} + 4489 T^{4} \))(\( 1 + 6 T + 130 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 + 6 T + 130 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 + 6 T + 63 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 + 6 T + 63 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 + 2 T + 181 T^{2} + 218 T^{3} + 12127 T^{4} + 8978 T^{5} + 300763 T^{6} \))(\( 1 - 8 T + 125 T^{2} - 536 T^{3} + 8375 T^{4} - 35912 T^{5} + 300763 T^{6} \))(\( 1 - 8 T + 125 T^{2} - 536 T^{3} + 8375 T^{4} - 35912 T^{5} + 300763 T^{6} \))(\( 1 - 10 T + 193 T^{2} - 1140 T^{3} + 12931 T^{4} - 44890 T^{5} + 300763 T^{6} \))(\( 1 + 36 T + 605 T^{2} + 6160 T^{3} + 40535 T^{4} + 161604 T^{5} + 300763 T^{6} \))(\( 1 + 11 T + 200 T^{2} + 1605 T^{3} + 20103 T^{4} + 135609 T^{5} + 1346901 T^{6} + 7204845 T^{7} + 60152600 T^{8} + 221662331 T^{9} + 1350125107 T^{10} \))(\( 1 + 11 T + 200 T^{2} + 1605 T^{3} + 20103 T^{4} + 135609 T^{5} + 1346901 T^{6} + 7204845 T^{7} + 60152600 T^{8} + 221662331 T^{9} + 1350125107 T^{10} \))(\( 1 + 3 T + 230 T^{2} + 228 T^{3} + 22853 T^{4} + 3146 T^{5} + 1531151 T^{6} + 1023492 T^{7} + 69175490 T^{8} + 60453363 T^{9} + 1350125107 T^{10} \))(\( 1 - 27 T + 645 T^{2} - 9607 T^{3} + 129139 T^{4} - 1305704 T^{5} + 12088494 T^{6} - 87482168 T^{7} + 579704971 T^{8} - 2889430141 T^{9} + 12997473045 T^{10} - 36453377889 T^{11} + 90458382169 T^{12} \))(\( 1 + 24 T + 472 T^{2} + 6040 T^{3} + 72643 T^{4} + 683720 T^{5} + 6437456 T^{6} + 51360592 T^{7} + 431309552 T^{8} + 3069219080 T^{9} + 21848326609 T^{10} + 121712770840 T^{11} + 637259050504 T^{12} + 2171001172056 T^{13} + 6060711605323 T^{14} \))(\( 1 + 24 T + 472 T^{2} + 6040 T^{3} + 72643 T^{4} + 683720 T^{5} + 6437456 T^{6} + 51360592 T^{7} + 431309552 T^{8} + 3069219080 T^{9} + 21848326609 T^{10} + 121712770840 T^{11} + 637259050504 T^{12} + 2171001172056 T^{13} + 6060711605323 T^{14} \))(\( 1 - 49 T + 1801 T^{2} - 48652 T^{3} + 1116265 T^{4} - 21935772 T^{5} + 384886511 T^{6} - 6079379447 T^{7} + 88015541222 T^{8} - 1175052922682 T^{9} + 14607671313010 T^{10} - 169826063101027 T^{11} + 1857414620972507 T^{12} - 19168380745213392 T^{13} + 187354457744892357 T^{14} - 1737460217921484366 T^{15} + 15320437388008044792 T^{16} - \)\(12\!\cdots\!50\)\( T^{17} + \)\(10\!\cdots\!64\)\( T^{18} - \)\(77\!\cdots\!74\)\( T^{19} + \)\(56\!\cdots\!91\)\( T^{20} - \)\(38\!\cdots\!32\)\( T^{21} + \)\(25\!\cdots\!49\)\( T^{22} - \)\(15\!\cdots\!63\)\( T^{23} + \)\(88\!\cdots\!30\)\( T^{24} - \)\(47\!\cdots\!62\)\( T^{25} + \)\(23\!\cdots\!34\)\( T^{26} - \)\(11\!\cdots\!03\)\( T^{27} + \)\(47\!\cdots\!13\)\( T^{28} - \)\(17\!\cdots\!92\)\( T^{29} + \)\(61\!\cdots\!55\)\( T^{30} - \)\(17\!\cdots\!08\)\( T^{31} + \)\(44\!\cdots\!43\)\( T^{32} - \)\(80\!\cdots\!69\)\( T^{33} + \)\(11\!\cdots\!27\)\( T^{34} \))(\( 1 - 49 T + 1801 T^{2} - 48652 T^{3} + 1116265 T^{4} - 21935772 T^{5} + 384886511 T^{6} - 6079379447 T^{7} + 88015541222 T^{8} - 1175052922682 T^{9} + 14607671313010 T^{10} - 169826063101027 T^{11} + 1857414620972507 T^{12} - 19168380745213392 T^{13} + 187354457744892357 T^{14} - 1737460217921484366 T^{15} + 15320437388008044792 T^{16} - \)\(12\!\cdots\!50\)\( T^{17} + \)\(10\!\cdots\!64\)\( T^{18} - \)\(77\!\cdots\!74\)\( T^{19} + \)\(56\!\cdots\!91\)\( T^{20} - \)\(38\!\cdots\!32\)\( T^{21} + \)\(25\!\cdots\!49\)\( T^{22} - \)\(15\!\cdots\!63\)\( T^{23} + \)\(88\!\cdots\!30\)\( T^{24} - \)\(47\!\cdots\!62\)\( T^{25} + \)\(23\!\cdots\!34\)\( T^{26} - \)\(11\!\cdots\!03\)\( T^{27} + \)\(47\!\cdots\!13\)\( T^{28} - \)\(17\!\cdots\!92\)\( T^{29} + \)\(61\!\cdots\!55\)\( T^{30} - \)\(17\!\cdots\!08\)\( T^{31} + \)\(44\!\cdots\!43\)\( T^{32} - \)\(80\!\cdots\!69\)\( T^{33} + \)\(11\!\cdots\!27\)\( T^{34} \))(\( 1 + 4 T + 508 T^{2} + 2676 T^{3} + 119783 T^{4} + 785404 T^{5} + 17867516 T^{6} + 138787264 T^{7} + 1993805958 T^{8} + 17121061356 T^{9} + 191693784190 T^{10} + 1640777965272 T^{11} + 17373926578870 T^{12} + 134842203434952 T^{13} + 1474761640508702 T^{14} + 10353104142184508 T^{15} + 112106275921829321 T^{16} + 773704682842873564 T^{17} + 7683496896669878492 T^{18} + 55515909626186811336 T^{19} + \)\(51\!\cdots\!50\)\( T^{20} + \)\(37\!\cdots\!12\)\( T^{21} + \)\(34\!\cdots\!88\)\( T^{22} + \)\(23\!\cdots\!32\)\( T^{23} + \)\(22\!\cdots\!41\)\( T^{24} + \)\(13\!\cdots\!56\)\( T^{25} + \)\(13\!\cdots\!38\)\( T^{26} + \)\(81\!\cdots\!96\)\( T^{27} + \)\(70\!\cdots\!70\)\( T^{28} + \)\(44\!\cdots\!84\)\( T^{29} + \)\(34\!\cdots\!10\)\( T^{30} + \)\(20\!\cdots\!48\)\( T^{31} + \)\(16\!\cdots\!38\)\( T^{32} + \)\(76\!\cdots\!68\)\( T^{33} + \)\(65\!\cdots\!64\)\( T^{34} + \)\(19\!\cdots\!72\)\( T^{35} + \)\(19\!\cdots\!23\)\( T^{36} + \)\(29\!\cdots\!52\)\( T^{37} + \)\(37\!\cdots\!72\)\( T^{38} + \)\(19\!\cdots\!12\)\( T^{39} + \)\(33\!\cdots\!01\)\( T^{40} \))(\( 1 + 4 T + 508 T^{2} + 2676 T^{3} + 119783 T^{4} + 785404 T^{5} + 17867516 T^{6} + 138787264 T^{7} + 1993805958 T^{8} + 17121061356 T^{9} + 191693784190 T^{10} + 1640777965272 T^{11} + 17373926578870 T^{12} + 134842203434952 T^{13} + 1474761640508702 T^{14} + 10353104142184508 T^{15} + 112106275921829321 T^{16} + 773704682842873564 T^{17} + 7683496896669878492 T^{18} + 55515909626186811336 T^{19} + \)\(51\!\cdots\!50\)\( T^{20} + \)\(37\!\cdots\!12\)\( T^{21} + \)\(34\!\cdots\!88\)\( T^{22} + \)\(23\!\cdots\!32\)\( T^{23} + \)\(22\!\cdots\!41\)\( T^{24} + \)\(13\!\cdots\!56\)\( T^{25} + \)\(13\!\cdots\!38\)\( T^{26} + \)\(81\!\cdots\!96\)\( T^{27} + \)\(70\!\cdots\!70\)\( T^{28} + \)\(44\!\cdots\!84\)\( T^{29} + \)\(34\!\cdots\!10\)\( T^{30} + \)\(20\!\cdots\!48\)\( T^{31} + \)\(16\!\cdots\!38\)\( T^{32} + \)\(76\!\cdots\!68\)\( T^{33} + \)\(65\!\cdots\!64\)\( T^{34} + \)\(19\!\cdots\!72\)\( T^{35} + \)\(19\!\cdots\!23\)\( T^{36} + \)\(29\!\cdots\!52\)\( T^{37} + \)\(37\!\cdots\!72\)\( T^{38} + \)\(19\!\cdots\!12\)\( T^{39} + \)\(33\!\cdots\!01\)\( T^{40} \))
$71$ (\( 1 - 6 T + 71 T^{2} - 426 T^{3} + 5041 T^{4} \))(\( 1 + 4 T + 141 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 + 25 T^{2} + 5041 T^{4} \))(\( 1 + 25 T^{2} + 5041 T^{4} \))(\( 1 + 20 T + 222 T^{2} + 1420 T^{3} + 5041 T^{4} \))(\( 1 + 20 T + 222 T^{2} + 1420 T^{3} + 5041 T^{4} \))(\( 1 - 20 T + 297 T^{2} - 2706 T^{3} + 21087 T^{4} - 100820 T^{5} + 357911 T^{6} \))(\( 1 + 10 T + 205 T^{2} + 1220 T^{3} + 14555 T^{4} + 50410 T^{5} + 357911 T^{6} \))(\( 1 + 10 T + 205 T^{2} + 1220 T^{3} + 14555 T^{4} + 50410 T^{5} + 357911 T^{6} \))(\( 1 + 14 T + 197 T^{2} + 1964 T^{3} + 13987 T^{4} + 70574 T^{5} + 357911 T^{6} \))(\( 1 + 2 T + 177 T^{2} + 276 T^{3} + 12567 T^{4} + 10082 T^{5} + 357911 T^{6} \))(\( 1 + 205 T^{2} + 61 T^{3} + 23652 T^{4} + 1421 T^{5} + 1679292 T^{6} + 307501 T^{7} + 73371755 T^{8} + 1804229351 T^{10} \))(\( 1 + 205 T^{2} + 61 T^{3} + 23652 T^{4} + 1421 T^{5} + 1679292 T^{6} + 307501 T^{7} + 73371755 T^{8} + 1804229351 T^{10} \))(\( 1 + 24 T + 396 T^{2} + 4954 T^{3} + 55267 T^{4} + 504628 T^{5} + 3923957 T^{6} + 24973114 T^{7} + 141732756 T^{8} + 609880344 T^{9} + 1804229351 T^{10} \))(\( 1 + 6 T + 321 T^{2} + 1680 T^{3} + 48347 T^{4} + 214362 T^{5} + 4349446 T^{6} + 15219702 T^{7} + 243717227 T^{8} + 601290480 T^{9} + 8157149601 T^{10} + 10825376106 T^{11} + 128100283921 T^{12} \))(\( 1 + 12 T + 291 T^{2} + 4116 T^{3} + 49600 T^{4} + 569260 T^{5} + 5785078 T^{6} + 47941040 T^{7} + 410740538 T^{8} + 2869639660 T^{9} + 17752385600 T^{10} + 104594478996 T^{11} + 525030741141 T^{12} + 1537203407052 T^{13} + 9095120158391 T^{14} \))(\( 1 + 12 T + 291 T^{2} + 4116 T^{3} + 49600 T^{4} + 569260 T^{5} + 5785078 T^{6} + 47941040 T^{7} + 410740538 T^{8} + 2869639660 T^{9} + 17752385600 T^{10} + 104594478996 T^{11} + 525030741141 T^{12} + 1537203407052 T^{13} + 9095120158391 T^{14} \))(\( 1 - 40 T + 1374 T^{2} - 33177 T^{3} + 715975 T^{4} - 13040936 T^{5} + 218184927 T^{6} - 3272019966 T^{7} + 45860802496 T^{8} - 592702948240 T^{9} + 7241747364173 T^{10} - 82885605229825 T^{11} + 903810471887914 T^{12} - 9319858469320218 T^{13} + 92021704416520370 T^{14} - 863959534379931611 T^{15} + 7789151191505478234 T^{16} - 66945292548611306582 T^{17} + \)\(55\!\cdots\!14\)\( T^{18} - \)\(43\!\cdots\!51\)\( T^{19} + \)\(32\!\cdots\!70\)\( T^{20} - \)\(23\!\cdots\!58\)\( T^{21} + \)\(16\!\cdots\!14\)\( T^{22} - \)\(10\!\cdots\!25\)\( T^{23} + \)\(65\!\cdots\!43\)\( T^{24} - \)\(38\!\cdots\!40\)\( T^{25} + \)\(21\!\cdots\!76\)\( T^{26} - \)\(10\!\cdots\!66\)\( T^{27} + \)\(50\!\cdots\!17\)\( T^{28} - \)\(21\!\cdots\!76\)\( T^{29} + \)\(83\!\cdots\!25\)\( T^{30} - \)\(27\!\cdots\!37\)\( T^{31} + \)\(80\!\cdots\!74\)\( T^{32} - \)\(16\!\cdots\!40\)\( T^{33} + \)\(29\!\cdots\!91\)\( T^{34} \))(\( 1 - 40 T + 1374 T^{2} - 33177 T^{3} + 715975 T^{4} - 13040936 T^{5} + 218184927 T^{6} - 3272019966 T^{7} + 45860802496 T^{8} - 592702948240 T^{9} + 7241747364173 T^{10} - 82885605229825 T^{11} + 903810471887914 T^{12} - 9319858469320218 T^{13} + 92021704416520370 T^{14} - 863959534379931611 T^{15} + 7789151191505478234 T^{16} - 66945292548611306582 T^{17} + \)\(55\!\cdots\!14\)\( T^{18} - \)\(43\!\cdots\!51\)\( T^{19} + \)\(32\!\cdots\!70\)\( T^{20} - \)\(23\!\cdots\!58\)\( T^{21} + \)\(16\!\cdots\!14\)\( T^{22} - \)\(10\!\cdots\!25\)\( T^{23} + \)\(65\!\cdots\!43\)\( T^{24} - \)\(38\!\cdots\!40\)\( T^{25} + \)\(21\!\cdots\!76\)\( T^{26} - \)\(10\!\cdots\!66\)\( T^{27} + \)\(50\!\cdots\!17\)\( T^{28} - \)\(21\!\cdots\!76\)\( T^{29} + \)\(83\!\cdots\!25\)\( T^{30} - \)\(27\!\cdots\!37\)\( T^{31} + \)\(80\!\cdots\!74\)\( T^{32} - \)\(16\!\cdots\!40\)\( T^{33} + \)\(29\!\cdots\!91\)\( T^{34} \))(\( 1 - 8 T + 762 T^{2} - 3576 T^{3} + 275000 T^{4} - 597800 T^{5} + 66381154 T^{6} - 16110776 T^{7} + 12386993870 T^{8} + 14552435320 T^{9} + 1904761586734 T^{10} + 4109636225576 T^{11} + 248644265143658 T^{12} + 692801064948840 T^{13} + 28008670199006558 T^{14} + 87750614257749208 T^{15} + 2749348361125969377 T^{16} + 8953364907147647152 T^{17} + \)\(23\!\cdots\!96\)\( T^{18} + \)\(75\!\cdots\!44\)\( T^{19} + \)\(17\!\cdots\!88\)\( T^{20} + \)\(53\!\cdots\!24\)\( T^{21} + \)\(11\!\cdots\!36\)\( T^{22} + \)\(32\!\cdots\!72\)\( T^{23} + \)\(69\!\cdots\!37\)\( T^{24} + \)\(15\!\cdots\!08\)\( T^{25} + \)\(35\!\cdots\!18\)\( T^{26} + \)\(63\!\cdots\!40\)\( T^{27} + \)\(16\!\cdots\!38\)\( T^{28} + \)\(18\!\cdots\!56\)\( T^{29} + \)\(62\!\cdots\!34\)\( T^{30} + \)\(33\!\cdots\!20\)\( T^{31} + \)\(20\!\cdots\!70\)\( T^{32} - \)\(18\!\cdots\!36\)\( T^{33} + \)\(54\!\cdots\!74\)\( T^{34} - \)\(35\!\cdots\!00\)\( T^{35} + \)\(11\!\cdots\!00\)\( T^{36} - \)\(10\!\cdots\!16\)\( T^{37} + \)\(16\!\cdots\!82\)\( T^{38} - \)\(11\!\cdots\!48\)\( T^{39} + \)\(10\!\cdots\!01\)\( T^{40} \))(\( 1 - 8 T + 762 T^{2} - 3576 T^{3} + 275000 T^{4} - 597800 T^{5} + 66381154 T^{6} - 16110776 T^{7} + 12386993870 T^{8} + 14552435320 T^{9} + 1904761586734 T^{10} + 4109636225576 T^{11} + 248644265143658 T^{12} + 692801064948840 T^{13} + 28008670199006558 T^{14} + 87750614257749208 T^{15} + 2749348361125969377 T^{16} + 8953364907147647152 T^{17} + \)\(23\!\cdots\!96\)\( T^{18} + \)\(75\!\cdots\!44\)\( T^{19} + \)\(17\!\cdots\!88\)\( T^{20} + \)\(53\!\cdots\!24\)\( T^{21} + \)\(11\!\cdots\!36\)\( T^{22} + \)\(32\!\cdots\!72\)\( T^{23} + \)\(69\!\cdots\!37\)\( T^{24} + \)\(15\!\cdots\!08\)\( T^{25} + \)\(35\!\cdots\!18\)\( T^{26} + \)\(63\!\cdots\!40\)\( T^{27} + \)\(16\!\cdots\!38\)\( T^{28} + \)\(18\!\cdots\!56\)\( T^{29} + \)\(62\!\cdots\!34\)\( T^{30} + \)\(33\!\cdots\!20\)\( T^{31} + \)\(20\!\cdots\!70\)\( T^{32} - \)\(18\!\cdots\!36\)\( T^{33} + \)\(54\!\cdots\!74\)\( T^{34} - \)\(35\!\cdots\!00\)\( T^{35} + \)\(11\!\cdots\!00\)\( T^{36} - \)\(10\!\cdots\!16\)\( T^{37} + \)\(16\!\cdots\!82\)\( T^{38} - \)\(11\!\cdots\!48\)\( T^{39} + \)\(10\!\cdots\!01\)\( T^{40} \))
$73$ (\( 1 - 2 T + 67 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( ( 1 - 15 T + 73 T^{2} )^{2} \))(\( 1 + 15 T + 199 T^{2} + 1095 T^{3} + 5329 T^{4} \))(\( 1 - 15 T + 199 T^{2} - 1095 T^{3} + 5329 T^{4} \))(\( 1 - 14 T + 175 T^{2} - 1022 T^{3} + 5329 T^{4} \))(\( 1 + 14 T + 175 T^{2} + 1022 T^{3} + 5329 T^{4} \))(\( 1 - 2 T + 39 T^{2} - 536 T^{3} + 2847 T^{4} - 10658 T^{5} + 389017 T^{6} \))(\( 1 + 10 T + 147 T^{2} + 956 T^{3} + 10731 T^{4} + 53290 T^{5} + 389017 T^{6} \))(\( 1 - 10 T + 147 T^{2} - 956 T^{3} + 10731 T^{4} - 53290 T^{5} + 389017 T^{6} \))(\( 1 - 4 T + 135 T^{2} - 192 T^{3} + 9855 T^{4} - 21316 T^{5} + 389017 T^{6} \))(\( 1 - 2 T + 183 T^{2} - 284 T^{3} + 13359 T^{4} - 10658 T^{5} + 389017 T^{6} \))(\( 1 - 13 T + 255 T^{2} - 2110 T^{3} + 24189 T^{4} - 166475 T^{5} + 1765797 T^{6} - 11244190 T^{7} + 99199335 T^{8} - 369177133 T^{9} + 2073071593 T^{10} \))(\( 1 + 13 T + 255 T^{2} + 2110 T^{3} + 24189 T^{4} + 166475 T^{5} + 1765797 T^{6} + 11244190 T^{7} + 99199335 T^{8} + 369177133 T^{9} + 2073071593 T^{10} \))(\( 1 + 40 T + 950 T^{2} + 15562 T^{3} + 192937 T^{4} + 1857916 T^{5} + 14084401 T^{6} + 82929898 T^{7} + 369566150 T^{8} + 1135929640 T^{9} + 2073071593 T^{10} \))(\( 1 + 52 T + 1447 T^{2} + 27846 T^{3} + 408023 T^{4} + 4752206 T^{5} + 44927922 T^{6} + 346911038 T^{7} + 2174354567 T^{8} + 10832567382 T^{9} + 41092254727 T^{10} + 107799722836 T^{11} + 151334226289 T^{12} \))(\( 1 + 14 T + 381 T^{2} + 5104 T^{3} + 72100 T^{4} + 815200 T^{5} + 8333298 T^{6} + 75539380 T^{7} + 608330754 T^{8} + 4344200800 T^{9} + 28048125700 T^{10} + 144944622064 T^{11} + 789840276933 T^{12} + 2118679168046 T^{13} + 11047398519097 T^{14} \))(\( 1 - 14 T + 381 T^{2} - 5104 T^{3} + 72100 T^{4} - 815200 T^{5} + 8333298 T^{6} - 75539380 T^{7} + 608330754 T^{8} - 4344200800 T^{9} + 28048125700 T^{10} - 144944622064 T^{11} + 789840276933 T^{12} - 2118679168046 T^{13} + 11047398519097 T^{14} \))(\( 1 - 14 T + 720 T^{2} - 9687 T^{3} + 270306 T^{4} - 3431349 T^{5} + 68849521 T^{6} - 816618430 T^{7} + 13172555356 T^{8} - 145309875303 T^{9} + 1994781329106 T^{10} - 20421139880276 T^{11} + 246535981040545 T^{12} - 2338641027340479 T^{13} + 25336379927237556 T^{14} - 222253591410494343 T^{15} + 2188948692794156785 T^{16} - 17697891775385147678 T^{17} + \)\(15\!\cdots\!05\)\( T^{18} - \)\(11\!\cdots\!47\)\( T^{19} + \)\(98\!\cdots\!52\)\( T^{20} - \)\(66\!\cdots\!39\)\( T^{21} + \)\(51\!\cdots\!85\)\( T^{22} - \)\(30\!\cdots\!64\)\( T^{23} + \)\(22\!\cdots\!82\)\( T^{24} - \)\(11\!\cdots\!43\)\( T^{25} + \)\(77\!\cdots\!28\)\( T^{26} - \)\(35\!\cdots\!70\)\( T^{27} + \)\(21\!\cdots\!17\)\( T^{28} - \)\(78\!\cdots\!29\)\( T^{29} + \)\(45\!\cdots\!98\)\( T^{30} - \)\(11\!\cdots\!83\)\( T^{31} + \)\(64\!\cdots\!40\)\( T^{32} - \)\(91\!\cdots\!54\)\( T^{33} + \)\(47\!\cdots\!53\)\( T^{34} \))(\( 1 + 14 T + 720 T^{2} + 9687 T^{3} + 270306 T^{4} + 3431349 T^{5} + 68849521 T^{6} + 816618430 T^{7} + 13172555356 T^{8} + 145309875303 T^{9} + 1994781329106 T^{10} + 20421139880276 T^{11} + 246535981040545 T^{12} + 2338641027340479 T^{13} + 25336379927237556 T^{14} + 222253591410494343 T^{15} + 2188948692794156785 T^{16} + 17697891775385147678 T^{17} + \)\(15\!\cdots\!05\)\( T^{18} + \)\(11\!\cdots\!47\)\( T^{19} + \)\(98\!\cdots\!52\)\( T^{20} + \)\(66\!\cdots\!39\)\( T^{21} + \)\(51\!\cdots\!85\)\( T^{22} + \)\(30\!\cdots\!64\)\( T^{23} + \)\(22\!\cdots\!82\)\( T^{24} + \)\(11\!\cdots\!43\)\( T^{25} + \)\(77\!\cdots\!28\)\( T^{26} + \)\(35\!\cdots\!70\)\( T^{27} + \)\(21\!\cdots\!17\)\( T^{28} + \)\(78\!\cdots\!29\)\( T^{29} + \)\(45\!\cdots\!98\)\( T^{30} + \)\(11\!\cdots\!83\)\( T^{31} + \)\(64\!\cdots\!40\)\( T^{32} + \)\(91\!\cdots\!54\)\( T^{33} + \)\(47\!\cdots\!53\)\( T^{34} \))(\( 1 + 48 T + 1942 T^{2} + 56264 T^{3} + 1433780 T^{4} + 31189032 T^{5} + 615525402 T^{6} + 10961436744 T^{7} + 180602859582 T^{8} + 2754197341656 T^{9} + 39361752586386 T^{10} + 528064119106464 T^{11} + 6697259691407002 T^{12} + 80430473082955408 T^{13} + 918686945721583994 T^{14} + 9992605985967244920 T^{15} + \)\(10\!\cdots\!45\)\( T^{16} + \)\(10\!\cdots\!04\)\( T^{17} + \)\(97\!\cdots\!60\)\( T^{18} + \)\(89\!\cdots\!64\)\( T^{19} + \)\(77\!\cdots\!20\)\( T^{20} + \)\(65\!\cdots\!72\)\( T^{21} + \)\(52\!\cdots\!40\)\( T^{22} + \)\(40\!\cdots\!68\)\( T^{23} + \)\(29\!\cdots\!45\)\( T^{24} + \)\(20\!\cdots\!60\)\( T^{25} + \)\(13\!\cdots\!66\)\( T^{26} + \)\(88\!\cdots\!76\)\( T^{27} + \)\(54\!\cdots\!62\)\( T^{28} + \)\(31\!\cdots\!32\)\( T^{29} + \)\(16\!\cdots\!14\)\( T^{30} + \)\(86\!\cdots\!12\)\( T^{31} + \)\(41\!\cdots\!22\)\( T^{32} + \)\(18\!\cdots\!52\)\( T^{33} + \)\(75\!\cdots\!18\)\( T^{34} + \)\(27\!\cdots\!24\)\( T^{35} + \)\(93\!\cdots\!80\)\( T^{36} + \)\(26\!\cdots\!92\)\( T^{37} + \)\(67\!\cdots\!98\)\( T^{38} + \)\(12\!\cdots\!76\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))(\( 1 - 48 T + 1942 T^{2} - 56264 T^{3} + 1433780 T^{4} - 31189032 T^{5} + 615525402 T^{6} - 10961436744 T^{7} + 180602859582 T^{8} - 2754197341656 T^{9} + 39361752586386 T^{10} - 528064119106464 T^{11} + 6697259691407002 T^{12} - 80430473082955408 T^{13} + 918686945721583994 T^{14} - 9992605985967244920 T^{15} + \)\(10\!\cdots\!45\)\( T^{16} - \)\(10\!\cdots\!04\)\( T^{17} + \)\(97\!\cdots\!60\)\( T^{18} - \)\(89\!\cdots\!64\)\( T^{19} + \)\(77\!\cdots\!20\)\( T^{20} - \)\(65\!\cdots\!72\)\( T^{21} + \)\(52\!\cdots\!40\)\( T^{22} - \)\(40\!\cdots\!68\)\( T^{23} + \)\(29\!\cdots\!45\)\( T^{24} - \)\(20\!\cdots\!60\)\( T^{25} + \)\(13\!\cdots\!66\)\( T^{26} - \)\(88\!\cdots\!76\)\( T^{27} + \)\(54\!\cdots\!62\)\( T^{28} - \)\(31\!\cdots\!32\)\( T^{29} + \)\(16\!\cdots\!14\)\( T^{30} - \)\(86\!\cdots\!12\)\( T^{31} + \)\(41\!\cdots\!22\)\( T^{32} - \)\(18\!\cdots\!52\)\( T^{33} + \)\(75\!\cdots\!18\)\( T^{34} - \)\(27\!\cdots\!24\)\( T^{35} + \)\(93\!\cdots\!80\)\( T^{36} - \)\(26\!\cdots\!92\)\( T^{37} + \)\(67\!\cdots\!98\)\( T^{38} - \)\(12\!\cdots\!76\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))
$79$ (\( 1 + 10 T + 138 T^{2} + 790 T^{3} + 6241 T^{4} \))(\( 1 + 2 T + 114 T^{2} + 158 T^{3} + 6241 T^{4} \))(\( 1 + 6 T - 41 T^{2} + 474 T^{3} + 6241 T^{4} \))(\( 1 + 6 T - 41 T^{2} + 474 T^{3} + 6241 T^{4} \))(\( ( 1 + T + 79 T^{2} )^{2} \))(\( ( 1 + T + 79 T^{2} )^{2} \))(\( 1 - 32 T + 565 T^{2} - 6146 T^{3} + 44635 T^{4} - 199712 T^{5} + 493039 T^{6} \))(\( ( 1 + 6 T + 79 T^{2} )^{3} \))(\( ( 1 + 6 T + 79 T^{2} )^{3} \))(\( 1 - 14 T + 269 T^{2} - 2156 T^{3} + 21251 T^{4} - 87374 T^{5} + 493039 T^{6} \))(\( 1 - 20 T + 333 T^{2} - 3224 T^{3} + 26307 T^{4} - 124820 T^{5} + 493039 T^{6} \))(\( 1 + 41 T + 948 T^{2} + 15081 T^{3} + 184951 T^{4} + 1815285 T^{5} + 14611129 T^{6} + 94120521 T^{7} + 467400972 T^{8} + 1596953321 T^{9} + 3077056399 T^{10} \))(\( 1 + 41 T + 948 T^{2} + 15081 T^{3} + 184951 T^{4} + 1815285 T^{5} + 14611129 T^{6} + 94120521 T^{7} + 467400972 T^{8} + 1596953321 T^{9} + 3077056399 T^{10} \))(\( 1 + 42 T + 967 T^{2} + 15192 T^{3} + 184214 T^{4} + 1801084 T^{5} + 14552906 T^{6} + 94813272 T^{7} + 476768713 T^{8} + 1635903402 T^{9} + 3077056399 T^{10} \))(\( 1 + 322 T^{2} - 96 T^{3} + 49695 T^{4} - 14720 T^{5} + 4820732 T^{6} - 1162880 T^{7} + 310146495 T^{8} - 47331744 T^{9} + 12541926082 T^{10} + 243087455521 T^{12} \))(\( 1 + 8 T + 273 T^{2} + 3016 T^{3} + 44397 T^{4} + 494520 T^{5} + 4907901 T^{6} + 49239664 T^{7} + 387724179 T^{8} + 3086299320 T^{9} + 21889452483 T^{10} + 117473444296 T^{11} + 840036396927 T^{12} + 1944699644168 T^{13} + 19203908986159 T^{14} \))(\( 1 + 8 T + 273 T^{2} + 3016 T^{3} + 44397 T^{4} + 494520 T^{5} + 4907901 T^{6} + 49239664 T^{7} + 387724179 T^{8} + 3086299320 T^{9} + 21889452483 T^{10} + 117473444296 T^{11} + 840036396927 T^{12} + 1944699644168 T^{13} + 19203908986159 T^{14} \))(\( 1 - 61 T + 2502 T^{2} - 75965 T^{3} + 1921212 T^{4} - 41664694 T^{5} + 803078539 T^{6} - 13949750004 T^{7} + 221918919163 T^{8} - 3258387952572 T^{9} + 44540686481580 T^{10} - 569446531924719 T^{11} + 6843743339160625 T^{12} - 77527861881114540 T^{13} + 830333552183309167 T^{14} - 8419647937183343721 T^{15} + 80964267131630511813 T^{16} - \)\(73\!\cdots\!77\)\( T^{17} + \)\(63\!\cdots\!27\)\( T^{18} - \)\(52\!\cdots\!61\)\( T^{19} + \)\(40\!\cdots\!13\)\( T^{20} - \)\(30\!\cdots\!40\)\( T^{21} + \)\(21\!\cdots\!75\)\( T^{22} - \)\(13\!\cdots\!99\)\( T^{23} + \)\(85\!\cdots\!20\)\( T^{24} - \)\(49\!\cdots\!92\)\( T^{25} + \)\(26\!\cdots\!97\)\( T^{26} - \)\(13\!\cdots\!04\)\( T^{27} + \)\(60\!\cdots\!81\)\( T^{28} - \)\(24\!\cdots\!54\)\( T^{29} + \)\(89\!\cdots\!68\)\( T^{30} - \)\(28\!\cdots\!65\)\( T^{31} + \)\(72\!\cdots\!98\)\( T^{32} - \)\(14\!\cdots\!81\)\( T^{33} + \)\(18\!\cdots\!59\)\( T^{34} \))(\( 1 - 61 T + 2502 T^{2} - 75965 T^{3} + 1921212 T^{4} - 41664694 T^{5} + 803078539 T^{6} - 13949750004 T^{7} + 221918919163 T^{8} - 3258387952572 T^{9} + 44540686481580 T^{10} - 569446531924719 T^{11} + 6843743339160625 T^{12} - 77527861881114540 T^{13} + 830333552183309167 T^{14} - 8419647937183343721 T^{15} + 80964267131630511813 T^{16} - \)\(73\!\cdots\!77\)\( T^{17} + \)\(63\!\cdots\!27\)\( T^{18} - \)\(52\!\cdots\!61\)\( T^{19} + \)\(40\!\cdots\!13\)\( T^{20} - \)\(30\!\cdots\!40\)\( T^{21} + \)\(21\!\cdots\!75\)\( T^{22} - \)\(13\!\cdots\!99\)\( T^{23} + \)\(85\!\cdots\!20\)\( T^{24} - \)\(49\!\cdots\!92\)\( T^{25} + \)\(26\!\cdots\!97\)\( T^{26} - \)\(13\!\cdots\!04\)\( T^{27} + \)\(60\!\cdots\!81\)\( T^{28} - \)\(24\!\cdots\!54\)\( T^{29} + \)\(89\!\cdots\!68\)\( T^{30} - \)\(28\!\cdots\!65\)\( T^{31} + \)\(72\!\cdots\!98\)\( T^{32} - \)\(14\!\cdots\!81\)\( T^{33} + \)\(18\!\cdots\!59\)\( T^{34} \))(\( 1 + 4 T + 744 T^{2} + 3204 T^{3} + 274302 T^{4} + 1114476 T^{5} + 66854640 T^{6} + 228599980 T^{7} + 12124345485 T^{8} + 30973250912 T^{9} + 1759640243608 T^{10} + 2880535376928 T^{11} + 216553343817768 T^{12} + 181564983044224 T^{13} + 23661783887002376 T^{14} + 7171924176109248 T^{15} + 2357550074150624818 T^{16} + 127612800881544008 T^{17} + \)\(21\!\cdots\!68\)\( T^{18} - 3227028660750646520 T^{19} + \)\(17\!\cdots\!04\)\( T^{20} - \)\(25\!\cdots\!80\)\( T^{21} + \)\(13\!\cdots\!88\)\( T^{22} + \)\(62\!\cdots\!12\)\( T^{23} + \)\(91\!\cdots\!58\)\( T^{24} + \)\(22\!\cdots\!52\)\( T^{25} + \)\(57\!\cdots\!96\)\( T^{26} + \)\(34\!\cdots\!16\)\( T^{27} + \)\(32\!\cdots\!48\)\( T^{28} + \)\(34\!\cdots\!32\)\( T^{29} + \)\(16\!\cdots\!08\)\( T^{30} + \)\(23\!\cdots\!48\)\( T^{31} + \)\(71\!\cdots\!85\)\( T^{32} + \)\(10\!\cdots\!20\)\( T^{33} + \)\(24\!\cdots\!40\)\( T^{34} + \)\(32\!\cdots\!24\)\( T^{35} + \)\(63\!\cdots\!42\)\( T^{36} + \)\(58\!\cdots\!36\)\( T^{37} + \)\(10\!\cdots\!84\)\( T^{38} + \)\(45\!\cdots\!76\)\( T^{39} + \)\(89\!\cdots\!01\)\( T^{40} \))(\( 1 + 4 T + 744 T^{2} + 3204 T^{3} + 274302 T^{4} + 1114476 T^{5} + 66854640 T^{6} + 228599980 T^{7} + 12124345485 T^{8} + 30973250912 T^{9} + 1759640243608 T^{10} + 2880535376928 T^{11} + 216553343817768 T^{12} + 181564983044224 T^{13} + 23661783887002376 T^{14} + 7171924176109248 T^{15} + 2357550074150624818 T^{16} + 127612800881544008 T^{17} + \)\(21\!\cdots\!68\)\( T^{18} - 3227028660750646520 T^{19} + \)\(17\!\cdots\!04\)\( T^{20} - \)\(25\!\cdots\!80\)\( T^{21} + \)\(13\!\cdots\!88\)\( T^{22} + \)\(62\!\cdots\!12\)\( T^{23} + \)\(91\!\cdots\!58\)\( T^{24} + \)\(22\!\cdots\!52\)\( T^{25} + \)\(57\!\cdots\!96\)\( T^{26} + \)\(34\!\cdots\!16\)\( T^{27} + \)\(32\!\cdots\!48\)\( T^{28} + \)\(34\!\cdots\!32\)\( T^{29} + \)\(16\!\cdots\!08\)\( T^{30} + \)\(23\!\cdots\!48\)\( T^{31} + \)\(71\!\cdots\!85\)\( T^{32} + \)\(10\!\cdots\!20\)\( T^{33} + \)\(24\!\cdots\!40\)\( T^{34} + \)\(32\!\cdots\!24\)\( T^{35} + \)\(63\!\cdots\!42\)\( T^{36} + \)\(58\!\cdots\!36\)\( T^{37} + \)\(10\!\cdots\!84\)\( T^{38} + \)\(45\!\cdots\!76\)\( T^{39} + \)\(89\!\cdots\!01\)\( T^{40} \))
$83$ (\( 1 - 2 T + 147 T^{2} - 166 T^{3} + 6889 T^{4} \))(\( 1 + 6 T + 95 T^{2} + 498 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 217 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 - 16 T + 217 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 182 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 + 12 T + 182 T^{2} + 996 T^{3} + 6889 T^{4} \))(\( 1 + 185 T^{2} + 128 T^{3} + 15355 T^{4} + 571787 T^{6} \))(\( 1 - 14 T + 281 T^{2} - 2268 T^{3} + 23323 T^{4} - 96446 T^{5} + 571787 T^{6} \))(\( 1 + 14 T + 281 T^{2} + 2268 T^{3} + 23323 T^{4} + 96446 T^{5} + 571787 T^{6} \))(\( 1 - 2 T + 181 T^{2} - 388 T^{3} + 15023 T^{4} - 13778 T^{5} + 571787 T^{6} \))(\( 1 - 6 T + 149 T^{2} - 332 T^{3} + 12367 T^{4} - 41334 T^{5} + 571787 T^{6} \))(\( 1 + 2 T + 338 T^{2} + 520 T^{3} + 50961 T^{4} + 61081 T^{5} + 4229763 T^{6} + 3582280 T^{7} + 193264006 T^{8} + 94916642 T^{9} + 3939040643 T^{10} \))(\( 1 - 2 T + 338 T^{2} - 520 T^{3} + 50961 T^{4} - 61081 T^{5} + 4229763 T^{6} - 3582280 T^{7} + 193264006 T^{8} - 94916642 T^{9} + 3939040643 T^{10} \))(\( 1 - 12 T + 156 T^{2} - 1442 T^{3} + 16075 T^{4} - 98732 T^{5} + 1334225 T^{6} - 9933938 T^{7} + 89198772 T^{8} - 569499852 T^{9} + 3939040643 T^{10} \))(\( 1 + 12 T + 371 T^{2} + 4410 T^{3} + 66551 T^{4} + 681302 T^{5} + 7059658 T^{6} + 56548066 T^{7} + 458469839 T^{8} + 2521580670 T^{9} + 17607037091 T^{10} + 47268487716 T^{11} + 326940373369 T^{12} \))(\( 1 + 14 T + 291 T^{2} + 1240 T^{3} + 22896 T^{4} + 53760 T^{5} + 3234166 T^{6} + 15310380 T^{7} + 268435778 T^{8} + 370352640 T^{9} + 13091635152 T^{10} + 58848318040 T^{11} + 1146260827113 T^{12} + 4577165227166 T^{13} + 27136050989627 T^{14} \))(\( 1 - 14 T + 291 T^{2} - 1240 T^{3} + 22896 T^{4} - 53760 T^{5} + 3234166 T^{6} - 15310380 T^{7} + 268435778 T^{8} - 370352640 T^{9} + 13091635152 T^{10} - 58848318040 T^{11} + 1146260827113 T^{12} - 4577165227166 T^{13} + 27136050989627 T^{14} \))(\( 1 - 18 T + 649 T^{2} - 8266 T^{3} + 187447 T^{4} - 1911189 T^{5} + 35451581 T^{6} - 305873841 T^{7} + 5175717576 T^{8} - 39367421468 T^{9} + 642998529916 T^{10} - 4466934544265 T^{11} + 71637393222865 T^{12} - 466445774476547 T^{13} + 7274839511346155 T^{14} - 44877481335368596 T^{15} + 670127463585613200 T^{16} - 3921599863597187412 T^{17} + 55620579477605895600 T^{18} - \)\(30\!\cdots\!44\)\( T^{19} + \)\(41\!\cdots\!85\)\( T^{20} - \)\(22\!\cdots\!87\)\( T^{21} + \)\(28\!\cdots\!95\)\( T^{22} - \)\(14\!\cdots\!85\)\( T^{23} + \)\(17\!\cdots\!32\)\( T^{24} - \)\(88\!\cdots\!88\)\( T^{25} + \)\(96\!\cdots\!28\)\( T^{26} - \)\(47\!\cdots\!09\)\( T^{27} + \)\(45\!\cdots\!27\)\( T^{28} - \)\(20\!\cdots\!29\)\( T^{29} + \)\(16\!\cdots\!61\)\( T^{30} - \)\(60\!\cdots\!14\)\( T^{31} + \)\(39\!\cdots\!43\)\( T^{32} - \)\(91\!\cdots\!58\)\( T^{33} + \)\(42\!\cdots\!23\)\( T^{34} \))(\( 1 + 18 T + 649 T^{2} + 8266 T^{3} + 187447 T^{4} + 1911189 T^{5} + 35451581 T^{6} + 305873841 T^{7} + 5175717576 T^{8} + 39367421468 T^{9} + 642998529916 T^{10} + 4466934544265 T^{11} + 71637393222865 T^{12} + 466445774476547 T^{13} + 7274839511346155 T^{14} + 44877481335368596 T^{15} + 670127463585613200 T^{16} + 3921599863597187412 T^{17} + 55620579477605895600 T^{18} + \)\(30\!\cdots\!44\)\( T^{19} + \)\(41\!\cdots\!85\)\( T^{20} + \)\(22\!\cdots\!87\)\( T^{21} + \)\(28\!\cdots\!95\)\( T^{22} + \)\(14\!\cdots\!85\)\( T^{23} + \)\(17\!\cdots\!32\)\( T^{24} + \)\(88\!\cdots\!88\)\( T^{25} + \)\(96\!\cdots\!28\)\( T^{26} + \)\(47\!\cdots\!09\)\( T^{27} + \)\(45\!\cdots\!27\)\( T^{28} + \)\(20\!\cdots\!29\)\( T^{29} + \)\(16\!\cdots\!61\)\( T^{30} + \)\(60\!\cdots\!14\)\( T^{31} + \)\(39\!\cdots\!43\)\( T^{32} + \)\(91\!\cdots\!58\)\( T^{33} + \)\(42\!\cdots\!23\)\( T^{34} \))(\( 1 + 8 T + 652 T^{2} + 3792 T^{3} + 203652 T^{4} + 810608 T^{5} + 41396172 T^{6} + 94217504 T^{7} + 6243872430 T^{8} + 3834384688 T^{9} + 752626097124 T^{10} - 814590982952 T^{11} + 75624310995034 T^{12} - 224318035845656 T^{13} + 6485612334199396 T^{14} - 34384736717270752 T^{15} + 488098252382532241 T^{16} - 4060655772846815224 T^{17} + 34603086671340481632 T^{18} - \)\(39\!\cdots\!64\)\( T^{19} + \)\(26\!\cdots\!36\)\( T^{20} - \)\(33\!\cdots\!12\)\( T^{21} + \)\(23\!\cdots\!48\)\( T^{22} - \)\(23\!\cdots\!88\)\( T^{23} + \)\(23\!\cdots\!61\)\( T^{24} - \)\(13\!\cdots\!36\)\( T^{25} + \)\(21\!\cdots\!24\)\( T^{26} - \)\(60\!\cdots\!12\)\( T^{27} + \)\(17\!\cdots\!94\)\( T^{28} - \)\(15\!\cdots\!56\)\( T^{29} + \)\(11\!\cdots\!76\)\( T^{30} + \)\(49\!\cdots\!96\)\( T^{31} + \)\(66\!\cdots\!30\)\( T^{32} + \)\(83\!\cdots\!52\)\( T^{33} + \)\(30\!\cdots\!88\)\( T^{34} + \)\(49\!\cdots\!56\)\( T^{35} + \)\(10\!\cdots\!12\)\( T^{36} + \)\(15\!\cdots\!16\)\( T^{37} + \)\(22\!\cdots\!68\)\( T^{38} + \)\(23\!\cdots\!76\)\( T^{39} + \)\(24\!\cdots\!01\)\( T^{40} \))(\( 1 - 8 T + 652 T^{2} - 3792 T^{3} + 203652 T^{4} - 810608 T^{5} + 41396172 T^{6} - 94217504 T^{7} + 6243872430 T^{8} - 3834384688 T^{9} + 752626097124 T^{10} + 814590982952 T^{11} + 75624310995034 T^{12} + 224318035845656 T^{13} + 6485612334199396 T^{14} + 34384736717270752 T^{15} + 488098252382532241 T^{16} + 4060655772846815224 T^{17} + 34603086671340481632 T^{18} + \)\(39\!\cdots\!64\)\( T^{19} + \)\(26\!\cdots\!36\)\( T^{20} + \)\(33\!\cdots\!12\)\( T^{21} + \)\(23\!\cdots\!48\)\( T^{22} + \)\(23\!\cdots\!88\)\( T^{23} + \)\(23\!\cdots\!61\)\( T^{24} + \)\(13\!\cdots\!36\)\( T^{25} + \)\(21\!\cdots\!24\)\( T^{26} + \)\(60\!\cdots\!12\)\( T^{27} + \)\(17\!\cdots\!94\)\( T^{28} + \)\(15\!\cdots\!56\)\( T^{29} + \)\(11\!\cdots\!76\)\( T^{30} - \)\(49\!\cdots\!96\)\( T^{31} + \)\(66\!\cdots\!30\)\( T^{32} - \)\(83\!\cdots\!52\)\( T^{33} + \)\(30\!\cdots\!88\)\( T^{34} - \)\(49\!\cdots\!56\)\( T^{35} + \)\(10\!\cdots\!12\)\( T^{36} - \)\(15\!\cdots\!16\)\( T^{37} + \)\(22\!\cdots\!68\)\( T^{38} - \)\(23\!\cdots\!76\)\( T^{39} + \)\(24\!\cdots\!01\)\( T^{40} \))
$89$ (\( 1 - 3 T + 119 T^{2} - 267 T^{3} + 7921 T^{4} \))(\( 1 - 9 T + 97 T^{2} - 801 T^{3} + 7921 T^{4} \))(\( 1 + 8 T + 181 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 - 8 T + 181 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( 1 - 24 T + 317 T^{2} - 2136 T^{3} + 7921 T^{4} \))(\( 1 + 24 T + 317 T^{2} + 2136 T^{3} + 7921 T^{4} \))(\( 1 - 6 T + 119 T^{2} - 148 T^{3} + 10591 T^{4} - 47526 T^{5} + 704969 T^{6} \))(\( 1 - 5 T + 249 T^{2} - 827 T^{3} + 22161 T^{4} - 39605 T^{5} + 704969 T^{6} \))(\( 1 + 5 T + 249 T^{2} + 827 T^{3} + 22161 T^{4} + 39605 T^{5} + 704969 T^{6} \))(\( 1 + 5 T + T^{2} - 911 T^{3} + 89 T^{4} + 39605 T^{5} + 704969 T^{6} \))(\( 1 - T + 55 T^{2} - 1227 T^{3} + 4895 T^{4} - 7921 T^{5} + 704969 T^{6} \))(\( 1 - 14 T + 194 T^{2} - 1342 T^{3} + 12493 T^{4} - 62707 T^{5} + 1111877 T^{6} - 10629982 T^{7} + 136763986 T^{8} - 878391374 T^{9} + 5584059449 T^{10} \))(\( 1 + 14 T + 194 T^{2} + 1342 T^{3} + 12493 T^{4} + 62707 T^{5} + 1111877 T^{6} + 10629982 T^{7} + 136763986 T^{8} + 878391374 T^{9} + 5584059449 T^{10} \))(\( 1 + 8 T + 457 T^{2} + 2846 T^{3} + 82405 T^{4} + 379849 T^{5} + 7334045 T^{6} + 22543166 T^{7} + 322170833 T^{8} + 501937928 T^{9} + 5584059449 T^{10} \))(\( 1 - 38 T + 938 T^{2} - 15970 T^{3} + 222014 T^{4} - 2537075 T^{5} + 25723552 T^{6} - 225799675 T^{7} + 1758572894 T^{8} - 11258354930 T^{9} + 58852222058 T^{10} - 212194259062 T^{11} + 496981290961 T^{12} \))(\( 1 - 19 T + 536 T^{2} - 8224 T^{3} + 130645 T^{4} - 1612251 T^{5} + 18578340 T^{6} - 183326933 T^{7} + 1653472260 T^{8} - 12770640171 T^{9} + 92100675005 T^{10} - 515992189984 T^{11} + 2993055864664 T^{12} - 9442644528259 T^{13} + 44231334895529 T^{14} \))(\( 1 + 19 T + 536 T^{2} + 8224 T^{3} + 130645 T^{4} + 1612251 T^{5} + 18578340 T^{6} + 183326933 T^{7} + 1653472260 T^{8} + 12770640171 T^{9} + 92100675005 T^{10} + 515992189984 T^{11} + 2993055864664 T^{12} + 9442644528259 T^{13} + 44231334895529 T^{14} \))(\( 1 + 18 T + 1210 T^{2} + 18248 T^{3} + 680740 T^{4} + 8864127 T^{5} + 240661821 T^{6} + 2762259374 T^{7} + 60681859080 T^{8} + 623143969383 T^{9} + 11705249565930 T^{10} + 108726466717854 T^{11} + 1803991540372945 T^{12} + 15276479424715949 T^{13} + 228369702398463766 T^{14} + 1771921614312460364 T^{15} + 24145001558824388947 T^{16} + \)\(17\!\cdots\!34\)\( T^{17} + \)\(21\!\cdots\!83\)\( T^{18} + \)\(14\!\cdots\!44\)\( T^{19} + \)\(16\!\cdots\!54\)\( T^{20} + \)\(95\!\cdots\!09\)\( T^{21} + \)\(10\!\cdots\!05\)\( T^{22} + \)\(54\!\cdots\!94\)\( T^{23} + \)\(51\!\cdots\!70\)\( T^{24} + \)\(24\!\cdots\!23\)\( T^{25} + \)\(21\!\cdots\!20\)\( T^{26} + \)\(86\!\cdots\!74\)\( T^{27} + \)\(66\!\cdots\!69\)\( T^{28} + \)\(21\!\cdots\!67\)\( T^{29} + \)\(14\!\cdots\!60\)\( T^{30} + \)\(35\!\cdots\!68\)\( T^{31} + \)\(21\!\cdots\!90\)\( T^{32} + \)\(27\!\cdots\!98\)\( T^{33} + \)\(13\!\cdots\!29\)\( T^{34} \))(\( 1 - 18 T + 1210 T^{2} - 18248 T^{3} + 680740 T^{4} - 8864127 T^{5} + 240661821 T^{6} - 2762259374 T^{7} + 60681859080 T^{8} - 623143969383 T^{9} + 11705249565930 T^{10} - 108726466717854 T^{11} + 1803991540372945 T^{12} - 15276479424715949 T^{13} + 228369702398463766 T^{14} - 1771921614312460364 T^{15} + 24145001558824388947 T^{16} - \)\(17\!\cdots\!34\)\( T^{17} + \)\(21\!\cdots\!83\)\( T^{18} - \)\(14\!\cdots\!44\)\( T^{19} + \)\(16\!\cdots\!54\)\( T^{20} - \)\(95\!\cdots\!09\)\( T^{21} + \)\(10\!\cdots\!05\)\( T^{22} - \)\(54\!\cdots\!94\)\( T^{23} + \)\(51\!\cdots\!70\)\( T^{24} - \)\(24\!\cdots\!23\)\( T^{25} + \)\(21\!\cdots\!20\)\( T^{26} - \)\(86\!\cdots\!74\)\( T^{27} + \)\(66\!\cdots\!69\)\( T^{28} - \)\(21\!\cdots\!67\)\( T^{29} + \)\(14\!\cdots\!60\)\( T^{30} - \)\(35\!\cdots\!68\)\( T^{31} + \)\(21\!\cdots\!90\)\( T^{32} - \)\(27\!\cdots\!98\)\( T^{33} + \)\(13\!\cdots\!29\)\( T^{34} \))(\( 1 + 20 T + 808 T^{2} + 12856 T^{3} + 314542 T^{4} + 4326688 T^{5} + 81767262 T^{6} + 1024025692 T^{7} + 16342815399 T^{8} + 192379723056 T^{9} + 2700529362264 T^{10} + 30408160260956 T^{11} + 383587331961062 T^{12} + 4167192887975976 T^{13} + 47960522080828044 T^{14} + 504816645425875312 T^{15} + 5374084024329144099 T^{16} + 54821471985120211132 T^{17} + \)\(54\!\cdots\!98\)\( T^{18} + \)\(53\!\cdots\!00\)\( T^{19} + \)\(50\!\cdots\!95\)\( T^{20} + \)\(47\!\cdots\!00\)\( T^{21} + \)\(43\!\cdots\!58\)\( T^{22} + \)\(38\!\cdots\!08\)\( T^{23} + \)\(33\!\cdots\!59\)\( T^{24} + \)\(28\!\cdots\!88\)\( T^{25} + \)\(23\!\cdots\!84\)\( T^{26} + \)\(18\!\cdots\!04\)\( T^{27} + \)\(15\!\cdots\!22\)\( T^{28} + \)\(10\!\cdots\!04\)\( T^{29} + \)\(84\!\cdots\!64\)\( T^{30} + \)\(53\!\cdots\!84\)\( T^{31} + \)\(40\!\cdots\!79\)\( T^{32} + \)\(22\!\cdots\!48\)\( T^{33} + \)\(15\!\cdots\!42\)\( T^{34} + \)\(75\!\cdots\!12\)\( T^{35} + \)\(48\!\cdots\!62\)\( T^{36} + \)\(17\!\cdots\!24\)\( T^{37} + \)\(99\!\cdots\!48\)\( T^{38} + \)\(21\!\cdots\!80\)\( T^{39} + \)\(97\!\cdots\!01\)\( T^{40} \))(\( 1 - 20 T + 808 T^{2} - 12856 T^{3} + 314542 T^{4} - 4326688 T^{5} + 81767262 T^{6} - 1024025692 T^{7} + 16342815399 T^{8} - 192379723056 T^{9} + 2700529362264 T^{10} - 30408160260956 T^{11} + 383587331961062 T^{12} - 4167192887975976 T^{13} + 47960522080828044 T^{14} - 504816645425875312 T^{15} + 5374084024329144099 T^{16} - 54821471985120211132 T^{17} + \)\(54\!\cdots\!98\)\( T^{18} - \)\(53\!\cdots\!00\)\( T^{19} + \)\(50\!\cdots\!95\)\( T^{20} - \)\(47\!\cdots\!00\)\( T^{21} + \)\(43\!\cdots\!58\)\( T^{22} - \)\(38\!\cdots\!08\)\( T^{23} + \)\(33\!\cdots\!59\)\( T^{24} - \)\(28\!\cdots\!88\)\( T^{25} + \)\(23\!\cdots\!84\)\( T^{26} - \)\(18\!\cdots\!04\)\( T^{27} + \)\(15\!\cdots\!22\)\( T^{28} - \)\(10\!\cdots\!04\)\( T^{29} + \)\(84\!\cdots\!64\)\( T^{30} - \)\(53\!\cdots\!84\)\( T^{31} + \)\(40\!\cdots\!79\)\( T^{32} - \)\(22\!\cdots\!48\)\( T^{33} + \)\(15\!\cdots\!42\)\( T^{34} - \)\(75\!\cdots\!12\)\( T^{35} + \)\(48\!\cdots\!62\)\( T^{36} - \)\(17\!\cdots\!24\)\( T^{37} + \)\(99\!\cdots\!48\)\( T^{38} - \)\(21\!\cdots\!80\)\( T^{39} + \)\(97\!\cdots\!01\)\( T^{40} \))
$97$ (\( 1 - 15 T + 149 T^{2} - 1455 T^{3} + 9409 T^{4} \))(\( 1 - 17 T + 255 T^{2} - 1649 T^{3} + 9409 T^{4} \))(\( 1 + 15 T + 247 T^{2} + 1455 T^{3} + 9409 T^{4} \))(\( 1 - 15 T + 247 T^{2} - 1455 T^{3} + 9409 T^{4} \))(\( 1 + 8 T + 190 T^{2} + 776 T^{3} + 9409 T^{4} \))(\( 1 - 8 T + 190 T^{2} - 776 T^{3} + 9409 T^{4} \))(\( 1 + 6 T + 239 T^{2} + 916 T^{3} + 23183 T^{4} + 56454 T^{5} + 912673 T^{6} \))(\( 1 - 19 T + 387 T^{2} - 3749 T^{3} + 37539 T^{4} - 178771 T^{5} + 912673 T^{6} \))(\( 1 + 19 T + 387 T^{2} + 3749 T^{3} + 37539 T^{4} + 178771 T^{5} + 912673 T^{6} \))(\( 1 + 27 T + 493 T^{2} + 5699 T^{3} + 47821 T^{4} + 254043 T^{5} + 912673 T^{6} \))(\( 1 + 11 T + 315 T^{2} + 2147 T^{3} + 30555 T^{4} + 103499 T^{5} + 912673 T^{6} \))(\( 1 + 27 T + 448 T^{2} + 5083 T^{3} + 45427 T^{4} + 421253 T^{5} + 4406419 T^{6} + 47825947 T^{7} + 408877504 T^{8} + 2390290587 T^{9} + 8587340257 T^{10} \))(\( 1 - 27 T + 448 T^{2} - 5083 T^{3} + 45427 T^{4} - 421253 T^{5} + 4406419 T^{6} - 47825947 T^{7} + 408877504 T^{8} - 2390290587 T^{9} + 8587340257 T^{10} \))(\( 1 + 16 T + 323 T^{2} + 4394 T^{3} + 51905 T^{4} + 561841 T^{5} + 5034785 T^{6} + 41343146 T^{7} + 294793379 T^{8} + 1416468496 T^{9} + 8587340257 T^{10} \))(\( 1 + 8 T + 266 T^{2} + 1362 T^{3} + 34864 T^{4} + 189883 T^{5} + 3886868 T^{6} + 18418651 T^{7} + 328035376 T^{8} + 1243060626 T^{9} + 23548788746 T^{10} + 68698722056 T^{11} + 832972004929 T^{12} \))(\( 1 + 23 T + 696 T^{2} + 10604 T^{3} + 188081 T^{4} + 2171679 T^{5} + 28535268 T^{6} + 263605149 T^{7} + 2767920996 T^{8} + 20433327711 T^{9} + 171656450513 T^{10} + 938764495724 T^{11} + 5976788818872 T^{12} + 19158356113367 T^{13} + 80798284478113 T^{14} \))(\( 1 - 23 T + 696 T^{2} - 10604 T^{3} + 188081 T^{4} - 2171679 T^{5} + 28535268 T^{6} - 263605149 T^{7} + 2767920996 T^{8} - 20433327711 T^{9} + 171656450513 T^{10} - 938764495724 T^{11} + 5976788818872 T^{12} - 19158356113367 T^{13} + 80798284478113 T^{14} \))(\( 1 + 26 T + 770 T^{2} + 14867 T^{3} + 292781 T^{4} + 4868120 T^{5} + 78821304 T^{6} + 1162618972 T^{7} + 16577872762 T^{8} + 221284097506 T^{9} + 2870029762020 T^{10} + 35191267282090 T^{11} + 421154908714594 T^{12} + 4794568498290144 T^{13} + 53333097252056137 T^{14} + 567616748953336231 T^{15} + 5895969216393339567 T^{16} + 58806362472633202712 T^{17} + \)\(57\!\cdots\!99\)\( T^{18} + \)\(53\!\cdots\!79\)\( T^{19} + \)\(48\!\cdots\!01\)\( T^{20} + \)\(42\!\cdots\!64\)\( T^{21} + \)\(36\!\cdots\!58\)\( T^{22} + \)\(29\!\cdots\!10\)\( T^{23} + \)\(23\!\cdots\!60\)\( T^{24} + \)\(17\!\cdots\!66\)\( T^{25} + \)\(12\!\cdots\!54\)\( T^{26} + \)\(85\!\cdots\!28\)\( T^{27} + \)\(56\!\cdots\!12\)\( T^{28} + \)\(33\!\cdots\!20\)\( T^{29} + \)\(19\!\cdots\!37\)\( T^{30} + \)\(97\!\cdots\!23\)\( T^{31} + \)\(48\!\cdots\!10\)\( T^{32} + \)\(15\!\cdots\!46\)\( T^{33} + \)\(59\!\cdots\!37\)\( T^{34} \))(\( 1 - 26 T + 770 T^{2} - 14867 T^{3} + 292781 T^{4} - 4868120 T^{5} + 78821304 T^{6} - 1162618972 T^{7} + 16577872762 T^{8} - 221284097506 T^{9} + 2870029762020 T^{10} - 35191267282090 T^{11} + 421154908714594 T^{12} - 4794568498290144 T^{13} + 53333097252056137 T^{14} - 567616748953336231 T^{15} + 5895969216393339567 T^{16} - 58806362472633202712 T^{17} + \)\(57\!\cdots\!99\)\( T^{18} - \)\(53\!\cdots\!79\)\( T^{19} + \)\(48\!\cdots\!01\)\( T^{20} - \)\(42\!\cdots\!64\)\( T^{21} + \)\(36\!\cdots\!58\)\( T^{22} - \)\(29\!\cdots\!10\)\( T^{23} + \)\(23\!\cdots\!60\)\( T^{24} - \)\(17\!\cdots\!66\)\( T^{25} + \)\(12\!\cdots\!54\)\( T^{26} - \)\(85\!\cdots\!28\)\( T^{27} + \)\(56\!\cdots\!12\)\( T^{28} - \)\(33\!\cdots\!20\)\( T^{29} + \)\(19\!\cdots\!37\)\( T^{30} - \)\(97\!\cdots\!23\)\( T^{31} + \)\(48\!\cdots\!10\)\( T^{32} - \)\(15\!\cdots\!46\)\( T^{33} + \)\(59\!\cdots\!37\)\( T^{34} \))(\( 1 + 8 T + 1066 T^{2} + 8140 T^{3} + 574822 T^{4} + 4231648 T^{5} + 208790556 T^{6} + 1486980364 T^{7} + 57301056433 T^{8} + 394664140872 T^{9} + 12625178523118 T^{10} + 83880214388348 T^{11} + 2315754575630556 T^{12} + 14783337728939600 T^{13} + 361857543145360578 T^{14} + 2208911135139695232 T^{15} + 48893254201549069627 T^{16} + \)\(28\!\cdots\!52\)\( T^{17} + \)\(57\!\cdots\!24\)\( T^{18} + \)\(31\!\cdots\!20\)\( T^{19} + \)\(59\!\cdots\!31\)\( T^{20} + \)\(30\!\cdots\!40\)\( T^{21} + \)\(54\!\cdots\!16\)\( T^{22} + \)\(25\!\cdots\!96\)\( T^{23} + \)\(43\!\cdots\!87\)\( T^{24} + \)\(18\!\cdots\!24\)\( T^{25} + \)\(30\!\cdots\!62\)\( T^{26} + \)\(11\!\cdots\!00\)\( T^{27} + \)\(18\!\cdots\!16\)\( T^{28} + \)\(63\!\cdots\!16\)\( T^{29} + \)\(93\!\cdots\!82\)\( T^{30} + \)\(28\!\cdots\!16\)\( T^{31} + \)\(39\!\cdots\!53\)\( T^{32} + \)\(10\!\cdots\!28\)\( T^{33} + \)\(13\!\cdots\!64\)\( T^{34} + \)\(26\!\cdots\!64\)\( T^{35} + \)\(35\!\cdots\!62\)\( T^{36} + \)\(48\!\cdots\!80\)\( T^{37} + \)\(61\!\cdots\!74\)\( T^{38} + \)\(44\!\cdots\!64\)\( T^{39} + \)\(54\!\cdots\!01\)\( T^{40} \))(\( 1 - 8 T + 1066 T^{2} - 8140 T^{3} + 574822 T^{4} - 4231648 T^{5} + 208790556 T^{6} - 1486980364 T^{7} + 57301056433 T^{8} - 394664140872 T^{9} + 12625178523118 T^{10} - 83880214388348 T^{11} + 2315754575630556 T^{12} - 14783337728939600 T^{13} + 361857543145360578 T^{14} - 2208911135139695232 T^{15} + 48893254201549069627 T^{16} - \)\(28\!\cdots\!52\)\( T^{17} + \)\(57\!\cdots\!24\)\( T^{18} - \)\(31\!\cdots\!20\)\( T^{19} + \)\(59\!\cdots\!31\)\( T^{20} - \)\(30\!\cdots\!40\)\( T^{21} + \)\(54\!\cdots\!16\)\( T^{22} - \)\(25\!\cdots\!96\)\( T^{23} + \)\(43\!\cdots\!87\)\( T^{24} - \)\(18\!\cdots\!24\)\( T^{25} + \)\(30\!\cdots\!62\)\( T^{26} - \)\(11\!\cdots\!00\)\( T^{27} + \)\(18\!\cdots\!16\)\( T^{28} - \)\(63\!\cdots\!16\)\( T^{29} + \)\(93\!\cdots\!82\)\( T^{30} - \)\(28\!\cdots\!16\)\( T^{31} + \)\(39\!\cdots\!53\)\( T^{32} - \)\(10\!\cdots\!28\)\( T^{33} + \)\(13\!\cdots\!64\)\( T^{34} - \)\(26\!\cdots\!64\)\( T^{35} + \)\(35\!\cdots\!62\)\( T^{36} - \)\(48\!\cdots\!80\)\( T^{37} + \)\(61\!\cdots\!74\)\( T^{38} - \)\(44\!\cdots\!64\)\( T^{39} + \)\(54\!\cdots\!01\)\( T^{40} \))
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