Properties

Label 4026.2.a
Level 4026
Weight 2
Character orbit a
Rep. character \(\chi_{4026}(1,\cdot)\)
Character field \(\Q\)
Dimension 101
Newform subspaces 29
Sturm bound 1488
Trace bound 11

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Defining parameters

Level: \( N \) \(=\) \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4026.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 29 \)
Sturm bound: \(1488\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4026))\).

Total New Old
Modular forms 752 101 651
Cusp forms 737 101 636
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.

\(2\)\(3\)\(11\)\(61\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(39\)
Minus space\(-\)\(62\)

Trace form

\( 101q + q^{2} + q^{3} + 101q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + 101q^{9} + O(q^{10}) \) \( 101q + q^{2} + q^{3} + 101q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + 101q^{9} + 6q^{10} + q^{11} + q^{12} + 14q^{13} + 8q^{14} + 6q^{15} + 101q^{16} + 2q^{17} + q^{18} + 4q^{19} + 6q^{20} + 8q^{21} + q^{22} - 24q^{23} + q^{24} + 99q^{25} + 14q^{26} + q^{27} + 8q^{28} - 50q^{29} + 6q^{30} + q^{32} - 3q^{33} + 10q^{34} - 16q^{35} + 101q^{36} + 6q^{37} + 4q^{38} + 14q^{39} + 6q^{40} - 6q^{41} + 12q^{43} + q^{44} + 6q^{45} + 8q^{46} + 32q^{47} + q^{48} + 117q^{49} + 31q^{50} + 18q^{51} + 14q^{52} + 6q^{53} + q^{54} + 6q^{55} + 8q^{56} + 20q^{57} + 22q^{58} + 12q^{59} + 6q^{60} + q^{61} + 16q^{62} + 8q^{63} + 101q^{64} + 52q^{65} + q^{66} + 44q^{67} + 2q^{68} - 16q^{69} + 16q^{70} + 24q^{71} + q^{72} - 6q^{73} + 38q^{74} + 31q^{75} + 4q^{76} + 8q^{77} - 26q^{78} + 16q^{79} + 6q^{80} + 101q^{81} + 2q^{82} - 12q^{83} + 8q^{84} - 4q^{85} - 4q^{86} - 2q^{87} + q^{88} - 38q^{89} + 6q^{90} - 24q^{92} + 24q^{93} - 16q^{94} - 56q^{95} + q^{96} + 58q^{97} + 25q^{98} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4026))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 11 61
4026.2.a.a \(1\) \(32.148\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
4026.2.a.b \(1\) \(32.148\) \(\Q\) None \(-1\) \(1\) \(3\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-4q^{7}+\cdots\)
4026.2.a.c \(1\) \(32.148\) \(\Q\) None \(-1\) \(1\) \(3\) \(-4\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-4q^{7}+\cdots\)
4026.2.a.d \(1\) \(32.148\) \(\Q\) None \(-1\) \(1\) \(4\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots\)
4026.2.a.e \(1\) \(32.148\) \(\Q\) None \(-1\) \(1\) \(4\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}+4q^{7}+\cdots\)
4026.2.a.f \(1\) \(32.148\) \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
4026.2.a.g \(1\) \(32.148\) \(\Q\) None \(1\) \(-1\) \(2\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
4026.2.a.h \(1\) \(32.148\) \(\Q\) None \(1\) \(-1\) \(3\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+2q^{7}+\cdots\)
4026.2.a.i \(1\) \(32.148\) \(\Q\) None \(1\) \(1\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)
4026.2.a.j \(1\) \(32.148\) \(\Q\) None \(1\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
4026.2.a.k \(2\) \(32.148\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-6\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-3+\beta )q^{5}-q^{6}+\cdots\)
4026.2.a.l \(2\) \(32.148\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(-2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
4026.2.a.m \(2\) \(32.148\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2\beta q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
4026.2.a.n \(3\) \(32.148\) \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(-3\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-1-\beta _{1})q^{5}-q^{6}+\cdots\)
4026.2.a.o \(3\) \(32.148\) 3.3.1129.1 None \(3\) \(-3\) \(-3\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
4026.2.a.p \(3\) \(32.148\) \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-5\) \(-6\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-2-\beta _{2})q^{5}+q^{6}+\cdots\)
4026.2.a.q \(4\) \(32.148\) 4.4.6809.1 None \(-4\) \(-4\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4026.2.a.r \(4\) \(32.148\) 4.4.7537.1 None \(-4\) \(4\) \(1\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
4026.2.a.s \(4\) \(32.148\) 4.4.26825.1 None \(4\) \(-4\) \(3\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{3})q^{5}-q^{6}+\cdots\)
4026.2.a.t \(4\) \(32.148\) 4.4.2777.1 None \(4\) \(4\) \(-4\) \(-6\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{2})q^{5}+q^{6}+\cdots\)
4026.2.a.u \(5\) \(32.148\) 5.5.9176805.1 None \(-5\) \(5\) \(-1\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
4026.2.a.v \(5\) \(32.148\) 5.5.11492689.1 None \(5\) \(-5\) \(7\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots\)
4026.2.a.w \(6\) \(32.148\) 6.6.30998405.1 None \(-6\) \(-6\) \(-1\) \(5\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
4026.2.a.x \(6\) \(32.148\) 6.6.46101901.1 None \(6\) \(-6\) \(-6\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots\)
4026.2.a.y \(7\) \(32.148\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-7\) \(-2\) \(1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+\beta _{6}q^{7}+\cdots\)
4026.2.a.z \(7\) \(32.148\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-7\) \(2\) \(-4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}+(\beta _{4}+\cdots)q^{7}+\cdots\)
4026.2.a.ba \(7\) \(32.148\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(7\) \(-5\) \(9\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
4026.2.a.bb \(8\) \(32.148\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(8\) \(5\) \(13\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta _{5})q^{5}+q^{6}+\cdots\)
4026.2.a.bc \(9\) \(32.148\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(9\) \(8\) \(9\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4026))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4026)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(122))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(366))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(671))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1342))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2013))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 + T )^{7} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{8} \))(\( ( 1 - T )^{9} \))
$3$ (\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{7} \))(\( ( 1 - T )^{8} \))(\( ( 1 - T )^{9} \))
$5$ (\( 1 - T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 6 T + 17 T^{2} + 30 T^{3} + 25 T^{4} \))(\( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 3 T + 15 T^{2} + 29 T^{3} + 75 T^{4} + 75 T^{5} + 125 T^{6} \))(\( 1 + 3 T + 11 T^{2} + 21 T^{3} + 55 T^{4} + 75 T^{5} + 125 T^{6} \))(\( 1 + 5 T + 21 T^{2} + 51 T^{3} + 105 T^{4} + 125 T^{5} + 125 T^{6} \))(\( 1 + 15 T^{2} - T^{3} + 101 T^{4} - 5 T^{5} + 375 T^{6} + 625 T^{8} \))(\( 1 - T + 14 T^{2} - 14 T^{3} + 96 T^{4} - 70 T^{5} + 350 T^{6} - 125 T^{7} + 625 T^{8} \))(\( 1 - 3 T + 8 T^{2} - 20 T^{3} + 68 T^{4} - 100 T^{5} + 200 T^{6} - 375 T^{7} + 625 T^{8} \))(\( 1 + 4 T + 21 T^{2} + 53 T^{3} + 159 T^{4} + 265 T^{5} + 525 T^{6} + 500 T^{7} + 625 T^{8} \))(\( 1 + T + 13 T^{2} + 13 T^{3} + 100 T^{4} + 100 T^{5} + 500 T^{6} + 325 T^{7} + 1625 T^{8} + 625 T^{9} + 3125 T^{10} \))(\( 1 - 7 T + 34 T^{2} - 122 T^{3} + 363 T^{4} - 877 T^{5} + 1815 T^{6} - 3050 T^{7} + 4250 T^{8} - 4375 T^{9} + 3125 T^{10} \))(\( 1 + T + 16 T^{2} + 22 T^{3} + 127 T^{4} + 213 T^{5} + 712 T^{6} + 1065 T^{7} + 3175 T^{8} + 2750 T^{9} + 10000 T^{10} + 3125 T^{11} + 15625 T^{12} \))(\( 1 + 6 T + 29 T^{2} + 117 T^{3} + 372 T^{4} + 1023 T^{5} + 2516 T^{6} + 5115 T^{7} + 9300 T^{8} + 14625 T^{9} + 18125 T^{10} + 18750 T^{11} + 15625 T^{12} \))(\( 1 + 2 T + 14 T^{2} + 21 T^{3} + 89 T^{4} + 70 T^{5} + 364 T^{6} + 142 T^{7} + 1820 T^{8} + 1750 T^{9} + 11125 T^{10} + 13125 T^{11} + 43750 T^{12} + 31250 T^{13} + 78125 T^{14} \))(\( 1 - 2 T + 17 T^{2} - 35 T^{3} + 179 T^{4} - 307 T^{5} + 1240 T^{6} - 1902 T^{7} + 6200 T^{8} - 7675 T^{9} + 22375 T^{10} - 21875 T^{11} + 53125 T^{12} - 31250 T^{13} + 78125 T^{14} \))(\( 1 + 5 T + 28 T^{2} + 94 T^{3} + 346 T^{4} + 932 T^{5} + 2603 T^{6} + 5690 T^{7} + 13015 T^{8} + 23300 T^{9} + 43250 T^{10} + 58750 T^{11} + 87500 T^{12} + 78125 T^{13} + 78125 T^{14} \))(\( 1 - 5 T + 21 T^{2} - 61 T^{3} + 192 T^{4} - 506 T^{5} + 1335 T^{6} - 2940 T^{7} + 6862 T^{8} - 14700 T^{9} + 33375 T^{10} - 63250 T^{11} + 120000 T^{12} - 190625 T^{13} + 328125 T^{14} - 390625 T^{15} + 390625 T^{16} \))(\( 1 - 8 T + 43 T^{2} - 173 T^{3} + 596 T^{4} - 1821 T^{5} + 5181 T^{6} - 13837 T^{7} + 34611 T^{8} - 80410 T^{9} + 173055 T^{10} - 345925 T^{11} + 647625 T^{12} - 1138125 T^{13} + 1862500 T^{14} - 2703125 T^{15} + 3359375 T^{16} - 3125000 T^{17} + 1953125 T^{18} \))
$7$ (\( 1 + 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( ( 1 - 2 T + 7 T^{2} )^{2} \))(\( 1 + 2 T - 2 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + T + 13 T^{2} + 7 T^{3} + 49 T^{4} \))(\( 1 + 18 T^{2} - T^{3} + 126 T^{4} + 343 T^{6} \))(\( 1 + 2 T + 8 T^{2} + 11 T^{3} + 56 T^{4} + 98 T^{5} + 343 T^{6} \))(\( 1 + 6 T + 26 T^{2} + 85 T^{3} + 182 T^{4} + 294 T^{5} + 343 T^{6} \))(\( 1 + 2 T + 17 T^{2} + 41 T^{3} + 150 T^{4} + 287 T^{5} + 833 T^{6} + 686 T^{7} + 2401 T^{8} \))(\( 1 + 4 T + 27 T^{2} + 69 T^{3} + 272 T^{4} + 483 T^{5} + 1323 T^{6} + 1372 T^{7} + 2401 T^{8} \))(\( 1 + 2 T + 17 T^{2} + 25 T^{3} + 136 T^{4} + 175 T^{5} + 833 T^{6} + 686 T^{7} + 2401 T^{8} \))(\( 1 + 6 T + 35 T^{2} + 121 T^{3} + 384 T^{4} + 847 T^{5} + 1715 T^{6} + 2058 T^{7} + 2401 T^{8} \))(\( 1 + 3 T + 9 T^{2} + 6 T^{4} - 109 T^{5} + 42 T^{6} + 3087 T^{8} + 7203 T^{9} + 16807 T^{10} \))(\( 1 + 14 T^{2} + 3 T^{3} + 99 T^{4} + 10 T^{5} + 693 T^{6} + 147 T^{7} + 4802 T^{8} + 16807 T^{10} \))(\( 1 - 5 T + 32 T^{2} - 93 T^{3} + 407 T^{4} - 1009 T^{5} + 3604 T^{6} - 7063 T^{7} + 19943 T^{8} - 31899 T^{9} + 76832 T^{10} - 84035 T^{11} + 117649 T^{12} \))(\( 1 - T + 24 T^{2} - 35 T^{3} + 307 T^{4} - 415 T^{5} + 2648 T^{6} - 2905 T^{7} + 15043 T^{8} - 12005 T^{9} + 57624 T^{10} - 16807 T^{11} + 117649 T^{12} \))(\( 1 - T + 25 T^{2} - 32 T^{3} + 329 T^{4} - 430 T^{5} + 2985 T^{6} - 3682 T^{7} + 20895 T^{8} - 21070 T^{9} + 112847 T^{10} - 76832 T^{11} + 420175 T^{12} - 117649 T^{13} + 823543 T^{14} \))(\( 1 + 4 T + 28 T^{2} + 63 T^{3} + 258 T^{4} + 284 T^{5} + 1327 T^{6} + 674 T^{7} + 9289 T^{8} + 13916 T^{9} + 88494 T^{10} + 151263 T^{11} + 470596 T^{12} + 470596 T^{13} + 823543 T^{14} \))(\( 1 - 9 T + 53 T^{2} - 218 T^{3} + 787 T^{4} - 2436 T^{5} + 7147 T^{6} - 19062 T^{7} + 50029 T^{8} - 119364 T^{9} + 269941 T^{10} - 523418 T^{11} + 890771 T^{12} - 1058841 T^{13} + 823543 T^{14} \))(\( 1 - 13 T + 104 T^{2} - 611 T^{3} + 2950 T^{4} - 12084 T^{5} + 43244 T^{6} - 136182 T^{7} + 381994 T^{8} - 953274 T^{9} + 2118956 T^{10} - 4144812 T^{11} + 7082950 T^{12} - 10269077 T^{13} + 12235496 T^{14} - 10706059 T^{15} + 5764801 T^{16} \))(\( 1 - 9 T + 57 T^{2} - 254 T^{3} + 1016 T^{4} - 3511 T^{5} + 11672 T^{6} - 34914 T^{7} + 101360 T^{8} - 270112 T^{9} + 709520 T^{10} - 1710786 T^{11} + 4003496 T^{12} - 8429911 T^{13} + 17075912 T^{14} - 29882846 T^{15} + 46941951 T^{16} - 51883209 T^{17} + 40353607 T^{18} \))
$11$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{7} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{8} \))(\( ( 1 - T )^{9} \))
$13$ (\( 1 + T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 3 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 3 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( ( 1 - 3 T + 13 T^{2} )^{2} \))(\( 1 - 5 T + 28 T^{2} - 65 T^{3} + 169 T^{4} \))(\( 1 - 3 T + 17 T^{2} - 39 T^{3} + 169 T^{4} \))(\( 1 + 3 T + 39 T^{2} + 75 T^{3} + 507 T^{4} + 507 T^{5} + 2197 T^{6} \))(\( 1 + 7 T + 29 T^{2} + 85 T^{3} + 377 T^{4} + 1183 T^{5} + 2197 T^{6} \))(\( 1 + 9 T + 59 T^{2} + 247 T^{3} + 767 T^{4} + 1521 T^{5} + 2197 T^{6} \))(\( 1 + 4 T + 31 T^{2} + 165 T^{3} + 485 T^{4} + 2145 T^{5} + 5239 T^{6} + 8788 T^{7} + 28561 T^{8} \))(\( 1 + 3 T + 20 T^{2} - 38 T^{3} + 4 T^{4} - 494 T^{5} + 3380 T^{6} + 6591 T^{7} + 28561 T^{8} \))(\( 1 - 13 T + 86 T^{2} - 374 T^{3} + 1384 T^{4} - 4862 T^{5} + 14534 T^{6} - 28561 T^{7} + 28561 T^{8} \))(\( 1 + 5 T + 40 T^{2} + 156 T^{3} + 680 T^{4} + 2028 T^{5} + 6760 T^{6} + 10985 T^{7} + 28561 T^{8} \))(\( 1 - 2 T + 31 T^{2} - 48 T^{3} + 557 T^{4} - 911 T^{5} + 7241 T^{6} - 8112 T^{7} + 68107 T^{8} - 57122 T^{9} + 371293 T^{10} \))(\( 1 + 2 T + 34 T^{2} + 81 T^{3} + 724 T^{4} + 1272 T^{5} + 9412 T^{6} + 13689 T^{7} + 74698 T^{8} + 57122 T^{9} + 371293 T^{10} \))(\( 1 - 2 T + 34 T^{2} - 26 T^{3} + 462 T^{4} + 219 T^{5} + 4820 T^{6} + 2847 T^{7} + 78078 T^{8} - 57122 T^{9} + 971074 T^{10} - 742586 T^{11} + 4826809 T^{12} \))(\( 1 - 2 T + 60 T^{2} - 108 T^{3} + 1668 T^{4} - 2487 T^{5} + 27484 T^{6} - 32331 T^{7} + 281892 T^{8} - 237276 T^{9} + 1713660 T^{10} - 742586 T^{11} + 4826809 T^{12} \))(\( 1 + 45 T^{2} + 28 T^{3} + 1098 T^{4} + 925 T^{5} + 19436 T^{6} + 14614 T^{7} + 252668 T^{8} + 156325 T^{9} + 2412306 T^{10} + 799708 T^{11} + 16708185 T^{12} + 62748517 T^{14} \))(\( 1 + 7 T + 64 T^{2} + 304 T^{3} + 1602 T^{4} + 5726 T^{5} + 23725 T^{6} + 76838 T^{7} + 308425 T^{8} + 967694 T^{9} + 3519594 T^{10} + 8682544 T^{11} + 23762752 T^{12} + 33787663 T^{13} + 62748517 T^{14} \))(\( 1 - 4 T + 28 T^{2} - 14 T^{3} + 319 T^{4} - 81 T^{5} + 6379 T^{6} - 3965 T^{7} + 82927 T^{8} - 13689 T^{9} + 700843 T^{10} - 399854 T^{11} + 10396204 T^{12} - 19307236 T^{13} + 62748517 T^{14} \))(\( 1 - 10 T + 107 T^{2} - 712 T^{3} + 4503 T^{4} - 22801 T^{5} + 107360 T^{6} - 441362 T^{7} + 1682040 T^{8} - 5737706 T^{9} + 18143840 T^{10} - 50093797 T^{11} + 128610183 T^{12} - 264360616 T^{13} + 516468563 T^{14} - 627485170 T^{15} + 815730721 T^{16} \))(\( 1 - 8 T + 78 T^{2} - 432 T^{3} + 2434 T^{4} - 10355 T^{5} + 44785 T^{6} - 159867 T^{7} + 628598 T^{8} - 2099508 T^{9} + 8171774 T^{10} - 27017523 T^{11} + 98392645 T^{12} - 295749155 T^{13} + 903727162 T^{14} - 2085181488 T^{15} + 4894384326 T^{16} - 6525845768 T^{17} + 10604499373 T^{18} \))
$17$ (\( 1 + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 26 T^{2} + 289 T^{4} \))(\( 1 - 2 T + 18 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 + 13 T + 75 T^{2} + 221 T^{3} + 289 T^{4} \))(\( 1 - 3 T + 42 T^{2} - 99 T^{3} + 714 T^{4} - 867 T^{5} + 4913 T^{6} \))(\( ( 1 - T + 17 T^{2} )^{3} \))(\( 1 - T + 42 T^{2} - 33 T^{3} + 714 T^{4} - 289 T^{5} + 4913 T^{6} \))(\( 1 + T + 43 T^{2} + 26 T^{3} + 892 T^{4} + 442 T^{5} + 12427 T^{6} + 4913 T^{7} + 83521 T^{8} \))(\( 1 + 3 T + 37 T^{2} + 122 T^{3} + 674 T^{4} + 2074 T^{5} + 10693 T^{6} + 14739 T^{7} + 83521 T^{8} \))(\( 1 - 3 T + 33 T^{2} - 178 T^{3} + 614 T^{4} - 3026 T^{5} + 9537 T^{6} - 14739 T^{7} + 83521 T^{8} \))(\( 1 + 10 T + 72 T^{2} + 332 T^{3} + 1521 T^{4} + 5644 T^{5} + 20808 T^{6} + 49130 T^{7} + 83521 T^{8} \))(\( 1 - 6 T + 54 T^{2} - 207 T^{3} + 995 T^{4} - 3429 T^{5} + 16915 T^{6} - 59823 T^{7} + 265302 T^{8} - 501126 T^{9} + 1419857 T^{10} \))(\( 1 - 2 T + 53 T^{2} - 110 T^{3} + 1457 T^{4} - 2648 T^{5} + 24769 T^{6} - 31790 T^{7} + 260389 T^{8} - 167042 T^{9} + 1419857 T^{10} \))(\( 1 + 4 T + 91 T^{2} + 279 T^{3} + 3523 T^{4} + 8442 T^{5} + 77012 T^{6} + 143514 T^{7} + 1018147 T^{8} + 1370727 T^{9} + 7600411 T^{10} + 5679428 T^{11} + 24137569 T^{12} \))(\( 1 + 13 T + 101 T^{2} + 479 T^{3} + 1466 T^{4} + 1913 T^{5} + 885 T^{6} + 32521 T^{7} + 423674 T^{8} + 2353327 T^{9} + 8435621 T^{10} + 18458141 T^{11} + 24137569 T^{12} \))(\( 1 - 3 T + 52 T^{2} - 106 T^{3} + 1445 T^{4} - 2240 T^{5} + 30621 T^{6} - 44620 T^{7} + 520557 T^{8} - 647360 T^{9} + 7099285 T^{10} - 8853226 T^{11} + 73832564 T^{12} - 72412707 T^{13} + 410338673 T^{14} \))(\( 1 + 4 T + 27 T^{2} + 62 T^{3} + 940 T^{4} + 3746 T^{5} + 18340 T^{6} + 38608 T^{7} + 311780 T^{8} + 1082594 T^{9} + 4618220 T^{10} + 5178302 T^{11} + 38336139 T^{12} + 96550276 T^{13} + 410338673 T^{14} \))(\( 1 + 6 T + 56 T^{2} + 245 T^{3} + 972 T^{4} + 1603 T^{5} + 2739 T^{6} - 28128 T^{7} + 46563 T^{8} + 463267 T^{9} + 4775436 T^{10} + 20462645 T^{11} + 79511992 T^{12} + 144825414 T^{13} + 410338673 T^{14} \))(\( 1 - 4 T + 73 T^{2} - 275 T^{3} + 3198 T^{4} - 10516 T^{5} + 89009 T^{6} - 258321 T^{7} + 1803046 T^{8} - 4391457 T^{9} + 25723601 T^{10} - 51665108 T^{11} + 267100158 T^{12} - 390460675 T^{13} + 1762042537 T^{14} - 1641354692 T^{15} + 6975757441 T^{16} \))(\( 1 - T + 90 T^{2} + 36 T^{3} + 3566 T^{4} + 7439 T^{5} + 84611 T^{6} + 338722 T^{7} + 1507336 T^{8} + 7734304 T^{9} + 25624712 T^{10} + 97890658 T^{11} + 415693843 T^{12} + 621312719 T^{13} + 5063210062 T^{14} + 868952484 T^{15} + 36930480570 T^{16} - 6975757441 T^{17} + 118587876497 T^{18} \))
$19$ (\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 8 T + 46 T^{2} - 152 T^{3} + 361 T^{4} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( 1 + 7 T + 49 T^{2} + 133 T^{3} + 361 T^{4} \))(\( 1 + 6 T + 48 T^{2} + 177 T^{3} + 912 T^{4} + 2166 T^{5} + 6859 T^{6} \))(\( 1 - 2 T + 32 T^{2} - 107 T^{3} + 608 T^{4} - 722 T^{5} + 6859 T^{6} \))(\( 1 + 8 T^{2} + 91 T^{3} + 152 T^{4} + 6859 T^{6} \))(\( 1 - 4 T + 35 T^{2} - 151 T^{3} + 600 T^{4} - 2869 T^{5} + 12635 T^{6} - 27436 T^{7} + 130321 T^{8} \))(\( 1 + 4 T + 69 T^{2} + 213 T^{3} + 1898 T^{4} + 4047 T^{5} + 24909 T^{6} + 27436 T^{7} + 130321 T^{8} \))(\( 1 - 2 T + 71 T^{2} - 107 T^{3} + 1980 T^{4} - 2033 T^{5} + 25631 T^{6} - 13718 T^{7} + 130321 T^{8} \))(\( 1 + 8 T + 77 T^{2} + 373 T^{3} + 2080 T^{4} + 7087 T^{5} + 27797 T^{6} + 54872 T^{7} + 130321 T^{8} \))(\( 1 - 7 T + 31 T^{2} - 114 T^{3} + 536 T^{4} - 3085 T^{5} + 10184 T^{6} - 41154 T^{7} + 212629 T^{8} - 912247 T^{9} + 2476099 T^{10} \))(\( 1 - 18 T + 200 T^{2} - 1571 T^{3} + 9599 T^{4} - 46478 T^{5} + 182381 T^{6} - 567131 T^{7} + 1371800 T^{8} - 2345778 T^{9} + 2476099 T^{10} \))(\( 1 + 5 T + 60 T^{2} + 225 T^{3} + 1851 T^{4} + 5521 T^{5} + 37764 T^{6} + 104899 T^{7} + 668211 T^{8} + 1543275 T^{9} + 7819260 T^{10} + 12380495 T^{11} + 47045881 T^{12} \))(\( 1 - T + 20 T^{2} - 113 T^{3} + 113 T^{4} + 189 T^{5} + 7116 T^{6} + 3591 T^{7} + 40793 T^{8} - 775067 T^{9} + 2606420 T^{10} - 2476099 T^{11} + 47045881 T^{12} \))(\( 1 + 5 T + 91 T^{2} + 450 T^{3} + 4229 T^{4} + 18354 T^{5} + 122757 T^{6} + 440582 T^{7} + 2332383 T^{8} + 6625794 T^{9} + 29006711 T^{10} + 58644450 T^{11} + 225325009 T^{12} + 235229405 T^{13} + 893871739 T^{14} \))(\( 1 + 4 T + 46 T^{2} + 167 T^{3} + 1308 T^{4} + 4592 T^{5} + 30835 T^{6} + 110842 T^{7} + 585865 T^{8} + 1657712 T^{9} + 8971572 T^{10} + 21763607 T^{11} + 113900554 T^{12} + 188183524 T^{13} + 893871739 T^{14} \))(\( 1 - 9 T + 111 T^{2} - 742 T^{3} + 5599 T^{4} - 30012 T^{5} + 166841 T^{6} - 718890 T^{7} + 3169979 T^{8} - 10834332 T^{9} + 38403541 T^{10} - 96698182 T^{11} + 274846989 T^{12} - 423412929 T^{13} + 893871739 T^{14} \))(\( 1 - 11 T + 118 T^{2} - 795 T^{3} + 5394 T^{4} - 28896 T^{5} + 156370 T^{6} - 714344 T^{7} + 3336682 T^{8} - 13572536 T^{9} + 56449570 T^{10} - 198197664 T^{11} + 702951474 T^{12} - 1968498705 T^{13} + 5551413958 T^{14} - 9832589129 T^{15} + 16983563041 T^{16} \))(\( 1 - 5 T + 71 T^{2} - 346 T^{3} + 2884 T^{4} - 14991 T^{5} + 90776 T^{6} - 444626 T^{7} + 2160454 T^{8} - 9570800 T^{9} + 41048626 T^{10} - 160509986 T^{11} + 622632584 T^{12} - 1953642111 T^{13} + 7141069516 T^{14} - 16277874826 T^{15} + 63464893469 T^{16} - 84917815205 T^{17} + 322687697779 T^{18} \))
$23$ (\( 1 + 4 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 38 T^{2} + 529 T^{4} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 2 T + 23 T^{2} )^{2} \))(\( 1 + 6 T + 78 T^{2} + 277 T^{3} + 1794 T^{4} + 3174 T^{5} + 12167 T^{6} \))(\( 1 + 4 T + 48 T^{2} + 103 T^{3} + 1104 T^{4} + 2116 T^{5} + 12167 T^{6} \))(\( 1 + 4 T + 44 T^{2} + 113 T^{3} + 1012 T^{4} + 2116 T^{5} + 12167 T^{6} \))(\( 1 - 16 T + 161 T^{2} - 1085 T^{3} + 5920 T^{4} - 24955 T^{5} + 85169 T^{6} - 194672 T^{7} + 279841 T^{8} \))(\( 1 - 10 T + 89 T^{2} - 413 T^{3} + 2352 T^{4} - 9499 T^{5} + 47081 T^{6} - 121670 T^{7} + 279841 T^{8} \))(\( 1 - 2 T + 87 T^{2} - 131 T^{3} + 2948 T^{4} - 3013 T^{5} + 46023 T^{6} - 24334 T^{7} + 279841 T^{8} \))(\( 1 + 7 T + 71 T^{2} + 397 T^{3} + 2311 T^{4} + 9131 T^{5} + 37559 T^{6} + 85169 T^{7} + 279841 T^{8} \))(\( 1 + 12 T + 128 T^{2} + 909 T^{3} + 5835 T^{4} + 29074 T^{5} + 134205 T^{6} + 480861 T^{7} + 1557376 T^{8} + 3358092 T^{9} + 6436343 T^{10} \))(\( 1 + T - 4 T^{2} + 200 T^{3} + 740 T^{4} - 1946 T^{5} + 17020 T^{6} + 105800 T^{7} - 48668 T^{8} + 279841 T^{9} + 6436343 T^{10} \))(\( 1 + 6 T + 79 T^{2} + 341 T^{3} + 3195 T^{4} + 11719 T^{5} + 88522 T^{6} + 269537 T^{7} + 1690155 T^{8} + 4148947 T^{9} + 22107439 T^{10} + 38618058 T^{11} + 148035889 T^{12} \))(\( 1 + 11 T + 113 T^{2} + 593 T^{3} + 3232 T^{4} + 9762 T^{5} + 53552 T^{6} + 224526 T^{7} + 1709728 T^{8} + 7215031 T^{9} + 31622033 T^{10} + 70799773 T^{11} + 148035889 T^{12} \))(\( 1 + 3 T + 84 T^{2} + 446 T^{3} + 3649 T^{4} + 23153 T^{5} + 117678 T^{6} + 665436 T^{7} + 2706594 T^{8} + 12247937 T^{9} + 44397383 T^{10} + 124809086 T^{11} + 540652812 T^{12} + 444107667 T^{13} + 3404825447 T^{14} \))(\( 1 + T + 54 T^{2} + 2 T^{3} + 1067 T^{4} - 5429 T^{5} + 5978 T^{6} - 217660 T^{7} + 137494 T^{8} - 2871941 T^{9} + 12982189 T^{10} + 559682 T^{11} + 347562522 T^{12} + 148035889 T^{13} + 3404825447 T^{14} \))(\( 1 + 8 T + 98 T^{2} + 441 T^{3} + 3648 T^{4} + 11744 T^{5} + 92871 T^{6} + 256318 T^{7} + 2136033 T^{8} + 6212576 T^{9} + 44385216 T^{10} + 123409881 T^{11} + 630761614 T^{12} + 1184287112 T^{13} + 3404825447 T^{14} \))(\( 1 - 2 T + 135 T^{2} - 249 T^{3} + 8858 T^{4} - 14627 T^{5} + 361913 T^{6} - 518212 T^{7} + 10011114 T^{8} - 11918876 T^{9} + 191451977 T^{10} - 177966709 T^{11} + 2478831578 T^{12} - 1602649407 T^{13} + 19984845015 T^{14} - 6809650894 T^{15} + 78310985281 T^{16} \))(\( 1 + T + 76 T^{2} + 222 T^{3} + 3176 T^{4} + 13616 T^{5} + 111494 T^{6} + 456274 T^{7} + 3308121 T^{8} + 11436478 T^{9} + 76086783 T^{10} + 241368946 T^{11} + 1356547498 T^{12} + 3810315056 T^{13} + 20441825368 T^{14} + 32863967358 T^{15} + 258766733972 T^{16} + 78310985281 T^{17} + 1801152661463 T^{18} \))
$29$ (\( 1 - 5 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 7 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 35 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 5 T + 60 T^{2} - 145 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 22 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 60 T^{2} - 297 T^{3} + 1740 T^{4} - 5046 T^{5} + 24389 T^{6} \))(\( 1 + 8 T + 76 T^{2} + 437 T^{3} + 2204 T^{4} + 6728 T^{5} + 24389 T^{6} \))(\( 1 + 12 T + 114 T^{2} + 669 T^{3} + 3306 T^{4} + 10092 T^{5} + 24389 T^{6} \))(\( 1 + 5 T + 83 T^{2} + 319 T^{3} + 3271 T^{4} + 9251 T^{5} + 69803 T^{6} + 121945 T^{7} + 707281 T^{8} \))(\( 1 + 10 T + 127 T^{2} + 793 T^{3} + 5546 T^{4} + 22997 T^{5} + 106807 T^{6} + 243890 T^{7} + 707281 T^{8} \))(\( 1 - 2 T + 99 T^{2} - 189 T^{3} + 4058 T^{4} - 5481 T^{5} + 83259 T^{6} - 48778 T^{7} + 707281 T^{8} \))(\( 1 + 4 T + 101 T^{2} + 309 T^{3} + 4178 T^{4} + 8961 T^{5} + 84941 T^{6} + 97556 T^{7} + 707281 T^{8} \))(\( 1 - 4 T + 96 T^{2} - 109 T^{3} + 3365 T^{4} + 970 T^{5} + 97585 T^{6} - 91669 T^{7} + 2341344 T^{8} - 2829124 T^{9} + 20511149 T^{10} \))(\( 1 - 7 T + 130 T^{2} - 728 T^{3} + 7066 T^{4} - 30476 T^{5} + 204914 T^{6} - 612248 T^{7} + 3170570 T^{8} - 4950967 T^{9} + 20511149 T^{10} \))(\( 1 + 10 T + 153 T^{2} + 1149 T^{3} + 9903 T^{4} + 58129 T^{5} + 365798 T^{6} + 1685741 T^{7} + 8328423 T^{8} + 28022961 T^{9} + 108213993 T^{10} + 205111490 T^{11} + 594823321 T^{12} \))(\( 1 + 14 T + 169 T^{2} + 1529 T^{3} + 11755 T^{4} + 77809 T^{5} + 446222 T^{6} + 2256461 T^{7} + 9885955 T^{8} + 37290781 T^{9} + 119530489 T^{10} + 287156086 T^{11} + 594823321 T^{12} \))(\( 1 + 14 T + 216 T^{2} + 2099 T^{3} + 18644 T^{4} + 138406 T^{5} + 888303 T^{6} + 5181922 T^{7} + 25760787 T^{8} + 116399446 T^{9} + 454708516 T^{10} + 1484582819 T^{11} + 4430408184 T^{12} + 8327526494 T^{13} + 17249876309 T^{14} \))(\( 1 - 6 T + 147 T^{2} - 583 T^{3} + 9622 T^{4} - 30403 T^{5} + 413142 T^{6} - 1095792 T^{7} + 11981118 T^{8} - 25568923 T^{9} + 234670958 T^{10} - 412344823 T^{11} + 3015138903 T^{12} - 3568939926 T^{13} + 17249876309 T^{14} \))(\( 1 + 4 T + 105 T^{2} + 485 T^{3} + 6144 T^{4} + 26521 T^{5} + 250044 T^{6} + 917740 T^{7} + 7251276 T^{8} + 22304161 T^{9} + 149846016 T^{10} + 343031285 T^{11} + 2153670645 T^{12} + 2379293284 T^{13} + 17249876309 T^{14} \))(\( 1 - 10 T + 154 T^{2} - 1061 T^{3} + 10523 T^{4} - 62366 T^{5} + 493342 T^{6} - 2543295 T^{7} + 16694912 T^{8} - 73755555 T^{9} + 414900622 T^{10} - 1521044374 T^{11} + 7442717963 T^{12} - 21762329089 T^{13} + 91602791434 T^{14} - 172498763090 T^{15} + 500246412961 T^{16} \))(\( 1 + 14 T + 245 T^{2} + 2481 T^{3} + 26187 T^{4} + 207825 T^{5} + 1655733 T^{6} + 10754403 T^{7} + 69370466 T^{8} + 375441946 T^{9} + 2011743514 T^{10} + 9044452923 T^{11} + 40381672137 T^{12} + 146990673825 T^{13} + 537125458863 T^{14} + 1475756659401 T^{15} + 4226219695705 T^{16} + 7003449781454 T^{17} + 14507145975869 T^{18} \))
$31$ (\( 1 - 7 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 - 9 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 10 T + 85 T^{2} - 310 T^{3} + 961 T^{4} \))(\( 1 - 3 T + 26 T^{2} - 93 T^{3} + 961 T^{4} \))(\( 1 + 2 T + 18 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 + 15 T + 129 T^{2} + 771 T^{3} + 3999 T^{4} + 14415 T^{5} + 29791 T^{6} \))(\( 1 + 17 T + 175 T^{2} + 1147 T^{3} + 5425 T^{4} + 16337 T^{5} + 29791 T^{6} \))(\( 1 + 3 T + 47 T^{2} + 89 T^{3} + 1457 T^{4} + 2883 T^{5} + 29791 T^{6} \))(\( 1 + 10 T + 97 T^{2} + 423 T^{3} + 2897 T^{4} + 13113 T^{5} + 93217 T^{6} + 297910 T^{7} + 923521 T^{8} \))(\( 1 + 9 T + 88 T^{2} + 326 T^{3} + 2380 T^{4} + 10106 T^{5} + 84568 T^{6} + 268119 T^{7} + 923521 T^{8} \))(\( 1 + T + 66 T^{2} - 52 T^{3} + 2298 T^{4} - 1612 T^{5} + 63426 T^{6} + 29791 T^{7} + 923521 T^{8} \))(\( 1 + 9 T + 74 T^{2} + 220 T^{3} + 1320 T^{4} + 6820 T^{5} + 71114 T^{6} + 268119 T^{7} + 923521 T^{8} \))(\( 1 + T + 133 T^{2} + 111 T^{3} + 7658 T^{4} + 5020 T^{5} + 237398 T^{6} + 106671 T^{7} + 3962203 T^{8} + 923521 T^{9} + 28629151 T^{10} \))(\( 1 + 100 T^{2} - 67 T^{3} + 5228 T^{4} - 2620 T^{5} + 162068 T^{6} - 64387 T^{7} + 2979100 T^{8} + 28629151 T^{10} \))(\( 1 + 15 T + 180 T^{2} + 1096 T^{3} + 5509 T^{4} + 9033 T^{5} + 36380 T^{6} + 280023 T^{7} + 5294149 T^{8} + 32650936 T^{9} + 166233780 T^{10} + 429437265 T^{11} + 887503681 T^{12} \))(\( 1 + 5 T + 94 T^{2} + 368 T^{3} + 4111 T^{4} + 12623 T^{5} + 133948 T^{6} + 391313 T^{7} + 3950671 T^{8} + 10963088 T^{9} + 86810974 T^{10} + 143145755 T^{11} + 887503681 T^{12} \))(\( 1 - 5 T + 161 T^{2} - 767 T^{3} + 12507 T^{4} - 52647 T^{5} + 591659 T^{6} - 2093338 T^{7} + 18341429 T^{8} - 50593767 T^{9} + 372596037 T^{10} - 708340607 T^{11} + 4609293311 T^{12} - 4437518405 T^{13} + 27512614111 T^{14} \))(\( 1 - 7 T + 140 T^{2} - 998 T^{3} + 10018 T^{4} - 66484 T^{5} + 455561 T^{6} - 2619926 T^{7} + 14122391 T^{8} - 63891124 T^{9} + 298446238 T^{10} - 921673958 T^{11} + 4008081140 T^{12} - 6212525767 T^{13} + 27512614111 T^{14} \))(\( 1 - 17 T + 230 T^{2} - 2084 T^{3} + 16120 T^{4} - 101370 T^{5} + 601321 T^{6} - 3294182 T^{7} + 18640951 T^{8} - 97416570 T^{9} + 480230920 T^{10} - 1924617764 T^{11} + 6584704730 T^{12} - 15087562577 T^{13} + 27512614111 T^{14} \))(\( 1 - 9 T + 197 T^{2} - 1601 T^{3} + 18414 T^{4} - 130354 T^{5} + 1050057 T^{6} - 6298538 T^{7} + 39612950 T^{8} - 195254678 T^{9} + 1009104777 T^{10} - 3883376014 T^{11} + 17005715694 T^{12} - 45835270751 T^{13} + 174838225157 T^{14} - 247613526999 T^{15} + 852891037441 T^{16} \))(\( 1 - 25 T + 462 T^{2} - 6008 T^{3} + 65765 T^{4} - 597525 T^{5} + 4812095 T^{6} - 34069348 T^{7} + 219678951 T^{8} - 1275714300 T^{9} + 6810047481 T^{10} - 32740643428 T^{11} + 143357122145 T^{12} - 551826885525 T^{13} + 1882796115515 T^{14} - 5332122115448 T^{15} + 12710827719282 T^{16} - 21322275936025 T^{17} + 26439622160671 T^{18} \))
$37$ (\( 1 + 6 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 + 37 T^{2} \))(\( 1 + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 2 T^{2} + 1369 T^{4} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( 1 - 13 T + 105 T^{2} - 481 T^{3} + 1369 T^{4} \))(\( 1 + 6 T + 66 T^{2} + 501 T^{3} + 2442 T^{4} + 8214 T^{5} + 50653 T^{6} \))(\( 1 + 14 T + 160 T^{2} + 1045 T^{3} + 5920 T^{4} + 19166 T^{5} + 50653 T^{6} \))(\( 1 + 6 T + 116 T^{2} + 445 T^{3} + 4292 T^{4} + 8214 T^{5} + 50653 T^{6} \))(\( 1 + 10 T + 91 T^{2} + 727 T^{3} + 5542 T^{4} + 26899 T^{5} + 124579 T^{6} + 506530 T^{7} + 1874161 T^{8} \))(\( 1 + 6 T + 69 T^{2} + 397 T^{3} + 3722 T^{4} + 14689 T^{5} + 94461 T^{6} + 303918 T^{7} + 1874161 T^{8} \))(\( 1 + 6 T + 49 T^{2} - 173 T^{3} - 706 T^{4} - 6401 T^{5} + 67081 T^{6} + 303918 T^{7} + 1874161 T^{8} \))(\( 1 + 11 T + 119 T^{2} + 827 T^{3} + 5511 T^{4} + 30599 T^{5} + 162911 T^{6} + 557183 T^{7} + 1874161 T^{8} \))(\( 1 - 3 T + 103 T^{2} - 174 T^{3} + 5588 T^{4} - 8037 T^{5} + 206756 T^{6} - 238206 T^{7} + 5217259 T^{8} - 5622483 T^{9} + 69343957 T^{10} \))(\( 1 - 11 T + 124 T^{2} - 916 T^{3} + 7078 T^{4} - 39344 T^{5} + 261886 T^{6} - 1254004 T^{7} + 6280972 T^{8} - 20615771 T^{9} + 69343957 T^{10} \))(\( 1 + 3 T + 76 T^{2} + 119 T^{3} + 4159 T^{4} + 5613 T^{5} + 166518 T^{6} + 207681 T^{7} + 5693671 T^{8} + 6027707 T^{9} + 142436236 T^{10} + 208031871 T^{11} + 2565726409 T^{12} \))(\( 1 + 6 T + 157 T^{2} + 492 T^{3} + 9721 T^{4} + 15403 T^{5} + 396453 T^{6} + 569911 T^{7} + 13308049 T^{8} + 24921276 T^{9} + 294243277 T^{10} + 416063742 T^{11} + 2565726409 T^{12} \))(\( 1 - 14 T + 198 T^{2} - 2012 T^{3} + 17566 T^{4} - 132995 T^{5} + 939334 T^{6} - 5754020 T^{7} + 34755358 T^{8} - 182070155 T^{9} + 889770598 T^{10} - 3770811932 T^{11} + 13730103486 T^{12} - 35920169726 T^{13} + 94931877133 T^{14} \))(\( 1 + 15 T + 276 T^{2} + 2934 T^{3} + 31287 T^{4} + 251475 T^{5} + 1939820 T^{6} + 12092656 T^{7} + 71773340 T^{8} + 344269275 T^{9} + 1584780411 T^{10} + 5498788374 T^{11} + 19138932132 T^{12} + 38485896135 T^{13} + 94931877133 T^{14} \))(\( 1 - 19 T + 357 T^{2} - 4142 T^{3} + 45451 T^{4} - 377480 T^{5} + 2956223 T^{6} - 18517834 T^{7} + 109380251 T^{8} - 516770120 T^{9} + 2302229503 T^{10} - 7762774862 T^{11} + 24755792649 T^{12} - 48748801771 T^{13} + 94931877133 T^{14} \))(\( 1 - 9 T + 98 T^{2} - 635 T^{3} + 5646 T^{4} - 26596 T^{5} + 181832 T^{6} - 675000 T^{7} + 6018774 T^{8} - 24975000 T^{9} + 248928008 T^{10} - 1347167188 T^{11} + 10581513006 T^{12} - 44033412695 T^{13} + 251441188082 T^{14} - 854386894197 T^{15} + 3512479453921 T^{16} \))(\( 1 - 16 T + 276 T^{2} - 2638 T^{3} + 23833 T^{4} - 133961 T^{5} + 638446 T^{6} - 297518 T^{7} - 11273464 T^{8} + 137497450 T^{9} - 417118168 T^{10} - 407302142 T^{11} + 32339205238 T^{12} - 251064481721 T^{13} + 1652674527181 T^{14} - 6768386266942 T^{15} + 26201198088708 T^{16} - 56199671262736 T^{17} + 129961739795077 T^{18} \))
$41$ (\( 1 + T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 + 2 T - 15 T^{2} + 82 T^{3} + 1681 T^{4} \))(\( 1 - 19 T + 168 T^{2} - 779 T^{3} + 1681 T^{4} \))(\( 1 + 8 T + 78 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 + 15 T + 186 T^{2} + 1287 T^{3} + 7626 T^{4} + 25215 T^{5} + 68921 T^{6} \))(\( 1 + 5 T + 66 T^{2} + 437 T^{3} + 2706 T^{4} + 8405 T^{5} + 68921 T^{6} \))(\( 1 + T + 58 T^{2} + 249 T^{3} + 2378 T^{4} + 1681 T^{5} + 68921 T^{6} \))(\( 1 - 16 T + 162 T^{2} - 984 T^{3} + 6251 T^{4} - 40344 T^{5} + 272322 T^{6} - 1102736 T^{7} + 2825761 T^{8} \))(\( 1 - 3 T + 115 T^{2} - 286 T^{3} + 6044 T^{4} - 11726 T^{5} + 193315 T^{6} - 206763 T^{7} + 2825761 T^{8} \))(\( 1 - 9 T + 169 T^{2} - 1026 T^{3} + 10410 T^{4} - 42066 T^{5} + 284089 T^{6} - 620289 T^{7} + 2825761 T^{8} \))(\( 1 + 17 T + 229 T^{2} + 2170 T^{3} + 15438 T^{4} + 88970 T^{5} + 384949 T^{6} + 1171657 T^{7} + 2825761 T^{8} \))(\( 1 + 3 T + 112 T^{2} + 213 T^{3} + 6631 T^{4} + 7488 T^{5} + 271871 T^{6} + 358053 T^{7} + 7719152 T^{8} + 8477283 T^{9} + 115856201 T^{10} \))(\( 1 - 8 T + 97 T^{2} - 558 T^{3} + 6329 T^{4} - 36766 T^{5} + 259489 T^{6} - 937998 T^{7} + 6685337 T^{8} - 22606088 T^{9} + 115856201 T^{10} \))(\( 1 + 9 T + 199 T^{2} + 1200 T^{3} + 16009 T^{4} + 73479 T^{5} + 787486 T^{6} + 3012639 T^{7} + 26911129 T^{8} + 82705200 T^{9} + 562326439 T^{10} + 1042705809 T^{11} + 4750104241 T^{12} \))(\( 1 + 25 T + 371 T^{2} + 3752 T^{3} + 30437 T^{4} + 211679 T^{5} + 1388622 T^{6} + 8678839 T^{7} + 51164597 T^{8} + 258591592 T^{9} + 1048357331 T^{10} + 2896405025 T^{11} + 4750104241 T^{12} \))(\( 1 + 7 T + 224 T^{2} + 1439 T^{3} + 23360 T^{4} + 130625 T^{5} + 1470535 T^{6} + 6839346 T^{7} + 60291935 T^{8} + 219580625 T^{9} + 1609994560 T^{10} + 4066270079 T^{11} + 25951789024 T^{12} + 33250729687 T^{13} + 194754273881 T^{14} \))(\( 1 - T + 169 T^{2} + 8 T^{3} + 15440 T^{4} + 3400 T^{5} + 918302 T^{6} + 260626 T^{7} + 37650382 T^{8} + 5715400 T^{9} + 1064140240 T^{10} + 22606088 T^{11} + 19579697969 T^{12} - 4750104241 T^{13} + 194754273881 T^{14} \))(\( 1 - 5 T + 243 T^{2} - 970 T^{3} + 26508 T^{4} - 86478 T^{5} + 1705372 T^{6} - 4521438 T^{7} + 69920252 T^{8} - 145369518 T^{9} + 1826957868 T^{10} - 2740988170 T^{11} + 28153056843 T^{12} - 23750521205 T^{13} + 194754273881 T^{14} \))(\( 1 - 3 T + 262 T^{2} - 677 T^{3} + 32119 T^{4} - 71264 T^{5} + 2398904 T^{6} - 4507824 T^{7} + 119184500 T^{8} - 184820784 T^{9} + 4032557624 T^{10} - 4911586144 T^{11} + 90760617559 T^{12} - 78434648077 T^{13} + 1244527311142 T^{14} - 584262821643 T^{15} + 7984925229121 T^{16} \))(\( 1 - 5 T + 139 T^{2} - 704 T^{3} + 12993 T^{4} - 63019 T^{5} + 880519 T^{6} - 3866896 T^{7} + 45589660 T^{8} - 183888032 T^{9} + 1869176060 T^{10} - 6500252176 T^{11} + 60686249999 T^{12} - 178076632459 T^{13} + 1505319619593 T^{14} - 3344073385664 T^{15} + 27070844069459 T^{16} - 39924626145605 T^{17} + 327381934393961 T^{18} \))
$43$ (\( 1 - 4 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 - 9 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( ( 1 + 6 T + 43 T^{2} )^{2} \))(\( 1 - 4 T + 22 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 90 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 78 T^{2} + 407 T^{3} + 3354 T^{4} + 11094 T^{5} + 79507 T^{6} \))(\( 1 + 122 T^{2} - 3 T^{3} + 5246 T^{4} + 79507 T^{6} \))(\( 1 + 2 T + 86 T^{2} + 45 T^{3} + 3698 T^{4} + 3698 T^{5} + 79507 T^{6} \))(\( 1 + 8 T + 121 T^{2} + 591 T^{3} + 5984 T^{4} + 25413 T^{5} + 223729 T^{6} + 636056 T^{7} + 3418801 T^{8} \))(\( 1 + 18 T + 225 T^{2} + 2065 T^{3} + 15776 T^{4} + 88795 T^{5} + 416025 T^{6} + 1431126 T^{7} + 3418801 T^{8} \))(\( 1 + 20 T + 313 T^{2} + 2989 T^{3} + 23632 T^{4} + 128527 T^{5} + 578737 T^{6} + 1590140 T^{7} + 3418801 T^{8} \))(\( 1 + 11 T + 107 T^{2} + 921 T^{3} + 7617 T^{4} + 39603 T^{5} + 197843 T^{6} + 874577 T^{7} + 3418801 T^{8} \))(\( 1 - 24 T + 400 T^{2} - 4559 T^{3} + 41953 T^{4} - 301526 T^{5} + 1803979 T^{6} - 8429591 T^{7} + 31802800 T^{8} - 82051224 T^{9} + 147008443 T^{10} \))(\( 1 + 7 T + 180 T^{2} + 1100 T^{3} + 14130 T^{4} + 69078 T^{5} + 607590 T^{6} + 2033900 T^{7} + 14311260 T^{8} + 23931607 T^{9} + 147008443 T^{10} \))(\( 1 - 10 T + 199 T^{2} - 1345 T^{3} + 15837 T^{4} - 82771 T^{5} + 790822 T^{6} - 3559153 T^{7} + 29282613 T^{8} - 106936915 T^{9} + 680341399 T^{10} - 1470084430 T^{11} + 6321363049 T^{12} \))(\( 1 - 19 T + 289 T^{2} - 2719 T^{3} + 23018 T^{4} - 149938 T^{5} + 1049156 T^{6} - 6447334 T^{7} + 42560282 T^{8} - 216179533 T^{9} + 988033489 T^{10} - 2793160417 T^{11} + 6321363049 T^{12} \))(\( 1 - T + 144 T^{2} - 432 T^{3} + 8369 T^{4} - 58109 T^{5} + 288954 T^{6} - 3543844 T^{7} + 12425022 T^{8} - 107443541 T^{9} + 665394083 T^{10} - 1476922032 T^{11} + 21169215792 T^{12} - 6321363049 T^{13} + 271818611107 T^{14} \))(\( 1 + 13 T + 222 T^{2} + 1874 T^{3} + 19311 T^{4} + 123943 T^{5} + 1041534 T^{6} + 5818180 T^{7} + 44785962 T^{8} + 229170607 T^{9} + 1535359677 T^{10} + 6406833074 T^{11} + 32635874346 T^{12} + 82177719637 T^{13} + 271818611107 T^{14} \))(\( 1 - 24 T + 458 T^{2} - 6071 T^{3} + 69138 T^{4} - 640436 T^{5} + 5252333 T^{6} - 36460442 T^{7} + 225850319 T^{8} - 1184166164 T^{9} + 5496954966 T^{10} - 20755540871 T^{11} + 67329866894 T^{12} - 151712713176 T^{13} + 271818611107 T^{14} \))(\( 1 - 16 T + 205 T^{2} - 1085 T^{3} + 3792 T^{4} + 28237 T^{5} - 134453 T^{6} + 817270 T^{7} + 4143710 T^{8} + 35142610 T^{9} - 248603597 T^{10} + 2245039159 T^{11} + 12964093392 T^{12} - 159504160655 T^{13} + 1295879425045 T^{14} - 4349097777712 T^{15} + 11688200277601 T^{16} \))(\( 1 - 5 T + 34 T^{2} - 310 T^{3} + 4140 T^{4} - 22044 T^{5} + 167878 T^{6} - 1100770 T^{7} + 9159643 T^{8} - 42641774 T^{9} + 393864649 T^{10} - 2035323730 T^{11} + 13347476146 T^{12} - 75364049244 T^{13} + 608614954020 T^{14} - 1959622545190 T^{15} + 9241832777638 T^{16} - 58441001388005 T^{17} + 502592611936843 T^{18} \))
$47$ (\( 1 + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( ( 1 + 6 T + 47 T^{2} )^{2} \))(\( 1 - 4 T + 30 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 - 5 T + 89 T^{2} - 235 T^{3} + 2209 T^{4} \))(\( 1 - 9 T + 51 T^{2} - 369 T^{3} + 2397 T^{4} - 19881 T^{5} + 103823 T^{6} \))(\( 1 + 5 T + 59 T^{2} + 303 T^{3} + 2773 T^{4} + 11045 T^{5} + 103823 T^{6} \))(\( 1 + 13 T + 181 T^{2} + 1251 T^{3} + 8507 T^{4} + 28717 T^{5} + 103823 T^{6} \))(\( 1 + 7 T + 120 T^{2} + 770 T^{3} + 8022 T^{4} + 36190 T^{5} + 265080 T^{6} + 726761 T^{7} + 4879681 T^{8} \))(\( 1 - 21 T + 304 T^{2} - 3062 T^{3} + 24182 T^{4} - 143914 T^{5} + 671536 T^{6} - 2180283 T^{7} + 4879681 T^{8} \))(\( 1 - 19 T + 270 T^{2} - 2616 T^{3} + 20342 T^{4} - 122952 T^{5} + 596430 T^{6} - 1972637 T^{7} + 4879681 T^{8} \))(\( 1 + 7 T + 156 T^{2} + 654 T^{3} + 9620 T^{4} + 30738 T^{5} + 344604 T^{6} + 726761 T^{7} + 4879681 T^{8} \))(\( 1 - 18 T + 261 T^{2} - 2562 T^{3} + 23795 T^{4} - 170127 T^{5} + 1118365 T^{6} - 5659458 T^{7} + 27097803 T^{8} - 87834258 T^{9} + 229345007 T^{10} \))(\( 1 - T + 73 T^{2} + 141 T^{3} + 1206 T^{4} + 19128 T^{5} + 56682 T^{6} + 311469 T^{7} + 7579079 T^{8} - 4879681 T^{9} + 229345007 T^{10} \))(\( 1 + 14 T + 142 T^{2} + 948 T^{3} + 7946 T^{4} + 74593 T^{5} + 596918 T^{6} + 3505871 T^{7} + 17552714 T^{8} + 98424204 T^{9} + 692914702 T^{10} + 3210830098 T^{11} + 10779215329 T^{12} \))(\( 1 + 10 T + 260 T^{2} + 2040 T^{3} + 29132 T^{4} + 178673 T^{5} + 1795972 T^{6} + 8397631 T^{7} + 64352588 T^{8} + 211798920 T^{9} + 1268717060 T^{10} + 2293450070 T^{11} + 10779215329 T^{12} \))(\( 1 + 143 T^{2} - 134 T^{3} + 10246 T^{4} - 3145 T^{5} + 606214 T^{6} + 298958 T^{7} + 28492058 T^{8} - 6947305 T^{9} + 1063770458 T^{10} - 653877254 T^{11} + 32796336001 T^{12} + 506623120463 T^{14} \))(\( 1 - 11 T + 293 T^{2} - 2333 T^{3} + 36491 T^{4} - 231353 T^{5} + 2683487 T^{6} - 13771198 T^{7} + 126123889 T^{8} - 511058777 T^{9} + 3788605093 T^{10} - 11384295773 T^{11} + 67198087051 T^{12} - 118571368619 T^{13} + 506623120463 T^{14} \))(\( 1 - 6 T + 209 T^{2} - 1150 T^{3} + 22680 T^{4} - 107719 T^{5} + 1559756 T^{6} - 6275246 T^{7} + 73308532 T^{8} - 237951271 T^{9} + 2354705640 T^{10} - 5611633150 T^{11} + 47933106463 T^{12} - 64675291974 T^{13} + 506623120463 T^{14} \))(\( 1 + 16 T + 206 T^{2} + 1802 T^{3} + 12129 T^{4} + 38819 T^{5} - 131698 T^{6} - 3691287 T^{7} - 32095452 T^{8} - 173490489 T^{9} - 290920882 T^{10} + 4030305037 T^{11} + 59185650849 T^{12} + 413279702614 T^{13} + 2220518357774 T^{14} + 8105969927408 T^{15} + 23811286661761 T^{16} \))(\( 1 - 8 T + 239 T^{2} - 1310 T^{3} + 24469 T^{4} - 102001 T^{5} + 1708823 T^{6} - 6577734 T^{7} + 100330640 T^{8} - 361481814 T^{9} + 4715540080 T^{10} - 14530214406 T^{11} + 177415130329 T^{12} - 497732341681 T^{13} + 5611842976283 T^{14} - 14120772080990 T^{15} + 121082925790657 T^{16} - 190490293294088 T^{17} + 1119130473102767 T^{18} \))
$53$ (\( 1 + 12 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 - 16 T + 162 T^{2} - 848 T^{3} + 2809 T^{4} \))(\( 1 + 2 T + 90 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 + 7 T + 87 T^{2} + 371 T^{3} + 2809 T^{4} \))(\( 1 - 6 T + 78 T^{2} - 439 T^{3} + 4134 T^{4} - 16854 T^{5} + 148877 T^{6} \))(\( 1 - 8 T + 106 T^{2} - 545 T^{3} + 5618 T^{4} - 22472 T^{5} + 148877 T^{6} \))(\( 1 + 16 T + 102 T^{2} + 435 T^{3} + 5406 T^{4} + 44944 T^{5} + 148877 T^{6} \))(\( 1 - 12 T + 143 T^{2} - 1135 T^{3} + 9944 T^{4} - 60155 T^{5} + 401687 T^{6} - 1786524 T^{7} + 7890481 T^{8} \))(\( 1 + 20 T + 295 T^{2} + 3005 T^{3} + 25640 T^{4} + 159265 T^{5} + 828655 T^{6} + 2977540 T^{7} + 7890481 T^{8} \))(\( 1 - 8 T + 207 T^{2} - 1227 T^{3} + 16334 T^{4} - 65031 T^{5} + 581463 T^{6} - 1191016 T^{7} + 7890481 T^{8} \))(\( 1 - 16 T + 227 T^{2} - 2271 T^{3} + 17942 T^{4} - 120363 T^{5} + 637643 T^{6} - 2382032 T^{7} + 7890481 T^{8} \))(\( 1 + 13 T + 305 T^{2} + 2764 T^{3} + 34410 T^{4} + 219955 T^{5} + 1823730 T^{6} + 7764076 T^{7} + 45407485 T^{8} + 102576253 T^{9} + 418195493 T^{10} \))(\( 1 - 10 T + 144 T^{2} - 1327 T^{3} + 13765 T^{4} - 89890 T^{5} + 729545 T^{6} - 3727543 T^{7} + 21438288 T^{8} - 78904810 T^{9} + 418195493 T^{10} \))(\( 1 + 11 T + 306 T^{2} + 2587 T^{3} + 39037 T^{4} + 257183 T^{5} + 2716878 T^{6} + 13630699 T^{7} + 109654933 T^{8} + 385144799 T^{9} + 2414487186 T^{10} + 4600150423 T^{11} + 22164361129 T^{12} \))(\( 1 + 17 T + 370 T^{2} + 4081 T^{3} + 50917 T^{4} + 409681 T^{5} + 3620938 T^{6} + 21713093 T^{7} + 143025853 T^{8} + 607567037 T^{9} + 2919477970 T^{10} + 7109323381 T^{11} + 22164361129 T^{12} \))(\( 1 + 3 T + 193 T^{2} + 46 T^{3} + 17551 T^{4} - 24658 T^{5} + 1181021 T^{6} - 1977370 T^{7} + 62594113 T^{8} - 69264322 T^{9} + 2612940227 T^{10} + 362962126 T^{11} + 80711730149 T^{12} + 66493083387 T^{13} + 1174711139837 T^{14} \))(\( 1 - 14 T + 306 T^{2} - 2995 T^{3} + 39352 T^{4} - 306178 T^{5} + 3066361 T^{6} - 19775306 T^{7} + 162517133 T^{8} - 860054002 T^{9} + 5858607704 T^{10} - 23631990595 T^{11} + 127967820858 T^{12} - 310301055806 T^{13} + 1174711139837 T^{14} \))(\( 1 - 3 T + 197 T^{2} - 1022 T^{3} + 20085 T^{4} - 128036 T^{5} + 1416341 T^{6} - 8781154 T^{7} + 75066073 T^{8} - 359653124 T^{9} + 2990194545 T^{10} - 8064071582 T^{11} + 82384512121 T^{12} - 66493083387 T^{13} + 1174711139837 T^{14} \))(\( 1 - 7 T + 208 T^{2} - 1453 T^{3} + 24474 T^{4} - 146432 T^{5} + 1962770 T^{6} - 10336604 T^{7} + 117577006 T^{8} - 547840012 T^{9} + 5513420930 T^{10} - 21800356864 T^{11} + 193111631994 T^{12} - 607638051329 T^{13} + 4610187114832 T^{14} - 8222977978859 T^{15} + 62259690411361 T^{16} \))(\( 1 - T + 201 T^{2} - 76 T^{3} + 21676 T^{4} - 4509 T^{5} + 1738900 T^{6} + 33540 T^{7} + 111004234 T^{8} + 21886428 T^{9} + 5883224402 T^{10} + 94213860 T^{11} + 258882215300 T^{12} - 35578178829 T^{13} + 9064805506268 T^{14} - 1684491445804 T^{15} + 236116939107237 T^{16} - 62259690411361 T^{17} + 3299763591802133 T^{18} \))
$59$ (\( 1 - 9 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 6 T - T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 + T + 114 T^{2} + 59 T^{3} + 3481 T^{4} \))(\( 1 + 17 T + 179 T^{2} + 1003 T^{3} + 3481 T^{4} \))(\( 1 + 9 T + 141 T^{2} + 891 T^{3} + 8319 T^{4} + 31329 T^{5} + 205379 T^{6} \))(\( 1 - 13 T + 127 T^{2} - 733 T^{3} + 7493 T^{4} - 45253 T^{5} + 205379 T^{6} \))(\( 1 + 21 T + 317 T^{2} + 2779 T^{3} + 18703 T^{4} + 73101 T^{5} + 205379 T^{6} \))(\( 1 - 2 T + 191 T^{2} - 175 T^{3} + 15451 T^{4} - 10325 T^{5} + 664871 T^{6} - 410758 T^{7} + 12117361 T^{8} \))(\( 1 - 5 T + 18 T^{2} + 2 T^{3} + 3718 T^{4} + 118 T^{5} + 62658 T^{6} - 1026895 T^{7} + 12117361 T^{8} \))(\( 1 - 13 T + 110 T^{2} - 288 T^{3} + 134 T^{4} - 16992 T^{5} + 382910 T^{6} - 2669927 T^{7} + 12117361 T^{8} \))(\( 1 - 3 T + 116 T^{2} - 704 T^{3} + 8072 T^{4} - 41536 T^{5} + 403796 T^{6} - 616137 T^{7} + 12117361 T^{8} \))(\( 1 + 16 T + 187 T^{2} + 2226 T^{3} + 21689 T^{4} + 167401 T^{5} + 1279651 T^{6} + 7748706 T^{7} + 38405873 T^{8} + 193877776 T^{9} + 714924299 T^{10} \))(\( 1 - 8 T + 228 T^{2} - 1307 T^{3} + 23296 T^{4} - 104348 T^{5} + 1374464 T^{6} - 4549667 T^{7} + 46826412 T^{8} - 96938888 T^{9} + 714924299 T^{10} \))(\( 1 + 20 T + 388 T^{2} + 5090 T^{3} + 59534 T^{4} + 557963 T^{5} + 4732406 T^{6} + 32919817 T^{7} + 207237854 T^{8} + 1045379110 T^{9} + 4701536068 T^{10} + 14298485980 T^{11} + 42180533641 T^{12} \))(\( 1 + 14 T + 254 T^{2} + 2290 T^{3} + 25172 T^{4} + 172633 T^{5} + 1628952 T^{6} + 10185347 T^{7} + 87623732 T^{8} + 470317910 T^{9} + 3077809694 T^{10} + 10008940186 T^{11} + 42180533641 T^{12} \))(\( 1 + 14 T + 413 T^{2} + 4220 T^{3} + 70038 T^{4} + 557747 T^{5} + 6665088 T^{6} + 42205670 T^{7} + 393240192 T^{8} + 1941517307 T^{9} + 14384334402 T^{10} + 51135263420 T^{11} + 295263735487 T^{12} + 590527470974 T^{13} + 2488651484819 T^{14} \))(\( 1 - 39 T + 922 T^{2} - 15604 T^{3} + 210106 T^{4} - 2343710 T^{5} + 22337347 T^{6} - 183953230 T^{7} + 1317903473 T^{8} - 8158454510 T^{9} + 43151360174 T^{10} - 189079301044 T^{11} + 659160203678 T^{12} - 1645040811999 T^{13} + 2488651484819 T^{14} \))(\( 1 - 10 T + 320 T^{2} - 2568 T^{3} + 45501 T^{4} - 306445 T^{5} + 3948285 T^{6} - 22395551 T^{7} + 232948815 T^{8} - 1066735045 T^{9} + 9344949879 T^{10} - 31117383048 T^{11} + 228775775680 T^{12} - 421805336410 T^{13} + 2488651484819 T^{14} \))(\( 1 + 14 T + 489 T^{2} + 5476 T^{3} + 102809 T^{4} + 934581 T^{5} + 12232504 T^{6} + 90236252 T^{7} + 904300590 T^{8} + 5323938868 T^{9} + 42581346424 T^{10} + 191943311199 T^{11} + 1245773767049 T^{12} + 3914925461324 T^{13} + 20626280950449 T^{14} + 34841120787466 T^{15} + 146830437604321 T^{16} \))(\( 1 - 4 T + 326 T^{2} - 690 T^{3} + 48930 T^{4} - 14953 T^{5} + 4598993 T^{6} + 5391123 T^{7} + 322789418 T^{8} + 553826680 T^{9} + 19044575662 T^{10} + 18766499163 T^{11} + 944536583347 T^{12} - 181190899033 T^{13} + 34981245950070 T^{14} - 29104568212290 T^{15} + 811300384050994 T^{16} - 587321750417284 T^{17} + 8662995818654939 T^{18} \))
$61$ (\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{7} \))(\( ( 1 - T )^{8} \))(\( ( 1 + T )^{9} \))
$67$ (\( 1 - 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))(\( 1 + 62 T^{2} + 4489 T^{4} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( 1 + 17 T + 195 T^{2} + 1139 T^{3} + 4489 T^{4} \))(\( 1 + 27 T + 333 T^{2} + 2915 T^{3} + 22311 T^{4} + 121203 T^{5} + 300763 T^{6} \))(\( 1 - 17 T + 283 T^{2} - 2371 T^{3} + 18961 T^{4} - 76313 T^{5} + 300763 T^{6} \))(\( 1 + T + 157 T^{2} + 217 T^{3} + 10519 T^{4} + 4489 T^{5} + 300763 T^{6} \))(\( 1 + 5 T + 116 T^{2} + 312 T^{3} + 5862 T^{4} + 20904 T^{5} + 520724 T^{6} + 1503815 T^{7} + 20151121 T^{8} \))(\( 1 + 3 T + 266 T^{2} + 598 T^{3} + 26668 T^{4} + 40066 T^{5} + 1194074 T^{6} + 902289 T^{7} + 20151121 T^{8} \))(\( 1 + 3 T + 188 T^{2} + 240 T^{3} + 16018 T^{4} + 16080 T^{5} + 843932 T^{6} + 902289 T^{7} + 20151121 T^{8} \))(\( 1 - 5 T + 236 T^{2} - 796 T^{3} + 22402 T^{4} - 53332 T^{5} + 1059404 T^{6} - 1503815 T^{7} + 20151121 T^{8} \))(\( 1 - 18 T + 279 T^{2} - 2904 T^{3} + 32349 T^{4} - 267409 T^{5} + 2167383 T^{6} - 13036056 T^{7} + 83912877 T^{8} - 362720178 T^{9} + 1350125107 T^{10} \))(\( 1 + 9 T + 331 T^{2} + 2311 T^{3} + 44086 T^{4} + 229080 T^{5} + 2953762 T^{6} + 10374079 T^{7} + 99552553 T^{8} + 181360089 T^{9} + 1350125107 T^{10} \))(\( 1 - 14 T + 298 T^{2} - 2778 T^{3} + 37102 T^{4} - 274023 T^{5} + 2934510 T^{6} - 18359541 T^{7} + 166550878 T^{8} - 835519614 T^{9} + 6005034058 T^{10} - 18901751498 T^{11} + 90458382169 T^{12} \))(\( 1 - 12 T + 260 T^{2} - 2692 T^{3} + 36308 T^{4} - 306087 T^{5} + 2989418 T^{6} - 20507829 T^{7} + 162986612 T^{8} - 809653996 T^{9} + 5239291460 T^{10} - 16201501284 T^{11} + 90458382169 T^{12} \))(\( 1 + 249 T^{2} - 612 T^{3} + 32316 T^{4} - 112395 T^{5} + 2965226 T^{6} - 9819458 T^{7} + 198670142 T^{8} - 504541155 T^{9} + 9719457108 T^{10} - 12332486052 T^{11} + 336181151643 T^{12} + 6060711605323 T^{14} \))(\( 1 + 3 T + 137 T^{2} + 123 T^{3} + 11105 T^{4} - 43679 T^{5} + 545553 T^{6} - 4043198 T^{7} + 36552051 T^{8} - 196075031 T^{9} + 3339973115 T^{10} + 2478587883 T^{11} + 184967139659 T^{12} + 271375146507 T^{13} + 6060711605323 T^{14} \))(\( 1 - 22 T + 421 T^{2} - 4788 T^{3} + 50240 T^{4} - 374709 T^{5} + 2994564 T^{6} - 20687394 T^{7} + 200635788 T^{8} - 1682068701 T^{9} + 15110333120 T^{10} - 96483567348 T^{11} + 568402670047 T^{12} - 1990084407718 T^{13} + 6060711605323 T^{14} \))(\( 1 - 8 T + 290 T^{2} - 2224 T^{3} + 49393 T^{4} - 334771 T^{5} + 5412530 T^{6} - 32410203 T^{7} + 430011908 T^{8} - 2171483601 T^{9} + 24296847170 T^{10} - 100686730273 T^{11} + 995324319553 T^{12} - 3002678237968 T^{13} + 26232930829010 T^{14} - 48485692842584 T^{15} + 406067677556641 T^{16} \))(\( 1 + 4 T + 441 T^{2} + 2236 T^{3} + 90751 T^{4} + 530455 T^{5} + 11694625 T^{6} + 71082416 T^{7} + 1060815410 T^{8} + 5946422690 T^{9} + 71074632470 T^{10} + 319088965424 T^{11} + 3517310498875 T^{12} + 10689262890055 T^{13} + 122525203585357 T^{14} + 202264942529884 T^{15} + 2672773817947443 T^{16} + 1624270710226564 T^{17} + 27206534396294947 T^{18} \))
$71$ (\( 1 - 6 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 - 15 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( 1 + 2 T + 126 T^{2} + 142 T^{3} + 5041 T^{4} \))(\( 1 - 10 T + 162 T^{2} - 710 T^{3} + 5041 T^{4} \))(\( 1 - 15 T + 225 T^{2} - 2111 T^{3} + 15975 T^{4} - 75615 T^{5} + 357911 T^{6} \))(\( 1 + 17 T + 295 T^{2} + 2507 T^{3} + 20945 T^{4} + 85697 T^{5} + 357911 T^{6} \))(\( 1 + 15 T + 239 T^{2} + 1961 T^{3} + 16969 T^{4} + 75615 T^{5} + 357911 T^{6} \))(\( 1 - 15 T + 288 T^{2} - 2726 T^{3} + 30728 T^{4} - 193546 T^{5} + 1451808 T^{6} - 5368665 T^{7} + 25411681 T^{8} \))(\( 1 + 9 T + 244 T^{2} + 1588 T^{3} + 24338 T^{4} + 112748 T^{5} + 1230004 T^{6} + 3221199 T^{7} + 25411681 T^{8} \))(\( 1 + T + 200 T^{2} + 174 T^{3} + 18314 T^{4} + 12354 T^{5} + 1008200 T^{6} + 357911 T^{7} + 25411681 T^{8} \))(\( 1 + 10 T + 199 T^{2} + 1427 T^{3} + 19545 T^{4} + 101317 T^{5} + 1003159 T^{6} + 3579110 T^{7} + 25411681 T^{8} \))(\( 1 + 31 T + 687 T^{2} + 10159 T^{3} + 122096 T^{4} + 1126272 T^{5} + 8668816 T^{6} + 51211519 T^{7} + 245884857 T^{8} + 787762111 T^{9} + 1804229351 T^{10} \))(\( 1 - 34 T + 622 T^{2} - 8033 T^{3} + 82242 T^{4} - 728020 T^{5} + 5839182 T^{6} - 40494353 T^{7} + 222620642 T^{8} - 863997154 T^{9} + 1804229351 T^{10} \))(\( 1 + 21 T + 456 T^{2} + 6236 T^{3} + 82897 T^{4} + 822655 T^{5} + 7859980 T^{6} + 58408505 T^{7} + 417883777 T^{8} + 2231932996 T^{9} + 11587726536 T^{10} + 37888816371 T^{11} + 128100283921 T^{12} \))(\( 1 - 6 T + 279 T^{2} - 1265 T^{3} + 36464 T^{4} - 129133 T^{5} + 3056036 T^{6} - 9168443 T^{7} + 183815024 T^{8} - 452757415 T^{9} + 7089858999 T^{10} - 10825376106 T^{11} + 128100283921 T^{12} \))(\( 1 + 22 T + 644 T^{2} + 9527 T^{3} + 156593 T^{4} + 1704816 T^{5} + 19630790 T^{6} + 161780134 T^{7} + 1393786090 T^{8} + 8593977456 T^{9} + 56046357223 T^{10} + 242097084887 T^{11} + 1161923702044 T^{12} + 2818206246262 T^{13} + 9095120158391 T^{14} \))(\( 1 - 12 T + 218 T^{2} - 1673 T^{3} + 28749 T^{4} - 224564 T^{5} + 2781012 T^{6} - 17115998 T^{7} + 197451852 T^{8} - 1132027124 T^{9} + 10289583339 T^{10} - 42513742313 T^{11} + 393321998518 T^{12} - 1537203407052 T^{13} + 9095120158391 T^{14} \))(\( 1 - T + 305 T^{2} - 211 T^{3} + 46407 T^{4} - 10643 T^{5} + 4574967 T^{6} - 345826 T^{7} + 324822657 T^{8} - 53651363 T^{9} + 16609575777 T^{10} - 5361864691 T^{11} + 550289952055 T^{12} - 128100283921 T^{13} + 9095120158391 T^{14} \))(\( 1 - 11 T + 302 T^{2} - 3528 T^{3} + 53098 T^{4} - 539286 T^{5} + 6310066 T^{6} - 54605825 T^{7} + 526561322 T^{8} - 3877013575 T^{9} + 31809042706 T^{10} - 193016391546 T^{11} + 1349309437738 T^{12} - 6365321150328 T^{13} + 38686285744142 T^{14} - 100046321742301 T^{15} + 645753531245761 T^{16} \))(\( 1 - 20 T + 504 T^{2} - 7263 T^{3} + 113232 T^{4} - 1332428 T^{5} + 15920938 T^{6} - 158399153 T^{7} + 1557834753 T^{8} - 13249712128 T^{9} + 110606267463 T^{10} - 798490130273 T^{11} + 5698278840518 T^{12} - 33859235291468 T^{13} + 204296497872432 T^{14} - 930392362118223 T^{15} + 4583940559829064 T^{16} - 12915070624915220 T^{17} + 45848500718449031 T^{18} \))
$73$ (\( 1 - 8 T + 73 T^{2} \))(\( 1 + 7 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 8 T + 130 T^{2} - 584 T^{3} + 5329 T^{4} \))(\( 1 - 2 T + 130 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 + 8 T + 142 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( 1 - 6 T + 102 T^{2} - 177 T^{3} + 7446 T^{4} - 31974 T^{5} + 389017 T^{6} \))(\( 1 - 10 T + 220 T^{2} - 1349 T^{3} + 16060 T^{4} - 53290 T^{5} + 389017 T^{6} \))(\( 1 + 18 T + 306 T^{2} + 2711 T^{3} + 22338 T^{4} + 95922 T^{5} + 389017 T^{6} \))(\( 1 + 28 T + 397 T^{2} + 3589 T^{3} + 29536 T^{4} + 261997 T^{5} + 2115613 T^{6} + 10892476 T^{7} + 28398241 T^{8} \))(\( 1 + 51 T^{2} - 377 T^{3} + 7094 T^{4} - 27521 T^{5} + 271779 T^{6} + 28398241 T^{8} \))(\( 1 + 2 T + 181 T^{2} + 461 T^{3} + 15934 T^{4} + 33653 T^{5} + 964549 T^{6} + 778034 T^{7} + 28398241 T^{8} \))(\( 1 + 9 T + 105 T^{2} + 741 T^{3} + 11403 T^{4} + 54093 T^{5} + 559545 T^{6} + 3501153 T^{7} + 28398241 T^{8} \))(\( 1 - 8 T + 176 T^{2} - 691 T^{3} + 12623 T^{4} - 18442 T^{5} + 921479 T^{6} - 3682339 T^{7} + 68466992 T^{8} - 227185928 T^{9} + 2073071593 T^{10} \))(\( 1 - 13 T + 170 T^{2} - 2170 T^{3} + 22014 T^{4} - 162898 T^{5} + 1607022 T^{6} - 11563930 T^{7} + 66132890 T^{8} - 369177133 T^{9} + 2073071593 T^{10} \))(\( 1 - 16 T + 391 T^{2} - 5055 T^{3} + 69949 T^{4} - 676281 T^{5} + 6823446 T^{6} - 49368513 T^{7} + 372758221 T^{8} - 1966480935 T^{9} + 11103712231 T^{10} - 33169145488 T^{11} + 151334226289 T^{12} \))(\( 1 + 29 T + 649 T^{2} + 9813 T^{3} + 128754 T^{4} + 1353010 T^{5} + 12719488 T^{6} + 98769730 T^{7} + 686130066 T^{8} + 3817423821 T^{9} + 18430458409 T^{10} + 60119076197 T^{11} + 151334226289 T^{12} \))(\( 1 - T + 364 T^{2} - 296 T^{3} + 61993 T^{4} - 30297 T^{5} + 6604954 T^{6} - 2048028 T^{7} + 482161642 T^{8} - 161452713 T^{9} + 24116330881 T^{10} - 8405879336 T^{11} + 754598059852 T^{12} - 151334226289 T^{13} + 11047398519097 T^{14} \))(\( 1 + 21 T + 570 T^{2} + 8142 T^{3} + 128073 T^{4} + 1380513 T^{5} + 15660896 T^{6} + 131172464 T^{7} + 1143245408 T^{8} + 7356753777 T^{9} + 49822574241 T^{10} + 231218478222 T^{11} + 1181650808010 T^{12} + 3178018752069 T^{13} + 11047398519097 T^{14} \))(\( 1 - 32 T + 738 T^{2} - 12977 T^{3} + 185644 T^{4} - 2261288 T^{5} + 23779529 T^{6} - 216674702 T^{7} + 1735905617 T^{8} - 12050403752 T^{9} + 72218671948 T^{10} - 368523973457 T^{11} + 1529926835634 T^{12} - 4842695241248 T^{13} + 11047398519097 T^{14} \))(\( 1 - 14 T + 343 T^{2} - 3319 T^{3} + 45652 T^{4} - 293923 T^{5} + 3108441 T^{6} - 13508928 T^{7} + 176953174 T^{8} - 986151744 T^{9} + 16564882089 T^{10} - 114341043691 T^{11} + 1296436498132 T^{12} - 6880524617167 T^{13} + 51907639617127 T^{14} - 154663579267358 T^{15} + 806460091894081 T^{16} \))(\( 1 - 15 T + 458 T^{2} - 5686 T^{3} + 104740 T^{4} - 1099794 T^{5} + 15228338 T^{6} - 137002922 T^{7} + 1543536703 T^{8} - 11861010366 T^{9} + 112678179319 T^{10} - 730088571338 T^{11} + 5924082363746 T^{12} - 31232215062354 T^{13} + 217133518650820 T^{14} - 860486410679254 T^{15} + 5059708521746426 T^{16} - 12096901378411215 T^{17} + 58871586708267913 T^{18} \))
$79$ (\( 1 + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( 1 - 15 T + 183 T^{2} - 1185 T^{3} + 6241 T^{4} \))(\( 1 + 3 T + 237 T^{2} + 473 T^{3} + 18723 T^{4} + 18723 T^{5} + 493039 T^{6} \))(\( 1 + 7 T + 227 T^{2} + 1009 T^{3} + 17933 T^{4} + 43687 T^{5} + 493039 T^{6} \))(\( 1 + 19 T + 313 T^{2} + 2863 T^{3} + 24727 T^{4} + 118579 T^{5} + 493039 T^{6} \))(\( 1 - 3 T + 200 T^{2} - 270 T^{3} + 20254 T^{4} - 21330 T^{5} + 1248200 T^{6} - 1479117 T^{7} + 38950081 T^{8} \))(\( 1 + 31 T + 594 T^{2} + 7924 T^{3} + 81606 T^{4} + 625996 T^{5} + 3707154 T^{6} + 15284209 T^{7} + 38950081 T^{8} \))(\( 1 - 19 T + 192 T^{2} - 1652 T^{3} + 15770 T^{4} - 130508 T^{5} + 1198272 T^{6} - 9367741 T^{7} + 38950081 T^{8} \))(\( 1 + 11 T + 278 T^{2} + 2478 T^{3} + 31770 T^{4} + 195762 T^{5} + 1734998 T^{6} + 5423429 T^{7} + 38950081 T^{8} \))(\( 1 - 32 T + 521 T^{2} - 6042 T^{3} + 60211 T^{4} - 551709 T^{5} + 4756669 T^{6} - 37708122 T^{7} + 256873319 T^{8} - 1246402592 T^{9} + 3077056399 T^{10} \))(\( 1 - 15 T + 349 T^{2} - 3743 T^{3} + 51768 T^{4} - 414980 T^{5} + 4089672 T^{6} - 23360063 T^{7} + 172070611 T^{8} - 584251215 T^{9} + 3077056399 T^{10} \))(\( 1 + 6 T + 162 T^{2} + 484 T^{3} + 16196 T^{4} + 36935 T^{5} + 1488670 T^{6} + 2917865 T^{7} + 101079236 T^{8} + 238630876 T^{9} + 6309913122 T^{10} + 18462338394 T^{11} + 243087455521 T^{12} \))(\( 1 + 24 T + 318 T^{2} + 2904 T^{3} + 29300 T^{4} + 312897 T^{5} + 3138590 T^{6} + 24718863 T^{7} + 182861300 T^{8} + 1431785256 T^{9} + 12386125758 T^{10} + 73849353576 T^{11} + 243087455521 T^{12} \))(\( 1 - 10 T + 363 T^{2} - 3814 T^{3} + 62168 T^{4} - 656547 T^{5} + 6793226 T^{6} - 66031034 T^{7} + 536664854 T^{8} - 4097509827 T^{9} + 30651248552 T^{10} - 148555608934 T^{11} + 1116971472837 T^{12} - 2430874555210 T^{13} + 19203908986159 T^{14} \))(\( 1 - 15 T + 479 T^{2} - 5323 T^{3} + 99247 T^{4} - 874109 T^{5} + 12066833 T^{6} - 86316370 T^{7} + 953279807 T^{8} - 5455314269 T^{9} + 48932641633 T^{10} - 207331281163 T^{11} + 1473910015121 T^{12} - 3646311832815 T^{13} + 19203908986159 T^{14} \))(\( 1 + 8 T + 261 T^{2} + 1286 T^{3} + 29164 T^{4} + 75261 T^{5} + 2431460 T^{6} + 3805370 T^{7} + 192085340 T^{8} + 469703901 T^{9} + 14378989396 T^{10} + 50089804166 T^{11} + 803111720139 T^{12} + 1944699644168 T^{13} + 19203908986159 T^{14} \))(\( 1 - 22 T + 620 T^{2} - 10382 T^{3} + 171351 T^{4} - 2215601 T^{5} + 27106408 T^{6} - 277046829 T^{7} + 2677646568 T^{8} - 21886699491 T^{9} + 169171092328 T^{10} - 1092377701439 T^{11} + 6674135329431 T^{12} - 31945999534418 T^{13} + 150714222423020 T^{14} - 422485997695498 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 2 T + 285 T^{2} + 432 T^{3} + 38669 T^{4} + 20555 T^{5} + 3899611 T^{6} + 509508 T^{7} + 349149658 T^{8} + 94271678 T^{9} + 27582822982 T^{10} + 3179839428 T^{11} + 1922660307829 T^{12} + 800618914955 T^{13} + 118986693892931 T^{14} + 105013780785072 T^{15} + 5473114061055315 T^{16} + 3034217619813122 T^{17} + 119851595982618319 T^{18} \))
$83$ (\( 1 - 4 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 74 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 - 4 T + 102 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 - 4 T - 10 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 - 6 T + 132 T^{2} - 675 T^{3} + 10956 T^{4} - 41334 T^{5} + 571787 T^{6} \))(\( 1 + 14 T + 168 T^{2} + 2063 T^{3} + 13944 T^{4} + 96446 T^{5} + 571787 T^{6} \))(\( 1 + 2 T + 66 T^{2} - 411 T^{3} + 5478 T^{4} + 13778 T^{5} + 571787 T^{6} \))(\( 1 - 32 T + 649 T^{2} - 8773 T^{3} + 92400 T^{4} - 728159 T^{5} + 4470961 T^{6} - 18297184 T^{7} + 47458321 T^{8} \))(\( 1 + 8 T + 267 T^{2} + 1711 T^{3} + 30448 T^{4} + 142013 T^{5} + 1839363 T^{6} + 4574296 T^{7} + 47458321 T^{8} \))(\( 1 - 12 T + 307 T^{2} - 2541 T^{3} + 36868 T^{4} - 210903 T^{5} + 2114923 T^{6} - 6861444 T^{7} + 47458321 T^{8} \))(\( 1 - 5 T + 269 T^{2} - 1083 T^{3} + 32009 T^{4} - 89889 T^{5} + 1853141 T^{6} - 2858935 T^{7} + 47458321 T^{8} \))(\( 1 - 8 T + 222 T^{2} - 875 T^{3} + 16877 T^{4} - 33826 T^{5} + 1400791 T^{6} - 6027875 T^{7} + 126936714 T^{8} - 379666568 T^{9} + 3939040643 T^{10} \))(\( 1 + 27 T + 376 T^{2} + 3000 T^{3} + 16368 T^{4} + 90878 T^{5} + 1358544 T^{6} + 20667000 T^{7} + 214991912 T^{8} + 1281374667 T^{9} + 3939040643 T^{10} \))(\( 1 + 10 T + 355 T^{2} + 2481 T^{3} + 55667 T^{4} + 305639 T^{5} + 5550770 T^{6} + 25368037 T^{7} + 383489963 T^{8} + 1418603547 T^{9} + 16847703955 T^{10} + 39390406430 T^{11} + 326940373369 T^{12} \))(\( 1 + 9 T - 3 T^{2} - 625 T^{3} + 1196 T^{4} + 19774 T^{5} + 127172 T^{6} + 1641242 T^{7} + 8239244 T^{8} - 357366875 T^{9} - 142374963 T^{10} + 35451365787 T^{11} + 326940373369 T^{12} \))(\( 1 + 17 T + 542 T^{2} + 6484 T^{3} + 119053 T^{4} + 1098807 T^{5} + 15033196 T^{6} + 112538360 T^{7} + 1247755268 T^{8} + 7569681423 T^{9} + 68072957711 T^{10} + 307719753364 T^{11} + 2134960028506 T^{12} + 5557986347273 T^{13} + 27136050989627 T^{14} \))(\( 1 - 5 T + 376 T^{2} - 1556 T^{3} + 70427 T^{4} - 248779 T^{5} + 8501768 T^{6} - 25379752 T^{7} + 705646744 T^{8} - 1713838531 T^{9} + 40269243049 T^{10} - 73845147476 T^{11} + 1481079281768 T^{12} - 1634701866845 T^{13} + 27136050989627 T^{14} \))(\( 1 + 30 T + 636 T^{2} + 10091 T^{3} + 132970 T^{4} + 1523538 T^{5} + 15733803 T^{6} + 148515002 T^{7} + 1305905649 T^{8} + 10495653282 T^{9} + 76030517390 T^{10} + 478901917211 T^{11} + 2505229848948 T^{12} + 9808211201070 T^{13} + 27136050989627 T^{14} \))(\( 1 + 16 T + 285 T^{2} + 3041 T^{3} + 38374 T^{4} + 345939 T^{5} + 4548555 T^{6} + 42313374 T^{7} + 456851282 T^{8} + 3512010042 T^{9} + 31334995395 T^{10} + 197803422993 T^{11} + 1821165610054 T^{12} + 11978622595363 T^{13} + 93178006410165 T^{14} + 434176815834032 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 21 T + 536 T^{2} - 8472 T^{3} + 135858 T^{4} - 1728950 T^{5} + 21746156 T^{6} - 232136504 T^{7} + 2452072257 T^{8} - 22440930506 T^{9} + 203521997331 T^{10} - 1599188376056 T^{11} + 12434169300772 T^{12} - 82053064092950 T^{13} + 535150183676694 T^{14} - 2769838843182168 T^{15} + 14544923330440072 T^{16} - 47298136874919861 T^{17} + 186940255267540403 T^{18} \))
$89$ (\( 1 - 15 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 - 13 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 17 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 6 T + 115 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 7 T + 84 T^{2} - 623 T^{3} + 7921 T^{4} \))(\( 1 + 26 T + 342 T^{2} + 2314 T^{3} + 7921 T^{4} \))(\( 1 - 3 T + 159 T^{2} - 747 T^{3} + 14151 T^{4} - 23763 T^{5} + 704969 T^{6} \))(\( 1 + 23 T + 261 T^{2} + 2357 T^{3} + 23229 T^{4} + 182183 T^{5} + 704969 T^{6} \))(\( 1 + 5 T - 21 T^{2} - 1461 T^{3} - 1869 T^{4} + 39605 T^{5} + 704969 T^{6} \))(\( 1 + 16 T + 447 T^{2} + 4489 T^{3} + 63905 T^{4} + 399521 T^{5} + 3540687 T^{6} + 11279504 T^{7} + 62742241 T^{8} \))(\( 1 - 5 T + 242 T^{2} - 1162 T^{3} + 28506 T^{4} - 103418 T^{5} + 1916882 T^{6} - 3524845 T^{7} + 62742241 T^{8} \))(\( 1 - 19 T + 306 T^{2} - 3602 T^{3} + 41100 T^{4} - 320578 T^{5} + 2423826 T^{6} - 13394411 T^{7} + 62742241 T^{8} \))(\( 1 - 8 T + 309 T^{2} - 1663 T^{3} + 38487 T^{4} - 148007 T^{5} + 2447589 T^{6} - 5639752 T^{7} + 62742241 T^{8} \))(\( 1 - T + 249 T^{2} + 215 T^{3} + 30584 T^{4} + 42508 T^{5} + 2721976 T^{6} + 1703015 T^{7} + 175537281 T^{8} - 62742241 T^{9} + 5584059449 T^{10} \))(\( 1 - 11 T + 286 T^{2} - 2392 T^{3} + 41643 T^{4} - 296243 T^{5} + 3706227 T^{6} - 18947032 T^{7} + 201621134 T^{8} - 690164651 T^{9} + 5584059449 T^{10} \))(\( 1 + 11 T + 348 T^{2} + 3384 T^{3} + 51315 T^{4} + 477593 T^{5} + 5047832 T^{6} + 42505777 T^{7} + 406466115 T^{8} + 2385615096 T^{9} + 21834299868 T^{10} + 61424653939 T^{11} + 496981290961 T^{12} \))(\( 1 + 4 T + 171 T^{2} + 1179 T^{3} + 28542 T^{4} + 151791 T^{5} + 2823324 T^{6} + 13509399 T^{7} + 226081182 T^{8} + 831158451 T^{9} + 10728923211 T^{10} + 22336237796 T^{11} + 496981290961 T^{12} \))(\( 1 + 18 T + 554 T^{2} + 7305 T^{3} + 124975 T^{4} + 1304968 T^{5} + 16362238 T^{6} + 141939378 T^{7} + 1456239182 T^{8} + 10336651528 T^{9} + 88103500775 T^{10} + 458332070505 T^{11} + 3093568934746 T^{12} + 8945663237298 T^{13} + 44231334895529 T^{14} \))(\( 1 + 8 T + 433 T^{2} + 3367 T^{3} + 90341 T^{4} + 655427 T^{5} + 11810964 T^{6} + 74474014 T^{7} + 1051175796 T^{8} + 5191637267 T^{9} + 63687604429 T^{10} + 211253125447 T^{11} + 2417897741417 T^{12} + 3975850327688 T^{13} + 44231334895529 T^{14} \))(\( 1 - 5 T + 472 T^{2} - 2248 T^{3} + 104236 T^{4} - 455178 T^{5} + 14046421 T^{6} - 52446858 T^{7} + 1250131469 T^{8} - 3605464938 T^{9} + 73483148684 T^{10} - 141044557768 T^{11} + 2635676059928 T^{12} - 2484906454805 T^{13} + 44231334895529 T^{14} \))(\( 1 - T + 221 T^{2} + 1243 T^{3} + 14742 T^{4} + 211258 T^{5} + 1643035 T^{6} + 2642040 T^{7} + 244871018 T^{8} + 235141560 T^{9} + 13014480235 T^{10} + 148930341002 T^{11} + 924946116822 T^{12} + 6940985895107 T^{13} + 109832865302381 T^{14} - 44231334895529 T^{15} + 3936588805702081 T^{16} \))(\( 1 - 10 T + 593 T^{2} - 5039 T^{3} + 167476 T^{4} - 1218985 T^{5} + 29632639 T^{6} - 185487881 T^{7} + 3642987927 T^{8} - 19566775250 T^{9} + 324225925503 T^{10} - 1469249505401 T^{11} + 20890091883191 T^{12} - 76481850645385 T^{13} + 935195940280724 T^{14} - 2504288725152479 T^{15} + 26229181593048697 T^{16} - 39365888057020810 T^{17} + 350356403707485209 T^{18} \))
$97$ (\( 1 + 11 T + 97 T^{2} \))(\( 1 - 11 T + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 13 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 3 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 10 T + 187 T^{2} - 970 T^{3} + 9409 T^{4} \))(\( 1 + T + 156 T^{2} + 97 T^{3} + 9409 T^{4} \))(\( 1 + 17 T + 205 T^{2} + 1649 T^{3} + 9409 T^{4} \))(\( 1 - 9 T + 261 T^{2} - 1439 T^{3} + 25317 T^{4} - 84681 T^{5} + 912673 T^{6} \))(\( 1 + 7 T + 161 T^{2} + 709 T^{3} + 15617 T^{4} + 65863 T^{5} + 912673 T^{6} \))(\( 1 - T + 261 T^{2} - 151 T^{3} + 25317 T^{4} - 9409 T^{5} + 912673 T^{6} \))(\( 1 - 2 T + 199 T^{2} - 105 T^{3} + 24953 T^{4} - 10185 T^{5} + 1872391 T^{6} - 1825346 T^{7} + 88529281 T^{8} \))(\( 1 + 25 T + 412 T^{2} + 5726 T^{3} + 65012 T^{4} + 555422 T^{5} + 3876508 T^{6} + 22816825 T^{7} + 88529281 T^{8} \))(\( 1 + T + 288 T^{2} + 782 T^{3} + 36368 T^{4} + 75854 T^{5} + 2709792 T^{6} + 912673 T^{7} + 88529281 T^{8} \))(\( 1 + 12 T + 289 T^{2} + 2645 T^{3} + 38579 T^{4} + 256565 T^{5} + 2719201 T^{6} + 10952076 T^{7} + 88529281 T^{8} \))(\( 1 + 4 T + 361 T^{2} + 1626 T^{3} + 61187 T^{4} + 232277 T^{5} + 5935139 T^{6} + 15299034 T^{7} + 329474953 T^{8} + 354117124 T^{9} + 8587340257 T^{10} \))(\( 1 - 37 T + 838 T^{2} - 13892 T^{3} + 182723 T^{4} - 1965609 T^{5} + 17724131 T^{6} - 130709828 T^{7} + 764819974 T^{8} - 3275583397 T^{9} + 8587340257 T^{10} \))(\( 1 - 2 T + 334 T^{2} - 368 T^{3} + 51532 T^{4} - 38707 T^{5} + 5558388 T^{6} - 3754579 T^{7} + 484864588 T^{8} - 335863664 T^{9} + 29568779854 T^{10} - 17174680514 T^{11} + 832972004929 T^{12} \))(\( 1 + 5 T + 334 T^{2} + 1183 T^{3} + 56850 T^{4} + 146998 T^{5} + 6383687 T^{6} + 14258806 T^{7} + 534901650 T^{8} + 1079692159 T^{9} + 29568779854 T^{10} + 42936701285 T^{11} + 832972004929 T^{12} \))(\( 1 - 25 T + 569 T^{2} - 7000 T^{3} + 76902 T^{4} - 419559 T^{5} + 2045781 T^{6} + 4237706 T^{7} + 198440757 T^{8} - 3947630631 T^{9} + 70186379046 T^{10} - 619704967000 T^{11} + 4886196606233 T^{12} - 20824300123225 T^{13} + 80798284478113 T^{14} \))(\( 1 + 20 T + 677 T^{2} + 10031 T^{3} + 194235 T^{4} + 2229699 T^{5} + 31031912 T^{6} + 280309906 T^{7} + 3010095464 T^{8} + 20979237891 T^{9} + 177273040155 T^{10} + 888037217711 T^{11} + 5813629353989 T^{12} + 16659440098580 T^{13} + 80798284478113 T^{14} \))(\( 1 - 14 T + 564 T^{2} - 5698 T^{3} + 133631 T^{4} - 1045409 T^{5} + 18848719 T^{6} - 121183741 T^{7} + 1828325743 T^{8} - 9836253281 T^{9} + 121961405663 T^{10} - 504439843138 T^{11} + 4843259904948 T^{12} - 11661608069006 T^{13} + 80798284478113 T^{14} \))(\( 1 - 24 T + 345 T^{2} - 4508 T^{3} + 52531 T^{4} - 526413 T^{5} + 5608724 T^{6} - 52037408 T^{7} + 460813184 T^{8} - 5047628576 T^{9} + 52772484116 T^{10} - 480442931949 T^{11} + 4650531660211 T^{12} - 38711729878556 T^{13} + 287375341700505 T^{14} - 1939158827474712 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 3 T + 242 T^{2} - 419 T^{3} + 45376 T^{4} - 11678 T^{5} + 5944026 T^{6} + 1244419 T^{7} + 663596572 T^{8} + 666908176 T^{9} + 64368867484 T^{10} + 11708738371 T^{11} + 5424952041498 T^{12} - 1033844943518 T^{13} + 389659151501632 T^{14} - 349015270065251 T^{15} + 19553184843703346 T^{16} - 23512300783130883 T^{17} + 760231058654565217 T^{18} \))
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