Properties

Label 4002.2.a
Level 4002
Weight 2
Character orbit a
Rep. character \(\chi_{4002}(1,\cdot)\)
Character field \(\Q\)
Dimension 101
Newform subspaces 37
Sturm bound 1440
Trace bound 7

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Defining parameters

Level: \( N \) \(=\) \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4002.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 37 \)
Sturm bound: \(1440\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4002))\).

Total New Old
Modular forms 728 101 627
Cusp forms 713 101 612
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.

\(2\)\(3\)\(23\)\(29\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(43\)
Minus space\(-\)\(58\)

Trace form

\( 101q + q^{2} - 3q^{3} + 101q^{4} + 6q^{5} + q^{6} + q^{8} + 101q^{9} + O(q^{10}) \) \( 101q + q^{2} - 3q^{3} + 101q^{4} + 6q^{5} + q^{6} + q^{8} + 101q^{9} + 6q^{10} + 12q^{11} - 3q^{12} + 6q^{13} + 8q^{14} + 6q^{15} + 101q^{16} + 18q^{17} + q^{18} - 4q^{19} + 6q^{20} - 16q^{21} + 12q^{22} + q^{23} + q^{24} + 115q^{25} + 14q^{26} - 3q^{27} + q^{29} + 6q^{30} + 8q^{31} + q^{32} + 12q^{33} + 18q^{34} + 48q^{35} + 101q^{36} + 14q^{37} + 20q^{38} - 26q^{39} + 6q^{40} + 26q^{41} + 8q^{42} + 4q^{43} + 12q^{44} + 6q^{45} - 7q^{46} + 16q^{47} - 3q^{48} + 117q^{49} + 15q^{50} + 18q^{51} + 6q^{52} - 10q^{53} + q^{54} + 8q^{55} + 8q^{56} - 4q^{57} - 3q^{58} + 4q^{59} + 6q^{60} + 22q^{61} + 8q^{62} + 101q^{64} - 28q^{65} + 12q^{66} - 28q^{67} + 18q^{68} - 7q^{69} + 16q^{70} - 56q^{71} + q^{72} - 14q^{73} - 34q^{74} + 3q^{75} - 4q^{76} - 48q^{77} - 2q^{78} - 40q^{79} + 6q^{80} + 101q^{81} - 6q^{82} - 84q^{83} - 16q^{84} - 36q^{85} - 20q^{86} + q^{87} + 12q^{88} - 70q^{89} + 6q^{90} + 32q^{91} + q^{92} - 24q^{93} - 8q^{94} - 88q^{95} + q^{96} - 6q^{97} + 25q^{98} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4002))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 23 29
4002.2.a.a \(1\) \(31.956\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots\)
4002.2.a.b \(1\) \(31.956\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
4002.2.a.c \(1\) \(31.956\) \(\Q\) None \(-1\) \(-1\) \(1\) \(4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
4002.2.a.d \(1\) \(31.956\) \(\Q\) None \(-1\) \(1\) \(-3\) \(-3\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
4002.2.a.e \(1\) \(31.956\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.f \(1\) \(31.956\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.g \(1\) \(31.956\) \(\Q\) None \(-1\) \(1\) \(4\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.h \(1\) \(31.956\) \(\Q\) None \(1\) \(-1\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
4002.2.a.i \(1\) \(31.956\) \(\Q\) None \(1\) \(-1\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+2q^{7}+\cdots\)
4002.2.a.j \(1\) \(31.956\) \(\Q\) None \(1\) \(-1\) \(1\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
4002.2.a.k \(1\) \(31.956\) \(\Q\) None \(1\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4002.2.a.l \(1\) \(31.956\) \(\Q\) None \(1\) \(-1\) \(2\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
4002.2.a.m \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(-3\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots\)
4002.2.a.n \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(-2\) \(-4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
4002.2.a.o \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(-1\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
4002.2.a.p \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4002.2.a.q \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(0\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
4002.2.a.r \(1\) \(31.956\) \(\Q\) None \(1\) \(1\) \(3\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
4002.2.a.s \(2\) \(31.956\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-3\) \(3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
4002.2.a.t \(2\) \(31.956\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+2\beta q^{5}+q^{6}+\beta q^{7}+\cdots\)
4002.2.a.u \(2\) \(31.956\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(1\) \(1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+\beta q^{7}+\cdots\)
4002.2.a.v \(2\) \(31.956\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
4002.2.a.w \(2\) \(31.956\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(6\) \(6\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+3q^{7}+\cdots\)
4002.2.a.x \(2\) \(31.956\) \(\Q(\sqrt{6}) \) None \(2\) \(2\) \(8\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+(2-\beta )q^{7}+\cdots\)
4002.2.a.y \(3\) \(31.956\) 3.3.1772.1 None \(-3\) \(-3\) \(-1\) \(6\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(2+\cdots)q^{7}+\cdots\)
4002.2.a.z \(3\) \(31.956\) 3.3.316.1 None \(3\) \(-3\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
4002.2.a.ba \(4\) \(31.956\) 4.4.16448.2 None \(-4\) \(-4\) \(2\) \(6\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
4002.2.a.bb \(4\) \(31.956\) 4.4.23252.1 None \(-4\) \(4\) \(-3\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots\)
4002.2.a.bc \(4\) \(31.956\) 4.4.11324.1 None \(4\) \(4\) \(-4\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
4002.2.a.bd \(4\) \(31.956\) 4.4.19796.1 None \(4\) \(4\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-\beta _{3}q^{5}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
4002.2.a.be \(5\) \(31.956\) 5.5.2389280.1 None \(-5\) \(-5\) \(1\) \(-4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bf \(6\) \(31.956\) 6.6.61157024.1 None \(-6\) \(6\) \(3\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta _{4}q^{5}-q^{6}+(\beta _{4}+\cdots)q^{7}+\cdots\)
4002.2.a.bg \(7\) \(31.956\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-7\) \(2\) \(-5\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-\beta _{5}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bh \(7\) \(31.956\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(7\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}-\beta _{6}q^{7}+\cdots\)
4002.2.a.bi \(8\) \(31.956\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(8\) \(-3\) \(-6\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-\beta _{4}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bj \(8\) \(31.956\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-8\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{4}q^{7}+\cdots\)
4002.2.a.bk \(8\) \(31.956\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-8\) \(2\) \(5\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(174))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(667))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1334))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2001))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{8} \))(\( ( 1 - T )^{8} \))(\( ( 1 - T )^{8} \))
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{7} \))(\( ( 1 - T )^{8} \))(\( ( 1 + T )^{8} \))(\( ( 1 + T )^{8} \))
$5$ (\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 + 2 T^{2} + 25 T^{4} \))(\( 1 - T + 6 T^{2} - 5 T^{3} + 25 T^{4} \))(\( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} \))(\( ( 1 - 3 T + 5 T^{2} )^{2} \))(\( ( 1 - 4 T + 5 T^{2} )^{2} \))(\( 1 + T + 3 T^{2} + 2 T^{3} + 15 T^{4} + 25 T^{5} + 125 T^{6} \))(\( 1 + 8 T^{2} - 2 T^{3} + 40 T^{4} + 125 T^{6} \))(\( 1 - 2 T + 9 T^{2} - 10 T^{3} + 36 T^{4} - 50 T^{5} + 225 T^{6} - 250 T^{7} + 625 T^{8} \))(\( 1 + 3 T + 13 T^{2} + 36 T^{3} + 94 T^{4} + 180 T^{5} + 325 T^{6} + 375 T^{7} + 625 T^{8} \))(\( 1 + 4 T + 17 T^{2} + 50 T^{3} + 124 T^{4} + 250 T^{5} + 425 T^{6} + 500 T^{7} + 625 T^{8} \))(\( 1 + T + 11 T^{2} + 20 T^{3} + 64 T^{4} + 100 T^{5} + 275 T^{6} + 125 T^{7} + 625 T^{8} \))(\( 1 - T + 7 T^{2} - 16 T^{3} + 65 T^{4} - 61 T^{5} + 325 T^{6} - 400 T^{7} + 875 T^{8} - 625 T^{9} + 3125 T^{10} \))(\( ( 1 - T + 6 T^{2} - 5 T^{3} + 25 T^{4} )^{3} \))(\( 1 - 2 T + 19 T^{2} - 26 T^{3} + 154 T^{4} - 112 T^{5} + 770 T^{6} - 328 T^{7} + 3850 T^{8} - 2800 T^{9} + 19250 T^{10} - 16250 T^{11} + 59375 T^{12} - 31250 T^{13} + 78125 T^{14} \))(\( 1 - T + 12 T^{2} - 9 T^{3} + 70 T^{4} + T^{5} + 297 T^{6} + 274 T^{7} + 1485 T^{8} + 25 T^{9} + 8750 T^{10} - 5625 T^{11} + 37500 T^{12} - 15625 T^{13} + 78125 T^{14} \))(\( 1 + 3 T + 18 T^{2} + 39 T^{3} + 107 T^{4} + 156 T^{5} + 72 T^{6} - 114 T^{7} - 1452 T^{8} - 570 T^{9} + 1800 T^{10} + 19500 T^{11} + 66875 T^{12} + 121875 T^{13} + 281250 T^{14} + 234375 T^{15} + 390625 T^{16} \))(\( 1 - T + 14 T^{2} - 31 T^{3} + 129 T^{4} - 312 T^{5} + 994 T^{6} - 2040 T^{7} + 5724 T^{8} - 10200 T^{9} + 24850 T^{10} - 39000 T^{11} + 80625 T^{12} - 96875 T^{13} + 218750 T^{14} - 78125 T^{15} + 390625 T^{16} \))(\( 1 - 2 T + 10 T^{2} - 18 T^{3} + 67 T^{4} - 102 T^{5} + 458 T^{6} - 790 T^{7} + 2768 T^{8} - 3950 T^{9} + 11450 T^{10} - 12750 T^{11} + 41875 T^{12} - 56250 T^{13} + 156250 T^{14} - 156250 T^{15} + 390625 T^{16} \))
$7$ (\( 1 + 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 3 T + 12 T^{2} - 21 T^{3} + 49 T^{4} \))(\( 1 + 12 T^{2} + 49 T^{4} \))(\( 1 - T + 10 T^{2} - 7 T^{3} + 49 T^{4} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 - 3 T + 7 T^{2} )^{2} \))(\( 1 - 4 T + 12 T^{2} - 28 T^{3} + 49 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 52 T^{3} + 133 T^{4} - 294 T^{5} + 343 T^{6} \))(\( 1 + 2 T + 6 T^{2} - 4 T^{3} + 42 T^{4} + 98 T^{5} + 343 T^{6} \))(\( 1 - 6 T + 29 T^{2} - 94 T^{3} + 276 T^{4} - 658 T^{5} + 1421 T^{6} - 2058 T^{7} + 2401 T^{8} \))(\( 1 + 2 T + 8 T^{2} + 38 T^{3} + 78 T^{4} + 266 T^{5} + 392 T^{6} + 686 T^{7} + 2401 T^{8} \))(\( 1 + 4 T + 25 T^{2} + 66 T^{3} + 248 T^{4} + 462 T^{5} + 1225 T^{6} + 1372 T^{7} + 2401 T^{8} \))(\( 1 - 2 T + 16 T^{2} - 22 T^{3} + 142 T^{4} - 154 T^{5} + 784 T^{6} - 686 T^{7} + 2401 T^{8} \))(\( 1 + 4 T + 28 T^{2} + 86 T^{3} + 363 T^{4} + 832 T^{5} + 2541 T^{6} + 4214 T^{7} + 9604 T^{8} + 9604 T^{9} + 16807 T^{10} \))(\( 1 - 2 T + 19 T^{2} - 30 T^{3} + 219 T^{4} - 264 T^{5} + 1682 T^{6} - 1848 T^{7} + 10731 T^{8} - 10290 T^{9} + 45619 T^{10} - 33614 T^{11} + 117649 T^{12} \))(\( 1 + 5 T + 31 T^{2} + 158 T^{3} + 571 T^{4} + 2123 T^{5} + 6749 T^{6} + 17700 T^{7} + 47243 T^{8} + 104027 T^{9} + 195853 T^{10} + 379358 T^{11} + 521017 T^{12} + 588245 T^{13} + 823543 T^{14} \))(\( 1 + 2 T + 23 T^{2} + 40 T^{3} + 255 T^{4} + 406 T^{5} + 1977 T^{6} + 2976 T^{7} + 13839 T^{8} + 19894 T^{9} + 87465 T^{10} + 96040 T^{11} + 386561 T^{12} + 235298 T^{13} + 823543 T^{14} \))(\( 1 + 6 T + 41 T^{2} + 150 T^{3} + 662 T^{4} + 1978 T^{5} + 7343 T^{6} + 19418 T^{7} + 61090 T^{8} + 135926 T^{9} + 359807 T^{10} + 678454 T^{11} + 1589462 T^{12} + 2521050 T^{13} + 4823609 T^{14} + 4941258 T^{15} + 5764801 T^{16} \))(\( 1 + 25 T^{2} + 10 T^{3} + 326 T^{4} + 182 T^{5} + 3343 T^{6} + 1532 T^{7} + 27186 T^{8} + 10724 T^{9} + 163807 T^{10} + 62426 T^{11} + 782726 T^{12} + 168070 T^{13} + 2941225 T^{14} + 5764801 T^{16} \))(\( 1 - 5 T + 24 T^{2} - 73 T^{3} + 288 T^{4} - 805 T^{5} + 2824 T^{6} - 7665 T^{7} + 24094 T^{8} - 53655 T^{9} + 138376 T^{10} - 276115 T^{11} + 691488 T^{12} - 1226911 T^{13} + 2823576 T^{14} - 4117715 T^{15} + 5764801 T^{16} \))
$11$ (\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( 1 - 2 T + 6 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 + T + 18 T^{2} + 11 T^{3} + 121 T^{4} \))(\( 1 + 2 T + 20 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 - 2 T^{2} + 121 T^{4} \))(\( 1 + T + 21 T^{2} + 14 T^{3} + 231 T^{4} + 121 T^{5} + 1331 T^{6} \))(\( 1 + 2 T + 27 T^{2} + 36 T^{3} + 297 T^{4} + 242 T^{5} + 1331 T^{6} \))(\( 1 + 18 T^{2} - 24 T^{3} + 162 T^{4} - 264 T^{5} + 2178 T^{6} + 14641 T^{8} \))(\( 1 + 11 T + 83 T^{2} + 408 T^{3} + 1586 T^{4} + 4488 T^{5} + 10043 T^{6} + 14641 T^{7} + 14641 T^{8} \))(\( 1 + 12 T + 82 T^{2} + 384 T^{3} + 1426 T^{4} + 4224 T^{5} + 9922 T^{6} + 15972 T^{7} + 14641 T^{8} \))(\( 1 - 15 T + 121 T^{2} - 648 T^{3} + 2512 T^{4} - 7128 T^{5} + 14641 T^{6} - 19965 T^{7} + 14641 T^{8} \))(\( 1 - 5 T + 38 T^{2} - 121 T^{3} + 527 T^{4} - 1410 T^{5} + 5797 T^{6} - 14641 T^{7} + 50578 T^{8} - 73205 T^{9} + 161051 T^{10} \))(\( 1 - 7 T + 72 T^{2} - 347 T^{3} + 2031 T^{4} - 7264 T^{5} + 29952 T^{6} - 79904 T^{7} + 245751 T^{8} - 461857 T^{9} + 1054152 T^{10} - 1127357 T^{11} + 1771561 T^{12} \))(\( 1 + T + 40 T^{2} + 19 T^{3} + 754 T^{4} - 49 T^{5} + 9543 T^{6} - 3190 T^{7} + 104973 T^{8} - 5929 T^{9} + 1003574 T^{10} + 278179 T^{11} + 6442040 T^{12} + 1771561 T^{13} + 19487171 T^{14} \))(\( 1 - 11 T + 94 T^{2} - 557 T^{3} + 2970 T^{4} - 13045 T^{5} + 52889 T^{6} - 182502 T^{7} + 581779 T^{8} - 1578445 T^{9} + 3953070 T^{10} - 8155037 T^{11} + 15138794 T^{12} - 19487171 T^{13} + 19487171 T^{14} \))(\( 1 + 7 T + 49 T^{2} + 224 T^{3} + 1080 T^{4} + 4308 T^{5} + 17831 T^{6} + 63439 T^{7} + 228190 T^{8} + 697829 T^{9} + 2157551 T^{10} + 5733948 T^{11} + 15812280 T^{12} + 36075424 T^{13} + 86806489 T^{14} + 136410197 T^{15} + 214358881 T^{16} \))(\( 1 - 3 T + 29 T^{2} + 2 T^{3} + 382 T^{4} + 258 T^{5} + 7307 T^{6} + 1497 T^{7} + 90306 T^{8} + 16467 T^{9} + 884147 T^{10} + 343398 T^{11} + 5592862 T^{12} + 322102 T^{13} + 51375269 T^{14} - 58461513 T^{15} + 214358881 T^{16} \))(\( 1 - 3 T + 39 T^{2} - 154 T^{3} + 974 T^{4} - 3596 T^{5} + 17345 T^{6} - 54121 T^{7} + 226690 T^{8} - 595331 T^{9} + 2098745 T^{10} - 4786276 T^{11} + 14260334 T^{12} - 24801854 T^{13} + 69090879 T^{14} - 58461513 T^{15} + 214358881 T^{16} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 10 T^{2} + 26 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 22 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + 2 T + 10 T^{2} + 26 T^{3} + 169 T^{4} \))(\( 1 - 5 T + 28 T^{2} - 65 T^{3} + 169 T^{4} \))(\( 1 - 6 T + 32 T^{2} - 78 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 6 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 - 7 T + 43 T^{2} - 162 T^{3} + 559 T^{4} - 1183 T^{5} + 2197 T^{6} \))(\( 1 + 8 T + 45 T^{2} + 164 T^{3} + 585 T^{4} + 1352 T^{5} + 2197 T^{6} \))(\( 1 + 10 T^{2} + 40 T^{3} - 70 T^{4} + 520 T^{5} + 1690 T^{6} + 28561 T^{8} \))(\( 1 + T + 29 T^{2} + 66 T^{3} + 438 T^{4} + 858 T^{5} + 4901 T^{6} + 2197 T^{7} + 28561 T^{8} \))(\( 1 + 6 T + 46 T^{2} + 170 T^{3} + 818 T^{4} + 2210 T^{5} + 7774 T^{6} + 13182 T^{7} + 28561 T^{8} \))(\( 1 - 11 T + 81 T^{2} - 430 T^{3} + 1730 T^{4} - 5590 T^{5} + 13689 T^{6} - 24167 T^{7} + 28561 T^{8} \))(\( 1 + 11 T + 102 T^{2} + 603 T^{3} + 3111 T^{4} + 11962 T^{5} + 40443 T^{6} + 101907 T^{7} + 224094 T^{8} + 314171 T^{9} + 371293 T^{10} \))(\( 1 - 3 T + 54 T^{2} - 177 T^{3} + 1371 T^{4} - 4424 T^{5} + 21772 T^{6} - 57512 T^{7} + 231699 T^{8} - 388869 T^{9} + 1542294 T^{10} - 1113879 T^{11} + 4826809 T^{12} \))(\( 1 - T + 44 T^{2} - 81 T^{3} + 1240 T^{4} - 2023 T^{5} + 22599 T^{6} - 35630 T^{7} + 293787 T^{8} - 341887 T^{9} + 2724280 T^{10} - 2313441 T^{11} + 16336892 T^{12} - 4826809 T^{13} + 62748517 T^{14} \))(\( 1 + T + 54 T^{2} + 45 T^{3} + 1424 T^{4} + 803 T^{5} + 24693 T^{6} + 10462 T^{7} + 321009 T^{8} + 135707 T^{9} + 3128528 T^{10} + 1285245 T^{11} + 20049822 T^{12} + 4826809 T^{13} + 62748517 T^{14} \))(\( 1 + 3 T + 47 T^{2} + 148 T^{3} + 1078 T^{4} + 3916 T^{5} + 16797 T^{6} + 70033 T^{7} + 223018 T^{8} + 910429 T^{9} + 2838693 T^{10} + 8603452 T^{11} + 30788758 T^{12} + 54951364 T^{13} + 226860023 T^{14} + 188245551 T^{15} + 815730721 T^{16} \))(\( 1 - 9 T + 81 T^{2} - 452 T^{3} + 2668 T^{4} - 11664 T^{5} + 54123 T^{6} - 199599 T^{7} + 800542 T^{8} - 2594787 T^{9} + 9146787 T^{10} - 25625808 T^{11} + 76200748 T^{12} - 167824436 T^{13} + 390971529 T^{14} - 564736653 T^{15} + 815730721 T^{16} \))(\( 1 - 13 T + 105 T^{2} - 522 T^{3} + 2068 T^{4} - 7084 T^{5} + 31911 T^{6} - 147353 T^{7} + 619590 T^{8} - 1915589 T^{9} + 5392959 T^{10} - 15563548 T^{11} + 59064148 T^{12} - 193814946 T^{13} + 506814945 T^{14} - 815730721 T^{15} + 815730721 T^{16} \))
$17$ (\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 5 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 + 9 T + 50 T^{2} + 153 T^{3} + 289 T^{4} \))(\( 1 + 26 T^{2} + 289 T^{4} \))(\( 1 + T + 30 T^{2} + 17 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 26 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 31 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 + 10 T^{2} + 289 T^{4} \))(\( ( 1 - 4 T + 17 T^{2} )^{3} \))(\( 1 + 44 T^{2} + 2 T^{3} + 748 T^{4} + 4913 T^{6} \))(\( 1 + 6 T + 37 T^{2} + 162 T^{3} + 736 T^{4} + 2754 T^{5} + 10693 T^{6} + 29478 T^{7} + 83521 T^{8} \))(\( 1 - 2 T + 48 T^{2} - 98 T^{3} + 1118 T^{4} - 1666 T^{5} + 13872 T^{6} - 9826 T^{7} + 83521 T^{8} \))(\( 1 + 2 T + 45 T^{2} + 62 T^{3} + 1016 T^{4} + 1054 T^{5} + 13005 T^{6} + 9826 T^{7} + 83521 T^{8} \))(\( 1 - 2 T + 56 T^{2} - 82 T^{3} + 1342 T^{4} - 1394 T^{5} + 16184 T^{6} - 9826 T^{7} + 83521 T^{8} \))(\( 1 - 4 T + 30 T^{2} - 118 T^{3} + 753 T^{4} - 3464 T^{5} + 12801 T^{6} - 34102 T^{7} + 147390 T^{8} - 334084 T^{9} + 1419857 T^{10} \))(\( 1 - 8 T + 83 T^{2} - 518 T^{3} + 3155 T^{4} - 15498 T^{5} + 69090 T^{6} - 263466 T^{7} + 911795 T^{8} - 2544934 T^{9} + 6932243 T^{10} - 11358856 T^{11} + 24137569 T^{12} \))(\( 1 + T + 75 T^{2} + 54 T^{3} + 2749 T^{4} + 1391 T^{5} + 65767 T^{6} + 25652 T^{7} + 1118039 T^{8} + 401999 T^{9} + 13505837 T^{10} + 4510134 T^{11} + 106489275 T^{12} + 24137569 T^{13} + 410338673 T^{14} \))(\( 1 - 18 T + 215 T^{2} - 1880 T^{3} + 13421 T^{4} - 80110 T^{5} + 409851 T^{6} - 1813456 T^{7} + 6967467 T^{8} - 23151790 T^{9} + 65937373 T^{10} - 157019480 T^{11} + 305269255 T^{12} - 434476242 T^{13} + 410338673 T^{14} \))(\( 1 + 12 T + 89 T^{2} + 390 T^{3} + 1214 T^{4} + 146 T^{5} - 19777 T^{6} - 165076 T^{7} - 756206 T^{8} - 2806292 T^{9} - 5715553 T^{10} + 717298 T^{11} + 101394494 T^{12} + 553744230 T^{13} + 2148243641 T^{14} + 4924064076 T^{15} + 6975757441 T^{16} \))(\( 1 - 8 T + 97 T^{2} - 638 T^{3} + 4566 T^{4} - 24906 T^{5} + 135183 T^{6} - 619840 T^{7} + 2744882 T^{8} - 10537280 T^{9} + 39067887 T^{10} - 122363178 T^{11} + 381356886 T^{12} - 905868766 T^{13} + 2341344193 T^{14} - 3282709384 T^{15} + 6975757441 T^{16} \))(\( 1 - 5 T + 80 T^{2} - 331 T^{3} + 3160 T^{4} - 11297 T^{5} + 83360 T^{6} - 263535 T^{7} + 1628590 T^{8} - 4480095 T^{9} + 24091040 T^{10} - 55502161 T^{11} + 263926360 T^{12} - 469972667 T^{13} + 1931005520 T^{14} - 2051693365 T^{15} + 6975757441 T^{16} \))
$19$ (\( 1 + 2 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - T + 34 T^{2} - 19 T^{3} + 361 T^{4} \))(\( 1 + 8 T + 52 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 + 9 T + 54 T^{2} + 171 T^{3} + 361 T^{4} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( 1 + 2 T + 27 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 36 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 6 T + 55 T^{2} - 220 T^{3} + 1045 T^{4} - 2166 T^{5} + 6859 T^{6} \))(\( 1 - 2 T + 26 T^{2} - 120 T^{3} + 494 T^{4} - 722 T^{5} + 6859 T^{6} \))(\( 1 - 2 T + 17 T^{2} - 54 T^{3} + 696 T^{4} - 1026 T^{5} + 6137 T^{6} - 13718 T^{7} + 130321 T^{8} \))(\( 1 - 8 T + 44 T^{2} - 236 T^{3} + 1182 T^{4} - 4484 T^{5} + 15884 T^{6} - 54872 T^{7} + 130321 T^{8} \))(\( 1 + 10 T + 89 T^{2} + 494 T^{3} + 2584 T^{4} + 9386 T^{5} + 32129 T^{6} + 68590 T^{7} + 130321 T^{8} \))(\( 1 + 2 T + 64 T^{2} + 94 T^{3} + 1726 T^{4} + 1786 T^{5} + 23104 T^{6} + 13718 T^{7} + 130321 T^{8} \))(\( 1 + 4 T + 40 T^{2} + 150 T^{3} + 1143 T^{4} + 4576 T^{5} + 21717 T^{6} + 54150 T^{7} + 274360 T^{8} + 521284 T^{9} + 2476099 T^{10} \))(\( 1 + 4 T + 67 T^{2} + 350 T^{3} + 2463 T^{4} + 11710 T^{5} + 59282 T^{6} + 222490 T^{7} + 889143 T^{8} + 2400650 T^{9} + 8731507 T^{10} + 9904396 T^{11} + 47045881 T^{12} \))(\( 1 + 9 T + 115 T^{2} + 722 T^{3} + 5539 T^{4} + 27143 T^{5} + 157953 T^{6} + 632300 T^{7} + 3001107 T^{8} + 9798623 T^{9} + 37992001 T^{10} + 94091762 T^{11} + 284751385 T^{12} + 423412929 T^{13} + 893871739 T^{14} \))(\( 1 - 6 T + 63 T^{2} - 288 T^{3} + 1339 T^{4} - 3666 T^{5} + 11005 T^{6} - 13520 T^{7} + 209095 T^{8} - 1323426 T^{9} + 9184201 T^{10} - 37532448 T^{11} + 155994237 T^{12} - 282275286 T^{13} + 893871739 T^{14} \))(\( 1 + 4 T + 41 T^{2} + 174 T^{3} + 1178 T^{4} + 3534 T^{5} + 17143 T^{6} + 49756 T^{7} + 281498 T^{8} + 945364 T^{9} + 6188623 T^{10} + 24239706 T^{11} + 153518138 T^{12} + 430841226 T^{13} + 1928881121 T^{14} + 3575486956 T^{15} + 16983563041 T^{16} \))(\( 1 + 121 T^{2} + 10 T^{3} + 6830 T^{4} + 782 T^{5} + 235447 T^{6} + 26684 T^{7} + 5414946 T^{8} + 506996 T^{9} + 84996367 T^{10} + 5363738 T^{11} + 890092430 T^{12} + 24760990 T^{13} + 5692551601 T^{14} + 16983563041 T^{16} \))(\( 1 - 7 T + 62 T^{2} - 259 T^{3} + 1524 T^{4} - 6555 T^{5} + 37058 T^{6} - 190391 T^{7} + 895158 T^{8} - 3617429 T^{9} + 13377938 T^{10} - 44960745 T^{11} + 198609204 T^{12} - 641309641 T^{13} + 2916844622 T^{14} - 6257102173 T^{15} + 16983563041 T^{16} \))
$23$ (\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{7} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{8} \))(\( ( 1 - T )^{8} \))(\( ( 1 + T )^{8} \))
$29$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{8} \))(\( ( 1 - T )^{8} \))(\( ( 1 + T )^{8} \))
$31$ (\( 1 + 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 6 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( 1 - 7 T + 70 T^{2} - 217 T^{3} + 961 T^{4} \))(\( 1 + 2 T + 60 T^{2} + 62 T^{3} + 961 T^{4} \))(\( ( 1 + 6 T + 31 T^{2} )^{2} \))(\( 1 - 7 T + 97 T^{2} - 414 T^{3} + 3007 T^{4} - 6727 T^{5} + 29791 T^{6} \))(\( 1 + 2 T + 39 T^{2} - 52 T^{3} + 1209 T^{4} + 1922 T^{5} + 29791 T^{6} \))(\( 1 - 8 T + 122 T^{2} - 648 T^{3} + 5514 T^{4} - 20088 T^{5} + 117242 T^{6} - 238328 T^{7} + 923521 T^{8} \))(\( 1 + 17 T + 215 T^{2} + 1724 T^{3} + 11352 T^{4} + 53444 T^{5} + 206615 T^{6} + 506447 T^{7} + 923521 T^{8} \))(\( 1 + 6 T + 26 T^{2} - 74 T^{3} - 150 T^{4} - 2294 T^{5} + 24986 T^{6} + 178746 T^{7} + 923521 T^{8} \))(\( 1 + 5 T + 91 T^{2} + 324 T^{3} + 3596 T^{4} + 10044 T^{5} + 87451 T^{6} + 148955 T^{7} + 923521 T^{8} \))(\( 1 - 5 T + 68 T^{2} + 11 T^{3} + 697 T^{4} + 10018 T^{5} + 21607 T^{6} + 10571 T^{7} + 2025788 T^{8} - 4617605 T^{9} + 28629151 T^{10} \))(\( 1 - T + 84 T^{2} + 107 T^{3} + 3407 T^{4} + 11204 T^{5} + 105304 T^{6} + 347324 T^{7} + 3274127 T^{8} + 3187637 T^{9} + 77575764 T^{10} - 28629151 T^{11} + 887503681 T^{12} \))(\( 1 + 19 T + 220 T^{2} + 1479 T^{3} + 7378 T^{4} + 24313 T^{5} + 98263 T^{6} + 386138 T^{7} + 3046153 T^{8} + 23364793 T^{9} + 219797998 T^{10} + 1365887559 T^{11} + 6298413220 T^{12} + 16862569939 T^{13} + 27512614111 T^{14} \))(\( 1 - 3 T + 108 T^{2} - 283 T^{3} + 6922 T^{4} - 18429 T^{5} + 294655 T^{6} - 669642 T^{7} + 9134305 T^{8} - 17710269 T^{9} + 206213302 T^{10} - 261356443 T^{11} + 3091948308 T^{12} - 2662511043 T^{13} + 27512614111 T^{14} \))(\( 1 + T + 89 T^{2} + 6 T^{3} + 3372 T^{4} - 9830 T^{5} + 76567 T^{6} - 684371 T^{7} + 1711558 T^{8} - 21215501 T^{9} + 73580887 T^{10} - 292845530 T^{11} + 3114112812 T^{12} + 171774906 T^{13} + 78987827609 T^{14} + 27512614111 T^{15} + 852891037441 T^{16} \))(\( 1 + 9 T + 79 T^{2} + 382 T^{3} + 1446 T^{4} + 4854 T^{5} + 9449 T^{6} - 76151 T^{7} - 291102 T^{8} - 2360681 T^{9} + 9080489 T^{10} + 144605514 T^{11} + 1335411366 T^{12} + 10936335682 T^{13} + 70112790799 T^{14} + 247613526999 T^{15} + 852891037441 T^{16} \))(\( 1 - 15 T + 273 T^{2} - 2596 T^{3} + 27084 T^{4} - 189138 T^{5} + 1460487 T^{6} - 8237389 T^{7} + 52912694 T^{8} - 255359059 T^{9} + 1403528007 T^{10} - 5634610158 T^{11} + 25012642764 T^{12} - 74321275996 T^{13} + 242288504913 T^{14} - 412689211665 T^{15} + 852891037441 T^{16} \))
$37$ (\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 - T + 70 T^{2} - 37 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 70 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 - 13 T + 112 T^{2} - 481 T^{3} + 1369 T^{4} \))(\( 1 + 11 T + 100 T^{2} + 407 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 51 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( 1 + 7 T + 79 T^{2} + 306 T^{3} + 2923 T^{4} + 9583 T^{5} + 50653 T^{6} \))(\( 1 + 14 T + 172 T^{2} + 1118 T^{3} + 6364 T^{4} + 19166 T^{5} + 50653 T^{6} \))(\( 1 - 10 T + 59 T^{2} - 102 T^{3} + 60 T^{4} - 3774 T^{5} + 80771 T^{6} - 506530 T^{7} + 1874161 T^{8} \))(\( 1 - 15 T + 137 T^{2} - 826 T^{3} + 4728 T^{4} - 30562 T^{5} + 187553 T^{6} - 759795 T^{7} + 1874161 T^{8} \))(\( 1 + 10 T + 125 T^{2} + 984 T^{3} + 6756 T^{4} + 36408 T^{5} + 171125 T^{6} + 506530 T^{7} + 1874161 T^{8} \))(\( 1 - 3 T + 71 T^{2} - 54 T^{3} + 2842 T^{4} - 1998 T^{5} + 97199 T^{6} - 151959 T^{7} + 1874161 T^{8} \))(\( 1 - 9 T + 119 T^{2} - 1024 T^{3} + 8109 T^{4} - 49469 T^{5} + 300033 T^{6} - 1401856 T^{7} + 6027707 T^{8} - 16867449 T^{9} + 69343957 T^{10} \))(\( 1 - 7 T + 145 T^{2} - 842 T^{3} + 10265 T^{4} - 51327 T^{5} + 461994 T^{6} - 1899099 T^{7} + 14052785 T^{8} - 42649826 T^{9} + 271753345 T^{10} - 485407699 T^{11} + 2565726409 T^{12} \))(\( 1 + 18 T + 243 T^{2} + 2064 T^{3} + 13554 T^{4} + 61166 T^{5} + 198486 T^{6} + 701672 T^{7} + 7343982 T^{8} + 83736254 T^{9} + 686550762 T^{10} + 3868268304 T^{11} + 16850581551 T^{12} + 46183075362 T^{13} + 94931877133 T^{14} \))(\( 1 - 5 T + 124 T^{2} - 703 T^{3} + 10192 T^{4} - 48303 T^{5} + 530823 T^{6} - 2259322 T^{7} + 19640451 T^{8} - 66126807 T^{9} + 516255376 T^{10} - 1317535183 T^{11} + 8598650668 T^{12} - 12828632045 T^{13} + 94931877133 T^{14} \))(\( 1 + 11 T + 226 T^{2} + 1803 T^{3} + 20923 T^{4} + 134628 T^{5} + 1171400 T^{6} + 6559782 T^{7} + 48561940 T^{8} + 242711934 T^{9} + 1603646600 T^{10} + 6819312084 T^{11} + 39213070603 T^{12} + 125027154471 T^{13} + 579854168434 T^{14} + 1044250648463 T^{15} + 3512479453921 T^{16} \))(\( 1 - 7 T + 128 T^{2} - 541 T^{3} + 7041 T^{4} - 19856 T^{5} + 287290 T^{6} - 682032 T^{7} + 10991528 T^{8} - 25235184 T^{9} + 393300010 T^{10} - 1005765968 T^{11} + 13195967601 T^{12} - 37515080737 T^{13} + 328412980352 T^{14} - 664523139931 T^{15} + 3512479453921 T^{16} \))(\( 1 - 22 T + 352 T^{2} - 4098 T^{3} + 40849 T^{4} - 345810 T^{5} + 2646836 T^{6} - 18170950 T^{7} + 115687748 T^{8} - 672325150 T^{9} + 3623518484 T^{10} - 17516313930 T^{11} + 76557602689 T^{12} - 284171535786 T^{13} + 903135695968 T^{14} - 2088501296926 T^{15} + 3512479453921 T^{16} \))
$41$ (\( 1 + 6 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 3 T + 80 T^{2} + 123 T^{3} + 1681 T^{4} \))(\( 1 + 74 T^{2} + 1681 T^{4} \))(\( 1 - 13 T + 120 T^{2} - 533 T^{3} + 1681 T^{4} \))(\( 1 - 9 T + 64 T^{2} - 369 T^{3} + 1681 T^{4} \))(\( 1 - 65 T^{2} + 1681 T^{4} \))(\( 1 + 8 T + 74 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 + 11 T + 115 T^{2} + 886 T^{3} + 4715 T^{4} + 18491 T^{5} + 68921 T^{6} \))(\( 1 + 10 T + 152 T^{2} + 842 T^{3} + 6232 T^{4} + 16810 T^{5} + 68921 T^{6} \))(\( 1 - 6 T + 143 T^{2} - 694 T^{3} + 8360 T^{4} - 28454 T^{5} + 240383 T^{6} - 413526 T^{7} + 2825761 T^{8} \))(\( 1 - T + 89 T^{2} + 42 T^{3} + 4370 T^{4} + 1722 T^{5} + 149609 T^{6} - 68921 T^{7} + 2825761 T^{8} \))(\( 1 + 4 T + 117 T^{2} + 216 T^{3} + 5900 T^{4} + 8856 T^{5} + 196677 T^{6} + 275684 T^{7} + 2825761 T^{8} \))(\( 1 - 11 T + 153 T^{2} - 1330 T^{3} + 9186 T^{4} - 54530 T^{5} + 257193 T^{6} - 758131 T^{7} + 2825761 T^{8} \))(\( 1 - 5 T + 169 T^{2} - 608 T^{3} + 12377 T^{4} - 33861 T^{5} + 507457 T^{6} - 1022048 T^{7} + 11647649 T^{8} - 14128805 T^{9} + 115856201 T^{10} \))(\( 1 - 13 T + 165 T^{2} - 1194 T^{3} + 9229 T^{4} - 55617 T^{5} + 387642 T^{6} - 2280297 T^{7} + 15513949 T^{8} - 82291674 T^{9} + 466250565 T^{10} - 1506130613 T^{11} + 4750104241 T^{12} \))(\( 1 - 4 T + 155 T^{2} - 598 T^{3} + 13564 T^{4} - 49070 T^{5} + 790272 T^{6} - 2430224 T^{7} + 32401152 T^{8} - 82486670 T^{9} + 934844444 T^{10} - 1689805078 T^{11} + 17957711155 T^{12} - 19000416964 T^{13} + 194754273881 T^{14} \))(\( 1 - 25 T + 386 T^{2} - 3905 T^{3} + 29516 T^{4} - 161567 T^{5} + 728617 T^{6} - 3510126 T^{7} + 29873297 T^{8} - 271594127 T^{9} + 2034272236 T^{10} - 11034596705 T^{11} + 44720493586 T^{12} - 118752606025 T^{13} + 194754273881 T^{14} \))(\( 1 + 17 T + 298 T^{2} + 3055 T^{3} + 31995 T^{4} + 245016 T^{5} + 1994164 T^{6} + 12858016 T^{7} + 91409676 T^{8} + 527178656 T^{9} + 3352189684 T^{10} + 16886747736 T^{11} + 90410223195 T^{12} + 353940694055 T^{13} + 1415531063818 T^{14} + 3310822655977 T^{15} + 7984925229121 T^{16} \))(\( 1 - 3 T + 178 T^{2} - 85 T^{3} + 12967 T^{4} + 38400 T^{5} + 522424 T^{6} + 4049448 T^{7} + 18123068 T^{8} + 166027368 T^{9} + 878194744 T^{10} + 2646566400 T^{11} + 36641642887 T^{12} - 9847777085 T^{13} + 845518554898 T^{14} - 584262821643 T^{15} + 7984925229121 T^{16} \))(\( 1 + 8 T + 194 T^{2} + 1052 T^{3} + 17737 T^{4} + 77524 T^{5} + 1130186 T^{6} + 4344968 T^{7} + 54209140 T^{8} + 178143688 T^{9} + 1899842666 T^{10} + 5343031604 T^{11} + 50120522857 T^{12} + 121880723452 T^{13} + 921520222754 T^{14} + 1558034191048 T^{15} + 7984925229121 T^{16} \))
$43$ (\( 1 + 2 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 11 T + 43 T^{2} \))(\( 1 - 11 T + 78 T^{2} - 473 T^{3} + 1849 T^{4} \))(\( 1 - 8 T + 84 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 - 9 T + 102 T^{2} - 387 T^{3} + 1849 T^{4} \))(\( 1 + 10 T + 94 T^{2} + 430 T^{3} + 1849 T^{4} \))(\( 1 + 10 T + 63 T^{2} + 430 T^{3} + 1849 T^{4} \))(\( 1 - 20 T + 180 T^{2} - 860 T^{3} + 1849 T^{4} \))(\( 1 - 4 T + 51 T^{2} - 524 T^{3} + 2193 T^{4} - 7396 T^{5} + 79507 T^{6} \))(\( 1 + 6 T + 134 T^{2} + 512 T^{3} + 5762 T^{4} + 11094 T^{5} + 79507 T^{6} \))(\( 1 - 14 T + 201 T^{2} - 1690 T^{3} + 13464 T^{4} - 72670 T^{5} + 371649 T^{6} - 1113098 T^{7} + 3418801 T^{8} \))(\( 1 - 4 T - 36 T^{2} - 20 T^{3} + 3558 T^{4} - 860 T^{5} - 66564 T^{6} - 318028 T^{7} + 3418801 T^{8} \))(\( 1 + 14 T + 213 T^{2} + 1822 T^{3} + 14600 T^{4} + 78346 T^{5} + 393837 T^{6} + 1113098 T^{7} + 3418801 T^{8} \))(\( 1 - 10 T + 144 T^{2} - 962 T^{3} + 8270 T^{4} - 41366 T^{5} + 266256 T^{6} - 795070 T^{7} + 3418801 T^{8} \))(\( 1 + 16 T + 280 T^{2} + 2730 T^{3} + 26615 T^{4} + 175444 T^{5} + 1144445 T^{6} + 5047770 T^{7} + 22261960 T^{8} + 54700816 T^{9} + 147008443 T^{10} \))(\( 1 + 219 T^{2} + 50 T^{3} + 21199 T^{4} + 6070 T^{5} + 1172466 T^{6} + 261010 T^{7} + 39196951 T^{8} + 3975350 T^{9} + 748717419 T^{10} + 6321363049 T^{12} \))(\( 1 + 9 T + 97 T^{2} + 242 T^{3} + 3553 T^{4} + 1999 T^{5} + 83529 T^{6} - 656164 T^{7} + 3591747 T^{8} + 3696151 T^{9} + 282488371 T^{10} + 827349842 T^{11} + 14259818971 T^{12} + 56892267441 T^{13} + 271818611107 T^{14} \))(\( 1 - 20 T + 371 T^{2} - 4284 T^{3} + 46807 T^{4} - 390556 T^{5} + 3171125 T^{6} - 20952040 T^{7} + 136358375 T^{8} - 722138044 T^{9} + 3721484149 T^{10} - 14646143484 T^{11} + 54540132353 T^{12} - 126427260980 T^{13} + 271818611107 T^{14} \))(\( 1 + 10 T + 185 T^{2} + 1458 T^{3} + 14574 T^{4} + 95914 T^{5} + 710911 T^{6} + 4244050 T^{7} + 29600770 T^{8} + 182494150 T^{9} + 1314474439 T^{10} + 7625834398 T^{11} + 49825605774 T^{12} + 214338309894 T^{13} + 1169452164065 T^{14} + 2718186111070 T^{15} + 11688200277601 T^{16} \))(\( 1 - 16 T + 269 T^{2} - 2994 T^{3} + 34966 T^{4} - 306106 T^{5} + 2700755 T^{6} - 19504080 T^{7} + 141734978 T^{8} - 838675440 T^{9} + 4993695995 T^{10} - 24337569742 T^{11} + 119541795766 T^{12} - 440143278342 T^{13} + 1700446660181 T^{14} - 4349097777712 T^{15} + 11688200277601 T^{16} \))(\( 1 + T + 216 T^{2} - 27 T^{3} + 23428 T^{4} - 14131 T^{5} + 1664632 T^{6} - 1274687 T^{7} + 83748086 T^{8} - 54811541 T^{9} + 3077904568 T^{10} - 1123513417 T^{11} + 80095669828 T^{12} - 3969227961 T^{13} + 1365414418584 T^{14} + 271818611107 T^{15} + 11688200277601 T^{16} \))
$47$ (\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 11 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 13 T + 47 T^{2} \))(\( 1 - 9 T + 110 T^{2} - 423 T^{3} + 2209 T^{4} \))(\( 1 - 34 T^{2} + 2209 T^{4} \))(\( 1 - 5 T + 62 T^{2} - 235 T^{3} + 2209 T^{4} \))(\( 1 - 14 T + 126 T^{2} - 658 T^{3} + 2209 T^{4} \))(\( 1 - 2 T - 13 T^{2} - 94 T^{3} + 2209 T^{4} \))(\( ( 1 - 4 T + 47 T^{2} )^{2} \))(\( 1 + 10 T + 125 T^{2} + 844 T^{3} + 5875 T^{4} + 22090 T^{5} + 103823 T^{6} \))(\( 1 + 14 T + 146 T^{2} + 1300 T^{3} + 6862 T^{4} + 30926 T^{5} + 103823 T^{6} \))(\( 1 - 10 T + 213 T^{2} - 1418 T^{3} + 15588 T^{4} - 66646 T^{5} + 470517 T^{6} - 1038230 T^{7} + 4879681 T^{8} \))(\( 1 - 6 T + 148 T^{2} - 810 T^{3} + 9670 T^{4} - 38070 T^{5} + 326932 T^{6} - 622938 T^{7} + 4879681 T^{8} \))(\( 1 - 6 T + 169 T^{2} - 834 T^{3} + 11484 T^{4} - 39198 T^{5} + 373321 T^{6} - 622938 T^{7} + 4879681 T^{8} \))(\( 1 - 10 T + 100 T^{2} - 278 T^{3} + 2646 T^{4} - 13066 T^{5} + 220900 T^{6} - 1038230 T^{7} + 4879681 T^{8} \))(\( 1 - 8 T + 48 T^{2} - 274 T^{3} + 1907 T^{4} - 25496 T^{5} + 89629 T^{6} - 605266 T^{7} + 4983504 T^{8} - 39037448 T^{9} + 229345007 T^{10} \))(\( 1 - 22 T + 443 T^{2} - 5526 T^{3} + 62811 T^{4} - 533680 T^{5} + 4153682 T^{6} - 25082960 T^{7} + 138749499 T^{8} - 573725898 T^{9} + 2161698683 T^{10} - 5045590154 T^{11} + 10779215329 T^{12} \))(\( 1 + 11 T + 261 T^{2} + 1882 T^{3} + 27069 T^{4} + 147189 T^{5} + 1731081 T^{6} + 7894028 T^{7} + 81360807 T^{8} + 325140501 T^{9} + 2810384787 T^{10} + 9183559642 T^{11} + 59859046827 T^{12} + 118571368619 T^{13} + 506623120463 T^{14} \))(\( 1 + 193 T^{2} + 148 T^{3} + 19597 T^{4} + 17136 T^{5} + 1313197 T^{6} + 1057272 T^{7} + 61720259 T^{8} + 37853424 T^{9} + 2034619331 T^{10} + 722192788 T^{11} + 44263586351 T^{12} + 506623120463 T^{14} \))(\( 1 + 26 T + 457 T^{2} + 5922 T^{3} + 65470 T^{4} + 628070 T^{5} + 5499191 T^{6} + 43324526 T^{7} + 312994370 T^{8} + 2036252722 T^{9} + 12147712919 T^{10} + 65208111610 T^{11} + 319472715070 T^{12} + 1358181131454 T^{13} + 4926101405353 T^{14} + 13172201132038 T^{15} + 23811286661761 T^{16} \))(\( 1 - 24 T + 449 T^{2} - 6138 T^{3} + 72934 T^{4} - 736450 T^{5} + 6670735 T^{6} - 53290128 T^{7} + 387139666 T^{8} - 2504636016 T^{9} + 14735653615 T^{10} - 76460448350 T^{11} + 355894654054 T^{12} - 1407719652966 T^{13} + 4839867682721 T^{14} - 12158954891112 T^{15} + 23811286661761 T^{16} \))(\( 1 + 9 T + 304 T^{2} + 2189 T^{3} + 41456 T^{4} + 247729 T^{5} + 3441408 T^{6} + 17318733 T^{7} + 193709886 T^{8} + 813980451 T^{9} + 7602070272 T^{10} + 25719967967 T^{11} + 202292055536 T^{12} + 502036220323 T^{13} + 3276881460016 T^{14} + 4559608084167 T^{15} + 23811286661761 T^{16} \))
$53$ (\( 1 + 6 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 8 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( ( 1 + 2 T + 53 T^{2} )^{2} \))(\( ( 1 - 4 T + 53 T^{2} )^{2} \))(\( 1 - 6 T + 98 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( 1 - 12 T + 130 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( 1 + 8 T + 98 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( 1 + 2 T + 111 T^{2} + 148 T^{3} + 5883 T^{4} + 5618 T^{5} + 148877 T^{6} \))(\( 1 + 10 T + 31 T^{2} + 84 T^{3} + 1643 T^{4} + 28090 T^{5} + 148877 T^{6} \))(\( 1 - 4 T + 112 T^{2} - 956 T^{3} + 5998 T^{4} - 50668 T^{5} + 314608 T^{6} - 595508 T^{7} + 7890481 T^{8} \))(\( 1 - 2 T + 104 T^{2} - 258 T^{3} + 5462 T^{4} - 13674 T^{5} + 292136 T^{6} - 297754 T^{7} + 7890481 T^{8} \))(\( 1 + 30 T + 480 T^{2} + 5282 T^{3} + 43886 T^{4} + 279946 T^{5} + 1348320 T^{6} + 4466310 T^{7} + 7890481 T^{8} \))(\( 1 - 24 T + 248 T^{2} - 1316 T^{3} + 6254 T^{4} - 69748 T^{5} + 696632 T^{6} - 3573048 T^{7} + 7890481 T^{8} \))(\( 1 + 4 T + 109 T^{2} + 532 T^{3} + 6806 T^{4} + 29440 T^{5} + 360718 T^{6} + 1494388 T^{7} + 16227593 T^{8} + 31561924 T^{9} + 418195493 T^{10} \))(\( 1 - 10 T + 230 T^{2} - 1882 T^{3} + 23799 T^{4} - 163908 T^{5} + 1527284 T^{6} - 8687124 T^{7} + 66851391 T^{8} - 280186514 T^{9} + 1814810630 T^{10} - 4181954930 T^{11} + 22164361129 T^{12} \))(\( 1 - 8 T + 131 T^{2} - 1092 T^{3} + 13885 T^{4} - 83832 T^{5} + 914503 T^{6} - 5669496 T^{7} + 48468659 T^{8} - 235484088 T^{9} + 2067157145 T^{10} - 8616405252 T^{11} + 54783609583 T^{12} - 177314889032 T^{13} + 1174711139837 T^{14} \))(\( 1 + 4 T + 235 T^{2} + 1148 T^{3} + 28293 T^{4} + 130940 T^{5} + 2232023 T^{6} + 8645640 T^{7} + 118297219 T^{8} + 367810460 T^{9} + 4212176961 T^{10} + 9058272188 T^{11} + 98275940855 T^{12} + 88657444516 T^{13} + 1174711139837 T^{14} \))(\( 1 + 2 T + 184 T^{2} + 298 T^{3} + 20580 T^{4} + 25998 T^{5} + 1608712 T^{6} + 1735078 T^{7} + 97850646 T^{8} + 91959134 T^{9} + 4518872008 T^{10} + 3870504246 T^{11} + 162386098980 T^{12} + 124622256914 T^{13} + 4078242447736 T^{14} + 2349422279674 T^{15} + 62259690411361 T^{16} \))(\( 1 - 8 T + 292 T^{2} - 1780 T^{3} + 40676 T^{4} - 209220 T^{5} + 3660732 T^{6} - 16048752 T^{7} + 229566358 T^{8} - 850583856 T^{9} + 10282996188 T^{10} - 31148045940 T^{11} + 320953205156 T^{12} - 744387977540 T^{13} + 6471993449668 T^{14} - 9397689118696 T^{15} + 62259690411361 T^{16} \))(\( 1 - 14 T + 300 T^{2} - 2958 T^{3} + 38988 T^{4} - 313626 T^{5} + 3319444 T^{6} - 23179914 T^{7} + 206455430 T^{8} - 1228535442 T^{9} + 9324318196 T^{10} - 46691698002 T^{11} + 307634073228 T^{12} - 1237022268294 T^{13} + 6649308338700 T^{14} - 16445955957718 T^{15} + 62259690411361 T^{16} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 + 5 T + 59 T^{2} \))(\( 1 + 7 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + 9 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 11 T + 59 T^{2} \))(\( 1 + 5 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - T + 114 T^{2} - 59 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 126 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 + 5 T + 86 T^{2} + 295 T^{3} + 3481 T^{4} \))(\( 1 - 5 T + 18 T^{2} - 295 T^{3} + 3481 T^{4} \))(\( 1 - 14 T + 155 T^{2} - 826 T^{3} + 3481 T^{4} \))(\( 1 + 94 T^{2} + 3481 T^{4} \))(\( 1 - 23 T + 341 T^{2} - 3074 T^{3} + 20119 T^{4} - 80063 T^{5} + 205379 T^{6} \))(\( 1 - 10 T + 58 T^{2} - 24 T^{3} + 3422 T^{4} - 34810 T^{5} + 205379 T^{6} \))(\( 1 + 22 T + 373 T^{2} + 4094 T^{3} + 36940 T^{4} + 241546 T^{5} + 1298413 T^{6} + 4518338 T^{7} + 12117361 T^{8} \))(\( 1 + 13 T + 219 T^{2} + 1544 T^{3} + 16476 T^{4} + 91096 T^{5} + 762339 T^{6} + 2669927 T^{7} + 12117361 T^{8} \))(\( 1 + 2 T + 153 T^{2} + 138 T^{3} + 11924 T^{4} + 8142 T^{5} + 532593 T^{6} + 410758 T^{7} + 12117361 T^{8} \))(\( 1 - T + 107 T^{2} - 360 T^{3} + 6260 T^{4} - 21240 T^{5} + 372467 T^{6} - 205379 T^{7} + 12117361 T^{8} \))(\( 1 - 23 T + 421 T^{2} - 5154 T^{3} + 55025 T^{4} - 451553 T^{5} + 3246475 T^{6} - 17941074 T^{7} + 86464559 T^{8} - 278699303 T^{9} + 714924299 T^{10} \))(\( 1 - 17 T + 245 T^{2} - 1866 T^{3} + 13171 T^{4} - 39341 T^{5} + 274958 T^{6} - 2321119 T^{7} + 45848251 T^{8} - 383237214 T^{9} + 2968753445 T^{10} - 12153713083 T^{11} + 42180533641 T^{12} \))(\( 1 - 12 T + 295 T^{2} - 2984 T^{3} + 43884 T^{4} - 358012 T^{5} + 3935974 T^{6} - 26495200 T^{7} + 232222466 T^{8} - 1246239772 T^{9} + 9012852036 T^{10} - 36158205224 T^{11} + 210902668205 T^{12} - 506166403692 T^{13} + 2488651484819 T^{14} \))(\( 1 + 17 T + 420 T^{2} + 5053 T^{3} + 72670 T^{4} + 669603 T^{5} + 6997663 T^{6} + 50801054 T^{7} + 412862117 T^{8} + 2330888043 T^{9} + 14924891930 T^{10} + 61229025133 T^{11} + 300268205580 T^{12} + 717069071897 T^{13} + 2488651484819 T^{14} \))(\( 1 + 25 T + 382 T^{2} + 4743 T^{3} + 54617 T^{4} + 590176 T^{5} + 5671518 T^{6} + 48070994 T^{7} + 379541188 T^{8} + 2836188646 T^{9} + 19742554158 T^{10} + 121209756704 T^{11} + 661813905737 T^{12} + 3390885950157 T^{13} + 16112963850862 T^{14} + 62216287120475 T^{15} + 146830437604321 T^{16} \))(\( 1 + 3 T + 150 T^{2} + 349 T^{3} + 13673 T^{4} + 12544 T^{5} + 816478 T^{6} - 190746 T^{7} + 48114580 T^{8} - 11254014 T^{9} + 2842159918 T^{10} + 2576274176 T^{11} + 165680676953 T^{12} + 249508580351 T^{13} + 6327080046150 T^{14} + 7465954454457 T^{15} + 146830437604321 T^{16} \))(\( 1 + 4 T + 222 T^{2} + 896 T^{3} + 27357 T^{4} + 102548 T^{5} + 2428622 T^{6} + 8399528 T^{7} + 163415196 T^{8} + 495572152 T^{9} + 8454033182 T^{10} + 21061205692 T^{11} + 331494644877 T^{12} + 640572171904 T^{13} + 9364078468302 T^{14} + 9954605939276 T^{15} + 146830437604321 T^{16} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 3 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 2 T + 106 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( 1 + 4 T + 94 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( 1 + 15 T + 140 T^{2} + 915 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 30 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( 1 + 4 T + 102 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 7 T + 187 T^{2} + 834 T^{3} + 11407 T^{4} + 26047 T^{5} + 226981 T^{6} \))(\( 1 + 18 T + 155 T^{2} + 988 T^{3} + 9455 T^{4} + 66978 T^{5} + 226981 T^{6} \))(\( 1 - 28 T + 432 T^{2} - 4484 T^{3} + 38094 T^{4} - 273524 T^{5} + 1607472 T^{6} - 6355468 T^{7} + 13845841 T^{8} \))(\( 1 + 13 T + 301 T^{2} + 2478 T^{3} + 29336 T^{4} + 151158 T^{5} + 1120021 T^{6} + 2950753 T^{7} + 13845841 T^{8} \))(\( 1 + 2 T + 92 T^{2} + 310 T^{3} + 3862 T^{4} + 18910 T^{5} + 342332 T^{6} + 453962 T^{7} + 13845841 T^{8} \))(\( 1 - 3 T + 79 T^{2} - 166 T^{3} + 7406 T^{4} - 10126 T^{5} + 293959 T^{6} - 680943 T^{7} + 13845841 T^{8} \))(\( 1 - 7 T + 54 T^{2} - 1097 T^{3} + 8949 T^{4} - 35032 T^{5} + 545889 T^{6} - 4081937 T^{7} + 12256974 T^{8} - 96920887 T^{9} + 844596301 T^{10} \))(\( 1 - T + 172 T^{2} - 153 T^{3} + 15631 T^{4} - 26114 T^{5} + 1085944 T^{6} - 1592954 T^{7} + 58162951 T^{8} - 34728093 T^{9} + 2381484652 T^{10} - 844596301 T^{11} + 51520374361 T^{12} \))(\( 1 + 5 T + 296 T^{2} + 1087 T^{3} + 41592 T^{4} + 118235 T^{5} + 3693539 T^{6} + 8582258 T^{7} + 225305879 T^{8} + 439952435 T^{9} + 9440593752 T^{10} + 15050429167 T^{11} + 250000505096 T^{12} + 257601871805 T^{13} + 3142742836021 T^{14} \))(\( 1 - 5 T + 340 T^{2} - 1419 T^{3} + 53696 T^{4} - 187719 T^{5} + 5080663 T^{6} - 14587154 T^{7} + 309920443 T^{8} - 698502399 T^{9} + 12187971776 T^{10} - 19647248379 T^{11} + 287162742340 T^{12} - 257601871805 T^{13} + 3142742836021 T^{14} \))(\( 1 - 3 T + 257 T^{2} - 320 T^{3} + 31936 T^{4} - 19322 T^{5} + 2892351 T^{6} - 2207999 T^{7} + 204160846 T^{8} - 134687939 T^{9} + 10762438071 T^{10} - 4385726882 T^{11} + 442180778176 T^{12} - 270270816320 T^{13} + 13240736210777 T^{14} - 9428228508063 T^{15} + 191707312997281 T^{16} \))(\( 1 - 31 T + 643 T^{2} - 9466 T^{3} + 118324 T^{4} - 1268360 T^{5} + 12490781 T^{6} - 110698579 T^{7} + 910240006 T^{8} - 6752613319 T^{9} + 46478196101 T^{10} - 287893621160 T^{11} + 1638295290484 T^{12} - 7994948585266 T^{13} + 33127600714123 T^{14} - 97425027916651 T^{15} + 191707312997281 T^{16} \))(\( 1 - 13 T + 509 T^{2} - 5236 T^{3} + 110804 T^{4} - 921462 T^{5} + 13630243 T^{6} - 91869197 T^{7} + 1041659494 T^{8} - 5604021017 T^{9} + 50718134203 T^{10} - 209154366222 T^{11} + 1534174566164 T^{12} - 4422306232036 T^{13} + 26223870549749 T^{14} - 40855656868273 T^{15} + 191707312997281 T^{16} \))
$67$ (\( 1 - 16 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 16 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( 1 - 12 T + 98 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 - 6 T + 126 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 + 5 T + 102 T^{2} + 335 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 158 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( ( 1 - 2 T + 67 T^{2} )^{2} \))(\( 1 + 7 T + 205 T^{2} + 918 T^{3} + 13735 T^{4} + 31423 T^{5} + 300763 T^{6} \))(\( 1 + 28 T + 433 T^{2} + 4264 T^{3} + 29011 T^{4} + 125692 T^{5} + 300763 T^{6} \))(\( 1 - 24 T + 332 T^{2} - 3608 T^{3} + 32886 T^{4} - 241736 T^{5} + 1490348 T^{6} - 7218312 T^{7} + 20151121 T^{8} \))(\( 1 + 13 T + 143 T^{2} + 134 T^{3} + 916 T^{4} + 8978 T^{5} + 641927 T^{6} + 3909919 T^{7} + 20151121 T^{8} \))(\( 1 + 2 T + 248 T^{2} + 370 T^{3} + 24286 T^{4} + 24790 T^{5} + 1113272 T^{6} + 601526 T^{7} + 20151121 T^{8} \))(\( 1 - 7 T + 125 T^{2} + 210 T^{3} + 3450 T^{4} + 14070 T^{5} + 561125 T^{6} - 2105341 T^{7} + 20151121 T^{8} \))(\( 1 - 5 T + 178 T^{2} - 381 T^{3} + 16941 T^{4} - 29612 T^{5} + 1135047 T^{6} - 1710309 T^{7} + 53535814 T^{8} - 100755605 T^{9} + 1350125107 T^{10} \))(\( 1 - 3 T + 244 T^{2} - 697 T^{3} + 30199 T^{4} - 78874 T^{5} + 2432664 T^{6} - 5284558 T^{7} + 135563311 T^{8} - 209631811 T^{9} + 4916873524 T^{10} - 4050375321 T^{11} + 90458382169 T^{12} \))(\( 1 + 13 T + 306 T^{2} + 2885 T^{3} + 42008 T^{4} + 341339 T^{5} + 3948099 T^{6} + 27861510 T^{7} + 264522633 T^{8} + 1532270771 T^{9} + 12634452104 T^{10} + 58135984085 T^{11} + 413138282742 T^{12} + 1175958968197 T^{13} + 6060711605323 T^{14} \))(\( 1 - 15 T + 378 T^{2} - 4975 T^{3} + 66408 T^{4} - 740105 T^{5} + 6961363 T^{6} - 63504594 T^{7} + 466411321 T^{8} - 3322331345 T^{9} + 19973069304 T^{10} - 100251826975 T^{11} + 510347290446 T^{12} - 1356875732535 T^{13} + 6060711605323 T^{14} \))(\( 1 - T + 169 T^{2} + 160 T^{3} + 17638 T^{4} + 14422 T^{5} + 1486335 T^{6} + 266089 T^{7} + 109608914 T^{8} + 17827963 T^{9} + 6672157815 T^{10} + 4337603986 T^{11} + 355425472198 T^{12} + 216020017120 T^{13} + 15287466586561 T^{14} - 6060711605323 T^{15} + 406067677556641 T^{16} \))(\( 1 + 11 T + 233 T^{2} + 1726 T^{3} + 28104 T^{4} + 179316 T^{5} + 2485199 T^{6} + 13095181 T^{7} + 173475598 T^{8} + 877377127 T^{9} + 11156058311 T^{10} + 53931618108 T^{11} + 566327104584 T^{12} + 2330315934682 T^{13} + 21076803045377 T^{14} + 66667827658553 T^{15} + 406067677556641 T^{16} \))(\( 1 + 3 T + 281 T^{2} - 216 T^{3} + 37366 T^{4} - 107138 T^{5} + 3826511 T^{6} - 10693043 T^{7} + 304683698 T^{8} - 716433881 T^{9} + 17177207879 T^{10} - 32223146294 T^{11} + 752966787286 T^{12} - 291627023112 T^{13} + 25418805389489 T^{14} + 18182134815969 T^{15} + 406067677556641 T^{16} \))
$71$ (\( 1 + 8 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 5 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 10 T + 71 T^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( 1 + 4 T + 74 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( 1 + 9 T + 158 T^{2} + 639 T^{3} + 5041 T^{4} \))(\( 1 + 6 T + 76 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 + 12 T + 154 T^{2} + 852 T^{3} + 5041 T^{4} \))(\( 1 + 15 T + 181 T^{2} + 1326 T^{3} + 12851 T^{4} + 75615 T^{5} + 357911 T^{6} \))(\( 1 - 34 T + 591 T^{2} - 6204 T^{3} + 41961 T^{4} - 171394 T^{5} + 357911 T^{6} \))(\( 1 - 28 T + 462 T^{2} - 5068 T^{3} + 46754 T^{4} - 359828 T^{5} + 2328942 T^{6} - 10021508 T^{7} + 25411681 T^{8} \))(\( 1 + 15 T + 215 T^{2} + 1804 T^{3} + 16664 T^{4} + 128084 T^{5} + 1083815 T^{6} + 5368665 T^{7} + 25411681 T^{8} \))(\( 1 - 10 T + 82 T^{2} - 962 T^{3} + 13978 T^{4} - 68302 T^{5} + 413362 T^{6} - 3579110 T^{7} + 25411681 T^{8} \))(\( 1 + 13 T + 247 T^{2} + 2036 T^{3} + 24016 T^{4} + 144556 T^{5} + 1245127 T^{6} + 4652843 T^{7} + 25411681 T^{8} \))(\( 1 + 21 T + 452 T^{2} + 5785 T^{3} + 69929 T^{4} + 608650 T^{5} + 4964959 T^{6} + 29162185 T^{7} + 161775772 T^{8} + 533645301 T^{9} + 1804229351 T^{10} \))(\( 1 - 11 T + 344 T^{2} - 2579 T^{3} + 48599 T^{4} - 277464 T^{5} + 4173216 T^{6} - 19699944 T^{7} + 244987559 T^{8} - 923052469 T^{9} + 8741618264 T^{10} - 19846522861 T^{11} + 128100283921 T^{12} \))(\( 1 + T + 272 T^{2} + 1253 T^{3} + 33218 T^{4} + 278403 T^{5} + 2689531 T^{6} + 27799598 T^{7} + 190956701 T^{8} + 1403429523 T^{9} + 11889087598 T^{10} + 31840836293 T^{11} + 490750383472 T^{12} + 128100283921 T^{13} + 9095120158391 T^{14} \))(\( 1 - 15 T + 392 T^{2} - 3679 T^{3} + 58458 T^{4} - 408289 T^{5} + 5414907 T^{6} - 32164450 T^{7} + 384458397 T^{8} - 2058184849 T^{9} + 20922761238 T^{10} - 93489574399 T^{11} + 707257905592 T^{12} - 1921504258815 T^{13} + 9095120158391 T^{14} \))(\( 1 + 27 T + 501 T^{2} + 5942 T^{3} + 59960 T^{4} + 486414 T^{5} + 4067907 T^{6} + 31459219 T^{7} + 274745214 T^{8} + 2233604549 T^{9} + 20506319187 T^{10} + 174092921154 T^{11} + 1523684392760 T^{12} + 10720730803642 T^{13} + 64178242244421 T^{14} + 245568244276557 T^{15} + 645753531245761 T^{16} \))(\( 1 - 7 T + 399 T^{2} - 2354 T^{3} + 77214 T^{4} - 388770 T^{5} + 9468465 T^{6} - 40765031 T^{7} + 800730306 T^{8} - 2894317201 T^{9} + 47730532065 T^{10} - 139145059470 T^{11} + 1962137536734 T^{12} - 4247155892254 T^{13} + 51112013284479 T^{14} - 63665841108737 T^{15} + 645753531245761 T^{16} \))(\( 1 - 7 T + 317 T^{2} - 2068 T^{3} + 46432 T^{4} - 298298 T^{5} + 4360091 T^{6} - 28261253 T^{7} + 327322606 T^{8} - 2006548963 T^{9} + 21979218731 T^{10} - 106764135478 T^{11} + 1179915172192 T^{12} - 3731146297868 T^{13} + 40607790002957 T^{14} - 63665841108737 T^{15} + 645753531245761 T^{16} \))
$73$ (\( 1 - 14 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( 1 - 12 T + 110 T^{2} - 876 T^{3} + 5329 T^{4} \))(\( 1 + 8 T + 94 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( 1 + 14 T + 178 T^{2} + 1022 T^{3} + 5329 T^{4} \))(\( 1 + 12 T + 134 T^{2} + 876 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 126 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 159 T^{2} + 440 T^{3} + 11607 T^{4} + 21316 T^{5} + 389017 T^{6} \))(\( ( 1 - 2 T + 73 T^{2} )^{3} \))(\( 1 + 92 T^{2} - 512 T^{3} + 3558 T^{4} - 37376 T^{5} + 490268 T^{6} + 28398241 T^{8} \))(\( 1 + 22 T + 388 T^{2} + 4710 T^{3} + 45518 T^{4} + 343830 T^{5} + 2067652 T^{6} + 8558374 T^{7} + 28398241 T^{8} \))(\( 1 + 12 T + 260 T^{2} + 2132 T^{3} + 27030 T^{4} + 155636 T^{5} + 1385540 T^{6} + 4668204 T^{7} + 28398241 T^{8} \))(\( 1 + 2 T + 140 T^{2} + 474 T^{3} + 12990 T^{4} + 34602 T^{5} + 746060 T^{6} + 778034 T^{7} + 28398241 T^{8} \))(\( 1 + 8 T + 49 T^{2} + 28 T^{3} + 7398 T^{4} + 71192 T^{5} + 540054 T^{6} + 149212 T^{7} + 19061833 T^{8} + 227185928 T^{9} + 2073071593 T^{10} \))(\( 1 + 282 T^{2} - 480 T^{3} + 35775 T^{4} - 105760 T^{5} + 2995564 T^{6} - 7720480 T^{7} + 190644975 T^{8} - 186728160 T^{9} + 8008303962 T^{10} + 151334226289 T^{12} \))(\( 1 + 26 T + 591 T^{2} + 9160 T^{3} + 130901 T^{4} + 1497526 T^{5} + 15859371 T^{6} + 140404368 T^{7} + 1157734083 T^{8} + 7980316054 T^{9} + 50922714317 T^{10} + 260127887560 T^{11} + 1225185311463 T^{12} + 3934689883514 T^{13} + 11047398519097 T^{14} \))(\( 1 - 14 T + 463 T^{2} - 5200 T^{3} + 92565 T^{4} - 854242 T^{5} + 10684267 T^{6} - 80209088 T^{7} + 779951491 T^{8} - 4552255618 T^{9} + 36009358605 T^{10} - 147670853200 T^{11} + 959832147559 T^{12} - 2118679168046 T^{13} + 11047398519097 T^{14} \))(\( 1 - 16 T + 428 T^{2} - 4396 T^{3} + 69276 T^{4} - 520252 T^{5} + 6654516 T^{6} - 41620584 T^{7} + 510058182 T^{8} - 3038302632 T^{9} + 35461915764 T^{10} - 202386872284 T^{11} + 1967316543516 T^{12} - 9113222722828 T^{13} + 64771048851692 T^{14} - 176758376305552 T^{15} + 806460091894081 T^{16} \))(\( 1 - 14 T + 240 T^{2} - 2054 T^{3} + 23828 T^{4} - 200586 T^{5} + 2457648 T^{6} - 19847266 T^{7} + 214335958 T^{8} - 1448850418 T^{9} + 13096806192 T^{10} - 78031363962 T^{11} + 676673286548 T^{12} - 4258089052022 T^{13} + 36320214309360 T^{14} - 154663579267358 T^{15} + 806460091894081 T^{16} \))(\( 1 - 16 T + 356 T^{2} - 4196 T^{3} + 53148 T^{4} - 507284 T^{5} + 4711356 T^{6} - 40976280 T^{7} + 340756294 T^{8} - 2991268440 T^{9} + 25106816124 T^{10} - 197342099828 T^{11} + 1509309712668 T^{12} - 8698608404228 T^{13} + 53874984558884 T^{14} - 176758376305552 T^{15} + 806460091894081 T^{16} \))
$79$ (\( 1 - 8 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 16 T + 154 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 - 20 T + 226 T^{2} - 1580 T^{3} + 6241 T^{4} \))(\( 1 - 8 T + 106 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 - 10 T + 166 T^{2} - 790 T^{3} + 6241 T^{4} \))(\( 1 + 10 T + 36 T^{2} + 790 T^{3} + 6241 T^{4} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( 1 + 6 T + 193 T^{2} + 748 T^{3} + 15247 T^{4} + 37446 T^{5} + 493039 T^{6} \))(\( 1 + 6 T + 111 T^{2} + 1276 T^{3} + 8769 T^{4} + 37446 T^{5} + 493039 T^{6} \))(\( 1 - 12 T + 214 T^{2} - 2500 T^{3} + 23066 T^{4} - 197500 T^{5} + 1335574 T^{6} - 5916468 T^{7} + 38950081 T^{8} \))(\( 1 + 26 T + 516 T^{2} + 6574 T^{3} + 69294 T^{4} + 519346 T^{5} + 3220356 T^{6} + 12819014 T^{7} + 38950081 T^{8} \))(\( 1 + 18 T + 414 T^{2} + 4386 T^{3} + 52746 T^{4} + 346494 T^{5} + 2583774 T^{6} + 8874702 T^{7} + 38950081 T^{8} \))(\( 1 + 22 T + 396 T^{2} + 4322 T^{3} + 45006 T^{4} + 341438 T^{5} + 2471436 T^{6} + 10846858 T^{7} + 38950081 T^{8} \))(\( 1 + 8 T + 393 T^{2} + 2460 T^{3} + 62016 T^{4} + 288800 T^{5} + 4899264 T^{6} + 15352860 T^{7} + 193764327 T^{8} + 311600648 T^{9} + 3077056399 T^{10} \))(\( 1 - 2 T - 16 T^{2} - 138 T^{3} + 18991 T^{4} - 23464 T^{5} - 200704 T^{6} - 1853656 T^{7} + 118522831 T^{8} - 68039382 T^{9} - 623201296 T^{10} - 6154112798 T^{11} + 243087455521 T^{12} \))(\( 1 + 38 T + 1065 T^{2} + 20520 T^{3} + 330517 T^{4} + 4291562 T^{5} + 48441997 T^{6} + 459493968 T^{7} + 3826917763 T^{8} + 26783638442 T^{9} + 162957771163 T^{10} + 799255662120 T^{11} + 3277065064935 T^{12} + 9237323309798 T^{13} + 19203908986159 T^{14} \))(\( 1 + 4 T + 253 T^{2} - 252 T^{3} + 26201 T^{4} - 193396 T^{5} + 1719485 T^{6} - 23900392 T^{7} + 135839315 T^{8} - 1206984436 T^{9} + 12918114839 T^{10} - 9815420412 T^{11} + 778495268947 T^{12} + 972349822084 T^{13} + 19203908986159 T^{14} \))(\( 1 + 6 T + 350 T^{2} + 1334 T^{3} + 57376 T^{4} + 152006 T^{5} + 6748130 T^{6} + 15515606 T^{7} + 617416446 T^{8} + 1225732874 T^{9} + 42115079330 T^{10} + 74944886234 T^{11} + 2234799847456 T^{12} + 4104793236266 T^{13} + 85080609432350 T^{14} + 115223453916954 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 12 T + 282 T^{2} - 1812 T^{3} + 29608 T^{4} - 94076 T^{5} + 2318678 T^{6} - 5620212 T^{7} + 196672526 T^{8} - 443996748 T^{9} + 14470869398 T^{10} - 46383136964 T^{11} + 1153233998248 T^{12} - 5575626194988 T^{13} + 68550662456922 T^{14} - 230446907833908 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 14 T + 480 T^{2} - 5706 T^{3} + 111164 T^{4} - 1111882 T^{5} + 15864416 T^{6} - 132890126 T^{7} + 1515327366 T^{8} - 10498319954 T^{9} + 99009820256 T^{10} - 548201189398 T^{11} + 4329846804284 T^{12} - 17557683812694 T^{13} + 116681978650080 T^{14} - 268854725806226 T^{15} + 1517108809906561 T^{16} \))
$83$ (\( 1 + 14 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 10 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 14 T + 198 T^{2} + 1162 T^{3} + 6889 T^{4} \))(\( 1 - 4 T - 72 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 - 2 T + 150 T^{2} - 166 T^{3} + 6889 T^{4} \))(\( 1 - 6 T + 22 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 218 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 + 8 T + 176 T^{2} + 664 T^{3} + 6889 T^{4} \))(\( 1 + 123 T^{2} - 324 T^{3} + 10209 T^{4} + 571787 T^{6} \))(\( 1 + 8 T + 253 T^{2} + 1296 T^{3} + 20999 T^{4} + 55112 T^{5} + 571787 T^{6} \))(\( 1 - 20 T + 408 T^{2} - 4916 T^{3} + 53726 T^{4} - 408028 T^{5} + 2810712 T^{6} - 11435740 T^{7} + 47458321 T^{8} \))(\( 1 + 22 T + 336 T^{2} + 3246 T^{3} + 31406 T^{4} + 269418 T^{5} + 2314704 T^{6} + 12579314 T^{7} + 47458321 T^{8} \))(\( 1 + 20 T + 432 T^{2} + 4868 T^{3} + 56846 T^{4} + 404044 T^{5} + 2976048 T^{6} + 11435740 T^{7} + 47458321 T^{8} \))(\( 1 + 16 T + 276 T^{2} + 2576 T^{3} + 29814 T^{4} + 213808 T^{5} + 1901364 T^{6} + 9148592 T^{7} + 47458321 T^{8} \))(\( 1 + 18 T + 103 T^{2} + 168 T^{3} + 11122 T^{4} + 192460 T^{5} + 923126 T^{6} + 1157352 T^{7} + 58894061 T^{8} + 854249778 T^{9} + 3939040643 T^{10} \))(\( 1 - 16 T + 518 T^{2} - 5724 T^{3} + 103567 T^{4} - 857596 T^{5} + 11183492 T^{6} - 71180468 T^{7} + 713473063 T^{8} - 3272908788 T^{9} + 24583410278 T^{10} - 63024650288 T^{11} + 326940373369 T^{12} \))(\( 1 + 6 T + 525 T^{2} + 2596 T^{3} + 121621 T^{4} + 493514 T^{5} + 16204881 T^{6} + 53015032 T^{7} + 1345005123 T^{8} + 3399817946 T^{9} + 69541306727 T^{10} + 123201801316 T^{11} + 2067996337575 T^{12} + 1961642240214 T^{13} + 27136050989627 T^{14} \))(\( 1 - 14 T + 539 T^{2} - 6100 T^{3} + 125791 T^{4} - 1160370 T^{5} + 16757717 T^{6} - 124585720 T^{7} + 1390890511 T^{8} - 7993788930 T^{9} + 71925658517 T^{10} - 289495758100 T^{11} + 2123142906577 T^{12} - 4577165227166 T^{13} + 27136050989627 T^{14} \))(\( 1 + 44 T + 1156 T^{2} + 21892 T^{3} + 330292 T^{4} + 4169940 T^{5} + 46199964 T^{6} + 463933500 T^{7} + 4353903798 T^{8} + 38506480500 T^{9} + 318271551996 T^{10} + 2384317482780 T^{11} + 15675103759732 T^{12} + 86233477756556 T^{13} + 377943071614564 T^{14} + 1193986243543588 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 8 T + 616 T^{2} + 4244 T^{3} + 169700 T^{4} + 995260 T^{5} + 27290104 T^{6} + 133633280 T^{7} + 2801581334 T^{8} + 11091562240 T^{9} + 188001526456 T^{10} + 569076729620 T^{11} + 8053677073700 T^{12} + 16717288488892 T^{13} + 201395269995304 T^{14} + 217088407917016 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 36 T + 1068 T^{2} - 21540 T^{3} + 379932 T^{4} - 5414068 T^{5} + 69163188 T^{6} - 750478036 T^{7} + 7372769638 T^{8} - 62289676988 T^{9} + 476465202132 T^{10} - 3095693699516 T^{11} + 18030934814172 T^{12} - 84846935450220 T^{13} + 349172318758092 T^{14} - 976897835626572 T^{15} + 2252292232139041 T^{16} \))
$89$ (\( 1 + 6 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 18 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 2 T + 162 T^{2} - 178 T^{3} + 7921 T^{4} \))(\( 1 + 16 T + 234 T^{2} + 1424 T^{3} + 7921 T^{4} \))(\( 1 - 10 T + 50 T^{2} - 890 T^{3} + 7921 T^{4} \))(\( 1 - 8 T + 126 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( 1 + 4 T + 170 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 - 16 T + 218 T^{2} - 1424 T^{3} + 7921 T^{4} \))(\( 1 + 10 T + 251 T^{2} + 1684 T^{3} + 22339 T^{4} + 79210 T^{5} + 704969 T^{6} \))(\( 1 + 14 T + 315 T^{2} + 2508 T^{3} + 28035 T^{4} + 110894 T^{5} + 704969 T^{6} \))(\( 1 + 24 T + 332 T^{2} + 2632 T^{3} + 21878 T^{4} + 234248 T^{5} + 2629772 T^{6} + 16919256 T^{7} + 62742241 T^{8} \))(\( 1 + 24 T + 312 T^{2} + 3412 T^{3} + 35918 T^{4} + 303668 T^{5} + 2471352 T^{6} + 16919256 T^{7} + 62742241 T^{8} \))(\( 1 + 8 T + 252 T^{2} + 952 T^{3} + 26070 T^{4} + 84728 T^{5} + 1996092 T^{6} + 5639752 T^{7} + 62742241 T^{8} \))(\( 1 + 8 T + 200 T^{2} + 244 T^{3} + 14638 T^{4} + 21716 T^{5} + 1584200 T^{6} + 5639752 T^{7} + 62742241 T^{8} \))(\( 1 - 32 T + 665 T^{2} - 9820 T^{3} + 122750 T^{4} - 1249656 T^{5} + 10924750 T^{6} - 77784220 T^{7} + 468804385 T^{8} - 2007751712 T^{9} + 5584059449 T^{10} \))(\( 1 - 16 T + 446 T^{2} - 5376 T^{3} + 82239 T^{4} - 803760 T^{5} + 8999332 T^{6} - 71534640 T^{7} + 651415119 T^{8} - 3789913344 T^{9} + 27983039486 T^{10} - 89344951184 T^{11} + 496981290961 T^{12} \))(\( 1 - 20 T + 695 T^{2} - 10156 T^{3} + 196005 T^{4} - 2192252 T^{5} + 29744563 T^{6} - 257527752 T^{7} + 2647266107 T^{8} - 17364828092 T^{9} + 138177448845 T^{10} - 637210199596 T^{11} + 3880921317055 T^{12} - 9939625819220 T^{13} + 44231334895529 T^{14} \))(\( 1 - 8 T + 195 T^{2} - 772 T^{3} + 28737 T^{4} - 119800 T^{5} + 3219435 T^{6} - 9854840 T^{7} + 286529715 T^{8} - 948935800 T^{9} + 20258694153 T^{10} - 48437010052 T^{11} + 1088891592555 T^{12} - 3975850327688 T^{13} + 44231334895529 T^{14} \))(\( 1 + 52 T + 1736 T^{2} + 41896 T^{3} + 809700 T^{4} + 12939536 T^{5} + 175733048 T^{6} + 2052055476 T^{7} + 20775355382 T^{8} + 182632937364 T^{9} + 1391981473208 T^{10} + 9121971754384 T^{11} + 50802392537700 T^{12} + 233949754675304 T^{13} + 862759521108296 T^{14} + 2300029414567508 T^{15} + 3936588805702081 T^{16} \))(\( 1 + 12 T + 316 T^{2} + 2504 T^{3} + 36260 T^{4} + 40992 T^{5} + 689796 T^{6} - 28701716 T^{7} - 131086986 T^{8} - 2554452724 T^{9} + 5463874116 T^{10} + 28898089248 T^{11} + 2275033658660 T^{12} + 13982484860296 T^{13} + 157046087943676 T^{14} + 530776018746348 T^{15} + 3936588805702081 T^{16} \))(\( 1 + 12 T + 480 T^{2} + 5664 T^{3} + 113508 T^{4} + 1285880 T^{5} + 17169344 T^{6} + 176415740 T^{7} + 1808026422 T^{8} + 15701000860 T^{9} + 135998373824 T^{10} + 906505537720 T^{11} + 7121746291428 T^{12} + 31628112719136 T^{13} + 238551019661280 T^{14} + 530776018746348 T^{15} + 3936588805702081 T^{16} \))
$97$ (\( 1 + 8 T + 97 T^{2} \))(\( 1 + 4 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 - 18 T + 258 T^{2} - 1746 T^{3} + 9409 T^{4} \))(\( 1 - 24 T + 336 T^{2} - 2328 T^{3} + 9409 T^{4} \))(\( ( 1 + 8 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 4 T + 97 T^{2} )^{2} \))(\( 1 + 4 T - 96 T^{2} + 388 T^{3} + 9409 T^{4} \))(\( 1 - 28 T + 509 T^{2} - 5732 T^{3} + 49373 T^{4} - 263452 T^{5} + 912673 T^{6} \))(\( 1 + 2 T + 67 T^{2} - 988 T^{3} + 6499 T^{4} + 18818 T^{5} + 912673 T^{6} \))(\( 1 + 32 T + 700 T^{2} + 10272 T^{3} + 117878 T^{4} + 996384 T^{5} + 6586300 T^{6} + 29205536 T^{7} + 88529281 T^{8} \))(\( 1 + 8 T + 152 T^{2} + 580 T^{3} + 16894 T^{4} + 56260 T^{5} + 1430168 T^{6} + 7301384 T^{7} + 88529281 T^{8} \))(\( 1 - 2 T + 24 T^{2} - 70 T^{3} + 16878 T^{4} - 6790 T^{5} + 225816 T^{6} - 1825346 T^{7} + 88529281 T^{8} \))(\( 1 + 4 T + 184 T^{2} + 944 T^{3} + 25342 T^{4} + 91568 T^{5} + 1731256 T^{6} + 3650692 T^{7} + 88529281 T^{8} \))(\( 1 + 16 T + 425 T^{2} + 4908 T^{3} + 75446 T^{4} + 664696 T^{5} + 7318262 T^{6} + 46179372 T^{7} + 387886025 T^{8} + 1416468496 T^{9} + 8587340257 T^{10} \))(\( 1 - 2 T + 290 T^{2} - 342 T^{3} + 49863 T^{4} - 57272 T^{5} + 5865804 T^{6} - 5555384 T^{7} + 469160967 T^{8} - 312134166 T^{9} + 25673491490 T^{10} - 17174680514 T^{11} + 832972004929 T^{12} \))(\( 1 + 8 T + 487 T^{2} + 3356 T^{3} + 114309 T^{4} + 672248 T^{5} + 16617651 T^{6} + 81458120 T^{7} + 1611912147 T^{8} + 6325181432 T^{9} + 104326737957 T^{10} + 297104267036 T^{11} + 4182034705159 T^{12} + 6663776039432 T^{13} + 80798284478113 T^{14} \))(\( 1 + 18 T + 517 T^{2} + 7512 T^{3} + 125323 T^{4} + 1485718 T^{5} + 18324399 T^{6} + 179829792 T^{7} + 1777466703 T^{8} + 13979120662 T^{9} + 114378918379 T^{10} + 665031958872 T^{11} + 4439654912869 T^{12} + 14993496088722 T^{13} + 80798284478113 T^{14} \))(\( 1 + 4 T + 152 T^{2} - 664 T^{3} + 7084 T^{4} - 93824 T^{5} + 482312 T^{6} - 2061036 T^{7} + 58267366 T^{8} - 199920492 T^{9} + 4538073608 T^{10} - 85630631552 T^{11} + 627141426604 T^{12} - 5701993930648 T^{13} + 126611744749208 T^{14} + 323193137912452 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 16 T + 596 T^{2} - 6800 T^{3} + 152260 T^{4} - 1383968 T^{5} + 24247644 T^{6} - 186238592 T^{7} + 2748802518 T^{8} - 18065143424 T^{9} + 228146082396 T^{10} - 1263110226464 T^{11} + 13479468325060 T^{12} - 58393913747600 T^{13} + 496451314937684 T^{14} - 1292772551649808 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 10 T + 524 T^{2} - 6122 T^{3} + 138388 T^{4} - 1555974 T^{5} + 24094964 T^{6} - 228532070 T^{7} + 2849699030 T^{8} - 22167610790 T^{9} + 226709516276 T^{10} - 1420095458502 T^{11} + 12251390139028 T^{12} - 52571697053354 T^{13} + 436477330582796 T^{14} - 807982844781130 T^{15} + 7837433594376961 T^{16} \))
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