Properties

Label 3234.2.a
Level 3234
Weight 2
Character orbit a
Rep. character \(\chi_{3234}(1,\cdot)\)
Character field \(\Q\)
Dimension 68
Newform subspaces 39
Sturm bound 1344
Trace bound 17

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Defining parameters

Level: \( N \) = \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3234.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 39 \)
Sturm bound: \(1344\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3234))\).

Total New Old
Modular forms 704 68 636
Cusp forms 641 68 573
Eisenstein series 63 0 63

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

\(2\)\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(24\)
Minus space\(-\)\(44\)

Trace form

\( 68q + 2q^{2} - 2q^{3} + 68q^{4} + 4q^{5} + 2q^{8} + 68q^{9} + O(q^{10}) \) \( 68q + 2q^{2} - 2q^{3} + 68q^{4} + 4q^{5} + 2q^{8} + 68q^{9} + 4q^{10} - 2q^{12} + 68q^{16} + 12q^{17} + 2q^{18} - 4q^{19} + 4q^{20} + 2q^{22} - 4q^{23} + 52q^{25} + 16q^{26} - 2q^{27} - 12q^{29} - 24q^{31} + 2q^{32} - 2q^{33} + 68q^{36} + 56q^{37} - 4q^{38} + 36q^{39} + 4q^{40} + 12q^{41} + 12q^{43} + 4q^{45} + 12q^{47} - 2q^{48} + 62q^{50} - 8q^{51} + 60q^{53} + 44q^{57} + 64q^{58} - 8q^{59} + 24q^{61} + 16q^{62} + 68q^{64} + 72q^{65} - 4q^{66} + 40q^{67} + 12q^{68} - 4q^{69} + 4q^{71} + 2q^{72} + 24q^{73} + 68q^{74} - 6q^{75} - 4q^{76} - 20q^{78} + 52q^{79} + 4q^{80} + 68q^{81} - 8q^{82} + 16q^{83} + 56q^{85} - 20q^{86} - 8q^{87} + 2q^{88} + 24q^{89} + 4q^{90} - 4q^{92} + 64q^{93} + 8q^{94} - 32q^{95} + 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3234))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 11
3234.2.a.a \(1\) \(25.824\) \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
3234.2.a.b \(1\) \(25.824\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.c \(1\) \(25.824\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.d \(1\) \(25.824\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.e \(1\) \(25.824\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.f \(1\) \(25.824\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.g \(1\) \(25.824\) \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
3234.2.a.h \(1\) \(25.824\) \(\Q\) None \(-1\) \(1\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.i \(1\) \(25.824\) \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.j \(1\) \(25.824\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.k \(1\) \(25.824\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.l \(1\) \(25.824\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.m \(1\) \(25.824\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.n \(1\) \(25.824\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.o \(1\) \(25.824\) \(\Q\) None \(-1\) \(1\) \(3\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.p \(1\) \(25.824\) \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.q \(1\) \(25.824\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
3234.2.a.r \(1\) \(25.824\) \(\Q\) None \(1\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.s \(1\) \(25.824\) \(\Q\) None \(1\) \(-1\) \(4\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.t \(1\) \(25.824\) \(\Q\) None \(1\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.u \(1\) \(25.824\) \(\Q\) None \(1\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.v \(1\) \(25.824\) \(\Q\) None \(1\) \(1\) \(4\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.w \(2\) \(25.824\) \(\Q(\sqrt{7}) \) None \(-2\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
3234.2.a.x \(2\) \(25.824\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
3234.2.a.y \(2\) \(25.824\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.z \(2\) \(25.824\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.ba \(2\) \(25.824\) \(\Q(\sqrt{7}) \) None \(-2\) \(2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.bb \(2\) \(25.824\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
3234.2.a.bc \(2\) \(25.824\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(4\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.bd \(2\) \(25.824\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-4\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.be \(2\) \(25.824\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
3234.2.a.bf \(3\) \(25.824\) 3.3.2700.1 None \(3\) \(-3\) \(0\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.bg \(3\) \(25.824\) 3.3.621.1 None \(3\) \(-3\) \(0\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.bh \(3\) \(25.824\) 3.3.2700.1 None \(3\) \(3\) \(0\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.bi \(3\) \(25.824\) 3.3.621.1 None \(3\) \(3\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.bj \(4\) \(25.824\) 4.4.14336.1 None \(-4\) \(-4\) \(0\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}-q^{8}+\cdots\)
3234.2.a.bk \(4\) \(25.824\) 4.4.14336.1 None \(-4\) \(4\) \(0\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.bl \(4\) \(25.824\) 4.4.4352.1 None \(4\) \(-4\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta _{3})q^{5}-q^{6}+\cdots\)
3234.2.a.bm \(4\) \(25.824\) 4.4.4352.1 None \(4\) \(4\) \(4\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta _{3})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3234))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3234)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1617))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))
$5$ (\( 1 + 3 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 3 T^{2} + 25 T^{4} \))(\( 1 - 2 T^{2} + 25 T^{4} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( 1 + 3 T^{2} + 25 T^{4} \))(\( 1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4} \))(\( ( 1 - 2 T + 5 T^{2} )^{2} \))(\( ( 1 + 2 T + 5 T^{2} )^{2} \))(\( 1 - 2 T + 6 T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 20 T^{3} + 125 T^{6} \))(\( 1 + 6 T^{2} - 4 T^{3} + 30 T^{4} + 125 T^{6} \))(\( 1 + 20 T^{3} + 125 T^{6} \))(\( 1 + 6 T^{2} + 4 T^{3} + 30 T^{4} + 125 T^{6} \))(\( 1 + 4 T^{2} + 46 T^{4} + 100 T^{6} + 625 T^{8} \))(\( 1 + 4 T^{2} + 46 T^{4} + 100 T^{6} + 625 T^{8} \))(\( 1 + 4 T + 16 T^{2} + 44 T^{3} + 118 T^{4} + 220 T^{5} + 400 T^{6} + 500 T^{7} + 625 T^{8} \))(\( 1 - 4 T + 16 T^{2} - 44 T^{3} + 118 T^{4} - 220 T^{5} + 400 T^{6} - 500 T^{7} + 625 T^{8} \))
$7$ 1
$11$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( 1 + 24 T^{2} + 169 T^{4} \))(\( 1 + 24 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 - 8 T + 40 T^{2} - 104 T^{3} + 169 T^{4} \))(\( 1 + 8 T + 40 T^{2} + 104 T^{3} + 169 T^{4} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{3} \))(\( 1 + 3 T^{2} - 32 T^{3} + 39 T^{4} + 2197 T^{6} \))(\( ( 1 + 13 T^{2} )^{3} \))(\( 1 + 3 T^{2} + 32 T^{3} + 39 T^{4} + 2197 T^{6} \))(\( 1 + 16 T^{2} + 32 T^{3} + 242 T^{4} + 416 T^{5} + 2704 T^{6} + 28561 T^{8} \))(\( 1 + 16 T^{2} - 32 T^{3} + 242 T^{4} - 416 T^{5} + 2704 T^{6} + 28561 T^{8} \))(\( 1 + 8 T + 48 T^{2} + 232 T^{3} + 882 T^{4} + 3016 T^{5} + 8112 T^{6} + 17576 T^{7} + 28561 T^{8} \))(\( 1 - 8 T + 48 T^{2} - 232 T^{3} + 882 T^{4} - 3016 T^{5} + 8112 T^{6} - 17576 T^{7} + 28561 T^{8} \))
$17$ (\( 1 - 5 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 5 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( ( 1 + 3 T + 17 T^{2} )^{2} \))(\( 1 + 22 T^{2} + 289 T^{4} \))(\( ( 1 - 4 T + 17 T^{2} )^{2} \))(\( ( 1 + 4 T + 17 T^{2} )^{2} \))(\( ( 1 - 3 T + 17 T^{2} )^{2} \))(\( 1 + 6 T + 38 T^{2} + 102 T^{3} + 289 T^{4} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( 1 - 6 T + 38 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - 3 T - 6 T^{2} + 37 T^{3} - 102 T^{4} - 867 T^{5} + 4913 T^{6} \))(\( ( 1 + T + 17 T^{2} )^{3} \))(\( 1 + 3 T - 6 T^{2} - 37 T^{3} - 102 T^{4} + 867 T^{5} + 4913 T^{6} \))(\( ( 1 - T + 17 T^{2} )^{3} \))(\( 1 + 36 T^{2} - 32 T^{3} + 638 T^{4} - 544 T^{5} + 10404 T^{6} + 83521 T^{8} \))(\( 1 + 36 T^{2} + 32 T^{3} + 638 T^{4} + 544 T^{5} + 10404 T^{6} + 83521 T^{8} \))(\( 1 + 4 T + 16 T^{2} + 92 T^{3} + 742 T^{4} + 1564 T^{5} + 4624 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 - 4 T + 16 T^{2} - 92 T^{3} + 742 T^{4} - 1564 T^{5} + 4624 T^{6} - 19652 T^{7} + 83521 T^{8} \))
$19$ (\( 1 + 6 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 3 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 10 T^{2} + 361 T^{4} \))(\( 1 + 4 T + 30 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 8 T + 52 T^{2} - 152 T^{3} + 361 T^{4} \))(\( 1 + 8 T + 52 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 + 10 T^{2} + 361 T^{4} \))(\( 1 + 2 T - 6 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 24 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 2 T - 6 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 + 9 T + 69 T^{2} + 314 T^{3} + 1311 T^{4} + 3249 T^{5} + 6859 T^{6} \))(\( 1 - 3 T + 21 T^{2} - 150 T^{3} + 399 T^{4} - 1083 T^{5} + 6859 T^{6} \))(\( 1 - 9 T + 69 T^{2} - 314 T^{3} + 1311 T^{4} - 3249 T^{5} + 6859 T^{6} \))(\( 1 + 3 T + 21 T^{2} + 150 T^{3} + 399 T^{4} + 1083 T^{5} + 6859 T^{6} \))(\( 1 + 40 T^{2} - 80 T^{3} + 794 T^{4} - 1520 T^{5} + 14440 T^{6} + 130321 T^{8} \))(\( 1 + 40 T^{2} + 80 T^{3} + 794 T^{4} + 1520 T^{5} + 14440 T^{6} + 130321 T^{8} \))(\( 1 + 12 T + 116 T^{2} + 708 T^{3} + 3658 T^{4} + 13452 T^{5} + 41876 T^{6} + 82308 T^{7} + 130321 T^{8} \))(\( 1 - 12 T + 116 T^{2} - 708 T^{3} + 3658 T^{4} - 13452 T^{5} + 41876 T^{6} - 82308 T^{7} + 130321 T^{8} \))
$23$ (\( 1 - 5 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 39 T^{2} + 529 T^{4} \))(\( 1 - 2 T^{2} + 529 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 39 T^{2} + 529 T^{4} \))(\( 1 - 4 T + 30 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 30 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 3 T + 42 T^{2} - 49 T^{3} + 966 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - 9 T + 72 T^{2} - 393 T^{3} + 1656 T^{4} - 4761 T^{5} + 12167 T^{6} \))(\( 1 - 3 T + 42 T^{2} - 49 T^{3} + 966 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - 9 T + 72 T^{2} - 393 T^{3} + 1656 T^{4} - 4761 T^{5} + 12167 T^{6} \))(\( 1 + 8 T + 36 T^{2} - 56 T^{3} - 570 T^{4} - 1288 T^{5} + 19044 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 36 T^{2} - 56 T^{3} - 570 T^{4} - 1288 T^{5} + 19044 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 92 T^{2} + 520 T^{3} + 3190 T^{4} + 11960 T^{5} + 48668 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 92 T^{2} + 520 T^{3} + 3190 T^{4} + 11960 T^{5} + 48668 T^{6} + 97336 T^{7} + 279841 T^{8} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 10 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( 1 + 26 T^{2} + 841 T^{4} \))(\( 1 + 26 T^{2} + 841 T^{4} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( 1 + 38 T^{2} + 841 T^{4} \))(\( 1 - 8 T + 42 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 42 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 + 38 T^{2} + 841 T^{4} \))(\( 1 - 9 T + 39 T^{2} - 174 T^{3} + 1131 T^{4} - 7569 T^{5} + 24389 T^{6} \))(\( 1 - 9 T + 87 T^{2} - 430 T^{3} + 2523 T^{4} - 7569 T^{5} + 24389 T^{6} \))(\( 1 - 9 T + 39 T^{2} - 174 T^{3} + 1131 T^{4} - 7569 T^{5} + 24389 T^{6} \))(\( 1 - 9 T + 87 T^{2} - 430 T^{3} + 2523 T^{4} - 7569 T^{5} + 24389 T^{6} \))(\( ( 1 + 50 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 50 T^{2} + 841 T^{4} )^{2} \))(\( 1 + 8 T + 84 T^{2} + 632 T^{3} + 3254 T^{4} + 18328 T^{5} + 70644 T^{6} + 195112 T^{7} + 707281 T^{8} \))(\( 1 + 8 T + 84 T^{2} + 632 T^{3} + 3254 T^{4} + 18328 T^{5} + 70644 T^{6} + 195112 T^{7} + 707281 T^{8} \))
$31$ (\( 1 + 4 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( 1 + 4 T + 54 T^{2} + 124 T^{3} + 961 T^{4} \))(\( 1 - 8 T + 28 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 28 T^{2} + 248 T^{3} + 961 T^{4} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( 1 + 10 T + 82 T^{2} + 310 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 48 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 + 4 T + 48 T^{2} + 124 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 82 T^{2} - 310 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 45 T^{2} + 180 T^{3} + 1395 T^{4} + 5766 T^{5} + 29791 T^{6} \))(\( 1 + 6 T - 3 T^{2} - 140 T^{3} - 93 T^{4} + 5766 T^{5} + 29791 T^{6} \))(\( 1 - 6 T + 45 T^{2} - 180 T^{3} + 1395 T^{4} - 5766 T^{5} + 29791 T^{6} \))(\( 1 - 6 T - 3 T^{2} + 140 T^{3} - 93 T^{4} - 5766 T^{5} + 29791 T^{6} \))(\( 1 + 16 T + 200 T^{2} + 1568 T^{3} + 10378 T^{4} + 48608 T^{5} + 192200 T^{6} + 476656 T^{7} + 923521 T^{8} \))(\( 1 - 16 T + 200 T^{2} - 1568 T^{3} + 10378 T^{4} - 48608 T^{5} + 192200 T^{6} - 476656 T^{7} + 923521 T^{8} \))(\( 1 + 4 T + 36 T^{2} + 44 T^{3} + 1274 T^{4} + 1364 T^{5} + 34596 T^{6} + 119164 T^{7} + 923521 T^{8} \))(\( 1 - 4 T + 36 T^{2} - 44 T^{3} + 1274 T^{4} - 1364 T^{5} + 34596 T^{6} - 119164 T^{7} + 923521 T^{8} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 8 T + 62 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 30 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 62 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( 1 + 4 T - 2 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 70 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 70 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T - 2 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 21 T + 243 T^{2} - 1782 T^{3} + 8991 T^{4} - 28749 T^{5} + 50653 T^{6} \))(\( 1 - 9 T + 99 T^{2} - 502 T^{3} + 3663 T^{4} - 12321 T^{5} + 50653 T^{6} \))(\( 1 - 21 T + 243 T^{2} - 1782 T^{3} + 8991 T^{4} - 28749 T^{5} + 50653 T^{6} \))(\( 1 - 9 T + 99 T^{2} - 502 T^{3} + 3663 T^{4} - 12321 T^{5} + 50653 T^{6} \))(\( 1 - 8 T + 76 T^{2} - 408 T^{3} + 2486 T^{4} - 15096 T^{5} + 104044 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( 1 - 8 T + 76 T^{2} - 408 T^{3} + 2486 T^{4} - 15096 T^{5} + 104044 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( 1 - 8 T + 116 T^{2} - 792 T^{3} + 5862 T^{4} - 29304 T^{5} + 158804 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( 1 - 8 T + 116 T^{2} - 792 T^{3} + 5862 T^{4} - 29304 T^{5} + 158804 T^{6} - 405224 T^{7} + 1874161 T^{8} \))
$41$ (\( 1 + 5 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( ( 1 - 9 T + 41 T^{2} )^{2} \))(\( 1 + 70 T^{2} + 1681 T^{4} \))(\( 1 - 8 T + 66 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 + 8 T + 66 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( ( 1 + 9 T + 41 T^{2} )^{2} \))(\( 1 + 6 T + 86 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 86 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 86 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 - 6 T + 86 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 96 T^{2} - 678 T^{3} + 3936 T^{4} - 20172 T^{5} + 68921 T^{6} \))(\( 1 + 12 T + 144 T^{2} + 902 T^{3} + 5904 T^{4} + 20172 T^{5} + 68921 T^{6} \))(\( 1 + 12 T + 96 T^{2} + 678 T^{3} + 3936 T^{4} + 20172 T^{5} + 68921 T^{6} \))(\( 1 - 12 T + 144 T^{2} - 902 T^{3} + 5904 T^{4} - 20172 T^{5} + 68921 T^{6} \))(\( 1 + 132 T^{2} + 32 T^{3} + 7454 T^{4} + 1312 T^{5} + 221892 T^{6} + 2825761 T^{8} \))(\( 1 + 132 T^{2} - 32 T^{3} + 7454 T^{4} - 1312 T^{5} + 221892 T^{6} + 2825761 T^{8} \))(\( 1 + 12 T + 80 T^{2} - 76 T^{3} - 1786 T^{4} - 3116 T^{5} + 134480 T^{6} + 827052 T^{7} + 2825761 T^{8} \))(\( 1 - 12 T + 80 T^{2} + 76 T^{3} - 1786 T^{4} + 3116 T^{5} + 134480 T^{6} - 827052 T^{7} + 2825761 T^{8} \))
$43$ (\( 1 + 10 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 11 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 11 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 8 T + 74 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 344 T^{3} + 1849 T^{4} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( 1 - 8 T + 74 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 - 4 T + 70 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 + 4 T + 82 T^{2} + 172 T^{3} + 1849 T^{4} \))(\( 1 + 4 T + 82 T^{2} + 172 T^{3} + 1849 T^{4} \))(\( 1 - 4 T + 70 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 - 3 T - 3 T^{2} + 146 T^{3} - 129 T^{4} - 5547 T^{5} + 79507 T^{6} \))(\( 1 - 9 T + 117 T^{2} - 610 T^{3} + 5031 T^{4} - 16641 T^{5} + 79507 T^{6} \))(\( 1 - 3 T - 3 T^{2} + 146 T^{3} - 129 T^{4} - 5547 T^{5} + 79507 T^{6} \))(\( 1 - 9 T + 117 T^{2} - 610 T^{3} + 5031 T^{4} - 16641 T^{5} + 79507 T^{6} \))(\( 1 - 8 T + 116 T^{2} - 424 T^{3} + 5110 T^{4} - 18232 T^{5} + 214484 T^{6} - 636056 T^{7} + 3418801 T^{8} \))(\( 1 - 8 T + 116 T^{2} - 424 T^{3} + 5110 T^{4} - 18232 T^{5} + 214484 T^{6} - 636056 T^{7} + 3418801 T^{8} \))(\( 1 + 8 T + 140 T^{2} + 936 T^{3} + 8358 T^{4} + 40248 T^{5} + 258860 T^{6} + 636056 T^{7} + 3418801 T^{8} \))(\( 1 + 8 T + 140 T^{2} + 936 T^{3} + 8358 T^{4} + 40248 T^{5} + 258860 T^{6} + 636056 T^{7} + 3418801 T^{8} \))
$47$ (\( 1 + 9 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 118 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 + 92 T^{2} + 2209 T^{4} \))(\( 1 + 92 T^{2} + 2209 T^{4} \))(\( 1 + 8 T + 47 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 6 T + 58 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 4 T - 188 T^{3} + 2209 T^{4} \))(\( 1 + 4 T + 188 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 58 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 3 T + 114 T^{2} - 273 T^{3} + 5358 T^{4} - 6627 T^{5} + 103823 T^{6} \))(\( 1 - 15 T + 192 T^{2} - 1391 T^{3} + 9024 T^{4} - 33135 T^{5} + 103823 T^{6} \))(\( 1 + 3 T + 114 T^{2} + 273 T^{3} + 5358 T^{4} + 6627 T^{5} + 103823 T^{6} \))(\( 1 + 15 T + 192 T^{2} + 1391 T^{3} + 9024 T^{4} + 33135 T^{5} + 103823 T^{6} \))(\( 1 + 16 T + 248 T^{2} + 2304 T^{3} + 18890 T^{4} + 108288 T^{5} + 547832 T^{6} + 1661168 T^{7} + 4879681 T^{8} \))(\( 1 - 16 T + 248 T^{2} - 2304 T^{3} + 18890 T^{4} - 108288 T^{5} + 547832 T^{6} - 1661168 T^{7} + 4879681 T^{8} \))(\( 1 + 4 T + 164 T^{2} + 572 T^{3} + 11002 T^{4} + 26884 T^{5} + 362276 T^{6} + 415292 T^{7} + 4879681 T^{8} \))(\( 1 - 4 T + 164 T^{2} - 572 T^{3} + 11002 T^{4} - 26884 T^{5} + 362276 T^{6} - 415292 T^{7} + 4879681 T^{8} \))
$53$ (\( 1 - 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( ( 1 - 4 T + 53 T^{2} )^{2} \))(\( 1 - 12 T + 94 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 78 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 78 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( ( 1 - 4 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( 1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 8 T + 53 T^{2} )^{3} \))(\( 1 + 123 T^{2} + 32 T^{3} + 6519 T^{4} + 148877 T^{6} \))(\( ( 1 - 8 T + 53 T^{2} )^{3} \))(\( 1 + 123 T^{2} + 32 T^{3} + 6519 T^{4} + 148877 T^{6} \))(\( 1 - 8 T + 140 T^{2} - 1048 T^{3} + 9334 T^{4} - 55544 T^{5} + 393260 T^{6} - 1191016 T^{7} + 7890481 T^{8} \))(\( 1 - 8 T + 140 T^{2} - 1048 T^{3} + 9334 T^{4} - 55544 T^{5} + 393260 T^{6} - 1191016 T^{7} + 7890481 T^{8} \))(\( 1 + 8 T + 52 T^{2} + 280 T^{3} + 3750 T^{4} + 14840 T^{5} + 146068 T^{6} + 1191016 T^{7} + 7890481 T^{8} \))(\( 1 + 8 T + 52 T^{2} + 280 T^{3} + 3750 T^{4} + 14840 T^{5} + 146068 T^{6} + 1191016 T^{7} + 7890481 T^{8} \))
$59$ (\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 7 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 9 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 7 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 9 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 8 T + 22 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 + 70 T^{2} + 3481 T^{4} \))(\( 1 - 8 T + 126 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 126 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 22 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 134 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 126 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 126 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 134 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 9 T + 129 T^{2} + 1014 T^{3} + 7611 T^{4} + 31329 T^{5} + 205379 T^{6} \))(\( 1 + 9 T + 81 T^{2} + 294 T^{3} + 4779 T^{4} + 31329 T^{5} + 205379 T^{6} \))(\( 1 - 9 T + 129 T^{2} - 1014 T^{3} + 7611 T^{4} - 31329 T^{5} + 205379 T^{6} \))(\( 1 - 9 T + 81 T^{2} - 294 T^{3} + 4779 T^{4} - 31329 T^{5} + 205379 T^{6} \))(\( ( 1 + 16 T + 174 T^{2} + 944 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 16 T + 174 T^{2} - 944 T^{3} + 3481 T^{4} )^{2} \))(\( 1 + 92 T^{2} - 512 T^{3} + 3446 T^{4} - 30208 T^{5} + 320252 T^{6} + 12117361 T^{8} \))(\( 1 + 92 T^{2} + 512 T^{3} + 3446 T^{4} + 30208 T^{5} + 320252 T^{6} + 12117361 T^{8} \))
$61$ (\( 1 - 5 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 8 T + 75 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( 1 + 120 T^{2} + 3721 T^{4} \))(\( 1 + 120 T^{2} + 3721 T^{4} \))(\( 1 + 8 T + 75 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( ( 1 + 61 T^{2} )^{2} \))(\( 1 - 8 T + 136 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 136 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( ( 1 + 61 T^{2} )^{2} \))(\( 1 + 6 T + 120 T^{2} + 830 T^{3} + 7320 T^{4} + 22326 T^{5} + 226981 T^{6} \))(\( 1 - 6 T + 54 T^{2} - 506 T^{3} + 3294 T^{4} - 22326 T^{5} + 226981 T^{6} \))(\( 1 - 6 T + 120 T^{2} - 830 T^{3} + 7320 T^{4} - 22326 T^{5} + 226981 T^{6} \))(\( 1 + 6 T + 54 T^{2} + 506 T^{3} + 3294 T^{4} + 22326 T^{5} + 226981 T^{6} \))(\( 1 + 16 T + 304 T^{2} + 2864 T^{3} + 29362 T^{4} + 174704 T^{5} + 1131184 T^{6} + 3631696 T^{7} + 13845841 T^{8} \))(\( 1 - 16 T + 304 T^{2} - 2864 T^{3} + 29362 T^{4} - 174704 T^{5} + 1131184 T^{6} - 3631696 T^{7} + 13845841 T^{8} \))(\( 1 + 24 T + 336 T^{2} + 3768 T^{3} + 33714 T^{4} + 229848 T^{5} + 1250256 T^{6} + 5447544 T^{7} + 13845841 T^{8} \))(\( 1 - 24 T + 336 T^{2} - 3768 T^{3} + 33714 T^{4} - 229848 T^{5} + 1250256 T^{6} - 5447544 T^{7} + 13845841 T^{8} \))
$67$ (\( 1 - 5 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 6 T + 31 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 - 16 T + 150 T^{2} - 1072 T^{3} + 4489 T^{4} \))(\( 1 + 6 T^{2} + 4489 T^{4} \))(\( 1 + 6 T^{2} + 4489 T^{4} \))(\( 1 + 6 T + 31 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 42 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 142 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 142 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 42 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 6 T + 138 T^{2} - 592 T^{3} + 9246 T^{4} - 26934 T^{5} + 300763 T^{6} \))(\( 1 - 6 T + 186 T^{2} - 720 T^{3} + 12462 T^{4} - 26934 T^{5} + 300763 T^{6} \))(\( 1 - 6 T + 138 T^{2} - 592 T^{3} + 9246 T^{4} - 26934 T^{5} + 300763 T^{6} \))(\( 1 - 6 T + 186 T^{2} - 720 T^{3} + 12462 T^{4} - 26934 T^{5} + 300763 T^{6} \))(\( 1 - 16 T + 124 T^{2} - 1104 T^{3} + 11510 T^{4} - 73968 T^{5} + 556636 T^{6} - 4812208 T^{7} + 20151121 T^{8} \))(\( 1 - 16 T + 124 T^{2} - 1104 T^{3} + 11510 T^{4} - 73968 T^{5} + 556636 T^{6} - 4812208 T^{7} + 20151121 T^{8} \))(\( 1 + 8 T + 228 T^{2} + 1576 T^{3} + 21606 T^{4} + 105592 T^{5} + 1023492 T^{6} + 2406104 T^{7} + 20151121 T^{8} \))(\( 1 + 8 T + 228 T^{2} + 1576 T^{3} + 21606 T^{4} + 105592 T^{5} + 1023492 T^{6} + 2406104 T^{7} + 20151121 T^{8} \))
$71$ (\( 1 - 4 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 16 T + 178 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( 1 - 16 T + 174 T^{2} - 1136 T^{3} + 5041 T^{4} \))(\( 1 - 16 T + 174 T^{2} - 1136 T^{3} + 5041 T^{4} \))(\( 1 + 16 T + 178 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 - 4 T + 126 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 + 110 T^{2} + 5041 T^{4} \))(\( 1 + 110 T^{2} + 5041 T^{4} \))(\( 1 - 4 T + 126 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 - 9 T + 105 T^{2} - 1170 T^{3} + 7455 T^{4} - 45369 T^{5} + 357911 T^{6} \))(\( 1 - 3 T + 189 T^{2} - 362 T^{3} + 13419 T^{4} - 15123 T^{5} + 357911 T^{6} \))(\( 1 - 9 T + 105 T^{2} - 1170 T^{3} + 7455 T^{4} - 45369 T^{5} + 357911 T^{6} \))(\( 1 - 3 T + 189 T^{2} - 362 T^{3} + 13419 T^{4} - 15123 T^{5} + 357911 T^{6} \))(\( 1 + 140 T^{2} - 256 T^{3} + 12422 T^{4} - 18176 T^{5} + 705740 T^{6} + 25411681 T^{8} \))(\( 1 + 140 T^{2} - 256 T^{3} + 12422 T^{4} - 18176 T^{5} + 705740 T^{6} + 25411681 T^{8} \))(\( 1 - 8 T + 60 T^{2} - 744 T^{3} + 10790 T^{4} - 52824 T^{5} + 302460 T^{6} - 2863288 T^{7} + 25411681 T^{8} \))(\( 1 - 8 T + 60 T^{2} - 744 T^{3} + 10790 T^{4} - 52824 T^{5} + 302460 T^{6} - 2863288 T^{7} + 25411681 T^{8} \))
$73$ (\( 1 + 12 T + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 + 20 T + 218 T^{2} + 1460 T^{3} + 5329 T^{4} \))(\( 1 - 8 T + 150 T^{2} - 584 T^{3} + 5329 T^{4} \))(\( ( 1 - 4 T + 73 T^{2} )^{2} \))(\( ( 1 + 4 T + 73 T^{2} )^{2} \))(\( 1 - 20 T + 218 T^{2} - 1460 T^{3} + 5329 T^{4} \))(\( 1 + 18 T + 182 T^{2} + 1314 T^{3} + 5329 T^{4} \))(\( 1 - 12 T + 150 T^{2} - 876 T^{3} + 5329 T^{4} \))(\( 1 + 12 T + 150 T^{2} + 876 T^{3} + 5329 T^{4} \))(\( 1 - 18 T + 182 T^{2} - 1314 T^{3} + 5329 T^{4} \))(\( 1 + 99 T^{2} - 480 T^{3} + 7227 T^{4} + 389017 T^{6} \))(\( 1 + 123 T^{2} + 192 T^{3} + 8979 T^{4} + 389017 T^{6} \))(\( 1 + 99 T^{2} + 480 T^{3} + 7227 T^{4} + 389017 T^{6} \))(\( 1 + 123 T^{2} - 192 T^{3} + 8979 T^{4} + 389017 T^{6} \))(\( 1 + 116 T^{2} + 448 T^{3} + 6462 T^{4} + 32704 T^{5} + 618164 T^{6} + 28398241 T^{8} \))(\( 1 + 116 T^{2} - 448 T^{3} + 6462 T^{4} - 32704 T^{5} + 618164 T^{6} + 28398241 T^{8} \))(\( 1 + 4 T + 224 T^{2} + 796 T^{3} + 22758 T^{4} + 58108 T^{5} + 1193696 T^{6} + 1556068 T^{7} + 28398241 T^{8} \))(\( 1 - 4 T + 224 T^{2} - 796 T^{3} + 22758 T^{4} - 58108 T^{5} + 1193696 T^{6} - 1556068 T^{7} + 28398241 T^{8} \))
$79$ (\( 1 + T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 17 T + 79 T^{2} \))(\( 1 - 17 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 16 T + 215 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 126 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 142 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 142 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 215 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 4 T - 18 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 + 16 T + 150 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 + 16 T + 150 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 + 4 T - 18 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 270 T^{2} - 1880 T^{3} + 21330 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 - 12 T + 204 T^{2} - 1528 T^{3} + 16116 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 - 12 T + 270 T^{2} - 1880 T^{3} + 21330 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 - 12 T + 204 T^{2} - 1528 T^{3} + 16116 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 - 16 T + 236 T^{2} - 2448 T^{3} + 24582 T^{4} - 193392 T^{5} + 1472876 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 - 16 T + 236 T^{2} - 2448 T^{3} + 24582 T^{4} - 193392 T^{5} + 1472876 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 + 8 T + 180 T^{2} + 904 T^{3} + 15990 T^{4} + 71416 T^{5} + 1123380 T^{6} + 3944312 T^{7} + 38950081 T^{8} \))(\( 1 + 8 T + 180 T^{2} + 904 T^{3} + 15990 T^{4} + 71416 T^{5} + 1123380 T^{6} + 3944312 T^{7} + 38950081 T^{8} \))
$83$ (\( 1 + T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 - 10 T + 79 T^{2} - 830 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 180 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 - 16 T + 180 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 + 10 T + 79 T^{2} + 830 T^{3} + 6889 T^{4} \))(\( 1 + 2 T + 162 T^{2} + 166 T^{3} + 6889 T^{4} \))(\( 1 + 4 T + 120 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 - 4 T + 120 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 - 2 T + 162 T^{2} - 166 T^{3} + 6889 T^{4} \))(\( 1 - 18 T + 282 T^{2} - 2824 T^{3} + 23406 T^{4} - 124002 T^{5} + 571787 T^{6} \))(\( 1 - 6 T + 138 T^{2} - 1184 T^{3} + 11454 T^{4} - 41334 T^{5} + 571787 T^{6} \))(\( 1 + 18 T + 282 T^{2} + 2824 T^{3} + 23406 T^{4} + 124002 T^{5} + 571787 T^{6} \))(\( 1 + 6 T + 138 T^{2} + 1184 T^{3} + 11454 T^{4} + 41334 T^{5} + 571787 T^{6} \))(\( 1 + 280 T^{2} + 48 T^{3} + 32794 T^{4} + 3984 T^{5} + 1928920 T^{6} + 47458321 T^{8} \))(\( 1 + 280 T^{2} - 48 T^{3} + 32794 T^{4} - 3984 T^{5} + 1928920 T^{6} + 47458321 T^{8} \))(\( 1 + 4 T + 228 T^{2} + 860 T^{3} + 26058 T^{4} + 71380 T^{5} + 1570692 T^{6} + 2287148 T^{7} + 47458321 T^{8} \))(\( 1 - 4 T + 228 T^{2} - 860 T^{3} + 26058 T^{4} - 71380 T^{5} + 1570692 T^{6} - 2287148 T^{7} + 47458321 T^{8} \))
$89$ (\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 16 T + 214 T^{2} - 1424 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 166 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 - 8 T + 192 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( 1 + 8 T + 192 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 + 16 T + 214 T^{2} + 1424 T^{3} + 7921 T^{4} \))(\( 1 + 4 T + 162 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 - 16 T + 224 T^{2} - 1424 T^{3} + 7921 T^{4} \))(\( 1 + 16 T + 224 T^{2} + 1424 T^{3} + 7921 T^{4} \))(\( 1 - 4 T + 162 T^{2} - 356 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 255 T^{2} + 2120 T^{3} + 22695 T^{4} + 95052 T^{5} + 704969 T^{6} \))(\( 1 - 36 T + 663 T^{2} - 7736 T^{3} + 59007 T^{4} - 285156 T^{5} + 704969 T^{6} \))(\( 1 - 12 T + 255 T^{2} - 2120 T^{3} + 22695 T^{4} - 95052 T^{5} + 704969 T^{6} \))(\( 1 + 36 T + 663 T^{2} + 7736 T^{3} + 59007 T^{4} + 285156 T^{5} + 704969 T^{6} \))(\( 1 + 16 T + 160 T^{2} + 1904 T^{3} + 24642 T^{4} + 169456 T^{5} + 1267360 T^{6} + 11279504 T^{7} + 62742241 T^{8} \))(\( 1 - 16 T + 160 T^{2} - 1904 T^{3} + 24642 T^{4} - 169456 T^{5} + 1267360 T^{6} - 11279504 T^{7} + 62742241 T^{8} \))(\( 1 + 24 T + 480 T^{2} + 6424 T^{3} + 69314 T^{4} + 571736 T^{5} + 3802080 T^{6} + 16919256 T^{7} + 62742241 T^{8} \))(\( 1 - 24 T + 480 T^{2} - 6424 T^{3} + 69314 T^{4} - 571736 T^{5} + 3802080 T^{6} - 16919256 T^{7} + 62742241 T^{8} \))
$97$ (\( 1 + 9 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 + 17 T + 97 T^{2} \))(\( 1 - 17 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 9 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 2 T + 83 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( 1 + 32 T^{2} + 9409 T^{4} \))(\( 1 + 32 T^{2} + 9409 T^{4} \))(\( 1 - 2 T + 83 T^{2} - 194 T^{3} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 + 96 T^{2} + 9409 T^{4} \))(\( 1 + 96 T^{2} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( ( 1 - 7 T + 97 T^{2} )^{3} \))(\( 1 + 9 T + 210 T^{2} + 1753 T^{3} + 20370 T^{4} + 84681 T^{5} + 912673 T^{6} \))(\( ( 1 + 7 T + 97 T^{2} )^{3} \))(\( 1 - 9 T + 210 T^{2} - 1753 T^{3} + 20370 T^{4} - 84681 T^{5} + 912673 T^{6} \))(\( 1 - 16 T + 352 T^{2} - 3984 T^{3} + 51458 T^{4} - 386448 T^{5} + 3311968 T^{6} - 14602768 T^{7} + 88529281 T^{8} \))(\( 1 + 16 T + 352 T^{2} + 3984 T^{3} + 51458 T^{4} + 386448 T^{5} + 3311968 T^{6} + 14602768 T^{7} + 88529281 T^{8} \))(\( 1 + 128 T^{2} - 1280 T^{3} + 4866 T^{4} - 124160 T^{5} + 1204352 T^{6} + 88529281 T^{8} \))(\( 1 + 128 T^{2} + 1280 T^{3} + 4866 T^{4} + 124160 T^{5} + 1204352 T^{6} + 88529281 T^{8} \))
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