Properties

Label 2450.2.a
Level 2450
Weight 2
Character orbit a
Rep. character \(\chi_{2450}(1,\cdot)\)
Character field \(\Q\)
Dimension 64
Newform subspaces 47
Sturm bound 840
Trace bound 17

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Defining parameters

Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2450.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 47 \)
Sturm bound: \(840\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\), \(17\), \(19\), \(23\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2450))\).

Total New Old
Modular forms 468 64 404
Cusp forms 373 64 309
Eisenstein series 95 0 95

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

\(2\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(11\)
Plus space\(+\)\(23\)
Minus space\(-\)\(41\)

Trace form

\( 64q - 2q^{3} + 64q^{4} + 4q^{6} + 66q^{9} + O(q^{10}) \) \( 64q - 2q^{3} + 64q^{4} + 4q^{6} + 66q^{9} + 10q^{11} - 2q^{12} - 10q^{13} + 64q^{16} + 8q^{17} - 8q^{19} + 8q^{22} + 8q^{23} + 4q^{24} + 10q^{26} + 4q^{27} + 24q^{29} - 8q^{31} + 2q^{34} + 66q^{36} + 24q^{37} - 2q^{38} + 24q^{39} + 18q^{41} + 40q^{43} + 10q^{44} + 4q^{46} - 4q^{47} - 2q^{48} + 2q^{51} - 10q^{52} - 20q^{53} + 22q^{54} + 24q^{57} - 12q^{58} - 2q^{59} + 2q^{61} + 12q^{62} + 64q^{64} + 6q^{66} + 16q^{67} + 8q^{68} + 36q^{69} + 32q^{71} + 4q^{73} - 24q^{74} - 8q^{76} - 16q^{78} + 36q^{79} + 96q^{81} - 4q^{82} + 2q^{83} + 8q^{86} + 12q^{87} + 8q^{88} + 58q^{89} + 8q^{92} + 40q^{93} + 28q^{94} + 4q^{96} - 8q^{97} + 148q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2450))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7
2450.2.a.a \(1\) \(19.563\) \(\Q\) None \(-1\) \(-3\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots\)
2450.2.a.b \(1\) \(19.563\) \(\Q\) None \(-1\) \(-3\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots\)
2450.2.a.c \(1\) \(19.563\) \(\Q\) None \(-1\) \(-3\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots\)
2450.2.a.d \(1\) \(19.563\) \(\Q\) None \(-1\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.e \(1\) \(19.563\) \(\Q\) None \(-1\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.f \(1\) \(19.563\) \(\Q\) None \(-1\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.g \(1\) \(19.563\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots\)
2450.2.a.h \(1\) \(19.563\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots\)
2450.2.a.i \(1\) \(19.563\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots\)
2450.2.a.j \(1\) \(19.563\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{8}-3q^{9}+3q^{11}-5q^{13}+\cdots\)
2450.2.a.k \(1\) \(19.563\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{8}-3q^{9}+3q^{11}+5q^{13}+\cdots\)
2450.2.a.l \(1\) \(19.563\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{8}-3q^{9}+4q^{11}-6q^{13}+\cdots\)
2450.2.a.m \(1\) \(19.563\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-2q^{9}+\cdots\)
2450.2.a.n \(1\) \(19.563\) \(\Q\) None \(-1\) \(2\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.o \(1\) \(19.563\) \(\Q\) None \(-1\) \(2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.p \(1\) \(19.563\) \(\Q\) None \(-1\) \(2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\)
2450.2.a.q \(1\) \(19.563\) \(\Q\) None \(-1\) \(3\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{8}+6q^{9}+\cdots\)
2450.2.a.r \(1\) \(19.563\) \(\Q\) None \(-1\) \(3\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{8}+6q^{9}+\cdots\)
2450.2.a.s \(1\) \(19.563\) \(\Q\) None \(1\) \(-3\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}-3q^{3}+q^{4}-3q^{6}+q^{8}+6q^{9}+\cdots\)
2450.2.a.t \(1\) \(19.563\) \(\Q\) None \(1\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots\)
2450.2.a.u \(1\) \(19.563\) \(\Q\) None \(1\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots\)
2450.2.a.v \(1\) \(19.563\) \(\Q\) None \(1\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots\)
2450.2.a.w \(1\) \(19.563\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots\)
2450.2.a.x \(1\) \(19.563\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots\)
2450.2.a.y \(1\) \(19.563\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots\)
2450.2.a.z \(1\) \(19.563\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots\)
2450.2.a.ba \(1\) \(19.563\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{8}-3q^{9}+3q^{11}-5q^{13}+\cdots\)
2450.2.a.bb \(1\) \(19.563\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{8}-3q^{9}+3q^{11}+5q^{13}+\cdots\)
2450.2.a.bc \(1\) \(19.563\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots\)
2450.2.a.bd \(1\) \(19.563\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots\)
2450.2.a.be \(1\) \(19.563\) \(\Q\) None \(1\) \(2\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots\)
2450.2.a.bf \(1\) \(19.563\) \(\Q\) None \(1\) \(2\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots\)
2450.2.a.bg \(1\) \(19.563\) \(\Q\) None \(1\) \(3\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots\)
2450.2.a.bh \(1\) \(19.563\) \(\Q\) None \(1\) \(3\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots\)
2450.2.a.bi \(2\) \(19.563\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{8}-3q^{9}-4q^{11}+3\beta q^{13}+\cdots\)
2450.2.a.bj \(2\) \(19.563\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}-q^{9}+\cdots\)
2450.2.a.bk \(2\) \(19.563\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}-q^{9}+\cdots\)
2450.2.a.bl \(2\) \(19.563\) \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+3q^{9}+\cdots\)
2450.2.a.bm \(2\) \(19.563\) \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+4q^{9}+\cdots\)
2450.2.a.bn \(2\) \(19.563\) \(\Q(\sqrt{2}) \) None \(2\) \(-4\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+(-2+\beta )q^{3}+q^{4}+(-2+\beta )q^{6}+\cdots\)
2450.2.a.bo \(2\) \(19.563\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{8}-3q^{9}-4q^{11}+3\beta q^{13}+\cdots\)
2450.2.a.bp \(2\) \(19.563\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}-q^{9}+\cdots\)
2450.2.a.bq \(2\) \(19.563\) \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}+3q^{9}+\cdots\)
2450.2.a.br \(2\) \(19.563\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}+4q^{9}+\cdots\)
2450.2.a.bs \(2\) \(19.563\) \(\Q(\sqrt{2}) \) None \(2\) \(4\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+(2+\beta )q^{3}+q^{4}+(2+\beta )q^{6}+\cdots\)
2450.2.a.bt \(4\) \(19.563\) \(\Q(\sqrt{2}, \sqrt{11})\) None \(-4\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-q^{8}+\cdots\)
2450.2.a.bu \(4\) \(19.563\) \(\Q(\sqrt{2}, \sqrt{11})\) None \(4\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2450))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2450)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1225))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( ( 1 + 3 T^{2} )^{2} \))(\( 1 + 4 T^{2} + 9 T^{4} \))(\( 1 + 4 T^{2} + 9 T^{4} \))(\( 1 + 9 T^{4} \))(\( 1 - T^{2} + 9 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4} \))(\( ( 1 + 3 T^{2} )^{2} \))(\( 1 + 4 T^{2} + 9 T^{4} \))(\( 1 + 9 T^{4} \))(\( 1 - T^{2} + 9 T^{4} \))(\( 1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4} \))(\( 1 + 7 T^{4} + 81 T^{8} \))(\( 1 + 7 T^{4} + 81 T^{8} \))
$5$ 1
$7$ 1
$11$ (\( 1 + 5 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 - 2 T^{2} + 121 T^{4} \))(\( ( 1 - 5 T + 11 T^{2} )^{2} \))(\( 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 - 2 T^{2} + 121 T^{4} \))(\( ( 1 - 5 T + 11 T^{2} )^{2} \))(\( 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} \))(\( ( 1 - 4 T + 15 T^{2} - 44 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 4 T + 15 T^{2} - 44 T^{3} + 121 T^{4} )^{2} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 8 T^{2} + 169 T^{4} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 + 8 T^{2} + 169 T^{4} \))(\( 1 + 4 T + 24 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 - 2 T^{2} + 169 T^{4} \))(\( 1 - 4 T + 22 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + 8 T^{2} + 169 T^{4} \))(\( 1 + 8 T^{2} + 169 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 2 T^{2} + 169 T^{4} \))(\( 1 + 4 T + 22 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 + 4 T^{2} + 166 T^{4} + 676 T^{6} + 28561 T^{8} \))(\( 1 + 4 T^{2} + 166 T^{4} + 676 T^{6} + 28561 T^{8} \))
$17$ (\( 1 + T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 16 T^{2} + 289 T^{4} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( 1 + 27 T^{2} + 289 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 + 16 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( 1 + 27 T^{2} + 289 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 136 T^{3} + 289 T^{4} \))(\( 1 + 8 T^{2} + 55 T^{4} + 2312 T^{6} + 83521 T^{8} \))(\( 1 + 8 T^{2} + 55 T^{4} + 2312 T^{6} + 83521 T^{8} \))
$19$ (\( 1 - 3 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 6 T^{2} + 361 T^{4} \))(\( 1 - 12 T^{2} + 361 T^{4} \))(\( 1 + 20 T^{2} + 361 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 - 25 T^{2} + 361 T^{4} \))(\( 1 - 4 T + 40 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 6 T^{2} + 361 T^{4} \))(\( 1 + 20 T^{2} + 361 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 - 25 T^{2} + 361 T^{4} \))(\( 1 + 4 T + 40 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 64 T^{2} + 1735 T^{4} + 23104 T^{6} + 130321 T^{8} \))(\( 1 + 64 T^{2} + 1735 T^{4} + 23104 T^{6} + 130321 T^{8} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 7 T + 23 T^{2} \))(\( 1 - 7 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 6 T + 23 T^{2} )^{2} \))(\( 1 + 4 T + 26 T^{2} + 92 T^{3} + 529 T^{4} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( 1 - 8 T + 54 T^{2} - 184 T^{3} + 529 T^{4} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 6 T + 23 T^{2} )^{2} \))(\( 1 - 4 T + 26 T^{2} - 92 T^{3} + 529 T^{4} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( 1 - 8 T + 54 T^{2} - 184 T^{3} + 529 T^{4} \))(\( ( 1 - 4 T + 6 T^{2} - 92 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 4 T + 6 T^{2} + 92 T^{3} + 529 T^{4} )^{2} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( ( 1 + 4 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( 1 - 4 T + 38 T^{2} - 116 T^{3} + 841 T^{4} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( 1 + 4 T + 54 T^{2} + 116 T^{3} + 841 T^{4} \))(\( ( 1 + 4 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( 1 - 4 T + 38 T^{2} - 116 T^{3} + 841 T^{4} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( 1 + 4 T + 54 T^{2} + 116 T^{3} + 841 T^{4} \))(\( ( 1 - 8 T + 30 T^{2} - 232 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 8 T + 30 T^{2} - 232 T^{3} + 841 T^{4} )^{2} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 30 T^{2} + 961 T^{4} \))(\( 1 - 10 T^{2} + 961 T^{4} \))(\( 1 - 10 T^{2} + 961 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 50 T^{2} + 961 T^{4} \))(\( 1 + 54 T^{2} + 961 T^{4} \))(\( 1 + 30 T^{2} + 961 T^{4} \))(\( 1 - 10 T^{2} + 961 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 50 T^{2} + 961 T^{4} \))(\( 1 + 54 T^{2} + 961 T^{4} \))(\( ( 1 + 30 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 30 T^{2} + 961 T^{4} )^{2} \))
$37$ (\( 1 + 8 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 11 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 11 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( ( 1 - 6 T + 37 T^{2} )^{2} \))(\( ( 1 + 10 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 4 T + 37 T^{2} )^{2} \))(\( 1 - 4 T + 46 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 6 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( 1 - 4 T + 46 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( ( 1 + 4 T + 34 T^{2} + 148 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 4 T + 34 T^{2} - 148 T^{3} + 1369 T^{4} )^{2} \))
$41$ (\( 1 + 11 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 11 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 80 T^{2} + 1681 T^{4} \))(\( 1 - 16 T^{2} + 1681 T^{4} \))(\( 1 + 10 T^{2} + 1681 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 + 75 T^{2} + 1681 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 + 80 T^{2} + 1681 T^{4} \))(\( 1 + 10 T^{2} + 1681 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 + 75 T^{2} + 1681 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 + 104 T^{2} + 5527 T^{4} + 174824 T^{6} + 2825761 T^{8} \))(\( 1 + 104 T^{2} + 5527 T^{4} + 174824 T^{6} + 2825761 T^{8} \))
$43$ (\( 1 - 8 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( ( 1 - 12 T + 43 T^{2} )^{2} \))(\( ( 1 + 2 T + 43 T^{2} )^{2} \))(\( ( 1 + 12 T + 43 T^{2} )^{2} \))(\( 1 - 8 T + 78 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( 1 - 12 T + 114 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( ( 1 + 12 T + 43 T^{2} )^{2} \))(\( ( 1 - 12 T + 43 T^{2} )^{2} \))(\( 1 + 8 T + 78 T^{2} + 344 T^{3} + 1849 T^{4} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( 1 - 12 T + 114 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( ( 1 + 42 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 + 42 T^{2} + 1849 T^{4} )^{2} \))
$47$ (\( 1 - 2 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( 1 + 86 T^{2} + 2209 T^{4} \))(\( 1 + 86 T^{2} + 2209 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 66 T^{2} + 2209 T^{4} \))(\( 1 + 16 T + 150 T^{2} + 752 T^{3} + 2209 T^{4} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( 1 + 86 T^{2} + 2209 T^{4} \))(\( 1 - 8 T + 86 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 66 T^{2} + 2209 T^{4} \))(\( 1 - 16 T + 150 T^{2} - 752 T^{3} + 2209 T^{4} \))(\( 1 + 140 T^{2} + 9142 T^{4} + 309260 T^{6} + 4879681 T^{8} \))(\( 1 + 140 T^{2} + 9142 T^{4} + 309260 T^{6} + 4879681 T^{8} \))
$53$ (\( 1 + 4 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( ( 1 - 12 T + 53 T^{2} )^{2} \))(\( ( 1 - 2 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( 1 + 12 T + 118 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( ( 1 + 4 T + 53 T^{2} )^{2} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( ( 1 + 12 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( 1 - 12 T + 118 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( ( 1 - 4 T + 53 T^{2} )^{2} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( ( 1 + 8 T + 53 T^{2} )^{4} \))(\( ( 1 - 8 T + 53 T^{2} )^{4} \))
$59$ (\( 1 + 4 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 2 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 2 T + 59 T^{2} \))(\( 1 - 2 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 2 T + 59 T^{2} \))(\( 1 - 10 T^{2} + 3481 T^{4} \))(\( 1 + 116 T^{2} + 3481 T^{4} \))(\( 1 + 100 T^{2} + 3481 T^{4} \))(\( 1 - 8 T + 128 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 90 T^{2} + 3481 T^{4} \))(\( 1 - 20 T + 216 T^{2} - 1180 T^{3} + 3481 T^{4} \))(\( 1 - 10 T^{2} + 3481 T^{4} \))(\( 1 + 100 T^{2} + 3481 T^{4} \))(\( 1 - 8 T + 128 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 90 T^{2} + 3481 T^{4} \))(\( 1 + 20 T + 216 T^{2} + 1180 T^{3} + 3481 T^{4} \))(\( 1 + 176 T^{2} + 14002 T^{4} + 612656 T^{6} + 12117361 T^{8} \))(\( 1 + 176 T^{2} + 14002 T^{4} + 612656 T^{6} + 12117361 T^{8} \))
$61$ (\( 1 - 2 T + 61 T^{2} \))(\( 1 - T + 61 T^{2} \))(\( 1 - 9 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 + 9 T + 61 T^{2} \))(\( 1 + 9 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 9 T + 61 T^{2} \))(\( 1 + 72 T^{2} + 3721 T^{4} \))(\( 1 + 114 T^{2} + 3721 T^{4} \))(\( 1 + 104 T^{2} + 3721 T^{4} \))(\( 1 + 12 T + 152 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 94 T^{2} + 3721 T^{4} \))(\( 1 + 4 T - 2 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 72 T^{2} + 3721 T^{4} \))(\( 1 + 104 T^{2} + 3721 T^{4} \))(\( 1 + 12 T + 152 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 94 T^{2} + 3721 T^{4} \))(\( 1 - 4 T - 2 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 196 T^{2} + 16870 T^{4} + 729316 T^{6} + 13845841 T^{8} \))(\( 1 + 196 T^{2} + 16870 T^{4} + 729316 T^{6} + 13845841 T^{8} \))
$67$ (\( 1 + 9 T + 67 T^{2} \))(\( 1 - 9 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 9 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 - 13 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 9 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( ( 1 - 12 T + 67 T^{2} )^{2} \))(\( ( 1 + 12 T + 67 T^{2} )^{2} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 5 T + 67 T^{2} )^{2} \))(\( 1 - 8 T + 118 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( ( 1 + 12 T + 67 T^{2} )^{2} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 5 T + 67 T^{2} )^{2} \))(\( 1 - 8 T + 118 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( ( 1 - 10 T + 115 T^{2} - 670 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 10 T + 115 T^{2} + 670 T^{3} + 4489 T^{4} )^{2} \))
$71$ (\( 1 + 10 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 16 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( 1 + 12 T + 154 T^{2} + 852 T^{3} + 5041 T^{4} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( 1 + 12 T + 154 T^{2} + 852 T^{3} + 5041 T^{4} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} \))(\( ( 1 + 2 T + 71 T^{2} )^{4} \))(\( ( 1 + 2 T + 71 T^{2} )^{4} \))
$73$ (\( 1 + 7 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 5 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 5 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 7 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 128 T^{2} + 5329 T^{4} \))(\( 1 + 144 T^{2} + 5329 T^{4} \))(\( 1 + 74 T^{2} + 5329 T^{4} \))(\( 1 - 4 T + 126 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( 1 + 139 T^{2} + 5329 T^{4} \))(\( 1 - 16 T + 208 T^{2} - 1168 T^{3} + 5329 T^{4} \))(\( 1 + 128 T^{2} + 5329 T^{4} \))(\( 1 + 74 T^{2} + 5329 T^{4} \))(\( 1 + 4 T + 126 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 + 139 T^{2} + 5329 T^{4} \))(\( 1 + 16 T + 208 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( 1 + 232 T^{2} + 23575 T^{4} + 1236328 T^{6} + 28398241 T^{8} \))(\( 1 + 232 T^{2} + 23575 T^{4} + 1236328 T^{6} + 28398241 T^{8} \))
$79$ (\( 1 + 2 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( 1 - 4 T + 138 T^{2} - 316 T^{3} + 6241 T^{4} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( 1 + 8 T + 166 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( 1 - 4 T + 138 T^{2} - 316 T^{3} + 6241 T^{4} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( 1 + 8 T + 166 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( ( 1 - 16 T + 178 T^{2} - 1264 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 16 T + 178 T^{2} - 1264 T^{3} + 6241 T^{4} )^{2} \))
$83$ (\( 1 - 11 T + 83 T^{2} \))(\( 1 - 7 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 7 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 11 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 122 T^{2} + 6889 T^{4} \))(\( 1 + 68 T^{2} + 6889 T^{4} \))(\( 1 - 76 T^{2} + 6889 T^{4} \))(\( 1 + 160 T^{2} + 6889 T^{4} \))(\( 1 + 159 T^{2} + 6889 T^{4} \))(\( 1 + 4 T + 152 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 - 122 T^{2} + 6889 T^{4} \))(\( 1 - 76 T^{2} + 6889 T^{4} \))(\( 1 + 160 T^{2} + 6889 T^{4} \))(\( 1 + 159 T^{2} + 6889 T^{4} \))(\( 1 - 4 T + 152 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 + 96 T^{2} + 13607 T^{4} + 661344 T^{6} + 47458321 T^{8} \))(\( 1 + 96 T^{2} + 13607 T^{4} + 661344 T^{6} + 47458321 T^{8} \))
$89$ (\( 1 - 11 T + 89 T^{2} \))(\( 1 - T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 - 3 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 + 7 T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + T + 89 T^{2} \))(\( 1 + 7 T + 89 T^{2} \))(\( 1 + 7 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 + 7 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 - 3 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 11 T + 89 T^{2} \))(\( 1 - 7 T + 89 T^{2} \))(\( 1 + 160 T^{2} + 7921 T^{4} \))(\( 1 + 128 T^{2} + 7921 T^{4} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( 1 + 3 T^{2} + 7921 T^{4} \))(\( 1 + 16 T^{2} + 7921 T^{4} \))(\( 1 + 160 T^{2} + 7921 T^{4} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( 1 + 3 T^{2} + 7921 T^{4} \))(\( 1 + 16 T^{2} + 7921 T^{4} \))(\( 1 + 248 T^{2} + 30327 T^{4} + 1964408 T^{6} + 62742241 T^{8} \))(\( 1 + 248 T^{2} + 30327 T^{4} + 1964408 T^{6} + 62742241 T^{8} \))
$97$ (\( 1 + 10 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 - 5 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 5 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 176 T^{2} + 9409 T^{4} \))(\( 1 + 96 T^{2} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 + 12 T + 134 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 - 24 T + 320 T^{2} - 2328 T^{3} + 9409 T^{4} \))(\( 1 + 176 T^{2} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 - 12 T + 134 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 + 24 T + 320 T^{2} + 2328 T^{3} + 9409 T^{4} \))(\( ( 1 + 176 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 + 176 T^{2} + 9409 T^{4} )^{2} \))
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