Properties

Label 4704.2.a
Level 4704
Weight 2
Character orbit a
Rep. character \(\chi_{4704}(1,\cdot)\)
Character field \(\Q\)
Dimension 82
Newform subspaces 52
Sturm bound 1792
Trace bound 19

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Defining parameters

Level: \( N \) \(=\) \( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4704.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 52 \)
Sturm bound: \(1792\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4704))\).

Total New Old
Modular forms 960 82 878
Cusp forms 833 82 751
Eisenstein series 127 0 127

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

\(2\)\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(-\)\(-\)\(+\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(12\)
Plus space\(+\)\(36\)
Minus space\(-\)\(46\)

Trace form

\( 82q + 4q^{5} + 82q^{9} + O(q^{10}) \) \( 82q + 4q^{5} + 82q^{9} + 12q^{13} - 12q^{17} + 62q^{25} + 4q^{29} - 8q^{33} + 12q^{37} - 28q^{41} + 4q^{45} - 12q^{53} + 8q^{57} - 4q^{61} - 40q^{65} - 12q^{73} + 82q^{81} + 40q^{85} - 12q^{89} - 8q^{93} + 36q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4704))\) 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
4704.2.a.a \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}-4q^{5}+q^{9}+6q^{11}+5q^{13}+\cdots\)
4704.2.a.b \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}-3q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
4704.2.a.c \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
4704.2.a.d \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{5}+q^{9}+2q^{11}+2q^{15}+\cdots\)
4704.2.a.e \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
4704.2.a.f \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{9}-q^{11}+q^{15}+8q^{17}+\cdots\)
4704.2.a.g \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+q^{9}-2q^{11}+q^{13}-2q^{17}+\cdots\)
4704.2.a.h \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+q^{9}-2q^{11}+5q^{13}-2q^{17}+\cdots\)
4704.2.a.i \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{9}+2q^{11}-5q^{13}+2q^{17}+\cdots\)
4704.2.a.j \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{9}+2q^{11}-q^{13}+2q^{17}+\cdots\)
4704.2.a.k \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{9}+2q^{11}+2q^{13}-4q^{17}+\cdots\)
4704.2.a.l \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}+q^{5}+q^{9}+q^{11}-q^{15}-8q^{17}+\cdots\)
4704.2.a.m \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
4704.2.a.n \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+2q^{5}+q^{9}-2q^{11}-2q^{15}+\cdots\)
4704.2.a.o \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(3\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+3q^{5}+q^{9}+q^{11}-4q^{13}+\cdots\)
4704.2.a.p \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(4\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+4q^{5}+q^{9}-6q^{11}-5q^{13}+\cdots\)
4704.2.a.q \(1\) \(37.562\) \(\Q\) None \(0\) \(-1\) \(4\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+4q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\)
4704.2.a.r \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(-4\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}-4q^{5}+q^{9}-6q^{11}+5q^{13}+\cdots\)
4704.2.a.s \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(-3\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}-3q^{5}+q^{9}+q^{11}+4q^{13}+\cdots\)
4704.2.a.t \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4704.2.a.u \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}-2q^{5}+q^{9}-2q^{11}-2q^{15}+\cdots\)
4704.2.a.v \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
4704.2.a.w \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}-q^{5}+q^{9}+q^{11}-q^{15}+8q^{17}+\cdots\)
4704.2.a.x \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{9}-2q^{11}-5q^{13}+2q^{17}+\cdots\)
4704.2.a.y \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{9}-2q^{11}-q^{13}+2q^{17}+\cdots\)
4704.2.a.z \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{9}-2q^{11}+2q^{13}-4q^{17}+\cdots\)
4704.2.a.ba \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{9}+2q^{11}+q^{13}-2q^{17}+\cdots\)
4704.2.a.bb \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+q^{9}+2q^{11}+5q^{13}-2q^{17}+\cdots\)
4704.2.a.bc \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+q^{9}-q^{11}+q^{15}-8q^{17}+\cdots\)
4704.2.a.bd \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+q^{9}+2q^{11}+2q^{15}+\cdots\)
4704.2.a.be \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
4704.2.a.bf \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(3\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+3q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
4704.2.a.bg \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+4q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\)
4704.2.a.bh \(1\) \(37.562\) \(\Q\) None \(0\) \(1\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+4q^{5}+q^{9}+6q^{11}-5q^{13}+\cdots\)
4704.2.a.bi \(2\) \(37.562\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+\beta q^{5}+q^{9}+\beta q^{11}-\beta q^{15}+\cdots\)
4704.2.a.bj \(2\) \(37.562\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+\beta q^{13}+\cdots\)
4704.2.a.bk \(2\) \(37.562\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{9}+\beta q^{11}+\beta q^{13}+\beta q^{17}+\cdots\)
4704.2.a.bl \(2\) \(37.562\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}-3\beta q^{13}+\cdots\)
4704.2.a.bm \(2\) \(37.562\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+\beta q^{5}+q^{9}+(2+\beta )q^{11}-2q^{13}+\cdots\)
4704.2.a.bn \(2\) \(37.562\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}+q^{9}+(-2-\beta )q^{11}+\cdots\)
4704.2.a.bo \(2\) \(37.562\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}-3\beta q^{13}+\cdots\)
4704.2.a.bp \(2\) \(37.562\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{9}-\beta q^{11}+\beta q^{13}+\beta q^{17}+\cdots\)
4704.2.a.bq \(2\) \(37.562\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}+\beta q^{13}+\cdots\)
4704.2.a.br \(2\) \(37.562\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+\beta q^{15}+\cdots\)
4704.2.a.bs \(3\) \(37.562\) 3.3.621.1 None \(0\) \(-3\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}+\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
4704.2.a.bt \(3\) \(37.562\) 3.3.621.1 None \(0\) \(-3\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}-\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
4704.2.a.bu \(3\) \(37.562\) 3.3.621.1 None \(0\) \(3\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
4704.2.a.bv \(3\) \(37.562\) 3.3.621.1 None \(0\) \(3\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}-\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
4704.2.a.bw \(4\) \(37.562\) 4.4.2624.1 None \(0\) \(-4\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)
4704.2.a.bx \(4\) \(37.562\) 4.4.2624.1 None \(0\) \(-4\) \(4\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}+(1+\beta _{3})q^{5}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)
4704.2.a.by \(4\) \(37.562\) 4.4.2624.1 None \(0\) \(4\) \(-4\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots\)
4704.2.a.bz \(4\) \(37.562\) 4.4.2624.1 None \(0\) \(4\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+(1+\beta _{3})q^{5}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4704))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4704)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1568))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2352))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))
$5$ (\( 1 + 4 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 2 T^{2} + 25 T^{4} \))(\( 1 + 8 T^{2} + 25 T^{4} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( 1 + 8 T^{2} + 25 T^{4} \))(\( 1 - 2 T^{2} + 25 T^{4} \))(\( 1 - 2 T^{2} + 25 T^{4} \))(\( 1 + 8 T^{2} + 25 T^{4} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( 1 + 8 T^{2} + 25 T^{4} \))(\( 1 + 2 T^{2} + 25 T^{4} \))(\( 1 + 6 T^{2} + 4 T^{3} + 30 T^{4} + 125 T^{6} \))(\( 1 + 6 T^{2} - 4 T^{3} + 30 T^{4} + 125 T^{6} \))(\( 1 + 6 T^{2} + 4 T^{3} + 30 T^{4} + 125 T^{6} \))(\( 1 + 6 T^{2} - 4 T^{3} + 30 T^{4} + 125 T^{6} \))(\( 1 + 4 T + 12 T^{2} + 36 T^{3} + 98 T^{4} + 180 T^{5} + 300 T^{6} + 500 T^{7} + 625 T^{8} \))(\( 1 - 4 T + 12 T^{2} - 36 T^{3} + 98 T^{4} - 180 T^{5} + 300 T^{6} - 500 T^{7} + 625 T^{8} \))(\( 1 + 4 T + 12 T^{2} + 36 T^{3} + 98 T^{4} + 180 T^{5} + 300 T^{6} + 500 T^{7} + 625 T^{8} \))(\( 1 - 4 T + 12 T^{2} - 36 T^{3} + 98 T^{4} - 180 T^{5} + 300 T^{6} - 500 T^{7} + 625 T^{8} \))
$7$ 1
$11$ (\( 1 - 6 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 4 T + 14 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 14 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 + 6 T^{2} - 38 T^{3} + 66 T^{4} + 1331 T^{6} \))(\( 1 + 6 T^{2} + 38 T^{3} + 66 T^{4} + 1331 T^{6} \))(\( 1 + 6 T^{2} + 38 T^{3} + 66 T^{4} + 1331 T^{6} \))(\( 1 + 6 T^{2} - 38 T^{3} + 66 T^{4} + 1331 T^{6} \))(\( 1 - 4 T + 24 T^{2} - 84 T^{3} + 302 T^{4} - 924 T^{5} + 2904 T^{6} - 5324 T^{7} + 14641 T^{8} \))(\( 1 + 4 T + 24 T^{2} + 84 T^{3} + 302 T^{4} + 924 T^{5} + 2904 T^{6} + 5324 T^{7} + 14641 T^{8} \))(\( 1 + 4 T + 24 T^{2} + 84 T^{3} + 302 T^{4} + 924 T^{5} + 2904 T^{6} + 5324 T^{7} + 14641 T^{8} \))(\( 1 - 4 T + 24 T^{2} - 84 T^{3} + 302 T^{4} - 924 T^{5} + 2904 T^{6} - 5324 T^{7} + 14641 T^{8} \))
$13$ (\( 1 - 5 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 + 24 T^{2} + 169 T^{4} \))(\( 1 - 6 T^{2} + 169 T^{4} \))(\( 1 + 8 T^{2} + 169 T^{4} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( 1 + 8 T^{2} + 169 T^{4} \))(\( 1 - 6 T^{2} + 169 T^{4} \))(\( 1 + 24 T^{2} + 169 T^{4} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 + 3 T + 3 T^{2} - 34 T^{3} + 39 T^{4} + 507 T^{5} + 2197 T^{6} \))(\( 1 - 3 T + 3 T^{2} + 34 T^{3} + 39 T^{4} - 507 T^{5} + 2197 T^{6} \))(\( 1 + 3 T + 3 T^{2} - 34 T^{3} + 39 T^{4} + 507 T^{5} + 2197 T^{6} \))(\( 1 - 3 T + 3 T^{2} + 34 T^{3} + 39 T^{4} - 507 T^{5} + 2197 T^{6} \))(\( 1 + 8 T + 48 T^{2} + 232 T^{3} + 978 T^{4} + 3016 T^{5} + 8112 T^{6} + 17576 T^{7} + 28561 T^{8} \))(\( 1 - 8 T + 48 T^{2} - 232 T^{3} + 978 T^{4} - 3016 T^{5} + 8112 T^{6} - 17576 T^{7} + 28561 T^{8} \))(\( 1 + 8 T + 48 T^{2} + 232 T^{3} + 978 T^{4} + 3016 T^{5} + 8112 T^{6} + 17576 T^{7} + 28561 T^{8} \))(\( 1 - 8 T + 48 T^{2} - 232 T^{3} + 978 T^{4} - 3016 T^{5} + 8112 T^{6} - 17576 T^{7} + 28561 T^{8} \))
$17$ (\( 1 - 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 26 T^{2} + 289 T^{4} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 + 16 T^{2} + 289 T^{4} \))(\( 1 + 8 T + 38 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 + 8 T + 38 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 + 16 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 + 26 T^{2} + 289 T^{4} \))(\( 1 - 6 T + 27 T^{2} - 108 T^{3} + 459 T^{4} - 1734 T^{5} + 4913 T^{6} \))(\( 1 + 6 T + 27 T^{2} + 108 T^{3} + 459 T^{4} + 1734 T^{5} + 4913 T^{6} \))(\( 1 - 6 T + 27 T^{2} - 108 T^{3} + 459 T^{4} - 1734 T^{5} + 4913 T^{6} \))(\( 1 + 6 T + 27 T^{2} + 108 T^{3} + 459 T^{4} + 1734 T^{5} + 4913 T^{6} \))(\( 1 + 4 T + 44 T^{2} + 84 T^{3} + 818 T^{4} + 1428 T^{5} + 12716 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 - 4 T + 44 T^{2} - 84 T^{3} + 818 T^{4} - 1428 T^{5} + 12716 T^{6} - 19652 T^{7} + 83521 T^{8} \))(\( 1 + 4 T + 44 T^{2} + 84 T^{3} + 818 T^{4} + 1428 T^{5} + 12716 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 - 4 T + 44 T^{2} - 84 T^{3} + 818 T^{4} - 1428 T^{5} + 12716 T^{6} - 19652 T^{7} + 83521 T^{8} \))
$19$ (\( 1 - T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + 3 T + 19 T^{2} \))(\( 1 + 3 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 8 T + 19 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 361 T^{4} \))(\( 1 - 10 T^{2} + 361 T^{4} \))(\( ( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( 1 + 3 T + 21 T^{2} + 2 T^{3} + 399 T^{4} + 1083 T^{5} + 6859 T^{6} \))(\( 1 + 3 T + 21 T^{2} + 2 T^{3} + 399 T^{4} + 1083 T^{5} + 6859 T^{6} \))(\( 1 - 3 T + 21 T^{2} - 2 T^{3} + 399 T^{4} - 1083 T^{5} + 6859 T^{6} \))(\( 1 - 3 T + 21 T^{2} - 2 T^{3} + 399 T^{4} - 1083 T^{5} + 6859 T^{6} \))(\( 1 + 8 T + 68 T^{2} + 392 T^{3} + 1926 T^{4} + 7448 T^{5} + 24548 T^{6} + 54872 T^{7} + 130321 T^{8} \))(\( 1 + 8 T + 68 T^{2} + 392 T^{3} + 1926 T^{4} + 7448 T^{5} + 24548 T^{6} + 54872 T^{7} + 130321 T^{8} \))(\( 1 - 8 T + 68 T^{2} - 392 T^{3} + 1926 T^{4} - 7448 T^{5} + 24548 T^{6} - 54872 T^{7} + 130321 T^{8} \))(\( 1 - 8 T + 68 T^{2} - 392 T^{3} + 1926 T^{4} - 7448 T^{5} + 24548 T^{6} - 54872 T^{7} + 130321 T^{8} \))
$23$ (\( 1 + 6 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 26 T^{2} + 529 T^{4} \))(\( 1 + 38 T^{2} + 529 T^{4} \))(\( 1 + 14 T^{2} + 529 T^{4} \))(\( 1 + 38 T^{2} + 529 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 38 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 38 T^{2} + 529 T^{4} \))(\( 1 + 14 T^{2} + 529 T^{4} \))(\( 1 + 38 T^{2} + 529 T^{4} \))(\( 1 - 26 T^{2} + 529 T^{4} \))(\( 1 - 6 T + 45 T^{2} - 180 T^{3} + 1035 T^{4} - 3174 T^{5} + 12167 T^{6} \))(\( 1 + 6 T + 45 T^{2} + 180 T^{3} + 1035 T^{4} + 3174 T^{5} + 12167 T^{6} \))(\( 1 + 6 T + 45 T^{2} + 180 T^{3} + 1035 T^{4} + 3174 T^{5} + 12167 T^{6} \))(\( 1 - 6 T + 45 T^{2} - 180 T^{3} + 1035 T^{4} - 3174 T^{5} + 12167 T^{6} \))(\( 1 - 12 T + 120 T^{2} - 780 T^{3} + 4350 T^{4} - 17940 T^{5} + 63480 T^{6} - 146004 T^{7} + 279841 T^{8} \))(\( 1 + 12 T + 120 T^{2} + 780 T^{3} + 4350 T^{4} + 17940 T^{5} + 63480 T^{6} + 146004 T^{7} + 279841 T^{8} \))(\( 1 + 12 T + 120 T^{2} + 780 T^{3} + 4350 T^{4} + 17940 T^{5} + 63480 T^{6} + 146004 T^{7} + 279841 T^{8} \))(\( 1 - 12 T + 120 T^{2} - 780 T^{3} + 4350 T^{4} - 17940 T^{5} + 63480 T^{6} - 146004 T^{7} + 279841 T^{8} \))
$29$ (\( 1 + 29 T^{2} \))(\( 1 + 7 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 7 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 7 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 7 T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( 1 - 4 T + 14 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 14 T^{2} - 116 T^{3} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( 1 - 12 T + 126 T^{2} - 728 T^{3} + 3654 T^{4} - 10092 T^{5} + 24389 T^{6} \))(\( 1 - 12 T + 126 T^{2} - 728 T^{3} + 3654 T^{4} - 10092 T^{5} + 24389 T^{6} \))(\( 1 - 12 T + 126 T^{2} - 728 T^{3} + 3654 T^{4} - 10092 T^{5} + 24389 T^{6} \))(\( 1 - 12 T + 126 T^{2} - 728 T^{3} + 3654 T^{4} - 10092 T^{5} + 24389 T^{6} \))(\( 1 + 60 T^{2} + 128 T^{3} + 1862 T^{4} + 3712 T^{5} + 50460 T^{6} + 707281 T^{8} \))(\( 1 + 60 T^{2} + 128 T^{3} + 1862 T^{4} + 3712 T^{5} + 50460 T^{6} + 707281 T^{8} \))(\( 1 + 60 T^{2} + 128 T^{3} + 1862 T^{4} + 3712 T^{5} + 50460 T^{6} + 707281 T^{8} \))(\( 1 + 60 T^{2} + 128 T^{3} + 1862 T^{4} + 3712 T^{5} + 50460 T^{6} + 707281 T^{8} \))
$31$ (\( 1 + 3 T + 31 T^{2} \))(\( 1 + 11 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - T + 31 T^{2} \))(\( 1 - T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 11 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 - 11 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 11 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( 1 - 8 T + 30 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 30 T^{2} + 248 T^{3} + 961 T^{4} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( 1 + 3 T + 72 T^{2} + 139 T^{3} + 2232 T^{4} + 2883 T^{5} + 29791 T^{6} \))(\( 1 + 3 T + 72 T^{2} + 139 T^{3} + 2232 T^{4} + 2883 T^{5} + 29791 T^{6} \))(\( 1 - 3 T + 72 T^{2} - 139 T^{3} + 2232 T^{4} - 2883 T^{5} + 29791 T^{6} \))(\( 1 - 3 T + 72 T^{2} - 139 T^{3} + 2232 T^{4} - 2883 T^{5} + 29791 T^{6} \))(\( 1 - 8 T + 84 T^{2} - 616 T^{3} + 3222 T^{4} - 19096 T^{5} + 80724 T^{6} - 238328 T^{7} + 923521 T^{8} \))(\( 1 - 8 T + 84 T^{2} - 616 T^{3} + 3222 T^{4} - 19096 T^{5} + 80724 T^{6} - 238328 T^{7} + 923521 T^{8} \))(\( 1 + 8 T + 84 T^{2} + 616 T^{3} + 3222 T^{4} + 19096 T^{5} + 80724 T^{6} + 238328 T^{7} + 923521 T^{8} \))(\( 1 + 8 T + 84 T^{2} + 616 T^{3} + 3222 T^{4} + 19096 T^{5} + 80724 T^{6} + 238328 T^{7} + 923521 T^{8} \))
$37$ (\( 1 - 3 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 9 T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 + 9 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 + 9 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 9 T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 4 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 4 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( 1 - 3 T + 27 T^{2} + 146 T^{3} + 999 T^{4} - 4107 T^{5} + 50653 T^{6} \))(\( 1 - 3 T + 27 T^{2} + 146 T^{3} + 999 T^{4} - 4107 T^{5} + 50653 T^{6} \))(\( 1 - 3 T + 27 T^{2} + 146 T^{3} + 999 T^{4} - 4107 T^{5} + 50653 T^{6} \))(\( 1 - 3 T + 27 T^{2} + 146 T^{3} + 999 T^{4} - 4107 T^{5} + 50653 T^{6} \))(\( ( 1 + 42 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 42 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 42 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 42 T^{2} + 1369 T^{4} )^{2} \))
$41$ (\( 1 + 6 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 10 T^{2} + 1681 T^{4} \))(\( 1 + 80 T^{2} + 1681 T^{4} \))(\( 1 + 50 T^{2} + 1681 T^{4} \))(\( 1 + 32 T^{2} + 1681 T^{4} \))(\( 1 + 16 T + 134 T^{2} + 656 T^{3} + 1681 T^{4} \))(\( 1 + 16 T + 134 T^{2} + 656 T^{3} + 1681 T^{4} \))(\( 1 + 32 T^{2} + 1681 T^{4} \))(\( 1 + 50 T^{2} + 1681 T^{4} \))(\( 1 + 80 T^{2} + 1681 T^{4} \))(\( 1 + 10 T^{2} + 1681 T^{4} \))(\( 1 + 6 T + 27 T^{2} - 20 T^{3} + 1107 T^{4} + 10086 T^{5} + 68921 T^{6} \))(\( 1 - 6 T + 27 T^{2} + 20 T^{3} + 1107 T^{4} - 10086 T^{5} + 68921 T^{6} \))(\( 1 + 6 T + 27 T^{2} - 20 T^{3} + 1107 T^{4} + 10086 T^{5} + 68921 T^{6} \))(\( 1 - 6 T + 27 T^{2} + 20 T^{3} + 1107 T^{4} - 10086 T^{5} + 68921 T^{6} \))(\( 1 + 20 T + 220 T^{2} + 1540 T^{3} + 9874 T^{4} + 63140 T^{5} + 369820 T^{6} + 1378420 T^{7} + 2825761 T^{8} \))(\( 1 - 20 T + 220 T^{2} - 1540 T^{3} + 9874 T^{4} - 63140 T^{5} + 369820 T^{6} - 1378420 T^{7} + 2825761 T^{8} \))(\( 1 + 20 T + 220 T^{2} + 1540 T^{3} + 9874 T^{4} + 63140 T^{5} + 369820 T^{6} + 1378420 T^{7} + 2825761 T^{8} \))(\( 1 - 20 T + 220 T^{2} - 1540 T^{3} + 9874 T^{4} - 63140 T^{5} + 369820 T^{6} - 1378420 T^{7} + 2825761 T^{8} \))
$43$ (\( 1 - 5 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 - 42 T^{2} + 1849 T^{4} \))(\( 1 + 54 T^{2} + 1849 T^{4} \))(\( ( 1 + 43 T^{2} )^{2} \))(\( 1 + 54 T^{2} + 1849 T^{4} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( 1 + 54 T^{2} + 1849 T^{4} \))(\( ( 1 + 43 T^{2} )^{2} \))(\( 1 + 54 T^{2} + 1849 T^{4} \))(\( 1 - 42 T^{2} + 1849 T^{4} \))(\( 1 + 15 T + 177 T^{2} + 1318 T^{3} + 7611 T^{4} + 27735 T^{5} + 79507 T^{6} \))(\( 1 - 15 T + 177 T^{2} - 1318 T^{3} + 7611 T^{4} - 27735 T^{5} + 79507 T^{6} \))(\( 1 - 15 T + 177 T^{2} - 1318 T^{3} + 7611 T^{4} - 27735 T^{5} + 79507 T^{6} \))(\( 1 + 15 T + 177 T^{2} + 1318 T^{3} + 7611 T^{4} + 27735 T^{5} + 79507 T^{6} \))(\( 1 + 8 T + 124 T^{2} + 648 T^{3} + 6710 T^{4} + 27864 T^{5} + 229276 T^{6} + 636056 T^{7} + 3418801 T^{8} \))(\( 1 - 8 T + 124 T^{2} - 648 T^{3} + 6710 T^{4} - 27864 T^{5} + 229276 T^{6} - 636056 T^{7} + 3418801 T^{8} \))(\( 1 - 8 T + 124 T^{2} - 648 T^{3} + 6710 T^{4} - 27864 T^{5} + 229276 T^{6} - 636056 T^{7} + 3418801 T^{8} \))(\( 1 + 8 T + 124 T^{2} + 648 T^{3} + 6710 T^{4} + 27864 T^{5} + 229276 T^{6} + 636056 T^{7} + 3418801 T^{8} \))
$47$ (\( 1 + 4 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 12 T + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 4 T + 47 T^{2} )^{2} \))(\( 1 + 8 T + 62 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 62 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( ( 1 - 4 T + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 12 T + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( 1 + 12 T + 153 T^{2} + 1016 T^{3} + 7191 T^{4} + 26508 T^{5} + 103823 T^{6} \))(\( 1 + 12 T + 153 T^{2} + 1016 T^{3} + 7191 T^{4} + 26508 T^{5} + 103823 T^{6} \))(\( 1 - 12 T + 153 T^{2} - 1016 T^{3} + 7191 T^{4} - 26508 T^{5} + 103823 T^{6} \))(\( 1 - 12 T + 153 T^{2} - 1016 T^{3} + 7191 T^{4} - 26508 T^{5} + 103823 T^{6} \))(\( 1 - 16 T + 164 T^{2} - 1232 T^{3} + 7990 T^{4} - 57904 T^{5} + 362276 T^{6} - 1661168 T^{7} + 4879681 T^{8} \))(\( 1 - 16 T + 164 T^{2} - 1232 T^{3} + 7990 T^{4} - 57904 T^{5} + 362276 T^{6} - 1661168 T^{7} + 4879681 T^{8} \))(\( 1 + 16 T + 164 T^{2} + 1232 T^{3} + 7990 T^{4} + 57904 T^{5} + 362276 T^{6} + 1661168 T^{7} + 4879681 T^{8} \))(\( 1 + 16 T + 164 T^{2} + 1232 T^{3} + 7990 T^{4} + 57904 T^{5} + 362276 T^{6} + 1661168 T^{7} + 4879681 T^{8} \))
$53$ (\( 1 + 6 T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 10 T + 53 T^{2} )^{2} \))(\( ( 1 + 2 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 2 T + 53 T^{2} )^{2} \))(\( ( 1 + 2 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 2 T + 53 T^{2} )^{2} \))(\( ( 1 - 10 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( 1 - 6 T + 78 T^{2} - 802 T^{3} + 4134 T^{4} - 16854 T^{5} + 148877 T^{6} \))(\( 1 - 6 T + 78 T^{2} - 802 T^{3} + 4134 T^{4} - 16854 T^{5} + 148877 T^{6} \))(\( 1 - 6 T + 78 T^{2} - 802 T^{3} + 4134 T^{4} - 16854 T^{5} + 148877 T^{6} \))(\( 1 - 6 T + 78 T^{2} - 802 T^{3} + 4134 T^{4} - 16854 T^{5} + 148877 T^{6} \))(\( 1 + 140 T^{2} - 128 T^{3} + 9494 T^{4} - 6784 T^{5} + 393260 T^{6} + 7890481 T^{8} \))(\( 1 + 140 T^{2} - 128 T^{3} + 9494 T^{4} - 6784 T^{5} + 393260 T^{6} + 7890481 T^{8} \))(\( 1 + 140 T^{2} - 128 T^{3} + 9494 T^{4} - 6784 T^{5} + 393260 T^{6} + 7890481 T^{8} \))(\( 1 + 140 T^{2} - 128 T^{3} + 9494 T^{4} - 6784 T^{5} + 393260 T^{6} + 7890481 T^{8} \))
$59$ (\( 1 + 6 T + 59 T^{2} \))(\( 1 + 7 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 9 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 9 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 7 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 7 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 9 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 9 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 7 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 - 8 T + 59 T^{2} )^{2} \))(\( 1 - 16 T + 134 T^{2} - 944 T^{3} + 3481 T^{4} \))(\( 1 + 16 T + 134 T^{2} + 944 T^{3} + 3481 T^{4} \))(\( ( 1 + 8 T + 59 T^{2} )^{2} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( 1 + 12 T + 198 T^{2} + 1334 T^{3} + 11682 T^{4} + 41772 T^{5} + 205379 T^{6} \))(\( 1 + 12 T + 198 T^{2} + 1334 T^{3} + 11682 T^{4} + 41772 T^{5} + 205379 T^{6} \))(\( 1 - 12 T + 198 T^{2} - 1334 T^{3} + 11682 T^{4} - 41772 T^{5} + 205379 T^{6} \))(\( 1 - 12 T + 198 T^{2} - 1334 T^{3} + 11682 T^{4} - 41772 T^{5} + 205379 T^{6} \))(\( 1 + 84 T^{2} - 960 T^{3} + 1350 T^{4} - 56640 T^{5} + 292404 T^{6} + 12117361 T^{8} \))(\( 1 + 84 T^{2} - 960 T^{3} + 1350 T^{4} - 56640 T^{5} + 292404 T^{6} + 12117361 T^{8} \))(\( 1 + 84 T^{2} + 960 T^{3} + 1350 T^{4} + 56640 T^{5} + 292404 T^{6} + 12117361 T^{8} \))(\( 1 + 84 T^{2} + 960 T^{3} + 1350 T^{4} + 56640 T^{5} + 292404 T^{6} + 12117361 T^{8} \))
$61$ (\( 1 + 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 12 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 12 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 12 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 12 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 90 T^{2} + 3721 T^{4} \))(\( 1 + 120 T^{2} + 3721 T^{4} \))(\( 1 + 90 T^{2} + 3721 T^{4} \))(\( 1 + 104 T^{2} + 3721 T^{4} \))(\( 1 - 4 T + 78 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 - 4 T + 78 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 104 T^{2} + 3721 T^{4} \))(\( 1 + 90 T^{2} + 3721 T^{4} \))(\( 1 + 120 T^{2} + 3721 T^{4} \))(\( 1 + 90 T^{2} + 3721 T^{4} \))(\( 1 + 18 T + 195 T^{2} + 1644 T^{3} + 11895 T^{4} + 66978 T^{5} + 226981 T^{6} \))(\( 1 - 18 T + 195 T^{2} - 1644 T^{3} + 11895 T^{4} - 66978 T^{5} + 226981 T^{6} \))(\( 1 + 18 T + 195 T^{2} + 1644 T^{3} + 11895 T^{4} + 66978 T^{5} + 226981 T^{6} \))(\( 1 - 18 T + 195 T^{2} - 1644 T^{3} + 11895 T^{4} - 66978 T^{5} + 226981 T^{6} \))(\( 1 + 16 T + 288 T^{2} + 2768 T^{3} + 27282 T^{4} + 168848 T^{5} + 1071648 T^{6} + 3631696 T^{7} + 13845841 T^{8} \))(\( 1 - 16 T + 288 T^{2} - 2768 T^{3} + 27282 T^{4} - 168848 T^{5} + 1071648 T^{6} - 3631696 T^{7} + 13845841 T^{8} \))(\( 1 + 16 T + 288 T^{2} + 2768 T^{3} + 27282 T^{4} + 168848 T^{5} + 1071648 T^{6} + 3631696 T^{7} + 13845841 T^{8} \))(\( 1 - 16 T + 288 T^{2} - 2768 T^{3} + 27282 T^{4} - 168848 T^{5} + 1071648 T^{6} - 3631696 T^{7} + 13845841 T^{8} \))
$67$ (\( 1 - 7 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))(\( 1 + 16 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 - 11 T + 67 T^{2} \))(\( 1 + 11 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 16 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 11 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 11 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 + 102 T^{2} + 4489 T^{4} \))(\( 1 + 6 T^{2} + 4489 T^{4} \))(\( 1 + 6 T^{2} + 4489 T^{4} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( 1 - 8 T + 102 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 102 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( 1 + 6 T^{2} + 4489 T^{4} \))(\( 1 + 6 T^{2} + 4489 T^{4} \))(\( 1 + 102 T^{2} + 4489 T^{4} \))(\( 1 + 9 T + 189 T^{2} + 1042 T^{3} + 12663 T^{4} + 40401 T^{5} + 300763 T^{6} \))(\( 1 - 9 T + 189 T^{2} - 1042 T^{3} + 12663 T^{4} - 40401 T^{5} + 300763 T^{6} \))(\( 1 - 9 T + 189 T^{2} - 1042 T^{3} + 12663 T^{4} - 40401 T^{5} + 300763 T^{6} \))(\( 1 + 9 T + 189 T^{2} + 1042 T^{3} + 12663 T^{4} + 40401 T^{5} + 300763 T^{6} \))(\( 1 + 8 T + 124 T^{2} - 56 T^{3} + 3286 T^{4} - 3752 T^{5} + 556636 T^{6} + 2406104 T^{7} + 20151121 T^{8} \))(\( 1 - 8 T + 124 T^{2} + 56 T^{3} + 3286 T^{4} + 3752 T^{5} + 556636 T^{6} - 2406104 T^{7} + 20151121 T^{8} \))(\( 1 - 8 T + 124 T^{2} + 56 T^{3} + 3286 T^{4} + 3752 T^{5} + 556636 T^{6} - 2406104 T^{7} + 20151121 T^{8} \))(\( 1 + 8 T + 124 T^{2} - 56 T^{3} + 3286 T^{4} - 3752 T^{5} + 556636 T^{6} + 2406104 T^{7} + 20151121 T^{8} \))
$71$ (\( 1 - 16 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 10 T + 71 T^{2} \))(\( 1 + 16 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 16 T + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 + 16 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 10 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 14 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 + 134 T^{2} + 5041 T^{4} \))(\( 1 + 134 T^{2} + 5041 T^{4} \))(\( 1 + 110 T^{2} + 5041 T^{4} \))(\( 1 - 58 T^{2} + 5041 T^{4} \))(\( 1 - 12 T + 166 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( 1 + 12 T + 166 T^{2} + 852 T^{3} + 5041 T^{4} \))(\( 1 - 58 T^{2} + 5041 T^{4} \))(\( 1 + 110 T^{2} + 5041 T^{4} \))(\( 1 + 134 T^{2} + 5041 T^{4} \))(\( 1 + 134 T^{2} + 5041 T^{4} \))(\( 1 + 177 T^{2} + 32 T^{3} + 12567 T^{4} + 357911 T^{6} \))(\( 1 + 177 T^{2} - 32 T^{3} + 12567 T^{4} + 357911 T^{6} \))(\( 1 + 177 T^{2} - 32 T^{3} + 12567 T^{4} + 357911 T^{6} \))(\( 1 + 177 T^{2} + 32 T^{3} + 12567 T^{4} + 357911 T^{6} \))(\( 1 - 12 T + 248 T^{2} - 2380 T^{3} + 25406 T^{4} - 168980 T^{5} + 1250168 T^{6} - 4294932 T^{7} + 25411681 T^{8} \))(\( 1 + 12 T + 248 T^{2} + 2380 T^{3} + 25406 T^{4} + 168980 T^{5} + 1250168 T^{6} + 4294932 T^{7} + 25411681 T^{8} \))(\( 1 + 12 T + 248 T^{2} + 2380 T^{3} + 25406 T^{4} + 168980 T^{5} + 1250168 T^{6} + 4294932 T^{7} + 25411681 T^{8} \))(\( 1 - 12 T + 248 T^{2} - 2380 T^{3} + 25406 T^{4} - 168980 T^{5} + 1250168 T^{6} - 4294932 T^{7} + 25411681 T^{8} \))
$73$ (\( 1 + 3 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 + 3 T + 73 T^{2} \))(\( 1 - 3 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 3 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 3 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 3 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 + 3 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 3 T + 73 T^{2} \))(\( 1 + 114 T^{2} + 5329 T^{4} \))(\( 1 - 16 T^{2} + 5329 T^{4} \))(\( 1 + 18 T^{2} + 5329 T^{4} \))(\( 1 + 144 T^{2} + 5329 T^{4} \))(\( 1 + 12 T + 134 T^{2} + 876 T^{3} + 5329 T^{4} \))(\( 1 + 12 T + 134 T^{2} + 876 T^{3} + 5329 T^{4} \))(\( 1 + 144 T^{2} + 5329 T^{4} \))(\( 1 + 18 T^{2} + 5329 T^{4} \))(\( 1 - 16 T^{2} + 5329 T^{4} \))(\( 1 + 114 T^{2} + 5329 T^{4} \))(\( 1 - 33 T + 555 T^{2} - 5814 T^{3} + 40515 T^{4} - 175857 T^{5} + 389017 T^{6} \))(\( 1 + 33 T + 555 T^{2} + 5814 T^{3} + 40515 T^{4} + 175857 T^{5} + 389017 T^{6} \))(\( 1 - 33 T + 555 T^{2} - 5814 T^{3} + 40515 T^{4} - 175857 T^{5} + 389017 T^{6} \))(\( 1 + 33 T + 555 T^{2} + 5814 T^{3} + 40515 T^{4} + 175857 T^{5} + 389017 T^{6} \))(\( 1 + 8 T + 256 T^{2} + 1608 T^{3} + 27170 T^{4} + 117384 T^{5} + 1364224 T^{6} + 3112136 T^{7} + 28398241 T^{8} \))(\( 1 - 8 T + 256 T^{2} - 1608 T^{3} + 27170 T^{4} - 117384 T^{5} + 1364224 T^{6} - 3112136 T^{7} + 28398241 T^{8} \))(\( 1 + 8 T + 256 T^{2} + 1608 T^{3} + 27170 T^{4} + 117384 T^{5} + 1364224 T^{6} + 3112136 T^{7} + 28398241 T^{8} \))(\( 1 - 8 T + 256 T^{2} - 1608 T^{3} + 27170 T^{4} - 117384 T^{5} + 1364224 T^{6} - 3112136 T^{7} + 28398241 T^{8} \))
$79$ (\( 1 - 11 T + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 9 T + 79 T^{2} \))(\( 1 + 5 T + 79 T^{2} \))(\( 1 + 17 T + 79 T^{2} \))(\( 1 - 17 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 9 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 9 T + 79 T^{2} \))(\( 1 + 17 T + 79 T^{2} \))(\( 1 + 5 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 - 17 T + 79 T^{2} \))(\( 1 - 9 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))(\( 1 + 126 T^{2} + 6241 T^{4} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 + 8 T + 126 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - 8 T + 126 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 + 126 T^{2} + 6241 T^{4} \))(\( 1 - 27 T + 432 T^{2} - 4619 T^{3} + 34128 T^{4} - 168507 T^{5} + 493039 T^{6} \))(\( 1 + 27 T + 432 T^{2} + 4619 T^{3} + 34128 T^{4} + 168507 T^{5} + 493039 T^{6} \))(\( 1 + 27 T + 432 T^{2} + 4619 T^{3} + 34128 T^{4} + 168507 T^{5} + 493039 T^{6} \))(\( 1 - 27 T + 432 T^{2} - 4619 T^{3} + 34128 T^{4} - 168507 T^{5} + 493039 T^{6} \))(\( 1 - 16 T + 284 T^{2} - 2768 T^{3} + 31366 T^{4} - 218672 T^{5} + 1772444 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 + 16 T + 284 T^{2} + 2768 T^{3} + 31366 T^{4} + 218672 T^{5} + 1772444 T^{6} + 7888624 T^{7} + 38950081 T^{8} \))(\( 1 + 16 T + 284 T^{2} + 2768 T^{3} + 31366 T^{4} + 218672 T^{5} + 1772444 T^{6} + 7888624 T^{7} + 38950081 T^{8} \))(\( 1 - 16 T + 284 T^{2} - 2768 T^{3} + 31366 T^{4} - 218672 T^{5} + 1772444 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))
$83$ (\( 1 - 12 T + 83 T^{2} \))(\( 1 + 11 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 11 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 11 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 11 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( 1 + 18 T + 234 T^{2} + 2040 T^{3} + 19422 T^{4} + 124002 T^{5} + 571787 T^{6} \))(\( 1 + 18 T + 234 T^{2} + 2040 T^{3} + 19422 T^{4} + 124002 T^{5} + 571787 T^{6} \))(\( 1 - 18 T + 234 T^{2} - 2040 T^{3} + 19422 T^{4} - 124002 T^{5} + 571787 T^{6} \))(\( 1 - 18 T + 234 T^{2} - 2040 T^{3} + 19422 T^{4} - 124002 T^{5} + 571787 T^{6} \))(\( 1 + 204 T^{2} - 256 T^{3} + 21878 T^{4} - 21248 T^{5} + 1405356 T^{6} + 47458321 T^{8} \))(\( 1 + 204 T^{2} - 256 T^{3} + 21878 T^{4} - 21248 T^{5} + 1405356 T^{6} + 47458321 T^{8} \))(\( 1 + 204 T^{2} + 256 T^{3} + 21878 T^{4} + 21248 T^{5} + 1405356 T^{6} + 47458321 T^{8} \))(\( 1 + 204 T^{2} + 256 T^{3} + 21878 T^{4} + 21248 T^{5} + 1405356 T^{6} + 47458321 T^{8} \))
$89$ (\( 1 - 4 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 - 4 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 + 170 T^{2} + 7921 T^{4} \))(\( 1 + 128 T^{2} + 7921 T^{4} \))(\( 1 + 146 T^{2} + 7921 T^{4} \))(\( 1 + 176 T^{2} + 7921 T^{4} \))(\( 1 + 166 T^{2} + 7921 T^{4} \))(\( 1 + 166 T^{2} + 7921 T^{4} \))(\( 1 + 176 T^{2} + 7921 T^{4} \))(\( 1 + 146 T^{2} + 7921 T^{4} \))(\( 1 + 128 T^{2} + 7921 T^{4} \))(\( 1 + 170 T^{2} + 7921 T^{4} \))(\( 1 + 12 T + 279 T^{2} + 2024 T^{3} + 24831 T^{4} + 95052 T^{5} + 704969 T^{6} \))(\( 1 - 12 T + 279 T^{2} - 2024 T^{3} + 24831 T^{4} - 95052 T^{5} + 704969 T^{6} \))(\( 1 + 12 T + 279 T^{2} + 2024 T^{3} + 24831 T^{4} + 95052 T^{5} + 704969 T^{6} \))(\( 1 - 12 T + 279 T^{2} - 2024 T^{3} + 24831 T^{4} - 95052 T^{5} + 704969 T^{6} \))(\( 1 + 28 T + 524 T^{2} + 6764 T^{3} + 72658 T^{4} + 601996 T^{5} + 4150604 T^{6} + 19739132 T^{7} + 62742241 T^{8} \))(\( 1 - 28 T + 524 T^{2} - 6764 T^{3} + 72658 T^{4} - 601996 T^{5} + 4150604 T^{6} - 19739132 T^{7} + 62742241 T^{8} \))(\( 1 + 28 T + 524 T^{2} + 6764 T^{3} + 72658 T^{4} + 601996 T^{5} + 4150604 T^{6} + 19739132 T^{7} + 62742241 T^{8} \))(\( 1 - 28 T + 524 T^{2} - 6764 T^{3} + 72658 T^{4} - 601996 T^{5} + 4150604 T^{6} - 19739132 T^{7} + 62742241 T^{8} \))
$97$ (\( 1 + 6 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 + 96 T^{2} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 + 32 T^{2} + 9409 T^{4} \))(\( 1 - 4 T + 150 T^{2} - 388 T^{3} + 9409 T^{4} \))(\( 1 - 4 T + 150 T^{2} - 388 T^{3} + 9409 T^{4} \))(\( 1 + 32 T^{2} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 + 96 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 + 264 T^{2} + 38 T^{3} + 25608 T^{4} + 912673 T^{6} \))(\( 1 + 264 T^{2} - 38 T^{3} + 25608 T^{4} + 912673 T^{6} \))(\( 1 + 264 T^{2} + 38 T^{3} + 25608 T^{4} + 912673 T^{6} \))(\( 1 + 264 T^{2} - 38 T^{3} + 25608 T^{4} + 912673 T^{6} \))(\( 1 + 40 T + 896 T^{2} + 13608 T^{3} + 153858 T^{4} + 1319976 T^{5} + 8430464 T^{6} + 36506920 T^{7} + 88529281 T^{8} \))(\( 1 - 40 T + 896 T^{2} - 13608 T^{3} + 153858 T^{4} - 1319976 T^{5} + 8430464 T^{6} - 36506920 T^{7} + 88529281 T^{8} \))(\( 1 + 40 T + 896 T^{2} + 13608 T^{3} + 153858 T^{4} + 1319976 T^{5} + 8430464 T^{6} + 36506920 T^{7} + 88529281 T^{8} \))(\( 1 - 40 T + 896 T^{2} - 13608 T^{3} + 153858 T^{4} - 1319976 T^{5} + 8430464 T^{6} - 36506920 T^{7} + 88529281 T^{8} \))
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