Properties

Label 2800.2.a
Level 2800
Weight 2
Character orbit a
Rep. character \(\chi_{2800}(1,\cdot)\)
Character field \(\Q\)
Dimension 57
Newform subspaces 44
Sturm bound 960
Trace bound 13

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Defining parameters

Level: \( N \) = \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2800.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 44 \)
Sturm bound: \(960\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2800))\).

Total New Old
Modular forms 516 57 459
Cusp forms 445 57 388
Eisenstein series 71 0 71

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.
\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(9\)
Plus space\(+\)\(26\)
Minus space\(-\)\(31\)

Trace form

\( 57q - q^{7} + 53q^{9} + O(q^{10}) \) \( 57q - q^{7} + 53q^{9} - 8q^{11} + 2q^{13} - 6q^{17} + 8q^{19} - 8q^{23} - 24q^{27} + 6q^{29} + 8q^{31} + 14q^{37} - 16q^{39} + 2q^{41} + 20q^{43} + 57q^{49} - 16q^{51} + 6q^{53} + 8q^{57} - 6q^{61} - 5q^{63} - 28q^{67} - 16q^{69} + 12q^{71} - 22q^{73} + 4q^{77} + 20q^{79} + 57q^{81} + 32q^{83} - 8q^{87} - 22q^{89} - 6q^{91} + 32q^{93} - 22q^{97} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2800))\) 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
2800.2.a.a \(1\) \(22.358\) \(\Q\) None \(0\) \(-3\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q-3q^{3}-q^{7}+6q^{9}-3q^{11}+q^{13}+\cdots\)
2800.2.a.b \(1\) \(22.358\) \(\Q\) None \(0\) \(-3\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-3q^{3}-q^{7}+6q^{9}+5q^{11}+6q^{13}+\cdots\)
2800.2.a.c \(1\) \(22.358\) \(\Q\) None \(0\) \(-3\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q-3q^{3}+q^{7}+6q^{9}+5q^{11}+5q^{13}+\cdots\)
2800.2.a.d \(1\) \(22.358\) \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-2q^{3}-q^{7}+q^{9}-5q^{11}+8q^{17}+\cdots\)
2800.2.a.e \(1\) \(22.358\) \(\Q\) None \(0\) \(-2\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q-2q^{3}+q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
2800.2.a.f \(1\) \(22.358\) \(\Q\) None \(0\) \(-2\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q-2q^{3}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
2800.2.a.g \(1\) \(22.358\) \(\Q\) None \(0\) \(-2\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q-2q^{3}+q^{7}+q^{9}+4q^{13}-6q^{17}+\cdots\)
2800.2.a.h \(1\) \(22.358\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{3}-q^{7}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
2800.2.a.i \(1\) \(22.358\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}-2q^{9}+5q^{11}-q^{13}+\cdots\)
2800.2.a.j \(1\) \(22.358\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}-2q^{9}+q^{11}-6q^{13}+\cdots\)
2800.2.a.k \(1\) \(22.358\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}-2q^{9}+q^{11}-q^{13}-3q^{17}+\cdots\)
2800.2.a.l \(1\) \(22.358\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q-q^{3}+q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
2800.2.a.m \(1\) \(22.358\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{7}-3q^{9}-4q^{11}+6q^{13}-2q^{17}+\cdots\)
2800.2.a.n \(1\) \(22.358\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{7}-3q^{9}-q^{11}-2q^{13}-4q^{17}+\cdots\)
2800.2.a.o \(1\) \(22.358\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{7}-3q^{9}+4q^{13}+4q^{17}-4q^{19}+\cdots\)
2800.2.a.p \(1\) \(22.358\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{7}-3q^{9}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
2800.2.a.q \(1\) \(22.358\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{7}-3q^{9}+5q^{11}-6q^{13}+4q^{17}+\cdots\)
2800.2.a.r \(1\) \(22.358\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q+q^{7}-3q^{9}-q^{11}+2q^{13}+4q^{17}+\cdots\)
2800.2.a.s \(1\) \(22.358\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+q^{7}-3q^{9}-4q^{13}-4q^{17}-4q^{19}+\cdots\)
2800.2.a.t \(1\) \(22.358\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+q^{7}-3q^{9}+5q^{11}+6q^{13}-4q^{17}+\cdots\)
2800.2.a.u \(1\) \(22.358\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(q+q^{3}-q^{7}-2q^{9}+q^{11}+q^{13}+3q^{17}+\cdots\)
2800.2.a.v \(1\) \(22.358\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q+q^{3}-q^{7}-2q^{9}+q^{11}+6q^{13}+\cdots\)
2800.2.a.w \(1\) \(22.358\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots\)
2800.2.a.x \(1\) \(22.358\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
2800.2.a.y \(1\) \(22.358\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}-2q^{9}-3q^{11}+q^{13}+\cdots\)
2800.2.a.z \(1\) \(22.358\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}-2q^{9}+3q^{11}-5q^{13}+\cdots\)
2800.2.a.ba \(1\) \(22.358\) \(\Q\) None \(0\) \(2\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q+2q^{3}-q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
2800.2.a.bb \(1\) \(22.358\) \(\Q\) None \(0\) \(2\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q+2q^{3}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
2800.2.a.bc \(1\) \(22.358\) \(\Q\) None \(0\) \(2\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q+2q^{3}+q^{7}+q^{9}-5q^{11}-8q^{17}+\cdots\)
2800.2.a.bd \(1\) \(22.358\) \(\Q\) None \(0\) \(2\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q+2q^{3}+q^{7}+q^{9}+2q^{17}+2q^{19}+\cdots\)
2800.2.a.be \(1\) \(22.358\) \(\Q\) None \(0\) \(3\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q+3q^{3}-q^{7}+6q^{9}+5q^{11}+3q^{13}+\cdots\)
2800.2.a.bf \(1\) \(22.358\) \(\Q\) None \(0\) \(3\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+3q^{3}+q^{7}+6q^{9}-3q^{11}-q^{13}+\cdots\)
2800.2.a.bg \(1\) \(22.358\) \(\Q\) None \(0\) \(3\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+3q^{3}+q^{7}+6q^{9}+5q^{11}-6q^{13}+\cdots\)
2800.2.a.bh \(2\) \(22.358\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+(-1-\beta )q^{3}+q^{7}+(3+2\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
2800.2.a.bi \(2\) \(22.358\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-\beta q^{3}-q^{7}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
2800.2.a.bj \(2\) \(22.358\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(q-\beta q^{3}-q^{7}+(1+\beta )q^{9}+(3-2\beta )q^{11}+\cdots\)
2800.2.a.bk \(2\) \(22.358\) \(\Q(\sqrt{33}) \) None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta q^{3}-q^{7}+(5+\beta )q^{9}+(-4+\beta )q^{11}+\cdots\)
2800.2.a.bl \(2\) \(22.358\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+\beta q^{3}-q^{7}+3q^{9}-2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
2800.2.a.bm \(2\) \(22.358\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+\beta q^{3}+q^{7}+3q^{9}+2\beta q^{11}+(2+\beta )q^{13}+\cdots\)
2800.2.a.bn \(2\) \(22.358\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{3}+q^{7}+(1+\beta )q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
2800.2.a.bo \(2\) \(22.358\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{3}+q^{7}+(1+\beta )q^{9}+(3-2\beta )q^{11}+\cdots\)
2800.2.a.bp \(2\) \(22.358\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{3}-q^{7}+(3+2\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
2800.2.a.bq \(3\) \(22.358\) 3.3.568.1 None \(0\) \(-1\) \(0\) \(3\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots\)
2800.2.a.br \(3\) \(22.358\) 3.3.568.1 None \(0\) \(1\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}-q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(700))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1400))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + T + 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 + T + 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 + 9 T^{4} \))(\( 1 + 9 T^{4} \))(\( 1 - T + 2 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - T + 2 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 + T + 3 T^{2} + 8 T^{3} + 9 T^{4} + 9 T^{5} + 27 T^{6} \))(\( 1 - T + 3 T^{2} - 8 T^{3} + 9 T^{4} - 9 T^{5} + 27 T^{6} \))
$5$ 1
$7$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))
$11$ (\( 1 + 3 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 4 T + 21 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + T + 18 T^{2} + 11 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 9 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 7 T + 26 T^{2} + 77 T^{3} + 121 T^{4} \))(\( 1 - 2 T^{2} + 121 T^{4} \))(\( 1 - 2 T^{2} + 121 T^{4} \))(\( 1 - T + 18 T^{2} - 11 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 9 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 21 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 7 T + 41 T^{2} + 146 T^{3} + 451 T^{4} + 847 T^{5} + 1331 T^{6} \))(\( 1 + 7 T + 41 T^{2} + 146 T^{3} + 451 T^{4} + 847 T^{5} + 1331 T^{6} \))
$13$ (\( 1 - T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 22 T^{2} - 26 T^{3} + 169 T^{4} \))(\( 1 + 5 T + 28 T^{2} + 65 T^{3} + 169 T^{4} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( 1 + 3 T + 20 T^{2} + 39 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 24 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + T - 12 T^{2} + 13 T^{3} + 169 T^{4} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( 1 + 2 T + 22 T^{2} + 26 T^{3} + 169 T^{4} \))(\( 1 + 5 T + 17 T^{2} + 24 T^{3} + 221 T^{4} + 845 T^{5} + 2197 T^{6} \))(\( 1 - 5 T + 17 T^{2} - 24 T^{3} + 221 T^{4} - 845 T^{5} + 2197 T^{6} \))
$17$ (\( 1 + 5 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - 5 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 - 4 T + 18 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 - 5 T + 36 T^{2} - 85 T^{3} + 289 T^{4} \))(\( 1 + T + 30 T^{2} + 17 T^{3} + 289 T^{4} \))(\( 1 + 5 T + 32 T^{2} + 85 T^{3} + 289 T^{4} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( 1 + 11 T + 60 T^{2} + 187 T^{3} + 289 T^{4} \))(\( 1 - T + 30 T^{2} - 17 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - T + 27 T^{2} - 54 T^{3} + 459 T^{4} - 289 T^{5} + 4913 T^{6} \))(\( 1 + T + 27 T^{2} + 54 T^{3} + 459 T^{4} + 289 T^{5} + 4913 T^{6} \))
$19$ (\( 1 - 8 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 + 18 T^{2} + 361 T^{4} \))(\( 1 - 6 T + 30 T^{2} - 114 T^{3} + 361 T^{4} \))(\( 1 + 3 T + 36 T^{2} + 57 T^{3} + 361 T^{4} \))(\( 1 + 2 T + 6 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 - 6 T + 30 T^{2} - 114 T^{3} + 361 T^{4} \))(\( 1 + 3 T + 36 T^{2} + 57 T^{3} + 361 T^{4} \))(\( 1 + 18 T^{2} + 361 T^{4} \))(\( 1 + 4 T + 43 T^{2} + 160 T^{3} + 817 T^{4} + 1444 T^{5} + 6859 T^{6} \))(\( 1 + 4 T + 43 T^{2} + 160 T^{3} + 817 T^{4} + 1444 T^{5} + 6859 T^{6} \))
$23$ (\( 1 + 2 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 7 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 5 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 8 T + 57 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 2 T + 30 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 + 7 T + 54 T^{2} + 161 T^{3} + 529 T^{4} \))(\( 1 - 2 T + 14 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 26 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 26 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 2 T + 30 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 - 7 T + 54 T^{2} - 161 T^{3} + 529 T^{4} \))(\( 1 + 8 T + 57 T^{2} + 184 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 41 T^{2} + 140 T^{3} + 943 T^{4} + 3174 T^{5} + 12167 T^{6} \))(\( 1 - 6 T + 41 T^{2} - 140 T^{3} + 943 T^{4} - 3174 T^{5} + 12167 T^{6} \))
$29$ (\( 1 + T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 7 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( ( 1 - 5 T + 29 T^{2} )^{2} \))(\( 1 - T + 20 T^{2} - 29 T^{3} + 841 T^{4} \))(\( 1 - 11 T + 84 T^{2} - 319 T^{3} + 841 T^{4} \))(\( 1 + 3 T + 52 T^{2} + 87 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 - 5 T + 60 T^{2} - 145 T^{3} + 841 T^{4} \))(\( 1 - 11 T + 84 T^{2} - 319 T^{3} + 841 T^{4} \))(\( ( 1 - 5 T + 29 T^{2} )^{2} \))(\( 1 - 3 T + 15 T^{2} - 66 T^{3} + 435 T^{4} - 2523 T^{5} + 24389 T^{6} \))(\( 1 - 3 T + 15 T^{2} - 66 T^{3} + 435 T^{4} - 2523 T^{5} + 24389 T^{6} \))
$31$ (\( 1 - 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 6 T + 26 T^{2} - 186 T^{3} + 961 T^{4} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( 1 - 10 T + 70 T^{2} - 310 T^{3} + 961 T^{4} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( 1 + 8 T + 54 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 4 T - 2 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 70 T^{2} - 310 T^{3} + 961 T^{4} \))(\( 1 - 6 T + 26 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 + 10 T + 101 T^{2} + 540 T^{3} + 3131 T^{4} + 9610 T^{5} + 29791 T^{6} \))(\( 1 + 10 T + 101 T^{2} + 540 T^{3} + 3131 T^{4} + 9610 T^{5} + 29791 T^{6} \))
$37$ (\( 1 - 10 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 - 9 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 + 9 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( ( 1 + 3 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( 1 + 3 T - 30 T^{2} + 111 T^{3} + 1369 T^{4} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( 1 + 6 T^{2} + 1369 T^{4} \))(\( 1 - 3 T - 30 T^{2} - 111 T^{3} + 1369 T^{4} \))(\( ( 1 - 3 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{3} \))(\( ( 1 - 6 T + 37 T^{2} )^{3} \))
$41$ (\( 1 + 6 T + 41 T^{2} \))(\( 1 - 11 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 11 T + 41 T^{2} \))(\( 1 - 14 T + 126 T^{2} - 574 T^{3} + 1681 T^{4} \))(\( 1 - 2 T + 66 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 + 9 T + 98 T^{2} + 369 T^{3} + 1681 T^{4} \))(\( 1 - 2 T + 50 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 94 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 94 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 - 6 T + 74 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 + 9 T + 98 T^{2} + 369 T^{3} + 1681 T^{4} \))(\( 1 - 14 T + 126 T^{2} - 574 T^{3} + 1681 T^{4} \))(\( 1 - 18 T + 191 T^{2} - 1388 T^{3} + 7831 T^{4} - 30258 T^{5} + 68921 T^{6} \))(\( 1 - 18 T + 191 T^{2} - 1388 T^{3} + 7831 T^{4} - 30258 T^{5} + 68921 T^{6} \))
$43$ (\( 1 - 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 3 T + 43 T^{2} \))(\( 1 - 11 T + 43 T^{2} \))(\( 1 + 9 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 11 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 + 11 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 11 T + 43 T^{2} \))(\( 1 - 9 T + 43 T^{2} \))(\( 1 - 3 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 8 T + 97 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 - 10 T + 94 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 + 9 T + 102 T^{2} + 387 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 62 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 - 8 T + 78 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 + 8 T + 78 T^{2} + 344 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 78 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 - 9 T + 102 T^{2} - 387 T^{3} + 1849 T^{4} \))(\( 1 + 8 T + 97 T^{2} + 344 T^{3} + 1849 T^{4} \))(\( 1 + 89 T^{2} + 64 T^{3} + 3827 T^{4} + 79507 T^{6} \))(\( 1 + 89 T^{2} - 64 T^{3} + 3827 T^{4} + 79507 T^{6} \))
$47$ (\( 1 + 11 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 - T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + T + 47 T^{2} \))(\( 1 - 11 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( ( 1 + 2 T + 47 T^{2} )^{2} \))(\( 1 + 5 T + 62 T^{2} + 235 T^{3} + 2209 T^{4} \))(\( 1 + 26 T^{2} + 2209 T^{4} \))(\( 1 - 3 T + 22 T^{2} - 141 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 86 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 9 T + 110 T^{2} - 423 T^{3} + 2209 T^{4} \))(\( 1 + 26 T^{2} + 2209 T^{4} \))(\( ( 1 - 2 T + 47 T^{2} )^{2} \))(\( 1 + 9 T + 93 T^{2} + 614 T^{3} + 4371 T^{4} + 19881 T^{5} + 103823 T^{6} \))(\( 1 - 9 T + 93 T^{2} - 614 T^{3} + 4371 T^{4} - 19881 T^{5} + 103823 T^{6} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 + 8 T + 102 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( 1 - 2 T + 90 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( 1 - 6 T + 98 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 98 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 - 12 T + 118 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( 1 + 12 T + 118 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( 1 - 18 T + 170 T^{2} - 954 T^{3} + 2809 T^{4} \))(\( 1 + 6 T + 98 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 8 T + 102 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 115 T^{2} + 588 T^{3} + 6095 T^{4} + 28090 T^{5} + 148877 T^{6} \))(\( 1 - 10 T + 115 T^{2} - 588 T^{3} + 6095 T^{4} - 28090 T^{5} + 148877 T^{6} \))
$59$ (\( 1 - 10 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 10 T + 98 T^{2} + 590 T^{3} + 3481 T^{4} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( 1 - 2 T - 34 T^{2} - 118 T^{3} + 3481 T^{4} \))(\( ( 1 + 8 T + 59 T^{2} )^{2} \))(\( 1 - 8 T + 128 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 128 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( 1 - 2 T - 34 T^{2} - 118 T^{3} + 3481 T^{4} \))(\( 1 + 10 T + 98 T^{2} + 590 T^{3} + 3481 T^{4} \))(\( 1 + 6 T + 99 T^{2} + 752 T^{3} + 5841 T^{4} + 20886 T^{5} + 205379 T^{6} \))(\( 1 + 6 T + 99 T^{2} + 752 T^{3} + 5841 T^{4} + 20886 T^{5} + 205379 T^{6} \))
$61$ (\( 1 + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 6 T + 86 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 - 6 T - 22 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 - 14 T + 154 T^{2} - 854 T^{3} + 3721 T^{4} \))(\( 1 - 6 T + 98 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 152 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 152 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 + 22 T + 226 T^{2} + 1342 T^{3} + 3721 T^{4} \))(\( 1 - 14 T + 154 T^{2} - 854 T^{3} + 3721 T^{4} \))(\( 1 + 6 T + 86 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 - 24 T + 365 T^{2} - 3368 T^{3} + 22265 T^{4} - 89304 T^{5} + 226981 T^{6} \))(\( 1 - 24 T + 365 T^{2} - 3368 T^{3} + 22265 T^{4} - 89304 T^{5} + 226981 T^{6} \))
$67$ (\( 1 - 10 T + 67 T^{2} \))(\( 1 - 9 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 + T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 + T + 67 T^{2} \))(\( 1 - 13 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 4 T + 133 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 70 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 24 T + 261 T^{2} + 1608 T^{3} + 4489 T^{4} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( 1 + 12 T + 102 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 - 24 T + 261 T^{2} - 1608 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 133 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 10 T + 137 T^{2} + 828 T^{3} + 9179 T^{4} + 44890 T^{5} + 300763 T^{6} \))(\( 1 - 10 T + 137 T^{2} - 828 T^{3} + 9179 T^{4} - 44890 T^{5} + 300763 T^{6} \))
$71$ (\( 1 + 71 T^{2} \))(\( 1 - 10 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 5 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 - 7 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 14 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 13 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 13 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 + 14 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 - 7 T + 71 T^{2} \))(\( 1 + 5 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 10 T + 71 T^{2} \))(\( 1 + 4 T + 101 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( 1 - 9 T + 124 T^{2} - 639 T^{3} + 5041 T^{4} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( 1 - 12 T + 154 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( 1 - 12 T + 154 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( 1 - 9 T + 124 T^{2} - 639 T^{3} + 5041 T^{4} \))(\( 1 + 4 T + 101 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 + 4 T + 193 T^{2} + 504 T^{3} + 13703 T^{4} + 20164 T^{5} + 357911 T^{6} \))(\( 1 + 4 T + 193 T^{2} + 504 T^{3} + 13703 T^{4} + 20164 T^{5} + 357911 T^{6} \))
$73$ (\( 1 + 10 T + 73 T^{2} \))(\( 1 - 7 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 5 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 15 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 15 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 5 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 7 T + 73 T^{2} \))(\( 1 - 22 T + 262 T^{2} - 1606 T^{3} + 5329 T^{4} \))(\( 1 - 8 T + 94 T^{2} - 584 T^{3} + 5329 T^{4} \))(\( 1 - 17 T + 214 T^{2} - 1241 T^{3} + 5329 T^{4} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( 1 - 4 T + 126 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 126 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 + 8 T + 94 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( 1 + 17 T + 214 T^{2} + 1241 T^{3} + 5329 T^{4} \))(\( 1 + 22 T + 262 T^{2} + 1606 T^{3} + 5329 T^{4} \))(\( 1 - 6 T + 191 T^{2} - 740 T^{3} + 13943 T^{4} - 31974 T^{5} + 389017 T^{6} \))(\( 1 + 6 T + 191 T^{2} + 740 T^{3} + 13943 T^{4} + 31974 T^{5} + 389017 T^{6} \))
$79$ (\( 1 - 7 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 - 3 T + 79 T^{2} \))(\( 1 - 13 T + 79 T^{2} \))(\( 1 - 7 T + 79 T^{2} \))(\( 1 - 9 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 - 3 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 9 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 - 9 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 + 5 T + 79 T^{2} \))(\( 1 - T + 79 T^{2} \))(\( 1 - 7 T + 79 T^{2} \))(\( 1 - 9 T + 79 T^{2} \))(\( 1 - 13 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 13 T + 79 T^{2} \))(\( 1 - 7 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 33 T^{2} + 6241 T^{4} \))(\( 1 - 9 T + 174 T^{2} - 711 T^{3} + 6241 T^{4} \))(\( 1 + T + 120 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 + 13 T + 126 T^{2} + 1027 T^{3} + 6241 T^{4} \))(\( 1 + 4 T + 138 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 + 4 T + 138 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 - 11 T + 150 T^{2} - 869 T^{3} + 6241 T^{4} \))(\( 1 + T + 120 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 + 33 T^{2} + 6241 T^{4} \))(\( 1 + 17 T + 205 T^{2} + 2138 T^{3} + 16195 T^{4} + 106097 T^{5} + 493039 T^{6} \))(\( 1 + 17 T + 205 T^{2} + 2138 T^{3} + 16195 T^{4} + 106097 T^{5} + 493039 T^{6} \))
$83$ (\( 1 + 12 T + 83 T^{2} \))(\( 1 - 11 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 10 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 10 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 11 T + 83 T^{2} \))(\( 1 + 2 T + 122 T^{2} + 166 T^{3} + 6889 T^{4} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( 1 - 15 T + 184 T^{2} - 1245 T^{3} + 6889 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 + 160 T^{2} + 6889 T^{4} \))(\( 1 + 160 T^{2} + 6889 T^{4} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( 1 + 15 T + 184 T^{2} + 1245 T^{3} + 6889 T^{4} \))(\( 1 - 2 T + 122 T^{2} - 166 T^{3} + 6889 T^{4} \))(\( 1 + 12 T + 107 T^{2} + 1168 T^{3} + 8881 T^{4} + 82668 T^{5} + 571787 T^{6} \))(\( 1 - 12 T + 107 T^{2} - 1168 T^{3} + 8881 T^{4} - 82668 T^{5} + 571787 T^{6} \))
$89$ (\( 1 - 8 T + 89 T^{2} \))(\( 1 + 11 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 + 16 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 4 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 + 11 T + 89 T^{2} \))(\( 1 - 30 T + 398 T^{2} - 2670 T^{3} + 7921 T^{4} \))(\( 1 - 6 T + 170 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 + T + 72 T^{2} + 89 T^{3} + 7921 T^{4} \))(\( 1 - 18 T + 226 T^{2} - 1602 T^{3} + 7921 T^{4} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( 1 - 2 T + 162 T^{2} - 178 T^{3} + 7921 T^{4} \))(\( 1 + T + 72 T^{2} + 89 T^{3} + 7921 T^{4} \))(\( 1 - 30 T + 398 T^{2} - 2670 T^{3} + 7921 T^{4} \))(\( 1 + 95 T^{2} - 464 T^{3} + 8455 T^{4} + 704969 T^{6} \))(\( 1 + 95 T^{2} - 464 T^{3} + 8455 T^{4} + 704969 T^{6} \))
$97$ (\( 1 - 3 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 13 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 16 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 + 19 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 19 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 17 T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 16 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 13 T + 97 T^{2} \))(\( 1 + 3 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 6 T + 198 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( 1 - 9 T + 108 T^{2} - 873 T^{3} + 9409 T^{4} \))(\( ( 1 - 6 T + 97 T^{2} )^{2} \))(\( 1 + 9 T + 8 T^{2} + 873 T^{3} + 9409 T^{4} \))(\( 1 + 12 T + 134 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( 1 - 12 T + 134 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( 1 + 15 T + 212 T^{2} + 1455 T^{3} + 9409 T^{4} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( 1 - 6 T + 198 T^{2} - 582 T^{3} + 9409 T^{4} \))(\( 1 - 9 T + 275 T^{2} - 1702 T^{3} + 26675 T^{4} - 84681 T^{5} + 912673 T^{6} \))(\( 1 + 9 T + 275 T^{2} + 1702 T^{3} + 26675 T^{4} + 84681 T^{5} + 912673 T^{6} \))
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