Properties

Label 3600.2.a
Level $3600$
Weight $2$
Character orbit 3600.a
Rep. character $\chi_{3600}(1,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $45$
Sturm bound $1440$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3600.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 45 \)
Sturm bound: \(1440\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3600))\).

Total New Old
Modular forms 792 49 743
Cusp forms 649 46 603
Eisenstein series 143 3 140

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

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(21\)
Minus space\(-\)\(25\)

Trace form

\( 46q + 2q^{7} + O(q^{10}) \) \( 46q + 2q^{7} - 4q^{11} - 2q^{17} + 8q^{19} + 6q^{23} - 2q^{29} - 4q^{37} + 2q^{41} + 2q^{43} - 22q^{47} + 42q^{49} - 2q^{53} - 28q^{59} - 8q^{61} - 18q^{67} - 20q^{71} + 20q^{73} - 16q^{77} + 20q^{79} - 10q^{83} - 2q^{89} + 4q^{91} + 12q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3600))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5
3600.2.a.a \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-5\) \(+\) \(-\) \(+\) \(q-5q^{7}-6q^{11}+3q^{13}-2q^{17}-q^{19}+\cdots\)
3600.2.a.b \(1\) \(28.746\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) \(-\) \(+\) \(-\) \(q-5q^{7}+5q^{13}+q^{19}+7q^{31}-10q^{37}+\cdots\)
3600.2.a.c \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q-4q^{7}-4q^{11}-4q^{13}+6q^{17}+4q^{19}+\cdots\)
3600.2.a.d \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q-4q^{7}-4q^{11}-4q^{17}+4q^{23}+6q^{29}+\cdots\)
3600.2.a.e \(1\) \(28.746\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q-4q^{7}-2q^{13}-8q^{19}+4q^{31}+10q^{37}+\cdots\)
3600.2.a.f \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(q-4q^{7}-2q^{13}+6q^{17}+4q^{19}+6q^{29}+\cdots\)
3600.2.a.g \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q-4q^{7}+4q^{11}-4q^{13}-6q^{17}+4q^{19}+\cdots\)
3600.2.a.h \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(q-4q^{7}+4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots\)
3600.2.a.i \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-3\) \(+\) \(-\) \(-\) \(q-3q^{7}+2q^{11}-3q^{13}-6q^{17}+7q^{19}+\cdots\)
3600.2.a.j \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(q-3q^{7}+2q^{11}-q^{13}+2q^{17}+5q^{19}+\cdots\)
3600.2.a.k \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q-2q^{7}-4q^{11}+4q^{13}+4q^{19}-2q^{23}+\cdots\)
3600.2.a.l \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q-2q^{7}-3q^{11}-4q^{13}+3q^{17}-5q^{19}+\cdots\)
3600.2.a.m \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q-2q^{7}+q^{11}+4q^{13}-5q^{17}-q^{19}+\cdots\)
3600.2.a.n \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q-2q^{7}+2q^{11}-2q^{13}+6q^{17}-8q^{19}+\cdots\)
3600.2.a.o \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q-2q^{7}+2q^{11}+6q^{13}-2q^{17}-4q^{23}+\cdots\)
3600.2.a.p \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{7}-4q^{11}-q^{13}+4q^{17}-q^{19}+\cdots\)
3600.2.a.q \(1\) \(28.746\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{7}+7q^{13}+7q^{19}-11q^{31}+10q^{37}+\cdots\)
3600.2.a.r \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{7}+4q^{11}-q^{13}-4q^{17}-q^{19}+\cdots\)
3600.2.a.s \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{7}+6q^{11}-5q^{13}-6q^{17}-5q^{19}+\cdots\)
3600.2.a.t \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-4q^{11}-6q^{13}-6q^{17}+4q^{19}+\cdots\)
3600.2.a.u \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q-4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots\)
3600.2.a.v \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots\)
3600.2.a.w \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q+q^{7}-4q^{11}+q^{13}-4q^{17}-q^{19}+\cdots\)
3600.2.a.x \(1\) \(28.746\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+q^{7}-7q^{13}+7q^{19}-11q^{31}-10q^{37}+\cdots\)
3600.2.a.y \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q+q^{7}+4q^{11}+q^{13}+4q^{17}-q^{19}+\cdots\)
3600.2.a.z \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+q^{7}+6q^{11}+5q^{13}+6q^{17}-5q^{19}+\cdots\)
3600.2.a.ba \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+2q^{7}-6q^{11}+4q^{13}+6q^{17}+4q^{19}+\cdots\)
3600.2.a.bb \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+2q^{7}-4q^{11}-4q^{13}+4q^{19}+2q^{23}+\cdots\)
3600.2.a.bc \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+2q^{7}-3q^{11}+4q^{13}-3q^{17}-5q^{19}+\cdots\)
3600.2.a.bd \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q+2q^{7}-2q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
3600.2.a.be \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+2q^{7}-2q^{13}-6q^{17}+4q^{19}-6q^{23}+\cdots\)
3600.2.a.bf \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+2q^{7}+q^{11}-4q^{13}+5q^{17}-q^{19}+\cdots\)
3600.2.a.bg \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+2q^{7}+2q^{11}-6q^{13}+2q^{17}+4q^{23}+\cdots\)
3600.2.a.bh \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q+2q^{7}+2q^{11}-4q^{13}-2q^{17}-4q^{19}+\cdots\)
3600.2.a.bi \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+2q^{7}+2q^{11}+2q^{13}-6q^{17}-8q^{19}+\cdots\)
3600.2.a.bj \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+2q^{7}+6q^{11}+4q^{13}-6q^{17}+4q^{19}+\cdots\)
3600.2.a.bk \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(3\) \(-\) \(-\) \(-\) \(q+3q^{7}+2q^{11}+q^{13}-2q^{17}+5q^{19}+\cdots\)
3600.2.a.bl \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(3\) \(+\) \(-\) \(+\) \(q+3q^{7}+2q^{11}+3q^{13}+6q^{17}+7q^{19}+\cdots\)
3600.2.a.bm \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+4q^{7}-4q^{11}+4q^{17}-4q^{23}+6q^{29}+\cdots\)
3600.2.a.bn \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+4q^{7}-4q^{11}+4q^{13}-6q^{17}+4q^{19}+\cdots\)
3600.2.a.bo \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q+4q^{7}+6q^{13}-2q^{17}-4q^{19}+8q^{23}+\cdots\)
3600.2.a.bp \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+4q^{7}+4q^{11}+4q^{13}+6q^{17}+4q^{19}+\cdots\)
3600.2.a.bq \(1\) \(28.746\) \(\Q\) None \(0\) \(0\) \(0\) \(5\) \(+\) \(-\) \(-\) \(q+5q^{7}-6q^{11}-3q^{13}+2q^{17}-q^{19}+\cdots\)
3600.2.a.br \(1\) \(28.746\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(-\) \(+\) \(+\) \(q+5q^{7}-5q^{13}+q^{19}+7q^{31}+10q^{37}+\cdots\)
3600.2.a.bs \(2\) \(28.746\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-\beta q^{17}-4q^{19}+2\beta q^{23}-8q^{31}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(900))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1800))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ 1
$7$ (\( 1 + 5 T + 7 T^{2} \))(\( 1 + 5 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))
$11$ (\( 1 + 6 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))
$13$ (\( 1 - 3 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 3 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 7 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 7 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 3 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))
$17$ (\( 1 + 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 5 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 5 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 14 T^{2} + 289 T^{4} \))
$19$ (\( 1 + T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))
$23$ (\( 1 - 2 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 34 T^{2} + 529 T^{4} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 10 T + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))
$31$ (\( 1 + 3 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 11 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 11 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))
$37$ (\( 1 - 6 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( ( 1 + 37 T^{2} )^{2} \))
$41$ (\( 1 + 4 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))
$43$ (\( 1 - 11 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 3 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + 13 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 - 13 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 - 3 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 11 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( ( 1 + 43 T^{2} )^{2} \))
$47$ (\( 1 - 10 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 14 T^{2} + 2209 T^{4} \))
$53$ (\( 1 + 8 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 86 T^{2} + 2809 T^{4} \))
$59$ (\( 1 + 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))
$61$ (\( 1 - 3 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 3 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))
$67$ (\( 1 + T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 16 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 + 14 T + 67 T^{2} \))(\( 1 - 13 T + 67 T^{2} \))(\( 1 - T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 - 11 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 - 11 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 13 T + 67 T^{2} \))(\( 1 + 11 T + 67 T^{2} \))(\( 1 - 13 T + 67 T^{2} \))(\( 1 + 11 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( ( 1 + 67 T^{2} )^{2} \))
$71$ (\( 1 + 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))
$73$ (\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 8 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 - 8 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 - 3 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 8 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 3 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 8 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( ( 1 + 73 T^{2} )^{2} \))
$79$ (\( 1 - 8 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 6 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 6 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))
$83$ (\( 1 - 6 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 13 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 13 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 154 T^{2} + 6889 T^{4} \))
$89$ (\( 1 - 16 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 16 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 - 9 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 9 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 16 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 16 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))
$97$ (\( 1 - 7 T + 97 T^{2} \))(\( 1 - 5 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 + 17 T + 97 T^{2} \))(\( 1 - 16 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 13 T + 97 T^{2} \))(\( 1 - 19 T + 97 T^{2} \))(\( 1 + 13 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 13 T + 97 T^{2} \))(\( 1 + 19 T + 97 T^{2} \))(\( 1 - 13 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 16 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 17 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( ( 1 + 97 T^{2} )^{2} \))
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