Properties

Label 4410.2.a
Level 4410
Weight 2
Character orbit a
Rep. character \(\chi_{4410}(1,\cdot)\)
Character field \(\Q\)
Dimension 67
Newform subspaces 53
Sturm bound 2016
Trace bound 17

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Defining parameters

Level: \( N \) \(=\) \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4410.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 53 \)
Sturm bound: \(2016\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4410))\).

Total New Old
Modular forms 1072 67 1005
Cusp forms 945 67 878
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.

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(26\)
Minus space\(-\)\(41\)

Trace form

\( 67q + q^{2} + 67q^{4} - q^{5} + q^{8} + O(q^{10}) \) \( 67q + q^{2} + 67q^{4} - q^{5} + q^{8} + q^{10} - 4q^{11} - 2q^{13} + 67q^{16} - 6q^{17} - 8q^{19} - q^{20} - 4q^{22} - 24q^{23} + 67q^{25} - 10q^{26} + 10q^{29} + 8q^{31} + q^{32} - 10q^{34} + 42q^{37} - 8q^{38} + q^{40} - 10q^{41} + 36q^{43} - 4q^{44} - 8q^{47} + q^{50} - 2q^{52} - 18q^{53} - 4q^{55} - 14q^{58} - 12q^{59} + 22q^{61} + 67q^{64} - 2q^{65} + 52q^{67} - 6q^{68} - 32q^{71} + 38q^{73} + 6q^{74} - 8q^{76} + 80q^{79} - q^{80} + 14q^{82} + 40q^{83} + 14q^{85} - 16q^{86} - 4q^{88} + 54q^{89} - 24q^{92} + 24q^{94} + 20q^{95} - 10q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4410))\) 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 7
4410.2.a.a \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
4410.2.a.b \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
4410.2.a.c \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-3q^{11}+\cdots\)
4410.2.a.d \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-2q^{11}+\cdots\)
4410.2.a.e \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-2q^{11}+\cdots\)
4410.2.a.f \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-2q^{13}+\cdots\)
4410.2.a.g \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots\)
4410.2.a.h \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+2q^{11}+\cdots\)
4410.2.a.i \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+4q^{11}+\cdots\)
4410.2.a.j \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+5q^{11}+\cdots\)
4410.2.a.k \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+6q^{11}+\cdots\)
4410.2.a.l \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-4q^{11}+\cdots\)
4410.2.a.m \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-3q^{11}+\cdots\)
4410.2.a.n \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
4410.2.a.o \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
4410.2.a.p \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{13}+\cdots\)
4410.2.a.q \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{11}+\cdots\)
4410.2.a.r \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+2q^{11}+\cdots\)
4410.2.a.s \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+4q^{11}+\cdots\)
4410.2.a.t \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+4q^{11}+\cdots\)
4410.2.a.u \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+5q^{11}+\cdots\)
4410.2.a.v \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-6q^{11}+\cdots\)
4410.2.a.w \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-3q^{11}+\cdots\)
4410.2.a.x \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-3q^{11}+\cdots\)
4410.2.a.y \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-2q^{13}+\cdots\)
4410.2.a.z \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-2q^{13}+\cdots\)
4410.2.a.ba \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{11}+\cdots\)
4410.2.a.bb \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+2q^{11}+\cdots\)
4410.2.a.bc \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+4q^{11}+\cdots\)
4410.2.a.bd \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+6q^{11}+\cdots\)
4410.2.a.be \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-6q^{11}+\cdots\)
4410.2.a.bf \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-6q^{11}+\cdots\)
4410.2.a.bg \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-3q^{11}+\cdots\)
4410.2.a.bh \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-3q^{11}+\cdots\)
4410.2.a.bi \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-2q^{13}+\cdots\)
4410.2.a.bj \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots\)
4410.2.a.bk \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+2q^{11}+\cdots\)
4410.2.a.bl \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots\)
4410.2.a.bm \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+6q^{11}+\cdots\)
4410.2.a.bn \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bo \(2\) \(35.214\) \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bp \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+(2+\beta )q^{11}+\cdots\)
4410.2.a.bq \(2\) \(35.214\) \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.br \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bs \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+(2+\beta )q^{11}+\cdots\)
4410.2.a.bt \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bu \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bv \(2\) \(35.214\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(2+\beta )q^{11}+\cdots\)
4410.2.a.bw \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(2+3\beta )q^{11}+\cdots\)
4410.2.a.bx \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.by \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bz \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+(2+3\beta )q^{11}+\cdots\)
4410.2.a.ca \(2\) \(35.214\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+(2+\beta )q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4410))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4410)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1470))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2205))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))
$3$ 1
$5$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))
$7$ 1
$11$ (\( 1 + 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 4 T + 24 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 19 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 19 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 24 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 24 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 19 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 8 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 24 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 8 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 19 T^{2} - 44 T^{3} + 121 T^{4} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 7 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 7 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 - 4 T + 23 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + 8 T + 34 T^{2} + 104 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 23 T^{2} + 52 T^{3} + 169 T^{4} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 - 8 T + 34 T^{2} - 104 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 22 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 - 8 T + 34 T^{2} - 104 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 23 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 - 6 T^{2} + 169 T^{4} \))(\( 1 + 8 T + 34 T^{2} + 104 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 22 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 6 T^{2} + 169 T^{4} \))(\( 1 - 4 T + 23 T^{2} - 52 T^{3} + 169 T^{4} \))
$17$ (\( 1 + 4 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 + 4 T + 10 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 36 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 10 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 + 4 T + 36 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 36 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 10 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 36 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 136 T^{3} + 289 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 136 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 10 T^{2} - 68 T^{3} + 289 T^{4} \))
$19$ (\( 1 + 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 3 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 30 T^{2} + 361 T^{4} \))(\( 1 + 2 T + 11 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 34 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 2 T + 11 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 + 30 T^{2} + 361 T^{4} \))(\( 1 - 4 T + 34 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 40 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 34 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 2 T + 11 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 + 8 T + 46 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 34 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 40 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 8 T + 46 T^{2} - 152 T^{3} + 361 T^{4} \))(\( 1 + 2 T + 11 T^{2} + 38 T^{3} + 361 T^{4} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} \))(\( ( 1 + 3 T + 23 T^{2} )^{2} \))(\( 1 - 4 T + 18 T^{2} - 92 T^{3} + 529 T^{4} \))(\( ( 1 + 3 T + 23 T^{2} )^{2} \))(\( 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 8 T + 54 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 92 T^{3} + 529 T^{4} \))(\( ( 1 - 3 T + 23 T^{2} )^{2} \))(\( 1 + 12 T + 74 T^{2} + 276 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 8 T + 54 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 12 T + 74 T^{2} + 276 T^{3} + 529 T^{4} \))(\( ( 1 - 3 T + 23 T^{2} )^{2} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 8 T + 56 T^{2} + 232 T^{3} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( 1 - 8 T + 72 T^{2} - 232 T^{3} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( 1 + 8 T + 56 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 72 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 54 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 72 T^{2} + 232 T^{3} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( 1 + 8 T + 72 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 72 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 54 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 72 T^{2} + 232 T^{3} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 4 T + 16 T^{2} + 124 T^{3} + 961 T^{4} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( 1 + 12 T + 96 T^{2} + 372 T^{3} + 961 T^{4} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( 1 - 4 T + 16 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 - 12 T + 96 T^{2} - 372 T^{3} + 961 T^{4} \))(\( 1 + 54 T^{2} + 961 T^{4} \))(\( 1 - 12 T + 96 T^{2} - 372 T^{3} + 961 T^{4} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( 1 + 12 T + 80 T^{2} + 372 T^{3} + 961 T^{4} \))(\( 1 + 12 T + 96 T^{2} + 372 T^{3} + 961 T^{4} \))(\( 1 + 54 T^{2} + 961 T^{4} \))(\( 1 - 12 T + 80 T^{2} - 372 T^{3} + 961 T^{4} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))
$37$ (\( 1 - 8 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 72 T^{2} + 1369 T^{4} \))(\( 1 - 4 T + 15 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 76 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 15 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 + 72 T^{2} + 1369 T^{4} \))(\( 1 + 4 T + 76 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 76 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 15 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 - 8 T + 72 T^{2} - 296 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 76 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 8 T + 72 T^{2} - 296 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 15 T^{2} - 148 T^{3} + 1369 T^{4} \))
$41$ (\( 1 + 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 11 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 11 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 12 T + 110 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 - 8 T + 91 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 - 4 T + 54 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 + 8 T + 91 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 110 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 + 4 T + 54 T^{2} + 164 T^{3} + 1681 T^{4} \))(\( 1 + 8 T + 48 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 - 4 T + 54 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 - 8 T + 91 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 + 4 T + 14 T^{2} + 164 T^{3} + 1681 T^{4} \))(\( 1 + 4 T + 54 T^{2} + 164 T^{3} + 1681 T^{4} \))(\( 1 - 8 T + 48 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 - 4 T + 14 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 + 8 T + 91 T^{2} + 328 T^{3} + 1681 T^{4} \))
$43$ (\( 1 + 2 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 - 12 T + 120 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 + 36 T^{2} + 1849 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 - 12 T + 120 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 + 36 T^{2} + 1849 T^{4} \))(\( 1 + 12 T + 114 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 + 36 T^{2} + 1849 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 - 4 T + 40 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 + 36 T^{2} + 1849 T^{4} \))(\( 1 + 12 T + 114 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 - 4 T + 40 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 516 T^{3} + 1849 T^{4} \))
$47$ (\( 1 + 10 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 11 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 11 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 5 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 5 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 4 T + 48 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 - 2 T - 17 T^{2} - 94 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 108 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 2 T - 17 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( 1 + 4 T + 48 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 108 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 16 T + 150 T^{2} + 752 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 108 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 - 2 T - 17 T^{2} - 94 T^{3} + 2209 T^{4} \))(\( 1 + 4 T + 80 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 108 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 16 T + 150 T^{2} - 752 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 80 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 + 2 T - 17 T^{2} + 94 T^{3} + 2209 T^{4} \))
$53$ (\( 1 - 14 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 11 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 11 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 4 T - 18 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 103 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 103 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 + 4 T - 18 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 103 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 12 T + 110 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 38 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 + 12 T + 110 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 103 T^{2} - 530 T^{3} + 2809 T^{4} \))
$59$ (\( 1 - 4 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 12 T + 82 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 106 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 4 T + 114 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 106 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 82 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 + 4 T + 114 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 + 20 T + 216 T^{2} + 1180 T^{3} + 3481 T^{4} \))(\( 1 - 4 T + 114 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 106 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 146 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 4 T + 114 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 20 T + 216 T^{2} - 1180 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 146 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 106 T^{2} - 472 T^{3} + 3481 T^{4} \))
$61$ (\( 1 - 8 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 12 T + 126 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 12 T + 130 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 106 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 130 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 126 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 - 8 T + 106 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( 1 + 4 T - 2 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 - 8 T + 106 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 130 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 + 12 T + 126 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 106 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( 1 - 4 T - 2 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 126 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 + 12 T + 130 T^{2} + 732 T^{3} + 3721 T^{4} \))
$67$ (\( 1 - 6 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 6 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 4 T + 40 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 - 20 T + 206 T^{2} - 1340 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 52 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 20 T + 206 T^{2} - 1340 T^{3} + 4489 T^{4} \))(\( 1 + 4 T + 40 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 52 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 118 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 52 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 20 T + 206 T^{2} - 1340 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 88 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 52 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 118 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 88 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 20 T + 206 T^{2} - 1340 T^{3} + 4489 T^{4} \))
$71$ (\( 1 + 2 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 16 T + 198 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 - 16 T + 178 T^{2} - 1136 T^{3} + 5041 T^{4} \))(\( 1 + 4 T + 74 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 - 16 T + 178 T^{2} - 1136 T^{3} + 5041 T^{4} \))(\( 1 + 16 T + 198 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 + 4 T + 74 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 - 4 T + 74 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 + 16 T + 178 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 - 4 T + 74 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 + 16 T + 178 T^{2} + 1136 T^{3} + 5041 T^{4} \))
$73$ (\( 1 - 10 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 4 T + 118 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( 1 + 20 T + 238 T^{2} + 1460 T^{3} + 5329 T^{4} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( 1 + 4 T + 118 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 - 20 T + 238 T^{2} - 1460 T^{3} + 5329 T^{4} \))(\( 1 + 16 T + 208 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( 1 - 20 T + 238 T^{2} - 1460 T^{3} + 5329 T^{4} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( 1 + 20 T + 238 T^{2} + 1460 T^{3} + 5329 T^{4} \))(\( 1 - 16 T + 208 T^{2} - 1168 T^{3} + 5329 T^{4} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))
$79$ (\( 1 - 16 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 - 12 T + 166 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 166 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 166 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 166 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 166 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( 1 - 12 T + 166 T^{2} - 948 T^{3} + 6241 T^{4} \))
$83$ (\( 1 - 8 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 7 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 7 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 - 16 T + 222 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 - 20 T + 238 T^{2} - 1660 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 158 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 + 20 T + 238 T^{2} + 1660 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 222 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 - 16 T + 158 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 + 4 T + 152 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 158 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 - 20 T + 238 T^{2} - 1660 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 222 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 - 16 T + 158 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 - 4 T + 152 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 - 16 T + 222 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 + 20 T + 238 T^{2} + 1660 T^{3} + 6889 T^{4} \))
$89$ (\( 1 + 2 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 + T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 18 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 18 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 4 T + 110 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 + 8 T + 82 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 142 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 8 T + 82 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( 1 - 4 T + 110 T^{2} - 356 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 142 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 + 16 T^{2} + 7921 T^{4} \))(\( 1 - 12 T + 142 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 + 8 T + 82 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 + 4 T + 174 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 142 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 + 16 T^{2} + 7921 T^{4} \))(\( 1 - 4 T + 174 T^{2} - 356 T^{3} + 7921 T^{4} \))(\( 1 - 8 T + 82 T^{2} - 712 T^{3} + 7921 T^{4} \))
$97$ (\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 16 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 16 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 16 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 16 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 12 T + 222 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( ( 1 - 4 T + 97 T^{2} )^{2} \))(\( 1 + 12 T + 158 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( 1 + 12 T + 222 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( 1 - 12 T + 158 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( 1 + 24 T + 320 T^{2} + 2328 T^{3} + 9409 T^{4} \))(\( 1 - 12 T + 158 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( 1 - 4 T + 126 T^{2} - 388 T^{3} + 9409 T^{4} \))(\( 1 + 12 T + 158 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( 1 - 24 T + 320 T^{2} - 2328 T^{3} + 9409 T^{4} \))(\( 1 + 4 T + 126 T^{2} + 388 T^{3} + 9409 T^{4} \))(\( ( 1 - 4 T + 97 T^{2} )^{2} \))
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