Properties

Label 5610.2.a
Level 5610
Weight 2
Character orbit a
Rep. character \(\chi_{5610}(1,\cdot)\)
Character field \(\Q\)
Dimension 111
Newform subspaces 63
Sturm bound 2592
Trace bound 13

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Defining parameters

Level: \( N \) = \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5610.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 63 \)
Sturm bound: \(2592\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(13\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5610))\).

Total New Old
Modular forms 1312 111 1201
Cusp forms 1281 111 1170
Eisenstein series 31 0 31

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

\(2\)\(3\)\(5\)\(11\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(44\)
Minus space\(-\)\(67\)

Trace form

\( 111q - q^{2} + 7q^{3} + 111q^{4} - q^{5} - q^{6} + 8q^{7} - q^{8} + 111q^{9} + O(q^{10}) \) \( 111q - q^{2} + 7q^{3} + 111q^{4} - q^{5} - q^{6} + 8q^{7} - q^{8} + 111q^{9} - q^{10} - q^{11} + 7q^{12} + 2q^{13} - 8q^{14} - q^{15} + 111q^{16} - q^{17} - q^{18} - 4q^{19} - q^{20} + 8q^{21} + 7q^{22} - 8q^{23} - q^{24} + 111q^{25} + 2q^{26} + 7q^{27} + 8q^{28} - 30q^{29} - q^{30} - q^{32} - q^{33} - q^{34} - 8q^{35} + 111q^{36} + 26q^{37} + 28q^{38} + 34q^{39} - q^{40} + 22q^{41} - 8q^{42} + 36q^{43} - q^{44} - q^{45} + 8q^{46} + 16q^{47} + 7q^{48} + 119q^{49} - q^{50} - q^{51} + 2q^{52} + 26q^{53} - q^{54} - q^{55} - 8q^{56} + 28q^{57} + 2q^{58} + 20q^{59} - q^{60} + 18q^{61} + 32q^{62} + 8q^{63} + 111q^{64} + 18q^{65} - q^{66} + 60q^{67} - q^{68} + 8q^{69} - 8q^{70} + 8q^{71} - q^{72} + 6q^{73} - 6q^{74} + 7q^{75} - 4q^{76} + 8q^{77} + 2q^{78} + 64q^{79} - q^{80} + 111q^{81} + 22q^{82} + 44q^{83} + 8q^{84} - q^{85} + 68q^{86} + 34q^{87} + 7q^{88} - 26q^{89} - q^{90} - 16q^{91} - 8q^{92} + 16q^{93} + 16q^{94} - 20q^{95} - q^{96} + 30q^{97} + 71q^{98} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5610))\) 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 11 17
5610.2.a.a \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
5610.2.a.b \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
5610.2.a.c \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5610.2.a.d \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
5610.2.a.e \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(4\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
5610.2.a.f \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-3\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
5610.2.a.g \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5610.2.a.h \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5610.2.a.i \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(1\) \(2\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
5610.2.a.j \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(1\) \(3\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
5610.2.a.k \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
5610.2.a.l \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
5610.2.a.m \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
5610.2.a.n \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
5610.2.a.o \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5610.2.a.p \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(3\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots\)
5610.2.a.q \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
5610.2.a.r \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.s \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.t \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(2\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
5610.2.a.u \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
5610.2.a.v \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(4\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
5610.2.a.w \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-4\) \(-\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
5610.2.a.x \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
5610.2.a.y \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.z \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.ba \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
5610.2.a.bb \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
5610.2.a.bc \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5610.2.a.bd \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(1\) \(3\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
5610.2.a.be \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots\)
5610.2.a.bf \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(-4\) \(-\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots\)
5610.2.a.bg \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
5610.2.a.bh \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5610.2.a.bi \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(4\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
5610.2.a.bj \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(5\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+5q^{7}+\cdots\)
5610.2.a.bk \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots\)
5610.2.a.bl \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5610.2.a.bm \(2\) \(44.796\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.bn \(2\) \(44.796\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta q^{7}+\cdots\)
5610.2.a.bo \(2\) \(44.796\) \(\Q(\sqrt{41}) \) None \(-2\) \(-2\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta q^{7}+\cdots\)
5610.2.a.bp \(2\) \(44.796\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(-2\) \(1\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta q^{7}+\cdots\)
5610.2.a.bq \(2\) \(44.796\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(2\) \(-1\) \(+\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta q^{7}+\cdots\)
5610.2.a.br \(2\) \(44.796\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(2\) \(2\) \(+\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta )q^{7}+\cdots\)
5610.2.a.bs \(2\) \(44.796\) \(\Q(\sqrt{13}) \) None \(-2\) \(2\) \(-2\) \(2\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
5610.2.a.bt \(2\) \(44.796\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
5610.2.a.bu \(2\) \(44.796\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
5610.2.a.bv \(2\) \(44.796\) \(\Q(\sqrt{41}) \) None \(2\) \(-2\) \(2\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.bw \(2\) \(44.796\) \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5610.2.a.bx \(2\) \(44.796\) \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(2\) \(1\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots\)
5610.2.a.by \(3\) \(44.796\) \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
5610.2.a.bz \(3\) \(44.796\) 3.3.148.1 None \(-3\) \(3\) \(3\) \(-4\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.ca \(3\) \(44.796\) 3.3.961.1 None \(-3\) \(3\) \(3\) \(1\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
5610.2.a.cb \(3\) \(44.796\) 3.3.2089.1 None \(-3\) \(3\) \(3\) \(3\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
5610.2.a.cc \(3\) \(44.796\) \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(3\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.cd \(3\) \(44.796\) 3.3.2089.1 None \(3\) \(3\) \(-3\) \(1\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{2}q^{7}+\cdots\)
5610.2.a.ce \(4\) \(44.796\) 4.4.2777.1 None \(-4\) \(-4\) \(4\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta _{1}q^{7}+\cdots\)
5610.2.a.cf \(4\) \(44.796\) 4.4.17428.1 None \(-4\) \(4\) \(-4\) \(5\) \(+\) \(-\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
5610.2.a.cg \(4\) \(44.796\) 4.4.54764.1 None \(4\) \(-4\) \(-4\) \(4\) \(-\) \(+\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
5610.2.a.ch \(4\) \(44.796\) 4.4.65905.1 None \(4\) \(4\) \(-4\) \(1\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{2}q^{7}+\cdots\)
5610.2.a.ci \(5\) \(44.796\) 5.5.18569692.1 None \(5\) \(-5\) \(5\) \(2\) \(-\) \(+\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-\beta _{3}q^{7}+\cdots\)
5610.2.a.cj \(5\) \(44.796\) 5.5.1284160.1 None \(5\) \(5\) \(5\) \(1\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots\)
5610.2.a.ck \(5\) \(44.796\) 5.5.19985813.1 None \(5\) \(5\) \(5\) \(2\) \(-\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5610))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5610)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(374))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(561))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(935))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1870))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2805))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{5} \))
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{5} \))
$5$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{5} \))
$7$ (\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T - 2 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + T + 10 T^{2} + 7 T^{3} + 49 T^{4} \))(\( 1 + T + 4 T^{2} + 7 T^{3} + 49 T^{4} \))(\( 1 - T + 6 T^{2} - 7 T^{3} + 49 T^{4} \))(\( 1 + T + 6 T^{2} + 7 T^{3} + 49 T^{4} \))(\( 1 - 2 T + 10 T^{2} - 14 T^{3} + 49 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( 1 - 2 T + 10 T^{2} - 14 T^{3} + 49 T^{4} \))(\( 1 + 3 T + 6 T^{2} + 21 T^{3} + 49 T^{4} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( 1 - T + 6 T^{2} - 7 T^{3} + 49 T^{4} \))(\( 1 + 9 T^{2} - 8 T^{3} + 63 T^{4} + 343 T^{6} \))(\( 1 + 4 T + 13 T^{2} + 40 T^{3} + 91 T^{4} + 196 T^{5} + 343 T^{6} \))(\( 1 - T + 11 T^{2} - 6 T^{3} + 77 T^{4} - 49 T^{5} + 343 T^{6} \))(\( 1 - 3 T + 11 T^{2} - 34 T^{3} + 77 T^{4} - 147 T^{5} + 343 T^{6} \))(\( 1 + 2 T + 13 T^{2} + 20 T^{3} + 91 T^{4} + 98 T^{5} + 343 T^{6} \))(\( 1 - T + 7 T^{2} + 2 T^{3} + 49 T^{4} - 49 T^{5} + 343 T^{6} \))(\( 1 + T + 20 T^{2} + 17 T^{3} + 190 T^{4} + 119 T^{5} + 980 T^{6} + 343 T^{7} + 2401 T^{8} \))(\( 1 - 5 T + 24 T^{2} - 81 T^{3} + 254 T^{4} - 567 T^{5} + 1176 T^{6} - 1715 T^{7} + 2401 T^{8} \))(\( 1 - 4 T + 15 T^{2} - 44 T^{3} + 96 T^{4} - 308 T^{5} + 735 T^{6} - 1372 T^{7} + 2401 T^{8} \))(\( 1 - T + 14 T^{2} - 13 T^{3} + 106 T^{4} - 91 T^{5} + 686 T^{6} - 343 T^{7} + 2401 T^{8} \))(\( 1 - 2 T + 8 T^{2} - 4 T^{3} + 91 T^{4} - 180 T^{5} + 637 T^{6} - 196 T^{7} + 2744 T^{8} - 4802 T^{9} + 16807 T^{10} \))(\( 1 - T + 11 T^{2} + 4 T^{3} + 50 T^{4} + 90 T^{5} + 350 T^{6} + 196 T^{7} + 3773 T^{8} - 2401 T^{9} + 16807 T^{10} \))(\( 1 - 2 T + 10 T^{2} + 6 T^{3} - 7 T^{4} + 200 T^{5} - 49 T^{6} + 294 T^{7} + 3430 T^{8} - 4802 T^{9} + 16807 T^{10} \))
$11$ (\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{5} \))
$13$ (\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 3 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 10 T^{2} - 26 T^{3} + 169 T^{4} \))(\( 1 + 2 T + 10 T^{2} + 26 T^{3} + 169 T^{4} \))(\( 1 - 3 T + 18 T^{2} - 39 T^{3} + 169 T^{4} \))(\( 1 - 3 T + 20 T^{2} - 39 T^{3} + 169 T^{4} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( 1 - 6 T + 30 T^{2} - 78 T^{3} + 169 T^{4} \))(\( 1 + 6 T + 22 T^{2} + 78 T^{3} + 169 T^{4} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( 1 + 2 T + 22 T^{2} + 26 T^{3} + 169 T^{4} \))(\( 1 + T + 16 T^{2} + 13 T^{3} + 169 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 78 T^{3} + 169 T^{4} \))(\( 1 + 2 T - 6 T^{2} + 26 T^{3} + 169 T^{4} \))(\( 1 - 6 T + 15 T^{2} - 20 T^{3} + 195 T^{4} - 1014 T^{5} + 2197 T^{6} \))(\( 1 + 2 T + 27 T^{2} + 44 T^{3} + 351 T^{4} + 338 T^{5} + 2197 T^{6} \))(\( 1 + 2 T - T^{2} - 12 T^{3} - 13 T^{4} + 338 T^{5} + 2197 T^{6} \))(\( ( 1 - 4 T + 13 T^{2} )^{3} \))(\( 1 + 4 T + 35 T^{2} + 96 T^{3} + 455 T^{4} + 676 T^{5} + 2197 T^{6} \))(\( 1 - 5 T + 33 T^{2} - 122 T^{3} + 429 T^{4} - 845 T^{5} + 2197 T^{6} \))(\( 1 - 3 T + 10 T^{2} + 11 T^{3} - 166 T^{4} + 143 T^{5} + 1690 T^{6} - 6591 T^{7} + 28561 T^{8} \))(\( 1 - 6 T + 40 T^{2} - 178 T^{3} + 766 T^{4} - 2314 T^{5} + 6760 T^{6} - 13182 T^{7} + 28561 T^{8} \))(\( 1 + T + 8 T^{2} - 21 T^{3} + 174 T^{4} - 273 T^{5} + 1352 T^{6} + 2197 T^{7} + 28561 T^{8} \))(\( 1 - 9 T + 68 T^{2} - 331 T^{3} + 1390 T^{4} - 4303 T^{5} + 11492 T^{6} - 19773 T^{7} + 28561 T^{8} \))(\( 1 + T + 33 T^{2} + 88 T^{3} + 554 T^{4} + 1822 T^{5} + 7202 T^{6} + 14872 T^{7} + 72501 T^{8} + 28561 T^{9} + 371293 T^{10} \))(\( 1 - 9 T + 73 T^{2} - 412 T^{3} + 1954 T^{4} - 7686 T^{5} + 25402 T^{6} - 69628 T^{7} + 160381 T^{8} - 257049 T^{9} + 371293 T^{10} \))(\( 1 - 9 T + 71 T^{2} - 384 T^{3} + 1876 T^{4} - 7070 T^{5} + 24388 T^{6} - 64896 T^{7} + 155987 T^{8} - 257049 T^{9} + 371293 T^{10} \))
$17$ (\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{5} \))
$19$ (\( 1 + 8 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + 3 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 2 T + 22 T^{2} + 38 T^{3} + 361 T^{4} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( 1 + 3 T + 30 T^{2} + 57 T^{3} + 361 T^{4} \))(\( 1 + T + 30 T^{2} + 19 T^{3} + 361 T^{4} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( 1 + 6 T + 42 T^{2} + 114 T^{3} + 361 T^{4} \))(\( 1 + 6 T + 34 T^{2} + 114 T^{3} + 361 T^{4} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( 1 + 2 T - 6 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 - 5 T + 34 T^{2} - 95 T^{3} + 361 T^{4} \))(\( 1 + 2 T + 22 T^{2} + 38 T^{3} + 361 T^{4} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( 1 - 6 T + 33 T^{2} - 92 T^{3} + 627 T^{4} - 2166 T^{5} + 6859 T^{6} \))(\( 1 + 41 T^{2} + 16 T^{3} + 779 T^{4} + 6859 T^{6} \))(\( 1 - 2 T + 17 T^{2} - 12 T^{3} + 323 T^{4} - 722 T^{5} + 6859 T^{6} \))(\( ( 1 + 19 T^{2} )^{3} \))(\( 1 + 29 T^{2} - 56 T^{3} + 551 T^{4} + 6859 T^{6} \))(\( 1 - 13 T + 99 T^{2} - 502 T^{3} + 1881 T^{4} - 4693 T^{5} + 6859 T^{6} \))(\( 1 + 9 T + 98 T^{2} + 521 T^{3} + 2994 T^{4} + 9899 T^{5} + 35378 T^{6} + 61731 T^{7} + 130321 T^{8} \))(\( 1 - 8 T + 60 T^{2} - 248 T^{3} + 1302 T^{4} - 4712 T^{5} + 21660 T^{6} - 54872 T^{7} + 130321 T^{8} \))(\( 1 - 5 T + 44 T^{2} - 173 T^{3} + 1206 T^{4} - 3287 T^{5} + 15884 T^{6} - 34295 T^{7} + 130321 T^{8} \))(\( 1 - 9 T + 92 T^{2} - 493 T^{3} + 2734 T^{4} - 9367 T^{5} + 33212 T^{6} - 61731 T^{7} + 130321 T^{8} \))(\( 1 + T + 63 T^{2} + 112 T^{3} + 1898 T^{4} + 3406 T^{5} + 36062 T^{6} + 40432 T^{7} + 432117 T^{8} + 130321 T^{9} + 2476099 T^{10} \))(\( 1 + 5 T + 31 T^{2} + 124 T^{3} + 602 T^{4} + 3342 T^{5} + 11438 T^{6} + 44764 T^{7} + 212629 T^{8} + 651605 T^{9} + 2476099 T^{10} \))(\( 1 - 11 T + 117 T^{2} - 768 T^{3} + 4752 T^{4} - 21370 T^{5} + 90288 T^{6} - 277248 T^{7} + 802503 T^{8} - 1433531 T^{9} + 2476099 T^{10} \))
$23$ (\( 1 + 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 - 7 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 5 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 2 T + 30 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 - 9 T + 62 T^{2} - 207 T^{3} + 529 T^{4} \))(\( 1 + 11 T + 66 T^{2} + 253 T^{3} + 529 T^{4} \))(\( 1 - T + 38 T^{2} - 23 T^{3} + 529 T^{4} \))(\( 1 + 9 T + 58 T^{2} + 207 T^{3} + 529 T^{4} \))(\( 1 - 10 T + 66 T^{2} - 230 T^{3} + 529 T^{4} \))(\( 1 + 2 T + 34 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 + 14 T^{2} + 529 T^{4} \))(\( 1 + 6 T + 50 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 3 T + 38 T^{2} + 69 T^{3} + 529 T^{4} \))(\( 1 + 10 T + 54 T^{2} + 230 T^{3} + 529 T^{4} \))(\( 1 + T + 38 T^{2} + 23 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 69 T^{2} + 252 T^{3} + 1587 T^{4} + 3174 T^{5} + 12167 T^{6} \))(\( 1 + 53 T^{2} + 16 T^{3} + 1219 T^{4} + 12167 T^{6} \))(\( 1 - 13 T + 115 T^{2} - 630 T^{3} + 2645 T^{4} - 6877 T^{5} + 12167 T^{6} \))(\( 1 + T + 13 T^{2} + 174 T^{3} + 299 T^{4} + 529 T^{5} + 12167 T^{6} \))(\( 1 + 8 T + 25 T^{2} + 24 T^{3} + 575 T^{4} + 4232 T^{5} + 12167 T^{6} \))(\( 1 + 11 T + 95 T^{2} + 514 T^{3} + 2185 T^{4} + 5819 T^{5} + 12167 T^{6} \))(\( 1 + T + 46 T^{2} + 53 T^{3} + 1546 T^{4} + 1219 T^{5} + 24334 T^{6} + 12167 T^{7} + 279841 T^{8} \))(\( 1 - T + 56 T^{2} - 149 T^{3} + 1470 T^{4} - 3427 T^{5} + 29624 T^{6} - 12167 T^{7} + 279841 T^{8} \))(\( 1 - 14 T + 105 T^{2} - 470 T^{3} + 2060 T^{4} - 10810 T^{5} + 55545 T^{6} - 170338 T^{7} + 279841 T^{8} \))(\( 1 - 7 T + 96 T^{2} - 455 T^{3} + 3334 T^{4} - 10465 T^{5} + 50784 T^{6} - 85169 T^{7} + 279841 T^{8} \))(\( 1 + 18 T^{2} + 76 T^{3} + 833 T^{4} - 1224 T^{5} + 19159 T^{6} + 40204 T^{7} + 219006 T^{8} + 6436343 T^{10} \))(\( 1 - 11 T + 59 T^{2} - 308 T^{3} + 2258 T^{4} - 13346 T^{5} + 51934 T^{6} - 162932 T^{7} + 717853 T^{8} - 3078251 T^{9} + 6436343 T^{10} \))(\( 1 - 4 T + 44 T^{2} - 342 T^{3} + 1715 T^{4} - 9100 T^{5} + 39445 T^{6} - 180918 T^{7} + 535348 T^{8} - 1119364 T^{9} + 6436343 T^{10} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 10 T^{2} + 841 T^{4} \))(\( 1 + 5 T + 60 T^{2} + 145 T^{3} + 841 T^{4} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( 1 + 7 T + 62 T^{2} + 203 T^{3} + 841 T^{4} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( 1 + 4 T + 30 T^{2} + 116 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 232 T^{3} + 841 T^{4} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( 1 + 10 T + 66 T^{2} + 290 T^{3} + 841 T^{4} \))(\( 1 - 11 T + 80 T^{2} - 319 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 51 T^{2} - 324 T^{3} + 1479 T^{4} - 5046 T^{5} + 24389 T^{6} \))(\( 1 - 2 T + 3 T^{2} - 12 T^{3} + 87 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( 1 - 3 T + 59 T^{2} - 82 T^{3} + 1711 T^{4} - 2523 T^{5} + 24389 T^{6} \))(\( 1 + 3 T + 77 T^{2} + 166 T^{3} + 2233 T^{4} + 2523 T^{5} + 24389 T^{6} \))(\( ( 1 + 6 T + 29 T^{2} )^{3} \))(\( ( 1 - 2 T + 29 T^{2} )^{3} \))(\( 1 + 8 T + 60 T^{2} + 344 T^{3} + 2390 T^{4} + 9976 T^{5} + 50460 T^{6} + 195112 T^{7} + 707281 T^{8} \))(\( 1 - T + 86 T^{2} - 35 T^{3} + 3378 T^{4} - 1015 T^{5} + 72326 T^{6} - 24389 T^{7} + 707281 T^{8} \))(\( 1 + 3 T - 30 T^{2} + 9 T^{3} + 1722 T^{4} + 261 T^{5} - 25230 T^{6} + 73167 T^{7} + 707281 T^{8} \))(\( ( 1 + 2 T + 29 T^{2} )^{4} \))(\( 1 - 17 T + 223 T^{2} - 1984 T^{3} + 14740 T^{4} - 86158 T^{5} + 427460 T^{6} - 1668544 T^{7} + 5438747 T^{8} - 12023777 T^{9} + 20511149 T^{10} \))(\( 1 + 2 T + 25 T^{2} - 72 T^{3} - 30 T^{4} - 7380 T^{5} - 870 T^{6} - 60552 T^{7} + 609725 T^{8} + 1414562 T^{9} + 20511149 T^{10} \))(\( 1 - 7 T + 119 T^{2} - 592 T^{3} + 6012 T^{4} - 23138 T^{5} + 174348 T^{6} - 497872 T^{7} + 2902291 T^{8} - 4950967 T^{9} + 20511149 T^{10} \))
$31$ (\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 - T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 9 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 - 9 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T - 2 T^{2} + 124 T^{3} + 961 T^{4} \))(\( 1 + 5 T + 30 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + 5 T + 58 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 - 9 T + 74 T^{2} - 279 T^{3} + 961 T^{4} \))(\( 1 + T - 12 T^{2} + 31 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 46 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 + 4 T + 14 T^{2} + 124 T^{3} + 961 T^{4} \))(\( 1 + 30 T^{2} + 961 T^{4} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( 1 + 3 T + 54 T^{2} + 93 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 54 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 - 15 T + 110 T^{2} - 465 T^{3} + 961 T^{4} \))(\( 1 + 45 T^{2} + 64 T^{3} + 1395 T^{4} + 29791 T^{6} \))(\( 1 + 12 T + 77 T^{2} + 424 T^{3} + 2387 T^{4} + 11532 T^{5} + 29791 T^{6} \))(\( 1 - 3 T + 65 T^{2} - 218 T^{3} + 2015 T^{4} - 2883 T^{5} + 29791 T^{6} \))(\( 1 - 3 T + 83 T^{2} - 170 T^{3} + 2573 T^{4} - 2883 T^{5} + 29791 T^{6} \))(\( 1 - 8 T + 77 T^{2} - 432 T^{3} + 2387 T^{4} - 7688 T^{5} + 29791 T^{6} \))(\( 1 - 5 T + 21 T^{2} + 58 T^{3} + 651 T^{4} - 4805 T^{5} + 29791 T^{6} \))(\( 1 + T - 40 T^{2} + 29 T^{3} + 2062 T^{4} + 899 T^{5} - 38440 T^{6} + 29791 T^{7} + 923521 T^{8} \))(\( 1 - 3 T + 80 T^{2} - 167 T^{3} + 2974 T^{4} - 5177 T^{5} + 76880 T^{6} - 89373 T^{7} + 923521 T^{8} \))(\( 1 + 4 T + 111 T^{2} + 332 T^{3} + 4944 T^{4} + 10292 T^{5} + 106671 T^{6} + 119164 T^{7} + 923521 T^{8} \))(\( 1 - 3 T + 40 T^{2} - 119 T^{3} + 2158 T^{4} - 3689 T^{5} + 38440 T^{6} - 89373 T^{7} + 923521 T^{8} \))(\( 1 - 10 T + 98 T^{2} - 470 T^{3} + 2437 T^{4} - 9600 T^{5} + 75547 T^{6} - 451670 T^{7} + 2919518 T^{8} - 9235210 T^{9} + 28629151 T^{10} \))(\( 1 + 7 T + 131 T^{2} + 772 T^{3} + 7506 T^{4} + 34666 T^{5} + 232686 T^{6} + 741892 T^{7} + 3902621 T^{8} + 6464647 T^{9} + 28629151 T^{10} \))(\( 1 - 10 T + 106 T^{2} - 806 T^{3} + 5949 T^{4} - 33952 T^{5} + 184419 T^{6} - 774566 T^{7} + 3157846 T^{8} - 9235210 T^{9} + 28629151 T^{10} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 6 T + 37 T^{2} )^{2} \))(\( 1 - 15 T + 120 T^{2} - 555 T^{3} + 1369 T^{4} \))(\( 1 + 11 T + 96 T^{2} + 407 T^{3} + 1369 T^{4} \))(\( 1 - 6 T + 50 T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 + 54 T^{2} + 1369 T^{4} \))(\( 1 + 22 T^{2} + 1369 T^{4} \))(\( 1 - 12 T + 78 T^{2} - 444 T^{3} + 1369 T^{4} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( 1 + T + 64 T^{2} + 37 T^{3} + 1369 T^{4} \))(\( 1 + 6 T + 66 T^{2} + 222 T^{3} + 1369 T^{4} \))(\( ( 1 + 10 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{3} \))(\( 1 + 10 T + 91 T^{2} + 604 T^{3} + 3367 T^{4} + 13690 T^{5} + 50653 T^{6} \))(\( ( 1 - 6 T + 37 T^{2} )^{3} \))(\( 1 - 4 T + 59 T^{2} - 312 T^{3} + 2183 T^{4} - 5476 T^{5} + 50653 T^{6} \))(\( 1 + 10 T + 107 T^{2} + 636 T^{3} + 3959 T^{4} + 13690 T^{5} + 50653 T^{6} \))(\( 1 - T + 59 T^{2} - 198 T^{3} + 2183 T^{4} - 1369 T^{5} + 50653 T^{6} \))(\( 1 - T + 46 T^{2} - 411 T^{3} + 962 T^{4} - 15207 T^{5} + 62974 T^{6} - 50653 T^{7} + 1874161 T^{8} \))(\( ( 1 - 2 T + 37 T^{2} )^{4} \))(\( 1 - 9 T + 102 T^{2} - 675 T^{3} + 5682 T^{4} - 24975 T^{5} + 139638 T^{6} - 455877 T^{7} + 1874161 T^{8} \))(\( 1 - 13 T + 54 T^{2} + 497 T^{3} - 5678 T^{4} + 18389 T^{5} + 73926 T^{6} - 658489 T^{7} + 1874161 T^{8} \))(\( 1 - T + 63 T^{2} - 336 T^{3} + 1676 T^{4} - 19374 T^{5} + 62012 T^{6} - 459984 T^{7} + 3191139 T^{8} - 1874161 T^{9} + 69343957 T^{10} \))(\( 1 - 23 T + 353 T^{2} - 3716 T^{3} + 31458 T^{4} - 209498 T^{5} + 1163946 T^{6} - 5087204 T^{7} + 17880509 T^{8} - 43105703 T^{9} + 69343957 T^{10} \))(\( 1 - 7 T + 87 T^{2} - 256 T^{3} + 2196 T^{4} + 350 T^{5} + 81252 T^{6} - 350464 T^{7} + 4406811 T^{8} - 13119127 T^{9} + 69343957 T^{10} \))
$41$ (\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( 1 + 6 T + 74 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 + 6 T + 50 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( 1 - 10 T + 74 T^{2} - 410 T^{3} + 1681 T^{4} \))(\( 1 + 2 T^{2} + 1681 T^{4} \))(\( 1 - 4 T + 34 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 - 4 T + 54 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 + 2 T^{2} + 1681 T^{4} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( 1 + 2 T + 66 T^{2} + 82 T^{3} + 1681 T^{4} \))(\( 1 + 14 T + 98 T^{2} + 574 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 123 T^{2} + 792 T^{3} + 5043 T^{4} + 20172 T^{5} + 68921 T^{6} \))(\( 1 + 22 T + 263 T^{2} + 2036 T^{3} + 10783 T^{4} + 36982 T^{5} + 68921 T^{6} \))(\( 1 + 8 T + 103 T^{2} + 528 T^{3} + 4223 T^{4} + 13448 T^{5} + 68921 T^{6} \))(\( 1 - 2 T + 67 T^{2} - 36 T^{3} + 2747 T^{4} - 3362 T^{5} + 68921 T^{6} \))(\( ( 1 + 8 T + 41 T^{2} )^{3} \))(\( ( 1 + 2 T + 41 T^{2} )^{3} \))(\( 1 - 2 T + 132 T^{2} - 214 T^{3} + 7590 T^{4} - 8774 T^{5} + 221892 T^{6} - 137842 T^{7} + 2825761 T^{8} \))(\( 1 - 2 T + 136 T^{2} - 206 T^{3} + 7886 T^{4} - 8446 T^{5} + 228616 T^{6} - 137842 T^{7} + 2825761 T^{8} \))(\( 1 + 6 T + 104 T^{2} + 554 T^{3} + 5198 T^{4} + 22714 T^{5} + 174824 T^{6} + 413526 T^{7} + 2825761 T^{8} \))(\( 1 - 6 T + 52 T^{2} - 130 T^{3} + 2310 T^{4} - 5330 T^{5} + 87412 T^{6} - 413526 T^{7} + 2825761 T^{8} \))(\( 1 - 12 T + 169 T^{2} - 1632 T^{3} + 13086 T^{4} - 93224 T^{5} + 536526 T^{6} - 2743392 T^{7} + 11647649 T^{8} - 33909132 T^{9} + 115856201 T^{10} \))(\( 1 - 14 T + 133 T^{2} - 1480 T^{3} + 11682 T^{4} - 71444 T^{5} + 478962 T^{6} - 2487880 T^{7} + 9166493 T^{8} - 39560654 T^{9} + 115856201 T^{10} \))(\( 1 - 4 T + 113 T^{2} - 432 T^{3} + 6134 T^{4} - 22744 T^{5} + 251494 T^{6} - 726192 T^{7} + 7788073 T^{8} - 11303044 T^{9} + 115856201 T^{10} \))
$43$ (\( 1 - 10 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 13 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 11 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 + 6 T + 78 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 + 5 T - 14 T^{2} + 215 T^{3} + 1849 T^{4} \))(\( 1 + 2 T + 46 T^{2} + 86 T^{3} + 1849 T^{4} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( 1 + 15 T + 134 T^{2} + 645 T^{3} + 1849 T^{4} \))(\( 1 - 10 T + 106 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 + 18 T + 154 T^{2} + 774 T^{3} + 1849 T^{4} \))(\( 1 + 54 T^{2} + 1849 T^{4} \))(\( 1 + 2 T + 82 T^{2} + 86 T^{3} + 1849 T^{4} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 43 T^{2} )^{2} \))(\( 1 - 9 T + 98 T^{2} - 387 T^{3} + 1849 T^{4} \))(\( 1 - 12 T + 165 T^{2} - 1040 T^{3} + 7095 T^{4} - 22188 T^{5} + 79507 T^{6} \))(\( 1 + 8 T + 89 T^{2} + 384 T^{3} + 3827 T^{4} + 14792 T^{5} + 79507 T^{6} \))(\( 1 - T + 119 T^{2} - 78 T^{3} + 5117 T^{4} - 1849 T^{5} + 79507 T^{6} \))(\( 1 - 21 T + 263 T^{2} - 2054 T^{3} + 11309 T^{4} - 38829 T^{5} + 79507 T^{6} \))(\( 1 - 6 T + 113 T^{2} - 412 T^{3} + 4859 T^{4} - 11094 T^{5} + 79507 T^{6} \))(\( 1 - 6 T + 89 T^{2} - 388 T^{3} + 3827 T^{4} - 11094 T^{5} + 79507 T^{6} \))(\( 1 - 4 T + 80 T^{2} - 92 T^{3} + 3694 T^{4} - 3956 T^{5} + 147920 T^{6} - 318028 T^{7} + 3418801 T^{8} \))(\( 1 - 9 T + 104 T^{2} - 785 T^{3} + 6958 T^{4} - 33755 T^{5} + 192296 T^{6} - 715563 T^{7} + 3418801 T^{8} \))(\( 1 + 11 T + 132 T^{2} + 955 T^{3} + 8166 T^{4} + 41065 T^{5} + 244068 T^{6} + 874577 T^{7} + 3418801 T^{8} \))(\( 1 - 2 T + 60 T^{2} + 198 T^{3} + 1814 T^{4} + 8514 T^{5} + 110940 T^{6} - 159014 T^{7} + 3418801 T^{8} \))(\( 1 - 7 T - 21 T^{2} + 420 T^{3} + 1550 T^{4} - 27722 T^{5} + 66650 T^{6} + 776580 T^{7} - 1669647 T^{8} - 23931607 T^{9} + 147008443 T^{10} \))(\( 1 + 8 T + 183 T^{2} + 1184 T^{3} + 14426 T^{4} + 72752 T^{5} + 620318 T^{6} + 2189216 T^{7} + 14549781 T^{8} + 27350408 T^{9} + 147008443 T^{10} \))(\( 1 - 11 T + 173 T^{2} - 1704 T^{3} + 13808 T^{4} - 105354 T^{5} + 593744 T^{6} - 3150696 T^{7} + 13754711 T^{8} - 37606811 T^{9} + 147008443 T^{10} \))
$47$ (\( 1 - 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( ( 1 + 4 T + 47 T^{2} )^{2} \))(\( 1 + 4 T + 30 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 + 6 T + 62 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 + 6 T + 70 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 10 T + 86 T^{2} - 470 T^{3} + 2209 T^{4} \))(\( 1 + 14 T^{2} + 2209 T^{4} \))(\( ( 1 - 12 T + 47 T^{2} )^{2} \))(\( ( 1 + 4 T + 47 T^{2} )^{2} \))(\( 1 + 4 T + 78 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 62 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 86 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 + 4 T - 34 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( ( 1 + 47 T^{2} )^{3} \))(\( ( 1 - 4 T + 47 T^{2} )^{3} \))(\( ( 1 + 4 T + 47 T^{2} )^{3} \))(\( 1 + 2 T + 85 T^{2} + 60 T^{3} + 3995 T^{4} + 4418 T^{5} + 103823 T^{6} \))(\( 1 + 29 T^{2} + 448 T^{3} + 1363 T^{4} + 103823 T^{6} \))(\( 1 - 10 T - 35 T^{2} + 852 T^{3} - 1645 T^{4} - 22090 T^{5} + 103823 T^{6} \))(\( 1 + 2 T + 108 T^{2} + 282 T^{3} + 6758 T^{4} + 13254 T^{5} + 238572 T^{6} + 207646 T^{7} + 4879681 T^{8} \))(\( ( 1 + 47 T^{2} )^{4} \))(\( 1 - 10 T + 60 T^{2} - 514 T^{3} + 5318 T^{4} - 24158 T^{5} + 132540 T^{6} - 1038230 T^{7} + 4879681 T^{8} \))(\( 1 - 6 T + 76 T^{2} - 238 T^{3} + 4134 T^{4} - 11186 T^{5} + 167884 T^{6} - 622938 T^{7} + 4879681 T^{8} \))(\( 1 - 12 T + 199 T^{2} - 1920 T^{3} + 17718 T^{4} - 127208 T^{5} + 832746 T^{6} - 4241280 T^{7} + 20660777 T^{8} - 58556172 T^{9} + 229345007 T^{10} \))(\( 1 - 6 T + 75 T^{2} - 40 T^{3} + 810 T^{4} + 19164 T^{5} + 38070 T^{6} - 88360 T^{7} + 7786725 T^{8} - 29278086 T^{9} + 229345007 T^{10} \))(\( 1 + 4 T + 143 T^{2} + 528 T^{3} + 9758 T^{4} + 32728 T^{5} + 458626 T^{6} + 1166352 T^{7} + 14846689 T^{8} + 19518724 T^{9} + 229345007 T^{10} \))
$53$ (\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 8 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 10 T + 114 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 - 14 T + 138 T^{2} - 742 T^{3} + 2809 T^{4} \))(\( ( 1 - 2 T + 53 T^{2} )^{2} \))(\( 1 - 26 T^{2} + 2809 T^{4} \))(\( ( 1 + 53 T^{2} )^{2} \))(\( 1 + 2 T + 62 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 118 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( ( 1 + 10 T + 53 T^{2} )^{2} \))(\( 1 - 2 T + 102 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( ( 1 + 2 T + 53 T^{2} )^{2} \))(\( ( 1 - 4 T + 53 T^{2} )^{2} \))(\( 1 - 10 T + 98 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 - 12 T + 123 T^{2} - 864 T^{3} + 6519 T^{4} - 33708 T^{5} + 148877 T^{6} \))(\( 1 - 6 T + 155 T^{2} - 628 T^{3} + 8215 T^{4} - 16854 T^{5} + 148877 T^{6} \))(\( 1 - 10 T + 151 T^{2} - 996 T^{3} + 8003 T^{4} - 28090 T^{5} + 148877 T^{6} \))(\( 1 + 2 T + 23 T^{2} + 724 T^{3} + 1219 T^{4} + 5618 T^{5} + 148877 T^{6} \))(\( 1 - 2 T + 39 T^{2} - 540 T^{3} + 2067 T^{4} - 5618 T^{5} + 148877 T^{6} \))(\( 1 - 12 T + 155 T^{2} - 1160 T^{3} + 8215 T^{4} - 33708 T^{5} + 148877 T^{6} \))(\( 1 - 6 T + 160 T^{2} - 858 T^{3} + 11326 T^{4} - 45474 T^{5} + 449440 T^{6} - 893262 T^{7} + 7890481 T^{8} \))(\( 1 + 2 T + 120 T^{2} + 550 T^{3} + 7006 T^{4} + 29150 T^{5} + 337080 T^{6} + 297754 T^{7} + 7890481 T^{8} \))(\( 1 - 6 T + 152 T^{2} - 770 T^{3} + 10526 T^{4} - 40810 T^{5} + 426968 T^{6} - 893262 T^{7} + 7890481 T^{8} \))(\( 1 + 4 T + 128 T^{2} + 404 T^{3} + 9438 T^{4} + 21412 T^{5} + 359552 T^{6} + 595508 T^{7} + 7890481 T^{8} \))(\( 1 - 6 T + 137 T^{2} - 552 T^{3} + 7610 T^{4} - 26084 T^{5} + 403330 T^{6} - 1550568 T^{7} + 20396149 T^{8} - 47342886 T^{9} + 418195493 T^{10} \))(\( 1 + 6 T + 209 T^{2} + 1064 T^{3} + 19842 T^{4} + 80964 T^{5} + 1051626 T^{6} + 2988776 T^{7} + 31115293 T^{8} + 47342886 T^{9} + 418195493 T^{10} \))(\( 1 - 12 T + 113 T^{2} - 760 T^{3} + 9650 T^{4} - 76888 T^{5} + 511450 T^{6} - 2134840 T^{7} + 16823101 T^{8} - 94685772 T^{9} + 418195493 T^{10} \))
$59$ (\( 1 - 6 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 2 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 6 T + 110 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 + 2 T + 102 T^{2} + 118 T^{3} + 3481 T^{4} \))(\( 1 + 14 T + 126 T^{2} + 826 T^{3} + 3481 T^{4} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( 1 - 14 T + 134 T^{2} - 826 T^{3} + 3481 T^{4} \))(\( 1 - 22 T + 234 T^{2} - 1298 T^{3} + 3481 T^{4} \))(\( 1 + 14 T + 154 T^{2} + 826 T^{3} + 3481 T^{4} \))(\( 1 - 10 T^{2} + 3481 T^{4} \))(\( 1 + 2 T + 114 T^{2} + 118 T^{3} + 3481 T^{4} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( 1 - 4 T + 54 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 10 T + 110 T^{2} + 590 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 213 T^{2} + 1440 T^{3} + 12567 T^{4} + 41772 T^{5} + 205379 T^{6} \))(\( 1 + 12 T + 105 T^{2} + 984 T^{3} + 6195 T^{4} + 41772 T^{5} + 205379 T^{6} \))(\( 1 + 4 T + 141 T^{2} + 456 T^{3} + 8319 T^{4} + 13924 T^{5} + 205379 T^{6} \))(\( 1 - 4 T + 125 T^{2} - 488 T^{3} + 7375 T^{4} - 13924 T^{5} + 205379 T^{6} \))(\( 1 + 14 T + 233 T^{2} + 1708 T^{3} + 13747 T^{4} + 48734 T^{5} + 205379 T^{6} \))(\( 1 - 6 T + 137 T^{2} - 580 T^{3} + 8083 T^{4} - 20886 T^{5} + 205379 T^{6} \))(\( 1 + 24 T + 384 T^{2} + 4176 T^{3} + 36846 T^{4} + 246384 T^{5} + 1336704 T^{6} + 4929096 T^{7} + 12117361 T^{8} \))(\( 1 + 2 T + 212 T^{2} + 322 T^{3} + 18150 T^{4} + 18998 T^{5} + 737972 T^{6} + 410758 T^{7} + 12117361 T^{8} \))(\( 1 - 2 T + 36 T^{2} + 446 T^{3} + 1254 T^{4} + 26314 T^{5} + 125316 T^{6} - 410758 T^{7} + 12117361 T^{8} \))(\( 1 - 6 T + 100 T^{2} + 178 T^{3} + 2438 T^{4} + 10502 T^{5} + 348100 T^{6} - 1232274 T^{7} + 12117361 T^{8} \))(\( 1 - 2 T + 71 T^{2} - 488 T^{3} + 3866 T^{4} - 31628 T^{5} + 228094 T^{6} - 1698728 T^{7} + 14581909 T^{8} - 24234722 T^{9} + 714924299 T^{10} \))(\( 1 - 20 T + 327 T^{2} - 3824 T^{3} + 39514 T^{4} - 320952 T^{5} + 2331326 T^{6} - 13311344 T^{7} + 67158933 T^{8} - 242347220 T^{9} + 714924299 T^{10} \))(\( 1 - 4 T + 183 T^{2} - 328 T^{3} + 14634 T^{4} - 11624 T^{5} + 863406 T^{6} - 1141768 T^{7} + 37584357 T^{8} - 48469444 T^{9} + 714924299 T^{10} \))
$61$ (\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 11 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - 13 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 6 T + 61 T^{2} )^{2} \))(\( 1 - 9 T + 132 T^{2} - 549 T^{3} + 3721 T^{4} \))(\( 1 - 9 T + 68 T^{2} - 549 T^{3} + 3721 T^{4} \))(\( 1 - 10 T^{2} + 3721 T^{4} \))(\( 1 + 12 T + 78 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( 1 - 4 T + 94 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( ( 1 - 6 T + 61 T^{2} )^{2} \))(\( 1 - 3 T + 32 T^{2} - 183 T^{3} + 3721 T^{4} \))(\( 1 + 54 T^{2} + 3721 T^{4} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( 1 + 6 T + 147 T^{2} + 580 T^{3} + 8967 T^{4} + 22326 T^{5} + 226981 T^{6} \))(\( ( 1 + 10 T + 61 T^{2} )^{3} \))(\( ( 1 - 2 T + 61 T^{2} )^{3} \))(\( ( 1 - 2 T + 61 T^{2} )^{3} \))(\( 1 + 2 T + 147 T^{2} + 236 T^{3} + 8967 T^{4} + 7442 T^{5} + 226981 T^{6} \))(\( 1 - 11 T + 171 T^{2} - 1058 T^{3} + 10431 T^{4} - 40931 T^{5} + 226981 T^{6} \))(\( 1 + 7 T + 242 T^{2} + 1221 T^{3} + 22074 T^{4} + 74481 T^{5} + 900482 T^{6} + 1588867 T^{7} + 13845841 T^{8} \))(\( 1 - 4 T + 148 T^{2} - 588 T^{3} + 12262 T^{4} - 35868 T^{5} + 550708 T^{6} - 907924 T^{7} + 13845841 T^{8} \))(\( 1 + 25 T + 402 T^{2} + 4571 T^{3} + 41274 T^{4} + 278831 T^{5} + 1495842 T^{6} + 5674525 T^{7} + 13845841 T^{8} \))(\( 1 - 13 T + 150 T^{2} - 439 T^{3} + 3922 T^{4} - 26779 T^{5} + 558150 T^{6} - 2950753 T^{7} + 13845841 T^{8} \))(\( 1 - 9 T + 165 T^{2} - 644 T^{3} + 11238 T^{4} - 32246 T^{5} + 685518 T^{6} - 2396324 T^{7} + 37451865 T^{8} - 124612569 T^{9} + 844596301 T^{10} \))(\( 1 + 5 T + 9 T^{2} - 436 T^{3} + 1298 T^{4} + 11246 T^{5} + 79178 T^{6} - 1622356 T^{7} + 2042829 T^{8} + 69229205 T^{9} + 844596301 T^{10} \))(\( 1 - 19 T + 273 T^{2} - 2900 T^{3} + 26602 T^{4} - 212386 T^{5} + 1622722 T^{6} - 10790900 T^{7} + 61965813 T^{8} - 263070979 T^{9} + 844596301 T^{10} \))
$67$ (\( 1 + 10 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 14 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 6 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 + 16 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 6 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 - 12 T + 67 T^{2} )^{2} \))(\( 1 + 23 T + 256 T^{2} + 1541 T^{3} + 4489 T^{4} \))(\( 1 - 7 T + 138 T^{2} - 469 T^{3} + 4489 T^{4} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( 1 + 8 T + 130 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( ( 1 + 10 T + 67 T^{2} )^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 - 6 T + 67 T^{2} )^{2} \))(\( 1 + 11 T + 154 T^{2} + 737 T^{3} + 4489 T^{4} \))(\( 1 + 22 T + 238 T^{2} + 1474 T^{3} + 4489 T^{4} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( 1 - 18 T + 261 T^{2} - 2276 T^{3} + 17487 T^{4} - 80802 T^{5} + 300763 T^{6} \))(\( 1 - 4 T + 73 T^{2} - 952 T^{3} + 4891 T^{4} - 17956 T^{5} + 300763 T^{6} \))(\( 1 + 4 T + 41 T^{2} + 24 T^{3} + 2747 T^{4} + 17956 T^{5} + 300763 T^{6} \))(\( 1 - 2 T + 121 T^{2} - 236 T^{3} + 8107 T^{4} - 8978 T^{5} + 300763 T^{6} \))(\( 1 + 2 T + 53 T^{2} + 36 T^{3} + 3551 T^{4} + 8978 T^{5} + 300763 T^{6} \))(\( 1 - 29 T + 429 T^{2} - 4142 T^{3} + 28743 T^{4} - 130181 T^{5} + 300763 T^{6} \))(\( 1 - 11 T + 242 T^{2} - 2135 T^{3} + 23538 T^{4} - 143045 T^{5} + 1086338 T^{6} - 3308393 T^{7} + 20151121 T^{8} \))(\( 1 - 12 T + 188 T^{2} - 1100 T^{3} + 12502 T^{4} - 73700 T^{5} + 843932 T^{6} - 3609156 T^{7} + 20151121 T^{8} \))(\( 1 + 5 T + 236 T^{2} + 893 T^{3} + 22902 T^{4} + 59831 T^{5} + 1059404 T^{6} + 1503815 T^{7} + 20151121 T^{8} \))(\( 1 - 11 T + 226 T^{2} - 1783 T^{3} + 22290 T^{4} - 119461 T^{5} + 1014514 T^{6} - 3308393 T^{7} + 20151121 T^{8} \))(\( 1 - 17 T + 259 T^{2} - 2544 T^{3} + 29182 T^{4} - 237678 T^{5} + 1955194 T^{6} - 11420016 T^{7} + 77897617 T^{8} - 342569057 T^{9} + 1350125107 T^{10} \))(\( 1 - 3 T + 231 T^{2} - 660 T^{3} + 24434 T^{4} - 61378 T^{5} + 1637078 T^{6} - 2962740 T^{7} + 69476253 T^{8} - 60453363 T^{9} + 1350125107 T^{10} \))(\( 1 + 9 T + 143 T^{2} + 1432 T^{3} + 16202 T^{4} + 102510 T^{5} + 1085534 T^{6} + 6428248 T^{7} + 43009109 T^{8} + 181360089 T^{9} + 1350125107 T^{10} \))
$71$ (\( 1 - 6 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 2 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 14 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 18 T + 206 T^{2} + 1278 T^{3} + 5041 T^{4} \))(\( 1 - 18 T + 206 T^{2} - 1278 T^{3} + 5041 T^{4} \))(\( 1 - 22 T^{2} + 5041 T^{4} \))(\( 1 + 2 T + 110 T^{2} + 142 T^{3} + 5041 T^{4} \))(\( 1 + 2 T + 110 T^{2} + 142 T^{3} + 5041 T^{4} \))(\( 1 - 6 T + 146 T^{2} - 426 T^{3} + 5041 T^{4} \))(\( 1 + 10 T + 154 T^{2} + 710 T^{3} + 5041 T^{4} \))(\( 1 + 110 T^{2} + 5041 T^{4} \))(\( 1 + 6 T + 146 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 - 10 T + 126 T^{2} - 710 T^{3} + 5041 T^{4} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( 1 - 14 T + 158 T^{2} - 994 T^{3} + 5041 T^{4} \))(\( 1 - 12 T + 249 T^{2} - 1728 T^{3} + 17679 T^{4} - 60492 T^{5} + 357911 T^{6} \))(\( 1 - 8 T + 173 T^{2} - 832 T^{3} + 12283 T^{4} - 40328 T^{5} + 357911 T^{6} \))(\( 1 - 20 T + 305 T^{2} - 2824 T^{3} + 21655 T^{4} - 100820 T^{5} + 357911 T^{6} \))(\( 1 - 16 T + 89 T^{2} - 176 T^{3} + 6319 T^{4} - 80656 T^{5} + 357911 T^{6} \))(\( 1 + 18 T + 293 T^{2} + 2660 T^{3} + 20803 T^{4} + 90738 T^{5} + 357911 T^{6} \))(\( 1 - 4 T + 137 T^{2} - 440 T^{3} + 9727 T^{4} - 20164 T^{5} + 357911 T^{6} \))(\( 1 + 22 T + 416 T^{2} + 4638 T^{3} + 47342 T^{4} + 329298 T^{5} + 2097056 T^{6} + 7874042 T^{7} + 25411681 T^{8} \))(\( 1 + 10 T + 116 T^{2} + 338 T^{3} + 5526 T^{4} + 23998 T^{5} + 584756 T^{6} + 3579110 T^{7} + 25411681 T^{8} \))(\( 1 - 24 T + 424 T^{2} - 5016 T^{3} + 48526 T^{4} - 356136 T^{5} + 2137384 T^{6} - 8589864 T^{7} + 25411681 T^{8} \))(\( 1 - 16 T + 128 T^{2} + 312 T^{3} - 7442 T^{4} + 22152 T^{5} + 645248 T^{6} - 5726576 T^{7} + 25411681 T^{8} \))(\( 1 - 20 T + 423 T^{2} - 5472 T^{3} + 64222 T^{4} - 576408 T^{5} + 4559762 T^{6} - 27584352 T^{7} + 151396353 T^{8} - 508233620 T^{9} + 1804229351 T^{10} \))(\( 1 + 2 T + 99 T^{2} + 952 T^{3} + 8874 T^{4} + 75724 T^{5} + 630054 T^{6} + 4799032 T^{7} + 35433189 T^{8} + 50823362 T^{9} + 1804229351 T^{10} \))(\( 1 + 2 T + 187 T^{2} + 1088 T^{3} + 14834 T^{4} + 133372 T^{5} + 1053214 T^{6} + 5484608 T^{7} + 66929357 T^{8} + 50823362 T^{9} + 1804229351 T^{10} \))
$73$ (\( 1 + 8 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 - 8 T + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 6 T + 138 T^{2} - 438 T^{3} + 5329 T^{4} \))(\( 1 + 8 T + 94 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( ( 1 + 8 T + 73 T^{2} )^{2} \))(\( 1 + 14 T + 162 T^{2} + 1022 T^{3} + 5329 T^{4} \))(\( ( 1 + 6 T + 73 T^{2} )^{2} \))(\( 1 + 10 T + 126 T^{2} + 730 T^{3} + 5329 T^{4} \))(\( 1 + 10 T + 158 T^{2} + 730 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 22 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 + 2 T + 142 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 - 10 T + 130 T^{2} - 730 T^{3} + 5329 T^{4} \))(\( 1 + 16 T + 142 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( ( 1 + 6 T + 73 T^{2} )^{2} \))(\( 1 - 6 T - 21 T^{2} + 988 T^{3} - 1533 T^{4} - 31974 T^{5} + 389017 T^{6} \))(\( 1 - 14 T + 223 T^{2} - 1700 T^{3} + 16279 T^{4} - 74606 T^{5} + 389017 T^{6} \))(\( 1 + 8 T + 199 T^{2} + 1040 T^{3} + 14527 T^{4} + 42632 T^{5} + 389017 T^{6} \))(\( 1 - 4 T + 143 T^{2} - 456 T^{3} + 10439 T^{4} - 21316 T^{5} + 389017 T^{6} \))(\( 1 + 4 T - 9 T^{2} + 16 T^{3} - 657 T^{4} + 21316 T^{5} + 389017 T^{6} \))(\( 1 - 10 T + 115 T^{2} - 436 T^{3} + 8395 T^{4} - 53290 T^{5} + 389017 T^{6} \))(\( 1 - 14 T + 212 T^{2} - 1522 T^{3} + 16006 T^{4} - 111106 T^{5} + 1129748 T^{6} - 5446238 T^{7} + 28398241 T^{8} \))(\( 1 - 16 T + 292 T^{2} - 3168 T^{3} + 31990 T^{4} - 231264 T^{5} + 1556068 T^{6} - 6224272 T^{7} + 28398241 T^{8} \))(\( 1 + 6 T + 128 T^{2} + 1098 T^{3} + 13150 T^{4} + 80154 T^{5} + 682112 T^{6} + 2334102 T^{7} + 28398241 T^{8} \))(\( 1 - 12 T + 88 T^{2} + 772 T^{3} - 9170 T^{4} + 56356 T^{5} + 468952 T^{6} - 4668204 T^{7} + 28398241 T^{8} \))(\( 1 - 4 T + 229 T^{2} - 1056 T^{3} + 24610 T^{4} - 111800 T^{5} + 1796530 T^{6} - 5627424 T^{7} + 89084893 T^{8} - 113592964 T^{9} + 2073071593 T^{10} \))(\( 1 - 12 T + 309 T^{2} - 3472 T^{3} + 41170 T^{4} - 378952 T^{5} + 3005410 T^{6} - 18502288 T^{7} + 120206253 T^{8} - 340778892 T^{9} + 2073071593 T^{10} \))(\( 1 - 14 T + 229 T^{2} - 2304 T^{3} + 28418 T^{4} - 230500 T^{5} + 2074514 T^{6} - 12278016 T^{7} + 89084893 T^{8} - 397575374 T^{9} + 2073071593 T^{10} \))
$79$ (\( 1 + 4 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 6 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 - 14 T + 190 T^{2} - 1106 T^{3} + 6241 T^{4} \))(\( ( 1 + 12 T + 79 T^{2} )^{2} \))(\( 1 - 2 T + 118 T^{2} - 158 T^{3} + 6241 T^{4} \))(\( 1 + 2 T + 126 T^{2} + 158 T^{3} + 6241 T^{4} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( 1 - 14 T + 202 T^{2} - 1106 T^{3} + 6241 T^{4} \))(\( 1 + 6 T + 154 T^{2} + 474 T^{3} + 6241 T^{4} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 + 6 T + 122 T^{2} + 474 T^{3} + 6241 T^{4} \))(\( 1 - 6 T + 126 T^{2} - 474 T^{3} + 6241 T^{4} \))(\( 1 + 2 T + 142 T^{2} + 158 T^{3} + 6241 T^{4} \))(\( 1 + 4 T + 30 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 - 6 T + 213 T^{2} - 812 T^{3} + 16827 T^{4} - 37446 T^{5} + 493039 T^{6} \))(\( 1 + 12 T + 141 T^{2} + 1816 T^{3} + 11139 T^{4} + 74892 T^{5} + 493039 T^{6} \))(\( 1 - 10 T + 229 T^{2} - 1516 T^{3} + 18091 T^{4} - 62410 T^{5} + 493039 T^{6} \))(\( 1 + 4 T + 13 T^{2} - 392 T^{3} + 1027 T^{4} + 24964 T^{5} + 493039 T^{6} \))(\( 1 + 12 T + 33 T^{2} - 560 T^{3} + 2607 T^{4} + 74892 T^{5} + 493039 T^{6} \))(\( 1 - 8 T + 177 T^{2} - 1088 T^{3} + 13983 T^{4} - 49928 T^{5} + 493039 T^{6} \))(\( 1 + 12 T + 272 T^{2} + 2132 T^{3} + 29838 T^{4} + 168428 T^{5} + 1697552 T^{6} + 5916468 T^{7} + 38950081 T^{8} \))(\( 1 - 12 T + 124 T^{2} - 1324 T^{3} + 17542 T^{4} - 104596 T^{5} + 773884 T^{6} - 5916468 T^{7} + 38950081 T^{8} \))(\( 1 - 26 T + 484 T^{2} - 5938 T^{3} + 60790 T^{4} - 469102 T^{5} + 3020644 T^{6} - 12819014 T^{7} + 38950081 T^{8} \))(\( 1 - 2 T + 168 T^{2} - 1130 T^{3} + 13566 T^{4} - 89270 T^{5} + 1048488 T^{6} - 986078 T^{7} + 38950081 T^{8} \))(\( 1 + 2 T + 255 T^{2} + 576 T^{3} + 33518 T^{4} + 61948 T^{5} + 2647922 T^{6} + 3594816 T^{7} + 125724945 T^{8} + 77900162 T^{9} + 3077056399 T^{10} \))(\( 1 - 14 T + 203 T^{2} - 2248 T^{3} + 23626 T^{4} - 245076 T^{5} + 1866454 T^{6} - 14029768 T^{7} + 100086917 T^{8} - 545301134 T^{9} + 3077056399 T^{10} \))(\( 1 - 16 T + 339 T^{2} - 3512 T^{3} + 44242 T^{4} - 351088 T^{5} + 3495118 T^{6} - 21918392 T^{7} + 167140221 T^{8} - 623201296 T^{9} + 3077056399 T^{10} \))
$83$ (\( 1 - 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 7 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 - 15 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 11 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( 1 - 4 T + 102 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 + 13 T + 198 T^{2} + 1079 T^{3} + 6889 T^{4} \))(\( 1 + 9 T + 178 T^{2} + 747 T^{3} + 6889 T^{4} \))(\( 1 + 4 T + 38 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 - 8 T + 102 T^{2} - 664 T^{3} + 6889 T^{4} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( 1 + 8 T + 102 T^{2} + 664 T^{3} + 6889 T^{4} \))(\( 1 + 11 T + 186 T^{2} + 913 T^{3} + 6889 T^{4} \))(\( 1 + 4 T + 102 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{3} \))(\( 1 - 4 T + 105 T^{2} + 168 T^{3} + 8715 T^{4} - 27556 T^{5} + 571787 T^{6} \))(\( 1 - 8 T + 105 T^{2} - 1200 T^{3} + 8715 T^{4} - 55112 T^{5} + 571787 T^{6} \))(\( 1 - 4 T + 25 T^{2} + 360 T^{3} + 2075 T^{4} - 27556 T^{5} + 571787 T^{6} \))(\( 1 - 8 T + 121 T^{2} - 816 T^{3} + 10043 T^{4} - 55112 T^{5} + 571787 T^{6} \))(\( 1 + 19 T + 289 T^{2} + 3138 T^{3} + 23987 T^{4} + 130891 T^{5} + 571787 T^{6} \))(\( 1 + 25 T + 484 T^{2} + 6353 T^{3} + 66054 T^{4} + 527299 T^{5} + 3334276 T^{6} + 14294675 T^{7} + 47458321 T^{8} \))(\( 1 - 4 T + 220 T^{2} - 676 T^{3} + 24278 T^{4} - 56108 T^{5} + 1515580 T^{6} - 2287148 T^{7} + 47458321 T^{8} \))(\( 1 - T + 168 T^{2} - 489 T^{3} + 16478 T^{4} - 40587 T^{5} + 1157352 T^{6} - 571787 T^{7} + 47458321 T^{8} \))(\( 1 + 19 T + 212 T^{2} + 1275 T^{3} + 7590 T^{4} + 105825 T^{5} + 1460468 T^{6} + 10863953 T^{7} + 47458321 T^{8} \))(\( 1 - T + 151 T^{2} + 484 T^{3} + 12370 T^{4} + 64426 T^{5} + 1026710 T^{6} + 3334276 T^{7} + 86339837 T^{8} - 47458321 T^{9} + 3939040643 T^{10} \))(\( 1 - 17 T + 351 T^{2} - 3308 T^{3} + 42970 T^{4} - 315158 T^{5} + 3566510 T^{6} - 22788812 T^{7} + 200697237 T^{8} - 806791457 T^{9} + 3939040643 T^{10} \))(\( 1 - 9 T + 271 T^{2} - 1820 T^{3} + 34314 T^{4} - 181190 T^{5} + 2848062 T^{6} - 12537980 T^{7} + 154954277 T^{8} - 427124889 T^{9} + 3939040643 T^{10} \))
$89$ (\( 1 + 18 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 8 T + 126 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 + 14 T + 210 T^{2} + 1246 T^{3} + 7921 T^{4} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( 1 - 6 T + 154 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( 1 - 4 T + 102 T^{2} - 356 T^{3} + 7921 T^{4} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( 1 - 8 T + 126 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( 1 - 22 T + 266 T^{2} - 1958 T^{3} + 7921 T^{4} \))(\( 1 + 6 T + 87 T^{2} + 180 T^{3} + 7743 T^{4} + 47526 T^{5} + 704969 T^{6} \))(\( 1 + 10 T + 247 T^{2} + 1644 T^{3} + 21983 T^{4} + 79210 T^{5} + 704969 T^{6} \))(\( 1 - 8 T + 247 T^{2} - 1296 T^{3} + 21983 T^{4} - 63368 T^{5} + 704969 T^{6} \))(\( 1 + 24 T + 407 T^{2} + 4400 T^{3} + 36223 T^{4} + 190104 T^{5} + 704969 T^{6} \))(\( 1 - 2 T + 119 T^{2} - 124 T^{3} + 10591 T^{4} - 15842 T^{5} + 704969 T^{6} \))(\( 1 + 2 T - 57 T^{2} - 36 T^{3} - 5073 T^{4} + 15842 T^{5} + 704969 T^{6} \))(\( 1 + 20 T + 356 T^{2} + 4620 T^{3} + 48278 T^{4} + 411180 T^{5} + 2819876 T^{6} + 14099380 T^{7} + 62742241 T^{8} \))(\( 1 - 18 T + 424 T^{2} - 4702 T^{3} + 59534 T^{4} - 418478 T^{5} + 3358504 T^{6} - 12689442 T^{7} + 62742241 T^{8} \))(\( 1 - 14 T + 264 T^{2} - 3234 T^{3} + 31118 T^{4} - 287826 T^{5} + 2091144 T^{6} - 9869566 T^{7} + 62742241 T^{8} \))(\( 1 + 12 T + 180 T^{2} + 1876 T^{3} + 16374 T^{4} + 166964 T^{5} + 1425780 T^{6} + 8459628 T^{7} + 62742241 T^{8} \))(\( 1 - 4 T + 301 T^{2} - 1088 T^{3} + 43114 T^{4} - 136184 T^{5} + 3837146 T^{6} - 8618048 T^{7} + 212195669 T^{8} - 250968964 T^{9} + 5584059449 T^{10} \))(\( 1 + 6 T + 229 T^{2} + 1672 T^{3} + 26738 T^{4} + 212004 T^{5} + 2379682 T^{6} + 13243912 T^{7} + 161437901 T^{8} + 376453446 T^{9} + 5584059449 T^{10} \))(\( 1 + 16 T + 365 T^{2} + 4720 T^{3} + 59946 T^{4} + 585728 T^{5} + 5335194 T^{6} + 37387120 T^{7} + 257313685 T^{8} + 1003875856 T^{9} + 5584059449 T^{10} \))
$97$ (\( 1 + 8 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( 1 + 15 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 9 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 - 13 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 13 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 + 16 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 + 16 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 - 17 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 126 T^{2} + 9409 T^{4} \))(\( 1 - 9 T + 176 T^{2} - 873 T^{3} + 9409 T^{4} \))(\( 1 - 13 T + 226 T^{2} - 1261 T^{3} + 9409 T^{4} \))(\( 1 - 13 T + 228 T^{2} - 1261 T^{3} + 9409 T^{4} \))(\( 1 + 7 T + 679 T^{3} + 9409 T^{4} \))(\( 1 + 8 T + 130 T^{2} + 776 T^{3} + 9409 T^{4} \))(\( 1 + 12 T + 178 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( 1 + 12 T + 198 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 - 11 T + 132 T^{2} - 1067 T^{3} + 9409 T^{4} \))(\( 1 - 14 T + 226 T^{2} - 1358 T^{3} + 9409 T^{4} \))(\( 1 + 13 T + 228 T^{2} + 1261 T^{3} + 9409 T^{4} \))(\( 1 - 12 T + 147 T^{2} - 1112 T^{3} + 14259 T^{4} - 112908 T^{5} + 912673 T^{6} \))(\( 1 - 6 T + 143 T^{2} - 1460 T^{3} + 13871 T^{4} - 56454 T^{5} + 912673 T^{6} \))(\( 1 - 5 T + 227 T^{2} - 1086 T^{3} + 22019 T^{4} - 47045 T^{5} + 912673 T^{6} \))(\( 1 + 5 T + 37 T^{2} + 1274 T^{3} + 3589 T^{4} + 47045 T^{5} + 912673 T^{6} \))(\( 1 + 16 T + 339 T^{2} + 3040 T^{3} + 32883 T^{4} + 150544 T^{5} + 912673 T^{6} \))(\( 1 - 9 T + 95 T^{2} - 110 T^{3} + 9215 T^{4} - 84681 T^{5} + 912673 T^{6} \))(\( 1 - 19 T + 404 T^{2} - 4393 T^{3} + 55782 T^{4} - 426121 T^{5} + 3801236 T^{6} - 17340787 T^{7} + 88529281 T^{8} \))(\( 1 - 11 T + 378 T^{2} - 2805 T^{3} + 53546 T^{4} - 272085 T^{5} + 3556602 T^{6} - 10039403 T^{7} + 88529281 T^{8} \))(\( 1 - 2 T + 265 T^{2} - 42 T^{3} + 32996 T^{4} - 4074 T^{5} + 2493385 T^{6} - 1825346 T^{7} + 88529281 T^{8} \))(\( 1 - 11 T + 276 T^{2} - 3473 T^{3} + 34534 T^{4} - 336881 T^{5} + 2596884 T^{6} - 10039403 T^{7} + 88529281 T^{8} \))(\( 1 + 8 T + 334 T^{2} + 3010 T^{3} + 51365 T^{4} + 434580 T^{5} + 4982405 T^{6} + 28321090 T^{7} + 304832782 T^{8} + 708234248 T^{9} + 8587340257 T^{10} \))(\( 1 - 23 T + 613 T^{2} - 8372 T^{3} + 124474 T^{4} - 1175786 T^{5} + 12073978 T^{6} - 78772148 T^{7} + 559468549 T^{8} - 2036173463 T^{9} + 8587340257 T^{10} \))(\( 1 - 8 T + 366 T^{2} - 1498 T^{3} + 53277 T^{4} - 132356 T^{5} + 5167869 T^{6} - 14094682 T^{7} + 334038318 T^{8} - 708234248 T^{9} + 8587340257 T^{10} \))
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