Properties

Label 2366.2.a
Level 2366
Weight 2
Character orbit a
Rep. character \(\chi_{2366}(1,\cdot)\)
Character field \(\Q\)
Dimension 78
Newform subspaces 34
Sturm bound 728
Trace bound 5

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Defining parameters

Level: \( N \) = \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2366.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 34 \)
Sturm bound: \(728\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2366))\).

Total New Old
Modular forms 392 78 314
Cusp forms 337 78 259
Eisenstein series 55 0 55

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

\(2\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(13\)
\(+\)\(-\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(28\)
Minus space\(-\)\(50\)

Trace form

\( 78q - 6q^{3} + 78q^{4} - 2q^{5} - 2q^{6} + 78q^{9} + O(q^{10}) \) \( 78q - 6q^{3} + 78q^{4} - 2q^{5} - 2q^{6} + 78q^{9} + 6q^{10} + 4q^{11} - 6q^{12} + 2q^{14} + 8q^{15} + 78q^{16} + 4q^{18} - 2q^{19} - 2q^{20} + 2q^{21} - 8q^{22} + 8q^{23} - 2q^{24} + 82q^{25} - 12q^{27} + 28q^{29} + 16q^{30} - 4q^{31} + 16q^{33} + 12q^{34} + 6q^{35} + 78q^{36} - 24q^{37} + 10q^{38} + 6q^{40} + 16q^{41} + 2q^{42} + 4q^{44} + 38q^{45} + 20q^{47} - 6q^{48} + 78q^{49} - 4q^{50} + 20q^{51} + 8q^{53} + 4q^{54} + 2q^{56} + 12q^{57} + 4q^{58} + 14q^{59} + 8q^{60} - 18q^{61} - 4q^{62} - 4q^{63} + 78q^{64} - 24q^{67} + 32q^{69} - 6q^{70} - 24q^{71} + 4q^{72} - 36q^{73} + 24q^{74} - 34q^{75} - 2q^{76} + 12q^{77} + 16q^{79} - 2q^{80} + 82q^{81} + 4q^{82} + 6q^{83} + 2q^{84} - 4q^{85} - 28q^{86} + 4q^{87} - 8q^{88} + 4q^{89} + 38q^{90} + 8q^{92} - 40q^{93} - 4q^{94} - 24q^{95} - 2q^{96} - 24q^{97} + 28q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2366))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 13
2366.2.a.a \(1\) \(18.893\) \(\Q\) None \(-1\) \(-2\) \(-3\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}+q^{7}+\cdots\)
2366.2.a.b \(1\) \(18.893\) \(\Q\) None \(-1\) \(-2\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
2366.2.a.c \(1\) \(18.893\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
2366.2.a.d \(1\) \(18.893\) \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
2366.2.a.e \(1\) \(18.893\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
2366.2.a.f \(1\) \(18.893\) \(\Q\) None \(-1\) \(1\) \(3\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
2366.2.a.g \(1\) \(18.893\) \(\Q\) None \(-1\) \(3\) \(-3\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}-3q^{5}-3q^{6}+q^{7}+\cdots\)
2366.2.a.h \(1\) \(18.893\) \(\Q\) None \(-1\) \(3\) \(4\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}+4q^{5}-3q^{6}+q^{7}+\cdots\)
2366.2.a.i \(1\) \(18.893\) \(\Q\) None \(1\) \(-2\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
2366.2.a.j \(1\) \(18.893\) \(\Q\) None \(1\) \(-2\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
2366.2.a.k \(1\) \(18.893\) \(\Q\) None \(1\) \(-2\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}-q^{7}+\cdots\)
2366.2.a.l \(1\) \(18.893\) \(\Q\) None \(1\) \(-1\) \(2\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
2366.2.a.m \(1\) \(18.893\) \(\Q\) None \(1\) \(1\) \(-4\) \(1\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
2366.2.a.n \(1\) \(18.893\) \(\Q\) None \(1\) \(1\) \(-3\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
2366.2.a.o \(1\) \(18.893\) \(\Q\) None \(1\) \(3\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+3q^{3}+q^{4}+3q^{6}-q^{7}+q^{8}+\cdots\)
2366.2.a.p \(1\) \(18.893\) \(\Q\) None \(1\) \(3\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+3q^{3}+q^{4}+3q^{5}+3q^{6}-q^{7}+\cdots\)
2366.2.a.q \(2\) \(18.893\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
2366.2.a.r \(2\) \(18.893\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-4\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}+(-2-\beta )q^{5}-\beta q^{6}+\cdots\)
2366.2.a.s \(2\) \(18.893\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
2366.2.a.t \(2\) \(18.893\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(4\) \(-2\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta q^{3}+q^{4}+(2+\beta )q^{5}+\beta q^{6}+\cdots\)
2366.2.a.u \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-5\) \(-2\) \(3\) \(+\) \(-\) \(+\) \(q-q^{2}+(-2-\beta _{2})q^{3}+q^{4}-2\beta _{1}q^{5}+\cdots\)
2366.2.a.v \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-4\) \(-2\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
2366.2.a.w \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(8\) \(3\) \(+\) \(-\) \(+\) \(q-q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(3+\beta _{2})q^{5}+\cdots\)
2366.2.a.x \(3\) \(18.893\) 3.3.1384.1 None \(-3\) \(1\) \(-2\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
2366.2.a.y \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(-3\) \(2\) \(0\) \(3\) \(+\) \(-\) \(-\) \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
2366.2.a.z \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(3\) \(-5\) \(2\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{2}+(-2-\beta _{2})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots\)
2366.2.a.ba \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(3\) \(-4\) \(2\) \(3\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2366.2.a.bb \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(-8\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-3+\cdots)q^{5}+\cdots\)
2366.2.a.bc \(3\) \(18.893\) 3.3.1384.1 None \(3\) \(1\) \(2\) \(3\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots\)
2366.2.a.bd \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(3\) \(2\) \(0\) \(-3\) \(-\) \(+\) \(+\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
2366.2.a.be \(6\) \(18.893\) 6.6.6052921.1 None \(-6\) \(1\) \(-4\) \(-6\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
2366.2.a.bf \(6\) \(18.893\) 6.6.285686784.1 None \(-6\) \(2\) \(2\) \(-6\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{1}+\beta _{5})q^{5}+\cdots\)
2366.2.a.bg \(6\) \(18.893\) 6.6.6052921.1 None \(6\) \(1\) \(4\) \(6\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{4})q^{5}+\beta _{1}q^{6}+\cdots\)
2366.2.a.bh \(6\) \(18.893\) 6.6.285686784.1 None \(6\) \(2\) \(-2\) \(6\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2366))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2366)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 + 5 T + 15 T^{2} + 31 T^{3} + 45 T^{4} + 45 T^{5} + 27 T^{6} \))(\( 1 + 4 T + 12 T^{2} + 23 T^{3} + 36 T^{4} + 36 T^{5} + 27 T^{6} \))(\( 1 + 2 T^{2} + 7 T^{3} + 6 T^{4} + 27 T^{6} \))(\( 1 - T - T^{2} + 8 T^{3} - 3 T^{4} - 9 T^{5} + 27 T^{6} \))(\( 1 - 2 T + 8 T^{2} - 11 T^{3} + 24 T^{4} - 18 T^{5} + 27 T^{6} \))(\( 1 + 5 T + 15 T^{2} + 31 T^{3} + 45 T^{4} + 45 T^{5} + 27 T^{6} \))(\( 1 + 4 T + 12 T^{2} + 23 T^{3} + 36 T^{4} + 36 T^{5} + 27 T^{6} \))(\( 1 + 2 T^{2} + 7 T^{3} + 6 T^{4} + 27 T^{6} \))(\( 1 - T - T^{2} + 8 T^{3} - 3 T^{4} - 9 T^{5} + 27 T^{6} \))(\( 1 - 2 T + 8 T^{2} - 11 T^{3} + 24 T^{4} - 18 T^{5} + 27 T^{6} \))(\( 1 - T + 7 T^{2} - 8 T^{3} + 36 T^{4} - 36 T^{5} + 117 T^{6} - 108 T^{7} + 324 T^{8} - 216 T^{9} + 567 T^{10} - 243 T^{11} + 729 T^{12} \))(\( 1 - 2 T + 8 T^{2} - 18 T^{3} + 36 T^{4} - 70 T^{5} + 124 T^{6} - 210 T^{7} + 324 T^{8} - 486 T^{9} + 648 T^{10} - 486 T^{11} + 729 T^{12} \))(\( 1 - T + 7 T^{2} - 8 T^{3} + 36 T^{4} - 36 T^{5} + 117 T^{6} - 108 T^{7} + 324 T^{8} - 216 T^{9} + 567 T^{10} - 243 T^{11} + 729 T^{12} \))(\( 1 - 2 T + 8 T^{2} - 18 T^{3} + 36 T^{4} - 70 T^{5} + 124 T^{6} - 210 T^{7} + 324 T^{8} - 486 T^{9} + 648 T^{10} - 486 T^{11} + 729 T^{12} \))
$5$ (\( 1 + 3 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( ( 1 - T + 5 T^{2} )^{2} \))(\( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} \))(\( ( 1 + T + 5 T^{2} )^{2} \))(\( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} \))(\( 1 + 2 T + 7 T^{2} + 12 T^{3} + 35 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 + 2 T + 14 T^{2} + 19 T^{3} + 70 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 - 8 T + 34 T^{2} - 93 T^{3} + 170 T^{4} - 200 T^{5} + 125 T^{6} \))(\( 1 + 2 T + 5 T^{2} + 16 T^{3} + 25 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 + 8 T^{2} - 7 T^{3} + 40 T^{4} + 125 T^{6} \))(\( 1 - 2 T + 7 T^{2} - 12 T^{3} + 35 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 - 2 T + 14 T^{2} - 19 T^{3} + 70 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 + 8 T + 34 T^{2} + 93 T^{3} + 170 T^{4} + 200 T^{5} + 125 T^{6} \))(\( 1 - 2 T + 5 T^{2} - 16 T^{3} + 25 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 + 8 T^{2} + 7 T^{3} + 40 T^{4} + 125 T^{6} \))(\( 1 + 4 T + 19 T^{2} + 43 T^{3} + 141 T^{4} + 257 T^{5} + 766 T^{6} + 1285 T^{7} + 3525 T^{8} + 5375 T^{9} + 11875 T^{10} + 12500 T^{11} + 15625 T^{12} \))(\( 1 - 2 T + 11 T^{2} - 26 T^{3} + 88 T^{4} - 150 T^{5} + 509 T^{6} - 750 T^{7} + 2200 T^{8} - 3250 T^{9} + 6875 T^{10} - 6250 T^{11} + 15625 T^{12} \))(\( 1 - 4 T + 19 T^{2} - 43 T^{3} + 141 T^{4} - 257 T^{5} + 766 T^{6} - 1285 T^{7} + 3525 T^{8} - 5375 T^{9} + 11875 T^{10} - 12500 T^{11} + 15625 T^{12} \))(\( 1 + 2 T + 11 T^{2} + 26 T^{3} + 88 T^{4} + 150 T^{5} + 509 T^{6} + 750 T^{7} + 2200 T^{8} + 3250 T^{9} + 6875 T^{10} + 6250 T^{11} + 15625 T^{12} \))
$7$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))
$11$ (\( 1 + 6 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 2 T + 20 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 14 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 2 T + 20 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 14 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 3 T + 15 T^{2} + 53 T^{3} + 165 T^{4} + 363 T^{5} + 1331 T^{6} \))(\( 1 - 11 T + 71 T^{2} - 283 T^{3} + 781 T^{4} - 1331 T^{5} + 1331 T^{6} \))(\( 1 - 9 T + 53 T^{2} - 211 T^{3} + 583 T^{4} - 1089 T^{5} + 1331 T^{6} \))(\( 1 + 7 T + 25 T^{2} + 66 T^{3} + 275 T^{4} + 847 T^{5} + 1331 T^{6} \))(\( 1 + T + 31 T^{2} + 21 T^{3} + 341 T^{4} + 121 T^{5} + 1331 T^{6} \))(\( 1 - 3 T + 15 T^{2} - 53 T^{3} + 165 T^{4} - 363 T^{5} + 1331 T^{6} \))(\( 1 + 11 T + 71 T^{2} + 283 T^{3} + 781 T^{4} + 1331 T^{5} + 1331 T^{6} \))(\( 1 + 9 T + 53 T^{2} + 211 T^{3} + 583 T^{4} + 1089 T^{5} + 1331 T^{6} \))(\( 1 - 7 T + 25 T^{2} - 66 T^{3} + 275 T^{4} - 847 T^{5} + 1331 T^{6} \))(\( 1 - T + 31 T^{2} - 21 T^{3} + 341 T^{4} - 121 T^{5} + 1331 T^{6} \))(\( 1 + 6 T + 61 T^{2} + 270 T^{3} + 1565 T^{4} + 5398 T^{5} + 22427 T^{6} + 59378 T^{7} + 189365 T^{8} + 359370 T^{9} + 893101 T^{10} + 966306 T^{11} + 1771561 T^{12} \))(\( 1 + 2 T + 24 T^{2} + 14 T^{3} + 335 T^{4} - 108 T^{5} + 3520 T^{6} - 1188 T^{7} + 40535 T^{8} + 18634 T^{9} + 351384 T^{10} + 322102 T^{11} + 1771561 T^{12} \))(\( 1 - 6 T + 61 T^{2} - 270 T^{3} + 1565 T^{4} - 5398 T^{5} + 22427 T^{6} - 59378 T^{7} + 189365 T^{8} - 359370 T^{9} + 893101 T^{10} - 966306 T^{11} + 1771561 T^{12} \))(\( 1 - 2 T + 24 T^{2} - 14 T^{3} + 335 T^{4} + 108 T^{5} + 3520 T^{6} + 1188 T^{7} + 40535 T^{8} - 18634 T^{9} + 351384 T^{10} - 322102 T^{11} + 1771561 T^{12} \))
$13$ 1
$17$ (\( 1 + 3 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 8 T + 47 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 + 22 T^{2} + 289 T^{4} \))(\( 1 + 8 T + 47 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 + 22 T^{2} + 289 T^{4} \))(\( 1 + 7 T + 65 T^{2} + 245 T^{3} + 1105 T^{4} + 2023 T^{5} + 4913 T^{6} \))(\( 1 + 2 T - 6 T^{2} - 3 T^{3} - 102 T^{4} + 578 T^{5} + 4913 T^{6} \))(\( 1 - 10 T + 40 T^{2} - 117 T^{3} + 680 T^{4} - 2890 T^{5} + 4913 T^{6} \))(\( 1 - 2 T + 7 T^{2} - 12 T^{3} + 119 T^{4} - 578 T^{5} + 4913 T^{6} \))(\( 1 - 2 T + 36 T^{2} - 81 T^{3} + 612 T^{4} - 578 T^{5} + 4913 T^{6} \))(\( 1 + 7 T + 65 T^{2} + 245 T^{3} + 1105 T^{4} + 2023 T^{5} + 4913 T^{6} \))(\( 1 + 2 T - 6 T^{2} - 3 T^{3} - 102 T^{4} + 578 T^{5} + 4913 T^{6} \))(\( 1 - 10 T + 40 T^{2} - 117 T^{3} + 680 T^{4} - 2890 T^{5} + 4913 T^{6} \))(\( 1 - 2 T + 7 T^{2} - 12 T^{3} + 119 T^{4} - 578 T^{5} + 4913 T^{6} \))(\( 1 - 2 T + 36 T^{2} - 81 T^{3} + 612 T^{4} - 578 T^{5} + 4913 T^{6} \))(\( 1 + 9 T + 101 T^{2} + 638 T^{3} + 4134 T^{4} + 19764 T^{5} + 92011 T^{6} + 335988 T^{7} + 1194726 T^{8} + 3134494 T^{9} + 8435621 T^{10} + 12778713 T^{11} + 24137569 T^{12} \))(\( 1 - 4 T + 63 T^{2} - 172 T^{3} + 1859 T^{4} - 3792 T^{5} + 36442 T^{6} - 64464 T^{7} + 537251 T^{8} - 845036 T^{9} + 5261823 T^{10} - 5679428 T^{11} + 24137569 T^{12} \))(\( 1 + 9 T + 101 T^{2} + 638 T^{3} + 4134 T^{4} + 19764 T^{5} + 92011 T^{6} + 335988 T^{7} + 1194726 T^{8} + 3134494 T^{9} + 8435621 T^{10} + 12778713 T^{11} + 24137569 T^{12} \))(\( 1 - 4 T + 63 T^{2} - 172 T^{3} + 1859 T^{4} - 3792 T^{5} + 36442 T^{6} - 64464 T^{7} + 537251 T^{8} - 845036 T^{9} + 5261823 T^{10} - 5679428 T^{11} + 24137569 T^{12} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 30 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 + 4 T + 30 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 - 11 T + 53 T^{2} - 207 T^{3} + 1007 T^{4} - 3971 T^{5} + 6859 T^{6} \))(\( 1 - 13 T + 111 T^{2} - 565 T^{3} + 2109 T^{4} - 4693 T^{5} + 6859 T^{6} \))(\( 1 - 7 T + 57 T^{2} - 259 T^{3} + 1083 T^{4} - 2527 T^{5} + 6859 T^{6} \))(\( 1 + 4 T + 51 T^{2} + 136 T^{3} + 969 T^{4} + 1444 T^{5} + 6859 T^{6} \))(\( 1 + 15 T + 125 T^{2} + 653 T^{3} + 2375 T^{4} + 5415 T^{5} + 6859 T^{6} \))(\( 1 + 11 T + 53 T^{2} + 207 T^{3} + 1007 T^{4} + 3971 T^{5} + 6859 T^{6} \))(\( 1 + 13 T + 111 T^{2} + 565 T^{3} + 2109 T^{4} + 4693 T^{5} + 6859 T^{6} \))(\( 1 + 7 T + 57 T^{2} + 259 T^{3} + 1083 T^{4} + 2527 T^{5} + 6859 T^{6} \))(\( 1 - 4 T + 51 T^{2} - 136 T^{3} + 969 T^{4} - 1444 T^{5} + 6859 T^{6} \))(\( 1 - 15 T + 125 T^{2} - 653 T^{3} + 2375 T^{4} - 5415 T^{5} + 6859 T^{6} \))(\( 1 + 10 T + 97 T^{2} + 568 T^{3} + 3695 T^{4} + 17488 T^{5} + 89105 T^{6} + 332272 T^{7} + 1333895 T^{8} + 3895912 T^{9} + 12641137 T^{10} + 24760990 T^{11} + 47045881 T^{12} \))(\( 1 - 4 T + 22 T^{2} - 76 T^{3} + 971 T^{4} - 2824 T^{5} + 15500 T^{6} - 53656 T^{7} + 350531 T^{8} - 521284 T^{9} + 2867062 T^{10} - 9904396 T^{11} + 47045881 T^{12} \))(\( 1 - 10 T + 97 T^{2} - 568 T^{3} + 3695 T^{4} - 17488 T^{5} + 89105 T^{6} - 332272 T^{7} + 1333895 T^{8} - 3895912 T^{9} + 12641137 T^{10} - 24760990 T^{11} + 47045881 T^{12} \))(\( 1 + 4 T + 22 T^{2} + 76 T^{3} + 971 T^{4} + 2824 T^{5} + 15500 T^{6} + 53656 T^{7} + 350531 T^{8} + 521284 T^{9} + 2867062 T^{10} + 9904396 T^{11} + 47045881 T^{12} \))
$23$ (\( 1 + 6 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 6 T + 52 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 10 T + 59 T^{2} - 230 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 52 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 10 T + 59 T^{2} - 230 T^{3} + 529 T^{4} \))(\( 1 + 14 T + 125 T^{2} + 700 T^{3} + 2875 T^{4} + 7406 T^{5} + 12167 T^{6} \))(\( 1 + 7 T + 69 T^{2} + 273 T^{3} + 1587 T^{4} + 3703 T^{5} + 12167 T^{6} \))(\( 1 - 3 T + 65 T^{2} - 125 T^{3} + 1495 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - 3 T + 53 T^{2} - 106 T^{3} + 1219 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - T + 53 T^{2} - 59 T^{3} + 1219 T^{4} - 529 T^{5} + 12167 T^{6} \))(\( 1 + 14 T + 125 T^{2} + 700 T^{3} + 2875 T^{4} + 7406 T^{5} + 12167 T^{6} \))(\( 1 + 7 T + 69 T^{2} + 273 T^{3} + 1587 T^{4} + 3703 T^{5} + 12167 T^{6} \))(\( 1 - 3 T + 65 T^{2} - 125 T^{3} + 1495 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - 3 T + 53 T^{2} - 106 T^{3} + 1219 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - T + 53 T^{2} - 59 T^{3} + 1219 T^{4} - 529 T^{5} + 12167 T^{6} \))(\( 1 - 21 T + 244 T^{2} - 1974 T^{3} + 13037 T^{4} - 74557 T^{5} + 380660 T^{6} - 1714811 T^{7} + 6896573 T^{8} - 24017658 T^{9} + 68281204 T^{10} - 135163203 T^{11} + 148035889 T^{12} \))(\( 1 + 6 T + 70 T^{2} + 202 T^{3} + 1572 T^{4} + 782 T^{5} + 25728 T^{6} + 17986 T^{7} + 831588 T^{8} + 2457734 T^{9} + 19588870 T^{10} + 38618058 T^{11} + 148035889 T^{12} \))(\( 1 - 21 T + 244 T^{2} - 1974 T^{3} + 13037 T^{4} - 74557 T^{5} + 380660 T^{6} - 1714811 T^{7} + 6896573 T^{8} - 24017658 T^{9} + 68281204 T^{10} - 135163203 T^{11} + 148035889 T^{12} \))(\( 1 + 6 T + 70 T^{2} + 202 T^{3} + 1572 T^{4} + 782 T^{5} + 25728 T^{6} + 17986 T^{7} + 831588 T^{8} + 2457734 T^{9} + 19588870 T^{10} + 38618058 T^{11} + 148035889 T^{12} \))
$29$ (\( 1 - 3 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( 1 - 4 T + 14 T^{2} - 116 T^{3} + 841 T^{4} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( 1 - 4 T + 14 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 - 2 T + 79 T^{2} - 108 T^{3} + 2291 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( 1 + 3 T + 41 T^{2} + 175 T^{3} + 1189 T^{4} + 2523 T^{5} + 24389 T^{6} \))(\( 1 - 5 T - 5 T^{2} + 87 T^{3} - 145 T^{4} - 4205 T^{5} + 24389 T^{6} \))(\( 1 - 8 T + 67 T^{2} - 288 T^{3} + 1943 T^{4} - 6728 T^{5} + 24389 T^{6} \))(\( 1 - 5 T + 65 T^{2} - 193 T^{3} + 1885 T^{4} - 4205 T^{5} + 24389 T^{6} \))(\( 1 - 2 T + 79 T^{2} - 108 T^{3} + 2291 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( 1 + 3 T + 41 T^{2} + 175 T^{3} + 1189 T^{4} + 2523 T^{5} + 24389 T^{6} \))(\( 1 - 5 T - 5 T^{2} + 87 T^{3} - 145 T^{4} - 4205 T^{5} + 24389 T^{6} \))(\( 1 - 8 T + 67 T^{2} - 288 T^{3} + 1943 T^{4} - 6728 T^{5} + 24389 T^{6} \))(\( 1 - 5 T + 65 T^{2} - 193 T^{3} + 1885 T^{4} - 4205 T^{5} + 24389 T^{6} \))(\( 1 + T + 60 T^{2} - 38 T^{3} + 1813 T^{4} - 5663 T^{5} + 52956 T^{6} - 164227 T^{7} + 1524733 T^{8} - 926782 T^{9} + 42436860 T^{10} + 20511149 T^{11} + 594823321 T^{12} \))(\( 1 - 10 T + 135 T^{2} - 898 T^{3} + 7715 T^{4} - 39852 T^{5} + 268810 T^{6} - 1155708 T^{7} + 6488315 T^{8} - 21901322 T^{9} + 95482935 T^{10} - 205111490 T^{11} + 594823321 T^{12} \))(\( 1 + T + 60 T^{2} - 38 T^{3} + 1813 T^{4} - 5663 T^{5} + 52956 T^{6} - 164227 T^{7} + 1524733 T^{8} - 926782 T^{9} + 42436860 T^{10} + 20511149 T^{11} + 594823321 T^{12} \))(\( 1 - 10 T + 135 T^{2} - 898 T^{3} + 7715 T^{4} - 39852 T^{5} + 268810 T^{6} - 1155708 T^{7} + 6488315 T^{8} - 21901322 T^{9} + 95482935 T^{10} - 205111490 T^{11} + 594823321 T^{12} \))
$31$ (\( 1 + 10 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 14 T + 108 T^{2} + 434 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 66 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 14 T + 108 T^{2} - 434 T^{3} + 961 T^{4} \))(\( 1 - 8 T + 66 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 - 14 T + 149 T^{2} - 924 T^{3} + 4619 T^{4} - 13454 T^{5} + 29791 T^{6} \))(\( 1 - 2 T + 64 T^{2} - 53 T^{3} + 1984 T^{4} - 1922 T^{5} + 29791 T^{6} \))(\( 1 - 24 T + 278 T^{2} - 1951 T^{3} + 8618 T^{4} - 23064 T^{5} + 29791 T^{6} \))(\( 1 - 7 T + 85 T^{2} - 346 T^{3} + 2635 T^{4} - 6727 T^{5} + 29791 T^{6} \))(\( 1 + 4 T + 54 T^{2} + 289 T^{3} + 1674 T^{4} + 3844 T^{5} + 29791 T^{6} \))(\( 1 + 14 T + 149 T^{2} + 924 T^{3} + 4619 T^{4} + 13454 T^{5} + 29791 T^{6} \))(\( 1 + 2 T + 64 T^{2} + 53 T^{3} + 1984 T^{4} + 1922 T^{5} + 29791 T^{6} \))(\( 1 + 24 T + 278 T^{2} + 1951 T^{3} + 8618 T^{4} + 23064 T^{5} + 29791 T^{6} \))(\( 1 + 7 T + 85 T^{2} + 346 T^{3} + 2635 T^{4} + 6727 T^{5} + 29791 T^{6} \))(\( 1 - 4 T + 54 T^{2} - 289 T^{3} + 1674 T^{4} - 3844 T^{5} + 29791 T^{6} \))(\( 1 + 20 T + 321 T^{2} + 3425 T^{3} + 31041 T^{4} + 220905 T^{5} + 1365586 T^{6} + 6848055 T^{7} + 29830401 T^{8} + 102034175 T^{9} + 296450241 T^{10} + 572583020 T^{11} + 887503681 T^{12} \))(\( 1 - 2 T + 144 T^{2} - 358 T^{3} + 9287 T^{4} - 23652 T^{5} + 358576 T^{6} - 733212 T^{7} + 8924807 T^{8} - 10665178 T^{9} + 132987024 T^{10} - 57258302 T^{11} + 887503681 T^{12} \))(\( 1 - 20 T + 321 T^{2} - 3425 T^{3} + 31041 T^{4} - 220905 T^{5} + 1365586 T^{6} - 6848055 T^{7} + 29830401 T^{8} - 102034175 T^{9} + 296450241 T^{10} - 572583020 T^{11} + 887503681 T^{12} \))(\( 1 + 2 T + 144 T^{2} + 358 T^{3} + 9287 T^{4} + 23652 T^{5} + 358576 T^{6} + 733212 T^{7} + 8924807 T^{8} + 10665178 T^{9} + 132987024 T^{10} + 57258302 T^{11} + 887503681 T^{12} \))
$37$ (\( 1 + T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + 9 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 47 T^{2} + 1369 T^{4} \))(\( 1 - 12 T + 98 T^{2} - 444 T^{3} + 1369 T^{4} \))(\( 1 + 47 T^{2} + 1369 T^{4} \))(\( 1 + 12 T + 98 T^{2} + 444 T^{3} + 1369 T^{4} \))(\( 1 - 8 T + 123 T^{2} - 584 T^{3} + 4551 T^{4} - 10952 T^{5} + 50653 T^{6} \))(\( 1 + 90 T^{2} + 7 T^{3} + 3330 T^{4} + 50653 T^{6} \))(\( 1 + 4 T + 72 T^{2} + 337 T^{3} + 2664 T^{4} + 5476 T^{5} + 50653 T^{6} \))(\( 1 + 9 T + 119 T^{2} + 622 T^{3} + 4403 T^{4} + 12321 T^{5} + 50653 T^{6} \))(\( 1 + 28 T + 370 T^{2} + 2863 T^{3} + 13690 T^{4} + 38332 T^{5} + 50653 T^{6} \))(\( 1 + 8 T + 123 T^{2} + 584 T^{3} + 4551 T^{4} + 10952 T^{5} + 50653 T^{6} \))(\( 1 + 90 T^{2} - 7 T^{3} + 3330 T^{4} + 50653 T^{6} \))(\( 1 - 4 T + 72 T^{2} - 337 T^{3} + 2664 T^{4} - 5476 T^{5} + 50653 T^{6} \))(\( 1 - 9 T + 119 T^{2} - 622 T^{3} + 4403 T^{4} - 12321 T^{5} + 50653 T^{6} \))(\( 1 - 28 T + 370 T^{2} - 2863 T^{3} + 13690 T^{4} - 38332 T^{5} + 50653 T^{6} \))(\( 1 + 16 T + 179 T^{2} + 1601 T^{3} + 12575 T^{4} + 87987 T^{5} + 557826 T^{6} + 3255519 T^{7} + 17215175 T^{8} + 81095453 T^{9} + 335474819 T^{10} + 1109503312 T^{11} + 2565726409 T^{12} \))(\( 1 + 67 T^{2} + 8 T^{3} + 3347 T^{4} + 280 T^{5} + 165506 T^{6} + 10360 T^{7} + 4582043 T^{8} + 405224 T^{9} + 125568787 T^{10} + 2565726409 T^{12} \))(\( 1 - 16 T + 179 T^{2} - 1601 T^{3} + 12575 T^{4} - 87987 T^{5} + 557826 T^{6} - 3255519 T^{7} + 17215175 T^{8} - 81095453 T^{9} + 335474819 T^{10} - 1109503312 T^{11} + 2565726409 T^{12} \))(\( 1 + 67 T^{2} - 8 T^{3} + 3347 T^{4} - 280 T^{5} + 165506 T^{6} - 10360 T^{7} + 4582043 T^{8} - 405224 T^{9} + 125568787 T^{10} + 2565726409 T^{12} \))
$41$ (\( 1 + 3 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 + 2 T + 71 T^{2} + 82 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 106 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 - 2 T + 71 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 106 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 - 9 T + 59 T^{2} - 205 T^{3} + 2419 T^{4} - 15129 T^{5} + 68921 T^{6} \))(\( 1 - 7 T + 25 T^{2} - 231 T^{3} + 1025 T^{4} - 11767 T^{5} + 68921 T^{6} \))(\( 1 + 3 T + 77 T^{2} + 289 T^{3} + 3157 T^{4} + 5043 T^{5} + 68921 T^{6} \))(\( 1 - 15 T + 179 T^{2} - 1274 T^{3} + 7339 T^{4} - 25215 T^{5} + 68921 T^{6} \))(\( 1 + 13 T + 149 T^{2} + 1067 T^{3} + 6109 T^{4} + 21853 T^{5} + 68921 T^{6} \))(\( 1 + 9 T + 59 T^{2} + 205 T^{3} + 2419 T^{4} + 15129 T^{5} + 68921 T^{6} \))(\( 1 + 7 T + 25 T^{2} + 231 T^{3} + 1025 T^{4} + 11767 T^{5} + 68921 T^{6} \))(\( 1 - 3 T + 77 T^{2} - 289 T^{3} + 3157 T^{4} - 5043 T^{5} + 68921 T^{6} \))(\( 1 + 15 T + 179 T^{2} + 1274 T^{3} + 7339 T^{4} + 25215 T^{5} + 68921 T^{6} \))(\( 1 - 13 T + 149 T^{2} - 1067 T^{3} + 6109 T^{4} - 21853 T^{5} + 68921 T^{6} \))(\( 1 + 2 T + 77 T^{2} - 18 T^{3} + 4625 T^{4} + 618 T^{5} + 215007 T^{6} + 25338 T^{7} + 7774625 T^{8} - 1240578 T^{9} + 217583597 T^{10} + 231712402 T^{11} + 4750104241 T^{12} \))(\( 1 + 6 T + 151 T^{2} + 878 T^{3} + 11883 T^{4} + 57724 T^{5} + 604554 T^{6} + 2366684 T^{7} + 19975323 T^{8} + 60512638 T^{9} + 426689911 T^{10} + 695137206 T^{11} + 4750104241 T^{12} \))(\( 1 - 2 T + 77 T^{2} + 18 T^{3} + 4625 T^{4} - 618 T^{5} + 215007 T^{6} - 25338 T^{7} + 7774625 T^{8} + 1240578 T^{9} + 217583597 T^{10} - 231712402 T^{11} + 4750104241 T^{12} \))(\( 1 - 6 T + 151 T^{2} - 878 T^{3} + 11883 T^{4} - 57724 T^{5} + 604554 T^{6} - 2366684 T^{7} + 19975323 T^{8} - 60512638 T^{9} + 426689911 T^{10} - 695137206 T^{11} + 4750104241 T^{12} \))
$43$ (\( 1 + 10 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 14 T + 108 T^{2} + 602 T^{3} + 1849 T^{4} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( 1 + 14 T + 108 T^{2} + 602 T^{3} + 1849 T^{4} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( 1 - 19 T + 219 T^{2} - 1663 T^{3} + 9417 T^{4} - 35131 T^{5} + 79507 T^{6} \))(\( 1 + 17 T + 209 T^{2} + 1533 T^{3} + 8987 T^{4} + 31433 T^{5} + 79507 T^{6} \))(\( 1 + 9 T + 149 T^{2} + 787 T^{3} + 6407 T^{4} + 16641 T^{5} + 79507 T^{6} \))(\( 1 + 8 T + 105 T^{2} + 560 T^{3} + 4515 T^{4} + 14792 T^{5} + 79507 T^{6} \))(\( 1 + T + 85 T^{2} + 169 T^{3} + 3655 T^{4} + 1849 T^{5} + 79507 T^{6} \))(\( 1 - 19 T + 219 T^{2} - 1663 T^{3} + 9417 T^{4} - 35131 T^{5} + 79507 T^{6} \))(\( 1 + 17 T + 209 T^{2} + 1533 T^{3} + 8987 T^{4} + 31433 T^{5} + 79507 T^{6} \))(\( 1 + 9 T + 149 T^{2} + 787 T^{3} + 6407 T^{4} + 16641 T^{5} + 79507 T^{6} \))(\( 1 + 8 T + 105 T^{2} + 560 T^{3} + 4515 T^{4} + 14792 T^{5} + 79507 T^{6} \))(\( 1 + T + 85 T^{2} + 169 T^{3} + 3655 T^{4} + 1849 T^{5} + 79507 T^{6} \))(\( 1 - 2 T + 25 T^{2} - 136 T^{3} + 5603 T^{4} - 9604 T^{5} + 92961 T^{6} - 412972 T^{7} + 10359947 T^{8} - 10812952 T^{9} + 85470025 T^{10} - 294016886 T^{11} + 6321363049 T^{12} \))(\( 1 - 26 T + 472 T^{2} - 5942 T^{3} + 61823 T^{4} - 518084 T^{5} + 3733280 T^{6} - 22277612 T^{7} + 114310727 T^{8} - 472430594 T^{9} + 1613674072 T^{10} - 3822219518 T^{11} + 6321363049 T^{12} \))(\( 1 - 2 T + 25 T^{2} - 136 T^{3} + 5603 T^{4} - 9604 T^{5} + 92961 T^{6} - 412972 T^{7} + 10359947 T^{8} - 10812952 T^{9} + 85470025 T^{10} - 294016886 T^{11} + 6321363049 T^{12} \))(\( 1 - 26 T + 472 T^{2} - 5942 T^{3} + 61823 T^{4} - 518084 T^{5} + 3733280 T^{6} - 22277612 T^{7} + 114310727 T^{8} - 472430594 T^{9} + 1613674072 T^{10} - 3822219518 T^{11} + 6321363049 T^{12} \))
$47$ (\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 13 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 13 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))(\( 1 - 8 T + 62 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 50 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 62 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 4 T + 50 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 + 14 T + 169 T^{2} + 1260 T^{3} + 7943 T^{4} + 30926 T^{5} + 103823 T^{6} \))(\( 1 + 5 T + 77 T^{2} + 499 T^{3} + 3619 T^{4} + 11045 T^{5} + 103823 T^{6} \))(\( 1 - 17 T + 235 T^{2} - 1767 T^{3} + 11045 T^{4} - 37553 T^{5} + 103823 T^{6} \))(\( 1 + 17 T + 213 T^{2} + 1686 T^{3} + 10011 T^{4} + 37553 T^{5} + 103823 T^{6} \))(\( 1 + 7 T + 43 T^{2} + 21 T^{3} + 2021 T^{4} + 15463 T^{5} + 103823 T^{6} \))(\( 1 - 14 T + 169 T^{2} - 1260 T^{3} + 7943 T^{4} - 30926 T^{5} + 103823 T^{6} \))(\( 1 - 5 T + 77 T^{2} - 499 T^{3} + 3619 T^{4} - 11045 T^{5} + 103823 T^{6} \))(\( 1 + 17 T + 235 T^{2} + 1767 T^{3} + 11045 T^{4} + 37553 T^{5} + 103823 T^{6} \))(\( 1 - 17 T + 213 T^{2} - 1686 T^{3} + 10011 T^{4} - 37553 T^{5} + 103823 T^{6} \))(\( 1 - 7 T + 43 T^{2} - 21 T^{3} + 2021 T^{4} - 15463 T^{5} + 103823 T^{6} \))(\( 1 - 5 T + 164 T^{2} - 954 T^{3} + 15413 T^{4} - 75645 T^{5} + 908724 T^{6} - 3555315 T^{7} + 34047317 T^{8} - 99047142 T^{9} + 800267684 T^{10} - 1146725035 T^{11} + 10779215329 T^{12} \))(\( 1 - 8 T + 178 T^{2} - 792 T^{3} + 11679 T^{4} - 26000 T^{5} + 524700 T^{6} - 1222000 T^{7} + 25798911 T^{8} - 82227816 T^{9} + 868583218 T^{10} - 1834760056 T^{11} + 10779215329 T^{12} \))(\( 1 + 5 T + 164 T^{2} + 954 T^{3} + 15413 T^{4} + 75645 T^{5} + 908724 T^{6} + 3555315 T^{7} + 34047317 T^{8} + 99047142 T^{9} + 800267684 T^{10} + 1146725035 T^{11} + 10779215329 T^{12} \))(\( 1 + 8 T + 178 T^{2} + 792 T^{3} + 11679 T^{4} + 26000 T^{5} + 524700 T^{6} + 1222000 T^{7} + 25798911 T^{8} + 82227816 T^{9} + 868583218 T^{10} + 1834760056 T^{11} + 10779215329 T^{12} \))
$53$ (\( 1 + 9 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 - 10 T + 119 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 58 T^{2} + 2809 T^{4} \))(\( 1 - 10 T + 119 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 58 T^{2} + 2809 T^{4} \))(\( 1 + 14 T + 215 T^{2} + 1540 T^{3} + 11395 T^{4} + 39326 T^{5} + 148877 T^{6} \))(\( 1 + 110 T^{2} + 91 T^{3} + 5830 T^{4} + 148877 T^{6} \))(\( 1 + 10 T + 176 T^{2} + 1019 T^{3} + 9328 T^{4} + 28090 T^{5} + 148877 T^{6} \))(\( ( 1 + 6 T + 53 T^{2} )^{3} \))(\( 1 + 12 T + 186 T^{2} + 1259 T^{3} + 9858 T^{4} + 33708 T^{5} + 148877 T^{6} \))(\( 1 + 14 T + 215 T^{2} + 1540 T^{3} + 11395 T^{4} + 39326 T^{5} + 148877 T^{6} \))(\( 1 + 110 T^{2} + 91 T^{3} + 5830 T^{4} + 148877 T^{6} \))(\( 1 + 10 T + 176 T^{2} + 1019 T^{3} + 9328 T^{4} + 28090 T^{5} + 148877 T^{6} \))(\( ( 1 + 6 T + 53 T^{2} )^{3} \))(\( 1 + 12 T + 186 T^{2} + 1259 T^{3} + 9858 T^{4} + 33708 T^{5} + 148877 T^{6} \))(\( 1 - 28 T + 551 T^{2} - 7735 T^{3} + 88485 T^{4} - 826301 T^{5} + 6574358 T^{6} - 43793953 T^{7} + 248554365 T^{8} - 1151563595 T^{9} + 4347655031 T^{10} - 11709473804 T^{11} + 22164361129 T^{12} \))(\( 1 - 18 T + 267 T^{2} - 3114 T^{3} + 31467 T^{4} - 273420 T^{5} + 2178178 T^{6} - 14491260 T^{7} + 88390803 T^{8} - 463602978 T^{9} + 2106758427 T^{10} - 7527518874 T^{11} + 22164361129 T^{12} \))(\( 1 - 28 T + 551 T^{2} - 7735 T^{3} + 88485 T^{4} - 826301 T^{5} + 6574358 T^{6} - 43793953 T^{7} + 248554365 T^{8} - 1151563595 T^{9} + 4347655031 T^{10} - 11709473804 T^{11} + 22164361129 T^{12} \))(\( 1 - 18 T + 267 T^{2} - 3114 T^{3} + 31467 T^{4} - 273420 T^{5} + 2178178 T^{6} - 14491260 T^{7} + 88390803 T^{8} - 463602978 T^{9} + 2106758427 T^{10} - 7527518874 T^{11} + 22164361129 T^{12} \))
$59$ (\( 1 + 6 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 - 9 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 9 T + 59 T^{2} \))(\( 1 - 18 T + 196 T^{2} - 1062 T^{3} + 3481 T^{4} \))(\( 1 + 16 T + 155 T^{2} + 944 T^{3} + 3481 T^{4} \))(\( 1 + 18 T + 196 T^{2} + 1062 T^{3} + 3481 T^{4} \))(\( 1 - 16 T + 155 T^{2} - 944 T^{3} + 3481 T^{4} \))(\( 1 - 9 T - 13 T^{2} + 745 T^{3} - 767 T^{4} - 31329 T^{5} + 205379 T^{6} \))(\( 1 - 17 T + 271 T^{2} - 2175 T^{3} + 15989 T^{4} - 59177 T^{5} + 205379 T^{6} \))(\( 1 + 3 T + 131 T^{2} + 355 T^{3} + 7729 T^{4} + 10443 T^{5} + 205379 T^{6} \))(\( 1 + 10 T + 83 T^{2} + 296 T^{3} + 4897 T^{4} + 34810 T^{5} + 205379 T^{6} \))(\( 1 - 3 T + 117 T^{2} - 481 T^{3} + 6903 T^{4} - 10443 T^{5} + 205379 T^{6} \))(\( 1 + 9 T - 13 T^{2} - 745 T^{3} - 767 T^{4} + 31329 T^{5} + 205379 T^{6} \))(\( 1 + 17 T + 271 T^{2} + 2175 T^{3} + 15989 T^{4} + 59177 T^{5} + 205379 T^{6} \))(\( 1 - 3 T + 131 T^{2} - 355 T^{3} + 7729 T^{4} - 10443 T^{5} + 205379 T^{6} \))(\( 1 - 10 T + 83 T^{2} - 296 T^{3} + 4897 T^{4} - 34810 T^{5} + 205379 T^{6} \))(\( 1 + 3 T + 117 T^{2} + 481 T^{3} + 6903 T^{4} + 10443 T^{5} + 205379 T^{6} \))(\( 1 - 12 T + 243 T^{2} - 1492 T^{3} + 18371 T^{4} - 52238 T^{5} + 891263 T^{6} - 3082042 T^{7} + 63949451 T^{8} - 306425468 T^{9} + 2944518723 T^{10} - 8579091588 T^{11} + 42180533641 T^{12} \))(\( 1 + 2 T + 272 T^{2} + 506 T^{3} + 32980 T^{4} + 54774 T^{5} + 2408732 T^{6} + 3231666 T^{7} + 114803380 T^{8} + 103921774 T^{9} + 3295922192 T^{10} + 1429848598 T^{11} + 42180533641 T^{12} \))(\( 1 + 12 T + 243 T^{2} + 1492 T^{3} + 18371 T^{4} + 52238 T^{5} + 891263 T^{6} + 3082042 T^{7} + 63949451 T^{8} + 306425468 T^{9} + 2944518723 T^{10} + 8579091588 T^{11} + 42180533641 T^{12} \))(\( 1 - 2 T + 272 T^{2} - 506 T^{3} + 32980 T^{4} - 54774 T^{5} + 2408732 T^{6} - 3231666 T^{7} + 114803380 T^{8} - 103921774 T^{9} + 3295922192 T^{10} - 1429848598 T^{11} + 42180533641 T^{12} \))
$61$ (\( 1 + 7 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 - 11 T + 61 T^{2} \))(\( 1 - 13 T + 61 T^{2} \))(\( 1 - T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 7 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 11 T + 61 T^{2} \))(\( 1 - 13 T + 61 T^{2} \))(\( 1 - 13 T + 61 T^{2} \))(\( 1 + 20 T + 219 T^{2} + 1220 T^{3} + 3721 T^{4} \))(\( 1 + 4 T + 99 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 20 T + 219 T^{2} + 1220 T^{3} + 3721 T^{4} \))(\( 1 + 4 T + 99 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 4 T + 123 T^{2} + 256 T^{3} + 7503 T^{4} + 14884 T^{5} + 226981 T^{6} \))(\( 1 - 3 T + 137 T^{2} - 367 T^{3} + 8357 T^{4} - 11163 T^{5} + 226981 T^{6} \))(\( 1 + 5 T + 105 T^{2} + 779 T^{3} + 6405 T^{4} + 18605 T^{5} + 226981 T^{6} \))(\( 1 - 5 T + 181 T^{2} - 608 T^{3} + 11041 T^{4} - 18605 T^{5} + 226981 T^{6} \))(\( 1 + 3 T + 95 T^{2} + 479 T^{3} + 5795 T^{4} + 11163 T^{5} + 226981 T^{6} \))(\( 1 + 4 T + 123 T^{2} + 256 T^{3} + 7503 T^{4} + 14884 T^{5} + 226981 T^{6} \))(\( 1 - 3 T + 137 T^{2} - 367 T^{3} + 8357 T^{4} - 11163 T^{5} + 226981 T^{6} \))(\( 1 + 5 T + 105 T^{2} + 779 T^{3} + 6405 T^{4} + 18605 T^{5} + 226981 T^{6} \))(\( 1 - 5 T + 181 T^{2} - 608 T^{3} + 11041 T^{4} - 18605 T^{5} + 226981 T^{6} \))(\( 1 + 3 T + 95 T^{2} + 479 T^{3} + 5795 T^{4} + 11163 T^{5} + 226981 T^{6} \))(\( 1 + 27 T + 598 T^{2} + 8766 T^{3} + 111115 T^{4} + 1098335 T^{5} + 9564612 T^{6} + 66998435 T^{7} + 413458915 T^{8} + 1989715446 T^{9} + 8279812918 T^{10} + 22804100127 T^{11} + 51520374361 T^{12} \))(\( 1 - 28 T + 435 T^{2} - 3956 T^{3} + 18488 T^{4} + 18948 T^{5} - 811259 T^{6} + 1155828 T^{7} + 68793848 T^{8} - 897936836 T^{9} + 6022940835 T^{10} - 23648696428 T^{11} + 51520374361 T^{12} \))(\( 1 + 27 T + 598 T^{2} + 8766 T^{3} + 111115 T^{4} + 1098335 T^{5} + 9564612 T^{6} + 66998435 T^{7} + 413458915 T^{8} + 1989715446 T^{9} + 8279812918 T^{10} + 22804100127 T^{11} + 51520374361 T^{12} \))(\( 1 - 28 T + 435 T^{2} - 3956 T^{3} + 18488 T^{4} + 18948 T^{5} - 811259 T^{6} + 1155828 T^{7} + 68793848 T^{8} - 897936836 T^{9} + 6022940835 T^{10} - 23648696428 T^{11} + 51520374361 T^{12} \))
$67$ (\( 1 - 2 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 11 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 6 T + 68 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 90 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 6 T + 68 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 + 4 T + 90 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 + 3 T + 141 T^{2} + 151 T^{3} + 9447 T^{4} + 13467 T^{5} + 300763 T^{6} \))(\( 1 - 21 T + 327 T^{2} - 3017 T^{3} + 21909 T^{4} - 94269 T^{5} + 300763 T^{6} \))(\( 1 + 5 T + 95 T^{2} + 867 T^{3} + 6365 T^{4} + 22445 T^{5} + 300763 T^{6} \))(\( 1 + 15 T + 257 T^{2} + 2026 T^{3} + 17219 T^{4} + 67335 T^{5} + 300763 T^{6} \))(\( 1 - 5 T + 151 T^{2} - 545 T^{3} + 10117 T^{4} - 22445 T^{5} + 300763 T^{6} \))(\( 1 - 3 T + 141 T^{2} - 151 T^{3} + 9447 T^{4} - 13467 T^{5} + 300763 T^{6} \))(\( 1 + 21 T + 327 T^{2} + 3017 T^{3} + 21909 T^{4} + 94269 T^{5} + 300763 T^{6} \))(\( 1 - 5 T + 95 T^{2} - 867 T^{3} + 6365 T^{4} - 22445 T^{5} + 300763 T^{6} \))(\( 1 - 15 T + 257 T^{2} - 2026 T^{3} + 17219 T^{4} - 67335 T^{5} + 300763 T^{6} \))(\( 1 + 5 T + 151 T^{2} + 545 T^{3} + 10117 T^{4} + 22445 T^{5} + 300763 T^{6} \))(\( 1 + 16 T + 259 T^{2} + 2960 T^{3} + 34347 T^{4} + 316274 T^{5} + 2882699 T^{6} + 21190358 T^{7} + 154183683 T^{8} + 890258480 T^{9} + 5219140339 T^{10} + 21602001712 T^{11} + 90458382169 T^{12} \))(\( 1 + 6 T + 280 T^{2} + 1562 T^{3} + 34127 T^{4} + 179068 T^{5} + 2660672 T^{6} + 11997556 T^{7} + 153196103 T^{8} + 469791806 T^{9} + 5642313880 T^{10} + 8100750642 T^{11} + 90458382169 T^{12} \))(\( 1 - 16 T + 259 T^{2} - 2960 T^{3} + 34347 T^{4} - 316274 T^{5} + 2882699 T^{6} - 21190358 T^{7} + 154183683 T^{8} - 890258480 T^{9} + 5219140339 T^{10} - 21602001712 T^{11} + 90458382169 T^{12} \))(\( 1 - 6 T + 280 T^{2} - 1562 T^{3} + 34127 T^{4} - 179068 T^{5} + 2660672 T^{6} - 11997556 T^{7} + 153196103 T^{8} - 469791806 T^{9} + 5642313880 T^{10} - 8100750642 T^{11} + 90458382169 T^{12} \))
$71$ (\( 1 + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 + 16 T + 71 T^{2} \))(\( 1 + 16 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 15 T + 71 T^{2} \))(\( 1 - 50 T^{2} + 5041 T^{4} \))(\( 1 + 2 T + 131 T^{2} + 142 T^{3} + 5041 T^{4} \))(\( 1 - 50 T^{2} + 5041 T^{4} \))(\( 1 - 2 T + 131 T^{2} - 142 T^{3} + 5041 T^{4} \))(\( 1 - 8 T + 169 T^{2} - 792 T^{3} + 11999 T^{4} - 40328 T^{5} + 357911 T^{6} \))(\( 1 + 16 T + 184 T^{2} + 1431 T^{3} + 13064 T^{4} + 80656 T^{5} + 357911 T^{6} \))(\( 1 - 24 T + 356 T^{2} - 3577 T^{3} + 25276 T^{4} - 120984 T^{5} + 357911 T^{6} \))(\( 1 - 4 T + 53 T^{2} + 328 T^{3} + 3763 T^{4} - 20164 T^{5} + 357911 T^{6} \))(\( 1 + 164 T^{2} + 91 T^{3} + 11644 T^{4} + 357911 T^{6} \))(\( 1 + 8 T + 169 T^{2} + 792 T^{3} + 11999 T^{4} + 40328 T^{5} + 357911 T^{6} \))(\( 1 - 16 T + 184 T^{2} - 1431 T^{3} + 13064 T^{4} - 80656 T^{5} + 357911 T^{6} \))(\( 1 + 24 T + 356 T^{2} + 3577 T^{3} + 25276 T^{4} + 120984 T^{5} + 357911 T^{6} \))(\( 1 + 4 T + 53 T^{2} - 328 T^{3} + 3763 T^{4} + 20164 T^{5} + 357911 T^{6} \))(\( 1 + 164 T^{2} - 91 T^{3} + 11644 T^{4} + 357911 T^{6} \))(\( 1 + 169 T^{2} + 35 T^{3} + 11271 T^{4} - 4445 T^{5} + 581862 T^{6} - 315595 T^{7} + 56817111 T^{8} + 12526885 T^{9} + 4294574089 T^{10} + 128100283921 T^{12} \))(\( 1 + 4 T + 272 T^{2} + 880 T^{3} + 36280 T^{4} + 92988 T^{5} + 3097886 T^{6} + 6602148 T^{7} + 182887480 T^{8} + 314961680 T^{9} + 6911977232 T^{10} + 7216917404 T^{11} + 128100283921 T^{12} \))(\( 1 + 169 T^{2} - 35 T^{3} + 11271 T^{4} + 4445 T^{5} + 581862 T^{6} + 315595 T^{7} + 56817111 T^{8} - 12526885 T^{9} + 4294574089 T^{10} + 128100283921 T^{12} \))(\( 1 - 4 T + 272 T^{2} - 880 T^{3} + 36280 T^{4} - 92988 T^{5} + 3097886 T^{6} - 6602148 T^{7} + 182887480 T^{8} - 314961680 T^{9} + 6911977232 T^{10} - 7216917404 T^{11} + 128100283921 T^{12} \))
$73$ (\( 1 + 7 T + 73 T^{2} \))(\( 1 + 3 T + 73 T^{2} \))(\( 1 - T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 5 T + 73 T^{2} \))(\( 1 - 3 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 7 T + 73 T^{2} \))(\( 1 + T + 73 T^{2} \))(\( 1 + 9 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 7 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 2 T + 39 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 - 8 T + 150 T^{2} - 584 T^{3} + 5329 T^{4} \))(\( 1 + 2 T + 39 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 8 T + 150 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( 1 - 13 T + 203 T^{2} - 1731 T^{3} + 14819 T^{4} - 69277 T^{5} + 389017 T^{6} \))(\( 1 + T + 203 T^{2} + 117 T^{3} + 14819 T^{4} + 5329 T^{5} + 389017 T^{6} \))(\( 1 - T + 189 T^{2} - 103 T^{3} + 13797 T^{4} - 5329 T^{5} + 389017 T^{6} \))(\( 1 - 11 T + 235 T^{2} - 1610 T^{3} + 17155 T^{4} - 58619 T^{5} + 389017 T^{6} \))(\( 1 + 21 T + 149 T^{2} + 707 T^{3} + 10877 T^{4} + 111909 T^{5} + 389017 T^{6} \))(\( 1 + 13 T + 203 T^{2} + 1731 T^{3} + 14819 T^{4} + 69277 T^{5} + 389017 T^{6} \))(\( 1 - T + 203 T^{2} - 117 T^{3} + 14819 T^{4} - 5329 T^{5} + 389017 T^{6} \))(\( 1 + T + 189 T^{2} + 103 T^{3} + 13797 T^{4} + 5329 T^{5} + 389017 T^{6} \))(\( 1 + 11 T + 235 T^{2} + 1610 T^{3} + 17155 T^{4} + 58619 T^{5} + 389017 T^{6} \))(\( 1 - 21 T + 149 T^{2} - 707 T^{3} + 10877 T^{4} - 111909 T^{5} + 389017 T^{6} \))(\( 1 + 38 T + 811 T^{2} + 12294 T^{3} + 150495 T^{4} + 1568896 T^{5} + 14314189 T^{6} + 114529408 T^{7} + 801987855 T^{8} + 4782574998 T^{9} + 23030973451 T^{10} + 78776720534 T^{11} + 151334226289 T^{12} \))(\( 1 - 22 T + 375 T^{2} - 3350 T^{3} + 25043 T^{4} - 71940 T^{5} + 489610 T^{6} - 5251620 T^{7} + 133454147 T^{8} - 1303206950 T^{9} + 10649340375 T^{10} - 45607575046 T^{11} + 151334226289 T^{12} \))(\( 1 - 38 T + 811 T^{2} - 12294 T^{3} + 150495 T^{4} - 1568896 T^{5} + 14314189 T^{6} - 114529408 T^{7} + 801987855 T^{8} - 4782574998 T^{9} + 23030973451 T^{10} - 78776720534 T^{11} + 151334226289 T^{12} \))(\( 1 + 22 T + 375 T^{2} + 3350 T^{3} + 25043 T^{4} + 71940 T^{5} + 489610 T^{6} + 5251620 T^{7} + 133454147 T^{8} + 1303206950 T^{9} + 10649340375 T^{10} + 45607575046 T^{11} + 151334226289 T^{12} \))
$79$ (\( 1 - 14 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 15 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 + 15 T + 79 T^{2} \))(\( 1 + 13 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 17 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 18 T + 212 T^{2} + 1422 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 174 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 18 T + 212 T^{2} + 1422 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 174 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 16 T + 201 T^{2} + 2296 T^{3} + 15879 T^{4} + 99856 T^{5} + 493039 T^{6} \))(\( 1 - 10 T + 212 T^{2} - 1455 T^{3} + 16748 T^{4} - 62410 T^{5} + 493039 T^{6} \))(\( 1 - 10 T + 128 T^{2} - 489 T^{3} + 10112 T^{4} - 62410 T^{5} + 493039 T^{6} \))(\( 1 + 7 T + 149 T^{2} + 1254 T^{3} + 11771 T^{4} + 43687 T^{5} + 493039 T^{6} \))(\( 1 + 2 T + 12 T^{2} - 931 T^{3} + 948 T^{4} + 12482 T^{5} + 493039 T^{6} \))(\( 1 + 16 T + 201 T^{2} + 2296 T^{3} + 15879 T^{4} + 99856 T^{5} + 493039 T^{6} \))(\( 1 - 10 T + 212 T^{2} - 1455 T^{3} + 16748 T^{4} - 62410 T^{5} + 493039 T^{6} \))(\( 1 - 10 T + 128 T^{2} - 489 T^{3} + 10112 T^{4} - 62410 T^{5} + 493039 T^{6} \))(\( 1 + 7 T + 149 T^{2} + 1254 T^{3} + 11771 T^{4} + 43687 T^{5} + 493039 T^{6} \))(\( 1 + 2 T + 12 T^{2} - 931 T^{3} + 948 T^{4} + 12482 T^{5} + 493039 T^{6} \))(\( 1 - 6 T + 337 T^{2} - 1579 T^{3} + 54647 T^{4} - 210917 T^{5} + 5415446 T^{6} - 16662443 T^{7} + 341051927 T^{8} - 778508581 T^{9} + 13126177297 T^{10} - 18462338394 T^{11} + 243087455521 T^{12} \))(\( 1 - 22 T + 536 T^{2} - 7106 T^{3} + 100727 T^{4} - 974028 T^{5} + 10218624 T^{6} - 76948212 T^{7} + 628637207 T^{8} - 3503535134 T^{9} + 20877243416 T^{10} - 67695240778 T^{11} + 243087455521 T^{12} \))(\( 1 - 6 T + 337 T^{2} - 1579 T^{3} + 54647 T^{4} - 210917 T^{5} + 5415446 T^{6} - 16662443 T^{7} + 341051927 T^{8} - 778508581 T^{9} + 13126177297 T^{10} - 18462338394 T^{11} + 243087455521 T^{12} \))(\( 1 - 22 T + 536 T^{2} - 7106 T^{3} + 100727 T^{4} - 974028 T^{5} + 10218624 T^{6} - 76948212 T^{7} + 628637207 T^{8} - 3503535134 T^{9} + 20877243416 T^{10} - 67695240778 T^{11} + 243087455521 T^{12} \))
$83$ (\( 1 + 18 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 18 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 - 18 T + 220 T^{2} - 1494 T^{3} + 6889 T^{4} \))(\( 1 + 58 T^{2} + 6889 T^{4} \))(\( 1 + 18 T + 220 T^{2} + 1494 T^{3} + 6889 T^{4} \))(\( 1 + 58 T^{2} + 6889 T^{4} \))(\( 1 - 21 T + 333 T^{2} - 3577 T^{3} + 27639 T^{4} - 144669 T^{5} + 571787 T^{6} \))(\( 1 - T + 149 T^{2} - 347 T^{3} + 12367 T^{4} - 6889 T^{5} + 571787 T^{6} \))(\( 1 + 7 T + 95 T^{2} + 371 T^{3} + 7885 T^{4} + 48223 T^{5} + 571787 T^{6} \))(\( 1 + 10 T + 123 T^{2} + 408 T^{3} + 10209 T^{4} + 68890 T^{5} + 571787 T^{6} \))(\( 1 - 5 T + 241 T^{2} - 789 T^{3} + 20003 T^{4} - 34445 T^{5} + 571787 T^{6} \))(\( 1 + 21 T + 333 T^{2} + 3577 T^{3} + 27639 T^{4} + 144669 T^{5} + 571787 T^{6} \))(\( 1 + T + 149 T^{2} + 347 T^{3} + 12367 T^{4} + 6889 T^{5} + 571787 T^{6} \))(\( 1 - 7 T + 95 T^{2} - 371 T^{3} + 7885 T^{4} - 48223 T^{5} + 571787 T^{6} \))(\( 1 - 10 T + 123 T^{2} - 408 T^{3} + 10209 T^{4} - 68890 T^{5} + 571787 T^{6} \))(\( 1 + 5 T + 241 T^{2} + 789 T^{3} + 20003 T^{4} + 34445 T^{5} + 571787 T^{6} \))(\( 1 - 6 T + 265 T^{2} - 1224 T^{3} + 35891 T^{4} - 128808 T^{5} + 3418761 T^{6} - 10691064 T^{7} + 247253099 T^{8} - 699867288 T^{9} + 12576455065 T^{10} - 23634243858 T^{11} + 326940373369 T^{12} \))(\( 1 - 10 T + 316 T^{2} - 2478 T^{3} + 41691 T^{4} - 288388 T^{5} + 3740088 T^{6} - 23936204 T^{7} + 287209299 T^{8} - 1416888186 T^{9} + 14996829436 T^{10} - 39390406430 T^{11} + 326940373369 T^{12} \))(\( 1 + 6 T + 265 T^{2} + 1224 T^{3} + 35891 T^{4} + 128808 T^{5} + 3418761 T^{6} + 10691064 T^{7} + 247253099 T^{8} + 699867288 T^{9} + 12576455065 T^{10} + 23634243858 T^{11} + 326940373369 T^{12} \))(\( 1 + 10 T + 316 T^{2} + 2478 T^{3} + 41691 T^{4} + 288388 T^{5} + 3740088 T^{6} + 23936204 T^{7} + 287209299 T^{8} + 1416888186 T^{9} + 14996829436 T^{10} + 39390406430 T^{11} + 326940373369 T^{12} \))
$89$ (\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 - 18 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 - 12 T + 202 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 24 T + 310 T^{2} - 2136 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 202 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 + 24 T + 310 T^{2} + 2136 T^{3} + 7921 T^{4} \))(\( 1 - 25 T + 431 T^{2} - 4547 T^{3} + 38359 T^{4} - 198025 T^{5} + 704969 T^{6} \))(\( 1 + 4 T + 158 T^{2} + 473 T^{3} + 14062 T^{4} + 31684 T^{5} + 704969 T^{6} \))(\( 1 - 2 T + 252 T^{2} - 327 T^{3} + 22428 T^{4} - 15842 T^{5} + 704969 T^{6} \))(\( 1 - 26 T + 447 T^{2} - 4860 T^{3} + 39783 T^{4} - 205946 T^{5} + 704969 T^{6} \))(\( 1 + 14 T + 176 T^{2} + 2191 T^{3} + 15664 T^{4} + 110894 T^{5} + 704969 T^{6} \))(\( 1 + 25 T + 431 T^{2} + 4547 T^{3} + 38359 T^{4} + 198025 T^{5} + 704969 T^{6} \))(\( 1 - 4 T + 158 T^{2} - 473 T^{3} + 14062 T^{4} - 31684 T^{5} + 704969 T^{6} \))(\( 1 + 2 T + 252 T^{2} + 327 T^{3} + 22428 T^{4} + 15842 T^{5} + 704969 T^{6} \))(\( 1 + 26 T + 447 T^{2} + 4860 T^{3} + 39783 T^{4} + 205946 T^{5} + 704969 T^{6} \))(\( 1 - 14 T + 176 T^{2} - 2191 T^{3} + 15664 T^{4} - 110894 T^{5} + 704969 T^{6} \))(\( 1 - T + 229 T^{2} + 94 T^{3} + 31324 T^{4} - 21644 T^{5} + 3356869 T^{6} - 1926316 T^{7} + 248117404 T^{8} + 66267086 T^{9} + 14367973189 T^{10} - 5584059449 T^{11} + 496981290961 T^{12} \))(\( 1 - 4 T + 334 T^{2} - 1140 T^{3} + 57807 T^{4} - 169576 T^{5} + 6306852 T^{6} - 15092264 T^{7} + 457889247 T^{8} - 803664660 T^{9} + 20955908494 T^{10} - 22336237796 T^{11} + 496981290961 T^{12} \))(\( 1 + T + 229 T^{2} - 94 T^{3} + 31324 T^{4} + 21644 T^{5} + 3356869 T^{6} + 1926316 T^{7} + 248117404 T^{8} - 66267086 T^{9} + 14367973189 T^{10} + 5584059449 T^{11} + 496981290961 T^{12} \))(\( 1 + 4 T + 334 T^{2} + 1140 T^{3} + 57807 T^{4} + 169576 T^{5} + 6306852 T^{6} + 15092264 T^{7} + 457889247 T^{8} + 803664660 T^{9} + 20955908494 T^{10} + 22336237796 T^{11} + 496981290961 T^{12} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 17 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 + 11 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 4 T + 186 T^{2} + 388 T^{3} + 9409 T^{4} \))(\( 1 - 20 T + 246 T^{2} - 1940 T^{3} + 9409 T^{4} \))(\( 1 - 4 T + 186 T^{2} - 388 T^{3} + 9409 T^{4} \))(\( 1 + 20 T + 246 T^{2} + 1940 T^{3} + 9409 T^{4} \))(\( 1 - 31 T + 609 T^{2} - 7093 T^{3} + 59073 T^{4} - 291679 T^{5} + 912673 T^{6} \))(\( 1 - 19 T + 311 T^{2} - 3225 T^{3} + 30167 T^{4} - 178771 T^{5} + 912673 T^{6} \))(\( 1 + 27 T + 527 T^{2} + 5911 T^{3} + 51119 T^{4} + 254043 T^{5} + 912673 T^{6} \))(\( 1 - 21 T + 419 T^{2} - 4270 T^{3} + 40643 T^{4} - 197589 T^{5} + 912673 T^{6} \))(\( 1 - 15 T + 359 T^{2} - 3007 T^{3} + 34823 T^{4} - 141135 T^{5} + 912673 T^{6} \))(\( 1 + 31 T + 609 T^{2} + 7093 T^{3} + 59073 T^{4} + 291679 T^{5} + 912673 T^{6} \))(\( 1 + 19 T + 311 T^{2} + 3225 T^{3} + 30167 T^{4} + 178771 T^{5} + 912673 T^{6} \))(\( 1 - 27 T + 527 T^{2} - 5911 T^{3} + 51119 T^{4} - 254043 T^{5} + 912673 T^{6} \))(\( 1 + 21 T + 419 T^{2} + 4270 T^{3} + 40643 T^{4} + 197589 T^{5} + 912673 T^{6} \))(\( 1 + 15 T + 359 T^{2} + 3007 T^{3} + 34823 T^{4} + 141135 T^{5} + 912673 T^{6} \))(\( 1 + 16 T + 511 T^{2} + 6198 T^{3} + 113769 T^{4} + 1087256 T^{5} + 14310613 T^{6} + 105463832 T^{7} + 1070452521 T^{8} + 5656747254 T^{9} + 45238462591 T^{10} + 137397444112 T^{11} + 832972004929 T^{12} \))(\( 1 - 12 T + 358 T^{2} - 3260 T^{3} + 59423 T^{4} - 424120 T^{5} + 6536564 T^{6} - 41139640 T^{7} + 559111007 T^{8} - 2975313980 T^{9} + 31693482598 T^{10} - 103048083084 T^{11} + 832972004929 T^{12} \))(\( 1 - 16 T + 511 T^{2} - 6198 T^{3} + 113769 T^{4} - 1087256 T^{5} + 14310613 T^{6} - 105463832 T^{7} + 1070452521 T^{8} - 5656747254 T^{9} + 45238462591 T^{10} - 137397444112 T^{11} + 832972004929 T^{12} \))(\( 1 + 12 T + 358 T^{2} + 3260 T^{3} + 59423 T^{4} + 424120 T^{5} + 6536564 T^{6} + 41139640 T^{7} + 559111007 T^{8} + 2975313980 T^{9} + 31693482598 T^{10} + 103048083084 T^{11} + 832972004929 T^{12} \))
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