Properties

Label 1155.2.a
Level 1155
Weight 2
Character orbit a
Rep. character \(\chi_{1155}(1,\cdot)\)
Character field \(\Q\)
Dimension 41
Newform subspaces 23
Sturm bound 384
Trace bound 5

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(384\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1155))\).

Total New Old
Modular forms 200 41 159
Cusp forms 185 41 144
Eisenstein series 15 0 15

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

\(3\)\(5\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(13\)
Minus space\(-\)\(28\)

Trace form

\( 41q + 3q^{2} + q^{3} + 39q^{4} + q^{5} - 5q^{6} + q^{7} + 15q^{8} + 41q^{9} + O(q^{10}) \) \( 41q + 3q^{2} + q^{3} + 39q^{4} + q^{5} - 5q^{6} + q^{7} + 15q^{8} + 41q^{9} - 5q^{10} + q^{11} + 7q^{12} + 14q^{13} + 3q^{14} - 7q^{15} + 47q^{16} + 2q^{17} + 3q^{18} - 12q^{19} + 7q^{20} + q^{21} - 5q^{22} - 8q^{23} - 9q^{24} + 41q^{25} + 26q^{26} + q^{27} + 7q^{28} + 14q^{29} + 3q^{30} + 63q^{32} + q^{33} + 38q^{34} + q^{35} + 39q^{36} + 6q^{37} + 12q^{38} + 14q^{39} - 9q^{40} - 6q^{41} - 5q^{42} + 12q^{43} + 7q^{44} + q^{45} + 8q^{46} + 31q^{48} + 41q^{49} + 3q^{50} - 14q^{51} + 98q^{52} + 6q^{53} - 5q^{54} + q^{55} + 15q^{56} + 20q^{57} + 42q^{58} - 4q^{59} - 17q^{60} - 2q^{61} - 64q^{62} + q^{63} + 15q^{64} - 2q^{65} + 3q^{66} - 28q^{67} - 34q^{68} - 24q^{69} - 5q^{70} - 56q^{71} + 15q^{72} + 10q^{73} - 94q^{74} + q^{75} - 36q^{76} + q^{77} + 10q^{78} - 16q^{79} - 33q^{80} + 41q^{81} - 2q^{82} - 28q^{83} + 7q^{84} - 14q^{85} + 4q^{86} - 18q^{87} - 9q^{88} + 10q^{89} - 5q^{90} - 2q^{91} - 40q^{92} + 16q^{93} - 32q^{94} + 4q^{95} + 7q^{96} - 14q^{97} + 3q^{98} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 7 11
1155.2.a.a \(1\) \(9.223\) \(\Q\) None \(-2\) \(-1\) \(1\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
1155.2.a.b \(1\) \(9.223\) \(\Q\) None \(-2\) \(1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
1155.2.a.c \(1\) \(9.223\) \(\Q\) None \(-2\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
1155.2.a.d \(1\) \(9.223\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.e \(1\) \(9.223\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.f \(1\) \(9.223\) \(\Q\) None \(-1\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.g \(1\) \(9.223\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+q^{11}+\cdots\)
1155.2.a.h \(1\) \(9.223\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
1155.2.a.i \(1\) \(9.223\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
1155.2.a.j \(1\) \(9.223\) \(\Q\) None \(1\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.k \(1\) \(9.223\) \(\Q\) None \(1\) \(-1\) \(1\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.l \(1\) \(9.223\) \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.m \(1\) \(9.223\) \(\Q\) None \(1\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
1155.2.a.n \(1\) \(9.223\) \(\Q\) None \(2\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
1155.2.a.o \(2\) \(9.223\) \(\Q(\sqrt{17}) \) None \(-1\) \(-2\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
1155.2.a.p \(2\) \(9.223\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-q^{7}-2\beta q^{8}+\cdots\)
1155.2.a.q \(2\) \(9.223\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(2\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+q^{3}+4q^{4}+q^{5}+\beta q^{6}+q^{7}+\cdots\)
1155.2.a.r \(2\) \(9.223\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}-q^{5}+\cdots\)
1155.2.a.s \(3\) \(9.223\) 3.3.316.1 None \(1\) \(-3\) \(3\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1155.2.a.t \(3\) \(9.223\) 3.3.316.1 None \(1\) \(3\) \(3\) \(-3\) \(-\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
1155.2.a.u \(4\) \(9.223\) 4.4.13448.1 None \(0\) \(4\) \(-4\) \(-4\) \(-\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
1155.2.a.v \(4\) \(9.223\) 4.4.7232.1 None \(2\) \(-4\) \(4\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
1155.2.a.w \(5\) \(9.223\) 5.5.352076.1 None \(1\) \(5\) \(-5\) \(5\) \(-\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1155))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1155)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))(\( 1 + 2 T + 2 T^{2} \))(\( 1 + 2 T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + 2 T^{2} \))(\( 1 + 2 T^{2} \))(\( 1 + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - 2 T + 2 T^{2} \))(\( 1 + T + 2 T^{3} + 4 T^{4} \))(\( 1 + 2 T^{2} + 4 T^{4} \))(\( 1 - 2 T^{2} + 4 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} \))(\( 1 - T + 2 T^{2} - 2 T^{3} + 4 T^{4} - 4 T^{5} + 8 T^{6} \))(\( 1 - T + 2 T^{2} - 2 T^{3} + 4 T^{4} - 4 T^{5} + 8 T^{6} \))(\( 1 + T^{2} - 2 T^{4} + 4 T^{6} + 16 T^{8} \))(\( 1 - 2 T + 3 T^{2} - 4 T^{3} + 6 T^{4} - 8 T^{5} + 12 T^{6} - 16 T^{7} + 16 T^{8} \))(\( 1 - T + T^{2} - T^{3} + 2 T^{4} - 2 T^{5} + 4 T^{6} - 4 T^{7} + 8 T^{8} - 16 T^{9} + 32 T^{10} \))
$3$ (\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{5} \))
$5$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{5} \))
$7$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{5} \))
$11$ (\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{5} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 6 T + 18 T^{2} + 78 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 28 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 2 T - 26 T^{3} + 169 T^{4} \))(\( 1 - 8 T + 53 T^{2} - 204 T^{3} + 689 T^{4} - 1352 T^{5} + 2197 T^{6} \))(\( 1 - 8 T + 53 T^{2} - 204 T^{3} + 689 T^{4} - 1352 T^{5} + 2197 T^{6} \))(\( 1 - 8 T + 50 T^{2} - 240 T^{3} + 1002 T^{4} - 3120 T^{5} + 8450 T^{6} - 17576 T^{7} + 28561 T^{8} \))(\( 1 - 4 T + 38 T^{2} - 132 T^{3} + 642 T^{4} - 1716 T^{5} + 6422 T^{6} - 8788 T^{7} + 28561 T^{8} \))(\( 1 - 8 T + 55 T^{2} - 252 T^{3} + 1260 T^{4} - 4632 T^{5} + 16380 T^{6} - 42588 T^{7} + 120835 T^{8} - 228488 T^{9} + 371293 T^{10} \))
$17$ (\( 1 + 3 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 5 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 3 T + 32 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 - 2 T + 27 T^{2} - 34 T^{3} + 289 T^{4} \))(\( ( 1 + 3 T + 17 T^{2} )^{2} \))(\( 1 + 6 T + 31 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 12 T + 92 T^{2} - 442 T^{3} + 1564 T^{4} - 3468 T^{5} + 4913 T^{6} \))(\( 1 - 8 T + 56 T^{2} - 226 T^{3} + 952 T^{4} - 2312 T^{5} + 4913 T^{6} \))(\( ( 1 + T + 24 T^{2} + 17 T^{3} + 289 T^{4} )^{2} \))(\( 1 - 6 T + 57 T^{2} - 302 T^{3} + 1364 T^{4} - 5134 T^{5} + 16473 T^{6} - 29478 T^{7} + 83521 T^{8} \))(\( 1 + 22 T^{2} + 70 T^{3} + 57 T^{4} + 1876 T^{5} + 969 T^{6} + 20230 T^{7} + 108086 T^{8} + 1419857 T^{10} \))
$19$ (\( 1 - T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 3 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + T + 34 T^{2} + 19 T^{3} + 361 T^{4} \))(\( 1 + 2 T + 31 T^{2} + 38 T^{3} + 361 T^{4} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( 1 + 10 T + 51 T^{2} + 190 T^{3} + 361 T^{4} \))(\( 1 - 2 T + 26 T^{2} - 120 T^{3} + 494 T^{4} - 722 T^{5} + 6859 T^{6} \))(\( 1 + 2 T + 26 T^{2} + 120 T^{3} + 494 T^{4} + 722 T^{5} + 6859 T^{6} \))(\( 1 - 10 T + 37 T^{2} + 78 T^{3} - 916 T^{4} + 1482 T^{5} + 13357 T^{6} - 68590 T^{7} + 130321 T^{8} \))(\( 1 + 6 T + 77 T^{2} + 318 T^{3} + 2188 T^{4} + 6042 T^{5} + 27797 T^{6} + 41154 T^{7} + 130321 T^{8} \))(\( 1 - 6 T + 92 T^{2} - 412 T^{3} + 3439 T^{4} - 11388 T^{5} + 65341 T^{6} - 148732 T^{7} + 631028 T^{8} - 781926 T^{9} + 2476099 T^{10} \))
$23$ (\( 1 + 7 T + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 5 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 7 T + 54 T^{2} + 161 T^{3} + 529 T^{4} \))(\( 1 + 2 T + 39 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 31 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 10 T + 59 T^{2} - 230 T^{3} + 529 T^{4} \))(\( 1 - 2 T + 54 T^{2} - 60 T^{3} + 1242 T^{4} - 1058 T^{5} + 12167 T^{6} \))(\( 1 + 6 T + 74 T^{2} + 268 T^{3} + 1702 T^{4} + 3174 T^{5} + 12167 T^{6} \))(\( 1 + 2 T + 21 T^{2} - 98 T^{3} - 108 T^{4} - 2254 T^{5} + 11109 T^{6} + 24334 T^{7} + 279841 T^{8} \))(\( 1 - 10 T + 53 T^{2} - 242 T^{3} + 1252 T^{4} - 5566 T^{5} + 28037 T^{6} - 121670 T^{7} + 279841 T^{8} \))(\( 1 + 2 T + 68 T^{2} + 260 T^{3} + 2175 T^{4} + 9652 T^{5} + 50025 T^{6} + 137540 T^{7} + 827356 T^{8} + 559682 T^{9} + 6436343 T^{10} \))
$29$ (\( 1 - T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 7 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 - 10 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 9 T + 40 T^{2} + 261 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 49 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 61 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 71 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 56 T^{2} - 314 T^{3} + 1624 T^{4} - 5046 T^{5} + 24389 T^{6} \))(\( 1 - 10 T + 116 T^{2} - 602 T^{3} + 3364 T^{4} - 8410 T^{5} + 24389 T^{6} \))(\( 1 + 2 T + 71 T^{2} + 210 T^{3} + 2432 T^{4} + 6090 T^{5} + 59711 T^{6} + 48778 T^{7} + 707281 T^{8} \))(\( 1 - 6 T + 71 T^{2} - 422 T^{3} + 2720 T^{4} - 12238 T^{5} + 59711 T^{6} - 146334 T^{7} + 707281 T^{8} \))(\( 1 - 6 T + 58 T^{2} - 142 T^{3} + 1365 T^{4} - 3016 T^{5} + 39585 T^{6} - 119422 T^{7} + 1414562 T^{8} - 4243686 T^{9} + 20511149 T^{10} \))
$31$ (\( 1 - 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 2 T + 46 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 64 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 12 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 + 14 T + 108 T^{2} + 434 T^{3} + 961 T^{4} \))(\( 1 + 2 T + 39 T^{2} - 52 T^{3} + 1209 T^{4} + 1922 T^{5} + 29791 T^{6} \))(\( 1 + 2 T + 79 T^{2} + 92 T^{3} + 2449 T^{4} + 1922 T^{5} + 29791 T^{6} \))(\( 1 - 24 T + 326 T^{2} - 2928 T^{3} + 19090 T^{4} - 90768 T^{5} + 313286 T^{6} - 714984 T^{7} + 923521 T^{8} \))(\( 1 + 8 T + 106 T^{2} + 552 T^{3} + 4394 T^{4} + 17112 T^{5} + 101866 T^{6} + 238328 T^{7} + 923521 T^{8} \))(\( 1 - 10 T + 145 T^{2} - 1040 T^{3} + 8424 T^{4} - 45388 T^{5} + 261144 T^{6} - 999440 T^{7} + 4319695 T^{8} - 9235210 T^{9} + 28629151 T^{10} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 12 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 6 T + 66 T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 60 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 72 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 - 2 T + 48 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 109 T^{2} - 292 T^{3} + 4033 T^{4} - 5476 T^{5} + 50653 T^{6} \))(\( 1 - 8 T + 53 T^{2} - 300 T^{3} + 1961 T^{4} - 10952 T^{5} + 50653 T^{6} \))(\( 1 - 8 T + 114 T^{2} - 688 T^{3} + 6282 T^{4} - 25456 T^{5} + 156066 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( 1 - 12 T + 118 T^{2} - 988 T^{3} + 6818 T^{4} - 36556 T^{5} + 161542 T^{6} - 607836 T^{7} + 1874161 T^{8} \))(\( 1 - 4 T + 71 T^{2} - 204 T^{3} + 1316 T^{4} - 4928 T^{5} + 48692 T^{6} - 279276 T^{7} + 3596363 T^{8} - 7496644 T^{9} + 69343957 T^{10} \))
$41$ (\( 1 + 8 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( 1 - 8 T + 48 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 + 76 T^{2} + 1681 T^{4} \))(\( 1 - 2 T + 8 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 + 89 T^{2} + 76 T^{3} + 3649 T^{4} + 68921 T^{6} \))(\( 1 - 4 T + 73 T^{2} - 396 T^{3} + 2993 T^{4} - 6724 T^{5} + 68921 T^{6} \))(\( 1 + 38 T^{2} + 402 T^{4} + 63878 T^{6} + 2825761 T^{8} \))(\( 1 + 58 T^{2} + 264 T^{3} + 2362 T^{4} + 10824 T^{5} + 97498 T^{6} + 2825761 T^{8} \))(\( 1 + 83 T^{2} - 260 T^{3} + 4964 T^{4} - 11192 T^{5} + 203524 T^{6} - 437060 T^{7} + 5720443 T^{8} + 115856201 T^{10} \))
$43$ (\( 1 - 9 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 11 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 - 13 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 - T + 82 T^{2} - 43 T^{3} + 1849 T^{4} \))(\( 1 + 10 T + 109 T^{2} + 430 T^{3} + 1849 T^{4} \))(\( 1 - 10 T + 105 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 + 83 T^{2} + 1849 T^{4} \))(\( 1 + 8 T + 126 T^{2} + 596 T^{3} + 5418 T^{4} + 14792 T^{5} + 79507 T^{6} \))(\( 1 + 86 T^{2} - 44 T^{3} + 3698 T^{4} + 79507 T^{6} \))(\( 1 - 6 T + 107 T^{2} - 470 T^{3} + 5520 T^{4} - 20210 T^{5} + 197843 T^{6} - 477042 T^{7} + 3418801 T^{8} \))(\( 1 - 6 T + 11 T^{2} - 238 T^{3} + 3504 T^{4} - 10234 T^{5} + 20339 T^{6} - 477042 T^{7} + 3418801 T^{8} \))(\( 1 + 48 T^{2} + 12 T^{3} + 2563 T^{4} + 12104 T^{5} + 110209 T^{6} + 22188 T^{7} + 3816336 T^{8} + 147008443 T^{10} \))
$47$ (\( 1 + 12 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 2 T + 78 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 112 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 124 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 100 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 119 T^{2} - 580 T^{3} + 5593 T^{4} - 13254 T^{5} + 103823 T^{6} \))(\( 1 - 2 T + 127 T^{2} - 156 T^{3} + 5969 T^{4} - 4418 T^{5} + 103823 T^{6} \))(\( 1 - 4 T + 54 T^{2} - 452 T^{3} + 786 T^{4} - 21244 T^{5} + 119286 T^{6} - 415292 T^{7} + 4879681 T^{8} \))(\( 1 + 42 T^{2} - 352 T^{3} + 1706 T^{4} - 16544 T^{5} + 92778 T^{6} + 4879681 T^{8} \))(\( 1 + 2 T + 97 T^{2} + 328 T^{3} + 6984 T^{4} + 12780 T^{5} + 328248 T^{6} + 724552 T^{7} + 10070831 T^{8} + 9759362 T^{9} + 229345007 T^{10} \))
$53$ (\( 1 + 5 T + 53 T^{2} \))(\( 1 + T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 + 15 T + 124 T^{2} + 795 T^{3} + 2809 T^{4} \))(\( 1 - 6 T + 83 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( ( 1 - 3 T + 53 T^{2} )^{2} \))(\( 1 - 2 T + 95 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( 1 - 16 T + 140 T^{2} - 974 T^{3} + 7420 T^{4} - 44944 T^{5} + 148877 T^{6} \))(\( 1 + 152 T^{2} + 2 T^{3} + 8056 T^{4} + 148877 T^{6} \))(\( 1 - 14 T + 161 T^{2} - 1198 T^{3} + 10012 T^{4} - 63494 T^{5} + 452249 T^{6} - 2084278 T^{7} + 7890481 T^{8} \))(\( 1 - 14 T + 233 T^{2} - 2118 T^{3} + 19148 T^{4} - 112254 T^{5} + 654497 T^{6} - 2084278 T^{7} + 7890481 T^{8} \))(\( 1 + 8 T + 194 T^{2} + 1338 T^{3} + 17981 T^{4} + 100460 T^{5} + 952993 T^{6} + 3758442 T^{7} + 28882138 T^{8} + 63123848 T^{9} + 418195493 T^{10} \))
$59$ (\( 1 - 3 T + 59 T^{2} \))(\( 1 - 9 T + 59 T^{2} \))(\( 1 + 5 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 5 T + 59 T^{2} \))(\( 1 - 15 T + 59 T^{2} \))(\( 1 + 11 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 11 T + 59 T^{2} \))(\( 1 - 17 T + 186 T^{2} - 1003 T^{3} + 3481 T^{4} \))(\( 1 - 26 T + 285 T^{2} - 1534 T^{3} + 3481 T^{4} \))(\( 1 - 6 T + 121 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 - 24 T + 259 T^{2} - 1416 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 174 T^{2} + 852 T^{3} + 10266 T^{4} + 27848 T^{5} + 205379 T^{6} \))(\( 1 + 12 T + 186 T^{2} + 1340 T^{3} + 10974 T^{4} + 41772 T^{5} + 205379 T^{6} \))(\( 1 + 2 T + 203 T^{2} + 238 T^{3} + 16912 T^{4} + 14042 T^{5} + 706643 T^{6} + 410758 T^{7} + 12117361 T^{8} \))(\( 1 - 2 T + 99 T^{2} - 266 T^{3} + 9056 T^{4} - 15694 T^{5} + 344619 T^{6} - 410758 T^{7} + 12117361 T^{8} \))(\( 1 + 4 T + 164 T^{2} + 404 T^{3} + 15719 T^{4} + 36528 T^{5} + 927421 T^{6} + 1406324 T^{7} + 33682156 T^{8} + 48469444 T^{9} + 714924299 T^{10} \))
$61$ (\( 1 - 13 T + 61 T^{2} \))(\( 1 + 11 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 7 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 + 11 T + 148 T^{2} + 671 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 115 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 + 14 T + 147 T^{2} + 854 T^{3} + 3721 T^{4} \))(\( 1 - 2 T + 15 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( 1 + 36 T^{2} + 578 T^{3} + 2196 T^{4} + 226981 T^{6} \))(\( 1 - 4 T + 132 T^{2} - 262 T^{3} + 8052 T^{4} - 14884 T^{5} + 226981 T^{6} \))(\( 1 - 6 T + 121 T^{2} - 866 T^{3} + 9380 T^{4} - 52826 T^{5} + 450241 T^{6} - 1361886 T^{7} + 13845841 T^{8} \))(\( 1 - 2 T + 193 T^{2} - 226 T^{3} + 16300 T^{4} - 13786 T^{5} + 718153 T^{6} - 453962 T^{7} + 13845841 T^{8} \))(\( 1 - 16 T + 246 T^{2} - 2642 T^{3} + 28105 T^{4} - 220396 T^{5} + 1714405 T^{6} - 9830882 T^{7} + 55837326 T^{8} - 221533456 T^{9} + 844596301 T^{10} \))
$67$ (\( 1 + 14 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 6 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 22 T + 238 T^{2} - 1474 T^{3} + 4489 T^{4} \))(\( ( 1 + 6 T + 67 T^{2} )^{2} \))(\( ( 1 - 2 T + 67 T^{2} )^{2} \))(\( 1 + 4 T + 90 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 - 8 T + 93 T^{2} - 224 T^{3} + 6231 T^{4} - 35912 T^{5} + 300763 T^{6} \))(\( 1 + 173 T^{2} - 16 T^{3} + 11591 T^{4} + 300763 T^{6} \))(\( 1 + 8 T + 176 T^{2} + 1176 T^{3} + 17358 T^{4} + 78792 T^{5} + 790064 T^{6} + 2406104 T^{7} + 20151121 T^{8} \))(\( 1 + 12 T + 96 T^{2} - 180 T^{3} - 2706 T^{4} - 12060 T^{5} + 430944 T^{6} + 3609156 T^{7} + 20151121 T^{8} \))(\( 1 - 16 T + 323 T^{2} - 3792 T^{3} + 43246 T^{4} - 364224 T^{5} + 2897482 T^{6} - 17022288 T^{7} + 97146449 T^{8} - 322417936 T^{9} + 1350125107 T^{10} \))
$71$ (\( 1 - 8 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 16 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 2 T + 126 T^{2} - 142 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 108 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 - 8 T^{2} + 5041 T^{4} \))(\( 1 + 2 T + 68 T^{2} + 142 T^{3} + 5041 T^{4} \))(\( 1 + 2 T + 119 T^{2} - 68 T^{3} + 8449 T^{4} + 10082 T^{5} + 357911 T^{6} \))(\( 1 + 18 T + 255 T^{2} + 2284 T^{3} + 18105 T^{4} + 90738 T^{5} + 357911 T^{6} \))(\( 1 + 258 T^{2} + 26682 T^{4} + 1300578 T^{6} + 25411681 T^{8} \))(\( 1 - 4 T + 190 T^{2} - 692 T^{3} + 19074 T^{4} - 49132 T^{5} + 957790 T^{6} - 1431644 T^{7} + 25411681 T^{8} \))(\( 1 + 6 T + 161 T^{2} + 392 T^{3} + 13184 T^{4} + 19748 T^{5} + 936064 T^{6} + 1976072 T^{7} + 57623671 T^{8} + 152470086 T^{9} + 1804229351 T^{10} \))
$73$ (\( 1 + 8 T + 73 T^{2} \))(\( 1 - 8 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 14 T + 178 T^{2} + 1022 T^{3} + 5329 T^{4} \))(\( 1 + 74 T^{2} + 5329 T^{4} \))(\( 1 - 16 T + 186 T^{2} - 1168 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 42 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 + 2 T + 203 T^{2} + 276 T^{3} + 14819 T^{4} + 10658 T^{5} + 389017 T^{6} \))(\( 1 - 14 T + 267 T^{2} - 2060 T^{3} + 19491 T^{4} - 74606 T^{5} + 389017 T^{6} \))(\( 1 - 4 T + 112 T^{2} + 148 T^{3} + 4318 T^{4} + 10804 T^{5} + 596848 T^{6} - 1556068 T^{7} + 28398241 T^{8} \))(\( 1 - 20 T + 416 T^{2} - 4604 T^{3} + 50046 T^{4} - 336092 T^{5} + 2216864 T^{6} - 7780340 T^{7} + 28398241 T^{8} \))(\( 1 - 2 T + 121 T^{2} + 240 T^{3} + 13998 T^{4} - 10908 T^{5} + 1021854 T^{6} + 1278960 T^{7} + 47071057 T^{8} - 56796482 T^{9} + 2073071593 T^{10} \))
$79$ (\( 1 + 14 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 4 T + 94 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 156 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 120 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 10 T + 108 T^{2} + 790 T^{3} + 6241 T^{4} \))(\( 1 + 18 T + 287 T^{2} + 2588 T^{3} + 22673 T^{4} + 112338 T^{5} + 493039 T^{6} \))(\( 1 - 2 T - 9 T^{2} + 292 T^{3} - 711 T^{4} - 12482 T^{5} + 493039 T^{6} \))(\( 1 + 290 T^{2} + 33466 T^{4} + 1809890 T^{6} + 38950081 T^{8} \))(\( 1 + 4 T + 206 T^{2} + 596 T^{3} + 21154 T^{4} + 47084 T^{5} + 1285646 T^{6} + 1972156 T^{7} + 38950081 T^{8} \))(\( 1 - 42 T + 1065 T^{2} - 18336 T^{3} + 239440 T^{4} - 2398060 T^{5} + 18915760 T^{6} - 114434976 T^{7} + 525086535 T^{8} - 1635903402 T^{9} + 3077056399 T^{10} \))
$83$ (\( 1 - 11 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 - 5 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 11 T + 83 T^{2} \))(\( 1 + 15 T + 218 T^{2} + 1245 T^{3} + 6889 T^{4} \))(\( 1 - 6 T - 25 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( ( 1 + 9 T + 83 T^{2} )^{2} \))(\( 1 + 2 T + 155 T^{2} + 166 T^{3} + 6889 T^{4} \))(\( 1 - 10 T + 190 T^{2} - 1584 T^{3} + 15770 T^{4} - 68890 T^{5} + 571787 T^{6} \))(\( 1 - 6 T + 114 T^{2} - 1288 T^{3} + 9462 T^{4} - 41334 T^{5} + 571787 T^{6} \))(\( 1 - 6 T + 117 T^{2} - 1478 T^{3} + 12284 T^{4} - 122674 T^{5} + 806013 T^{6} - 3430722 T^{7} + 47458321 T^{8} \))(\( 1 - 14 T + 285 T^{2} - 3094 T^{3} + 34668 T^{4} - 256802 T^{5} + 1963365 T^{6} - 8005018 T^{7} + 47458321 T^{8} \))(\( 1 + 22 T + 432 T^{2} + 5200 T^{3} + 64115 T^{4} + 577172 T^{5} + 5321545 T^{6} + 35822800 T^{7} + 247011984 T^{8} + 1044083062 T^{9} + 3939040643 T^{10} \))
$89$ (\( 1 + 9 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 3 T + 89 T^{2} \))(\( 1 + 9 T + 89 T^{2} \))(\( 1 - 13 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 7 T + 89 T^{2} \))(\( 1 + 17 T + 212 T^{2} + 1513 T^{3} + 7921 T^{4} \))(\( 1 - 14 T + 177 T^{2} - 1246 T^{3} + 7921 T^{4} \))(\( 1 + 6 T + 133 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 139 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 2 T - 28 T^{2} + 1106 T^{3} - 2492 T^{4} - 15842 T^{5} + 704969 T^{6} \))(\( 1 + 10 T + 200 T^{2} + 1778 T^{3} + 17800 T^{4} + 79210 T^{5} + 704969 T^{6} \))(\( 1 - 18 T + 255 T^{2} - 2594 T^{3} + 29096 T^{4} - 230866 T^{5} + 2019855 T^{6} - 12689442 T^{7} + 62742241 T^{8} \))(\( 1 + 6 T + 231 T^{2} + 1758 T^{3} + 25464 T^{4} + 156462 T^{5} + 1829751 T^{6} + 4229814 T^{7} + 62742241 T^{8} \))(\( 1 + 10 T + 202 T^{2} + 1822 T^{3} + 26405 T^{4} + 244592 T^{5} + 2350045 T^{6} + 14432062 T^{7} + 142403738 T^{8} + 627422410 T^{9} + 5584059449 T^{10} \))
$97$ (\( 1 - 5 T + 97 T^{2} \))(\( 1 + 13 T + 97 T^{2} \))(\( 1 - 3 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 - 17 T + 97 T^{2} \))(\( 1 + 19 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 + 15 T + 144 T^{2} + 1455 T^{3} + 9409 T^{4} \))(\( 1 + 6 T + 185 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( 1 + 2 T + 189 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 + 8 T + 207 T^{2} + 776 T^{3} + 9409 T^{4} \))(\( 1 - 18 T + 308 T^{2} - 2830 T^{3} + 29876 T^{4} - 169362 T^{5} + 912673 T^{6} \))(\( 1 - 10 T + 84 T^{2} - 118 T^{3} + 8148 T^{4} - 94090 T^{5} + 912673 T^{6} \))(\( 1 + 6 T + 111 T^{2} - 834 T^{3} - 984 T^{4} - 80898 T^{5} + 1044399 T^{6} + 5476038 T^{7} + 88529281 T^{8} \))(\( 1 + 14 T + 447 T^{2} + 4150 T^{3} + 67896 T^{4} + 402550 T^{5} + 4205823 T^{6} + 12777422 T^{7} + 88529281 T^{8} \))(\( 1 + 2 T + 58 T^{2} + 502 T^{3} + 12309 T^{4} + 560 T^{5} + 1193973 T^{6} + 4723318 T^{7} + 52935034 T^{8} + 177058562 T^{9} + 8587340257 T^{10} \))
show more
show less