Properties

Label 1183.2.a
Level 1183
Weight 2
Character orbit a
Rep. character \(\chi_{1183}(1,\cdot)\)
Character field \(\Q\)
Dimension 77
Newform subspaces 18
Sturm bound 242
Trace bound 6

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Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(242\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1183))\).

Total New Old
Modular forms 134 77 57
Cusp forms 107 77 30
Eisenstein series 27 0 27

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

\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(17\)
\(+\)\(-\)\(-\)\(21\)
\(-\)\(+\)\(-\)\(24\)
\(-\)\(-\)\(+\)\(15\)
Plus space\(+\)\(32\)
Minus space\(-\)\(45\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 13
1183.2.a.a \(1\) \(9.446\) \(\Q\) None \(0\) \(-2\) \(3\) \(-1\) \(+\) \(+\) \(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+4q^{12}+\cdots\)
1183.2.a.b \(1\) \(9.446\) \(\Q\) None \(2\) \(0\) \(3\) \(1\) \(-\) \(+\) \(q+2q^{2}+2q^{4}+3q^{5}+q^{7}-3q^{9}+\cdots\)
1183.2.a.c \(2\) \(9.446\) \(\Q(\sqrt{5}) \) None \(-3\) \(-3\) \(-3\) \(-2\) \(+\) \(+\) \(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1183.2.a.d \(2\) \(9.446\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-6\) \(-2\) \(+\) \(+\) \(q+\beta q^{2}+\beta q^{3}+(-3+\beta )q^{5}+2q^{6}+\cdots\)
1183.2.a.e \(2\) \(9.446\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(+\) \(q+\beta q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(-3+\cdots)q^{6}+\cdots\)
1183.2.a.f \(2\) \(9.446\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(+\) \(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(3+\cdots)q^{6}+\cdots\)
1183.2.a.g \(2\) \(9.446\) \(\Q(\sqrt{5}) \) None \(3\) \(-3\) \(3\) \(2\) \(-\) \(+\) \(q+(1+\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1183.2.a.h \(3\) \(9.446\) 3.3.148.1 None \(-2\) \(0\) \(-3\) \(3\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.i \(3\) \(9.446\) 3.3.316.1 None \(-1\) \(-2\) \(-2\) \(3\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1183.2.a.j \(3\) \(9.446\) 3.3.148.1 None \(2\) \(0\) \(3\) \(-3\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.k \(4\) \(9.446\) 4.4.27004.1 None \(-1\) \(1\) \(-7\) \(-4\) \(+\) \(+\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.l \(4\) \(9.446\) 4.4.27004.1 None \(1\) \(1\) \(7\) \(4\) \(-\) \(+\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.m \(6\) \(9.446\) 6.6.7674048.1 None \(-4\) \(0\) \(-6\) \(6\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.2.a.n \(6\) \(9.446\) 6.6.1279733.1 None \(-2\) \(-4\) \(-2\) \(6\) \(-\) \(-\) \(q+(-1+\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
1183.2.a.o \(6\) \(9.446\) 6.6.1279733.1 None \(2\) \(-4\) \(2\) \(-6\) \(+\) \(+\) \(q+(1-\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
1183.2.a.p \(6\) \(9.446\) 6.6.7674048.1 None \(4\) \(0\) \(6\) \(-6\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.2.a.q \(12\) \(9.446\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(8\) \(4\) \(-12\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
1183.2.a.r \(12\) \(9.446\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(8\) \(-4\) \(12\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1183))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1183)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T^{2} \))(\( 1 - 2 T + 2 T^{2} \))(\( 1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4} \))(\( 1 + 2 T^{2} + 4 T^{4} \))(\( 1 + T^{2} + 4 T^{4} \))(\( 1 + T^{2} + 4 T^{4} \))(\( 1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4} \))(\( 1 + 2 T + 4 T^{2} + 6 T^{3} + 8 T^{4} + 8 T^{5} + 8 T^{6} \))(\( 1 + T + 2 T^{2} + 2 T^{3} + 4 T^{4} + 4 T^{5} + 8 T^{6} \))(\( 1 - 2 T + 4 T^{2} - 6 T^{3} + 8 T^{4} - 8 T^{5} + 8 T^{6} \))(\( 1 + T + 2 T^{2} + 3 T^{3} + T^{4} + 6 T^{5} + 8 T^{6} + 8 T^{7} + 16 T^{8} \))(\( 1 - T + 2 T^{2} - 3 T^{3} + T^{4} - 6 T^{5} + 8 T^{6} - 8 T^{7} + 16 T^{8} \))(\( 1 + 4 T + 12 T^{2} + 28 T^{3} + 56 T^{4} + 96 T^{5} + 145 T^{6} + 192 T^{7} + 224 T^{8} + 224 T^{9} + 192 T^{10} + 128 T^{11} + 64 T^{12} \))(\( 1 + 2 T + 4 T^{2} + 5 T^{3} + 10 T^{4} + 18 T^{5} + 31 T^{6} + 36 T^{7} + 40 T^{8} + 40 T^{9} + 64 T^{10} + 64 T^{11} + 64 T^{12} \))(\( 1 - 2 T + 4 T^{2} - 5 T^{3} + 10 T^{4} - 18 T^{5} + 31 T^{6} - 36 T^{7} + 40 T^{8} - 40 T^{9} + 64 T^{10} - 64 T^{11} + 64 T^{12} \))(\( 1 - 4 T + 12 T^{2} - 28 T^{3} + 56 T^{4} - 96 T^{5} + 145 T^{6} - 192 T^{7} + 224 T^{8} - 224 T^{9} + 192 T^{10} - 128 T^{11} + 64 T^{12} \))(\( 1 + 3 T + 9 T^{2} + 20 T^{3} + 44 T^{4} + 78 T^{5} + 141 T^{6} + 218 T^{7} + 354 T^{8} + 514 T^{9} + 783 T^{10} + 1085 T^{11} + 1625 T^{12} + 2170 T^{13} + 3132 T^{14} + 4112 T^{15} + 5664 T^{16} + 6976 T^{17} + 9024 T^{18} + 9984 T^{19} + 11264 T^{20} + 10240 T^{21} + 9216 T^{22} + 6144 T^{23} + 4096 T^{24} \))(\( 1 - 3 T + 9 T^{2} - 20 T^{3} + 44 T^{4} - 78 T^{5} + 141 T^{6} - 218 T^{7} + 354 T^{8} - 514 T^{9} + 783 T^{10} - 1085 T^{11} + 1625 T^{12} - 2170 T^{13} + 3132 T^{14} - 4112 T^{15} + 5664 T^{16} - 6976 T^{17} + 9024 T^{18} - 9984 T^{19} + 11264 T^{20} - 10240 T^{21} + 9216 T^{22} - 6144 T^{23} + 4096 T^{24} \))
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4} \))(\( 1 + 4 T^{2} + 9 T^{4} \))(\( 1 - 2 T + 4 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 - 2 T + 4 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4} \))(\( 1 + 5 T^{2} + 2 T^{3} + 15 T^{4} + 27 T^{6} \))(\( 1 + 2 T + 3 T^{2} + 4 T^{3} + 9 T^{4} + 18 T^{5} + 27 T^{6} \))(\( 1 + 5 T^{2} + 2 T^{3} + 15 T^{4} + 27 T^{6} \))(\( 1 - T + 3 T^{2} + 7 T^{3} - 6 T^{4} + 21 T^{5} + 27 T^{6} - 27 T^{7} + 81 T^{8} \))(\( 1 - T + 3 T^{2} + 7 T^{3} - 6 T^{4} + 21 T^{5} + 27 T^{6} - 27 T^{7} + 81 T^{8} \))(\( 1 + 7 T^{2} - 2 T^{3} + 28 T^{4} + 2 T^{5} + 100 T^{6} + 6 T^{7} + 252 T^{8} - 54 T^{9} + 567 T^{10} + 729 T^{12} \))(\( 1 + 4 T + 17 T^{2} + 46 T^{3} + 122 T^{4} + 245 T^{5} + 481 T^{6} + 735 T^{7} + 1098 T^{8} + 1242 T^{9} + 1377 T^{10} + 972 T^{11} + 729 T^{12} \))(\( 1 + 4 T + 17 T^{2} + 46 T^{3} + 122 T^{4} + 245 T^{5} + 481 T^{6} + 735 T^{7} + 1098 T^{8} + 1242 T^{9} + 1377 T^{10} + 972 T^{11} + 729 T^{12} \))(\( 1 + 7 T^{2} - 2 T^{3} + 28 T^{4} + 2 T^{5} + 100 T^{6} + 6 T^{7} + 252 T^{8} - 54 T^{9} + 567 T^{10} + 729 T^{12} \))(\( 1 - 8 T + 37 T^{2} - 128 T^{3} + 375 T^{4} - 979 T^{5} + 2342 T^{6} - 5167 T^{7} + 10609 T^{8} - 20575 T^{9} + 38357 T^{10} - 69347 T^{11} + 121870 T^{12} - 208041 T^{13} + 345213 T^{14} - 555525 T^{15} + 859329 T^{16} - 1255581 T^{17} + 1707318 T^{18} - 2141073 T^{19} + 2460375 T^{20} - 2519424 T^{21} + 2184813 T^{22} - 1417176 T^{23} + 531441 T^{24} \))(\( 1 - 8 T + 37 T^{2} - 128 T^{3} + 375 T^{4} - 979 T^{5} + 2342 T^{6} - 5167 T^{7} + 10609 T^{8} - 20575 T^{9} + 38357 T^{10} - 69347 T^{11} + 121870 T^{12} - 208041 T^{13} + 345213 T^{14} - 555525 T^{15} + 859329 T^{16} - 1255581 T^{17} + 1707318 T^{18} - 2141073 T^{19} + 2460375 T^{20} - 2519424 T^{21} + 2184813 T^{22} - 1417176 T^{23} + 531441 T^{24} \))
$5$ (\( 1 - 3 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 3 T + 11 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 + 6 T + 17 T^{2} + 30 T^{3} + 25 T^{4} \))(\( 1 + 7 T^{2} + 25 T^{4} \))(\( 1 + 7 T^{2} + 25 T^{4} \))(\( 1 - 3 T + 11 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 + 3 T + 14 T^{2} + 29 T^{3} + 70 T^{4} + 75 T^{5} + 125 T^{6} \))(\( 1 + 2 T + 12 T^{2} + 18 T^{3} + 60 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 - 3 T + 14 T^{2} - 29 T^{3} + 70 T^{4} - 75 T^{5} + 125 T^{6} \))(\( 1 + 7 T + 32 T^{2} + 104 T^{3} + 261 T^{4} + 520 T^{5} + 800 T^{6} + 875 T^{7} + 625 T^{8} \))(\( 1 - 7 T + 32 T^{2} - 104 T^{3} + 261 T^{4} - 520 T^{5} + 800 T^{6} - 875 T^{7} + 625 T^{8} \))(\( 1 + 6 T + 28 T^{2} + 100 T^{3} + 333 T^{4} + 878 T^{5} + 2121 T^{6} + 4390 T^{7} + 8325 T^{8} + 12500 T^{9} + 17500 T^{10} + 18750 T^{11} + 15625 T^{12} \))(\( 1 + 2 T + 22 T^{2} + 35 T^{3} + 229 T^{4} + 303 T^{5} + 1447 T^{6} + 1515 T^{7} + 5725 T^{8} + 4375 T^{9} + 13750 T^{10} + 6250 T^{11} + 15625 T^{12} \))(\( 1 - 2 T + 22 T^{2} - 35 T^{3} + 229 T^{4} - 303 T^{5} + 1447 T^{6} - 1515 T^{7} + 5725 T^{8} - 4375 T^{9} + 13750 T^{10} - 6250 T^{11} + 15625 T^{12} \))(\( 1 - 6 T + 28 T^{2} - 100 T^{3} + 333 T^{4} - 878 T^{5} + 2121 T^{6} - 4390 T^{7} + 8325 T^{8} - 12500 T^{9} + 17500 T^{10} - 18750 T^{11} + 15625 T^{12} \))(\( 1 - 4 T + 22 T^{2} - 63 T^{3} + 250 T^{4} - 557 T^{5} + 1853 T^{6} - 3600 T^{7} + 11381 T^{8} - 19648 T^{9} + 62597 T^{10} - 102004 T^{11} + 320128 T^{12} - 510020 T^{13} + 1564925 T^{14} - 2456000 T^{15} + 7113125 T^{16} - 11250000 T^{17} + 28953125 T^{18} - 43515625 T^{19} + 97656250 T^{20} - 123046875 T^{21} + 214843750 T^{22} - 195312500 T^{23} + 244140625 T^{24} \))(\( 1 + 4 T + 22 T^{2} + 63 T^{3} + 250 T^{4} + 557 T^{5} + 1853 T^{6} + 3600 T^{7} + 11381 T^{8} + 19648 T^{9} + 62597 T^{10} + 102004 T^{11} + 320128 T^{12} + 510020 T^{13} + 1564925 T^{14} + 2456000 T^{15} + 7113125 T^{16} + 11250000 T^{17} + 28953125 T^{18} + 43515625 T^{19} + 97656250 T^{20} + 123046875 T^{21} + 214843750 T^{22} + 195312500 T^{23} + 244140625 T^{24} \))
$7$ (\( 1 + T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{12} \))(\( ( 1 - T )^{12} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 - 3 T + 13 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 + 4 T^{2} + 121 T^{4} \))(\( 1 + 6 T + 28 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 - 6 T + 28 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 + 3 T + 13 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + 8 T + 51 T^{2} + 186 T^{3} + 561 T^{4} + 968 T^{5} + 1331 T^{6} \))(\( 1 + 2 T + 27 T^{2} + 36 T^{3} + 297 T^{4} + 242 T^{5} + 1331 T^{6} \))(\( 1 - 8 T + 51 T^{2} - 186 T^{3} + 561 T^{4} - 968 T^{5} + 1331 T^{6} \))(\( 1 + T + 35 T^{2} + 17 T^{3} + 522 T^{4} + 187 T^{5} + 4235 T^{6} + 1331 T^{7} + 14641 T^{8} \))(\( 1 - T + 35 T^{2} - 17 T^{3} + 522 T^{4} - 187 T^{5} + 4235 T^{6} - 1331 T^{7} + 14641 T^{8} \))(\( 1 + 4 T + 49 T^{2} + 204 T^{3} + 1152 T^{4} + 4240 T^{5} + 16164 T^{6} + 46640 T^{7} + 139392 T^{8} + 271524 T^{9} + 717409 T^{10} + 644204 T^{11} + 1771561 T^{12} \))(\( 1 + 8 T + 50 T^{2} + 243 T^{3} + 1083 T^{4} + 4383 T^{5} + 15277 T^{6} + 48213 T^{7} + 131043 T^{8} + 323433 T^{9} + 732050 T^{10} + 1288408 T^{11} + 1771561 T^{12} \))(\( 1 - 8 T + 50 T^{2} - 243 T^{3} + 1083 T^{4} - 4383 T^{5} + 15277 T^{6} - 48213 T^{7} + 131043 T^{8} - 323433 T^{9} + 732050 T^{10} - 1288408 T^{11} + 1771561 T^{12} \))(\( 1 - 4 T + 49 T^{2} - 204 T^{3} + 1152 T^{4} - 4240 T^{5} + 16164 T^{6} - 46640 T^{7} + 139392 T^{8} - 271524 T^{9} + 717409 T^{10} - 644204 T^{11} + 1771561 T^{12} \))(\( 1 + 12 T + 119 T^{2} + 839 T^{3} + 5562 T^{4} + 31178 T^{5} + 165247 T^{6} + 777143 T^{7} + 3489086 T^{8} + 14271228 T^{9} + 55872520 T^{10} + 201068300 T^{11} + 693943541 T^{12} + 2211751300 T^{13} + 6760574920 T^{14} + 18995004468 T^{15} + 51083708126 T^{16} + 125159657293 T^{17} + 292745140567 T^{18} + 607571017438 T^{19} + 1192264096122 T^{20} + 1978318112749 T^{21} + 3086553527519 T^{22} + 3423740047332 T^{23} + 3138428376721 T^{24} \))(\( 1 - 12 T + 119 T^{2} - 839 T^{3} + 5562 T^{4} - 31178 T^{5} + 165247 T^{6} - 777143 T^{7} + 3489086 T^{8} - 14271228 T^{9} + 55872520 T^{10} - 201068300 T^{11} + 693943541 T^{12} - 2211751300 T^{13} + 6760574920 T^{14} - 18995004468 T^{15} + 51083708126 T^{16} - 125159657293 T^{17} + 292745140567 T^{18} - 607571017438 T^{19} + 1192264096122 T^{20} - 1978318112749 T^{21} + 3086553527519 T^{22} - 3423740047332 T^{23} + 3138428376721 T^{24} \))
$13$ 1
$17$ (\( 1 + 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 6 T + 23 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 + 12 T + 67 T^{2} + 204 T^{3} + 289 T^{4} \))(\( 1 + 12 T + 67 T^{2} + 204 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 23 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 43 T^{2} - 102 T^{3} + 731 T^{4} - 1156 T^{5} + 4913 T^{6} \))(\( 1 - 4 T + 41 T^{2} - 140 T^{3} + 697 T^{4} - 1156 T^{5} + 4913 T^{6} \))(\( 1 - 4 T + 43 T^{2} - 102 T^{3} + 731 T^{4} - 1156 T^{5} + 4913 T^{6} \))(\( 1 + 4 T + 56 T^{2} + 144 T^{3} + 1273 T^{4} + 2448 T^{5} + 16184 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 + 4 T + 56 T^{2} + 144 T^{3} + 1273 T^{4} + 2448 T^{5} + 16184 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 + 4 T + 81 T^{2} + 280 T^{3} + 3074 T^{4} + 8724 T^{5} + 67033 T^{6} + 148308 T^{7} + 888386 T^{8} + 1375640 T^{9} + 6765201 T^{10} + 5679428 T^{11} + 24137569 T^{12} \))(\( 1 + 23 T + 292 T^{2} + 2540 T^{3} + 16936 T^{4} + 91115 T^{5} + 409523 T^{6} + 1548955 T^{7} + 4894504 T^{8} + 12479020 T^{9} + 24388132 T^{10} + 32656711 T^{11} + 24137569 T^{12} \))(\( 1 + 23 T + 292 T^{2} + 2540 T^{3} + 16936 T^{4} + 91115 T^{5} + 409523 T^{6} + 1548955 T^{7} + 4894504 T^{8} + 12479020 T^{9} + 24388132 T^{10} + 32656711 T^{11} + 24137569 T^{12} \))(\( 1 + 4 T + 81 T^{2} + 280 T^{3} + 3074 T^{4} + 8724 T^{5} + 67033 T^{6} + 148308 T^{7} + 888386 T^{8} + 1375640 T^{9} + 6765201 T^{10} + 5679428 T^{11} + 24137569 T^{12} \))(\( 1 - 31 T + 568 T^{2} - 7546 T^{3} + 80093 T^{4} - 711892 T^{5} + 5469505 T^{6} - 37077989 T^{7} + 225308737 T^{8} - 1241326188 T^{9} + 6256554679 T^{10} - 29025017842 T^{11} + 124423663010 T^{12} - 493425303314 T^{13} + 1808144302231 T^{14} - 6098635561644 T^{15} + 18818011022977 T^{16} - 52645442227573 T^{17} + 132020554333345 T^{18} - 292116818599316 T^{19} + 558709340722013 T^{20} - 894864116046362 T^{21} + 1145084535455032 T^{22} - 1062428785536623 T^{23} + 582622237229761 T^{24} \))(\( 1 - 31 T + 568 T^{2} - 7546 T^{3} + 80093 T^{4} - 711892 T^{5} + 5469505 T^{6} - 37077989 T^{7} + 225308737 T^{8} - 1241326188 T^{9} + 6256554679 T^{10} - 29025017842 T^{11} + 124423663010 T^{12} - 493425303314 T^{13} + 1808144302231 T^{14} - 6098635561644 T^{15} + 18818011022977 T^{16} - 52645442227573 T^{17} + 132020554333345 T^{18} - 292116818599316 T^{19} + 558709340722013 T^{20} - 894864116046362 T^{21} + 1145084535455032 T^{22} - 1062428785536623 T^{23} + 582622237229761 T^{24} \))
$19$ (\( 1 - 7 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + 3 T + 29 T^{2} + 57 T^{3} + 361 T^{4} \))(\( 1 - 6 T + 29 T^{2} - 114 T^{3} + 361 T^{4} \))(\( ( 1 + 2 T + 19 T^{2} )^{2} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( 1 - 3 T + 29 T^{2} - 57 T^{3} + 361 T^{4} \))(\( 1 + T - 2 T^{2} - 155 T^{3} - 38 T^{4} + 361 T^{5} + 6859 T^{6} \))(\( 1 - 4 T + 58 T^{2} - 148 T^{3} + 1102 T^{4} - 1444 T^{5} + 6859 T^{6} \))(\( 1 - T - 2 T^{2} + 155 T^{3} - 38 T^{4} - 361 T^{5} + 6859 T^{6} \))(\( 1 - T + 21 T^{2} - 57 T^{3} + 576 T^{4} - 1083 T^{5} + 7581 T^{6} - 6859 T^{7} + 130321 T^{8} \))(\( 1 + T + 21 T^{2} + 57 T^{3} + 576 T^{4} + 1083 T^{5} + 7581 T^{6} + 6859 T^{7} + 130321 T^{8} \))(\( 1 + 2 T + 87 T^{2} + 190 T^{3} + 3512 T^{4} + 7188 T^{5} + 84124 T^{6} + 136572 T^{7} + 1267832 T^{8} + 1303210 T^{9} + 11337927 T^{10} + 4952198 T^{11} + 47045881 T^{12} \))(\( 1 - 13 T + 161 T^{2} - 1215 T^{3} + 8665 T^{4} - 45671 T^{5} + 227327 T^{6} - 867749 T^{7} + 3128065 T^{8} - 8333685 T^{9} + 20981681 T^{10} - 32189287 T^{11} + 47045881 T^{12} \))(\( 1 + 13 T + 161 T^{2} + 1215 T^{3} + 8665 T^{4} + 45671 T^{5} + 227327 T^{6} + 867749 T^{7} + 3128065 T^{8} + 8333685 T^{9} + 20981681 T^{10} + 32189287 T^{11} + 47045881 T^{12} \))(\( 1 - 2 T + 87 T^{2} - 190 T^{3} + 3512 T^{4} - 7188 T^{5} + 84124 T^{6} - 136572 T^{7} + 1267832 T^{8} - 1303210 T^{9} + 11337927 T^{10} - 4952198 T^{11} + 47045881 T^{12} \))(\( 1 - 3 T + 97 T^{2} - 331 T^{3} + 5018 T^{4} - 17630 T^{5} + 182052 T^{6} - 621452 T^{7} + 5139665 T^{8} - 16723937 T^{9} + 119795163 T^{10} - 372021619 T^{11} + 2418532296 T^{12} - 7068410761 T^{13} + 43246053843 T^{14} - 114709483883 T^{15} + 669806282465 T^{16} - 1538776675748 T^{17} + 8564796727812 T^{18} - 15758958758570 T^{19} + 85223519339738 T^{20} - 106809627964849 T^{21} + 594713427006697 T^{22} - 349470776694657 T^{23} + 2213314919066161 T^{24} \))(\( 1 + 3 T + 97 T^{2} + 331 T^{3} + 5018 T^{4} + 17630 T^{5} + 182052 T^{6} + 621452 T^{7} + 5139665 T^{8} + 16723937 T^{9} + 119795163 T^{10} + 372021619 T^{11} + 2418532296 T^{12} + 7068410761 T^{13} + 43246053843 T^{14} + 114709483883 T^{15} + 669806282465 T^{16} + 1538776675748 T^{17} + 8564796727812 T^{18} + 15758958758570 T^{19} + 85223519339738 T^{20} + 106809627964849 T^{21} + 594713427006697 T^{22} + 349470776694657 T^{23} + 2213314919066161 T^{24} \))
$23$ (\( 1 - 3 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 26 T^{2} + 529 T^{4} \))(\( 1 + 6 T + 47 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 52 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 52 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 + 26 T^{2} + 529 T^{4} \))(\( 1 + 3 T + 44 T^{2} + 59 T^{3} + 1012 T^{4} + 1587 T^{5} + 12167 T^{6} \))(\( 1 - 10 T + 70 T^{2} - 324 T^{3} + 1610 T^{4} - 5290 T^{5} + 12167 T^{6} \))(\( 1 + 3 T + 44 T^{2} + 59 T^{3} + 1012 T^{4} + 1587 T^{5} + 12167 T^{6} \))(\( 1 + 2 T + 54 T^{2} + 82 T^{3} + 1498 T^{4} + 1886 T^{5} + 28566 T^{6} + 24334 T^{7} + 279841 T^{8} \))(\( 1 + 2 T + 54 T^{2} + 82 T^{3} + 1498 T^{4} + 1886 T^{5} + 28566 T^{6} + 24334 T^{7} + 279841 T^{8} \))(\( 1 + 12 T + 118 T^{2} + 772 T^{3} + 4479 T^{4} + 23000 T^{5} + 111732 T^{6} + 529000 T^{7} + 2369391 T^{8} + 9392924 T^{9} + 33021238 T^{10} + 77236116 T^{11} + 148035889 T^{12} \))(\( 1 + 18 T + 235 T^{2} + 2091 T^{3} + 15661 T^{4} + 94020 T^{5} + 495523 T^{6} + 2162460 T^{7} + 8284669 T^{8} + 25441197 T^{9} + 65762635 T^{10} + 115854174 T^{11} + 148035889 T^{12} \))(\( 1 + 18 T + 235 T^{2} + 2091 T^{3} + 15661 T^{4} + 94020 T^{5} + 495523 T^{6} + 2162460 T^{7} + 8284669 T^{8} + 25441197 T^{9} + 65762635 T^{10} + 115854174 T^{11} + 148035889 T^{12} \))(\( 1 + 12 T + 118 T^{2} + 772 T^{3} + 4479 T^{4} + 23000 T^{5} + 111732 T^{6} + 529000 T^{7} + 2369391 T^{8} + 9392924 T^{9} + 33021238 T^{10} + 77236116 T^{11} + 148035889 T^{12} \))(\( 1 - 18 T + 288 T^{2} - 3107 T^{3} + 30473 T^{4} - 245131 T^{5} + 1836488 T^{6} - 12056167 T^{7} + 75169797 T^{8} - 425099506 T^{9} + 2324537664 T^{10} - 11781456452 T^{11} + 58451275845 T^{12} - 270973498396 T^{13} + 1229680424256 T^{14} - 5172185689502 T^{15} + 21035591162277 T^{16} - 77597626077281 T^{17} + 271866133717832 T^{18} - 834628266648557 T^{19} + 2386370654467913 T^{20} - 5596181319165541 T^{21} + 11930835229530912 T^{22} - 17150575642450686 T^{23} + 21914624432020321 T^{24} \))(\( 1 - 18 T + 288 T^{2} - 3107 T^{3} + 30473 T^{4} - 245131 T^{5} + 1836488 T^{6} - 12056167 T^{7} + 75169797 T^{8} - 425099506 T^{9} + 2324537664 T^{10} - 11781456452 T^{11} + 58451275845 T^{12} - 270973498396 T^{13} + 1229680424256 T^{14} - 5172185689502 T^{15} + 21035591162277 T^{16} - 77597626077281 T^{17} + 271866133717832 T^{18} - 834628266648557 T^{19} + 2386370654467913 T^{20} - 5596181319165541 T^{21} + 11930835229530912 T^{22} - 17150575642450686 T^{23} + 21914624432020321 T^{24} \))
$29$ (\( 1 + 9 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 59 T^{2} - 174 T^{3} + 841 T^{4} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( 1 - 3 T + 29 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 + 7 T + 66 T^{2} + 411 T^{3} + 1914 T^{4} + 5887 T^{5} + 24389 T^{6} \))(\( 1 - 24 T + 272 T^{2} - 1846 T^{3} + 7888 T^{4} - 20184 T^{5} + 24389 T^{6} \))(\( 1 + 7 T + 66 T^{2} + 411 T^{3} + 1914 T^{4} + 5887 T^{5} + 24389 T^{6} \))(\( 1 - T + 94 T^{2} - 108 T^{3} + 3765 T^{4} - 3132 T^{5} + 79054 T^{6} - 24389 T^{7} + 707281 T^{8} \))(\( 1 - T + 94 T^{2} - 108 T^{3} + 3765 T^{4} - 3132 T^{5} + 79054 T^{6} - 24389 T^{7} + 707281 T^{8} \))(\( 1 + 8 T + 130 T^{2} + 594 T^{3} + 6099 T^{4} + 18374 T^{5} + 187029 T^{6} + 532846 T^{7} + 5129259 T^{8} + 14487066 T^{9} + 91946530 T^{10} + 164089192 T^{11} + 594823321 T^{12} \))(\( 1 + 15 T + 183 T^{2} + 1577 T^{3} + 12663 T^{4} + 80831 T^{5} + 478995 T^{6} + 2344099 T^{7} + 10649583 T^{8} + 38461453 T^{9} + 129432423 T^{10} + 307667235 T^{11} + 594823321 T^{12} \))(\( 1 + 15 T + 183 T^{2} + 1577 T^{3} + 12663 T^{4} + 80831 T^{5} + 478995 T^{6} + 2344099 T^{7} + 10649583 T^{8} + 38461453 T^{9} + 129432423 T^{10} + 307667235 T^{11} + 594823321 T^{12} \))(\( 1 + 8 T + 130 T^{2} + 594 T^{3} + 6099 T^{4} + 18374 T^{5} + 187029 T^{6} + 532846 T^{7} + 5129259 T^{8} + 14487066 T^{9} + 91946530 T^{10} + 164089192 T^{11} + 594823321 T^{12} \))(\( 1 - 15 T + 324 T^{2} - 3564 T^{3} + 44939 T^{4} - 393247 T^{5} + 3697678 T^{6} - 27010904 T^{7} + 207877679 T^{8} - 1310438539 T^{9} + 8672615780 T^{10} - 48262071296 T^{11} + 282259550511 T^{12} - 1399600067584 T^{13} + 7293669870980 T^{14} - 31960285527671 T^{15} + 147027932680799 T^{16} - 554024676568696 T^{17} + 2199465107948638 T^{18} - 6783462108885323 T^{19} + 22480573552054379 T^{20} - 51703468257997116 T^{21} + 136309143589265124 T^{22} - 183007646485587435 T^{23} + 353814783205469041 T^{24} \))(\( 1 - 15 T + 324 T^{2} - 3564 T^{3} + 44939 T^{4} - 393247 T^{5} + 3697678 T^{6} - 27010904 T^{7} + 207877679 T^{8} - 1310438539 T^{9} + 8672615780 T^{10} - 48262071296 T^{11} + 282259550511 T^{12} - 1399600067584 T^{13} + 7293669870980 T^{14} - 31960285527671 T^{15} + 147027932680799 T^{16} - 554024676568696 T^{17} + 2199465107948638 T^{18} - 6783462108885323 T^{19} + 22480573552054379 T^{20} - 51703468257997116 T^{21} + 136309143589265124 T^{22} - 183007646485587435 T^{23} + 353814783205469041 T^{24} \))
$31$ (\( 1 + 5 T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 + 4 T + 21 T^{2} + 124 T^{3} + 961 T^{4} \))(\( 1 - 2 T + 45 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 - 2 T + 36 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 + 2 T + 36 T^{2} + 62 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 21 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 + 11 T + 112 T^{2} + 617 T^{3} + 3472 T^{4} + 10571 T^{5} + 29791 T^{6} \))(\( 1 - 4 T + 74 T^{2} - 264 T^{3} + 2294 T^{4} - 3844 T^{5} + 29791 T^{6} \))(\( 1 - 11 T + 112 T^{2} - 617 T^{3} + 3472 T^{4} - 10571 T^{5} + 29791 T^{6} \))(\( 1 + 4 T + 111 T^{2} + 346 T^{3} + 5014 T^{4} + 10726 T^{5} + 106671 T^{6} + 119164 T^{7} + 923521 T^{8} \))(\( 1 - 4 T + 111 T^{2} - 346 T^{3} + 5014 T^{4} - 10726 T^{5} + 106671 T^{6} - 119164 T^{7} + 923521 T^{8} \))(\( 1 - 14 T + 216 T^{2} - 1972 T^{3} + 17840 T^{4} - 117486 T^{5} + 749554 T^{6} - 3642066 T^{7} + 17144240 T^{8} - 58747852 T^{9} + 199480536 T^{10} - 400808114 T^{11} + 887503681 T^{12} \))(\( 1 + 3 T + 29 T^{2} - 99 T^{3} + 1365 T^{4} + 1247 T^{5} + 67011 T^{6} + 38657 T^{7} + 1311765 T^{8} - 2949309 T^{9} + 26782109 T^{10} + 85887453 T^{11} + 887503681 T^{12} \))(\( 1 - 3 T + 29 T^{2} + 99 T^{3} + 1365 T^{4} - 1247 T^{5} + 67011 T^{6} - 38657 T^{7} + 1311765 T^{8} + 2949309 T^{9} + 26782109 T^{10} - 85887453 T^{11} + 887503681 T^{12} \))(\( 1 + 14 T + 216 T^{2} + 1972 T^{3} + 17840 T^{4} + 117486 T^{5} + 749554 T^{6} + 3642066 T^{7} + 17144240 T^{8} + 58747852 T^{9} + 199480536 T^{10} + 400808114 T^{11} + 887503681 T^{12} \))(\( 1 - 21 T + 379 T^{2} - 4981 T^{3} + 57158 T^{4} - 568830 T^{5} + 5110446 T^{6} - 41827128 T^{7} + 315883869 T^{8} - 2216417859 T^{9} + 14507944551 T^{10} - 88982695273 T^{11} + 511191760792 T^{12} - 2758463553463 T^{13} + 13942134713511 T^{14} - 66029304437469 T^{15} + 291725386582749 T^{16} - 1197475163408328 T^{17} + 4535539636551726 T^{18} - 15650000284760130 T^{19} + 48749545918052678 T^{20} - 131695757982302251 T^{21} + 310639120765723579 T^{22} - 533578014824501451 T^{23} + 787662783788549761 T^{24} \))(\( 1 + 21 T + 379 T^{2} + 4981 T^{3} + 57158 T^{4} + 568830 T^{5} + 5110446 T^{6} + 41827128 T^{7} + 315883869 T^{8} + 2216417859 T^{9} + 14507944551 T^{10} + 88982695273 T^{11} + 511191760792 T^{12} + 2758463553463 T^{13} + 13942134713511 T^{14} + 66029304437469 T^{15} + 291725386582749 T^{16} + 1197475163408328 T^{17} + 4535539636551726 T^{18} + 15650000284760130 T^{19} + 48749545918052678 T^{20} + 131695757982302251 T^{21} + 310639120765723579 T^{22} + 533578014824501451 T^{23} + 787662783788549761 T^{24} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( 1 - 4 T + 60 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( ( 1 - 7 T + 37 T^{2} )^{2} \))(\( ( 1 + 7 T + 37 T^{2} )^{2} \))(\( ( 1 - 4 T + 37 T^{2} )^{2} \))(\( 1 + 12 T + 129 T^{2} + 834 T^{3} + 4773 T^{4} + 16428 T^{5} + 50653 T^{6} \))(\( 1 + 53 T^{2} + 124 T^{3} + 1961 T^{4} + 50653 T^{6} \))(\( 1 - 12 T + 129 T^{2} - 834 T^{3} + 4773 T^{4} - 16428 T^{5} + 50653 T^{6} \))(\( 1 + 10 T + 165 T^{2} + 1066 T^{3} + 9456 T^{4} + 39442 T^{5} + 225885 T^{6} + 506530 T^{7} + 1874161 T^{8} \))(\( 1 - 10 T + 165 T^{2} - 1066 T^{3} + 9456 T^{4} - 39442 T^{5} + 225885 T^{6} - 506530 T^{7} + 1874161 T^{8} \))(\( 1 + 12 T + 135 T^{2} + 1176 T^{3} + 10575 T^{4} + 70860 T^{5} + 472322 T^{6} + 2621820 T^{7} + 14477175 T^{8} + 59567928 T^{9} + 253011735 T^{10} + 832127484 T^{11} + 2565726409 T^{12} \))(\( 1 - 13 T + 227 T^{2} - 2287 T^{3} + 21261 T^{4} - 165075 T^{5} + 1053087 T^{6} - 6107775 T^{7} + 29106309 T^{8} - 115843411 T^{9} + 425434547 T^{10} - 901471441 T^{11} + 2565726409 T^{12} \))(\( 1 + 13 T + 227 T^{2} + 2287 T^{3} + 21261 T^{4} + 165075 T^{5} + 1053087 T^{6} + 6107775 T^{7} + 29106309 T^{8} + 115843411 T^{9} + 425434547 T^{10} + 901471441 T^{11} + 2565726409 T^{12} \))(\( 1 - 12 T + 135 T^{2} - 1176 T^{3} + 10575 T^{4} - 70860 T^{5} + 472322 T^{6} - 2621820 T^{7} + 14477175 T^{8} - 59567928 T^{9} + 253011735 T^{10} - 832127484 T^{11} + 2565726409 T^{12} \))(\( 1 + 5 T + 192 T^{2} + 1172 T^{3} + 21221 T^{4} + 140227 T^{5} + 1678192 T^{6} + 11205720 T^{7} + 104159167 T^{8} + 662961305 T^{9} + 5221320672 T^{10} + 30647237568 T^{11} + 213700265471 T^{12} + 1133947790016 T^{13} + 7147987999968 T^{14} + 33580978982165 T^{15} + 195211048583887 T^{16} + 777048965834040 T^{17} + 4305781533772528 T^{18} + 13312012334729191 T^{19} + 74538326491657541 T^{20} + 152315159039830244 T^{21} + 923248199504227008 T^{22} + 889588108897302065 T^{23} + 6582952005840035281 T^{24} \))(\( 1 - 5 T + 192 T^{2} - 1172 T^{3} + 21221 T^{4} - 140227 T^{5} + 1678192 T^{6} - 11205720 T^{7} + 104159167 T^{8} - 662961305 T^{9} + 5221320672 T^{10} - 30647237568 T^{11} + 213700265471 T^{12} - 1133947790016 T^{13} + 7147987999968 T^{14} - 33580978982165 T^{15} + 195211048583887 T^{16} - 777048965834040 T^{17} + 4305781533772528 T^{18} - 13312012334729191 T^{19} + 74538326491657541 T^{20} - 152315159039830244 T^{21} + 923248199504227008 T^{22} - 889588108897302065 T^{23} + 6582952005840035281 T^{24} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 6 T + 86 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 110 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 + 55 T^{2} + 1681 T^{4} \))(\( 1 + 55 T^{2} + 1681 T^{4} \))(\( 1 - 6 T + 86 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 + 2 T + 71 T^{2} + 124 T^{3} + 2911 T^{4} + 3362 T^{5} + 68921 T^{6} \))(\( 1 + 2 T + 95 T^{2} + 172 T^{3} + 3895 T^{4} + 3362 T^{5} + 68921 T^{6} \))(\( 1 - 2 T + 71 T^{2} - 124 T^{3} + 2911 T^{4} - 3362 T^{5} + 68921 T^{6} \))(\( 1 + 22 T + 313 T^{2} + 2932 T^{3} + 21740 T^{4} + 120212 T^{5} + 526153 T^{6} + 1516262 T^{7} + 2825761 T^{8} \))(\( 1 - 22 T + 313 T^{2} - 2932 T^{3} + 21740 T^{4} - 120212 T^{5} + 526153 T^{6} - 1516262 T^{7} + 2825761 T^{8} \))(\( 1 + 28 T + 503 T^{2} + 6376 T^{3} + 64135 T^{4} + 528684 T^{5} + 3676082 T^{6} + 21676044 T^{7} + 107810935 T^{8} + 439440296 T^{9} + 1421357783 T^{10} + 3243973628 T^{11} + 4750104241 T^{12} \))(\( 1 - 4 T + 131 T^{2} - 292 T^{3} + 6158 T^{4} - 3460 T^{5} + 202879 T^{6} - 141860 T^{7} + 10351598 T^{8} - 20124932 T^{9} + 370174691 T^{10} - 463424804 T^{11} + 4750104241 T^{12} \))(\( 1 + 4 T + 131 T^{2} + 292 T^{3} + 6158 T^{4} + 3460 T^{5} + 202879 T^{6} + 141860 T^{7} + 10351598 T^{8} + 20124932 T^{9} + 370174691 T^{10} + 463424804 T^{11} + 4750104241 T^{12} \))(\( 1 - 28 T + 503 T^{2} - 6376 T^{3} + 64135 T^{4} - 528684 T^{5} + 3676082 T^{6} - 21676044 T^{7} + 107810935 T^{8} - 439440296 T^{9} + 1421357783 T^{10} - 3243973628 T^{11} + 4750104241 T^{12} \))(\( 1 - 16 T + 357 T^{2} - 3684 T^{3} + 49551 T^{4} - 390244 T^{5} + 4189980 T^{6} - 28050332 T^{7} + 270848157 T^{8} - 1645568508 T^{9} + 14674605695 T^{10} - 81741178960 T^{11} + 663362111078 T^{12} - 3351388337360 T^{13} + 24668012173295 T^{14} - 113414227139868 T^{15} + 765352158972477 T^{16} - 3249804902308732 T^{17} + 19902841767705180 T^{18} - 76001686856416964 T^{19} + 395661030028174671 T^{20} - 1206075046307352324 T^{21} + 4791889373724407157 T^{22} - 8805264507459975056 T^{23} + 22563490300366186081 T^{24} \))(\( 1 + 16 T + 357 T^{2} + 3684 T^{3} + 49551 T^{4} + 390244 T^{5} + 4189980 T^{6} + 28050332 T^{7} + 270848157 T^{8} + 1645568508 T^{9} + 14674605695 T^{10} + 81741178960 T^{11} + 663362111078 T^{12} + 3351388337360 T^{13} + 24668012173295 T^{14} + 113414227139868 T^{15} + 765352158972477 T^{16} + 3249804902308732 T^{17} + 19902841767705180 T^{18} + 76001686856416964 T^{19} + 395661030028174671 T^{20} + 1206075046307352324 T^{21} + 4791889373724407157 T^{22} + 8805264507459975056 T^{23} + 22563490300366186081 T^{24} \))
$43$ (\( 1 + T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 - 5 T - 9 T^{2} - 215 T^{3} + 1849 T^{4} \))(\( ( 1 + 5 T + 43 T^{2} )^{2} \))(\( 1 - 10 T + 84 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 - 10 T + 84 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 - 5 T - 9 T^{2} - 215 T^{3} + 1849 T^{4} \))(\( 1 - 13 T + 164 T^{2} - 1101 T^{3} + 7052 T^{4} - 24037 T^{5} + 79507 T^{6} \))(\( 1 - 10 T + 58 T^{2} - 232 T^{3} + 2494 T^{4} - 18490 T^{5} + 79507 T^{6} \))(\( 1 - 13 T + 164 T^{2} - 1101 T^{3} + 7052 T^{4} - 24037 T^{5} + 79507 T^{6} \))(\( 1 - 3 T + 169 T^{2} - 379 T^{3} + 10834 T^{4} - 16297 T^{5} + 312481 T^{6} - 238521 T^{7} + 3418801 T^{8} \))(\( 1 - 3 T + 169 T^{2} - 379 T^{3} + 10834 T^{4} - 16297 T^{5} + 312481 T^{6} - 238521 T^{7} + 3418801 T^{8} \))(\( 1 - 2 T + 149 T^{2} - 340 T^{3} + 11408 T^{4} - 21594 T^{5} + 590652 T^{6} - 928542 T^{7} + 21093392 T^{8} - 27032380 T^{9} + 509401349 T^{10} - 294016886 T^{11} + 6321363049 T^{12} \))(\( 1 + 18 T + 311 T^{2} + 3496 T^{3} + 35744 T^{4} + 284555 T^{5} + 2083101 T^{6} + 12235865 T^{7} + 66090656 T^{8} + 277956472 T^{9} + 1063247111 T^{10} + 2646151974 T^{11} + 6321363049 T^{12} \))(\( 1 + 18 T + 311 T^{2} + 3496 T^{3} + 35744 T^{4} + 284555 T^{5} + 2083101 T^{6} + 12235865 T^{7} + 66090656 T^{8} + 277956472 T^{9} + 1063247111 T^{10} + 2646151974 T^{11} + 6321363049 T^{12} \))(\( 1 - 2 T + 149 T^{2} - 340 T^{3} + 11408 T^{4} - 21594 T^{5} + 590652 T^{6} - 928542 T^{7} + 21093392 T^{8} - 27032380 T^{9} + 509401349 T^{10} - 294016886 T^{11} + 6321363049 T^{12} \))(\( 1 + 22 T + 488 T^{2} + 6678 T^{3} + 88352 T^{4} + 884517 T^{5} + 8597269 T^{6} + 67064082 T^{7} + 520023521 T^{8} + 3313340282 T^{9} + 22407318040 T^{10} + 129779666728 T^{11} + 897781203465 T^{12} + 5580525669304 T^{13} + 41431131055960 T^{14} + 263433745800974 T^{15} + 1777856933618321 T^{16} + 9858986276044326 T^{17} + 54346458578913181 T^{18} + 240428182440530319 T^{19} + 1032675870926603552 T^{20} + 3356313462514237554 T^{21} + 10546403368882713512 T^{22} + 20444462268366899554 T^{23} + 39959630797262576401 T^{24} \))(\( 1 + 22 T + 488 T^{2} + 6678 T^{3} + 88352 T^{4} + 884517 T^{5} + 8597269 T^{6} + 67064082 T^{7} + 520023521 T^{8} + 3313340282 T^{9} + 22407318040 T^{10} + 129779666728 T^{11} + 897781203465 T^{12} + 5580525669304 T^{13} + 41431131055960 T^{14} + 263433745800974 T^{15} + 1777856933618321 T^{16} + 9858986276044326 T^{17} + 54346458578913181 T^{18} + 240428182440530319 T^{19} + 1032675870926603552 T^{20} + 3356313462514237554 T^{21} + 10546403368882713512 T^{22} + 20444462268366899554 T^{23} + 39959630797262576401 T^{24} \))
$47$ (\( 1 + 3 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 + 89 T^{2} + 2209 T^{4} \))(\( 1 + 6 T + 101 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 82 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 82 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 + 89 T^{2} + 2209 T^{4} \))(\( 1 + 19 T + 246 T^{2} + 1923 T^{3} + 11562 T^{4} + 41971 T^{5} + 103823 T^{6} \))(\( 1 - 8 T + 62 T^{2} - 208 T^{3} + 2914 T^{4} - 17672 T^{5} + 103823 T^{6} \))(\( 1 - 19 T + 246 T^{2} - 1923 T^{3} + 11562 T^{4} - 41971 T^{5} + 103823 T^{6} \))(\( 1 - 2 T + 137 T^{2} - 294 T^{3} + 8560 T^{4} - 13818 T^{5} + 302633 T^{6} - 207646 T^{7} + 4879681 T^{8} \))(\( 1 + 2 T + 137 T^{2} + 294 T^{3} + 8560 T^{4} + 13818 T^{5} + 302633 T^{6} + 207646 T^{7} + 4879681 T^{8} \))(\( 1 + 14 T + 244 T^{2} + 2532 T^{3} + 25548 T^{4} + 209078 T^{5} + 1534242 T^{6} + 9826666 T^{7} + 56435532 T^{8} + 262879836 T^{9} + 1190642164 T^{10} + 3210830098 T^{11} + 10779215329 T^{12} \))(\( 1 - 16 T + 260 T^{2} - 2471 T^{3} + 24701 T^{4} - 179041 T^{5} + 1411093 T^{6} - 8414927 T^{7} + 54564509 T^{8} - 256546633 T^{9} + 1268717060 T^{10} - 3669520112 T^{11} + 10779215329 T^{12} \))(\( 1 + 16 T + 260 T^{2} + 2471 T^{3} + 24701 T^{4} + 179041 T^{5} + 1411093 T^{6} + 8414927 T^{7} + 54564509 T^{8} + 256546633 T^{9} + 1268717060 T^{10} + 3669520112 T^{11} + 10779215329 T^{12} \))(\( 1 - 14 T + 244 T^{2} - 2532 T^{3} + 25548 T^{4} - 209078 T^{5} + 1534242 T^{6} - 9826666 T^{7} + 56435532 T^{8} - 262879836 T^{9} + 1190642164 T^{10} - 3210830098 T^{11} + 10779215329 T^{12} \))(\( 1 - 4 T + 302 T^{2} - 1611 T^{3} + 46080 T^{4} - 291499 T^{5} + 4844787 T^{6} - 32306172 T^{7} + 394622569 T^{8} - 2514725020 T^{9} + 25802776751 T^{10} - 148951322836 T^{11} + 1355290855372 T^{12} - 7000712173292 T^{13} + 56998333842959 T^{14} - 261086295751460 T^{15} + 1925632252120489 T^{16} - 7409259243483204 T^{17} + 52223002296139923 T^{18} - 147680132991844037 T^{19} + 1097224089373946880 T^{20} - 1802919192168557637 T^{21} + 15884937935220674798 T^{22} - 9888636860336049212 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 4 T + 302 T^{2} + 1611 T^{3} + 46080 T^{4} + 291499 T^{5} + 4844787 T^{6} + 32306172 T^{7} + 394622569 T^{8} + 2514725020 T^{9} + 25802776751 T^{10} + 148951322836 T^{11} + 1355290855372 T^{12} + 7000712173292 T^{13} + 56998333842959 T^{14} + 261086295751460 T^{15} + 1925632252120489 T^{16} + 7409259243483204 T^{17} + 52223002296139923 T^{18} + 147680132991844037 T^{19} + 1097224089373946880 T^{20} + 1802919192168557637 T^{21} + 15884937935220674798 T^{22} + 9888636860336049212 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))
$53$ (\( 1 + 9 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 12 T + 137 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( 1 + 6 T + 107 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 6 T + 67 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 6 T + 67 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 12 T + 137 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( 1 - T + 150 T^{2} - 93 T^{3} + 7950 T^{4} - 2809 T^{5} + 148877 T^{6} \))(\( 1 - 8 T + 124 T^{2} - 870 T^{3} + 6572 T^{4} - 22472 T^{5} + 148877 T^{6} \))(\( 1 - T + 150 T^{2} - 93 T^{3} + 7950 T^{4} - 2809 T^{5} + 148877 T^{6} \))(\( 1 - 2 T + 72 T^{2} + 572 T^{3} + 625 T^{4} + 30316 T^{5} + 202248 T^{6} - 297754 T^{7} + 7890481 T^{8} \))(\( 1 - 2 T + 72 T^{2} + 572 T^{3} + 625 T^{4} + 30316 T^{5} + 202248 T^{6} - 297754 T^{7} + 7890481 T^{8} \))(\( 1 + 22 T + 409 T^{2} + 5130 T^{3} + 58074 T^{4} + 513982 T^{5} + 4153497 T^{6} + 27241046 T^{7} + 163129866 T^{8} + 763739010 T^{9} + 3227206729 T^{10} + 9200300846 T^{11} + 22164361129 T^{12} \))(\( 1 + 25 T + 429 T^{2} + 5407 T^{3} + 58624 T^{4} + 523460 T^{5} + 4125969 T^{6} + 27743380 T^{7} + 164674816 T^{8} + 804977939 T^{9} + 3385016349 T^{10} + 10454887325 T^{11} + 22164361129 T^{12} \))(\( 1 + 25 T + 429 T^{2} + 5407 T^{3} + 58624 T^{4} + 523460 T^{5} + 4125969 T^{6} + 27743380 T^{7} + 164674816 T^{8} + 804977939 T^{9} + 3385016349 T^{10} + 10454887325 T^{11} + 22164361129 T^{12} \))(\( 1 + 22 T + 409 T^{2} + 5130 T^{3} + 58074 T^{4} + 513982 T^{5} + 4153497 T^{6} + 27241046 T^{7} + 163129866 T^{8} + 763739010 T^{9} + 3227206729 T^{10} + 9200300846 T^{11} + 22164361129 T^{12} \))(\( 1 - 53 T + 1690 T^{2} - 39432 T^{3} + 742118 T^{4} - 11784588 T^{5} + 162742979 T^{6} - 1990565860 T^{7} + 21854781923 T^{8} - 217266658693 T^{9} + 1968301968594 T^{10} - 16312473390394 T^{11} + 123975115151263 T^{12} - 864561089690882 T^{13} + 5528960229780546 T^{14} - 32346008346237761 T^{15} + 172444741522574963 T^{16} - 832445671171668980 T^{17} + 3607094157765263291 T^{18} - 13843486801989432156 T^{19} + 46204036928698402598 T^{20} - \)\(13\!\cdots\!56\)\( T^{21} + \)\(29\!\cdots\!10\)\( T^{22} - \)\(49\!\cdots\!41\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - 53 T + 1690 T^{2} - 39432 T^{3} + 742118 T^{4} - 11784588 T^{5} + 162742979 T^{6} - 1990565860 T^{7} + 21854781923 T^{8} - 217266658693 T^{9} + 1968301968594 T^{10} - 16312473390394 T^{11} + 123975115151263 T^{12} - 864561089690882 T^{13} + 5528960229780546 T^{14} - 32346008346237761 T^{15} + 172444741522574963 T^{16} - 832445671171668980 T^{17} + 3607094157765263291 T^{18} - 13843486801989432156 T^{19} + 46204036928698402598 T^{20} - \)\(13\!\cdots\!56\)\( T^{21} + \)\(29\!\cdots\!10\)\( T^{22} - \)\(49\!\cdots\!41\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 113 T^{2} + 3481 T^{4} \))(\( 1 + 12 T + 122 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 + 18 T + 196 T^{2} + 1062 T^{3} + 3481 T^{4} \))(\( 1 - 18 T + 196 T^{2} - 1062 T^{3} + 3481 T^{4} \))(\( 1 + 113 T^{2} + 3481 T^{4} \))(\( 1 + 2 T + 145 T^{2} + 288 T^{3} + 8555 T^{4} + 6962 T^{5} + 205379 T^{6} \))(\( 1 - 4 T + 21 T^{2} + 216 T^{3} + 1239 T^{4} - 13924 T^{5} + 205379 T^{6} \))(\( 1 - 2 T + 145 T^{2} - 288 T^{3} + 8555 T^{4} - 6962 T^{5} + 205379 T^{6} \))(\( 1 + 8 T + 159 T^{2} + 866 T^{3} + 11094 T^{4} + 51094 T^{5} + 553479 T^{6} + 1643032 T^{7} + 12117361 T^{8} \))(\( 1 - 8 T + 159 T^{2} - 866 T^{3} + 11094 T^{4} - 51094 T^{5} + 553479 T^{6} - 1643032 T^{7} + 12117361 T^{8} \))(\( 1 - 2 T + 192 T^{2} - 380 T^{3} + 20828 T^{4} - 39642 T^{5} + 1464142 T^{6} - 2338878 T^{7} + 72502268 T^{8} - 78044020 T^{9} + 2326533312 T^{10} - 1429848598 T^{11} + 42180533641 T^{12} \))(\( 1 + 18 T + 231 T^{2} + 2285 T^{3} + 20723 T^{4} + 164956 T^{5} + 1340761 T^{6} + 9732404 T^{7} + 72136763 T^{8} + 469291015 T^{9} + 2799110391 T^{10} + 12868637382 T^{11} + 42180533641 T^{12} \))(\( 1 - 18 T + 231 T^{2} - 2285 T^{3} + 20723 T^{4} - 164956 T^{5} + 1340761 T^{6} - 9732404 T^{7} + 72136763 T^{8} - 469291015 T^{9} + 2799110391 T^{10} - 12868637382 T^{11} + 42180533641 T^{12} \))(\( 1 + 2 T + 192 T^{2} + 380 T^{3} + 20828 T^{4} + 39642 T^{5} + 1464142 T^{6} + 2338878 T^{7} + 72502268 T^{8} + 78044020 T^{9} + 2326533312 T^{10} + 1429848598 T^{11} + 42180533641 T^{12} \))(\( 1 - 26 T + 773 T^{2} - 13175 T^{3} + 235106 T^{4} - 3083462 T^{5} + 41573240 T^{6} - 449706923 T^{7} + 4982524361 T^{8} - 46123793209 T^{9} + 437701285395 T^{10} - 3538343532723 T^{11} + 29361055210472 T^{12} - 208762268430657 T^{13} + 1523638174459995 T^{14} - 9472858525471211 T^{15} + 60375046373531321 T^{16} - 321506406681221977 T^{17} + 1753581448385366840 T^{18} - 7673662284682963378 T^{19} + 34520716863401493026 T^{20} - \)\(11\!\cdots\!25\)\( T^{21} + \)\(39\!\cdots\!73\)\( T^{22} - \)\(78\!\cdots\!34\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 + 26 T + 773 T^{2} + 13175 T^{3} + 235106 T^{4} + 3083462 T^{5} + 41573240 T^{6} + 449706923 T^{7} + 4982524361 T^{8} + 46123793209 T^{9} + 437701285395 T^{10} + 3538343532723 T^{11} + 29361055210472 T^{12} + 208762268430657 T^{13} + 1523638174459995 T^{14} + 9472858525471211 T^{15} + 60375046373531321 T^{16} + 321506406681221977 T^{17} + 1753581448385366840 T^{18} + 7673662284682963378 T^{19} + 34520716863401493026 T^{20} + \)\(11\!\cdots\!25\)\( T^{21} + \)\(39\!\cdots\!73\)\( T^{22} + \)\(78\!\cdots\!34\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( ( 1 + 6 T + 61 T^{2} )^{2} \))(\( ( 1 - 6 T + 61 T^{2} )^{2} \))(\( 1 + 20 T + 195 T^{2} + 1220 T^{3} + 3721 T^{4} \))(\( 1 + 20 T + 195 T^{2} + 1220 T^{3} + 3721 T^{4} \))(\( ( 1 + 6 T + 61 T^{2} )^{2} \))(\( 1 - 14 T + 211 T^{2} - 1556 T^{3} + 12871 T^{4} - 52094 T^{5} + 226981 T^{6} \))(\( ( 1 + 2 T + 61 T^{2} )^{3} \))(\( 1 - 14 T + 211 T^{2} - 1556 T^{3} + 12871 T^{4} - 52094 T^{5} + 226981 T^{6} \))(\( 1 - 8 T + 229 T^{2} - 1288 T^{3} + 20396 T^{4} - 78568 T^{5} + 852109 T^{6} - 1815848 T^{7} + 13845841 T^{8} \))(\( 1 - 8 T + 229 T^{2} - 1288 T^{3} + 20396 T^{4} - 78568 T^{5} + 852109 T^{6} - 1815848 T^{7} + 13845841 T^{8} \))(\( 1 + 14 T + 279 T^{2} + 2854 T^{3} + 32699 T^{4} + 263412 T^{5} + 2369290 T^{6} + 16068132 T^{7} + 121672979 T^{8} + 647803774 T^{9} + 3862989639 T^{10} + 11824348214 T^{11} + 51520374361 T^{12} \))(\( 1 - 16 T + 311 T^{2} - 3792 T^{3} + 44666 T^{4} - 408293 T^{5} + 3575773 T^{6} - 24905873 T^{7} + 166202186 T^{8} - 860711952 T^{9} + 4306056551 T^{10} - 13513540816 T^{11} + 51520374361 T^{12} \))(\( 1 - 16 T + 311 T^{2} - 3792 T^{3} + 44666 T^{4} - 408293 T^{5} + 3575773 T^{6} - 24905873 T^{7} + 166202186 T^{8} - 860711952 T^{9} + 4306056551 T^{10} - 13513540816 T^{11} + 51520374361 T^{12} \))(\( 1 + 14 T + 279 T^{2} + 2854 T^{3} + 32699 T^{4} + 263412 T^{5} + 2369290 T^{6} + 16068132 T^{7} + 121672979 T^{8} + 647803774 T^{9} + 3862989639 T^{10} + 11824348214 T^{11} + 51520374361 T^{12} \))(\( 1 - 22 T + 603 T^{2} - 9418 T^{3} + 147071 T^{4} - 1764999 T^{5} + 19928830 T^{6} - 191653031 T^{7} + 1725978769 T^{8} - 13879813535 T^{9} + 109588022583 T^{10} - 809459548819 T^{11} + 6414765325406 T^{12} - 49377032477959 T^{13} + 407777032031343 T^{14} - 3150453955987835 T^{15} + 23897627604949729 T^{16} - 161869441058038331 T^{17} + 1026740782176727630 T^{18} - 5546937962834228979 T^{19} + 28194586229823113951 T^{20} - \)\(11\!\cdots\!38\)\( T^{21} + \)\(43\!\cdots\!03\)\( T^{22} - \)\(95\!\cdots\!42\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 22 T + 603 T^{2} - 9418 T^{3} + 147071 T^{4} - 1764999 T^{5} + 19928830 T^{6} - 191653031 T^{7} + 1725978769 T^{8} - 13879813535 T^{9} + 109588022583 T^{10} - 809459548819 T^{11} + 6414765325406 T^{12} - 49377032477959 T^{13} + 407777032031343 T^{14} - 3150453955987835 T^{15} + 23897627604949729 T^{16} - 161869441058038331 T^{17} + 1026740782176727630 T^{18} - 5546937962834228979 T^{19} + 28194586229823113951 T^{20} - \)\(11\!\cdots\!38\)\( T^{21} + \)\(43\!\cdots\!03\)\( T^{22} - \)\(95\!\cdots\!42\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))
$67$ (\( 1 + 14 T + 67 T^{2} \))(\( 1 - 6 T + 67 T^{2} \))(\( 1 - 12 T + 125 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 98 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 - 2 T + 108 T^{2} - 134 T^{3} + 4489 T^{4} \))(\( 1 + 2 T + 108 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 125 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 233 T^{2} - 1592 T^{3} + 15611 T^{4} - 53868 T^{5} + 300763 T^{6} \))(\( 1 - 12 T + 77 T^{2} - 632 T^{3} + 5159 T^{4} - 53868 T^{5} + 300763 T^{6} \))(\( 1 + 12 T + 233 T^{2} + 1592 T^{3} + 15611 T^{4} + 53868 T^{5} + 300763 T^{6} \))(\( 1 + 6 T + 57 T^{2} + 572 T^{3} + 9670 T^{4} + 38324 T^{5} + 255873 T^{6} + 1804578 T^{7} + 20151121 T^{8} \))(\( 1 - 6 T + 57 T^{2} - 572 T^{3} + 9670 T^{4} - 38324 T^{5} + 255873 T^{6} - 1804578 T^{7} + 20151121 T^{8} \))(\( 1 + 24 T + 496 T^{2} + 6632 T^{3} + 80672 T^{4} + 775096 T^{5} + 6983258 T^{6} + 51931432 T^{7} + 362136608 T^{8} + 1994660216 T^{9} + 9994956016 T^{10} + 32403002568 T^{11} + 90458382169 T^{12} \))(\( 1 + 16 T + 296 T^{2} + 2748 T^{3} + 28371 T^{4} + 190491 T^{5} + 1772499 T^{6} + 12762897 T^{7} + 127357419 T^{8} + 826496724 T^{9} + 5964731816 T^{10} + 21602001712 T^{11} + 90458382169 T^{12} \))(\( 1 - 16 T + 296 T^{2} - 2748 T^{3} + 28371 T^{4} - 190491 T^{5} + 1772499 T^{6} - 12762897 T^{7} + 127357419 T^{8} - 826496724 T^{9} + 5964731816 T^{10} - 21602001712 T^{11} + 90458382169 T^{12} \))(\( 1 - 24 T + 496 T^{2} - 6632 T^{3} + 80672 T^{4} - 775096 T^{5} + 6983258 T^{6} - 51931432 T^{7} + 362136608 T^{8} - 1994660216 T^{9} + 9994956016 T^{10} - 32403002568 T^{11} + 90458382169 T^{12} \))(\( 1 + 12 T + 605 T^{2} + 6840 T^{3} + 174280 T^{4} + 1817687 T^{5} + 31736675 T^{6} + 301001100 T^{7} + 4095931922 T^{8} + 35017153676 T^{9} + 398002971834 T^{10} + 3047044319596 T^{11} + 30078417682499 T^{12} + 204151969412932 T^{13} + 1786635340562826 T^{14} + 10531864191054788 T^{15} + 82537619767984562 T^{16} + 406389142344617700 T^{17} + 2870848275923348075 T^{18} + 11016476695744747901 T^{19} + 70769474844571393480 T^{20} + \)\(18\!\cdots\!80\)\( T^{21} + \)\(11\!\cdots\!45\)\( T^{22} + \)\(14\!\cdots\!96\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 - 12 T + 605 T^{2} - 6840 T^{3} + 174280 T^{4} - 1817687 T^{5} + 31736675 T^{6} - 301001100 T^{7} + 4095931922 T^{8} - 35017153676 T^{9} + 398002971834 T^{10} - 3047044319596 T^{11} + 30078417682499 T^{12} - 204151969412932 T^{13} + 1786635340562826 T^{14} - 10531864191054788 T^{15} + 82537619767984562 T^{16} - 406389142344617700 T^{17} + 2870848275923348075 T^{18} - 11016476695744747901 T^{19} + 70769474844571393480 T^{20} - \)\(18\!\cdots\!80\)\( T^{21} + \)\(11\!\cdots\!45\)\( T^{22} - \)\(14\!\cdots\!96\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))
$71$ (\( 1 - 6 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 6 T + 26 T^{2} - 426 T^{3} + 5041 T^{4} \))(\( 1 - 12 T + 128 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( 1 + 6 T + 26 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 + 14 T + 159 T^{2} + 1098 T^{3} + 11289 T^{4} + 70574 T^{5} + 357911 T^{6} \))(\( 1 - 6 T + 191 T^{2} - 868 T^{3} + 13561 T^{4} - 30246 T^{5} + 357911 T^{6} \))(\( 1 - 14 T + 159 T^{2} - 1098 T^{3} + 11289 T^{4} - 70574 T^{5} + 357911 T^{6} \))(\( 1 + 14 T + 268 T^{2} + 2270 T^{3} + 25942 T^{4} + 161170 T^{5} + 1350988 T^{6} + 5010754 T^{7} + 25411681 T^{8} \))(\( 1 - 14 T + 268 T^{2} - 2270 T^{3} + 25942 T^{4} - 161170 T^{5} + 1350988 T^{6} - 5010754 T^{7} + 25411681 T^{8} \))(\( 1 + 4 T + 358 T^{2} + 1164 T^{3} + 57375 T^{4} + 149608 T^{5} + 5246868 T^{6} + 10622168 T^{7} + 289227375 T^{8} + 416608404 T^{9} + 9097381798 T^{10} + 7216917404 T^{11} + 128100283921 T^{12} \))(\( 1 + 25 T + 450 T^{2} + 5633 T^{3} + 66618 T^{4} + 665639 T^{5} + 6202577 T^{6} + 47260369 T^{7} + 335821338 T^{8} + 2016112663 T^{9} + 11435256450 T^{10} + 45105733775 T^{11} + 128100283921 T^{12} \))(\( 1 - 25 T + 450 T^{2} - 5633 T^{3} + 66618 T^{4} - 665639 T^{5} + 6202577 T^{6} - 47260369 T^{7} + 335821338 T^{8} - 2016112663 T^{9} + 11435256450 T^{10} - 45105733775 T^{11} + 128100283921 T^{12} \))(\( 1 - 4 T + 358 T^{2} - 1164 T^{3} + 57375 T^{4} - 149608 T^{5} + 5246868 T^{6} - 10622168 T^{7} + 289227375 T^{8} - 416608404 T^{9} + 9097381798 T^{10} - 7216917404 T^{11} + 128100283921 T^{12} \))(\( 1 + 21 T + 727 T^{2} + 12190 T^{3} + 244065 T^{4} + 3390521 T^{5} + 50728302 T^{6} + 599872706 T^{7} + 7342499572 T^{8} + 75238897929 T^{9} + 784539982090 T^{10} + 7029442696200 T^{11} + 63652953856239 T^{12} + 499090431430200 T^{13} + 3954866049715690 T^{14} + 26928829196666319 T^{15} + 186585256866300532 T^{16} + 1082307943028993806 T^{17} + 6498309889030232142 T^{18} + 30837195894548011711 T^{19} + \)\(15\!\cdots\!65\)\( T^{20} + \)\(55\!\cdots\!90\)\( T^{21} + \)\(23\!\cdots\!27\)\( T^{22} + \)\(48\!\cdots\!91\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 - 21 T + 727 T^{2} - 12190 T^{3} + 244065 T^{4} - 3390521 T^{5} + 50728302 T^{6} - 599872706 T^{7} + 7342499572 T^{8} - 75238897929 T^{9} + 784539982090 T^{10} - 7029442696200 T^{11} + 63652953856239 T^{12} - 499090431430200 T^{13} + 3954866049715690 T^{14} - 26928829196666319 T^{15} + 186585256866300532 T^{16} - 1082307943028993806 T^{17} + 6498309889030232142 T^{18} - 30837195894548011711 T^{19} + \)\(15\!\cdots\!65\)\( T^{20} - \)\(55\!\cdots\!90\)\( T^{21} + \)\(23\!\cdots\!27\)\( T^{22} - \)\(48\!\cdots\!91\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))
$73$ (\( 1 + 11 T + 73 T^{2} \))(\( 1 - 13 T + 73 T^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( 1 - 10 T + 153 T^{2} - 730 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 123 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 - 4 T + 123 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( 1 - 9 T + 128 T^{2} - 1345 T^{3} + 9344 T^{4} - 47961 T^{5} + 389017 T^{6} \))(\( 1 - 10 T + 120 T^{2} - 1186 T^{3} + 8760 T^{4} - 53290 T^{5} + 389017 T^{6} \))(\( 1 + 9 T + 128 T^{2} + 1345 T^{3} + 9344 T^{4} + 47961 T^{5} + 389017 T^{6} \))(\( 1 + 8 T + 173 T^{2} + 1664 T^{3} + 16372 T^{4} + 121472 T^{5} + 921917 T^{6} + 3112136 T^{7} + 28398241 T^{8} \))(\( 1 - 8 T + 173 T^{2} - 1664 T^{3} + 16372 T^{4} - 121472 T^{5} + 921917 T^{6} - 3112136 T^{7} + 28398241 T^{8} \))(\( 1 + 36 T + 919 T^{2} + 15928 T^{3} + 225311 T^{4} + 2516900 T^{5} + 23841506 T^{6} + 183733700 T^{7} + 1200682319 T^{8} + 6196262776 T^{9} + 26097983479 T^{10} + 74630577348 T^{11} + 151334226289 T^{12} \))(\( 1 - 5 T + 262 T^{2} - 1812 T^{3} + 33912 T^{4} - 262035 T^{5} + 2891423 T^{6} - 19128555 T^{7} + 180717048 T^{8} - 704898804 T^{9} + 7440339142 T^{10} - 10365357965 T^{11} + 151334226289 T^{12} \))(\( 1 + 5 T + 262 T^{2} + 1812 T^{3} + 33912 T^{4} + 262035 T^{5} + 2891423 T^{6} + 19128555 T^{7} + 180717048 T^{8} + 704898804 T^{9} + 7440339142 T^{10} + 10365357965 T^{11} + 151334226289 T^{12} \))(\( 1 - 36 T + 919 T^{2} - 15928 T^{3} + 225311 T^{4} - 2516900 T^{5} + 23841506 T^{6} - 183733700 T^{7} + 1200682319 T^{8} - 6196262776 T^{9} + 26097983479 T^{10} - 74630577348 T^{11} + 151334226289 T^{12} \))(\( 1 - 15 T + 470 T^{2} - 6338 T^{3} + 113941 T^{4} - 1395230 T^{5} + 18986387 T^{6} - 208861651 T^{7} + 2393521289 T^{8} - 23604957926 T^{9} + 238883501575 T^{10} - 2120985896592 T^{11} + 19309354982914 T^{12} - 154831970451216 T^{13} + 1273010179893175 T^{14} - 9182729917498742 T^{15} + 67971794403652649 T^{16} - 432985155555180043 T^{17} + 2873290186668527843 T^{18} - 15413661835799707310 T^{19} + 91888869330503483221 T^{20} - \)\(37\!\cdots\!94\)\( T^{21} + \)\(20\!\cdots\!30\)\( T^{22} - \)\(47\!\cdots\!55\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 + 15 T + 470 T^{2} + 6338 T^{3} + 113941 T^{4} + 1395230 T^{5} + 18986387 T^{6} + 208861651 T^{7} + 2393521289 T^{8} + 23604957926 T^{9} + 238883501575 T^{10} + 2120985896592 T^{11} + 19309354982914 T^{12} + 154831970451216 T^{13} + 1273010179893175 T^{14} + 9182729917498742 T^{15} + 67971794403652649 T^{16} + 432985155555180043 T^{17} + 2873290186668527843 T^{18} + 15413661835799707310 T^{19} + 91888869330503483221 T^{20} + \)\(37\!\cdots\!94\)\( T^{21} + \)\(20\!\cdots\!30\)\( T^{22} + \)\(47\!\cdots\!55\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))
$79$ (\( 1 + T + 79 T^{2} \))(\( 1 - 3 T + 79 T^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( 1 - 14 T + 135 T^{2} - 1106 T^{3} + 6241 T^{4} \))(\( 1 - 22 T + 252 T^{2} - 1738 T^{3} + 6241 T^{4} \))(\( 1 - 22 T + 252 T^{2} - 1738 T^{3} + 6241 T^{4} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( 1 - 13 T + 200 T^{2} - 1869 T^{3} + 15800 T^{4} - 81133 T^{5} + 493039 T^{6} \))(\( 1 + 14 T + 242 T^{2} + 2196 T^{3} + 19118 T^{4} + 87374 T^{5} + 493039 T^{6} \))(\( 1 - 13 T + 200 T^{2} - 1869 T^{3} + 15800 T^{4} - 81133 T^{5} + 493039 T^{6} \))(\( 1 + 26 T + 450 T^{2} + 5138 T^{3} + 50938 T^{4} + 405902 T^{5} + 2808450 T^{6} + 12819014 T^{7} + 38950081 T^{8} \))(\( 1 + 26 T + 450 T^{2} + 5138 T^{3} + 50938 T^{4} + 405902 T^{5} + 2808450 T^{6} + 12819014 T^{7} + 38950081 T^{8} \))(\( 1 + 28 T + 686 T^{2} + 11252 T^{3} + 159023 T^{4} + 1794648 T^{5} + 17548548 T^{6} + 141777192 T^{7} + 992462543 T^{8} + 5547674828 T^{9} + 26719755566 T^{10} + 86157579172 T^{11} + 243087455521 T^{12} \))(\( 1 - 2 T + 307 T^{2} - 689 T^{3} + 48091 T^{4} - 95350 T^{5} + 4742205 T^{6} - 7532650 T^{7} + 300135931 T^{8} - 339703871 T^{9} + 11957674867 T^{10} - 6154112798 T^{11} + 243087455521 T^{12} \))(\( 1 - 2 T + 307 T^{2} - 689 T^{3} + 48091 T^{4} - 95350 T^{5} + 4742205 T^{6} - 7532650 T^{7} + 300135931 T^{8} - 339703871 T^{9} + 11957674867 T^{10} - 6154112798 T^{11} + 243087455521 T^{12} \))(\( 1 + 28 T + 686 T^{2} + 11252 T^{3} + 159023 T^{4} + 1794648 T^{5} + 17548548 T^{6} + 141777192 T^{7} + 992462543 T^{8} + 5547674828 T^{9} + 26719755566 T^{10} + 86157579172 T^{11} + 243087455521 T^{12} \))(\( 1 - 2 T + 584 T^{2} - 1395 T^{3} + 168539 T^{4} - 450057 T^{5} + 31930200 T^{6} - 89980411 T^{7} + 4451310839 T^{8} - 12583796510 T^{9} + 484433738906 T^{10} - 1306073996328 T^{11} + 42443514423483 T^{12} - 103179845709912 T^{13} + 3023350964512346 T^{14} - 6204302447493890 T^{15} + 173378917735227959 T^{16} - 276874799452199989 T^{17} + 7761831072276634200 T^{18} - 8642853666583761063 T^{19} + \)\(25\!\cdots\!79\)\( T^{20} - \)\(16\!\cdots\!05\)\( T^{21} + \)\(55\!\cdots\!84\)\( T^{22} - \)\(14\!\cdots\!58\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 - 2 T + 584 T^{2} - 1395 T^{3} + 168539 T^{4} - 450057 T^{5} + 31930200 T^{6} - 89980411 T^{7} + 4451310839 T^{8} - 12583796510 T^{9} + 484433738906 T^{10} - 1306073996328 T^{11} + 42443514423483 T^{12} - 103179845709912 T^{13} + 3023350964512346 T^{14} - 6204302447493890 T^{15} + 173378917735227959 T^{16} - 276874799452199989 T^{17} + 7761831072276634200 T^{18} - 8642853666583761063 T^{19} + \)\(25\!\cdots\!79\)\( T^{20} - \)\(16\!\cdots\!05\)\( T^{21} + \)\(55\!\cdots\!84\)\( T^{22} - \)\(14\!\cdots\!58\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))
$83$ (\( 1 + 3 T + 83 T^{2} \))(\( 1 + 15 T + 83 T^{2} \))(\( 1 + 121 T^{2} + 6889 T^{4} \))(\( 1 + 18 T + 229 T^{2} + 1494 T^{3} + 6889 T^{4} \))(\( 1 + 6 T + 148 T^{2} + 498 T^{3} + 6889 T^{4} \))(\( 1 - 6 T + 148 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( 1 + 121 T^{2} + 6889 T^{4} \))(\( 1 + T + 136 T^{2} + 3 T^{3} + 11288 T^{4} + 6889 T^{5} + 571787 T^{6} \))(\( 1 - 12 T - 22 T^{2} + 1276 T^{3} - 1826 T^{4} - 82668 T^{5} + 571787 T^{6} \))(\( 1 - T + 136 T^{2} - 3 T^{3} + 11288 T^{4} - 6889 T^{5} + 571787 T^{6} \))(\( 1 + 235 T^{2} - 442 T^{3} + 24806 T^{4} - 36686 T^{5} + 1618915 T^{6} + 47458321 T^{8} \))(\( 1 + 235 T^{2} + 442 T^{3} + 24806 T^{4} + 36686 T^{5} + 1618915 T^{6} + 47458321 T^{8} \))(\( 1 + 26 T + 684 T^{2} + 10460 T^{3} + 156752 T^{4} + 1683426 T^{5} + 17728366 T^{6} + 139724358 T^{7} + 1079864528 T^{8} + 5980892020 T^{9} + 32461491564 T^{10} + 102415056718 T^{11} + 326940373369 T^{12} \))(\( 1 - 7 T + 226 T^{2} - 2485 T^{3} + 35590 T^{4} - 306775 T^{5} + 3896483 T^{6} - 25462325 T^{7} + 245179510 T^{8} - 1420890695 T^{9} + 10725580546 T^{10} - 27573284501 T^{11} + 326940373369 T^{12} \))(\( 1 + 7 T + 226 T^{2} + 2485 T^{3} + 35590 T^{4} + 306775 T^{5} + 3896483 T^{6} + 25462325 T^{7} + 245179510 T^{8} + 1420890695 T^{9} + 10725580546 T^{10} + 27573284501 T^{11} + 326940373369 T^{12} \))(\( 1 - 26 T + 684 T^{2} - 10460 T^{3} + 156752 T^{4} - 1683426 T^{5} + 17728366 T^{6} - 139724358 T^{7} + 1079864528 T^{8} - 5980892020 T^{9} + 32461491564 T^{10} - 102415056718 T^{11} + 326940373369 T^{12} \))(\( 1 - 9 T + 748 T^{2} - 5855 T^{3} + 267849 T^{4} - 1850302 T^{5} + 61117591 T^{6} - 375534386 T^{7} + 9932124121 T^{8} - 54413960281 T^{9} + 1212981331253 T^{10} - 5908493820239 T^{11} + 114217701170938 T^{12} - 490404987079837 T^{13} + 8356228391001917 T^{14} - 31113195107192147 T^{15} + 471361934746260841 T^{16} - 1479245209298050198 T^{17} + 19981808020953834079 T^{18} - 50209889418208817354 T^{19} + \)\(60\!\cdots\!09\)\( T^{20} - \)\(10\!\cdots\!65\)\( T^{21} + \)\(11\!\cdots\!52\)\( T^{22} - \)\(11\!\cdots\!03\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + 9 T + 748 T^{2} + 5855 T^{3} + 267849 T^{4} + 1850302 T^{5} + 61117591 T^{6} + 375534386 T^{7} + 9932124121 T^{8} + 54413960281 T^{9} + 1212981331253 T^{10} + 5908493820239 T^{11} + 114217701170938 T^{12} + 490404987079837 T^{13} + 8356228391001917 T^{14} + 31113195107192147 T^{15} + 471361934746260841 T^{16} + 1479245209298050198 T^{17} + 19981808020953834079 T^{18} + 50209889418208817354 T^{19} + \)\(60\!\cdots\!09\)\( T^{20} + \)\(10\!\cdots\!65\)\( T^{21} + \)\(11\!\cdots\!52\)\( T^{22} + \)\(11\!\cdots\!03\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))
$89$ (\( 1 + 15 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))(\( 1 + 21 T + 257 T^{2} + 1869 T^{3} + 7921 T^{4} \))(\( 1 + 6 T + 185 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 166 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 166 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 21 T + 257 T^{2} - 1869 T^{3} + 7921 T^{4} \))(\( 1 + 3 T + 212 T^{2} + 307 T^{3} + 18868 T^{4} + 23763 T^{5} + 704969 T^{6} \))(\( 1 + 2 T + 172 T^{2} - 66 T^{3} + 15308 T^{4} + 15842 T^{5} + 704969 T^{6} \))(\( 1 - 3 T + 212 T^{2} - 307 T^{3} + 18868 T^{4} - 23763 T^{5} + 704969 T^{6} \))(\( 1 + T + 285 T^{2} + 83 T^{3} + 34780 T^{4} + 7387 T^{5} + 2257485 T^{6} + 704969 T^{7} + 62742241 T^{8} \))(\( 1 - T + 285 T^{2} - 83 T^{3} + 34780 T^{4} - 7387 T^{5} + 2257485 T^{6} - 704969 T^{7} + 62742241 T^{8} \))(\( 1 + 42 T + 1087 T^{2} + 20330 T^{3} + 304908 T^{4} + 3736348 T^{5} + 38506140 T^{6} + 332534972 T^{7} + 2415176268 T^{8} + 14332019770 T^{9} + 68200815967 T^{10} + 234530496858 T^{11} + 496981290961 T^{12} \))(\( 1 - 10 T + 292 T^{2} - 2764 T^{3} + 48371 T^{4} - 414955 T^{5} + 5171855 T^{6} - 36930995 T^{7} + 383146691 T^{8} - 1948534316 T^{9} + 18320734372 T^{10} - 55840594490 T^{11} + 496981290961 T^{12} \))(\( 1 + 10 T + 292 T^{2} + 2764 T^{3} + 48371 T^{4} + 414955 T^{5} + 5171855 T^{6} + 36930995 T^{7} + 383146691 T^{8} + 1948534316 T^{9} + 18320734372 T^{10} + 55840594490 T^{11} + 496981290961 T^{12} \))(\( 1 - 42 T + 1087 T^{2} - 20330 T^{3} + 304908 T^{4} - 3736348 T^{5} + 38506140 T^{6} - 332534972 T^{7} + 2415176268 T^{8} - 14332019770 T^{9} + 68200815967 T^{10} - 234530496858 T^{11} + 496981290961 T^{12} \))(\( 1 - 22 T + 708 T^{2} - 10390 T^{3} + 187172 T^{4} - 1990489 T^{5} + 25852105 T^{6} - 199935153 T^{7} + 2114359661 T^{8} - 10231800017 T^{9} + 107906121907 T^{10} - 117505330649 T^{11} + 5586713487164 T^{12} - 10457974427761 T^{13} + 854724391625347 T^{14} - 7213101826184473 T^{15} + 132659663411140301 T^{16} - 1116449780296910697 T^{17} + 12848012516959322905 T^{18} - 88041985564866623681 T^{19} + \)\(73\!\cdots\!32\)\( T^{20} - \)\(36\!\cdots\!10\)\( T^{21} + \)\(22\!\cdots\!08\)\( T^{22} - \)\(61\!\cdots\!58\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 22 T + 708 T^{2} + 10390 T^{3} + 187172 T^{4} + 1990489 T^{5} + 25852105 T^{6} + 199935153 T^{7} + 2114359661 T^{8} + 10231800017 T^{9} + 107906121907 T^{10} + 117505330649 T^{11} + 5586713487164 T^{12} + 10457974427761 T^{13} + 854724391625347 T^{14} + 7213101826184473 T^{15} + 132659663411140301 T^{16} + 1116449780296910697 T^{17} + 12848012516959322905 T^{18} + 88041985564866623681 T^{19} + \)\(73\!\cdots\!32\)\( T^{20} + \)\(36\!\cdots\!10\)\( T^{21} + \)\(22\!\cdots\!08\)\( T^{22} + \)\(61\!\cdots\!58\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))
$97$ (\( 1 - T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 + 31 T + 423 T^{2} + 3007 T^{3} + 9409 T^{4} \))(\( 1 - 2 T + 33 T^{2} - 194 T^{3} + 9409 T^{4} \))(\( 1 - 8 T + 102 T^{2} - 776 T^{3} + 9409 T^{4} \))(\( 1 + 8 T + 102 T^{2} + 776 T^{3} + 9409 T^{4} \))(\( 1 - 31 T + 423 T^{2} - 3007 T^{3} + 9409 T^{4} \))(\( 1 + 15 T + 116 T^{2} + 727 T^{3} + 11252 T^{4} + 141135 T^{5} + 912673 T^{6} \))(\( 1 - 10 T + 320 T^{2} - 1962 T^{3} + 31040 T^{4} - 94090 T^{5} + 912673 T^{6} \))(\( 1 - 15 T + 116 T^{2} - 727 T^{3} + 11252 T^{4} - 141135 T^{5} + 912673 T^{6} \))(\( 1 - 3 T + 83 T^{2} - 205 T^{3} + 12976 T^{4} - 19885 T^{5} + 780947 T^{6} - 2738019 T^{7} + 88529281 T^{8} \))(\( 1 + 3 T + 83 T^{2} + 205 T^{3} + 12976 T^{4} + 19885 T^{5} + 780947 T^{6} + 2738019 T^{7} + 88529281 T^{8} \))(\( 1 + 24 T + 679 T^{2} + 10706 T^{3} + 174956 T^{4} + 2000590 T^{5} + 22996700 T^{6} + 194057230 T^{7} + 1646161004 T^{8} + 9771077138 T^{9} + 60111381799 T^{10} + 206096166168 T^{11} + 832972004929 T^{12} \))(\( 1 - 5 T + 286 T^{2} - 1431 T^{3} + 39905 T^{4} - 196126 T^{5} + 4141037 T^{6} - 19024222 T^{7} + 375466145 T^{8} - 1306035063 T^{9} + 25319374366 T^{10} - 42936701285 T^{11} + 832972004929 T^{12} \))(\( 1 + 5 T + 286 T^{2} + 1431 T^{3} + 39905 T^{4} + 196126 T^{5} + 4141037 T^{6} + 19024222 T^{7} + 375466145 T^{8} + 1306035063 T^{9} + 25319374366 T^{10} + 42936701285 T^{11} + 832972004929 T^{12} \))(\( 1 - 24 T + 679 T^{2} - 10706 T^{3} + 174956 T^{4} - 2000590 T^{5} + 22996700 T^{6} - 194057230 T^{7} + 1646161004 T^{8} - 9771077138 T^{9} + 60111381799 T^{10} - 206096166168 T^{11} + 832972004929 T^{12} \))(\( 1 + 9 T + 676 T^{2} + 4541 T^{3} + 226390 T^{4} + 1212365 T^{5} + 51019981 T^{6} + 227397355 T^{7} + 8639580341 T^{8} + 33084442880 T^{9} + 1153564648063 T^{10} + 3894500343298 T^{11} + 124194015909192 T^{12} + 377766533299906 T^{13} + 10853889773624767 T^{14} + 30195277736618240 T^{15} + 764855835730464821 T^{16} + 1952738460926820235 T^{17} + 42498215865009486349 T^{18} + 97957012161307467245 T^{19} + \)\(17\!\cdots\!90\)\( T^{20} + \)\(34\!\cdots\!97\)\( T^{21} + \)\(49\!\cdots\!24\)\( T^{22} + \)\(64\!\cdots\!77\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 9 T + 676 T^{2} - 4541 T^{3} + 226390 T^{4} - 1212365 T^{5} + 51019981 T^{6} - 227397355 T^{7} + 8639580341 T^{8} - 33084442880 T^{9} + 1153564648063 T^{10} - 3894500343298 T^{11} + 124194015909192 T^{12} - 377766533299906 T^{13} + 10853889773624767 T^{14} - 30195277736618240 T^{15} + 764855835730464821 T^{16} - 1952738460926820235 T^{17} + 42498215865009486349 T^{18} - 97957012161307467245 T^{19} + \)\(17\!\cdots\!90\)\( T^{20} - \)\(34\!\cdots\!97\)\( T^{21} + \)\(49\!\cdots\!24\)\( T^{22} - \)\(64\!\cdots\!77\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))
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