Properties

Label 2006.2.a
Level 2006
Weight 2
Character orbit a
Rep. character \(\chi_{2006}(1,\cdot)\)
Character field \(\Q\)
Dimension 79
Newform subspaces 23
Sturm bound 540
Trace bound 5

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Defining parameters

Level: \( N \) \(=\) \( 2006 = 2 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2006.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(540\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2006))\).

Total New Old
Modular forms 274 79 195
Cusp forms 267 79 188
Eisenstein series 7 0 7

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

\(2\)\(17\)\(59\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(13\)
\(+\)\(-\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(13\)
Plus space\(+\)\(28\)
Minus space\(-\)\(51\)

Trace form

\( 79q - q^{2} + 79q^{4} - 2q^{5} + 4q^{6} + 8q^{7} - q^{8} + 83q^{9} + O(q^{10}) \) \( 79q - q^{2} + 79q^{4} - 2q^{5} + 4q^{6} + 8q^{7} - q^{8} + 83q^{9} - 6q^{10} - 12q^{11} + 10q^{13} - 16q^{15} + 79q^{16} + 3q^{17} - 5q^{18} + 20q^{19} - 2q^{20} + 16q^{21} - 8q^{22} - 16q^{23} + 4q^{24} + 73q^{25} + 2q^{26} + 8q^{28} + 14q^{29} + 8q^{30} + 8q^{31} - q^{32} + 16q^{33} - q^{34} - 24q^{35} + 83q^{36} + 18q^{37} + 12q^{38} + 8q^{39} - 6q^{40} + 14q^{41} + 8q^{42} + 4q^{43} - 12q^{44} - 2q^{45} + 8q^{46} + 32q^{47} + 95q^{49} + 17q^{50} + 10q^{52} - 38q^{53} + 16q^{54} - 16q^{55} + 8q^{57} - 6q^{58} - q^{59} - 16q^{60} + 42q^{61} - 16q^{63} + 79q^{64} - 36q^{65} + 40q^{66} - 4q^{67} + 3q^{68} - 40q^{69} - 24q^{70} - 8q^{71} - 5q^{72} - 18q^{73} - 18q^{74} + 8q^{75} + 20q^{76} + 32q^{77} + 48q^{78} - 16q^{79} - 2q^{80} + 111q^{81} + 6q^{82} + 4q^{83} + 16q^{84} + 6q^{85} - 20q^{86} + 16q^{87} - 8q^{88} - 66q^{89} - 6q^{90} + 32q^{91} - 16q^{92} + 56q^{93} + 48q^{95} + 4q^{96} - 10q^{97} - 17q^{98} - 28q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2006))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 17 59
2006.2.a.a \(1\) \(16.018\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-5\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-5q^{7}+\cdots\)
2006.2.a.b \(1\) \(16.018\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
2006.2.a.c \(1\) \(16.018\) \(\Q\) None \(-1\) \(-1\) \(2\) \(4\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
2006.2.a.d \(1\) \(16.018\) \(\Q\) None \(-1\) \(0\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+2q^{7}-q^{8}-3q^{9}+4q^{11}+\cdots\)
2006.2.a.e \(1\) \(16.018\) \(\Q\) None \(-1\) \(1\) \(-3\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
2006.2.a.f \(1\) \(16.018\) \(\Q\) None \(-1\) \(3\) \(2\) \(4\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}+2q^{5}-3q^{6}+4q^{7}+\cdots\)
2006.2.a.g \(1\) \(16.018\) \(\Q\) None \(1\) \(-3\) \(-3\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{2}-3q^{3}+q^{4}-3q^{5}-3q^{6}-q^{7}+\cdots\)
2006.2.a.h \(1\) \(16.018\) \(\Q\) None \(1\) \(-1\) \(-3\) \(1\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
2006.2.a.i \(1\) \(16.018\) \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2006.2.a.j \(1\) \(16.018\) \(\Q\) None \(1\) \(0\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}-6q^{11}+\cdots\)
2006.2.a.k \(1\) \(16.018\) \(\Q\) None \(1\) \(2\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+2q^{7}+\cdots\)
2006.2.a.l \(2\) \(16.018\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(0\) \(-6\) \(+\) \(+\) \(+\) \(q-q^{2}-\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}-3q^{7}+\cdots\)
2006.2.a.m \(2\) \(16.018\) \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(-5\) \(2\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+(-2-\beta )q^{5}+\beta q^{6}+\cdots\)
2006.2.a.n \(3\) \(16.018\) 3.3.229.1 None \(-3\) \(2\) \(-2\) \(3\) \(+\) \(+\) \(+\) \(q-q^{2}+(1+\beta _{2})q^{3}+q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
2006.2.a.o \(3\) \(16.018\) 3.3.568.1 None \(3\) \(-1\) \(5\) \(7\) \(-\) \(+\) \(+\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(2-\beta _{1})q^{5}-\beta _{1}q^{6}+\cdots\)
2006.2.a.p \(4\) \(16.018\) 4.4.2225.1 None \(-4\) \(-1\) \(-5\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
2006.2.a.q \(4\) \(16.018\) \(\Q(\zeta_{20})^+\) None \(-4\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}+(-\beta _{2}+\beta _{3})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
2006.2.a.r \(4\) \(16.018\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(4\) \(-4\) \(4\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
2006.2.a.s \(4\) \(16.018\) 4.4.13676.1 None \(4\) \(-3\) \(3\) \(-12\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2006.2.a.t \(8\) \(16.018\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(5\) \(-5\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+(1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{7})q^{5}+\cdots\)
2006.2.a.u \(9\) \(16.018\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-1\) \(7\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{6})q^{5}+\beta _{1}q^{6}+\cdots\)
2006.2.a.v \(12\) \(16.018\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-3\) \(-1\) \(4\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots\)
2006.2.a.w \(13\) \(16.018\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(13\) \(7\) \(1\) \(8\) \(-\) \(-\) \(-\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+\beta _{8}q^{5}+(1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2006))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1003))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{8} \))(\( ( 1 + T )^{9} \))(\( ( 1 + T )^{12} \))(\( ( 1 - T )^{13} \))
$3$ (\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 + T^{2} + 9 T^{4} \))(\( 1 - T + 5 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - 2 T + 5 T^{2} - 5 T^{3} + 15 T^{4} - 18 T^{5} + 27 T^{6} \))(\( 1 + T + 3 T^{2} + 8 T^{3} + 9 T^{4} + 9 T^{5} + 27 T^{6} \))(\( 1 + T + 7 T^{2} + 7 T^{3} + 28 T^{4} + 21 T^{5} + 63 T^{6} + 27 T^{7} + 81 T^{8} \))(\( 1 + 2 T^{2} - T^{4} + 18 T^{6} + 81 T^{8} \))(\( ( 1 + 2 T + 5 T^{2} + 6 T^{3} + 9 T^{4} )^{2} \))(\( 1 + 3 T + 8 T^{2} + 18 T^{3} + 35 T^{4} + 54 T^{5} + 72 T^{6} + 81 T^{7} + 81 T^{8} \))(\( 1 - 5 T + 16 T^{2} - 48 T^{3} + 134 T^{4} - 315 T^{5} + 664 T^{6} - 1319 T^{7} + 2423 T^{8} - 3957 T^{9} + 5976 T^{10} - 8505 T^{11} + 10854 T^{12} - 11664 T^{13} + 11664 T^{14} - 10935 T^{15} + 6561 T^{16} \))(\( 1 + T + 4 T^{2} + 6 T^{3} + 26 T^{4} + 19 T^{5} + 81 T^{6} + 48 T^{7} + 254 T^{8} + 152 T^{9} + 762 T^{10} + 432 T^{11} + 2187 T^{12} + 1539 T^{13} + 6318 T^{14} + 4374 T^{15} + 8748 T^{16} + 6561 T^{17} + 19683 T^{18} \))(\( 1 + 3 T + 15 T^{2} + 37 T^{3} + 108 T^{4} + 229 T^{5} + 521 T^{6} + 1013 T^{7} + 2100 T^{8} + 3881 T^{9} + 7795 T^{10} + 13443 T^{11} + 25502 T^{12} + 40329 T^{13} + 70155 T^{14} + 104787 T^{15} + 170100 T^{16} + 246159 T^{17} + 379809 T^{18} + 500823 T^{19} + 708588 T^{20} + 728271 T^{21} + 885735 T^{22} + 531441 T^{23} + 531441 T^{24} \))(\( 1 - 7 T + 36 T^{2} - 134 T^{3} + 427 T^{4} - 1154 T^{5} + 2837 T^{6} - 6264 T^{7} + 12985 T^{8} - 24934 T^{9} + 46135 T^{10} - 81370 T^{11} + 142787 T^{12} - 245642 T^{13} + 428361 T^{14} - 732330 T^{15} + 1245645 T^{16} - 2019654 T^{17} + 3155355 T^{18} - 4566456 T^{19} + 6204519 T^{20} - 7571394 T^{21} + 8404641 T^{22} - 7912566 T^{23} + 6377292 T^{24} - 3720087 T^{25} + 1594323 T^{26} \))
$5$ (\( 1 + T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} + 25 T^{4} \))(\( 1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4} \))(\( 1 + 2 T + 11 T^{2} + 13 T^{3} + 55 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 - 5 T + 17 T^{2} - 40 T^{3} + 85 T^{4} - 125 T^{5} + 125 T^{6} \))(\( 1 + 5 T + 19 T^{2} + 55 T^{3} + 124 T^{4} + 275 T^{5} + 475 T^{6} + 625 T^{7} + 625 T^{8} \))(\( 1 - 2 T + 14 T^{2} - 28 T^{3} + 91 T^{4} - 140 T^{5} + 350 T^{6} - 250 T^{7} + 625 T^{8} \))(\( 1 - 4 T + 20 T^{2} - 52 T^{3} + 149 T^{4} - 260 T^{5} + 500 T^{6} - 500 T^{7} + 625 T^{8} \))(\( 1 - 3 T + 16 T^{2} - 36 T^{3} + 115 T^{4} - 180 T^{5} + 400 T^{6} - 375 T^{7} + 625 T^{8} \))(\( 1 + 5 T + 18 T^{2} + 48 T^{3} + 147 T^{4} + 346 T^{5} + 858 T^{6} + 2025 T^{7} + 5212 T^{8} + 10125 T^{9} + 21450 T^{10} + 43250 T^{11} + 91875 T^{12} + 150000 T^{13} + 281250 T^{14} + 390625 T^{15} + 390625 T^{16} \))(\( 1 - 7 T + 37 T^{2} - 155 T^{3} + 581 T^{4} - 1894 T^{5} + 5637 T^{6} - 15233 T^{7} + 38408 T^{8} - 88766 T^{9} + 192040 T^{10} - 380825 T^{11} + 704625 T^{12} - 1183750 T^{13} + 1815625 T^{14} - 2421875 T^{15} + 2890625 T^{16} - 2734375 T^{17} + 1953125 T^{18} \))(\( 1 + T + 21 T^{2} + 21 T^{3} + 243 T^{4} + 186 T^{5} + 2054 T^{6} + 1220 T^{7} + 14247 T^{8} + 7907 T^{9} + 87297 T^{10} + 46785 T^{11} + 471018 T^{12} + 233925 T^{13} + 2182425 T^{14} + 988375 T^{15} + 8904375 T^{16} + 3812500 T^{17} + 32093750 T^{18} + 14531250 T^{19} + 94921875 T^{20} + 41015625 T^{21} + 205078125 T^{22} + 48828125 T^{23} + 244140625 T^{24} \))(\( 1 - T + 26 T^{2} + 2 T^{3} + 296 T^{4} + 367 T^{5} + 2267 T^{6} + 5088 T^{7} + 16069 T^{8} + 38041 T^{9} + 112164 T^{10} + 210942 T^{11} + 681293 T^{12} + 1063858 T^{13} + 3406465 T^{14} + 5273550 T^{15} + 14020500 T^{16} + 23775625 T^{17} + 50215625 T^{18} + 79500000 T^{19} + 177109375 T^{20} + 143359375 T^{21} + 578125000 T^{22} + 19531250 T^{23} + 1269531250 T^{24} - 244140625 T^{25} + 1220703125 T^{26} \))
$7$ (\( 1 + 5 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( ( 1 + 3 T + 7 T^{2} )^{2} \))(\( ( 1 - T + 7 T^{2} )^{2} \))(\( 1 - 3 T + 8 T^{2} - 19 T^{3} + 56 T^{4} - 147 T^{5} + 343 T^{6} \))(\( 1 - 7 T + 29 T^{2} - 90 T^{3} + 203 T^{4} - 343 T^{5} + 343 T^{6} \))(\( 1 + 2 T + 23 T^{2} + 36 T^{3} + 228 T^{4} + 252 T^{5} + 1127 T^{6} + 686 T^{7} + 2401 T^{8} \))(\( 1 - 2 T + 22 T^{2} - 40 T^{3} + 211 T^{4} - 280 T^{5} + 1078 T^{6} - 686 T^{7} + 2401 T^{8} \))(\( 1 + 4 T + 20 T^{2} + 60 T^{3} + 173 T^{4} + 420 T^{5} + 980 T^{6} + 1372 T^{7} + 2401 T^{8} \))(\( ( 1 + 3 T + 7 T^{2} )^{4} \))(\( 1 + 14 T^{2} - 16 T^{3} + 129 T^{4} - 320 T^{5} + 894 T^{6} - 3760 T^{7} + 5252 T^{8} - 26320 T^{9} + 43806 T^{10} - 109760 T^{11} + 309729 T^{12} - 268912 T^{13} + 1647086 T^{14} + 5764801 T^{16} \))(\( 1 + 25 T^{2} + 28 T^{3} + 371 T^{4} + 508 T^{5} + 4397 T^{6} + 5604 T^{7} + 38578 T^{8} + 47624 T^{9} + 270046 T^{10} + 274596 T^{11} + 1508171 T^{12} + 1219708 T^{13} + 6235397 T^{14} + 3294172 T^{15} + 20588575 T^{16} + 40353607 T^{18} \))(\( 1 - 4 T + 35 T^{2} - 120 T^{3} + 675 T^{4} - 2136 T^{5} + 9472 T^{6} - 28428 T^{7} + 105013 T^{8} - 295208 T^{9} + 954701 T^{10} - 2504352 T^{11} + 7273198 T^{12} - 17530464 T^{13} + 46780349 T^{14} - 101256344 T^{15} + 252136213 T^{16} - 477789396 T^{17} + 1114371328 T^{18} - 1759087848 T^{19} + 3891240675 T^{20} - 4842432840 T^{21} + 9886633715 T^{22} - 7909306972 T^{23} + 13841287201 T^{24} \))(\( 1 - 8 T + 66 T^{2} - 336 T^{3} + 1720 T^{4} - 6764 T^{5} + 26605 T^{6} - 86652 T^{7} + 285141 T^{8} - 806848 T^{9} + 2356712 T^{10} - 6099380 T^{11} + 16916673 T^{12} - 42760216 T^{13} + 118416711 T^{14} - 298869620 T^{15} + 808352216 T^{16} - 1937242048 T^{17} + 4792364787 T^{18} - 10194521148 T^{19} + 21910361515 T^{20} - 38993113964 T^{21} + 69408204040 T^{22} - 94911683664 T^{23} + 130503565038 T^{24} - 110730297608 T^{25} + 96889010407 T^{26} \))
$11$ (\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 2 T + 18 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 + 3 T + 23 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 - 3 T + 32 T^{2} - 64 T^{3} + 352 T^{4} - 363 T^{5} + 1331 T^{6} \))(\( 1 + 2 T + 9 T^{2} + 60 T^{3} + 99 T^{4} + 242 T^{5} + 1331 T^{6} \))(\( 1 - T + 9 T^{2} - 11 T^{3} + 120 T^{4} - 121 T^{5} + 1089 T^{6} - 1331 T^{7} + 14641 T^{8} \))(\( 1 + 2 T + 38 T^{2} + 54 T^{3} + 590 T^{4} + 594 T^{5} + 4598 T^{6} + 2662 T^{7} + 14641 T^{8} \))(\( 1 + 8 T + 62 T^{2} + 272 T^{3} + 1118 T^{4} + 2992 T^{5} + 7502 T^{6} + 10648 T^{7} + 14641 T^{8} \))(\( 1 + 5 T + 27 T^{2} + 81 T^{3} + 344 T^{4} + 891 T^{5} + 3267 T^{6} + 6655 T^{7} + 14641 T^{8} \))(\( 1 + 5 T + 53 T^{2} + 241 T^{3} + 1534 T^{4} + 5953 T^{5} + 28787 T^{6} + 95053 T^{7} + 376194 T^{8} + 1045583 T^{9} + 3483227 T^{10} + 7923443 T^{11} + 22459294 T^{12} + 38813291 T^{13} + 93892733 T^{14} + 97435855 T^{15} + 214358881 T^{16} \))(\( 1 - 5 T + 22 T^{2} - 68 T^{3} + 259 T^{4} - 980 T^{5} + 5563 T^{6} - 17500 T^{7} + 61433 T^{8} - 189102 T^{9} + 675763 T^{10} - 2117500 T^{11} + 7404353 T^{12} - 14348180 T^{13} + 41712209 T^{14} - 120466148 T^{15} + 428717762 T^{16} - 1071794405 T^{17} + 2357947691 T^{18} \))(\( 1 + 3 T + 45 T^{2} + 139 T^{3} + 1006 T^{4} + 3189 T^{5} + 14765 T^{6} + 49253 T^{7} + 170823 T^{8} + 606246 T^{9} + 1847326 T^{10} + 6800742 T^{11} + 20101748 T^{12} + 74808162 T^{13} + 223526446 T^{14} + 806913426 T^{15} + 2501019543 T^{16} + 7932244903 T^{17} + 26157098165 T^{18} + 62144588319 T^{19} + 215645034286 T^{20} + 327754729049 T^{21} + 1167184107045 T^{22} + 855935011833 T^{23} + 3138428376721 T^{24} \))(\( 1 - 13 T + 144 T^{2} - 1118 T^{3} + 7877 T^{4} - 46914 T^{5} + 259479 T^{6} - 1285750 T^{7} + 5994038 T^{8} - 25715027 T^{9} + 104684723 T^{10} - 397378108 T^{11} + 1438032038 T^{12} - 4880619548 T^{13} + 15818352418 T^{14} - 48082751068 T^{15} + 139335366313 T^{16} - 376493710307 T^{17} + 965345813938 T^{18} - 2277784555750 T^{19} + 5056511643909 T^{20} - 10056432543234 T^{21} + 18573553962007 T^{22} - 28998040703918 T^{23} + 41084880567984 T^{24} - 40799568897373 T^{25} + 34522712143931 T^{26} \))
$13$ (\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 7 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 4 T + 10 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 + T + 15 T^{2} + 13 T^{3} + 169 T^{4} \))(\( 1 + 5 T + 32 T^{2} + 132 T^{3} + 416 T^{4} + 845 T^{5} + 2197 T^{6} \))(\( ( 1 - 2 T + 13 T^{2} )^{3} \))(\( 1 - T + 37 T^{2} - 47 T^{3} + 628 T^{4} - 611 T^{5} + 6253 T^{6} - 2197 T^{7} + 28561 T^{8} \))(\( 1 + 14 T + 118 T^{2} + 670 T^{3} + 2806 T^{4} + 8710 T^{5} + 19942 T^{6} + 30758 T^{7} + 28561 T^{8} \))(\( 1 + 12 T + 90 T^{2} + 460 T^{3} + 1878 T^{4} + 5980 T^{5} + 15210 T^{6} + 26364 T^{7} + 28561 T^{8} \))(\( 1 + T + 23 T^{2} + 31 T^{3} + 432 T^{4} + 403 T^{5} + 3887 T^{6} + 2197 T^{7} + 28561 T^{8} \))(\( 1 - T + 27 T^{2} - 51 T^{3} + 785 T^{4} - 1318 T^{5} + 12886 T^{6} - 23252 T^{7} + 210258 T^{8} - 302276 T^{9} + 2177734 T^{10} - 2895646 T^{11} + 22420385 T^{12} - 18935943 T^{13} + 130323843 T^{14} - 62748517 T^{15} + 815730721 T^{16} \))(\( 1 - 25 T + 337 T^{2} - 3167 T^{3} + 23273 T^{4} - 142416 T^{5} + 755453 T^{6} - 3553721 T^{7} + 14994976 T^{8} - 56957102 T^{9} + 194934688 T^{10} - 600578849 T^{11} + 1659730241 T^{12} - 4067543376 T^{13} + 8641101989 T^{14} - 15286504103 T^{15} + 21146250229 T^{16} - 20393268025 T^{17} + 10604499373 T^{18} \))(\( 1 - 15 T + 179 T^{2} - 1567 T^{3} + 11849 T^{4} - 77442 T^{5} + 456600 T^{6} - 2443672 T^{7} + 12065123 T^{8} - 55115149 T^{9} + 234941297 T^{10} - 934050723 T^{11} + 3483192654 T^{12} - 12142659399 T^{13} + 39705079193 T^{14} - 121087982353 T^{15} + 344591978003 T^{16} - 907318307896 T^{17} + 2203920989400 T^{18} - 4859370653514 T^{19} + 9665593313129 T^{20} - 16617250517491 T^{21} + 24676670040971 T^{22} - 26882405910555 T^{23} + 23298085122481 T^{24} \))(\( 1 - 9 T + 124 T^{2} - 814 T^{3} + 6432 T^{4} - 33675 T^{5} + 198449 T^{6} - 891478 T^{7} + 4416951 T^{8} - 18122987 T^{9} + 80563304 T^{10} - 309304564 T^{11} + 1251935103 T^{12} - 4427496946 T^{13} + 16275156339 T^{14} - 52272471316 T^{15} + 176997578888 T^{16} - 517610631707 T^{17} + 1639982987643 T^{18} - 4302994033702 T^{19} + 12452380450133 T^{20} - 27469732029675 T^{21} + 68208139967136 T^{22} - 112216812365086 T^{23} + 222227888860588 T^{24} - 209682766102329 T^{25} + 302875106592253 T^{26} \))
$17$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{8} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{12} \))(\( ( 1 - T )^{13} \))
$19$ (\( 1 + 7 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 8 T + 49 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 + 8 T + 49 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 + 9 T + 68 T^{2} + 313 T^{3} + 1292 T^{4} + 3249 T^{5} + 6859 T^{6} \))(\( 1 - 7 T + 65 T^{2} - 258 T^{3} + 1235 T^{4} - 2527 T^{5} + 6859 T^{6} \))(\( 1 + 8 T + 59 T^{2} + 204 T^{3} + 1056 T^{4} + 3876 T^{5} + 21299 T^{6} + 54872 T^{7} + 130321 T^{8} \))(\( 1 + 4 T + 62 T^{2} + 232 T^{3} + 1635 T^{4} + 4408 T^{5} + 22382 T^{6} + 27436 T^{7} + 130321 T^{8} \))(\( 1 + 8 T + 70 T^{2} + 368 T^{3} + 1859 T^{4} + 6992 T^{5} + 25270 T^{6} + 54872 T^{7} + 130321 T^{8} \))(\( 1 + 6 T + 64 T^{2} + 248 T^{3} + 1649 T^{4} + 4712 T^{5} + 23104 T^{6} + 41154 T^{7} + 130321 T^{8} \))(\( 1 - 8 T + 74 T^{2} - 532 T^{3} + 3597 T^{4} - 20536 T^{5} + 110914 T^{6} - 536796 T^{7} + 2523516 T^{8} - 10199124 T^{9} + 40039954 T^{10} - 140856424 T^{11} + 468764637 T^{12} - 1317284668 T^{13} + 3481395194 T^{14} - 7150973912 T^{15} + 16983563041 T^{16} \))(\( 1 - 14 T + 155 T^{2} - 1186 T^{3} + 8155 T^{4} - 46564 T^{5} + 253349 T^{6} - 1234926 T^{7} + 5897444 T^{8} - 25864540 T^{9} + 112051436 T^{10} - 445808286 T^{11} + 1737720791 T^{12} - 6068267044 T^{13} + 20192587345 T^{14} - 55796414866 T^{15} + 138550119545 T^{16} - 237769882574 T^{17} + 322687697779 T^{18} \))(\( 1 - 16 T + 261 T^{2} - 2688 T^{3} + 26727 T^{4} - 210296 T^{5} + 1589984 T^{6} - 10272224 T^{7} + 63862929 T^{8} - 351016096 T^{9} + 1859742523 T^{10} - 8846921064 T^{11} + 40604855566 T^{12} - 168091500216 T^{13} + 671367050803 T^{14} - 2407619402464 T^{15} + 8322680770209 T^{16} - 25435043574176 T^{17} + 74802198055904 T^{18} - 187977651224744 T^{19} + 453919689396807 T^{20} - 867384531629952 T^{21} + 1600208293286061 T^{22} - 1863844142371504 T^{23} + 2213314919066161 T^{24} \))(\( 1 - 16 T + 268 T^{2} - 2880 T^{3} + 29778 T^{4} - 246976 T^{5} + 1954021 T^{6} - 13358704 T^{7} + 87231249 T^{8} - 508918704 T^{9} + 2843071818 T^{10} - 14422538064 T^{11} + 70182797219 T^{12} - 312256382976 T^{13} + 1333473147161 T^{14} - 5206536241104 T^{15} + 19500629599662 T^{16} - 66322794423984 T^{17} + 215993208417651 T^{18} - 628471998698224 T^{19} + 1746644149312519 T^{20} - 4194532465614016 T^{21} + 9608994264463062 T^{22} - 17657470822466880 T^{23} + 31219389384722692 T^{24} - 35413038705058576 T^{25} + 42052983462257059 T^{26} \))
$23$ (\( 1 + 2 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 5 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 8 T + 42 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 26 T^{2} + 529 T^{4} \))(\( 1 - 4 T + 49 T^{2} - 168 T^{3} + 1127 T^{4} - 2116 T^{5} + 12167 T^{6} \))(\( 1 + 4 T + 23 T^{2} - 16 T^{3} + 529 T^{4} + 2116 T^{5} + 12167 T^{6} \))(\( 1 + 2 T + 52 T^{2} + 82 T^{3} + 1318 T^{4} + 1886 T^{5} + 27508 T^{6} + 24334 T^{7} + 279841 T^{8} \))(\( 1 + 6 T + 58 T^{2} + 330 T^{3} + 1926 T^{4} + 7590 T^{5} + 30682 T^{6} + 73002 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 110 T^{2} + 560 T^{3} + 3998 T^{4} + 12880 T^{5} + 58190 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 + 4 T + 48 T^{2} + 116 T^{3} + 1278 T^{4} + 2668 T^{5} + 25392 T^{6} + 48668 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 96 T^{2} + 574 T^{3} + 4285 T^{4} + 21200 T^{5} + 130460 T^{6} + 585898 T^{7} + 3233116 T^{8} + 13475654 T^{9} + 69013340 T^{10} + 257940400 T^{11} + 1199118685 T^{12} + 3694460882 T^{13} + 14211445344 T^{14} + 27238603576 T^{15} + 78310985281 T^{16} \))(\( 1 - 2 T + 102 T^{2} - 170 T^{3} + 5031 T^{4} - 8896 T^{5} + 169283 T^{6} - 342854 T^{7} + 4503033 T^{8} - 9370140 T^{9} + 103569759 T^{10} - 181369766 T^{11} + 2059666261 T^{12} - 2489465536 T^{13} + 32381241633 T^{14} - 25166101130 T^{15} + 347292195594 T^{16} - 156621970562 T^{17} + 1801152661463 T^{18} \))(\( 1 + 14 T + 244 T^{2} + 2264 T^{3} + 23527 T^{4} + 171320 T^{5} + 1369928 T^{6} + 8514454 T^{7} + 57362923 T^{8} + 314751856 T^{9} + 1850915772 T^{10} + 9072435224 T^{11} + 47464514058 T^{12} + 208666010152 T^{13} + 979134443388 T^{14} + 3829585831952 T^{15} + 16052497735243 T^{16} + 54801946401722 T^{17} + 202798509345992 T^{18} + 583314695580040 T^{19} + 1842422550706087 T^{20} + 4077809625552232 T^{21} + 10108068736130356 T^{22} + 13339336610794978 T^{23} + 21914624432020321 T^{24} \))(\( 1 - 18 T + 281 T^{2} - 3306 T^{3} + 33759 T^{4} - 303440 T^{5} + 2461491 T^{6} - 18254162 T^{7} + 125170815 T^{8} - 797177646 T^{9} + 4751393631 T^{10} - 26531291140 T^{11} + 139356005780 T^{12} - 688627179424 T^{13} + 3205188132940 T^{14} - 14035053013060 T^{15} + 57810206308377 T^{16} - 223082989634286 T^{17} + 805642298929545 T^{18} - 2702271099620018 T^{19} + 8380947194361477 T^{20} - 23762685373666640 T^{21} + 60805112698329417 T^{22} - 136956046072323594 T^{23} + 267739541973813487 T^{24} - 394463239776365778 T^{25} + 504036361936467383 T^{26} \))
$29$ (\( 1 + 3 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 7 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 53 T^{2} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( 1 + 13 T + 111 T^{2} + 642 T^{3} + 3219 T^{4} + 10933 T^{5} + 24389 T^{6} \))(\( 1 + 17 T + 153 T^{2} + 936 T^{3} + 4437 T^{4} + 14297 T^{5} + 24389 T^{6} \))(\( ( 1 - 4 T + 42 T^{2} - 116 T^{3} + 841 T^{4} )^{2} \))(\( 1 + 14 T + 122 T^{2} + 772 T^{3} + 4135 T^{4} + 22388 T^{5} + 102602 T^{6} + 341446 T^{7} + 707281 T^{8} \))(\( 1 - 8 T + 36 T^{2} - 132 T^{3} + 1045 T^{4} - 3828 T^{5} + 30276 T^{6} - 195112 T^{7} + 707281 T^{8} \))(\( 1 + 18 T + 225 T^{2} + 1826 T^{3} + 11576 T^{4} + 52954 T^{5} + 189225 T^{6} + 439002 T^{7} + 707281 T^{8} \))(\( 1 - 20 T + 301 T^{2} - 3040 T^{3} + 25479 T^{4} - 171624 T^{5} + 1027640 T^{6} - 5570800 T^{7} + 30043906 T^{8} - 161553200 T^{9} + 864245240 T^{10} - 4185737736 T^{11} + 18020812599 T^{12} - 62353892960 T^{13} + 179041819621 T^{14} - 344997526180 T^{15} + 500246412961 T^{16} \))(\( 1 - 18 T + 269 T^{2} - 2518 T^{3} + 21323 T^{4} - 138552 T^{5} + 897387 T^{6} - 4941534 T^{7} + 29325628 T^{8} - 151665492 T^{9} + 850443212 T^{10} - 4155830094 T^{11} + 21886371543 T^{12} - 97995197112 T^{13} + 437359230127 T^{14} - 1497765122278 T^{15} + 4640216727121 T^{16} - 9004435433298 T^{17} + 14507145975869 T^{18} \))(\( 1 - 14 T + 264 T^{2} - 2638 T^{3} + 31540 T^{4} - 260510 T^{5} + 2422814 T^{6} - 17170302 T^{7} + 133571644 T^{8} - 831267018 T^{9} + 5601858552 T^{10} - 30863724854 T^{11} + 183138331706 T^{12} - 895048020766 T^{13} + 4711163042232 T^{14} - 20273771302002 T^{15} + 94472685939964 T^{16} - 352182622696998 T^{17} + 1441146269645294 T^{18} - 4493765277257590 T^{19} + 15777771864789940 T^{20} - 38269851084342422 T^{21} + 111066709591253064 T^{22} - 170807136719881606 T^{23} + 353814783205469041 T^{24} \))(\( 1 - 8 T + 257 T^{2} - 2274 T^{3} + 34244 T^{4} - 295418 T^{5} + 3075772 T^{6} - 23969200 T^{7} + 200540380 T^{8} - 1378527222 T^{9} + 9793335244 T^{10} - 59459255774 T^{11} + 366126101218 T^{12} - 1965003767312 T^{13} + 10617656935322 T^{14} - 50005234105934 T^{15} + 238849653265916 T^{16} - 975006112103382 T^{17} + 4113313614696620 T^{18} - 14257439145713200 T^{19} + 53056686554685548 T^{20} - 147781794824112698 T^{21} + 496782706797658036 T^{22} - 956688248524657074 T^{23} + 3135531009786398053 T^{24} - 2830518265643752328 T^{25} + 10260628712958602189 T^{26} \))
$31$ (\( 1 + 4 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( 1 + 8 T + 73 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + 12 T + 98 T^{2} + 530 T^{3} + 3038 T^{4} + 11532 T^{5} + 29791 T^{6} \))(\( 1 + 6 T + 95 T^{2} + 368 T^{3} + 2945 T^{4} + 5766 T^{5} + 29791 T^{6} \))(\( 1 + 8 T + 113 T^{2} + 586 T^{3} + 4960 T^{4} + 18166 T^{5} + 108593 T^{6} + 238328 T^{7} + 923521 T^{8} \))(\( 1 + 2 T + 118 T^{2} + 174 T^{3} + 5390 T^{4} + 5394 T^{5} + 113398 T^{6} + 59582 T^{7} + 923521 T^{8} \))(\( 1 + 8 T + 102 T^{2} + 552 T^{3} + 4438 T^{4} + 17112 T^{5} + 98022 T^{6} + 238328 T^{7} + 923521 T^{8} \))(\( 1 + 8 T + 31 T^{2} - 60 T^{3} - 1252 T^{4} - 1860 T^{5} + 29791 T^{6} + 238328 T^{7} + 923521 T^{8} \))(\( 1 - 18 T + 257 T^{2} - 2472 T^{3} + 22255 T^{4} - 165226 T^{5} + 1189712 T^{6} - 7347290 T^{7} + 43961322 T^{8} - 227765990 T^{9} + 1143313232 T^{10} - 4922247766 T^{11} + 20552959855 T^{12} - 70771261272 T^{13} + 228088446017 T^{14} - 495227053998 T^{15} + 852891037441 T^{16} \))(\( 1 - 6 T + 153 T^{2} - 896 T^{3} + 11671 T^{4} - 61590 T^{5} + 589229 T^{6} - 2767300 T^{7} + 22355870 T^{8} - 95509856 T^{9} + 693031970 T^{10} - 2659375300 T^{11} + 17553721139 T^{12} - 56879658390 T^{13} + 334130821321 T^{14} - 795203298176 T^{15} + 4209429958983 T^{16} - 5117346224646 T^{17} + 26439622160671 T^{18} \))(\( 1 - 26 T + 547 T^{2} - 8198 T^{3} + 106345 T^{4} - 1163148 T^{5} + 11421262 T^{6} - 99743564 T^{7} + 798152525 T^{8} - 5816402750 T^{9} + 39279992855 T^{10} - 244266556194 T^{11} + 1414933329258 T^{12} - 7572263242014 T^{13} + 37748073133655 T^{14} - 173276454325250 T^{15} + 737110618040525 T^{16} - 2855573555034164 T^{17} + 10136412066665422 T^{18} - 32001242077981428 T^{19} + 90700697376663145 T^{20} - 216752022473180858 T^{21} + 448336672978498147 T^{22} - 660620399306525606 T^{23} + 787662783788549761 T^{24} \))(\( 1 - 32 T + 666 T^{2} - 9564 T^{3} + 108410 T^{4} - 976340 T^{5} + 7313971 T^{6} - 45406772 T^{7} + 243247527 T^{8} - 1152371368 T^{9} + 5449230586 T^{10} - 27819669584 T^{11} + 159739329413 T^{12} - 902314296936 T^{13} + 4951919211803 T^{14} - 26734702470224 T^{15} + 162338028387526 T^{16} - 1064239158146728 T^{17} + 6963970180859577 T^{18} - 40298677292327732 T^{19} + 201226461742044781 T^{20} - 832711635495145940 T^{21} + 2866319438438343110 T^{22} - 7838924936684380764 T^{23} + 16922045613005617446 T^{24} - 25205209081233592352 T^{25} + 24417546297445042591 T^{26} \))
$37$ (\( 1 + 8 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( ( 1 - 8 T + 37 T^{2} )^{2} \))(\( 1 + 3 T + 65 T^{2} + 111 T^{3} + 1369 T^{4} \))(\( 1 + 13 T + 140 T^{2} + 870 T^{3} + 5180 T^{4} + 17797 T^{5} + 50653 T^{6} \))(\( 1 + 4 T + 83 T^{2} + 264 T^{3} + 3071 T^{4} + 5476 T^{5} + 50653 T^{6} \))(\( 1 + 11 T + 149 T^{2} + 957 T^{3} + 7764 T^{4} + 35409 T^{5} + 203981 T^{6} + 557183 T^{7} + 1874161 T^{8} \))(\( ( 1 + 4 T + 58 T^{2} + 148 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 37 T^{2} )^{4} \))(\( 1 - 7 T + 83 T^{2} - 297 T^{3} + 2892 T^{4} - 10989 T^{5} + 113627 T^{6} - 354571 T^{7} + 1874161 T^{8} \))(\( 1 + 7 T + 217 T^{2} + 1221 T^{3} + 21770 T^{4} + 103307 T^{5} + 1368751 T^{6} + 5552353 T^{7} + 59865450 T^{8} + 205437061 T^{9} + 1873820119 T^{10} + 5232809471 T^{11} + 40800484970 T^{12} + 84668971497 T^{13} + 556762630753 T^{14} + 664523139931 T^{15} + 3512479453921 T^{16} \))(\( 1 - 11 T + 254 T^{2} - 2422 T^{3} + 30535 T^{4} - 249560 T^{5} + 2290849 T^{6} - 15980026 T^{7} + 118475221 T^{8} - 703375642 T^{9} + 4383583177 T^{10} - 21876655594 T^{11} + 116038374397 T^{12} - 467715619160 T^{13} + 2117417726995 T^{14} - 6214189362598 T^{15} + 24112696791782 T^{16} - 38637273993131 T^{17} + 129961739795077 T^{18} \))(\( 1 - 15 T + 371 T^{2} - 4249 T^{3} + 60460 T^{4} - 568993 T^{5} + 5993263 T^{6} - 48372815 T^{7} + 415375767 T^{8} - 2952574278 T^{9} + 21748879462 T^{10} - 138145122794 T^{11} + 898969143960 T^{12} - 5111369543378 T^{13} + 29774215983478 T^{14} - 149556744903534 T^{15} + 778481062856487 T^{16} - 3354362403328955 T^{17} + 15377073155182567 T^{18} - 54015573565537069 T^{19} + 212364507784063660 T^{20} - 552207432389282173 T^{21} + 1783984802167021979 T^{22} - 2668764326691906195 T^{23} + 6582952005840035281 T^{24} \))(\( 1 + 3 T + 160 T^{2} - 366 T^{3} + 10435 T^{4} - 90710 T^{5} + 670307 T^{6} - 6580934 T^{7} + 51746890 T^{8} - 332137171 T^{9} + 2890344233 T^{10} - 16941169308 T^{11} + 116257378150 T^{12} - 736847956500 T^{13} + 4301522991550 T^{14} - 23192460782652 T^{15} + 146404606434149 T^{16} - 622478532538531 T^{17} + 3588334115043730 T^{18} - 16884876159686006 T^{19} + 63633501765389831 T^{20} - 318617011265173910 T^{21} + 1356150754761628495 T^{22} - 1759941880304932734 T^{23} + 28466819484713666080 T^{24} + 19748856017520105843 T^{25} + \)\(24\!\cdots\!97\)\( T^{26} \))
$41$ (\( 1 - 5 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - T + 41 T^{2} \))(\( 1 + 11 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( ( 1 + 9 T + 41 T^{2} )^{2} \))(\( 1 - 2 T + 78 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 + 7 T + 89 T^{2} + 338 T^{3} + 3649 T^{4} + 11767 T^{5} + 68921 T^{6} \))(\( 1 + T + 115 T^{2} + 78 T^{3} + 4715 T^{4} + 1681 T^{5} + 68921 T^{6} \))(\( 1 - 6 T + 116 T^{2} - 442 T^{3} + 5846 T^{4} - 18122 T^{5} + 194996 T^{6} - 413526 T^{7} + 2825761 T^{8} \))(\( 1 + 54 T^{2} - 120 T^{3} + 2271 T^{4} - 4920 T^{5} + 90774 T^{6} + 2825761 T^{8} \))(\( 1 + 4 T + 106 T^{2} + 528 T^{3} + 5411 T^{4} + 21648 T^{5} + 178186 T^{6} + 275684 T^{7} + 2825761 T^{8} \))(\( 1 + 8 T + 69 T^{2} - 14 T^{3} + 228 T^{4} - 574 T^{5} + 115989 T^{6} + 551368 T^{7} + 2825761 T^{8} \))(\( 1 - 12 T + 189 T^{2} - 1046 T^{3} + 9990 T^{4} - 31830 T^{5} + 485027 T^{6} - 2224088 T^{7} + 27559314 T^{8} - 91187608 T^{9} + 815330387 T^{10} - 2193755430 T^{11} + 28229352390 T^{12} - 121185586246 T^{13} + 897769701549 T^{14} - 2337051286572 T^{15} + 7984925229121 T^{16} \))(\( 1 - 18 T + 354 T^{2} - 4312 T^{3} + 51123 T^{4} - 477280 T^{5} + 4275321 T^{6} - 32743240 T^{7} + 241418057 T^{8} - 1573224796 T^{9} + 9898140337 T^{10} - 55041386440 T^{11} + 294659398641 T^{12} - 1348679210080 T^{13} + 5922916563723 T^{14} - 20482449487192 T^{15} + 68943012953874 T^{16} - 143728654124178 T^{17} + 327381934393961 T^{18} \))(\( 1 + 2 T + 118 T^{2} - 326 T^{3} + 8923 T^{4} - 36660 T^{5} + 710750 T^{6} - 2786744 T^{7} + 40275739 T^{8} - 194404514 T^{9} + 2032738764 T^{10} - 9040665806 T^{11} + 93927876882 T^{12} - 370667298046 T^{13} + 3417033862284 T^{14} - 13398553509394 T^{15} + 113809612512379 T^{16} - 322861572999544 T^{17} + 3376136589290750 T^{18} - 7139691680477460 T^{19} + 71249487819446683 T^{20} - 106726510612431286 T^{21} + 1583873798597983318 T^{22} + 1100658063432496882 T^{23} + 22563490300366186081 T^{24} \))(\( 1 - 24 T + 527 T^{2} - 8188 T^{3} + 114637 T^{4} - 1369284 T^{5} + 15007105 T^{6} - 148396356 T^{7} + 1365373845 T^{8} - 11605117704 T^{9} + 92573162899 T^{10} - 689681040768 T^{11} + 4844590450162 T^{12} - 31923164193848 T^{13} + 198628208456642 T^{14} - 1159353829531008 T^{15} + 6380234960161979 T^{16} - 32793289008372744 T^{17} + 158187026626462845 T^{18} - 704898159984545796 T^{19} + 2922697837330924505 T^{20} - 10933630357431719364 T^{21} + 37530082813120507157 T^{22} - \)\(10\!\cdots\!88\)\( T^{23} + \)\(29\!\cdots\!07\)\( T^{24} - \)\(54\!\cdots\!44\)\( T^{25} + \)\(92\!\cdots\!21\)\( T^{26} \))
$43$ (\( 1 - 4 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( 1 + 14 T + 115 T^{2} + 602 T^{3} + 1849 T^{4} \))(\( 1 + 16 T + 202 T^{2} + 1450 T^{3} + 8686 T^{4} + 29584 T^{5} + 79507 T^{6} \))(\( 1 - 6 T + 101 T^{2} - 380 T^{3} + 4343 T^{4} - 11094 T^{5} + 79507 T^{6} \))(\( 1 - 14 T + 229 T^{2} - 1882 T^{3} + 16012 T^{4} - 80926 T^{5} + 423421 T^{6} - 1113098 T^{7} + 3418801 T^{8} \))(\( 1 + 14 T + 98 T^{2} + 330 T^{3} + 1446 T^{4} + 14190 T^{5} + 181202 T^{6} + 1113098 T^{7} + 3418801 T^{8} \))(\( 1 - 8 T + 150 T^{2} - 880 T^{3} + 9518 T^{4} - 37840 T^{5} + 277350 T^{6} - 636056 T^{7} + 3418801 T^{8} \))(\( 1 + 18 T + 209 T^{2} + 1558 T^{3} + 10968 T^{4} + 66994 T^{5} + 386441 T^{6} + 1431126 T^{7} + 3418801 T^{8} \))(\( 1 + 8 T + 197 T^{2} + 1054 T^{3} + 16890 T^{4} + 71282 T^{5} + 1055955 T^{6} + 4085524 T^{7} + 52913706 T^{8} + 175677532 T^{9} + 1952460795 T^{10} + 5667417974 T^{11} + 57743548890 T^{12} + 154946898922 T^{13} + 1245308520653 T^{14} + 2174548888856 T^{15} + 11688200277601 T^{16} \))(\( 1 + 10 T + 196 T^{2} + 872 T^{3} + 10465 T^{4} - 11080 T^{5} + 176697 T^{6} - 2882664 T^{7} + 4220119 T^{8} - 136800580 T^{9} + 181465117 T^{10} - 5330045736 T^{11} + 14048648379 T^{12} - 37880315080 T^{13} + 1538443355995 T^{14} + 5512228578728 T^{15} + 53276447776972 T^{16} + 116882002776010 T^{17} + 502592611936843 T^{18} \))(\( 1 - 8 T + 307 T^{2} - 1994 T^{3} + 44142 T^{4} - 237906 T^{5} + 4083763 T^{6} - 18693220 T^{7} + 281389223 T^{8} - 1122646572 T^{9} + 15650263074 T^{10} - 55988114880 T^{11} + 730515926580 T^{12} - 2407488939840 T^{13} + 28937336423826 T^{14} - 89258261000004 T^{15} + 962013756981623 T^{16} - 2748061166856460 T^{17} + 25814948529073387 T^{18} - 64667278494021942 T^{19} + 515940536653863342 T^{20} - 1002169668202064942 T^{21} + 6634725070178264443 T^{22} - 7434349915769781656 T^{23} + 39959630797262576401 T^{24} \))(\( 1 + 2 T + 286 T^{2} + 644 T^{3} + 44391 T^{4} + 100972 T^{5} + 4762029 T^{6} + 10557892 T^{7} + 387156688 T^{8} + 816924734 T^{9} + 24974157159 T^{10} + 49195107608 T^{11} + 1308531680386 T^{12} + 2361238468456 T^{13} + 56266862256598 T^{14} + 90961753967192 T^{15} + 1985620313240613 T^{16} + 2792903097523934 T^{17} + 56915301899916784 T^{18} + 66740268364132708 T^{19} + 1294408108831256103 T^{20} + 1180180958429928172 T^{21} + 22310588636488397613 T^{22} + 13917794609755056356 T^{23} + \)\(26\!\cdots\!02\)\( T^{24} + 79919261594525152802 T^{25} + \)\(17\!\cdots\!43\)\( T^{26} \))
$47$ (\( 1 + 8 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 6 T + 58 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 + 10 T + 99 T^{2} + 470 T^{3} + 2209 T^{4} \))(\( 1 - 10 T + 124 T^{2} - 678 T^{3} + 5828 T^{4} - 22090 T^{5} + 103823 T^{6} \))(\( 1 - 2 T + 45 T^{2} - 348 T^{3} + 2115 T^{4} - 4418 T^{5} + 103823 T^{6} \))(\( 1 - 26 T + 425 T^{2} - 4570 T^{3} + 36748 T^{4} - 214790 T^{5} + 938825 T^{6} - 2699398 T^{7} + 4879681 T^{8} \))(\( 1 - 8 T + 72 T^{2} - 480 T^{3} + 1946 T^{4} - 22560 T^{5} + 159048 T^{6} - 830584 T^{7} + 4879681 T^{8} \))(\( 1 + 12 T + 196 T^{2} + 1364 T^{3} + 13042 T^{4} + 64108 T^{5} + 432964 T^{6} + 1245876 T^{7} + 4879681 T^{8} \))(\( 1 + 16 T + 259 T^{2} + 2348 T^{3} + 19920 T^{4} + 110356 T^{5} + 572131 T^{6} + 1661168 T^{7} + 4879681 T^{8} \))(\( 1 - 30 T + 615 T^{2} - 8800 T^{3} + 102782 T^{4} - 987276 T^{5} + 8382105 T^{6} - 63473482 T^{7} + 451752642 T^{8} - 2983253654 T^{9} + 18516069945 T^{10} - 102501956148 T^{11} + 501543372542 T^{12} - 2018236061600 T^{13} + 6629217427335 T^{14} - 15198693613890 T^{15} + 23811286661761 T^{16} \))(\( 1 + 20 T + 434 T^{2} + 5756 T^{3} + 77279 T^{4} + 794248 T^{5} + 8055739 T^{6} + 67353796 T^{7} + 551888765 T^{8} + 3827019080 T^{9} + 25938771955 T^{10} + 148784535364 T^{11} + 836370990197 T^{12} + 3875676874888 T^{13} + 17723552795953 T^{14} + 62045163433724 T^{15} + 219874434280942 T^{16} + 476225733235220 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 6 T + 321 T^{2} + 1714 T^{3} + 50816 T^{4} + 245782 T^{5} + 5310121 T^{6} + 23764226 T^{7} + 414761391 T^{8} + 1736438204 T^{9} + 25866207606 T^{10} + 100848531492 T^{11} + 1331382964384 T^{12} + 4739880980124 T^{13} + 57138452601654 T^{14} + 180282223653892 T^{15} + 2023903279196271 T^{16} + 5450206578319582 T^{17} + 57238937682044809 T^{18} + 124518843793637066 T^{19} + 1209994343004046976 T^{20} + 1918189630898142638 T^{21} + 16884321447701445729 T^{22} + 14832955290504073818 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 - 26 T + 476 T^{2} - 6224 T^{3} + 73815 T^{4} - 751524 T^{5} + 7216961 T^{6} - 61657216 T^{7} + 508454170 T^{8} - 3839940326 T^{9} + 28635107119 T^{10} - 199893627952 T^{11} + 1418279873626 T^{12} - 9597659887032 T^{13} + 66659154060422 T^{14} - 441565024145968 T^{15} + 2972982726415937 T^{16} - 18737683849916006 T^{17} + 116611425177829190 T^{18} - 664616407850664064 T^{19} + 3656279302079772943 T^{20} - 17894753397193273764 T^{21} + 82608615872080746105 T^{22} - \)\(32\!\cdots\!76\)\( T^{23} + \)\(11\!\cdots\!28\)\( T^{24} - \)\(30\!\cdots\!66\)\( T^{25} + \)\(54\!\cdots\!27\)\( T^{26} \))
$53$ (\( 1 - T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 + T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 13 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 16 T + 165 T^{2} + 848 T^{3} + 2809 T^{4} \))(\( 1 - 3 T + 47 T^{2} - 159 T^{3} + 2809 T^{4} \))(\( 1 - 2 T + 23 T^{2} - 199 T^{3} + 1219 T^{4} - 5618 T^{5} + 148877 T^{6} \))(\( 1 + 15 T + 159 T^{2} + 1306 T^{3} + 8427 T^{4} + 42135 T^{5} + 148877 T^{6} \))(\( 1 - 3 T - 23 T^{2} - 213 T^{3} + 4588 T^{4} - 11289 T^{5} - 64607 T^{6} - 446631 T^{7} + 7890481 T^{8} \))(\( 1 + 2 T + 86 T^{2} + 316 T^{3} + 6499 T^{4} + 16748 T^{5} + 241574 T^{6} + 297754 T^{7} + 7890481 T^{8} \))(\( 1 + 4 T + 172 T^{2} + 508 T^{3} + 12813 T^{4} + 26924 T^{5} + 483148 T^{6} + 595508 T^{7} + 7890481 T^{8} \))(\( 1 - 11 T + 250 T^{2} - 1792 T^{3} + 20893 T^{4} - 94976 T^{5} + 702250 T^{6} - 1637647 T^{7} + 7890481 T^{8} \))(\( 1 + 5 T + 182 T^{2} + 684 T^{3} + 19035 T^{4} + 68334 T^{5} + 1460550 T^{6} + 4926557 T^{7} + 87135696 T^{8} + 261107521 T^{9} + 4102684950 T^{10} + 10173360918 T^{11} + 150195305835 T^{12} + 286045717212 T^{13} + 4033913725478 T^{14} + 5873555699185 T^{15} + 62259690411361 T^{16} \))(\( 1 + 7 T + 305 T^{2} + 1733 T^{3} + 43573 T^{4} + 212104 T^{5} + 3999425 T^{6} + 17151299 T^{7} + 269626512 T^{8} + 1031550466 T^{9} + 14290205136 T^{10} + 48177998891 T^{11} + 595422395725 T^{12} + 1673602582024 T^{13} + 18222032216489 T^{14} + 38410837836557 T^{15} + 358286897650285 T^{16} + 435817832879527 T^{17} + 3299763591802133 T^{18} \))(\( 1 - T + 453 T^{2} - 257 T^{3} + 100405 T^{4} - 29798 T^{5} + 14381034 T^{6} - 1939180 T^{7} + 1479105845 T^{8} - 68864311 T^{9} + 114861409425 T^{10} - 1069492365 T^{11} + 6897740428042 T^{12} - 56683095345 T^{13} + 322645699074825 T^{14} - 10252312028747 T^{15} + 11670856566961445 T^{16} - 810956336115740 T^{17} + 318746430984427386 T^{18} - 35004042544862926 T^{19} + 6251184215752701205 T^{20} - 848039243093148181 T^{21} + 79224024075577411197 T^{22} - 9269035929372191597 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 + 27 T + 616 T^{2} + 9626 T^{3} + 131062 T^{4} + 1475683 T^{5} + 14916867 T^{6} + 132631696 T^{7} + 1086939077 T^{8} + 8103582909 T^{9} + 57699524838 T^{10} + 390091387382 T^{11} + 2692887174231 T^{12} + 18878676414922 T^{13} + 142723020234243 T^{14} + 1095766707156038 T^{15} + 8590132159306926 T^{16} + 63941166975389229 T^{17} + 454553023166979961 T^{18} + 2939696807295744784 T^{19} + 17523009836366930679 T^{20} + 91875566725308434563 T^{21} + \)\(43\!\cdots\!46\)\( T^{22} + \)\(16\!\cdots\!74\)\( T^{23} + \)\(57\!\cdots\!52\)\( T^{24} + \)\(13\!\cdots\!07\)\( T^{25} + \)\(26\!\cdots\!73\)\( T^{26} \))
$59$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{8} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{12} \))(\( ( 1 - T )^{13} \))
$61$ (\( 1 - 14 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( 1 + 8 T + 133 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( 1 + 2 T + 64 T^{2} + 572 T^{3} + 3904 T^{4} + 7442 T^{5} + 226981 T^{6} \))(\( 1 + 4 T + 155 T^{2} + 456 T^{3} + 9455 T^{4} + 14884 T^{5} + 226981 T^{6} \))(\( 1 + 46 T + 1021 T^{2} + 14102 T^{3} + 132196 T^{4} + 860222 T^{5} + 3799141 T^{6} + 10441126 T^{7} + 13845841 T^{8} \))(\( 1 + 10 T + 274 T^{2} + 1850 T^{3} + 25966 T^{4} + 112850 T^{5} + 1019554 T^{6} + 2269810 T^{7} + 13845841 T^{8} \))(\( 1 - 4 T + 154 T^{2} - 604 T^{3} + 13070 T^{4} - 36844 T^{5} + 573034 T^{6} - 907924 T^{7} + 13845841 T^{8} \))(\( 1 + 20 T + 363 T^{2} + 3772 T^{3} + 36252 T^{4} + 230092 T^{5} + 1350723 T^{6} + 4539620 T^{7} + 13845841 T^{8} \))(\( 1 - 12 T + 145 T^{2} - 1270 T^{3} + 14126 T^{4} - 102382 T^{5} + 1141063 T^{6} - 9105672 T^{7} + 84473058 T^{8} - 555445992 T^{9} + 4245895423 T^{10} - 23238768742 T^{11} + 195586349966 T^{12} - 1072637302270 T^{13} + 7470454282345 T^{14} - 37712914032252 T^{15} + 191707312997281 T^{16} \))(\( 1 - 30 T + 860 T^{2} - 15286 T^{3} + 253753 T^{4} - 3235612 T^{5} + 38874855 T^{6} - 385362330 T^{7} + 3633540311 T^{8} - 29042737420 T^{9} + 221645958971 T^{10} - 1433933229930 T^{11} + 8823853462755 T^{12} - 44799769289692 T^{13} + 214318845167653 T^{14} - 787540442482246 T^{15} + 2702758838978060 T^{16} - 5751219389918430 T^{17} + 11694146092834141 T^{18} \))(\( 1 - 30 T + 845 T^{2} - 15312 T^{3} + 259810 T^{4} - 3521908 T^{5} + 45510957 T^{6} - 507323994 T^{7} + 5457925815 T^{8} - 52396647280 T^{9} + 488029577998 T^{10} - 4114740878476 T^{11} + 33710840965484 T^{12} - 250999193587036 T^{13} + 1815958059730558 T^{14} - 11893043396261680 T^{15} + 75569573024285415 T^{16} - 428483968740946194 T^{17} + 2344741542167373477 T^{18} - 11068451136125048068 T^{19} + 49807476989823576610 T^{20} - \)\(17\!\cdots\!92\)\( T^{21} + \)\(60\!\cdots\!45\)\( T^{22} - \)\(13\!\cdots\!30\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 20 T + 544 T^{2} - 8026 T^{3} + 131201 T^{4} - 1574944 T^{5} + 19967157 T^{6} - 207066506 T^{7} + 2242997518 T^{8} - 20813716444 T^{9} + 200734484589 T^{10} - 1692844063148 T^{11} + 14762691756822 T^{12} - 113515846533216 T^{13} + 900524197166142 T^{14} - 6299072758973708 T^{15} + 45562914046495809 T^{16} - 288183408502709404 T^{17} + 1894427406854980918 T^{18} - 10668143906744252666 T^{19} + 62751639617456562297 T^{20} - \)\(30\!\cdots\!64\)\( T^{21} + \)\(15\!\cdots\!41\)\( T^{22} - \)\(57\!\cdots\!26\)\( T^{23} + \)\(23\!\cdots\!84\)\( T^{24} - \)\(53\!\cdots\!20\)\( T^{25} + \)\(16\!\cdots\!81\)\( T^{26} \))
$67$ (\( 1 + 10 T + 67 T^{2} \))(\( 1 + 14 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 11 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 6 T + 98 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 - 16 T + 193 T^{2} - 1072 T^{3} + 4489 T^{4} \))(\( 1 + 2 T + 152 T^{2} + 366 T^{3} + 10184 T^{4} + 8978 T^{5} + 300763 T^{6} \))(\( 1 - 6 T + 173 T^{2} - 668 T^{3} + 11591 T^{4} - 26934 T^{5} + 300763 T^{6} \))(\( 1 + 20 T + 339 T^{2} + 3580 T^{3} + 34512 T^{4} + 239860 T^{5} + 1521771 T^{6} + 6015260 T^{7} + 20151121 T^{8} \))(\( 1 - 10 T + 118 T^{2} - 1190 T^{3} + 14014 T^{4} - 79730 T^{5} + 529702 T^{6} - 3007630 T^{7} + 20151121 T^{8} \))(\( 1 + 16 T + 230 T^{2} + 1560 T^{3} + 15118 T^{4} + 104520 T^{5} + 1032470 T^{6} + 4812208 T^{7} + 20151121 T^{8} \))(\( 1 - 4 T + 175 T^{2} - 624 T^{3} + 16736 T^{4} - 41808 T^{5} + 785575 T^{6} - 1203052 T^{7} + 20151121 T^{8} \))(\( 1 + 4 T + 285 T^{2} + 572 T^{3} + 42221 T^{4} + 42928 T^{5} + 4314514 T^{6} + 2289624 T^{7} + 329961806 T^{8} + 153404808 T^{9} + 19367853346 T^{10} + 12911154064 T^{11} + 850800479741 T^{12} + 772271561204 T^{13} + 25780638918165 T^{14} + 24242846421292 T^{15} + 406067677556641 T^{16} \))(\( 1 - 6 T + 415 T^{2} - 2698 T^{3} + 84967 T^{4} - 545428 T^{5} + 11242261 T^{6} - 66001446 T^{7} + 1045711948 T^{8} - 5329208588 T^{9} + 70062700516 T^{10} - 296280491094 T^{11} + 3381256145143 T^{12} - 10990985624788 T^{13} + 114716079966469 T^{14} - 244056715091962 T^{15} + 2515195316209045 T^{16} - 2436406065339846 T^{17} + 27206534396294947 T^{18} \))(\( 1 - 10 T + 423 T^{2} - 4288 T^{3} + 92721 T^{4} - 931010 T^{5} + 14128236 T^{6} - 135353322 T^{7} + 1647274031 T^{8} - 14617061424 T^{9} + 152224374785 T^{10} - 1230518540338 T^{11} + 11332033650726 T^{12} - 82444742202646 T^{13} + 683335218409865 T^{14} - 4396271245066512 T^{15} + 33194418318838751 T^{16} - 182743918348055454 T^{17} + 1278017371461823884 T^{18} - 5642583111671766230 T^{19} + 37651001130729310161 T^{20} - \)\(11\!\cdots\!36\)\( T^{21} + \)\(77\!\cdots\!27\)\( T^{22} - \)\(12\!\cdots\!30\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 - 4 T + 470 T^{2} - 1112 T^{3} + 104618 T^{4} - 32892 T^{5} + 14488811 T^{6} + 33214400 T^{7} + 1404725659 T^{8} + 7881819756 T^{9} + 104997348282 T^{10} + 978413992360 T^{11} + 6914061187553 T^{12} + 79373387531784 T^{13} + 463242099566051 T^{14} + 4392100411704040 T^{15} + 31579317461339166 T^{16} + 158827503603346476 T^{17} + 1896555380663020513 T^{18} + 3004520888714033600 T^{19} + 87812504975031540953 T^{20} - 13356378050193035772 T^{21} + \)\(28\!\cdots\!46\)\( T^{22} - \)\(20\!\cdots\!88\)\( T^{23} + \)\(57\!\cdots\!10\)\( T^{24} - \)\(32\!\cdots\!44\)\( T^{25} + \)\(54\!\cdots\!87\)\( T^{26} \))
$71$ (\( 1 + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 14 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 14 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 12 T + 158 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( 1 - 10 T + 147 T^{2} - 710 T^{3} + 5041 T^{4} \))(\( 1 - 32 T + 548 T^{2} - 5692 T^{3} + 38908 T^{4} - 161312 T^{5} + 357911 T^{6} \))(\( 1 - 28 T + 397 T^{2} - 3816 T^{3} + 28187 T^{4} - 141148 T^{5} + 357911 T^{6} \))(\( 1 - 10 T + 103 T^{2} - 380 T^{3} + 3588 T^{4} - 26980 T^{5} + 519223 T^{6} - 3579110 T^{7} + 25411681 T^{8} \))(\( 1 + 16 T + 320 T^{2} + 3104 T^{3} + 34414 T^{4} + 220384 T^{5} + 1613120 T^{6} + 5726576 T^{7} + 25411681 T^{8} \))(\( 1 + 20 T + 344 T^{2} + 3860 T^{3} + 38366 T^{4} + 274060 T^{5} + 1734104 T^{6} + 7158220 T^{7} + 25411681 T^{8} \))(\( 1 + 22 T + 321 T^{2} + 3310 T^{3} + 30956 T^{4} + 235010 T^{5} + 1618161 T^{6} + 7874042 T^{7} + 25411681 T^{8} \))(\( 1 - 4 T + 271 T^{2} - 332 T^{3} + 39810 T^{4} - 13948 T^{5} + 4248449 T^{6} + 1104588 T^{7} + 334658746 T^{8} + 78425748 T^{9} + 21416431409 T^{10} - 4992142628 T^{11} + 1011639020610 T^{12} - 599004144532 T^{13} + 34715176942591 T^{14} - 36380480633564 T^{15} + 645753531245761 T^{16} \))(\( 1 - 30 T + 784 T^{2} - 13780 T^{3} + 221345 T^{4} - 2895792 T^{5} + 35299797 T^{6} - 371421676 T^{7} + 3668237899 T^{8} - 31877631204 T^{9} + 260444890829 T^{10} - 1872336668716 T^{11} + 12634185644067 T^{12} - 73586942546352 T^{13} + 399357145697095 T^{14} - 1765221912431380 T^{15} + 7130574204178544 T^{16} - 19372605937372830 T^{17} + 45848500718449031 T^{18} \))(\( 1 - 6 T + 525 T^{2} - 3322 T^{3} + 141004 T^{4} - 879022 T^{5} + 25222521 T^{6} - 149416274 T^{7} + 3312269639 T^{8} - 18233363260 T^{9} + 334942231402 T^{10} - 1679356025828 T^{11} + 26694600815384 T^{12} - 119234277833788 T^{13} + 1688443788497482 T^{14} - 6525921277749860 T^{15} + 84170339452253159 T^{16} - 269581227067858174 T^{17} + 3231012101303384841 T^{18} - 7994810711869173602 T^{19} + 91053830919777284044 T^{20} - \)\(15\!\cdots\!82\)\( T^{21} + \)\(17\!\cdots\!25\)\( T^{22} - \)\(13\!\cdots\!26\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 8 T + 342 T^{2} + 1636 T^{3} + 51441 T^{4} + 144424 T^{5} + 5379051 T^{6} + 11871892 T^{7} + 498066940 T^{8} + 1243759896 T^{9} + 40146192175 T^{10} + 97580161992 T^{11} + 2777632457890 T^{12} + 6343911234928 T^{13} + 197211904510190 T^{14} + 491901596601672 T^{15} + 14368763787546425 T^{16} + 31606029717745176 T^{17} + 898626991910755940 T^{18} + 1520792735879448532 T^{19} + 48923115183113266941 T^{20} + 93262307996637786664 T^{21} + \)\(23\!\cdots\!71\)\( T^{22} + \)\(53\!\cdots\!36\)\( T^{23} + \)\(79\!\cdots\!82\)\( T^{24} + \)\(13\!\cdots\!28\)\( T^{25} + \)\(11\!\cdots\!11\)\( T^{26} \))
$73$ (\( 1 + 16 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 8 T + 73 T^{2} \))(\( 1 - 8 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 - 2 T + 142 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 + 6 T + 75 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( 1 + 6 T + 188 T^{2} + 904 T^{3} + 13724 T^{4} + 31974 T^{5} + 389017 T^{6} \))(\( 1 - 12 T + 257 T^{2} - 1768 T^{3} + 18761 T^{4} - 63948 T^{5} + 389017 T^{6} \))(\( 1 + 16 T + 227 T^{2} + 1372 T^{3} + 13668 T^{4} + 100156 T^{5} + 1209683 T^{6} + 6224272 T^{7} + 28398241 T^{8} \))(\( 1 - 10 T + 242 T^{2} - 1530 T^{3} + 23454 T^{4} - 111690 T^{5} + 1289618 T^{6} - 3890170 T^{7} + 28398241 T^{8} \))(\( 1 + 4 T + 178 T^{2} + 340 T^{3} + 15686 T^{4} + 24820 T^{5} + 948562 T^{6} + 1556068 T^{7} + 28398241 T^{8} \))(\( 1 + 4 T + 207 T^{2} + 692 T^{3} + 21432 T^{4} + 50516 T^{5} + 1103103 T^{6} + 1556068 T^{7} + 28398241 T^{8} \))(\( 1 + 18 T + 557 T^{2} + 7514 T^{3} + 135010 T^{4} + 1445030 T^{5} + 18962823 T^{6} + 164841486 T^{7} + 1706540402 T^{8} + 12033428478 T^{9} + 101052883767 T^{10} + 562141235510 T^{11} + 3834046517410 T^{12} + 15577059949802 T^{13} + 84293164042973 T^{14} + 198853173343746 T^{15} + 806460091894081 T^{16} \))(\( 1 + 400 T^{2} + 872 T^{3} + 79077 T^{4} + 266028 T^{5} + 10618687 T^{6} + 37235608 T^{7} + 1051425123 T^{8} + 3277017640 T^{9} + 76754033979 T^{10} + 198428555032 T^{11} + 4130849760679 T^{12} + 7554727256748 T^{13} + 163932282359661 T^{14} + 131963445324008 T^{15} + 4418959407638800 T^{16} + 58871586708267913 T^{18} \))(\( 1 - 26 T + 821 T^{2} - 13822 T^{3} + 257424 T^{4} - 3277314 T^{5} + 46051925 T^{6} - 480171702 T^{7} + 5644907911 T^{8} - 50859800704 T^{9} + 532261120998 T^{10} - 4327640260624 T^{11} + 41856954693808 T^{12} - 315917739025552 T^{13} + 2836419513798342 T^{14} - 19785327090467968 T^{15} + 160305455279384551 T^{16} - 995430315178661286 T^{17} + 6969232438994056325 T^{18} - 36205793830215865458 T^{19} + \)\(20\!\cdots\!44\)\( T^{20} - \)\(81\!\cdots\!86\)\( T^{21} + \)\(35\!\cdots\!29\)\( T^{22} - \)\(81\!\cdots\!02\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 10 T + 582 T^{2} - 5502 T^{3} + 168075 T^{4} - 1473092 T^{5} + 32003115 T^{6} - 257438430 T^{7} + 4502273508 T^{8} - 33142502022 T^{9} + 496088688477 T^{10} - 3338596229764 T^{11} + 44178945631506 T^{12} - 270618197034712 T^{13} + 3225063031099938 T^{14} - 17791379308412356 T^{15} + 192986933325257109 T^{16} - 941188759763743302 T^{17} + 9333535313351258244 T^{18} - 38959245621104886270 T^{19} + \)\(35\!\cdots\!55\)\( T^{20} - \)\(11\!\cdots\!52\)\( T^{21} + \)\(98\!\cdots\!75\)\( T^{22} - \)\(23\!\cdots\!98\)\( T^{23} + \)\(18\!\cdots\!14\)\( T^{24} - \)\(22\!\cdots\!10\)\( T^{25} + \)\(16\!\cdots\!33\)\( T^{26} \))
$79$ (\( 1 - T + 79 T^{2} \))(\( 1 - T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 - 17 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 7 T + 79 T^{2} \))(\( 1 - 7 T + 79 T^{2} \))(\( 1 - T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 + 14 T + 187 T^{2} + 1106 T^{3} + 6241 T^{4} \))(\( 1 - 11 T + 177 T^{2} - 869 T^{3} + 6241 T^{4} \))(\( 1 + 12 T + 237 T^{2} + 1667 T^{3} + 18723 T^{4} + 74892 T^{5} + 493039 T^{6} \))(\( 1 - 17 T + 261 T^{2} - 2222 T^{3} + 20619 T^{4} - 106097 T^{5} + 493039 T^{6} \))(\( 1 - T + 163 T^{2} - 851 T^{3} + 13708 T^{4} - 67229 T^{5} + 1017283 T^{6} - 493039 T^{7} + 38950081 T^{8} \))(\( 1 + 26 T + 522 T^{2} + 6568 T^{3} + 69255 T^{4} + 518872 T^{5} + 3257802 T^{6} + 12819014 T^{7} + 38950081 T^{8} \))(\( 1 + 12 T + 204 T^{2} + 1516 T^{3} + 18261 T^{4} + 119764 T^{5} + 1273164 T^{6} + 5916468 T^{7} + 38950081 T^{8} \))(\( 1 + 31 T + 610 T^{2} + 7950 T^{3} + 81533 T^{4} + 628050 T^{5} + 3807010 T^{6} + 15284209 T^{7} + 38950081 T^{8} \))(\( 1 + 17 T + 672 T^{2} + 9296 T^{3} + 193495 T^{4} + 2186634 T^{5} + 31287596 T^{6} + 286822203 T^{7} + 3112979816 T^{8} + 22658954037 T^{9} + 195265886636 T^{10} + 1078095840726 T^{11} + 7536645923095 T^{12} + 28604316285104 T^{13} + 163354770110112 T^{14} + 326466452764703 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 29 T + 777 T^{2} - 14373 T^{3} + 233985 T^{4} - 3224718 T^{5} + 39878627 T^{6} - 441075323 T^{7} + 4479272042 T^{8} - 41351651050 T^{9} + 353862491318 T^{10} - 2752751090843 T^{11} + 19661718377453 T^{12} - 125603027302158 T^{13} + 719985041520015 T^{14} - 3493895998203333 T^{15} + 14921437282245543 T^{16} - 43996155487290269 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 11 T + 547 T^{2} + 5925 T^{3} + 155841 T^{4} + 1586030 T^{5} + 29955546 T^{6} + 281260924 T^{7} + 4275435585 T^{8} + 36718875821 T^{9} + 474760587171 T^{10} + 3694320377573 T^{11} + 41927698245050 T^{12} + 291851309828267 T^{13} + 2962980824534211 T^{14} + 18103837815910019 T^{15} + 166528562346032385 T^{16} + 865455725982852676 T^{17} + 7281817455882269466 T^{18} + 30457975769317758770 T^{19} + \)\(23\!\cdots\!01\)\( T^{20} + \)\(71\!\cdots\!75\)\( T^{21} + \)\(51\!\cdots\!47\)\( T^{22} + \)\(82\!\cdots\!69\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 - 35 T + 788 T^{2} - 13780 T^{3} + 206198 T^{4} - 2758711 T^{5} + 34518453 T^{6} - 409171560 T^{7} + 4631528969 T^{8} - 49967627633 T^{9} + 514314224226 T^{10} - 5038400964548 T^{11} + 47353128594203 T^{12} - 428336019297898 T^{13} + 3740897158942037 T^{14} - 31444660419744068 T^{15} + 253576970798162814 T^{16} - 1946243143683188273 T^{17} + 14251475851215322631 T^{18} - 99464473391958182760 T^{19} + \)\(66\!\cdots\!27\)\( T^{20} - \)\(41\!\cdots\!71\)\( T^{21} + \)\(24\!\cdots\!62\)\( T^{22} - \)\(13\!\cdots\!80\)\( T^{23} + \)\(58\!\cdots\!52\)\( T^{24} - \)\(20\!\cdots\!35\)\( T^{25} + \)\(46\!\cdots\!39\)\( T^{26} \))
$83$ (\( 1 + 6 T + 83 T^{2} \))(\( 1 - 18 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 2 T + 42 T^{2} - 166 T^{3} + 6889 T^{4} \))(\( 1 + 5 T + 111 T^{2} + 415 T^{3} + 6889 T^{4} \))(\( 1 + 3 T + 248 T^{2} + 496 T^{3} + 20584 T^{4} + 20667 T^{5} + 571787 T^{6} \))(\( 1 - 2 T + 153 T^{2} - 492 T^{3} + 12699 T^{4} - 13778 T^{5} + 571787 T^{6} \))(\( 1 - T + 109 T^{2} - 473 T^{3} + 13132 T^{4} - 39259 T^{5} + 750901 T^{6} - 571787 T^{7} + 47458321 T^{8} \))(\( 1 - 18 T + 406 T^{2} - 4374 T^{3} + 53214 T^{4} - 363042 T^{5} + 2796934 T^{6} - 10292166 T^{7} + 47458321 T^{8} \))(\( 1 + 16 T + 334 T^{2} + 3848 T^{3} + 41502 T^{4} + 319384 T^{5} + 2300926 T^{6} + 9148592 T^{7} + 47458321 T^{8} \))(\( 1 + 27 T + 449 T^{2} + 4807 T^{3} + 46844 T^{4} + 398981 T^{5} + 3093161 T^{6} + 15438249 T^{7} + 47458321 T^{8} \))(\( 1 - 9 T + 255 T^{2} - 1971 T^{3} + 31025 T^{4} - 180452 T^{5} + 2354790 T^{6} - 9790966 T^{7} + 158803434 T^{8} - 812650178 T^{9} + 16222148310 T^{10} - 103180107724 T^{11} + 1472394409025 T^{12} - 7763849107353 T^{13} + 83369795209095 T^{14} - 244224458906643 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 9 T + 187 T^{2} + 847 T^{3} + 7433 T^{4} + 125246 T^{5} + 2889291 T^{6} + 3848041 T^{7} + 194916836 T^{8} + 1805383478 T^{9} + 16178097388 T^{10} + 26509154449 T^{11} + 1652059033017 T^{12} + 5943964871966 T^{13} + 29278889099419 T^{14} + 276918496243543 T^{15} + 5074441535060249 T^{16} - 20270630089251369 T^{17} + 186940255267540403 T^{18} \))(\( 1 + 21 T + 683 T^{2} + 11831 T^{3} + 227681 T^{4} + 3292394 T^{5} + 48639832 T^{6} + 602279336 T^{7} + 7455134083 T^{8} + 80998178327 T^{9} + 873330483361 T^{10} + 8455930784271 T^{11} + 80994677535854 T^{12} + 701842255094493 T^{13} + 6016373699873929 T^{14} + 46313705391060349 T^{15} + 353808146409054643 T^{16} + 2372402782943053048 T^{17} + 15902324834685434008 T^{18} + 89342571461941997038 T^{19} + \)\(51\!\cdots\!21\)\( T^{20} + \)\(22\!\cdots\!93\)\( T^{21} + \)\(10\!\cdots\!67\)\( T^{22} + \)\(27\!\cdots\!07\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + T + 720 T^{2} + 908 T^{3} + 252436 T^{4} + 353343 T^{5} + 57331819 T^{6} + 82831042 T^{7} + 9467567023 T^{8} + 13448870843 T^{9} + 1208479816668 T^{10} + 1627434752034 T^{11} + 123398352811583 T^{12} + 152538403306826 T^{13} + 10242063283361389 T^{14} + 11211398006762226 T^{15} + 690993048933145716 T^{16} + 638260829554634603 T^{17} + 37293131293923515789 T^{18} + 27080811798023320498 T^{19} + \)\(15\!\cdots\!13\)\( T^{20} + \)\(79\!\cdots\!63\)\( T^{21} + \)\(47\!\cdots\!08\)\( T^{22} + \)\(14\!\cdots\!92\)\( T^{23} + \)\(92\!\cdots\!40\)\( T^{24} + \)\(10\!\cdots\!61\)\( T^{25} + \)\(88\!\cdots\!63\)\( T^{26} \))
$89$ (\( 1 + 14 T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 - 4 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 4 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 - 18 T + 254 T^{2} - 1602 T^{3} + 7921 T^{4} \))(\( 1 + 2 T - T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 + 14 T + 320 T^{2} + 2548 T^{3} + 28480 T^{4} + 110894 T^{5} + 704969 T^{6} \))(\( 1 - 16 T + 231 T^{2} - 1872 T^{3} + 20559 T^{4} - 126736 T^{5} + 704969 T^{6} \))(\( 1 + 6 T + 113 T^{2} + 1486 T^{3} + 5348 T^{4} + 132254 T^{5} + 895073 T^{6} + 4229814 T^{7} + 62742241 T^{8} \))(\( 1 + 16 T + 312 T^{2} + 3288 T^{3} + 37610 T^{4} + 292632 T^{5} + 2471352 T^{6} + 11279504 T^{7} + 62742241 T^{8} \))(\( 1 + 32 T + 664 T^{2} + 9056 T^{3} + 98706 T^{4} + 805984 T^{5} + 5259544 T^{6} + 22559008 T^{7} + 62742241 T^{8} \))(\( 1 - 18 T + 377 T^{2} - 4142 T^{3} + 49316 T^{4} - 368638 T^{5} + 2986217 T^{6} - 12689442 T^{7} + 62742241 T^{8} \))(\( 1 + 12 T + 301 T^{2} + 2174 T^{3} + 28430 T^{4} + 170414 T^{5} + 2097443 T^{6} + 21016344 T^{7} + 220856418 T^{8} + 1870454616 T^{9} + 16613846003 T^{10} + 120136587166 T^{11} + 1783761911630 T^{12} + 12139745242126 T^{13} + 149591368579261 T^{14} + 530776018746348 T^{15} + 3936588805702081 T^{16} \))(\( 1 - 8 T + 302 T^{2} - 3410 T^{3} + 60239 T^{4} - 711596 T^{5} + 8868685 T^{6} - 98494286 T^{7} + 1009140445 T^{8} - 10142158104 T^{9} + 89813499605 T^{10} - 780173239406 T^{11} + 6252147995765 T^{12} - 44647127726636 T^{13} + 336378157148311 T^{14} - 1694706202177010 T^{15} + 13357863138449758 T^{16} - 31492710445616648 T^{17} + 350356403707485209 T^{18} \))(\( 1 + 2 T + 369 T^{2} + 50 T^{3} + 66736 T^{4} - 148054 T^{5} + 8374409 T^{6} - 33799254 T^{7} + 937838159 T^{8} - 3631138492 T^{9} + 103130162870 T^{10} - 271260913292 T^{11} + 10097512554560 T^{12} - 24142221282988 T^{13} + 816894020093270 T^{14} - 2559840071566748 T^{15} + 58842067790974319 T^{16} - 188737043667851046 T^{17} + 4161924595855417049 T^{18} - 6548626056622650566 T^{19} + \)\(26\!\cdots\!16\)\( T^{20} + 17517820185374260450 T^{21} + \)\(11\!\cdots\!69\)\( T^{22} + \)\(55\!\cdots\!78\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 20 T + 850 T^{2} + 12486 T^{3} + 307425 T^{4} + 3533556 T^{5} + 66275561 T^{6} + 622934726 T^{7} + 10087517520 T^{8} + 80939403884 T^{9} + 1216995481829 T^{10} + 8701176690580 T^{11} + 124632503324494 T^{12} + 821026020848408 T^{13} + 11092292795879966 T^{14} + 68922020566084180 T^{15} + 857944087829508301 T^{16} + 5078319584886264044 T^{17} + 56329297524509046480 T^{18} + \)\(30\!\cdots\!86\)\( T^{19} + \)\(29\!\cdots\!69\)\( T^{20} + \)\(13\!\cdots\!36\)\( T^{21} + \)\(10\!\cdots\!25\)\( T^{22} + \)\(38\!\cdots\!86\)\( T^{23} + \)\(23\!\cdots\!50\)\( T^{24} + \)\(49\!\cdots\!20\)\( T^{25} + \)\(21\!\cdots\!69\)\( T^{26} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 - 5 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 16 T + 97 T^{2} \))(\( 1 - 17 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 + 10 T + 174 T^{2} + 970 T^{3} + 9409 T^{4} \))(\( 1 + 27 T + 345 T^{2} + 2619 T^{3} + 9409 T^{4} \))(\( 1 - 15 T + 266 T^{2} - 2410 T^{3} + 25802 T^{4} - 141135 T^{5} + 912673 T^{6} \))(\( 1 - 16 T + 297 T^{2} - 2776 T^{3} + 28809 T^{4} - 150544 T^{5} + 912673 T^{6} \))(\( 1 - 19 T + 309 T^{2} - 3893 T^{3} + 47864 T^{4} - 377621 T^{5} + 2907381 T^{6} - 17340787 T^{7} + 88529281 T^{8} \))(\( 1 + 16 T + 344 T^{2} + 3832 T^{3} + 49674 T^{4} + 371704 T^{5} + 3236696 T^{6} + 14602768 T^{7} + 88529281 T^{8} \))(\( 1 - 24 T + 408 T^{2} - 5496 T^{3} + 61298 T^{4} - 533112 T^{5} + 3838872 T^{6} - 21904152 T^{7} + 88529281 T^{8} \))(\( 1 - 9 T + 209 T^{2} - 1775 T^{3} + 26532 T^{4} - 172175 T^{5} + 1966481 T^{6} - 8214057 T^{7} + 88529281 T^{8} \))(\( 1 + 11 T + 503 T^{2} + 4215 T^{3} + 115409 T^{4} + 724012 T^{5} + 16459682 T^{6} + 81717036 T^{7} + 1764760090 T^{8} + 7926552492 T^{9} + 154869147938 T^{10} + 660786204076 T^{11} + 10217075790929 T^{12} + 36195639183255 T^{13} + 418984918479287 T^{14} + 888781129259243 T^{15} + 7837433594376961 T^{16} \))(\( 1 + 13 T + 329 T^{2} + 3523 T^{3} + 60439 T^{4} + 580574 T^{5} + 7676031 T^{6} + 70350185 T^{7} + 821742080 T^{8} + 7354262258 T^{9} + 79708981760 T^{10} + 661924890665 T^{11} + 7005706240863 T^{12} + 51397798787294 T^{13} + 519010257792823 T^{14} + 2934560373364867 T^{15} + 26582635593299177 T^{16} + 101886636726900493 T^{17} + 760231058654565217 T^{18} \))(\( 1 - 27 T + 721 T^{2} - 12841 T^{3} + 222129 T^{4} - 3091368 T^{5} + 42301152 T^{6} - 491222500 T^{7} + 5721330571 T^{8} - 58641346705 T^{9} + 621415347747 T^{10} - 5960877552271 T^{11} + 61248612374678 T^{12} - 578205122570287 T^{13} + 5846897006951523 T^{14} - 53520373821292465 T^{15} + 506505281813949451 T^{16} - 4218294749394182500 T^{17} + 35235675392246378208 T^{18} - \)\(24\!\cdots\!84\)\( T^{19} + \)\(17\!\cdots\!69\)\( T^{20} - \)\(97\!\cdots\!97\)\( T^{21} + \)\(53\!\cdots\!29\)\( T^{22} - \)\(19\!\cdots\!31\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 + 3 T + 790 T^{2} + 3202 T^{3} + 300226 T^{4} + 1455403 T^{5} + 73842555 T^{6} + 393498292 T^{7} + 13335345967 T^{8} + 73073225497 T^{9} + 1895678973554 T^{10} + 10126088833522 T^{11} + 220623322560795 T^{12} + 1099944951657954 T^{13} + 21400462288397115 T^{14} + 95276369834608498 T^{15} + 1730135015830449842 T^{16} + 6469120113600277657 T^{17} + \)\(11\!\cdots\!19\)\( T^{18} + \)\(32\!\cdots\!68\)\( T^{19} + \)\(59\!\cdots\!15\)\( T^{20} + \)\(11\!\cdots\!83\)\( T^{21} + \)\(22\!\cdots\!42\)\( T^{22} + \)\(23\!\cdots\!98\)\( T^{23} + \)\(56\!\cdots\!70\)\( T^{24} + \)\(20\!\cdots\!23\)\( T^{25} + \)\(67\!\cdots\!77\)\( T^{26} \))
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