Properties

Label 490.6.a
Level 490
Weight 6
Character orbit a
Rep. character \(\chi_{490}(1,\cdot)\)
Character field \(\Q\)
Dimension 67
Newform subspaces 31
Sturm bound 504
Trace bound 3

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Defining parameters

Level: \( N \) = \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 490.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 31 \)
Sturm bound: \(504\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(490))\).

Total New Old
Modular forms 436 67 369
Cusp forms 404 67 337
Eisenstein series 32 0 32

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

\(2\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(11\)
Plus space\(+\)\(31\)
Minus space\(-\)\(36\)

Trace form

\( 67q - 4q^{2} + 40q^{3} + 1072q^{4} + 25q^{5} - 48q^{6} - 64q^{8} + 5155q^{9} + O(q^{10}) \) \( 67q - 4q^{2} + 40q^{3} + 1072q^{4} + 25q^{5} - 48q^{6} - 64q^{8} + 5155q^{9} + 100q^{10} - 1184q^{11} + 640q^{12} + 694q^{13} - 1100q^{15} + 17152q^{16} + 1062q^{17} - 1908q^{18} - 80q^{19} + 400q^{20} - 1456q^{22} + 2880q^{23} - 768q^{24} + 41875q^{25} - 5864q^{26} - 9920q^{27} + 2342q^{29} + 2000q^{30} - 1384q^{31} - 1024q^{32} - 18080q^{33} + 14648q^{34} + 82480q^{36} - 38094q^{37} + 320q^{38} + 16272q^{39} + 1600q^{40} - 30818q^{41} + 61092q^{43} - 18944q^{44} + 8925q^{45} + 33456q^{46} + 39848q^{47} + 10240q^{48} - 2500q^{50} + 50064q^{51} + 11104q^{52} + 21522q^{53} - 61344q^{54} + 10100q^{55} + 264920q^{57} - 86072q^{58} + 37944q^{59} - 17600q^{60} + 50494q^{61} + 87168q^{62} + 274432q^{64} + 16550q^{65} + 21696q^{66} + 83716q^{67} + 16992q^{68} + 14056q^{69} - 44152q^{71} - 30528q^{72} + 62102q^{73} + 33144q^{74} + 25000q^{75} - 1280q^{76} + 14336q^{78} + 460736q^{79} + 6400q^{80} + 423555q^{81} - 21448q^{82} - 82192q^{83} + 5150q^{85} + 40144q^{86} - 450480q^{87} - 23296q^{88} - 202866q^{89} + 111700q^{90} + 46080q^{92} + 173464q^{93} + 102096q^{94} + 18100q^{95} - 12288q^{96} + 116342q^{97} - 953168q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(490))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7
490.6.a.a \(1\) \(78.588\) \(\Q\) None \(-4\) \(-24\) \(-25\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}-24q^{3}+2^{4}q^{4}-5^{2}q^{5}+96q^{6}+\cdots\)
490.6.a.b \(1\) \(78.588\) \(\Q\) None \(-4\) \(-18\) \(25\) \(0\) \(+\) \(-\) \(+\) \(q-4q^{2}-18q^{3}+2^{4}q^{4}+5^{2}q^{5}+72q^{6}+\cdots\)
490.6.a.c \(1\) \(78.588\) \(\Q\) None \(-4\) \(-11\) \(25\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}-11q^{3}+2^{4}q^{4}+5^{2}q^{5}+44q^{6}+\cdots\)
490.6.a.d \(1\) \(78.588\) \(\Q\) None \(-4\) \(-5\) \(-25\) \(0\) \(+\) \(+\) \(+\) \(q-4q^{2}-5q^{3}+2^{4}q^{4}-5^{2}q^{5}+20q^{6}+\cdots\)
490.6.a.e \(1\) \(78.588\) \(\Q\) None \(-4\) \(3\) \(25\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+3q^{3}+2^{4}q^{4}+5^{2}q^{5}-12q^{6}+\cdots\)
490.6.a.f \(1\) \(78.588\) \(\Q\) None \(-4\) \(5\) \(25\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+5q^{3}+2^{4}q^{4}+5^{2}q^{5}-20q^{6}+\cdots\)
490.6.a.g \(1\) \(78.588\) \(\Q\) None \(-4\) \(9\) \(-25\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-5^{2}q^{5}-6^{2}q^{6}+\cdots\)
490.6.a.h \(1\) \(78.588\) \(\Q\) None \(-4\) \(18\) \(-25\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}+18q^{3}+2^{4}q^{4}-5^{2}q^{5}-72q^{6}+\cdots\)
490.6.a.i \(1\) \(78.588\) \(\Q\) None \(-4\) \(23\) \(-25\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}+23q^{3}+2^{4}q^{4}-5^{2}q^{5}-92q^{6}+\cdots\)
490.6.a.j \(1\) \(78.588\) \(\Q\) None \(-4\) \(26\) \(25\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+26q^{3}+2^{4}q^{4}+5^{2}q^{5}-104q^{6}+\cdots\)
490.6.a.k \(1\) \(78.588\) \(\Q\) None \(4\) \(-6\) \(25\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}-6q^{3}+2^{4}q^{4}+5^{2}q^{5}-24q^{6}+\cdots\)
490.6.a.l \(1\) \(78.588\) \(\Q\) None \(4\) \(11\) \(25\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+11q^{3}+2^{4}q^{4}+5^{2}q^{5}+44q^{6}+\cdots\)
490.6.a.m \(1\) \(78.588\) \(\Q\) None \(4\) \(17\) \(-25\) \(0\) \(-\) \(+\) \(-\) \(q+4q^{2}+17q^{3}+2^{4}q^{4}-5^{2}q^{5}+68q^{6}+\cdots\)
490.6.a.n \(2\) \(78.588\) \(\Q(\sqrt{106}) \) None \(-8\) \(-22\) \(-50\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}+(-11+\beta )q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
490.6.a.o \(2\) \(78.588\) \(\Q(\sqrt{337}) \) None \(-8\) \(-20\) \(50\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+(-10-\beta )q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
490.6.a.p \(2\) \(78.588\) \(\Q(\sqrt{79}) \) None \(-8\) \(-6\) \(50\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+(-3+\beta )q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
490.6.a.q \(2\) \(78.588\) \(\Q(\sqrt{79}) \) None \(-8\) \(6\) \(-50\) \(0\) \(+\) \(+\) \(+\) \(q-4q^{2}+(3+\beta )q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
490.6.a.r \(2\) \(78.588\) \(\Q(\sqrt{337}) \) None \(-8\) \(20\) \(-50\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}+(10-\beta )q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
490.6.a.s \(2\) \(78.588\) \(\Q(\sqrt{106}) \) None \(-8\) \(22\) \(50\) \(0\) \(+\) \(-\) \(+\) \(q-4q^{2}+(11+\beta )q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
490.6.a.t \(2\) \(78.588\) \(\Q(\sqrt{46}) \) None \(8\) \(-18\) \(-50\) \(0\) \(-\) \(+\) \(-\) \(q+4q^{2}+(-9+\beta )q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
490.6.a.u \(2\) \(78.588\) \(\Q(\sqrt{1129}) \) None \(8\) \(-5\) \(-50\) \(0\) \(-\) \(+\) \(-\) \(q+4q^{2}+(-2-\beta )q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
490.6.a.v \(2\) \(78.588\) \(\Q(\sqrt{3369}) \) None \(8\) \(-3\) \(50\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+(-1-\beta )q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
490.6.a.w \(2\) \(78.588\) \(\Q(\sqrt{46}) \) None \(8\) \(18\) \(50\) \(0\) \(-\) \(-\) \(+\) \(q+4q^{2}+(9+\beta )q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
490.6.a.x \(3\) \(78.588\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(12\) \(-2\) \(75\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+(-1+\beta _{1})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
490.6.a.y \(3\) \(78.588\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(12\) \(2\) \(-75\) \(0\) \(-\) \(+\) \(-\) \(q+4q^{2}+(1-\beta _{1})q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
490.6.a.z \(4\) \(78.588\) \(\Q(\sqrt{2}, \sqrt{193})\) None \(16\) \(-40\) \(100\) \(0\) \(-\) \(-\) \(+\) \(q+4q^{2}+(-10-\beta _{1})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
490.6.a.ba \(4\) \(78.588\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(16\) \(-23\) \(-100\) \(0\) \(-\) \(+\) \(+\) \(q+4q^{2}+(-6+\beta _{1})q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
490.6.a.bb \(4\) \(78.588\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(16\) \(23\) \(100\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+(6-\beta _{1})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
490.6.a.bc \(4\) \(78.588\) \(\Q(\sqrt{2}, \sqrt{193})\) None \(16\) \(40\) \(-100\) \(0\) \(-\) \(+\) \(+\) \(q+4q^{2}+(10-\beta _{1})q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
490.6.a.bd \(6\) \(78.588\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-24\) \(-4\) \(150\) \(0\) \(+\) \(-\) \(+\) \(q-4q^{2}+(-1-\beta _{2})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
490.6.a.be \(6\) \(78.588\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-24\) \(4\) \(-150\) \(0\) \(+\) \(+\) \(+\) \(q-4q^{2}+(1+\beta _{2})q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(490))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(490)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 - 4 T \))(\( 1 - 4 T \))(\( 1 - 4 T \))(\( ( 1 + 4 T )^{2} \))(\( ( 1 + 4 T )^{2} \))(\( ( 1 + 4 T )^{2} \))(\( ( 1 + 4 T )^{2} \))(\( ( 1 + 4 T )^{2} \))(\( ( 1 + 4 T )^{2} \))(\( ( 1 - 4 T )^{2} \))(\( ( 1 - 4 T )^{2} \))(\( ( 1 - 4 T )^{2} \))(\( ( 1 - 4 T )^{2} \))(\( ( 1 - 4 T )^{3} \))(\( ( 1 - 4 T )^{3} \))(\( ( 1 - 4 T )^{4} \))(\( ( 1 - 4 T )^{4} \))(\( ( 1 - 4 T )^{4} \))(\( ( 1 - 4 T )^{4} \))(\( ( 1 + 4 T )^{6} \))(\( ( 1 + 4 T )^{6} \))
$3$ (\( 1 + 24 T + 243 T^{2} \))(\( 1 + 18 T + 243 T^{2} \))(\( 1 + 11 T + 243 T^{2} \))(\( 1 + 5 T + 243 T^{2} \))(\( 1 - 3 T + 243 T^{2} \))(\( 1 - 5 T + 243 T^{2} \))(\( 1 - 9 T + 243 T^{2} \))(\( 1 - 18 T + 243 T^{2} \))(\( 1 - 23 T + 243 T^{2} \))(\( 1 - 26 T + 243 T^{2} \))(\( 1 + 6 T + 243 T^{2} \))(\( 1 - 11 T + 243 T^{2} \))(\( 1 - 17 T + 243 T^{2} \))(\( 1 + 22 T + 501 T^{2} + 5346 T^{3} + 59049 T^{4} \))(\( 1 + 20 T + 249 T^{2} + 4860 T^{3} + 59049 T^{4} \))(\( 1 + 6 T + 179 T^{2} + 1458 T^{3} + 59049 T^{4} \))(\( 1 - 6 T + 179 T^{2} - 1458 T^{3} + 59049 T^{4} \))(\( 1 - 20 T + 249 T^{2} - 4860 T^{3} + 59049 T^{4} \))(\( 1 - 22 T + 501 T^{2} - 5346 T^{3} + 59049 T^{4} \))(\( 1 + 18 T + 521 T^{2} + 4374 T^{3} + 59049 T^{4} \))(\( 1 + 5 T + 210 T^{2} + 1215 T^{3} + 59049 T^{4} \))(\( 1 + 3 T - 354 T^{2} + 729 T^{3} + 59049 T^{4} \))(\( 1 - 18 T + 521 T^{2} - 4374 T^{3} + 59049 T^{4} \))(\( 1 + 2 T + 292 T^{2} - 1002 T^{3} + 70956 T^{4} + 118098 T^{5} + 14348907 T^{6} \))(\( 1 - 2 T + 292 T^{2} + 1002 T^{3} + 70956 T^{4} - 118098 T^{5} + 14348907 T^{6} \))(\( 1 + 40 T + 1150 T^{2} + 24720 T^{3} + 439227 T^{4} + 6006960 T^{5} + 67906350 T^{6} + 573956280 T^{7} + 3486784401 T^{8} \))(\( 1 + 23 T + 513 T^{2} + 9300 T^{3} + 139410 T^{4} + 2259900 T^{5} + 30292137 T^{6} + 330024861 T^{7} + 3486784401 T^{8} \))(\( 1 - 23 T + 513 T^{2} - 9300 T^{3} + 139410 T^{4} - 2259900 T^{5} + 30292137 T^{6} - 330024861 T^{7} + 3486784401 T^{8} \))(\( 1 - 40 T + 1150 T^{2} - 24720 T^{3} + 439227 T^{4} - 6006960 T^{5} + 67906350 T^{6} - 573956280 T^{7} + 3486784401 T^{8} \))(\( 1 + 4 T + 358 T^{2} + 492 T^{3} + 102596 T^{4} + 56388 T^{5} + 28101636 T^{6} + 13702284 T^{7} + 6058191204 T^{8} + 7059662244 T^{9} + 1248268815558 T^{10} + 3389154437772 T^{11} + 205891132094649 T^{12} \))(\( 1 - 4 T + 358 T^{2} - 492 T^{3} + 102596 T^{4} - 56388 T^{5} + 28101636 T^{6} - 13702284 T^{7} + 6058191204 T^{8} - 7059662244 T^{9} + 1248268815558 T^{10} - 3389154437772 T^{11} + 205891132094649 T^{12} \))
$5$ (\( 1 + 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 + 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 + 25 T \))(\( 1 + 25 T \))(\( 1 + 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 + 25 T \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 - 25 T )^{2} \))(\( ( 1 - 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 - 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 - 25 T )^{2} \))(\( ( 1 - 25 T )^{2} \))(\( ( 1 - 25 T )^{3} \))(\( ( 1 + 25 T )^{3} \))(\( ( 1 - 25 T )^{4} \))(\( ( 1 + 25 T )^{4} \))(\( ( 1 - 25 T )^{4} \))(\( ( 1 + 25 T )^{4} \))(\( ( 1 - 25 T )^{6} \))(\( ( 1 + 25 T )^{6} \))
$7$ 1
$11$ (\( 1 - 132 T + 161051 T^{2} \))(\( 1 + 505 T + 161051 T^{2} \))(\( 1 - 83 T + 161051 T^{2} \))(\( 1 - 198 T + 161051 T^{2} \))(\( 1 - 405 T + 161051 T^{2} \))(\( 1 - 198 T + 161051 T^{2} \))(\( 1 + 187 T + 161051 T^{2} \))(\( 1 + 505 T + 161051 T^{2} \))(\( 1 - 555 T + 161051 T^{2} \))(\( 1 + 768 T + 161051 T^{2} \))(\( 1 - 192 T + 161051 T^{2} \))(\( 1 + 267 T + 161051 T^{2} \))(\( 1 + 715 T + 161051 T^{2} \))(\( 1 - 876 T + 418546 T^{2} - 141080676 T^{3} + 25937424601 T^{4} \))(\( 1 + 860 T + 498577 T^{2} + 138503860 T^{3} + 25937424601 T^{4} \))(\( 1 + 76 T + 322282 T^{2} + 12239876 T^{3} + 25937424601 T^{4} \))(\( 1 + 76 T + 322282 T^{2} + 12239876 T^{3} + 25937424601 T^{4} \))(\( 1 + 860 T + 498577 T^{2} + 138503860 T^{3} + 25937424601 T^{4} \))(\( 1 - 876 T + 418546 T^{2} - 141080676 T^{3} + 25937424601 T^{4} \))(\( 1 + 252 T + 240642 T^{2} + 40584852 T^{3} + 25937424601 T^{4} \))(\( 1 - 415 T + 317458 T^{2} - 66836165 T^{3} + 25937424601 T^{4} \))(\( 1 - 959 T + 544442 T^{2} - 154447909 T^{3} + 25937424601 T^{4} \))(\( 1 + 252 T + 240642 T^{2} + 40584852 T^{3} + 25937424601 T^{4} \))(\( 1 + 144 T + 177588 T^{2} + 83096788 T^{3} + 28600724988 T^{4} + 3734989142544 T^{5} + 4177248169415651 T^{6} \))(\( 1 + 144 T + 177588 T^{2} + 83096788 T^{3} + 28600724988 T^{4} + 3734989142544 T^{5} + 4177248169415651 T^{6} \))(\( 1 + 432 T + 424946 T^{2} + 155685072 T^{3} + 100205028739 T^{4} + 25073236530672 T^{5} + 11022004834496546 T^{6} + 1804571209187561232 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 - 149 T + 190026 T^{2} - 71657169 T^{3} + 47399395810 T^{4} - 11540458724619 T^{5} + 4928785047229626 T^{6} - 622409977242931999 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 - 149 T + 190026 T^{2} - 71657169 T^{3} + 47399395810 T^{4} - 11540458724619 T^{5} + 4928785047229626 T^{6} - 622409977242931999 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 + 432 T + 424946 T^{2} + 155685072 T^{3} + 100205028739 T^{4} + 25073236530672 T^{5} + 11022004834496546 T^{6} + 1804571209187561232 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 - 52 T + 496036 T^{2} - 14909060 T^{3} + 138706644832 T^{4} - 2542152571780 T^{5} + 26545532307181978 T^{6} - 409416213837740780 T^{7} + \)\(35\!\cdots\!32\)\( T^{8} - \)\(62\!\cdots\!60\)\( T^{9} + \)\(33\!\cdots\!36\)\( T^{10} - \)\(56\!\cdots\!52\)\( T^{11} + \)\(17\!\cdots\!01\)\( T^{12} \))(\( 1 - 52 T + 496036 T^{2} - 14909060 T^{3} + 138706644832 T^{4} - 2542152571780 T^{5} + 26545532307181978 T^{6} - 409416213837740780 T^{7} + \)\(35\!\cdots\!32\)\( T^{8} - \)\(62\!\cdots\!60\)\( T^{9} + \)\(33\!\cdots\!36\)\( T^{10} - \)\(56\!\cdots\!52\)\( T^{11} + \)\(17\!\cdots\!01\)\( T^{12} \))
$13$ (\( 1 - 946 T + 371293 T^{2} \))(\( 1 + 897 T + 371293 T^{2} \))(\( 1 - 83 T + 371293 T^{2} \))(\( 1 + 340 T + 371293 T^{2} \))(\( 1 - 391 T + 371293 T^{2} \))(\( 1 - 340 T + 371293 T^{2} \))(\( 1 + 627 T + 371293 T^{2} \))(\( 1 - 897 T + 371293 T^{2} \))(\( 1 - 241 T + 371293 T^{2} \))(\( 1 - 46 T + 371293 T^{2} \))(\( 1 + 1106 T + 371293 T^{2} \))(\( 1 - 1087 T + 371293 T^{2} \))(\( 1 + 331 T + 371293 T^{2} \))(\( 1 - 284 T + 518526 T^{2} - 105447212 T^{3} + 137858491849 T^{4} \))(\( 1 - 1270 T + 982703 T^{2} - 471542110 T^{3} + 137858491849 T^{4} \))(\( 1 + 732 T + 723598 T^{2} + 271786476 T^{3} + 137858491849 T^{4} \))(\( 1 - 732 T + 723598 T^{2} - 271786476 T^{3} + 137858491849 T^{4} \))(\( 1 + 1270 T + 982703 T^{2} + 471542110 T^{3} + 137858491849 T^{4} \))(\( 1 + 284 T + 518526 T^{2} + 105447212 T^{3} + 137858491849 T^{4} \))(\( 1 - 1588 T + 1313406 T^{2} - 589613284 T^{3} + 137858491849 T^{4} \))(\( 1 + 429 T + 754444 T^{2} + 159284697 T^{3} + 137858491849 T^{4} \))(\( 1 - 393 T + 591692 T^{2} - 145918149 T^{3} + 137858491849 T^{4} \))(\( 1 + 1588 T + 1313406 T^{2} + 589613284 T^{3} + 137858491849 T^{4} \))(\( 1 - 288 T + 686016 T^{2} - 240976874 T^{3} + 254712938688 T^{4} - 39703245652512 T^{5} + 51185893014090757 T^{6} \))(\( 1 + 288 T + 686016 T^{2} + 240976874 T^{3} + 254712938688 T^{4} + 39703245652512 T^{5} + 51185893014090757 T^{6} \))(\( 1 + 620 T + 1364814 T^{2} + 630975960 T^{3} + 736096010131 T^{4} + 234276957116280 T^{5} + 188151199694401086 T^{6} + 31735253668736269340 T^{7} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( 1 + 983 T + 1473692 T^{2} + 900421677 T^{3} + 784741488614 T^{4} + 334320265718361 T^{5} + 203160956569936508 T^{6} + 50315732832851214131 T^{7} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( 1 - 983 T + 1473692 T^{2} - 900421677 T^{3} + 784741488614 T^{4} - 334320265718361 T^{5} + 203160956569936508 T^{6} - 50315732832851214131 T^{7} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( 1 - 620 T + 1364814 T^{2} - 630975960 T^{3} + 736096010131 T^{4} - 234276957116280 T^{5} + 188151199694401086 T^{6} - 31735253668736269340 T^{7} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( 1 - 1024 T + 1331556 T^{2} - 1090818548 T^{3} + 1025333968848 T^{4} - 662788445405112 T^{5} + 465340609107443454 T^{6} - \)\(24\!\cdots\!16\)\( T^{7} + \)\(14\!\cdots\!52\)\( T^{8} - \)\(55\!\cdots\!36\)\( T^{9} + \)\(25\!\cdots\!56\)\( T^{10} - \)\(72\!\cdots\!32\)\( T^{11} + \)\(26\!\cdots\!49\)\( T^{12} \))(\( 1 + 1024 T + 1331556 T^{2} + 1090818548 T^{3} + 1025333968848 T^{4} + 662788445405112 T^{5} + 465340609107443454 T^{6} + \)\(24\!\cdots\!16\)\( T^{7} + \)\(14\!\cdots\!52\)\( T^{8} + \)\(55\!\cdots\!36\)\( T^{9} + \)\(25\!\cdots\!56\)\( T^{10} + \)\(72\!\cdots\!32\)\( T^{11} + \)\(26\!\cdots\!49\)\( T^{12} \))
$17$ (\( 1 - 222 T + 1419857 T^{2} \))(\( 1 + 782 T + 1419857 T^{2} \))(\( 1 - 177 T + 1419857 T^{2} \))(\( 1 - 1848 T + 1419857 T^{2} \))(\( 1 + 999 T + 1419857 T^{2} \))(\( 1 + 1848 T + 1419857 T^{2} \))(\( 1 + 1813 T + 1419857 T^{2} \))(\( 1 - 782 T + 1419857 T^{2} \))(\( 1 - 1491 T + 1419857 T^{2} \))(\( 1 + 378 T + 1419857 T^{2} \))(\( 1 + 762 T + 1419857 T^{2} \))(\( 1 - 513 T + 1419857 T^{2} \))(\( 1 - 1699 T + 1419857 T^{2} \))(\( 1 - 516 T + 2768902 T^{2} - 732646212 T^{3} + 2015993900449 T^{4} \))(\( 1 + 250 T + 908827 T^{2} + 354964250 T^{3} + 2015993900449 T^{4} \))(\( 1 - 3012 T + 5096374 T^{2} - 4276609284 T^{3} + 2015993900449 T^{4} \))(\( 1 + 3012 T + 5096374 T^{2} + 4276609284 T^{3} + 2015993900449 T^{4} \))(\( 1 - 250 T + 908827 T^{2} - 354964250 T^{3} + 2015993900449 T^{4} \))(\( 1 + 516 T + 2768902 T^{2} + 732646212 T^{3} + 2015993900449 T^{4} \))(\( 1 - 716 T + 318278 T^{2} - 1016617612 T^{3} + 2015993900449 T^{4} \))(\( 1 + 1319 T + 2082148 T^{2} + 1872791383 T^{3} + 2015993900449 T^{4} \))(\( 1 - 2231 T + 4015832 T^{2} - 3167700967 T^{3} + 2015993900449 T^{4} \))(\( 1 + 716 T + 318278 T^{2} + 1016617612 T^{3} + 2015993900449 T^{4} \))(\( 1 - 1182 T + 2224164 T^{2} - 1631354924 T^{3} + 3157994824548 T^{4} - 2382904790330718 T^{5} + 2862423051509815793 T^{6} \))(\( 1 + 1182 T + 2224164 T^{2} + 1631354924 T^{3} + 3157994824548 T^{4} + 2382904790330718 T^{5} + 2862423051509815793 T^{6} \))(\( 1 + 2260 T + 6689558 T^{2} + 9325180360 T^{3} + 14902549646075 T^{4} + 13240422610408520 T^{5} + 13486108124699811542 T^{6} + \)\(64\!\cdots\!80\)\( T^{7} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( 1 + 218 T + 2775480 T^{2} + 952184262 T^{3} + 5551636110286 T^{4} + 1351965489690534 T^{5} + 5595350750818190520 T^{6} + \)\(62\!\cdots\!74\)\( T^{7} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( 1 - 218 T + 2775480 T^{2} - 952184262 T^{3} + 5551636110286 T^{4} - 1351965489690534 T^{5} + 5595350750818190520 T^{6} - \)\(62\!\cdots\!74\)\( T^{7} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( 1 - 2260 T + 6689558 T^{2} - 9325180360 T^{3} + 14902549646075 T^{4} - 13240422610408520 T^{5} + 13486108124699811542 T^{6} - \)\(64\!\cdots\!80\)\( T^{7} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( 1 - 1812 T + 4521846 T^{2} - 9193036640 T^{3} + 14007968825388 T^{4} - 19623137225736012 T^{5} + 26786499218696823804 T^{6} - \)\(27\!\cdots\!84\)\( T^{7} + \)\(28\!\cdots\!12\)\( T^{8} - \)\(26\!\cdots\!20\)\( T^{9} + \)\(18\!\cdots\!46\)\( T^{10} - \)\(10\!\cdots\!84\)\( T^{11} + \)\(81\!\cdots\!49\)\( T^{12} \))(\( 1 + 1812 T + 4521846 T^{2} + 9193036640 T^{3} + 14007968825388 T^{4} + 19623137225736012 T^{5} + 26786499218696823804 T^{6} + \)\(27\!\cdots\!84\)\( T^{7} + \)\(28\!\cdots\!12\)\( T^{8} + \)\(26\!\cdots\!20\)\( T^{9} + \)\(18\!\cdots\!46\)\( T^{10} + \)\(10\!\cdots\!84\)\( T^{11} + \)\(81\!\cdots\!49\)\( T^{12} \))
$19$ (\( 1 + 500 T + 2476099 T^{2} \))(\( 1 - 1683 T + 2476099 T^{2} \))(\( 1 - 2082 T + 2476099 T^{2} \))(\( 1 + 1210 T + 2476099 T^{2} \))(\( 1 + 2342 T + 2476099 T^{2} \))(\( 1 - 1210 T + 2476099 T^{2} \))(\( 1 + 258 T + 2476099 T^{2} \))(\( 1 + 1683 T + 2476099 T^{2} \))(\( 1 - 2038 T + 2476099 T^{2} \))(\( 1 + 1100 T + 2476099 T^{2} \))(\( 1 - 2740 T + 2476099 T^{2} \))(\( 1 - 802 T + 2476099 T^{2} \))(\( 1 - 1718 T + 2476099 T^{2} \))(\( 1 + 1024 T + 5199078 T^{2} + 2535525376 T^{3} + 6131066257801 T^{4} \))(\( 1 + 460 T + 3446810 T^{2} + 1139005540 T^{3} + 6131066257801 T^{4} \))(\( 1 + 1160 T + 3163814 T^{2} + 2872274840 T^{3} + 6131066257801 T^{4} \))(\( 1 - 1160 T + 3163814 T^{2} - 2872274840 T^{3} + 6131066257801 T^{4} \))(\( 1 - 460 T + 3446810 T^{2} - 1139005540 T^{3} + 6131066257801 T^{4} \))(\( 1 - 1024 T + 5199078 T^{2} - 2535525376 T^{3} + 6131066257801 T^{4} \))(\( 1 - 1032 T + 625078 T^{2} - 2555334168 T^{3} + 6131066257801 T^{4} \))(\( 1 + 1918 T + 2203758 T^{2} + 4749157882 T^{3} + 6131066257801 T^{4} \))(\( 1 + 3342 T + 7714118 T^{2} + 8275122858 T^{3} + 6131066257801 T^{4} \))(\( 1 + 1032 T + 625078 T^{2} + 2555334168 T^{3} + 6131066257801 T^{4} \))(\( 1 - 1134 T + 7023429 T^{2} - 5066355420 T^{3} + 17390705523471 T^{4} - 6952629136346334 T^{5} + 15181127029874798299 T^{6} \))(\( 1 + 1134 T + 7023429 T^{2} + 5066355420 T^{3} + 17390705523471 T^{4} + 6952629136346334 T^{5} + 15181127029874798299 T^{6} \))(\( 1 + 1480 T + 9396964 T^{2} + 10144231720 T^{3} + 34421947075670 T^{4} + 25118122017660280 T^{5} + 57613408906170716164 T^{6} + \)\(22\!\cdots\!20\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} \))(\( 1 + 599 T + 6325406 T^{2} + 4625107935 T^{3} + 20894051165666 T^{4} + 11452225132745565 T^{5} + 38781483293491992206 T^{6} + \)\(90\!\cdots\!01\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} \))(\( 1 - 599 T + 6325406 T^{2} - 4625107935 T^{3} + 20894051165666 T^{4} - 11452225132745565 T^{5} + 38781483293491992206 T^{6} - \)\(90\!\cdots\!01\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} \))(\( 1 - 1480 T + 9396964 T^{2} - 10144231720 T^{3} + 34421947075670 T^{4} - 25118122017660280 T^{5} + 57613408906170716164 T^{6} - \)\(22\!\cdots\!20\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} \))(\( 1 + 36 T + 2258844 T^{2} + 2367090188 T^{3} + 12028551753471 T^{4} + 5413421593852056 T^{5} + 23183550638346746968 T^{6} + \)\(13\!\cdots\!44\)\( T^{7} + \)\(73\!\cdots\!71\)\( T^{8} + \)\(35\!\cdots\!12\)\( T^{9} + \)\(84\!\cdots\!44\)\( T^{10} + \)\(33\!\cdots\!64\)\( T^{11} + \)\(23\!\cdots\!01\)\( T^{12} \))(\( 1 - 36 T + 2258844 T^{2} - 2367090188 T^{3} + 12028551753471 T^{4} - 5413421593852056 T^{5} + 23183550638346746968 T^{6} - \)\(13\!\cdots\!44\)\( T^{7} + \)\(73\!\cdots\!71\)\( T^{8} - \)\(35\!\cdots\!12\)\( T^{9} + \)\(84\!\cdots\!44\)\( T^{10} - \)\(33\!\cdots\!64\)\( T^{11} + \)\(23\!\cdots\!01\)\( T^{12} \))
$23$ (\( 1 - 3564 T + 6436343 T^{2} \))(\( 1 + 1371 T + 6436343 T^{2} \))(\( 1 + 3170 T + 6436343 T^{2} \))(\( 1 - 2823 T + 6436343 T^{2} \))(\( 1 - 2430 T + 6436343 T^{2} \))(\( 1 - 2823 T + 6436343 T^{2} \))(\( 1 - 2970 T + 6436343 T^{2} \))(\( 1 + 1371 T + 6436343 T^{2} \))(\( 1 + 1230 T + 6436343 T^{2} \))(\( 1 + 1986 T + 6436343 T^{2} \))(\( 1 - 1566 T + 6436343 T^{2} \))(\( 1 + 1290 T + 6436343 T^{2} \))(\( 1 + 3950 T + 6436343 T^{2} \))(\( 1 - 234 T + 6314269 T^{2} - 1506104262 T^{3} + 41426511213649 T^{4} \))(\( 1 + 2468 T + 14361742 T^{2} + 15884894524 T^{3} + 41426511213649 T^{4} \))(\( 1 + 3518 T + 15079123 T^{2} + 22643054674 T^{3} + 41426511213649 T^{4} \))(\( 1 + 3518 T + 15079123 T^{2} + 22643054674 T^{3} + 41426511213649 T^{4} \))(\( 1 + 2468 T + 14361742 T^{2} + 15884894524 T^{3} + 41426511213649 T^{4} \))(\( 1 - 234 T + 6314269 T^{2} - 1506104262 T^{3} + 41426511213649 T^{4} \))(\( 1 + 2242 T + 12042353 T^{2} + 14430281006 T^{3} + 41426511213649 T^{4} \))(\( 1 + 1334 T + 10606846 T^{2} + 8586081562 T^{3} + 41426511213649 T^{4} \))(\( 1 + 450 T - 6027314 T^{2} + 2896354350 T^{3} + 41426511213649 T^{4} \))(\( 1 + 2242 T + 12042353 T^{2} + 14430281006 T^{3} + 41426511213649 T^{4} \))(\( 1 - 1872 T + 15510357 T^{2} - 24609547616 T^{3} + 99829977704451 T^{4} - 77550428991950928 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 - 1872 T + 15510357 T^{2} - 24609547616 T^{3} + 99829977704451 T^{4} - 77550428991950928 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 - 1968 T + 9987488 T^{2} - 32046096912 T^{3} + 52040993557570 T^{4} - 206259671536872816 T^{5} + \)\(41\!\cdots\!12\)\( T^{6} - \)\(52\!\cdots\!76\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 3942 T + 19536020 T^{2} - 54100449288 T^{3} + 166644073569165 T^{4} - 348209048071673784 T^{5} + \)\(80\!\cdots\!80\)\( T^{6} - \)\(10\!\cdots\!94\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 3942 T + 19536020 T^{2} - 54100449288 T^{3} + 166644073569165 T^{4} - 348209048071673784 T^{5} + \)\(80\!\cdots\!80\)\( T^{6} - \)\(10\!\cdots\!94\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 1968 T + 9987488 T^{2} - 32046096912 T^{3} + 52040993557570 T^{4} - 206259671536872816 T^{5} + \)\(41\!\cdots\!12\)\( T^{6} - \)\(52\!\cdots\!76\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 1640 T + 30670998 T^{2} - 48341994104 T^{3} + 433913289297363 T^{4} - 595124448729285936 T^{5} + \)\(35\!\cdots\!28\)\( T^{6} - \)\(38\!\cdots\!48\)\( T^{7} + \)\(17\!\cdots\!87\)\( T^{8} - \)\(12\!\cdots\!28\)\( T^{9} + \)\(52\!\cdots\!98\)\( T^{10} - \)\(18\!\cdots\!20\)\( T^{11} + \)\(71\!\cdots\!49\)\( T^{12} \))(\( 1 - 1640 T + 30670998 T^{2} - 48341994104 T^{3} + 433913289297363 T^{4} - 595124448729285936 T^{5} + \)\(35\!\cdots\!28\)\( T^{6} - \)\(38\!\cdots\!48\)\( T^{7} + \)\(17\!\cdots\!87\)\( T^{8} - \)\(12\!\cdots\!28\)\( T^{9} + \)\(52\!\cdots\!98\)\( T^{10} - \)\(18\!\cdots\!20\)\( T^{11} + \)\(71\!\cdots\!49\)\( T^{12} \))
$29$ (\( 1 - 2190 T + 20511149 T^{2} \))(\( 1 - 4374 T + 20511149 T^{2} \))(\( 1 + 8681 T + 20511149 T^{2} \))(\( 1 + 4539 T + 20511149 T^{2} \))(\( 1 - 8259 T + 20511149 T^{2} \))(\( 1 + 4539 T + 20511149 T^{2} \))(\( 1 - 1299 T + 20511149 T^{2} \))(\( 1 - 4374 T + 20511149 T^{2} \))(\( 1 + 5001 T + 20511149 T^{2} \))(\( 1 + 5610 T + 20511149 T^{2} \))(\( 1 - 5910 T + 20511149 T^{2} \))(\( 1 - 1779 T + 20511149 T^{2} \))(\( 1 - 4579 T + 20511149 T^{2} \))(\( 1 + 4218 T + 33926779 T^{2} + 86516026482 T^{3} + 420707233300201 T^{4} \))(\( 1 - 682 T + 40296079 T^{2} - 13988603618 T^{3} + 420707233300201 T^{4} \))(\( 1 - 3286 T + 42427411 T^{2} - 67399635614 T^{3} + 420707233300201 T^{4} \))(\( 1 - 3286 T + 42427411 T^{2} - 67399635614 T^{3} + 420707233300201 T^{4} \))(\( 1 - 682 T + 40296079 T^{2} - 13988603618 T^{3} + 420707233300201 T^{4} \))(\( 1 + 4218 T + 33926779 T^{2} + 86516026482 T^{3} + 420707233300201 T^{4} \))(\( 1 + 8330 T + 46216507 T^{2} + 170857871170 T^{3} + 420707233300201 T^{4} \))(\( 1 + 1131 T + 38900908 T^{2} + 23198109519 T^{3} + 420707233300201 T^{4} \))(\( 1 + 4515 T + 21490372 T^{2} + 92607837735 T^{3} + 420707233300201 T^{4} \))(\( 1 + 8330 T + 46216507 T^{2} + 170857871170 T^{3} + 420707233300201 T^{4} \))(\( 1 + 5724 T + 5668896 T^{2} - 64003334922 T^{3} + 116275570521504 T^{4} + 2408128203410350524 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( 1 + 5724 T + 5668896 T^{2} - 64003334922 T^{3} + 116275570521504 T^{4} + 2408128203410350524 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( 1 + 564 T + 69433474 T^{2} + 9006757936 T^{3} + 1994184496605979 T^{4} + 184738954032228464 T^{5} + \)\(29\!\cdots\!74\)\( T^{6} + \)\(48\!\cdots\!36\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 6513 T + 78001481 T^{2} - 384959254518 T^{3} + 2365670893077330 T^{4} - 7895956628347621182 T^{5} + \)\(32\!\cdots\!81\)\( T^{6} - \)\(56\!\cdots\!37\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 6513 T + 78001481 T^{2} - 384959254518 T^{3} + 2365670893077330 T^{4} - 7895956628347621182 T^{5} + \)\(32\!\cdots\!81\)\( T^{6} - \)\(56\!\cdots\!37\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 + 564 T + 69433474 T^{2} + 9006757936 T^{3} + 1994184496605979 T^{4} + 184738954032228464 T^{5} + \)\(29\!\cdots\!74\)\( T^{6} + \)\(48\!\cdots\!36\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 10152 T + 118912584 T^{2} - 690987730076 T^{3} + 4690951280224224 T^{4} - 19754501095214942568 T^{5} + \)\(10\!\cdots\!66\)\( T^{6} - \)\(40\!\cdots\!32\)\( T^{7} + \)\(19\!\cdots\!24\)\( T^{8} - \)\(59\!\cdots\!24\)\( T^{9} + \)\(21\!\cdots\!84\)\( T^{10} - \)\(36\!\cdots\!48\)\( T^{11} + \)\(74\!\cdots\!01\)\( T^{12} \))(\( 1 - 10152 T + 118912584 T^{2} - 690987730076 T^{3} + 4690951280224224 T^{4} - 19754501095214942568 T^{5} + \)\(10\!\cdots\!66\)\( T^{6} - \)\(40\!\cdots\!32\)\( T^{7} + \)\(19\!\cdots\!24\)\( T^{8} - \)\(59\!\cdots\!24\)\( T^{9} + \)\(21\!\cdots\!84\)\( T^{10} - \)\(36\!\cdots\!48\)\( T^{11} + \)\(74\!\cdots\!01\)\( T^{12} \))
$31$ (\( 1 + 2312 T + 28629151 T^{2} \))(\( 1 + 7600 T + 28629151 T^{2} \))(\( 1 + 1636 T + 28629151 T^{2} \))(\( 1 + 712 T + 28629151 T^{2} \))(\( 1 + 4016 T + 28629151 T^{2} \))(\( 1 - 712 T + 28629151 T^{2} \))(\( 1 + 1916 T + 28629151 T^{2} \))(\( 1 - 7600 T + 28629151 T^{2} \))(\( 1 + 5696 T + 28629151 T^{2} \))(\( 1 - 3988 T + 28629151 T^{2} \))(\( 1 - 6868 T + 28629151 T^{2} \))(\( 1 - 2584 T + 28629151 T^{2} \))(\( 1 + 6756 T + 28629151 T^{2} \))(\( 1 + 7756 T + 72201786 T^{2} + 222047695156 T^{3} + 819628286980801 T^{4} \))(\( 1 - 5740 T + 62389410 T^{2} - 164331326740 T^{3} + 819628286980801 T^{4} \))(\( 1 + 18228 T + 140242402 T^{2} + 521852164428 T^{3} + 819628286980801 T^{4} \))(\( 1 - 18228 T + 140242402 T^{2} - 521852164428 T^{3} + 819628286980801 T^{4} \))(\( 1 + 5740 T + 62389410 T^{2} + 164331326740 T^{3} + 819628286980801 T^{4} \))(\( 1 - 7756 T + 72201786 T^{2} - 222047695156 T^{3} + 819628286980801 T^{4} \))(\( 1 - 7652 T + 42013322 T^{2} - 219070263452 T^{3} + 819628286980801 T^{4} \))(\( 1 - 5472 T + 8095294 T^{2} - 156658714272 T^{3} + 819628286980801 T^{4} \))(\( 1 - 2036 T + 23243550 T^{2} - 58288951436 T^{3} + 819628286980801 T^{4} \))(\( 1 + 7652 T + 42013322 T^{2} + 219070263452 T^{3} + 819628286980801 T^{4} \))(\( 1 - 2184 T + 25269921 T^{2} - 256728066880 T^{3} + 723456384067071 T^{4} - 1790068178766069384 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( 1 + 2184 T + 25269921 T^{2} + 256728066880 T^{3} + 723456384067071 T^{4} + 1790068178766069384 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( 1 + 10240 T + 148124560 T^{2} + 917751994240 T^{3} + 6856056611517602 T^{4} + 26274460423648090240 T^{5} + \)\(12\!\cdots\!60\)\( T^{6} + \)\(24\!\cdots\!40\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 + 1660 T + 51120016 T^{2} - 25882292468 T^{3} + 1205059842304030 T^{4} - 740988059292534668 T^{5} + \)\(41\!\cdots\!16\)\( T^{6} + \)\(38\!\cdots\!60\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 - 1660 T + 51120016 T^{2} + 25882292468 T^{3} + 1205059842304030 T^{4} + 740988059292534668 T^{5} + \)\(41\!\cdots\!16\)\( T^{6} - \)\(38\!\cdots\!60\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 - 10240 T + 148124560 T^{2} - 917751994240 T^{3} + 6856056611517602 T^{4} - 26274460423648090240 T^{5} + \)\(12\!\cdots\!60\)\( T^{6} - \)\(24\!\cdots\!40\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 - 6720 T + 83882054 T^{2} - 149953144320 T^{3} + 1096980856438083 T^{4} + 12257980657524960960 T^{5} - \)\(28\!\cdots\!92\)\( T^{6} + \)\(35\!\cdots\!60\)\( T^{7} + \)\(89\!\cdots\!83\)\( T^{8} - \)\(35\!\cdots\!20\)\( T^{9} + \)\(56\!\cdots\!54\)\( T^{10} - \)\(12\!\cdots\!20\)\( T^{11} + \)\(55\!\cdots\!01\)\( T^{12} \))(\( 1 + 6720 T + 83882054 T^{2} + 149953144320 T^{3} + 1096980856438083 T^{4} - 12257980657524960960 T^{5} - \)\(28\!\cdots\!92\)\( T^{6} - \)\(35\!\cdots\!60\)\( T^{7} + \)\(89\!\cdots\!83\)\( T^{8} + \)\(35\!\cdots\!20\)\( T^{9} + \)\(56\!\cdots\!54\)\( T^{10} + \)\(12\!\cdots\!20\)\( T^{11} + \)\(55\!\cdots\!01\)\( T^{12} \))
$37$ (\( 1 + 11242 T + 69343957 T^{2} \))(\( 1 + 11263 T + 69343957 T^{2} \))(\( 1 - 4298 T + 69343957 T^{2} \))(\( 1 + 7324 T + 69343957 T^{2} \))(\( 1 + 7042 T + 69343957 T^{2} \))(\( 1 + 7324 T + 69343957 T^{2} \))(\( 1 - 6578 T + 69343957 T^{2} \))(\( 1 + 11263 T + 69343957 T^{2} \))(\( 1 + 5602 T + 69343957 T^{2} \))(\( 1 + 142 T + 69343957 T^{2} \))(\( 1 + 5518 T + 69343957 T^{2} \))(\( 1 - 13862 T + 69343957 T^{2} \))(\( 1 + 16518 T + 69343957 T^{2} \))(\( 1 - 11968 T + 151279626 T^{2} - 829908477376 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 2532 T + 14892970 T^{2} - 175578899124 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 2896 T + 94188522 T^{2} - 200820099472 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 2896 T + 94188522 T^{2} - 200820099472 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 2532 T + 14892970 T^{2} - 175578899124 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 11968 T + 151279626 T^{2} - 829908477376 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 11168 T + 169832906 T^{2} + 774433311776 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 9156 T + 152420398 T^{2} + 634913270292 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 1928 T + 133674294 T^{2} + 133695149096 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 11168 T + 169832906 T^{2} + 774433311776 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 10698 T + 130381287 T^{2} - 640617332132 T^{3} + 9041154359332659 T^{4} - 51442235616126148602 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( 1 - 10698 T + 130381287 T^{2} - 640617332132 T^{3} + 9041154359332659 T^{4} - 51442235616126148602 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( 1 + 1648 T + 161896744 T^{2} + 101725654768 T^{3} + 13339828319781218 T^{4} + 7054059430029036976 T^{5} + \)\(77\!\cdots\!56\)\( T^{6} + \)\(54\!\cdots\!64\)\( T^{7} + \)\(23\!\cdots\!01\)\( T^{8} \))(\( 1 - 4295 T + 191480032 T^{2} - 753861222713 T^{3} + 18343565056616782 T^{4} - 52275720211777695341 T^{5} + \)\(92\!\cdots\!68\)\( T^{6} - \)\(14\!\cdots\!35\)\( T^{7} + \)\(23\!\cdots\!01\)\( T^{8} \))(\( 1 - 4295 T + 191480032 T^{2} - 753861222713 T^{3} + 18343565056616782 T^{4} - 52275720211777695341 T^{5} + \)\(92\!\cdots\!68\)\( T^{6} - \)\(14\!\cdots\!35\)\( T^{7} + \)\(23\!\cdots\!01\)\( T^{8} \))(\( 1 + 1648 T + 161896744 T^{2} + 101725654768 T^{3} + 13339828319781218 T^{4} + 7054059430029036976 T^{5} + \)\(77\!\cdots\!56\)\( T^{6} + \)\(54\!\cdots\!64\)\( T^{7} + \)\(23\!\cdots\!01\)\( T^{8} \))(\( 1 + 3828 T + 229257302 T^{2} + 1348898078180 T^{3} + 30083396450792907 T^{4} + \)\(15\!\cdots\!20\)\( T^{5} + \)\(26\!\cdots\!88\)\( T^{6} + \)\(10\!\cdots\!40\)\( T^{7} + \)\(14\!\cdots\!43\)\( T^{8} + \)\(44\!\cdots\!40\)\( T^{9} + \)\(53\!\cdots\!02\)\( T^{10} + \)\(61\!\cdots\!96\)\( T^{11} + \)\(11\!\cdots\!49\)\( T^{12} \))(\( 1 + 3828 T + 229257302 T^{2} + 1348898078180 T^{3} + 30083396450792907 T^{4} + \)\(15\!\cdots\!20\)\( T^{5} + \)\(26\!\cdots\!88\)\( T^{6} + \)\(10\!\cdots\!40\)\( T^{7} + \)\(14\!\cdots\!43\)\( T^{8} + \)\(44\!\cdots\!40\)\( T^{9} + \)\(53\!\cdots\!02\)\( T^{10} + \)\(61\!\cdots\!96\)\( T^{11} + \)\(11\!\cdots\!49\)\( T^{12} \))
$41$ (\( 1 + 1242 T + 115856201 T^{2} \))(\( 1 + 13493 T + 115856201 T^{2} \))(\( 1 + 2356 T + 115856201 T^{2} \))(\( 1 - 15633 T + 115856201 T^{2} \))(\( 1 + 3336 T + 115856201 T^{2} \))(\( 1 + 15633 T + 115856201 T^{2} \))(\( 1 + 6676 T + 115856201 T^{2} \))(\( 1 - 13493 T + 115856201 T^{2} \))(\( 1 - 2424 T + 115856201 T^{2} \))(\( 1 + 1542 T + 115856201 T^{2} \))(\( 1 - 378 T + 115856201 T^{2} \))(\( 1 - 11904 T + 115856201 T^{2} \))(\( 1 + 18876 T + 115856201 T^{2} \))(\( 1 + 28806 T + 427615411 T^{2} + 3337353726006 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 22560 T + 333650190 T^{2} + 2613715894560 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 26174 T + 371825635 T^{2} - 3032420204974 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 26174 T + 371825635 T^{2} + 3032420204974 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 22560 T + 333650190 T^{2} - 2613715894560 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 28806 T + 427615411 T^{2} - 3337353726006 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 8990 T + 75564283 T^{2} + 1041547246990 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 7822 T + 243078274 T^{2} - 906227204222 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 19318 T + 258029594 T^{2} + 2238110090918 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 8990 T + 75564283 T^{2} - 1041547246990 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 6204 T + 357228231 T^{2} - 1437873089320 T^{3} + 41387105733610431 T^{4} - 83274178360185495804 T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( 1 + 6204 T + 357228231 T^{2} + 1437873089320 T^{3} + 41387105733610431 T^{4} + 83274178360185495804 T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( 1 + 32320 T + 609845624 T^{2} + 7548797241280 T^{3} + 84857018876077202 T^{4} + \)\(87\!\cdots\!80\)\( T^{5} + \)\(81\!\cdots\!24\)\( T^{6} + \)\(50\!\cdots\!20\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 + 7034 T + 344624304 T^{2} + 2804261926836 T^{3} + 52716916518379105 T^{4} + \)\(32\!\cdots\!36\)\( T^{5} + \)\(46\!\cdots\!04\)\( T^{6} + \)\(10\!\cdots\!34\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 - 7034 T + 344624304 T^{2} - 2804261926836 T^{3} + 52716916518379105 T^{4} - \)\(32\!\cdots\!36\)\( T^{5} + \)\(46\!\cdots\!04\)\( T^{6} - \)\(10\!\cdots\!34\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 - 32320 T + 609845624 T^{2} - 7548797241280 T^{3} + 84857018876077202 T^{4} - \)\(87\!\cdots\!80\)\( T^{5} + \)\(81\!\cdots\!24\)\( T^{6} - \)\(50\!\cdots\!20\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 + 9832 T + 450004072 T^{2} + 4806591418280 T^{3} + 108214618636339555 T^{4} + \)\(95\!\cdots\!92\)\( T^{5} + \)\(16\!\cdots\!64\)\( T^{6} + \)\(11\!\cdots\!92\)\( T^{7} + \)\(14\!\cdots\!55\)\( T^{8} + \)\(74\!\cdots\!80\)\( T^{9} + \)\(81\!\cdots\!72\)\( T^{10} + \)\(20\!\cdots\!32\)\( T^{11} + \)\(24\!\cdots\!01\)\( T^{12} \))(\( 1 - 9832 T + 450004072 T^{2} - 4806591418280 T^{3} + 108214618636339555 T^{4} - \)\(95\!\cdots\!92\)\( T^{5} + \)\(16\!\cdots\!64\)\( T^{6} - \)\(11\!\cdots\!92\)\( T^{7} + \)\(14\!\cdots\!55\)\( T^{8} - \)\(74\!\cdots\!80\)\( T^{9} + \)\(81\!\cdots\!72\)\( T^{10} - \)\(20\!\cdots\!32\)\( T^{11} + \)\(24\!\cdots\!01\)\( T^{12} \))
$43$ (\( 1 - 20624 T + 147008443 T^{2} \))(\( 1 + 6830 T + 147008443 T^{2} \))(\( 1 - 8738 T + 147008443 T^{2} \))(\( 1 - 15827 T + 147008443 T^{2} \))(\( 1 + 23518 T + 147008443 T^{2} \))(\( 1 - 15827 T + 147008443 T^{2} \))(\( 1 - 3178 T + 147008443 T^{2} \))(\( 1 + 6830 T + 147008443 T^{2} \))(\( 1 - 602 T + 147008443 T^{2} \))(\( 1 + 5026 T + 147008443 T^{2} \))(\( 1 + 2434 T + 147008443 T^{2} \))(\( 1 + 598 T + 147008443 T^{2} \))(\( 1 - 2258 T + 147008443 T^{2} \))(\( 1 + 8930 T + 66789837 T^{2} + 1312785395990 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 6484 T + 77928650 T^{2} - 953202744412 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 13298 T + 238774251 T^{2} + 1954918275014 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 13298 T + 238774251 T^{2} + 1954918275014 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 6484 T + 77928650 T^{2} - 953202744412 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 8930 T + 66789837 T^{2} + 1312785395990 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 6502 T + 167071601 T^{2} + 955848896386 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 2078 T - 70429762 T^{2} - 305483544554 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 14146 T + 330672654 T^{2} + 2079581434678 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 6502 T + 167071601 T^{2} + 955848896386 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 10728 T + 218609349 T^{2} + 3888257298944 T^{3} + 32137420021733607 T^{4} + \)\(23\!\cdots\!72\)\( T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( 1 + 10728 T + 218609349 T^{2} + 3888257298944 T^{3} + 32137420021733607 T^{4} + \)\(23\!\cdots\!72\)\( T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( 1 - 19320 T + 647664324 T^{2} - 8553439555800 T^{3} + 147201745308735542 T^{4} - \)\(12\!\cdots\!00\)\( T^{5} + \)\(13\!\cdots\!76\)\( T^{6} - \)\(61\!\cdots\!40\)\( T^{7} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( 1 - 22113 T + 536918297 T^{2} - 7794797939172 T^{3} + 114944785067371194 T^{4} - \)\(11\!\cdots\!96\)\( T^{5} + \)\(11\!\cdots\!53\)\( T^{6} - \)\(70\!\cdots\!91\)\( T^{7} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( 1 - 22113 T + 536918297 T^{2} - 7794797939172 T^{3} + 114944785067371194 T^{4} - \)\(11\!\cdots\!96\)\( T^{5} + \)\(11\!\cdots\!53\)\( T^{6} - \)\(70\!\cdots\!91\)\( T^{7} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( 1 - 19320 T + 647664324 T^{2} - 8553439555800 T^{3} + 147201745308735542 T^{4} - \)\(12\!\cdots\!00\)\( T^{5} + \)\(13\!\cdots\!76\)\( T^{6} - \)\(61\!\cdots\!40\)\( T^{7} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( 1 - 17212 T + 511306198 T^{2} - 5471181239044 T^{3} + 106746528822874647 T^{4} - \)\(79\!\cdots\!88\)\( T^{5} + \)\(15\!\cdots\!20\)\( T^{6} - \)\(11\!\cdots\!84\)\( T^{7} + \)\(23\!\cdots\!03\)\( T^{8} - \)\(17\!\cdots\!08\)\( T^{9} + \)\(23\!\cdots\!98\)\( T^{10} - \)\(11\!\cdots\!16\)\( T^{11} + \)\(10\!\cdots\!49\)\( T^{12} \))(\( 1 - 17212 T + 511306198 T^{2} - 5471181239044 T^{3} + 106746528822874647 T^{4} - \)\(79\!\cdots\!88\)\( T^{5} + \)\(15\!\cdots\!20\)\( T^{6} - \)\(11\!\cdots\!84\)\( T^{7} + \)\(23\!\cdots\!03\)\( T^{8} - \)\(17\!\cdots\!08\)\( T^{9} + \)\(23\!\cdots\!98\)\( T^{10} - \)\(11\!\cdots\!16\)\( T^{11} + \)\(10\!\cdots\!49\)\( T^{12} \))
$47$ (\( 1 + 6588 T + 229345007 T^{2} \))(\( 1 + 19067 T + 229345007 T^{2} \))(\( 1 - 3641 T + 229345007 T^{2} \))(\( 1 + 3192 T + 229345007 T^{2} \))(\( 1 + 10317 T + 229345007 T^{2} \))(\( 1 - 3192 T + 229345007 T^{2} \))(\( 1 - 22001 T + 229345007 T^{2} \))(\( 1 - 19067 T + 229345007 T^{2} \))(\( 1 - 23163 T + 229345007 T^{2} \))(\( 1 + 24738 T + 229345007 T^{2} \))(\( 1 + 13122 T + 229345007 T^{2} \))(\( 1 - 17019 T + 229345007 T^{2} \))(\( 1 - 537 T + 229345007 T^{2} \))(\( 1 + 8604 T + 302439682 T^{2} + 1973284440228 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 1840 T + 456985661 T^{2} + 421994812880 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 16472 T + 262536574 T^{2} - 3777770955304 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 16472 T + 262536574 T^{2} + 3777770955304 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 1840 T + 456985661 T^{2} - 421994812880 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 8604 T + 302439682 T^{2} - 1973284440228 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 30364 T + 659743138 T^{2} + 6963831792548 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 8507 T - 114195314 T^{2} - 1951037974549 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 19745 T + 544626710 T^{2} - 4528417163215 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 30364 T + 659743138 T^{2} - 6963831792548 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 23556 T + 555980028 T^{2} - 10660071906676 T^{3} + 127511243413520196 T^{4} - \)\(12\!\cdots\!44\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 + 23556 T + 555980028 T^{2} + 10660071906676 T^{3} + 127511243413520196 T^{4} + \)\(12\!\cdots\!44\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 + 15600 T + 589104950 T^{2} + 3062232126720 T^{3} + 126459226732351027 T^{4} + \)\(70\!\cdots\!40\)\( T^{5} + \)\(30\!\cdots\!50\)\( T^{6} + \)\(18\!\cdots\!00\)\( T^{7} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 + 2537 T + 386558172 T^{2} + 624254884725 T^{3} + 126348532724187526 T^{4} + \)\(14\!\cdots\!75\)\( T^{5} + \)\(20\!\cdots\!28\)\( T^{6} + \)\(30\!\cdots\!91\)\( T^{7} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 - 2537 T + 386558172 T^{2} - 624254884725 T^{3} + 126348532724187526 T^{4} - \)\(14\!\cdots\!75\)\( T^{5} + \)\(20\!\cdots\!28\)\( T^{6} - \)\(30\!\cdots\!91\)\( T^{7} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 - 15600 T + 589104950 T^{2} - 3062232126720 T^{3} + 126459226732351027 T^{4} - \)\(70\!\cdots\!40\)\( T^{5} + \)\(30\!\cdots\!50\)\( T^{6} - \)\(18\!\cdots\!00\)\( T^{7} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 - 7584 T + 780425660 T^{2} - 5474144646128 T^{3} + 337812510741153416 T^{4} - \)\(20\!\cdots\!08\)\( T^{5} + \)\(94\!\cdots\!30\)\( T^{6} - \)\(46\!\cdots\!56\)\( T^{7} + \)\(17\!\cdots\!84\)\( T^{8} - \)\(66\!\cdots\!04\)\( T^{9} + \)\(21\!\cdots\!60\)\( T^{10} - \)\(48\!\cdots\!88\)\( T^{11} + \)\(14\!\cdots\!49\)\( T^{12} \))(\( 1 + 7584 T + 780425660 T^{2} + 5474144646128 T^{3} + 337812510741153416 T^{4} + \)\(20\!\cdots\!08\)\( T^{5} + \)\(94\!\cdots\!30\)\( T^{6} + \)\(46\!\cdots\!56\)\( T^{7} + \)\(17\!\cdots\!84\)\( T^{8} + \)\(66\!\cdots\!04\)\( T^{9} + \)\(21\!\cdots\!60\)\( T^{10} + \)\(48\!\cdots\!88\)\( T^{11} + \)\(14\!\cdots\!49\)\( T^{12} \))
$53$ (\( 1 + 21066 T + 418195493 T^{2} \))(\( 1 - 12569 T + 418195493 T^{2} \))(\( 1 - 33268 T + 418195493 T^{2} \))(\( 1 + 20046 T + 418195493 T^{2} \))(\( 1 - 3084 T + 418195493 T^{2} \))(\( 1 + 20046 T + 418195493 T^{2} \))(\( 1 - 26168 T + 418195493 T^{2} \))(\( 1 - 12569 T + 418195493 T^{2} \))(\( 1 + 25296 T + 418195493 T^{2} \))(\( 1 + 14166 T + 418195493 T^{2} \))(\( 1 + 9174 T + 418195493 T^{2} \))(\( 1 - 27852 T + 418195493 T^{2} \))(\( 1 + 10984 T + 418195493 T^{2} \))(\( 1 - 19200 T + 885674410 T^{2} - 8029353465600 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 26508 T + 493888302 T^{2} - 11085526128444 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 14960 T + 888790810 T^{2} + 6256204575280 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 14960 T + 888790810 T^{2} + 6256204575280 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 26508 T + 493888302 T^{2} - 11085526128444 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 19200 T + 885674410 T^{2} - 8029353465600 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 22888 T + 397397722 T^{2} + 9571658443784 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 34242 T + 846139498 T^{2} + 14319850071306 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 26378 T + 911827778 T^{2} - 11031160714354 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 22888 T + 397397722 T^{2} + 9571658443784 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 13218 T + 552727275 T^{2} + 14121258149708 T^{3} + 231148055263171575 T^{4} + \)\(23\!\cdots\!82\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( 1 + 13218 T + 552727275 T^{2} + 14121258149708 T^{3} + 231148055263171575 T^{4} + \)\(23\!\cdots\!82\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( 1 - 28928 T + 1635333216 T^{2} - 31852579536384 T^{3} + 1005064993135837554 T^{4} - \)\(13\!\cdots\!12\)\( T^{5} + \)\(28\!\cdots\!84\)\( T^{6} - \)\(21\!\cdots\!96\)\( T^{7} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( 1 - 12401 T + 988925790 T^{2} - 15703469072751 T^{3} + 489556243824360346 T^{4} - \)\(65\!\cdots\!43\)\( T^{5} + \)\(17\!\cdots\!10\)\( T^{6} - \)\(90\!\cdots\!57\)\( T^{7} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( 1 - 12401 T + 988925790 T^{2} - 15703469072751 T^{3} + 489556243824360346 T^{4} - \)\(65\!\cdots\!43\)\( T^{5} + \)\(17\!\cdots\!10\)\( T^{6} - \)\(90\!\cdots\!57\)\( T^{7} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( 1 - 28928 T + 1635333216 T^{2} - 31852579536384 T^{3} + 1005064993135837554 T^{4} - \)\(13\!\cdots\!12\)\( T^{5} + \)\(28\!\cdots\!84\)\( T^{6} - \)\(21\!\cdots\!96\)\( T^{7} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( 1 + 18644 T + 621550822 T^{2} - 1091704138908 T^{3} + 20244284055688779 T^{4} - \)\(80\!\cdots\!32\)\( T^{5} + \)\(39\!\cdots\!44\)\( T^{6} - \)\(33\!\cdots\!76\)\( T^{7} + \)\(35\!\cdots\!71\)\( T^{8} - \)\(79\!\cdots\!56\)\( T^{9} + \)\(19\!\cdots\!22\)\( T^{10} + \)\(23\!\cdots\!92\)\( T^{11} + \)\(53\!\cdots\!49\)\( T^{12} \))(\( 1 + 18644 T + 621550822 T^{2} - 1091704138908 T^{3} + 20244284055688779 T^{4} - \)\(80\!\cdots\!32\)\( T^{5} + \)\(39\!\cdots\!44\)\( T^{6} - \)\(33\!\cdots\!76\)\( T^{7} + \)\(35\!\cdots\!71\)\( T^{8} - \)\(79\!\cdots\!56\)\( T^{9} + \)\(19\!\cdots\!22\)\( T^{10} + \)\(23\!\cdots\!92\)\( T^{11} + \)\(53\!\cdots\!49\)\( T^{12} \))
$59$ (\( 1 + 7980 T + 714924299 T^{2} \))(\( 1 + 26488 T + 714924299 T^{2} \))(\( 1 - 30968 T + 714924299 T^{2} \))(\( 1 - 23046 T + 714924299 T^{2} \))(\( 1 - 18816 T + 714924299 T^{2} \))(\( 1 + 23046 T + 714924299 T^{2} \))(\( 1 + 3932 T + 714924299 T^{2} \))(\( 1 - 26488 T + 714924299 T^{2} \))(\( 1 + 5724 T + 714924299 T^{2} \))(\( 1 + 28380 T + 714924299 T^{2} \))(\( 1 - 34980 T + 714924299 T^{2} \))(\( 1 + 30912 T + 714924299 T^{2} \))(\( 1 - 25956 T + 714924299 T^{2} \))(\( 1 - 7464 T - 949863002 T^{2} - 5336194967736 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 35520 T + 1379363730 T^{2} + 25394111100480 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 37816 T + 1487579446 T^{2} + 27035577290984 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 37816 T + 1487579446 T^{2} - 27035577290984 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 35520 T + 1379363730 T^{2} - 25394111100480 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 7464 T - 949863002 T^{2} + 5336194967736 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 992 T + 1046429590 T^{2} - 709204904608 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 6952 T + 1381163878 T^{2} + 4970153726648 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 11104 T + 899856086 T^{2} - 7938519416096 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 992 T + 1046429590 T^{2} + 709204904608 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 83226 T + 4368725469 T^{2} - 137977877115220 T^{3} + 3123307993448271231 T^{4} - \)\(42\!\cdots\!26\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( 1 + 83226 T + 4368725469 T^{2} + 137977877115220 T^{3} + 3123307993448271231 T^{4} + \)\(42\!\cdots\!26\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( 1 + 5800 T - 228430544 T^{2} + 9932648143800 T^{3} + 786538339437354002 T^{4} + \)\(71\!\cdots\!00\)\( T^{5} - \)\(11\!\cdots\!44\)\( T^{6} + \)\(21\!\cdots\!00\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 - 16118 T + 1463792268 T^{2} - 35724021066486 T^{3} + 1126615118465122582 T^{4} - \)\(25\!\cdots\!14\)\( T^{5} + \)\(74\!\cdots\!68\)\( T^{6} - \)\(58\!\cdots\!82\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 + 16118 T + 1463792268 T^{2} + 35724021066486 T^{3} + 1126615118465122582 T^{4} + \)\(25\!\cdots\!14\)\( T^{5} + \)\(74\!\cdots\!68\)\( T^{6} + \)\(58\!\cdots\!82\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 - 5800 T - 228430544 T^{2} - 9932648143800 T^{3} + 786538339437354002 T^{4} - \)\(71\!\cdots\!00\)\( T^{5} - \)\(11\!\cdots\!44\)\( T^{6} - \)\(21\!\cdots\!00\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 - 63820 T + 4133539032 T^{2} - 164835478648900 T^{3} + 6459959775045425739 T^{4} - \)\(19\!\cdots\!20\)\( T^{5} + \)\(57\!\cdots\!44\)\( T^{6} - \)\(13\!\cdots\!80\)\( T^{7} + \)\(33\!\cdots\!39\)\( T^{8} - \)\(60\!\cdots\!00\)\( T^{9} + \)\(10\!\cdots\!32\)\( T^{10} - \)\(11\!\cdots\!80\)\( T^{11} + \)\(13\!\cdots\!01\)\( T^{12} \))(\( 1 + 63820 T + 4133539032 T^{2} + 164835478648900 T^{3} + 6459959775045425739 T^{4} + \)\(19\!\cdots\!20\)\( T^{5} + \)\(57\!\cdots\!44\)\( T^{6} + \)\(13\!\cdots\!80\)\( T^{7} + \)\(33\!\cdots\!39\)\( T^{8} + \)\(60\!\cdots\!00\)\( T^{9} + \)\(10\!\cdots\!32\)\( T^{10} + \)\(11\!\cdots\!80\)\( T^{11} + \)\(13\!\cdots\!01\)\( T^{12} \))
$61$ (\( 1 + 16622 T + 844596301 T^{2} \))(\( 1 + 18224 T + 844596301 T^{2} \))(\( 1 + 4560 T + 844596301 T^{2} \))(\( 1 + 379 T + 844596301 T^{2} \))(\( 1 + 21668 T + 844596301 T^{2} \))(\( 1 - 379 T + 844596301 T^{2} \))(\( 1 - 48740 T + 844596301 T^{2} \))(\( 1 - 18224 T + 844596301 T^{2} \))(\( 1 - 36112 T + 844596301 T^{2} \))(\( 1 + 5522 T + 844596301 T^{2} \))(\( 1 - 9838 T + 844596301 T^{2} \))(\( 1 - 1780 T + 844596301 T^{2} \))(\( 1 + 39188 T + 844596301 T^{2} \))(\( 1 + 51154 T + 1750994955 T^{2} + 43204479181354 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 68220 T + 2580926554 T^{2} - 57618359654220 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 3274 T - 95070973 T^{2} - 2765208289474 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 3274 T - 95070973 T^{2} + 2765208289474 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 68220 T + 2580926554 T^{2} + 57618359654220 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 51154 T + 1750994955 T^{2} - 43204479181354 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 37242 T + 1695607843 T^{2} + 31454455441842 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 45138 T + 2092145242 T^{2} - 38123387834538 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 3554 T + 491608410 T^{2} + 3001695253754 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 37242 T + 1695607843 T^{2} - 31454455441842 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 24330 T + 2178954975 T^{2} - 40865490255620 T^{3} + 1840337311930547475 T^{4} - \)\(17\!\cdots\!30\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( 1 + 24330 T + 2178954975 T^{2} + 40865490255620 T^{3} + 1840337311930547475 T^{4} + \)\(17\!\cdots\!30\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( 1 + 83720 T + 4627195636 T^{2} + 172113870704120 T^{3} + 5572286308486140470 T^{4} + \)\(14\!\cdots\!20\)\( T^{5} + \)\(33\!\cdots\!36\)\( T^{6} + \)\(50\!\cdots\!20\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} \))(\( 1 + 4221 T + 678336575 T^{2} + 1261547015454 T^{3} - 244770010134034536 T^{4} + \)\(10\!\cdots\!54\)\( T^{5} + \)\(48\!\cdots\!75\)\( T^{6} + \)\(25\!\cdots\!21\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} \))(\( 1 - 4221 T + 678336575 T^{2} - 1261547015454 T^{3} - 244770010134034536 T^{4} - \)\(10\!\cdots\!54\)\( T^{5} + \)\(48\!\cdots\!75\)\( T^{6} - \)\(25\!\cdots\!21\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} \))(\( 1 - 83720 T + 4627195636 T^{2} - 172113870704120 T^{3} + 5572286308486140470 T^{4} - \)\(14\!\cdots\!20\)\( T^{5} + \)\(33\!\cdots\!36\)\( T^{6} - \)\(50\!\cdots\!20\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} \))(\( 1 + 2204 T + 2514991794 T^{2} - 5084528767172 T^{3} + 2869836688198904439 T^{4} - \)\(19\!\cdots\!36\)\( T^{5} + \)\(24\!\cdots\!92\)\( T^{6} - \)\(16\!\cdots\!36\)\( T^{7} + \)\(20\!\cdots\!39\)\( T^{8} - \)\(30\!\cdots\!72\)\( T^{9} + \)\(12\!\cdots\!94\)\( T^{10} + \)\(94\!\cdots\!04\)\( T^{11} + \)\(36\!\cdots\!01\)\( T^{12} \))(\( 1 - 2204 T + 2514991794 T^{2} + 5084528767172 T^{3} + 2869836688198904439 T^{4} + \)\(19\!\cdots\!36\)\( T^{5} + \)\(24\!\cdots\!92\)\( T^{6} + \)\(16\!\cdots\!36\)\( T^{7} + \)\(20\!\cdots\!39\)\( T^{8} + \)\(30\!\cdots\!72\)\( T^{9} + \)\(12\!\cdots\!94\)\( T^{10} - \)\(94\!\cdots\!04\)\( T^{11} + \)\(36\!\cdots\!01\)\( T^{12} \))
$67$ (\( 1 - 1808 T + 1350125107 T^{2} \))(\( 1 + 13032 T + 1350125107 T^{2} \))(\( 1 - 37788 T + 1350125107 T^{2} \))(\( 1 + 35473 T + 1350125107 T^{2} \))(\( 1 - 52124 T + 1350125107 T^{2} \))(\( 1 + 35473 T + 1350125107 T^{2} \))(\( 1 + 44832 T + 1350125107 T^{2} \))(\( 1 + 13032 T + 1350125107 T^{2} \))(\( 1 - 66104 T + 1350125107 T^{2} \))(\( 1 + 24742 T + 1350125107 T^{2} \))(\( 1 - 33722 T + 1350125107 T^{2} \))(\( 1 - 25052 T + 1350125107 T^{2} \))(\( 1 - 4416 T + 1350125107 T^{2} \))(\( 1 + 24446 T + 2305848093 T^{2} + 33005158365722 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 22640 T + 2718901314 T^{2} + 30566832422480 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 41438 T + 3129223499 T^{2} - 55946484183866 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 41438 T + 3129223499 T^{2} - 55946484183866 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 22640 T + 2718901314 T^{2} + 30566832422480 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 24446 T + 2305848093 T^{2} + 33005158365722 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 64830 T + 3739158185 T^{2} - 87528610686810 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 54556 T + 3349390598 T^{2} + 73657425337492 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 65208 T + 2645517686 T^{2} - 88038957977256 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 64830 T + 3739158185 T^{2} - 87528610686810 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 37836 T + 765294261 T^{2} - 32007616310696 T^{3} + 1033242996019110927 T^{4} + \)\(68\!\cdots\!64\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( 1 + 37836 T + 765294261 T^{2} - 32007616310696 T^{3} + 1033242996019110927 T^{4} + \)\(68\!\cdots\!64\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( 1 + 33000 T + 5259529240 T^{2} + 125466399418200 T^{3} + 10527764775076193698 T^{4} + \)\(16\!\cdots\!00\)\( T^{5} + \)\(95\!\cdots\!60\)\( T^{6} + \)\(81\!\cdots\!00\)\( T^{7} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( 1 - 92923 T + 7317977555 T^{2} - 375075181209756 T^{3} + 16014048816352970828 T^{4} - \)\(50\!\cdots\!92\)\( T^{5} + \)\(13\!\cdots\!95\)\( T^{6} - \)\(22\!\cdots\!89\)\( T^{7} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( 1 - 92923 T + 7317977555 T^{2} - 375075181209756 T^{3} + 16014048816352970828 T^{4} - \)\(50\!\cdots\!92\)\( T^{5} + \)\(13\!\cdots\!95\)\( T^{6} - \)\(22\!\cdots\!89\)\( T^{7} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( 1 + 33000 T + 5259529240 T^{2} + 125466399418200 T^{3} + 10527764775076193698 T^{4} + \)\(16\!\cdots\!00\)\( T^{5} + \)\(95\!\cdots\!60\)\( T^{6} + \)\(81\!\cdots\!00\)\( T^{7} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( 1 + 71952 T + 5427158478 T^{2} + 293642751770144 T^{3} + 15433060608573106587 T^{4} + \)\(63\!\cdots\!56\)\( T^{5} + \)\(26\!\cdots\!44\)\( T^{6} + \)\(85\!\cdots\!92\)\( T^{7} + \)\(28\!\cdots\!63\)\( T^{8} + \)\(72\!\cdots\!92\)\( T^{9} + \)\(18\!\cdots\!78\)\( T^{10} + \)\(32\!\cdots\!64\)\( T^{11} + \)\(60\!\cdots\!49\)\( T^{12} \))(\( 1 + 71952 T + 5427158478 T^{2} + 293642751770144 T^{3} + 15433060608573106587 T^{4} + \)\(63\!\cdots\!56\)\( T^{5} + \)\(26\!\cdots\!44\)\( T^{6} + \)\(85\!\cdots\!92\)\( T^{7} + \)\(28\!\cdots\!63\)\( T^{8} + \)\(72\!\cdots\!92\)\( T^{9} + \)\(18\!\cdots\!78\)\( T^{10} + \)\(32\!\cdots\!64\)\( T^{11} + \)\(60\!\cdots\!49\)\( T^{12} \))
$71$ (\( 1 + 24528 T + 1804229351 T^{2} \))(\( 1 - 77056 T + 1804229351 T^{2} \))(\( 1 + 59304 T + 1804229351 T^{2} \))(\( 1 - 71814 T + 1804229351 T^{2} \))(\( 1 + 28560 T + 1804229351 T^{2} \))(\( 1 - 71814 T + 1804229351 T^{2} \))(\( 1 - 63736 T + 1804229351 T^{2} \))(\( 1 - 77056 T + 1804229351 T^{2} \))(\( 1 - 16080 T + 1804229351 T^{2} \))(\( 1 - 42372 T + 1804229351 T^{2} \))(\( 1 - 70212 T + 1804229351 T^{2} \))(\( 1 + 51984 T + 1804229351 T^{2} \))(\( 1 + 31880 T + 1804229351 T^{2} \))(\( 1 + 77496 T + 4875166942 T^{2} + 139820557785096 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 33928 T + 2679665998 T^{2} + 61213893420728 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 8520 T + 3293960686 T^{2} - 15372034070520 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 8520 T + 3293960686 T^{2} - 15372034070520 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 33928 T + 2679665998 T^{2} + 61213893420728 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 77496 T + 4875166942 T^{2} + 139820557785096 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 82800 T + 5183788686 T^{2} + 149390190262800 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 62272 T + 3502450894 T^{2} + 112352970145472 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 17104 T + 3301248782 T^{2} - 30859538819504 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 82800 T + 5183788686 T^{2} + 149390190262800 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 996 T + 5284207893 T^{2} + 3087495817080 T^{3} + 9533922977336467443 T^{4} + \)\(32\!\cdots\!96\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( 1 + 996 T + 5284207893 T^{2} + 3087495817080 T^{3} + 9533922977336467443 T^{4} + \)\(32\!\cdots\!96\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( 1 - 4112 T + 162751908 T^{2} - 37355181830544 T^{3} + 877858340675496870 T^{4} - \)\(67\!\cdots\!44\)\( T^{5} + \)\(52\!\cdots\!08\)\( T^{6} - \)\(24\!\cdots\!12\)\( T^{7} + \)\(10\!\cdots\!01\)\( T^{8} \))(\( 1 - 123154 T + 9917624532 T^{2} - 512649131256378 T^{3} + 23979389590658065078 T^{4} - \)\(92\!\cdots\!78\)\( T^{5} + \)\(32\!\cdots\!32\)\( T^{6} - \)\(72\!\cdots\!54\)\( T^{7} + \)\(10\!\cdots\!01\)\( T^{8} \))(\( 1 - 123154 T + 9917624532 T^{2} - 512649131256378 T^{3} + 23979389590658065078 T^{4} - \)\(92\!\cdots\!78\)\( T^{5} + \)\(32\!\cdots\!32\)\( T^{6} - \)\(72\!\cdots\!54\)\( T^{7} + \)\(10\!\cdots\!01\)\( T^{8} \))(\( 1 - 4112 T + 162751908 T^{2} - 37355181830544 T^{3} + 877858340675496870 T^{4} - \)\(67\!\cdots\!44\)\( T^{5} + \)\(52\!\cdots\!08\)\( T^{6} - \)\(24\!\cdots\!12\)\( T^{7} + \)\(10\!\cdots\!01\)\( T^{8} \))(\( 1 + 87000 T + 9976525050 T^{2} + 594195534260872 T^{3} + 38893897059875342127 T^{4} + \)\(17\!\cdots\!96\)\( T^{5} + \)\(87\!\cdots\!80\)\( T^{6} + \)\(32\!\cdots\!96\)\( T^{7} + \)\(12\!\cdots\!27\)\( T^{8} + \)\(34\!\cdots\!72\)\( T^{9} + \)\(10\!\cdots\!50\)\( T^{10} + \)\(16\!\cdots\!00\)\( T^{11} + \)\(34\!\cdots\!01\)\( T^{12} \))(\( 1 + 87000 T + 9976525050 T^{2} + 594195534260872 T^{3} + 38893897059875342127 T^{4} + \)\(17\!\cdots\!96\)\( T^{5} + \)\(87\!\cdots\!80\)\( T^{6} + \)\(32\!\cdots\!96\)\( T^{7} + \)\(12\!\cdots\!27\)\( T^{8} + \)\(34\!\cdots\!72\)\( T^{9} + \)\(10\!\cdots\!50\)\( T^{10} + \)\(16\!\cdots\!00\)\( T^{11} + \)\(34\!\cdots\!01\)\( T^{12} \))
$73$ (\( 1 + 20474 T + 2073071593 T^{2} \))(\( 1 - 2540 T + 2073071593 T^{2} \))(\( 1 - 8910 T + 2073071593 T^{2} \))(\( 1 - 31664 T + 2073071593 T^{2} \))(\( 1 - 70342 T + 2073071593 T^{2} \))(\( 1 + 31664 T + 2073071593 T^{2} \))(\( 1 + 60470 T + 2073071593 T^{2} \))(\( 1 + 2540 T + 2073071593 T^{2} \))(\( 1 - 80482 T + 2073071593 T^{2} \))(\( 1 - 52126 T + 2073071593 T^{2} \))(\( 1 + 21986 T + 2073071593 T^{2} \))(\( 1 + 47690 T + 2073071593 T^{2} \))(\( 1 - 5018 T + 2073071593 T^{2} \))(\( 1 - 13892 T + 4163480502 T^{2} - 28799110569956 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 18140 T + 4108700294 T^{2} - 37605518697020 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 28676 T + 114084326 T^{2} + 59447401000868 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 28676 T + 114084326 T^{2} - 59447401000868 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 18140 T + 4108700294 T^{2} + 37605518697020 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 13892 T + 4163480502 T^{2} + 28799110569956 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 8516 T + 1155149526 T^{2} + 17654277685988 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 40896 T + 3740866126 T^{2} + 84780335867328 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 36740 T + 1141498182 T^{2} - 76164650326820 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 8516 T + 1155149526 T^{2} - 17654277685988 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 167256 T + 14886868767 T^{2} - 826942238928544 T^{3} + 30861544749586635831 T^{4} - \)\(71\!\cdots\!44\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( 1 + 167256 T + 14886868767 T^{2} + 826942238928544 T^{3} + 30861544749586635831 T^{4} + \)\(71\!\cdots\!44\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( 1 + 84400 T + 8395914132 T^{2} + 436767418008080 T^{3} + 25012278932128479110 T^{4} + \)\(90\!\cdots\!40\)\( T^{5} + \)\(36\!\cdots\!68\)\( T^{6} + \)\(75\!\cdots\!00\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 - 70484 T + 3062731816 T^{2} + 111828103856548 T^{3} - 7770306300233393042 T^{4} + \)\(23\!\cdots\!64\)\( T^{5} + \)\(13\!\cdots\!84\)\( T^{6} - \)\(62\!\cdots\!88\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 + 70484 T + 3062731816 T^{2} - 111828103856548 T^{3} - 7770306300233393042 T^{4} - \)\(23\!\cdots\!64\)\( T^{5} + \)\(13\!\cdots\!84\)\( T^{6} + \)\(62\!\cdots\!88\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 - 84400 T + 8395914132 T^{2} - 436767418008080 T^{3} + 25012278932128479110 T^{4} - \)\(90\!\cdots\!40\)\( T^{5} + \)\(36\!\cdots\!68\)\( T^{6} - \)\(75\!\cdots\!00\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 + 88464 T + 8555939780 T^{2} + 612102154254320 T^{3} + 39809268201842804055 T^{4} + \)\(20\!\cdots\!84\)\( T^{5} + \)\(10\!\cdots\!96\)\( T^{6} + \)\(43\!\cdots\!12\)\( T^{7} + \)\(17\!\cdots\!95\)\( T^{8} + \)\(54\!\cdots\!40\)\( T^{9} + \)\(15\!\cdots\!80\)\( T^{10} + \)\(33\!\cdots\!52\)\( T^{11} + \)\(79\!\cdots\!49\)\( T^{12} \))(\( 1 - 88464 T + 8555939780 T^{2} - 612102154254320 T^{3} + 39809268201842804055 T^{4} - \)\(20\!\cdots\!84\)\( T^{5} + \)\(10\!\cdots\!96\)\( T^{6} - \)\(43\!\cdots\!12\)\( T^{7} + \)\(17\!\cdots\!95\)\( T^{8} - \)\(54\!\cdots\!40\)\( T^{9} + \)\(15\!\cdots\!80\)\( T^{10} - \)\(33\!\cdots\!52\)\( T^{11} + \)\(79\!\cdots\!49\)\( T^{12} \))
$79$ (\( 1 + 46240 T + 3077056399 T^{2} \))(\( 1 + 530 T + 3077056399 T^{2} \))(\( 1 - 27589 T + 3077056399 T^{2} \))(\( 1 - 8534 T + 3077056399 T^{2} \))(\( 1 - 58823 T + 3077056399 T^{2} \))(\( 1 - 8534 T + 3077056399 T^{2} \))(\( 1 + 43721 T + 3077056399 T^{2} \))(\( 1 + 530 T + 3077056399 T^{2} \))(\( 1 + 64147 T + 3077056399 T^{2} \))(\( 1 + 39640 T + 3077056399 T^{2} \))(\( 1 - 4520 T + 3077056399 T^{2} \))(\( 1 + 102121 T + 3077056399 T^{2} \))(\( 1 + 27977 T + 3077056399 T^{2} \))(\( 1 - 17944 T + 5384465838 T^{2} - 55214700023656 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 23600 T + 475376373 T^{2} - 72618531016400 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 3552 T + 6073781038 T^{2} - 10929704329248 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 3552 T + 6073781038 T^{2} - 10929704329248 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 23600 T + 475376373 T^{2} - 72618531016400 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 17944 T + 5384465838 T^{2} - 55214700023656 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 85136 T + 5230299998 T^{2} + 261968273585264 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 62069 T + 5500962758 T^{2} - 190989813629531 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 72245 T + 6817044654 T^{2} - 222301939545755 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 85136 T + 5230299998 T^{2} + 261968273585264 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 8796 T + 6777348012 T^{2} + 13639242317108 T^{3} + 20854282068574528788 T^{4} + \)\(83\!\cdots\!96\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( 1 + 8796 T + 6777348012 T^{2} + 13639242317108 T^{3} + 20854282068574528788 T^{4} + \)\(83\!\cdots\!96\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( 1 + 44648 T + 3915859882 T^{2} + 198304071878096 T^{3} + 23368298036236933259 T^{4} + \)\(61\!\cdots\!04\)\( T^{5} + \)\(37\!\cdots\!82\)\( T^{6} + \)\(13\!\cdots\!52\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} \))(\( 1 - 190524 T + 24312482576 T^{2} - 2033714917891788 T^{3} + \)\(13\!\cdots\!46\)\( T^{4} - \)\(62\!\cdots\!12\)\( T^{5} + \)\(23\!\cdots\!76\)\( T^{6} - \)\(55\!\cdots\!76\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} \))(\( 1 - 190524 T + 24312482576 T^{2} - 2033714917891788 T^{3} + \)\(13\!\cdots\!46\)\( T^{4} - \)\(62\!\cdots\!12\)\( T^{5} + \)\(23\!\cdots\!76\)\( T^{6} - \)\(55\!\cdots\!76\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} \))(\( 1 + 44648 T + 3915859882 T^{2} + 198304071878096 T^{3} + 23368298036236933259 T^{4} + \)\(61\!\cdots\!04\)\( T^{5} + \)\(37\!\cdots\!82\)\( T^{6} + \)\(13\!\cdots\!52\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} \))(\( 1 - 174624 T + 18535506032 T^{2} - 1289538846863048 T^{3} + 77895867205793408136 T^{4} - \)\(42\!\cdots\!56\)\( T^{5} + \)\(24\!\cdots\!62\)\( T^{6} - \)\(13\!\cdots\!44\)\( T^{7} + \)\(73\!\cdots\!36\)\( T^{8} - \)\(37\!\cdots\!52\)\( T^{9} + \)\(16\!\cdots\!32\)\( T^{10} - \)\(48\!\cdots\!76\)\( T^{11} + \)\(84\!\cdots\!01\)\( T^{12} \))(\( 1 - 174624 T + 18535506032 T^{2} - 1289538846863048 T^{3} + 77895867205793408136 T^{4} - \)\(42\!\cdots\!56\)\( T^{5} + \)\(24\!\cdots\!62\)\( T^{6} - \)\(13\!\cdots\!44\)\( T^{7} + \)\(73\!\cdots\!36\)\( T^{8} - \)\(37\!\cdots\!52\)\( T^{9} + \)\(16\!\cdots\!32\)\( T^{10} - \)\(48\!\cdots\!76\)\( T^{11} + \)\(84\!\cdots\!01\)\( T^{12} \))
$83$ (\( 1 - 51576 T + 3939040643 T^{2} \))(\( 1 + 78344 T + 3939040643 T^{2} \))(\( 1 + 67676 T + 3939040643 T^{2} \))(\( 1 + 106551 T + 3939040643 T^{2} \))(\( 1 + 756 T + 3939040643 T^{2} \))(\( 1 - 106551 T + 3939040643 T^{2} \))(\( 1 + 97276 T + 3939040643 T^{2} \))(\( 1 - 78344 T + 3939040643 T^{2} \))(\( 1 - 106284 T + 3939040643 T^{2} \))(\( 1 - 59826 T + 3939040643 T^{2} \))(\( 1 - 109074 T + 3939040643 T^{2} \))(\( 1 - 83676 T + 3939040643 T^{2} \))(\( 1 + 37644 T + 3939040643 T^{2} \))(\( 1 + 74694 T + 7297411861 T^{2} + 294222701788242 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 67840 T + 5922418934 T^{2} + 267224517221120 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 54982 T + 8517406483 T^{2} - 216576332633426 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 54982 T + 8517406483 T^{2} + 216576332633426 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 67840 T + 5922418934 T^{2} - 267224517221120 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 74694 T + 7297411861 T^{2} - 294222701788242 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 9930 T + 4650013585 T^{2} + 39114673584990 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 189600 T + 16864958710 T^{2} + 746842105912800 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 99676 T + 8405717894 T^{2} + 392627815131668 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 9930 T + 4650013585 T^{2} - 39114673584990 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 2418 T + 11189413017 T^{2} + 19315102603532 T^{3} + 44075552645276249931 T^{4} + \)\(37\!\cdots\!82\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 - 2418 T + 11189413017 T^{2} - 19315102603532 T^{3} + 44075552645276249931 T^{4} - \)\(37\!\cdots\!82\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 + 129120 T + 20912281996 T^{2} + 1580873942983520 T^{3} + \)\(13\!\cdots\!02\)\( T^{4} + \)\(62\!\cdots\!60\)\( T^{5} + \)\(32\!\cdots\!04\)\( T^{6} + \)\(78\!\cdots\!40\)\( T^{7} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 - 205189 T + 22470089835 T^{2} - 1618232342295012 T^{3} + \)\(10\!\cdots\!88\)\( T^{4} - \)\(63\!\cdots\!16\)\( T^{5} + \)\(34\!\cdots\!15\)\( T^{6} - \)\(12\!\cdots\!23\)\( T^{7} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 + 205189 T + 22470089835 T^{2} + 1618232342295012 T^{3} + \)\(10\!\cdots\!88\)\( T^{4} + \)\(63\!\cdots\!16\)\( T^{5} + \)\(34\!\cdots\!15\)\( T^{6} + \)\(12\!\cdots\!23\)\( T^{7} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 - 129120 T + 20912281996 T^{2} - 1580873942983520 T^{3} + \)\(13\!\cdots\!02\)\( T^{4} - \)\(62\!\cdots\!60\)\( T^{5} + \)\(32\!\cdots\!04\)\( T^{6} - \)\(78\!\cdots\!40\)\( T^{7} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 + 63324 T + 10564443988 T^{2} + 748236327493476 T^{3} + 68989120112715563423 T^{4} + \)\(42\!\cdots\!60\)\( T^{5} + \)\(31\!\cdots\!12\)\( T^{6} + \)\(16\!\cdots\!80\)\( T^{7} + \)\(10\!\cdots\!27\)\( T^{8} + \)\(45\!\cdots\!32\)\( T^{9} + \)\(25\!\cdots\!88\)\( T^{10} + \)\(60\!\cdots\!32\)\( T^{11} + \)\(37\!\cdots\!49\)\( T^{12} \))(\( 1 - 63324 T + 10564443988 T^{2} - 748236327493476 T^{3} + 68989120112715563423 T^{4} - \)\(42\!\cdots\!60\)\( T^{5} + \)\(31\!\cdots\!12\)\( T^{6} - \)\(16\!\cdots\!80\)\( T^{7} + \)\(10\!\cdots\!27\)\( T^{8} - \)\(45\!\cdots\!32\)\( T^{9} + \)\(25\!\cdots\!88\)\( T^{10} - \)\(60\!\cdots\!32\)\( T^{11} + \)\(37\!\cdots\!49\)\( T^{12} \))
$89$ (\( 1 - 110310 T + 5584059449 T^{2} \))(\( 1 - 90758 T + 5584059449 T^{2} \))(\( 1 + 10700 T + 5584059449 T^{2} \))(\( 1 + 12303 T + 5584059449 T^{2} \))(\( 1 + 135384 T + 5584059449 T^{2} \))(\( 1 - 12303 T + 5584059449 T^{2} \))(\( 1 + 45560 T + 5584059449 T^{2} \))(\( 1 + 90758 T + 5584059449 T^{2} \))(\( 1 - 71676 T + 5584059449 T^{2} \))(\( 1 + 57690 T + 5584059449 T^{2} \))(\( 1 + 38490 T + 5584059449 T^{2} \))(\( 1 - 32400 T + 5584059449 T^{2} \))(\( 1 - 17216 T + 5584059449 T^{2} \))(\( 1 - 4662 T + 6539386795 T^{2} - 26032885151238 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 72380 T + 12375892498 T^{2} - 404174222918620 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 81578 T + 10636136683 T^{2} + 455536401730522 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 81578 T + 10636136683 T^{2} - 455536401730522 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 72380 T + 12375892498 T^{2} + 404174222918620 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 4662 T + 6539386795 T^{2} + 26032885151238 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 181530 T + 18938890299 T^{2} + 1013674311776970 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 64190 T + 10032531898 T^{2} + 358440776031310 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 82454 T + 5676583178 T^{2} + 460428037807846 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 181530 T + 18938890299 T^{2} - 1013674311776970 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 14292 T + 8217900747 T^{2} - 187245812389784 T^{3} + 45889246317229508403 T^{4} + \)\(44\!\cdots\!92\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( 1 - 14292 T + 8217900747 T^{2} + 187245812389784 T^{3} + 45889246317229508403 T^{4} - \)\(44\!\cdots\!92\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( 1 + 309800 T + 51469973748 T^{2} + 5970269052356280 T^{3} + \)\(51\!\cdots\!02\)\( T^{4} + \)\(33\!\cdots\!20\)\( T^{5} + \)\(16\!\cdots\!48\)\( T^{6} + \)\(53\!\cdots\!00\)\( T^{7} + \)\(97\!\cdots\!01\)\( T^{8} \))(\( 1 + 295903 T + 45929634153 T^{2} + 5172270437119674 T^{3} + \)\(44\!\cdots\!78\)\( T^{4} + \)\(28\!\cdots\!26\)\( T^{5} + \)\(14\!\cdots\!53\)\( T^{6} + \)\(51\!\cdots\!47\)\( T^{7} + \)\(97\!\cdots\!01\)\( T^{8} \))(\( 1 - 295903 T + 45929634153 T^{2} - 5172270437119674 T^{3} + \)\(44\!\cdots\!78\)\( T^{4} - \)\(28\!\cdots\!26\)\( T^{5} + \)\(14\!\cdots\!53\)\( T^{6} - \)\(51\!\cdots\!47\)\( T^{7} + \)\(97\!\cdots\!01\)\( T^{8} \))(\( 1 - 309800 T + 51469973748 T^{2} - 5970269052356280 T^{3} + \)\(51\!\cdots\!02\)\( T^{4} - \)\(33\!\cdots\!20\)\( T^{5} + \)\(16\!\cdots\!48\)\( T^{6} - \)\(53\!\cdots\!00\)\( T^{7} + \)\(97\!\cdots\!01\)\( T^{8} \))(\( 1 - 72520 T + 20045674724 T^{2} - 771639579634840 T^{3} + \)\(15\!\cdots\!71\)\( T^{4} - \)\(23\!\cdots\!80\)\( T^{5} + \)\(86\!\cdots\!08\)\( T^{6} - \)\(12\!\cdots\!20\)\( T^{7} + \)\(49\!\cdots\!71\)\( T^{8} - \)\(13\!\cdots\!60\)\( T^{9} + \)\(19\!\cdots\!24\)\( T^{10} - \)\(39\!\cdots\!80\)\( T^{11} + \)\(30\!\cdots\!01\)\( T^{12} \))(\( 1 + 72520 T + 20045674724 T^{2} + 771639579634840 T^{3} + \)\(15\!\cdots\!71\)\( T^{4} + \)\(23\!\cdots\!80\)\( T^{5} + \)\(86\!\cdots\!08\)\( T^{6} + \)\(12\!\cdots\!20\)\( T^{7} + \)\(49\!\cdots\!71\)\( T^{8} + \)\(13\!\cdots\!60\)\( T^{9} + \)\(19\!\cdots\!24\)\( T^{10} + \)\(39\!\cdots\!80\)\( T^{11} + \)\(30\!\cdots\!01\)\( T^{12} \))
$97$ (\( 1 - 78382 T + 8587340257 T^{2} \))(\( 1 - 116750 T + 8587340257 T^{2} \))(\( 1 + 65075 T + 8587340257 T^{2} \))(\( 1 + 102802 T + 8587340257 T^{2} \))(\( 1 + 110435 T + 8587340257 T^{2} \))(\( 1 - 102802 T + 8587340257 T^{2} \))(\( 1 - 57295 T + 8587340257 T^{2} \))(\( 1 + 116750 T + 8587340257 T^{2} \))(\( 1 + 151025 T + 8587340257 T^{2} \))(\( 1 - 144382 T + 8587340257 T^{2} \))(\( 1 - 1918 T + 8587340257 T^{2} \))(\( 1 - 148645 T + 8587340257 T^{2} \))(\( 1 - 63175 T + 8587340257 T^{2} \))(\( 1 + 29068 T + 12461384934 T^{2} + 249616806590476 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 143650 T + 22148969939 T^{2} + 1233571427918050 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 106964 T + 17911970214 T^{2} - 918536263249748 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 106964 T + 17911970214 T^{2} + 918536263249748 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 143650 T + 22148969939 T^{2} - 1233571427918050 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 29068 T + 12461384934 T^{2} - 249616806590476 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 78948 T + 10795370374 T^{2} - 677953338609636 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 155547 T + 22978754524 T^{2} + 1335735014955579 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 104627 T + 12436884864 T^{2} - 898467649069139 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 78948 T + 10795370374 T^{2} + 677953338609636 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 103710 T + 14791745196 T^{2} - 1416915438419940 T^{3} + \)\(12\!\cdots\!72\)\( T^{4} - \)\(76\!\cdots\!90\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( 1 + 103710 T + 14791745196 T^{2} + 1416915438419940 T^{3} + \)\(12\!\cdots\!72\)\( T^{4} + \)\(76\!\cdots\!90\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( 1 - 5220 T + 27657295382 T^{2} + 978769401240 T^{3} + \)\(32\!\cdots\!79\)\( T^{4} + \)\(84\!\cdots\!80\)\( T^{5} + \)\(20\!\cdots\!18\)\( T^{6} - \)\(33\!\cdots\!60\)\( T^{7} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( 1 - 237344 T + 40866891628 T^{2} - 5179571017419296 T^{3} + \)\(55\!\cdots\!34\)\( T^{4} - \)\(44\!\cdots\!72\)\( T^{5} + \)\(30\!\cdots\!72\)\( T^{6} - \)\(15\!\cdots\!92\)\( T^{7} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( 1 + 237344 T + 40866891628 T^{2} + 5179571017419296 T^{3} + \)\(55\!\cdots\!34\)\( T^{4} + \)\(44\!\cdots\!72\)\( T^{5} + \)\(30\!\cdots\!72\)\( T^{6} + \)\(15\!\cdots\!92\)\( T^{7} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( 1 + 5220 T + 27657295382 T^{2} - 978769401240 T^{3} + \)\(32\!\cdots\!79\)\( T^{4} - \)\(84\!\cdots\!80\)\( T^{5} + \)\(20\!\cdots\!18\)\( T^{6} + \)\(33\!\cdots\!60\)\( T^{7} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( 1 + 230036 T + 46112153542 T^{2} + 4760347862078224 T^{3} + \)\(44\!\cdots\!28\)\( T^{4} + \)\(20\!\cdots\!68\)\( T^{5} + \)\(18\!\cdots\!56\)\( T^{6} + \)\(17\!\cdots\!76\)\( T^{7} + \)\(32\!\cdots\!72\)\( T^{8} + \)\(30\!\cdots\!32\)\( T^{9} + \)\(25\!\cdots\!42\)\( T^{10} + \)\(10\!\cdots\!52\)\( T^{11} + \)\(40\!\cdots\!49\)\( T^{12} \))(\( 1 - 230036 T + 46112153542 T^{2} - 4760347862078224 T^{3} + \)\(44\!\cdots\!28\)\( T^{4} - \)\(20\!\cdots\!68\)\( T^{5} + \)\(18\!\cdots\!56\)\( T^{6} - \)\(17\!\cdots\!76\)\( T^{7} + \)\(32\!\cdots\!72\)\( T^{8} - \)\(30\!\cdots\!32\)\( T^{9} + \)\(25\!\cdots\!42\)\( T^{10} - \)\(10\!\cdots\!52\)\( T^{11} + \)\(40\!\cdots\!49\)\( T^{12} \))
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