Properties

Label 525.4.a
Level $525$
Weight $4$
Character orbit 525.a
Rep. character $\chi_{525}(1,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $24$
Sturm bound $320$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 525.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(320\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(525))\).

Total New Old
Modular forms 252 56 196
Cusp forms 228 56 172
Eisenstein series 24 0 24

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

\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(31\)
Minus space\(-\)\(25\)

Trace form

\( 56q + 6q^{2} + 194q^{4} + 12q^{6} + 14q^{7} + 30q^{8} + 504q^{9} + O(q^{10}) \) \( 56q + 6q^{2} + 194q^{4} + 12q^{6} + 14q^{7} + 30q^{8} + 504q^{9} + 20q^{11} - 24q^{12} + 112q^{13} - 70q^{14} + 858q^{16} - 56q^{17} + 54q^{18} + 40q^{19} - 42q^{21} - 152q^{22} - 212q^{23} + 324q^{24} + 868q^{26} + 70q^{28} + 920q^{29} - 72q^{31} + 1086q^{32} + 288q^{33} + 644q^{34} + 1746q^{36} + 152q^{37} - 712q^{38} - 336q^{39} + 176q^{41} + 84q^{42} + 240q^{43} + 716q^{44} + 2228q^{46} - 824q^{47} + 432q^{48} + 2744q^{49} + 276q^{51} + 1636q^{52} - 480q^{53} + 108q^{54} - 378q^{56} + 192q^{57} - 268q^{58} - 952q^{59} - 3832q^{61} + 2520q^{62} + 126q^{63} + 3790q^{64} + 1896q^{66} - 168q^{67} + 2596q^{68} + 336q^{69} - 1676q^{71} + 270q^{72} - 2520q^{73} - 9280q^{74} + 3672q^{76} - 1176q^{77} + 1464q^{78} + 336q^{79} + 4536q^{81} + 1604q^{82} - 4208q^{83} - 504q^{84} - 9340q^{86} + 792q^{87} - 4952q^{88} - 5120q^{89} - 1148q^{91} - 1568q^{92} - 816q^{93} + 9904q^{94} + 7764q^{96} + 4520q^{97} + 294q^{98} + 180q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(525))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 7
525.4.a.a \(1\) \(30.976\) \(\Q\) None \(-5\) \(3\) \(0\) \(-7\) \(-\) \(+\) \(+\) \(q-5q^{2}+3q^{3}+17q^{4}-15q^{6}-7q^{7}+\cdots\)
525.4.a.b \(1\) \(30.976\) \(\Q\) None \(-4\) \(3\) \(0\) \(7\) \(-\) \(+\) \(-\) \(q-4q^{2}+3q^{3}+8q^{4}-12q^{6}+7q^{7}+\cdots\)
525.4.a.c \(1\) \(30.976\) \(\Q\) None \(-3\) \(-3\) \(0\) \(7\) \(+\) \(-\) \(-\) \(q-3q^{2}-3q^{3}+q^{4}+9q^{6}+7q^{7}+\cdots\)
525.4.a.d \(1\) \(30.976\) \(\Q\) None \(-2\) \(3\) \(0\) \(-7\) \(-\) \(+\) \(+\) \(q-2q^{2}+3q^{3}-4q^{4}-6q^{6}-7q^{7}+\cdots\)
525.4.a.e \(1\) \(30.976\) \(\Q\) None \(0\) \(3\) \(0\) \(-7\) \(-\) \(+\) \(+\) \(q+3q^{3}-8q^{4}-7q^{7}+9q^{9}+42q^{11}+\cdots\)
525.4.a.f \(1\) \(30.976\) \(\Q\) None \(2\) \(-3\) \(0\) \(7\) \(+\) \(-\) \(-\) \(q+2q^{2}-3q^{3}-4q^{4}-6q^{6}+7q^{7}+\cdots\)
525.4.a.g \(1\) \(30.976\) \(\Q\) None \(3\) \(3\) \(0\) \(-7\) \(-\) \(+\) \(+\) \(q+3q^{2}+3q^{3}+q^{4}+9q^{6}-7q^{7}+\cdots\)
525.4.a.h \(1\) \(30.976\) \(\Q\) None \(3\) \(3\) \(0\) \(-7\) \(-\) \(+\) \(+\) \(q+3q^{2}+3q^{3}+q^{4}+9q^{6}-7q^{7}+\cdots\)
525.4.a.i \(2\) \(30.976\) \(\Q(\sqrt{41}) \) None \(-3\) \(-6\) \(0\) \(-14\) \(+\) \(+\) \(+\) \(q+(-1-\beta )q^{2}-3q^{3}+(3+3\beta )q^{4}+\cdots\)
525.4.a.j \(2\) \(30.976\) \(\Q(\sqrt{17}) \) None \(-3\) \(6\) \(0\) \(14\) \(-\) \(-\) \(-\) \(q+(-1-\beta )q^{2}+3q^{3}+(-3+3\beta )q^{4}+\cdots\)
525.4.a.k \(2\) \(30.976\) \(\Q(\sqrt{65}) \) None \(-1\) \(-6\) \(0\) \(14\) \(+\) \(+\) \(-\) \(q-\beta q^{2}-3q^{3}+(8+\beta )q^{4}+3\beta q^{6}+\cdots\)
525.4.a.l \(2\) \(30.976\) \(\Q(\sqrt{2}) \) None \(2\) \(6\) \(0\) \(14\) \(-\) \(+\) \(-\) \(q+(1+\beta )q^{2}+3q^{3}+(1+2\beta )q^{4}+(3+\cdots)q^{6}+\cdots\)
525.4.a.m \(2\) \(30.976\) \(\Q(\sqrt{17}) \) None \(3\) \(-6\) \(0\) \(-14\) \(+\) \(+\) \(+\) \(q+(1+\beta )q^{2}-3q^{3}+(-3+3\beta )q^{4}+\cdots\)
525.4.a.n \(2\) \(30.976\) \(\Q(\sqrt{57}) \) None \(3\) \(-6\) \(0\) \(-14\) \(+\) \(+\) \(+\) \(q+(1+\beta )q^{2}-3q^{3}+(7+3\beta )q^{4}+(-3+\cdots)q^{6}+\cdots\)
525.4.a.o \(2\) \(30.976\) \(\Q(\sqrt{5}) \) None \(4\) \(-6\) \(0\) \(14\) \(+\) \(+\) \(-\) \(q+(2+\beta )q^{2}-3q^{3}+(1+4\beta )q^{4}+(-6+\cdots)q^{6}+\cdots\)
525.4.a.p \(2\) \(30.976\) \(\Q(\sqrt{17}) \) None \(7\) \(6\) \(0\) \(14\) \(-\) \(+\) \(-\) \(q+(4-\beta )q^{2}+3q^{3}+(12-7\beta )q^{4}+(12+\cdots)q^{6}+\cdots\)
525.4.a.q \(3\) \(30.976\) 3.3.2292.1 None \(-1\) \(9\) \(0\) \(21\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+3q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
525.4.a.r \(3\) \(30.976\) 3.3.2292.1 None \(1\) \(-9\) \(0\) \(-21\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
525.4.a.s \(4\) \(30.976\) 4.4.26729725.1 None \(-6\) \(-12\) \(0\) \(28\) \(+\) \(+\) \(-\) \(q+(-1-\beta _{1})q^{2}-3q^{3}+(3+3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
525.4.a.t \(4\) \(30.976\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-12\) \(0\) \(-28\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+3\beta _{1}q^{6}+\cdots\)
525.4.a.u \(4\) \(30.976\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(12\) \(0\) \(28\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+3\beta _{1}q^{6}+\cdots\)
525.4.a.v \(4\) \(30.976\) 4.4.26729725.1 None \(6\) \(12\) \(0\) \(-28\) \(-\) \(-\) \(+\) \(q+(1+\beta _{1})q^{2}+3q^{3}+(3+3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
525.4.a.w \(5\) \(30.976\) 5.5.78066700.1 None \(-1\) \(15\) \(0\) \(-35\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+3q^{3}+(5-\beta _{1}-\beta _{3})q^{4}+\cdots\)
525.4.a.x \(5\) \(30.976\) 5.5.78066700.1 None \(1\) \(-15\) \(0\) \(35\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(5-\beta _{1}-\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(525))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(525)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 5 T + 8 T^{2} \))(\( 1 + 4 T + 8 T^{2} \))(\( 1 + 3 T + 8 T^{2} \))(\( 1 + 2 T + 8 T^{2} \))(\( 1 + 8 T^{2} \))(\( 1 - 2 T + 8 T^{2} \))(\( 1 - 3 T + 8 T^{2} \))(\( 1 - 3 T + 8 T^{2} \))(\( 1 + 3 T + 8 T^{2} + 24 T^{3} + 64 T^{4} \))(\( 1 + 3 T + 14 T^{2} + 24 T^{3} + 64 T^{4} \))(\( 1 + T + 8 T^{3} + 64 T^{4} \))(\( 1 - 2 T + 9 T^{2} - 16 T^{3} + 64 T^{4} \))(\( 1 - 3 T + 14 T^{2} - 24 T^{3} + 64 T^{4} \))(\( 1 - 3 T + 4 T^{2} - 24 T^{3} + 64 T^{4} \))(\( 1 - 4 T + 15 T^{2} - 32 T^{3} + 64 T^{4} \))(\( 1 - 7 T + 24 T^{2} - 56 T^{3} + 64 T^{4} \))(\( 1 + T + 11 T^{2} + 15 T^{3} + 88 T^{4} + 64 T^{5} + 512 T^{6} \))(\( 1 - T + 11 T^{2} - 15 T^{3} + 88 T^{4} - 64 T^{5} + 512 T^{6} \))(\( 1 + 6 T + 26 T^{2} + 99 T^{3} + 298 T^{4} + 792 T^{5} + 1664 T^{6} + 3072 T^{7} + 4096 T^{8} \))(\( 1 + 8 T^{2} + 3 T^{3} + 46 T^{4} + 24 T^{5} + 512 T^{6} + 4096 T^{8} \))(\( 1 + 8 T^{2} - 3 T^{3} + 46 T^{4} - 24 T^{5} + 512 T^{6} + 4096 T^{8} \))(\( 1 - 6 T + 26 T^{2} - 99 T^{3} + 298 T^{4} - 792 T^{5} + 1664 T^{6} - 3072 T^{7} + 4096 T^{8} \))(\( 1 + T + 7 T^{2} + 15 T^{3} + 48 T^{4} + 32 T^{5} + 384 T^{6} + 960 T^{7} + 3584 T^{8} + 4096 T^{9} + 32768 T^{10} \))(\( 1 - T + 7 T^{2} - 15 T^{3} + 48 T^{4} - 32 T^{5} + 384 T^{6} - 960 T^{7} + 3584 T^{8} - 4096 T^{9} + 32768 T^{10} \))
$3$ (\( 1 - 3 T \))(\( 1 - 3 T \))(\( 1 + 3 T \))(\( 1 - 3 T \))(\( 1 - 3 T \))(\( 1 + 3 T \))(\( 1 - 3 T \))(\( 1 - 3 T \))(\( ( 1 + 3 T )^{2} \))(\( ( 1 - 3 T )^{2} \))(\( ( 1 + 3 T )^{2} \))(\( ( 1 - 3 T )^{2} \))(\( ( 1 + 3 T )^{2} \))(\( ( 1 + 3 T )^{2} \))(\( ( 1 + 3 T )^{2} \))(\( ( 1 - 3 T )^{2} \))(\( ( 1 - 3 T )^{3} \))(\( ( 1 + 3 T )^{3} \))(\( ( 1 + 3 T )^{4} \))(\( ( 1 + 3 T )^{4} \))(\( ( 1 - 3 T )^{4} \))(\( ( 1 - 3 T )^{4} \))(\( ( 1 - 3 T )^{5} \))(\( ( 1 + 3 T )^{5} \))
$5$ 1
$7$ (\( 1 + 7 T \))(\( 1 - 7 T \))(\( 1 - 7 T \))(\( 1 + 7 T \))(\( 1 + 7 T \))(\( 1 - 7 T \))(\( 1 + 7 T \))(\( 1 + 7 T \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 - 7 T )^{2} \))(\( ( 1 - 7 T )^{2} \))(\( ( 1 - 7 T )^{2} \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 - 7 T )^{2} \))(\( ( 1 - 7 T )^{2} \))(\( ( 1 - 7 T )^{3} \))(\( ( 1 + 7 T )^{3} \))(\( ( 1 - 7 T )^{4} \))(\( ( 1 + 7 T )^{4} \))(\( ( 1 - 7 T )^{4} \))(\( ( 1 + 7 T )^{4} \))(\( ( 1 + 7 T )^{5} \))(\( ( 1 - 7 T )^{5} \))
$11$ (\( 1 - 12 T + 1331 T^{2} \))(\( 1 - 62 T + 1331 T^{2} \))(\( 1 + 6 T + 1331 T^{2} \))(\( 1 + 21 T + 1331 T^{2} \))(\( 1 - 42 T + 1331 T^{2} \))(\( 1 + 21 T + 1331 T^{2} \))(\( 1 + 36 T + 1331 T^{2} \))(\( 1 + 6 T + 1331 T^{2} \))(\( 1 - 62 T + 3582 T^{2} - 82522 T^{3} + 1771561 T^{4} \))(\( 1 + 31 T + 2796 T^{2} + 41261 T^{3} + 1771561 T^{4} \))(\( 1 + 22 T + 2718 T^{2} + 29282 T^{3} + 1771561 T^{4} \))(\( 1 + 16 T - 474 T^{2} + 21296 T^{3} + 1771561 T^{4} \))(\( 1 + 31 T + 2796 T^{2} + 41261 T^{3} + 1771561 T^{4} \))(\( 1 + 6 T + 1246 T^{2} + 7986 T^{3} + 1771561 T^{4} \))(\( 1 + 92 T + 4758 T^{2} + 122452 T^{3} + 1771561 T^{4} \))(\( 1 + 26 T + 2406 T^{2} + 34606 T^{3} + 1771561 T^{4} \))(\( 1 + 66 T + 3717 T^{2} + 169572 T^{3} + 4947327 T^{4} + 116923026 T^{5} + 2357947691 T^{6} \))(\( 1 + 66 T + 3717 T^{2} + 169572 T^{3} + 4947327 T^{4} + 116923026 T^{5} + 2357947691 T^{6} \))(\( 1 - 57 T + 4001 T^{2} - 182772 T^{3} + 7206874 T^{4} - 243269532 T^{5} + 7088015561 T^{6} - 134403018387 T^{7} + 3138428376721 T^{8} \))(\( 1 - 21 T + 2681 T^{2} - 22236 T^{3} + 3289690 T^{4} - 29596116 T^{5} + 4749555041 T^{6} - 49516901511 T^{7} + 3138428376721 T^{8} \))(\( 1 - 21 T + 2681 T^{2} - 22236 T^{3} + 3289690 T^{4} - 29596116 T^{5} + 4749555041 T^{6} - 49516901511 T^{7} + 3138428376721 T^{8} \))(\( 1 - 57 T + 4001 T^{2} - 182772 T^{3} + 7206874 T^{4} - 243269532 T^{5} + 7088015561 T^{6} - 134403018387 T^{7} + 3138428376721 T^{8} \))(\( 1 - 66 T + 4555 T^{2} - 210928 T^{3} + 10802758 T^{4} - 383496700 T^{5} + 14378470898 T^{6} - 373671818608 T^{7} + 10740451732505 T^{8} - 207136272863586 T^{9} + 4177248169415651 T^{10} \))(\( 1 - 66 T + 4555 T^{2} - 210928 T^{3} + 10802758 T^{4} - 383496700 T^{5} + 14378470898 T^{6} - 373671818608 T^{7} + 10740451732505 T^{8} - 207136272863586 T^{9} + 4177248169415651 T^{10} \))
$13$ (\( 1 + 30 T + 2197 T^{2} \))(\( 1 - 62 T + 2197 T^{2} \))(\( 1 - 41 T + 2197 T^{2} \))(\( 1 - 24 T + 2197 T^{2} \))(\( 1 + 20 T + 2197 T^{2} \))(\( 1 + 24 T + 2197 T^{2} \))(\( 1 - 34 T + 2197 T^{2} \))(\( 1 + 41 T + 2197 T^{2} \))(\( 1 - 6 T + 3378 T^{2} - 13182 T^{3} + 4826809 T^{4} \))(\( 1 + 39 T + 3546 T^{2} + 85683 T^{3} + 4826809 T^{4} \))(\( 1 - 22 T + 4450 T^{2} - 48334 T^{3} + 4826809 T^{4} \))(\( 1 - 76 T + 5806 T^{2} - 166972 T^{3} + 4826809 T^{4} \))(\( 1 - 39 T + 3546 T^{2} - 85683 T^{3} + 4826809 T^{4} \))(\( 1 + 16 T + 2406 T^{2} + 35152 T^{3} + 4826809 T^{4} \))(\( 1 + 8 T - 2810 T^{2} + 17576 T^{3} + 4826809 T^{4} \))(\( 1 + 14 T + 2386 T^{2} + 30758 T^{3} + 4826809 T^{4} \))(\( 1 + 102 T + 9675 T^{2} + 476884 T^{3} + 21255975 T^{4} + 492334518 T^{5} + 10604499373 T^{6} \))(\( 1 - 102 T + 9675 T^{2} - 476884 T^{3} + 21255975 T^{4} - 492334518 T^{5} + 10604499373 T^{6} \))(\( 1 + 43 T + 4464 T^{2} + 221093 T^{3} + 13201958 T^{4} + 485741321 T^{5} + 21546875376 T^{6} + 455993473039 T^{7} + 23298085122481 T^{8} \))(\( 1 + 5 T + 1848 T^{2} - 69653 T^{3} - 988138 T^{4} - 153027641 T^{5} + 8919943032 T^{6} + 53022496865 T^{7} + 23298085122481 T^{8} \))(\( 1 - 5 T + 1848 T^{2} + 69653 T^{3} - 988138 T^{4} + 153027641 T^{5} + 8919943032 T^{6} - 53022496865 T^{7} + 23298085122481 T^{8} \))(\( 1 - 43 T + 4464 T^{2} - 221093 T^{3} + 13201958 T^{4} - 485741321 T^{5} + 21546875376 T^{6} - 455993473039 T^{7} + 23298085122481 T^{8} \))(\( 1 - 2 T + 6833 T^{2} - 33080 T^{3} + 25238338 T^{4} - 84665324 T^{5} + 55448628586 T^{6} - 159670841720 T^{7} + 72460544215709 T^{8} - 46596170244962 T^{9} + 51185893014090757 T^{10} \))(\( 1 + 2 T + 6833 T^{2} + 33080 T^{3} + 25238338 T^{4} + 84665324 T^{5} + 55448628586 T^{6} + 159670841720 T^{7} + 72460544215709 T^{8} + 46596170244962 T^{9} + 51185893014090757 T^{10} \))
$17$ (\( 1 - 134 T + 4913 T^{2} \))(\( 1 + 84 T + 4913 T^{2} \))(\( 1 - 27 T + 4913 T^{2} \))(\( 1 + 22 T + 4913 T^{2} \))(\( 1 + 66 T + 4913 T^{2} \))(\( 1 - 22 T + 4913 T^{2} \))(\( 1 + 42 T + 4913 T^{2} \))(\( 1 + 27 T + 4913 T^{2} \))(\( 1 + 40 T + 8750 T^{2} + 196520 T^{3} + 24137569 T^{4} \))(\( 1 - 79 T + 8288 T^{2} - 388127 T^{3} + 24137569 T^{4} \))(\( 1 + 116 T + 9030 T^{2} + 569908 T^{3} + 24137569 T^{4} \))(\( 1 - 124 T + 13638 T^{2} - 609212 T^{3} + 24137569 T^{4} \))(\( 1 + 79 T + 8288 T^{2} + 388127 T^{3} + 24137569 T^{4} \))(\( 1 - 6 T + 9778 T^{2} - 29478 T^{3} + 24137569 T^{4} \))(\( 1 - 44 T + 630 T^{2} - 216172 T^{3} + 24137569 T^{4} \))(\( 1 + 16 T + 6558 T^{2} + 78608 T^{3} + 24137569 T^{4} \))(\( 1 + 152 T + 20867 T^{2} + 1561824 T^{3} + 102519571 T^{4} + 3668910488 T^{5} + 118587876497 T^{6} \))(\( 1 - 152 T + 20867 T^{2} - 1561824 T^{3} + 102519571 T^{4} - 3668910488 T^{5} + 118587876497 T^{6} \))(\( 1 + 99 T + 13790 T^{2} + 926229 T^{3} + 90687946 T^{4} + 4550563077 T^{5} + 332857076510 T^{6} + 11740199773203 T^{7} + 582622237229761 T^{8} \))(\( 1 + 99 T + 13298 T^{2} + 508917 T^{3} + 56706418 T^{4} + 2500309221 T^{5} + 320981392562 T^{6} + 11740199773203 T^{7} + 582622237229761 T^{8} \))(\( 1 - 99 T + 13298 T^{2} - 508917 T^{3} + 56706418 T^{4} - 2500309221 T^{5} + 320981392562 T^{6} - 11740199773203 T^{7} + 582622237229761 T^{8} \))(\( 1 - 99 T + 13790 T^{2} - 926229 T^{3} + 90687946 T^{4} - 4550563077 T^{5} + 332857076510 T^{6} - 11740199773203 T^{7} + 582622237229761 T^{8} \))(\( 1 + 108 T + 7625 T^{2} + 580624 T^{3} + 28716998 T^{4} + 723515208 T^{5} + 141086611174 T^{6} + 14014851863056 T^{7} + 904232558289625 T^{8} + 62923201620814188 T^{9} + 2862423051509815793 T^{10} \))(\( 1 - 108 T + 7625 T^{2} - 580624 T^{3} + 28716998 T^{4} - 723515208 T^{5} + 141086611174 T^{6} - 14014851863056 T^{7} + 904232558289625 T^{8} - 62923201620814188 T^{9} + 2862423051509815793 T^{10} \))
$19$ (\( 1 + 92 T + 6859 T^{2} \))(\( 1 - 100 T + 6859 T^{2} \))(\( 1 + 4 T + 6859 T^{2} \))(\( 1 - 16 T + 6859 T^{2} \))(\( 1 - 38 T + 6859 T^{2} \))(\( 1 - 16 T + 6859 T^{2} \))(\( 1 + 124 T + 6859 T^{2} \))(\( 1 + 4 T + 6859 T^{2} \))(\( 1 + 122 T + 17398 T^{2} + 836798 T^{3} + 47045881 T^{4} \))(\( 1 + 56 T + 1174 T^{2} + 384104 T^{3} + 47045881 T^{4} \))(\( 1 - 102 T + 13134 T^{2} - 699618 T^{3} + 47045881 T^{4} \))(\( 1 + 96 T + 13974 T^{2} + 658464 T^{3} + 47045881 T^{4} \))(\( 1 + 56 T + 1174 T^{2} + 384104 T^{3} + 47045881 T^{4} \))(\( 1 - 64 T + 6534 T^{2} - 438976 T^{3} + 47045881 T^{4} \))(\( 1 + 108 T + 13254 T^{2} + 740772 T^{3} + 47045881 T^{4} \))(\( 1 - 174 T + 18414 T^{2} - 1193466 T^{3} + 47045881 T^{4} \))(\( 1 + 138 T + 26205 T^{2} + 1963716 T^{3} + 179740095 T^{4} + 6492331578 T^{5} + 322687697779 T^{6} \))(\( 1 + 138 T + 26205 T^{2} + 1963716 T^{3} + 179740095 T^{4} + 6492331578 T^{5} + 322687697779 T^{6} \))(\( 1 + 12 T - 10212 T^{2} + 154020 T^{3} + 95206646 T^{4} + 1056423180 T^{5} - 480432536772 T^{6} + 3872252373348 T^{7} + 2213314919066161 T^{8} \))(\( 1 - 72 T + 25164 T^{2} - 1424592 T^{3} + 252125750 T^{4} - 9771276528 T^{5} + 1183862549484 T^{6} - 23233514240088 T^{7} + 2213314919066161 T^{8} \))(\( 1 - 72 T + 25164 T^{2} - 1424592 T^{3} + 252125750 T^{4} - 9771276528 T^{5} + 1183862549484 T^{6} - 23233514240088 T^{7} + 2213314919066161 T^{8} \))(\( 1 + 12 T - 10212 T^{2} + 154020 T^{3} + 95206646 T^{4} + 1056423180 T^{5} - 480432536772 T^{6} + 3872252373348 T^{7} + 2213314919066161 T^{8} \))(\( 1 - 174 T + 30655 T^{2} - 3260120 T^{3} + 355132498 T^{4} - 29134734196 T^{5} + 2435853803782 T^{6} - 153375217565720 T^{7} + 9891991375415245 T^{8} - 385116795917512014 T^{9} + 15181127029874798299 T^{10} \))(\( 1 - 174 T + 30655 T^{2} - 3260120 T^{3} + 355132498 T^{4} - 29134734196 T^{5} + 2435853803782 T^{6} - 153375217565720 T^{7} + 9891991375415245 T^{8} - 385116795917512014 T^{9} + 15181127029874798299 T^{10} \))
$23$ (\( 1 + 112 T + 12167 T^{2} \))(\( 1 - 42 T + 12167 T^{2} \))(\( 1 - 75 T + 12167 T^{2} \))(\( 1 + 25 T + 12167 T^{2} \))(\( 1 + 12 T + 12167 T^{2} \))(\( 1 - 25 T + 12167 T^{2} \))(\( 1 + 12167 T^{2} \))(\( 1 + 75 T + 12167 T^{2} \))(\( 1 + 16 T + 782 T^{2} + 194672 T^{3} + 148035889 T^{4} \))(\( 1 + 254 T + 38015 T^{2} + 3090418 T^{3} + 148035889 T^{4} \))(\( 1 + 260 T + 34734 T^{2} + 3163420 T^{3} + 148035889 T^{4} \))(\( 1 - 16 T + 15150 T^{2} - 194672 T^{3} + 148035889 T^{4} \))(\( 1 - 254 T + 38015 T^{2} - 3090418 T^{3} + 148035889 T^{4} \))(\( 1 + 6 T + 7870 T^{2} + 73002 T^{3} + 148035889 T^{4} \))(\( 1 - 320 T + 47934 T^{2} - 3893440 T^{3} + 148035889 T^{4} \))(\( 1 + 184 T + 19470 T^{2} + 2238728 T^{3} + 148035889 T^{4} \))(\( 1 - 180 T + 40221 T^{2} - 4151304 T^{3} + 489368907 T^{4} - 26646460020 T^{5} + 1801152661463 T^{6} \))(\( 1 + 180 T + 40221 T^{2} + 4151304 T^{3} + 489368907 T^{4} + 26646460020 T^{5} + 1801152661463 T^{6} \))(\( 1 + 156 T + 28082 T^{2} + 3613896 T^{3} + 479553835 T^{4} + 43970272632 T^{5} + 4157143834898 T^{6} + 280979815188228 T^{7} + 21914624432020321 T^{8} \))(\( 1 + 102 T + 38528 T^{2} + 3477336 T^{3} + 641077657 T^{4} + 42308747112 T^{5} + 5703526731392 T^{6} + 183717571469226 T^{7} + 21914624432020321 T^{8} \))(\( 1 - 102 T + 38528 T^{2} - 3477336 T^{3} + 641077657 T^{4} - 42308747112 T^{5} + 5703526731392 T^{6} - 183717571469226 T^{7} + 21914624432020321 T^{8} \))(\( 1 - 156 T + 28082 T^{2} - 3613896 T^{3} + 479553835 T^{4} - 43970272632 T^{5} + 4157143834898 T^{6} - 280979815188228 T^{7} + 21914624432020321 T^{8} \))(\( 1 - 116 T + 41159 T^{2} - 2945168 T^{3} + 716339614 T^{4} - 37811551864 T^{5} + 8715704083538 T^{6} - 435990563134352 T^{7} + 74133642393155617 T^{8} - 2542096434114357236 T^{9} + \)\(26\!\cdots\!07\)\( T^{10} \))(\( 1 + 116 T + 41159 T^{2} + 2945168 T^{3} + 716339614 T^{4} + 37811551864 T^{5} + 8715704083538 T^{6} + 435990563134352 T^{7} + 74133642393155617 T^{8} + 2542096434114357236 T^{9} + \)\(26\!\cdots\!07\)\( T^{10} \))
$29$ (\( 1 + 58 T + 24389 T^{2} \))(\( 1 + 10 T + 24389 T^{2} \))(\( 1 + 123 T + 24389 T^{2} \))(\( 1 - 167 T + 24389 T^{2} \))(\( 1 + 258 T + 24389 T^{2} \))(\( 1 - 167 T + 24389 T^{2} \))(\( 1 - 102 T + 24389 T^{2} \))(\( 1 + 123 T + 24389 T^{2} \))(\( 1 - 352 T + 78278 T^{2} - 8584928 T^{3} + 594823321 T^{4} \))(\( 1 + 62 T + 19751 T^{2} + 1512118 T^{3} + 594823321 T^{4} \))(\( 1 + 196 T + 20942 T^{2} + 4780244 T^{3} + 594823321 T^{4} \))(\( 1 - 188 T + 34286 T^{2} - 4585132 T^{3} + 594823321 T^{4} \))(\( 1 + 62 T + 19751 T^{2} + 1512118 T^{3} + 594823321 T^{4} \))(\( 1 + 252 T + 56446 T^{2} + 6146028 T^{3} + 594823321 T^{4} \))(\( 1 + 236 T + 61982 T^{2} + 5755804 T^{3} + 594823321 T^{4} \))(\( 1 + 32 T + 19046 T^{2} + 780448 T^{3} + 594823321 T^{4} \))(\( 1 - 170 T + 65051 T^{2} - 6611676 T^{3} + 1586528839 T^{4} - 101119964570 T^{5} + 14507145975869 T^{6} \))(\( 1 - 170 T + 65051 T^{2} - 6611676 T^{3} + 1586528839 T^{4} - 101119964570 T^{5} + 14507145975869 T^{6} \))(\( 1 - 378 T + 143760 T^{2} - 29729988 T^{3} + 5852097929 T^{4} - 725084677332 T^{5} + 85511800626960 T^{6} - 5483701178878482 T^{7} + 353814783205469041 T^{8} \))(\( 1 + 240 T + 86430 T^{2} + 14441664 T^{3} + 3156579983 T^{4} + 352217743296 T^{5} + 51410579634030 T^{6} + 3481715034208560 T^{7} + 353814783205469041 T^{8} \))(\( 1 + 240 T + 86430 T^{2} + 14441664 T^{3} + 3156579983 T^{4} + 352217743296 T^{5} + 51410579634030 T^{6} + 3481715034208560 T^{7} + 353814783205469041 T^{8} \))(\( 1 - 378 T + 143760 T^{2} - 29729988 T^{3} + 5852097929 T^{4} - 725084677332 T^{5} + 85511800626960 T^{6} - 5483701178878482 T^{7} + 353814783205469041 T^{8} \))(\( 1 - 370 T + 160385 T^{2} - 37125560 T^{3} + 8745786530 T^{4} - 1370740158092 T^{5} + 213300987680170 T^{6} - 22083148893184760 T^{7} + 2326728607339749565 T^{8} - \)\(13\!\cdots\!70\)\( T^{9} + \)\(86\!\cdots\!49\)\( T^{10} \))(\( 1 - 370 T + 160385 T^{2} - 37125560 T^{3} + 8745786530 T^{4} - 1370740158092 T^{5} + 213300987680170 T^{6} - 22083148893184760 T^{7} + 2326728607339749565 T^{8} - \)\(13\!\cdots\!70\)\( T^{9} + \)\(86\!\cdots\!49\)\( T^{10} \))
$31$ (\( 1 + 224 T + 29791 T^{2} \))(\( 1 + 48 T + 29791 T^{2} \))(\( 1 + 205 T + 29791 T^{2} \))(\( 1 - 10 T + 29791 T^{2} \))(\( 1 - 146 T + 29791 T^{2} \))(\( 1 - 10 T + 29791 T^{2} \))(\( 1 + 160 T + 29791 T^{2} \))(\( 1 + 205 T + 29791 T^{2} \))(\( 1 - 66 T + 45870 T^{2} - 1966206 T^{3} + 887503681 T^{4} \))(\( 1 + 135 T + 63420 T^{2} + 4021785 T^{3} + 887503681 T^{4} \))(\( 1 - 150 T + 36542 T^{2} - 4468650 T^{3} + 887503681 T^{4} \))(\( 1 + 120 T + 60590 T^{2} + 3574920 T^{3} + 887503681 T^{4} \))(\( 1 + 135 T + 63420 T^{2} + 4021785 T^{3} + 887503681 T^{4} \))(\( 1 - 40 T - 13890 T^{2} - 1191640 T^{3} + 887503681 T^{4} \))(\( 1 + 60 T + 8462 T^{2} + 1787460 T^{3} + 887503681 T^{4} \))(\( 1 - 330 T + 85430 T^{2} - 9831030 T^{3} + 887503681 T^{4} \))(\( 1 + 366 T + 102201 T^{2} + 18296380 T^{3} + 3044669991 T^{4} + 324826347246 T^{5} + 26439622160671 T^{6} \))(\( 1 + 366 T + 102201 T^{2} + 18296380 T^{3} + 3044669991 T^{4} + 324826347246 T^{5} + 26439622160671 T^{6} \))(\( 1 + 93 T + 16330 T^{2} - 936891 T^{3} + 385099458 T^{4} - 27910919781 T^{5} + 14492935110730 T^{6} + 2458884860942403 T^{7} + 787662783788549761 T^{8} \))(\( 1 - 351 T + 102010 T^{2} - 21726711 T^{3} + 4440563682 T^{4} - 647260447401 T^{5} + 90534250498810 T^{6} - 9280307378395521 T^{7} + 787662783788549761 T^{8} \))(\( 1 - 351 T + 102010 T^{2} - 21726711 T^{3} + 4440563682 T^{4} - 647260447401 T^{5} + 90534250498810 T^{6} - 9280307378395521 T^{7} + 787662783788549761 T^{8} \))(\( 1 + 93 T + 16330 T^{2} - 936891 T^{3} + 385099458 T^{4} - 27910919781 T^{5} + 14492935110730 T^{6} + 2458884860942403 T^{7} + 787662783788549761 T^{8} \))(\( 1 - 342 T + 142051 T^{2} - 26927448 T^{3} + 6639779138 T^{4} - 944601593732 T^{5} + 197805660300158 T^{6} - 23898209219936088 T^{7} + 3755774767545476221 T^{8} - \)\(26\!\cdots\!62\)\( T^{9} + \)\(23\!\cdots\!51\)\( T^{10} \))(\( 1 - 342 T + 142051 T^{2} - 26927448 T^{3} + 6639779138 T^{4} - 944601593732 T^{5} + 197805660300158 T^{6} - 23898209219936088 T^{7} + 3755774767545476221 T^{8} - \)\(26\!\cdots\!62\)\( T^{9} + \)\(23\!\cdots\!51\)\( T^{10} \))
$37$ (\( 1 - 146 T + 50653 T^{2} \))(\( 1 - 246 T + 50653 T^{2} \))(\( 1 + 262 T + 50653 T^{2} \))(\( 1 + 133 T + 50653 T^{2} \))(\( 1 + 434 T + 50653 T^{2} \))(\( 1 - 133 T + 50653 T^{2} \))(\( 1 + 398 T + 50653 T^{2} \))(\( 1 - 262 T + 50653 T^{2} \))(\( 1 - 188 T + 44542 T^{2} - 9522764 T^{3} + 2565726409 T^{4} \))(\( 1 + 113 T + 102964 T^{2} + 5723789 T^{3} + 2565726409 T^{4} \))(\( 1 - 96 T + 82550 T^{2} - 4862688 T^{3} + 2565726409 T^{4} \))(\( 1 - 132 T + 70814 T^{2} - 6686196 T^{3} + 2565726409 T^{4} \))(\( 1 - 113 T + 102964 T^{2} - 5723789 T^{3} + 2565726409 T^{4} \))(\( 1 - 248 T + 98214 T^{2} - 12561944 T^{3} + 2565726409 T^{4} \))(\( 1 + 204 T + 108830 T^{2} + 10333212 T^{3} + 2565726409 T^{4} \))(\( 1 - 132 T + 103214 T^{2} - 6686196 T^{3} + 2565726409 T^{4} \))(\( 1 + 252 T + 99399 T^{2} + 17307224 T^{3} + 5034857547 T^{4} + 646563055068 T^{5} + 129961739795077 T^{6} \))(\( 1 - 252 T + 99399 T^{2} - 17307224 T^{3} + 5034857547 T^{4} - 646563055068 T^{5} + 129961739795077 T^{6} \))(\( 1 + 81 T + 107185 T^{2} + 469746 T^{3} + 5937897606 T^{4} + 23794044138 T^{5} + 275007385148665 T^{6} + 10526900923401237 T^{7} + 6582952005840035281 T^{8} \))(\( 1 + 399 T + 123385 T^{2} + 25924734 T^{3} + 6891314910 T^{4} + 1313165551302 T^{5} + 316572152974465 T^{6} + 51854734178235723 T^{7} + 6582952005840035281 T^{8} \))(\( 1 - 399 T + 123385 T^{2} - 25924734 T^{3} + 6891314910 T^{4} - 1313165551302 T^{5} + 316572152974465 T^{6} - 51854734178235723 T^{7} + 6582952005840035281 T^{8} \))(\( 1 - 81 T + 107185 T^{2} - 469746 T^{3} + 5937897606 T^{4} - 23794044138 T^{5} + 275007385148665 T^{6} - 10526900923401237 T^{7} + 6582952005840035281 T^{8} \))(\( 1 - 408 T + 163665 T^{2} - 51926944 T^{3} + 15115947738 T^{4} - 3482080406928 T^{5} + 765668100772914 T^{6} - 133230331559464096 T^{7} + 21270188143561277205 T^{8} - \)\(26\!\cdots\!48\)\( T^{9} + \)\(33\!\cdots\!93\)\( T^{10} \))(\( 1 + 408 T + 163665 T^{2} + 51926944 T^{3} + 15115947738 T^{4} + 3482080406928 T^{5} + 765668100772914 T^{6} + 133230331559464096 T^{7} + 21270188143561277205 T^{8} + \)\(26\!\cdots\!48\)\( T^{9} + \)\(33\!\cdots\!93\)\( T^{10} \))
$41$ (\( 1 - 18 T + 68921 T^{2} \))(\( 1 + 248 T + 68921 T^{2} \))(\( 1 - 57 T + 68921 T^{2} \))(\( 1 + 168 T + 68921 T^{2} \))(\( 1 + 282 T + 68921 T^{2} \))(\( 1 + 168 T + 68921 T^{2} \))(\( 1 + 318 T + 68921 T^{2} \))(\( 1 - 57 T + 68921 T^{2} \))(\( 1 - 16 T + 18350 T^{2} - 1102736 T^{3} + 4750104241 T^{4} \))(\( 1 - 235 T + 143042 T^{2} - 16196435 T^{3} + 4750104241 T^{4} \))(\( 1 + 176 T - 16914 T^{2} + 12130096 T^{3} + 4750104241 T^{4} \))(\( 1 - 100 T + 89142 T^{2} - 6892100 T^{3} + 4750104241 T^{4} \))(\( 1 - 235 T + 143042 T^{2} - 16196435 T^{3} + 4750104241 T^{4} \))(\( 1 + 450 T + 175642 T^{2} + 31014450 T^{3} + 4750104241 T^{4} \))(\( 1 - 44 T + 106326 T^{2} - 3032524 T^{3} + 4750104241 T^{4} \))(\( 1 - 200 T + 64542 T^{2} - 13784200 T^{3} + 4750104241 T^{4} \))(\( 1 + 206 T + 68783 T^{2} + 10173252 T^{3} + 4740593143 T^{4} + 978521473646 T^{5} + 327381934393961 T^{6} \))(\( 1 + 206 T + 68783 T^{2} + 10173252 T^{3} + 4740593143 T^{4} + 978521473646 T^{5} + 327381934393961 T^{6} \))(\( 1 + 465 T + 105716 T^{2} + 566235 T^{3} - 2050285754 T^{4} + 39025482435 T^{5} + 502162019941556 T^{6} + 152232599493191865 T^{7} + 22563490300366186081 T^{8} \))(\( 1 - 381 T + 273692 T^{2} - 71526783 T^{3} + 28134293782 T^{4} - 4929697411143 T^{5} + 1300065529927772 T^{6} - 124732517004099141 T^{7} + 22563490300366186081 T^{8} \))(\( 1 - 381 T + 273692 T^{2} - 71526783 T^{3} + 28134293782 T^{4} - 4929697411143 T^{5} + 1300065529927772 T^{6} - 124732517004099141 T^{7} + 22563490300366186081 T^{8} \))(\( 1 + 465 T + 105716 T^{2} + 566235 T^{3} - 2050285754 T^{4} + 39025482435 T^{5} + 502162019941556 T^{6} + 152232599493191865 T^{7} + 22563490300366186081 T^{8} \))(\( 1 - 802 T + 392457 T^{2} - 146273472 T^{3} + 44792512462 T^{4} - 12012058617212 T^{5} + 3087144751393502 T^{6} - 694814239692994752 T^{7} + \)\(12\!\cdots\!77\)\( T^{8} - \)\(18\!\cdots\!62\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} \))(\( 1 - 802 T + 392457 T^{2} - 146273472 T^{3} + 44792512462 T^{4} - 12012058617212 T^{5} + 3087144751393502 T^{6} - 694814239692994752 T^{7} + \)\(12\!\cdots\!77\)\( T^{8} - \)\(18\!\cdots\!62\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} \))
$43$ (\( 1 + 340 T + 79507 T^{2} \))(\( 1 + 68 T + 79507 T^{2} \))(\( 1 - 407 T + 79507 T^{2} \))(\( 1 + 97 T + 79507 T^{2} \))(\( 1 + 20 T + 79507 T^{2} \))(\( 1 - 97 T + 79507 T^{2} \))(\( 1 - 268 T + 79507 T^{2} \))(\( 1 + 407 T + 79507 T^{2} \))(\( 1 - 396 T + 95718 T^{2} - 31484772 T^{3} + 6321363049 T^{4} \))(\( 1 + 804 T + 306321 T^{2} + 63923628 T^{3} + 6321363049 T^{4} \))(\( 1 - 344 T + 171958 T^{2} - 27350408 T^{3} + 6321363049 T^{4} \))(\( 1 - 536 T + 200086 T^{2} - 42615752 T^{3} + 6321363049 T^{4} \))(\( 1 - 804 T + 306321 T^{2} - 63923628 T^{3} + 6321363049 T^{4} \))(\( 1 + 376 T + 161526 T^{2} + 29894632 T^{3} + 6321363049 T^{4} \))(\( 1 + 136 T + 81718 T^{2} + 10812952 T^{3} + 6321363049 T^{4} \))(\( 1 + 364 T + 172486 T^{2} + 28940548 T^{3} + 6321363049 T^{4} \))(\( 1 - 108 T + 76905 T^{2} - 30874696 T^{3} + 6114485835 T^{4} - 682707209292 T^{5} + 502592611936843 T^{6} \))(\( 1 + 108 T + 76905 T^{2} + 30874696 T^{3} + 6114485835 T^{4} + 682707209292 T^{5} + 502592611936843 T^{6} \))(\( 1 - 64 T + 64662 T^{2} + 2492176 T^{3} + 5477627255 T^{4} + 198145437232 T^{5} + 408751977474438 T^{6} - 32165927163957952 T^{7} + 39959630797262576401 T^{8} \))(\( 1 + 460 T + 241338 T^{2} + 78643232 T^{3} + 29430041627 T^{4} + 6252687446624 T^{5} + 1525585115519562 T^{6} + 231192601490947780 T^{7} + 39959630797262576401 T^{8} \))(\( 1 - 460 T + 241338 T^{2} - 78643232 T^{3} + 29430041627 T^{4} - 6252687446624 T^{5} + 1525585115519562 T^{6} - 231192601490947780 T^{7} + 39959630797262576401 T^{8} \))(\( 1 + 64 T + 64662 T^{2} - 2492176 T^{3} + 5477627255 T^{4} - 198145437232 T^{5} + 408751977474438 T^{6} + 32165927163957952 T^{7} + 39959630797262576401 T^{8} \))(\( 1 - 584 T + 413407 T^{2} - 149329184 T^{3} + 61499850522 T^{4} - 16229990754224 T^{5} + 4889668615452654 T^{6} - 943963985874922016 T^{7} + \)\(20\!\cdots\!01\)\( T^{8} - \)\(23\!\cdots\!84\)\( T^{9} + \)\(31\!\cdots\!07\)\( T^{10} \))(\( 1 + 584 T + 413407 T^{2} + 149329184 T^{3} + 61499850522 T^{4} + 16229990754224 T^{5} + 4889668615452654 T^{6} + 943963985874922016 T^{7} + \)\(20\!\cdots\!01\)\( T^{8} + \)\(23\!\cdots\!84\)\( T^{9} + \)\(31\!\cdots\!07\)\( T^{10} \))
$47$ (\( 1 + 208 T + 103823 T^{2} \))(\( 1 + 324 T + 103823 T^{2} \))(\( 1 + 60 T + 103823 T^{2} \))(\( 1 + 400 T + 103823 T^{2} \))(\( 1 - 72 T + 103823 T^{2} \))(\( 1 - 400 T + 103823 T^{2} \))(\( 1 + 240 T + 103823 T^{2} \))(\( 1 - 60 T + 103823 T^{2} \))(\( 1 - 188 T + 15582 T^{2} - 19518724 T^{3} + 10779215329 T^{4} \))(\( 1 + 152 T + 180510 T^{2} + 15781096 T^{3} + 10779215329 T^{4} \))(\( 1 + 560 T + 248606 T^{2} + 58140880 T^{3} + 10779215329 T^{4} \))(\( 1 - 928 T + 408830 T^{2} - 96347744 T^{3} + 10779215329 T^{4} \))(\( 1 - 152 T + 180510 T^{2} - 15781096 T^{3} + 10779215329 T^{4} \))(\( 1 - 12 T + 141790 T^{2} - 1245876 T^{3} + 10779215329 T^{4} \))(\( 1 + 400 T + 106526 T^{2} + 41529200 T^{3} + 10779215329 T^{4} \))(\( 1 + 292 T + 179390 T^{2} + 30316316 T^{3} + 10779215329 T^{4} \))(\( 1 - 24 T + 84141 T^{2} - 25877328 T^{3} + 8735771043 T^{4} - 258701167896 T^{5} + 1119130473102767 T^{6} \))(\( 1 + 24 T + 84141 T^{2} + 25877328 T^{3} + 8735771043 T^{4} + 258701167896 T^{5} + 1119130473102767 T^{6} \))(\( 1 + 744 T + 588276 T^{2} + 247094976 T^{3} + 101020317878 T^{4} + 25654141693248 T^{5} + 6341153676882804 T^{6} + 832633071988458648 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 60 T + 130548 T^{2} + 11848116 T^{3} + 16872903254 T^{4} + 1230106947468 T^{5} + 1407205002770292 T^{6} + 67147828386166020 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 - 60 T + 130548 T^{2} - 11848116 T^{3} + 16872903254 T^{4} - 1230106947468 T^{5} + 1407205002770292 T^{6} - 67147828386166020 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 - 744 T + 588276 T^{2} - 247094976 T^{3} + 101020317878 T^{4} - 25654141693248 T^{5} + 6341153676882804 T^{6} - 832633071988458648 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 716 T + 507419 T^{2} + 209415632 T^{3} + 90503203546 T^{4} + 27982753228744 T^{5} + 9396314101756358 T^{6} + 2257336190586622928 T^{7} + \)\(56\!\cdots\!73\)\( T^{8} + \)\(83\!\cdots\!56\)\( T^{9} + \)\(12\!\cdots\!43\)\( T^{10} \))(\( 1 - 716 T + 507419 T^{2} - 209415632 T^{3} + 90503203546 T^{4} - 27982753228744 T^{5} + 9396314101756358 T^{6} - 2257336190586622928 T^{7} + \)\(56\!\cdots\!73\)\( T^{8} - \)\(83\!\cdots\!56\)\( T^{9} + \)\(12\!\cdots\!43\)\( T^{10} \))
$53$ (\( 1 - 754 T + 148877 T^{2} \))(\( 1 + 258 T + 148877 T^{2} \))(\( 1 - 327 T + 148877 T^{2} \))(\( 1 + 182 T + 148877 T^{2} \))(\( 1 + 336 T + 148877 T^{2} \))(\( 1 - 182 T + 148877 T^{2} \))(\( 1 - 498 T + 148877 T^{2} \))(\( 1 + 327 T + 148877 T^{2} \))(\( 1 + 982 T + 504354 T^{2} + 146197214 T^{3} + 22164361129 T^{4} \))(\( 1 + 149 T + 269640 T^{2} + 22182673 T^{3} + 22164361129 T^{4} \))(\( 1 + 326 T + 204138 T^{2} + 48533902 T^{3} + 22164361129 T^{4} \))(\( 1 + 884 T + 460350 T^{2} + 131607268 T^{3} + 22164361129 T^{4} \))(\( 1 - 149 T + 269640 T^{2} - 22182673 T^{3} + 22164361129 T^{4} \))(\( 1 - 1104 T + 602230 T^{2} - 164360208 T^{3} + 22164361129 T^{4} \))(\( 1 + 16 T + 260838 T^{2} + 2382032 T^{3} + 22164361129 T^{4} \))(\( 1 + 34 T + 103410 T^{2} + 5061818 T^{3} + 22164361129 T^{4} \))(\( 1 + 354 T + 295827 T^{2} + 51866076 T^{3} + 44041836279 T^{4} + 7846183839666 T^{5} + 3299763591802133 T^{6} \))(\( 1 - 354 T + 295827 T^{2} - 51866076 T^{3} + 44041836279 T^{4} - 7846183839666 T^{5} + 3299763591802133 T^{6} \))(\( 1 + 729 T + 333446 T^{2} + 137056347 T^{3} + 63585804370 T^{4} + 20404537772319 T^{5} + 7390617561020534 T^{6} + 2405527658423754957 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 + 873 T + 701906 T^{2} + 368908875 T^{3} + 161980949146 T^{4} + 54922046583375 T^{5} + 15557298062611874 T^{6} + 2880693615643262109 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 873 T + 701906 T^{2} - 368908875 T^{3} + 161980949146 T^{4} - 54922046583375 T^{5} + 15557298062611874 T^{6} - 2880693615643262109 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 729 T + 333446 T^{2} - 137056347 T^{3} + 63585804370 T^{4} - 20404537772319 T^{5} + 7390617561020534 T^{6} - 2405527658423754957 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 + 98 T + 503305 T^{2} + 71121272 T^{3} + 122661090658 T^{4} + 16369960190572 T^{5} + 18261415193891066 T^{6} + 1576357556561836088 T^{7} + \)\(16\!\cdots\!65\)\( T^{8} + \)\(48\!\cdots\!18\)\( T^{9} + \)\(73\!\cdots\!57\)\( T^{10} \))(\( 1 - 98 T + 503305 T^{2} - 71121272 T^{3} + 122661090658 T^{4} - 16369960190572 T^{5} + 18261415193891066 T^{6} - 1576357556561836088 T^{7} + \)\(16\!\cdots\!65\)\( T^{8} - \)\(48\!\cdots\!18\)\( T^{9} + \)\(73\!\cdots\!57\)\( T^{10} \))
$59$ (\( 1 - 380 T + 205379 T^{2} \))(\( 1 - 120 T + 205379 T^{2} \))(\( 1 - 33 T + 205379 T^{2} \))(\( 1 - 488 T + 205379 T^{2} \))(\( 1 + 360 T + 205379 T^{2} \))(\( 1 - 488 T + 205379 T^{2} \))(\( 1 + 132 T + 205379 T^{2} \))(\( 1 - 33 T + 205379 T^{2} \))(\( 1 - 516 T + 418118 T^{2} - 105975564 T^{3} + 42180533641 T^{4} \))(\( 1 + 441 T + 273734 T^{2} + 90572139 T^{3} + 42180533641 T^{4} \))(\( 1 + 844 T + 474182 T^{2} + 173339876 T^{3} + 42180533641 T^{4} \))(\( 1 - 104 T + 80534 T^{2} - 21359416 T^{3} + 42180533641 T^{4} \))(\( 1 + 441 T + 273734 T^{2} + 90572139 T^{3} + 42180533641 T^{4} \))(\( 1 - 804 T + 380614 T^{2} - 165124716 T^{3} + 42180533641 T^{4} \))(\( 1 + 464 T + 458102 T^{2} + 95295856 T^{3} + 42180533641 T^{4} \))(\( 1 - 364 T + 438374 T^{2} - 74757956 T^{3} + 42180533641 T^{4} \))(\( 1 + 880 T + 706697 T^{2} + 338588064 T^{3} + 145140723163 T^{4} + 37118869604080 T^{5} + 8662995818654939 T^{6} \))(\( 1 + 880 T + 706697 T^{2} + 338588064 T^{3} + 145140723163 T^{4} + 37118869604080 T^{5} + 8662995818654939 T^{6} \))(\( 1 - 231 T + 701280 T^{2} - 148812447 T^{3} + 204019205798 T^{4} - 30562951552413 T^{5} + 29580364631760480 T^{6} - 2001152034109290909 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 + 855 T + 767616 T^{2} + 344685519 T^{3} + 195821792246 T^{4} + 70791167206701 T^{5} + 32378452511369856 T^{6} + 7406861424949972845 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 + 855 T + 767616 T^{2} + 344685519 T^{3} + 195821792246 T^{4} + 70791167206701 T^{5} + 32378452511369856 T^{6} + 7406861424949972845 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 - 231 T + 701280 T^{2} - 148812447 T^{3} + 204019205798 T^{4} - 30562951552413 T^{5} + 29580364631760480 T^{6} - 2001152034109290909 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 - 704 T + 427487 T^{2} - 197865856 T^{3} + 99740405354 T^{4} - 55609053370240 T^{5} + 20484584711199166 T^{6} - 8346087395413261696 T^{7} + \)\(37\!\cdots\!93\)\( T^{8} - \)\(12\!\cdots\!24\)\( T^{9} + \)\(36\!\cdots\!99\)\( T^{10} \))(\( 1 - 704 T + 427487 T^{2} - 197865856 T^{3} + 99740405354 T^{4} - 55609053370240 T^{5} + 20484584711199166 T^{6} - 8346087395413261696 T^{7} + \)\(37\!\cdots\!93\)\( T^{8} - \)\(12\!\cdots\!24\)\( T^{9} + \)\(36\!\cdots\!99\)\( T^{10} \))
$61$ (\( 1 - 718 T + 226981 T^{2} \))(\( 1 - 622 T + 226981 T^{2} \))(\( 1 + 427 T + 226981 T^{2} \))(\( 1 - 28 T + 226981 T^{2} \))(\( 1 + 682 T + 226981 T^{2} \))(\( 1 - 28 T + 226981 T^{2} \))(\( 1 - 398 T + 226981 T^{2} \))(\( 1 + 427 T + 226981 T^{2} \))(\( 1 + 880 T + 575238 T^{2} + 199743280 T^{3} + 51520374361 T^{4} \))(\( 1 + 223 T + 149646 T^{2} + 50616763 T^{3} + 51520374361 T^{4} \))(\( 1 + 204 T + 455006 T^{2} + 46304124 T^{3} + 51520374361 T^{4} \))(\( 1 + 468 T + 494606 T^{2} + 106227108 T^{3} + 51520374361 T^{4} \))(\( 1 + 223 T + 149646 T^{2} + 50616763 T^{3} + 51520374361 T^{4} \))(\( 1 + 428 T + 425886 T^{2} + 97147868 T^{3} + 51520374361 T^{4} \))(\( 1 + 684 T + 535646 T^{2} + 155255004 T^{3} + 51520374361 T^{4} \))(\( 1 - 792 T + 340886 T^{2} - 179768952 T^{3} + 51520374361 T^{4} \))(\( 1 + 870 T + 582363 T^{2} + 282478148 T^{3} + 132185336103 T^{4} + 44822725694070 T^{5} + 11694146092834141 T^{6} \))(\( 1 + 870 T + 582363 T^{2} + 282478148 T^{3} + 132185336103 T^{4} + 44822725694070 T^{5} + 11694146092834141 T^{6} \))(\( 1 + 1353 T + 1374808 T^{2} + 931878711 T^{3} + 511309944510 T^{4} + 211518761701491 T^{5} + 70830622834497688 T^{6} + 15822179663604592773 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 - 687 T + 715504 T^{2} - 385624593 T^{3} + 235308406830 T^{4} - 87529455743733 T^{5} + 36863033936792944 T^{6} - 8033878365777054867 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 - 687 T + 715504 T^{2} - 385624593 T^{3} + 235308406830 T^{4} - 87529455743733 T^{5} + 36863033936792944 T^{6} - 8033878365777054867 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 + 1353 T + 1374808 T^{2} + 931878711 T^{3} + 511309944510 T^{4} + 211518761701491 T^{5} + 70830622834497688 T^{6} + 15822179663604592773 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 - 650 T + 689345 T^{2} - 375251480 T^{3} + 259020342850 T^{4} - 102268282520348 T^{5} + 58792696440435850 T^{6} - 19333096729119304280 T^{7} + \)\(80\!\cdots\!45\)\( T^{8} - \)\(17\!\cdots\!50\)\( T^{9} + \)\(60\!\cdots\!01\)\( T^{10} \))(\( 1 - 650 T + 689345 T^{2} - 375251480 T^{3} + 259020342850 T^{4} - 102268282520348 T^{5} + 58792696440435850 T^{6} - 19333096729119304280 T^{7} + \)\(80\!\cdots\!45\)\( T^{8} - \)\(17\!\cdots\!50\)\( T^{9} + \)\(60\!\cdots\!01\)\( T^{10} \))
$67$ (\( 1 + 412 T + 300763 T^{2} \))(\( 1 + 904 T + 300763 T^{2} \))(\( 1 + 628 T + 300763 T^{2} \))(\( 1 + 967 T + 300763 T^{2} \))(\( 1 + 812 T + 300763 T^{2} \))(\( 1 - 967 T + 300763 T^{2} \))(\( 1 + 92 T + 300763 T^{2} \))(\( 1 - 628 T + 300763 T^{2} \))(\( 1 - 356 T + 100374 T^{2} - 107071628 T^{3} + 90458382169 T^{4} \))(\( 1 + 1157 T + 871890 T^{2} + 347982791 T^{3} + 90458382169 T^{4} \))(\( 1 - 104 T + 537670 T^{2} - 31279352 T^{3} + 90458382169 T^{4} \))(\( 1 - 1688 T + 1302310 T^{2} - 507687944 T^{3} + 90458382169 T^{4} \))(\( 1 - 1157 T + 871890 T^{2} - 347982791 T^{3} + 90458382169 T^{4} \))(\( 1 + 148 T + 440790 T^{2} + 44512924 T^{3} + 90458382169 T^{4} \))(\( 1 + 736 T + 602470 T^{2} + 221361568 T^{3} + 90458382169 T^{4} \))(\( 1 - 788 T + 753430 T^{2} - 237001244 T^{3} + 90458382169 T^{4} \))(\( 1 - 96 T + 555537 T^{2} - 22556608 T^{3} + 167084974731 T^{4} - 8684004688224 T^{5} + 27206534396294947 T^{6} \))(\( 1 + 96 T + 555537 T^{2} + 22556608 T^{3} + 167084974731 T^{4} + 8684004688224 T^{5} + 27206534396294947 T^{6} \))(\( 1 + 1487 T + 1603371 T^{2} + 1080212116 T^{3} + 674138302124 T^{4} + 324887836644508 T^{5} + 145038346676691699 T^{6} + 40456116647290586189 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 503 T + 452451 T^{2} - 193160692 T^{3} + 211333484900 T^{4} - 58095589207996 T^{5} + 40927985470746219 T^{6} - 13684886801336358341 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 + 503 T + 452451 T^{2} + 193160692 T^{3} + 211333484900 T^{4} + 58095589207996 T^{5} + 40927985470746219 T^{6} + 13684886801336358341 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 1487 T + 1603371 T^{2} - 1080212116 T^{3} + 674138302124 T^{4} - 324887836644508 T^{5} + 145038346676691699 T^{6} - 40456116647290586189 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 + 180 T + 1024695 T^{2} - 16666000 T^{3} + 437663187690 T^{4} - 44169474067848 T^{5} + 131632893319207470 T^{6} - 1507579397228554000 T^{7} + \)\(27\!\cdots\!65\)\( T^{8} + \)\(14\!\cdots\!80\)\( T^{9} + \)\(24\!\cdots\!43\)\( T^{10} \))(\( 1 - 180 T + 1024695 T^{2} + 16666000 T^{3} + 437663187690 T^{4} + 44169474067848 T^{5} + 131632893319207470 T^{6} + 1507579397228554000 T^{7} + \)\(27\!\cdots\!65\)\( T^{8} - \)\(14\!\cdots\!80\)\( T^{9} + \)\(24\!\cdots\!43\)\( T^{10} \))
$71$ (\( 1 + 960 T + 357911 T^{2} \))(\( 1 + 678 T + 357911 T^{2} \))(\( 1 - 300 T + 357911 T^{2} \))(\( 1 + 285 T + 357911 T^{2} \))(\( 1 - 810 T + 357911 T^{2} \))(\( 1 + 285 T + 357911 T^{2} \))(\( 1 + 720 T + 357911 T^{2} \))(\( 1 - 300 T + 357911 T^{2} \))(\( 1 - 310 T + 664038 T^{2} - 110952410 T^{3} + 128100283921 T^{4} \))(\( 1 - 619 T + 576906 T^{2} - 221546909 T^{3} + 128100283921 T^{4} \))(\( 1 - 1670 T + 1384382 T^{2} - 597711370 T^{3} + 128100283921 T^{4} \))(\( 1 + 136 T + 540446 T^{2} + 48675896 T^{3} + 128100283921 T^{4} \))(\( 1 - 619 T + 576906 T^{2} - 221546909 T^{3} + 128100283921 T^{4} \))(\( 1 - 954 T + 930526 T^{2} - 341447094 T^{3} + 128100283921 T^{4} \))(\( 1 + 740 T + 757502 T^{2} + 264854140 T^{3} + 128100283921 T^{4} \))(\( 1 - 454 T + 304526 T^{2} - 162491594 T^{3} + 128100283921 T^{4} \))(\( 1 + 1018 T + 1108049 T^{2} + 595462884 T^{3} + 396582925639 T^{4} + 130406089031578 T^{5} + 45848500718449031 T^{6} \))(\( 1 + 1018 T + 1108049 T^{2} + 595462884 T^{3} + 396582925639 T^{4} + 130406089031578 T^{5} + 45848500718449031 T^{6} \))(\( 1 + 1725 T + 1434819 T^{2} + 706812600 T^{3} + 347044577276 T^{4} + 252976004478600 T^{5} + 183800721275245299 T^{6} + 79088663739324578475 T^{7} + \)\(16\!\cdots\!41\)\( T^{8} \))(\( 1 + 681 T + 1310019 T^{2} + 668258544 T^{3} + 678493576820 T^{4} + 239177083741584 T^{5} + 167813805841904499 T^{6} + 31222828989263790111 T^{7} + \)\(16\!\cdots\!41\)\( T^{8} \))(\( 1 + 681 T + 1310019 T^{2} + 668258544 T^{3} + 678493576820 T^{4} + 239177083741584 T^{5} + 167813805841904499 T^{6} + 31222828989263790111 T^{7} + \)\(16\!\cdots\!41\)\( T^{8} \))(\( 1 + 1725 T + 1434819 T^{2} + 706812600 T^{3} + 347044577276 T^{4} + 252976004478600 T^{5} + 183800721275245299 T^{6} + 79088663739324578475 T^{7} + \)\(16\!\cdots\!41\)\( T^{8} \))(\( 1 - 1470 T + 1881615 T^{2} - 1727909680 T^{3} + 1338943951990 T^{4} - 860023408325220 T^{5} + 479222768800692890 T^{6} - \)\(22\!\cdots\!80\)\( T^{7} + \)\(86\!\cdots\!65\)\( T^{8} - \)\(24\!\cdots\!70\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} \))(\( 1 - 1470 T + 1881615 T^{2} - 1727909680 T^{3} + 1338943951990 T^{4} - 860023408325220 T^{5} + 479222768800692890 T^{6} - \)\(22\!\cdots\!80\)\( T^{7} + \)\(86\!\cdots\!65\)\( T^{8} - \)\(24\!\cdots\!70\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} \))
$73$ (\( 1 + 1066 T + 389017 T^{2} \))(\( 1 - 642 T + 389017 T^{2} \))(\( 1 - 98 T + 389017 T^{2} \))(\( 1 + 838 T + 389017 T^{2} \))(\( 1 - 124 T + 389017 T^{2} \))(\( 1 - 838 T + 389017 T^{2} \))(\( 1 - 502 T + 389017 T^{2} \))(\( 1 + 98 T + 389017 T^{2} \))(\( 1 + 326 T + 789802 T^{2} + 126819542 T^{3} + 151334226289 T^{4} \))(\( 1 + 268 T + 763078 T^{2} + 104256556 T^{3} + 151334226289 T^{4} \))(\( 1 - 386 T + 152218 T^{2} - 150160562 T^{3} + 151334226289 T^{4} \))(\( 1 + 508 T + 13078 T^{2} + 197620636 T^{3} + 151334226289 T^{4} \))(\( 1 - 268 T + 763078 T^{2} - 104256556 T^{3} + 151334226289 T^{4} \))(\( 1 + 1072 T + 1063278 T^{2} + 417026224 T^{3} + 151334226289 T^{4} \))(\( 1 + 424 T + 748558 T^{2} + 164943208 T^{3} + 151334226289 T^{4} \))(\( 1 + 778 T + 794698 T^{2} + 302655226 T^{3} + 151334226289 T^{4} \))(\( 1 + 1554 T + 1505463 T^{2} + 1009418700 T^{3} + 585650699871 T^{4} + 235173387653106 T^{5} + 58871586708267913 T^{6} \))(\( 1 - 1554 T + 1505463 T^{2} - 1009418700 T^{3} + 585650699871 T^{4} - 235173387653106 T^{5} + 58871586708267913 T^{6} \))(\( 1 + 512 T + 1030980 T^{2} + 484092568 T^{3} + 566560915526 T^{4} + 188320238525656 T^{5} + 156022560619433220 T^{6} + 30142252394633171456 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 + 1228 T + 618972 T^{2} - 228294532 T^{3} - 319091414218 T^{4} - 88810453955044 T^{5} + 93671648714554908 T^{6} + 72294308477752997164 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 1228 T + 618972 T^{2} + 228294532 T^{3} - 319091414218 T^{4} + 88810453955044 T^{5} + 93671648714554908 T^{6} - 72294308477752997164 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 512 T + 1030980 T^{2} - 484092568 T^{3} + 566560915526 T^{4} - 188320238525656 T^{5} + 156022560619433220 T^{6} - 30142252394633171456 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 534 T + 1342021 T^{2} - 930732232 T^{3} + 817882087762 T^{4} - 560574711779204 T^{5} + 318170036134909954 T^{6} - \)\(14\!\cdots\!48\)\( T^{7} + \)\(79\!\cdots\!73\)\( T^{8} - \)\(12\!\cdots\!14\)\( T^{9} + \)\(89\!\cdots\!57\)\( T^{10} \))(\( 1 + 534 T + 1342021 T^{2} + 930732232 T^{3} + 817882087762 T^{4} + 560574711779204 T^{5} + 318170036134909954 T^{6} + \)\(14\!\cdots\!48\)\( T^{7} + \)\(79\!\cdots\!73\)\( T^{8} + \)\(12\!\cdots\!14\)\( T^{9} + \)\(89\!\cdots\!57\)\( T^{10} \))
$79$ (\( 1 - 896 T + 493039 T^{2} \))(\( 1 - 740 T + 493039 T^{2} \))(\( 1 - 686 T + 493039 T^{2} \))(\( 1 + 469 T + 493039 T^{2} \))(\( 1 - 1136 T + 493039 T^{2} \))(\( 1 + 469 T + 493039 T^{2} \))(\( 1 + 1024 T + 493039 T^{2} \))(\( 1 - 686 T + 493039 T^{2} \))(\( 1 - 1832 T + 1824478 T^{2} - 903247448 T^{3} + 243087455521 T^{4} \))(\( 1 + 427 T + 986572 T^{2} + 210527653 T^{3} + 243087455521 T^{4} \))(\( 1 + 888 T + 1007454 T^{2} + 437818632 T^{3} + 243087455521 T^{4} \))(\( 1 + 432 T + 602142 T^{2} + 212992848 T^{3} + 243087455521 T^{4} \))(\( 1 + 427 T + 986572 T^{2} + 210527653 T^{3} + 243087455521 T^{4} \))(\( 1 + 572 T + 901662 T^{2} + 282018308 T^{3} + 243087455521 T^{4} \))(\( 1 + 408 T - 143586 T^{2} + 201159912 T^{3} + 243087455521 T^{4} \))(\( 1 - 408 T + 994782 T^{2} - 201159912 T^{3} + 243087455521 T^{4} \))(\( 1 + 1620 T + 1787517 T^{2} + 1338821912 T^{3} + 881315594163 T^{4} + 393801677944020 T^{5} + 119851595982618319 T^{6} \))(\( 1 + 1620 T + 1787517 T^{2} + 1338821912 T^{3} + 881315594163 T^{4} + 393801677944020 T^{5} + 119851595982618319 T^{6} \))(\( 1 - 1629 T + 1989837 T^{2} - 1837769472 T^{3} + 1504809477470 T^{4} - 906092022705408 T^{5} + 483704413231540077 T^{6} - \)\(19\!\cdots\!51\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 - 345 T + 1235121 T^{2} - 721148448 T^{3} + 716751093026 T^{4} - 355554309653472 T^{5} + 300242421150553041 T^{6} - 41348800614003320055 T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 - 345 T + 1235121 T^{2} - 721148448 T^{3} + 716751093026 T^{4} - 355554309653472 T^{5} + 300242421150553041 T^{6} - 41348800614003320055 T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 - 1629 T + 1989837 T^{2} - 1837769472 T^{3} + 1504809477470 T^{4} - 906092022705408 T^{5} + 483704413231540077 T^{6} - \)\(19\!\cdots\!51\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 + 820 T + 1736795 T^{2} + 1027136240 T^{3} + 1389341527610 T^{4} + 657402503393464 T^{5} + 684999557431306790 T^{6} + \)\(24\!\cdots\!40\)\( T^{7} + \)\(20\!\cdots\!05\)\( T^{8} + \)\(48\!\cdots\!20\)\( T^{9} + \)\(29\!\cdots\!99\)\( T^{10} \))(\( 1 + 820 T + 1736795 T^{2} + 1027136240 T^{3} + 1389341527610 T^{4} + 657402503393464 T^{5} + 684999557431306790 T^{6} + \)\(24\!\cdots\!40\)\( T^{7} + \)\(20\!\cdots\!05\)\( T^{8} + \)\(48\!\cdots\!20\)\( T^{9} + \)\(29\!\cdots\!99\)\( T^{10} \))
$83$ (\( 1 + 436 T + 571787 T^{2} \))(\( 1 + 468 T + 571787 T^{2} \))(\( 1 - 1401 T + 571787 T^{2} \))(\( 1 + 406 T + 571787 T^{2} \))(\( 1 + 156 T + 571787 T^{2} \))(\( 1 - 406 T + 571787 T^{2} \))(\( 1 - 204 T + 571787 T^{2} \))(\( 1 + 1401 T + 571787 T^{2} \))(\( 1 - 680 T + 744870 T^{2} - 388815160 T^{3} + 326940373369 T^{4} \))(\( 1 + 1211 T + 720720 T^{2} + 692434057 T^{3} + 326940373369 T^{4} \))(\( 1 + 928 T + 600710 T^{2} + 530618336 T^{3} + 326940373369 T^{4} \))(\( 1 - 584 T + 1172390 T^{2} - 333923608 T^{3} + 326940373369 T^{4} \))(\( 1 - 1211 T + 720720 T^{2} - 692434057 T^{3} + 326940373369 T^{4} \))(\( 1 + 1944 T + 1957030 T^{2} + 1111553928 T^{3} + 326940373369 T^{4} \))(\( 1 + 608 T + 1200710 T^{2} + 347646496 T^{3} + 326940373369 T^{4} \))(\( 1 + 1136 T + 1169990 T^{2} + 649550032 T^{3} + 326940373369 T^{4} \))(\( 1 - 872 T + 923489 T^{2} - 308826096 T^{3} + 528039004843 T^{4} - 285092005577768 T^{5} + 186940255267540403 T^{6} \))(\( 1 + 872 T + 923489 T^{2} + 308826096 T^{3} + 528039004843 T^{4} + 285092005577768 T^{5} + 186940255267540403 T^{6} \))(\( 1 + 321 T + 661434 T^{2} + 144132717 T^{3} + 79870144034 T^{4} + 82413213855279 T^{5} + 216249478918951146 T^{6} + 60007821940880469363 T^{7} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 + 1509 T + 2187990 T^{2} + 1588008513 T^{3} + 1474125264218 T^{4} + 908002623622731 T^{5} + 715342267527638310 T^{6} + \)\(28\!\cdots\!27\)\( T^{7} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 - 1509 T + 2187990 T^{2} - 1588008513 T^{3} + 1474125264218 T^{4} - 908002623622731 T^{5} + 715342267527638310 T^{6} - \)\(28\!\cdots\!27\)\( T^{7} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 - 321 T + 661434 T^{2} - 144132717 T^{3} + 79870144034 T^{4} - 82413213855279 T^{5} + 216249478918951146 T^{6} - 60007821940880469363 T^{7} + \)\(10\!\cdots\!61\)\( T^{8} \))(\( 1 + 1520 T + 3526775 T^{2} + 3535501120 T^{3} + 4405187467130 T^{4} + 3049079895261856 T^{5} + 2518828926267861310 T^{6} + \)\(11\!\cdots\!80\)\( T^{7} + \)\(65\!\cdots\!25\)\( T^{8} + \)\(16\!\cdots\!20\)\( T^{9} + \)\(61\!\cdots\!07\)\( T^{10} \))(\( 1 - 1520 T + 3526775 T^{2} - 3535501120 T^{3} + 4405187467130 T^{4} - 3049079895261856 T^{5} + 2518828926267861310 T^{6} - \)\(11\!\cdots\!80\)\( T^{7} + \)\(65\!\cdots\!25\)\( T^{8} - \)\(16\!\cdots\!20\)\( T^{9} + \)\(61\!\cdots\!07\)\( T^{10} \))
$89$ (\( 1 + 1038 T + 704969 T^{2} \))(\( 1 - 200 T + 704969 T^{2} \))(\( 1 - 714 T + 704969 T^{2} \))(\( 1 - 324 T + 704969 T^{2} \))(\( 1 + 1038 T + 704969 T^{2} \))(\( 1 - 324 T + 704969 T^{2} \))(\( 1 - 354 T + 704969 T^{2} \))(\( 1 - 714 T + 704969 T^{2} \))(\( 1 - 796 T + 411158 T^{2} - 561155324 T^{3} + 496981290961 T^{4} \))(\( 1 - 466 T + 306170 T^{2} - 328515554 T^{3} + 496981290961 T^{4} \))(\( 1 - 588 T + 1495334 T^{2} - 414521772 T^{3} + 496981290961 T^{4} \))(\( 1 + 1404 T + 1802390 T^{2} + 989776476 T^{3} + 496981290961 T^{4} \))(\( 1 - 466 T + 306170 T^{2} - 328515554 T^{3} + 496981290961 T^{4} \))(\( 1 - 366 T + 1156090 T^{2} - 258018654 T^{3} + 496981290961 T^{4} \))(\( 1 + 1332 T + 1790774 T^{2} + 939018708 T^{3} + 496981290961 T^{4} \))(\( 1 - 36 T - 842170 T^{2} - 25378884 T^{3} + 496981290961 T^{4} \))(\( 1 + 1938 T + 3246255 T^{2} + 2913932892 T^{3} + 2288509141095 T^{4} + 963149741882418 T^{5} + 350356403707485209 T^{6} \))(\( 1 + 1938 T + 3246255 T^{2} + 2913932892 T^{3} + 2288509141095 T^{4} + 963149741882418 T^{5} + 350356403707485209 T^{6} \))(\( 1 + 978 T + 526228 T^{2} - 159100050 T^{3} - 360762420714 T^{4} - 112160603148450 T^{5} + 261525470779825108 T^{6} + \)\(34\!\cdots\!02\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 + 198 T + 1184884 T^{2} - 492558966 T^{3} + 650980125750 T^{4} - 347238801702054 T^{5} + 588865179959033524 T^{6} + 69370567934082071382 T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 + 198 T + 1184884 T^{2} - 492558966 T^{3} + 650980125750 T^{4} - 347238801702054 T^{5} + 588865179959033524 T^{6} + 69370567934082071382 T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 + 978 T + 526228 T^{2} - 159100050 T^{3} - 360762420714 T^{4} - 112160603148450 T^{5} + 261525470779825108 T^{6} + \)\(34\!\cdots\!02\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 - 286 T + 2177465 T^{2} - 600135040 T^{3} + 2162009088238 T^{4} - 560754412921604 T^{5} + 1524149384926054622 T^{6} - \)\(29\!\cdots\!40\)\( T^{7} + \)\(76\!\cdots\!85\)\( T^{8} - \)\(70\!\cdots\!06\)\( T^{9} + \)\(17\!\cdots\!49\)\( T^{10} \))(\( 1 - 286 T + 2177465 T^{2} - 600135040 T^{3} + 2162009088238 T^{4} - 560754412921604 T^{5} + 1524149384926054622 T^{6} - \)\(29\!\cdots\!40\)\( T^{7} + \)\(76\!\cdots\!85\)\( T^{8} - \)\(70\!\cdots\!06\)\( T^{9} + \)\(17\!\cdots\!49\)\( T^{10} \))
$97$ (\( 1 - 702 T + 912673 T^{2} \))(\( 1 - 1266 T + 912673 T^{2} \))(\( 1 - 494 T + 912673 T^{2} \))(\( 1 + 114 T + 912673 T^{2} \))(\( 1 + 1208 T + 912673 T^{2} \))(\( 1 - 114 T + 912673 T^{2} \))(\( 1 - 286 T + 912673 T^{2} \))(\( 1 + 494 T + 912673 T^{2} \))(\( 1 - 670 T + 1145410 T^{2} - 611490910 T^{3} + 832972004929 T^{4} \))(\( 1 + 172 T - 273626 T^{2} + 156979756 T^{3} + 832972004929 T^{4} \))(\( 1 + 522 T + 291282 T^{2} + 476415306 T^{3} + 832972004929 T^{4} \))(\( 1 - 1188 T + 2161254 T^{2} - 1084255524 T^{3} + 832972004929 T^{4} \))(\( 1 - 172 T - 273626 T^{2} - 156979756 T^{3} + 832972004929 T^{4} \))(\( 1 + 808 T + 903054 T^{2} + 737439784 T^{3} + 832972004929 T^{4} \))(\( 1 - 2448 T + 3286542 T^{2} - 2234223504 T^{3} + 832972004929 T^{4} \))(\( 1 - 498 T + 1796754 T^{2} - 454511154 T^{3} + 832972004929 T^{4} \))(\( 1 + 1878 T + 3431919 T^{2} + 3287491396 T^{3} + 3132219809487 T^{4} + 1564321425256662 T^{5} + 760231058654565217 T^{6} \))(\( 1 - 1878 T + 3431919 T^{2} - 3287491396 T^{3} + 3132219809487 T^{4} - 1564321425256662 T^{5} + 760231058654565217 T^{6} \))(\( 1 + 2616 T + 5183100 T^{2} + 6945540936 T^{3} + 7789652954246 T^{4} + 6339007682681928 T^{5} + 4317377198747499900 T^{6} + \)\(19\!\cdots\!72\)\( T^{7} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 - 372 T + 1910724 T^{2} - 1429297356 T^{3} + 2012229372278 T^{4} - 1304481105792588 T^{5} + 1591579601145958596 T^{6} - \)\(28\!\cdots\!24\)\( T^{7} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 + 372 T + 1910724 T^{2} + 1429297356 T^{3} + 2012229372278 T^{4} + 1304481105792588 T^{5} + 1591579601145958596 T^{6} + \)\(28\!\cdots\!24\)\( T^{7} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 - 2616 T + 5183100 T^{2} - 6945540936 T^{3} + 7789652954246 T^{4} - 6339007682681928 T^{5} + 4317377198747499900 T^{6} - \)\(19\!\cdots\!72\)\( T^{7} + \)\(69\!\cdots\!41\)\( T^{8} \))(\( 1 + 278 T + 3429709 T^{2} + 1008794696 T^{3} + 5371131513042 T^{4} + 1398135665763908 T^{5} + 4902086711402581266 T^{6} + \)\(84\!\cdots\!84\)\( T^{7} + \)\(26\!\cdots\!53\)\( T^{8} + \)\(19\!\cdots\!98\)\( T^{9} + \)\(63\!\cdots\!93\)\( T^{10} \))(\( 1 - 278 T + 3429709 T^{2} - 1008794696 T^{3} + 5371131513042 T^{4} - 1398135665763908 T^{5} + 4902086711402581266 T^{6} - \)\(84\!\cdots\!84\)\( T^{7} + \)\(26\!\cdots\!53\)\( T^{8} - \)\(19\!\cdots\!98\)\( T^{9} + \)\(63\!\cdots\!93\)\( T^{10} \))
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