Properties

Label 400.6.a
Level 400
Weight 6
Character orbit a
Rep. character \(\chi_{400}(1,\cdot)\)
Character field \(\Q\)
Dimension 46
Newform subspaces 27
Sturm bound 360
Trace bound 9

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Defining parameters

Level: \( N \) = \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 400.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(360\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(400))\).

Total New Old
Modular forms 318 49 269
Cusp forms 282 46 236
Eisenstein series 36 3 33

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

\(2\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(11\)
\(-\)\(-\)\(+\)\(11\)
Plus space\(+\)\(22\)
Minus space\(-\)\(24\)

Trace form

\( 46q - 10q^{3} + 110q^{7} + 3462q^{9} + O(q^{10}) \) \( 46q - 10q^{3} + 110q^{7} + 3462q^{9} + 64q^{11} - 60q^{13} - 400q^{17} + 644q^{19} - 580q^{21} + 90q^{23} - 7180q^{27} - 196q^{29} + 2868q^{31} + 5920q^{33} + 620q^{37} - 28540q^{39} - 2540q^{41} + 20630q^{43} + 41950q^{47} + 97098q^{49} - 22904q^{51} + 11060q^{53} + 10040q^{57} + 38968q^{59} + 40648q^{61} + 4190q^{63} - 64350q^{67} + 9284q^{69} - 37300q^{71} + 43520q^{73} - 16880q^{77} - 151360q^{79} + 307602q^{81} - 94130q^{83} - 23580q^{87} + 58760q^{89} + 266308q^{91} - 163560q^{93} + 32760q^{97} - 93644q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(400))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
400.6.a.a \(1\) \(64.154\) \(\Q\) None \(0\) \(-26\) \(0\) \(-22\) \(-\) \(+\) \(q-26q^{3}-22q^{7}+433q^{9}+768q^{11}+\cdots\)
400.6.a.b \(1\) \(64.154\) \(\Q\) None \(0\) \(-18\) \(0\) \(242\) \(+\) \(+\) \(q-18q^{3}+242q^{7}+3^{4}q^{9}-656q^{11}+\cdots\)
400.6.a.c \(1\) \(64.154\) \(\Q\) None \(0\) \(-14\) \(0\) \(-158\) \(-\) \(-\) \(q-14q^{3}-158q^{7}-47q^{9}+148q^{11}+\cdots\)
400.6.a.d \(1\) \(64.154\) \(\Q\) None \(0\) \(-12\) \(0\) \(-88\) \(-\) \(+\) \(q-12q^{3}-88q^{7}-99q^{9}-540q^{11}+\cdots\)
400.6.a.e \(1\) \(64.154\) \(\Q\) None \(0\) \(-11\) \(0\) \(-142\) \(-\) \(+\) \(q-11q^{3}-142q^{7}-122q^{9}-777q^{11}+\cdots\)
400.6.a.f \(1\) \(64.154\) \(\Q\) None \(0\) \(-8\) \(0\) \(-108\) \(+\) \(+\) \(q-8q^{3}-108q^{7}-179q^{9}+604q^{11}+\cdots\)
400.6.a.g \(1\) \(64.154\) \(\Q\) None \(0\) \(-4\) \(0\) \(192\) \(-\) \(+\) \(q-4q^{3}+192q^{7}-227q^{9}+148q^{11}+\cdots\)
400.6.a.h \(1\) \(64.154\) \(\Q\) None \(0\) \(-2\) \(0\) \(-62\) \(+\) \(+\) \(q-2q^{3}-62q^{7}-239q^{9}+12^{2}q^{11}+\cdots\)
400.6.a.i \(1\) \(64.154\) \(\Q\) None \(0\) \(6\) \(0\) \(-118\) \(-\) \(+\) \(q+6q^{3}-118q^{7}-207q^{9}-192q^{11}+\cdots\)
400.6.a.j \(1\) \(64.154\) \(\Q\) None \(0\) \(11\) \(0\) \(142\) \(-\) \(-\) \(q+11q^{3}+142q^{7}-122q^{9}-777q^{11}+\cdots\)
400.6.a.k \(1\) \(64.154\) \(\Q\) None \(0\) \(14\) \(0\) \(158\) \(-\) \(-\) \(q+14q^{3}+158q^{7}-47q^{9}+148q^{11}+\cdots\)
400.6.a.l \(1\) \(64.154\) \(\Q\) None \(0\) \(20\) \(0\) \(-24\) \(+\) \(+\) \(q+20q^{3}-24q^{7}+157q^{9}-124q^{11}+\cdots\)
400.6.a.m \(1\) \(64.154\) \(\Q\) None \(0\) \(22\) \(0\) \(218\) \(-\) \(+\) \(q+22q^{3}+218q^{7}+241q^{9}+480q^{11}+\cdots\)
400.6.a.n \(1\) \(64.154\) \(\Q\) None \(0\) \(24\) \(0\) \(-172\) \(-\) \(+\) \(q+24q^{3}-172q^{7}+333q^{9}-132q^{11}+\cdots\)
400.6.a.o \(2\) \(64.154\) \(\Q(\sqrt{241}) \) None \(0\) \(-20\) \(0\) \(-200\) \(-\) \(-\) \(q+(-10-\beta )q^{3}+(-10^{2}-2\beta )q^{7}+\cdots\)
400.6.a.p \(2\) \(64.154\) \(\Q(\sqrt{409}) \) None \(0\) \(-20\) \(0\) \(40\) \(-\) \(+\) \(q+(-10-\beta )q^{3}+(20+6\beta )q^{7}+(266+\cdots)q^{9}+\cdots\)
400.6.a.q \(2\) \(64.154\) \(\Q(\sqrt{129}) \) None \(0\) \(-12\) \(0\) \(52\) \(+\) \(+\) \(q+(-6-\beta )q^{3}+(26-3\beta )q^{7}+(309+\cdots)q^{9}+\cdots\)
400.6.a.r \(2\) \(64.154\) \(\Q(\sqrt{241}) \) None \(0\) \(-8\) \(0\) \(8\) \(+\) \(+\) \(q+(-4-\beta )q^{3}+(4+2\beta )q^{7}+(14+8\beta )q^{9}+\cdots\)
400.6.a.s \(2\) \(64.154\) \(\Q(\sqrt{31}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+\beta q^{3}-11\beta q^{7}-119q^{9}+10^{2}q^{11}+\cdots\)
400.6.a.t \(2\) \(64.154\) \(\Q(\sqrt{11}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+3\beta q^{3}-9\beta q^{7}+153q^{9}-252q^{11}+\cdots\)
400.6.a.u \(2\) \(64.154\) \(\Q(\sqrt{241}) \) None \(0\) \(8\) \(0\) \(-8\) \(+\) \(-\) \(q+(4+\beta )q^{3}+(-4-2\beta )q^{7}+(14+8\beta )q^{9}+\cdots\)
400.6.a.v \(2\) \(64.154\) \(\Q(\sqrt{409}) \) None \(0\) \(20\) \(0\) \(-40\) \(-\) \(-\) \(q+(10-\beta )q^{3}+(-20+6\beta )q^{7}+(266+\cdots)q^{9}+\cdots\)
400.6.a.w \(2\) \(64.154\) \(\Q(\sqrt{241}) \) None \(0\) \(20\) \(0\) \(200\) \(-\) \(+\) \(q+(10-\beta )q^{3}+(10^{2}-2\beta )q^{7}+(98-20\beta )q^{9}+\cdots\)
400.6.a.x \(3\) \(64.154\) 3.3.47217.1 None \(0\) \(-1\) \(0\) \(70\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(24-\beta _{1}-\beta _{2})q^{7}+(50+5\beta _{1}+\cdots)q^{9}+\cdots\)
400.6.a.y \(3\) \(64.154\) 3.3.47217.1 None \(0\) \(1\) \(0\) \(-70\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(-24+\beta _{1}+\beta _{2})q^{7}+(50+\cdots)q^{9}+\cdots\)
400.6.a.z \(4\) \(64.154\) 4.4.1595208.1 None \(0\) \(-4\) \(0\) \(-148\) \(+\) \(-\) \(q+(-1-\beta _{1})q^{3}+(-37-\beta _{1}+\beta _{3})q^{7}+\cdots\)
400.6.a.ba \(4\) \(64.154\) 4.4.1595208.1 None \(0\) \(4\) \(0\) \(148\) \(+\) \(-\) \(q+(1+\beta _{1})q^{3}+(37+\beta _{1}-\beta _{3})q^{7}+(5^{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(400))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(400)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 26 T + 243 T^{2} \))(\( 1 + 18 T + 243 T^{2} \))(\( 1 + 14 T + 243 T^{2} \))(\( 1 + 12 T + 243 T^{2} \))(\( 1 + 11 T + 243 T^{2} \))(\( 1 + 8 T + 243 T^{2} \))(\( 1 + 4 T + 243 T^{2} \))(\( 1 + 2 T + 243 T^{2} \))(\( 1 - 6 T + 243 T^{2} \))(\( 1 - 11 T + 243 T^{2} \))(\( 1 - 14 T + 243 T^{2} \))(\( 1 - 20 T + 243 T^{2} \))(\( 1 - 22 T + 243 T^{2} \))(\( 1 - 24 T + 243 T^{2} \))(\( 1 + 20 T + 345 T^{2} + 4860 T^{3} + 59049 T^{4} \))(\( 1 + 20 T + 177 T^{2} + 4860 T^{3} + 59049 T^{4} \))(\( 1 + 12 T + 6 T^{2} + 2916 T^{3} + 59049 T^{4} \))(\( 1 + 8 T + 261 T^{2} + 1944 T^{3} + 59049 T^{4} \))(\( 1 + 362 T^{2} + 59049 T^{4} \))(\( 1 + 90 T^{2} + 59049 T^{4} \))(\( 1 - 8 T + 261 T^{2} - 1944 T^{3} + 59049 T^{4} \))(\( 1 - 20 T + 177 T^{2} - 4860 T^{3} + 59049 T^{4} \))(\( 1 - 20 T + 345 T^{2} - 4860 T^{3} + 59049 T^{4} \))(\( 1 + T + 288 T^{2} + 1581 T^{3} + 69984 T^{4} + 59049 T^{5} + 14348907 T^{6} \))(\( 1 - T + 288 T^{2} - 1581 T^{3} + 69984 T^{4} - 59049 T^{5} + 14348907 T^{6} \))(\( 1 + 4 T + 244 T^{2} + 3348 T^{3} + 18486 T^{4} + 813564 T^{5} + 14407956 T^{6} + 57395628 T^{7} + 3486784401 T^{8} \))(\( 1 - 4 T + 244 T^{2} - 3348 T^{3} + 18486 T^{4} - 813564 T^{5} + 14407956 T^{6} - 57395628 T^{7} + 3486784401 T^{8} \))
$5$ 1
$7$ (\( 1 + 22 T + 16807 T^{2} \))(\( 1 - 242 T + 16807 T^{2} \))(\( 1 + 158 T + 16807 T^{2} \))(\( 1 + 88 T + 16807 T^{2} \))(\( 1 + 142 T + 16807 T^{2} \))(\( 1 + 108 T + 16807 T^{2} \))(\( 1 - 192 T + 16807 T^{2} \))(\( 1 + 62 T + 16807 T^{2} \))(\( 1 + 118 T + 16807 T^{2} \))(\( 1 - 142 T + 16807 T^{2} \))(\( 1 - 158 T + 16807 T^{2} \))(\( 1 + 24 T + 16807 T^{2} \))(\( 1 - 218 T + 16807 T^{2} \))(\( 1 + 172 T + 16807 T^{2} \))(\( 1 + 200 T + 42650 T^{2} + 3361400 T^{3} + 282475249 T^{4} \))(\( 1 - 40 T + 19290 T^{2} - 672280 T^{3} + 282475249 T^{4} \))(\( 1 - 52 T + 29646 T^{2} - 873964 T^{3} + 282475249 T^{4} \))(\( 1 - 8 T + 32666 T^{2} - 134456 T^{3} + 282475249 T^{4} \))(\( 1 + 18610 T^{2} + 282475249 T^{4} \))(\( 1 + 30050 T^{2} + 282475249 T^{4} \))(\( 1 + 8 T + 32666 T^{2} + 134456 T^{3} + 282475249 T^{4} \))(\( 1 + 40 T + 19290 T^{2} + 672280 T^{3} + 282475249 T^{4} \))(\( 1 - 200 T + 42650 T^{2} - 3361400 T^{3} + 282475249 T^{4} \))(\( 1 - 70 T - 5551 T^{2} + 3221636 T^{3} - 93295657 T^{4} - 19773267430 T^{5} + 4747561509943 T^{6} \))(\( 1 + 70 T - 5551 T^{2} - 3221636 T^{3} - 93295657 T^{4} + 19773267430 T^{5} + 4747561509943 T^{6} \))(\( 1 + 148 T + 33316 T^{2} + 2108948 T^{3} + 503710694 T^{4} + 35445089036 T^{5} + 9410945395684 T^{6} + 702639103471564 T^{7} + 79792266297612001 T^{8} \))(\( 1 - 148 T + 33316 T^{2} - 2108948 T^{3} + 503710694 T^{4} - 35445089036 T^{5} + 9410945395684 T^{6} - 702639103471564 T^{7} + 79792266297612001 T^{8} \))
$11$ (\( 1 - 768 T + 161051 T^{2} \))(\( 1 + 656 T + 161051 T^{2} \))(\( 1 - 148 T + 161051 T^{2} \))(\( 1 + 540 T + 161051 T^{2} \))(\( 1 + 777 T + 161051 T^{2} \))(\( 1 - 604 T + 161051 T^{2} \))(\( 1 - 148 T + 161051 T^{2} \))(\( 1 - 144 T + 161051 T^{2} \))(\( 1 + 192 T + 161051 T^{2} \))(\( 1 + 777 T + 161051 T^{2} \))(\( 1 - 148 T + 161051 T^{2} \))(\( 1 + 124 T + 161051 T^{2} \))(\( 1 - 480 T + 161051 T^{2} \))(\( 1 + 132 T + 161051 T^{2} \))(\( 1 - 196 T + 181081 T^{2} - 31565996 T^{3} + 25937424601 T^{4} \))(\( 1 - 60 T + 230977 T^{2} - 9663060 T^{3} + 25937424601 T^{4} \))(\( 1 + 560 T + 381926 T^{2} + 90188560 T^{3} + 25937424601 T^{4} \))(\( 1 - 200 T + 225821 T^{2} - 32210200 T^{3} + 25937424601 T^{4} \))(\( ( 1 - 100 T + 161051 T^{2} )^{2} \))(\( ( 1 + 252 T + 161051 T^{2} )^{2} \))(\( 1 - 200 T + 225821 T^{2} - 32210200 T^{3} + 25937424601 T^{4} \))(\( 1 - 60 T + 230977 T^{2} - 9663060 T^{3} + 25937424601 T^{4} \))(\( 1 - 196 T + 181081 T^{2} - 31565996 T^{3} + 25937424601 T^{4} \))(\( 1 - 19 T + 398752 T^{2} - 4577119 T^{3} + 64219408352 T^{4} - 492811067419 T^{5} + 4177248169415651 T^{6} \))(\( 1 - 19 T + 398752 T^{2} - 4577119 T^{3} + 64219408352 T^{4} - 492811067419 T^{5} + 4177248169415651 T^{6} \))(\( 1 - 368 T + 176204 T^{2} - 51158896 T^{3} + 42277949270 T^{4} - 8239191359696 T^{5} + 4570277964394604 T^{6} - 1537227326344959568 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 - 368 T + 176204 T^{2} - 51158896 T^{3} + 42277949270 T^{4} - 8239191359696 T^{5} + 4570277964394604 T^{6} - 1537227326344959568 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))
$13$ (\( 1 - 46 T + 371293 T^{2} \))(\( 1 - 206 T + 371293 T^{2} \))(\( 1 - 684 T + 371293 T^{2} \))(\( 1 - 418 T + 371293 T^{2} \))(\( 1 + 884 T + 371293 T^{2} \))(\( 1 - 306 T + 371293 T^{2} \))(\( 1 + 286 T + 371293 T^{2} \))(\( 1 - 654 T + 371293 T^{2} \))(\( 1 + 1106 T + 371293 T^{2} \))(\( 1 - 884 T + 371293 T^{2} \))(\( 1 + 684 T + 371293 T^{2} \))(\( 1 + 478 T + 371293 T^{2} \))(\( 1 - 622 T + 371293 T^{2} \))(\( 1 - 946 T + 371293 T^{2} \))(\( 1 + 360 T + 713290 T^{2} + 133665480 T^{3} + 137858491849 T^{4} \))(\( 1 - 920 T + 718602 T^{2} - 341589560 T^{3} + 137858491849 T^{4} \))(\( 1 + 1388 T + 1149918 T^{2} + 515354684 T^{3} + 137858491849 T^{4} \))(\( 1 + 592 T + 178538 T^{2} + 219805456 T^{3} + 137858491849 T^{4} \))(\( 1 + 202442 T^{2} + 137858491849 T^{4} \))(\( 1 + 728330 T^{2} + 137858491849 T^{4} \))(\( 1 - 592 T + 178538 T^{2} - 219805456 T^{3} + 137858491849 T^{4} \))(\( 1 + 920 T + 718602 T^{2} + 341589560 T^{3} + 137858491849 T^{4} \))(\( 1 - 360 T + 713290 T^{2} - 133665480 T^{3} + 137858491849 T^{4} \))(\( 1 + 196 T + 642439 T^{2} + 197315624 T^{3} + 238533103627 T^{4} + 27020264402404 T^{5} + 51185893014090757 T^{6} \))(\( 1 - 196 T + 642439 T^{2} - 197315624 T^{3} + 238533103627 T^{4} - 27020264402404 T^{5} + 51185893014090757 T^{6} \))(\( 1 - 440 T + 886036 T^{2} - 564452872 T^{3} + 392923998710 T^{4} - 209577400203496 T^{5} + 122147586683920564 T^{6} - 22521792926199933080 T^{7} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( 1 + 440 T + 886036 T^{2} + 564452872 T^{3} + 392923998710 T^{4} + 209577400203496 T^{5} + 122147586683920564 T^{6} + 22521792926199933080 T^{7} + \)\(19\!\cdots\!01\)\( T^{8} \))
$17$ (\( 1 + 378 T + 1419857 T^{2} \))(\( 1 + 1690 T + 1419857 T^{2} \))(\( 1 - 2048 T + 1419857 T^{2} \))(\( 1 + 594 T + 1419857 T^{2} \))(\( 1 - 27 T + 1419857 T^{2} \))(\( 1 + 930 T + 1419857 T^{2} \))(\( 1 - 1678 T + 1419857 T^{2} \))(\( 1 - 1190 T + 1419857 T^{2} \))(\( 1 + 762 T + 1419857 T^{2} \))(\( 1 + 27 T + 1419857 T^{2} \))(\( 1 + 2048 T + 1419857 T^{2} \))(\( 1 - 1198 T + 1419857 T^{2} \))(\( 1 + 186 T + 1419857 T^{2} \))(\( 1 - 222 T + 1419857 T^{2} \))(\( 1 - 1490 T + 2280355 T^{2} - 2115586930 T^{3} + 2015993900449 T^{4} \))(\( 1 - 2910 T + 4897843 T^{2} - 4131783870 T^{3} + 2015993900449 T^{4} \))(\( 1 + 148 T - 795706 T^{2} + 210138836 T^{3} + 2015993900449 T^{4} \))(\( 1 - 278 T + 2797339 T^{2} - 394720246 T^{3} + 2015993900449 T^{4} \))(\( 1 + 1879458 T^{2} + 2015993900449 T^{4} \))(\( 1 + 2363810 T^{2} + 2015993900449 T^{4} \))(\( 1 + 278 T + 2797339 T^{2} + 394720246 T^{3} + 2015993900449 T^{4} \))(\( 1 + 2910 T + 4897843 T^{2} + 4131783870 T^{3} + 2015993900449 T^{4} \))(\( 1 + 1490 T + 2280355 T^{2} + 2115586930 T^{3} + 2015993900449 T^{4} \))(\( 1 - 1223 T + 2296046 T^{2} - 2818923747 T^{3} + 3260056985422 T^{4} - 2465560540249127 T^{5} + 2862423051509815793 T^{6} \))(\( 1 + 1223 T + 2296046 T^{2} + 2818923747 T^{3} + 3260056985422 T^{4} + 2465560540249127 T^{5} + 2862423051509815793 T^{6} \))(\( 1 + 672 T + 3356228 T^{2} + 3540729312 T^{3} + 5520858237894 T^{4} + 5027329298748384 T^{5} + 6766135176516146372 T^{6} + \)\(19\!\cdots\!96\)\( T^{7} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( 1 - 672 T + 3356228 T^{2} - 3540729312 T^{3} + 5520858237894 T^{4} - 5027329298748384 T^{5} + 6766135176516146372 T^{6} - \)\(19\!\cdots\!96\)\( T^{7} + \)\(40\!\cdots\!01\)\( T^{8} \))
$19$ (\( 1 + 1100 T + 2476099 T^{2} \))(\( 1 - 1364 T + 2476099 T^{2} \))(\( 1 + 2220 T + 2476099 T^{2} \))(\( 1 + 836 T + 2476099 T^{2} \))(\( 1 + 1145 T + 2476099 T^{2} \))(\( 1 - 1324 T + 2476099 T^{2} \))(\( 1 + 1060 T + 2476099 T^{2} \))(\( 1 + 556 T + 2476099 T^{2} \))(\( 1 - 2740 T + 2476099 T^{2} \))(\( 1 + 1145 T + 2476099 T^{2} \))(\( 1 + 2220 T + 2476099 T^{2} \))(\( 1 + 3044 T + 2476099 T^{2} \))(\( 1 - 1204 T + 2476099 T^{2} \))(\( 1 + 500 T + 2476099 T^{2} \))(\( 1 - 3180 T + 7185073 T^{2} - 7873994820 T^{3} + 6131066257801 T^{4} \))(\( 1 + 2092 T + 5218089 T^{2} + 5179999108 T^{3} + 6131066257801 T^{4} \))(\( 1 - 1000 T + 4533462 T^{2} - 2476099000 T^{3} + 6131066257801 T^{4} \))(\( 1 - 840 T + 4289677 T^{2} - 2079923160 T^{3} + 6131066257801 T^{4} \))(\( ( 1 - 2244 T + 2476099 T^{2} )^{2} \))(\( ( 1 + 220 T + 2476099 T^{2} )^{2} \))(\( 1 - 840 T + 4289677 T^{2} - 2079923160 T^{3} + 6131066257801 T^{4} \))(\( 1 + 2092 T + 5218089 T^{2} + 5179999108 T^{3} + 6131066257801 T^{4} \))(\( 1 - 3180 T + 7185073 T^{2} - 7873994820 T^{3} + 6131066257801 T^{4} \))(\( 1 + 1221 T + 2478936 T^{2} - 986654423 T^{3} + 6138090950664 T^{4} + 7486031900775021 T^{5} + 15181127029874798299 T^{6} \))(\( 1 + 1221 T + 2478936 T^{2} - 986654423 T^{3} + 6138090950664 T^{4} + 7486031900775021 T^{5} + 15181127029874798299 T^{6} \))(\( 1 - 688 T + 5308396 T^{2} - 6058136368 T^{3} + 15069081422710 T^{4} - 15000545402668432 T^{5} + 32546127598645797196 T^{6} - \)\(10\!\cdots\!12\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} \))(\( 1 - 688 T + 5308396 T^{2} - 6058136368 T^{3} + 15069081422710 T^{4} - 15000545402668432 T^{5} + 32546127598645797196 T^{6} - \)\(10\!\cdots\!12\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} \))
$23$ (\( 1 + 1986 T + 6436343 T^{2} \))(\( 1 - 2198 T + 6436343 T^{2} \))(\( 1 - 1246 T + 6436343 T^{2} \))(\( 1 + 4104 T + 6436343 T^{2} \))(\( 1 - 1854 T + 6436343 T^{2} \))(\( 1 + 852 T + 6436343 T^{2} \))(\( 1 - 2976 T + 6436343 T^{2} \))(\( 1 - 2182 T + 6436343 T^{2} \))(\( 1 - 1566 T + 6436343 T^{2} \))(\( 1 + 1854 T + 6436343 T^{2} \))(\( 1 + 1246 T + 6436343 T^{2} \))(\( 1 - 184 T + 6436343 T^{2} \))(\( 1 + 3186 T + 6436343 T^{2} \))(\( 1 - 3564 T + 6436343 T^{2} \))(\( 1 + 1560 T + 13472410 T^{2} + 10040695080 T^{3} + 41426511213649 T^{4} \))(\( 1 + 120 T + 5087290 T^{2} + 772361160 T^{3} + 41426511213649 T^{4} \))(\( 1 + 2452 T + 6569198 T^{2} + 15781913036 T^{3} + 41426511213649 T^{4} \))(\( 1 - 1952 T + 11510698 T^{2} - 12563741536 T^{3} + 41426511213649 T^{4} \))(\( 1 + 1185810 T^{2} + 41426511213649 T^{4} \))(\( 1 + 6946370 T^{2} + 41426511213649 T^{4} \))(\( 1 + 1952 T + 11510698 T^{2} + 12563741536 T^{3} + 41426511213649 T^{4} \))(\( 1 - 120 T + 5087290 T^{2} - 772361160 T^{3} + 41426511213649 T^{4} \))(\( 1 - 1560 T + 13472410 T^{2} - 10040695080 T^{3} + 41426511213649 T^{4} \))(\( 1 - 2490 T + 1075617 T^{2} + 18384852604 T^{3} + 6923039948631 T^{4} - 103152012921986010 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 + 2490 T + 1075617 T^{2} - 18384852604 T^{3} + 6923039948631 T^{4} + 103152012921986010 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 + 4492 T + 27426980 T^{2} + 79192657228 T^{3} + 264562508116390 T^{4} + 509711105000837204 T^{5} + \)\(11\!\cdots\!20\)\( T^{6} + \)\(11\!\cdots\!44\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 4492 T + 27426980 T^{2} - 79192657228 T^{3} + 264562508116390 T^{4} - 509711105000837204 T^{5} + \)\(11\!\cdots\!20\)\( T^{6} - \)\(11\!\cdots\!44\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))
$29$ (\( 1 + 5610 T + 20511149 T^{2} \))(\( 1 + 2218 T + 20511149 T^{2} \))(\( 1 + 270 T + 20511149 T^{2} \))(\( 1 + 594 T + 20511149 T^{2} \))(\( 1 + 4920 T + 20511149 T^{2} \))(\( 1 - 5902 T + 20511149 T^{2} \))(\( 1 + 3410 T + 20511149 T^{2} \))(\( 1 + 1578 T + 20511149 T^{2} \))(\( 1 - 5910 T + 20511149 T^{2} \))(\( 1 + 4920 T + 20511149 T^{2} \))(\( 1 + 270 T + 20511149 T^{2} \))(\( 1 + 3282 T + 20511149 T^{2} \))(\( 1 - 5526 T + 20511149 T^{2} \))(\( 1 - 2190 T + 20511149 T^{2} \))(\( 1 + 3920 T + 44478298 T^{2} + 80403704080 T^{3} + 420707233300201 T^{4} \))(\( 1 - 3552 T + 20618074 T^{2} - 72855601248 T^{3} + 420707233300201 T^{4} \))(\( 1 - 1340 T - 8758306 T^{2} - 27484939660 T^{3} + 420707233300201 T^{4} \))(\( 1 + 4680 T + 41219034 T^{2} + 95992177320 T^{3} + 420707233300201 T^{4} \))(\( ( 1 + 7854 T + 20511149 T^{2} )^{2} \))(\( ( 1 - 6930 T + 20511149 T^{2} )^{2} \))(\( 1 + 4680 T + 41219034 T^{2} + 95992177320 T^{3} + 420707233300201 T^{4} \))(\( 1 - 3552 T + 20618074 T^{2} - 72855601248 T^{3} + 420707233300201 T^{4} \))(\( 1 + 3920 T + 44478298 T^{2} + 80403704080 T^{3} + 420707233300201 T^{4} \))(\( 1 - 11912 T + 107337223 T^{2} - 544650638288 T^{3} + 2201609774199227 T^{4} - 5011464563071994312 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( 1 - 11912 T + 107337223 T^{2} - 544650638288 T^{3} + 2201609774199227 T^{4} - 5011464563071994312 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( 1 + 2936 T + 58625996 T^{2} + 77951973928 T^{3} + 1466411094282230 T^{4} + 1598884552081323272 T^{5} + \)\(24\!\cdots\!96\)\( T^{6} + \)\(25\!\cdots\!64\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 + 2936 T + 58625996 T^{2} + 77951973928 T^{3} + 1466411094282230 T^{4} + 1598884552081323272 T^{5} + \)\(24\!\cdots\!96\)\( T^{6} + \)\(25\!\cdots\!64\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))
$31$ (\( 1 - 3988 T + 28629151 T^{2} \))(\( 1 - 1700 T + 28629151 T^{2} \))(\( 1 - 2048 T + 28629151 T^{2} \))(\( 1 + 4256 T + 28629151 T^{2} \))(\( 1 + 1802 T + 28629151 T^{2} \))(\( 1 - 3320 T + 28629151 T^{2} \))(\( 1 - 2448 T + 28629151 T^{2} \))(\( 1 + 9660 T + 28629151 T^{2} \))(\( 1 - 6868 T + 28629151 T^{2} \))(\( 1 + 1802 T + 28629151 T^{2} \))(\( 1 - 2048 T + 28629151 T^{2} \))(\( 1 - 5728 T + 28629151 T^{2} \))(\( 1 + 9356 T + 28629151 T^{2} \))(\( 1 + 2312 T + 28629151 T^{2} \))(\( 1 - 1096 T - 15343894 T^{2} - 31377549496 T^{3} + 819628286980801 T^{4} \))(\( 1 - 8888 T + 67804938 T^{2} - 254455894088 T^{3} + 819628286980801 T^{4} \))(\( 1 - 2248 T + 57017022 T^{2} - 64358331448 T^{3} + 819628286980801 T^{4} \))(\( 1 - 5008 T + 33327162 T^{2} - 143374788208 T^{3} + 819628286980801 T^{4} \))(\( ( 1 - 2144 T + 28629151 T^{2} )^{2} \))(\( ( 1 + 6752 T + 28629151 T^{2} )^{2} \))(\( 1 - 5008 T + 33327162 T^{2} - 143374788208 T^{3} + 819628286980801 T^{4} \))(\( 1 - 8888 T + 67804938 T^{2} - 254455894088 T^{3} + 819628286980801 T^{4} \))(\( 1 - 1096 T - 15343894 T^{2} - 31377549496 T^{3} + 819628286980801 T^{4} \))(\( 1 + 7442 T + 82803193 T^{2} + 411681472084 T^{3} + 2370585115679143 T^{4} + 6099673711711121042 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( 1 + 7442 T + 82803193 T^{2} + 411681472084 T^{3} + 2370585115679143 T^{4} + 6099673711711121042 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( 1 + 2112 T + 80187004 T^{2} + 163080265536 T^{3} + 3196344720873606 T^{4} + 4668849547150239936 T^{5} + \)\(65\!\cdots\!04\)\( T^{6} + \)\(49\!\cdots\!12\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 + 2112 T + 80187004 T^{2} + 163080265536 T^{3} + 3196344720873606 T^{4} + 4668849547150239936 T^{5} + \)\(65\!\cdots\!04\)\( T^{6} + \)\(49\!\cdots\!12\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))
$37$ (\( 1 - 142 T + 69343957 T^{2} \))(\( 1 - 846 T + 69343957 T^{2} \))(\( 1 + 4372 T + 69343957 T^{2} \))(\( 1 - 298 T + 69343957 T^{2} \))(\( 1 + 13178 T + 69343957 T^{2} \))(\( 1 + 10774 T + 69343957 T^{2} \))(\( 1 + 182 T + 69343957 T^{2} \))(\( 1 - 3534 T + 69343957 T^{2} \))(\( 1 - 5518 T + 69343957 T^{2} \))(\( 1 - 13178 T + 69343957 T^{2} \))(\( 1 - 4372 T + 69343957 T^{2} \))(\( 1 + 10326 T + 69343957 T^{2} \))(\( 1 + 5618 T + 69343957 T^{2} \))(\( 1 - 11242 T + 69343957 T^{2} \))(\( 1 - 2020 T + 130823790 T^{2} - 140074793140 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 12140 T + 90486990 T^{2} - 841835637980 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 5940 T + 123434318 T^{2} - 411903104580 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 12500 T + 121294718 T^{2} - 866799462500 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 30515770 T^{2} + 4808584372417849 T^{4} \))(\( 1 - 56462470 T^{2} + 4808584372417849 T^{4} \))(\( 1 + 12500 T + 121294718 T^{2} + 866799462500 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 12140 T + 90486990 T^{2} + 841835637980 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 2020 T + 130823790 T^{2} + 140074793140 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 14766 T + 175309995 T^{2} - 1612649497908 T^{3} + 12156688754950215 T^{4} - 71003556843121958334 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( 1 + 14766 T + 175309995 T^{2} + 1612649497908 T^{3} + 12156688754950215 T^{4} + 71003556843121958334 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( 1 - 8792 T + 164536948 T^{2} - 653354012200 T^{3} + 11523689002604438 T^{4} - 45306152527774275400 T^{5} + \)\(79\!\cdots\!52\)\( T^{6} - \)\(29\!\cdots\!56\)\( T^{7} + \)\(23\!\cdots\!01\)\( T^{8} \))(\( 1 + 8792 T + 164536948 T^{2} + 653354012200 T^{3} + 11523689002604438 T^{4} + 45306152527774275400 T^{5} + \)\(79\!\cdots\!52\)\( T^{6} + \)\(29\!\cdots\!56\)\( T^{7} + \)\(23\!\cdots\!01\)\( T^{8} \))
$41$ (\( 1 - 1542 T + 115856201 T^{2} \))(\( 1 + 1818 T + 115856201 T^{2} \))(\( 1 + 2398 T + 115856201 T^{2} \))(\( 1 - 17226 T + 115856201 T^{2} \))(\( 1 + 15123 T + 115856201 T^{2} \))(\( 1 + 17958 T + 115856201 T^{2} \))(\( 1 + 9398 T + 115856201 T^{2} \))(\( 1 - 7462 T + 115856201 T^{2} \))(\( 1 + 378 T + 115856201 T^{2} \))(\( 1 + 15123 T + 115856201 T^{2} \))(\( 1 + 2398 T + 115856201 T^{2} \))(\( 1 + 8886 T + 115856201 T^{2} \))(\( 1 + 14394 T + 115856201 T^{2} \))(\( 1 - 1242 T + 115856201 T^{2} \))(\( 1 - 27754 T + 414643531 T^{2} - 3215473002554 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 12438 T + 217381963 T^{2} + 1441019428038 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 23076 T + 352280470 T^{2} - 2673497694276 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 5334 T + 27686155 T^{2} + 617976976134 T^{3} + 13422659310152401 T^{4} \))(\( ( 1 + 7414 T + 115856201 T^{2} )^{2} \))(\( ( 1 + 198 T + 115856201 T^{2} )^{2} \))(\( 1 + 5334 T + 27686155 T^{2} + 617976976134 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 12438 T + 217381963 T^{2} + 1441019428038 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 27754 T + 414643531 T^{2} - 3215473002554 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 3223 T + 204190518 T^{2} - 833781103267 T^{3} + 23656737695702118 T^{4} - 43261230956621188423 T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( 1 - 3223 T + 204190518 T^{2} - 833781103267 T^{3} + 23656737695702118 T^{4} - 43261230956621188423 T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( 1 - 11800 T + 337909340 T^{2} - 2943020124776 T^{3} + 51155654972384870 T^{4} - \)\(34\!\cdots\!76\)\( T^{5} + \)\(45\!\cdots\!40\)\( T^{6} - \)\(18\!\cdots\!00\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 - 11800 T + 337909340 T^{2} - 2943020124776 T^{3} + 51155654972384870 T^{4} - \)\(34\!\cdots\!76\)\( T^{5} + \)\(45\!\cdots\!40\)\( T^{6} - \)\(18\!\cdots\!00\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))
$43$ (\( 1 + 5026 T + 147008443 T^{2} \))(\( 1 - 10534 T + 147008443 T^{2} \))(\( 1 + 2294 T + 147008443 T^{2} \))(\( 1 + 12100 T + 147008443 T^{2} \))(\( 1 - 7844 T + 147008443 T^{2} \))(\( 1 - 9264 T + 147008443 T^{2} \))(\( 1 + 1244 T + 147008443 T^{2} \))(\( 1 + 7114 T + 147008443 T^{2} \))(\( 1 + 2434 T + 147008443 T^{2} \))(\( 1 + 7844 T + 147008443 T^{2} \))(\( 1 - 2294 T + 147008443 T^{2} \))(\( 1 + 9188 T + 147008443 T^{2} \))(\( 1 + 370 T + 147008443 T^{2} \))(\( 1 - 20624 T + 147008443 T^{2} \))(\( 1 - 3000 T + 23431750 T^{2} - 441025329000 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 1160 T + 270794886 T^{2} + 170529793880 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 17684 T + 312898614 T^{2} - 2599697306012 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 224 T + 15005414 T^{2} + 32929891232 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 21442214 T^{2} + 21611482313284249 T^{4} \))(\( 1 + 293842250 T^{2} + 21611482313284249 T^{4} \))(\( 1 - 224 T + 15005414 T^{2} - 32929891232 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 1160 T + 270794886 T^{2} - 170529793880 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 3000 T + 23431750 T^{2} + 441025329000 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 41060 T + 882414881 T^{2} - 12733285389272 T^{3} + 129722437735840283 T^{4} - \)\(88\!\cdots\!40\)\( T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( 1 + 41060 T + 882414881 T^{2} + 12733285389272 T^{3} + 129722437735840283 T^{4} + \)\(88\!\cdots\!40\)\( T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( 1 + 48276 T + 1306891924 T^{2} + 24102642735684 T^{3} + 333606713965182294 T^{4} + \)\(35\!\cdots\!12\)\( T^{5} + \)\(28\!\cdots\!76\)\( T^{6} + \)\(15\!\cdots\!32\)\( T^{7} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( 1 - 48276 T + 1306891924 T^{2} - 24102642735684 T^{3} + 333606713965182294 T^{4} - \)\(35\!\cdots\!12\)\( T^{5} + \)\(28\!\cdots\!76\)\( T^{6} - \)\(15\!\cdots\!32\)\( T^{7} + \)\(46\!\cdots\!01\)\( T^{8} \))
$47$ (\( 1 - 24738 T + 229345007 T^{2} \))(\( 1 - 12074 T + 229345007 T^{2} \))(\( 1 - 10682 T + 229345007 T^{2} \))(\( 1 + 1296 T + 229345007 T^{2} \))(\( 1 + 6732 T + 229345007 T^{2} \))(\( 1 + 9796 T + 229345007 T^{2} \))(\( 1 + 12088 T + 229345007 T^{2} \))(\( 1 + 28294 T + 229345007 T^{2} \))(\( 1 - 13122 T + 229345007 T^{2} \))(\( 1 - 6732 T + 229345007 T^{2} \))(\( 1 + 10682 T + 229345007 T^{2} \))(\( 1 - 23664 T + 229345007 T^{2} \))(\( 1 - 16146 T + 229345007 T^{2} \))(\( 1 - 6588 T + 229345007 T^{2} \))(\( 1 + 25760 T + 480952270 T^{2} + 5907927380320 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 1200 T + 451923598 T^{2} - 275214008400 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 2908 T + 56660030 T^{2} + 666935280356 T^{3} + 52599132235830049 T^{4} \))(\( ( 1 + 13036 T + 229345007 T^{2} )^{2} \))(\( 1 + 369731298 T^{2} + 52599132235830049 T^{4} \))(\( 1 + 347593490 T^{2} + 52599132235830049 T^{4} \))(\( ( 1 - 13036 T + 229345007 T^{2} )^{2} \))(\( 1 + 1200 T + 451923598 T^{2} + 275214008400 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 25760 T + 480952270 T^{2} - 5907927380320 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 29188 T + 677809469 T^{2} + 13063893267768 T^{3} + 155452217412471283 T^{4} + \)\(15\!\cdots\!12\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 - 29188 T + 677809469 T^{2} - 13063893267768 T^{3} + 155452217412471283 T^{4} - \)\(15\!\cdots\!12\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 + 14724 T + 590074244 T^{2} + 7755349482468 T^{3} + 177012391425566214 T^{4} + \)\(17\!\cdots\!76\)\( T^{5} + \)\(31\!\cdots\!56\)\( T^{6} + \)\(17\!\cdots\!32\)\( T^{7} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 - 14724 T + 590074244 T^{2} - 7755349482468 T^{3} + 177012391425566214 T^{4} - \)\(17\!\cdots\!76\)\( T^{5} + \)\(31\!\cdots\!56\)\( T^{6} - \)\(17\!\cdots\!32\)\( T^{7} + \)\(27\!\cdots\!01\)\( T^{8} \))
$53$ (\( 1 - 14166 T + 418195493 T^{2} \))(\( 1 + 32586 T + 418195493 T^{2} \))(\( 1 - 2964 T + 418195493 T^{2} \))(\( 1 + 19494 T + 418195493 T^{2} \))(\( 1 + 3414 T + 418195493 T^{2} \))(\( 1 - 31434 T + 418195493 T^{2} \))(\( 1 + 23846 T + 418195493 T^{2} \))(\( 1 - 13046 T + 418195493 T^{2} \))(\( 1 - 9174 T + 418195493 T^{2} \))(\( 1 - 3414 T + 418195493 T^{2} \))(\( 1 + 2964 T + 418195493 T^{2} \))(\( 1 + 11686 T + 418195493 T^{2} \))(\( 1 - 4374 T + 418195493 T^{2} \))(\( 1 - 21066 T + 418195493 T^{2} \))(\( 1 + 26980 T + 984299470 T^{2} + 11282914401140 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 26340 T + 941756110 T^{2} - 11015269285620 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 5412 T + 693247822 T^{2} - 2263274008116 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 46812 T + 1352998222 T^{2} + 19576567418316 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 248174170 T^{2} + 174887470365513049 T^{4} \))(\( 1 + 802472090 T^{2} + 174887470365513049 T^{4} \))(\( 1 - 46812 T + 1352998222 T^{2} - 19576567418316 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 26340 T + 941756110 T^{2} + 11015269285620 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 26980 T + 984299470 T^{2} - 11282914401140 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 12878 T + 18166107 T^{2} - 11553992883916 T^{3} + 7596984072755751 T^{4} + \)\(22\!\cdots\!22\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( 1 - 12878 T + 18166107 T^{2} + 11553992883916 T^{3} + 7596984072755751 T^{4} - \)\(22\!\cdots\!22\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( 1 - 84296 T + 4144600628 T^{2} - 135070817073080 T^{3} + 3234464962764166486 T^{4} - \)\(56\!\cdots\!40\)\( T^{5} + \)\(72\!\cdots\!72\)\( T^{6} - \)\(61\!\cdots\!72\)\( T^{7} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( 1 + 84296 T + 4144600628 T^{2} + 135070817073080 T^{3} + 3234464962764166486 T^{4} + \)\(56\!\cdots\!40\)\( T^{5} + \)\(72\!\cdots\!72\)\( T^{6} + \)\(61\!\cdots\!72\)\( T^{7} + \)\(30\!\cdots\!01\)\( T^{8} \))
$59$ (\( 1 + 28380 T + 714924299 T^{2} \))(\( 1 + 8668 T + 714924299 T^{2} \))(\( 1 - 39740 T + 714924299 T^{2} \))(\( 1 - 7668 T + 714924299 T^{2} \))(\( 1 + 33960 T + 714924299 T^{2} \))(\( 1 + 33228 T + 714924299 T^{2} \))(\( 1 - 20020 T + 714924299 T^{2} \))(\( 1 - 37092 T + 714924299 T^{2} \))(\( 1 - 34980 T + 714924299 T^{2} \))(\( 1 + 33960 T + 714924299 T^{2} \))(\( 1 - 39740 T + 714924299 T^{2} \))(\( 1 + 16876 T + 714924299 T^{2} \))(\( 1 - 11748 T + 714924299 T^{2} \))(\( 1 + 7980 T + 714924299 T^{2} \))(\( 1 + 11960 T + 1234152598 T^{2} + 8550494616040 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 36696 T + 1234961302 T^{2} - 26234862076104 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 62584 T + 2277965606 T^{2} + 44742822328616 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 81776 T + 3059970646 T^{2} - 58463649475024 T^{3} + 511116753300641401 T^{4} \))(\( ( 1 + 25972 T + 714924299 T^{2} )^{2} \))(\( ( 1 + 24660 T + 714924299 T^{2} )^{2} \))(\( 1 - 81776 T + 3059970646 T^{2} - 58463649475024 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 36696 T + 1234961302 T^{2} - 26234862076104 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 11960 T + 1234152598 T^{2} + 8550494616040 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 64912 T + 3469849057 T^{2} + 101432669884000 T^{3} + 2480679404711536043 T^{4} + \)\(33\!\cdots\!12\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( 1 + 64912 T + 3469849057 T^{2} + 101432669884000 T^{3} + 2480679404711536043 T^{4} + \)\(33\!\cdots\!12\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( 1 - 45840 T + 3064286732 T^{2} - 94721285480976 T^{3} + 3348109683185502486 T^{4} - \)\(67\!\cdots\!24\)\( T^{5} + \)\(15\!\cdots\!32\)\( T^{6} - \)\(16\!\cdots\!60\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 - 45840 T + 3064286732 T^{2} - 94721285480976 T^{3} + 3348109683185502486 T^{4} - \)\(67\!\cdots\!24\)\( T^{5} + \)\(15\!\cdots\!32\)\( T^{6} - \)\(16\!\cdots\!60\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} \))
$61$ (\( 1 - 5522 T + 844596301 T^{2} \))(\( 1 + 34670 T + 844596301 T^{2} \))(\( 1 + 42298 T + 844596301 T^{2} \))(\( 1 + 34738 T + 844596301 T^{2} \))(\( 1 - 47402 T + 844596301 T^{2} \))(\( 1 + 40210 T + 844596301 T^{2} \))(\( 1 - 32302 T + 844596301 T^{2} \))(\( 1 - 39570 T + 844596301 T^{2} \))(\( 1 + 9838 T + 844596301 T^{2} \))(\( 1 - 47402 T + 844596301 T^{2} \))(\( 1 + 42298 T + 844596301 T^{2} \))(\( 1 + 18482 T + 844596301 T^{2} \))(\( 1 - 13202 T + 844596301 T^{2} \))(\( 1 - 16622 T + 844596301 T^{2} \))(\( 1 + 24396 T + 1596983806 T^{2} + 20604771359196 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 19204 T + 627029406 T^{2} - 16219627364404 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 14108 T + 1110042462 T^{2} - 11915564614508 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 46932 T + 2239379182 T^{2} + 39638593598532 T^{3} + 713342911662882601 T^{4} \))(\( ( 1 + 3058 T + 844596301 T^{2} )^{2} \))(\( ( 1 + 5698 T + 844596301 T^{2} )^{2} \))(\( 1 + 46932 T + 2239379182 T^{2} + 39638593598532 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 19204 T + 627029406 T^{2} - 16219627364404 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 24396 T + 1596983806 T^{2} + 20604771359196 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 22478 T + 1331345683 T^{2} - 9784946414356 T^{3} + 1124449639214118583 T^{4} - \)\(16\!\cdots\!78\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( 1 - 22478 T + 1331345683 T^{2} - 9784946414356 T^{3} + 1124449639214118583 T^{4} - \)\(16\!\cdots\!78\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( 1 - 61928 T + 3903014764 T^{2} - 145287706763384 T^{3} + 5198153942066716726 T^{4} - \)\(12\!\cdots\!84\)\( T^{5} + \)\(27\!\cdots\!64\)\( T^{6} - \)\(37\!\cdots\!28\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} \))(\( 1 - 61928 T + 3903014764 T^{2} - 145287706763384 T^{3} + 5198153942066716726 T^{4} - \)\(12\!\cdots\!84\)\( T^{5} + \)\(27\!\cdots\!64\)\( T^{6} - \)\(37\!\cdots\!28\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} \))
$67$ (\( 1 + 24742 T + 1350125107 T^{2} \))(\( 1 + 47566 T + 1350125107 T^{2} \))(\( 1 + 32098 T + 1350125107 T^{2} \))(\( 1 - 21812 T + 1350125107 T^{2} \))(\( 1 + 13177 T + 1350125107 T^{2} \))(\( 1 - 58864 T + 1350125107 T^{2} \))(\( 1 - 60972 T + 1350125107 T^{2} \))(\( 1 + 56734 T + 1350125107 T^{2} \))(\( 1 - 33722 T + 1350125107 T^{2} \))(\( 1 - 13177 T + 1350125107 T^{2} \))(\( 1 - 32098 T + 1350125107 T^{2} \))(\( 1 + 15532 T + 1350125107 T^{2} \))(\( 1 + 11542 T + 1350125107 T^{2} \))(\( 1 - 1808 T + 1350125107 T^{2} \))(\( 1 - 40060 T + 2949898505 T^{2} - 54086011786420 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 90460 T + 4578999825 T^{2} - 122132317179220 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 85412 T + 4371910566 T^{2} + 115316885639084 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 68808 T + 3858742141 T^{2} + 92899408362456 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 755362070 T^{2} + 1822837804551761449 T^{4} \))(\( 1 + 795787610 T^{2} + 1822837804551761449 T^{4} \))(\( 1 - 68808 T + 3858742141 T^{2} - 92899408362456 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 90460 T + 4578999825 T^{2} + 122132317179220 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 40060 T + 2949898505 T^{2} + 54086011786420 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 26499 T + 3645391656 T^{2} + 72815104048223 T^{3} + 4921734799613907192 T^{4} + \)\(48\!\cdots\!51\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( 1 - 26499 T + 3645391656 T^{2} - 72815104048223 T^{3} + 4921734799613907192 T^{4} - \)\(48\!\cdots\!51\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( 1 + 72700 T + 7283604532 T^{2} + 314621051775212 T^{3} + 16093744308113184182 T^{4} + \)\(42\!\cdots\!84\)\( T^{5} + \)\(13\!\cdots\!68\)\( T^{6} + \)\(17\!\cdots\!00\)\( T^{7} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( 1 - 72700 T + 7283604532 T^{2} - 314621051775212 T^{3} + 16093744308113184182 T^{4} - \)\(42\!\cdots\!84\)\( T^{5} + \)\(13\!\cdots\!68\)\( T^{6} - \)\(17\!\cdots\!00\)\( T^{7} + \)\(33\!\cdots\!01\)\( T^{8} \))
$71$ (\( 1 + 42372 T + 1804229351 T^{2} \))(\( 1 + 948 T + 1804229351 T^{2} \))(\( 1 - 4248 T + 1804229351 T^{2} \))(\( 1 - 46872 T + 1804229351 T^{2} \))(\( 1 - 7548 T + 1804229351 T^{2} \))(\( 1 - 55312 T + 1804229351 T^{2} \))(\( 1 - 32648 T + 1804229351 T^{2} \))(\( 1 + 45588 T + 1804229351 T^{2} \))(\( 1 + 70212 T + 1804229351 T^{2} \))(\( 1 - 7548 T + 1804229351 T^{2} \))(\( 1 - 4248 T + 1804229351 T^{2} \))(\( 1 - 31960 T + 1804229351 T^{2} \))(\( 1 - 29532 T + 1804229351 T^{2} \))(\( 1 - 24528 T + 1804229351 T^{2} \))(\( 1 - 87296 T + 5453356606 T^{2} - 157502005424896 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 2736 T + 2006886526 T^{2} + 4936371504336 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 47208 T + 4011779662 T^{2} + 85174059202008 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 7448 T + 3593807902 T^{2} + 13437900206248 T^{3} + 3255243551009881201 T^{4} \))(\( ( 1 + 37608 T + 1804229351 T^{2} )^{2} \))(\( ( 1 + 53352 T + 1804229351 T^{2} )^{2} \))(\( 1 + 7448 T + 3593807902 T^{2} + 13437900206248 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 2736 T + 2006886526 T^{2} + 4936371504336 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 87296 T + 5453356606 T^{2} - 157502005424896 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 86676 T + 6149511717 T^{2} + 281168787837912 T^{3} + 11095129534129805667 T^{4} + \)\(28\!\cdots\!76\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( 1 + 86676 T + 6149511717 T^{2} + 281168787837912 T^{3} + 11095129534129805667 T^{4} + \)\(28\!\cdots\!76\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( 1 - 62816 T + 3398787356 T^{2} - 184024084124896 T^{3} + 8353296562609817510 T^{4} - \)\(33\!\cdots\!96\)\( T^{5} + \)\(11\!\cdots\!56\)\( T^{6} - \)\(36\!\cdots\!16\)\( T^{7} + \)\(10\!\cdots\!01\)\( T^{8} \))(\( 1 - 62816 T + 3398787356 T^{2} - 184024084124896 T^{3} + 8353296562609817510 T^{4} - \)\(33\!\cdots\!96\)\( T^{5} + \)\(11\!\cdots\!56\)\( T^{6} - \)\(36\!\cdots\!16\)\( T^{7} + \)\(10\!\cdots\!01\)\( T^{8} \))
$73$ (\( 1 - 52126 T + 2073071593 T^{2} \))(\( 1 - 63102 T + 2073071593 T^{2} \))(\( 1 - 30104 T + 2073071593 T^{2} \))(\( 1 + 67562 T + 2073071593 T^{2} \))(\( 1 - 59821 T + 2073071593 T^{2} \))(\( 1 + 27258 T + 2073071593 T^{2} \))(\( 1 - 38774 T + 2073071593 T^{2} \))(\( 1 + 11842 T + 2073071593 T^{2} \))(\( 1 + 21986 T + 2073071593 T^{2} \))(\( 1 + 59821 T + 2073071593 T^{2} \))(\( 1 + 30104 T + 2073071593 T^{2} \))(\( 1 - 4886 T + 2073071593 T^{2} \))(\( 1 + 33698 T + 2073071593 T^{2} \))(\( 1 + 20474 T + 2073071593 T^{2} \))(\( 1 + 70290 T + 5306812435 T^{2} + 145716202271970 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 12770 T + 4184025507 T^{2} - 26473124242610 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 67452 T + 4400780438 T^{2} - 139832825091036 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 108822 T + 7105450763 T^{2} + 225595796893446 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 3569749522 T^{2} + 4297625829703557649 T^{4} \))(\( 1 - 883886830 T^{2} + 4297625829703557649 T^{4} \))(\( 1 - 108822 T + 7105450763 T^{2} - 225595796893446 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 12770 T + 4184025507 T^{2} + 26473124242610 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 70290 T + 5306812435 T^{2} - 145716202271970 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 8305 T - 51125178 T^{2} + 126365418680971 T^{3} - 105986154198868554 T^{4} - \)\(35\!\cdots\!45\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( 1 + 8305 T - 51125178 T^{2} - 126365418680971 T^{3} - 105986154198868554 T^{4} + \)\(35\!\cdots\!45\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( 1 - 133072 T + 13424418340 T^{2} - 846379227250928 T^{3} + 45561026057566462310 T^{4} - \)\(17\!\cdots\!04\)\( T^{5} + \)\(57\!\cdots\!60\)\( T^{6} - \)\(11\!\cdots\!04\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 + 133072 T + 13424418340 T^{2} + 846379227250928 T^{3} + 45561026057566462310 T^{4} + \)\(17\!\cdots\!04\)\( T^{5} + \)\(57\!\cdots\!60\)\( T^{6} + \)\(11\!\cdots\!04\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))
$79$ (\( 1 - 39640 T + 3077056399 T^{2} \))(\( 1 + 46536 T + 3077056399 T^{2} \))(\( 1 + 35280 T + 3077056399 T^{2} \))(\( 1 - 76912 T + 3077056399 T^{2} \))(\( 1 + 75830 T + 3077056399 T^{2} \))(\( 1 + 31456 T + 3077056399 T^{2} \))(\( 1 - 33360 T + 3077056399 T^{2} \))(\( 1 + 94216 T + 3077056399 T^{2} \))(\( 1 + 4520 T + 3077056399 T^{2} \))(\( 1 + 75830 T + 3077056399 T^{2} \))(\( 1 + 35280 T + 3077056399 T^{2} \))(\( 1 + 44560 T + 3077056399 T^{2} \))(\( 1 + 31208 T + 3077056399 T^{2} \))(\( 1 - 46240 T + 3077056399 T^{2} \))(\( 1 + 65480 T + 5707696298 T^{2} + 201485653006520 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 16184 T + 6157384362 T^{2} - 49799080761416 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 65904 T + 3994274078 T^{2} - 202790324919696 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 108104 T + 6816153098 T^{2} - 332642104957496 T^{3} + 9468276082626847201 T^{4} \))(\( ( 1 + 79728 T + 3077056399 T^{2} )^{2} \))(\( ( 1 - 51920 T + 3077056399 T^{2} )^{2} \))(\( 1 - 108104 T + 6816153098 T^{2} - 332642104957496 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 16184 T + 6157384362 T^{2} - 49799080761416 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 65480 T + 5707696298 T^{2} + 201485653006520 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 21982 T + 8034849513 T^{2} + 109220050198796 T^{3} + 24723685108978683687 T^{4} + \)\(20\!\cdots\!82\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( 1 + 21982 T + 8034849513 T^{2} + 109220050198796 T^{3} + 24723685108978683687 T^{4} + \)\(20\!\cdots\!82\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( 1 - 21632 T + 7152876604 T^{2} - 332616618908288 T^{3} + 24121899620797566790 T^{4} - \)\(10\!\cdots\!12\)\( T^{5} + \)\(67\!\cdots\!04\)\( T^{6} - \)\(63\!\cdots\!68\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} \))(\( 1 - 21632 T + 7152876604 T^{2} - 332616618908288 T^{3} + 24121899620797566790 T^{4} - \)\(10\!\cdots\!12\)\( T^{5} + \)\(67\!\cdots\!04\)\( T^{6} - \)\(63\!\cdots\!68\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} \))
$83$ (\( 1 + 59826 T + 3939040643 T^{2} \))(\( 1 + 88778 T + 3939040643 T^{2} \))(\( 1 - 27826 T + 3939040643 T^{2} \))(\( 1 - 67716 T + 3939040643 T^{2} \))(\( 1 - 46299 T + 3939040643 T^{2} \))(\( 1 - 24552 T + 3939040643 T^{2} \))(\( 1 - 16716 T + 3939040643 T^{2} \))(\( 1 + 31482 T + 3939040643 T^{2} \))(\( 1 + 109074 T + 3939040643 T^{2} \))(\( 1 + 46299 T + 3939040643 T^{2} \))(\( 1 + 27826 T + 3939040643 T^{2} \))(\( 1 - 67364 T + 3939040643 T^{2} \))(\( 1 + 38466 T + 3939040643 T^{2} \))(\( 1 + 51576 T + 3939040643 T^{2} \))(\( 1 + 92580 T + 9976491505 T^{2} + 364676382728940 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 30300 T + 4057027705 T^{2} - 119352931482900 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 108724 T + 10572459494 T^{2} - 428268254869532 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 27224 T + 4507827109 T^{2} + 107236442465032 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 7612675530 T^{2} + 15516041187205853449 T^{4} \))(\( 1 + 4053674810 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 27224 T + 4507827109 T^{2} - 107236442465032 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 30300 T + 4057027705 T^{2} + 119352931482900 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 92580 T + 9976491505 T^{2} - 364676382728940 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 213353 T + 26132961424 T^{2} - 1969967057862869 T^{3} + \)\(10\!\cdots\!32\)\( T^{4} - \)\(33\!\cdots\!97\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 + 213353 T + 26132961424 T^{2} + 1969967057862869 T^{3} + \)\(10\!\cdots\!32\)\( T^{4} + \)\(33\!\cdots\!97\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 + 74660 T + 6167006708 T^{2} + 554766838355444 T^{3} + 42874466663031633142 T^{4} + \)\(21\!\cdots\!92\)\( T^{5} + \)\(95\!\cdots\!92\)\( T^{6} + \)\(45\!\cdots\!20\)\( T^{7} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 - 74660 T + 6167006708 T^{2} - 554766838355444 T^{3} + 42874466663031633142 T^{4} - \)\(21\!\cdots\!92\)\( T^{5} + \)\(95\!\cdots\!92\)\( T^{6} - \)\(45\!\cdots\!20\)\( T^{7} + \)\(24\!\cdots\!01\)\( T^{8} \))
$89$ (\( 1 - 57690 T + 5584059449 T^{2} \))(\( 1 + 104934 T + 5584059449 T^{2} \))(\( 1 + 85210 T + 5584059449 T^{2} \))(\( 1 - 29754 T + 5584059449 T^{2} \))(\( 1 + 30585 T + 5584059449 T^{2} \))(\( 1 + 90854 T + 5584059449 T^{2} \))(\( 1 - 101370 T + 5584059449 T^{2} \))(\( 1 + 94054 T + 5584059449 T^{2} \))(\( 1 - 38490 T + 5584059449 T^{2} \))(\( 1 + 30585 T + 5584059449 T^{2} \))(\( 1 + 85210 T + 5584059449 T^{2} \))(\( 1 - 71994 T + 5584059449 T^{2} \))(\( 1 - 119514 T + 5584059449 T^{2} \))(\( 1 + 110310 T + 5584059449 T^{2} \))(\( 1 + 72810 T + 5926578523 T^{2} + 406575368481690 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 47322 T - 1006825781 T^{2} + 264248861245578 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 55020 T + 10818978262 T^{2} + 307234950883980 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 70990 T + 6345035107 T^{2} - 396412380284510 T^{3} + 31181719929966183601 T^{4} \))(\( ( 1 + 826 T + 5584059449 T^{2} )^{2} \))(\( ( 1 - 9990 T + 5584059449 T^{2} )^{2} \))(\( 1 - 70990 T + 6345035107 T^{2} - 396412380284510 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 47322 T - 1006825781 T^{2} + 264248861245578 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 72810 T + 5926578523 T^{2} + 406575368481690 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 182381 T + 27173913486 T^{2} - 2227663367824697 T^{3} + \)\(15\!\cdots\!14\)\( T^{4} - \)\(56\!\cdots\!81\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( 1 - 182381 T + 27173913486 T^{2} - 2227663367824697 T^{3} + \)\(15\!\cdots\!14\)\( T^{4} - \)\(56\!\cdots\!81\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( 1 - 20952 T + 16118164796 T^{2} - 497915996461992 T^{3} + \)\(11\!\cdots\!30\)\( T^{4} - \)\(27\!\cdots\!08\)\( T^{5} + \)\(50\!\cdots\!96\)\( T^{6} - \)\(36\!\cdots\!48\)\( T^{7} + \)\(97\!\cdots\!01\)\( T^{8} \))(\( 1 - 20952 T + 16118164796 T^{2} - 497915996461992 T^{3} + \)\(11\!\cdots\!30\)\( T^{4} - \)\(27\!\cdots\!08\)\( T^{5} + \)\(50\!\cdots\!96\)\( T^{6} - \)\(36\!\cdots\!48\)\( T^{7} + \)\(97\!\cdots\!01\)\( T^{8} \))
$97$ (\( 1 - 144382 T + 8587340257 T^{2} \))(\( 1 - 36254 T + 8587340257 T^{2} \))(\( 1 + 97232 T + 8587340257 T^{2} \))(\( 1 - 122398 T + 8587340257 T^{2} \))(\( 1 + 104018 T + 8587340257 T^{2} \))(\( 1 + 154706 T + 8587340257 T^{2} \))(\( 1 - 119038 T + 8587340257 T^{2} \))(\( 1 + 23714 T + 8587340257 T^{2} \))(\( 1 - 1918 T + 8587340257 T^{2} \))(\( 1 - 104018 T + 8587340257 T^{2} \))(\( 1 - 97232 T + 8587340257 T^{2} \))(\( 1 + 48866 T + 8587340257 T^{2} \))(\( 1 + 94658 T + 8587340257 T^{2} \))(\( 1 - 78382 T + 8587340257 T^{2} \))(\( 1 + 126140 T + 13936294470 T^{2} + 1083207100017980 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 2980 T + 14115250950 T^{2} + 25590273965860 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 147668 T + 11612429670 T^{2} + 1268075361070676 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 96852 T + 16039717990 T^{2} + 831701078570964 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 15761405890 T^{2} + 73742412689492826049 T^{4} \))(\( 1 + 6923133890 T^{2} + 73742412689492826049 T^{4} \))(\( 1 - 96852 T + 16039717990 T^{2} - 831701078570964 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 2980 T + 14115250950 T^{2} - 25590273965860 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 126140 T + 13936294470 T^{2} - 1083207100017980 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 76342 T + 16917659759 T^{2} - 1144576356113332 T^{3} + \)\(14\!\cdots\!63\)\( T^{4} - \)\(56\!\cdots\!58\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( 1 + 76342 T + 16917659759 T^{2} + 1144576356113332 T^{3} + \)\(14\!\cdots\!63\)\( T^{4} + \)\(56\!\cdots\!58\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( 1 - 59456 T + 24399465604 T^{2} - 684112850575552 T^{3} + \)\(25\!\cdots\!74\)\( T^{4} - \)\(58\!\cdots\!64\)\( T^{5} + \)\(17\!\cdots\!96\)\( T^{6} - \)\(37\!\cdots\!08\)\( T^{7} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( 1 + 59456 T + 24399465604 T^{2} + 684112850575552 T^{3} + \)\(25\!\cdots\!74\)\( T^{4} + \)\(58\!\cdots\!64\)\( T^{5} + \)\(17\!\cdots\!96\)\( T^{6} + \)\(37\!\cdots\!08\)\( T^{7} + \)\(54\!\cdots\!01\)\( T^{8} \))
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