Properties

Label 294.6.a
Level $294$
Weight $6$
Character orbit 294.a
Rep. character $\chi_{294}(1,\cdot)$
Character field $\Q$
Dimension $33$
Newform subspaces $23$
Sturm bound $336$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 294.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(336\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(294))\).

Total New Old
Modular forms 296 33 263
Cusp forms 264 33 231
Eisenstein series 32 0 32

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

\(2\)\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(14\)
Minus space\(-\)\(19\)

Trace form

\( 33q + 4q^{2} + 9q^{3} + 528q^{4} + 22q^{5} + 36q^{6} + 64q^{8} + 2673q^{9} + O(q^{10}) \) \( 33q + 4q^{2} + 9q^{3} + 528q^{4} + 22q^{5} + 36q^{6} + 64q^{8} + 2673q^{9} - 360q^{10} - 652q^{11} + 144q^{12} + 694q^{13} + 198q^{15} + 8448q^{16} - 1054q^{17} + 324q^{18} + 3124q^{19} + 352q^{20} - 1696q^{22} + 5424q^{23} + 576q^{24} + 24427q^{25} - 4392q^{26} + 729q^{27} + 1262q^{29} - 5976q^{30} + 616q^{31} + 1024q^{32} + 180q^{33} + 13704q^{34} + 42768q^{36} - 31658q^{37} + 2192q^{38} - 10134q^{39} - 5760q^{40} - 20742q^{41} + 3684q^{43} - 10432q^{44} + 1782q^{45} + 14080q^{46} + 13776q^{47} + 2304q^{48} - 89124q^{50} + 11718q^{51} + 11104q^{52} - 63538q^{53} + 2916q^{54} - 69672q^{55} + 80100q^{57} + 2440q^{58} - 80900q^{59} + 3168q^{60} + 86566q^{61} + 106848q^{62} + 135168q^{64} + 146500q^{65} + 37008q^{66} + 123956q^{67} - 16864q^{68} - 88920q^{69} + 161888q^{71} + 5184q^{72} + 105274q^{73} + 349528q^{74} + 48807q^{75} + 49984q^{76} - 48024q^{78} + 212748q^{79} + 5632q^{80} + 216513q^{81} + 13800q^{82} + 62612q^{83} + 158524q^{85} - 172368q^{86} + 188982q^{87} - 27136q^{88} - 121398q^{89} - 29160q^{90} + 86784q^{92} + 235656q^{93} + 129024q^{94} + 302848q^{95} + 9216q^{96} - 163646q^{97} - 52812q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(294))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7
294.6.a.a \(1\) \(47.153\) \(\Q\) None \(-4\) \(-9\) \(-26\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}-26q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.b \(1\) \(47.153\) \(\Q\) None \(-4\) \(-9\) \(-26\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}-26q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.c \(1\) \(47.153\) \(\Q\) None \(-4\) \(-9\) \(72\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+72q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.d \(1\) \(47.153\) \(\Q\) None \(-4\) \(-9\) \(86\) \(0\) \(+\) \(+\) \(+\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+86q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.e \(1\) \(47.153\) \(\Q\) None \(-4\) \(9\) \(-86\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-86q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.f \(1\) \(47.153\) \(\Q\) None \(-4\) \(9\) \(-44\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-44q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.g \(1\) \(47.153\) \(\Q\) None \(-4\) \(9\) \(26\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+26q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.h \(1\) \(47.153\) \(\Q\) None \(-4\) \(9\) \(54\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+54q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.i \(1\) \(47.153\) \(\Q\) None \(4\) \(-9\) \(-24\) \(0\) \(-\) \(+\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}-24q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.j \(1\) \(47.153\) \(\Q\) None \(4\) \(-9\) \(6\) \(0\) \(-\) \(+\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+6q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.k \(1\) \(47.153\) \(\Q\) None \(4\) \(9\) \(-76\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}-76q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.l \(1\) \(47.153\) \(\Q\) None \(4\) \(9\) \(-6\) \(0\) \(-\) \(-\) \(+\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}-6q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.m \(1\) \(47.153\) \(\Q\) None \(4\) \(9\) \(66\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+66q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.n \(2\) \(47.153\) \(\Q(\sqrt{2}) \) None \(-8\) \(-18\) \(-108\) \(0\) \(+\) \(+\) \(+\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-54+5\beta )q^{5}+\cdots\)
294.6.a.o \(2\) \(47.153\) \(\Q(\sqrt{505}) \) None \(-8\) \(-18\) \(-17\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-9-\beta )q^{5}+\cdots\)
294.6.a.p \(2\) \(47.153\) \(\Q(\sqrt{505}) \) None \(-8\) \(18\) \(17\) \(0\) \(+\) \(-\) \(+\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(9+\beta )q^{5}+\cdots\)
294.6.a.q \(2\) \(47.153\) \(\Q(\sqrt{2}) \) None \(-8\) \(18\) \(108\) \(0\) \(+\) \(-\) \(+\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(54+5\beta )q^{5}+\cdots\)
294.6.a.r \(2\) \(47.153\) \(\Q(\sqrt{9601}) \) None \(8\) \(-18\) \(-53\) \(0\) \(-\) \(+\) \(+\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-26-\beta )q^{5}+\cdots\)
294.6.a.s \(2\) \(47.153\) \(\Q(\sqrt{4705}) \) None \(8\) \(-18\) \(-18\) \(0\) \(-\) \(+\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-9-\beta )q^{5}+\cdots\)
294.6.a.t \(2\) \(47.153\) \(\Q(\sqrt{2}) \) None \(8\) \(-18\) \(108\) \(0\) \(-\) \(+\) \(+\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(54+5\beta )q^{5}+\cdots\)
294.6.a.u \(2\) \(47.153\) \(\Q(\sqrt{2}) \) None \(8\) \(18\) \(-108\) \(0\) \(-\) \(-\) \(+\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(-54+5\beta )q^{5}+\cdots\)
294.6.a.v \(2\) \(47.153\) \(\Q(\sqrt{4705}) \) None \(8\) \(18\) \(18\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(9-\beta )q^{5}+\cdots\)
294.6.a.w \(2\) \(47.153\) \(\Q(\sqrt{9601}) \) None \(8\) \(18\) \(53\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(3^{3}-\beta )q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(294))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(294)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 + 4 T \))(\( 1 - 4 T \))(\( 1 - 4 T \))(\( 1 - 4 T \))(\( 1 - 4 T \))(\( 1 - 4 T \))(\( ( 1 + 4 T )^{2} \))(\( ( 1 + 4 T )^{2} \))(\( ( 1 + 4 T )^{2} \))(\( ( 1 + 4 T )^{2} \))(\( ( 1 - 4 T )^{2} \))(\( ( 1 - 4 T )^{2} \))(\( ( 1 - 4 T )^{2} \))(\( ( 1 - 4 T )^{2} \))(\( ( 1 - 4 T )^{2} \))(\( ( 1 - 4 T )^{2} \))
$3$ (\( 1 + 9 T \))(\( 1 + 9 T \))(\( 1 + 9 T \))(\( 1 + 9 T \))(\( 1 - 9 T \))(\( 1 - 9 T \))(\( 1 - 9 T \))(\( 1 - 9 T \))(\( 1 + 9 T \))(\( 1 + 9 T \))(\( 1 - 9 T \))(\( 1 - 9 T \))(\( 1 - 9 T \))(\( ( 1 + 9 T )^{2} \))(\( ( 1 + 9 T )^{2} \))(\( ( 1 - 9 T )^{2} \))(\( ( 1 - 9 T )^{2} \))(\( ( 1 + 9 T )^{2} \))(\( ( 1 + 9 T )^{2} \))(\( ( 1 + 9 T )^{2} \))(\( ( 1 - 9 T )^{2} \))(\( ( 1 - 9 T )^{2} \))(\( ( 1 - 9 T )^{2} \))
$5$ (\( 1 + 26 T + 3125 T^{2} \))(\( 1 + 26 T + 3125 T^{2} \))(\( 1 - 72 T + 3125 T^{2} \))(\( 1 - 86 T + 3125 T^{2} \))(\( 1 + 86 T + 3125 T^{2} \))(\( 1 + 44 T + 3125 T^{2} \))(\( 1 - 26 T + 3125 T^{2} \))(\( 1 - 54 T + 3125 T^{2} \))(\( 1 + 24 T + 3125 T^{2} \))(\( 1 - 6 T + 3125 T^{2} \))(\( 1 + 76 T + 3125 T^{2} \))(\( 1 + 6 T + 3125 T^{2} \))(\( 1 - 66 T + 3125 T^{2} \))(\( 1 + 108 T + 6716 T^{2} + 337500 T^{3} + 9765625 T^{4} \))(\( 1 + 17 T + 136 T^{2} + 53125 T^{3} + 9765625 T^{4} \))(\( 1 - 17 T + 136 T^{2} - 53125 T^{3} + 9765625 T^{4} \))(\( 1 - 108 T + 6716 T^{2} - 337500 T^{3} + 9765625 T^{4} \))(\( 1 + 53 T + 4552 T^{2} + 165625 T^{3} + 9765625 T^{4} \))(\( 1 + 18 T + 1626 T^{2} + 56250 T^{3} + 9765625 T^{4} \))(\( 1 - 108 T + 9116 T^{2} - 337500 T^{3} + 9765625 T^{4} \))(\( 1 + 108 T + 9116 T^{2} + 337500 T^{3} + 9765625 T^{4} \))(\( 1 - 18 T + 1626 T^{2} - 56250 T^{3} + 9765625 T^{4} \))(\( 1 - 53 T + 4552 T^{2} - 165625 T^{3} + 9765625 T^{4} \))
$7$ 1
$11$ (\( 1 + 358 T + 161051 T^{2} \))(\( 1 - 664 T + 161051 T^{2} \))(\( 1 + 414 T + 161051 T^{2} \))(\( 1 - 34 T + 161051 T^{2} \))(\( 1 - 34 T + 161051 T^{2} \))(\( 1 + 470 T + 161051 T^{2} \))(\( 1 + 358 T + 161051 T^{2} \))(\( 1 - 216 T + 161051 T^{2} \))(\( 1 - 66 T + 161051 T^{2} \))(\( 1 + 666 T + 161051 T^{2} \))(\( 1 - 650 T + 161051 T^{2} \))(\( 1 + 666 T + 161051 T^{2} \))(\( 1 + 60 T + 161051 T^{2} \))(\( 1 - 124 T + 294194 T^{2} - 19970324 T^{3} + 25937424601 T^{4} \))(\( 1 - 145 T + 24232 T^{2} - 23352395 T^{3} + 25937424601 T^{4} \))(\( 1 - 145 T + 24232 T^{2} - 23352395 T^{3} + 25937424601 T^{4} \))(\( 1 - 124 T + 294194 T^{2} - 19970324 T^{3} + 25937424601 T^{4} \))(\( 1 - 191 T + 271216 T^{2} - 30760741 T^{3} + 25937424601 T^{4} \))(\( 1 - 2 T - 59002 T^{2} - 322102 T^{3} + 25937424601 T^{4} \))(\( 1 + 124 T + 325298 T^{2} + 19970324 T^{3} + 25937424601 T^{4} \))(\( 1 + 124 T + 325298 T^{2} + 19970324 T^{3} + 25937424601 T^{4} \))(\( 1 - 2 T - 59002 T^{2} - 322102 T^{3} + 25937424601 T^{4} \))(\( 1 - 191 T + 271216 T^{2} - 30760741 T^{3} + 25937424601 T^{4} \))
$13$ (\( 1 + 332 T + 371293 T^{2} \))(\( 1 + 318 T + 371293 T^{2} \))(\( 1 - 1054 T + 371293 T^{2} \))(\( 1 + 3 T + 371293 T^{2} \))(\( 1 - 3 T + 371293 T^{2} \))(\( 1 - 1158 T + 371293 T^{2} \))(\( 1 - 332 T + 371293 T^{2} \))(\( 1 + 998 T + 371293 T^{2} \))(\( 1 + 98 T + 371293 T^{2} \))(\( 1 - 559 T + 371293 T^{2} \))(\( 1 + 762 T + 371293 T^{2} \))(\( 1 + 559 T + 371293 T^{2} \))(\( 1 - 658 T + 371293 T^{2} \))(\( 1 + 720 T + 673736 T^{2} + 267330960 T^{3} + 137858491849 T^{4} \))(\( 1 - 715 T + 864206 T^{2} - 265474495 T^{3} + 137858491849 T^{4} \))(\( 1 + 715 T + 864206 T^{2} + 265474495 T^{3} + 137858491849 T^{4} \))(\( 1 - 720 T + 673736 T^{2} - 267330960 T^{3} + 137858491849 T^{4} \))(\( 1 + 379 T + 488066 T^{2} + 140720047 T^{3} + 137858491849 T^{4} \))(\( 1 + 288 T + 688042 T^{2} + 106932384 T^{3} + 137858491849 T^{4} \))(\( 1 - 720 T + 716504 T^{2} - 267330960 T^{3} + 137858491849 T^{4} \))(\( 1 + 720 T + 716504 T^{2} + 267330960 T^{3} + 137858491849 T^{4} \))(\( 1 - 288 T + 688042 T^{2} - 106932384 T^{3} + 137858491849 T^{4} \))(\( 1 - 379 T + 488066 T^{2} - 140720047 T^{3} + 137858491849 T^{4} \))
$17$ (\( 1 + 126 T + 1419857 T^{2} \))(\( 1 + 1582 T + 1419857 T^{2} \))(\( 1 - 1848 T + 1419857 T^{2} \))(\( 1 + 1904 T + 1419857 T^{2} \))(\( 1 - 1904 T + 1419857 T^{2} \))(\( 1 + 1204 T + 1419857 T^{2} \))(\( 1 - 126 T + 1419857 T^{2} \))(\( 1 + 1302 T + 1419857 T^{2} \))(\( 1 - 216 T + 1419857 T^{2} \))(\( 1 - 1740 T + 1419857 T^{2} \))(\( 1 - 556 T + 1419857 T^{2} \))(\( 1 + 1740 T + 1419857 T^{2} \))(\( 1 - 414 T + 1419857 T^{2} \))(\( 1 - 1260 T + 2796692 T^{2} - 1789019820 T^{3} + 2015993900449 T^{4} \))(\( 1 + 1372 T + 835810 T^{2} + 1948043804 T^{3} + 2015993900449 T^{4} \))(\( 1 - 1372 T + 835810 T^{2} - 1948043804 T^{3} + 2015993900449 T^{4} \))(\( 1 + 1260 T + 2796692 T^{2} + 1789019820 T^{3} + 2015993900449 T^{4} \))(\( 1 + 340 T + 1908514 T^{2} + 482751380 T^{3} + 2015993900449 T^{4} \))(\( 1 + 1530 T + 2366314 T^{2} + 2172381210 T^{3} + 2015993900449 T^{4} \))(\( 1 - 612 T - 146812 T^{2} - 868952484 T^{3} + 2015993900449 T^{4} \))(\( 1 + 612 T - 146812 T^{2} + 868952484 T^{3} + 2015993900449 T^{4} \))(\( 1 - 1530 T + 2366314 T^{2} - 2172381210 T^{3} + 2015993900449 T^{4} \))(\( 1 - 340 T + 1908514 T^{2} - 482751380 T^{3} + 2015993900449 T^{4} \))
$19$ (\( 1 - 2200 T + 2476099 T^{2} \))(\( 1 + 236 T + 2476099 T^{2} \))(\( 1 + 236 T + 2476099 T^{2} \))(\( 1 + 1489 T + 2476099 T^{2} \))(\( 1 - 1489 T + 2476099 T^{2} \))(\( 1 - 2644 T + 2476099 T^{2} \))(\( 1 + 2200 T + 2476099 T^{2} \))(\( 1 + 884 T + 2476099 T^{2} \))(\( 1 - 340 T + 2476099 T^{2} \))(\( 1 + 1157 T + 2476099 T^{2} \))(\( 1 - 2452 T + 2476099 T^{2} \))(\( 1 - 1157 T + 2476099 T^{2} \))(\( 1 + 956 T + 2476099 T^{2} \))(\( 1 + 360 T + 4777230 T^{2} + 891395640 T^{3} + 6131066257801 T^{4} \))(\( 1 + 1081 T + 734562 T^{2} + 2676663019 T^{3} + 6131066257801 T^{4} \))(\( 1 - 1081 T + 734562 T^{2} - 2676663019 T^{3} + 6131066257801 T^{4} \))(\( 1 - 360 T + 4777230 T^{2} - 891395640 T^{3} + 6131066257801 T^{4} \))(\( 1 + 1769 T + 2083758 T^{2} + 4380219131 T^{3} + 6131066257801 T^{4} \))(\( 1 + 1188 T + 4834534 T^{2} + 2941605612 T^{3} + 6131066257801 T^{4} \))(\( 1 - 2088 T + 3803406 T^{2} - 5170094712 T^{3} + 6131066257801 T^{4} \))(\( 1 + 2088 T + 3803406 T^{2} + 5170094712 T^{3} + 6131066257801 T^{4} \))(\( 1 - 1188 T + 4834534 T^{2} - 2941605612 T^{3} + 6131066257801 T^{4} \))(\( 1 - 1769 T + 2083758 T^{2} - 4380219131 T^{3} + 6131066257801 T^{4} \))
$23$ (\( 1 + 2142 T + 6436343 T^{2} \))(\( 1 - 2212 T + 6436343 T^{2} \))(\( 1 - 2898 T + 6436343 T^{2} \))(\( 1 + 224 T + 6436343 T^{2} \))(\( 1 + 224 T + 6436343 T^{2} \))(\( 1 + 1190 T + 6436343 T^{2} \))(\( 1 + 2142 T + 6436343 T^{2} \))(\( 1 + 2268 T + 6436343 T^{2} \))(\( 1 + 1038 T + 6436343 T^{2} \))(\( 1 + 3468 T + 6436343 T^{2} \))(\( 1 + 2950 T + 6436343 T^{2} \))(\( 1 + 3468 T + 6436343 T^{2} \))(\( 1 - 600 T + 6436343 T^{2} \))(\( 1 - 6524 T + 23227562 T^{2} - 41990701732 T^{3} + 41426511213649 T^{4} \))(\( 1 + 4508 T + 17854222 T^{2} + 29015034244 T^{3} + 41426511213649 T^{4} \))(\( 1 + 4508 T + 17854222 T^{2} + 29015034244 T^{3} + 41426511213649 T^{4} \))(\( 1 - 6524 T + 23227562 T^{2} - 41990701732 T^{3} + 41426511213649 T^{4} \))(\( 1 - 3236 T + 15452206 T^{2} - 20828005948 T^{3} + 41426511213649 T^{4} \))(\( 1 - 3390 T + 6218086 T^{2} - 21819202770 T^{3} + 41426511213649 T^{4} \))(\( 1 - 772 T + 11336234 T^{2} - 4968856796 T^{3} + 41426511213649 T^{4} \))(\( 1 - 772 T + 11336234 T^{2} - 4968856796 T^{3} + 41426511213649 T^{4} \))(\( 1 - 3390 T + 6218086 T^{2} - 21819202770 T^{3} + 41426511213649 T^{4} \))(\( 1 - 3236 T + 15452206 T^{2} - 20828005948 T^{3} + 41426511213649 T^{4} \))
$29$ (\( 1 + 3610 T + 20511149 T^{2} \))(\( 1 + 4954 T + 20511149 T^{2} \))(\( 1 + 6522 T + 20511149 T^{2} \))(\( 1 + 6508 T + 20511149 T^{2} \))(\( 1 + 6508 T + 20511149 T^{2} \))(\( 1 - 3614 T + 20511149 T^{2} \))(\( 1 + 3610 T + 20511149 T^{2} \))(\( 1 + 1482 T + 20511149 T^{2} \))(\( 1 + 2490 T + 20511149 T^{2} \))(\( 1 - 3372 T + 20511149 T^{2} \))(\( 1 + 674 T + 20511149 T^{2} \))(\( 1 - 3372 T + 20511149 T^{2} \))(\( 1 - 5574 T + 20511149 T^{2} \))(\( 1 - 7088 T + 48216146 T^{2} - 145383024112 T^{3} + 420707233300201 T^{4} \))(\( 1 - 7865 T + 34952518 T^{2} - 161320186885 T^{3} + 420707233300201 T^{4} \))(\( 1 - 7865 T + 34952518 T^{2} - 161320186885 T^{3} + 420707233300201 T^{4} \))(\( 1 - 7088 T + 48216146 T^{2} - 145383024112 T^{3} + 420707233300201 T^{4} \))(\( 1 - 4459 T + 37061638 T^{2} - 91459213391 T^{3} + 420707233300201 T^{4} \))(\( 1 + 3976 T + 31254662 T^{2} + 81552328424 T^{3} + 420707233300201 T^{4} \))(\( 1 + 4592 T + 40196882 T^{2} + 94187196208 T^{3} + 420707233300201 T^{4} \))(\( 1 + 4592 T + 40196882 T^{2} + 94187196208 T^{3} + 420707233300201 T^{4} \))(\( 1 + 3976 T + 31254662 T^{2} + 81552328424 T^{3} + 420707233300201 T^{4} \))(\( 1 - 4459 T + 37061638 T^{2} - 91459213391 T^{3} + 420707233300201 T^{4} \))
$31$ (\( 1 + 5668 T + 28629151 T^{2} \))(\( 1 - 7128 T + 28629151 T^{2} \))(\( 1 + 6200 T + 28629151 T^{2} \))(\( 1 - 1731 T + 28629151 T^{2} \))(\( 1 + 1731 T + 28629151 T^{2} \))(\( 1 + 5616 T + 28629151 T^{2} \))(\( 1 - 5668 T + 28629151 T^{2} \))(\( 1 + 8360 T + 28629151 T^{2} \))(\( 1 - 7048 T + 28629151 T^{2} \))(\( 1 + 6293 T + 28629151 T^{2} \))(\( 1 - 3024 T + 28629151 T^{2} \))(\( 1 - 6293 T + 28629151 T^{2} \))(\( 1 - 3592 T + 28629151 T^{2} \))(\( 1 + 5904 T + 58828406 T^{2} + 169026507504 T^{3} + 819628286980801 T^{4} \))(\( 1 + 8816 T + 75476261 T^{2} + 252394595216 T^{3} + 819628286980801 T^{4} \))(\( 1 - 8816 T + 75476261 T^{2} - 252394595216 T^{3} + 819628286980801 T^{4} \))(\( 1 - 5904 T + 58828406 T^{2} - 169026507504 T^{3} + 819628286980801 T^{4} \))(\( 1 - 1994 T - 6304813 T^{2} - 57086527094 T^{3} + 819628286980801 T^{4} \))(\( 1 + 7596 T + 61727326 T^{2} + 217467030996 T^{3} + 819628286980801 T^{4} \))(\( 1 - 9792 T + 81095990 T^{2} - 280336646592 T^{3} + 819628286980801 T^{4} \))(\( 1 + 9792 T + 81095990 T^{2} + 280336646592 T^{3} + 819628286980801 T^{4} \))(\( 1 - 7596 T + 61727326 T^{2} - 217467030996 T^{3} + 819628286980801 T^{4} \))(\( 1 + 1994 T - 6304813 T^{2} + 57086527094 T^{3} + 819628286980801 T^{4} \))
$37$ (\( 1 + 2922 T + 69343957 T^{2} \))(\( 1 - 4358 T + 69343957 T^{2} \))(\( 1 - 9650 T + 69343957 T^{2} \))(\( 1 + 7633 T + 69343957 T^{2} \))(\( 1 + 7633 T + 69343957 T^{2} \))(\( 1 + 6478 T + 69343957 T^{2} \))(\( 1 + 2922 T + 69343957 T^{2} \))(\( 1 + 4714 T + 69343957 T^{2} \))(\( 1 + 12238 T + 69343957 T^{2} \))(\( 1 - 3131 T + 69343957 T^{2} \))(\( 1 - 7730 T + 69343957 T^{2} \))(\( 1 - 3131 T + 69343957 T^{2} \))(\( 1 + 8458 T + 69343957 T^{2} \))(\( 1 + 6040 T + 111103002 T^{2} + 418837500280 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 14573 T + 151193010 T^{2} + 1010549485361 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 14573 T + 151193010 T^{2} + 1010549485361 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 6040 T + 111103002 T^{2} + 418837500280 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 20587 T + 238401006 T^{2} - 1427584042759 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 2688 T + 126774470 T^{2} - 186396556416 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 5992 T + 51114522 T^{2} + 415508990344 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 5992 T + 51114522 T^{2} + 415508990344 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 2688 T + 126774470 T^{2} - 186396556416 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 20587 T + 238401006 T^{2} - 1427584042759 T^{3} + 4808584372417849 T^{4} \))
$41$ (\( 1 - 2142 T + 115856201 T^{2} \))(\( 1 + 10542 T + 115856201 T^{2} \))(\( 1 + 8484 T + 115856201 T^{2} \))(\( 1 - 15414 T + 115856201 T^{2} \))(\( 1 + 15414 T + 115856201 T^{2} \))(\( 1 + 2856 T + 115856201 T^{2} \))(\( 1 + 2142 T + 115856201 T^{2} \))(\( 1 - 9786 T + 115856201 T^{2} \))(\( 1 + 6468 T + 115856201 T^{2} \))(\( 1 - 4866 T + 115856201 T^{2} \))(\( 1 - 17016 T + 115856201 T^{2} \))(\( 1 + 4866 T + 115856201 T^{2} \))(\( 1 + 19194 T + 115856201 T^{2} \))(\( 1 - 17388 T + 216792980 T^{2} - 2014507622988 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 7350 T + 218270722 T^{2} + 851543077350 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 7350 T + 218270722 T^{2} - 851543077350 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 17388 T + 216792980 T^{2} + 2014507622988 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 8814 T + 240678562 T^{2} - 1021156555614 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 36630 T + 559995322 T^{2} + 4243812642630 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 20196 T + 324853604 T^{2} - 2339831835396 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 20196 T + 324853604 T^{2} + 2339831835396 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 36630 T + 559995322 T^{2} - 4243812642630 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 8814 T + 240678562 T^{2} + 1021156555614 T^{3} + 13422659310152401 T^{4} \))
$43$ (\( 1 - 6388 T + 147008443 T^{2} \))(\( 1 + 8452 T + 147008443 T^{2} \))(\( 1 + 10804 T + 147008443 T^{2} \))(\( 1 - 18491 T + 147008443 T^{2} \))(\( 1 - 18491 T + 147008443 T^{2} \))(\( 1 + 13492 T + 147008443 T^{2} \))(\( 1 - 6388 T + 147008443 T^{2} \))(\( 1 - 19436 T + 147008443 T^{2} \))(\( 1 + 15412 T + 147008443 T^{2} \))(\( 1 + 11407 T + 147008443 T^{2} \))(\( 1 - 21836 T + 147008443 T^{2} \))(\( 1 + 11407 T + 147008443 T^{2} \))(\( 1 - 13316 T + 147008443 T^{2} \))(\( 1 + 608 T + 164053110 T^{2} + 89381133344 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 5921 T + 278228220 T^{2} + 870436991003 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 5921 T + 278228220 T^{2} + 870436991003 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 608 T + 164053110 T^{2} + 89381133344 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 15853 T + 338678796 T^{2} - 2330524846879 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 23032 T + 329072262 T^{2} + 3385898459176 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 1136 T + 157222710 T^{2} + 167001591248 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 1136 T + 157222710 T^{2} + 167001591248 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 23032 T + 329072262 T^{2} + 3385898459176 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 15853 T + 338678796 T^{2} - 2330524846879 T^{3} + 21611482313284249 T^{4} \))
$47$ (\( 1 - 6520 T + 229345007 T^{2} \))(\( 1 + 5352 T + 229345007 T^{2} \))(\( 1 + 60 T + 229345007 T^{2} \))(\( 1 - 18462 T + 229345007 T^{2} \))(\( 1 + 18462 T + 229345007 T^{2} \))(\( 1 - 18372 T + 229345007 T^{2} \))(\( 1 + 6520 T + 229345007 T^{2} \))(\( 1 + 22200 T + 229345007 T^{2} \))(\( 1 + 20604 T + 229345007 T^{2} \))(\( 1 + 2310 T + 229345007 T^{2} \))(\( 1 - 23940 T + 229345007 T^{2} \))(\( 1 - 2310 T + 229345007 T^{2} \))(\( 1 - 19680 T + 229345007 T^{2} \))(\( 1 - 30456 T + 629420198 T^{2} - 6984931533192 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 44808 T + 952611850 T^{2} + 10276491073656 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 44808 T + 952611850 T^{2} - 10276491073656 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 30456 T + 629420198 T^{2} + 6984931533192 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 33912 T + 687783466 T^{2} - 7777547877384 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 864 T + 46643358 T^{2} + 198154086048 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 36936 T + 775004390 T^{2} - 8471087178552 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 36936 T + 775004390 T^{2} + 8471087178552 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 864 T + 46643358 T^{2} - 198154086048 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 33912 T + 687783466 T^{2} + 7777547877384 T^{3} + 52599132235830049 T^{4} \))
$53$ (\( 1 + 10702 T + 418195493 T^{2} \))(\( 1 + 33354 T + 418195493 T^{2} \))(\( 1 - 22506 T + 418195493 T^{2} \))(\( 1 + 19956 T + 418195493 T^{2} \))(\( 1 + 19956 T + 418195493 T^{2} \))(\( 1 + 4374 T + 418195493 T^{2} \))(\( 1 + 10702 T + 418195493 T^{2} \))(\( 1 - 26790 T + 418195493 T^{2} \))(\( 1 - 32490 T + 418195493 T^{2} \))(\( 1 + 28296 T + 418195493 T^{2} \))(\( 1 - 15594 T + 418195493 T^{2} \))(\( 1 + 28296 T + 418195493 T^{2} \))(\( 1 + 31266 T + 418195493 T^{2} \))(\( 1 - 3964 T + 594431822 T^{2} - 1657726934252 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 9417 T + 846033802 T^{2} - 3938146957581 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 9417 T + 846033802 T^{2} - 3938146957581 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 3964 T + 594431822 T^{2} - 1657726934252 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 49239 T + 1320998110 T^{2} - 20591527879827 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 32920 T + 983844566 T^{2} + 13766995629560 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 16708 T + 904428110 T^{2} + 6987210297044 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 16708 T + 904428110 T^{2} + 6987210297044 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 32920 T + 983844566 T^{2} + 13766995629560 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 49239 T + 1320998110 T^{2} - 20591527879827 T^{3} + 174887470365513049 T^{4} \))
$59$ (\( 1 + 42524 T + 714924299 T^{2} \))(\( 1 - 15436 T + 714924299 T^{2} \))(\( 1 - 28176 T + 714924299 T^{2} \))(\( 1 + 31828 T + 714924299 T^{2} \))(\( 1 - 31828 T + 714924299 T^{2} \))(\( 1 + 30248 T + 714924299 T^{2} \))(\( 1 - 42524 T + 714924299 T^{2} \))(\( 1 + 28092 T + 714924299 T^{2} \))(\( 1 + 34224 T + 714924299 T^{2} \))(\( 1 + 20544 T + 714924299 T^{2} \))(\( 1 + 5608 T + 714924299 T^{2} \))(\( 1 - 20544 T + 714924299 T^{2} \))(\( 1 + 26340 T + 714924299 T^{2} \))(\( 1 + 40752 T + 1841031182 T^{2} + 29134595032848 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 5077 T + 557047054 T^{2} - 3629670666023 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 5077 T + 557047054 T^{2} + 3629670666023 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 40752 T + 1841031182 T^{2} - 29134595032848 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 56735 T + 2230528834 T^{2} + 40561230103765 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 26712 T + 697343334 T^{2} - 19097057874888 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 74592 T + 2772859406 T^{2} - 53327633311008 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 74592 T + 2772859406 T^{2} + 53327633311008 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 26712 T + 697343334 T^{2} + 19097057874888 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 56735 T + 2230528834 T^{2} - 40561230103765 T^{3} + 511116753300641401 T^{4} \))
$61$ (\( 1 - 44840 T + 844596301 T^{2} \))(\( 1 - 36762 T + 844596301 T^{2} \))(\( 1 - 35194 T + 844596301 T^{2} \))(\( 1 + 57654 T + 844596301 T^{2} \))(\( 1 - 57654 T + 844596301 T^{2} \))(\( 1 + 19542 T + 844596301 T^{2} \))(\( 1 + 44840 T + 844596301 T^{2} \))(\( 1 - 38866 T + 844596301 T^{2} \))(\( 1 + 35654 T + 844596301 T^{2} \))(\( 1 - 4630 T + 844596301 T^{2} \))(\( 1 + 150 T + 844596301 T^{2} \))(\( 1 + 4630 T + 844596301 T^{2} \))(\( 1 - 31090 T + 844596301 T^{2} \))(\( 1 - 1368 T + 1545466296 T^{2} - 1155407739768 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 42368 T + 2085594038 T^{2} + 35783856080768 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 42368 T + 2085594038 T^{2} - 35783856080768 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 1368 T + 1545466296 T^{2} + 1155407739768 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 67508 T + 2826067262 T^{2} - 57017007087908 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 20412 T + 1230091258 T^{2} + 17239899696012 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 18648 T + 1674996936 T^{2} + 15750031821048 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 18648 T + 1674996936 T^{2} - 15750031821048 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 20412 T + 1230091258 T^{2} - 17239899696012 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 67508 T + 2826067262 T^{2} + 57017007087908 T^{3} + 713342911662882601 T^{4} \))
$67$ (\( 1 + 1448 T + 1350125107 T^{2} \))(\( 1 - 40972 T + 1350125107 T^{2} \))(\( 1 + 28216 T + 1350125107 T^{2} \))(\( 1 + 60563 T + 1350125107 T^{2} \))(\( 1 + 60563 T + 1350125107 T^{2} \))(\( 1 - 54328 T + 1350125107 T^{2} \))(\( 1 + 1448 T + 1350125107 T^{2} \))(\( 1 - 23948 T + 1350125107 T^{2} \))(\( 1 - 12680 T + 1350125107 T^{2} \))(\( 1 + 18745 T + 1350125107 T^{2} \))(\( 1 + 43784 T + 1350125107 T^{2} \))(\( 1 + 18745 T + 1350125107 T^{2} \))(\( 1 + 16804 T + 1350125107 T^{2} \))(\( 1 + 16224 T + 813179750 T^{2} + 21904429735968 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 30501 T + 2311177888 T^{2} - 41180165888607 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 30501 T + 2311177888 T^{2} - 41180165888607 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 16224 T + 813179750 T^{2} + 21904429735968 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 75723 T + 3861149404 T^{2} - 102235523477361 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 36172 T + 2220935430 T^{2} + 48836725370404 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 67344 T + 3672053798 T^{2} - 90922825205808 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 67344 T + 3672053798 T^{2} - 90922825205808 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 36172 T + 2220935430 T^{2} + 48836725370404 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 75723 T + 3861149404 T^{2} - 102235523477361 T^{3} + 1822837804551761449 T^{4} \))
$71$ (\( 1 + 4402 T + 1804229351 T^{2} \))(\( 1 + 9092 T + 1804229351 T^{2} \))(\( 1 + 6642 T + 1804229351 T^{2} \))(\( 1 + 44834 T + 1804229351 T^{2} \))(\( 1 + 44834 T + 1804229351 T^{2} \))(\( 1 + 10730 T + 1804229351 T^{2} \))(\( 1 + 4402 T + 1804229351 T^{2} \))(\( 1 + 20628 T + 1804229351 T^{2} \))(\( 1 + 42642 T + 1804229351 T^{2} \))(\( 1 + 38226 T + 1804229351 T^{2} \))(\( 1 + 39178 T + 1804229351 T^{2} \))(\( 1 + 38226 T + 1804229351 T^{2} \))(\( 1 - 6120 T + 1804229351 T^{2} \))(\( 1 + 3204 T - 212201462 T^{2} + 5780750840604 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 91744 T + 5413284586 T^{2} - 165527217578144 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 91744 T + 5413284586 T^{2} - 165527217578144 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 3204 T - 212201462 T^{2} + 5780750840604 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 8992 T - 681216182 T^{2} + 16223630324192 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 73706 T + 3356433686 T^{2} - 132982528544806 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 76548 T + 3345343306 T^{2} - 138110148360348 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 76548 T + 3345343306 T^{2} - 138110148360348 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 73706 T + 3356433686 T^{2} - 132982528544806 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 8992 T - 681216182 T^{2} + 16223630324192 T^{3} + 3255243551009881201 T^{4} \))
$73$ (\( 1 + 20500 T + 2073071593 T^{2} \))(\( 1 - 73454 T + 2073071593 T^{2} \))(\( 1 - 52090 T + 2073071593 T^{2} \))(\( 1 - 20821 T + 2073071593 T^{2} \))(\( 1 + 20821 T + 2073071593 T^{2} \))(\( 1 + 35374 T + 2073071593 T^{2} \))(\( 1 - 20500 T + 2073071593 T^{2} \))(\( 1 + 290 T + 2073071593 T^{2} \))(\( 1 + 33734 T + 2073071593 T^{2} \))(\( 1 + 70589 T + 2073071593 T^{2} \))(\( 1 - 23570 T + 2073071593 T^{2} \))(\( 1 - 70589 T + 2073071593 T^{2} \))(\( 1 - 25558 T + 2073071593 T^{2} \))(\( 1 + 23976 T + 68704368 T^{2} + 49703964513768 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 85665 T + 4403117836 T^{2} - 177589678014345 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 85665 T + 4403117836 T^{2} + 177589678014345 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 23976 T + 68704368 T^{2} - 49703964513768 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 3201 T + 2311013380 T^{2} + 6635902169193 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 74772 T + 3993671602 T^{2} - 155007709151796 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 47304 T + 4525629840 T^{2} - 98064578635272 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 47304 T + 4525629840 T^{2} + 98064578635272 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 74772 T + 3993671602 T^{2} + 155007709151796 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 3201 T + 2311013380 T^{2} - 6635902169193 T^{3} + 4297625829703557649 T^{4} \))
$79$ (\( 1 - 65236 T + 3077056399 T^{2} \))(\( 1 - 89400 T + 3077056399 T^{2} \))(\( 1 - 43340 T + 3077056399 T^{2} \))(\( 1 + 30531 T + 3077056399 T^{2} \))(\( 1 + 30531 T + 3077056399 T^{2} \))(\( 1 + 49956 T + 3077056399 T^{2} \))(\( 1 - 65236 T + 3077056399 T^{2} \))(\( 1 + 99544 T + 3077056399 T^{2} \))(\( 1 + 85108 T + 3077056399 T^{2} \))(\( 1 + 62293 T + 3077056399 T^{2} \))(\( 1 + 17892 T + 3077056399 T^{2} \))(\( 1 + 62293 T + 3077056399 T^{2} \))(\( 1 - 74408 T + 3077056399 T^{2} \))(\( 1 + 82160 T + 7785668670 T^{2} + 252810953741840 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 94646 T + 5465354807 T^{2} - 291231079939754 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 94646 T + 5465354807 T^{2} - 291231079939754 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 82160 T + 7785668670 T^{2} + 252810953741840 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 26612 T + 3997648985 T^{2} - 81886624890188 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 23116 T + 6249589662 T^{2} + 71129235719284 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 140656 T + 10301739582 T^{2} - 432806444857744 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 140656 T + 10301739582 T^{2} - 432806444857744 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 23116 T + 6249589662 T^{2} + 71129235719284 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 26612 T + 3997648985 T^{2} - 81886624890188 T^{3} + 9468276082626847201 T^{4} \))
$83$ (\( 1 - 102804 T + 3939040643 T^{2} \))(\( 1 - 6428 T + 3939040643 T^{2} \))(\( 1 + 25716 T + 3939040643 T^{2} \))(\( 1 - 110602 T + 3939040643 T^{2} \))(\( 1 + 110602 T + 3939040643 T^{2} \))(\( 1 - 26948 T + 3939040643 T^{2} \))(\( 1 + 102804 T + 3939040643 T^{2} \))(\( 1 + 19308 T + 3939040643 T^{2} \))(\( 1 - 106764 T + 3939040643 T^{2} \))(\( 1 + 79818 T + 3939040643 T^{2} \))(\( 1 + 38972 T + 3939040643 T^{2} \))(\( 1 - 79818 T + 3939040643 T^{2} \))(\( 1 - 6468 T + 3939040643 T^{2} \))(\( 1 + 173736 T + 14732805782 T^{2} + 684353165152248 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 33841 T + 8158439620 T^{2} + 133301074399763 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 33841 T + 8158439620 T^{2} - 133301074399763 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 173736 T + 14732805782 T^{2} - 684353165152248 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 949 T + 367057696 T^{2} + 3738149570207 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 147816 T + 13316083030 T^{2} + 582253231685688 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 94104 T + 8432170262 T^{2} - 370679480668872 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 94104 T + 8432170262 T^{2} + 370679480668872 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 147816 T + 13316083030 T^{2} - 582253231685688 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 949 T + 367057696 T^{2} - 3738149570207 T^{3} + 15516041187205853449 T^{4} \))
$89$ (\( 1 - 128006 T + 5584059449 T^{2} \))(\( 1 - 122658 T + 5584059449 T^{2} \))(\( 1 + 98724 T + 5584059449 T^{2} \))(\( 1 + 58992 T + 5584059449 T^{2} \))(\( 1 - 58992 T + 5584059449 T^{2} \))(\( 1 + 100776 T + 5584059449 T^{2} \))(\( 1 + 128006 T + 5584059449 T^{2} \))(\( 1 + 36390 T + 5584059449 T^{2} \))(\( 1 + 34884 T + 5584059449 T^{2} \))(\( 1 - 18120 T + 5584059449 T^{2} \))(\( 1 + 6024 T + 5584059449 T^{2} \))(\( 1 + 18120 T + 5584059449 T^{2} \))(\( 1 - 32742 T + 5584059449 T^{2} \))(\( 1 + 200556 T + 21158382260 T^{2} + 1119916626853644 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 27558 T + 11170684834 T^{2} + 153885510295542 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 27558 T + 11170684834 T^{2} - 153885510295542 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 200556 T + 21158382260 T^{2} - 1119916626853644 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 176562 T + 18855802834 T^{2} - 985932704434338 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 164646 T + 17878567722 T^{2} + 919393052040054 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 17604 T + 7609766564 T^{2} + 98301782540196 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 17604 T + 7609766564 T^{2} - 98301782540196 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 164646 T + 17878567722 T^{2} - 919393052040054 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 176562 T + 18855802834 T^{2} + 985932704434338 T^{3} + 31181719929966183601 T^{4} \))
$97$ (\( 1 - 113324 T + 8587340257 T^{2} \))(\( 1 + 21370 T + 8587340257 T^{2} \))(\( 1 - 148954 T + 8587340257 T^{2} \))(\( 1 + 119846 T + 8587340257 T^{2} \))(\( 1 - 119846 T + 8587340257 T^{2} \))(\( 1 + 77134 T + 8587340257 T^{2} \))(\( 1 + 113324 T + 8587340257 T^{2} \))(\( 1 - 79078 T + 8587340257 T^{2} \))(\( 1 + 18662 T + 8587340257 T^{2} \))(\( 1 + 124754 T + 8587340257 T^{2} \))(\( 1 + 108430 T + 8587340257 T^{2} \))(\( 1 - 124754 T + 8587340257 T^{2} \))(\( 1 + 166082 T + 8587340257 T^{2} \))(\( 1 + 251928 T + 32348722272 T^{2} + 2163391456265496 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 46671 T + 13111898848 T^{2} - 400779757134447 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 46671 T + 13111898848 T^{2} + 400779757134447 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 251928 T + 32348722272 T^{2} - 2163391456265496 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 129423 T + 11942811256 T^{2} + 1111399338081711 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 162036 T + 20528488258 T^{2} + 1391458265883252 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 85176 T + 11802571296 T^{2} - 731435293730232 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 85176 T + 11802571296 T^{2} + 731435293730232 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 162036 T + 20528488258 T^{2} - 1391458265883252 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 129423 T + 11942811256 T^{2} - 1111399338081711 T^{3} + 73742412689492826049 T^{4} \))
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