# Properties

 Degree 74 Conductor $5^{37} \cdot 11^{37} \cdot 73^{37}$ Sign $1$ Motivic weight 1 Primitive no Self-dual yes Analytic rank 0

# Origins of factors

## Dirichlet series

 L(s)  = 1 + 5·2-s + 3·3-s − 3·4-s + 37·5-s + 15·6-s + 6·7-s − 56·8-s − 26·9-s + 185·10-s + 37·11-s − 9·12-s + 11·13-s + 30·14-s + 111·15-s − 55·16-s + 38·17-s − 130·18-s + 34·19-s − 111·20-s + 18·21-s + 185·22-s + 4·23-s − 168·24-s + 703·25-s + 55·26-s − 89·27-s − 18·28-s + ⋯
 L(s)  = 1 + 3.53·2-s + 1.73·3-s − 3/2·4-s + 16.5·5-s + 6.12·6-s + 2.26·7-s − 19.7·8-s − 8.66·9-s + 58.5·10-s + 11.1·11-s − 2.59·12-s + 3.05·13-s + 8.01·14-s + 28.6·15-s − 13.7·16-s + 9.21·17-s − 30.6·18-s + 7.80·19-s − 24.8·20-s + 3.92·21-s + 39.4·22-s + 0.834·23-s − 34.2·24-s + 140.·25-s + 10.7·26-s − 17.1·27-s − 3.40·28-s + ⋯

## Functional equation

\begin{aligned} \Lambda(s)=\mathstrut &\left(5^{37} \cdot 11^{37} \cdot 73^{37}\right)^{s/2} \, \Gamma_{\C}(s)^{37} \, L(s)\cr =\mathstrut & \,\Lambda(2-s) \end{aligned}
\begin{aligned} \Lambda(s)=\mathstrut &\left(5^{37} \cdot 11^{37} \cdot 73^{37}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{37} \, L(s)\cr =\mathstrut & \,\Lambda(1-s) \end{aligned}

## Invariants

 $$d$$ = $$74$$ $$N$$ = $$5^{37} \cdot 11^{37} \cdot 73^{37}$$ $$\varepsilon$$ = $1$ motivic weight = $$1$$ character : induced by $\chi_{4015} (1, \cdot )$ primitive : no self-dual : yes analytic rank = 0 Selberg data = $(74,\ 5^{37} \cdot 11^{37} \cdot 73^{37} ,\ ( \ : [1/2]^{37} ),\ 1 )$ $L(1)$ $\approx$ $4.593545883e9$ $L(\frac12)$ $\approx$ $4.593545883e9$ $L(\frac{3}{2})$ not available $L(1)$ not available

## Euler product

$L(s) = \prod_{p \text{ prime}} F_p(p^{-s})^{-1}$ where, for $p \notin \{5,\;11,\;73\}$, $$F_p$$ is a polynomial of degree 74. If $p \in \{5,\;11,\;73\}$, then $F_p$ is a polynomial of degree at most 73.
$p$$F_p$
bad5 $$( 1 - T )^{37}$$
11 $$( 1 - T )^{37}$$
73 $$( 1 - T )^{37}$$
good2 $$1 - 5 T + 7 p^{2} T^{2} - 99 T^{3} + 177 p T^{4} - 255 p^{2} T^{5} + 2917 T^{6} - 3661 p T^{7} + 71 p^{8} T^{8} - 41253 T^{9} + 92595 T^{10} - 12153 p^{4} T^{11} + 404299 T^{12} - 398975 p T^{13} + 1561725 T^{14} - 2929971 T^{15} + 5459319 T^{16} - 4909225 p T^{17} + 17560145 T^{18} - 30465341 T^{19} + 6576943 p^{3} T^{20} - 22117751 p^{2} T^{21} + 37051393 p^{2} T^{22} - 60593763 p^{2} T^{23} + 197573381 p T^{24} - 630209337 T^{25} + 501245907 p T^{26} - 390630467 p^{2} T^{27} + 607536233 p^{2} T^{28} - 3707887665 T^{29} + 1411835319 p^{2} T^{30} - 8446167681 T^{31} + 12613262623 T^{32} - 9254609097 p T^{33} + 13563211339 p T^{34} - 9770551995 p^{2} T^{35} + 7030285297 p^{3} T^{36} - 4973941477 p^{4} T^{37} + 7030285297 p^{4} T^{38} - 9770551995 p^{4} T^{39} + 13563211339 p^{4} T^{40} - 9254609097 p^{5} T^{41} + 12613262623 p^{5} T^{42} - 8446167681 p^{6} T^{43} + 1411835319 p^{9} T^{44} - 3707887665 p^{8} T^{45} + 607536233 p^{11} T^{46} - 390630467 p^{12} T^{47} + 501245907 p^{12} T^{48} - 630209337 p^{12} T^{49} + 197573381 p^{14} T^{50} - 60593763 p^{16} T^{51} + 37051393 p^{17} T^{52} - 22117751 p^{18} T^{53} + 6576943 p^{20} T^{54} - 30465341 p^{18} T^{55} + 17560145 p^{19} T^{56} - 4909225 p^{21} T^{57} + 5459319 p^{21} T^{58} - 2929971 p^{22} T^{59} + 1561725 p^{23} T^{60} - 398975 p^{25} T^{61} + 404299 p^{25} T^{62} - 12153 p^{30} T^{63} + 92595 p^{27} T^{64} - 41253 p^{28} T^{65} + 71 p^{37} T^{66} - 3661 p^{31} T^{67} + 2917 p^{31} T^{68} - 255 p^{34} T^{69} + 177 p^{34} T^{70} - 99 p^{34} T^{71} + 7 p^{37} T^{72} - 5 p^{36} T^{73} + p^{37} T^{74}$$
3 $$1 - p T + 35 T^{2} - 94 T^{3} + 622 T^{4} - 1526 T^{5} + 31 p^{5} T^{6} - 5705 p T^{7} + 70166 T^{8} - 149174 T^{9} + 179218 p T^{10} - 359624 p T^{11} + 3540952 T^{12} - 27806 p^{5} T^{13} + 20675600 T^{14} - 37768418 T^{15} + 36502795 p T^{16} - 64202323 p T^{17} + 6605725 p^{4} T^{18} - 910438532 T^{19} + 2441156875 T^{20} - 4033293683 T^{21} + 10488175822 T^{22} - 16871598314 T^{23} + 42684850004 T^{24} - 66983676857 T^{25} + 55083258226 p T^{26} - 84446845615 p T^{27} + 203493039367 p T^{28} - 305121323050 p T^{29} + 719129295265 p T^{30} - 3166637500475 T^{31} + 270624201703 p^{3} T^{32} - 1167339924367 p^{2} T^{33} + 7916685269429 p T^{34} - 11155458371197 p T^{35} + 24716223597658 p T^{36} - 102419532848570 T^{37} + 24716223597658 p^{2} T^{38} - 11155458371197 p^{3} T^{39} + 7916685269429 p^{4} T^{40} - 1167339924367 p^{6} T^{41} + 270624201703 p^{8} T^{42} - 3166637500475 p^{6} T^{43} + 719129295265 p^{8} T^{44} - 305121323050 p^{9} T^{45} + 203493039367 p^{10} T^{46} - 84446845615 p^{11} T^{47} + 55083258226 p^{12} T^{48} - 66983676857 p^{12} T^{49} + 42684850004 p^{13} T^{50} - 16871598314 p^{14} T^{51} + 10488175822 p^{15} T^{52} - 4033293683 p^{16} T^{53} + 2441156875 p^{17} T^{54} - 910438532 p^{18} T^{55} + 6605725 p^{23} T^{56} - 64202323 p^{21} T^{57} + 36502795 p^{22} T^{58} - 37768418 p^{22} T^{59} + 20675600 p^{23} T^{60} - 27806 p^{29} T^{61} + 3540952 p^{25} T^{62} - 359624 p^{27} T^{63} + 179218 p^{28} T^{64} - 149174 p^{28} T^{65} + 70166 p^{29} T^{66} - 5705 p^{31} T^{67} + 31 p^{36} T^{68} - 1526 p^{32} T^{69} + 622 p^{33} T^{70} - 94 p^{34} T^{71} + 35 p^{35} T^{72} - p^{37} T^{73} + p^{37} T^{74}$$
7 $$1 - 6 T + 118 T^{2} - 592 T^{3} + 6743 T^{4} - 29443 T^{5} + 252622 T^{6} - 982222 T^{7} + 143384 p^{2} T^{8} - 3522192 p T^{9} + 155138770 T^{10} - 495183247 T^{11} + 2836098332 T^{12} - 8264375716 T^{13} + 44174271977 T^{14} - 117596134461 T^{15} + 598944276354 T^{16} - 1454173789004 T^{17} + 7194943341108 T^{18} - 15880384820894 T^{19} + 77816860429645 T^{20} - 155604567919099 T^{21} + 110008064472748 p T^{22} - 1393322578624803 T^{23} + 7091001194309475 T^{24} - 11661799858985051 T^{25} + 61803902600767710 T^{26} - 93634851530842488 T^{27} + 73917292358887828 p T^{28} - 738108864530385378 T^{29} + 4199169077871462497 T^{30} - 5774580083456353654 T^{31} + 33090655917894105814 T^{32} - 44580221222706442023 T^{33} +$$$$25\!\cdots\!12$$$$T^{34} -$$$$33\!\cdots\!39$$$$T^{35} +$$$$18\!\cdots\!46$$$$T^{36} -$$$$23\!\cdots\!28$$$$T^{37} +$$$$18\!\cdots\!46$$$$p T^{38} -$$$$33\!\cdots\!39$$$$p^{2} T^{39} +$$$$25\!\cdots\!12$$$$p^{3} T^{40} - 44580221222706442023 p^{4} T^{41} + 33090655917894105814 p^{5} T^{42} - 5774580083456353654 p^{6} T^{43} + 4199169077871462497 p^{7} T^{44} - 738108864530385378 p^{8} T^{45} + 73917292358887828 p^{10} T^{46} - 93634851530842488 p^{10} T^{47} + 61803902600767710 p^{11} T^{48} - 11661799858985051 p^{12} T^{49} + 7091001194309475 p^{13} T^{50} - 1393322578624803 p^{14} T^{51} + 110008064472748 p^{16} T^{52} - 155604567919099 p^{16} T^{53} + 77816860429645 p^{17} T^{54} - 15880384820894 p^{18} T^{55} + 7194943341108 p^{19} T^{56} - 1454173789004 p^{20} T^{57} + 598944276354 p^{21} T^{58} - 117596134461 p^{22} T^{59} + 44174271977 p^{23} T^{60} - 8264375716 p^{24} T^{61} + 2836098332 p^{25} T^{62} - 495183247 p^{26} T^{63} + 155138770 p^{27} T^{64} - 3522192 p^{29} T^{65} + 143384 p^{31} T^{66} - 982222 p^{30} T^{67} + 252622 p^{31} T^{68} - 29443 p^{32} T^{69} + 6743 p^{33} T^{70} - 592 p^{34} T^{71} + 118 p^{35} T^{72} - 6 p^{36} T^{73} + p^{37} T^{74}$$
13 $$1 - 11 T + 281 T^{2} - 2559 T^{3} + 37464 T^{4} - 294672 T^{5} + 3216659 T^{6} - 22489068 T^{7} + 202539174 T^{8} - 1285112758 T^{9} + 10065275209 T^{10} - 58870216594 T^{11} + 413952060333 T^{12} - 2258582820563 T^{13} + 14560083903371 T^{14} - 74792533215669 T^{15} + 448524873226242 T^{16} - 2184654362846685 T^{17} + 12316175985374539 T^{18} - 57198442373434142 T^{19} + 305512952372224334 T^{20} - 104519165506325852 p T^{21} + 532062817560352440 p T^{22} - 29559961689731414306 T^{23} +$$$$14\!\cdots\!97$$$$T^{24} -$$$$59\!\cdots\!85$$$$T^{25} +$$$$27\!\cdots\!07$$$$T^{26} -$$$$11\!\cdots\!91$$$$T^{27} +$$$$49\!\cdots\!26$$$$T^{28} -$$$$19\!\cdots\!39$$$$T^{29} +$$$$83\!\cdots\!80$$$$T^{30} -$$$$31\!\cdots\!24$$$$T^{31} +$$$$13\!\cdots\!08$$$$T^{32} -$$$$47\!\cdots\!33$$$$T^{33} +$$$$19\!\cdots\!00$$$$T^{34} -$$$$67\!\cdots\!99$$$$T^{35} +$$$$26\!\cdots\!11$$$$T^{36} -$$$$90\!\cdots\!64$$$$T^{37} +$$$$26\!\cdots\!11$$$$p T^{38} -$$$$67\!\cdots\!99$$$$p^{2} T^{39} +$$$$19\!\cdots\!00$$$$p^{3} T^{40} -$$$$47\!\cdots\!33$$$$p^{4} T^{41} +$$$$13\!\cdots\!08$$$$p^{5} T^{42} -$$$$31\!\cdots\!24$$$$p^{6} T^{43} +$$$$83\!\cdots\!80$$$$p^{7} T^{44} -$$$$19\!\cdots\!39$$$$p^{8} T^{45} +$$$$49\!\cdots\!26$$$$p^{9} T^{46} -$$$$11\!\cdots\!91$$$$p^{10} T^{47} +$$$$27\!\cdots\!07$$$$p^{11} T^{48} -$$$$59\!\cdots\!85$$$$p^{12} T^{49} +$$$$14\!\cdots\!97$$$$p^{13} T^{50} - 29559961689731414306 p^{14} T^{51} + 532062817560352440 p^{16} T^{52} - 104519165506325852 p^{17} T^{53} + 305512952372224334 p^{17} T^{54} - 57198442373434142 p^{18} T^{55} + 12316175985374539 p^{19} T^{56} - 2184654362846685 p^{20} T^{57} + 448524873226242 p^{21} T^{58} - 74792533215669 p^{22} T^{59} + 14560083903371 p^{23} T^{60} - 2258582820563 p^{24} T^{61} + 413952060333 p^{25} T^{62} - 58870216594 p^{26} T^{63} + 10065275209 p^{27} T^{64} - 1285112758 p^{28} T^{65} + 202539174 p^{29} T^{66} - 22489068 p^{30} T^{67} + 3216659 p^{31} T^{68} - 294672 p^{32} T^{69} + 37464 p^{33} T^{70} - 2559 p^{34} T^{71} + 281 p^{35} T^{72} - 11 p^{36} T^{73} + p^{37} T^{74}$$
17 $$1 - 38 T + 1001 T^{2} - 19679 T^{3} + 324756 T^{4} - 4627356 T^{5} + 58931335 T^{6} - 680959714 T^{7} + 7251722126 T^{8} - 71824843797 T^{9} + 667461458400 T^{10} - 5854894882241 T^{11} + 48749930089441 T^{12} - 386926278089633 T^{13} + 172862258975383 p T^{14} - 1260171866569021 p T^{15} + 150323626216866332 T^{16} - 1017667288673934842 T^{17} + 6660774627152806202 T^{18} - 42224360192857224552 T^{19} +$$$$25\!\cdots\!31$$$$T^{20} -$$$$15\!\cdots\!08$$$$T^{21} +$$$$90\!\cdots\!04$$$$T^{22} -$$$$51\!\cdots\!52$$$$T^{23} +$$$$28\!\cdots\!95$$$$T^{24} -$$$$15\!\cdots\!84$$$$T^{25} +$$$$79\!\cdots\!61$$$$T^{26} -$$$$40\!\cdots\!78$$$$T^{27} +$$$$20\!\cdots\!93$$$$T^{28} -$$$$10\!\cdots\!67$$$$T^{29} +$$$$48\!\cdots\!82$$$$T^{30} -$$$$22\!\cdots\!98$$$$T^{31} +$$$$10\!\cdots\!58$$$$T^{32} -$$$$47\!\cdots\!65$$$$T^{33} +$$$$20\!\cdots\!10$$$$T^{34} -$$$$90\!\cdots\!17$$$$T^{35} +$$$$38\!\cdots\!49$$$$T^{36} -$$$$16\!\cdots\!60$$$$T^{37} +$$$$38\!\cdots\!49$$$$p T^{38} -$$$$90\!\cdots\!17$$$$p^{2} T^{39} +$$$$20\!\cdots\!10$$$$p^{3} T^{40} -$$$$47\!\cdots\!65$$$$p^{4} T^{41} +$$$$10\!\cdots\!58$$$$p^{5} T^{42} -$$$$22\!\cdots\!98$$$$p^{6} T^{43} +$$$$48\!\cdots\!82$$$$p^{7} T^{44} -$$$$10\!\cdots\!67$$$$p^{8} T^{45} +$$$$20\!\cdots\!93$$$$p^{9} T^{46} -$$$$40\!\cdots\!78$$$$p^{10} T^{47} +$$$$79\!\cdots\!61$$$$p^{11} T^{48} -$$$$15\!\cdots\!84$$$$p^{12} T^{49} +$$$$28\!\cdots\!95$$$$p^{13} T^{50} -$$$$51\!\cdots\!52$$$$p^{14} T^{51} +$$$$90\!\cdots\!04$$$$p^{15} T^{52} -$$$$15\!\cdots\!08$$$$p^{16} T^{53} +$$$$25\!\cdots\!31$$$$p^{17} T^{54} - 42224360192857224552 p^{18} T^{55} + 6660774627152806202 p^{19} T^{56} - 1017667288673934842 p^{20} T^{57} + 150323626216866332 p^{21} T^{58} - 1260171866569021 p^{23} T^{59} + 172862258975383 p^{24} T^{60} - 386926278089633 p^{24} T^{61} + 48749930089441 p^{25} T^{62} - 5854894882241 p^{26} T^{63} + 667461458400 p^{27} T^{64} - 71824843797 p^{28} T^{65} + 7251722126 p^{29} T^{66} - 680959714 p^{30} T^{67} + 58931335 p^{31} T^{68} - 4627356 p^{32} T^{69} + 324756 p^{33} T^{70} - 19679 p^{34} T^{71} + 1001 p^{35} T^{72} - 38 p^{36} T^{73} + p^{37} T^{74}$$
19 $$1 - 34 T + 910 T^{2} - 17690 T^{3} + 298911 T^{4} - 4337906 T^{5} + 57162994 T^{6} - 683702364 T^{7} + 7605041136 T^{8} - 4148691871 p T^{9} + 771076711987 T^{10} - 7134624659848 T^{11} + 62914834631689 T^{12} - 529808560700892 T^{13} + 4281161885202045 T^{14} - 33252092853286779 T^{15} + 249066365749363400 T^{16} - 1801593850785372066 T^{17} + 12614163879905397284 T^{18} - 85588247504823921349 T^{19} +$$$$56\!\cdots\!51$$$$T^{20} -$$$$36\!\cdots\!67$$$$T^{21} +$$$$22\!\cdots\!63$$$$T^{22} -$$$$13\!\cdots\!42$$$$T^{23} +$$$$80\!\cdots\!86$$$$T^{24} -$$$$46\!\cdots\!54$$$$T^{25} +$$$$26\!\cdots\!94$$$$T^{26} -$$$$14\!\cdots\!14$$$$T^{27} +$$$$76\!\cdots\!65$$$$T^{28} -$$$$40\!\cdots\!28$$$$T^{29} +$$$$20\!\cdots\!29$$$$T^{30} -$$$$10\!\cdots\!79$$$$T^{31} +$$$$50\!\cdots\!12$$$$T^{32} -$$$$24\!\cdots\!77$$$$T^{33} +$$$$11\!\cdots\!96$$$$T^{34} -$$$$27\!\cdots\!33$$$$p T^{35} +$$$$23\!\cdots\!27$$$$T^{36} -$$$$10\!\cdots\!10$$$$T^{37} +$$$$23\!\cdots\!27$$$$p T^{38} -$$$$27\!\cdots\!33$$$$p^{3} T^{39} +$$$$11\!\cdots\!96$$$$p^{3} T^{40} -$$$$24\!\cdots\!77$$$$p^{4} T^{41} +$$$$50\!\cdots\!12$$$$p^{5} T^{42} -$$$$10\!\cdots\!79$$$$p^{6} T^{43} +$$$$20\!\cdots\!29$$$$p^{7} T^{44} -$$$$40\!\cdots\!28$$$$p^{8} T^{45} +$$$$76\!\cdots\!65$$$$p^{9} T^{46} -$$$$14\!\cdots\!14$$$$p^{10} T^{47} +$$$$26\!\cdots\!94$$$$p^{11} T^{48} -$$$$46\!\cdots\!54$$$$p^{12} T^{49} +$$$$80\!\cdots\!86$$$$p^{13} T^{50} -$$$$13\!\cdots\!42$$$$p^{14} T^{51} +$$$$22\!\cdots\!63$$$$p^{15} T^{52} -$$$$36\!\cdots\!67$$$$p^{16} T^{53} +$$$$56\!\cdots\!51$$$$p^{17} T^{54} - 85588247504823921349 p^{18} T^{55} + 12614163879905397284 p^{19} T^{56} - 1801593850785372066 p^{20} T^{57} + 249066365749363400 p^{21} T^{58} - 33252092853286779 p^{22} T^{59} + 4281161885202045 p^{23} T^{60} - 529808560700892 p^{24} T^{61} + 62914834631689 p^{25} T^{62} - 7134624659848 p^{26} T^{63} + 771076711987 p^{27} T^{64} - 4148691871 p^{29} T^{65} + 7605041136 p^{29} T^{66} - 683702364 p^{30} T^{67} + 57162994 p^{31} T^{68} - 4337906 p^{32} T^{69} + 298911 p^{33} T^{70} - 17690 p^{34} T^{71} + 910 p^{35} T^{72} - 34 p^{36} T^{73} + p^{37} T^{74}$$
23 $$1 - 4 T + 417 T^{2} - 1517 T^{3} + 87605 T^{4} - 291360 T^{5} + 12363286 T^{6} - 37683818 T^{7} + 1317799514 T^{8} - 3681575519 T^{9} + 113060352599 T^{10} - 288903450256 T^{11} + 8124465056492 T^{12} - 18908495217474 T^{13} + 502437530052577 T^{14} - 1058197153787684 T^{15} + 27271171091085067 T^{16} - 51522699077916532 T^{17} + 1318661285879464800 T^{18} - 2209754956773436801 T^{19} + 57474465118364939040 T^{20} - 84250781092006302513 T^{21} +$$$$22\!\cdots\!62$$$$T^{22} -$$$$28\!\cdots\!45$$$$T^{23} +$$$$82\!\cdots\!82$$$$T^{24} -$$$$38\!\cdots\!04$$$$p T^{25} +$$$$12\!\cdots\!04$$$$p T^{26} -$$$$24\!\cdots\!06$$$$T^{27} +$$$$87\!\cdots\!89$$$$T^{28} -$$$$62\!\cdots\!47$$$$T^{29} +$$$$25\!\cdots\!51$$$$T^{30} -$$$$14\!\cdots\!58$$$$T^{31} +$$$$69\!\cdots\!39$$$$T^{32} -$$$$33\!\cdots\!35$$$$T^{33} +$$$$17\!\cdots\!33$$$$T^{34} -$$$$73\!\cdots\!55$$$$T^{35} +$$$$43\!\cdots\!16$$$$T^{36} -$$$$16\!\cdots\!44$$$$T^{37} +$$$$43\!\cdots\!16$$$$p T^{38} -$$$$73\!\cdots\!55$$$$p^{2} T^{39} +$$$$17\!\cdots\!33$$$$p^{3} T^{40} -$$$$33\!\cdots\!35$$$$p^{4} T^{41} +$$$$69\!\cdots\!39$$$$p^{5} T^{42} -$$$$14\!\cdots\!58$$$$p^{6} T^{43} +$$$$25\!\cdots\!51$$$$p^{7} T^{44} -$$$$62\!\cdots\!47$$$$p^{8} T^{45} +$$$$87\!\cdots\!89$$$$p^{9} T^{46} -$$$$24\!\cdots\!06$$$$p^{10} T^{47} +$$$$12\!\cdots\!04$$$$p^{12} T^{48} -$$$$38\!\cdots\!04$$$$p^{13} T^{49} +$$$$82\!\cdots\!82$$$$p^{13} T^{50} -$$$$28\!\cdots\!45$$$$p^{14} T^{51} +$$$$22\!\cdots\!62$$$$p^{15} T^{52} - 84250781092006302513 p^{16} T^{53} + 57474465118364939040 p^{17} T^{54} - 2209754956773436801 p^{18} T^{55} + 1318661285879464800 p^{19} T^{56} - 51522699077916532 p^{20} T^{57} + 27271171091085067 p^{21} T^{58} - 1058197153787684 p^{22} T^{59} + 502437530052577 p^{23} T^{60} - 18908495217474 p^{24} T^{61} + 8124465056492 p^{25} T^{62} - 288903450256 p^{26} T^{63} + 113060352599 p^{27} T^{64} - 3681575519 p^{28} T^{65} + 1317799514 p^{29} T^{66} - 37683818 p^{30} T^{67} + 12363286 p^{31} T^{68} - 291360 p^{32} T^{69} + 87605 p^{33} T^{70} - 1517 p^{34} T^{71} + 417 p^{35} T^{72} - 4 p^{36} T^{73} + p^{37} T^{74}$$
29 $$1 - 2 p T + 2183 T^{2} - 61268 T^{3} + 1423162 T^{4} - 28441306 T^{5} + 504905661 T^{6} - 8106727537 T^{7} + 119503727766 T^{8} - 1633987438977 T^{9} + 20902460868805 T^{10} - 251793492095318 T^{11} + 2872149177964270 T^{12} - 31161070875676654 T^{13} + 322801712461013242 T^{14} - 3203059496985887500 T^{15} + 30529473146514645043 T^{16} -$$$$28\!\cdots\!53$$$$T^{17} +$$$$24\!\cdots\!14$$$$T^{18} -$$$$21\!\cdots\!96$$$$T^{19} +$$$$17\!\cdots\!60$$$$T^{20} -$$$$14\!\cdots\!60$$$$T^{21} +$$$$11\!\cdots\!98$$$$T^{22} -$$$$83\!\cdots\!77$$$$T^{23} +$$$$61\!\cdots\!45$$$$T^{24} -$$$$44\!\cdots\!28$$$$T^{25} +$$$$31\!\cdots\!47$$$$T^{26} -$$$$21\!\cdots\!22$$$$T^{27} +$$$$14\!\cdots\!26$$$$T^{28} -$$$$92\!\cdots\!59$$$$T^{29} +$$$$58\!\cdots\!24$$$$T^{30} -$$$$36\!\cdots\!39$$$$T^{31} +$$$$22\!\cdots\!09$$$$T^{32} -$$$$13\!\cdots\!26$$$$T^{33} +$$$$76\!\cdots\!49$$$$T^{34} -$$$$43\!\cdots\!74$$$$T^{35} +$$$$24\!\cdots\!31$$$$T^{36} -$$$$13\!\cdots\!56$$$$T^{37} +$$$$24\!\cdots\!31$$$$p T^{38} -$$$$43\!\cdots\!74$$$$p^{2} T^{39} +$$$$76\!\cdots\!49$$$$p^{3} T^{40} -$$$$13\!\cdots\!26$$$$p^{4} T^{41} +$$$$22\!\cdots\!09$$$$p^{5} T^{42} -$$$$36\!\cdots\!39$$$$p^{6} T^{43} +$$$$58\!\cdots\!24$$$$p^{7} T^{44} -$$$$92\!\cdots\!59$$$$p^{8} T^{45} +$$$$14\!\cdots\!26$$$$p^{9} T^{46} -$$$$21\!\cdots\!22$$$$p^{10} T^{47} +$$$$31\!\cdots\!47$$$$p^{11} T^{48} -$$$$44\!\cdots\!28$$$$p^{12} T^{49} +$$$$61\!\cdots\!45$$$$p^{13} T^{50} -$$$$83\!\cdots\!77$$$$p^{14} T^{51} +$$$$11\!\cdots\!98$$$$p^{15} T^{52} -$$$$14\!\cdots\!60$$$$p^{16} T^{53} +$$$$17\!\cdots\!60$$$$p^{17} T^{54} -$$$$21\!\cdots\!96$$$$p^{18} T^{55} +$$$$24\!\cdots\!14$$$$p^{19} T^{56} -$$$$28\!\cdots\!53$$$$p^{20} T^{57} + 30529473146514645043 p^{21} T^{58} - 3203059496985887500 p^{22} T^{59} + 322801712461013242 p^{23} T^{60} - 31161070875676654 p^{24} T^{61} + 2872149177964270 p^{25} T^{62} - 251793492095318 p^{26} T^{63} + 20902460868805 p^{27} T^{64} - 1633987438977 p^{28} T^{65} + 119503727766 p^{29} T^{66} - 8106727537 p^{30} T^{67} + 504905661 p^{31} T^{68} - 28441306 p^{32} T^{69} + 1423162 p^{33} T^{70} - 61268 p^{34} T^{71} + 2183 p^{35} T^{72} - 2 p^{37} T^{73} + p^{37} T^{74}$$
31 $$1 - 8 T + 609 T^{2} - 4539 T^{3} + 184331 T^{4} - 1297651 T^{5} + 37109719 T^{6} - 249681701 T^{7} + 5604175250 T^{8} - 36402820661 T^{9} + 678194947613 T^{10} - 4289571993919 T^{11} + 68562149473639 T^{12} - 425266223068313 T^{13} + 5957239543917211 T^{14} - 36443181225904593 T^{15} + 454084189466302971 T^{16} - 2751665155485526260 T^{17} + 30833722965496934101 T^{18} -$$$$18\!\cdots\!37$$$$T^{19} +$$$$18\!\cdots\!64$$$$T^{20} -$$$$11\!\cdots\!84$$$$T^{21} +$$$$10\!\cdots\!78$$$$T^{22} -$$$$62\!\cdots\!24$$$$T^{23} +$$$$53\!\cdots\!65$$$$T^{24} -$$$$31\!\cdots\!28$$$$T^{25} +$$$$25\!\cdots\!77$$$$T^{26} -$$$$14\!\cdots\!68$$$$T^{27} +$$$$11\!\cdots\!61$$$$T^{28} -$$$$64\!\cdots\!79$$$$T^{29} +$$$$44\!\cdots\!65$$$$T^{30} -$$$$25\!\cdots\!40$$$$T^{31} +$$$$16\!\cdots\!94$$$$T^{32} -$$$$95\!\cdots\!79$$$$T^{33} +$$$$59\!\cdots\!65$$$$T^{34} -$$$$33\!\cdots\!71$$$$T^{35} +$$$$19\!\cdots\!22$$$$T^{36} -$$$$10\!\cdots\!42$$$$T^{37} +$$$$19\!\cdots\!22$$$$p T^{38} -$$$$33\!\cdots\!71$$$$p^{2} T^{39} +$$$$59\!\cdots\!65$$$$p^{3} T^{40} -$$$$95\!\cdots\!79$$$$p^{4} T^{41} +$$$$16\!\cdots\!94$$$$p^{5} T^{42} -$$$$25\!\cdots\!40$$$$p^{6} T^{43} +$$$$44\!\cdots\!65$$$$p^{7} T^{44} -$$$$64\!\cdots\!79$$$$p^{8} T^{45} +$$$$11\!\cdots\!61$$$$p^{9} T^{46} -$$$$14\!\cdots\!68$$$$p^{10} T^{47} +$$$$25\!\cdots\!77$$$$p^{11} T^{48} -$$$$31\!\cdots\!28$$$$p^{12} T^{49} +$$$$53\!\cdots\!65$$$$p^{13} T^{50} -$$$$62\!\cdots\!24$$$$p^{14} T^{51} +$$$$10\!\cdots\!78$$$$p^{15} T^{52} -$$$$11\!\cdots\!84$$$$p^{16} T^{53} +$$$$18\!\cdots\!64$$$$p^{17} T^{54} -$$$$18\!\cdots\!37$$$$p^{18} T^{55} + 30833722965496934101 p^{19} T^{56} - 2751665155485526260 p^{20} T^{57} + 454084189466302971 p^{21} T^{58} - 36443181225904593 p^{22} T^{59} + 5957239543917211 p^{23} T^{60} - 425266223068313 p^{24} T^{61} + 68562149473639 p^{25} T^{62} - 4289571993919 p^{26} T^{63} + 678194947613 p^{27} T^{64} - 36402820661 p^{28} T^{65} + 5604175250 p^{29} T^{66} - 249681701 p^{30} T^{67} + 37109719 p^{31} T^{68} - 1297651 p^{32} T^{69} + 184331 p^{33} T^{70} - 4539 p^{34} T^{71} + 609 p^{35} T^{72} - 8 p^{36} T^{73} + p^{37} T^{74}$$
37 $$1 - 2 T + 737 T^{2} - 1659 T^{3} + 270230 T^{4} - 668309 T^{5} + 65789268 T^{6} - 175462293 T^{7} + 11974905719 T^{8} - 33942771741 T^{9} + 1739686666274 T^{10} - 5180479464072 T^{11} + 210283664836267 T^{12} - 651802654154043 T^{13} + 21766825467024037 T^{14} - 69706477899150110 T^{15} + 1970734843693426529 T^{16} - 6480211856491786024 T^{17} +$$$$15\!\cdots\!66$$$$T^{18} -$$$$53\!\cdots\!65$$$$T^{19} +$$$$11\!\cdots\!55$$$$T^{20} -$$$$39\!\cdots\!85$$$$T^{21} +$$$$75\!\cdots\!22$$$$T^{22} -$$$$26\!\cdots\!81$$$$T^{23} +$$$$45\!\cdots\!03$$$$T^{24} -$$$$15\!\cdots\!09$$$$T^{25} +$$$$25\!\cdots\!72$$$$T^{26} -$$$$88\!\cdots\!57$$$$T^{27} +$$$$13\!\cdots\!99$$$$T^{28} -$$$$45\!\cdots\!15$$$$T^{29} +$$$$63\!\cdots\!23$$$$T^{30} -$$$$21\!\cdots\!76$$$$T^{31} +$$$$28\!\cdots\!86$$$$T^{32} -$$$$96\!\cdots\!30$$$$T^{33} +$$$$11\!\cdots\!37$$$$T^{34} -$$$$39\!\cdots\!59$$$$T^{35} +$$$$47\!\cdots\!91$$$$T^{36} -$$$$41\!\cdots\!64$$$$p T^{37} +$$$$47\!\cdots\!91$$$$p T^{38} -$$$$39\!\cdots\!59$$$$p^{2} T^{39} +$$$$11\!\cdots\!37$$$$p^{3} T^{40} -$$$$96\!\cdots\!30$$$$p^{4} T^{41} +$$$$28\!\cdots\!86$$$$p^{5} T^{42} -$$$$21\!\cdots\!76$$$$p^{6} T^{43} +$$$$63\!\cdots\!23$$$$p^{7} T^{44} -$$$$45\!\cdots\!15$$$$p^{8} T^{45} +$$$$13\!\cdots\!99$$$$p^{9} T^{46} -$$$$88\!\cdots\!57$$$$p^{10} T^{47} +$$$$25\!\cdots\!72$$$$p^{11} T^{48} -$$$$15\!\cdots\!09$$$$p^{12} T^{49} +$$$$45\!\cdots\!03$$$$p^{13} T^{50} -$$$$26\!\cdots\!81$$$$p^{14} T^{51} +$$$$75\!\cdots\!22$$$$p^{15} T^{52} -$$$$39\!\cdots\!85$$$$p^{16} T^{53} +$$$$11\!\cdots\!55$$$$p^{17} T^{54} -$$$$53\!\cdots\!65$$$$p^{18} T^{55} +$$$$15\!\cdots\!66$$$$p^{19} T^{56} - 6480211856491786024 p^{20} T^{57} + 1970734843693426529 p^{21} T^{58} - 69706477899150110 p^{22} T^{59} + 21766825467024037 p^{23} T^{60} - 651802654154043 p^{24} T^{61} + 210283664836267 p^{25} T^{62} - 5180479464072 p^{26} T^{63} + 1739686666274 p^{27} T^{64} - 33942771741 p^{28} T^{65} + 11974905719 p^{29} T^{66} - 175462293 p^{30} T^{67} + 65789268 p^{31} T^{68} - 668309 p^{32} T^{69} + 270230 p^{33} T^{70} - 1659 p^{34} T^{71} + 737 p^{35} T^{72} - 2 p^{36} T^{73} + p^{37} T^{74}$$
41 $$1 - 62 T + 2681 T^{2} - 86339 T^{3} + 2331454 T^{4} - 54224361 T^{5} + 1124400951 T^{6} - 21092361372 T^{7} + 363534371768 T^{8} - 5808302084520 T^{9} + 86777727457808 T^{10} - 1219524995521692 T^{11} + 16210742457399822 T^{12} - 204671501430776919 T^{13} + 2463915898157194768 T^{14} - 28369441158307521603 T^{15} +$$$$31\!\cdots\!49$$$$T^{16} -$$$$33\!\cdots\!02$$$$T^{17} +$$$$34\!\cdots\!45$$$$T^{18} -$$$$33\!\cdots\!67$$$$T^{19} +$$$$32\!\cdots\!22$$$$T^{20} -$$$$72\!\cdots\!88$$$$p T^{21} +$$$$26\!\cdots\!11$$$$T^{22} -$$$$23\!\cdots\!06$$$$T^{23} +$$$$19\!\cdots\!76$$$$T^{24} -$$$$16\!\cdots\!72$$$$T^{25} +$$$$13\!\cdots\!82$$$$T^{26} -$$$$10\!\cdots\!90$$$$T^{27} +$$$$79\!\cdots\!45$$$$T^{28} -$$$$59\!\cdots\!65$$$$T^{29} +$$$$43\!\cdots\!41$$$$T^{30} -$$$$31\!\cdots\!87$$$$T^{31} +$$$$22\!\cdots\!28$$$$T^{32} -$$$$37\!\cdots\!00$$$$p T^{33} +$$$$10\!\cdots\!94$$$$T^{34} -$$$$69\!\cdots\!84$$$$T^{35} +$$$$45\!\cdots\!90$$$$T^{36} -$$$$29\!\cdots\!14$$$$T^{37} +$$$$45\!\cdots\!90$$$$p T^{38} -$$$$69\!\cdots\!84$$$$p^{2} T^{39} +$$$$10\!\cdots\!94$$$$p^{3} T^{40} -$$$$37\!\cdots\!00$$$$p^{5} T^{41} +$$$$22\!\cdots\!28$$$$p^{5} T^{42} -$$$$31\!\cdots\!87$$$$p^{6} T^{43} +$$$$43\!\cdots\!41$$$$p^{7} T^{44} -$$$$59\!\cdots\!65$$$$p^{8} T^{45} +$$$$79\!\cdots\!45$$$$p^{9} T^{46} -$$$$10\!\cdots\!90$$$$p^{10} T^{47} +$$$$13\!\cdots\!82$$$$p^{11} T^{48} -$$$$16\!\cdots\!72$$$$p^{12} T^{49} +$$$$19\!\cdots\!76$$$$p^{13} T^{50} -$$$$23\!\cdots\!06$$$$p^{14} T^{51} +$$$$26\!\cdots\!11$$$$p^{15} T^{52} -$$$$72\!\cdots\!88$$$$p^{17} T^{53} +$$$$32\!\cdots\!22$$$$p^{17} T^{54} -$$$$33\!\cdots\!67$$$$p^{18} T^{55} +$$$$34\!\cdots\!45$$$$p^{19} T^{56} -$$$$33\!\cdots\!02$$$$p^{20} T^{57} +$$$$31\!\cdots\!49$$$$p^{21} T^{58} - 28369441158307521603 p^{22} T^{59} + 2463915898157194768 p^{23} T^{60} - 204671501430776919 p^{24} T^{61} + 16210742457399822 p^{25} T^{62} - 1219524995521692 p^{26} T^{63} + 86777727457808 p^{27} T^{64} - 5808302084520 p^{28} T^{65} + 363534371768 p^{29} T^{66} - 21092361372 p^{30} T^{67} + 1124400951 p^{31} T^{68} - 54224361 p^{32} T^{69} + 2331454 p^{33} T^{70} - 86339 p^{34} T^{71} + 2681 p^{35} T^{72} - 62 p^{36} T^{73} + p^{37} T^{74}$$
43 $$1 - 30 T + 1153 T^{2} - 26209 T^{3} + 619912 T^{4} - 11592252 T^{5} + 4971819 p T^{6} - 3448073470 T^{7} + 53980210834 T^{8} - 773753978559 T^{9} + 10723421510548 T^{10} - 139409648033100 T^{11} + 1752774414514702 T^{12} - 20966988957155590 T^{13} + 242965672233926097 T^{14} - 2702786095703890961 T^{15} + 29184908263019590821 T^{16} -$$$$30\!\cdots\!20$$$$T^{17} +$$$$30\!\cdots\!73$$$$T^{18} -$$$$30\!\cdots\!30$$$$T^{19} +$$$$29\!\cdots\!08$$$$T^{20} -$$$$27\!\cdots\!07$$$$T^{21} +$$$$24\!\cdots\!73$$$$T^{22} -$$$$21\!\cdots\!70$$$$T^{23} +$$$$18\!\cdots\!24$$$$T^{24} -$$$$16\!\cdots\!41$$$$T^{25} +$$$$13\!\cdots\!01$$$$T^{26} -$$$$25\!\cdots\!55$$$$p T^{27} +$$$$85\!\cdots\!26$$$$T^{28} -$$$$66\!\cdots\!78$$$$T^{29} +$$$$50\!\cdots\!99$$$$T^{30} -$$$$37\!\cdots\!26$$$$T^{31} +$$$$27\!\cdots\!01$$$$T^{32} -$$$$19\!\cdots\!78$$$$T^{33} +$$$$13\!\cdots\!06$$$$T^{34} -$$$$94\!\cdots\!09$$$$T^{35} +$$$$64\!\cdots\!42$$$$T^{36} -$$$$42\!\cdots\!50$$$$T^{37} +$$$$64\!\cdots\!42$$$$p T^{38} -$$$$94\!\cdots\!09$$$$p^{2} T^{39} +$$$$13\!\cdots\!06$$$$p^{3} T^{40} -$$$$19\!\cdots\!78$$$$p^{4} T^{41} +$$$$27\!\cdots\!01$$$$p^{5} T^{42} -$$$$37\!\cdots\!26$$$$p^{6} T^{43} +$$$$50\!\cdots\!99$$$$p^{7} T^{44} -$$$$66\!\cdots\!78$$$$p^{8} T^{45} +$$$$85\!\cdots\!26$$$$p^{9} T^{46} -$$$$25\!\cdots\!55$$$$p^{11} T^{47} +$$$$13\!\cdots\!01$$$$p^{11} T^{48} -$$$$16\!\cdots\!41$$$$p^{12} T^{49} +$$$$18\!\cdots\!24$$$$p^{13} T^{50} -$$$$21\!\cdots\!70$$$$p^{14} T^{51} +$$$$24\!\cdots\!73$$$$p^{15} T^{52} -$$$$27\!\cdots\!07$$$$p^{16} T^{53} +$$$$29\!\cdots\!08$$$$p^{17} T^{54} -$$$$30\!\cdots\!30$$$$p^{18} T^{55} +$$$$30\!\cdots\!73$$$$p^{19} T^{56} -$$$$30\!\cdots\!20$$$$p^{20} T^{57} + 29184908263019590821 p^{21} T^{58} - 2702786095703890961 p^{22} T^{59} + 242965672233926097 p^{23} T^{60} - 20966988957155590 p^{24} T^{61} + 1752774414514702 p^{25} T^{62} - 139409648033100 p^{26} T^{63} + 10723421510548 p^{27} T^{64} - 773753978559 p^{28} T^{65} + 53980210834 p^{29} T^{66} - 3448073470 p^{30} T^{67} + 4971819 p^{32} T^{68} - 11592252 p^{32} T^{69} + 619912 p^{33} T^{70} - 26209 p^{34} T^{71} + 1153 p^{35} T^{72} - 30 p^{36} T^{73} + p^{37} T^{74}$$
47 $$1 - 5 T + 766 T^{2} - 3590 T^{3} + 297374 T^{4} - 1325079 T^{5} + 78036870 T^{6} - 335767492 T^{7} + 15566942159 T^{8} - 65719763002 T^{9} + 2515719401762 T^{10} - 10588368700584 T^{11} + 342699705713142 T^{12} - 1460103512364316 T^{13} + 40426387906733974 T^{14} - 176809349022352954 T^{15} + 4210748162312733807 T^{16} - 19134169831095669454 T^{17} +$$$$39\!\cdots\!15$$$$T^{18} -$$$$18\!\cdots\!96$$$$T^{19} +$$$$33\!\cdots\!68$$$$T^{20} -$$$$16\!\cdots\!32$$$$T^{21} +$$$$25\!\cdots\!92$$$$T^{22} -$$$$13\!\cdots\!52$$$$T^{23} +$$$$18\!\cdots\!43$$$$T^{24} -$$$$10\!\cdots\!25$$$$T^{25} +$$$$12\!\cdots\!70$$$$T^{26} -$$$$72\!\cdots\!51$$$$T^{27} +$$$$75\!\cdots\!53$$$$T^{28} -$$$$47\!\cdots\!16$$$$T^{29} +$$$$43\!\cdots\!63$$$$T^{30} -$$$$28\!\cdots\!69$$$$T^{31} +$$$$24\!\cdots\!66$$$$T^{32} -$$$$34\!\cdots\!62$$$$p T^{33} +$$$$12\!\cdots\!23$$$$T^{34} -$$$$83\!\cdots\!12$$$$T^{35} +$$$$62\!\cdots\!02$$$$T^{36} -$$$$40\!\cdots\!54$$$$T^{37} +$$$$62\!\cdots\!02$$$$p T^{38} -$$$$83\!\cdots\!12$$$$p^{2} T^{39} +$$$$12\!\cdots\!23$$$$p^{3} T^{40} -$$$$34\!\cdots\!62$$$$p^{5} T^{41} +$$$$24\!\cdots\!66$$$$p^{5} T^{42} -$$$$28\!\cdots\!69$$$$p^{6} T^{43} +$$$$43\!\cdots\!63$$$$p^{7} T^{44} -$$$$47\!\cdots\!16$$$$p^{8} T^{45} +$$$$75\!\cdots\!53$$$$p^{9} T^{46} -$$$$72\!\cdots\!51$$$$p^{10} T^{47} +$$$$12\!\cdots\!70$$$$p^{11} T^{48} -$$$$10\!\cdots\!25$$$$p^{12} T^{49} +$$$$18\!\cdots\!43$$$$p^{13} T^{50} -$$$$13\!\cdots\!52$$$$p^{14} T^{51} +$$$$25\!\cdots\!92$$$$p^{15} T^{52} -$$$$16\!\cdots\!32$$$$p^{16} T^{53} +$$$$33\!\cdots\!68$$$$p^{17} T^{54} -$$$$18\!\cdots\!96$$$$p^{18} T^{55} +$$$$39\!\cdots\!15$$$$p^{19} T^{56} - 19134169831095669454 p^{20} T^{57} + 4210748162312733807 p^{21} T^{58} - 176809349022352954 p^{22} T^{59} + 40426387906733974 p^{23} T^{60} - 1460103512364316 p^{24} T^{61} + 342699705713142 p^{25} T^{62} - 10588368700584 p^{26} T^{63} + 2515719401762 p^{27} T^{64} - 65719763002 p^{28} T^{65} + 15566942159 p^{29} T^{66} - 335767492 p^{30} T^{67} + 78036870 p^{31} T^{68} - 1325079 p^{32} T^{69} + 297374 p^{33} T^{70} - 3590 p^{34} T^{71} + 766 p^{35} T^{72} - 5 p^{36} T^{73} + p^{37} T^{74}$$
53 $$1 - 18 T + 972 T^{2} - 15954 T^{3} + 474394 T^{4} - 7116368 T^{5} + 154448202 T^{6} - 2130096314 T^{7} + 37679402451 T^{8} - 481211465305 T^{9} + 7345254247572 T^{10} - 87491145010460 T^{11} + 1192214873114439 T^{12} - 13332310037046908 T^{13} + 165817572011667119 T^{14} - 1751181980868577100 T^{15} + 20187509096563627020 T^{16} -$$$$20\!\cdots\!25$$$$T^{17} +$$$$21\!\cdots\!41$$$$T^{18} -$$$$20\!\cdots\!47$$$$T^{19} +$$$$21\!\cdots\!46$$$$T^{20} -$$$$19\!\cdots\!56$$$$T^{21} +$$$$19\!\cdots\!53$$$$T^{22} -$$$$16\!\cdots\!89$$$$T^{23} +$$$$15\!\cdots\!22$$$$T^{24} -$$$$13\!\cdots\!42$$$$T^{25} +$$$$11\!\cdots\!91$$$$T^{26} -$$$$96\!\cdots\!89$$$$T^{27} +$$$$83\!\cdots\!34$$$$T^{28} -$$$$66\!\cdots\!40$$$$T^{29} +$$$$55\!\cdots\!32$$$$T^{30} -$$$$42\!\cdots\!53$$$$T^{31} +$$$$34\!\cdots\!00$$$$T^{32} -$$$$48\!\cdots\!78$$$$p T^{33} +$$$$20\!\cdots\!74$$$$T^{34} -$$$$14\!\cdots\!18$$$$T^{35} +$$$$11\!\cdots\!29$$$$T^{36} -$$$$15\!\cdots\!40$$$$p T^{37} +$$$$11\!\cdots\!29$$$$p T^{38} -$$$$14\!\cdots\!18$$$$p^{2} T^{39} +$$$$20\!\cdots\!74$$$$p^{3} T^{40} -$$$$48\!\cdots\!78$$$$p^{5} T^{41} +$$$$34\!\cdots\!00$$$$p^{5} T^{42} -$$$$42\!\cdots\!53$$$$p^{6} T^{43} +$$$$55\!\cdots\!32$$$$p^{7} T^{44} -$$$$66\!\cdots\!40$$$$p^{8} T^{45} +$$$$83\!\cdots\!34$$$$p^{9} T^{46} -$$$$96\!\cdots\!89$$$$p^{10} T^{47} +$$$$11\!\cdots\!91$$$$p^{11} T^{48} -$$$$13\!\cdots\!42$$$$p^{12} T^{49} +$$$$15\!\cdots\!22$$$$p^{13} T^{50} -$$$$16\!\cdots\!89$$$$p^{14} T^{51} +$$$$19\!\cdots\!53$$$$p^{15} T^{52} -$$$$19\!\cdots\!56$$$$p^{16} T^{53} +$$$$21\!\cdots\!46$$$$p^{17} T^{54} -$$$$20\!\cdots\!47$$$$p^{18} T^{55} +$$$$21\!\cdots\!41$$$$p^{19} T^{56} -$$$$20\!\cdots\!25$$$$p^{20} T^{57} + 20187509096563627020 p^{21} T^{58} - 1751181980868577100 p^{22} T^{59} + 165817572011667119 p^{23} T^{60} - 13332310037046908 p^{24} T^{61} + 1192214873114439 p^{25} T^{62} - 87491145010460 p^{26} T^{63} + 7345254247572 p^{27} T^{64} - 481211465305 p^{28} T^{65} + 37679402451 p^{29} T^{66} - 2130096314 p^{30} T^{67} + 154448202 p^{31} T^{68} - 7116368 p^{32} T^{69} + 474394 p^{33} T^{70} - 15954 p^{34} T^{71} + 972 p^{35} T^{72} - 18 p^{36} T^{73} + p^{37} T^{74}$$
59 $$1 - 15 T + 1186 T^{2} - 15491 T^{3} + 687604 T^{4} - 7970891 T^{5} + 261813768 T^{6} - 2728837270 T^{7} + 74037791164 T^{8} - 700093962882 T^{9} + 16647624077546 T^{10} - 143701801277783 T^{11} + 3108742923073211 T^{12} - 24599676054190416 T^{13} + 496877615978616476 T^{14} - 3614513680698981355 T^{15} + 69493544625978585189 T^{16} -$$$$46\!\cdots\!20$$$$T^{17} +$$$$86\!\cdots\!36$$$$T^{18} -$$$$90\!\cdots\!13$$$$p T^{19} +$$$$97\!\cdots\!36$$$$T^{20} -$$$$55\!\cdots\!32$$$$T^{21} +$$$$99\!\cdots\!15$$$$T^{22} -$$$$52\!\cdots\!94$$$$T^{23} +$$$$93\!\cdots\!95$$$$T^{24} -$$$$45\!\cdots\!72$$$$T^{25} +$$$$81\!\cdots\!40$$$$T^{26} -$$$$36\!\cdots\!40$$$$T^{27} +$$$$65\!\cdots\!57$$$$T^{28} -$$$$27\!\cdots\!20$$$$T^{29} +$$$$49\!\cdots\!32$$$$T^{30} -$$$$19\!\cdots\!38$$$$T^{31} +$$$$35\!\cdots\!16$$$$T^{32} -$$$$13\!\cdots\!55$$$$T^{33} +$$$$23\!\cdots\!29$$$$T^{34} -$$$$85\!\cdots\!70$$$$T^{35} +$$$$14\!\cdots\!43$$$$T^{36} -$$$$51\!\cdots\!58$$$$T^{37} +$$$$14\!\cdots\!43$$$$p T^{38} -$$$$85\!\cdots\!70$$$$p^{2} T^{39} +$$$$23\!\cdots\!29$$$$p^{3} T^{40} -$$$$13\!\cdots\!55$$$$p^{4} T^{41} +$$$$35\!\cdots\!16$$$$p^{5} T^{42} -$$$$19\!\cdots\!38$$$$p^{6} T^{43} +$$$$49\!\cdots\!32$$$$p^{7} T^{44} -$$$$27\!\cdots\!20$$$$p^{8} T^{45} +$$$$65\!\cdots\!57$$$$p^{9} T^{46} -$$$$36\!\cdots\!40$$$$p^{10} T^{47} +$$$$81\!\cdots\!40$$$$p^{11} T^{48} -$$$$45\!\cdots\!72$$$$p^{12} T^{49} +$$$$93\!\cdots\!95$$$$p^{13} T^{50} -$$$$52\!\cdots\!94$$$$p^{14} T^{51} +$$$$99\!\cdots\!15$$$$p^{15} T^{52} -$$$$55\!\cdots\!32$$$$p^{16} T^{53} +$$$$97\!\cdots\!36$$$$p^{17} T^{54} -$$$$90\!\cdots\!13$$$$p^{19} T^{55} +$$$$86\!\cdots\!36$$$$p^{19} T^{56} -$$$$46\!\cdots\!20$$$$p^{20} T^{57} + 69493544625978585189 p^{21} T^{58} - 3614513680698981355 p^{22} T^{59} + 496877615978616476 p^{23} T^{60} - 24599676054190416 p^{24} T^{61} + 3108742923073211 p^{25} T^{62} - 143701801277783 p^{26} T^{63} + 16647624077546 p^{27} T^{64} - 700093962882 p^{28} T^{65} + 74037791164 p^{29} T^{66} - 2728837270 p^{30} T^{67} + 261813768 p^{31} T^{68} - 7970891 p^{32} T^{69} + 687604 p^{33} T^{70} - 15491 p^{34} T^{71} + 1186 p^{35} T^{72} - 15 p^{36} T^{73} + p^{37} T^{74}$$
61 $$1 - 57 T + 2902 T^{2} - 102324 T^{3} + 3256248 T^{4} - 87172039 T^{5} + 2150507921 T^{6} - 47593622895 T^{7} + 985802886425 T^{8} - 18880529404958 T^{9} + 342197179105808 T^{10} - 5833788857715001 T^{11} + 94876187290822765 T^{12} - 1467162119205391836 T^{13} + 21773906311851530028 T^{14} -$$$$30\!\cdots\!71$$$$T^{15} +$$$$42\!\cdots\!80$$$$T^{16} -$$$$55\!\cdots\!74$$$$T^{17} +$$$$71\!\cdots\!78$$$$T^{18} -$$$$88\!\cdots\!00$$$$T^{19} +$$$$10\!\cdots\!17$$$$T^{20} -$$$$12\!\cdots\!84$$$$T^{21} +$$$$13\!\cdots\!29$$$$T^{22} -$$$$15\!\cdots\!31$$$$T^{23} +$$$$16\!\cdots\!80$$$$T^{24} -$$$$16\!\cdots\!82$$$$T^{25} +$$$$17\!\cdots\!06$$$$T^{26} -$$$$17\!\cdots\!24$$$$T^{27} +$$$$16\!\cdots\!40$$$$T^{28} -$$$$15\!\cdots\!68$$$$T^{29} +$$$$14\!\cdots\!39$$$$T^{30} -$$$$12\!\cdots\!08$$$$T^{31} +$$$$11\!\cdots\!41$$$$T^{32} -$$$$98\!\cdots\!97$$$$T^{33} +$$$$83\!\cdots\!79$$$$T^{34} -$$$$68\!\cdots\!86$$$$T^{35} +$$$$55\!\cdots\!69$$$$T^{36} -$$$$43\!\cdots\!22$$$$T^{37} +$$$$55\!\cdots\!69$$$$p T^{38} -$$$$68\!\cdots\!86$$$$p^{2} T^{39} +$$$$83\!\cdots\!79$$$$p^{3} T^{40} -$$$$98\!\cdots\!97$$$$p^{4} T^{41} +$$$$11\!\cdots\!41$$$$p^{5} T^{42} -$$$$12\!\cdots\!08$$$$p^{6} T^{43} +$$$$14\!\cdots\!39$$$$p^{7} T^{44} -$$$$15\!\cdots\!68$$$$p^{8} T^{45} +$$$$16\!\cdots\!40$$$$p^{9} T^{46} -$$$$17\!\cdots\!24$$$$p^{10} T^{47} +$$$$17\!\cdots\!06$$$$p^{11} T^{48} -$$$$16\!\cdots\!82$$$$p^{12} T^{49} +$$$$16\!\cdots\!80$$$$p^{13} T^{50} -$$$$15\!\cdots\!31$$$$p^{14} T^{51} +$$$$13\!\cdots\!29$$$$p^{15} T^{52} -$$$$12\!\cdots\!84$$$$p^{16} T^{53} +$$$$10\!\cdots\!17$$$$p^{17} T^{54} -$$$$88\!\cdots\!00$$$$p^{18} T^{55} +$$$$71\!\cdots\!78$$$$p^{19} T^{56} -$$$$55\!\cdots\!74$$$$p^{20} T^{57} +$$$$42\!\cdots\!80$$$$p^{21} T^{58} -$$$$30\!\cdots\!71$$$$p^{22} T^{59} + 21773906311851530028 p^{23} T^{60} - 1467162119205391836 p^{24} T^{61} + 94876187290822765 p^{25} T^{62} - 5833788857715001 p^{26} T^{63} + 342197179105808 p^{27} T^{64} - 18880529404958 p^{28} T^{65} + 985802886425 p^{29} T^{66} - 47593622895 p^{30} T^{67} + 2150507921 p^{31} T^{68} - 87172039 p^{32} T^{69} + 3256248 p^{33} T^{70} - 102324 p^{34} T^{71} + 2902 p^{35} T^{72} - 57 p^{36} T^{73} + p^{37} T^{74}$$
67 $$1 + 14 T + 1314 T^{2} + 16590 T^{3} + 839476 T^{4} + 9682452 T^{5} + 348898171 T^{6} + 3714868148 T^{7} + 106433942489 T^{8} + 1055731026189 T^{9} + 25490345188328 T^{10} + 237566256931531 T^{11} + 5006752993639019 T^{12} + 44216251839057588 T^{13} + 832169961838726464 T^{14} + 7025079342081843000 T^{15} +$$$$11\!\cdots\!84$$$$T^{16} +$$$$97\!\cdots\!56$$$$T^{17} +$$$$15\!\cdots\!60$$$$T^{18} +$$$$12\!\cdots\!51$$$$T^{19} +$$$$17\!\cdots\!45$$$$T^{20} +$$$$13\!\cdots\!15$$$$T^{21} +$$$$18\!\cdots\!86$$$$T^{22} +$$$$14\!\cdots\!93$$$$T^{23} +$$$$17\!\cdots\!08$$$$T^{24} +$$$$13\!\cdots\!39$$$$T^{25} +$$$$15\!\cdots\!27$$$$T^{26} +$$$$12\!\cdots\!90$$$$T^{27} +$$$$13\!\cdots\!93$$$$T^{28} +$$$$10\!\cdots\!67$$$$T^{29} +$$$$10\!\cdots\!28$$$$T^{30} +$$$$83\!\cdots\!29$$$$T^{31} +$$$$82\!\cdots\!37$$$$T^{32} +$$$$64\!\cdots\!78$$$$T^{33} +$$$$60\!\cdots\!40$$$$T^{34} +$$$$46\!\cdots\!52$$$$T^{35} +$$$$42\!\cdots\!38$$$$T^{36} +$$$$31\!\cdots\!52$$$$T^{37} +$$$$42\!\cdots\!38$$$$p T^{38} +$$$$46\!\cdots\!52$$$$p^{2} T^{39} +$$$$60\!\cdots\!40$$$$p^{3} T^{40} +$$$$64\!\cdots\!78$$$$p^{4} T^{41} +$$$$82\!\cdots\!37$$$$p^{5} T^{42} +$$$$83\!\cdots\!29$$$$p^{6} T^{43} +$$$$10\!\cdots\!28$$$$p^{7} T^{44} +$$$$10\!\cdots\!67$$$$p^{8} T^{45} +$$$$13\!\cdots\!93$$$$p^{9} T^{46} +$$$$12\!\cdots\!90$$$$p^{10} T^{47} +$$$$15\!\cdots\!27$$$$p^{11} T^{48} +$$$$13\!\cdots\!39$$$$p^{12} T^{49} +$$$$17\!\cdots\!08$$$$p^{13} T^{50} +$$$$14\!\cdots\!93$$$$p^{14} T^{51} +$$$$18\!\cdots\!86$$$$p^{15} T^{52} +$$$$13\!\cdots\!15$$$$p^{16} T^{53} +$$$$17\!\cdots\!45$$$$p^{17} T^{54} +$$$$12\!\cdots\!51$$$$p^{18} T^{55} +$$$$15\!\cdots\!60$$$$p^{19} T^{56} +$$$$97\!\cdots\!56$$$$p^{20} T^{57} +$$$$11\!\cdots\!84$$$$p^{21} T^{58} + 7025079342081843000 p^{22} T^{59} + 832169961838726464 p^{23} T^{60} + 44216251839057588 p^{24} T^{61} + 5006752993639019 p^{25} T^{62} + 237566256931531 p^{26} T^{63} + 25490345188328 p^{27} T^{64} + 1055731026189 p^{28} T^{65} + 106433942489 p^{29} T^{66} + 3714868148 p^{30} T^{67} + 348898171 p^{31} T^{68} + 9682452 p^{32} T^{69} + 839476 p^{33} T^{70} + 16590 p^{34} T^{71} + 1314 p^{35} T^{72} + 14 p^{36} T^{73} + p^{37} T^{74}$$
71 $$1 - 8 T + 1380 T^{2} - 10988 T^{3} + 960290 T^{4} - 7586748 T^{5} + 448285645 T^{6} - 3505761715 T^{7} + 157638972908 T^{8} - 1217807349931 T^{9} + 44466185857948 T^{10} - 338704111345632 T^{11} + 10464940002742994 T^{12} - 78456329482563870 T^{13} + 2110808410051594745 T^{14} - 15548490171895775644 T^{15} +$$$$37\!\cdots\!04$$$$T^{16} -$$$$26\!\cdots\!12$$$$T^{17} +$$$$58\!\cdots\!24$$$$T^{18} -$$$$41\!\cdots\!24$$$$T^{19} +$$$$81\!\cdots\!48$$$$T^{20} -$$$$56\!\cdots\!45$$$$T^{21} +$$$$10\!\cdots\!30$$$$T^{22} -$$$$70\!\cdots\!76$$$$T^{23} +$$$$12\!\cdots\!39$$$$T^{24} -$$$$79\!\cdots\!96$$$$T^{25} +$$$$12\!\cdots\!48$$$$T^{26} -$$$$82\!\cdots\!42$$$$T^{27} +$$$$17\!\cdots\!63$$$$p T^{28} -$$$$79\!\cdots\!43$$$$T^{29} +$$$$11\!\cdots\!45$$$$T^{30} -$$$$70\!\cdots\!38$$$$T^{31} +$$$$99\!\cdots\!36$$$$T^{32} -$$$$59\!\cdots\!55$$$$T^{33} +$$$$80\!\cdots\!00$$$$T^{34} -$$$$46\!\cdots\!38$$$$T^{35} +$$$$60\!\cdots\!12$$$$T^{36} -$$$$33\!\cdots\!50$$$$T^{37} +$$$$60\!\cdots\!12$$$$p T^{38} -$$$$46\!\cdots\!38$$$$p^{2} T^{39} +$$$$80\!\cdots\!00$$$$p^{3} T^{40} -$$$$59\!\cdots\!55$$$$p^{4} T^{41} +$$$$99\!\cdots\!36$$$$p^{5} T^{42} -$$$$70\!\cdots\!38$$$$p^{6} T^{43} +$$$$11\!\cdots\!45$$$$p^{7} T^{44} -$$$$79\!\cdots\!43$$$$p^{8} T^{45} +$$$$17\!\cdots\!63$$$$p^{10} T^{46} -$$$$82\!\cdots\!42$$$$p^{10} T^{47} +$$$$12\!\cdots\!48$$$$p^{11} T^{48} -$$$$79\!\cdots\!96$$$$p^{12} T^{49} +$$$$12\!\cdots\!39$$$$p^{13} T^{50} -$$$$70\!\cdots\!76$$$$p^{14} T^{51} +$$$$10\!\cdots\!30$$$$p^{15} T^{52} -$$$$56\!\cdots\!45$$$$p^{16} T^{53} +$$$$81\!\cdots\!48$$$$p^{17} T^{54} -$$$$41\!\cdots\!24$$$$p^{18} T^{55} +$$$$58\!\cdots\!24$$$$p^{19} T^{56} -$$$$26\!\cdots\!12$$$$p^{20} T^{57} +$$$$37\!\cdots\!04$$$$p^{21} T^{58} - 15548490171895775644 p^{22} T^{59} + 2110808410051594745 p^{23} T^{60} - 78456329482563870 p^{24} T^{61} + 10464940002742994 p^{25} T^{62} - 338704111345632 p^{26} T^{63} + 44466185857948 p^{27} T^{64} - 1217807349931 p^{28} T^{65} + 157638972908 p^{29} T^{66} - 3505761715 p^{30} T^{67} + 448285645 p^{31} T^{68} - 7586748 p^{32} T^{69} + 960290 p^{33} T^{70} - 10988 p^{34} T^{71} + 1380 p^{35} T^{72} - 8 p^{36} T^{73} + p^{37} T^{74}$$
79 $$1 - 42 T + 2172 T^{2} - 67949 T^{3} + 2160995 T^{4} - 55076474 T^{5} + 1364573356 T^{6} - 29813639552 T^{7} + 626616120208 T^{8} - 12120389457202 T^{9} + 225425289771448 T^{10} - 3945290330840761 T^{11} + 66558937739414139 T^{12} - 1070411920962872641 T^{13} + 16645448966301470756 T^{14} -$$$$24\!\cdots\!13$$$$T^{15} +$$$$36\!\cdots\!15$$$$T^{16} -$$$$50\!\cdots\!76$$$$T^{17} +$$$$68\!\cdots\!79$$$$T^{18} -$$$$90\!\cdots\!01$$$$T^{19} +$$$$11\!\cdots\!79$$$$T^{20} -$$$$14\!\cdots\!10$$$$T^{21} +$$$$17\!\cdots\!17$$$$T^{22} -$$$$21\!\cdots\!86$$$$T^{23} +$$$$25\!\cdots\!85$$$$T^{24} -$$$$28\!\cdots\!90$$$$T^{25} +$$$$31\!\cdots\!95$$$$T^{26} -$$$$34\!\cdots\!00$$$$T^{27} +$$$$37\!\cdots\!24$$$$T^{28} -$$$$38\!\cdots\!71$$$$T^{29} +$$$$39\!\cdots\!75$$$$T^{30} -$$$$40\!\cdots\!22$$$$T^{31} +$$$$39\!\cdots\!19$$$$T^{32} -$$$$38\!\cdots\!10$$$$T^{33} +$$$$36\!\cdots\!58$$$$T^{34} -$$$$33\!\cdots\!12$$$$T^{35} +$$$$31\!\cdots\!27$$$$T^{36} -$$$$27\!\cdots\!16$$$$T^{37} +$$$$31\!\cdots\!27$$$$p T^{38} -$$$$33\!\cdots\!12$$$$p^{2} T^{39} +$$$$36\!\cdots\!58$$$$p^{3} T^{40} -$$$$38\!\cdots\!10$$$$p^{4} T^{41} +$$$$39\!\cdots\!19$$$$p^{5} T^{42} -$$$$40\!\cdots\!22$$$$p^{6} T^{43} +$$$$39\!\cdots\!75$$$$p^{7} T^{44} -$$$$38\!\cdots\!71$$$$p^{8} T^{45} +$$$$37\!\cdots\!24$$$$p^{9} T^{46} -$$$$34\!\cdots\!00$$$$p^{10} T^{47} +$$$$31\!\cdots\!95$$$$p^{11} T^{48} -$$$$28\!\cdots\!90$$$$p^{12} T^{49} +$$$$25\!\cdots\!85$$$$p^{13} T^{50} -$$$$21\!\cdots\!86$$$$p^{14} T^{51} +$$$$17\!\cdots\!17$$$$p^{15} T^{52} -$$$$14\!\cdots\!10$$$$p^{16} T^{53} +$$$$11\!\cdots\!79$$$$p^{17} T^{54} -$$$$90\!\cdots\!01$$$$p^{18} T^{55} +$$$$68\!\cdots\!79$$$$p^{19} T^{56} -$$$$50\!\cdots\!76$$$$p^{20} T^{57} +$$$$36\!\cdots\!15$$$$p^{21} T^{58} -$$$$24\!\cdots\!13$$$$p^{22} T^{59} + 16645448966301470756 p^{23} T^{60} - 1070411920962872641 p^{24} T^{61} + 66558937739414139 p^{25} T^{62} - 3945290330840761 p^{26} T^{63} + 225425289771448 p^{27} T^{64} - 12120389457202 p^{28} T^{65} + 626616120208 p^{29} T^{66} - 29813639552 p^{30} T^{67} + 1364573356 p^{31} T^{68} - 55076474 p^{32} T^{69} + 2160995 p^{33} T^{70} - 67949 p^{34} T^{71} + 2172 p^{35} T^{72} - 42 p^{36} T^{73} + p^{37} T^{74}$$
83 $$1 - 44 T + 2206 T^{2} - 67800 T^{3} + 2086113 T^{4} - 50896700 T^{5} + 1210311044 T^{6} - 24992306880 T^{7} + 500346700531 T^{8} - 9087615668327 T^{9} + 160148023727714 T^{10} - 2625243785001341 T^{11} + 41862955614011189 T^{12} - 630938481437882110 T^{13} + 9277413273166309600 T^{14} -$$$$13\!\cdots\!81$$$$T^{15} +$$$$17\!\cdots\!05$$$$T^{16} -$$$$23\!\cdots\!90$$$$T^{17} +$$$$30\!\cdots\!90$$$$T^{18} -$$$$46\!\cdots\!86$$$$p T^{19} +$$$$47\!\cdots\!49$$$$T^{20} -$$$$57\!\cdots\!21$$$$T^{21} +$$$$67\!\cdots\!38$$$$T^{22} -$$$$77\!\cdots\!02$$$$T^{23} +$$$$88\!\cdots\!25$$$$T^{24} -$$$$98\!\cdots\!52$$$$T^{25} +$$$$10\!\cdots\!92$$$$T^{26} -$$$$11\!\cdots\!60$$$$T^{27} +$$$$14\!\cdots\!40$$$$p T^{28} -$$$$12\!\cdots\!55$$$$T^{29} +$$$$12\!\cdots\!49$$$$T^{30} -$$$$12\!\cdots\!57$$$$T^{31} +$$$$12\!\cdots\!27$$$$T^{32} -$$$$12\!\cdots\!27$$$$T^{33} +$$$$11\!\cdots\!97$$$$T^{34} -$$$$11\!\cdots\!17$$$$T^{35} +$$$$10\!\cdots\!82$$$$T^{36} -$$$$96\!\cdots\!96$$$$T^{37} +$$$$10\!\cdots\!82$$$$p T^{38} -$$$$11\!\cdots\!17$$$$p^{2} T^{39} +$$$$11\!\cdots\!97$$$$p^{3} T^{40} -$$$$12\!\cdots\!27$$$$p^{4} T^{41} +$$$$12\!\cdots\!27$$$$p^{5} T^{42} -$$$$12\!\cdots\!57$$$$p^{6} T^{43} +$$$$12\!\cdots\!49$$$$p^{7} T^{44} -$$$$12\!\cdots\!55$$$$p^{8} T^{45} +$$$$14\!\cdots\!40$$$$p^{10} T^{46} -$$$$11\!\cdots\!60$$$$p^{10} T^{47} +$$$$10\!\cdots\!92$$$$p^{11} T^{48} -$$$$98\!\cdots\!52$$$$p^{12} T^{49} +$$$$88\!\cdots\!25$$$$p^{13} T^{50} -$$$$77\!\cdots\!02$$$$p^{14} T^{51} +$$$$67\!\cdots\!38$$$$p^{15} T^{52} -$$$$57\!\cdots\!21$$$$p^{16} T^{53} +$$$$47\!\cdots\!49$$$$p^{17} T^{54} -$$$$46\!\cdots\!86$$$$p^{19} T^{55} +$$$$30\!\cdots\!90$$$$p^{19} T^{56} -$$$$23\!\cdots\!90$$$$p^{20} T^{57} +$$$$17\!\cdots\!05$$$$p^{21} T^{58} -$$$$13\!\cdots\!81$$$$p^{22} T^{59} + 9277413273166309600 p^{23} T^{60} - 630938481437882110 p^{24} T^{61} + 41862955614011189 p^{25} T^{62} - 2625243785001341 p^{26} T^{63} + 160148023727714 p^{27} T^{64} - 9087615668327 p^{28} T^{65} + 500346700531 p^{29} T^{66} - 24992306880 p^{30} T^{67} + 1210311044 p^{31} T^{68} - 50896700 p^{32} T^{69} + 2086113 p^{33} T^{70} - 67800 p^{34} T^{71} + 2206 p^{35} T^{72} - 44 p^{36} T^{73} + p^{37} T^{74}$$
89 $$1 - 69 T + 4086 T^{2} - 169838 T^{3} + 6273098 T^{4} - 195755255 T^{5} + 5583272608 T^{6} - 143035141959 T^{7} + 3412595459822 T^{8} - 75301066114637 T^{9} + 1567550817236526 T^{10} - 30695134007156151 T^{11} + 572370851388024025 T^{12} - 10150933526634695075 T^{13} +$$$$17\!\cdots\!46$$$$T^{14} -$$$$28\!\cdots\!42$$$$T^{15} +$$$$44\!\cdots\!00$$$$T^{16} -$$$$67\!\cdots\!32$$$$T^{17} +$$$$98\!\cdots\!70$$$$T^{18} -$$$$13\!\cdots\!11$$$$T^{19} +$$$$19\!\cdots\!62$$$$T^{20} -$$$$25\!\cdots\!76$$$$T^{21} +$$$$33\!\cdots\!34$$$$T^{22} -$$$$42\!\cdots\!59$$$$T^{23} +$$$$53\!\cdots\!40$$$$T^{24} -$$$$64\!\cdots\!75$$$$T^{25} +$$$$76\!\cdots\!18$$$$T^{26} -$$$$88\!\cdots\!96$$$$T^{27} +$$$$11\!\cdots\!04$$$$p T^{28} -$$$$11\!\cdots\!91$$$$T^{29} +$$$$12\!\cdots\!08$$$$T^{30} -$$$$13\!\cdots\!86$$$$T^{31} +$$$$13\!\cdots\!11$$$$T^{32} -$$$$13\!\cdots\!70$$$$T^{33} +$$$$14\!\cdots\!67$$$$T^{34} -$$$$13\!\cdots\!21$$$$T^{35} +$$$$13\!\cdots\!90$$$$T^{36} -$$$$12\!\cdots\!34$$$$T^{37} +$$$$13\!\cdots\!90$$$$p T^{38} -$$$$13\!\cdots\!21$$$$p^{2} T^{39} +$$$$14\!\cdots\!67$$$$p^{3} T^{40} -$$$$13\!\cdots\!70$$$$p^{4} T^{41} +$$$$13\!\cdots\!11$$$$p^{5} T^{42} -$$$$13\!\cdots\!86$$$$p^{6} T^{43} +$$$$12\!\cdots\!08$$$$p^{7} T^{44} -$$$$11\!\cdots\!91$$$$p^{8} T^{45} +$$$$11\!\cdots\!04$$$$p^{10} T^{46} -$$$$88\!\cdots\!96$$$$p^{10} T^{47} +$$$$76\!\cdots\!18$$$$p^{11} T^{48} -$$$$64\!\cdots\!75$$$$p^{12} T^{49} +$$$$53\!\cdots\!40$$$$p^{13} T^{50} -$$$$42\!\cdots\!59$$$$p^{14} T^{51} +$$$$33\!\cdots\!34$$$$p^{15} T^{52} -$$$$25\!\cdots\!76$$$$p^{16} T^{53} +$$$$19\!\cdots\!62$$$$p^{17} T^{54} -$$$$13\!\cdots\!11$$$$p^{18} T^{55} +$$$$98\!\cdots\!70$$$$p^{19} T^{56} -$$$$67\!\cdots\!32$$$$p^{20} T^{57} +$$$$44\!\cdots\!00$$$$p^{21} T^{58} -$$$$28\!\cdots\!42$$$$p^{22} T^{59} +$$$$17\!\cdots\!46$$$$p^{23} T^{60} - 10150933526634695075 p^{24} T^{61} + 572370851388024025 p^{25} T^{62} - 30695134007156151 p^{26} T^{63} + 1567550817236526 p^{27} T^{64} - 75301066114637 p^{28} T^{65} + 3412595459822 p^{29} T^{66} - 143035141959 p^{30} T^{67} + 5583272608 p^{31} T^{68} - 195755255 p^{32} T^{69} + 6273098 p^{33} T^{70} - 169838 p^{34} T^{71} + 4086 p^{35} T^{72} - 69 p^{36} T^{73} + p^{37} T^{74}$$
97 $$1 - 37 T + 2655 T^{2} - 79537 T^{3} + 3259664 T^{4} - 82714723 T^{5} + 2509272855 T^{6} - 55556198767 T^{7} + 1376538935732 T^{8} - 27156750644696 T^{9} + 578196822037273 T^{10} - 10326563587968865 T^{11} + 194850033357154762 T^{12} - 3190384070551897666 T^{13} + 54479011522236291750 T^{14} -$$$$82\!\cdots\!98$$$$T^{15} +$$$$12\!\cdots\!15$$$$T^{16} -$$$$18\!\cdots\!45$$$$T^{17} +$$$$26\!\cdots\!60$$$$T^{18} -$$$$35\!\cdots\!45$$$$T^{19} +$$$$49\!\cdots\!19$$$$T^{20} -$$$$62\!\cdots\!29$$$$T^{21} +$$$$81\!\cdots\!06$$$$T^{22} -$$$$98\!\cdots\!15$$$$T^{23} +$$$$12\!\cdots\!58$$$$T^{24} -$$$$14\!\cdots\!48$$$$T^{25} +$$$$16\!\cdots\!17$$$$T^{26} -$$$$18\!\cdots\!97$$$$T^{27} +$$$$21\!\cdots\!66$$$$T^{28} -$$$$23\!\cdots\!25$$$$T^{29} +$$$$26\!\cdots\!07$$$$T^{30} -$$$$27\!\cdots\!51$$$$T^{31} +$$$$29\!\cdots\!37$$$$T^{32} -$$$$30\!\cdots\!40$$$$T^{33} +$$$$32\!\cdots\!88$$$$T^{34} -$$$$32\!\cdots\!45$$$$T^{35} +$$$$32\!\cdots\!55$$$$T^{36} -$$$$31\!\cdots\!38$$$$T^{37} +$$$$32\!\cdots\!55$$$$p T^{38} -$$$$32\!\cdots\!45$$$$p^{2} T^{39} +$$$$32\!\cdots\!88$$$$p^{3} T^{40} -$$$$30\!\cdots\!40$$$$p^{4} T^{41} +$$$$29\!\cdots\!37$$$$p^{5} T^{42} -$$$$27\!\cdots\!51$$$$p^{6} T^{43} +$$$$26\!\cdots\!07$$$$p^{7} T^{44} -$$$$23\!\cdots\!25$$$$p^{8} T^{45} +$$$$21\!\cdots\!66$$$$p^{9} T^{46} -$$$$18\!\cdots\!97$$$$p^{10} T^{47} +$$$$16\!\cdots\!17$$$$p^{11} T^{48} -$$$$14\!\cdots\!48$$$$p^{12} T^{49} +$$$$12\!\cdots\!58$$$$p^{13} T^{50} -$$$$98\!\cdots\!15$$$$p^{14} T^{51} +$$$$81\!\cdots\!06$$$$p^{15} T^{52} -$$$$62\!\cdots\!29$$$$p^{16} T^{53} +$$$$49\!\cdots\!19$$$$p^{17} T^{54} -$$$$35\!\cdots\!45$$$$p^{18} T^{55} +$$$$26\!\cdots\!60$$$$p^{19} T^{56} -$$$$18\!\cdots\!45$$$$p^{20} T^{57} +$$$$12\!\cdots\!15$$$$p^{21} T^{58} -$$$$82\!\cdots\!98$$$$p^{22} T^{59} + 54479011522236291750 p^{23} T^{60} - 3190384070551897666 p^{24} T^{61} + 194850033357154762 p^{25} T^{62} - 10326563587968865 p^{26} T^{63} + 578196822037273 p^{27} T^{64} - 27156750644696 p^{28} T^{65} + 1376538935732 p^{29} T^{66} - 55556198767 p^{30} T^{67} + 2509272855 p^{31} T^{68} - 82714723 p^{32} T^{69} + 3259664 p^{33} T^{70} - 79537 p^{34} T^{71} + 2655 p^{35} T^{72} - 37 p^{36} T^{73} + p^{37} T^{74}$$
\begin{aligned} L(s) = \prod_p \ \prod_{j=1}^{74} (1 - \alpha_{j,p}\, p^{-s})^{-1} \end{aligned}