# Properties

 Degree 104 Conductor $3^{52} \cdot 7^{52} \cdot 383^{52}$ Sign $1$ Motivic weight 1 Primitive no Self-dual yes Analytic rank 0

# Origins of factors

## Dirichlet series

 L(s)  = 1 + 3·2-s − 52·3-s − 17·4-s − 7·5-s − 156·6-s + 52·7-s − 54·8-s + 1.37e3·9-s − 21·10-s + 9·11-s + 884·12-s + 44·13-s + 156·14-s + 364·15-s + 149·16-s − 6·17-s + 4.13e3·18-s + 7·19-s + 119·20-s − 2.70e3·21-s + 27·22-s − 4·23-s + 2.80e3·24-s − 64·25-s + 132·26-s − 2.48e4·27-s − 884·28-s + ⋯
 L(s)  = 1 + 2.12·2-s − 30.0·3-s − 8.5·4-s − 3.13·5-s − 63.6·6-s + 19.6·7-s − 19.0·8-s + 459.·9-s − 6.64·10-s + 2.71·11-s + 255.·12-s + 12.2·13-s + 41.6·14-s + 93.9·15-s + 37.2·16-s − 1.45·17-s + 974.·18-s + 1.60·19-s + 26.6·20-s − 590.·21-s + 5.75·22-s − 0.834·23-s + 573.·24-s − 12.7·25-s + 25.8·26-s − 4.77e3·27-s − 167.·28-s + ⋯

## Functional equation

\begin{aligned} \Lambda(s)=\mathstrut &\left(3^{52} \cdot 7^{52} \cdot 383^{52}\right)^{s/2} \, \Gamma_{\C}(s)^{52} \, L(s)\cr =\mathstrut & \,\Lambda(2-s) \end{aligned}
\begin{aligned} \Lambda(s)=\mathstrut &\left(3^{52} \cdot 7^{52} \cdot 383^{52}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{52} \, L(s)\cr =\mathstrut & \,\Lambda(1-s) \end{aligned}

## Invariants

 $$d$$ = $$104$$ $$N$$ = $$3^{52} \cdot 7^{52} \cdot 383^{52}$$ $$\varepsilon$$ = $1$ motivic weight = $$1$$ character : induced by $\chi_{8043} (1, \cdot )$ primitive : no self-dual : yes analytic rank = 0 Selberg data = $(104,\ 3^{52} \cdot 7^{52} \cdot 383^{52} ,\ ( \ : [1/2]^{52} ),\ 1 )$ $L(1)$ $\approx$ $2569.273410$ $L(\frac12)$ $\approx$ $2569.273410$ $L(\frac{3}{2})$ not available $L(1)$ not available

## Euler product

$L(s) = \prod_{p \text{ prime}} F_p(p^{-s})^{-1}$ where, for $p \notin \{3,\;7,\;383\}$, $$F_p$$ is a polynomial of degree 104. If $p \in \{3,\;7,\;383\}$, then $F_p$ is a polynomial of degree at most 103.
$p$$F_p$
bad3 $$( 1 + T )^{52}$$
7 $$( 1 - T )^{52}$$
383 $$( 1 + T )^{52}$$
good2 $$1 - 3 T + 13 p T^{2} - 75 T^{3} + 89 p^{2} T^{4} - 973 T^{5} + 425 p^{3} T^{6} - 8733 T^{7} + 25305 T^{8} - 60983 T^{9} + 38933 p^{2} T^{10} - 353171 T^{11} + 822823 T^{12} - 1765423 T^{13} + 3832703 T^{14} - 7827953 T^{15} + 16056537 T^{16} - 15701775 p T^{17} + 61452493 T^{18} - 115707441 T^{19} + 217571365 T^{20} - 99048669 p^{2} T^{21} + 359928551 p T^{22} - 636353523 p T^{23} + 561089189 p^{2} T^{24} - 1932654571 p T^{25} + 6639674195 T^{26} - 11170554545 T^{27} + 4686869703 p^{2} T^{28} - 7721474299 p^{2} T^{29} + 1586656231 p^{5} T^{30} - 82082276819 T^{31} + 66225658875 p T^{32} - 105250970455 p T^{33} + 334028078427 T^{34} - 261339335545 p T^{35} + 816844721153 T^{36} - 630046927717 p T^{37} + 970949803101 p T^{38} - 2956359527141 T^{39} + 4497112461523 T^{40} - 1690553721035 p^{2} T^{41} + 10161376689075 T^{42} - 7550418145233 p T^{43} + 22428389173955 T^{44} - 16477847573329 p T^{45} + 48398644948457 T^{46} - 1098995948047 p^{6} T^{47} + 6385248285313 p^{4} T^{48} - 2294815109771 p^{6} T^{49} + 52756718456419 p^{2} T^{50} - 18757463894785 p^{4} T^{51} + 13331526826765 p^{5} T^{52} - 18757463894785 p^{5} T^{53} + 52756718456419 p^{4} T^{54} - 2294815109771 p^{9} T^{55} + 6385248285313 p^{8} T^{56} - 1098995948047 p^{11} T^{57} + 48398644948457 p^{6} T^{58} - 16477847573329 p^{8} T^{59} + 22428389173955 p^{8} T^{60} - 7550418145233 p^{10} T^{61} + 10161376689075 p^{10} T^{62} - 1690553721035 p^{13} T^{63} + 4497112461523 p^{12} T^{64} - 2956359527141 p^{13} T^{65} + 970949803101 p^{15} T^{66} - 630046927717 p^{16} T^{67} + 816844721153 p^{16} T^{68} - 261339335545 p^{18} T^{69} + 334028078427 p^{18} T^{70} - 105250970455 p^{20} T^{71} + 66225658875 p^{21} T^{72} - 82082276819 p^{21} T^{73} + 1586656231 p^{27} T^{74} - 7721474299 p^{25} T^{75} + 4686869703 p^{26} T^{76} - 11170554545 p^{25} T^{77} + 6639674195 p^{26} T^{78} - 1932654571 p^{28} T^{79} + 561089189 p^{30} T^{80} - 636353523 p^{30} T^{81} + 359928551 p^{31} T^{82} - 99048669 p^{33} T^{83} + 217571365 p^{32} T^{84} - 115707441 p^{33} T^{85} + 61452493 p^{34} T^{86} - 15701775 p^{36} T^{87} + 16056537 p^{36} T^{88} - 7827953 p^{37} T^{89} + 3832703 p^{38} T^{90} - 1765423 p^{39} T^{91} + 822823 p^{40} T^{92} - 353171 p^{41} T^{93} + 38933 p^{44} T^{94} - 60983 p^{43} T^{95} + 25305 p^{44} T^{96} - 8733 p^{45} T^{97} + 425 p^{49} T^{98} - 973 p^{47} T^{99} + 89 p^{50} T^{100} - 75 p^{49} T^{101} + 13 p^{51} T^{102} - 3 p^{51} T^{103} + p^{52} T^{104}$$
5 $$1 + 7 T + 113 T^{2} + 664 T^{3} + 1222 p T^{4} + 6243 p T^{5} + 42706 p T^{6} + 972331 T^{7} + 5476932 T^{8} + 22645992 T^{9} + 110786118 T^{10} + 84394261 p T^{11} + 1851989051 T^{12} + 6572503111 T^{13} + 26448123926 T^{14} + 88260749243 T^{15} + 330749074981 T^{16} + 1045671256914 T^{17} + 3691986088967 T^{18} + 11126252150509 T^{19} + 37349848731262 T^{20} + 21568767336639 p T^{21} + 13868571897796 p^{2} T^{22} + 963344289040444 T^{23} + 2983978388228639 T^{24} + 8008159706342594 T^{25} + 24019609143144113 T^{26} + 62466656290683767 T^{27} + 182200806923996778 T^{28} + 460498016449016156 T^{29} + 1310906106052914949 T^{30} + 3228129172418446864 T^{31} + 8996361066763510371 T^{32} + 21633569040970041504 T^{33} + 59173491264013458033 T^{34} +$$$$13\!\cdots\!42$$$$T^{35} + 2996529979750456753 p^{3} T^{36} +$$$$86\!\cdots\!33$$$$T^{37} +$$$$22\!\cdots\!94$$$$T^{38} +$$$$51\!\cdots\!08$$$$T^{39} +$$$$13\!\cdots\!18$$$$T^{40} +$$$$60\!\cdots\!88$$$$p T^{41} +$$$$77\!\cdots\!59$$$$T^{42} +$$$$17\!\cdots\!83$$$$T^{43} +$$$$43\!\cdots\!03$$$$T^{44} +$$$$93\!\cdots\!06$$$$T^{45} +$$$$47\!\cdots\!83$$$$p T^{46} +$$$$50\!\cdots\!87$$$$T^{47} +$$$$12\!\cdots\!22$$$$T^{48} +$$$$26\!\cdots\!08$$$$T^{49} +$$$$65\!\cdots\!91$$$$T^{50} +$$$$54\!\cdots\!54$$$$p^{2} T^{51} +$$$$32\!\cdots\!54$$$$T^{52} +$$$$54\!\cdots\!54$$$$p^{3} T^{53} +$$$$65\!\cdots\!91$$$$p^{2} T^{54} +$$$$26\!\cdots\!08$$$$p^{3} T^{55} +$$$$12\!\cdots\!22$$$$p^{4} T^{56} +$$$$50\!\cdots\!87$$$$p^{5} T^{57} +$$$$47\!\cdots\!83$$$$p^{7} T^{58} +$$$$93\!\cdots\!06$$$$p^{7} T^{59} +$$$$43\!\cdots\!03$$$$p^{8} T^{60} +$$$$17\!\cdots\!83$$$$p^{9} T^{61} +$$$$77\!\cdots\!59$$$$p^{10} T^{62} +$$$$60\!\cdots\!88$$$$p^{12} T^{63} +$$$$13\!\cdots\!18$$$$p^{12} T^{64} +$$$$51\!\cdots\!08$$$$p^{13} T^{65} +$$$$22\!\cdots\!94$$$$p^{14} T^{66} +$$$$86\!\cdots\!33$$$$p^{15} T^{67} + 2996529979750456753 p^{19} T^{68} +$$$$13\!\cdots\!42$$$$p^{17} T^{69} + 59173491264013458033 p^{18} T^{70} + 21633569040970041504 p^{19} T^{71} + 8996361066763510371 p^{20} T^{72} + 3228129172418446864 p^{21} T^{73} + 1310906106052914949 p^{22} T^{74} + 460498016449016156 p^{23} T^{75} + 182200806923996778 p^{24} T^{76} + 62466656290683767 p^{25} T^{77} + 24019609143144113 p^{26} T^{78} + 8008159706342594 p^{27} T^{79} + 2983978388228639 p^{28} T^{80} + 963344289040444 p^{29} T^{81} + 13868571897796 p^{32} T^{82} + 21568767336639 p^{32} T^{83} + 37349848731262 p^{32} T^{84} + 11126252150509 p^{33} T^{85} + 3691986088967 p^{34} T^{86} + 1045671256914 p^{35} T^{87} + 330749074981 p^{36} T^{88} + 88260749243 p^{37} T^{89} + 26448123926 p^{38} T^{90} + 6572503111 p^{39} T^{91} + 1851989051 p^{40} T^{92} + 84394261 p^{42} T^{93} + 110786118 p^{42} T^{94} + 22645992 p^{43} T^{95} + 5476932 p^{44} T^{96} + 972331 p^{45} T^{97} + 42706 p^{47} T^{98} + 6243 p^{48} T^{99} + 1222 p^{49} T^{100} + 664 p^{49} T^{101} + 113 p^{50} T^{102} + 7 p^{51} T^{103} + p^{52} T^{104}$$
11 $$1 - 9 T + 272 T^{2} - 2127 T^{3} + 36107 T^{4} - 251689 T^{5} + 3147322 T^{6} - 19920437 T^{7} + 18542397 p T^{8} - 1188548926 T^{9} + 10532892423 T^{10} - 57116046661 T^{11} + 453120573970 T^{12} - 2305926738602 T^{13} + 16748935115435 T^{14} - 80533390429232 T^{15} + 49467681613622 p T^{16} - 2485616013031490 T^{17} + 15808108669807467 T^{18} - 6264335753542365 p T^{19} + 416224901301613443 T^{20} - 1737715024143332315 T^{21} + 10039632711654150695 T^{22} - 40267719675617306988 T^{23} +$$$$22\!\cdots\!91$$$$T^{24} - 7144744646058630341 p^{2} T^{25} +$$$$46\!\cdots\!26$$$$T^{26} -$$$$17\!\cdots\!77$$$$T^{27} +$$$$81\!\cdots\!64$$$$p T^{28} -$$$$32\!\cdots\!18$$$$T^{29} +$$$$16\!\cdots\!59$$$$T^{30} -$$$$57\!\cdots\!69$$$$T^{31} +$$$$28\!\cdots\!45$$$$T^{32} -$$$$96\!\cdots\!74$$$$T^{33} +$$$$46\!\cdots\!98$$$$T^{34} -$$$$15\!\cdots\!64$$$$T^{35} +$$$$72\!\cdots\!63$$$$T^{36} -$$$$23\!\cdots\!50$$$$T^{37} +$$$$10\!\cdots\!35$$$$T^{38} -$$$$33\!\cdots\!56$$$$T^{39} +$$$$15\!\cdots\!98$$$$T^{40} -$$$$42\!\cdots\!15$$$$p T^{41} +$$$$20\!\cdots\!69$$$$T^{42} -$$$$62\!\cdots\!93$$$$T^{43} +$$$$24\!\cdots\!68$$$$p T^{44} -$$$$72\!\cdots\!57$$$$p T^{45} +$$$$34\!\cdots\!68$$$$T^{46} -$$$$98\!\cdots\!15$$$$T^{47} +$$$$41\!\cdots\!32$$$$T^{48} -$$$$11\!\cdots\!60$$$$T^{49} +$$$$48\!\cdots\!59$$$$T^{50} -$$$$13\!\cdots\!80$$$$T^{51} +$$$$54\!\cdots\!66$$$$T^{52} -$$$$13\!\cdots\!80$$$$p T^{53} +$$$$48\!\cdots\!59$$$$p^{2} T^{54} -$$$$11\!\cdots\!60$$$$p^{3} T^{55} +$$$$41\!\cdots\!32$$$$p^{4} T^{56} -$$$$98\!\cdots\!15$$$$p^{5} T^{57} +$$$$34\!\cdots\!68$$$$p^{6} T^{58} -$$$$72\!\cdots\!57$$$$p^{8} T^{59} +$$$$24\!\cdots\!68$$$$p^{9} T^{60} -$$$$62\!\cdots\!93$$$$p^{9} T^{61} +$$$$20\!\cdots\!69$$$$p^{10} T^{62} -$$$$42\!\cdots\!15$$$$p^{12} T^{63} +$$$$15\!\cdots\!98$$$$p^{12} T^{64} -$$$$33\!\cdots\!56$$$$p^{13} T^{65} +$$$$10\!\cdots\!35$$$$p^{14} T^{66} -$$$$23\!\cdots\!50$$$$p^{15} T^{67} +$$$$72\!\cdots\!63$$$$p^{16} T^{68} -$$$$15\!\cdots\!64$$$$p^{17} T^{69} +$$$$46\!\cdots\!98$$$$p^{18} T^{70} -$$$$96\!\cdots\!74$$$$p^{19} T^{71} +$$$$28\!\cdots\!45$$$$p^{20} T^{72} -$$$$57\!\cdots\!69$$$$p^{21} T^{73} +$$$$16\!\cdots\!59$$$$p^{22} T^{74} -$$$$32\!\cdots\!18$$$$p^{23} T^{75} +$$$$81\!\cdots\!64$$$$p^{25} T^{76} -$$$$17\!\cdots\!77$$$$p^{25} T^{77} +$$$$46\!\cdots\!26$$$$p^{26} T^{78} - 7144744646058630341 p^{29} T^{79} +$$$$22\!\cdots\!91$$$$p^{28} T^{80} - 40267719675617306988 p^{29} T^{81} + 10039632711654150695 p^{30} T^{82} - 1737715024143332315 p^{31} T^{83} + 416224901301613443 p^{32} T^{84} - 6264335753542365 p^{34} T^{85} + 15808108669807467 p^{34} T^{86} - 2485616013031490 p^{35} T^{87} + 49467681613622 p^{37} T^{88} - 80533390429232 p^{37} T^{89} + 16748935115435 p^{38} T^{90} - 2305926738602 p^{39} T^{91} + 453120573970 p^{40} T^{92} - 57116046661 p^{41} T^{93} + 10532892423 p^{42} T^{94} - 1188548926 p^{43} T^{95} + 18542397 p^{45} T^{96} - 19920437 p^{45} T^{97} + 3147322 p^{46} T^{98} - 251689 p^{47} T^{99} + 36107 p^{48} T^{100} - 2127 p^{49} T^{101} + 272 p^{50} T^{102} - 9 p^{51} T^{103} + p^{52} T^{104}$$
13 $$1 - 44 T + 1242 T^{2} - 26202 T^{3} + 457248 T^{4} - 6878050 T^{5} + 92021446 T^{6} - 1115769295 T^{7} + 12444211515 T^{8} - 129016033794 T^{9} + 1254091267089 T^{10} - 11505733140923 T^{11} + 100187109962463 T^{12} - 831751689249807 T^{13} + 6609065276959875 T^{14} - 50427887798610461 T^{15} + 370524095942869358 T^{16} - 2628095522262293497 T^{17} + 18033497372935269565 T^{18} - 9225964313833607917 p T^{19} +$$$$77\!\cdots\!69$$$$T^{20} -$$$$48\!\cdots\!39$$$$T^{21} +$$$$29\!\cdots\!28$$$$T^{22} -$$$$17\!\cdots\!22$$$$T^{23} +$$$$10\!\cdots\!61$$$$T^{24} -$$$$58\!\cdots\!06$$$$T^{25} +$$$$32\!\cdots\!20$$$$T^{26} -$$$$17\!\cdots\!86$$$$T^{27} +$$$$94\!\cdots\!50$$$$T^{28} -$$$$49\!\cdots\!72$$$$T^{29} +$$$$25\!\cdots\!28$$$$T^{30} -$$$$12\!\cdots\!98$$$$T^{31} +$$$$62\!\cdots\!64$$$$T^{32} -$$$$30\!\cdots\!78$$$$T^{33} +$$$$14\!\cdots\!93$$$$T^{34} -$$$$66\!\cdots\!68$$$$T^{35} +$$$$30\!\cdots\!91$$$$T^{36} -$$$$13\!\cdots\!13$$$$T^{37} +$$$$61\!\cdots\!06$$$$T^{38} -$$$$27\!\cdots\!46$$$$T^{39} +$$$$11\!\cdots\!66$$$$T^{40} -$$$$49\!\cdots\!03$$$$T^{41} +$$$$20\!\cdots\!20$$$$T^{42} -$$$$85\!\cdots\!44$$$$T^{43} +$$$$34\!\cdots\!83$$$$T^{44} -$$$$13\!\cdots\!88$$$$T^{45} +$$$$54\!\cdots\!64$$$$T^{46} -$$$$21\!\cdots\!66$$$$T^{47} +$$$$81\!\cdots\!95$$$$T^{48} -$$$$31\!\cdots\!82$$$$T^{49} +$$$$11\!\cdots\!36$$$$T^{50} -$$$$42\!\cdots\!55$$$$T^{51} +$$$$15\!\cdots\!60$$$$T^{52} -$$$$42\!\cdots\!55$$$$p T^{53} +$$$$11\!\cdots\!36$$$$p^{2} T^{54} -$$$$31\!\cdots\!82$$$$p^{3} T^{55} +$$$$81\!\cdots\!95$$$$p^{4} T^{56} -$$$$21\!\cdots\!66$$$$p^{5} T^{57} +$$$$54\!\cdots\!64$$$$p^{6} T^{58} -$$$$13\!\cdots\!88$$$$p^{7} T^{59} +$$$$34\!\cdots\!83$$$$p^{8} T^{60} -$$$$85\!\cdots\!44$$$$p^{9} T^{61} +$$$$20\!\cdots\!20$$$$p^{10} T^{62} -$$$$49\!\cdots\!03$$$$p^{11} T^{63} +$$$$11\!\cdots\!66$$$$p^{12} T^{64} -$$$$27\!\cdots\!46$$$$p^{13} T^{65} +$$$$61\!\cdots\!06$$$$p^{14} T^{66} -$$$$13\!\cdots\!13$$$$p^{15} T^{67} +$$$$30\!\cdots\!91$$$$p^{16} T^{68} -$$$$66\!\cdots\!68$$$$p^{17} T^{69} +$$$$14\!\cdots\!93$$$$p^{18} T^{70} -$$$$30\!\cdots\!78$$$$p^{19} T^{71} +$$$$62\!\cdots\!64$$$$p^{20} T^{72} -$$$$12\!\cdots\!98$$$$p^{21} T^{73} +$$$$25\!\cdots\!28$$$$p^{22} T^{74} -$$$$49\!\cdots\!72$$$$p^{23} T^{75} +$$$$94\!\cdots\!50$$$$p^{24} T^{76} -$$$$17\!\cdots\!86$$$$p^{25} T^{77} +$$$$32\!\cdots\!20$$$$p^{26} T^{78} -$$$$58\!\cdots\!06$$$$p^{27} T^{79} +$$$$10\!\cdots\!61$$$$p^{28} T^{80} -$$$$17\!\cdots\!22$$$$p^{29} T^{81} +$$$$29\!\cdots\!28$$$$p^{30} T^{82} -$$$$48\!\cdots\!39$$$$p^{31} T^{83} +$$$$77\!\cdots\!69$$$$p^{32} T^{84} - 9225964313833607917 p^{34} T^{85} + 18033497372935269565 p^{34} T^{86} - 2628095522262293497 p^{35} T^{87} + 370524095942869358 p^{36} T^{88} - 50427887798610461 p^{37} T^{89} + 6609065276959875 p^{38} T^{90} - 831751689249807 p^{39} T^{91} + 100187109962463 p^{40} T^{92} - 11505733140923 p^{41} T^{93} + 1254091267089 p^{42} T^{94} - 129016033794 p^{43} T^{95} + 12444211515 p^{44} T^{96} - 1115769295 p^{45} T^{97} + 92021446 p^{46} T^{98} - 6878050 p^{47} T^{99} + 457248 p^{48} T^{100} - 26202 p^{49} T^{101} + 1242 p^{50} T^{102} - 44 p^{51} T^{103} + p^{52} T^{104}$$
17 $$1 + 6 T + 414 T^{2} + 2392 T^{3} + 85223 T^{4} + 477749 T^{5} + 11658353 T^{6} + 63826060 T^{7} + 1194955907 T^{8} + 6424204438 T^{9} + 98087136938 T^{10} + 520129423723 T^{11} + 6728882058948 T^{12} + 35312416523488 T^{13} + 397444177438614 T^{14} + 2068886517528783 T^{15} + 20661038855175961 T^{16} + 106819191958294620 T^{17} + 961335236810144101 T^{18} + 290498522574706415 p T^{19} + 40567451037550133840 T^{20} + 12177159585715639704 p T^{21} +$$$$15\!\cdots\!77$$$$T^{22} +$$$$79\!\cdots\!44$$$$T^{23} +$$$$32\!\cdots\!12$$$$p T^{24} +$$$$28\!\cdots\!26$$$$T^{25} +$$$$18\!\cdots\!82$$$$T^{26} +$$$$92\!\cdots\!09$$$$T^{27} +$$$$58\!\cdots\!78$$$$T^{28} +$$$$28\!\cdots\!56$$$$T^{29} +$$$$17\!\cdots\!22$$$$T^{30} +$$$$82\!\cdots\!67$$$$T^{31} +$$$$47\!\cdots\!75$$$$T^{32} +$$$$22\!\cdots\!13$$$$T^{33} +$$$$12\!\cdots\!38$$$$T^{34} +$$$$58\!\cdots\!82$$$$T^{35} +$$$$30\!\cdots\!16$$$$T^{36} +$$$$14\!\cdots\!91$$$$T^{37} +$$$$72\!\cdots\!64$$$$T^{38} +$$$$33\!\cdots\!29$$$$T^{39} +$$$$16\!\cdots\!45$$$$T^{40} +$$$$73\!\cdots\!93$$$$T^{41} +$$$$35\!\cdots\!53$$$$T^{42} +$$$$15\!\cdots\!03$$$$T^{43} +$$$$73\!\cdots\!42$$$$T^{44} +$$$$31\!\cdots\!81$$$$T^{45} +$$$$14\!\cdots\!07$$$$T^{46} +$$$$61\!\cdots\!13$$$$T^{47} +$$$$27\!\cdots\!51$$$$T^{48} +$$$$11\!\cdots\!00$$$$T^{49} +$$$$49\!\cdots\!37$$$$T^{50} +$$$$20\!\cdots\!03$$$$T^{51} +$$$$85\!\cdots\!94$$$$T^{52} +$$$$20\!\cdots\!03$$$$p T^{53} +$$$$49\!\cdots\!37$$$$p^{2} T^{54} +$$$$11\!\cdots\!00$$$$p^{3} T^{55} +$$$$27\!\cdots\!51$$$$p^{4} T^{56} +$$$$61\!\cdots\!13$$$$p^{5} T^{57} +$$$$14\!\cdots\!07$$$$p^{6} T^{58} +$$$$31\!\cdots\!81$$$$p^{7} T^{59} +$$$$73\!\cdots\!42$$$$p^{8} T^{60} +$$$$15\!\cdots\!03$$$$p^{9} T^{61} +$$$$35\!\cdots\!53$$$$p^{10} T^{62} +$$$$73\!\cdots\!93$$$$p^{11} T^{63} +$$$$16\!\cdots\!45$$$$p^{12} T^{64} +$$$$33\!\cdots\!29$$$$p^{13} T^{65} +$$$$72\!\cdots\!64$$$$p^{14} T^{66} +$$$$14\!\cdots\!91$$$$p^{15} T^{67} +$$$$30\!\cdots\!16$$$$p^{16} T^{68} +$$$$58\!\cdots\!82$$$$p^{17} T^{69} +$$$$12\!\cdots\!38$$$$p^{18} T^{70} +$$$$22\!\cdots\!13$$$$p^{19} T^{71} +$$$$47\!\cdots\!75$$$$p^{20} T^{72} +$$$$82\!\cdots\!67$$$$p^{21} T^{73} +$$$$17\!\cdots\!22$$$$p^{22} T^{74} +$$$$28\!\cdots\!56$$$$p^{23} T^{75} +$$$$58\!\cdots\!78$$$$p^{24} T^{76} +$$$$92\!\cdots\!09$$$$p^{25} T^{77} +$$$$18\!\cdots\!82$$$$p^{26} T^{78} +$$$$28\!\cdots\!26$$$$p^{27} T^{79} +$$$$32\!\cdots\!12$$$$p^{29} T^{80} +$$$$79\!\cdots\!44$$$$p^{29} T^{81} +$$$$15\!\cdots\!77$$$$p^{30} T^{82} + 12177159585715639704 p^{32} T^{83} + 40567451037550133840 p^{32} T^{84} + 290498522574706415 p^{34} T^{85} + 961335236810144101 p^{34} T^{86} + 106819191958294620 p^{35} T^{87} + 20661038855175961 p^{36} T^{88} + 2068886517528783 p^{37} T^{89} + 397444177438614 p^{38} T^{90} + 35312416523488 p^{39} T^{91} + 6728882058948 p^{40} T^{92} + 520129423723 p^{41} T^{93} + 98087136938 p^{42} T^{94} + 6424204438 p^{43} T^{95} + 1194955907 p^{44} T^{96} + 63826060 p^{45} T^{97} + 11658353 p^{46} T^{98} + 477749 p^{47} T^{99} + 85223 p^{48} T^{100} + 2392 p^{49} T^{101} + 414 p^{50} T^{102} + 6 p^{51} T^{103} + p^{52} T^{104}$$
19 $$1 - 7 T + 452 T^{2} - 2998 T^{3} + 102268 T^{4} - 645059 T^{5} + 15462339 T^{6} - 93047703 T^{7} + 1759284433 T^{8} - 10129352018 T^{9} + 160805189034 T^{10} - 888072648668 T^{11} + 12307172320323 T^{12} - 65334662335047 T^{13} + 811569143111740 T^{14} - 4148902250776685 T^{15} + 47082781785604557 T^{16} - 232132663229163386 T^{17} + 2441449609262768750 T^{18} - 11622552972665225395 T^{19} +$$$$11\!\cdots\!08$$$$T^{20} -$$$$52\!\cdots\!67$$$$T^{21} +$$$$49\!\cdots\!87$$$$T^{22} -$$$$21\!\cdots\!34$$$$T^{23} +$$$$19\!\cdots\!16$$$$T^{24} -$$$$83\!\cdots\!90$$$$T^{25} +$$$$71\!\cdots\!40$$$$T^{26} -$$$$29\!\cdots\!68$$$$T^{27} +$$$$24\!\cdots\!59$$$$T^{28} -$$$$98\!\cdots\!06$$$$T^{29} +$$$$78\!\cdots\!90$$$$T^{30} -$$$$30\!\cdots\!17$$$$T^{31} +$$$$23\!\cdots\!25$$$$T^{32} -$$$$89\!\cdots\!46$$$$T^{33} +$$$$67\!\cdots\!97$$$$T^{34} -$$$$24\!\cdots\!36$$$$T^{35} +$$$$18\!\cdots\!51$$$$T^{36} -$$$$64\!\cdots\!29$$$$T^{37} +$$$$46\!\cdots\!98$$$$T^{38} -$$$$16\!\cdots\!28$$$$T^{39} +$$$$11\!\cdots\!39$$$$T^{40} -$$$$38\!\cdots\!67$$$$T^{41} +$$$$27\!\cdots\!28$$$$T^{42} -$$$$87\!\cdots\!52$$$$T^{43} +$$$$61\!\cdots\!78$$$$T^{44} -$$$$19\!\cdots\!91$$$$T^{45} +$$$$13\!\cdots\!04$$$$T^{46} -$$$$40\!\cdots\!73$$$$T^{47} +$$$$27\!\cdots\!93$$$$T^{48} -$$$$82\!\cdots\!18$$$$T^{49} +$$$$55\!\cdots\!29$$$$T^{50} -$$$$16\!\cdots\!30$$$$T^{51} +$$$$10\!\cdots\!62$$$$T^{52} -$$$$16\!\cdots\!30$$$$p T^{53} +$$$$55\!\cdots\!29$$$$p^{2} T^{54} -$$$$82\!\cdots\!18$$$$p^{3} T^{55} +$$$$27\!\cdots\!93$$$$p^{4} T^{56} -$$$$40\!\cdots\!73$$$$p^{5} T^{57} +$$$$13\!\cdots\!04$$$$p^{6} T^{58} -$$$$19\!\cdots\!91$$$$p^{7} T^{59} +$$$$61\!\cdots\!78$$$$p^{8} T^{60} -$$$$87\!\cdots\!52$$$$p^{9} T^{61} +$$$$27\!\cdots\!28$$$$p^{10} T^{62} -$$$$38\!\cdots\!67$$$$p^{11} T^{63} +$$$$11\!\cdots\!39$$$$p^{12} T^{64} -$$$$16\!\cdots\!28$$$$p^{13} T^{65} +$$$$46\!\cdots\!98$$$$p^{14} T^{66} -$$$$64\!\cdots\!29$$$$p^{15} T^{67} +$$$$18\!\cdots\!51$$$$p^{16} T^{68} -$$$$24\!\cdots\!36$$$$p^{17} T^{69} +$$$$67\!\cdots\!97$$$$p^{18} T^{70} -$$$$89\!\cdots\!46$$$$p^{19} T^{71} +$$$$23\!\cdots\!25$$$$p^{20} T^{72} -$$$$30\!\cdots\!17$$$$p^{21} T^{73} +$$$$78\!\cdots\!90$$$$p^{22} T^{74} -$$$$98\!\cdots\!06$$$$p^{23} T^{75} +$$$$24\!\cdots\!59$$$$p^{24} T^{76} -$$$$29\!\cdots\!68$$$$p^{25} T^{77} +$$$$71\!\cdots\!40$$$$p^{26} T^{78} -$$$$83\!\cdots\!90$$$$p^{27} T^{79} +$$$$19\!\cdots\!16$$$$p^{28} T^{80} -$$$$21\!\cdots\!34$$$$p^{29} T^{81} +$$$$49\!\cdots\!87$$$$p^{30} T^{82} -$$$$52\!\cdots\!67$$$$p^{31} T^{83} +$$$$11\!\cdots\!08$$$$p^{32} T^{84} - 11622552972665225395 p^{33} T^{85} + 2441449609262768750 p^{34} T^{86} - 232132663229163386 p^{35} T^{87} + 47082781785604557 p^{36} T^{88} - 4148902250776685 p^{37} T^{89} + 811569143111740 p^{38} T^{90} - 65334662335047 p^{39} T^{91} + 12307172320323 p^{40} T^{92} - 888072648668 p^{41} T^{93} + 160805189034 p^{42} T^{94} - 10129352018 p^{43} T^{95} + 1759284433 p^{44} T^{96} - 93047703 p^{45} T^{97} + 15462339 p^{46} T^{98} - 645059 p^{47} T^{99} + 102268 p^{48} T^{100} - 2998 p^{49} T^{101} + 452 p^{50} T^{102} - 7 p^{51} T^{103} + p^{52} T^{104}$$
23 $$1 + 4 T + 491 T^{2} + 71 p T^{3} + 122279 T^{4} + 341865 T^{5} + 20661000 T^{6} + 49016087 T^{7} + 2667121506 T^{8} + 5420739399 T^{9} + 280505383378 T^{10} + 933230876 p^{2} T^{11} + 1087614116489 p T^{12} + 38603206989552 T^{13} + 1943468719693726 T^{14} + 2667992781849177 T^{15} + 134123286388937193 T^{16} + 166455349630022514 T^{17} + 8342821454168002464 T^{18} + 9522566107808230007 T^{19} +$$$$47\!\cdots\!47$$$$T^{20} +$$$$50\!\cdots\!66$$$$T^{21} +$$$$24\!\cdots\!94$$$$T^{22} +$$$$25\!\cdots\!31$$$$T^{23} +$$$$11\!\cdots\!50$$$$T^{24} +$$$$11\!\cdots\!99$$$$T^{25} +$$$$53\!\cdots\!37$$$$T^{26} +$$$$51\!\cdots\!57$$$$T^{27} +$$$$22\!\cdots\!63$$$$T^{28} +$$$$21\!\cdots\!33$$$$T^{29} +$$$$90\!\cdots\!63$$$$T^{30} +$$$$84\!\cdots\!63$$$$T^{31} +$$$$33\!\cdots\!14$$$$T^{32} +$$$$31\!\cdots\!10$$$$T^{33} +$$$$11\!\cdots\!37$$$$T^{34} +$$$$11\!\cdots\!06$$$$T^{35} +$$$$17\!\cdots\!71$$$$p T^{36} +$$$$38\!\cdots\!34$$$$T^{37} +$$$$12\!\cdots\!22$$$$T^{38} +$$$$12\!\cdots\!99$$$$T^{39} +$$$$39\!\cdots\!53$$$$T^{40} +$$$$37\!\cdots\!32$$$$T^{41} +$$$$11\!\cdots\!75$$$$T^{42} +$$$$11\!\cdots\!97$$$$T^{43} +$$$$32\!\cdots\!30$$$$T^{44} +$$$$30\!\cdots\!41$$$$T^{45} +$$$$86\!\cdots\!65$$$$T^{46} +$$$$81\!\cdots\!82$$$$T^{47} +$$$$22\!\cdots\!55$$$$T^{48} +$$$$20\!\cdots\!69$$$$T^{49} +$$$$54\!\cdots\!20$$$$T^{50} +$$$$49\!\cdots\!35$$$$T^{51} +$$$$12\!\cdots\!54$$$$T^{52} +$$$$49\!\cdots\!35$$$$p T^{53} +$$$$54\!\cdots\!20$$$$p^{2} T^{54} +$$$$20\!\cdots\!69$$$$p^{3} T^{55} +$$$$22\!\cdots\!55$$$$p^{4} T^{56} +$$$$81\!\cdots\!82$$$$p^{5} T^{57} +$$$$86\!\cdots\!65$$$$p^{6} T^{58} +$$$$30\!\cdots\!41$$$$p^{7} T^{59} +$$$$32\!\cdots\!30$$$$p^{8} T^{60} +$$$$11\!\cdots\!97$$$$p^{9} T^{61} +$$$$11\!\cdots\!75$$$$p^{10} T^{62} +$$$$37\!\cdots\!32$$$$p^{11} T^{63} +$$$$39\!\cdots\!53$$$$p^{12} T^{64} +$$$$12\!\cdots\!99$$$$p^{13} T^{65} +$$$$12\!\cdots\!22$$$$p^{14} T^{66} +$$$$38\!\cdots\!34$$$$p^{15} T^{67} +$$$$17\!\cdots\!71$$$$p^{17} T^{68} +$$$$11\!\cdots\!06$$$$p^{17} T^{69} +$$$$11\!\cdots\!37$$$$p^{18} T^{70} +$$$$31\!\cdots\!10$$$$p^{19} T^{71} +$$$$33\!\cdots\!14$$$$p^{20} T^{72} +$$$$84\!\cdots\!63$$$$p^{21} T^{73} +$$$$90\!\cdots\!63$$$$p^{22} T^{74} +$$$$21\!\cdots\!33$$$$p^{23} T^{75} +$$$$22\!\cdots\!63$$$$p^{24} T^{76} +$$$$51\!\cdots\!57$$$$p^{25} T^{77} +$$$$53\!\cdots\!37$$$$p^{26} T^{78} +$$$$11\!\cdots\!99$$$$p^{27} T^{79} +$$$$11\!\cdots\!50$$$$p^{28} T^{80} +$$$$25\!\cdots\!31$$$$p^{29} T^{81} +$$$$24\!\cdots\!94$$$$p^{30} T^{82} +$$$$50\!\cdots\!66$$$$p^{31} T^{83} +$$$$47\!\cdots\!47$$$$p^{32} T^{84} + 9522566107808230007 p^{33} T^{85} + 8342821454168002464 p^{34} T^{86} + 166455349630022514 p^{35} T^{87} + 134123286388937193 p^{36} T^{88} + 2667992781849177 p^{37} T^{89} + 1943468719693726 p^{38} T^{90} + 38603206989552 p^{39} T^{91} + 1087614116489 p^{41} T^{92} + 933230876 p^{43} T^{93} + 280505383378 p^{42} T^{94} + 5420739399 p^{43} T^{95} + 2667121506 p^{44} T^{96} + 49016087 p^{45} T^{97} + 20661000 p^{46} T^{98} + 341865 p^{47} T^{99} + 122279 p^{48} T^{100} + 71 p^{50} T^{101} + 491 p^{50} T^{102} + 4 p^{51} T^{103} + p^{52} T^{104}$$
29 $$1 - 31 T + 1196 T^{2} - 27242 T^{3} + 640424 T^{4} - 11806584 T^{5} + 214207364 T^{6} - 3368916074 T^{7} + 51413346879 T^{8} - 712687200082 T^{9} + 9553764190043 T^{10} - 4114436803877 p T^{11} + 1441669974545738 T^{12} - 16478789167590758 T^{13} + 182541212903466146 T^{14} - 1932110945294116052 T^{15} + 19861041333865595085 T^{16} -$$$$19\!\cdots\!76$$$$T^{17} +$$$$18\!\cdots\!07$$$$T^{18} -$$$$17\!\cdots\!24$$$$T^{19} +$$$$15\!\cdots\!83$$$$T^{20} -$$$$14\!\cdots\!63$$$$T^{21} +$$$$12\!\cdots\!67$$$$T^{22} -$$$$10\!\cdots\!04$$$$T^{23} +$$$$83\!\cdots\!94$$$$T^{24} -$$$$66\!\cdots\!26$$$$T^{25} +$$$$52\!\cdots\!79$$$$T^{26} -$$$$40\!\cdots\!48$$$$T^{27} +$$$$30\!\cdots\!56$$$$T^{28} -$$$$22\!\cdots\!89$$$$T^{29} +$$$$56\!\cdots\!36$$$$p T^{30} -$$$$11\!\cdots\!71$$$$T^{31} +$$$$81\!\cdots\!59$$$$T^{32} -$$$$56\!\cdots\!88$$$$T^{33} +$$$$38\!\cdots\!55$$$$T^{34} -$$$$25\!\cdots\!72$$$$T^{35} +$$$$16\!\cdots\!36$$$$T^{36} -$$$$10\!\cdots\!80$$$$T^{37} +$$$$69\!\cdots\!11$$$$T^{38} -$$$$44\!\cdots\!91$$$$T^{39} +$$$$27\!\cdots\!27$$$$T^{40} -$$$$16\!\cdots\!17$$$$T^{41} +$$$$10\!\cdots\!73$$$$T^{42} -$$$$61\!\cdots\!30$$$$T^{43} +$$$$36\!\cdots\!06$$$$T^{44} -$$$$21\!\cdots\!94$$$$T^{45} +$$$$12\!\cdots\!79$$$$T^{46} -$$$$71\!\cdots\!80$$$$T^{47} +$$$$40\!\cdots\!59$$$$T^{48} -$$$$22\!\cdots\!84$$$$T^{49} +$$$$12\!\cdots\!84$$$$T^{50} -$$$$68\!\cdots\!63$$$$T^{51} +$$$$37\!\cdots\!70$$$$T^{52} -$$$$68\!\cdots\!63$$$$p T^{53} +$$$$12\!\cdots\!84$$$$p^{2} T^{54} -$$$$22\!\cdots\!84$$$$p^{3} T^{55} +$$$$40\!\cdots\!59$$$$p^{4} T^{56} -$$$$71\!\cdots\!80$$$$p^{5} T^{57} +$$$$12\!\cdots\!79$$$$p^{6} T^{58} -$$$$21\!\cdots\!94$$$$p^{7} T^{59} +$$$$36\!\cdots\!06$$$$p^{8} T^{60} -$$$$61\!\cdots\!30$$$$p^{9} T^{61} +$$$$10\!\cdots\!73$$$$p^{10} T^{62} -$$$$16\!\cdots\!17$$$$p^{11} T^{63} +$$$$27\!\cdots\!27$$$$p^{12} T^{64} -$$$$44\!\cdots\!91$$$$p^{13} T^{65} +$$$$69\!\cdots\!11$$$$p^{14} T^{66} -$$$$10\!\cdots\!80$$$$p^{15} T^{67} +$$$$16\!\cdots\!36$$$$p^{16} T^{68} -$$$$25\!\cdots\!72$$$$p^{17} T^{69} +$$$$38\!\cdots\!55$$$$p^{18} T^{70} -$$$$56\!\cdots\!88$$$$p^{19} T^{71} +$$$$81\!\cdots\!59$$$$p^{20} T^{72} -$$$$11\!\cdots\!71$$$$p^{21} T^{73} +$$$$56\!\cdots\!36$$$$p^{23} T^{74} -$$$$22\!\cdots\!89$$$$p^{23} T^{75} +$$$$30\!\cdots\!56$$$$p^{24} T^{76} -$$$$40\!\cdots\!48$$$$p^{25} T^{77} +$$$$52\!\cdots\!79$$$$p^{26} T^{78} -$$$$66\!\cdots\!26$$$$p^{27} T^{79} +$$$$83\!\cdots\!94$$$$p^{28} T^{80} -$$$$10\!\cdots\!04$$$$p^{29} T^{81} +$$$$12\!\cdots\!67$$$$p^{30} T^{82} -$$$$14\!\cdots\!63$$$$p^{31} T^{83} +$$$$15\!\cdots\!83$$$$p^{32} T^{84} -$$$$17\!\cdots\!24$$$$p^{33} T^{85} +$$$$18\!\cdots\!07$$$$p^{34} T^{86} -$$$$19\!\cdots\!76$$$$p^{35} T^{87} + 19861041333865595085 p^{36} T^{88} - 1932110945294116052 p^{37} T^{89} + 182541212903466146 p^{38} T^{90} - 16478789167590758 p^{39} T^{91} + 1441669974545738 p^{40} T^{92} - 4114436803877 p^{42} T^{93} + 9553764190043 p^{42} T^{94} - 712687200082 p^{43} T^{95} + 51413346879 p^{44} T^{96} - 3368916074 p^{45} T^{97} + 214207364 p^{46} T^{98} - 11806584 p^{47} T^{99} + 640424 p^{48} T^{100} - 27242 p^{49} T^{101} + 1196 p^{50} T^{102} - 31 p^{51} T^{103} + p^{52} T^{104}$$
31 $$1 - 11 T + 849 T^{2} - 9479 T^{3} + 366844 T^{4} - 4090542 T^{5} + 107277051 T^{6} - 1180010987 T^{7} + 23819492480 T^{8} - 256160308735 T^{9} + 4272275582350 T^{10} - 44647543986430 T^{11} + 643317337293813 T^{12} - 6508078179582989 T^{13} + 83488271874534422 T^{14} - 815823170382756959 T^{15} + 9517285823784961859 T^{16} - 89742064963225611783 T^{17} +$$$$96\!\cdots\!25$$$$T^{18} -$$$$87\!\cdots\!65$$$$T^{19} +$$$$88\!\cdots\!34$$$$T^{20} -$$$$77\!\cdots\!33$$$$T^{21} +$$$$73\!\cdots\!32$$$$T^{22} -$$$$62\!\cdots\!16$$$$T^{23} +$$$$18\!\cdots\!67$$$$p T^{24} -$$$$46\!\cdots\!83$$$$T^{25} +$$$$39\!\cdots\!15$$$$T^{26} -$$$$31\!\cdots\!00$$$$T^{27} +$$$$25\!\cdots\!26$$$$T^{28} -$$$$19\!\cdots\!28$$$$T^{29} +$$$$15\!\cdots\!04$$$$T^{30} -$$$$11\!\cdots\!77$$$$T^{31} +$$$$88\!\cdots\!83$$$$T^{32} -$$$$63\!\cdots\!92$$$$T^{33} +$$$$46\!\cdots\!41$$$$T^{34} -$$$$32\!\cdots\!28$$$$T^{35} +$$$$23\!\cdots\!39$$$$T^{36} -$$$$15\!\cdots\!01$$$$T^{37} +$$$$10\!\cdots\!13$$$$T^{38} -$$$$72\!\cdots\!76$$$$T^{39} +$$$$48\!\cdots\!34$$$$T^{40} -$$$$10\!\cdots\!62$$$$p T^{41} +$$$$20\!\cdots\!52$$$$T^{42} -$$$$12\!\cdots\!60$$$$T^{43} +$$$$79\!\cdots\!49$$$$T^{44} -$$$$48\!\cdots\!29$$$$T^{45} +$$$$29\!\cdots\!09$$$$T^{46} -$$$$17\!\cdots\!36$$$$T^{47} +$$$$10\!\cdots\!30$$$$T^{48} -$$$$61\!\cdots\!97$$$$T^{49} +$$$$35\!\cdots\!25$$$$T^{50} -$$$$19\!\cdots\!32$$$$T^{51} +$$$$11\!\cdots\!66$$$$T^{52} -$$$$19\!\cdots\!32$$$$p T^{53} +$$$$35\!\cdots\!25$$$$p^{2} T^{54} -$$$$61\!\cdots\!97$$$$p^{3} T^{55} +$$$$10\!\cdots\!30$$$$p^{4} T^{56} -$$$$17\!\cdots\!36$$$$p^{5} T^{57} +$$$$29\!\cdots\!09$$$$p^{6} T^{58} -$$$$48\!\cdots\!29$$$$p^{7} T^{59} +$$$$79\!\cdots\!49$$$$p^{8} T^{60} -$$$$12\!\cdots\!60$$$$p^{9} T^{61} +$$$$20\!\cdots\!52$$$$p^{10} T^{62} -$$$$10\!\cdots\!62$$$$p^{12} T^{63} +$$$$48\!\cdots\!34$$$$p^{12} T^{64} -$$$$72\!\cdots\!76$$$$p^{13} T^{65} +$$$$10\!\cdots\!13$$$$p^{14} T^{66} -$$$$15\!\cdots\!01$$$$p^{15} T^{67} +$$$$23\!\cdots\!39$$$$p^{16} T^{68} -$$$$32\!\cdots\!28$$$$p^{17} T^{69} +$$$$46\!\cdots\!41$$$$p^{18} T^{70} -$$$$63\!\cdots\!92$$$$p^{19} T^{71} +$$$$88\!\cdots\!83$$$$p^{20} T^{72} -$$$$11\!\cdots\!77$$$$p^{21} T^{73} +$$$$15\!\cdots\!04$$$$p^{22} T^{74} -$$$$19\!\cdots\!28$$$$p^{23} T^{75} +$$$$25\!\cdots\!26$$$$p^{24} T^{76} -$$$$31\!\cdots\!00$$$$p^{25} T^{77} +$$$$39\!\cdots\!15$$$$p^{26} T^{78} -$$$$46\!\cdots\!83$$$$p^{27} T^{79} +$$$$18\!\cdots\!67$$$$p^{29} T^{80} -$$$$62\!\cdots\!16$$$$p^{29} T^{81} +$$$$73\!\cdots\!32$$$$p^{30} T^{82} -$$$$77\!\cdots\!33$$$$p^{31} T^{83} +$$$$88\!\cdots\!34$$$$p^{32} T^{84} -$$$$87\!\cdots\!65$$$$p^{33} T^{85} +$$$$96\!\cdots\!25$$$$p^{34} T^{86} - 89742064963225611783 p^{35} T^{87} + 9517285823784961859 p^{36} T^{88} - 815823170382756959 p^{37} T^{89} + 83488271874534422 p^{38} T^{90} - 6508078179582989 p^{39} T^{91} + 643317337293813 p^{40} T^{92} - 44647543986430 p^{41} T^{93} + 4272275582350 p^{42} T^{94} - 256160308735 p^{43} T^{95} + 23819492480 p^{44} T^{96} - 1180010987 p^{45} T^{97} + 107277051 p^{46} T^{98} - 4090542 p^{47} T^{99} + 366844 p^{48} T^{100} - 9479 p^{49} T^{101} + 849 p^{50} T^{102} - 11 p^{51} T^{103} + p^{52} T^{104}$$
37 $$1 - 71 T + 3384 T^{2} - 120672 T^{3} + 3591511 T^{4} - 92302266 T^{5} + 2116547624 T^{6} - 44029508046 T^{7} + 843548484385 T^{8} - 15029100201456 T^{9} + 251152778762591 T^{10} - 3961344524026601 T^{11} + 59298056669030898 T^{12} - 22867163446333910 p T^{13} + 11551171246552891663 T^{14} -$$$$15\!\cdots\!82$$$$T^{15} +$$$$19\!\cdots\!14$$$$T^{16} -$$$$23\!\cdots\!76$$$$T^{17} +$$$$27\!\cdots\!38$$$$T^{18} -$$$$31\!\cdots\!69$$$$T^{19} +$$$$34\!\cdots\!05$$$$T^{20} -$$$$37\!\cdots\!83$$$$T^{21} +$$$$38\!\cdots\!57$$$$T^{22} -$$$$39\!\cdots\!95$$$$T^{23} +$$$$39\!\cdots\!85$$$$T^{24} -$$$$38\!\cdots\!47$$$$T^{25} +$$$$36\!\cdots\!23$$$$T^{26} -$$$$33\!\cdots\!20$$$$T^{27} +$$$$30\!\cdots\!47$$$$T^{28} -$$$$27\!\cdots\!28$$$$T^{29} +$$$$23\!\cdots\!86$$$$T^{30} -$$$$20\!\cdots\!21$$$$T^{31} +$$$$16\!\cdots\!08$$$$T^{32} -$$$$13\!\cdots\!33$$$$T^{33} +$$$$11\!\cdots\!69$$$$T^{34} -$$$$24\!\cdots\!91$$$$p T^{35} +$$$$69\!\cdots\!53$$$$T^{36} -$$$$53\!\cdots\!29$$$$T^{37} +$$$$40\!\cdots\!59$$$$T^{38} -$$$$30\!\cdots\!54$$$$T^{39} +$$$$21\!\cdots\!30$$$$T^{40} -$$$$15\!\cdots\!55$$$$T^{41} +$$$$11\!\cdots\!29$$$$T^{42} -$$$$78\!\cdots\!73$$$$T^{43} +$$$$53\!\cdots\!43$$$$T^{44} -$$$$36\!\cdots\!84$$$$T^{45} +$$$$24\!\cdots\!92$$$$T^{46} -$$$$16\!\cdots\!55$$$$T^{47} +$$$$10\!\cdots\!97$$$$T^{48} -$$$$66\!\cdots\!73$$$$T^{49} +$$$$41\!\cdots\!41$$$$T^{50} -$$$$26\!\cdots\!94$$$$T^{51} +$$$$15\!\cdots\!86$$$$T^{52} -$$$$26\!\cdots\!94$$$$p T^{53} +$$$$41\!\cdots\!41$$$$p^{2} T^{54} -$$$$66\!\cdots\!73$$$$p^{3} T^{55} +$$$$10\!\cdots\!97$$$$p^{4} T^{56} -$$$$16\!\cdots\!55$$$$p^{5} T^{57} +$$$$24\!\cdots\!92$$$$p^{6} T^{58} -$$$$36\!\cdots\!84$$$$p^{7} T^{59} +$$$$53\!\cdots\!43$$$$p^{8} T^{60} -$$$$78\!\cdots\!73$$$$p^{9} T^{61} +$$$$11\!\cdots\!29$$$$p^{10} T^{62} -$$$$15\!\cdots\!55$$$$p^{11} T^{63} +$$$$21\!\cdots\!30$$$$p^{12} T^{64} -$$$$30\!\cdots\!54$$$$p^{13} T^{65} +$$$$40\!\cdots\!59$$$$p^{14} T^{66} -$$$$53\!\cdots\!29$$$$p^{15} T^{67} +$$$$69\!\cdots\!53$$$$p^{16} T^{68} -$$$$24\!\cdots\!91$$$$p^{18} T^{69} +$$$$11\!\cdots\!69$$$$p^{18} T^{70} -$$$$13\!\cdots\!33$$$$p^{19} T^{71} +$$$$16\!\cdots\!08$$$$p^{20} T^{72} -$$$$20\!\cdots\!21$$$$p^{21} T^{73} +$$$$23\!\cdots\!86$$$$p^{22} T^{74} -$$$$27\!\cdots\!28$$$$p^{23} T^{75} +$$$$30\!\cdots\!47$$$$p^{24} T^{76} -$$$$33\!\cdots\!20$$$$p^{25} T^{77} +$$$$36\!\cdots\!23$$$$p^{26} T^{78} -$$$$38\!\cdots\!47$$$$p^{27} T^{79} +$$$$39\!\cdots\!85$$$$p^{28} T^{80} -$$$$39\!\cdots\!95$$$$p^{29} T^{81} +$$$$38\!\cdots\!57$$$$p^{30} T^{82} -$$$$37\!\cdots\!83$$$$p^{31} T^{83} +$$$$34\!\cdots\!05$$$$p^{32} T^{84} -$$$$31\!\cdots\!69$$$$p^{33} T^{85} +$$$$27\!\cdots\!38$$$$p^{34} T^{86} -$$$$23\!\cdots\!76$$$$p^{35} T^{87} +$$$$19\!\cdots\!14$$$$p^{36} T^{88} -$$$$15\!\cdots\!82$$$$p^{37} T^{89} + 11551171246552891663 p^{38} T^{90} - 22867163446333910 p^{40} T^{91} + 59298056669030898 p^{40} T^{92} - 3961344524026601 p^{41} T^{93} + 251152778762591 p^{42} T^{94} - 15029100201456 p^{43} T^{95} + 843548484385 p^{44} T^{96} - 44029508046 p^{45} T^{97} + 2116547624 p^{46} T^{98} - 92302266 p^{47} T^{99} + 3591511 p^{48} T^{100} - 120672 p^{49} T^{101} + 3384 p^{50} T^{102} - 71 p^{51} T^{103} + p^{52} T^{104}$$
41 $$1 + 25 T + 1404 T^{2} + 29342 T^{3} + 938916 T^{4} + 17036215 T^{5} + 9859628 p T^{6} + 6531807957 T^{7} + 127110244047 T^{8} + 1862380325891 T^{9} + 31308175741476 T^{10} + 421603435697161 T^{11} + 6316814948016862 T^{12} + 79000024806066371 T^{13} + 1076948860515551691 T^{14} + 12612369446659968166 T^{15} +$$$$15\!\cdots\!88$$$$T^{16} +$$$$17\!\cdots\!82$$$$T^{17} +$$$$20\!\cdots\!07$$$$T^{18} +$$$$21\!\cdots\!67$$$$T^{19} +$$$$23\!\cdots\!12$$$$T^{20} +$$$$23\!\cdots\!06$$$$T^{21} +$$$$24\!\cdots\!42$$$$T^{22} +$$$$23\!\cdots\!65$$$$T^{23} +$$$$23\!\cdots\!39$$$$T^{24} +$$$$21\!\cdots\!46$$$$T^{25} +$$$$20\!\cdots\!51$$$$T^{26} +$$$$18\!\cdots\!95$$$$T^{27} +$$$$16\!\cdots\!47$$$$T^{28} +$$$$14\!\cdots\!48$$$$T^{29} +$$$$12\!\cdots\!16$$$$T^{30} +$$$$10\!\cdots\!44$$$$T^{31} +$$$$87\!\cdots\!90$$$$T^{32} +$$$$69\!\cdots\!15$$$$T^{33} +$$$$57\!\cdots\!72$$$$T^{34} +$$$$44\!\cdots\!57$$$$T^{35} +$$$$35\!\cdots\!99$$$$T^{36} +$$$$26\!\cdots\!16$$$$T^{37} +$$$$20\!\cdots\!44$$$$T^{38} +$$$$15\!\cdots\!09$$$$T^{39} +$$$$11\!\cdots\!42$$$$T^{40} +$$$$82\!\cdots\!73$$$$T^{41} +$$$$61\!\cdots\!42$$$$T^{42} +$$$$42\!\cdots\!39$$$$T^{43} +$$$$30\!\cdots\!99$$$$T^{44} +$$$$21\!\cdots\!34$$$$T^{45} +$$$$14\!\cdots\!04$$$$T^{46} +$$$$98\!\cdots\!72$$$$T^{47} +$$$$67\!\cdots\!77$$$$T^{48} +$$$$44\!\cdots\!35$$$$T^{49} +$$$$29\!\cdots\!31$$$$T^{50} +$$$$18\!\cdots\!97$$$$T^{51} +$$$$12\!\cdots\!50$$$$T^{52} +$$$$18\!\cdots\!97$$$$p T^{53} +$$$$29\!\cdots\!31$$$$p^{2} T^{54} +$$$$44\!\cdots\!35$$$$p^{3} T^{55} +$$$$67\!\cdots\!77$$$$p^{4} T^{56} +$$$$98\!\cdots\!72$$$$p^{5} T^{57} +$$$$14\!\cdots\!04$$$$p^{6} T^{58} +$$$$21\!\cdots\!34$$$$p^{7} T^{59} +$$$$30\!\cdots\!99$$$$p^{8} T^{60} +$$$$42\!\cdots\!39$$$$p^{9} T^{61} +$$$$61\!\cdots\!42$$$$p^{10} T^{62} +$$$$82\!\cdots\!73$$$$p^{11} T^{63} +$$$$11\!\cdots\!42$$$$p^{12} T^{64} +$$$$15\!\cdots\!09$$$$p^{13} T^{65} +$$$$20\!\cdots\!44$$$$p^{14} T^{66} +$$$$26\!\cdots\!16$$$$p^{15} T^{67} +$$$$35\!\cdots\!99$$$$p^{16} T^{68} +$$$$44\!\cdots\!57$$$$p^{17} T^{69} +$$$$57\!\cdots\!72$$$$p^{18} T^{70} +$$$$69\!\cdots\!15$$$$p^{19} T^{71} +$$$$87\!\cdots\!90$$$$p^{20} T^{72} +$$$$10\!\cdots\!44$$$$p^{21} T^{73} +$$$$12\!\cdots\!16$$$$p^{22} T^{74} +$$$$14\!\cdots\!48$$$$p^{23} T^{75} +$$$$16\!\cdots\!47$$$$p^{24} T^{76} +$$$$18\!\cdots\!95$$$$p^{25} T^{77} +$$$$20\!\cdots\!51$$$$p^{26} T^{78} +$$$$21\!\cdots\!46$$$$p^{27} T^{79} +$$$$23\!\cdots\!39$$$$p^{28} T^{80} +$$$$23\!\cdots\!65$$$$p^{29} T^{81} +$$$$24\!\cdots\!42$$$$p^{30} T^{82} +$$$$23\!\cdots\!06$$$$p^{31} T^{83} +$$$$23\!\cdots\!12$$$$p^{32} T^{84} +$$$$21\!\cdots\!67$$$$p^{33} T^{85} +$$$$20\!\cdots\!07$$$$p^{34} T^{86} +$$$$17\!\cdots\!82$$$$p^{35} T^{87} +$$$$15\!\cdots\!88$$$$p^{36} T^{88} + 12612369446659968166 p^{37} T^{89} + 1076948860515551691 p^{38} T^{90} + 79000024806066371 p^{39} T^{91} + 6316814948016862 p^{40} T^{92} + 421603435697161 p^{41} T^{93} + 31308175741476 p^{42} T^{94} + 1862380325891 p^{43} T^{95} + 127110244047 p^{44} T^{96} + 6531807957 p^{45} T^{97} + 9859628 p^{47} T^{98} + 17036215 p^{47} T^{99} + 938916 p^{48} T^{100} + 29342 p^{49} T^{101} + 1404 p^{50} T^{102} + 25 p^{51} T^{103} + p^{52} T^{104}$$
43 $$1 - 75 T + 3964 T^{2} - 155062 T^{3} + 5099655 T^{4} - 144165456 T^{5} + 84625298 p T^{6} - 83070561848 T^{7} + 1744758756167 T^{8} - 33994667795756 T^{9} + 620329635918828 T^{10} - 10661689242777951 T^{11} + 173641574839633175 T^{12} - 2690795524097447162 T^{13} + 39840460768946881394 T^{14} -$$$$56\!\cdots\!94$$$$T^{15} +$$$$77\!\cdots\!68$$$$T^{16} -$$$$10\!\cdots\!46$$$$T^{17} +$$$$12\!\cdots\!83$$$$T^{18} -$$$$15\!\cdots\!11$$$$T^{19} +$$$$18\!\cdots\!07$$$$T^{20} -$$$$21\!\cdots\!78$$$$T^{21} +$$$$24\!\cdots\!05$$$$T^{22} -$$$$26\!\cdots\!69$$$$T^{23} +$$$$28\!\cdots\!58$$$$T^{24} -$$$$29\!\cdots\!66$$$$T^{25} +$$$$30\!\cdots\!47$$$$T^{26} -$$$$30\!\cdots\!74$$$$T^{27} +$$$$29\!\cdots\!46$$$$T^{28} -$$$$28\!\cdots\!46$$$$T^{29} +$$$$26\!\cdots\!91$$$$T^{30} -$$$$24\!\cdots\!39$$$$T^{31} +$$$$21\!\cdots\!33$$$$T^{32} -$$$$19\!\cdots\!44$$$$T^{33} +$$$$16\!\cdots\!72$$$$T^{34} -$$$$14\!\cdots\!21$$$$T^{35} +$$$$11\!\cdots\!80$$$$T^{36} -$$$$97\!\cdots\!47$$$$T^{37} +$$$$18\!\cdots\!70$$$$p T^{38} -$$$$14\!\cdots\!35$$$$p T^{39} +$$$$49\!\cdots\!83$$$$T^{40} -$$$$38\!\cdots\!89$$$$T^{41} +$$$$29\!\cdots\!53$$$$T^{42} -$$$$22\!\cdots\!61$$$$T^{43} +$$$$16\!\cdots\!39$$$$T^{44} -$$$$11\!\cdots\!94$$$$T^{45} +$$$$85\!\cdots\!07$$$$T^{46} -$$$$60\!\cdots\!50$$$$T^{47} +$$$$98\!\cdots\!22$$$$p T^{48} -$$$$29\!\cdots\!49$$$$T^{49} +$$$$19\!\cdots\!52$$$$T^{50} -$$$$13\!\cdots\!31$$$$T^{51} +$$$$87\!\cdots\!16$$$$T^{52} -$$$$13\!\cdots\!31$$$$p T^{53} +$$$$19\!\cdots\!52$$$$p^{2} T^{54} -$$$$29\!\cdots\!49$$$$p^{3} T^{55} +$$$$98\!\cdots\!22$$$$p^{5} T^{56} -$$$$60\!\cdots\!50$$$$p^{5} T^{57} +$$$$85\!\cdots\!07$$$$p^{6} T^{58} -$$$$11\!\cdots\!94$$$$p^{7} T^{59} +$$$$16\!\cdots\!39$$$$p^{8} T^{60} -$$$$22\!\cdots\!61$$$$p^{9} T^{61} +$$$$29\!\cdots\!53$$$$p^{10} T^{62} -$$$$38\!\cdots\!89$$$$p^{11} T^{63} +$$$$49\!\cdots\!83$$$$p^{12} T^{64} -$$$$14\!\cdots\!35$$$$p^{14} T^{65} +$$$$18\!\cdots\!70$$$$p^{15} T^{66} -$$$$97\!\cdots\!47$$$$p^{15} T^{67} +$$$$11\!\cdots\!80$$$$p^{16} T^{68} -$$$$14\!\cdots\!21$$$$p^{17} T^{69} +$$$$16\!\cdots\!72$$$$p^{18} T^{70} -$$$$19\!\cdots\!44$$$$p^{19} T^{71} +$$$$21\!\cdots\!33$$$$p^{20} T^{72} -$$$$24\!\cdots\!39$$$$p^{21} T^{73} +$$$$26\!\cdots\!91$$$$p^{22} T^{74} -$$$$28\!\cdots\!46$$$$p^{23} T^{75} +$$$$29\!\cdots\!46$$$$p^{24} T^{76} -$$$$30\!\cdots\!74$$$$p^{25} T^{77} +$$$$30\!\cdots\!47$$$$p^{26} T^{78} -$$$$29\!\cdots\!66$$$$p^{27} T^{79} +$$$$28\!\cdots\!58$$$$p^{28} T^{80} -$$$$26\!\cdots\!69$$$$p^{29} T^{81} +$$$$24\!\cdots\!05$$$$p^{30} T^{82} -$$$$21\!\cdots\!78$$$$p^{31} T^{83} +$$$$18\!\cdots\!07$$$$p^{32} T^{84} -$$$$15\!\cdots\!11$$$$p^{33} T^{85} +$$$$12\!\cdots\!83$$$$p^{34} T^{86} -$$$$10\!\cdots\!46$$$$p^{35} T^{87} +$$$$77\!\cdots\!68$$$$p^{36} T^{88} -$$$$56\!\cdots\!94$$$$p^{37} T^{89} + 39840460768946881394 p^{38} T^{90} - 2690795524097447162 p^{39} T^{91} + 173641574839633175 p^{40} T^{92} - 10661689242777951 p^{41} T^{93} + 620329635918828 p^{42} T^{94} - 33994667795756 p^{43} T^{95} + 1744758756167 p^{44} T^{96} - 83070561848 p^{45} T^{97} + 84625298 p^{47} T^{98} - 144165456 p^{47} T^{99} + 5099655 p^{48} T^{100} - 155062 p^{49} T^{101} + 3964 p^{50} T^{102} - 75 p^{51} T^{103} + p^{52} T^{104}$$
47 $$1 + 20 T + 1340 T^{2} + 23908 T^{3} + 883612 T^{4} + 14322990 T^{5} + 384310300 T^{6} + 5738977688 T^{7} + 124501792036 T^{8} + 1731576031354 T^{9} + 32136994582504 T^{10} + 419912104467130 T^{11} + 6899550934080095 T^{12} + 85292414101374981 T^{13} + 1269209345115551925 T^{14} + 14929570597438688975 T^{15} +$$$$20\!\cdots\!50$$$$T^{16} +$$$$22\!\cdots\!98$$$$T^{17} +$$$$29\!\cdots\!45$$$$T^{18} +$$$$31\!\cdots\!50$$$$T^{19} +$$$$37\!\cdots\!55$$$$T^{20} +$$$$39\!\cdots\!83$$$$T^{21} +$$$$44\!\cdots\!34$$$$T^{22} +$$$$44\!\cdots\!09$$$$T^{23} +$$$$48\!\cdots\!72$$$$T^{24} +$$$$46\!\cdots\!14$$$$T^{25} +$$$$48\!\cdots\!22$$$$T^{26} +$$$$45\!\cdots\!31$$$$T^{27} +$$$$44\!\cdots\!73$$$$T^{28} +$$$$41\!\cdots\!31$$$$T^{29} +$$$$39\!\cdots\!23$$$$T^{30} +$$$$34\!\cdots\!31$$$$T^{31} +$$$$31\!\cdots\!91$$$$T^{32} +$$$$27\!\cdots\!73$$$$T^{33} +$$$$24\!\cdots\!20$$$$T^{34} +$$$$20\!\cdots\!04$$$$T^{35} +$$$$17\!\cdots\!85$$$$T^{36} +$$$$14\!\cdots\!30$$$$T^{37} +$$$$12\!\cdots\!18$$$$T^{38} +$$$$97\!\cdots\!59$$$$T^{39} +$$$$78\!\cdots\!66$$$$T^{40} +$$$$61\!\cdots\!39$$$$T^{41} +$$$$48\!\cdots\!29$$$$T^{42} +$$$$37\!\cdots\!89$$$$T^{43} +$$$$28\!\cdots\!44$$$$T^{44} +$$$$21\!\cdots\!06$$$$T^{45} +$$$$15\!\cdots\!45$$$$T^{46} +$$$$11\!\cdots\!65$$$$T^{47} +$$$$84\!\cdots\!44$$$$T^{48} +$$$$59\!\cdots\!01$$$$T^{49} +$$$$42\!\cdots\!79$$$$T^{50} +$$$$29\!\cdots\!89$$$$T^{51} +$$$$20\!\cdots\!76$$$$T^{52} +$$$$29\!\cdots\!89$$$$p T^{53} +$$$$42\!\cdots\!79$$$$p^{2} T^{54} +$$$$59\!\cdots\!01$$$$p^{3} T^{55} +$$$$84\!\cdots\!44$$$$p^{4} T^{56} +$$$$11\!\cdots\!65$$$$p^{5} T^{57} +$$$$15\!\cdots\!45$$$$p^{6} T^{58} +$$$$21\!\cdots\!06$$$$p^{7} T^{59} +$$$$28\!\cdots\!44$$$$p^{8} T^{60} +$$$$37\!\cdots\!89$$$$p^{9} T^{61} +$$$$48\!\cdots\!29$$$$p^{10} T^{62} +$$$$61\!\cdots\!39$$$$p^{11} T^{63} +$$$$78\!\cdots\!66$$$$p^{12} T^{64} +$$$$97\!\cdots\!59$$$$p^{13} T^{65} +$$$$12\!\cdots\!18$$$$p^{14} T^{66} +$$$$14\!\cdots\!30$$$$p^{15} T^{67} +$$$$17\!\cdots\!85$$$$p^{16} T^{68} +$$$$20\!\cdots\!04$$$$p^{17} T^{69} +$$$$24\!\cdots\!20$$$$p^{18} T^{70} +$$$$27\!\cdots\!73$$$$p^{19} T^{71} +$$$$31\!\cdots\!91$$$$p^{20} T^{72} +$$$$34\!\cdots\!31$$$$p^{21} T^{73} +$$$$39\!\cdots\!23$$$$p^{22} T^{74} +$$$$41\!\cdots\!31$$$$p^{23} T^{75} +$$$$44\!\cdots\!73$$$$p^{24} T^{76} +$$$$45\!\cdots\!31$$$$p^{25} T^{77} +$$$$48\!\cdots\!22$$$$p^{26} T^{78} +$$$$46\!\cdots\!14$$$$p^{27} T^{79} +$$$$48\!\cdots\!72$$$$p^{28} T^{80} +$$$$44\!\cdots\!09$$$$p^{29} T^{81} +$$$$44\!\cdots\!34$$$$p^{30} T^{82} +$$$$39\!\cdots\!83$$$$p^{31} T^{83} +$$$$37\!\cdots\!55$$$$p^{32} T^{84} +$$$$31\!\cdots\!50$$$$p^{33} T^{85} +$$$$29\!\cdots\!45$$$$p^{34} T^{86} +$$$$22\!\cdots\!98$$$$p^{35} T^{87} +$$$$20\!\cdots\!50$$$$p^{36} T^{88} + 14929570597438688975 p^{37} T^{89} + 1269209345115551925 p^{38} T^{90} + 85292414101374981 p^{39} T^{91} + 6899550934080095 p^{40} T^{92} + 419912104467130 p^{41} T^{93} + 32136994582504 p^{42} T^{94} + 1731576031354 p^{43} T^{95} + 124501792036 p^{44} T^{96} + 5738977688 p^{45} T^{97} + 384310300 p^{46} T^{98} + 14322990 p^{47} T^{99} + 883612 p^{48} T^{100} + 23908 p^{49} T^{101} + 1340 p^{50} T^{102} + 20 p^{51} T^{103} + p^{52} T^{104}$$
53 $$1 - 70 T + 3751 T^{2} - 148151 T^{3} + 5019017 T^{4} - 146687024 T^{5} + 3860607751 T^{6} - 92261186220 T^{7} + 2038445929791 T^{8} - 41917817827473 T^{9} + 809897346594737 T^{10} - 14776500978496040 T^{11} + 256054473123539078 T^{12} - 4230085355615323287 T^{13} + 66882763252309635870 T^{14} -$$$$10\!\cdots\!76$$$$T^{15} +$$$$14\!\cdots\!17$$$$T^{16} -$$$$20\!\cdots\!73$$$$T^{17} +$$$$28\!\cdots\!42$$$$T^{18} -$$$$37\!\cdots\!99$$$$T^{19} +$$$$48\!\cdots\!99$$$$T^{20} -$$$$59\!\cdots\!38$$$$T^{21} +$$$$72\!\cdots\!73$$$$T^{22} -$$$$85\!\cdots\!49$$$$T^{23} +$$$$98\!\cdots\!06$$$$T^{24} -$$$$11\!\cdots\!80$$$$T^{25} +$$$$12\!\cdots\!58$$$$T^{26} -$$$$12\!\cdots\!08$$$$T^{27} +$$$$13\!\cdots\!17$$$$T^{28} -$$$$14\!\cdots\!40$$$$T^{29} +$$$$14\!\cdots\!86$$$$T^{30} -$$$$13\!\cdots\!74$$$$T^{31} +$$$$13\!\cdots\!53$$$$T^{32} -$$$$12\!\cdots\!26$$$$T^{33} +$$$$12\!\cdots\!58$$$$T^{34} -$$$$11\!\cdots\!67$$$$T^{35} +$$$$10\!\cdots\!31$$$$T^{36} -$$$$90\!\cdots\!96$$$$T^{37} +$$$$79\!\cdots\!82$$$$T^{38} -$$$$68\!\cdots\!76$$$$T^{39} +$$$$58\!\cdots\!09$$$$T^{40} -$$$$49\!\cdots\!15$$$$T^{41} +$$$$41\!\cdots\!05$$$$T^{42} -$$$$33\!\cdots\!12$$$$T^{43} +$$$$27\!\cdots\!17$$$$T^{44} -$$$$21\!\cdots\!17$$$$T^{45} +$$$$17\!\cdots\!16$$$$T^{46} -$$$$13\!\cdots\!34$$$$T^{47} +$$$$10\!\cdots\!99$$$$T^{48} -$$$$77\!\cdots\!30$$$$T^{49} +$$$$10\!\cdots\!55$$$$p T^{50} -$$$$43\!\cdots\!05$$$$T^{51} +$$$$31\!\cdots\!42$$$$T^{52} -$$$$43\!\cdots\!05$$$$p T^{53} +$$$$10\!\cdots\!55$$$$p^{3} T^{54} -$$$$77\!\cdots\!30$$$$p^{3} T^{55} +$$$$10\!\cdots\!99$$$$p^{4} T^{56} -$$$$13\!\cdots\!34$$$$p^{5} T^{57} +$$$$17\!\cdots\!16$$$$p^{6} T^{58} -$$$$21\!\cdots\!17$$$$p^{7} T^{59} +$$$$27\!\cdots\!17$$$$p^{8} T^{60} -$$$$33\!\cdots\!12$$$$p^{9} T^{61} +$$$$41\!\cdots\!05$$$$p^{10} T^{62} -$$$$49\!\cdots\!15$$$$p^{11} T^{63} +$$$$58\!\cdots\!09$$$$p^{12} T^{64} -$$$$68\!\cdots\!76$$$$p^{13} T^{65} +$$$$79\!\cdots\!82$$$$p^{14} T^{66} -$$$$90\!\cdots\!96$$$$p^{15} T^{67} +$$$$10\!\cdots\!31$$$$p^{16} T^{68} -$$$$11\!\cdots\!67$$$$p^{17} T^{69} +$$$$12\!\cdots\!58$$$$p^{18} T^{70} -$$$$12\!\cdots\!26$$$$p^{19} T^{71} +$$$$13\!\cdots\!53$$$$p^{20} T^{72} -$$$$13\!\cdots\!74$$$$p^{21} T^{73} +$$$$14\!\cdots\!86$$$$p^{22} T^{74} -$$$$14\!\cdots\!40$$$$p^{23} T^{75} +$$$$13\!\cdots\!17$$$$p^{24} T^{76} -$$$$12\!\cdots\!08$$$$p^{25} T^{77} +$$$$12\!\cdots\!58$$$$p^{26} T^{78} -$$$$11\!\cdots\!80$$$$p^{27} T^{79} +$$$$98\!\cdots\!06$$$$p^{28} T^{80} -$$$$85\!\cdots\!49$$$$p^{29} T^{81} +$$$$72\!\cdots\!73$$$$p^{30} T^{82} -$$$$59\!\cdots\!38$$$$p^{31} T^{83} +$$$$48\!\cdots\!99$$$$p^{32} T^{84} -$$$$37\!\cdots\!99$$$$p^{33} T^{85} +$$$$28\!\cdots\!42$$$$p^{34} T^{86} -$$$$20\!\cdots\!73$$$$p^{35} T^{87} +$$$$14\!\cdots\!17$$$$p^{36} T^{88} -$$$$10\!\cdots\!76$$$$p^{37} T^{89} + 66882763252309635870 p^{38} T^{90} - 4230085355615323287 p^{39} T^{91} + 256054473123539078 p^{40} T^{92} - 14776500978496040 p^{41} T^{93} + 809897346594737 p^{42} T^{94} - 41917817827473 p^{43} T^{95} + 2038445929791 p^{44} T^{96} - 92261186220 p^{45} T^{97} + 3860607751 p^{46} T^{98} - 146687024 p^{47} T^{99} + 5019017 p^{48} T^{100} - 148151 p^{49} T^{101} + 3751 p^{50} T^{102} - 70 p^{51} T^{103} + p^{52} T^{104}$$
59 $$1 + 27 T + 1696 T^{2} + 40543 T^{3} + 1440550 T^{4} + 30915146 T^{5} + 816690684 T^{6} + 15931130699 T^{7} + 347645410662 T^{8} + 105609821371 p T^{9} + 118523920772151 T^{10} + 1969992841747097 T^{11} + 33713022775936434 T^{12} + 523719355210639524 T^{13} + 8228464686231623136 T^{14} +$$$$12\!\cdots\!92$$$$T^{15} +$$$$17\!\cdots\!71$$$$T^{16} +$$$$24\!\cdots\!50$$$$T^{17} +$$$$33\!\cdots\!93$$$$T^{18} +$$$$43\!\cdots\!15$$$$T^{19} +$$$$57\!\cdots\!09$$$$T^{20} +$$$$71\!\cdots\!17$$$$T^{21} +$$$$89\!\cdots\!23$$$$T^{22} +$$$$10\!\cdots\!20$$$$T^{23} +$$$$12\!\cdots\!31$$$$T^{24} +$$$$14\!\cdots\!93$$$$T^{25} +$$$$16\!\cdots\!56$$$$T^{26} +$$$$18\!\cdots\!81$$$$T^{27} +$$$$20\!\cdots\!29$$$$T^{28} +$$$$21\!\cdots\!82$$$$T^{29} +$$$$23\!\cdots\!57$$$$T^{30} +$$$$24\!\cdots\!36$$$$T^{31} +$$$$24\!\cdots\!02$$$$T^{32} +$$$$24\!\cdots\!33$$$$T^{33} +$$$$24\!\cdots\!01$$$$T^{34} +$$$$23\!\cdots\!90$$$$T^{35} +$$$$22\!\cdots\!93$$$$T^{36} +$$$$21\!\cdots\!01$$$$T^{37} +$$$$20\!\cdots\!21$$$$T^{38} +$$$$18\!\cdots\!11$$$$T^{39} +$$$$16\!\cdots\!59$$$$T^{40} +$$$$15\!\cdots\!53$$$$T^{41} +$$$$13\!\cdots\!00$$$$T^{42} +$$$$11\!\cdots\!59$$$$T^{43} +$$$$99\!\cdots\!77$$$$T^{44} +$$$$84\!\cdots\!79$$$$T^{45} +$$$$70\!\cdots\!76$$$$T^{46} +$$$$58\!\cdots\!39$$$$T^{47} +$$$$47\!\cdots\!66$$$$T^{48} +$$$$37\!\cdots\!20$$$$T^{49} +$$$$30\!\cdots\!78$$$$T^{50} +$$$$23\!\cdots\!80$$$$T^{51} +$$$$18\!\cdots\!00$$$$T^{52} +$$$$23\!\cdots\!80$$$$p T^{53} +$$$$30\!\cdots\!78$$$$p^{2} T^{54} +$$$$37\!\cdots\!20$$$$p^{3} T^{55} +$$$$47\!\cdots\!66$$$$p^{4} T^{56} +$$$$58\!\cdots\!39$$$$p^{5} T^{57} +$$$$70\!\cdots\!76$$$$p^{6} T^{58} +$$$$84\!\cdots\!79$$$$p^{7} T^{59} +$$$$99\!\cdots\!77$$$$p^{8} T^{60} +$$$$11\!\cdots\!59$$$$p^{9} T^{61} +$$$$13\!\cdots\!00$$$$p^{10} T^{62} +$$$$15\!\cdots\!53$$$$p^{11} T^{63} +$$$$16\!\cdots\!59$$$$p^{12} T^{64} +$$$$18\!\cdots\!11$$$$p^{13} T^{65} +$$$$20\!\cdots\!21$$$$p^{14} T^{66} +$$$$21\!\cdots\!01$$$$p^{15} T^{67} +$$$$22\!\cdots\!93$$$$p^{16} T^{68} +$$$$23\!\cdots\!90$$$$p^{17} T^{69} +$$$$24\!\cdots\!01$$$$p^{18} T^{70} +$$$$24\!\cdots\!33$$$$p^{19} T^{71} +$$$$24\!\cdots\!02$$$$p^{20} T^{72} +$$$$24\!\cdots\!36$$$$p^{21} T^{73} +$$$$23\!\cdots\!57$$$$p^{22} T^{74} +$$$$21\!\cdots\!82$$$$p^{23} T^{75} +$$$$20\!\cdots\!29$$$$p^{24} T^{76} +$$$$18\!\cdots\!81$$$$p^{25} T^{77} +$$$$16\!\cdots\!56$$$$p^{26} T^{78} +$$$$14\!\cdots\!93$$$$p^{27} T^{79} +$$$$12\!\cdots\!31$$$$p^{28} T^{80} +$$$$10\!\cdots\!20$$$$p^{29} T^{81} +$$$$89\!\cdots\!23$$$$p^{30} T^{82} +$$$$71\!\cdots\!17$$$$p^{31} T^{83} +$$$$57\!\cdots\!09$$$$p^{32} T^{84} +$$$$43\!\cdots\!15$$$$p^{33} T^{85} +$$$$33\!\cdots\!93$$$$p^{34} T^{86} +$$$$24\!\cdots\!50$$$$p^{35} T^{87} +$$$$17\!\cdots\!71$$$$p^{36} T^{88} +$$$$12\!\cdots\!92$$$$p^{37} T^{89} + 8228464686231623136 p^{38} T^{90} + 523719355210639524 p^{39} T^{91} + 33713022775936434 p^{40} T^{92} + 1969992841747097 p^{41} T^{93} + 118523920772151 p^{42} T^{94} + 105609821371 p^{44} T^{95} + 347645410662 p^{44} T^{96} + 15931130699 p^{45} T^{97} + 816690684 p^{46} T^{98} + 30915146 p^{47} T^{99} + 1440550 p^{48} T^{100} + 40543 p^{49} T^{101} + 1696 p^{50} T^{102} + 27 p^{51} T^{103} + p^{52} T^{104}$$
61 $$1 - 59 T + 3543 T^{2} - 140680 T^{3} + 5262273 T^{4} - 163119945 T^{5} + 4742204807 T^{6} - 123060212006 T^{7} + 3013007884762 T^{8} - 68114975895608 T^{9} + 1463035857414157 T^{10} - 29555811911978820 T^{11} + 570773706496214929 T^{12} - 10485586013726108934 T^{13} +$$$$18\!\cdots\!29$$$$T^{14} -$$$$31\!\cdots\!92$$$$T^{15} +$$$$51\!\cdots\!43$$$$T^{16} -$$$$80\!\cdots\!00$$$$T^{17} +$$$$12\!\cdots\!55$$$$T^{18} -$$$$18\!\cdots\!66$$$$T^{19} +$$$$25\!\cdots\!17$$$$T^{20} -$$$$35\!\cdots\!40$$$$T^{21} +$$$$48\!\cdots\!58$$$$T^{22} -$$$$63\!\cdots\!23$$$$T^{23} +$$$$82\!\cdots\!69$$$$T^{24} -$$$$10\!\cdots\!27$$$$T^{25} +$$$$12\!\cdots\!57$$$$T^{26} -$$$$15\!\cdots\!88$$$$T^{27} +$$$$17\!\cdots\!17$$$$T^{28} -$$$$20\!\cdots\!33$$$$T^{29} +$$$$22\!\cdots\!66$$$$T^{30} -$$$$24\!\cdots\!01$$$$T^{31} +$$$$26\!\cdots\!62$$$$T^{32} -$$$$28\!\cdots\!94$$$$T^{33} +$$$$29\!\cdots\!94$$$$T^{34} -$$$$49\!\cdots\!37$$$$p T^{35} +$$$$30\!\cdots\!49$$$$T^{36} -$$$$29\!\cdots\!82$$$$T^{37} +$$$$28\!\cdots\!76$$$$T^{38} -$$$$27\!\cdots\!15$$$$T^{39} +$$$$25\!\cdots\!23$$$$T^{40} -$$$$23\!\cdots\!99$$$$T^{41} +$$$$21\!\cdots\!07$$$$T^{42} -$$$$19\!\cdots\!73$$$$T^{43} +$$$$17\!\cdots\!34$$$$T^{44} -$$$$14\!\cdots\!84$$$$T^{45} +$$$$12\!\cdots\!28$$$$T^{46} -$$$$10\!\cdots\!57$$$$T^{47} +$$$$89\!\cdots\!84$$$$T^{48} -$$$$73\!\cdots\!11$$$$T^{49} +$$$$96\!\cdots\!99$$$$p T^{50} -$$$$47\!\cdots\!26$$$$T^{51} +$$$$37\!\cdots\!66$$$$T^{52} -$$$$47\!\cdots\!26$$$$p T^{53} +$$$$96\!\cdots\!99$$$$p^{3} T^{54} -$$$$73\!\cdots\!11$$$$p^{3} T^{55} +$$$$89\!\cdots\!84$$$$p^{4} T^{56} -$$$$10\!\cdots\!57$$$$p^{5} T^{57} +$$$$12\!\cdots\!28$$$$p^{6} T^{58} -$$$$14\!\cdots\!84$$$$p^{7} T^{59} +$$$$17\!\cdots\!34$$$$p^{8} T^{60} -$$$$19\!\cdots\!73$$$$p^{9} T^{61} +$$$$21\!\cdots\!07$$$$p^{10} T^{62} -$$$$23\!\cdots\!99$$$$p^{11} T^{63} +$$$$25\!\cdots\!23$$$$p^{12} T^{64} -$$$$27\!\cdots\!15$$$$p^{13} T^{65} +$$$$28\!\cdots\!76$$$$p^{14} T^{66} -$$$$29\!\cdots\!82$$$$p^{15} T^{67} +$$$$30\!\cdots\!49$$$$p^{16} T^{68} -$$$$49\!\cdots\!37$$$$p^{18} T^{69} +$$$$29\!\cdots\!94$$$$p^{18} T^{70} -$$$$28\!\cdots\!94$$$$p^{19} T^{71} +$$$$26\!\cdots\!62$$$$p^{20} T^{72} -$$$$24\!\cdots\!01$$$$p^{21} T^{73} +$$$$22\!\cdots\!66$$$$p^{22} T^{74} -$$$$20\!\cdots\!33$$$$p^{23} T^{75} +$$$$17\!\cdots\!17$$$$p^{24} T^{76} -$$$$15\!\cdots\!88$$$$p^{25} T^{77} +$$$$12\!\cdots\!57$$$$p^{26} T^{78} -$$$$10\!\cdots\!27$$$$p^{27} T^{79} +$$$$82\!\cdots\!69$$$$p^{28} T^{80} -$$$$63\!\cdots\!23$$$$p^{29} T^{81} +$$$$48\!\cdots\!58$$$$p^{30} T^{82} -$$$$35\!\cdots\!40$$$$p^{31} T^{83} +$$$$25\!\cdots\!17$$$$p^{32} T^{84} -$$$$18\!\cdots\!66$$$$p^{33} T^{85} +$$$$12\!\cdots\!55$$$$p^{34} T^{86} -$$$$80\!\cdots\!00$$$$p^{35} T^{87} +$$$$51\!\cdots\!43$$$$p^{36} T^{88} -$$$$31\!\cdots\!92$$$$p^{37} T^{89} +$$$$18\!\cdots\!29$$$$p^{38} T^{90} - 10485586013726108934 p^{39} T^{91} + 570773706496214929 p^{40} T^{92} - 29555811911978820 p^{41} T^{93} + 1463035857414157 p^{42} T^{94} - 68114975895608 p^{43} T^{95} + 3013007884762 p^{44} T^{96} - 123060212006 p^{45} T^{97} + 4742204807 p^{46} T^{98} - 163119945 p^{47} T^{99} + 5262273 p^{48} T^{100} - 140680 p^{49} T^{101} + 3543 p^{50} T^{102} - 59 p^{51} T^{103} + p^{52} T^{104}$$
67 $$1 - 65 T + 3952 T^{2} - 163439 T^{3} + 6208895 T^{4} - 197014518 T^{5} + 5813325741 T^{6} - 153414335980 T^{7} + 3810354196512 T^{8} - 87403212357549 T^{9} + 1904758729921419 T^{10} - 39037347954719234 T^{11} + 765610982000206499 T^{12} - 14283661795084294357 T^{13} +$$$$25\!\cdots\!66$$$$T^{14} -$$$$44\!\cdots\!50$$$$T^{15} +$$$$73\!\cdots\!02$$$$T^{16} -$$$$11\!\cdots\!22$$$$T^{17} +$$$$18\!\cdots\!57$$$$T^{18} -$$$$27\!\cdots\!63$$$$T^{19} +$$$$40\!\cdots\!42$$$$T^{20} -$$$$57\!\cdots\!01$$$$T^{21} +$$$$80\!\cdots\!53$$$$T^{22} -$$$$10\!\cdots\!20$$$$T^{23} +$$$$21\!\cdots\!10$$$$p T^{24} -$$$$18\!\cdots\!80$$$$T^{25} +$$$$23\!\cdots\!36$$$$T^{26} -$$$$28\!\cdots\!07$$$$T^{27} +$$$$34\!\cdots\!84$$$$T^{28} -$$$$41\!\cdots\!29$$$$T^{29} +$$$$48\!\cdots\!73$$$$T^{30} -$$$$54\!\cdots\!36$$$$T^{31} +$$$$61\!\cdots\!69$$$$T^{32} -$$$$67\!\cdots\!14$$$$T^{33} +$$$$73\!\cdots\!71$$$$T^{34} -$$$$77\!\cdots\!06$$$$T^{35} +$$$$81\!\cdots\!33$$$$T^{36} -$$$$83\!\cdots\!48$$$$T^{37} +$$$$84\!\cdots\!23$$$$T^{38} -$$$$84\!\cdots\!72$$$$T^{39} +$$$$82\!\cdots\!39$$$$T^{40} -$$$$79\!\cdots\!78$$$$T^{41} +$$$$75\!\cdots\!49$$$$T^{42} -$$$$70\!\cdots\!18$$$$T^{43} +$$$$65\!\cdots\!31$$$$T^{44} -$$$$59\!\cdots\!13$$$$T^{45} +$$$$53\!\cdots\!97$$$$T^{46} -$$$$47\!\cdots\!13$$$$T^{47} +$$$$41\!\cdots\!95$$$$T^{48} -$$$$35\!\cdots\!27$$$$T^{49} +$$$$30\!\cdots\!23$$$$T^{50} -$$$$37\!\cdots\!13$$$$p T^{51} +$$$$20\!\cdots\!32$$$$T^{52} -$$$$37\!\cdots\!13$$$$p^{2} T^{53} +$$$$30\!\cdots\!23$$$$p^{2} T^{54} -$$$$35\!\cdots\!27$$$$p^{3} T^{55} +$$$$41\!\cdots\!95$$$$p^{4} T^{56} -$$$$47\!\cdots\!13$$$$p^{5} T^{57} +$$$$53\!\cdots\!97$$$$p^{6} T^{58} -$$$$59\!\cdots\!13$$$$p^{7} T^{59} +$$$$65\!\cdots\!31$$$$p^{8} T^{60} -$$$$70\!\cdots\!18$$$$p^{9} T^{61} +$$$$75\!\cdots\!49$$$$p^{10} T^{62} -$$$$79\!\cdots\!78$$$$p^{11} T^{63} +$$$$82\!\cdots\!39$$$$p^{12} T^{64} -$$$$84\!\cdots\!72$$$$p^{13} T^{65} +$$$$84\!\cdots\!23$$$$p^{14} T^{66} -$$$$83\!\cdots\!48$$$$p^{15} T^{67} +$$$$81\!\cdots\!33$$$$p^{16} T^{68} -$$$$77\!\cdots\!06$$$$p^{17} T^{69} +$$$$73\!\cdots\!71$$$$p^{18} T^{70} -$$$$67\!\cdots\!14$$$$p^{19} T^{71} +$$$$61\!\cdots\!69$$$$p^{20} T^{72} -$$$$54\!\cdots\!36$$$$p^{21} T^{73} +$$$$48\!\cdots\!73$$$$p^{22} T^{74} -$$$$41\!\cdots\!29$$$$p^{23} T^{75} +$$$$34\!\cdots\!84$$$$p^{24} T^{76} -$$$$28\!\cdots\!07$$$$p^{25} T^{77} +$$$$23\!\cdots\!36$$$$p^{26} T^{78} -$$$$18\!\cdots\!80$$$$p^{27} T^{79} +$$$$21\!\cdots\!10$$$$p^{29} T^{80} -$$$$10\!\cdots\!20$$$$p^{29} T^{81} +$$$$80\!\cdots\!53$$$$p^{30} T^{82} -$$$$57\!\cdots\!01$$$$p^{31} T^{83} +$$$$40\!\cdots\!42$$$$p^{32} T^{84} -$$$$27\!\cdots\!63$$$$p^{33} T^{85} +$$$$18\!\cdots\!57$$$$p^{34} T^{86} -$$$$11\!\cdots\!22$$$$p^{35} T^{87} +$$$$73\!\cdots\!02$$$$p^{36} T^{88} -$$$$44\!\cdots\!50$$$$p^{37} T^{89} +$$$$25\!\cdots\!66$$$$p^{38} T^{90} - 14283661795084294357 p^{39} T^{91} + 765610982000206499 p^{40} T^{92} - 39037347954719234 p^{41} T^{93} + 1904758729921419 p^{42} T^{94} - 87403212357549 p^{43} T^{95} + 3810354196512 p^{44} T^{96} - 153414335980 p^{45} T^{97} + 5813325741 p^{46} T^{98} - 197014518 p^{47} T^{99} + 6208895 p^{48} T^{100} - 163439 p^{49} T^{101} + 3952 p^{50} T^{102} - 65 p^{51} T^{103} + p^{52} T^{104}$$
71 $$1 + 11 T + 1855 T^{2} + 19054 T^{3} + 1695172 T^{4} + 16291744 T^{5} + 1018440492 T^{6} + 9171890558 T^{7} + 452958102671 T^{8} + 3827409322244 T^{9} + 159236816128943 T^{10} + 1264092936185928 T^{11} + 46144258384375100 T^{12} + 344707566406683609 T^{13} + 11352560178336407200 T^{14} + 79989112495842779222 T^{15} +$$$$24\!\cdots\!66$$$$T^{16} +$$$$16\!\cdots\!39$$$$T^{17} +$$$$45\!\cdots\!03$$$$T^{18} +$$$$29\!\cdots\!20$$$$T^{19} +$$$$77\!\cdots\!53$$$$T^{20} +$$$$46\!\cdots\!05$$$$T^{21} +$$$$11\!\cdots\!92$$$$T^{22} +$$$$69\!\cdots\!67$$$$T^{23} +$$$$16\!\cdots\!82$$$$T^{24} +$$$$95\!\cdots\!96$$$$T^{25} +$$$$21\!\cdots\!00$$$$T^{26} +$$$$12\!\cdots\!23$$$$T^{27} +$$$$26\!\cdots\!04$$$$T^{28} +$$$$14\!\cdots\!32$$$$T^{29} +$$$$29\!\cdots\!50$$$$T^{30} +$$$$16\!\cdots\!54$$$$T^{31} +$$$$31\!\cdots\!94$$$$T^{32} +$$$$18\!\cdots\!77$$$$T^{33} +$$$$32\!\cdots\!41$$$$T^{34} +$$$$18\!\cdots\!98$$$$T^{35} +$$$$31\!\cdots\!32$$$$T^{36} +$$$$18\!\cdots\!26$$$$T^{37} +$$$$29\!\cdots\!04$$$$T^{38} +$$$$17\!\cdots\!08$$$$T^{39} +$$$$25\!\cdots\!00$$$$T^{40} +$$$$15\!\cdots\!38$$$$T^{41} +$$$$22\!\cdots\!29$$$$T^{42} +$$$$13\!\cdots\!76$$$$T^{43} +$$$$18\!\cdots\!76$$$$T^{44} +$$$$11\!\cdots\!62$$$$T^{45} +$$$$14\!\cdots\!26$$$$T^{46} +$$$$90\!\cdots\!10$$$$T^{47} +$$$$11\!\cdots\!26$$$$T^{48} +$$$$69\!\cdots\!26$$$$T^{49} +$$$$83\!\cdots\!05$$$$T^{50} +$$$$51\!\cdots\!75$$$$T^{51} +$$$$60\!\cdots\!90$$$$T^{52} +$$$$51\!\cdots\!75$$$$p T^{53} +$$$$83\!\cdots\!05$$$$p^{2} T^{54} +$$$$69\!\cdots\!26$$$$p^{3} T^{55} +$$$$11\!\cdots\!26$$$$p^{4} T^{56} +$$$$90\!\cdots\!10$$$$p^{5} T^{57} +$$$$14\!\cdots\!26$$$$p^{6} T^{58} +$$$$11\!\cdots\!62$$$$p^{7} T^{59} +$$$$18\!\cdots\!76$$$$p^{8} T^{60} +$$$$13\!\cdots\!76$$$$p^{9} T^{61} +$$$$22\!\cdots\!29$$$$p^{10} T^{62} +$$$$15\!\cdots\!38$$$$p^{11} T^{63} +$$$$25\!\cdots\!00$$$$p^{12} T^{64} +$$$$17\!\cdots\!08$$$$p^{13} T^{65} +$$$$29\!\cdots\!04$$$$p^{14} T^{66} +$$$$18\!\cdots\!26$$$$p^{15} T^{67} +$$$$31\!\cdots\!32$$$$p^{16} T^{68} +$$$$18\!\cdots\!98$$$$p^{17} T^{69} +$$$$32\!\cdots\!41$$$$p^{18} T^{70} +$$$$18\!\cdots\!77$$$$p^{19} T^{71} +$$$$31\!\cdots\!94$$$$p^{20} T^{72} +$$$$16\!\cdots\!54$$$$p^{21} T^{73} +$$$$29\!\cdots\!50$$$$p^{22} T^{74} +$$$$14\!\cdots\!32$$$$p^{23} T^{75} +$$$$26\!\cdots\!04$$$$p^{24} T^{76} +$$$$12\!\cdots\!23$$$$p^{25} T^{77} +$$$$21\!\cdots\!00$$$$p^{26} T^{78} +$$$$95\!\cdots\!96$$$$p^{27} T^{79} +$$$$16\!\cdots\!82$$$$p^{28} T^{80} +$$$$69\!\cdots\!67$$$$p^{29} T^{81} +$$$$11\!\cdots\!92$$$$p^{30} T^{82} +$$$$46\!\cdots\!05$$$$p^{31} T^{83} +$$$$77\!\cdots\!53$$$$p^{32} T^{84} +$$$$29\!\cdots\!20$$$$p^{33} T^{85} +$$$$45\!\cdots\!03$$$$p^{34} T^{86} +$$$$16\!\cdots\!39$$$$p^{35} T^{87} +$$$$24\!\cdots\!66$$$$p^{36} T^{88} + 79989112495842779222 p^{37} T^{89} + 11352560178336407200 p^{38} T^{90} + 344707566406683609 p^{39} T^{91} + 46144258384375100 p^{40} T^{92} + 1264092936185928 p^{41} T^{93} + 159236816128943 p^{42} T^{94} + 3827409322244 p^{43} T^{95} + 452958102671 p^{44} T^{96} + 9171890558 p^{45} T^{97} + 1018440492 p^{46} T^{98} + 16291744 p^{47} T^{99} + 1695172 p^{48} T^{100} + 19054 p^{49} T^{101} + 1855 p^{50} T^{102} + 11 p^{51} T^{103} + p^{52} T^{104}$$
73 $$1 - 34 T + 2490 T^{2} - 69709 T^{3} + 2933456 T^{4} - 70777640 T^{5} + 2220863961 T^{6} - 47557466704 T^{7} + 1228824084669 T^{8} - 23834365962758 T^{9} + 533757774567962 T^{10} - 9517514682531821 T^{11} + 190498918663545330 T^{12} - 3158093216524907368 T^{13} + 57657066804992420294 T^{14} -$$$$89\!\cdots\!34$$$$T^{15} +$$$$15\!\cdots\!84$$$$T^{16} -$$$$22\!\cdots\!91$$$$T^{17} +$$$$35\!\cdots\!62$$$$T^{18} -$$$$49\!\cdots\!19$$$$T^{19} +$$$$73\!\cdots\!57$$$$T^{20} -$$$$97\!\cdots\!28$$$$T^{21} +$$$$13\!\cdots\!41$$$$T^{22} -$$$$17\!\cdots\!48$$$$T^{23} +$$$$23\!\cdots\!05$$$$T^{24} -$$$$28\!\cdots\!64$$$$T^{25} +$$$$37\!\cdots\!38$$$$T^{26} -$$$$44\!\cdots\!71$$$$T^{27} +$$$$54\!\cdots\!01$$$$T^{28} -$$$$62\!\cdots\!93$$$$T^{29} +$$$$74\!\cdots\!59$$$$T^{30} -$$$$82\!\cdots\!89$$$$T^{31} +$$$$95\!\cdots\!91$$$$T^{32} -$$$$10\!\cdots\!95$$$$T^{33} +$$$$11\!\cdots\!23$$$$T^{34} -$$$$16\!\cdots\!78$$$$p T^{35} +$$$$12\!\cdots\!27$$$$T^{36} -$$$$13\!\cdots\!59$$$$T^{37} +$$$$13\!\cdots\!28$$$$T^{38} -$$$$13\!\cdots\!23$$$$T^{39} +$$$$13\!\cdots\!09$$$$T^{40} -$$$$13\!\cdots\!63$$$$T^{41} +$$$$13\!\cdots\!81$$$$T^{42} -$$$$12\!\cdots\!16$$$$T^{43} +$$$$12\!\cdots\!77$$$$T^{44} -$$$$11\!\cdots\!31$$$$T^{45} +$$$$10\!\cdots\!86$$$$T^{46} -$$$$93\!\cdots\!84$$$$T^{47} +$$$$86\!\cdots\!89$$$$T^{48} -$$$$75\!\cdots\!41$$$$T^{49} +$$$$67\!\cdots\!07$$$$T^{50} -$$$$57\!\cdots\!11$$$$T^{51} +$$$$50\!\cdots\!36$$$$T^{52} -$$$$57\!\cdots\!11$$$$p T^{53} +$$$$67\!\cdots\!07$$$$p^{2} T^{54} -$$$$75\!\cdots\!41$$$$p^{3} T^{55} +$$$$86\!\cdots\!89$$$$p^{4} T^{56} -$$$$93\!\cdots\!84$$$$p^{5} T^{57} +$$$$10\!\cdots\!86$$$$p^{6} T^{58} -$$$$11\!\cdots\!31$$$$p^{7} T^{59} +$$$$12\!\cdots\!77$$$$p^{8} T^{60} -$$$$12\!\cdots\!16$$$$p^{9} T^{61} +$$$$13\!\cdots\!81$$$$p^{10} T^{62} -$$$$13\!\cdots\!63$$$$p^{11} T^{63} +$$$$13\!\cdots\!09$$$$p^{12} T^{64} -$$$$13\!\cdots\!23$$$$p^{13} T^{65} +$$$$13\!\cdots\!28$$$$p^{14} T^{66} -$$$$13\!\cdots\!59$$$$p^{15} T^{67} +$$$$12\!\cdots\!27$$$$p^{16} T^{68} -$$$$16\!\cdots\!78$$$$p^{18} T^{69} +$$$$11\!\cdots\!23$$$$p^{18} T^{70} -$$$$10\!\cdots\!95$$$$p^{19} T^{71} +$$$$95\!\cdots\!91$$$$p^{20} T^{72} -$$$$82\!\cdots\!89$$$$p^{21} T^{73} +$$$$74\!\cdots\!59$$$$p^{22} T^{74} -$$$$62\!\cdots\!93$$$$p^{23} T^{75} +$$$$54\!\cdots\!01$$$$p^{24} T^{76} -$$$$44\!\cdots\!71$$$$p^{25} T^{77} +$$$$37\!\cdots\!38$$$$p^{26} T^{78} -$$$$28\!\cdots\!64$$$$p^{27} T^{79} +$$$$23\!\cdots\!05$$$$p^{28} T^{80} -$$$$17\!\cdots\!48$$$$p^{29} T^{81} +$$$$13\!\cdots\!41$$$$p^{30} T^{82} -$$$$97\!\cdots\!28$$$$p^{31} T^{83} +$$$$73\!\cdots\!57$$$$p^{32} T^{84} -$$$$49\!\cdots\!19$$$$p^{33} T^{85} +$$$$35\!\cdots\!62$$$$p^{34} T^{86} -$$$$22\!\cdots\!91$$$$p^{35} T^{87} +$$$$15\!\cdots\!84$$$$p^{36} T^{88} -$$$$89\!\cdots\!34$$$$p^{37} T^{89} + 57657066804992420294 p^{38} T^{90} - 3158093216524907368 p^{39} T^{91} + 190498918663545330 p^{40} T^{92} - 9517514682531821 p^{41} T^{93} + 533757774567962 p^{42} T^{94} - 23834365962758 p^{43} T^{95} + 1228824084669 p^{44} T^{96} - 47557466704 p^{45} T^{97} + 2220863961 p^{46} T^{98} - 70777640 p^{47} T^{99} + 2933456 p^{48} T^{100} - 69709 p^{49} T^{101} + 2490 p^{50} T^{102} - 34 p^{51} T^{103} + p^{52} T^{104}$$
79 $$1 - 74 T + 4873 T^{2} - 223911 T^{3} + 9267466 T^{4} - 324299194 T^{5} + 10448492413 T^{6} - 303092536078 T^{7} + 8226815870644 T^{8} - 207058284411455 T^{9} + 4932644537396531 T^{10} - 110791490026202880 T^{11} + 2375171567331148801 T^{12} - 48520845768565731819 T^{13} +$$$$95\!\cdots\!79$$$$T^{14} -$$$$17\!\cdots\!81$$$$T^{15} +$$$$32\!\cdots\!08$$$$T^{16} -$$$$57\!\cdots\!95$$$$T^{17} +$$$$97\!\cdots\!94$$$$T^{18} -$$$$16\!\cdots\!33$$$$T^{19} +$$$$25\!\cdots\!70$$$$T^{20} -$$$$39\!\cdots\!70$$$$T^{21} +$$$$60\!\cdots\!56$$$$T^{22} -$$$$89\!\cdots\!02$$$$T^{23} +$$$$12\!\cdots\!17$$$$T^{24} -$$$$18\!\cdots\!08$$$$T^{25} +$$$$24\!\cdots\!70$$$$T^{26} -$$$$33\!\cdots\!86$$$$T^{27} +$$$$44\!\cdots\!32$$$$T^{28} -$$$$57\!\cdots\!37$$$$T^{29} +$$$$72\!\cdots\!64$$$$T^{30} -$$$$90\!\cdots\!57$$$$T^{31} +$$$$11\!\cdots\!34$$$$T^{32} -$$$$13\!\cdots\!29$$$$T^{33} +$$$$15\!\cdots\!92$$$$T^{34} -$$$$17\!\cdots\!94$$$$T^{35} +$$$$20\!\cdots\!04$$$$T^{36} -$$$$22\!\cdots\!23$$$$T^{37} +$$$$25\!\cdots\!86$$$$T^{38} -$$$$27\!\cdots\!77$$$$T^{39} +$$$$29\!\cdots\!15$$$$T^{40} -$$$$30\!\cdots\!44$$$$T^{41} +$$$$31\!\cdots\!11$$$$T^{42} -$$$$32\!\cdots\!47$$$$T^{43} +$$$$32\!\cdots\!31$$$$T^{44} -$$$$32\!\cdots\!09$$$$T^{45} +$$$$31\!\cdots\!73$$$$T^{46} -$$$$30\!\cdots\!65$$$$T^{47} +$$$$28\!\cdots\!37$$$$T^{48} -$$$$26\!\cdots\!59$$$$T^{49} +$$$$24\!\cdots\!34$$$$T^{50} -$$$$22\!\cdots\!85$$$$T^{51} +$$$$19\!\cdots\!00$$$$T^{52} -$$$$22\!\cdots\!85$$$$p T^{53} +$$$$24\!\cdots\!34$$$$p^{2} T^{54} -$$$$26\!\cdots\!59$$$$p^{3} T^{55} +$$$$28\!\cdots\!37$$$$p^{4} T^{56} -$$$$30\!\cdots\!65$$$$p^{5} T^{57} +$$$$31\!\cdots\!73$$$$p^{6} T^{58} -$$$$32\!\cdots\!09$$$$p^{7} T^{59} +$$$$32\!\cdots\!31$$$$p^{8} T^{60} -$$$$32\!\cdots\!47$$$$p^{9} T^{61} +$$$$31\!\cdots\!11$$$$p^{10} T^{62} -$$$$30\!\cdots\!44$$$$p^{11} T^{63} +$$$$29\!\cdots\!15$$$$p^{12} T^{64} -$$$$27\!\cdots\!77$$$$p^{13} T^{65} +$$$$25\!\cdots\!86$$$$p^{14} T^{66} -$$$$22\!\cdots\!23$$$$p^{15} T^{67} +$$$$20\!\cdots\!04$$$$p^{16} T^{68} -$$$$17\!\cdots\!94$$$$p^{17} T^{69} +$$$$15\!\cdots\!92$$$$p^{18} T^{70} -$$$$13\!\cdots\!29$$$$p^{19} T^{71} +$$$$11\!\cdots\!34$$$$p^{20} T^{72} -$$$$90\!\cdots\!57$$$$p^{21} T^{73} +$$$$72\!\cdots\!64$$$$p^{22} T^{74} -$$$$57\!\cdots\!37$$$$p^{23} T^{75} +$$$$44\!\cdots\!32$$$$p^{24} T^{76} -$$$$33\!\cdots\!86$$$$p^{25} T^{77} +$$$$24\!\cdots\!70$$$$p^{26} T^{78} -$$$$18\!\cdots\!08$$$$p^{27} T^{79} +$$$$12\!\cdots\!17$$$$p^{28} T^{80} -$$$$89\!\cdots\!02$$$$p^{29} T^{81} +$$$$60\!\cdots\!56$$$$p^{30} T^{82} -$$$$39\!\cdots\!70$$$$p^{31} T^{83} +$$$$25\!\cdots\!70$$$$p^{32} T^{84} -$$$$16\!\cdots\!33$$$$p^{33} T^{85} +$$$$97\!\cdots\!94$$$$p^{34} T^{86} -$$$$57\!\cdots\!95$$$$p^{35} T^{87} +$$$$32\!\cdots\!08$$$$p^{36} T^{88} -$$$$17\!\cdots\!81$$$$p^{37} T^{89} +$$$$95\!\cdots\!79$$$$p^{38} T^{90} - 48520845768565731819 p^{39} T^{91} + 2375171567331148801 p^{40} T^{92} - 110791490026202880 p^{41} T^{93} + 4932644537396531 p^{42} T^{94} - 207058284411455 p^{43} T^{95} + 8226815870644 p^{44} T^{96} - 303092536078 p^{45} T^{97} + 10448492413 p^{46} T^{98} - 324299194 p^{47} T^{99} + 9267466 p^{48} T^{100} - 223911 p^{49} T^{101} + 4873 p^{50} T^{102} - 74 p^{51} T^{103} + p^{52} T^{104}$$
83 $$1 + 30 T + 2674 T^{2} + 70295 T^{3} + 3488682 T^{4} + 82302574 T^{5} + 2983304579 T^{6} + 64243119867 T^{7} + 1890185990801 T^{8} + 37627367780102 T^{9} + 949491172052154 T^{10} + 17643026544541903 T^{11} + 394746676454024548 T^{12} + 6899118443365918048 T^{13} +$$$$13\!\cdots\!19$$$$T^{14} +$$$$23\!\cdots\!40$$$$T^{15} +$$$$43\!\cdots\!84$$$$T^{16} +$$$$67\!\cdots\!67$$$$T^{17} +$$$$11\!\cdots\!60$$$$T^{18} +$$$$17\!\cdots\!75$$$$T^{19} +$$$$28\!\cdots\!30$$$$T^{20} +$$$$41\!\cdots\!58$$$$T^{21} +$$$$77\!\cdots\!08$$$$p T^{22} +$$$$89\!\cdots\!64$$$$T^{23} +$$$$13\!\cdots\!80$$$$T^{24} +$$$$17\!\cdots\!94$$$$T^{25} +$$$$24\!\cdots\!53$$$$T^{26} +$$$$31\!\cdots\!32$$$$T^{27} +$$$$42\!\cdots\!65$$$$T^{28} +$$$$52\!\cdots\!25$$$$T^{29} +$$$$67\!\cdots\!92$$$$T^{30} +$$$$81\!\cdots\!45$$$$T^{31} +$$$$10\!\cdots\!74$$$$T^{32} +$$$$11\!\cdots\!95$$$$T^{33} +$$$$14\!\cdots\!40$$$$T^{34} +$$$$16\!\cdots\!23$$$$T^{35} +$$$$18\!\cdots\!24$$$$T^{36} +$$$$20\!\cdots\!56$$$$T^{37} +$$$$23\!\cdots\!93$$$$T^{38} +$$$$25\!\cdots\!24$$$$T^{39} +$$$$27\!\cdots\!18$$$$T^{40} +$$$$28\!\cdots\!85$$$$T^{41} +$$$$30\!\cdots\!70$$$$T^{42} +$$$$31\!\cdots\!86$$$$T^{43} +$$$$32\!\cdots\!07$$$$T^{44} +$$$$31\!\cdots\!92$$$$T^{45} +$$$$32\!\cdots\!28$$$$T^{46} +$$$$30\!\cdots\!00$$$$T^{47} +$$$$30\!\cdots\!34$$$$T^{48} +$$$$28\!\cdots\!35$$$$T^{49} +$$$$27\!\cdots\!66$$$$T^{50} +$$$$24\!\cdots\!55$$$$T^{51} +$$$$23\!\cdots\!00$$$$T^{52} +$$$$24\!\cdots\!55$$$$p T^{53} +$$$$27\!\cdots\!66$$$$p^{2} T^{54} +$$$$28\!\cdots\!35$$$$p^{3} T^{55} +$$$$30\!\cdots\!34$$$$p^{4} T^{56} +$$$$30\!\cdots\!00$$$$p^{5} T^{57} +$$$$32\!\cdots\!28$$$$p^{6} T^{58} +$$$$31\!\cdots\!92$$$$p^{7} T^{59} +$$$$32\!\cdots\!07$$$$p^{8} T^{60} +$$$$31\!\cdots\!86$$$$p^{9} T^{61} +$$$$30\!\cdots\!70$$$$p^{10} T^{62} +$$$$28\!\cdots\!85$$$$p^{11} T^{63} +$$$$27\!\cdots\!18$$$$p^{12} T^{64} +$$$$25\!\cdots\!24$$$$p^{13} T^{65} +$$$$23\!\cdots\!93$$$$p^{14} T^{66} +$$$$20\!\cdots\!56$$$$p^{15} T^{67} +$$$$18\!\cdots\!24$$$$p^{16} T^{68} +$$$$16\!\cdots\!23$$$$p^{17} T^{69} +$$$$14\!\cdots\!40$$$$p^{18} T^{70} +$$$$11\!\cdots\!95$$$$p^{19} T^{71} +$$$$10\!\cdots\!74$$$$p^{20} T^{72} +$$$$81\!\cdots\!45$$$$p^{21} T^{73} +$$$$67\!\cdots\!92$$$$p^{22} T^{74} +$$$$52\!\cdots\!25$$$$p^{23} T^{75} +$$$$42\!\cdots\!65$$$$p^{24} T^{76} +$$$$31\!\cdots\!32$$$$p^{25} T^{77} +$$$$24\!\cdots\!53$$$$p^{26} T^{78} +$$$$17\!\cdots\!94$$$$p^{27} T^{79} +$$$$13\!\cdots\!80$$$$p^{28} T^{80} +$$$$89\!\cdots\!64$$$$p^{29} T^{81} +$$$$77\!\cdots\!08$$$$p^{31} T^{82} +$$$$41\!\cdots\!58$$$$p^{31} T^{83} +$$$$28\!\cdots\!30$$$$p^{32} T^{84} +$$$$17\!\cdots\!75$$$$p^{33} T^{85} +$$$$11\!\cdots\!60$$$$p^{34} T^{86} +$$$$67\!\cdots\!67$$$$p^{35} T^{87} +$$$$43\!\cdots\!84$$$$p^{36} T^{88} +$$$$23\!\cdots\!40$$$$p^{37} T^{89} +$$$$13\!\cdots\!19$$$$p^{38} T^{90} + 6899118443365918048 p^{39} T^{91} + 394746676454024548 p^{40} T^{92} + 17643026544541903 p^{41} T^{93} + 949491172052154 p^{42} T^{94} + 37627367780102 p^{43} T^{95} + 1890185990801 p^{44} T^{96} + 64243119867 p^{45} T^{97} + 2983304579 p^{46} T^{98} + 82302574 p^{47} T^{99} + 3488682 p^{48} T^{100} + 70295 p^{49} T^{101} + 2674 p^{50} T^{102} + 30 p^{51} T^{103} + p^{52} T^{104}$$
89 $$1 + T + 2632 T^{2} + 3565 T^{3} + 3451067 T^{4} + 5730125 T^{5} + 3003459454 T^{6} + 5755692144 T^{7} + 1950305421890 T^{8} + 4136860194414 T^{9} + 1007079027533583 T^{10} + 2289739688506925 T^{11} + 430381923301512112 T^{12} + 1021257021706497417 T^{13} +$$$$15\!\cdots\!26$$$$T^{14} +$$$$37\!\cdots\!36$$$$T^{15} +$$$$49\!\cdots\!73$$$$T^{16} +$$$$11\!\cdots\!83$$$$T^{17} +$$$$13\!\cdots\!54$$$$T^{18} +$$$$32\!\cdots\!48$$$$T^{19} +$$$$33\!\cdots\!77$$$$T^{20} +$$$$74\!\cdots\!50$$$$T^{21} +$$$$75\!\cdots\!82$$$$T^{22} +$$$$15\!\cdots\!20$$$$T^{23} +$$$$15\!\cdots\!76$$$$T^{24} +$$$$26\!\cdots\!95$$$$T^{25} +$$$$27\!\cdots\!32$$$$T^{26} +$$$$40\!\cdots\!51$$$$T^{27} +$$$$46\!\cdots\!96$$$$T^{28} +$$$$50\!\cdots\!34$$$$T^{29} +$$$$71\!\cdots\!16$$$$T^{30} +$$$$43\!\cdots\!57$$$$T^{31} +$$$$10\!\cdots\!33$$$$T^{32} +$$$$58\!\cdots\!85$$$$T^{33} +$$$$13\!\cdots\!17$$$$T^{34} -$$$$80\!\cdots\!34$$$$T^{35} +$$$$16\!\cdots\!64$$$$T^{36} -$$$$22\!\cdots\!10$$$$T^{37} +$$$$18\!\cdots\!41$$$$T^{38} -$$$$42\!\cdots\!40$$$$T^{39} +$$$$20\!\cdots\!92$$$$T^{40} -$$$$66\!\cdots\!27$$$$T^{41} +$$$$20\!\cdots\!85$$$$T^{42} -$$$$90\!\cdots\!51$$$$T^{43} +$$$$20\!\cdots\!96$$$$T^{44} -$$$$11\!\cdots\!48$$$$T^{45} +$$$$18\!\cdots\!66$$$$T^{46} -$$$$12\!\cdots\!51$$$$T^{47} +$$$$17\!\cdots\!95$$$$T^{48} -$$$$12\!\cdots\!81$$$$T^{49} +$$$$15\!\cdots\!52$$$$T^{50} -$$$$12\!\cdots\!24$$$$T^{51} +$$$$13\!\cdots\!04$$$$T^{52} -$$$$12\!\cdots\!24$$$$p T^{53} +$$$$15\!\cdots\!52$$$$p^{2} T^{54} -$$$$12\!\cdots\!81$$$$p^{3} T^{55} +$$$$17\!\cdots\!95$$$$p^{4} T^{56} -$$$$12\!\cdots\!51$$$$p^{5} T^{57} +$$$$18\!\cdots\!66$$$$p^{6} T^{58} -$$$$11\!\cdots\!48$$$$p^{7} T^{59} +$$$$20\!\cdots\!96$$$$p^{8} T^{60} -$$$$90\!\cdots\!51$$$$p^{9} T^{61} +$$$$20\!\cdots\!85$$$$p^{10} T^{62} -$$$$66\!\cdots\!27$$$$p^{11} T^{63} +$$$$20\!\cdots\!92$$$$p^{12} T^{64} -$$$$42\!\cdots\!40$$$$p^{13} T^{65} +$$$$18\!\cdots\!41$$$$p^{14} T^{66} -$$$$22\!\cdots\!10$$$$p^{15} T^{67} +$$$$16\!\cdots\!64$$$$p^{16} T^{68} -$$$$80\!\cdots\!34$$$$p^{17} T^{69} +$$$$13\!\cdots\!17$$$$p^{18} T^{70} +$$$$58\!\cdots\!85$$$$p^{19} T^{71} +$$$$10\!\cdots\!33$$$$p^{20} T^{72} +$$$$43\!\cdots\!57$$$$p^{21} T^{73} +$$$$71\!\cdots\!16$$$$p^{22} T^{74} +$$$$50\!\cdots\!34$$$$p^{23} T^{75} +$$$$46\!\cdots\!96$$$$p^{24} T^{76} +$$$$40\!\cdots\!51$$$$p^{25} T^{77} +$$$$27\!\cdots\!32$$$$p^{26} T^{78} +$$$$26\!\cdots\!95$$$$p^{27} T^{79} +$$$$15\!\cdots\!76$$$$p^{28} T^{80} +$$$$15\!\cdots\!20$$$$p^{29} T^{81} +$$$$75\!\cdots\!82$$$$p^{30} T^{82} +$$$$74\!\cdots\!50$$$$p^{31} T^{83} +$$$$33\!\cdots\!77$$$$p^{32} T^{84} +$$$$32\!\cdots\!48$$$$p^{33} T^{85} +$$$$13\!\cdots\!54$$$$p^{34} T^{86} +$$$$11\!\cdots\!83$$$$p^{35} T^{87} +$$$$49\!\cdots\!73$$$$p^{36} T^{88} +$$$$37\!\cdots\!36$$$$p^{37} T^{89} +$$$$15\!\cdots\!26$$$$p^{38} T^{90} + 1021257021706497417 p^{39} T^{91} + 430381923301512112 p^{40} T^{92} + 2289739688506925 p^{41} T^{93} + 1007079027533583 p^{42} T^{94} + 4136860194414 p^{43} T^{95} + 1950305421890 p^{44} T^{96} + 5755692144 p^{45} T^{97} + 3003459454 p^{46} T^{98} + 5730125 p^{47} T^{99} + 3451067 p^{48} T^{100} + 3565 p^{49} T^{101} + 2632 p^{50} T^{102} + p^{51} T^{103} + p^{52} T^{104}$$
97 $$1 - 73 T + 5098 T^{2} - 241474 T^{3} + 10558016 T^{4} - 386395858 T^{5} + 13158561217 T^{6} - 401965324868 T^{7} + 11550176928595 T^{8} - 307376038861409 T^{9} + 7764743354504903 T^{10} - 184907341879343730 T^{11} + 4209980467234106598 T^{12} - 91362718127164434823 T^{13} +$$$$19\!\cdots\!55$$$$T^{14} -$$$$38\!\cdots\!75$$$$T^{15} +$$$$73\!\cdots\!79$$$$T^{16} -$$$$13\!\cdots\!25$$$$T^{17} +$$$$25\!\cdots\!45$$$$T^{18} -$$$$43\!\cdots\!37$$$$T^{19} +$$$$74\!\cdots\!55$$$$T^{20} -$$$$12\!\cdots\!05$$$$T^{21} +$$$$20\!\cdots\!73$$$$T^{22} -$$$$31\!\cdots\!91$$$$T^{23} +$$$$48\!\cdots\!34$$$$T^{24} -$$$$73\!\cdots\!12$$$$T^{25} +$$$$10\!\cdots\!61$$$$T^{26} -$$$$15\!\cdots\!76$$$$T^{27} +$$$$22\!\cdots\!16$$$$T^{28} -$$$$30\!\cdots\!27$$$$T^{29} +$$$$41\!\cdots\!97$$$$T^{30} -$$$$55\!\cdots\!29$$$$T^{31} +$$$$72\!\cdots\!77$$$$T^{32} -$$$$93\!\cdots\!45$$$$T^{33} +$$$$11\!\cdots\!13$$$$T^{34} -$$$$14\!\cdots\!74$$$$T^{35} +$$$$17\!\cdots\!93$$$$T^{36} -$$$$21\!\cdots\!33$$$$T^{37} +$$$$26\!\cdots\!97$$$$p T^{38} -$$$$30\!\cdots\!79$$$$T^{39} +$$$$34\!\cdots\!63$$$$T^{40} -$$$$39\!\cdots\!65$$$$T^{41} +$$$$44\!\cdots\!71$$$$T^{42} -$$$$49\!\cdots\!76$$$$T^{43} +$$$$53\!\cdots\!06$$$$T^{44} -$$$$58\!\cdots\!20$$$$T^{45} +$$$$62\!\cdots\!73$$$$T^{46} -$$$$65\!\cdots\!34$$$$T^{47} +$$$$67\!\cdots\!55$$$$T^{48} -$$$$69\!\cdots\!51$$$$T^{49} +$$$$70\!\cdots\!77$$$$T^{50} -$$$$70\!\cdots\!43$$$$T^{51} +$$$$70\!\cdots\!64$$$$T^{52} -$$$$70\!\cdots\!43$$$$p T^{53} +$$$$70\!\cdots\!77$$$$p^{2} T^{54} -$$$$69\!\cdots\!51$$$$p^{3} T^{55} +$$$$67\!\cdots\!55$$$$p^{4} T^{56} -$$$$65\!\cdots\!34$$$$p^{5} T^{57} +$$$$62\!\cdots\!73$$$$p^{6} T^{58} -$$$$58\!\cdots\!20$$$$p^{7} T^{59} +$$$$53\!\cdots\!06$$$$p^{8} T^{60} -$$$$49\!\cdots\!76$$$$p^{9} T^{61} +$$$$44\!\cdots\!71$$$$p^{10} T^{62} -$$$$39\!\cdots\!65$$$$p^{11} T^{63} +$$$$34\!\cdots\!63$$$$p^{12} T^{64} -$$$$30\!\cdots\!79$$$$p^{13} T^{65} +$$$$26\!\cdots\!97$$$$p^{15} T^{66} -$$$$21\!\cdots\!33$$$$p^{15} T^{67} +$$$$17\!\cdots\!93$$$$p^{16} T^{68} -$$$$14\!\cdots\!74$$$$p^{17} T^{69} +$$$$11\!\cdots\!13$$$$p^{18} T^{70} -$$$$93\!\cdots\!45$$$$p^{19} T^{71} +$$$$72\!\cdots\!77$$$$p^{20} T^{72} -$$$$55\!\cdots\!29$$$$p^{21} T^{73} +$$$$41\!\cdots\!97$$$$p^{22} T^{74} -$$$$30\!\cdots\!27$$$$p^{23} T^{75} +$$$$22\!\cdots\!16$$$$p^{24} T^{76} -$$$$15\!\cdots\!76$$$$p^{25} T^{77} +$$$$10\!\cdots\!61$$$$p^{26} T^{78} -$$$$73\!\cdots\!12$$$$p^{27} T^{79} +$$$$48\!\cdots\!34$$$$p^{28} T^{80} -$$$$31\!\cdots\!91$$$$p^{29} T^{81} +$$$$20\!\cdots\!73$$$$p^{30} T^{82} -$$$$12\!\cdots\!05$$$$p^{31} T^{83} +$$$$74\!\cdots\!55$$$$p^{32} T^{84} -$$$$43\!\cdots\!37$$$$p^{33} T^{85} +$$$$25\!\cdots\!45$$$$p^{34} T^{86} -$$$$13\!\cdots\!25$$$$p^{35} T^{87} +$$$$73\!\cdots\!79$$$$p^{36} T^{88} -$$$$38\!\cdots\!75$$$$p^{37} T^{89} +$$$$19\!\cdots\!55$$$$p^{38} T^{90} - 91362718127164434823 p^{39} T^{91} + 4209980467234106598 p^{40} T^{92} - 184907341879343730 p^{41} T^{93} + 7764743354504903 p^{42} T^{94} - 307376038861409 p^{43} T^{95} + 11550176928595 p^{44} T^{96} - 401965324868 p^{45} T^{97} + 13158561217 p^{46} T^{98} - 386395858 p^{47} T^{99} + 10558016 p^{48} T^{100} - 241474 p^{49} T^{101} + 5098 p^{50} T^{102} - 73 p^{51} T^{103} + p^{52} T^{104}$$
\begin{aligned} L(s) = \prod_p \ \prod_{j=1}^{104} (1 - \alpha_{j,p}\, p^{-s})^{-1} \end{aligned}