# Properties

 Degree 124 Conductor $5^{62} \cdot 7^{62} \cdot 229^{62}$ Sign $1$ Motivic weight 1 Primitive no Self-dual yes Analytic rank 0

# Origins of factors

## Dirichlet series

 L(s)  = 1 + 11·3-s − 62·5-s − 62·7-s + 2·9-s − 13·11-s + 31·13-s − 682·15-s + 30·17-s + 20·19-s − 682·21-s + 1.95e3·25-s − 413·27-s − 29·29-s + 20·31-s − 143·33-s + 3.84e3·35-s + 35·37-s + 341·39-s + 13·41-s − 4·43-s − 124·45-s + 58·47-s + 1.95e3·49-s + 330·51-s + 18·53-s + 806·55-s + 220·57-s + ⋯
 L(s)  = 1 + 6.35·3-s − 27.7·5-s − 23.4·7-s + 2/3·9-s − 3.91·11-s + 8.59·13-s − 176.·15-s + 7.27·17-s + 4.58·19-s − 148.·21-s + 390.·25-s − 79.4·27-s − 5.38·29-s + 3.59·31-s − 24.8·33-s + 649.·35-s + 5.75·37-s + 54.6·39-s + 2.03·41-s − 0.609·43-s − 18.4·45-s + 8.46·47-s + 279·49-s + 46.2·51-s + 2.47·53-s + 108.·55-s + 29.1·57-s + ⋯

## Functional equation

\begin{aligned} \Lambda(s)=\mathstrut &\left(5^{62} \cdot 7^{62} \cdot 229^{62}\right)^{s/2} \, \Gamma_{\C}(s)^{62} \, L(s)\cr =\mathstrut & \,\Lambda(2-s) \end{aligned}
\begin{aligned} \Lambda(s)=\mathstrut &\left(5^{62} \cdot 7^{62} \cdot 229^{62}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{62} \, L(s)\cr =\mathstrut & \,\Lambda(1-s) \end{aligned}

## Invariants

 $$d$$ = $$124$$ $$N$$ = $$5^{62} \cdot 7^{62} \cdot 229^{62}$$ $$\varepsilon$$ = $1$ motivic weight = $$1$$ character : induced by $\chi_{8015} (1, \cdot )$ primitive : no self-dual : yes analytic rank = 0 Selberg data = $(124,\ 5^{62} \cdot 7^{62} \cdot 229^{62} ,\ ( \ : [1/2]^{62} ),\ 1 )$ $L(1)$ $\approx$ $0.0005888383407$ $L(\frac12)$ $\approx$ $0.0005888383407$ $L(\frac{3}{2})$ not available $L(1)$ not available

## Euler product

$L(s) = \prod_{p \text{ prime}} F_p(p^{-s})^{-1}$ where, for $p \notin \{5,\;7,\;229\}$, $$F_p(T)$$ is a polynomial of degree 124. If $p \in \{5,\;7,\;229\}$, then $F_p(T)$ is a polynomial of degree at most 123.
$p$$F_p(T)$
bad5 $$( 1 + T )^{62}$$
7 $$( 1 + T )^{62}$$
229 $$( 1 - T )^{62}$$
good2 $$1+O(T)$$
3 $$1 - 11 T + 119 T^{2} - 874 T^{3} + 664 p^{2} T^{4} - 11465 p T^{5} + 184990 T^{6} - 897928 T^{7} + 1370998 p T^{8} - 17547016 T^{9} + 71278568 T^{10} - 91449913 p T^{11} + 1012767169 T^{12} - 3580208299 T^{13} + 12208454335 T^{14} - 40152176914 T^{15} + 42655139395 p T^{16} - 395368902893 T^{17} + 1188061721215 T^{18} - 3474438934994 T^{19} + 9911803270361 T^{20} - 27602418522208 T^{21} + 75168084046453 T^{22} - 200312165767574 T^{23} + 523079613357289 T^{24} - 1339337493337418 T^{25} + 1122110359863098 p T^{26} - 8310350014679150 T^{27} + 6722871842243825 p T^{28} - 48145368447454892 T^{29} + 113133316622108629 T^{30} - 261812071999453816 T^{31} + 199030206435700600 p T^{32} - 1342544265915778927 T^{33} + 330874895276569837 p^{2} T^{34} - 6518434309499429540 T^{35} + 14088427989500003477 T^{36} - 30076010914381752985 T^{37} + 63447891463743474127 T^{38} -$$$$13\!\cdots\!24$$$$T^{39} +$$$$27\!\cdots\!13$$$$T^{40} -$$$$18\!\cdots\!53$$$$p T^{41} +$$$$37\!\cdots\!13$$$$p T^{42} -$$$$22\!\cdots\!68$$$$T^{43} +$$$$44\!\cdots\!75$$$$T^{44} -$$$$87\!\cdots\!17$$$$T^{45} +$$$$56\!\cdots\!95$$$$p T^{46} -$$$$32\!\cdots\!43$$$$T^{47} +$$$$62\!\cdots\!62$$$$T^{48} -$$$$11\!\cdots\!80$$$$T^{49} +$$$$22\!\cdots\!31$$$$T^{50} -$$$$41\!\cdots\!93$$$$T^{51} +$$$$76\!\cdots\!70$$$$T^{52} -$$$$46\!\cdots\!96$$$$p T^{53} +$$$$28\!\cdots\!87$$$$p^{2} T^{54} -$$$$46\!\cdots\!08$$$$T^{55} +$$$$83\!\cdots\!09$$$$T^{56} -$$$$14\!\cdots\!85$$$$T^{57} +$$$$26\!\cdots\!54$$$$T^{58} -$$$$47\!\cdots\!63$$$$T^{59} +$$$$91\!\cdots\!44$$$$p^{2} T^{60} -$$$$53\!\cdots\!93$$$$p^{3} T^{61} +$$$$27\!\cdots\!94$$$$p^{2} T^{62} -$$$$53\!\cdots\!93$$$$p^{4} T^{63} +$$$$91\!\cdots\!44$$$$p^{4} T^{64} -$$$$47\!\cdots\!63$$$$p^{3} T^{65} +$$$$26\!\cdots\!54$$$$p^{4} T^{66} -$$$$14\!\cdots\!85$$$$p^{5} T^{67} +$$$$83\!\cdots\!09$$$$p^{6} T^{68} -$$$$46\!\cdots\!08$$$$p^{7} T^{69} +$$$$28\!\cdots\!87$$$$p^{10} T^{70} -$$$$46\!\cdots\!96$$$$p^{10} T^{71} +$$$$76\!\cdots\!70$$$$p^{10} T^{72} -$$$$41\!\cdots\!93$$$$p^{11} T^{73} +$$$$22\!\cdots\!31$$$$p^{12} T^{74} -$$$$11\!\cdots\!80$$$$p^{13} T^{75} +$$$$62\!\cdots\!62$$$$p^{14} T^{76} -$$$$32\!\cdots\!43$$$$p^{15} T^{77} +$$$$56\!\cdots\!95$$$$p^{17} T^{78} -$$$$87\!\cdots\!17$$$$p^{17} T^{79} +$$$$44\!\cdots\!75$$$$p^{18} T^{80} -$$$$22\!\cdots\!68$$$$p^{19} T^{81} +$$$$37\!\cdots\!13$$$$p^{21} T^{82} -$$$$18\!\cdots\!53$$$$p^{22} T^{83} +$$$$27\!\cdots\!13$$$$p^{22} T^{84} -$$$$13\!\cdots\!24$$$$p^{23} T^{85} + 63447891463743474127 p^{24} T^{86} - 30076010914381752985 p^{25} T^{87} + 14088427989500003477 p^{26} T^{88} - 6518434309499429540 p^{27} T^{89} + 330874895276569837 p^{30} T^{90} - 1342544265915778927 p^{29} T^{91} + 199030206435700600 p^{31} T^{92} - 261812071999453816 p^{31} T^{93} + 113133316622108629 p^{32} T^{94} - 48145368447454892 p^{33} T^{95} + 6722871842243825 p^{35} T^{96} - 8310350014679150 p^{35} T^{97} + 1122110359863098 p^{37} T^{98} - 1339337493337418 p^{37} T^{99} + 523079613357289 p^{38} T^{100} - 200312165767574 p^{39} T^{101} + 75168084046453 p^{40} T^{102} - 27602418522208 p^{41} T^{103} + 9911803270361 p^{42} T^{104} - 3474438934994 p^{43} T^{105} + 1188061721215 p^{44} T^{106} - 395368902893 p^{45} T^{107} + 42655139395 p^{47} T^{108} - 40152176914 p^{47} T^{109} + 12208454335 p^{48} T^{110} - 3580208299 p^{49} T^{111} + 1012767169 p^{50} T^{112} - 91449913 p^{52} T^{113} + 71278568 p^{52} T^{114} - 17547016 p^{53} T^{115} + 1370998 p^{55} T^{116} - 897928 p^{55} T^{117} + 184990 p^{56} T^{118} - 11465 p^{58} T^{119} + 664 p^{60} T^{120} - 874 p^{59} T^{121} + 119 p^{60} T^{122} - 11 p^{61} T^{123} + p^{62} T^{124}$$
11 $$1 + 13 T + 348 T^{2} + 3855 T^{3} + 59149 T^{4} + 573948 T^{5} + 6586109 T^{6} + 57144451 T^{7} + 542595561 T^{8} + 388777126 p T^{9} + 35373145602 T^{10} + 256406003047 T^{11} + 1904389810542 T^{12} + 12821115755376 T^{13} + 87203026814243 T^{14} + 49967808783020 p T^{15} + 3470359130418242 T^{16} + 20613718269385374 T^{17} + 122022021267963442 T^{18} + 686791060948136469 T^{19} + 3840293281251926405 T^{20} + 20575955215549810721 T^{21} +$$$$10\!\cdots\!51$$$$T^{22} +$$$$55\!\cdots\!40$$$$T^{23} +$$$$28\!\cdots\!52$$$$T^{24} +$$$$13\!\cdots\!49$$$$T^{25} +$$$$67\!\cdots\!73$$$$T^{26} +$$$$32\!\cdots\!58$$$$T^{27} +$$$$14\!\cdots\!20$$$$T^{28} +$$$$62\!\cdots\!97$$$$p T^{29} +$$$$30\!\cdots\!90$$$$T^{30} +$$$$12\!\cdots\!22$$$$p T^{31} +$$$$59\!\cdots\!32$$$$T^{32} +$$$$25\!\cdots\!51$$$$T^{33} +$$$$97\!\cdots\!89$$$$p T^{34} +$$$$44\!\cdots\!19$$$$T^{35} +$$$$18\!\cdots\!41$$$$T^{36} +$$$$73\!\cdots\!85$$$$T^{37} +$$$$29\!\cdots\!41$$$$T^{38} +$$$$11\!\cdots\!02$$$$T^{39} +$$$$41\!\cdots\!85$$$$p T^{40} +$$$$17\!\cdots\!17$$$$T^{41} +$$$$67\!\cdots\!99$$$$T^{42} +$$$$25\!\cdots\!87$$$$T^{43} +$$$$95\!\cdots\!45$$$$T^{44} +$$$$35\!\cdots\!27$$$$T^{45} +$$$$12\!\cdots\!39$$$$T^{46} +$$$$47\!\cdots\!37$$$$T^{47} +$$$$17\!\cdots\!98$$$$T^{48} +$$$$61\!\cdots\!40$$$$T^{49} +$$$$20\!\cdots\!13$$$$p T^{50} +$$$$78\!\cdots\!06$$$$T^{51} +$$$$27\!\cdots\!38$$$$T^{52} +$$$$96\!\cdots\!30$$$$T^{53} +$$$$33\!\cdots\!07$$$$T^{54} +$$$$11\!\cdots\!26$$$$T^{55} +$$$$40\!\cdots\!55$$$$T^{56} +$$$$13\!\cdots\!90$$$$T^{57} +$$$$46\!\cdots\!73$$$$T^{58} +$$$$15\!\cdots\!69$$$$T^{59} +$$$$53\!\cdots\!71$$$$T^{60} +$$$$17\!\cdots\!78$$$$T^{61} +$$$$59\!\cdots\!64$$$$T^{62} +$$$$17\!\cdots\!78$$$$p T^{63} +$$$$53\!\cdots\!71$$$$p^{2} T^{64} +$$$$15\!\cdots\!69$$$$p^{3} T^{65} +$$$$46\!\cdots\!73$$$$p^{4} T^{66} +$$$$13\!\cdots\!90$$$$p^{5} T^{67} +$$$$40\!\cdots\!55$$$$p^{6} T^{68} +$$$$11\!\cdots\!26$$$$p^{7} T^{69} +$$$$33\!\cdots\!07$$$$p^{8} T^{70} +$$$$96\!\cdots\!30$$$$p^{9} T^{71} +$$$$27\!\cdots\!38$$$$p^{10} T^{72} +$$$$78\!\cdots\!06$$$$p^{11} T^{73} +$$$$20\!\cdots\!13$$$$p^{13} T^{74} +$$$$61\!\cdots\!40$$$$p^{13} T^{75} +$$$$17\!\cdots\!98$$$$p^{14} T^{76} +$$$$47\!\cdots\!37$$$$p^{15} T^{77} +$$$$12\!\cdots\!39$$$$p^{16} T^{78} +$$$$35\!\cdots\!27$$$$p^{17} T^{79} +$$$$95\!\cdots\!45$$$$p^{18} T^{80} +$$$$25\!\cdots\!87$$$$p^{19} T^{81} +$$$$67\!\cdots\!99$$$$p^{20} T^{82} +$$$$17\!\cdots\!17$$$$p^{21} T^{83} +$$$$41\!\cdots\!85$$$$p^{23} T^{84} +$$$$11\!\cdots\!02$$$$p^{23} T^{85} +$$$$29\!\cdots\!41$$$$p^{24} T^{86} +$$$$73\!\cdots\!85$$$$p^{25} T^{87} +$$$$18\!\cdots\!41$$$$p^{26} T^{88} +$$$$44\!\cdots\!19$$$$p^{27} T^{89} +$$$$97\!\cdots\!89$$$$p^{29} T^{90} +$$$$25\!\cdots\!51$$$$p^{29} T^{91} +$$$$59\!\cdots\!32$$$$p^{30} T^{92} +$$$$12\!\cdots\!22$$$$p^{32} T^{93} +$$$$30\!\cdots\!90$$$$p^{32} T^{94} +$$$$62\!\cdots\!97$$$$p^{34} T^{95} +$$$$14\!\cdots\!20$$$$p^{34} T^{96} +$$$$32\!\cdots\!58$$$$p^{35} T^{97} +$$$$67\!\cdots\!73$$$$p^{36} T^{98} +$$$$13\!\cdots\!49$$$$p^{37} T^{99} +$$$$28\!\cdots\!52$$$$p^{38} T^{100} +$$$$55\!\cdots\!40$$$$p^{39} T^{101} +$$$$10\!\cdots\!51$$$$p^{40} T^{102} + 20575955215549810721 p^{41} T^{103} + 3840293281251926405 p^{42} T^{104} + 686791060948136469 p^{43} T^{105} + 122022021267963442 p^{44} T^{106} + 20613718269385374 p^{45} T^{107} + 3470359130418242 p^{46} T^{108} + 49967808783020 p^{48} T^{109} + 87203026814243 p^{48} T^{110} + 12821115755376 p^{49} T^{111} + 1904389810542 p^{50} T^{112} + 256406003047 p^{51} T^{113} + 35373145602 p^{52} T^{114} + 388777126 p^{54} T^{115} + 542595561 p^{54} T^{116} + 57144451 p^{55} T^{117} + 6586109 p^{56} T^{118} + 573948 p^{57} T^{119} + 59149 p^{58} T^{120} + 3855 p^{59} T^{121} + 348 p^{60} T^{122} + 13 p^{61} T^{123} + p^{62} T^{124}$$
13 $$1 - 31 T + 796 T^{2} - 14589 T^{3} + 235463 T^{4} - 3238153 T^{5} + 40603434 T^{6} - 459879257 T^{7} + 4850010859 T^{8} - 47505313874 T^{9} + 439273597563 T^{10} - 3833571665253 T^{11} + 31888610883084 T^{12} - 252970326815157 T^{13} + 1926314387204719 T^{14} - 14091804654459712 T^{15} + 99487393300748019 T^{16} - 678449336360193465 T^{17} + 4484113223475335837 T^{18} - 28749015539555278299 T^{19} +$$$$17\!\cdots\!67$$$$T^{20} -$$$$10\!\cdots\!09$$$$T^{21} +$$$$64\!\cdots\!87$$$$T^{22} -$$$$37\!\cdots\!99$$$$T^{23} +$$$$21\!\cdots\!98$$$$T^{24} -$$$$11\!\cdots\!49$$$$T^{25} +$$$$62\!\cdots\!44$$$$T^{26} -$$$$33\!\cdots\!81$$$$T^{27} +$$$$17\!\cdots\!28$$$$T^{28} -$$$$89\!\cdots\!67$$$$T^{29} +$$$$34\!\cdots\!61$$$$p T^{30} -$$$$22\!\cdots\!28$$$$T^{31} +$$$$10\!\cdots\!93$$$$T^{32} -$$$$52\!\cdots\!24$$$$T^{33} +$$$$24\!\cdots\!29$$$$T^{34} -$$$$11\!\cdots\!73$$$$T^{35} +$$$$52\!\cdots\!55$$$$T^{36} -$$$$24\!\cdots\!43$$$$T^{37} +$$$$10\!\cdots\!14$$$$T^{38} -$$$$36\!\cdots\!77$$$$p T^{39} +$$$$21\!\cdots\!33$$$$T^{40} -$$$$91\!\cdots\!27$$$$T^{41} +$$$$30\!\cdots\!12$$$$p T^{42} -$$$$12\!\cdots\!12$$$$p T^{43} +$$$$54\!\cdots\!69$$$$p T^{44} -$$$$29\!\cdots\!33$$$$T^{45} +$$$$12\!\cdots\!99$$$$T^{46} -$$$$49\!\cdots\!50$$$$T^{47} +$$$$20\!\cdots\!58$$$$T^{48} -$$$$62\!\cdots\!42$$$$p T^{49} +$$$$32\!\cdots\!32$$$$T^{50} -$$$$97\!\cdots\!24$$$$p T^{51} +$$$$49\!\cdots\!83$$$$T^{52} -$$$$19\!\cdots\!69$$$$T^{53} +$$$$74\!\cdots\!29$$$$T^{54} -$$$$28\!\cdots\!33$$$$T^{55} +$$$$10\!\cdots\!66$$$$T^{56} -$$$$40\!\cdots\!13$$$$T^{57} +$$$$15\!\cdots\!15$$$$T^{58} -$$$$56\!\cdots\!56$$$$T^{59} +$$$$20\!\cdots\!16$$$$T^{60} -$$$$75\!\cdots\!65$$$$T^{61} +$$$$27\!\cdots\!30$$$$T^{62} -$$$$75\!\cdots\!65$$$$p T^{63} +$$$$20\!\cdots\!16$$$$p^{2} T^{64} -$$$$56\!\cdots\!56$$$$p^{3} T^{65} +$$$$15\!\cdots\!15$$$$p^{4} T^{66} -$$$$40\!\cdots\!13$$$$p^{5} T^{67} +$$$$10\!\cdots\!66$$$$p^{6} T^{68} -$$$$28\!\cdots\!33$$$$p^{7} T^{69} +$$$$74\!\cdots\!29$$$$p^{8} T^{70} -$$$$19\!\cdots\!69$$$$p^{9} T^{71} +$$$$49\!\cdots\!83$$$$p^{10} T^{72} -$$$$97\!\cdots\!24$$$$p^{12} T^{73} +$$$$32\!\cdots\!32$$$$p^{12} T^{74} -$$$$62\!\cdots\!42$$$$p^{14} T^{75} +$$$$20\!\cdots\!58$$$$p^{14} T^{76} -$$$$49\!\cdots\!50$$$$p^{15} T^{77} +$$$$12\!\cdots\!99$$$$p^{16} T^{78} -$$$$29\!\cdots\!33$$$$p^{17} T^{79} +$$$$54\!\cdots\!69$$$$p^{19} T^{80} -$$$$12\!\cdots\!12$$$$p^{20} T^{81} +$$$$30\!\cdots\!12$$$$p^{21} T^{82} -$$$$91\!\cdots\!27$$$$p^{21} T^{83} +$$$$21\!\cdots\!33$$$$p^{22} T^{84} -$$$$36\!\cdots\!77$$$$p^{24} T^{85} +$$$$10\!\cdots\!14$$$$p^{24} T^{86} -$$$$24\!\cdots\!43$$$$p^{25} T^{87} +$$$$52\!\cdots\!55$$$$p^{26} T^{88} -$$$$11\!\cdots\!73$$$$p^{27} T^{89} +$$$$24\!\cdots\!29$$$$p^{28} T^{90} -$$$$52\!\cdots\!24$$$$p^{29} T^{91} +$$$$10\!\cdots\!93$$$$p^{30} T^{92} -$$$$22\!\cdots\!28$$$$p^{31} T^{93} +$$$$34\!\cdots\!61$$$$p^{33} T^{94} -$$$$89\!\cdots\!67$$$$p^{33} T^{95} +$$$$17\!\cdots\!28$$$$p^{34} T^{96} -$$$$33\!\cdots\!81$$$$p^{35} T^{97} +$$$$62\!\cdots\!44$$$$p^{36} T^{98} -$$$$11\!\cdots\!49$$$$p^{37} T^{99} +$$$$21\!\cdots\!98$$$$p^{38} T^{100} -$$$$37\!\cdots\!99$$$$p^{39} T^{101} +$$$$64\!\cdots\!87$$$$p^{40} T^{102} -$$$$10\!\cdots\!09$$$$p^{41} T^{103} +$$$$17\!\cdots\!67$$$$p^{42} T^{104} - 28749015539555278299 p^{43} T^{105} + 4484113223475335837 p^{44} T^{106} - 678449336360193465 p^{45} T^{107} + 99487393300748019 p^{46} T^{108} - 14091804654459712 p^{47} T^{109} + 1926314387204719 p^{48} T^{110} - 252970326815157 p^{49} T^{111} + 31888610883084 p^{50} T^{112} - 3833571665253 p^{51} T^{113} + 439273597563 p^{52} T^{114} - 47505313874 p^{53} T^{115} + 4850010859 p^{54} T^{116} - 459879257 p^{55} T^{117} + 40603434 p^{56} T^{118} - 3238153 p^{57} T^{119} + 235463 p^{58} T^{120} - 14589 p^{59} T^{121} + 796 p^{60} T^{122} - 31 p^{61} T^{123} + p^{62} T^{124}$$
17 $$1 - 30 T + 865 T^{2} - 16910 T^{3} + 305602 T^{4} - 4622931 T^{5} + 65125064 T^{6} - 822970311 T^{7} + 9788088636 T^{8} - 107816102656 T^{9} + 1127916192135 T^{10} - 11123514496531 T^{11} + 104938585104554 T^{12} - 943676382821862 T^{13} + 480235101599270 p T^{14} - 67836640168257305 T^{15} + 544734585033831297 T^{16} - 4224463289303252302 T^{17} + 31777025296365468004 T^{18} -$$$$23\!\cdots\!98$$$$T^{19} +$$$$16\!\cdots\!52$$$$T^{20} -$$$$11\!\cdots\!59$$$$T^{21} +$$$$76\!\cdots\!24$$$$T^{22} -$$$$50\!\cdots\!59$$$$T^{23} +$$$$32\!\cdots\!82$$$$T^{24} -$$$$20\!\cdots\!01$$$$T^{25} +$$$$12\!\cdots\!14$$$$T^{26} -$$$$75\!\cdots\!90$$$$T^{27} +$$$$44\!\cdots\!90$$$$T^{28} -$$$$25\!\cdots\!34$$$$T^{29} +$$$$14\!\cdots\!98$$$$T^{30} -$$$$82\!\cdots\!61$$$$T^{31} +$$$$45\!\cdots\!67$$$$T^{32} -$$$$24\!\cdots\!94$$$$T^{33} +$$$$13\!\cdots\!08$$$$T^{34} -$$$$40\!\cdots\!69$$$$p T^{35} +$$$$35\!\cdots\!64$$$$T^{36} -$$$$18\!\cdots\!90$$$$T^{37} +$$$$92\!\cdots\!13$$$$T^{38} -$$$$46\!\cdots\!30$$$$T^{39} +$$$$22\!\cdots\!45$$$$T^{40} -$$$$11\!\cdots\!80$$$$T^{41} +$$$$31\!\cdots\!06$$$$p T^{42} -$$$$25\!\cdots\!47$$$$T^{43} +$$$$12\!\cdots\!48$$$$T^{44} -$$$$56\!\cdots\!72$$$$T^{45} +$$$$26\!\cdots\!36$$$$T^{46} -$$$$12\!\cdots\!87$$$$T^{47} +$$$$55\!\cdots\!67$$$$T^{48} -$$$$25\!\cdots\!80$$$$T^{49} +$$$$11\!\cdots\!34$$$$T^{50} -$$$$50\!\cdots\!17$$$$T^{51} +$$$$22\!\cdots\!06$$$$T^{52} -$$$$98\!\cdots\!66$$$$T^{53} +$$$$42\!\cdots\!00$$$$T^{54} -$$$$18\!\cdots\!85$$$$T^{55} +$$$$80\!\cdots\!51$$$$T^{56} -$$$$34\!\cdots\!06$$$$T^{57} +$$$$14\!\cdots\!62$$$$T^{58} -$$$$61\!\cdots\!90$$$$T^{59} +$$$$25\!\cdots\!44$$$$T^{60} -$$$$10\!\cdots\!43$$$$T^{61} +$$$$44\!\cdots\!18$$$$T^{62} -$$$$10\!\cdots\!43$$$$p T^{63} +$$$$25\!\cdots\!44$$$$p^{2} T^{64} -$$$$61\!\cdots\!90$$$$p^{3} T^{65} +$$$$14\!\cdots\!62$$$$p^{4} T^{66} -$$$$34\!\cdots\!06$$$$p^{5} T^{67} +$$$$80\!\cdots\!51$$$$p^{6} T^{68} -$$$$18\!\cdots\!85$$$$p^{7} T^{69} +$$$$42\!\cdots\!00$$$$p^{8} T^{70} -$$$$98\!\cdots\!66$$$$p^{9} T^{71} +$$$$22\!\cdots\!06$$$$p^{10} T^{72} -$$$$50\!\cdots\!17$$$$p^{11} T^{73} +$$$$11\!\cdots\!34$$$$p^{12} T^{74} -$$$$25\!\cdots\!80$$$$p^{13} T^{75} +$$$$55\!\cdots\!67$$$$p^{14} T^{76} -$$$$12\!\cdots\!87$$$$p^{15} T^{77} +$$$$26\!\cdots\!36$$$$p^{16} T^{78} -$$$$56\!\cdots\!72$$$$p^{17} T^{79} +$$$$12\!\cdots\!48$$$$p^{18} T^{80} -$$$$25\!\cdots\!47$$$$p^{19} T^{81} +$$$$31\!\cdots\!06$$$$p^{21} T^{82} -$$$$11\!\cdots\!80$$$$p^{21} T^{83} +$$$$22\!\cdots\!45$$$$p^{22} T^{84} -$$$$46\!\cdots\!30$$$$p^{23} T^{85} +$$$$92\!\cdots\!13$$$$p^{24} T^{86} -$$$$18\!\cdots\!90$$$$p^{25} T^{87} +$$$$35\!\cdots\!64$$$$p^{26} T^{88} -$$$$40\!\cdots\!69$$$$p^{28} T^{89} +$$$$13\!\cdots\!08$$$$p^{28} T^{90} -$$$$24\!\cdots\!94$$$$p^{29} T^{91} +$$$$45\!\cdots\!67$$$$p^{30} T^{92} -$$$$82\!\cdots\!61$$$$p^{31} T^{93} +$$$$14\!\cdots\!98$$$$p^{32} T^{94} -$$$$25\!\cdots\!34$$$$p^{33} T^{95} +$$$$44\!\cdots\!90$$$$p^{34} T^{96} -$$$$75\!\cdots\!90$$$$p^{35} T^{97} +$$$$12\!\cdots\!14$$$$p^{36} T^{98} -$$$$20\!\cdots\!01$$$$p^{37} T^{99} +$$$$32\!\cdots\!82$$$$p^{38} T^{100} -$$$$50\!\cdots\!59$$$$p^{39} T^{101} +$$$$76\!\cdots\!24$$$$p^{40} T^{102} -$$$$11\!\cdots\!59$$$$p^{41} T^{103} +$$$$16\!\cdots\!52$$$$p^{42} T^{104} -$$$$23\!\cdots\!98$$$$p^{43} T^{105} + 31777025296365468004 p^{44} T^{106} - 4224463289303252302 p^{45} T^{107} + 544734585033831297 p^{46} T^{108} - 67836640168257305 p^{47} T^{109} + 480235101599270 p^{49} T^{110} - 943676382821862 p^{49} T^{111} + 104938585104554 p^{50} T^{112} - 11123514496531 p^{51} T^{113} + 1127916192135 p^{52} T^{114} - 107816102656 p^{53} T^{115} + 9788088636 p^{54} T^{116} - 822970311 p^{55} T^{117} + 65125064 p^{56} T^{118} - 4622931 p^{57} T^{119} + 305602 p^{58} T^{120} - 16910 p^{59} T^{121} + 865 p^{60} T^{122} - 30 p^{61} T^{123} + p^{62} T^{124}$$
19 $$1 - 20 T + 664 T^{2} - 10071 T^{3} + 196345 T^{4} - 2444918 T^{5} + 35913399 T^{6} - 384095078 T^{7} + 4672295093 T^{8} - 44185173023 T^{9} + 467725107483 T^{10} - 3991573331791 T^{11} + 37919971276668 T^{12} - 296485896128443 T^{13} + 2582387143018823 T^{14} - 18717387344424794 T^{15} + 151873672663889505 T^{16} - 1030092903471434389 T^{17} + 7884146044477847438 T^{18} - 50424395243989364418 T^{19} +$$$$36\!\cdots\!91$$$$T^{20} -$$$$22\!\cdots\!25$$$$T^{21} +$$$$15\!\cdots\!10$$$$T^{22} -$$$$90\!\cdots\!82$$$$T^{23} +$$$$61\!\cdots\!82$$$$T^{24} -$$$$33\!\cdots\!62$$$$T^{25} +$$$$22\!\cdots\!51$$$$T^{26} -$$$$11\!\cdots\!37$$$$T^{27} +$$$$76\!\cdots\!67$$$$T^{28} -$$$$39\!\cdots\!33$$$$T^{29} +$$$$24\!\cdots\!90$$$$T^{30} -$$$$12\!\cdots\!83$$$$T^{31} +$$$$76\!\cdots\!74$$$$T^{32} -$$$$36\!\cdots\!27$$$$T^{33} +$$$$22\!\cdots\!89$$$$T^{34} -$$$$55\!\cdots\!21$$$$p T^{35} +$$$$63\!\cdots\!46$$$$T^{36} -$$$$15\!\cdots\!37$$$$p T^{37} +$$$$17\!\cdots\!22$$$$T^{38} -$$$$76\!\cdots\!78$$$$T^{39} +$$$$45\!\cdots\!57$$$$T^{40} -$$$$19\!\cdots\!37$$$$T^{41} +$$$$11\!\cdots\!10$$$$T^{42} -$$$$48\!\cdots\!67$$$$T^{43} +$$$$28\!\cdots\!70$$$$T^{44} -$$$$11\!\cdots\!90$$$$T^{45} +$$$$66\!\cdots\!41$$$$T^{46} -$$$$14\!\cdots\!85$$$$p T^{47} +$$$$15\!\cdots\!97$$$$T^{48} -$$$$61\!\cdots\!93$$$$T^{49} +$$$$34\!\cdots\!61$$$$T^{50} -$$$$13\!\cdots\!14$$$$T^{51} +$$$$75\!\cdots\!07$$$$T^{52} -$$$$29\!\cdots\!71$$$$T^{53} +$$$$84\!\cdots\!63$$$$p T^{54} -$$$$60\!\cdots\!43$$$$T^{55} +$$$$33\!\cdots\!11$$$$T^{56} -$$$$12\!\cdots\!60$$$$T^{57} +$$$$67\!\cdots\!32$$$$T^{58} -$$$$24\!\cdots\!46$$$$T^{59} +$$$$70\!\cdots\!66$$$$p T^{60} -$$$$48\!\cdots\!50$$$$T^{61} +$$$$25\!\cdots\!08$$$$T^{62} -$$$$48\!\cdots\!50$$$$p T^{63} +$$$$70\!\cdots\!66$$$$p^{3} T^{64} -$$$$24\!\cdots\!46$$$$p^{3} T^{65} +$$$$67\!\cdots\!32$$$$p^{4} T^{66} -$$$$12\!\cdots\!60$$$$p^{5} T^{67} +$$$$33\!\cdots\!11$$$$p^{6} T^{68} -$$$$60\!\cdots\!43$$$$p^{7} T^{69} +$$$$84\!\cdots\!63$$$$p^{9} T^{70} -$$$$29\!\cdots\!71$$$$p^{9} T^{71} +$$$$75\!\cdots\!07$$$$p^{10} T^{72} -$$$$13\!\cdots\!14$$$$p^{11} T^{73} +$$$$34\!\cdots\!61$$$$p^{12} T^{74} -$$$$61\!\cdots\!93$$$$p^{13} T^{75} +$$$$15\!\cdots\!97$$$$p^{14} T^{76} -$$$$14\!\cdots\!85$$$$p^{16} T^{77} +$$$$66\!\cdots\!41$$$$p^{16} T^{78} -$$$$11\!\cdots\!90$$$$p^{17} T^{79} +$$$$28\!\cdots\!70$$$$p^{18} T^{80} -$$$$48\!\cdots\!67$$$$p^{19} T^{81} +$$$$11\!\cdots\!10$$$$p^{20} T^{82} -$$$$19\!\cdots\!37$$$$p^{21} T^{83} +$$$$45\!\cdots\!57$$$$p^{22} T^{84} -$$$$76\!\cdots\!78$$$$p^{23} T^{85} +$$$$17\!\cdots\!22$$$$p^{24} T^{86} -$$$$15\!\cdots\!37$$$$p^{26} T^{87} +$$$$63\!\cdots\!46$$$$p^{26} T^{88} -$$$$55\!\cdots\!21$$$$p^{28} T^{89} +$$$$22\!\cdots\!89$$$$p^{28} T^{90} -$$$$36\!\cdots\!27$$$$p^{29} T^{91} +$$$$76\!\cdots\!74$$$$p^{30} T^{92} -$$$$12\!\cdots\!83$$$$p^{31} T^{93} +$$$$24\!\cdots\!90$$$$p^{32} T^{94} -$$$$39\!\cdots\!33$$$$p^{33} T^{95} +$$$$76\!\cdots\!67$$$$p^{34} T^{96} -$$$$11\!\cdots\!37$$$$p^{35} T^{97} +$$$$22\!\cdots\!51$$$$p^{36} T^{98} -$$$$33\!\cdots\!62$$$$p^{37} T^{99} +$$$$61\!\cdots\!82$$$$p^{38} T^{100} -$$$$90\!\cdots\!82$$$$p^{39} T^{101} +$$$$15\!\cdots\!10$$$$p^{40} T^{102} -$$$$22\!\cdots\!25$$$$p^{41} T^{103} +$$$$36\!\cdots\!91$$$$p^{42} T^{104} - 50424395243989364418 p^{43} T^{105} + 7884146044477847438 p^{44} T^{106} - 1030092903471434389 p^{45} T^{107} + 151873672663889505 p^{46} T^{108} - 18717387344424794 p^{47} T^{109} + 2582387143018823 p^{48} T^{110} - 296485896128443 p^{49} T^{111} + 37919971276668 p^{50} T^{112} - 3991573331791 p^{51} T^{113} + 467725107483 p^{52} T^{114} - 44185173023 p^{53} T^{115} + 4672295093 p^{54} T^{116} - 384095078 p^{55} T^{117} + 35913399 p^{56} T^{118} - 2444918 p^{57} T^{119} + 196345 p^{58} T^{120} - 10071 p^{59} T^{121} + 664 p^{60} T^{122} - 20 p^{61} T^{123} + p^{62} T^{124}$$
23 $$1 + 618 T^{2} - 9 p T^{3} + 193024 T^{4} - 122964 T^{5} + 1766562 p T^{6} - 36979223 T^{7} + 6483933530 T^{8} - 7503345868 T^{9} + 836545435517 T^{10} - 1155092737221 T^{11} + 90866686756235 T^{12} - 143835216523101 T^{13} + 8543973444907455 T^{14} - 15084279881819169 T^{15} + 709635441791067748 T^{16} - 1369711459703168685 T^{17} + 52867138649957586404 T^{18} -$$$$10\!\cdots\!25$$$$T^{19} +$$$$35\!\cdots\!69$$$$T^{20} -$$$$79\!\cdots\!21$$$$T^{21} +$$$$22\!\cdots\!84$$$$T^{22} -$$$$51\!\cdots\!69$$$$T^{23} +$$$$12\!\cdots\!63$$$$T^{24} -$$$$30\!\cdots\!18$$$$T^{25} +$$$$67\!\cdots\!37$$$$T^{26} -$$$$17\!\cdots\!35$$$$T^{27} +$$$$14\!\cdots\!07$$$$p T^{28} -$$$$88\!\cdots\!82$$$$T^{29} +$$$$15\!\cdots\!21$$$$T^{30} -$$$$42\!\cdots\!30$$$$T^{31} +$$$$69\!\cdots\!98$$$$T^{32} -$$$$19\!\cdots\!86$$$$T^{33} +$$$$28\!\cdots\!98$$$$T^{34} -$$$$81\!\cdots\!24$$$$T^{35} +$$$$11\!\cdots\!04$$$$T^{36} -$$$$32\!\cdots\!07$$$$T^{37} +$$$$43\!\cdots\!87$$$$T^{38} -$$$$12\!\cdots\!26$$$$T^{39} +$$$$15\!\cdots\!29$$$$T^{40} -$$$$46\!\cdots\!43$$$$T^{41} +$$$$53\!\cdots\!42$$$$T^{42} -$$$$15\!\cdots\!16$$$$T^{43} +$$$$17\!\cdots\!02$$$$T^{44} -$$$$52\!\cdots\!20$$$$T^{45} +$$$$55\!\cdots\!09$$$$T^{46} -$$$$16\!\cdots\!10$$$$T^{47} +$$$$16\!\cdots\!13$$$$T^{48} -$$$$51\!\cdots\!11$$$$T^{49} +$$$$49\!\cdots\!75$$$$T^{50} -$$$$14\!\cdots\!47$$$$T^{51} +$$$$13\!\cdots\!29$$$$T^{52} -$$$$41\!\cdots\!23$$$$T^{53} +$$$$37\!\cdots\!43$$$$T^{54} -$$$$11\!\cdots\!81$$$$T^{55} +$$$$97\!\cdots\!45$$$$T^{56} -$$$$28\!\cdots\!96$$$$T^{57} +$$$$24\!\cdots\!48$$$$T^{58} -$$$$72\!\cdots\!74$$$$T^{59} +$$$$59\!\cdots\!09$$$$T^{60} -$$$$17\!\cdots\!12$$$$T^{61} +$$$$13\!\cdots\!88$$$$T^{62} -$$$$17\!\cdots\!12$$$$p T^{63} +$$$$59\!\cdots\!09$$$$p^{2} T^{64} -$$$$72\!\cdots\!74$$$$p^{3} T^{65} +$$$$24\!\cdots\!48$$$$p^{4} T^{66} -$$$$28\!\cdots\!96$$$$p^{5} T^{67} +$$$$97\!\cdots\!45$$$$p^{6} T^{68} -$$$$11\!\cdots\!81$$$$p^{7} T^{69} +$$$$37\!\cdots\!43$$$$p^{8} T^{70} -$$$$41\!\cdots\!23$$$$p^{9} T^{71} +$$$$13\!\cdots\!29$$$$p^{10} T^{72} -$$$$14\!\cdots\!47$$$$p^{11} T^{73} +$$$$49\!\cdots\!75$$$$p^{12} T^{74} -$$$$51\!\cdots\!11$$$$p^{13} T^{75} +$$$$16\!\cdots\!13$$$$p^{14} T^{76} -$$$$16\!\cdots\!10$$$$p^{15} T^{77} +$$$$55\!\cdots\!09$$$$p^{16} T^{78} -$$$$52\!\cdots\!20$$$$p^{17} T^{79} +$$$$17\!\cdots\!02$$$$p^{18} T^{80} -$$$$15\!\cdots\!16$$$$p^{19} T^{81} +$$$$53\!\cdots\!42$$$$p^{20} T^{82} -$$$$46\!\cdots\!43$$$$p^{21} T^{83} +$$$$15\!\cdots\!29$$$$p^{22} T^{84} -$$$$12\!\cdots\!26$$$$p^{23} T^{85} +$$$$43\!\cdots\!87$$$$p^{24} T^{86} -$$$$32\!\cdots\!07$$$$p^{25} T^{87} +$$$$11\!\cdots\!04$$$$p^{26} T^{88} -$$$$81\!\cdots\!24$$$$p^{27} T^{89} +$$$$28\!\cdots\!98$$$$p^{28} T^{90} -$$$$19\!\cdots\!86$$$$p^{29} T^{91} +$$$$69\!\cdots\!98$$$$p^{30} T^{92} -$$$$42\!\cdots\!30$$$$p^{31} T^{93} +$$$$15\!\cdots\!21$$$$p^{32} T^{94} -$$$$88\!\cdots\!82$$$$p^{33} T^{95} +$$$$14\!\cdots\!07$$$$p^{35} T^{96} -$$$$17\!\cdots\!35$$$$p^{35} T^{97} +$$$$67\!\cdots\!37$$$$p^{36} T^{98} -$$$$30\!\cdots\!18$$$$p^{37} T^{99} +$$$$12\!\cdots\!63$$$$p^{38} T^{100} -$$$$51\!\cdots\!69$$$$p^{39} T^{101} +$$$$22\!\cdots\!84$$$$p^{40} T^{102} -$$$$79\!\cdots\!21$$$$p^{41} T^{103} +$$$$35\!\cdots\!69$$$$p^{42} T^{104} -$$$$10\!\cdots\!25$$$$p^{43} T^{105} + 52867138649957586404 p^{44} T^{106} - 1369711459703168685 p^{45} T^{107} + 709635441791067748 p^{46} T^{108} - 15084279881819169 p^{47} T^{109} + 8543973444907455 p^{48} T^{110} - 143835216523101 p^{49} T^{111} + 90866686756235 p^{50} T^{112} - 1155092737221 p^{51} T^{113} + 836545435517 p^{52} T^{114} - 7503345868 p^{53} T^{115} + 6483933530 p^{54} T^{116} - 36979223 p^{55} T^{117} + 1766562 p^{57} T^{118} - 122964 p^{57} T^{119} + 193024 p^{58} T^{120} - 9 p^{60} T^{121} + 618 p^{60} T^{122} + p^{62} T^{124}$$
29 $$1 + p T + 1151 T^{2} + 24949 T^{3} + 592843 T^{4} + 10459661 T^{5} + 189372949 T^{6} + 2852150373 T^{7} + 42986574078 T^{8} + 569476260387 T^{9} + 7471321071543 T^{10} + 88853528070600 T^{11} + 1042077885720216 T^{12} + 11289337427540265 T^{13} + 120453178246094682 T^{14} + 1201834094988667006 T^{15} + 11812307750526894128 T^{16} +$$$$10\!\cdots\!82$$$$T^{17} +$$$$10\!\cdots\!40$$$$T^{18} +$$$$86\!\cdots\!01$$$$T^{19} +$$$$74\!\cdots\!23$$$$T^{20} +$$$$60\!\cdots\!24$$$$T^{21} +$$$$48\!\cdots\!53$$$$T^{22} +$$$$37\!\cdots\!00$$$$T^{23} +$$$$28\!\cdots\!54$$$$T^{24} +$$$$21\!\cdots\!16$$$$T^{25} +$$$$15\!\cdots\!57$$$$T^{26} +$$$$10\!\cdots\!15$$$$T^{27} +$$$$74\!\cdots\!43$$$$T^{28} +$$$$49\!\cdots\!50$$$$T^{29} +$$$$32\!\cdots\!59$$$$T^{30} +$$$$20\!\cdots\!17$$$$T^{31} +$$$$13\!\cdots\!77$$$$T^{32} +$$$$82\!\cdots\!76$$$$T^{33} +$$$$51\!\cdots\!44$$$$T^{34} +$$$$29\!\cdots\!67$$$$T^{35} +$$$$18\!\cdots\!82$$$$T^{36} +$$$$10\!\cdots\!28$$$$T^{37} +$$$$59\!\cdots\!07$$$$T^{38} +$$$$32\!\cdots\!50$$$$T^{39} +$$$$18\!\cdots\!01$$$$T^{40} +$$$$95\!\cdots\!62$$$$T^{41} +$$$$54\!\cdots\!33$$$$T^{42} +$$$$26\!\cdots\!83$$$$T^{43} +$$$$14\!\cdots\!36$$$$T^{44} +$$$$65\!\cdots\!35$$$$T^{45} +$$$$36\!\cdots\!10$$$$T^{46} +$$$$14\!\cdots\!78$$$$T^{47} +$$$$78\!\cdots\!68$$$$T^{48} +$$$$23\!\cdots\!67$$$$T^{49} +$$$$13\!\cdots\!92$$$$T^{50} +$$$$61\!\cdots\!78$$$$T^{51} +$$$$61\!\cdots\!38$$$$T^{52} -$$$$17\!\cdots\!55$$$$T^{53} -$$$$77\!\cdots\!17$$$$T^{54} -$$$$10\!\cdots\!33$$$$T^{55} -$$$$48\!\cdots\!91$$$$T^{56} -$$$$44\!\cdots\!84$$$$T^{57} -$$$$20\!\cdots\!52$$$$T^{58} -$$$$15\!\cdots\!60$$$$T^{59} -$$$$70\!\cdots\!17$$$$T^{60} -$$$$50\!\cdots\!07$$$$T^{61} -$$$$21\!\cdots\!34$$$$T^{62} -$$$$50\!\cdots\!07$$$$p T^{63} -$$$$70\!\cdots\!17$$$$p^{2} T^{64} -$$$$15\!\cdots\!60$$$$p^{3} T^{65} -$$$$20\!\cdots\!52$$$$p^{4} T^{66} -$$$$44\!\cdots\!84$$$$p^{5} T^{67} -$$$$48\!\cdots\!91$$$$p^{6} T^{68} -$$$$10\!\cdots\!33$$$$p^{7} T^{69} -$$$$77\!\cdots\!17$$$$p^{8} T^{70} -$$$$17\!\cdots\!55$$$$p^{9} T^{71} +$$$$61\!\cdots\!38$$$$p^{10} T^{72} +$$$$61\!\cdots\!78$$$$p^{11} T^{73} +$$$$13\!\cdots\!92$$$$p^{12} T^{74} +$$$$23\!\cdots\!67$$$$p^{13} T^{75} +$$$$78\!\cdots\!68$$$$p^{14} T^{76} +$$$$14\!\cdots\!78$$$$p^{15} T^{77} +$$$$36\!\cdots\!10$$$$p^{16} T^{78} +$$$$65\!\cdots\!35$$$$p^{17} T^{79} +$$$$14\!\cdots\!36$$$$p^{18} T^{80} +$$$$26\!\cdots\!83$$$$p^{19} T^{81} +$$$$54\!\cdots\!33$$$$p^{20} T^{82} +$$$$95\!\cdots\!62$$$$p^{21} T^{83} +$$$$18\!\cdots\!01$$$$p^{22} T^{84} +$$$$32\!\cdots\!50$$$$p^{23} T^{85} +$$$$59\!\cdots\!07$$$$p^{24} T^{86} +$$$$10\!\cdots\!28$$$$p^{25} T^{87} +$$$$18\!\cdots\!82$$$$p^{26} T^{88} +$$$$29\!\cdots\!67$$$$p^{27} T^{89} +$$$$51\!\cdots\!44$$$$p^{28} T^{90} +$$$$82\!\cdots\!76$$$$p^{29} T^{91} +$$$$13\!\cdots\!77$$$$p^{30} T^{92} +$$$$20\!\cdots\!17$$$$p^{31} T^{93} +$$$$32\!\cdots\!59$$$$p^{32} T^{94} +$$$$49\!\cdots\!50$$$$p^{33} T^{95} +$$$$74\!\cdots\!43$$$$p^{34} T^{96} +$$$$10\!\cdots\!15$$$$p^{35} T^{97} +$$$$15\!\cdots\!57$$$$p^{36} T^{98} +$$$$21\!\cdots\!16$$$$p^{37} T^{99} +$$$$28\!\cdots\!54$$$$p^{38} T^{100} +$$$$37\!\cdots\!00$$$$p^{39} T^{101} +$$$$48\!\cdots\!53$$$$p^{40} T^{102} +$$$$60\!\cdots\!24$$$$p^{41} T^{103} +$$$$74\!\cdots\!23$$$$p^{42} T^{104} +$$$$86\!\cdots\!01$$$$p^{43} T^{105} +$$$$10\!\cdots\!40$$$$p^{44} T^{106} +$$$$10\!\cdots\!82$$$$p^{45} T^{107} + 11812307750526894128 p^{46} T^{108} + 1201834094988667006 p^{47} T^{109} + 120453178246094682 p^{48} T^{110} + 11289337427540265 p^{49} T^{111} + 1042077885720216 p^{50} T^{112} + 88853528070600 p^{51} T^{113} + 7471321071543 p^{52} T^{114} + 569476260387 p^{53} T^{115} + 42986574078 p^{54} T^{116} + 2852150373 p^{55} T^{117} + 189372949 p^{56} T^{118} + 10459661 p^{57} T^{119} + 592843 p^{58} T^{120} + 24949 p^{59} T^{121} + 1151 p^{60} T^{122} + p^{62} T^{123} + p^{62} T^{124}$$
31 $$1 - 20 T + 1099 T^{2} - 20368 T^{3} + 613911 T^{4} - 10482659 T^{5} + 230760911 T^{6} - 3632253834 T^{7} + 65370958778 T^{8} - 952174617676 T^{9} + 14846885883464 T^{10} - 201174793786034 T^{11} + 2811524574670439 T^{12} - 35639394722807664 T^{13} + 456148234544252928 T^{14} - 5438823086723966720 T^{15} + 64684184137789569500 T^{16} -$$$$72\!\cdots\!85$$$$T^{17} +$$$$26\!\cdots\!79$$$$p T^{18} -$$$$87\!\cdots\!02$$$$T^{19} +$$$$92\!\cdots\!09$$$$T^{20} -$$$$93\!\cdots\!67$$$$T^{21} +$$$$94\!\cdots\!88$$$$T^{22} -$$$$92\!\cdots\!12$$$$T^{23} +$$$$88\!\cdots\!86$$$$T^{24} -$$$$82\!\cdots\!83$$$$T^{25} +$$$$76\!\cdots\!13$$$$T^{26} -$$$$68\!\cdots\!74$$$$T^{27} +$$$$60\!\cdots\!47$$$$T^{28} -$$$$52\!\cdots\!38$$$$T^{29} +$$$$45\!\cdots\!45$$$$T^{30} -$$$$37\!\cdots\!52$$$$T^{31} +$$$$31\!\cdots\!04$$$$T^{32} -$$$$25\!\cdots\!73$$$$T^{33} +$$$$20\!\cdots\!67$$$$T^{34} -$$$$16\!\cdots\!32$$$$T^{35} +$$$$12\!\cdots\!38$$$$T^{36} -$$$$95\!\cdots\!50$$$$T^{37} +$$$$71\!\cdots\!69$$$$T^{38} -$$$$53\!\cdots\!24$$$$T^{39} +$$$$39\!\cdots\!41$$$$T^{40} -$$$$28\!\cdots\!84$$$$T^{41} +$$$$20\!\cdots\!54$$$$T^{42} -$$$$14\!\cdots\!98$$$$T^{43} +$$$$98\!\cdots\!05$$$$T^{44} -$$$$67\!\cdots\!79$$$$T^{45} +$$$$45\!\cdots\!01$$$$T^{46} -$$$$30\!\cdots\!78$$$$T^{47} +$$$$20\!\cdots\!44$$$$T^{48} -$$$$13\!\cdots\!38$$$$T^{49} +$$$$84\!\cdots\!48$$$$T^{50} -$$$$53\!\cdots\!25$$$$T^{51} +$$$$33\!\cdots\!60$$$$T^{52} -$$$$20\!\cdots\!65$$$$T^{53} +$$$$12\!\cdots\!30$$$$T^{54} -$$$$77\!\cdots\!82$$$$T^{55} +$$$$46\!\cdots\!26$$$$T^{56} -$$$$27\!\cdots\!85$$$$T^{57} +$$$$16\!\cdots\!14$$$$T^{58} -$$$$94\!\cdots\!98$$$$T^{59} +$$$$53\!\cdots\!53$$$$T^{60} -$$$$30\!\cdots\!83$$$$T^{61} +$$$$17\!\cdots\!48$$$$T^{62} -$$$$30\!\cdots\!83$$$$p T^{63} +$$$$53\!\cdots\!53$$$$p^{2} T^{64} -$$$$94\!\cdots\!98$$$$p^{3} T^{65} +$$$$16\!\cdots\!14$$$$p^{4} T^{66} -$$$$27\!\cdots\!85$$$$p^{5} T^{67} +$$$$46\!\cdots\!26$$$$p^{6} T^{68} -$$$$77\!\cdots\!82$$$$p^{7} T^{69} +$$$$12\!\cdots\!30$$$$p^{8} T^{70} -$$$$20\!\cdots\!65$$$$p^{9} T^{71} +$$$$33\!\cdots\!60$$$$p^{10} T^{72} -$$$$53\!\cdots\!25$$$$p^{11} T^{73} +$$$$84\!\cdots\!48$$$$p^{12} T^{74} -$$$$13\!\cdots\!38$$$$p^{13} T^{75} +$$$$20\!\cdots\!44$$$$p^{14} T^{76} -$$$$30\!\cdots\!78$$$$p^{15} T^{77} +$$$$45\!\cdots\!01$$$$p^{16} T^{78} -$$$$67\!\cdots\!79$$$$p^{17} T^{79} +$$$$98\!\cdots\!05$$$$p^{18} T^{80} -$$$$14\!\cdots\!98$$$$p^{19} T^{81} +$$$$20\!\cdots\!54$$$$p^{20} T^{82} -$$$$28\!\cdots\!84$$$$p^{21} T^{83} +$$$$39\!\cdots\!41$$$$p^{22} T^{84} -$$$$53\!\cdots\!24$$$$p^{23} T^{85} +$$$$71\!\cdots\!69$$$$p^{24} T^{86} -$$$$95\!\cdots\!50$$$$p^{25} T^{87} +$$$$12\!\cdots\!38$$$$p^{26} T^{88} -$$$$16\!\cdots\!32$$$$p^{27} T^{89} +$$$$20\!\cdots\!67$$$$p^{28} T^{90} -$$$$25\!\cdots\!73$$$$p^{29} T^{91} +$$$$31\!\cdots\!04$$$$p^{30} T^{92} -$$$$37\!\cdots\!52$$$$p^{31} T^{93} +$$$$45\!\cdots\!45$$$$p^{32} T^{94} -$$$$52\!\cdots\!38$$$$p^{33} T^{95} +$$$$60\!\cdots\!47$$$$p^{34} T^{96} -$$$$68\!\cdots\!74$$$$p^{35} T^{97} +$$$$76\!\cdots\!13$$$$p^{36} T^{98} -$$$$82\!\cdots\!83$$$$p^{37} T^{99} +$$$$88\!\cdots\!86$$$$p^{38} T^{100} -$$$$92\!\cdots\!12$$$$p^{39} T^{101} +$$$$94\!\cdots\!88$$$$p^{40} T^{102} -$$$$93\!\cdots\!67$$$$p^{41} T^{103} +$$$$92\!\cdots\!09$$$$p^{42} T^{104} -$$$$87\!\cdots\!02$$$$p^{43} T^{105} +$$$$26\!\cdots\!79$$$$p^{45} T^{106} -$$$$72\!\cdots\!85$$$$p^{45} T^{107} + 64684184137789569500 p^{46} T^{108} - 5438823086723966720 p^{47} T^{109} + 456148234544252928 p^{48} T^{110} - 35639394722807664 p^{49} T^{111} + 2811524574670439 p^{50} T^{112} - 201174793786034 p^{51} T^{113} + 14846885883464 p^{52} T^{114} - 952174617676 p^{53} T^{115} + 65370958778 p^{54} T^{116} - 3632253834 p^{55} T^{117} + 230760911 p^{56} T^{118} - 10482659 p^{57} T^{119} + 613911 p^{58} T^{120} - 20368 p^{59} T^{121} + 1099 p^{60} T^{122} - 20 p^{61} T^{123} + p^{62} T^{124}$$
37 $$1 - 35 T + 1552 T^{2} - 40398 T^{3} + 1091304 T^{4} - 23136378 T^{5} + 483178993 T^{6} - 8775598435 T^{7} + 154541477744 T^{8} - 2482116534067 T^{9} + 38503520323611 T^{10} - 558812913955331 T^{11} + 7836213448823241 T^{12} - 104378495933838552 T^{13} + 1345969608201650981 T^{14} - 16647464493229023219 T^{15} +$$$$19\!\cdots\!12$$$$T^{16} -$$$$23\!\cdots\!91$$$$T^{17} +$$$$26\!\cdots\!95$$$$T^{18} -$$$$28\!\cdots\!06$$$$T^{19} +$$$$30\!\cdots\!79$$$$T^{20} -$$$$31\!\cdots\!78$$$$T^{21} +$$$$32\!\cdots\!26$$$$T^{22} -$$$$31\!\cdots\!85$$$$T^{23} +$$$$30\!\cdots\!77$$$$T^{24} -$$$$29\!\cdots\!24$$$$T^{25} +$$$$27\!\cdots\!25$$$$T^{26} -$$$$24\!\cdots\!54$$$$T^{27} +$$$$22\!\cdots\!08$$$$T^{28} -$$$$19\!\cdots\!28$$$$T^{29} +$$$$17\!\cdots\!62$$$$T^{30} -$$$$14\!\cdots\!47$$$$T^{31} +$$$$12\!\cdots\!64$$$$T^{32} -$$$$10\!\cdots\!42$$$$T^{33} +$$$$82\!\cdots\!89$$$$T^{34} -$$$$65\!\cdots\!69$$$$T^{35} +$$$$52\!\cdots\!12$$$$T^{36} -$$$$40\!\cdots\!06$$$$T^{37} +$$$$31\!\cdots\!08$$$$T^{38} -$$$$24\!\cdots\!35$$$$T^{39} +$$$$18\!\cdots\!18$$$$T^{40} -$$$$13\!\cdots\!13$$$$T^{41} +$$$$99\!\cdots\!57$$$$T^{42} -$$$$72\!\cdots\!25$$$$T^{43} +$$$$52\!\cdots\!02$$$$T^{44} -$$$$37\!\cdots\!40$$$$T^{45} +$$$$26\!\cdots\!11$$$$T^{46} -$$$$18\!\cdots\!73$$$$T^{47} +$$$$12\!\cdots\!73$$$$T^{48} -$$$$87\!\cdots\!49$$$$T^{49} +$$$$59\!\cdots\!69$$$$T^{50} -$$$$40\!\cdots\!10$$$$T^{51} +$$$$26\!\cdots\!59$$$$T^{52} -$$$$17\!\cdots\!56$$$$T^{53} +$$$$11\!\cdots\!53$$$$T^{54} -$$$$74\!\cdots\!63$$$$T^{55} +$$$$48\!\cdots\!67$$$$T^{56} -$$$$30\!\cdots\!81$$$$T^{57} +$$$$19\!\cdots\!66$$$$T^{58} -$$$$12\!\cdots\!33$$$$T^{59} +$$$$75\!\cdots\!79$$$$T^{60} -$$$$12\!\cdots\!01$$$$p T^{61} +$$$$28\!\cdots\!36$$$$T^{62} -$$$$12\!\cdots\!01$$$$p^{2} T^{63} +$$$$75\!\cdots\!79$$$$p^{2} T^{64} -$$$$12\!\cdots\!33$$$$p^{3} T^{65} +$$$$19\!\cdots\!66$$$$p^{4} T^{66} -$$$$30\!\cdots\!81$$$$p^{5} T^{67} +$$$$48\!\cdots\!67$$$$p^{6} T^{68} -$$$$74\!\cdots\!63$$$$p^{7} T^{69} +$$$$11\!\cdots\!53$$$$p^{8} T^{70} -$$$$17\!\cdots\!56$$$$p^{9} T^{71} +$$$$26\!\cdots\!59$$$$p^{10} T^{72} -$$$$40\!\cdots\!10$$$$p^{11} T^{73} +$$$$59\!\cdots\!69$$$$p^{12} T^{74} -$$$$87\!\cdots\!49$$$$p^{13} T^{75} +$$$$12\!\cdots\!73$$$$p^{14} T^{76} -$$$$18\!\cdots\!73$$$$p^{15} T^{77} +$$$$26\!\cdots\!11$$$$p^{16} T^{78} -$$$$37\!\cdots\!40$$$$p^{17} T^{79} +$$$$52\!\cdots\!02$$$$p^{18} T^{80} -$$$$72\!\cdots\!25$$$$p^{19} T^{81} +$$$$99\!\cdots\!57$$$$p^{20} T^{82} -$$$$13\!\cdots\!13$$$$p^{21} T^{83} +$$$$18\!\cdots\!18$$$$p^{22} T^{84} -$$$$24\!\cdots\!35$$$$p^{23} T^{85} +$$$$31\!\cdots\!08$$$$p^{24} T^{86} -$$$$40\!\cdots\!06$$$$p^{25} T^{87} +$$$$52\!\cdots\!12$$$$p^{26} T^{88} -$$$$65\!\cdots\!69$$$$p^{27} T^{89} +$$$$82\!\cdots\!89$$$$p^{28} T^{90} -$$$$10\!\cdots\!42$$$$p^{29} T^{91} +$$$$12\!\cdots\!64$$$$p^{30} T^{92} -$$$$14\!\cdots\!47$$$$p^{31} T^{93} +$$$$17\!\cdots\!62$$$$p^{32} T^{94} -$$$$19\!\cdots\!28$$$$p^{33} T^{95} +$$$$22\!\cdots\!08$$$$p^{34} T^{96} -$$$$24\!\cdots\!54$$$$p^{35} T^{97} +$$$$27\!\cdots\!25$$$$p^{36} T^{98} -$$$$29\!\cdots\!24$$$$p^{37} T^{99} +$$$$30\!\cdots\!77$$$$p^{38} T^{100} -$$$$31\!\cdots\!85$$$$p^{39} T^{101} +$$$$32\!\cdots\!26$$$$p^{40} T^{102} -$$$$31\!\cdots\!78$$$$p^{41} T^{103} +$$$$30\!\cdots\!79$$$$p^{42} T^{104} -$$$$28\!\cdots\!06$$$$p^{43} T^{105} +$$$$26\!\cdots\!95$$$$p^{44} T^{106} -$$$$23\!\cdots\!91$$$$p^{45} T^{107} +$$$$19\!\cdots\!12$$$$p^{46} T^{108} - 16647464493229023219 p^{47} T^{109} + 1345969608201650981 p^{48} T^{110} - 104378495933838552 p^{49} T^{111} + 7836213448823241 p^{50} T^{112} - 558812913955331 p^{51} T^{113} + 38503520323611 p^{52} T^{114} - 2482116534067 p^{53} T^{115} + 154541477744 p^{54} T^{116} - 8775598435 p^{55} T^{117} + 483178993 p^{56} T^{118} - 23136378 p^{57} T^{119} + 1091304 p^{58} T^{120} - 40398 p^{59} T^{121} + 1552 p^{60} T^{122} - 35 p^{61} T^{123} + p^{62} T^{124}$$
41 $$1 - 13 T + 1187 T^{2} - 13497 T^{3} + 681478 T^{4} - 6835121 T^{5} + 253401446 T^{6} - 2250072841 T^{7} + 68889563541 T^{8} - 541186391309 T^{9} + 14648663407429 T^{10} - 101293438863789 T^{11} + 2545023114822986 T^{12} - 15332170561691967 T^{13} + 372666076372715501 T^{14} - 46904174320175773 p T^{15} + 47096732432936447727 T^{16} -$$$$20\!\cdots\!54$$$$T^{17} +$$$$52\!\cdots\!94$$$$T^{18} -$$$$18\!\cdots\!80$$$$T^{19} +$$$$52\!\cdots\!05$$$$T^{20} -$$$$13\!\cdots\!21$$$$T^{21} +$$$$46\!\cdots\!26$$$$T^{22} -$$$$79\!\cdots\!26$$$$T^{23} +$$$$23\!\cdots\!49$$$$p^{2} T^{24} -$$$$31\!\cdots\!40$$$$T^{25} +$$$$29\!\cdots\!48$$$$T^{26} +$$$$14\!\cdots\!94$$$$T^{27} +$$$$21\!\cdots\!93$$$$T^{28} +$$$$19\!\cdots\!08$$$$T^{29} +$$$$14\!\cdots\!12$$$$T^{30} +$$$$24\!\cdots\!94$$$$T^{31} +$$$$96\!\cdots\!24$$$$T^{32} +$$$$22\!\cdots\!23$$$$T^{33} +$$$$60\!\cdots\!95$$$$T^{34} +$$$$17\!\cdots\!78$$$$T^{35} +$$$$36\!\cdots\!28$$$$T^{36} +$$$$12\!\cdots\!45$$$$T^{37} +$$$$20\!\cdots\!48$$$$T^{38} +$$$$82\!\cdots\!18$$$$T^{39} +$$$$11\!\cdots\!20$$$$T^{40} +$$$$50\!\cdots\!51$$$$T^{41} +$$$$62\!\cdots\!02$$$$T^{42} +$$$$29\!\cdots\!64$$$$T^{43} +$$$$32\!\cdots\!01$$$$T^{44} +$$$$16\!\cdots\!09$$$$T^{45} +$$$$16\!\cdots\!75$$$$T^{46} +$$$$84\!\cdots\!57$$$$T^{47} +$$$$81\!\cdots\!07$$$$T^{48} +$$$$43\!\cdots\!19$$$$T^{49} +$$$$39\!\cdots\!13$$$$T^{50} +$$$$21\!\cdots\!83$$$$T^{51} +$$$$18\!\cdots\!16$$$$T^{52} +$$$$99\!\cdots\!07$$$$T^{53} +$$$$82\!\cdots\!84$$$$T^{54} +$$$$45\!\cdots\!47$$$$T^{55} +$$$$36\!\cdots\!85$$$$T^{56} +$$$$20\!\cdots\!94$$$$T^{57} +$$$$15\!\cdots\!91$$$$T^{58} +$$$$88\!\cdots\!37$$$$T^{59} +$$$$67\!\cdots\!53$$$$T^{60} +$$$$37\!\cdots\!15$$$$T^{61} +$$$$27\!\cdots\!98$$$$T^{62} +$$$$37\!\cdots\!15$$$$p T^{63} +$$$$67\!\cdots\!53$$$$p^{2} T^{64} +$$$$88\!\cdots\!37$$$$p^{3} T^{65} +$$$$15\!\cdots\!91$$$$p^{4} T^{66} +$$$$20\!\cdots\!94$$$$p^{5} T^{67} +$$$$36\!\cdots\!85$$$$p^{6} T^{68} +$$$$45\!\cdots\!47$$$$p^{7} T^{69} +$$$$82\!\cdots\!84$$$$p^{8} T^{70} +$$$$99\!\cdots\!07$$$$p^{9} T^{71} +$$$$18\!\cdots\!16$$$$p^{10} T^{72} +$$$$21\!\cdots\!83$$$$p^{11} T^{73} +$$$$39\!\cdots\!13$$$$p^{12} T^{74} +$$$$43\!\cdots\!19$$$$p^{13} T^{75} +$$$$81\!\cdots\!07$$$$p^{14} T^{76} +$$$$84\!\cdots\!57$$$$p^{15} T^{77} +$$$$16\!\cdots\!75$$$$p^{16} T^{78} +$$$$16\!\cdots\!09$$$$p^{17} T^{79} +$$$$32\!\cdots\!01$$$$p^{18} T^{80} +$$$$29\!\cdots\!64$$$$p^{19} T^{81} +$$$$62\!\cdots\!02$$$$p^{20} T^{82} +$$$$50\!\cdots\!51$$$$p^{21} T^{83} +$$$$11\!\cdots\!20$$$$p^{22} T^{84} +$$$$82\!\cdots\!18$$$$p^{23} T^{85} +$$$$20\!\cdots\!48$$$$p^{24} T^{86} +$$$$12\!\cdots\!45$$$$p^{25} T^{87} +$$$$36\!\cdots\!28$$$$p^{26} T^{88} +$$$$17\!\cdots\!78$$$$p^{27} T^{89} +$$$$60\!\cdots\!95$$$$p^{28} T^{90} +$$$$22\!\cdots\!23$$$$p^{29} T^{91} +$$$$96\!\cdots\!24$$$$p^{30} T^{92} +$$$$24\!\cdots\!94$$$$p^{31} T^{93} +$$$$14\!\cdots\!12$$$$p^{32} T^{94} +$$$$19\!\cdots\!08$$$$p^{33} T^{95} +$$$$21\!\cdots\!93$$$$p^{34} T^{96} +$$$$14\!\cdots\!94$$$$p^{35} T^{97} +$$$$29\!\cdots\!48$$$$p^{36} T^{98} -$$$$31\!\cdots\!40$$$$p^{37} T^{99} +$$$$23\!\cdots\!49$$$$p^{40} T^{100} -$$$$79\!\cdots\!26$$$$p^{39} T^{101} +$$$$46\!\cdots\!26$$$$p^{40} T^{102} -$$$$13\!\cdots\!21$$$$p^{41} T^{103} +$$$$52\!\cdots\!05$$$$p^{42} T^{104} -$$$$18\!\cdots\!80$$$$p^{43} T^{105} +$$$$52\!\cdots\!94$$$$p^{44} T^{106} -$$$$20\!\cdots\!54$$$$p^{45} T^{107} + 47096732432936447727 p^{46} T^{108} - 46904174320175773 p^{48} T^{109} + 372666076372715501 p^{48} T^{110} - 15332170561691967 p^{49} T^{111} + 2545023114822986 p^{50} T^{112} - 101293438863789 p^{51} T^{113} + 14648663407429 p^{52} T^{114} - 541186391309 p^{53} T^{115} + 68889563541 p^{54} T^{116} - 2250072841 p^{55} T^{117} + 253401446 p^{56} T^{118} - 6835121 p^{57} T^{119} + 681478 p^{58} T^{120} - 13497 p^{59} T^{121} + 1187 p^{60} T^{122} - 13 p^{61} T^{123} + p^{62} T^{124}$$
43 $$1 + 4 T + 1291 T^{2} + 4991 T^{3} + 835574 T^{4} + 3091538 T^{5} + 361232298 T^{6} + 1268095124 T^{7} + 117291243837 T^{8} + 387652389533 T^{9} + 30501922854490 T^{10} + 94246069967358 T^{11} + 6616913672389734 T^{12} + 18992239266566040 T^{13} + 1231693622031158359 T^{14} + 3265243641984663247 T^{15} +$$$$20\!\cdots\!18$$$$T^{16} +$$$$48\!\cdots\!40$$$$T^{17} +$$$$29\!\cdots\!89$$$$T^{18} +$$$$65\!\cdots\!29$$$$T^{19} +$$$$38\!\cdots\!91$$$$T^{20} +$$$$77\!\cdots\!27$$$$T^{21} +$$$$45\!\cdots\!30$$$$T^{22} +$$$$84\!\cdots\!56$$$$T^{23} +$$$$49\!\cdots\!74$$$$T^{24} +$$$$84\!\cdots\!50$$$$T^{25} +$$$$50\!\cdots\!98$$$$T^{26} +$$$$77\!\cdots\!00$$$$T^{27} +$$$$47\!\cdots\!88$$$$T^{28} +$$$$67\!\cdots\!37$$$$T^{29} +$$$$42\!\cdots\!82$$$$T^{30} +$$$$54\!\cdots\!73$$$$T^{31} +$$$$34\!\cdots\!62$$$$T^{32} +$$$$42\!\cdots\!67$$$$T^{33} +$$$$27\!\cdots\!08$$$$T^{34} +$$$$31\!\cdots\!20$$$$T^{35} +$$$$20\!\cdots\!71$$$$T^{36} +$$$$21\!\cdots\!68$$$$T^{37} +$$$$14\!\cdots\!32$$$$T^{38} +$$$$14\!\cdots\!97$$$$T^{39} +$$$$96\!\cdots\!42$$$$T^{40} +$$$$95\!\cdots\!51$$$$T^{41} +$$$$61\!\cdots\!29$$$$T^{42} +$$$$60\!\cdots\!65$$$$T^{43} +$$$$37\!\cdots\!32$$$$T^{44} +$$$$36\!\cdots\!51$$$$T^{45} +$$$$22\!\cdots\!81$$$$T^{46} +$$$$21\!\cdots\!48$$$$T^{47} +$$$$12\!\cdots\!80$$$$T^{48} +$$$$27\!\cdots\!13$$$$p T^{49} +$$$$68\!\cdots\!32$$$$T^{50} +$$$$64\!\cdots\!47$$$$T^{51} +$$$$35\!\cdots\!26$$$$T^{52} +$$$$33\!\cdots\!58$$$$T^{53} +$$$$41\!\cdots\!68$$$$p T^{54} +$$$$16\!\cdots\!62$$$$T^{55} +$$$$87\!\cdots\!29$$$$T^{56} +$$$$81\!\cdots\!25$$$$T^{57} +$$$$41\!\cdots\!63$$$$T^{58} +$$$$37\!\cdots\!99$$$$T^{59} +$$$$18\!\cdots\!57$$$$T^{60} +$$$$16\!\cdots\!92$$$$T^{61} +$$$$81\!\cdots\!24$$$$T^{62} +$$$$16\!\cdots\!92$$$$p T^{63} +$$$$18\!\cdots\!57$$$$p^{2} T^{64} +$$$$37\!\cdots\!99$$$$p^{3} T^{65} +$$$$41\!\cdots\!63$$$$p^{4} T^{66} +$$$$81\!\cdots\!25$$$$p^{5} T^{67} +$$$$87\!\cdots\!29$$$$p^{6} T^{68} +$$$$16\!\cdots\!62$$$$p^{7} T^{69} +$$$$41\!\cdots\!68$$$$p^{9} T^{70} +$$$$33\!\cdots\!58$$$$p^{9} T^{71} +$$$$35\!\cdots\!26$$$$p^{10} T^{72} +$$$$64\!\cdots\!47$$$$p^{11} T^{73} +$$$$68\!\cdots\!32$$$$p^{12} T^{74} +$$$$27\!\cdots\!13$$$$p^{14} T^{75} +$$$$12\!\cdots\!80$$$$p^{14} T^{76} +$$$$21\!\cdots\!48$$$$p^{15} T^{77} +$$$$22\!\cdots\!81$$$$p^{16} T^{78} +$$$$36\!\cdots\!51$$$$p^{17} T^{79} +$$$$37\!\cdots\!32$$$$p^{18} T^{80} +$$$$60\!\cdots\!65$$$$p^{19} T^{81} +$$$$61\!\cdots\!29$$$$p^{20} T^{82} +$$$$95\!\cdots\!51$$$$p^{21} T^{83} +$$$$96\!\cdots\!42$$$$p^{22} T^{84} +$$$$14\!\cdots\!97$$$$p^{23} T^{85} +$$$$14\!\cdots\!32$$$$p^{24} T^{86} +$$$$21\!\cdots\!68$$$$p^{25} T^{87} +$$$$20\!\cdots\!71$$$$p^{26} T^{88} +$$$$31\!\cdots\!20$$$$p^{27} T^{89} +$$$$27\!\cdots\!08$$$$p^{28} T^{90} +$$$$42\!\cdots\!67$$$$p^{29} T^{91} +$$$$34\!\cdots\!62$$$$p^{30} T^{92} +$$$$54\!\cdots\!73$$$$p^{31} T^{93} +$$$$42\!\cdots\!82$$$$p^{32} T^{94} +$$$$67\!\cdots\!37$$$$p^{33} T^{95} +$$$$47\!\cdots\!88$$$$p^{34} T^{96} +$$$$77\!\cdots\!00$$$$p^{35} T^{97} +$$$$50\!\cdots\!98$$$$p^{36} T^{98} +$$$$84\!\cdots\!50$$$$p^{37} T^{99} +$$$$49\!\cdots\!74$$$$p^{38} T^{100} +$$$$84\!\cdots\!56$$$$p^{39} T^{101} +$$$$45\!\cdots\!30$$$$p^{40} T^{102} +$$$$77\!\cdots\!27$$$$p^{41} T^{103} +$$$$38\!\cdots\!91$$$$p^{42} T^{104} +$$$$65\!\cdots\!29$$$$p^{43} T^{105} +$$$$29\!\cdots\!89$$$$p^{44} T^{106} +$$$$48\!\cdots\!40$$$$p^{45} T^{107} +$$$$20\!\cdots\!18$$$$p^{46} T^{108} + 3265243641984663247 p^{47} T^{109} + 1231693622031158359 p^{48} T^{110} + 18992239266566040 p^{49} T^{111} + 6616913672389734 p^{50} T^{112} + 94246069967358 p^{51} T^{113} + 30501922854490 p^{52} T^{114} + 387652389533 p^{53} T^{115} + 117291243837 p^{54} T^{116} + 1268095124 p^{55} T^{117} + 361232298 p^{56} T^{118} + 3091538 p^{57} T^{119} + 835574 p^{58} T^{120} + 4991 p^{59} T^{121} + 1291 p^{60} T^{122} + 4 p^{61} T^{123} + p^{62} T^{124}$$
47 $$1 - 58 T + 2942 T^{2} - 105997 T^{3} + 3414756 T^{4} - 94011213 T^{5} + 2375478474 T^{6} - 54431258896 T^{7} + 1165715541299 T^{8} - 23269781103594 T^{9} + 439632108294533 T^{10} - 7862475882419363 T^{11} + 134279559653727518 T^{12} - 2192341887005516902 T^{13} + 34407335051097870235 T^{14} -$$$$51\!\cdots\!18$$$$T^{15} +$$$$75\!\cdots\!46$$$$T^{16} -$$$$10\!\cdots\!35$$$$T^{17} +$$$$14\!\cdots\!80$$$$T^{18} -$$$$19\!\cdots\!32$$$$T^{19} +$$$$25\!\cdots\!90$$$$T^{20} -$$$$31\!\cdots\!62$$$$T^{21} +$$$$39\!\cdots\!79$$$$T^{22} -$$$$99\!\cdots\!63$$$$p T^{23} +$$$$54\!\cdots\!01$$$$T^{24} -$$$$62\!\cdots\!36$$$$T^{25} +$$$$70\!\cdots\!73$$$$T^{26} -$$$$77\!\cdots\!55$$$$T^{27} +$$$$84\!\cdots\!97$$$$T^{28} -$$$$89\!\cdots\!65$$$$T^{29} +$$$$92\!\cdots\!67$$$$T^{30} -$$$$94\!\cdots\!21$$$$T^{31} +$$$$95\!\cdots\!51$$$$T^{32} -$$$$93\!\cdots\!68$$$$T^{33} +$$$$91\!\cdots\!41$$$$T^{34} -$$$$87\!\cdots\!04$$$$T^{35} +$$$$82\!\cdots\!25$$$$T^{36} -$$$$76\!\cdots\!81$$$$T^{37} +$$$$70\!\cdots\!14$$$$T^{38} -$$$$63\!\cdots\!74$$$$T^{39} +$$$$56\!\cdots\!08$$$$T^{40} -$$$$49\!\cdots\!80$$$$T^{41} +$$$$42\!\cdots\!38$$$$T^{42} -$$$$36\!\cdots\!60$$$$T^{43} +$$$$30\!\cdots\!54$$$$T^{44} -$$$$25\!\cdots\!12$$$$T^{45} +$$$$21\!\cdots\!23$$$$T^{46} -$$$$17\!\cdots\!76$$$$T^{47} +$$$$13\!\cdots\!02$$$$T^{48} -$$$$11\!\cdots\!40$$$$T^{49} +$$$$87\!\cdots\!69$$$$T^{50} -$$$$67\!\cdots\!62$$$$T^{51} +$$$$52\!\cdots\!95$$$$T^{52} -$$$$39\!\cdots\!52$$$$T^{53} +$$$$29\!\cdots\!33$$$$T^{54} -$$$$22\!\cdots\!85$$$$T^{55} +$$$$16\!\cdots\!42$$$$T^{56} -$$$$11\!\cdots\!09$$$$T^{57} +$$$$84\!\cdots\!20$$$$T^{58} -$$$$60\!\cdots\!31$$$$T^{59} +$$$$42\!\cdots\!71$$$$T^{60} -$$$$29\!\cdots\!52$$$$T^{61} +$$$$20\!\cdots\!50$$$$T^{62} -$$$$29\!\cdots\!52$$$$p T^{63} +$$$$42\!\cdots\!71$$$$p^{2} T^{64} -$$$$60\!\cdots\!31$$$$p^{3} T^{65} +$$$$84\!\cdots\!20$$$$p^{4} T^{66} -$$$$11\!\cdots\!09$$$$p^{5} T^{67} +$$$$16\!\cdots\!42$$$$p^{6} T^{68} -$$$$22\!\cdots\!85$$$$p^{7} T^{69} +$$$$29\!\cdots\!33$$$$p^{8} T^{70} -$$$$39\!\cdots\!52$$$$p^{9} T^{71} +$$$$52\!\cdots\!95$$$$p^{10} T^{72} -$$$$67\!\cdots\!62$$$$p^{11} T^{73} +$$$$87\!\cdots\!69$$$$p^{12} T^{74} -$$$$11\!\cdots\!40$$$$p^{13} T^{75} +$$$$13\!\cdots\!02$$$$p^{14} T^{76} -$$$$17\!\cdots\!76$$$$p^{15} T^{77} +$$$$21\!\cdots\!23$$$$p^{16} T^{78} -$$$$25\!\cdots\!12$$$$p^{17} T^{79} +$$$$30\!\cdots\!54$$$$p^{18} T^{80} -$$$$36\!\cdots\!60$$$$p^{19} T^{81} +$$$$42\!\cdots\!38$$$$p^{20} T^{82} -$$$$49\!\cdots\!80$$$$p^{21} T^{83} +$$$$56\!\cdots\!08$$$$p^{22} T^{84} -$$$$63\!\cdots\!74$$$$p^{23} T^{85} +$$$$70\!\cdots\!14$$$$p^{24} T^{86} -$$$$76\!\cdots\!81$$$$p^{25} T^{87} +$$$$82\!\cdots\!25$$$$p^{26} T^{88} -$$$$87\!\cdots\!04$$$$p^{27} T^{89} +$$$$91\!\cdots\!41$$$$p^{28} T^{90} -$$$$93\!\cdots\!68$$$$p^{29} T^{91} +$$$$95\!\cdots\!51$$$$p^{30} T^{92} -$$$$94\!\cdots\!21$$$$p^{31} T^{93} +$$$$92\!\cdots\!67$$$$p^{32} T^{94} -$$$$89\!\cdots\!65$$$$p^{33} T^{95} +$$$$84\!\cdots\!97$$$$p^{34} T^{96} -$$$$77\!\cdots\!55$$$$p^{35} T^{97} +$$$$70\!\cdots\!73$$$$p^{36} T^{98} -$$$$62\!\cdots\!36$$$$p^{37} T^{99} +$$$$54\!\cdots\!01$$$$p^{38} T^{100} -$$$$99\!\cdots\!63$$$$p^{40} T^{101} +$$$$39\!\cdots\!79$$$$p^{40} T^{102} -$$$$31\!\cdots\!62$$$$p^{41} T^{103} +$$$$25\!\cdots\!90$$$$p^{42} T^{104} -$$$$19\!\cdots\!32$$$$p^{43} T^{105} +$$$$14\!\cdots\!80$$$$p^{44} T^{106} -$$$$10\!\cdots\!35$$$$p^{45} T^{107} +$$$$75\!\cdots\!46$$$$p^{46} T^{108} -$$$$51\!\cdots\!18$$$$p^{47} T^{109} + 34407335051097870235 p^{48} T^{110} - 2192341887005516902 p^{49} T^{111} + 134279559653727518 p^{50} T^{112} - 7862475882419363 p^{51} T^{113} + 439632108294533 p^{52} T^{114} - 23269781103594 p^{53} T^{115} + 1165715541299 p^{54} T^{116} - 54431258896 p^{55} T^{117} + 2375478474 p^{56} T^{118} - 94011213 p^{57} T^{119} + 3414756 p^{58} T^{120} - 105997 p^{59} T^{121} + 2942 p^{60} T^{122} - 58 p^{61} T^{123} + p^{62} T^{124}$$
53 $$1 - 18 T + 1587 T^{2} - 26943 T^{3} + 1262396 T^{4} - 20240508 T^{5} + 12647652 p T^{6} - 10169848048 T^{7} + 267069777756 T^{8} - 3842736017241 T^{9} + 85103255588112 T^{10} - 1164062870258647 T^{11} + 22580181244701689 T^{12} - 294294657183565413 T^{13} + 5128266231035475277 T^{14} - 63827188809015906902 T^{15} +$$$$10\!\cdots\!41$$$$T^{16} -$$$$12\!\cdots\!88$$$$T^{17} +$$$$17\!\cdots\!13$$$$T^{18} -$$$$20\!\cdots\!88$$$$T^{19} +$$$$28\!\cdots\!06$$$$T^{20} -$$$$30\!\cdots\!43$$$$T^{21} +$$$$40\!\cdots\!43$$$$T^{22} -$$$$42\!\cdots\!68$$$$T^{23} +$$$$52\!\cdots\!59$$$$T^{24} -$$$$53\!\cdots\!18$$$$T^{25} +$$$$63\!\cdots\!70$$$$T^{26} -$$$$61\!\cdots\!82$$$$T^{27} +$$$$69\!\cdots\!32$$$$T^{28} -$$$$65\!\cdots\!53$$$$T^{29} +$$$$71\!\cdots\!55$$$$T^{30} -$$$$64\!\cdots\!03$$$$T^{31} +$$$$68\!\cdots\!22$$$$T^{32} -$$$$59\!\cdots\!40$$$$T^{33} +$$$$60\!\cdots\!12$$$$T^{34} -$$$$50\!\cdots\!22$$$$T^{35} +$$$$49\!\cdots\!07$$$$T^{36} -$$$$40\!\cdots\!94$$$$T^{37} +$$$$38\!\cdots\!67$$$$T^{38} -$$$$29\!\cdots\!65$$$$T^{39} +$$$$27\!\cdots\!58$$$$T^{40} -$$$$20\!\cdots\!20$$$$T^{41} +$$$$18\!\cdots\!41$$$$T^{42} -$$$$13\!\cdots\!92$$$$T^{43} +$$$$11\!\cdots\!59$$$$T^{44} -$$$$77\!\cdots\!06$$$$T^{45} +$$$$69\!\cdots\!27$$$$T^{46} -$$$$41\!\cdots\!47$$$$T^{47} +$$$$36\!\cdots\!87$$$$T^{48} -$$$$19\!\cdots\!33$$$$T^{49} +$$$$17\!\cdots\!78$$$$T^{50} -$$$$75\!\cdots\!27$$$$T^{51} +$$$$75\!\cdots\!88$$$$T^{52} -$$$$19\!\cdots\!44$$$$T^{53} +$$$$26\!\cdots\!18$$$$T^{54} +$$$$27\!\cdots\!62$$$$T^{55} +$$$$57\!\cdots\!18$$$$T^{56} +$$$$82\!\cdots\!51$$$$T^{57} -$$$$89\!\cdots\!85$$$$T^{58} +$$$$72\!\cdots\!28$$$$T^{59} -$$$$19\!\cdots\!67$$$$T^{60} +$$$$46\!\cdots\!04$$$$T^{61} -$$$$13\!\cdots\!82$$$$T^{62} +$$$$46\!\cdots\!04$$$$p T^{63} -$$$$19\!\cdots\!67$$$$p^{2} T^{64} +$$$$72\!\cdots\!28$$$$p^{3} T^{65} -$$$$89\!\cdots\!85$$$$p^{4} T^{66} +$$$$82\!\cdots\!51$$$$p^{5} T^{67} +$$$$57\!\cdots\!18$$$$p^{6} T^{68} +$$$$27\!\cdots\!62$$$$p^{7} T^{69} +$$$$26\!\cdots\!18$$$$p^{8} T^{70} -$$$$19\!\cdots\!44$$$$p^{9} T^{71} +$$$$75\!\cdots\!88$$$$p^{10} T^{72} -$$$$75\!\cdots\!27$$$$p^{11} T^{73} +$$$$17\!\cdots\!78$$$$p^{12} T^{74} -$$$$19\!\cdots\!33$$$$p^{13} T^{75} +$$$$36\!\cdots\!87$$$$p^{14} T^{76} -$$$$41\!\cdots\!47$$$$p^{15} T^{77} +$$$$69\!\cdots\!27$$$$p^{16} T^{78} -$$$$77\!\cdots\!06$$$$p^{17} T^{79} +$$$$11\!\cdots\!59$$$$p^{18} T^{80} -$$$$13\!\cdots\!92$$$$p^{19} T^{81} +$$$$18\!\cdots\!41$$$$p^{20} T^{82} -$$$$20\!\cdots\!20$$$$p^{21} T^{83} +$$$$27\!\cdots\!58$$$$p^{22} T^{84} -$$$$29\!\cdots\!65$$$$p^{23} T^{85} +$$$$38\!\cdots\!67$$$$p^{24} T^{86} -$$$$40\!\cdots\!94$$$$p^{25} T^{87} +$$$$49\!\cdots\!07$$$$p^{26} T^{88} -$$$$50\!\cdots\!22$$$$p^{27} T^{89} +$$$$60\!\cdots\!12$$$$p^{28} T^{90} -$$$$59\!\cdots\!40$$$$p^{29} T^{91} +$$$$68\!\cdots\!22$$$$p^{30} T^{92} -$$$$64\!\cdots\!03$$$$p^{31} T^{93} +$$$$71\!\cdots\!55$$$$p^{32} T^{94} -$$$$65\!\cdots\!53$$$$p^{33} T^{95} +$$$$69\!\cdots\!32$$$$p^{34} T^{96} -$$$$61\!\cdots\!82$$$$p^{35} T^{97} +$$$$63\!\cdots\!70$$$$p^{36} T^{98} -$$$$53\!\cdots\!18$$$$p^{37} T^{99} +$$$$52\!\cdots\!59$$$$p^{38} T^{100} -$$$$42\!\cdots\!68$$$$p^{39} T^{101} +$$$$40\!\cdots\!43$$$$p^{40} T^{102} -$$$$30\!\cdots\!43$$$$p^{41} T^{103} +$$$$28\!\cdots\!06$$$$p^{42} T^{104} -$$$$20\!\cdots\!88$$$$p^{43} T^{105} +$$$$17\!\cdots\!13$$$$p^{44} T^{106} -$$$$12\!\cdots\!88$$$$p^{45} T^{107} +$$$$10\!\cdots\!41$$$$p^{46} T^{108} - 63827188809015906902 p^{47} T^{109} + 5128266231035475277 p^{48} T^{110} - 294294657183565413 p^{49} T^{111} + 22580181244701689 p^{50} T^{112} - 1164062870258647 p^{51} T^{113} + 85103255588112 p^{52} T^{114} - 3842736017241 p^{53} T^{115} + 267069777756 p^{54} T^{116} - 10169848048 p^{55} T^{117} + 12647652 p^{57} T^{118} - 20240508 p^{57} T^{119} + 1262396 p^{58} T^{120} - 26943 p^{59} T^{121} + 1587 p^{60} T^{122} - 18 p^{61} T^{123} + p^{62} T^{124}$$
59 $$1 + 11 T + 1628 T^{2} + 20554 T^{3} + 1367760 T^{4} + 18960536 T^{5} + 791019135 T^{6} + 11606502661 T^{7} + 353552557056 T^{8} + 5331425381954 T^{9} + 129791918658904 T^{10} + 1966654798928420 T^{11} + 40588918729200848 T^{12} + 10305910329276912 p T^{13} + 11074080289318361917 T^{14} +$$$$16\!\cdots\!33$$$$T^{15} +$$$$26\!\cdots\!61$$$$T^{16} +$$$$38\!\cdots\!77$$$$T^{17} +$$$$58\!\cdots\!50$$$$T^{18} +$$$$80\!\cdots\!80$$$$T^{19} +$$$$11\!\cdots\!11$$$$T^{20} +$$$$15\!\cdots\!06$$$$T^{21} +$$$$20\!\cdots\!46$$$$T^{22} +$$$$26\!\cdots\!29$$$$T^{23} +$$$$34\!\cdots\!42$$$$T^{24} +$$$$42\!\cdots\!02$$$$T^{25} +$$$$53\!\cdots\!49$$$$T^{26} +$$$$63\!\cdots\!56$$$$T^{27} +$$$$76\!\cdots\!81$$$$T^{28} +$$$$88\!\cdots\!24$$$$T^{29} +$$$$10\!\cdots\!28$$$$T^{30} +$$$$11\!\cdots\!10$$$$T^{31} +$$$$12\!\cdots\!71$$$$T^{32} +$$$$14\!\cdots\!38$$$$T^{33} +$$$$15\!\cdots\!37$$$$T^{34} +$$$$16\!\cdots\!29$$$$T^{35} +$$$$17\!\cdots\!13$$$$T^{36} +$$$$17\!\cdots\!81$$$$T^{37} +$$$$18\!\cdots\!77$$$$T^{38} +$$$$18\!\cdots\!78$$$$T^{39} +$$$$18\!\cdots\!25$$$$T^{40} +$$$$17\!\cdots\!45$$$$T^{41} +$$$$17\!\cdots\!91$$$$T^{42} +$$$$16\!\cdots\!03$$$$T^{43} +$$$$15\!\cdots\!47$$$$T^{44} +$$$$14\!\cdots\!10$$$$T^{45} +$$$$13\!\cdots\!86$$$$T^{46} +$$$$12\!\cdots\!93$$$$T^{47} +$$$$11\!\cdots\!76$$$$T^{48} +$$$$98\!\cdots\!60$$$$T^{49} +$$$$86\!\cdots\!89$$$$T^{50} +$$$$75\!\cdots\!62$$$$T^{51} +$$$$65\!\cdots\!54$$$$T^{52} +$$$$55\!\cdots\!69$$$$T^{53} +$$$$46\!\cdots\!84$$$$T^{54} +$$$$38\!\cdots\!41$$$$T^{55} +$$$$32\!\cdots\!46$$$$T^{56} +$$$$26\!\cdots\!38$$$$T^{57} +$$$$21\!\cdots\!31$$$$T^{58} +$$$$16\!\cdots\!04$$$$T^{59} +$$$$13\!\cdots\!73$$$$T^{60} +$$$$10\!\cdots\!70$$$$T^{61} +$$$$80\!\cdots\!82$$$$T^{62} +$$$$10\!\cdots\!70$$$$p T^{63} +$$$$13\!\cdots\!73$$$$p^{2} T^{64} +$$$$16\!\cdots\!04$$$$p^{3} T^{65} +$$$$21\!\cdots\!31$$$$p^{4} T^{66} +$$$$26\!\cdots\!38$$$$p^{5} T^{67} +$$$$32\!\cdots\!46$$$$p^{6} T^{68} +$$$$38\!\cdots\!41$$$$p^{7} T^{69} +$$$$46\!\cdots\!84$$$$p^{8} T^{70} +$$$$55\!\cdots\!69$$$$p^{9} T^{71} +$$$$65\!\cdots\!54$$$$p^{10} T^{72} +$$$$75\!\cdots\!62$$$$p^{11} T^{73} +$$$$86\!\cdots\!89$$$$p^{12} T^{74} +$$$$98\!\cdots\!60$$$$p^{13} T^{75} +$$$$11\!\cdots\!76$$$$p^{14} T^{76} +$$$$12\!\cdots\!93$$$$p^{15} T^{77} +$$$$13\!\cdots\!86$$$$p^{16} T^{78} +$$$$14\!\cdots\!10$$$$p^{17} T^{79} +$$$$15\!\cdots\!47$$$$p^{18} T^{80} +$$$$16\!\cdots\!03$$$$p^{19} T^{81} +$$$$17\!\cdots\!91$$$$p^{20} T^{82} +$$$$17\!\cdots\!45$$$$p^{21} T^{83} +$$$$18\!\cdots\!25$$$$p^{22} T^{84} +$$$$18\!\cdots\!78$$$$p^{23} T^{85} +$$$$18\!\cdots\!77$$$$p^{24} T^{86} +$$$$17\!\cdots\!81$$$$p^{25} T^{87} +$$$$17\!\cdots\!13$$$$p^{26} T^{88} +$$$$16\!\cdots\!29$$$$p^{27} T^{89} +$$$$15\!\cdots\!37$$$$p^{28} T^{90} +$$$$14\!\cdots\!38$$$$p^{29} T^{91} +$$$$12\!\cdots\!71$$$$p^{30} T^{92} +$$$$11\!\cdots\!10$$$$p^{31} T^{93} +$$$$10\!\cdots\!28$$$$p^{32} T^{94} +$$$$88\!\cdots\!24$$$$p^{33} T^{95} +$$$$76\!\cdots\!81$$$$p^{34} T^{96} +$$$$63\!\cdots\!56$$$$p^{35} T^{97} +$$$$53\!\cdots\!49$$$$p^{36} T^{98} +$$$$42\!\cdots\!02$$$$p^{37} T^{99} +$$$$34\!\cdots\!42$$$$p^{38} T^{100} +$$$$26\!\cdots\!29$$$$p^{39} T^{101} +$$$$20\!\cdots\!46$$$$p^{40} T^{102} +$$$$15\!\cdots\!06$$$$p^{41} T^{103} +$$$$11\!\cdots\!11$$$$p^{42} T^{104} +$$$$80\!\cdots\!80$$$$p^{43} T^{105} +$$$$58\!\cdots\!50$$$$p^{44} T^{106} +$$$$38\!\cdots\!77$$$$p^{45} T^{107} +$$$$26\!\cdots\!61$$$$p^{46} T^{108} +$$$$16\!\cdots\!33$$$$p^{47} T^{109} + 11074080289318361917 p^{48} T^{110} + 10305910329276912 p^{50} T^{111} + 40588918729200848 p^{50} T^{112} + 1966654798928420 p^{51} T^{113} + 129791918658904 p^{52} T^{114} + 5331425381954 p^{53} T^{115} + 353552557056 p^{54} T^{116} + 11606502661 p^{55} T^{117} + 791019135 p^{56} T^{118} + 18960536 p^{57} T^{119} + 1367760 p^{58} T^{120} + 20554 p^{59} T^{121} + 1628 p^{60} T^{122} + 11 p^{61} T^{123} + p^{62} T^{124}$$
61 $$1 - 24 T + 1964 T^{2} - 39835 T^{3} + 1848989 T^{4} - 32708574 T^{5} + 1127538511 T^{6} - 17758854828 T^{7} + 505364054650 T^{8} - 7186713201635 T^{9} + 178634805598575 T^{10} - 2315936487981061 T^{11} + 52102630187818127 T^{12} - 619868947724148474 T^{13} + 12942329593174633282 T^{14} -$$$$14\!\cdots\!11$$$$T^{15} +$$$$28\!\cdots\!21$$$$T^{16} -$$$$28\!\cdots\!67$$$$T^{17} +$$$$88\!\cdots\!57$$$$p T^{18} -$$$$50\!\cdots\!02$$$$T^{19} +$$$$93\!\cdots\!17$$$$T^{20} -$$$$80\!\cdots\!91$$$$T^{21} +$$$$14\!\cdots\!99$$$$T^{22} -$$$$11\!\cdots\!37$$$$T^{23} +$$$$21\!\cdots\!42$$$$T^{24} -$$$$15\!\cdots\!43$$$$T^{25} +$$$$28\!\cdots\!12$$$$T^{26} -$$$$31\!\cdots\!09$$$$p T^{27} +$$$$36\!\cdots\!00$$$$T^{28} -$$$$22\!\cdots\!74$$$$T^{29} +$$$$42\!\cdots\!24$$$$T^{30} -$$$$23\!\cdots\!47$$$$T^{31} +$$$$48\!\cdots\!12$$$$T^{32} -$$$$23\!\cdots\!63$$$$T^{33} +$$$$51\!\cdots\!68$$$$T^{34} -$$$$22\!\cdots\!38$$$$T^{35} +$$$$51\!\cdots\!78$$$$T^{36} -$$$$20\!\cdots\!72$$$$T^{37} +$$$$49\!\cdots\!38$$$$T^{38} -$$$$17\!\cdots\!04$$$$T^{39} +$$$$46\!\cdots\!51$$$$T^{40} -$$$$13\!\cdots\!85$$$$T^{41} +$$$$40\!\cdots\!99$$$$T^{42} -$$$$10\!\cdots\!09$$$$T^{43} +$$$$34\!\cdots\!33$$$$T^{44} -$$$$78\!\cdots\!66$$$$T^{45} +$$$$28\!\cdots\!60$$$$T^{46} -$$$$54\!\cdots\!09$$$$T^{47} +$$$$22\!\cdots\!67$$$$T^{48} -$$$$37\!\cdots\!15$$$$T^{49} +$$$$17\!\cdots\!81$$$$T^{50} -$$$$24\!\cdots\!18$$$$T^{51} +$$$$12\!\cdots\!62$$$$T^{52} -$$$$15\!\cdots\!53$$$$T^{53} +$$$$91\!\cdots\!96$$$$T^{54} -$$$$92\!\cdots\!65$$$$T^{55} +$$$$62\!\cdots\!75$$$$T^{56} -$$$$55\!\cdots\!44$$$$T^{57} +$$$$41\!\cdots\!56$$$$T^{58} -$$$$33\!\cdots\!28$$$$T^{59} +$$$$26\!\cdots\!15$$$$T^{60} -$$$$20\!\cdots\!51$$$$T^{61} +$$$$16\!\cdots\!60$$$$T^{62} -$$$$20\!\cdots\!51$$$$p T^{63} +$$$$26\!\cdots\!15$$$$p^{2} T^{64} -$$$$33\!\cdots\!28$$$$p^{3} T^{65} +$$$$41\!\cdots\!56$$$$p^{4} T^{66} -$$$$55\!\cdots\!44$$$$p^{5} T^{67} +$$$$62\!\cdots\!75$$$$p^{6} T^{68} -$$$$92\!\cdots\!65$$$$p^{7} T^{69} +$$$$91\!\cdots\!96$$$$p^{8} T^{70} -$$$$15\!\cdots\!53$$$$p^{9} T^{71} +$$$$12\!\cdots\!62$$$$p^{10} T^{72} -$$$$24\!\cdots\!18$$$$p^{11} T^{73} +$$$$17\!\cdots\!81$$$$p^{12} T^{74} -$$$$37\!\cdots\!15$$$$p^{13} T^{75} +$$$$22\!\cdots\!67$$$$p^{14} T^{76} -$$$$54\!\cdots\!09$$$$p^{15} T^{77} +$$$$28\!\cdots\!60$$$$p^{16} T^{78} -$$$$78\!\cdots\!66$$$$p^{17} T^{79} +$$$$34\!\cdots\!33$$$$p^{18} T^{80} -$$$$10\!\cdots\!09$$$$p^{19} T^{81} +$$$$40\!\cdots\!99$$$$p^{20} T^{82} -$$$$13\!\cdots\!85$$$$p^{21} T^{83} +$$$$46\!\cdots\!51$$$$p^{22} T^{84} -$$$$17\!\cdots\!04$$$$p^{23} T^{85} +$$$$49\!\cdots\!38$$$$p^{24} T^{86} -$$$$20\!\cdots\!72$$$$p^{25} T^{87} +$$$$51\!\cdots\!78$$$$p^{26} T^{88} -$$$$22\!\cdots\!38$$$$p^{27} T^{89} +$$$$51\!\cdots\!68$$$$p^{28} T^{90} -$$$$23\!\cdots\!63$$$$p^{29} T^{91} +$$$$48\!\cdots\!12$$$$p^{30} T^{92} -$$$$23\!\cdots\!47$$$$p^{31} T^{93} +$$$$42\!\cdots\!24$$$$p^{32} T^{94} -$$$$22\!\cdots\!74$$$$p^{33} T^{95} +$$$$36\!\cdots\!00$$$$p^{34} T^{96} -$$$$31\!\cdots\!09$$$$p^{36} T^{97} +$$$$28\!\cdots\!12$$$$p^{36} T^{98} -$$$$15\!\cdots\!43$$$$p^{37} T^{99} +$$$$21\!\cdots\!42$$$$p^{38} T^{100} -$$$$11\!\cdots\!37$$$$p^{39} T^{101} +$$$$14\!\cdots\!99$$$$p^{40} T^{102} -$$$$80\!\cdots\!91$$$$p^{41} T^{103} +$$$$93\!\cdots\!17$$$$p^{42} T^{104} -$$$$50\!\cdots\!02$$$$p^{43} T^{105} +$$$$88\!\cdots\!57$$$$p^{45} T^{106} -$$$$28\!\cdots\!67$$$$p^{45} T^{107} +$$$$28\!\cdots\!21$$$$p^{46} T^{108} -$$$$14\!\cdots\!11$$$$p^{47} T^{109} + 12942329593174633282 p^{48} T^{110} - 619868947724148474 p^{49} T^{111} + 52102630187818127 p^{50} T^{112} - 2315936487981061 p^{51} T^{113} + 178634805598575 p^{52} T^{114} - 7186713201635 p^{53} T^{115} + 505364054650 p^{54} T^{116} - 17758854828 p^{55} T^{117} + 1127538511 p^{56} T^{118} - 32708574 p^{57} T^{119} + 1848989 p^{58} T^{120} - 39835 p^{59} T^{121} + 1964 p^{60} T^{122} - 24 p^{61} T^{123} + p^{62} T^{124}$$
67 $$1 + 6 T + 1919 T^{2} + 10706 T^{3} + 1835554 T^{4} + 9576587 T^{5} + 1168064042 T^{6} + 5731443014 T^{7} + 556778294511 T^{8} + 2583626495896 T^{9} + 212188236079779 T^{10} + 936055187493532 T^{11} + 67379862329475947 T^{12} + 283962317323365690 T^{13} + 18344921127585997436 T^{14} + 74182328686515599204 T^{15} +$$$$43\!\cdots\!81$$$$T^{16} +$$$$17\!\cdots\!65$$$$T^{17} +$$$$92\!\cdots\!37$$$$T^{18} +$$$$34\!\cdots\!59$$$$T^{19} +$$$$17\!\cdots\!69$$$$T^{20} +$$$$64\!\cdots\!48$$$$T^{21} +$$$$30\!\cdots\!76$$$$T^{22} +$$$$10\!\cdots\!27$$$$T^{23} +$$$$49\!\cdots\!92$$$$T^{24} +$$$$16\!\cdots\!07$$$$T^{25} +$$$$72\!\cdots\!66$$$$T^{26} +$$$$24\!\cdots\!78$$$$T^{27} +$$$$10\!\cdots\!82$$$$T^{28} +$$$$32\!\cdots\!07$$$$T^{29} +$$$$12\!\cdots\!95$$$$T^{30} +$$$$40\!\cdots\!90$$$$T^{31} +$$$$15\!\cdots\!68$$$$T^{32} +$$$$47\!\cdots\!96$$$$T^{33} +$$$$17\!\cdots\!21$$$$T^{34} +$$$$52\!\cdots\!00$$$$T^{35} +$$$$19\!\cdots\!05$$$$T^{36} +$$$$54\!\cdots\!74$$$$T^{37} +$$$$19\!\cdots\!93$$$$T^{38} +$$$$53\!\cdots\!16$$$$T^{39} +$$$$19\!\cdots\!15$$$$T^{40} +$$$$50\!\cdots\!88$$$$T^{41} +$$$$18\!\cdots\!21$$$$T^{42} +$$$$45\!\cdots\!20$$$$T^{43} +$$$$16\!\cdots\!71$$$$T^{44} +$$$$39\!\cdots\!50$$$$T^{45} +$$$$14\!\cdots\!09$$$$T^{46} +$$$$32\!\cdots\!20$$$$T^{47} +$$$$12\!\cdots\!38$$$$T^{48} +$$$$25\!\cdots\!51$$$$T^{49} +$$$$98\!\cdots\!90$$$$T^{50} +$$$$19\!\cdots\!69$$$$T^{51} +$$$$77\!\cdots\!06$$$$T^{52} +$$$$14\!\cdots\!77$$$$T^{53} +$$$$58\!\cdots\!97$$$$T^{54} +$$$$10\!\cdots\!57$$$$T^{55} +$$$$43\!\cdots\!03$$$$T^{56} +$$$$77\!\cdots\!52$$$$T^{57} +$$$$31\!\cdots\!32$$$$T^{58} +$$$$54\!\cdots\!43$$$$T^{59} +$$$$21\!\cdots\!57$$$$T^{60} +$$$$37\!\cdots\!33$$$$T^{61} +$$$$14\!\cdots\!50$$$$T^{62} +$$$$37\!\cdots\!33$$$$p T^{63} +$$$$21\!\cdots\!57$$$$p^{2} T^{64} +$$$$54\!\cdots\!43$$$$p^{3} T^{65} +$$$$31\!\cdots\!32$$$$p^{4} T^{66} +$$$$77\!\cdots\!52$$$$p^{5} T^{67} +$$$$43\!\cdots\!03$$$$p^{6} T^{68} +$$$$10\!\cdots\!57$$$$p^{7} T^{69} +$$$$58\!\cdots\!97$$$$p^{8} T^{70} +$$$$14\!\cdots\!77$$$$p^{9} T^{71} +$$$$77\!\cdots\!06$$$$p^{10} T^{72} +$$$$19\!\cdots\!69$$$$p^{11} T^{73} +$$$$98\!\cdots\!90$$$$p^{12} T^{74} +$$$$25\!\cdots\!51$$$$p^{13} T^{75} +$$$$12\!\cdots\!38$$$$p^{14} T^{76} +$$$$32\!\cdots\!20$$$$p^{15} T^{77} +$$$$14\!\cdots\!09$$$$p^{16} T^{78} +$$$$39\!\cdots\!50$$$$p^{17} T^{79} +$$$$16\!\cdots\!71$$$$p^{18} T^{80} +$$$$45\!\cdots\!20$$$$p^{19} T^{81} +$$$$18\!\cdots\!21$$$$p^{20} T^{82} +$$$$50\!\cdots\!88$$$$p^{21} T^{83} +$$$$19\!\cdots\!15$$$$p^{22} T^{84} +$$$$53\!\cdots\!16$$$$p^{23} T^{85} +$$$$19\!\cdots\!93$$$$p^{24} T^{86} +$$$$54\!\cdots\!74$$$$p^{25} T^{87} +$$$$19\!\cdots\!05$$$$p^{26} T^{88} +$$$$52\!\cdots\!00$$$$p^{27} T^{89} +$$$$17\!\cdots\!21$$$$p^{28} T^{90} +$$$$47\!\cdots\!96$$$$p^{29} T^{91} +$$$$15\!\cdots\!68$$$$p^{30} T^{92} +$$$$40\!\cdots\!90$$$$p^{31} T^{93} +$$$$12\!\cdots\!95$$$$p^{32} T^{94} +$$$$32\!\cdots\!07$$$$p^{33} T^{95} +$$$$10\!\cdots\!82$$$$p^{34} T^{96} +$$$$24\!\cdots\!78$$$$p^{35} T^{97} +$$$$72\!\cdots\!66$$$$p^{36} T^{98} +$$$$16\!\cdots\!07$$$$p^{37} T^{99} +$$$$49\!\cdots\!92$$$$p^{38} T^{100} +$$$$10\!\cdots\!27$$$$p^{39} T^{101} +$$$$30\!\cdots\!76$$$$p^{40} T^{102} +$$$$64\!\cdots\!48$$$$p^{41} T^{103} +$$$$17\!\cdots\!69$$$$p^{42} T^{104} +$$$$34\!\cdots\!59$$$$p^{43} T^{105} +$$$$92\!\cdots\!37$$$$p^{44} T^{106} +$$$$17\!\cdots\!65$$$$p^{45} T^{107} +$$$$43\!\cdots\!81$$$$p^{46} T^{108} + 74182328686515599204 p^{47} T^{109} + 18344921127585997436 p^{48} T^{110} + 283962317323365690 p^{49} T^{111} + 67379862329475947 p^{50} T^{112} + 936055187493532 p^{51} T^{113} + 212188236079779 p^{52} T^{114} + 2583626495896 p^{53} T^{115} + 556778294511 p^{54} T^{116} + 5731443014 p^{55} T^{117} + 1168064042 p^{56} T^{118} + 9576587 p^{57} T^{119} + 1835554 p^{58} T^{120} + 10706 p^{59} T^{121} + 1919 p^{60} T^{122} + 6 p^{61} T^{123} + p^{62} T^{124}$$
71 $$1 + 35 T + 2438 T^{2} + 67677 T^{3} + 2743162 T^{4} + 64342189 T^{5} + 1960542218 T^{6} + 40369399936 T^{7} + 1019396229502 T^{8} + 18900837452644 T^{9} + 416007810030832 T^{10} + 7071541155009838 T^{11} + 139863643487517676 T^{12} + 2208919044616640797 T^{13} + 40061267596327976361 T^{14} + 8364446084319039107 p T^{15} +$$$$10\!\cdots\!81$$$$T^{16} +$$$$14\!\cdots\!04$$$$T^{17} +$$$$22\!\cdots\!48$$$$T^{18} +$$$$29\!\cdots\!86$$$$T^{19} +$$$$44\!\cdots\!72$$$$T^{20} +$$$$57\!\cdots\!70$$$$T^{21} +$$$$81\!\cdots\!67$$$$T^{22} +$$$$10\!\cdots\!80$$$$T^{23} +$$$$13\!\cdots\!65$$$$T^{24} +$$$$16\!\cdots\!29$$$$T^{25} +$$$$21\!\cdots\!00$$$$T^{26} +$$$$24\!\cdots\!28$$$$T^{27} +$$$$31\!\cdots\!48$$$$T^{28} +$$$$35\!\cdots\!33$$$$T^{29} +$$$$43\!\cdots\!32$$$$T^{30} +$$$$47\!\cdots\!45$$$$T^{31} +$$$$57\!\cdots\!56$$$$T^{32} +$$$$60\!\cdots\!62$$$$T^{33} +$$$$70\!\cdots\!06$$$$T^{34} +$$$$72\!\cdots\!69$$$$T^{35} +$$$$82\!\cdots\!09$$$$T^{36} +$$$$83\!\cdots\!88$$$$T^{37} +$$$$92\!\cdots\!22$$$$T^{38} +$$$$91\!\cdots\!62$$$$T^{39} +$$$$99\!\cdots\!90$$$$T^{40} +$$$$13\!\cdots\!32$$$$p T^{41} +$$$$10\!\cdots\!63$$$$T^{42} +$$$$96\!\cdots\!13$$$$T^{43} +$$$$10\!\cdots\!94$$$$T^{44} +$$$$93\!\cdots\!22$$$$T^{45} +$$$$95\!\cdots\!79$$$$T^{46} +$$$$87\!\cdots\!42$$$$T^{47} +$$$$87\!\cdots\!10$$$$T^{48} +$$$$78\!\cdots\!16$$$$T^{49} +$$$$77\!\cdots\!70$$$$T^{50} +$$$$67\!\cdots\!35$$$$T^{51} +$$$$65\!\cdots\!18$$$$T^{52} +$$$$56\!\cdots\!57$$$$T^{53} +$$$$54\!\cdots\!17$$$$T^{54} +$$$$46\!\cdots\!24$$$$T^{55} +$$$$43\!\cdots\!85$$$$T^{56} +$$$$36\!\cdots\!24$$$$T^{57} +$$$$33\!\cdots\!08$$$$T^{58} +$$$$27\!\cdots\!89$$$$T^{59} +$$$$24\!\cdots\!87$$$$T^{60} +$$$$20\!\cdots\!67$$$$T^{61} +$$$$17\!\cdots\!38$$$$T^{62} +$$$$20\!\cdots\!67$$$$p T^{63} +$$$$24\!\cdots\!87$$$$p^{2} T^{64} +$$$$27\!\cdots\!89$$$$p^{3} T^{65} +$$$$33\!\cdots\!08$$$$p^{4} T^{66} +$$$$36\!\cdots\!24$$$$p^{5} T^{67} +$$$$43\!\cdots\!85$$$$p^{6} T^{68} +$$$$46\!\cdots\!24$$$$p^{7} T^{69} +$$$$54\!\cdots\!17$$$$p^{8} T^{70} +$$$$56\!\cdots\!57$$$$p^{9} T^{71} +$$$$65\!\cdots\!18$$$$p^{10} T^{72} +$$$$67\!\cdots\!35$$$$p^{11} T^{73} +$$$$77\!\cdots\!70$$$$p^{12} T^{74} +$$$$78\!\cdots\!16$$$$p^{13} T^{75} +$$$$87\!\cdots\!10$$$$p^{14} T^{76} +$$$$87\!\cdots\!42$$$$p^{15} T^{77} +$$$$95\!\cdots\!79$$$$p^{16} T^{78} +$$$$93\!\cdots\!22$$$$p^{17} T^{79} +$$$$10\!\cdots\!94$$$$p^{18} T^{80} +$$$$96\!\cdots\!13$$$$p^{19} T^{81} +$$$$10\!\cdots\!63$$$$p^{20} T^{82} +$$$$13\!\cdots\!32$$$$p^{22} T^{83} +$$$$99\!\cdots\!90$$$$p^{22} T^{84} +$$$$91\!\cdots\!62$$$$p^{23} T^{85} +$$$$92\!\cdots\!22$$$$p^{24} T^{86} +$$$$83\!\cdots\!88$$$$p^{25} T^{87} +$$$$82\!\cdots\!09$$$$p^{26} T^{88} +$$$$72\!\cdots\!69$$$$p^{27} T^{89} +$$$$70\!\cdots\!06$$$$p^{28} T^{90} +$$$$60\!\cdots\!62$$$$p^{29} T^{91} +$$$$57\!\cdots\!56$$$$p^{30} T^{92} +$$$$47\!\cdots\!45$$$$p^{31} T^{93} +$$$$43\!\cdots\!32$$$$p^{32} T^{94} +$$$$35\!\cdots\!33$$$$p^{33} T^{95} +$$$$31\!\cdots\!48$$$$p^{34} T^{96} +$$$$24\!\cdots\!28$$$$p^{35} T^{97} +$$$$21\!\cdots\!00$$$$p^{36} T^{98} +$$$$16\!\cdots\!29$$$$p^{37} T^{99} +$$$$13\!\cdots\!65$$$$p^{38} T^{100} +$$$$10\!\cdots\!80$$$$p^{39} T^{101} +$$$$81\!\cdots\!67$$$$p^{40} T^{102} +$$$$57\!\cdots\!70$$$$p^{41} T^{103} +$$$$44\!\cdots\!72$$$$p^{42} T^{104} +$$$$29\!\cdots\!86$$$$p^{43} T^{105} +$$$$22\!\cdots\!48$$$$p^{44} T^{106} +$$$$14\!\cdots\!04$$$$p^{45} T^{107} +$$$$10\!\cdots\!81$$$$p^{46} T^{108} + 8364446084319039107 p^{48} T^{109} + 40061267596327976361 p^{48} T^{110} + 2208919044616640797 p^{49} T^{111} + 139863643487517676 p^{50} T^{112} + 7071541155009838 p^{51} T^{113} + 416007810030832 p^{52} T^{114} + 18900837452644 p^{53} T^{115} + 1019396229502 p^{54} T^{116} + 40369399936 p^{55} T^{117} + 1960542218 p^{56} T^{118} + 64342189 p^{57} T^{119} + 2743162 p^{58} T^{120} + 67677 p^{59} T^{121} + 2438 p^{60} T^{122} + 35 p^{61} T^{123} + p^{62} T^{124}$$
73 $$1 - 116 T + 8584 T^{2} - 472146 T^{3} + 21401821 T^{4} - 832952939 T^{5} + 28745595856 T^{6} - 896331652625 T^{7} + 25643513108567 T^{8} - 680344133233820 T^{9} + 16888833141921747 T^{10} - 394957694624394629 T^{11} + 8752089129544776660 T^{12} -$$$$18\!\cdots\!27$$$$T^{13} +$$$$37\!\cdots\!64$$$$T^{14} -$$$$72\!\cdots\!52$$$$T^{15} +$$$$13\!\cdots\!75$$$$T^{16} -$$$$24\!\cdots\!10$$$$T^{17} +$$$$41\!\cdots\!78$$$$T^{18} -$$$$70\!\cdots\!54$$$$T^{19} +$$$$11\!\cdots\!01$$$$T^{20} -$$$$18\!\cdots\!00$$$$T^{21} +$$$$28\!\cdots\!81$$$$T^{22} -$$$$42\!\cdots\!37$$$$T^{23} +$$$$62\!\cdots\!79$$$$T^{24} -$$$$89\!\cdots\!77$$$$T^{25} +$$$$12\!\cdots\!70$$$$T^{26} -$$$$17\!\cdots\!07$$$$T^{27} +$$$$23\!\cdots\!37$$$$T^{28} -$$$$31\!\cdots\!35$$$$T^{29} +$$$$40\!\cdots\!48$$$$T^{30} -$$$$51\!\cdots\!76$$$$T^{31} +$$$$64\!\cdots\!41$$$$T^{32} -$$$$79\!\cdots\!60$$$$T^{33} +$$$$96\!\cdots\!65$$$$T^{34} -$$$$11\!\cdots\!25$$$$T^{35} +$$$$13\!\cdots\!88$$$$T^{36} -$$$$15\!\cdots\!58$$$$T^{37} +$$$$17\!\cdots\!72$$$$T^{38} -$$$$20\!\cdots\!39$$$$T^{39} +$$$$22\!\cdots\!86$$$$T^{40} -$$$$24\!\cdots\!12$$$$T^{41} +$$$$26\!\cdots\!09$$$$T^{42} -$$$$28\!\cdots\!45$$$$T^{43} +$$$$29\!\cdots\!67$$$$T^{44} -$$$$30\!\cdots\!57$$$$T^{45} +$$$$31\!\cdots\!14$$$$T^{46} -$$$$32\!\cdots\!92$$$$T^{47} +$$$$32\!\cdots\!70$$$$T^{48} -$$$$31\!\cdots\!16$$$$T^{49} +$$$$31\!\cdots\!58$$$$T^{50} -$$$$30\!\cdots\!50$$$$T^{51} +$$$$28\!\cdots\!38$$$$T^{52} -$$$$27\!\cdots\!16$$$$T^{53} +$$$$25\!\cdots\!55$$$$T^{54} -$$$$23\!\cdots\!58$$$$T^{55} +$$$$21\!\cdots\!12$$$$T^{56} -$$$$19\!\cdots\!48$$$$T^{57} +$$$$17\!\cdots\!97$$$$T^{58} -$$$$15\!\cdots\!05$$$$T^{59} +$$$$13\!\cdots\!09$$$$T^{60} -$$$$11\!\cdots\!93$$$$T^{61} +$$$$10\!\cdots\!48$$$$T^{62} -$$$$11\!\cdots\!93$$$$p T^{63} +$$$$13\!\cdots\!09$$$$p^{2} T^{64} -$$$$15\!\cdots\!05$$$$p^{3} T^{65} +$$$$17\!\cdots\!97$$$$p^{4} T^{66} -$$$$19\!\cdots\!48$$$$p^{5} T^{67} +$$$$21\!\cdots\!12$$$$p^{6} T^{68} -$$$$23\!\cdots\!58$$$$p^{7} T^{69} +$$$$25\!\cdots\!55$$$$p^{8} T^{70} -$$$$27\!\cdots\!16$$$$p^{9} T^{71} +$$$$28\!\cdots\!38$$$$p^{10} T^{72} -$$$$30\!\cdots\!50$$$$p^{11} T^{73} +$$$$31\!\cdots\!58$$$$p^{12} T^{74} -$$$$31\!\cdots\!16$$$$p^{13} T^{75} +$$$$32\!\cdots\!70$$$$p^{14} T^{76} -$$$$32\!\cdots\!92$$$$p^{15} T^{77} +$$$$31\!\cdots\!14$$$$p^{16} T^{78} -$$$$30\!\cdots\!57$$$$p^{17} T^{79} +$$$$29\!\cdots\!67$$$$p^{18} T^{80} -$$$$28\!\cdots\!45$$$$p^{19} T^{81} +$$$$26\!\cdots\!09$$$$p^{20} T^{82} -$$$$24\!\cdots\!12$$$$p^{21} T^{83} +$$$$22\!\cdots\!86$$$$p^{22} T^{84} -$$$$20\!\cdots\!39$$$$p^{23} T^{85} +$$$$17\!\cdots\!72$$$$p^{24} T^{86} -$$$$15\!\cdots\!58$$$$p^{25} T^{87} +$$$$13\!\cdots\!88$$$$p^{26} T^{88} -$$$$11\!\cdots\!25$$$$p^{27} T^{89} +$$$$96\!\cdots\!65$$$$p^{28} T^{90} -$$$$79\!\cdots\!60$$$$p^{29} T^{91} +$$$$64\!\cdots\!41$$$$p^{30} T^{92} -$$$$51\!\cdots\!76$$$$p^{31} T^{93} +$$$$40\!\cdots\!48$$$$p^{32} T^{94} -$$$$31\!\cdots\!35$$$$p^{33} T^{95} +$$$$23\!\cdots\!37$$$$p^{34} T^{96} -$$$$17\!\cdots\!07$$$$p^{35} T^{97} +$$$$12\!\cdots\!70$$$$p^{36} T^{98} -$$$$89\!\cdots\!77$$$$p^{37} T^{99} +$$$$62\!\cdots\!79$$$$p^{38} T^{100} -$$$$42\!\cdots\!37$$$$p^{39} T^{101} +$$$$28\!\cdots\!81$$$$p^{40} T^{102} -$$$$18\!\cdots\!00$$$$p^{41} T^{103} +$$$$11\!\cdots\!01$$$$p^{42} T^{104} -$$$$70\!\cdots\!54$$$$p^{43} T^{105} +$$$$41\!\cdots\!78$$$$p^{44} T^{106} -$$$$24\!\cdots\!10$$$$p^{45} T^{107} +$$$$13\!\cdots\!75$$$$p^{46} T^{108} -$$$$72\!\cdots\!52$$$$p^{47} T^{109} +$$$$37\!\cdots\!64$$$$p^{48} T^{110} -$$$$18\!\cdots\!27$$$$p^{49} T^{111} + 8752089129544776660 p^{50} T^{112} - 394957694624394629 p^{51} T^{113} + 16888833141921747 p^{52} T^{114} - 680344133233820 p^{53} T^{115} + 25643513108567 p^{54} T^{116} - 896331652625 p^{55} T^{117} + 28745595856 p^{56} T^{118} - 832952939 p^{57} T^{119} + 21401821 p^{58} T^{120} - 472146 p^{59} T^{121} + 8584 p^{60} T^{122} - 116 p^{61} T^{123} + p^{62} T^{124}$$
79 $$1 + 83 T + 5247 T^{2} + 242631 T^{3} + 9649077 T^{4} + 329713044 T^{5} + 10174852766 T^{6} + 284657890914 T^{7} + 7382325860822 T^{8} + 178165328659936 T^{9} + 4050350573989094 T^{10} + 87018633390370250 T^{11} + 1780139265761225352 T^{12} + 34766334372656567924 T^{13} +$$$$65\!\cdots\!26$$$$T^{14} +$$$$11\!\cdots\!61$$$$T^{15} +$$$$20\!\cdots\!53$$$$T^{16} +$$$$34\!\cdots\!30$$$$T^{17} +$$$$55\!\cdots\!67$$$$T^{18} +$$$$88\!\cdots\!05$$$$T^{19} +$$$$13\!\cdots\!24$$$$T^{20} +$$$$20\!\cdots\!25$$$$T^{21} +$$$$30\!\cdots\!16$$$$T^{22} +$$$$42\!\cdots\!01$$$$T^{23} +$$$$60\!\cdots\!94$$$$T^{24} +$$$$82\!\cdots\!66$$$$T^{25} +$$$$11\!\cdots\!33$$$$T^{26} +$$$$14\!\cdots\!39$$$$T^{27} +$$$$18\!\cdots\!65$$$$T^{28} +$$$$24\!\cdots\!40$$$$T^{29} +$$$$30\!\cdots\!10$$$$T^{30} +$$$$37\!\cdots\!72$$$$T^{31} +$$$$45\!\cdots\!14$$$$T^{32} +$$$$54\!\cdots\!00$$$$T^{33} +$$$$63\!\cdots\!55$$$$T^{34} +$$$$74\!\cdots\!67$$$$T^{35} +$$$$85\!\cdots\!42$$$$T^{36} +$$$$97\!\cdots\!54$$$$T^{37} +$$$$10\!\cdots\!87$$$$T^{38} +$$$$12\!\cdots\!41$$$$T^{39} +$$$$13\!\cdots\!44$$$$T^{40} +$$$$14\!\cdots\!11$$$$T^{41} +$$$$15\!\cdots\!35$$$$T^{42} +$$$$16\!\cdots\!96$$$$T^{43} +$$$$17\!\cdots\!28$$$$T^{44} +$$$$17\!\cdots\!94$$$$T^{45} +$$$$18\!\cdots\!68$$$$T^{46} +$$$$18\!\cdots\!59$$$$T^{47} +$$$$18\!\cdots\!47$$$$T^{48} +$$$$18\!\cdots\!94$$$$T^{49} +$$$$18\!\cdots\!48$$$$T^{50} +$$$$18\!\cdots\!12$$$$T^{51} +$$$$17\!\cdots\!22$$$$T^{52} +$$$$17\!\cdots\!80$$$$T^{53} +$$$$16\!\cdots\!79$$$$T^{54} +$$$$15\!\cdots\!63$$$$T^{55} +$$$$14\!\cdots\!55$$$$T^{56} +$$$$13\!\cdots\!58$$$$T^{57} +$$$$12\!\cdots\!05$$$$T^{58} +$$$$11\!\cdots\!94$$$$T^{59} +$$$$10\!\cdots\!00$$$$T^{60} +$$$$93\!\cdots\!26$$$$T^{61} +$$$$83\!\cdots\!36$$$$T^{62} +$$$$93\!\cdots\!26$$$$p T^{63} +$$$$10\!\cdots\!00$$$$p^{2} T^{64} +$$$$11\!\cdots\!94$$$$p^{3} T^{65} +$$$$12\!\cdots\!05$$$$p^{4} T^{66} +$$$$13\!\cdots\!58$$$$p^{5} T^{67} +$$$$14\!\cdots\!55$$$$p^{6} T^{68} +$$$$15\!\cdots\!63$$$$p^{7} T^{69} +$$$$16\!\cdots\!79$$$$p^{8} T^{70} +$$$$17\!\cdots\!80$$$$p^{9} T^{71} +$$$$17\!\cdots\!22$$$$p^{10} T^{72} +$$$$18\!\cdots\!12$$$$p^{11} T^{73} +$$$$18\!\cdots\!48$$$$p^{12} T^{74} +$$$$18\!\cdots\!94$$$$p^{13} T^{75} +$$$$18\!\cdots\!47$$$$p^{14} T^{76} +$$$$18\!\cdots\!59$$$$p^{15} T^{77} +$$$$18\!\cdots\!68$$$$p^{16} T^{78} +$$$$17\!\cdots\!94$$$$p^{17} T^{79} +$$$$17\!\cdots\!28$$$$p^{18} T^{80} +$$$$16\!\cdots\!96$$$$p^{19} T^{81} +$$$$15\!\cdots\!35$$$$p^{20} T^{82} +$$$$14\!\cdots\!11$$$$p^{21} T^{83} +$$$$13\!\cdots\!44$$$$p^{22} T^{84} +$$$$12\!\cdots\!41$$$$p^{23} T^{85} +$$$$10\!\cdots\!87$$$$p^{24} T^{86} +$$$$97\!\cdots\!54$$$$p^{25} T^{87} +$$$$85\!\cdots\!42$$$$p^{26} T^{88} +$$$$74\!\cdots\!67$$$$p^{27} T^{89} +$$$$63\!\cdots\!55$$$$p^{28} T^{90} +$$$$54\!\cdots\!00$$$$p^{29} T^{91} +$$$$45\!\cdots\!14$$$$p^{30} T^{92} +$$$$37\!\cdots\!72$$$$p^{31} T^{93} +$$$$30\!\cdots\!10$$$$p^{32} T^{94} +$$$$24\!\cdots\!40$$$$p^{33} T^{95} +$$$$18\!\cdots\!65$$$$p^{34} T^{96} +$$$$14\!\cdots\!39$$$$p^{35} T^{97} +$$$$11\!\cdots\!33$$$$p^{36} T^{98} +$$$$82\!\cdots\!66$$$$p^{37} T^{99} +$$$$60\!\cdots\!94$$$$p^{38} T^{100} +$$$$42\!\cdots\!01$$$$p^{39} T^{101} +$$$$30\!\cdots\!16$$$$p^{40} T^{102} +$$$$20\!\cdots\!25$$$$p^{41} T^{103} +$$$$13\!\cdots\!24$$$$p^{42} T^{104} +$$$$88\!\cdots\!05$$$$p^{43} T^{105} +$$$$55\!\cdots\!67$$$$p^{44} T^{106} +$$$$34\!\cdots\!30$$$$p^{45} T^{107} +$$$$20\!\cdots\!53$$$$p^{46} T^{108} +$$$$11\!\cdots\!61$$$$p^{47} T^{109} +$$$$65\!\cdots\!26$$$$p^{48} T^{110} + 34766334372656567924 p^{49} T^{111} + 1780139265761225352 p^{50} T^{112} + 87018633390370250 p^{51} T^{113} + 4050350573989094 p^{52} T^{114} + 178165328659936 p^{53} T^{115} + 7382325860822 p^{54} T^{116} + 284657890914 p^{55} T^{117} + 10174852766 p^{56} T^{118} + 329713044 p^{57} T^{119} + 9649077 p^{58} T^{120} + 242631 p^{59} T^{121} + 5247 p^{60} T^{122} + 83 p^{61} T^{123} + p^{62} T^{124}$$
83 $$1 - 84 T + 5681 T^{2} - 279883 T^{3} + 12024699 T^{4} - 444762492 T^{5} + 14938025594 T^{6} - 455911649586 T^{7} + 12932698479688 T^{8} - 342021808340934 T^{9} + 8531968844895750 T^{10} - 201386159508198554 T^{11} + 4529011707765080572 T^{12} - 97305949052096417179 T^{13} +$$$$20\!\cdots\!76$$$$T^{14} -$$$$39\!\cdots\!53$$$$T^{15} +$$$$76\!\cdots\!15$$$$T^{16} -$$$$14\!\cdots\!27$$$$T^{17} +$$$$25\!\cdots\!93$$$$T^{18} -$$$$43\!\cdots\!64$$$$T^{19} +$$$$74\!\cdots\!45$$$$T^{20} -$$$$12\!\cdots\!20$$$$T^{21} +$$$$19\!\cdots\!80$$$$T^{22} -$$$$30\!\cdots\!88$$$$T^{23} +$$$$46\!\cdots\!74$$$$T^{24} -$$$$70\!\cdots\!15$$$$T^{25} +$$$$10\!\cdots\!49$$$$T^{26} -$$$$14\!\cdots\!79$$$$T^{27} +$$$$20\!\cdots\!19$$$$T^{28} -$$$$28\!\cdots\!85$$$$T^{29} +$$$$38\!\cdots\!12$$$$T^{30} -$$$$51\!\cdots\!06$$$$T^{31} +$$$$66\!\cdots\!39$$$$T^{32} -$$$$85\!\cdots\!36$$$$T^{33} +$$$$10\!\cdots\!61$$$$T^{34} -$$$$13\!\cdots\!12$$$$T^{35} +$$$$16\!\cdots\!69$$$$T^{36} -$$$$19\!\cdots\!86$$$$T^{37} +$$$$23\!\cdots\!60$$$$T^{38} -$$$$27\!\cdots\!20$$$$T^{39} +$$$$32\!\cdots\!56$$$$T^{40} -$$$$36\!\cdots\!92$$$$T^{41} +$$$$41\!\cdots\!77$$$$T^{42} -$$$$45\!\cdots\!14$$$$T^{43} +$$$$50\!\cdots\!87$$$$T^{44} -$$$$54\!\cdots\!08$$$$T^{45} +$$$$58\!\cdots\!62$$$$T^{46} -$$$$62\!\cdots\!88$$$$T^{47} +$$$$65\!\cdots\!57$$$$T^{48} -$$$$67\!\cdots\!40$$$$T^{49} +$$$$69\!\cdots\!28$$$$T^{50} -$$$$70\!\cdots\!45$$$$T^{51} +$$$$70\!\cdots\!75$$$$T^{52} -$$$$70\!\cdots\!15$$$$T^{53} +$$$$69\!\cdots\!96$$$$T^{54} -$$$$67\!\cdots\!12$$$$T^{55} +$$$$65\!\cdots\!86$$$$T^{56} -$$$$62\!\cdots\!82$$$$T^{57} +$$$$59\!\cdots\!09$$$$T^{58} -$$$$55\!\cdots\!35$$$$T^{59} +$$$$51\!\cdots\!13$$$$T^{60} -$$$$47\!\cdots\!98$$$$T^{61} +$$$$43\!\cdots\!70$$$$T^{62} -$$$$47\!\cdots\!98$$$$p T^{63} +$$$$51\!\cdots\!13$$$$p^{2} T^{64} -$$$$55\!\cdots\!35$$$$p^{3} T^{65} +$$$$59\!\cdots\!09$$$$p^{4} T^{66} -$$$$62\!\cdots\!82$$$$p^{5} T^{67} +$$$$65\!\cdots\!86$$$$p^{6} T^{68} -$$$$67\!\cdots\!12$$$$p^{7} T^{69} +$$$$69\!\cdots\!96$$$$p^{8} T^{70} -$$$$70\!\cdots\!15$$$$p^{9} T^{71} +$$$$70\!\cdots\!75$$$$p^{10} T^{72} -$$$$70\!\cdots\!45$$$$p^{11} T^{73} +$$$$69\!\cdots\!28$$$$p^{12} T^{74} -$$$$67\!\cdots\!40$$$$p^{13} T^{75} +$$$$65\!\cdots\!57$$$$p^{14} T^{76} -$$$$62\!\cdots\!88$$$$p^{15} T^{77} +$$$$58\!\cdots\!62$$$$p^{16} T^{78} -$$$$54\!\cdots\!08$$$$p^{17} T^{79} +$$$$50\!\cdots\!87$$$$p^{18} T^{80} -$$$$45\!\cdots\!14$$$$p^{19} T^{81} +$$$$41\!\cdots\!77$$$$p^{20} T^{82} -$$$$36\!\cdots\!92$$$$p^{21} T^{83} +$$$$32\!\cdots\!56$$$$p^{22} T^{84} -$$$$27\!\cdots\!20$$$$p^{23} T^{85} +$$$$23\!\cdots\!60$$$$p^{24} T^{86} -$$$$19\!\cdots\!86$$$$p^{25} T^{87} +$$$$16\!\cdots\!69$$$$p^{26} T^{88} -$$$$13\!\cdots\!12$$$$p^{27} T^{89} +$$$$10\!\cdots\!61$$$$p^{28} T^{90} -$$$$85\!\cdots\!36$$$$p^{29} T^{91} +$$$$66\!\cdots\!39$$$$p^{30} T^{92} -$$$$51\!\cdots\!06$$$$p^{31} T^{93} +$$$$38\!\cdots\!12$$$$p^{32} T^{94} -$$$$28\!\cdots\!85$$$$p^{33} T^{95} +$$$$20\!\cdots\!19$$$$p^{34} T^{96} -$$$$14\!\cdots\!79$$$$p^{35} T^{97} +$$$$10\!\cdots\!49$$$$p^{36} T^{98} -$$$$70\!\cdots\!15$$$$p^{37} T^{99} +$$$$46\!\cdots\!74$$$$p^{38} T^{100} -$$$$30\!\cdots\!88$$$$p^{39} T^{101} +$$$$19\!\cdots\!80$$$$p^{40} T^{102} -$$$$12\!\cdots\!20$$$$p^{41} T^{103} +$$$$74\!\cdots\!45$$$$p^{42} T^{104} -$$$$43\!\cdots\!64$$$$p^{43} T^{105} +$$$$25\!\cdots\!93$$$$p^{44} T^{106} -$$$$14\!\cdots\!27$$$$p^{45} T^{107} +$$$$76\!\cdots\!15$$$$p^{46} T^{108} -$$$$39\!\cdots\!53$$$$p^{47} T^{109} +$$$$20\!\cdots\!76$$$$p^{48} T^{110} - 97305949052096417179 p^{49} T^{111} + 4529011707765080572 p^{50} T^{112} - 201386159508198554 p^{51} T^{113} + 8531968844895750 p^{52} T^{114} - 342021808340934 p^{53} T^{115} + 12932698479688 p^{54} T^{116} - 455911649586 p^{55} T^{117} + 14938025594 p^{56} T^{118} - 444762492 p^{57} T^{119} + 12024699 p^{58} T^{120} - 279883 p^{59} T^{121} + 5681 p^{60} T^{122} - 84 p^{61} T^{123} + p^{62} T^{124}$$
89 $$1 + 16 T + 2561 T^{2} + 41687 T^{3} + 3341162 T^{4} + 54671340 T^{5} + 2953656486 T^{6} + 48139973692 T^{7} + 1985876550391 T^{8} + 32018833779141 T^{9} + 1080934519050722 T^{10} + 17155217440171633 T^{11} + 495263989104796457 T^{12} + 7709886471987653863 T^{13} +$$$$19\!\cdots\!13$$$$T^{14} +$$$$29\!\cdots\!93$$$$T^{15} +$$$$68\!\cdots\!96$$$$T^{16} +$$$$10\!\cdots\!05$$$$T^{17} +$$$$21\!\cdots\!50$$$$T^{18} +$$$$31\!\cdots\!84$$$$T^{19} +$$$$60\!\cdots\!38$$$$T^{20} +$$$$85\!\cdots\!19$$$$T^{21} +$$$$15\!\cdots\!83$$$$T^{22} +$$$$21\!\cdots\!37$$$$T^{23} +$$$$36\!\cdots\!51$$$$T^{24} +$$$$49\!\cdots\!99$$$$T^{25} +$$$$80\!\cdots\!08$$$$T^{26} +$$$$10\!\cdots\!17$$$$T^{27} +$$$$16\!\cdots\!35$$$$T^{28} +$$$$21\!\cdots\!72$$$$T^{29} +$$$$31\!\cdots\!36$$$$T^{30} +$$$$39\!\cdots\!88$$$$T^{31} +$$$$56\!\cdots\!59$$$$T^{32} +$$$$69\!\cdots\!74$$$$T^{33} +$$$$95\!\cdots\!75$$$$T^{34} +$$$$11\!\cdots\!55$$$$T^{35} +$$$$15\!\cdots\!44$$$$T^{36} +$$$$17\!\cdots\!69$$$$T^{37} +$$$$23\!\cdots\!24$$$$T^{38} +$$$$26\!\cdots\!86$$$$T^{39} +$$$$33\!\cdots\!86$$$$T^{40} +$$$$37\!\cdots\!63$$$$T^{41} +$$$$45\!\cdots\!42$$$$T^{42} +$$$$49\!\cdots\!09$$$$T^{43} +$$$$59\!\cdots\!37$$$$T^{44} +$$$$63\!\cdots\!30$$$$T^{45} +$$$$73\!\cdots\!78$$$$T^{46} +$$$$77\!\cdots\!74$$$$T^{47} +$$$$88\!\cdots\!11$$$$T^{48} +$$$$91\!\cdots\!31$$$$T^{49} +$$$$10\!\cdots\!55$$$$T^{50} +$$$$10\!\cdots\!31$$$$T^{51} +$$$$11\!\cdots\!88$$$$T^{52} +$$$$11\!\cdots\!85$$$$T^{53} +$$$$11\!\cdots\!00$$$$T^{54} +$$$$11\!\cdots\!96$$$$T^{55} +$$$$11\!\cdots\!59$$$$T^{56} +$$$$11\!\cdots\!48$$$$T^{57} +$$$$11\!\cdots\!49$$$$T^{58} +$$$$10\!\cdots\!43$$$$T^{59} +$$$$10\!\cdots\!69$$$$T^{60} +$$$$10\!\cdots\!96$$$$T^{61} +$$$$99\!\cdots\!80$$$$T^{62} +$$$$10\!\cdots\!96$$$$p T^{63} +$$$$10\!\cdots\!69$$$$p^{2} T^{64} +$$$$10\!\cdots\!43$$$$p^{3} T^{65} +$$$$11\!\cdots\!49$$$$p^{4} T^{66} +$$$$11\!\cdots\!48$$$$p^{5} T^{67} +$$$$11\!\cdots\!59$$$$p^{6} T^{68} +$$$$11\!\cdots\!96$$$$p^{7} T^{69} +$$$$11\!\cdots\!00$$$$p^{8} T^{70} +$$$$11\!\cdots\!85$$$$p^{9} T^{71} +$$$$11\!\cdots\!88$$$$p^{10} T^{72} +$$$$10\!\cdots\!31$$$$p^{11} T^{73} +$$$$10\!\cdots\!55$$$$p^{12} T^{74} +$$$$91\!\cdots\!31$$$$p^{13} T^{75} +$$$$88\!\cdots\!11$$$$p^{14} T^{76} +$$$$77\!\cdots\!74$$$$p^{15} T^{77} +$$$$73\!\cdots\!78$$$$p^{16} T^{78} +$$$$63\!\cdots\!30$$$$p^{17} T^{79} +$$$$59\!\cdots\!37$$$$p^{18} T^{80} +$$$$49\!\cdots\!09$$$$p^{19} T^{81} +$$$$45\!\cdots\!42$$$$p^{20} T^{82} +$$$$37\!\cdots\!63$$$$p^{21} T^{83} +$$$$33\!\cdots\!86$$$$p^{22} T^{84} +$$$$26\!\cdots\!86$$$$p^{23} T^{85} +$$$$23\!\cdots\!24$$$$p^{24} T^{86} +$$$$17\!\cdots\!69$$$$p^{25} T^{87} +$$$$15\!\cdots\!44$$$$p^{26} T^{88} +$$$$11\!\cdots\!55$$$$p^{27} T^{89} +$$$$95\!\cdots\!75$$$$p^{28} T^{90} +$$$$69\!\cdots\!74$$$$p^{29} T^{91} +$$$$56\!\cdots\!59$$$$p^{30} T^{92} +$$$$39\!\cdots\!88$$$$p^{31} T^{93} +$$$$31\!\cdots\!36$$$$p^{32} T^{94} +$$$$21\!\cdots\!72$$$$p^{33} T^{95} +$$$$16\!\cdots\!35$$$$p^{34} T^{96} +$$$$10\!\cdots\!17$$$$p^{35} T^{97} +$$$$80\!\cdots\!08$$$$p^{36} T^{98} +$$$$49\!\cdots\!99$$$$p^{37} T^{99} +$$$$36\!\cdots\!51$$$$p^{38} T^{100} +$$$$21\!\cdots\!37$$$$p^{39} T^{101} +$$$$15\!\cdots\!83$$$$p^{40} T^{102} +$$$$85\!\cdots\!19$$$$p^{41} T^{103} +$$$$60\!\cdots\!38$$$$p^{42} T^{104} +$$$$31\!\cdots\!84$$$$p^{43} T^{105} +$$$$21\!\cdots\!50$$$$p^{44} T^{106} +$$$$10\!\cdots\!05$$$$p^{45} T^{107} +$$$$68\!\cdots\!96$$$$p^{46} T^{108} +$$$$29\!\cdots\!93$$$$p^{47} T^{109} +$$$$19\!\cdots\!13$$$$p^{48} T^{110} + 7709886471987653863 p^{49} T^{111} + 495263989104796457 p^{50} T^{112} + 17155217440171633 p^{51} T^{113} + 1080934519050722 p^{52} T^{114} + 32018833779141 p^{53} T^{115} + 1985876550391 p^{54} T^{116} + 48139973692 p^{55} T^{117} + 2953656486 p^{56} T^{118} + 54671340 p^{57} T^{119} + 3341162 p^{58} T^{120} + 41687 p^{59} T^{121} + 2561 p^{60} T^{122} + 16 p^{61} T^{123} + p^{62} T^{124}$$
97 $$1 - 155 T + 14285 T^{2} - 967590 T^{3} + 547999 p T^{4} - 2487821104 T^{5} + 102426058958 T^{6} - 3789266909560 T^{7} + 127954676259383 T^{8} - 3990280726298721 T^{9} + 115987671412167072 T^{10} - 3165837607374239192 T^{11} + 81634766710884967582 T^{12} -$$$$19\!\cdots\!19$$$$T^{13} +$$$$46\!\cdots\!56$$$$T^{14} -$$$$10\!\cdots\!04$$$$T^{15} +$$$$22\!\cdots\!80$$$$T^{16} -$$$$46\!\cdots\!82$$$$T^{17} +$$$$92\!\cdots\!05$$$$T^{18} -$$$$17\!\cdots\!68$$$$T^{19} +$$$$33\!\cdots\!01$$$$T^{20} -$$$$60\!\cdots\!30$$$$T^{21} +$$$$10\!\cdots\!90$$$$T^{22} -$$$$18\!\cdots\!93$$$$T^{23} +$$$$30\!\cdots\!82$$$$T^{24} -$$$$50\!\cdots\!89$$$$T^{25} +$$$$80\!\cdots\!58$$$$T^{26} -$$$$12\!\cdots\!46$$$$T^{27} +$$$$19\!\cdots\!63$$$$T^{28} -$$$$28\!\cdots\!50$$$$T^{29} +$$$$42\!\cdots\!85$$$$T^{30} -$$$$61\!\cdots\!28$$$$T^{31} +$$$$86\!\cdots\!90$$$$T^{32} -$$$$12\!\cdots\!45$$$$T^{33} +$$$$16\!\cdots\!79$$$$T^{34} -$$$$22\!\cdots\!68$$$$T^{35} +$$$$29\!\cdots\!12$$$$T^{36} -$$$$38\!\cdots\!83$$$$T^{37} +$$$$50\!\cdots\!15$$$$T^{38} -$$$$63\!\cdots\!04$$$$T^{39} +$$$$79\!\cdots\!01$$$$T^{40} -$$$$98\!\cdots\!09$$$$T^{41} +$$$$11\!\cdots\!42$$$$T^{42} -$$$$14\!\cdots\!74$$$$T^{43} +$$$$17\!\cdots\!89$$$$T^{44} -$$$$20\!\cdots\!73$$$$T^{45} +$$$$23\!\cdots\!39$$$$T^{46} -$$$$26\!\cdots\!03$$$$T^{47} +$$$$30\!\cdots\!62$$$$T^{48} -$$$$34\!\cdots\!60$$$$T^{49} +$$$$37\!\cdots\!28$$$$T^{50} -$$$$41\!\cdots\!36$$$$T^{51} +$$$$45\!\cdots\!12$$$$T^{52} -$$$$48\!\cdots\!11$$$$T^{53} +$$$$51\!\cdots\!53$$$$T^{54} -$$$$54\!\cdots\!96$$$$T^{55} +$$$$58\!\cdots\!12$$$$p T^{56} -$$$$59\!\cdots\!54$$$$T^{57} +$$$$60\!\cdots\!67$$$$T^{58} -$$$$61\!\cdots\!35$$$$T^{59} +$$$$62\!\cdots\!91$$$$T^{60} -$$$$62\!\cdots\!54$$$$T^{61} +$$$$61\!\cdots\!20$$$$T^{62} -$$$$62\!\cdots\!54$$$$p T^{63} +$$$$62\!\cdots\!91$$$$p^{2} T^{64} -$$$$61\!\cdots\!35$$$$p^{3} T^{65} +$$$$60\!\cdots\!67$$$$p^{4} T^{66} -$$$$59\!\cdots\!54$$$$p^{5} T^{67} +$$$$58\!\cdots\!12$$$$p^{7} T^{68} -$$$$54\!\cdots\!96$$$$p^{7} T^{69} +$$$$51\!\cdots\!53$$$$p^{8} T^{70} -$$$$48\!\cdots\!11$$$$p^{9} T^{71} +$$$$45\!\cdots\!12$$$$p^{10} T^{72} -$$$$41\!\cdots\!36$$$$p^{11} T^{73} +$$$$37\!\cdots\!28$$$$p^{12} T^{74} -$$$$34\!\cdots\!60$$$$p^{13} T^{75} +$$$$30\!\cdots\!62$$$$p^{14} T^{76} -$$$$26\!\cdots\!03$$$$p^{15} T^{77} +$$$$23\!\cdots\!39$$$$p^{16} T^{78} -$$$$20\!\cdots\!73$$$$p^{17} T^{79} +$$$$17\!\cdots\!89$$$$p^{18} T^{80} -$$$$14\!\cdots\!74$$$$p^{19} T^{81} +$$$$11\!\cdots\!42$$$$p^{20} T^{82} -$$$$98\!\cdots\!09$$$$p^{21} T^{83} +$$$$79\!\cdots\!01$$$$p^{22} T^{84} -$$$$63\!\cdots\!04$$$$p^{23} T^{85} +$$$$50\!\cdots\!15$$$$p^{24} T^{86} -$$$$38\!\cdots\!83$$$$p^{25} T^{87} +$$$$29\!\cdots\!12$$$$p^{26} T^{88} -$$$$22\!\cdots\!68$$$$p^{27} T^{89} +$$$$16\!\cdots\!79$$$$p^{28} T^{90} -$$$$12\!\cdots\!45$$$$p^{29} T^{91} +$$$$86\!\cdots\!90$$$$p^{30} T^{92} -$$$$61\!\cdots\!28$$$$p^{31} T^{93} +$$$$42\!\cdots\!85$$$$p^{32} T^{94} -$$$$28\!\cdots\!50$$$$p^{33} T^{95} +$$$$19\!\cdots\!63$$$$p^{34} T^{96} -$$$$12\!\cdots\!46$$$$p^{35} T^{97} +$$$$80\!\cdots\!58$$$$p^{36} T^{98} -$$$$50\!\cdots\!89$$$$p^{37} T^{99} +$$$$30\!\cdots\!82$$$$p^{38} T^{100} -$$$$18\!\cdots\!93$$$$p^{39} T^{101} +$$$$10\!\cdots\!90$$$$p^{40} T^{102} -$$$$60\!\cdots\!30$$$$p^{41} T^{103} +$$$$33\!\cdots\!01$$$$p^{42} T^{104} -$$$$17\!\cdots\!68$$$$p^{43} T^{105} +$$$$92\!\cdots\!05$$$$p^{44} T^{106} -$$$$46\!\cdots\!82$$$$p^{45} T^{107} +$$$$22\!\cdots\!80$$$$p^{46} T^{108} -$$$$10\!\cdots\!04$$$$p^{47} T^{109} +$$$$46\!\cdots\!56$$$$p^{48} T^{110} -$$$$19\!\cdots\!19$$$$p^{49} T^{111} + 81634766710884967582 p^{50} T^{112} - 3165837607374239192 p^{51} T^{113} + 115987671412167072 p^{52} T^{114} - 3990280726298721 p^{53} T^{115} + 127954676259383 p^{54} T^{116} - 3789266909560 p^{55} T^{117} + 102426058958 p^{56} T^{118} - 2487821104 p^{57} T^{119} + 547999 p^{59} T^{120} - 967590 p^{59} T^{121} + 14285 p^{60} T^{122} - 155 p^{61} T^{123} + p^{62} T^{124}$$
\begin{aligned} L(s) = \prod_p \ \prod_{j=1}^{124} (1 - \alpha_{j,p}\, p^{-s})^{-1} \end{aligned}