# Properties

 Degree 158 Conductor $37^{79} \cdot 109^{79}$ Sign $-1$ Motivic weight 1 Primitive no Self-dual yes Analytic rank 79

# Origins of factors

## Dirichlet series

 L(s)  = 1 − 11·2-s − 11·3-s + 21·4-s − 16·5-s + 121·6-s − 15·7-s + 206·8-s − 20·9-s + 176·10-s − 5·11-s − 231·12-s − 18·13-s + 165·14-s + 176·15-s − 945·16-s − 62·17-s + 220·18-s − 25·19-s − 336·20-s + 165·21-s + 55·22-s − 94·23-s − 2.26e3·24-s − 34·25-s + 198·26-s + 659·27-s − 315·28-s + ⋯
 L(s)  = 1 − 7.77·2-s − 6.35·3-s + 21/2·4-s − 7.15·5-s + 49.3·6-s − 5.66·7-s + 72.8·8-s − 6.66·9-s + 55.6·10-s − 1.50·11-s − 66.6·12-s − 4.99·13-s + 44.0·14-s + 45.4·15-s − 236.·16-s − 15.0·17-s + 51.8·18-s − 5.73·19-s − 75.1·20-s + 36.0·21-s + 11.7·22-s − 19.6·23-s − 462.·24-s − 6.79·25-s + 38.8·26-s + 126.·27-s − 59.5·28-s + ⋯

## Functional equation

\begin{aligned} \Lambda(s)=\mathstrut &\left(37^{79} \cdot 109^{79}\right)^{s/2} \, \Gamma_{\C}(s)^{79} \, L(s)\cr =\mathstrut & -\,\Lambda(2-s) \end{aligned}
\begin{aligned} \Lambda(s)=\mathstrut &\left(37^{79} \cdot 109^{79}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{79} \, L(s)\cr =\mathstrut & -\,\Lambda(1-s) \end{aligned}

## Invariants

 $$d$$ = $$158$$ $$N$$ = $$37^{79} \cdot 109^{79}$$ $$\varepsilon$$ = $-1$ motivic weight = $$1$$ character : induced by $\chi_{4033} (1, \cdot )$ primitive : no self-dual : yes analytic rank = 79 Selberg data = $(158,\ 37^{79} \cdot 109^{79} ,\ ( \ : [1/2]^{79} ),\ -1 )$ $L(1)$ $=$ $0$ $L(\frac12)$ $=$ $0$ $L(\frac{3}{2})$ not available $L(1)$ not available

## Euler product

$L(s) = \prod_{p \text{ prime}} F_p(p^{-s})^{-1}$ where, for $p \notin \{37,\;109\}$, $$F_p$$ is a polynomial of degree 158. If $p \in \{37,\;109\}$, then $F_p$ is a polynomial of degree at most 157.
$p$$F_p$
bad37 $$( 1 + T )^{79}$$
109 $$( 1 + T )^{79}$$
good2 $$1 + 11 T + 25 p^{2} T^{2} + 663 T^{3} + 121 p^{5} T^{4} + 19563 T^{5} + 90351 T^{6} + 95321 p^{2} T^{7} + 1503871 T^{8} + 5560363 T^{9} + 4873049 p^{2} T^{10} + 64996575 T^{11} + 207511373 T^{12} + 318066095 p T^{13} + 1880317521 T^{14} + 2685855201 p T^{15} + 3718713339 p^{2} T^{16} + 40002090283 T^{17} + 104694963185 T^{18} + 267091811107 T^{19} + 41578856759 p^{4} T^{20} + 404966857615 p^{2} T^{21} + 965202189209 p^{2} T^{22} + 4508392303573 p T^{23} + 10328097572125 p T^{24} + 46458125622341 T^{25} + 3208541096299 p^{5} T^{26} + 223133900207517 T^{27} + 238598217562127 p T^{28} + 1004920635710269 T^{29} + 521283226619761 p^{2} T^{30} + 4265237581847705 T^{31} + 8605718090231957 T^{32} + 2141822369694789 p^{3} T^{33} + 4210258040734075 p^{3} T^{34} + 65394992655431009 T^{35} + 125453412655095169 T^{36} + 118943943075140423 p T^{37} + 223015593232784063 p T^{38} + 827184958002532997 T^{39} + 1517814820637936969 T^{40} + 2756385836338027439 T^{41} + 4955489170366046283 T^{42} + 8822102412658655829 T^{43} + 7778133627906228003 p T^{44} + 27176269497542482805 T^{45} + 11761554092691108399 p^{2} T^{46} + 40362216350691437737 p T^{47} +$$$$13\!\cdots\!51$$$$T^{48} + 14475895524978367559 p^{4} T^{49} +$$$$38\!\cdots\!35$$$$T^{50} +$$$$64\!\cdots\!25$$$$T^{51} +$$$$10\!\cdots\!63$$$$T^{52} +$$$$17\!\cdots\!61$$$$T^{53} +$$$$14\!\cdots\!93$$$$p T^{54} +$$$$28\!\cdots\!77$$$$p^{4} T^{55} +$$$$18\!\cdots\!87$$$$p^{2} T^{56} +$$$$11\!\cdots\!15$$$$T^{57} + 35240815786035582963 p^{9} T^{58} +$$$$28\!\cdots\!81$$$$T^{59} +$$$$68\!\cdots\!77$$$$p^{6} T^{60} +$$$$67\!\cdots\!13$$$$T^{61} +$$$$10\!\cdots\!39$$$$T^{62} +$$$$39\!\cdots\!91$$$$p^{2} T^{63} +$$$$60\!\cdots\!73$$$$p^{2} T^{64} +$$$$18\!\cdots\!65$$$$p T^{65} +$$$$27\!\cdots\!89$$$$p T^{66} +$$$$51\!\cdots\!53$$$$p^{4} T^{67} +$$$$12\!\cdots\!57$$$$T^{68} +$$$$45\!\cdots\!37$$$$p^{2} T^{69} +$$$$66\!\cdots\!89$$$$p^{2} T^{70} +$$$$38\!\cdots\!03$$$$T^{71} +$$$$56\!\cdots\!13$$$$T^{72} +$$$$10\!\cdots\!71$$$$p^{3} T^{73} +$$$$11\!\cdots\!79$$$$T^{74} +$$$$21\!\cdots\!29$$$$p^{3} T^{75} +$$$$24\!\cdots\!51$$$$T^{76} +$$$$17\!\cdots\!53$$$$p T^{77} +$$$$24\!\cdots\!37$$$$p T^{78} +$$$$88\!\cdots\!25$$$$p^{3} T^{79} +$$$$24\!\cdots\!37$$$$p^{2} T^{80} +$$$$17\!\cdots\!53$$$$p^{3} T^{81} +$$$$24\!\cdots\!51$$$$p^{3} T^{82} +$$$$21\!\cdots\!29$$$$p^{7} T^{83} +$$$$11\!\cdots\!79$$$$p^{5} T^{84} +$$$$10\!\cdots\!71$$$$p^{9} T^{85} +$$$$56\!\cdots\!13$$$$p^{7} T^{86} +$$$$38\!\cdots\!03$$$$p^{8} T^{87} +$$$$66\!\cdots\!89$$$$p^{11} T^{88} +$$$$45\!\cdots\!37$$$$p^{12} T^{89} +$$$$12\!\cdots\!57$$$$p^{11} T^{90} +$$$$51\!\cdots\!53$$$$p^{16} T^{91} +$$$$27\!\cdots\!89$$$$p^{14} T^{92} +$$$$18\!\cdots\!65$$$$p^{15} T^{93} +$$$$60\!\cdots\!73$$$$p^{17} T^{94} +$$$$39\!\cdots\!91$$$$p^{18} T^{95} +$$$$10\!\cdots\!39$$$$p^{17} T^{96} +$$$$67\!\cdots\!13$$$$p^{18} T^{97} +$$$$68\!\cdots\!77$$$$p^{25} T^{98} +$$$$28\!\cdots\!81$$$$p^{20} T^{99} + 35240815786035582963 p^{30} T^{100} +$$$$11\!\cdots\!15$$$$p^{22} T^{101} +$$$$18\!\cdots\!87$$$$p^{25} T^{102} +$$$$28\!\cdots\!77$$$$p^{28} T^{103} +$$$$14\!\cdots\!93$$$$p^{26} T^{104} +$$$$17\!\cdots\!61$$$$p^{26} T^{105} +$$$$10\!\cdots\!63$$$$p^{27} T^{106} +$$$$64\!\cdots\!25$$$$p^{28} T^{107} +$$$$38\!\cdots\!35$$$$p^{29} T^{108} + 14475895524978367559 p^{34} T^{109} +$$$$13\!\cdots\!51$$$$p^{31} T^{110} + 40362216350691437737 p^{33} T^{111} + 11761554092691108399 p^{35} T^{112} + 27176269497542482805 p^{34} T^{113} + 7778133627906228003 p^{36} T^{114} + 8822102412658655829 p^{36} T^{115} + 4955489170366046283 p^{37} T^{116} + 2756385836338027439 p^{38} T^{117} + 1517814820637936969 p^{39} T^{118} + 827184958002532997 p^{40} T^{119} + 223015593232784063 p^{42} T^{120} + 118943943075140423 p^{43} T^{121} + 125453412655095169 p^{43} T^{122} + 65394992655431009 p^{44} T^{123} + 4210258040734075 p^{48} T^{124} + 2141822369694789 p^{49} T^{125} + 8605718090231957 p^{47} T^{126} + 4265237581847705 p^{48} T^{127} + 521283226619761 p^{51} T^{128} + 1004920635710269 p^{50} T^{129} + 238598217562127 p^{52} T^{130} + 223133900207517 p^{52} T^{131} + 3208541096299 p^{58} T^{132} + 46458125622341 p^{54} T^{133} + 10328097572125 p^{56} T^{134} + 4508392303573 p^{57} T^{135} + 965202189209 p^{59} T^{136} + 404966857615 p^{60} T^{137} + 41578856759 p^{63} T^{138} + 267091811107 p^{60} T^{139} + 104694963185 p^{61} T^{140} + 40002090283 p^{62} T^{141} + 3718713339 p^{65} T^{142} + 2685855201 p^{65} T^{143} + 1880317521 p^{65} T^{144} + 318066095 p^{67} T^{145} + 207511373 p^{67} T^{146} + 64996575 p^{68} T^{147} + 4873049 p^{71} T^{148} + 5560363 p^{70} T^{149} + 1503871 p^{71} T^{150} + 95321 p^{74} T^{151} + 90351 p^{73} T^{152} + 19563 p^{74} T^{153} + 121 p^{80} T^{154} + 663 p^{76} T^{155} + 25 p^{79} T^{156} + 11 p^{78} T^{157} + p^{79} T^{158}$$
3 $$1 + 11 T + 47 p T^{2} + 1112 T^{3} + 8815 T^{4} + 55963 T^{5} + 345625 T^{6} + 1873603 T^{7} + 9805736 T^{8} + 47011189 T^{9} + 217535051 T^{10} + 34957574 p^{3} T^{11} + 3960496124 T^{12} + 195120622 p^{4} T^{13} + 61152774907 T^{14} + 75708622822 p T^{15} + 30371420744 p^{3} T^{16} + 953441524532 p T^{17} + 3240620790809 p T^{18} + 10691258476130 p T^{19} + 34443108046352 p T^{20} + 36030238331242 p^{2} T^{21} + 995597368208030 T^{22} + 995304940183055 p T^{23} + 8775539535952132 T^{24} + 25249702495330229 T^{25} + 71296422620180261 T^{26} + 197449232224595291 T^{27} + 537306428231735347 T^{28} + 1436224945844005262 T^{29} + 3776470231847055224 T^{30} + 9766503548670632855 T^{31} + 307042645527377405 p^{4} T^{32} + 62358195299588169646 T^{33} +$$$$15\!\cdots\!60$$$$T^{34} +$$$$37\!\cdots\!12$$$$T^{35} +$$$$30\!\cdots\!18$$$$p T^{36} +$$$$21\!\cdots\!90$$$$T^{37} +$$$$16\!\cdots\!36$$$$p T^{38} +$$$$38\!\cdots\!86$$$$p T^{39} +$$$$29\!\cdots\!06$$$$p^{2} T^{40} +$$$$59\!\cdots\!68$$$$T^{41} +$$$$13\!\cdots\!83$$$$T^{42} +$$$$28\!\cdots\!47$$$$T^{43} +$$$$20\!\cdots\!94$$$$p T^{44} +$$$$13\!\cdots\!66$$$$T^{45} +$$$$28\!\cdots\!11$$$$T^{46} +$$$$60\!\cdots\!96$$$$T^{47} +$$$$42\!\cdots\!84$$$$p T^{48} +$$$$26\!\cdots\!46$$$$T^{49} +$$$$53\!\cdots\!81$$$$T^{50} +$$$$10\!\cdots\!89$$$$T^{51} +$$$$21\!\cdots\!28$$$$T^{52} +$$$$42\!\cdots\!47$$$$T^{53} +$$$$84\!\cdots\!90$$$$T^{54} +$$$$16\!\cdots\!40$$$$T^{55} +$$$$32\!\cdots\!87$$$$T^{56} +$$$$68\!\cdots\!81$$$$p^{2} T^{57} +$$$$39\!\cdots\!98$$$$p T^{58} +$$$$22\!\cdots\!80$$$$T^{59} +$$$$13\!\cdots\!01$$$$p T^{60} +$$$$77\!\cdots\!24$$$$T^{61} +$$$$16\!\cdots\!80$$$$p^{2} T^{62} +$$$$88\!\cdots\!72$$$$p T^{63} +$$$$48\!\cdots\!79$$$$T^{64} +$$$$99\!\cdots\!15$$$$p^{2} T^{65} +$$$$16\!\cdots\!93$$$$T^{66} +$$$$29\!\cdots\!74$$$$T^{67} +$$$$52\!\cdots\!73$$$$T^{68} +$$$$93\!\cdots\!96$$$$T^{69} +$$$$16\!\cdots\!31$$$$T^{70} +$$$$29\!\cdots\!28$$$$T^{71} +$$$$52\!\cdots\!69$$$$T^{72} +$$$$92\!\cdots\!73$$$$T^{73} +$$$$16\!\cdots\!97$$$$T^{74} +$$$$10\!\cdots\!87$$$$p^{3} T^{75} +$$$$49\!\cdots\!65$$$$T^{76} +$$$$87\!\cdots\!26$$$$T^{77} +$$$$50\!\cdots\!28$$$$p T^{78} +$$$$26\!\cdots\!98$$$$T^{79} +$$$$50\!\cdots\!28$$$$p^{2} T^{80} +$$$$87\!\cdots\!26$$$$p^{2} T^{81} +$$$$49\!\cdots\!65$$$$p^{3} T^{82} +$$$$10\!\cdots\!87$$$$p^{7} T^{83} +$$$$16\!\cdots\!97$$$$p^{5} T^{84} +$$$$92\!\cdots\!73$$$$p^{6} T^{85} +$$$$52\!\cdots\!69$$$$p^{7} T^{86} +$$$$29\!\cdots\!28$$$$p^{8} T^{87} +$$$$16\!\cdots\!31$$$$p^{9} T^{88} +$$$$93\!\cdots\!96$$$$p^{10} T^{89} +$$$$52\!\cdots\!73$$$$p^{11} T^{90} +$$$$29\!\cdots\!74$$$$p^{12} T^{91} +$$$$16\!\cdots\!93$$$$p^{13} T^{92} +$$$$99\!\cdots\!15$$$$p^{16} T^{93} +$$$$48\!\cdots\!79$$$$p^{15} T^{94} +$$$$88\!\cdots\!72$$$$p^{17} T^{95} +$$$$16\!\cdots\!80$$$$p^{19} T^{96} +$$$$77\!\cdots\!24$$$$p^{18} T^{97} +$$$$13\!\cdots\!01$$$$p^{20} T^{98} +$$$$22\!\cdots\!80$$$$p^{20} T^{99} +$$$$39\!\cdots\!98$$$$p^{22} T^{100} +$$$$68\!\cdots\!81$$$$p^{24} T^{101} +$$$$32\!\cdots\!87$$$$p^{23} T^{102} +$$$$16\!\cdots\!40$$$$p^{24} T^{103} +$$$$84\!\cdots\!90$$$$p^{25} T^{104} +$$$$42\!\cdots\!47$$$$p^{26} T^{105} +$$$$21\!\cdots\!28$$$$p^{27} T^{106} +$$$$10\!\cdots\!89$$$$p^{28} T^{107} +$$$$53\!\cdots\!81$$$$p^{29} T^{108} +$$$$26\!\cdots\!46$$$$p^{30} T^{109} +$$$$42\!\cdots\!84$$$$p^{32} T^{110} +$$$$60\!\cdots\!96$$$$p^{32} T^{111} +$$$$28\!\cdots\!11$$$$p^{33} T^{112} +$$$$13\!\cdots\!66$$$$p^{34} T^{113} +$$$$20\!\cdots\!94$$$$p^{36} T^{114} +$$$$28\!\cdots\!47$$$$p^{36} T^{115} +$$$$13\!\cdots\!83$$$$p^{37} T^{116} +$$$$59\!\cdots\!68$$$$p^{38} T^{117} +$$$$29\!\cdots\!06$$$$p^{41} T^{118} +$$$$38\!\cdots\!86$$$$p^{41} T^{119} +$$$$16\!\cdots\!36$$$$p^{42} T^{120} +$$$$21\!\cdots\!90$$$$p^{42} T^{121} +$$$$30\!\cdots\!18$$$$p^{44} T^{122} +$$$$37\!\cdots\!12$$$$p^{44} T^{123} +$$$$15\!\cdots\!60$$$$p^{45} T^{124} + 62358195299588169646 p^{46} T^{125} + 307042645527377405 p^{51} T^{126} + 9766503548670632855 p^{48} T^{127} + 3776470231847055224 p^{49} T^{128} + 1436224945844005262 p^{50} T^{129} + 537306428231735347 p^{51} T^{130} + 197449232224595291 p^{52} T^{131} + 71296422620180261 p^{53} T^{132} + 25249702495330229 p^{54} T^{133} + 8775539535952132 p^{55} T^{134} + 995304940183055 p^{57} T^{135} + 995597368208030 p^{57} T^{136} + 36030238331242 p^{60} T^{137} + 34443108046352 p^{60} T^{138} + 10691258476130 p^{61} T^{139} + 3240620790809 p^{62} T^{140} + 953441524532 p^{63} T^{141} + 30371420744 p^{66} T^{142} + 75708622822 p^{65} T^{143} + 61152774907 p^{65} T^{144} + 195120622 p^{70} T^{145} + 3960496124 p^{67} T^{146} + 34957574 p^{71} T^{147} + 217535051 p^{69} T^{148} + 47011189 p^{70} T^{149} + 9805736 p^{71} T^{150} + 1873603 p^{72} T^{151} + 345625 p^{73} T^{152} + 55963 p^{74} T^{153} + 8815 p^{75} T^{154} + 1112 p^{76} T^{155} + 47 p^{78} T^{156} + 11 p^{78} T^{157} + p^{79} T^{158}$$
5 $$1 + 16 T + 58 p T^{2} + 651 p T^{3} + 36338 T^{4} + 324529 T^{5} + 2807303 T^{6} + 21238501 T^{7} + 154843333 T^{8} + 1029685196 T^{9} + 6603769088 T^{10} + 39540952321 T^{11} + 228896595992 T^{12} + 1255030166307 T^{13} + 6671257390741 T^{14} + 33912267661294 T^{15} + 33513849731258 p T^{16} + 797218417202436 T^{17} + 3695625663640299 T^{18} + 3315546910352442 p T^{19} + 72612156515261892 T^{20} + 308952036588923512 T^{21} + 257191570671933471 p T^{22} + 5215279305831282806 T^{23} + 20724786789712462884 T^{24} + 16088348356576576222 p T^{25} +$$$$30\!\cdots\!36$$$$T^{26} +$$$$22\!\cdots\!21$$$$p T^{27} +$$$$41\!\cdots\!36$$$$T^{28} +$$$$30\!\cdots\!47$$$$p T^{29} +$$$$53\!\cdots\!51$$$$T^{30} +$$$$18\!\cdots\!07$$$$T^{31} +$$$$62\!\cdots\!91$$$$T^{32} +$$$$21\!\cdots\!08$$$$T^{33} +$$$$13\!\cdots\!56$$$$p T^{34} +$$$$22\!\cdots\!83$$$$T^{35} +$$$$72\!\cdots\!81$$$$T^{36} +$$$$23\!\cdots\!18$$$$T^{37} +$$$$71\!\cdots\!49$$$$T^{38} +$$$$22\!\cdots\!49$$$$T^{39} +$$$$67\!\cdots\!49$$$$T^{40} +$$$$20\!\cdots\!79$$$$T^{41} +$$$$11\!\cdots\!88$$$$p T^{42} +$$$$17\!\cdots\!68$$$$T^{43} +$$$$50\!\cdots\!13$$$$T^{44} +$$$$14\!\cdots\!94$$$$T^{45} +$$$$40\!\cdots\!96$$$$T^{46} +$$$$22\!\cdots\!48$$$$p T^{47} +$$$$31\!\cdots\!49$$$$T^{48} +$$$$17\!\cdots\!32$$$$p T^{49} +$$$$23\!\cdots\!82$$$$T^{50} +$$$$62\!\cdots\!12$$$$T^{51} +$$$$16\!\cdots\!97$$$$T^{52} +$$$$43\!\cdots\!19$$$$T^{53} +$$$$11\!\cdots\!26$$$$T^{54} +$$$$29\!\cdots\!04$$$$T^{55} +$$$$76\!\cdots\!67$$$$T^{56} +$$$$19\!\cdots\!14$$$$T^{57} +$$$$98\!\cdots\!07$$$$p T^{58} +$$$$24\!\cdots\!37$$$$p T^{59} +$$$$30\!\cdots\!94$$$$T^{60} +$$$$75\!\cdots\!01$$$$T^{61} +$$$$18\!\cdots\!33$$$$T^{62} +$$$$45\!\cdots\!96$$$$T^{63} +$$$$10\!\cdots\!97$$$$T^{64} +$$$$26\!\cdots\!74$$$$T^{65} +$$$$63\!\cdots\!58$$$$T^{66} +$$$$15\!\cdots\!94$$$$T^{67} +$$$$71\!\cdots\!47$$$$p T^{68} +$$$$16\!\cdots\!19$$$$p T^{69} +$$$$19\!\cdots\!66$$$$T^{70} +$$$$45\!\cdots\!03$$$$T^{71} +$$$$21\!\cdots\!96$$$$p T^{72} +$$$$97\!\cdots\!03$$$$p^{2} T^{73} +$$$$56\!\cdots\!23$$$$T^{74} +$$$$12\!\cdots\!59$$$$T^{75} +$$$$29\!\cdots\!06$$$$T^{76} +$$$$65\!\cdots\!29$$$$T^{77} +$$$$14\!\cdots\!27$$$$T^{78} +$$$$33\!\cdots\!22$$$$T^{79} +$$$$14\!\cdots\!27$$$$p T^{80} +$$$$65\!\cdots\!29$$$$p^{2} T^{81} +$$$$29\!\cdots\!06$$$$p^{3} T^{82} +$$$$12\!\cdots\!59$$$$p^{4} T^{83} +$$$$56\!\cdots\!23$$$$p^{5} T^{84} +$$$$97\!\cdots\!03$$$$p^{8} T^{85} +$$$$21\!\cdots\!96$$$$p^{8} T^{86} +$$$$45\!\cdots\!03$$$$p^{8} T^{87} +$$$$19\!\cdots\!66$$$$p^{9} T^{88} +$$$$16\!\cdots\!19$$$$p^{11} T^{89} +$$$$71\!\cdots\!47$$$$p^{12} T^{90} +$$$$15\!\cdots\!94$$$$p^{12} T^{91} +$$$$63\!\cdots\!58$$$$p^{13} T^{92} +$$$$26\!\cdots\!74$$$$p^{14} T^{93} +$$$$10\!\cdots\!97$$$$p^{15} T^{94} +$$$$45\!\cdots\!96$$$$p^{16} T^{95} +$$$$18\!\cdots\!33$$$$p^{17} T^{96} +$$$$75\!\cdots\!01$$$$p^{18} T^{97} +$$$$30\!\cdots\!94$$$$p^{19} T^{98} +$$$$24\!\cdots\!37$$$$p^{21} T^{99} +$$$$98\!\cdots\!07$$$$p^{22} T^{100} +$$$$19\!\cdots\!14$$$$p^{22} T^{101} +$$$$76\!\cdots\!67$$$$p^{23} T^{102} +$$$$29\!\cdots\!04$$$$p^{24} T^{103} +$$$$11\!\cdots\!26$$$$p^{25} T^{104} +$$$$43\!\cdots\!19$$$$p^{26} T^{105} +$$$$16\!\cdots\!97$$$$p^{27} T^{106} +$$$$62\!\cdots\!12$$$$p^{28} T^{107} +$$$$23\!\cdots\!82$$$$p^{29} T^{108} +$$$$17\!\cdots\!32$$$$p^{31} T^{109} +$$$$31\!\cdots\!49$$$$p^{31} T^{110} +$$$$22\!\cdots\!48$$$$p^{33} T^{111} +$$$$40\!\cdots\!96$$$$p^{33} T^{112} +$$$$14\!\cdots\!94$$$$p^{34} T^{113} +$$$$50\!\cdots\!13$$$$p^{35} T^{114} +$$$$17\!\cdots\!68$$$$p^{36} T^{115} +$$$$11\!\cdots\!88$$$$p^{38} T^{116} +$$$$20\!\cdots\!79$$$$p^{38} T^{117} +$$$$67\!\cdots\!49$$$$p^{39} T^{118} +$$$$22\!\cdots\!49$$$$p^{40} T^{119} +$$$$71\!\cdots\!49$$$$p^{41} T^{120} +$$$$23\!\cdots\!18$$$$p^{42} T^{121} +$$$$72\!\cdots\!81$$$$p^{43} T^{122} +$$$$22\!\cdots\!83$$$$p^{44} T^{123} +$$$$13\!\cdots\!56$$$$p^{46} T^{124} +$$$$21\!\cdots\!08$$$$p^{46} T^{125} +$$$$62\!\cdots\!91$$$$p^{47} T^{126} +$$$$18\!\cdots\!07$$$$p^{48} T^{127} +$$$$53\!\cdots\!51$$$$p^{49} T^{128} +$$$$30\!\cdots\!47$$$$p^{51} T^{129} +$$$$41\!\cdots\!36$$$$p^{51} T^{130} +$$$$22\!\cdots\!21$$$$p^{53} T^{131} +$$$$30\!\cdots\!36$$$$p^{53} T^{132} + 16088348356576576222 p^{55} T^{133} + 20724786789712462884 p^{55} T^{134} + 5215279305831282806 p^{56} T^{135} + 257191570671933471 p^{58} T^{136} + 308952036588923512 p^{58} T^{137} + 72612156515261892 p^{59} T^{138} + 3315546910352442 p^{61} T^{139} + 3695625663640299 p^{61} T^{140} + 797218417202436 p^{62} T^{141} + 33513849731258 p^{64} T^{142} + 33912267661294 p^{64} T^{143} + 6671257390741 p^{65} T^{144} + 1255030166307 p^{66} T^{145} + 228896595992 p^{67} T^{146} + 39540952321 p^{68} T^{147} + 6603769088 p^{69} T^{148} + 1029685196 p^{70} T^{149} + 154843333 p^{71} T^{150} + 21238501 p^{72} T^{151} + 2807303 p^{73} T^{152} + 324529 p^{74} T^{153} + 36338 p^{75} T^{154} + 651 p^{77} T^{155} + 58 p^{78} T^{156} + 16 p^{78} T^{157} + p^{79} T^{158}$$
7 $$1 + 15 T + 348 T^{2} + 4057 T^{3} + 55841 T^{4} + 542611 T^{5} + 5679033 T^{6} + 47920718 T^{7} + 418230684 T^{8} + 3147454418 T^{9} + 24005489124 T^{10} + 478554918 p^{3} T^{11} + 1125052430511 T^{12} + 7085740194234 T^{13} + 907270329005 p^{2} T^{14} + 37227393158330 p T^{15} + 1516245336568692 T^{16} + 8340003798775461 T^{17} + 45441208879764041 T^{18} + 236092609921867240 T^{19} + 1213679390974337216 T^{20} + 5988744125814625277 T^{21} + 29221582664938280021 T^{22} +$$$$13\!\cdots\!31$$$$T^{23} +$$$$64\!\cdots\!42$$$$T^{24} +$$$$28\!\cdots\!63$$$$T^{25} +$$$$12\!\cdots\!99$$$$T^{26} +$$$$55\!\cdots\!38$$$$T^{27} +$$$$23\!\cdots\!64$$$$T^{28} +$$$$99\!\cdots\!87$$$$T^{29} +$$$$41\!\cdots\!93$$$$T^{30} +$$$$16\!\cdots\!30$$$$T^{31} +$$$$66\!\cdots\!91$$$$T^{32} +$$$$26\!\cdots\!59$$$$T^{33} +$$$$10\!\cdots\!17$$$$T^{34} +$$$$38\!\cdots\!71$$$$T^{35} +$$$$14\!\cdots\!70$$$$T^{36} +$$$$53\!\cdots\!56$$$$T^{37} +$$$$27\!\cdots\!23$$$$p T^{38} +$$$$69\!\cdots\!36$$$$T^{39} +$$$$24\!\cdots\!99$$$$T^{40} +$$$$87\!\cdots\!40$$$$T^{41} +$$$$43\!\cdots\!06$$$$p T^{42} +$$$$14\!\cdots\!28$$$$p T^{43} +$$$$35\!\cdots\!66$$$$T^{44} +$$$$12\!\cdots\!32$$$$T^{45} +$$$$40\!\cdots\!42$$$$T^{46} +$$$$13\!\cdots\!10$$$$T^{47} +$$$$61\!\cdots\!79$$$$p T^{48} +$$$$14\!\cdots\!02$$$$T^{49} +$$$$45\!\cdots\!61$$$$T^{50} +$$$$14\!\cdots\!65$$$$T^{51} +$$$$45\!\cdots\!64$$$$T^{52} +$$$$14\!\cdots\!77$$$$T^{53} +$$$$62\!\cdots\!25$$$$p T^{54} +$$$$13\!\cdots\!95$$$$T^{55} +$$$$41\!\cdots\!30$$$$T^{56} +$$$$12\!\cdots\!97$$$$T^{57} +$$$$37\!\cdots\!62$$$$T^{58} +$$$$11\!\cdots\!64$$$$T^{59} +$$$$48\!\cdots\!87$$$$p T^{60} +$$$$99\!\cdots\!93$$$$T^{61} +$$$$29\!\cdots\!08$$$$T^{62} +$$$$85\!\cdots\!72$$$$T^{63} +$$$$24\!\cdots\!95$$$$T^{64} +$$$$70\!\cdots\!38$$$$T^{65} +$$$$20\!\cdots\!43$$$$T^{66} +$$$$57\!\cdots\!43$$$$T^{67} +$$$$23\!\cdots\!93$$$$p T^{68} +$$$$45\!\cdots\!62$$$$T^{69} +$$$$12\!\cdots\!86$$$$T^{70} +$$$$35\!\cdots\!11$$$$T^{71} +$$$$97\!\cdots\!58$$$$T^{72} +$$$$26\!\cdots\!88$$$$T^{73} +$$$$73\!\cdots\!78$$$$T^{74} +$$$$19\!\cdots\!01$$$$T^{75} +$$$$53\!\cdots\!36$$$$T^{76} +$$$$14\!\cdots\!64$$$$T^{77} +$$$$38\!\cdots\!42$$$$T^{78} +$$$$10\!\cdots\!08$$$$T^{79} +$$$$38\!\cdots\!42$$$$p T^{80} +$$$$14\!\cdots\!64$$$$p^{2} T^{81} +$$$$53\!\cdots\!36$$$$p^{3} T^{82} +$$$$19\!\cdots\!01$$$$p^{4} T^{83} +$$$$73\!\cdots\!78$$$$p^{5} T^{84} +$$$$26\!\cdots\!88$$$$p^{6} T^{85} +$$$$97\!\cdots\!58$$$$p^{7} T^{86} +$$$$35\!\cdots\!11$$$$p^{8} T^{87} +$$$$12\!\cdots\!86$$$$p^{9} T^{88} +$$$$45\!\cdots\!62$$$$p^{10} T^{89} +$$$$23\!\cdots\!93$$$$p^{12} T^{90} +$$$$57\!\cdots\!43$$$$p^{12} T^{91} +$$$$20\!\cdots\!43$$$$p^{13} T^{92} +$$$$70\!\cdots\!38$$$$p^{14} T^{93} +$$$$24\!\cdots\!95$$$$p^{15} T^{94} +$$$$85\!\cdots\!72$$$$p^{16} T^{95} +$$$$29\!\cdots\!08$$$$p^{17} T^{96} +$$$$99\!\cdots\!93$$$$p^{18} T^{97} +$$$$48\!\cdots\!87$$$$p^{20} T^{98} +$$$$11\!\cdots\!64$$$$p^{20} T^{99} +$$$$37\!\cdots\!62$$$$p^{21} T^{100} +$$$$12\!\cdots\!97$$$$p^{22} T^{101} +$$$$41\!\cdots\!30$$$$p^{23} T^{102} +$$$$13\!\cdots\!95$$$$p^{24} T^{103} +$$$$62\!\cdots\!25$$$$p^{26} T^{104} +$$$$14\!\cdots\!77$$$$p^{26} T^{105} +$$$$45\!\cdots\!64$$$$p^{27} T^{106} +$$$$14\!\cdots\!65$$$$p^{28} T^{107} +$$$$45\!\cdots\!61$$$$p^{29} T^{108} +$$$$14\!\cdots\!02$$$$p^{30} T^{109} +$$$$61\!\cdots\!79$$$$p^{32} T^{110} +$$$$13\!\cdots\!10$$$$p^{32} T^{111} +$$$$40\!\cdots\!42$$$$p^{33} T^{112} +$$$$12\!\cdots\!32$$$$p^{34} T^{113} +$$$$35\!\cdots\!66$$$$p^{35} T^{114} +$$$$14\!\cdots\!28$$$$p^{37} T^{115} +$$$$43\!\cdots\!06$$$$p^{38} T^{116} +$$$$87\!\cdots\!40$$$$p^{38} T^{117} +$$$$24\!\cdots\!99$$$$p^{39} T^{118} +$$$$69\!\cdots\!36$$$$p^{40} T^{119} +$$$$27\!\cdots\!23$$$$p^{42} T^{120} +$$$$53\!\cdots\!56$$$$p^{42} T^{121} +$$$$14\!\cdots\!70$$$$p^{43} T^{122} +$$$$38\!\cdots\!71$$$$p^{44} T^{123} +$$$$10\!\cdots\!17$$$$p^{45} T^{124} +$$$$26\!\cdots\!59$$$$p^{46} T^{125} +$$$$66\!\cdots\!91$$$$p^{47} T^{126} +$$$$16\!\cdots\!30$$$$p^{48} T^{127} +$$$$41\!\cdots\!93$$$$p^{49} T^{128} +$$$$99\!\cdots\!87$$$$p^{50} T^{129} +$$$$23\!\cdots\!64$$$$p^{51} T^{130} +$$$$55\!\cdots\!38$$$$p^{52} T^{131} +$$$$12\!\cdots\!99$$$$p^{53} T^{132} +$$$$28\!\cdots\!63$$$$p^{54} T^{133} +$$$$64\!\cdots\!42$$$$p^{55} T^{134} +$$$$13\!\cdots\!31$$$$p^{56} T^{135} + 29221582664938280021 p^{57} T^{136} + 5988744125814625277 p^{58} T^{137} + 1213679390974337216 p^{59} T^{138} + 236092609921867240 p^{60} T^{139} + 45441208879764041 p^{61} T^{140} + 8340003798775461 p^{62} T^{141} + 1516245336568692 p^{63} T^{142} + 37227393158330 p^{65} T^{143} + 907270329005 p^{67} T^{144} + 7085740194234 p^{66} T^{145} + 1125052430511 p^{67} T^{146} + 478554918 p^{71} T^{147} + 24005489124 p^{69} T^{148} + 3147454418 p^{70} T^{149} + 418230684 p^{71} T^{150} + 47920718 p^{72} T^{151} + 5679033 p^{73} T^{152} + 542611 p^{74} T^{153} + 55841 p^{75} T^{154} + 4057 p^{76} T^{155} + 348 p^{77} T^{156} + 15 p^{78} T^{157} + p^{79} T^{158}$$
11 $$1 + 5 T + 412 T^{2} + 182 p T^{3} + 85192 T^{4} + 36616 p T^{5} + 11785864 T^{6} + 54271675 T^{7} + 1227030741 T^{8} + 5508299425 T^{9} + 102524644613 T^{10} + 449059092428 T^{11} + 650933071112 p T^{12} + 30622774055004 T^{13} + 429848066777688 T^{14} + 1796248679715616 T^{15} + 22639513200135268 T^{16} + 8408717631492547 p T^{17} + 1062563433579355365 T^{18} + 4246757974720694918 T^{19} + 44989184689545532464 T^{20} +$$$$17\!\cdots\!01$$$$T^{21} +$$$$17\!\cdots\!73$$$$T^{22} +$$$$60\!\cdots\!17$$$$p T^{23} +$$$$61\!\cdots\!65$$$$T^{24} +$$$$20\!\cdots\!23$$$$p T^{25} +$$$$20\!\cdots\!15$$$$T^{26} +$$$$74\!\cdots\!39$$$$T^{27} +$$$$55\!\cdots\!04$$$$p T^{28} +$$$$22\!\cdots\!34$$$$T^{29} +$$$$17\!\cdots\!19$$$$T^{30} +$$$$61\!\cdots\!19$$$$T^{31} +$$$$46\!\cdots\!51$$$$T^{32} +$$$$16\!\cdots\!63$$$$T^{33} +$$$$11\!\cdots\!53$$$$T^{34} +$$$$40\!\cdots\!97$$$$T^{35} +$$$$28\!\cdots\!57$$$$T^{36} +$$$$85\!\cdots\!09$$$$p T^{37} +$$$$64\!\cdots\!67$$$$T^{38} +$$$$21\!\cdots\!51$$$$T^{39} +$$$$13\!\cdots\!83$$$$T^{40} +$$$$44\!\cdots\!62$$$$T^{41} +$$$$28\!\cdots\!05$$$$T^{42} +$$$$89\!\cdots\!76$$$$T^{43} +$$$$50\!\cdots\!41$$$$p T^{44} +$$$$15\!\cdots\!62$$$$p T^{45} +$$$$10\!\cdots\!38$$$$T^{46} +$$$$32\!\cdots\!76$$$$T^{47} +$$$$19\!\cdots\!57$$$$T^{48} +$$$$57\!\cdots\!53$$$$T^{49} +$$$$33\!\cdots\!80$$$$T^{50} +$$$$98\!\cdots\!98$$$$T^{51} +$$$$55\!\cdots\!57$$$$T^{52} +$$$$16\!\cdots\!90$$$$T^{53} +$$$$89\!\cdots\!42$$$$T^{54} +$$$$25\!\cdots\!45$$$$T^{55} +$$$$14\!\cdots\!23$$$$T^{56} +$$$$39\!\cdots\!61$$$$T^{57} +$$$$21\!\cdots\!45$$$$T^{58} +$$$$58\!\cdots\!29$$$$T^{59} +$$$$30\!\cdots\!13$$$$T^{60} +$$$$84\!\cdots\!02$$$$T^{61} +$$$$43\!\cdots\!58$$$$T^{62} +$$$$11\!\cdots\!52$$$$T^{63} +$$$$49\!\cdots\!59$$$$p^{2} T^{64} +$$$$16\!\cdots\!91$$$$T^{65} +$$$$73\!\cdots\!47$$$$p T^{66} +$$$$21\!\cdots\!00$$$$T^{67} +$$$$10\!\cdots\!47$$$$T^{68} +$$$$26\!\cdots\!70$$$$T^{69} +$$$$13\!\cdots\!24$$$$T^{70} +$$$$33\!\cdots\!64$$$$T^{71} +$$$$16\!\cdots\!11$$$$T^{72} +$$$$40\!\cdots\!00$$$$T^{73} +$$$$17\!\cdots\!89$$$$p T^{74} +$$$$43\!\cdots\!72$$$$p T^{75} +$$$$22\!\cdots\!64$$$$T^{76} +$$$$54\!\cdots\!84$$$$T^{77} +$$$$25\!\cdots\!98$$$$T^{78} +$$$$60\!\cdots\!79$$$$T^{79} +$$$$25\!\cdots\!98$$$$p T^{80} +$$$$54\!\cdots\!84$$$$p^{2} T^{81} +$$$$22\!\cdots\!64$$$$p^{3} T^{82} +$$$$43\!\cdots\!72$$$$p^{5} T^{83} +$$$$17\!\cdots\!89$$$$p^{6} T^{84} +$$$$40\!\cdots\!00$$$$p^{6} T^{85} +$$$$16\!\cdots\!11$$$$p^{7} T^{86} +$$$$33\!\cdots\!64$$$$p^{8} T^{87} +$$$$13\!\cdots\!24$$$$p^{9} T^{88} +$$$$26\!\cdots\!70$$$$p^{10} T^{89} +$$$$10\!\cdots\!47$$$$p^{11} T^{90} +$$$$21\!\cdots\!00$$$$p^{12} T^{91} +$$$$73\!\cdots\!47$$$$p^{14} T^{92} +$$$$16\!\cdots\!91$$$$p^{14} T^{93} +$$$$49\!\cdots\!59$$$$p^{17} T^{94} +$$$$11\!\cdots\!52$$$$p^{16} T^{95} +$$$$43\!\cdots\!58$$$$p^{17} T^{96} +$$$$84\!\cdots\!02$$$$p^{18} T^{97} +$$$$30\!\cdots\!13$$$$p^{19} T^{98} +$$$$58\!\cdots\!29$$$$p^{20} T^{99} +$$$$21\!\cdots\!45$$$$p^{21} T^{100} +$$$$39\!\cdots\!61$$$$p^{22} T^{101} +$$$$14\!\cdots\!23$$$$p^{23} T^{102} +$$$$25\!\cdots\!45$$$$p^{24} T^{103} +$$$$89\!\cdots\!42$$$$p^{25} T^{104} +$$$$16\!\cdots\!90$$$$p^{26} T^{105} +$$$$55\!\cdots\!57$$$$p^{27} T^{106} +$$$$98\!\cdots\!98$$$$p^{28} T^{107} +$$$$33\!\cdots\!80$$$$p^{29} T^{108} +$$$$57\!\cdots\!53$$$$p^{30} T^{109} +$$$$19\!\cdots\!57$$$$p^{31} T^{110} +$$$$32\!\cdots\!76$$$$p^{32} T^{111} +$$$$10\!\cdots\!38$$$$p^{33} T^{112} +$$$$15\!\cdots\!62$$$$p^{35} T^{113} +$$$$50\!\cdots\!41$$$$p^{36} T^{114} +$$$$89\!\cdots\!76$$$$p^{36} T^{115} +$$$$28\!\cdots\!05$$$$p^{37} T^{116} +$$$$44\!\cdots\!62$$$$p^{38} T^{117} +$$$$13\!\cdots\!83$$$$p^{39} T^{118} +$$$$21\!\cdots\!51$$$$p^{40} T^{119} +$$$$64\!\cdots\!67$$$$p^{41} T^{120} +$$$$85\!\cdots\!09$$$$p^{43} T^{121} +$$$$28\!\cdots\!57$$$$p^{43} T^{122} +$$$$40\!\cdots\!97$$$$p^{44} T^{123} +$$$$11\!\cdots\!53$$$$p^{45} T^{124} +$$$$16\!\cdots\!63$$$$p^{46} T^{125} +$$$$46\!\cdots\!51$$$$p^{47} T^{126} +$$$$61\!\cdots\!19$$$$p^{48} T^{127} +$$$$17\!\cdots\!19$$$$p^{49} T^{128} +$$$$22\!\cdots\!34$$$$p^{50} T^{129} +$$$$55\!\cdots\!04$$$$p^{52} T^{130} +$$$$74\!\cdots\!39$$$$p^{52} T^{131} +$$$$20\!\cdots\!15$$$$p^{53} T^{132} +$$$$20\!\cdots\!23$$$$p^{55} T^{133} +$$$$61\!\cdots\!65$$$$p^{55} T^{134} +$$$$60\!\cdots\!17$$$$p^{57} T^{135} +$$$$17\!\cdots\!73$$$$p^{57} T^{136} +$$$$17\!\cdots\!01$$$$p^{58} T^{137} + 44989184689545532464 p^{59} T^{138} + 4246757974720694918 p^{60} T^{139} + 1062563433579355365 p^{61} T^{140} + 8408717631492547 p^{63} T^{141} + 22639513200135268 p^{63} T^{142} + 1796248679715616 p^{64} T^{143} + 429848066777688 p^{65} T^{144} + 30622774055004 p^{66} T^{145} + 650933071112 p^{68} T^{146} + 449059092428 p^{68} T^{147} + 102524644613 p^{69} T^{148} + 5508299425 p^{70} T^{149} + 1227030741 p^{71} T^{150} + 54271675 p^{72} T^{151} + 11785864 p^{73} T^{152} + 36616 p^{75} T^{153} + 85192 p^{75} T^{154} + 182 p^{77} T^{155} + 412 p^{77} T^{156} + 5 p^{78} T^{157} + p^{79} T^{158}$$
13 $$1 + 18 T + 622 T^{2} + 9104 T^{3} + 182574 T^{4} + 2284662 T^{5} + 34392298 T^{6} + 379756003 T^{7} + 4728999786 T^{8} + 47078973086 T^{9} + 509689783774 T^{10} + 4646395347272 T^{11} + 45051422238644 T^{12} + 380476207151270 T^{13} + 3369177335740254 T^{14} + 26599106088416983 T^{15} + 16776411567766287 p T^{16} + 1621133312632187345 T^{17} + 12433378669438632977 T^{18} + 6732476993275053764 p T^{19} + 48677609840123029443 p T^{20} +$$$$42\!\cdots\!49$$$$T^{21} +$$$$29\!\cdots\!74$$$$T^{22} +$$$$18\!\cdots\!09$$$$T^{23} +$$$$12\!\cdots\!14$$$$T^{24} +$$$$74\!\cdots\!67$$$$T^{25} +$$$$46\!\cdots\!41$$$$T^{26} +$$$$27\!\cdots\!36$$$$T^{27} +$$$$16\!\cdots\!14$$$$T^{28} +$$$$94\!\cdots\!96$$$$T^{29} +$$$$54\!\cdots\!11$$$$T^{30} +$$$$29\!\cdots\!05$$$$T^{31} +$$$$16\!\cdots\!65$$$$T^{32} +$$$$68\!\cdots\!32$$$$p T^{33} +$$$$48\!\cdots\!57$$$$T^{34} +$$$$24\!\cdots\!66$$$$T^{35} +$$$$13\!\cdots\!68$$$$T^{36} +$$$$65\!\cdots\!39$$$$T^{37} +$$$$33\!\cdots\!27$$$$T^{38} +$$$$16\!\cdots\!91$$$$T^{39} +$$$$80\!\cdots\!62$$$$T^{40} +$$$$38\!\cdots\!86$$$$T^{41} +$$$$18\!\cdots\!38$$$$T^{42} +$$$$85\!\cdots\!45$$$$T^{43} +$$$$40\!\cdots\!13$$$$T^{44} +$$$$18\!\cdots\!32$$$$T^{45} +$$$$84\!\cdots\!81$$$$T^{46} +$$$$37\!\cdots\!71$$$$T^{47} +$$$$16\!\cdots\!03$$$$T^{48} +$$$$72\!\cdots\!87$$$$T^{49} +$$$$32\!\cdots\!83$$$$T^{50} +$$$$13\!\cdots\!45$$$$T^{51} +$$$$59\!\cdots\!19$$$$T^{52} +$$$$24\!\cdots\!69$$$$T^{53} +$$$$10\!\cdots\!56$$$$T^{54} +$$$$42\!\cdots\!08$$$$T^{55} +$$$$13\!\cdots\!24$$$$p T^{56} +$$$$71\!\cdots\!35$$$$T^{57} +$$$$29\!\cdots\!29$$$$T^{58} +$$$$11\!\cdots\!03$$$$T^{59} +$$$$48\!\cdots\!54$$$$T^{60} +$$$$18\!\cdots\!23$$$$T^{61} +$$$$75\!\cdots\!52$$$$T^{62} +$$$$28\!\cdots\!84$$$$T^{63} +$$$$11\!\cdots\!19$$$$T^{64} +$$$$25\!\cdots\!45$$$$p^{2} T^{65} +$$$$17\!\cdots\!98$$$$T^{66} +$$$$63\!\cdots\!11$$$$T^{67} +$$$$25\!\cdots\!84$$$$T^{68} +$$$$70\!\cdots\!19$$$$p T^{69} +$$$$36\!\cdots\!74$$$$T^{70} +$$$$12\!\cdots\!54$$$$T^{71} +$$$$50\!\cdots\!59$$$$T^{72} +$$$$17\!\cdots\!81$$$$T^{73} +$$$$69\!\cdots\!94$$$$T^{74} +$$$$24\!\cdots\!04$$$$T^{75} +$$$$94\!\cdots\!06$$$$T^{76} +$$$$32\!\cdots\!99$$$$T^{77} +$$$$12\!\cdots\!61$$$$T^{78} +$$$$42\!\cdots\!32$$$$T^{79} +$$$$12\!\cdots\!61$$$$p T^{80} +$$$$32\!\cdots\!99$$$$p^{2} T^{81} +$$$$94\!\cdots\!06$$$$p^{3} T^{82} +$$$$24\!\cdots\!04$$$$p^{4} T^{83} +$$$$69\!\cdots\!94$$$$p^{5} T^{84} +$$$$17\!\cdots\!81$$$$p^{6} T^{85} +$$$$50\!\cdots\!59$$$$p^{7} T^{86} +$$$$12\!\cdots\!54$$$$p^{8} T^{87} +$$$$36\!\cdots\!74$$$$p^{9} T^{88} +$$$$70\!\cdots\!19$$$$p^{11} T^{89} +$$$$25\!\cdots\!84$$$$p^{11} T^{90} +$$$$63\!\cdots\!11$$$$p^{12} T^{91} +$$$$17\!\cdots\!98$$$$p^{13} T^{92} +$$$$25\!\cdots\!45$$$$p^{16} T^{93} +$$$$11\!\cdots\!19$$$$p^{15} T^{94} +$$$$28\!\cdots\!84$$$$p^{16} T^{95} +$$$$75\!\cdots\!52$$$$p^{17} T^{96} +$$$$18\!\cdots\!23$$$$p^{18} T^{97} +$$$$48\!\cdots\!54$$$$p^{19} T^{98} +$$$$11\!\cdots\!03$$$$p^{20} T^{99} +$$$$29\!\cdots\!29$$$$p^{21} T^{100} +$$$$71\!\cdots\!35$$$$p^{22} T^{101} +$$$$13\!\cdots\!24$$$$p^{24} T^{102} +$$$$42\!\cdots\!08$$$$p^{24} T^{103} +$$$$10\!\cdots\!56$$$$p^{25} T^{104} +$$$$24\!\cdots\!69$$$$p^{26} T^{105} +$$$$59\!\cdots\!19$$$$p^{27} T^{106} +$$$$13\!\cdots\!45$$$$p^{28} T^{107} +$$$$32\!\cdots\!83$$$$p^{29} T^{108} +$$$$72\!\cdots\!87$$$$p^{30} T^{109} +$$$$16\!\cdots\!03$$$$p^{31} T^{110} +$$$$37\!\cdots\!71$$$$p^{32} T^{111} +$$$$84\!\cdots\!81$$$$p^{33} T^{112} +$$$$18\!\cdots\!32$$$$p^{34} T^{113} +$$$$40\!\cdots\!13$$$$p^{35} T^{114} +$$$$85\!\cdots\!45$$$$p^{36} T^{115} +$$$$18\!\cdots\!38$$$$p^{37} T^{116} +$$$$38\!\cdots\!86$$$$p^{38} T^{117} +$$$$80\!\cdots\!62$$$$p^{39} T^{118} +$$$$16\!\cdots\!91$$$$p^{40} T^{119} +$$$$33\!\cdots\!27$$$$p^{41} T^{120} +$$$$65\!\cdots\!39$$$$p^{42} T^{121} +$$$$13\!\cdots\!68$$$$p^{43} T^{122} +$$$$24\!\cdots\!66$$$$p^{44} T^{123} +$$$$48\!\cdots\!57$$$$p^{45} T^{124} +$$$$68\!\cdots\!32$$$$p^{47} T^{125} +$$$$16\!\cdots\!65$$$$p^{47} T^{126} +$$$$29\!\cdots\!05$$$$p^{48} T^{127} +$$$$54\!\cdots\!11$$$$p^{49} T^{128} +$$$$94\!\cdots\!96$$$$p^{50} T^{129} +$$$$16\!\cdots\!14$$$$p^{51} T^{130} +$$$$27\!\cdots\!36$$$$p^{52} T^{131} +$$$$46\!\cdots\!41$$$$p^{53} T^{132} +$$$$74\!\cdots\!67$$$$p^{54} T^{133} +$$$$12\!\cdots\!14$$$$p^{55} T^{134} +$$$$18\!\cdots\!09$$$$p^{56} T^{135} +$$$$29\!\cdots\!74$$$$p^{57} T^{136} +$$$$42\!\cdots\!49$$$$p^{58} T^{137} + 48677609840123029443 p^{60} T^{138} + 6732476993275053764 p^{61} T^{139} + 12433378669438632977 p^{61} T^{140} + 1621133312632187345 p^{62} T^{141} + 16776411567766287 p^{64} T^{142} + 26599106088416983 p^{64} T^{143} + 3369177335740254 p^{65} T^{144} + 380476207151270 p^{66} T^{145} + 45051422238644 p^{67} T^{146} + 4646395347272 p^{68} T^{147} + 509689783774 p^{69} T^{148} + 47078973086 p^{70} T^{149} + 4728999786 p^{71} T^{150} + 379756003 p^{72} T^{151} + 34392298 p^{73} T^{152} + 2284662 p^{74} T^{153} + 182574 p^{75} T^{154} + 9104 p^{76} T^{155} + 622 p^{77} T^{156} + 18 p^{78} T^{157} + p^{79} T^{158}$$
17 $$1 + 62 T + 2524 T^{2} + 76787 T^{3} + 1939635 T^{4} + 42234908 T^{5} + 818554472 T^{6} + 845438123 p T^{7} + 232074951639 T^{8} + 3481307735913 T^{9} + 48934697411849 T^{10} + 648745571793149 T^{11} + 8157196570610002 T^{12} + 97716201776331089 T^{13} + 1119562569891104174 T^{14} + 12308563681781964467 T^{15} +$$$$13\!\cdots\!30$$$$T^{16} +$$$$13\!\cdots\!93$$$$T^{17} +$$$$77\!\cdots\!62$$$$p T^{18} +$$$$12\!\cdots\!93$$$$T^{19} +$$$$11\!\cdots\!55$$$$T^{20} +$$$$10\!\cdots\!93$$$$T^{21} +$$$$92\!\cdots\!66$$$$T^{22} +$$$$78\!\cdots\!45$$$$T^{23} +$$$$65\!\cdots\!57$$$$T^{24} +$$$$53\!\cdots\!93$$$$T^{25} +$$$$42\!\cdots\!81$$$$T^{26} +$$$$33\!\cdots\!04$$$$T^{27} +$$$$25\!\cdots\!27$$$$T^{28} +$$$$19\!\cdots\!59$$$$T^{29} +$$$$13\!\cdots\!17$$$$T^{30} +$$$$59\!\cdots\!65$$$$p T^{31} +$$$$71\!\cdots\!40$$$$T^{32} +$$$$49\!\cdots\!09$$$$T^{33} +$$$$33\!\cdots\!78$$$$T^{34} +$$$$22\!\cdots\!88$$$$T^{35} +$$$$15\!\cdots\!62$$$$T^{36} +$$$$98\!\cdots\!98$$$$T^{37} +$$$$63\!\cdots\!88$$$$T^{38} +$$$$39\!\cdots\!19$$$$T^{39} +$$$$24\!\cdots\!43$$$$T^{40} +$$$$15\!\cdots\!80$$$$T^{41} +$$$$92\!\cdots\!48$$$$T^{42} +$$$$55\!\cdots\!41$$$$T^{43} +$$$$32\!\cdots\!37$$$$T^{44} +$$$$19\!\cdots\!33$$$$T^{45} +$$$$10\!\cdots\!73$$$$T^{46} +$$$$62\!\cdots\!47$$$$T^{47} +$$$$34\!\cdots\!70$$$$T^{48} +$$$$19\!\cdots\!91$$$$T^{49} +$$$$10\!\cdots\!61$$$$T^{50} +$$$$57\!\cdots\!42$$$$T^{51} +$$$$30\!\cdots\!65$$$$T^{52} +$$$$16\!\cdots\!99$$$$T^{53} +$$$$85\!\cdots\!63$$$$T^{54} +$$$$44\!\cdots\!34$$$$T^{55} +$$$$22\!\cdots\!45$$$$T^{56} +$$$$11\!\cdots\!16$$$$T^{57} +$$$$58\!\cdots\!51$$$$T^{58} +$$$$29\!\cdots\!51$$$$T^{59} +$$$$14\!\cdots\!85$$$$T^{60} +$$$$69\!\cdots\!49$$$$T^{61} +$$$$33\!\cdots\!86$$$$T^{62} +$$$$16\!\cdots\!17$$$$T^{63} +$$$$76\!\cdots\!95$$$$T^{64} +$$$$35\!\cdots\!69$$$$T^{65} +$$$$16\!\cdots\!56$$$$T^{66} +$$$$77\!\cdots\!50$$$$T^{67} +$$$$35\!\cdots\!05$$$$T^{68} +$$$$15\!\cdots\!38$$$$T^{69} +$$$$71\!\cdots\!33$$$$T^{70} +$$$$31\!\cdots\!43$$$$T^{71} +$$$$14\!\cdots\!93$$$$T^{72} +$$$$61\!\cdots\!64$$$$T^{73} +$$$$26\!\cdots\!60$$$$T^{74} +$$$$11\!\cdots\!18$$$$T^{75} +$$$$48\!\cdots\!27$$$$T^{76} +$$$$20\!\cdots\!68$$$$T^{77} +$$$$84\!\cdots\!25$$$$T^{78} +$$$$35\!\cdots\!70$$$$T^{79} +$$$$84\!\cdots\!25$$$$p T^{80} +$$$$20\!\cdots\!68$$$$p^{2} T^{81} +$$$$48\!\cdots\!27$$$$p^{3} T^{82} +$$$$11\!\cdots\!18$$$$p^{4} T^{83} +$$$$26\!\cdots\!60$$$$p^{5} T^{84} +$$$$61\!\cdots\!64$$$$p^{6} T^{85} +$$$$14\!\cdots\!93$$$$p^{7} T^{86} +$$$$31\!\cdots\!43$$$$p^{8} T^{87} +$$$$71\!\cdots\!33$$$$p^{9} T^{88} +$$$$15\!\cdots\!38$$$$p^{10} T^{89} +$$$$35\!\cdots\!05$$$$p^{11} T^{90} +$$$$77\!\cdots\!50$$$$p^{12} T^{91} +$$$$16\!\cdots\!56$$$$p^{13} T^{92} +$$$$35\!\cdots\!69$$$$p^{14} T^{93} +$$$$76\!\cdots\!95$$$$p^{15} T^{94} +$$$$16\!\cdots\!17$$$$p^{16} T^{95} +$$$$33\!\cdots\!86$$$$p^{17} T^{96} +$$$$69\!\cdots\!49$$$$p^{18} T^{97} +$$$$14\!\cdots\!85$$$$p^{19} T^{98} +$$$$29\!\cdots\!51$$$$p^{20} T^{99} +$$$$58\!\cdots\!51$$$$p^{21} T^{100} +$$$$11\!\cdots\!16$$$$p^{22} T^{101} +$$$$22\!\cdots\!45$$$$p^{23} T^{102} +$$$$44\!\cdots\!34$$$$p^{24} T^{103} +$$$$85\!\cdots\!63$$$$p^{25} T^{104} +$$$$16\!\cdots\!99$$$$p^{26} T^{105} +$$$$30\!\cdots\!65$$$$p^{27} T^{106} +$$$$57\!\cdots\!42$$$$p^{28} T^{107} +$$$$10\!\cdots\!61$$$$p^{29} T^{108} +$$$$19\!\cdots\!91$$$$p^{30} T^{109} +$$$$34\!\cdots\!70$$$$p^{31} T^{110} +$$$$62\!\cdots\!47$$$$p^{32} T^{111} +$$$$10\!\cdots\!73$$$$p^{33} T^{112} +$$$$19\!\cdots\!33$$$$p^{34} T^{113} +$$$$32\!\cdots\!37$$$$p^{35} T^{114} +$$$$55\!\cdots\!41$$$$p^{36} T^{115} +$$$$92\!\cdots\!48$$$$p^{37} T^{116} +$$$$15\!\cdots\!80$$$$p^{38} T^{117} +$$$$24\!\cdots\!43$$$$p^{39} T^{118} +$$$$39\!\cdots\!19$$$$p^{40} T^{119} +$$$$63\!\cdots\!88$$$$p^{41} T^{120} +$$$$98\!\cdots\!98$$$$p^{42} T^{121} +$$$$15\!\cdots\!62$$$$p^{43} T^{122} +$$$$22\!\cdots\!88$$$$p^{44} T^{123} +$$$$33\!\cdots\!78$$$$p^{45} T^{124} +$$$$49\!\cdots\!09$$$$p^{46} T^{125} +$$$$71\!\cdots\!40$$$$p^{47} T^{126} +$$$$59\!\cdots\!65$$$$p^{49} T^{127} +$$$$13\!\cdots\!17$$$$p^{49} T^{128} +$$$$19\!\cdots\!59$$$$p^{50} T^{129} +$$$$25\!\cdots\!27$$$$p^{51} T^{130} +$$$$33\!\cdots\!04$$$$p^{52} T^{131} +$$$$42\!\cdots\!81$$$$p^{53} T^{132} +$$$$53\!\cdots\!93$$$$p^{54} T^{133} +$$$$65\!\cdots\!57$$$$p^{55} T^{134} +$$$$78\!\cdots\!45$$$$p^{56} T^{135} +$$$$92\!\cdots\!66$$$$p^{57} T^{136} +$$$$10\!\cdots\!93$$$$p^{58} T^{137} +$$$$11\!\cdots\!55$$$$p^{59} T^{138} +$$$$12\!\cdots\!93$$$$p^{60} T^{139} +$$$$77\!\cdots\!62$$$$p^{62} T^{140} +$$$$13\!\cdots\!93$$$$p^{62} T^{141} +$$$$13\!\cdots\!30$$$$p^{63} T^{142} + 12308563681781964467 p^{64} T^{143} + 1119562569891104174 p^{65} T^{144} + 97716201776331089 p^{66} T^{145} + 8157196570610002 p^{67} T^{146} + 648745571793149 p^{68} T^{147} + 48934697411849 p^{69} T^{148} + 3481307735913 p^{70} T^{149} + 232074951639 p^{71} T^{150} + 845438123 p^{73} T^{151} + 818554472 p^{73} T^{152} + 42234908 p^{74} T^{153} + 1939635 p^{75} T^{154} + 76787 p^{76} T^{155} + 2524 p^{77} T^{156} + 62 p^{78} T^{157} + p^{79} T^{158}$$
19 $$1 + 25 T + 935 T^{2} + 18122 T^{3} + 405067 T^{4} + 6540668 T^{5} + 111819960 T^{6} + 1568834809 T^{7} + 22475954660 T^{8} + 281574410707 T^{9} + 3540516736890 T^{10} + 40365653627632 T^{11} + 457906084016053 T^{12} + 4817658347513556 T^{13} + 50207709028764853 T^{14} + 492656277597662535 T^{15} + 251456452738491617 p T^{16} + 2320379091370335802 p T^{17} +$$$$40\!\cdots\!94$$$$T^{18} +$$$$35\!\cdots\!37$$$$T^{19} +$$$$30\!\cdots\!39$$$$T^{20} +$$$$25\!\cdots\!93$$$$T^{21} +$$$$20\!\cdots\!82$$$$T^{22} +$$$$16\!\cdots\!24$$$$T^{23} +$$$$12\!\cdots\!28$$$$T^{24} +$$$$98\!\cdots\!08$$$$T^{25} +$$$$74\!\cdots\!11$$$$T^{26} +$$$$54\!\cdots\!09$$$$T^{27} +$$$$39\!\cdots\!89$$$$T^{28} +$$$$28\!\cdots\!28$$$$T^{29} +$$$$19\!\cdots\!59$$$$T^{30} +$$$$13\!\cdots\!57$$$$T^{31} +$$$$92\!\cdots\!83$$$$T^{32} +$$$$61\!\cdots\!74$$$$T^{33} +$$$$40\!\cdots\!04$$$$T^{34} +$$$$26\!\cdots\!35$$$$T^{35} +$$$$17\!\cdots\!94$$$$T^{36} +$$$$10\!\cdots\!47$$$$T^{37} +$$$$67\!\cdots\!52$$$$T^{38} +$$$$41\!\cdots\!01$$$$T^{39} +$$$$25\!\cdots\!92$$$$T^{40} +$$$$15\!\cdots\!81$$$$T^{41} +$$$$91\!\cdots\!37$$$$T^{42} +$$$$53\!\cdots\!50$$$$T^{43} +$$$$31\!\cdots\!34$$$$T^{44} +$$$$18\!\cdots\!38$$$$T^{45} +$$$$10\!\cdots\!75$$$$T^{46} +$$$$58\!\cdots\!20$$$$T^{47} +$$$$32\!\cdots\!27$$$$T^{48} +$$$$18\!\cdots\!09$$$$T^{49} +$$$$99\!\cdots\!39$$$$T^{50} +$$$$53\!\cdots\!23$$$$T^{51} +$$$$29\!\cdots\!28$$$$T^{52} +$$$$15\!\cdots\!28$$$$T^{53} +$$$$82\!\cdots\!75$$$$T^{54} +$$$$43\!\cdots\!70$$$$T^{55} +$$$$22\!\cdots\!57$$$$T^{56} +$$$$11\!\cdots\!02$$$$T^{57} +$$$$59\!\cdots\!02$$$$T^{58} +$$$$30\!\cdots\!72$$$$T^{59} +$$$$15\!\cdots\!50$$$$T^{60} +$$$$75\!\cdots\!01$$$$T^{61} +$$$$37\!\cdots\!55$$$$T^{62} +$$$$18\!\cdots\!51$$$$T^{63} +$$$$90\!\cdots\!28$$$$T^{64} +$$$$43\!\cdots\!07$$$$T^{65} +$$$$21\!\cdots\!52$$$$T^{66} +$$$$10\!\cdots\!40$$$$T^{67} +$$$$47\!\cdots\!60$$$$T^{68} +$$$$22\!\cdots\!27$$$$T^{69} +$$$$10\!\cdots\!52$$$$T^{70} +$$$$48\!\cdots\!38$$$$T^{71} +$$$$22\!\cdots\!32$$$$T^{72} +$$$$10\!\cdots\!06$$$$T^{73} +$$$$46\!\cdots\!01$$$$T^{74} +$$$$20\!\cdots\!18$$$$T^{75} +$$$$92\!\cdots\!75$$$$T^{76} +$$$$41\!\cdots\!69$$$$T^{77} +$$$$18\!\cdots\!85$$$$T^{78} +$$$$79\!\cdots\!02$$$$T^{79} +$$$$18\!\cdots\!85$$$$p T^{80} +$$$$41\!\cdots\!69$$$$p^{2} T^{81} +$$$$92\!\cdots\!75$$$$p^{3} T^{82} +$$$$20\!\cdots\!18$$$$p^{4} T^{83} +$$$$46\!\cdots\!01$$$$p^{5} T^{84} +$$$$10\!\cdots\!06$$$$p^{6} T^{85} +$$$$22\!\cdots\!32$$$$p^{7} T^{86} +$$$$48\!\cdots\!38$$$$p^{8} T^{87} +$$$$10\!\cdots\!52$$$$p^{9} T^{88} +$$$$22\!\cdots\!27$$$$p^{10} T^{89} +$$$$47\!\cdots\!60$$$$p^{11} T^{90} +$$$$10\!\cdots\!40$$$$p^{12} T^{91} +$$$$21\!\cdots\!52$$$$p^{13} T^{92} +$$$$43\!\cdots\!07$$$$p^{14} T^{93} +$$$$90\!\cdots\!28$$$$p^{15} T^{94} +$$$$18\!\cdots\!51$$$$p^{16} T^{95} +$$$$37\!\cdots\!55$$$$p^{17} T^{96} +$$$$75\!\cdots\!01$$$$p^{18} T^{97} +$$$$15\!\cdots\!50$$$$p^{19} T^{98} +$$$$30\!\cdots\!72$$$$p^{20} T^{99} +$$$$59\!\cdots\!02$$$$p^{21} T^{100} +$$$$11\!\cdots\!02$$$$p^{22} T^{101} +$$$$22\!\cdots\!57$$$$p^{23} T^{102} +$$$$43\!\cdots\!70$$$$p^{24} T^{103} +$$$$82\!\cdots\!75$$$$p^{25} T^{104} +$$$$15\!\cdots\!28$$$$p^{26} T^{105} +$$$$29\!\cdots\!28$$$$p^{27} T^{106} +$$$$53\!\cdots\!23$$$$p^{28} T^{107} +$$$$99\!\cdots\!39$$$$p^{29} T^{108} +$$$$18\!\cdots\!09$$$$p^{30} T^{109} +$$$$32\!\cdots\!27$$$$p^{31} T^{110} +$$$$58\!\cdots\!20$$$$p^{32} T^{111} +$$$$10\!\cdots\!75$$$$p^{33} T^{112} +$$$$18\!\cdots\!38$$$$p^{34} T^{113} +$$$$31\!\cdots\!34$$$$p^{35} T^{114} +$$$$53\!\cdots\!50$$$$p^{36} T^{115} +$$$$91\!\cdots\!37$$$$p^{37} T^{116} +$$$$15\!\cdots\!81$$$$p^{38} T^{117} +$$$$25\!\cdots\!92$$$$p^{39} T^{118} +$$$$41\!\cdots\!01$$$$p^{40} T^{119} +$$$$67\!\cdots\!52$$$$p^{41} T^{120} +$$$$10\!\cdots\!47$$$$p^{42} T^{121} +$$$$17\!\cdots\!94$$$$p^{43} T^{122} +$$$$26\!\cdots\!35$$$$p^{44} T^{123} +$$$$40\!\cdots\!04$$$$p^{45} T^{124} +$$$$61\!\cdots\!74$$$$p^{46} T^{125} +$$$$92\!\cdots\!83$$$$p^{47} T^{126} +$$$$13\!\cdots\!57$$$$p^{48} T^{127} +$$$$19\!\cdots\!59$$$$p^{49} T^{128} +$$$$28\!\cdots\!28$$$$p^{50} T^{129} +$$$$39\!\cdots\!89$$$$p^{51} T^{130} +$$$$54\!\cdots\!09$$$$p^{52} T^{131} +$$$$74\!\cdots\!11$$$$p^{53} T^{132} +$$$$98\!\cdots\!08$$$$p^{54} T^{133} +$$$$12\!\cdots\!28$$$$p^{55} T^{134} +$$$$16\!\cdots\!24$$$$p^{56} T^{135} +$$$$20\!\cdots\!82$$$$p^{57} T^{136} +$$$$25\!\cdots\!93$$$$p^{58} T^{137} +$$$$30\!\cdots\!39$$$$p^{59} T^{138} +$$$$35\!\cdots\!37$$$$p^{60} T^{139} +$$$$40\!\cdots\!94$$$$p^{61} T^{140} + 2320379091370335802 p^{63} T^{141} + 251456452738491617 p^{64} T^{142} + 492656277597662535 p^{64} T^{143} + 50207709028764853 p^{65} T^{144} + 4817658347513556 p^{66} T^{145} + 457906084016053 p^{67} T^{146} + 40365653627632 p^{68} T^{147} + 3540516736890 p^{69} T^{148} + 281574410707 p^{70} T^{149} + 22475954660 p^{71} T^{150} + 1568834809 p^{72} T^{151} + 111819960 p^{73} T^{152} + 6540668 p^{74} T^{153} + 405067 p^{75} T^{154} + 18122 p^{76} T^{155} + 935 p^{77} T^{156} + 25 p^{78} T^{157} + p^{79} T^{158}$$
23 $$1 + 94 T + 231 p T^{2} + 222368 T^{3} + 7588695 T^{4} + 221589955 T^{5} + 5710753924 T^{6} + 132603388011 T^{7} + 2816238686718 T^{8} + 55326382030339 T^{9} + 1014319224720956 T^{10} + 17476596227978617 T^{11} + 284633275559708678 T^{12} + 4402971818526207258 T^{13} + 64953098368976348636 T^{14} +$$$$91\!\cdots\!50$$$$T^{15} +$$$$12\!\cdots\!65$$$$T^{16} +$$$$16\!\cdots\!56$$$$T^{17} +$$$$20\!\cdots\!14$$$$T^{18} +$$$$24\!\cdots\!94$$$$T^{19} +$$$$29\!\cdots\!71$$$$T^{20} +$$$$33\!\cdots\!90$$$$T^{21} +$$$$36\!\cdots\!73$$$$T^{22} +$$$$39\!\cdots\!39$$$$T^{23} +$$$$41\!\cdots\!21$$$$T^{24} +$$$$42\!\cdots\!17$$$$T^{25} +$$$$42\!\cdots\!08$$$$T^{26} +$$$$41\!\cdots\!67$$$$T^{27} +$$$$39\!\cdots\!51$$$$T^{28} +$$$$37\!\cdots\!89$$$$T^{29} +$$$$34\!\cdots\!64$$$$T^{30} +$$$$30\!\cdots\!00$$$$T^{31} +$$$$26\!\cdots\!85$$$$T^{32} +$$$$23\!\cdots\!47$$$$T^{33} +$$$$19\!\cdots\!57$$$$T^{34} +$$$$16\!\cdots\!36$$$$T^{35} +$$$$13\!\cdots\!55$$$$T^{36} +$$$$10\!\cdots\!56$$$$T^{37} +$$$$84\!\cdots\!59$$$$T^{38} +$$$$65\!\cdots\!28$$$$T^{39} +$$$$50\!\cdots\!21$$$$T^{40} +$$$$37\!\cdots\!08$$$$T^{41} +$$$$27\!\cdots\!24$$$$T^{42} +$$$$20\!\cdots\!48$$$$T^{43} +$$$$14\!\cdots\!48$$$$T^{44} +$$$$10\!\cdots\!73$$$$T^{45} +$$$$73\!\cdots\!62$$$$T^{46} +$$$$50\!\cdots\!68$$$$T^{47} +$$$$34\!\cdots\!45$$$$T^{48} +$$$$23\!\cdots\!44$$$$T^{49} +$$$$15\!\cdots\!90$$$$T^{50} +$$$$10\!\cdots\!19$$$$T^{51} +$$$$65\!\cdots\!98$$$$T^{52} +$$$$41\!\cdots\!90$$$$T^{53} +$$$$26\!\cdots\!53$$$$T^{54} +$$$$16\!\cdots\!89$$$$T^{55} +$$$$10\!\cdots\!57$$$$T^{56} +$$$$61\!\cdots\!83$$$$T^{57} +$$$$37\!\cdots\!65$$$$T^{58} +$$$$22\!\cdots\!36$$$$T^{59} +$$$$13\!\cdots\!13$$$$T^{60} +$$$$75\!\cdots\!03$$$$T^{61} +$$$$43\!\cdots\!59$$$$T^{62} +$$$$24\!\cdots\!06$$$$T^{63} +$$$$14\!\cdots\!93$$$$T^{64} +$$$$78\!\cdots\!65$$$$T^{65} +$$$$43\!\cdots\!55$$$$T^{66} +$$$$23\!\cdots\!38$$$$T^{67} +$$$$12\!\cdots\!80$$$$T^{68} +$$$$67\!\cdots\!82$$$$T^{69} +$$$$35\!\cdots\!26$$$$T^{70} +$$$$18\!\cdots\!30$$$$T^{71} +$$$$97\!\cdots\!17$$$$T^{72} +$$$$49\!\cdots\!88$$$$T^{73} +$$$$25\!\cdots\!96$$$$T^{74} +$$$$12\!\cdots\!34$$$$T^{75} +$$$$62\!\cdots\!47$$$$T^{76} +$$$$30\!\cdots\!35$$$$T^{77} +$$$$15\!\cdots\!24$$$$T^{78} +$$$$72\!\cdots\!34$$$$T^{79} +$$$$15\!\cdots\!24$$$$p T^{80} +$$$$30\!\cdots\!35$$$$p^{2} T^{81} +$$$$62\!\cdots\!47$$$$p^{3} T^{82} +$$$$12\!\cdots\!34$$$$p^{4} T^{83} +$$$$25\!\cdots\!96$$$$p^{5} T^{84} +$$$$49\!\cdots\!88$$$$p^{6} T^{85} +$$$$97\!\cdots\!17$$$$p^{7} T^{86} +$$$$18\!\cdots\!30$$$$p^{8} T^{87} +$$$$35\!\cdots\!26$$$$p^{9} T^{88} +$$$$67\!\cdots\!82$$$$p^{10} T^{89} +$$$$12\!\cdots\!80$$$$p^{11} T^{90} +$$$$23\!\cdots\!38$$$$p^{12} T^{91} +$$$$43\!\cdots\!55$$$$p^{13} T^{92} +$$$$78\!\cdots\!65$$$$p^{14} T^{93} +$$$$14\!\cdots\!93$$$$p^{15} T^{94} +$$$$24\!\cdots\!06$$$$p^{16} T^{95} +$$$$43\!\cdots\!59$$$$p^{17} T^{96} +$$$$75\!\cdots\!03$$$$p^{18} T^{97} +$$$$13\!\cdots\!13$$$$p^{19} T^{98} +$$$$22\!\cdots\!36$$$$p^{20} T^{99} +$$$$37\!\cdots\!65$$$$p^{21} T^{100} +$$$$61\!\cdots\!83$$$$p^{22} T^{101} +$$$$10\!\cdots\!57$$$$p^{23} T^{102} +$$$$16\!\cdots\!89$$$$p^{24} T^{103} +$$$$26\!\cdots\!53$$$$p^{25} T^{104} +$$$$41\!\cdots\!90$$$$p^{26} T^{105} +$$$$65\!\cdots\!98$$$$p^{27} T^{106} +$$$$10\!\cdots\!19$$$$p^{28} T^{107} +$$$$15\!\cdots\!90$$$$p^{29} T^{108} +$$$$23\!\cdots\!44$$$$p^{30} T^{109} +$$$$34\!\cdots\!45$$$$p^{31} T^{110} +$$$$50\!\cdots\!68$$$$p^{32} T^{111} +$$$$73\!\cdots\!62$$$$p^{33} T^{112} +$$$$10\!\cdots\!73$$$$p^{34} T^{113} +$$$$14\!\cdots\!48$$$$p^{35} T^{114} +$$$$20\!\cdots\!48$$$$p^{36} T^{115} +$$$$27\!\cdots\!24$$$$p^{37} T^{116} +$$$$37\!\cdots\!08$$$$p^{38} T^{117} +$$$$50\!\cdots\!21$$$$p^{39} T^{118} +$$$$65\!\cdots\!28$$$$p^{40} T^{119} +$$$$84\!\cdots\!59$$$$p^{41} T^{120} +$$$$10\!\cdots\!56$$$$p^{42} T^{121} +$$$$13\!\cdots\!55$$$$p^{43} T^{122} +$$$$16\!\cdots\!36$$$$p^{44} T^{123} +$$$$19\!\cdots\!57$$$$p^{45} T^{124} +$$$$23\!\cdots\!47$$$$p^{46} T^{125} +$$$$26\!\cdots\!85$$$$p^{47} T^{126} +$$$$30\!\cdots\!00$$$$p^{48} T^{127} +$$$$34\!\cdots\!64$$$$p^{49} T^{128} +$$$$37\!\cdots\!89$$$$p^{50} T^{129} +$$$$39\!\cdots\!51$$$$p^{51} T^{130} +$$$$41\!\cdots\!67$$$$p^{52} T^{131} +$$$$42\!\cdots\!08$$$$p^{53} T^{132} +$$$$42\!\cdots\!17$$$$p^{54} T^{133} +$$$$41\!\cdots\!21$$$$p^{55} T^{134} +$$$$39\!\cdots\!39$$$$p^{56} T^{135} +$$$$36\!\cdots\!73$$$$p^{57} T^{136} +$$$$33\!\cdots\!90$$$$p^{58} T^{137} +$$$$29\!\cdots\!71$$$$p^{59} T^{138} +$$$$24\!\cdots\!94$$$$p^{60} T^{139} +$$$$20\!\cdots\!14$$$$p^{61} T^{140} +$$$$16\!\cdots\!56$$$$p^{62} T^{141} +$$$$12\!\cdots\!65$$$$p^{63} T^{142} +$$$$91\!\cdots\!50$$$$p^{64} T^{143} + 64953098368976348636 p^{65} T^{144} + 4402971818526207258 p^{66} T^{145} + 284633275559708678 p^{67} T^{146} + 17476596227978617 p^{68} T^{147} + 1014319224720956 p^{69} T^{148} + 55326382030339 p^{70} T^{149} + 2816238686718 p^{71} T^{150} + 132603388011 p^{72} T^{151} + 5710753924 p^{73} T^{152} + 221589955 p^{74} T^{153} + 7588695 p^{75} T^{154} + 222368 p^{76} T^{155} + 231 p^{78} T^{156} + 94 p^{78} T^{157} + p^{79} T^{158}$$
29 $$1 + 17 T + 1278 T^{2} + 19596 T^{3} + 802503 T^{4} + 11258501 T^{5} + 331392551 T^{6} + 4300951541 T^{7} + 101526590378 T^{8} + 1229667212584 T^{9} + 24666229024494 T^{10} + 280785860257365 T^{11} + 4958578940768389 T^{12} + 53362508427957110 T^{13} + 849479378522137105 T^{14} + 8684998528404280391 T^{15} +$$$$12\!\cdots\!69$$$$T^{16} +$$$$12\!\cdots\!13$$$$T^{17} +$$$$16\!\cdots\!34$$$$T^{18} +$$$$15\!\cdots\!62$$$$T^{19} +$$$$19\!\cdots\!33$$$$T^{20} +$$$$61\!\cdots\!22$$$$p T^{21} +$$$$21\!\cdots\!97$$$$T^{22} +$$$$18\!\cdots\!51$$$$T^{23} +$$$$20\!\cdots\!25$$$$T^{24} +$$$$17\!\cdots\!23$$$$T^{25} +$$$$19\!\cdots\!89$$$$T^{26} +$$$$15\!\cdots\!88$$$$T^{27} +$$$$16\!\cdots\!12$$$$T^{28} +$$$$12\!\cdots\!40$$$$T^{29} +$$$$12\!\cdots\!70$$$$T^{30} +$$$$95\!\cdots\!22$$$$T^{31} +$$$$31\!\cdots\!25$$$$p T^{32} +$$$$68\!\cdots\!14$$$$T^{33} +$$$$63\!\cdots\!72$$$$T^{34} +$$$$45\!\cdots\!91$$$$T^{35} +$$$$41\!\cdots\!72$$$$T^{36} +$$$$29\!\cdots\!65$$$$T^{37} +$$$$25\!\cdots\!61$$$$T^{38} +$$$$17\!\cdots\!16$$$$T^{39} +$$$$15\!\cdots\!88$$$$T^{40} +$$$$10\!\cdots\!23$$$$T^{41} +$$$$85\!\cdots\!89$$$$T^{42} +$$$$55\!\cdots\!40$$$$T^{43} +$$$$45\!\cdots\!35$$$$T^{44} +$$$$29\!\cdots\!21$$$$T^{45} +$$$$23\!\cdots\!70$$$$T^{46} +$$$$14\!\cdots\!54$$$$T^{47} +$$$$11\!\cdots\!33$$$$T^{48} +$$$$70\!\cdots\!17$$$$T^{49} +$$$$54\!\cdots\!11$$$$T^{50} +$$$$32\!\cdots\!03$$$$T^{51} +$$$$24\!\cdots\!64$$$$T^{52} +$$$$14\!\cdots\!30$$$$T^{53} +$$$$10\!\cdots\!93$$$$T^{54} +$$$$63\!\cdots\!80$$$$T^{55} +$$$$45\!\cdots\!33$$$$T^{56} +$$$$26\!\cdots\!23$$$$T^{57} +$$$$18\!\cdots\!02$$$$T^{58} +$$$$10\!\cdots\!45$$$$T^{59} +$$$$73\!\cdots\!37$$$$T^{60} +$$$$40\!\cdots\!13$$$$T^{61} +$$$$27\!\cdots\!36$$$$T^{62} +$$$$15\!\cdots\!44$$$$T^{63} +$$$$10\!\cdots\!65$$$$T^{64} +$$$$55\!\cdots\!75$$$$T^{65} +$$$$36\!\cdots\!80$$$$T^{66} +$$$$19\!\cdots\!32$$$$T^{67} +$$$$12\!\cdots\!19$$$$T^{68} +$$$$66\!\cdots\!63$$$$T^{69} +$$$$42\!\cdots\!94$$$$T^{70} +$$$$22\!\cdots\!00$$$$T^{71} +$$$$14\!\cdots\!19$$$$T^{72} +$$$$24\!\cdots\!69$$$$p T^{73} +$$$$44\!\cdots\!29$$$$T^{74} +$$$$22\!\cdots\!52$$$$T^{75} +$$$$13\!\cdots\!61$$$$T^{76} +$$$$66\!\cdots\!21$$$$T^{77} +$$$$40\!\cdots\!61$$$$T^{78} +$$$$19\!\cdots\!44$$$$T^{79} +$$$$40\!\cdots\!61$$$$p T^{80} +$$$$66\!\cdots\!21$$$$p^{2} T^{81} +$$$$13\!\cdots\!61$$$$p^{3} T^{82} +$$$$22\!\cdots\!52$$$$p^{4} T^{83} +$$$$44\!\cdots\!29$$$$p^{5} T^{84} +$$$$24\!\cdots\!69$$$$p^{7} T^{85} +$$$$14\!\cdots\!19$$$$p^{7} T^{86} +$$$$22\!\cdots\!00$$$$p^{8} T^{87} +$$$$42\!\cdots\!94$$$$p^{9} T^{88} +$$$$66\!\cdots\!63$$$$p^{10} T^{89} +$$$$12\!\cdots\!19$$$$p^{11} T^{90} +$$$$19\!\cdots\!32$$$$p^{12} T^{91} +$$$$36\!\cdots\!80$$$$p^{13} T^{92} +$$$$55\!\cdots\!75$$$$p^{14} T^{93} +$$$$10\!\cdots\!65$$$$p^{15} T^{94} +$$$$15\!\cdots\!44$$$$p^{16} T^{95} +$$$$27\!\cdots\!36$$$$p^{17} T^{96} +$$$$40\!\cdots\!13$$$$p^{18} T^{97} +$$$$73\!\cdots\!37$$$$p^{19} T^{98} +$$$$10\!\cdots\!45$$$$p^{20} T^{99} +$$$$18\!\cdots\!02$$$$p^{21} T^{100} +$$$$26\!\cdots\!23$$$$p^{22} T^{101} +$$$$45\!\cdots\!33$$$$p^{23} T^{102} +$$$$63\!\cdots\!80$$$$p^{24} T^{103} +$$$$10\!\cdots\!93$$$$p^{25} T^{104} +$$$$14\!\cdots\!30$$$$p^{26} T^{105} +$$$$24\!\cdots\!64$$$$p^{27} T^{106} +$$$$32\!\cdots\!03$$$$p^{28} T^{107} +$$$$54\!\cdots\!11$$$$p^{29} T^{108} +$$$$70\!\cdots\!17$$$$p^{30} T^{109} +$$$$11\!\cdots\!33$$$$p^{31} T^{110} +$$$$14\!\cdots\!54$$$$p^{32} T^{111} +$$$$23\!\cdots\!70$$$$p^{33} T^{112} +$$$$29\!\cdots\!21$$$$p^{34} T^{113} +$$$$45\!\cdots\!35$$$$p^{35} T^{114} +$$$$55\!\cdots\!40$$$$p^{36} T^{115} +$$$$85\!\cdots\!89$$$$p^{37} T^{116} +$$$$10\!\cdots\!23$$$$p^{38} T^{117} +$$$$15\!\cdots\!88$$$$p^{39} T^{118} +$$$$17\!\cdots\!16$$$$p^{40} T^{119} +$$$$25\!\cdots\!61$$$$p^{41} T^{120} +$$$$29\!\cdots\!65$$$$p^{42} T^{121} +$$$$41\!\cdots\!72$$$$p^{43} T^{122} +$$$$45\!\cdots\!91$$$$p^{44} T^{123} +$$$$63\!\cdots\!72$$$$p^{45} T^{124} +$$$$68\!\cdots\!14$$$$p^{46} T^{125} +$$$$31\!\cdots\!25$$$$p^{48} T^{126} +$$$$95\!\cdots\!22$$$$p^{48} T^{127} +$$$$12\!\cdots\!70$$$$p^{49} T^{128} +$$$$12\!\cdots\!40$$$$p^{50} T^{129} +$$$$16\!\cdots\!12$$$$p^{51} T^{130} +$$$$15\!\cdots\!88$$$$p^{52} T^{131} +$$$$19\!\cdots\!89$$$$p^{53} T^{132} +$$$$17\!\cdots\!23$$$$p^{54} T^{133} +$$$$20\!\cdots\!25$$$$p^{55} T^{134} +$$$$18\!\cdots\!51$$$$p^{56} T^{135} +$$$$21\!\cdots\!97$$$$p^{57} T^{136} +$$$$61\!\cdots\!22$$$$p^{59} T^{137} +$$$$19\!\cdots\!33$$$$p^{59} T^{138} +$$$$15\!\cdots\!62$$$$p^{60} T^{139} +$$$$16\!\cdots\!34$$$$p^{61} T^{140} +$$$$12\!\cdots\!13$$$$p^{62} T^{141} +$$$$12\!\cdots\!69$$$$p^{63} T^{142} + 8684998528404280391 p^{64} T^{143} + 849479378522137105 p^{65} T^{144} + 53362508427957110 p^{66} T^{145} + 4958578940768389 p^{67} T^{146} + 280785860257365 p^{68} T^{147} + 24666229024494 p^{69} T^{148} + 1229667212584 p^{70} T^{149} + 101526590378 p^{71} T^{150} + 4300951541 p^{72} T^{151} + 331392551 p^{73} T^{152} + 11258501 p^{74} T^{153} + 802503 p^{75} T^{154} + 19596 p^{76} T^{155} + 1278 p^{77} T^{156} + 17 p^{78} T^{157} + p^{79} T^{158}$$
31 $$1 + 37 T + 1842 T^{2} + 50463 T^{3} + 1514894 T^{4} + 33836413 T^{5} + 778912846 T^{6} + 14939807015 T^{7} + 288284254304 T^{8} + 4902969593850 T^{9} + 82994140001099 T^{10} + 1278939754407686 T^{11} + 19516876266374065 T^{12} + 276747034705191010 T^{13} + 3876939752769073142 T^{14} + 51172415552388673171 T^{15} +$$$$66\!\cdots\!19$$$$T^{16} +$$$$82\!\cdots\!13$$$$T^{17} +$$$$10\!\cdots\!95$$$$T^{18} +$$$$11\!\cdots\!96$$$$T^{19} +$$$$13\!\cdots\!95$$$$T^{20} +$$$$15\!\cdots\!62$$$$T^{21} +$$$$16\!\cdots\!71$$$$T^{22} +$$$$17\!\cdots\!38$$$$T^{23} +$$$$18\!\cdots\!43$$$$T^{24} +$$$$19\!\cdots\!95$$$$T^{25} +$$$$19\!\cdots\!67$$$$T^{26} +$$$$19\!\cdots\!09$$$$T^{27} +$$$$18\!\cdots\!92$$$$T^{28} +$$$$17\!\cdots\!38$$$$T^{29} +$$$$16\!\cdots\!42$$$$T^{30} +$$$$15\!\cdots\!29$$$$T^{31} +$$$$13\!\cdots\!48$$$$T^{32} +$$$$12\!\cdots\!76$$$$T^{33} +$$$$10\!\cdots\!03$$$$T^{34} +$$$$94\!\cdots\!90$$$$T^{35} +$$$$80\!\cdots\!51$$$$T^{36} +$$$$67\!\cdots\!11$$$$T^{37} +$$$$56\!\cdots\!12$$$$T^{38} +$$$$46\!\cdots\!11$$$$T^{39} +$$$$37\!\cdots\!61$$$$T^{40} +$$$$30\!\cdots\!30$$$$T^{41} +$$$$23\!\cdots\!76$$$$T^{42} +$$$$18\!\cdots\!97$$$$T^{43} +$$$$14\!\cdots\!99$$$$T^{44} +$$$$10\!\cdots\!31$$$$T^{45} +$$$$83\!\cdots\!34$$$$T^{46} +$$$$61\!\cdots\!34$$$$T^{47} +$$$$45\!\cdots\!36$$$$T^{48} +$$$$33\!\cdots\!72$$$$T^{49} +$$$$78\!\cdots\!66$$$$p T^{50} +$$$$17\!\cdots\!41$$$$T^{51} +$$$$12\!\cdots\!19$$$$T^{52} +$$$$86\!\cdots\!06$$$$T^{53} +$$$$60\!\cdots\!58$$$$T^{54} +$$$$41\!\cdots\!05$$$$T^{55} +$$$$28\!\cdots\!69$$$$T^{56} +$$$$19\!\cdots\!53$$$$T^{57} +$$$$12\!\cdots\!67$$$$T^{58} +$$$$84\!\cdots\!33$$$$T^{59} +$$$$55\!\cdots\!02$$$$T^{60} +$$$$36\!\cdots\!92$$$$T^{61} +$$$$23\!\cdots\!28$$$$T^{62} +$$$$15\!\cdots\!73$$$$T^{63} +$$$$95\!\cdots\!57$$$$T^{64} +$$$$59\!\cdots\!34$$$$T^{65} +$$$$37\!\cdots\!98$$$$T^{66} +$$$$23\!\cdots\!89$$$$T^{67} +$$$$14\!\cdots\!35$$$$T^{68} +$$$$85\!\cdots\!75$$$$T^{69} +$$$$51\!\cdots\!94$$$$T^{70} +$$$$30\!\cdots\!62$$$$T^{71} +$$$$18\!\cdots\!80$$$$T^{72} +$$$$10\!\cdots\!83$$$$T^{73} +$$$$62\!\cdots\!01$$$$T^{74} +$$$$36\!\cdots\!13$$$$T^{75} +$$$$20\!\cdots\!50$$$$T^{76} +$$$$11\!\cdots\!63$$$$T^{77} +$$$$66\!\cdots\!23$$$$T^{78} +$$$$37\!\cdots\!66$$$$T^{79} +$$$$66\!\cdots\!23$$$$p T^{80} +$$$$11\!\cdots\!63$$$$p^{2} T^{81} +$$$$20\!\cdots\!50$$$$p^{3} T^{82} +$$$$36\!\cdots\!13$$$$p^{4} T^{83} +$$$$62\!\cdots\!01$$$$p^{5} T^{84} +$$$$10\!\cdots\!83$$$$p^{6} T^{85} +$$$$18\!\cdots\!80$$$$p^{7} T^{86} +$$$$30\!\cdots\!62$$$$p^{8} T^{87} +$$$$51\!\cdots\!94$$$$p^{9} T^{88} +$$$$85\!\cdots\!75$$$$p^{10} T^{89} +$$$$14\!\cdots\!35$$$$p^{11} T^{90} +$$$$23\!\cdots\!89$$$$p^{12} T^{91} +$$$$37\!\cdots\!98$$$$p^{13} T^{92} +$$$$59\!\cdots\!34$$$$p^{14} T^{93} +$$$$95\!\cdots\!57$$$$p^{15} T^{94} +$$$$15\!\cdots\!73$$$$p^{16} T^{95} +$$$$23\!\cdots\!28$$$$p^{17} T^{96} +$$$$36\!\cdots\!92$$$$p^{18} T^{97} +$$$$55\!\cdots\!02$$$$p^{19} T^{98} +$$$$84\!\cdots\!33$$$$p^{20} T^{99} +$$$$12\!\cdots\!67$$$$p^{21} T^{100} +$$$$19\!\cdots\!53$$$$p^{22} T^{101} +$$$$28\!\cdots\!69$$$$p^{23} T^{102} +$$$$41\!\cdots\!05$$$$p^{24} T^{103} +$$$$60\!\cdots\!58$$$$p^{25} T^{104} +$$$$86\!\cdots\!06$$$$p^{26} T^{105} +$$$$12\!\cdots\!19$$$$p^{27} T^{106} +$$$$17\!\cdots\!41$$$$p^{28} T^{107} +$$$$78\!\cdots\!66$$$$p^{30} T^{108} +$$$$33\!\cdots\!72$$$$p^{30} T^{109} +$$$$45\!\cdots\!36$$$$p^{31} T^{110} +$$$$61\!\cdots\!34$$$$p^{32} T^{111} +$$$$83\!\cdots\!34$$$$p^{33} T^{112} +$$$$10\!\cdots\!31$$$$p^{34} T^{113} +$$$$14\!\cdots\!99$$$$p^{35} T^{114} +$$$$18\!\cdots\!97$$$$p^{36} T^{115} +$$$$23\!\cdots\!76$$$$p^{37} T^{116} +$$$$30\!\cdots\!30$$$$p^{38} T^{117} +$$$$37\!\cdots\!61$$$$p^{39} T^{118} +$$$$46\!\cdots\!11$$$$p^{40} T^{119} +$$$$56\!\cdots\!12$$$$p^{41} T^{120} +$$$$67\!\cdots\!11$$$$p^{42} T^{121} +$$$$80\!\cdots\!51$$$$p^{43} T^{122} +$$$$94\!\cdots\!90$$$$p^{44} T^{123} +$$$$10\!\cdots\!03$$$$p^{45} T^{124} +$$$$12\!\cdots\!76$$$$p^{46} T^{125} +$$$$13\!\cdots\!48$$$$p^{47} T^{126} +$$$$15\!\cdots\!29$$$$p^{48} T^{127} +$$$$16\!\cdots\!42$$$$p^{49} T^{128} +$$$$17\!\cdots\!38$$$$p^{50} T^{129} +$$$$18\!\cdots\!92$$$$p^{51} T^{130} +$$$$19\!\cdots\!09$$$$p^{52} T^{131} +$$$$19\!\cdots\!67$$$$p^{53} T^{132} +$$$$19\!\cdots\!95$$$$p^{54} T^{133} +$$$$18\!\cdots\!43$$$$p^{55} T^{134} +$$$$17\!\cdots\!38$$$$p^{56} T^{135} +$$$$16\!\cdots\!71$$$$p^{57} T^{136} +$$$$15\!\cdots\!62$$$$p^{58} T^{137} +$$$$13\!\cdots\!95$$$$p^{59} T^{138} +$$$$11\!\cdots\!96$$$$p^{60} T^{139} +$$$$10\!\cdots\!95$$$$p^{61} T^{140} +$$$$82\!\cdots\!13$$$$p^{62} T^{141} +$$$$66\!\cdots\!19$$$$p^{63} T^{142} + 51172415552388673171 p^{64} T^{143} + 3876939752769073142 p^{65} T^{144} + 276747034705191010 p^{66} T^{145} + 19516876266374065 p^{67} T^{146} + 1278939754407686 p^{68} T^{147} + 82994140001099 p^{69} T^{148} + 4902969593850 p^{70} T^{149} + 288284254304 p^{71} T^{150} + 14939807015 p^{72} T^{151} + 778912846 p^{73} T^{152} + 33836413 p^{74} T^{153} + 1514894 p^{75} T^{154} + 50463 p^{76} T^{155} + 1842 p^{77} T^{156} + 37 p^{78} T^{157} + p^{79} T^{158}$$
41 $$1 + 37 T + 2225 T^{2} + 64917 T^{3} + 2302829 T^{4} + 56468440 T^{5} + 1519298307 T^{6} + 32534034910 T^{7} + 729333764913 T^{8} + 13988374572243 T^{9} + 274093674334243 T^{10} + 4793319307665725 T^{11} + 84473252073261779 T^{12} + 1364822421771898808 T^{13} + 22043550871417417813 T^{14} +$$$$33\!\cdots\!84$$$$T^{15} +$$$$49\!\cdots\!32$$$$T^{16} +$$$$70\!\cdots\!39$$$$T^{17} +$$$$99\!\cdots\!07$$$$T^{18} +$$$$13\!\cdots\!24$$$$T^{19} +$$$$17\!\cdots\!39$$$$T^{20} +$$$$22\!\cdots\!70$$$$T^{21} +$$$$28\!\cdots\!43$$$$T^{22} +$$$$35\!\cdots\!07$$$$T^{23} +$$$$42\!\cdots\!53$$$$T^{24} +$$$$49\!\cdots\!20$$$$T^{25} +$$$$57\!\cdots\!63$$$$T^{26} +$$$$64\!\cdots\!98$$$$T^{27} +$$$$72\!\cdots\!94$$$$T^{28} +$$$$78\!\cdots\!92$$$$T^{29} +$$$$84\!\cdots\!28$$$$T^{30} +$$$$88\!\cdots\!46$$$$T^{31} +$$$$92\!\cdots\!21$$$$T^{32} +$$$$93\!\cdots\!24$$$$T^{33} +$$$$94\!\cdots\!33$$$$T^{34} +$$$$93\!\cdots\!53$$$$T^{35} +$$$$91\!\cdots\!37$$$$T^{36} +$$$$88\!\cdots\!73$$$$T^{37} +$$$$84\!\cdots\!59$$$$T^{38} +$$$$78\!\cdots\!61$$$$T^{39} +$$$$73\!\cdots\!61$$$$T^{40} +$$$$66\!\cdots\!47$$$$T^{41} +$$$$60\!\cdots\!55$$$$T^{42} +$$$$53\!\cdots\!38$$$$T^{43} +$$$$47\!\cdots\!04$$$$T^{44} +$$$$41\!\cdots\!47$$$$T^{45} +$$$$35\!\cdots\!84$$$$T^{46} +$$$$30\!\cdots\!04$$$$T^{47} +$$$$25\!\cdots\!40$$$$T^{48} +$$$$21\!\cdots\!38$$$$T^{49} +$$$$17\!\cdots\!24$$$$T^{50} +$$$$14\!\cdots\!35$$$$T^{51} +$$$$11\!\cdots\!69$$$$T^{52} +$$$$94\!\cdots\!05$$$$T^{53} +$$$$75\!\cdots\!53$$$$T^{54} +$$$$59\!\cdots\!07$$$$T^{55} +$$$$46\!\cdots\!54$$$$T^{56} +$$$$35\!\cdots\!77$$$$T^{57} +$$$$27\!\cdots\!96$$$$T^{58} +$$$$20\!\cdots\!80$$$$T^{59} +$$$$15\!\cdots\!88$$$$T^{60} +$$$$11\!\cdots\!48$$$$T^{61} +$$$$20\!\cdots\!60$$$$p T^{62} +$$$$62\!\cdots\!50$$$$T^{63} +$$$$45\!\cdots\!92$$$$T^{64} +$$$$32\!\cdots\!96$$$$T^{65} +$$$$23\!\cdots\!25$$$$T^{66} +$$$$16\!\cdots\!97$$$$T^{67} +$$$$11\!\cdots\!96$$$$T^{68} +$$$$80\!\cdots\!19$$$$T^{69} +$$$$55\!\cdots\!35$$$$T^{70} +$$$$38\!\cdots\!41$$$$T^{71} +$$$$25\!\cdots\!74$$$$T^{72} +$$$$17\!\cdots\!33$$$$T^{73} +$$$$11\!\cdots\!42$$$$T^{74} +$$$$77\!\cdots\!81$$$$T^{75} +$$$$50\!\cdots\!02$$$$T^{76} +$$$$33\!\cdots\!08$$$$T^{77} +$$$$21\!\cdots\!07$$$$T^{78} +$$$$13\!\cdots\!80$$$$T^{79} +$$$$21\!\cdots\!07$$$$p T^{80} +$$$$33\!\cdots\!08$$$$p^{2} T^{81} +$$$$50\!\cdots\!02$$$$p^{3} T^{82} +$$$$77\!\cdots\!81$$$$p^{4} T^{83} +$$$$11\!\cdots\!42$$$$p^{5} T^{84} +$$$$17\!\cdots\!33$$$$p^{6} T^{85} +$$$$25\!\cdots\!74$$$$p^{7} T^{86} +$$$$38\!\cdots\!41$$$$p^{8} T^{87} +$$$$55\!\cdots\!35$$$$p^{9} T^{88} +$$$$80\!\cdots\!19$$$$p^{10} T^{89} +$$$$11\!\cdots\!96$$$$p^{11} T^{90} +$$$$16\!\cdots\!97$$$$p^{12} T^{91} +$$$$23\!\cdots\!25$$$$p^{13} T^{92} +$$$$32\!\cdots\!96$$$$p^{14} T^{93} +$$$$45\!\cdots\!92$$$$p^{15} T^{94} +$$$$62\!\cdots\!50$$$$p^{16} T^{95} +$$$$20\!\cdots\!60$$$$p^{18} T^{96} +$$$$11\!\cdots\!48$$$$p^{18} T^{97} +$$$$15\!\cdots\!88$$$$p^{19} T^{98} +$$$$20\!\cdots\!80$$$$p^{20} T^{99} +$$$$27\!\cdots\!96$$$$p^{21} T^{100} +$$$$35\!\cdots\!77$$$$p^{22} T^{101} +$$$$46\!\cdots\!54$$$$p^{23} T^{102} +$$$$59\!\cdots\!07$$$$p^{24} T^{103} +$$$$75\!\cdots\!53$$$$p^{25} T^{104} +$$$$94\!\cdots\!05$$$$p^{26} T^{105} +$$$$11\!\cdots\!69$$$$p^{27} T^{106} +$$$$14\!\cdots\!35$$$$p^{28} T^{107} +$$$$17\!\cdots\!24$$$$p^{29} T^{108} +$$$$21\!\cdots\!38$$$$p^{30} T^{109} +$$$$25\!\cdots\!40$$$$p^{31} T^{110} +$$$$30\!\cdots\!04$$$$p^{32} T^{111} +$$$$35\!\cdots\!84$$$$p^{33} T^{112} +$$$$41\!\cdots\!47$$$$p^{34} T^{113} +$$$$47\!\cdots\!04$$$$p^{35} T^{114} +$$$$53\!\cdots\!38$$$$p^{36} T^{115} +$$$$60\!\cdots\!55$$$$p^{37} T^{116} +$$$$66\!\cdots\!47$$$$p^{38} T^{117} +$$$$73\!\cdots\!61$$$$p^{39} T^{118} +$$$$78\!\cdots\!61$$$$p^{40} T^{119} +$$$$84\!\cdots\!59$$$$p^{41} T^{120} +$$$$88\!\cdots\!73$$$$p^{42} T^{121} +$$$$91\!\cdots\!37$$$$p^{43} T^{122} +$$$$93\!\cdots\!53$$$$p^{44} T^{123} +$$$$94\!\cdots\!33$$$$p^{45} T^{124} +$$$$93\!\cdots\!24$$$$p^{46} T^{125} +$$$$92\!\cdots\!21$$$$p^{47} T^{126} +$$$$88\!\cdots\!46$$$$p^{48} T^{127} +$$$$84\!\cdots\!28$$$$p^{49} T^{128} +$$$$78\!\cdots\!92$$$$p^{50} T^{129} +$$$$72\!\cdots\!94$$$$p^{51} T^{130} +$$$$64\!\cdots\!98$$$$p^{52} T^{131} +$$$$57\!\cdots\!63$$$$p^{53} T^{132} +$$$$49\!\cdots\!20$$$$p^{54} T^{133} +$$$$42\!\cdots\!53$$$$p^{55} T^{134} +$$$$35\!\cdots\!07$$$$p^{56} T^{135} +$$$$28\!\cdots\!43$$$$p^{57} T^{136} +$$$$22\!\cdots\!70$$$$p^{58} T^{137} +$$$$17\!\cdots\!39$$$$p^{59} T^{138} +$$$$13\!\cdots\!24$$$$p^{60} T^{139} +$$$$99\!\cdots\!07$$$$p^{61} T^{140} +$$$$70\!\cdots\!39$$$$p^{62} T^{141} +$$$$49\!\cdots\!32$$$$p^{63} T^{142} +$$$$33\!\cdots\!84$$$$p^{64} T^{143} + 22043550871417417813 p^{65} T^{144} + 1364822421771898808 p^{66} T^{145} + 84473252073261779 p^{67} T^{146} + 4793319307665725 p^{68} T^{147} + 274093674334243 p^{69} T^{148} + 13988374572243 p^{70} T^{149} + 729333764913 p^{71} T^{150} + 32534034910 p^{72} T^{151} + 1519298307 p^{73} T^{152} + 56468440 p^{74} T^{153} + 2302829 p^{75} T^{154} + 64917 p^{76} T^{155} + 2225 p^{77} T^{156} + 37 p^{78} T^{157} + p^{79} T^{158}$$
43 $$1 + 20 T + 1922 T^{2} + 36758 T^{3} + 1853272 T^{4} + 33856551 T^{5} + 1194404226 T^{6} + 20835555295 T^{7} + 578420660271 T^{8} + 9637099428982 T^{9} + 224383361581036 T^{10} + 3573065363320925 T^{11} + 72594841730146963 T^{12} + 1105998779672384451 T^{13} + 20139242545385060783 T^{14} +$$$$29\!\cdots\!87$$$$T^{15} +$$$$48\!\cdots\!19$$$$T^{16} +$$$$68\!\cdots\!42$$$$T^{17} +$$$$10\!\cdots\!31$$$$T^{18} +$$$$14\!\cdots\!99$$$$T^{19} +$$$$20\!\cdots\!36$$$$T^{20} +$$$$26\!\cdots\!05$$$$T^{21} +$$$$36\!\cdots\!35$$$$T^{22} +$$$$45\!\cdots\!08$$$$T^{23} +$$$$58\!\cdots\!56$$$$T^{24} +$$$$70\!\cdots\!49$$$$T^{25} +$$$$86\!\cdots\!36$$$$T^{26} +$$$$10\!\cdots\!60$$$$T^{27} +$$$$11\!\cdots\!93$$$$T^{28} +$$$$13\!\cdots\!08$$$$T^{29} +$$$$15\!\cdots\!83$$$$T^{30} +$$$$16\!\cdots\!45$$$$T^{31} +$$$$18\!\cdots\!52$$$$T^{32} +$$$$19\!\cdots\!33$$$$T^{33} +$$$$20\!\cdots\!72$$$$T^{34} +$$$$21\!\cdots\!61$$$$T^{35} +$$$$22\!\cdots\!71$$$$T^{36} +$$$$22\!\cdots\!14$$$$T^{37} +$$$$22\!\cdots\!48$$$$T^{38} +$$$$22\!\cdots\!80$$$$T^{39} +$$$$21\!\cdots\!38$$$$T^{40} +$$$$20\!\cdots\!06$$$$T^{41} +$$$$19\!\cdots\!08$$$$T^{42} +$$$$18\!\cdots\!41$$$$T^{43} +$$$$16\!\cdots\!62$$$$T^{44} +$$$$15\!\cdots\!39$$$$T^{45} +$$$$13\!\cdots\!88$$$$T^{46} +$$$$12\!\cdots\!00$$$$T^{47} +$$$$10\!\cdots\!17$$$$T^{48} +$$$$95\!\cdots\!50$$$$T^{49} +$$$$82\!\cdots\!04$$$$T^{50} +$$$$70\!\cdots\!91$$$$T^{51} +$$$$59\!\cdots\!25$$$$T^{52} +$$$$49\!\cdots\!97$$$$T^{53} +$$$$41\!\cdots\!46$$$$T^{54} +$$$$33\!\cdots\!60$$$$T^{55} +$$$$27\!\cdots\!74$$$$T^{56} +$$$$22\!\cdots\!69$$$$T^{57} +$$$$17\!\cdots\!31$$$$T^{58} +$$$$13\!\cdots\!12$$$$T^{59} +$$$$10\!\cdots\!11$$$$T^{60} +$$$$83\!\cdots\!71$$$$T^{61} +$$$$63\!\cdots\!96$$$$T^{62} +$$$$48\!\cdots\!64$$$$T^{63} +$$$$36\!\cdots\!23$$$$T^{64} +$$$$27\!\cdots\!53$$$$T^{65} +$$$$20\!\cdots\!17$$$$T^{66} +$$$$14\!\cdots\!67$$$$T^{67} +$$$$10\!\cdots\!71$$$$T^{68} +$$$$76\!\cdots\!81$$$$T^{69} +$$$$54\!\cdots\!62$$$$T^{70} +$$$$38\!\cdots\!97$$$$T^{71} +$$$$26\!\cdots\!43$$$$T^{72} +$$$$18\!\cdots\!61$$$$T^{73} +$$$$12\!\cdots\!11$$$$T^{74} +$$$$87\!\cdots\!21$$$$T^{75} +$$$$59\!\cdots\!82$$$$T^{76} +$$$$39\!\cdots\!94$$$$T^{77} +$$$$26\!\cdots\!81$$$$T^{78} +$$$$17\!\cdots\!30$$$$T^{79} +$$$$26\!\cdots\!81$$$$p T^{80} +$$$$39\!\cdots\!94$$$$p^{2} T^{81} +$$$$59\!\cdots\!82$$$$p^{3} T^{82} +$$$$87\!\cdots\!21$$$$p^{4} T^{83} +$$$$12\!\cdots\!11$$$$p^{5} T^{84} +$$$$18\!\cdots\!61$$$$p^{6} T^{85} +$$$$26\!\cdots\!43$$$$p^{7} T^{86} +$$$$38\!\cdots\!97$$$$p^{8} T^{87} +$$$$54\!\cdots\!62$$$$p^{9} T^{88} +$$$$76\!\cdots\!81$$$$p^{10} T^{89} +$$$$10\!\cdots\!71$$$$p^{11} T^{90} +$$$$14\!\cdots\!67$$$$p^{12} T^{91} +$$$$20\!\cdots\!17$$$$p^{13} T^{92} +$$$$27\!\cdots\!53$$$$p^{14} T^{93} +$$$$36\!\cdots\!23$$$$p^{15} T^{94} +$$$$48\!\cdots\!64$$$$p^{16} T^{95} +$$$$63\!\cdots\!96$$$$p^{17} T^{96} +$$$$83\!\cdots\!71$$$$p^{18} T^{97} +$$$$10\!\cdots\!11$$$$p^{19} T^{98} +$$$$13\!\cdots\!12$$$$p^{20} T^{99} +$$$$17\!\cdots\!31$$$$p^{21} T^{100} +$$$$22\!\cdots\!69$$$$p^{22} T^{101} +$$$$27\!\cdots\!74$$$$p^{23} T^{102} +$$$$33\!\cdots\!60$$$$p^{24} T^{103} +$$$$41\!\cdots\!46$$$$p^{25} T^{104} +$$$$49\!\cdots\!97$$$$p^{26} T^{105} +$$$$59\!\cdots\!25$$$$p^{27} T^{106} +$$$$70\!\cdots\!91$$$$p^{28} T^{107} +$$$$82\!\cdots\!04$$$$p^{29} T^{108} +$$$$95\!\cdots\!50$$$$p^{30} T^{109} +$$$$10\!\cdots\!17$$$$p^{31} T^{110} +$$$$12\!\cdots\!00$$$$p^{32} T^{111} +$$$$13\!\cdots\!88$$$$p^{33} T^{112} +$$$$15\!\cdots\!39$$$$p^{34} T^{113} +$$$$16\!\cdots\!62$$$$p^{35} T^{114} +$$$$18\!\cdots\!41$$$$p^{36} T^{115} +$$$$19\!\cdots\!08$$$$p^{37} T^{116} +$$$$20\!\cdots\!06$$$$p^{38} T^{117} +$$$$21\!\cdots\!38$$$$p^{39} T^{118} +$$$$22\!\cdots\!80$$$$p^{40} T^{119} +$$$$22\!\cdots\!48$$$$p^{41} T^{120} +$$$$22\!\cdots\!14$$$$p^{42} T^{121} +$$$$22\!\cdots\!71$$$$p^{43} T^{122} +$$$$21\!\cdots\!61$$$$p^{44} T^{123} +$$$$20\!\cdots\!72$$$$p^{45} T^{124} +$$$$19\!\cdots\!33$$$$p^{46} T^{125} +$$$$18\!\cdots\!52$$$$p^{47} T^{126} +$$$$16\!\cdots\!45$$$$p^{48} T^{127} +$$$$15\!\cdots\!83$$$$p^{49} T^{128} +$$$$13\!\cdots\!08$$$$p^{50} T^{129} +$$$$11\!\cdots\!93$$$$p^{51} T^{130} +$$$$10\!\cdots\!60$$$$p^{52} T^{131} +$$$$86\!\cdots\!36$$$$p^{53} T^{132} +$$$$70\!\cdots\!49$$$$p^{54} T^{133} +$$$$58\!\cdots\!56$$$$p^{55} T^{134} +$$$$45\!\cdots\!08$$$$p^{56} T^{135} +$$$$36\!\cdots\!35$$$$p^{57} T^{136} +$$$$26\!\cdots\!05$$$$p^{58} T^{137} +$$$$20\!\cdots\!36$$$$p^{59} T^{138} +$$$$14\!\cdots\!99$$$$p^{60} T^{139} +$$$$10\!\cdots\!31$$$$p^{61} T^{140} +$$$$68\!\cdots\!42$$$$p^{62} T^{141} +$$$$48\!\cdots\!19$$$$p^{63} T^{142} +$$$$29\!\cdots\!87$$$$p^{64} T^{143} + 20139242545385060783 p^{65} T^{144} + 1105998779672384451 p^{66} T^{145} + 72594841730146963 p^{67} T^{146} + 3573065363320925 p^{68} T^{147} + 224383361581036 p^{69} T^{148} + 9637099428982 p^{70} T^{149} + 578420660271 p^{71} T^{150} + 20835555295 p^{72} T^{151} + 1194404226 p^{73} T^{152} + 33856551 p^{74} T^{153} + 1853272 p^{75} T^{154} + 36758 p^{76} T^{155} + 1922 p^{77} T^{156} + 20 p^{78} T^{157} + p^{79} T^{158}$$
47 $$1 + 148 T + 12649 T^{2} + 789366 T^{3} + 39723278 T^{4} + 1697622122 T^{5} + 63649232868 T^{6} + 2140035289880 T^{7} + 65556654872000 T^{8} + 1851676953906481 T^{9} + 48675876977285871 T^{10} + 1199774822208351695 T^{11} + 27897904228442691404 T^{12} +$$$$61\!\cdots\!10$$$$T^{13} +$$$$12\!\cdots\!01$$$$T^{14} +$$$$25\!\cdots\!18$$$$T^{15} +$$$$49\!\cdots\!53$$$$T^{16} +$$$$92\!\cdots\!40$$$$T^{17} +$$$$16\!\cdots\!24$$$$T^{18} +$$$$28\!\cdots\!38$$$$T^{19} +$$$$47\!\cdots\!28$$$$T^{20} +$$$$76\!\cdots\!04$$$$T^{21} +$$$$11\!\cdots\!34$$$$T^{22} +$$$$18\!\cdots\!39$$$$T^{23} +$$$$27\!\cdots\!42$$$$T^{24} +$$$$39\!\cdots\!96$$$$T^{25} +$$$$55\!\cdots\!36$$$$T^{26} +$$$$75\!\cdots\!19$$$$T^{27} +$$$$10\!\cdots\!62$$$$T^{28} +$$$$13\!\cdots\!84$$$$T^{29} +$$$$17\!\cdots\!43$$$$T^{30} +$$$$21\!\cdots\!28$$$$T^{31} +$$$$27\!\cdots\!74$$$$T^{32} +$$$$33\!\cdots\!35$$$$T^{33} +$$$$39\!\cdots\!92$$$$T^{34} +$$$$46\!\cdots\!70$$$$T^{35} +$$$$53\!\cdots\!13$$$$T^{36} +$$$$60\!\cdots\!47$$$$T^{37} +$$$$67\!\cdots\!55$$$$T^{38} +$$$$73\!\cdots\!30$$$$T^{39} +$$$$79\!\cdots\!98$$$$T^{40} +$$$$84\!\cdots\!47$$$$T^{41} +$$$$88\!\cdots\!47$$$$T^{42} +$$$$90\!\cdots\!00$$$$T^{43} +$$$$19\!\cdots\!80$$$$p T^{44} +$$$$92\!\cdots\!93$$$$T^{45} +$$$$91\!\cdots\!78$$$$T^{46} +$$$$89\!\cdots\!73$$$$T^{47} +$$$$85\!\cdots\!03$$$$T^{48} +$$$$81\!\cdots\!82$$$$T^{49} +$$$$76\!\cdots\!77$$$$T^{50} +$$$$70\!\cdots\!97$$$$T^{51} +$$$$64\!\cdots\!02$$$$T^{52} +$$$$58\!\cdots\!44$$$$T^{53} +$$$$52\!\cdots\!71$$$$T^{54} +$$$$46\!\cdots\!69$$$$T^{55} +$$$$40\!\cdots\!91$$$$T^{56} +$$$$34\!\cdots\!17$$$$T^{57} +$$$$29\!\cdots\!06$$$$T^{58} +$$$$25\!\cdots\!51$$$$T^{59} +$$$$20\!\cdots\!02$$$$T^{60} +$$$$17\!\cdots\!03$$$$T^{61} +$$$$14\!\cdots\!44$$$$T^{62} +$$$$11\!\cdots\!68$$$$T^{63} +$$$$90\!\cdots\!71$$$$T^{64} +$$$$71\!\cdots\!06$$$$T^{65} +$$$$56\!\cdots\!71$$$$T^{66} +$$$$43\!\cdots\!49$$$$T^{67} +$$$$33\!\cdots\!87$$$$T^{68} +$$$$25\!\cdots\!21$$$$T^{69} +$$$$40\!\cdots\!24$$$$p T^{70} +$$$$14\!\cdots\!61$$$$T^{71} +$$$$10\!\cdots\!41$$$$T^{72} +$$$$76\!\cdots\!71$$$$T^{73} +$$$$55\!\cdots\!39$$$$T^{74} +$$$$39\!\cdots\!00$$$$T^{75} +$$$$28\!\cdots\!90$$$$T^{76} +$$$$19\!\cdots\!36$$$$T^{77} +$$$$13\!\cdots\!33$$$$T^{78} +$$$$94\!\cdots\!25$$$$T^{79} +$$$$13\!\cdots\!33$$$$p T^{80} +$$$$19\!\cdots\!36$$$$p^{2} T^{81} +$$$$28\!\cdots\!90$$$$p^{3} T^{82} +$$$$39\!\cdots\!00$$$$p^{4} T^{83} +$$$$55\!\cdots\!39$$$$p^{5} T^{84} +$$$$76\!\cdots\!71$$$$p^{6} T^{85} +$$$$10\!\cdots\!41$$$$p^{7} T^{86} +$$$$14\!\cdots\!61$$$$p^{8} T^{87} +$$$$40\!\cdots\!24$$$$p^{10} T^{88} +$$$$25\!\cdots\!21$$$$p^{10} T^{89} +$$$$33\!\cdots\!87$$$$p^{11} T^{90} +$$$$43\!\cdots\!49$$$$p^{12} T^{91} +$$$$56\!\cdots\!71$$$$p^{13} T^{92} +$$$$71\!\cdots\!06$$$$p^{14} T^{93} +$$$$90\!\cdots\!71$$$$p^{15} T^{94} +$$$$11\!\cdots\!68$$$$p^{16} T^{95} +$$$$14\!\cdots\!44$$$$p^{17} T^{96} +$$$$17\!\cdots\!03$$$$p^{18} T^{97} +$$$$20\!\cdots\!02$$$$p^{19} T^{98} +$$$$25\!\cdots\!51$$$$p^{20} T^{99} +$$$$29\!\cdots\!06$$$$p^{21} T^{100} +$$$$34\!\cdots\!17$$$$p^{22} T^{101} +$$$$40\!\cdots\!91$$$$p^{23} T^{102} +$$$$46\!\cdots\!69$$$$p^{24} T^{103} +$$$$52\!\cdots\!71$$$$p^{25} T^{104} +$$$$58\!\cdots\!44$$$$p^{26} T^{105} +$$$$64\!\cdots\!02$$$$p^{27} T^{106} +$$$$70\!\cdots\!97$$$$p^{28} T^{107} +$$$$76\!\cdots\!77$$$$p^{29} T^{108} +$$$$81\!\cdots\!82$$$$p^{30} T^{109} +$$$$85\!\cdots\!03$$$$p^{31} T^{110} +$$$$89\!\cdots\!73$$$$p^{32} T^{111} +$$$$91\!\cdots\!78$$$$p^{33} T^{112} +$$$$92\!\cdots\!93$$$$p^{34} T^{113} +$$$$19\!\cdots\!80$$$$p^{36} T^{114} +$$$$90\!\cdots\!00$$$$p^{36} T^{115} +$$$$88\!\cdots\!47$$$$p^{37} T^{116} +$$$$84\!\cdots\!47$$$$p^{38} T^{117} +$$$$79\!\cdots\!98$$$$p^{39} T^{118} +$$$$73\!\cdots\!30$$$$p^{40} T^{119} +$$$$67\!\cdots\!55$$$$p^{41} T^{120} +$$$$60\!\cdots\!47$$$$p^{42} T^{121} +$$$$53\!\cdots\!13$$$$p^{43} T^{122} +$$$$46\!\cdots\!70$$$$p^{44} T^{123} +$$$$39\!\cdots\!92$$$$p^{45} T^{124} +$$$$33\!\cdots\!35$$$$p^{46} T^{125} +$$$$27\!\cdots\!74$$$$p^{47} T^{126} +$$$$21\!\cdots\!28$$$$p^{48} T^{127} +$$$$17\!\cdots\!43$$$$p^{49} T^{128} +$$$$13\!\cdots\!84$$$$p^{50} T^{129} +$$$$10\!\cdots\!62$$$$p^{51} T^{130} +$$$$75\!\cdots\!19$$$$p^{52} T^{131} +$$$$55\!\cdots\!36$$$$p^{53} T^{132} +$$$$39\!\cdots\!96$$$$p^{54} T^{133} +$$$$27\!\cdots\!42$$$$p^{55} T^{134} +$$$$18\!\cdots\!39$$$$p^{56} T^{135} +$$$$11\!\cdots\!34$$$$p^{57} T^{136} +$$$$76\!\cdots\!04$$$$p^{58} T^{137} +$$$$47\!\cdots\!28$$$$p^{59} T^{138} +$$$$28\!\cdots\!38$$$$p^{60} T^{139} +$$$$16\!\cdots\!24$$$$p^{61} T^{140} +$$$$92\!\cdots\!40$$$$p^{62} T^{141} +$$$$49\!\cdots\!53$$$$p^{63} T^{142} +$$$$25\!\cdots\!18$$$$p^{64} T^{143} +$$$$12\!\cdots\!01$$$$p^{65} T^{144} +$$$$61\!\cdots\!10$$$$p^{66} T^{145} + 27897904228442691404 p^{67} T^{146} + 1199774822208351695 p^{68} T^{147} + 48675876977285871 p^{69} T^{148} + 1851676953906481 p^{70} T^{149} + 65556654872000 p^{71} T^{150} + 2140035289880 p^{72} T^{151} + 63649232868 p^{73} T^{152} + 1697622122 p^{74} T^{153} + 39723278 p^{75} T^{154} + 789366 p^{76} T^{155} + 12649 p^{77} T^{156} + 148 p^{78} T^{157} + p^{79} T^{158}$$
53 $$1 + 70 T + 4195 T^{2} + 178957 T^{3} + 6785612 T^{4} + 219676468 T^{5} + 6511273082 T^{6} + 174799835050 T^{7} + 4380534180052 T^{8} + 102221267840227 T^{9} + 2256137872401499 T^{10} + 47106106683139699 T^{11} + 938931056908882735 T^{12} + 17884788090335013107 T^{13} +$$$$32\!\cdots\!81$$$$T^{14} +$$$$57\!\cdots\!59$$$$T^{15} +$$$$98\!\cdots\!20$$$$T^{16} +$$$$16\!\cdots\!70$$$$T^{17} +$$$$25\!\cdots\!70$$$$T^{18} +$$$$40\!\cdots\!28$$$$T^{19} +$$$$60\!\cdots\!41$$$$T^{20} +$$$$89\!\cdots\!81$$$$T^{21} +$$$$12\!\cdots\!73$$$$T^{22} +$$$$17\!\cdots\!26$$$$T^{23} +$$$$24\!\cdots\!99$$$$T^{24} +$$$$11\!\cdots\!07$$$$p^{2} T^{25} +$$$$43\!\cdots\!97$$$$T^{26} +$$$$56\!\cdots\!20$$$$T^{27} +$$$$71\!\cdots\!55$$$$T^{28} +$$$$89\!\cdots\!22$$$$T^{29} +$$$$10\!\cdots\!73$$$$T^{30} +$$$$24\!\cdots\!88$$$$p T^{31} +$$$$15\!\cdots\!00$$$$T^{32} +$$$$18\!\cdots\!69$$$$T^{33} +$$$$20\!\cdots\!60$$$$T^{34} +$$$$23\!\cdots\!51$$$$T^{35} +$$$$26\!\cdots\!82$$$$T^{36} +$$$$28\!\cdots\!83$$$$T^{37} +$$$$31\!\cdots\!57$$$$T^{38} +$$$$33\!\cdots\!84$$$$T^{39} +$$$$35\!\cdots\!03$$$$T^{40} +$$$$36\!\cdots\!33$$$$T^{41} +$$$$37\!\cdots\!00$$$$T^{42} +$$$$38\!\cdots\!60$$$$T^{43} +$$$$38\!\cdots\!56$$$$T^{44} +$$$$38\!\cdots\!37$$$$T^{45} +$$$$38\!\cdots\!72$$$$T^{46} +$$$$37\!\cdots\!54$$$$T^{47} +$$$$35\!\cdots\!66$$$$T^{48} +$$$$34\!\cdots\!70$$$$T^{49} +$$$$32\!\cdots\!16$$$$T^{50} +$$$$29\!\cdots\!24$$$$T^{51} +$$$$27\!\cdots\!27$$$$T^{52} +$$$$25\!\cdots\!13$$$$T^{53} +$$$$22\!\cdots\!68$$$$T^{54} +$$$$20\!\cdots\!55$$$$T^{55} +$$$$18\!\cdots\!28$$$$T^{56} +$$$$16\!\cdots\!52$$$$T^{57} +$$$$14\!\cdots\!86$$$$T^{58} +$$$$12\!\cdots\!14$$$$T^{59} +$$$$10\!\cdots\!86$$$$T^{60} +$$$$16\!\cdots\!22$$$$p T^{61} +$$$$74\!\cdots\!54$$$$T^{62} +$$$$62\!\cdots\!65$$$$T^{63} +$$$$51\!\cdots\!97$$$$T^{64} +$$$$42\!\cdots\!57$$$$T^{65} +$$$$34\!\cdots\!63$$$$T^{66} +$$$$27\!\cdots\!48$$$$T^{67} +$$$$22\!\cdots\!46$$$$T^{68} +$$$$17\!\cdots\!05$$$$T^{69} +$$$$13\!\cdots\!22$$$$T^{70} +$$$$10\!\cdots\!77$$$$T^{71} +$$$$83\!\cdots\!33$$$$T^{72} +$$$$64\!\cdots\!66$$$$T^{73} +$$$$48\!\cdots\!44$$$$T^{74} +$$$$36\!\cdots\!92$$$$T^{75} +$$$$27\!\cdots\!51$$$$T^{76} +$$$$20\!\cdots\!09$$$$T^{77} +$$$$15\!\cdots\!90$$$$T^{78} +$$$$20\!\cdots\!42$$$$p T^{79} +$$$$15\!\cdots\!90$$$$p T^{80} +$$$$20\!\cdots\!09$$$$p^{2} T^{81} +$$$$27\!\cdots\!51$$$$p^{3} T^{82} +$$$$36\!\cdots\!92$$$$p^{4} T^{83} +$$$$48\!\cdots\!44$$$$p^{5} T^{84} +$$$$64\!\cdots\!66$$$$p^{6} T^{85} +$$$$83\!\cdots\!33$$$$p^{7} T^{86} +$$$$10\!\cdots\!77$$$$p^{8} T^{87} +$$$$13\!\cdots\!22$$$$p^{9} T^{88} +$$$$17\!\cdots\!05$$$$p^{10} T^{89} +$$$$22\!\cdots\!46$$$$p^{11} T^{90} +$$$$27\!\cdots\!48$$$$p^{12} T^{91} +$$$$34\!\cdots\!63$$$$p^{13} T^{92} +$$$$42\!\cdots\!57$$$$p^{14} T^{93} +$$$$51\!\cdots\!97$$$$p^{15} T^{94} +$$$$62\!\cdots\!65$$$$p^{16} T^{95} +$$$$74\!\cdots\!54$$$$p^{17} T^{96} +$$$$16\!\cdots\!22$$$$p^{19} T^{97} +$$$$10\!\cdots\!86$$$$p^{19} T^{98} +$$$$12\!\cdots\!14$$$$p^{20} T^{99} +$$$$14\!\cdots\!86$$$$p^{21} T^{100} +$$$$16\!\cdots\!52$$$$p^{22} T^{101} +$$$$18\!\cdots\!28$$$$p^{23} T^{102} +$$$$20\!\cdots\!55$$$$p^{24} T^{103} +$$$$22\!\cdots\!68$$$$p^{25} T^{104} +$$$$25\!\cdots\!13$$$$p^{26} T^{105} +$$$$27\!\cdots\!27$$$$p^{27} T^{106} +$$$$29\!\cdots\!24$$$$p^{28} T^{107} +$$$$32\!\cdots\!16$$$$p^{29} T^{108} +$$$$34\!\cdots\!70$$$$p^{30} T^{109} +$$$$35\!\cdots\!66$$$$p^{31} T^{110} +$$$$37\!\cdots\!54$$$$p^{32} T^{111} +$$$$38\!\cdots\!72$$$$p^{33} T^{112} +$$$$38\!\cdots\!37$$$$p^{34} T^{113} +$$$$38\!\cdots\!56$$$$p^{35} T^{114} +$$$$38\!\cdots\!60$$$$p^{36} T^{115} +$$$$37\!\cdots\!00$$$$p^{37} T^{116} +$$$$36\!\cdots\!33$$$$p^{38} T^{117} +$$$$35\!\cdots\!03$$$$p^{39} T^{118} +$$$$33\!\cdots\!84$$$$p^{40} T^{119} +$$$$31\!\cdots\!57$$$$p^{41} T^{120} +$$$$28\!\cdots\!83$$$$p^{42} T^{121} +$$$$26\!\cdots\!82$$$$p^{43} T^{122} +$$$$23\!\cdots\!51$$$$p^{44} T^{123} +$$$$20\!\cdots\!60$$$$p^{45} T^{124} +$$$$18\!\cdots\!69$$$$p^{46} T^{125} +$$$$15\!\cdots\!00$$$$p^{47} T^{126} +$$$$24\!\cdots\!88$$$$p^{49} T^{127} +$$$$10\!\cdots\!73$$$$p^{49} T^{128} +$$$$89\!\cdots\!22$$$$p^{50} T^{129} +$$$$71\!\cdots\!55$$$$p^{51} T^{130} +$$$$56\!\cdots\!20$$$$p^{52} T^{131} +$$$$43\!\cdots\!97$$$$p^{53} T^{132} +$$$$11\!\cdots\!07$$$$p^{56} T^{133} +$$$$24\!\cdots\!99$$$$p^{55} T^{134} +$$$$17\!\cdots\!26$$$$p^{56} T^{135} +$$$$12\!\cdots\!73$$$$p^{57} T^{136} +$$$$89\!\cdots\!81$$$$p^{58} T^{137} +$$$$60\!\cdots\!41$$$$p^{59} T^{138} +$$$$40\!\cdots\!28$$$$p^{60} T^{139} +$$$$25\!\cdots\!70$$$$p^{61} T^{140} +$$$$16\!\cdots\!70$$$$p^{62} T^{141} +$$$$98\!\cdots\!20$$$$p^{63} T^{142} +$$$$57\!\cdots\!59$$$$p^{64} T^{143} +$$$$32\!\cdots\!81$$$$p^{65} T^{144} + 17884788090335013107 p^{66} T^{145} + 938931056908882735 p^{67} T^{146} + 47106106683139699 p^{68} T^{147} + 2256137872401499 p^{69} T^{148} + 102221267840227 p^{70} T^{149} + 4380534180052 p^{71} T^{150} + 174799835050 p^{72} T^{151} + 6511273082 p^{73} T^{152} + 219676468 p^{74} T^{153} + 6785612 p^{75} T^{154} + 178957 p^{76} T^{155} + 4195 p^{77} T^{156} + 70 p^{78} T^{157} + p^{79} T^{158}$$
59 $$1 + 96 T + 6802 T^{2} + 355381 T^{3} + 15789204 T^{4} + 603501911 T^{5} + 350750865 p T^{6} + 642613364512 T^{7} + 311953535593 p T^{8} + 489524359518093 T^{9} + 12211419152964229 T^{10} + 287119840838423674 T^{11} + 6402434192988946190 T^{12} +$$$$13\!\cdots\!96$$$$T^{13} +$$$$27\!\cdots\!43$$$$T^{14} +$$$$53\!\cdots\!23$$$$T^{15} +$$$$10\!\cdots\!92$$$$T^{16} +$$$$18\!\cdots\!94$$$$T^{17} +$$$$31\!\cdots\!43$$$$T^{18} +$$$$53\!\cdots\!22$$$$T^{19} +$$$$86\!\cdots\!96$$$$T^{20} +$$$$13\!\cdots\!06$$$$T^{21} +$$$$21\!\cdots\!24$$$$T^{22} +$$$$31\!\cdots\!25$$$$T^{23} +$$$$46\!\cdots\!33$$$$T^{24} +$$$$66\!\cdots\!10$$$$T^{25} +$$$$92\!\cdots\!22$$$$T^{26} +$$$$12\!\cdots\!16$$$$T^{27} +$$$$16\!\cdots\!16$$$$T^{28} +$$$$37\!\cdots\!16$$$$p T^{29} +$$$$28\!\cdots\!48$$$$T^{30} +$$$$35\!\cdots\!72$$$$T^{31} +$$$$43\!\cdots\!42$$$$T^{32} +$$$$52\!\cdots\!16$$$$T^{33} +$$$$62\!\cdots\!35$$$$T^{34} +$$$$72\!\cdots\!22$$$$T^{35} +$$$$83\!\cdots\!28$$$$T^{36} +$$$$94\!\cdots\!26$$$$T^{37} +$$$$10\!\cdots\!63$$$$T^{38} +$$$$11\!\cdots\!17$$$$T^{39} +$$$$12\!\cdots\!07$$$$T^{40} +$$$$13\!\cdots\!61$$$$T^{41} +$$$$14\!\cdots\!20$$$$T^{42} +$$$$14\!\cdots\!58$$$$T^{43} +$$$$14\!\cdots\!44$$$$T^{44} +$$$$15\!\cdots\!08$$$$T^{45} +$$$$15\!\cdots\!84$$$$T^{46} +$$$$14\!\cdots\!72$$$$T^{47} +$$$$14\!\cdots\!56$$$$T^{48} +$$$$13\!\cdots\!72$$$$T^{49} +$$$$13\!\cdots\!37$$$$T^{50} +$$$$12\!\cdots\!53$$$$T^{51} +$$$$11\!\cdots\!38$$$$T^{52} +$$$$10\!\cdots\!27$$$$T^{53} +$$$$98\!\cdots\!39$$$$T^{54} +$$$$88\!\cdots\!26$$$$T^{55} +$$$$13\!\cdots\!36$$$$p T^{56} +$$$$70\!\cdots\!80$$$$T^{57} +$$$$62\!\cdots\!58$$$$T^{58} +$$$$54\!\cdots\!49$$$$T^{59} +$$$$46\!\cdots\!34$$$$T^{60} +$$$$39\!\cdots\!30$$$$T^{61} +$$$$33\!\cdots\!08$$$$T^{62} +$$$$28\!\cdots\!43$$$$T^{63} +$$$$23\!\cdots\!88$$$$T^{64} +$$$$19\!\cdots\!04$$$$T^{65} +$$$$16\!\cdots\!84$$$$T^{66} +$$$$13\!\cdots\!09$$$$T^{67} +$$$$10\!\cdots\!61$$$$T^{68} +$$$$88\!\cdots\!37$$$$T^{69} +$$$$71\!\cdots\!30$$$$T^{70} +$$$$56\!\cdots\!66$$$$T^{71} +$$$$45\!\cdots\!09$$$$T^{72} +$$$$35\!\cdots\!20$$$$T^{73} +$$$$28\!\cdots\!25$$$$T^{74} +$$$$22\!\cdots\!47$$$$T^{75} +$$$$17\!\cdots\!08$$$$T^{76} +$$$$13\!\cdots\!61$$$$T^{77} +$$$$10\!\cdots\!97$$$$T^{78} +$$$$79\!\cdots\!70$$$$T^{79} +$$$$10\!\cdots\!97$$$$p T^{80} +$$$$13\!\cdots\!61$$$$p^{2} T^{81} +$$$$17\!\cdots\!08$$$$p^{3} T^{82} +$$$$22\!\cdots\!47$$$$p^{4} T^{83} +$$$$28\!\cdots\!25$$$$p^{5} T^{84} +$$$$35\!\cdots\!20$$$$p^{6} T^{85} +$$$$45\!\cdots\!09$$$$p^{7} T^{86} +$$$$56\!\cdots\!66$$$$p^{8} T^{87} +$$$$71\!\cdots\!30$$$$p^{9} T^{88} +$$$$88\!\cdots\!37$$$$p^{10} T^{89} +$$$$10\!\cdots\!61$$$$p^{11} T^{90} +$$$$13\!\cdots\!09$$$$p^{12} T^{91} +$$$$16\!\cdots\!84$$$$p^{13} T^{92} +$$$$19\!\cdots\!04$$$$p^{14} T^{93} +$$$$23\!\cdots\!88$$$$p^{15} T^{94} +$$$$28\!\cdots\!43$$$$p^{16} T^{95} +$$$$33\!\cdots\!08$$$$p^{17} T^{96} +$$$$39\!\cdots\!30$$$$p^{18} T^{97} +$$$$46\!\cdots\!34$$$$p^{19} T^{98} +$$$$54\!\cdots\!49$$$$p^{20} T^{99} +$$$$62\!\cdots\!58$$$$p^{21} T^{100} +$$$$70\!\cdots\!80$$$$p^{22} T^{101} +$$$$13\!\cdots\!36$$$$p^{24} T^{102} +$$$$88\!\cdots\!26$$$$p^{24} T^{103} +$$$$98\!\cdots\!39$$$$p^{25} T^{104} +$$$$10\!\cdots\!27$$$$p^{26} T^{105} +$$$$11\!\cdots\!38$$$$p^{27} T^{106} +$$$$12\!\cdots\!53$$$$p^{28} T^{107} +$$$$13\!\cdots\!37$$$$p^{29} T^{108} +$$$$13\!\cdots\!72$$$$p^{30} T^{109} +$$$$14\!\cdots\!56$$$$p^{31} T^{110} +$$$$14\!\cdots\!72$$$$p^{32} T^{111} +$$$$15\!\cdots\!84$$$$p^{33} T^{112} +$$$$15\!\cdots\!08$$$$p^{34} T^{113} +$$$$14\!\cdots\!44$$$$p^{35} T^{114} +$$$$14\!\cdots\!58$$$$p^{36} T^{115} +$$$$14\!\cdots\!20$$$$p^{37} T^{116} +$$$$13\!\cdots\!61$$$$p^{38} T^{117} +$$$$12\!\cdots\!07$$$$p^{39} T^{118} +$$$$11\!\cdots\!17$$$$p^{40} T^{119} +$$$$10\!\cdots\!63$$$$p^{41} T^{120} +$$$$94\!\cdots\!26$$$$p^{42} T^{121} +$$$$83\!\cdots\!28$$$$p^{43} T^{122} +$$$$72\!\cdots\!22$$$$p^{44} T^{123} +$$$$62\!\cdots\!35$$$$p^{45} T^{124} +$$$$52\!\cdots\!16$$$$p^{46} T^{125} +$$$$43\!\cdots\!42$$$$p^{47} T^{126} +$$$$35\!\cdots\!72$$$$p^{48} T^{127} +$$$$28\!\cdots\!48$$$$p^{49} T^{128} +$$$$37\!\cdots\!16$$$$p^{51} T^{129} +$$$$16\!\cdots\!16$$$$p^{51} T^{130} +$$$$12\!\cdots\!16$$$$p^{52} T^{131} +$$$$92\!\cdots\!22$$$$p^{53} T^{132} +$$$$66\!\cdots\!10$$$$p^{54} T^{133} +$$$$46\!\cdots\!33$$$$p^{55} T^{134} +$$$$31\!\cdots\!25$$$$p^{56} T^{135} +$$$$21\!\cdots\!24$$$$p^{57} T^{136} +$$$$13\!\cdots\!06$$$$p^{58} T^{137} +$$$$86\!\cdots\!96$$$$p^{59} T^{138} +$$$$53\!\cdots\!22$$$$p^{60} T^{139} +$$$$31\!\cdots\!43$$$$p^{61} T^{140} +$$$$18\!\cdots\!94$$$$p^{62} T^{141} +$$$$10\!\cdots\!92$$$$p^{63} T^{142} +$$$$53\!\cdots\!23$$$$p^{64} T^{143} +$$$$27\!\cdots\!43$$$$p^{65} T^{144} +$$$$13\!\cdots\!96$$$$p^{66} T^{145} + 6402434192988946190 p^{67} T^{146} + 287119840838423674 p^{68} T^{147} + 12211419152964229 p^{69} T^{148} + 489524359518093 p^{70} T^{149} + 311953535593 p^{72} T^{150} + 642613364512 p^{72} T^{151} + 350750865 p^{74} T^{152} + 603501911 p^{74} T^{153} + 15789204 p^{75} T^{154} + 355381 p^{76} T^{155} + 6802 p^{77} T^{156} + 96 p^{78} T^{157} + p^{79} T^{158}$$
61 $$1 + 21 T + 2490 T^{2} + 49133 T^{3} + 50823 p T^{4} + 57733425 T^{5} + 2573403037 T^{6} + 45409977051 T^{7} + 1602221229828 T^{8} + 26887749094468 T^{9} + 798163232055444 T^{10} + 12780385912746908 T^{11} + 331419902938337546 T^{12} + 5078613827273129645 T^{13} +$$$$11\!\cdots\!53$$$$T^{14} +$$$$17\!\cdots\!10$$$$T^{15} +$$$$36\!\cdots\!96$$$$T^{16} +$$$$52\!\cdots\!94$$$$T^{17} +$$$$10\!\cdots\!99$$$$T^{18} +$$$$13\!\cdots\!03$$$$T^{19} +$$$$25\!\cdots\!09$$$$T^{20} +$$$$33\!\cdots\!10$$$$T^{21} +$$$$57\!\cdots\!06$$$$T^{22} +$$$$12\!\cdots\!29$$$$p T^{23} +$$$$12\!\cdots\!94$$$$T^{24} +$$$$14\!\cdots\!86$$$$T^{25} +$$$$23\!\cdots\!36$$$$T^{26} +$$$$27\!\cdots\!01$$$$T^{27} +$$$$41\!\cdots\!87$$$$T^{28} +$$$$48\!\cdots\!21$$$$T^{29} +$$$$69\!\cdots\!93$$$$T^{30} +$$$$78\!\cdots\!53$$$$T^{31} +$$$$10\!\cdots\!77$$$$T^{32} +$$$$11\!\cdots\!03$$$$T^{33} +$$$$15\!\cdots\!40$$$$T^{34} +$$$$17\!\cdots\!91$$$$T^{35} +$$$$22\!\cdots\!81$$$$T^{36} +$$$$23\!\cdots\!30$$$$T^{37} +$$$$29\!\cdots\!81$$$$T^{38} +$$$$30\!\cdots\!31$$$$T^{39} +$$$$36\!\cdots\!64$$$$T^{40} +$$$$37\!\cdots\!54$$$$T^{41} +$$$$44\!\cdots\!36$$$$T^{42} +$$$$43\!\cdots\!03$$$$T^{43} +$$$$50\!\cdots\!05$$$$T^{44} +$$$$48\!\cdots\!43$$$$T^{45} +$$$$55\!\cdots\!91$$$$T^{46} +$$$$52\!\cdots\!08$$$$T^{47} +$$$$57\!\cdots\!58$$$$T^{48} +$$$$53\!\cdots\!78$$$$T^{49} +$$$$58\!\cdots\!11$$$$T^{50} +$$$$53\!\cdots\!11$$$$T^{51} +$$$$56\!\cdots\!72$$$$T^{52} +$$$$50\!\cdots\!68$$$$T^{53} +$$$$52\!\cdots\!82$$$$T^{54} +$$$$46\!\cdots\!45$$$$T^{55} +$$$$47\!\cdots\!97$$$$T^{56} +$$$$66\!\cdots\!59$$$$p T^{57} +$$$$40\!\cdots\!61$$$$T^{58} +$$$$34\!\cdots\!80$$$$T^{59} +$$$$34\!\cdots\!52$$$$T^{60} +$$$$28\!\cdots\!43$$$$T^{61} +$$$$27\!\cdots\!34$$$$T^{62} +$$$$22\!\cdots\!13$$$$T^{63} +$$$$21\!\cdots\!09$$$$T^{64} +$$$$17\!\cdots\!87$$$$T^{65} +$$$$16\!\cdots\!82$$$$T^{66} +$$$$13\!\cdots\!63$$$$T^{67} +$$$$12\!\cdots\!60$$$$T^{68} +$$$$93\!\cdots\!08$$$$T^{69} +$$$$85\!\cdots\!04$$$$T^{70} +$$$$65\!\cdots\!23$$$$T^{71} +$$$$58\!\cdots\!78$$$$T^{72} +$$$$44\!\cdots\!06$$$$T^{73} +$$$$39\!\cdots\!42$$$$T^{74} +$$$$29\!\cdots\!98$$$$T^{75} +$$$$25\!\cdots\!90$$$$T^{76} +$$$$18\!\cdots\!28$$$$T^{77} +$$$$16\!\cdots\!64$$$$T^{78} +$$$$11\!\cdots\!10$$$$T^{79} +$$$$16\!\cdots\!64$$$$p T^{80} +$$$$18\!\cdots\!28$$$$p^{2} T^{81} +$$$$25\!\cdots\!90$$$$p^{3} T^{82} +$$$$29\!\cdots\!98$$$$p^{4} T^{83} +$$$$39\!\cdots\!42$$$$p^{5} T^{84} +$$$$44\!\cdots\!06$$$$p^{6} T^{85} +$$$$58\!\cdots\!78$$$$p^{7} T^{86} +$$$$65\!\cdots\!23$$$$p^{8} T^{87} +$$$$85\!\cdots\!04$$$$p^{9} T^{88} +$$$$93\!\cdots\!08$$$$p^{10} T^{89} +$$$$12\!\cdots\!60$$$$p^{11} T^{90} +$$$$13\!\cdots\!63$$$$p^{12} T^{91} +$$$$16\!\cdots\!82$$$$p^{13} T^{92} +$$$$17\!\cdots\!87$$$$p^{14} T^{93} +$$$$21\!\cdots\!09$$$$p^{15} T^{94} +$$$$22\!\cdots\!13$$$$p^{16} T^{95} +$$$$27\!\cdots\!34$$$$p^{17} T^{96} +$$$$28\!\cdots\!43$$$$p^{18} T^{97} +$$$$34\!\cdots\!52$$$$p^{19} T^{98} +$$$$34\!\cdots\!80$$$$p^{20} T^{99} +$$$$40\!\cdots\!61$$$$p^{21} T^{100} +$$$$66\!\cdots\!59$$$$p^{23} T^{101} +$$$$47\!\cdots\!97$$$$p^{23} T^{102} +$$$$46\!\cdots\!45$$$$p^{24} T^{103} +$$$$52\!\cdots\!82$$$$p^{25} T^{104} +$$$$50\!\cdots\!68$$$$p^{26} T^{105} +$$$$56\!\cdots\!72$$$$p^{27} T^{106} +$$$$53\!\cdots\!11$$$$p^{28} T^{107} +$$$$58\!\cdots\!11$$$$p^{29} T^{108} +$$$$53\!\cdots\!78$$$$p^{30} T^{109} +$$$$57\!\cdots\!58$$$$p^{31} T^{110} +$$$$52\!\cdots\!08$$$$p^{32} T^{111} +$$$$55\!\cdots\!91$$$$p^{33} T^{112} +$$$$48\!\cdots\!43$$$$p^{34} T^{113} +$$$$50\!\cdots\!05$$$$p^{35} T^{114} +$$$$43\!\cdots\!03$$$$p^{36} T^{115} +$$$$44\!\cdots\!36$$$$p^{37} T^{116} +$$$$37\!\cdots\!54$$$$p^{38} T^{117} +$$$$36\!\cdots\!64$$$$p^{39} T^{118} +$$$$30\!\cdots\!31$$$$p^{40} T^{119} +$$$$29\!\cdots\!81$$$$p^{41} T^{120} +$$$$23\!\cdots\!30$$$$p^{42} T^{121} +$$$$22\!\cdots\!81$$$$p^{43} T^{122} +$$$$17\!\cdots\!91$$$$p^{44} T^{123} +$$$$15\!\cdots\!40$$$$p^{45} T^{124} +$$$$11\!\cdots\!03$$$$p^{46} T^{125} +$$$$10\!\cdots\!77$$$$p^{47} T^{126} +$$$$78\!\cdots\!53$$$$p^{48} T^{127} +$$$$69\!\cdots\!93$$$$p^{49} T^{128} +$$$$48\!\cdots\!21$$$$p^{50} T^{129} +$$$$41\!\cdots\!87$$$$p^{51} T^{130} +$$$$27\!\cdots\!01$$$$p^{52} T^{131} +$$$$23\!\cdots\!36$$$$p^{53} T^{132} +$$$$14\!\cdots\!86$$$$p^{54} T^{133} +$$$$12\!\cdots\!94$$$$p^{55} T^{134} +$$$$12\!\cdots\!29$$$$p^{57} T^{135} +$$$$57\!\cdots\!06$$$$p^{57} T^{136} +$$$$33\!\cdots\!10$$$$p^{58} T^{137} +$$$$25\!\cdots\!09$$$$p^{59} T^{138} +$$$$13\!\cdots\!03$$$$p^{60} T^{139} +$$$$10\!\cdots\!99$$$$p^{61} T^{140} +$$$$52\!\cdots\!94$$$$p^{62} T^{141} +$$$$36\!\cdots\!96$$$$p^{63} T^{142} +$$$$17\!\cdots\!10$$$$p^{64} T^{143} +$$$$11\!\cdots\!53$$$$p^{65} T^{144} + 5078613827273129645 p^{66} T^{145} + 331419902938337546 p^{67} T^{146} + 12780385912746908 p^{68} T^{147} + 798163232055444 p^{69} T^{148} + 26887749094468 p^{70} T^{149} + 1602221229828 p^{71} T^{150} + 45409977051 p^{72} T^{151} + 2573403037 p^{73} T^{152} + 57733425 p^{74} T^{153} + 50823 p^{76} T^{154} + 49133 p^{76} T^{155} + 2490 p^{77} T^{156} + 21 p^{78} T^{157} + p^{79} T^{158}$$
67 $$1 + 44 T + 3686 T^{2} + 133193 T^{3} + 6443423 T^{4} + 199666920 T^{5} + 7230325399 T^{6} + 197687327746 T^{7} + 5910235131976 T^{8} + 145463221439670 T^{9} + 3774544704206526 T^{10} + 84869457641847425 T^{11} + 1969094066061511523 T^{12} + 40906453772766177644 T^{13} +$$$$86\!\cdots\!13$$$$T^{14} +$$$$16\!\cdots\!83$$$$T^{15} +$$$$32\!\cdots\!71$$$$T^{16} +$$$$59\!\cdots\!23$$$$T^{17} +$$$$10\!\cdots\!07$$$$T^{18} +$$$$18\!\cdots\!66$$$$T^{19} +$$$$32\!\cdots\!22$$$$T^{20} +$$$$52\!\cdots\!96$$$$T^{21} +$$$$84\!\cdots\!48$$$$T^{22} +$$$$13\!\cdots\!40$$$$T^{23} +$$$$20\!\cdots\!49$$$$T^{24} +$$$$30\!\cdots\!48$$$$T^{25} +$$$$44\!\cdots\!13$$$$T^{26} +$$$$63\!\cdots\!59$$$$T^{27} +$$$$90\!\cdots\!08$$$$T^{28} +$$$$12\!\cdots\!39$$$$T^{29} +$$$$16\!\cdots\!94$$$$T^{30} +$$$$22\!\cdots\!94$$$$T^{31} +$$$$29\!\cdots\!75$$$$T^{32} +$$$$37\!\cdots\!74$$$$T^{33} +$$$$47\!\cdots\!57$$$$T^{34} +$$$$59\!\cdots\!54$$$$T^{35} +$$$$72\!\cdots\!70$$$$T^{36} +$$$$87\!\cdots\!50$$$$T^{37} +$$$$10\!\cdots\!84$$$$T^{38} +$$$$12\!\cdots\!24$$$$T^{39} +$$$$14\!\cdots\!82$$$$T^{40} +$$$$16\!\cdots\!34$$$$T^{41} +$$$$18\!\cdots\!00$$$$T^{42} +$$$$20\!\cdots\!84$$$$T^{43} +$$$$22\!\cdots\!47$$$$T^{44} +$$$$24\!\cdots\!48$$$$T^{45} +$$$$25\!\cdots\!09$$$$T^{46} +$$$$27\!\cdots\!79$$$$T^{47} +$$$$28\!\cdots\!58$$$$T^{48} +$$$$29\!\cdots\!35$$$$T^{49} +$$$$30\!\cdots\!92$$$$T^{50} +$$$$31\!\cdots\!11$$$$T^{51} +$$$$31\!\cdots\!32$$$$T^{52} +$$$$31\!\cdots\!79$$$$T^{53} +$$$$31\!\cdots\!50$$$$T^{54} +$$$$30\!\cdots\!06$$$$T^{55} +$$$$29\!\cdots\!55$$$$T^{56} +$$$$28\!\cdots\!56$$$$T^{57} +$$$$27\!\cdots\!23$$$$T^{58} +$$$$25\!\cdots\!46$$$$T^{59} +$$$$24\!\cdots\!42$$$$T^{60} +$$$$22\!\cdots\!77$$$$T^{61} +$$$$21\!\cdots\!24$$$$T^{62} +$$$$19\!\cdots\!75$$$$T^{63} +$$$$17\!\cdots\!00$$$$T^{64} +$$$$15\!\cdots\!05$$$$T^{65} +$$$$14\!\cdots\!40$$$$T^{66} +$$$$12\!\cdots\!26$$$$T^{67} +$$$$11\!\cdots\!61$$$$T^{68} +$$$$98\!\cdots\!61$$$$T^{69} +$$$$85\!\cdots\!53$$$$T^{70} +$$$$74\!\cdots\!47$$$$T^{71} +$$$$64\!\cdots\!14$$$$T^{72} +$$$$54\!\cdots\!78$$$$T^{73} +$$$$46\!\cdots\!18$$$$T^{74} +$$$$39\!\cdots\!20$$$$T^{75} +$$$$32\!\cdots\!70$$$$T^{76} +$$$$27\!\cdots\!95$$$$T^{77} +$$$$22\!\cdots\!79$$$$T^{78} +$$$$18\!\cdots\!56$$$$T^{79} +$$$$22\!\cdots\!79$$$$p T^{80} +$$$$27\!\cdots\!95$$$$p^{2} T^{81} +$$$$32\!\cdots\!70$$$$p^{3} T^{82} +$$$$39\!\cdots\!20$$$$p^{4} T^{83} +$$$$46\!\cdots\!18$$$$p^{5} T^{84} +$$$$54\!\cdots\!78$$$$p^{6} T^{85} +$$$$64\!\cdots\!14$$$$p^{7} T^{86} +$$$$74\!\cdots\!47$$$$p^{8} T^{87} +$$$$85\!\cdots\!53$$$$p^{9} T^{88} +$$$$98\!\cdots\!61$$$$p^{10} T^{89} +$$$$11\!\cdots\!61$$$$p^{11} T^{90} +$$$$12\!\cdots\!26$$$$p^{12} T^{91} +$$$$14\!\cdots\!40$$$$p^{13} T^{92} +$$$$15\!\cdots\!05$$$$p^{14} T^{93} +$$$$17\!\cdots\!00$$$$p^{15} T^{94} +$$$$19\!\cdots\!75$$$$p^{16} T^{95} +$$$$21\!\cdots\!24$$$$p^{17} T^{96} +$$$$22\!\cdots\!77$$$$p^{18} T^{97} +$$$$24\!\cdots\!42$$$$p^{19} T^{98} +$$$$25\!\cdots\!46$$$$p^{20} T^{99} +$$$$27\!\cdots\!23$$$$p^{21} T^{100} +$$$$28\!\cdots\!56$$$$p^{22} T^{101} +$$$$29\!\cdots\!55$$$$p^{23} T^{102} +$$$$30\!\cdots\!06$$$$p^{24} T^{103} +$$$$31\!\cdots\!50$$$$p^{25} T^{104} +$$$$31\!\cdots\!79$$$$p^{26} T^{105} +$$$$31\!\cdots\!32$$$$p^{27} T^{106} +$$$$31\!\cdots\!11$$$$p^{28} T^{107} +$$$$30\!\cdots\!92$$$$p^{29} T^{108} +$$$$29\!\cdots\!35$$$$p^{30} T^{109} +$$$$28\!\cdots\!58$$$$p^{31} T^{110} +$$$$27\!\cdots\!79$$$$p^{32} T^{111} +$$$$25\!\cdots\!09$$$$p^{33} T^{112} +$$$$24\!\cdots\!48$$$$p^{34} T^{113} +$$$$22\!\cdots\!47$$$$p^{35} T^{114} +$$$$20\!\cdots\!84$$$$p^{36} T^{115} +$$$$18\!\cdots\!00$$$$p^{37} T^{116} +$$$$16\!\cdots\!34$$$$p^{38} T^{117} +$$$$14\!\cdots\!82$$$$p^{39} T^{118} +$$$$12\!\cdots\!24$$$$p^{40} T^{119} +$$$$10\!\cdots\!84$$$$p^{41} T^{120} +$$$$87\!\cdots\!50$$$$p^{42} T^{121} +$$$$72\!\cdots\!70$$$$p^{43} T^{122} +$$$$59\!\cdots\!54$$$$p^{44} T^{123} +$$$$47\!\cdots\!57$$$$p^{45} T^{124} +$$$$37\!\cdots\!74$$$$p^{46} T^{125} +$$$$29\!\cdots\!75$$$$p^{47} T^{126} +$$$$22\!\cdots\!94$$$$p^{48} T^{127} +$$$$16\!\cdots\!94$$$$p^{49} T^{128} +$$$$12\!\cdots\!39$$$$p^{50} T^{129} +$$$$90\!\cdots\!08$$$$p^{51} T^{130} +$$$$63\!\cdots\!59$$$$p^{52} T^{131} +$$$$44\!\cdots\!13$$$$p^{53} T^{132} +$$$$30\!\cdots\!48$$$$p^{54} T^{133} +$$$$20\!\cdots\!49$$$$p^{55} T^{134} +$$$$13\!\cdots\!40$$$$p^{56} T^{135} +$$$$84\!\cdots\!48$$$$p^{57} T^{136} +$$$$52\!\cdots\!96$$$$p^{58} T^{137} +$$$$32\!\cdots\!22$$$$p^{59} T^{138} +$$$$18\!\cdots\!66$$$$p^{60} T^{139} +$$$$10\!\cdots\!07$$$$p^{61} T^{140} +$$$$59\!\cdots\!23$$$$p^{62} T^{141} +$$$$32\!\cdots\!71$$$$p^{63} T^{142} +$$$$16\!\cdots\!83$$$$p^{64} T^{143} +$$$$86\!\cdots\!13$$$$p^{65} T^{144} + 40906453772766177644 p^{66} T^{145} + 1969094066061511523 p^{67} T^{146} + 84869457641847425 p^{68} T^{147} + 3774544704206526 p^{69} T^{148} + 145463221439670 p^{70} T^{149} + 5910235131976 p^{71} T^{150} + 197687327746 p^{72} T^{151} + 7230325399 p^{73} T^{152} + 199666920 p^{74} T^{153} + 6443423 p^{75} T^{154} + 133193 p^{76} T^{155} + 3686 p^{77} T^{156} + 44 p^{78} T^{157} + p^{79} T^{158}$$
71 $$1 + 55 T + 4322 T^{2} + 179821 T^{3} + 8435974 T^{4} + 288446364 T^{5} + 10314049065 T^{6} + 303667665179 T^{7} + 9061942469005 T^{8} + 236649850924446 T^{9} + 6172557455938269 T^{10} + 145918816486423283 T^{11} + 3420173946416943149 T^{12} + 74280864544070033520 T^{13} +$$$$15\!\cdots\!96$$$$T^{14} +$$$$32\!\cdots\!03$$$$T^{15} +$$$$63\!\cdots\!38$$$$T^{16} +$$$$12\!\cdots\!16$$$$T^{17} +$$$$22\!\cdots\!09$$$$T^{18} +$$$$40\!\cdots\!23$$$$T^{19} +$$$$70\!\cdots\!95$$$$T^{20} +$$$$11\!\cdots\!09$$$$T^{21} +$$$$19\!\cdots\!02$$$$T^{22} +$$$$32\!\cdots\!06$$$$T^{23} +$$$$51\!\cdots\!06$$$$T^{24} +$$$$79\!\cdots\!56$$$$T^{25} +$$$$12\!\cdots\!98$$$$T^{26} +$$$$18\!\cdots\!60$$$$T^{27} +$$$$26\!\cdots\!62$$$$T^{28} +$$$$37\!\cdots\!86$$$$T^{29} +$$$$53\!\cdots\!67$$$$T^{30} +$$$$74\!\cdots\!12$$$$T^{31} +$$$$10\!\cdots\!12$$$$T^{32} +$$$$13\!\cdots\!92$$$$T^{33} +$$$$17\!\cdots\!71$$$$T^{34} +$$$$23\!\cdots\!95$$$$T^{35} +$$$$30\!\cdots\!52$$$$T^{36} +$$$$37\!\cdots\!27$$$$T^{37} +$$$$47\!\cdots\!00$$$$T^{38} +$$$$58\!\cdots\!82$$$$T^{39} +$$$$71\!\cdots\!44$$$$T^{40} +$$$$85\!\cdots\!36$$$$T^{41} +$$$$10\!\cdots\!09$$$$T^{42} +$$$$11\!\cdots\!07$$$$T^{43} +$$$$13\!\cdots\!84$$$$T^{44} +$$$$15\!\cdots\!45$$$$T^{45} +$$$$17\!\cdots\!00$$$$T^{46} +$$$$19\!\cdots\!58$$$$T^{47} +$$$$22\!\cdots\!56$$$$T^{48} +$$$$24\!\cdots\!18$$$$T^{49} +$$$$26\!\cdots\!46$$$$T^{50} +$$$$28\!\cdots\!92$$$$T^{51} +$$$$29\!\cdots\!66$$$$T^{52} +$$$$31\!\cdots\!80$$$$T^{53} +$$$$32\!\cdots\!21$$$$T^{54} +$$$$33\!\cdots\!96$$$$T^{55} +$$$$34\!\cdots\!71$$$$T^{56} +$$$$35\!\cdots\!68$$$$T^{57} +$$$$35\!\cdots\!60$$$$T^{58} +$$$$35\!\cdots\!58$$$$T^{59} +$$$$34\!\cdots\!69$$$$T^{60} +$$$$34\!\cdots\!84$$$$T^{61} +$$$$33\!\cdots\!58$$$$T^{62} +$$$$31\!\cdots\!44$$$$T^{63} +$$$$30\!\cdots\!73$$$$T^{64} +$$$$28\!\cdots\!04$$$$T^{65} +$$$$26\!\cdots\!10$$$$T^{66} +$$$$25\!\cdots\!75$$$$T^{67} +$$$$23\!\cdots\!33$$$$T^{68} +$$$$21\!\cdots\!85$$$$T^{69} +$$$$19\!\cdots\!09$$$$T^{70} +$$$$17\!\cdots\!02$$$$T^{71} +$$$$15\!\cdots\!48$$$$T^{72} +$$$$13\!\cdots\!98$$$$T^{73} +$$$$12\!\cdots\!24$$$$T^{74} +$$$$10\!\cdots\!87$$$$T^{75} +$$$$91\!\cdots\!53$$$$T^{76} +$$$$78\!\cdots\!57$$$$T^{77} +$$$$93\!\cdots\!05$$$$p T^{78} +$$$$56\!\cdots\!54$$$$T^{79} +$$$$93\!\cdots\!05$$$$p^{2} T^{80} +$$$$78\!\cdots\!57$$$$p^{2} T^{81} +$$$$91\!\cdots\!53$$$$p^{3} T^{82} +$$$$10\!\cdots\!87$$$$p^{4} T^{83} +$$$$12\!\cdots\!24$$$$p^{5} T^{84} +$$$$13\!\cdots\!98$$$$p^{6} T^{85} +$$$$15\!\cdots\!48$$$$p^{7} T^{86} +$$$$17\!\cdots\!02$$$$p^{8} T^{87} +$$$$19\!\cdots\!09$$$$p^{9} T^{88} +$$$$21\!\cdots\!85$$$$p^{10} T^{89} +$$$$23\!\cdots\!33$$$$p^{11} T^{90} +$$$$25\!\cdots\!75$$$$p^{12} T^{91} +$$$$26\!\cdots\!10$$$$p^{13} T^{92} +$$$$28\!\cdots\!04$$$$p^{14} T^{93} +$$$$30\!\cdots\!73$$$$p^{15} T^{94} +$$$$31\!\cdots\!44$$$$p^{16} T^{95} +$$$$33\!\cdots\!58$$$$p^{17} T^{96} +$$$$34\!\cdots\!84$$$$p^{18} T^{97} +$$$$34\!\cdots\!69$$$$p^{19} T^{98} +$$$$35\!\cdots\!58$$$$p^{20} T^{99} +$$$$35\!\cdots\!60$$$$p^{21} T^{100} +$$$$35\!\cdots\!68$$$$p^{22} T^{101} +$$$$34\!\cdots\!71$$$$p^{23} T^{102} +$$$$33\!\cdots\!96$$$$p^{24} T^{103} +$$$$32\!\cdots\!21$$$$p^{25} T^{104} +$$$$31\!\cdots\!80$$$$p^{26} T^{105} +$$$$29\!\cdots\!66$$$$p^{27} T^{106} +$$$$28\!\cdots\!92$$$$p^{28} T^{107} +$$$$26\!\cdots\!46$$$$p^{29} T^{108} +$$$$24\!\cdots\!18$$$$p^{30} T^{109} +$$$$22\!\cdots\!56$$$$p^{31} T^{110} +$$$$19\!\cdots\!58$$$$p^{32} T^{111} +$$$$17\!\cdots\!00$$$$p^{33} T^{112} +$$$$15\!\cdots\!45$$$$p^{34} T^{113} +$$$$13\!\cdots\!84$$$$p^{35} T^{114} +$$$$11\!\cdots\!07$$$$p^{36} T^{115} +$$$$10\!\cdots\!09$$$$p^{37} T^{116} +$$$$85\!\cdots\!36$$$$p^{38} T^{117} +$$$$71\!\cdots\!44$$$$p^{39} T^{118} +$$$$58\!\cdots\!82$$$$p^{40} T^{119} +$$$$47\!\cdots\!00$$$$p^{41} T^{120} +$$$$37\!\cdots\!27$$$$p^{42} T^{121} +$$$$30\!\cdots\!52$$$$p^{43} T^{122} +$$$$23\!\cdots\!95$$$$p^{44} T^{123} +$$$$17\!\cdots\!71$$$$p^{45} T^{124} +$$$$13\!\cdots\!92$$$$p^{46} T^{125} +$$$$10\!\cdots\!12$$$$p^{47} T^{126} +$$$$74\!\cdots\!12$$$$p^{48} T^{127} +$$$$53\!\cdots\!67$$$$p^{49} T^{128} +$$$$37\!\cdots\!86$$$$p^{50} T^{129} +$$$$26\!\cdots\!62$$$$p^{51} T^{130} +$$$$18\!\cdots\!60$$$$p^{52} T^{131} +$$$$12\!\cdots\!98$$$$p^{53} T^{132} +$$$$79\!\cdots\!56$$$$p^{54} T^{133} +$$$$51\!\cdots\!06$$$$p^{55} T^{134} +$$$$32\!\cdots\!06$$$$p^{56} T^{135} +$$$$19\!\cdots\!02$$$$p^{57} T^{136} +$$$$11\!\cdots\!09$$$$p^{58} T^{137} +$$$$70\!\cdots\!95$$$$p^{59} T^{138} +$$$$40\!\cdots\!23$$$$p^{60} T^{139} +$$$$22\!\cdots\!09$$$$p^{61} T^{140} +$$$$12\!\cdots\!16$$$$p^{62} T^{141} +$$$$63\!\cdots\!38$$$$p^{63} T^{142} +$$$$32\!\cdots\!03$$$$p^{64} T^{143} +$$$$15\!\cdots\!96$$$$p^{65} T^{144} + 74280864544070033520 p^{66} T^{145} + 3420173946416943149 p^{67} T^{146} + 145918816486423283 p^{68} T^{147} + 6172557455938269 p^{69} T^{148} + 236649850924446 p^{70} T^{149} + 9061942469005 p^{71} T^{150} + 303667665179 p^{72} T^{151} + 10314049065 p^{73} T^{152} + 288446364 p^{74} T^{153} + 8435974 p^{75} T^{154} + 179821 p^{76} T^{155} + 4322 p^{77} T^{156} + 55 p^{78} T^{157} + p^{79} T^{158}$$
73 $$1 + 27T + 3.34e3T^{2} + 8.41e4T^{3} + 5.54e6T^{4} + 1.30e8T^{5} + 6.09e9T^{6} + 1.35e11T^{7} + 4.99e12T^{8} + 1.04e14T^{9} + 3.26e15T^{10} + 6.49e16T^{11} + 1.76e18T^{12} + 3.34e19T^{13} + 8.14e20T^{14} + 1.47e22T^{15} + 3.27e23T^{16} + 5.66e24T^{17} + 1.16e26T^{18} + 1.93e27T^{19} + 3.70e28T^{20} + 5.93e29T^{21} + 1.06e31T^{22} + 1.65e32T^{23} + 2.81e33T^{24} + 4.19e34T^{25} + 6.83e35T^{26} + 9.84e36T^{27} + 1.53e38T^{28} + 2.14e39T^{29} + 3.19e40T^{30} + 4.33e41T^{31} + 6.23e42T^{32} + 8.20e43T^{33} + 1.13e45T^{34} + 1.46e46T^{35} + 1.96e47T^{36} + 2.45e48T^{37} + 3.19e49T^{38} + 3.88e50T^{39} + 4.92e51T^{40} + 5.85e52T^{41} + 7.20e53T^{42} + 8.37e54T^{43} + 1.00e56T^{44} + 1.14e57T^{45} + 1.33e58T^{46} + 1.48e59T^{47} + 1.70e60T^{48} + 1.85e61T^{49} + 2.07e62T^{50} + 2.21e63T^{51} + 2.42e64T^{52} + 2.54e65T^{53} + 2.72e66T^{54} + 2.80e67T^{55} + 2.94e68T^{56} + 2.97e69T^{57} + 3.07e70T^{58} + 3.04e71T^{59} + 3.08e72T^{60} + 3.01e73T^{61} + 2.99e74T^{62} + 2.87e75T^{63} + 2.81e76T^{64} + 2.65e77T^{65} + 2.55e78T^{66} + 2.37e79T^{67} + 2.24e80T^{68} + 2.05e81T^{69} + 1.90e82T^{70} + 1.71e83T^{71} + 1.57e84T^{72} + 1.39e85T^{73} + 1.26e86T^{74} + 1.10e87T^{75} + 9.77e87T^{76} + 8.40e88T^{77} + 7.35e89T^{78}+O(T^{79})$$
79 $$1 + 49T + 4.18e3T^{2} + 1.66e5T^{3} + 8.29e6T^{4} + 2.81e8T^{5} + 1.06e10T^{6} + 3.17e11T^{7} + 9.95e12T^{8} + 2.67e14T^{9} + 7.34e15T^{10} + 1.80e17T^{11} + 4.44e18T^{12} + 1.01e20T^{13} + 2.28e21T^{14} + 4.85e22T^{15} + 1.02e24T^{16} + 2.03e25T^{17} + 4.01e26T^{18} + 7.58e27T^{19} + 1.41e29T^{20} + 2.54e30T^{21} + 4.49e31T^{22} + 7.72e32T^{23} + 1.30e34T^{24} + 2.15e35T^{25} + 3.48e36T^{26} + 5.51e37T^{27} + 8.60e38T^{28} + 1.31e40T^{29} + 1.97e41T^{30} + 2.91e42T^{31} + 4.23e43T^{32} + 6.04e44T^{33} + 8.51e45T^{34} + 1.17e47T^{35} + 1.61e48T^{36} + 2.16e49T^{37} + 2.88e50T^{38} + 3.77e51T^{39} + 4.87e52T^{40} + 6.22e53T^{41} + 7.83e54T^{42} + 9.74e55T^{43} + 1.19e57T^{44} + 1.45e58T^{45} + 1.74e59T^{46} + 2.07e60T^{47} + 2.43e61T^{48} + 2.82e62T^{49} + 3.24e63T^{50} + 3.68e64T^{51} + 4.14e65T^{52} + 4.60e66T^{53} + 5.07e67T^{54} + 5.53e68T^{55} + 5.98e69T^{56} + 6.39e70T^{57} + 6.78e71T^{58} + 7.12e72T^{59} + 7.41e73T^{60} + 7.64e74T^{61} + 7.81e75T^{62} + 7.91e76T^{63} + 7.95e77T^{64} + 7.92e78T^{65} + 7.82e79T^{66} + 7.66e80T^{67} + 7.44e81T^{68} + 7.17e82T^{69} + 6.86e83T^{70} + 6.51e84T^{71} + 6.12e85T^{72} + 5.72e86T^{73} + 5.30e87T^{74} + 4.87e88T^{75} + 4.45e89T^{76} + 4.03e90T^{77}+O(T^{78})$$
83 $$1 + 52T + 4.49e3T^{2} + 1.85e5T^{3} + 9.39e6T^{4} + 3.25e8T^{5} + 1.25e10T^{6} + 3.78e11T^{7} + 1.20e13T^{8} + 3.26e14T^{9} + 9.09e15T^{10} + 2.23e17T^{11} + 5.58e18T^{12} + 1.26e20T^{13} + 2.88e21T^{14} + 6.08e22T^{15} + 1.28e24T^{16} + 2.53e25T^{17} + 5.00e26T^{18} + 9.34e27T^{19} + 1.73e29T^{20} + 3.06e30T^{21} + 5.39e31T^{22} + 9.09e32T^{23} + 1.52e34T^{24} + 2.44e35T^{25} + 3.91e36T^{26} + 6.03e37T^{27} + 9.25e38T^{28} + 1.37e40T^{29} + 2.02e41T^{30} + 2.88e42T^{31} + 4.09e43T^{32} + 5.65e44T^{33} + 7.74e45T^{34} + 1.03e47T^{35} + 1.37e48T^{36} + 1.77e49T^{37} + 2.28e50T^{38} + 2.86e51T^{39} + 3.58e52T^{40} + 4.37e53T^{41} + 5.31e54T^{42} + 6.32e55T^{43} + 7.48e56T^{44} + 8.68e57T^{45} + 1.00e59T^{46} + 1.13e60T^{47} + 1.28e61T^{48} + 1.42e62T^{49} + 1.58e63T^{50} + 1.71e64T^{51} + 1.86e65T^{52} + 1.98e66T^{53} + 2.11e67T^{54} + 2.21e68T^{55} + 2.32e69T^{56} + 2.39e70T^{57} + 2.46e71T^{58} + 2.50e72T^{59} + 2.54e73T^{60} + 2.54e74T^{61} + 2.55e75T^{62} + 2.51e76T^{63} + 2.49e77T^{64} + 2.42e78T^{65} + 2.37e79T^{66} + 2.28e80T^{67} + 2.21e81T^{68} + 2.10e82T^{69} + 2.02e83T^{70} + 1.90e84T^{71} + 1.80e85T^{72} + 1.68e86T^{73} + 1.58e87T^{74} + 1.46e88T^{75} + 1.36e89T^{76}+O(T^{77})$$
89 $$1 + 68T + 5.99e3T^{2} + 3.00e5T^{3} + 1.60e7T^{4} + 6.50e8T^{5} + 2.66e10T^{6} + 9.25e11T^{7} + 3.17e13T^{8} + 9.73e14T^{9} + 2.92e16T^{10} + 8.08e17T^{11} + 2.18e19T^{12} + 5.53e20T^{13} + 1.37e22T^{14} + 3.21e23T^{15} + 7.38e24T^{16} + 1.62e26T^{17} + 3.47e27T^{18} + 7.19e28T^{19} + 1.45e30T^{20} + 2.84e31T^{21} + 5.46e32T^{22} + 1.01e34T^{23} + 1.86e35T^{24} + 3.31e36T^{25} + 5.78e37T^{26} + 9.86e38T^{27} + 1.65e40T^{28} + 2.71e41T^{29} + 4.37e42T^{30} + 6.90e43T^{31} + 1.07e45T^{32} + 1.63e46T^{33} + 2.46e47T^{34} + 3.63e48T^{35} + 5.29e49T^{36} + 7.58e50T^{37} + 1.07e52T^{38} + 1.48e53T^{39} + 2.04e54T^{40} + 2.75e55T^{41} + 3.68e56T^{42} + 4.84e57T^{43} + 6.30e58T^{44} + 8.08e59T^{45} + 1.02e61T^{46} + 1.28e62T^{47} + 1.58e63T^{48} + 1.94e64T^{49} + 2.35e65T^{50} + 2.81e66T^{51} + 3.33e67T^{52} + 3.90e68T^{53} + 4.53e69T^{54} + 5.20e70T^{55} + 5.92e71T^{56} + 6.66e72T^{57} + 7.44e73T^{58} + 8.22e74T^{59} + 9.01e75T^{60} + 9.79e76T^{61} + 1.05e78T^{62} + 1.12e79T^{63} + 1.19e80T^{64} + 1.25e81T^{65} + 1.30e82T^{66} + 1.34e83T^{67} + 1.38e84T^{68} + 1.40e85T^{69} + 1.42e86T^{70} + 1.42e87T^{71} + 1.42e88T^{72} + 1.40e89T^{73} + 1.37e90T^{74} + 1.34e91T^{75}+O(T^{76})$$
97 $$1 + 57T + 5.73e3T^{2} + 2.59e5T^{3} + 1.52e7T^{4} + 5.81e8T^{5} + 2.56e10T^{6} + 8.55e11T^{7} + 3.11e13T^{8} + 9.31e14T^{9} + 2.94e16T^{10} + 8.02e17T^{11} + 2.27e19T^{12} + 5.69e20T^{13} + 1.47e22T^{14} + 3.44e23T^{15} + 8.21e24T^{16} + 1.80e26T^{17} + 4.02e27T^{18} + 8.34e28T^{19} + 1.75e30T^{20} + 3.45e31T^{21} + 6.87e32T^{22} + 1.29e34T^{23} + 2.45e35T^{24} + 4.42e36T^{25} + 8.01e37T^{26} + 1.38e39T^{27} + 2.41e40T^{28} + 4.03e41T^{29} + 6.77e42T^{30} + 1.09e44T^{31} + 1.77e45T^{32} + 2.76e46T^{33} + 4.33e47T^{34} + 6.57e48T^{35} + 1.00e50T^{36} + 1.47e51T^{37} + 2.17e52T^{38} + 3.12e53T^{39} + 4.49e54T^{40} + 6.28e55T^{41} + 8.82e56T^{42} + 1.20e58T^{43} + 1.64e59T^{44} + 2.19e60T^{45} + 2.93e61T^{46} + 3.83e62T^{47} + 5.01e63T^{48} + 6.40e64T^{49} + 8.19e65T^{50} + 1.02e67T^{51} + 1.28e68T^{52} + 1.57e69T^{53} + 1.93e70T^{54} + 2.33e71T^{55} + 2.81e72T^{56} + 3.32e73T^{57} + 3.93e74T^{58} + 4.56e75T^{59} + 5.30e76T^{60} + 6.04e77T^{61} + 6.90e78T^{62} + 7.73e79T^{63} + 8.68e80T^{64} + 9.56e81T^{65} + 1.05e83T^{66} + 1.14e84T^{67} + 1.24e85T^{68} + 1.32e86T^{69} + 1.41e87T^{70} + 1.48e88T^{71} + 1.55e89T^{72} + 1.60e90T^{73}+O(T^{74})$$
\begin{aligned} L(s) = \prod_p \ \prod_{j=1}^{158} (1 - \alpha_{j,p}\, p^{-s})^{-1} \end{aligned}