# Properties

 Degree 134 Conductor $2^{67} \cdot 4021^{67}$ Sign $-1$ Motivic weight 1 Primitive no Self-dual yes Analytic rank 67

# Origins of factors

## Dirichlet series

 L(s)  = 1 + 67·2-s − 11·3-s + 2.27e3·4-s − 20·5-s − 737·6-s − 40·7-s + 5.23e4·8-s − 28·9-s − 1.34e3·10-s − 13·11-s − 2.50e4·12-s − 51·13-s − 2.68e3·14-s + 220·15-s + 9.16e5·16-s − 34·17-s − 1.87e3·18-s − 33·19-s − 4.55e4·20-s + 440·21-s − 871·22-s − 43·23-s − 5.76e5·24-s + 28·25-s − 3.41e3·26-s + 753·27-s − 9.11e4·28-s + ⋯
 L(s)  = 1 + 47.3·2-s − 6.35·3-s + 1.13e3·4-s − 8.94·5-s − 300.·6-s − 15.1·7-s + 1.85e4·8-s − 9.33·9-s − 423.·10-s − 3.91·11-s − 7.23e3·12-s − 14.1·13-s − 716.·14-s + 56.8·15-s + 2.29e5·16-s − 8.24·17-s − 442.·18-s − 7.57·19-s − 1.01e4·20-s + 96.0·21-s − 185.·22-s − 8.96·23-s − 1.17e5·24-s + 28/5·25-s − 670.·26-s + 144.·27-s − 1.72e4·28-s + ⋯

## Functional equation

\begin{aligned} \Lambda(s)=\mathstrut &\left(2^{67} \cdot 4021^{67}\right)^{s/2} \, \Gamma_{\C}(s)^{67} \, L(s)\cr =\mathstrut & -\,\Lambda(2-s) \end{aligned}
\begin{aligned} \Lambda(s)=\mathstrut &\left(2^{67} \cdot 4021^{67}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{67} \, L(s)\cr =\mathstrut & -\,\Lambda(1-s) \end{aligned}

## Invariants

 $$d$$ = $$134$$ $$N$$ = $$2^{67} \cdot 4021^{67}$$ $$\varepsilon$$ = $-1$ motivic weight = $$1$$ character : induced by $\chi_{8042} (1, \cdot )$ primitive : no self-dual : yes analytic rank = 67 Selberg data = $(134,\ 2^{67} \cdot 4021^{67} ,\ ( \ : [1/2]^{67} ),\ -1 )$ $L(1)$ $=$ $0$ $L(\frac12)$ $=$ $0$ $L(\frac{3}{2})$ not available $L(1)$ not available

## Euler product

$L(s) = \prod_{p \text{ prime}} F_p(p^{-s})^{-1}$ where, for $p \notin \{2,\;4021\}$, $$F_p$$ is a polynomial of degree 134. If $p \in \{2,\;4021\}$, then $F_p$ is a polynomial of degree at most 133.
$p$$F_p$
bad2 $$( 1 - T )^{67}$$
4021 $$1+O(T)$$
good3 $$1 + 11 T + 149 T^{2} + 398 p T^{3} + 3301 p T^{4} + 64241 T^{5} + 412585 T^{6} + 2289829 T^{7} + 12409189 T^{8} + 60932347 T^{9} + 290995841 T^{10} + 430885793 p T^{11} + 1861036063 p T^{12} + 7597750475 p T^{13} + 30190734713 p T^{14} + 343813786096 T^{15} + 424094479187 p T^{16} + 1510335845123 p T^{17} + 1750722158552 p^{2} T^{18} + 53017308150938 T^{19} + 174473917679743 T^{20} + 185946379772560 p T^{21} + 1747007875160372 T^{22} + 5332469347406987 T^{23} + 15964846236601147 T^{24} + 46703896604886455 T^{25} + 44726117188652024 p T^{26} + 377454485926538494 T^{27} + 1043930705816403032 T^{28} + 2831906285589006635 T^{29} + 7560411530540539936 T^{30} + 2202917973620644840 p^{2} T^{31} + 51213586387525341007 T^{32} + 43368272059515175445 p T^{33} +$$$$32\!\cdots\!53$$$$T^{34} +$$$$80\!\cdots\!81$$$$T^{35} +$$$$19\!\cdots\!81$$$$T^{36} +$$$$15\!\cdots\!77$$$$p T^{37} +$$$$11\!\cdots\!97$$$$T^{38} +$$$$86\!\cdots\!36$$$$p T^{39} +$$$$59\!\cdots\!64$$$$T^{40} +$$$$13\!\cdots\!97$$$$T^{41} +$$$$33\!\cdots\!41$$$$p^{2} T^{42} +$$$$67\!\cdots\!24$$$$T^{43} +$$$$14\!\cdots\!15$$$$T^{44} +$$$$32\!\cdots\!03$$$$T^{45} +$$$$69\!\cdots\!22$$$$T^{46} +$$$$48\!\cdots\!12$$$$p T^{47} +$$$$30\!\cdots\!95$$$$T^{48} +$$$$23\!\cdots\!53$$$$p^{3} T^{49} +$$$$43\!\cdots\!91$$$$p T^{50} +$$$$26\!\cdots\!35$$$$T^{51} +$$$$53\!\cdots\!15$$$$T^{52} +$$$$35\!\cdots\!96$$$$p T^{53} +$$$$20\!\cdots\!38$$$$T^{54} +$$$$40\!\cdots\!84$$$$T^{55} +$$$$78\!\cdots\!06$$$$T^{56} +$$$$50\!\cdots\!00$$$$p T^{57} +$$$$28\!\cdots\!28$$$$T^{58} +$$$$53\!\cdots\!76$$$$T^{59} +$$$$99\!\cdots\!75$$$$T^{60} +$$$$67\!\cdots\!74$$$$p^{3} T^{61} +$$$$33\!\cdots\!65$$$$T^{62} +$$$$60\!\cdots\!46$$$$T^{63} +$$$$10\!\cdots\!68$$$$T^{64} +$$$$19\!\cdots\!55$$$$T^{65} +$$$$33\!\cdots\!67$$$$T^{66} +$$$$58\!\cdots\!91$$$$T^{67} +$$$$33\!\cdots\!67$$$$p T^{68} +$$$$19\!\cdots\!55$$$$p^{2} T^{69} +$$$$10\!\cdots\!68$$$$p^{3} T^{70} +$$$$60\!\cdots\!46$$$$p^{4} T^{71} +$$$$33\!\cdots\!65$$$$p^{5} T^{72} +$$$$67\!\cdots\!74$$$$p^{9} T^{73} +$$$$99\!\cdots\!75$$$$p^{7} T^{74} +$$$$53\!\cdots\!76$$$$p^{8} T^{75} +$$$$28\!\cdots\!28$$$$p^{9} T^{76} +$$$$50\!\cdots\!00$$$$p^{11} T^{77} +$$$$78\!\cdots\!06$$$$p^{11} T^{78} +$$$$40\!\cdots\!84$$$$p^{12} T^{79} +$$$$20\!\cdots\!38$$$$p^{13} T^{80} +$$$$35\!\cdots\!96$$$$p^{15} T^{81} +$$$$53\!\cdots\!15$$$$p^{15} T^{82} +$$$$26\!\cdots\!35$$$$p^{16} T^{83} +$$$$43\!\cdots\!91$$$$p^{18} T^{84} +$$$$23\!\cdots\!53$$$$p^{21} T^{85} +$$$$30\!\cdots\!95$$$$p^{19} T^{86} +$$$$48\!\cdots\!12$$$$p^{21} T^{87} +$$$$69\!\cdots\!22$$$$p^{21} T^{88} +$$$$32\!\cdots\!03$$$$p^{22} T^{89} +$$$$14\!\cdots\!15$$$$p^{23} T^{90} +$$$$67\!\cdots\!24$$$$p^{24} T^{91} +$$$$33\!\cdots\!41$$$$p^{27} T^{92} +$$$$13\!\cdots\!97$$$$p^{26} T^{93} +$$$$59\!\cdots\!64$$$$p^{27} T^{94} +$$$$86\!\cdots\!36$$$$p^{29} T^{95} +$$$$11\!\cdots\!97$$$$p^{29} T^{96} +$$$$15\!\cdots\!77$$$$p^{31} T^{97} +$$$$19\!\cdots\!81$$$$p^{31} T^{98} +$$$$80\!\cdots\!81$$$$p^{32} T^{99} +$$$$32\!\cdots\!53$$$$p^{33} T^{100} + 43368272059515175445 p^{35} T^{101} + 51213586387525341007 p^{35} T^{102} + 2202917973620644840 p^{38} T^{103} + 7560411530540539936 p^{37} T^{104} + 2831906285589006635 p^{38} T^{105} + 1043930705816403032 p^{39} T^{106} + 377454485926538494 p^{40} T^{107} + 44726117188652024 p^{42} T^{108} + 46703896604886455 p^{42} T^{109} + 15964846236601147 p^{43} T^{110} + 5332469347406987 p^{44} T^{111} + 1747007875160372 p^{45} T^{112} + 185946379772560 p^{47} T^{113} + 174473917679743 p^{47} T^{114} + 53017308150938 p^{48} T^{115} + 1750722158552 p^{51} T^{116} + 1510335845123 p^{51} T^{117} + 424094479187 p^{52} T^{118} + 343813786096 p^{52} T^{119} + 30190734713 p^{54} T^{120} + 7597750475 p^{55} T^{121} + 1861036063 p^{56} T^{122} + 430885793 p^{57} T^{123} + 290995841 p^{57} T^{124} + 60932347 p^{58} T^{125} + 12409189 p^{59} T^{126} + 2289829 p^{60} T^{127} + 412585 p^{61} T^{128} + 64241 p^{62} T^{129} + 3301 p^{64} T^{130} + 398 p^{65} T^{131} + 149 p^{65} T^{132} + 11 p^{66} T^{133} + p^{67} T^{134}$$
5 $$1 + 4 p T + 372 T^{2} + 4756 T^{3} + 55521 T^{4} + 545529 T^{5} + 4961807 T^{6} + 40583602 T^{7} + 311352737 T^{8} + 2214796248 T^{9} + 119440707 p^{3} T^{10} + 94924983314 T^{11} + 576413898119 T^{12} + 3336838564691 T^{13} + 18559895576243 T^{14} + 99138221978734 T^{15} + 511191193589498 T^{16} + 508958986945287 p T^{17} + 12275024574068108 T^{18} + 57393375452712518 T^{19} + 52161240468520824 p T^{20} + 1152414512989398447 T^{21} + 4961362381754110863 T^{22} + 20822161800695105197 T^{23} + 17064300103696879123 p T^{24} + 2732224832450842733 p^{3} T^{25} +$$$$13\!\cdots\!37$$$$T^{26} +$$$$10\!\cdots\!52$$$$p T^{27} +$$$$19\!\cdots\!12$$$$T^{28} +$$$$70\!\cdots\!73$$$$T^{29} +$$$$25\!\cdots\!36$$$$T^{30} +$$$$90\!\cdots\!52$$$$T^{31} +$$$$31\!\cdots\!79$$$$T^{32} +$$$$10\!\cdots\!04$$$$T^{33} +$$$$35\!\cdots\!43$$$$T^{34} +$$$$11\!\cdots\!01$$$$T^{35} +$$$$38\!\cdots\!52$$$$T^{36} +$$$$12\!\cdots\!32$$$$T^{37} +$$$$77\!\cdots\!71$$$$p T^{38} +$$$$12\!\cdots\!52$$$$T^{39} +$$$$36\!\cdots\!41$$$$T^{40} +$$$$88\!\cdots\!01$$$$p^{3} T^{41} +$$$$32\!\cdots\!88$$$$T^{42} +$$$$95\!\cdots\!01$$$$T^{43} +$$$$27\!\cdots\!19$$$$T^{44} +$$$$15\!\cdots\!13$$$$p T^{45} +$$$$88\!\cdots\!84$$$$p^{2} T^{46} +$$$$61\!\cdots\!86$$$$T^{47} +$$$$33\!\cdots\!78$$$$p T^{48} +$$$$45\!\cdots\!88$$$$T^{49} +$$$$12\!\cdots\!03$$$$T^{50} +$$$$32\!\cdots\!42$$$$T^{51} +$$$$85\!\cdots\!38$$$$T^{52} +$$$$22\!\cdots\!57$$$$T^{53} +$$$$56\!\cdots\!64$$$$T^{54} +$$$$14\!\cdots\!01$$$$T^{55} +$$$$35\!\cdots\!78$$$$T^{56} +$$$$88\!\cdots\!88$$$$T^{57} +$$$$21\!\cdots\!54$$$$T^{58} +$$$$52\!\cdots\!58$$$$T^{59} +$$$$12\!\cdots\!66$$$$T^{60} +$$$$30\!\cdots\!51$$$$T^{61} +$$$$71\!\cdots\!53$$$$T^{62} +$$$$16\!\cdots\!12$$$$T^{63} +$$$$38\!\cdots\!73$$$$T^{64} +$$$$88\!\cdots\!72$$$$T^{65} +$$$$40\!\cdots\!37$$$$p T^{66} +$$$$45\!\cdots\!27$$$$T^{67} +$$$$40\!\cdots\!37$$$$p^{2} T^{68} +$$$$88\!\cdots\!72$$$$p^{2} T^{69} +$$$$38\!\cdots\!73$$$$p^{3} T^{70} +$$$$16\!\cdots\!12$$$$p^{4} T^{71} +$$$$71\!\cdots\!53$$$$p^{5} T^{72} +$$$$30\!\cdots\!51$$$$p^{6} T^{73} +$$$$12\!\cdots\!66$$$$p^{7} T^{74} +$$$$52\!\cdots\!58$$$$p^{8} T^{75} +$$$$21\!\cdots\!54$$$$p^{9} T^{76} +$$$$88\!\cdots\!88$$$$p^{10} T^{77} +$$$$35\!\cdots\!78$$$$p^{11} T^{78} +$$$$14\!\cdots\!01$$$$p^{12} T^{79} +$$$$56\!\cdots\!64$$$$p^{13} T^{80} +$$$$22\!\cdots\!57$$$$p^{14} T^{81} +$$$$85\!\cdots\!38$$$$p^{15} T^{82} +$$$$32\!\cdots\!42$$$$p^{16} T^{83} +$$$$12\!\cdots\!03$$$$p^{17} T^{84} +$$$$45\!\cdots\!88$$$$p^{18} T^{85} +$$$$33\!\cdots\!78$$$$p^{20} T^{86} +$$$$61\!\cdots\!86$$$$p^{20} T^{87} +$$$$88\!\cdots\!84$$$$p^{23} T^{88} +$$$$15\!\cdots\!13$$$$p^{23} T^{89} +$$$$27\!\cdots\!19$$$$p^{23} T^{90} +$$$$95\!\cdots\!01$$$$p^{24} T^{91} +$$$$32\!\cdots\!88$$$$p^{25} T^{92} +$$$$88\!\cdots\!01$$$$p^{29} T^{93} +$$$$36\!\cdots\!41$$$$p^{27} T^{94} +$$$$12\!\cdots\!52$$$$p^{28} T^{95} +$$$$77\!\cdots\!71$$$$p^{30} T^{96} +$$$$12\!\cdots\!32$$$$p^{30} T^{97} +$$$$38\!\cdots\!52$$$$p^{31} T^{98} +$$$$11\!\cdots\!01$$$$p^{32} T^{99} +$$$$35\!\cdots\!43$$$$p^{33} T^{100} +$$$$10\!\cdots\!04$$$$p^{34} T^{101} +$$$$31\!\cdots\!79$$$$p^{35} T^{102} +$$$$90\!\cdots\!52$$$$p^{36} T^{103} +$$$$25\!\cdots\!36$$$$p^{37} T^{104} +$$$$70\!\cdots\!73$$$$p^{38} T^{105} +$$$$19\!\cdots\!12$$$$p^{39} T^{106} +$$$$10\!\cdots\!52$$$$p^{41} T^{107} +$$$$13\!\cdots\!37$$$$p^{41} T^{108} + 2732224832450842733 p^{45} T^{109} + 17064300103696879123 p^{44} T^{110} + 20822161800695105197 p^{44} T^{111} + 4961362381754110863 p^{45} T^{112} + 1152414512989398447 p^{46} T^{113} + 52161240468520824 p^{48} T^{114} + 57393375452712518 p^{48} T^{115} + 12275024574068108 p^{49} T^{116} + 508958986945287 p^{51} T^{117} + 511191193589498 p^{51} T^{118} + 99138221978734 p^{52} T^{119} + 18559895576243 p^{53} T^{120} + 3336838564691 p^{54} T^{121} + 576413898119 p^{55} T^{122} + 94924983314 p^{56} T^{123} + 119440707 p^{60} T^{124} + 2214796248 p^{58} T^{125} + 311352737 p^{59} T^{126} + 40583602 p^{60} T^{127} + 4961807 p^{61} T^{128} + 545529 p^{62} T^{129} + 55521 p^{63} T^{130} + 4756 p^{64} T^{131} + 372 p^{65} T^{132} + 4 p^{67} T^{133} + p^{67} T^{134}$$
7 $$1 + 40 T + 1034 T^{2} + 19981 T^{3} + 319393 T^{4} + 4396036 T^{5} + 53739957 T^{6} + 594325779 T^{7} + 6034049991 T^{8} + 56827555147 T^{9} + 500685163066 T^{10} + 593464150562 p T^{11} + 32639761977173 T^{12} + 243949472612855 T^{13} + 1741168658041203 T^{14} + 11907055993752574 T^{15} + 78242316635153117 T^{16} + 495268656991353157 T^{17} + 3026667692279020073 T^{18} + 17892276501699709997 T^{19} +$$$$10\!\cdots\!81$$$$T^{20} +$$$$56\!\cdots\!41$$$$T^{21} +$$$$30\!\cdots\!68$$$$T^{22} +$$$$16\!\cdots\!92$$$$T^{23} +$$$$82\!\cdots\!24$$$$T^{24} +$$$$41\!\cdots\!50$$$$T^{25} +$$$$28\!\cdots\!48$$$$p T^{26} +$$$$96\!\cdots\!08$$$$T^{27} +$$$$45\!\cdots\!63$$$$T^{28} +$$$$29\!\cdots\!51$$$$p T^{29} +$$$$91\!\cdots\!18$$$$T^{30} +$$$$40\!\cdots\!21$$$$T^{31} +$$$$17\!\cdots\!21$$$$T^{32} +$$$$73\!\cdots\!83$$$$T^{33} +$$$$30\!\cdots\!27$$$$T^{34} +$$$$12\!\cdots\!21$$$$T^{35} +$$$$49\!\cdots\!24$$$$T^{36} +$$$$19\!\cdots\!58$$$$T^{37} +$$$$75\!\cdots\!73$$$$T^{38} +$$$$28\!\cdots\!57$$$$T^{39} +$$$$10\!\cdots\!45$$$$T^{40} +$$$$56\!\cdots\!84$$$$p T^{41} +$$$$14\!\cdots\!68$$$$T^{42} +$$$$51\!\cdots\!62$$$$T^{43} +$$$$18\!\cdots\!75$$$$T^{44} +$$$$63\!\cdots\!88$$$$T^{45} +$$$$31\!\cdots\!14$$$$p T^{46} +$$$$74\!\cdots\!95$$$$T^{47} +$$$$24\!\cdots\!32$$$$T^{48} +$$$$11\!\cdots\!82$$$$p T^{49} +$$$$26\!\cdots\!36$$$$T^{50} +$$$$85\!\cdots\!98$$$$T^{51} +$$$$27\!\cdots\!29$$$$T^{52} +$$$$85\!\cdots\!40$$$$T^{53} +$$$$26\!\cdots\!04$$$$T^{54} +$$$$81\!\cdots\!36$$$$T^{55} +$$$$24\!\cdots\!03$$$$T^{56} +$$$$73\!\cdots\!65$$$$T^{57} +$$$$21\!\cdots\!25$$$$T^{58} +$$$$63\!\cdots\!33$$$$T^{59} +$$$$18\!\cdots\!71$$$$T^{60} +$$$$51\!\cdots\!81$$$$T^{61} +$$$$14\!\cdots\!52$$$$T^{62} +$$$$40\!\cdots\!34$$$$T^{63} +$$$$11\!\cdots\!57$$$$T^{64} +$$$$30\!\cdots\!19$$$$T^{65} +$$$$82\!\cdots\!88$$$$T^{66} +$$$$21\!\cdots\!87$$$$T^{67} +$$$$82\!\cdots\!88$$$$p T^{68} +$$$$30\!\cdots\!19$$$$p^{2} T^{69} +$$$$11\!\cdots\!57$$$$p^{3} T^{70} +$$$$40\!\cdots\!34$$$$p^{4} T^{71} +$$$$14\!\cdots\!52$$$$p^{5} T^{72} +$$$$51\!\cdots\!81$$$$p^{6} T^{73} +$$$$18\!\cdots\!71$$$$p^{7} T^{74} +$$$$63\!\cdots\!33$$$$p^{8} T^{75} +$$$$21\!\cdots\!25$$$$p^{9} T^{76} +$$$$73\!\cdots\!65$$$$p^{10} T^{77} +$$$$24\!\cdots\!03$$$$p^{11} T^{78} +$$$$81\!\cdots\!36$$$$p^{12} T^{79} +$$$$26\!\cdots\!04$$$$p^{13} T^{80} +$$$$85\!\cdots\!40$$$$p^{14} T^{81} +$$$$27\!\cdots\!29$$$$p^{15} T^{82} +$$$$85\!\cdots\!98$$$$p^{16} T^{83} +$$$$26\!\cdots\!36$$$$p^{17} T^{84} +$$$$11\!\cdots\!82$$$$p^{19} T^{85} +$$$$24\!\cdots\!32$$$$p^{19} T^{86} +$$$$74\!\cdots\!95$$$$p^{20} T^{87} +$$$$31\!\cdots\!14$$$$p^{22} T^{88} +$$$$63\!\cdots\!88$$$$p^{22} T^{89} +$$$$18\!\cdots\!75$$$$p^{23} T^{90} +$$$$51\!\cdots\!62$$$$p^{24} T^{91} +$$$$14\!\cdots\!68$$$$p^{25} T^{92} +$$$$56\!\cdots\!84$$$$p^{27} T^{93} +$$$$10\!\cdots\!45$$$$p^{27} T^{94} +$$$$28\!\cdots\!57$$$$p^{28} T^{95} +$$$$75\!\cdots\!73$$$$p^{29} T^{96} +$$$$19\!\cdots\!58$$$$p^{30} T^{97} +$$$$49\!\cdots\!24$$$$p^{31} T^{98} +$$$$12\!\cdots\!21$$$$p^{32} T^{99} +$$$$30\!\cdots\!27$$$$p^{33} T^{100} +$$$$73\!\cdots\!83$$$$p^{34} T^{101} +$$$$17\!\cdots\!21$$$$p^{35} T^{102} +$$$$40\!\cdots\!21$$$$p^{36} T^{103} +$$$$91\!\cdots\!18$$$$p^{37} T^{104} +$$$$29\!\cdots\!51$$$$p^{39} T^{105} +$$$$45\!\cdots\!63$$$$p^{39} T^{106} +$$$$96\!\cdots\!08$$$$p^{40} T^{107} +$$$$28\!\cdots\!48$$$$p^{42} T^{108} +$$$$41\!\cdots\!50$$$$p^{42} T^{109} +$$$$82\!\cdots\!24$$$$p^{43} T^{110} +$$$$16\!\cdots\!92$$$$p^{44} T^{111} +$$$$30\!\cdots\!68$$$$p^{45} T^{112} +$$$$56\!\cdots\!41$$$$p^{46} T^{113} +$$$$10\!\cdots\!81$$$$p^{47} T^{114} + 17892276501699709997 p^{48} T^{115} + 3026667692279020073 p^{49} T^{116} + 495268656991353157 p^{50} T^{117} + 78242316635153117 p^{51} T^{118} + 11907055993752574 p^{52} T^{119} + 1741168658041203 p^{53} T^{120} + 243949472612855 p^{54} T^{121} + 32639761977173 p^{55} T^{122} + 593464150562 p^{57} T^{123} + 500685163066 p^{57} T^{124} + 56827555147 p^{58} T^{125} + 6034049991 p^{59} T^{126} + 594325779 p^{60} T^{127} + 53739957 p^{61} T^{128} + 4396036 p^{62} T^{129} + 319393 p^{63} T^{130} + 19981 p^{64} T^{131} + 1034 p^{65} T^{132} + 40 p^{66} T^{133} + p^{67} T^{134}$$
11 $$1 + 13 T + 4 p^{2} T^{2} + 5428 T^{3} + 112407 T^{4} + 1114752 T^{5} + 16825988 T^{6} + 150200594 T^{7} + 1835127933 T^{8} + 1358490648 p T^{9} + 156087600887 T^{10} + 1171466762040 T^{11} + 10812812791557 T^{12} + 75414705197311 T^{13} + 628804195222969 T^{14} + 4103083899256448 T^{15} + 31392772949971738 T^{16} + 192726713155301142 T^{17} + 1369085596909639567 T^{18} + 7945846939487147117 T^{19} + 52893100975072838485 T^{20} +$$$$29\!\cdots\!35$$$$T^{21} +$$$$18\!\cdots\!09$$$$T^{22} +$$$$96\!\cdots\!98$$$$T^{23} +$$$$57\!\cdots\!84$$$$T^{24} +$$$$28\!\cdots\!03$$$$T^{25} +$$$$16\!\cdots\!00$$$$T^{26} +$$$$79\!\cdots\!12$$$$T^{27} +$$$$43\!\cdots\!80$$$$T^{28} +$$$$20\!\cdots\!93$$$$T^{29} +$$$$10\!\cdots\!96$$$$T^{30} +$$$$47\!\cdots\!78$$$$T^{31} +$$$$24\!\cdots\!73$$$$T^{32} +$$$$10\!\cdots\!81$$$$T^{33} +$$$$51\!\cdots\!29$$$$T^{34} +$$$$21\!\cdots\!71$$$$T^{35} +$$$$10\!\cdots\!65$$$$T^{36} +$$$$38\!\cdots\!97$$$$p T^{37} +$$$$19\!\cdots\!13$$$$T^{38} +$$$$77\!\cdots\!02$$$$T^{39} +$$$$35\!\cdots\!91$$$$T^{40} +$$$$13\!\cdots\!54$$$$T^{41} +$$$$46\!\cdots\!33$$$$p^{3} T^{42} +$$$$23\!\cdots\!51$$$$T^{43} +$$$$10\!\cdots\!90$$$$T^{44} +$$$$37\!\cdots\!14$$$$T^{45} +$$$$16\!\cdots\!55$$$$T^{46} +$$$$58\!\cdots\!04$$$$T^{47} +$$$$24\!\cdots\!02$$$$T^{48} +$$$$87\!\cdots\!85$$$$T^{49} +$$$$36\!\cdots\!51$$$$T^{50} +$$$$12\!\cdots\!61$$$$T^{51} +$$$$46\!\cdots\!46$$$$p T^{52} +$$$$17\!\cdots\!29$$$$T^{53} +$$$$70\!\cdots\!66$$$$T^{54} +$$$$23\!\cdots\!50$$$$T^{55} +$$$$93\!\cdots\!32$$$$T^{56} +$$$$30\!\cdots\!39$$$$T^{57} +$$$$12\!\cdots\!74$$$$T^{58} +$$$$35\!\cdots\!83$$$$p T^{59} +$$$$14\!\cdots\!11$$$$T^{60} +$$$$47\!\cdots\!34$$$$T^{61} +$$$$18\!\cdots\!63$$$$T^{62} +$$$$56\!\cdots\!43$$$$T^{63} +$$$$21\!\cdots\!70$$$$T^{64} +$$$$59\!\cdots\!81$$$$p T^{65} +$$$$19\!\cdots\!59$$$$p^{2} T^{66} +$$$$72\!\cdots\!85$$$$T^{67} +$$$$19\!\cdots\!59$$$$p^{3} T^{68} +$$$$59\!\cdots\!81$$$$p^{3} T^{69} +$$$$21\!\cdots\!70$$$$p^{3} T^{70} +$$$$56\!\cdots\!43$$$$p^{4} T^{71} +$$$$18\!\cdots\!63$$$$p^{5} T^{72} +$$$$47\!\cdots\!34$$$$p^{6} T^{73} +$$$$14\!\cdots\!11$$$$p^{7} T^{74} +$$$$35\!\cdots\!83$$$$p^{9} T^{75} +$$$$12\!\cdots\!74$$$$p^{9} T^{76} +$$$$30\!\cdots\!39$$$$p^{10} T^{77} +$$$$93\!\cdots\!32$$$$p^{11} T^{78} +$$$$23\!\cdots\!50$$$$p^{12} T^{79} +$$$$70\!\cdots\!66$$$$p^{13} T^{80} +$$$$17\!\cdots\!29$$$$p^{14} T^{81} +$$$$46\!\cdots\!46$$$$p^{16} T^{82} +$$$$12\!\cdots\!61$$$$p^{16} T^{83} +$$$$36\!\cdots\!51$$$$p^{17} T^{84} +$$$$87\!\cdots\!85$$$$p^{18} T^{85} +$$$$24\!\cdots\!02$$$$p^{19} T^{86} +$$$$58\!\cdots\!04$$$$p^{20} T^{87} +$$$$16\!\cdots\!55$$$$p^{21} T^{88} +$$$$37\!\cdots\!14$$$$p^{22} T^{89} +$$$$10\!\cdots\!90$$$$p^{23} T^{90} +$$$$23\!\cdots\!51$$$$p^{24} T^{91} +$$$$46\!\cdots\!33$$$$p^{28} T^{92} +$$$$13\!\cdots\!54$$$$p^{26} T^{93} +$$$$35\!\cdots\!91$$$$p^{27} T^{94} +$$$$77\!\cdots\!02$$$$p^{28} T^{95} +$$$$19\!\cdots\!13$$$$p^{29} T^{96} +$$$$38\!\cdots\!97$$$$p^{31} T^{97} +$$$$10\!\cdots\!65$$$$p^{31} T^{98} +$$$$21\!\cdots\!71$$$$p^{32} T^{99} +$$$$51\!\cdots\!29$$$$p^{33} T^{100} +$$$$10\!\cdots\!81$$$$p^{34} T^{101} +$$$$24\!\cdots\!73$$$$p^{35} T^{102} +$$$$47\!\cdots\!78$$$$p^{36} T^{103} +$$$$10\!\cdots\!96$$$$p^{37} T^{104} +$$$$20\!\cdots\!93$$$$p^{38} T^{105} +$$$$43\!\cdots\!80$$$$p^{39} T^{106} +$$$$79\!\cdots\!12$$$$p^{40} T^{107} +$$$$16\!\cdots\!00$$$$p^{41} T^{108} +$$$$28\!\cdots\!03$$$$p^{42} T^{109} +$$$$57\!\cdots\!84$$$$p^{43} T^{110} +$$$$96\!\cdots\!98$$$$p^{44} T^{111} +$$$$18\!\cdots\!09$$$$p^{45} T^{112} +$$$$29\!\cdots\!35$$$$p^{46} T^{113} + 52893100975072838485 p^{47} T^{114} + 7945846939487147117 p^{48} T^{115} + 1369085596909639567 p^{49} T^{116} + 192726713155301142 p^{50} T^{117} + 31392772949971738 p^{51} T^{118} + 4103083899256448 p^{52} T^{119} + 628804195222969 p^{53} T^{120} + 75414705197311 p^{54} T^{121} + 10812812791557 p^{55} T^{122} + 1171466762040 p^{56} T^{123} + 156087600887 p^{57} T^{124} + 1358490648 p^{59} T^{125} + 1835127933 p^{59} T^{126} + 150200594 p^{60} T^{127} + 16825988 p^{61} T^{128} + 1114752 p^{62} T^{129} + 112407 p^{63} T^{130} + 5428 p^{64} T^{131} + 4 p^{67} T^{132} + 13 p^{66} T^{133} + p^{67} T^{134}$$
13 $$1 + 51 T + 1763 T^{2} + 45544 T^{3} + 982313 T^{4} + 18272061 T^{5} + 302907925 T^{6} + 4548346070 T^{7} + 62798058091 T^{8} + 804873042174 T^{9} + 9658312745648 T^{10} + 109183371713055 T^{11} + 1169159268529042 T^{12} + 916178042580195 p T^{13} + 115867711792283317 T^{14} + 1079840450864831754 T^{15} + 743687219635443907 p T^{16} + 83353678251907675369 T^{17} +$$$$69\!\cdots\!60$$$$T^{18} +$$$$55\!\cdots\!51$$$$T^{19} +$$$$43\!\cdots\!72$$$$T^{20} +$$$$32\!\cdots\!65$$$$T^{21} +$$$$24\!\cdots\!10$$$$T^{22} +$$$$17\!\cdots\!19$$$$T^{23} +$$$$11\!\cdots\!98$$$$T^{24} +$$$$81\!\cdots\!59$$$$T^{25} +$$$$53\!\cdots\!73$$$$T^{26} +$$$$34\!\cdots\!01$$$$T^{27} +$$$$21\!\cdots\!96$$$$T^{28} +$$$$13\!\cdots\!98$$$$T^{29} +$$$$80\!\cdots\!81$$$$T^{30} +$$$$47\!\cdots\!14$$$$T^{31} +$$$$27\!\cdots\!65$$$$T^{32} +$$$$15\!\cdots\!90$$$$T^{33} +$$$$87\!\cdots\!97$$$$T^{34} +$$$$47\!\cdots\!54$$$$T^{35} +$$$$25\!\cdots\!36$$$$T^{36} +$$$$13\!\cdots\!46$$$$T^{37} +$$$$69\!\cdots\!60$$$$T^{38} +$$$$35\!\cdots\!47$$$$T^{39} +$$$$17\!\cdots\!59$$$$T^{40} +$$$$86\!\cdots\!56$$$$T^{41} +$$$$41\!\cdots\!65$$$$T^{42} +$$$$19\!\cdots\!49$$$$T^{43} +$$$$93\!\cdots\!61$$$$T^{44} +$$$$43\!\cdots\!29$$$$T^{45} +$$$$19\!\cdots\!86$$$$T^{46} +$$$$88\!\cdots\!95$$$$T^{47} +$$$$39\!\cdots\!64$$$$T^{48} +$$$$17\!\cdots\!53$$$$T^{49} +$$$$73\!\cdots\!01$$$$T^{50} +$$$$23\!\cdots\!57$$$$p T^{51} +$$$$10\!\cdots\!41$$$$p T^{52} +$$$$41\!\cdots\!61$$$$p T^{53} +$$$$22\!\cdots\!96$$$$T^{54} +$$$$89\!\cdots\!68$$$$T^{55} +$$$$27\!\cdots\!15$$$$p T^{56} +$$$$14\!\cdots\!72$$$$T^{57} +$$$$55\!\cdots\!64$$$$T^{58} +$$$$16\!\cdots\!24$$$$p T^{59} +$$$$82\!\cdots\!44$$$$T^{60} +$$$$31\!\cdots\!62$$$$T^{61} +$$$$90\!\cdots\!84$$$$p T^{62} +$$$$44\!\cdots\!16$$$$T^{63} +$$$$12\!\cdots\!93$$$$p T^{64} +$$$$60\!\cdots\!74$$$$T^{65} +$$$$21\!\cdots\!39$$$$T^{66} +$$$$79\!\cdots\!35$$$$T^{67} +$$$$21\!\cdots\!39$$$$p T^{68} +$$$$60\!\cdots\!74$$$$p^{2} T^{69} +$$$$12\!\cdots\!93$$$$p^{4} T^{70} +$$$$44\!\cdots\!16$$$$p^{4} T^{71} +$$$$90\!\cdots\!84$$$$p^{6} T^{72} +$$$$31\!\cdots\!62$$$$p^{6} T^{73} +$$$$82\!\cdots\!44$$$$p^{7} T^{74} +$$$$16\!\cdots\!24$$$$p^{9} T^{75} +$$$$55\!\cdots\!64$$$$p^{9} T^{76} +$$$$14\!\cdots\!72$$$$p^{10} T^{77} +$$$$27\!\cdots\!15$$$$p^{12} T^{78} +$$$$89\!\cdots\!68$$$$p^{12} T^{79} +$$$$22\!\cdots\!96$$$$p^{13} T^{80} +$$$$41\!\cdots\!61$$$$p^{15} T^{81} +$$$$10\!\cdots\!41$$$$p^{16} T^{82} +$$$$23\!\cdots\!57$$$$p^{17} T^{83} +$$$$73\!\cdots\!01$$$$p^{17} T^{84} +$$$$17\!\cdots\!53$$$$p^{18} T^{85} +$$$$39\!\cdots\!64$$$$p^{19} T^{86} +$$$$88\!\cdots\!95$$$$p^{20} T^{87} +$$$$19\!\cdots\!86$$$$p^{21} T^{88} +$$$$43\!\cdots\!29$$$$p^{22} T^{89} +$$$$93\!\cdots\!61$$$$p^{23} T^{90} +$$$$19\!\cdots\!49$$$$p^{24} T^{91} +$$$$41\!\cdots\!65$$$$p^{25} T^{92} +$$$$86\!\cdots\!56$$$$p^{26} T^{93} +$$$$17\!\cdots\!59$$$$p^{27} T^{94} +$$$$35\!\cdots\!47$$$$p^{28} T^{95} +$$$$69\!\cdots\!60$$$$p^{29} T^{96} +$$$$13\!\cdots\!46$$$$p^{30} T^{97} +$$$$25\!\cdots\!36$$$$p^{31} T^{98} +$$$$47\!\cdots\!54$$$$p^{32} T^{99} +$$$$87\!\cdots\!97$$$$p^{33} T^{100} +$$$$15\!\cdots\!90$$$$p^{34} T^{101} +$$$$27\!\cdots\!65$$$$p^{35} T^{102} +$$$$47\!\cdots\!14$$$$p^{36} T^{103} +$$$$80\!\cdots\!81$$$$p^{37} T^{104} +$$$$13\!\cdots\!98$$$$p^{38} T^{105} +$$$$21\!\cdots\!96$$$$p^{39} T^{106} +$$$$34\!\cdots\!01$$$$p^{40} T^{107} +$$$$53\!\cdots\!73$$$$p^{41} T^{108} +$$$$81\!\cdots\!59$$$$p^{42} T^{109} +$$$$11\!\cdots\!98$$$$p^{43} T^{110} +$$$$17\!\cdots\!19$$$$p^{44} T^{111} +$$$$24\!\cdots\!10$$$$p^{45} T^{112} +$$$$32\!\cdots\!65$$$$p^{46} T^{113} +$$$$43\!\cdots\!72$$$$p^{47} T^{114} +$$$$55\!\cdots\!51$$$$p^{48} T^{115} +$$$$69\!\cdots\!60$$$$p^{49} T^{116} + 83353678251907675369 p^{50} T^{117} + 743687219635443907 p^{52} T^{118} + 1079840450864831754 p^{52} T^{119} + 115867711792283317 p^{53} T^{120} + 916178042580195 p^{55} T^{121} + 1169159268529042 p^{55} T^{122} + 109183371713055 p^{56} T^{123} + 9658312745648 p^{57} T^{124} + 804873042174 p^{58} T^{125} + 62798058091 p^{59} T^{126} + 4548346070 p^{60} T^{127} + 302907925 p^{61} T^{128} + 18272061 p^{62} T^{129} + 982313 p^{63} T^{130} + 45544 p^{64} T^{131} + 1763 p^{65} T^{132} + 51 p^{66} T^{133} + p^{67} T^{134}$$
17 $$1 + 2 p T + 1192 T^{2} + 27292 T^{3} + 593619 T^{4} + 10619273 T^{5} + 179140036 T^{6} + 2685186078 T^{7} + 38117363278 T^{8} + 498271409753 T^{9} + 6205219183281 T^{10} + 72574479333240 T^{11} + 813127869805589 T^{12} + 8660610044554107 T^{13} + 88784692853634147 T^{14} + 51314155809658726 p T^{15} + 8282294805925665013 T^{16} + 75805998517838795044 T^{17} +$$$$67\!\cdots\!63$$$$T^{18} +$$$$57\!\cdots\!66$$$$T^{19} +$$$$48\!\cdots\!82$$$$T^{20} +$$$$39\!\cdots\!01$$$$T^{21} +$$$$30\!\cdots\!18$$$$T^{22} +$$$$23\!\cdots\!53$$$$T^{23} +$$$$17\!\cdots\!06$$$$T^{24} +$$$$13\!\cdots\!19$$$$T^{25} +$$$$94\!\cdots\!77$$$$T^{26} +$$$$66\!\cdots\!89$$$$T^{27} +$$$$45\!\cdots\!61$$$$T^{28} +$$$$30\!\cdots\!14$$$$T^{29} +$$$$20\!\cdots\!88$$$$T^{30} +$$$$13\!\cdots\!66$$$$T^{31} +$$$$84\!\cdots\!13$$$$T^{32} +$$$$52\!\cdots\!16$$$$T^{33} +$$$$32\!\cdots\!72$$$$T^{34} +$$$$19\!\cdots\!18$$$$T^{35} +$$$$11\!\cdots\!29$$$$T^{36} +$$$$68\!\cdots\!81$$$$T^{37} +$$$$39\!\cdots\!49$$$$T^{38} +$$$$22\!\cdots\!09$$$$T^{39} +$$$$12\!\cdots\!05$$$$T^{40} +$$$$69\!\cdots\!97$$$$T^{41} +$$$$22\!\cdots\!26$$$$p T^{42} +$$$$20\!\cdots\!96$$$$T^{43} +$$$$10\!\cdots\!07$$$$T^{44} +$$$$56\!\cdots\!14$$$$T^{45} +$$$$28\!\cdots\!77$$$$T^{46} +$$$$14\!\cdots\!78$$$$T^{47} +$$$$74\!\cdots\!92$$$$T^{48} +$$$$21\!\cdots\!11$$$$p T^{49} +$$$$18\!\cdots\!75$$$$T^{50} +$$$$88\!\cdots\!82$$$$T^{51} +$$$$42\!\cdots\!03$$$$T^{52} +$$$$20\!\cdots\!11$$$$T^{53} +$$$$95\!\cdots\!12$$$$T^{54} +$$$$26\!\cdots\!57$$$$p T^{55} +$$$$20\!\cdots\!07$$$$T^{56} +$$$$93\!\cdots\!66$$$$T^{57} +$$$$42\!\cdots\!35$$$$T^{58} +$$$$18\!\cdots\!70$$$$T^{59} +$$$$83\!\cdots\!55$$$$T^{60} +$$$$36\!\cdots\!70$$$$T^{61} +$$$$15\!\cdots\!31$$$$T^{62} +$$$$68\!\cdots\!46$$$$T^{63} +$$$$29\!\cdots\!88$$$$T^{64} +$$$$12\!\cdots\!08$$$$T^{65} +$$$$51\!\cdots\!07$$$$T^{66} +$$$$21\!\cdots\!57$$$$T^{67} +$$$$51\!\cdots\!07$$$$p T^{68} +$$$$12\!\cdots\!08$$$$p^{2} T^{69} +$$$$29\!\cdots\!88$$$$p^{3} T^{70} +$$$$68\!\cdots\!46$$$$p^{4} T^{71} +$$$$15\!\cdots\!31$$$$p^{5} T^{72} +$$$$36\!\cdots\!70$$$$p^{6} T^{73} +$$$$83\!\cdots\!55$$$$p^{7} T^{74} +$$$$18\!\cdots\!70$$$$p^{8} T^{75} +$$$$42\!\cdots\!35$$$$p^{9} T^{76} +$$$$93\!\cdots\!66$$$$p^{10} T^{77} +$$$$20\!\cdots\!07$$$$p^{11} T^{78} +$$$$26\!\cdots\!57$$$$p^{13} T^{79} +$$$$95\!\cdots\!12$$$$p^{13} T^{80} +$$$$20\!\cdots\!11$$$$p^{14} T^{81} +$$$$42\!\cdots\!03$$$$p^{15} T^{82} +$$$$88\!\cdots\!82$$$$p^{16} T^{83} +$$$$18\!\cdots\!75$$$$p^{17} T^{84} +$$$$21\!\cdots\!11$$$$p^{19} T^{85} +$$$$74\!\cdots\!92$$$$p^{19} T^{86} +$$$$14\!\cdots\!78$$$$p^{20} T^{87} +$$$$28\!\cdots\!77$$$$p^{21} T^{88} +$$$$56\!\cdots\!14$$$$p^{22} T^{89} +$$$$10\!\cdots\!07$$$$p^{23} T^{90} +$$$$20\!\cdots\!96$$$$p^{24} T^{91} +$$$$22\!\cdots\!26$$$$p^{26} T^{92} +$$$$69\!\cdots\!97$$$$p^{26} T^{93} +$$$$12\!\cdots\!05$$$$p^{27} T^{94} +$$$$22\!\cdots\!09$$$$p^{28} T^{95} +$$$$39\!\cdots\!49$$$$p^{29} T^{96} +$$$$68\!\cdots\!81$$$$p^{30} T^{97} +$$$$11\!\cdots\!29$$$$p^{31} T^{98} +$$$$19\!\cdots\!18$$$$p^{32} T^{99} +$$$$32\!\cdots\!72$$$$p^{33} T^{100} +$$$$52\!\cdots\!16$$$$p^{34} T^{101} +$$$$84\!\cdots\!13$$$$p^{35} T^{102} +$$$$13\!\cdots\!66$$$$p^{36} T^{103} +$$$$20\!\cdots\!88$$$$p^{37} T^{104} +$$$$30\!\cdots\!14$$$$p^{38} T^{105} +$$$$45\!\cdots\!61$$$$p^{39} T^{106} +$$$$66\!\cdots\!89$$$$p^{40} T^{107} +$$$$94\!\cdots\!77$$$$p^{41} T^{108} +$$$$13\!\cdots\!19$$$$p^{42} T^{109} +$$$$17\!\cdots\!06$$$$p^{43} T^{110} +$$$$23\!\cdots\!53$$$$p^{44} T^{111} +$$$$30\!\cdots\!18$$$$p^{45} T^{112} +$$$$39\!\cdots\!01$$$$p^{46} T^{113} +$$$$48\!\cdots\!82$$$$p^{47} T^{114} +$$$$57\!\cdots\!66$$$$p^{48} T^{115} +$$$$67\!\cdots\!63$$$$p^{49} T^{116} + 75805998517838795044 p^{50} T^{117} + 8282294805925665013 p^{51} T^{118} + 51314155809658726 p^{53} T^{119} + 88784692853634147 p^{53} T^{120} + 8660610044554107 p^{54} T^{121} + 813127869805589 p^{55} T^{122} + 72574479333240 p^{56} T^{123} + 6205219183281 p^{57} T^{124} + 498271409753 p^{58} T^{125} + 38117363278 p^{59} T^{126} + 2685186078 p^{60} T^{127} + 179140036 p^{61} T^{128} + 10619273 p^{62} T^{129} + 593619 p^{63} T^{130} + 27292 p^{64} T^{131} + 1192 p^{65} T^{132} + 2 p^{67} T^{133} + p^{67} T^{134}$$
19 $$1 + 33 T + 1214 T^{2} + 27732 T^{3} + 627954 T^{4} + 11357818 T^{5} + 198986074 T^{6} + 3041452026 T^{7} + 44843146976 T^{8} + 601569832243 T^{9} + 7791674445994 T^{10} + 94012116657970 T^{11} + 1097724515452723 T^{12} + 12116872924031875 T^{13} + 6829642993183582 p T^{14} + 1326737096626391583 T^{15} + 13192668488352364213 T^{16} +$$$$12\!\cdots\!66$$$$T^{17} +$$$$11\!\cdots\!64$$$$T^{18} +$$$$10\!\cdots\!61$$$$T^{19} +$$$$93\!\cdots\!39$$$$T^{20} +$$$$79\!\cdots\!86$$$$T^{21} +$$$$66\!\cdots\!23$$$$T^{22} +$$$$53\!\cdots\!51$$$$T^{23} +$$$$42\!\cdots\!51$$$$T^{24} +$$$$33\!\cdots\!35$$$$T^{25} +$$$$13\!\cdots\!19$$$$p T^{26} +$$$$18\!\cdots\!69$$$$T^{27} +$$$$13\!\cdots\!38$$$$T^{28} +$$$$98\!\cdots\!81$$$$T^{29} +$$$$69\!\cdots\!92$$$$T^{30} +$$$$48\!\cdots\!05$$$$T^{31} +$$$$32\!\cdots\!76$$$$T^{32} +$$$$21\!\cdots\!22$$$$T^{33} +$$$$14\!\cdots\!25$$$$T^{34} +$$$$92\!\cdots\!59$$$$T^{35} +$$$$59\!\cdots\!71$$$$T^{36} +$$$$36\!\cdots\!61$$$$T^{37} +$$$$22\!\cdots\!63$$$$T^{38} +$$$$13\!\cdots\!39$$$$T^{39} +$$$$83\!\cdots\!07$$$$T^{40} +$$$$49\!\cdots\!97$$$$T^{41} +$$$$28\!\cdots\!58$$$$T^{42} +$$$$16\!\cdots\!69$$$$T^{43} +$$$$94\!\cdots\!08$$$$T^{44} +$$$$52\!\cdots\!39$$$$T^{45} +$$$$29\!\cdots\!95$$$$T^{46} +$$$$16\!\cdots\!63$$$$T^{47} +$$$$86\!\cdots\!98$$$$T^{48} +$$$$46\!\cdots\!51$$$$T^{49} +$$$$24\!\cdots\!42$$$$T^{50} +$$$$12\!\cdots\!51$$$$T^{51} +$$$$65\!\cdots\!11$$$$T^{52} +$$$$33\!\cdots\!66$$$$T^{53} +$$$$16\!\cdots\!85$$$$T^{54} +$$$$44\!\cdots\!82$$$$p T^{55} +$$$$41\!\cdots\!00$$$$T^{56} +$$$$20\!\cdots\!24$$$$T^{57} +$$$$97\!\cdots\!10$$$$T^{58} +$$$$46\!\cdots\!10$$$$T^{59} +$$$$21\!\cdots\!77$$$$T^{60} +$$$$10\!\cdots\!77$$$$T^{61} +$$$$47\!\cdots\!84$$$$T^{62} +$$$$21\!\cdots\!68$$$$T^{63} +$$$$97\!\cdots\!30$$$$T^{64} +$$$$22\!\cdots\!18$$$$p T^{65} +$$$$19\!\cdots\!58$$$$T^{66} +$$$$84\!\cdots\!93$$$$T^{67} +$$$$19\!\cdots\!58$$$$p T^{68} +$$$$22\!\cdots\!18$$$$p^{3} T^{69} +$$$$97\!\cdots\!30$$$$p^{3} T^{70} +$$$$21\!\cdots\!68$$$$p^{4} T^{71} +$$$$47\!\cdots\!84$$$$p^{5} T^{72} +$$$$10\!\cdots\!77$$$$p^{6} T^{73} +$$$$21\!\cdots\!77$$$$p^{7} T^{74} +$$$$46\!\cdots\!10$$$$p^{8} T^{75} +$$$$97\!\cdots\!10$$$$p^{9} T^{76} +$$$$20\!\cdots\!24$$$$p^{10} T^{77} +$$$$41\!\cdots\!00$$$$p^{11} T^{78} +$$$$44\!\cdots\!82$$$$p^{13} T^{79} +$$$$16\!\cdots\!85$$$$p^{13} T^{80} +$$$$33\!\cdots\!66$$$$p^{14} T^{81} +$$$$65\!\cdots\!11$$$$p^{15} T^{82} +$$$$12\!\cdots\!51$$$$p^{16} T^{83} +$$$$24\!\cdots\!42$$$$p^{17} T^{84} +$$$$46\!\cdots\!51$$$$p^{18} T^{85} +$$$$86\!\cdots\!98$$$$p^{19} T^{86} +$$$$16\!\cdots\!63$$$$p^{20} T^{87} +$$$$29\!\cdots\!95$$$$p^{21} T^{88} +$$$$52\!\cdots\!39$$$$p^{22} T^{89} +$$$$94\!\cdots\!08$$$$p^{23} T^{90} +$$$$16\!\cdots\!69$$$$p^{24} T^{91} +$$$$28\!\cdots\!58$$$$p^{25} T^{92} +$$$$49\!\cdots\!97$$$$p^{26} T^{93} +$$$$83\!\cdots\!07$$$$p^{27} T^{94} +$$$$13\!\cdots\!39$$$$p^{28} T^{95} +$$$$22\!\cdots\!63$$$$p^{29} T^{96} +$$$$36\!\cdots\!61$$$$p^{30} T^{97} +$$$$59\!\cdots\!71$$$$p^{31} T^{98} +$$$$92\!\cdots\!59$$$$p^{32} T^{99} +$$$$14\!\cdots\!25$$$$p^{33} T^{100} +$$$$21\!\cdots\!22$$$$p^{34} T^{101} +$$$$32\!\cdots\!76$$$$p^{35} T^{102} +$$$$48\!\cdots\!05$$$$p^{36} T^{103} +$$$$69\!\cdots\!92$$$$p^{37} T^{104} +$$$$98\!\cdots\!81$$$$p^{38} T^{105} +$$$$13\!\cdots\!38$$$$p^{39} T^{106} +$$$$18\!\cdots\!69$$$$p^{40} T^{107} +$$$$13\!\cdots\!19$$$$p^{42} T^{108} +$$$$33\!\cdots\!35$$$$p^{42} T^{109} +$$$$42\!\cdots\!51$$$$p^{43} T^{110} +$$$$53\!\cdots\!51$$$$p^{44} T^{111} +$$$$66\!\cdots\!23$$$$p^{45} T^{112} +$$$$79\!\cdots\!86$$$$p^{46} T^{113} +$$$$93\!\cdots\!39$$$$p^{47} T^{114} +$$$$10\!\cdots\!61$$$$p^{48} T^{115} +$$$$11\!\cdots\!64$$$$p^{49} T^{116} +$$$$12\!\cdots\!66$$$$p^{50} T^{117} + 13192668488352364213 p^{51} T^{118} + 1326737096626391583 p^{52} T^{119} + 6829642993183582 p^{54} T^{120} + 12116872924031875 p^{54} T^{121} + 1097724515452723 p^{55} T^{122} + 94012116657970 p^{56} T^{123} + 7791674445994 p^{57} T^{124} + 601569832243 p^{58} T^{125} + 44843146976 p^{59} T^{126} + 3041452026 p^{60} T^{127} + 198986074 p^{61} T^{128} + 11357818 p^{62} T^{129} + 627954 p^{63} T^{130} + 27732 p^{64} T^{131} + 1214 p^{65} T^{132} + 33 p^{66} T^{133} + p^{67} T^{134}$$
23 $$1 + 43 T + 1721 T^{2} + 47111 T^{3} + 1177598 T^{4} + 24686945 T^{5} + 478841921 T^{6} + 8330144197 T^{7} + 135828703113 T^{8} + 2049397162289 T^{9} + 29279373527585 T^{10} + 393910785716521 T^{11} + 5057441927355674 T^{12} + 61825786869194071 T^{13} + 725671207486485565 T^{14} + 8171700269241586671 T^{15} + 88776221547428996953 T^{16} +$$$$93\!\cdots\!69$$$$T^{17} +$$$$94\!\cdots\!80$$$$T^{18} +$$$$92\!\cdots\!88$$$$T^{19} +$$$$88\!\cdots\!75$$$$T^{20} +$$$$82\!\cdots\!94$$$$T^{21} +$$$$74\!\cdots\!93$$$$T^{22} +$$$$65\!\cdots\!93$$$$T^{23} +$$$$56\!\cdots\!77$$$$T^{24} +$$$$47\!\cdots\!38$$$$T^{25} +$$$$39\!\cdots\!49$$$$T^{26} +$$$$31\!\cdots\!72$$$$T^{27} +$$$$24\!\cdots\!22$$$$T^{28} +$$$$19\!\cdots\!25$$$$T^{29} +$$$$14\!\cdots\!03$$$$T^{30} +$$$$10\!\cdots\!38$$$$T^{31} +$$$$78\!\cdots\!97$$$$T^{32} +$$$$56\!\cdots\!99$$$$T^{33} +$$$$39\!\cdots\!76$$$$T^{34} +$$$$27\!\cdots\!95$$$$T^{35} +$$$$18\!\cdots\!33$$$$T^{36} +$$$$12\!\cdots\!61$$$$T^{37} +$$$$84\!\cdots\!40$$$$T^{38} +$$$$55\!\cdots\!83$$$$T^{39} +$$$$35\!\cdots\!32$$$$T^{40} +$$$$22\!\cdots\!87$$$$T^{41} +$$$$14\!\cdots\!28$$$$T^{42} +$$$$87\!\cdots\!08$$$$T^{43} +$$$$53\!\cdots\!08$$$$T^{44} +$$$$32\!\cdots\!90$$$$T^{45} +$$$$19\!\cdots\!00$$$$T^{46} +$$$$11\!\cdots\!53$$$$T^{47} +$$$$66\!\cdots\!56$$$$T^{48} +$$$$38\!\cdots\!02$$$$T^{49} +$$$$21\!\cdots\!73$$$$T^{50} +$$$$12\!\cdots\!14$$$$T^{51} +$$$$67\!\cdots\!64$$$$T^{52} +$$$$37\!\cdots\!09$$$$T^{53} +$$$$20\!\cdots\!19$$$$T^{54} +$$$$11\!\cdots\!51$$$$T^{55} +$$$$58\!\cdots\!12$$$$T^{56} +$$$$31\!\cdots\!91$$$$T^{57} +$$$$16\!\cdots\!32$$$$T^{58} +$$$$36\!\cdots\!41$$$$p T^{59} +$$$$43\!\cdots\!36$$$$T^{60} +$$$$22\!\cdots\!70$$$$T^{61} +$$$$11\!\cdots\!37$$$$T^{62} +$$$$56\!\cdots\!97$$$$T^{63} +$$$$27\!\cdots\!24$$$$T^{64} +$$$$13\!\cdots\!39$$$$T^{65} +$$$$66\!\cdots\!96$$$$T^{66} +$$$$31\!\cdots\!11$$$$T^{67} +$$$$66\!\cdots\!96$$$$p T^{68} +$$$$13\!\cdots\!39$$$$p^{2} T^{69} +$$$$27\!\cdots\!24$$$$p^{3} T^{70} +$$$$56\!\cdots\!97$$$$p^{4} T^{71} +$$$$11\!\cdots\!37$$$$p^{5} T^{72} +$$$$22\!\cdots\!70$$$$p^{6} T^{73} +$$$$43\!\cdots\!36$$$$p^{7} T^{74} +$$$$36\!\cdots\!41$$$$p^{9} T^{75} +$$$$16\!\cdots\!32$$$$p^{9} T^{76} +$$$$31\!\cdots\!91$$$$p^{10} T^{77} +$$$$58\!\cdots\!12$$$$p^{11} T^{78} +$$$$11\!\cdots\!51$$$$p^{12} T^{79} +$$$$20\!\cdots\!19$$$$p^{13} T^{80} +$$$$37\!\cdots\!09$$$$p^{14} T^{81} +$$$$67\!\cdots\!64$$$$p^{15} T^{82} +$$$$12\!\cdots\!14$$$$p^{16} T^{83} +$$$$21\!\cdots\!73$$$$p^{17} T^{84} +$$$$38\!\cdots\!02$$$$p^{18} T^{85} +$$$$66\!\cdots\!56$$$$p^{19} T^{86} +$$$$11\!\cdots\!53$$$$p^{20} T^{87} +$$$$19\!\cdots\!00$$$$p^{21} T^{88} +$$$$32\!\cdots\!90$$$$p^{22} T^{89} +$$$$53\!\cdots\!08$$$$p^{23} T^{90} +$$$$87\!\cdots\!08$$$$p^{24} T^{91} +$$$$14\!\cdots\!28$$$$p^{25} T^{92} +$$$$22\!\cdots\!87$$$$p^{26} T^{93} +$$$$35\!\cdots\!32$$$$p^{27} T^{94} +$$$$55\!\cdots\!83$$$$p^{28} T^{95} +$$$$84\!\cdots\!40$$$$p^{29} T^{96} +$$$$12\!\cdots\!61$$$$p^{30} T^{97} +$$$$18\!\cdots\!33$$$$p^{31} T^{98} +$$$$27\!\cdots\!95$$$$p^{32} T^{99} +$$$$39\!\cdots\!76$$$$p^{33} T^{100} +$$$$56\!\cdots\!99$$$$p^{34} T^{101} +$$$$78\!\cdots\!97$$$$p^{35} T^{102} +$$$$10\!\cdots\!38$$$$p^{36} T^{103} +$$$$14\!\cdots\!03$$$$p^{37} T^{104} +$$$$19\!\cdots\!25$$$$p^{38} T^{105} +$$$$24\!\cdots\!22$$$$p^{39} T^{106} +$$$$31\!\cdots\!72$$$$p^{40} T^{107} +$$$$39\!\cdots\!49$$$$p^{41} T^{108} +$$$$47\!\cdots\!38$$$$p^{42} T^{109} +$$$$56\!\cdots\!77$$$$p^{43} T^{110} +$$$$65\!\cdots\!93$$$$p^{44} T^{111} +$$$$74\!\cdots\!93$$$$p^{45} T^{112} +$$$$82\!\cdots\!94$$$$p^{46} T^{113} +$$$$88\!\cdots\!75$$$$p^{47} T^{114} +$$$$92\!\cdots\!88$$$$p^{48} T^{115} +$$$$94\!\cdots\!80$$$$p^{49} T^{116} +$$$$93\!\cdots\!69$$$$p^{50} T^{117} + 88776221547428996953 p^{51} T^{118} + 8171700269241586671 p^{52} T^{119} + 725671207486485565 p^{53} T^{120} + 61825786869194071 p^{54} T^{121} + 5057441927355674 p^{55} T^{122} + 393910785716521 p^{56} T^{123} + 29279373527585 p^{57} T^{124} + 2049397162289 p^{58} T^{125} + 135828703113 p^{59} T^{126} + 8330144197 p^{60} T^{127} + 478841921 p^{61} T^{128} + 24686945 p^{62} T^{129} + 1177598 p^{63} T^{130} + 47111 p^{64} T^{131} + 1721 p^{65} T^{132} + 43 p^{66} T^{133} + p^{67} T^{134}$$
29 $$1 + 63 T + 2956 T^{2} + 102545 T^{3} + 3034627 T^{4} + 77450312 T^{5} + 1776951121 T^{6} + 36992748857 T^{7} + 711418818065 T^{8} + 12724953934347 T^{9} + 213739798937402 T^{10} + 3388105461421858 T^{11} + 50985064928951449 T^{12} + 731029315876604291 T^{13} + 10026986048448459382 T^{14} +$$$$13\!\cdots\!10$$$$T^{15} +$$$$16\!\cdots\!37$$$$T^{16} +$$$$20\!\cdots\!41$$$$T^{17} +$$$$24\!\cdots\!20$$$$T^{18} +$$$$27\!\cdots\!00$$$$T^{19} +$$$$30\!\cdots\!35$$$$T^{20} +$$$$32\!\cdots\!95$$$$T^{21} +$$$$34\!\cdots\!45$$$$T^{22} +$$$$34\!\cdots\!63$$$$T^{23} +$$$$34\!\cdots\!39$$$$T^{24} +$$$$33\!\cdots\!81$$$$T^{25} +$$$$31\!\cdots\!98$$$$T^{26} +$$$$29\!\cdots\!38$$$$T^{27} +$$$$26\!\cdots\!33$$$$T^{28} +$$$$23\!\cdots\!32$$$$T^{29} +$$$$20\!\cdots\!43$$$$T^{30} +$$$$17\!\cdots\!80$$$$T^{31} +$$$$14\!\cdots\!92$$$$T^{32} +$$$$11\!\cdots\!45$$$$T^{33} +$$$$93\!\cdots\!55$$$$T^{34} +$$$$74\!\cdots\!52$$$$T^{35} +$$$$57\!\cdots\!73$$$$T^{36} +$$$$43\!\cdots\!14$$$$T^{37} +$$$$33\!\cdots\!37$$$$T^{38} +$$$$24\!\cdots\!58$$$$T^{39} +$$$$17\!\cdots\!74$$$$T^{40} +$$$$12\!\cdots\!40$$$$T^{41} +$$$$90\!\cdots\!42$$$$T^{42} +$$$$63\!\cdots\!69$$$$T^{43} +$$$$43\!\cdots\!50$$$$T^{44} +$$$$29\!\cdots\!58$$$$T^{45} +$$$$19\!\cdots\!92$$$$T^{46} +$$$$13\!\cdots\!86$$$$T^{47} +$$$$86\!\cdots\!87$$$$T^{48} +$$$$56\!\cdots\!90$$$$T^{49} +$$$$35\!\cdots\!04$$$$T^{50} +$$$$22\!\cdots\!95$$$$T^{51} +$$$$14\!\cdots\!67$$$$T^{52} +$$$$87\!\cdots\!00$$$$T^{53} +$$$$53\!\cdots\!92$$$$T^{54} +$$$$32\!\cdots\!48$$$$T^{55} +$$$$19\!\cdots\!88$$$$T^{56} +$$$$11\!\cdots\!15$$$$T^{57} +$$$$68\!\cdots\!19$$$$T^{58} +$$$$39\!\cdots\!78$$$$T^{59} +$$$$22\!\cdots\!43$$$$T^{60} +$$$$13\!\cdots\!14$$$$T^{61} +$$$$74\!\cdots\!74$$$$T^{62} +$$$$41\!\cdots\!70$$$$T^{63} +$$$$23\!\cdots\!37$$$$T^{64} +$$$$12\!\cdots\!28$$$$T^{65} +$$$$69\!\cdots\!91$$$$T^{66} +$$$$37\!\cdots\!45$$$$T^{67} +$$$$69\!\cdots\!91$$$$p T^{68} +$$$$12\!\cdots\!28$$$$p^{2} T^{69} +$$$$23\!\cdots\!37$$$$p^{3} T^{70} +$$$$41\!\cdots\!70$$$$p^{4} T^{71} +$$$$74\!\cdots\!74$$$$p^{5} T^{72} +$$$$13\!\cdots\!14$$$$p^{6} T^{73} +$$$$22\!\cdots\!43$$$$p^{7} T^{74} +$$$$39\!\cdots\!78$$$$p^{8} T^{75} +$$$$68\!\cdots\!19$$$$p^{9} T^{76} +$$$$11\!\cdots\!15$$$$p^{10} T^{77} +$$$$19\!\cdots\!88$$$$p^{11} T^{78} +$$$$32\!\cdots\!48$$$$p^{12} T^{79} +$$$$53\!\cdots\!92$$$$p^{13} T^{80} +$$$$87\!\cdots\!00$$$$p^{14} T^{81} +$$$$14\!\cdots\!67$$$$p^{15} T^{82} +$$$$22\!\cdots\!95$$$$p^{16} T^{83} +$$$$35\!\cdots\!04$$$$p^{17} T^{84} +$$$$56\!\cdots\!90$$$$p^{18} T^{85} +$$$$86\!\cdots\!87$$$$p^{19} T^{86} +$$$$13\!\cdots\!86$$$$p^{20} T^{87} +$$$$19\!\cdots\!92$$$$p^{21} T^{88} +$$$$29\!\cdots\!58$$$$p^{22} T^{89} +$$$$43\!\cdots\!50$$$$p^{23} T^{90} +$$$$63\!\cdots\!69$$$$p^{24} T^{91} +$$$$90\!\cdots\!42$$$$p^{25} T^{92} +$$$$12\!\cdots\!40$$$$p^{26} T^{93} +$$$$17\!\cdots\!74$$$$p^{27} T^{94} +$$$$24\!\cdots\!58$$$$p^{28} T^{95} +$$$$33\!\cdots\!37$$$$p^{29} T^{96} +$$$$43\!\cdots\!14$$$$p^{30} T^{97} +$$$$57\!\cdots\!73$$$$p^{31} T^{98} +$$$$74\!\cdots\!52$$$$p^{32} T^{99} +$$$$93\!\cdots\!55$$$$p^{33} T^{100} +$$$$11\!\cdots\!45$$$$p^{34} T^{101} +$$$$14\!\cdots\!92$$$$p^{35} T^{102} +$$$$17\!\cdots\!80$$$$p^{36} T^{103} +$$$$20\!\cdots\!43$$$$p^{37} T^{104} +$$$$23\!\cdots\!32$$$$p^{38} T^{105} +$$$$26\!\cdots\!33$$$$p^{39} T^{106} +$$$$29\!\cdots\!38$$$$p^{40} T^{107} +$$$$31\!\cdots\!98$$$$p^{41} T^{108} +$$$$33\!\cdots\!81$$$$p^{42} T^{109} +$$$$34\!\cdots\!39$$$$p^{43} T^{110} +$$$$34\!\cdots\!63$$$$p^{44} T^{111} +$$$$34\!\cdots\!45$$$$p^{45} T^{112} +$$$$32\!\cdots\!95$$$$p^{46} T^{113} +$$$$30\!\cdots\!35$$$$p^{47} T^{114} +$$$$27\!\cdots\!00$$$$p^{48} T^{115} +$$$$24\!\cdots\!20$$$$p^{49} T^{116} +$$$$20\!\cdots\!41$$$$p^{50} T^{117} +$$$$16\!\cdots\!37$$$$p^{51} T^{118} +$$$$13\!\cdots\!10$$$$p^{52} T^{119} + 10026986048448459382 p^{53} T^{120} + 731029315876604291 p^{54} T^{121} + 50985064928951449 p^{55} T^{122} + 3388105461421858 p^{56} T^{123} + 213739798937402 p^{57} T^{124} + 12724953934347 p^{58} T^{125} + 711418818065 p^{59} T^{126} + 36992748857 p^{60} T^{127} + 1776951121 p^{61} T^{128} + 77450312 p^{62} T^{129} + 3034627 p^{63} T^{130} + 102545 p^{64} T^{131} + 2956 p^{65} T^{132} + 63 p^{66} T^{133} + p^{67} T^{134}$$
31 $$1 + 43 T + 1938 T^{2} + 56213 T^{3} + 1565150 T^{4} + 35484473 T^{5} + 764023462 T^{6} + 14512657139 T^{7} + 262386004236 T^{8} + 4345451327902 T^{9} + 68816855888140 T^{10} + 32885443815832 p T^{11} + 14508720291942649 T^{12} + 195703029170726481 T^{13} + 2546629025197024237 T^{14} + 31688248835721339282 T^{15} + 12314762810638004897 p T^{16} +$$$$44\!\cdots\!74$$$$T^{17} +$$$$49\!\cdots\!17$$$$T^{18} +$$$$54\!\cdots\!91$$$$T^{19} +$$$$57\!\cdots\!39$$$$T^{20} +$$$$59\!\cdots\!54$$$$T^{21} +$$$$59\!\cdots\!38$$$$T^{22} +$$$$58\!\cdots\!39$$$$T^{23} +$$$$55\!\cdots\!07$$$$T^{24} +$$$$51\!\cdots\!31$$$$T^{25} +$$$$47\!\cdots\!42$$$$T^{26} +$$$$42\!\cdots\!87$$$$T^{27} +$$$$37\!\cdots\!92$$$$T^{28} +$$$$32\!\cdots\!57$$$$T^{29} +$$$$27\!\cdots\!93$$$$T^{30} +$$$$22\!\cdots\!31$$$$T^{31} +$$$$18\!\cdots\!77$$$$T^{32} +$$$$14\!\cdots\!93$$$$T^{33} +$$$$11\!\cdots\!24$$$$T^{34} +$$$$90\!\cdots\!74$$$$T^{35} +$$$$69\!\cdots\!88$$$$T^{36} +$$$$52\!\cdots\!27$$$$T^{37} +$$$$39\!\cdots\!33$$$$T^{38} +$$$$28\!\cdots\!08$$$$T^{39} +$$$$20\!\cdots\!21$$$$T^{40} +$$$$14\!\cdots\!84$$$$T^{41} +$$$$10\!\cdots\!27$$$$T^{42} +$$$$73\!\cdots\!04$$$$T^{43} +$$$$50\!\cdots\!21$$$$T^{44} +$$$$34\!\cdots\!84$$$$T^{45} +$$$$23\!\cdots\!89$$$$T^{46} +$$$$15\!\cdots\!54$$$$T^{47} +$$$$10\!\cdots\!02$$$$T^{48} +$$$$68\!\cdots\!24$$$$T^{49} +$$$$44\!\cdots\!71$$$$T^{50} +$$$$28\!\cdots\!42$$$$T^{51} +$$$$18\!\cdots\!29$$$$T^{52} +$$$$11\!\cdots\!32$$$$T^{53} +$$$$71\!\cdots\!02$$$$T^{54} +$$$$44\!\cdots\!62$$$$T^{55} +$$$$27\!\cdots\!04$$$$T^{56} +$$$$16\!\cdots\!61$$$$T^{57} +$$$$98\!\cdots\!85$$$$T^{58} +$$$$59\!\cdots\!32$$$$T^{59} +$$$$35\!\cdots\!21$$$$T^{60} +$$$$20\!\cdots\!00$$$$T^{61} +$$$$11\!\cdots\!42$$$$T^{62} +$$$$22\!\cdots\!35$$$$p T^{63} +$$$$39\!\cdots\!87$$$$T^{64} +$$$$22\!\cdots\!22$$$$T^{65} +$$$$12\!\cdots\!25$$$$T^{66} +$$$$71\!\cdots\!81$$$$T^{67} +$$$$12\!\cdots\!25$$$$p T^{68} +$$$$22\!\cdots\!22$$$$p^{2} T^{69} +$$$$39\!\cdots\!87$$$$p^{3} T^{70} +$$$$22\!\cdots\!35$$$$p^{5} T^{71} +$$$$11\!\cdots\!42$$$$p^{5} T^{72} +$$$$20\!\cdots\!00$$$$p^{6} T^{73} +$$$$35\!\cdots\!21$$$$p^{7} T^{74} +$$$$59\!\cdots\!32$$$$p^{8} T^{75} +$$$$98\!\cdots\!85$$$$p^{9} T^{76} +$$$$16\!\cdots\!61$$$$p^{10} T^{77} +$$$$27\!\cdots\!04$$$$p^{11} T^{78} +$$$$44\!\cdots\!62$$$$p^{12} T^{79} +$$$$71\!\cdots\!02$$$$p^{13} T^{80} +$$$$11\!\cdots\!32$$$$p^{14} T^{81} +$$$$18\!\cdots\!29$$$$p^{15} T^{82} +$$$$28\!\cdots\!42$$$$p^{16} T^{83} +$$$$44\!\cdots\!71$$$$p^{17} T^{84} +$$$$68\!\cdots\!24$$$$p^{18} T^{85} +$$$$10\!\cdots\!02$$$$p^{19} T^{86} +$$$$15\!\cdots\!54$$$$p^{20} T^{87} +$$$$23\!\cdots\!89$$$$p^{21} T^{88} +$$$$34\!\cdots\!84$$$$p^{22} T^{89} +$$$$50\!\cdots\!21$$$$p^{23} T^{90} +$$$$73\!\cdots\!04$$$$p^{24} T^{91} +$$$$10\!\cdots\!27$$$$p^{25} T^{92} +$$$$14\!\cdots\!84$$$$p^{26} T^{93} +$$$$20\!\cdots\!21$$$$p^{27} T^{94} +$$$$28\!\cdots\!08$$$$p^{28} T^{95} +$$$$39\!\cdots\!33$$$$p^{29} T^{96} +$$$$52\!\cdots\!27$$$$p^{30} T^{97} +$$$$69\!\cdots\!88$$$$p^{31} T^{98} +$$$$90\!\cdots\!74$$$$p^{32} T^{99} +$$$$11\!\cdots\!24$$$$p^{33} T^{100} +$$$$14\!\cdots\!93$$$$p^{34} T^{101} +$$$$18\!\cdots\!77$$$$p^{35} T^{102} +$$$$22\!\cdots\!31$$$$p^{36} T^{103} +$$$$27\!\cdots\!93$$$$p^{37} T^{104} +$$$$32\!\cdots\!57$$$$p^{38} T^{105} +$$$$37\!\cdots\!92$$$$p^{39} T^{106} +$$$$42\!\cdots\!87$$$$p^{40} T^{107} +$$$$47\!\cdots\!42$$$$p^{41} T^{108} +$$$$51\!\cdots\!31$$$$p^{42} T^{109} +$$$$55\!\cdots\!07$$$$p^{43} T^{110} +$$$$58\!\cdots\!39$$$$p^{44} T^{111} +$$$$59\!\cdots\!38$$$$p^{45} T^{112} +$$$$59\!\cdots\!54$$$$p^{46} T^{113} +$$$$57\!\cdots\!39$$$$p^{47} T^{114} +$$$$54\!\cdots\!91$$$$p^{48} T^{115} +$$$$49\!\cdots\!17$$$$p^{49} T^{116} +$$$$44\!\cdots\!74$$$$p^{50} T^{117} + 12314762810638004897 p^{52} T^{118} + 31688248835721339282 p^{52} T^{119} + 2546629025197024237 p^{53} T^{120} + 195703029170726481 p^{54} T^{121} + 14508720291942649 p^{55} T^{122} + 32885443815832 p^{57} T^{123} + 68816855888140 p^{57} T^{124} + 4345451327902 p^{58} T^{125} + 262386004236 p^{59} T^{126} + 14512657139 p^{60} T^{127} + 764023462 p^{61} T^{128} + 35484473 p^{62} T^{129} + 1565150 p^{63} T^{130} + 56213 p^{64} T^{131} + 1938 p^{65} T^{132} + 43 p^{66} T^{133} + p^{67} T^{134}$$
37 $$1 + 77 T + 4229 T^{2} + 172059 T^{3} + 5907572 T^{4} + 174613644 T^{5} + 4617882460 T^{6} + 110600219288 T^{7} + 2440612878876 T^{8} + 50014507161417 T^{9} + 960909076264104 T^{10} + 17403022100860803 T^{11} + 298900320806624229 T^{12} + 4887679124375559038 T^{13} + 76408148344531889789 T^{14} +$$$$11\!\cdots\!30$$$$T^{15} +$$$$16\!\cdots\!58$$$$T^{16} +$$$$22\!\cdots\!02$$$$T^{17} +$$$$30\!\cdots\!71$$$$T^{18} +$$$$40\!\cdots\!25$$$$T^{19} +$$$$50\!\cdots\!60$$$$T^{20} +$$$$61\!\cdots\!33$$$$T^{21} +$$$$73\!\cdots\!44$$$$T^{22} +$$$$85\!\cdots\!77$$$$T^{23} +$$$$96\!\cdots\!06$$$$T^{24} +$$$$10\!\cdots\!60$$$$T^{25} +$$$$11\!\cdots\!17$$$$T^{26} +$$$$12\!\cdots\!62$$$$T^{27} +$$$$12\!\cdots\!16$$$$T^{28} +$$$$12\!\cdots\!68$$$$T^{29} +$$$$12\!\cdots\!95$$$$T^{30} +$$$$12\!\cdots\!82$$$$T^{31} +$$$$11\!\cdots\!22$$$$T^{32} +$$$$10\!\cdots\!85$$$$T^{33} +$$$$98\!\cdots\!16$$$$T^{34} +$$$$88\!\cdots\!00$$$$T^{35} +$$$$78\!\cdots\!49$$$$T^{36} +$$$$68\!\cdots\!33$$$$T^{37} +$$$$59\!\cdots\!96$$$$T^{38} +$$$$50\!\cdots\!50$$$$T^{39} +$$$$41\!\cdots\!28$$$$T^{40} +$$$$34\!\cdots\!70$$$$T^{41} +$$$$27\!\cdots\!22$$$$T^{42} +$$$$22\!\cdots\!94$$$$T^{43} +$$$$17\!\cdots\!48$$$$T^{44} +$$$$13\!\cdots\!51$$$$T^{45} +$$$$10\!\cdots\!35$$$$T^{46} +$$$$79\!\cdots\!79$$$$T^{47} +$$$$59\!\cdots\!58$$$$T^{48} +$$$$44\!\cdots\!45$$$$T^{49} +$$$$32\!\cdots\!44$$$$T^{50} +$$$$63\!\cdots\!77$$$$p T^{51} +$$$$16\!\cdots\!45$$$$T^{52} +$$$$11\!\cdots\!56$$$$T^{53} +$$$$82\!\cdots\!95$$$$T^{54} +$$$$56\!\cdots\!92$$$$T^{55} +$$$$38\!\cdots\!01$$$$T^{56} +$$$$26\!\cdots\!02$$$$T^{57} +$$$$17\!\cdots\!39$$$$T^{58} +$$$$11\!\cdots\!95$$$$T^{59} +$$$$76\!\cdots\!63$$$$T^{60} +$$$$49\!\cdots\!96$$$$T^{61} +$$$$31\!\cdots\!64$$$$T^{62} +$$$$20\!\cdots\!31$$$$T^{63} +$$$$12\!\cdots\!59$$$$T^{64} +$$$$79\!\cdots\!27$$$$T^{65} +$$$$49\!\cdots\!27$$$$T^{66} +$$$$30\!\cdots\!91$$$$T^{67} +$$$$49\!\cdots\!27$$$$p T^{68} +$$$$79\!\cdots\!27$$$$p^{2} T^{69} +$$$$12\!\cdots\!59$$$$p^{3} T^{70} +$$$$20\!\cdots\!31$$$$p^{4} T^{71} +$$$$31\!\cdots\!64$$$$p^{5} T^{72} +$$$$49\!\cdots\!96$$$$p^{6} T^{73} +$$$$76\!\cdots\!63$$$$p^{7} T^{74} +$$$$11\!\cdots\!95$$$$p^{8} T^{75} +$$$$17\!\cdots\!39$$$$p^{9} T^{76} +$$$$26\!\cdots\!02$$$$p^{10} T^{77} +$$$$38\!\cdots\!01$$$$p^{11} T^{78} +$$$$56\!\cdots\!92$$$$p^{12} T^{79} +$$$$82\!\cdots\!95$$$$p^{13} T^{80} +$$$$11\!\cdots\!56$$$$p^{14} T^{81} +$$$$16\!\cdots\!45$$$$p^{15} T^{82} +$$$$63\!\cdots\!77$$$$p^{17} T^{83} +$$$$32\!\cdots\!44$$$$p^{17} T^{84} +$$$$44\!\cdots\!45$$$$p^{18} T^{85} +$$$$59\!\cdots\!58$$$$p^{19} T^{86} +$$$$79\!\cdots\!79$$$$p^{20} T^{87} +$$$$10\!\cdots\!35$$$$p^{21} T^{88} +$$$$13\!\cdots\!51$$$$p^{22} T^{89} +$$$$17\!\cdots\!48$$$$p^{23} T^{90} +$$$$22\!\cdots\!94$$$$p^{24} T^{91} +$$$$27\!\cdots\!22$$$$p^{25} T^{92} +$$$$34\!\cdots\!70$$$$p^{26} T^{93} +$$$$41\!\cdots\!28$$$$p^{27} T^{94} +$$$$50\!\cdots\!50$$$$p^{28} T^{95} +$$$$59\!\cdots\!96$$$$p^{29} T^{96} +$$$$68\!\cdots\!33$$$$p^{30} T^{97} +$$$$78\!\cdots\!49$$$$p^{31} T^{98} +$$$$88\!\cdots\!00$$$$p^{32} T^{99} +$$$$98\!\cdots\!16$$$$p^{33} T^{100} +$$$$10\!\cdots\!85$$$$p^{34} T^{101} +$$$$11\!\cdots\!22$$$$p^{35} T^{102} +$$$$12\!\cdots\!82$$$$p^{36} T^{103} +$$$$12\!\cdots\!95$$$$p^{37} T^{104} +$$$$12\!\cdots\!68$$$$p^{38} T^{105} +$$$$12\!\cdots\!16$$$$p^{39} T^{106} +$$$$12\!\cdots\!62$$$$p^{40} T^{107} +$$$$11\!\cdots\!17$$$$p^{41} T^{108} +$$$$10\!\cdots\!60$$$$p^{42} T^{109} +$$$$96\!\cdots\!06$$$$p^{43} T^{110} +$$$$85\!\cdots\!77$$$$p^{44} T^{111} +$$$$73\!\cdots\!44$$$$p^{45} T^{112} +$$$$61\!\cdots\!33$$$$p^{46} T^{113} +$$$$50\!\cdots\!60$$$$p^{47} T^{114} +$$$$40\!\cdots\!25$$$$p^{48} T^{115} +$$$$30\!\cdots\!71$$$$p^{49} T^{116} +$$$$22\!\cdots\!02$$$$p^{50} T^{117} +$$$$16\!\cdots\!58$$$$p^{51} T^{118} +$$$$11\!\cdots\!30$$$$p^{52} T^{119} + 76408148344531889789 p^{53} T^{120} + 4887679124375559038 p^{54} T^{121} + 298900320806624229 p^{55} T^{122} + 17403022100860803 p^{56} T^{123} + 960909076264104 p^{57} T^{124} + 50014507161417 p^{58} T^{125} + 2440612878876 p^{59} T^{126} + 110600219288 p^{60} T^{127} + 4617882460 p^{61} T^{128} + 174613644 p^{62} T^{129} + 5907572 p^{63} T^{130} + 172059 p^{64} T^{131} + 4229 p^{65} T^{132} + 77 p^{66} T^{133} + p^{67} T^{134}$$
41 $$1 + 50 T + 2715 T^{2} + 93900 T^{3} + 3153628 T^{4} + 86168945 T^{5} + 2245240037 T^{6} + 51721511011 T^{7} + 1135610127860 T^{8} + 22907244907396 T^{9} + 441980941203046 T^{10} + 8001140800538430 T^{11} + 139128531995107744 T^{12} + 2299258607972322174 T^{13} + 36643166862236263158 T^{14} +$$$$55\!\cdots\!32$$$$T^{15} +$$$$82\!\cdots\!89$$$$T^{16} +$$$$11\!\cdots\!85$$$$T^{17} +$$$$16\!\cdots\!06$$$$T^{18} +$$$$21\!\cdots\!97$$$$T^{19} +$$$$28\!\cdots\!24$$$$T^{20} +$$$$36\!\cdots\!27$$$$T^{21} +$$$$10\!\cdots\!61$$$$p T^{22} +$$$$53\!\cdots\!44$$$$T^{23} +$$$$63\!\cdots\!26$$$$T^{24} +$$$$72\!\cdots\!90$$$$T^{25} +$$$$82\!\cdots\!25$$$$T^{26} +$$$$90\!\cdots\!00$$$$T^{27} +$$$$97\!\cdots\!33$$$$T^{28} +$$$$10\!\cdots\!36$$$$T^{29} +$$$$10\!\cdots\!22$$$$T^{30} +$$$$26\!\cdots\!25$$$$p T^{31} +$$$$10\!\cdots\!90$$$$T^{32} +$$$$10\!\cdots\!79$$$$T^{33} +$$$$10\!\cdots\!76$$$$T^{34} +$$$$99\!\cdots\!05$$$$T^{35} +$$$$92\!\cdots\!97$$$$T^{36} +$$$$85\!\cdots\!68$$$$T^{37} +$$$$77\!\cdots\!58$$$$T^{38} +$$$$69\!\cdots\!24$$$$T^{39} +$$$$61\!\cdots\!35$$$$T^{40} +$$$$53\!\cdots\!54$$$$T^{41} +$$$$45\!\cdots\!29$$$$T^{42} +$$$$38\!\cdots\!66$$$$T^{43} +$$$$32\!\cdots\!94$$$$T^{44} +$$$$26\!\cdots\!80$$$$T^{45} +$$$$21\!\cdots\!27$$$$T^{46} +$$$$17\!\cdots\!17$$$$T^{47} +$$$$13\!\cdots\!55$$$$T^{48} +$$$$10\!\cdots\!13$$$$T^{49} +$$$$83\!\cdots\!33$$$$T^{50} +$$$$63\!\cdots\!58$$$$T^{51} +$$$$48\!\cdots\!13$$$$T^{52} +$$$$36\!\cdots\!55$$$$T^{53} +$$$$26\!\cdots\!81$$$$T^{54} +$$$$19\!\cdots\!71$$$$T^{55} +$$$$14\!\cdots\!46$$$$T^{56} +$$$$10\!\cdots\!11$$$$T^{57} +$$$$71\!\cdots\!30$$$$T^{58} +$$$$49\!\cdots\!54$$$$T^{59} +$$$$34\!\cdots\!68$$$$T^{60} +$$$$23\!\cdots\!44$$$$T^{61} +$$$$16\!\cdots\!85$$$$T^{62} +$$$$10\!\cdots\!83$$$$T^{63} +$$$$71\!\cdots\!19$$$$T^{64} +$$$$46\!\cdots\!71$$$$T^{65} +$$$$30\!\cdots\!20$$$$T^{66} +$$$$19\!\cdots\!49$$$$T^{67} +$$$$30\!\cdots\!20$$$$p T^{68} +$$$$46\!\cdots\!71$$$$p^{2} T^{69} +$$$$71\!\cdots\!19$$$$p^{3} T^{70} +$$$$10\!\cdots\!83$$$$p^{4} T^{71} +$$$$16\!\cdots\!85$$$$p^{5} T^{72} +$$$$23\!\cdots\!44$$$$p^{6} T^{73} +$$$$34\!\cdots\!68$$$$p^{7} T^{74} +$$$$49\!\cdots\!54$$$$p^{8} T^{75} +$$$$71\!\cdots\!30$$$$p^{9} T^{76} +$$$$10\!\cdots\!11$$$$p^{10} T^{77} +$$$$14\!\cdots\!46$$$$p^{11} T^{78} +$$$$19\!\cdots\!71$$$$p^{12} T^{79} +$$$$26\!\cdots\!81$$$$p^{13} T^{80} +$$$$36\!\cdots\!55$$$$p^{14} T^{81} +$$$$48\!\cdots\!13$$$$p^{15} T^{82} +$$$$63\!\cdots\!58$$$$p^{16} T^{83} +$$$$83\!\cdots\!33$$$$p^{17} T^{84} +$$$$10\!\cdots\!13$$$$p^{18} T^{85} +$$$$13\!\cdots\!55$$$$p^{19} T^{86} +$$$$17\!\cdots\!17$$$$p^{20} T^{87} +$$$$21\!\cdots\!27$$$$p^{21} T^{88} +$$$$26\!\cdots\!80$$$$p^{22} T^{89} +$$$$32\!\cdots\!94$$$$p^{23} T^{90} +$$$$38\!\cdots\!66$$$$p^{24} T^{91} +$$$$45\!\cdots\!29$$$$p^{25} T^{92} +$$$$53\!\cdots\!54$$$$p^{26} T^{93} +$$$$61\!\cdots\!35$$$$p^{27} T^{94} +$$$$69\!\cdots\!24$$$$p^{28} T^{95} +$$$$77\!\cdots\!58$$$$p^{29} T^{96} +$$$$85\!\cdots\!68$$$$p^{30} T^{97} +$$$$92\!\cdots\!97$$$$p^{31} T^{98} +$$$$99\!\cdots\!05$$$$p^{32} T^{99} +$$$$10\!\cdots\!76$$$$p^{33} T^{100} +$$$$10\!\cdots\!79$$$$p^{34} T^{101} +$$$$10\!\cdots\!90$$$$p^{35} T^{102} +$$$$26\!\cdots\!25$$$$p^{37} T^{103} +$$$$10\!\cdots\!22$$$$p^{37} T^{104} +$$$$10\!\cdots\!36$$$$p^{38} T^{105} +$$$$97\!\cdots\!33$$$$p^{39} T^{106} +$$$$90\!\cdots\!00$$$$p^{40} T^{107} +$$$$82\!\cdots\!25$$$$p^{41} T^{108} +$$$$72\!\cdots\!90$$$$p^{42} T^{109} +$$$$63\!\cdots\!26$$$$p^{43} T^{110} +$$$$53\!\cdots\!44$$$$p^{44} T^{111} +$$$$10\!\cdots\!61$$$$p^{46} T^{112} +$$$$36\!\cdots\!27$$$$p^{46} T^{113} +$$$$28\!\cdots\!24$$$$p^{47} T^{114} +$$$$21\!\cdots\!97$$$$p^{48} T^{115} +$$$$16\!\cdots\!06$$$$p^{49} T^{116} +$$$$11\!\cdots\!85$$$$p^{50} T^{117} +$$$$82\!\cdots\!89$$$$p^{51} T^{118} +$$$$55\!\cdots\!32$$$$p^{52} T^{119} + 36643166862236263158 p^{53} T^{120} + 2299258607972322174 p^{54} T^{121} + 139128531995107744 p^{55} T^{122} + 8001140800538430 p^{56} T^{123} + 441980941203046 p^{57} T^{124} + 22907244907396 p^{58} T^{125} + 1135610127860 p^{59} T^{126} + 51721511011 p^{60} T^{127} + 2245240037 p^{61} T^{128} + 86168945 p^{62} T^{129} + 3153628 p^{63} T^{130} + 93900 p^{64} T^{131} + 2715 p^{65} T^{132} + 50 p^{66} T^{133} + p^{67} T^{134}$$
43 $$1 + 56 T + 3214 T^{2} + 120412 T^{3} + 4280699 T^{4} + 124922107 T^{5} + 3437823272 T^{6} + 83887169840 T^{7} + 1939013444807 T^{8} + 41191139349771 T^{9} + 833805916662397 T^{10} + 15823119317833759 T^{11} + 287681108866043085 T^{12} + 4964309194013449987 T^{13} + 82452023089453507711 T^{14} +$$$$13\!\cdots\!80$$$$T^{15} +$$$$20\!\cdots\!78$$$$T^{16} +$$$$29\!\cdots\!67$$$$T^{17} +$$$$42\!\cdots\!91$$$$T^{18} +$$$$59\!\cdots\!39$$$$T^{19} +$$$$79\!\cdots\!07$$$$T^{20} +$$$$10\!\cdots\!78$$$$T^{21} +$$$$13\!\cdots\!67$$$$T^{22} +$$$$16\!\cdots\!49$$$$T^{23} +$$$$19\!\cdots\!86$$$$T^{24} +$$$$23\!\cdots\!62$$$$T^{25} +$$$$27\!\cdots\!40$$$$T^{26} +$$$$30\!\cdots\!94$$$$T^{27} +$$$$33\!\cdots\!75$$$$T^{28} +$$$$36\!\cdots\!19$$$$T^{29} +$$$$89\!\cdots\!40$$$$p T^{30} +$$$$40\!\cdots\!95$$$$T^{31} +$$$$41\!\cdots\!23$$$$T^{32} +$$$$41\!\cdots\!44$$$$T^{33} +$$$$40\!\cdots\!30$$$$T^{34} +$$$$39\!\cdots\!22$$$$T^{35} +$$$$37\!\cdots\!90$$$$T^{36} +$$$$34\!\cdots\!95$$$$T^{37} +$$$$31\!\cdots\!95$$$$T^{38} +$$$$67\!\cdots\!26$$$$p T^{39} +$$$$25\!\cdots\!48$$$$T^{40} +$$$$22\!\cdots\!99$$$$T^{41} +$$$$19\!\cdots\!13$$$$T^{42} +$$$$16\!\cdots\!26$$$$T^{43} +$$$$14\!\cdots\!36$$$$T^{44} +$$$$11\!\cdots\!44$$$$T^{45} +$$$$97\!\cdots\!60$$$$T^{46} +$$$$79\!\cdots\!21$$$$T^{47} +$$$$63\!\cdots\!91$$$$T^{48} +$$$$50\!\cdots\!40$$$$T^{49} +$$$$39\!\cdots\!25$$$$T^{50} +$$$$30\!\cdots\!78$$$$T^{51} +$$$$23\!\cdots\!01$$$$T^{52} +$$$$41\!\cdots\!25$$$$p T^{53} +$$$$13\!\cdots\!71$$$$T^{54} +$$$$97\!\cdots\!10$$$$T^{55} +$$$$71\!\cdots\!51$$$$T^{56} +$$$$52\!\cdots\!75$$$$T^{57} +$$$$37\!\cdots\!65$$$$T^{58} +$$$$26\!\cdots\!58$$$$T^{59} +$$$$18\!\cdots\!02$$$$T^{60} +$$$$13\!\cdots\!60$$$$T^{61} +$$$$90\!\cdots\!62$$$$T^{62} +$$$$61\!\cdots\!84$$$$T^{63} +$$$$41\!\cdots\!70$$$$T^{64} +$$$$28\!\cdots\!89$$$$T^{65} +$$$$18\!\cdots\!18$$$$T^{66} +$$$$12\!\cdots\!57$$$$T^{67} +$$$$18\!\cdots\!18$$$$p T^{68} +$$$$28\!\cdots\!89$$$$p^{2} T^{69} +$$$$41\!\cdots\!70$$$$p^{3} T^{70} +$$$$61\!\cdots\!84$$$$p^{4} T^{71} +$$$$90\!\cdots\!62$$$$p^{5} T^{72} +$$$$13\!\cdots\!60$$$$p^{6} T^{73} +$$$$18\!\cdots\!02$$$$p^{7} T^{74} +$$$$26\!\cdots\!58$$$$p^{8} T^{75} +$$$$37\!\cdots\!65$$$$p^{9} T^{76} +$$$$52\!\cdots\!75$$$$p^{10} T^{77} +$$$$71\!\cdots\!51$$$$p^{11} T^{78} +$$$$97\!\cdots\!10$$$$p^{12} T^{79} +$$$$13\!\cdots\!71$$$$p^{13} T^{80} +$$$$41\!\cdots\!25$$$$p^{15} T^{81} +$$$$23\!\cdots\!01$$$$p^{15} T^{82} +$$$$30\!\cdots\!78$$$$p^{16} T^{83} +$$$$39\!\cdots\!25$$$$p^{17} T^{84} +$$$$50\!\cdots\!40$$$$p^{18} T^{85} +$$$$63\!\cdots\!91$$$$p^{19} T^{86} +$$$$79\!\cdots\!21$$$$p^{20} T^{87} +$$$$97\!\cdots\!60$$$$p^{21} T^{88} +$$$$11\!\cdots\!44$$$$p^{22} T^{89} +$$$$14\!\cdots\!36$$$$p^{23} T^{90} +$$$$16\!\cdots\!26$$$$p^{24} T^{91} +$$$$19\!\cdots\!13$$$$p^{25} T^{92} +$$$$22\!\cdots\!99$$$$p^{26} T^{93} +$$$$25\!\cdots\!48$$$$p^{27} T^{94} +$$$$67\!\cdots\!26$$$$p^{29} T^{95} +$$$$31\!\cdots\!95$$$$p^{29} T^{96} +$$$$34\!\cdots\!95$$$$p^{30} T^{97} +$$$$37\!\cdots\!90$$$$p^{31} T^{98} +$$$$39\!\cdots\!22$$$$p^{32} T^{99} +$$$$40\!\cdots\!30$$$$p^{33} T^{100} +$$$$41\!\cdots\!44$$$$p^{34} T^{101} +$$$$41\!\cdots\!23$$$$p^{35} T^{102} +$$$$40\!\cdots\!95$$$$p^{36} T^{103} +$$$$89\!\cdots\!40$$$$p^{38} T^{104} +$$$$36\!\cdots\!19$$$$p^{38} T^{105} +$$$$33\!\cdots\!75$$$$p^{39} T^{106} +$$$$30\!\cdots\!94$$$$p^{40} T^{107} +$$$$27\!\cdots\!40$$$$p^{41} T^{108} +$$$$23\!\cdots\!62$$$$p^{42} T^{109} +$$$$19\!\cdots\!86$$$$p^{43} T^{110} +$$$$16\!\cdots\!49$$$$p^{44} T^{111} +$$$$13\!\cdots\!67$$$$p^{45} T^{112} +$$$$10\!\cdots\!78$$$$p^{46} T^{113} +$$$$79\!\cdots\!07$$$$p^{47} T^{114} +$$$$59\!\cdots\!39$$$$p^{48} T^{115} +$$$$42\!\cdots\!91$$$$p^{49} T^{116} +$$$$29\!\cdots\!67$$$$p^{50} T^{117} +$$$$20\!\cdots\!78$$$$p^{51} T^{118} +$$$$13\!\cdots\!80$$$$p^{52} T^{119} + 82452023089453507711 p^{53} T^{120} + 4964309194013449987 p^{54} T^{121} + 287681108866043085 p^{55} T^{122} + 15823119317833759 p^{56} T^{123} + 833805916662397 p^{57} T^{124} + 41191139349771 p^{58} T^{125} + 1939013444807 p^{59} T^{126} + 83887169840 p^{60} T^{127} + 3437823272 p^{61} T^{128} + 124922107 p^{62} T^{129} + 4280699 p^{63} T^{130} + 120412 p^{64} T^{131} + 3214 p^{65} T^{132} + 56 p^{66} T^{133} + p^{67} T^{134}$$
47 $$1 + 48 T + 2804 T^{2} + 97719 T^{3} + 3491923 T^{4} + 98182340 T^{5} + 2712666985 T^{6} + 65041082635 T^{7} + 1513400112788 T^{8} + 32001190720922 T^{9} + 654734494988595 T^{10} + 12485033646357158 T^{11} + 230450863901207457 T^{12} + 4025859562547666285 T^{13} + 68186813898444496388 T^{14} +$$$$11\!\cdots\!97$$$$T^{15} +$$$$17\!\cdots\!65$$$$T^{16} +$$$$26\!\cdots\!69$$$$T^{17} +$$$$38\!\cdots\!73$$$$T^{18} +$$$$55\!\cdots\!38$$$$T^{19} +$$$$76\!\cdots\!57$$$$T^{20} +$$$$10\!\cdots\!81$$$$T^{21} +$$$$13\!\cdots\!80$$$$T^{22} +$$$$17\!\cdots\!55$$$$T^{23} +$$$$22\!\cdots\!22$$$$T^{24} +$$$$27\!\cdots\!00$$$$T^{25} +$$$$32\!\cdots\!12$$$$T^{26} +$$$$38\!\cdots\!95$$$$T^{27} +$$$$44\!\cdots\!05$$$$T^{28} +$$$$50\!\cdots\!15$$$$T^{29} +$$$$55\!\cdots\!46$$$$T^{30} +$$$$60\!\cdots\!74$$$$T^{31} +$$$$64\!\cdots\!23$$$$T^{32} +$$$$68\!\cdots\!95$$$$T^{33} +$$$$70\!\cdots\!38$$$$T^{34} +$$$$71\!\cdots\!60$$$$T^{35} +$$$$71\!\cdots\!58$$$$T^{36} +$$$$70\!\cdots\!09$$$$T^{37} +$$$$68\!\cdots\!98$$$$T^{38} +$$$$65\!\cdots\!07$$$$T^{39} +$$$$61\!\cdots\!18$$$$T^{40} +$$$$57\!\cdots\!26$$$$T^{41} +$$$$52\!\cdots\!58$$$$T^{42} +$$$$47\!\cdots\!78$$$$T^{43} +$$$$42\!\cdots\!40$$$$T^{44} +$$$$36\!\cdots\!66$$$$T^{45} +$$$$32\!\cdots\!72$$$$T^{46} +$$$$27\!\cdots\!37$$$$T^{47} +$$$$23\!\cdots\!47$$$$T^{48} +$$$$19\!\cdots\!61$$$$T^{49} +$$$$16\!\cdots\!99$$$$T^{50} +$$$$13\!\cdots\!98$$$$T^{51} +$$$$10\!\cdots\!94$$$$T^{52} +$$$$84\!\cdots\!34$$$$T^{53} +$$$$66\!\cdots\!88$$$$T^{54} +$$$$51\!\cdots\!26$$$$T^{55} +$$$$40\!\cdots\!22$$$$T^{56} +$$$$30\!\cdots\!26$$$$T^{57} +$$$$23\!\cdots\!26$$$$T^{58} +$$$$17\!\cdots\!05$$$$T^{59} +$$$$12\!\cdots\!99$$$$T^{60} +$$$$93\!\cdots\!35$$$$T^{61} +$$$$67\!\cdots\!05$$$$T^{62} +$$$$48\!\cdots\!42$$$$T^{63} +$$$$34\!\cdots\!60$$$$T^{64} +$$$$24\!\cdots\!50$$$$T^{65} +$$$$16\!\cdots\!85$$$$T^{66} +$$$$11\!\cdots\!31$$$$T^{67} +$$$$16\!\cdots\!85$$$$p T^{68} +$$$$24\!\cdots\!50$$$$p^{2} T^{69} +$$$$34\!\cdots\!60$$$$p^{3} T^{70} +$$$$48\!\cdots\!42$$$$p^{4} T^{71} +$$$$67\!\cdots\!05$$$$p^{5} T^{72} +$$$$93\!\cdots\!35$$$$p^{6} T^{73} +$$$$12\!\cdots\!99$$$$p^{7} T^{74} +$$$$17\!\cdots\!05$$$$p^{8} T^{75} +$$$$23\!\cdots\!26$$$$p^{9} T^{76} +$$$$30\!\cdots\!26$$$$p^{10} T^{77} +$$$$40\!\cdots\!22$$$$p^{11} T^{78} +$$$$51\!\cdots\!26$$$$p^{12} T^{79} +$$$$66\!\cdots\!88$$$$p^{13} T^{80} +$$$$84\!\cdots\!34$$$$p^{14} T^{81} +$$$$10\!\cdots\!94$$$$p^{15} T^{82} +$$$$13\!\cdots\!98$$$$p^{16} T^{83} +$$$$16\!\cdots\!99$$$$p^{17} T^{84} +$$$$19\!\cdots\!61$$$$p^{18} T^{85} +$$$$23\!\cdots\!47$$$$p^{19} T^{86} +$$$$27\!\cdots\!37$$$$p^{20} T^{87} +$$$$32\!\cdots\!72$$$$p^{21} T^{88} +$$$$36\!\cdots\!66$$$$p^{22} T^{89} +$$$$42\!\cdots\!40$$$$p^{23} T^{90} +$$$$47\!\cdots\!78$$$$p^{24} T^{91} +$$$$52\!\cdots\!58$$$$p^{25} T^{92} +$$$$57\!\cdots\!26$$$$p^{26} T^{93} +$$$$61\!\cdots\!18$$$$p^{27} T^{94} +$$$$65\!\cdots\!07$$$$p^{28} T^{95} +$$$$68\!\cdots\!98$$$$p^{29} T^{96} +$$$$70\!\cdots\!09$$$$p^{30} T^{97} +$$$$71\!\cdots\!58$$$$p^{31} T^{98} +$$$$71\!\cdots\!60$$$$p^{32} T^{99} +$$$$70\!\cdots\!38$$$$p^{33} T^{100} +$$$$68\!\cdots\!95$$$$p^{34} T^{101} +$$$$64\!\cdots\!23$$$$p^{35} T^{102} +$$$$60\!\cdots\!74$$$$p^{36} T^{103} +$$$$55\!\cdots\!46$$$$p^{37} T^{104} +$$$$50\!\cdots\!15$$$$p^{38} T^{105} +$$$$44\!\cdots\!05$$$$p^{39} T^{106} +$$$$38\!\cdots\!95$$$$p^{40} T^{107} +$$$$32\!\cdots\!12$$$$p^{41} T^{108} +$$$$27\!\cdots\!00$$$$p^{42} T^{109} +$$$$22\!\cdots\!22$$$$p^{43} T^{110} +$$$$17\!\cdots\!55$$$$p^{44} T^{111} +$$$$13\!\cdots\!80$$$$p^{45} T^{112} +$$$$10\!\cdots\!81$$$$p^{46} T^{113} +$$$$76\!\cdots\!57$$$$p^{47} T^{114} +$$$$55\!\cdots\!38$$$$p^{48} T^{115} +$$$$38\!\cdots\!73$$$$p^{49} T^{116} +$$$$26\!\cdots\!69$$$$p^{50} T^{117} +$$$$17\!\cdots\!65$$$$p^{51} T^{118} +$$$$11\!\cdots\!97$$$$p^{52} T^{119} + 68186813898444496388 p^{53} T^{120} + 4025859562547666285 p^{54} T^{121} + 230450863901207457 p^{55} T^{122} + 12485033646357158 p^{56} T^{123} + 654734494988595 p^{57} T^{124} + 32001190720922 p^{58} T^{125} + 1513400112788 p^{59} T^{126} + 65041082635 p^{60} T^{127} + 2712666985 p^{61} T^{128} + 98182340 p^{62} T^{129} + 3491923 p^{63} T^{130} + 97719 p^{64} T^{131} + 2804 p^{65} T^{132} + 48 p^{66} T^{133} + p^{67} T^{134}$$
53 $$1 + 91 T + 6036 T^{2} + 296847 T^{3} + 12381151 T^{4} + 445401529 T^{5} + 14366962592 T^{6} + 420342724694 T^{7} + 11345296669491 T^{8} + 284702754590666 T^{9} + 6703885694412894 T^{10} + 148934658680427617 T^{11} + 3139721591818198836 T^{12} + 63057937909602841884 T^{13} +$$$$12\!\cdots\!56$$$$T^{14} +$$$$22\!\cdots\!43$$$$T^{15} +$$$$39\!\cdots\!97$$$$T^{16} +$$$$67\!\cdots\!67$$$$T^{17} +$$$$11\!\cdots\!28$$$$T^{18} +$$$$17\!\cdots\!59$$$$T^{19} +$$$$27\!\cdots\!72$$$$T^{20} +$$$$41\!\cdots\!40$$$$T^{21} +$$$$61\!\cdots\!62$$$$T^{22} +$$$$87\!\cdots\!78$$$$T^{23} +$$$$12\!\cdots\!06$$$$T^{24} +$$$$16\!\cdots\!66$$$$T^{25} +$$$$21\!\cdots\!16$$$$T^{26} +$$$$28\!\cdots\!08$$$$T^{27} +$$$$35\!\cdots\!23$$$$T^{28} +$$$$44\!\cdots\!24$$$$T^{29} +$$$$54\!\cdots\!84$$$$T^{30} +$$$$64\!\cdots\!50$$$$T^{31} +$$$$75\!\cdots\!21$$$$T^{32} +$$$$86\!\cdots\!38$$$$T^{33} +$$$$97\!\cdots\!48$$$$T^{34} +$$$$10\!\cdots\!37$$$$T^{35} +$$$$11\!\cdots\!22$$$$T^{36} +$$$$12\!\cdots\!26$$$$T^{37} +$$$$13\!\cdots\!15$$$$T^{38} +$$$$13\!\cdots\!44$$$$T^{39} +$$$$13\!\cdots\!49$$$$T^{40} +$$$$14\!\cdots\!39$$$$T^{41} +$$$$13\!\cdots\!42$$$$T^{42} +$$$$13\!\cdots\!67$$$$T^{43} +$$$$13\!\cdots\!06$$$$T^{44} +$$$$12\!\cdots\!28$$$$T^{45} +$$$$11\!\cdots\!14$$$$T^{46} +$$$$10\!\cdots\!46$$$$T^{47} +$$$$97\!\cdots\!47$$$$T^{48} +$$$$87\!\cdots\!75$$$$T^{49} +$$$$77\!\cdots\!16$$$$T^{50} +$$$$68\!\cdots\!59$$$$T^{51} +$$$$58\!\cdots\!61$$$$T^{52} +$$$$50\!\cdots\!09$$$$T^{53} +$$$$42\!\cdots\!92$$$$T^{54} +$$$$35\!\cdots\!12$$$$T^{55} +$$$$29\!\cdots\!45$$$$T^{56} +$$$$23\!\cdots\!25$$$$T^{57} +$$$$19\!\cdots\!71$$$$T^{58} +$$$$15\!\cdots\!78$$$$T^{59} +$$$$12\!\cdots\!25$$$$T^{60} +$$$$94\!\cdots\!84$$$$T^{61} +$$$$73\!\cdots\!12$$$$T^{62} +$$$$55\!\cdots\!62$$$$T^{63} +$$$$42\!\cdots\!05$$$$T^{64} +$$$$31\!\cdots\!26$$$$T^{65} +$$$$23\!\cdots\!71$$$$T^{66} +$$$$17\!\cdots\!01$$$$T^{67} +$$$$23\!\cdots\!71$$$$p T^{68} +$$$$31\!\cdots\!26$$$$p^{2} T^{69} +$$$$42\!\cdots\!05$$$$p^{3} T^{70} +$$$$55\!\cdots\!62$$$$p^{4} T^{71} +$$$$73\!\cdots\!12$$$$p^{5} T^{72} +$$$$94\!\cdots\!84$$$$p^{6} T^{73} +$$$$12\!\cdots\!25$$$$p^{7} T^{74} +$$$$15\!\cdots\!78$$$$p^{8} T^{75} +$$$$19\!\cdots\!71$$$$p^{9} T^{76} +$$$$23\!\cdots\!25$$$$p^{10} T^{77} +$$$$29\!\cdots\!45$$$$p^{11} T^{78} +$$$$35\!\cdots\!12$$$$p^{12} T^{79} +$$$$42\!\cdots\!92$$$$p^{13} T^{80} +$$$$50\!\cdots\!09$$$$p^{14} T^{81} +$$$$58\!\cdots\!61$$$$p^{15} T^{82} +$$$$68\!\cdots\!59$$$$p^{16} T^{83} +$$$$77\!\cdots\!16$$$$p^{17} T^{84} +$$$$87\!\cdots\!75$$$$p^{18} T^{85} +$$$$97\!\cdots\!47$$$$p^{19} T^{86} +$$$$10\!\cdots\!46$$$$p^{20} T^{87} +$$$$11\!\cdots\!14$$$$p^{21} T^{88} +$$$$12\!\cdots\!28$$$$p^{22} T^{89} +$$$$13\!\cdots\!06$$$$p^{23} T^{90} +$$$$13\!\cdots\!67$$$$p^{24} T^{91} +$$$$13\!\cdots\!42$$$$p^{25} T^{92} +$$$$14\!\cdots\!39$$$$p^{26} T^{93} +$$$$13\!\cdots\!49$$$$p^{27} T^{94} +$$$$13\!\cdots\!44$$$$p^{28} T^{95} +$$$$13\!\cdots\!15$$$$p^{29} T^{96} +$$$$12\!\cdots\!26$$$$p^{30} T^{97} +$$$$11\!\cdots\!22$$$$p^{31} T^{98} +$$$$10\!\cdots\!37$$$$p^{32} T^{99} +$$$$97\!\cdots\!48$$$$p^{33} T^{100} +$$$$86\!\cdots\!38$$$$p^{34} T^{101} +$$$$75\!\cdots\!21$$$$p^{35} T^{102} +$$$$64\!\cdots\!50$$$$p^{36} T^{103} +$$$$54\!\cdots\!84$$$$p^{37} T^{104} +$$$$44\!\cdots\!24$$$$p^{38} T^{105} +$$$$35\!\cdots\!23$$$$p^{39} T^{106} +$$$$28\!\cdots\!08$$$$p^{40} T^{107} +$$$$21\!\cdots\!16$$$$p^{41} T^{108} +$$$$16\!\cdots\!66$$$$p^{42} T^{109} +$$$$12\!\cdots\!06$$$$p^{43} T^{110} +$$$$87\!\cdots\!78$$$$p^{44} T^{111} +$$$$61\!\cdots\!62$$$$p^{45} T^{112} +$$$$41\!\cdots\!40$$$$p^{46} T^{113} +$$$$27\!\cdots\!72$$$$p^{47} T^{114} +$$$$17\!\cdots\!59$$$$p^{48} T^{115} +$$$$11\!\cdots\!28$$$$p^{49} T^{116} +$$$$67\!\cdots\!67$$$$p^{50} T^{117} +$$$$39\!\cdots\!97$$$$p^{51} T^{118} +$$$$22\!\cdots\!43$$$$p^{52} T^{119} +$$$$12\!\cdots\!56$$$$p^{53} T^{120} + 63057937909602841884 p^{54} T^{121} + 3139721591818198836 p^{55} T^{122} + 148934658680427617 p^{56} T^{123} + 6703885694412894 p^{57} T^{124} + 284702754590666 p^{58} T^{125} + 11345296669491 p^{59} T^{126} + 420342724694 p^{60} T^{127} + 14366962592 p^{61} T^{128} + 445401529 p^{62} T^{129} + 12381151 p^{63} T^{130} + 296847 p^{64} T^{131} + 6036 p^{65} T^{132} + 91 p^{66} T^{133} + p^{67} T^{134}$$
59 $$1 + 17 T + 2297 T^{2} + 36959 T^{3} + 2609664 T^{4} + 39886022 T^{5} + 1956137450 T^{6} + 28490462267 T^{7} + 1088743014240 T^{8} + 15154142500539 T^{9} + 480114910900073 T^{10} + 6402972579108270 T^{11} + 174797363643672727 T^{12} + 2238887835068474353 T^{13} + 54059973958971195369 T^{14} +$$$$66\!\cdots\!86$$$$T^{15} +$$$$14\!\cdots\!74$$$$T^{16} +$$$$17\!\cdots\!31$$$$T^{17} +$$$$34\!\cdots\!80$$$$T^{18} +$$$$39\!\cdots\!47$$$$T^{19} +$$$$72\!\cdots\!60$$$$T^{20} +$$$$80\!\cdots\!92$$$$T^{21} +$$$$13\!\cdots\!07$$$$T^{22} +$$$$14\!\cdots\!91$$$$T^{23} +$$$$23\!\cdots\!75$$$$T^{24} +$$$$25\!\cdots\!33$$$$T^{25} +$$$$38\!\cdots\!61$$$$T^{26} +$$$$38\!\cdots\!84$$$$T^{27} +$$$$55\!\cdots\!34$$$$T^{28} +$$$$55\!\cdots\!69$$$$T^{29} +$$$$76\!\cdots\!18$$$$T^{30} +$$$$74\!\cdots\!57$$$$T^{31} +$$$$97\!\cdots\!31$$$$T^{32} +$$$$92\!\cdots\!04$$$$T^{33} +$$$$11\!\cdots\!61$$$$T^{34} +$$$$10\!\cdots\!17$$$$T^{35} +$$$$13\!\cdots\!38$$$$T^{36} +$$$$11\!\cdots\!63$$$$T^{37} +$$$$13\!\cdots\!55$$$$T^{38} +$$$$12\!\cdots\!53$$$$T^{39} +$$$$23\!\cdots\!24$$$$p T^{40} +$$$$12\!\cdots\!08$$$$T^{41} +$$$$13\!\cdots\!03$$$$T^{42} +$$$$11\!\cdots\!74$$$$T^{43} +$$$$12\!\cdots\!57$$$$T^{44} +$$$$10\!\cdots\!00$$$$T^{45} +$$$$10\!\cdots\!23$$$$T^{46} +$$$$90\!\cdots\!90$$$$T^{47} +$$$$89\!\cdots\!83$$$$T^{48} +$$$$75\!\cdots\!18$$$$T^{49} +$$$$71\!\cdots\!57$$$$T^{50} +$$$$59\!\cdots\!18$$$$T^{51} +$$$$55\!\cdots\!96$$$$T^{52} +$$$$45\!\cdots\!34$$$$T^{53} +$$$$41\!\cdots\!13$$$$T^{54} +$$$$33\!\cdots\!15$$$$T^{55} +$$$$29\!\cdots\!11$$$$T^{56} +$$$$24\!\cdots\!81$$$$T^{57} +$$$$20\!\cdots\!97$$$$T^{58} +$$$$16\!\cdots\!32$$$$T^{59} +$$$$13\!\cdots\!17$$$$T^{60} +$$$$18\!\cdots\!72$$$$p T^{61} +$$$$90\!\cdots\!67$$$$T^{62} +$$$$70\!\cdots\!73$$$$T^{63} +$$$$57\!\cdots\!25$$$$T^{64} +$$$$43\!\cdots\!93$$$$T^{65} +$$$$34\!\cdots\!38$$$$T^{66} +$$$$26\!\cdots\!63$$$$T^{67} +$$$$34\!\cdots\!38$$$$p T^{68} +$$$$43\!\cdots\!93$$$$p^{2} T^{69} +$$$$57\!\cdots\!25$$$$p^{3} T^{70} +$$$$70\!\cdots\!73$$$$p^{4} T^{71} +$$$$90\!\cdots\!67$$$$p^{5} T^{72} +$$$$18\!\cdots\!72$$$$p^{7} T^{73} +$$$$13\!\cdots\!17$$$$p^{7} T^{74} +$$$$16\!\cdots\!32$$$$p^{8} T^{75} +$$$$20\!\cdots\!97$$$$p^{9} T^{76} +$$$$24\!\cdots\!81$$$$p^{10} T^{77} +$$$$29\!\cdots\!11$$$$p^{11} T^{78} +$$$$33\!\cdots\!15$$$$p^{12} T^{79} +$$$$41\!\cdots\!13$$$$p^{13} T^{80} +$$$$45\!\cdots\!34$$$$p^{14} T^{81} +$$$$55\!\cdots\!96$$$$p^{15} T^{82} +$$$$59\!\cdots\!18$$$$p^{16} T^{83} +$$$$71\!\cdots\!57$$$$p^{17} T^{84} +$$$$75\!\cdots\!18$$$$p^{18} T^{85} +$$$$89\!\cdots\!83$$$$p^{19} T^{86} +$$$$90\!\cdots\!90$$$$p^{20} T^{87} +$$$$10\!\cdots\!23$$$$p^{21} T^{88} +$$$$10\!\cdots\!00$$$$p^{22} T^{89} +$$$$12\!\cdots\!57$$$$p^{23} T^{90} +$$$$11\!\cdots\!74$$$$p^{24} T^{91} +$$$$13\!\cdots\!03$$$$p^{25} T^{92} +$$$$12\!\cdots\!08$$$$p^{26} T^{93} +$$$$23\!\cdots\!24$$$$p^{28} T^{94} +$$$$12\!\cdots\!53$$$$p^{28} T^{95} +$$$$13\!\cdots\!55$$$$p^{29} T^{96} +$$$$11\!\cdots\!63$$$$p^{30} T^{97} +$$$$13\!\cdots\!38$$$$p^{31} T^{98} +$$$$10\!\cdots\!17$$$$p^{32} T^{99} +$$$$11\!\cdots\!61$$$$p^{33} T^{100} +$$$$92\!\cdots\!04$$$$p^{34} T^{101} +$$$$97\!\cdots\!31$$$$p^{35} T^{102} +$$$$74\!\cdots\!57$$$$p^{36} T^{103} +$$$$76\!\cdots\!18$$$$p^{37} T^{104} +$$$$55\!\cdots\!69$$$$p^{38} T^{105} +$$$$55\!\cdots\!34$$$$p^{39} T^{106} +$$$$38\!\cdots\!84$$$$p^{40} T^{107} +$$$$38\!\cdots\!61$$$$p^{41} T^{108} +$$$$25\!\cdots\!33$$$$p^{42} T^{109} +$$$$23\!\cdots\!75$$$$p^{43} T^{110} +$$$$14\!\cdots\!91$$$$p^{44} T^{111} +$$$$13\!\cdots\!07$$$$p^{45} T^{112} +$$$$80\!\cdots\!92$$$$p^{46} T^{113} +$$$$72\!\cdots\!60$$$$p^{47} T^{114} +$$$$39\!\cdots\!47$$$$p^{48} T^{115} +$$$$34\!\cdots\!80$$$$p^{49} T^{116} +$$$$17\!\cdots\!31$$$$p^{50} T^{117} +$$$$14\!\cdots\!74$$$$p^{51} T^{118} +$$$$66\!\cdots\!86$$$$p^{52} T^{119} + 54059973958971195369 p^{53} T^{120} + 2238887835068474353 p^{54} T^{121} + 174797363643672727 p^{55} T^{122} + 6402972579108270 p^{56} T^{123} + 480114910900073 p^{57} T^{124} + 15154142500539 p^{58} T^{125} + 1088743014240 p^{59} T^{126} + 28490462267 p^{60} T^{127} + 1956137450 p^{61} T^{128} + 39886022 p^{62} T^{129} + 2609664 p^{63} T^{130} + 36959 p^{64} T^{131} + 2297 p^{65} T^{132} + 17 p^{66} T^{133} + p^{67} T^{134}$$
61 $$1 + 45 T + 3136 T^{2} + 110130 T^{3} + 4541189 T^{4} + 133013764 T^{5} + 4163834533 T^{6} + 105836589702 T^{7} + 2759277656633 T^{8} + 62470129093837 T^{9} + 1421640020176839 T^{10} + 29197681046570618 T^{11} + 596420158699690682 T^{12} + 11262760374142660049 T^{13} +$$$$21\!\cdots\!38$$$$T^{14} +$$$$36\!\cdots\!84$$$$T^{15} +$$$$63\!\cdots\!67$$$$T^{16} +$$$$10\!\cdots\!16$$$$T^{17} +$$$$16\!\cdots\!47$$$$T^{18} +$$$$26\!\cdots\!60$$$$T^{19} +$$$$40\!\cdots\!07$$$$T^{20} +$$$$58\!\cdots\!86$$$$T^{21} +$$$$84\!\cdots\!66$$$$T^{22} +$$$$11\!\cdots\!45$$$$T^{23} +$$$$16\!\cdots\!87$$$$T^{24} +$$$$21\!\cdots\!69$$$$T^{25} +$$$$28\!\cdots\!72$$$$T^{26} +$$$$36\!\cdots\!73$$$$T^{27} +$$$$45\!\cdots\!41$$$$T^{28} +$$$$56\!\cdots\!16$$$$T^{29} +$$$$68\!\cdots\!85$$$$T^{30} +$$$$81\!\cdots\!33$$$$T^{31} +$$$$94\!\cdots\!95$$$$T^{32} +$$$$10\!\cdots\!38$$$$T^{33} +$$$$12\!\cdots\!30$$$$T^{34} +$$$$13\!\cdots\!23$$$$T^{35} +$$$$14\!\cdots\!42$$$$T^{36} +$$$$15\!\cdots\!75$$$$T^{37} +$$$$16\!\cdots\!26$$$$T^{38} +$$$$17\!\cdots\!29$$$$T^{39} +$$$$18\!\cdots\!20$$$$T^{40} +$$$$18\!\cdots\!73$$$$T^{41} +$$$$18\!\cdots\!52$$$$T^{42} +$$$$18\!\cdots\!29$$$$T^{43} +$$$$17\!\cdots\!14$$$$T^{44} +$$$$17\!\cdots\!08$$$$T^{45} +$$$$16\!\cdots\!60$$$$T^{46} +$$$$15\!\cdots\!36$$$$T^{47} +$$$$14\!\cdots\!89$$$$T^{48} +$$$$13\!\cdots\!30$$$$T^{49} +$$$$12\!\cdots\!95$$$$T^{50} +$$$$10\!\cdots\!55$$$$T^{51} +$$$$97\!\cdots\!58$$$$T^{52} +$$$$85\!\cdots\!08$$$$T^{53} +$$$$75\!\cdots\!72$$$$T^{54} +$$$$65\!\cdots\!26$$$$T^{55} +$$$$55\!\cdots\!78$$$$T^{56} +$$$$47\!\cdots\!07$$$$T^{57} +$$$$40\!\cdots\!61$$$$T^{58} +$$$$33\!\cdots\!95$$$$T^{59} +$$$$27\!\cdots\!25$$$$T^{60} +$$$$22\!\cdots\!04$$$$T^{61} +$$$$30\!\cdots\!85$$$$p T^{62} +$$$$15\!\cdots\!50$$$$T^{63} +$$$$12\!\cdots\!13$$$$T^{64} +$$$$95\!\cdots\!63$$$$T^{65} +$$$$75\!\cdots\!08$$$$T^{66} +$$$$59\!\cdots\!87$$$$T^{67} +$$$$75\!\cdots\!08$$$$p T^{68} +$$$$95\!\cdots\!63$$$$p^{2} T^{69} +$$$$12\!\cdots\!13$$$$p^{3} T^{70} +$$$$15\!\cdots\!50$$$$p^{4} T^{71} +$$$$30\!\cdots\!85$$$$p^{6} T^{72} +$$$$22\!\cdots\!04$$$$p^{6} T^{73} +$$$$27\!\cdots\!25$$$$p^{7} T^{74} +$$$$33\!\cdots\!95$$$$p^{8} T^{75} +$$$$40\!\cdots\!61$$$$p^{9} T^{76} +$$$$47\!\cdots\!07$$$$p^{10} T^{77} +$$$$55\!\cdots\!78$$$$p^{11} T^{78} +$$$$65\!\cdots\!26$$$$p^{12} T^{79} +$$$$75\!\cdots\!72$$$$p^{13} T^{80} +$$$$85\!\cdots\!08$$$$p^{14} T^{81} +$$$$97\!\cdots\!58$$$$p^{15} T^{82} +$$$$10\!\cdots\!55$$$$p^{16} T^{83} +$$$$12\!\cdots\!95$$$$p^{17} T^{84} +$$$$13\!\cdots\!30$$$$p^{18} T^{85} +$$$$14\!\cdots\!89$$$$p^{19} T^{86} +$$$$15\!\cdots\!36$$$$p^{20} T^{87} +$$$$16\!\cdots\!60$$$$p^{21} T^{88} +$$$$17\!\cdots\!08$$$$p^{22} T^{89} +$$$$17\!\cdots\!14$$$$p^{23} T^{90} +$$$$18\!\cdots\!29$$$$p^{24} T^{91} +$$$$18\!\cdots\!52$$$$p^{25} T^{92} +$$$$18\!\cdots\!73$$$$p^{26} T^{93} +$$$$18\!\cdots\!20$$$$p^{27} T^{94} +$$$$17\!\cdots\!29$$$$p^{28} T^{95} +$$$$16\!\cdots\!26$$$$p^{29} T^{96} +$$$$15\!\cdots\!75$$$$p^{30} T^{97} +$$$$14\!\cdots\!42$$$$p^{31} T^{98} +$$$$13\!\cdots\!23$$$$p^{32} T^{99} +$$$$12\!\cdots\!30$$$$p^{33} T^{100} +$$$$10\!\cdots\!38$$$$p^{34} T^{101} +$$$$94\!\cdots\!95$$$$p^{35} T^{102} +$$$$81\!\cdots\!33$$$$p^{36} T^{103} +$$$$68\!\cdots\!85$$$$p^{37} T^{104} +$$$$56\!\cdots\!16$$$$p^{38} T^{105} +$$$$45\!\cdots\!41$$$$p^{39} T^{106} +$$$$36\!\cdots\!73$$$$p^{40} T^{107} +$$$$28\!\cdots\!72$$$$p^{41} T^{108} +$$$$21\!\cdots\!69$$$$p^{42} T^{109} +$$$$16\!\cdots\!87$$$$p^{43} T^{110} +$$$$11\!\cdots\!45$$$$p^{44} T^{111} +$$$$84\!\cdots\!66$$$$p^{45} T^{112} +$$$$58\!\cdots\!86$$$$p^{46} T^{113} +$$$$40\!\cdots\!07$$$$p^{47} T^{114} +$$$$26\!\cdots\!60$$$$p^{48} T^{115} +$$$$16\!\cdots\!47$$$$p^{49} T^{116} +$$$$10\!\cdots\!16$$$$p^{50} T^{117} +$$$$63\!\cdots\!67$$$$p^{51} T^{118} +$$$$36\!\cdots\!84$$$$p^{52} T^{119} +$$$$21\!\cdots\!38$$$$p^{53} T^{120} + 11262760374142660049 p^{54} T^{121} + 596420158699690682 p^{55} T^{122} + 29197681046570618 p^{56} T^{123} + 1421640020176839 p^{57} T^{124} + 62470129093837 p^{58} T^{125} + 2759277656633 p^{59} T^{126} + 105836589702 p^{60} T^{127} + 4163834533 p^{61} T^{128} + 133013764 p^{62} T^{129} + 4541189 p^{63} T^{130} + 110130 p^{64} T^{131} + 3136 p^{65} T^{132} + 45 p^{66} T^{133} + p^{67} T^{134}$$
67 $$1 + 112 T + 8527 T^{2} + 481571 T^{3} + 22660750 T^{4} + 915262318 T^{5} + 32856872020 T^{6} + 1064469478717 T^{7} + 31624123424762 T^{8} + 869476794334138 T^{9} + 22325021000845617 T^{10} + 538577733329561040 T^{11} + 12278873926029122530 T^{12} +$$$$26\!\cdots\!63$$$$T^{13} +$$$$54\!\cdots\!55$$$$T^{14} +$$$$10\!\cdots\!88$$$$T^{15} +$$$$20\!\cdots\!19$$$$T^{16} +$$$$37\!\cdots\!66$$$$T^{17} +$$$$64\!\cdots\!34$$$$T^{18} +$$$$10\!\cdots\!38$$$$T^{19} +$$$$17\!\cdots\!27$$$$T^{20} +$$$$28\!\cdots\!90$$$$T^{21} +$$$$43\!\cdots\!13$$$$T^{22} +$$$$64\!\cdots\!57$$$$T^{23} +$$$$94\!\cdots\!17$$$$T^{24} +$$$$13\!\cdots\!69$$$$T^{25} +$$$$18\!\cdots\!35$$$$T^{26} +$$$$24\!\cdots\!49$$$$T^{27} +$$$$32\!\cdots\!26$$$$T^{28} +$$$$41\!\cdots\!73$$$$T^{29} +$$$$51\!\cdots\!97$$$$T^{30} +$$$$63\!\cdots\!85$$$$T^{31} +$$$$76\!\cdots\!95$$$$T^{32} +$$$$90\!\cdots\!80$$$$T^{33} +$$$$10\!\cdots\!02$$$$T^{34} +$$$$11\!\cdots\!60$$$$T^{35} +$$$$13\!\cdots\!18$$$$T^{36} +$$$$14\!\cdots\!23$$$$T^{37} +$$$$15\!\cdots\!70$$$$T^{38} +$$$$16\!\cdots\!73$$$$T^{39} +$$$$17\!\cdots\!15$$$$T^{40} +$$$$26\!\cdots\!60$$$$p T^{41} +$$$$18\!\cdots\!32$$$$T^{42} +$$$$18\!\cdots\!55$$$$T^{43} +$$$$17\!\cdots\!56$$$$T^{44} +$$$$17\!\cdots\!97$$$$T^{45} +$$$$16\!\cdots\!69$$$$T^{46} +$$$$15\!\cdots\!76$$$$T^{47} +$$$$14\!\cdots\!37$$$$T^{48} +$$$$13\!\cdots\!27$$$$T^{49} +$$$$12\!\cdots\!92$$$$T^{50} +$$$$11\!\cdots\!88$$$$T^{51} +$$$$10\!\cdots\!04$$$$T^{52} +$$$$91\!\cdots\!61$$$$T^{53} +$$$$80\!\cdots\!39$$$$T^{54} +$$$$70\!\cdots\!81$$$$T^{55} +$$$$60\!\cdots\!78$$$$T^{56} +$$$$52\!\cdots\!26$$$$T^{57} +$$$$44\!\cdots\!43$$$$T^{58} +$$$$37\!\cdots\!65$$$$T^{59} +$$$$31\!\cdots\!63$$$$T^{60} +$$$$26\!\cdots\!54$$$$T^{61} +$$$$22\!\cdots\!73$$$$T^{62} +$$$$18\!\cdots\!79$$$$T^{63} +$$$$15\!\cdots\!12$$$$T^{64} +$$$$12\!\cdots\!45$$$$T^{65} +$$$$10\!\cdots\!62$$$$T^{66} +$$$$84\!\cdots\!55$$$$T^{67} +$$$$10\!\cdots\!62$$$$p T^{68} +$$$$12\!\cdots\!45$$$$p^{2} T^{69} +$$$$15\!\cdots\!12$$$$p^{3} T^{70} +$$$$18\!\cdots\!79$$$$p^{4} T^{71} +$$$$22\!\cdots\!73$$$$p^{5} T^{72} +$$$$26\!\cdots\!54$$$$p^{6} T^{73} +$$$$31\!\cdots\!63$$$$p^{7} T^{74} +$$$$37\!\cdots\!65$$$$p^{8} T^{75} +$$$$44\!\cdots\!43$$$$p^{9} T^{76} +$$$$52\!\cdots\!26$$$$p^{10} T^{77} +$$$$60\!\cdots\!78$$$$p^{11} T^{78} +$$$$70\!\cdots\!81$$$$p^{12} T^{79} +$$$$80\!\cdots\!39$$$$p^{13} T^{80} +$$$$91\!\cdots\!61$$$$p^{14} T^{81} +$$$$10\!\cdots\!04$$$$p^{15} T^{82} +$$$$11\!\cdots\!88$$$$p^{16} T^{83} +$$$$12\!\cdots\!92$$$$p^{17} T^{84} +$$$$13\!\cdots\!27$$$$p^{18} T^{85} +$$$$14\!\cdots\!37$$$$p^{19} T^{86} +$$$$15\!\cdots\!76$$$$p^{20} T^{87} +$$$$16\!\cdots\!69$$$$p^{21} T^{88} +$$$$17\!\cdots\!97$$$$p^{22} T^{89} +$$$$17\!\cdots\!56$$$$p^{23} T^{90} +$$$$18\!\cdots\!55$$$$p^{24} T^{91} +$$$$18\!\cdots\!32$$$$p^{25} T^{92} +$$$$26\!\cdots\!60$$$$p^{27} T^{93} +$$$$17\!\cdots\!15$$$$p^{27} T^{94} +$$$$16\!\cdots\!73$$$$p^{28} T^{95} +$$$$15\!\cdots\!70$$$$p^{29} T^{96} +$$$$14\!\cdots\!23$$$$p^{30} T^{97} +$$$$13\!\cdots\!18$$$$p^{31} T^{98} +$$$$11\!\cdots\!60$$$$p^{32} T^{99} +$$$$10\!\cdots\!02$$$$p^{33} T^{100} +$$$$90\!\cdots\!80$$$$p^{34} T^{101} +$$$$76\!\cdots\!95$$$$p^{35} T^{102} +$$$$63\!\cdots\!85$$$$p^{36} T^{103} +$$$$51\!\cdots\!97$$$$p^{37} T^{104} +$$$$41\!\cdots\!73$$$$p^{38} T^{105} +$$$$32\!\cdots\!26$$$$p^{39} T^{106} +$$$$24\!\cdots\!49$$$$p^{40} T^{107} +$$$$18\!\cdots\!35$$$$p^{41} T^{108} +$$$$13\!\cdots\!69$$$$p^{42} T^{109} +$$$$94\!\cdots\!17$$$$p^{43} T^{110} +$$$$64\!\cdots\!57$$$$p^{44} T^{111} +$$$$43\!\cdots\!13$$$$p^{45} T^{112} +$$$$28\!\cdots\!90$$$$p^{46} T^{113} +$$$$17\!\cdots\!27$$$$p^{47} T^{114} +$$$$10\!\cdots\!38$$$$p^{48} T^{115} +$$$$64\!\cdots\!34$$$$p^{49} T^{116} +$$$$37\!\cdots\!66$$$$p^{50} T^{117} +$$$$20\!\cdots\!19$$$$p^{51} T^{118} +$$$$10\!\cdots\!88$$$$p^{52} T^{119} +$$$$54\!\cdots\!55$$$$p^{53} T^{120} +$$$$26\!\cdots\!63$$$$p^{54} T^{121} + 12278873926029122530 p^{55} T^{122} + 538577733329561040 p^{56} T^{123} + 22325021000845617 p^{57} T^{124} + 869476794334138 p^{58} T^{125} + 31624123424762 p^{59} T^{126} + 1064469478717 p^{60} T^{127} + 32856872020 p^{61} T^{128} + 915262318 p^{62} T^{129} + 22660750 p^{63} T^{130} + 481571 p^{64} T^{131} + 8527 p^{65} T^{132} + 112 p^{66} T^{133} + p^{67} T^{134}$$
71 $$1 + 75 T + 5390 T^{2} + 258378 T^{3} + 11502937 T^{4} + 422574648 T^{5} + 14523338310 T^{6} + 442625006617 T^{7} + 12742750537029 T^{8} + 336625910084543 T^{9} + 8468907035594062 T^{10} + 199342475749826218 T^{11} + 4497617800359238333 T^{12} + 96121022990977942344 T^{13} +$$$$19\!\cdots\!86$$$$T^{14} +$$$$38\!\cdots\!68$$$$T^{15} +$$$$74\!\cdots\!84$$$$T^{16} +$$$$13\!\cdots\!00$$$$T^{17} +$$$$24\!\cdots\!09$$$$T^{18} +$$$$41\!\cdots\!25$$$$T^{19} +$$$$68\!\cdots\!85$$$$T^{20} +$$$$11\!\cdots\!43$$$$T^{21} +$$$$17\!\cdots\!29$$$$T^{22} +$$$$26\!\cdots\!47$$$$T^{23} +$$$$40\!\cdots\!78$$$$T^{24} +$$$$58\!\cdots\!78$$$$T^{25} +$$$$84\!\cdots\!55$$$$T^{26} +$$$$11\!\cdots\!33$$$$T^{27} +$$$$16\!\cdots\!10$$$$T^{28} +$$$$21\!\cdots\!01$$$$T^{29} +$$$$28\!\cdots\!35$$$$T^{30} +$$$$36\!\cdots\!37$$$$T^{31} +$$$$45\!\cdots\!71$$$$T^{32} +$$$$56\!\cdots\!25$$$$T^{33} +$$$$68\!\cdots\!48$$$$T^{34} +$$$$81\!\cdots\!48$$$$T^{35} +$$$$94\!\cdots\!47$$$$T^{36} +$$$$10\!\cdots\!55$$$$T^{37} +$$$$12\!\cdots\!47$$$$T^{38} +$$$$13\!\cdots\!87$$$$T^{39} +$$$$14\!\cdots\!48$$$$T^{40} +$$$$16\!\cdots\!05$$$$T^{41} +$$$$16\!\cdots\!11$$$$T^{42} +$$$$17\!\cdots\!69$$$$T^{43} +$$$$18\!\cdots\!69$$$$T^{44} +$$$$18\!\cdots\!64$$$$T^{45} +$$$$17\!\cdots\!18$$$$T^{46} +$$$$17\!\cdots\!74$$$$T^{47} +$$$$16\!\cdots\!67$$$$T^{48} +$$$$15\!\cdots\!65$$$$T^{49} +$$$$14\!\cdots\!97$$$$T^{50} +$$$$13\!\cdots\!16$$$$T^{51} +$$$$11\!\cdots\!75$$$$T^{52} +$$$$10\!\cdots\!25$$$$T^{53} +$$$$88\!\cdots\!95$$$$T^{54} +$$$$74\!\cdots\!12$$$$T^{55} +$$$$61\!\cdots\!27$$$$T^{56} +$$$$49\!\cdots\!41$$$$T^{57} +$$$$39\!\cdots\!48$$$$T^{58} +$$$$30\!\cdots\!46$$$$T^{59} +$$$$23\!\cdots\!73$$$$T^{60} +$$$$17\!\cdots\!48$$$$T^{61} +$$$$12\!\cdots\!18$$$$T^{62} +$$$$91\!\cdots\!67$$$$T^{63} +$$$$66\!\cdots\!40$$$$T^{64} +$$$$48\!\cdots\!33$$$$T^{65} +$$$$37\!\cdots\!91$$$$T^{66} +$$$$30\!\cdots\!33$$$$T^{67} +$$$$37\!\cdots\!91$$$$p T^{68} +$$$$48\!\cdots\!33$$$$p^{2} T^{69} +$$$$66\!\cdots\!40$$$$p^{3} T^{70} +$$$$91\!\cdots\!67$$$$p^{4} T^{71} +$$$$12\!\cdots\!18$$$$p^{5} T^{72} +$$$$17\!\cdots\!48$$$$p^{6} T^{73} +$$$$23\!\cdots\!73$$$$p^{7} T^{74} +$$$$30\!\cdots\!46$$$$p^{8} T^{75} +$$$$39\!\cdots\!48$$$$p^{9} T^{76} +$$$$49\!\cdots\!41$$$$p^{10} T^{77} +$$$$61\!\cdots\!27$$$$p^{11} T^{78} +$$$$74\!\cdots\!12$$$$p^{12} T^{79} +$$$$88\!\cdots\!95$$$$p^{13} T^{80} +$$$$10\!\cdots\!25$$$$p^{14} T^{81} +$$$$11\!\cdots\!75$$$$p^{15} T^{82} +$$$$13\!\cdots\!16$$$$p^{16} T^{83} +$$$$14\!\cdots\!97$$$$p^{17} T^{84} +$$$$15\!\cdots\!65$$$$p^{18} T^{85} +$$$$16\!\cdots\!67$$$$p^{19} T^{86} +$$$$17\!\cdots\!74$$$$p^{20} T^{87} +$$$$17\!\cdots\!18$$$$p^{21} T^{88} +$$$$18\!\cdots\!64$$$$p^{22} T^{89} +$$$$18\!\cdots\!69$$$$p^{23} T^{90} +$$$$17\!\cdots\!69$$$$p^{24} T^{91} +$$$$16\!\cdots\!11$$$$p^{25} T^{92} +$$$$16\!\cdots\!05$$$$p^{26} T^{93} +$$$$14\!\cdots\!48$$$$p^{27} T^{94} +$$$$13\!\cdots\!87$$$$p^{28} T^{95} +$$$$12\!\cdots\!47$$$$p^{29} T^{96} +$$$$10\!\cdots\!55$$$$p^{30} T^{97} +$$$$94\!\cdots\!47$$$$p^{31} T^{98} +$$$$81\!\cdots\!48$$$$p^{32} T^{99} +$$$$68\!\cdots\!48$$$$p^{33} T^{100} +$$$$56\!\cdots\!25$$$$p^{34} T^{101} +$$$$45\!\cdots\!71$$$$p^{35} T^{102} +$$$$36\!\cdots\!37$$$$p^{36} T^{103} +$$$$28\!\cdots\!35$$$$p^{37} T^{104} +$$$$21\!\cdots\!01$$$$p^{38} T^{105} +$$$$16\!\cdots\!10$$$$p^{39} T^{106} +$$$$11\!\cdots\!33$$$$p^{40} T^{107} +$$$$84\!\cdots\!55$$$$p^{41} T^{108} +$$$$58\!\cdots\!78$$$$p^{42} T^{109} +$$$$40\!\cdots\!78$$$$p^{43} T^{110} +$$$$26\!\cdots\!47$$$$p^{44} T^{111} +$$$$17\!\cdots\!29$$$$p^{45} T^{112} +$$$$11\!\cdots\!43$$$$p^{46} T^{113} +$$$$68\!\cdots\!85$$$$p^{47} T^{114} +$$$$41\!\cdots\!25$$$$p^{48} T^{115} +$$$$24\!\cdots\!09$$$$p^{49} T^{116} +$$$$13\!\cdots\!00$$$$p^{50} T^{117} +$$$$74\!\cdots\!84$$$$p^{51} T^{118} +$$$$38\!\cdots\!68$$$$p^{52} T^{119} +$$$$19\!\cdots\!86$$$$p^{53} T^{120} + 96121022990977942344 p^{54} T^{121} + 4497617800359238333 p^{55} T^{122} + 199342475749826218 p^{56} T^{123} + 8468907035594062 p^{57} T^{124} + 336625910084543 p^{58} T^{125} + 12742750537029 p^{59} T^{126} + 442625006617 p^{60} T^{127} + 14523338310 p^{61} T^{128} + 422574648 p^{62} T^{129} + 11502937 p^{63} T^{130} + 258378 p^{64} T^{131} + 5390 p^{65} T^{132} + 75 p^{66} T^{133} + p^{67} T^{134}$$
73 $$1 + 79 T + 5519 T^{2} + 268793 T^{3} + 11751050 T^{4} + 433521824 T^{5} + 14686290557 T^{6} + 446959744092 T^{7} + 12698206306304 T^{8} + 333750286080657 T^{9} + 113489671402153 p T^{10} + 193452287082833490 T^{11} + 4302551270821871198 T^{12} + 90977699800228244544 T^{13} +$$$$18\!\cdots\!16$$$$T^{14} +$$$$35\!\cdots\!92$$$$T^{15} +$$$$66\!\cdots\!96$$$$T^{16} +$$$$12\!\cdots\!69$$$$T^{17} +$$$$20\!\cdots\!74$$$$T^{18} +$$$$35\!\cdots\!01$$$$T^{19} +$$$$57\!\cdots\!99$$$$T^{20} +$$$$91\!\cdots\!24$$$$T^{21} +$$$$14\!\cdots\!17$$$$T^{22} +$$$$21\!\cdots\!21$$$$T^{23} +$$$$30\!\cdots\!01$$$$T^{24} +$$$$44\!\cdots\!81$$$$T^{25} +$$$$61\!\cdots\!33$$$$T^{26} +$$$$83\!\cdots\!82$$$$T^{27} +$$$$11\!\cdots\!99$$$$T^{28} +$$$$14\!\cdots\!54$$$$T^{29} +$$$$18\!\cdots\!67$$$$T^{30} +$$$$22\!\cdots\!89$$$$T^{31} +$$$$28\!\cdots\!19$$$$T^{32} +$$$$33\!\cdots\!55$$$$T^{33} +$$$$39\!\cdots\!13$$$$T^{34} +$$$$46\!\cdots\!84$$$$T^{35} +$$$$52\!\cdots\!11$$$$T^{36} +$$$$59\!\cdots\!72$$$$T^{37} +$$$$65\!\cdots\!95$$$$T^{38} +$$$$70\!\cdots\!70$$$$T^{39} +$$$$75\!\cdots\!22$$$$T^{40} +$$$$79\!\cdots\!24$$$$T^{41} +$$$$82\!\cdots\!83$$$$T^{42} +$$$$83\!\cdots\!71$$$$T^{43} +$$$$84\!\cdots\!14$$$$T^{44} +$$$$83\!\cdots\!90$$$$T^{45} +$$$$82\!\cdots\!13$$$$T^{46} +$$$$79\!\cdots\!16$$$$T^{47} +$$$$75\!\cdots\!02$$$$T^{48} +$$$$71\!\cdots\!75$$$$T^{49} +$$$$66\!\cdots\!88$$$$T^{50} +$$$$61\!\cdots\!60$$$$T^{51} +$$$$55\!\cdots\!11$$$$T^{52} +$$$$50\!\cdots\!99$$$$T^{53} +$$$$44\!\cdots\!03$$$$T^{54} +$$$$39\!\cdots\!23$$$$T^{55} +$$$$34\!\cdots\!71$$$$T^{56} +$$$$29\!\cdots\!14$$$$T^{57} +$$$$25\!\cdots\!20$$$$T^{58} +$$$$21\!\cdots\!50$$$$T^{59} +$$$$18\!\cdots\!40$$$$T^{60} +$$$$15\!\cdots\!91$$$$T^{61} +$$$$13\!\cdots\!73$$$$T^{62} +$$$$11\!\cdots\!98$$$$T^{63} +$$$$93\!\cdots\!66$$$$T^{64} +$$$$78\!\cdots\!83$$$$T^{65} +$$$$66\!\cdots\!25$$$$T^{66} +$$$$56\!\cdots\!91$$$$T^{67} +$$$$66\!\cdots\!25$$$$p T^{68} +$$$$78\!\cdots\!83$$$$p^{2} T^{69} +$$$$93\!\cdots\!66$$$$p^{3} T^{70} +$$$$11\!\cdots\!98$$$$p^{4} T^{71} +$$$$13\!\cdots\!73$$$$p^{5} T^{72} +$$$$15\!\cdots\!91$$$$p^{6} T^{73} +$$$$18\!\cdots\!40$$$$p^{7} T^{74} +$$$$21\!\cdots\!50$$$$p^{8} T^{75} +$$$$25\!\cdots\!20$$$$p^{9} T^{76} +$$$$29\!\cdots\!14$$$$p^{10} T^{77} +$$$$34\!\cdots\!71$$$$p^{11} T^{78} +$$$$39\!\cdots\!23$$$$p^{12} T^{79} +$$$$44\!\cdots\!03$$$$p^{13} T^{80} +$$$$50\!\cdots\!99$$$$p^{14} T^{81} +$$$$55\!\cdots\!11$$$$p^{15} T^{82} +$$$$61\!\cdots\!60$$$$p^{16} T^{83} +$$$$66\!\cdots\!88$$$$p^{17} T^{84} +$$$$71\!\cdots\!75$$$$p^{18} T^{85} +$$$$75\!\cdots\!02$$$$p^{19} T^{86} +$$$$79\!\cdots\!16$$$$p^{20} T^{87} +$$$$82\!\cdots\!13$$$$p^{21} T^{88} +$$$$83\!\cdots\!90$$$$p^{22} T^{89} +$$$$84\!\cdots\!14$$$$p^{23} T^{90} +$$$$83\!\cdots\!71$$$$p^{24} T^{91} +$$$$82\!\cdots\!83$$$$p^{25} T^{92} +$$$$79\!\cdots\!24$$$$p^{26} T^{93} +$$$$75\!\cdots\!22$$$$p^{27} T^{94} +$$$$70\!\cdots\!70$$$$p^{28} T^{95} +$$$$65\!\cdots\!95$$$$p^{29} T^{96} +$$$$59\!\cdots\!72$$$$p^{30} T^{97} +$$$$52\!\cdots\!11$$$$p^{31} T^{98} +$$$$46\!\cdots\!84$$$$p^{32} T^{99} +$$$$39\!\cdots\!13$$$$p^{33} T^{100} +$$$$33\!\cdots\!55$$$$p^{34} T^{101} +$$$$28\!\cdots\!19$$$$p^{35} T^{102} +$$$$22\!\cdots\!89$$$$p^{36} T^{103} +$$$$18\!\cdots\!67$$$$p^{37} T^{104} +$$$$14\!\cdots\!54$$$$p^{38} T^{105} +$$$$11\!\cdots\!99$$$$p^{39} T^{106} +$$$$83\!\cdots\!82$$$$p^{40} T^{107} +$$$$61\!\cdots\!33$$$$p^{41} T^{108} +$$$$44\!\cdots\!81$$$$p^{42} T^{109} +$$$$30\!\cdots\!01$$$$p^{43} T^{110} +$$$$21\!\cdots\!21$$$$p^{44} T^{111} +$$$$14\!\cdots\!17$$$$p^{45} T^{112} +$$$$91\!\cdots\!24$$$$p^{46} T^{113} +$$$$57\!\cdots\!99$$$$p^{47} T^{114} +$$$$35\!\cdots\!01$$$$p^{48} T^{115} +$$$$20\!\cdots\!74$$$$p^{49} T^{116} +$$$$12\!\cdots\!69$$$$p^{50} T^{117} +$$$$66\!\cdots\!96$$$$p^{51} T^{118} +$$$$35\!\cdots\!92$$$$p^{52} T^{119} +$$$$18\!\cdots\!16$$$$p^{53} T^{120} + 90977699800228244544 p^{54} T^{121} + 4302551270821871198 p^{55} T^{122} + 193452287082833490 p^{56} T^{123} + 113489671402153 p^{58} T^{124} + 333750286080657 p^{58} T^{125} + 12698206306304 p^{59} T^{126} + 446959744092 p^{60} T^{127} + 14686290557 p^{61} T^{128} + 433521824 p^{62} T^{129} + 11751050 p^{63} T^{130} + 268793 p^{64} T^{131} + 5519 p^{65} T^{132} + 79 p^{66} T^{133} + p^{67} T^{134}$$
79 $$1 + 80 T + 5790 T^{2} + 289550 T^{3} + 13123270 T^{4} + 500567421 T^{5} + 17630659736 T^{6} + 557777624052 T^{7} + 16538040267267 T^{8} + 454126167158912 T^{9} + 11815045977479346 T^{10} + 289653310763408806 T^{11} + 6782721107873626153 T^{12} +$$$$15\!\cdots\!43$$$$T^{13} +$$$$32\!\cdots\!78$$$$T^{14} +$$$$66\!\cdots\!38$$$$T^{15} +$$$$13\!\cdots\!60$$$$T^{16} +$$$$25\!\cdots\!14$$$$T^{17} +$$$$47\!\cdots\!55$$$$T^{18} +$$$$85\!\cdots\!89$$$$T^{19} +$$$$14\!\cdots\!55$$$$T^{20} +$$$$25\!\cdots\!49$$$$T^{21} +$$$$42\!\cdots\!53$$$$T^{22} +$$$$68\!\cdots\!04$$$$T^{23} +$$$$10\!\cdots\!36$$$$T^{24} +$$$$16\!\cdots\!61$$$$T^{25} +$$$$25\!\cdots\!45$$$$T^{26} +$$$$37\!\cdots\!32$$$$T^{27} +$$$$55\!\cdots\!93$$$$T^{28} +$$$$78\!\cdots\!50$$$$T^{29} +$$$$10\!\cdots\!08$$$$T^{30} +$$$$15\!\cdots\!58$$$$T^{31} +$$$$20\!\cdots\!16$$$$T^{32} +$$$$27\!\cdots\!42$$$$T^{33} +$$$$35\!\cdots\!65$$$$T^{34} +$$$$45\!\cdots\!78$$$$T^{35} +$$$$57\!\cdots\!78$$$$T^{36} +$$$$71\!\cdots\!49$$$$T^{37} +$$$$88\!\cdots\!10$$$$T^{38} +$$$$10\!\cdots\!15$$$$T^{39} +$$$$12\!\cdots\!04$$$$T^{40} +$$$$15\!\cdots\!71$$$$T^{41} +$$$$17\!\cdots\!19$$$$T^{42} +$$$$20\!\cdots\!83$$$$T^{43} +$$$$22\!\cdots\!60$$$$T^{44} +$$$$25\!\cdots\!40$$$$T^{45} +$$$$28\!\cdots\!02$$$$T^{46} +$$$$30\!\cdots\!93$$$$T^{47} +$$$$33\!\cdots\!85$$$$T^{48} +$$$$35\!\cdots\!24$$$$T^{49} +$$$$37\!\cdots\!40$$$$T^{50} +$$$$39\!\cdots\!11$$$$T^{51} +$$$$40\!\cdots\!01$$$$T^{52} +$$$$41\!\cdots\!61$$$$T^{53} +$$$$42\!\cdots\!92$$$$T^{54} +$$$$42\!\cdots\!31$$$$T^{55} +$$$$42\!\cdots\!25$$$$T^{56} +$$$$41\!\cdots\!63$$$$T^{57} +$$$$40\!\cdots\!89$$$$T^{58} +$$$$38\!\cdots\!13$$$$T^{59} +$$$$37\!\cdots\!65$$$$T^{60} +$$$$35\!\cdots\!55$$$$T^{61} +$$$$32\!\cdots\!18$$$$T^{62} +$$$$30\!\cdots\!00$$$$T^{63} +$$$$27\!\cdots\!19$$$$T^{64} +$$$$25\!\cdots\!07$$$$T^{65} +$$$$22\!\cdots\!32$$$$T^{66} +$$$$20\!\cdots\!97$$$$T^{67} +$$$$22\!\cdots\!32$$$$p T^{68} +$$$$25\!\cdots\!07$$$$p^{2} T^{69} +$$$$27\!\cdots\!19$$$$p^{3} T^{70} +$$$$30\!\cdots\!00$$$$p^{4} T^{71} +$$$$32\!\cdots\!18$$$$p^{5} T^{72} +$$$$35\!\cdots\!55$$$$p^{6} T^{73} +$$$$37\!\cdots\!65$$$$p^{7} T^{74} +$$$$38\!\cdots\!13$$$$p^{8} T^{75} +$$$$40\!\cdots\!89$$$$p^{9} T^{76} +$$$$41\!\cdots\!63$$$$p^{10} T^{77} +$$$$42\!\cdots\!25$$$$p^{11} T^{78} +$$$$42\!\cdots\!31$$$$p^{12} T^{79} +$$$$42\!\cdots\!92$$$$p^{13} T^{80} +$$$$41\!\cdots\!61$$$$p^{14} T^{81} +$$$$40\!\cdots\!01$$$$p^{15} T^{82} +$$$$39\!\cdots\!11$$$$p^{16} T^{83} +$$$$37\!\cdots\!40$$$$p^{17} T^{84} +$$$$35\!\cdots\!24$$$$p^{18} T^{85} +$$$$33\!\cdots\!85$$$$p^{19} T^{86} +$$$$30\!\cdots\!93$$$$p^{20} T^{87} +$$$$28\!\cdots\!02$$$$p^{21} T^{88} +$$$$25\!\cdots\!40$$$$p^{22} T^{89} +$$$$22\!\cdots\!60$$$$p^{23} T^{90} +$$$$20\!\cdots\!83$$$$p^{24} T^{91} +$$$$17\!\cdots\!19$$$$p^{25} T^{92} +$$$$15\!\cdots\!71$$$$p^{26} T^{93} +$$$$12\!\cdots\!04$$$$p^{27} T^{94} +$$$$10\!\cdots\!15$$$$p^{28} T^{95} +$$$$88\!\cdots\!10$$$$p^{29} T^{96} +$$$$71\!\cdots\!49$$$$p^{30} T^{97} +$$$$57\!\cdots\!78$$$$p^{31} T^{98} +$$$$45\!\cdots\!78$$$$p^{32} T^{99} +$$$$35\!\cdots\!65$$$$p^{33} T^{100} +$$$$27\!\cdots\!42$$$$p^{34} T^{101} +$$$$20\!\cdots\!16$$$$p^{35} T^{102} +$$$$15\!\cdots\!58$$$$p^{36} T^{103} +$$$$10\!\cdots\!08$$$$p^{37} T^{104} +$$$$78\!\cdots\!50$$$$p^{38} T^{105} +$$$$55\!\cdots\!93$$$$p^{39} T^{106} +$$$$37\!\cdots\!32$$$$p^{40} T^{107} +$$$$25\!\cdots\!45$$$$p^{41} T^{108} +$$$$16\!\cdots\!61$$$$p^{42} T^{109} +$$$$10\!\cdots\!36$$$$p^{43} T^{110} +$$$$68\!\cdots\!04$$$$p^{44} T^{111} +$$$$42\!\cdots\!53$$$$p^{45} T^{112} +$$$$25\!\cdots\!49$$$$p^{46} T^{113} +$$$$14\!\cdots\!55$$$$p^{47} T^{114} +$$$$85\!\cdots\!89$$$$p^{48} T^{115} +$$$$47\!\cdots\!55$$$$p^{49} T^{116} +$$$$25\!\cdots\!14$$$$p^{50} T^{117} +$$$$13\!\cdots\!60$$$$p^{51} T^{118} +$$$$66\!\cdots\!38$$$$p^{52} T^{119} +$$$$32\!\cdots\!78$$$$p^{53} T^{120} +$$$$15\!\cdots\!43$$$$p^{54} T^{121} + 6782721107873626153 p^{55} T^{122} + 289653310763408806 p^{56} T^{123} + 11815045977479346 p^{57} T^{124} + 454126167158912 p^{58} T^{125} + 16538040267267 p^{59} T^{126} + 557777624052 p^{60} T^{127} + 17630659736 p^{61} T^{128} + 500567421 p^{62} T^{129} + 13123270 p^{63} T^{130} + 289550 p^{64} T^{131} + 5790 p^{65} T^{132} + 80 p^{66} T^{133} + p^{67} T^{134}$$
83 $$1 + 22 T + 3114 T^{2} + 67268 T^{3} + 4851752 T^{4} + 102411932 T^{5} + 5039680426 T^{6} + 103535434550 T^{7} + 3923934810855 T^{8} + 78212385451636 T^{9} + 2441422706529647 T^{10} + 47101517591381987 T^{11} + 1263811593184140120 T^{12} + 23560686774628929683 T^{13} +$$$$55\!\cdots\!86$$$$T^{14} +$$$$10\!\cdots\!92$$$$T^{15} +$$$$21\!\cdots\!68$$$$T^{16} +$$$$37\!\cdots\!89$$$$T^{17} +$$$$74\!\cdots\!11$$$$T^{18} +$$$$12\!\cdots\!97$$$$T^{19} +$$$$22\!\cdots\!06$$$$T^{20} +$$$$36\!\cdots\!16$$$$T^{21} +$$$$63\!\cdots\!91$$$$T^{22} +$$$$99\!\cdots\!35$$$$T^{23} +$$$$16\!\cdots\!11$$$$T^{24} +$$$$24\!\cdots\!47$$$$T^{25} +$$$$37\!\cdots\!62$$$$T^{26} +$$$$55\!\cdots\!31$$$$T^{27} +$$$$82\!\cdots\!47$$$$T^{28} +$$$$11\!\cdots\!33$$$$T^{29} +$$$$16\!\cdots\!72$$$$T^{30} +$$$$22\!\cdots\!29$$$$T^{31} +$$$$31\!\cdots\!00$$$$T^{32} +$$$$41\!\cdots\!65$$$$T^{33} +$$$$55\!\cdots\!62$$$$T^{34} +$$$$71\!\cdots\!66$$$$T^{35} +$$$$92\!\cdots\!86$$$$T^{36} +$$$$11\!\cdots\!09$$$$T^{37} +$$$$14\!\cdots\!21$$$$T^{38} +$$$$17\!\cdots\!66$$$$T^{39} +$$$$21\!\cdots\!52$$$$T^{40} +$$$$25\!\cdots\!42$$$$T^{41} +$$$$30\!\cdots\!11$$$$T^{42} +$$$$35\!\cdots\!16$$$$T^{43} +$$$$41\!\cdots\!01$$$$T^{44} +$$$$46\!\cdots\!46$$$$T^{45} +$$$$53\!\cdots\!03$$$$T^{46} +$$$$58\!\cdots\!95$$$$T^{47} +$$$$65\!\cdots\!35$$$$T^{48} +$$$$70\!\cdots\!60$$$$T^{49} +$$$$76\!\cdots\!69$$$$T^{50} +$$$$81\!\cdots\!86$$$$T^{51} +$$$$86\!\cdots\!81$$$$T^{52} +$$$$89\!\cdots\!25$$$$T^{53} +$$$$93\!\cdots\!72$$$$T^{54} +$$$$95\!\cdots\!98$$$$T^{55} +$$$$96\!\cdots\!01$$$$T^{56} +$$$$96\!\cdots\!70$$$$T^{57} +$$$$96\!\cdots\!24$$$$T^{58} +$$$$95\!\cdots\!65$$$$T^{59} +$$$$92\!\cdots\!44$$$$T^{60} +$$$$89\!\cdots\!29$$$$T^{61} +$$$$85\!\cdots\!47$$$$T^{62} +$$$$81\!\cdots\!99$$$$T^{63} +$$$$76\!\cdots\!47$$$$T^{64} +$$$$71\!\cdots\!06$$$$T^{65} +$$$$66\!\cdots\!31$$$$T^{66} +$$$$60\!\cdots\!09$$$$T^{67} +$$$$66\!\cdots\!31$$$$p T^{68} +$$$$71\!\cdots\!06$$$$p^{2} T^{69} +$$$$76\!\cdots\!47$$$$p^{3} T^{70} +$$$$81\!\cdots\!99$$$$p^{4} T^{71} +$$$$85\!\cdots\!47$$$$p^{5} T^{72} +$$$$89\!\cdots\!29$$$$p^{6} T^{73} +$$$$92\!\cdots\!44$$$$p^{7} T^{74} +$$$$95\!\cdots\!65$$$$p^{8} T^{75} +$$$$96\!\cdots\!24$$$$p^{9} T^{76} +$$$$96\!\cdots\!70$$$$p^{10} T^{77} +$$$$96\!\cdots\!01$$$$p^{11} T^{78} +$$$$95\!\cdots\!98$$$$p^{12} T^{79} +$$$$93\!\cdots\!72$$$$p^{13} T^{80} +$$$$89\!\cdots\!25$$$$p^{14} T^{81} +$$$$86\!\cdots\!81$$$$p^{15} T^{82} +$$$$81\!\cdots\!86$$$$p^{16} T^{83} +$$$$76\!\cdots\!69$$$$p^{17} T^{84} +$$$$70\!\cdots\!60$$$$p^{18} T^{85} +$$$$65\!\cdots\!35$$$$p^{19} T^{86} +$$$$58\!\cdots\!95$$$$p^{20} T^{87} +$$$$53\!\cdots\!03$$$$p^{21} T^{88} +$$$$46\!\cdots\!46$$$$p^{22} T^{89} +$$$$41\!\cdots\!01$$$$p^{23} T^{90} +$$$$35\!\cdots\!16$$$$p^{24} T^{91} +$$$$30\!\cdots\!11$$$$p^{25} T^{92} +$$$$25\!\cdots\!42$$$$p^{26} T^{93} +$$$$21\!\cdots\!52$$$$p^{27} T^{94} +$$$$17\!\cdots\!66$$$$p^{28} T^{95} +$$$$14\!\cdots\!21$$$$p^{29} T^{96} +$$$$11\!\cdots\!09$$$$p^{30} T^{97} +$$$$92\!\cdots\!86$$$$p^{31} T^{98} +$$$$71\!\cdots\!66$$$$p^{32} T^{99} +$$$$55\!\cdots\!62$$$$p^{33} T^{100} +$$$$41\!\cdots\!65$$$$p^{34} T^{101} +$$$$31\!\cdots\!00$$$$p^{35} T^{102} +$$$$22\!\cdots\!29$$$$p^{36} T^{103} +$$$$16\!\cdots\!72$$$$p^{37} T^{104} +$$$$11\!\cdots\!33$$$$p^{38} T^{105} +$$$$82\!\cdots\!47$$$$p^{39} T^{106} +$$$$55\!\cdots\!31$$$$p^{40} T^{107} +$$$$37\!\cdots\!62$$$$p^{41} T^{108} +$$$$24\!\cdots\!47$$$$p^{42} T^{109} +$$$$16\!\cdots\!11$$$$p^{43} T^{110} +$$$$99\!\cdots\!35$$$$p^{44} T^{111} +$$$$63\!\cdots\!91$$$$p^{45} T^{112} +$$$$36\!\cdots\!16$$$$p^{46} T^{113} +$$$$22\!\cdots\!06$$$$p^{47} T^{114} +$$$$12\!\cdots\!97$$$$p^{48} T^{115} +$$$$74\!\cdots\!11$$$$p^{49} T^{116} +$$$$37\!\cdots\!89$$$$p^{50} T^{117} +$$$$21\!\cdots\!68$$$$p^{51} T^{118} +$$$$10\!\cdots\!92$$$$p^{52} T^{119} +$$$$55\!\cdots\!86$$$$p^{53} T^{120} + 23560686774628929683 p^{54} T^{121} + 1263811593184140120 p^{55} T^{122} + 47101517591381987 p^{56} T^{123} + 2441422706529647 p^{57} T^{124} + 78212385451636 p^{58} T^{125} + 3923934810855 p^{59} T^{126} + 103535434550 p^{60} T^{127} + 5039680426 p^{61} T^{128} + 102411932 p^{62} T^{129} + 4851752 p^{63} T^{130} + 67268 p^{64} T^{131} + 3114 p^{65} T^{132} + 22 p^{66} T^{133} + p^{67} T^{134}$$
89 $$1 + 77 T + 5606 T^{2} + 279945 T^{3} + 12855134 T^{4} + 497337437 T^{5} + 17887378753 T^{6} + 579624726668 T^{7} + 17673301335002 T^{8} + 500714156911552 T^{9} + 13478959614619919 T^{10} + 342961453436748540 T^{11} + 8353817614896642096 T^{12} +$$$$19\!\cdots\!17$$$$T^{13} +$$$$43\!\cdots\!80$$$$T^{14} +$$$$93\!\cdots\!16$$$$T^{15} +$$$$19\!\cdots\!03$$$$T^{16} +$$$$39\!\cdots\!79$$$$T^{17} +$$$$77\!\cdots\!69$$$$T^{18} +$$$$14\!\cdots\!54$$$$T^{19} +$$$$27\!\cdots\!84$$$$T^{20} +$$$$49\!\cdots\!59$$$$T^{21} +$$$$86\!\cdots\!38$$$$T^{22} +$$$$14\!\cdots\!48$$$$T^{23} +$$$$24\!\cdots\!79$$$$T^{24} +$$$$41\!\cdots\!69$$$$T^{25} +$$$$66\!\cdots\!78$$$$T^{26} +$$$$10\!\cdots\!92$$$$T^{27} +$$$$16\!\cdots\!34$$$$T^{28} +$$$$24\!\cdots\!47$$$$T^{29} +$$$$36\!\cdots\!74$$$$T^{30} +$$$$53\!\cdots\!12$$$$T^{31} +$$$$77\!\cdots\!75$$$$T^{32} +$$$$11\!\cdots\!88$$$$T^{33} +$$$$15\!\cdots\!07$$$$T^{34} +$$$$21\!\cdots\!20$$$$T^{35} +$$$$28\!\cdots\!90$$$$T^{36} +$$$$38\!\cdots\!92$$$$T^{37} +$$$$50\!\cdots\!92$$$$T^{38} +$$$$65\!\cdots\!70$$$$T^{39} +$$$$83\!\cdots\!46$$$$T^{40} +$$$$10\!\cdots\!13$$$$T^{41} +$$$$13\!\cdots\!26$$$$T^{42} +$$$$16\!\cdots\!27$$$$T^{43} +$$$$19\!\cdots\!81$$$$T^{44} +$$$$23\!\cdots\!86$$$$T^{45} +$$$$27\!\cdots\!40$$$$T^{46} +$$$$32\!\cdots\!01$$$$T^{47} +$$$$37\!\cdots\!48$$$$T^{48} +$$$$43\!\cdots\!49$$$$T^{49} +$$$$48\!\cdots\!42$$$$T^{50} +$$$$54\!\cdots\!26$$$$T^{51} +$$$$60\!\cdots\!78$$$$T^{52} +$$$$65\!\cdots\!71$$$$T^{53} +$$$$71\!\cdots\!20$$$$T^{54} +$$$$76\!\cdots\!56$$$$T^{55} +$$$$80\!\cdots\!26$$$$T^{56} +$$$$84\!\cdots\!08$$$$T^{57} +$$$$87\!\cdots\!21$$$$T^{58} +$$$$90\!\cdots\!34$$$$T^{59} +$$$$91\!\cdots\!94$$$$T^{60} +$$$$92\!\cdots\!26$$$$T^{61} +$$$$91\!\cdots\!04$$$$T^{62} +$$$$90\!\cdots\!05$$$$T^{63} +$$$$88\!\cdots\!30$$$$T^{64} +$$$$85\!\cdots\!41$$$$T^{65} +$$$$81\!\cdots\!36$$$$T^{66} +$$$$77\!\cdots\!47$$$$T^{67} +$$$$81\!\cdots\!36$$$$p T^{68} +$$$$85\!\cdots\!41$$$$p^{2} T^{69} +$$$$88\!\cdots\!30$$$$p^{3} T^{70} +$$$$90\!\cdots\!05$$$$p^{4} T^{71} +$$$$91\!\cdots\!04$$$$p^{5} T^{72} +$$$$92\!\cdots\!26$$$$p^{6} T^{73} +$$$$91\!\cdots\!94$$$$p^{7} T^{74} +$$$$90\!\cdots\!34$$$$p^{8} T^{75} +$$$$87\!\cdots\!21$$$$p^{9} T^{76} +$$$$84\!\cdots\!08$$$$p^{10} T^{77} +$$$$80\!\cdots\!26$$$$p^{11} T^{78} +$$$$76\!\cdots\!56$$$$p^{12} T^{79} +$$$$71\!\cdots\!20$$$$p^{13} T^{80} +$$$$65\!\cdots\!71$$$$p^{14} T^{81} +$$$$60\!\cdots\!78$$$$p^{15} T^{82} +$$$$54\!\cdots\!26$$$$p^{16} T^{83} +$$$$48\!\cdots\!42$$$$p^{17} T^{84} +$$$$43\!\cdots\!49$$$$p^{18} T^{85} +$$$$37\!\cdots\!48$$$$p^{19} T^{86} +$$$$32\!\cdots\!01$$$$p^{20} T^{87} +$$$$27\!\cdots\!40$$$$p^{21} T^{88} +$$$$23\!\cdots\!86$$$$p^{22} T^{89} +$$$$19\!\cdots\!81$$$$p^{23} T^{90} +$$$$16\!\cdots\!27$$$$p^{24} T^{91} +$$$$13\!\cdots\!26$$$$p^{25} T^{92} +$$$$10\!\cdots\!13$$$$p^{26} T^{93} +$$$$83\!\cdots\!46$$$$p^{27} T^{94} +$$$$65\!\cdots\!70$$$$p^{28} T^{95} +$$$$50\!\cdots\!92$$$$p^{29} T^{96} +$$$$38\!\cdots\!92$$$$p^{30} T^{97} +$$$$28\!\cdots\!90$$$$p^{31} T^{98} +$$$$21\!\cdots\!20$$$$p^{32} T^{99} +$$$$15\!\cdots\!07$$$$p^{33} T^{100} +$$$$11\!\cdots\!88$$$$p^{34} T^{101} +$$$$77\!\cdots\!75$$$$p^{35} T^{102} +$$$$53\!\cdots\!12$$$$p^{36} T^{103} +$$$$36\!\cdots\!74$$$$p^{37} T^{104} +$$$$24\!\cdots\!47$$$$p^{38} T^{105} +$$$$16\!\cdots\!34$$$$p^{39} T^{106} +$$$$10\!\cdots\!92$$$$p^{40} T^{107} +$$$$66\!\cdots\!78$$$$p^{41} T^{108} +$$$$41\!\cdots\!69$$$$p^{42} T^{109} +$$$$24\!\cdots\!79$$$$p^{43} T^{110} +$$$$14\!\cdots\!48$$$$p^{44} T^{111} +$$$$86\!\cdots\!38$$$$p^{45} T^{112} +$$$$49\!\cdots\!59$$$$p^{46} T^{113} +$$$$27\!\cdots\!84$$$$p^{47} T^{114} +$$$$14\!\cdots\!54$$$$p^{48} T^{115} +$$$$77\!\cdots\!69$$$$p^{49} T^{116} +$$$$39\!\cdots\!79$$$$p^{50} T^{117} +$$$$19\!\cdots\!03$$$$p^{51} T^{118} +$$$$93\!\cdots\!16$$$$p^{52} T^{119} +$$$$43\!\cdots\!80$$$$p^{53} T^{120} +$$$$19\!\cdots\!17$$$$p^{54} T^{121} + 8353817614896642096 p^{55} T^{122} + 342961453436748540 p^{56} T^{123} + 13478959614619919 p^{57} T^{124} + 500714156911552 p^{58} T^{125} + 17673301335002 p^{59} T^{126} + 579624726668 p^{60} T^{127} + 17887378753 p^{61} T^{128} + 497337437 p^{62} T^{129} + 12855134 p^{63} T^{130} + 279945 p^{64} T^{131} + 5606 p^{65} T^{132} + 77 p^{66} T^{133} + p^{67} T^{134}$$
97 $$1 + 87 T + 6953 T^{2} + 387357 T^{3} + 19588096 T^{4} + 841166996 T^{5} + 33345062249 T^{6} + 1195923154147 T^{7} + 40188164413894 T^{8} + 1257711490375879 T^{9} + 37294951945510751 T^{10} + 1046566289950815406 T^{11} + 28059924087961162913 T^{12} +$$$$71\!\cdots\!00$$$$T^{13} +$$$$17\!\cdots\!98$$$$T^{14} +$$$$42\!\cdots\!27$$$$T^{15} +$$$$96\!\cdots\!81$$$$T^{16} +$$$$21\!\cdots\!68$$$$T^{17} +$$$$45\!\cdots\!32$$$$T^{18} +$$$$95\!\cdots\!61$$$$T^{19} +$$$$19\!\cdots\!21$$$$T^{20} +$$$$38\!\cdots\!28$$$$T^{21} +$$$$74\!\cdots\!19$$$$T^{22} +$$$$13\!\cdots\!46$$$$T^{23} +$$$$25\!\cdots\!20$$$$T^{24} +$$$$47\!\cdots\!52$$$$p T^{25} +$$$$81\!\cdots\!34$$$$T^{26} +$$$$13\!\cdots\!56$$$$T^{27} +$$$$23\!\cdots\!51$$$$T^{28} +$$$$39\!\cdots\!29$$$$T^{29} +$$$$63\!\cdots\!44$$$$T^{30} +$$$$10\!\cdots\!46$$$$T^{31} +$$$$16\!\cdots\!36$$$$T^{32} +$$$$24\!\cdots\!42$$$$T^{33} +$$$$37\!\cdots\!86$$$$T^{34} +$$$$56\!\cdots\!13$$$$T^{35} +$$$$82\!\cdots\!39$$$$T^{36} +$$$$11\!\cdots\!97$$$$T^{37} +$$$$16\!\cdots\!45$$$$T^{38} +$$$$23\!\cdots\!76$$$$T^{39} +$$$$32\!\cdots\!90$$$$T^{40} +$$$$44\!\cdots\!82$$$$T^{41} +$$$$60\!\cdots\!01$$$$T^{42} +$$$$80\!\cdots\!72$$$$T^{43} +$$$$10\!\cdots\!95$$$$T^{44} +$$$$13\!\cdots\!45$$$$T^{45} +$$$$17\!\cdots\!59$$$$T^{46} +$$$$21\!\cdots\!35$$$$T^{47} +$$$$26\!\cdots\!47$$$$T^{48} +$$$$33\!\cdots\!52$$$$T^{49} +$$$$39\!\cdots\!15$$$$T^{50} +$$$$47\!\cdots\!14$$$$T^{51} +$$$$56\!\cdots\!58$$$$T^{52} +$$$$65\!\cdots\!64$$$$T^{53} +$$$$75\!\cdots\!59$$$$T^{54} +$$$$86\!\cdots\!00$$$$T^{55} +$$$$97\!\cdots\!45$$$$T^{56} +$$$$10\!\cdots\!68$$$$T^{57} +$$$$11\!\cdots\!08$$$$T^{58} +$$$$12\!\cdots\!87$$$$T^{59} +$$$$13\!\cdots\!64$$$$T^{60} +$$$$14\!\cdots\!61$$$$T^{61} +$$$$15\!\cdots\!55$$$$T^{62} +$$$$15\!\cdots\!97$$$$T^{63} +$$$$16\!\cdots\!79$$$$T^{64} +$$$$16\!\cdots\!71$$$$T^{65} +$$$$16\!\cdots\!72$$$$T^{66} +$$$$16\!\cdots\!77$$$$T^{67} +$$$$16\!\cdots\!72$$$$p T^{68} +$$$$16\!\cdots\!71$$$$p^{2} T^{69} +$$$$16\!\cdots\!79$$$$p^{3} T^{70} +$$$$15\!\cdots\!97$$$$p^{4} T^{71} +$$$$15\!\cdots\!55$$$$p^{5} T^{72} +$$$$14\!\cdots\!61$$$$p^{6} T^{73} +$$$$13\!\cdots\!64$$$$p^{7} T^{74} +$$$$12\!\cdots\!87$$$$p^{8} T^{75} +$$$$11\!\cdots\!08$$$$p^{9} T^{76} +$$$$10\!\cdots\!68$$$$p^{10} T^{77} +$$$$97\!\cdots\!45$$$$p^{11} T^{78} +$$$$86\!\cdots\!00$$$$p^{12} T^{79} +$$$$75\!\cdots\!59$$$$p^{13} T^{80} +$$$$65\!\cdots\!64$$$$p^{14} T^{81} +$$$$56\!\cdots\!58$$$$p^{15} T^{82} +$$$$47\!\cdots\!14$$$$p^{16} T^{83} +$$$$39\!\cdots\!15$$$$p^{17} T^{84} +$$$$33\!\cdots\!52$$$$p^{18} T^{85} +$$$$26\!\cdots\!47$$$$p^{19} T^{86} +$$$$21\!\cdots\!35$$$$p^{20} T^{87} +$$$$17\!\cdots\!59$$$$p^{21} T^{88} +$$$$13\!\cdots\!45$$$$p^{22} T^{89} +$$$$10\!\cdots\!95$$$$p^{23} T^{90} +$$$$80\!\cdots\!72$$$$p^{24} T^{91} +$$$$60\!\cdots\!01$$$$p^{25} T^{92} +$$$$44\!\cdots\!82$$$$p^{26} T^{93} +$$$$32\!\cdots\!90$$$$p^{27} T^{94} +$$$$23\!\cdots\!76$$$$p^{28} T^{95} +$$$$16\!\cdots\!45$$$$p^{29} T^{96} +$$$$11\!\cdots\!97$$$$p^{30} T^{97} +$$$$82\!\cdots\!39$$$$p^{31} T^{98} +$$$$56\!\cdots\!13$$$$p^{32} T^{99} +$$$$37\!\cdots\!86$$$$p^{33} T^{100} +$$$$24\!\cdots\!42$$$$p^{34} T^{101} +$$$$16\!\cdots\!36$$$$p^{35} T^{102} +$$$$10\!\cdots\!46$$$$p^{36} T^{103} +$$$$63\!\cdots\!44$$$$p^{37} T^{104} +$$$$39\!\cdots\!29$$$$p^{38} T^{105} +$$$$23\!\cdots\!51$$$$p^{39} T^{106} +$$$$13\!\cdots\!56$$$$p^{40} T^{107} +$$$$81\!\cdots\!34$$$$p^{41} T^{108} +$$$$47\!\cdots\!52$$$$p^{43} T^{109} +$$$$25\!\cdots\!20$$$$p^{43} T^{110} +$$$$13\!\cdots\!46$$$$p^{44} T^{111} +$$$$74\!\cdots\!19$$$$p^{45} T^{112} +$$$$38\!\cdots\!28$$$$p^{46} T^{113} +$$$$19\!\cdots\!21$$$$p^{47} T^{114} +$$$$95\!\cdots\!61$$$$p^{48} T^{115} +$$$$45\!\cdots\!32$$$$p^{49} T^{116} +$$$$21\!\cdots\!68$$$$p^{50} T^{117} +$$$$96\!\cdots\!81$$$$p^{51} T^{118} +$$$$42\!\cdots\!27$$$$p^{52} T^{119} +$$$$17\!\cdots\!98$$$$p^{53} T^{120} +$$$$71\!\cdots\!00$$$$p^{54} T^{121} + 28059924087961162913 p^{55} T^{122} + 1046566289950815406 p^{56} T^{123} + 37294951945510751 p^{57} T^{124} + 1257711490375879 p^{58} T^{125} + 40188164413894 p^{59} T^{126} + 1195923154147 p^{60} T^{127} + 33345062249 p^{61} T^{128} + 841166996 p^{62} T^{129} + 19588096 p^{63} T^{130} + 387357 p^{64} T^{131} + 6953 p^{65} T^{132} + 87 p^{66} T^{133} + p^{67} T^{134}$$
\begin{aligned} L(s) = \prod_p \ \prod_{j=1}^{134} (1 - \alpha_{j,p}\, p^{-s})^{-1} \end{aligned}