# Properties

 Degree 154 Conductor $2^{77} \cdot 4001^{77}$ Sign $1$ Motivic weight 1 Primitive no Self-dual yes Analytic rank 0

# Origins of factors

## Dirichlet series

 L(s)  = 1 − 77·2-s + 10·3-s + 3.00e3·4-s + 18·5-s − 770·6-s + 21·7-s − 7.90e4·8-s − 30·9-s − 1.38e3·10-s + 30·11-s + 3.00e4·12-s − 2·13-s − 1.61e3·14-s + 180·15-s + 1.58e6·16-s + 60·17-s + 2.31e3·18-s − 3·19-s + 5.40e4·20-s + 210·21-s − 2.31e3·22-s + 53·23-s − 7.90e5·24-s − 25-s + 154·26-s − 629·27-s + 6.30e4·28-s + ⋯
 L(s)  = 1 − 54.4·2-s + 5.77·3-s + 1.50e3·4-s + 8.04·5-s − 314.·6-s + 7.93·7-s − 2.79e4·8-s − 10·9-s − 438.·10-s + 9.04·11-s + 8.66e3·12-s − 0.554·13-s − 432.·14-s + 46.4·15-s + 3.95e5·16-s + 14.5·17-s + 544.·18-s − 0.688·19-s + 1.20e4·20-s + 45.8·21-s − 492.·22-s + 11.0·23-s − 1.61e5·24-s − 1/5·25-s + 30.2·26-s − 121.·27-s + 1.19e4·28-s + ⋯

## Functional equation

\begin{aligned} \Lambda(s)=\mathstrut &\left(2^{77} \cdot 4001^{77}\right)^{s/2} \, \Gamma_{\C}(s)^{77} \, L(s)\cr =\mathstrut & \,\Lambda(2-s) \end{aligned}
\begin{aligned} \Lambda(s)=\mathstrut &\left(2^{77} \cdot 4001^{77}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{77} \, L(s)\cr =\mathstrut & \,\Lambda(1-s) \end{aligned}

## Invariants

 $$d$$ = $$154$$ $$N$$ = $$2^{77} \cdot 4001^{77}$$ $$\varepsilon$$ = $1$ motivic weight = $$1$$ character : induced by $\chi_{8002} (1, \cdot )$ primitive : no self-dual : yes analytic rank = 0 Selberg data = $(154,\ 2^{77} \cdot 4001^{77} ,\ ( \ : [1/2]^{77} ),\ 1 )$ $L(1)$ $\approx$ $0.008193097521$ $L(\frac12)$ $\approx$ $0.008193097521$ $L(\frac{3}{2})$ not available $L(1)$ not available

## Euler product

$L(s) = \prod_{p \text{ prime}} F_p(p^{-s})^{-1}$ where, for $p \notin \{2,\;4001\}$, $$F_p(T)$$ is a polynomial of degree 154. If $p \in \{2,\;4001\}$, then $F_p(T)$ is a polynomial of degree at most 153.
$p$$F_p(T)$
bad2 $$( 1 + T )^{77}$$
4001 $$1+O(T)$$
good3 $$1 - 10 T + 130 T^{2} - 971 T^{3} + 7700 T^{4} - 47138 T^{5} + 289549 T^{6} - 1528439 T^{7} + 7938389 T^{8} - 12430693 p T^{9} + 57059680 p T^{10} - 731062166 T^{11} + 3044911741 T^{12} - 12003888611 T^{13} + 5128897957 p^{2} T^{14} - 169902919148 T^{15} + 610654429967 T^{16} - 2117042026363 T^{17} + 2392266941080 p T^{18} - 23598435659530 T^{19} + 75987801569558 T^{20} - 238317675559858 T^{21} + 732994933602037 T^{22} - 734281441234654 p T^{23} + 6501056302447247 T^{24} - 18793921204409747 T^{25} + 53420248449741763 T^{26} - 49681056774965360 p T^{27} + 136439860442999986 p T^{28} - 1105243580777019205 T^{29} + 980210070157355782 p T^{30} - 855919797330763693 p^{2} T^{31} + 19902017397396464249 T^{32} - 50685749432975065244 T^{33} + 42471703672278077357 p T^{34} -$$$$31\!\cdots\!46$$$$T^{35} +$$$$77\!\cdots\!76$$$$T^{36} -$$$$18\!\cdots\!41$$$$T^{37} +$$$$44\!\cdots\!12$$$$T^{38} -$$$$35\!\cdots\!71$$$$p T^{39} +$$$$82\!\cdots\!88$$$$p T^{40} -$$$$19\!\cdots\!65$$$$p T^{41} +$$$$13\!\cdots\!64$$$$T^{42} -$$$$29\!\cdots\!75$$$$T^{43} +$$$$66\!\cdots\!67$$$$T^{44} -$$$$14\!\cdots\!50$$$$T^{45} +$$$$10\!\cdots\!45$$$$p T^{46} -$$$$70\!\cdots\!61$$$$T^{47} +$$$$16\!\cdots\!65$$$$p^{2} T^{48} -$$$$32\!\cdots\!86$$$$T^{49} +$$$$69\!\cdots\!49$$$$T^{50} -$$$$14\!\cdots\!95$$$$T^{51} +$$$$30\!\cdots\!43$$$$T^{52} -$$$$62\!\cdots\!58$$$$T^{53} +$$$$42\!\cdots\!12$$$$p T^{54} -$$$$26\!\cdots\!58$$$$T^{55} +$$$$17\!\cdots\!88$$$$p T^{56} -$$$$10\!\cdots\!18$$$$T^{57} +$$$$21\!\cdots\!36$$$$T^{58} -$$$$41\!\cdots\!98$$$$T^{59} +$$$$81\!\cdots\!53$$$$T^{60} -$$$$15\!\cdots\!84$$$$T^{61} +$$$$33\!\cdots\!61$$$$p^{2} T^{62} -$$$$19\!\cdots\!63$$$$p T^{63} +$$$$36\!\cdots\!90$$$$p T^{64} -$$$$77\!\cdots\!47$$$$p^{3} T^{65} +$$$$39\!\cdots\!36$$$$T^{66} -$$$$72\!\cdots\!31$$$$T^{67} +$$$$13\!\cdots\!11$$$$T^{68} -$$$$24\!\cdots\!87$$$$T^{69} +$$$$44\!\cdots\!65$$$$T^{70} -$$$$27\!\cdots\!45$$$$p T^{71} +$$$$14\!\cdots\!21$$$$T^{72} -$$$$26\!\cdots\!05$$$$T^{73} +$$$$46\!\cdots\!60$$$$T^{74} -$$$$27\!\cdots\!62$$$$p T^{75} +$$$$14\!\cdots\!35$$$$T^{76} -$$$$24\!\cdots\!76$$$$T^{77} +$$$$14\!\cdots\!35$$$$p T^{78} -$$$$27\!\cdots\!62$$$$p^{3} T^{79} +$$$$46\!\cdots\!60$$$$p^{3} T^{80} -$$$$26\!\cdots\!05$$$$p^{4} T^{81} +$$$$14\!\cdots\!21$$$$p^{5} T^{82} -$$$$27\!\cdots\!45$$$$p^{7} T^{83} +$$$$44\!\cdots\!65$$$$p^{7} T^{84} -$$$$24\!\cdots\!87$$$$p^{8} T^{85} +$$$$13\!\cdots\!11$$$$p^{9} T^{86} -$$$$72\!\cdots\!31$$$$p^{10} T^{87} +$$$$39\!\cdots\!36$$$$p^{11} T^{88} -$$$$77\!\cdots\!47$$$$p^{15} T^{89} +$$$$36\!\cdots\!90$$$$p^{14} T^{90} -$$$$19\!\cdots\!63$$$$p^{15} T^{91} +$$$$33\!\cdots\!61$$$$p^{17} T^{92} -$$$$15\!\cdots\!84$$$$p^{16} T^{93} +$$$$81\!\cdots\!53$$$$p^{17} T^{94} -$$$$41\!\cdots\!98$$$$p^{18} T^{95} +$$$$21\!\cdots\!36$$$$p^{19} T^{96} -$$$$10\!\cdots\!18$$$$p^{20} T^{97} +$$$$17\!\cdots\!88$$$$p^{22} T^{98} -$$$$26\!\cdots\!58$$$$p^{22} T^{99} +$$$$42\!\cdots\!12$$$$p^{24} T^{100} -$$$$62\!\cdots\!58$$$$p^{24} T^{101} +$$$$30\!\cdots\!43$$$$p^{25} T^{102} -$$$$14\!\cdots\!95$$$$p^{26} T^{103} +$$$$69\!\cdots\!49$$$$p^{27} T^{104} -$$$$32\!\cdots\!86$$$$p^{28} T^{105} +$$$$16\!\cdots\!65$$$$p^{31} T^{106} -$$$$70\!\cdots\!61$$$$p^{30} T^{107} +$$$$10\!\cdots\!45$$$$p^{32} T^{108} -$$$$14\!\cdots\!50$$$$p^{32} T^{109} +$$$$66\!\cdots\!67$$$$p^{33} T^{110} -$$$$29\!\cdots\!75$$$$p^{34} T^{111} +$$$$13\!\cdots\!64$$$$p^{35} T^{112} -$$$$19\!\cdots\!65$$$$p^{37} T^{113} +$$$$82\!\cdots\!88$$$$p^{38} T^{114} -$$$$35\!\cdots\!71$$$$p^{39} T^{115} +$$$$44\!\cdots\!12$$$$p^{39} T^{116} -$$$$18\!\cdots\!41$$$$p^{40} T^{117} +$$$$77\!\cdots\!76$$$$p^{41} T^{118} -$$$$31\!\cdots\!46$$$$p^{42} T^{119} + 42471703672278077357 p^{44} T^{120} - 50685749432975065244 p^{44} T^{121} + 19902017397396464249 p^{45} T^{122} - 855919797330763693 p^{48} T^{123} + 980210070157355782 p^{48} T^{124} - 1105243580777019205 p^{48} T^{125} + 136439860442999986 p^{50} T^{126} - 49681056774965360 p^{51} T^{127} + 53420248449741763 p^{51} T^{128} - 18793921204409747 p^{52} T^{129} + 6501056302447247 p^{53} T^{130} - 734281441234654 p^{55} T^{131} + 732994933602037 p^{55} T^{132} - 238317675559858 p^{56} T^{133} + 75987801569558 p^{57} T^{134} - 23598435659530 p^{58} T^{135} + 2392266941080 p^{60} T^{136} - 2117042026363 p^{60} T^{137} + 610654429967 p^{61} T^{138} - 169902919148 p^{62} T^{139} + 5128897957 p^{65} T^{140} - 12003888611 p^{64} T^{141} + 3044911741 p^{65} T^{142} - 731062166 p^{66} T^{143} + 57059680 p^{68} T^{144} - 12430693 p^{69} T^{145} + 7938389 p^{69} T^{146} - 1528439 p^{70} T^{147} + 289549 p^{71} T^{148} - 47138 p^{72} T^{149} + 7700 p^{73} T^{150} - 971 p^{74} T^{151} + 130 p^{75} T^{152} - 10 p^{76} T^{153} + p^{77} T^{154}$$
5 $$1 - 18 T + 13 p^{2} T^{2} - 3909 T^{3} + 44209 T^{4} - 415949 T^{5} + 3676001 T^{6} - 5818512 p T^{7} + 8712993 p^{2} T^{8} - 60432821 p^{2} T^{9} + 9987781761 T^{10} - 62315235854 T^{11} + 74586791276 p T^{12} - 2130785335979 T^{13} + 11738739467538 T^{14} - 62220359482593 T^{15} + 319342893034076 T^{16} - 1585659643067954 T^{17} + 1530067055256837 p T^{18} - 7171384100836203 p T^{19} + 163766109457825771 T^{20} - 728933335779915817 T^{21} + 3169158004885925434 T^{22} - 13462369160014157784 T^{23} + 55970768252304645389 T^{24} -$$$$22\!\cdots\!39$$$$T^{25} +$$$$18\!\cdots\!09$$$$p T^{26} -$$$$35\!\cdots\!31$$$$T^{27} +$$$$13\!\cdots\!48$$$$T^{28} -$$$$51\!\cdots\!03$$$$T^{29} +$$$$19\!\cdots\!61$$$$T^{30} -$$$$13\!\cdots\!09$$$$p T^{31} +$$$$25\!\cdots\!89$$$$T^{32} -$$$$88\!\cdots\!48$$$$T^{33} +$$$$30\!\cdots\!39$$$$T^{34} -$$$$10\!\cdots\!32$$$$T^{35} +$$$$35\!\cdots\!57$$$$T^{36} -$$$$11\!\cdots\!93$$$$T^{37} +$$$$39\!\cdots\!81$$$$T^{38} -$$$$12\!\cdots\!13$$$$T^{39} +$$$$41\!\cdots\!23$$$$T^{40} -$$$$13\!\cdots\!88$$$$T^{41} +$$$$40\!\cdots\!76$$$$T^{42} -$$$$12\!\cdots\!28$$$$T^{43} +$$$$38\!\cdots\!64$$$$T^{44} -$$$$11\!\cdots\!84$$$$T^{45} +$$$$34\!\cdots\!74$$$$T^{46} -$$$$10\!\cdots\!99$$$$T^{47} +$$$$60\!\cdots\!09$$$$p T^{48} -$$$$17\!\cdots\!01$$$$p T^{49} +$$$$24\!\cdots\!68$$$$T^{50} -$$$$70\!\cdots\!11$$$$T^{51} +$$$$79\!\cdots\!37$$$$p^{2} T^{52} -$$$$54\!\cdots\!63$$$$T^{53} +$$$$15\!\cdots\!88$$$$T^{54} -$$$$41\!\cdots\!58$$$$T^{55} +$$$$11\!\cdots\!87$$$$T^{56} -$$$$29\!\cdots\!08$$$$T^{57} +$$$$78\!\cdots\!96$$$$T^{58} -$$$$20\!\cdots\!37$$$$T^{59} +$$$$53\!\cdots\!41$$$$T^{60} -$$$$13\!\cdots\!47$$$$T^{61} +$$$$35\!\cdots\!68$$$$T^{62} -$$$$88\!\cdots\!56$$$$T^{63} +$$$$22\!\cdots\!22$$$$T^{64} -$$$$55\!\cdots\!67$$$$T^{65} +$$$$27\!\cdots\!27$$$$p T^{66} -$$$$33\!\cdots\!94$$$$T^{67} +$$$$80\!\cdots\!47$$$$T^{68} -$$$$19\!\cdots\!53$$$$T^{69} +$$$$18\!\cdots\!96$$$$p^{2} T^{70} -$$$$21\!\cdots\!46$$$$p T^{71} +$$$$25\!\cdots\!93$$$$T^{72} -$$$$59\!\cdots\!64$$$$T^{73} +$$$$13\!\cdots\!48$$$$T^{74} -$$$$31\!\cdots\!43$$$$T^{75} +$$$$70\!\cdots\!77$$$$T^{76} -$$$$15\!\cdots\!72$$$$T^{77} +$$$$70\!\cdots\!77$$$$p T^{78} -$$$$31\!\cdots\!43$$$$p^{2} T^{79} +$$$$13\!\cdots\!48$$$$p^{3} T^{80} -$$$$59\!\cdots\!64$$$$p^{4} T^{81} +$$$$25\!\cdots\!93$$$$p^{5} T^{82} -$$$$21\!\cdots\!46$$$$p^{7} T^{83} +$$$$18\!\cdots\!96$$$$p^{9} T^{84} -$$$$19\!\cdots\!53$$$$p^{8} T^{85} +$$$$80\!\cdots\!47$$$$p^{9} T^{86} -$$$$33\!\cdots\!94$$$$p^{10} T^{87} +$$$$27\!\cdots\!27$$$$p^{12} T^{88} -$$$$55\!\cdots\!67$$$$p^{12} T^{89} +$$$$22\!\cdots\!22$$$$p^{13} T^{90} -$$$$88\!\cdots\!56$$$$p^{14} T^{91} +$$$$35\!\cdots\!68$$$$p^{15} T^{92} -$$$$13\!\cdots\!47$$$$p^{16} T^{93} +$$$$53\!\cdots\!41$$$$p^{17} T^{94} -$$$$20\!\cdots\!37$$$$p^{18} T^{95} +$$$$78\!\cdots\!96$$$$p^{19} T^{96} -$$$$29\!\cdots\!08$$$$p^{20} T^{97} +$$$$11\!\cdots\!87$$$$p^{21} T^{98} -$$$$41\!\cdots\!58$$$$p^{22} T^{99} +$$$$15\!\cdots\!88$$$$p^{23} T^{100} -$$$$54\!\cdots\!63$$$$p^{24} T^{101} +$$$$79\!\cdots\!37$$$$p^{27} T^{102} -$$$$70\!\cdots\!11$$$$p^{26} T^{103} +$$$$24\!\cdots\!68$$$$p^{27} T^{104} -$$$$17\!\cdots\!01$$$$p^{29} T^{105} +$$$$60\!\cdots\!09$$$$p^{30} T^{106} -$$$$10\!\cdots\!99$$$$p^{30} T^{107} +$$$$34\!\cdots\!74$$$$p^{31} T^{108} -$$$$11\!\cdots\!84$$$$p^{32} T^{109} +$$$$38\!\cdots\!64$$$$p^{33} T^{110} -$$$$12\!\cdots\!28$$$$p^{34} T^{111} +$$$$40\!\cdots\!76$$$$p^{35} T^{112} -$$$$13\!\cdots\!88$$$$p^{36} T^{113} +$$$$41\!\cdots\!23$$$$p^{37} T^{114} -$$$$12\!\cdots\!13$$$$p^{38} T^{115} +$$$$39\!\cdots\!81$$$$p^{39} T^{116} -$$$$11\!\cdots\!93$$$$p^{40} T^{117} +$$$$35\!\cdots\!57$$$$p^{41} T^{118} -$$$$10\!\cdots\!32$$$$p^{42} T^{119} +$$$$30\!\cdots\!39$$$$p^{43} T^{120} -$$$$88\!\cdots\!48$$$$p^{44} T^{121} +$$$$25\!\cdots\!89$$$$p^{45} T^{122} -$$$$13\!\cdots\!09$$$$p^{47} T^{123} +$$$$19\!\cdots\!61$$$$p^{47} T^{124} -$$$$51\!\cdots\!03$$$$p^{48} T^{125} +$$$$13\!\cdots\!48$$$$p^{49} T^{126} -$$$$35\!\cdots\!31$$$$p^{50} T^{127} +$$$$18\!\cdots\!09$$$$p^{52} T^{128} -$$$$22\!\cdots\!39$$$$p^{52} T^{129} + 55970768252304645389 p^{53} T^{130} - 13462369160014157784 p^{54} T^{131} + 3169158004885925434 p^{55} T^{132} - 728933335779915817 p^{56} T^{133} + 163766109457825771 p^{57} T^{134} - 7171384100836203 p^{59} T^{135} + 1530067055256837 p^{60} T^{136} - 1585659643067954 p^{60} T^{137} + 319342893034076 p^{61} T^{138} - 62220359482593 p^{62} T^{139} + 11738739467538 p^{63} T^{140} - 2130785335979 p^{64} T^{141} + 74586791276 p^{66} T^{142} - 62315235854 p^{66} T^{143} + 9987781761 p^{67} T^{144} - 60432821 p^{70} T^{145} + 8712993 p^{71} T^{146} - 5818512 p^{71} T^{147} + 3676001 p^{71} T^{148} - 415949 p^{72} T^{149} + 44209 p^{73} T^{150} - 3909 p^{74} T^{151} + 13 p^{77} T^{152} - 18 p^{76} T^{153} + p^{77} T^{154}$$
7 $$1 - 3 p T + 478 T^{2} - 6964 T^{3} + 98432 T^{4} - 162290 p T^{5} + 12500585 T^{6} - 17421347 p T^{7} + 1134218025 T^{8} - 9713244843 T^{9} + 79608779624 T^{10} - 613298849614 T^{11} + 4541662960861 T^{12} - 32014298102513 T^{13} + 217803278056257 T^{14} - 1422319623798729 T^{15} + 8996074343090367 T^{16} - 54938689322042798 T^{17} + 325937517240344463 T^{18} - 1875220177376264896 T^{19} + 10507833436044945218 T^{20} - 8184513884695912362 p T^{21} +$$$$30\!\cdots\!92$$$$T^{22} -$$$$15\!\cdots\!59$$$$T^{23} +$$$$80\!\cdots\!80$$$$T^{24} -$$$$39\!\cdots\!34$$$$T^{25} +$$$$19\!\cdots\!60$$$$T^{26} -$$$$92\!\cdots\!32$$$$T^{27} +$$$$43\!\cdots\!28$$$$T^{28} -$$$$19\!\cdots\!48$$$$T^{29} +$$$$89\!\cdots\!32$$$$T^{30} -$$$$39\!\cdots\!78$$$$T^{31} +$$$$17\!\cdots\!05$$$$T^{32} -$$$$73\!\cdots\!34$$$$T^{33} +$$$$43\!\cdots\!98$$$$p T^{34} -$$$$12\!\cdots\!78$$$$T^{35} +$$$$51\!\cdots\!50$$$$T^{36} -$$$$20\!\cdots\!93$$$$T^{37} +$$$$11\!\cdots\!77$$$$p T^{38} -$$$$32\!\cdots\!35$$$$T^{39} +$$$$17\!\cdots\!01$$$$p T^{40} -$$$$47\!\cdots\!82$$$$T^{41} +$$$$17\!\cdots\!21$$$$T^{42} -$$$$93\!\cdots\!67$$$$p T^{43} +$$$$23\!\cdots\!50$$$$T^{44} -$$$$85\!\cdots\!87$$$$T^{45} +$$$$30\!\cdots\!54$$$$T^{46} -$$$$10\!\cdots\!80$$$$T^{47} +$$$$37\!\cdots\!70$$$$T^{48} -$$$$12\!\cdots\!79$$$$T^{49} +$$$$44\!\cdots\!95$$$$T^{50} -$$$$14\!\cdots\!52$$$$T^{51} +$$$$49\!\cdots\!75$$$$T^{52} -$$$$16\!\cdots\!75$$$$T^{53} +$$$$53\!\cdots\!40$$$$T^{54} -$$$$17\!\cdots\!05$$$$T^{55} +$$$$55\!\cdots\!14$$$$T^{56} -$$$$24\!\cdots\!64$$$$p T^{57} +$$$$78\!\cdots\!44$$$$p T^{58} -$$$$16\!\cdots\!25$$$$T^{59} +$$$$52\!\cdots\!16$$$$T^{60} -$$$$15\!\cdots\!26$$$$T^{61} +$$$$48\!\cdots\!29$$$$T^{62} -$$$$20\!\cdots\!76$$$$p T^{63} +$$$$60\!\cdots\!33$$$$p T^{64} -$$$$12\!\cdots\!04$$$$T^{65} +$$$$36\!\cdots\!24$$$$T^{66} -$$$$15\!\cdots\!25$$$$p T^{67} +$$$$30\!\cdots\!48$$$$T^{68} -$$$$85\!\cdots\!46$$$$T^{69} +$$$$24\!\cdots\!37$$$$T^{70} -$$$$67\!\cdots\!23$$$$T^{71} +$$$$18\!\cdots\!70$$$$T^{72} -$$$$51\!\cdots\!01$$$$T^{73} +$$$$13\!\cdots\!19$$$$T^{74} -$$$$37\!\cdots\!69$$$$T^{75} +$$$$10\!\cdots\!51$$$$T^{76} -$$$$26\!\cdots\!92$$$$T^{77} +$$$$10\!\cdots\!51$$$$p T^{78} -$$$$37\!\cdots\!69$$$$p^{2} T^{79} +$$$$13\!\cdots\!19$$$$p^{3} T^{80} -$$$$51\!\cdots\!01$$$$p^{4} T^{81} +$$$$18\!\cdots\!70$$$$p^{5} T^{82} -$$$$67\!\cdots\!23$$$$p^{6} T^{83} +$$$$24\!\cdots\!37$$$$p^{7} T^{84} -$$$$85\!\cdots\!46$$$$p^{8} T^{85} +$$$$30\!\cdots\!48$$$$p^{9} T^{86} -$$$$15\!\cdots\!25$$$$p^{11} T^{87} +$$$$36\!\cdots\!24$$$$p^{11} T^{88} -$$$$12\!\cdots\!04$$$$p^{12} T^{89} +$$$$60\!\cdots\!33$$$$p^{14} T^{90} -$$$$20\!\cdots\!76$$$$p^{15} T^{91} +$$$$48\!\cdots\!29$$$$p^{15} T^{92} -$$$$15\!\cdots\!26$$$$p^{16} T^{93} +$$$$52\!\cdots\!16$$$$p^{17} T^{94} -$$$$16\!\cdots\!25$$$$p^{18} T^{95} +$$$$78\!\cdots\!44$$$$p^{20} T^{96} -$$$$24\!\cdots\!64$$$$p^{21} T^{97} +$$$$55\!\cdots\!14$$$$p^{21} T^{98} -$$$$17\!\cdots\!05$$$$p^{22} T^{99} +$$$$53\!\cdots\!40$$$$p^{23} T^{100} -$$$$16\!\cdots\!75$$$$p^{24} T^{101} +$$$$49\!\cdots\!75$$$$p^{25} T^{102} -$$$$14\!\cdots\!52$$$$p^{26} T^{103} +$$$$44\!\cdots\!95$$$$p^{27} T^{104} -$$$$12\!\cdots\!79$$$$p^{28} T^{105} +$$$$37\!\cdots\!70$$$$p^{29} T^{106} -$$$$10\!\cdots\!80$$$$p^{30} T^{107} +$$$$30\!\cdots\!54$$$$p^{31} T^{108} -$$$$85\!\cdots\!87$$$$p^{32} T^{109} +$$$$23\!\cdots\!50$$$$p^{33} T^{110} -$$$$93\!\cdots\!67$$$$p^{35} T^{111} +$$$$17\!\cdots\!21$$$$p^{35} T^{112} -$$$$47\!\cdots\!82$$$$p^{36} T^{113} +$$$$17\!\cdots\!01$$$$p^{38} T^{114} -$$$$32\!\cdots\!35$$$$p^{38} T^{115} +$$$$11\!\cdots\!77$$$$p^{40} T^{116} -$$$$20\!\cdots\!93$$$$p^{40} T^{117} +$$$$51\!\cdots\!50$$$$p^{41} T^{118} -$$$$12\!\cdots\!78$$$$p^{42} T^{119} +$$$$43\!\cdots\!98$$$$p^{44} T^{120} -$$$$73\!\cdots\!34$$$$p^{44} T^{121} +$$$$17\!\cdots\!05$$$$p^{45} T^{122} -$$$$39\!\cdots\!78$$$$p^{46} T^{123} +$$$$89\!\cdots\!32$$$$p^{47} T^{124} -$$$$19\!\cdots\!48$$$$p^{48} T^{125} +$$$$43\!\cdots\!28$$$$p^{49} T^{126} -$$$$92\!\cdots\!32$$$$p^{50} T^{127} +$$$$19\!\cdots\!60$$$$p^{51} T^{128} -$$$$39\!\cdots\!34$$$$p^{52} T^{129} +$$$$80\!\cdots\!80$$$$p^{53} T^{130} -$$$$15\!\cdots\!59$$$$p^{54} T^{131} +$$$$30\!\cdots\!92$$$$p^{55} T^{132} - 8184513884695912362 p^{57} T^{133} + 10507833436044945218 p^{57} T^{134} - 1875220177376264896 p^{58} T^{135} + 325937517240344463 p^{59} T^{136} - 54938689322042798 p^{60} T^{137} + 8996074343090367 p^{61} T^{138} - 1422319623798729 p^{62} T^{139} + 217803278056257 p^{63} T^{140} - 32014298102513 p^{64} T^{141} + 4541662960861 p^{65} T^{142} - 613298849614 p^{66} T^{143} + 79608779624 p^{67} T^{144} - 9713244843 p^{68} T^{145} + 1134218025 p^{69} T^{146} - 17421347 p^{71} T^{147} + 12500585 p^{71} T^{148} - 162290 p^{73} T^{149} + 98432 p^{73} T^{150} - 6964 p^{74} T^{151} + 478 p^{75} T^{152} - 3 p^{77} T^{153} + p^{77} T^{154}$$
11 $$1 - 30 T + 857 T^{2} - 16611 T^{3} + 296697 T^{4} - 4432266 T^{5} + 5596676 p T^{6} - 766249486 T^{7} + 8967182067 T^{8} - 97093872162 T^{9} + 997707172304 T^{10} - 9656579600763 T^{11} + 89350209638554 T^{12} - 787507602105669 T^{13} + 6673643620736826 T^{14} - 54286171632753559 T^{15} + 426532403557477579 T^{16} - 3234807761892696634 T^{17} + 23784199540874907146 T^{18} -$$$$16\!\cdots\!63$$$$T^{19} +$$$$11\!\cdots\!20$$$$T^{20} -$$$$79\!\cdots\!12$$$$T^{21} +$$$$52\!\cdots\!67$$$$T^{22} -$$$$33\!\cdots\!69$$$$T^{23} +$$$$20\!\cdots\!14$$$$T^{24} -$$$$12\!\cdots\!53$$$$T^{25} +$$$$76\!\cdots\!21$$$$T^{26} -$$$$44\!\cdots\!07$$$$T^{27} +$$$$25\!\cdots\!85$$$$T^{28} -$$$$14\!\cdots\!01$$$$T^{29} +$$$$80\!\cdots\!32$$$$T^{30} -$$$$43\!\cdots\!31$$$$T^{31} +$$$$23\!\cdots\!49$$$$T^{32} -$$$$12\!\cdots\!96$$$$T^{33} +$$$$63\!\cdots\!90$$$$T^{34} -$$$$32\!\cdots\!07$$$$T^{35} +$$$$16\!\cdots\!83$$$$T^{36} -$$$$79\!\cdots\!16$$$$T^{37} +$$$$38\!\cdots\!49$$$$T^{38} -$$$$18\!\cdots\!44$$$$T^{39} +$$$$88\!\cdots\!04$$$$T^{40} -$$$$41\!\cdots\!82$$$$T^{41} +$$$$18\!\cdots\!60$$$$T^{42} -$$$$86\!\cdots\!76$$$$T^{43} +$$$$38\!\cdots\!21$$$$T^{44} -$$$$17\!\cdots\!63$$$$T^{45} +$$$$75\!\cdots\!74$$$$T^{46} -$$$$32\!\cdots\!87$$$$T^{47} +$$$$12\!\cdots\!30$$$$p T^{48} -$$$$60\!\cdots\!89$$$$T^{49} +$$$$25\!\cdots\!86$$$$T^{50} -$$$$10\!\cdots\!94$$$$T^{51} +$$$$43\!\cdots\!59$$$$T^{52} -$$$$17\!\cdots\!67$$$$T^{53} +$$$$71\!\cdots\!20$$$$T^{54} -$$$$28\!\cdots\!53$$$$T^{55} +$$$$11\!\cdots\!63$$$$T^{56} -$$$$44\!\cdots\!27$$$$T^{57} +$$$$17\!\cdots\!82$$$$T^{58} -$$$$66\!\cdots\!48$$$$T^{59} +$$$$25\!\cdots\!08$$$$T^{60} -$$$$95\!\cdots\!05$$$$T^{61} +$$$$36\!\cdots\!67$$$$T^{62} -$$$$13\!\cdots\!46$$$$T^{63} +$$$$49\!\cdots\!11$$$$T^{64} -$$$$18\!\cdots\!54$$$$T^{65} +$$$$65\!\cdots\!00$$$$T^{66} -$$$$23\!\cdots\!80$$$$T^{67} +$$$$84\!\cdots\!65$$$$T^{68} -$$$$29\!\cdots\!63$$$$T^{69} +$$$$10\!\cdots\!52$$$$T^{70} -$$$$36\!\cdots\!53$$$$T^{71} +$$$$12\!\cdots\!51$$$$T^{72} -$$$$43\!\cdots\!21$$$$T^{73} +$$$$14\!\cdots\!55$$$$T^{74} -$$$$50\!\cdots\!83$$$$T^{75} +$$$$16\!\cdots\!03$$$$T^{76} -$$$$56\!\cdots\!56$$$$T^{77} +$$$$16\!\cdots\!03$$$$p T^{78} -$$$$50\!\cdots\!83$$$$p^{2} T^{79} +$$$$14\!\cdots\!55$$$$p^{3} T^{80} -$$$$43\!\cdots\!21$$$$p^{4} T^{81} +$$$$12\!\cdots\!51$$$$p^{5} T^{82} -$$$$36\!\cdots\!53$$$$p^{6} T^{83} +$$$$10\!\cdots\!52$$$$p^{7} T^{84} -$$$$29\!\cdots\!63$$$$p^{8} T^{85} +$$$$84\!\cdots\!65$$$$p^{9} T^{86} -$$$$23\!\cdots\!80$$$$p^{10} T^{87} +$$$$65\!\cdots\!00$$$$p^{11} T^{88} -$$$$18\!\cdots\!54$$$$p^{12} T^{89} +$$$$49\!\cdots\!11$$$$p^{13} T^{90} -$$$$13\!\cdots\!46$$$$p^{14} T^{91} +$$$$36\!\cdots\!67$$$$p^{15} T^{92} -$$$$95\!\cdots\!05$$$$p^{16} T^{93} +$$$$25\!\cdots\!08$$$$p^{17} T^{94} -$$$$66\!\cdots\!48$$$$p^{18} T^{95} +$$$$17\!\cdots\!82$$$$p^{19} T^{96} -$$$$44\!\cdots\!27$$$$p^{20} T^{97} +$$$$11\!\cdots\!63$$$$p^{21} T^{98} -$$$$28\!\cdots\!53$$$$p^{22} T^{99} +$$$$71\!\cdots\!20$$$$p^{23} T^{100} -$$$$17\!\cdots\!67$$$$p^{24} T^{101} +$$$$43\!\cdots\!59$$$$p^{25} T^{102} -$$$$10\!\cdots\!94$$$$p^{26} T^{103} +$$$$25\!\cdots\!86$$$$p^{27} T^{104} -$$$$60\!\cdots\!89$$$$p^{28} T^{105} +$$$$12\!\cdots\!30$$$$p^{30} T^{106} -$$$$32\!\cdots\!87$$$$p^{30} T^{107} +$$$$75\!\cdots\!74$$$$p^{31} T^{108} -$$$$17\!\cdots\!63$$$$p^{32} T^{109} +$$$$38\!\cdots\!21$$$$p^{33} T^{110} -$$$$86\!\cdots\!76$$$$p^{34} T^{111} +$$$$18\!\cdots\!60$$$$p^{35} T^{112} -$$$$41\!\cdots\!82$$$$p^{36} T^{113} +$$$$88\!\cdots\!04$$$$p^{37} T^{114} -$$$$18\!\cdots\!44$$$$p^{38} T^{115} +$$$$38\!\cdots\!49$$$$p^{39} T^{116} -$$$$79\!\cdots\!16$$$$p^{40} T^{117} +$$$$16\!\cdots\!83$$$$p^{41} T^{118} -$$$$32\!\cdots\!07$$$$p^{42} T^{119} +$$$$63\!\cdots\!90$$$$p^{43} T^{120} -$$$$12\!\cdots\!96$$$$p^{44} T^{121} +$$$$23\!\cdots\!49$$$$p^{45} T^{122} -$$$$43\!\cdots\!31$$$$p^{46} T^{123} +$$$$80\!\cdots\!32$$$$p^{47} T^{124} -$$$$14\!\cdots\!01$$$$p^{48} T^{125} +$$$$25\!\cdots\!85$$$$p^{49} T^{126} -$$$$44\!\cdots\!07$$$$p^{50} T^{127} +$$$$76\!\cdots\!21$$$$p^{51} T^{128} -$$$$12\!\cdots\!53$$$$p^{52} T^{129} +$$$$20\!\cdots\!14$$$$p^{53} T^{130} -$$$$33\!\cdots\!69$$$$p^{54} T^{131} +$$$$52\!\cdots\!67$$$$p^{55} T^{132} -$$$$79\!\cdots\!12$$$$p^{56} T^{133} +$$$$11\!\cdots\!20$$$$p^{57} T^{134} -$$$$16\!\cdots\!63$$$$p^{58} T^{135} + 23784199540874907146 p^{59} T^{136} - 3234807761892696634 p^{60} T^{137} + 426532403557477579 p^{61} T^{138} - 54286171632753559 p^{62} T^{139} + 6673643620736826 p^{63} T^{140} - 787507602105669 p^{64} T^{141} + 89350209638554 p^{65} T^{142} - 9656579600763 p^{66} T^{143} + 997707172304 p^{67} T^{144} - 97093872162 p^{68} T^{145} + 8967182067 p^{69} T^{146} - 766249486 p^{70} T^{147} + 5596676 p^{72} T^{148} - 4432266 p^{72} T^{149} + 296697 p^{73} T^{150} - 16611 p^{74} T^{151} + 857 p^{75} T^{152} - 30 p^{76} T^{153} + p^{77} T^{154}$$
13 $$1 + 2 T + 508 T^{2} + 1042 T^{3} + 129782 T^{4} + 272470 T^{5} + 22226891 T^{6} + 47666620 T^{7} + 2870055102 T^{8} + 6274776801 T^{9} + 297957282814 T^{10} + 662811452506 T^{11} + 25898307876537 T^{12} + 58507254679922 T^{13} + 1937968879952341 T^{14} + 4437970317568377 T^{15} + 127409921615909796 T^{16} + 295231471103510147 T^{17} + 7473899365421986505 T^{18} + 17493593224160709976 T^{19} +$$$$39\!\cdots\!89$$$$T^{20} +$$$$93\!\cdots\!88$$$$T^{21} +$$$$19\!\cdots\!52$$$$T^{22} +$$$$45\!\cdots\!93$$$$T^{23} +$$$$84\!\cdots\!38$$$$T^{24} +$$$$20\!\cdots\!81$$$$T^{25} +$$$$34\!\cdots\!60$$$$T^{26} +$$$$83\!\cdots\!18$$$$T^{27} +$$$$13\!\cdots\!13$$$$T^{28} +$$$$32\!\cdots\!67$$$$T^{29} +$$$$47\!\cdots\!90$$$$T^{30} +$$$$11\!\cdots\!81$$$$T^{31} +$$$$16\!\cdots\!94$$$$T^{32} +$$$$38\!\cdots\!32$$$$T^{33} +$$$$50\!\cdots\!86$$$$T^{34} +$$$$12\!\cdots\!76$$$$T^{35} +$$$$15\!\cdots\!93$$$$T^{36} +$$$$36\!\cdots\!41$$$$T^{37} +$$$$43\!\cdots\!63$$$$T^{38} +$$$$10\!\cdots\!55$$$$T^{39} +$$$$11\!\cdots\!77$$$$T^{40} +$$$$27\!\cdots\!00$$$$T^{41} +$$$$29\!\cdots\!07$$$$T^{42} +$$$$70\!\cdots\!01$$$$T^{43} +$$$$73\!\cdots\!01$$$$T^{44} +$$$$17\!\cdots\!68$$$$T^{45} +$$$$13\!\cdots\!77$$$$p T^{46} +$$$$40\!\cdots\!63$$$$T^{47} +$$$$38\!\cdots\!97$$$$T^{48} +$$$$89\!\cdots\!93$$$$T^{49} +$$$$63\!\cdots\!23$$$$p T^{50} +$$$$19\!\cdots\!10$$$$T^{51} +$$$$17\!\cdots\!69$$$$T^{52} +$$$$39\!\cdots\!79$$$$T^{53} +$$$$34\!\cdots\!20$$$$T^{54} +$$$$76\!\cdots\!68$$$$T^{55} +$$$$65\!\cdots\!46$$$$T^{56} +$$$$14\!\cdots\!55$$$$T^{57} +$$$$11\!\cdots\!03$$$$T^{58} +$$$$26\!\cdots\!61$$$$T^{59} +$$$$21\!\cdots\!23$$$$T^{60} +$$$$35\!\cdots\!43$$$$p T^{61} +$$$$36\!\cdots\!99$$$$T^{62} +$$$$78\!\cdots\!60$$$$T^{63} +$$$$59\!\cdots\!21$$$$T^{64} +$$$$12\!\cdots\!50$$$$T^{65} +$$$$95\!\cdots\!16$$$$T^{66} +$$$$20\!\cdots\!33$$$$T^{67} +$$$$14\!\cdots\!37$$$$T^{68} +$$$$30\!\cdots\!74$$$$T^{69} +$$$$21\!\cdots\!22$$$$T^{70} +$$$$34\!\cdots\!51$$$$p T^{71} +$$$$31\!\cdots\!13$$$$T^{72} +$$$$63\!\cdots\!55$$$$T^{73} +$$$$43\!\cdots\!41$$$$T^{74} +$$$$86\!\cdots\!33$$$$T^{75} +$$$$58\!\cdots\!17$$$$T^{76} +$$$$11\!\cdots\!60$$$$T^{77} +$$$$58\!\cdots\!17$$$$p T^{78} +$$$$86\!\cdots\!33$$$$p^{2} T^{79} +$$$$43\!\cdots\!41$$$$p^{3} T^{80} +$$$$63\!\cdots\!55$$$$p^{4} T^{81} +$$$$31\!\cdots\!13$$$$p^{5} T^{82} +$$$$34\!\cdots\!51$$$$p^{7} T^{83} +$$$$21\!\cdots\!22$$$$p^{7} T^{84} +$$$$30\!\cdots\!74$$$$p^{8} T^{85} +$$$$14\!\cdots\!37$$$$p^{9} T^{86} +$$$$20\!\cdots\!33$$$$p^{10} T^{87} +$$$$95\!\cdots\!16$$$$p^{11} T^{88} +$$$$12\!\cdots\!50$$$$p^{12} T^{89} +$$$$59\!\cdots\!21$$$$p^{13} T^{90} +$$$$78\!\cdots\!60$$$$p^{14} T^{91} +$$$$36\!\cdots\!99$$$$p^{15} T^{92} +$$$$35\!\cdots\!43$$$$p^{17} T^{93} +$$$$21\!\cdots\!23$$$$p^{17} T^{94} +$$$$26\!\cdots\!61$$$$p^{18} T^{95} +$$$$11\!\cdots\!03$$$$p^{19} T^{96} +$$$$14\!\cdots\!55$$$$p^{20} T^{97} +$$$$65\!\cdots\!46$$$$p^{21} T^{98} +$$$$76\!\cdots\!68$$$$p^{22} T^{99} +$$$$34\!\cdots\!20$$$$p^{23} T^{100} +$$$$39\!\cdots\!79$$$$p^{24} T^{101} +$$$$17\!\cdots\!69$$$$p^{25} T^{102} +$$$$19\!\cdots\!10$$$$p^{26} T^{103} +$$$$63\!\cdots\!23$$$$p^{28} T^{104} +$$$$89\!\cdots\!93$$$$p^{28} T^{105} +$$$$38\!\cdots\!97$$$$p^{29} T^{106} +$$$$40\!\cdots\!63$$$$p^{30} T^{107} +$$$$13\!\cdots\!77$$$$p^{32} T^{108} +$$$$17\!\cdots\!68$$$$p^{32} T^{109} +$$$$73\!\cdots\!01$$$$p^{33} T^{110} +$$$$70\!\cdots\!01$$$$p^{34} T^{111} +$$$$29\!\cdots\!07$$$$p^{35} T^{112} +$$$$27\!\cdots\!00$$$$p^{36} T^{113} +$$$$11\!\cdots\!77$$$$p^{37} T^{114} +$$$$10\!\cdots\!55$$$$p^{38} T^{115} +$$$$43\!\cdots\!63$$$$p^{39} T^{116} +$$$$36\!\cdots\!41$$$$p^{40} T^{117} +$$$$15\!\cdots\!93$$$$p^{41} T^{118} +$$$$12\!\cdots\!76$$$$p^{42} T^{119} +$$$$50\!\cdots\!86$$$$p^{43} T^{120} +$$$$38\!\cdots\!32$$$$p^{44} T^{121} +$$$$16\!\cdots\!94$$$$p^{45} T^{122} +$$$$11\!\cdots\!81$$$$p^{46} T^{123} +$$$$47\!\cdots\!90$$$$p^{47} T^{124} +$$$$32\!\cdots\!67$$$$p^{48} T^{125} +$$$$13\!\cdots\!13$$$$p^{49} T^{126} +$$$$83\!\cdots\!18$$$$p^{50} T^{127} +$$$$34\!\cdots\!60$$$$p^{51} T^{128} +$$$$20\!\cdots\!81$$$$p^{52} T^{129} +$$$$84\!\cdots\!38$$$$p^{53} T^{130} +$$$$45\!\cdots\!93$$$$p^{54} T^{131} +$$$$19\!\cdots\!52$$$$p^{55} T^{132} +$$$$93\!\cdots\!88$$$$p^{56} T^{133} +$$$$39\!\cdots\!89$$$$p^{57} T^{134} + 17493593224160709976 p^{58} T^{135} + 7473899365421986505 p^{59} T^{136} + 295231471103510147 p^{60} T^{137} + 127409921615909796 p^{61} T^{138} + 4437970317568377 p^{62} T^{139} + 1937968879952341 p^{63} T^{140} + 58507254679922 p^{64} T^{141} + 25898307876537 p^{65} T^{142} + 662811452506 p^{66} T^{143} + 297957282814 p^{67} T^{144} + 6274776801 p^{68} T^{145} + 2870055102 p^{69} T^{146} + 47666620 p^{70} T^{147} + 22226891 p^{71} T^{148} + 272470 p^{72} T^{149} + 129782 p^{73} T^{150} + 1042 p^{74} T^{151} + 508 p^{75} T^{152} + 2 p^{76} T^{153} + p^{77} T^{154}$$
17 $$1 - 60 T + 2488 T^{2} - 76761 T^{3} + 1984425 T^{4} - 44189849 T^{5} + 878054884 T^{6} - 929335187 p T^{7} + 261561857097 T^{8} - 4020585960621 T^{9} + 57900067367523 T^{10} - 785869229713245 T^{11} + 10111258477814278 T^{12} - 123848988962214978 T^{13} + 1449941236079744487 T^{14} - 16276146656437411085 T^{15} +$$$$17\!\cdots\!22$$$$T^{16} -$$$$18\!\cdots\!03$$$$T^{17} +$$$$18\!\cdots\!40$$$$T^{18} -$$$$17\!\cdots\!36$$$$T^{19} +$$$$16\!\cdots\!57$$$$T^{20} -$$$$15\!\cdots\!36$$$$T^{21} +$$$$13\!\cdots\!87$$$$T^{22} -$$$$11\!\cdots\!32$$$$T^{23} +$$$$10\!\cdots\!31$$$$T^{24} -$$$$83\!\cdots\!75$$$$T^{25} +$$$$67\!\cdots\!18$$$$T^{26} -$$$$53\!\cdots\!70$$$$T^{27} +$$$$41\!\cdots\!35$$$$T^{28} -$$$$31\!\cdots\!66$$$$T^{29} +$$$$23\!\cdots\!00$$$$T^{30} -$$$$16\!\cdots\!91$$$$T^{31} +$$$$12\!\cdots\!33$$$$T^{32} -$$$$85\!\cdots\!78$$$$T^{33} +$$$$58\!\cdots\!71$$$$T^{34} -$$$$39\!\cdots\!65$$$$T^{35} +$$$$26\!\cdots\!10$$$$T^{36} -$$$$17\!\cdots\!01$$$$T^{37} +$$$$11\!\cdots\!00$$$$T^{38} -$$$$72\!\cdots\!19$$$$T^{39} +$$$$45\!\cdots\!73$$$$T^{40} -$$$$16\!\cdots\!81$$$$p T^{41} +$$$$17\!\cdots\!22$$$$T^{42} -$$$$10\!\cdots\!43$$$$T^{43} +$$$$60\!\cdots\!94$$$$T^{44} -$$$$35\!\cdots\!53$$$$T^{45} +$$$$20\!\cdots\!31$$$$T^{46} -$$$$11\!\cdots\!49$$$$T^{47} +$$$$38\!\cdots\!27$$$$p T^{48} -$$$$36\!\cdots\!56$$$$T^{49} +$$$$20\!\cdots\!83$$$$T^{50} -$$$$10\!\cdots\!07$$$$T^{51} +$$$$58\!\cdots\!63$$$$T^{52} -$$$$31\!\cdots\!48$$$$T^{53} +$$$$16\!\cdots\!86$$$$T^{54} -$$$$85\!\cdots\!15$$$$T^{55} +$$$$43\!\cdots\!66$$$$T^{56} -$$$$22\!\cdots\!61$$$$T^{57} +$$$$11\!\cdots\!97$$$$T^{58} -$$$$55\!\cdots\!91$$$$T^{59} +$$$$27\!\cdots\!29$$$$T^{60} -$$$$13\!\cdots\!98$$$$T^{61} +$$$$63\!\cdots\!68$$$$T^{62} -$$$$30\!\cdots\!82$$$$T^{63} +$$$$14\!\cdots\!09$$$$T^{64} -$$$$66\!\cdots\!06$$$$T^{65} +$$$$30\!\cdots\!43$$$$T^{66} -$$$$14\!\cdots\!49$$$$T^{67} +$$$$63\!\cdots\!25$$$$T^{68} -$$$$28\!\cdots\!02$$$$T^{69} +$$$$12\!\cdots\!41$$$$T^{70} -$$$$55\!\cdots\!13$$$$T^{71} +$$$$24\!\cdots\!10$$$$T^{72} -$$$$10\!\cdots\!55$$$$T^{73} +$$$$44\!\cdots\!06$$$$T^{74} -$$$$18\!\cdots\!88$$$$T^{75} +$$$$78\!\cdots\!48$$$$T^{76} -$$$$32\!\cdots\!78$$$$T^{77} +$$$$78\!\cdots\!48$$$$p T^{78} -$$$$18\!\cdots\!88$$$$p^{2} T^{79} +$$$$44\!\cdots\!06$$$$p^{3} T^{80} -$$$$10\!\cdots\!55$$$$p^{4} T^{81} +$$$$24\!\cdots\!10$$$$p^{5} T^{82} -$$$$55\!\cdots\!13$$$$p^{6} T^{83} +$$$$12\!\cdots\!41$$$$p^{7} T^{84} -$$$$28\!\cdots\!02$$$$p^{8} T^{85} +$$$$63\!\cdots\!25$$$$p^{9} T^{86} -$$$$14\!\cdots\!49$$$$p^{10} T^{87} +$$$$30\!\cdots\!43$$$$p^{11} T^{88} -$$$$66\!\cdots\!06$$$$p^{12} T^{89} +$$$$14\!\cdots\!09$$$$p^{13} T^{90} -$$$$30\!\cdots\!82$$$$p^{14} T^{91} +$$$$63\!\cdots\!68$$$$p^{15} T^{92} -$$$$13\!\cdots\!98$$$$p^{16} T^{93} +$$$$27\!\cdots\!29$$$$p^{17} T^{94} -$$$$55\!\cdots\!91$$$$p^{18} T^{95} +$$$$11\!\cdots\!97$$$$p^{19} T^{96} -$$$$22\!\cdots\!61$$$$p^{20} T^{97} +$$$$43\!\cdots\!66$$$$p^{21} T^{98} -$$$$85\!\cdots\!15$$$$p^{22} T^{99} +$$$$16\!\cdots\!86$$$$p^{23} T^{100} -$$$$31\!\cdots\!48$$$$p^{24} T^{101} +$$$$58\!\cdots\!63$$$$p^{25} T^{102} -$$$$10\!\cdots\!07$$$$p^{26} T^{103} +$$$$20\!\cdots\!83$$$$p^{27} T^{104} -$$$$36\!\cdots\!56$$$$p^{28} T^{105} +$$$$38\!\cdots\!27$$$$p^{30} T^{106} -$$$$11\!\cdots\!49$$$$p^{30} T^{107} +$$$$20\!\cdots\!31$$$$p^{31} T^{108} -$$$$35\!\cdots\!53$$$$p^{32} T^{109} +$$$$60\!\cdots\!94$$$$p^{33} T^{110} -$$$$10\!\cdots\!43$$$$p^{34} T^{111} +$$$$17\!\cdots\!22$$$$p^{35} T^{112} -$$$$16\!\cdots\!81$$$$p^{37} T^{113} +$$$$45\!\cdots\!73$$$$p^{37} T^{114} -$$$$72\!\cdots\!19$$$$p^{38} T^{115} +$$$$11\!\cdots\!00$$$$p^{39} T^{116} -$$$$17\!\cdots\!01$$$$p^{40} T^{117} +$$$$26\!\cdots\!10$$$$p^{41} T^{118} -$$$$39\!\cdots\!65$$$$p^{42} T^{119} +$$$$58\!\cdots\!71$$$$p^{43} T^{120} -$$$$85\!\cdots\!78$$$$p^{44} T^{121} +$$$$12\!\cdots\!33$$$$p^{45} T^{122} -$$$$16\!\cdots\!91$$$$p^{46} T^{123} +$$$$23\!\cdots\!00$$$$p^{47} T^{124} -$$$$31\!\cdots\!66$$$$p^{48} T^{125} +$$$$41\!\cdots\!35$$$$p^{49} T^{126} -$$$$53\!\cdots\!70$$$$p^{50} T^{127} +$$$$67\!\cdots\!18$$$$p^{51} T^{128} -$$$$83\!\cdots\!75$$$$p^{52} T^{129} +$$$$10\!\cdots\!31$$$$p^{53} T^{130} -$$$$11\!\cdots\!32$$$$p^{54} T^{131} +$$$$13\!\cdots\!87$$$$p^{55} T^{132} -$$$$15\!\cdots\!36$$$$p^{56} T^{133} +$$$$16\!\cdots\!57$$$$p^{57} T^{134} -$$$$17\!\cdots\!36$$$$p^{58} T^{135} +$$$$18\!\cdots\!40$$$$p^{59} T^{136} -$$$$18\!\cdots\!03$$$$p^{60} T^{137} +$$$$17\!\cdots\!22$$$$p^{61} T^{138} - 16276146656437411085 p^{62} T^{139} + 1449941236079744487 p^{63} T^{140} - 123848988962214978 p^{64} T^{141} + 10111258477814278 p^{65} T^{142} - 785869229713245 p^{66} T^{143} + 57900067367523 p^{67} T^{144} - 4020585960621 p^{68} T^{145} + 261561857097 p^{69} T^{146} - 929335187 p^{71} T^{147} + 878054884 p^{71} T^{148} - 44189849 p^{72} T^{149} + 1984425 p^{73} T^{150} - 76761 p^{74} T^{151} + 2488 p^{75} T^{152} - 60 p^{76} T^{153} + p^{77} T^{154}$$
19 $$1 + 3 T + 735 T^{2} + 2466 T^{3} + 271048 T^{4} + 996031 T^{5} + 66895348 T^{6} + 264765806 T^{7} + 12433456127 T^{8} + 52276043182 T^{9} + 1856520932156 T^{10} + 8196764028174 T^{11} + 231970389945689 T^{12} + 1065060859551722 T^{13} + 24944086187192167 T^{14} + 118118286151912540 T^{15} + 2355991024927685748 T^{16} + 11425538305891049554 T^{17} +$$$$19\!\cdots\!47$$$$T^{18} +$$$$98\!\cdots\!59$$$$T^{19} +$$$$15\!\cdots\!63$$$$T^{20} +$$$$75\!\cdots\!04$$$$T^{21} +$$$$10\!\cdots\!62$$$$T^{22} +$$$$52\!\cdots\!37$$$$T^{23} +$$$$66\!\cdots\!02$$$$T^{24} +$$$$33\!\cdots\!55$$$$T^{25} +$$$$39\!\cdots\!19$$$$T^{26} +$$$$20\!\cdots\!19$$$$T^{27} +$$$$21\!\cdots\!90$$$$T^{28} +$$$$10\!\cdots\!64$$$$T^{29} +$$$$11\!\cdots\!33$$$$T^{30} +$$$$56\!\cdots\!88$$$$T^{31} +$$$$53\!\cdots\!78$$$$T^{32} +$$$$26\!\cdots\!33$$$$T^{33} +$$$$24\!\cdots\!00$$$$T^{34} +$$$$12\!\cdots\!91$$$$T^{35} +$$$$10\!\cdots\!29$$$$T^{36} +$$$$51\!\cdots\!48$$$$T^{37} +$$$$42\!\cdots\!05$$$$T^{38} +$$$$21\!\cdots\!37$$$$T^{39} +$$$$16\!\cdots\!75$$$$T^{40} +$$$$42\!\cdots\!57$$$$p T^{41} +$$$$16\!\cdots\!46$$$$p^{2} T^{42} +$$$$29\!\cdots\!00$$$$T^{43} +$$$$21\!\cdots\!86$$$$T^{44} +$$$$10\!\cdots\!18$$$$T^{45} +$$$$72\!\cdots\!62$$$$T^{46} +$$$$34\!\cdots\!97$$$$T^{47} +$$$$23\!\cdots\!85$$$$T^{48} +$$$$10\!\cdots\!36$$$$T^{49} +$$$$72\!\cdots\!86$$$$T^{50} +$$$$33\!\cdots\!10$$$$T^{51} +$$$$21\!\cdots\!10$$$$T^{52} +$$$$51\!\cdots\!29$$$$p T^{53} +$$$$62\!\cdots\!54$$$$T^{54} +$$$$27\!\cdots\!11$$$$T^{55} +$$$$17\!\cdots\!75$$$$T^{56} +$$$$75\!\cdots\!15$$$$T^{57} +$$$$45\!\cdots\!35$$$$T^{58} +$$$$19\!\cdots\!25$$$$T^{59} +$$$$11\!\cdots\!25$$$$T^{60} +$$$$50\!\cdots\!64$$$$T^{61} +$$$$28\!\cdots\!95$$$$T^{62} +$$$$12\!\cdots\!12$$$$T^{63} +$$$$69\!\cdots\!13$$$$T^{64} +$$$$28\!\cdots\!94$$$$T^{65} +$$$$16\!\cdots\!09$$$$T^{66} +$$$$66\!\cdots\!68$$$$T^{67} +$$$$35\!\cdots\!07$$$$T^{68} +$$$$14\!\cdots\!55$$$$T^{69} +$$$$77\!\cdots\!00$$$$T^{70} +$$$$31\!\cdots\!30$$$$T^{71} +$$$$16\!\cdots\!22$$$$T^{72} +$$$$64\!\cdots\!51$$$$T^{73} +$$$$32\!\cdots\!65$$$$T^{74} +$$$$12\!\cdots\!14$$$$T^{75} +$$$$64\!\cdots\!63$$$$T^{76} +$$$$24\!\cdots\!66$$$$T^{77} +$$$$64\!\cdots\!63$$$$p T^{78} +$$$$12\!\cdots\!14$$$$p^{2} T^{79} +$$$$32\!\cdots\!65$$$$p^{3} T^{80} +$$$$64\!\cdots\!51$$$$p^{4} T^{81} +$$$$16\!\cdots\!22$$$$p^{5} T^{82} +$$$$31\!\cdots\!30$$$$p^{6} T^{83} +$$$$77\!\cdots\!00$$$$p^{7} T^{84} +$$$$14\!\cdots\!55$$$$p^{8} T^{85} +$$$$35\!\cdots\!07$$$$p^{9} T^{86} +$$$$66\!\cdots\!68$$$$p^{10} T^{87} +$$$$16\!\cdots\!09$$$$p^{11} T^{88} +$$$$28\!\cdots\!94$$$$p^{12} T^{89} +$$$$69\!\cdots\!13$$$$p^{13} T^{90} +$$$$12\!\cdots\!12$$$$p^{14} T^{91} +$$$$28\!\cdots\!95$$$$p^{15} T^{92} +$$$$50\!\cdots\!64$$$$p^{16} T^{93} +$$$$11\!\cdots\!25$$$$p^{17} T^{94} +$$$$19\!\cdots\!25$$$$p^{18} T^{95} +$$$$45\!\cdots\!35$$$$p^{19} T^{96} +$$$$75\!\cdots\!15$$$$p^{20} T^{97} +$$$$17\!\cdots\!75$$$$p^{21} T^{98} +$$$$27\!\cdots\!11$$$$p^{22} T^{99} +$$$$62\!\cdots\!54$$$$p^{23} T^{100} +$$$$51\!\cdots\!29$$$$p^{25} T^{101} +$$$$21\!\cdots\!10$$$$p^{25} T^{102} +$$$$33\!\cdots\!10$$$$p^{26} T^{103} +$$$$72\!\cdots\!86$$$$p^{27} T^{104} +$$$$10\!\cdots\!36$$$$p^{28} T^{105} +$$$$23\!\cdots\!85$$$$p^{29} T^{106} +$$$$34\!\cdots\!97$$$$p^{30} T^{107} +$$$$72\!\cdots\!62$$$$p^{31} T^{108} +$$$$10\!\cdots\!18$$$$p^{32} T^{109} +$$$$21\!\cdots\!86$$$$p^{33} T^{110} +$$$$29\!\cdots\!00$$$$p^{34} T^{111} +$$$$16\!\cdots\!46$$$$p^{37} T^{112} +$$$$42\!\cdots\!57$$$$p^{37} T^{113} +$$$$16\!\cdots\!75$$$$p^{37} T^{114} +$$$$21\!\cdots\!37$$$$p^{38} T^{115} +$$$$42\!\cdots\!05$$$$p^{39} T^{116} +$$$$51\!\cdots\!48$$$$p^{40} T^{117} +$$$$10\!\cdots\!29$$$$p^{41} T^{118} +$$$$12\!\cdots\!91$$$$p^{42} T^{119} +$$$$24\!\cdots\!00$$$$p^{43} T^{120} +$$$$26\!\cdots\!33$$$$p^{44} T^{121} +$$$$53\!\cdots\!78$$$$p^{45} T^{122} +$$$$56\!\cdots\!88$$$$p^{46} T^{123} +$$$$11\!\cdots\!33$$$$p^{47} T^{124} +$$$$10\!\cdots\!64$$$$p^{48} T^{125} +$$$$21\!\cdots\!90$$$$p^{49} T^{126} +$$$$20\!\cdots\!19$$$$p^{50} T^{127} +$$$$39\!\cdots\!19$$$$p^{51} T^{128} +$$$$33\!\cdots\!55$$$$p^{52} T^{129} +$$$$66\!\cdots\!02$$$$p^{53} T^{130} +$$$$52\!\cdots\!37$$$$p^{54} T^{131} +$$$$10\!\cdots\!62$$$$p^{55} T^{132} +$$$$75\!\cdots\!04$$$$p^{56} T^{133} +$$$$15\!\cdots\!63$$$$p^{57} T^{134} +$$$$98\!\cdots\!59$$$$p^{58} T^{135} +$$$$19\!\cdots\!47$$$$p^{59} T^{136} + 11425538305891049554 p^{60} T^{137} + 2355991024927685748 p^{61} T^{138} + 118118286151912540 p^{62} T^{139} + 24944086187192167 p^{63} T^{140} + 1065060859551722 p^{64} T^{141} + 231970389945689 p^{65} T^{142} + 8196764028174 p^{66} T^{143} + 1856520932156 p^{67} T^{144} + 52276043182 p^{68} T^{145} + 12433456127 p^{69} T^{146} + 264765806 p^{70} T^{147} + 66895348 p^{71} T^{148} + 996031 p^{72} T^{149} + 271048 p^{73} T^{150} + 2466 p^{74} T^{151} + 735 p^{75} T^{152} + 3 p^{76} T^{153} + p^{77} T^{154}$$
23 $$1 - 53 T + 2325 T^{2} - 73059 T^{3} + 2018099 T^{4} - 47596491 T^{5} + 1021981593 T^{6} - 19841646448 T^{7} + 358237948140 T^{8} - 6009486592536 T^{9} + 95057747325374 T^{10} - 1419037377645284 T^{11} + 876879411169714 p T^{12} - 273263576804679212 T^{13} + 3549847668354252135 T^{14} - 1924918713014496542 p T^{15} +$$$$53\!\cdots\!50$$$$T^{16} -$$$$61\!\cdots\!65$$$$T^{17} +$$$$69\!\cdots\!89$$$$T^{18} -$$$$75\!\cdots\!81$$$$T^{19} +$$$$34\!\cdots\!09$$$$p T^{20} -$$$$81\!\cdots\!18$$$$T^{21} +$$$$81\!\cdots\!45$$$$T^{22} -$$$$79\!\cdots\!11$$$$T^{23} +$$$$75\!\cdots\!26$$$$T^{24} -$$$$70\!\cdots\!07$$$$T^{25} +$$$$63\!\cdots\!18$$$$T^{26} -$$$$56\!\cdots\!27$$$$T^{27} +$$$$49\!\cdots\!07$$$$T^{28} -$$$$42\!\cdots\!32$$$$T^{29} +$$$$35\!\cdots\!24$$$$T^{30} -$$$$28\!\cdots\!42$$$$T^{31} +$$$$23\!\cdots\!78$$$$T^{32} -$$$$18\!\cdots\!07$$$$T^{33} +$$$$14\!\cdots\!63$$$$T^{34} -$$$$10\!\cdots\!37$$$$T^{35} +$$$$82\!\cdots\!99$$$$T^{36} -$$$$60\!\cdots\!62$$$$T^{37} +$$$$44\!\cdots\!04$$$$T^{38} -$$$$31\!\cdots\!06$$$$T^{39} +$$$$22\!\cdots\!50$$$$T^{40} -$$$$15\!\cdots\!94$$$$T^{41} +$$$$10\!\cdots\!92$$$$T^{42} -$$$$73\!\cdots\!83$$$$T^{43} +$$$$48\!\cdots\!80$$$$T^{44} -$$$$32\!\cdots\!31$$$$T^{45} +$$$$21\!\cdots\!89$$$$T^{46} -$$$$13\!\cdots\!78$$$$T^{47} +$$$$86\!\cdots\!62$$$$T^{48} -$$$$54\!\cdots\!94$$$$T^{49} +$$$$33\!\cdots\!30$$$$T^{50} -$$$$20\!\cdots\!04$$$$T^{51} +$$$$12\!\cdots\!92$$$$T^{52} -$$$$75\!\cdots\!81$$$$T^{53} +$$$$44\!\cdots\!07$$$$T^{54} -$$$$26\!\cdots\!49$$$$T^{55} +$$$$15\!\cdots\!46$$$$T^{56} -$$$$87\!\cdots\!26$$$$T^{57} +$$$$49\!\cdots\!11$$$$T^{58} -$$$$27\!\cdots\!00$$$$T^{59} +$$$$15\!\cdots\!04$$$$T^{60} -$$$$86\!\cdots\!77$$$$T^{61} +$$$$47\!\cdots\!95$$$$T^{62} -$$$$11\!\cdots\!01$$$$p T^{63} +$$$$13\!\cdots\!20$$$$T^{64} -$$$$73\!\cdots\!84$$$$T^{65} +$$$$38\!\cdots\!80$$$$T^{66} -$$$$20\!\cdots\!22$$$$T^{67} +$$$$10\!\cdots\!42$$$$T^{68} -$$$$54\!\cdots\!64$$$$T^{69} +$$$$27\!\cdots\!82$$$$T^{70} -$$$$13\!\cdots\!69$$$$T^{71} +$$$$69\!\cdots\!96$$$$T^{72} -$$$$34\!\cdots\!93$$$$T^{73} +$$$$17\!\cdots\!52$$$$T^{74} -$$$$84\!\cdots\!48$$$$T^{75} +$$$$40\!\cdots\!01$$$$T^{76} -$$$$19\!\cdots\!82$$$$T^{77} +$$$$40\!\cdots\!01$$$$p T^{78} -$$$$84\!\cdots\!48$$$$p^{2} T^{79} +$$$$17\!\cdots\!52$$$$p^{3} T^{80} -$$$$34\!\cdots\!93$$$$p^{4} T^{81} +$$$$69\!\cdots\!96$$$$p^{5} T^{82} -$$$$13\!\cdots\!69$$$$p^{6} T^{83} +$$$$27\!\cdots\!82$$$$p^{7} T^{84} -$$$$54\!\cdots\!64$$$$p^{8} T^{85} +$$$$10\!\cdots\!42$$$$p^{9} T^{86} -$$$$20\!\cdots\!22$$$$p^{10} T^{87} +$$$$38\!\cdots\!80$$$$p^{11} T^{88} -$$$$73\!\cdots\!84$$$$p^{12} T^{89} +$$$$13\!\cdots\!20$$$$p^{13} T^{90} -$$$$11\!\cdots\!01$$$$p^{15} T^{91} +$$$$47\!\cdots\!95$$$$p^{15} T^{92} -$$$$86\!\cdots\!77$$$$p^{16} T^{93} +$$$$15\!\cdots\!04$$$$p^{17} T^{94} -$$$$27\!\cdots\!00$$$$p^{18} T^{95} +$$$$49\!\cdots\!11$$$$p^{19} T^{96} -$$$$87\!\cdots\!26$$$$p^{20} T^{97} +$$$$15\!\cdots\!46$$$$p^{21} T^{98} -$$$$26\!\cdots\!49$$$$p^{22} T^{99} +$$$$44\!\cdots\!07$$$$p^{23} T^{100} -$$$$75\!\cdots\!81$$$$p^{24} T^{101} +$$$$12\!\cdots\!92$$$$p^{25} T^{102} -$$$$20\!\cdots\!04$$$$p^{26} T^{103} +$$$$33\!\cdots\!30$$$$p^{27} T^{104} -$$$$54\!\cdots\!94$$$$p^{28} T^{105} +$$$$86\!\cdots\!62$$$$p^{29} T^{106} -$$$$13\!\cdots\!78$$$$p^{30} T^{107} +$$$$21\!\cdots\!89$$$$p^{31} T^{108} -$$$$32\!\cdots\!31$$$$p^{32} T^{109} +$$$$48\!\cdots\!80$$$$p^{33} T^{110} -$$$$73\!\cdots\!83$$$$p^{34} T^{111} +$$$$10\!\cdots\!92$$$$p^{35} T^{112} -$$$$15\!\cdots\!94$$$$p^{36} T^{113} +$$$$22\!\cdots\!50$$$$p^{37} T^{114} -$$$$31\!\cdots\!06$$$$p^{38} T^{115} +$$$$44\!\cdots\!04$$$$p^{39} T^{116} -$$$$60\!\cdots\!62$$$$p^{40} T^{117} +$$$$82\!\cdots\!99$$$$p^{41} T^{118} -$$$$10\!\cdots\!37$$$$p^{42} T^{119} +$$$$14\!\cdots\!63$$$$p^{43} T^{120} -$$$$18\!\cdots\!07$$$$p^{44} T^{121} +$$$$23\!\cdots\!78$$$$p^{45} T^{122} -$$$$28\!\cdots\!42$$$$p^{46} T^{123} +$$$$35\!\cdots\!24$$$$p^{47} T^{124} -$$$$42\!\cdots\!32$$$$p^{48} T^{125} +$$$$49\!\cdots\!07$$$$p^{49} T^{126} -$$$$56\!\cdots\!27$$$$p^{50} T^{127} +$$$$63\!\cdots\!18$$$$p^{51} T^{128} -$$$$70\!\cdots\!07$$$$p^{52} T^{129} +$$$$75\!\cdots\!26$$$$p^{53} T^{130} -$$$$79\!\cdots\!11$$$$p^{54} T^{131} +$$$$81\!\cdots\!45$$$$p^{55} T^{132} -$$$$81\!\cdots\!18$$$$p^{56} T^{133} +$$$$34\!\cdots\!09$$$$p^{58} T^{134} -$$$$75\!\cdots\!81$$$$p^{58} T^{135} +$$$$69\!\cdots\!89$$$$p^{59} T^{136} -$$$$61\!\cdots\!65$$$$p^{60} T^{137} +$$$$53\!\cdots\!50$$$$p^{61} T^{138} - 1924918713014496542 p^{63} T^{139} + 3549847668354252135 p^{63} T^{140} - 273263576804679212 p^{64} T^{141} + 876879411169714 p^{66} T^{142} - 1419037377645284 p^{66} T^{143} + 95057747325374 p^{67} T^{144} - 6009486592536 p^{68} T^{145} + 358237948140 p^{69} T^{146} - 19841646448 p^{70} T^{147} + 1021981593 p^{71} T^{148} - 47596491 p^{72} T^{149} + 2018099 p^{73} T^{150} - 73059 p^{74} T^{151} + 2325 p^{75} T^{152} - 53 p^{76} T^{153} + p^{77} T^{154}$$
29 $$1 - 30 T + 1555 T^{2} - 37483 T^{3} + 1136826 T^{4} - 801521 p T^{5} + 532230375 T^{6} - 329248735 p T^{7} + 181614892334 T^{8} - 2925035884015 T^{9} + 48520854443770 T^{10} - 713190590957015 T^{11} + 10620271870761246 T^{12} - 144228788266955179 T^{13} + 67757487252016990 p T^{14} - 858303804846523632 p T^{15} +$$$$31\!\cdots\!54$$$$T^{16} -$$$$37\!\cdots\!51$$$$T^{17} +$$$$44\!\cdots\!83$$$$T^{18} -$$$$49\!\cdots\!29$$$$T^{19} +$$$$55\!\cdots\!64$$$$T^{20} -$$$$59\!\cdots\!12$$$$T^{21} +$$$$62\!\cdots\!62$$$$T^{22} -$$$$64\!\cdots\!87$$$$T^{23} +$$$$64\!\cdots\!69$$$$T^{24} -$$$$63\!\cdots\!09$$$$T^{25} +$$$$61\!\cdots\!59$$$$T^{26} -$$$$57\!\cdots\!25$$$$T^{27} +$$$$53\!\cdots\!54$$$$T^{28} -$$$$48\!\cdots\!49$$$$T^{29} +$$$$14\!\cdots\!33$$$$p T^{30} -$$$$37\!\cdots\!12$$$$T^{31} +$$$$32\!\cdots\!23$$$$T^{32} -$$$$27\!\cdots\!85$$$$T^{33} +$$$$23\!\cdots\!31$$$$T^{34} -$$$$18\!\cdots\!81$$$$T^{35} +$$$$15\!\cdots\!05$$$$T^{36} -$$$$12\!\cdots\!28$$$$T^{37} +$$$$33\!\cdots\!36$$$$p T^{38} -$$$$74\!\cdots\!95$$$$T^{39} +$$$$57\!\cdots\!82$$$$T^{40} -$$$$43\!\cdots\!00$$$$T^{41} +$$$$11\!\cdots\!94$$$$p T^{42} -$$$$23\!\cdots\!69$$$$T^{43} +$$$$17\!\cdots\!70$$$$T^{44} -$$$$12\!\cdots\!53$$$$T^{45} +$$$$87\!\cdots\!56$$$$T^{46} -$$$$61\!\cdots\!94$$$$T^{47} +$$$$42\!\cdots\!09$$$$T^{48} -$$$$29\!\cdots\!31$$$$T^{49} +$$$$19\!\cdots\!98$$$$T^{50} -$$$$13\!\cdots\!10$$$$T^{51} +$$$$89\!\cdots\!68$$$$T^{52} -$$$$58\!\cdots\!92$$$$T^{53} +$$$$38\!\cdots\!66$$$$T^{54} -$$$$24\!\cdots\!90$$$$T^{55} +$$$$15\!\cdots\!57$$$$T^{56} -$$$$10\!\cdots\!71$$$$T^{57} +$$$$63\!\cdots\!68$$$$T^{58} -$$$$39\!\cdots\!98$$$$T^{59} +$$$$24\!\cdots\!17$$$$T^{60} -$$$$14\!\cdots\!47$$$$T^{61} +$$$$91\!\cdots\!08$$$$T^{62} -$$$$54\!\cdots\!77$$$$T^{63} +$$$$32\!\cdots\!02$$$$T^{64} -$$$$19\!\cdots\!06$$$$T^{65} +$$$$11\!\cdots\!82$$$$T^{66} -$$$$66\!\cdots\!53$$$$T^{67} +$$$$38\!\cdots\!48$$$$T^{68} -$$$$22\!\cdots\!81$$$$T^{69} +$$$$12\!\cdots\!52$$$$T^{70} -$$$$71\!\cdots\!21$$$$T^{71} +$$$$39\!\cdots\!51$$$$T^{72} -$$$$22\!\cdots\!38$$$$T^{73} +$$$$12\!\cdots\!62$$$$T^{74} -$$$$67\!\cdots\!46$$$$T^{75} +$$$$36\!\cdots\!76$$$$T^{76} -$$$$19\!\cdots\!64$$$$T^{77} +$$$$36\!\cdots\!76$$$$p T^{78} -$$$$67\!\cdots\!46$$$$p^{2} T^{79} +$$$$12\!\cdots\!62$$$$p^{3} T^{80} -$$$$22\!\cdots\!38$$$$p^{4} T^{81} +$$$$39\!\cdots\!51$$$$p^{5} T^{82} -$$$$71\!\cdots\!21$$$$p^{6} T^{83} +$$$$12\!\cdots\!52$$$$p^{7} T^{84} -$$$$22\!\cdots\!81$$$$p^{8} T^{85} +$$$$38\!\cdots\!48$$$$p^{9} T^{86} -$$$$66\!\cdots\!53$$$$p^{10} T^{87} +$$$$11\!\cdots\!82$$$$p^{11} T^{88} -$$$$19\!\cdots\!06$$$$p^{12} T^{89} +$$$$32\!\cdots\!02$$$$p^{13} T^{90} -$$$$54\!\cdots\!77$$$$p^{14} T^{91} +$$$$91\!\cdots\!08$$$$p^{15} T^{92} -$$$$14\!\cdots\!47$$$$p^{16} T^{93} +$$$$24\!\cdots\!17$$$$p^{17} T^{94} -$$$$39\!\cdots\!98$$$$p^{18} T^{95} +$$$$63\!\cdots\!68$$$$p^{19} T^{96} -$$$$10\!\cdots\!71$$$$p^{20} T^{97} +$$$$15\!\cdots\!57$$$$p^{21} T^{98} -$$$$24\!\cdots\!90$$$$p^{22} T^{99} +$$$$38\!\cdots\!66$$$$p^{23} T^{100} -$$$$58\!\cdots\!92$$$$p^{24} T^{101} +$$$$89\!\cdots\!68$$$$p^{25} T^{102} -$$$$13\!\cdots\!10$$$$p^{26} T^{103} +$$$$19\!\cdots\!98$$$$p^{27} T^{104} -$$$$29\!\cdots\!31$$$$p^{28} T^{105} +$$$$42\!\cdots\!09$$$$p^{29} T^{106} -$$$$61\!\cdots\!94$$$$p^{30} T^{107} +$$$$87\!\cdots\!56$$$$p^{31} T^{108} -$$$$12\!\cdots\!53$$$$p^{32} T^{109} +$$$$17\!\cdots\!70$$$$p^{33} T^{110} -$$$$23\!\cdots\!69$$$$p^{34} T^{111} +$$$$11\!\cdots\!94$$$$p^{36} T^{112} -$$$$43\!\cdots\!00$$$$p^{36} T^{113} +$$$$57\!\cdots\!82$$$$p^{37} T^{114} -$$$$74\!\cdots\!95$$$$p^{38} T^{115} +$$$$33\!\cdots\!36$$$$p^{40} T^{116} -$$$$12\!\cdots\!28$$$$p^{40} T^{117} +$$$$15\!\cdots\!05$$$$p^{41} T^{118} -$$$$18\!\cdots\!81$$$$p^{42} T^{119} +$$$$23\!\cdots\!31$$$$p^{43} T^{120} -$$$$27\!\cdots\!85$$$$p^{44} T^{121} +$$$$32\!\cdots\!23$$$$p^{45} T^{122} -$$$$37\!\cdots\!12$$$$p^{46} T^{123} +$$$$14\!\cdots\!33$$$$p^{48} T^{124} -$$$$48\!\cdots\!49$$$$p^{48} T^{125} +$$$$53\!\cdots\!54$$$$p^{49} T^{126} -$$$$57\!\cdots\!25$$$$p^{50} T^{127} +$$$$61\!\cdots\!59$$$$p^{51} T^{128} -$$$$63\!\cdots\!09$$$$p^{52} T^{129} +$$$$64\!\cdots\!69$$$$p^{53} T^{130} -$$$$64\!\cdots\!87$$$$p^{54} T^{131} +$$$$62\!\cdots\!62$$$$p^{55} T^{132} -$$$$59\!\cdots\!12$$$$p^{56} T^{133} +$$$$55\!\cdots\!64$$$$p^{57} T^{134} -$$$$49\!\cdots\!29$$$$p^{58} T^{135} +$$$$44\!\cdots\!83$$$$p^{59} T^{136} -$$$$37\!\cdots\!51$$$$p^{60} T^{137} +$$$$31\!\cdots\!54$$$$p^{61} T^{138} - 858303804846523632 p^{63} T^{139} + 67757487252016990 p^{64} T^{140} - 144228788266955179 p^{64} T^{141} + 10620271870761246 p^{65} T^{142} - 713190590957015 p^{66} T^{143} + 48520854443770 p^{67} T^{144} - 2925035884015 p^{68} T^{145} + 181614892334 p^{69} T^{146} - 329248735 p^{71} T^{147} + 532230375 p^{71} T^{148} - 801521 p^{73} T^{149} + 1136826 p^{73} T^{150} - 37483 p^{74} T^{151} + 1555 p^{75} T^{152} - 30 p^{76} T^{153} + p^{77} T^{154}$$
31 $$1 - 22 T + 1530 T^{2} - 29790 T^{3} + 1145138 T^{4} - 20124851 T^{5} + 562053525 T^{6} - 9046395328 T^{7} + 204257398084 T^{8} - 3044763033852 T^{9} + 58775164288549 T^{10} - 26406681106451 p T^{11} + 13975237669476237 T^{12} - 183160761292398250 T^{13} + 2828185627210261945 T^{14} - 35083668496157557153 T^{15} +$$$$49\!\cdots\!42$$$$T^{16} -$$$$58\!\cdots\!39$$$$T^{17} +$$$$77\!\cdots\!47$$$$T^{18} -$$$$87\!\cdots\!48$$$$T^{19} +$$$$10\!\cdots\!87$$$$T^{20} -$$$$11\!\cdots\!02$$$$T^{21} +$$$$13\!\cdots\!87$$$$T^{22} -$$$$14\!\cdots\!78$$$$T^{23} +$$$$15\!\cdots\!13$$$$T^{24} -$$$$50\!\cdots\!63$$$$p T^{25} +$$$$16\!\cdots\!84$$$$T^{26} -$$$$16\!\cdots\!57$$$$T^{27} +$$$$16\!\cdots\!24$$$$T^{28} -$$$$15\!\cdots\!31$$$$T^{29} +$$$$14\!\cdots\!84$$$$T^{30} -$$$$13\!\cdots\!32$$$$T^{31} +$$$$12\!\cdots\!65$$$$T^{32} -$$$$11\!\cdots\!00$$$$T^{33} +$$$$10\!\cdots\!06$$$$T^{34} -$$$$87\!\cdots\!19$$$$T^{35} +$$$$77\!\cdots\!81$$$$T^{36} -$$$$64\!\cdots\!22$$$$T^{37} +$$$$54\!\cdots\!30$$$$T^{38} -$$$$44\!\cdots\!03$$$$T^{39} +$$$$37\!\cdots\!28$$$$T^{40} -$$$$29\!\cdots\!95$$$$T^{41} +$$$$23\!\cdots\!36$$$$T^{42} -$$$$18\!\cdots\!17$$$$T^{43} +$$$$14\!\cdots\!31$$$$T^{44} -$$$$10\!\cdots\!70$$$$T^{45} +$$$$84\!\cdots\!59$$$$T^{46} -$$$$62\!\cdots\!01$$$$T^{47} +$$$$46\!\cdots\!17$$$$T^{48} -$$$$33\!\cdots\!24$$$$T^{49} +$$$$24\!\cdots\!71$$$$T^{50} -$$$$17\!\cdots\!89$$$$T^{51} +$$$$12\!\cdots\!60$$$$T^{52} -$$$$87\!\cdots\!07$$$$T^{53} +$$$$61\!\cdots\!57$$$$T^{54} -$$$$41\!\cdots\!37$$$$T^{55} +$$$$28\!\cdots\!16$$$$T^{56} -$$$$19\!\cdots\!31$$$$T^{57} +$$$$12\!\cdots\!58$$$$T^{58} -$$$$84\!\cdots\!51$$$$T^{59} +$$$$55\!\cdots\!70$$$$T^{60} -$$$$35\!\cdots\!61$$$$T^{61} +$$$$22\!\cdots\!25$$$$T^{62} -$$$$14\!\cdots\!10$$$$T^{63} +$$$$91\!\cdots\!94$$$$T^{64} -$$$$57\!\cdots\!95$$$$T^{65} +$$$$35\!\cdots\!24$$$$T^{66} -$$$$21\!\cdots\!84$$$$T^{67} +$$$$13\!\cdots\!87$$$$T^{68} -$$$$78\!\cdots\!08$$$$T^{69} +$$$$47\!\cdots\!28$$$$T^{70} -$$$$27\!\cdots\!44$$$$T^{71} +$$$$16\!\cdots\!23$$$$T^{72} -$$$$93\!\cdots\!93$$$$T^{73} +$$$$54\!\cdots\!46$$$$T^{74} -$$$$30\!\cdots\!26$$$$T^{75} +$$$$17\!\cdots\!41$$$$T^{76} -$$$$96\!\cdots\!84$$$$T^{77} +$$$$17\!\cdots\!41$$$$p T^{78} -$$$$30\!\cdots\!26$$$$p^{2} T^{79} +$$$$54\!\cdots\!46$$$$p^{3} T^{80} -$$$$93\!\cdots\!93$$$$p^{4} T^{81} +$$$$16\!\cdots\!23$$$$p^{5} T^{82} -$$$$27\!\cdots\!44$$$$p^{6} T^{83} +$$$$47\!\cdots\!28$$$$p^{7} T^{84} -$$$$78\!\cdots\!08$$$$p^{8} T^{85} +$$$$13\!\cdots\!87$$$$p^{9} T^{86} -$$$$21\!\cdots\!84$$$$p^{10} T^{87} +$$$$35\!\cdots\!24$$$$p^{11} T^{88} -$$$$57\!\cdots\!95$$$$p^{12} T^{89} +$$$$91\!\cdots\!94$$$$p^{13} T^{90} -$$$$14\!\cdots\!10$$$$p^{14} T^{91} +$$$$22\!\cdots\!25$$$$p^{15} T^{92} -$$$$35\!\cdots\!61$$$$p^{16} T^{93} +$$$$55\!\cdots\!70$$$$p^{17} T^{94} -$$$$84\!\cdots\!51$$$$p^{18} T^{95} +$$$$12\!\cdots\!58$$$$p^{19} T^{96} -$$$$19\!\cdots\!31$$$$p^{20} T^{97} +$$$$28\!\cdots\!16$$$$p^{21} T^{98} -$$$$41\!\cdots\!37$$$$p^{22} T^{99} +$$$$61\!\cdots\!57$$$$p^{23} T^{100} -$$$$87\!\cdots\!07$$$$p^{24} T^{101} +$$$$12\!\cdots\!60$$$$p^{25} T^{102} -$$$$17\!\cdots\!89$$$$p^{26} T^{103} +$$$$24\!\cdots\!71$$$$p^{27} T^{104} -$$$$33\!\cdots\!24$$$$p^{28} T^{105} +$$$$46\!\cdots\!17$$$$p^{29} T^{106} -$$$$62\!\cdots\!01$$$$p^{30} T^{107} +$$$$84\!\cdots\!59$$$$p^{31} T^{108} -$$$$10\!\cdots\!70$$$$p^{32} T^{109} +$$$$14\!\cdots\!31$$$$p^{33} T^{110} -$$$$18\!\cdots\!17$$$$p^{34} T^{111} +$$$$23\!\cdots\!36$$$$p^{35} T^{112} -$$$$29\!\cdots\!95$$$$p^{36} T^{113} +$$$$37\!\cdots\!28$$$$p^{37} T^{114} -$$$$44\!\cdots\!03$$$$p^{38} T^{115} +$$$$54\!\cdots\!30$$$$p^{39} T^{116} -$$$$64\!\cdots\!22$$$$p^{40} T^{117} +$$$$77\!\cdots\!81$$$$p^{41} T^{118} -$$$$87\!\cdots\!19$$$$p^{42} T^{119} +$$$$10\!\cdots\!06$$$$p^{43} T^{120} -$$$$11\!\cdots\!00$$$$p^{44} T^{121} +$$$$12\!\cdots\!65$$$$p^{45} T^{122} -$$$$13\!\cdots\!32$$$$p^{46} T^{123} +$$$$14\!\cdots\!84$$$$p^{47} T^{124} -$$$$15\!\cdots\!31$$$$p^{48} T^{125} +$$$$16\!\cdots\!24$$$$p^{49} T^{126} -$$$$16\!\cdots\!57$$$$p^{50} T^{127} +$$$$16\!\cdots\!84$$$$p^{51} T^{128} -$$$$50\!\cdots\!63$$$$p^{53} T^{129} +$$$$15\!\cdots\!13$$$$p^{53} T^{130} -$$$$14\!\cdots\!78$$$$p^{54} T^{131} +$$$$13\!\cdots\!87$$$$p^{55} T^{132} -$$$$11\!\cdots\!02$$$$p^{56} T^{133} +$$$$10\!\cdots\!87$$$$p^{57} T^{134} -$$$$87\!\cdots\!48$$$$p^{58} T^{135} +$$$$77\!\cdots\!47$$$$p^{59} T^{136} -$$$$58\!\cdots\!39$$$$p^{60} T^{137} +$$$$49\!\cdots\!42$$$$p^{61} T^{138} - 35083668496157557153 p^{62} T^{139} + 2828185627210261945 p^{63} T^{140} - 183160761292398250 p^{64} T^{141} + 13975237669476237 p^{65} T^{142} - 26406681106451 p^{67} T^{143} + 58775164288549 p^{67} T^{144} - 3044763033852 p^{68} T^{145} + 204257398084 p^{69} T^{146} - 9046395328 p^{70} T^{147} + 562053525 p^{71} T^{148} - 20124851 p^{72} T^{149} + 1145138 p^{73} T^{150} - 29790 p^{74} T^{151} + 1530 p^{75} T^{152} - 22 p^{76} T^{153} + p^{77} T^{154}$$
37 $$1 + 3 T + 45 p T^{2} + 5691 T^{3} + 1382211 T^{4} + 5276065 T^{5} + 763140974 T^{6} + 3200585970 T^{7} + 315365942199 T^{8} + 1433497067262 T^{9} + 104077631527262 T^{10} + 506768937425473 T^{11} + 28579280224674787 T^{12} + 147551168396133658 T^{13} + 6717168626904910855 T^{14} + 36442971047168443210 T^{15} +$$$$13\!\cdots\!71$$$$T^{16} +$$$$78\!\cdots\!14$$$$T^{17} +$$$$25\!\cdots\!19$$$$T^{18} +$$$$14\!\cdots\!93$$$$T^{19} +$$$$41\!\cdots\!89$$$$T^{20} +$$$$24\!\cdots\!32$$$$T^{21} +$$$$61\!\cdots\!30$$$$T^{22} +$$$$37\!\cdots\!26$$$$T^{23} +$$$$83\!\cdots\!25$$$$T^{24} +$$$$52\!\cdots\!49$$$$T^{25} +$$$$10\!\cdots\!31$$$$T^{26} +$$$$66\!\cdots\!86$$$$T^{27} +$$$$12\!\cdots\!56$$$$T^{28} +$$$$77\!\cdots\!17$$$$T^{29} +$$$$13\!\cdots\!76$$$$T^{30} +$$$$84\!\cdots\!29$$$$T^{31} +$$$$13\!\cdots\!58$$$$T^{32} +$$$$85\!\cdots\!85$$$$T^{33} +$$$$12\!\cdots\!72$$$$T^{34} +$$$$81\!\cdots\!64$$$$T^{35} +$$$$11\!\cdots\!93$$$$T^{36} +$$$$72\!\cdots\!51$$$$T^{37} +$$$$94\!\cdots\!99$$$$T^{38} +$$$$61\!\cdots\!46$$$$T^{39} +$$$$75\!\cdots\!90$$$$T^{40} +$$$$48\!\cdots\!86$$$$T^{41} +$$$$57\!\cdots\!82$$$$T^{42} +$$$$98\!\cdots\!97$$$$p T^{43} +$$$$41\!\cdots\!62$$$$T^{44} +$$$$26\!\cdots\!17$$$$T^{45} +$$$$28\!\cdots\!30$$$$T^{46} +$$$$17\!\cdots\!05$$$$T^{47} +$$$$18\!\cdots\!01$$$$T^{48} +$$$$11\!\cdots\!94$$$$T^{49} +$$$$11\!\cdots\!43$$$$T^{50} +$$$$70\!\cdots\!05$$$$T^{51} +$$$$69\!\cdots\!63$$$$T^{52} +$$$$41\!\cdots\!48$$$$T^{53} +$$$$40\!\cdots\!36$$$$T^{54} +$$$$23\!\cdots\!72$$$$T^{55} +$$$$22\!\cdots\!91$$$$T^{56} +$$$$12\!\cdots\!75$$$$T^{57} +$$$$11\!\cdots\!90$$$$T^{58} +$$$$67\!\cdots\!14$$$$T^{59} +$$$$59\!\cdots\!03$$$$T^{60} +$$$$33\!\cdots\!25$$$$T^{61} +$$$$29\!\cdots\!11$$$$T^{62} +$$$$16\!\cdots\!37$$$$T^{63} +$$$$13\!\cdots\!46$$$$T^{64} +$$$$76\!\cdots\!78$$$$T^{65} +$$$$62\!\cdots\!28$$$$T^{66} +$$$$34\!\cdots\!83$$$$T^{67} +$$$$27\!\cdots\!45$$$$T^{68} +$$$$14\!\cdots\!32$$$$T^{69} +$$$$11\!\cdots\!42$$$$T^{70} +$$$$62\!\cdots\!74$$$$T^{71} +$$$$48\!\cdots\!34$$$$T^{72} +$$$$25\!\cdots\!26$$$$T^{73} +$$$$19\!\cdots\!52$$$$T^{74} +$$$$97\!\cdots\!25$$$$T^{75} +$$$$72\!\cdots\!78$$$$T^{76} +$$$$36\!\cdots\!70$$$$T^{77} +$$$$72\!\cdots\!78$$$$p T^{78} +$$$$97\!\cdots\!25$$$$p^{2} T^{79} +$$$$19\!\cdots\!52$$$$p^{3} T^{80} +$$$$25\!\cdots\!26$$$$p^{4} T^{81} +$$$$48\!\cdots\!34$$$$p^{5} T^{82} +$$$$62\!\cdots\!74$$$$p^{6} T^{83} +$$$$11\!\cdots\!42$$$$p^{7} T^{84} +$$$$14\!\cdots\!32$$$$p^{8} T^{85} +$$$$27\!\cdots\!45$$$$p^{9} T^{86} +$$$$34\!\cdots\!83$$$$p^{10} T^{87} +$$$$62\!\cdots\!28$$$$p^{11} T^{88} +$$$$76\!\cdots\!78$$$$p^{12} T^{89} +$$$$13\!\cdots\!46$$$$p^{13} T^{90} +$$$$16\!\cdots\!37$$$$p^{14} T^{91} +$$$$29\!\cdots\!11$$$$p^{15} T^{92} +$$$$33\!\cdots\!25$$$$p^{16} T^{93} +$$$$59\!\cdots\!03$$$$p^{17} T^{94} +$$$$67\!\cdots\!14$$$$p^{18} T^{95} +$$$$11\!\cdots\!90$$$$p^{19} T^{96} +$$$$12\!\cdots\!75$$$$p^{20} T^{97} +$$$$22\!\cdots\!91$$$$p^{21} T^{98} +$$$$23\!\cdots\!72$$$$p^{22} T^{99} +$$$$40\!\cdots\!36$$$$p^{23} T^{100} +$$$$41\!\cdots\!48$$$$p^{24} T^{101} +$$$$69\!\cdots\!63$$$$p^{25} T^{102} +$$$$70\!\cdots\!05$$$$p^{26} T^{103} +$$$$11\!\cdots\!43$$$$p^{27} T^{104} +$$$$11\!\cdots\!94$$$$p^{28} T^{105} +$$$$18\!\cdots\!01$$$$p^{29} T^{106} +$$$$17\!\cdots\!05$$$$p^{30} T^{107} +$$$$28\!\cdots\!30$$$$p^{31} T^{108} +$$$$26\!\cdots\!17$$$$p^{32} T^{109} +$$$$41\!\cdots\!62$$$$p^{33} T^{110} +$$$$98\!\cdots\!97$$$$p^{35} T^{111} +$$$$57\!\cdots\!82$$$$p^{35} T^{112} +$$$$48\!\cdots\!86$$$$p^{36} T^{113} +$$$$75\!\cdots\!90$$$$p^{37} T^{114} +$$$$61\!\cdots\!46$$$$p^{38} T^{115} +$$$$94\!\cdots\!99$$$$p^{39} T^{116} +$$$$72\!\cdots\!51$$$$p^{40} T^{117} +$$$$11\!\cdots\!93$$$$p^{41} T^{118} +$$$$81\!\cdots\!64$$$$p^{42} T^{119} +$$$$12\!\cdots\!72$$$$p^{43} T^{120} +$$$$85\!\cdots\!85$$$$p^{44} T^{121} +$$$$13\!\cdots\!58$$$$p^{45} T^{122} +$$$$84\!\cdots\!29$$$$p^{46} T^{123} +$$$$13\!\cdots\!76$$$$p^{47} T^{124} +$$$$77\!\cdots\!17$$$$p^{48} T^{125} +$$$$12\!\cdots\!56$$$$p^{49} T^{126} +$$$$66\!\cdots\!86$$$$p^{50} T^{127} +$$$$10\!\cdots\!31$$$$p^{51} T^{128} +$$$$52\!\cdots\!49$$$$p^{52} T^{129} +$$$$83\!\cdots\!25$$$$p^{53} T^{130} +$$$$37\!\cdots\!26$$$$p^{54} T^{131} +$$$$61\!\cdots\!30$$$$p^{55} T^{132} +$$$$24\!\cdots\!32$$$$p^{56} T^{133} +$$$$41\!\cdots\!89$$$$p^{57} T^{134} +$$$$14\!\cdots\!93$$$$p^{58} T^{135} +$$$$25\!\cdots\!19$$$$p^{59} T^{136} +$$$$78\!\cdots\!14$$$$p^{60} T^{137} +$$$$13\!\cdots\!71$$$$p^{61} T^{138} + 36442971047168443210 p^{62} T^{139} + 6717168626904910855 p^{63} T^{140} + 147551168396133658 p^{64} T^{141} + 28579280224674787 p^{65} T^{142} + 506768937425473 p^{66} T^{143} + 104077631527262 p^{67} T^{144} + 1433497067262 p^{68} T^{145} + 315365942199 p^{69} T^{146} + 3200585970 p^{70} T^{147} + 763140974 p^{71} T^{148} + 5276065 p^{72} T^{149} + 1382211 p^{73} T^{150} + 5691 p^{74} T^{151} + 45 p^{76} T^{152} + 3 p^{76} T^{153} + p^{77} T^{154}$$
41 $$1 - 48 T + 2933 T^{2} - 101923 T^{3} + 3764788 T^{4} - 105324662 T^{5} + 2979832946 T^{6} - 70939413816 T^{7} + 1677543359209 T^{8} - 35146017548888 T^{9} + 726310191216633 T^{10} - 13694372835002975 T^{11} + 254019667338681675 T^{12} - 4379113552739315930 T^{13} + 74219115219349896042 T^{14} -$$$$11\!\cdots\!30$$$$T^{15} +$$$$18\!\cdots\!55$$$$T^{16} -$$$$27\!\cdots\!84$$$$T^{17} +$$$$40\!\cdots\!46$$$$T^{18} -$$$$56\!\cdots\!29$$$$T^{19} +$$$$78\!\cdots\!87$$$$T^{20} -$$$$10\!\cdots\!34$$$$T^{21} +$$$$13\!\cdots\!86$$$$T^{22} -$$$$16\!\cdots\!21$$$$T^{23} +$$$$21\!\cdots\!92$$$$T^{24} -$$$$25\!\cdots\!26$$$$T^{25} +$$$$29\!\cdots\!37$$$$T^{26} -$$$$34\!\cdots\!13$$$$T^{27} +$$$$39\!\cdots\!31$$$$T^{28} -$$$$43\!\cdots\!82$$$$T^{29} +$$$$47\!\cdots\!95$$$$T^{30} -$$$$50\!\cdots\!51$$$$T^{31} +$$$$52\!\cdots\!82$$$$T^{32} -$$$$53\!\cdots\!05$$$$T^{33} +$$$$54\!\cdots\!69$$$$T^{34} -$$$$54\!\cdots\!09$$$$T^{35} +$$$$53\!\cdots\!76$$$$T^{36} -$$$$51\!\cdots\!41$$$$T^{37} +$$$$48\!\cdots\!15$$$$T^{38} -$$$$45\!\cdots\!21$$$$T^{39} +$$$$41\!\cdots\!56$$$$T^{40} -$$$$37\!\cdots\!29$$$$T^{41} +$$$$33\!\cdots\!52$$$$T^{42} -$$$$29\!\cdots\!64$$$$T^{43} +$$$$26\!\cdots\!28$$$$T^{44} -$$$$22\!\cdots\!69$$$$T^{45} +$$$$19\!\cdots\!24$$$$T^{46} -$$$$15\!\cdots\!04$$$$T^{47} +$$$$13\!\cdots\!34$$$$T^{48} -$$$$10\!\cdots\!89$$$$T^{49} +$$$$87\!\cdots\!69$$$$T^{50} -$$$$69\!\cdots\!58$$$$T^{51} +$$$$55\!\cdots\!47$$$$T^{52} -$$$$43\!\cdots\!59$$$$T^{53} +$$$$33\!\cdots\!08$$$$T^{54} -$$$$25\!\cdots\!42$$$$T^{55} +$$$$19\!\cdots\!00$$$$T^{56} -$$$$14\!\cdots\!02$$$$T^{57} +$$$$11\!\cdots\!88$$$$T^{58} -$$$$81\!\cdots\!97$$$$T^{59} +$$$$60\!\cdots\!03$$$$T^{60} -$$$$43\!\cdots\!70$$$$T^{61} +$$$$31\!\cdots\!91$$$$T^{62} -$$$$22\!\cdots\!65$$$$T^{63} +$$$$15\!\cdots\!86$$$$T^{64} -$$$$11\!\cdots\!51$$$$T^{65} +$$$$77\!\cdots\!13$$$$T^{66} -$$$$53\!\cdots\!71$$$$T^{67} +$$$$36\!\cdots\!69$$$$T^{68} -$$$$24\!\cdots\!28$$$$T^{69} +$$$$16\!\cdots\!56$$$$T^{70} -$$$$11\!\cdots\!66$$$$T^{71} +$$$$75\!\cdots\!91$$$$T^{72} -$$$$49\!\cdots\!82$$$$T^{73} +$$$$32\!\cdots\!14$$$$T^{74} -$$$$21\!\cdots\!65$$$$T^{75} +$$$$13\!\cdots\!81$$$$T^{76} -$$$$87\!\cdots\!38$$$$T^{77} +$$$$13\!\cdots\!81$$$$p T^{78} -$$$$21\!\cdots\!65$$$$p^{2} T^{79} +$$$$32\!\cdots\!14$$$$p^{3} T^{80} -$$$$49\!\cdots\!82$$$$p^{4} T^{81} +$$$$75\!\cdots\!91$$$$p^{5} T^{82} -$$$$11\!\cdots\!66$$$$p^{6} T^{83} +$$$$16\!\cdots\!56$$$$p^{7} T^{84} -$$$$24\!\cdots\!28$$$$p^{8} T^{85} +$$$$36\!\cdots\!69$$$$p^{9} T^{86} -$$$$53\!\cdots\!71$$$$p^{10} T^{87} +$$$$77\!\cdots\!13$$$$p^{11} T^{88} -$$$$11\!\cdots\!51$$$$p^{12} T^{89} +$$$$15\!\cdots\!86$$$$p^{13} T^{90} -$$$$22\!\cdots\!65$$$$p^{14} T^{91} +$$$$31\!\cdots\!91$$$$p^{15} T^{92} -$$$$43\!\cdots\!70$$$$p^{16} T^{93} +$$$$60\!\cdots\!03$$$$p^{17} T^{94} -$$$$81\!\cdots\!97$$$$p^{18} T^{95} +$$$$11\!\cdots\!88$$$$p^{19} T^{96} -$$$$14\!\cdots\!02$$$$p^{20} T^{97} +$$$$19\!\cdots\!00$$$$p^{21} T^{98} -$$$$25\!\cdots\!42$$$$p^{22} T^{99} +$$$$33\!\cdots\!08$$$$p^{23} T^{100} -$$$$43\!\cdots\!59$$$$p^{24} T^{101} +$$$$55\!\cdots\!47$$$$p^{25} T^{102} -$$$$69\!\cdots\!58$$$$p^{26} T^{103} +$$$$87\!\cdots\!69$$$$p^{27} T^{104} -$$$$10\!\cdots\!89$$$$p^{28} T^{105} +$$$$13\!\cdots\!34$$$$p^{29} T^{106} -$$$$15\!\cdots\!04$$$$p^{30} T^{107} +$$$$19\!\cdots\!24$$$$p^{31} T^{108} -$$$$22\!\cdots\!69$$$$p^{32} T^{109} +$$$$26\!\cdots\!28$$$$p^{33} T^{110} -$$$$29\!\cdots\!64$$$$p^{34} T^{111} +$$$$33\!\cdots\!52$$$$p^{35} T^{112} -$$$$37\!\cdots\!29$$$$p^{36} T^{113} +$$$$41\!\cdots\!56$$$$p^{37} T^{114} -$$$$45\!\cdots\!21$$$$p^{38} T^{115} +$$$$48\!\cdots\!15$$$$p^{39} T^{116} -$$$$51\!\cdots\!41$$$$p^{40} T^{117} +$$$$53\!\cdots\!76$$$$p^{41} T^{118} -$$$$54\!\cdots\!09$$$$p^{42} T^{119} +$$$$54\!\cdots\!69$$$$p^{43} T^{120} -$$$$53\!\cdots\!05$$$$p^{44} T^{121} +$$$$52\!\cdots\!82$$$$p^{45} T^{122} -$$$$50\!\cdots\!51$$$$p^{46} T^{123} +$$$$47\!\cdots\!95$$$$p^{47} T^{124} -$$$$43\!\cdots\!82$$$$p^{48} T^{125} +$$$$39\!\cdots\!31$$$$p^{49} T^{126} -$$$$34\!\cdots\!13$$$$p^{50} T^{127} +$$$$29\!\cdots\!37$$$$p^{51} T^{128} -$$$$25\!\cdots\!26$$$$p^{52} T^{129} +$$$$21\!\cdots\!92$$$$p^{53} T^{130} -$$$$16\!\cdots\!21$$$$p^{54} T^{131} +$$$$13\!\cdots\!86$$$$p^{55} T^{132} -$$$$10\!\cdots\!34$$$$p^{56} T^{133} +$$$$78\!\cdots\!87$$$$p^{57} T^{134} -$$$$56\!\cdots\!29$$$$p^{58} T^{135} +$$$$40\!\cdots\!46$$$$p^{59} T^{136} -$$$$27\!\cdots\!84$$$$p^{60} T^{137} +$$$$18\!\cdots\!55$$$$p^{61} T^{138} -$$$$11\!\cdots\!30$$$$p^{62} T^{139} + 74219115219349896042 p^{63} T^{140} - 4379113552739315930 p^{64} T^{141} + 254019667338681675 p^{65} T^{142} - 13694372835002975 p^{66} T^{143} + 726310191216633 p^{67} T^{144} - 35146017548888 p^{68} T^{145} + 1677543359209 p^{69} T^{146} - 70939413816 p^{70} T^{147} + 2979832946 p^{71} T^{148} - 105324662 p^{72} T^{149} + 3764788 p^{73} T^{150} - 101923 p^{74} T^{151} + 2933 p^{75} T^{152} - 48 p^{76} T^{153} + p^{77} T^{154}$$
43 $$1 - 21 T + 2078 T^{2} - 38280 T^{3} + 2089253 T^{4} - 34317254 T^{5} + 1362606657 T^{6} - 20185188296 T^{7} + 651117110853 T^{8} - 8767800372601 T^{9} + 243897190094112 T^{10} - 69792212886917 p T^{11} + 74785300446495752 T^{12} - 843392897854857419 T^{13} + 19348259833961080520 T^{14} -$$$$20\!\cdots\!48$$$$T^{15} +$$$$10\!\cdots\!60$$$$p T^{16} -$$$$40\!\cdots\!10$$$$T^{17} +$$$$84\!\cdots\!20$$$$T^{18} -$$$$73\!\cdots\!72$$$$T^{19} +$$$$14\!\cdots\!15$$$$T^{20} -$$$$11\!\cdots\!65$$$$T^{21} +$$$$23\!\cdots\!58$$$$T^{22} -$$$$16\!\cdots\!50$$$$T^{23} +$$$$33\!\cdots\!76$$$$T^{24} -$$$$21\!\cdots\!26$$$$T^{25} +$$$$43\!\cdots\!97$$$$T^{26} -$$$$24\!\cdots\!81$$$$T^{27} +$$$$53\!\cdots\!16$$$$T^{28} -$$$$25\!\cdots\!83$$$$T^{29} +$$$$60\!\cdots\!59$$$$T^{30} -$$$$24\!\cdots\!55$$$$T^{31} +$$$$64\!\cdots\!40$$$$T^{32} -$$$$20\!\cdots\!63$$$$T^{33} +$$$$64\!\cdots\!47$$$$T^{34} -$$$$15\!\cdots\!55$$$$T^{35} +$$$$60\!\cdots\!06$$$$T^{36} -$$$$10\!\cdots\!46$$$$T^{37} +$$$$54\!\cdots\!63$$$$T^{38} -$$$$48\!\cdots\!80$$$$T^{39} +$$$$47\!\cdots\!21$$$$T^{40} -$$$$55\!\cdots\!08$$$$T^{41} +$$$$38\!\cdots\!80$$$$T^{42} +$$$$23\!\cdots\!21$$$$T^{43} +$$$$30\!\cdots\!19$$$$T^{44} +$$$$39\!\cdots\!52$$$$T^{45} +$$$$23\!\cdots\!82$$$$T^{46} +$$$$10\!\cdots\!96$$$$p T^{47} +$$$$16\!\cdots\!64$$$$T^{48} +$$$$41\!\cdots\!82$$$$T^{49} +$$$$11\!\cdots\!44$$$$T^{50} +$$$$34\!\cdots\!73$$$$T^{51} +$$$$79\!\cdots\!38$$$$T^{52} +$$$$27\!\cdots\!98$$$$T^{53} +$$$$51\!\cdots\!61$$$$T^{54} +$$$$19\!\cdots\!09$$$$T^{55} +$$$$32\!\cdots\!58$$$$T^{56} +$$$$13\!\cdots\!12$$$$T^{57} +$$$$19\!\cdots\!02$$$$T^{58} +$$$$85\!\cdots\!79$$$$T^{59} +$$$$11\!\cdots\!51$$$$T^{60} +$$$$52\!\cdots\!07$$$$T^{61} +$$$$65\!\cdots\!44$$$$T^{62} +$$$$30\!\cdots\!85$$$$T^{63} +$$$$36\!\cdots\!27$$$$T^{64} +$$$$17\!\cdots\!38$$$$T^{65} +$$$$19\!\cdots\!48$$$$T^{66} +$$$$92\!\cdots\!34$$$$T^{67} +$$$$97\!\cdots\!65$$$$T^{68} +$$$$47\!\cdots\!47$$$$T^{69} +$$$$47\!\cdots\!69$$$$T^{70} +$$$$23\!\cdots\!25$$$$T^{71} +$$$$22\!\cdots\!44$$$$T^{72} +$$$$11\!\cdots\!21$$$$T^{73} +$$$$10\!\cdots\!76$$$$T^{74} +$$$$50\!\cdots\!70$$$$T^{75} +$$$$46\!\cdots\!94$$$$T^{76} +$$$$22\!\cdots\!22$$$$T^{77} +$$$$46\!\cdots\!94$$$$p T^{78} +$$$$50\!\cdots\!70$$$$p^{2} T^{79} +$$$$10\!\cdots\!76$$$$p^{3} T^{80} +$$$$11\!\cdots\!21$$$$p^{4} T^{81} +$$$$22\!\cdots\!44$$$$p^{5} T^{82} +$$$$23\!\cdots\!25$$$$p^{6} T^{83} +$$$$47\!\cdots\!69$$$$p^{7} T^{84} +$$$$47\!\cdots\!47$$$$p^{8} T^{85} +$$$$97\!\cdots\!65$$$$p^{9} T^{86} +$$$$92\!\cdots\!34$$$$p^{10} T^{87} +$$$$19\!\cdots\!48$$$$p^{11} T^{88} +$$$$17\!\cdots\!38$$$$p^{12} T^{89} +$$$$36\!\cdots\!27$$$$p^{13} T^{90} +$$$$30\!\cdots\!85$$$$p^{14} T^{91} +$$$$65\!\cdots\!44$$$$p^{15} T^{92} +$$$$52\!\cdots\!07$$$$p^{16} T^{93} +$$$$11\!\cdots\!51$$$$p^{17} T^{94} +$$$$85\!\cdots\!79$$$$p^{18} T^{95} +$$$$19\!\cdots\!02$$$$p^{19} T^{96} +$$$$13\!\cdots\!12$$$$p^{20} T^{97} +$$$$32\!\cdots\!58$$$$p^{21} T^{98} +$$$$19\!\cdots\!09$$$$p^{22} T^{99} +$$$$51\!\cdots\!61$$$$p^{23} T^{100} +$$$$27\!\cdots\!98$$$$p^{24} T^{101} +$$$$79\!\cdots\!38$$$$p^{25} T^{102} +$$$$34\!\cdots\!73$$$$p^{26} T^{103} +$$$$11\!\cdots\!44$$$$p^{27} T^{104} +$$$$41\!\cdots\!82$$$$p^{28} T^{105} +$$$$16\!\cdots\!64$$$$p^{29} T^{106} +$$$$10\!\cdots\!96$$$$p^{31} T^{107} +$$$$23\!\cdots\!82$$$$p^{31} T^{108} +$$$$39\!\cdots\!52$$$$p^{32} T^{109} +$$$$30\!\cdots\!19$$$$p^{33} T^{110} +$$$$23\!\cdots\!21$$$$p^{34} T^{111} +$$$$38\!\cdots\!80$$$$p^{35} T^{112} -$$$$55\!\cdots\!08$$$$p^{36} T^{113} +$$$$47\!\cdots\!21$$$$p^{37} T^{114} -$$$$48\!\cdots\!80$$$$p^{38} T^{115} +$$$$54\!\cdots\!63$$$$p^{39} T^{116} -$$$$10\!\cdots\!46$$$$p^{40} T^{117} +$$$$60\!\cdots\!06$$$$p^{41} T^{118} -$$$$15\!\cdots\!55$$$$p^{42} T^{119} +$$$$64\!\cdots\!47$$$$p^{43} T^{120} -$$$$20\!\cdots\!63$$$$p^{44} T^{121} +$$$$64\!\cdots\!40$$$$p^{45} T^{122} -$$$$24\!\cdots\!55$$$$p^{46} T^{123} +$$$$60\!\cdots\!59$$$$p^{47} T^{124} -$$$$25\!\cdots\!83$$$$p^{48} T^{125} +$$$$53\!\cdots\!16$$$$p^{49} T^{126} -$$$$24\!\cdots\!81$$$$p^{50} T^{127} +$$$$43\!\cdots\!97$$$$p^{51} T^{128} -$$$$21\!\cdots\!26$$$$p^{52} T^{129} +$$$$33\!\cdots\!76$$$$p^{53} T^{130} -$$$$16\!\cdots\!50$$$$p^{54} T^{131} +$$$$23\!\cdots\!58$$$$p^{55} T^{132} -$$$$11\!\cdots\!65$$$$p^{56} T^{133} +$$$$14\!\cdots\!15$$$$p^{57} T^{134} -$$$$73\!\cdots\!72$$$$p^{58} T^{135} +$$$$84\!\cdots\!20$$$$p^{59} T^{136} -$$$$40\!\cdots\!10$$$$p^{60} T^{137} +$$$$10\!\cdots\!60$$$$p^{62} T^{138} -$$$$20\!\cdots\!48$$$$p^{62} T^{139} + 19348259833961080520 p^{63} T^{140} - 843392897854857419 p^{64} T^{141} + 74785300446495752 p^{65} T^{142} - 69792212886917 p^{67} T^{143} + 243897190094112 p^{67} T^{144} - 8767800372601 p^{68} T^{145} + 651117110853 p^{69} T^{146} - 20185188296 p^{70} T^{147} + 1362606657 p^{71} T^{148} - 34317254 p^{72} T^{149} + 2089253 p^{73} T^{150} - 38280 p^{74} T^{151} + 2078 p^{75} T^{152} - 21 p^{76} T^{153} + p^{77} T^{154}$$
47 $$1 - 107 T + 7653 T^{2} - 410089 T^{3} + 18307310 T^{4} - 705485926 T^{5} + 24221824048 T^{6} - 753745589064 T^{7} + 458988576965 p T^{8} - 573495504430996 T^{9} + 14280970261577657 T^{10} - 335231912265454172 T^{11} + 7458501393165727253 T^{12} -$$$$15\!\cdots\!56$$$$T^{13} +$$$$31\!\cdots\!13$$$$T^{14} -$$$$62\!\cdots\!54$$$$T^{15} +$$$$11\!\cdots\!11$$$$T^{16} -$$$$20\!\cdots\!42$$$$T^{17} +$$$$76\!\cdots\!32$$$$p T^{18} -$$$$60\!\cdots\!48$$$$T^{19} +$$$$98\!\cdots\!80$$$$T^{20} -$$$$15\!\cdots\!65$$$$T^{21} +$$$$24\!\cdots\!71$$$$T^{22} -$$$$35\!\cdots\!75$$$$T^{23} +$$$$52\!\cdots\!04$$$$T^{24} -$$$$74\!\cdots\!81$$$$T^{25} +$$$$10\!\cdots\!71$$$$T^{26} -$$$$14\!\cdots\!75$$$$T^{27} +$$$$18\!\cdots\!04$$$$T^{28} -$$$$51\!\cdots\!49$$$$p T^{29} +$$$$30\!\cdots\!04$$$$T^{30} -$$$$38\!\cdots\!32$$$$T^{31} +$$$$47\!\cdots\!46$$$$T^{32} -$$$$56\!\cdots\!69$$$$T^{33} +$$$$66\!\cdots\!60$$$$T^{34} -$$$$77\!\cdots\!31$$$$T^{35} +$$$$88\!\cdots\!84$$$$T^{36} -$$$$98\!\cdots\!75$$$$T^{37} +$$$$10\!\cdots\!25$$$$T^{38} -$$$$11\!\cdots\!12$$$$T^{39} +$$$$12\!\cdots\!65$$$$T^{40} -$$$$13\!\cdots\!91$$$$T^{41} +$$$$13\!\cdots\!86$$$$T^{42} -$$$$13\!\cdots\!92$$$$T^{43} +$$$$14\!\cdots\!78$$$$T^{44} -$$$$13\!\cdots\!01$$$$T^{45} +$$$$13\!\cdots\!07$$$$T^{46} -$$$$13\!\cdots\!52$$$$T^{47} +$$$$12\!\cdots\!00$$$$T^{48} -$$$$11\!\cdots\!43$$$$T^{49} +$$$$10\!\cdots\!03$$$$T^{50} -$$$$10\!\cdots\!73$$$$T^{51} +$$$$90\!\cdots\!09$$$$T^{52} -$$$$81\!\cdots\!56$$$$T^{53} +$$$$71\!\cdots\!64$$$$T^{54} -$$$$62\!\cdots\!63$$$$T^{55} +$$$$54\!\cdots\!27$$$$T^{56} -$$$$46\!\cdots\!45$$$$T^{57} +$$$$38\!\cdots\!65$$$$T^{58} -$$$$32\!\cdots\!12$$$$T^{59} +$$$$26\!\cdots\!61$$$$T^{60} -$$$$21\!\cdots\!08$$$$T^{61} +$$$$17\!\cdots\!74$$$$T^{62} -$$$$13\!\cdots\!52$$$$T^{63} +$$$$11\!\cdots\!08$$$$T^{64} -$$$$86\!\cdots\!46$$$$T^{65} +$$$$66\!\cdots\!22$$$$T^{66} -$$$$50\!\cdots\!13$$$$T^{67} +$$$$38\!\cdots\!31$$$$T^{68} -$$$$28\!\cdots\!98$$$$T^{69} +$$$$21\!\cdots\!40$$$$T^{70} -$$$$15\!\cdots\!36$$$$T^{71} +$$$$11\!\cdots\!45$$$$T^{72} -$$$$81\!\cdots\!60$$$$T^{73} +$$$$57\!\cdots\!01$$$$T^{74} -$$$$40\!\cdots\!43$$$$T^{75} +$$$$28\!\cdots\!52$$$$T^{76} -$$$$19\!\cdots\!96$$$$T^{77} +$$$$28\!\cdots\!52$$$$p T^{78} -$$$$40\!\cdots\!43$$$$p^{2} T^{79} +$$$$57\!\cdots\!01$$$$p^{3} T^{80} -$$$$81\!\cdots\!60$$$$p^{4} T^{81} +$$$$11\!\cdots\!45$$$$p^{5} T^{82} -$$$$15\!\cdots\!36$$$$p^{6} T^{83} +$$$$21\!\cdots\!40$$$$p^{7} T^{84} -$$$$28\!\cdots\!98$$$$p^{8} T^{85} +$$$$38\!\cdots\!31$$$$p^{9} T^{86} -$$$$50\!\cdots\!13$$$$p^{10} T^{87} +$$$$66\!\cdots\!22$$$$p^{11} T^{88} -$$$$86\!\cdots\!46$$$$p^{12} T^{89} +$$$$11\!\cdots\!08$$$$p^{13} T^{90} -$$$$13\!\cdots\!52$$$$p^{14} T^{91} +$$$$17\!\cdots\!74$$$$p^{15} T^{92} -$$$$21\!\cdots\!08$$$$p^{16} T^{93} +$$$$26\!\cdots\!61$$$$p^{17} T^{94} -$$$$32\!\cdots\!12$$$$p^{18} T^{95} +$$$$38\!\cdots\!65$$$$p^{19} T^{96} -$$$$46\!\cdots\!45$$$$p^{20} T^{97} +$$$$54\!\cdots\!27$$$$p^{21} T^{98} -$$$$62\!\cdots\!63$$$$p^{22} T^{99} +$$$$71\!\cdots\!64$$$$p^{23} T^{100} -$$$$81\!\cdots\!56$$$$p^{24} T^{101} +$$$$90\!\cdots\!09$$$$p^{25} T^{102} -$$$$10\!\cdots\!73$$$$p^{26} T^{103} +$$$$10\!\cdots\!03$$$$p^{27} T^{104} -$$$$11\!\cdots\!43$$$$p^{28} T^{105} +$$$$12\!\cdots\!00$$$$p^{29} T^{106} -$$$$13\!\cdots\!52$$$$p^{30} T^{107} +$$$$13\!\cdots\!07$$$$p^{31} T^{108} -$$$$13\!\cdots\!01$$$$p^{32} T^{109} +$$$$14\!\cdots\!78$$$$p^{33} T^{110} -$$$$13\!\cdots\!92$$$$p^{34} T^{111} +$$$$13\!\cdots\!86$$$$p^{35} T^{112} -$$$$13\!\cdots\!91$$$$p^{36} T^{113} +$$$$12\!\cdots\!65$$$$p^{37} T^{114} -$$$$11\!\cdots\!12$$$$p^{38} T^{115} +$$$$10\!\cdots\!25$$$$p^{39} T^{116} -$$$$98\!\cdots\!75$$$$p^{40} T^{117} +$$$$88\!\cdots\!84$$$$p^{41} T^{118} -$$$$77\!\cdots\!31$$$$p^{42} T^{119} +$$$$66\!\cdots\!60$$$$p^{43} T^{120} -$$$$56\!\cdots\!69$$$$p^{44} T^{121} +$$$$47\!\cdots\!46$$$$p^{45} T^{122} -$$$$38\!\cdots\!32$$$$p^{46} T^{123} +$$$$30\!\cdots\!04$$$$p^{47} T^{124} -$$$$51\!\cdots\!49$$$$p^{49} T^{125} +$$$$18\!\cdots\!04$$$$p^{49} T^{126} -$$$$14\!\cdots\!75$$$$p^{50} T^{127} +$$$$10\!\cdots\!71$$$$p^{51} T^{128} -$$$$74\!\cdots\!81$$$$p^{52} T^{129} +$$$$52\!\cdots\!04$$$$p^{53} T^{130} -$$$$35\!\cdots\!75$$$$p^{54} T^{131} +$$$$24\!\cdots\!71$$$$p^{55} T^{132} -$$$$15\!\cdots\!65$$$$p^{56} T^{133} +$$$$98\!\cdots\!80$$$$p^{57} T^{134} -$$$$60\!\cdots\!48$$$$p^{58} T^{135} +$$$$76\!\cdots\!32$$$$p^{60} T^{136} -$$$$20\!\cdots\!42$$$$p^{60} T^{137} +$$$$11\!\cdots\!11$$$$p^{61} T^{138} -$$$$62\!\cdots\!54$$$$p^{62} T^{139} +$$$$31\!\cdots\!13$$$$p^{63} T^{140} -$$$$15\!\cdots\!56$$$$p^{64} T^{141} + 7458501393165727253 p^{65} T^{142} - 335231912265454172 p^{66} T^{143} + 14280970261577657 p^{67} T^{144} - 573495504430996 p^{68} T^{145} + 458988576965 p^{70} T^{146} - 753745589064 p^{70} T^{147} + 24221824048 p^{71} T^{148} - 705485926 p^{72} T^{149} + 18307310 p^{73} T^{150} - 410089 p^{74} T^{151} + 7653 p^{75} T^{152} - 107 p^{76} T^{153} + p^{77} T^{154}$$
53 $$1 - 42 T + 3188 T^{2} - 108877 T^{3} + 4790735 T^{4} - 139481456 T^{5} + 4604736362 T^{6} - 117840526638 T^{7} + 3216920621116 T^{8} - 73916071417618 T^{9} + 1753437252868697 T^{10} - 36741273697995162 T^{11} + 780093892862054716 T^{12} - 15083930469072097976 T^{13} +$$$$29\!\cdots\!31$$$$T^{14} -$$$$52\!\cdots\!33$$$$T^{15} +$$$$94\!\cdots\!02$$$$T^{16} -$$$$15\!\cdots\!62$$$$T^{17} +$$$$26\!\cdots\!20$$$$T^{18} -$$$$42\!\cdots\!28$$$$T^{19} +$$$$67\!\cdots\!29$$$$T^{20} -$$$$10\!\cdots\!04$$$$T^{21} +$$$$15\!\cdots\!51$$$$T^{22} -$$$$21\!\cdots\!12$$$$T^{23} +$$$$31\!\cdots\!49$$$$T^{24} -$$$$43\!\cdots\!39$$$$T^{25} +$$$$58\!\cdots\!49$$$$T^{26} -$$$$77\!\cdots\!79$$$$T^{27} +$$$$10\!\cdots\!87$$$$T^{28} -$$$$12\!\cdots\!13$$$$T^{29} +$$$$16\!\cdots\!83$$$$T^{30} -$$$$19\!\cdots\!22$$$$T^{31} +$$$$24\!\cdots\!36$$$$T^{32} -$$$$28\!\cdots\!44$$$$T^{33} +$$$$33\!\cdots\!89$$$$T^{34} -$$$$38\!\cdots\!19$$$$T^{35} +$$$$43\!\cdots\!60$$$$T^{36} -$$$$48\!\cdots\!65$$$$T^{37} +$$$$53\!\cdots\!63$$$$T^{38} -$$$$58\!\cdots\!16$$$$T^{39} +$$$$62\!\cdots\!56$$$$T^{40} -$$$$65\!\cdots\!00$$$$T^{41} +$$$$68\!\cdots\!87$$$$T^{42} -$$$$70\!\cdots\!16$$$$T^{43} +$$$$71\!\cdots\!57$$$$T^{44} -$$$$71\!\cdots\!35$$$$T^{45} +$$$$70\!\cdots\!60$$$$T^{46} -$$$$69\!\cdots\!75$$$$T^{47} +$$$$66\!\cdots\!87$$$$T^{48} -$$$$63\!\cdots\!30$$$$T^{49} +$$$$60\!\cdots\!36$$$$T^{50} -$$$$56\!\cdots\!53$$$$T^{51} +$$$$52\!\cdots\!79$$$$T^{52} -$$$$47\!\cdots\!97$$$$T^{53} +$$$$43\!\cdots\!87$$$$T^{54} -$$$$38\!\cdots\!68$$$$T^{55} +$$$$34\!\cdots\!95$$$$T^{56} -$$$$30\!\cdots\!63$$$$T^{57} +$$$$26\!\cdots\!32$$$$T^{58} -$$$$22\!\cdots\!66$$$$T^{59} +$$$$19\!\cdots\!65$$$$T^{60} -$$$$16\!\cdots\!87$$$$T^{61} +$$$$13\!\cdots\!49$$$$T^{62} -$$$$11\!\cdots\!22$$$$T^{63} +$$$$91\!\cdots\!12$$$$T^{64} -$$$$74\!\cdots\!26$$$$T^{65} +$$$$60\!\cdots\!96$$$$T^{66} -$$$$47\!\cdots\!68$$$$T^{67} +$$$$37\!\cdots\!44$$$$T^{68} -$$$$29\!\cdots\!03$$$$T^{69} +$$$$23\!\cdots\!28$$$$T^{70} -$$$$17\!\cdots\!48$$$$T^{71} +$$$$13\!\cdots\!41$$$$T^{72} -$$$$10\!\cdots\!86$$$$T^{73} +$$$$77\!\cdots\!23$$$$T^{74} -$$$$57\!\cdots\!02$$$$T^{75} +$$$$42\!\cdots\!38$$$$T^{76} -$$$$31\!\cdots\!60$$$$T^{77} +$$$$42\!\cdots\!38$$$$p T^{78} -$$$$57\!\cdots\!02$$$$p^{2} T^{79} +$$$$77\!\cdots\!23$$$$p^{3} T^{80} -$$$$10\!\cdots\!86$$$$p^{4} T^{81} +$$$$13\!\cdots\!41$$$$p^{5} T^{82} -$$$$17\!\cdots\!48$$$$p^{6} T^{83} +$$$$23\!\cdots\!28$$$$p^{7} T^{84} -$$$$29\!\cdots\!03$$$$p^{8} T^{85} +$$$$37\!\cdots\!44$$$$p^{9} T^{86} -$$$$47\!\cdots\!68$$$$p^{10} T^{87} +$$$$60\!\cdots\!96$$$$p^{11} T^{88} -$$$$74\!\cdots\!26$$$$p^{12} T^{89} +$$$$91\!\cdots\!12$$$$p^{13} T^{90} -$$$$11\!\cdots\!22$$$$p^{14} T^{91} +$$$$13\!\cdots\!49$$$$p^{15} T^{92} -$$$$16\!\cdots\!87$$$$p^{16} T^{93} +$$$$19\!\cdots\!65$$$$p^{17} T^{94} -$$$$22\!\cdots\!66$$$$p^{18} T^{95} +$$$$26\!\cdots\!32$$$$p^{19} T^{96} -$$$$30\!\cdots\!63$$$$p^{20} T^{97} +$$$$34\!\cdots\!95$$$$p^{21} T^{98} -$$$$38\!\cdots\!68$$$$p^{22} T^{99} +$$$$43\!\cdots\!87$$$$p^{23} T^{100} -$$$$47\!\cdots\!97$$$$p^{24} T^{101} +$$$$52\!\cdots\!79$$$$p^{25} T^{102} -$$$$56\!\cdots\!53$$$$p^{26} T^{103} +$$$$60\!\cdots\!36$$$$p^{27} T^{104} -$$$$63\!\cdots\!30$$$$p^{28} T^{105} +$$$$66\!\cdots\!87$$$$p^{29} T^{106} -$$$$69\!\cdots\!75$$$$p^{30} T^{107} +$$$$70\!\cdots\!60$$$$p^{31} T^{108} -$$$$71\!\cdots\!35$$$$p^{32} T^{109} +$$$$71\!\cdots\!57$$$$p^{33} T^{110} -$$$$70\!\cdots\!16$$$$p^{34} T^{111} +$$$$68\!\cdots\!87$$$$p^{35} T^{112} -$$$$65\!\cdots\!00$$$$p^{36} T^{113} +$$$$62\!\cdots\!56$$$$p^{37} T^{114} -$$$$58\!\cdots\!16$$$$p^{38} T^{115} +$$$$53\!\cdots\!63$$$$p^{39} T^{116} -$$$$48\!\cdots\!65$$$$p^{40} T^{117} +$$$$43\!\cdots\!60$$$$p^{41} T^{118} -$$$$38\!\cdots\!19$$$$p^{42} T^{119} +$$$$33\!\cdots\!89$$$$p^{43} T^{120} -$$$$28\!\cdots\!44$$$$p^{44} T^{121} +$$$$24\!\cdots\!36$$$$p^{45} T^{122} -$$$$19\!\cdots\!22$$$$p^{46} T^{123} +$$$$16\!\cdots\!83$$$$p^{47} T^{124} -$$$$12\!\cdots\!13$$$$p^{48} T^{125} +$$$$10\!\cdots\!87$$$$p^{49} T^{126} -$$$$77\!\cdots\!79$$$$p^{50} T^{127} +$$$$58\!\cdots\!49$$$$p^{51} T^{128} -$$$$43\!\cdots\!39$$$$p^{52} T^{129} +$$$$31\!\cdots\!49$$$$p^{53} T^{130} -$$$$21\!\cdots\!12$$$$p^{54} T^{131} +$$$$15\!\cdots\!51$$$$p^{55} T^{132} -$$$$10\!\cdots\!04$$$$p^{56} T^{133} +$$$$67\!\cdots\!29$$$$p^{57} T^{134} -$$$$42\!\cdots\!28$$$$p^{58} T^{135} +$$$$26\!\cdots\!20$$$$p^{59} T^{136} -$$$$15\!\cdots\!62$$$$p^{60} T^{137} +$$$$94\!\cdots\!02$$$$p^{61} T^{138} -$$$$52\!\cdots\!33$$$$p^{62} T^{139} +$$$$29\!\cdots\!31$$$$p^{63} T^{140} - 15083930469072097976 p^{64} T^{141} + 780093892862054716 p^{65} T^{142} - 36741273697995162 p^{66} T^{143} + 1753437252868697 p^{67} T^{144} - 73916071417618 p^{68} T^{145} + 3216920621116 p^{69} T^{146} - 117840526638 p^{70} T^{147} + 4604736362 p^{71} T^{148} - 139481456 p^{72} T^{149} + 4790735 p^{73} T^{150} - 108877 p^{74} T^{151} + 3188 p^{75} T^{152} - 42 p^{76} T^{153} + p^{77} T^{154}$$
59 $$1 - 42 T + 3281 T^{2} - 111010 T^{3} + 5031181 T^{4} - 144663374 T^{5} + 4915483212 T^{6} - 124185488348 T^{7} + 3485199416669 T^{8} - 79135234503731 T^{9} + 1927674749660257 T^{10} - 39982826596819965 T^{11} + 870895704497822983 T^{12} - 16703252743035726470 T^{13} +$$$$33\!\cdots\!80$$$$T^{14} -$$$$59\!\cdots\!31$$$$T^{15} +$$$$10\!\cdots\!70$$$$T^{16} -$$$$18\!\cdots\!09$$$$T^{17} +$$$$31\!\cdots\!48$$$$T^{18} -$$$$50\!\cdots\!80$$$$T^{19} +$$$$81\!\cdots\!01$$$$T^{20} -$$$$12\!\cdots\!82$$$$T^{21} +$$$$18\!\cdots\!40$$$$T^{22} -$$$$27\!\cdots\!16$$$$T^{23} +$$$$39\!\cdots\!33$$$$T^{24} -$$$$55\!\cdots\!07$$$$T^{25} +$$$$77\!\cdots\!19$$$$T^{26} -$$$$10\!\cdots\!42$$$$T^{27} +$$$$13\!\cdots\!37$$$$T^{28} -$$$$17\!\cdots\!89$$$$T^{29} +$$$$22\!\cdots\!57$$$$T^{30} -$$$$28\!\cdots\!90$$$$T^{31} +$$$$35\!\cdots\!57$$$$T^{32} -$$$$42\!\cdots\!74$$$$T^{33} +$$$$51\!\cdots\!68$$$$T^{34} -$$$$60\!\cdots\!55$$$$T^{35} +$$$$70\!\cdots\!98$$$$T^{36} -$$$$80\!\cdots\!61$$$$T^{37} +$$$$91\!\cdots\!75$$$$T^{38} -$$$$10\!\cdots\!68$$$$T^{39} +$$$$11\!\cdots\!45$$$$T^{40} -$$$$12\!\cdots\!55$$$$T^{41} +$$$$12\!\cdots\!97$$$$T^{42} -$$$$13\!\cdots\!64$$$$T^{43} +$$$$14\!\cdots\!84$$$$T^{44} -$$$$14\!\cdots\!74$$$$T^{45} +$$$$15\!\cdots\!04$$$$T^{46} -$$$$15\!\cdots\!61$$$$T^{47} +$$$$15\!\cdots\!12$$$$T^{48} -$$$$15\!\cdots\!59$$$$T^{49} +$$$$14\!\cdots\!74$$$$T^{50} -$$$$14\!\cdots\!22$$$$T^{51} +$$$$13\!\cdots\!75$$$$T^{52} -$$$$13\!\cdots\!79$$$$T^{53} +$$$$12\!\cdots\!01$$$$T^{54} -$$$$11\!\cdots\!74$$$$T^{55} +$$$$10\!\cdots\!24$$$$T^{56} -$$$$95\!\cdots\!58$$$$T^{57} +$$$$87\!\cdots\!03$$$$T^{58} -$$$$77\!\cdots\!88$$$$T^{59} +$$$$69\!\cdots\!88$$$$T^{60} -$$$$60\!\cdots\!53$$$$T^{61} +$$$$53\!\cdots\!91$$$$T^{62} -$$$$46\!\cdots\!82$$$$T^{63} +$$$$39\!\cdots\!79$$$$T^{64} -$$$$33\!\cdots\!59$$$$T^{65} +$$$$28\!\cdots\!20$$$$T^{66} -$$$$23\!\cdots\!79$$$$T^{67} +$$$$33\!\cdots\!26$$$$p T^{68} -$$$$16\!\cdots\!63$$$$T^{69} +$$$$13\!\cdots\!99$$$$T^{70} -$$$$10\!\cdots\!41$$$$T^{71} +$$$$86\!\cdots\!86$$$$T^{72} -$$$$68\!\cdots\!96$$$$T^{73} +$$$$54\!\cdots\!89$$$$T^{74} -$$$$42\!\cdots\!36$$$$T^{75} +$$$$33\!\cdots\!14$$$$T^{76} -$$$$25\!\cdots\!14$$$$T^{77} +$$$$33\!\cdots\!14$$$$p T^{78} -$$$$42\!\cdots\!36$$$$p^{2} T^{79} +$$$$54\!\cdots\!89$$$$p^{3} T^{80} -$$$$68\!\cdots\!96$$$$p^{4} T^{81} +$$$$86\!\cdots\!86$$$$p^{5} T^{82} -$$$$10\!\cdots\!41$$$$p^{6} T^{83} +$$$$13\!\cdots\!99$$$$p^{7} T^{84} -$$$$16\!\cdots\!63$$$$p^{8} T^{85} +$$$$33\!\cdots\!26$$$$p^{10} T^{86} -$$$$23\!\cdots\!79$$$$p^{10} T^{87} +$$$$28\!\cdots\!20$$$$p^{11} T^{88} -$$$$33\!\cdots\!59$$$$p^{12} T^{89} +$$$$39\!\cdots\!79$$$$p^{13} T^{90} -$$$$46\!\cdots\!82$$$$p^{14} T^{91} +$$$$53\!\cdots\!91$$$$p^{15} T^{92} -$$$$60\!\cdots\!53$$$$p^{16} T^{93} +$$$$69\!\cdots\!88$$$$p^{17} T^{94} -$$$$77\!\cdots\!88$$$$p^{18} T^{95} +$$$$87\!\cdots\!03$$$$p^{19} T^{96} -$$$$95\!\cdots\!58$$$$p^{20} T^{97} +$$$$10\!\cdots\!24$$$$p^{21} T^{98} -$$$$11\!\cdots\!74$$$$p^{22} T^{99} +$$$$12\!\cdots\!01$$$$p^{23} T^{100} -$$$$13\!\cdots\!79$$$$p^{24} T^{101} +$$$$13\!\cdots\!75$$$$p^{25} T^{102} -$$$$14\!\cdots\!22$$$$p^{26} T^{103} +$$$$14\!\cdots\!74$$$$p^{27} T^{104} -$$$$15\!\cdots\!59$$$$p^{28} T^{105} +$$$$15\!\cdots\!12$$$$p^{29} T^{106} -$$$$15\!\cdots\!61$$$$p^{30} T^{107} +$$$$15\!\cdots\!04$$$$p^{31} T^{108} -$$$$14\!\cdots\!74$$$$p^{32} T^{109} +$$$$14\!\cdots\!84$$$$p^{33} T^{110} -$$$$13\!\cdots\!64$$$$p^{34} T^{111} +$$$$12\!\cdots\!97$$$$p^{35} T^{112} -$$$$12\!\cdots\!55$$$$p^{36} T^{113} +$$$$11\!\cdots\!45$$$$p^{37} T^{114} -$$$$10\!\cdots\!68$$$$p^{38} T^{115} +$$$$91\!\cdots\!75$$$$p^{39} T^{116} -$$$$80\!\cdots\!61$$$$p^{40} T^{117} +$$$$70\!\cdots\!98$$$$p^{41} T^{118} -$$$$60\!\cdots\!55$$$$p^{42} T^{119} +$$$$51\!\cdots\!68$$$$p^{43} T^{120} -$$$$42\!\cdots\!74$$$$p^{44} T^{121} +$$$$35\!\cdots\!57$$$$p^{45} T^{122} -$$$$28\!\cdots\!90$$$$p^{46} T^{123} +$$$$22\!\cdots\!57$$$$p^{47} T^{124} -$$$$17\!\cdots\!89$$$$p^{48} T^{125} +$$$$13\!\cdots\!37$$$$p^{49} T^{126} -$$$$10\!\cdots\!42$$$$p^{50} T^{127} +$$$$77\!\cdots\!19$$$$p^{51} T^{128} -$$$$55\!\cdots\!07$$$$p^{52} T^{129} +$$$$39\!\cdots\!33$$$$p^{53} T^{130} -$$$$27\!\cdots\!16$$$$p^{54} T^{131} +$$$$18\!\cdots\!40$$$$p^{55} T^{132} -$$$$12\!\cdots\!82$$$$p^{56} T^{133} +$$$$81\!\cdots\!01$$$$p^{57} T^{134} -$$$$50\!\cdots\!80$$$$p^{58} T^{135} +$$$$31\!\cdots\!48$$$$p^{59} T^{136} -$$$$18\!\cdots\!09$$$$p^{60} T^{137} +$$$$10\!\cdots\!70$$$$p^{61} T^{138} -$$$$59\!\cdots\!31$$$$p^{62} T^{139} +$$$$33\!\cdots\!80$$$$p^{63} T^{140} - 16703252743035726470 p^{64} T^{141} + 870895704497822983 p^{65} T^{142} - 39982826596819965 p^{66} T^{143} + 1927674749660257 p^{67} T^{144} - 79135234503731 p^{68} T^{145} + 3485199416669 p^{69} T^{146} - 124185488348 p^{70} T^{147} + 4915483212 p^{71} T^{148} - 144663374 p^{72} T^{149} + 5031181 p^{73} T^{150} - 111010 p^{74} T^{151} + 3281 p^{75} T^{152} - 42 p^{76} T^{153} + p^{77} T^{154}$$
61 $$1 + 31 T + 2861 T^{2} + 77225 T^{3} + 3969850 T^{4} + 95651011 T^{5} + 3590608929 T^{6} + 78611522289 T^{7} + 2394031588845 T^{8} + 791224792010 p T^{9} + 1259731199371166 T^{10} + 23628160194186241 T^{11} + 546389037786209820 T^{12} + 157589780589269916 p T^{13} +$$$$20\!\cdots\!03$$$$T^{14} + 54831351357996516414 p T^{15} +$$$$64\!\cdots\!45$$$$T^{16} +$$$$10\!\cdots\!52$$$$T^{17} +$$$$18\!\cdots\!16$$$$T^{18} +$$$$27\!\cdots\!03$$$$T^{19} +$$$$46\!\cdots\!08$$$$T^{20} +$$$$66\!\cdots\!20$$$$T^{21} +$$$$10\!\cdots\!36$$$$T^{22} +$$$$14\!\cdots\!75$$$$T^{23} +$$$$22\!\cdots\!04$$$$T^{24} +$$$$29\!\cdots\!60$$$$T^{25} +$$$$42\!\cdots\!98$$$$T^{26} +$$$$55\!\cdots\!49$$$$T^{27} +$$$$76\!\cdots\!29$$$$T^{28} +$$$$95\!\cdots\!15$$$$T^{29} +$$$$12\!\cdots\!46$$$$T^{30} +$$$$15\!\cdots\!62$$$$T^{31} +$$$$32\!\cdots\!18$$$$p T^{32} +$$$$23\!\cdots\!03$$$$T^{33} +$$$$28\!\cdots\!65$$$$T^{34} +$$$$33\!\cdots\!28$$$$T^{35} +$$$$39\!\cdots\!31$$$$T^{36} +$$$$44\!\cdots\!18$$$$T^{37} +$$$$51\!\cdots\!21$$$$T^{38} +$$$$56\!\cdots\!94$$$$T^{39} +$$$$64\!\cdots\!42$$$$T^{40} +$$$$68\!\cdots\!57$$$$T^{41} +$$$$76\!\cdots\!23$$$$T^{42} +$$$$79\!\cdots\!61$$$$T^{43} +$$$$85\!\cdots\!73$$$$T^{44} +$$$$87\!\cdots\!50$$$$T^{45} +$$$$92\!\cdots\!04$$$$T^{46} +$$$$91\!\cdots\!79$$$$T^{47} +$$$$94\!\cdots\!66$$$$T^{48} +$$$$92\!\cdots\!61$$$$T^{49} +$$$$93\!\cdots\!36$$$$T^{50} +$$$$89\!\cdots\!31$$$$T^{51} +$$$$89\!\cdots\!11$$$$T^{52} +$$$$83\!\cdots\!62$$$$T^{53} +$$$$81\!\cdots\!26$$$$T^{54} +$$$$75\!\cdots\!35$$$$T^{55} +$$$$71\!\cdots\!36$$$$T^{56} +$$$$65\!\cdots\!42$$$$T^{57} +$$$$60\!\cdots\!79$$$$T^{58} +$$$$54\!\cdots\!18$$$$T^{59} +$$$$49\!\cdots\!94$$$$T^{60} +$$$$43\!\cdots\!57$$$$T^{61} +$$$$39\!\cdots\!42$$$$T^{62} +$$$$33\!\cdots\!35$$$$T^{63} +$$$$30\!\cdots\!23$$$$T^{64} +$$$$41\!\cdots\!82$$$$p T^{65} +$$$$22\!\cdots\!98$$$$T^{66} +$$$$18\!\cdots\!89$$$$T^{67} +$$$$15\!\cdots\!87$$$$T^{68} +$$$$13\!\cdots\!72$$$$T^{69} +$$$$11\!\cdots\!84$$$$T^{70} +$$$$89\!\cdots\!37$$$$T^{71} +$$$$73\!\cdots\!74$$$$T^{72} +$$$$58\!\cdots\!74$$$$T^{73} +$$$$47\!\cdots\!92$$$$T^{74} +$$$$37\!\cdots\!99$$$$T^{75} +$$$$30\!\cdots\!90$$$$T^{76} +$$$$23\!\cdots\!98$$$$T^{77} +$$$$30\!\cdots\!90$$$$p T^{78} +$$$$37\!\cdots\!99$$$$p^{2} T^{79} +$$$$47\!\cdots\!92$$$$p^{3} T^{80} +$$$$58\!\cdots\!74$$$$p^{4} T^{81} +$$$$73\!\cdots\!74$$$$p^{5} T^{82} +$$$$89\!\cdots\!37$$$$p^{6} T^{83} +$$$$11\!\cdots\!84$$$$p^{7} T^{84} +$$$$13\!\cdots\!72$$$$p^{8} T^{85} +$$$$15\!\cdots\!87$$$$p^{9} T^{86} +$$$$18\!\cdots\!89$$$$p^{10} T^{87} +$$$$22\!\cdots\!98$$$$p^{11} T^{88} +$$$$41\!\cdots\!82$$$$p^{13} T^{89} +$$$$30\!\cdots\!23$$$$p^{13} T^{90} +$$$$33\!\cdots\!35$$$$p^{14} T^{91} +$$$$39\!\cdots\!42$$$$p^{15} T^{92} +$$$$43\!\cdots\!57$$$$p^{16} T^{93} +$$$$49\!\cdots\!94$$$$p^{17} T^{94} +$$$$54\!\cdots\!18$$$$p^{18} T^{95} +$$$$60\!\cdots\!79$$$$p^{19} T^{96} +$$$$65\!\cdots\!42$$$$p^{20} T^{97} +$$$$71\!\cdots\!36$$$$p^{21} T^{98} +$$$$75\!\cdots\!35$$$$p^{22} T^{99} +$$$$81\!\cdots\!26$$$$p^{23} T^{100} +$$$$83\!\cdots\!62$$$$p^{24} T^{101} +$$$$89\!\cdots\!11$$$$p^{25} T^{102} +$$$$89\!\cdots\!31$$$$p^{26} T^{103} +$$$$93\!\cdots\!36$$$$p^{27} T^{104} +$$$$92\!\cdots\!61$$$$p^{28} T^{105} +$$$$94\!\cdots\!66$$$$p^{29} T^{106} +$$$$91\!\cdots\!79$$$$p^{30} T^{107} +$$$$92\!\cdots\!04$$$$p^{31} T^{108} +$$$$87\!\cdots\!50$$$$p^{32} T^{109} +$$$$85\!\cdots\!73$$$$p^{33} T^{110} +$$$$79\!\cdots\!61$$$$p^{34} T^{111} +$$$$76\!\cdots\!23$$$$p^{35} T^{112} +$$$$68\!\cdots\!57$$$$p^{36} T^{113} +$$$$64\!\cdots\!42$$$$p^{37} T^{114} +$$$$56\!\cdots\!94$$$$p^{38} T^{115} +$$$$51\!\cdots\!21$$$$p^{39} T^{116} +$$$$44\!\cdots\!18$$$$p^{40} T^{117} +$$$$39\!\cdots\!31$$$$p^{41} T^{118} +$$$$33\!\cdots\!28$$$$p^{42} T^{119} +$$$$28\!\cdots\!65$$$$p^{43} T^{120} +$$$$23\!\cdots\!03$$$$p^{44} T^{121} +$$$$32\!\cdots\!18$$$$p^{46} T^{122} +$$$$15\!\cdots\!62$$$$p^{46} T^{123} +$$$$12\!\cdots\!46$$$$p^{47} T^{124} +$$$$95\!\cdots\!15$$$$p^{48} T^{125} +$$$$76\!\cdots\!29$$$$p^{49} T^{126} +$$$$55\!\cdots\!49$$$$p^{50} T^{127} +$$$$42\!\cdots\!98$$$$p^{51} T^{128} +$$$$29\!\cdots\!60$$$$p^{52} T^{129} +$$$$22\!\cdots\!04$$$$p^{53} T^{130} +$$$$14\!\cdots\!75$$$$p^{54} T^{131} +$$$$10\!\cdots\!36$$$$p^{55} T^{132} +$$$$66\!\cdots\!20$$$$p^{56} T^{133} +$$$$46\!\cdots\!08$$$$p^{57} T^{134} +$$$$27\!\cdots\!03$$$$p^{58} T^{135} +$$$$18\!\cdots\!16$$$$p^{59} T^{136} +$$$$10\!\cdots\!52$$$$p^{60} T^{137} +$$$$64\!\cdots\!45$$$$p^{61} T^{138} + 54831351357996516414 p^{63} T^{139} +$$$$20\!\cdots\!03$$$$p^{63} T^{140} + 157589780589269916 p^{65} T^{141} + 546389037786209820 p^{65} T^{142} + 23628160194186241 p^{66} T^{143} + 1259731199371166 p^{67} T^{144} + 791224792010 p^{69} T^{145} + 2394031588845 p^{69} T^{146} + 78611522289 p^{70} T^{147} + 3590608929 p^{71} T^{148} + 95651011 p^{72} T^{149} + 3969850 p^{73} T^{150} + 77225 p^{74} T^{151} + 2861 p^{75} T^{152} + 31 p^{76} T^{153} + p^{77} T^{154}$$
67 $$1 + T + 2644 T^{2} + 2045 T^{3} + 3504010 T^{4} + 1929663 T^{5} + 3102712671 T^{6} + 1029687433 T^{7} + 2064657996221 T^{8} + 241790670241 T^{9} + 1101110605070290 T^{10} - 102807184047396 T^{11} + 490168628429711595 T^{12} - 146721135612176873 T^{13} +$$$$18\!\cdots\!09$$$$T^{14} - 93752788792849997742 T^{15} +$$$$93\!\cdots\!49$$$$p T^{16} -$$$$43\!\cdots\!46$$$$T^{17} +$$$$18\!\cdots\!31$$$$T^{18} -$$$$16\!\cdots\!28$$$$T^{19} +$$$$50\!\cdots\!41$$$$T^{20} -$$$$53\!\cdots\!80$$$$T^{21} +$$$$12\!\cdots\!21$$$$T^{22} -$$$$15\!\cdots\!02$$$$T^{23} +$$$$27\!\cdots\!11$$$$T^{24} -$$$$39\!\cdots\!75$$$$T^{25} +$$$$56\!\cdots\!51$$$$T^{26} -$$$$90\!\cdots\!04$$$$T^{27} +$$$$10\!\cdots\!40$$$$T^{28} -$$$$19\!\cdots\!32$$$$T^{29} +$$$$19\!\cdots\!05$$$$T^{30} -$$$$37\!\cdots\!71$$$$T^{31} +$$$$33\!\cdots\!41$$$$T^{32} -$$$$68\!\cdots\!05$$$$T^{33} +$$$$52\!\cdots\!63$$$$T^{34} -$$$$11\!\cdots\!36$$$$T^{35} +$$$$78\!\cdots\!42$$$$T^{36} -$$$$18\!\cdots\!98$$$$T^{37} +$$$$11\!\cdots\!32$$$$T^{38} -$$$$27\!\cdots\!45$$$$T^{39} +$$$$15\!\cdots\!93$$$$T^{40} -$$$$39\!\cdots\!72$$$$T^{41} +$$$$19\!\cdots\!57$$$$T^{42} -$$$$52\!\cdots\!14$$$$T^{43} +$$$$23\!\cdots\!94$$$$T^{44} -$$$$66\!\cdots\!81$$$$T^{45} +$$$$27\!\cdots\!93$$$$T^{46} -$$$$81\!\cdots\!26$$$$T^{47} +$$$$31\!\cdots\!24$$$$T^{48} -$$$$94\!\cdots\!41$$$$T^{49} +$$$$33\!\cdots\!52$$$$T^{50} -$$$$10\!\cdots\!09$$$$T^{51} +$$$$35\!\cdots\!85$$$$T^{52} -$$$$11\!\cdots\!65$$$$T^{53} +$$$$34\!\cdots\!67$$$$T^{54} -$$$$11\!\cdots\!43$$$$T^{55} +$$$$33\!\cdots\!78$$$$T^{56} -$$$$11\!\cdots\!33$$$$T^{57} +$$$$31\!\cdots\!44$$$$T^{58} -$$$$10\!\cdots\!42$$$$T^{59} +$$$$27\!\cdots\!03$$$$T^{60} -$$$$94\!\cdots\!46$$$$T^{61} +$$$$23\!\cdots\!00$$$$T^{62} -$$$$82\!\cdots\!46$$$$T^{63} +$$$$20\!\cdots\!89$$$$T^{64} -$$$$68\!\cdots\!02$$$$T^{65} +$$$$16\!\cdots\!05$$$$T^{66} -$$$$55\!\cdots\!33$$$$T^{67} +$$$$12\!\cdots\!26$$$$T^{68} -$$$$43\!\cdots\!02$$$$T^{69} +$$$$96\!\cdots\!42$$$$T^{70} -$$$$33\!\cdots\!54$$$$T^{71} +$$$$70\!\cdots\!17$$$$T^{72} -$$$$24\!\cdots\!16$$$$T^{73} +$$$$50\!\cdots\!33$$$$T^{74} -$$$$17\!\cdots\!11$$$$T^{75} +$$$$34\!\cdots\!60$$$$T^{76} -$$$$11\!\cdots\!04$$$$T^{77} +$$$$34\!\cdots\!60$$$$p T^{78} -$$$$17\!\cdots\!11$$$$p^{2} T^{79} +$$$$50\!\cdots\!33$$$$p^{3} T^{80} -$$$$24\!\cdots\!16$$$$p^{4} T^{81} +$$$$70\!\cdots\!17$$$$p^{5} T^{82} -$$$$33\!\cdots\!54$$$$p^{6} T^{83} +$$$$96\!\cdots\!42$$$$p^{7} T^{84} -$$$$43\!\cdots\!02$$$$p^{8} T^{85} +$$$$12\!\cdots\!26$$$$p^{9} T^{86} -$$$$55\!\cdots\!33$$$$p^{10} T^{87} +$$$$16\!\cdots\!05$$$$p^{11} T^{88} -$$$$68\!\cdots\!02$$$$p^{12} T^{89} +$$$$20\!\cdots\!89$$$$p^{13} T^{90} -$$$$82\!\cdots\!46$$$$p^{14} T^{91} +$$$$23\!\cdots\!00$$$$p^{15} T^{92} -$$$$94\!\cdots\!46$$$$p^{16} T^{93} +$$$$27\!\cdots\!03$$$$p^{17} T^{94} -$$$$10\!\cdots\!42$$$$p^{18} T^{95} +$$$$31\!\cdots\!44$$$$p^{19} T^{96} -$$$$11\!\cdots\!33$$$$p^{20} T^{97} +$$$$33\!\cdots\!78$$$$p^{21} T^{98} -$$$$11\!\cdots\!43$$$$p^{22} T^{99} +$$$$34\!\cdots\!67$$$$p^{23} T^{100} -$$$$11\!\cdots\!65$$$$p^{24} T^{101} +$$$$35\!\cdots\!85$$$$p^{25} T^{102} -$$$$10\!\cdots\!09$$$$p^{26} T^{103} +$$$$33\!\cdots\!52$$$$p^{27} T^{104} -$$$$94\!\cdots\!41$$$$p^{28} T^{105} +$$$$31\!\cdots\!24$$$$p^{29} T^{106} -$$$$81\!\cdots\!26$$$$p^{30} T^{107} +$$$$27\!\cdots\!93$$$$p^{31} T^{108} -$$$$66\!\cdots\!81$$$$p^{32} T^{109} +$$$$23\!\cdots\!94$$$$p^{33} T^{110} -$$$$52\!\cdots\!14$$$$p^{34} T^{111} +$$$$19\!\cdots\!57$$$$p^{35} T^{112} -$$$$39\!\cdots\!72$$$$p^{36} T^{113} +$$$$15\!\cdots\!93$$$$p^{37} T^{114} -$$$$27\!\cdots\!45$$$$p^{38} T^{115} +$$$$11\!\cdots\!32$$$$p^{39} T^{116} -$$$$18\!\cdots\!98$$$$p^{40} T^{117} +$$$$78\!\cdots\!42$$$$p^{41} T^{118} -$$$$11\!\cdots\!36$$$$p^{42} T^{119} +$$$$52\!\cdots\!63$$$$p^{43} T^{120} -$$$$68\!\cdots\!05$$$$p^{44} T^{121} +$$$$33\!\cdots\!41$$$$p^{45} T^{122} -$$$$37\!\cdots\!71$$$$p^{46} T^{123} +$$$$19\!\cdots\!05$$$$p^{47} T^{124} -$$$$19\!\cdots\!32$$$$p^{48} T^{125} +$$$$10\!\cdots\!40$$$$p^{49} T^{126} -$$$$90\!\cdots\!04$$$$p^{50} T^{127} +$$$$56\!\cdots\!51$$$$p^{51} T^{128} -$$$$39\!\cdots\!75$$$$p^{52} T^{129} +$$$$27\!\cdots\!11$$$$p^{53} T^{130} -$$$$15\!\cdots\!02$$$$p^{54} T^{131} +$$$$12\!\cdots\!21$$$$p^{55} T^{132} -$$$$53\!\cdots\!80$$$$p^{56} T^{133} +$$$$50\!\cdots\!41$$$$p^{57} T^{134} -$$$$16\!\cdots\!28$$$$p^{58} T^{135} +$$$$18\!\cdots\!31$$$$p^{59} T^{136} -$$$$43\!\cdots\!46$$$$p^{60} T^{137} +$$$$93\!\cdots\!49$$$$p^{62} T^{138} - 93752788792849997742 p^{62} T^{139} +$$$$18\!\cdots\!09$$$$p^{63} T^{140} - 146721135612176873 p^{64} T^{141} + 490168628429711595 p^{65} T^{142} - 102807184047396 p^{66} T^{143} + 1101110605070290 p^{67} T^{144} + 241790670241 p^{68} T^{145} + 2064657996221 p^{69} T^{146} + 1029687433 p^{70} T^{147} + 3102712671 p^{71} T^{148} + 1929663 p^{72} T^{149} + 3504010 p^{73} T^{150} + 2045 p^{74} T^{151} + 2644 p^{75} T^{152} + p^{76} T^{153} + p^{77} T^{154}$$
71 $$1 - 58 T + 4112 T^{2} - 175858 T^{3} + 7677810 T^{4} - 267060014 T^{5} + 9079513754 T^{6} - 270863529711 T^{7} + 7807614887013 T^{8} - 206415798497575 T^{9} + 5263870027021224 T^{10} - 126062858435869571 T^{11} + 2916563715039560024 T^{12} - 64262948819932640554 T^{13} +$$$$13\!\cdots\!71$$$$T^{14} -$$$$28\!\cdots\!64$$$$T^{15} +$$$$55\!\cdots\!18$$$$T^{16} -$$$$10\!\cdots\!59$$$$T^{17} +$$$$20\!\cdots\!95$$$$T^{18} -$$$$36\!\cdots\!83$$$$T^{19} +$$$$65\!\cdots\!11$$$$T^{20} -$$$$11\!\cdots\!32$$$$T^{21} +$$$$19\!\cdots\!16$$$$T^{22} -$$$$31\!\cdots\!62$$$$T^{23} +$$$$51\!\cdots\!93$$$$T^{24} -$$$$80\!\cdots\!80$$$$T^{25} +$$$$12\!\cdots\!73$$$$T^{26} -$$$$19\!\cdots\!29$$$$T^{27} +$$$$28\!\cdots\!40$$$$T^{28} -$$$$42\!\cdots\!09$$$$T^{29} +$$$$60\!\cdots\!56$$$$T^{30} -$$$$86\!\cdots\!33$$$$T^{31} +$$$$12\!\cdots\!70$$$$T^{32} -$$$$16\!\cdots\!26$$$$T^{33} +$$$$22\!\cdots\!23$$$$T^{34} -$$$$29\!\cdots\!29$$$$T^{35} +$$$$39\!\cdots\!77$$$$T^{36} -$$$$50\!\cdots\!75$$$$T^{37} +$$$$64\!\cdots\!00$$$$T^{38} -$$$$81\!\cdots\!50$$$$T^{39} +$$$$10\!\cdots\!20$$$$T^{40} -$$$$12\!\cdots\!29$$$$T^{41} +$$$$15\!\cdots\!92$$$$T^{42} -$$$$18\!\cdots\!27$$$$T^{43} +$$$$21\!\cdots\!77$$$$T^{44} -$$$$24\!\cdots\!58$$$$T^{45} +$$$$28\!\cdots\!58$$$$T^{46} -$$$$32\!\cdots\!90$$$$T^{47} +$$$$37\!\cdots\!70$$$$T^{48} -$$$$41\!\cdots\!36$$$$T^{49} +$$$$45\!\cdots\!59$$$$T^{50} -$$$$49\!\cdots\!51$$$$T^{51} +$$$$53\!\cdots\!42$$$$T^{52} -$$$$57\!\cdots\!48$$$$T^{53} +$$$$60\!\cdots\!38$$$$T^{54} -$$$$63\!\cdots\!16$$$$T^{55} +$$$$65\!\cdots\!59$$$$T^{56} -$$$$66\!\cdots\!08$$$$T^{57} +$$$$67\!\cdots\!29$$$$T^{58} -$$$$67\!\cdots\!53$$$$T^{59} +$$$$67\!\cdots\!13$$$$T^{60} -$$$$66\!\cdots\!58$$$$T^{61} +$$$$64\!\cdots\!40$$$$T^{62} -$$$$62\!\cdots\!57$$$$T^{63} +$$$$59\!\cdots\!42$$$$T^{64} -$$$$56\!\cdots\!22$$$$T^{65} +$$$$52\!\cdots\!79$$$$T^{66} -$$$$48\!\cdots\!69$$$$T^{67} +$$$$45\!\cdots\!23$$$$T^{68} -$$$$41\!\cdots\!75$$$$T^{69} +$$$$37\!\cdots\!41$$$$T^{70} -$$$$33\!\cdots\!91$$$$T^{71} +$$$$29\!\cdots\!61$$$$T^{72} -$$$$25\!\cdots\!71$$$$T^{73} +$$$$22\!\cdots\!45$$$$T^{74} -$$$$19\!\cdots\!00$$$$T^{75} +$$$$16\!\cdots\!77$$$$T^{76} -$$$$14\!\cdots\!74$$$$T^{77} +$$$$16\!\cdots\!77$$$$p T^{78} -$$$$19\!\cdots\!00$$$$p^{2} T^{79} +$$$$22\!\cdots\!45$$$$p^{3} T^{80} -$$$$25\!\cdots\!71$$$$p^{4} T^{81} +$$$$29\!\cdots\!61$$$$p^{5} T^{82} -$$$$33\!\cdots\!91$$$$p^{6} T^{83} +$$$$37\!\cdots\!41$$$$p^{7} T^{84} -$$$$41\!\cdots\!75$$$$p^{8} T^{85} +$$$$45\!\cdots\!23$$$$p^{9} T^{86} -$$$$48\!\cdots\!69$$$$p^{10} T^{87} +$$$$52\!\cdots\!79$$$$p^{11} T^{88} -$$$$56\!\cdots\!22$$$$p^{12} T^{89} +$$$$59\!\cdots\!42$$$$p^{13} T^{90} -$$$$62\!\cdots\!57$$$$p^{14} T^{91} +$$$$64\!\cdots\!40$$$$p^{15} T^{92} -$$$$66\!\cdots\!58$$$$p^{16} T^{93} +$$$$67\!\cdots\!13$$$$p^{17} T^{94} -$$$$67\!\cdots\!53$$$$p^{18} T^{95} +$$$$67\!\cdots\!29$$$$p^{19} T^{96} -$$$$66\!\cdots\!08$$$$p^{20} T^{97} +$$$$65\!\cdots\!59$$$$p^{21} T^{98} -$$$$63\!\cdots\!16$$$$p^{22} T^{99} +$$$$60\!\cdots\!38$$$$p^{23} T^{100} -$$$$57\!\cdots\!48$$$$p^{24} T^{101} +$$$$53\!\cdots\!42$$$$p^{25} T^{102} -$$$$49\!\cdots\!51$$$$p^{26} T^{103} +$$$$45\!\cdots\!59$$$$p^{27} T^{104} -$$$$41\!\cdots\!36$$$$p^{28} T^{105} +$$$$37\!\cdots\!70$$$$p^{29} T^{106} -$$$$32\!\cdots\!90$$$$p^{30} T^{107} +$$$$28\!\cdots\!58$$$$p^{31} T^{108} -$$$$24\!\cdots\!58$$$$p^{32} T^{109} +$$$$21\!\cdots\!77$$$$p^{33} T^{110} -$$$$18\!\cdots\!27$$$$p^{34} T^{111} +$$$$15\!\cdots\!92$$$$p^{35} T^{112} -$$$$12\!\cdots\!29$$$$p^{36} T^{113} +$$$$10\!\cdots\!20$$$$p^{37} T^{114} -$$$$81\!\cdots\!50$$$$p^{38} T^{115} +$$$$64\!\cdots\!00$$$$p^{39} T^{116} -$$$$50\!\cdots\!75$$$$p^{40} T^{117} +$$$$39\!\cdots\!77$$$$p^{41} T^{118} -$$$$29\!\cdots\!29$$$$p^{42} T^{119} +$$$$22\!\cdots\!23$$$$p^{43} T^{120} -$$$$16\!\cdots\!26$$$$p^{44} T^{121} +$$$$12\!\cdots\!70$$$$p^{45} T^{122} -$$$$86\!\cdots\!33$$$$p^{46} T^{123} +$$$$60\!\cdots\!56$$$$p^{47} T^{124} -$$$$42\!\cdots\!09$$$$p^{48} T^{125} +$$$$28\!\cdots\!40$$$$p^{49} T^{126} -$$$$19\!\cdots\!29$$$$p^{50} T^{127} +$$$$12\!\cdots\!73$$$$p^{51} T^{128} -$$$$80\!\cdots\!80$$$$p^{52} T^{129} +$$$$51\!\cdots\!93$$$$p^{53} T^{130} -$$$$31\!\cdots\!62$$$$p^{54} T^{131} +$$$$19\!\cdots\!16$$$$p^{55} T^{132} -$$$$11\!\cdots\!32$$$$p^{56} T^{133} +$$$$65\!\cdots\!11$$$$p^{57} T^{134} -$$$$36\!\cdots\!83$$$$p^{58} T^{135} +$$$$20\!\cdots\!95$$$$p^{59} T^{136} -$$$$10\!\cdots\!59$$$$p^{60} T^{137} +$$$$55\!\cdots\!18$$$$p^{61} T^{138} -$$$$28\!\cdots\!64$$$$p^{62} T^{139} +$$$$13\!\cdots\!71$$$$p^{63} T^{140} - 64262948819932640554 p^{64} T^{141} + 2916563715039560024 p^{65} T^{142} - 126062858435869571 p^{66} T^{143} + 5263870027021224 p^{67} T^{144} - 206415798497575 p^{68} T^{145} + 7807614887013 p^{69} T^{146} - 270863529711 p^{70} T^{147} + 9079513754 p^{71} T^{148} - 267060014 p^{72} T^{149} + 7677810 p^{73} T^{150} - 175858 p^{74} T^{151} + 4112 p^{75} T^{152} - 58 p^{76} T^{153} + p^{77} T^{154}$$
73 $$1 - 35 T + 3465 T^{2} - 106086 T^{3} + 5842098 T^{4} - 159988086 T^{5} + 6432015064 T^{6} - 160150297920 T^{7} + 5224998455219 T^{8} - 119767188898010 T^{9} + 3350914396962404 T^{10} - 71405626395464054 T^{11} + 1771362883264984468 T^{12} - 35367794994281976996 T^{13} + 10894260540515323014 p T^{14} -$$$$14\!\cdots\!26$$$$T^{15} +$$$$31\!\cdots\!04$$$$T^{16} -$$$$55\!\cdots\!24$$$$T^{17} +$$$$10\!\cdots\!85$$$$T^{18} -$$$$18\!\cdots\!83$$$$T^{19} +$$$$32\!\cdots\!08$$$$T^{20} -$$$$53\!\cdots\!41$$$$T^{21} +$$$$91\!\cdots\!10$$$$T^{22} -$$$$14\!\cdots\!72$$$$T^{23} +$$$$23\!\cdots\!92$$$$T^{24} -$$$$34\!\cdots\!09$$$$T^{25} +$$$$54\!\cdots\!20$$$$T^{26} -$$$$78\!\cdots\!84$$$$T^{27} +$$$$11\!\cdots\!11$$$$T^{28} -$$$$16\!\cdots\!90$$$$T^{29} +$$$$23\!\cdots\!15$$$$T^{30} -$$$$32\!\cdots\!25$$$$T^{31} +$$$$44\!\cdots\!83$$$$T^{32} -$$$$58\!\cdots\!34$$$$T^{33} +$$$$79\!\cdots\!07$$$$T^{34} -$$$$10\!\cdots\!11$$$$T^{35} +$$$$13\!\cdots\!34$$$$T^{36} -$$$$16\!\cdots\!90$$$$T^{37} +$$$$20\!\cdots\!26$$$$T^{38} -$$$$25\!\cdots\!24$$$$T^{39} +$$$$42\!\cdots\!13$$$$p T^{40} -$$$$36\!\cdots\!10$$$$T^{41} +$$$$44\!\cdots\!71$$$$T^{42} -$$$$51\!\cdots\!67$$$$T^{43} +$$$$59\!\cdots\!04$$$$T^{44} -$$$$67\!\cdots\!72$$$$T^{45} +$$$$77\!\cdots\!85$$$$T^{46} -$$$$85\!\cdots\!42$$$$T^{47} +$$$$96\!\cdots\!47$$$$T^{48} -$$$$10\!\cdots\!42$$$$T^{49} +$$$$11\!\cdots\!97$$$$T^{50} -$$$$12\!\cdots\!29$$$$T^{51} +$$$$13\!\cdots\!04$$$$T^{52} -$$$$13\!\cdots\!47$$$$T^{53} +$$$$14\!\cdots\!35$$$$T^{54} -$$$$14\!\cdots\!52$$$$T^{55} +$$$$15\!\cdots\!66$$$$T^{56} -$$$$15\!\cdots\!06$$$$T^{57} +$$$$15\!\cdots\!15$$$$T^{58} -$$$$15\!\cdots\!19$$$$T^{59} +$$$$15\!\cdots\!12$$$$T^{60} -$$$$14\!\cdots\!83$$$$T^{61} +$$$$14\!\cdots\!32$$$$T^{62} -$$$$13\!\cdots\!67$$$$T^{63} +$$$$13\!\cdots\!18$$$$T^{64} -$$$$12\!\cdots\!73$$$$T^{65} +$$$$11\!\cdots\!42$$$$T^{66} -$$$$10\!\cdots\!30$$$$T^{67} +$$$$99\!\cdots\!00$$$$T^{68} -$$$$90\!\cdots\!94$$$$T^{69} +$$$$82\!\cdots\!43$$$$T^{70} -$$$$73\!\cdots\!69$$$$T^{71} +$$$$66\!\cdots\!72$$$$T^{72} -$$$$58\!\cdots\!49$$$$T^{73} +$$$$51\!\cdots\!63$$$$T^{74} -$$$$44\!\cdots\!40$$$$T^{75} +$$$$38\!\cdots\!41$$$$T^{76} -$$$$33\!\cdots\!46$$$$T^{77} +$$$$38\!\cdots\!41$$$$p T^{78} -$$$$44\!\cdots\!40$$$$p^{2} T^{79} +$$$$51\!\cdots\!63$$$$p^{3} T^{80} -$$$$58\!\cdots\!49$$$$p^{4} T^{81} +$$$$66\!\cdots\!72$$$$p^{5} T^{82} -$$$$73\!\cdots\!69$$$$p^{6} T^{83} +$$$$82\!\cdots\!43$$$$p^{7} T^{84} -$$$$90\!\cdots\!94$$$$p^{8} T^{85} +$$$$99\!\cdots\!00$$$$p^{9} T^{86} -$$$$10\!\cdots\!30$$$$p^{10} T^{87} +$$$$11\!\cdots\!42$$$$p^{11} T^{88} -$$$$12\!\cdots\!73$$$$p^{12} T^{89} +$$$$13\!\cdots\!18$$$$p^{13} T^{90} -$$$$13\!\cdots\!67$$$$p^{14} T^{91} +$$$$14\!\cdots\!32$$$$p^{15} T^{92} -$$$$14\!\cdots\!83$$$$p^{16} T^{93} +$$$$15\!\cdots\!12$$$$p^{17} T^{94} -$$$$15\!\cdots\!19$$$$p^{18} T^{95} +$$$$15\!\cdots\!15$$$$p^{19} T^{96} -$$$$15\!\cdots\!06$$$$p^{20} T^{97} +$$$$15\!\cdots\!66$$$$p^{21} T^{98} -$$$$14\!\cdots\!52$$$$p^{22} T^{99} +$$$$14\!\cdots\!35$$$$p^{23} T^{100} -$$$$13\!\cdots\!47$$$$p^{24} T^{101} +$$$$13\!\cdots\!04$$$$p^{25} T^{102} -$$$$12\!\cdots\!29$$$$p^{26} T^{103} +$$$$11\!\cdots\!97$$$$p^{27} T^{104} -$$$$10\!\cdots\!42$$$$p^{28} T^{105} +$$$$96\!\cdots\!47$$$$p^{29} T^{106} -$$$$85\!\cdots\!42$$$$p^{30} T^{107} +$$$$77\!\cdots\!85$$$$p^{31} T^{108} -$$$$67\!\cdots\!72$$$$p^{32} T^{109} +$$$$59\!\cdots\!04$$$$p^{33} T^{110} -$$$$51\!\cdots\!67$$$$p^{34} T^{111} +$$$$44\!\cdots\!71$$$$p^{35} T^{112} -$$$$36\!\cdots\!10$$$$p^{36} T^{113} +$$$$42\!\cdots\!13$$$$p^{38} T^{114} -$$$$25\!\cdots\!24$$$$p^{38} T^{115} +$$$$20\!\cdots\!26$$$$p^{39} T^{116} -$$$$16\!\cdots\!90$$$$p^{40} T^{117} +$$$$13\!\cdots\!34$$$$p^{41} T^{118} -$$$$10\!\cdots\!11$$$$p^{42} T^{119} +$$$$79\!\cdots\!07$$$$p^{43} T^{120} -$$$$58\!\cdots\!34$$$$p^{44} T^{121} +$$$$44\!\cdots\!83$$$$p^{45} T^{122} -$$$$32\!\cdots\!25$$$$p^{46} T^{123} +$$$$23\!\cdots\!15$$$$p^{47} T^{124} -$$$$16\!\cdots\!90$$$$p^{48} T^{125} +$$$$11\!\cdots\!11$$$$p^{49} T^{126} -$$$$78\!\cdots\!84$$$$p^{50} T^{127} +$$$$54\!\cdots\!20$$$$p^{51} T^{128} -$$$$34\!\cdots\!09$$$$p^{52} T^{129} +$$$$23\!\cdots\!92$$$$p^{53} T^{130} -$$$$14\!\cdots\!72$$$$p^{54} T^{131} +$$$$91\!\cdots\!10$$$$p^{55} T^{132} -$$$$53\!\cdots\!41$$$$p^{56} T^{133} +$$$$32\!\cdots\!08$$$$p^{57} T^{134} -$$$$18\!\cdots\!83$$$$p^{58} T^{135} +$$$$10\!\cdots\!85$$$$p^{59} T^{136} -$$$$55\!\cdots\!24$$$$p^{60} T^{137} +$$$$31\!\cdots\!04$$$$p^{61} T^{138} -$$$$14\!\cdots\!26$$$$p^{62} T^{139} + 10894260540515323014 p^{64} T^{140} - 35367794994281976996 p^{64} T^{141} + 1771362883264984468 p^{65} T^{142} - 71405626395464054 p^{66} T^{143} + 3350914396962404 p^{67} T^{144} - 119767188898010 p^{68} T^{145} + 5224998455219 p^{69} T^{146} - 160150297920 p^{70} T^{147} + 6432015064 p^{71} T^{148} - 159988086 p^{72} T^{149} + 5842098 p^{73} T^{150} - 106086 p^{74} T^{151} + 3465 p^{75} T^{152} - 35 p^{76} T^{153} + p^{77} T^{154}$$
79 $$1 - 25 T + 3447 T^{2} - 77566 T^{3} + 5803108 T^{4} - 118987461 T^{5} + 6384181264 T^{6} - 120396105903 T^{7} + 5176830121828 T^{8} - 90446162336333 T^{9} + 3307226601028602 T^{10} - 53838183538585169 T^{11} + 1736905818104649284 T^{12} - 26464854178148836682 T^{13} +$$$$77\!\cdots\!95$$$$T^{14} -$$$$11\!\cdots\!43$$$$T^{15} +$$$$29\!\cdots\!55$$$$T^{16} -$$$$40\!\cdots\!34$$$$T^{17} +$$$$10\!\cdots\!41$$$$T^{18} -$$$$12\!\cdots\!74$$$$T^{19} +$$$$30\!\cdots\!09$$$$T^{20} -$$$$36\!\cdots\!36$$$$T^{21} +$$$$83\!\cdots\!08$$$$T^{22} -$$$$94\!\cdots\!19$$$$T^{23} +$$$$20\!\cdots\!02$$$$T^{24} -$$$$22\!\cdots\!87$$$$T^{25} +$$$$47\!\cdots\!91$$$$T^{26} -$$$$48\!\cdots\!39$$$$T^{27} +$$$$99\!\cdots\!24$$$$T^{28} -$$$$96\!\cdots\!92$$$$T^{29} +$$$$19\!\cdots\!91$$$$T^{30} -$$$$17\!\cdots\!17$$$$T^{31} +$$$$35\!\cdots\!97$$$$T^{32} -$$$$31\!\cdots\!11$$$$T^{33} +$$$$61\!\cdots\!78$$$$T^{34} -$$$$51\!\cdots\!19$$$$T^{35} +$$$$10\!\cdots\!81$$$$T^{36} -$$$$78\!\cdots\!45$$$$T^{37} +$$$$15\!\cdots\!21$$$$T^{38} -$$$$11\!\cdots\!76$$$$T^{39} +$$$$22\!\cdots\!85$$$$T^{40} -$$$$15\!\cdots\!12$$$$T^{41} +$$$$31\!\cdots\!75$$$$T^{42} -$$$$20\!\cdots\!53$$$$T^{43} +$$$$42\!\cdots\!49$$$$T^{44} -$$$$26\!\cdots\!73$$$$T^{45} +$$$$54\!\cdots\!77$$$$T^{46} -$$$$31\!\cdots\!60$$$$T^{47} +$$$$66\!\cdots\!74$$$$T^{48} -$$$$36\!\cdots\!10$$$$T^{49} +$$$$79\!\cdots\!35$$$$T^{50} -$$$$40\!\cdots\!26$$$$T^{51} +$$$$90\!\cdots\!00$$$$T^{52} -$$$$55\!\cdots\!35$$$$p T^{53} +$$$$10\!\cdots\!23$$$$T^{54} -$$$$45\!\cdots\!40$$$$T^{55} +$$$$10\!\cdots\!73$$$$T^{56} -$$$$45\!\cdots\!08$$$$T^{57} +$$$$11\!\cdots\!67$$$$T^{58} -$$$$43\!\cdots\!56$$$$T^{59} +$$$$11\!\cdots\!33$$$$T^{60} -$$$$41\!\cdots\!28$$$$T^{61} +$$$$10\!\cdots\!35$$$$T^{62} -$$$$37\!\cdots\!66$$$$T^{63} +$$$$10\!\cdots\!06$$$$T^{64} -$$$$33\!\cdots\!86$$$$T^{65} +$$$$95\!\cdots\!81$$$$T^{66} -$$$$29\!\cdots\!68$$$$T^{67} +$$$$85\!\cdots\!38$$$$T^{68} -$$$$25\!\cdots\!63$$$$T^{69} +$$$$74\!\cdots\!10$$$$T^{70} -$$$$21\!\cdots\!53$$$$T^{71} +$$$$63\!\cdots\!44$$$$T^{72} -$$$$17\!\cdots\!94$$$$T^{73} +$$$$52\!\cdots\!00$$$$T^{74} -$$$$14\!\cdots\!97$$$$T^{75} +$$$$42\!\cdots\!82$$$$T^{76} -$$$$11\!\cdots\!18$$$$T^{77} +$$$$42\!\cdots\!82$$$$p T^{78} -$$$$14\!\cdots\!97$$$$p^{2} T^{79} +$$$$52\!\cdots\!00$$$$p^{3} T^{80} -$$$$17\!\cdots\!94$$$$p^{4} T^{81} +$$$$63\!\cdots\!44$$$$p^{5} T^{82} -$$$$21\!\cdots\!53$$$$p^{6} T^{83} +$$$$74\!\cdots\!10$$$$p^{7} T^{84} -$$$$25\!\cdots\!63$$$$p^{8} T^{85} +$$$$85\!\cdots\!38$$$$p^{9} T^{86} -$$$$29\!\cdots\!68$$$$p^{10} T^{87} +$$$$95\!\cdots\!81$$$$p^{11} T^{88} -$$$$33\!\cdots\!86$$$$p^{12} T^{89} +$$$$10\!\cdots\!06$$$$p^{13} T^{90} -$$$$37\!\cdots\!66$$$$p^{14} T^{91} +$$$$10\!\cdots\!35$$$$p^{15} T^{92} -$$$$41\!\cdots\!28$$$$p^{16} T^{93} +$$$$11\!\cdots\!33$$$$p^{17} T^{94} -$$$$43\!\cdots\!56$$$$p^{18} T^{95} +$$$$11\!\cdots\!67$$$$p^{19} T^{96} -$$$$45\!\cdots\!08$$$$p^{20} T^{97} +$$$$10\!\cdots\!73$$$$p^{21} T^{98} -$$$$45\!\cdots\!40$$$$p^{22} T^{99} +$$$$10\!\cdots\!23$$$$p^{23} T^{100} -$$$$55\!\cdots\!35$$$$p^{25} T^{101} +$$$$90\!\cdots\!00$$$$p^{25} T^{102} -$$$$40\!\cdots\!26$$$$p^{26} T^{103} +$$$$79\!\cdots\!35$$$$p^{27} T^{104} -$$$$36\!\cdots\!10$$$$p^{28} T^{105} +$$$$66\!\cdots\!74$$$$p^{29} T^{106} -$$$$31\!\cdots\!60$$$$p^{30} T^{107} +$$$$54\!\cdots\!77$$$$p^{31} T^{108} -$$$$26\!\cdots\!73$$$$p^{32} T^{109} +$$$$42\!\cdots\!49$$$$p^{33} T^{110} -$$$$20\!\cdots\!53$$$$p^{34} T^{111} +$$$$31\!\cdots\!75$$$$p^{35} T^{112} -$$$$15\!\cdots\!12$$$$p^{36} T^{113} +$$$$22\!\cdots\!85$$$$p^{37} T^{114} -$$$$11\!\cdots\!76$$$$p^{38} T^{115} +$$$$15\!\cdots\!21$$$$p^{39} T^{116} -$$$$78\!\cdots\!45$$$$p^{40} T^{117} +$$$$10\!\cdots\!81$$$$p^{41} T^{118} -$$$$51\!\cdots\!19$$$$p^{42} T^{119} +$$$$61\!\cdots\!78$$$$p^{43} T^{120} -$$$$31\!\cdots\!11$$$$p^{44} T^{121} +$$$$35\!\cdots\!97$$$$p^{45} T^{122} -$$$$17\!\cdots\!17$$$$p^{46} T^{123} +$$$$19\!\cdots\!91$$$$p^{47} T^{124} -$$$$96\!\cdots\!92$$$$p^{48} T^{125} +$$$$99\!\cdots\!24$$$$p^{49} T^{126} -$$$$48\!\cdots\!39$$$$p^{50} T^{127} +$$$$47\!\cdots\!91$$$$p^{51} T^{128} -$$$$22\!\cdots\!87$$$$p^{52} T^{129} +$$$$20\!\cdots\!02$$$$p^{53} T^{130} -$$$$94\!\cdots\!19$$$$p^{54} T^{131} +$$$$83\!\cdots\!08$$$$p^{55} T^{132} -$$$$36\!\cdots\!36$$$$p^{56} T^{133} +$$$$30\!\cdots\!09$$$$p^{57} T^{134} -$$$$12\!\cdots\!74$$$$p^{58} T^{135} +$$$$10\!\cdots\!41$$$$p^{59} T^{136} -$$$$40\!\cdots\!34$$$$p^{60} T^{137} +$$$$29\!\cdots\!55$$$$p^{61} T^{138} -$$$$11\!\cdots\!43$$$$p^{62} T^{139} +$$$$77\!\cdots\!95$$$$p^{63} T^{140} - 26464854178148836682 p^{64} T^{141} + 1736905818104649284 p^{65} T^{142} - 53838183538585169 p^{66} T^{143} + 3307226601028602 p^{67} T^{144} - 90446162336333 p^{68} T^{145} + 5176830121828 p^{69} T^{146} - 120396105903 p^{70} T^{147} + 6384181264 p^{71} T^{148} - 118987461 p^{72} T^{149} + 5803108 p^{73} T^{150} - 77566 p^{74} T^{151} + 3447 p^{75} T^{152} - 25 p^{76} T^{153} + p^{77} T^{154}$$
83 $$1 - 107T + 9.33e3T^{2} - 5.85e5T^{3} + 3.21e7T^{4} - 1.50e9T^{5} + 6.40e10T^{6} - 2.46e12T^{7} + 8.78e13T^{8} - 2.90e15T^{9} + 9.06e16T^{10} - 2.66e18T^{11} + 7.44e19T^{12} - 1.98e21T^{13} + 5.04e22T^{14} - 1.23e24T^{15} + 2.89e25T^{16} - 6.57e26T^{17} + 1.44e28T^{18} - 3.05e29T^{19} + 6.29e30T^{20} - 1.25e32T^{21} + 2.44e33T^{22} - 4.62e34T^{23} + 8.52e35T^{24} - 1.53e37T^{25} + 2.69e38T^{26} - 4.63e39T^{27} + 7.78e40T^{28} - 1.28e42T^{29} + 2.06e43T^{30} - 3.26e44T^{31} + 5.05e45T^{32} - 7.69e46T^{33} + 1.14e48T^{34} - 1.68e49T^{35} + 2.43e50T^{36} - 3.45e51T^{37} + 4.82e52T^{38} - 6.62e53T^{39} + 8.95e54T^{40} - 1.19e56T^{41} + 1.56e57T^{42} - 2.02e58T^{43} + 2.58e59T^{44} - 3.25e60T^{45} + 4.04e61T^{46} - 4.95e62T^{47} + 6.00e63T^{48} - 7.17e64T^{49} + 8.46e65T^{50} - 9.86e66T^{51} + 1.13e68T^{52} - 1.29e69T^{53} + 1.45e70T^{54} - 1.62e71T^{55} + 1.79e72T^{56} - 1.95e73T^{57} + 2.10e74T^{58} - 2.24e75T^{59} + 2.37e76T^{60} - 2.49e77T^{61} + 2.58e78T^{62} - 2.65e79T^{63} + 2.70e80T^{64} - 2.72e81T^{65} + 2.72e82T^{66} - 2.70e83T^{67} + 2.65e84T^{68} - 2.59e85T^{69} + 2.50e86T^{70} - 2.40e87T^{71} + 2.28e88T^{72} - 2.15e89T^{73} + 2.01e90T^{74} - 1.87e91T^{75} + 1.72e92T^{76}+O(T^{77})$$
89 $$1 - 34T + 3.93e3T^{2} - 1.19e5T^{3} + 7.59e6T^{4} - 2.10e8T^{5} + 9.61e9T^{6} - 2.45e11T^{7} + 9.02e12T^{8} - 2.13e14T^{9} + 6.69e15T^{10} - 1.48e17T^{11} + 4.10e18T^{12} - 8.57e19T^{13} + 2.13e21T^{14} - 4.22e22T^{15} + 9.68e23T^{16} - 1.82e25T^{17} + 3.87e26T^{18} - 6.94e27T^{19} + 1.38e29T^{20} - 2.37e30T^{21} + 4.47e31T^{22} - 7.38e32T^{23} + 1.31e34T^{24} - 2.09e35T^{25} + 3.57e36T^{26} - 5.47e37T^{27} + 8.93e38T^{28} - 1.32e40T^{29} + 2.07e41T^{30} - 2.97e42T^{31} + 4.49e43T^{32} - 6.24e44T^{33} + 9.11e45T^{34} - 1.22e47T^{35} + 1.73e48T^{36} - 2.27e49T^{37} + 3.10e50T^{38} - 3.95e51T^{39} + 5.25e52T^{40} - 6.51e53T^{41} + 8.40e54T^{42} - 1.01e56T^{43} + 1.27e57T^{44} - 1.49e58T^{45} + 1.82e59T^{46} - 2.08e60T^{47} + 2.47e61T^{48} - 2.75e62T^{49} + 3.19e63T^{50} - 3.45e64T^{51} + 3.91e65T^{52} - 4.11e66T^{53} + 4.53e67T^{54} - 4.62e68T^{55} + 4.97e69T^{56} - 4.91e70T^{57} + 5.15e71T^{58} - 4.91e72T^{59} + 5.02e73T^{60} - 4.60e74T^{61} + 4.58e75T^{62} - 4.00e76T^{63} + 3.88e77T^{64} - 3.19e78T^{65} + 3.00e79T^{66} - 2.27e80T^{67} + 2.08e81T^{68} - 1.37e82T^{69} + 1.23e83T^{70} - 6.09e83T^{71} + 5.52e84T^{72} - 5.55e84T^{73} + 1.05e86T^{74} + 2.48e87T^{75}+O(T^{76})$$
97 $$1 + 13T + 3.72e3T^{2} + 4.70e4T^{3} + 6.92e6T^{4} + 8.49e7T^{5} + 8.57e9T^{6} + 1.02e11T^{7} + 7.95e12T^{8} + 9.22e13T^{9} + 5.90e15T^{10} + 6.65e16T^{11} + 3.64e18T^{12} + 4.00e19T^{13} + 1.93e21T^{14} + 2.07e22T^{15} + 8.96e23T^{16} + 9.36e24T^{17} + 3.69e26T^{18} + 3.76e27T^{19} + 1.37e29T^{20} + 1.36e30T^{21} + 4.63e31T^{22} + 4.52e32T^{23} + 1.43e34T^{24} + 1.37e35T^{25} + 4.12e36T^{26} + 3.85e37T^{27} + 1.10e39T^{28} + 1.00e40T^{29} + 2.74e41T^{30} + 2.46e42T^{31} + 6.42e43T^{32} + 5.65e44T^{33} + 1.41e46T^{34} + 1.22e47T^{35} + 2.96e48T^{36} + 2.52e49T^{37} + 5.87e50T^{38} + 4.91e51T^{39} + 1.10e53T^{40} + 9.14e53T^{41} + 1.99e55T^{42} + 1.62e56T^{43} + 3.43e57T^{44} + 2.75e58T^{45} + 5.66e59T^{46} + 4.48e60T^{47} + 8.96e61T^{48} + 7.02e62T^{49} + 1.36e64T^{50} + 1.05e65T^{51} + 2.00e66T^{52} + 1.53e67T^{53} + 2.82e68T^{54} + 2.14e69T^{55} + 3.85e70T^{56} + 2.89e71T^{57} + 5.08e72T^{58} + 3.77e73T^{59} + 6.48e74T^{60} + 4.76e75T^{61} + 8.00e76T^{62} + 5.82e77T^{63} + 9.56e78T^{64} + 6.89e79T^{65} + 1.10e81T^{66} + 7.91e81T^{67} + 1.24e83T^{68} + 8.79e83T^{69} + 1.36e85T^{70} + 9.48e85T^{71} + 1.44e87T^{72} + 9.92e87T^{73} + 1.48e89T^{74}+O(T^{75})$$
\begin{aligned} L(s) = \prod_p \ \prod_{j=1}^{154} (1 - \alpha_{j,p}\, p^{-s})^{-1} \end{aligned}