# Properties

 Degree 96 Conductor $29^{48}$ Sign $1$ Motivic weight 2 Primitive no Self-dual yes Analytic rank 0

# Origins of factors

## Dirichlet series

 L(s)  = 1 − 16·2-s − 12·3-s + 121·4-s − 14·5-s + 192·6-s − 10·7-s − 564·8-s + 65·9-s + 224·10-s − 8·11-s − 1.45e3·12-s − 14·13-s + 160·14-s + 168·15-s + 1.74e3·16-s − 26·17-s − 1.04e3·18-s + 2·19-s − 1.69e3·20-s + 120·21-s + 128·22-s + 56·23-s + 6.76e3·24-s − 19·25-s + 224·26-s − 156·27-s − 1.21e3·28-s + ⋯
 L(s)  = 1 − 8·2-s − 4·3-s + 30.2·4-s − 2.79·5-s + 32·6-s − 1.42·7-s − 70.5·8-s + 65/9·9-s + 22.3·10-s − 0.727·11-s − 121·12-s − 1.07·13-s + 80/7·14-s + 56/5·15-s + 109.·16-s − 1.52·17-s − 57.7·18-s + 2/19·19-s − 84.6·20-s + 40/7·21-s + 5.81·22-s + 2.43·23-s + 282·24-s − 0.759·25-s + 8.61·26-s − 5.77·27-s − 43.2·28-s + ⋯

## Functional equation

\begin{aligned} \Lambda(s)=\mathstrut &\left(29^{48}\right)^{s/2} \, \Gamma_{\C}(s)^{48} \, L(s)\cr =\mathstrut & \,\Lambda(3-s) \end{aligned}
\begin{aligned} \Lambda(s)=\mathstrut &\left(29^{48}\right)^{s/2} \, \Gamma_{\C}(s+1)^{48} \, L(s)\cr =\mathstrut & \,\Lambda(1-s) \end{aligned}

## Invariants

 $$d$$ = $$96$$ $$N$$ = $$29^{48}$$ $$\varepsilon$$ = $1$ motivic weight = $$2$$ character : induced by $\chi_{29} (1, \cdot )$ primitive : no self-dual : yes analytic rank = 0 Selberg data = $(96,\ 29^{48} ,\ ( \ : [1]^{48} ),\ 1 )$ $L(\frac{3}{2})$ $\approx$ $1.18733e-6$ $L(\frac12)$ $\approx$ $1.18733e-6$ $L(2)$ not available $L(1)$ not available

## Euler product

$L(s) = \prod_{p \text{ prime}} F_p(p^{-s})^{-1}$ where, for $p \neq 29$, $$F_p$$ is a polynomial of degree 96. If $p = 29$, then $F_p$ is a polynomial of degree at most 95.
$p$$F_p$
bad29 $$1 + 170T + 1.64e4T^{2} + 1.15e6T^{3} + 6.75e7T^{4} + 3.39e9T^{5} + 1.49e11T^{6} + 5.78e12T^{7} + 1.96e14T^{8} + 5.75e15T^{9} + 1.34e17T^{10} + 1.80e18T^{11} - 3.61e19T^{12} - 4.07e21T^{13} - 2.04e23T^{14} - 7.82e24T^{15} - 2.51e26T^{16} - 6.88e27T^{17} - 1.54e29T^{18} - 2.38e30T^{19} + 5.70e30T^{20} + 2.37e33T^{21} + 1.23e35T^{22} + 4.66e36T^{23} + 1.46e38T^{24} + 3.92e39T^{25} + 8.75e40T^{26} + 1.41e42T^{27} + 2.85e42T^{28} - 1.00e45T^{29} - 5.47e46T^{30} - 2.04e48T^{31} - 6.29e49T^{32} - 1.64e51T^{33} - 3.61e52T^{34} - 6.06e53T^{35} - 4.52e54T^{36} + 1.90e56T^{37} + 1.18e58T^{38} + 4.28e59T^{39}+O(T^{40})$$
good2 $$1 + p^{4} T + 135 T^{2} + 197 p^{2} T^{3} + 111 p^{5} T^{4} + 1643 p^{3} T^{5} + 41739 T^{6} + 29633 p^{2} T^{7} + 78709 p^{2} T^{8} + 204397 p^{2} T^{9} + 1067567 p T^{10} + 175195 p^{5} T^{11} + 1815039 p^{3} T^{12} + 9114211 p^{2} T^{13} + 88397463 T^{14} + 13057715 p^{4} T^{15} + 488323459 T^{16} + 71231285 p^{4} T^{17} + 1327396905 p T^{18} + 1531728025 p^{2} T^{19} + 13919718399 T^{20} + 972461967 p^{5} T^{21} + 34412748821 p T^{22} + 37906073985 p^{2} T^{23} + 166932494989 p T^{24} + 183384212547 p^{2} T^{25} + 800528189889 p T^{26} + 865156445521 p^{2} T^{27} + 7411178034935 T^{28} + 246614249921 p^{6} T^{29} + 33566605723417 T^{30} + 17855922361445 p^{2} T^{31} + 75927672355019 p T^{32} + 80400348114177 p^{2} T^{33} + 676768432312661 T^{34} + 353728268225691 p^{2} T^{35} + 1472463936933815 p T^{36} + 764813411152363 p^{3} T^{37} + 3177093668793159 p^{2} T^{38} + 6593080706599709 p^{2} T^{39} + 27282480931142745 p T^{40} + 3510281784395543 p^{5} T^{41} + 229914341232963609 T^{42} + 29268993727661163 p^{4} T^{43} + 950885806896528813 T^{44} + 240893643149222809 p^{3} T^{45} + 974484947948979345 p^{2} T^{46} + 491095797463312935 p^{4} T^{47} + 15760107896406852297 T^{48} + 491095797463312935 p^{6} T^{49} + 974484947948979345 p^{6} T^{50} + 240893643149222809 p^{9} T^{51} + 950885806896528813 p^{8} T^{52} + 29268993727661163 p^{14} T^{53} + 229914341232963609 p^{12} T^{54} + 3510281784395543 p^{19} T^{55} + 27282480931142745 p^{17} T^{56} + 6593080706599709 p^{20} T^{57} + 3177093668793159 p^{22} T^{58} + 764813411152363 p^{25} T^{59} + 1472463936933815 p^{25} T^{60} + 353728268225691 p^{28} T^{61} + 676768432312661 p^{28} T^{62} + 80400348114177 p^{32} T^{63} + 75927672355019 p^{33} T^{64} + 17855922361445 p^{36} T^{65} + 33566605723417 p^{36} T^{66} + 246614249921 p^{44} T^{67} + 7411178034935 p^{40} T^{68} + 865156445521 p^{44} T^{69} + 800528189889 p^{45} T^{70} + 183384212547 p^{48} T^{71} + 166932494989 p^{49} T^{72} + 37906073985 p^{52} T^{73} + 34412748821 p^{53} T^{74} + 972461967 p^{59} T^{75} + 13919718399 p^{56} T^{76} + 1531728025 p^{60} T^{77} + 1327396905 p^{61} T^{78} + 71231285 p^{66} T^{79} + 488323459 p^{64} T^{80} + 13057715 p^{70} T^{81} + 88397463 p^{68} T^{82} + 9114211 p^{72} T^{83} + 1815039 p^{75} T^{84} + 175195 p^{79} T^{85} + 1067567 p^{77} T^{86} + 204397 p^{80} T^{87} + 78709 p^{82} T^{88} + 29633 p^{84} T^{89} + 41739 p^{84} T^{90} + 1643 p^{89} T^{91} + 111 p^{93} T^{92} + 197 p^{92} T^{93} + 135 p^{92} T^{94} + p^{98} T^{95} + p^{96} T^{96}$$
3 $$1 + 4 p T + 79 T^{2} + 4 p^{4} T^{3} + 748 T^{4} - 494 T^{5} - 130 p^{4} T^{6} - 39118 T^{7} - 48541 T^{8} + 128030 T^{9} + 482833 T^{10} - 1998106 T^{11} - 16783124 T^{12} - 46528514 T^{13} + 1792499 p^{2} T^{14} + 536701510 T^{15} + 601721455 p T^{16} + 837911930 T^{17} - 9844192510 T^{18} - 22942460714 T^{19} + 27230985275 p T^{20} + 60653437636 p^{2} T^{21} + 1087074533884 T^{22} - 739642668232 p T^{23} - 15067957643603 T^{24} - 26011599498430 T^{25} + 53989809057728 T^{26} + 266577710253134 T^{27} + 2137734182375 p^{3} T^{28} - 3281217034587490 T^{29} - 3137678687282555 p T^{30} - 4065963991456922 T^{31} + 52011350594684165 T^{32} + 18587655913801294 p T^{33} - 312758690152830590 T^{34} - 1216210783148992826 T^{35} + 3463181333041964018 T^{36} + 8039407714287583988 p T^{37} + 48467602177176134969 T^{38} - 97610757960846102472 T^{39} -$$$$15\!\cdots\!00$$$$p T^{40} +$$$$11\!\cdots\!36$$$$T^{41} +$$$$72\!\cdots\!95$$$$T^{42} +$$$$59\!\cdots\!60$$$$p T^{43} -$$$$14\!\cdots\!58$$$$T^{44} -$$$$24\!\cdots\!82$$$$T^{45} -$$$$50\!\cdots\!52$$$$T^{46} +$$$$45\!\cdots\!90$$$$p^{2} T^{47} +$$$$51\!\cdots\!02$$$$T^{48} +$$$$45\!\cdots\!90$$$$p^{4} T^{49} -$$$$50\!\cdots\!52$$$$p^{4} T^{50} -$$$$24\!\cdots\!82$$$$p^{6} T^{51} -$$$$14\!\cdots\!58$$$$p^{8} T^{52} +$$$$59\!\cdots\!60$$$$p^{11} T^{53} +$$$$72\!\cdots\!95$$$$p^{12} T^{54} +$$$$11\!\cdots\!36$$$$p^{14} T^{55} -$$$$15\!\cdots\!00$$$$p^{17} T^{56} - 97610757960846102472 p^{18} T^{57} + 48467602177176134969 p^{20} T^{58} + 8039407714287583988 p^{23} T^{59} + 3463181333041964018 p^{24} T^{60} - 1216210783148992826 p^{26} T^{61} - 312758690152830590 p^{28} T^{62} + 18587655913801294 p^{31} T^{63} + 52011350594684165 p^{32} T^{64} - 4065963991456922 p^{34} T^{65} - 3137678687282555 p^{37} T^{66} - 3281217034587490 p^{38} T^{67} + 2137734182375 p^{43} T^{68} + 266577710253134 p^{42} T^{69} + 53989809057728 p^{44} T^{70} - 26011599498430 p^{46} T^{71} - 15067957643603 p^{48} T^{72} - 739642668232 p^{51} T^{73} + 1087074533884 p^{52} T^{74} + 60653437636 p^{56} T^{75} + 27230985275 p^{57} T^{76} - 22942460714 p^{58} T^{77} - 9844192510 p^{60} T^{78} + 837911930 p^{62} T^{79} + 601721455 p^{65} T^{80} + 536701510 p^{66} T^{81} + 1792499 p^{70} T^{82} - 46528514 p^{70} T^{83} - 16783124 p^{72} T^{84} - 1998106 p^{74} T^{85} + 482833 p^{76} T^{86} + 128030 p^{78} T^{87} - 48541 p^{80} T^{88} - 39118 p^{82} T^{89} - 130 p^{88} T^{90} - 494 p^{86} T^{91} + 748 p^{88} T^{92} + 4 p^{94} T^{93} + 79 p^{92} T^{94} + 4 p^{95} T^{95} + p^{96} T^{96}$$
5 $$1 + 14 T + 43 p T^{2} + 1834 T^{3} + 3573 p T^{4} + 123158 T^{5} + 1009721 T^{6} + 6275206 T^{7} + 45581307 T^{8} + 254470454 T^{9} + 1643397299 T^{10} + 8282968722 T^{11} + 48998384761 T^{12} + 226606387504 T^{13} + 9995099042 p^{3} T^{14} + 5328052129288 T^{15} + 28456162978762 T^{16} + 119252280051548 T^{17} + 136912490888736 p T^{18} + 3196076151689568 T^{19} + 20754317597334414 T^{20} + 110475331409659104 T^{21} + 741356750745407536 T^{22} + 4062946872613183716 T^{23} + 25607985795088903054 T^{24} +$$$$13\!\cdots\!52$$$$T^{25} +$$$$77\!\cdots\!94$$$$T^{26} +$$$$37\!\cdots\!72$$$$T^{27} +$$$$19\!\cdots\!83$$$$T^{28} +$$$$36\!\cdots\!86$$$$p^{2} T^{29} +$$$$88\!\cdots\!69$$$$p T^{30} +$$$$20\!\cdots\!46$$$$T^{31} +$$$$97\!\cdots\!81$$$$T^{32} +$$$$47\!\cdots\!54$$$$T^{33} +$$$$24\!\cdots\!31$$$$T^{34} +$$$$13\!\cdots\!02$$$$T^{35} +$$$$76\!\cdots\!19$$$$T^{36} +$$$$44\!\cdots\!58$$$$T^{37} +$$$$24\!\cdots\!93$$$$T^{38} +$$$$13\!\cdots\!54$$$$T^{39} +$$$$72\!\cdots\!23$$$$T^{40} +$$$$37\!\cdots\!32$$$$T^{41} +$$$$72\!\cdots\!24$$$$p^{2} T^{42} +$$$$87\!\cdots\!44$$$$T^{43} +$$$$38\!\cdots\!64$$$$T^{44} +$$$$18\!\cdots\!56$$$$T^{45} +$$$$77\!\cdots\!16$$$$T^{46} +$$$$75\!\cdots\!08$$$$p T^{47} +$$$$17\!\cdots\!76$$$$T^{48} +$$$$75\!\cdots\!08$$$$p^{3} T^{49} +$$$$77\!\cdots\!16$$$$p^{4} T^{50} +$$$$18\!\cdots\!56$$$$p^{6} T^{51} +$$$$38\!\cdots\!64$$$$p^{8} T^{52} +$$$$87\!\cdots\!44$$$$p^{10} T^{53} +$$$$72\!\cdots\!24$$$$p^{14} T^{54} +$$$$37\!\cdots\!32$$$$p^{14} T^{55} +$$$$72\!\cdots\!23$$$$p^{16} T^{56} +$$$$13\!\cdots\!54$$$$p^{18} T^{57} +$$$$24\!\cdots\!93$$$$p^{20} T^{58} +$$$$44\!\cdots\!58$$$$p^{22} T^{59} +$$$$76\!\cdots\!19$$$$p^{24} T^{60} +$$$$13\!\cdots\!02$$$$p^{26} T^{61} +$$$$24\!\cdots\!31$$$$p^{28} T^{62} +$$$$47\!\cdots\!54$$$$p^{30} T^{63} +$$$$97\!\cdots\!81$$$$p^{32} T^{64} +$$$$20\!\cdots\!46$$$$p^{34} T^{65} +$$$$88\!\cdots\!69$$$$p^{37} T^{66} +$$$$36\!\cdots\!86$$$$p^{40} T^{67} +$$$$19\!\cdots\!83$$$$p^{40} T^{68} +$$$$37\!\cdots\!72$$$$p^{42} T^{69} +$$$$77\!\cdots\!94$$$$p^{44} T^{70} +$$$$13\!\cdots\!52$$$$p^{46} T^{71} + 25607985795088903054 p^{48} T^{72} + 4062946872613183716 p^{50} T^{73} + 741356750745407536 p^{52} T^{74} + 110475331409659104 p^{54} T^{75} + 20754317597334414 p^{56} T^{76} + 3196076151689568 p^{58} T^{77} + 136912490888736 p^{61} T^{78} + 119252280051548 p^{62} T^{79} + 28456162978762 p^{64} T^{80} + 5328052129288 p^{66} T^{81} + 9995099042 p^{71} T^{82} + 226606387504 p^{70} T^{83} + 48998384761 p^{72} T^{84} + 8282968722 p^{74} T^{85} + 1643397299 p^{76} T^{86} + 254470454 p^{78} T^{87} + 45581307 p^{80} T^{88} + 6275206 p^{82} T^{89} + 1009721 p^{84} T^{90} + 123158 p^{86} T^{91} + 3573 p^{89} T^{92} + 1834 p^{90} T^{93} + 43 p^{93} T^{94} + 14 p^{94} T^{95} + p^{96} T^{96}$$
7 $$1 + 10 T - 57 p T^{2} - 4236 T^{3} + 88012 T^{4} + 961236 T^{5} - 289276 p^{2} T^{6} - 155492966 T^{7} + 265275399 p T^{8} + 20094259140 T^{9} - 208698108449 T^{10} - 2199633719140 T^{11} + 20758293283115 T^{12} + 210987582526270 T^{13} - 1865195037242882 T^{14} - 18111952270636036 T^{15} + 153584251691602171 T^{16} + 1410417772300341874 T^{17} - 11707484613660681198 T^{18} -$$$$10\!\cdots\!46$$$$T^{19} +$$$$11\!\cdots\!81$$$$p T^{20} +$$$$65\!\cdots\!40$$$$T^{21} -$$$$55\!\cdots\!76$$$$T^{22} -$$$$39\!\cdots\!98$$$$T^{23} +$$$$34\!\cdots\!90$$$$T^{24} +$$$$21\!\cdots\!42$$$$T^{25} -$$$$29\!\cdots\!80$$$$p T^{26} -$$$$10\!\cdots\!08$$$$T^{27} +$$$$11\!\cdots\!89$$$$T^{28} +$$$$70\!\cdots\!38$$$$p T^{29} -$$$$85\!\cdots\!42$$$$p T^{30} -$$$$18\!\cdots\!14$$$$T^{31} +$$$$29\!\cdots\!61$$$$T^{32} +$$$$53\!\cdots\!40$$$$T^{33} -$$$$13\!\cdots\!02$$$$T^{34} -$$$$38\!\cdots\!02$$$$T^{35} +$$$$56\!\cdots\!64$$$$T^{36} -$$$$85\!\cdots\!82$$$$T^{37} -$$$$21\!\cdots\!74$$$$T^{38} +$$$$81\!\cdots\!00$$$$T^{39} +$$$$67\!\cdots\!27$$$$T^{40} -$$$$70\!\cdots\!30$$$$p T^{41} -$$$$15\!\cdots\!86$$$$T^{42} +$$$$33\!\cdots\!62$$$$p T^{43} +$$$$44\!\cdots\!35$$$$T^{44} -$$$$81\!\cdots\!68$$$$T^{45} +$$$$21\!\cdots\!04$$$$T^{46} +$$$$14\!\cdots\!90$$$$T^{47} -$$$$14\!\cdots\!86$$$$T^{48} +$$$$14\!\cdots\!90$$$$p^{2} T^{49} +$$$$21\!\cdots\!04$$$$p^{4} T^{50} -$$$$81\!\cdots\!68$$$$p^{6} T^{51} +$$$$44\!\cdots\!35$$$$p^{8} T^{52} +$$$$33\!\cdots\!62$$$$p^{11} T^{53} -$$$$15\!\cdots\!86$$$$p^{12} T^{54} -$$$$70\!\cdots\!30$$$$p^{15} T^{55} +$$$$67\!\cdots\!27$$$$p^{16} T^{56} +$$$$81\!\cdots\!00$$$$p^{18} T^{57} -$$$$21\!\cdots\!74$$$$p^{20} T^{58} -$$$$85\!\cdots\!82$$$$p^{22} T^{59} +$$$$56\!\cdots\!64$$$$p^{24} T^{60} -$$$$38\!\cdots\!02$$$$p^{26} T^{61} -$$$$13\!\cdots\!02$$$$p^{28} T^{62} +$$$$53\!\cdots\!40$$$$p^{30} T^{63} +$$$$29\!\cdots\!61$$$$p^{32} T^{64} -$$$$18\!\cdots\!14$$$$p^{34} T^{65} -$$$$85\!\cdots\!42$$$$p^{37} T^{66} +$$$$70\!\cdots\!38$$$$p^{39} T^{67} +$$$$11\!\cdots\!89$$$$p^{40} T^{68} -$$$$10\!\cdots\!08$$$$p^{42} T^{69} -$$$$29\!\cdots\!80$$$$p^{45} T^{70} +$$$$21\!\cdots\!42$$$$p^{46} T^{71} +$$$$34\!\cdots\!90$$$$p^{48} T^{72} -$$$$39\!\cdots\!98$$$$p^{50} T^{73} -$$$$55\!\cdots\!76$$$$p^{52} T^{74} +$$$$65\!\cdots\!40$$$$p^{54} T^{75} +$$$$11\!\cdots\!81$$$$p^{57} T^{76} -$$$$10\!\cdots\!46$$$$p^{58} T^{77} - 11707484613660681198 p^{60} T^{78} + 1410417772300341874 p^{62} T^{79} + 153584251691602171 p^{64} T^{80} - 18111952270636036 p^{66} T^{81} - 1865195037242882 p^{68} T^{82} + 210987582526270 p^{70} T^{83} + 20758293283115 p^{72} T^{84} - 2199633719140 p^{74} T^{85} - 208698108449 p^{76} T^{86} + 20094259140 p^{78} T^{87} + 265275399 p^{81} T^{88} - 155492966 p^{82} T^{89} - 289276 p^{86} T^{90} + 961236 p^{86} T^{91} + 88012 p^{88} T^{92} - 4236 p^{90} T^{93} - 57 p^{93} T^{94} + 10 p^{94} T^{95} + p^{96} T^{96}$$
11 $$1 + 8 T + 375 T^{2} - 3272 T^{3} + 2241 T^{4} - 2162458 T^{5} + 5347517 T^{6} - 157814138 T^{7} + 7201185249 T^{8} + 9877404696 T^{9} + 917857593905 T^{10} - 13867055165844 T^{11} - 55986550658351 T^{12} - 261730948803364 p T^{13} + 12885112707636822 T^{14} + 123497906965345760 T^{15} + 6429964586798756808 T^{16} + 18962958071140584144 T^{17} - 56515688687913417570 T^{18} -$$$$99\!\cdots\!24$$$$T^{19} -$$$$10\!\cdots\!34$$$$T^{20} -$$$$41\!\cdots\!72$$$$T^{21} +$$$$93\!\cdots\!42$$$$T^{22} +$$$$23\!\cdots\!84$$$$T^{23} +$$$$16\!\cdots\!72$$$$T^{24} +$$$$26\!\cdots\!04$$$$T^{25} -$$$$33\!\cdots\!30$$$$T^{26} -$$$$34\!\cdots\!04$$$$T^{27} -$$$$30\!\cdots\!73$$$$T^{28} +$$$$29\!\cdots\!32$$$$T^{29} +$$$$51\!\cdots\!07$$$$T^{30} +$$$$73\!\cdots\!92$$$$T^{31} +$$$$13\!\cdots\!03$$$$T^{32} -$$$$51\!\cdots\!58$$$$T^{33} -$$$$11\!\cdots\!53$$$$T^{34} -$$$$61\!\cdots\!30$$$$T^{35} +$$$$21\!\cdots\!43$$$$T^{36} +$$$$13\!\cdots\!88$$$$T^{37} +$$$$14\!\cdots\!69$$$$T^{38} +$$$$43\!\cdots\!00$$$$T^{39} -$$$$10\!\cdots\!25$$$$T^{40} -$$$$21\!\cdots\!84$$$$T^{41} -$$$$12\!\cdots\!40$$$$T^{42} +$$$$17\!\cdots\!20$$$$T^{43} +$$$$24\!\cdots\!56$$$$p T^{44} +$$$$22\!\cdots\!56$$$$T^{45} +$$$$13\!\cdots\!08$$$$T^{46} -$$$$24\!\cdots\!36$$$$p T^{47} -$$$$31\!\cdots\!20$$$$T^{48} -$$$$24\!\cdots\!36$$$$p^{3} T^{49} +$$$$13\!\cdots\!08$$$$p^{4} T^{50} +$$$$22\!\cdots\!56$$$$p^{6} T^{51} +$$$$24\!\cdots\!56$$$$p^{9} T^{52} +$$$$17\!\cdots\!20$$$$p^{10} T^{53} -$$$$12\!\cdots\!40$$$$p^{12} T^{54} -$$$$21\!\cdots\!84$$$$p^{14} T^{55} -$$$$10\!\cdots\!25$$$$p^{16} T^{56} +$$$$43\!\cdots\!00$$$$p^{18} T^{57} +$$$$14\!\cdots\!69$$$$p^{20} T^{58} +$$$$13\!\cdots\!88$$$$p^{22} T^{59} +$$$$21\!\cdots\!43$$$$p^{24} T^{60} -$$$$61\!\cdots\!30$$$$p^{26} T^{61} -$$$$11\!\cdots\!53$$$$p^{28} T^{62} -$$$$51\!\cdots\!58$$$$p^{30} T^{63} +$$$$13\!\cdots\!03$$$$p^{32} T^{64} +$$$$73\!\cdots\!92$$$$p^{34} T^{65} +$$$$51\!\cdots\!07$$$$p^{36} T^{66} +$$$$29\!\cdots\!32$$$$p^{38} T^{67} -$$$$30\!\cdots\!73$$$$p^{40} T^{68} -$$$$34\!\cdots\!04$$$$p^{42} T^{69} -$$$$33\!\cdots\!30$$$$p^{44} T^{70} +$$$$26\!\cdots\!04$$$$p^{46} T^{71} +$$$$16\!\cdots\!72$$$$p^{48} T^{72} +$$$$23\!\cdots\!84$$$$p^{50} T^{73} +$$$$93\!\cdots\!42$$$$p^{52} T^{74} -$$$$41\!\cdots\!72$$$$p^{54} T^{75} -$$$$10\!\cdots\!34$$$$p^{56} T^{76} -$$$$99\!\cdots\!24$$$$p^{58} T^{77} - 56515688687913417570 p^{60} T^{78} + 18962958071140584144 p^{62} T^{79} + 6429964586798756808 p^{64} T^{80} + 123497906965345760 p^{66} T^{81} + 12885112707636822 p^{68} T^{82} - 261730948803364 p^{71} T^{83} - 55986550658351 p^{72} T^{84} - 13867055165844 p^{74} T^{85} + 917857593905 p^{76} T^{86} + 9877404696 p^{78} T^{87} + 7201185249 p^{80} T^{88} - 157814138 p^{82} T^{89} + 5347517 p^{84} T^{90} - 2162458 p^{86} T^{91} + 2241 p^{88} T^{92} - 3272 p^{90} T^{93} + 375 p^{92} T^{94} + 8 p^{94} T^{95} + p^{96} T^{96}$$
13 $$1 + 14 T + 87 p T^{2} + 7182 T^{3} + 513722 T^{4} - 21532 p T^{5} + 140514018 T^{6} - 1045192008 T^{7} + 28981359188 T^{8} - 395007332664 T^{9} + 4185090585476 T^{10} - 85414188632556 T^{11} + 195249953381758 T^{12} - 7527599672416894 T^{13} - 84934009480748863 T^{14} + 1866452920027596922 T^{15} - 35643886055783294108 T^{16} +$$$$87\!\cdots\!46$$$$T^{17} -$$$$86\!\cdots\!77$$$$T^{18} +$$$$18\!\cdots\!58$$$$T^{19} -$$$$13\!\cdots\!10$$$$T^{20} +$$$$23\!\cdots\!60$$$$T^{21} -$$$$10\!\cdots\!86$$$$T^{22} +$$$$65\!\cdots\!88$$$$T^{23} +$$$$13\!\cdots\!01$$$$T^{24} -$$$$38\!\cdots\!70$$$$T^{25} +$$$$63\!\cdots\!87$$$$T^{26} -$$$$94\!\cdots\!58$$$$T^{27} +$$$$10\!\cdots\!90$$$$T^{28} -$$$$11\!\cdots\!18$$$$T^{29} +$$$$63\!\cdots\!13$$$$T^{30} -$$$$61\!\cdots\!34$$$$T^{31} -$$$$73\!\cdots\!61$$$$T^{32} -$$$$10\!\cdots\!40$$$$T^{33} -$$$$64\!\cdots\!34$$$$T^{34} -$$$$18\!\cdots\!12$$$$T^{35} +$$$$69\!\cdots\!87$$$$T^{36} -$$$$92\!\cdots\!88$$$$T^{37} +$$$$27\!\cdots\!60$$$$T^{38} -$$$$21\!\cdots\!80$$$$T^{39} +$$$$52\!\cdots\!67$$$$T^{40} -$$$$27\!\cdots\!64$$$$T^{41} +$$$$35\!\cdots\!20$$$$p T^{42} +$$$$62\!\cdots\!52$$$$T^{43} -$$$$50\!\cdots\!65$$$$T^{44} +$$$$12\!\cdots\!10$$$$T^{45} -$$$$29\!\cdots\!93$$$$T^{46} +$$$$34\!\cdots\!42$$$$T^{47} -$$$$64\!\cdots\!72$$$$T^{48} +$$$$34\!\cdots\!42$$$$p^{2} T^{49} -$$$$29\!\cdots\!93$$$$p^{4} T^{50} +$$$$12\!\cdots\!10$$$$p^{6} T^{51} -$$$$50\!\cdots\!65$$$$p^{8} T^{52} +$$$$62\!\cdots\!52$$$$p^{10} T^{53} +$$$$35\!\cdots\!20$$$$p^{13} T^{54} -$$$$27\!\cdots\!64$$$$p^{14} T^{55} +$$$$52\!\cdots\!67$$$$p^{16} T^{56} -$$$$21\!\cdots\!80$$$$p^{18} T^{57} +$$$$27\!\cdots\!60$$$$p^{20} T^{58} -$$$$92\!\cdots\!88$$$$p^{22} T^{59} +$$$$69\!\cdots\!87$$$$p^{24} T^{60} -$$$$18\!\cdots\!12$$$$p^{26} T^{61} -$$$$64\!\cdots\!34$$$$p^{28} T^{62} -$$$$10\!\cdots\!40$$$$p^{30} T^{63} -$$$$73\!\cdots\!61$$$$p^{32} T^{64} -$$$$61\!\cdots\!34$$$$p^{34} T^{65} +$$$$63\!\cdots\!13$$$$p^{36} T^{66} -$$$$11\!\cdots\!18$$$$p^{38} T^{67} +$$$$10\!\cdots\!90$$$$p^{40} T^{68} -$$$$94\!\cdots\!58$$$$p^{42} T^{69} +$$$$63\!\cdots\!87$$$$p^{44} T^{70} -$$$$38\!\cdots\!70$$$$p^{46} T^{71} +$$$$13\!\cdots\!01$$$$p^{48} T^{72} +$$$$65\!\cdots\!88$$$$p^{50} T^{73} -$$$$10\!\cdots\!86$$$$p^{52} T^{74} +$$$$23\!\cdots\!60$$$$p^{54} T^{75} -$$$$13\!\cdots\!10$$$$p^{56} T^{76} +$$$$18\!\cdots\!58$$$$p^{58} T^{77} -$$$$86\!\cdots\!77$$$$p^{60} T^{78} +$$$$87\!\cdots\!46$$$$p^{62} T^{79} - 35643886055783294108 p^{64} T^{80} + 1866452920027596922 p^{66} T^{81} - 84934009480748863 p^{68} T^{82} - 7527599672416894 p^{70} T^{83} + 195249953381758 p^{72} T^{84} - 85414188632556 p^{74} T^{85} + 4185090585476 p^{76} T^{86} - 395007332664 p^{78} T^{87} + 28981359188 p^{80} T^{88} - 1045192008 p^{82} T^{89} + 140514018 p^{84} T^{90} - 21532 p^{87} T^{91} + 513722 p^{88} T^{92} + 7182 p^{90} T^{93} + 87 p^{93} T^{94} + 14 p^{94} T^{95} + p^{96} T^{96}$$
17 $$1 + 26T + 338T^{2} + 1.08e4T^{3} + 3.76e5T^{4} + 8.81e6T^{5} + 1.60e8T^{6} + 4.07e9T^{7} + 9.66e10T^{8} + 1.90e12T^{9} + 3.92e13T^{10} + 8.31e14T^{11} + 1.72e16T^{12} + 3.35e17T^{13} + 6.64e18T^{14} + 1.28e20T^{15} + 2.45e21T^{16} + 4.71e22T^{17} + 8.69e23T^{18} + 1.59e25T^{19} + 2.91e26T^{20} + 5.31e27T^{21} + 9.25e28T^{22} + 1.62e30T^{23} + 2.80e31T^{24} + 4.71e32T^{25} + 7.86e33T^{26} + 1.27e35T^{27} + 2.02e36T^{28} + 3.08e37T^{29} + 4.61e38T^{30} + 6.24e39T^{31} + 7.61e40T^{32} + 8.44e41T^{33} + 4.06e42T^{34} - 1.22e44T^{35} - 5.33e45T^{36} - 1.43e47T^{37} - 3.42e48T^{38} - 7.45e49T^{39} - 1.52e51T^{40} - 3.04e52T^{41} - 5.78e53T^{42} - 1.08e55T^{43} - 2.00e56T^{44} - 3.60e57T^{45}+O(T^{46})$$
19 $$1 - 2T + 555T^{2} + 1.86e3T^{3} - 1.33e4T^{4} + 7.25e6T^{5} - 6.55e7T^{6} + 4.32e9T^{7} - 1.17e10T^{8} + 1.04e12T^{9} + 4.40e12T^{10} - 7.96e13T^{11} + 1.17e16T^{12} - 2.26e17T^{13} + 9.25e18T^{14} - 1.26e20T^{15} + 2.30e21T^{16} - 1.30e22T^{17} - 4.02e23T^{18} + 1.91e25T^{19} - 4.63e26T^{20} + 1.12e28T^{21} - 2.14e29T^{22} + 3.39e30T^{23} - 5.93e31T^{24} + 2.22e32T^{25} + 8.49e33T^{26} - 5.09e35T^{27} + 1.35e37T^{28} - 3.06e38T^{29} + 4.62e39T^{30} - 7.45e40T^{31} + 7.45e41T^{32} - 3.29e42T^{33} - 1.04e44T^{34} + 6.25e45T^{35} - 1.87e47T^{36} + 4.64e48T^{37} - 8.61e49T^{38} + 1.52e51T^{39} - 1.47e52T^{40} + 1.57e53T^{41} + 1.14e54T^{42} - 2.29e55T^{43} + 1.32e57T^{44}+O(T^{45})$$
23 $$1 - 56T + 177T^{2} + 3.90e4T^{3} - 3.54e5T^{4} - 6.63e6T^{5} + 1.98e7T^{6} - 2.13e10T^{7} + 6.02e11T^{8} + 1.71e13T^{9} - 5.38e14T^{10} - 5.08e15T^{11} + 9.76e16T^{12} - 3.87e17T^{13} + 1.82e20T^{14} + 7.36e20T^{15} - 1.93e23T^{16} + 7.16e22T^{17} + 7.83e25T^{18} + 5.70e24T^{19} + 6.23e27T^{20} - 2.20e29T^{21} - 3.05e31T^{22} + 2.95e32T^{23} + 1.90e34T^{24} - 1.92e35T^{25} - 2.59e36T^{26} + 2.16e37T^{27} - 3.99e39T^{28} + 5.77e40T^{29} + 3.24e42T^{30} - 5.33e43T^{31} - 6.81e44T^{32} + 1.32e46T^{33} - 4.70e47T^{34} + 9.04e48T^{35} + 4.68e50T^{36} - 1.06e52T^{37} - 1.55e53T^{38} + 4.53e54T^{39} - 2.49e55T^{40} + 2.18e56T^{41}+O(T^{42})$$
31 $$1 + 88T + 5.37e3T^{2} + 3.60e5T^{3} + 1.99e7T^{4} + 9.66e8T^{5} + 4.62e10T^{6} + 2.05e12T^{7} + 8.43e13T^{8} + 3.42e15T^{9} + 1.32e17T^{10} + 4.88e18T^{11} + 1.79e20T^{12} + 6.43e21T^{13} + 2.21e23T^{14} + 7.72e24T^{15} + 2.64e26T^{16} + 8.82e27T^{17} + 2.97e29T^{18} + 9.95e30T^{19} + 3.22e32T^{20} + 1.05e34T^{21} + 3.41e35T^{22} + 1.06e37T^{23} + 3.32e38T^{24} + 1.02e40T^{25} + 2.99e41T^{26} + 8.79e42T^{27} + 2.52e44T^{28} + 6.73e45T^{29} + 1.77e47T^{30} + 4.48e48T^{31} + 9.56e49T^{32} + 1.78e51T^{33} + 1.99e52T^{34} - 7.50e53T^{35} - 5.98e55T^{36} - 2.90e57T^{37} - 1.29e59T^{38}+O(T^{39})$$
37 $$1 + 56T + 4.66e3T^{2} + 1.32e5T^{3} + 5.13e6T^{4} - 2.61e8T^{5} - 1.47e10T^{6} - 1.46e12T^{7} - 3.43e13T^{8} - 1.59e15T^{9} + 5.51e16T^{10} + 2.78e18T^{11} + 3.04e20T^{12} + 7.14e21T^{13} + 3.53e23T^{14} - 7.23e24T^{15} - 3.54e26T^{16} - 4.59e28T^{17} - 1.08e30T^{18} - 5.40e31T^{19} + 7.56e32T^{20} + 4.11e34T^{21} + 5.74e36T^{22} + 1.45e38T^{23} + 6.90e39T^{24} - 5.06e40T^{25} - 4.13e42T^{26} - 5.96e44T^{27} - 1.65e46T^{28} - 7.27e47T^{29} + 1.75e48T^{30} + 4.03e50T^{31} + 5.46e52T^{32} + 1.71e54T^{33} + 6.80e55T^{34} + 1.86e56T^{35} - 3.50e58T^{36}+O(T^{37})$$
41 $$1 + 34T + 578T^{2} + 1.34e5T^{3} + 3.17e6T^{4} - 1.04e8T^{5} + 3.71e9T^{6} - 2.00e11T^{7} - 3.88e13T^{8} - 8.45e13T^{9} - 1.38e16T^{10} - 3.03e18T^{11} + 8.23e19T^{12} + 5.20e21T^{13} - 6.26e22T^{14} + 1.34e25T^{15} + 6.22e26T^{16} - 1.28e28T^{17} + 4.46e29T^{18} + 2.01e31T^{19} - 2.99e33T^{20} - 3.96e34T^{21} + 8.65e35T^{22} - 2.34e38T^{23} - 1.38e39T^{24} + 3.25e41T^{25} - 6.35e42T^{26} + 2.29e44T^{27} + 4.25e46T^{28} - 1.52e47T^{29} + 3.23e47T^{30} + 2.44e51T^{31} - 5.78e52T^{32} - 3.44e54T^{33} + 8.37e55T^{34} - 5.94e57T^{35}+O(T^{36})$$
43 $$1 - 176T + 1.10e4T^{2} - 1.60e5T^{3} - 1.60e7T^{4} + 1.57e9T^{5} - 1.15e11T^{6} + 4.18e12T^{7} + 1.48e14T^{8} - 2.14e16T^{9} + 1.03e18T^{10} - 3.45e19T^{11} + 5.35e18T^{12} + 1.35e23T^{13} - 9.48e24T^{14} + 2.65e26T^{15} + 7.85e26T^{16} - 6.45e29T^{17} + 5.68e31T^{18} - 2.43e33T^{19} + 1.75e34T^{20} + 3.64e36T^{21} - 2.78e38T^{22} + 1.36e40T^{23} - 2.98e41T^{24} - 1.41e43T^{25} + 1.50e45T^{26} - 6.94e46T^{27} + 1.93e48T^{28} + 2.18e49T^{29} - 6.32e51T^{30} + 3.57e53T^{31} - 1.04e55T^{32} + 2.08e55T^{33} + 2.12e58T^{34} - 1.56e60T^{35}+O(T^{36})$$
47 $$1 - 208T + 1.75e4T^{2} - 5.35e5T^{3} - 3.12e7T^{4} + 3.59e9T^{5} - 6.21e10T^{6} - 8.93e12T^{7} + 5.48e14T^{8} + 7.72e15T^{9} - 2.15e18T^{10} + 6.89e19T^{11} + 3.05e21T^{12} - 2.84e23T^{13} + 2.48e24T^{14} + 6.02e26T^{15} - 2.43e28T^{16} - 6.88e29T^{17} + 7.66e31T^{18} - 8.14e32T^{19} - 1.45e35T^{20} + 6.08e36T^{21} + 1.22e38T^{22} - 1.42e40T^{23} + 1.03e41T^{24} + 2.39e43T^{25} - 6.71e44T^{26} - 3.37e46T^{27} + 1.68e48T^{28} + 3.43e49T^{29} - 2.68e51T^{30} - 9.40e52T^{31} + 9.23e54T^{32} + 1.59e56T^{33} - 3.18e58T^{34}+O(T^{35})$$
53 $$1 + 14T - 1.77e4T^{2} + 3.03e5T^{3} + 1.58e8T^{4} - 6.32e9T^{5} - 8.00e11T^{6} + 4.96e13T^{7} + 2.32e15T^{8} - 2.07e17T^{9} - 4.20e18T^{10} + 4.92e20T^{11} + 1.15e22T^{12} - 7.67e23T^{13} - 4.90e25T^{14} + 1.22e27T^{15} + 6.29e28T^{16} + 4.33e30T^{17} + 2.95e32T^{18} - 6.60e34T^{19} - 6.48e35T^{20} + 3.06e38T^{21} - 2.20e39T^{22} - 7.83e41T^{23} + 5.27e42T^{24} + 1.59e45T^{25} + 1.86e46T^{26} - 3.45e48T^{27} - 8.29e49T^{28} + 2.77e51T^{29} + 2.94e53T^{30} + 2.44e55T^{31} - 1.74e57T^{32} - 1.20e59T^{33}+O(T^{34})$$
59 $$1 + 44T + 1.14e5T^{2} + 5.03e6T^{3} + 6.45e9T^{4} + 2.85e11T^{5} + 2.41e14T^{6} + 1.06e16T^{7} + 6.70e18T^{8} + 2.95e20T^{9} + 1.47e23T^{10} + 6.47e24T^{11} + 2.68e27T^{12} + 1.17e29T^{13} + 4.14e31T^{14} + 1.79e33T^{15} + 5.54e35T^{16} + 2.38e37T^{17} + 6.54e39T^{18} + 2.77e41T^{19} + 6.87e43T^{20} + 2.88e45T^{21} + 6.49e47T^{22} + 2.69e49T^{23} + 5.57e51T^{24} + 2.27e53T^{25} + 4.36e55T^{26} + 1.75e57T^{27} + 3.14e59T^{28} + 1.24e61T^{29} + 2.08e63T^{30} + 8.07e64T^{31} + 1.28e67T^{32}+O(T^{33})$$
61 $$1 + 30T + 7.93e3T^{2} + 1.89e6T^{3} + 1.04e8T^{4} + 1.58e10T^{5} + 1.94e12T^{6} + 1.46e14T^{7} + 1.59e16T^{8} + 1.46e18T^{9} + 1.22e20T^{10} + 1.09e22T^{11} + 8.86e23T^{12} + 7.29e25T^{13} + 5.77e27T^{14} + 4.41e29T^{15} + 3.40e31T^{16} + 2.50e33T^{17} + 1.83e35T^{18} + 1.32e37T^{19} + 9.25e38T^{20} + 6.50e40T^{21} + 4.45e42T^{22} + 2.99e44T^{23} + 2.01e46T^{24} + 1.32e48T^{25} + 8.62e49T^{26} + 5.57e51T^{27} + 3.52e53T^{28} + 2.21e55T^{29} + 1.37e57T^{30} + 8.41e58T^{31} + 5.11e60T^{32}+O(T^{33})$$
67 $$1 + 574T + 1.83e5T^{2} + 4.17e7T^{3} + 7.45e9T^{4} + 1.09e12T^{5} + 1.33e14T^{6} + 1.37e16T^{7} + 1.18e18T^{8} + 8.08e19T^{9} + 3.75e21T^{10} + 8.54e21T^{11} - 2.14e25T^{12} - 2.85e27T^{13} - 2.50e29T^{14} - 1.72e31T^{15} - 1.02e33T^{16} - 5.93e34T^{17} - 4.06e36T^{18} - 3.26e38T^{19} - 2.45e40T^{20} - 1.30e42T^{21} - 9.57e42T^{22} + 7.81e45T^{23} + 1.12e48T^{24} + 1.02e50T^{25} + 7.00e51T^{26} + 3.73e53T^{27} + 1.57e55T^{28} + 5.91e56T^{29} + 3.20e58T^{30} + 2.66e60T^{31}+O(T^{32})$$
71 $$1 - 224T + 3.68e4T^{2} - 3.98e6T^{3} + 3.24e8T^{4} - 2.21e10T^{5} + 1.69e12T^{6} - 1.95e14T^{7} + 2.40e16T^{8} - 2.44e18T^{9} + 1.93e20T^{10} - 1.28e22T^{11} + 8.70e23T^{12} - 7.97e25T^{13} + 8.72e27T^{14} - 8.50e29T^{15} + 6.90e31T^{16} - 4.74e33T^{17} + 3.16e35T^{18} - 2.50e37T^{19} + 2.34e39T^{20} - 2.17e41T^{21} + 1.78e43T^{22} - 1.28e45T^{23} + 8.68e46T^{24} - 6.35e48T^{25} + 5.26e50T^{26} - 4.55e52T^{27} + 3.73e54T^{28} - 2.77e56T^{29} + 1.94e58T^{30} - 1.37e60T^{31}+O(T^{32})$$
73 $$1 + 22T + 3.04e4T^{2} - 3.43e5T^{3} + 4.88e8T^{4} - 2.77e10T^{5} + 6.09e12T^{6} - 6.05e14T^{7} + 7.45e16T^{8} - 8.57e18T^{9} + 9.09e20T^{10} - 9.94e22T^{11} + 1.01e25T^{12} - 1.04e27T^{13} + 1.02e29T^{14} - 1.00e31T^{15} + 9.49e32T^{16} - 8.91e34T^{17} + 8.15e36T^{18} - 7.31e38T^{19} + 6.50e40T^{20} - 5.61e42T^{21} + 4.81e44T^{22} - 4.03e46T^{23} + 3.32e48T^{24} - 2.69e50T^{25} + 2.14e52T^{26} - 1.67e54T^{27} + 1.28e56T^{28} - 9.59e57T^{29} + 7.00e59T^{30}+O(T^{31})$$
79 $$1 - 564T + 1.61e5T^{2} - 3.02e7T^{3} + 4.06e9T^{4} - 4.05e11T^{5} + 3.00e13T^{6} - 1.70e15T^{7} + 1.00e17T^{8} - 1.08e19T^{9} + 1.35e21T^{10} - 1.14e23T^{11} + 4.19e24T^{12} + 2.65e26T^{13} - 4.07e28T^{14} + 3.89e29T^{15} + 3.70e32T^{16} - 4.31e34T^{17} + 1.69e36T^{18} + 9.97e37T^{19} - 1.40e40T^{20} - 7.76e40T^{21} + 1.44e44T^{22} - 1.43e46T^{23} + 4.54e47T^{24} + 3.17e49T^{25} - 2.80e51T^{26} - 2.21e53T^{27} + 5.38e55T^{28} - 4.20e57T^{29} + 1.06e59T^{30}+O(T^{31})$$
83 $$1 + 126T - 2.97e4T^{2} - 3.22e6T^{3} + 5.37e8T^{4} + 4.91e10T^{5} - 6.27e12T^{6} - 5.24e14T^{7} + 6.21e16T^{8} + 4.97e18T^{9} - 6.04e20T^{10} - 4.29e22T^{11} + 5.88e24T^{12} + 3.59e26T^{13} - 4.98e28T^{14} - 2.74e30T^{15} + 3.57e32T^{16} + 1.65e34T^{17} - 2.26e36T^{18} - 6.54e37T^{19} + 1.38e40T^{20} + 5.70e40T^{21} - 8.81e43T^{22} + 1.71e45T^{23} + 4.47e47T^{24} - 2.48e49T^{25} - 9.30e50T^{26} + 2.59e53T^{27} - 7.41e54T^{28} - 2.37e57T^{29} + 8.84e58T^{30}+O(T^{31})$$
89 $$1 + 160T + 1.74e4T^{2} + 5.00e6T^{3} + 6.45e8T^{4} + 6.27e10T^{5} + 1.09e13T^{6} + 1.16e15T^{7} + 9.98e16T^{8} + 1.36e19T^{9} + 1.24e21T^{10} + 9.96e22T^{11} + 1.23e25T^{12} + 1.04e27T^{13} + 9.22e28T^{14} + 1.11e31T^{15} + 9.94e32T^{16} + 1.03e35T^{17} + 1.15e37T^{18} + 1.04e39T^{19} + 1.12e41T^{20} + 1.10e43T^{21} + 9.77e44T^{22} + 1.02e47T^{23} + 9.28e48T^{24} + 8.28e50T^{25} + 8.53e52T^{26} + 7.58e54T^{27} + 6.97e56T^{28} + 6.90e58T^{29}+O(T^{30})$$
97 $$1 - 604T + 2.20e5T^{2} - 6.01e7T^{3} + 1.32e10T^{4} - 2.45e12T^{5} + 3.94e14T^{6} - 5.54e16T^{7} + 6.86e18T^{8} - 7.42e20T^{9} + 6.96e22T^{10} - 5.50e24T^{11} + 3.49e26T^{12} - 1.58e28T^{13} + 4.09e29T^{14} - 2.49e31T^{15} + 8.06e33T^{16} - 1.56e36T^{17} + 1.70e38T^{18} - 9.74e39T^{19} - 5.27e41T^{20} + 2.23e44T^{21} - 3.30e46T^{22} + 3.53e48T^{23} - 2.72e50T^{24} + 1.59e52T^{25} - 5.51e53T^{26} - 1.14e55T^{27} + 3.42e57T^{28} - 8.90e59T^{29}+O(T^{30})$$
\begin{aligned} L(s) = \prod_p \ \prod_{j=1}^{96} (1 - \alpha_{j,p}\, p^{-s})^{-1} \end{aligned}