Dirichlet series
| L(s) = 1 | + 15·2-s + 7·3-s − 613·4-s + 3.89e3·5-s + 105·6-s − 7.13e3·7-s − 9.24e3·8-s − 2.73e4·9-s + 5.84e4·10-s + 1.72e5·11-s − 4.29e3·12-s + 1.09e5·13-s − 1.06e5·14-s + 2.72e4·15-s + 2.58e5·16-s + 5.83e5·17-s − 4.10e5·18-s + 1.04e6·19-s − 2.38e6·20-s − 4.99e4·21-s + 2.59e6·22-s − 2.29e6·23-s − 6.47e4·24-s − 1.28e5·25-s + 1.63e6·26-s − 5.32e6·27-s + 4.37e6·28-s + ⋯ |
| L(s) = 1 | + 0.662·2-s + 0.0498·3-s − 1.19·4-s + 2.78·5-s + 0.0330·6-s − 1.12·7-s − 0.797·8-s − 1.38·9-s + 1.84·10-s + 3.55·11-s − 0.0597·12-s + 1.06·13-s − 0.744·14-s + 0.139·15-s + 0.987·16-s + 1.69·17-s − 0.921·18-s + 1.83·19-s − 3.33·20-s − 0.0560·21-s + 2.35·22-s − 1.70·23-s − 0.0398·24-s − 0.0656·25-s + 0.703·26-s − 1.92·27-s + 1.34·28-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(19^{8}\right)^{s/2} \, \Gamma_{\C}(s)^{8} \, L(s)\cr=\mathstrut & \,\Lambda(10-s)\end{aligned}\]
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(19^{8}\right)^{s/2} \, \Gamma_{\C}(s+9/2)^{8} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}\]
Invariants
| Degree: | \(16\) |
| Conductor: | \(19^{8}\) |
| Sign: | $1$ |
| Analytic conductor: | \(8.40869\times 10^{7}\) |
| Root analytic conductor: | \(3.12820\) |
| Motivic weight: | \(9\) |
| Rational: | yes |
| Arithmetic: | yes |
| Character: | Trivial |
| Primitive: | no |
| Self-dual: | yes |
| Analytic rank: | \(0\) |
| Selberg data: | \((16,\ 19^{8} ,\ ( \ : [9/2]^{8} ),\ 1 )\) |
Particular Values
| \(L(5)\) | \(\approx\) | \(1.578117061\) |
| \(L(\frac12)\) | \(\approx\) | \(1.578117061\) |
| \(L(\frac{11}{2})\) | not available | |
| \(L(1)\) | not available |
Euler product
\(L(s) = \displaystyle \prod_{p} F_p(p^{-s})^{-1} \)
| $p$ | $F_p(T)$ | |
|---|---|---|
| bad | 19 | \( ( 1 - p^{4} T )^{8} \) |
| good | 2 | \( 1 - 15 T + 419 p T^{2} - 6261 p T^{3} + 38003 p^{3} T^{4} - 13383 p^{3} T^{5} + 3117095 p^{5} T^{6} - 12013023 p^{7} T^{7} + 47792567 p^{9} T^{8} - 12013023 p^{16} T^{9} + 3117095 p^{23} T^{10} - 13383 p^{30} T^{11} + 38003 p^{39} T^{12} - 6261 p^{46} T^{13} + 419 p^{55} T^{14} - 15 p^{63} T^{15} + p^{72} T^{16} \) |
| 3 | \( 1 - 7 T + 9133 p T^{2} + 183016 p^{3} T^{3} + 4666286 p^{4} T^{4} + 736515446 p^{5} T^{5} + 10136437651 p^{7} T^{6} + 2700678800887 p^{6} T^{7} + 315725629189574 p^{7} T^{8} + 2700678800887 p^{15} T^{9} + 10136437651 p^{25} T^{10} + 736515446 p^{32} T^{11} + 4666286 p^{40} T^{12} + 183016 p^{48} T^{13} + 9133 p^{55} T^{14} - 7 p^{63} T^{15} + p^{72} T^{16} \) | |
| 5 | \( 1 - 3894 T + 15291454 T^{2} - 39592589754 T^{3} + 97974686225209 T^{4} - 193926452620339728 T^{5} + 72888798925476291302 p T^{6} - \)\(23\!\cdots\!28\)\( p^{2} T^{7} + \)\(69\!\cdots\!52\)\( p^{3} T^{8} - \)\(23\!\cdots\!28\)\( p^{11} T^{9} + 72888798925476291302 p^{19} T^{10} - 193926452620339728 p^{27} T^{11} + 97974686225209 p^{36} T^{12} - 39592589754 p^{45} T^{13} + 15291454 p^{54} T^{14} - 3894 p^{63} T^{15} + p^{72} T^{16} \) | |
| 7 | \( 1 + 1019 p T + 18710247 p T^{2} + 985871673442 T^{3} + 1748903147974751 p T^{4} + 1615669669640346639 p^{2} T^{5} + \)\(22\!\cdots\!58\)\( p^{3} T^{6} + \)\(18\!\cdots\!41\)\( p^{4} T^{7} + \)\(21\!\cdots\!62\)\( p^{5} T^{8} + \)\(18\!\cdots\!41\)\( p^{13} T^{9} + \)\(22\!\cdots\!58\)\( p^{21} T^{10} + 1615669669640346639 p^{29} T^{11} + 1748903147974751 p^{37} T^{12} + 985871673442 p^{45} T^{13} + 18710247 p^{55} T^{14} + 1019 p^{64} T^{15} + p^{72} T^{16} \) | |
| 11 | \( 1 - 172818 T + 23592385162 T^{2} - 201704841517590 p T^{3} + \)\(18\!\cdots\!57\)\( T^{4} - \)\(12\!\cdots\!20\)\( T^{5} + \)\(78\!\cdots\!02\)\( T^{6} - \)\(42\!\cdots\!92\)\( T^{7} + \)\(22\!\cdots\!16\)\( T^{8} - \)\(42\!\cdots\!92\)\( p^{9} T^{9} + \)\(78\!\cdots\!02\)\( p^{18} T^{10} - \)\(12\!\cdots\!20\)\( p^{27} T^{11} + \)\(18\!\cdots\!57\)\( p^{36} T^{12} - 201704841517590 p^{46} T^{13} + 23592385162 p^{54} T^{14} - 172818 p^{63} T^{15} + p^{72} T^{16} \) | |
| 13 | \( 1 - 8407 p T + 3320653425 p T^{2} - 5154256155442958 T^{3} + \)\(89\!\cdots\!28\)\( T^{4} - \)\(98\!\cdots\!60\)\( T^{5} + \)\(13\!\cdots\!23\)\( T^{6} - \)\(11\!\cdots\!95\)\( T^{7} + \)\(15\!\cdots\!22\)\( T^{8} - \)\(11\!\cdots\!95\)\( p^{9} T^{9} + \)\(13\!\cdots\!23\)\( p^{18} T^{10} - \)\(98\!\cdots\!60\)\( p^{27} T^{11} + \)\(89\!\cdots\!28\)\( p^{36} T^{12} - 5154256155442958 p^{45} T^{13} + 3320653425 p^{55} T^{14} - 8407 p^{64} T^{15} + p^{72} T^{16} \) | |
| 17 | \( 1 - 583575 T + 836436120727 T^{2} - 351333641594829684 T^{3} + \)\(29\!\cdots\!95\)\( T^{4} - \)\(99\!\cdots\!19\)\( T^{5} + \)\(63\!\cdots\!86\)\( T^{6} - \)\(17\!\cdots\!19\)\( T^{7} + \)\(91\!\cdots\!88\)\( T^{8} - \)\(17\!\cdots\!19\)\( p^{9} T^{9} + \)\(63\!\cdots\!86\)\( p^{18} T^{10} - \)\(99\!\cdots\!19\)\( p^{27} T^{11} + \)\(29\!\cdots\!95\)\( p^{36} T^{12} - 351333641594829684 p^{45} T^{13} + 836436120727 p^{54} T^{14} - 583575 p^{63} T^{15} + p^{72} T^{16} \) | |
| 23 | \( 1 + 2292405 T + 11138212731967 T^{2} + 21924823966421407104 T^{3} + \)\(60\!\cdots\!98\)\( T^{4} + \)\(99\!\cdots\!70\)\( T^{5} + \)\(19\!\cdots\!09\)\( T^{6} + \)\(27\!\cdots\!35\)\( T^{7} + \)\(18\!\cdots\!82\)\( p T^{8} + \)\(27\!\cdots\!35\)\( p^{9} T^{9} + \)\(19\!\cdots\!09\)\( p^{18} T^{10} + \)\(99\!\cdots\!70\)\( p^{27} T^{11} + \)\(60\!\cdots\!98\)\( p^{36} T^{12} + 21924823966421407104 p^{45} T^{13} + 11138212731967 p^{54} T^{14} + 2292405 p^{63} T^{15} + p^{72} T^{16} \) | |
| 29 | \( 1 - 4546335 T + 79161257246173 T^{2} - \)\(28\!\cdots\!22\)\( T^{3} + \)\(29\!\cdots\!52\)\( T^{4} - \)\(87\!\cdots\!16\)\( T^{5} + \)\(69\!\cdots\!07\)\( T^{6} - \)\(17\!\cdots\!39\)\( T^{7} + \)\(11\!\cdots\!34\)\( T^{8} - \)\(17\!\cdots\!39\)\( p^{9} T^{9} + \)\(69\!\cdots\!07\)\( p^{18} T^{10} - \)\(87\!\cdots\!16\)\( p^{27} T^{11} + \)\(29\!\cdots\!52\)\( p^{36} T^{12} - \)\(28\!\cdots\!22\)\( p^{45} T^{13} + 79161257246173 p^{54} T^{14} - 4546335 p^{63} T^{15} + p^{72} T^{16} \) | |
| 31 | \( 1 + 8277416 T + 133496259942552 T^{2} + \)\(10\!\cdots\!56\)\( T^{3} + \)\(95\!\cdots\!92\)\( T^{4} + \)\(61\!\cdots\!56\)\( T^{5} + \)\(43\!\cdots\!52\)\( T^{6} + \)\(23\!\cdots\!44\)\( T^{7} + \)\(13\!\cdots\!22\)\( T^{8} + \)\(23\!\cdots\!44\)\( p^{9} T^{9} + \)\(43\!\cdots\!52\)\( p^{18} T^{10} + \)\(61\!\cdots\!56\)\( p^{27} T^{11} + \)\(95\!\cdots\!92\)\( p^{36} T^{12} + \)\(10\!\cdots\!56\)\( p^{45} T^{13} + 133496259942552 p^{54} T^{14} + 8277416 p^{63} T^{15} + p^{72} T^{16} \) | |
| 37 | \( 1 - 24485536 T + 729676315318776 T^{2} - \)\(89\!\cdots\!52\)\( T^{3} + \)\(15\!\cdots\!60\)\( T^{4} - \)\(13\!\cdots\!64\)\( T^{5} + \)\(25\!\cdots\!76\)\( T^{6} - \)\(21\!\cdots\!48\)\( T^{7} + \)\(39\!\cdots\!98\)\( T^{8} - \)\(21\!\cdots\!48\)\( p^{9} T^{9} + \)\(25\!\cdots\!76\)\( p^{18} T^{10} - \)\(13\!\cdots\!64\)\( p^{27} T^{11} + \)\(15\!\cdots\!60\)\( p^{36} T^{12} - \)\(89\!\cdots\!52\)\( p^{45} T^{13} + 729676315318776 p^{54} T^{14} - 24485536 p^{63} T^{15} + p^{72} T^{16} \) | |
| 41 | \( 1 - 35051946 T + 1987196667762736 T^{2} - \)\(48\!\cdots\!54\)\( T^{3} + \)\(17\!\cdots\!00\)\( T^{4} - \)\(33\!\cdots\!54\)\( T^{5} + \)\(93\!\cdots\!48\)\( T^{6} - \)\(15\!\cdots\!54\)\( T^{7} + \)\(35\!\cdots\!06\)\( T^{8} - \)\(15\!\cdots\!54\)\( p^{9} T^{9} + \)\(93\!\cdots\!48\)\( p^{18} T^{10} - \)\(33\!\cdots\!54\)\( p^{27} T^{11} + \)\(17\!\cdots\!00\)\( p^{36} T^{12} - \)\(48\!\cdots\!54\)\( p^{45} T^{13} + 1987196667762736 p^{54} T^{14} - 35051946 p^{63} T^{15} + p^{72} T^{16} \) | |
| 43 | \( 1 - 36624268 T + 3144072390924366 T^{2} - \)\(99\!\cdots\!84\)\( T^{3} + \)\(10\!\cdots\!43\)\( p T^{4} - \)\(12\!\cdots\!96\)\( T^{5} + \)\(42\!\cdots\!10\)\( T^{6} - \)\(96\!\cdots\!32\)\( T^{7} + \)\(25\!\cdots\!16\)\( T^{8} - \)\(96\!\cdots\!32\)\( p^{9} T^{9} + \)\(42\!\cdots\!10\)\( p^{18} T^{10} - \)\(12\!\cdots\!96\)\( p^{27} T^{11} + \)\(10\!\cdots\!43\)\( p^{37} T^{12} - \)\(99\!\cdots\!84\)\( p^{45} T^{13} + 3144072390924366 p^{54} T^{14} - 36624268 p^{63} T^{15} + p^{72} T^{16} \) | |
| 47 | \( 1 - 9865524 T + 5203582909578334 T^{2} - \)\(36\!\cdots\!16\)\( T^{3} + \)\(11\!\cdots\!05\)\( T^{4} + \)\(13\!\cdots\!24\)\( T^{5} + \)\(15\!\cdots\!42\)\( T^{6} + \)\(36\!\cdots\!56\)\( T^{7} + \)\(17\!\cdots\!28\)\( T^{8} + \)\(36\!\cdots\!56\)\( p^{9} T^{9} + \)\(15\!\cdots\!42\)\( p^{18} T^{10} + \)\(13\!\cdots\!24\)\( p^{27} T^{11} + \)\(11\!\cdots\!05\)\( p^{36} T^{12} - \)\(36\!\cdots\!16\)\( p^{45} T^{13} + 5203582909578334 p^{54} T^{14} - 9865524 p^{63} T^{15} + p^{72} T^{16} \) | |
| 53 | \( 1 - 13963683 T + 17073484815670069 T^{2} - \)\(26\!\cdots\!98\)\( T^{3} + \)\(14\!\cdots\!36\)\( T^{4} - \)\(22\!\cdots\!28\)\( T^{5} + \)\(76\!\cdots\!99\)\( T^{6} - \)\(11\!\cdots\!71\)\( T^{7} + \)\(29\!\cdots\!10\)\( T^{8} - \)\(11\!\cdots\!71\)\( p^{9} T^{9} + \)\(76\!\cdots\!99\)\( p^{18} T^{10} - \)\(22\!\cdots\!28\)\( p^{27} T^{11} + \)\(14\!\cdots\!36\)\( p^{36} T^{12} - \)\(26\!\cdots\!98\)\( p^{45} T^{13} + 17073484815670069 p^{54} T^{14} - 13963683 p^{63} T^{15} + p^{72} T^{16} \) | |
| 59 | \( 1 - 21215463 T + 51939655106856319 T^{2} - \)\(11\!\cdots\!56\)\( T^{3} + \)\(12\!\cdots\!22\)\( T^{4} - \)\(26\!\cdots\!26\)\( T^{5} + \)\(20\!\cdots\!73\)\( T^{6} - \)\(36\!\cdots\!61\)\( T^{7} + \)\(21\!\cdots\!10\)\( T^{8} - \)\(36\!\cdots\!61\)\( p^{9} T^{9} + \)\(20\!\cdots\!73\)\( p^{18} T^{10} - \)\(26\!\cdots\!26\)\( p^{27} T^{11} + \)\(12\!\cdots\!22\)\( p^{36} T^{12} - \)\(11\!\cdots\!56\)\( p^{45} T^{13} + 51939655106856319 p^{54} T^{14} - 21215463 p^{63} T^{15} + p^{72} T^{16} \) | |
| 61 | \( 1 - 180552112 T + 63384711665992446 T^{2} - \)\(10\!\cdots\!84\)\( T^{3} + \)\(21\!\cdots\!45\)\( T^{4} - \)\(30\!\cdots\!20\)\( T^{5} + \)\(44\!\cdots\!66\)\( T^{6} - \)\(52\!\cdots\!16\)\( T^{7} + \)\(63\!\cdots\!08\)\( T^{8} - \)\(52\!\cdots\!16\)\( p^{9} T^{9} + \)\(44\!\cdots\!66\)\( p^{18} T^{10} - \)\(30\!\cdots\!20\)\( p^{27} T^{11} + \)\(21\!\cdots\!45\)\( p^{36} T^{12} - \)\(10\!\cdots\!84\)\( p^{45} T^{13} + 63384711665992446 p^{54} T^{14} - 180552112 p^{63} T^{15} + p^{72} T^{16} \) | |
| 67 | \( 1 - 1767355 T + 128860418793589167 T^{2} - \)\(52\!\cdots\!20\)\( p T^{3} + \)\(87\!\cdots\!50\)\( T^{4} - \)\(28\!\cdots\!58\)\( T^{5} + \)\(39\!\cdots\!73\)\( T^{6} - \)\(12\!\cdots\!01\)\( T^{7} + \)\(12\!\cdots\!78\)\( T^{8} - \)\(12\!\cdots\!01\)\( p^{9} T^{9} + \)\(39\!\cdots\!73\)\( p^{18} T^{10} - \)\(28\!\cdots\!58\)\( p^{27} T^{11} + \)\(87\!\cdots\!50\)\( p^{36} T^{12} - \)\(52\!\cdots\!20\)\( p^{46} T^{13} + 128860418793589167 p^{54} T^{14} - 1767355 p^{63} T^{15} + p^{72} T^{16} \) | |
| 71 | \( 1 - 273631578 T + 157335255139337836 T^{2} - \)\(37\!\cdots\!98\)\( T^{3} + \)\(15\!\cdots\!64\)\( T^{4} - \)\(31\!\cdots\!74\)\( T^{5} + \)\(10\!\cdots\!28\)\( T^{6} - \)\(19\!\cdots\!22\)\( T^{7} + \)\(55\!\cdots\!26\)\( T^{8} - \)\(19\!\cdots\!22\)\( p^{9} T^{9} + \)\(10\!\cdots\!28\)\( p^{18} T^{10} - \)\(31\!\cdots\!74\)\( p^{27} T^{11} + \)\(15\!\cdots\!64\)\( p^{36} T^{12} - \)\(37\!\cdots\!98\)\( p^{45} T^{13} + 157335255139337836 p^{54} T^{14} - 273631578 p^{63} T^{15} + p^{72} T^{16} \) | |
| 73 | \( 1 + 263711543 T + 331465751377699875 T^{2} + \)\(77\!\cdots\!48\)\( T^{3} + \)\(50\!\cdots\!03\)\( T^{4} + \)\(10\!\cdots\!11\)\( T^{5} + \)\(48\!\cdots\!62\)\( T^{6} + \)\(92\!\cdots\!27\)\( T^{7} + \)\(33\!\cdots\!60\)\( T^{8} + \)\(92\!\cdots\!27\)\( p^{9} T^{9} + \)\(48\!\cdots\!62\)\( p^{18} T^{10} + \)\(10\!\cdots\!11\)\( p^{27} T^{11} + \)\(50\!\cdots\!03\)\( p^{36} T^{12} + \)\(77\!\cdots\!48\)\( p^{45} T^{13} + 331465751377699875 p^{54} T^{14} + 263711543 p^{63} T^{15} + p^{72} T^{16} \) | |
| 79 | \( 1 - 744472174 T + 699588345246686052 T^{2} - \)\(39\!\cdots\!10\)\( T^{3} + \)\(23\!\cdots\!32\)\( T^{4} - \)\(10\!\cdots\!26\)\( T^{5} + \)\(48\!\cdots\!80\)\( T^{6} - \)\(18\!\cdots\!38\)\( T^{7} + \)\(69\!\cdots\!70\)\( T^{8} - \)\(18\!\cdots\!38\)\( p^{9} T^{9} + \)\(48\!\cdots\!80\)\( p^{18} T^{10} - \)\(10\!\cdots\!26\)\( p^{27} T^{11} + \)\(23\!\cdots\!32\)\( p^{36} T^{12} - \)\(39\!\cdots\!10\)\( p^{45} T^{13} + 699588345246686052 p^{54} T^{14} - 744472174 p^{63} T^{15} + p^{72} T^{16} \) | |
| 83 | \( 1 - 832139910 T + 1067812716222727228 T^{2} - \)\(71\!\cdots\!58\)\( T^{3} + \)\(55\!\cdots\!64\)\( T^{4} - \)\(30\!\cdots\!10\)\( T^{5} + \)\(18\!\cdots\!80\)\( T^{6} - \)\(84\!\cdots\!14\)\( T^{7} + \)\(40\!\cdots\!38\)\( T^{8} - \)\(84\!\cdots\!14\)\( p^{9} T^{9} + \)\(18\!\cdots\!80\)\( p^{18} T^{10} - \)\(30\!\cdots\!10\)\( p^{27} T^{11} + \)\(55\!\cdots\!64\)\( p^{36} T^{12} - \)\(71\!\cdots\!58\)\( p^{45} T^{13} + 1067812716222727228 p^{54} T^{14} - 832139910 p^{63} T^{15} + p^{72} T^{16} \) | |
| 89 | \( 1 + 3274806 p T + 1214581057689547912 T^{2} + \)\(29\!\cdots\!18\)\( T^{3} + \)\(80\!\cdots\!64\)\( T^{4} + \)\(26\!\cdots\!26\)\( T^{5} + \)\(38\!\cdots\!52\)\( T^{6} + \)\(13\!\cdots\!74\)\( T^{7} + \)\(14\!\cdots\!42\)\( T^{8} + \)\(13\!\cdots\!74\)\( p^{9} T^{9} + \)\(38\!\cdots\!52\)\( p^{18} T^{10} + \)\(26\!\cdots\!26\)\( p^{27} T^{11} + \)\(80\!\cdots\!64\)\( p^{36} T^{12} + \)\(29\!\cdots\!18\)\( p^{45} T^{13} + 1214581057689547912 p^{54} T^{14} + 3274806 p^{64} T^{15} + p^{72} T^{16} \) | |
| 97 | \( 1 + 3483837140 T + 8339577434333907816 T^{2} + \)\(14\!\cdots\!08\)\( T^{3} + \)\(20\!\cdots\!40\)\( T^{4} + \)\(24\!\cdots\!56\)\( T^{5} + \)\(27\!\cdots\!24\)\( T^{6} + \)\(28\!\cdots\!32\)\( T^{7} + \)\(25\!\cdots\!14\)\( T^{8} + \)\(28\!\cdots\!32\)\( p^{9} T^{9} + \)\(27\!\cdots\!24\)\( p^{18} T^{10} + \)\(24\!\cdots\!56\)\( p^{27} T^{11} + \)\(20\!\cdots\!40\)\( p^{36} T^{12} + \)\(14\!\cdots\!08\)\( p^{45} T^{13} + 8339577434333907816 p^{54} T^{14} + 3483837140 p^{63} T^{15} + p^{72} T^{16} \) | |
| show more | ||
| show less | ||
\(L(s) = \displaystyle\prod_p \ \prod_{j=1}^{16} (1 - \alpha_{j,p}\, p^{-s})^{-1}\)
Imaginary part of the first few zeros on the critical line
−6.62357282519856290156939118643, −6.51541552220294343060417129569, −6.43451479849802655833808649133, −5.86644379450180981655201839797, −5.82221975383444593390774571152, −5.75764131181370034865569555017, −5.61574120257359910981275363064, −5.57493630076643760082596225634, −5.36094187061282492011121092138, −4.67813865591330012935620387254, −4.28319713573947044517676925415, −4.11215004203933638632913066381, −3.80111585915551779389143063999, −3.78694178789874056213798447836, −3.50831063442538838526369635463, −3.38729000783488099910422988935, −2.71222295477195927780166534522, −2.42044760528025127860201510800, −2.28324465436453339856357915132, −1.63120280561633983834314855180, −1.47771595416754314027295505814, −1.42405251684325837671702240186, −0.952445434843203143590712223714, −0.68830806815822460384622222861, −0.094726626200472959111459146522, 0.094726626200472959111459146522, 0.68830806815822460384622222861, 0.952445434843203143590712223714, 1.42405251684325837671702240186, 1.47771595416754314027295505814, 1.63120280561633983834314855180, 2.28324465436453339856357915132, 2.42044760528025127860201510800, 2.71222295477195927780166534522, 3.38729000783488099910422988935, 3.50831063442538838526369635463, 3.78694178789874056213798447836, 3.80111585915551779389143063999, 4.11215004203933638632913066381, 4.28319713573947044517676925415, 4.67813865591330012935620387254, 5.36094187061282492011121092138, 5.57493630076643760082596225634, 5.61574120257359910981275363064, 5.75764131181370034865569555017, 5.82221975383444593390774571152, 5.86644379450180981655201839797, 6.43451479849802655833808649133, 6.51541552220294343060417129569, 6.62357282519856290156939118643
Graph of the $Z$-function along the critical line
Plot not available for L-functions of degree greater than 10.