Dirichlet series
| L(s) = 1 | − 54·3-s + 40·4-s + 1.53e3·9-s − 2.16e3·12-s + 688·16-s + 268·17-s − 452·23-s + 513·25-s − 3.07e4·27-s − 1.09e3·29-s + 6.15e4·36-s − 316·43-s − 3.71e4·48-s + 2.44e3·49-s − 1.44e4·51-s + 2.79e3·53-s + 4.18e3·61-s + 5.44e3·64-s + 1.07e4·68-s + 2.44e4·69-s − 2.77e4·75-s − 230·79-s + 4.84e5·81-s + 5.90e4·87-s − 1.80e4·92-s + 2.05e4·100-s + 522·101-s + ⋯ |
| L(s) = 1 | − 10.3·3-s + 5·4-s + 57·9-s − 51.9·12-s + 43/4·16-s + 3.82·17-s − 4.09·23-s + 4.10·25-s − 219.·27-s − 7.00·29-s + 285·36-s − 1.12·43-s − 111.·48-s + 7.12·49-s − 39.7·51-s + 7.25·53-s + 8.78·61-s + 10.6·64-s + 19.1·68-s + 42.5·69-s − 42.6·75-s − 0.327·79-s + 665·81-s + 72.8·87-s − 20.4·92-s + 20.5·100-s + 0.514·101-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(3^{18} \cdot 13^{36}\right)^{s/2} \, \Gamma_{\C}(s)^{18} \, L(s)\cr=\mathstrut & \,\Lambda(4-s)\end{aligned}\]
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(3^{18} \cdot 13^{36}\right)^{s/2} \, \Gamma_{\C}(s+3/2)^{18} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}\]
Invariants
| Degree: | \(36\) |
| Conductor: | \(3^{18} \cdot 13^{36}\) |
| Sign: | $1$ |
| Analytic conductor: | \(3.67902\times 10^{26}\) |
| Root analytic conductor: | \(5.46936\) |
| Motivic weight: | \(3\) |
| Rational: | yes |
| Arithmetic: | yes |
| Character: | Trivial |
| Primitive: | no |
| Self-dual: | yes |
| Analytic rank: | \(0\) |
| Selberg data: | \((36,\ 3^{18} \cdot 13^{36} ,\ ( \ : [3/2]^{18} ),\ 1 )\) |
Particular Values
| \(L(2)\) | \(\approx\) | \(0.02264727338\) |
| \(L(\frac12)\) | \(\approx\) | \(0.02264727338\) |
| \(L(\frac{5}{2})\) | not available | |
| \(L(1)\) | not available |
Euler product
\(L(s) = \displaystyle \prod_{p} F_p(p^{-s})^{-1} \)
| $p$ | $F_p(T)$ | |
|---|---|---|
| bad | 3 | \( ( 1 + p T )^{18} \) |
| 13 | \( 1 \) | |
| good | 2 | \( 1 - 5 p^{3} T^{2} + 57 p^{4} T^{4} - 14405 T^{6} + 87647 p T^{8} - 1724947 T^{10} + 14494565 T^{12} - 27347243 p^{2} T^{14} + 25084699 p^{5} T^{16} - 96106895 p^{6} T^{18} + 25084699 p^{11} T^{20} - 27347243 p^{14} T^{22} + 14494565 p^{18} T^{24} - 1724947 p^{24} T^{26} + 87647 p^{31} T^{28} - 14405 p^{36} T^{30} + 57 p^{46} T^{32} - 5 p^{51} T^{34} + p^{54} T^{36} \) |
| 5 | \( 1 - 513 T^{2} + 148221 T^{4} - 35411651 T^{6} + 1398775227 p T^{8} - 1194952434711 T^{10} + 188893926307086 T^{12} - 27017006882653257 T^{14} + 3630332321004416757 T^{16} - \)\(46\!\cdots\!79\)\( T^{18} + 3630332321004416757 p^{6} T^{20} - 27017006882653257 p^{12} T^{22} + 188893926307086 p^{18} T^{24} - 1194952434711 p^{24} T^{26} + 1398775227 p^{31} T^{28} - 35411651 p^{36} T^{30} + 148221 p^{42} T^{32} - 513 p^{48} T^{34} + p^{54} T^{36} \) | |
| 7 | \( 1 - 2445 T^{2} + 3218081 T^{4} - 3039641919 T^{6} + 324841151177 p T^{8} - 202220442293969 p T^{10} + 107918770266567230 p T^{12} - 7176399945187288741 p^{2} T^{14} + \)\(29\!\cdots\!13\)\( p^{2} T^{16} - \)\(10\!\cdots\!95\)\( p^{2} T^{18} + \)\(29\!\cdots\!13\)\( p^{8} T^{20} - 7176399945187288741 p^{14} T^{22} + 107918770266567230 p^{19} T^{24} - 202220442293969 p^{25} T^{26} + 324841151177 p^{31} T^{28} - 3039641919 p^{36} T^{30} + 3218081 p^{42} T^{32} - 2445 p^{48} T^{34} + p^{54} T^{36} \) | |
| 11 | \( 1 - 9319 T^{2} + 46858038 T^{4} - 168837173710 T^{6} + 483251663348903 T^{8} - 1155074022126235477 T^{10} + \)\(21\!\cdots\!64\)\( p T^{12} - \)\(42\!\cdots\!05\)\( T^{14} + \)\(67\!\cdots\!32\)\( T^{16} - \)\(95\!\cdots\!85\)\( T^{18} + \)\(67\!\cdots\!32\)\( p^{6} T^{20} - \)\(42\!\cdots\!05\)\( p^{12} T^{22} + \)\(21\!\cdots\!64\)\( p^{19} T^{24} - 1155074022126235477 p^{24} T^{26} + 483251663348903 p^{30} T^{28} - 168837173710 p^{36} T^{30} + 46858038 p^{42} T^{32} - 9319 p^{48} T^{34} + p^{54} T^{36} \) | |
| 17 | \( ( 1 - 134 T + 31870 T^{2} - 2895632 T^{3} + 389871107 T^{4} - 25426400680 T^{5} + 2595913829472 T^{6} - 127839526448684 T^{7} + 12429944904049430 T^{8} - 559326357383412308 T^{9} + 12429944904049430 p^{3} T^{10} - 127839526448684 p^{6} T^{11} + 2595913829472 p^{9} T^{12} - 25426400680 p^{12} T^{13} + 389871107 p^{15} T^{14} - 2895632 p^{18} T^{15} + 31870 p^{21} T^{16} - 134 p^{24} T^{17} + p^{27} T^{18} )^{2} \) | |
| 19 | \( 1 - 49944 T^{2} + 1375568226 T^{4} - 26579498442244 T^{6} + 398908858127042313 T^{8} - \)\(49\!\cdots\!40\)\( T^{10} + \)\(51\!\cdots\!44\)\( T^{12} - \)\(24\!\cdots\!02\)\( p T^{14} + \)\(37\!\cdots\!32\)\( T^{16} - \)\(27\!\cdots\!52\)\( T^{18} + \)\(37\!\cdots\!32\)\( p^{6} T^{20} - \)\(24\!\cdots\!02\)\( p^{13} T^{22} + \)\(51\!\cdots\!44\)\( p^{18} T^{24} - \)\(49\!\cdots\!40\)\( p^{24} T^{26} + 398908858127042313 p^{30} T^{28} - 26579498442244 p^{36} T^{30} + 1375568226 p^{42} T^{32} - 49944 p^{48} T^{34} + p^{54} T^{36} \) | |
| 23 | \( ( 1 + 226 T + 81815 T^{2} + 16258082 T^{3} + 3468064857 T^{4} + 557247960198 T^{5} + 90899581520090 T^{6} + 12044943239754990 T^{7} + 1588739302979220263 T^{8} + \)\(17\!\cdots\!68\)\( T^{9} + 1588739302979220263 p^{3} T^{10} + 12044943239754990 p^{6} T^{11} + 90899581520090 p^{9} T^{12} + 557247960198 p^{12} T^{13} + 3468064857 p^{15} T^{14} + 16258082 p^{18} T^{15} + 81815 p^{21} T^{16} + 226 p^{24} T^{17} + p^{27} T^{18} )^{2} \) | |
| 29 | \( ( 1 + 547 T + 257397 T^{2} + 76666599 T^{3} + 20293099631 T^{4} + 4094154725297 T^{5} + 763499956425928 T^{6} + 117635069996325623 T^{7} + 18495766143723554001 T^{8} + \)\(27\!\cdots\!45\)\( T^{9} + 18495766143723554001 p^{3} T^{10} + 117635069996325623 p^{6} T^{11} + 763499956425928 p^{9} T^{12} + 4094154725297 p^{12} T^{13} + 20293099631 p^{15} T^{14} + 76666599 p^{18} T^{15} + 257397 p^{21} T^{16} + 547 p^{24} T^{17} + p^{27} T^{18} )^{2} \) | |
| 31 | \( 1 - 314837 T^{2} + 46896621725 T^{4} - 4416626336483407 T^{6} + \)\(29\!\cdots\!67\)\( T^{8} - \)\(15\!\cdots\!51\)\( T^{10} + \)\(66\!\cdots\!62\)\( T^{12} - \)\(24\!\cdots\!01\)\( T^{14} + \)\(82\!\cdots\!05\)\( T^{16} - \)\(25\!\cdots\!87\)\( T^{18} + \)\(82\!\cdots\!05\)\( p^{6} T^{20} - \)\(24\!\cdots\!01\)\( p^{12} T^{22} + \)\(66\!\cdots\!62\)\( p^{18} T^{24} - \)\(15\!\cdots\!51\)\( p^{24} T^{26} + \)\(29\!\cdots\!67\)\( p^{30} T^{28} - 4416626336483407 p^{36} T^{30} + 46896621725 p^{42} T^{32} - 314837 p^{48} T^{34} + p^{54} T^{36} \) | |
| 37 | \( 1 - 464158 T^{2} + 102657574519 T^{4} - 14242654505264502 T^{6} + \)\(13\!\cdots\!67\)\( T^{8} - \)\(90\!\cdots\!32\)\( T^{10} + \)\(39\!\cdots\!60\)\( T^{12} - \)\(56\!\cdots\!44\)\( T^{14} - \)\(57\!\cdots\!43\)\( T^{16} + \)\(48\!\cdots\!68\)\( T^{18} - \)\(57\!\cdots\!43\)\( p^{6} T^{20} - \)\(56\!\cdots\!44\)\( p^{12} T^{22} + \)\(39\!\cdots\!60\)\( p^{18} T^{24} - \)\(90\!\cdots\!32\)\( p^{24} T^{26} + \)\(13\!\cdots\!67\)\( p^{30} T^{28} - 14242654505264502 p^{36} T^{30} + 102657574519 p^{42} T^{32} - 464158 p^{48} T^{34} + p^{54} T^{36} \) | |
| 41 | \( 1 - 605896 T^{2} + 189063195150 T^{4} - 40326653719449464 T^{6} + \)\(65\!\cdots\!17\)\( T^{8} - \)\(87\!\cdots\!48\)\( T^{10} + \)\(97\!\cdots\!96\)\( T^{12} - \)\(93\!\cdots\!10\)\( T^{14} + \)\(78\!\cdots\!28\)\( T^{16} - \)\(57\!\cdots\!84\)\( T^{18} + \)\(78\!\cdots\!28\)\( p^{6} T^{20} - \)\(93\!\cdots\!10\)\( p^{12} T^{22} + \)\(97\!\cdots\!96\)\( p^{18} T^{24} - \)\(87\!\cdots\!48\)\( p^{24} T^{26} + \)\(65\!\cdots\!17\)\( p^{30} T^{28} - 40326653719449464 p^{36} T^{30} + 189063195150 p^{42} T^{32} - 605896 p^{48} T^{34} + p^{54} T^{36} \) | |
| 43 | \( ( 1 + 158 T + 414734 T^{2} + 70335996 T^{3} + 91129375254 T^{4} + 14698619715102 T^{5} + 13437400325294869 T^{6} + 1968909046011777708 T^{7} + \)\(14\!\cdots\!28\)\( T^{8} + \)\(18\!\cdots\!08\)\( T^{9} + \)\(14\!\cdots\!28\)\( p^{3} T^{10} + 1968909046011777708 p^{6} T^{11} + 13437400325294869 p^{9} T^{12} + 14698619715102 p^{12} T^{13} + 91129375254 p^{15} T^{14} + 70335996 p^{18} T^{15} + 414734 p^{21} T^{16} + 158 p^{24} T^{17} + p^{27} T^{18} )^{2} \) | |
| 47 | \( 1 - 493088 T^{2} + 110907180766 T^{4} - 15566641050041936 T^{6} + \)\(15\!\cdots\!93\)\( T^{8} - \)\(11\!\cdots\!20\)\( T^{10} + \)\(54\!\cdots\!16\)\( T^{12} + \)\(20\!\cdots\!34\)\( T^{14} - \)\(90\!\cdots\!64\)\( T^{16} + \)\(12\!\cdots\!88\)\( T^{18} - \)\(90\!\cdots\!64\)\( p^{6} T^{20} + \)\(20\!\cdots\!34\)\( p^{12} T^{22} + \)\(54\!\cdots\!16\)\( p^{18} T^{24} - \)\(11\!\cdots\!20\)\( p^{24} T^{26} + \)\(15\!\cdots\!93\)\( p^{30} T^{28} - 15566641050041936 p^{36} T^{30} + 110907180766 p^{42} T^{32} - 493088 p^{48} T^{34} + p^{54} T^{36} \) | |
| 53 | \( ( 1 - 1399 T + 1838846 T^{2} - 1568203054 T^{3} + 1236563700767 T^{4} - 774676352395257 T^{5} + 451502726866177032 T^{6} - \)\(22\!\cdots\!09\)\( T^{7} + \)\(10\!\cdots\!84\)\( T^{8} - \)\(40\!\cdots\!57\)\( T^{9} + \)\(10\!\cdots\!84\)\( p^{3} T^{10} - \)\(22\!\cdots\!09\)\( p^{6} T^{11} + 451502726866177032 p^{9} T^{12} - 774676352395257 p^{12} T^{13} + 1236563700767 p^{15} T^{14} - 1568203054 p^{18} T^{15} + 1838846 p^{21} T^{16} - 1399 p^{24} T^{17} + p^{27} T^{18} )^{2} \) | |
| 59 | \( 1 - 1585421 T^{2} + 1425053114479 T^{4} - 902128703822262515 T^{6} + \)\(44\!\cdots\!14\)\( T^{8} - \)\(17\!\cdots\!62\)\( T^{10} + \)\(60\!\cdots\!90\)\( T^{12} - \)\(17\!\cdots\!57\)\( T^{14} + \)\(44\!\cdots\!88\)\( T^{16} - \)\(97\!\cdots\!62\)\( T^{18} + \)\(44\!\cdots\!88\)\( p^{6} T^{20} - \)\(17\!\cdots\!57\)\( p^{12} T^{22} + \)\(60\!\cdots\!90\)\( p^{18} T^{24} - \)\(17\!\cdots\!62\)\( p^{24} T^{26} + \)\(44\!\cdots\!14\)\( p^{30} T^{28} - 902128703822262515 p^{36} T^{30} + 1425053114479 p^{42} T^{32} - 1585421 p^{48} T^{34} + p^{54} T^{36} \) | |
| 61 | \( ( 1 - 2092 T + 2899914 T^{2} - 2746264024 T^{3} + 2107526963381 T^{4} - 1297704122709412 T^{5} + 700467654937121908 T^{6} - \)\(33\!\cdots\!26\)\( T^{7} + \)\(15\!\cdots\!76\)\( T^{8} - \)\(69\!\cdots\!56\)\( T^{9} + \)\(15\!\cdots\!76\)\( p^{3} T^{10} - \)\(33\!\cdots\!26\)\( p^{6} T^{11} + 700467654937121908 p^{9} T^{12} - 1297704122709412 p^{12} T^{13} + 2107526963381 p^{15} T^{14} - 2746264024 p^{18} T^{15} + 2899914 p^{21} T^{16} - 2092 p^{24} T^{17} + p^{27} T^{18} )^{2} \) | |
| 67 | \( 1 - 2624932 T^{2} + 3557264917814 T^{4} - 3303507939519540420 T^{6} + \)\(23\!\cdots\!29\)\( T^{8} - \)\(13\!\cdots\!52\)\( T^{10} + \)\(66\!\cdots\!48\)\( T^{12} - \)\(27\!\cdots\!74\)\( T^{14} + \)\(10\!\cdots\!88\)\( T^{16} - \)\(32\!\cdots\!60\)\( T^{18} + \)\(10\!\cdots\!88\)\( p^{6} T^{20} - \)\(27\!\cdots\!74\)\( p^{12} T^{22} + \)\(66\!\cdots\!48\)\( p^{18} T^{24} - \)\(13\!\cdots\!52\)\( p^{24} T^{26} + \)\(23\!\cdots\!29\)\( p^{30} T^{28} - 3303507939519540420 p^{36} T^{30} + 3557264917814 p^{42} T^{32} - 2624932 p^{48} T^{34} + p^{54} T^{36} \) | |
| 71 | \( 1 - 2233402 T^{2} + 2827392454395 T^{4} - 2593483622986925722 T^{6} + \)\(19\!\cdots\!75\)\( T^{8} - \)\(11\!\cdots\!60\)\( T^{10} + \)\(63\!\cdots\!72\)\( T^{12} - \)\(30\!\cdots\!92\)\( T^{14} + \)\(12\!\cdots\!57\)\( T^{16} - \)\(48\!\cdots\!92\)\( T^{18} + \)\(12\!\cdots\!57\)\( p^{6} T^{20} - \)\(30\!\cdots\!92\)\( p^{12} T^{22} + \)\(63\!\cdots\!72\)\( p^{18} T^{24} - \)\(11\!\cdots\!60\)\( p^{24} T^{26} + \)\(19\!\cdots\!75\)\( p^{30} T^{28} - 2593483622986925722 p^{36} T^{30} + 2827392454395 p^{42} T^{32} - 2233402 p^{48} T^{34} + p^{54} T^{36} \) | |
| 73 | \( 1 - 3427705 T^{2} + 6176110861025 T^{4} - 7673125785767653451 T^{6} + \)\(73\!\cdots\!63\)\( T^{8} - \)\(56\!\cdots\!87\)\( T^{10} + \)\(36\!\cdots\!26\)\( T^{12} - \)\(20\!\cdots\!21\)\( T^{14} + \)\(96\!\cdots\!17\)\( T^{16} - \)\(40\!\cdots\!11\)\( T^{18} + \)\(96\!\cdots\!17\)\( p^{6} T^{20} - \)\(20\!\cdots\!21\)\( p^{12} T^{22} + \)\(36\!\cdots\!26\)\( p^{18} T^{24} - \)\(56\!\cdots\!87\)\( p^{24} T^{26} + \)\(73\!\cdots\!63\)\( p^{30} T^{28} - 7673125785767653451 p^{36} T^{30} + 6176110861025 p^{42} T^{32} - 3427705 p^{48} T^{34} + p^{54} T^{36} \) | |
| 79 | \( ( 1 + 115 T + 1593876 T^{2} + 798800090 T^{3} + 1772916753533 T^{4} + 999425306482225 T^{5} + 1431928934682659048 T^{6} + \)\(86\!\cdots\!41\)\( T^{7} + \)\(91\!\cdots\!76\)\( T^{8} + \)\(47\!\cdots\!49\)\( T^{9} + \)\(91\!\cdots\!76\)\( p^{3} T^{10} + \)\(86\!\cdots\!41\)\( p^{6} T^{11} + 1431928934682659048 p^{9} T^{12} + 999425306482225 p^{12} T^{13} + 1772916753533 p^{15} T^{14} + 798800090 p^{18} T^{15} + 1593876 p^{21} T^{16} + 115 p^{24} T^{17} + p^{27} T^{18} )^{2} \) | |
| 83 | \( 1 - 6805485 T^{2} + 22392720914925 T^{4} - 47610846207061680607 T^{6} + \)\(73\!\cdots\!19\)\( T^{8} - \)\(89\!\cdots\!27\)\( T^{10} + \)\(88\!\cdots\!26\)\( T^{12} - \)\(73\!\cdots\!29\)\( T^{14} + \)\(52\!\cdots\!77\)\( T^{16} - \)\(32\!\cdots\!31\)\( T^{18} + \)\(52\!\cdots\!77\)\( p^{6} T^{20} - \)\(73\!\cdots\!29\)\( p^{12} T^{22} + \)\(88\!\cdots\!26\)\( p^{18} T^{24} - \)\(89\!\cdots\!27\)\( p^{24} T^{26} + \)\(73\!\cdots\!19\)\( p^{30} T^{28} - 47610846207061680607 p^{36} T^{30} + 22392720914925 p^{42} T^{32} - 6805485 p^{48} T^{34} + p^{54} T^{36} \) | |
| 89 | \( 1 - 7198632 T^{2} + 25184079858474 T^{4} - 57181344404590688092 T^{6} + \)\(95\!\cdots\!77\)\( T^{8} - \)\(12\!\cdots\!80\)\( T^{10} + \)\(13\!\cdots\!64\)\( T^{12} - \)\(12\!\cdots\!22\)\( T^{14} + \)\(10\!\cdots\!00\)\( T^{16} - \)\(79\!\cdots\!32\)\( T^{18} + \)\(10\!\cdots\!00\)\( p^{6} T^{20} - \)\(12\!\cdots\!22\)\( p^{12} T^{22} + \)\(13\!\cdots\!64\)\( p^{18} T^{24} - \)\(12\!\cdots\!80\)\( p^{24} T^{26} + \)\(95\!\cdots\!77\)\( p^{30} T^{28} - 57181344404590688092 p^{36} T^{30} + 25184079858474 p^{42} T^{32} - 7198632 p^{48} T^{34} + p^{54} T^{36} \) | |
| 97 | \( 1 - 12640255 T^{2} + 77541271499756 T^{4} - \)\(30\!\cdots\!86\)\( T^{6} + \)\(88\!\cdots\!08\)\( T^{8} - \)\(19\!\cdots\!06\)\( T^{10} + \)\(34\!\cdots\!79\)\( T^{12} - \)\(49\!\cdots\!56\)\( T^{14} + \)\(58\!\cdots\!48\)\( T^{16} - \)\(58\!\cdots\!53\)\( T^{18} + \)\(58\!\cdots\!48\)\( p^{6} T^{20} - \)\(49\!\cdots\!56\)\( p^{12} T^{22} + \)\(34\!\cdots\!79\)\( p^{18} T^{24} - \)\(19\!\cdots\!06\)\( p^{24} T^{26} + \)\(88\!\cdots\!08\)\( p^{30} T^{28} - \)\(30\!\cdots\!86\)\( p^{36} T^{30} + 77541271499756 p^{42} T^{32} - 12640255 p^{48} T^{34} + p^{54} T^{36} \) | |
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\(L(s) = \displaystyle\prod_p \ \prod_{j=1}^{36} (1 - \alpha_{j,p}\, p^{-s})^{-1}\)
Imaginary part of the first few zeros on the critical line
−2.19293725959522632958770235059, −2.04364423733717798384418442882, −2.01496570462266934776951620744, −1.96260434981297914041113557653, −1.84779260447903593185903640195, −1.79701058404250593486670906511, −1.70972719723493968409670822122, −1.45178745493421556620983353311, −1.41978054510127668077786699809, −1.35508676638821066039434631935, −1.17098645101626331140246385563, −1.13611915921552176665054512630, −1.10380722348191702687264336400, −1.09793783484110532465089841422, −1.07222135825094982655384104508, −0.802023352556778800832928409682, −0.77444573066904663437004541807, −0.75269549250615826138947308949, −0.65455162804122289254578698461, −0.61538407868374294310533134902, −0.57801041169481246713897488801, −0.33329725382282219916228210878, −0.18572356053548876116708486509, −0.099264995065449032974765772272, −0.02860859180482005132891422410, 0.02860859180482005132891422410, 0.099264995065449032974765772272, 0.18572356053548876116708486509, 0.33329725382282219916228210878, 0.57801041169481246713897488801, 0.61538407868374294310533134902, 0.65455162804122289254578698461, 0.75269549250615826138947308949, 0.77444573066904663437004541807, 0.802023352556778800832928409682, 1.07222135825094982655384104508, 1.09793783484110532465089841422, 1.10380722348191702687264336400, 1.13611915921552176665054512630, 1.17098645101626331140246385563, 1.35508676638821066039434631935, 1.41978054510127668077786699809, 1.45178745493421556620983353311, 1.70972719723493968409670822122, 1.79701058404250593486670906511, 1.84779260447903593185903640195, 1.96260434981297914041113557653, 2.01496570462266934776951620744, 2.04364423733717798384418442882, 2.19293725959522632958770235059
Graph of the $Z$-function along the critical line
Plot not available for L-functions of degree greater than 10.