Dirichlet series
| L(s) = 1 | + 2·2-s − 6·4-s + 3·5-s − 3·7-s − 14·8-s + 6·10-s + 12·11-s + 13·13-s − 6·14-s + 12·16-s + 14·17-s − 9·19-s − 18·20-s + 24·22-s + 14·23-s − 24·25-s + 26·26-s + 18·28-s + 14·29-s − 28·31-s + 36·32-s + 28·34-s − 9·35-s − 12·37-s − 18·38-s − 42·40-s + 25·41-s + ⋯ |
| L(s) = 1 | + 1.41·2-s − 3·4-s + 1.34·5-s − 1.13·7-s − 4.94·8-s + 1.89·10-s + 3.61·11-s + 3.60·13-s − 1.60·14-s + 3·16-s + 3.39·17-s − 2.06·19-s − 4.02·20-s + 5.11·22-s + 2.91·23-s − 4.79·25-s + 5.09·26-s + 3.40·28-s + 2.59·29-s − 5.02·31-s + 6.36·32-s + 4.80·34-s − 1.52·35-s − 1.97·37-s − 2.91·38-s − 6.64·40-s + 3.90·41-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(3^{28} \cdot 23^{14} \cdot 29^{14}\right)^{s/2} \, \Gamma_{\C}(s)^{14} \, L(s)\cr=\mathstrut & \,\Lambda(2-s)\end{aligned}\]
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(3^{28} \cdot 23^{14} \cdot 29^{14}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{14} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}\]
Invariants
| Degree: | \(28\) |
| Conductor: | \(3^{28} \cdot 23^{14} \cdot 29^{14}\) |
| Sign: | $1$ |
| Analytic conductor: | \(3.38093\times 10^{23}\) |
| Root analytic conductor: | \(6.92345\) |
| Motivic weight: | \(1\) |
| Rational: | yes |
| Arithmetic: | yes |
| Character: | Trivial |
| Primitive: | no |
| Self-dual: | yes |
| Analytic rank: | \(0\) |
| Selberg data: | \((28,\ 3^{28} \cdot 23^{14} \cdot 29^{14} ,\ ( \ : [1/2]^{14} ),\ 1 )\) |
Particular Values
| \(L(1)\) | \(\approx\) | \(30.27705097\) |
| \(L(\frac12)\) | \(\approx\) | \(30.27705097\) |
| \(L(\frac{3}{2})\) | not available | |
| \(L(1)\) | not available |
Euler product
\(L(s) = \displaystyle \prod_{p} F_p(p^{-s})^{-1} \)
| $p$ | $F_p(T)$ | |
|---|---|---|
| bad | 3 | \( 1 \) |
| 23 | \( ( 1 - T )^{14} \) | |
| 29 | \( ( 1 - T )^{14} \) | |
| good | 2 | \( 1 - p T + 5 p T^{2} - 9 p T^{3} + 7 p^{3} T^{4} - 23 p^{2} T^{5} + 55 p^{2} T^{6} - 337 T^{7} + 343 p T^{8} - 985 T^{9} + 1787 T^{10} - 1219 p T^{11} + p^{12} T^{12} - 669 p^{3} T^{13} + 1065 p^{3} T^{14} - 669 p^{4} T^{15} + p^{14} T^{16} - 1219 p^{4} T^{17} + 1787 p^{4} T^{18} - 985 p^{5} T^{19} + 343 p^{7} T^{20} - 337 p^{7} T^{21} + 55 p^{10} T^{22} - 23 p^{11} T^{23} + 7 p^{13} T^{24} - 9 p^{12} T^{25} + 5 p^{13} T^{26} - p^{14} T^{27} + p^{14} T^{28} \) |
| 5 | \( 1 - 3 T + 33 T^{2} - 99 T^{3} + 534 T^{4} - 319 p T^{5} + 1172 p T^{6} - 17183 T^{7} + 50676 T^{8} - 141937 T^{9} + 369399 T^{10} - 963721 T^{11} + 92437 p^{2} T^{12} - 1114138 p T^{13} + 12445672 T^{14} - 1114138 p^{2} T^{15} + 92437 p^{4} T^{16} - 963721 p^{3} T^{17} + 369399 p^{4} T^{18} - 141937 p^{5} T^{19} + 50676 p^{6} T^{20} - 17183 p^{7} T^{21} + 1172 p^{9} T^{22} - 319 p^{10} T^{23} + 534 p^{10} T^{24} - 99 p^{11} T^{25} + 33 p^{12} T^{26} - 3 p^{13} T^{27} + p^{14} T^{28} \) | |
| 7 | \( 1 + 3 T + 45 T^{2} + 99 T^{3} + 970 T^{4} + 1612 T^{5} + 13841 T^{6} + 17081 T^{7} + 149698 T^{8} + 18472 p T^{9} + 1326607 T^{10} + 104600 p T^{11} + 10262627 T^{12} + 3642781 T^{13} + 73555142 T^{14} + 3642781 p T^{15} + 10262627 p^{2} T^{16} + 104600 p^{4} T^{17} + 1326607 p^{4} T^{18} + 18472 p^{6} T^{19} + 149698 p^{6} T^{20} + 17081 p^{7} T^{21} + 13841 p^{8} T^{22} + 1612 p^{9} T^{23} + 970 p^{10} T^{24} + 99 p^{11} T^{25} + 45 p^{12} T^{26} + 3 p^{13} T^{27} + p^{14} T^{28} \) | |
| 11 | \( 1 - 12 T + 139 T^{2} - 1121 T^{3} + 8287 T^{4} - 52293 T^{5} + 27674 p T^{6} - 1606898 T^{7} + 7904531 T^{8} - 36145022 T^{9} + 155180105 T^{10} - 626725645 T^{11} + 217058503 p T^{12} - 8604818257 T^{13} + 29318443452 T^{14} - 8604818257 p T^{15} + 217058503 p^{3} T^{16} - 626725645 p^{3} T^{17} + 155180105 p^{4} T^{18} - 36145022 p^{5} T^{19} + 7904531 p^{6} T^{20} - 1606898 p^{7} T^{21} + 27674 p^{9} T^{22} - 52293 p^{9} T^{23} + 8287 p^{10} T^{24} - 1121 p^{11} T^{25} + 139 p^{12} T^{26} - 12 p^{13} T^{27} + p^{14} T^{28} \) | |
| 13 | \( 1 - p T + 177 T^{2} - 1487 T^{3} + 12289 T^{4} - 78917 T^{5} + 38192 p T^{6} - 2629018 T^{7} + 13720162 T^{8} - 62633382 T^{9} + 284605872 T^{10} - 1157550439 T^{11} + 4740009622 T^{12} - 17623247216 T^{13} + 66511477178 T^{14} - 17623247216 p T^{15} + 4740009622 p^{2} T^{16} - 1157550439 p^{3} T^{17} + 284605872 p^{4} T^{18} - 62633382 p^{5} T^{19} + 13720162 p^{6} T^{20} - 2629018 p^{7} T^{21} + 38192 p^{9} T^{22} - 78917 p^{9} T^{23} + 12289 p^{10} T^{24} - 1487 p^{11} T^{25} + 177 p^{12} T^{26} - p^{14} T^{27} + p^{14} T^{28} \) | |
| 17 | \( 1 - 14 T + 208 T^{2} - 1889 T^{3} + 16926 T^{4} - 117195 T^{5} + 798635 T^{6} - 4583479 T^{7} + 26201988 T^{8} - 132050361 T^{9} + 671563025 T^{10} - 3086940621 T^{11} + 14399017325 T^{12} - 61266330337 T^{13} + 264303495568 T^{14} - 61266330337 p T^{15} + 14399017325 p^{2} T^{16} - 3086940621 p^{3} T^{17} + 671563025 p^{4} T^{18} - 132050361 p^{5} T^{19} + 26201988 p^{6} T^{20} - 4583479 p^{7} T^{21} + 798635 p^{8} T^{22} - 117195 p^{9} T^{23} + 16926 p^{10} T^{24} - 1889 p^{11} T^{25} + 208 p^{12} T^{26} - 14 p^{13} T^{27} + p^{14} T^{28} \) | |
| 19 | \( 1 + 9 T + 184 T^{2} + 1407 T^{3} + 16433 T^{4} + 109832 T^{5} + 951768 T^{6} + 5660364 T^{7} + 2110984 p T^{8} + 214599308 T^{9} + 1304579992 T^{10} + 6316022728 T^{11} + 33841102070 T^{12} + 148435363378 T^{13} + 712050960576 T^{14} + 148435363378 p T^{15} + 33841102070 p^{2} T^{16} + 6316022728 p^{3} T^{17} + 1304579992 p^{4} T^{18} + 214599308 p^{5} T^{19} + 2110984 p^{7} T^{20} + 5660364 p^{7} T^{21} + 951768 p^{8} T^{22} + 109832 p^{9} T^{23} + 16433 p^{10} T^{24} + 1407 p^{11} T^{25} + 184 p^{12} T^{26} + 9 p^{13} T^{27} + p^{14} T^{28} \) | |
| 31 | \( 1 + 28 T + 572 T^{2} + 8327 T^{3} + 101681 T^{4} + 1034552 T^{5} + 9267436 T^{6} + 72684144 T^{7} + 513558687 T^{8} + 3250981745 T^{9} + 18879768188 T^{10} + 100774249494 T^{11} + 515723640143 T^{12} + 2609190143976 T^{13} + 14031300428920 T^{14} + 2609190143976 p T^{15} + 515723640143 p^{2} T^{16} + 100774249494 p^{3} T^{17} + 18879768188 p^{4} T^{18} + 3250981745 p^{5} T^{19} + 513558687 p^{6} T^{20} + 72684144 p^{7} T^{21} + 9267436 p^{8} T^{22} + 1034552 p^{9} T^{23} + 101681 p^{10} T^{24} + 8327 p^{11} T^{25} + 572 p^{12} T^{26} + 28 p^{13} T^{27} + p^{14} T^{28} \) | |
| 37 | \( 1 + 12 T + 304 T^{2} + 2885 T^{3} + 42862 T^{4} + 341274 T^{5} + 3808952 T^{6} + 26105941 T^{7} + 241811446 T^{8} + 1455530727 T^{9} + 11923120230 T^{10} + 64695546402 T^{11} + 495142685963 T^{12} + 2521698703959 T^{13} + 18795047013204 T^{14} + 2521698703959 p T^{15} + 495142685963 p^{2} T^{16} + 64695546402 p^{3} T^{17} + 11923120230 p^{4} T^{18} + 1455530727 p^{5} T^{19} + 241811446 p^{6} T^{20} + 26105941 p^{7} T^{21} + 3808952 p^{8} T^{22} + 341274 p^{9} T^{23} + 42862 p^{10} T^{24} + 2885 p^{11} T^{25} + 304 p^{12} T^{26} + 12 p^{13} T^{27} + p^{14} T^{28} \) | |
| 41 | \( 1 - 25 T + 563 T^{2} - 8607 T^{3} + 121790 T^{4} - 1433577 T^{5} + 15853304 T^{6} - 156316437 T^{7} + 1459584908 T^{8} - 12547879865 T^{9} + 102600090629 T^{10} - 785560142479 T^{11} + 5735202560101 T^{12} - 39539710215930 T^{13} + 260203302026272 T^{14} - 39539710215930 p T^{15} + 5735202560101 p^{2} T^{16} - 785560142479 p^{3} T^{17} + 102600090629 p^{4} T^{18} - 12547879865 p^{5} T^{19} + 1459584908 p^{6} T^{20} - 156316437 p^{7} T^{21} + 15853304 p^{8} T^{22} - 1433577 p^{9} T^{23} + 121790 p^{10} T^{24} - 8607 p^{11} T^{25} + 563 p^{12} T^{26} - 25 p^{13} T^{27} + p^{14} T^{28} \) | |
| 43 | \( 1 - 5 T + 297 T^{2} - 1219 T^{3} + 46823 T^{4} - 174090 T^{5} + 5132797 T^{6} - 17834622 T^{7} + 430864094 T^{8} - 1416867538 T^{9} + 29103005409 T^{10} - 90407818422 T^{11} + 1625566361842 T^{12} - 4719120486698 T^{13} + 76160620269810 T^{14} - 4719120486698 p T^{15} + 1625566361842 p^{2} T^{16} - 90407818422 p^{3} T^{17} + 29103005409 p^{4} T^{18} - 1416867538 p^{5} T^{19} + 430864094 p^{6} T^{20} - 17834622 p^{7} T^{21} + 5132797 p^{8} T^{22} - 174090 p^{9} T^{23} + 46823 p^{10} T^{24} - 1219 p^{11} T^{25} + 297 p^{12} T^{26} - 5 p^{13} T^{27} + p^{14} T^{28} \) | |
| 47 | \( 1 - 17 T + 476 T^{2} - 5509 T^{3} + 90642 T^{4} - 798086 T^{5} + 10209828 T^{6} - 74193631 T^{7} + 843621786 T^{8} - 5421861566 T^{9} + 57988161744 T^{10} - 341708483626 T^{11} + 3434636562755 T^{12} - 18683810508297 T^{13} + 174525409046848 T^{14} - 18683810508297 p T^{15} + 3434636562755 p^{2} T^{16} - 341708483626 p^{3} T^{17} + 57988161744 p^{4} T^{18} - 5421861566 p^{5} T^{19} + 843621786 p^{6} T^{20} - 74193631 p^{7} T^{21} + 10209828 p^{8} T^{22} - 798086 p^{9} T^{23} + 90642 p^{10} T^{24} - 5509 p^{11} T^{25} + 476 p^{12} T^{26} - 17 p^{13} T^{27} + p^{14} T^{28} \) | |
| 53 | \( 1 - 17 T + 451 T^{2} - 6199 T^{3} + 103714 T^{4} - 1212805 T^{5} + 15785236 T^{6} - 162135273 T^{7} + 1781542164 T^{8} - 16346188245 T^{9} + 157363232837 T^{10} - 24593719095 p T^{11} + 11220283418081 T^{12} - 84285002735454 T^{13} + 655369971693480 T^{14} - 84285002735454 p T^{15} + 11220283418081 p^{2} T^{16} - 24593719095 p^{4} T^{17} + 157363232837 p^{4} T^{18} - 16346188245 p^{5} T^{19} + 1781542164 p^{6} T^{20} - 162135273 p^{7} T^{21} + 15785236 p^{8} T^{22} - 1212805 p^{9} T^{23} + 103714 p^{10} T^{24} - 6199 p^{11} T^{25} + 451 p^{12} T^{26} - 17 p^{13} T^{27} + p^{14} T^{28} \) | |
| 59 | \( 1 - 18 T + 638 T^{2} - 9332 T^{3} + 189406 T^{4} - 2362986 T^{5} + 35603330 T^{6} - 389556630 T^{7} + 4800237280 T^{8} - 46805333984 T^{9} + 494611111946 T^{10} - 4334161949190 T^{11} + 40310964925849 T^{12} - 318364997149716 T^{13} + 2644086692075628 T^{14} - 318364997149716 p T^{15} + 40310964925849 p^{2} T^{16} - 4334161949190 p^{3} T^{17} + 494611111946 p^{4} T^{18} - 46805333984 p^{5} T^{19} + 4800237280 p^{6} T^{20} - 389556630 p^{7} T^{21} + 35603330 p^{8} T^{22} - 2362986 p^{9} T^{23} + 189406 p^{10} T^{24} - 9332 p^{11} T^{25} + 638 p^{12} T^{26} - 18 p^{13} T^{27} + p^{14} T^{28} \) | |
| 61 | \( 1 + 13 T + 596 T^{2} + 6434 T^{3} + 165632 T^{4} + 1535224 T^{5} + 29236284 T^{6} + 238761328 T^{7} + 3747057210 T^{8} + 27488969596 T^{9} + 374836174492 T^{10} + 2499571361745 T^{11} + 30415369892253 T^{12} + 185108931897456 T^{13} + 2037221839194280 T^{14} + 185108931897456 p T^{15} + 30415369892253 p^{2} T^{16} + 2499571361745 p^{3} T^{17} + 374836174492 p^{4} T^{18} + 27488969596 p^{5} T^{19} + 3747057210 p^{6} T^{20} + 238761328 p^{7} T^{21} + 29236284 p^{8} T^{22} + 1535224 p^{9} T^{23} + 165632 p^{10} T^{24} + 6434 p^{11} T^{25} + 596 p^{12} T^{26} + 13 p^{13} T^{27} + p^{14} T^{28} \) | |
| 67 | \( 1 - 2 T + 412 T^{2} - 85 T^{3} + 81873 T^{4} + 59025 T^{5} + 11064257 T^{6} + 6768182 T^{7} + 1156961567 T^{8} - 227617176 T^{9} + 98345725864 T^{10} - 115483783745 T^{11} + 7193333316815 T^{12} - 13468582820631 T^{13} + 489649450710742 T^{14} - 13468582820631 p T^{15} + 7193333316815 p^{2} T^{16} - 115483783745 p^{3} T^{17} + 98345725864 p^{4} T^{18} - 227617176 p^{5} T^{19} + 1156961567 p^{6} T^{20} + 6768182 p^{7} T^{21} + 11064257 p^{8} T^{22} + 59025 p^{9} T^{23} + 81873 p^{10} T^{24} - 85 p^{11} T^{25} + 412 p^{12} T^{26} - 2 p^{13} T^{27} + p^{14} T^{28} \) | |
| 71 | \( 1 - 55 T + 1906 T^{2} - 47988 T^{3} + 984493 T^{4} - 17083015 T^{5} + 260576902 T^{6} - 3557771614 T^{7} + 44369235966 T^{8} - 510923883358 T^{9} + 5499327498984 T^{10} - 55655727934707 T^{11} + 533182660015140 T^{12} - 4844300269336289 T^{13} + 41867190182528960 T^{14} - 4844300269336289 p T^{15} + 533182660015140 p^{2} T^{16} - 55655727934707 p^{3} T^{17} + 5499327498984 p^{4} T^{18} - 510923883358 p^{5} T^{19} + 44369235966 p^{6} T^{20} - 3557771614 p^{7} T^{21} + 260576902 p^{8} T^{22} - 17083015 p^{9} T^{23} + 984493 p^{10} T^{24} - 47988 p^{11} T^{25} + 1906 p^{12} T^{26} - 55 p^{13} T^{27} + p^{14} T^{28} \) | |
| 73 | \( 1 - 19 T + 865 T^{2} - 13222 T^{3} + 339511 T^{4} - 4344852 T^{5} + 81804908 T^{6} - 899882588 T^{7} + 13751393653 T^{8} - 132600600224 T^{9} + 1735580768935 T^{10} - 14902256067743 T^{11} + 172536300488083 T^{12} - 1334594221796352 T^{13} + 13913248462638488 T^{14} - 1334594221796352 p T^{15} + 172536300488083 p^{2} T^{16} - 14902256067743 p^{3} T^{17} + 1735580768935 p^{4} T^{18} - 132600600224 p^{5} T^{19} + 13751393653 p^{6} T^{20} - 899882588 p^{7} T^{21} + 81804908 p^{8} T^{22} - 4344852 p^{9} T^{23} + 339511 p^{10} T^{24} - 13222 p^{11} T^{25} + 865 p^{12} T^{26} - 19 p^{13} T^{27} + p^{14} T^{28} \) | |
| 79 | \( 1 + 68 T + 2854 T^{2} + 87913 T^{3} + 2199796 T^{4} + 46646952 T^{5} + 865021420 T^{6} + 14282158063 T^{7} + 212976079418 T^{8} + 2894813443275 T^{9} + 36133541437366 T^{10} + 416213385145996 T^{11} + 4441578912784593 T^{12} + 44010249013254925 T^{13} + 405564900431154960 T^{14} + 44010249013254925 p T^{15} + 4441578912784593 p^{2} T^{16} + 416213385145996 p^{3} T^{17} + 36133541437366 p^{4} T^{18} + 2894813443275 p^{5} T^{19} + 212976079418 p^{6} T^{20} + 14282158063 p^{7} T^{21} + 865021420 p^{8} T^{22} + 46646952 p^{9} T^{23} + 2199796 p^{10} T^{24} + 87913 p^{11} T^{25} + 2854 p^{12} T^{26} + 68 p^{13} T^{27} + p^{14} T^{28} \) | |
| 83 | \( 1 - 21 T + 889 T^{2} - 15799 T^{3} + 375156 T^{4} - 5788987 T^{5} + 100461402 T^{6} - 1370905001 T^{7} + 19213943114 T^{8} - 234724212595 T^{9} + 2794963467615 T^{10} - 30778046565473 T^{11} + 320655847170681 T^{12} - 3188405195562274 T^{13} + 29585454778993340 T^{14} - 3188405195562274 p T^{15} + 320655847170681 p^{2} T^{16} - 30778046565473 p^{3} T^{17} + 2794963467615 p^{4} T^{18} - 234724212595 p^{5} T^{19} + 19213943114 p^{6} T^{20} - 1370905001 p^{7} T^{21} + 100461402 p^{8} T^{22} - 5788987 p^{9} T^{23} + 375156 p^{10} T^{24} - 15799 p^{11} T^{25} + 889 p^{12} T^{26} - 21 p^{13} T^{27} + p^{14} T^{28} \) | |
| 89 | \( 1 - 17 T + 605 T^{2} - 7757 T^{3} + 170857 T^{4} - 1865051 T^{5} + 32707576 T^{6} - 317061790 T^{7} + 4820161984 T^{8} - 42568948494 T^{9} + 590976178888 T^{10} - 4867467377397 T^{11} + 63043309074110 T^{12} - 487765585730110 T^{13} + 5943840388880014 T^{14} - 487765585730110 p T^{15} + 63043309074110 p^{2} T^{16} - 4867467377397 p^{3} T^{17} + 590976178888 p^{4} T^{18} - 42568948494 p^{5} T^{19} + 4820161984 p^{6} T^{20} - 317061790 p^{7} T^{21} + 32707576 p^{8} T^{22} - 1865051 p^{9} T^{23} + 170857 p^{10} T^{24} - 7757 p^{11} T^{25} + 605 p^{12} T^{26} - 17 p^{13} T^{27} + p^{14} T^{28} \) | |
| 97 | \( 1 - 25 T + 998 T^{2} - 18478 T^{3} + 440564 T^{4} - 6808974 T^{5} + 124249438 T^{6} - 1688787414 T^{7} + 25703112526 T^{8} - 313958756704 T^{9} + 4151947080722 T^{10} - 46013431741105 T^{11} + 541103217274109 T^{12} - 5455834895034788 T^{13} + 57822196357889364 T^{14} - 5455834895034788 p T^{15} + 541103217274109 p^{2} T^{16} - 46013431741105 p^{3} T^{17} + 4151947080722 p^{4} T^{18} - 313958756704 p^{5} T^{19} + 25703112526 p^{6} T^{20} - 1688787414 p^{7} T^{21} + 124249438 p^{8} T^{22} - 6808974 p^{9} T^{23} + 440564 p^{10} T^{24} - 18478 p^{11} T^{25} + 998 p^{12} T^{26} - 25 p^{13} T^{27} + p^{14} T^{28} \) | |
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\(L(s) = \displaystyle\prod_p \ \prod_{j=1}^{28} (1 - \alpha_{j,p}\, p^{-s})^{-1}\)
Imaginary part of the first few zeros on the critical line
−2.09765062397600237641417520601, −2.00558619250340789660390041345, −1.89631702379212417942193942191, −1.79758807088500697952401231412, −1.72819578611237098670166914272, −1.67077604061314462488831009190, −1.65621822437505364208645221316, −1.61984698257582156379821866742, −1.53905382151830616755905666487, −1.51572792803160518849906876088, −1.47566987411980651846488624403, −1.37337487048175230261794793739, −1.27508864535061539091508769514, −1.12183582808623980891327138323, −0.874773419823097028254651712328, −0.835108296712397940733919997224, −0.78024268530186785547632331366, −0.76156525780055603072790582606, −0.72937253535316334272205189088, −0.56085573486905571726020081517, −0.54537786476120804254674032466, −0.51145215109474234986679481817, −0.49284258480015612216479727796, −0.35758276752957612552772851501, −0.06037015171813126189267670696, 0.06037015171813126189267670696, 0.35758276752957612552772851501, 0.49284258480015612216479727796, 0.51145215109474234986679481817, 0.54537786476120804254674032466, 0.56085573486905571726020081517, 0.72937253535316334272205189088, 0.76156525780055603072790582606, 0.78024268530186785547632331366, 0.835108296712397940733919997224, 0.874773419823097028254651712328, 1.12183582808623980891327138323, 1.27508864535061539091508769514, 1.37337487048175230261794793739, 1.47566987411980651846488624403, 1.51572792803160518849906876088, 1.53905382151830616755905666487, 1.61984698257582156379821866742, 1.65621822437505364208645221316, 1.67077604061314462488831009190, 1.72819578611237098670166914272, 1.79758807088500697952401231412, 1.89631702379212417942193942191, 2.00558619250340789660390041345, 2.09765062397600237641417520601
Graph of the $Z$-function along the critical line
Plot not available for L-functions of degree greater than 10.