Dirichlet series
| L(s) = 1 | + 3·2-s + 4·3-s − 4-s + 12·6-s + 14·7-s − 13·8-s − 4·9-s + 5·11-s − 4·12-s + 11·13-s + 42·14-s − 12·16-s + 3·17-s − 12·18-s − 2·19-s + 56·21-s + 15·22-s + 14·23-s − 52·24-s + 33·26-s − 33·27-s − 14·28-s + 7·29-s − 3·31-s + 19·32-s + 20·33-s + 9·34-s + ⋯ |
| L(s) = 1 | + 2.12·2-s + 2.30·3-s − 1/2·4-s + 4.89·6-s + 5.29·7-s − 4.59·8-s − 4/3·9-s + 1.50·11-s − 1.15·12-s + 3.05·13-s + 11.2·14-s − 3·16-s + 0.727·17-s − 2.82·18-s − 0.458·19-s + 12.2·21-s + 3.19·22-s + 2.91·23-s − 10.6·24-s + 6.47·26-s − 6.35·27-s − 2.64·28-s + 1.29·29-s − 0.538·31-s + 3.35·32-s + 3.48·33-s + 1.54·34-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(5^{28} \cdot 7^{14} \cdot 23^{14}\right)^{s/2} \, \Gamma_{\C}(s)^{14} \, L(s)\cr=\mathstrut & \,\Lambda(2-s)\end{aligned}\]
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(5^{28} \cdot 7^{14} \cdot 23^{14}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{14} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}\]
Invariants
| Degree: | \(28\) |
| Conductor: | \(5^{28} \cdot 7^{14} \cdot 23^{14}\) |
| Sign: | $1$ |
| Analytic conductor: | \(1.25487\times 10^{21}\) |
| Root analytic conductor: | \(5.66919\) |
| Motivic weight: | \(1\) |
| Rational: | yes |
| Arithmetic: | yes |
| Character: | Trivial |
| Primitive: | no |
| Self-dual: | yes |
| Analytic rank: | \(0\) |
| Selberg data: | \((28,\ 5^{28} \cdot 7^{14} \cdot 23^{14} ,\ ( \ : [1/2]^{14} ),\ 1 )\) |
Particular Values
| \(L(1)\) | \(\approx\) | \(1595.684288\) |
| \(L(\frac12)\) | \(\approx\) | \(1595.684288\) |
| \(L(\frac{3}{2})\) | not available | |
| \(L(1)\) | not available |
Euler product
\(L(s) = \displaystyle \prod_{p} F_p(p^{-s})^{-1} \)
| $p$ | $F_p(T)$ | |
|---|---|---|
| bad | 5 | \( 1 \) |
| 7 | \( ( 1 - T )^{14} \) | |
| 23 | \( ( 1 - T )^{14} \) | |
| good | 2 | \( 1 - 3 T + 5 p T^{2} - 5 p^{2} T^{3} + 43 T^{4} - 37 p T^{5} + 17 p^{3} T^{6} - 113 p T^{7} + 385 T^{8} - 609 T^{9} + 951 T^{10} - 1439 T^{11} + 1061 p T^{12} - 3131 T^{13} + 4407 T^{14} - 3131 p T^{15} + 1061 p^{3} T^{16} - 1439 p^{3} T^{17} + 951 p^{4} T^{18} - 609 p^{5} T^{19} + 385 p^{6} T^{20} - 113 p^{8} T^{21} + 17 p^{11} T^{22} - 37 p^{10} T^{23} + 43 p^{10} T^{24} - 5 p^{13} T^{25} + 5 p^{13} T^{26} - 3 p^{13} T^{27} + p^{14} T^{28} \) |
| 3 | \( 1 - 4 T + 20 T^{2} - 7 p^{2} T^{3} + 209 T^{4} - 554 T^{5} + 1508 T^{6} - 3520 T^{7} + 2791 p T^{8} - 5909 p T^{9} + 38002 T^{10} - 73930 T^{11} + 145099 T^{12} - 260483 T^{13} + 471199 T^{14} - 260483 p T^{15} + 145099 p^{2} T^{16} - 73930 p^{3} T^{17} + 38002 p^{4} T^{18} - 5909 p^{6} T^{19} + 2791 p^{7} T^{20} - 3520 p^{7} T^{21} + 1508 p^{8} T^{22} - 554 p^{9} T^{23} + 209 p^{10} T^{24} - 7 p^{13} T^{25} + 20 p^{12} T^{26} - 4 p^{13} T^{27} + p^{14} T^{28} \) | |
| 11 | \( 1 - 5 T + 76 T^{2} - 272 T^{3} + 2324 T^{4} - 5905 T^{5} + 38186 T^{6} - 61069 T^{7} + 353283 T^{8} - 56808 T^{9} + 805238 T^{10} + 9768951 T^{11} - 32652216 T^{12} + 199091648 T^{13} - 572672536 T^{14} + 199091648 p T^{15} - 32652216 p^{2} T^{16} + 9768951 p^{3} T^{17} + 805238 p^{4} T^{18} - 56808 p^{5} T^{19} + 353283 p^{6} T^{20} - 61069 p^{7} T^{21} + 38186 p^{8} T^{22} - 5905 p^{9} T^{23} + 2324 p^{10} T^{24} - 272 p^{11} T^{25} + 76 p^{12} T^{26} - 5 p^{13} T^{27} + p^{14} T^{28} \) | |
| 13 | \( 1 - 11 T + 126 T^{2} - 870 T^{3} + 36 p^{2} T^{4} - 33289 T^{5} + 186025 T^{6} - 893691 T^{7} + 4340781 T^{8} - 18757848 T^{9} + 6279044 p T^{10} - 323152792 T^{11} + 1299676347 T^{12} - 4804492671 T^{13} + 18074146521 T^{14} - 4804492671 p T^{15} + 1299676347 p^{2} T^{16} - 323152792 p^{3} T^{17} + 6279044 p^{5} T^{18} - 18757848 p^{5} T^{19} + 4340781 p^{6} T^{20} - 893691 p^{7} T^{21} + 186025 p^{8} T^{22} - 33289 p^{9} T^{23} + 36 p^{12} T^{24} - 870 p^{11} T^{25} + 126 p^{12} T^{26} - 11 p^{13} T^{27} + p^{14} T^{28} \) | |
| 17 | \( 1 - 3 T + 111 T^{2} - 267 T^{3} + 6459 T^{4} - 12043 T^{5} + 256809 T^{6} - 359254 T^{7} + 7809940 T^{8} - 7858562 T^{9} + 193283627 T^{10} - 137606996 T^{11} + 4049124032 T^{12} - 2194603371 T^{13} + 73593772698 T^{14} - 2194603371 p T^{15} + 4049124032 p^{2} T^{16} - 137606996 p^{3} T^{17} + 193283627 p^{4} T^{18} - 7858562 p^{5} T^{19} + 7809940 p^{6} T^{20} - 359254 p^{7} T^{21} + 256809 p^{8} T^{22} - 12043 p^{9} T^{23} + 6459 p^{10} T^{24} - 267 p^{11} T^{25} + 111 p^{12} T^{26} - 3 p^{13} T^{27} + p^{14} T^{28} \) | |
| 19 | \( 1 + 2 T + 117 T^{2} + 164 T^{3} + 7048 T^{4} + 6613 T^{5} + 294219 T^{6} + 176952 T^{7} + 9630855 T^{8} + 3751931 T^{9} + 262568065 T^{10} + 70881973 T^{11} + 322966848 p T^{12} + 1299950195 T^{13} + 124727554846 T^{14} + 1299950195 p T^{15} + 322966848 p^{3} T^{16} + 70881973 p^{3} T^{17} + 262568065 p^{4} T^{18} + 3751931 p^{5} T^{19} + 9630855 p^{6} T^{20} + 176952 p^{7} T^{21} + 294219 p^{8} T^{22} + 6613 p^{9} T^{23} + 7048 p^{10} T^{24} + 164 p^{11} T^{25} + 117 p^{12} T^{26} + 2 p^{13} T^{27} + p^{14} T^{28} \) | |
| 29 | \( 1 - 7 T + 157 T^{2} - 1077 T^{3} + 13907 T^{4} - 90207 T^{5} + 890241 T^{6} - 5279677 T^{7} + 44297446 T^{8} - 240998825 T^{9} + 1812178993 T^{10} - 9157766584 T^{11} + 63364064656 T^{12} - 300806471186 T^{13} + 1947499885897 T^{14} - 300806471186 p T^{15} + 63364064656 p^{2} T^{16} - 9157766584 p^{3} T^{17} + 1812178993 p^{4} T^{18} - 240998825 p^{5} T^{19} + 44297446 p^{6} T^{20} - 5279677 p^{7} T^{21} + 890241 p^{8} T^{22} - 90207 p^{9} T^{23} + 13907 p^{10} T^{24} - 1077 p^{11} T^{25} + 157 p^{12} T^{26} - 7 p^{13} T^{27} + p^{14} T^{28} \) | |
| 31 | \( 1 + 3 T + 188 T^{2} + 550 T^{3} + 515 p T^{4} + 43204 T^{5} + 779963 T^{6} + 1855224 T^{7} + 21382677 T^{8} + 42888527 T^{9} + 114325175 T^{10} + 171574022 T^{11} - 17281079762 T^{12} - 23731916416 T^{13} - 822309308409 T^{14} - 23731916416 p T^{15} - 17281079762 p^{2} T^{16} + 171574022 p^{3} T^{17} + 114325175 p^{4} T^{18} + 42888527 p^{5} T^{19} + 21382677 p^{6} T^{20} + 1855224 p^{7} T^{21} + 779963 p^{8} T^{22} + 43204 p^{9} T^{23} + 515 p^{11} T^{24} + 550 p^{11} T^{25} + 188 p^{12} T^{26} + 3 p^{13} T^{27} + p^{14} T^{28} \) | |
| 37 | \( 1 - 22 T + 522 T^{2} - 7817 T^{3} + 115272 T^{4} - 1356664 T^{5} + 15428426 T^{6} - 151665750 T^{7} + 1434199673 T^{8} - 12154351467 T^{9} + 99018715088 T^{10} - 736205811706 T^{11} + 5263209408638 T^{12} - 34643930511858 T^{13} + 219325179695320 T^{14} - 34643930511858 p T^{15} + 5263209408638 p^{2} T^{16} - 736205811706 p^{3} T^{17} + 99018715088 p^{4} T^{18} - 12154351467 p^{5} T^{19} + 1434199673 p^{6} T^{20} - 151665750 p^{7} T^{21} + 15428426 p^{8} T^{22} - 1356664 p^{9} T^{23} + 115272 p^{10} T^{24} - 7817 p^{11} T^{25} + 522 p^{12} T^{26} - 22 p^{13} T^{27} + p^{14} T^{28} \) | |
| 41 | \( 1 + 17 T + 378 T^{2} + 5316 T^{3} + 73453 T^{4} + 840084 T^{5} + 9214851 T^{6} + 89272404 T^{7} + 831682317 T^{8} + 7065105151 T^{9} + 57747973055 T^{10} + 438152240282 T^{11} + 3205596096524 T^{12} + 21938127627268 T^{13} + 145091451945897 T^{14} + 21938127627268 p T^{15} + 3205596096524 p^{2} T^{16} + 438152240282 p^{3} T^{17} + 57747973055 p^{4} T^{18} + 7065105151 p^{5} T^{19} + 831682317 p^{6} T^{20} + 89272404 p^{7} T^{21} + 9214851 p^{8} T^{22} + 840084 p^{9} T^{23} + 73453 p^{10} T^{24} + 5316 p^{11} T^{25} + 378 p^{12} T^{26} + 17 p^{13} T^{27} + p^{14} T^{28} \) | |
| 43 | \( 1 - 18 T + 478 T^{2} - 5787 T^{3} + 89169 T^{4} - 806610 T^{5} + 9355076 T^{6} - 67553931 T^{7} + 677579870 T^{8} - 4226402868 T^{9} + 40623384000 T^{10} - 236903394387 T^{11} + 2211069001608 T^{12} - 12144130144285 T^{13} + 104422411826012 T^{14} - 12144130144285 p T^{15} + 2211069001608 p^{2} T^{16} - 236903394387 p^{3} T^{17} + 40623384000 p^{4} T^{18} - 4226402868 p^{5} T^{19} + 677579870 p^{6} T^{20} - 67553931 p^{7} T^{21} + 9355076 p^{8} T^{22} - 806610 p^{9} T^{23} + 89169 p^{10} T^{24} - 5787 p^{11} T^{25} + 478 p^{12} T^{26} - 18 p^{13} T^{27} + p^{14} T^{28} \) | |
| 47 | \( 1 - 30 T + 757 T^{2} - 13956 T^{3} + 226130 T^{4} - 3145061 T^{5} + 39751893 T^{6} - 453037275 T^{7} + 4780591274 T^{8} - 46507325725 T^{9} + 423391135294 T^{10} - 3594201351750 T^{11} + 28722881382201 T^{12} - 215242935935997 T^{13} + 1522545273662593 T^{14} - 215242935935997 p T^{15} + 28722881382201 p^{2} T^{16} - 3594201351750 p^{3} T^{17} + 423391135294 p^{4} T^{18} - 46507325725 p^{5} T^{19} + 4780591274 p^{6} T^{20} - 453037275 p^{7} T^{21} + 39751893 p^{8} T^{22} - 3145061 p^{9} T^{23} + 226130 p^{10} T^{24} - 13956 p^{11} T^{25} + 757 p^{12} T^{26} - 30 p^{13} T^{27} + p^{14} T^{28} \) | |
| 53 | \( 1 - 11 T + 459 T^{2} - 4050 T^{3} + 95108 T^{4} - 659652 T^{5} + 11697724 T^{6} - 59472636 T^{7} + 942701787 T^{8} - 2806666614 T^{9} + 52282455135 T^{10} - 214461969 p T^{11} + 2178795550640 T^{12} + 7016039332924 T^{13} + 94871220818868 T^{14} + 7016039332924 p T^{15} + 2178795550640 p^{2} T^{16} - 214461969 p^{4} T^{17} + 52282455135 p^{4} T^{18} - 2806666614 p^{5} T^{19} + 942701787 p^{6} T^{20} - 59472636 p^{7} T^{21} + 11697724 p^{8} T^{22} - 659652 p^{9} T^{23} + 95108 p^{10} T^{24} - 4050 p^{11} T^{25} + 459 p^{12} T^{26} - 11 p^{13} T^{27} + p^{14} T^{28} \) | |
| 59 | \( 1 + 22 T + 614 T^{2} + 9721 T^{3} + 169952 T^{4} + 2196912 T^{5} + 29980987 T^{6} + 333692017 T^{7} + 3847134473 T^{8} + 37895606369 T^{9} + 382954251456 T^{10} + 3387468788676 T^{11} + 30588576474205 T^{12} + 244652170345875 T^{13} + 1993147423237107 T^{14} + 244652170345875 p T^{15} + 30588576474205 p^{2} T^{16} + 3387468788676 p^{3} T^{17} + 382954251456 p^{4} T^{18} + 37895606369 p^{5} T^{19} + 3847134473 p^{6} T^{20} + 333692017 p^{7} T^{21} + 29980987 p^{8} T^{22} + 2196912 p^{9} T^{23} + 169952 p^{10} T^{24} + 9721 p^{11} T^{25} + 614 p^{12} T^{26} + 22 p^{13} T^{27} + p^{14} T^{28} \) | |
| 61 | \( 1 + 8 T + 526 T^{2} + 4031 T^{3} + 137780 T^{4} + 1022326 T^{5} + 23833533 T^{6} + 171989587 T^{7} + 3049610443 T^{8} + 21304378998 T^{9} + 306010094100 T^{10} + 2042085853071 T^{11} + 24878939119392 T^{12} + 155308290678935 T^{13} + 1667120075729314 T^{14} + 155308290678935 p T^{15} + 24878939119392 p^{2} T^{16} + 2042085853071 p^{3} T^{17} + 306010094100 p^{4} T^{18} + 21304378998 p^{5} T^{19} + 3049610443 p^{6} T^{20} + 171989587 p^{7} T^{21} + 23833533 p^{8} T^{22} + 1022326 p^{9} T^{23} + 137780 p^{10} T^{24} + 4031 p^{11} T^{25} + 526 p^{12} T^{26} + 8 p^{13} T^{27} + p^{14} T^{28} \) | |
| 67 | \( 1 - 39 T + 1009 T^{2} - 18287 T^{3} + 273624 T^{4} - 3409810 T^{5} + 38266001 T^{6} - 386317903 T^{7} + 3713668585 T^{8} - 33551472462 T^{9} + 298538213605 T^{10} - 2551754474434 T^{11} + 21842282044670 T^{12} - 180850389231113 T^{13} + 1505220801615634 T^{14} - 180850389231113 p T^{15} + 21842282044670 p^{2} T^{16} - 2551754474434 p^{3} T^{17} + 298538213605 p^{4} T^{18} - 33551472462 p^{5} T^{19} + 3713668585 p^{6} T^{20} - 386317903 p^{7} T^{21} + 38266001 p^{8} T^{22} - 3409810 p^{9} T^{23} + 273624 p^{10} T^{24} - 18287 p^{11} T^{25} + 1009 p^{12} T^{26} - 39 p^{13} T^{27} + p^{14} T^{28} \) | |
| 71 | \( 1 + 5 T + 301 T^{2} + 887 T^{3} + 47257 T^{4} + 105001 T^{5} + 5092609 T^{6} + 8882415 T^{7} + 362758064 T^{8} + 426597757 T^{9} + 15099109549 T^{10} + 10059265392 T^{11} + 54382732686 T^{12} - 650360712684 T^{13} - 31591977346715 T^{14} - 650360712684 p T^{15} + 54382732686 p^{2} T^{16} + 10059265392 p^{3} T^{17} + 15099109549 p^{4} T^{18} + 426597757 p^{5} T^{19} + 362758064 p^{6} T^{20} + 8882415 p^{7} T^{21} + 5092609 p^{8} T^{22} + 105001 p^{9} T^{23} + 47257 p^{10} T^{24} + 887 p^{11} T^{25} + 301 p^{12} T^{26} + 5 p^{13} T^{27} + p^{14} T^{28} \) | |
| 73 | \( 1 - 18 T + 596 T^{2} - 7217 T^{3} + 150439 T^{4} - 1482612 T^{5} + 25965976 T^{6} - 230470980 T^{7} + 3558209497 T^{8} - 28542821925 T^{9} + 392859833814 T^{10} - 2878115746178 T^{11} + 36436831583161 T^{12} - 248126005750359 T^{13} + 2891953096870395 T^{14} - 248126005750359 p T^{15} + 36436831583161 p^{2} T^{16} - 2878115746178 p^{3} T^{17} + 392859833814 p^{4} T^{18} - 28542821925 p^{5} T^{19} + 3558209497 p^{6} T^{20} - 230470980 p^{7} T^{21} + 25965976 p^{8} T^{22} - 1482612 p^{9} T^{23} + 150439 p^{10} T^{24} - 7217 p^{11} T^{25} + 596 p^{12} T^{26} - 18 p^{13} T^{27} + p^{14} T^{28} \) | |
| 79 | \( 1 - 10 T + 492 T^{2} - 4862 T^{3} + 133358 T^{4} - 1236539 T^{5} + 25248098 T^{6} - 217682804 T^{7} + 3684169111 T^{8} - 29521156037 T^{9} + 437078923458 T^{10} - 3258625021461 T^{11} + 43548923964458 T^{12} - 302143143647501 T^{13} + 3709096196507328 T^{14} - 302143143647501 p T^{15} + 43548923964458 p^{2} T^{16} - 3258625021461 p^{3} T^{17} + 437078923458 p^{4} T^{18} - 29521156037 p^{5} T^{19} + 3684169111 p^{6} T^{20} - 217682804 p^{7} T^{21} + 25248098 p^{8} T^{22} - 1236539 p^{9} T^{23} + 133358 p^{10} T^{24} - 4862 p^{11} T^{25} + 492 p^{12} T^{26} - 10 p^{13} T^{27} + p^{14} T^{28} \) | |
| 83 | \( 1 - 24 T + 731 T^{2} - 13603 T^{3} + 260411 T^{4} - 3964887 T^{5} + 59666939 T^{6} - 778011917 T^{7} + 9968714740 T^{8} - 114820087847 T^{9} + 1303030698647 T^{10} - 13560161394564 T^{11} + 139457980760552 T^{12} - 1330096080532638 T^{13} + 12559576595348166 T^{14} - 1330096080532638 p T^{15} + 139457980760552 p^{2} T^{16} - 13560161394564 p^{3} T^{17} + 1303030698647 p^{4} T^{18} - 114820087847 p^{5} T^{19} + 9968714740 p^{6} T^{20} - 778011917 p^{7} T^{21} + 59666939 p^{8} T^{22} - 3964887 p^{9} T^{23} + 260411 p^{10} T^{24} - 13603 p^{11} T^{25} + 731 p^{12} T^{26} - 24 p^{13} T^{27} + p^{14} T^{28} \) | |
| 89 | \( 1 - 25 T + 794 T^{2} - 14006 T^{3} + 277865 T^{4} - 3948430 T^{5} + 61379150 T^{6} - 746774942 T^{7} + 9908005206 T^{8} - 107104187344 T^{9} + 1271677533784 T^{10} - 12552819431873 T^{11} + 1544458161840 p T^{12} - 1264112781649036 T^{13} + 12992236516231040 T^{14} - 1264112781649036 p T^{15} + 1544458161840 p^{3} T^{16} - 12552819431873 p^{3} T^{17} + 1271677533784 p^{4} T^{18} - 107104187344 p^{5} T^{19} + 9908005206 p^{6} T^{20} - 746774942 p^{7} T^{21} + 61379150 p^{8} T^{22} - 3948430 p^{9} T^{23} + 277865 p^{10} T^{24} - 14006 p^{11} T^{25} + 794 p^{12} T^{26} - 25 p^{13} T^{27} + p^{14} T^{28} \) | |
| 97 | \( 1 - 43 T + 1592 T^{2} - 39590 T^{3} + 887293 T^{4} - 16234448 T^{5} + 276616898 T^{6} - 4130832308 T^{7} + 58811863262 T^{8} - 760864401164 T^{9} + 9522564908486 T^{10} - 110245919746819 T^{11} + 1241634039076756 T^{12} - 13016470869116572 T^{13} + 132803983609724832 T^{14} - 13016470869116572 p T^{15} + 1241634039076756 p^{2} T^{16} - 110245919746819 p^{3} T^{17} + 9522564908486 p^{4} T^{18} - 760864401164 p^{5} T^{19} + 58811863262 p^{6} T^{20} - 4130832308 p^{7} T^{21} + 276616898 p^{8} T^{22} - 16234448 p^{9} T^{23} + 887293 p^{10} T^{24} - 39590 p^{11} T^{25} + 1592 p^{12} T^{26} - 43 p^{13} T^{27} + p^{14} T^{28} \) | |
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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
−2.26826548753711988856267068653, −2.26111261471750003723890686898, −2.26039522819372306877901065916, −2.10902917444615967832749605799, −1.96702533262071546680335582997, −1.85069697287401507322486717209, −1.85036518241716423618512677044, −1.74832355979982010719576310558, −1.69144712667100677822749591640, −1.69066897336750622716707259815, −1.46762026509206570030002595144, −1.35542207027426133420161013888, −1.24841601062711051979791278823, −1.24770722411394475762557333430, −1.18713443169925525527359219889, −1.00466836282336089018158179509, −0.984012084437720631301636677887, −0.77008632289525629250303105000, −0.74712138223180042487659514695, −0.74174875977937740455301077034, −0.69468320945008885659519272048, −0.67536264485154824121101761773, −0.65929983161705763368958156862, −0.32492387752611122890980391350, −0.19432614217148083023337277042, 0.19432614217148083023337277042, 0.32492387752611122890980391350, 0.65929983161705763368958156862, 0.67536264485154824121101761773, 0.69468320945008885659519272048, 0.74174875977937740455301077034, 0.74712138223180042487659514695, 0.77008632289525629250303105000, 0.984012084437720631301636677887, 1.00466836282336089018158179509, 1.18713443169925525527359219889, 1.24770722411394475762557333430, 1.24841601062711051979791278823, 1.35542207027426133420161013888, 1.46762026509206570030002595144, 1.69066897336750622716707259815, 1.69144712667100677822749591640, 1.74832355979982010719576310558, 1.85036518241716423618512677044, 1.85069697287401507322486717209, 1.96702533262071546680335582997, 2.10902917444615967832749605799, 2.26039522819372306877901065916, 2.26111261471750003723890686898, 2.26826548753711988856267068653
Graph of the $Z$-function along the critical line
Plot not available for L-functions of degree greater than 10.