Dirichlet series
| L(s) = 1 | − 14·2-s − 14·3-s + 105·4-s − 5-s + 196·6-s + 5·7-s − 560·8-s + 105·9-s + 14·10-s − 11-s − 1.47e3·12-s − 14·13-s − 70·14-s + 14·15-s + 2.38e3·16-s − 12·17-s − 1.47e3·18-s + 10·19-s − 105·20-s − 70·21-s + 14·22-s − 23-s + 7.84e3·24-s − 25·25-s + 196·26-s − 560·27-s + 525·28-s + ⋯ |
| L(s) = 1 | − 9.89·2-s − 8.08·3-s + 52.5·4-s − 0.447·5-s + 80.0·6-s + 1.88·7-s − 197.·8-s + 35·9-s + 4.42·10-s − 0.301·11-s − 424.·12-s − 3.88·13-s − 18.7·14-s + 3.61·15-s + 595·16-s − 2.91·17-s − 346.·18-s + 2.29·19-s − 23.4·20-s − 15.2·21-s + 2.98·22-s − 0.208·23-s + 1.60e3·24-s − 5·25-s + 38.4·26-s − 107.·27-s + 99.2·28-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{14} \cdot 3^{14} \cdot 13^{14} \cdot 103^{14}\right)^{s/2} \, \Gamma_{\C}(s)^{14} \, L(s)\cr=\mathstrut & \,\Lambda(2-s)\end{aligned}\]
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{14} \cdot 3^{14} \cdot 13^{14} \cdot 103^{14}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{14} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}\]
Invariants
| Degree: | \(28\) |
| Conductor: | \(2^{14} \cdot 3^{14} \cdot 13^{14} \cdot 103^{14}\) |
| Sign: | $1$ |
| Analytic conductor: | \(1.99951\times 10^{25}\) |
| Root analytic conductor: | \(8.00948\) |
| Motivic weight: | \(1\) |
| Rational: | yes |
| Arithmetic: | yes |
| Character: | Trivial |
| Primitive: | no |
| Self-dual: | yes |
| Analytic rank: | \(0\) |
| Selberg data: | \((28,\ 2^{14} \cdot 3^{14} \cdot 13^{14} \cdot 103^{14} ,\ ( \ : [1/2]^{14} ),\ 1 )\) |
Particular Values
| \(L(1)\) | \(\approx\) | \(0.003791444111\) |
| \(L(\frac12)\) | \(\approx\) | \(0.003791444111\) |
| \(L(\frac{3}{2})\) | not available | |
| \(L(1)\) | not available |
Euler product
\(L(s) = \displaystyle \prod_{p} F_p(p^{-s})^{-1} \)
| $p$ | $F_p(T)$ | |
|---|---|---|
| bad | 2 | \( ( 1 + T )^{14} \) |
| 3 | \( ( 1 + T )^{14} \) | |
| 13 | \( ( 1 + T )^{14} \) | |
| 103 | \( ( 1 - T )^{14} \) | |
| good | 5 | \( 1 + T + 26 T^{2} + 29 T^{3} + 357 T^{4} + 421 T^{5} + 3562 T^{6} + 4277 T^{7} + 28796 T^{8} + 35021 T^{9} + 197621 T^{10} + 241828 T^{11} + 1189074 T^{12} + 1418301 T^{13} + 6329698 T^{14} + 1418301 p T^{15} + 1189074 p^{2} T^{16} + 241828 p^{3} T^{17} + 197621 p^{4} T^{18} + 35021 p^{5} T^{19} + 28796 p^{6} T^{20} + 4277 p^{7} T^{21} + 3562 p^{8} T^{22} + 421 p^{9} T^{23} + 357 p^{10} T^{24} + 29 p^{11} T^{25} + 26 p^{12} T^{26} + p^{13} T^{27} + p^{14} T^{28} \) |
| 7 | \( 1 - 5 T + 57 T^{2} - 239 T^{3} + 1611 T^{4} - 5855 T^{5} + 4303 p T^{6} - 97176 T^{7} + 59844 p T^{8} - 1219306 T^{9} + 659192 p T^{10} - 12255191 T^{11} + 41803831 T^{12} - 102002004 T^{13} + 318158398 T^{14} - 102002004 p T^{15} + 41803831 p^{2} T^{16} - 12255191 p^{3} T^{17} + 659192 p^{5} T^{18} - 1219306 p^{5} T^{19} + 59844 p^{7} T^{20} - 97176 p^{7} T^{21} + 4303 p^{9} T^{22} - 5855 p^{9} T^{23} + 1611 p^{10} T^{24} - 239 p^{11} T^{25} + 57 p^{12} T^{26} - 5 p^{13} T^{27} + p^{14} T^{28} \) | |
| 11 | \( 1 + T + 47 T^{2} - 9 T^{3} + 1093 T^{4} - 1167 T^{5} + 18072 T^{6} - 28964 T^{7} + 240068 T^{8} - 401230 T^{9} + 2852393 T^{10} - 302704 p T^{11} + 32846446 T^{12} - 18794541 T^{13} + 367939200 T^{14} - 18794541 p T^{15} + 32846446 p^{2} T^{16} - 302704 p^{4} T^{17} + 2852393 p^{4} T^{18} - 401230 p^{5} T^{19} + 240068 p^{6} T^{20} - 28964 p^{7} T^{21} + 18072 p^{8} T^{22} - 1167 p^{9} T^{23} + 1093 p^{10} T^{24} - 9 p^{11} T^{25} + 47 p^{12} T^{26} + p^{13} T^{27} + p^{14} T^{28} \) | |
| 17 | \( 1 + 12 T + 146 T^{2} + 1179 T^{3} + 9205 T^{4} + 57844 T^{5} + 354707 T^{6} + 1891121 T^{7} + 10018184 T^{8} + 48084616 T^{9} + 233639956 T^{10} + 61777073 p T^{11} + 4794849506 T^{12} + 20320486587 T^{13} + 87060872590 T^{14} + 20320486587 p T^{15} + 4794849506 p^{2} T^{16} + 61777073 p^{4} T^{17} + 233639956 p^{4} T^{18} + 48084616 p^{5} T^{19} + 10018184 p^{6} T^{20} + 1891121 p^{7} T^{21} + 354707 p^{8} T^{22} + 57844 p^{9} T^{23} + 9205 p^{10} T^{24} + 1179 p^{11} T^{25} + 146 p^{12} T^{26} + 12 p^{13} T^{27} + p^{14} T^{28} \) | |
| 19 | \( 1 - 10 T + 120 T^{2} - 786 T^{3} + 358 p T^{4} - 39806 T^{5} + 293600 T^{6} - 80951 p T^{7} + 9895152 T^{8} - 47448685 T^{9} + 278127368 T^{10} - 1237611429 T^{11} + 6641904965 T^{12} - 27317844823 T^{13} + 135542121088 T^{14} - 27317844823 p T^{15} + 6641904965 p^{2} T^{16} - 1237611429 p^{3} T^{17} + 278127368 p^{4} T^{18} - 47448685 p^{5} T^{19} + 9895152 p^{6} T^{20} - 80951 p^{8} T^{21} + 293600 p^{8} T^{22} - 39806 p^{9} T^{23} + 358 p^{11} T^{24} - 786 p^{11} T^{25} + 120 p^{12} T^{26} - 10 p^{13} T^{27} + p^{14} T^{28} \) | |
| 23 | \( 1 + T + 146 T^{2} + 24 T^{3} + 10990 T^{4} - 4388 T^{5} + 580134 T^{6} - 461554 T^{7} + 23923309 T^{8} - 25743097 T^{9} + 811618435 T^{10} - 1003391134 T^{11} + 23330385884 T^{12} - 29594442892 T^{13} + 577062042746 T^{14} - 29594442892 p T^{15} + 23330385884 p^{2} T^{16} - 1003391134 p^{3} T^{17} + 811618435 p^{4} T^{18} - 25743097 p^{5} T^{19} + 23923309 p^{6} T^{20} - 461554 p^{7} T^{21} + 580134 p^{8} T^{22} - 4388 p^{9} T^{23} + 10990 p^{10} T^{24} + 24 p^{11} T^{25} + 146 p^{12} T^{26} + p^{13} T^{27} + p^{14} T^{28} \) | |
| 29 | \( 1 - 6 T + 221 T^{2} - 1312 T^{3} + 25500 T^{4} - 145405 T^{5} + 1992382 T^{6} - 10821112 T^{7} + 117210411 T^{8} - 601700609 T^{9} + 5479693190 T^{10} - 26359011388 T^{11} + 209605421418 T^{12} - 934182931232 T^{13} + 6656663786778 T^{14} - 934182931232 p T^{15} + 209605421418 p^{2} T^{16} - 26359011388 p^{3} T^{17} + 5479693190 p^{4} T^{18} - 601700609 p^{5} T^{19} + 117210411 p^{6} T^{20} - 10821112 p^{7} T^{21} + 1992382 p^{8} T^{22} - 145405 p^{9} T^{23} + 25500 p^{10} T^{24} - 1312 p^{11} T^{25} + 221 p^{12} T^{26} - 6 p^{13} T^{27} + p^{14} T^{28} \) | |
| 31 | \( 1 - 20 T + 460 T^{2} - 6228 T^{3} + 86212 T^{4} - 910676 T^{5} + 9578480 T^{6} - 84341457 T^{7} + 733512374 T^{8} - 5576136615 T^{9} + 41749585244 T^{10} - 279324702071 T^{11} + 1838783091861 T^{12} - 10933646049901 T^{13} + 63949041245744 T^{14} - 10933646049901 p T^{15} + 1838783091861 p^{2} T^{16} - 279324702071 p^{3} T^{17} + 41749585244 p^{4} T^{18} - 5576136615 p^{5} T^{19} + 733512374 p^{6} T^{20} - 84341457 p^{7} T^{21} + 9578480 p^{8} T^{22} - 910676 p^{9} T^{23} + 86212 p^{10} T^{24} - 6228 p^{11} T^{25} + 460 p^{12} T^{26} - 20 p^{13} T^{27} + p^{14} T^{28} \) | |
| 37 | \( 1 + 3 T + 321 T^{2} + 1045 T^{3} + 50594 T^{4} + 168589 T^{5} + 5241883 T^{6} + 17060148 T^{7} + 401317130 T^{8} + 1236128166 T^{9} + 24116562479 T^{10} + 69122313326 T^{11} + 1177989745387 T^{12} + 3113686396783 T^{13} + 47707103466890 T^{14} + 3113686396783 p T^{15} + 1177989745387 p^{2} T^{16} + 69122313326 p^{3} T^{17} + 24116562479 p^{4} T^{18} + 1236128166 p^{5} T^{19} + 401317130 p^{6} T^{20} + 17060148 p^{7} T^{21} + 5241883 p^{8} T^{22} + 168589 p^{9} T^{23} + 50594 p^{10} T^{24} + 1045 p^{11} T^{25} + 321 p^{12} T^{26} + 3 p^{13} T^{27} + p^{14} T^{28} \) | |
| 41 | \( 1 - T + 392 T^{2} - 431 T^{3} + 74963 T^{4} - 84808 T^{5} + 9312788 T^{6} - 10451117 T^{7} + 842827407 T^{8} - 916471376 T^{9} + 58956181431 T^{10} - 60864919040 T^{11} + 3293709367305 T^{12} - 3156265964107 T^{13} + 149454356867042 T^{14} - 3156265964107 p T^{15} + 3293709367305 p^{2} T^{16} - 60864919040 p^{3} T^{17} + 58956181431 p^{4} T^{18} - 916471376 p^{5} T^{19} + 842827407 p^{6} T^{20} - 10451117 p^{7} T^{21} + 9312788 p^{8} T^{22} - 84808 p^{9} T^{23} + 74963 p^{10} T^{24} - 431 p^{11} T^{25} + 392 p^{12} T^{26} - p^{13} T^{27} + p^{14} T^{28} \) | |
| 43 | \( 1 - 6 T + 318 T^{2} - 1234 T^{3} + 49771 T^{4} - 123850 T^{5} + 5264265 T^{6} - 7515939 T^{7} + 424310419 T^{8} - 280342639 T^{9} + 27762581682 T^{10} - 4792935707 T^{11} + 1520722018593 T^{12} + 78771451359 T^{13} + 70801844302318 T^{14} + 78771451359 p T^{15} + 1520722018593 p^{2} T^{16} - 4792935707 p^{3} T^{17} + 27762581682 p^{4} T^{18} - 280342639 p^{5} T^{19} + 424310419 p^{6} T^{20} - 7515939 p^{7} T^{21} + 5264265 p^{8} T^{22} - 123850 p^{9} T^{23} + 49771 p^{10} T^{24} - 1234 p^{11} T^{25} + 318 p^{12} T^{26} - 6 p^{13} T^{27} + p^{14} T^{28} \) | |
| 47 | \( 1 + 13 T + 419 T^{2} + 4853 T^{3} + 89575 T^{4} + 923795 T^{5} + 12655911 T^{6} + 117246364 T^{7} + 1313017147 T^{8} + 10991750001 T^{9} + 105566329709 T^{10} + 801112719728 T^{11} + 6777279818617 T^{12} + 46613745020802 T^{13} + 352861467105682 T^{14} + 46613745020802 p T^{15} + 6777279818617 p^{2} T^{16} + 801112719728 p^{3} T^{17} + 105566329709 p^{4} T^{18} + 10991750001 p^{5} T^{19} + 1313017147 p^{6} T^{20} + 117246364 p^{7} T^{21} + 12655911 p^{8} T^{22} + 923795 p^{9} T^{23} + 89575 p^{10} T^{24} + 4853 p^{11} T^{25} + 419 p^{12} T^{26} + 13 p^{13} T^{27} + p^{14} T^{28} \) | |
| 53 | \( 1 + 27 T + 770 T^{2} + 14162 T^{3} + 250695 T^{4} + 3591117 T^{5} + 48939583 T^{6} + 581612670 T^{7} + 6580518292 T^{8} + 67135844393 T^{9} + 653741569860 T^{10} + 5837714316066 T^{11} + 49860139272540 T^{12} + 393743995952773 T^{13} + 2977411680612566 T^{14} + 393743995952773 p T^{15} + 49860139272540 p^{2} T^{16} + 5837714316066 p^{3} T^{17} + 653741569860 p^{4} T^{18} + 67135844393 p^{5} T^{19} + 6580518292 p^{6} T^{20} + 581612670 p^{7} T^{21} + 48939583 p^{8} T^{22} + 3591117 p^{9} T^{23} + 250695 p^{10} T^{24} + 14162 p^{11} T^{25} + 770 p^{12} T^{26} + 27 p^{13} T^{27} + p^{14} T^{28} \) | |
| 59 | \( 1 + 6 T + 525 T^{2} + 3815 T^{3} + 139996 T^{4} + 1108393 T^{5} + 24939893 T^{6} + 202044681 T^{7} + 3281310437 T^{8} + 26097232160 T^{9} + 334899389329 T^{10} + 2532993097652 T^{11} + 27215924996070 T^{12} + 190432727322865 T^{13} + 1784179620381802 T^{14} + 190432727322865 p T^{15} + 27215924996070 p^{2} T^{16} + 2532993097652 p^{3} T^{17} + 334899389329 p^{4} T^{18} + 26097232160 p^{5} T^{19} + 3281310437 p^{6} T^{20} + 202044681 p^{7} T^{21} + 24939893 p^{8} T^{22} + 1108393 p^{9} T^{23} + 139996 p^{10} T^{24} + 3815 p^{11} T^{25} + 525 p^{12} T^{26} + 6 p^{13} T^{27} + p^{14} T^{28} \) | |
| 61 | \( 1 + 4 T + 484 T^{2} + 1314 T^{3} + 115319 T^{4} + 201434 T^{5} + 18326791 T^{6} + 19012883 T^{7} + 2192118347 T^{8} + 1180380893 T^{9} + 209538594860 T^{10} + 46690441853 T^{11} + 16545695495773 T^{12} + 1220607119195 T^{13} + 1098037338250994 T^{14} + 1220607119195 p T^{15} + 16545695495773 p^{2} T^{16} + 46690441853 p^{3} T^{17} + 209538594860 p^{4} T^{18} + 1180380893 p^{5} T^{19} + 2192118347 p^{6} T^{20} + 19012883 p^{7} T^{21} + 18326791 p^{8} T^{22} + 201434 p^{9} T^{23} + 115319 p^{10} T^{24} + 1314 p^{11} T^{25} + 484 p^{12} T^{26} + 4 p^{13} T^{27} + p^{14} T^{28} \) | |
| 67 | \( 1 - 13 T + 680 T^{2} - 7544 T^{3} + 211176 T^{4} - 2018649 T^{5} + 39849212 T^{6} - 330189361 T^{7} + 5155084593 T^{8} - 37314891084 T^{9} + 496316070080 T^{10} - 3199008307173 T^{11} + 38737076756099 T^{12} - 231279252876556 T^{13} + 2689074296203136 T^{14} - 231279252876556 p T^{15} + 38737076756099 p^{2} T^{16} - 3199008307173 p^{3} T^{17} + 496316070080 p^{4} T^{18} - 37314891084 p^{5} T^{19} + 5155084593 p^{6} T^{20} - 330189361 p^{7} T^{21} + 39849212 p^{8} T^{22} - 2018649 p^{9} T^{23} + 211176 p^{10} T^{24} - 7544 p^{11} T^{25} + 680 p^{12} T^{26} - 13 p^{13} T^{27} + p^{14} T^{28} \) | |
| 71 | \( 1 - 18 T + 713 T^{2} - 11370 T^{3} + 255495 T^{4} - 3554696 T^{5} + 59554379 T^{6} - 727778567 T^{7} + 9998837755 T^{8} - 108358619322 T^{9} + 1275902745998 T^{10} - 12340757125686 T^{11} + 127482062456591 T^{12} - 1103461769654179 T^{13} + 10126899044108824 T^{14} - 1103461769654179 p T^{15} + 127482062456591 p^{2} T^{16} - 12340757125686 p^{3} T^{17} + 1275902745998 p^{4} T^{18} - 108358619322 p^{5} T^{19} + 9998837755 p^{6} T^{20} - 727778567 p^{7} T^{21} + 59554379 p^{8} T^{22} - 3554696 p^{9} T^{23} + 255495 p^{10} T^{24} - 11370 p^{11} T^{25} + 713 p^{12} T^{26} - 18 p^{13} T^{27} + p^{14} T^{28} \) | |
| 73 | \( 1 - 11 T + 693 T^{2} - 5745 T^{3} + 219235 T^{4} - 1334368 T^{5} + 42455980 T^{6} - 171947317 T^{7} + 5691712425 T^{8} - 11648551898 T^{9} + 574015416074 T^{10} - 93417125842 T^{11} + 47527580757994 T^{12} + 53350058703113 T^{13} + 3559539737657822 T^{14} + 53350058703113 p T^{15} + 47527580757994 p^{2} T^{16} - 93417125842 p^{3} T^{17} + 574015416074 p^{4} T^{18} - 11648551898 p^{5} T^{19} + 5691712425 p^{6} T^{20} - 171947317 p^{7} T^{21} + 42455980 p^{8} T^{22} - 1334368 p^{9} T^{23} + 219235 p^{10} T^{24} - 5745 p^{11} T^{25} + 693 p^{12} T^{26} - 11 p^{13} T^{27} + p^{14} T^{28} \) | |
| 79 | \( 1 - 33 T + 1089 T^{2} - 21955 T^{3} + 435186 T^{4} - 6543527 T^{5} + 97884339 T^{6} - 1191992050 T^{7} + 14697771336 T^{8} - 151921536064 T^{9} + 1632154963579 T^{10} - 14939958274018 T^{11} + 147514063862501 T^{12} - 1259006663805439 T^{13} + 11989712661479842 T^{14} - 1259006663805439 p T^{15} + 147514063862501 p^{2} T^{16} - 14939958274018 p^{3} T^{17} + 1632154963579 p^{4} T^{18} - 151921536064 p^{5} T^{19} + 14697771336 p^{6} T^{20} - 1191992050 p^{7} T^{21} + 97884339 p^{8} T^{22} - 6543527 p^{9} T^{23} + 435186 p^{10} T^{24} - 21955 p^{11} T^{25} + 1089 p^{12} T^{26} - 33 p^{13} T^{27} + p^{14} T^{28} \) | |
| 83 | \( 1 + 25 T + 826 T^{2} + 14837 T^{3} + 300177 T^{4} + 4364942 T^{5} + 68402706 T^{6} + 852425088 T^{7} + 11274422479 T^{8} + 124553623990 T^{9} + 1454382814530 T^{10} + 14570091380449 T^{11} + 154285125617853 T^{12} + 1421274293530685 T^{13} + 13852164490995784 T^{14} + 1421274293530685 p T^{15} + 154285125617853 p^{2} T^{16} + 14570091380449 p^{3} T^{17} + 1454382814530 p^{4} T^{18} + 124553623990 p^{5} T^{19} + 11274422479 p^{6} T^{20} + 852425088 p^{7} T^{21} + 68402706 p^{8} T^{22} + 4364942 p^{9} T^{23} + 300177 p^{10} T^{24} + 14837 p^{11} T^{25} + 826 p^{12} T^{26} + 25 p^{13} T^{27} + p^{14} T^{28} \) | |
| 89 | \( 1 - 3 T + 629 T^{2} - 1848 T^{3} + 186017 T^{4} - 533416 T^{5} + 34890189 T^{6} - 93023627 T^{7} + 4727064917 T^{8} - 10662916229 T^{9} + 503981695563 T^{10} - 855474831760 T^{11} + 46288243965721 T^{12} - 58080317869029 T^{13} + 4082640989018310 T^{14} - 58080317869029 p T^{15} + 46288243965721 p^{2} T^{16} - 855474831760 p^{3} T^{17} + 503981695563 p^{4} T^{18} - 10662916229 p^{5} T^{19} + 4727064917 p^{6} T^{20} - 93023627 p^{7} T^{21} + 34890189 p^{8} T^{22} - 533416 p^{9} T^{23} + 186017 p^{10} T^{24} - 1848 p^{11} T^{25} + 629 p^{12} T^{26} - 3 p^{13} T^{27} + p^{14} T^{28} \) | |
| 97 | \( 1 - 11 T + 624 T^{2} - 5689 T^{3} + 175816 T^{4} - 1324798 T^{5} + 29812767 T^{6} - 188735535 T^{7} + 3513075222 T^{8} - 20153207198 T^{9} + 333728514676 T^{10} - 2026678003970 T^{11} + 30373819549249 T^{12} - 210293383957295 T^{13} + 2887845488774970 T^{14} - 210293383957295 p T^{15} + 30373819549249 p^{2} T^{16} - 2026678003970 p^{3} T^{17} + 333728514676 p^{4} T^{18} - 20153207198 p^{5} T^{19} + 3513075222 p^{6} T^{20} - 188735535 p^{7} T^{21} + 29812767 p^{8} T^{22} - 1324798 p^{9} T^{23} + 175816 p^{10} T^{24} - 5689 p^{11} T^{25} + 624 p^{12} T^{26} - 11 p^{13} T^{27} + p^{14} T^{28} \) | |
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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
−1.64671562415157740440563440307, −1.62110962744451062155198913911, −1.59768554207614817148655157060, −1.54681861106467407428261788737, −1.54619037512751622868281149254, −1.53721710403238630585466723072, −1.51937347645770170240588977204, −1.51612031366663910191337103872, −1.46444779705088097774795430065, −1.42141121113758165444200392351, −1.34858878400570633391812850815, −0.966650487979642404321199326636, −0.945936293955441338155437069543, −0.807915567537481501233445692527, −0.63282210881924992784611707381, −0.63001145263019747997391466181, −0.60408568698448996241862773379, −0.59389553833442049994122446076, −0.47841399512480290524082160846, −0.43870123530732401506963949410, −0.41991649614098024565453622333, −0.33103669072318425855869482144, −0.32390962819546747079550265035, −0.31285552070410861934162807343, −0.10995244218046691468045906696, 0.10995244218046691468045906696, 0.31285552070410861934162807343, 0.32390962819546747079550265035, 0.33103669072318425855869482144, 0.41991649614098024565453622333, 0.43870123530732401506963949410, 0.47841399512480290524082160846, 0.59389553833442049994122446076, 0.60408568698448996241862773379, 0.63001145263019747997391466181, 0.63282210881924992784611707381, 0.807915567537481501233445692527, 0.945936293955441338155437069543, 0.966650487979642404321199326636, 1.34858878400570633391812850815, 1.42141121113758165444200392351, 1.46444779705088097774795430065, 1.51612031366663910191337103872, 1.51937347645770170240588977204, 1.53721710403238630585466723072, 1.54619037512751622868281149254, 1.54681861106467407428261788737, 1.59768554207614817148655157060, 1.62110962744451062155198913911, 1.64671562415157740440563440307
Graph of the $Z$-function along the critical line
Plot not available for L-functions of degree greater than 10.