Dirichlet series
| L(s) = 1 | + 8·3-s − 8·4-s − 2·7-s + 28·9-s + 6·11-s − 64·12-s − 10·13-s + 36·16-s + 18·19-s − 16·21-s + 32·23-s − 20·25-s + 48·27-s + 16·28-s − 4·29-s − 12·31-s + 48·33-s − 224·36-s − 80·39-s − 18·41-s − 32·43-s − 48·44-s − 66·47-s + 288·48-s + 13·49-s + 80·52-s + 2·53-s + ⋯ |
| L(s) = 1 | + 4.61·3-s − 4·4-s − 0.755·7-s + 28/3·9-s + 1.80·11-s − 18.4·12-s − 2.77·13-s + 9·16-s + 4.12·19-s − 3.49·21-s + 6.67·23-s − 4·25-s + 9.23·27-s + 3.02·28-s − 0.742·29-s − 2.15·31-s + 8.35·33-s − 37.3·36-s − 12.8·39-s − 2.81·41-s − 4.87·43-s − 7.23·44-s − 9.62·47-s + 41.5·48-s + 13/7·49-s + 11.0·52-s + 0.274·53-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{16} \cdot 3^{16} \cdot 7^{16} \cdot 13^{16}\right)^{s/2} \, \Gamma_{\C}(s)^{16} \, L(s)\cr=\mathstrut & \,\Lambda(2-s)\end{aligned}\]
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{16} \cdot 3^{16} \cdot 7^{16} \cdot 13^{16}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{16} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}\]
Invariants
| Degree: | \(32\) |
| Conductor: | \(2^{16} \cdot 3^{16} \cdot 7^{16} \cdot 13^{16}\) |
| Sign: | $1$ |
| Analytic conductor: | \(1.70418\times 10^{10}\) |
| Root analytic conductor: | \(2.08802\) |
| Motivic weight: | \(1\) |
| Rational: | yes |
| Arithmetic: | yes |
| Character: | Trivial |
| Primitive: | no |
| Self-dual: | yes |
| Analytic rank: | \(0\) |
| Selberg data: | \((32,\ 2^{16} \cdot 3^{16} \cdot 7^{16} \cdot 13^{16} ,\ ( \ : [1/2]^{16} ),\ 1 )\) |
Particular Values
| \(L(1)\) | \(\approx\) | \(0.01630871166\) |
| \(L(\frac12)\) | \(\approx\) | \(0.01630871166\) |
| \(L(\frac{3}{2})\) | not available | |
| \(L(1)\) | not available |
Euler product
\(L(s) = \displaystyle \prod_{p} F_p(p^{-s})^{-1} \)
| $p$ | $F_p(T)$ | |
|---|---|---|
| bad | 2 | \( ( 1 + T^{2} )^{8} \) |
| 3 | \( ( 1 - T + T^{2} )^{8} \) | |
| 7 | \( 1 + 2 T - 9 T^{2} + 2 T^{3} + 178 T^{4} + 138 T^{5} - 169 p T^{6} + 460 T^{7} + 12447 T^{8} + 460 p T^{9} - 169 p^{3} T^{10} + 138 p^{3} T^{11} + 178 p^{4} T^{12} + 2 p^{5} T^{13} - 9 p^{6} T^{14} + 2 p^{7} T^{15} + p^{8} T^{16} \) | |
| 13 | \( 1 + 10 T + 23 T^{2} - 6 p T^{3} - 506 T^{4} - 1726 T^{5} - 4623 T^{6} + 17920 T^{7} + 163851 T^{8} + 17920 p T^{9} - 4623 p^{2} T^{10} - 1726 p^{3} T^{11} - 506 p^{4} T^{12} - 6 p^{6} T^{13} + 23 p^{6} T^{14} + 10 p^{7} T^{15} + p^{8} T^{16} \) | |
| good | 5 | \( 1 + 4 p T^{2} + 47 p T^{4} + 24 p T^{5} + 1888 T^{6} + 1938 T^{7} + 11808 T^{8} + 3792 p T^{9} + 67872 T^{10} + 121746 T^{11} + 76729 p T^{12} + 120954 p T^{13} + 2201808 T^{14} + 2694924 T^{15} + 11530099 T^{16} + 2694924 p T^{17} + 2201808 p^{2} T^{18} + 120954 p^{4} T^{19} + 76729 p^{5} T^{20} + 121746 p^{5} T^{21} + 67872 p^{6} T^{22} + 3792 p^{8} T^{23} + 11808 p^{8} T^{24} + 1938 p^{9} T^{25} + 1888 p^{10} T^{26} + 24 p^{12} T^{27} + 47 p^{13} T^{28} + 4 p^{15} T^{30} + p^{16} T^{32} \) |
| 11 | \( 1 - 6 T + 72 T^{2} - 360 T^{3} + 2518 T^{4} - 10086 T^{5} + 52598 T^{6} - 1380 p^{2} T^{7} + 702971 T^{8} - 1649982 T^{9} + 5978343 T^{10} - 7325682 T^{11} + 27802483 T^{12} + 44723634 T^{13} - 8219647 T^{14} + 109492164 p T^{15} - 106661683 p T^{16} + 109492164 p^{2} T^{17} - 8219647 p^{2} T^{18} + 44723634 p^{3} T^{19} + 27802483 p^{4} T^{20} - 7325682 p^{5} T^{21} + 5978343 p^{6} T^{22} - 1649982 p^{7} T^{23} + 702971 p^{8} T^{24} - 1380 p^{11} T^{25} + 52598 p^{10} T^{26} - 10086 p^{11} T^{27} + 2518 p^{12} T^{28} - 360 p^{13} T^{29} + 72 p^{14} T^{30} - 6 p^{15} T^{31} + p^{16} T^{32} \) | |
| 17 | \( ( 1 + 82 T^{2} - 2 T^{3} + 3340 T^{4} - 116 T^{5} + 90557 T^{6} - 1892 T^{7} + 1787081 T^{8} - 1892 p T^{9} + 90557 p^{2} T^{10} - 116 p^{3} T^{11} + 3340 p^{4} T^{12} - 2 p^{5} T^{13} + 82 p^{6} T^{14} + p^{8} T^{16} )^{2} \) | |
| 19 | \( 1 - 18 T + 226 T^{2} - 2124 T^{3} + 16541 T^{4} - 112542 T^{5} + 684130 T^{6} - 3856542 T^{7} + 20450576 T^{8} - 104232144 T^{9} + 517354848 T^{10} - 2524594800 T^{11} + 12200231931 T^{12} - 3066796092 p T^{13} + 273798293704 T^{14} - 66011210070 p T^{15} + 5564171904503 T^{16} - 66011210070 p^{2} T^{17} + 273798293704 p^{2} T^{18} - 3066796092 p^{4} T^{19} + 12200231931 p^{4} T^{20} - 2524594800 p^{5} T^{21} + 517354848 p^{6} T^{22} - 104232144 p^{7} T^{23} + 20450576 p^{8} T^{24} - 3856542 p^{9} T^{25} + 684130 p^{10} T^{26} - 112542 p^{11} T^{27} + 16541 p^{12} T^{28} - 2124 p^{13} T^{29} + 226 p^{14} T^{30} - 18 p^{15} T^{31} + p^{16} T^{32} \) | |
| 23 | \( ( 1 - 16 T + 190 T^{2} - 1590 T^{3} + 10826 T^{4} - 61216 T^{5} + 302541 T^{6} - 1399166 T^{7} + 6519277 T^{8} - 1399166 p T^{9} + 302541 p^{2} T^{10} - 61216 p^{3} T^{11} + 10826 p^{4} T^{12} - 1590 p^{5} T^{13} + 190 p^{6} T^{14} - 16 p^{7} T^{15} + p^{8} T^{16} )^{2} \) | |
| 29 | \( 1 + 4 T - 86 T^{2} + 88 T^{3} + 5202 T^{4} - 20786 T^{5} - 127570 T^{6} + 1350404 T^{7} - 713179 T^{8} - 38405408 T^{9} + 185121661 T^{10} + 383989708 T^{11} - 6091484475 T^{12} + 10535407228 T^{13} + 3124876821 p T^{14} - 229396275918 T^{15} - 808236948365 T^{16} - 229396275918 p T^{17} + 3124876821 p^{3} T^{18} + 10535407228 p^{3} T^{19} - 6091484475 p^{4} T^{20} + 383989708 p^{5} T^{21} + 185121661 p^{6} T^{22} - 38405408 p^{7} T^{23} - 713179 p^{8} T^{24} + 1350404 p^{9} T^{25} - 127570 p^{10} T^{26} - 20786 p^{11} T^{27} + 5202 p^{12} T^{28} + 88 p^{13} T^{29} - 86 p^{14} T^{30} + 4 p^{15} T^{31} + p^{16} T^{32} \) | |
| 31 | \( 1 + 12 T + 178 T^{2} + 1560 T^{3} + 13526 T^{4} + 88560 T^{5} + 18310 p T^{6} + 2643174 T^{7} + 12175877 T^{8} + 22216488 T^{9} - 24227007 T^{10} - 1509848178 T^{11} - 9626729415 T^{12} - 72584640054 T^{13} - 309976990523 T^{14} - 1999645319814 T^{15} - 8070164087269 T^{16} - 1999645319814 p T^{17} - 309976990523 p^{2} T^{18} - 72584640054 p^{3} T^{19} - 9626729415 p^{4} T^{20} - 1509848178 p^{5} T^{21} - 24227007 p^{6} T^{22} + 22216488 p^{7} T^{23} + 12175877 p^{8} T^{24} + 2643174 p^{9} T^{25} + 18310 p^{11} T^{26} + 88560 p^{11} T^{27} + 13526 p^{12} T^{28} + 1560 p^{13} T^{29} + 178 p^{14} T^{30} + 12 p^{15} T^{31} + p^{16} T^{32} \) | |
| 37 | \( 1 - 160 T^{2} + 15312 T^{4} - 1032986 T^{6} + 56274050 T^{8} - 2707257990 T^{10} + 121584478885 T^{12} - 5160026463562 T^{14} + 200332997367093 T^{16} - 5160026463562 p^{2} T^{18} + 121584478885 p^{4} T^{20} - 2707257990 p^{6} T^{22} + 56274050 p^{8} T^{24} - 1032986 p^{10} T^{26} + 15312 p^{12} T^{28} - 160 p^{14} T^{30} + p^{16} T^{32} \) | |
| 41 | \( 1 + 18 T + 358 T^{2} + 4500 T^{3} + 54840 T^{4} + 546582 T^{5} + 5282002 T^{6} + 45829452 T^{7} + 391371517 T^{8} + 3136234194 T^{9} + 24733354269 T^{10} + 186013158912 T^{11} + 1365943595003 T^{12} + 234854728914 p T^{13} + 66175973009543 T^{14} + 10725583636596 p T^{15} + 2857961563758879 T^{16} + 10725583636596 p^{2} T^{17} + 66175973009543 p^{2} T^{18} + 234854728914 p^{4} T^{19} + 1365943595003 p^{4} T^{20} + 186013158912 p^{5} T^{21} + 24733354269 p^{6} T^{22} + 3136234194 p^{7} T^{23} + 391371517 p^{8} T^{24} + 45829452 p^{9} T^{25} + 5282002 p^{10} T^{26} + 546582 p^{11} T^{27} + 54840 p^{12} T^{28} + 4500 p^{13} T^{29} + 358 p^{14} T^{30} + 18 p^{15} T^{31} + p^{16} T^{32} \) | |
| 43 | \( 1 + 32 T + 386 T^{2} + 1956 T^{3} + 3028 T^{4} + 21752 T^{5} + 145614 T^{6} - 5040252 T^{7} - 76956731 T^{8} - 431456972 T^{9} - 1420003353 T^{10} - 10453792098 T^{11} - 69895637053 T^{12} + 208576009948 T^{13} + 5960716600089 T^{14} + 38060480693916 T^{15} + 189113657800291 T^{16} + 38060480693916 p T^{17} + 5960716600089 p^{2} T^{18} + 208576009948 p^{3} T^{19} - 69895637053 p^{4} T^{20} - 10453792098 p^{5} T^{21} - 1420003353 p^{6} T^{22} - 431456972 p^{7} T^{23} - 76956731 p^{8} T^{24} - 5040252 p^{9} T^{25} + 145614 p^{10} T^{26} + 21752 p^{11} T^{27} + 3028 p^{12} T^{28} + 1956 p^{13} T^{29} + 386 p^{14} T^{30} + 32 p^{15} T^{31} + p^{16} T^{32} \) | |
| 47 | \( 1 + 66 T + 2301 T^{2} + 56034 T^{3} + 1061827 T^{4} + 16584684 T^{5} + 221550956 T^{6} + 2600902890 T^{7} + 27436895546 T^{8} + 265294801890 T^{9} + 2393966242239 T^{10} + 20471188232046 T^{11} + 167711622861328 T^{12} + 28160940748968 p T^{13} + 10066116607722236 T^{14} + 73587368388097878 T^{15} + 515611185246520285 T^{16} + 73587368388097878 p T^{17} + 10066116607722236 p^{2} T^{18} + 28160940748968 p^{4} T^{19} + 167711622861328 p^{4} T^{20} + 20471188232046 p^{5} T^{21} + 2393966242239 p^{6} T^{22} + 265294801890 p^{7} T^{23} + 27436895546 p^{8} T^{24} + 2600902890 p^{9} T^{25} + 221550956 p^{10} T^{26} + 16584684 p^{11} T^{27} + 1061827 p^{12} T^{28} + 56034 p^{13} T^{29} + 2301 p^{14} T^{30} + 66 p^{15} T^{31} + p^{16} T^{32} \) | |
| 53 | \( 1 - 2 T - 195 T^{2} - 1318 T^{3} + 22409 T^{4} + 269300 T^{5} - 557738 T^{6} - 27538680 T^{7} - 96170256 T^{8} + 1346417800 T^{9} + 12401375043 T^{10} - 17177770406 T^{11} - 633298455796 T^{12} - 1787982426838 T^{13} + 14498252101676 T^{14} + 62417595792192 T^{15} - 108566606387647 T^{16} + 62417595792192 p T^{17} + 14498252101676 p^{2} T^{18} - 1787982426838 p^{3} T^{19} - 633298455796 p^{4} T^{20} - 17177770406 p^{5} T^{21} + 12401375043 p^{6} T^{22} + 1346417800 p^{7} T^{23} - 96170256 p^{8} T^{24} - 27538680 p^{9} T^{25} - 557738 p^{10} T^{26} + 269300 p^{11} T^{27} + 22409 p^{12} T^{28} - 1318 p^{13} T^{29} - 195 p^{14} T^{30} - 2 p^{15} T^{31} + p^{16} T^{32} \) | |
| 59 | \( 1 - 380 T^{2} + 68018 T^{4} - 7713172 T^{6} + 646336299 T^{8} - 46563852812 T^{10} + 3301553751524 T^{12} - 231962799484800 T^{14} + 14737262425784917 T^{16} - 231962799484800 p^{2} T^{18} + 3301553751524 p^{4} T^{20} - 46563852812 p^{6} T^{22} + 646336299 p^{8} T^{24} - 7713172 p^{10} T^{26} + 68018 p^{12} T^{28} - 380 p^{14} T^{30} + p^{16} T^{32} \) | |
| 61 | \( 1 - 4 T - 316 T^{2} - 312 T^{3} + 61324 T^{4} + 245132 T^{5} - 7198536 T^{6} - 55299324 T^{7} + 556284058 T^{8} + 6963620032 T^{9} - 19845563172 T^{10} - 599541342300 T^{11} - 953172266128 T^{12} + 33168551975332 T^{13} + 211771076298780 T^{14} - 841283718375456 T^{15} - 16826358225960461 T^{16} - 841283718375456 p T^{17} + 211771076298780 p^{2} T^{18} + 33168551975332 p^{3} T^{19} - 953172266128 p^{4} T^{20} - 599541342300 p^{5} T^{21} - 19845563172 p^{6} T^{22} + 6963620032 p^{7} T^{23} + 556284058 p^{8} T^{24} - 55299324 p^{9} T^{25} - 7198536 p^{10} T^{26} + 245132 p^{11} T^{27} + 61324 p^{12} T^{28} - 312 p^{13} T^{29} - 316 p^{14} T^{30} - 4 p^{15} T^{31} + p^{16} T^{32} \) | |
| 67 | \( 1 - 36 T + 835 T^{2} - 14508 T^{3} + 201800 T^{4} - 2276208 T^{5} + 20516915 T^{6} - 134114418 T^{7} + 361268522 T^{8} + 5542022646 T^{9} - 109812124426 T^{10} + 1139839347762 T^{11} - 7532359492173 T^{12} + 17374023669942 T^{13} + 339151764941754 T^{14} - 6101687687866866 T^{15} + 60614188125948085 T^{16} - 6101687687866866 p T^{17} + 339151764941754 p^{2} T^{18} + 17374023669942 p^{3} T^{19} - 7532359492173 p^{4} T^{20} + 1139839347762 p^{5} T^{21} - 109812124426 p^{6} T^{22} + 5542022646 p^{7} T^{23} + 361268522 p^{8} T^{24} - 134114418 p^{9} T^{25} + 20516915 p^{10} T^{26} - 2276208 p^{11} T^{27} + 201800 p^{12} T^{28} - 14508 p^{13} T^{29} + 835 p^{14} T^{30} - 36 p^{15} T^{31} + p^{16} T^{32} \) | |
| 71 | \( 1 + 30 T + 496 T^{2} + 5880 T^{3} + 47763 T^{4} + 239550 T^{5} - 184432 T^{6} - 17087508 T^{7} - 154821892 T^{8} - 456732348 T^{9} + 8514713412 T^{10} + 158385211890 T^{11} + 1465807912525 T^{12} + 7253307274650 T^{13} - 20262310103312 T^{14} - 798123905876142 T^{15} - 8825867569357317 T^{16} - 798123905876142 p T^{17} - 20262310103312 p^{2} T^{18} + 7253307274650 p^{3} T^{19} + 1465807912525 p^{4} T^{20} + 158385211890 p^{5} T^{21} + 8514713412 p^{6} T^{22} - 456732348 p^{7} T^{23} - 154821892 p^{8} T^{24} - 17087508 p^{9} T^{25} - 184432 p^{10} T^{26} + 239550 p^{11} T^{27} + 47763 p^{12} T^{28} + 5880 p^{13} T^{29} + 496 p^{14} T^{30} + 30 p^{15} T^{31} + p^{16} T^{32} \) | |
| 73 | \( 1 - 18 T + 301 T^{2} - 3474 T^{3} + 27698 T^{4} - 113148 T^{5} - 236309 T^{6} + 20620026 T^{7} - 249891430 T^{8} + 2525884308 T^{9} - 21352907538 T^{10} + 134607558612 T^{11} - 277508772423 T^{12} - 33901633560 p T^{13} + 104687240819980 T^{14} - 1238446915840422 T^{15} + 11497606771536233 T^{16} - 1238446915840422 p T^{17} + 104687240819980 p^{2} T^{18} - 33901633560 p^{4} T^{19} - 277508772423 p^{4} T^{20} + 134607558612 p^{5} T^{21} - 21352907538 p^{6} T^{22} + 2525884308 p^{7} T^{23} - 249891430 p^{8} T^{24} + 20620026 p^{9} T^{25} - 236309 p^{10} T^{26} - 113148 p^{11} T^{27} + 27698 p^{12} T^{28} - 3474 p^{13} T^{29} + 301 p^{14} T^{30} - 18 p^{15} T^{31} + p^{16} T^{32} \) | |
| 79 | \( 1 + 24 T - 116 T^{2} - 6316 T^{3} + 8751 T^{4} + 1024592 T^{5} - 1057936 T^{6} - 117334194 T^{7} + 354271940 T^{8} + 10928923888 T^{9} - 72443598888 T^{10} - 846862897898 T^{11} + 9962166960773 T^{12} + 50168591523642 T^{13} - 1051373374276888 T^{14} - 1522192926505076 T^{15} + 90217363743814155 T^{16} - 1522192926505076 p T^{17} - 1051373374276888 p^{2} T^{18} + 50168591523642 p^{3} T^{19} + 9962166960773 p^{4} T^{20} - 846862897898 p^{5} T^{21} - 72443598888 p^{6} T^{22} + 10928923888 p^{7} T^{23} + 354271940 p^{8} T^{24} - 117334194 p^{9} T^{25} - 1057936 p^{10} T^{26} + 1024592 p^{11} T^{27} + 8751 p^{12} T^{28} - 6316 p^{13} T^{29} - 116 p^{14} T^{30} + 24 p^{15} T^{31} + p^{16} T^{32} \) | |
| 83 | \( 1 - 484 T^{2} + 142268 T^{4} - 29580086 T^{6} + 4879595558 T^{8} - 662523125234 T^{10} + 76909497524985 T^{12} - 7735213826859018 T^{14} + 684662977430406493 T^{16} - 7735213826859018 p^{2} T^{18} + 76909497524985 p^{4} T^{20} - 662523125234 p^{6} T^{22} + 4879595558 p^{8} T^{24} - 29580086 p^{10} T^{26} + 142268 p^{12} T^{28} - 484 p^{14} T^{30} + p^{16} T^{32} \) | |
| 89 | \( 1 - 682 T^{2} + 241445 T^{4} - 58677170 T^{6} + 10958822348 T^{8} - 1669148292560 T^{10} + 214384262179515 T^{12} - 23643926104661220 T^{14} + 2258387111623449559 T^{16} - 23643926104661220 p^{2} T^{18} + 214384262179515 p^{4} T^{20} - 1669148292560 p^{6} T^{22} + 10958822348 p^{8} T^{24} - 58677170 p^{10} T^{26} + 241445 p^{12} T^{28} - 682 p^{14} T^{30} + p^{16} T^{32} \) | |
| 97 | \( 1 + 6 T + 503 T^{2} + 2946 T^{3} + 127209 T^{4} + 657234 T^{5} + 21377574 T^{6} + 92067138 T^{7} + 2753435634 T^{8} + 9901707102 T^{9} + 312594305607 T^{10} + 1072349902938 T^{11} + 35099100528878 T^{12} + 134138470329528 T^{13} + 3917180676344122 T^{14} + 16065358655112540 T^{15} + 403313590778631681 T^{16} + 16065358655112540 p T^{17} + 3917180676344122 p^{2} T^{18} + 134138470329528 p^{3} T^{19} + 35099100528878 p^{4} T^{20} + 1072349902938 p^{5} T^{21} + 312594305607 p^{6} T^{22} + 9901707102 p^{7} T^{23} + 2753435634 p^{8} T^{24} + 92067138 p^{9} T^{25} + 21377574 p^{10} T^{26} + 657234 p^{11} T^{27} + 127209 p^{12} T^{28} + 2946 p^{13} T^{29} + 503 p^{14} T^{30} + 6 p^{15} T^{31} + p^{16} T^{32} \) | |
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\(L(s) = \displaystyle\prod_p \ \prod_{j=1}^{32} (1 - \alpha_{j,p}\, p^{-s})^{-1}\)
Imaginary part of the first few zeros on the critical line
−3.01534754416965105059576603767, −2.99560091667272494599143010667, −2.94917551639980725287890159655, −2.79563435271506823255602946122, −2.71023934173279386951431837579, −2.44547401757216040483785278640, −2.41034220037222588806990022564, −2.37287121678518858364714997789, −2.32828196035130107862290784931, −2.27118124369825206277496307852, −2.09663465265701728166494637766, −2.06239806830425956199200972732, −1.81044907795594355182357955362, −1.53226803201635069116792718134, −1.49098084801636304034477323097, −1.48066036583139500849598561982, −1.47821720146009888914686830739, −1.40106047996286010359251346329, −1.32515195004577955275153823722, −1.25131761854073082846487029069, −1.07116278357664680618666519713, −0.810436400435397330114672722315, −0.30299746939185432956876707004, −0.11655987403281761737740896794, −0.04107877727315629491260816125, 0.04107877727315629491260816125, 0.11655987403281761737740896794, 0.30299746939185432956876707004, 0.810436400435397330114672722315, 1.07116278357664680618666519713, 1.25131761854073082846487029069, 1.32515195004577955275153823722, 1.40106047996286010359251346329, 1.47821720146009888914686830739, 1.48066036583139500849598561982, 1.49098084801636304034477323097, 1.53226803201635069116792718134, 1.81044907795594355182357955362, 2.06239806830425956199200972732, 2.09663465265701728166494637766, 2.27118124369825206277496307852, 2.32828196035130107862290784931, 2.37287121678518858364714997789, 2.41034220037222588806990022564, 2.44547401757216040483785278640, 2.71023934173279386951431837579, 2.79563435271506823255602946122, 2.94917551639980725287890159655, 2.99560091667272494599143010667, 3.01534754416965105059576603767
Graph of the $Z$-function along the critical line
Plot not available for L-functions of degree greater than 10.