Dirichlet series
| L(s) = 1 | + 4.39e3·3-s − 5.73e4·4-s + 6.97e4·5-s − 1.83e7·9-s + 2.01e7·11-s − 2.51e8·12-s + 3.06e8·15-s + 1.87e9·16-s − 4.00e9·20-s − 7.30e9·23-s − 3.06e10·25-s − 1.04e11·27-s − 3.35e10·31-s + 8.85e10·33-s + 1.05e12·36-s + 7.31e10·37-s − 1.15e12·44-s − 1.27e12·45-s − 1.61e12·47-s + 8.25e12·48-s + 6.45e12·49-s − 3.53e12·53-s + 1.40e12·55-s − 8.18e11·59-s − 1.75e13·60-s − 4.61e13·64-s + 1.64e13·67-s + ⋯ |
| L(s) = 1 | + 2.00·3-s − 7/2·4-s + 0.892·5-s − 3.83·9-s + 1.03·11-s − 7.03·12-s + 1.79·15-s + 7·16-s − 3.12·20-s − 2.14·23-s − 5.02·25-s − 9.98·27-s − 1.22·31-s + 2.07·33-s + 13.4·36-s + 0.770·37-s − 3.61·44-s − 3.41·45-s − 3.18·47-s + 14.0·48-s + 9.52·49-s − 3.00·53-s + 0.922·55-s − 0.328·59-s − 6.27·60-s − 10.5·64-s + 2.72·67-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{14} \cdot 11^{14}\right)^{s/2} \, \Gamma_{\C}(s)^{14} \, L(s)\cr=\mathstrut & \,\Lambda(15-s)\end{aligned}\]
\[\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{14} \cdot 11^{14}\right)^{s/2} \, \Gamma_{\C}(s+7)^{14} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}\]
Invariants
| Degree: | \(28\) |
| Conductor: | \(2^{14} \cdot 11^{14}\) |
| Sign: | $1$ |
| Analytic conductor: | \(1.31198\times 10^{20}\) |
| Root analytic conductor: | \(5.22994\) |
| Motivic weight: | \(14\) |
| Rational: | yes |
| Arithmetic: | yes |
| Character: | Trivial |
| Primitive: | no |
| Self-dual: | yes |
| Analytic rank: | \(0\) |
| Selberg data: | \((28,\ 2^{14} \cdot 11^{14} ,\ ( \ : [7]^{14} ),\ 1 )\) |
Particular Values
| \(L(\frac{15}{2})\) | \(\approx\) | \(0.06778492348\) |
| \(L(\frac12)\) | \(\approx\) | \(0.06778492348\) |
| \(L(8)\) | not available | |
| \(L(1)\) | not available |
Euler product
\(L(s) = \displaystyle \prod_{p} F_p(p^{-s})^{-1} \)
| $p$ | $F_p(T)$ | |
|---|---|---|
| bad | 2 | \( ( 1 + p^{13} T^{2} )^{7} \) |
| 11 | \( 1 - 20143042 T + 10111913126009 p T^{2} + 869390528442718976 p^{4} T^{3} - 7972776854862344192 p^{9} T^{4} - \)\(18\!\cdots\!16\)\( p^{12} T^{5} + \)\(78\!\cdots\!08\)\( p^{16} T^{6} + \)\(17\!\cdots\!52\)\( p^{22} T^{7} + \)\(78\!\cdots\!08\)\( p^{30} T^{8} - \)\(18\!\cdots\!16\)\( p^{40} T^{9} - 7972776854862344192 p^{51} T^{10} + 869390528442718976 p^{60} T^{11} + 10111913126009 p^{71} T^{12} - 20143042 p^{84} T^{13} + p^{98} T^{14} \) | |
| good | 3 | \( ( 1 - 2197 T + 5466551 p T^{2} - 11558238008 p T^{3} + 5378035687996 p^{3} T^{4} - 1118379084232864 p^{5} T^{5} + 138272932443665770 p^{8} T^{6} - 8435939261283857930 p^{11} T^{7} + 138272932443665770 p^{22} T^{8} - 1118379084232864 p^{33} T^{9} + 5378035687996 p^{45} T^{10} - 11558238008 p^{57} T^{11} + 5466551 p^{71} T^{12} - 2197 p^{84} T^{13} + p^{98} T^{14} )^{2} \) |
| 5 | \( ( 1 - 34879 T + 3429521429 p T^{2} - 57218522208996 p T^{3} + 5511502276909670124 p^{2} T^{4} + \)\(36\!\cdots\!04\)\( p^{2} T^{5} + \)\(13\!\cdots\!38\)\( p^{4} T^{6} + \)\(10\!\cdots\!34\)\( p^{6} T^{7} + \)\(13\!\cdots\!38\)\( p^{18} T^{8} + \)\(36\!\cdots\!04\)\( p^{30} T^{9} + 5511502276909670124 p^{44} T^{10} - 57218522208996 p^{57} T^{11} + 3429521429 p^{71} T^{12} - 34879 p^{84} T^{13} + p^{98} T^{14} )^{2} \) | |
| 7 | \( 1 - 6459862772438 T^{2} + \)\(29\!\cdots\!45\)\( p T^{4} - \)\(88\!\cdots\!56\)\( p^{2} T^{6} + \)\(19\!\cdots\!87\)\( p^{3} T^{8} - \)\(32\!\cdots\!94\)\( p^{4} T^{10} + \)\(43\!\cdots\!65\)\( p^{5} T^{12} - \)\(46\!\cdots\!24\)\( p^{6} T^{14} + \)\(43\!\cdots\!65\)\( p^{33} T^{16} - \)\(32\!\cdots\!94\)\( p^{60} T^{18} + \)\(19\!\cdots\!87\)\( p^{87} T^{20} - \)\(88\!\cdots\!56\)\( p^{114} T^{22} + \)\(29\!\cdots\!45\)\( p^{141} T^{24} - 6459862772438 p^{168} T^{26} + p^{196} T^{28} \) | |
| 13 | \( 1 - 17115533219989574 T^{2} + \)\(11\!\cdots\!51\)\( p^{2} T^{4} - \)\(52\!\cdots\!72\)\( p^{4} T^{6} + \)\(20\!\cdots\!61\)\( p^{6} T^{8} - \)\(52\!\cdots\!18\)\( p^{9} T^{10} + \)\(19\!\cdots\!07\)\( p^{10} T^{12} - \)\(48\!\cdots\!48\)\( p^{12} T^{14} + \)\(19\!\cdots\!07\)\( p^{38} T^{16} - \)\(52\!\cdots\!18\)\( p^{65} T^{18} + \)\(20\!\cdots\!61\)\( p^{90} T^{20} - \)\(52\!\cdots\!72\)\( p^{116} T^{22} + \)\(11\!\cdots\!51\)\( p^{142} T^{24} - 17115533219989574 p^{168} T^{26} + p^{196} T^{28} \) | |
| 17 | \( 1 - 745158408686455286 T^{2} + \)\(34\!\cdots\!39\)\( T^{4} - \)\(69\!\cdots\!00\)\( p T^{6} + \)\(33\!\cdots\!57\)\( T^{8} - \)\(80\!\cdots\!66\)\( T^{10} + \)\(16\!\cdots\!63\)\( T^{12} - \)\(29\!\cdots\!24\)\( T^{14} + \)\(16\!\cdots\!63\)\( p^{28} T^{16} - \)\(80\!\cdots\!66\)\( p^{56} T^{18} + \)\(33\!\cdots\!57\)\( p^{84} T^{20} - \)\(69\!\cdots\!00\)\( p^{113} T^{22} + \)\(34\!\cdots\!39\)\( p^{140} T^{24} - 745158408686455286 p^{168} T^{26} + p^{196} T^{28} \) | |
| 19 | \( 1 - 8370367638427904006 T^{2} + \)\(33\!\cdots\!99\)\( T^{4} - \)\(88\!\cdots\!28\)\( T^{6} + \)\(16\!\cdots\!09\)\( T^{8} - \)\(23\!\cdots\!46\)\( T^{10} + \)\(26\!\cdots\!23\)\( T^{12} - \)\(23\!\cdots\!52\)\( T^{14} + \)\(26\!\cdots\!23\)\( p^{28} T^{16} - \)\(23\!\cdots\!46\)\( p^{56} T^{18} + \)\(16\!\cdots\!09\)\( p^{84} T^{20} - \)\(88\!\cdots\!28\)\( p^{112} T^{22} + \)\(33\!\cdots\!99\)\( p^{140} T^{24} - 8370367638427904006 p^{168} T^{26} + p^{196} T^{28} \) | |
| 23 | \( ( 1 + 3652877771 T + 34836934137830560621 T^{2} + \)\(58\!\cdots\!12\)\( T^{3} + \)\(47\!\cdots\!68\)\( T^{4} + \)\(55\!\cdots\!88\)\( T^{5} + \)\(62\!\cdots\!34\)\( T^{6} + \)\(83\!\cdots\!66\)\( T^{7} + \)\(62\!\cdots\!34\)\( p^{14} T^{8} + \)\(55\!\cdots\!88\)\( p^{28} T^{9} + \)\(47\!\cdots\!68\)\( p^{42} T^{10} + \)\(58\!\cdots\!12\)\( p^{56} T^{11} + 34836934137830560621 p^{70} T^{12} + 3652877771 p^{84} T^{13} + p^{98} T^{14} )^{2} \) | |
| 29 | \( 1 - \)\(90\!\cdots\!86\)\( T^{2} + \)\(68\!\cdots\!87\)\( T^{4} - \)\(37\!\cdots\!24\)\( T^{6} + \)\(17\!\cdots\!25\)\( T^{8} - \)\(69\!\cdots\!02\)\( T^{10} + \)\(24\!\cdots\!07\)\( T^{12} - \)\(77\!\cdots\!68\)\( T^{14} + \)\(24\!\cdots\!07\)\( p^{28} T^{16} - \)\(69\!\cdots\!02\)\( p^{56} T^{18} + \)\(17\!\cdots\!25\)\( p^{84} T^{20} - \)\(37\!\cdots\!24\)\( p^{112} T^{22} + \)\(68\!\cdots\!87\)\( p^{140} T^{24} - \)\(90\!\cdots\!86\)\( p^{168} T^{26} + p^{196} T^{28} \) | |
| 31 | \( ( 1 + 16784936971 T + \)\(15\!\cdots\!25\)\( T^{2} + \)\(61\!\cdots\!76\)\( T^{3} + \)\(69\!\cdots\!40\)\( T^{4} + \)\(11\!\cdots\!44\)\( T^{5} + \)\(67\!\cdots\!38\)\( T^{6} + \)\(25\!\cdots\!50\)\( T^{7} + \)\(67\!\cdots\!38\)\( p^{14} T^{8} + \)\(11\!\cdots\!44\)\( p^{28} T^{9} + \)\(69\!\cdots\!40\)\( p^{42} T^{10} + \)\(61\!\cdots\!76\)\( p^{56} T^{11} + \)\(15\!\cdots\!25\)\( p^{70} T^{12} + 16784936971 p^{84} T^{13} + p^{98} T^{14} )^{2} \) | |
| 37 | \( ( 1 - 36583911983 T + \)\(28\!\cdots\!81\)\( T^{2} - \)\(19\!\cdots\!48\)\( T^{3} + \)\(54\!\cdots\!68\)\( T^{4} - \)\(31\!\cdots\!72\)\( T^{5} + \)\(69\!\cdots\!74\)\( T^{6} - \)\(37\!\cdots\!42\)\( T^{7} + \)\(69\!\cdots\!74\)\( p^{14} T^{8} - \)\(31\!\cdots\!72\)\( p^{28} T^{9} + \)\(54\!\cdots\!68\)\( p^{42} T^{10} - \)\(19\!\cdots\!48\)\( p^{56} T^{11} + \)\(28\!\cdots\!81\)\( p^{70} T^{12} - 36583911983 p^{84} T^{13} + p^{98} T^{14} )^{2} \) | |
| 41 | \( 1 - \)\(21\!\cdots\!22\)\( T^{2} + \)\(26\!\cdots\!07\)\( T^{4} - \)\(23\!\cdots\!76\)\( T^{6} + \)\(16\!\cdots\!05\)\( T^{8} - \)\(92\!\cdots\!26\)\( T^{10} + \)\(44\!\cdots\!07\)\( T^{12} - \)\(18\!\cdots\!44\)\( T^{14} + \)\(44\!\cdots\!07\)\( p^{28} T^{16} - \)\(92\!\cdots\!26\)\( p^{56} T^{18} + \)\(16\!\cdots\!05\)\( p^{84} T^{20} - \)\(23\!\cdots\!76\)\( p^{112} T^{22} + \)\(26\!\cdots\!07\)\( p^{140} T^{24} - \)\(21\!\cdots\!22\)\( p^{168} T^{26} + p^{196} T^{28} \) | |
| 43 | \( 1 - \)\(42\!\cdots\!54\)\( T^{2} + \)\(10\!\cdots\!87\)\( T^{4} - \)\(18\!\cdots\!56\)\( T^{6} + \)\(24\!\cdots\!45\)\( T^{8} - \)\(27\!\cdots\!78\)\( T^{10} + \)\(25\!\cdots\!07\)\( T^{12} - \)\(10\!\cdots\!48\)\( p^{2} T^{14} + \)\(25\!\cdots\!07\)\( p^{28} T^{16} - \)\(27\!\cdots\!78\)\( p^{56} T^{18} + \)\(24\!\cdots\!45\)\( p^{84} T^{20} - \)\(18\!\cdots\!56\)\( p^{112} T^{22} + \)\(10\!\cdots\!87\)\( p^{140} T^{24} - \)\(42\!\cdots\!54\)\( p^{168} T^{26} + p^{196} T^{28} \) | |
| 47 | \( ( 1 + 806358693062 T + \)\(14\!\cdots\!91\)\( T^{2} + \)\(95\!\cdots\!12\)\( T^{3} + \)\(96\!\cdots\!53\)\( T^{4} + \)\(52\!\cdots\!98\)\( T^{5} + \)\(39\!\cdots\!59\)\( T^{6} + \)\(17\!\cdots\!68\)\( T^{7} + \)\(39\!\cdots\!59\)\( p^{14} T^{8} + \)\(52\!\cdots\!98\)\( p^{28} T^{9} + \)\(96\!\cdots\!53\)\( p^{42} T^{10} + \)\(95\!\cdots\!12\)\( p^{56} T^{11} + \)\(14\!\cdots\!91\)\( p^{70} T^{12} + 806358693062 p^{84} T^{13} + p^{98} T^{14} )^{2} \) | |
| 53 | \( ( 1 + 1765032034082 T + \)\(59\!\cdots\!47\)\( T^{2} + \)\(92\!\cdots\!72\)\( T^{3} + \)\(18\!\cdots\!17\)\( T^{4} + \)\(24\!\cdots\!54\)\( T^{5} + \)\(35\!\cdots\!15\)\( T^{6} + \)\(42\!\cdots\!52\)\( T^{7} + \)\(35\!\cdots\!15\)\( p^{14} T^{8} + \)\(24\!\cdots\!54\)\( p^{28} T^{9} + \)\(18\!\cdots\!17\)\( p^{42} T^{10} + \)\(92\!\cdots\!72\)\( p^{56} T^{11} + \)\(59\!\cdots\!47\)\( p^{70} T^{12} + 1765032034082 p^{84} T^{13} + p^{98} T^{14} )^{2} \) | |
| 59 | \( ( 1 + 409248282035 T + \)\(14\!\cdots\!01\)\( T^{2} - \)\(14\!\cdots\!80\)\( T^{3} + \)\(92\!\cdots\!60\)\( T^{4} - \)\(21\!\cdots\!00\)\( T^{5} + \)\(80\!\cdots\!42\)\( T^{6} - \)\(12\!\cdots\!70\)\( T^{7} + \)\(80\!\cdots\!42\)\( p^{14} T^{8} - \)\(21\!\cdots\!00\)\( p^{28} T^{9} + \)\(92\!\cdots\!60\)\( p^{42} T^{10} - \)\(14\!\cdots\!80\)\( p^{56} T^{11} + \)\(14\!\cdots\!01\)\( p^{70} T^{12} + 409248282035 p^{84} T^{13} + p^{98} T^{14} )^{2} \) | |
| 61 | \( 1 - \)\(81\!\cdots\!26\)\( T^{2} + \)\(33\!\cdots\!03\)\( T^{4} - \)\(91\!\cdots\!08\)\( T^{6} + \)\(18\!\cdots\!53\)\( T^{8} - \)\(29\!\cdots\!94\)\( T^{10} + \)\(37\!\cdots\!19\)\( T^{12} - \)\(40\!\cdots\!16\)\( T^{14} + \)\(37\!\cdots\!19\)\( p^{28} T^{16} - \)\(29\!\cdots\!94\)\( p^{56} T^{18} + \)\(18\!\cdots\!53\)\( p^{84} T^{20} - \)\(91\!\cdots\!08\)\( p^{112} T^{22} + \)\(33\!\cdots\!03\)\( p^{140} T^{24} - \)\(81\!\cdots\!26\)\( p^{168} T^{26} + p^{196} T^{28} \) | |
| 67 | \( ( 1 - 8242732638461 T + \)\(13\!\cdots\!69\)\( T^{2} - \)\(82\!\cdots\!92\)\( T^{3} + \)\(74\!\cdots\!32\)\( T^{4} - \)\(39\!\cdots\!08\)\( T^{5} + \)\(28\!\cdots\!34\)\( T^{6} - \)\(15\!\cdots\!54\)\( T^{7} + \)\(28\!\cdots\!34\)\( p^{14} T^{8} - \)\(39\!\cdots\!08\)\( p^{28} T^{9} + \)\(74\!\cdots\!32\)\( p^{42} T^{10} - \)\(82\!\cdots\!92\)\( p^{56} T^{11} + \)\(13\!\cdots\!69\)\( p^{70} T^{12} - 8242732638461 p^{84} T^{13} + p^{98} T^{14} )^{2} \) | |
| 71 | \( ( 1 + 9690439589939 T + \)\(34\!\cdots\!25\)\( T^{2} + \)\(22\!\cdots\!24\)\( T^{3} + \)\(47\!\cdots\!40\)\( T^{4} + \)\(18\!\cdots\!76\)\( T^{5} + \)\(41\!\cdots\!38\)\( T^{6} + \)\(98\!\cdots\!70\)\( T^{7} + \)\(41\!\cdots\!38\)\( p^{14} T^{8} + \)\(18\!\cdots\!76\)\( p^{28} T^{9} + \)\(47\!\cdots\!40\)\( p^{42} T^{10} + \)\(22\!\cdots\!24\)\( p^{56} T^{11} + \)\(34\!\cdots\!25\)\( p^{70} T^{12} + 9690439589939 p^{84} T^{13} + p^{98} T^{14} )^{2} \) | |
| 73 | \( 1 - \)\(77\!\cdots\!62\)\( T^{2} + \)\(25\!\cdots\!15\)\( T^{4} - \)\(45\!\cdots\!28\)\( T^{6} + \)\(48\!\cdots\!89\)\( T^{8} - \)\(44\!\cdots\!90\)\( T^{10} + \)\(66\!\cdots\!35\)\( T^{12} - \)\(99\!\cdots\!20\)\( T^{14} + \)\(66\!\cdots\!35\)\( p^{28} T^{16} - \)\(44\!\cdots\!90\)\( p^{56} T^{18} + \)\(48\!\cdots\!89\)\( p^{84} T^{20} - \)\(45\!\cdots\!28\)\( p^{112} T^{22} + \)\(25\!\cdots\!15\)\( p^{140} T^{24} - \)\(77\!\cdots\!62\)\( p^{168} T^{26} + p^{196} T^{28} \) | |
| 79 | \( 1 - \)\(19\!\cdots\!74\)\( T^{2} + \)\(23\!\cdots\!39\)\( T^{4} - \)\(20\!\cdots\!20\)\( T^{6} + \)\(14\!\cdots\!57\)\( T^{8} - \)\(80\!\cdots\!74\)\( T^{10} + \)\(38\!\cdots\!03\)\( T^{12} - \)\(15\!\cdots\!76\)\( T^{14} + \)\(38\!\cdots\!03\)\( p^{28} T^{16} - \)\(80\!\cdots\!74\)\( p^{56} T^{18} + \)\(14\!\cdots\!57\)\( p^{84} T^{20} - \)\(20\!\cdots\!20\)\( p^{112} T^{22} + \)\(23\!\cdots\!39\)\( p^{140} T^{24} - \)\(19\!\cdots\!74\)\( p^{168} T^{26} + p^{196} T^{28} \) | |
| 83 | \( 1 - \)\(23\!\cdots\!22\)\( T^{2} + \)\(32\!\cdots\!07\)\( T^{4} - \)\(32\!\cdots\!52\)\( T^{6} + \)\(25\!\cdots\!25\)\( T^{8} - \)\(15\!\cdots\!98\)\( T^{10} + \)\(81\!\cdots\!91\)\( T^{12} - \)\(47\!\cdots\!40\)\( T^{14} + \)\(81\!\cdots\!91\)\( p^{28} T^{16} - \)\(15\!\cdots\!98\)\( p^{56} T^{18} + \)\(25\!\cdots\!25\)\( p^{84} T^{20} - \)\(32\!\cdots\!52\)\( p^{112} T^{22} + \)\(32\!\cdots\!07\)\( p^{140} T^{24} - \)\(23\!\cdots\!22\)\( p^{168} T^{26} + p^{196} T^{28} \) | |
| 89 | \( ( 1 + 58885370993825 T + \)\(11\!\cdots\!53\)\( T^{2} + \)\(46\!\cdots\!88\)\( T^{3} + \)\(52\!\cdots\!64\)\( T^{4} + \)\(16\!\cdots\!20\)\( T^{5} + \)\(14\!\cdots\!98\)\( T^{6} + \)\(37\!\cdots\!66\)\( T^{7} + \)\(14\!\cdots\!98\)\( p^{14} T^{8} + \)\(16\!\cdots\!20\)\( p^{28} T^{9} + \)\(52\!\cdots\!64\)\( p^{42} T^{10} + \)\(46\!\cdots\!88\)\( p^{56} T^{11} + \)\(11\!\cdots\!53\)\( p^{70} T^{12} + 58885370993825 p^{84} T^{13} + p^{98} T^{14} )^{2} \) | |
| 97 | \( ( 1 - 61699069421783 T + \)\(34\!\cdots\!85\)\( T^{2} - \)\(20\!\cdots\!48\)\( T^{3} + \)\(58\!\cdots\!08\)\( T^{4} - \)\(29\!\cdots\!16\)\( T^{5} + \)\(59\!\cdots\!34\)\( T^{6} - \)\(24\!\cdots\!62\)\( T^{7} + \)\(59\!\cdots\!34\)\( p^{14} T^{8} - \)\(29\!\cdots\!16\)\( p^{28} T^{9} + \)\(58\!\cdots\!08\)\( p^{42} T^{10} - \)\(20\!\cdots\!48\)\( p^{56} T^{11} + \)\(34\!\cdots\!85\)\( p^{70} T^{12} - 61699069421783 p^{84} T^{13} + p^{98} T^{14} )^{2} \) | |
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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
−3.41039496749508973876093498128, −2.94341338633077971979140930811, −2.90410251880749723935268862753, −2.89338038396831308292647474868, −2.79165556004428670444084988910, −2.78392170010192233131805544996, −2.51513572476022727763718295137, −2.42712898030687205343769343696, −2.24942545601451412778193869569, −2.18721260970537895286577726841, −1.91760238664358447240096101591, −1.84283299679148058346412909954, −1.75157132721269429988802412892, −1.68802688611684828054128366462, −1.44265268820598830142604279930, −1.41393477304014995334514304937, −1.03621594426067674437051484649, −0.952311557750251638138716450303, −0.65012169554358746384284258235, −0.60361094649306319310037058107, −0.55652942421769051825639611318, −0.39870686365676598234023793100, −0.28148925222632453705540448363, −0.22337133490353459945202739371, −0.02557120376394272374021293483, 0.02557120376394272374021293483, 0.22337133490353459945202739371, 0.28148925222632453705540448363, 0.39870686365676598234023793100, 0.55652942421769051825639611318, 0.60361094649306319310037058107, 0.65012169554358746384284258235, 0.952311557750251638138716450303, 1.03621594426067674437051484649, 1.41393477304014995334514304937, 1.44265268820598830142604279930, 1.68802688611684828054128366462, 1.75157132721269429988802412892, 1.84283299679148058346412909954, 1.91760238664358447240096101591, 2.18721260970537895286577726841, 2.24942545601451412778193869569, 2.42712898030687205343769343696, 2.51513572476022727763718295137, 2.78392170010192233131805544996, 2.79165556004428670444084988910, 2.89338038396831308292647474868, 2.90410251880749723935268862753, 2.94341338633077971979140930811, 3.41039496749508973876093498128
Graph of the $Z$-function along the critical line
Plot not available for L-functions of degree greater than 10.