Properties

Degree 28
Conductor $ 3^{28} \cdot 11^{14} \cdot 61^{14} $
Sign $1$
Motivic weight 1
Primitive no
Self-dual yes
Analytic rank 0

Origins

Origins of factors

Downloads

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Normalization:  

Dirichlet series

L(s)  = 1  + 2-s − 6·4-s − 5-s + 9·7-s − 7·8-s − 10-s + 14·11-s + 13-s + 9·14-s + 14·16-s + 9·17-s + 22·19-s + 6·20-s + 14·22-s − 23-s − 22·25-s + 26-s − 54·28-s + 6·29-s + 9·31-s + 20·32-s + 9·34-s − 9·35-s + 18·37-s + 22·38-s + 7·40-s + 25·41-s + ⋯
L(s)  = 1  + 0.707·2-s − 3·4-s − 0.447·5-s + 3.40·7-s − 2.47·8-s − 0.316·10-s + 4.22·11-s + 0.277·13-s + 2.40·14-s + 7/2·16-s + 2.18·17-s + 5.04·19-s + 1.34·20-s + 2.98·22-s − 0.208·23-s − 4.39·25-s + 0.196·26-s − 10.2·28-s + 1.11·29-s + 1.61·31-s + 3.53·32-s + 1.54·34-s − 1.52·35-s + 2.95·37-s + 3.56·38-s + 1.10·40-s + 3.90·41-s + ⋯

Functional equation

\[\begin{aligned} \Lambda(s)=\mathstrut &\left(3^{28} \cdot 11^{14} \cdot 61^{14}\right)^{s/2} \, \Gamma_{\C}(s)^{14} \, L(s)\cr =\mathstrut & \,\Lambda(2-s) \end{aligned} \]
\[\begin{aligned} \Lambda(s)=\mathstrut &\left(3^{28} \cdot 11^{14} \cdot 61^{14}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{14} \, L(s)\cr =\mathstrut & \,\Lambda(1-s) \end{aligned} \]

Invariants

\( d \)  =  \(28\)
\( N \)  =  \(3^{28} \cdot 11^{14} \cdot 61^{14}\)
\( \varepsilon \)  =  $1$
motivic weight  =  \(1\)
character  :  induced by $\chi_{6039} (1, \cdot )$
primitive  :  no
self-dual  :  yes
analytic rank  =  0
Selberg data  =  $(28,\ 3^{28} \cdot 11^{14} \cdot 61^{14} ,\ ( \ : [1/2]^{14} ),\ 1 )$
$L(1)$  $\approx$  $1260.061585$
$L(\frac12)$  $\approx$  $1260.061585$
$L(\frac{3}{2})$   not available
$L(1)$   not available

Euler product

\[L(s) = \prod_{p \text{ prime}} F_p(p^{-s})^{-1} \] where, for $p \notin \{3,\;11,\;61\}$, \(F_p\) is a polynomial of degree 28. If $p \in \{3,\;11,\;61\}$, then $F_p$ is a polynomial of degree at most 27.
$p$$F_p$
bad3 \( 1 \)
11 \( ( 1 - T )^{14} \)
61 \( ( 1 - T )^{14} \)
good2 \( 1 - T + 7 T^{2} - 3 p T^{3} + 27 T^{4} - 5 p^{2} T^{5} + 81 T^{6} - 55 T^{7} + 207 T^{8} - 139 T^{9} + 257 p T^{10} - 89 p^{2} T^{11} + 615 p T^{12} - 851 T^{13} + 2615 T^{14} - 851 p T^{15} + 615 p^{3} T^{16} - 89 p^{5} T^{17} + 257 p^{5} T^{18} - 139 p^{5} T^{19} + 207 p^{6} T^{20} - 55 p^{7} T^{21} + 81 p^{8} T^{22} - 5 p^{11} T^{23} + 27 p^{10} T^{24} - 3 p^{12} T^{25} + 7 p^{12} T^{26} - p^{13} T^{27} + p^{14} T^{28} \)
5 \( 1 + T + 23 T^{2} + 7 p T^{3} + 331 T^{4} + 561 T^{5} + 3552 T^{6} + 2 p^{5} T^{7} + 6142 p T^{8} + 53589 T^{9} + 222534 T^{10} + 374432 T^{11} + 1380392 T^{12} + 2199712 T^{13} + 1480746 p T^{14} + 2199712 p T^{15} + 1380392 p^{2} T^{16} + 374432 p^{3} T^{17} + 222534 p^{4} T^{18} + 53589 p^{5} T^{19} + 6142 p^{7} T^{20} + 2 p^{12} T^{21} + 3552 p^{8} T^{22} + 561 p^{9} T^{23} + 331 p^{10} T^{24} + 7 p^{12} T^{25} + 23 p^{12} T^{26} + p^{13} T^{27} + p^{14} T^{28} \)
7 \( 1 - 9 T + 11 p T^{2} - 432 T^{3} + 2270 T^{4} - 9803 T^{5} + 40388 T^{6} - 149410 T^{7} + 533718 T^{8} - 1782087 T^{9} + 819597 p T^{10} - 17535815 T^{11} + 51464307 T^{12} - 144627270 T^{13} + 390279048 T^{14} - 144627270 p T^{15} + 51464307 p^{2} T^{16} - 17535815 p^{3} T^{17} + 819597 p^{5} T^{18} - 1782087 p^{5} T^{19} + 533718 p^{6} T^{20} - 149410 p^{7} T^{21} + 40388 p^{8} T^{22} - 9803 p^{9} T^{23} + 2270 p^{10} T^{24} - 432 p^{11} T^{25} + 11 p^{13} T^{26} - 9 p^{13} T^{27} + p^{14} T^{28} \)
13 \( 1 - T + 81 T^{2} - 98 T^{3} + 3422 T^{4} - 4866 T^{5} + 100104 T^{6} - 160773 T^{7} + 2269434 T^{8} - 3949833 T^{9} + 42329042 T^{10} - 76600455 T^{11} + 51805101 p T^{12} - 1208879886 T^{13} + 9341312614 T^{14} - 1208879886 p T^{15} + 51805101 p^{3} T^{16} - 76600455 p^{3} T^{17} + 42329042 p^{4} T^{18} - 3949833 p^{5} T^{19} + 2269434 p^{6} T^{20} - 160773 p^{7} T^{21} + 100104 p^{8} T^{22} - 4866 p^{9} T^{23} + 3422 p^{10} T^{24} - 98 p^{11} T^{25} + 81 p^{12} T^{26} - p^{13} T^{27} + p^{14} T^{28} \)
17 \( 1 - 9 T + 161 T^{2} - 1229 T^{3} + 12271 T^{4} - 79788 T^{5} + 588756 T^{6} - 3306669 T^{7} + 20089312 T^{8} - 99501923 T^{9} + 526646471 T^{10} - 2355773010 T^{11} + 11265239146 T^{12} - 46479022192 T^{13} + 205561578844 T^{14} - 46479022192 p T^{15} + 11265239146 p^{2} T^{16} - 2355773010 p^{3} T^{17} + 526646471 p^{4} T^{18} - 99501923 p^{5} T^{19} + 20089312 p^{6} T^{20} - 3306669 p^{7} T^{21} + 588756 p^{8} T^{22} - 79788 p^{9} T^{23} + 12271 p^{10} T^{24} - 1229 p^{11} T^{25} + 161 p^{12} T^{26} - 9 p^{13} T^{27} + p^{14} T^{28} \)
19 \( 1 - 22 T + 405 T^{2} - 5162 T^{3} + 58169 T^{4} - 545208 T^{5} + 4656573 T^{6} - 35148668 T^{7} + 245940070 T^{8} - 82286142 p T^{9} + 9305286079 T^{10} - 51028457017 T^{11} + 263455290000 T^{12} - 1261886979845 T^{13} + 5704736463782 T^{14} - 1261886979845 p T^{15} + 263455290000 p^{2} T^{16} - 51028457017 p^{3} T^{17} + 9305286079 p^{4} T^{18} - 82286142 p^{6} T^{19} + 245940070 p^{6} T^{20} - 35148668 p^{7} T^{21} + 4656573 p^{8} T^{22} - 545208 p^{9} T^{23} + 58169 p^{10} T^{24} - 5162 p^{11} T^{25} + 405 p^{12} T^{26} - 22 p^{13} T^{27} + p^{14} T^{28} \)
23 \( 1 + T + 162 T^{2} + 129 T^{3} + 13736 T^{4} + 351 p T^{5} + 796428 T^{6} + 295782 T^{7} + 1526932 p T^{8} + 6199464 T^{9} + 1245290749 T^{10} + 41635747 T^{11} + 36690460719 T^{12} - 1399840196 T^{13} + 914656857314 T^{14} - 1399840196 p T^{15} + 36690460719 p^{2} T^{16} + 41635747 p^{3} T^{17} + 1245290749 p^{4} T^{18} + 6199464 p^{5} T^{19} + 1526932 p^{7} T^{20} + 295782 p^{7} T^{21} + 796428 p^{8} T^{22} + 351 p^{10} T^{23} + 13736 p^{10} T^{24} + 129 p^{11} T^{25} + 162 p^{12} T^{26} + p^{13} T^{27} + p^{14} T^{28} \)
29 \( 1 - 6 T + 164 T^{2} - 548 T^{3} + 11705 T^{4} - 21353 T^{5} + 580119 T^{6} - 778214 T^{7} + 25224091 T^{8} - 43384579 T^{9} + 965373316 T^{10} - 1935780164 T^{11} + 30569274113 T^{12} - 61567478972 T^{13} + 883259702894 T^{14} - 61567478972 p T^{15} + 30569274113 p^{2} T^{16} - 1935780164 p^{3} T^{17} + 965373316 p^{4} T^{18} - 43384579 p^{5} T^{19} + 25224091 p^{6} T^{20} - 778214 p^{7} T^{21} + 580119 p^{8} T^{22} - 21353 p^{9} T^{23} + 11705 p^{10} T^{24} - 548 p^{11} T^{25} + 164 p^{12} T^{26} - 6 p^{13} T^{27} + p^{14} T^{28} \)
31 \( 1 - 9 T + 239 T^{2} - 1595 T^{3} + 24505 T^{4} - 122870 T^{5} + 1461485 T^{6} - 5328640 T^{7} + 58869289 T^{8} - 145579448 T^{9} + 1870221962 T^{10} - 3013751093 T^{11} + 56112840139 T^{12} - 69208980055 T^{13} + 55702274272 p T^{14} - 69208980055 p T^{15} + 56112840139 p^{2} T^{16} - 3013751093 p^{3} T^{17} + 1870221962 p^{4} T^{18} - 145579448 p^{5} T^{19} + 58869289 p^{6} T^{20} - 5328640 p^{7} T^{21} + 1461485 p^{8} T^{22} - 122870 p^{9} T^{23} + 24505 p^{10} T^{24} - 1595 p^{11} T^{25} + 239 p^{12} T^{26} - 9 p^{13} T^{27} + p^{14} T^{28} \)
37 \( 1 - 18 T + 432 T^{2} - 5905 T^{3} + 85438 T^{4} - 946870 T^{5} + 10472125 T^{6} - 98228108 T^{7} + 903726227 T^{8} - 7378741926 T^{9} + 58846420685 T^{10} - 425956868704 T^{11} + 3011460506632 T^{12} - 19535248148689 T^{13} + 123848656581976 T^{14} - 19535248148689 p T^{15} + 3011460506632 p^{2} T^{16} - 425956868704 p^{3} T^{17} + 58846420685 p^{4} T^{18} - 7378741926 p^{5} T^{19} + 903726227 p^{6} T^{20} - 98228108 p^{7} T^{21} + 10472125 p^{8} T^{22} - 946870 p^{9} T^{23} + 85438 p^{10} T^{24} - 5905 p^{11} T^{25} + 432 p^{12} T^{26} - 18 p^{13} T^{27} + p^{14} T^{28} \)
41 \( 1 - 25 T + 555 T^{2} - 8481 T^{3} + 115073 T^{4} - 1302241 T^{5} + 13419824 T^{6} - 122695156 T^{7} + 1044133400 T^{8} - 8136457371 T^{9} + 60228332496 T^{10} - 418792302802 T^{11} + 2832480690002 T^{12} - 18464723912586 T^{13} + 119639509456198 T^{14} - 18464723912586 p T^{15} + 2832480690002 p^{2} T^{16} - 418792302802 p^{3} T^{17} + 60228332496 p^{4} T^{18} - 8136457371 p^{5} T^{19} + 1044133400 p^{6} T^{20} - 122695156 p^{7} T^{21} + 13419824 p^{8} T^{22} - 1302241 p^{9} T^{23} + 115073 p^{10} T^{24} - 8481 p^{11} T^{25} + 555 p^{12} T^{26} - 25 p^{13} T^{27} + p^{14} T^{28} \)
43 \( 1 - 25 T + 532 T^{2} - 8239 T^{3} + 114958 T^{4} - 1374000 T^{5} + 15215678 T^{6} - 152200843 T^{7} + 1433865593 T^{8} - 12506182861 T^{9} + 103731364030 T^{10} - 807115680118 T^{11} + 6006992048132 T^{12} - 42217165145506 T^{13} + 284592836335592 T^{14} - 42217165145506 p T^{15} + 6006992048132 p^{2} T^{16} - 807115680118 p^{3} T^{17} + 103731364030 p^{4} T^{18} - 12506182861 p^{5} T^{19} + 1433865593 p^{6} T^{20} - 152200843 p^{7} T^{21} + 15215678 p^{8} T^{22} - 1374000 p^{9} T^{23} + 114958 p^{10} T^{24} - 8239 p^{11} T^{25} + 532 p^{12} T^{26} - 25 p^{13} T^{27} + p^{14} T^{28} \)
47 \( 1 + 36 T + 781 T^{2} + 11882 T^{3} + 146937 T^{4} + 1545655 T^{5} + 14728490 T^{6} + 128324787 T^{7} + 1055895172 T^{8} + 8241399586 T^{9} + 63121300759 T^{10} + 471780048623 T^{11} + 3479881314414 T^{12} + 24801469326359 T^{13} + 173052355308364 T^{14} + 24801469326359 p T^{15} + 3479881314414 p^{2} T^{16} + 471780048623 p^{3} T^{17} + 63121300759 p^{4} T^{18} + 8241399586 p^{5} T^{19} + 1055895172 p^{6} T^{20} + 128324787 p^{7} T^{21} + 14728490 p^{8} T^{22} + 1545655 p^{9} T^{23} + 146937 p^{10} T^{24} + 11882 p^{11} T^{25} + 781 p^{12} T^{26} + 36 p^{13} T^{27} + p^{14} T^{28} \)
53 \( 1 + 402 T^{2} - 227 T^{3} + 1578 p T^{4} - 79457 T^{5} + 11882258 T^{6} - 14130355 T^{7} + 1278036905 T^{8} - 1675943848 T^{9} + 109466085477 T^{10} - 146445928242 T^{11} + 7669739305332 T^{12} - 9873375239069 T^{13} + 445518985784738 T^{14} - 9873375239069 p T^{15} + 7669739305332 p^{2} T^{16} - 146445928242 p^{3} T^{17} + 109466085477 p^{4} T^{18} - 1675943848 p^{5} T^{19} + 1278036905 p^{6} T^{20} - 14130355 p^{7} T^{21} + 11882258 p^{8} T^{22} - 79457 p^{9} T^{23} + 1578 p^{11} T^{24} - 227 p^{11} T^{25} + 402 p^{12} T^{26} + p^{14} T^{28} \)
59 \( 1 + 17 T + 389 T^{2} + 4740 T^{3} + 64287 T^{4} + 608577 T^{5} + 6371355 T^{6} + 49592532 T^{7} + 442577701 T^{8} + 2858040770 T^{9} + 22812298546 T^{10} + 115897267986 T^{11} + 906553113883 T^{12} + 61873551798 p T^{13} + 39630010779372 T^{14} + 61873551798 p^{2} T^{15} + 906553113883 p^{2} T^{16} + 115897267986 p^{3} T^{17} + 22812298546 p^{4} T^{18} + 2858040770 p^{5} T^{19} + 442577701 p^{6} T^{20} + 49592532 p^{7} T^{21} + 6371355 p^{8} T^{22} + 608577 p^{9} T^{23} + 64287 p^{10} T^{24} + 4740 p^{11} T^{25} + 389 p^{12} T^{26} + 17 p^{13} T^{27} + p^{14} T^{28} \)
67 \( 1 - 22 T + 681 T^{2} - 10157 T^{3} + 186696 T^{4} - 2114640 T^{5} + 29260327 T^{6} - 261335976 T^{7} + 2995953959 T^{8} - 21040316696 T^{9} + 216281497981 T^{10} - 1160965161854 T^{11} + 12304472925340 T^{12} - 52683459033475 T^{13} + 722943372345054 T^{14} - 52683459033475 p T^{15} + 12304472925340 p^{2} T^{16} - 1160965161854 p^{3} T^{17} + 216281497981 p^{4} T^{18} - 21040316696 p^{5} T^{19} + 2995953959 p^{6} T^{20} - 261335976 p^{7} T^{21} + 29260327 p^{8} T^{22} - 2114640 p^{9} T^{23} + 186696 p^{10} T^{24} - 10157 p^{11} T^{25} + 681 p^{12} T^{26} - 22 p^{13} T^{27} + p^{14} T^{28} \)
71 \( 1 - 13 T + 466 T^{2} - 4633 T^{3} + 99121 T^{4} - 892267 T^{5} + 14927077 T^{6} - 133506138 T^{7} + 1828465207 T^{8} - 15985056605 T^{9} + 184637787060 T^{10} - 1563978150040 T^{11} + 16068717568391 T^{12} - 130982142754738 T^{13} + 1226932266157194 T^{14} - 130982142754738 p T^{15} + 16068717568391 p^{2} T^{16} - 1563978150040 p^{3} T^{17} + 184637787060 p^{4} T^{18} - 15985056605 p^{5} T^{19} + 1828465207 p^{6} T^{20} - 133506138 p^{7} T^{21} + 14927077 p^{8} T^{22} - 892267 p^{9} T^{23} + 99121 p^{10} T^{24} - 4633 p^{11} T^{25} + 466 p^{12} T^{26} - 13 p^{13} T^{27} + p^{14} T^{28} \)
73 \( 1 - 20 T + 815 T^{2} - 13122 T^{3} + 300368 T^{4} - 3986354 T^{5} + 66684005 T^{6} - 744919067 T^{7} + 10089838918 T^{8} - 96900011919 T^{9} + 1130454581090 T^{10} - 9593322829902 T^{11} + 101395062590991 T^{12} - 788574260711128 T^{13} + 7838904257943112 T^{14} - 788574260711128 p T^{15} + 101395062590991 p^{2} T^{16} - 9593322829902 p^{3} T^{17} + 1130454581090 p^{4} T^{18} - 96900011919 p^{5} T^{19} + 10089838918 p^{6} T^{20} - 744919067 p^{7} T^{21} + 66684005 p^{8} T^{22} - 3986354 p^{9} T^{23} + 300368 p^{10} T^{24} - 13122 p^{11} T^{25} + 815 p^{12} T^{26} - 20 p^{13} T^{27} + p^{14} T^{28} \)
79 \( 1 - 31 T + 1023 T^{2} - 21323 T^{3} + 433671 T^{4} - 7070910 T^{5} + 110900735 T^{6} - 1512216248 T^{7} + 19835673362 T^{8} - 234800713163 T^{9} + 2683673218946 T^{10} - 28224264814010 T^{11} + 3642310673466 p T^{12} - 2726029592624301 T^{13} + 25095925876714032 T^{14} - 2726029592624301 p T^{15} + 3642310673466 p^{3} T^{16} - 28224264814010 p^{3} T^{17} + 2683673218946 p^{4} T^{18} - 234800713163 p^{5} T^{19} + 19835673362 p^{6} T^{20} - 1512216248 p^{7} T^{21} + 110900735 p^{8} T^{22} - 7070910 p^{9} T^{23} + 433671 p^{10} T^{24} - 21323 p^{11} T^{25} + 1023 p^{12} T^{26} - 31 p^{13} T^{27} + p^{14} T^{28} \)
83 \( 1 + 32 T + 1197 T^{2} + 27366 T^{3} + 616486 T^{4} + 11110672 T^{5} + 190171157 T^{6} + 2848502518 T^{7} + 40231880855 T^{8} + 516914651030 T^{9} + 6266878895874 T^{10} + 70420077805961 T^{11} + 9015283209310 p T^{12} + 89575113078661 p T^{13} + 69953545105194072 T^{14} + 89575113078661 p^{2} T^{15} + 9015283209310 p^{3} T^{16} + 70420077805961 p^{3} T^{17} + 6266878895874 p^{4} T^{18} + 516914651030 p^{5} T^{19} + 40231880855 p^{6} T^{20} + 2848502518 p^{7} T^{21} + 190171157 p^{8} T^{22} + 11110672 p^{9} T^{23} + 616486 p^{10} T^{24} + 27366 p^{11} T^{25} + 1197 p^{12} T^{26} + 32 p^{13} T^{27} + p^{14} T^{28} \)
89 \( 1 - 21 T + 607 T^{2} - 8920 T^{3} + 171262 T^{4} - 23615 p T^{5} + 32830164 T^{6} - 352108686 T^{7} + 4829265654 T^{8} - 46726972789 T^{9} + 586211633725 T^{10} - 5219427228739 T^{11} + 61415310081737 T^{12} - 512935261401252 T^{13} + 5745185914786624 T^{14} - 512935261401252 p T^{15} + 61415310081737 p^{2} T^{16} - 5219427228739 p^{3} T^{17} + 586211633725 p^{4} T^{18} - 46726972789 p^{5} T^{19} + 4829265654 p^{6} T^{20} - 352108686 p^{7} T^{21} + 32830164 p^{8} T^{22} - 23615 p^{10} T^{23} + 171262 p^{10} T^{24} - 8920 p^{11} T^{25} + 607 p^{12} T^{26} - 21 p^{13} T^{27} + p^{14} T^{28} \)
97 \( 1 - 37 T + 1265 T^{2} - 30962 T^{3} + 679791 T^{4} - 12841719 T^{5} + 221642161 T^{6} - 3474922608 T^{7} + 50579995695 T^{8} - 684170650429 T^{9} + 8690333561707 T^{10} - 103729058988553 T^{11} + 1171015994366347 T^{12} - 12490999256601712 T^{13} + 126454166386797242 T^{14} - 12490999256601712 p T^{15} + 1171015994366347 p^{2} T^{16} - 103729058988553 p^{3} T^{17} + 8690333561707 p^{4} T^{18} - 684170650429 p^{5} T^{19} + 50579995695 p^{6} T^{20} - 3474922608 p^{7} T^{21} + 221642161 p^{8} T^{22} - 12841719 p^{9} T^{23} + 679791 p^{10} T^{24} - 30962 p^{11} T^{25} + 1265 p^{12} T^{26} - 37 p^{13} T^{27} + p^{14} T^{28} \)
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\[\begin{aligned} L(s) = \prod_p \ \prod_{j=1}^{28} (1 - \alpha_{j,p}\, p^{-s})^{-1} \end{aligned}\]

Imaginary part of the first few zeros on the critical line

−2.02581154554017747141564947613, −1.99008670884630616827382981468, −1.90365766311106273815355062741, −1.81510747478904852956750515620, −1.65322550260515605774620357453, −1.59056212457827549864428479331, −1.57545068657445943036227458046, −1.57024127347974521585597910517, −1.56156717444436071913658005399, −1.49517454072277944232370809450, −1.45344622938096362104872830700, −1.37191044461190353140393294081, −1.15978805539640306195740486671, −1.11791820589654811379857328239, −1.04218039491255058316551189340, −0.849488502495908868069502440206, −0.78339505709521181828766037710, −0.76646874793059205121306802660, −0.72938973837820853887462298201, −0.67828378037022359312773144964, −0.53416547355162579861083366993, −0.48811443910286370109187285428, −0.45410945173783718289007838765, −0.39700894289407426371349317147, −0.37441049610034581639960265431, 0.37441049610034581639960265431, 0.39700894289407426371349317147, 0.45410945173783718289007838765, 0.48811443910286370109187285428, 0.53416547355162579861083366993, 0.67828378037022359312773144964, 0.72938973837820853887462298201, 0.76646874793059205121306802660, 0.78339505709521181828766037710, 0.849488502495908868069502440206, 1.04218039491255058316551189340, 1.11791820589654811379857328239, 1.15978805539640306195740486671, 1.37191044461190353140393294081, 1.45344622938096362104872830700, 1.49517454072277944232370809450, 1.56156717444436071913658005399, 1.57024127347974521585597910517, 1.57545068657445943036227458046, 1.59056212457827549864428479331, 1.65322550260515605774620357453, 1.81510747478904852956750515620, 1.90365766311106273815355062741, 1.99008670884630616827382981468, 2.02581154554017747141564947613

Graph of the $Z$-function along the critical line

Plot not available for L-functions of degree greater than 10.