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Properties

Label 16-1250e8-1.1-c3e8-0-0
Degree 1616
Conductor 5.960×10245.960\times 10^{24}
Sign 11
Analytic cond. 8.75404×10148.75404\times 10^{14}
Root an. cond. 8.587928.58792
Motivic weight 33
Arithmetic yes
Rational yes
Primitive no
Self-dual yes
Analytic rank 00

Origins

Origins of factors

Downloads

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Normalization:  

Dirichlet series

L(s)  = 1  − 16·2-s + 4·3-s + 144·4-s − 64·6-s + 27·7-s − 960·8-s − 62·9-s − 39·11-s + 576·12-s + 179·13-s − 432·14-s + 5.28e3·16-s + 247·17-s + 992·18-s − 25·19-s + 108·21-s + 624·22-s + 179·23-s − 3.84e3·24-s − 2.86e3·26-s − 102·27-s + 3.88e3·28-s − 565·29-s − 89·31-s − 2.53e4·32-s − 156·33-s − 3.95e3·34-s + ⋯
L(s)  = 1  − 5.65·2-s + 0.769·3-s + 18·4-s − 4.35·6-s + 1.45·7-s − 42.4·8-s − 2.29·9-s − 1.06·11-s + 13.8·12-s + 3.81·13-s − 8.24·14-s + 82.5·16-s + 3.52·17-s + 12.9·18-s − 0.301·19-s + 1.12·21-s + 6.04·22-s + 1.62·23-s − 32.6·24-s − 21.6·26-s − 0.727·27-s + 26.2·28-s − 3.61·29-s − 0.515·31-s − 140.·32-s − 0.822·33-s − 19.9·34-s + ⋯

Functional equation

Λ(s)=((28⋅532)s/2 ΓC(s)8 L(s)=( Λ(4−s)\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{8} \cdot 5^{32}\right)^{s/2} \, \Gamma_{\C}(s)^{8} \, L(s)\cr=\mathstrut & \,\Lambda(4-s)\end{aligned}
Λ(s)=((28⋅532)s/2 ΓC(s+3/2)8 L(s)=( Λ(1−s)\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{8} \cdot 5^{32}\right)^{s/2} \, \Gamma_{\C}(s+3/2)^{8} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}

Invariants

Degree: 1616
Conductor: 28⋅5322^{8} \cdot 5^{32}
Sign: 11
Analytic conductor: 8.75404×10148.75404\times 10^{14}
Root analytic conductor: 8.587928.58792
Motivic weight: 33
Rational: yes
Arithmetic: yes
Character: Trivial
Primitive: no
Self-dual: yes
Analytic rank: 00
Selberg data: (16, 28⋅532, ( :[3/2]8), 1)(16,\ 2^{8} \cdot 5^{32} ,\ ( \ : [3/2]^{8} ),\ 1 )

Particular Values

L(2)L(2) ≈\approx 1.3377260041.337726004
L(12)L(\frac12) ≈\approx 1.3377260041.337726004
L(52)L(\frac{5}{2}) not available
L(1)L(1) not available

Euler product

   L(s)=∏pFp(p−s)−1L(s) = \displaystyle \prod_{p} F_p(p^{-s})^{-1}
ppFp(T)F_p(T)
bad2 (1+pT)8 ( 1 + p T )^{8}
5 1 1
good3 1−4T+26pT2−458T3+3736T4−21284T5+47725pT6−689974T7+4284844T8−689974p3T9+47725p7T10−21284p9T11+3736p12T12−458p15T13+26p19T14−4p21T15+p24T16 1 - 4 T + 26 p T^{2} - 458 T^{3} + 3736 T^{4} - 21284 T^{5} + 47725 p T^{6} - 689974 T^{7} + 4284844 T^{8} - 689974 p^{3} T^{9} + 47725 p^{7} T^{10} - 21284 p^{9} T^{11} + 3736 p^{12} T^{12} - 458 p^{15} T^{13} + 26 p^{19} T^{14} - 4 p^{21} T^{15} + p^{24} T^{16}
7 1−27T+1312T2−21346T3+754721T4−1255896pT5+303427660T6−2702813353T7+104452113604T8−2702813353p3T9+303427660p6T10−1255896p10T11+754721p12T12−21346p15T13+1312p18T14−27p21T15+p24T16 1 - 27 T + 1312 T^{2} - 21346 T^{3} + 754721 T^{4} - 1255896 p T^{5} + 303427660 T^{6} - 2702813353 T^{7} + 104452113604 T^{8} - 2702813353 p^{3} T^{9} + 303427660 p^{6} T^{10} - 1255896 p^{10} T^{11} + 754721 p^{12} T^{12} - 21346 p^{15} T^{13} + 1312 p^{18} T^{14} - 27 p^{21} T^{15} + p^{24} T^{16}
11 1+39T+3350T2+111410T3+774335pT4+295217122T5+17381158818T6+489155464115T7+23841275119380T8+489155464115p3T9+17381158818p6T10+295217122p9T11+774335p13T12+111410p15T13+3350p18T14+39p21T15+p24T16 1 + 39 T + 3350 T^{2} + 111410 T^{3} + 774335 p T^{4} + 295217122 T^{5} + 17381158818 T^{6} + 489155464115 T^{7} + 23841275119380 T^{8} + 489155464115 p^{3} T^{9} + 17381158818 p^{6} T^{10} + 295217122 p^{9} T^{11} + 774335 p^{13} T^{12} + 111410 p^{15} T^{13} + 3350 p^{18} T^{14} + 39 p^{21} T^{15} + p^{24} T^{16}
13 1−179T+18963T2−1425043T3+83285016T4−3916072579T5+156156827690T6−5745676940154T7+237221890478099T8−5745676940154p3T9+156156827690p6T10−3916072579p9T11+83285016p12T12−1425043p15T13+18963p18T14−179p21T15+p24T16 1 - 179 T + 18963 T^{2} - 1425043 T^{3} + 83285016 T^{4} - 3916072579 T^{5} + 156156827690 T^{6} - 5745676940154 T^{7} + 237221890478099 T^{8} - 5745676940154 p^{3} T^{9} + 156156827690 p^{6} T^{10} - 3916072579 p^{9} T^{11} + 83285016 p^{12} T^{12} - 1425043 p^{15} T^{13} + 18963 p^{18} T^{14} - 179 p^{21} T^{15} + p^{24} T^{16}
17 1−247T+43092T2−5416366T3+35109328pT4−56707178117T5+5053326009255T6−403779423876048T7+29993946177008184T8−403779423876048p3T9+5053326009255p6T10−56707178117p9T11+35109328p13T12−5416366p15T13+43092p18T14−247p21T15+p24T16 1 - 247 T + 43092 T^{2} - 5416366 T^{3} + 35109328 p T^{4} - 56707178117 T^{5} + 5053326009255 T^{6} - 403779423876048 T^{7} + 29993946177008184 T^{8} - 403779423876048 p^{3} T^{9} + 5053326009255 p^{6} T^{10} - 56707178117 p^{9} T^{11} + 35109328 p^{13} T^{12} - 5416366 p^{15} T^{13} + 43092 p^{18} T^{14} - 247 p^{21} T^{15} + p^{24} T^{16}
19 1+25T+29022T2+1048310T3+24456062pT4+16885403025T5+5078356152059T6+173645627039000T7+40137236328736080T8+173645627039000p3T9+5078356152059p6T10+16885403025p9T11+24456062p13T12+1048310p15T13+29022p18T14+25p21T15+p24T16 1 + 25 T + 29022 T^{2} + 1048310 T^{3} + 24456062 p T^{4} + 16885403025 T^{5} + 5078356152059 T^{6} + 173645627039000 T^{7} + 40137236328736080 T^{8} + 173645627039000 p^{3} T^{9} + 5078356152059 p^{6} T^{10} + 16885403025 p^{9} T^{11} + 24456062 p^{13} T^{12} + 1048310 p^{15} T^{13} + 29022 p^{18} T^{14} + 25 p^{21} T^{15} + p^{24} T^{16}
23 1−179T+39323T2−4116143T3+845669571T4−109920609624T5+17395875133180T6−1630691152015284T7+205047824474561674T8−1630691152015284p3T9+17395875133180p6T10−109920609624p9T11+845669571p12T12−4116143p15T13+39323p18T14−179p21T15+p24T16 1 - 179 T + 39323 T^{2} - 4116143 T^{3} + 845669571 T^{4} - 109920609624 T^{5} + 17395875133180 T^{6} - 1630691152015284 T^{7} + 205047824474561674 T^{8} - 1630691152015284 p^{3} T^{9} + 17395875133180 p^{6} T^{10} - 109920609624 p^{9} T^{11} + 845669571 p^{12} T^{12} - 4116143 p^{15} T^{13} + 39323 p^{18} T^{14} - 179 p^{21} T^{15} + p^{24} T^{16}
29 1+565T+265917T2+82588765T3+22616657268T4+4944757781865T5+998019534529924T6+173320809150848750T7+28784408280803237505T8+173320809150848750p3T9+998019534529924p6T10+4944757781865p9T11+22616657268p12T12+82588765p15T13+265917p18T14+565p21T15+p24T16 1 + 565 T + 265917 T^{2} + 82588765 T^{3} + 22616657268 T^{4} + 4944757781865 T^{5} + 998019534529924 T^{6} + 173320809150848750 T^{7} + 28784408280803237505 T^{8} + 173320809150848750 p^{3} T^{9} + 998019534529924 p^{6} T^{10} + 4944757781865 p^{9} T^{11} + 22616657268 p^{12} T^{12} + 82588765 p^{15} T^{13} + 265917 p^{18} T^{14} + 565 p^{21} T^{15} + p^{24} T^{16}
31 1+89T+204085T2+522785pT3+19028053945T4+1325266015752T5+1059716594028998T6+62973270985320070T7+38581577327933099030T8+62973270985320070p3T9+1059716594028998p6T10+1325266015752p9T11+19028053945p12T12+522785p16T13+204085p18T14+89p21T15+p24T16 1 + 89 T + 204085 T^{2} + 522785 p T^{3} + 19028053945 T^{4} + 1325266015752 T^{5} + 1059716594028998 T^{6} + 62973270985320070 T^{7} + 38581577327933099030 T^{8} + 62973270985320070 p^{3} T^{9} + 1059716594028998 p^{6} T^{10} + 1325266015752 p^{9} T^{11} + 19028053945 p^{12} T^{12} + 522785 p^{16} T^{13} + 204085 p^{18} T^{14} + 89 p^{21} T^{15} + p^{24} T^{16}
37 1−287T+263247T2−41739741T3+25397450946T4−1211311720107T5+1241716482853020T6+90589591335584382T7+50710454906087085309T8+90589591335584382p3T9+1241716482853020p6T10−1211311720107p9T11+25397450946p12T12−41739741p15T13+263247p18T14−287p21T15+p24T16 1 - 287 T + 263247 T^{2} - 41739741 T^{3} + 25397450946 T^{4} - 1211311720107 T^{5} + 1241716482853020 T^{6} + 90589591335584382 T^{7} + 50710454906087085309 T^{8} + 90589591335584382 p^{3} T^{9} + 1241716482853020 p^{6} T^{10} - 1211311720107 p^{9} T^{11} + 25397450946 p^{12} T^{12} - 41739741 p^{15} T^{13} + 263247 p^{18} T^{14} - 287 p^{21} T^{15} + p^{24} T^{16}
41 1+394T+520380T2+175897160T3+120118591240T4+34514935457472T5+16109872456033553T6+3861648373034550680T7+ 1 + 394 T + 520380 T^{2} + 175897160 T^{3} + 120118591240 T^{4} + 34514935457472 T^{5} + 16109872456033553 T^{6} + 3861648373034550680 T^{7} + 13 ⁣⋯ ⁣8013\!\cdots\!80T8+3861648373034550680p3T9+16109872456033553p6T10+34514935457472p9T11+120118591240p12T12+175897160p15T13+520380p18T14+394p21T15+p24T16 T^{8} + 3861648373034550680 p^{3} T^{9} + 16109872456033553 p^{6} T^{10} + 34514935457472 p^{9} T^{11} + 120118591240 p^{12} T^{12} + 175897160 p^{15} T^{13} + 520380 p^{18} T^{14} + 394 p^{21} T^{15} + p^{24} T^{16}
43 1−529T+414328T2−139331268T3+64713221751T4−16515039487214T5+6454461910629660T6−1478695245459034599T7+ 1 - 529 T + 414328 T^{2} - 139331268 T^{3} + 64713221751 T^{4} - 16515039487214 T^{5} + 6454461910629660 T^{6} - 1478695245459034599 T^{7} + 54 ⁣⋯ ⁣2454\!\cdots\!24T8−1478695245459034599p3T9+6454461910629660p6T10−16515039487214p9T11+64713221751p12T12−139331268p15T13+414328p18T14−529p21T15+p24T16 T^{8} - 1478695245459034599 p^{3} T^{9} + 6454461910629660 p^{6} T^{10} - 16515039487214 p^{9} T^{11} + 64713221751 p^{12} T^{12} - 139331268 p^{15} T^{13} + 414328 p^{18} T^{14} - 529 p^{21} T^{15} + p^{24} T^{16}
47 1+758T+784692T2+439041634T3+271966134346T4+2521337641614pT5+54533132602498955T6+19158219614764220602T7+ 1 + 758 T + 784692 T^{2} + 439041634 T^{3} + 271966134346 T^{4} + 2521337641614 p T^{5} + 54533132602498955 T^{6} + 19158219614764220602 T^{7} + 69 ⁣⋯ ⁣8469\!\cdots\!84T8+19158219614764220602p3T9+54533132602498955p6T10+2521337641614p10T11+271966134346p12T12+439041634p15T13+784692p18T14+758p21T15+p24T16 T^{8} + 19158219614764220602 p^{3} T^{9} + 54533132602498955 p^{6} T^{10} + 2521337641614 p^{10} T^{11} + 271966134346 p^{12} T^{12} + 439041634 p^{15} T^{13} + 784692 p^{18} T^{14} + 758 p^{21} T^{15} + p^{24} T^{16}
53 1+56T+861328T2+20068102T3+354725727136T4+1894129166506T5+91932536311490645T6−103035379136580124T7+ 1 + 56 T + 861328 T^{2} + 20068102 T^{3} + 354725727136 T^{4} + 1894129166506 T^{5} + 91932536311490645 T^{6} - 103035379136580124 T^{7} + 16 ⁣⋯ ⁣6416\!\cdots\!64T8−103035379136580124p3T9+91932536311490645p6T10+1894129166506p9T11+354725727136p12T12+20068102p15T13+861328p18T14+56p21T15+p24T16 T^{8} - 103035379136580124 p^{3} T^{9} + 91932536311490645 p^{6} T^{10} + 1894129166506 p^{9} T^{11} + 354725727136 p^{12} T^{12} + 20068102 p^{15} T^{13} + 861328 p^{18} T^{14} + 56 p^{21} T^{15} + p^{24} T^{16}
59 1+1220T+2036087T2+1793989770T3+1664695350853T4+1121489731769670T5+733224544342936169T6+ 1 + 1220 T + 2036087 T^{2} + 1793989770 T^{3} + 1664695350853 T^{4} + 1121489731769670 T^{5} + 733224544342936169 T^{6} + 38 ⁣⋯ ⁣0038\!\cdots\!00T7+ T^{7} + 19 ⁣⋯ ⁣8019\!\cdots\!80T8+ T^{8} + 38 ⁣⋯ ⁣0038\!\cdots\!00p3T9+733224544342936169p6T10+1121489731769670p9T11+1664695350853p12T12+1793989770p15T13+2036087p18T14+1220p21T15+p24T16 p^{3} T^{9} + 733224544342936169 p^{6} T^{10} + 1121489731769670 p^{9} T^{11} + 1664695350853 p^{12} T^{12} + 1793989770 p^{15} T^{13} + 2036087 p^{18} T^{14} + 1220 p^{21} T^{15} + p^{24} T^{16}
61 1+489T+1575055T2+621459855T3+1111083730090T4+361578972829797T5+467005356774259768T6+ 1 + 489 T + 1575055 T^{2} + 621459855 T^{3} + 1111083730090 T^{4} + 361578972829797 T^{5} + 467005356774259768 T^{6} + 12 ⁣⋯ ⁣3012\!\cdots\!30T7+ T^{7} + 12 ⁣⋯ ⁣6512\!\cdots\!65T8+ T^{8} + 12 ⁣⋯ ⁣3012\!\cdots\!30p3T9+467005356774259768p6T10+361578972829797p9T11+1111083730090p12T12+621459855p15T13+1575055p18T14+489p21T15+p24T16 p^{3} T^{9} + 467005356774259768 p^{6} T^{10} + 361578972829797 p^{9} T^{11} + 1111083730090 p^{12} T^{12} + 621459855 p^{15} T^{13} + 1575055 p^{18} T^{14} + 489 p^{21} T^{15} + p^{24} T^{16}
67 1−2547T+4137912T2−4723504026T3+4326889325011T4−3285937502563142T5+2194176556517022280T6− 1 - 2547 T + 4137912 T^{2} - 4723504026 T^{3} + 4326889325011 T^{4} - 3285937502563142 T^{5} + 2194176556517022280 T^{6} - 13 ⁣⋯ ⁣0313\!\cdots\!03T7+ T^{7} + 74 ⁣⋯ ⁣2474\!\cdots\!24T8− T^{8} - 13 ⁣⋯ ⁣0313\!\cdots\!03p3T9+2194176556517022280p6T10−3285937502563142p9T11+4326889325011p12T12−4723504026p15T13+4137912p18T14−2547p21T15+p24T16 p^{3} T^{9} + 2194176556517022280 p^{6} T^{10} - 3285937502563142 p^{9} T^{11} + 4326889325011 p^{12} T^{12} - 4723504026 p^{15} T^{13} + 4137912 p^{18} T^{14} - 2547 p^{21} T^{15} + p^{24} T^{16}
71 1−1576T+2062240T2−1802050730T3+1564601142700T4−1075368517244678T5+753772981185501113T6− 1 - 1576 T + 2062240 T^{2} - 1802050730 T^{3} + 1564601142700 T^{4} - 1075368517244678 T^{5} + 753772981185501113 T^{6} - 44 ⁣⋯ ⁣4044\!\cdots\!40T7+56118484608830905460p2T8− T^{7} + 56118484608830905460 p^{2} T^{8} - 44 ⁣⋯ ⁣4044\!\cdots\!40p3T9+753772981185501113p6T10−1075368517244678p9T11+1564601142700p12T12−1802050730p15T13+2062240p18T14−1576p21T15+p24T16 p^{3} T^{9} + 753772981185501113 p^{6} T^{10} - 1075368517244678 p^{9} T^{11} + 1564601142700 p^{12} T^{12} - 1802050730 p^{15} T^{13} + 2062240 p^{18} T^{14} - 1576 p^{21} T^{15} + p^{24} T^{16}
73 1+166T+1843928T2−4132708T3+1618846353956T4−128675140372744T5+995478281705972145T6−75680988855895892424T7+ 1 + 166 T + 1843928 T^{2} - 4132708 T^{3} + 1618846353956 T^{4} - 128675140372744 T^{5} + 995478281705972145 T^{6} - 75680988855895892424 T^{7} + 45 ⁣⋯ ⁣4445\!\cdots\!44T8−75680988855895892424p3T9+995478281705972145p6T10−128675140372744p9T11+1618846353956p12T12−4132708p15T13+1843928p18T14+166p21T15+p24T16 T^{8} - 75680988855895892424 p^{3} T^{9} + 995478281705972145 p^{6} T^{10} - 128675140372744 p^{9} T^{11} + 1618846353956 p^{12} T^{12} - 4132708 p^{15} T^{13} + 1843928 p^{18} T^{14} + 166 p^{21} T^{15} + p^{24} T^{16}
79 1+1540T+3069157T2+3430256170T3+54859141207pT4+3921664767097740T5+3798209682014350499T6+ 1 + 1540 T + 3069157 T^{2} + 3430256170 T^{3} + 54859141207 p T^{4} + 3921664767097740 T^{5} + 3798209682014350499 T^{6} + 28 ⁣⋯ ⁣5028\!\cdots\!50T7+ T^{7} + 22 ⁣⋯ ⁣8022\!\cdots\!80T8+ T^{8} + 28 ⁣⋯ ⁣5028\!\cdots\!50p3T9+3798209682014350499p6T10+3921664767097740p9T11+54859141207p13T12+3430256170p15T13+3069157p18T14+1540p21T15+p24T16 p^{3} T^{9} + 3798209682014350499 p^{6} T^{10} + 3921664767097740 p^{9} T^{11} + 54859141207 p^{13} T^{12} + 3430256170 p^{15} T^{13} + 3069157 p^{18} T^{14} + 1540 p^{21} T^{15} + p^{24} T^{16}
83 1−929T+3192013T2−2114311123T3+4453876755901T4−2243553413996524T5+3873090378397321250T6− 1 - 929 T + 3192013 T^{2} - 2114311123 T^{3} + 4453876755901 T^{4} - 2243553413996524 T^{5} + 3873090378397321250 T^{6} - 15 ⁣⋯ ⁣5415\!\cdots\!54T7+ T^{7} + 24 ⁣⋯ ⁣5424\!\cdots\!54T8− T^{8} - 15 ⁣⋯ ⁣5415\!\cdots\!54p3T9+3873090378397321250p6T10−2243553413996524p9T11+4453876755901p12T12−2114311123p15T13+3192013p18T14−929p21T15+p24T16 p^{3} T^{9} + 3873090378397321250 p^{6} T^{10} - 2243553413996524 p^{9} T^{11} + 4453876755901 p^{12} T^{12} - 2114311123 p^{15} T^{13} + 3192013 p^{18} T^{14} - 929 p^{21} T^{15} + p^{24} T^{16}
89 1+1150T+3775147T2+2886348600T3+6042067745463T4+3499900267843900T5+6365375889650535029T6+ 1 + 1150 T + 3775147 T^{2} + 2886348600 T^{3} + 6042067745463 T^{4} + 3499900267843900 T^{5} + 6365375889650535029 T^{6} + 31 ⁣⋯ ⁣5031\!\cdots\!50T7+ T^{7} + 51 ⁣⋯ ⁣2051\!\cdots\!20T8+ T^{8} + 31 ⁣⋯ ⁣5031\!\cdots\!50p3T9+6365375889650535029p6T10+3499900267843900p9T11+6042067745463p12T12+2886348600p15T13+3775147p18T14+1150p21T15+p24T16 p^{3} T^{9} + 6365375889650535029 p^{6} T^{10} + 3499900267843900 p^{9} T^{11} + 6042067745463 p^{12} T^{12} + 2886348600 p^{15} T^{13} + 3775147 p^{18} T^{14} + 1150 p^{21} T^{15} + p^{24} T^{16}
97 1−632T+4051692T2−1487361826T3+7677909587811T4−1053131834623492T5+9327233457339635510T6+ 1 - 632 T + 4051692 T^{2} - 1487361826 T^{3} + 7677909587811 T^{4} - 1053131834623492 T^{5} + 9327233457339635510 T^{6} + 22 ⁣⋯ ⁣5222\!\cdots\!52T7+ T^{7} + 90 ⁣⋯ ⁣3990\!\cdots\!39T8+ T^{8} + 22 ⁣⋯ ⁣5222\!\cdots\!52p3T9+9327233457339635510p6T10−1053131834623492p9T11+7677909587811p12T12−1487361826p15T13+4051692p18T14−632p21T15+p24T16 p^{3} T^{9} + 9327233457339635510 p^{6} T^{10} - 1053131834623492 p^{9} T^{11} + 7677909587811 p^{12} T^{12} - 1487361826 p^{15} T^{13} + 4051692 p^{18} T^{14} - 632 p^{21} T^{15} + p^{24} T^{16}
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   L(s)=∏p ∏j=116(1−αj,p p−s)−1L(s) = \displaystyle\prod_p \ \prod_{j=1}^{16} (1 - \alpha_{j,p}\, p^{-s})^{-1}

Imaginary part of the first few zeros on the critical line

−3.66144241289903067333037111553, −3.30163130689450921631176645128, −3.17331508518770915275983494402, −3.05697198066675454806759565248, −2.96507106992486802284538267408, −2.94169301659605556175930482926, −2.89505184765455542519566561686, −2.86381884765811122199979320967, −2.67314695962071250172624552724, −2.23555965677225500777846211872, −2.23051924417237627269898298389, −1.91104870107562838974905869903, −1.74736175494083124537429285420, −1.71294857450523396937078706039, −1.69941050166545581097406100181, −1.56735006731892549212051452426, −1.47519469060589493827059673935, −1.21844710552070063501257751982, −1.20702059904232830410970580587, −0.67574071779948984728446194366, −0.63890998982087346687774393905, −0.62538239499700763597809751549, −0.60638455703089458103342337627, −0.45541027852408461052568422885, −0.14532312328804863226173401609, 0.14532312328804863226173401609, 0.45541027852408461052568422885, 0.60638455703089458103342337627, 0.62538239499700763597809751549, 0.63890998982087346687774393905, 0.67574071779948984728446194366, 1.20702059904232830410970580587, 1.21844710552070063501257751982, 1.47519469060589493827059673935, 1.56735006731892549212051452426, 1.69941050166545581097406100181, 1.71294857450523396937078706039, 1.74736175494083124537429285420, 1.91104870107562838974905869903, 2.23051924417237627269898298389, 2.23555965677225500777846211872, 2.67314695962071250172624552724, 2.86381884765811122199979320967, 2.89505184765455542519566561686, 2.94169301659605556175930482926, 2.96507106992486802284538267408, 3.05697198066675454806759565248, 3.17331508518770915275983494402, 3.30163130689450921631176645128, 3.66144241289903067333037111553

Graph of the ZZ-function along the critical line

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