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Properties

Label 32-630e16-1.1-c1e16-0-9
Degree 3232
Conductor 6.158×10446.158\times 10^{44}
Sign 11
Analytic cond. 1.68221×10111.68221\times 10^{11}
Root an. cond. 2.242892.24289
Motivic weight 11
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  + 12·5-s + 8·7-s + 12·11-s + 2·16-s + 36·17-s + 4·23-s + 78·25-s + 24·31-s + 96·35-s + 4·37-s − 8·43-s − 12·47-s + 32·49-s + 28·53-s + 144·55-s − 12·61-s + 32·67-s − 16·71-s − 12·73-s + 96·77-s + 24·80-s + 432·85-s − 60·101-s + 24·103-s − 20·107-s + 16·112-s + 8·113-s + ⋯
L(s)  = 1  + 5.36·5-s + 3.02·7-s + 3.61·11-s + 1/2·16-s + 8.73·17-s + 0.834·23-s + 78/5·25-s + 4.31·31-s + 16.2·35-s + 0.657·37-s − 1.21·43-s − 1.75·47-s + 32/7·49-s + 3.84·53-s + 19.4·55-s − 1.53·61-s + 3.90·67-s − 1.89·71-s − 1.40·73-s + 10.9·77-s + 2.68·80-s + 46.8·85-s − 5.97·101-s + 2.36·103-s − 1.93·107-s + 1.51·112-s + 0.752·113-s + ⋯

Functional equation

Λ(s)=((216⋅332⋅516⋅716)s/2 ΓC(s)16 L(s)=( Λ(2−s)\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{16} \cdot 3^{32} \cdot 5^{16} \cdot 7^{16}\right)^{s/2} \, \Gamma_{\C}(s)^{16} \, L(s)\cr=\mathstrut & \,\Lambda(2-s)\end{aligned}
Λ(s)=((216⋅332⋅516⋅716)s/2 ΓC(s+1/2)16 L(s)=( Λ(1−s)\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{16} \cdot 3^{32} \cdot 5^{16} \cdot 7^{16}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{16} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}

Invariants

Degree: 3232
Conductor: 216⋅332⋅516⋅7162^{16} \cdot 3^{32} \cdot 5^{16} \cdot 7^{16}
Sign: 11
Analytic conductor: 1.68221×10111.68221\times 10^{11}
Root analytic conductor: 2.242892.24289
Motivic weight: 11
Rational: yes
Arithmetic: yes
Character: Trivial
Primitive: no
Self-dual: yes
Analytic rank: 00
Selberg data: (32, 216⋅332⋅516⋅716, ( :[1/2]16), 1)(32,\ 2^{16} \cdot 3^{32} \cdot 5^{16} \cdot 7^{16} ,\ ( \ : [1/2]^{16} ),\ 1 )

Particular Values

L(1)L(1) ≈\approx 1105.1132891105.113289
L(12)L(\frac12) ≈\approx 1105.1132891105.113289
L(32)L(\frac{3}{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−T4+T8)2 ( 1 - T^{4} + T^{8} )^{2}
3 1 1
5 1−12T+66T2−216T3+18p2T4−468T5−864T6+6252T7−18241T8+6252pT9−864p2T10−468p3T11+18p6T12−216p5T13+66p6T14−12p7T15+p8T16 1 - 12 T + 66 T^{2} - 216 T^{3} + 18 p^{2} T^{4} - 468 T^{5} - 864 T^{6} + 6252 T^{7} - 18241 T^{8} + 6252 p T^{9} - 864 p^{2} T^{10} - 468 p^{3} T^{11} + 18 p^{6} T^{12} - 216 p^{5} T^{13} + 66 p^{6} T^{14} - 12 p^{7} T^{15} + p^{8} T^{16}
7 1−8T+32T2−80T3+73T4+160T5−416T6−696T7+4944T8−696pT9−416p2T10+160p3T11+73p4T12−80p5T13+32p6T14−8p7T15+p8T16 1 - 8 T + 32 T^{2} - 80 T^{3} + 73 T^{4} + 160 T^{5} - 416 T^{6} - 696 T^{7} + 4944 T^{8} - 696 p T^{9} - 416 p^{2} T^{10} + 160 p^{3} T^{11} + 73 p^{4} T^{12} - 80 p^{5} T^{13} + 32 p^{6} T^{14} - 8 p^{7} T^{15} + p^{8} T^{16}
good11 (1−6T+5T2+18T3−29T4+252T5−544T6+516T7−6650T8+516pT9−544p2T10+252p3T11−29p4T12+18p5T13+5p6T14−6p7T15+p8T16)2 ( 1 - 6 T + 5 T^{2} + 18 T^{3} - 29 T^{4} + 252 T^{5} - 544 T^{6} + 516 T^{7} - 6650 T^{8} + 516 p T^{9} - 544 p^{2} T^{10} + 252 p^{3} T^{11} - 29 p^{4} T^{12} + 18 p^{5} T^{13} + 5 p^{6} T^{14} - 6 p^{7} T^{15} + p^{8} T^{16} )^{2}
13 1+714T4+266977T8+68653746T12+13237862628T16+68653746p4T20+266977p8T24+714p12T28+p16T32 1 + 714 T^{4} + 266977 T^{8} + 68653746 T^{12} + 13237862628 T^{16} + 68653746 p^{4} T^{20} + 266977 p^{8} T^{24} + 714 p^{12} T^{28} + p^{16} T^{32}
17 1−36T+648T2−7776T3+70080T4−507420T5+3088368T6−16357284T7+77768530T8−343436904T9+1468660248T10−6351048828T11+28493424864T12−131692528476T13+608521516920T14−2723900163624T15+11569567164915T16−2723900163624pT17+608521516920p2T18−131692528476p3T19+28493424864p4T20−6351048828p5T21+1468660248p6T22−343436904p7T23+77768530p8T24−16357284p9T25+3088368p10T26−507420p11T27+70080p12T28−7776p13T29+648p14T30−36p15T31+p16T32 1 - 36 T + 648 T^{2} - 7776 T^{3} + 70080 T^{4} - 507420 T^{5} + 3088368 T^{6} - 16357284 T^{7} + 77768530 T^{8} - 343436904 T^{9} + 1468660248 T^{10} - 6351048828 T^{11} + 28493424864 T^{12} - 131692528476 T^{13} + 608521516920 T^{14} - 2723900163624 T^{15} + 11569567164915 T^{16} - 2723900163624 p T^{17} + 608521516920 p^{2} T^{18} - 131692528476 p^{3} T^{19} + 28493424864 p^{4} T^{20} - 6351048828 p^{5} T^{21} + 1468660248 p^{6} T^{22} - 343436904 p^{7} T^{23} + 77768530 p^{8} T^{24} - 16357284 p^{9} T^{25} + 3088368 p^{10} T^{26} - 507420 p^{11} T^{27} + 70080 p^{12} T^{28} - 7776 p^{13} T^{29} + 648 p^{14} T^{30} - 36 p^{15} T^{31} + p^{16} T^{32}
19 1−90T2+4011T4−123414T6+3034057T8−61998180T10+1094493006T12−18780034728T14+344074548210T16−18780034728p2T18+1094493006p4T20−61998180p6T22+3034057p8T24−123414p10T26+4011p12T28−90p14T30+p16T32 1 - 90 T^{2} + 4011 T^{4} - 123414 T^{6} + 3034057 T^{8} - 61998180 T^{10} + 1094493006 T^{12} - 18780034728 T^{14} + 344074548210 T^{16} - 18780034728 p^{2} T^{18} + 1094493006 p^{4} T^{20} - 61998180 p^{6} T^{22} + 3034057 p^{8} T^{24} - 123414 p^{10} T^{26} + 4011 p^{12} T^{28} - 90 p^{14} T^{30} + p^{16} T^{32}
23 1−4T+8T2+128T3−198T4+292T5+8608T6−3564T7−17335T8−1017836T9+5500848T10+18484pT11+20115594T12−929862264T13+4560471720T14+14572270428T15−102219015884T16+14572270428pT17+4560471720p2T18−929862264p3T19+20115594p4T20+18484p6T21+5500848p6T22−1017836p7T23−17335p8T24−3564p9T25+8608p10T26+292p11T27−198p12T28+128p13T29+8p14T30−4p15T31+p16T32 1 - 4 T + 8 T^{2} + 128 T^{3} - 198 T^{4} + 292 T^{5} + 8608 T^{6} - 3564 T^{7} - 17335 T^{8} - 1017836 T^{9} + 5500848 T^{10} + 18484 p T^{11} + 20115594 T^{12} - 929862264 T^{13} + 4560471720 T^{14} + 14572270428 T^{15} - 102219015884 T^{16} + 14572270428 p T^{17} + 4560471720 p^{2} T^{18} - 929862264 p^{3} T^{19} + 20115594 p^{4} T^{20} + 18484 p^{6} T^{21} + 5500848 p^{6} T^{22} - 1017836 p^{7} T^{23} - 17335 p^{8} T^{24} - 3564 p^{9} T^{25} + 8608 p^{10} T^{26} + 292 p^{11} T^{27} - 198 p^{12} T^{28} + 128 p^{13} T^{29} + 8 p^{14} T^{30} - 4 p^{15} T^{31} + p^{16} T^{32}
29 (1−70T2+2685T4−80906T6+2505752T8−80906p2T10+2685p4T12−70p6T14+p8T16)2 ( 1 - 70 T^{2} + 2685 T^{4} - 80906 T^{6} + 2505752 T^{8} - 80906 p^{2} T^{10} + 2685 p^{4} T^{12} - 70 p^{6} T^{14} + p^{8} T^{16} )^{2}
31 (1−12T+156T2−1296T3+10686T4−72996T5+489600T6−2919012T7+17046947T8−2919012pT9+489600p2T10−72996p3T11+10686p4T12−1296p5T13+156p6T14−12p7T15+p8T16)2 ( 1 - 12 T + 156 T^{2} - 1296 T^{3} + 10686 T^{4} - 72996 T^{5} + 489600 T^{6} - 2919012 T^{7} + 17046947 T^{8} - 2919012 p T^{9} + 489600 p^{2} T^{10} - 72996 p^{3} T^{11} + 10686 p^{4} T^{12} - 1296 p^{5} T^{13} + 156 p^{6} T^{14} - 12 p^{7} T^{15} + p^{8} T^{16} )^{2}
37 1−4T+8T2+240T3−3049T4+13544T5−984T6−514972T7+3800209T8−12256568T9−16248928T10+7999752pT11+119383314T12−6433305488T13+16607500784T14+478842888760T15−3828375485890T16+478842888760pT17+16607500784p2T18−6433305488p3T19+119383314p4T20+7999752p6T21−16248928p6T22−12256568p7T23+3800209p8T24−514972p9T25−984p10T26+13544p11T27−3049p12T28+240p13T29+8p14T30−4p15T31+p16T32 1 - 4 T + 8 T^{2} + 240 T^{3} - 3049 T^{4} + 13544 T^{5} - 984 T^{6} - 514972 T^{7} + 3800209 T^{8} - 12256568 T^{9} - 16248928 T^{10} + 7999752 p T^{11} + 119383314 T^{12} - 6433305488 T^{13} + 16607500784 T^{14} + 478842888760 T^{15} - 3828375485890 T^{16} + 478842888760 p T^{17} + 16607500784 p^{2} T^{18} - 6433305488 p^{3} T^{19} + 119383314 p^{4} T^{20} + 7999752 p^{6} T^{21} - 16248928 p^{6} T^{22} - 12256568 p^{7} T^{23} + 3800209 p^{8} T^{24} - 514972 p^{9} T^{25} - 984 p^{10} T^{26} + 13544 p^{11} T^{27} - 3049 p^{12} T^{28} + 240 p^{13} T^{29} + 8 p^{14} T^{30} - 4 p^{15} T^{31} + p^{16} T^{32}
41 (1−188T2+17802T4−1146544T6+54447827T8−1146544p2T10+17802p4T12−188p6T14+p8T16)2 ( 1 - 188 T^{2} + 17802 T^{4} - 1146544 T^{6} + 54447827 T^{8} - 1146544 p^{2} T^{10} + 17802 p^{4} T^{12} - 188 p^{6} T^{14} + p^{8} T^{16} )^{2}
43 (1+4T+8T2+32T3+3425T4+20696T5+55896T6+651228T7+6527152T8+651228pT9+55896p2T10+20696p3T11+3425p4T12+32p5T13+8p6T14+4p7T15+p8T16)2 ( 1 + 4 T + 8 T^{2} + 32 T^{3} + 3425 T^{4} + 20696 T^{5} + 55896 T^{6} + 651228 T^{7} + 6527152 T^{8} + 651228 p T^{9} + 55896 p^{2} T^{10} + 20696 p^{3} T^{11} + 3425 p^{4} T^{12} + 32 p^{5} T^{13} + 8 p^{6} T^{14} + 4 p^{7} T^{15} + p^{8} T^{16} )^{2}
47 1+12T+72T2+288T3−449T4−2880T5+39240T6+500820T7+44673T8−37644384T9−288946944T10−1723474464T11+9984376994T12+179746348152T13+1044056404368T14+4096130163936T15+8350203627806T16+4096130163936pT17+1044056404368p2T18+179746348152p3T19+9984376994p4T20−1723474464p5T21−288946944p6T22−37644384p7T23+44673p8T24+500820p9T25+39240p10T26−2880p11T27−449p12T28+288p13T29+72p14T30+12p15T31+p16T32 1 + 12 T + 72 T^{2} + 288 T^{3} - 449 T^{4} - 2880 T^{5} + 39240 T^{6} + 500820 T^{7} + 44673 T^{8} - 37644384 T^{9} - 288946944 T^{10} - 1723474464 T^{11} + 9984376994 T^{12} + 179746348152 T^{13} + 1044056404368 T^{14} + 4096130163936 T^{15} + 8350203627806 T^{16} + 4096130163936 p T^{17} + 1044056404368 p^{2} T^{18} + 179746348152 p^{3} T^{19} + 9984376994 p^{4} T^{20} - 1723474464 p^{5} T^{21} - 288946944 p^{6} T^{22} - 37644384 p^{7} T^{23} + 44673 p^{8} T^{24} + 500820 p^{9} T^{25} + 39240 p^{10} T^{26} - 2880 p^{11} T^{27} - 449 p^{12} T^{28} + 288 p^{13} T^{29} + 72 p^{14} T^{30} + 12 p^{15} T^{31} + p^{16} T^{32}
53 1−28T+392T2−1808T3−25321T4+567704T5−4335448T6−1435172T7+392677969T8−4105212392T9+14977011104T10+124625519288T11−2189877391278T12+14281594759536T13−14623477702416T14−648224117593688T15+7103959219709822T16−648224117593688pT17−14623477702416p2T18+14281594759536p3T19−2189877391278p4T20+124625519288p5T21+14977011104p6T22−4105212392p7T23+392677969p8T24−1435172p9T25−4335448p10T26+567704p11T27−25321p12T28−1808p13T29+392p14T30−28p15T31+p16T32 1 - 28 T + 392 T^{2} - 1808 T^{3} - 25321 T^{4} + 567704 T^{5} - 4335448 T^{6} - 1435172 T^{7} + 392677969 T^{8} - 4105212392 T^{9} + 14977011104 T^{10} + 124625519288 T^{11} - 2189877391278 T^{12} + 14281594759536 T^{13} - 14623477702416 T^{14} - 648224117593688 T^{15} + 7103959219709822 T^{16} - 648224117593688 p T^{17} - 14623477702416 p^{2} T^{18} + 14281594759536 p^{3} T^{19} - 2189877391278 p^{4} T^{20} + 124625519288 p^{5} T^{21} + 14977011104 p^{6} T^{22} - 4105212392 p^{7} T^{23} + 392677969 p^{8} T^{24} - 1435172 p^{9} T^{25} - 4335448 p^{10} T^{26} + 567704 p^{11} T^{27} - 25321 p^{12} T^{28} - 1808 p^{13} T^{29} + 392 p^{14} T^{30} - 28 p^{15} T^{31} + p^{16} T^{32}
59 1−320T2+54244T4−6209920T6+532238186T8−36082424000T10+2045329177232T12−105925693186240T14+5808829694261683T16−105925693186240p2T18+2045329177232p4T20−36082424000p6T22+532238186p8T24−6209920p10T26+54244p12T28−320p14T30+p16T32 1 - 320 T^{2} + 54244 T^{4} - 6209920 T^{6} + 532238186 T^{8} - 36082424000 T^{10} + 2045329177232 T^{12} - 105925693186240 T^{14} + 5808829694261683 T^{16} - 105925693186240 p^{2} T^{18} + 2045329177232 p^{4} T^{20} - 36082424000 p^{6} T^{22} + 532238186 p^{8} T^{24} - 6209920 p^{10} T^{26} + 54244 p^{12} T^{28} - 320 p^{14} T^{30} + p^{16} T^{32}
61 (1+6T+207T2+1170T3+23079T4+119796T5+1969284T6+9244740T7+135493478T8+9244740pT9+1969284p2T10+119796p3T11+23079p4T12+1170p5T13+207p6T14+6p7T15+p8T16)2 ( 1 + 6 T + 207 T^{2} + 1170 T^{3} + 23079 T^{4} + 119796 T^{5} + 1969284 T^{6} + 9244740 T^{7} + 135493478 T^{8} + 9244740 p T^{9} + 1969284 p^{2} T^{10} + 119796 p^{3} T^{11} + 23079 p^{4} T^{12} + 1170 p^{5} T^{13} + 207 p^{6} T^{14} + 6 p^{7} T^{15} + p^{8} T^{16} )^{2}
67 1−32T+512T2−3896T3−10509T4+663104T5−8249312T6+44834240T7+165963557T8−5505231928T9+49681319072T10−159136747544T11−1412717145882T12+21627811976512T13−103082665870656T14−335467607852040T15+7552610469365206T16−335467607852040pT17−103082665870656p2T18+21627811976512p3T19−1412717145882p4T20−159136747544p5T21+49681319072p6T22−5505231928p7T23+165963557p8T24+44834240p9T25−8249312p10T26+663104p11T27−10509p12T28−3896p13T29+512p14T30−32p15T31+p16T32 1 - 32 T + 512 T^{2} - 3896 T^{3} - 10509 T^{4} + 663104 T^{5} - 8249312 T^{6} + 44834240 T^{7} + 165963557 T^{8} - 5505231928 T^{9} + 49681319072 T^{10} - 159136747544 T^{11} - 1412717145882 T^{12} + 21627811976512 T^{13} - 103082665870656 T^{14} - 335467607852040 T^{15} + 7552610469365206 T^{16} - 335467607852040 p T^{17} - 103082665870656 p^{2} T^{18} + 21627811976512 p^{3} T^{19} - 1412717145882 p^{4} T^{20} - 159136747544 p^{5} T^{21} + 49681319072 p^{6} T^{22} - 5505231928 p^{7} T^{23} + 165963557 p^{8} T^{24} + 44834240 p^{9} T^{25} - 8249312 p^{10} T^{26} + 663104 p^{11} T^{27} - 10509 p^{12} T^{28} - 3896 p^{13} T^{29} + 512 p^{14} T^{30} - 32 p^{15} T^{31} + p^{16} T^{32}
71 (1+4T+94T2−964T3−1158T4−964pT5+94p2T6+4p3T7+p4T8)4 ( 1 + 4 T + 94 T^{2} - 964 T^{3} - 1158 T^{4} - 964 p T^{5} + 94 p^{2} T^{6} + 4 p^{3} T^{7} + p^{4} T^{8} )^{4}
73 1+12T+72T2+288T3+12064T4+83700T5+177264T6−3613524T7+19255890T8−96865032T9−2225167272T10−39441388620T11+6056513120T12−1050679100940T13−2551121523144T14−71385024146568T15+865631164724531T16−71385024146568pT17−2551121523144p2T18−1050679100940p3T19+6056513120p4T20−39441388620p5T21−2225167272p6T22−96865032p7T23+19255890p8T24−3613524p9T25+177264p10T26+83700p11T27+12064p12T28+288p13T29+72p14T30+12p15T31+p16T32 1 + 12 T + 72 T^{2} + 288 T^{3} + 12064 T^{4} + 83700 T^{5} + 177264 T^{6} - 3613524 T^{7} + 19255890 T^{8} - 96865032 T^{9} - 2225167272 T^{10} - 39441388620 T^{11} + 6056513120 T^{12} - 1050679100940 T^{13} - 2551121523144 T^{14} - 71385024146568 T^{15} + 865631164724531 T^{16} - 71385024146568 p T^{17} - 2551121523144 p^{2} T^{18} - 1050679100940 p^{3} T^{19} + 6056513120 p^{4} T^{20} - 39441388620 p^{5} T^{21} - 2225167272 p^{6} T^{22} - 96865032 p^{7} T^{23} + 19255890 p^{8} T^{24} - 3613524 p^{9} T^{25} + 177264 p^{10} T^{26} + 83700 p^{11} T^{27} + 12064 p^{12} T^{28} + 288 p^{13} T^{29} + 72 p^{14} T^{30} + 12 p^{15} T^{31} + p^{16} T^{32}
79 1+344T2+56836T4+6614224T6+630756554T8+45125337896T10+2052833339792T12+54520165812136T14+1660868031271123T16+54520165812136p2T18+2052833339792p4T20+45125337896p6T22+630756554p8T24+6614224p10T26+56836p12T28+344p14T30+p16T32 1 + 344 T^{2} + 56836 T^{4} + 6614224 T^{6} + 630756554 T^{8} + 45125337896 T^{10} + 2052833339792 T^{12} + 54520165812136 T^{14} + 1660868031271123 T^{16} + 54520165812136 p^{2} T^{18} + 2052833339792 p^{4} T^{20} + 45125337896 p^{6} T^{22} + 630756554 p^{8} T^{24} + 6614224 p^{10} T^{26} + 56836 p^{12} T^{28} + 344 p^{14} T^{30} + p^{16} T^{32}
83 1−25638T4+318852241T8−2957648820318T12+22747905510477444T16−2957648820318p4T20+318852241p8T24−25638p12T28+p16T32 1 - 25638 T^{4} + 318852241 T^{8} - 2957648820318 T^{12} + 22747905510477444 T^{16} - 2957648820318 p^{4} T^{20} + 318852241 p^{8} T^{24} - 25638 p^{12} T^{28} + p^{16} T^{32}
89 1−522T2+144915T4−27754278T6+4091335849T8−494840689332T10+51768593923950T12−4926383904774360T14+445675116984224850T16−4926383904774360p2T18+51768593923950p4T20−494840689332p6T22+4091335849p8T24−27754278p10T26+144915p12T28−522p14T30+p16T32 1 - 522 T^{2} + 144915 T^{4} - 27754278 T^{6} + 4091335849 T^{8} - 494840689332 T^{10} + 51768593923950 T^{12} - 4926383904774360 T^{14} + 445675116984224850 T^{16} - 4926383904774360 p^{2} T^{18} + 51768593923950 p^{4} T^{20} - 494840689332 p^{6} T^{22} + 4091335849 p^{8} T^{24} - 27754278 p^{10} T^{26} + 144915 p^{12} T^{28} - 522 p^{14} T^{30} + p^{16} T^{32}
97 (1+3868T4+90482118T8+3868p4T12+p8T16)2 ( 1 + 3868 T^{4} + 90482118 T^{8} + 3868 p^{4} T^{12} + p^{8} T^{16} )^{2}
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   L(s)=∏p ∏j=132(1−αj,p p−s)−1L(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

−2.75841717720257866238299995902, −2.72640420678823942159950493606, −2.63484634073159485401117583238, −2.60421717837181026570780493793, −2.52391863492926282631861118635, −2.51927265441559047764650928932, −2.25499030152367403283208101337, −2.16919217681946424645019821924, −2.11812145018474310328442749794, −1.99735540798851866062670092075, −1.82530149626850066439324096428, −1.79629812043631793362247417639, −1.62668413371298413934532213010, −1.60815948809842461146701914419, −1.47045975906220467538209455184, −1.44983713360727171187961998959, −1.38823176069122681008577388684, −1.37076850971702774257066682277, −1.12892687118478778412766127055, −1.11659055317809220023476540030, −1.00997864481205690381397040070, −0.981609851928948372742980243870, −0.882854889155919811856378915011, −0.74917322387410588225036565539, −0.63912672160233422288413676949, 0.63912672160233422288413676949, 0.74917322387410588225036565539, 0.882854889155919811856378915011, 0.981609851928948372742980243870, 1.00997864481205690381397040070, 1.11659055317809220023476540030, 1.12892687118478778412766127055, 1.37076850971702774257066682277, 1.38823176069122681008577388684, 1.44983713360727171187961998959, 1.47045975906220467538209455184, 1.60815948809842461146701914419, 1.62668413371298413934532213010, 1.79629812043631793362247417639, 1.82530149626850066439324096428, 1.99735540798851866062670092075, 2.11812145018474310328442749794, 2.16919217681946424645019821924, 2.25499030152367403283208101337, 2.51927265441559047764650928932, 2.52391863492926282631861118635, 2.60421717837181026570780493793, 2.63484634073159485401117583238, 2.72640420678823942159950493606, 2.75841717720257866238299995902

Graph of the ZZ-function along the critical line

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