↑

Properties

Label 20-67e10-1.1-c1e10-0-1
Degree 2020
Conductor 1.823×10181.823\times 10^{18}
Sign 11
Analytic cond. 0.001920960.00192096
Root an. cond. 0.7314350.731435
Motivic weight 11
Arithmetic yes
Rational yes
Primitive no
Self-dual yes
Analytic rank 00

Origins

Origins of factors

Downloads

Learn more

Normalization:  

Dirichlet series

L(s)  = 1  − 6·2-s − 2·3-s + 24·4-s + 3·5-s + 12·6-s − 66·8-s + 3·9-s − 18·10-s + 15·11-s − 48·12-s − 18·13-s − 6·15-s + 143·16-s − 26·17-s − 18·18-s − 19-s + 72·20-s − 90·22-s − 6·23-s + 132·24-s + 5·25-s + 108·26-s − 22·27-s + 28·29-s + 36·30-s − 10·31-s − 242·32-s + ⋯
L(s)  = 1  − 4.24·2-s − 1.15·3-s + 12·4-s + 1.34·5-s + 4.89·6-s − 23.3·8-s + 9-s − 5.69·10-s + 4.52·11-s − 13.8·12-s − 4.99·13-s − 1.54·15-s + 35.7·16-s − 6.30·17-s − 4.24·18-s − 0.229·19-s + 16.0·20-s − 19.1·22-s − 1.25·23-s + 26.9·24-s + 25-s + 21.1·26-s − 4.23·27-s + 5.19·29-s + 6.57·30-s − 1.79·31-s − 42.7·32-s + ⋯

Functional equation

Λ(s)=((6710)s/2 ΓC(s)10 L(s)=( Λ(2−s)\begin{aligned}\Lambda(s)=\mathstrut &\left(67^{10}\right)^{s/2} \, \Gamma_{\C}(s)^{10} \, L(s)\cr=\mathstrut & \,\Lambda(2-s)\end{aligned}
Λ(s)=((6710)s/2 ΓC(s+1/2)10 L(s)=( Λ(1−s)\begin{aligned}\Lambda(s)=\mathstrut &\left(67^{10}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{10} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}

Invariants

Degree: 2020
Conductor: 671067^{10}
Sign: 11
Analytic conductor: 0.001920960.00192096
Root analytic conductor: 0.7314350.731435
Motivic weight: 11
Rational: yes
Arithmetic: yes
Character: Trivial
Primitive: no
Self-dual: yes
Analytic rank: 00
Selberg data: (20, 6710, ( :[1/2]10), 1)(20,\ 67^{10} ,\ ( \ : [1/2]^{10} ),\ 1 )

Particular Values

L(1)L(1) ≈\approx 0.078871261180.07887126118
L(12)L(\frac12) ≈\approx 0.078871261180.07887126118
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)
bad67 1−23T+111T2+967T3−6379T4−13685T5−6379pT6+967p2T7+111p3T8−23p4T9+p5T10 1 - 23 T + 111 T^{2} + 967 T^{3} - 6379 T^{4} - 13685 T^{5} - 6379 p T^{6} + 967 p^{2} T^{7} + 111 p^{3} T^{8} - 23 p^{4} T^{9} + p^{5} T^{10}
good2 1+3pT+3p2T2−3pT3−71T4−53pT5+39pT6+115p2T7+459T8−509T9−1673T10−509pT11+459p2T12+115p5T13+39p5T14−53p6T15−71p6T16−3p8T17+3p10T18+3p10T19+p10T20 1 + 3 p T + 3 p^{2} T^{2} - 3 p T^{3} - 71 T^{4} - 53 p T^{5} + 39 p T^{6} + 115 p^{2} T^{7} + 459 T^{8} - 509 T^{9} - 1673 T^{10} - 509 p T^{11} + 459 p^{2} T^{12} + 115 p^{5} T^{13} + 39 p^{5} T^{14} - 53 p^{6} T^{15} - 71 p^{6} T^{16} - 3 p^{8} T^{17} + 3 p^{10} T^{18} + 3 p^{10} T^{19} + p^{10} T^{20}
3 1+2T+T2+2p2T3+11pT4+4pT5+41pT6+232T7+95T8+44p2T9+1189T10+44p3T11+95p2T12+232p3T13+41p5T14+4p6T15+11p7T16+2p9T17+p8T18+2p9T19+p10T20 1 + 2 T + T^{2} + 2 p^{2} T^{3} + 11 p T^{4} + 4 p T^{5} + 41 p T^{6} + 232 T^{7} + 95 T^{8} + 44 p^{2} T^{9} + 1189 T^{10} + 44 p^{3} T^{11} + 95 p^{2} T^{12} + 232 p^{3} T^{13} + 41 p^{5} T^{14} + 4 p^{6} T^{15} + 11 p^{7} T^{16} + 2 p^{9} T^{17} + p^{8} T^{18} + 2 p^{9} T^{19} + p^{10} T^{20}
5 1−3T+4T2−6pT3+14pT4−159T5+644T6−1137T7+3491T8−9023T9+12881T10−9023pT11+3491p2T12−1137p3T13+644p4T14−159p5T15+14p7T16−6p8T17+4p8T18−3p9T19+p10T20 1 - 3 T + 4 T^{2} - 6 p T^{3} + 14 p T^{4} - 159 T^{5} + 644 T^{6} - 1137 T^{7} + 3491 T^{8} - 9023 T^{9} + 12881 T^{10} - 9023 p T^{11} + 3491 p^{2} T^{12} - 1137 p^{3} T^{13} + 644 p^{4} T^{14} - 159 p^{5} T^{15} + 14 p^{7} T^{16} - 6 p^{8} T^{17} + 4 p^{8} T^{18} - 3 p^{9} T^{19} + p^{10} T^{20}
7 1−pT2+55T3+93T4−440T5+1175T6+5577T7−8962T8−1562T9+146939T10−1562pT11−8962p2T12+5577p3T13+1175p4T14−440p5T15+93p6T16+55p7T17−p9T18+p10T20 1 - p T^{2} + 55 T^{3} + 93 T^{4} - 440 T^{5} + 1175 T^{6} + 5577 T^{7} - 8962 T^{8} - 1562 T^{9} + 146939 T^{10} - 1562 p T^{11} - 8962 p^{2} T^{12} + 5577 p^{3} T^{13} + 1175 p^{4} T^{14} - 440 p^{5} T^{15} + 93 p^{6} T^{16} + 55 p^{7} T^{17} - p^{9} T^{18} + p^{10} T^{20}
11 1−15T+126T2−757T3+3479T4−12112T5+27955T6−8431T7−315526T8+1986795T9−7797811T10+1986795pT11−315526p2T12−8431p3T13+27955p4T14−12112p5T15+3479p6T16−757p7T17+126p8T18−15p9T19+p10T20 1 - 15 T + 126 T^{2} - 757 T^{3} + 3479 T^{4} - 12112 T^{5} + 27955 T^{6} - 8431 T^{7} - 315526 T^{8} + 1986795 T^{9} - 7797811 T^{10} + 1986795 p T^{11} - 315526 p^{2} T^{12} - 8431 p^{3} T^{13} + 27955 p^{4} T^{14} - 12112 p^{5} T^{15} + 3479 p^{6} T^{16} - 757 p^{7} T^{17} + 126 p^{8} T^{18} - 15 p^{9} T^{19} + p^{10} T^{20}
13 1+18T+146T2+53pT3+2155T4+5402T5+13418T6+33039T7+136842T8+73910pT9+4602685T10+73910p2T11+136842p2T12+33039p3T13+13418p4T14+5402p5T15+2155p6T16+53p8T17+146p8T18+18p9T19+p10T20 1 + 18 T + 146 T^{2} + 53 p T^{3} + 2155 T^{4} + 5402 T^{5} + 13418 T^{6} + 33039 T^{7} + 136842 T^{8} + 73910 p T^{9} + 4602685 T^{10} + 73910 p^{2} T^{11} + 136842 p^{2} T^{12} + 33039 p^{3} T^{13} + 13418 p^{4} T^{14} + 5402 p^{5} T^{15} + 2155 p^{6} T^{16} + 53 p^{8} T^{17} + 146 p^{8} T^{18} + 18 p^{9} T^{19} + p^{10} T^{20}
17 1+26T+373T2+3888T3+32366T4+226300T5+1375228T6+7447050T7+36667420T8+166910084T9+710331073T10+166910084pT11+36667420p2T12+7447050p3T13+1375228p4T14+226300p5T15+32366p6T16+3888p7T17+373p8T18+26p9T19+p10T20 1 + 26 T + 373 T^{2} + 3888 T^{3} + 32366 T^{4} + 226300 T^{5} + 1375228 T^{6} + 7447050 T^{7} + 36667420 T^{8} + 166910084 T^{9} + 710331073 T^{10} + 166910084 p T^{11} + 36667420 p^{2} T^{12} + 7447050 p^{3} T^{13} + 1375228 p^{4} T^{14} + 226300 p^{5} T^{15} + 32366 p^{6} T^{16} + 3888 p^{7} T^{17} + 373 p^{8} T^{18} + 26 p^{9} T^{19} + p^{10} T^{20}
19 1+T+26T2+216T3+745T4+7223T5+26552T6+180606T7+43618pT8+3043374T9+21110165T10+3043374pT11+43618p3T12+180606p3T13+26552p4T14+7223p5T15+745p6T16+216p7T17+26p8T18+p9T19+p10T20 1 + T + 26 T^{2} + 216 T^{3} + 745 T^{4} + 7223 T^{5} + 26552 T^{6} + 180606 T^{7} + 43618 p T^{8} + 3043374 T^{9} + 21110165 T^{10} + 3043374 p T^{11} + 43618 p^{3} T^{12} + 180606 p^{3} T^{13} + 26552 p^{4} T^{14} + 7223 p^{5} T^{15} + 745 p^{6} T^{16} + 216 p^{7} T^{17} + 26 p^{8} T^{18} + p^{9} T^{19} + p^{10} T^{20}
23 1+6T+2pT2+292T3+2014T4+12892T5+71697T6+391682T7+2068724T8+10751196T9+57015969T10+10751196pT11+2068724p2T12+391682p3T13+71697p4T14+12892p5T15+2014p6T16+292p7T17+2p9T18+6p9T19+p10T20 1 + 6 T + 2 p T^{2} + 292 T^{3} + 2014 T^{4} + 12892 T^{5} + 71697 T^{6} + 391682 T^{7} + 2068724 T^{8} + 10751196 T^{9} + 57015969 T^{10} + 10751196 p T^{11} + 2068724 p^{2} T^{12} + 391682 p^{3} T^{13} + 71697 p^{4} T^{14} + 12892 p^{5} T^{15} + 2014 p^{6} T^{16} + 292 p^{7} T^{17} + 2 p^{9} T^{18} + 6 p^{9} T^{19} + p^{10} T^{20}
29 (1−14T+186T2−1499T3+11494T4−63593T5+11494pT6−1499p2T7+186p3T8−14p4T9+p5T10)2 ( 1 - 14 T + 186 T^{2} - 1499 T^{3} + 11494 T^{4} - 63593 T^{5} + 11494 p T^{6} - 1499 p^{2} T^{7} + 186 p^{3} T^{8} - 14 p^{4} T^{9} + p^{5} T^{10} )^{2}
31 1+10T+102T2+1249T3+10329T4+81687T5+630673T6+4474506T7+28121671T8+171796966T9+1032212413T10+171796966pT11+28121671p2T12+4474506p3T13+630673p4T14+81687p5T15+10329p6T16+1249p7T17+102p8T18+10p9T19+p10T20 1 + 10 T + 102 T^{2} + 1249 T^{3} + 10329 T^{4} + 81687 T^{5} + 630673 T^{6} + 4474506 T^{7} + 28121671 T^{8} + 171796966 T^{9} + 1032212413 T^{10} + 171796966 p T^{11} + 28121671 p^{2} T^{12} + 4474506 p^{3} T^{13} + 630673 p^{4} T^{14} + 81687 p^{5} T^{15} + 10329 p^{6} T^{16} + 1249 p^{7} T^{17} + 102 p^{8} T^{18} + 10 p^{9} T^{19} + p^{10} T^{20}
37 (1+11T+130T2+1177T3+9389T4+56001T5+9389pT6+1177p2T7+130p3T8+11p4T9+p5T10)2 ( 1 + 11 T + 130 T^{2} + 1177 T^{3} + 9389 T^{4} + 56001 T^{5} + 9389 p T^{6} + 1177 p^{2} T^{7} + 130 p^{3} T^{8} + 11 p^{4} T^{9} + p^{5} T^{10} )^{2}
41 1−9T+40T2+306T3+160T4−11313T5+147826T6+497850T7−658742T8−2759394T9+350382319T10−2759394pT11−658742p2T12+497850p3T13+147826p4T14−11313p5T15+160p6T16+306p7T17+40p8T18−9p9T19+p10T20 1 - 9 T + 40 T^{2} + 306 T^{3} + 160 T^{4} - 11313 T^{5} + 147826 T^{6} + 497850 T^{7} - 658742 T^{8} - 2759394 T^{9} + 350382319 T^{10} - 2759394 p T^{11} - 658742 p^{2} T^{12} + 497850 p^{3} T^{13} + 147826 p^{4} T^{14} - 11313 p^{5} T^{15} + 160 p^{6} T^{16} + 306 p^{7} T^{17} + 40 p^{8} T^{18} - 9 p^{9} T^{19} + p^{10} T^{20}
43 1−21T+288T2−2769T3+21840T4−140055T5+652423T6−1065890T7−17392825T8+230128679T9−1793081113T10+230128679pT11−17392825p2T12−1065890p3T13+652423p4T14−140055p5T15+21840p6T16−2769p7T17+288p8T18−21p9T19+p10T20 1 - 21 T + 288 T^{2} - 2769 T^{3} + 21840 T^{4} - 140055 T^{5} + 652423 T^{6} - 1065890 T^{7} - 17392825 T^{8} + 230128679 T^{9} - 1793081113 T^{10} + 230128679 p T^{11} - 17392825 p^{2} T^{12} - 1065890 p^{3} T^{13} + 652423 p^{4} T^{14} - 140055 p^{5} T^{15} + 21840 p^{6} T^{16} - 2769 p^{7} T^{17} + 288 p^{8} T^{18} - 21 p^{9} T^{19} + p^{10} T^{20}
47 1+22T+250T2+1386T3−1982T4−113916T5−1065993T6−4765420T7+5013254T8+268925668T9+2504576689T10+268925668pT11+5013254p2T12−4765420p3T13−1065993p4T14−113916p5T15−1982p6T16+1386p7T17+250p8T18+22p9T19+p10T20 1 + 22 T + 250 T^{2} + 1386 T^{3} - 1982 T^{4} - 113916 T^{5} - 1065993 T^{6} - 4765420 T^{7} + 5013254 T^{8} + 268925668 T^{9} + 2504576689 T^{10} + 268925668 p T^{11} + 5013254 p^{2} T^{12} - 4765420 p^{3} T^{13} - 1065993 p^{4} T^{14} - 113916 p^{5} T^{15} - 1982 p^{6} T^{16} + 1386 p^{7} T^{17} + 250 p^{8} T^{18} + 22 p^{9} T^{19} + p^{10} T^{20}
53 1−20T+116T2+489T3−12903T4+90166T5−42792T6−3807843T7+23205826T8−707784T9−545699835T10−707784pT11+23205826p2T12−3807843p3T13−42792p4T14+90166p5T15−12903p6T16+489p7T17+116p8T18−20p9T19+p10T20 1 - 20 T + 116 T^{2} + 489 T^{3} - 12903 T^{4} + 90166 T^{5} - 42792 T^{6} - 3807843 T^{7} + 23205826 T^{8} - 707784 T^{9} - 545699835 T^{10} - 707784 p T^{11} + 23205826 p^{2} T^{12} - 3807843 p^{3} T^{13} - 42792 p^{4} T^{14} + 90166 p^{5} T^{15} - 12903 p^{6} T^{16} + 489 p^{7} T^{17} + 116 p^{8} T^{18} - 20 p^{9} T^{19} + p^{10} T^{20}
59 1+17T+241T2+2599T3+22814T4+177187T5+1323866T6+8330851T7+63828025T8+477832256T9+3640127217T10+477832256pT11+63828025p2T12+8330851p3T13+1323866p4T14+177187p5T15+22814p6T16+2599p7T17+241p8T18+17p9T19+p10T20 1 + 17 T + 241 T^{2} + 2599 T^{3} + 22814 T^{4} + 177187 T^{5} + 1323866 T^{6} + 8330851 T^{7} + 63828025 T^{8} + 477832256 T^{9} + 3640127217 T^{10} + 477832256 p T^{11} + 63828025 p^{2} T^{12} + 8330851 p^{3} T^{13} + 1323866 p^{4} T^{14} + 177187 p^{5} T^{15} + 22814 p^{6} T^{16} + 2599 p^{7} T^{17} + 241 p^{8} T^{18} + 17 p^{9} T^{19} + p^{10} T^{20}
61 1−13T+174T2−1337T3+19571T4−174296T5+1981255T6−12996507T7+132793130T8−952257907T9+9819441367T10−952257907pT11+132793130p2T12−12996507p3T13+1981255p4T14−174296p5T15+19571p6T16−1337p7T17+174p8T18−13p9T19+p10T20 1 - 13 T + 174 T^{2} - 1337 T^{3} + 19571 T^{4} - 174296 T^{5} + 1981255 T^{6} - 12996507 T^{7} + 132793130 T^{8} - 952257907 T^{9} + 9819441367 T^{10} - 952257907 p T^{11} + 132793130 p^{2} T^{12} - 12996507 p^{3} T^{13} + 1981255 p^{4} T^{14} - 174296 p^{5} T^{15} + 19571 p^{6} T^{16} - 1337 p^{7} T^{17} + 174 p^{8} T^{18} - 13 p^{9} T^{19} + p^{10} T^{20}
71 1−T−81T2+603T3−9581T4−22881T5+1272030T6−6773213T7+338422pT8+397226390T9−8711303457T10+397226390pT11+338422p3T12−6773213p3T13+1272030p4T14−22881p5T15−9581p6T16+603p7T17−81p8T18−p9T19+p10T20 1 - T - 81 T^{2} + 603 T^{3} - 9581 T^{4} - 22881 T^{5} + 1272030 T^{6} - 6773213 T^{7} + 338422 p T^{8} + 397226390 T^{9} - 8711303457 T^{10} + 397226390 p T^{11} + 338422 p^{3} T^{12} - 6773213 p^{3} T^{13} + 1272030 p^{4} T^{14} - 22881 p^{5} T^{15} - 9581 p^{6} T^{16} + 603 p^{7} T^{17} - 81 p^{8} T^{18} - p^{9} T^{19} + p^{10} T^{20}
73 1+18T+207T2+1796T3+19065T4+229904T5+2431707T6+18414708T7+149245213T8+1425344942T9+13293131103T10+1425344942pT11+149245213p2T12+18414708p3T13+2431707p4T14+229904p5T15+19065p6T16+1796p7T17+207p8T18+18p9T19+p10T20 1 + 18 T + 207 T^{2} + 1796 T^{3} + 19065 T^{4} + 229904 T^{5} + 2431707 T^{6} + 18414708 T^{7} + 149245213 T^{8} + 1425344942 T^{9} + 13293131103 T^{10} + 1425344942 p T^{11} + 149245213 p^{2} T^{12} + 18414708 p^{3} T^{13} + 2431707 p^{4} T^{14} + 229904 p^{5} T^{15} + 19065 p^{6} T^{16} + 1796 p^{7} T^{17} + 207 p^{8} T^{18} + 18 p^{9} T^{19} + p^{10} T^{20}
79 1−5T−76T2+2590T3−1270T4−218797T5+2276594T6+15204858T7−184964002T8+26446076T9+19410983107T10+26446076pT11−184964002p2T12+15204858p3T13+2276594p4T14−218797p5T15−1270p6T16+2590p7T17−76p8T18−5p9T19+p10T20 1 - 5 T - 76 T^{2} + 2590 T^{3} - 1270 T^{4} - 218797 T^{5} + 2276594 T^{6} + 15204858 T^{7} - 184964002 T^{8} + 26446076 T^{9} + 19410983107 T^{10} + 26446076 p T^{11} - 184964002 p^{2} T^{12} + 15204858 p^{3} T^{13} + 2276594 p^{4} T^{14} - 218797 p^{5} T^{15} - 1270 p^{6} T^{16} + 2590 p^{7} T^{17} - 76 p^{8} T^{18} - 5 p^{9} T^{19} + p^{10} T^{20}
83 1+12T−115T2−1540T3+6465T4+30181T5−945413T6−42680pT7+7145785T8+397493039T9+7663760257T10+397493039pT11+7145785p2T12−42680p4T13−945413p4T14+30181p5T15+6465p6T16−1540p7T17−115p8T18+12p9T19+p10T20 1 + 12 T - 115 T^{2} - 1540 T^{3} + 6465 T^{4} + 30181 T^{5} - 945413 T^{6} - 42680 p T^{7} + 7145785 T^{8} + 397493039 T^{9} + 7663760257 T^{10} + 397493039 p T^{11} + 7145785 p^{2} T^{12} - 42680 p^{4} T^{13} - 945413 p^{4} T^{14} + 30181 p^{5} T^{15} + 6465 p^{6} T^{16} - 1540 p^{7} T^{17} - 115 p^{8} T^{18} + 12 p^{9} T^{19} + p^{10} T^{20}
89 1−51T+1126T2−15003T3+164417T4−1953568T5+22220139T6−202706651T7+1729561976T8−17858590849T9+185096728543T10−17858590849pT11+1729561976p2T12−202706651p3T13+22220139p4T14−1953568p5T15+164417p6T16−15003p7T17+1126p8T18−51p9T19+p10T20 1 - 51 T + 1126 T^{2} - 15003 T^{3} + 164417 T^{4} - 1953568 T^{5} + 22220139 T^{6} - 202706651 T^{7} + 1729561976 T^{8} - 17858590849 T^{9} + 185096728543 T^{10} - 17858590849 p T^{11} + 1729561976 p^{2} T^{12} - 202706651 p^{3} T^{13} + 22220139 p^{4} T^{14} - 1953568 p^{5} T^{15} + 164417 p^{6} T^{16} - 15003 p^{7} T^{17} + 1126 p^{8} T^{18} - 51 p^{9} T^{19} + p^{10} T^{20}
97 (1+5T+396T2+1653T3+69681T4+225603T5+69681pT6+1653p2T7+396p3T8+5p4T9+p5T10)2 ( 1 + 5 T + 396 T^{2} + 1653 T^{3} + 69681 T^{4} + 225603 T^{5} + 69681 p T^{6} + 1653 p^{2} T^{7} + 396 p^{3} T^{8} + 5 p^{4} T^{9} + p^{5} T^{10} )^{2}
show more
show less
   L(s)=∏p ∏j=120(1−αj,p p−s)−1L(s) = \displaystyle\prod_p \ \prod_{j=1}^{20} (1 - \alpha_{j,p}\, p^{-s})^{-1}

Imaginary part of the first few zeros on the critical line

−6.36482481701108108846189516670, −6.34075392809389608307121277984, −6.33339869963557778593805852611, −6.07500849640953219260349586335, −5.96497745018869722875971425292, −5.87441071277092371701818614499, −5.41294864253551256224147896572, −5.03773897762151392801797217235, −4.98974771778447620779401953629, −4.87753131370298889005593320325, −4.80551532546529382123211624942, −4.72610928698281295875661100000, −4.18178578843873943528256330715, −4.04353129471180137993356740970, −4.00649036787726745642882726746, −3.89270894046844294842534682873, −3.71232404412472618660734369885, −2.75257143067634281787472220995, −2.51637970927187035342813907583, −2.48231968057767050624373350024, −2.27074473713084819478402558799, −2.13604216291331806054805858341, −1.81691943013905374783199452849, −1.75870967665180397768350887951, −1.49269717254852779529034636948, 1.49269717254852779529034636948, 1.75870967665180397768350887951, 1.81691943013905374783199452849, 2.13604216291331806054805858341, 2.27074473713084819478402558799, 2.48231968057767050624373350024, 2.51637970927187035342813907583, 2.75257143067634281787472220995, 3.71232404412472618660734369885, 3.89270894046844294842534682873, 4.00649036787726745642882726746, 4.04353129471180137993356740970, 4.18178578843873943528256330715, 4.72610928698281295875661100000, 4.80551532546529382123211624942, 4.87753131370298889005593320325, 4.98974771778447620779401953629, 5.03773897762151392801797217235, 5.41294864253551256224147896572, 5.87441071277092371701818614499, 5.96497745018869722875971425292, 6.07500849640953219260349586335, 6.33339869963557778593805852611, 6.34075392809389608307121277984, 6.36482481701108108846189516670

Graph of the ZZ-function along the critical line

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