↑

Properties

Label 24-338e12-1.1-c5e12-0-0
Degree 2424
Conductor 2.223×10302.223\times 10^{30}
Sign 11
Analytic cond. 6.44061×10206.44061\times 10^{20}
Root an. cond. 7.362727.36272
Motivic weight 55
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  − 72·3-s − 96·4-s + 1.42e3·9-s + 6.91e3·12-s + 5.37e3·16-s + 1.96e3·17-s + 1.08e4·23-s + 2.12e4·25-s + 1.71e4·27-s + 6.55e3·29-s − 1.37e5·36-s + 3.21e4·43-s − 3.87e5·48-s + 1.62e5·49-s − 1.41e5·51-s − 4.46e4·53-s − 1.36e5·61-s − 2.29e5·64-s − 1.88e5·68-s − 7.78e5·69-s − 1.53e6·75-s − 1.32e5·79-s − 9.21e5·81-s − 4.72e5·87-s − 1.03e6·92-s − 2.04e6·100-s + 2.58e5·101-s + ⋯
L(s)  = 1  − 4.61·3-s − 3·4-s + 5.87·9-s + 13.8·12-s + 21/4·16-s + 1.64·17-s + 4.26·23-s + 6.80·25-s + 4.53·27-s + 1.44·29-s − 17.6·36-s + 2.64·43-s − 24.2·48-s + 9.66·49-s − 7.59·51-s − 2.18·53-s − 4.69·61-s − 7·64-s − 4.93·68-s − 19.6·69-s − 31.4·75-s − 2.38·79-s − 15.6·81-s − 6.68·87-s − 12.7·92-s − 20.4·100-s + 2.52·101-s + ⋯

Functional equation

Λ(s)=((212⋅1324)s/2 ΓC(s)12 L(s)=( Λ(6−s)\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{12} \cdot 13^{24}\right)^{s/2} \, \Gamma_{\C}(s)^{12} \, L(s)\cr=\mathstrut & \,\Lambda(6-s)\end{aligned}
Λ(s)=((212⋅1324)s/2 ΓC(s+5/2)12 L(s)=( Λ(1−s)\begin{aligned}\Lambda(s)=\mathstrut &\left(2^{12} \cdot 13^{24}\right)^{s/2} \, \Gamma_{\C}(s+5/2)^{12} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}

Invariants

Degree: 2424
Conductor: 212⋅13242^{12} \cdot 13^{24}
Sign: 11
Analytic conductor: 6.44061×10206.44061\times 10^{20}
Root analytic conductor: 7.362727.36272
Motivic weight: 55
Rational: yes
Arithmetic: yes
Character: Trivial
Primitive: no
Self-dual: yes
Analytic rank: 00
Selberg data: (24, 212⋅1324, ( :[5/2]12), 1)(24,\ 2^{12} \cdot 13^{24} ,\ ( \ : [5/2]^{12} ),\ 1 )

Particular Values

L(3)L(3) ≈\approx 0.95384370190.9538437019
L(12)L(\frac12) ≈\approx 0.95384370190.9538437019
L(72)L(\frac{7}{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+p4T2)6 ( 1 + p^{4} T^{2} )^{6}
13 1 1
good3 (1+4p2T+410pT2+30944T3+78494p2T4+1466794p2T5+8145559p3T6+1466794p7T7+78494p12T8+30944p15T9+410p21T10+4p27T11+p30T12)2 ( 1 + 4 p^{2} T + 410 p T^{2} + 30944 T^{3} + 78494 p^{2} T^{4} + 1466794 p^{2} T^{5} + 8145559 p^{3} T^{6} + 1466794 p^{7} T^{7} + 78494 p^{12} T^{8} + 30944 p^{15} T^{9} + 410 p^{21} T^{10} + 4 p^{27} T^{11} + p^{30} T^{12} )^{2}
5 1−21272T2+211527624T4−1314676986882T6+233797705572432p2T8−20806687438165628592T10+ 1 - 21272 T^{2} + 211527624 T^{4} - 1314676986882 T^{6} + 233797705572432 p^{2} T^{8} - 20806687438165628592 T^{10} + 66 ⁣⋯ ⁣7966\!\cdots\!79T12−20806687438165628592p10T14+233797705572432p22T16−1314676986882p30T18+211527624p40T20−21272p50T22+p60T24 T^{12} - 20806687438165628592 p^{10} T^{14} + 233797705572432 p^{22} T^{16} - 1314676986882 p^{30} T^{18} + 211527624 p^{40} T^{20} - 21272 p^{50} T^{22} + p^{60} T^{24}
7 1−162502T2+12562749307T4−611612142299164T6+2986331094606780247pT8− 1 - 162502 T^{2} + 12562749307 T^{4} - 611612142299164 T^{6} + 2986331094606780247 p T^{8} - 10 ⁣⋯ ⁣5810\!\cdots\!58p2T10+ p^{2} T^{10} + 20 ⁣⋯ ⁣7520\!\cdots\!75p2T12− p^{2} T^{12} - 10 ⁣⋯ ⁣5810\!\cdots\!58p12T14+2986331094606780247p21T16−611612142299164p30T18+12562749307p40T20−162502p50T22+p60T24 p^{12} T^{14} + 2986331094606780247 p^{21} T^{16} - 611612142299164 p^{30} T^{18} + 12562749307 p^{40} T^{20} - 162502 p^{50} T^{22} + p^{60} T^{24}
11 1−1187236T2+705589763408T4−278602603717994762T6+ 1 - 1187236 T^{2} + 705589763408 T^{4} - 278602603717994762 T^{6} + 81 ⁣⋯ ⁣7681\!\cdots\!76T8− T^{8} - 18 ⁣⋯ ⁣0418\!\cdots\!04T10+ T^{10} + 33 ⁣⋯ ⁣7533\!\cdots\!75T12− T^{12} - 18 ⁣⋯ ⁣0418\!\cdots\!04p10T14+ p^{10} T^{14} + 81 ⁣⋯ ⁣7681\!\cdots\!76p20T16−278602603717994762p30T18+705589763408p40T20−1187236p50T22+p60T24 p^{20} T^{16} - 278602603717994762 p^{30} T^{18} + 705589763408 p^{40} T^{20} - 1187236 p^{50} T^{22} + p^{60} T^{24}
17 (1−980T+5433784T2−4928833714T3+13758820110808T4−11762601649747648T5+22893103492509283075T6−11762601649747648p5T7+13758820110808p10T8−4928833714p15T9+5433784p20T10−980p25T11+p30T12)2 ( 1 - 980 T + 5433784 T^{2} - 4928833714 T^{3} + 13758820110808 T^{4} - 11762601649747648 T^{5} + 22893103492509283075 T^{6} - 11762601649747648 p^{5} T^{7} + 13758820110808 p^{10} T^{8} - 4928833714 p^{15} T^{9} + 5433784 p^{20} T^{10} - 980 p^{25} T^{11} + p^{30} T^{12} )^{2}
19 1−17357500T2+154229688109308T4− 1 - 17357500 T^{2} + 154229688109308 T^{4} - 92 ⁣⋯ ⁣5092\!\cdots\!50T6+ T^{6} + 41 ⁣⋯ ⁣1241\!\cdots\!12T8− T^{8} - 14 ⁣⋯ ⁣2014\!\cdots\!20T10+ T^{10} + 39 ⁣⋯ ⁣7939\!\cdots\!79T12− T^{12} - 14 ⁣⋯ ⁣2014\!\cdots\!20p10T14+ p^{10} T^{14} + 41 ⁣⋯ ⁣1241\!\cdots\!12p20T16− p^{20} T^{16} - 92 ⁣⋯ ⁣5092\!\cdots\!50p30T18+154229688109308p40T20−17357500p50T22+p60T24 p^{30} T^{18} + 154229688109308 p^{40} T^{20} - 17357500 p^{50} T^{22} + p^{60} T^{24}
23 (1−5408T+30022239T2−99076121168T3+350443092650398T4−885852301500460448T5+ ( 1 - 5408 T + 30022239 T^{2} - 99076121168 T^{3} + 350443092650398 T^{4} - 885852301500460448 T^{5} + 25 ⁣⋯ ⁣7125\!\cdots\!71T6−885852301500460448p5T7+350443092650398p10T8−99076121168p15T9+30022239p20T10−5408p25T11+p30T12)2 T^{6} - 885852301500460448 p^{5} T^{7} + 350443092650398 p^{10} T^{8} - 99076121168 p^{15} T^{9} + 30022239 p^{20} T^{10} - 5408 p^{25} T^{11} + p^{30} T^{12} )^{2}
29 (1−3278T+81260211T2−252294509008T3+3420929052034245T4−9130400891772958686T5+ ( 1 - 3278 T + 81260211 T^{2} - 252294509008 T^{3} + 3420929052034245 T^{4} - 9130400891772958686 T^{5} + 86 ⁣⋯ ⁣3586\!\cdots\!35T6−9130400891772958686p5T7+3420929052034245p10T8−252294509008p15T9+81260211p20T10−3278p25T11+p30T12)2 T^{6} - 9130400891772958686 p^{5} T^{7} + 3420929052034245 p^{10} T^{8} - 252294509008 p^{15} T^{9} + 81260211 p^{20} T^{10} - 3278 p^{25} T^{11} + p^{30} T^{12} )^{2}
31 1−298934606T2+41987933783418427T4− 1 - 298934606 T^{2} + 41987933783418427 T^{4} - 36 ⁣⋯ ⁣8036\!\cdots\!80T6+ T^{6} + 22 ⁣⋯ ⁣6122\!\cdots\!61T8− T^{8} - 97 ⁣⋯ ⁣5497\!\cdots\!54T10+ T^{10} + 32 ⁣⋯ ⁣4332\!\cdots\!43T12− T^{12} - 97 ⁣⋯ ⁣5497\!\cdots\!54p10T14+ p^{10} T^{14} + 22 ⁣⋯ ⁣6122\!\cdots\!61p20T16− p^{20} T^{16} - 36 ⁣⋯ ⁣8036\!\cdots\!80p30T18+41987933783418427p40T20−298934606p50T22+p60T24 p^{30} T^{18} + 41987933783418427 p^{40} T^{20} - 298934606 p^{50} T^{22} + p^{60} T^{24}
37 1−483817864T2+119508967478929816T4− 1 - 483817864 T^{2} + 119508967478929816 T^{4} - 19 ⁣⋯ ⁣4219\!\cdots\!42T6+ T^{6} + 24 ⁣⋯ ⁣4424\!\cdots\!44T8− T^{8} - 23 ⁣⋯ ⁣9223\!\cdots\!92T10+ T^{10} + 18 ⁣⋯ ⁣5518\!\cdots\!55T12− T^{12} - 23 ⁣⋯ ⁣9223\!\cdots\!92p10T14+ p^{10} T^{14} + 24 ⁣⋯ ⁣4424\!\cdots\!44p20T16− p^{20} T^{16} - 19 ⁣⋯ ⁣4219\!\cdots\!42p30T18+119508967478929816p40T20−483817864p50T22+p60T24 p^{30} T^{18} + 119508967478929816 p^{40} T^{20} - 483817864 p^{50} T^{22} + p^{60} T^{24}
41 1−2242606T2−14660280441481091T4− 1 - 2242606 T^{2} - 14660280441481091 T^{4} - 17 ⁣⋯ ⁣7417\!\cdots\!74T6− T^{6} - 11 ⁣⋯ ⁣1411\!\cdots\!14T8+ T^{8} + 95 ⁣⋯ ⁣2295\!\cdots\!22T10+ T^{10} + 39 ⁣⋯ ⁣5339\!\cdots\!53T12+ T^{12} + 95 ⁣⋯ ⁣2295\!\cdots\!22p10T14− p^{10} T^{14} - 11 ⁣⋯ ⁣1411\!\cdots\!14p20T16− p^{20} T^{16} - 17 ⁣⋯ ⁣7417\!\cdots\!74p30T18−14660280441481091p40T20−2242606p50T22+p60T24 p^{30} T^{18} - 14660280441481091 p^{40} T^{20} - 2242606 p^{50} T^{22} + p^{60} T^{24}
43 (1−16050T+355188653T2−6051355408264T3+87899237304223639T4− ( 1 - 16050 T + 355188653 T^{2} - 6051355408264 T^{3} + 87899237304223639 T^{4} - 11 ⁣⋯ ⁣2811\!\cdots\!28T5+ T^{5} + 15 ⁣⋯ ⁣2115\!\cdots\!21T6− T^{6} - 11 ⁣⋯ ⁣2811\!\cdots\!28p5T7+87899237304223639p10T8−6051355408264p15T9+355188653p20T10−16050p25T11+p30T12)2 p^{5} T^{7} + 87899237304223639 p^{10} T^{8} - 6051355408264 p^{15} T^{9} + 355188653 p^{20} T^{10} - 16050 p^{25} T^{11} + p^{30} T^{12} )^{2}
47 1−1288428420T2+858054130838034256T4− 1 - 1288428420 T^{2} + 858054130838034256 T^{4} - 38 ⁣⋯ ⁣6238\!\cdots\!62T6+ T^{6} + 13 ⁣⋯ ⁣0013\!\cdots\!00T8− T^{8} - 37 ⁣⋯ ⁣5637\!\cdots\!56T10+ T^{10} + 90 ⁣⋯ ⁣7590\!\cdots\!75T12− T^{12} - 37 ⁣⋯ ⁣5637\!\cdots\!56p10T14+ p^{10} T^{14} + 13 ⁣⋯ ⁣0013\!\cdots\!00p20T16− p^{20} T^{16} - 38 ⁣⋯ ⁣6238\!\cdots\!62p30T18+858054130838034256p40T20−1288428420p50T22+p60T24 p^{30} T^{18} + 858054130838034256 p^{40} T^{20} - 1288428420 p^{50} T^{22} + p^{60} T^{24}
53 (1+22326T+1787665859T2+32764270404244T3+1541935343094270589T4+ ( 1 + 22326 T + 1787665859 T^{2} + 32764270404244 T^{3} + 1541935343094270589 T^{4} + 23 ⁣⋯ ⁣3823\!\cdots\!38T5+ T^{5} + 80 ⁣⋯ ⁣6380\!\cdots\!63T6+ T^{6} + 23 ⁣⋯ ⁣3823\!\cdots\!38p5T7+1541935343094270589p10T8+32764270404244p15T9+1787665859p20T10+22326p25T11+p30T12)2 p^{5} T^{7} + 1541935343094270589 p^{10} T^{8} + 32764270404244 p^{15} T^{9} + 1787665859 p^{20} T^{10} + 22326 p^{25} T^{11} + p^{30} T^{12} )^{2}
59 1−5625510046T2+15505742527393176045T4− 1 - 5625510046 T^{2} + 15505742527393176045 T^{4} - 27 ⁣⋯ ⁣7827\!\cdots\!78T6+ T^{6} + 36 ⁣⋯ ⁣7036\!\cdots\!70T8− T^{8} - 37 ⁣⋯ ⁣1837\!\cdots\!18T10+ T^{10} + 29 ⁣⋯ ⁣3329\!\cdots\!33T12− T^{12} - 37 ⁣⋯ ⁣1837\!\cdots\!18p10T14+ p^{10} T^{14} + 36 ⁣⋯ ⁣7036\!\cdots\!70p20T16− p^{20} T^{16} - 27 ⁣⋯ ⁣7827\!\cdots\!78p30T18+15505742527393176045p40T20−5625510046p50T22+p60T24 p^{30} T^{18} + 15505742527393176045 p^{40} T^{20} - 5625510046 p^{50} T^{22} + p^{60} T^{24}
61 (1+68204T+5614052356T2+249120175624274T3+12083767206480375752T4+ ( 1 + 68204 T + 5614052356 T^{2} + 249120175624274 T^{3} + 12083767206480375752 T^{4} + 39 ⁣⋯ ⁣6839\!\cdots\!68T5+ T^{5} + 13 ⁣⋯ ⁣5113\!\cdots\!51T6+ T^{6} + 39 ⁣⋯ ⁣6839\!\cdots\!68p5T7+12083767206480375752p10T8+249120175624274p15T9+5614052356p20T10+68204p25T11+p30T12)2 p^{5} T^{7} + 12083767206480375752 p^{10} T^{8} + 249120175624274 p^{15} T^{9} + 5614052356 p^{20} T^{10} + 68204 p^{25} T^{11} + p^{30} T^{12} )^{2}
67 1−7350772150T2+30015657607535269871T4− 1 - 7350772150 T^{2} + 30015657607535269871 T^{4} - 87 ⁣⋯ ⁣4087\!\cdots\!40T6+ T^{6} + 19 ⁣⋯ ⁣9719\!\cdots\!97T8− T^{8} - 35 ⁣⋯ ⁣5035\!\cdots\!50T10+ T^{10} + 53 ⁣⋯ ⁣8353\!\cdots\!83T12− T^{12} - 35 ⁣⋯ ⁣5035\!\cdots\!50p10T14+ p^{10} T^{14} + 19 ⁣⋯ ⁣9719\!\cdots\!97p20T16− p^{20} T^{16} - 87 ⁣⋯ ⁣4087\!\cdots\!40p30T18+30015657607535269871p40T20−7350772150p50T22+p60T24 p^{30} T^{18} + 30015657607535269871 p^{40} T^{20} - 7350772150 p^{50} T^{22} + p^{60} T^{24}
71 1−4774597258T2+12520702858599514575T4− 1 - 4774597258 T^{2} + 12520702858599514575 T^{4} - 31 ⁣⋯ ⁣6031\!\cdots\!60T6+ T^{6} + 79 ⁣⋯ ⁣4979\!\cdots\!49T8− T^{8} - 15 ⁣⋯ ⁣2615\!\cdots\!26T10+ T^{10} + 26 ⁣⋯ ⁣1926\!\cdots\!19T12− T^{12} - 15 ⁣⋯ ⁣2615\!\cdots\!26p10T14+ p^{10} T^{14} + 79 ⁣⋯ ⁣4979\!\cdots\!49p20T16− p^{20} T^{16} - 31 ⁣⋯ ⁣6031\!\cdots\!60p30T18+12520702858599514575p40T20−4774597258p50T22+p60T24 p^{30} T^{18} + 12520702858599514575 p^{40} T^{20} - 4774597258 p^{50} T^{22} + p^{60} T^{24}
73 1−9552593482T2+48177285345398086899T4− 1 - 9552593482 T^{2} + 48177285345398086899 T^{4} - 18 ⁣⋯ ⁣4018\!\cdots\!40T6+ T^{6} + 57 ⁣⋯ ⁣2157\!\cdots\!21T8− T^{8} - 15 ⁣⋯ ⁣6615\!\cdots\!66T10+ T^{10} + 33 ⁣⋯ ⁣3533\!\cdots\!35T12− T^{12} - 15 ⁣⋯ ⁣6615\!\cdots\!66p10T14+ p^{10} T^{14} + 57 ⁣⋯ ⁣2157\!\cdots\!21p20T16− p^{20} T^{16} - 18 ⁣⋯ ⁣4018\!\cdots\!40p30T18+48177285345398086899p40T20−9552593482p50T22+p60T24 p^{30} T^{18} + 48177285345398086899 p^{40} T^{20} - 9552593482 p^{50} T^{22} + p^{60} T^{24}
79 (1+66206T+4544241147T2+483703469494T3+5641007475847372879T4+ ( 1 + 66206 T + 4544241147 T^{2} + 483703469494 T^{3} + 5641007475847372879 T^{4} + 14 ⁣⋯ ⁣6414\!\cdots\!64T5+ T^{5} + 50 ⁣⋯ ⁣5350\!\cdots\!53T6+ T^{6} + 14 ⁣⋯ ⁣6414\!\cdots\!64p5T7+5641007475847372879p10T8+483703469494p15T9+4544241147p20T10+66206p25T11+p30T12)2 p^{5} T^{7} + 5641007475847372879 p^{10} T^{8} + 483703469494 p^{15} T^{9} + 4544241147 p^{20} T^{10} + 66206 p^{25} T^{11} + p^{30} T^{12} )^{2}
83 1−11195217826T2+99208519853795290879T4− 1 - 11195217826 T^{2} + 99208519853795290879 T^{4} - 63 ⁣⋯ ⁣6063\!\cdots\!60T6+ T^{6} + 34 ⁣⋯ ⁣6534\!\cdots\!65T8− T^{8} - 16 ⁣⋯ ⁣9016\!\cdots\!90T10+ T^{10} + 67 ⁣⋯ ⁣7167\!\cdots\!71T12− T^{12} - 16 ⁣⋯ ⁣9016\!\cdots\!90p10T14+ p^{10} T^{14} + 34 ⁣⋯ ⁣6534\!\cdots\!65p20T16− p^{20} T^{16} - 63 ⁣⋯ ⁣6063\!\cdots\!60p30T18+99208519853795290879p40T20−11195217826p50T22+p60T24 p^{30} T^{18} + 99208519853795290879 p^{40} T^{20} - 11195217826 p^{50} T^{22} + p^{60} T^{24}
89 1−39744869562T2+ 1 - 39744869562 T^{2} + 74 ⁣⋯ ⁣8374\!\cdots\!83T4− T^{4} - 88 ⁣⋯ ⁣9688\!\cdots\!96T6+ T^{6} + 74 ⁣⋯ ⁣8174\!\cdots\!81T8− T^{8} - 49 ⁣⋯ ⁣6249\!\cdots\!62T10+ T^{10} + 28 ⁣⋯ ⁣5128\!\cdots\!51T12− T^{12} - 49 ⁣⋯ ⁣6249\!\cdots\!62p10T14+ p^{10} T^{14} + 74 ⁣⋯ ⁣8174\!\cdots\!81p20T16− p^{20} T^{16} - 88 ⁣⋯ ⁣9688\!\cdots\!96p30T18+ p^{30} T^{18} + 74 ⁣⋯ ⁣8374\!\cdots\!83p40T20−39744869562p50T22+p60T24 p^{40} T^{20} - 39744869562 p^{50} T^{22} + p^{60} T^{24}
97 1−46890378730T2+ 1 - 46890378730 T^{2} + 11 ⁣⋯ ⁣9111\!\cdots\!91T4− T^{4} - 18 ⁣⋯ ⁣9618\!\cdots\!96T6+ T^{6} + 22 ⁣⋯ ⁣3322\!\cdots\!33T8− T^{8} - 22 ⁣⋯ ⁣9022\!\cdots\!90T10+ T^{10} + 20 ⁣⋯ ⁣4320\!\cdots\!43T12− T^{12} - 22 ⁣⋯ ⁣9022\!\cdots\!90p10T14+ p^{10} T^{14} + 22 ⁣⋯ ⁣3322\!\cdots\!33p20T16− p^{20} T^{16} - 18 ⁣⋯ ⁣9618\!\cdots\!96p30T18+ p^{30} T^{18} + 11 ⁣⋯ ⁣9111\!\cdots\!91p40T20−46890378730p50T22+p60T24 p^{40} T^{20} - 46890378730 p^{50} T^{22} + p^{60} T^{24}
show more
show less
   L(s)=∏p ∏j=124(1−αj,p p−s)−1L(s) = \displaystyle\prod_p \ \prod_{j=1}^{24} (1 - \alpha_{j,p}\, p^{-s})^{-1}

Imaginary part of the first few zeros on the critical line

−2.96645480635832094116647350863, −2.95269351849685868150387010381, −2.88248654514464903411341706473, −2.69766364114234477399900453727, −2.68910260661456744412751390563, −2.60329493881020499147359156422, −2.27982005608374476364554169900, −2.24905047136271101041411470925, −2.15859646210862122855225398426, −1.92224117907262701330698405021, −1.49896563525021399970706860437, −1.34198845724976464221997413310, −1.30466601500246473987225316950, −1.22914563203969532833643333119, −1.12685071667879053083840302596, −1.10171756134007784484192969754, −0.943246242829028352767280161751, −0.76524932317131826944508084362, −0.67795552097630002957149073389, −0.59866564152673520650368664728, −0.59014141769556175699904993578, −0.50951498449683050153812740499, −0.34808911513049686040642931012, −0.21494319667386406552196360088, −0.15474624214874617988940589715, 0.15474624214874617988940589715, 0.21494319667386406552196360088, 0.34808911513049686040642931012, 0.50951498449683050153812740499, 0.59014141769556175699904993578, 0.59866564152673520650368664728, 0.67795552097630002957149073389, 0.76524932317131826944508084362, 0.943246242829028352767280161751, 1.10171756134007784484192969754, 1.12685071667879053083840302596, 1.22914563203969532833643333119, 1.30466601500246473987225316950, 1.34198845724976464221997413310, 1.49896563525021399970706860437, 1.92224117907262701330698405021, 2.15859646210862122855225398426, 2.24905047136271101041411470925, 2.27982005608374476364554169900, 2.60329493881020499147359156422, 2.68910260661456744412751390563, 2.69766364114234477399900453727, 2.88248654514464903411341706473, 2.95269351849685868150387010381, 2.96645480635832094116647350863

Graph of the ZZ-function along the critical line

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