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Properties

Label 24-425e12-1.1-c1e12-0-8
Degree 2424
Conductor 3.473×10313.473\times 10^{31}
Sign 11
Analytic cond. 2.33341×1062.33341\times 10^{6}
Root an. cond. 1.842181.84218
Motivic weight 11
Arithmetic yes
Rational yes
Primitive no
Self-dual yes
Analytic rank 00

Origins

Origins of factors

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Normalization:  

Dirichlet series

L(s)  = 1  + 4·3-s + 6·4-s + 8·9-s − 4·11-s + 24·12-s + 13·16-s − 12·17-s − 12·23-s + 16·27-s − 12·29-s − 16·33-s + 48·36-s − 12·37-s − 24·41-s − 24·44-s + 48·47-s + 52·48-s − 48·51-s + 40·61-s + 12·64-s + 8·67-s − 72·68-s − 48·69-s + 28·71-s + 48·73-s − 8·79-s + 42·81-s + ⋯
L(s)  = 1  + 2.30·3-s + 3·4-s + 8/3·9-s − 1.20·11-s + 6.92·12-s + 13/4·16-s − 2.91·17-s − 2.50·23-s + 3.07·27-s − 2.22·29-s − 2.78·33-s + 8·36-s − 1.97·37-s − 3.74·41-s − 3.61·44-s + 7.00·47-s + 7.50·48-s − 6.72·51-s + 5.12·61-s + 3/2·64-s + 0.977·67-s − 8.73·68-s − 5.77·69-s + 3.32·71-s + 5.61·73-s − 0.900·79-s + 14/3·81-s + ⋯

Functional equation

Λ(s)=((524⋅1712)s/2 ΓC(s)12 L(s)=( Λ(2−s)\begin{aligned}\Lambda(s)=\mathstrut &\left(5^{24} \cdot 17^{12}\right)^{s/2} \, \Gamma_{\C}(s)^{12} \, L(s)\cr=\mathstrut & \,\Lambda(2-s)\end{aligned}
Λ(s)=((524⋅1712)s/2 ΓC(s+1/2)12 L(s)=( Λ(1−s)\begin{aligned}\Lambda(s)=\mathstrut &\left(5^{24} \cdot 17^{12}\right)^{s/2} \, \Gamma_{\C}(s+1/2)^{12} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned}

Invariants

Degree: 2424
Conductor: 524⋅17125^{24} \cdot 17^{12}
Sign: 11
Analytic conductor: 2.33341×1062.33341\times 10^{6}
Root analytic conductor: 1.842181.84218
Motivic weight: 11
Rational: yes
Arithmetic: yes
Character: Trivial
Primitive: no
Self-dual: yes
Analytic rank: 00
Selberg data: (24, 524⋅1712, ( :[1/2]12), 1)(24,\ 5^{24} \cdot 17^{12} ,\ ( \ : [1/2]^{12} ),\ 1 )

Particular Values

L(1)L(1) ≈\approx 25.3076913925.30769139
L(12)L(\frac12) ≈\approx 25.3076913925.30769139
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)
bad5 1 1
17 1+12T+82T2+516T3+3079T4+14512T5+60188T6+14512pT7+3079p2T8+516p3T9+82p4T10+12p5T11+p6T12 1 + 12 T + 82 T^{2} + 516 T^{3} + 3079 T^{4} + 14512 T^{5} + 60188 T^{6} + 14512 p T^{7} + 3079 p^{2} T^{8} + 516 p^{3} T^{9} + 82 p^{4} T^{10} + 12 p^{5} T^{11} + p^{6} T^{12}
good2 1−3pT2+23T4−9p3T6+203T8−237pT10+993T12−237p3T14+203p4T16−9p9T18+23p8T20−3p11T22+p12T24 1 - 3 p T^{2} + 23 T^{4} - 9 p^{3} T^{6} + 203 T^{8} - 237 p T^{10} + 993 T^{12} - 237 p^{3} T^{14} + 203 p^{4} T^{16} - 9 p^{9} T^{18} + 23 p^{8} T^{20} - 3 p^{11} T^{22} + p^{12} T^{24}
3 1−4T+8T2−16T3+22T4−16T5+16T6−28T7−29T8+304T9−760T10+1928T11−4304T12+1928pT13−760p2T14+304p3T15−29p4T16−28p5T17+16p6T18−16p7T19+22p8T20−16p9T21+8p10T22−4p11T23+p12T24 1 - 4 T + 8 T^{2} - 16 T^{3} + 22 T^{4} - 16 T^{5} + 16 T^{6} - 28 T^{7} - 29 T^{8} + 304 T^{9} - 760 T^{10} + 1928 T^{11} - 4304 T^{12} + 1928 p T^{13} - 760 p^{2} T^{14} + 304 p^{3} T^{15} - 29 p^{4} T^{16} - 28 p^{5} T^{17} + 16 p^{6} T^{18} - 16 p^{7} T^{19} + 22 p^{8} T^{20} - 16 p^{9} T^{21} + 8 p^{10} T^{22} - 4 p^{11} T^{23} + p^{12} T^{24}
7 1−4pT3+6pT4+212T5+8p2T6−928T7−3125T8+6744T9+31992T10+888pT11−376p3T12+888p2T13+31992p2T14+6744p3T15−3125p4T16−928p5T17+8p8T18+212p7T19+6p9T20−4p10T21+p12T24 1 - 4 p T^{3} + 6 p T^{4} + 212 T^{5} + 8 p^{2} T^{6} - 928 T^{7} - 3125 T^{8} + 6744 T^{9} + 31992 T^{10} + 888 p T^{11} - 376 p^{3} T^{12} + 888 p^{2} T^{13} + 31992 p^{2} T^{14} + 6744 p^{3} T^{15} - 3125 p^{4} T^{16} - 928 p^{5} T^{17} + 8 p^{8} T^{18} + 212 p^{7} T^{19} + 6 p^{9} T^{20} - 4 p^{10} T^{21} + p^{12} T^{24}
11 1+4T+8T2+64T3+74T4−72pT5−1712T6−13364T7−46833T8+42384T9+129224T10+1266064T11+10886032T12+1266064pT13+129224p2T14+42384p3T15−46833p4T16−13364p5T17−1712p6T18−72p8T19+74p8T20+64p9T21+8p10T22+4p11T23+p12T24 1 + 4 T + 8 T^{2} + 64 T^{3} + 74 T^{4} - 72 p T^{5} - 1712 T^{6} - 13364 T^{7} - 46833 T^{8} + 42384 T^{9} + 129224 T^{10} + 1266064 T^{11} + 10886032 T^{12} + 1266064 p T^{13} + 129224 p^{2} T^{14} + 42384 p^{3} T^{15} - 46833 p^{4} T^{16} - 13364 p^{5} T^{17} - 1712 p^{6} T^{18} - 72 p^{8} T^{19} + 74 p^{8} T^{20} + 64 p^{9} T^{21} + 8 p^{10} T^{22} + 4 p^{11} T^{23} + p^{12} T^{24}
13 (1+20T2−12T3+255T4+124T5+3948T6+124pT7+255p2T8−12p3T9+20p4T10+p6T12)2 ( 1 + 20 T^{2} - 12 T^{3} + 255 T^{4} + 124 T^{5} + 3948 T^{6} + 124 p T^{7} + 255 p^{2} T^{8} - 12 p^{3} T^{9} + 20 p^{4} T^{10} + p^{6} T^{12} )^{2}
19 1−92T2+4626T4−167116T6+4842975T8−117605944T10+2422842556T12−117605944p2T14+4842975p4T16−167116p6T18+4626p8T20−92p10T22+p12T24 1 - 92 T^{2} + 4626 T^{4} - 167116 T^{6} + 4842975 T^{8} - 117605944 T^{10} + 2422842556 T^{12} - 117605944 p^{2} T^{14} + 4842975 p^{4} T^{16} - 167116 p^{6} T^{18} + 4626 p^{8} T^{20} - 92 p^{10} T^{22} + p^{12} T^{24}
23 1+12T+72T2+400T3+2878T4+18936T5+100016T6+521948T7+2709363T8+13154744T9+63001992T10+314746192T11+1561862208T12+314746192pT13+63001992p2T14+13154744p3T15+2709363p4T16+521948p5T17+100016p6T18+18936p7T19+2878p8T20+400p9T21+72p10T22+12p11T23+p12T24 1 + 12 T + 72 T^{2} + 400 T^{3} + 2878 T^{4} + 18936 T^{5} + 100016 T^{6} + 521948 T^{7} + 2709363 T^{8} + 13154744 T^{9} + 63001992 T^{10} + 314746192 T^{11} + 1561862208 T^{12} + 314746192 p T^{13} + 63001992 p^{2} T^{14} + 13154744 p^{3} T^{15} + 2709363 p^{4} T^{16} + 521948 p^{5} T^{17} + 100016 p^{6} T^{18} + 18936 p^{7} T^{19} + 2878 p^{8} T^{20} + 400 p^{9} T^{21} + 72 p^{10} T^{22} + 12 p^{11} T^{23} + p^{12} T^{24}
29 1+12T+72T2+708T3+5562T4+21252T5+105192T6+726444T7+804479T8−8873352T9−9334512T10−305351640T11−3778100564T12−305351640pT13−9334512p2T14−8873352p3T15+804479p4T16+726444p5T17+105192p6T18+21252p7T19+5562p8T20+708p9T21+72p10T22+12p11T23+p12T24 1 + 12 T + 72 T^{2} + 708 T^{3} + 5562 T^{4} + 21252 T^{5} + 105192 T^{6} + 726444 T^{7} + 804479 T^{8} - 8873352 T^{9} - 9334512 T^{10} - 305351640 T^{11} - 3778100564 T^{12} - 305351640 p T^{13} - 9334512 p^{2} T^{14} - 8873352 p^{3} T^{15} + 804479 p^{4} T^{16} + 726444 p^{5} T^{17} + 105192 p^{6} T^{18} + 21252 p^{7} T^{19} + 5562 p^{8} T^{20} + 708 p^{9} T^{21} + 72 p^{10} T^{22} + 12 p^{11} T^{23} + p^{12} T^{24}
31 1−156T3−2754T4+452T5+12168T6+245112T7+3961447T8+323440T9−4624648T10−168645768T11−4098407752T12−168645768pT13−4624648p2T14+323440p3T15+3961447p4T16+245112p5T17+12168p6T18+452p7T19−2754p8T20−156p9T21+p12T24 1 - 156 T^{3} - 2754 T^{4} + 452 T^{5} + 12168 T^{6} + 245112 T^{7} + 3961447 T^{8} + 323440 T^{9} - 4624648 T^{10} - 168645768 T^{11} - 4098407752 T^{12} - 168645768 p T^{13} - 4624648 p^{2} T^{14} + 323440 p^{3} T^{15} + 3961447 p^{4} T^{16} + 245112 p^{5} T^{17} + 12168 p^{6} T^{18} + 452 p^{7} T^{19} - 2754 p^{8} T^{20} - 156 p^{9} T^{21} + p^{12} T^{24}
37 1+12T+72T2+308T3+2250T4+13364T5+45800T6−79636T7−905p2T8−18417192T9−170081904T10−1483635480T11−9533058292T12−1483635480pT13−170081904p2T14−18417192p3T15−905p6T16−79636p5T17+45800p6T18+13364p7T19+2250p8T20+308p9T21+72p10T22+12p11T23+p12T24 1 + 12 T + 72 T^{2} + 308 T^{3} + 2250 T^{4} + 13364 T^{5} + 45800 T^{6} - 79636 T^{7} - 905 p^{2} T^{8} - 18417192 T^{9} - 170081904 T^{10} - 1483635480 T^{11} - 9533058292 T^{12} - 1483635480 p T^{13} - 170081904 p^{2} T^{14} - 18417192 p^{3} T^{15} - 905 p^{6} T^{16} - 79636 p^{5} T^{17} + 45800 p^{6} T^{18} + 13364 p^{7} T^{19} + 2250 p^{8} T^{20} + 308 p^{9} T^{21} + 72 p^{10} T^{22} + 12 p^{11} T^{23} + p^{12} T^{24}
41 1+24T+288T2+2680T3+20998T4+135832T5+803744T6+4720696T7+28651119T8+187625072T9+744256p2T10+199495088pT11+52761079188T12+199495088p2T13+744256p4T14+187625072p3T15+28651119p4T16+4720696p5T17+803744p6T18+135832p7T19+20998p8T20+2680p9T21+288p10T22+24p11T23+p12T24 1 + 24 T + 288 T^{2} + 2680 T^{3} + 20998 T^{4} + 135832 T^{5} + 803744 T^{6} + 4720696 T^{7} + 28651119 T^{8} + 187625072 T^{9} + 744256 p^{2} T^{10} + 199495088 p T^{11} + 52761079188 T^{12} + 199495088 p^{2} T^{13} + 744256 p^{4} T^{14} + 187625072 p^{3} T^{15} + 28651119 p^{4} T^{16} + 4720696 p^{5} T^{17} + 803744 p^{6} T^{18} + 135832 p^{7} T^{19} + 20998 p^{8} T^{20} + 2680 p^{9} T^{21} + 288 p^{10} T^{22} + 24 p^{11} T^{23} + p^{12} T^{24}
43 1−184T2+18790T4−1391328T6+81780959T8−4113094280T10+185743711652T12−4113094280p2T14+81780959p4T16−1391328p6T18+18790p8T20−184p10T22+p12T24 1 - 184 T^{2} + 18790 T^{4} - 1391328 T^{6} + 81780959 T^{8} - 4113094280 T^{10} + 185743711652 T^{12} - 4113094280 p^{2} T^{14} + 81780959 p^{4} T^{16} - 1391328 p^{6} T^{18} + 18790 p^{8} T^{20} - 184 p^{10} T^{22} + p^{12} T^{24}
47 (1−24T+392T2−4556T3+43823T4−353156T5+2577076T6−353156pT7+43823p2T8−4556p3T9+392p4T10−24p5T11+p6T12)2 ( 1 - 24 T + 392 T^{2} - 4556 T^{3} + 43823 T^{4} - 353156 T^{5} + 2577076 T^{6} - 353156 p T^{7} + 43823 p^{2} T^{8} - 4556 p^{3} T^{9} + 392 p^{4} T^{10} - 24 p^{5} T^{11} + p^{6} T^{12} )^{2}
53 1−204T2+26562T4−2416476T6+178063743T8−11083541624T10+618583405660T12−11083541624p2T14+178063743p4T16−2416476p6T18+26562p8T20−204p10T22+p12T24 1 - 204 T^{2} + 26562 T^{4} - 2416476 T^{6} + 178063743 T^{8} - 11083541624 T^{10} + 618583405660 T^{12} - 11083541624 p^{2} T^{14} + 178063743 p^{4} T^{16} - 2416476 p^{6} T^{18} + 26562 p^{8} T^{20} - 204 p^{10} T^{22} + p^{12} T^{24}
59 1−468T2+102802T4−14182372T6+1399420159T8−107717762600T10+6886886586172T12−107717762600p2T14+1399420159p4T16−14182372p6T18+102802p8T20−468p10T22+p12T24 1 - 468 T^{2} + 102802 T^{4} - 14182372 T^{6} + 1399420159 T^{8} - 107717762600 T^{10} + 6886886586172 T^{12} - 107717762600 p^{2} T^{14} + 1399420159 p^{4} T^{16} - 14182372 p^{6} T^{18} + 102802 p^{8} T^{20} - 468 p^{10} T^{22} + p^{12} T^{24}
61 1−40T+800T2−12504T3+184598T4−40056pT5+28233248T6−305052840T7+3158111167T8−30151790672T9+267303164864T10−2283320825520T11+18527414094644T12−2283320825520pT13+267303164864p2T14−30151790672p3T15+3158111167p4T16−305052840p5T17+28233248p6T18−40056p8T19+184598p8T20−12504p9T21+800p10T22−40p11T23+p12T24 1 - 40 T + 800 T^{2} - 12504 T^{3} + 184598 T^{4} - 40056 p T^{5} + 28233248 T^{6} - 305052840 T^{7} + 3158111167 T^{8} - 30151790672 T^{9} + 267303164864 T^{10} - 2283320825520 T^{11} + 18527414094644 T^{12} - 2283320825520 p T^{13} + 267303164864 p^{2} T^{14} - 30151790672 p^{3} T^{15} + 3158111167 p^{4} T^{16} - 305052840 p^{5} T^{17} + 28233248 p^{6} T^{18} - 40056 p^{8} T^{19} + 184598 p^{8} T^{20} - 12504 p^{9} T^{21} + 800 p^{10} T^{22} - 40 p^{11} T^{23} + p^{12} T^{24}
67 (1−4T+356T2−1240T3+55175T4−159748T5+4798716T6−159748pT7+55175p2T8−1240p3T9+356p4T10−4p5T11+p6T12)2 ( 1 - 4 T + 356 T^{2} - 1240 T^{3} + 55175 T^{4} - 159748 T^{5} + 4798716 T^{6} - 159748 p T^{7} + 55175 p^{2} T^{8} - 1240 p^{3} T^{9} + 356 p^{4} T^{10} - 4 p^{5} T^{11} + p^{6} T^{12} )^{2}
71 1−28T+392T2−4432T3+35314T4−151184T5+211376T6+3536900T7−37488993T8+144764696T9−1069498168T10+21338963608T11−259039666848T12+21338963608pT13−1069498168p2T14+144764696p3T15−37488993p4T16+3536900p5T17+211376p6T18−151184p7T19+35314p8T20−4432p9T21+392p10T22−28p11T23+p12T24 1 - 28 T + 392 T^{2} - 4432 T^{3} + 35314 T^{4} - 151184 T^{5} + 211376 T^{6} + 3536900 T^{7} - 37488993 T^{8} + 144764696 T^{9} - 1069498168 T^{10} + 21338963608 T^{11} - 259039666848 T^{12} + 21338963608 p T^{13} - 1069498168 p^{2} T^{14} + 144764696 p^{3} T^{15} - 37488993 p^{4} T^{16} + 3536900 p^{5} T^{17} + 211376 p^{6} T^{18} - 151184 p^{7} T^{19} + 35314 p^{8} T^{20} - 4432 p^{9} T^{21} + 392 p^{10} T^{22} - 28 p^{11} T^{23} + p^{12} T^{24}
73 1−48T+1152T2−19520T3+277734T4−3608128T5+43755776T6−498961648T7+5387964143T8−54979433440T9+528636621952T10−4817379931648T11+41994385065940T12−4817379931648pT13+528636621952p2T14−54979433440p3T15+5387964143p4T16−498961648p5T17+43755776p6T18−3608128p7T19+277734p8T20−19520p9T21+1152p10T22−48p11T23+p12T24 1 - 48 T + 1152 T^{2} - 19520 T^{3} + 277734 T^{4} - 3608128 T^{5} + 43755776 T^{6} - 498961648 T^{7} + 5387964143 T^{8} - 54979433440 T^{9} + 528636621952 T^{10} - 4817379931648 T^{11} + 41994385065940 T^{12} - 4817379931648 p T^{13} + 528636621952 p^{2} T^{14} - 54979433440 p^{3} T^{15} + 5387964143 p^{4} T^{16} - 498961648 p^{5} T^{17} + 43755776 p^{6} T^{18} - 3608128 p^{7} T^{19} + 277734 p^{8} T^{20} - 19520 p^{9} T^{21} + 1152 p^{10} T^{22} - 48 p^{11} T^{23} + p^{12} T^{24}
79 1+8T+32T2−1220T3+5350T4+114868T5+1491944T6−12162584T7−38174937T8+233812952T9+16545882392T10−38512918912T11−355031479032T12−38512918912pT13+16545882392p2T14+233812952p3T15−38174937p4T16−12162584p5T17+1491944p6T18+114868p7T19+5350p8T20−1220p9T21+32p10T22+8p11T23+p12T24 1 + 8 T + 32 T^{2} - 1220 T^{3} + 5350 T^{4} + 114868 T^{5} + 1491944 T^{6} - 12162584 T^{7} - 38174937 T^{8} + 233812952 T^{9} + 16545882392 T^{10} - 38512918912 T^{11} - 355031479032 T^{12} - 38512918912 p T^{13} + 16545882392 p^{2} T^{14} + 233812952 p^{3} T^{15} - 38174937 p^{4} T^{16} - 12162584 p^{5} T^{17} + 1491944 p^{6} T^{18} + 114868 p^{7} T^{19} + 5350 p^{8} T^{20} - 1220 p^{9} T^{21} + 32 p^{10} T^{22} + 8 p^{11} T^{23} + p^{12} T^{24}
83 1−776T2+288430T4−67950336T6+11308890671T8−1401355662904T10+132600210726644T12−1401355662904p2T14+11308890671p4T16−67950336p6T18+288430p8T20−776p10T22+p12T24 1 - 776 T^{2} + 288430 T^{4} - 67950336 T^{6} + 11308890671 T^{8} - 1401355662904 T^{10} + 132600210726644 T^{12} - 1401355662904 p^{2} T^{14} + 11308890671 p^{4} T^{16} - 67950336 p^{6} T^{18} + 288430 p^{8} T^{20} - 776 p^{10} T^{22} + p^{12} T^{24}
89 (1−12T+354T2−4000T3+61415T4−604868T5+6702448T6−604868pT7+61415p2T8−4000p3T9+354p4T10−12p5T11+p6T12)2 ( 1 - 12 T + 354 T^{2} - 4000 T^{3} + 61415 T^{4} - 604868 T^{5} + 6702448 T^{6} - 604868 p T^{7} + 61415 p^{2} T^{8} - 4000 p^{3} T^{9} + 354 p^{4} T^{10} - 12 p^{5} T^{11} + p^{6} T^{12} )^{2}
97 1+4T+8T2−20T3−17958T4−32004T5+15848T6+4133236T7+241837519T8+226090952T9−316274672T10−41141248808T11−2546305955668T12−41141248808pT13−316274672p2T14+226090952p3T15+241837519p4T16+4133236p5T17+15848p6T18−32004p7T19−17958p8T20−20p9T21+8p10T22+4p11T23+p12T24 1 + 4 T + 8 T^{2} - 20 T^{3} - 17958 T^{4} - 32004 T^{5} + 15848 T^{6} + 4133236 T^{7} + 241837519 T^{8} + 226090952 T^{9} - 316274672 T^{10} - 41141248808 T^{11} - 2546305955668 T^{12} - 41141248808 p T^{13} - 316274672 p^{2} T^{14} + 226090952 p^{3} T^{15} + 241837519 p^{4} T^{16} + 4133236 p^{5} T^{17} + 15848 p^{6} T^{18} - 32004 p^{7} T^{19} - 17958 p^{8} T^{20} - 20 p^{9} T^{21} + 8 p^{10} T^{22} + 4 p^{11} T^{23} + p^{12} T^{24}
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   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

−3.75600823870450447334562151096, −3.69086205948017133142668399181, −3.57083841786235917877760601424, −3.45882879475510456915603280400, −3.28986629576383943473126540518, −3.24758644841945179823625589409, −2.90861653426051887263425095461, −2.90247002571030957063690467903, −2.82596095726175182370677088746, −2.57896880192536085953765257936, −2.44791485572697754172012076659, −2.41923256804051677742879643610, −2.26689207800569984707263466951, −2.21478924343758568121041337397, −2.20640820135803467913573115292, −2.13474387297100110461170401022, −2.13296026176283081126478299432, −1.94812258682500143143470157713, −1.73346879741093572899547184143, −1.72211865247491794086935508072, −1.40601133373346756352026358988, −1.10099095083585080560776985323, −0.798235789122958250204344552123, −0.53938213434604074267978219897, −0.45878954507378967587357711680, 0.45878954507378967587357711680, 0.53938213434604074267978219897, 0.798235789122958250204344552123, 1.10099095083585080560776985323, 1.40601133373346756352026358988, 1.72211865247491794086935508072, 1.73346879741093572899547184143, 1.94812258682500143143470157713, 2.13296026176283081126478299432, 2.13474387297100110461170401022, 2.20640820135803467913573115292, 2.21478924343758568121041337397, 2.26689207800569984707263466951, 2.41923256804051677742879643610, 2.44791485572697754172012076659, 2.57896880192536085953765257936, 2.82596095726175182370677088746, 2.90247002571030957063690467903, 2.90861653426051887263425095461, 3.24758644841945179823625589409, 3.28986629576383943473126540518, 3.45882879475510456915603280400, 3.57083841786235917877760601424, 3.69086205948017133142668399181, 3.75600823870450447334562151096

Graph of the ZZ-function along the critical line

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