L(s) = 1 | − 8.38e6·4-s + 2.00e11·9-s − 1.38e12·11-s + 5.27e13·16-s + 1.94e15·19-s + 8.07e16·29-s − 1.09e17·31-s − 1.68e18·36-s − 8.54e18·41-s + 1.16e19·44-s + 6.48e19·49-s − 8.03e19·59-s + 1.60e21·61-s − 2.95e20·64-s + 1.43e21·71-s − 1.62e22·76-s + 1.41e22·79-s + 1.31e22·81-s + 3.96e20·89-s − 2.77e23·99-s + 9.33e22·101-s + 1.20e24·109-s − 6.77e23·116-s − 2.23e24·121-s + 9.19e23·124-s + 127-s + 131-s + ⋯ |
L(s) = 1 | − 4-s + 2.12·9-s − 1.46·11-s + 3/4·16-s + 3.82·19-s + 1.22·29-s − 0.774·31-s − 2.12·36-s − 2.42·41-s + 1.46·44-s + 2.37·49-s − 0.347·59-s + 4.72·61-s − 1/2·64-s + 0.737·71-s − 3.82·76-s + 2.12·79-s + 1.48·81-s + 0.0151·89-s − 3.11·99-s + 0.832·101-s + 4.48·109-s − 1.22·116-s − 2.49·121-s + 0.774·124-s + ⋯ |
Λ(s)=(=(6250000s/2ΓC(s)4L(s)Λ(24−s)
Λ(s)=(=(6250000s/2ΓC(s+23/2)4L(s)Λ(1−s)
Degree: |
8 |
Conductor: |
6250000
= 24⋅58
|
Sign: |
1
|
Analytic conductor: |
7.89072×108 |
Root analytic conductor: |
12.9461 |
Motivic weight: |
23 |
Rational: |
yes |
Arithmetic: |
yes |
Character: |
Trivial
|
Primitive: |
no
|
Self-dual: |
yes
|
Analytic rank: |
0
|
Selberg data: |
(8, 6250000, ( :23/2,23/2,23/2,23/2), 1)
|
Particular Values
L(12) |
≈ |
0.7733313634 |
L(21) |
≈ |
0.7733313634 |
L(225) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1
L(s)=p∏ j=1∏8(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−7.26267989440015201953483595839, −7.13604840584669986906481464201, −7.12509578474095856742407051083, −6.38558577042684424347480818659, −6.28342854487835865733797376851, −5.61245033721831569276492278109, −5.50023356415719037548480259330, −5.16056459698266726918008805581, −4.91063633745120909202895613576, −4.85980729291180296776594604691, −4.68273509971737381633048310653, −3.80144027922060055569715841749, −3.72074234548431133137519782365, −3.64688561076860561966045627701, −3.55381115303999432463981783678, −2.75033803246208929373718409054, −2.68844007942149560517496901297, −2.24880426914318431734225795638, −2.11637932776584669049868861872, −1.39185870470309711112928146636, −1.29979859032035994580253769868, −1.05606265038972972883681836332, −0.842146679937357100442094222784, −0.61085242407239084228608677716, −0.07813250672482166511139869778,
0.07813250672482166511139869778, 0.61085242407239084228608677716, 0.842146679937357100442094222784, 1.05606265038972972883681836332, 1.29979859032035994580253769868, 1.39185870470309711112928146636, 2.11637932776584669049868861872, 2.24880426914318431734225795638, 2.68844007942149560517496901297, 2.75033803246208929373718409054, 3.55381115303999432463981783678, 3.64688561076860561966045627701, 3.72074234548431133137519782365, 3.80144027922060055569715841749, 4.68273509971737381633048310653, 4.85980729291180296776594604691, 4.91063633745120909202895613576, 5.16056459698266726918008805581, 5.50023356415719037548480259330, 5.61245033721831569276492278109, 6.28342854487835865733797376851, 6.38558577042684424347480818659, 7.12509578474095856742407051083, 7.13604840584669986906481464201, 7.26267989440015201953483595839