L(s) = 1 | + 897·2-s − 4.37e6·4-s − 3.90e7·5-s − 2.34e8·7-s − 4.81e9·8-s − 3.50e10·10-s − 3.14e10·11-s − 2.70e10·13-s − 2.10e11·14-s + 6.70e12·16-s + 2.94e12·17-s − 2.42e13·19-s + 1.70e14·20-s − 2.82e13·22-s − 1.03e13·23-s + 9.53e14·25-s − 2.42e13·26-s + 1.02e15·28-s − 4.72e15·29-s − 1.09e15·31-s + 8.96e15·32-s + 2.64e15·34-s + 9.16e15·35-s + 4.81e15·37-s − 2.17e16·38-s + 1.88e17·40-s − 2.89e17·41-s + ⋯ |
L(s) = 1 | + 0.619·2-s − 2.08·4-s − 1.78·5-s − 0.313·7-s − 1.58·8-s − 1.10·10-s − 0.366·11-s − 0.0543·13-s − 0.194·14-s + 1.52·16-s + 0.354·17-s − 0.908·19-s + 3.73·20-s − 0.226·22-s − 0.0520·23-s + 2·25-s − 0.0336·26-s + 0.654·28-s − 2.08·29-s − 0.239·31-s + 1.40·32-s + 0.219·34-s + 0.561·35-s + 0.164·37-s − 0.562·38-s + 2.83·40-s − 3.37·41-s + ⋯ |
Λ(s)=(=(4100625s/2ΓC(s)4L(s)Λ(22−s)
Λ(s)=(=(4100625s/2ΓC(s+21/2)4L(s)Λ(1−s)
Degree: |
8 |
Conductor: |
4100625
= 38⋅54
|
Sign: |
1
|
Analytic conductor: |
2.50170×108 |
Root analytic conductor: |
11.2144 |
Motivic weight: |
21 |
Rational: |
yes |
Arithmetic: |
yes |
Character: |
Trivial
|
Primitive: |
no
|
Self-dual: |
yes
|
Analytic rank: |
0
|
Selberg data: |
(8, 4100625, ( :21/2,21/2,21/2,21/2), 1)
|
Particular Values
L(11) |
≈ |
0.01920876667 |
L(21) |
≈ |
0.01920876667 |
L(223) |
|
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
−7.925661808048971603484989154936, −7.47400900377655106709746858276, −7.11931413950061897356061873488, −6.71548747807764158673202294660, −6.69661646011760205096314348576, −6.08379063346739706529498170478, −5.49282207059025500609540872302, −5.48762596346637760272339649288, −5.37802426682904202908343187039, −4.64948348735575554198424198864, −4.55586248848710531257708936492, −4.28034506390677916071463978657, −4.25595363719694055877070508889, −3.83725941632738691745049331827, −3.34414659808914850725861468710, −3.21115415125424645186078196694, −3.20942321412360675521358032589, −2.63281472626392836416860681181, −1.98420057947417468079924546350, −1.67414911027982636189640623942, −1.63762515646515751208863686285, −0.838567829295619169433666960052, −0.50659759460686242462831000900, −0.44074888670186003444212388732, −0.03115564611230382885270971954,
0.03115564611230382885270971954, 0.44074888670186003444212388732, 0.50659759460686242462831000900, 0.838567829295619169433666960052, 1.63762515646515751208863686285, 1.67414911027982636189640623942, 1.98420057947417468079924546350, 2.63281472626392836416860681181, 3.20942321412360675521358032589, 3.21115415125424645186078196694, 3.34414659808914850725861468710, 3.83725941632738691745049331827, 4.25595363719694055877070508889, 4.28034506390677916071463978657, 4.55586248848710531257708936492, 4.64948348735575554198424198864, 5.37802426682904202908343187039, 5.48762596346637760272339649288, 5.49282207059025500609540872302, 6.08379063346739706529498170478, 6.69661646011760205096314348576, 6.71548747807764158673202294660, 7.11931413950061897356061873488, 7.47400900377655106709746858276, 7.925661808048971603484989154936