L(s) = 1 | − 4.09e3·2-s − 1.85e4·3-s + 1.25e7·4-s + 9.76e7·5-s + 7.58e7·6-s − 4.41e9·7-s − 3.43e10·8-s − 1.31e11·9-s − 4.00e11·10-s + 1.95e11·11-s − 2.32e11·12-s + 2.58e12·13-s + 1.80e13·14-s − 1.80e12·15-s + 8.79e13·16-s + 1.31e14·17-s + 5.36e14·18-s − 1.76e12·19-s + 1.22e15·20-s + 8.17e13·21-s − 7.98e14·22-s + 4.01e15·23-s + 6.36e14·24-s + 7.15e15·25-s − 1.05e16·26-s + 3.11e15·27-s − 5.55e16·28-s + ⋯ |
L(s) = 1 | − 1.41·2-s − 0.0603·3-s + 3/2·4-s + 0.894·5-s + 0.0853·6-s − 0.844·7-s − 1.41·8-s − 1.39·9-s − 1.26·10-s + 0.206·11-s − 0.0905·12-s + 0.399·13-s + 1.19·14-s − 0.0539·15-s + 5/4·16-s + 0.931·17-s + 1.96·18-s − 0.00346·19-s + 1.34·20-s + 0.0509·21-s − 0.291·22-s + 0.878·23-s + 0.0853·24-s + 3/5·25-s − 0.565·26-s + 0.107·27-s − 1.26·28-s + ⋯ |
Λ(s)=(=(100s/2ΓC(s)2L(s)Λ(24−s)
Λ(s)=(=(100s/2ΓC(s+23/2)2L(s)Λ(1−s)
Degree: |
4 |
Conductor: |
100
= 22⋅52
|
Sign: |
1
|
Analytic conductor: |
1123.61 |
Root analytic conductor: |
5.78968 |
Motivic weight: |
23 |
Rational: |
yes |
Arithmetic: |
yes |
Character: |
Trivial
|
Primitive: |
no
|
Self-dual: |
yes
|
Analytic rank: |
2
|
Selberg data: |
(4, 100, ( :23/2,23/2), 1)
|
Particular Values
L(12) |
= |
0 |
L(21) |
= |
0 |
L(225) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1
L(s)=p∏ j=1∏4(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−14.69390718322505392582060265338, −14.58169983205091940843880867931, −13.25939727512564272838476998147, −12.79049491196663800966999533364, −11.42728542323827566773725694286, −11.35150879129843082742683915823, −10.08346713543973632897355434531, −9.828036761207862126136814570754, −8.795024627342551685736053765080, −8.624538790419002043482374226643, −7.35627020794432526751101012849, −6.69201322082391387620331792881, −5.77645227090916990841145681726, −5.40606186739822459580152865245, −3.38027992499909036996118919657, −3.06197370869439677911210663828, −1.87873178612466061232391881201, −1.36549710130965868341011250098, 0, 0,
1.36549710130965868341011250098, 1.87873178612466061232391881201, 3.06197370869439677911210663828, 3.38027992499909036996118919657, 5.40606186739822459580152865245, 5.77645227090916990841145681726, 6.69201322082391387620331792881, 7.35627020794432526751101012849, 8.624538790419002043482374226643, 8.795024627342551685736053765080, 9.828036761207862126136814570754, 10.08346713543973632897355434531, 11.35150879129843082742683915823, 11.42728542323827566773725694286, 12.79049491196663800966999533364, 13.25939727512564272838476998147, 14.58169983205091940843880867931, 14.69390718322505392582060265338