L(s) = 1 | + 4.09e3·2-s − 9.18e4·3-s + 1.25e7·4-s − 9.76e7·5-s − 3.76e8·6-s + 2.14e9·7-s + 3.43e10·8-s − 9.60e10·9-s − 4.00e11·10-s − 6.92e11·11-s − 1.15e12·12-s − 1.70e12·13-s + 8.79e12·14-s + 8.97e12·15-s + 8.79e13·16-s − 9.31e13·17-s − 3.93e14·18-s − 9.70e14·19-s − 1.22e15·20-s − 1.97e14·21-s − 2.83e15·22-s − 9.62e14·23-s − 3.15e15·24-s + 7.15e15·25-s − 6.99e15·26-s + 9.76e15·27-s + 2.70e16·28-s + ⋯ |
L(s) = 1 | + 1.41·2-s − 0.299·3-s + 3/2·4-s − 0.894·5-s − 0.423·6-s + 0.410·7-s + 1.41·8-s − 1.01·9-s − 1.26·10-s − 0.731·11-s − 0.449·12-s − 0.264·13-s + 0.580·14-s + 0.267·15-s + 5/4·16-s − 0.659·17-s − 1.44·18-s − 1.91·19-s − 1.34·20-s − 0.122·21-s − 1.03·22-s − 0.210·23-s − 0.423·24-s + 3/5·25-s − 0.373·26-s + 0.338·27-s + 0.615·28-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
−14.55430448726141694530821031557, −14.52714145053782251705922784833, −13.20883757430877632738312681175, −12.92354923669322687883018516492, −11.95917950019260127343796694263, −11.43494994566668803452833107465, −10.94698648401794219119414465327, −10.13369762318517327652199063516, −8.392302418733245324373918091481, −8.288694230353171644476465211036, −6.94103249727586938170408291690, −6.49645296786283932791073601534, −5.23431630705502910321398833247, −5.06211035121655743552037750147, −3.98167045682760011718907147567, −3.39131263719406303899277868045, −2.39426470800482057139001456287, −1.75844881679893128551930352218, 0, 0,
1.75844881679893128551930352218, 2.39426470800482057139001456287, 3.39131263719406303899277868045, 3.98167045682760011718907147567, 5.06211035121655743552037750147, 5.23431630705502910321398833247, 6.49645296786283932791073601534, 6.94103249727586938170408291690, 8.288694230353171644476465211036, 8.392302418733245324373918091481, 10.13369762318517327652199063516, 10.94698648401794219119414465327, 11.43494994566668803452833107465, 11.95917950019260127343796694263, 12.92354923669322687883018516492, 13.20883757430877632738312681175, 14.52714145053782251705922784833, 14.55430448726141694530821031557