L(s) = 1 | − 4.09e3·2-s + 6.86e5·3-s + 1.25e7·4-s − 9.76e7·5-s − 2.81e9·6-s − 3.52e9·7-s − 3.43e10·8-s + 2.25e11·9-s + 4.00e11·10-s + 9.36e11·11-s + 8.63e12·12-s + 9.96e12·13-s + 1.44e13·14-s − 6.70e13·15-s + 8.79e13·16-s − 1.60e12·17-s − 9.25e14·18-s − 2.56e14·19-s − 1.22e15·20-s − 2.42e15·21-s − 3.83e15·22-s + 3.59e15·23-s − 2.35e16·24-s + 7.15e15·25-s − 4.08e16·26-s + 5.13e16·27-s − 4.44e16·28-s + ⋯ |
L(s) = 1 | − 1.41·2-s + 2.23·3-s + 3/2·4-s − 0.894·5-s − 3.16·6-s − 0.674·7-s − 1.41·8-s + 2.40·9-s + 1.26·10-s + 0.989·11-s + 3.35·12-s + 1.54·13-s + 0.954·14-s − 2.00·15-s + 5/4·16-s − 0.0113·17-s − 3.39·18-s − 0.505·19-s − 1.34·20-s − 1.50·21-s − 1.39·22-s + 0.786·23-s − 3.16·24-s + 3/5·25-s − 2.18·26-s + 1.77·27-s − 1.01·28-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: |
0
|
Selberg data: |
(4, 100, ( :23/2,23/2), 1)
|
Particular Values
L(12) |
≈ |
4.041866136 |
L(21) |
≈ |
4.041866136 |
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
−15.50997745658585319492659493277, −15.19117359675760961223231492886, −14.13413588294952209331189303042, −13.83123498308352105226391530833, −12.69464495104874652409336596793, −11.93366291452725969285456019802, −10.94404979533563908472560842663, −10.21339686114719998896677824859, −9.152373569808496861084334929293, −8.993758261191315894266003781862, −8.115597605634270287552641704517, −8.101830958496358041931908930425, −6.77114373542903646842451922125, −6.41371313771799990709877614830, −4.27934146385728398294270129474, −3.56112422779799500224801165446, −2.88858060961328901916219702569, −2.40954745454556075414213239421, −1.05751238210411616523404130839, −0.863674310779455764603152532422,
0.863674310779455764603152532422, 1.05751238210411616523404130839, 2.40954745454556075414213239421, 2.88858060961328901916219702569, 3.56112422779799500224801165446, 4.27934146385728398294270129474, 6.41371313771799990709877614830, 6.77114373542903646842451922125, 8.101830958496358041931908930425, 8.115597605634270287552641704517, 8.993758261191315894266003781862, 9.152373569808496861084334929293, 10.21339686114719998896677824859, 10.94404979533563908472560842663, 11.93366291452725969285456019802, 12.69464495104874652409336596793, 13.83123498308352105226391530833, 14.13413588294952209331189303042, 15.19117359675760961223231492886, 15.50997745658585319492659493277