L(s) = 1 | − 1.63e4·2-s − 3.34e6·3-s + 2.01e8·4-s + 2.44e9·5-s + 5.47e10·6-s − 5.87e10·7-s − 2.19e12·8-s − 3.43e12·9-s − 4.00e13·10-s − 1.48e14·11-s − 6.72e14·12-s + 7.00e14·13-s + 9.61e14·14-s − 8.15e15·15-s + 2.25e16·16-s + 3.83e16·17-s + 5.62e16·18-s + 2.31e17·19-s + 4.91e17·20-s + 1.96e17·21-s + 2.43e18·22-s − 1.05e18·23-s + 7.34e18·24-s + 4.47e18·25-s − 1.14e19·26-s + 3.47e19·27-s − 1.18e19·28-s + ⋯ |
L(s) = 1 | − 1.41·2-s − 1.20·3-s + 3/2·4-s + 0.894·5-s + 1.71·6-s − 0.229·7-s − 1.41·8-s − 0.450·9-s − 1.26·10-s − 1.29·11-s − 1.81·12-s + 0.641·13-s + 0.323·14-s − 1.08·15-s + 5/4·16-s + 0.939·17-s + 0.636·18-s + 1.26·19-s + 1.34·20-s + 0.277·21-s + 1.83·22-s − 0.435·23-s + 1.71·24-s + 3/5·25-s − 0.906·26-s + 1.64·27-s − 0.343·28-s + ⋯ |
Λ(s)=(=(100s/2ΓC(s)2L(s)Λ(28−s)
Λ(s)=(=(100s/2ΓC(s+27/2)2L(s)Λ(1−s)
Degree: |
4 |
Conductor: |
100
= 22⋅52
|
Sign: |
1
|
Analytic conductor: |
2133.10 |
Root analytic conductor: |
6.79599 |
Motivic weight: |
27 |
Rational: |
yes |
Arithmetic: |
yes |
Character: |
Trivial
|
Primitive: |
no
|
Self-dual: |
yes
|
Analytic rank: |
2
|
Selberg data: |
(4, 100, ( :27/2,27/2), 1)
|
Particular Values
L(14) |
= |
0 |
L(21) |
= |
0 |
L(229) |
|
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
−13.97756821922551499166121253593, −13.49467399399764701293582925178, −12.08816433248692243662481854452, −12.07522271487377906900866341107, −10.82351813602922164737248597228, −10.72478428543871405819678904805, −9.840799220441137020884259230077, −9.349324796154985816624834683360, −8.190493865173437379062652528635, −7.926125608269574303601018424469, −6.61010164811198320189881389167, −6.23138509488249428180098377454, −5.44049308993059938142364929025, −5.03604025707529726661101869382, −3.05300331982851093961720436755, −2.88574255606246008863666505496, −1.56573529971417964589857727623, −1.13126610315316071062535865744, 0, 0,
1.13126610315316071062535865744, 1.56573529971417964589857727623, 2.88574255606246008863666505496, 3.05300331982851093961720436755, 5.03604025707529726661101869382, 5.44049308993059938142364929025, 6.23138509488249428180098377454, 6.61010164811198320189881389167, 7.926125608269574303601018424469, 8.190493865173437379062652528635, 9.349324796154985816624834683360, 9.840799220441137020884259230077, 10.72478428543871405819678904805, 10.82351813602922164737248597228, 12.07522271487377906900866341107, 12.08816433248692243662481854452, 13.49467399399764701293582925178, 13.97756821922551499166121253593