L(s) = 1 | + (−0.580 − 0.814i)2-s + (0.502 − 0.864i)3-s + (−0.326 + 0.945i)4-s + (−0.995 + 0.0919i)6-s + (−0.507 + 0.861i)7-s + (0.959 − 0.282i)8-s + (−0.494 − 0.869i)9-s + (−0.783 + 0.621i)11-s + (0.652 + 0.757i)12-s + (−0.856 + 0.516i)13-s + (0.996 − 0.0868i)14-s + (−0.786 − 0.617i)16-s + (−0.940 + 0.340i)17-s + (−0.421 + 0.906i)18-s + (0.0306 − 0.999i)19-s + ⋯ |
L(s) = 1 | + (−0.580 − 0.814i)2-s + (0.502 − 0.864i)3-s + (−0.326 + 0.945i)4-s + (−0.995 + 0.0919i)6-s + (−0.507 + 0.861i)7-s + (0.959 − 0.282i)8-s + (−0.494 − 0.869i)9-s + (−0.783 + 0.621i)11-s + (0.652 + 0.757i)12-s + (−0.856 + 0.516i)13-s + (0.996 − 0.0868i)14-s + (−0.786 − 0.617i)16-s + (−0.940 + 0.340i)17-s + (−0.421 + 0.906i)18-s + (0.0306 − 0.999i)19-s + ⋯ |
Λ(s)=(=(6145s/2ΓR(s)L(s)(0.472−0.881i)Λ(1−s)
Λ(s)=(=(6145s/2ΓR(s)L(s)(0.472−0.881i)Λ(1−s)
Degree: |
1 |
Conductor: |
6145
= 5⋅1229
|
Sign: |
0.472−0.881i
|
Analytic conductor: |
28.5372 |
Root analytic conductor: |
28.5372 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ6145(1058,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 6145, (0: ), 0.472−0.881i)
|
Particular Values
L(21) |
≈ |
0.5319752965−0.3184594073i |
L(21) |
≈ |
0.5319752965−0.3184594073i |
L(1) |
≈ |
0.5685109529−0.2999685124i |
L(1) |
≈ |
0.5685109529−0.2999685124i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1 |
| 1229 | 1 |
good | 2 | 1+(−0.580−0.814i)T |
| 3 | 1+(0.502−0.864i)T |
| 7 | 1+(−0.507+0.861i)T |
| 11 | 1+(−0.783+0.621i)T |
| 13 | 1+(−0.856+0.516i)T |
| 17 | 1+(−0.940+0.340i)T |
| 19 | 1+(0.0306−0.999i)T |
| 23 | 1+(0.0664−0.997i)T |
| 29 | 1+(−0.444+0.895i)T |
| 31 | 1+(−0.719−0.694i)T |
| 37 | 1+(0.989−0.142i)T |
| 41 | 1+(−0.946+0.321i)T |
| 43 | 1+(−0.999+0.0255i)T |
| 47 | 1+(0.122−0.992i)T |
| 53 | 1+(0.262+0.964i)T |
| 59 | 1+(−0.307+0.951i)T |
| 61 | 1+(0.297−0.954i)T |
| 67 | 1+(−0.360−0.932i)T |
| 71 | 1+(0.808+0.588i)T |
| 73 | 1+(0.934−0.355i)T |
| 79 | 1+(−0.959−0.282i)T |
| 83 | 1+(0.277+0.960i)T |
| 89 | 1+(−0.257−0.966i)T |
| 97 | 1+(0.831+0.555i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−17.55041401314568534994580488639, −16.99600521110305104013773356768, −16.38669758763412374753001074670, −15.91190823690152927718699264988, −15.30909586428321947040805063284, −14.69914244657928110179524018923, −13.99961508543527597588673673230, −13.42087969000973751459253158234, −12.93306119906143305790631130714, −11.52570619658309596547578573694, −10.88742859179347779527676536171, −10.21760791928908637583349431115, −9.82458876334856559616086329587, −9.2187856905840488391308796009, −8.350596716429191713951060634536, −7.8162067990466725706934399607, −7.27933778521859868513079027860, −6.386244872067486463670417430537, −5.51025372122959945917842107567, −5.047736275729757027832833593115, −4.18180742081836033299138908009, −3.47823476236066734458302064481, −2.62811171900313289700656673900, −1.67025427861072879306518076088, −0.368045378690619827414812590081,
0.421027170833228002698477649000, 1.7458339174978584147630929789, 2.30199848491676097836843164534, 2.66398275502964029221177713854, 3.516102484350772875825796272331, 4.5163441991625161789428567559, 5.217021458954842147290851689876, 6.4122022403937383941477381166, 6.97162310241425966102947095832, 7.585087484388624218922176611382, 8.409763117773822325629833038821, 8.96742561384977022942682541553, 9.44193727508466683434075425542, 10.17496096770014878417455235267, 11.0723162075178658303584474623, 11.7164423408376637194765755703, 12.37243787411230571091325076663, 12.93805893895929074734132829988, 13.20411681259893031740736725535, 14.13369984019420661425548374699, 15.09149535069831728417780685968, 15.382160049173301214974389731432, 16.57845183643142231077052229922, 17.000334394405997554839833815870, 18.00143214487960113419836568395