L(s) = 1 | + (0.999 + 0.0245i)2-s + (−0.376 + 0.926i)3-s + (0.998 + 0.0491i)4-s + (−0.163 + 0.986i)5-s + (−0.399 + 0.916i)6-s + (0.997 − 0.0687i)7-s + (0.997 + 0.0736i)8-s + (−0.716 − 0.697i)9-s + (−0.188 + 0.982i)10-s + (0.625 − 0.780i)11-s + (−0.421 + 0.906i)12-s + (−0.652 − 0.758i)13-s + (0.999 − 0.0442i)14-s + (−0.852 − 0.523i)15-s + (0.995 + 0.0981i)16-s + (0.723 + 0.690i)17-s + ⋯ |
L(s) = 1 | + (0.999 + 0.0245i)2-s + (−0.376 + 0.926i)3-s + (0.998 + 0.0491i)4-s + (−0.163 + 0.986i)5-s + (−0.399 + 0.916i)6-s + (0.997 − 0.0687i)7-s + (0.997 + 0.0736i)8-s + (−0.716 − 0.697i)9-s + (−0.188 + 0.982i)10-s + (0.625 − 0.780i)11-s + (−0.421 + 0.906i)12-s + (−0.652 − 0.758i)13-s + (0.999 − 0.0442i)14-s + (−0.852 − 0.523i)15-s + (0.995 + 0.0981i)16-s + (0.723 + 0.690i)17-s + ⋯ |
Λ(s)=(=(2557s/2ΓR(s)L(s)(0.647+0.761i)Λ(1−s)
Λ(s)=(=(2557s/2ΓR(s)L(s)(0.647+0.761i)Λ(1−s)
Degree: |
1 |
Conductor: |
2557
|
Sign: |
0.647+0.761i
|
Analytic conductor: |
11.8746 |
Root analytic conductor: |
11.8746 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2557(1024,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 2557, (0: ), 0.647+0.761i)
|
Particular Values
L(21) |
≈ |
3.168126170+1.465141377i |
L(21) |
≈ |
3.168126170+1.465141377i |
L(1) |
≈ |
1.907838869+0.6494351277i |
L(1) |
≈ |
1.907838869+0.6494351277i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2557 | 1 |
good | 2 | 1+(0.999+0.0245i)T |
| 3 | 1+(−0.376+0.926i)T |
| 5 | 1+(−0.163+0.986i)T |
| 7 | 1+(0.997−0.0687i)T |
| 11 | 1+(0.625−0.780i)T |
| 13 | 1+(−0.652−0.758i)T |
| 17 | 1+(0.723+0.690i)T |
| 19 | 1+(0.316−0.948i)T |
| 23 | 1+(0.288−0.957i)T |
| 29 | 1+(−0.833+0.552i)T |
| 31 | 1+(−0.941−0.337i)T |
| 37 | 1+(0.808−0.588i)T |
| 41 | 1+(0.983+0.180i)T |
| 43 | 1+(0.302+0.953i)T |
| 47 | 1+(0.652−0.758i)T |
| 53 | 1+(−0.367+0.930i)T |
| 59 | 1+(0.867+0.497i)T |
| 61 | 1+(0.984−0.176i)T |
| 67 | 1+(0.946+0.323i)T |
| 71 | 1+(−0.681+0.731i)T |
| 73 | 1+(−0.0712−0.997i)T |
| 79 | 1+(−0.759+0.650i)T |
| 83 | 1+(−0.969+0.243i)T |
| 89 | 1+(0.864−0.502i)T |
| 97 | 1+(−0.709−0.704i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−19.35154331497472180770516217705, −18.79225694761908964327421085514, −17.66128328678139289116513205010, −17.107229096669617077523000199609, −16.55872990642417657057141591017, −15.78375678495109277995903705277, −14.58741515468172223890826495089, −14.393654010243148278308518830645, −13.52340674181893381372043821886, −12.73247145530824249131491392783, −12.16209979331469440201833765787, −11.66478402539764162173989381700, −11.22667205306990379718762499290, −9.910700306706066731120036951288, −9.08719298042319109130691572248, −7.86104832509135416349665707284, −7.55981985255908429547031741368, −6.81471174608863476899993015025, −5.59670394233836366994343627153, −5.34453358660579760247255509062, −4.47999805200553908344532921688, −3.759294272377352677313578589209, −2.35395791094079317968316788864, −1.690296351590607385631773326908, −1.10734199031522568235584043016,
0.96398893087729547446126398731, 2.38996243698242909034504092504, 3.05864417726710304189918942477, 3.88683304312991433176858606112, 4.44642014655177608914834542683, 5.53015103498019650402993804875, 5.78732227227171010271350929200, 6.87063993054943394652772627782, 7.57884293012718184499153679027, 8.45037356865529025004238788295, 9.55845749859105170586145286798, 10.508956116925095478487629415361, 11.02163274850482372474307982885, 11.36915637707140857316139868101, 12.20479694927843117331333210472, 13.072279139241911065103157831121, 14.22513255934227536692458365410, 14.66096395160104813110753849027, 14.87141555809546238781839359856, 15.78254084129263976655828083795, 16.56067098257232481217689417100, 17.18928577680974961669925809395, 17.91625208573045188999812479847, 18.88140860833991509747336291758, 19.8317876808738562312347127773