L(s) = 1 | + (0.173 − 0.984i)2-s + (−0.939 − 0.342i)4-s + (−0.939 − 0.342i)5-s + (0.173 − 0.984i)7-s + (−0.5 + 0.866i)8-s + (−0.5 + 0.866i)10-s + (0.173 − 0.984i)11-s + (0.766 − 0.642i)13-s + (−0.939 − 0.342i)14-s + (0.766 + 0.642i)16-s + 17-s + (−0.5 − 0.866i)19-s + (0.766 + 0.642i)20-s + (−0.939 − 0.342i)22-s + (−0.939 − 0.342i)23-s + ⋯ |
L(s) = 1 | + (0.173 − 0.984i)2-s + (−0.939 − 0.342i)4-s + (−0.939 − 0.342i)5-s + (0.173 − 0.984i)7-s + (−0.5 + 0.866i)8-s + (−0.5 + 0.866i)10-s + (0.173 − 0.984i)11-s + (0.766 − 0.642i)13-s + (−0.939 − 0.342i)14-s + (0.766 + 0.642i)16-s + 17-s + (−0.5 − 0.866i)19-s + (0.766 + 0.642i)20-s + (−0.939 − 0.342i)22-s + (−0.939 − 0.342i)23-s + ⋯ |
Λ(s)=(=(837s/2ΓR(s)L(s)(−0.832+0.554i)Λ(1−s)
Λ(s)=(=(837s/2ΓR(s)L(s)(−0.832+0.554i)Λ(1−s)
Degree: |
1 |
Conductor: |
837
= 33⋅31
|
Sign: |
−0.832+0.554i
|
Analytic conductor: |
3.88701 |
Root analytic conductor: |
3.88701 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ837(211,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 837, (0: ), −0.832+0.554i)
|
Particular Values
L(21) |
≈ |
−0.2795210902−0.9233743951i |
L(21) |
≈ |
−0.2795210902−0.9233743951i |
L(1) |
≈ |
0.5426009565−0.7033947860i |
L(1) |
≈ |
0.5426009565−0.7033947860i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 31 | 1 |
good | 2 | 1+(0.173−0.984i)T |
| 5 | 1+(−0.939−0.342i)T |
| 7 | 1+(0.173−0.984i)T |
| 11 | 1+(0.173−0.984i)T |
| 13 | 1+(0.766−0.642i)T |
| 17 | 1+T |
| 19 | 1+(−0.5−0.866i)T |
| 23 | 1+(−0.939−0.342i)T |
| 29 | 1+(0.173−0.984i)T |
| 37 | 1+T |
| 41 | 1+(0.766−0.642i)T |
| 43 | 1+(−0.939+0.342i)T |
| 47 | 1+(−0.939+0.342i)T |
| 53 | 1+(−0.5−0.866i)T |
| 59 | 1+(0.173+0.984i)T |
| 61 | 1+(−0.939+0.342i)T |
| 67 | 1+(0.766−0.642i)T |
| 71 | 1+(−0.5+0.866i)T |
| 73 | 1+T |
| 79 | 1+(0.766+0.642i)T |
| 83 | 1+(−0.939+0.342i)T |
| 89 | 1+(−0.5+0.866i)T |
| 97 | 1+(0.766+0.642i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−22.93790829920366788525905438166, −21.939875640694783630734810082721, −21.30854428164351125543199610951, −20.20405667262241832998589474945, −19.12742451415380360807816527542, −18.44322257744090815977976263208, −17.9867722002471993522661394528, −16.713468150729921582622048784986, −16.12117778895505281773922771506, −15.33858582771681524350132185597, −14.67987132487743595391619165763, −14.13626580218933184470800990099, −12.739837831617862575105246735887, −12.216216612071731858242033306374, −11.41801023932726726889626560454, −10.09106174774072470267657032157, −9.207676615367139353633210380164, −8.23689005484238027986657768347, −7.743687598910512814422693765034, −6.66937581984665671939995375556, −5.96168583482975737174752586078, −4.87510911381457181264032661248, −4.029549035699780651224572515, −3.16631399880366833335798775406, −1.62835854754914343868293388592,
0.48394942690683491190607863022, 1.231716236662423631446878509217, 2.83487595861323451039271446472, 3.72848300904082654645183362569, 4.26653286085631802008983425116, 5.34822994791832354319972787484, 6.43021109922029242548751440238, 7.976304228825323436498191744242, 8.21802116243810890104988520393, 9.409873251142760890163008837919, 10.42465469777515193763704456146, 11.11141096128315099257366901685, 11.69049131684138389031946384185, 12.70947005529559737326655129279, 13.40652209432363653789820155216, 14.16098123049558390037482613040, 15.073645110815418239343942450221, 16.14255050268134029025633882242, 16.86840519319257338713749252069, 17.84818612842030176446563297646, 18.7225239251309307747179809772, 19.5461401484713571070215492999, 19.97680094291757290367642240896, 20.85383270058277845501886021589, 21.40902132411900585842731349750