L(s) = 1 | + (−0.995 − 0.0995i)3-s + (0.797 + 0.603i)4-s + (0.878 + 0.478i)7-s + (0.980 + 0.198i)9-s + (−0.733 − 0.680i)12-s + (0.0291 + 1.16i)13-s + (0.270 + 0.962i)16-s + (−0.623 + 0.781i)19-s + (−0.826 − 0.563i)21-s + (0.661 − 0.749i)25-s + (−0.955 − 0.294i)27-s + (0.411 + 0.911i)28-s − 0.248·31-s + (0.661 + 0.749i)36-s + (−0.355 − 1.15i)37-s + ⋯ |
L(s) = 1 | + (−0.995 − 0.0995i)3-s + (0.797 + 0.603i)4-s + (0.878 + 0.478i)7-s + (0.980 + 0.198i)9-s + (−0.733 − 0.680i)12-s + (0.0291 + 1.16i)13-s + (0.270 + 0.962i)16-s + (−0.623 + 0.781i)19-s + (−0.826 − 0.563i)21-s + (0.661 − 0.749i)25-s + (−0.955 − 0.294i)27-s + (0.411 + 0.911i)28-s − 0.248·31-s + (0.661 + 0.749i)36-s + (−0.355 − 1.15i)37-s + ⋯ |
Λ(s)=(=(2793s/2ΓC(s)L(s)(0.320−0.947i)Λ(1−s)
Λ(s)=(=(2793s/2ΓC(s)L(s)(0.320−0.947i)Λ(1−s)
Degree: |
2 |
Conductor: |
2793
= 3⋅72⋅19
|
Sign: |
0.320−0.947i
|
Analytic conductor: |
1.39388 |
Root analytic conductor: |
1.18063 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2793(59,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 2793, ( :0), 0.320−0.947i)
|
Particular Values
L(21) |
≈ |
1.168127500 |
L(21) |
≈ |
1.168127500 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1+(0.995+0.0995i)T |
| 7 | 1+(−0.878−0.478i)T |
| 19 | 1+(0.623−0.781i)T |
good | 2 | 1+(−0.797−0.603i)T2 |
| 5 | 1+(−0.661+0.749i)T2 |
| 11 | 1+(−0.955−0.294i)T2 |
| 13 | 1+(−0.0291−1.16i)T+(−0.998+0.0498i)T2 |
| 17 | 1+(0.270−0.962i)T2 |
| 23 | 1+(−0.698+0.715i)T2 |
| 29 | 1+(0.995+0.0995i)T2 |
| 31 | 1+0.248T+T2 |
| 37 | 1+(0.355+1.15i)T+(−0.826+0.563i)T2 |
| 41 | 1+(0.661−0.749i)T2 |
| 43 | 1+(1.36−1.40i)T+(−0.0249−0.999i)T2 |
| 47 | 1+(−0.998+0.0498i)T2 |
| 53 | 1+(0.270+0.962i)T2 |
| 59 | 1+(−0.878−0.478i)T2 |
| 61 | 1+(−0.0989+1.98i)T+(−0.995−0.0995i)T2 |
| 67 | 1+(−0.555+1.52i)T+(−0.766−0.642i)T2 |
| 71 | 1+(−0.411+0.911i)T2 |
| 73 | 1+(0.405−0.662i)T+(−0.456−0.889i)T2 |
| 79 | 1+(−1.65−0.291i)T+(0.939+0.342i)T2 |
| 83 | 1+(−0.733−0.680i)T2 |
| 89 | 1+(0.797−0.603i)T2 |
| 97 | 1+(0.126−0.719i)T+(−0.939−0.342i)T2 |
show more | |
show less | |
L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−9.052942964092469222530198109160, −8.180479836816819405950066189998, −7.63440060872504004188407868388, −6.60127022981642426696479412788, −6.36173208351702387120660740339, −5.28457978908542921449131386640, −4.52133199842339210066712441502, −3.66798667894789175671536885976, −2.24111002940490541059634356186, −1.60367011562447023104986250902,
0.876152224907721286852884589432, 1.84755600743347367936142450609, 3.11877183712131143467764878037, 4.33644953942454780574853568770, 5.23053078649997077764970330092, 5.54974581311665881689706655915, 6.67198288578743062934858346463, 7.07006309192422271934809489011, 7.905029934748291642530194987633, 8.824791817086813376618559023465