L(s) = 1 | + (0.187 + 0.187i)2-s + (1.67 + 0.692i)3-s − 1.92i·4-s + (0.183 + 0.443i)6-s + (1.88 + 4.55i)7-s + (0.737 − 0.737i)8-s + (0.193 + 0.193i)9-s + (1.50 + 3.62i)11-s + (1.33 − 3.22i)12-s − 2.07·13-s + (−0.500 + 1.20i)14-s − 3.58·16-s + (3.19 − 2.60i)17-s + 0.0724i·18-s + (2.08 − 2.08i)19-s + ⋯ |
L(s) = 1 | + (0.132 + 0.132i)2-s + (0.965 + 0.399i)3-s − 0.964i·4-s + (0.0749 + 0.181i)6-s + (0.712 + 1.72i)7-s + (0.260 − 0.260i)8-s + (0.0643 + 0.0643i)9-s + (0.452 + 1.09i)11-s + (0.385 − 0.931i)12-s − 0.574·13-s + (−0.133 + 0.322i)14-s − 0.895·16-s + (0.774 − 0.632i)17-s + 0.0170i·18-s + (0.478 − 0.478i)19-s + ⋯ |
Λ(s)=(=(425s/2ΓC(s)L(s)(0.905−0.424i)Λ(2−s)
Λ(s)=(=(425s/2ΓC(s+1/2)L(s)(0.905−0.424i)Λ(1−s)
Degree: |
2 |
Conductor: |
425
= 52⋅17
|
Sign: |
0.905−0.424i
|
Analytic conductor: |
3.39364 |
Root analytic conductor: |
1.84218 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ425(399,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 425, ( :1/2), 0.905−0.424i)
|
Particular Values
L(1) |
≈ |
2.06063+0.459262i |
L(21) |
≈ |
2.06063+0.459262i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1 |
| 17 | 1+(−3.19+2.60i)T |
good | 2 | 1+(−0.187−0.187i)T+2iT2 |
| 3 | 1+(−1.67−0.692i)T+(2.12+2.12i)T2 |
| 7 | 1+(−1.88−4.55i)T+(−4.94+4.94i)T2 |
| 11 | 1+(−1.50−3.62i)T+(−7.77+7.77i)T2 |
| 13 | 1+2.07T+13T2 |
| 19 | 1+(−2.08+2.08i)T−19iT2 |
| 23 | 1+(−3.58+1.48i)T+(16.2−16.2i)T2 |
| 29 | 1+(3.22+1.33i)T+(20.5+20.5i)T2 |
| 31 | 1+(−2.23+5.40i)T+(−21.9−21.9i)T2 |
| 37 | 1+(−1.88−0.781i)T+(26.1+26.1i)T2 |
| 41 | 1+(10.9−4.53i)T+(28.9−28.9i)T2 |
| 43 | 1+(3.91−3.91i)T−43iT2 |
| 47 | 1−0.453T+47T2 |
| 53 | 1+(4.60+4.60i)T+53iT2 |
| 59 | 1+(4.92+4.92i)T+59iT2 |
| 61 | 1+(0.0429−0.0177i)T+(43.1−43.1i)T2 |
| 67 | 1−10.0iT−67T2 |
| 71 | 1+(−5.85+14.1i)T+(−50.2−50.2i)T2 |
| 73 | 1+(3.36−8.12i)T+(−51.6−51.6i)T2 |
| 79 | 1+(−0.991−2.39i)T+(−55.8+55.8i)T2 |
| 83 | 1+(−1.09−1.09i)T+83iT2 |
| 89 | 1+10.2iT−89T2 |
| 97 | 1+(−4.07+9.83i)T+(−68.5−68.5i)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
−11.43994162221925196446847665223, −9.836690255785868884321173755802, −9.532184480758723548532244556726, −8.737869730365920918948175381110, −7.69667715795434720304308103422, −6.43526397990775080776048439553, −5.28721668235906179083098737706, −4.65297434152227968381561248336, −2.90199890300939264194537822132, −1.89914338663940957540077541034,
1.51149568025201142211707020345, 3.22043460509630503315525633359, 3.76076808004203484857378622314, 5.09364683911584494416424922718, 6.88166058986387754114295195860, 7.64062707622858507009144247302, 8.153664336305076514741308141030, 9.005291885841410862586449785574, 10.36362286428967090563915268301, 11.14030006319458540483479804287