L(s) = 1 | − 1.97·2-s − 3-s + 1.89·4-s + (1.38 + 1.75i)5-s + 1.97·6-s − 0.520i·7-s + 0.214·8-s + 9-s + (−2.72 − 3.46i)10-s + 2.16i·11-s − 1.89·12-s − 1.53i·13-s + 1.02i·14-s + (−1.38 − 1.75i)15-s − 4.20·16-s + 2.47·17-s + ⋯ |
L(s) = 1 | − 1.39·2-s − 0.577·3-s + 0.945·4-s + (0.617 + 0.786i)5-s + 0.805·6-s − 0.196i·7-s + 0.0758·8-s + 0.333·9-s + (−0.861 − 1.09i)10-s + 0.652i·11-s − 0.545·12-s − 0.425i·13-s + 0.274i·14-s + (−0.356 − 0.454i)15-s − 1.05·16-s + 0.601·17-s + ⋯ |
Λ(s)=(=(435s/2ΓC(s)L(s)(0.448−0.893i)Λ(2−s)
Λ(s)=(=(435s/2ΓC(s+1/2)L(s)(0.448−0.893i)Λ(1−s)
Degree: |
2 |
Conductor: |
435
= 3⋅5⋅29
|
Sign: |
0.448−0.893i
|
Analytic conductor: |
3.47349 |
Root analytic conductor: |
1.86373 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ435(289,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 435, ( :1/2), 0.448−0.893i)
|
Particular Values
L(1) |
≈ |
0.501384+0.309462i |
L(21) |
≈ |
0.501384+0.309462i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1+T |
| 5 | 1+(−1.38−1.75i)T |
| 29 | 1+(−2.29−4.87i)T |
good | 2 | 1+1.97T+2T2 |
| 7 | 1+0.520iT−7T2 |
| 11 | 1−2.16iT−11T2 |
| 13 | 1+1.53iT−13T2 |
| 17 | 1−2.47T+17T2 |
| 19 | 1+4.70iT−19T2 |
| 23 | 1−1.46iT−23T2 |
| 31 | 1−4.64iT−31T2 |
| 37 | 1−1.77T+37T2 |
| 41 | 1−9.71iT−41T2 |
| 43 | 1−5.39T+43T2 |
| 47 | 1−3.68T+47T2 |
| 53 | 1−7.74iT−53T2 |
| 59 | 1+1.91T+59T2 |
| 61 | 1−7.66iT−61T2 |
| 67 | 1−7.88iT−67T2 |
| 71 | 1+9.78T+71T2 |
| 73 | 1+4.70T+73T2 |
| 79 | 1+12.3iT−79T2 |
| 83 | 1−7.32iT−83T2 |
| 89 | 1+7.66iT−89T2 |
| 97 | 1+1.64T+97T2 |
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
−10.84229579715468130348142278173, −10.36244088380221644216095378385, −9.636508696064823728799599702272, −8.786248311154622492071496998094, −7.46136687014584946002846181141, −7.03758658382554884502711087736, −5.88797078196181595215712003270, −4.63372524825557059587573872200, −2.79363568961288372718918188206, −1.28314545827527783757071887383,
0.74035514304204564601057686220, 2.05689704942115635023617649873, 4.19185150448646007936721143228, 5.50199111514738442427427111391, 6.30520536078259477546922755290, 7.60591039136979406012883783845, 8.422400883984321005602303818435, 9.227828649709376807035745704167, 9.963177360252382493408876557808, 10.67305537593214080853953781178