L(s) = 1 | + (0.0236 + 0.0236i)2-s + (1.39 − 1.03i)3-s − 1.99i·4-s − 5-s + (0.0572 + 0.00855i)6-s + 3.42·7-s + (0.0944 − 0.0944i)8-s + (0.877 − 2.86i)9-s + (−0.0236 − 0.0236i)10-s + (−4.10 − 4.10i)11-s + (−2.05 − 2.78i)12-s + 3.19i·13-s + (0.0809 + 0.0809i)14-s + (−1.39 + 1.03i)15-s − 3.99·16-s + (4.08 + 4.08i)17-s + ⋯ |
L(s) = 1 | + (0.0167 + 0.0167i)2-s + (0.803 − 0.594i)3-s − 0.999i·4-s − 0.447·5-s + (0.0233 + 0.00349i)6-s + 1.29·7-s + (0.0334 − 0.0334i)8-s + (0.292 − 0.956i)9-s + (−0.00747 − 0.00747i)10-s + (−1.23 − 1.23i)11-s + (−0.594 − 0.803i)12-s + 0.886i·13-s + (0.0216 + 0.0216i)14-s + (−0.359 + 0.266i)15-s − 0.998·16-s + (0.991 + 0.991i)17-s + ⋯ |
Λ(s)=(=(435s/2ΓC(s)L(s)(0.0254+0.999i)Λ(2−s)
Λ(s)=(=(435s/2ΓC(s+1/2)L(s)(0.0254+0.999i)Λ(1−s)
Degree: |
2 |
Conductor: |
435
= 3⋅5⋅29
|
Sign: |
0.0254+0.999i
|
Analytic conductor: |
3.47349 |
Root analytic conductor: |
1.86373 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ435(191,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 435, ( :1/2), 0.0254+0.999i)
|
Particular Values
L(1) |
≈ |
1.27994−1.24771i |
L(21) |
≈ |
1.27994−1.24771i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1+(−1.39+1.03i)T |
| 5 | 1+T |
| 29 | 1+(−4.91−2.20i)T |
good | 2 | 1+(−0.0236−0.0236i)T+2iT2 |
| 7 | 1−3.42T+7T2 |
| 11 | 1+(4.10+4.10i)T+11iT2 |
| 13 | 1−3.19iT−13T2 |
| 17 | 1+(−4.08−4.08i)T+17iT2 |
| 19 | 1+(1.51−1.51i)T−19iT2 |
| 23 | 1+3.49iT−23T2 |
| 31 | 1+(0.896−0.896i)T−31iT2 |
| 37 | 1+(1.53+1.53i)T+37iT2 |
| 41 | 1+(−4.78+4.78i)T−41iT2 |
| 43 | 1+(2.79−2.79i)T−43iT2 |
| 47 | 1+(−3.94+3.94i)T−47iT2 |
| 53 | 1+0.219iT−53T2 |
| 59 | 1−14.4iT−59T2 |
| 61 | 1+(−7.78+7.78i)T−61iT2 |
| 67 | 1−11.2iT−67T2 |
| 71 | 1+9.21T+71T2 |
| 73 | 1+(−10.7−10.7i)T+73iT2 |
| 79 | 1+(−1.49+1.49i)T−79iT2 |
| 83 | 1−1.76iT−83T2 |
| 89 | 1+(−6.11−6.11i)T+89iT2 |
| 97 | 1+(5.10+5.10i)T+97iT2 |
show more | |
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L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−10.84535247001714738357918066167, −10.18807492218347895753598785646, −8.714103004388807454009552751520, −8.342807998924989513783188531996, −7.38773267118106232231392313357, −6.19405814086199974213811061445, −5.20788547953232194174530409715, −3.96911021512214635763628011280, −2.41151709122145508756592823456, −1.15469390156596609730449845957,
2.30755848805507095047063974169, 3.28477833901139002699005209096, 4.60381246969465014438343304023, 5.08047621668424795019586620121, 7.39547770995674206698928546158, 7.78083408612144466835026009229, 8.341958926279087772042391396612, 9.523260654606446791907346061436, 10.45011887061128635348232343316, 11.34011938489439266124600458529