L(s) = 1 | + (−1.13 − 0.844i)2-s + (−1.79 + 1.03i)3-s + (0.572 + 1.91i)4-s + 5-s + (2.91 + 0.341i)6-s + (3.65 + 2.10i)7-s + (0.969 − 2.65i)8-s + (0.658 − 1.14i)9-s + (−1.13 − 0.844i)10-s + (−2.34 − 4.05i)11-s + (−3.02 − 2.85i)12-s + (3.60 + 0.189i)13-s + (−2.36 − 5.48i)14-s + (−1.79 + 1.03i)15-s + (−3.34 + 2.19i)16-s + (1.44 − 2.49i)17-s + ⋯ |
L(s) = 1 | + (−0.801 − 0.597i)2-s + (−1.03 + 0.599i)3-s + (0.286 + 0.958i)4-s + 0.447·5-s + (1.19 + 0.139i)6-s + (1.38 + 0.797i)7-s + (0.342 − 0.939i)8-s + (0.219 − 0.380i)9-s + (−0.358 − 0.267i)10-s + (−0.705 − 1.22i)11-s + (−0.872 − 0.823i)12-s + (0.998 + 0.0524i)13-s + (−0.631 − 1.46i)14-s + (−0.464 + 0.268i)15-s + (−0.836 + 0.548i)16-s + (0.349 − 0.605i)17-s + ⋯ |
Λ(s)=(=(520s/2ΓC(s)L(s)(0.806−0.590i)Λ(2−s)
Λ(s)=(=(520s/2ΓC(s+1/2)L(s)(0.806−0.590i)Λ(1−s)
Degree: |
2 |
Conductor: |
520
= 23⋅5⋅13
|
Sign: |
0.806−0.590i
|
Analytic conductor: |
4.15222 |
Root analytic conductor: |
2.03769 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ520(101,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 520, ( :1/2), 0.806−0.590i)
|
Particular Values
L(1) |
≈ |
0.796381+0.260381i |
L(21) |
≈ |
0.796381+0.260381i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(1.13+0.844i)T |
| 5 | 1−T |
| 13 | 1+(−3.60−0.189i)T |
good | 3 | 1+(1.79−1.03i)T+(1.5−2.59i)T2 |
| 7 | 1+(−3.65−2.10i)T+(3.5+6.06i)T2 |
| 11 | 1+(2.34+4.05i)T+(−5.5+9.52i)T2 |
| 17 | 1+(−1.44+2.49i)T+(−8.5−14.7i)T2 |
| 19 | 1+(3.09−5.36i)T+(−9.5−16.4i)T2 |
| 23 | 1+(−3.36−5.82i)T+(−11.5+19.9i)T2 |
| 29 | 1+(−4.64+2.68i)T+(14.5−25.1i)T2 |
| 31 | 1+0.540iT−31T2 |
| 37 | 1+(0.815+1.41i)T+(−18.5+32.0i)T2 |
| 41 | 1+(−1.36+0.789i)T+(20.5−35.5i)T2 |
| 43 | 1+(−4.99−2.88i)T+(21.5+37.2i)T2 |
| 47 | 1−4.24iT−47T2 |
| 53 | 1−10.7iT−53T2 |
| 59 | 1+(6.90−11.9i)T+(−29.5−51.0i)T2 |
| 61 | 1+(−6.45−3.72i)T+(30.5+52.8i)T2 |
| 67 | 1+(−5.52−9.57i)T+(−33.5+58.0i)T2 |
| 71 | 1+(8.93+5.15i)T+(35.5+61.4i)T2 |
| 73 | 1+8.13iT−73T2 |
| 79 | 1−1.61T+79T2 |
| 83 | 1−3.34T+83T2 |
| 89 | 1+(2.76−1.59i)T+(44.5−77.0i)T2 |
| 97 | 1+(12.2+7.09i)T+(48.5+84.0i)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
−10.86627605005663370706689251218, −10.45787369327991265725909781866, −9.241408818864349201915985013040, −8.429008603942203539794412099271, −7.74588590102519224213577279417, −6.01421454827691421676884965076, −5.51478778382515855011436974036, −4.29108469513602712416664195519, −2.78417040457083400144545837934, −1.28739766371890923452365242269,
0.882103951370454201762910237446, 2.00470521090412996144851018655, 4.66518865462716043984814554871, 5.26703748379984168530997338460, 6.51331477354060702325042643280, 6.98686164863124459060446955017, 8.026225366806255322250961459473, 8.769090280003424979757663586119, 10.12339430246743244909521323978, 10.86122329163413485650858103004