L(s) = 1 | + (−1.48 − 1.48i)2-s + (−1.36 − 1.06i)3-s + 2.43i·4-s − 5-s + (0.442 + 3.61i)6-s − 1.31·7-s + (0.641 − 0.641i)8-s + (0.722 + 2.91i)9-s + (1.48 + 1.48i)10-s + (1.11 + 1.11i)11-s + (2.59 − 3.31i)12-s − 0.320i·13-s + (1.95 + 1.95i)14-s + (1.36 + 1.06i)15-s + 2.95·16-s + (0.771 + 0.771i)17-s + ⋯ |
L(s) = 1 | + (−1.05 − 1.05i)2-s + (−0.787 − 0.616i)3-s + 1.21i·4-s − 0.447·5-s + (0.180 + 1.47i)6-s − 0.495·7-s + (0.226 − 0.226i)8-s + (0.240 + 0.970i)9-s + (0.470 + 0.470i)10-s + (0.335 + 0.335i)11-s + (0.748 − 0.957i)12-s − 0.0889i·13-s + (0.521 + 0.521i)14-s + (0.352 + 0.275i)15-s + 0.737·16-s + (0.187 + 0.187i)17-s + ⋯ |
Λ(s)=(=(435s/2ΓC(s)L(s)(0.680+0.733i)Λ(2−s)
Λ(s)=(=(435s/2ΓC(s+1/2)L(s)(0.680+0.733i)Λ(1−s)
Degree: |
2 |
Conductor: |
435
= 3⋅5⋅29
|
Sign: |
0.680+0.733i
|
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), 0.680+0.733i)
|
Particular Values
L(1) |
≈ |
0.399959−0.174497i |
L(21) |
≈ |
0.399959−0.174497i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1+(1.36+1.06i)T |
| 5 | 1+T |
| 29 | 1+(−0.168−5.38i)T |
good | 2 | 1+(1.48+1.48i)T+2iT2 |
| 7 | 1+1.31T+7T2 |
| 11 | 1+(−1.11−1.11i)T+11iT2 |
| 13 | 1+0.320iT−13T2 |
| 17 | 1+(−0.771−0.771i)T+17iT2 |
| 19 | 1+(0.562−0.562i)T−19iT2 |
| 23 | 1−1.90iT−23T2 |
| 31 | 1+(−3.49+3.49i)T−31iT2 |
| 37 | 1+(−0.254−0.254i)T+37iT2 |
| 41 | 1+(−0.109+0.109i)T−41iT2 |
| 43 | 1+(−3.91+3.91i)T−43iT2 |
| 47 | 1+(−5.63+5.63i)T−47iT2 |
| 53 | 1−6.38iT−53T2 |
| 59 | 1+1.03iT−59T2 |
| 61 | 1+(−4.99+4.99i)T−61iT2 |
| 67 | 1−11.6iT−67T2 |
| 71 | 1−10.0T+71T2 |
| 73 | 1+(−9.52−9.52i)T+73iT2 |
| 79 | 1+(2.05−2.05i)T−79iT2 |
| 83 | 1−7.00iT−83T2 |
| 89 | 1+(−9.17−9.17i)T+89iT2 |
| 97 | 1+(−12.7−12.7i)T+97iT2 |
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
−11.00176034004970483847244536196, −10.28689695831280127253165491397, −9.436925119715321190673758099760, −8.397034731394763267544243934218, −7.52544723665090371543662049473, −6.53103120698840672275236048061, −5.33712713902563494376740281136, −3.78061632158098811023586836836, −2.34367457863809190828622754121, −0.965252506768556545714564581588,
0.59177154996541453191102467639, 3.42207333922996409433069980393, 4.70003408437216877628501510838, 5.99741176434406665835994340154, 6.55241697779050255746690284012, 7.56035191936343516769876321145, 8.585177676078175682085043566278, 9.401736569831760691257947625890, 10.09242796393090462916498535005, 11.01537137133939779218708317244