L(s) = 1 | + (−0.951 − 0.309i)3-s + (0.809 + 0.587i)5-s − 1.61i·7-s + (−1.30 − 0.951i)13-s + (−0.587 − 0.809i)15-s + (−0.587 + 0.190i)19-s + (−0.500 + 1.53i)21-s + (−0.587 − 0.809i)23-s + (0.309 + 0.951i)25-s + (0.587 + 0.809i)27-s + (0.190 − 0.587i)29-s + (−0.951 + 0.309i)31-s + (0.951 − 1.30i)35-s + (−0.809 − 0.587i)37-s + (0.951 + 1.30i)39-s + ⋯ |
L(s) = 1 | + (−0.951 − 0.309i)3-s + (0.809 + 0.587i)5-s − 1.61i·7-s + (−1.30 − 0.951i)13-s + (−0.587 − 0.809i)15-s + (−0.587 + 0.190i)19-s + (−0.500 + 1.53i)21-s + (−0.587 − 0.809i)23-s + (0.309 + 0.951i)25-s + (0.587 + 0.809i)27-s + (0.190 − 0.587i)29-s + (−0.951 + 0.309i)31-s + (0.951 − 1.30i)35-s + (−0.809 − 0.587i)37-s + (0.951 + 1.30i)39-s + ⋯ |
Λ(s)=(=(1600s/2ΓC(s)L(s)(−0.481+0.876i)Λ(1−s)
Λ(s)=(=(1600s/2ΓC(s)L(s)(−0.481+0.876i)Λ(1−s)
Degree: |
2 |
Conductor: |
1600
= 26⋅52
|
Sign: |
−0.481+0.876i
|
Analytic conductor: |
0.798504 |
Root analytic conductor: |
0.893590 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1600(511,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1600, ( :0), −0.481+0.876i)
|
Particular Values
L(21) |
≈ |
0.6292167620 |
L(21) |
≈ |
0.6292167620 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1+(−0.809−0.587i)T |
good | 3 | 1+(0.951+0.309i)T+(0.809+0.587i)T2 |
| 7 | 1+1.61iT−T2 |
| 11 | 1+(−0.309+0.951i)T2 |
| 13 | 1+(1.30+0.951i)T+(0.309+0.951i)T2 |
| 17 | 1+(−0.809+0.587i)T2 |
| 19 | 1+(0.587−0.190i)T+(0.809−0.587i)T2 |
| 23 | 1+(0.587+0.809i)T+(−0.309+0.951i)T2 |
| 29 | 1+(−0.190+0.587i)T+(−0.809−0.587i)T2 |
| 31 | 1+(0.951−0.309i)T+(0.809−0.587i)T2 |
| 37 | 1+(0.809+0.587i)T+(0.309+0.951i)T2 |
| 41 | 1+(0.309+0.951i)T2 |
| 43 | 1+0.618iT−T2 |
| 47 | 1+(−1.53−0.5i)T+(0.809+0.587i)T2 |
| 53 | 1+(−0.309+0.951i)T+(−0.809−0.587i)T2 |
| 59 | 1+(−0.363+0.5i)T+(−0.309−0.951i)T2 |
| 61 | 1+(−0.809+0.587i)T+(0.309−0.951i)T2 |
| 67 | 1+(0.809−0.587i)T2 |
| 71 | 1+(1.53+0.5i)T+(0.809+0.587i)T2 |
| 73 | 1+(0.809−0.587i)T+(0.309−0.951i)T2 |
| 79 | 1+(−0.587−0.190i)T+(0.809+0.587i)T2 |
| 83 | 1+(0.951−0.309i)T+(0.809−0.587i)T2 |
| 89 | 1+(0.309−0.951i)T2 |
| 97 | 1+(−0.5+1.53i)T+(−0.809−0.587i)T2 |
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
−9.676063369975670327358227614116, −8.470376387066196046239116137976, −7.26163154048967855301474884764, −7.08423195379189921771599361265, −6.08015600499275755730860184357, −5.41737684590961161715778816135, −4.42592180628927913427954571332, −3.30988391685286884074583068171, −2.07436226681351332262030798644, −0.52204646233237342968962369278,
1.88760119127643573341215305044, 2.63601913108886195616824733752, 4.37787100980143940373335555199, 5.16146807250773369423992958735, 5.65520188947811627115000272402, 6.29977771566192042382548132901, 7.35898576839707447428980619559, 8.669052122839764660360191335202, 9.025815959157027317747516900662, 9.838088196271625464117919703082