L(s) = 1 | − 2·4-s − 5-s − 4·9-s + 3·11-s + 5·19-s + 2·20-s − 4·25-s + 11·29-s − 6·31-s + 8·36-s − 41-s − 6·44-s + 4·45-s − 6·49-s − 3·55-s + 59-s − 2·61-s + 8·64-s − 3·71-s − 10·76-s − 15·79-s + 7·81-s − 9·89-s − 5·95-s − 12·99-s + 8·100-s + 15·101-s + ⋯ |
L(s) = 1 | − 4-s − 0.447·5-s − 4/3·9-s + 0.904·11-s + 1.14·19-s + 0.447·20-s − 4/5·25-s + 2.04·29-s − 1.07·31-s + 4/3·36-s − 0.156·41-s − 0.904·44-s + 0.596·45-s − 6/7·49-s − 0.404·55-s + 0.130·59-s − 0.256·61-s + 64-s − 0.356·71-s − 1.14·76-s − 1.68·79-s + 7/9·81-s − 0.953·89-s − 0.512·95-s − 1.20·99-s + 4/5·100-s + 1.49·101-s + ⋯ |
Λ(s)=(=(1025s/2ΓC(s)2L(s)Λ(2−s)
Λ(s)=(=(1025s/2ΓC(s+1/2)2L(s)Λ(1−s)
Degree: |
4 |
Conductor: |
1025
= 52⋅41
|
Sign: |
1
|
Analytic conductor: |
0.0653548 |
Root analytic conductor: |
0.505614 |
Motivic weight: |
1 |
Rational: |
yes |
Arithmetic: |
yes |
Character: |
Trivial
|
Primitive: |
yes
|
Self-dual: |
yes
|
Analytic rank: |
0
|
Selberg data: |
(4, 1025, ( :1/2,1/2), 1)
|
Particular Values
L(1) |
≈ |
0.4222141590 |
L(21) |
≈ |
0.4222141590 |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1
L(s)=p∏ j=1∏4(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−14.19454045717374451127091353927, −13.78836223859467724349513577428, −13.02132215935876782760497681759, −12.16321002560880394673395714560, −11.64675702466879730087811532096, −11.19128473596752981447430276521, −10.09738201918885273142298867748, −9.423661061919065844869674749372, −8.748731100307867456017587191214, −8.282454962036726379628037425237, −7.29437775775195108905884201252, −6.23530102487327827298160382161, −5.31271891550307177711333795025, −4.34036075847737870492735412284, −3.22692316031770542346454550404,
3.22692316031770542346454550404, 4.34036075847737870492735412284, 5.31271891550307177711333795025, 6.23530102487327827298160382161, 7.29437775775195108905884201252, 8.282454962036726379628037425237, 8.748731100307867456017587191214, 9.423661061919065844869674749372, 10.09738201918885273142298867748, 11.19128473596752981447430276521, 11.64675702466879730087811532096, 12.16321002560880394673395714560, 13.02132215935876782760497681759, 13.78836223859467724349513577428, 14.19454045717374451127091353927