L(s) = 1 | − 2.84i·3-s + (0.691 + 2.12i)5-s + 0.145i·7-s − 5.10·9-s + 5.71·11-s − 5.24i·13-s + (6.05 − 1.96i)15-s + 7.15i·17-s + 19-s + 0.412·21-s − 0.622i·23-s + (−4.04 + 2.94i)25-s + 6.00i·27-s + 5.46·29-s + 3.77·31-s + ⋯ |
L(s) = 1 | − 1.64i·3-s + (0.309 + 0.950i)5-s + 0.0548i·7-s − 1.70·9-s + 1.72·11-s − 1.45i·13-s + (1.56 − 0.508i)15-s + 1.73i·17-s + 0.229·19-s + 0.0901·21-s − 0.129i·23-s + (−0.808 + 0.588i)25-s + 1.15i·27-s + 1.01·29-s + 0.678·31-s + ⋯ |
Λ(s)=(=(1520s/2ΓC(s)L(s)(0.309+0.950i)Λ(2−s)
Λ(s)=(=(1520s/2ΓC(s+1/2)L(s)(0.309+0.950i)Λ(1−s)
Degree: |
2 |
Conductor: |
1520
= 24⋅5⋅19
|
Sign: |
0.309+0.950i
|
Analytic conductor: |
12.1372 |
Root analytic conductor: |
3.48385 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1520(609,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1520, ( :1/2), 0.309+0.950i)
|
Particular Values
L(1) |
≈ |
1.962373912 |
L(21) |
≈ |
1.962373912 |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1+(−0.691−2.12i)T |
| 19 | 1−T |
good | 3 | 1+2.84iT−3T2 |
| 7 | 1−0.145iT−7T2 |
| 11 | 1−5.71T+11T2 |
| 13 | 1+5.24iT−13T2 |
| 17 | 1−7.15iT−17T2 |
| 23 | 1+0.622iT−23T2 |
| 29 | 1−5.46T+29T2 |
| 31 | 1−3.77T+31T2 |
| 37 | 1+5.03iT−37T2 |
| 41 | 1−5.77T+41T2 |
| 43 | 1+3.32iT−43T2 |
| 47 | 1+5.85iT−47T2 |
| 53 | 1−6.97iT−53T2 |
| 59 | 1−9.09T+59T2 |
| 61 | 1+8.16T+61T2 |
| 67 | 1+13.6iT−67T2 |
| 71 | 1+2.41T+71T2 |
| 73 | 1+7.44iT−73T2 |
| 79 | 1+9.69T+79T2 |
| 83 | 1+2.17iT−83T2 |
| 89 | 1+3.90T+89T2 |
| 97 | 1−4.98iT−97T2 |
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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
−9.116874323884118177732056541440, −8.287086326222519113161816348626, −7.60760274764492804996292881954, −6.81132953531931430246541974082, −6.20654788642185527333516964842, −5.72846058891521949810104398215, −3.96817626991333269538831862234, −2.98443584051759968539176604089, −1.96345648673209389123102334946, −0.975240058292870222364100414435,
1.18480890710461835710753949727, 2.79602950245416530076975536493, 4.11978257236709199208711908587, 4.39913364856039961940055294990, 5.20191899164261512619694374484, 6.22497232793593668368454619660, 7.09949181505727591634125011624, 8.587509997347669803833019339851, 8.994478917215631643926262168220, 9.688145478827945684007999974394