L(s) = 1 | + (−0.669 + 0.743i)2-s + (−0.309 + 0.951i)3-s + (−0.104 − 0.994i)4-s + (−0.994 − 0.104i)5-s + (−0.499 − 0.866i)6-s + (0.809 + 0.587i)8-s + (−0.809 − 0.587i)9-s + (0.743 − 0.669i)10-s + (0.978 + 0.207i)12-s + (0.406 − 0.913i)15-s + (−0.978 + 0.207i)16-s + (−0.692 + 1.80i)17-s + (0.978 − 0.207i)18-s + (0.278 + 0.309i)19-s + i·20-s + ⋯ |
L(s) = 1 | + (−0.669 + 0.743i)2-s + (−0.309 + 0.951i)3-s + (−0.104 − 0.994i)4-s + (−0.994 − 0.104i)5-s + (−0.499 − 0.866i)6-s + (0.809 + 0.587i)8-s + (−0.809 − 0.587i)9-s + (0.743 − 0.669i)10-s + (0.978 + 0.207i)12-s + (0.406 − 0.913i)15-s + (−0.978 + 0.207i)16-s + (−0.692 + 1.80i)17-s + (0.978 − 0.207i)18-s + (0.278 + 0.309i)19-s + i·20-s + ⋯ |
Λ(s)=(=(3660s/2ΓC(s)L(s)(−0.880+0.473i)Λ(1−s)
Λ(s)=(=(3660s/2ΓC(s)L(s)(−0.880+0.473i)Λ(1−s)
Degree: |
2 |
Conductor: |
3660
= 22⋅3⋅5⋅61
|
Sign: |
−0.880+0.473i
|
Analytic conductor: |
1.82657 |
Root analytic conductor: |
1.35150 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3660(1499,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3660, ( :0), −0.880+0.473i)
|
Particular Values
L(21) |
≈ |
0.3409351122 |
L(21) |
≈ |
0.3409351122 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.669−0.743i)T |
| 3 | 1+(0.309−0.951i)T |
| 5 | 1+(0.994+0.104i)T |
| 61 | 1+(0.406+0.913i)T |
good | 7 | 1+(0.994−0.104i)T2 |
| 11 | 1−iT2 |
| 13 | 1+(0.5−0.866i)T2 |
| 17 | 1+(0.692−1.80i)T+(−0.743−0.669i)T2 |
| 19 | 1+(−0.278−0.309i)T+(−0.104+0.994i)T2 |
| 23 | 1+(−1.65+0.262i)T+(0.951−0.309i)T2 |
| 29 | 1+(0.866−0.5i)T2 |
| 31 | 1+(−0.685−1.05i)T+(−0.406+0.913i)T2 |
| 37 | 1+(−0.587−0.809i)T2 |
| 41 | 1+(−0.809+0.587i)T2 |
| 43 | 1+(0.743−0.669i)T2 |
| 47 | 1+(0.866+0.5i)T+(0.5+0.866i)T2 |
| 53 | 1+(1.84+0.292i)T+(0.951+0.309i)T2 |
| 59 | 1+(−0.406−0.913i)T2 |
| 67 | 1+(−0.207+0.978i)T2 |
| 71 | 1+(0.207+0.978i)T2 |
| 73 | 1+(0.978−0.207i)T2 |
| 79 | 1+(1.86−0.715i)T+(0.743−0.669i)T2 |
| 83 | 1+(−0.413−1.94i)T+(−0.913+0.406i)T2 |
| 89 | 1+(0.587−0.809i)T2 |
| 97 | 1+(0.913+0.406i)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
−8.987182642751449053505569908335, −8.383788397578421986479561391089, −7.951831777308973066696511015687, −6.75273126037143117693904434080, −6.42162960347068694172849721479, −5.29328990245356391732924262436, −4.74531633995892321812693304287, −3.96401774883402352644709289494, −3.03512931337064082545594591630, −1.34600873716073931441511683207,
0.29298030986127345739884771779, 1.37394029671026281640817388332, 2.76570477647167372070340684524, 3.06590545734824126885768566291, 4.47953758195477566558072649696, 5.01891149735695364660395637676, 6.42834913700042059532181949502, 7.12894884136875445192092234452, 7.53932689314145538570568423444, 8.231474357195028088817389313281