L(s) = 1 | + (0.793 − 0.608i)5-s + (0.866 + 0.5i)9-s + (−0.541 + 0.541i)13-s + (0.478 − 1.78i)17-s + (0.258 − 0.965i)25-s − 1.41i·29-s + (0.517 + 1.93i)37-s − 0.765i·41-s + (0.991 − 0.130i)45-s + (−0.366 + 1.36i)53-s + (1.60 + 0.923i)61-s + (−0.0999 + 0.758i)65-s + (−1.78 − 0.478i)73-s + (0.499 + 0.866i)81-s + (−0.707 − 1.70i)85-s + ⋯ |
L(s) = 1 | + (0.793 − 0.608i)5-s + (0.866 + 0.5i)9-s + (−0.541 + 0.541i)13-s + (0.478 − 1.78i)17-s + (0.258 − 0.965i)25-s − 1.41i·29-s + (0.517 + 1.93i)37-s − 0.765i·41-s + (0.991 − 0.130i)45-s + (−0.366 + 1.36i)53-s + (1.60 + 0.923i)61-s + (−0.0999 + 0.758i)65-s + (−1.78 − 0.478i)73-s + (0.499 + 0.866i)81-s + (−0.707 − 1.70i)85-s + ⋯ |
Λ(s)=(=(3920s/2ΓC(s)L(s)(0.868+0.495i)Λ(1−s)
Λ(s)=(=(3920s/2ΓC(s)L(s)(0.868+0.495i)Λ(1−s)
Degree: |
2 |
Conductor: |
3920
= 24⋅5⋅72
|
Sign: |
0.868+0.495i
|
Analytic conductor: |
1.95633 |
Root analytic conductor: |
1.39869 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3920(3743,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3920, ( :0), 0.868+0.495i)
|
Particular Values
L(21) |
≈ |
1.608297393 |
L(21) |
≈ |
1.608297393 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1+(−0.793+0.608i)T |
| 7 | 1 |
good | 3 | 1+(−0.866−0.5i)T2 |
| 11 | 1+(0.5−0.866i)T2 |
| 13 | 1+(0.541−0.541i)T−iT2 |
| 17 | 1+(−0.478+1.78i)T+(−0.866−0.5i)T2 |
| 19 | 1+(0.5+0.866i)T2 |
| 23 | 1+(−0.866+0.5i)T2 |
| 29 | 1+1.41iT−T2 |
| 31 | 1+(−0.5+0.866i)T2 |
| 37 | 1+(−0.517−1.93i)T+(−0.866+0.5i)T2 |
| 41 | 1+0.765iT−T2 |
| 43 | 1−iT2 |
| 47 | 1+(−0.866+0.5i)T2 |
| 53 | 1+(0.366−1.36i)T+(−0.866−0.5i)T2 |
| 59 | 1+(0.5−0.866i)T2 |
| 61 | 1+(−1.60−0.923i)T+(0.5+0.866i)T2 |
| 67 | 1+(−0.866−0.5i)T2 |
| 71 | 1−T2 |
| 73 | 1+(1.78+0.478i)T+(0.866+0.5i)T2 |
| 79 | 1+(−0.5−0.866i)T2 |
| 83 | 1+iT2 |
| 89 | 1+(−0.923+1.60i)T+(−0.5−0.866i)T2 |
| 97 | 1+(0.541+0.541i)T+iT2 |
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
−8.696358143695240585103962442378, −7.74065845048154658784118847085, −7.20656476810111780840406174094, −6.37339735985710400985152353964, −5.51523762732652894597236929835, −4.75956931242118190008385768078, −4.32286267813383801777840362948, −2.89191777140031939999129033948, −2.11460060210026892770636273291, −1.04984633787087071444886035687,
1.34256831903997319395807278827, 2.21552425600660151434293592183, 3.32517142781782395039134914499, 3.96608629379632026969066007405, 5.09911076583759005315648494763, 5.80449049587021431529521091221, 6.51830231797661923038663009140, 7.15266152344893349109050268087, 7.897243252996568563497430707466, 8.756400538122844241157240636970