L(s) = 1 | + (−0.866 − 1.5i)3-s + (0.866 + 0.5i)5-s + (−1 + 1.73i)9-s + (1.5 − 0.866i)11-s − i·13-s − 1.73i·15-s + (−0.866 + 0.5i)17-s + (0.499 + 0.866i)25-s + 1.73·27-s + 29-s + (−2.59 − 1.5i)33-s + (−1.5 + 0.866i)39-s + (−1.73 + i)45-s + (0.866 − 1.5i)47-s + (1.5 + 0.866i)51-s + ⋯ |
L(s) = 1 | + (−0.866 − 1.5i)3-s + (0.866 + 0.5i)5-s + (−1 + 1.73i)9-s + (1.5 − 0.866i)11-s − i·13-s − 1.73i·15-s + (−0.866 + 0.5i)17-s + (0.499 + 0.866i)25-s + 1.73·27-s + 29-s + (−2.59 − 1.5i)33-s + (−1.5 + 0.866i)39-s + (−1.73 + i)45-s + (0.866 − 1.5i)47-s + (1.5 + 0.866i)51-s + ⋯ |
Λ(s)=(=(3920s/2ΓC(s)L(s)(−0.126+0.991i)Λ(1−s)
Λ(s)=(=(3920s/2ΓC(s)L(s)(−0.126+0.991i)Λ(1−s)
Degree: |
2 |
Conductor: |
3920
= 24⋅5⋅72
|
Sign: |
−0.126+0.991i
|
Analytic conductor: |
1.95633 |
Root analytic conductor: |
1.39869 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3920(79,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3920, ( :0), −0.126+0.991i)
|
Particular Values
L(21) |
≈ |
1.176973663 |
L(21) |
≈ |
1.176973663 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1+(−0.866−0.5i)T |
| 7 | 1 |
good | 3 | 1+(0.866+1.5i)T+(−0.5+0.866i)T2 |
| 11 | 1+(−1.5+0.866i)T+(0.5−0.866i)T2 |
| 13 | 1+iT−T2 |
| 17 | 1+(0.866−0.5i)T+(0.5−0.866i)T2 |
| 19 | 1+(0.5+0.866i)T2 |
| 23 | 1+(−0.5−0.866i)T2 |
| 29 | 1−T+T2 |
| 31 | 1+(0.5−0.866i)T2 |
| 37 | 1+(0.5+0.866i)T2 |
| 41 | 1+T2 |
| 43 | 1+T2 |
| 47 | 1+(−0.866+1.5i)T+(−0.5−0.866i)T2 |
| 53 | 1+(0.5−0.866i)T2 |
| 59 | 1+(0.5−0.866i)T2 |
| 61 | 1+(−0.5−0.866i)T2 |
| 67 | 1+(−0.5+0.866i)T2 |
| 71 | 1−T2 |
| 73 | 1+(−1.73+i)T+(0.5−0.866i)T2 |
| 79 | 1+(1.5+0.866i)T+(0.5+0.866i)T2 |
| 83 | 1+T2 |
| 89 | 1+(−0.5−0.866i)T2 |
| 97 | 1+iT−T2 |
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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
−8.422560090860266100169737297152, −7.47790620575857058783219289449, −6.74820330966894489907027367120, −6.29873762451492276310206779757, −5.84493380529083506430228611510, −5.02876880062995945555256154068, −3.69727127327979788426684530546, −2.63846362083070419968824588903, −1.73596519740185243795890036969, −0.854098872692307461386070715311,
1.28252119891128638503113506162, 2.49155783054687746995112091030, 3.88288851643952576735041598032, 4.45816290496048886686061733694, 4.86385865335616126534606945838, 5.82269870666592923038987107978, 6.47646797089000081532844112003, 7.00781082583790177782876355732, 8.563450192513929530138433165883, 9.146701213304379015003254928309