L(s) = 1 | + (0.5 − 0.866i)3-s + (0.5 − 0.866i)4-s + 7-s + (−0.499 − 0.866i)9-s + (−0.499 − 0.866i)12-s + (−0.499 − 0.866i)16-s + (−1.5 + 0.866i)19-s + (0.5 − 0.866i)21-s + (0.5 − 0.866i)25-s − 0.999·27-s + (0.5 − 0.866i)28-s − 0.999·36-s + (1.5 − 0.866i)37-s − 43-s − 0.999·48-s + 49-s + ⋯ |
L(s) = 1 | + (0.5 − 0.866i)3-s + (0.5 − 0.866i)4-s + 7-s + (−0.499 − 0.866i)9-s + (−0.499 − 0.866i)12-s + (−0.499 − 0.866i)16-s + (−1.5 + 0.866i)19-s + (0.5 − 0.866i)21-s + (0.5 − 0.866i)25-s − 0.999·27-s + (0.5 − 0.866i)28-s − 0.999·36-s + (1.5 − 0.866i)37-s − 43-s − 0.999·48-s + 49-s + ⋯ |
Λ(s)=(=(3549s/2ΓC(s)L(s)(−0.301+0.953i)Λ(1−s)
Λ(s)=(=(3549s/2ΓC(s)L(s)(−0.301+0.953i)Λ(1−s)
Degree: |
2 |
Conductor: |
3549
= 3⋅7⋅132
|
Sign: |
−0.301+0.953i
|
Analytic conductor: |
1.77118 |
Root analytic conductor: |
1.33085 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3549(2027,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3549, ( :0), −0.301+0.953i)
|
Particular Values
L(21) |
≈ |
1.787713112 |
L(21) |
≈ |
1.787713112 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1+(−0.5+0.866i)T |
| 7 | 1−T |
| 13 | 1 |
good | 2 | 1+(−0.5+0.866i)T2 |
| 5 | 1+(−0.5+0.866i)T2 |
| 11 | 1+(−0.5−0.866i)T2 |
| 17 | 1+(0.5+0.866i)T2 |
| 19 | 1+(1.5−0.866i)T+(0.5−0.866i)T2 |
| 23 | 1+(0.5−0.866i)T2 |
| 29 | 1−T2 |
| 31 | 1+(0.5+0.866i)T2 |
| 37 | 1+(−1.5+0.866i)T+(0.5−0.866i)T2 |
| 41 | 1+T2 |
| 43 | 1+T+T2 |
| 47 | 1+(−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)T+(−0.5+0.866i)T2 |
| 67 | 1+(0.5+0.866i)T2 |
| 71 | 1+T2 |
| 73 | 1+(−1.5−0.866i)T+(0.5+0.866i)T2 |
| 79 | 1+(−1−1.73i)T+(−0.5+0.866i)T2 |
| 83 | 1+T2 |
| 89 | 1+(−0.5+0.866i)T2 |
| 97 | 1−1.73iT−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
−8.258345313121635897283444974163, −7.956596336802892185859258476163, −6.95075417051349831004792024554, −6.38289178660233816174991139505, −5.71184273714645165269111202039, −4.78435313950115788866885312619, −3.85003789344574746861109999485, −2.48642925924334335410721501670, −1.99002971842997088432551101453, −0.988385079620251236830817418952,
1.84470622892116988754578254410, 2.65549216054901037730773800983, 3.47547224503991014085091806831, 4.44098704077502661031754280930, 4.80937070239286446947957214667, 5.97051657210641814828685143893, 6.89935756452107476950234747110, 7.69223739874119623098489933960, 8.313887837299748150858049095623, 8.777046709203537479112421379895