L(s) = 1 | + 1.82i·2-s − 2.33·4-s − 2.44i·8-s + 2.12·16-s − 1.95i·17-s − 1.82·19-s − 1.33i·23-s − 1.95·31-s + 1.44i·32-s + 3.57·34-s − 3.33i·38-s + 2.44·46-s − 1.61i·47-s − 49-s + 0.209i·53-s + ⋯ |
L(s) = 1 | + 1.82i·2-s − 2.33·4-s − 2.44i·8-s + 2.12·16-s − 1.95i·17-s − 1.82·19-s − 1.33i·23-s − 1.95·31-s + 1.44i·32-s + 3.57·34-s − 3.33i·38-s + 2.44·46-s − 1.61i·47-s − 49-s + 0.209i·53-s + ⋯ |
Λ(s)=(=(3375s/2ΓC(s)L(s)Λ(1−s)
Λ(s)=(=(3375s/2ΓC(s)L(s)Λ(1−s)
Degree: |
2 |
Conductor: |
3375
= 33⋅53
|
Sign: |
1
|
Analytic conductor: |
1.68434 |
Root analytic conductor: |
1.29782 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3375(1376,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3375, ( :0), 1)
|
Particular Values
L(21) |
≈ |
0.4934673226 |
L(21) |
≈ |
0.4934673226 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 5 | 1 |
good | 2 | 1−1.82iT−T2 |
| 7 | 1+T2 |
| 11 | 1−T2 |
| 13 | 1+T2 |
| 17 | 1+1.95iT−T2 |
| 19 | 1+1.82T+T2 |
| 23 | 1+1.33iT−T2 |
| 29 | 1−T2 |
| 31 | 1+1.95T+T2 |
| 37 | 1+T2 |
| 41 | 1−T2 |
| 43 | 1+T2 |
| 47 | 1+1.61iT−T2 |
| 53 | 1−0.209iT−T2 |
| 59 | 1−T2 |
| 61 | 1+0.209T+T2 |
| 67 | 1+T2 |
| 71 | 1−T2 |
| 73 | 1+T2 |
| 79 | 1−0.209T+T2 |
| 83 | 1−0.209iT−T2 |
| 89 | 1−T2 |
| 97 | 1+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
−8.717264712716054537128525624295, −7.906527286251642073995642334849, −7.15106380006571344023232963896, −6.69214490164254775148805924891, −5.95420778777228819897130092559, −5.08489111882806646051148188378, −4.58733612137639498434243925582, −3.65401444200827237478620781999, −2.29642077818196458777941923242, −0.28790709775048257262888530787,
1.56062405406771046491979877722, 2.04440955693775002631801303930, 3.26461522100164185967484200541, 3.89168356983238406897511778764, 4.53367544624759941134443907771, 5.58742358961995843535992270371, 6.34305891947895765050659309041, 7.60876447986094351396841774604, 8.435397445188503102837135430982, 8.955515271445652244572887865592