L(s) = 1 | − i·2-s − 4-s − 2i·5-s + i·8-s − 2·10-s + 16-s − 2i·17-s + 2i·20-s − 3·25-s + 2i·29-s − i·32-s − 2·34-s − 37-s + 2·40-s + 49-s + 3i·50-s + ⋯ |
L(s) = 1 | − i·2-s − 4-s − 2i·5-s + i·8-s − 2·10-s + 16-s − 2i·17-s + 2i·20-s − 3·25-s + 2i·29-s − i·32-s − 2·34-s − 37-s + 2·40-s + 49-s + 3i·50-s + ⋯ |
Λ(s)=(=(1332s/2ΓC(s)L(s)−Λ(1−s)
Λ(s)=(=(1332s/2ΓC(s)L(s)−Λ(1−s)
Degree: |
2 |
Conductor: |
1332
= 22⋅32⋅37
|
Sign: |
−1
|
Analytic conductor: |
0.664754 |
Root analytic conductor: |
0.815324 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1332(739,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1332, ( :0), −1)
|
Particular Values
L(21) |
≈ |
0.8518879111 |
L(21) |
≈ |
0.8518879111 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+iT |
| 3 | 1 |
| 37 | 1+T |
good | 5 | 1+2iT−T2 |
| 7 | 1−T2 |
| 11 | 1−T2 |
| 13 | 1−T2 |
| 17 | 1+2iT−T2 |
| 19 | 1+T2 |
| 23 | 1+T2 |
| 29 | 1−2iT−T2 |
| 31 | 1+T2 |
| 41 | 1+T2 |
| 43 | 1+T2 |
| 47 | 1−T2 |
| 53 | 1+T2 |
| 59 | 1+T2 |
| 61 | 1−T2 |
| 67 | 1−T2 |
| 71 | 1−T2 |
| 73 | 1−2T+T2 |
| 79 | 1+T2 |
| 83 | 1−T2 |
| 89 | 1+2iT−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
−9.263316578553629191612984165716, −8.948198610174952362307836033265, −8.174508012512069959233592352296, −7.16664658589124262904547794499, −5.50116656458830640152099860584, −5.06240638219309506615955028832, −4.35031676942568073193058559590, −3.21418910234419495105039951092, −1.84593576095628764278001514242, −0.74639961767412490699413610569,
2.20670773972408657015567492181, 3.52071921081218638260797079824, 4.10210315070514634945543175068, 5.63725486358125138537236851318, 6.28692990200769658556860899977, 6.81329015461849506235384451688, 7.73669272123748992875920331166, 8.244531112739665959405529418217, 9.449464391846759011155041588538, 10.27430262381862409988665993183