L(s) = 1 | + (0.959 − 0.281i)3-s + (0.142 + 0.989i)4-s + (−0.544 − 1.19i)5-s + (0.841 − 0.540i)9-s + (0.654 + 0.755i)11-s + (0.415 + 0.909i)12-s + (−0.857 − 0.989i)15-s + (−0.959 + 0.281i)16-s + (1.10 − 0.708i)20-s + (−0.654 − 0.755i)23-s + (−0.468 + 0.540i)25-s + (0.654 − 0.755i)27-s + (0.698 + 0.449i)31-s + (0.841 + 0.540i)33-s + (0.654 + 0.755i)36-s + (−1.80 − 0.822i)37-s + ⋯ |
L(s) = 1 | + (0.959 − 0.281i)3-s + (0.142 + 0.989i)4-s + (−0.544 − 1.19i)5-s + (0.841 − 0.540i)9-s + (0.654 + 0.755i)11-s + (0.415 + 0.909i)12-s + (−0.857 − 0.989i)15-s + (−0.959 + 0.281i)16-s + (1.10 − 0.708i)20-s + (−0.654 − 0.755i)23-s + (−0.468 + 0.540i)25-s + (0.654 − 0.755i)27-s + (0.698 + 0.449i)31-s + (0.841 + 0.540i)33-s + (0.654 + 0.755i)36-s + (−1.80 − 0.822i)37-s + ⋯ |
Λ(s)=(=(759s/2ΓC(s)L(s)(0.985+0.167i)Λ(1−s)
Λ(s)=(=(759s/2ΓC(s)L(s)(0.985+0.167i)Λ(1−s)
Degree: |
2 |
Conductor: |
759
= 3⋅11⋅23
|
Sign: |
0.985+0.167i
|
Analytic conductor: |
0.378790 |
Root analytic conductor: |
0.615459 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ759(329,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 759, ( :0), 0.985+0.167i)
|
Particular Values
L(21) |
≈ |
1.259786761 |
L(21) |
≈ |
1.259786761 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1+(−0.959+0.281i)T |
| 11 | 1+(−0.654−0.755i)T |
| 23 | 1+(0.654+0.755i)T |
good | 2 | 1+(−0.142−0.989i)T2 |
| 5 | 1+(0.544+1.19i)T+(−0.654+0.755i)T2 |
| 7 | 1+(0.841−0.540i)T2 |
| 13 | 1+(−0.841−0.540i)T2 |
| 17 | 1+(0.959+0.281i)T2 |
| 19 | 1+(−0.959+0.281i)T2 |
| 29 | 1+(−0.959−0.281i)T2 |
| 31 | 1+(−0.698−0.449i)T+(0.415+0.909i)T2 |
| 37 | 1+(1.80+0.822i)T+(0.654+0.755i)T2 |
| 41 | 1+(−0.654+0.755i)T2 |
| 43 | 1+(0.415−0.909i)T2 |
| 47 | 1−1.81iT−T2 |
| 53 | 1+(0.273−0.0801i)T+(0.841−0.540i)T2 |
| 59 | 1+(0.557−1.89i)T+(−0.841−0.540i)T2 |
| 61 | 1+(0.415+0.909i)T2 |
| 67 | 1+(0.425+0.368i)T+(0.142+0.989i)T2 |
| 71 | 1+(1.14+0.989i)T+(0.142+0.989i)T2 |
| 73 | 1+(0.959−0.281i)T2 |
| 79 | 1+(0.841+0.540i)T2 |
| 83 | 1+(0.654+0.755i)T2 |
| 89 | 1+(−1.61+1.03i)T+(0.415−0.909i)T2 |
| 97 | 1+(1.65−0.755i)T+(0.654−0.755i)T2 |
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
−10.39907543668218576076302340619, −9.190106398187520352676815178396, −8.818802799117354863527613955680, −7.988931455894788268670224082279, −7.39085575890482624132304394274, −6.41483789461924228818846850239, −4.62953953977017547443132414986, −4.13169368230537108057237909656, −3.01332629440400930167828346057, −1.66851182074270606768332203879,
1.82068606928102639317806062344, 3.10427308500204328268688528516, 3.86755288993258236671664488487, 5.16186917082149028258544852879, 6.39971705183491492453100326513, 7.01978389951912351677596866016, 8.043249648737376402116090207370, 8.913790189027861216309503947952, 9.887718951952190899246854234660, 10.39318469500331951905401857812