L(s) = 1 | + (0.991 + 0.130i)3-s + (0.258 − 0.965i)7-s + (0.965 + 0.258i)9-s + (−0.608 − 0.793i)11-s + (0.866 − 0.5i)17-s + (0.793 + 0.608i)19-s + (0.382 − 0.923i)21-s + (−0.258 − 0.965i)23-s + (0.923 + 0.382i)27-s + (0.991 + 0.130i)29-s − 31-s + (−0.5 − 0.866i)33-s + (−0.793 + 0.608i)37-s + (0.258 + 0.965i)41-s + (0.991 − 0.130i)43-s + ⋯ |
L(s) = 1 | + (0.991 + 0.130i)3-s + (0.258 − 0.965i)7-s + (0.965 + 0.258i)9-s + (−0.608 − 0.793i)11-s + (0.866 − 0.5i)17-s + (0.793 + 0.608i)19-s + (0.382 − 0.923i)21-s + (−0.258 − 0.965i)23-s + (0.923 + 0.382i)27-s + (0.991 + 0.130i)29-s − 31-s + (−0.5 − 0.866i)33-s + (−0.793 + 0.608i)37-s + (0.258 + 0.965i)41-s + (0.991 − 0.130i)43-s + ⋯ |
Λ(s)=(=(4160s/2ΓR(s)L(s)(0.587−0.809i)Λ(1−s)
Λ(s)=(=(4160s/2ΓR(s)L(s)(0.587−0.809i)Λ(1−s)
Degree: |
1 |
Conductor: |
4160
= 26⋅5⋅13
|
Sign: |
0.587−0.809i
|
Analytic conductor: |
19.3189 |
Root analytic conductor: |
19.3189 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ4160(2629,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 4160, (0: ), 0.587−0.809i)
|
Particular Values
L(21) |
≈ |
2.540334749−1.294578236i |
L(21) |
≈ |
2.540334749−1.294578236i |
L(1) |
≈ |
1.586842502−0.2765977031i |
L(1) |
≈ |
1.586842502−0.2765977031i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1 |
| 13 | 1 |
good | 3 | 1+(0.991+0.130i)T |
| 7 | 1+(0.258−0.965i)T |
| 11 | 1+(−0.608−0.793i)T |
| 17 | 1+(0.866−0.5i)T |
| 19 | 1+(0.793+0.608i)T |
| 23 | 1+(−0.258−0.965i)T |
| 29 | 1+(0.991+0.130i)T |
| 31 | 1−T |
| 37 | 1+(−0.793+0.608i)T |
| 41 | 1+(0.258+0.965i)T |
| 43 | 1+(0.991−0.130i)T |
| 47 | 1−iT |
| 53 | 1+(0.382−0.923i)T |
| 59 | 1+(−0.130−0.991i)T |
| 61 | 1+(0.608−0.793i)T |
| 67 | 1+(0.991+0.130i)T |
| 71 | 1+(−0.258+0.965i)T |
| 73 | 1+(0.707−0.707i)T |
| 79 | 1+iT |
| 83 | 1+(0.923−0.382i)T |
| 89 | 1+(−0.965+0.258i)T |
| 97 | 1+(−0.5−0.866i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−18.529964529272654646716433315119, −17.93925993016366482759483219997, −17.427032181782684822944420970204, −16.160295203586301733756803639004, −15.67437231199667731029742408088, −15.1106517998476027282280957474, −14.50472341825260143631553237803, −13.797243557377629392564858739467, −13.12802216882438172250565888797, −12.232701897429831745190308492349, −12.07208196386280635052749454501, −10.82904522672209050337295424100, −10.12770084606912539917039245565, −9.3517898780635661841314695904, −8.91761872790421031105749328262, −8.01999418385559123315489369868, −7.52701959550597445408694666719, −6.84634009050970244673327523946, −5.64425956909201189137886232858, −5.21285665524734845772828085975, −4.17042032135467262612176873726, −3.40488872036763717159469516348, −2.56850325664154634364326071128, −2.025466599980187138656698055310, −1.127844251308407303791490559523,
0.74066883754819810151392704620, 1.52104565341009899135081855406, 2.60889451075428999348807251542, 3.276829856714278080352161804089, 3.890002486645476301645578793269, 4.77875024375957074507518074605, 5.46584712016367970423273593591, 6.587958510043321134164045688593, 7.290854628992893051727153972713, 8.108145627309084580669820681233, 8.26960835229514446766097979177, 9.43721884467812678630483880242, 9.97473728821821574857698928849, 10.6294282571066314975628846171, 11.29524739045764382246484877464, 12.35889836074532788838798216189, 12.94577295083900879101760170283, 13.84194159845455492102681426546, 14.14785656911669440937063211134, 14.635915338618845187904925847378, 15.74992602995279451559522347456, 16.19806677019779967573267709250, 16.72778348978788500084932012585, 17.76669593271242013847069615070, 18.44874116265442339003469185957