L(s) = 1 | + (0.608 − 0.793i)3-s + (−0.793 + 0.608i)5-s + (−0.258 − 0.965i)9-s + (−0.991 + 0.130i)11-s + (0.923 − 0.382i)13-s + i·15-s + (0.866 − 0.5i)17-s + (0.130 − 0.991i)19-s + (0.258 + 0.965i)23-s + (0.258 − 0.965i)25-s + (−0.923 − 0.382i)27-s + (0.382 + 0.923i)29-s + (−0.5 − 0.866i)31-s + (−0.5 + 0.866i)33-s + (−0.793 + 0.608i)37-s + ⋯ |
L(s) = 1 | + (0.608 − 0.793i)3-s + (−0.793 + 0.608i)5-s + (−0.258 − 0.965i)9-s + (−0.991 + 0.130i)11-s + (0.923 − 0.382i)13-s + i·15-s + (0.866 − 0.5i)17-s + (0.130 − 0.991i)19-s + (0.258 + 0.965i)23-s + (0.258 − 0.965i)25-s + (−0.923 − 0.382i)27-s + (0.382 + 0.923i)29-s + (−0.5 − 0.866i)31-s + (−0.5 + 0.866i)33-s + (−0.793 + 0.608i)37-s + ⋯ |
Λ(s)=(=(448s/2ΓR(s+1)L(s)(−0.955+0.294i)Λ(1−s)
Λ(s)=(=(448s/2ΓR(s+1)L(s)(−0.955+0.294i)Λ(1−s)
Degree: |
1 |
Conductor: |
448
= 26⋅7
|
Sign: |
−0.955+0.294i
|
Analytic conductor: |
48.1442 |
Root analytic conductor: |
48.1442 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ448(101,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 448, (1: ), −0.955+0.294i)
|
Particular Values
L(21) |
≈ |
−0.05550970081−0.3689407831i |
L(21) |
≈ |
−0.05550970081−0.3689407831i |
L(1) |
≈ |
0.8895647157−0.2409906112i |
L(1) |
≈ |
0.8895647157−0.2409906112i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 7 | 1 |
good | 3 | 1+(0.608−0.793i)T |
| 5 | 1+(−0.793+0.608i)T |
| 11 | 1+(−0.991+0.130i)T |
| 13 | 1+(0.923−0.382i)T |
| 17 | 1+(0.866−0.5i)T |
| 19 | 1+(0.130−0.991i)T |
| 23 | 1+(0.258+0.965i)T |
| 29 | 1+(0.382+0.923i)T |
| 31 | 1+(−0.5−0.866i)T |
| 37 | 1+(−0.793+0.608i)T |
| 41 | 1+(−0.707+0.707i)T |
| 43 | 1+(−0.382+0.923i)T |
| 47 | 1+(−0.866−0.5i)T |
| 53 | 1+(−0.991+0.130i)T |
| 59 | 1+(−0.130−0.991i)T |
| 61 | 1+(−0.991−0.130i)T |
| 67 | 1+(−0.608+0.793i)T |
| 71 | 1+(−0.707−0.707i)T |
| 73 | 1+(−0.965−0.258i)T |
| 79 | 1+(−0.866−0.5i)T |
| 83 | 1+(−0.923+0.382i)T |
| 89 | 1+(0.965−0.258i)T |
| 97 | 1+T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−24.24563850253877180855659574347, −23.33134907699755213646677598102, −22.69555765883932748063407813790, −21.26810162952520828559651306354, −20.94142661320427949470791928338, −20.17783813785894052535757751795, −19.124288797681558246652787115145, −18.58216833221244129432238321258, −17.04040951983722662778029056886, −16.19293143926940080857128331241, −15.772154647080950614926602388207, −14.782990737848933162459154576616, −13.88920276096920045541272590665, −12.88813794101112799608368262690, −11.95293901564504722348889690284, −10.78203049880714527966960637792, −10.15214939256587009685910446417, −8.83691981535194550486461107419, −8.31882947363972465259445815593, −7.47260874372959525277329074642, −5.82824153968301976699010254302, −4.85831174730109996648278028384, −3.887145872969541022817114133739, −3.11966934671431905001849969167, −1.59431096980984718142311351891,
0.08999905859207553216574115552, 1.43610000062465562158171005714, 2.96665375341500324763864592027, 3.3450962670397629741230629247, 4.938640394563178200953655259506, 6.23186690566686091259078406412, 7.27078919408517300290836250701, 7.84256600341177834053287787516, 8.73097253497320050729068280212, 9.94819565723532180812501925619, 11.09084804447802483229671911643, 11.83142717778900542939811646266, 12.9504358614471800855955876506, 13.57368330201616099989507496281, 14.636770175596803043476154317, 15.39525899992975950361451946518, 16.140073906336520904278088216121, 17.63096934462669825240622773556, 18.38833815278955724374055600466, 18.88997399840896482721930214086, 19.88669488740148246427275332206, 20.522387123570902666828106114674, 21.5257814790876111214011047313, 22.77727318835814174451938066402, 23.508323431670134043208621424454