L(s) = 1 | + (−0.984 − 0.173i)5-s − i·11-s + (0.642 + 0.766i)13-s + (0.939 − 0.342i)17-s + (0.766 − 0.642i)23-s + (0.939 + 0.342i)25-s + (0.984 − 0.173i)29-s + (0.5 − 0.866i)31-s + (0.866 + 0.5i)37-s + (−0.766 − 0.642i)41-s + (−0.342 − 0.939i)43-s + (0.939 + 0.342i)47-s + (−0.984 + 0.173i)53-s + (−0.173 + 0.984i)55-s + (−0.342 − 0.939i)59-s + ⋯ |
L(s) = 1 | + (−0.984 − 0.173i)5-s − i·11-s + (0.642 + 0.766i)13-s + (0.939 − 0.342i)17-s + (0.766 − 0.642i)23-s + (0.939 + 0.342i)25-s + (0.984 − 0.173i)29-s + (0.5 − 0.866i)31-s + (0.866 + 0.5i)37-s + (−0.766 − 0.642i)41-s + (−0.342 − 0.939i)43-s + (0.939 + 0.342i)47-s + (−0.984 + 0.173i)53-s + (−0.173 + 0.984i)55-s + (−0.342 − 0.939i)59-s + ⋯ |
Λ(s)=(=(6384s/2ΓR(s)L(s)(0.556−0.830i)Λ(1−s)
Λ(s)=(=(6384s/2ΓR(s)L(s)(0.556−0.830i)Λ(1−s)
Degree: |
1 |
Conductor: |
6384
= 24⋅3⋅7⋅19
|
Sign: |
0.556−0.830i
|
Analytic conductor: |
29.6471 |
Root analytic conductor: |
29.6471 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ6384(4421,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 6384, (0: ), 0.556−0.830i)
|
Particular Values
L(21) |
≈ |
1.462140325−0.7801942553i |
L(21) |
≈ |
1.462140325−0.7801942553i |
L(1) |
≈ |
1.011745294−0.1572129498i |
L(1) |
≈ |
1.011745294−0.1572129498i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1 |
| 7 | 1 |
| 19 | 1 |
good | 5 | 1+(−0.984−0.173i)T |
| 11 | 1−iT |
| 13 | 1+(0.642+0.766i)T |
| 17 | 1+(0.939−0.342i)T |
| 23 | 1+(0.766−0.642i)T |
| 29 | 1+(0.984−0.173i)T |
| 31 | 1+(0.5−0.866i)T |
| 37 | 1+(0.866+0.5i)T |
| 41 | 1+(−0.766−0.642i)T |
| 43 | 1+(−0.342−0.939i)T |
| 47 | 1+(0.939+0.342i)T |
| 53 | 1+(−0.984+0.173i)T |
| 59 | 1+(−0.342−0.939i)T |
| 61 | 1+(−0.642−0.766i)T |
| 67 | 1+(0.642+0.766i)T |
| 71 | 1+(0.939−0.342i)T |
| 73 | 1+(−0.173+0.984i)T |
| 79 | 1+(0.939−0.342i)T |
| 83 | 1+(0.866−0.5i)T |
| 89 | 1+(−0.173−0.984i)T |
| 97 | 1+(−0.173+0.984i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−17.96140153687661869688119054474, −16.955383284094044982069384087712, −16.40062994588271793492169805366, −15.56567083893767664602487821973, −15.223250593953587323089596381714, −14.63333375990882846405403739490, −13.82468582474277472187146006527, −13.01452451719799532067874451742, −12.346297795977560422131705534676, −11.97904357417837522002414899505, −11.048598565992540297837217153274, −10.57516173504817047134138137880, −9.8432507858685457408731402261, −9.0836807300146914357765289536, −8.11344995863137608255281731845, −7.9000453090036320947263596554, −7.0270665076616598085673522208, −6.44214451413306837119863396153, −5.46900134535313342936864162041, −4.78287883082557324238935767654, −4.08956345004920239390214188114, −3.24682962315173024236838324818, −2.826585689632739196993424841858, −1.532243809562216880143864621019, −0.863213666397516738694208682074,
0.59679203075880184256121467807, 1.16870014498054614407652339327, 2.41443861358874561196418702789, 3.2487248911620359715941926339, 3.76931000490613298335505762780, 4.585555413096241797879118345771, 5.22614980047788836530544382319, 6.21274200209819930160010598474, 6.70268878758377887555522908673, 7.64377228794236905110090218265, 8.19189519870745932976850355270, 8.7725163375532700152927893108, 9.44039452031512024745282514013, 10.39233791663695490564622722856, 11.05513898145465892856570136906, 11.59962779425397344658169993618, 12.15002913078597703230649014280, 12.864443138972833446100829752793, 13.743814278629911730219720468704, 14.13046746063773618840827816966, 14.99059279228035770081729568066, 15.67089624493083902694064054372, 16.16109255758950030198472685933, 16.80125144264204281318316634373, 17.25244492102289413482509261569