L(s) = 1 | + (−0.802 + 0.597i)2-s + (0.286 − 0.957i)4-s + (0.727 + 0.686i)7-s + (0.342 + 0.939i)8-s + (−0.893 + 0.448i)11-s + (−0.918 + 0.396i)13-s + (−0.993 − 0.116i)14-s + (−0.835 − 0.549i)16-s + (0.642 + 0.766i)17-s + (−0.766 − 0.642i)19-s + (0.448 − 0.893i)22-s + (−0.727 + 0.686i)23-s + (0.5 − 0.866i)26-s + (0.866 − 0.5i)28-s + (−0.993 + 0.116i)29-s + ⋯ |
L(s) = 1 | + (−0.802 + 0.597i)2-s + (0.286 − 0.957i)4-s + (0.727 + 0.686i)7-s + (0.342 + 0.939i)8-s + (−0.893 + 0.448i)11-s + (−0.918 + 0.396i)13-s + (−0.993 − 0.116i)14-s + (−0.835 − 0.549i)16-s + (0.642 + 0.766i)17-s + (−0.766 − 0.642i)19-s + (0.448 − 0.893i)22-s + (−0.727 + 0.686i)23-s + (0.5 − 0.866i)26-s + (0.866 − 0.5i)28-s + (−0.993 + 0.116i)29-s + ⋯ |
Λ(s)=(=(405s/2ΓR(s)L(s)(−0.860+0.509i)Λ(1−s)
Λ(s)=(=(405s/2ΓR(s)L(s)(−0.860+0.509i)Λ(1−s)
Degree: |
1 |
Conductor: |
405
= 34⋅5
|
Sign: |
−0.860+0.509i
|
Analytic conductor: |
1.88081 |
Root analytic conductor: |
1.88081 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ405(68,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 405, (0: ), −0.860+0.509i)
|
Particular Values
L(21) |
≈ |
0.1484976303+0.5426975094i |
L(21) |
≈ |
0.1484976303+0.5426975094i |
L(1) |
≈ |
0.5677567659+0.3011414098i |
L(1) |
≈ |
0.5677567659+0.3011414098i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 5 | 1 |
good | 2 | 1+(−0.802+0.597i)T |
| 7 | 1+(0.727+0.686i)T |
| 11 | 1+(−0.893+0.448i)T |
| 13 | 1+(−0.918+0.396i)T |
| 17 | 1+(0.642+0.766i)T |
| 19 | 1+(−0.766−0.642i)T |
| 23 | 1+(−0.727+0.686i)T |
| 29 | 1+(−0.993+0.116i)T |
| 31 | 1+(0.973−0.230i)T |
| 37 | 1+(0.984−0.173i)T |
| 41 | 1+(−0.597+0.802i)T |
| 43 | 1+(−0.998−0.0581i)T |
| 47 | 1+(−0.230+0.973i)T |
| 53 | 1+(−0.866+0.5i)T |
| 59 | 1+(0.893+0.448i)T |
| 61 | 1+(−0.286−0.957i)T |
| 67 | 1+(−0.116+0.993i)T |
| 71 | 1+(0.939+0.342i)T |
| 73 | 1+(−0.342−0.939i)T |
| 79 | 1+(−0.597−0.802i)T |
| 83 | 1+(0.802−0.597i)T |
| 89 | 1+(−0.939+0.342i)T |
| 97 | 1+(−0.549+0.835i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−24.10361362386469726867411984196, −23.06379923503337875430297139806, −22.03630026376413968011332469806, −21.04067396725087930279056404726, −20.56855009917833284759098330807, −19.66307248411057468687184479795, −18.65135847036034343696313153703, −18.05052674434539483252247424532, −16.98725592184498180738353401389, −16.495255799378405626622985825070, −15.26266047539316017129774841551, −14.1547707264071881205243350670, −13.14737764487833832875308060860, −12.18896432083288000340667955407, −11.29557473149284132886022348583, −10.34941634034489148189035977103, −9.82707564327056906846244887799, −8.31614845971689378627806860679, −7.887865846004559003568367445672, −6.859447022479149982210245778646, −5.30115653866991875812160106804, −4.15777323096005154603077709312, −2.940421396772922472485577914599, −1.879416087574081320121585548926, −0.41179945595950939092545481793,
1.654928351442686683479568920847, 2.54827918026250769883967896993, 4.55815583134634373336947563088, 5.391993215309500032555830505976, 6.398417439490760220890385700718, 7.658139532819536058373119008638, 8.14759091009233406683114242085, 9.3128188556228152269406910073, 10.09750204047206017881294144929, 11.12720872823633736109272082387, 12.04256185447591521949378026046, 13.241684984872373700411693468148, 14.58872972071446141362386368944, 15.01875401976241364286493339477, 15.90475972696474286724394394498, 17.023822203890635715488533182, 17.63399457179764130898758075124, 18.5291377433820512716017741017, 19.23142427583638895925347252082, 20.20579325378811297786367478773, 21.203808510254329983474805763017, 22.013536690352963290778712735998, 23.44894918092018187241120702452, 23.88436008326287100807279539310, 24.77259961284391456819738518933