L(s) = 1 | + (0.258 + 0.965i)2-s + (−0.5 + 0.133i)3-s + (−0.866 + 0.499i)4-s + (−0.258 − 0.448i)6-s + (−0.707 − 0.707i)8-s + (−0.633 + 0.366i)9-s + (−0.448 + 1.67i)11-s + (0.366 − 0.366i)12-s + (0.500 − 0.866i)16-s + (0.607 + 0.465i)17-s + (−0.517 − 0.517i)18-s + (−1.70 + 0.707i)19-s − 1.73·22-s + (0.448 + 0.258i)24-s + (−0.965 − 0.258i)25-s + ⋯ |
L(s) = 1 | + (0.258 + 0.965i)2-s + (−0.5 + 0.133i)3-s + (−0.866 + 0.499i)4-s + (−0.258 − 0.448i)6-s + (−0.707 − 0.707i)8-s + (−0.633 + 0.366i)9-s + (−0.448 + 1.67i)11-s + (0.366 − 0.366i)12-s + (0.500 − 0.866i)16-s + (0.607 + 0.465i)17-s + (−0.517 − 0.517i)18-s + (−1.70 + 0.707i)19-s − 1.73·22-s + (0.448 + 0.258i)24-s + (−0.965 − 0.258i)25-s + ⋯ |
Λ(s)=(=(776s/2ΓC(s)L(s)(−0.988−0.150i)Λ(1−s)
Λ(s)=(=(776s/2ΓC(s)L(s)(−0.988−0.150i)Λ(1−s)
Degree: |
2 |
Conductor: |
776
= 23⋅97
|
Sign: |
−0.988−0.150i
|
Analytic conductor: |
0.387274 |
Root analytic conductor: |
0.622313 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ776(539,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 776, ( :0), −0.988−0.150i)
|
Particular Values
L(21) |
≈ |
0.6159303363 |
L(21) |
≈ |
0.6159303363 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.258−0.965i)T |
| 97 | 1+(−0.965+0.258i)T |
good | 3 | 1+(0.5−0.133i)T+(0.866−0.5i)T2 |
| 5 | 1+(0.965+0.258i)T2 |
| 7 | 1+(−0.258+0.965i)T2 |
| 11 | 1+(0.448−1.67i)T+(−0.866−0.5i)T2 |
| 13 | 1+(0.965+0.258i)T2 |
| 17 | 1+(−0.607−0.465i)T+(0.258+0.965i)T2 |
| 19 | 1+(1.70−0.707i)T+(0.707−0.707i)T2 |
| 23 | 1+(0.258+0.965i)T2 |
| 29 | 1+(−0.965−0.258i)T2 |
| 31 | 1+(−0.866+0.5i)T2 |
| 37 | 1+(0.258−0.965i)T2 |
| 41 | 1+(−1.83−0.241i)T+(0.965+0.258i)T2 |
| 43 | 1+(−1.67−0.965i)T+(0.5+0.866i)T2 |
| 47 | 1+T2 |
| 53 | 1+(0.866−0.5i)T2 |
| 59 | 1+(0.465+0.607i)T+(−0.258+0.965i)T2 |
| 61 | 1+(0.5+0.866i)T2 |
| 67 | 1+(1.83−0.758i)T+(0.707−0.707i)T2 |
| 71 | 1+(−0.965+0.258i)T2 |
| 73 | 1+(0.5+0.866i)T2 |
| 79 | 1−iT2 |
| 83 | 1+(−0.965−0.741i)T+(0.258+0.965i)T2 |
| 89 | 1+(−1.36−1.36i)T+iT2 |
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
−10.73818409727594933778739849942, −10.05088531229595852296275932457, −9.126815958579719719589482102132, −8.037831727905725490350999759741, −7.57285033966932380270249165507, −6.35275262755267581849566263579, −5.76689320552756515461892229368, −4.72744558259182194716843405847, −4.03481393650677739636832972219, −2.34931219759139854850813734566,
0.61880480843703651093382163743, 2.48455882516805052692740620302, 3.42335981777669448746719898302, 4.55781201495843219272400564559, 5.87058753213018978890023400031, 5.97913435975849543813228924201, 7.67220622493348100173052151093, 8.765967120107860215228710268017, 9.189515313106483178959743360759, 10.60615728948549847803231219739