L(s) = 1 | + (2.40 − 0.511i)2-s + (3.70 − 1.64i)4-s + (0.968 + 0.205i)5-s + (−0.451 + 4.29i)7-s + (4.08 − 2.96i)8-s + 2.43·10-s + (0.155 − 3.31i)11-s + (2.42 + 2.68i)13-s + (1.11 + 10.5i)14-s + (2.89 − 3.21i)16-s + (−0.816 − 2.51i)17-s + (3.09 − 2.24i)19-s + (3.92 − 0.834i)20-s + (−1.31 − 8.05i)22-s + (1.72 − 2.98i)23-s + ⋯ |
L(s) = 1 | + (1.70 − 0.361i)2-s + (1.85 − 0.824i)4-s + (0.432 + 0.0920i)5-s + (−0.170 + 1.62i)7-s + (1.44 − 1.04i)8-s + 0.770·10-s + (0.0469 − 0.998i)11-s + (0.671 + 0.745i)13-s + (0.297 + 2.82i)14-s + (0.723 − 0.803i)16-s + (−0.197 − 0.609i)17-s + (0.710 − 0.516i)19-s + (0.877 − 0.186i)20-s + (−0.281 − 1.71i)22-s + (0.359 − 0.623i)23-s + ⋯ |
Λ(s)=(=(891s/2ΓC(s)L(s)(0.990+0.140i)Λ(2−s)
Λ(s)=(=(891s/2ΓC(s+1/2)L(s)(0.990+0.140i)Λ(1−s)
Degree: |
2 |
Conductor: |
891
= 34⋅11
|
Sign: |
0.990+0.140i
|
Analytic conductor: |
7.11467 |
Root analytic conductor: |
2.66733 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ891(757,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 891, ( :1/2), 0.990+0.140i)
|
Particular Values
L(1) |
≈ |
4.42418−0.312123i |
L(21) |
≈ |
4.42418−0.312123i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 11 | 1+(−0.155+3.31i)T |
good | 2 | 1+(−2.40+0.511i)T+(1.82−0.813i)T2 |
| 5 | 1+(−0.968−0.205i)T+(4.56+2.03i)T2 |
| 7 | 1+(0.451−4.29i)T+(−6.84−1.45i)T2 |
| 13 | 1+(−2.42−2.68i)T+(−1.35+12.9i)T2 |
| 17 | 1+(0.816+2.51i)T+(−13.7+9.99i)T2 |
| 19 | 1+(−3.09+2.24i)T+(5.87−18.0i)T2 |
| 23 | 1+(−1.72+2.98i)T+(−11.5−19.9i)T2 |
| 29 | 1+(1.08−10.3i)T+(−28.3−6.02i)T2 |
| 31 | 1+(1.12+1.25i)T+(−3.24+30.8i)T2 |
| 37 | 1+(2.61+1.90i)T+(11.4+35.1i)T2 |
| 41 | 1+(1.24+11.8i)T+(−40.1+8.52i)T2 |
| 43 | 1+(−1.06−1.83i)T+(−21.5+37.2i)T2 |
| 47 | 1+(3.92+1.74i)T+(31.4+34.9i)T2 |
| 53 | 1+(−2.93+9.01i)T+(−42.8−31.1i)T2 |
| 59 | 1+(5.91−2.63i)T+(39.4−43.8i)T2 |
| 61 | 1+(3.21−3.57i)T+(−6.37−60.6i)T2 |
| 67 | 1+(0.427−0.739i)T+(−33.5−58.0i)T2 |
| 71 | 1+(−1.16−3.59i)T+(−57.4+41.7i)T2 |
| 73 | 1+(9.22+6.70i)T+(22.5+69.4i)T2 |
| 79 | 1+(6.00−1.27i)T+(72.1−32.1i)T2 |
| 83 | 1+(2.24−2.49i)T+(−8.67−82.5i)T2 |
| 89 | 1−13.2T+89T2 |
| 97 | 1+(−0.363+0.0772i)T+(88.6−39.4i)T2 |
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
−10.47816670841153272496103047246, −9.098389659957915538880545821012, −8.751535908361366577935742036509, −7.05203255987818527624130482980, −6.21857358287926170952894117388, −5.58364717309963409274586113271, −4.95691965399885821795442019260, −3.61169253743977768494079199209, −2.82506193142502707552818805080, −1.88798523699328536316986320375,
1.58212490171419412707799817306, 3.17082825136683945634482695062, 3.97955608428232424236535543204, 4.68056085876662608124649361239, 5.76927335604584504447847276979, 6.42643179221788652259541841331, 7.42187035951023263550635236665, 7.87135028197470768330131227626, 9.601061112522684990626619581954, 10.26128479348517042014509573644