L(s) = 1 | + (−0.288 − 0.128i)2-s + (−1.27 − 1.41i)4-s + (3.70 − 1.64i)5-s + (−3.33 + 0.709i)7-s + (0.380 + 1.17i)8-s − 1.28·10-s + (−3.27 + 0.553i)11-s + (−0.144 − 1.37i)13-s + (1.05 + 0.224i)14-s + (−0.356 + 3.39i)16-s + (−5.20 − 3.78i)17-s + (−1.07 − 3.31i)19-s + (−7.03 − 3.13i)20-s + (1.01 + 0.260i)22-s + (−1.86 + 3.23i)23-s + ⋯ |
L(s) = 1 | + (−0.204 − 0.0909i)2-s + (−0.635 − 0.706i)4-s + (1.65 − 0.737i)5-s + (−1.26 + 0.267i)7-s + (0.134 + 0.414i)8-s − 0.405·10-s + (−0.985 + 0.166i)11-s + (−0.0400 − 0.381i)13-s + (0.281 + 0.0599i)14-s + (−0.0891 + 0.847i)16-s + (−1.26 − 0.916i)17-s + (−0.247 − 0.760i)19-s + (−1.57 − 0.700i)20-s + (0.216 + 0.0555i)22-s + (−0.389 + 0.675i)23-s + ⋯ |
Λ(s)=(=(891s/2ΓC(s)L(s)(−0.999+0.00433i)Λ(2−s)
Λ(s)=(=(891s/2ΓC(s+1/2)L(s)(−0.999+0.00433i)Λ(1−s)
Degree: |
2 |
Conductor: |
891
= 34⋅11
|
Sign: |
−0.999+0.00433i
|
Analytic conductor: |
7.11467 |
Root analytic conductor: |
2.66733 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ891(190,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 891, ( :1/2), −0.999+0.00433i)
|
Particular Values
L(1) |
≈ |
0.00115226−0.531559i |
L(21) |
≈ |
0.00115226−0.531559i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 11 | 1+(3.27−0.553i)T |
good | 2 | 1+(0.288+0.128i)T+(1.33+1.48i)T2 |
| 5 | 1+(−3.70+1.64i)T+(3.34−3.71i)T2 |
| 7 | 1+(3.33−0.709i)T+(6.39−2.84i)T2 |
| 13 | 1+(0.144+1.37i)T+(−12.7+2.70i)T2 |
| 17 | 1+(5.20+3.78i)T+(5.25+16.1i)T2 |
| 19 | 1+(1.07+3.31i)T+(−15.3+11.1i)T2 |
| 23 | 1+(1.86−3.23i)T+(−11.5−19.9i)T2 |
| 29 | 1+(−0.0729+0.0155i)T+(26.4−11.7i)T2 |
| 31 | 1+(−0.390−3.71i)T+(−30.3+6.44i)T2 |
| 37 | 1+(0.381−1.17i)T+(−29.9−21.7i)T2 |
| 41 | 1+(9.11+1.93i)T+(37.4+16.6i)T2 |
| 43 | 1+(−0.228−0.395i)T+(−21.5+37.2i)T2 |
| 47 | 1+(1.46−1.63i)T+(−4.91−46.7i)T2 |
| 53 | 1+(−0.729+0.530i)T+(16.3−50.4i)T2 |
| 59 | 1+(5.36+5.96i)T+(−6.16+58.6i)T2 |
| 61 | 1+(0.603−5.74i)T+(−59.6−12.6i)T2 |
| 67 | 1+(−2.92+5.06i)T+(−33.5−58.0i)T2 |
| 71 | 1+(−7.66−5.56i)T+(21.9+67.5i)T2 |
| 73 | 1+(−4.34+13.3i)T+(−59.0−42.9i)T2 |
| 79 | 1+(10.0+4.47i)T+(52.8+58.7i)T2 |
| 83 | 1+(−0.143+1.36i)T+(−81.1−17.2i)T2 |
| 89 | 1+10.3T+89T2 |
| 97 | 1+(7.53+3.35i)T+(64.9+72.0i)T2 |
show more | |
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L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−9.694558936970992613104005823819, −9.127802581382164894047161295964, −8.457855380942469724906773910636, −6.86614908218732695497382061168, −6.08063363506701710749316199875, −5.29444794265520374157331139724, −4.71998437767867085207444612431, −2.87604010199922948996205297448, −1.87107594056148905012902826354, −0.25106705897357914654426306222,
2.14522994141274730155497868810, 3.08028494503808089961125791481, 4.15890571420937113982065556049, 5.49334389544747919111213988714, 6.41282177375271595741202485169, 6.88673982472043462244172891557, 8.157172991634048557322116524693, 8.976392102205863571291652830059, 9.884082252155495719460718097397, 10.14902832145782431836813511781