L(s) = 1 | + (0.342 − 0.939i)2-s + (0.984 − 0.173i)3-s + (−0.766 − 0.642i)4-s + (0.173 − 0.984i)6-s + (−0.866 − 0.5i)7-s + (−0.866 + 0.5i)8-s + (0.939 − 0.342i)9-s + (−0.5 − 0.866i)11-s + (−0.866 − 0.5i)12-s + (−0.984 − 0.173i)13-s + (−0.766 + 0.642i)14-s + (0.173 + 0.984i)16-s + (0.342 − 0.939i)17-s − i·18-s + (−0.939 − 0.342i)21-s + (−0.984 + 0.173i)22-s + ⋯ |
L(s) = 1 | + (0.342 − 0.939i)2-s + (0.984 − 0.173i)3-s + (−0.766 − 0.642i)4-s + (0.173 − 0.984i)6-s + (−0.866 − 0.5i)7-s + (−0.866 + 0.5i)8-s + (0.939 − 0.342i)9-s + (−0.5 − 0.866i)11-s + (−0.866 − 0.5i)12-s + (−0.984 − 0.173i)13-s + (−0.766 + 0.642i)14-s + (0.173 + 0.984i)16-s + (0.342 − 0.939i)17-s − i·18-s + (−0.939 − 0.342i)21-s + (−0.984 + 0.173i)22-s + ⋯ |
Λ(s)=(=(95s/2ΓR(s+1)L(s)(−0.982−0.187i)Λ(1−s)
Λ(s)=(=(95s/2ΓR(s+1)L(s)(−0.982−0.187i)Λ(1−s)
Degree: |
1 |
Conductor: |
95
= 5⋅19
|
Sign: |
−0.982−0.187i
|
Analytic conductor: |
10.2091 |
Root analytic conductor: |
10.2091 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ95(17,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 95, (1: ), −0.982−0.187i)
|
Particular Values
L(21) |
≈ |
0.1767802170−1.868072433i |
L(21) |
≈ |
0.1767802170−1.868072433i |
L(1) |
≈ |
0.9223565861−0.9931757242i |
L(1) |
≈ |
0.9223565861−0.9931757242i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1 |
| 19 | 1 |
good | 2 | 1+(0.342−0.939i)T |
| 3 | 1+(0.984−0.173i)T |
| 7 | 1+(−0.866−0.5i)T |
| 11 | 1+(−0.5−0.866i)T |
| 13 | 1+(−0.984−0.173i)T |
| 17 | 1+(0.342−0.939i)T |
| 23 | 1+(0.642−0.766i)T |
| 29 | 1+(0.939−0.342i)T |
| 31 | 1+(−0.5+0.866i)T |
| 37 | 1+iT |
| 41 | 1+(0.173+0.984i)T |
| 43 | 1+(−0.642−0.766i)T |
| 47 | 1+(−0.342−0.939i)T |
| 53 | 1+(0.642−0.766i)T |
| 59 | 1+(0.939+0.342i)T |
| 61 | 1+(0.766+0.642i)T |
| 67 | 1+(−0.342−0.939i)T |
| 71 | 1+(0.766−0.642i)T |
| 73 | 1+(0.984−0.173i)T |
| 79 | 1+(−0.173−0.984i)T |
| 83 | 1+(0.866+0.5i)T |
| 89 | 1+(−0.173+0.984i)T |
| 97 | 1+(0.342−0.939i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−30.98135770518217531849514316454, −29.62812808914594419659100819449, −28.09104119273540869789990167435, −26.91429010043483726294250617971, −25.92172520323100338441854735468, −25.407476203211366458521523823429, −24.37425853069745485940614474263, −23.19992730323075993973255197939, −22.01392563004468109425444409266, −21.19720271091912799640121382338, −19.71348438815784601881966168497, −18.76154287650181773569324831111, −17.418043975058359146609800650165, −16.10412777332303770928350032251, −15.22478334540377254566419336291, −14.46433164496284062734975852764, −13.087480482507805945294002787446, −12.44098821233523486340195659076, −9.97829340533415089742588057409, −9.1514200243059098579517436602, −7.86017759675165875025532754001, −6.86568591240963037166991393461, −5.27218632101250518940891513829, −3.89119442824375811129816938206, −2.55597237984191897337141684415,
0.66769473517189660564445617831, 2.61136917444070395285106627891, 3.41231115360505481604069947558, 4.948119818026468540083078003138, 6.80971678393313520431257633691, 8.375271067209906133229225270198, 9.61021203171702628485831432351, 10.43667545784786827476793935019, 12.08531733577547896342186510867, 13.165931551949986314580798249970, 13.88806909531061409519570712478, 15.007569792172347794277779056984, 16.4244020102644219776892076580, 18.198270858395307907851027038190, 19.16426091763895587643733981010, 19.86815435623128000085061756300, 20.84607498271861998889276216975, 21.85294329714583465939167076019, 23.018794871997052769039860065100, 24.1190196008869760289567351059, 25.26897192213336807253471232055, 26.70738251597767160050846473916, 27.07796898200707536148837042582, 28.90450713008216150070872378823, 29.48330036745819583981651496752