L(s) = 1 | + (−0.766 + 0.642i)2-s + (0.326 + 0.118i)3-s + (0.173 − 0.984i)4-s + (−0.326 + 0.118i)6-s + (0.500 + 0.866i)8-s + (−0.673 − 0.565i)9-s + (−0.173 − 0.300i)11-s + (0.173 − 0.300i)12-s + (−0.939 − 0.342i)16-s + (−1.53 + 1.28i)17-s + 0.879·18-s + (−0.939 + 0.342i)19-s + (0.326 + 0.118i)22-s + (0.0603 + 0.342i)24-s + (−0.326 − 0.565i)27-s + ⋯ |
L(s) = 1 | + (−0.766 + 0.642i)2-s + (0.326 + 0.118i)3-s + (0.173 − 0.984i)4-s + (−0.326 + 0.118i)6-s + (0.500 + 0.866i)8-s + (−0.673 − 0.565i)9-s + (−0.173 − 0.300i)11-s + (0.173 − 0.300i)12-s + (−0.939 − 0.342i)16-s + (−1.53 + 1.28i)17-s + 0.879·18-s + (−0.939 + 0.342i)19-s + (0.326 + 0.118i)22-s + (0.0603 + 0.342i)24-s + (−0.326 − 0.565i)27-s + ⋯ |
Λ(s)=(=(3800s/2ΓC(s)L(s)(−0.944+0.327i)Λ(1−s)
Λ(s)=(=(3800s/2ΓC(s)L(s)(−0.944+0.327i)Λ(1−s)
Degree: |
2 |
Conductor: |
3800
= 23⋅52⋅19
|
Sign: |
−0.944+0.327i
|
Analytic conductor: |
1.89644 |
Root analytic conductor: |
1.37711 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3800(1051,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3800, ( :0), −0.944+0.327i)
|
Particular Values
L(21) |
≈ |
0.1036343074 |
L(21) |
≈ |
0.1036343074 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.766−0.642i)T |
| 5 | 1 |
| 19 | 1+(0.939−0.342i)T |
good | 3 | 1+(−0.326−0.118i)T+(0.766+0.642i)T2 |
| 7 | 1+(0.5+0.866i)T2 |
| 11 | 1+(0.173+0.300i)T+(−0.5+0.866i)T2 |
| 13 | 1+(−0.766+0.642i)T2 |
| 17 | 1+(1.53−1.28i)T+(0.173−0.984i)T2 |
| 23 | 1+(0.939+0.342i)T2 |
| 29 | 1+(−0.173−0.984i)T2 |
| 31 | 1+(0.5+0.866i)T2 |
| 37 | 1−T2 |
| 41 | 1+(1.43+0.524i)T+(0.766+0.642i)T2 |
| 43 | 1+(−0.173−0.984i)T+(−0.939+0.342i)T2 |
| 47 | 1+(−0.173−0.984i)T2 |
| 53 | 1+(0.939+0.342i)T2 |
| 59 | 1+(1.43−1.20i)T+(0.173−0.984i)T2 |
| 61 | 1+(0.939+0.342i)T2 |
| 67 | 1+(1.17+0.984i)T+(0.173+0.984i)T2 |
| 71 | 1+(0.939−0.342i)T2 |
| 73 | 1+(−1.43−0.524i)T+(0.766+0.642i)T2 |
| 79 | 1+(−0.766−0.642i)T2 |
| 83 | 1+(0.939−1.62i)T+(−0.5−0.866i)T2 |
| 89 | 1+(−0.939+0.342i)T+(0.766−0.642i)T2 |
| 97 | 1+(0.266−0.223i)T+(0.173−0.984i)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
−8.881021293318728160751902383405, −8.410582605413685325449442453312, −7.896597841356794731488206918501, −6.71878242464560178446231330295, −6.35688661564013329079372763177, −5.62897233144176985526571212329, −4.61285802541679709603768043216, −3.75110389753935244370787086989, −2.56971745405072568368513128421, −1.64588176062350009232667802072,
0.06633626023977120830009807562, 1.82684618122980062342493503958, 2.50249483844104010825832177651, 3.23144642428906930605384559330, 4.41212893395538740889793640553, 5.00251187336911850766062152029, 6.31877777882005621787775285791, 7.01762484749934931403913945566, 7.70650018667620485029779266731, 8.470070722979701079321455517613