L(s) = 1 | + (−0.984 − 0.173i)3-s + (0.939 + 0.342i)9-s + (0.984 + 1.70i)11-s + (0.592 − 1.62i)17-s + (−0.642 + 0.766i)19-s + (−0.173 + 0.984i)25-s + (−0.866 − 0.5i)27-s + (−0.673 − 1.85i)33-s + (−1.26 + 0.223i)41-s + (0.642 + 0.766i)43-s + (0.5 + 0.866i)49-s + (−0.866 + 1.5i)51-s + (0.766 − 0.642i)57-s + (−1.85 − 0.673i)59-s + (0.524 + 1.43i)67-s + ⋯ |
L(s) = 1 | + (−0.984 − 0.173i)3-s + (0.939 + 0.342i)9-s + (0.984 + 1.70i)11-s + (0.592 − 1.62i)17-s + (−0.642 + 0.766i)19-s + (−0.173 + 0.984i)25-s + (−0.866 − 0.5i)27-s + (−0.673 − 1.85i)33-s + (−1.26 + 0.223i)41-s + (0.642 + 0.766i)43-s + (0.5 + 0.866i)49-s + (−0.866 + 1.5i)51-s + (0.766 − 0.642i)57-s + (−1.85 − 0.673i)59-s + (0.524 + 1.43i)67-s + ⋯ |
Λ(s)=(=(3648s/2ΓC(s)L(s)(0.605−0.796i)Λ(1−s)
Λ(s)=(=(3648s/2ΓC(s)L(s)(0.605−0.796i)Λ(1−s)
Degree: |
2 |
Conductor: |
3648
= 26⋅3⋅19
|
Sign: |
0.605−0.796i
|
Analytic conductor: |
1.82058 |
Root analytic conductor: |
1.34929 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3648(1505,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3648, ( :0), 0.605−0.796i)
|
Particular Values
L(21) |
≈ |
0.9085915699 |
L(21) |
≈ |
0.9085915699 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1+(0.984+0.173i)T |
| 19 | 1+(0.642−0.766i)T |
good | 5 | 1+(0.173−0.984i)T2 |
| 7 | 1+(−0.5−0.866i)T2 |
| 11 | 1+(−0.984−1.70i)T+(−0.5+0.866i)T2 |
| 13 | 1+(0.939+0.342i)T2 |
| 17 | 1+(−0.592+1.62i)T+(−0.766−0.642i)T2 |
| 23 | 1+(−0.173−0.984i)T2 |
| 29 | 1+(0.766−0.642i)T2 |
| 31 | 1+(−0.5−0.866i)T2 |
| 37 | 1−T2 |
| 41 | 1+(1.26−0.223i)T+(0.939−0.342i)T2 |
| 43 | 1+(−0.642−0.766i)T+(−0.173+0.984i)T2 |
| 47 | 1+(−0.766+0.642i)T2 |
| 53 | 1+(0.173+0.984i)T2 |
| 59 | 1+(1.85+0.673i)T+(0.766+0.642i)T2 |
| 61 | 1+(−0.173−0.984i)T2 |
| 67 | 1+(−0.524−1.43i)T+(−0.766+0.642i)T2 |
| 71 | 1+(−0.173+0.984i)T2 |
| 73 | 1+(−0.0603−0.342i)T+(−0.939+0.342i)T2 |
| 79 | 1+(−0.939+0.342i)T2 |
| 83 | 1+(−0.642+1.11i)T+(−0.5−0.866i)T2 |
| 89 | 1+(−1.70−0.300i)T+(0.939+0.342i)T2 |
| 97 | 1+(−1.43−0.524i)T+(0.766+0.642i)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
−9.046177996000430152599418881754, −7.72417050364374406191145910916, −7.31427812042360150274331182320, −6.62952644180159345017646989457, −5.90036291239744746574374349583, −4.94031957492068916623235705917, −4.51075627322303465225344372698, −3.49778610977098627295068948667, −2.11723730331922405806782540303, −1.24062896913672562036949296670,
0.68529853637957071323424076704, 1.85086461583153684310014563429, 3.38882095797686306738419972778, 3.95080974156989587079909946634, 4.86084515338218338495273825090, 5.87642455379467619072930858915, 6.18730148648049152962670743626, 6.85324967163724525071091901285, 7.961146535835328700498458934862, 8.646729523464233782790298168360