L(s) = 1 | + (−0.290 + 0.956i)2-s + (−0.0980 − 0.995i)3-s + (−0.831 − 0.555i)4-s + (0.881 + 0.471i)5-s + (0.980 + 0.195i)6-s + (0.773 − 0.634i)8-s + (−0.980 + 0.195i)9-s + (−0.707 + 0.707i)10-s + (−0.471 + 0.881i)12-s + (0.382 − 0.923i)15-s + (0.382 + 0.923i)16-s + (0.360 + 0.871i)17-s + (0.0980 − 0.995i)18-s + (0.448 − 1.47i)19-s + (−0.471 − 0.881i)20-s + ⋯ |
L(s) = 1 | + (−0.290 + 0.956i)2-s + (−0.0980 − 0.995i)3-s + (−0.831 − 0.555i)4-s + (0.881 + 0.471i)5-s + (0.980 + 0.195i)6-s + (0.773 − 0.634i)8-s + (−0.980 + 0.195i)9-s + (−0.707 + 0.707i)10-s + (−0.471 + 0.881i)12-s + (0.382 − 0.923i)15-s + (0.382 + 0.923i)16-s + (0.360 + 0.871i)17-s + (0.0980 − 0.995i)18-s + (0.448 − 1.47i)19-s + (−0.471 − 0.881i)20-s + ⋯ |
Λ(s)=(=(1920s/2ΓC(s)L(s)(0.941−0.336i)Λ(1−s)
Λ(s)=(=(1920s/2ΓC(s)L(s)(0.941−0.336i)Λ(1−s)
Degree: |
2 |
Conductor: |
1920
= 27⋅3⋅5
|
Sign: |
0.941−0.336i
|
Analytic conductor: |
0.958204 |
Root analytic conductor: |
0.978879 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1920(1589,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1920, ( :0), 0.941−0.336i)
|
Particular Values
L(21) |
≈ |
1.042752545 |
L(21) |
≈ |
1.042752545 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.290−0.956i)T |
| 3 | 1+(0.0980+0.995i)T |
| 5 | 1+(−0.881−0.471i)T |
good | 7 | 1+(0.923+0.382i)T2 |
| 11 | 1+(0.195−0.980i)T2 |
| 13 | 1+(0.555−0.831i)T2 |
| 17 | 1+(−0.360−0.871i)T+(−0.707+0.707i)T2 |
| 19 | 1+(−0.448+1.47i)T+(−0.831−0.555i)T2 |
| 23 | 1+(−1.59−1.06i)T+(0.382+0.923i)T2 |
| 29 | 1+(−0.195−0.980i)T2 |
| 31 | 1+(1.17+1.17i)T+iT2 |
| 37 | 1+(−0.831+0.555i)T2 |
| 41 | 1+(0.382+0.923i)T2 |
| 43 | 1+(0.980+0.195i)T2 |
| 47 | 1+(−1.83+0.761i)T+(0.707−0.707i)T2 |
| 53 | 1+(−0.301+0.247i)T+(0.195−0.980i)T2 |
| 59 | 1+(0.555+0.831i)T2 |
| 61 | 1+(−1.26+0.124i)T+(0.980−0.195i)T2 |
| 67 | 1+(−0.980+0.195i)T2 |
| 71 | 1+(−0.923−0.382i)T2 |
| 73 | 1+(0.923−0.382i)T2 |
| 79 | 1+(−0.707−0.292i)T+(0.707+0.707i)T2 |
| 83 | 1+(1.87+0.569i)T+(0.831+0.555i)T2 |
| 89 | 1+(−0.382+0.923i)T2 |
| 97 | 1−iT2 |
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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
−9.163933745373036149093871193706, −8.677061245747683996535880742050, −7.50846344472881775201866301683, −7.16203717701029736901789038156, −6.40565218644316870527369658182, −5.60524600912997447131616002552, −5.11722866394464969010825842335, −3.54826147450151661954165612300, −2.30776179858977917781816227474, −1.13497901164359435096039850187,
1.18460624136507505350009319289, 2.55225176479048293361818252346, 3.35868147002420190777648456915, 4.39673322907077775785415046406, 5.16859284503079845222837618126, 5.73620210111394689392220766630, 7.08244962936253591615489374387, 8.240194235697336982575661041314, 8.943035410316241211890130633184, 9.425711979736080864640419452248