L(s) = 1 | + (0.258 + 0.448i)3-s + (0.707 − 0.707i)7-s + (0.366 − 0.633i)9-s + (0.965 + 1.67i)11-s − 1.73·13-s + (0.5 + 0.866i)17-s + (0.5 + 0.133i)21-s + (0.707 − 1.22i)23-s + (−0.5 − 0.866i)25-s + 0.896·27-s + (0.707 + 1.22i)31-s + (−0.500 + 0.866i)33-s + (−0.448 − 0.776i)39-s − 1.00i·49-s + (−0.258 + 0.448i)51-s + ⋯ |
L(s) = 1 | + (0.258 + 0.448i)3-s + (0.707 − 0.707i)7-s + (0.366 − 0.633i)9-s + (0.965 + 1.67i)11-s − 1.73·13-s + (0.5 + 0.866i)17-s + (0.5 + 0.133i)21-s + (0.707 − 1.22i)23-s + (−0.5 − 0.866i)25-s + 0.896·27-s + (0.707 + 1.22i)31-s + (−0.500 + 0.866i)33-s + (−0.448 − 0.776i)39-s − 1.00i·49-s + (−0.258 + 0.448i)51-s + ⋯ |
Λ(s)=(=(1904s/2ΓC(s)L(s)(0.947−0.319i)Λ(1−s)
Λ(s)=(=(1904s/2ΓC(s)L(s)(0.947−0.319i)Λ(1−s)
Degree: |
2 |
Conductor: |
1904
= 24⋅7⋅17
|
Sign: |
0.947−0.319i
|
Analytic conductor: |
0.950219 |
Root analytic conductor: |
0.974792 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1904(1087,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1904, ( :0), 0.947−0.319i)
|
Particular Values
L(21) |
≈ |
1.407230799 |
L(21) |
≈ |
1.407230799 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 7 | 1+(−0.707+0.707i)T |
| 17 | 1+(−0.5−0.866i)T |
good | 3 | 1+(−0.258−0.448i)T+(−0.5+0.866i)T2 |
| 5 | 1+(0.5+0.866i)T2 |
| 11 | 1+(−0.965−1.67i)T+(−0.5+0.866i)T2 |
| 13 | 1+1.73T+T2 |
| 19 | 1+(0.5+0.866i)T2 |
| 23 | 1+(−0.707+1.22i)T+(−0.5−0.866i)T2 |
| 29 | 1−T2 |
| 31 | 1+(−0.707−1.22i)T+(−0.5+0.866i)T2 |
| 37 | 1+(0.5+0.866i)T2 |
| 41 | 1−T2 |
| 43 | 1−T2 |
| 47 | 1+(0.5+0.866i)T2 |
| 53 | 1+(0.5+0.866i)T+(−0.5+0.866i)T2 |
| 59 | 1+(0.5−0.866i)T2 |
| 61 | 1+(0.5+0.866i)T2 |
| 67 | 1+(0.5−0.866i)T2 |
| 71 | 1−0.517T+T2 |
| 73 | 1+(0.5−0.866i)T2 |
| 79 | 1+(0.965−1.67i)T+(−0.5−0.866i)T2 |
| 83 | 1−T2 |
| 89 | 1+(0.866−1.5i)T+(−0.5−0.866i)T2 |
| 97 | 1−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
−9.740248162771570853240250596059, −8.700673569528244637719563459587, −7.87001746568159633302244459892, −6.95538959104009455157782318602, −6.64714787118121580465943028301, −5.03154550080646598404801402229, −4.49014095554876158102073627022, −3.88443343824757777748563736116, −2.52242672025114502018330956210, −1.38916341217935043774936476899,
1.29745561833815317456190818249, 2.42700677316046928072194148738, 3.28201020192719296336047208311, 4.60927433503944038424059727621, 5.34657057497909776470652159709, 6.09387281382190571911162767529, 7.35769986456912140334666104618, 7.62067515437959437802463736576, 8.568441108228104584382883085086, 9.286464979299899153861114562677