L(s) = 1 | + (0.841 − 0.540i)2-s + (0.415 − 0.909i)4-s + (−0.654 + 0.755i)7-s + (−0.142 − 0.989i)8-s + (0.959 − 0.281i)9-s + (0.239 − 0.153i)11-s + (−0.142 + 0.989i)14-s + (−0.654 − 0.755i)16-s + (0.654 − 0.755i)18-s + (0.118 − 0.258i)22-s + (−0.959 − 0.281i)23-s + (−0.841 − 0.540i)25-s + (0.415 + 0.909i)28-s + (−0.698 + 1.53i)29-s + (−0.959 − 0.281i)32-s + ⋯ |
L(s) = 1 | + (0.841 − 0.540i)2-s + (0.415 − 0.909i)4-s + (−0.654 + 0.755i)7-s + (−0.142 − 0.989i)8-s + (0.959 − 0.281i)9-s + (0.239 − 0.153i)11-s + (−0.142 + 0.989i)14-s + (−0.654 − 0.755i)16-s + (0.654 − 0.755i)18-s + (0.118 − 0.258i)22-s + (−0.959 − 0.281i)23-s + (−0.841 − 0.540i)25-s + (0.415 + 0.909i)28-s + (−0.698 + 1.53i)29-s + (−0.959 − 0.281i)32-s + ⋯ |
Λ(s)=(=(644s/2ΓC(s)L(s)(0.603+0.797i)Λ(1−s)
Λ(s)=(=(644s/2ΓC(s)L(s)(0.603+0.797i)Λ(1−s)
Degree: |
2 |
Conductor: |
644
= 22⋅7⋅23
|
Sign: |
0.603+0.797i
|
Analytic conductor: |
0.321397 |
Root analytic conductor: |
0.566919 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ644(251,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 644, ( :0), 0.603+0.797i)
|
Particular Values
L(21) |
≈ |
1.426212687 |
L(21) |
≈ |
1.426212687 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.841+0.540i)T |
| 7 | 1+(0.654−0.755i)T |
| 23 | 1+(0.959+0.281i)T |
good | 3 | 1+(−0.959+0.281i)T2 |
| 5 | 1+(0.841+0.540i)T2 |
| 11 | 1+(−0.239+0.153i)T+(0.415−0.909i)T2 |
| 13 | 1+(0.142−0.989i)T2 |
| 17 | 1+(−0.654−0.755i)T2 |
| 19 | 1+(0.654−0.755i)T2 |
| 29 | 1+(0.698−1.53i)T+(−0.654−0.755i)T2 |
| 31 | 1+(−0.959−0.281i)T2 |
| 37 | 1+(−0.425−1.45i)T+(−0.841+0.540i)T2 |
| 41 | 1+(−0.841−0.540i)T2 |
| 43 | 1+(−0.273−1.89i)T+(−0.959+0.281i)T2 |
| 47 | 1+T2 |
| 53 | 1+(0.817+0.708i)T+(0.142+0.989i)T2 |
| 59 | 1+(−0.142+0.989i)T2 |
| 61 | 1+(−0.959−0.281i)T2 |
| 67 | 1+(0.698+0.449i)T+(0.415+0.909i)T2 |
| 71 | 1+(−1.07+1.66i)T+(−0.415−0.909i)T2 |
| 73 | 1+(0.654−0.755i)T2 |
| 79 | 1+(−1.10−1.27i)T+(−0.142+0.989i)T2 |
| 83 | 1+(−0.841+0.540i)T2 |
| 89 | 1+(−0.959+0.281i)T2 |
| 97 | 1+(0.841+0.540i)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
−10.72869189528752176476262576347, −9.790095331077183246732334318377, −9.346896719593310270676999816702, −7.982255642059685181861509489900, −6.67661229051591541463817605022, −6.16439433008079971530569168618, −5.02818209323460077533481917708, −3.99550467749531639950049967792, −3.02464921740565158653968290842, −1.70321731499122355163687785107,
2.13638851526052235030581545632, 3.78017519468288730713362677628, 4.18210096799366597931473876415, 5.53159195079931390018441952677, 6.40855376916982194746710992602, 7.38028101660177667425654918050, 7.78503816095351405743086324151, 9.222557338681238592414041832958, 10.04966148117687477186386969782, 10.98159086231213536672194083891