L(s) = 1 | + (1.65 + 1.65i)5-s − 7-s + (−0.993 + 0.993i)11-s + (2.62 + 2.62i)13-s + 2.77i·17-s + (−1.56 + 1.56i)19-s − 1.05i·23-s + 0.491i·25-s + (−3.47 + 3.47i)29-s + 1.06i·31-s + (−1.65 − 1.65i)35-s + (−0.0657 + 0.0657i)37-s − 6.31·41-s + (2.38 + 2.38i)43-s − 1.47·47-s + ⋯ |
L(s) = 1 | + (0.741 + 0.741i)5-s − 0.377·7-s + (−0.299 + 0.299i)11-s + (0.728 + 0.728i)13-s + 0.673i·17-s + (−0.358 + 0.358i)19-s − 0.219i·23-s + 0.0982i·25-s + (−0.645 + 0.645i)29-s + 0.190i·31-s + (−0.280 − 0.280i)35-s + (−0.0108 + 0.0108i)37-s − 0.985·41-s + (0.364 + 0.364i)43-s − 0.214·47-s + ⋯ |
Λ(s)=(=(4032s/2ΓC(s)L(s)(−0.717−0.696i)Λ(2−s)
Λ(s)=(=(4032s/2ΓC(s+1/2)L(s)(−0.717−0.696i)Λ(1−s)
Degree: |
2 |
Conductor: |
4032
= 26⋅32⋅7
|
Sign: |
−0.717−0.696i
|
Analytic conductor: |
32.1956 |
Root analytic conductor: |
5.67412 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ4032(1583,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 4032, ( :1/2), −0.717−0.696i)
|
Particular Values
L(1) |
≈ |
1.404674316 |
L(21) |
≈ |
1.404674316 |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1 |
| 7 | 1+T |
good | 5 | 1+(−1.65−1.65i)T+5iT2 |
| 11 | 1+(0.993−0.993i)T−11iT2 |
| 13 | 1+(−2.62−2.62i)T+13iT2 |
| 17 | 1−2.77iT−17T2 |
| 19 | 1+(1.56−1.56i)T−19iT2 |
| 23 | 1+1.05iT−23T2 |
| 29 | 1+(3.47−3.47i)T−29iT2 |
| 31 | 1−1.06iT−31T2 |
| 37 | 1+(0.0657−0.0657i)T−37iT2 |
| 41 | 1+6.31T+41T2 |
| 43 | 1+(−2.38−2.38i)T+43iT2 |
| 47 | 1+1.47T+47T2 |
| 53 | 1+(−7.63−7.63i)T+53iT2 |
| 59 | 1+(4.15−4.15i)T−59iT2 |
| 61 | 1+(7.78+7.78i)T+61iT2 |
| 67 | 1+(1.98−1.98i)T−67iT2 |
| 71 | 1+13.0iT−71T2 |
| 73 | 1+9.50iT−73T2 |
| 79 | 1−9.85iT−79T2 |
| 83 | 1+(−1.13−1.13i)T+83iT2 |
| 89 | 1+7.04T+89T2 |
| 97 | 1−5.35T+97T2 |
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
−8.847702869112784531978719333117, −7.956255658529928597910527181976, −7.13820764440150482564899379575, −6.34847438452488549620784510907, −6.06840498316618870284943607846, −5.03313296254870035107094108523, −4.05772522590265725506838375011, −3.27105020908619148892613646080, −2.30497765930989401547153806697, −1.49756696195347056290504230550,
0.38431836768571028454798239769, 1.50617121741805089086650618208, 2.58363325280024470568732950231, 3.46715483715206153871686312412, 4.42853934597530084830170912839, 5.43362085222428549493167822614, 5.70631132137435664322787825657, 6.63974439577708854312654955243, 7.44887374654742652649007259479, 8.340024727182592496724007660883