L(s) = 1 | + (1.02 − 1.77i)3-s − 2.32·5-s + (−0.804 − 2.52i)7-s + (−0.609 − 1.05i)9-s + (−1.44 − 2.49i)11-s + (−0.126 + 0.219i)13-s + (−2.38 + 4.13i)15-s + (−2.14 + 3.71i)17-s + (−3.08 − 3.07i)19-s + (−5.30 − 1.15i)21-s + (−0.926 − 1.60i)23-s + 0.399·25-s + 3.65·27-s + (0.114 − 0.199i)29-s + (−4.46 − 7.73i)31-s + ⋯ |
L(s) = 1 | + (0.592 − 1.02i)3-s − 1.03·5-s + (−0.303 − 0.952i)7-s + (−0.203 − 0.351i)9-s + (−0.434 − 0.752i)11-s + (−0.0350 + 0.0607i)13-s + (−0.616 + 1.06i)15-s + (−0.519 + 0.900i)17-s + (−0.707 − 0.706i)19-s + (−1.15 − 0.252i)21-s + (−0.193 − 0.334i)23-s + 0.0798·25-s + 0.704·27-s + (0.0213 − 0.0369i)29-s + (−0.801 − 1.38i)31-s + ⋯ |
Λ(s)=(=(532s/2ΓC(s)L(s)(−0.912+0.409i)Λ(2−s)
Λ(s)=(=(532s/2ΓC(s+1/2)L(s)(−0.912+0.409i)Λ(1−s)
Degree: |
2 |
Conductor: |
532
= 22⋅7⋅19
|
Sign: |
−0.912+0.409i
|
Analytic conductor: |
4.24804 |
Root analytic conductor: |
2.06107 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ532(121,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 532, ( :1/2), −0.912+0.409i)
|
Particular Values
L(1) |
≈ |
0.202160−0.943319i |
L(21) |
≈ |
0.202160−0.943319i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 7 | 1+(0.804+2.52i)T |
| 19 | 1+(3.08+3.07i)T |
good | 3 | 1+(−1.02+1.77i)T+(−1.5−2.59i)T2 |
| 5 | 1+2.32T+5T2 |
| 11 | 1+(1.44+2.49i)T+(−5.5+9.52i)T2 |
| 13 | 1+(0.126−0.219i)T+(−6.5−11.2i)T2 |
| 17 | 1+(2.14−3.71i)T+(−8.5−14.7i)T2 |
| 23 | 1+(0.926+1.60i)T+(−11.5+19.9i)T2 |
| 29 | 1+(−0.114+0.199i)T+(−14.5−25.1i)T2 |
| 31 | 1+(4.46+7.73i)T+(−15.5+26.8i)T2 |
| 37 | 1+(−3.34+5.80i)T+(−18.5−32.0i)T2 |
| 41 | 1+(−5.50−9.53i)T+(−20.5+35.5i)T2 |
| 43 | 1+(−2.09−3.62i)T+(−21.5+37.2i)T2 |
| 47 | 1+(4.61+7.99i)T+(−23.5+40.7i)T2 |
| 53 | 1−8.63T+53T2 |
| 59 | 1+(0.351−0.608i)T+(−29.5−51.0i)T2 |
| 61 | 1+(5.19+8.98i)T+(−30.5+52.8i)T2 |
| 67 | 1−10.1T+67T2 |
| 71 | 1+(1.57+2.72i)T+(−35.5+61.4i)T2 |
| 73 | 1+(−3.48+6.03i)T+(−36.5−63.2i)T2 |
| 79 | 1−15.9T+79T2 |
| 83 | 1−5.34T+83T2 |
| 89 | 1+(−1.53−2.66i)T+(−44.5+77.0i)T2 |
| 97 | 1+(6.80+11.7i)T+(−48.5+84.0i)T2 |
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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
−10.77190909612069317551444660071, −9.427073963706286224619922104553, −8.219035205876954078239487341131, −7.908900981269931580130792961496, −7.01234797174486410887663575251, −6.16587615637386606697608460449, −4.45588020045093140429281636415, −3.57959478931039603925445838423, −2.25459845731733058026308325112, −0.50714348904975422759098615716,
2.45609162453092156430452731459, 3.55654279440074419731740476251, 4.41852493561199756847949320626, 5.39353633202998682681040387242, 6.80415577368535854649862277613, 7.83504756968586306380081868369, 8.724139142375890055864385483960, 9.380960180921460277208555307885, 10.22248624328120474478790531564, 11.12001732857196545225460228898