L(s) = 1 | + (−0.529 + 1.62i)3-s + (0.809 − 0.587i)5-s + (−1.14 − 3.52i)7-s + (0.0536 + 0.0389i)9-s + (−2.68 + 1.94i)11-s + (0.952 + 0.692i)13-s + (0.529 + 1.62i)15-s + (4.36 − 3.17i)17-s + (1.18 − 3.65i)19-s + 6.34·21-s + 8.68·23-s + (0.309 − 0.951i)25-s + (−4.24 + 3.08i)27-s + (−2.12 − 6.53i)29-s + (7.08 + 5.14i)31-s + ⋯ |
L(s) = 1 | + (−0.305 + 0.940i)3-s + (0.361 − 0.262i)5-s + (−0.432 − 1.33i)7-s + (0.0178 + 0.0129i)9-s + (−0.810 + 0.585i)11-s + (0.264 + 0.191i)13-s + (0.136 + 0.420i)15-s + (1.05 − 0.769i)17-s + (0.272 − 0.839i)19-s + 1.38·21-s + 1.81·23-s + (0.0618 − 0.190i)25-s + (−0.817 + 0.594i)27-s + (−0.394 − 1.21i)29-s + (1.27 + 0.924i)31-s + ⋯ |
Λ(s)=(=(880s/2ΓC(s)L(s)(0.999−0.0206i)Λ(2−s)
Λ(s)=(=(880s/2ΓC(s+1/2)L(s)(0.999−0.0206i)Λ(1−s)
Degree: |
2 |
Conductor: |
880
= 24⋅5⋅11
|
Sign: |
0.999−0.0206i
|
Analytic conductor: |
7.02683 |
Root analytic conductor: |
2.65081 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ880(81,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 880, ( :1/2), 0.999−0.0206i)
|
Particular Values
L(1) |
≈ |
1.46702+0.0151531i |
L(21) |
≈ |
1.46702+0.0151531i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1+(−0.809+0.587i)T |
| 11 | 1+(2.68−1.94i)T |
good | 3 | 1+(0.529−1.62i)T+(−2.42−1.76i)T2 |
| 7 | 1+(1.14+3.52i)T+(−5.66+4.11i)T2 |
| 13 | 1+(−0.952−0.692i)T+(4.01+12.3i)T2 |
| 17 | 1+(−4.36+3.17i)T+(5.25−16.1i)T2 |
| 19 | 1+(−1.18+3.65i)T+(−15.3−11.1i)T2 |
| 23 | 1−8.68T+23T2 |
| 29 | 1+(2.12+6.53i)T+(−23.4+17.0i)T2 |
| 31 | 1+(−7.08−5.14i)T+(9.57+29.4i)T2 |
| 37 | 1+(−0.696−2.14i)T+(−29.9+21.7i)T2 |
| 41 | 1+(−0.493+1.51i)T+(−33.1−24.0i)T2 |
| 43 | 1+4.11T+43T2 |
| 47 | 1+(−3.91+12.0i)T+(−38.0−27.6i)T2 |
| 53 | 1+(−10.0−7.27i)T+(16.3+50.4i)T2 |
| 59 | 1+(−0.121−0.374i)T+(−47.7+34.6i)T2 |
| 61 | 1+(1.45−1.05i)T+(18.8−58.0i)T2 |
| 67 | 1−14.3T+67T2 |
| 71 | 1+(5.54−4.02i)T+(21.9−67.5i)T2 |
| 73 | 1+(−3.10−9.56i)T+(−59.0+42.9i)T2 |
| 79 | 1+(0.901+0.654i)T+(24.4+75.1i)T2 |
| 83 | 1+(−0.0140+0.0101i)T+(25.6−78.9i)T2 |
| 89 | 1+8.49T+89T2 |
| 97 | 1+(8.50+6.18i)T+(29.9+92.2i)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
−9.977594936828869547794769026406, −9.771342812357913233112602303310, −8.613663049774648429577697359287, −7.35753528003260948837647022914, −6.92560663873292625204511944421, −5.42851477283673468607801903771, −4.83868485731211605093477501688, −3.96195757863562109447506473000, −2.81207590913558847250912048115, −0.911416885261561487896070151605,
1.19565574960920464737606746182, 2.52854666005754416282488818944, 3.43291701645815627572933881042, 5.27873287334432058356071670836, 5.86282266250004501275117678070, 6.53321568154535794901707201465, 7.59424945243083614328021437332, 8.347298224645001258267515195103, 9.279739187375656034973836881718, 10.12928589997160058287104293080