L(s) = 1 | + (−0.342 − 0.939i)5-s + (0.173 − 0.984i)7-s + (0.5 − 0.866i)11-s + (−0.984 − 0.173i)13-s + (−0.342 + 0.939i)17-s + (−0.984 − 0.173i)19-s + (−0.866 + 0.5i)23-s + (−0.766 + 0.642i)25-s + (0.866 + 0.5i)29-s + (0.866 + 0.5i)31-s + (−0.984 + 0.173i)35-s + (0.173 − 0.984i)41-s + (−0.866 + 0.5i)43-s − 47-s + (−0.939 − 0.342i)49-s + ⋯ |
L(s) = 1 | + (−0.342 − 0.939i)5-s + (0.173 − 0.984i)7-s + (0.5 − 0.866i)11-s + (−0.984 − 0.173i)13-s + (−0.342 + 0.939i)17-s + (−0.984 − 0.173i)19-s + (−0.866 + 0.5i)23-s + (−0.766 + 0.642i)25-s + (0.866 + 0.5i)29-s + (0.866 + 0.5i)31-s + (−0.984 + 0.173i)35-s + (0.173 − 0.984i)41-s + (−0.866 + 0.5i)43-s − 47-s + (−0.939 − 0.342i)49-s + ⋯ |
Λ(s)=(=(2664s/2ΓR(s)L(s)(−0.159+0.987i)Λ(1−s)
Λ(s)=(=(2664s/2ΓR(s)L(s)(−0.159+0.987i)Λ(1−s)
Degree: |
1 |
Conductor: |
2664
= 23⋅32⋅37
|
Sign: |
−0.159+0.987i
|
Analytic conductor: |
12.3715 |
Root analytic conductor: |
12.3715 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2664(389,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 2664, (0: ), −0.159+0.987i)
|
Particular Values
L(21) |
≈ |
0.1063666151+0.1249257499i |
L(21) |
≈ |
0.1063666151+0.1249257499i |
L(1) |
≈ |
0.7585431822−0.2192755646i |
L(1) |
≈ |
0.7585431822−0.2192755646i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1 |
| 37 | 1 |
good | 5 | 1+(−0.342−0.939i)T |
| 7 | 1+(0.173−0.984i)T |
| 11 | 1+(0.5−0.866i)T |
| 13 | 1+(−0.984−0.173i)T |
| 17 | 1+(−0.342+0.939i)T |
| 19 | 1+(−0.984−0.173i)T |
| 23 | 1+(−0.866+0.5i)T |
| 29 | 1+(0.866+0.5i)T |
| 31 | 1+(0.866+0.5i)T |
| 41 | 1+(0.173−0.984i)T |
| 43 | 1+(−0.866+0.5i)T |
| 47 | 1−T |
| 53 | 1+(0.766−0.642i)T |
| 59 | 1+(−0.984+0.173i)T |
| 61 | 1+(−0.642+0.766i)T |
| 67 | 1+(−0.939+0.342i)T |
| 71 | 1+(−0.173+0.984i)T |
| 73 | 1−T |
| 79 | 1+(0.984+0.173i)T |
| 83 | 1+(0.173+0.984i)T |
| 89 | 1+(0.642+0.766i)T |
| 97 | 1+iT |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−19.13917728228059924570631486248, −18.357697613696450320863304503876, −17.879090918345086766436209947449, −17.123636898221716816380732021076, −16.20702025724596560686651936919, −15.32067389740730253582280051262, −14.97224824922215182166393697016, −14.34890956727427669322001799130, −13.55025074909861522672037253981, −12.38855647474892004232801831963, −11.96302738383135921113464532323, −11.43805178166847545809503388023, −10.35562553293041235653994541970, −9.8220604136507480544377047689, −9.02597008340267074067501889821, −8.09680971081403518680871358163, −7.45093647836336975994082365073, −6.50353884638863420583750250648, −6.159679568431212537349951508074, −4.74327599563276546091203948567, −4.45711278273509181058416587795, −3.166008590786255852951666880659, −2.42501865508862742996717799572, −1.878478285048580787266842078884, −0.054062523317448217638035289405,
1.0403569031286043170706319099, 1.83279853234796858894215279018, 3.10998516183033193670900258034, 4.04755177324360537193800351108, 4.48832919642972825567015984412, 5.38992162873383024579039165098, 6.340795110537366190108157446757, 7.07612542821534744330847290319, 8.12413115058605738957007764469, 8.39728440688342327969987905899, 9.34543116124594793184746351051, 10.2347796288342088834054946958, 10.81183550129270327352020847765, 11.77888383537995203025953940880, 12.29811365657586243566705157061, 13.1818461446410143256782275184, 13.70550427730226016461956690225, 14.54958617335519323414791757574, 15.247977896024993628719360612466, 16.215642003885223226981992171716, 16.65166048738450244918885511240, 17.38768613639008850646495903920, 17.75964643117056677742347141220, 19.19815213627936393017082560648, 19.62023575357459646130607137432