L(s) = 1 | + (−0.309 − 0.951i)3-s + 7-s + (−0.809 + 0.587i)9-s + (0.809 + 0.587i)11-s + (0.809 − 0.587i)13-s + (0.309 − 0.951i)17-s + (−0.309 + 0.951i)19-s + (−0.309 − 0.951i)21-s + (−0.809 − 0.587i)23-s + (0.809 + 0.587i)27-s + (−0.309 − 0.951i)29-s + (0.309 − 0.951i)31-s + (0.309 − 0.951i)33-s + (0.809 − 0.587i)37-s + (−0.809 − 0.587i)39-s + ⋯ |
L(s) = 1 | + (−0.309 − 0.951i)3-s + 7-s + (−0.809 + 0.587i)9-s + (0.809 + 0.587i)11-s + (0.809 − 0.587i)13-s + (0.309 − 0.951i)17-s + (−0.309 + 0.951i)19-s + (−0.309 − 0.951i)21-s + (−0.809 − 0.587i)23-s + (0.809 + 0.587i)27-s + (−0.309 − 0.951i)29-s + (0.309 − 0.951i)31-s + (0.309 − 0.951i)33-s + (0.809 − 0.587i)37-s + (−0.809 − 0.587i)39-s + ⋯ |
Λ(s)=(=(200s/2ΓR(s)L(s)(0.535−0.844i)Λ(1−s)
Λ(s)=(=(200s/2ΓR(s)L(s)(0.535−0.844i)Λ(1−s)
Degree: |
1 |
Conductor: |
200
= 23⋅52
|
Sign: |
0.535−0.844i
|
Analytic conductor: |
0.928796 |
Root analytic conductor: |
0.928796 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ200(21,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 200, (0: ), 0.535−0.844i)
|
Particular Values
L(21) |
≈ |
1.040693357−0.5721260147i |
L(21) |
≈ |
1.040693357−0.5721260147i |
L(1) |
≈ |
1.032624294−0.3319573545i |
L(1) |
≈ |
1.032624294−0.3319573545i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1 |
good | 3 | 1+(−0.309−0.951i)T |
| 7 | 1+T |
| 11 | 1+(0.809+0.587i)T |
| 13 | 1+(0.809−0.587i)T |
| 17 | 1+(0.309−0.951i)T |
| 19 | 1+(−0.309+0.951i)T |
| 23 | 1+(−0.809−0.587i)T |
| 29 | 1+(−0.309−0.951i)T |
| 31 | 1+(0.309−0.951i)T |
| 37 | 1+(0.809−0.587i)T |
| 41 | 1+(−0.809+0.587i)T |
| 43 | 1−T |
| 47 | 1+(0.309+0.951i)T |
| 53 | 1+(−0.309−0.951i)T |
| 59 | 1+(0.809−0.587i)T |
| 61 | 1+(0.809+0.587i)T |
| 67 | 1+(−0.309+0.951i)T |
| 71 | 1+(0.309+0.951i)T |
| 73 | 1+(−0.809−0.587i)T |
| 79 | 1+(0.309+0.951i)T |
| 83 | 1+(−0.309+0.951i)T |
| 89 | 1+(−0.809−0.587i)T |
| 97 | 1+(0.309+0.951i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−27.16648536375092136918154233581, −26.26319024656322280711311972661, −25.327939929239203759111454250542, −23.92438971402613971126642870101, −23.46240934071449897012221980182, −21.80057543319904379808371179324, −21.72745084588767567378441814007, −20.54416147113324436426753536110, −19.608846609683568961856634849881, −18.26935404298679345531803455744, −17.273854273843435924379402119545, −16.53129423109257270860148445048, −15.4267173826685565637825413485, −14.5514829134894910930326577621, −13.65940039807263016811371895021, −11.95857912684032758683550202463, −11.243920251523204464556676901985, −10.390064341480197906218815357206, −9.017827924832673812419031925172, −8.35762918882993024295670316128, −6.62409005725283799438506788200, −5.53166484364844090124808636854, −4.38736573001378531112502530712, −3.4508369809728700803769304941, −1.51913789710526858107221771566,
1.16678896088193981694731306773, 2.31006237250729210363208505240, 4.10181513124177438500224428307, 5.46778875770818886817227743445, 6.47266908409354110707482063383, 7.71404037427088751884778188494, 8.396610716358763270866166752734, 9.93853993881460957367553307906, 11.30802136675975427035154910783, 11.90187025148506168750763510395, 13.022889194788427487500870169461, 14.08060849347568135755753762639, 14.864947711313681533897428250826, 16.3599073387843128993688030911, 17.352760247028595610641327830618, 18.12694528527520289282473158893, 18.86802489067200219529053873949, 20.18261053979356186310876355564, 20.81074083548657058008753405540, 22.32162199326546611890079520802, 23.02904895817732906152786642958, 23.94730394736278481492288779724, 24.94998306851510643653632825282, 25.37009877295466429648652677538, 26.88877084334063813598467113632