L(s) = 1 | + (−0.984 + 0.173i)2-s + (−0.642 − 0.766i)3-s + (0.939 − 0.342i)4-s + (0.766 + 0.642i)6-s + (−0.866 − 0.5i)7-s + (−0.866 + 0.5i)8-s + (−0.173 + 0.984i)9-s + (−0.5 − 0.866i)11-s + (−0.866 − 0.5i)12-s + (0.642 − 0.766i)13-s + (0.939 + 0.342i)14-s + (0.766 − 0.642i)16-s + (−0.984 + 0.173i)17-s − i·18-s + (0.173 + 0.984i)21-s + (0.642 + 0.766i)22-s + ⋯ |
L(s) = 1 | + (−0.984 + 0.173i)2-s + (−0.642 − 0.766i)3-s + (0.939 − 0.342i)4-s + (0.766 + 0.642i)6-s + (−0.866 − 0.5i)7-s + (−0.866 + 0.5i)8-s + (−0.173 + 0.984i)9-s + (−0.5 − 0.866i)11-s + (−0.866 − 0.5i)12-s + (0.642 − 0.766i)13-s + (0.939 + 0.342i)14-s + (0.766 − 0.642i)16-s + (−0.984 + 0.173i)17-s − i·18-s + (0.173 + 0.984i)21-s + (0.642 + 0.766i)22-s + ⋯ |
Λ(s)=(=(95s/2ΓR(s+1)L(s)(−0.0451+0.998i)Λ(1−s)
Λ(s)=(=(95s/2ΓR(s+1)L(s)(−0.0451+0.998i)Λ(1−s)
Degree: |
1 |
Conductor: |
95
= 5⋅19
|
Sign: |
−0.0451+0.998i
|
Analytic conductor: |
10.2091 |
Root analytic conductor: |
10.2091 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ95(92,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 95, (1: ), −0.0451+0.998i)
|
Particular Values
L(21) |
≈ |
0.1436520836+0.1502856956i |
L(21) |
≈ |
0.1436520836+0.1502856956i |
L(1) |
≈ |
0.4282553284−0.07429059458i |
L(1) |
≈ |
0.4282553284−0.07429059458i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1 |
| 19 | 1 |
good | 2 | 1+(−0.984+0.173i)T |
| 3 | 1+(−0.642−0.766i)T |
| 7 | 1+(−0.866−0.5i)T |
| 11 | 1+(−0.5−0.866i)T |
| 13 | 1+(0.642−0.766i)T |
| 17 | 1+(−0.984+0.173i)T |
| 23 | 1+(0.342+0.939i)T |
| 29 | 1+(−0.173+0.984i)T |
| 31 | 1+(−0.5+0.866i)T |
| 37 | 1+iT |
| 41 | 1+(0.766−0.642i)T |
| 43 | 1+(−0.342+0.939i)T |
| 47 | 1+(0.984+0.173i)T |
| 53 | 1+(0.342+0.939i)T |
| 59 | 1+(−0.173−0.984i)T |
| 61 | 1+(−0.939+0.342i)T |
| 67 | 1+(0.984+0.173i)T |
| 71 | 1+(−0.939−0.342i)T |
| 73 | 1+(−0.642−0.766i)T |
| 79 | 1+(−0.766+0.642i)T |
| 83 | 1+(0.866+0.5i)T |
| 89 | 1+(−0.766−0.642i)T |
| 97 | 1+(−0.984+0.173i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−28.98207773829777556462098702207, −28.64620442062038688021277548182, −27.79473234980270382714075231076, −26.46597324209583734090848817216, −26.001659616700418680822838293722, −24.68672870966788838053691453419, −23.233670971268265299863330672420, −22.16059673645781580087053050218, −21.07716623454390098936151145511, −20.17532364676240719416143179907, −18.81161269493234259520004378751, −17.91540886093386327651935445586, −16.75248617732612879162796910551, −15.88786249077670719304804100951, −15.10830166560752309934109080180, −12.887228404319183504174151722832, −11.75955261472416264979917393433, −10.70369060064943568160829002882, −9.63116013788155677338138631695, −8.83377921553808442683990748986, −6.98453444571699646198474453849, −5.93498314677774285899199666290, −4.10282439469411230378226608506, −2.41258825556532452438266435794, −0.15518387887657380654473755102,
1.16225815372873234039051529892, 3.01812984420647006410439813981, 5.59641487452379385536890181018, 6.58408259083114614173576690756, 7.65157725652973523181411817443, 8.8805329070016079178899259681, 10.49446631512216074692268867514, 11.14330033557221085818200844883, 12.66743581375039627476725981991, 13.67297813569562799299730140174, 15.61667657476936079905809927336, 16.42722451519169957063327377927, 17.48034766461596565548568706886, 18.39389439070306364600676040959, 19.34335187342176277943929746003, 20.22214943951463734361671605533, 21.84342577904824549139746254562, 23.205890710466354952890694488867, 23.985468045312825624233939621947, 25.1188035496286303116888543477, 26.00084504398287557169846927817, 27.146122014673284149389232200670, 28.22306528457869866498943386305, 29.26158723496086771981993327484, 29.6037496225037409061991213510