L(s) = 1 | + (−0.766 + 0.642i)2-s + (1.43 + 0.524i)3-s + (0.173 − 0.984i)4-s + (−1.43 + 0.524i)6-s + (0.500 + 0.866i)8-s + (1.03 + 0.866i)9-s + (0.939 + 1.62i)11-s + (0.766 − 1.32i)12-s + (−0.939 − 0.342i)16-s + (0.766 − 0.642i)17-s − 1.34·18-s + (0.173 − 0.984i)19-s + (−1.76 − 0.642i)22-s + (0.266 + 1.50i)24-s + (0.266 + 0.460i)27-s + ⋯ |
L(s) = 1 | + (−0.766 + 0.642i)2-s + (1.43 + 0.524i)3-s + (0.173 − 0.984i)4-s + (−1.43 + 0.524i)6-s + (0.500 + 0.866i)8-s + (1.03 + 0.866i)9-s + (0.939 + 1.62i)11-s + (0.766 − 1.32i)12-s + (−0.939 − 0.342i)16-s + (0.766 − 0.642i)17-s − 1.34·18-s + (0.173 − 0.984i)19-s + (−1.76 − 0.642i)22-s + (0.266 + 1.50i)24-s + (0.266 + 0.460i)27-s + ⋯ |
Λ(s)=(=(3800s/2ΓC(s)L(s)(0.188−0.982i)Λ(1−s)
Λ(s)=(=(3800s/2ΓC(s)L(s)(0.188−0.982i)Λ(1−s)
Degree: |
2 |
Conductor: |
3800
= 23⋅52⋅19
|
Sign: |
0.188−0.982i
|
Analytic conductor: |
1.89644 |
Root analytic conductor: |
1.37711 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3800(1051,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3800, ( :0), 0.188−0.982i)
|
Particular Values
L(21) |
≈ |
1.596863017 |
L(21) |
≈ |
1.596863017 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.766−0.642i)T |
| 5 | 1 |
| 19 | 1+(−0.173+0.984i)T |
good | 3 | 1+(−1.43−0.524i)T+(0.766+0.642i)T2 |
| 7 | 1+(0.5+0.866i)T2 |
| 11 | 1+(−0.939−1.62i)T+(−0.5+0.866i)T2 |
| 13 | 1+(−0.766+0.642i)T2 |
| 17 | 1+(−0.766+0.642i)T+(0.173−0.984i)T2 |
| 23 | 1+(0.939+0.342i)T2 |
| 29 | 1+(−0.173−0.984i)T2 |
| 31 | 1+(0.5+0.866i)T2 |
| 37 | 1−T2 |
| 41 | 1+(0.326+0.118i)T+(0.766+0.642i)T2 |
| 43 | 1+(−0.173−0.984i)T+(−0.939+0.342i)T2 |
| 47 | 1+(−0.173−0.984i)T2 |
| 53 | 1+(0.939+0.342i)T2 |
| 59 | 1+(1.43−1.20i)T+(0.173−0.984i)T2 |
| 61 | 1+(0.939+0.342i)T2 |
| 67 | 1+(0.266+0.223i)T+(0.173+0.984i)T2 |
| 71 | 1+(0.939−0.342i)T2 |
| 73 | 1+(1.76+0.642i)T+(0.766+0.642i)T2 |
| 79 | 1+(−0.766−0.642i)T2 |
| 83 | 1+(−0.173+0.300i)T+(−0.5−0.866i)T2 |
| 89 | 1+(−0.939+0.342i)T+(0.766−0.642i)T2 |
| 97 | 1+(0.266−0.223i)T+(0.173−0.984i)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
−9.059766421456119454654556736060, −8.146668712539112828265315621407, −7.42436031717628799647343862578, −7.05711739594252258225790290505, −6.07855195727046430716903194470, −4.85272830430224999361430437319, −4.44115732235627118357036754470, −3.27763253592235253427778556120, −2.35681088816189261826820645353, −1.45223696666061835205671100235,
1.16414841980705346392993377780, 1.86393399172571876064177440809, 3.07546935319514519677801288150, 3.40855795502559021738878300642, 4.15490901312524603297962828187, 5.76433482287113747945226134915, 6.53885836229998901212250633226, 7.46175747900631215452995322388, 8.063757410138753036047283010885, 8.518728157273354778866535136424