L(s) = 1 | + (0.984 + 0.173i)2-s + (0.939 + 0.342i)4-s + (−1.62 + 0.939i)7-s + (0.866 + 0.5i)8-s + (−0.173 − 0.984i)9-s + (−0.173 + 0.300i)11-s + (0.642 + 0.766i)13-s + (−1.76 + 0.642i)14-s + (0.766 + 0.642i)16-s − 0.999i·18-s + (−0.173 + 0.984i)19-s + (−0.223 + 0.266i)22-s + (−0.524 + 1.43i)23-s + (0.5 + 0.866i)26-s + (−1.85 + 0.326i)28-s + ⋯ |
L(s) = 1 | + (0.984 + 0.173i)2-s + (0.939 + 0.342i)4-s + (−1.62 + 0.939i)7-s + (0.866 + 0.5i)8-s + (−0.173 − 0.984i)9-s + (−0.173 + 0.300i)11-s + (0.642 + 0.766i)13-s + (−1.76 + 0.642i)14-s + (0.766 + 0.642i)16-s − 0.999i·18-s + (−0.173 + 0.984i)19-s + (−0.223 + 0.266i)22-s + (−0.524 + 1.43i)23-s + (0.5 + 0.866i)26-s + (−1.85 + 0.326i)28-s + ⋯ |
Λ(s)=(=(3800s/2ΓC(s)L(s)(0.0158−0.999i)Λ(1−s)
Λ(s)=(=(3800s/2ΓC(s)L(s)(0.0158−0.999i)Λ(1−s)
Degree: |
2 |
Conductor: |
3800
= 23⋅52⋅19
|
Sign: |
0.0158−0.999i
|
Analytic conductor: |
1.89644 |
Root analytic conductor: |
1.37711 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3800(1651,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3800, ( :0), 0.0158−0.999i)
|
Particular Values
L(21) |
≈ |
1.896470727 |
L(21) |
≈ |
1.896470727 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.984−0.173i)T |
| 5 | 1 |
| 19 | 1+(0.173−0.984i)T |
good | 3 | 1+(0.173+0.984i)T2 |
| 7 | 1+(1.62−0.939i)T+(0.5−0.866i)T2 |
| 11 | 1+(0.173−0.300i)T+(−0.5−0.866i)T2 |
| 13 | 1+(−0.642−0.766i)T+(−0.173+0.984i)T2 |
| 17 | 1+(−0.939−0.342i)T2 |
| 23 | 1+(0.524−1.43i)T+(−0.766−0.642i)T2 |
| 29 | 1+(0.939−0.342i)T2 |
| 31 | 1+(0.5−0.866i)T2 |
| 37 | 1−1.53iT−T2 |
| 41 | 1+(−0.266−0.223i)T+(0.173+0.984i)T2 |
| 43 | 1+(0.766−0.642i)T2 |
| 47 | 1+(−0.984+0.173i)T+(0.939−0.342i)T2 |
| 53 | 1+(−0.642+1.76i)T+(−0.766−0.642i)T2 |
| 59 | 1+(−0.173+0.984i)T+(−0.939−0.342i)T2 |
| 61 | 1+(−0.766−0.642i)T2 |
| 67 | 1+(−0.939+0.342i)T2 |
| 71 | 1+(−0.766+0.642i)T2 |
| 73 | 1+(0.173+0.984i)T2 |
| 79 | 1+(−0.173−0.984i)T2 |
| 83 | 1+(−0.5+0.866i)T2 |
| 89 | 1+(1.17−0.984i)T+(0.173−0.984i)T2 |
| 97 | 1+(−0.939−0.342i)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
−8.835804266530214422716900350144, −8.092098597735882409760399676329, −6.96546758081173651114206750943, −6.50524459964501095070624854249, −5.91800571150585852249597302897, −5.34841066461703795745045914192, −4.00480182367781979592688722360, −3.55598764224215274574476419270, −2.80366746769176514471843634747, −1.71637813427509189513980870520,
0.74751150436094506008877153765, 2.44514766464527012564157558600, 2.97341384824334508680579613313, 3.94143699379803011195751617190, 4.48901229309227030261335219642, 5.67897811625941526547607156317, 6.04239541180613775939514651349, 6.99351047441964366713600417438, 7.41910970068768186657221465644, 8.406013416656313386893228889050