L(s) = 1 | + (−0.891 − 0.453i)2-s + (1.84 − 0.763i)3-s + (0.587 + 0.809i)4-s + (−0.399 + 0.965i)5-s + (−1.98 − 0.156i)6-s + (0.707 + 0.707i)7-s + (−0.156 − 0.987i)8-s + (2.10 − 2.10i)9-s + (0.794 − 0.678i)10-s + (1.70 + 1.04i)12-s + (−0.309 − 0.951i)14-s + 2.08i·15-s + (−0.309 + 0.951i)16-s − i·17-s + (−2.82 + 0.919i)18-s + ⋯ |
L(s) = 1 | + (−0.891 − 0.453i)2-s + (1.84 − 0.763i)3-s + (0.587 + 0.809i)4-s + (−0.399 + 0.965i)5-s + (−1.98 − 0.156i)6-s + (0.707 + 0.707i)7-s + (−0.156 − 0.987i)8-s + (2.10 − 2.10i)9-s + (0.794 − 0.678i)10-s + (1.70 + 1.04i)12-s + (−0.309 − 0.951i)14-s + 2.08i·15-s + (−0.309 + 0.951i)16-s − i·17-s + (−2.82 + 0.919i)18-s + ⋯ |
Λ(s)=(=(3808s/2ΓC(s)L(s)(0.831+0.555i)Λ(1−s)
Λ(s)=(=(3808s/2ΓC(s)L(s)(0.831+0.555i)Λ(1−s)
Degree: |
2 |
Conductor: |
3808
= 25⋅7⋅17
|
Sign: |
0.831+0.555i
|
Analytic conductor: |
1.90043 |
Root analytic conductor: |
1.37856 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3808(3093,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3808, ( :0), 0.831+0.555i)
|
Particular Values
L(21) |
≈ |
1.735182533 |
L(21) |
≈ |
1.735182533 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.891+0.453i)T |
| 7 | 1+(−0.707−0.707i)T |
| 17 | 1+iT |
good | 3 | 1+(−1.84+0.763i)T+(0.707−0.707i)T2 |
| 5 | 1+(0.399−0.965i)T+(−0.707−0.707i)T2 |
| 11 | 1+(−0.707−0.707i)T2 |
| 13 | 1+(0.707−0.707i)T2 |
| 19 | 1+(0.707−0.707i)T2 |
| 23 | 1+iT2 |
| 29 | 1+(−0.707+0.707i)T2 |
| 31 | 1+1.61T+T2 |
| 37 | 1+(0.707+0.707i)T2 |
| 41 | 1+(−0.437+0.437i)T−iT2 |
| 43 | 1+(−1.40−0.581i)T+(0.707+0.707i)T2 |
| 47 | 1+T2 |
| 53 | 1+(0.431+0.178i)T+(0.707+0.707i)T2 |
| 59 | 1+(0.707+0.707i)T2 |
| 61 | 1+(−0.144+0.0600i)T+(0.707−0.707i)T2 |
| 67 | 1+(1.79−0.744i)T+(0.707−0.707i)T2 |
| 71 | 1−iT2 |
| 73 | 1+(1.26−1.26i)T−iT2 |
| 79 | 1+T2 |
| 83 | 1+(0.707−0.707i)T2 |
| 89 | 1−iT2 |
| 97 | 1+0.312T+T2 |
show more | |
show less | |
L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−8.656018247697836241172255719718, −7.913369755834157983232969404453, −7.28544362525349604902473821146, −7.11649380365519185913604281375, −5.98477640933943450798636176260, −4.34905309751552634578316664804, −3.46416038552818959516292458513, −2.79252869485261193126758995328, −2.28068133989515754350352580782, −1.33681695998981928058494434061,
1.36665105871206143372463233264, 2.08333300721499710021826087433, 3.30282161001141153782728478825, 4.24670188848403994767315032047, 4.68589039847777592632955905059, 5.69124173671094522658253436976, 7.09938866695727644459531909972, 7.68630105563150734356371123895, 8.096247387074179449215996984122, 8.797203119174070195323187953777