L(s) = 1 | + (−0.707 + 0.707i)2-s + (0.707 − 0.707i)3-s − 1.00i·4-s + (−0.707 − 0.707i)5-s + 1.00i·6-s + (0.707 + 0.707i)8-s − 1.00i·9-s + 1.00·10-s + (−0.707 − 0.707i)12-s − 1.00·15-s − 1.00·16-s + 1.41·17-s + (0.707 + 0.707i)18-s + (−1 + i)19-s + (−0.707 + 0.707i)20-s + ⋯ |
L(s) = 1 | + (−0.707 + 0.707i)2-s + (0.707 − 0.707i)3-s − 1.00i·4-s + (−0.707 − 0.707i)5-s + 1.00i·6-s + (0.707 + 0.707i)8-s − 1.00i·9-s + 1.00·10-s + (−0.707 − 0.707i)12-s − 1.00·15-s − 1.00·16-s + 1.41·17-s + (0.707 + 0.707i)18-s + (−1 + i)19-s + (−0.707 + 0.707i)20-s + ⋯ |
Λ(s)=(=(240s/2ΓC(s)L(s)(0.923+0.382i)Λ(1−s)
Λ(s)=(=(240s/2ΓC(s)L(s)(0.923+0.382i)Λ(1−s)
Degree: |
2 |
Conductor: |
240
= 24⋅3⋅5
|
Sign: |
0.923+0.382i
|
Analytic conductor: |
0.119775 |
Root analytic conductor: |
0.346086 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ240(149,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 240, ( :0), 0.923+0.382i)
|
Particular Values
L(21) |
≈ |
0.5917809861 |
L(21) |
≈ |
0.5917809861 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.707−0.707i)T |
| 3 | 1+(−0.707+0.707i)T |
| 5 | 1+(0.707+0.707i)T |
good | 7 | 1+T2 |
| 11 | 1−iT2 |
| 13 | 1+iT2 |
| 17 | 1−1.41T+T2 |
| 19 | 1+(1−i)T−iT2 |
| 23 | 1−1.41iT−T2 |
| 29 | 1+iT2 |
| 31 | 1+T2 |
| 37 | 1−iT2 |
| 41 | 1+T2 |
| 43 | 1−iT2 |
| 47 | 1+1.41T+T2 |
| 53 | 1+iT2 |
| 59 | 1−iT2 |
| 61 | 1+(−1+i)T−iT2 |
| 67 | 1+iT2 |
| 71 | 1+T2 |
| 73 | 1+T2 |
| 79 | 1−2T+T2 |
| 83 | 1−iT2 |
| 89 | 1+T2 |
| 97 | 1−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
−12.36936163496750345326236536554, −11.42609557929333522777040228548, −9.987440746581778878235120595066, −9.152244553984701345408037980079, −8.043005708260171471716271182966, −7.80746578592877739633446267261, −6.52446969123786007095903519098, −5.31144419502214469638598438828, −3.67167826288751907376634774032, −1.51939273448247247661441585868,
2.53553620062341549250040701672, 3.53036680717894158420722420130, 4.62319019308263877060332591515, 6.77479150238894859714644007434, 7.909413203481590687250027947400, 8.542877462261970093053789337113, 9.682864892071757417871083182559, 10.49354232776174795576261236325, 11.14349063871715647995098067786, 12.19935326316781195879732182893