L(s) = 1 | − 84i·3-s − 82i·5-s − 456·7-s − 4.86e3·9-s + 2.52e3i·11-s + 1.07e4i·13-s − 6.88e3·15-s − 1.11e4·17-s + 4.12e3i·19-s + 3.83e4i·21-s + 8.17e4·23-s + 7.14e4·25-s + 2.25e5i·27-s − 9.97e4i·29-s + 4.04e4·31-s + ⋯ |
L(s) = 1 | − 1.79i·3-s − 0.293i·5-s − 0.502·7-s − 2.22·9-s + 0.571i·11-s + 1.36i·13-s − 0.526·15-s − 0.550·17-s + 0.137i·19-s + 0.902i·21-s + 1.40·23-s + 0.913·25-s + 2.20i·27-s − 0.759i·29-s + 0.244·31-s + ⋯ |
Λ(s)=(=(256s/2ΓC(s)L(s)(0.707+0.707i)Λ(8−s)
Λ(s)=(=(256s/2ΓC(s+7/2)L(s)(0.707+0.707i)Λ(1−s)
Degree: |
2 |
Conductor: |
256
= 28
|
Sign: |
0.707+0.707i
|
Analytic conductor: |
79.9705 |
Root analytic conductor: |
8.94262 |
Motivic weight: |
7 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ256(129,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 256, ( :7/2), 0.707+0.707i)
|
Particular Values
L(4) |
≈ |
1.549272590 |
L(21) |
≈ |
1.549272590 |
L(29) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
good | 3 | 1+84iT−2.18e3T2 |
| 5 | 1+82iT−7.81e4T2 |
| 7 | 1+456T+8.23e5T2 |
| 11 | 1−2.52e3iT−1.94e7T2 |
| 13 | 1−1.07e4iT−6.27e7T2 |
| 17 | 1+1.11e4T+4.10e8T2 |
| 19 | 1−4.12e3iT−8.93e8T2 |
| 23 | 1−8.17e4T+3.40e9T2 |
| 29 | 1+9.97e4iT−1.72e10T2 |
| 31 | 1−4.04e4T+2.75e10T2 |
| 37 | 1+4.19e5iT−9.49e10T2 |
| 41 | 1+1.41e5T+1.94e11T2 |
| 43 | 1−6.90e5iT−2.71e11T2 |
| 47 | 1−6.82e5T+5.06e11T2 |
| 53 | 1−1.81e6iT−1.17e12T2 |
| 59 | 1−9.66e5iT−2.48e12T2 |
| 61 | 1+1.88e6iT−3.14e12T2 |
| 67 | 1−2.96e6iT−6.06e12T2 |
| 71 | 1+2.54e6T+9.09e12T2 |
| 73 | 1−1.68e6T+1.10e13T2 |
| 79 | 1+4.03e6T+1.92e13T2 |
| 83 | 1+5.38e6iT−2.71e13T2 |
| 89 | 1−6.47e6T+4.42e13T2 |
| 97 | 1+6.06e6T+8.07e13T2 |
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
−10.97734890127892479495126572898, −9.365883977455520315836849266810, −8.656889447820584858065578686080, −7.41712254529445219031962533083, −6.83916982901611453655435057768, −5.99199671231005306230123201707, −4.53184309673845843615059793608, −2.80368740528986447017807180074, −1.79989325446240354791157743987, −0.790579660537015334073372346359,
0.49445813957090068385499906448, 2.93857860247985236165877282021, 3.40843528008567585308453970880, 4.77293247286325986846104780945, 5.52457963273437033508747688568, 6.77294091715555615425052614033, 8.388551218446734898895550144371, 9.076568408744682903115659674472, 10.11831912229091367840177474291, 10.66906969307949070777471613965