L(s) = 1 | + 10.2i·3-s + (−17.9 − 17.4i)5-s + 84.8·7-s − 23.1·9-s − 71.3·11-s + 109.·13-s + (177. − 182. i)15-s − 151. i·17-s + 368.·19-s + 865. i·21-s + 358.·23-s + (16.8 + 624. i)25-s + 590. i·27-s + 387. i·29-s + 1.68e3i·31-s + ⋯ |
L(s) = 1 | + 1.13i·3-s + (−0.716 − 0.697i)5-s + 1.73·7-s − 0.285·9-s − 0.589·11-s + 0.646·13-s + (0.790 − 0.812i)15-s − 0.523i·17-s + 1.02·19-s + 1.96i·21-s + 0.676·23-s + (0.0269 + 0.999i)25-s + 0.810i·27-s + 0.460i·29-s + 1.75i·31-s + ⋯ |
Λ(s)=(=(160s/2ΓC(s)L(s)(0.603−0.797i)Λ(5−s)
Λ(s)=(=(160s/2ΓC(s+2)L(s)(0.603−0.797i)Λ(1−s)
Degree: |
2 |
Conductor: |
160
= 25⋅5
|
Sign: |
0.603−0.797i
|
Analytic conductor: |
16.5391 |
Root analytic conductor: |
4.06684 |
Motivic weight: |
4 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ160(79,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 160, ( :2), 0.603−0.797i)
|
Particular Values
L(25) |
≈ |
1.80343+0.897000i |
L(21) |
≈ |
1.80343+0.897000i |
L(3) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1+(17.9+17.4i)T |
good | 3 | 1−10.2iT−81T2 |
| 7 | 1−84.8T+2.40e3T2 |
| 11 | 1+71.3T+1.46e4T2 |
| 13 | 1−109.T+2.85e4T2 |
| 17 | 1+151.iT−8.35e4T2 |
| 19 | 1−368.T+1.30e5T2 |
| 23 | 1−358.T+2.79e5T2 |
| 29 | 1−387.iT−7.07e5T2 |
| 31 | 1−1.68e3iT−9.23e5T2 |
| 37 | 1−1.15e3T+1.87e6T2 |
| 41 | 1+2.54e3T+2.82e6T2 |
| 43 | 1−1.35e3iT−3.41e6T2 |
| 47 | 1−901.T+4.87e6T2 |
| 53 | 1−3.40e3T+7.89e6T2 |
| 59 | 1−1.45e3T+1.21e7T2 |
| 61 | 1+5.32e3iT−1.38e7T2 |
| 67 | 1+657.iT−2.01e7T2 |
| 71 | 1+6.74e3iT−2.54e7T2 |
| 73 | 1+4.13e3iT−2.83e7T2 |
| 79 | 1+2.30e3iT−3.89e7T2 |
| 83 | 1+2.14e3iT−4.74e7T2 |
| 89 | 1−5.11e3T+6.27e7T2 |
| 97 | 1−9.16e3iT−8.85e7T2 |
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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
−12.06151281197882829495649520041, −11.23415252899902936913459246593, −10.52020821573441040155825766065, −9.167438183231429660007285542419, −8.353512170449444356540942243401, −7.39237361974203979368967402064, −5.08550044810980707015917115485, −4.86223929605148465555977339859, −3.48360990661710555179389504313, −1.24504847065828227518791032617,
1.00437875591018459466059527539, 2.35138360309546054606804760191, 4.14039761011167712352643206034, 5.62803349330889621039155606211, 7.06525281747640682501795036568, 7.78832032366844223920108451254, 8.431970469185465419649538882799, 10.32218211050857635435805804216, 11.41071113444472734184258341992, 11.78218690026861009636622556525