L(s) = 1 | + 4.79i·3-s + (−4.35 − 2.46i)5-s − 7.67·7-s − 13.9·9-s + 0.472·11-s + 4.10·13-s + (11.7 − 20.8i)15-s − 2.26i·17-s − 26.3·19-s − 36.7i·21-s − 9.73·23-s + (12.8 + 21.4i)25-s − 23.6i·27-s + 41.6i·29-s + 22.0i·31-s + ⋯ |
L(s) = 1 | + 1.59i·3-s + (−0.870 − 0.492i)5-s − 1.09·7-s − 1.54·9-s + 0.0429·11-s + 0.316·13-s + (0.785 − 1.38i)15-s − 0.133i·17-s − 1.38·19-s − 1.75i·21-s − 0.423·23-s + (0.515 + 0.856i)25-s − 0.877i·27-s + 1.43i·29-s + 0.710i·31-s + ⋯ |
Λ(s)=(=(160s/2ΓC(s)L(s)(−0.949+0.313i)Λ(3−s)
Λ(s)=(=(160s/2ΓC(s+1)L(s)(−0.949+0.313i)Λ(1−s)
Degree: |
2 |
Conductor: |
160
= 25⋅5
|
Sign: |
−0.949+0.313i
|
Analytic conductor: |
4.35968 |
Root analytic conductor: |
2.08798 |
Motivic weight: |
2 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ160(79,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 160, ( :1), −0.949+0.313i)
|
Particular Values
L(23) |
≈ |
0.0669978−0.416961i |
L(21) |
≈ |
0.0669978−0.416961i |
L(2) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1+(4.35+2.46i)T |
good | 3 | 1−4.79iT−9T2 |
| 7 | 1+7.67T+49T2 |
| 11 | 1−0.472T+121T2 |
| 13 | 1−4.10T+169T2 |
| 17 | 1+2.26iT−289T2 |
| 19 | 1+26.3T+361T2 |
| 23 | 1+9.73T+529T2 |
| 29 | 1−41.6iT−841T2 |
| 31 | 1−22.0iT−961T2 |
| 37 | 1+51.7T+1.36e3T2 |
| 41 | 1−15.0T+1.68e3T2 |
| 43 | 1−9.31iT−1.84e3T2 |
| 47 | 1+8.76T+2.20e3T2 |
| 53 | 1−39.9T+2.80e3T2 |
| 59 | 1−77.1T+3.48e3T2 |
| 61 | 1−14.7iT−3.72e3T2 |
| 67 | 1+75.8iT−4.48e3T2 |
| 71 | 1−81.0iT−5.04e3T2 |
| 73 | 1−83.4iT−5.32e3T2 |
| 79 | 1+100.iT−6.24e3T2 |
| 83 | 1+0.266iT−6.88e3T2 |
| 89 | 1−85.5T+7.92e3T2 |
| 97 | 1−99.1iT−9.40e3T2 |
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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
−13.05328635291272971641202443112, −12.15190037070252163789830133682, −10.94408528717801768996126414159, −10.23314446510900431782984038463, −9.140797653733188351427275684040, −8.479577009065566716211189839671, −6.78108835037866087607389921621, −5.29686078788369774286768562172, −4.14891265575917097426570443984, −3.32190675510560422555138442292,
0.25201815960446320434649560492, 2.37135386090958401251202593006, 3.84169213511014197246134519234, 6.12503656842603105568442048196, 6.75100669789164617622683493149, 7.74227072789023623619549216181, 8.646773809056524844614992209307, 10.21217482539657267923065126312, 11.42267679623298232955151169418, 12.26156590532806190951887762405