L(s) = 1 | + (0.707 − 0.707i)2-s − 1.00i·4-s + (−0.707 − 0.707i)5-s + (−0.707 − 0.707i)8-s − 1.00·10-s − 1.00·16-s − 1.41i·17-s + (1 − i)19-s + (−0.707 + 0.707i)20-s + 1.41i·23-s + 1.00i·25-s + 2i·31-s + (−0.707 + 0.707i)32-s + (−1.00 − 1.00i)34-s − 1.41i·38-s + ⋯ |
L(s) = 1 | + (0.707 − 0.707i)2-s − 1.00i·4-s + (−0.707 − 0.707i)5-s + (−0.707 − 0.707i)8-s − 1.00·10-s − 1.00·16-s − 1.41i·17-s + (1 − i)19-s + (−0.707 + 0.707i)20-s + 1.41i·23-s + 1.00i·25-s + 2i·31-s + (−0.707 + 0.707i)32-s + (−1.00 − 1.00i)34-s − 1.41i·38-s + ⋯ |
Λ(s)=(=(720s/2ΓC(s)L(s)(−0.382+0.923i)Λ(1−s)
Λ(s)=(=(720s/2ΓC(s)L(s)(−0.382+0.923i)Λ(1−s)
Degree: |
2 |
Conductor: |
720
= 24⋅32⋅5
|
Sign: |
−0.382+0.923i
|
Analytic conductor: |
0.359326 |
Root analytic conductor: |
0.599438 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ720(19,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 720, ( :0), −0.382+0.923i)
|
Particular Values
L(21) |
≈ |
1.172592230 |
L(21) |
≈ |
1.172592230 |
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 |
| 5 | 1+(0.707+0.707i)T |
good | 7 | 1−T2 |
| 11 | 1+iT2 |
| 13 | 1−iT2 |
| 17 | 1+1.41iT−T2 |
| 19 | 1+(−1+i)T−iT2 |
| 23 | 1−1.41iT−T2 |
| 29 | 1+iT2 |
| 31 | 1−2iT−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−T2 |
| 83 | 1+(−1.41−1.41i)T+iT2 |
| 89 | 1−T2 |
| 97 | 1−T2 |
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show less | |
L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−10.58622698184824029020416472264, −9.383612710503227533419508223958, −9.042360657172713694227520769634, −7.62033086590413236406189592231, −6.85744546489755928801315468096, −5.34522420386373569232417709751, −4.95770460266557193651478883978, −3.76971133479913460119449386306, −2.83457145538099995172097371699, −1.13445124268816426143868428178,
2.51040726453255872723452292787, 3.71103122058905116286250460304, 4.32768987079081907197032935784, 5.74710953651620593703347171559, 6.36693237660249894171426637406, 7.45237123227378816983632751686, 7.970036923532743868076785153349, 8.873034328356344227895818577097, 10.18655162890125860536696265526, 10.97317434809376828717867320608