L(s) = 1 | + (0.106 − 2.99i)3-s + (1.83 + 1.06i)5-s + (3.42 + 5.93i)7-s + (−8.97 − 0.640i)9-s + (−4.54 + 2.62i)11-s + (10.0 − 17.3i)13-s + (3.38 − 5.40i)15-s + 0.0666i·17-s + 27.2·19-s + (18.1 − 9.63i)21-s + (18.5 + 10.7i)23-s + (−10.2 − 17.7i)25-s + (−2.87 + 26.8i)27-s + (37.2 − 21.5i)29-s + (−8.06 + 13.9i)31-s + ⋯ |
L(s) = 1 | + (0.0356 − 0.999i)3-s + (0.367 + 0.212i)5-s + (0.489 + 0.847i)7-s + (−0.997 − 0.0711i)9-s + (−0.413 + 0.238i)11-s + (0.770 − 1.33i)13-s + (0.225 − 0.360i)15-s + 0.00392i·17-s + 1.43·19-s + (0.864 − 0.458i)21-s + (0.807 + 0.466i)23-s + (−0.409 − 0.709i)25-s + (−0.106 + 0.994i)27-s + (1.28 − 0.742i)29-s + (−0.260 + 0.450i)31-s + ⋯ |
Λ(s)=(=(576s/2ΓC(s)L(s)(0.586+0.809i)Λ(3−s)
Λ(s)=(=(576s/2ΓC(s+1)L(s)(0.586+0.809i)Λ(1−s)
Degree: |
2 |
Conductor: |
576
= 26⋅32
|
Sign: |
0.586+0.809i
|
Analytic conductor: |
15.6948 |
Root analytic conductor: |
3.96167 |
Motivic weight: |
2 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ576(257,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 576, ( :1), 0.586+0.809i)
|
Particular Values
L(23) |
≈ |
2.043577010 |
L(21) |
≈ |
2.043577010 |
L(2) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1+(−0.106+2.99i)T |
good | 5 | 1+(−1.83−1.06i)T+(12.5+21.6i)T2 |
| 7 | 1+(−3.42−5.93i)T+(−24.5+42.4i)T2 |
| 11 | 1+(4.54−2.62i)T+(60.5−104.i)T2 |
| 13 | 1+(−10.0+17.3i)T+(−84.5−146.i)T2 |
| 17 | 1−0.0666iT−289T2 |
| 19 | 1−27.2T+361T2 |
| 23 | 1+(−18.5−10.7i)T+(264.5+458.i)T2 |
| 29 | 1+(−37.2+21.5i)T+(420.5−728.i)T2 |
| 31 | 1+(8.06−13.9i)T+(−480.5−832.i)T2 |
| 37 | 1−22.3T+1.36e3T2 |
| 41 | 1+(2.56+1.48i)T+(840.5+1.45e3i)T2 |
| 43 | 1+(14.6+25.4i)T+(−924.5+1.60e3i)T2 |
| 47 | 1+(−38.3+22.1i)T+(1.10e3−1.91e3i)T2 |
| 53 | 1+12.8iT−2.80e3T2 |
| 59 | 1+(75.0+43.3i)T+(1.74e3+3.01e3i)T2 |
| 61 | 1+(6.45+11.1i)T+(−1.86e3+3.22e3i)T2 |
| 67 | 1+(−61.4+106.i)T+(−2.24e3−3.88e3i)T2 |
| 71 | 1−125.iT−5.04e3T2 |
| 73 | 1−90.7T+5.32e3T2 |
| 79 | 1+(−24.2−42.0i)T+(−3.12e3+5.40e3i)T2 |
| 83 | 1+(101.−58.3i)T+(3.44e3−5.96e3i)T2 |
| 89 | 1+116.iT−7.92e3T2 |
| 97 | 1+(23.2+40.3i)T+(−4.70e3+8.14e3i)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
−10.47628395090163586435058987425, −9.427313218800120014500764125148, −8.345442671255185502195502939687, −7.87181188631952727650196371136, −6.77074643681996985673715684715, −5.74400509742010354067270575030, −5.19800916084386062084031510884, −3.22919756395402004104486871318, −2.32075456872554048094271353916, −0.952488186198548823411073231514,
1.22723324482679191610823912440, 2.98140840326563792902481448458, 4.12596176640771670478676034871, 4.90696895364564271116015387307, 5.89719798850846193679312256636, 7.08232359798382649269554073847, 8.152691011916206412423431546776, 9.105596342749499816262993467844, 9.685750188458949670580929033949, 10.77863096220156390089044629289