L(s) = 1 | + (−1.55 + 1.26i)2-s + (2.10 + 2.10i)3-s + (0.813 − 3.91i)4-s + (−4.62 − 4.62i)5-s + (−5.91 − 0.608i)6-s + 3.04·7-s + (3.68 + 7.10i)8-s − 0.156i·9-s + (13.0 + 1.33i)10-s + (−9.15 + 9.15i)11-s + (9.94 − 6.52i)12-s + (−5.78 + 5.78i)13-s + (−4.72 + 3.84i)14-s − 19.4i·15-s + (−14.6 − 6.37i)16-s + 17.6·17-s + ⋯ |
L(s) = 1 | + (−0.775 + 0.631i)2-s + (0.700 + 0.700i)3-s + (0.203 − 0.979i)4-s + (−0.925 − 0.925i)5-s + (−0.986 − 0.101i)6-s + 0.435·7-s + (0.460 + 0.887i)8-s − 0.0174i·9-s + (1.30 + 0.133i)10-s + (−0.831 + 0.831i)11-s + (0.828 − 0.543i)12-s + (−0.444 + 0.444i)13-s + (−0.337 + 0.274i)14-s − 1.29i·15-s + (−0.917 − 0.398i)16-s + 1.03·17-s + ⋯ |
Λ(s)=(=(16s/2ΓC(s)L(s)(0.718−0.695i)Λ(3−s)
Λ(s)=(=(16s/2ΓC(s+1)L(s)(0.718−0.695i)Λ(1−s)
Degree: |
2 |
Conductor: |
16
= 24
|
Sign: |
0.718−0.695i
|
Analytic conductor: |
0.435968 |
Root analytic conductor: |
0.660279 |
Motivic weight: |
2 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ16(11,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 16, ( :1), 0.718−0.695i)
|
Particular Values
L(23) |
≈ |
0.595321+0.240695i |
L(21) |
≈ |
0.595321+0.240695i |
L(2) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(1.55−1.26i)T |
good | 3 | 1+(−2.10−2.10i)T+9iT2 |
| 5 | 1+(4.62+4.62i)T+25iT2 |
| 7 | 1−3.04T+49T2 |
| 11 | 1+(9.15−9.15i)T−121iT2 |
| 13 | 1+(5.78−5.78i)T−169iT2 |
| 17 | 1−17.6T+289T2 |
| 19 | 1+(1.15+1.15i)T+361iT2 |
| 23 | 1+3.45T+529T2 |
| 29 | 1+(−12.1+12.1i)T−841iT2 |
| 31 | 1−38.5iT−961T2 |
| 37 | 1+(0.0972+0.0972i)T+1.36e3iT2 |
| 41 | 1+51.5iT−1.68e3T2 |
| 43 | 1+(1.70−1.70i)T−1.84e3iT2 |
| 47 | 1−24.1iT−2.20e3T2 |
| 53 | 1+(−27.0−27.0i)T+2.80e3iT2 |
| 59 | 1+(−19.5+19.5i)T−3.48e3iT2 |
| 61 | 1+(−16.7+16.7i)T−3.72e3iT2 |
| 67 | 1+(75.8+75.8i)T+4.48e3iT2 |
| 71 | 1+134.T+5.04e3T2 |
| 73 | 1−112.iT−5.32e3T2 |
| 79 | 1+135.iT−6.24e3T2 |
| 83 | 1+(−74.9−74.9i)T+6.88e3iT2 |
| 89 | 1+31.4iT−7.92e3T2 |
| 97 | 1−31.5T+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
−19.24631576833940179260032195605, −17.69273754984693331912412168442, −16.27321399969846010193682678422, −15.44155438872578373344285833964, −14.38367411776500791876881749275, −12.12711696639815969211762356962, −10.14434279059121646655929681001, −8.811955731886072562243428547535, −7.66736938703655029869243953012, −4.75617402699940195329251308925,
2.98931204697392862733797842527, 7.49795545202933616860365622989, 8.200020929716778120328955933920, 10.43946517157300583994667948221, 11.66918127289927349514823795935, 13.21334748146507348543615789638, 14.76304392848751706692529374921, 16.35332775477675652668389363409, 18.15104896815027068919475755278, 18.93018841176314664890974775170