L(s) = 1 | + (−5.25 + 2.08i)2-s + (−3.18 + 3.18i)3-s + (23.3 − 21.9i)4-s + (−67.3 − 67.3i)5-s + (10.0 − 23.3i)6-s − 148. i·7-s + (−76.8 + 163. i)8-s + 222. i·9-s + (494. + 213. i)10-s + (−256. − 256. i)11-s + (−4.40 + 143. i)12-s + (−218. + 218. i)13-s + (309. + 780. i)14-s + 428.·15-s + (62.6 − 1.02e3i)16-s − 463.·17-s + ⋯ |
L(s) = 1 | + (−0.929 + 0.368i)2-s + (−0.203 + 0.203i)3-s + (0.728 − 0.685i)4-s + (−1.20 − 1.20i)5-s + (0.114 − 0.264i)6-s − 1.14i·7-s + (−0.424 + 0.905i)8-s + 0.916i·9-s + (1.56 + 0.676i)10-s + (−0.638 − 0.638i)11-s + (−0.00883 + 0.288i)12-s + (−0.358 + 0.358i)13-s + (0.421 + 1.06i)14-s + 0.491·15-s + (0.0612 − 0.998i)16-s − 0.388·17-s + ⋯ |
Λ(s)=(=(16s/2ΓC(s)L(s)(−0.438+0.898i)Λ(6−s)
Λ(s)=(=(16s/2ΓC(s+5/2)L(s)(−0.438+0.898i)Λ(1−s)
Degree: |
2 |
Conductor: |
16
= 24
|
Sign: |
−0.438+0.898i
|
Analytic conductor: |
2.56614 |
Root analytic conductor: |
1.60191 |
Motivic weight: |
5 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ16(5,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 16, ( :5/2), −0.438+0.898i)
|
Particular Values
L(3) |
≈ |
0.210995−0.337730i |
L(21) |
≈ |
0.210995−0.337730i |
L(27) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(5.25−2.08i)T |
good | 3 | 1+(3.18−3.18i)T−243iT2 |
| 5 | 1+(67.3+67.3i)T+3.12e3iT2 |
| 7 | 1+148.iT−1.68e4T2 |
| 11 | 1+(256.+256.i)T+1.61e5iT2 |
| 13 | 1+(218.−218.i)T−3.71e5iT2 |
| 17 | 1+463.T+1.41e6T2 |
| 19 | 1+(−920.+920.i)T−2.47e6iT2 |
| 23 | 1+1.05e3iT−6.43e6T2 |
| 29 | 1+(−1.29e3+1.29e3i)T−2.05e7iT2 |
| 31 | 1−1.00e4T+2.86e7T2 |
| 37 | 1+(9.40e3+9.40e3i)T+6.93e7iT2 |
| 41 | 1+368.iT−1.15e8T2 |
| 43 | 1+(9.16e3+9.16e3i)T+1.47e8iT2 |
| 47 | 1+7.63e3T+2.29e8T2 |
| 53 | 1+(1.24e3+1.24e3i)T+4.18e8iT2 |
| 59 | 1+(−1.62e4−1.62e4i)T+7.14e8iT2 |
| 61 | 1+(1.39e3−1.39e3i)T−8.44e8iT2 |
| 67 | 1+(1.74e4−1.74e4i)T−1.35e9iT2 |
| 71 | 1+6.74e4iT−1.80e9T2 |
| 73 | 1−1.95e4iT−2.07e9T2 |
| 79 | 1+4.39e4T+3.07e9T2 |
| 83 | 1+(−7.32e4+7.32e4i)T−3.93e9iT2 |
| 89 | 1+8.86e4iT−5.58e9T2 |
| 97 | 1+7.36e4T+8.58e9T2 |
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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
−17.27902877545504515397432796494, −16.36340503006134644564080391006, −15.71346196556097066651134229779, −13.62289444803675834282333149306, −11.67565796960300762207303695214, −10.43719155874263528887439559439, −8.540704259673022286301772849491, −7.45027409225376373282120830400, −4.80753998200646947807092815008, −0.43939093951647305052290854050,
3.01657100555993255521868084764, 6.74994216799754702145016294433, 8.143753279263710150802104525325, 10.01022599308652725891341363539, 11.58502301029810087392385118216, 12.27938409902557999445249061825, 15.12454182340914749096485639956, 15.64505095177883040817335796060, 17.75346985063103747577406280728, 18.47743739538236651393092908756