L(s) = 1 | + (−0.473 + 0.345i)2-s + (0.902 + 0.0126i)3-s + (−0.525 − 0.327i)4-s + (−0.0303 − 0.847i)5-s + (−0.431 + 0.306i)6-s + (−0.348 − 0.611i)7-s + (0.187 − 0.590i)8-s + (0.799 + 0.0227i)9-s + (0.307 + 0.391i)10-s + (0.256 + 0.745i)11-s + (−0.470 − 0.302i)12-s + (−0.477 + 0.472i)13-s + (0.376 + 0.169i)14-s + (−0.0167 − 0.765i)15-s + (−0.209 + 0.551i)16-s + (0.205 − 0.140i)17-s + ⋯ |
Λ(s)=(=(ΓR(s−22.5i)ΓR(s−0.877i)ΓR(s+8.89i)ΓR(s+14.5i)L(s)Λ(1−s)
Degree: |
4 |
Conductor: |
1
|
Sign: |
1
|
Analytic conductor: |
1.25130 |
Root analytic conductor: |
1.05764 |
Rational: |
no |
Arithmetic: |
no |
Primitive: |
yes
|
Self-dual: |
no
|
Selberg data: |
(4, 1, (−22.5224000508i,−0.877793680384i,8.89271031532i,14.50748341588i: ), 1)
|
L(s)=p∏ j=1∏4(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−24.67850357, −22.71078844, −21.38370873, −19.52958908, −18.29701111, −2.90315745,
4.36082312, 7.21584682, 8.92106206, 9.81023223, 12.66475243, 13.96602377, 15.62993783, 17.17431380, 18.94507322, 20.35447110, 24.40107476