L(s) = 1 | − 4-s − 2·5-s + 4·13-s + 16-s + 2·20-s + 2·25-s − 2·29-s + 2·37-s + 2·41-s − 4·52-s + 2·61-s − 64-s − 8·65-s − 2·73-s − 2·80-s − 81-s − 4·89-s − 2·97-s − 2·100-s + 4·101-s + 2·109-s − 2·113-s + 2·116-s − 2·125-s + 127-s + 131-s + 137-s + ⋯ |
L(s) = 1 | − 4-s − 2·5-s + 4·13-s + 16-s + 2·20-s + 2·25-s − 2·29-s + 2·37-s + 2·41-s − 4·52-s + 2·61-s − 64-s − 8·65-s − 2·73-s − 2·80-s − 81-s − 4·89-s − 2·97-s − 2·100-s + 4·101-s + 2·109-s − 2·113-s + 2·116-s − 2·125-s + 127-s + 131-s + 137-s + ⋯ |
Λ(s)=(=(11102224s/2ΓC(s)2L(s)Λ(1−s)
Λ(s)=(=(11102224s/2ΓC(s)2L(s)Λ(1−s)
Degree: |
4 |
Conductor: |
11102224
= 24⋅74⋅172
|
Sign: |
1
|
Analytic conductor: |
2.76518 |
Root analytic conductor: |
1.28952 |
Motivic weight: |
0 |
Rational: |
yes |
Arithmetic: |
yes |
Character: |
Trivial
|
Primitive: |
no
|
Self-dual: |
yes
|
Analytic rank: |
0
|
Selberg data: |
(4, 11102224, ( :0,0), 1)
|
Particular Values
L(21) |
≈ |
0.8856150876 |
L(21) |
≈ |
0.8856150876 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1
L(s)=p∏ j=1∏4(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−8.790390094214946818624091041978, −8.548549548274563564144906219624, −8.274342717562745769936631149975, −8.098908181856115567616957731689, −7.48358014587181380502623646717, −7.41986238014984211437602090300, −6.84314331405163844154461594750, −6.15038956349376653971524218849, −6.00542313895195228226626409227, −5.69325487277978777709354685503, −5.26087062239580847145273039016, −4.40871171970737961750501582965, −4.13088693244731173451210324301, −3.94905446137667590140928639264, −3.85246361645720185831238690570, −3.11611928451943545657526856909, −2.96896215101482196034074936860, −1.77697439988707306132956663952, −1.15790871148051782974946018628, −0.71656054501944727655211663883,
0.71656054501944727655211663883, 1.15790871148051782974946018628, 1.77697439988707306132956663952, 2.96896215101482196034074936860, 3.11611928451943545657526856909, 3.85246361645720185831238690570, 3.94905446137667590140928639264, 4.13088693244731173451210324301, 4.40871171970737961750501582965, 5.26087062239580847145273039016, 5.69325487277978777709354685503, 6.00542313895195228226626409227, 6.15038956349376653971524218849, 6.84314331405163844154461594750, 7.41986238014984211437602090300, 7.48358014587181380502623646717, 8.098908181856115567616957731689, 8.274342717562745769936631149975, 8.548549548274563564144906219624, 8.790390094214946818624091041978