L(s) = 1 | − 2·2-s + 3·4-s − 4·8-s + 9-s + 2·13-s + 5·16-s + 2·17-s − 2·18-s + 2·25-s − 4·26-s − 6·32-s − 4·34-s + 3·36-s − 4·50-s + 6·52-s − 2·53-s + 7·64-s + 6·68-s − 4·72-s + 2·89-s + 6·100-s − 4·101-s − 8·104-s + 4·106-s + 2·117-s + 121-s + 127-s + ⋯ |
L(s) = 1 | − 2·2-s + 3·4-s − 4·8-s + 9-s + 2·13-s + 5·16-s + 2·17-s − 2·18-s + 2·25-s − 4·26-s − 6·32-s − 4·34-s + 3·36-s − 4·50-s + 6·52-s − 2·53-s + 7·64-s + 6·68-s − 4·72-s + 2·89-s + 6·100-s − 4·101-s − 8·104-s + 4·106-s + 2·117-s + 121-s + 127-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) |
≈ |
0.8765862764 |
L(21) |
≈ |
0.8765862764 |
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
−8.973293562638251319724270053544, −8.620933075111954257645631536986, −8.200686561090330194341197503467, −8.056522561671168512024461503494, −7.68363495275501182808579406818, −7.10350550302749743541646205977, −7.03636006340168503341862007103, −6.52341598717714413264105181402, −6.07660500680430133180969592635, −5.98925987369782933819195683307, −5.31004788033584759314288198884, −4.98726622899125756363525248303, −4.21815871410334199376265175633, −3.64031054439535941364333605260, −3.29416024314644885509815301305, −3.00803724595188655270512892113, −2.34786515678965719531469512308, −1.54204151387104326027237222343, −1.28017951305091991985577267014, −0.960671531228963139956870116350,
0.960671531228963139956870116350, 1.28017951305091991985577267014, 1.54204151387104326027237222343, 2.34786515678965719531469512308, 3.00803724595188655270512892113, 3.29416024314644885509815301305, 3.64031054439535941364333605260, 4.21815871410334199376265175633, 4.98726622899125756363525248303, 5.31004788033584759314288198884, 5.98925987369782933819195683307, 6.07660500680430133180969592635, 6.52341598717714413264105181402, 7.03636006340168503341862007103, 7.10350550302749743541646205977, 7.68363495275501182808579406818, 8.056522561671168512024461503494, 8.200686561090330194341197503467, 8.620933075111954257645631536986, 8.973293562638251319724270053544