L(s) = 1 | + 2·2-s + 3·4-s + 4·8-s + 6·9-s − 4·13-s + 5·16-s − 2·17-s + 12·18-s − 16·19-s − 25-s − 8·26-s + 6·32-s − 4·34-s + 18·36-s − 32·38-s − 16·43-s + 10·49-s − 2·50-s − 12·52-s + 20·53-s + 8·59-s + 7·64-s − 8·67-s − 6·68-s + 24·72-s − 48·76-s + 27·81-s + ⋯ |
L(s) = 1 | + 1.41·2-s + 3/2·4-s + 1.41·8-s + 2·9-s − 1.10·13-s + 5/4·16-s − 0.485·17-s + 2.82·18-s − 3.67·19-s − 1/5·25-s − 1.56·26-s + 1.06·32-s − 0.685·34-s + 3·36-s − 5.19·38-s − 2.43·43-s + 10/7·49-s − 0.282·50-s − 1.66·52-s + 2.74·53-s + 1.04·59-s + 7/8·64-s − 0.977·67-s − 0.727·68-s + 2.82·72-s − 5.50·76-s + 3·81-s + ⋯ |
Λ(s)=(=(28900s/2ΓC(s)2L(s)Λ(2−s)
Λ(s)=(=(28900s/2ΓC(s+1/2)2L(s)Λ(1−s)
Degree: |
4 |
Conductor: |
28900
= 22⋅52⋅172
|
Sign: |
1
|
Analytic conductor: |
1.84268 |
Root analytic conductor: |
1.16509 |
Motivic weight: |
1 |
Rational: |
yes |
Arithmetic: |
yes |
Character: |
Trivial
|
Primitive: |
no
|
Self-dual: |
yes
|
Analytic rank: |
0
|
Selberg data: |
(4, 28900, ( :1/2,1/2), 1)
|
Particular Values
L(1) |
≈ |
2.878557579 |
L(21) |
≈ |
2.878557579 |
L(23) |
|
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
−12.94407642036537484328674743374, −12.71991391950053845994315374925, −12.19336794839424565471569783485, −11.85433668855291833341100897616, −11.05543305765230238128605601836, −10.55622503560228451325784433348, −10.11639100699523557853309705068, −9.945609295567579133963362296170, −8.719628844099429559617781278284, −8.538087315103129226148980569814, −7.37919842515154954497070386172, −7.26835572617531933661978272572, −6.45168467505020539170819963411, −6.34769481191182450507979128760, −5.21583820190124830450662575045, −4.66481553244488061897850650772, −4.16309584125763120004185199517, −3.81144439505337770209116126257, −2.35577095351504871124232407459, −1.96873713218844423806568882524,
1.96873713218844423806568882524, 2.35577095351504871124232407459, 3.81144439505337770209116126257, 4.16309584125763120004185199517, 4.66481553244488061897850650772, 5.21583820190124830450662575045, 6.34769481191182450507979128760, 6.45168467505020539170819963411, 7.26835572617531933661978272572, 7.37919842515154954497070386172, 8.538087315103129226148980569814, 8.719628844099429559617781278284, 9.945609295567579133963362296170, 10.11639100699523557853309705068, 10.55622503560228451325784433348, 11.05543305765230238128605601836, 11.85433668855291833341100897616, 12.19336794839424565471569783485, 12.71991391950053845994315374925, 12.94407642036537484328674743374