L(s) = 1 | + (−0.866 − 0.5i)2-s + (−0.866 + 0.5i)3-s + (0.499 + 0.866i)4-s + (0.866 − 0.5i)5-s + 0.999·6-s − 0.999i·8-s + (0.499 − 0.866i)9-s − 0.999·10-s + (−0.866 − 0.499i)12-s + (−0.499 + 0.866i)15-s + (−0.5 + 0.866i)16-s + (−0.866 − 1.5i)17-s + (−0.866 + 0.499i)18-s + (−0.5 − 0.866i)19-s + (0.866 + 0.499i)20-s + ⋯ |
L(s) = 1 | + (−0.866 − 0.5i)2-s + (−0.866 + 0.5i)3-s + (0.499 + 0.866i)4-s + (0.866 − 0.5i)5-s + 0.999·6-s − 0.999i·8-s + (0.499 − 0.866i)9-s − 0.999·10-s + (−0.866 − 0.499i)12-s + (−0.499 + 0.866i)15-s + (−0.5 + 0.866i)16-s + (−0.866 − 1.5i)17-s + (−0.866 + 0.499i)18-s + (−0.5 − 0.866i)19-s + (0.866 + 0.499i)20-s + ⋯ |
Λ(s)=(=(2280s/2ΓC(s)L(s)(−0.582+0.813i)Λ(1−s)
Λ(s)=(=(2280s/2ΓC(s)L(s)(−0.582+0.813i)Λ(1−s)
Degree: |
2 |
Conductor: |
2280
= 23⋅3⋅5⋅19
|
Sign: |
−0.582+0.813i
|
Analytic conductor: |
1.13786 |
Root analytic conductor: |
1.06670 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2280(1019,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 2280, ( :0), −0.582+0.813i)
|
Particular Values
L(21) |
≈ |
0.4385765222 |
L(21) |
≈ |
0.4385765222 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.866+0.5i)T |
| 3 | 1+(0.866−0.5i)T |
| 5 | 1+(−0.866+0.5i)T |
| 19 | 1+(0.5+0.866i)T |
good | 7 | 1+T2 |
| 11 | 1−T2 |
| 13 | 1+(0.5+0.866i)T2 |
| 17 | 1+(0.866+1.5i)T+(−0.5+0.866i)T2 |
| 23 | 1+(1.73+i)T+(0.5+0.866i)T2 |
| 29 | 1+(0.5+0.866i)T2 |
| 31 | 1+T+T2 |
| 37 | 1−T2 |
| 41 | 1+(−0.5+0.866i)T2 |
| 43 | 1+(0.5−0.866i)T2 |
| 47 | 1+(−0.866−0.5i)T+(0.5+0.866i)T2 |
| 53 | 1+(0.866−1.5i)T+(−0.5−0.866i)T2 |
| 59 | 1+(−0.5+0.866i)T2 |
| 61 | 1+(0.5+0.866i)T2 |
| 67 | 1+(−0.5−0.866i)T2 |
| 71 | 1+(0.5−0.866i)T2 |
| 73 | 1+(0.5−0.866i)T2 |
| 79 | 1+(1+1.73i)T+(−0.5+0.866i)T2 |
| 83 | 1−1.73T+T2 |
| 89 | 1+(−0.5−0.866i)T2 |
| 97 | 1+(−0.5+0.866i)T2 |
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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
−9.302134231497134795045542596163, −8.489372371023483302818291525857, −7.38242635935274160224688200692, −6.56222195710315610346723321764, −5.94550263447709024774483588216, −4.80415369779446560094778212880, −4.23147360148348476275492269912, −2.83103000977866775778828528583, −1.86082495664824207388427668846, −0.42107034883101781765897788991,
1.69614120498622067077696646814, 2.06286263321466900389891292489, 3.86076126554646135307943579802, 5.18021362259896222464727290424, 5.98203917410106343785344125743, 6.25774733151626002877519464436, 7.07074505029389312970365652991, 7.901563131776355809926065744134, 8.542076005864833592040376969577, 9.652981417897061763135296384406