L(s) = 1 | + i·5-s − i·7-s + i·11-s − i·19-s + 23-s − 25-s + 29-s + i·31-s + 35-s + i·37-s + i·41-s + 43-s − i·47-s − 49-s − 53-s + ⋯ |
L(s) = 1 | + i·5-s − i·7-s + i·11-s − i·19-s + 23-s − 25-s + 29-s + i·31-s + 35-s + i·37-s + i·41-s + 43-s − i·47-s − 49-s − 53-s + ⋯ |
Λ(s)=(=(2652s/2ΓR(s+1)L(s)(0.289+0.957i)Λ(1−s)
Λ(s)=(=(2652s/2ΓR(s+1)L(s)(0.289+0.957i)Λ(1−s)
Degree: |
1 |
Conductor: |
2652
= 22⋅3⋅13⋅17
|
Sign: |
0.289+0.957i
|
Analytic conductor: |
284.996 |
Root analytic conductor: |
284.996 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2652(203,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 2652, (1: ), 0.289+0.957i)
|
Particular Values
L(21) |
≈ |
1.643877838+1.219849362i |
L(21) |
≈ |
1.643877838+1.219849362i |
L(1) |
≈ |
1.075618898+0.1842456970i |
L(1) |
≈ |
1.075618898+0.1842456970i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1 |
| 13 | 1 |
| 17 | 1 |
good | 5 | 1 |
| 7 | 1 |
| 11 | 1 |
| 19 | 1−iT |
| 23 | 1 |
| 29 | 1 |
| 31 | 1 |
| 37 | 1+iT |
| 41 | 1 |
| 43 | 1 |
| 47 | 1 |
| 53 | 1 |
| 59 | 1 |
| 61 | 1 |
| 67 | 1 |
| 71 | 1−iT |
| 73 | 1 |
| 79 | 1 |
| 83 | 1 |
| 89 | 1+T |
| 97 | 1 |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−19.10956064636441266752044591556, −18.39839401862955188135216063870, −17.48981246494809953304747523198, −16.88276877422785777681644106888, −16.03568852323072417840652775504, −15.75098451281606064143654806189, −14.722255341152508721348282572454, −14.03566329615061796427885474951, −13.17834829732965333787803956383, −12.54009602222527183157285568826, −11.96164207785894910024052951095, −11.21429136814709594949187819434, −10.36122982571962732343073083333, −9.28034492782624357656800554962, −8.9417584090894607363851337144, −8.19557378970015794381274494239, −7.50161740104936835524152294297, −6.13157231923907737778152466677, −5.80090288172321568368146165004, −4.97879612694454144513622772018, −4.12869669708688481371458180387, −3.17473240890460697593794793333, −2.28826144508215462356608315416, −1.29488249763888711895309197462, −0.43725738136437255845062952910,
0.76413261241354197522231600514, 1.77795092247748605156493586096, 2.81891249739205050324702558859, 3.41414858487303379050400182490, 4.50768020148246360295445045797, 4.97644780078939820155912710355, 6.393761151498034007044642702302, 6.830356242139791647672047262835, 7.4254792294155592477579334814, 8.23054868929958096977486016744, 9.36123508126607548216047082043, 9.97855572221918606945473014626, 10.72496352159313116172129331176, 11.16976182411773541550636072146, 12.12986818959568642817900725196, 12.94303539004129030711808944684, 13.7427225502222050807743849393, 14.248082290083688128775216467057, 15.12415842868160741006042007330, 15.53129080935302200488606887593, 16.55814624498709684893815778434, 17.36149520085207346143707275365, 17.789749420702633933183960062933, 18.51039017039806790702231562002, 19.48641617190070176595273425397