L(s) = 1 | + (1.26 + 1.00i)2-s + (1.57 + 0.360i)3-s + (0.137 + 0.602i)4-s + (1.77 − 2.23i)5-s + (1.63 + 2.04i)6-s + (−0.497 + 2.18i)7-s + (0.970 − 2.01i)8-s + (−0.344 − 0.165i)9-s + (4.50 − 1.02i)10-s + (−1.56 − 3.25i)11-s + 1.00i·12-s + (3.81 − 1.83i)13-s + (−2.82 + 2.25i)14-s + (3.61 − 2.87i)15-s + (4.37 − 2.10i)16-s + 6.61i·17-s + ⋯ |
L(s) = 1 | + (0.894 + 0.713i)2-s + (0.910 + 0.207i)3-s + (0.0687 + 0.301i)4-s + (0.795 − 0.997i)5-s + (0.666 + 0.835i)6-s + (−0.188 + 0.823i)7-s + (0.343 − 0.712i)8-s + (−0.114 − 0.0552i)9-s + (1.42 − 0.324i)10-s + (−0.473 − 0.982i)11-s + 0.288i·12-s + (1.05 − 0.509i)13-s + (−0.755 + 0.602i)14-s + (0.932 − 0.743i)15-s + (1.09 − 0.526i)16-s + 1.60i·17-s + ⋯ |
Λ(s)=(=(841s/2ΓC(s)L(s)(0.959−0.280i)Λ(2−s)
Λ(s)=(=(841s/2ΓC(s+1/2)L(s)(0.959−0.280i)Λ(1−s)
Degree: |
2 |
Conductor: |
841
= 292
|
Sign: |
0.959−0.280i
|
Analytic conductor: |
6.71541 |
Root analytic conductor: |
2.59141 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ841(267,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 841, ( :1/2), 0.959−0.280i)
|
Particular Values
L(1) |
≈ |
3.56357+0.510476i |
L(21) |
≈ |
3.56357+0.510476i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 29 | 1 |
good | 2 | 1+(−1.26−1.00i)T+(0.445+1.94i)T2 |
| 3 | 1+(−1.57−0.360i)T+(2.70+1.30i)T2 |
| 5 | 1+(−1.77+2.23i)T+(−1.11−4.87i)T2 |
| 7 | 1+(0.497−2.18i)T+(−6.30−3.03i)T2 |
| 11 | 1+(1.56+3.25i)T+(−6.85+8.60i)T2 |
| 13 | 1+(−3.81+1.83i)T+(8.10−10.1i)T2 |
| 17 | 1−6.61iT−17T2 |
| 19 | 1+(1.80−0.412i)T+(17.1−8.24i)T2 |
| 23 | 1+(−2.01−2.53i)T+(−5.11+22.4i)T2 |
| 31 | 1+(0.852+0.679i)T+(6.89+30.2i)T2 |
| 37 | 1+(3.77−7.84i)T+(−23.0−28.9i)T2 |
| 41 | 1+2.85iT−41T2 |
| 43 | 1+(2.16−1.72i)T+(9.56−41.9i)T2 |
| 47 | 1+(−3.03−6.30i)T+(−29.3+36.7i)T2 |
| 53 | 1+(1.24−1.56i)T+(−11.7−51.6i)T2 |
| 59 | 1+5.09T+59T2 |
| 61 | 1+(−1.57−0.360i)T+(54.9+26.4i)T2 |
| 67 | 1+(9.43+4.54i)T+(41.7+52.3i)T2 |
| 71 | 1+(−1.37+0.662i)T+(44.2−55.5i)T2 |
| 73 | 1+(−0.228+0.181i)T+(16.2−71.1i)T2 |
| 79 | 1+(2.20−4.58i)T+(−49.2−61.7i)T2 |
| 83 | 1+(1.76+7.74i)T+(−74.7+36.0i)T2 |
| 89 | 1+(−6.80−5.42i)T+(19.8+86.7i)T2 |
| 97 | 1+(16.1−3.68i)T+(87.3−42.0i)T2 |
show more | |
show less | |
L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−10.06682987919344548204969540805, −9.052160203208064210463738058588, −8.618188044414003652862840199657, −7.903961569297964390331995437891, −6.15259605036803085048843365473, −5.94472390643231611120454723163, −5.13197325992148277534690842822, −3.89145938384438975128674028620, −3.03333062305319084686000263179, −1.46872239749463051132675734107,
1.95645642266319388705832797008, 2.66562146827826425217981085698, 3.47183867962492087864633506577, 4.49122125106732550969704939503, 5.58441961295847694734647593917, 6.87023441184350434624557932110, 7.40104474000624904890102273759, 8.533374657031389249073099125875, 9.441775439072635246256442818914, 10.43799395037140158032300775303