L(s) = 1 | + (1.15 − 2.00i)2-s + (0.115 − 0.0667i)3-s + (−1.68 − 2.92i)4-s + (−2.18 − 1.26i)5-s − 0.309i·6-s − 3.19·8-s + (−1.49 + 2.58i)9-s + (−5.07 + 2.92i)10-s + (−4.29 + 2.48i)11-s + (−0.390 − 0.225i)12-s − 2.86·13-s − 0.337·15-s + (−0.331 + 0.573i)16-s + (−3.19 + 2.60i)17-s + (3.45 + 5.99i)18-s + (2.98 − 5.17i)19-s + ⋯ |
L(s) = 1 | + (0.820 − 1.42i)2-s + (0.0667 − 0.0385i)3-s + (−0.844 − 1.46i)4-s + (−0.978 − 0.564i)5-s − 0.126i·6-s − 1.13·8-s + (−0.497 + 0.860i)9-s + (−1.60 + 0.926i)10-s + (−1.29 + 0.748i)11-s + (−0.112 − 0.0651i)12-s − 0.793·13-s − 0.0870·15-s + (−0.0828 + 0.143i)16-s + (−0.774 + 0.632i)17-s + (0.815 + 1.41i)18-s + (0.685 − 1.18i)19-s + ⋯ |
Λ(s)=(=(833s/2ΓC(s)L(s)(−0.0346−0.999i)Λ(2−s)
Λ(s)=(=(833s/2ΓC(s+1/2)L(s)(−0.0346−0.999i)Λ(1−s)
Degree: |
2 |
Conductor: |
833
= 72⋅17
|
Sign: |
−0.0346−0.999i
|
Analytic conductor: |
6.65153 |
Root analytic conductor: |
2.57905 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ833(373,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 833, ( :1/2), −0.0346−0.999i)
|
Particular Values
L(1) |
≈ |
0.304477+0.315228i |
L(21) |
≈ |
0.304477+0.315228i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 7 | 1 |
| 17 | 1+(3.19−2.60i)T |
good | 2 | 1+(−1.15+2.00i)T+(−1−1.73i)T2 |
| 3 | 1+(−0.115+0.0667i)T+(1.5−2.59i)T2 |
| 5 | 1+(2.18+1.26i)T+(2.5+4.33i)T2 |
| 11 | 1+(4.29−2.48i)T+(5.5−9.52i)T2 |
| 13 | 1+2.86T+13T2 |
| 19 | 1+(−2.98+5.17i)T+(−9.5−16.4i)T2 |
| 23 | 1+(−2.59−1.49i)T+(11.5+19.9i)T2 |
| 29 | 1+4.37iT−29T2 |
| 31 | 1+(2.33−1.35i)T+(15.5−26.8i)T2 |
| 37 | 1+(5.41+3.12i)T+(18.5+32.0i)T2 |
| 41 | 1+6.74iT−41T2 |
| 43 | 1+6.21T+43T2 |
| 47 | 1+(0.788−1.36i)T+(−23.5−40.7i)T2 |
| 53 | 1+(−0.0987−0.171i)T+(−26.5+45.8i)T2 |
| 59 | 1+(−4.06−7.04i)T+(−29.5+51.0i)T2 |
| 61 | 1+(−0.472−0.272i)T+(30.5+52.8i)T2 |
| 67 | 1+(0.358+0.620i)T+(−33.5+58.0i)T2 |
| 71 | 1+10.8iT−71T2 |
| 73 | 1+(−4.66+2.69i)T+(36.5−63.2i)T2 |
| 79 | 1+(−12.0−6.95i)T+(39.5+68.4i)T2 |
| 83 | 1+10.7T+83T2 |
| 89 | 1+(8.48−14.7i)T+(−44.5−77.0i)T2 |
| 97 | 1+5.73iT−97T2 |
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
−9.928765097665671839747476066593, −8.897872461020180742175418615087, −7.903207643878317620976985868819, −7.19000576250155887900002754535, −5.28794098626800608744054381893, −4.94443298387792135733673451021, −4.05530200738932691228740310494, −2.83717653740312175916028321825, −2.05815181510093366959111780404, −0.15197690145134078323907594760,
3.00245931137684906308100495780, 3.64050583450964964075349361215, 4.88132078002752064541744543477, 5.56588816500957629652754692378, 6.62065157487354341303826817708, 7.26779959437147901851550264371, 8.026076113010620730789115202761, 8.658057609869900541223110187208, 9.913863209820265767993395371802, 11.00881798078988051217537918319