L(s) = 1 | + (−0.726 + 2.23i)2-s + (−2.85 − 2.07i)4-s + (−2.13 + 0.694i)5-s + (−2.38 + 3.27i)7-s + (2.90 − 2.10i)8-s − 5.28i·10-s + (3.31 − 0.0200i)11-s + (4.42 + 1.43i)13-s + (−5.59 − 7.70i)14-s + (0.427 + 1.31i)16-s + (0.0235 + 0.0725i)17-s + (1.40 + 1.93i)19-s + (7.53 + 2.44i)20-s + (−2.36 + 7.42i)22-s + 3.22i·23-s + ⋯ |
L(s) = 1 | + (−0.513 + 1.58i)2-s + (−1.42 − 1.03i)4-s + (−0.956 + 0.310i)5-s + (−0.899 + 1.23i)7-s + (1.02 − 0.745i)8-s − 1.67i·10-s + (0.999 − 0.00604i)11-s + (1.22 + 0.398i)13-s + (−1.49 − 2.05i)14-s + (0.106 + 0.328i)16-s + (0.00571 + 0.0175i)17-s + (0.323 + 0.444i)19-s + (1.68 + 0.547i)20-s + (−0.504 + 1.58i)22-s + 0.672i·23-s + ⋯ |
Λ(s)=(=(99s/2ΓC(s)L(s)(−0.999−0.00310i)Λ(2−s)
Λ(s)=(=(99s/2ΓC(s+1/2)L(s)(−0.999−0.00310i)Λ(1−s)
Degree: |
2 |
Conductor: |
99
= 32⋅11
|
Sign: |
−0.999−0.00310i
|
Analytic conductor: |
0.790518 |
Root analytic conductor: |
0.889111 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ99(35,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 99, ( :1/2), −0.999−0.00310i)
|
Particular Values
L(1) |
≈ |
0.000880781+0.568205i |
L(21) |
≈ |
0.000880781+0.568205i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 11 | 1+(−3.31+0.0200i)T |
good | 2 | 1+(0.726−2.23i)T+(−1.61−1.17i)T2 |
| 5 | 1+(2.13−0.694i)T+(4.04−2.93i)T2 |
| 7 | 1+(2.38−3.27i)T+(−2.16−6.65i)T2 |
| 13 | 1+(−4.42−1.43i)T+(10.5+7.64i)T2 |
| 17 | 1+(−0.0235−0.0725i)T+(−13.7+9.99i)T2 |
| 19 | 1+(−1.40−1.93i)T+(−5.87+18.0i)T2 |
| 23 | 1−3.22iT−23T2 |
| 29 | 1+(1.48+1.08i)T+(8.96+27.5i)T2 |
| 31 | 1+(−0.517+1.59i)T+(−25.0−18.2i)T2 |
| 37 | 1+(5.87+4.27i)T+(11.4+35.1i)T2 |
| 41 | 1+(−6.82+4.96i)T+(12.6−38.9i)T2 |
| 43 | 1−4.28iT−43T2 |
| 47 | 1+(−3.65−5.02i)T+(−14.5+44.6i)T2 |
| 53 | 1+(1.16+0.379i)T+(42.8+31.1i)T2 |
| 59 | 1+(−0.341+0.469i)T+(−18.2−56.1i)T2 |
| 61 | 1+(3.59−1.16i)T+(49.3−35.8i)T2 |
| 67 | 1−12.9T+67T2 |
| 71 | 1+(1.06−0.346i)T+(57.4−41.7i)T2 |
| 73 | 1+(−7.82+10.7i)T+(−22.5−69.4i)T2 |
| 79 | 1+(−0.627−0.203i)T+(63.9+46.4i)T2 |
| 83 | 1+(−3.15−9.71i)T+(−67.1+48.7i)T2 |
| 89 | 1+6.58iT−89T2 |
| 97 | 1+(−5.08+15.6i)T+(−78.4−57.0i)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
−14.82329736041423648954689826432, −13.82385061502975220616048624790, −12.33090517676581196959596342690, −11.31763942722825184534517235082, −9.463378423603972416847587503809, −8.838386943022131644960127744666, −7.69750669254702180655329149614, −6.53124109005508026100759207173, −5.73717545520714436180078245035, −3.73667479960224348845956228086,
0.855652997329293444855679185769, 3.43283514169905169840176564669, 4.12774478154439322216338921883, 6.72540443750132085188246097818, 8.232672145853905120298687386574, 9.274735293173336602986796233262, 10.37661599593391814969964488364, 11.18008677430688746017387332576, 12.11986899844358967670279363634, 13.03546170021631902199781450422