L(s) = 1 | + (0.698 + 1.87i)2-s + 0.798·3-s + (−3.02 + 2.61i)4-s + (−2.31 + 4.43i)5-s + (0.557 + 1.49i)6-s − 0.222·7-s + (−7.01 − 3.84i)8-s − 8.36·9-s + (−9.92 − 1.23i)10-s + 3.31i·11-s + (−2.41 + 2.08i)12-s − 4.74i·13-s + (−0.155 − 0.416i)14-s + (−1.84 + 3.53i)15-s + (2.30 − 15.8i)16-s − 4.87i·17-s + ⋯ |
L(s) = 1 | + (0.349 + 0.937i)2-s + 0.266·3-s + (−0.756 + 0.654i)4-s + (−0.462 + 0.886i)5-s + (0.0929 + 0.249i)6-s − 0.0317·7-s + (−0.877 − 0.480i)8-s − 0.929·9-s + (−0.992 − 0.123i)10-s + 0.301i·11-s + (−0.201 + 0.174i)12-s − 0.365i·13-s + (−0.0110 − 0.0297i)14-s + (−0.123 + 0.235i)15-s + (0.143 − 0.989i)16-s − 0.286i·17-s + ⋯ |
Λ(s)=(=(220s/2ΓC(s)L(s)(−0.973+0.230i)Λ(3−s)
Λ(s)=(=(220s/2ΓC(s+1)L(s)(−0.973+0.230i)Λ(1−s)
Degree: |
2 |
Conductor: |
220
= 22⋅5⋅11
|
Sign: |
−0.973+0.230i
|
Analytic conductor: |
5.99456 |
Root analytic conductor: |
2.44838 |
Motivic weight: |
2 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ220(199,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 220, ( :1), −0.973+0.230i)
|
Particular Values
L(23) |
≈ |
0.122421−1.04848i |
L(21) |
≈ |
0.122421−1.04848i |
L(2) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.698−1.87i)T |
| 5 | 1+(2.31−4.43i)T |
| 11 | 1−3.31iT |
good | 3 | 1−0.798T+9T2 |
| 7 | 1+0.222T+49T2 |
| 13 | 1+4.74iT−169T2 |
| 17 | 1+4.87iT−289T2 |
| 19 | 1−35.8iT−361T2 |
| 23 | 1+2.86T+529T2 |
| 29 | 1+12.9T+841T2 |
| 31 | 1−34.8iT−961T2 |
| 37 | 1−39.3iT−1.36e3T2 |
| 41 | 1−51.7T+1.68e3T2 |
| 43 | 1−44.8T+1.84e3T2 |
| 47 | 1−28.0T+2.20e3T2 |
| 53 | 1−0.246iT−2.80e3T2 |
| 59 | 1−50.0iT−3.48e3T2 |
| 61 | 1+77.8T+3.72e3T2 |
| 67 | 1−107.T+4.48e3T2 |
| 71 | 1+58.5iT−5.04e3T2 |
| 73 | 1−84.8iT−5.32e3T2 |
| 79 | 1−74.9iT−6.24e3T2 |
| 83 | 1−118.T+6.88e3T2 |
| 89 | 1+38.5T+7.92e3T2 |
| 97 | 1−3.24iT−9.40e3T2 |
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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
−12.61174304935243743961123215059, −11.82962845720794083680094437901, −10.62269872428733109725544079424, −9.468899615293090551670557578647, −8.233755388717407171686883107335, −7.63312324188658900247085432964, −6.45585845368145093339211283764, −5.51464146054469358930842658754, −3.96235642424518456297574414530, −2.92519775773711760217770662140,
0.49319211900431443884806113052, 2.41223248329212558846555768472, 3.80281381164776706647241601594, 4.89733078939604365153376500082, 6.00114005099320067634799861615, 7.80870106658886933914313985691, 8.976781378975942821525567704874, 9.324911264206499200765617605609, 11.00760463479028083650801241264, 11.43539168141309929731676402533