L(s) = 1 | + (0.130 + 1.40i)2-s + (0.00582 − 1.73i)3-s + (−1.96 + 0.367i)4-s + (0.965 + 0.258i)5-s + (2.43 − 0.217i)6-s + (−1.28 + 2.22i)7-s + (−0.774 − 2.72i)8-s + (−2.99 − 0.0201i)9-s + (−0.238 + 1.39i)10-s + (−1.49 + 0.400i)11-s + (0.625 + 3.40i)12-s + (−4.35 − 1.16i)13-s + (−3.30 − 1.52i)14-s + (0.453 − 1.67i)15-s + (3.72 − 1.44i)16-s − 3.11i·17-s + ⋯ |
L(s) = 1 | + (0.0923 + 0.995i)2-s + (0.00336 − 0.999i)3-s + (−0.982 + 0.183i)4-s + (0.431 + 0.115i)5-s + (0.996 − 0.0889i)6-s + (−0.486 + 0.842i)7-s + (−0.273 − 0.961i)8-s + (−0.999 − 0.00672i)9-s + (−0.0753 + 0.440i)10-s + (−0.451 + 0.120i)11-s + (0.180 + 0.983i)12-s + (−1.20 − 0.323i)13-s + (−0.883 − 0.406i)14-s + (0.117 − 0.431i)15-s + (0.932 − 0.361i)16-s − 0.754i·17-s + ⋯ |
Λ(s)=(=(720s/2ΓC(s)L(s)(−0.835+0.549i)Λ(2−s)
Λ(s)=(=(720s/2ΓC(s+1/2)L(s)(−0.835+0.549i)Λ(1−s)
Degree: |
2 |
Conductor: |
720
= 24⋅32⋅5
|
Sign: |
−0.835+0.549i
|
Analytic conductor: |
5.74922 |
Root analytic conductor: |
2.39775 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ720(11,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 720, ( :1/2), −0.835+0.549i)
|
Particular Values
L(1) |
≈ |
0.00940660−0.0314534i |
L(21) |
≈ |
0.00940660−0.0314534i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.130−1.40i)T |
| 3 | 1+(−0.00582+1.73i)T |
| 5 | 1+(−0.965−0.258i)T |
good | 7 | 1+(1.28−2.22i)T+(−3.5−6.06i)T2 |
| 11 | 1+(1.49−0.400i)T+(9.52−5.5i)T2 |
| 13 | 1+(4.35+1.16i)T+(11.2+6.5i)T2 |
| 17 | 1+3.11iT−17T2 |
| 19 | 1+(−0.356−0.356i)T+19iT2 |
| 23 | 1+(1.88−1.08i)T+(11.5−19.9i)T2 |
| 29 | 1+(8.55−2.29i)T+(25.1−14.5i)T2 |
| 31 | 1+(3.82−2.20i)T+(15.5−26.8i)T2 |
| 37 | 1+(6.60+6.60i)T+37iT2 |
| 41 | 1+(0.181+0.315i)T+(−20.5+35.5i)T2 |
| 43 | 1+(0.153+0.574i)T+(−37.2+21.5i)T2 |
| 47 | 1+(3.01−5.21i)T+(−23.5−40.7i)T2 |
| 53 | 1+(−0.622+0.622i)T−53iT2 |
| 59 | 1+(−1.61+6.02i)T+(−51.0−29.5i)T2 |
| 61 | 1+(3.62+13.5i)T+(−52.8+30.5i)T2 |
| 67 | 1+(−0.917+3.42i)T+(−58.0−33.5i)T2 |
| 71 | 1−14.8iT−71T2 |
| 73 | 1+9.34iT−73T2 |
| 79 | 1+(−9.07−5.23i)T+(39.5+68.4i)T2 |
| 83 | 1+(−3.29−12.2i)T+(−71.8+41.5i)T2 |
| 89 | 1−1.43T+89T2 |
| 97 | 1+(4.05−7.02i)T+(−48.5−84.0i)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
−10.91120173630113558360895929595, −9.576553422327924511987290768798, −9.196032864939841762466347740601, −8.049829385650412957317565327426, −7.34316085782793591663124508397, −6.64415270673930089875724048064, −5.56429213878310479950102084928, −5.20795705724363344152107776057, −3.32763188504648325377424907581, −2.17368790193936033928381371875,
0.01525003720748647956386551917, 2.10344874499992121721149740529, 3.32427697246923842203579617107, 4.17365864933031444062647052025, 5.06923027596488162687057155024, 5.96394123067477398620859153069, 7.42767422268728794398596595299, 8.583043874597592735721880157841, 9.416185838586804786163713356912, 10.11893839866746439125138847191