L(s) = 1 | + (−0.866 − 0.5i)7-s + (0.913 − 0.406i)11-s + (−0.406 + 0.913i)13-s + (−0.951 − 0.309i)17-s + (0.309 − 0.951i)19-s + (−0.994 − 0.104i)23-s + (0.978 + 0.207i)29-s + (−0.978 + 0.207i)31-s + (0.587 + 0.809i)37-s + (−0.913 − 0.406i)41-s + (−0.866 − 0.5i)43-s + (−0.207 + 0.978i)47-s + (0.5 + 0.866i)49-s + (0.951 − 0.309i)53-s + (−0.913 − 0.406i)59-s + ⋯ |
L(s) = 1 | + (−0.866 − 0.5i)7-s + (0.913 − 0.406i)11-s + (−0.406 + 0.913i)13-s + (−0.951 − 0.309i)17-s + (0.309 − 0.951i)19-s + (−0.994 − 0.104i)23-s + (0.978 + 0.207i)29-s + (−0.978 + 0.207i)31-s + (0.587 + 0.809i)37-s + (−0.913 − 0.406i)41-s + (−0.866 − 0.5i)43-s + (−0.207 + 0.978i)47-s + (0.5 + 0.866i)49-s + (0.951 − 0.309i)53-s + (−0.913 − 0.406i)59-s + ⋯ |
Λ(s)=(=(1800s/2ΓR(s)L(s)(−0.916+0.400i)Λ(1−s)
Λ(s)=(=(1800s/2ΓR(s)L(s)(−0.916+0.400i)Λ(1−s)
Degree: |
1 |
Conductor: |
1800
= 23⋅32⋅52
|
Sign: |
−0.916+0.400i
|
Analytic conductor: |
8.35916 |
Root analytic conductor: |
8.35916 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1800(797,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 1800, (0: ), −0.916+0.400i)
|
Particular Values
L(21) |
≈ |
0.01821360798+0.08718362399i |
L(21) |
≈ |
0.01821360798+0.08718362399i |
L(1) |
≈ |
0.7768512248−0.04057857096i |
L(1) |
≈ |
0.7768512248−0.04057857096i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1 |
| 5 | 1 |
good | 7 | 1+(−0.866−0.5i)T |
| 11 | 1+(0.913−0.406i)T |
| 13 | 1+(−0.406+0.913i)T |
| 17 | 1+(−0.951−0.309i)T |
| 19 | 1+(0.309−0.951i)T |
| 23 | 1+(−0.994−0.104i)T |
| 29 | 1+(0.978+0.207i)T |
| 31 | 1+(−0.978+0.207i)T |
| 37 | 1+(0.587+0.809i)T |
| 41 | 1+(−0.913−0.406i)T |
| 43 | 1+(−0.866−0.5i)T |
| 47 | 1+(−0.207+0.978i)T |
| 53 | 1+(0.951−0.309i)T |
| 59 | 1+(−0.913−0.406i)T |
| 61 | 1+(−0.913+0.406i)T |
| 67 | 1+(0.207+0.978i)T |
| 71 | 1+(−0.309−0.951i)T |
| 73 | 1+(−0.587+0.809i)T |
| 79 | 1+(0.978+0.207i)T |
| 83 | 1+(0.743−0.669i)T |
| 89 | 1+(−0.809−0.587i)T |
| 97 | 1+(0.207−0.978i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−19.97236623115307685855769066160, −19.30043608022803010809077455372, −18.23700527230334048320940291235, −17.86588342757115182376955178126, −16.7932503301040042388298746879, −16.30041967375302641937854273012, −15.28473289309303850360963298766, −14.92514348035875340397341507731, −13.89011071756739865593758560655, −13.13653814336921165837567160839, −12.27827380057505682597795897765, −11.94189578557000306750857650480, −10.76964435490155694283807959341, −9.963386998108973456465548981671, −9.40985431488211004007568394528, −8.52189210079761378516233626984, −7.70854429024353612977880870246, −6.70112867863060703467247783007, −6.11197134574765969413198205528, −5.275923721086239778285965910127, −4.1688125644052255920238933643, −3.44580727836090186451572894791, −2.46682915415177816566459204601, −1.54945204285917583171935493470, −0.031367621228065306024729233575,
1.26828126876440409836568455908, 2.38676243395002914970236697474, 3.34025837824566655591982472881, 4.17049968899917446178297714866, 4.89749339374391682989505597670, 6.19070376484107263608869170034, 6.7057311575465062681584268673, 7.33674126806694326900945073517, 8.58821497131260930588988180623, 9.20735228253521492446660698547, 9.87649007984227046767674254103, 10.77836686492040468025498735112, 11.63362549928744006564165945932, 12.188758653495869856234995688181, 13.28391316178291896840935777368, 13.75877911677391204759327410453, 14.471495034197165472237325638056, 15.46797303921547229625921334277, 16.19830460733234878184453669072, 16.7538210511278644365060612166, 17.49748786778897665866618397664, 18.34957828263001729622130698515, 19.16901768775666979523176864875, 20.00052986313866687513969422657, 20.04262028328982029032844459784