L(s) = 1 | + (−0.890 − 0.454i)2-s + (−0.222 − 0.974i)3-s + (0.586 + 0.809i)4-s + (0.932 − 0.359i)5-s + (−0.244 + 0.969i)6-s + (0.0976 + 0.995i)7-s + (−0.154 − 0.987i)8-s + (−0.900 + 0.433i)9-s + (−0.994 − 0.103i)10-s + (−0.0402 + 0.999i)11-s + (0.658 − 0.752i)12-s + (−0.988 + 0.149i)13-s + (0.365 − 0.930i)14-s + (−0.558 − 0.829i)15-s + (−0.311 + 0.950i)16-s + (0.529 − 0.848i)17-s + ⋯ |
L(s) = 1 | + (−0.890 − 0.454i)2-s + (−0.222 − 0.974i)3-s + (0.586 + 0.809i)4-s + (0.932 − 0.359i)5-s + (−0.244 + 0.969i)6-s + (0.0976 + 0.995i)7-s + (−0.154 − 0.987i)8-s + (−0.900 + 0.433i)9-s + (−0.994 − 0.103i)10-s + (−0.0402 + 0.999i)11-s + (0.658 − 0.752i)12-s + (−0.988 + 0.149i)13-s + (0.365 − 0.930i)14-s + (−0.558 − 0.829i)15-s + (−0.311 + 0.950i)16-s + (0.529 − 0.848i)17-s + ⋯ |
Λ(s)=(=(547s/2ΓR(s)L(s)(0.985+0.167i)Λ(1−s)
Λ(s)=(=(547s/2ΓR(s)L(s)(0.985+0.167i)Λ(1−s)
Degree: |
1 |
Conductor: |
547
|
Sign: |
0.985+0.167i
|
Analytic conductor: |
2.54025 |
Root analytic conductor: |
2.54025 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ547(36,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 547, (0: ), 0.985+0.167i)
|
Particular Values
L(21) |
≈ |
0.7952607846+0.06727297201i |
L(21) |
≈ |
0.7952607846+0.06727297201i |
L(1) |
≈ |
0.7085519630−0.1540552521i |
L(1) |
≈ |
0.7085519630−0.1540552521i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 547 | 1 |
good | 2 | 1+(−0.890−0.454i)T |
| 3 | 1+(−0.222−0.974i)T |
| 5 | 1+(0.932−0.359i)T |
| 7 | 1+(0.0976+0.995i)T |
| 11 | 1+(−0.0402+0.999i)T |
| 13 | 1+(−0.988+0.149i)T |
| 17 | 1+(0.529−0.848i)T |
| 19 | 1+(−0.131+0.991i)T |
| 23 | 1+(−0.999−0.0115i)T |
| 29 | 1+(0.725−0.688i)T |
| 31 | 1+(−0.0172+0.999i)T |
| 37 | 1+(0.905+0.423i)T |
| 41 | 1+(−0.5+0.866i)T |
| 43 | 1+(−0.763+0.645i)T |
| 47 | 1+(0.987−0.160i)T |
| 53 | 1+(−0.439+0.898i)T |
| 59 | 1+(0.692−0.721i)T |
| 61 | 1+(0.605+0.795i)T |
| 67 | 1+(−0.980−0.194i)T |
| 71 | 1+(0.166+0.986i)T |
| 73 | 1+(−0.558+0.829i)T |
| 79 | 1+(0.940+0.338i)T |
| 83 | 1+(0.428+0.903i)T |
| 89 | 1+(0.386+0.922i)T |
| 97 | 1+(0.756−0.654i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−23.657897041689639937782735244692, −22.312237125909265622184882527737, −21.72243783838231234881411135137, −20.80075416397644584277585190438, −19.96563749524808066149130503236, −19.1943544171457127042007803389, −17.98299694807602283520647440543, −17.26492508398336613293161944495, −16.81203882466075186651304704674, −16.00730059071841661939476039792, −14.879031333660728696893491605977, −14.33046966845576855768047480997, −13.445346082771619816036962639319, −11.78237973245354354304947515523, −10.71243881846618670848930270645, −10.36988799014082871101038179458, −9.587029126742063497786931393666, −8.68382284265615719663886189193, −7.61272417697209810660338746022, −6.49509075785249700490776957388, −5.74254813959298432463602391739, −4.799960789487089196837664600218, −3.40065826295764636375503481607, −2.19156968026769410872139694475, −0.5984012852344834796304731649,
1.29093616844429552896838375101, 2.160981933206195448545108725623, 2.76049777942216612519257161095, 4.78296214648464411778405704466, 5.86144962036720168955479872328, 6.75156715059451950924367358597, 7.76778455032757770100749109209, 8.53868501052158658774591410613, 9.6507467511664968655285075940, 10.09279158518995136272965122383, 11.62407464275624255951530069531, 12.24080547787799686739936236193, 12.67905582862115985012242561108, 13.88077139566065678770144338039, 14.852954125242345622233549768753, 16.20728327209022911782768074947, 16.96361401744871630215347203788, 17.84356040230517954905037258814, 18.19211660529103753221950585774, 19.028486154515767735837417148905, 19.97423258107967017276886393134, 20.69663207979031507990494668103, 21.685029729157742388323372406563, 22.32577161118346032049983719079, 23.50815929017519464880902621096