L(s) = 1 | + (0.841 + 0.540i)3-s + (0.959 + 0.281i)7-s + (0.415 + 0.909i)9-s + (0.654 − 0.755i)11-s + (−0.959 + 0.281i)13-s + (0.142 + 0.989i)17-s + (0.142 − 0.989i)19-s + (0.654 + 0.755i)21-s + (−0.142 + 0.989i)27-s + (0.142 + 0.989i)29-s + (0.841 − 0.540i)31-s + (0.959 − 0.281i)33-s + (0.415 + 0.909i)37-s + (−0.959 − 0.281i)39-s + (0.415 − 0.909i)41-s + ⋯ |
L(s) = 1 | + (0.841 + 0.540i)3-s + (0.959 + 0.281i)7-s + (0.415 + 0.909i)9-s + (0.654 − 0.755i)11-s + (−0.959 + 0.281i)13-s + (0.142 + 0.989i)17-s + (0.142 − 0.989i)19-s + (0.654 + 0.755i)21-s + (−0.142 + 0.989i)27-s + (0.142 + 0.989i)29-s + (0.841 − 0.540i)31-s + (0.959 − 0.281i)33-s + (0.415 + 0.909i)37-s + (−0.959 − 0.281i)39-s + (0.415 − 0.909i)41-s + ⋯ |
Λ(s)=(=(920s/2ΓR(s)L(s)(0.635+0.771i)Λ(1−s)
Λ(s)=(=(920s/2ΓR(s)L(s)(0.635+0.771i)Λ(1−s)
Degree: |
1 |
Conductor: |
920
= 23⋅5⋅23
|
Sign: |
0.635+0.771i
|
Analytic conductor: |
4.27246 |
Root analytic conductor: |
4.27246 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ920(29,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 920, (0: ), 0.635+0.771i)
|
Particular Values
L(21) |
≈ |
2.087358173+0.9850567605i |
L(21) |
≈ |
2.087358173+0.9850567605i |
L(1) |
≈ |
1.528708790+0.3863474512i |
L(1) |
≈ |
1.528708790+0.3863474512i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1 |
| 23 | 1 |
good | 3 | 1+(0.841+0.540i)T |
| 7 | 1+(0.959+0.281i)T |
| 11 | 1+(0.654−0.755i)T |
| 13 | 1+(−0.959+0.281i)T |
| 17 | 1+(0.142+0.989i)T |
| 19 | 1+(0.142−0.989i)T |
| 29 | 1+(0.142+0.989i)T |
| 31 | 1+(0.841−0.540i)T |
| 37 | 1+(0.415+0.909i)T |
| 41 | 1+(0.415−0.909i)T |
| 43 | 1+(0.841+0.540i)T |
| 47 | 1−T |
| 53 | 1+(−0.959−0.281i)T |
| 59 | 1+(0.959−0.281i)T |
| 61 | 1+(−0.841+0.540i)T |
| 67 | 1+(−0.654−0.755i)T |
| 71 | 1+(−0.654−0.755i)T |
| 73 | 1+(0.142−0.989i)T |
| 79 | 1+(−0.959+0.281i)T |
| 83 | 1+(0.415+0.909i)T |
| 89 | 1+(0.841+0.540i)T |
| 97 | 1+(−0.415+0.909i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−21.558520284373004111210404590269, −20.7751353391280672645232472593, −20.23078702876610283768723397817, −19.49281643181592478913283280939, −18.67934204077557038900158181147, −17.728500278262349235835489212203, −17.373436511447444959715471193390, −16.15047119838922199358249674739, −15.101228628884374293638842948782, −14.42153652776897388947578597351, −14.0557907313109038423958816641, −12.93715654108195515753594644393, −12.112269973181270956075507614462, −11.53270581158297446006979938424, −10.13089547718020274707650315567, −9.55917958149019308526551110396, −8.54172728829168396008697938249, −7.62970378513755154548535874309, −7.2675320467051106129607813293, −6.09491108196236120919749881847, −4.81718092129310798422793972039, −4.09519037061779428741393713528, −2.86795605554387530816153055150, −1.99104954647287218252188057157, −1.04132034427300331374314339370,
1.36617228174320900524573103931, 2.37865442856570264536102922133, 3.303578316188690573237726371063, 4.39805265924032939252494038752, 4.99056161697838324829776770406, 6.19442059254755922025941629112, 7.37302922756997024369483299182, 8.19380748941047269704468349980, 8.87854483020825412682890447350, 9.61802310797944349537130188812, 10.66049190409409281569834469550, 11.36290732552191066750549399789, 12.30843774147590066894963541838, 13.39256221890587421628878481716, 14.207856725285278069437271322140, 14.756994435427869797817998472832, 15.40778599583018127346580503629, 16.435642418226846299464033927894, 17.170542758958772330146404420663, 18.018527630116882910640803546673, 19.278335491707554995519882120443, 19.42677038476604668101565737053, 20.50459094322522013262229066384, 21.24615587353164187535377444186, 21.86474801497870127934628243215