L(s) = 1 | + (0.891 + 0.453i)3-s − i·7-s + (0.587 + 0.809i)9-s + (0.156 + 0.987i)11-s + (−0.156 + 0.987i)13-s + (0.309 − 0.951i)17-s + (−0.453 − 0.891i)19-s + (−0.453 + 0.891i)21-s + (−0.587 + 0.809i)23-s + (0.156 + 0.987i)27-s + (0.891 + 0.453i)29-s + (−0.309 + 0.951i)31-s + (−0.309 + 0.951i)33-s + (−0.987 − 0.156i)37-s + (−0.587 + 0.809i)39-s + ⋯ |
L(s) = 1 | + (0.891 + 0.453i)3-s − i·7-s + (0.587 + 0.809i)9-s + (0.156 + 0.987i)11-s + (−0.156 + 0.987i)13-s + (0.309 − 0.951i)17-s + (−0.453 − 0.891i)19-s + (−0.453 + 0.891i)21-s + (−0.587 + 0.809i)23-s + (0.156 + 0.987i)27-s + (0.891 + 0.453i)29-s + (−0.309 + 0.951i)31-s + (−0.309 + 0.951i)33-s + (−0.987 − 0.156i)37-s + (−0.587 + 0.809i)39-s + ⋯ |
Λ(s)=(=(800s/2ΓR(s+1)L(s)(−0.943+0.331i)Λ(1−s)
Λ(s)=(=(800s/2ΓR(s+1)L(s)(−0.943+0.331i)Λ(1−s)
Degree: |
1 |
Conductor: |
800
= 25⋅52
|
Sign: |
−0.943+0.331i
|
Analytic conductor: |
85.9719 |
Root analytic conductor: |
85.9719 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ800(779,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 800, (1: ), −0.943+0.331i)
|
Particular Values
L(21) |
≈ |
0.3799684810+2.228762210i |
L(21) |
≈ |
0.3799684810+2.228762210i |
L(1) |
≈ |
1.196461047+0.6592294560i |
L(1) |
≈ |
1.196461047+0.6592294560i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1 |
good | 3 | 1+(0.891+0.453i)T |
| 7 | 1−iT |
| 11 | 1+(0.156+0.987i)T |
| 13 | 1+(−0.156+0.987i)T |
| 17 | 1+(0.309−0.951i)T |
| 19 | 1+(−0.453−0.891i)T |
| 23 | 1+(−0.587+0.809i)T |
| 29 | 1+(0.891+0.453i)T |
| 31 | 1+(−0.309+0.951i)T |
| 37 | 1+(−0.987−0.156i)T |
| 41 | 1+(0.587+0.809i)T |
| 43 | 1+(0.707+0.707i)T |
| 47 | 1+(−0.309−0.951i)T |
| 53 | 1+(0.453−0.891i)T |
| 59 | 1+(−0.987−0.156i)T |
| 61 | 1+(−0.987+0.156i)T |
| 67 | 1+(−0.453−0.891i)T |
| 71 | 1+(0.951−0.309i)T |
| 73 | 1+(0.587−0.809i)T |
| 79 | 1+(0.309+0.951i)T |
| 83 | 1+(0.453+0.891i)T |
| 89 | 1+(0.587−0.809i)T |
| 97 | 1+(−0.309−0.951i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−21.52415827683957179623689671079, −20.71925447942360211003789091784, −20.14070271173987503190620891244, −19.2610069813026992380304570104, −18.7961662613985079402204772585, −17.65832384580732881298841722372, −16.97891919179595103576709684589, −16.01264284359210740851456392971, −15.05231846477880587601552086637, −14.22305089491121112498122482739, −13.71013920680552180006341135196, −12.78405738081055304724578514394, −12.14293922964949666068987666454, −10.66849223795124802528454527360, −10.28172664945795097654179500320, −9.083174566574143960172080792, −8.08174146923236115223995465453, −7.77605869816092889933442354531, −6.53896830371780428935490681749, −5.8014043023100791503109409471, −4.20004999552268975202379051391, −3.607975893302877523308788451271, −2.58204867061173302166492394753, −1.3611994440470848792626405374, −0.42134481896145305080555257678,
1.65505481805767116929737565904, 2.423003100294004604873275633144, 3.36117296601461950655829751250, 4.572788022242712626678944632489, 5.11968312433681392095443829216, 6.57875136282770770860188561664, 7.38520158756651284698645173408, 8.42833581429427614159540274038, 9.29278270995359054180895324309, 9.6296502844109400523244297085, 10.824369800296612516002794033107, 11.88780832805376205361966851350, 12.55251332416426536328641385441, 13.69547274645564004246317714225, 14.34624878208430235245343384996, 15.169905348608206259514875936120, 15.78667459868389767169638410796, 16.5485410828388972619923732247, 17.81910297035260688767373130155, 18.40458260069302661549504401722, 19.61779318667383235266794334844, 19.71455907212950007280737054880, 21.08644262796859199261931893776, 21.39103082900966791143589859062, 22.22801227467772730859461231391