L(s) = 1 | + (0.382 + 0.923i)5-s + (−0.991 + 0.130i)7-s + (0.793 − 0.608i)11-s + (−0.258 + 0.965i)19-s + (−0.793 + 0.608i)23-s + (−0.707 + 0.707i)25-s + (0.991 + 0.130i)29-s + (0.923 − 0.382i)31-s + (−0.5 − 0.866i)35-s + (−0.130 + 0.991i)37-s + (0.608 + 0.793i)41-s + (0.965 + 0.258i)43-s − i·47-s + (0.965 − 0.258i)49-s + (−0.707 − 0.707i)53-s + ⋯ |
L(s) = 1 | + (0.382 + 0.923i)5-s + (−0.991 + 0.130i)7-s + (0.793 − 0.608i)11-s + (−0.258 + 0.965i)19-s + (−0.793 + 0.608i)23-s + (−0.707 + 0.707i)25-s + (0.991 + 0.130i)29-s + (0.923 − 0.382i)31-s + (−0.5 − 0.866i)35-s + (−0.130 + 0.991i)37-s + (0.608 + 0.793i)41-s + (0.965 + 0.258i)43-s − i·47-s + (0.965 − 0.258i)49-s + (−0.707 − 0.707i)53-s + ⋯ |
Λ(s)=(=(2652s/2ΓR(s+1)L(s)(−0.840+0.541i)Λ(1−s)
Λ(s)=(=(2652s/2ΓR(s+1)L(s)(−0.840+0.541i)Λ(1−s)
Degree: |
1 |
Conductor: |
2652
= 22⋅3⋅13⋅17
|
Sign: |
−0.840+0.541i
|
Analytic conductor: |
284.996 |
Root analytic conductor: |
284.996 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2652(1043,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 2652, (1: ), −0.840+0.541i)
|
Particular Values
L(21) |
≈ |
0.4197487021+1.426034953i |
L(21) |
≈ |
0.4197487021+1.426034953i |
L(1) |
≈ |
0.9781229660+0.2944174048i |
L(1) |
≈ |
0.9781229660+0.2944174048i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1 |
| 13 | 1 |
| 17 | 1 |
good | 5 | 1+(0.382+0.923i)T |
| 7 | 1+(−0.991+0.130i)T |
| 11 | 1+(0.793−0.608i)T |
| 19 | 1+(−0.258+0.965i)T |
| 23 | 1+(−0.793+0.608i)T |
| 29 | 1+(0.991+0.130i)T |
| 31 | 1+(0.923−0.382i)T |
| 37 | 1+(−0.130+0.991i)T |
| 41 | 1+(0.608+0.793i)T |
| 43 | 1+(0.965+0.258i)T |
| 47 | 1−iT |
| 53 | 1+(−0.707−0.707i)T |
| 59 | 1+(0.965+0.258i)T |
| 61 | 1+(−0.991+0.130i)T |
| 67 | 1+(−0.5+0.866i)T |
| 71 | 1+(−0.793−0.608i)T |
| 73 | 1+(−0.382−0.923i)T |
| 79 | 1+(0.923+0.382i)T |
| 83 | 1+(−0.707−0.707i)T |
| 89 | 1+(0.866+0.5i)T |
| 97 | 1+(0.608−0.793i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−19.14943529017215171461144769844, −17.890414995226999851841651596233, −17.44014936462869014162020454061, −16.81181523637003677543925566394, −15.867935323136193317586930911429, −15.716487838625904533900592276366, −14.41606287459808644454378074568, −13.87013094788824451603987547103, −13.07333552842349183446737426963, −12.36977872078218512177664006502, −12.05038015720129504079313498598, −10.81431427876218324353893079927, −10.08393691010274737231012777819, −9.31150201930935789290712863495, −8.94981979594930409331845080728, −7.97861648026047582147654303494, −6.98272937810770310833551974986, −6.339480715991104721545028656632, −5.644336883992699243324393679910, −4.483398567978237712978230427161, −4.187632989910046573629909650210, −2.93091932124531220587989698504, −2.126680187970077188717698079347, −1.04731265176656922548235883934, −0.28249288749659633628818599770,
0.992222098972732578481186904568, 2.049803342180077873125766046585, 3.00109629395805215679271735460, 3.52525004831393134750533593024, 4.41767641709613423481008905698, 5.7898361197320845564785712582, 6.18769424450956338784043968657, 6.76860306628629709434896811092, 7.728502092256102604518964926013, 8.572703087904781246984182780091, 9.50812934511415463587915894706, 10.027580083603000217550538664938, 10.664434855394660953292352571557, 11.68207333628929870774928714480, 12.11691377516409633922466903495, 13.21577994691050521459921349799, 13.74884492294468926904873839064, 14.44013129598091177913678021121, 15.119094198059400950577609856169, 15.98834607109985387057871318193, 16.53622971898261652948973729025, 17.395720247243251009516728484329, 18.03303376022229965218950356243, 18.93433436891792240633257629820, 19.248160004155800182192620928076