L(s) = 1 | + (−0.947 + 0.318i)2-s + (0.847 + 0.531i)3-s + (0.796 − 0.604i)4-s + (0.943 + 0.332i)5-s + (−0.972 − 0.233i)6-s + (−0.960 − 0.276i)7-s + (−0.562 + 0.826i)8-s + (0.434 + 0.900i)9-s + (−0.999 − 0.0147i)10-s + (0.876 + 0.480i)11-s + (0.996 − 0.0883i)12-s + (0.353 + 0.935i)13-s + (0.999 − 0.0442i)14-s + (0.621 + 0.783i)15-s + (0.269 − 0.963i)16-s + (0.805 − 0.592i)17-s + ⋯ |
L(s) = 1 | + (−0.947 + 0.318i)2-s + (0.847 + 0.531i)3-s + (0.796 − 0.604i)4-s + (0.943 + 0.332i)5-s + (−0.972 − 0.233i)6-s + (−0.960 − 0.276i)7-s + (−0.562 + 0.826i)8-s + (0.434 + 0.900i)9-s + (−0.999 − 0.0147i)10-s + (0.876 + 0.480i)11-s + (0.996 − 0.0883i)12-s + (0.353 + 0.935i)13-s + (0.999 − 0.0442i)14-s + (0.621 + 0.783i)15-s + (0.269 − 0.963i)16-s + (0.805 − 0.592i)17-s + ⋯ |
Λ(s)=(=(2557s/2ΓR(s)L(s)(0.260+0.965i)Λ(1−s)
Λ(s)=(=(2557s/2ΓR(s)L(s)(0.260+0.965i)Λ(1−s)
Degree: |
1 |
Conductor: |
2557
|
Sign: |
0.260+0.965i
|
Analytic conductor: |
11.8746 |
Root analytic conductor: |
11.8746 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2557(1001,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 2557, (0: ), 0.260+0.965i)
|
Particular Values
L(21) |
≈ |
1.546085253+1.184037138i |
L(21) |
≈ |
1.546085253+1.184037138i |
L(1) |
≈ |
1.085965551+0.4557660553i |
L(1) |
≈ |
1.085965551+0.4557660553i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2557 | 1 |
good | 2 | 1+(−0.947+0.318i)T |
| 3 | 1+(0.847+0.531i)T |
| 5 | 1+(0.943+0.332i)T |
| 7 | 1+(−0.960−0.276i)T |
| 11 | 1+(0.876+0.480i)T |
| 13 | 1+(0.353+0.935i)T |
| 17 | 1+(0.805−0.592i)T |
| 19 | 1+(0.989+0.146i)T |
| 23 | 1+(−0.394−0.918i)T |
| 29 | 1+(−0.688−0.725i)T |
| 31 | 1+(0.168−0.985i)T |
| 37 | 1+(0.720+0.693i)T |
| 41 | 1+(0.869−0.493i)T |
| 43 | 1+(−0.610−0.792i)T |
| 47 | 1+(−0.353+0.935i)T |
| 53 | 1+(−0.367+0.930i)T |
| 59 | 1+(−0.339+0.940i)T |
| 61 | 1+(0.984−0.176i)T |
| 67 | 1+(−0.778−0.627i)T |
| 71 | 1+(0.890−0.454i)T |
| 73 | 1+(0.586−0.809i)T |
| 79 | 1+(−0.759+0.650i)T |
| 83 | 1+(0.994+0.103i)T |
| 89 | 1+(0.339−0.940i)T |
| 97 | 1+(0.964−0.262i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−19.299466026618316095837427135518, −18.5758275262474780272518687096, −17.920070884143166806923548218956, −17.42900256779181592624905103894, −16.36803543367942731942875484735, −16.04322875149264242940669709906, −14.95616572370942668333639753570, −14.23925664744485987969481754401, −13.28326810923038480031775815134, −12.85177945845245204113875706029, −12.1996125445083795555593284835, −11.30772249449489439431197236334, −10.16842920414176482924776766194, −9.6732087712819335073712706096, −9.156372979287453487528774986625, −8.45986539817824019751118916039, −7.739828726583691001589540188719, −6.81984153904016366693096683678, −6.17088364051014690231596141052, −5.4779193564961846484501372090, −3.562259477223439600405412577475, −3.36491658255377835354433490714, −2.41261636763512944954253173625, −1.43219667387071215335100903399, −0.91944789901868166044670283936,
1.0754516023301491808797170964, 2.006912954130299806552310273128, 2.729153304974566746816727558257, 3.59274162352899428908045141950, 4.59289681241361072415106669308, 5.78996793208095855282908316460, 6.40087321468073400149375352069, 7.18350083873164230398007203578, 7.823758756177087175524991682786, 8.990116537342853878033512526644, 9.49017778173801220258692784149, 9.749423163843909644311432684349, 10.47937576540061630934899705422, 11.397043804922429175005358501058, 12.299696379026905443989960249578, 13.48771538571356815771956961563, 14.0138708181733665673501462826, 14.58706970089193548036882204001, 15.34049294067616233207055118032, 16.24654608102986013117718438800, 16.64234215574047413047620661272, 17.24178286541822559773550398495, 18.43838867249248144511352448078, 18.71215827345587451601533295816, 19.44826914396023234492815368073