L(s) = 1 | + (−0.939 − 0.342i)5-s + (0.939 − 0.342i)11-s + (0.766 − 0.642i)13-s + (0.5 + 0.866i)17-s + (−0.5 + 0.866i)19-s + (0.173 + 0.984i)23-s + (0.766 + 0.642i)25-s + (−0.766 − 0.642i)29-s + (−0.173 − 0.984i)31-s + (0.5 + 0.866i)37-s + (−0.766 + 0.642i)41-s + (0.939 − 0.342i)43-s + (−0.173 + 0.984i)47-s − 53-s − 55-s + ⋯ |
L(s) = 1 | + (−0.939 − 0.342i)5-s + (0.939 − 0.342i)11-s + (0.766 − 0.642i)13-s + (0.5 + 0.866i)17-s + (−0.5 + 0.866i)19-s + (0.173 + 0.984i)23-s + (0.766 + 0.642i)25-s + (−0.766 − 0.642i)29-s + (−0.173 − 0.984i)31-s + (0.5 + 0.866i)37-s + (−0.766 + 0.642i)41-s + (0.939 − 0.342i)43-s + (−0.173 + 0.984i)47-s − 53-s − 55-s + ⋯ |
Λ(s)=(=(1512s/2ΓR(s+1)L(s)(0.116+0.993i)Λ(1−s)
Λ(s)=(=(1512s/2ΓR(s+1)L(s)(0.116+0.993i)Λ(1−s)
Degree: |
1 |
Conductor: |
1512
= 23⋅33⋅7
|
Sign: |
0.116+0.993i
|
Analytic conductor: |
162.486 |
Root analytic conductor: |
162.486 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1512(517,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 1512, (1: ), 0.116+0.993i)
|
Particular Values
L(21) |
≈ |
0.9682481973+0.8616677314i |
L(21) |
≈ |
0.9682481973+0.8616677314i |
L(1) |
≈ |
0.9386139308+0.02876477769i |
L(1) |
≈ |
0.9386139308+0.02876477769i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1 |
| 7 | 1 |
good | 5 | 1+(−0.939−0.342i)T |
| 11 | 1+(0.939−0.342i)T |
| 13 | 1+(0.766−0.642i)T |
| 17 | 1+(0.5+0.866i)T |
| 19 | 1+(−0.5+0.866i)T |
| 23 | 1+(0.173+0.984i)T |
| 29 | 1+(−0.766−0.642i)T |
| 31 | 1+(−0.173−0.984i)T |
| 37 | 1+(0.5+0.866i)T |
| 41 | 1+(−0.766+0.642i)T |
| 43 | 1+(0.939−0.342i)T |
| 47 | 1+(−0.173+0.984i)T |
| 53 | 1−T |
| 59 | 1+(−0.939−0.342i)T |
| 61 | 1+(0.173−0.984i)T |
| 67 | 1+(−0.766+0.642i)T |
| 71 | 1+(−0.5−0.866i)T |
| 73 | 1+(0.5−0.866i)T |
| 79 | 1+(0.766+0.642i)T |
| 83 | 1+(0.766+0.642i)T |
| 89 | 1+(0.5−0.866i)T |
| 97 | 1+(0.939−0.342i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−20.13845070932247019675766864074, −19.53390578420467860852291960394, −18.74612089840363804314395778276, −18.20229039541939547784660860413, −17.19463271401509668753935421769, −16.333129471298763641269019694601, −15.88438008506985446249523534699, −14.80808389266050556057350294321, −14.43883696430113239690479110872, −13.48160901024381398916124446518, −12.456298749948777664499323679620, −11.86236517526837462669802275851, −11.09909101844126560993240958409, −10.499253549726711816702562792496, −9.16470211467158719887459822650, −8.8449109406728435280423595892, −7.69930328883675126700291220892, −6.93840401333473737992810435167, −6.40677583887943168595835802912, −5.094190492805490187336681501791, −4.2466212434148353722001468451, −3.56823882758145740415582309353, −2.5886703146960842256255394864, −1.37717685740516128047297166038, −0.30177908935094189634151479084,
0.915081681858848643349225585844, 1.7092633805063098317785643579, 3.32819058294500559537633800554, 3.73334130035465721472195483940, 4.62172597723626895692250800704, 5.83030844217871552936217539432, 6.33670466162845926507169542724, 7.718270210286064293888776700579, 8.01551580184058831961156746637, 8.953997958663959201488116031540, 9.760131627440575898419212261696, 10.86361373622374790851331000759, 11.405582693616021140733351542185, 12.22840983026363607194811667643, 12.91804084474078961192675427991, 13.73308309359414041176064055215, 14.81157469850015209838050101600, 15.221627504010549677080033210806, 16.126111844590178211853958181909, 16.86666203865229692343102397913, 17.38016561498520009201261991412, 18.6598368681721943681760672716, 19.05221568739165581612825640143, 19.825524534783789984681950498276, 20.562211042751507008008439590499