L(s) = 1 | + (−0.999 + 0.0348i)2-s + (−0.173 + 0.984i)3-s + (0.997 − 0.0697i)4-s + (0.139 − 0.990i)6-s + (−0.669 + 0.743i)7-s + (−0.994 + 0.104i)8-s + (−0.939 − 0.342i)9-s + (0.994 − 0.104i)11-s + (−0.104 + 0.994i)12-s + (−0.990 − 0.139i)13-s + (0.642 − 0.766i)14-s + (0.990 − 0.139i)16-s + (0.559 − 0.829i)17-s + (0.951 + 0.309i)18-s + (−0.615 − 0.788i)21-s + (−0.990 + 0.139i)22-s + ⋯ |
L(s) = 1 | + (−0.999 + 0.0348i)2-s + (−0.173 + 0.984i)3-s + (0.997 − 0.0697i)4-s + (0.139 − 0.990i)6-s + (−0.669 + 0.743i)7-s + (−0.994 + 0.104i)8-s + (−0.939 − 0.342i)9-s + (0.994 − 0.104i)11-s + (−0.104 + 0.994i)12-s + (−0.990 − 0.139i)13-s + (0.642 − 0.766i)14-s + (0.990 − 0.139i)16-s + (0.559 − 0.829i)17-s + (0.951 + 0.309i)18-s + (−0.615 − 0.788i)21-s + (−0.990 + 0.139i)22-s + ⋯ |
Λ(s)=(=(3895s/2ΓR(s)L(s)(0.882−0.469i)Λ(1−s)
Λ(s)=(=(3895s/2ΓR(s)L(s)(0.882−0.469i)Λ(1−s)
Degree: |
1 |
Conductor: |
3895
= 5⋅19⋅41
|
Sign: |
0.882−0.469i
|
Analytic conductor: |
18.0883 |
Root analytic conductor: |
18.0883 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3895(1112,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 3895, (0: ), 0.882−0.469i)
|
Particular Values
L(21) |
≈ |
0.3331840046−0.08307650940i |
L(21) |
≈ |
0.3331840046−0.08307650940i |
L(1) |
≈ |
0.4813751189+0.1827111585i |
L(1) |
≈ |
0.4813751189+0.1827111585i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1 |
| 19 | 1 |
| 41 | 1 |
good | 2 | 1+(−0.999+0.0348i)T |
| 3 | 1+(−0.173+0.984i)T |
| 7 | 1+(−0.669+0.743i)T |
| 11 | 1+(0.994−0.104i)T |
| 13 | 1+(−0.990−0.139i)T |
| 17 | 1+(0.559−0.829i)T |
| 23 | 1+(−0.927+0.374i)T |
| 29 | 1+(−0.829+0.559i)T |
| 31 | 1+(−0.913−0.406i)T |
| 37 | 1+(−0.587+0.809i)T |
| 43 | 1+(0.529+0.848i)T |
| 47 | 1+(−0.615+0.788i)T |
| 53 | 1+(0.997−0.0697i)T |
| 59 | 1+(0.0348+0.999i)T |
| 61 | 1+(−0.848−0.529i)T |
| 67 | 1+(−0.559−0.829i)T |
| 71 | 1+(−0.0697+0.997i)T |
| 73 | 1+(0.984+0.173i)T |
| 79 | 1+(0.984+0.173i)T |
| 83 | 1+(−0.866+0.5i)T |
| 89 | 1+(−0.469−0.882i)T |
| 97 | 1+(−0.961−0.275i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−18.63734203904475401923206247105, −17.85474163842472535263805370318, −17.24636788566784302142183667769, −16.71989710995136131505813271255, −16.37432397378044117063171021011, −15.16292825510392736607060350521, −14.48739961156515456037737257422, −13.8544081108912175675919930406, −12.825153315327616551035469707600, −12.294357485925285119614793057910, −11.80396422287057401407333929706, −10.876836007634071260573451998094, −10.26739812047585084839414530780, −9.50671879974317387494001863343, −8.84754001279226516559695651932, −7.96078634165682135453872476974, −7.33539322129259013093796505811, −6.85650817635135623300429704290, −6.16114198462811791175326500167, −5.470135760511311663912986830995, −4.0097184576113295180772330748, −3.34522224134044227563686723603, −2.21003736435635871403508884153, −1.6978592503376652024637666804, −0.700357705144076132764314019602,
0.19448682840761018319693935661, 1.52789708365689646734435946439, 2.58585529627990326816864723406, 3.19534582288748022853196520965, 4.0053052977559661111591961582, 5.19196420857499214921584708095, 5.75462289503290195286222560216, 6.499814351764884522390592834182, 7.311455492304168595823843398601, 8.167228366956848637278759232958, 9.06134926986536424239588696197, 9.50121273551572345943580337393, 9.8399791488595180504859704957, 10.733884722814648380117486479631, 11.56464113025738178174801253547, 11.978270300671408767030754847600, 12.64438661507643441266989722268, 14.00535262764910926311312397083, 14.71145751938874441803484120572, 15.21191224646077765942076798317, 15.94600384244654591637138561268, 16.58910399819682878887425085864, 16.87998383301943133714448291137, 17.79622208995664544559349770316, 18.39124258440616878482310485905