L(s) = 1 | + (−0.719 − 0.694i)2-s + (0.0348 + 0.999i)4-s + (0.241 + 0.970i)5-s + (0.615 − 0.788i)7-s + (0.669 − 0.743i)8-s + (0.5 − 0.866i)10-s + (−0.438 − 0.898i)13-s + (−0.990 + 0.139i)14-s + (−0.997 + 0.0697i)16-s + (0.913 − 0.406i)17-s + (−0.669 + 0.743i)19-s + (−0.961 + 0.275i)20-s + (0.939 − 0.342i)23-s + (−0.882 + 0.469i)25-s + (−0.309 + 0.951i)26-s + ⋯ |
L(s) = 1 | + (−0.719 − 0.694i)2-s + (0.0348 + 0.999i)4-s + (0.241 + 0.970i)5-s + (0.615 − 0.788i)7-s + (0.669 − 0.743i)8-s + (0.5 − 0.866i)10-s + (−0.438 − 0.898i)13-s + (−0.990 + 0.139i)14-s + (−0.997 + 0.0697i)16-s + (0.913 − 0.406i)17-s + (−0.669 + 0.743i)19-s + (−0.961 + 0.275i)20-s + (0.939 − 0.342i)23-s + (−0.882 + 0.469i)25-s + (−0.309 + 0.951i)26-s + ⋯ |
Λ(s)=(=(297s/2ΓR(s)L(s)(0.828−0.560i)Λ(1−s)
Λ(s)=(=(297s/2ΓR(s)L(s)(0.828−0.560i)Λ(1−s)
Degree: |
1 |
Conductor: |
297
= 33⋅11
|
Sign: |
0.828−0.560i
|
Analytic conductor: |
1.37926 |
Root analytic conductor: |
1.37926 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ297(281,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 297, (0: ), 0.828−0.560i)
|
Particular Values
L(21) |
≈ |
0.9322571655−0.2856748913i |
L(21) |
≈ |
0.9322571655−0.2856748913i |
L(1) |
≈ |
0.8412760621−0.1871520907i |
L(1) |
≈ |
0.8412760621−0.1871520907i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 11 | 1 |
good | 2 | 1+(−0.719−0.694i)T |
| 5 | 1+(0.241+0.970i)T |
| 7 | 1+(0.615−0.788i)T |
| 13 | 1+(−0.438−0.898i)T |
| 17 | 1+(0.913−0.406i)T |
| 19 | 1+(−0.669+0.743i)T |
| 23 | 1+(0.939−0.342i)T |
| 29 | 1+(0.990+0.139i)T |
| 31 | 1+(0.559−0.829i)T |
| 37 | 1+(0.669+0.743i)T |
| 41 | 1+(0.990−0.139i)T |
| 43 | 1+(−0.766+0.642i)T |
| 47 | 1+(−0.0348+0.999i)T |
| 53 | 1+(0.809−0.587i)T |
| 59 | 1+(−0.848+0.529i)T |
| 61 | 1+(−0.559−0.829i)T |
| 67 | 1+(0.173−0.984i)T |
| 71 | 1+(−0.913+0.406i)T |
| 73 | 1+(0.978−0.207i)T |
| 79 | 1+(0.719+0.694i)T |
| 83 | 1+(0.438−0.898i)T |
| 89 | 1+(0.5+0.866i)T |
| 97 | 1+(−0.241+0.970i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−25.20728289326402455200025623966, −24.870532006627376344932392764448, −23.853087572040120573610520563667, −23.29975998649956191433222649617, −21.5858952685222655363936114967, −21.13014033599953625054437046065, −19.77537017932262927673023368851, −19.12330052173328964739989595321, −18.03417823722034948621553403334, −17.21747367767355361564304984302, −16.53983644976030508063397226874, −15.5229753751894470647056242962, −14.67813816544697138378075513697, −13.7123020390355927987658119091, −12.42540091563479663296693881505, −11.481797941217888724852525170241, −10.22579588965766746400438806153, −9.10157693868066694723606588209, −8.64819779947675809207446785121, −7.56571235231214379639768316890, −6.3190060068991040011749838566, −5.27849171201231072732389774838, −4.545153612408934811008592172553, −2.300150260486458924617535444241, −1.17509968267510206327350712590,
1.063882247922954773191676500917, 2.49676685849325928365549591997, 3.4143953226431046260472805062, 4.71105263001272074092344434051, 6.37485372391784877197530334376, 7.53998164979235187555600221519, 8.10087300239479282283303833222, 9.651018193439537212264361878481, 10.38515358413118030062406454483, 11.02942217388390378773380807163, 12.0878028773230256679286724012, 13.19820840040140021335009034478, 14.23503639239979014598690192112, 15.1322451857645809242936825805, 16.59045498584676376152297197582, 17.32944660717615330231320497267, 18.13073634404845958423661361353, 18.935511419006281672984990948425, 19.83086672823258861178282662257, 20.84040780494387620980856635884, 21.42411699933484185684619877833, 22.6390897311062395081305105662, 23.17111267657824639898824780290, 24.74444892805627159335047315435, 25.52763714077386424576618261039