L(s) = 1 | + (0.241 − 0.970i)2-s + (−0.882 − 0.469i)4-s + (−0.173 + 0.984i)5-s + (−0.374 − 0.927i)7-s + (−0.669 + 0.743i)8-s + (0.913 + 0.406i)10-s + (−0.374 − 0.927i)11-s + (−0.961 − 0.275i)13-s + (−0.990 + 0.139i)14-s + (0.559 + 0.829i)16-s + (0.309 + 0.951i)17-s + (−0.104 − 0.994i)19-s + (0.615 − 0.788i)20-s + (−0.990 + 0.139i)22-s + (0.990 − 0.139i)23-s + ⋯ |
L(s) = 1 | + (0.241 − 0.970i)2-s + (−0.882 − 0.469i)4-s + (−0.173 + 0.984i)5-s + (−0.374 − 0.927i)7-s + (−0.669 + 0.743i)8-s + (0.913 + 0.406i)10-s + (−0.374 − 0.927i)11-s + (−0.961 − 0.275i)13-s + (−0.990 + 0.139i)14-s + (0.559 + 0.829i)16-s + (0.309 + 0.951i)17-s + (−0.104 − 0.994i)19-s + (0.615 − 0.788i)20-s + (−0.990 + 0.139i)22-s + (0.990 − 0.139i)23-s + ⋯ |
Λ(s)=(=(837s/2ΓR(s)L(s)(0.181+0.983i)Λ(1−s)
Λ(s)=(=(837s/2ΓR(s)L(s)(0.181+0.983i)Λ(1−s)
Degree: |
1 |
Conductor: |
837
= 33⋅31
|
Sign: |
0.181+0.983i
|
Analytic conductor: |
3.88701 |
Root analytic conductor: |
3.88701 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ837(290,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 837, (0: ), 0.181+0.983i)
|
Particular Values
L(21) |
≈ |
0.1787348468+0.1487098168i |
L(21) |
≈ |
0.1787348468+0.1487098168i |
L(1) |
≈ |
0.6804731767−0.3106859780i |
L(1) |
≈ |
0.6804731767−0.3106859780i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 31 | 1 |
good | 2 | 1+(0.241−0.970i)T |
| 5 | 1+(−0.173+0.984i)T |
| 7 | 1+(−0.374−0.927i)T |
| 11 | 1+(−0.374−0.927i)T |
| 13 | 1+(−0.961−0.275i)T |
| 17 | 1+(0.309+0.951i)T |
| 19 | 1+(−0.104−0.994i)T |
| 23 | 1+(0.990−0.139i)T |
| 29 | 1+(−0.241+0.970i)T |
| 37 | 1−T |
| 41 | 1+(−0.559+0.829i)T |
| 43 | 1+(0.719+0.694i)T |
| 47 | 1+(−0.438+0.898i)T |
| 53 | 1+(−0.978−0.207i)T |
| 59 | 1+(0.241+0.970i)T |
| 61 | 1+(−0.173−0.984i)T |
| 67 | 1+(−0.939+0.342i)T |
| 71 | 1+(−0.669+0.743i)T |
| 73 | 1+(−0.309+0.951i)T |
| 79 | 1+(−0.0348+0.999i)T |
| 83 | 1+(−0.719−0.694i)T |
| 89 | 1+(−0.978+0.207i)T |
| 97 | 1+(−0.615+0.788i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−22.27114418581190267512355830762, −21.08217624820813644856608384646, −20.71658708808897080345989445869, −19.34475113343539265168581990660, −18.73945837154701940301804209535, −17.72707613319804943595662929020, −17.00022987418383868591353003580, −16.303237099361914594436445285942, −15.49095667633959393159700718997, −14.97967788328898308293177353076, −13.93384686886645705929511004075, −13.0109687083417732752228135268, −12.261755777967972160058562098882, −11.91726792043515546955938932521, −10.01568280776849600024420199225, −9.379227705458800964567149600969, −8.675578037375206478709209697006, −7.68848821240691490829738080443, −7.01733554549047541286861055184, −5.76561799718499988113867545588, −5.131340721855797380387963113036, −4.44286144702105178286905862773, −3.211247024378378803302052098451, −1.93628319467738991940538699285, −0.09967539429190812140300733156,
1.29912843918233579136075035532, 2.80368174876354367137681794871, 3.182860202025205165056576696715, 4.221749370270646616204240413242, 5.247178509938208327234309945057, 6.35825852620610494622438943287, 7.27467049246044877907898087120, 8.28542276635956487582806097325, 9.413289225139513879889157974699, 10.33268209631269274303308927811, 10.80595402645652939579360436354, 11.46721394158328598080044394531, 12.695999380860477194970616043011, 13.234199941280800350469914733311, 14.21902928372182039903450410792, 14.72244826542823301228038796852, 15.73761841561003587621524666430, 16.977197835249805679152404907868, 17.62114399132685624505999689459, 18.61754809108834049810397228713, 19.39773355729714044582642214482, 19.65440337116646694070208882348, 20.77125249677341265111705695237, 21.63226670803103030275001732057, 22.18511692229752866062442619287