L(s) = 1 | + (0.173 − 0.984i)2-s + (−0.939 − 0.342i)4-s + (0.766 − 0.642i)5-s + (0.173 + 0.984i)7-s + (−0.5 + 0.866i)8-s + (−0.5 − 0.866i)10-s + 11-s + (−0.939 − 0.342i)13-s + 14-s + (0.766 + 0.642i)16-s + (0.173 − 0.984i)17-s + (0.766 − 0.642i)19-s + (−0.939 + 0.342i)20-s + (0.173 − 0.984i)22-s + 23-s + ⋯ |
L(s) = 1 | + (0.173 − 0.984i)2-s + (−0.939 − 0.342i)4-s + (0.766 − 0.642i)5-s + (0.173 + 0.984i)7-s + (−0.5 + 0.866i)8-s + (−0.5 − 0.866i)10-s + 11-s + (−0.939 − 0.342i)13-s + 14-s + (0.766 + 0.642i)16-s + (0.173 − 0.984i)17-s + (0.766 − 0.642i)19-s + (−0.939 + 0.342i)20-s + (0.173 − 0.984i)22-s + 23-s + ⋯ |
Λ(s)=(=(333s/2ΓR(s)L(s)(−0.116−0.993i)Λ(1−s)
Λ(s)=(=(333s/2ΓR(s)L(s)(−0.116−0.993i)Λ(1−s)
Degree: |
1 |
Conductor: |
333
= 32⋅37
|
Sign: |
−0.116−0.993i
|
Analytic conductor: |
1.54644 |
Root analytic conductor: |
1.54644 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ333(16,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 333, (0: ), −0.116−0.993i)
|
Particular Values
L(21) |
≈ |
0.9867866418−1.109324692i |
L(21) |
≈ |
0.9867866418−1.109324692i |
L(1) |
≈ |
1.038393196−0.6755684971i |
L(1) |
≈ |
1.038393196−0.6755684971i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 37 | 1 |
good | 2 | 1+(0.173−0.984i)T |
| 5 | 1+(0.766−0.642i)T |
| 7 | 1+(0.173+0.984i)T |
| 11 | 1+T |
| 13 | 1+(−0.939−0.342i)T |
| 17 | 1+(0.173−0.984i)T |
| 19 | 1+(0.766−0.642i)T |
| 23 | 1+T |
| 29 | 1+T |
| 31 | 1+(−0.5+0.866i)T |
| 41 | 1+(−0.939−0.342i)T |
| 43 | 1+(−0.5−0.866i)T |
| 47 | 1+(−0.5+0.866i)T |
| 53 | 1+(−0.939+0.342i)T |
| 59 | 1+(0.173−0.984i)T |
| 61 | 1+(0.766−0.642i)T |
| 67 | 1+(0.766−0.642i)T |
| 71 | 1+(0.766−0.642i)T |
| 73 | 1+T |
| 79 | 1+(0.173+0.984i)T |
| 83 | 1+(−0.939+0.342i)T |
| 89 | 1+(−0.939+0.342i)T |
| 97 | 1+(−0.5+0.866i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−25.155686908813516881758937284349, −24.49656314219346037949741276331, −23.50011219620443818119959319714, −22.658979935775596987993633659119, −21.938588406297954218022923903904, −21.1207971783743502750068018374, −19.76360275119755296537225329362, −18.82154697003463634491043631467, −17.74258804958770484253900122936, −17.04565889517109368223544383165, −16.55813424721194738656738864119, −14.96853626174470553390700725786, −14.4790049629310347306676144758, −13.745001614735229101393307770116, −12.799089470975516342227741895807, −11.50992849448290623165480953217, −10.13741553114765054769053871892, −9.563452434401704370192216623641, −8.25467002932208685376391917224, −7.115186725295542807295391876513, −6.58658183095729945882101608230, −5.43948745266473352266167242973, −4.287819894153456810248999028068, −3.2482993072762183627299923344, −1.42654963444816590623548338629,
1.071894934054544037184761387144, 2.24681802382805703626686859716, 3.20630478861928221861678551105, 4.97547700772600019210421816042, 5.17865719451864113993895686030, 6.668912892563185108798627392381, 8.38611544653446383218269346067, 9.31088412060338763950360699340, 9.71074034665526928196639260679, 11.13107612795282973455433267150, 12.098602661923174354284345637813, 12.59794864718415169073296597769, 13.80530463714977649064562199836, 14.45012923159921027221430537764, 15.63174751048524412852009765211, 17.02169549462131228478859934793, 17.71187167219137112356517056845, 18.57432554783162999972839137316, 19.62597733033401481319124202199, 20.340171915939189166506909191079, 21.28825613405900391803241738438, 21.989503655739647546288364842110, 22.555165525269976631826524906, 23.90546496529967394016084244905, 24.83951794370680020471204241240