L(s) = 1 | + (0.142 − 0.989i)2-s + (−0.959 − 0.281i)4-s + (−0.841 − 0.540i)5-s + (−0.142 + 0.989i)7-s + (−0.415 + 0.909i)8-s + (−0.654 + 0.755i)10-s + (−0.841 − 0.540i)11-s + (0.415 + 0.909i)13-s + (0.959 + 0.281i)14-s + (0.841 + 0.540i)16-s + (0.959 − 0.281i)17-s + (−0.142 − 0.989i)19-s + (0.654 + 0.755i)20-s + (−0.654 + 0.755i)22-s + (0.654 + 0.755i)23-s + ⋯ |
L(s) = 1 | + (0.142 − 0.989i)2-s + (−0.959 − 0.281i)4-s + (−0.841 − 0.540i)5-s + (−0.142 + 0.989i)7-s + (−0.415 + 0.909i)8-s + (−0.654 + 0.755i)10-s + (−0.841 − 0.540i)11-s + (0.415 + 0.909i)13-s + (0.959 + 0.281i)14-s + (0.841 + 0.540i)16-s + (0.959 − 0.281i)17-s + (−0.142 − 0.989i)19-s + (0.654 + 0.755i)20-s + (−0.654 + 0.755i)22-s + (0.654 + 0.755i)23-s + ⋯ |
Λ(s)=(=(201s/2ΓR(s+1)L(s)(0.709−0.704i)Λ(1−s)
Λ(s)=(=(201s/2ΓR(s+1)L(s)(0.709−0.704i)Λ(1−s)
Degree: |
1 |
Conductor: |
201
= 3⋅67
|
Sign: |
0.709−0.704i
|
Analytic conductor: |
21.6004 |
Root analytic conductor: |
21.6004 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ201(107,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 201, (1: ), 0.709−0.704i)
|
Particular Values
L(21) |
≈ |
1.146247699−0.4724760902i |
L(21) |
≈ |
1.146247699−0.4724760902i |
L(1) |
≈ |
0.8082091995−0.3732655514i |
L(1) |
≈ |
0.8082091995−0.3732655514i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 67 | 1 |
good | 2 | 1+(0.142−0.989i)T |
| 5 | 1+(−0.841−0.540i)T |
| 7 | 1+(−0.142+0.989i)T |
| 11 | 1+(−0.841−0.540i)T |
| 13 | 1+(0.415+0.909i)T |
| 17 | 1+(0.959−0.281i)T |
| 19 | 1+(−0.142−0.989i)T |
| 23 | 1+(0.654+0.755i)T |
| 29 | 1−T |
| 31 | 1+(0.415−0.909i)T |
| 37 | 1+T |
| 41 | 1+(0.959−0.281i)T |
| 43 | 1+(−0.959+0.281i)T |
| 47 | 1+(0.654+0.755i)T |
| 53 | 1+(0.959+0.281i)T |
| 59 | 1+(−0.415+0.909i)T |
| 61 | 1+(0.841−0.540i)T |
| 71 | 1+(0.959+0.281i)T |
| 73 | 1+(0.841−0.540i)T |
| 79 | 1+(0.415+0.909i)T |
| 83 | 1+(−0.841−0.540i)T |
| 89 | 1+(0.654−0.755i)T |
| 97 | 1+T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−26.65783135394762275626955221493, −25.86476904099438104965386597267, −24.96946964775565187096361668628, −23.63288123698428726024814303745, −23.152247135534811170447869919694, −22.62013512878655759130813198566, −21.11844326223632057193038128885, −20.09411275820296425902411702186, −18.83022229301939483354488957514, −18.12974292459116676287135433485, −16.912555324432205463639902099855, −16.13245872301576382978789307084, −15.110518530283715655972809978670, −14.43676863081987731301125856267, −13.1914565348247579982771239711, −12.37939429445369669136847428818, −10.7237973643220412130378440561, −9.98245058090883535650531143572, −8.222128581487104733225169195105, −7.659556199024587608930365567245, −6.71094024114766304814003515674, −5.39772863040307031805469259814, −4.117808813969726399929157892350, −3.21550359017672807966267793389, −0.62044266161014960683572930918,
0.83518459625097134655474403359, 2.459049809441171939378033500121, 3.57851500082463261216568641220, 4.826216491778506748182979619010, 5.78481496443997430672018049139, 7.72075166586118105697388151180, 8.80399116157203896722261984291, 9.51894839612342809859266740051, 11.13892269573694015038976248710, 11.640994185884680893324283400248, 12.7145029648627178961967999034, 13.49010155458249238711945575988, 14.88483886224965438993566863013, 15.81166560551020960685667124001, 16.92722293434075628475539857487, 18.46124614261334904090918431589, 18.900806721882261665817642438105, 19.82289338460632055699920443855, 21.023026303909956289424846819033, 21.46278454059425829987353007903, 22.69992535220316300313935682770, 23.61416726254760323013492137345, 24.29123844349032713793146469329, 25.780796881346326522292441935844, 26.76520049557103919897558057246