L(s) = 1 | + (0.809 − 0.587i)2-s + (0.309 − 0.951i)4-s − 5-s + (0.309 − 0.951i)7-s + (−0.309 − 0.951i)8-s + (−0.809 + 0.587i)10-s + (0.309 − 0.951i)11-s + (0.809 + 0.587i)13-s + (−0.309 − 0.951i)14-s + (−0.809 − 0.587i)16-s + (0.309 + 0.951i)17-s + (−0.809 + 0.587i)19-s + (−0.309 + 0.951i)20-s + (−0.309 − 0.951i)22-s + (0.309 + 0.951i)23-s + ⋯ |
L(s) = 1 | + (0.809 − 0.587i)2-s + (0.309 − 0.951i)4-s − 5-s + (0.309 − 0.951i)7-s + (−0.309 − 0.951i)8-s + (−0.809 + 0.587i)10-s + (0.309 − 0.951i)11-s + (0.809 + 0.587i)13-s + (−0.309 − 0.951i)14-s + (−0.809 − 0.587i)16-s + (0.309 + 0.951i)17-s + (−0.809 + 0.587i)19-s + (−0.309 + 0.951i)20-s + (−0.309 − 0.951i)22-s + (0.309 + 0.951i)23-s + ⋯ |
Λ(s)=(=(93s/2ΓR(s)L(s)(0.0525−0.998i)Λ(1−s)
Λ(s)=(=(93s/2ΓR(s)L(s)(0.0525−0.998i)Λ(1−s)
Degree: |
1 |
Conductor: |
93
= 3⋅31
|
Sign: |
0.0525−0.998i
|
Analytic conductor: |
0.431890 |
Root analytic conductor: |
0.431890 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ93(89,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 93, (0: ), 0.0525−0.998i)
|
Particular Values
L(21) |
≈ |
0.9782381678−0.9281326887i |
L(21) |
≈ |
0.9782381678−0.9281326887i |
L(1) |
≈ |
1.202644646−0.6658986055i |
L(1) |
≈ |
1.202644646−0.6658986055i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 31 | 1 |
good | 2 | 1+(0.809−0.587i)T |
| 5 | 1−T |
| 7 | 1+(0.309−0.951i)T |
| 11 | 1+(0.309−0.951i)T |
| 13 | 1+(0.809+0.587i)T |
| 17 | 1+(0.309+0.951i)T |
| 19 | 1+(−0.809+0.587i)T |
| 23 | 1+(0.309+0.951i)T |
| 29 | 1+(−0.809+0.587i)T |
| 37 | 1−T |
| 41 | 1+(0.809−0.587i)T |
| 43 | 1+(0.809−0.587i)T |
| 47 | 1+(0.809+0.587i)T |
| 53 | 1+(0.309+0.951i)T |
| 59 | 1+(0.809+0.587i)T |
| 61 | 1−T |
| 67 | 1+T |
| 71 | 1+(−0.309−0.951i)T |
| 73 | 1+(−0.309+0.951i)T |
| 79 | 1+(−0.309−0.951i)T |
| 83 | 1+(−0.809+0.587i)T |
| 89 | 1+(0.309−0.951i)T |
| 97 | 1+(0.309−0.951i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−30.79124894015829289723596599561, −30.00867265895377296861066386542, −28.25927197397302585222928400450, −27.4835183363561622952919706946, −26.12224366491822319645525641238, −25.1152322646238317480482902495, −24.270345749508353371359040835142, −23.02508093084276483667213169390, −22.54249574519075862231088200189, −21.09414945295063846291512142256, −20.22838607319401959310375852852, −18.72104723631273324657235463439, −17.54805493033819584622572372606, −16.13622220002828122486254090057, −15.307995515443696091418335569523, −14.58065474927166684717111377317, −12.95004560292508977338778669109, −12.08084430478710381751845001639, −11.10205564286380500246871041991, −8.9276175806391470516547624184, −7.8817436202865462067016407300, −6.68804968489805835544211952249, −5.221665571838384525805213317176, −4.094585611232969422776071046362, −2.61350784459411592742076044349,
1.337164301210660044853081870010, 3.56419428996830271227761802187, 4.14085078041530229204433032287, 5.86691937682772208089113420988, 7.26894266026897109327844619209, 8.76039133740248175945812175545, 10.64163506488860945026731176311, 11.212849696832466897972327454307, 12.43999371410464506265174488843, 13.67183526420510332857306485372, 14.598905809076479871800947254062, 15.81746317334278001306744440233, 16.91636931563261481081097101910, 18.846635092319132867681865055498, 19.45228867468449102582393636072, 20.60291274004950308356703845729, 21.48201957037279086979732780652, 22.828282907040982759489286425855, 23.66967212516826229747218658683, 24.201079187263207767076125848679, 25.932229656431034208360948114801, 27.2602305833281809562448977389, 27.927654995891986742446422875769, 29.337074005970340900005553393562, 30.14890436982753007601308595579