L(s) = 1 | + (0.0255 + 0.999i)2-s + (−0.277 + 0.960i)3-s + (−0.998 + 0.0511i)4-s + (−0.967 − 0.253i)6-s + (−0.0817 − 0.996i)7-s + (−0.0766 − 0.997i)8-s + (−0.845 − 0.533i)9-s + (0.893 + 0.448i)11-s + (0.228 − 0.973i)12-s + (0.690 + 0.723i)13-s + (0.994 − 0.107i)14-s + (0.994 − 0.102i)16-s + (0.909 − 0.416i)17-s + (0.511 − 0.859i)18-s + (−0.820 + 0.571i)19-s + ⋯ |
L(s) = 1 | + (0.0255 + 0.999i)2-s + (−0.277 + 0.960i)3-s + (−0.998 + 0.0511i)4-s + (−0.967 − 0.253i)6-s + (−0.0817 − 0.996i)7-s + (−0.0766 − 0.997i)8-s + (−0.845 − 0.533i)9-s + (0.893 + 0.448i)11-s + (0.228 − 0.973i)12-s + (0.690 + 0.723i)13-s + (0.994 − 0.107i)14-s + (0.994 − 0.102i)16-s + (0.909 − 0.416i)17-s + (0.511 − 0.859i)18-s + (−0.820 + 0.571i)19-s + ⋯ |
Λ(s)=(=(6145s/2ΓR(s)L(s)(−0.309+0.951i)Λ(1−s)
Λ(s)=(=(6145s/2ΓR(s)L(s)(−0.309+0.951i)Λ(1−s)
Degree: |
1 |
Conductor: |
6145
= 5⋅1229
|
Sign: |
−0.309+0.951i
|
Analytic conductor: |
28.5372 |
Root analytic conductor: |
28.5372 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ6145(1037,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 6145, (0: ), −0.309+0.951i)
|
Particular Values
L(21) |
≈ |
0.8804784725+1.211893864i |
L(21) |
≈ |
0.8804784725+1.211893864i |
L(1) |
≈ |
0.7327822206+0.6142257263i |
L(1) |
≈ |
0.7327822206+0.6142257263i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1 |
| 1229 | 1 |
good | 2 | 1+(0.0255+0.999i)T |
| 3 | 1+(−0.277+0.960i)T |
| 7 | 1+(−0.0817−0.996i)T |
| 11 | 1+(0.893+0.448i)T |
| 13 | 1+(0.690+0.723i)T |
| 17 | 1+(0.909−0.416i)T |
| 19 | 1+(−0.820+0.571i)T |
| 23 | 1+(−0.999+0.0102i)T |
| 29 | 1+(0.957+0.287i)T |
| 31 | 1+(0.467−0.884i)T |
| 37 | 1+(0.733+0.679i)T |
| 41 | 1+(0.307+0.951i)T |
| 43 | 1+(−0.243+0.969i)T |
| 47 | 1+(0.648−0.760i)T |
| 53 | 1+(0.0409−0.999i)T |
| 59 | 1+(−0.168−0.985i)T |
| 61 | 1+(−0.529+0.848i)T |
| 67 | 1+(−0.853+0.520i)T |
| 71 | 1+(0.764−0.644i)T |
| 73 | 1+(−0.789−0.613i)T |
| 79 | 1+(−0.0766+0.997i)T |
| 83 | 1+(0.904−0.425i)T |
| 89 | 1+(−0.316−0.948i)T |
| 97 | 1+(0.592−0.805i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−17.60608027540599907642978068758, −17.22648979142415363302206673442, −16.29360226527848454339696418019, −15.4517437344985778027678254653, −14.567786049002425330831630093776, −14.01623368469305671982657349026, −13.41785378146691488441069027533, −12.642727776704828191303729170535, −12.085564882500408527255094746969, −11.913013114599086380727337997511, −10.825870479640502567023271024, −10.57361532277947946177281921414, −9.449853355218193864840676468, −8.7412698612476723649272801499, −8.35566510877246847195396636956, −7.63123816710959468047555707295, −6.41993880654686334764526201439, −5.94659039497043914002577493888, −5.42071331870792205643885813196, −4.40310915092320793339972665710, −3.53540342963945370818518721845, −2.79992862023806985325397099118, −2.16894038013319413261728233237, −1.32757876870322187383382379702, −0.670594660964857492099442675831,
0.65567521886132509725566993195, 1.56231103429109732016782002734, 3.11833759350324699531191244472, 3.832631238494413421671757650562, 4.37309501811315089886362232097, 4.74340403453545361266977449407, 5.97798917266330450641766820547, 6.25572770315689038324040942142, 6.97724424039083482344367153444, 7.90715970055691268132836908930, 8.45178344063553868507052117905, 9.29454522656184675049636574906, 9.956141909419418176352467780694, 10.19487056042745100247942332754, 11.294401054941880228758932729313, 11.88067789251076688260348318253, 12.703755608276964800187074911153, 13.65710779338225699785673102896, 14.136911726363256112099936031193, 14.66050011870406887925777966787, 15.25080073283059237011557527534, 16.15437683166205773848314023109, 16.611494548492755521630667461006, 16.80925624501018199441874485139, 17.67139827961263486991624177178