L(s) = 1 | + (0.453 − 0.891i)3-s − 7-s + (−0.587 − 0.809i)9-s + (0.156 + 0.987i)11-s + (0.987 + 0.156i)13-s + (0.951 + 0.309i)17-s + (0.453 + 0.891i)19-s + (−0.453 + 0.891i)21-s + (0.809 + 0.587i)23-s + (−0.987 + 0.156i)27-s + (−0.891 − 0.453i)29-s + (−0.309 + 0.951i)31-s + (0.951 + 0.309i)33-s + (0.156 − 0.987i)37-s + (0.587 − 0.809i)39-s + ⋯ |
L(s) = 1 | + (0.453 − 0.891i)3-s − 7-s + (−0.587 − 0.809i)9-s + (0.156 + 0.987i)11-s + (0.987 + 0.156i)13-s + (0.951 + 0.309i)17-s + (0.453 + 0.891i)19-s + (−0.453 + 0.891i)21-s + (0.809 + 0.587i)23-s + (−0.987 + 0.156i)27-s + (−0.891 − 0.453i)29-s + (−0.309 + 0.951i)31-s + (0.951 + 0.309i)33-s + (0.156 − 0.987i)37-s + (0.587 − 0.809i)39-s + ⋯ |
Λ(s)=(=(800s/2ΓR(s)L(s)(0.943−0.331i)Λ(1−s)
Λ(s)=(=(800s/2ΓR(s)L(s)(0.943−0.331i)Λ(1−s)
Degree: |
1 |
Conductor: |
800
= 25⋅52
|
Sign: |
0.943−0.331i
|
Analytic conductor: |
3.71518 |
Root analytic conductor: |
3.71518 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ800(203,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 800, (0: ), 0.943−0.331i)
|
Particular Values
L(21) |
≈ |
1.564890101−0.2667888534i |
L(21) |
≈ |
1.564890101−0.2667888534i |
L(1) |
≈ |
1.176460567−0.2135914542i |
L(1) |
≈ |
1.176460567−0.2135914542i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1 |
good | 3 | 1+(0.453−0.891i)T |
| 7 | 1−T |
| 11 | 1+(0.156+0.987i)T |
| 13 | 1+(0.987+0.156i)T |
| 17 | 1+(0.951+0.309i)T |
| 19 | 1+(0.453+0.891i)T |
| 23 | 1+(0.809+0.587i)T |
| 29 | 1+(−0.891−0.453i)T |
| 31 | 1+(−0.309+0.951i)T |
| 37 | 1+(0.156−0.987i)T |
| 41 | 1+(0.587+0.809i)T |
| 43 | 1+(0.707−0.707i)T |
| 47 | 1+(0.951−0.309i)T |
| 53 | 1+(−0.891−0.453i)T |
| 59 | 1+(0.987+0.156i)T |
| 61 | 1+(−0.987+0.156i)T |
| 67 | 1+(0.891−0.453i)T |
| 71 | 1+(0.951−0.309i)T |
| 73 | 1+(−0.809−0.587i)T |
| 79 | 1+(−0.309−0.951i)T |
| 83 | 1+(0.891−0.453i)T |
| 89 | 1+(−0.587+0.809i)T |
| 97 | 1+(0.951−0.309i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−22.30434955430763241589215907108, −21.51078585192475316540638266374, −20.66307251317736102418968395648, −20.1001723832411680319312914670, −18.97915577322678678994388953062, −18.71567588165450980322825887111, −17.19562182425847401877177340960, −16.44207868204857959452981831044, −15.9357959045383751320487216409, −15.155443175079268114678532884935, −14.139509856873528641640699758993, −13.492526911384214054537941087404, −12.667172833509268223642603209486, −11.298354234991355832766630602334, −10.8313977352943789232451513351, −9.71616739986069479311449095129, −9.14696360302764131953794020734, −8.35233706765050951465420901982, −7.26137798308098764298792414149, −6.06682217407497231204502785135, −5.38642717806264489963518580811, −4.11343453148609494065001774351, −3.3037168997172482154742390367, −2.70440579497188739389730290229, −0.8721029348536107078872622582,
1.07331531458267205083056637467, 2.03139654512712820433984274566, 3.26979189687397718020628051038, 3.85143949480079200101432890811, 5.52342712399884843335194541249, 6.26287680965498834342314819667, 7.1996790707245220572753415145, 7.81508977674867091796939313302, 9.01361792743997393923233207948, 9.56723627229344401071864443504, 10.64486932767953015700186370356, 11.837078480779564063952854177223, 12.56181309187655294637717053, 13.12195145896467848302784160236, 14.03717207367121668613304409234, 14.7916130613090582978804606681, 15.73092369447890599219878728181, 16.625160239263284931410401975036, 17.51303595272677106731842062584, 18.41113921672592863460655025413, 18.9956370584325379705339027001, 19.71884343902956687539022183646, 20.53195762769872787886017206744, 21.201523404615499026253427444622, 22.517118258519888819447232274281