L(s) = 1 | + (−0.809 − 0.587i)2-s + (−0.809 + 0.587i)3-s + (0.309 + 0.951i)4-s + 6-s + (−0.809 + 0.587i)7-s + (0.309 − 0.951i)8-s + (0.309 − 0.951i)9-s + (−0.809 − 0.587i)12-s + (0.309 − 0.951i)13-s + 14-s + (−0.809 + 0.587i)16-s + 17-s + (−0.809 + 0.587i)18-s + (0.309 − 0.951i)19-s + (0.309 − 0.951i)21-s + ⋯ |
L(s) = 1 | + (−0.809 − 0.587i)2-s + (−0.809 + 0.587i)3-s + (0.309 + 0.951i)4-s + 6-s + (−0.809 + 0.587i)7-s + (0.309 − 0.951i)8-s + (0.309 − 0.951i)9-s + (−0.809 − 0.587i)12-s + (0.309 − 0.951i)13-s + 14-s + (−0.809 + 0.587i)16-s + 17-s + (−0.809 + 0.587i)18-s + (0.309 − 0.951i)19-s + (0.309 − 0.951i)21-s + ⋯ |
Λ(s)=(=(275s/2ΓR(s)L(s)(0.920+0.390i)Λ(1−s)
Λ(s)=(=(275s/2ΓR(s)L(s)(0.920+0.390i)Λ(1−s)
Degree: |
1 |
Conductor: |
275
= 52⋅11
|
Sign: |
0.920+0.390i
|
Analytic conductor: |
1.27709 |
Root analytic conductor: |
1.27709 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ275(81,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 275, (0: ), 0.920+0.390i)
|
Particular Values
L(21) |
≈ |
0.5358035249+0.1088261455i |
L(21) |
≈ |
0.5358035249+0.1088261455i |
L(1) |
≈ |
0.5572156589+0.01158921178i |
L(1) |
≈ |
0.5572156589+0.01158921178i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 5 | 1 |
| 11 | 1 |
good | 2 | 1+(−0.809−0.587i)T |
| 3 | 1+(−0.809+0.587i)T |
| 7 | 1+(−0.809+0.587i)T |
| 13 | 1+(0.309−0.951i)T |
| 17 | 1+T |
| 19 | 1+(0.309−0.951i)T |
| 23 | 1+(−0.809+0.587i)T |
| 29 | 1+(0.309+0.951i)T |
| 31 | 1+(−0.809+0.587i)T |
| 37 | 1+T |
| 41 | 1+(0.309+0.951i)T |
| 43 | 1+T |
| 47 | 1+(−0.809+0.587i)T |
| 53 | 1+T |
| 59 | 1+T |
| 61 | 1+(0.309+0.951i)T |
| 67 | 1+(0.309+0.951i)T |
| 71 | 1+(−0.809−0.587i)T |
| 73 | 1+(0.309−0.951i)T |
| 79 | 1+T |
| 83 | 1+T |
| 89 | 1+(−0.809+0.587i)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
−25.66492522289357348241506021912, −24.73615159599267806041147778923, −23.825252838399760814898339706, −23.17695697568710537304115456080, −22.410124469989206401391132517882, −20.94487226185938439681154492400, −19.770442163325035183607263531976, −18.895122905244347943321441749774, −18.37601059651843983691447352964, −17.19987525892713430647096670242, −16.48113948938932077152657828466, −16.03448300307487093184295266078, −14.44831637828559341445328529221, −13.61571437804501153164826917861, −12.36600474888201353580576775989, −11.37420115107748664717048580096, −10.30282649204222813218818796402, −9.58882531192305288732438177766, −8.11250650898948395007034966285, −7.26970323099735153927866780976, −6.33806123465386558457809836795, −5.635563494074773163229228018593, −4.08588013410465699498974937844, −2.06551520229285675499152554494, −0.73665531557745548622824922782,
0.96623093423362030673724791765, 2.84462841825438907357748116374, 3.72970909250513521801030085677, 5.29577749161086339942291747683, 6.340936356416545270122581282682, 7.5704440342260404464332707072, 8.91441521184222427529836997094, 9.72773872532122672438801505889, 10.500348980810899878186160096223, 11.491149000135388669402231113693, 12.35873228781197843818968410048, 13.12582002659810144930315519702, 14.95741306635116640870049582961, 16.06755159378783048666536070122, 16.38302004832361561614090099893, 17.78404450286734800077417051606, 18.12688048081422992699761909938, 19.37896505488588278200529235583, 20.20478033036462334522320005434, 21.28554489577554742665462866649, 21.98424908858744254070136948888, 22.692875842100864035966214620045, 23.81375574391377771445147763187, 25.25957122225176993582784832095, 25.836587163247311547662727373229