L(s) = 1 | + (0.951 + 0.309i)3-s − i·7-s + (0.809 + 0.587i)9-s + (−0.809 + 0.587i)11-s + (−0.587 + 0.809i)13-s + (0.951 − 0.309i)17-s + (−0.309 − 0.951i)19-s + (−0.309 + 0.951i)21-s + (0.587 + 0.809i)23-s + (0.587 + 0.809i)27-s + (0.309 − 0.951i)29-s + (−0.309 − 0.951i)31-s + (−0.951 + 0.309i)33-s + (0.587 − 0.809i)37-s + (−0.809 + 0.587i)39-s + ⋯ |
L(s) = 1 | + (0.951 + 0.309i)3-s − i·7-s + (0.809 + 0.587i)9-s + (−0.809 + 0.587i)11-s + (−0.587 + 0.809i)13-s + (0.951 − 0.309i)17-s + (−0.309 − 0.951i)19-s + (−0.309 + 0.951i)21-s + (0.587 + 0.809i)23-s + (0.587 + 0.809i)27-s + (0.309 − 0.951i)29-s + (−0.309 − 0.951i)31-s + (−0.951 + 0.309i)33-s + (0.587 − 0.809i)37-s + (−0.809 + 0.587i)39-s + ⋯ |
Λ(s)=(=(200s/2ΓR(s)L(s)(0.535+0.844i)Λ(1−s)
Λ(s)=(=(200s/2ΓR(s)L(s)(0.535+0.844i)Λ(1−s)
Degree: |
1 |
Conductor: |
200
= 23⋅52
|
Sign: |
0.535+0.844i
|
Analytic conductor: |
0.928796 |
Root analytic conductor: |
0.928796 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ200(83,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 200, (0: ), 0.535+0.844i)
|
Particular Values
L(21) |
≈ |
1.330437507+0.7314142092i |
L(21) |
≈ |
1.330437507+0.7314142092i |
L(1) |
≈ |
1.301618751+0.3720137471i |
L(1) |
≈ |
1.301618751+0.3720137471i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1 |
good | 3 | 1+(0.951+0.309i)T |
| 7 | 1−iT |
| 11 | 1+(−0.809+0.587i)T |
| 13 | 1+(−0.587+0.809i)T |
| 17 | 1+(0.951−0.309i)T |
| 19 | 1+(−0.309−0.951i)T |
| 23 | 1+(0.587+0.809i)T |
| 29 | 1+(0.309−0.951i)T |
| 31 | 1+(−0.309−0.951i)T |
| 37 | 1+(0.587−0.809i)T |
| 41 | 1+(−0.809−0.587i)T |
| 43 | 1+iT |
| 47 | 1+(0.951+0.309i)T |
| 53 | 1+(−0.951−0.309i)T |
| 59 | 1+(0.809+0.587i)T |
| 61 | 1+(0.809−0.587i)T |
| 67 | 1+(0.951−0.309i)T |
| 71 | 1+(−0.309+0.951i)T |
| 73 | 1+(−0.587−0.809i)T |
| 79 | 1+(0.309−0.951i)T |
| 83 | 1+(−0.951+0.309i)T |
| 89 | 1+(0.809−0.587i)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
−26.93185889189180907294698077233, −25.69478187993929259586589584740, −25.057218372201281526907852093831, −23.84695358308389793125871893659, −23.30533120330761862689100286570, −21.85997820066507556020114056308, −20.76089583319993999275251674066, −20.21149632525028058632342280305, −19.12791804142954286390912164308, −18.37519083131514066993121095758, −17.10719173790124431731447556198, −16.12000491240526747016399347158, −14.855835132561706732964236497766, −14.15270260689941362030684742724, −13.11512965548114286876473234699, −12.37289117543238648538428729218, −10.597158553225062970959311192553, −10.01796944526591975294227213176, −8.47748487471459852625527952871, −7.791733326699066738017825111254, −6.76095418778843723688424577846, −5.193424260483532687942049777694, −3.723723069796121488762553762351, −2.80465940372880438118563426778, −1.164500797690574424686146980997,
2.06791314829376274656001823342, 2.888127830577544412438039938, 4.40498455688820979195841030927, 5.44849896318942906127635971978, 7.11820679673594287153428588896, 8.06452406711782498167433745646, 9.255870255293980056937233389367, 9.82906002786716369283017325983, 11.30629698701654437072885696411, 12.49474840171789441244327410161, 13.445251537726938769291721117835, 14.622531484576252527918404202943, 15.30786164225082126748149628534, 16.1657579770685404264022749728, 17.53150472669407552651181828207, 18.77260196357613596072976214332, 19.27861724351885856650081797036, 20.53141859857687723526072586041, 21.32212972887423024688155582477, 22.00651947624602412083201430630, 23.37515030046129041314211087271, 24.41368278561819095663549465435, 25.353133961191990065029031752152, 25.96281983928991448547171721798, 26.94959744336115842910097857188