L(s) = 1 | − i·3-s + i·7-s − 9-s + 11-s − i·17-s − 19-s + 21-s + i·23-s + i·27-s + 29-s − 31-s − i·33-s − i·37-s − 41-s − i·43-s + ⋯ |
L(s) = 1 | − i·3-s + i·7-s − 9-s + 11-s − i·17-s − 19-s + 21-s + i·23-s + i·27-s + 29-s − 31-s − i·33-s − i·37-s − 41-s − i·43-s + ⋯ |
Λ(s)=(=(520s/2ΓR(s+1)L(s)(−0.850+0.525i)Λ(1−s)
Λ(s)=(=(520s/2ΓR(s+1)L(s)(−0.850+0.525i)Λ(1−s)
Degree: |
1 |
Conductor: |
520
= 23⋅5⋅13
|
Sign: |
−0.850+0.525i
|
Analytic conductor: |
55.8817 |
Root analytic conductor: |
55.8817 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ520(493,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 520, (1: ), −0.850+0.525i)
|
Particular Values
L(21) |
≈ |
0.01930139266−0.06794373990i |
L(21) |
≈ |
0.01930139266−0.06794373990i |
L(1) |
≈ |
0.8480123126−0.2001885515i |
L(1) |
≈ |
0.8480123126−0.2001885515i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1 |
| 13 | 1 |
good | 3 | 1+T |
| 7 | 1−iT |
| 11 | 1 |
| 17 | 1 |
| 19 | 1+iT |
| 23 | 1 |
| 29 | 1−T |
| 31 | 1 |
| 37 | 1+T |
| 41 | 1 |
| 43 | 1 |
| 47 | 1 |
| 53 | 1 |
| 59 | 1 |
| 61 | 1−iT |
| 67 | 1 |
| 71 | 1−T |
| 73 | 1 |
| 79 | 1+T |
| 83 | 1 |
| 89 | 1+iT |
| 97 | 1 |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−23.56218803276308000524481410951, −23.00492538527100197324209269156, −21.971086305800787782571113277775, −21.464765442764555908696234518357, −20.31840612311396798709513458692, −19.923128081188688595991809990167, −18.946172486106917322991229230647, −17.53810431449030372007993160239, −16.90591125439961488089495610285, −16.394746397736307090195233211229, −15.14600155069740803304946760773, −14.57410951031407983921122063622, −13.7275296936409919341543304530, −12.59333644712353988160682835280, −11.5099390177137716255848484271, −10.58436502027786263374803948811, −10.09418311986337203823996064975, −8.92473220832702080804350338515, −8.216172161163277057462121740285, −6.81439233338221299678401321338, −6.026551160440865668399088586225, −4.57899389776792031405443250448, −4.09665955017170492073809404139, −3.06143435230847750324050643443, −1.48378498217064249556033326121,
0.01735230950147015540040240873, 1.45633552525518536843757208962, 2.3713881735861690967443408574, 3.48120666243944729733399832592, 4.98951631022137095977471961425, 5.9869815085371620619738077486, 6.751515667655515034639847054659, 7.730657252379397089936852931009, 8.80725972413671467002348224740, 9.34359653656719836718119895229, 10.89425172352993276556532382311, 11.84621675824583380136748736478, 12.29653052955928705646995156961, 13.33045800773207979073688812662, 14.20847034031471918753003124793, 14.98107530401516279808912800761, 16.044153620186619589674954899086, 17.10524271783263660829155274176, 17.84489551938149370332448568582, 18.6404338334639499412801417873, 19.37414921225198071260376136809, 20.05285991863407142204632498253, 21.23832838138698756719441007555, 22.08991291743246108139949298546, 22.88921246451969237927829954438