L(s) = 1 | + (0.342 + 0.939i)5-s + (0.173 − 0.984i)7-s + (0.5 − 0.866i)11-s + (0.984 + 0.173i)13-s + (0.342 − 0.939i)17-s + (0.984 + 0.173i)19-s + (0.866 − 0.5i)23-s + (−0.766 + 0.642i)25-s + (−0.866 − 0.5i)29-s + (−0.866 − 0.5i)31-s + (0.984 − 0.173i)35-s + (0.173 − 0.984i)41-s + (0.866 − 0.5i)43-s − 47-s + (−0.939 − 0.342i)49-s + ⋯ |
L(s) = 1 | + (0.342 + 0.939i)5-s + (0.173 − 0.984i)7-s + (0.5 − 0.866i)11-s + (0.984 + 0.173i)13-s + (0.342 − 0.939i)17-s + (0.984 + 0.173i)19-s + (0.866 − 0.5i)23-s + (−0.766 + 0.642i)25-s + (−0.866 − 0.5i)29-s + (−0.866 − 0.5i)31-s + (0.984 − 0.173i)35-s + (0.173 − 0.984i)41-s + (0.866 − 0.5i)43-s − 47-s + (−0.939 − 0.342i)49-s + ⋯ |
Λ(s)=(=(2664s/2ΓR(s)L(s)(0.580−0.814i)Λ(1−s)
Λ(s)=(=(2664s/2ΓR(s)L(s)(0.580−0.814i)Λ(1−s)
Degree: |
1 |
Conductor: |
2664
= 23⋅32⋅37
|
Sign: |
0.580−0.814i
|
Analytic conductor: |
12.3715 |
Root analytic conductor: |
12.3715 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2664(1757,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 2664, (0: ), 0.580−0.814i)
|
Particular Values
L(21) |
≈ |
1.787046923−0.9209819060i |
L(21) |
≈ |
1.787046923−0.9209819060i |
L(1) |
≈ |
1.266748816−0.1638616787i |
L(1) |
≈ |
1.266748816−0.1638616787i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1 |
| 37 | 1 |
good | 5 | 1+(0.342+0.939i)T |
| 7 | 1+(0.173−0.984i)T |
| 11 | 1+(0.5−0.866i)T |
| 13 | 1+(0.984+0.173i)T |
| 17 | 1+(0.342−0.939i)T |
| 19 | 1+(0.984+0.173i)T |
| 23 | 1+(0.866−0.5i)T |
| 29 | 1+(−0.866−0.5i)T |
| 31 | 1+(−0.866−0.5i)T |
| 41 | 1+(0.173−0.984i)T |
| 43 | 1+(0.866−0.5i)T |
| 47 | 1−T |
| 53 | 1+(0.766−0.642i)T |
| 59 | 1+(0.984−0.173i)T |
| 61 | 1+(0.642−0.766i)T |
| 67 | 1+(−0.939+0.342i)T |
| 71 | 1+(−0.173+0.984i)T |
| 73 | 1−T |
| 79 | 1+(−0.984−0.173i)T |
| 83 | 1+(0.173+0.984i)T |
| 89 | 1+(−0.642−0.766i)T |
| 97 | 1−iT |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−19.52509235190191143822643768867, −18.64350408337510424136261304220, −17.835262058971030677601383112942, −17.53105592396844917309568334416, −16.41068284037348856124638653423, −16.10095365609329026129711336975, −14.99979669114173616437490744887, −14.73099834735813099687370748934, −13.5401869511208129511844953047, −12.95255271862714015977815965166, −12.35928662663850941221966292312, −11.65356751286269128889043840505, −10.89468503145473923506637744420, −9.81835181811317629387615829928, −9.20518341851779447448152958118, −8.70533109146204004548694327002, −7.888757037633846076729405340197, −6.98606431753546536310906392658, −5.89158634056349430563134364341, −5.51270290274360306812294113970, −4.66684344678875691115167897648, −3.77457039121442837459546136306, −2.83514117553307943837729541150, −1.58949991617223102070881323201, −1.33464908362865461855691718704,
0.67173549718373974998255348774, 1.55889409917435191359413257201, 2.71279075005694890055165351182, 3.546481689796046377413064652649, 4.00855360358497443743768083010, 5.339290017495637292301806414004, 5.92843775746629074899377030610, 6.94817190555672716002224360662, 7.25887799296095361383359624348, 8.25051010051955787760978482709, 9.18402345040282907471496268507, 9.851417186507439671800710838170, 10.71902105452544246966028277813, 11.245126587514847676374840599571, 11.727263947105716431958996847135, 13.14091709903948739766057623078, 13.545550300108075140087242480455, 14.309199248583292654644590271118, 14.63237758934733041045029111749, 15.841076919448110921102940799532, 16.366660427100981182624792091617, 17.11756306317553354769745073832, 17.83248355531007965717114770039, 18.65036551958964657639245513354, 18.94928257615967752004089157037