L(s) = 1 | + (2.23 + 2i)3-s + (2.23 − 4.47i)5-s + 8i·7-s + (1.00 + 8.94i)9-s − 8.94i·11-s − 12i·13-s + (13.9 − 5.52i)15-s − 31.3·17-s − 6·19-s + (−16 + 17.8i)21-s + 4.47·23-s + (−15.0 − 20.0i)25-s + (−15.6 + 22.0i)27-s − 26.8i·29-s + 34·31-s + ⋯ |
L(s) = 1 | + (0.745 + 0.666i)3-s + (0.447 − 0.894i)5-s + 1.14i·7-s + (0.111 + 0.993i)9-s − 0.813i·11-s − 0.923i·13-s + (0.929 − 0.368i)15-s − 1.84·17-s − 0.315·19-s + (−0.761 + 0.851i)21-s + 0.194·23-s + (−0.600 − 0.800i)25-s + (−0.579 + 0.814i)27-s − 0.925i·29-s + 1.09·31-s + ⋯ |
Λ(s)=(=(60s/2ΓC(s)L(s)(0.929−0.368i)Λ(3−s)
Λ(s)=(=(60s/2ΓC(s+1)L(s)(0.929−0.368i)Λ(1−s)
Degree: |
2 |
Conductor: |
60
= 22⋅3⋅5
|
Sign: |
0.929−0.368i
|
Analytic conductor: |
1.63488 |
Root analytic conductor: |
1.27862 |
Motivic weight: |
2 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ60(29,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 60, ( :1), 0.929−0.368i)
|
Particular Values
L(23) |
≈ |
1.45178+0.277265i |
L(21) |
≈ |
1.45178+0.277265i |
L(2) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1+(−2.23−2i)T |
| 5 | 1+(−2.23+4.47i)T |
good | 7 | 1−8iT−49T2 |
| 11 | 1+8.94iT−121T2 |
| 13 | 1+12iT−169T2 |
| 17 | 1+31.3T+289T2 |
| 19 | 1+6T+361T2 |
| 23 | 1−4.47T+529T2 |
| 29 | 1+26.8iT−841T2 |
| 31 | 1−34T+961T2 |
| 37 | 1−44iT−1.36e3T2 |
| 41 | 1−17.8iT−1.68e3T2 |
| 43 | 1−28iT−1.84e3T2 |
| 47 | 1−4.47T+2.20e3T2 |
| 53 | 1−40.2T+2.80e3T2 |
| 59 | 1−98.3iT−3.48e3T2 |
| 61 | 1−74T+3.72e3T2 |
| 67 | 1+92iT−4.48e3T2 |
| 71 | 1−53.6iT−5.04e3T2 |
| 73 | 1+56iT−5.32e3T2 |
| 79 | 1+78T+6.24e3T2 |
| 83 | 1+102.T+6.88e3T2 |
| 89 | 1+17.8iT−7.92e3T2 |
| 97 | 1+32iT−9.40e3T2 |
show more | |
show less | |
L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−15.20792972282815476015571279133, −13.68175108496696622664396584733, −12.96917461784470061224317786048, −11.48153338687204257967085112029, −10.05556224265148204549474634162, −8.850276241935608498957155139665, −8.347297233587131691794432032574, −5.94137585119197281268068358720, −4.62424247316482503301892295422, −2.58186362428924905480915729866,
2.17131723727890984097766088136, 4.08223328678377031679040300796, 6.70381367980156212657825159348, 7.18236054184151654360121377292, 8.880679047898305080751982526464, 10.12245583978878001683934168376, 11.30211096781844578266825975358, 12.87789159468169518770330368802, 13.78758732139391218205172937444, 14.47621702430565846663890279212