L(s) = 1 | + (−0.0871 + 0.996i)2-s + (−0.984 − 0.173i)4-s + (2.82 + 1.31i)5-s + (1.97 − 0.718i)7-s + (0.258 − 0.965i)8-s + (−1.55 + 2.70i)10-s + (1.33 + 2.31i)11-s + (−0.527 − 0.753i)13-s + (0.543 + 2.02i)14-s + (0.939 + 0.342i)16-s + (2.87 − 4.11i)17-s + (−2.92 + 0.256i)19-s + (−2.55 − 1.78i)20-s + (−2.42 + 1.13i)22-s + (2.70 − 0.725i)23-s + ⋯ |
L(s) = 1 | + (−0.0616 + 0.704i)2-s + (−0.492 − 0.0868i)4-s + (1.26 + 0.589i)5-s + (0.745 − 0.271i)7-s + (0.0915 − 0.341i)8-s + (−0.493 + 0.853i)10-s + (0.403 + 0.699i)11-s + (−0.146 − 0.208i)13-s + (0.145 + 0.541i)14-s + (0.234 + 0.0855i)16-s + (0.698 − 0.997i)17-s + (−0.671 + 0.0587i)19-s + (−0.571 − 0.399i)20-s + (−0.517 + 0.241i)22-s + (0.564 − 0.151i)23-s + ⋯ |
Λ(s)=(=(666s/2ΓC(s)L(s)(0.387−0.921i)Λ(2−s)
Λ(s)=(=(666s/2ΓC(s+1/2)L(s)(0.387−0.921i)Λ(1−s)
Degree: |
2 |
Conductor: |
666
= 2⋅32⋅37
|
Sign: |
0.387−0.921i
|
Analytic conductor: |
5.31803 |
Root analytic conductor: |
2.30608 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ666(557,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 666, ( :1/2), 0.387−0.921i)
|
Particular Values
L(1) |
≈ |
1.56561+1.04030i |
L(21) |
≈ |
1.56561+1.04030i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.0871−0.996i)T |
| 3 | 1 |
| 37 | 1+(1.40−5.91i)T |
good | 5 | 1+(−2.82−1.31i)T+(3.21+3.83i)T2 |
| 7 | 1+(−1.97+0.718i)T+(5.36−4.49i)T2 |
| 11 | 1+(−1.33−2.31i)T+(−5.5+9.52i)T2 |
| 13 | 1+(0.527+0.753i)T+(−4.44+12.2i)T2 |
| 17 | 1+(−2.87+4.11i)T+(−5.81−15.9i)T2 |
| 19 | 1+(2.92−0.256i)T+(18.7−3.29i)T2 |
| 23 | 1+(−2.70+0.725i)T+(19.9−11.5i)T2 |
| 29 | 1+(−4.95−1.32i)T+(25.1+14.5i)T2 |
| 31 | 1+(1.88+1.88i)T+31iT2 |
| 41 | 1+(−0.366+2.08i)T+(−38.5−14.0i)T2 |
| 43 | 1+(6.00−6.00i)T−43iT2 |
| 47 | 1+(5.03+2.90i)T+(23.5+40.7i)T2 |
| 53 | 1+(2.29−6.30i)T+(−40.6−34.0i)T2 |
| 59 | 1+(−5.91−12.6i)T+(−37.9+45.1i)T2 |
| 61 | 1+(−5.22+3.66i)T+(20.8−57.3i)T2 |
| 67 | 1+(2.91+8.01i)T+(−51.3+43.0i)T2 |
| 71 | 1+(3.95−4.70i)T+(−12.3−69.9i)T2 |
| 73 | 1+9.01iT−73T2 |
| 79 | 1+(−0.222+0.477i)T+(−50.7−60.5i)T2 |
| 83 | 1+(−3.14+0.553i)T+(77.9−28.3i)T2 |
| 89 | 1+(2.30−1.07i)T+(57.2−68.1i)T2 |
| 97 | 1+(3.13+11.7i)T+(−84.0+48.5i)T2 |
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
−10.35937220729102904450986140745, −9.853452071277632350371678865646, −8.982929162523023011411829650493, −7.937292644071499692821751439151, −7.02414480565474753880706727354, −6.35091290453543996089214000968, −5.30146397779020743162623120981, −4.53305569734583568005297171668, −2.89932060180985196214627727927, −1.53153405760086804788538302080,
1.30070275762464398403898104830, 2.19456359278047186289657695644, 3.64827434496443977905683515959, 4.92318160071648507152453236569, 5.62193150200311203186662534628, 6.61141629423193906764529125501, 8.202780556715153584199118587787, 8.704686625731457118749532313132, 9.575171353809628216111936808074, 10.33265028025473195684854587540