L(s) = 1 | + (0.0871 − 0.996i)2-s + (−0.984 − 0.173i)4-s + (−3.03 − 1.41i)5-s + (−1.63 + 0.593i)7-s + (−0.258 + 0.965i)8-s + (−1.67 + 2.90i)10-s + (0.408 + 0.708i)11-s + (3.82 + 5.46i)13-s + (0.449 + 1.67i)14-s + (0.939 + 0.342i)16-s + (−0.771 + 1.10i)17-s + (−1.63 + 0.143i)19-s + (2.74 + 1.92i)20-s + (0.741 − 0.345i)22-s + (4.85 − 1.30i)23-s + ⋯ |
L(s) = 1 | + (0.0616 − 0.704i)2-s + (−0.492 − 0.0868i)4-s + (−1.35 − 0.633i)5-s + (−0.616 + 0.224i)7-s + (−0.0915 + 0.341i)8-s + (−0.529 + 0.917i)10-s + (0.123 + 0.213i)11-s + (1.06 + 1.51i)13-s + (0.120 + 0.447i)14-s + (0.234 + 0.0855i)16-s + (−0.187 + 0.267i)17-s + (−0.375 + 0.0328i)19-s + (0.613 + 0.429i)20-s + (0.158 − 0.0736i)22-s + (1.01 − 0.271i)23-s + ⋯ |
Λ(s)=(=(666s/2ΓC(s)L(s)(0.793−0.609i)Λ(2−s)
Λ(s)=(=(666s/2ΓC(s+1/2)L(s)(0.793−0.609i)Λ(1−s)
Degree: |
2 |
Conductor: |
666
= 2⋅32⋅37
|
Sign: |
0.793−0.609i
|
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), 0.793−0.609i)
|
Particular Values
L(1) |
≈ |
0.692346+0.235240i |
L(21) |
≈ |
0.692346+0.235240i |
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+(−4.15+4.44i)T |
good | 5 | 1+(3.03+1.41i)T+(3.21+3.83i)T2 |
| 7 | 1+(1.63−0.593i)T+(5.36−4.49i)T2 |
| 11 | 1+(−0.408−0.708i)T+(−5.5+9.52i)T2 |
| 13 | 1+(−3.82−5.46i)T+(−4.44+12.2i)T2 |
| 17 | 1+(0.771−1.10i)T+(−5.81−15.9i)T2 |
| 19 | 1+(1.63−0.143i)T+(18.7−3.29i)T2 |
| 23 | 1+(−4.85+1.30i)T+(19.9−11.5i)T2 |
| 29 | 1+(3.12+0.836i)T+(25.1+14.5i)T2 |
| 31 | 1+(−5.52−5.52i)T+31iT2 |
| 41 | 1+(0.631−3.58i)T+(−38.5−14.0i)T2 |
| 43 | 1+(7.38−7.38i)T−43iT2 |
| 47 | 1+(2.69+1.55i)T+(23.5+40.7i)T2 |
| 53 | 1+(1.64−4.52i)T+(−40.6−34.0i)T2 |
| 59 | 1+(−3.21−6.88i)T+(−37.9+45.1i)T2 |
| 61 | 1+(9.61−6.73i)T+(20.8−57.3i)T2 |
| 67 | 1+(−1.99−5.49i)T+(−51.3+43.0i)T2 |
| 71 | 1+(7.41−8.83i)T+(−12.3−69.9i)T2 |
| 73 | 1−6.79iT−73T2 |
| 79 | 1+(−3.68+7.89i)T+(−50.7−60.5i)T2 |
| 83 | 1+(−8.80+1.55i)T+(77.9−28.3i)T2 |
| 89 | 1+(4.08−1.90i)T+(57.2−68.1i)T2 |
| 97 | 1+(2.31+8.63i)T+(−84.0+48.5i)T2 |
show more | |
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L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−10.89907079499436518003660856464, −9.669646127144300892904142293545, −8.847580127483380161942492587755, −8.348726023114897360418677680308, −7.10285527230391148202890227951, −6.15884312984330382919257187675, −4.63203312481063445882096467510, −4.10456004055660333727060006002, −3.05007891741258367612622883405, −1.34685332882723795604818224346,
0.43049277759133843827155740965, 3.18422521082688788867308286986, 3.68454885456507905286486386586, 4.95890576675275804469076101246, 6.18283122525973951605841583670, 6.88136915696703809660136602134, 7.86177788437599141743705070693, 8.311175144417039071428391503374, 9.459690649792886892853163294730, 10.55654072460096924278946238585