L(s) = 1 | + (0.573 − 0.819i)2-s + (−0.342 − 0.939i)4-s + (1.60 − 0.140i)5-s + (1.53 + 1.29i)7-s + (−0.965 − 0.258i)8-s + (0.807 − 1.39i)10-s + (2.64 + 4.57i)11-s + (4.54 + 2.11i)13-s + (1.94 − 0.520i)14-s + (−0.766 + 0.642i)16-s + (−5.07 + 2.36i)17-s + (−0.363 + 0.254i)19-s + (−0.682 − 1.46i)20-s + (5.26 + 0.460i)22-s + (−1.51 − 5.64i)23-s + ⋯ |
L(s) = 1 | + (0.405 − 0.579i)2-s + (−0.171 − 0.469i)4-s + (0.719 − 0.0629i)5-s + (0.582 + 0.488i)7-s + (−0.341 − 0.0915i)8-s + (0.255 − 0.442i)10-s + (0.797 + 1.38i)11-s + (1.25 + 0.587i)13-s + (0.518 − 0.139i)14-s + (−0.191 + 0.160i)16-s + (−1.23 + 0.574i)17-s + (−0.0833 + 0.0583i)19-s + (−0.152 − 0.327i)20-s + (1.12 + 0.0982i)22-s + (−0.315 − 1.17i)23-s + ⋯ |
Λ(s)=(=(666s/2ΓC(s)L(s)(0.917+0.397i)Λ(2−s)
Λ(s)=(=(666s/2ΓC(s+1/2)L(s)(0.917+0.397i)Λ(1−s)
Degree: |
2 |
Conductor: |
666
= 2⋅32⋅37
|
Sign: |
0.917+0.397i
|
Analytic conductor: |
5.31803 |
Root analytic conductor: |
2.30608 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ666(17,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 666, ( :1/2), 0.917+0.397i)
|
Particular Values
L(1) |
≈ |
2.19610−0.455345i |
L(21) |
≈ |
2.19610−0.455345i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.573+0.819i)T |
| 3 | 1 |
| 37 | 1+(−6.05+0.580i)T |
good | 5 | 1+(−1.60+0.140i)T+(4.92−0.868i)T2 |
| 7 | 1+(−1.53−1.29i)T+(1.21+6.89i)T2 |
| 11 | 1+(−2.64−4.57i)T+(−5.5+9.52i)T2 |
| 13 | 1+(−4.54−2.11i)T+(8.35+9.95i)T2 |
| 17 | 1+(5.07−2.36i)T+(10.9−13.0i)T2 |
| 19 | 1+(0.363−0.254i)T+(6.49−17.8i)T2 |
| 23 | 1+(1.51+5.64i)T+(−19.9+11.5i)T2 |
| 29 | 1+(−1.91+7.15i)T+(−25.1−14.5i)T2 |
| 31 | 1+(−5.12+5.12i)T−31iT2 |
| 41 | 1+(6.41−2.33i)T+(31.4−26.3i)T2 |
| 43 | 1+(−7.63−7.63i)T+43iT2 |
| 47 | 1+(4.34+2.50i)T+(23.5+40.7i)T2 |
| 53 | 1+(7.64+9.10i)T+(−9.20+52.1i)T2 |
| 59 | 1+(0.615−7.03i)T+(−58.1−10.2i)T2 |
| 61 | 1+(2.86−6.14i)T+(−39.2−46.7i)T2 |
| 67 | 1+(3.96−4.72i)T+(−11.6−65.9i)T2 |
| 71 | 1+(−1.49−0.263i)T+(66.7+24.2i)T2 |
| 73 | 1+8.32iT−73T2 |
| 79 | 1+(1.28+14.6i)T+(−77.7+13.7i)T2 |
| 83 | 1+(−4.01+11.0i)T+(−63.5−53.3i)T2 |
| 89 | 1+(−0.608−0.0532i)T+(87.6+15.4i)T2 |
| 97 | 1+(10.0−2.68i)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
−10.47706073524551139610497026620, −9.666591199277376639515890363414, −8.949073978952302716409244764907, −8.037633087817109939441594986333, −6.42074675187870982951887562369, −6.15252398632920891017384069389, −4.60746494129152478702314836668, −4.16077695441224458188823795813, −2.34665891852775666872476327467, −1.64432667647500478986682845600,
1.31120314410692083616165421117, 3.09994781852700510341549573371, 4.09470659987592817940757681654, 5.28221747098021808848138468568, 6.11997862195577031412884525595, 6.78509281540242035832510768952, 8.020237004679782455679235952686, 8.702094989049313242475059069220, 9.512575989818398696700072185753, 10.91452220725059644218594116290