L(s) = 1 | + (−0.573 + 0.819i)2-s + (−0.342 − 0.939i)4-s + (3.66 − 0.320i)5-s + (−1.19 − 0.999i)7-s + (0.965 + 0.258i)8-s + (−1.83 + 3.18i)10-s + (−1.53 − 2.65i)11-s + (4.68 + 2.18i)13-s + (1.50 − 0.402i)14-s + (−0.766 + 0.642i)16-s + (3.89 − 1.81i)17-s + (−3.65 + 2.55i)19-s + (−1.55 − 3.33i)20-s + (3.05 + 0.267i)22-s + (−1.44 − 5.38i)23-s + ⋯ |
L(s) = 1 | + (−0.405 + 0.579i)2-s + (−0.171 − 0.469i)4-s + (1.63 − 0.143i)5-s + (−0.450 − 0.377i)7-s + (0.341 + 0.0915i)8-s + (−0.581 + 1.00i)10-s + (−0.462 − 0.801i)11-s + (1.29 + 0.605i)13-s + (0.401 − 0.107i)14-s + (−0.191 + 0.160i)16-s + (0.945 − 0.440i)17-s + (−0.837 + 0.586i)19-s + (−0.347 − 0.744i)20-s + (0.651 + 0.0570i)22-s + (−0.300 − 1.12i)23-s + ⋯ |
Λ(s)=(=(666s/2ΓC(s)L(s)(0.997−0.0714i)Λ(2−s)
Λ(s)=(=(666s/2ΓC(s+1/2)L(s)(0.997−0.0714i)Λ(1−s)
Degree: |
2 |
Conductor: |
666
= 2⋅32⋅37
|
Sign: |
0.997−0.0714i
|
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), 0.997−0.0714i)
|
Particular Values
L(1) |
≈ |
1.55292+0.0555605i |
L(21) |
≈ |
1.55292+0.0555605i |
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+(5.10−3.31i)T |
good | 5 | 1+(−3.66+0.320i)T+(4.92−0.868i)T2 |
| 7 | 1+(1.19+0.999i)T+(1.21+6.89i)T2 |
| 11 | 1+(1.53+2.65i)T+(−5.5+9.52i)T2 |
| 13 | 1+(−4.68−2.18i)T+(8.35+9.95i)T2 |
| 17 | 1+(−3.89+1.81i)T+(10.9−13.0i)T2 |
| 19 | 1+(3.65−2.55i)T+(6.49−17.8i)T2 |
| 23 | 1+(1.44+5.38i)T+(−19.9+11.5i)T2 |
| 29 | 1+(−1.43+5.35i)T+(−25.1−14.5i)T2 |
| 31 | 1+(−0.808+0.808i)T−31iT2 |
| 41 | 1+(−4.40+1.60i)T+(31.4−26.3i)T2 |
| 43 | 1+(−2.81−2.81i)T+43iT2 |
| 47 | 1+(−6.67−3.85i)T+(23.5+40.7i)T2 |
| 53 | 1+(−1.78−2.12i)T+(−9.20+52.1i)T2 |
| 59 | 1+(0.929−10.6i)T+(−58.1−10.2i)T2 |
| 61 | 1+(2.73−5.86i)T+(−39.2−46.7i)T2 |
| 67 | 1+(−6.26+7.46i)T+(−11.6−65.9i)T2 |
| 71 | 1+(−11.1−1.96i)T+(66.7+24.2i)T2 |
| 73 | 1−2.09iT−73T2 |
| 79 | 1+(−1.21−13.8i)T+(−77.7+13.7i)T2 |
| 83 | 1+(−2.26+6.23i)T+(−63.5−53.3i)T2 |
| 89 | 1+(14.6+1.28i)T+(87.6+15.4i)T2 |
| 97 | 1+(14.4−3.88i)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
−10.32745307667119458471774512897, −9.656044536472782210415892855262, −8.800876161710643613887500664219, −8.097188838757360590588017625815, −6.71786846975459772153326352265, −6.08788313286003947902415905480, −5.52101604817882667001764387166, −4.09045980449910228017278275112, −2.53803843537838431534469920188, −1.11621145299750387991400729783,
1.47911902498247134106064971528, 2.49474574925409342399167363478, 3.60307484550655430361175741680, 5.23637195017736311208778862978, 5.93729975741712590088684410789, 6.90236187474009634465107637447, 8.141043167702910780469743263708, 9.079570306056151527952820417984, 9.695107791312777313322390472617, 10.46141512037160129374146564937