L(s) = 1 | + (0.602 + 0.137i)2-s + (−0.268 − 0.556i)3-s + (−1.45 − 0.702i)4-s + (0.857 − 3.75i)5-s + (−0.0849 − 0.372i)6-s + (2.01 − 0.970i)7-s + (−1.74 − 1.39i)8-s + (1.63 − 2.04i)9-s + (1.03 − 2.14i)10-s + (−1.08 + 0.861i)11-s + 0.999i·12-s + (0.147 + 0.184i)13-s + (1.34 − 0.307i)14-s + (−2.32 + 0.530i)15-s + (1.15 + 1.44i)16-s + 4.38i·17-s + ⋯ |
L(s) = 1 | + (0.426 + 0.0972i)2-s + (−0.154 − 0.321i)3-s + (−0.728 − 0.351i)4-s + (0.383 − 1.68i)5-s + (−0.0346 − 0.152i)6-s + (0.761 − 0.366i)7-s + (−0.618 − 0.492i)8-s + (0.544 − 0.682i)9-s + (0.326 − 0.678i)10-s + (−0.325 + 0.259i)11-s + 0.288i·12-s + (0.0408 + 0.0511i)13-s + (0.360 − 0.0821i)14-s + (−0.599 + 0.136i)15-s + (0.289 + 0.362i)16-s + 1.06i·17-s + ⋯ |
Λ(s)=(=(841s/2ΓC(s)L(s)(−0.722+0.691i)Λ(2−s)
Λ(s)=(=(841s/2ΓC(s+1/2)L(s)(−0.722+0.691i)Λ(1−s)
Degree: |
2 |
Conductor: |
841
= 292
|
Sign: |
−0.722+0.691i
|
Analytic conductor: |
6.71541 |
Root analytic conductor: |
2.59141 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ841(236,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 841, ( :1/2), −0.722+0.691i)
|
Particular Values
L(1) |
≈ |
0.593149−1.47739i |
L(21) |
≈ |
0.593149−1.47739i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 29 | 1 |
good | 2 | 1+(−0.602−0.137i)T+(1.80+0.867i)T2 |
| 3 | 1+(0.268+0.556i)T+(−1.87+2.34i)T2 |
| 5 | 1+(−0.857+3.75i)T+(−4.50−2.16i)T2 |
| 7 | 1+(−2.01+0.970i)T+(4.36−5.47i)T2 |
| 11 | 1+(1.08−0.861i)T+(2.44−10.7i)T2 |
| 13 | 1+(−0.147−0.184i)T+(−2.89+12.6i)T2 |
| 17 | 1−4.38iT−17T2 |
| 19 | 1+(−2.10+4.37i)T+(−11.8−14.8i)T2 |
| 23 | 1+(−0.275−1.20i)T+(−20.7+9.97i)T2 |
| 31 | 1+(9.83+2.24i)T+(27.9+13.4i)T2 |
| 37 | 1+(−3.68−2.93i)T+(8.23+36.0i)T2 |
| 41 | 1−3.85iT−41T2 |
| 43 | 1+(−7.05+1.61i)T+(38.7−18.6i)T2 |
| 47 | 1+(−5.47+4.36i)T+(10.4−45.8i)T2 |
| 53 | 1+(−0.445+1.94i)T+(−47.7−22.9i)T2 |
| 59 | 1−6.09T+59T2 |
| 61 | 1+(0.268+0.556i)T+(−38.0+47.6i)T2 |
| 67 | 1+(−0.952+1.19i)T+(−14.9−65.3i)T2 |
| 71 | 1+(6.52+8.18i)T+(−15.7+69.2i)T2 |
| 73 | 1+(13.3−3.05i)T+(65.7−31.6i)T2 |
| 79 | 1+(−4.76−3.79i)T+(17.5+77.0i)T2 |
| 83 | 1+(−8.95−4.31i)T+(51.7+64.8i)T2 |
| 89 | 1+(−4.59−1.04i)T+(80.1+38.6i)T2 |
| 97 | 1+(−1.54+3.20i)T+(−60.4−75.8i)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
−9.581730373499390680853704278969, −9.148952049578102968618056733825, −8.308902978706365989800471135546, −7.35082858792306486311687453680, −6.06138624430064679643079823633, −5.32694917169042794239738236893, −4.57365950531642123150022631104, −3.89188825909699118911716807304, −1.66930958910473202140614148004, −0.74777230526507620978422880461,
2.18598908661274994856123770033, 3.15371891342622954475905353511, 4.15882857936807437477033626047, 5.27458069048673251551626962767, 5.84304655800974596398353553383, 7.30303339091413949275275113997, 7.72136539330966355463836871035, 8.950222457770236381750950945920, 9.816078606163824635050792755728, 10.62596789140238629011876802314