L(s) = 1 | − 2i·3-s + (1 − i)5-s + (−1 + i)7-s − 9-s + (3 − 3i)11-s + (3 + 2i)13-s + (−2 − 2i)15-s − 4i·17-s + (−3 − 3i)19-s + (2 + 2i)21-s + 3i·25-s − 4i·27-s + 6·29-s + (−3 − 3i)31-s + (−6 − 6i)33-s + ⋯ |
L(s) = 1 | − 1.15i·3-s + (0.447 − 0.447i)5-s + (−0.377 + 0.377i)7-s − 0.333·9-s + (0.904 − 0.904i)11-s + (0.832 + 0.554i)13-s + (−0.516 − 0.516i)15-s − 0.970i·17-s + (−0.688 − 0.688i)19-s + (0.436 + 0.436i)21-s + 0.600i·25-s − 0.769i·27-s + 1.11·29-s + (−0.538 − 0.538i)31-s + (−1.04 − 1.04i)33-s + ⋯ |
Λ(s)=(=(832s/2ΓC(s)L(s)(−0.289+0.957i)Λ(2−s)
Λ(s)=(=(832s/2ΓC(s+1/2)L(s)(−0.289+0.957i)Λ(1−s)
Degree: |
2 |
Conductor: |
832
= 26⋅13
|
Sign: |
−0.289+0.957i
|
Analytic conductor: |
6.64355 |
Root analytic conductor: |
2.57750 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ832(447,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 832, ( :1/2), −0.289+0.957i)
|
Particular Values
L(1) |
≈ |
1.00220−1.35058i |
L(21) |
≈ |
1.00220−1.35058i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 13 | 1+(−3−2i)T |
good | 3 | 1+2iT−3T2 |
| 5 | 1+(−1+i)T−5iT2 |
| 7 | 1+(1−i)T−7iT2 |
| 11 | 1+(−3+3i)T−11iT2 |
| 17 | 1+4iT−17T2 |
| 19 | 1+(3+3i)T+19iT2 |
| 23 | 1+23T2 |
| 29 | 1−6T+29T2 |
| 31 | 1+(3+3i)T+31iT2 |
| 37 | 1+(3+3i)T+37iT2 |
| 41 | 1+(−1+i)T−41iT2 |
| 43 | 1+4T+43T2 |
| 47 | 1+(5−5i)T−47iT2 |
| 53 | 1+6T+53T2 |
| 59 | 1+(−7+7i)T−59iT2 |
| 61 | 1+14T+61T2 |
| 67 | 1+(−5−5i)T+67iT2 |
| 71 | 1+(−5−5i)T+71iT2 |
| 73 | 1+(−9−9i)T+73iT2 |
| 79 | 1+6iT−79T2 |
| 83 | 1+(7+7i)T+83iT2 |
| 89 | 1+(−5−5i)T+89iT2 |
| 97 | 1+(−13+13i)T−97iT2 |
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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
−9.708403092534637786804036800911, −8.995431566054248029515318066996, −8.396730058539729071390433655237, −7.21698868902712111422462086917, −6.46051528107077955140448040257, −5.90751983764270213542656122899, −4.62534235882220824563664931861, −3.28913799709141643361790041770, −1.98793623399283218921870429115, −0.895926574942647178341408004396,
1.71074380767192155364519340326, 3.36549589406317037280628271231, 4.01739117261477378838166576793, 4.96637276383498824820393105142, 6.23806116816370123029569142599, 6.73358889978087964893655867521, 8.100381838567916013992286606119, 8.958583613492962289766076424109, 9.903280872059627338439098261168, 10.33194415367299669034685782811