L(s) = 1 | + (−0.988 − 0.149i)2-s + (1.36 − 0.930i)3-s + (0.955 + 0.294i)4-s + (−1.48 + 0.716i)6-s + (−0.900 − 0.433i)7-s + (−0.900 − 0.433i)8-s + (0.632 − 1.61i)9-s + (−0.722 − 1.84i)11-s + (1.57 − 0.487i)12-s + (−1.23 + 1.54i)13-s + (0.826 + 0.563i)14-s + (0.826 + 0.563i)16-s + (−0.733 − 0.680i)17-s + (−0.865 + 1.49i)18-s + (−1.63 + 0.246i)21-s + (0.440 + 1.92i)22-s + ⋯ |
L(s) = 1 | + (−0.988 − 0.149i)2-s + (1.36 − 0.930i)3-s + (0.955 + 0.294i)4-s + (−1.48 + 0.716i)6-s + (−0.900 − 0.433i)7-s + (−0.900 − 0.433i)8-s + (0.632 − 1.61i)9-s + (−0.722 − 1.84i)11-s + (1.57 − 0.487i)12-s + (−1.23 + 1.54i)13-s + (0.826 + 0.563i)14-s + (0.826 + 0.563i)16-s + (−0.733 − 0.680i)17-s + (−0.865 + 1.49i)18-s + (−1.63 + 0.246i)21-s + (0.440 + 1.92i)22-s + ⋯ |
Λ(s)=(=(3332s/2ΓC(s)L(s)(−0.999+0.0213i)Λ(1−s)
Λ(s)=(=(3332s/2ΓC(s)L(s)(−0.999+0.0213i)Λ(1−s)
Degree: |
2 |
Conductor: |
3332
= 22⋅72⋅17
|
Sign: |
−0.999+0.0213i
|
Analytic conductor: |
1.66288 |
Root analytic conductor: |
1.28952 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3332(1019,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3332, ( :0), −0.999+0.0213i)
|
Particular Values
L(21) |
≈ |
0.6365970018 |
L(21) |
≈ |
0.6365970018 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.988+0.149i)T |
| 7 | 1+(0.900+0.433i)T |
| 17 | 1+(0.733+0.680i)T |
good | 3 | 1+(−1.36+0.930i)T+(0.365−0.930i)T2 |
| 5 | 1+(0.988−0.149i)T2 |
| 11 | 1+(0.722+1.84i)T+(−0.733+0.680i)T2 |
| 13 | 1+(1.23−1.54i)T+(−0.222−0.974i)T2 |
| 19 | 1+(0.5−0.866i)T2 |
| 23 | 1+(0.914−0.848i)T+(0.0747−0.997i)T2 |
| 29 | 1+(0.900+0.433i)T2 |
| 31 | 1+(−0.900+1.56i)T+(−0.5−0.866i)T2 |
| 37 | 1+(−0.826+0.563i)T2 |
| 41 | 1+(−0.623−0.781i)T2 |
| 43 | 1+(−0.623+0.781i)T2 |
| 47 | 1+(−0.955−0.294i)T2 |
| 53 | 1+(−0.142−0.0440i)T+(0.826+0.563i)T2 |
| 59 | 1+(0.988+0.149i)T2 |
| 61 | 1+(−0.826+0.563i)T2 |
| 67 | 1+(0.5+0.866i)T2 |
| 71 | 1+(0.0332+0.145i)T+(−0.900+0.433i)T2 |
| 73 | 1+(−0.955+0.294i)T2 |
| 79 | 1+(0.365+0.632i)T+(−0.5+0.866i)T2 |
| 83 | 1+(0.222−0.974i)T2 |
| 89 | 1+(−0.603+1.53i)T+(−0.733−0.680i)T2 |
| 97 | 1−T2 |
show more | |
show less | |
L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−8.452625942674940758798023324813, −7.68934024666247813350762222416, −7.33526194752282588818220495134, −6.50729787810129263289045536202, −5.89521950536175138939555653031, −4.14394098951933334701633974088, −3.25534866867893562519068498499, −2.58272558800112628394128685031, −1.88249436121175035318284909304, −0.38138126468301668637445155566,
2.24987563009292359872437994132, 2.45987664307698134294671040315, 3.40951926012116440636312238566, 4.53136103298114367708003542646, 5.30888816172932698089532784204, 6.42620800854709266235115683421, 7.30041025606778135741464332554, 7.942895458115921150392549335789, 8.440617595385013351159142691851, 9.262195685670523470235311211918