L(s) = 1 | + (0.558 + 0.966i)2-s + (−1.69 − 0.975i)3-s + (0.376 − 0.652i)4-s + (1.29 − 0.749i)5-s − 2.17i·6-s + 3.07·8-s + (0.404 + 0.700i)9-s + (1.44 + 0.836i)10-s + (−0.854 − 0.493i)11-s + (−1.27 + 0.735i)12-s + 5.99·13-s − 2.92·15-s + (0.962 + 1.66i)16-s + (−4.12 − 0.155i)17-s + (−0.451 + 0.781i)18-s + (−2.38 − 4.13i)19-s + ⋯ |
L(s) = 1 | + (0.394 + 0.683i)2-s + (−0.975 − 0.563i)3-s + (0.188 − 0.326i)4-s + (0.580 − 0.335i)5-s − 0.889i·6-s + 1.08·8-s + (0.134 + 0.233i)9-s + (0.458 + 0.264i)10-s + (−0.257 − 0.148i)11-s + (−0.367 + 0.212i)12-s + 1.66·13-s − 0.755·15-s + (0.240 + 0.416i)16-s + (−0.999 − 0.0378i)17-s + (−0.106 + 0.184i)18-s + (−0.547 − 0.948i)19-s + ⋯ |
Λ(s)=(=(833s/2ΓC(s)L(s)(0.574+0.818i)Λ(2−s)
Λ(s)=(=(833s/2ΓC(s+1/2)L(s)(0.574+0.818i)Λ(1−s)
Degree: |
2 |
Conductor: |
833
= 72⋅17
|
Sign: |
0.574+0.818i
|
Analytic conductor: |
6.65153 |
Root analytic conductor: |
2.57905 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ833(67,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 833, ( :1/2), 0.574+0.818i)
|
Particular Values
L(1) |
≈ |
1.47103−0.764229i |
L(21) |
≈ |
1.47103−0.764229i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 7 | 1 |
| 17 | 1+(4.12+0.155i)T |
good | 2 | 1+(−0.558−0.966i)T+(−1+1.73i)T2 |
| 3 | 1+(1.69+0.975i)T+(1.5+2.59i)T2 |
| 5 | 1+(−1.29+0.749i)T+(2.5−4.33i)T2 |
| 11 | 1+(0.854+0.493i)T+(5.5+9.52i)T2 |
| 13 | 1−5.99T+13T2 |
| 19 | 1+(2.38+4.13i)T+(−9.5+16.4i)T2 |
| 23 | 1+(−0.807+0.466i)T+(11.5−19.9i)T2 |
| 29 | 1+4.13iT−29T2 |
| 31 | 1+(−1.49−0.863i)T+(15.5+26.8i)T2 |
| 37 | 1+(−6.78+3.91i)T+(18.5−32.0i)T2 |
| 41 | 1+9.93iT−41T2 |
| 43 | 1+5.60T+43T2 |
| 47 | 1+(1.68+2.92i)T+(−23.5+40.7i)T2 |
| 53 | 1+(−3.06+5.30i)T+(−26.5−45.8i)T2 |
| 59 | 1+(−3.33+5.77i)T+(−29.5−51.0i)T2 |
| 61 | 1+(−0.508+0.293i)T+(30.5−52.8i)T2 |
| 67 | 1+(−0.414+0.717i)T+(−33.5−58.0i)T2 |
| 71 | 1−15.0iT−71T2 |
| 73 | 1+(−6.04−3.49i)T+(36.5+63.2i)T2 |
| 79 | 1+(12.0−6.93i)T+(39.5−68.4i)T2 |
| 83 | 1+0.776T+83T2 |
| 89 | 1+(−2.05−3.55i)T+(−44.5+77.0i)T2 |
| 97 | 1−11.1iT−97T2 |
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
−10.27717106630534099691905201721, −9.130463402305738117011021481123, −8.291951456552624225477974663646, −7.00125782219619327217361119497, −6.49182222612513142061087506186, −5.78780699237402195412794877060, −5.18900262774008565473486604423, −4.01696498071171556752773589847, −2.09731829418034522084713968197, −0.851408012030401378719557818789,
1.64044979015583883931899813320, 2.88834439543483075956355722302, 4.04638058138357284045229089763, 4.78076410591545723497900158374, 6.03451100833405478945671243778, 6.45242704142157638394633487254, 7.84829697546058358239009431071, 8.693855875893417992005933616653, 10.04538960735165715063312646311, 10.50366375730109256509075809984