L(s) = 1 | + (−0.382 + 0.923i)2-s + (−0.567 + 2.85i)3-s + (−0.707 − 0.707i)4-s + (−2.41 − 1.61i)6-s + (−3.60 − 2.40i)7-s + (0.923 − 0.382i)8-s + (−5.03 − 2.08i)9-s + (−0.113 + 0.170i)11-s + (2.41 − 1.61i)12-s − 3.32·13-s + (3.60 − 2.40i)14-s + i·16-s + (4.05 + 0.761i)17-s + (3.85 − 3.85i)18-s + (1.76 − 0.729i)19-s + ⋯ |
L(s) = 1 | + (−0.270 + 0.653i)2-s + (−0.327 + 1.64i)3-s + (−0.353 − 0.353i)4-s + (−0.986 − 0.659i)6-s + (−1.36 − 0.910i)7-s + (0.326 − 0.135i)8-s + (−1.67 − 0.695i)9-s + (−0.0343 + 0.0513i)11-s + (0.697 − 0.466i)12-s − 0.923·13-s + (0.963 − 0.643i)14-s + 0.250i·16-s + (0.982 + 0.184i)17-s + (0.908 − 0.908i)18-s + (0.403 − 0.167i)19-s + ⋯ |
Λ(s)=(=(850s/2ΓC(s)L(s)(0.994+0.105i)Λ(2−s)
Λ(s)=(=(850s/2ΓC(s+1/2)L(s)(0.994+0.105i)Λ(1−s)
Degree: |
2 |
Conductor: |
850
= 2⋅52⋅17
|
Sign: |
0.994+0.105i
|
Analytic conductor: |
6.78728 |
Root analytic conductor: |
2.60524 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ850(607,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 850, ( :1/2), 0.994+0.105i)
|
Particular Values
L(1) |
≈ |
0.451150−0.0239362i |
L(21) |
≈ |
0.451150−0.0239362i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.382−0.923i)T |
| 5 | 1 |
| 17 | 1+(−4.05−0.761i)T |
good | 3 | 1+(0.567−2.85i)T+(−2.77−1.14i)T2 |
| 7 | 1+(3.60+2.40i)T+(2.67+6.46i)T2 |
| 11 | 1+(0.113−0.170i)T+(−4.20−10.1i)T2 |
| 13 | 1+3.32T+13T2 |
| 19 | 1+(−1.76+0.729i)T+(13.4−13.4i)T2 |
| 23 | 1+(−0.769+0.153i)T+(21.2−8.80i)T2 |
| 29 | 1+(−8.95−1.78i)T+(26.7+11.0i)T2 |
| 31 | 1+(4.85+7.26i)T+(−11.8+28.6i)T2 |
| 37 | 1+(−1.88−0.374i)T+(34.1+14.1i)T2 |
| 41 | 1+(3.42−0.682i)T+(37.8−15.6i)T2 |
| 43 | 1+(2.60+6.29i)T+(−30.4+30.4i)T2 |
| 47 | 1+11.8iT−47T2 |
| 53 | 1+(4.78+1.97i)T+(37.4+37.4i)T2 |
| 59 | 1+(1.58−3.81i)T+(−41.7−41.7i)T2 |
| 61 | 1+(−0.209−1.05i)T+(−56.3+23.3i)T2 |
| 67 | 1+(−5.49+5.49i)T−67iT2 |
| 71 | 1+(1.33−0.892i)T+(27.1−65.5i)T2 |
| 73 | 1+(−0.677+0.452i)T+(27.9−67.4i)T2 |
| 79 | 1+(10.3+6.88i)T+(30.2+72.9i)T2 |
| 83 | 1+(−0.269+0.650i)T+(−58.6−58.6i)T2 |
| 89 | 1+(3.70+3.70i)T+89iT2 |
| 97 | 1+(0.124−0.0834i)T+(37.1−89.6i)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
−10.04840074768538533562769633934, −9.625057851939711604608791267963, −8.732195016204312741206035036603, −7.52247157310671172684127863944, −6.68255214991630524970430679637, −5.69022163170318472863001571510, −4.86932847019500070346631145408, −3.92443068860585512214208154773, −3.11818862907535521845264012272, −0.27974926916691776952022264735,
1.19583869276393190277515027660, 2.56031316805578467828222110629, 3.16057735503618230763323069177, 5.08535889889313820511632622543, 6.04363807512117715649180958557, 6.79022048630667136972888252063, 7.62452829100637807521515551650, 8.460236291608044343246667899756, 9.451410513292605134779543800520, 10.09179652712484264230762781049