L(s) = 1 | + (2.09 + 0.934i)2-s + (2.19 + 2.43i)4-s + (1.55 − 0.690i)5-s + (−0.203 + 0.0431i)7-s + (0.910 + 2.80i)8-s + 3.90·10-s + (2.04 − 2.60i)11-s + (−0.144 − 1.37i)13-s + (−0.466 − 0.0992i)14-s + (−0.0217 + 0.206i)16-s + (2.97 + 2.15i)17-s + (2.50 + 7.70i)19-s + (5.08 + 2.26i)20-s + (6.73 − 3.56i)22-s + (−1.99 + 3.45i)23-s + ⋯ |
L(s) = 1 | + (1.48 + 0.660i)2-s + (1.09 + 1.21i)4-s + (0.693 − 0.308i)5-s + (−0.0767 + 0.0163i)7-s + (0.321 + 0.990i)8-s + 1.23·10-s + (0.617 − 0.786i)11-s + (−0.0400 − 0.381i)13-s + (−0.124 − 0.0265i)14-s + (−0.00542 + 0.0516i)16-s + (0.720 + 0.523i)17-s + (0.574 + 1.76i)19-s + (1.13 + 0.506i)20-s + (1.43 − 0.759i)22-s + (−0.416 + 0.721i)23-s + ⋯ |
Λ(s)=(=(891s/2ΓC(s)L(s)(0.737−0.675i)Λ(2−s)
Λ(s)=(=(891s/2ΓC(s+1/2)L(s)(0.737−0.675i)Λ(1−s)
Degree: |
2 |
Conductor: |
891
= 34⋅11
|
Sign: |
0.737−0.675i
|
Analytic conductor: |
7.11467 |
Root analytic conductor: |
2.66733 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ891(190,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 891, ( :1/2), 0.737−0.675i)
|
Particular Values
L(1) |
≈ |
3.74667+1.45669i |
L(21) |
≈ |
3.74667+1.45669i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 11 | 1+(−2.04+2.60i)T |
good | 2 | 1+(−2.09−0.934i)T+(1.33+1.48i)T2 |
| 5 | 1+(−1.55+0.690i)T+(3.34−3.71i)T2 |
| 7 | 1+(0.203−0.0431i)T+(6.39−2.84i)T2 |
| 13 | 1+(0.144+1.37i)T+(−12.7+2.70i)T2 |
| 17 | 1+(−2.97−2.15i)T+(5.25+16.1i)T2 |
| 19 | 1+(−2.50−7.70i)T+(−15.3+11.1i)T2 |
| 23 | 1+(1.99−3.45i)T+(−11.5−19.9i)T2 |
| 29 | 1+(0.530−0.112i)T+(26.4−11.7i)T2 |
| 31 | 1+(1.02+9.77i)T+(−30.3+6.44i)T2 |
| 37 | 1+(0.381−1.17i)T+(−29.9−21.7i)T2 |
| 41 | 1+(9.13+1.94i)T+(37.4+16.6i)T2 |
| 43 | 1+(3.96+6.86i)T+(−21.5+37.2i)T2 |
| 47 | 1+(5.25−5.83i)T+(−4.91−46.7i)T2 |
| 53 | 1+(5.30−3.85i)T+(16.3−50.4i)T2 |
| 59 | 1+(−5.26−5.84i)T+(−6.16+58.6i)T2 |
| 61 | 1+(−0.145+1.38i)T+(−59.6−12.6i)T2 |
| 67 | 1+(−2.92+5.06i)T+(−33.5−58.0i)T2 |
| 71 | 1+(−10.3−7.49i)T+(21.9+67.5i)T2 |
| 73 | 1+(−2.36+7.27i)T+(−59.0−42.9i)T2 |
| 79 | 1+(5.30+2.36i)T+(52.8+58.7i)T2 |
| 83 | 1+(−1.45+13.7i)T+(−81.1−17.2i)T2 |
| 89 | 1+6.19T+89T2 |
| 97 | 1+(6.41+2.85i)T+(64.9+72.0i)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
−10.10967024684845905861342676053, −9.502238422272909581961902565532, −8.198303965349340324822779579843, −7.54599599710368279524250782657, −6.26598472196005653006616284984, −5.83472643061899524898232460934, −5.20398337179677778083050404602, −3.85670447607201129126650059095, −3.33634410245590151166350592195, −1.65555379681884070845652021226,
1.64873074716557662719826053874, 2.66765120688604185935686543274, 3.57950605457240475530221167268, 4.79036417587050639679405463928, 5.22464122100216280999376401174, 6.59822860697523277573296913829, 6.81927020877516601420296670426, 8.415699260225294192664390608482, 9.614124654046048214090131294665, 10.08894674811143812754101736841