L(s) = 1 | + (−0.491 − 0.641i)2-s + (−1.73 − 0.0616i)3-s + (0.348 − 1.30i)4-s + (−3.10 − 0.203i)5-s + (0.812 + 1.14i)6-s + (0.330 + 5.03i)7-s + (−2.49 + 1.03i)8-s + (2.99 + 0.213i)9-s + (1.39 + 2.09i)10-s + (0.620 + 0.543i)11-s + (−0.683 + 2.23i)12-s + (−4.35 − 1.16i)13-s + (3.06 − 2.68i)14-s + (5.36 + 0.544i)15-s + (−0.439 − 0.253i)16-s + (−3.78 + 1.62i)17-s + ⋯ |
L(s) = 1 | + (−0.347 − 0.453i)2-s + (−0.999 − 0.0355i)3-s + (0.174 − 0.650i)4-s + (−1.38 − 0.0910i)5-s + (0.331 + 0.465i)6-s + (0.124 + 1.90i)7-s + (−0.883 + 0.365i)8-s + (0.997 + 0.0711i)9-s + (0.442 + 0.661i)10-s + (0.186 + 0.163i)11-s + (−0.197 + 0.643i)12-s + (−1.20 − 0.323i)13-s + (0.819 − 0.718i)14-s + (1.38 + 0.140i)15-s + (−0.109 − 0.0634i)16-s + (−0.918 + 0.394i)17-s + ⋯ |
Λ(s)=(=(153s/2ΓC(s)L(s)(−0.532−0.846i)Λ(2−s)
Λ(s)=(=(153s/2ΓC(s+1/2)L(s)(−0.532−0.846i)Λ(1−s)
Degree: |
2 |
Conductor: |
153
= 32⋅17
|
Sign: |
−0.532−0.846i
|
Analytic conductor: |
1.22171 |
Root analytic conductor: |
1.10531 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ153(11,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 153, ( :1/2), −0.532−0.846i)
|
Particular Values
L(1) |
≈ |
0.0541702+0.0980327i |
L(21) |
≈ |
0.0541702+0.0980327i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1+(1.73+0.0616i)T |
| 17 | 1+(3.78−1.62i)T |
good | 2 | 1+(0.491+0.641i)T+(−0.517+1.93i)T2 |
| 5 | 1+(3.10+0.203i)T+(4.95+0.652i)T2 |
| 7 | 1+(−0.330−5.03i)T+(−6.94+0.913i)T2 |
| 11 | 1+(−0.620−0.543i)T+(1.43+10.9i)T2 |
| 13 | 1+(4.35+1.16i)T+(11.2+6.5i)T2 |
| 19 | 1+(1.95+0.811i)T+(13.4+13.4i)T2 |
| 23 | 1+(1.27+3.75i)T+(−18.2+14.0i)T2 |
| 29 | 1+(0.376−0.185i)T+(17.6−23.0i)T2 |
| 31 | 1+(−0.875−0.997i)T+(−4.04+30.7i)T2 |
| 37 | 1+(−0.0132−0.0664i)T+(−34.1+14.1i)T2 |
| 41 | 1+(1.49−3.03i)T+(−24.9−32.5i)T2 |
| 43 | 1+(−0.945+7.17i)T+(−41.5−11.1i)T2 |
| 47 | 1+(−5.19+1.39i)T+(40.7−23.5i)T2 |
| 53 | 1+(2.70−6.52i)T+(−37.4−37.4i)T2 |
| 59 | 1+(−2.70−2.07i)T+(15.2+56.9i)T2 |
| 61 | 1+(1.71−0.112i)T+(60.4−7.96i)T2 |
| 67 | 1+(−1.90+1.10i)T+(33.5−58.0i)T2 |
| 71 | 1+(−2.14+0.426i)T+(65.5−27.1i)T2 |
| 73 | 1+(−4.79−3.20i)T+(27.9+67.4i)T2 |
| 79 | 1+(8.73−9.96i)T+(−10.3−78.3i)T2 |
| 83 | 1+(−2.91+2.23i)T+(21.4−80.1i)T2 |
| 89 | 1+(−3.26+3.26i)T−89iT2 |
| 97 | 1+(7.70+15.6i)T+(−59.0+76.9i)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
−12.55579666855536863108987263465, −12.10517407385019901856278059508, −11.46375151161172470180743164009, −10.55492145852882428459090496528, −9.322125179535131581951425056634, −8.313830547522934722300177127016, −6.80024524917110073677011067369, −5.64769813068704992929984324311, −4.60510031441731250312130063482, −2.34900520282817117173279599828,
0.13025874741519588135431229501, 3.79654564902860757534203212875, 4.53504156313230080304912482018, 6.70178983575682585054858635929, 7.29221030998669266807354599325, 7.963238341496359655204618606188, 9.652077465655337179577980936569, 10.90490618955604656301266177575, 11.54533851305612557559681762898, 12.39075473239613536621729768044