L(s) = 1 | + (0.923 − 0.382i)2-s + (2.22 − 0.442i)3-s + (0.707 − 0.707i)4-s + (−2.23 + 0.151i)5-s + (1.88 − 1.26i)6-s + (−1.29 − 1.93i)7-s + (0.382 − 0.923i)8-s + (1.98 − 0.820i)9-s + (−2.00 + 0.993i)10-s + (1.86 + 2.78i)11-s + (1.26 − 1.88i)12-s + 4.73i·13-s + (−1.93 − 1.29i)14-s + (−4.89 + 1.32i)15-s − i·16-s + (−2.38 + 3.36i)17-s + ⋯ |
L(s) = 1 | + (0.653 − 0.270i)2-s + (1.28 − 0.255i)3-s + (0.353 − 0.353i)4-s + (−0.997 + 0.0677i)5-s + (0.769 − 0.514i)6-s + (−0.488 − 0.731i)7-s + (0.135 − 0.326i)8-s + (0.660 − 0.273i)9-s + (−0.633 + 0.314i)10-s + (0.561 + 0.840i)11-s + (0.363 − 0.544i)12-s + 1.31i·13-s + (−0.517 − 0.345i)14-s + (−1.26 + 0.341i)15-s − 0.250i·16-s + (−0.578 + 0.815i)17-s + ⋯ |
Λ(s)=(=(170s/2ΓC(s)L(s)(0.809+0.587i)Λ(2−s)
Λ(s)=(=(170s/2ΓC(s+1/2)L(s)(0.809+0.587i)Λ(1−s)
Degree: |
2 |
Conductor: |
170
= 2⋅5⋅17
|
Sign: |
0.809+0.587i
|
Analytic conductor: |
1.35745 |
Root analytic conductor: |
1.16509 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ170(27,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 170, ( :1/2), 0.809+0.587i)
|
Particular Values
L(1) |
≈ |
1.84165−0.598368i |
L(21) |
≈ |
1.84165−0.598368i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.923+0.382i)T |
| 5 | 1+(2.23−0.151i)T |
| 17 | 1+(2.38−3.36i)T |
good | 3 | 1+(−2.22+0.442i)T+(2.77−1.14i)T2 |
| 7 | 1+(1.29+1.93i)T+(−2.67+6.46i)T2 |
| 11 | 1+(−1.86−2.78i)T+(−4.20+10.1i)T2 |
| 13 | 1−4.73iT−13T2 |
| 19 | 1+(0.786+0.325i)T+(13.4+13.4i)T2 |
| 23 | 1+(−0.820+4.12i)T+(−21.2−8.80i)T2 |
| 29 | 1+(3.83−0.762i)T+(26.7−11.0i)T2 |
| 31 | 1+(−4.45+6.66i)T+(−11.8−28.6i)T2 |
| 37 | 1+(1.97+9.93i)T+(−34.1+14.1i)T2 |
| 41 | 1+(0.472+0.0940i)T+(37.8+15.6i)T2 |
| 43 | 1+(1.69+0.702i)T+(30.4+30.4i)T2 |
| 47 | 1+6.52T+47T2 |
| 53 | 1+(1.33+3.22i)T+(−37.4+37.4i)T2 |
| 59 | 1+(−5.52−13.3i)T+(−41.7+41.7i)T2 |
| 61 | 1+(1.17−5.90i)T+(−56.3−23.3i)T2 |
| 67 | 1+(−0.912+0.912i)T−67iT2 |
| 71 | 1+(−10.9−7.33i)T+(27.1+65.5i)T2 |
| 73 | 1+(−6.77+10.1i)T+(−27.9−67.4i)T2 |
| 79 | 1+(6.77−4.52i)T+(30.2−72.9i)T2 |
| 83 | 1+(−8.98+3.72i)T+(58.6−58.6i)T2 |
| 89 | 1+(−2.75+2.75i)T−89iT2 |
| 97 | 1+(−5.10+7.64i)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
−12.85857313168255122028732215247, −11.87723548467617622600407286098, −10.83826517501801376305601339019, −9.553983861690429916709552052481, −8.569783594700855363556149286097, −7.35439135503079463903444302565, −6.63876437114795644422938866588, −4.30068144099397489002780006071, −3.76015925729211120159307257457, −2.17161809543178633388177045178,
2.97084625111728967830771443197, 3.53464645156611179257062771608, 5.09550115874366027846193529090, 6.57980643998744719428883760454, 7.947502380965745963085479806865, 8.545152286351369513032897564569, 9.569909543159726963229556606200, 11.12554260362077296909596802253, 12.05144162684747411653747677642, 13.06949243232466328623981461422