L(s) = 1 | + (0.342 + 0.939i)2-s + (3.03 + 1.10i)3-s + (−0.766 + 0.642i)4-s + (−0.984 + 0.173i)5-s + 3.23i·6-s + (0.130 + 0.739i)7-s + (−0.866 − 0.500i)8-s + (5.70 + 4.78i)9-s + (−0.5 − 0.866i)10-s + (1.20 − 2.08i)11-s + (−3.03 + 1.10i)12-s + (−2.83 − 3.37i)13-s + (−0.650 + 0.375i)14-s + (−3.18 − 0.561i)15-s + (0.173 − 0.984i)16-s + (−0.673 + 0.803i)17-s + ⋯ |
L(s) = 1 | + (0.241 + 0.664i)2-s + (1.75 + 0.638i)3-s + (−0.383 + 0.321i)4-s + (−0.440 + 0.0776i)5-s + 1.31i·6-s + (0.0492 + 0.279i)7-s + (−0.306 − 0.176i)8-s + (1.90 + 1.59i)9-s + (−0.158 − 0.273i)10-s + (0.363 − 0.628i)11-s + (−0.876 + 0.319i)12-s + (−0.784 − 0.935i)13-s + (−0.173 + 0.100i)14-s + (−0.821 − 0.144i)15-s + (0.0434 − 0.246i)16-s + (−0.163 + 0.194i)17-s + ⋯ |
Λ(s)=(=(370s/2ΓC(s)L(s)(−0.000155−0.999i)Λ(2−s)
Λ(s)=(=(370s/2ΓC(s+1/2)L(s)(−0.000155−0.999i)Λ(1−s)
Degree: |
2 |
Conductor: |
370
= 2⋅5⋅37
|
Sign: |
−0.000155−0.999i
|
Analytic conductor: |
2.95446 |
Root analytic conductor: |
1.71885 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ370(141,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 370, ( :1/2), −0.000155−0.999i)
|
Particular Values
L(1) |
≈ |
1.65181+1.65207i |
L(21) |
≈ |
1.65181+1.65207i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.342−0.939i)T |
| 5 | 1+(0.984−0.173i)T |
| 37 | 1+(−5.29−2.99i)T |
good | 3 | 1+(−3.03−1.10i)T+(2.29+1.92i)T2 |
| 7 | 1+(−0.130−0.739i)T+(−6.57+2.39i)T2 |
| 11 | 1+(−1.20+2.08i)T+(−5.5−9.52i)T2 |
| 13 | 1+(2.83+3.37i)T+(−2.25+12.8i)T2 |
| 17 | 1+(0.673−0.803i)T+(−2.95−16.7i)T2 |
| 19 | 1+(1.37−3.78i)T+(−14.5−12.2i)T2 |
| 23 | 1+(−2.42+1.40i)T+(11.5−19.9i)T2 |
| 29 | 1+(5.43+3.13i)T+(14.5+25.1i)T2 |
| 31 | 1+10.5iT−31T2 |
| 41 | 1+(6.67−5.59i)T+(7.11−40.3i)T2 |
| 43 | 1+6.19iT−43T2 |
| 47 | 1+(−1.01−1.76i)T+(−23.5+40.7i)T2 |
| 53 | 1+(−0.313+1.77i)T+(−49.8−18.1i)T2 |
| 59 | 1+(−5.19−0.916i)T+(55.4+20.1i)T2 |
| 61 | 1+(−6.70−7.98i)T+(−10.5+60.0i)T2 |
| 67 | 1+(0.144+0.820i)T+(−62.9+22.9i)T2 |
| 71 | 1+(14.1+5.15i)T+(54.3+45.6i)T2 |
| 73 | 1+2.93T+73T2 |
| 79 | 1+(7.33−1.29i)T+(74.2−27.0i)T2 |
| 83 | 1+(−3.30−2.77i)T+(14.4+81.7i)T2 |
| 89 | 1+(13.8+2.43i)T+(83.6+30.4i)T2 |
| 97 | 1+(−3.56+2.05i)T+(48.5−84.0i)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
−11.69409276457493748180815893237, −10.34597313185570058924709313858, −9.564750896622276423249593309503, −8.617136327553931455590084274987, −8.037829238447073534527240462939, −7.28882188846954998085426961735, −5.75082969928043520198765973238, −4.40714072176432070206307398827, −3.58477055598346365970824975802, −2.50732300401944597452733146494,
1.59568043697594910680473416229, 2.69884218255453287285036696783, 3.80138245452446769701476272020, 4.72888112997376833318795747664, 6.94990927770477433062854290329, 7.30799408686354881782644381400, 8.672424516974074227739199346710, 9.149962203642225313137040126739, 10.03981251870544168212313889430, 11.34207348682325376245377493114