L(s) = 1 | + (0.327 + 0.945i)2-s + (−0.458 + 0.888i)3-s + (−0.786 + 0.618i)4-s + (4.16 + 0.397i)5-s + (−0.989 − 0.142i)6-s + (0.0805 − 2.64i)7-s + (−0.841 − 0.540i)8-s + (−0.580 − 0.814i)9-s + (0.986 + 4.06i)10-s + (−0.191 − 0.0663i)11-s + (−0.189 − 0.981i)12-s + (−1.51 + 5.17i)13-s + (2.52 − 0.788i)14-s + (−2.26 + 3.52i)15-s + (0.235 − 0.971i)16-s + (−4.53 + 1.81i)17-s + ⋯ |
L(s) = 1 | + (0.231 + 0.668i)2-s + (−0.264 + 0.513i)3-s + (−0.393 + 0.309i)4-s + (1.86 + 0.177i)5-s + (−0.404 − 0.0580i)6-s + (0.0304 − 0.999i)7-s + (−0.297 − 0.191i)8-s + (−0.193 − 0.271i)9-s + (0.312 + 1.28i)10-s + (−0.0577 − 0.0199i)11-s + (−0.0546 − 0.283i)12-s + (−0.421 + 1.43i)13-s + (0.674 − 0.210i)14-s + (−0.584 + 0.909i)15-s + (0.0589 − 0.242i)16-s + (−1.09 + 0.439i)17-s + ⋯ |
Λ(s)=(=(966s/2ΓC(s)L(s)(−0.115−0.993i)Λ(2−s)
Λ(s)=(=(966s/2ΓC(s+1/2)L(s)(−0.115−0.993i)Λ(1−s)
Degree: |
2 |
Conductor: |
966
= 2⋅3⋅7⋅23
|
Sign: |
−0.115−0.993i
|
Analytic conductor: |
7.71354 |
Root analytic conductor: |
2.77732 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ966(145,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 966, ( :1/2), −0.115−0.993i)
|
Particular Values
L(1) |
≈ |
1.40353+1.57614i |
L(21) |
≈ |
1.40353+1.57614i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.327−0.945i)T |
| 3 | 1+(0.458−0.888i)T |
| 7 | 1+(−0.0805+2.64i)T |
| 23 | 1+(−4.79+0.0590i)T |
good | 5 | 1+(−4.16−0.397i)T+(4.90+0.946i)T2 |
| 11 | 1+(0.191+0.0663i)T+(8.64+6.79i)T2 |
| 13 | 1+(1.51−5.17i)T+(−10.9−7.02i)T2 |
| 17 | 1+(4.53−1.81i)T+(12.3−11.7i)T2 |
| 19 | 1+(−3.26−1.30i)T+(13.7+13.1i)T2 |
| 29 | 1+(0.707−4.91i)T+(−27.8−8.17i)T2 |
| 31 | 1+(−7.82−0.372i)T+(30.8+2.94i)T2 |
| 37 | 1+(−0.879+0.626i)T+(12.1−34.9i)T2 |
| 41 | 1+(2.62−1.19i)T+(26.8−30.9i)T2 |
| 43 | 1+(−3.34−5.20i)T+(−17.8+39.1i)T2 |
| 47 | 1+(−6.61−3.81i)T+(23.5+40.7i)T2 |
| 53 | 1+(−5.18+5.43i)T+(−2.52−52.9i)T2 |
| 59 | 1+(9.75−2.36i)T+(52.4−27.0i)T2 |
| 61 | 1+(5.15−2.65i)T+(35.3−49.6i)T2 |
| 67 | 1+(−2.09+10.8i)T+(−62.2−24.9i)T2 |
| 71 | 1+(0.0174−0.0201i)T+(−10.1−70.2i)T2 |
| 73 | 1+(6.57+8.35i)T+(−17.2+70.9i)T2 |
| 79 | 1+(11.2+11.7i)T+(−3.75+78.9i)T2 |
| 83 | 1+(−2.10+4.61i)T+(−54.3−62.7i)T2 |
| 89 | 1+(0.851+17.8i)T+(−88.5+8.45i)T2 |
| 97 | 1+(−0.146−0.319i)T+(−63.5+73.3i)T2 |
show more | |
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L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−10.20002275987643518175222047544, −9.296989870655800868987581621995, −8.943079773817086416515425759613, −7.41014134055542205028763651078, −6.60302939096078644575704072954, −6.11737633422254186102237775296, −4.96938010183692141537760458437, −4.41790060266786597967338410328, −2.97058208040942605884474541146, −1.54521121956127400412314571178,
1.04152375191357281607644659567, 2.44998082761253187135990805081, 2.70307141083735519411170467899, 4.83282920147797419995459804031, 5.48374741153471837107504663861, 6.02610783133198924828183897899, 7.05485132944321026551131966206, 8.427536209016755234714463516721, 9.157310918321573950048726752941, 9.850047583490697204394387924670