L(s) = 1 | + (−1.32 + 0.487i)2-s + (1.69 + 0.373i)3-s + (1.52 − 1.29i)4-s + (1.73 + 3.00i)5-s + (−2.42 + 0.328i)6-s − 2.47i·7-s + (−1.39 + 2.46i)8-s + (2.72 + 1.26i)9-s + (−3.76 − 3.14i)10-s + (−1.61 − 2.79i)11-s + (3.06 − 1.61i)12-s + (−3.34 − 1.35i)13-s + (1.20 + 3.29i)14-s + (1.81 + 5.72i)15-s + (0.653 − 3.94i)16-s + (2.89 + 5.01i)17-s + ⋯ |
L(s) = 1 | + (−0.938 + 0.344i)2-s + (0.976 + 0.215i)3-s + (0.762 − 0.646i)4-s + (0.775 + 1.34i)5-s + (−0.990 + 0.134i)6-s − 0.936i·7-s + (−0.493 + 0.869i)8-s + (0.907 + 0.420i)9-s + (−1.19 − 0.993i)10-s + (−0.487 − 0.843i)11-s + (0.884 − 0.467i)12-s + (−0.926 − 0.375i)13-s + (0.322 + 0.879i)14-s + (0.467 + 1.47i)15-s + (0.163 − 0.986i)16-s + (0.701 + 1.21i)17-s + ⋯ |
Λ(s)=(=(936s/2ΓC(s)L(s)(0.434−0.900i)Λ(2−s)
Λ(s)=(=(936s/2ΓC(s+1/2)L(s)(0.434−0.900i)Λ(1−s)
Degree: |
2 |
Conductor: |
936
= 23⋅32⋅13
|
Sign: |
0.434−0.900i
|
Analytic conductor: |
7.47399 |
Root analytic conductor: |
2.73386 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ936(277,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 936, ( :1/2), 0.434−0.900i)
|
Particular Values
L(1) |
≈ |
1.43133+0.898666i |
L(21) |
≈ |
1.43133+0.898666i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(1.32−0.487i)T |
| 3 | 1+(−1.69−0.373i)T |
| 13 | 1+(3.34+1.35i)T |
good | 5 | 1+(−1.73−3.00i)T+(−2.5+4.33i)T2 |
| 7 | 1+2.47iT−7T2 |
| 11 | 1+(1.61+2.79i)T+(−5.5+9.52i)T2 |
| 17 | 1+(−2.89−5.01i)T+(−8.5+14.7i)T2 |
| 19 | 1+(−2.26−3.92i)T+(−9.5+16.4i)T2 |
| 23 | 1−9.31T+23T2 |
| 29 | 1+(3.40−1.96i)T+(14.5−25.1i)T2 |
| 31 | 1+(−5.59+3.23i)T+(15.5−26.8i)T2 |
| 37 | 1+(1.66−2.87i)T+(−18.5−32.0i)T2 |
| 41 | 1−2.56iT−41T2 |
| 43 | 1−9.40iT−43T2 |
| 47 | 1+(7.93+4.57i)T+(23.5+40.7i)T2 |
| 53 | 1−0.880iT−53T2 |
| 59 | 1+(−4.67+8.09i)T+(−29.5−51.0i)T2 |
| 61 | 1+12.6iT−61T2 |
| 67 | 1+3.65T+67T2 |
| 71 | 1+(3.31−1.91i)T+(35.5−61.4i)T2 |
| 73 | 1+6.92iT−73T2 |
| 79 | 1+(5.76−9.99i)T+(−39.5−68.4i)T2 |
| 83 | 1+(1.07−1.86i)T+(−41.5−71.8i)T2 |
| 89 | 1+(1.67+0.964i)T+(44.5+77.0i)T2 |
| 97 | 1+5.53iT−97T2 |
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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
−9.964704638453795236912296838263, −9.704329892686110152046446505937, −8.378465636182048336616705988597, −7.75691997805107698673856682838, −7.06493655858251159553227894951, −6.24885429073123646576956806240, −5.15264707265935279447055567600, −3.37957626673582434836735811855, −2.79599798944543426730691111469, −1.46478118585463904424441606733,
1.08629804717760564042892262567, 2.26920103125289776549597752972, 2.88232555875016317050562788605, 4.67209280832052748577046586245, 5.40939807609641499522197616645, 7.01040290588439635361953595146, 7.48077040965802014854332265496, 8.681586515020954770600510034464, 9.088987661161376868761418268954, 9.550286548385151835811706696527