L(s) = 1 | + (0.616 + 1.89i)3-s + (0.139 − 0.430i)7-s + (−0.797 + 0.579i)9-s + (1.01 + 3.15i)11-s + (5.32 − 3.87i)13-s + (−0.959 − 0.696i)17-s + (0.575 + 1.77i)19-s + 0.903·21-s + 5.37·23-s + (3.25 + 2.36i)27-s + (−2.35 + 7.25i)29-s + (−2.83 + 2.05i)31-s + (−5.36 + 3.87i)33-s + (1.78 − 5.50i)37-s + (10.6 + 7.72i)39-s + ⋯ |
L(s) = 1 | + (0.356 + 1.09i)3-s + (0.0528 − 0.162i)7-s + (−0.265 + 0.193i)9-s + (0.306 + 0.951i)11-s + (1.47 − 1.07i)13-s + (−0.232 − 0.168i)17-s + (0.132 + 0.406i)19-s + 0.197·21-s + 1.11·23-s + (0.626 + 0.454i)27-s + (−0.437 + 1.34i)29-s + (−0.508 + 0.369i)31-s + (−0.934 + 0.675i)33-s + (0.294 − 0.904i)37-s + (1.70 + 1.23i)39-s + ⋯ |
Λ(s)=(=(1100s/2ΓC(s)L(s)(0.333−0.942i)Λ(2−s)
Λ(s)=(=(1100s/2ΓC(s+1/2)L(s)(0.333−0.942i)Λ(1−s)
Degree: |
2 |
Conductor: |
1100
= 22⋅52⋅11
|
Sign: |
0.333−0.942i
|
Analytic conductor: |
8.78354 |
Root analytic conductor: |
2.96370 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1100(201,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1100, ( :1/2), 0.333−0.942i)
|
Particular Values
L(1) |
≈ |
2.027484937 |
L(21) |
≈ |
2.027484937 |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1 |
| 11 | 1+(−1.01−3.15i)T |
good | 3 | 1+(−0.616−1.89i)T+(−2.42+1.76i)T2 |
| 7 | 1+(−0.139+0.430i)T+(−5.66−4.11i)T2 |
| 13 | 1+(−5.32+3.87i)T+(4.01−12.3i)T2 |
| 17 | 1+(0.959+0.696i)T+(5.25+16.1i)T2 |
| 19 | 1+(−0.575−1.77i)T+(−15.3+11.1i)T2 |
| 23 | 1−5.37T+23T2 |
| 29 | 1+(2.35−7.25i)T+(−23.4−17.0i)T2 |
| 31 | 1+(2.83−2.05i)T+(9.57−29.4i)T2 |
| 37 | 1+(−1.78+5.50i)T+(−29.9−21.7i)T2 |
| 41 | 1+(−0.103−0.317i)T+(−33.1+24.0i)T2 |
| 43 | 1+10.9T+43T2 |
| 47 | 1+(−1.98−6.09i)T+(−38.0+27.6i)T2 |
| 53 | 1+(−1.85+1.34i)T+(16.3−50.4i)T2 |
| 59 | 1+(−0.449+1.38i)T+(−47.7−34.6i)T2 |
| 61 | 1+(7.22+5.25i)T+(18.8+58.0i)T2 |
| 67 | 1+4.37T+67T2 |
| 71 | 1+(−8.91−6.47i)T+(21.9+67.5i)T2 |
| 73 | 1+(−1.09+3.36i)T+(−59.0−42.9i)T2 |
| 79 | 1+(−2.46+1.79i)T+(24.4−75.1i)T2 |
| 83 | 1+(7.95+5.78i)T+(25.6+78.9i)T2 |
| 89 | 1+12.7T+89T2 |
| 97 | 1+(−11.2+8.14i)T+(29.9−92.2i)T2 |
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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
−10.03618256127712093917466993124, −9.160259433824650837182874010031, −8.678504594239662058413322518028, −7.58505125601291003457702591486, −6.71176678924710145473234029711, −5.55590767046173357915791620526, −4.72292847622825239641666668641, −3.77094475484248375579283793374, −3.10733758403803069709267989494, −1.39739620367811548993509045386,
1.03548185214962837627981561849, 2.05948770301400677078185571941, 3.28937156521283294639204650881, 4.32136561355290715626797695441, 5.68673039256893310767262011345, 6.51070959804564568603951208413, 7.06812684004826972520958144585, 8.198100081661643437888171141825, 8.651394545916483888951272032762, 9.434270840305318780711532454578