L(s) = 1 | + (1.27 + 1.27i)5-s + 0.158i·7-s + (3.79 + 3.79i)11-s + (4.21 − 4.21i)13-s − 3.05·17-s + (−2.15 + 2.15i)19-s + 2.82i·23-s − 1.76i·25-s + (2.09 − 2.09i)29-s − 4.15·31-s + (−0.202 + 0.202i)35-s + (5.98 + 5.98i)37-s + 2.60i·41-s + (5.75 + 5.75i)43-s − 2.82·47-s + ⋯ |
L(s) = 1 | + (0.568 + 0.568i)5-s + 0.0600i·7-s + (1.14 + 1.14i)11-s + (1.16 − 1.16i)13-s − 0.740·17-s + (−0.495 + 0.495i)19-s + 0.589i·23-s − 0.353i·25-s + (0.389 − 0.389i)29-s − 0.746·31-s + (−0.0341 + 0.0341i)35-s + (0.984 + 0.984i)37-s + 0.406i·41-s + (0.877 + 0.877i)43-s − 0.412·47-s + ⋯ |
Λ(s)=(=(1152s/2ΓC(s)L(s)(0.757−0.653i)Λ(2−s)
Λ(s)=(=(1152s/2ΓC(s+1/2)L(s)(0.757−0.653i)Λ(1−s)
Degree: |
2 |
Conductor: |
1152
= 27⋅32
|
Sign: |
0.757−0.653i
|
Analytic conductor: |
9.19876 |
Root analytic conductor: |
3.03294 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1152(865,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1152, ( :1/2), 0.757−0.653i)
|
Particular Values
L(1) |
≈ |
1.954019831 |
L(21) |
≈ |
1.954019831 |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1 |
good | 5 | 1+(−1.27−1.27i)T+5iT2 |
| 7 | 1−0.158iT−7T2 |
| 11 | 1+(−3.79−3.79i)T+11iT2 |
| 13 | 1+(−4.21+4.21i)T−13iT2 |
| 17 | 1+3.05T+17T2 |
| 19 | 1+(2.15−2.15i)T−19iT2 |
| 23 | 1−2.82iT−23T2 |
| 29 | 1+(−2.09+2.09i)T−29iT2 |
| 31 | 1+4.15T+31T2 |
| 37 | 1+(−5.98−5.98i)T+37iT2 |
| 41 | 1−2.60iT−41T2 |
| 43 | 1+(−5.75−5.75i)T+43iT2 |
| 47 | 1+2.82T+47T2 |
| 53 | 1+(−3.55−3.55i)T+53iT2 |
| 59 | 1+(4+4i)T+59iT2 |
| 61 | 1+(3.66−3.66i)T−61iT2 |
| 67 | 1+(−0.767+0.767i)T−67iT2 |
| 71 | 1−0.317iT−71T2 |
| 73 | 1+1.33iT−73T2 |
| 79 | 1−9.69T+79T2 |
| 83 | 1+(0.115−0.115i)T−83iT2 |
| 89 | 1+14.3iT−89T2 |
| 97 | 1+0.571T+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
−9.908061140295156459774469313942, −9.181591890857744269363114246181, −8.273827107360188888101989604245, −7.36263027631526199523235205070, −6.34742267793101433786463625577, −5.98918906986356418278015658041, −4.62712912396091530873137679414, −3.72819861477195252743292953035, −2.54678918931375897201650328347, −1.38580784535627046025192429030,
0.997252152018289728472507164930, 2.14163664663664782010807357065, 3.67880576484288635016962254215, 4.36196111504773499221150372404, 5.60669306153293526584838384314, 6.32604237750801891687825335406, 6.99303375124325256222142254107, 8.399888304026330515510494738994, 9.094699989510457135688956135952, 9.219172782856626451711334234547