L(s) = 1 | + (−1.5 − 0.866i)5-s + 7-s + (−0.5 + 0.866i)9-s + (1.5 − 0.866i)17-s + (0.5 − 0.866i)19-s + (−1.5 − 0.866i)23-s + (1 + 1.73i)25-s + (−1.5 − 0.866i)35-s − 1.73i·43-s + (1.5 − 0.866i)45-s + (1 − 1.73i)47-s + 49-s + (−0.5 + 0.866i)63-s + (−0.499 − 0.866i)81-s − 83-s + ⋯ |
L(s) = 1 | + (−1.5 − 0.866i)5-s + 7-s + (−0.5 + 0.866i)9-s + (1.5 − 0.866i)17-s + (0.5 − 0.866i)19-s + (−1.5 − 0.866i)23-s + (1 + 1.73i)25-s + (−1.5 − 0.866i)35-s − 1.73i·43-s + (1.5 − 0.866i)45-s + (1 − 1.73i)47-s + 49-s + (−0.5 + 0.866i)63-s + (−0.499 − 0.866i)81-s − 83-s + ⋯ |
Λ(s)=(=(2128s/2ΓC(s)L(s)(0.386+0.922i)Λ(1−s)
Λ(s)=(=(2128s/2ΓC(s)L(s)(0.386+0.922i)Λ(1−s)
Degree: |
2 |
Conductor: |
2128
= 24⋅7⋅19
|
Sign: |
0.386+0.922i
|
Analytic conductor: |
1.06201 |
Root analytic conductor: |
1.03053 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2128(607,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 2128, ( :0), 0.386+0.922i)
|
Particular Values
L(21) |
≈ |
0.9013283135 |
L(21) |
≈ |
0.9013283135 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 7 | 1−T |
| 19 | 1+(−0.5+0.866i)T |
good | 3 | 1+(0.5−0.866i)T2 |
| 5 | 1+(1.5+0.866i)T+(0.5+0.866i)T2 |
| 11 | 1+(0.5−0.866i)T2 |
| 13 | 1+T2 |
| 17 | 1+(−1.5+0.866i)T+(0.5−0.866i)T2 |
| 23 | 1+(1.5+0.866i)T+(0.5+0.866i)T2 |
| 29 | 1−T2 |
| 31 | 1+(0.5−0.866i)T2 |
| 37 | 1+(0.5+0.866i)T2 |
| 41 | 1+T2 |
| 43 | 1+1.73iT−T2 |
| 47 | 1+(−1+1.73i)T+(−0.5−0.866i)T2 |
| 53 | 1+(0.5−0.866i)T2 |
| 59 | 1+(0.5−0.866i)T2 |
| 61 | 1+(0.5+0.866i)T2 |
| 67 | 1+(−0.5+0.866i)T2 |
| 71 | 1+T2 |
| 73 | 1+(0.5−0.866i)T2 |
| 79 | 1+(−0.5−0.866i)T2 |
| 83 | 1+T+T2 |
| 89 | 1+(−0.5−0.866i)T2 |
| 97 | 1+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
−8.659330615228117947383402275993, −8.470507690608842951038007020025, −7.57033008933390230494106598631, −7.30165757746488259783406120048, −5.62415852236648704299354914853, −5.05820642195303694774687866612, −4.37513906216833030932583372844, −3.46851343277349167427868613284, −2.21075619522109966132077998261, −0.72206824961062071798645446657,
1.35089012953080285445316301409, 2.95540018165320772393406118273, 3.69695136520859988420538150719, 4.27568027461664598340555195316, 5.61091398054100387808665124673, 6.22611235115667258567388439865, 7.40471070474306594963870286449, 7.911992987174439869646672830492, 8.246857951311914064867923837188, 9.447518534286920168368871786696