Interference yields an integer signal
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The samples are exact integers, even though the individual waves have complex amplitudes. Pairing conjugates gives
\[
c_{12}(n)=2\cos(\pi n/6)+2\cos(5\pi n/6).
\]
\[
(c_{12}(0),\ldots,c_{12}(11))=(4,0,2,0,-2,0,-4,0,-2,0,2,0).
\]
The antisymmetry \(c_{12}(n+6)=-c_{12}(n)\) will later expose why erasing the signs changes the recovered arithmetic.