Consider the complex numbers $z_1, z_2, z_3$ and $z_4$ in the following picture,
with the various angles between the line segments marked: Here, we have that $|z_1| = |z_3| = 3$ and $|z_2| = |z_4| = 2$. Then calculate the ordered list \[ z_1^6, z_2^6, z_3^6, z_4^6.\]Enter in your answers in order, in rectangular form.
