We need to Find a non constant map $f:\mathbb{C}^3\to \mathbb{C}$ such that for any three distinct complex numbers $z_1,z_2,z_3$ and any automorphism $\phi$ of $\mathbb{C}$, we have $f(z_1,z_2,z_3)= f(\phi(z_1),\phi(z_2),\phi(z_3))$

Thank you for help and discussion.