The lowest degree $0,1$-polynomial divisible by cyclotomic polynomial

Let $n$ be an even positive integer with at most three distinct prime factors and let ${\text{ze}}_n$ be a primitive $n$-th root of unity. In this study, we made an attempt to find the lowest-degree $0,1$-polynomial $f(x)\in \text{Q}[x]$ having at least three terms such that $f({\text{ze}}_n)$ is a minimal vanishing sum of the $n$-th roots of unity.