Let $h>0$ be a positive odd integer. Let $n=4h^2.$

Let $R(t)=r_0+r_1t+ \cdots + r_{n-1}t^{n-1}$

be a polynomial with integer coefficients in $\{-1,1\}$ such that

$R(\omega)$ is a nonzero integer for all complex $\omega \notin ${-1,1} such that

(a)

$$ \omega^n=1 $$

and

(b)

$R(1) = 2h$

Can we deduce that all these integers $R(\omega)$ have the same sign ???