Zeros of even and odd period polynomials

Let $f\in S_k({\mathrm{\Gamma }}_0(N))$ be a newform, and let $r_f^{\pm }(X)$ denote its corresponding even and odd period polynomials. For sufficiently large level and weight, we show that the zeros of $r_f^{\pm }(X)$ all lie on the circle $\mathrm{\mid }X\mathrm{\mid }=\frac{1}{\sqrt{N}}$.