  Given arbitrary integers $k$ and $d$ with $0 \leq 2k \leq d$, we construct a
Gorenstein Fano polytope $\Pc \subset \RR^d$ of dimension $d$ such that (i) its
Ehrhart polynomial $i(\Pc, n)$ possesses $d$ distinct roots; (ii) $i(\Pc, n)$
possesses exactly $2k$ imaginary roots; (iii) $i(\Pc, n)$ possesses exactly $d
- 2k$ real roots; (iv) the real part of each of the imaginary roots is equal to
$- 1 / 2$; (v) all of the real roots belong to the open interval $(-1, 0)$.
