The characteristic polynomials of abelian varieties of dimensions three and four over finite fields (Q1326979)

Let \(\mathbb{F}_ q\) be a finite field and let \(A\) be an abelian variety over \(\mathbb{F}_ q\) with Frobenius endomorphism \(\pi_ a\). The characteristic polynomial \(f_ A(t)\) of \(\pi_ a\) is a polynomial of degree \(2\cdot\dim A\) with integer coefficients. The author determines all the possible \(f_ A(t)\) of degree 6 and 8 for fixed \(\mathbb{F}_ q\).