  Let $\mathcal{M}_g^0(q)$ denote the isogeny class (if it is unique) of
$g$-dimensional abelian varieties defined over $\mathbb{F}_q$ with maximal
number of rational points among those with endomorphism algebra being a field.
We describe a polynomial $h_g(t,X)$ such that for every even power $q$ of a
prime and verifying mild conditions, $h_g(t,\sqrt{q})$ is the Weil polynomial
of $\mathcal{M}_g^0(q)$. It turns out that in this case, $\mathcal{M}_g^0(q)$
is ordinary and cyclic outside the primes dividing an integer $N_g$ that only
depends on $g$. We also give explicitly $h_3(t,X)$ and prove that
$\mathcal{M}_3^0(q)$ is ordinary and cyclic.
