  We study the inequities in the distribution of Frobenius elements in Galois
extensions of the rational numbers with Galois groups that are either dihedral
$D_{2n}$ or (generalized) quaternion $\mathbb H_{2n}$ of two-power order. In
the spirit of recent work of Fiorilli and Jouve arXiv:2001.05428, we study,
under natural hypotheses, some families of such extensions, in a horizontal
aspect, where the degree is fixed, and in a vertical aspect, where the degree
goes to infinity. Our main contribution uncovers in families of extensions a
phenomenon, for which Ng gave numerical evidence : real zeros of Artin
L-functions sometimes have a radical influence on the distribution of Frobenius
elements.
