Chebyshev’s bias in dihedral and generalized quaternion Galois groups

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