An explicit hybrid estimate for $L(1\mathrm{/}2+it,\chi )$

An explicit hybrid estimate for $L(1\mathrm{/}2+it,\chi )$ is derived, where $\chi$ is a Dirichlet character modulo $q$. The estimate applies when $t$ is bounded away from zero, and is most effective when $q$ is powerfull, yielding an explicit Weyl bound in this case. The estimate takes a particularly simple form if $q$ is a sixth power. Several hybrid lemmas of van der Corput–Weyl type are presented.