  In this article, we study microscopic properties of a two-dimensional
eigenvalue ensemble near a conical singularity arising from insertion of a
point charge in the bulk of the support of eigenvalues. In particular, we
characterize all rotationally symmetric scaling limits ('Mittag-Leffler
fields') and obtain universality of them when the underlying potential is
algebraic. Applications include a result on the asymptotic distribution of
$\log|p_n(\zeta)|$ where $p_n$ is the characteristic polynomial of an $n$:th
order random normal matrix.
