  We investigate two-dimensional canonical systems $y'=zJHy$ on an interval,
with positive semi-definite Hamiltonian $H$, such that limit circle case
prevails at the left endpoint and limit point case at the right . Let $q_H$ be
the Weyl coefficient of the system. We prove a formula that determines the
imaginary part of $q_H$ along the imaginary axis up to multiplicative
constants, which are independent of $H$. Using classical Abelian-Tauberian
theorems, we deduce characterizations of spectral properties such as
integrability of a given comparison function w.r.t. the spectral measure
$\mu_H$, and boundedness of the distribution function of $\mu_H$ relative to a
given comparison function. We study in depth Hamiltonians for which $\arg
q_H(ir)$ approaches $0$ or $\pi$ (at least on a subsequence). We show that
tangential behavior of $q_H(ir)$ imposes a substantial restriction on the
growth of $|q_H(ir)|$. An example is provided where $\arg q_H(ir)$ heavily
oscillates. Our results in this context are interesting also from a function
theoretic point of view.

Spectral Theory