Coherent numerical shadow of a matrix $A$ is defined as a probability distribution $P_A(z)$ on the complex plane, supported on the coherent numerical range $W^\mathrm{ent}(A)$. $P_A(z) := \int_{\Omega} {\rm d} \mu(\psi) \delta\Bigl( z-\langle \psi|A|\psi\rangle\Bigr),$ where $\mu(\psi)$ denotes the unique unitarily invariant (Fubini-Study) measure on the set of $SU(2)$ coherent states.