  The differential equations governing the late-time ring-down of the
perturbations of the Kerr metric, the Teukolsky Angular Equation and the
Teukolsky Radial Equation, can be solved analytically in terms of confluent
Heun functions. In this article, for the first time, we use those exact
solutions to obtain the electromagnetic (EM) quasinormal spectra of the Kerr
black hole . This is done by imposing the appropriate boundary conditions on
the solutions and solving numerically the so-obtained two-dimensional
transcendental system.
  The EM QNM spectra are compared with already published results, evaluated
through the continued fraction method. The comparison shows that the modes with
lower $n$ coincide for both methods, while those with higher $n$ may
demonstrate significant deviations. To study those deviations, we employ the
$\epsilon$-method which introduces small variations in the argument of the
complex radial variable. Using the $\epsilon$-method one can move in the
complex $r-$plane the branch cuts of the solutions of the radial equation and
examine the dependence of the spectrum on their position.
  For different values of $\epsilon$, one can obtain both the frequencies
evaluated through the well-established continued fraction method or somewhat
different spectra calculated here for the first time. This result raises the
question what spectrum should be compared with the observational data and why.
This choice should come from better understanding of the physics of the problem
and it may become particularly important considering the recent interest in the
spectra of the electromagnetic counterparts of events producing gravitational
waves.
