  Rotating waves (RW) bifurcating from the axisymmetric basic magnetized
spherical Couette (MSC) flow are computed by means of Newton-Krylov
continuation techniques for periodic orbits. In addition, their stability is
analysed in the framework of Floquet theory. The inner sphere rotates whilst
the outer is kept at rest and the fluid is subjected to an axial magnetic
field. For a moderate Reynolds number ${\rm Re}=10^3$ (measuring inner
rotation) the effect of increasing the magnetic field strength (measured by the
Hartmann number ${\rm Ha}$) is addressed in the range ${\rm Ha}\in(0,80)$
corresponding to the working conditions of the HEDGEHOG experiment at
Helmholtz-Zentrum Dresden-Rossendorf. The study reveals several regions of
multistability of waves with azimuthal wave number $m=2,3,4$, and several
transitions to quasiperiodic flows, i.e modulated rotating waves (MRW). These
nonlinear flows can be classified as the three different instabilities of the
radial jet, the return flow and the shear-layer, as found in previous studies.
These two flows are continuously linked, and part of the same branch, as the
magnetic forcing is increased. Midway between the two instabilities, at a
certain critical ${\rm Ha}$, the nonaxisymmetric component of the flow is
maximum.
