  All known solutions of the Dirac equation describing states of electrons
endowed with angular momentum are very far from our notion of the electron as a
spinning charged bullet because they are not localized in the direction of
propagation. We present here analytic exact solutions, eigenstates of the total
angular momentum component $M_z$, that come very close to this notion. These
new solutions of the Dirac equation have also intricate topological properties
similar to the hopfion solutions of the Maxwell equations.
