  We define a morphic subshift as a subshift generated by the image of a
substitution subshift by another substitution. In other words, it is the
subshift associated with a ultimately periodic directive sequence. We present
an efficient algorithm for computing eigenvalues of morphic subshifts using
coboundaries. We show that continuous eigenvalues of S-adic subshifts for
primitive directive sequences are always associated with some coboundary. For
morphic subshifts, we provide a characterization of the dimension of the
Q-vector space generated by eigenvalues. Additionally, if the substitutions are
unimodular and without coboundaries, we give a necessary and sufficient
condition for weak mixing of the subshift.
