  We provide Fourier expansions of vector-valued eigenfunctions of the
hyperbolic Laplacian that are twist-periodic in a horocycle direction. The
twist may be given by any endomorphism of a finite-dimensional vector space; no
assumptions on invertibility or unitarity are made. Examples of such
eigenfunctions include vector-valued twisted automorphic forms of Fuchsian
groups. We further provide a detailed description of the Fourier coefficients
and explicitly identify each of their constituents, which intimately depend on
the eigenvalues of the twisting endomorphism and the size of its Jordan blocks.
In addition, we determine the growth properties of the Fourier coefficients.
