Kellendonk J. Exact spectral values for discrete Quantum Pendulum-Integrals (333K, postscript, compressed and uuencoded) ABSTRACT. For specific choice of parameters the spectrum of the discrete Quantum Pendulum-Integral contains the eigenvalues of a finite matrix which depends analytically on the flux. Under natural continuity assumptions these eigenvalues include the spectral values which may be obtained by the algebraic Bethe-ansatz.