We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time t and thus periodic in imaginary (Matsubara) frequency i pi n. The formalism requires a generalization of the Dyson equation G (G0, S) and the Baym-Kadanoff-Luttinger-Ward functional for the free energy beta O = G (G). A conformal transformation is used to analytically continue the periodized Matsubara Green's function to real frequencies in a way that conserves the discontinuity at t = 0 of the corresponding real-time Green's function. This allows numerical Green's function calculations of very high precision and it appears to give a well controlled convergent approximation in the t discretization. The formalism is tested on dynamical mean field theory calculations of the paramagnetic Hubbard model.