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This paper presents an analysis of a flat slotted waveguide by the spectral domain method finalized by a complex root search procedure. Matching of fields from bounded and unbounded regions at the common interface is explained and applied to satisfy the boundary conditions in the spectral domain. New theoretical findings are reported, and the dispersion characteristics of particular modes are shown and discussed with regard to their potential application. The different behaviour of the odd and even modes is pointed out. Their affinity to the modes in a standard rectangular waveguide is noted. A hint is given of a modification of the line cross-section resulting in the propagation of a bound mode besides the propagation of the space leaky modes.