In this work, the values of the parameters of the eigenstate lattice network are obtained by using only analytical means. The procedure is applied to a simple structure, consisting of a bi-periodic surface made of a slotted metallic plane. The slot is very narrow and is slightly rotated. The analytical values are obtained by using a multi-mode expansion approach that only requires information about the normalized field in the slot. The equivalent circuit and the procedure are simple and provide physical insight into the structure. Very good agreement is found for analytical values and simulated ones.