We perform a method-of-moments (MoM) analysis of a circular array of cylindrical dipoles. The array is known from earlier theoretical and experimental studies to possess very narrow resonances. The earlier theoretical studies were carried out using the "two-term theory." The present paper is a direct continuation of a recent work showing that the problem possesses unique and particular difficulties. The main difficulties are overcome herein using a set of improved kernels in the usual Hallén-type integral equations (these kernels had been developed in previous works, and were successfully incorporated into the aforementioned two-term theory analyses). We make a detailed comparison of our MoM results to two-term theory results and, also, to the earlier experimental results.