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Properly dimensioned circular arrays of cylindrical dipoles are known to possess very narrow resonances. It is also known that analyzing such arrays using moment methods presents unique and particular difficulties, as application of such methods to the usual Hallen-type integral equations can yield meaningless results from which no further conclusions should be drawn. In the present paper, we apply moment methods to properly modified integral equations and obtain much more reliable results. We also observe that certain difficulties still remain, and discuss them in detail.