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conditions 32 conformal symmetries corresponding and lower corresponding expressions determinant for consideration direct periodic conformal e2 are primitive e2Xe ei(ei eie2 eliminate X(-i equations 29 expressed in X's expressions for Kt factored into transformations form kn form of 79 functional equation Furthermore given transformation independent irreducible period Kt and Kt-i left member lower orders members of 25 method of Section necessary condition observe order kn order t/2 orders of X periodic function periodic reverse conformal periodic transformations polynomial in lower polynomial in X's power series primitive root Qt-i rational integral functions relations 12 resulting from 93 reverse conformal transformation root of unity satisfied series in xi Similarly solution Suppose taken arbitrarily takes the form terms of X's Theorem transformation F(z transformations of order transformations of period uniquely vanish identically variables write X's and n's X's of corresponding X's of lower X's of order yield