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We give an algorithm for calculating the RO(S^1)-graded TR-groups of F_p,completing the calculation started by the second author. We also calculate theRO(S^1)-graded TR-groups of Z with mod p coefficients and of the Adams summand\ell of connective complex K-theory with V(1)-coefficients. Some of thesecalculations are used elsewhere to compute the algebraic K-theory of certainZ-algebras.

RO(S^1)-graded TR-groups of F_p, Z and \ell