  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 the
RO(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 these
calculations are used elsewhere to compute the algebraic K-theory of certain
Z-algebras.
