Moduli and Arguments of U and P at Trivial and Nontrivial Zeros

This paper computes the moduli and arguments of the U-space and P-space values at the trivial and nontrivial zeros of the Riemann zeta function. For nontrivial zeros s = 1/2 + iγ, numerical values of |u|, arg(u), |p|, and arg(p) are presented. For trivial zeros s = -2, -4, -6, ..., the corresponding values are also given. All data are presented in tables, and the U-P duality relation is verified at the listed zeros. Based on the numerical results, the necessary and sufficient condition for u to be real is derived, along with several observations on the behavior of U and P at the listed zeros. Numerical observations on the factors in the analytic continuation formula are also provided. Correction: The original version incorrectly used the W_{-1} branch for the P-space fixed point. This corrected version uses the principal branch W_0, which corresponds to the dynamically accessible attractor. All numerical tables for the P-space and U-P duality have been recomputed accordingly. Key changes: at nontrivial zeros, |p| < 1 (previously > 1) and arg(p) = 0° (previously ≈ -150°); at trivial zero s=-2, p is complex with |p| ≈ 2.144; U-P duality gives |p/u| < 1 (previously > 1).