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We improve the estimation of the distribution of the nontrivial zeros of Riemann zeta function ζ(σ+it) for sufficiently large t, which is based on an exact calculation of some special logarithmic integrals of nonvanishing ζ(σ+it) along well-chosen contours. A special and single-valued coordinate transformation s=τ(z) is chosen as the inverse of z=χ(s), and the functional equation ζ(s) = χ(s)ζ(1-s) is simplified as G(z) = z G_-(1/z) in the z coordinate, where G(z)=ζ(s)=ζ∘τ(z) and G_- is thearXiv:2005.04568v2 fatcat:6rkc5hbpmrduvjomok6gcajss4