Riemann Zeta Zeros — Critical Line Spiral

Riemann Hypothesis (1859, unproven): all non-trivial zeros of ζ(s) lie on Re(s) = ½.

First zeros (imaginary parts):

t₁ ≈ 14.135

t₂ ≈ 21.022

t₃ ≈ 25.011

t₄ ≈ 30.425

t₅ ≈ 32.935

Computed via Euler-Maclaurin sum: ζ(s) ≈ Σₙ n^{-s} with corrections. The spiral winds around the origin, touching it exactly at each zero.

The functional equation: ζ(s) = 2^s π^{s-1} sin(πs/2) Γ(1-s) ζ(1-s) forces zeros to be symmetric about Re(s)=½.