English: The Riemann zeta function ζ(s) is plotted for s values along the critical line Re(s) = 1/2.

Real values are on the horizontal axis and imaginary values are on the vertical axis.
Re(ζ(1/2 + it), Im(ζ(1/2 + it) is plotted with t ranging between −30 and 30.
The curve starts for t = -30 at ζ(1/2 - 30 i) = -0.12 + 0.58 i, and ends symmetrically below the starting point at ζ(1/2 + 30 i) = -0.12 - 0.58 i.
Six zeros of ζ(s) are found along the trajectory when the origin (0,0) is traversed, corresponding to imaginary parts of s Im(s) = ±14.135, ±21.022 and ±25.011.

Values for ζ can be found by calculating, e.g., zeta(1/2 - 30 i) using https://www.wolframalpha.com/input of Wolframalpha computational intelligence. Consulted 2 October 2022.