Left arg(ζ) mod 2π, right abs(ζ) mod 1
(-reflected for ease of comparison)
 
Showing the pole s = 1, nine trivial zeroes and the first five zeroes on the critical line.
 
Read -π (purple to yellow) 0 (blue to olive) π. A full spectrum matches 15^2 gain in height. So the size of abs(ζ) is nearly 15^13 (or 10^15) in the upper corner already.

Signed magnitude mod 1:
left im(ζ), right re(ζ) (-reflected)
 
Negative values are coloured red-orange, positive values blue-green.

ζ-transformation of line re(s) = 1/2, with im(s) between 0 and 35.
 
Compare with the critical strip in the above diagrams, just next to the imaginary axis.

Complex log of the secant transformation associated with zeta (Miró blobs)
 
Of the three zeroes shown, the upper two are regular (i.e., sources), while the other is the first exceptional one: a sink.

Same mapping: signed magnitude

Phase portrait of the same region for comparison with both previous diagrams.