ζ, ξ and Davenport–Heilbronn painted in the s-plane, in w = 1/(s − ½), and on the Riemann sphere with ½ in front; Hardy's Z(t) along the strut, with the off-line zero at t ≈ 85.7 marked.
open explorer → + +Turn the ball about the ½–∞ strut: s − ½ ↦ eiθ(s − ½). A quarter turn is the Wick rotation (cosh onto cos), a half turn is s ↦ 1 − s, a full turn is q = −1. Three sheets: ξ (even), (s − ½)·ξ (odd, with a zero at ½), and F(u) with u = (s − ½)², turning at double speed.
+ open explorer → +The earlier picture: ζ on a ball of diameter ½ resting at ½, turned by quaternion quarter-turns; 3b1b's grid as the ball's own latitude–longitude, bent by η.