  We have studied some properties of the special Gram points of the Riemann
zeta function which lie on contour lines ${\bf Im}(\zeta ( s )) = 0$ which do
not contain zeroes of $\zeta ( s )$. We find that certain functions of these
points, which all lie on the critical line ${\bf Re}( s ) = 1/2$, are
correlated in remarkable and unexpected ways. We have data up to a height of $t
= 10^4$, where $s = \sigma + it$.
