  The usual Riemann-Siegel Z(t) is a real-valued function. We construct a
complex function depending from t and from distance from critical line. It is
linked to Riemann Xi(s) function by the same real scaling factor of the usual
Riemann-Siegel Z(t) on critical line. Errors are not greater than the errors of
Riemann-Siegel Z(t) on the critical line, while this result covers at least the
whole critical strip.
