D(z)-quadruples in the ring Z[−2], for some exceptional cases of z

We present some new formulas for D(z)-quadruples in these remaining cases, involving some congruence conditions modulo 11 on integers a and b. We show the existence of D(z)-quadruple for significant proportion of the remaining three cases. These new formulas then together with previous results on this subject allow us to almost completely characterize elements z of Z[−2] for which a Diophantine quadruple with the property D(z) exists.