  We introduce two explicit examples of polynomials orthogonal on the unit
circle. Moments and the reflection coefficients are expressed in terms of
Jacobi elliptic functions. We find explicit expression for these polynomials in
terms of a new type of elliptic hypergeometric function. We show that obtained
polynomials are orthogonal on the unit circle with respect to a dense point
meausure, i.e. the spectrum consists from infinite number points of increase
which are dense on the unit circle. We construct also corresponding explicit
systems of polynomials orthogonal on the interval of the real axis with respect
to a dense point measure. They can be considered as an elliptic generalization
of the Askey-Wilson polynomials of a special type.
