  We consider generic 2 x 2 singular Liouville systems on a smooth bounded
domain in the plane having some symmetry with respect to the origin. We
construct a family of solutions to which blow-up at the origin and whose local
mass at the origin is a given quantity depending on the parameters of the
system. We can get either finitely many possible blow-up values of the local
mass or infinitely many. The blow-up values are produced using an explicit
formula which involves Chebyshev polynomials.
