The spectrum of the Orlik-Terao algebra, also called the reciprocal plane, is useful in studying various properties of the associated hyperplane arrangement. We begin this discussion by trying to compute the Poincar\'e polynomial of the intersection cohomology on the reciprocal plane. This story closely parallels the classical Kazhdan-Lusztig polynomials in the study of Hecke algebras for Coxeter groups. It turns out that these polynomials are combinatorial and can be computed via some recursion. We will discuss some geometry of the reciprocal plane which build this recursion. Then the recursion can be used to compute many cases. In particular, the case of uniform matroids of rank n with n+1 elements gives rise to the so called symmetric reciprocal plane and has connections to counting dissections of polygons and some representation theory.