  We present an approximate converse theorem which measures how close a given
set of irreducible admissible unramified unitary generic local representations
of GL(n) is to a genuine cuspidal representation. To get a formula for the
measure, we introduce a quasi-Maass form on the generalized upper half plane
for a given set of local representations. We also construct an annihilating
operator which enables us to write down an explicit cuspidal automorphic
function.
