  In this paper we compute the minimal polynomials of Ramanujan values
$27t_n^{-12}$ for discriminants D\equiv5mod24. Our method is based on Shimura
Reciprocity Law as which was made computationally explicit by A.Gee and P.
Stevenhagen. However, since these Ramanujan values are not class invariants, we
present a modification of the above method which can be applied on modular
functions that do not necessarily yield class invariants.
