CHAMP is a computer algebra package based on Magma for performing basic computations in rational Cherednik algebras at arbitrary parameters and in Verma modules for restricted rational Cherednik algebras. Part of this package is a new Las Vegas algorithm for computing the head and the constituents of a local module in characteristic zero. We used this method to compute the Calogero–Moser families, the decomposition matrices of the Verma modules, and the structure of the simple modules as graded G-modules for generic restricted rational Cherednik algebras for around half of the exceptional complex reflection groups.