  We consider the two-dimensional $\mathfrak{sl}_n$ quantum Toda field theory
with an imaginary background charge. This conformal field theory has a higher
spin symmetry ($W_n$ algebra), a central charge $c \leq n-1$ and a continuous
spectrum. Using the conformal bootstrap, we compute structure constants
involving two arbitrary scalar fields and a semi-degenerate field of Wyllard
type. The solution obtained is not the analytic continuation of the usual Toda
three-point function. Non-scalar primary fields and their three-point functions
are also discussed. Non-scalar primary fields are classified by conjugacy
classes of the permutation group $\mathfrak{S}_n$, and their structure
constants are computed explicitly, up to an overall factor.
