  The central charge $C_T$ is computed for scalar and Dirac fields propagating
according to GJMS-type kinetic operators acting on odd $d$-dimensional spheres
in the presence of a spherical monodromy. The relation of $C_T$ to the
derivatives of the free energy on the conically deformed sphere via the
Perlmutter factor leads to a numerical quadrature. The variation of $C_T$ with
the monodromy flux, $\delta$, displays sign changes, exactly as in even
dimensions. Closed forms for $C_T$ are derived when $\delta$ equals 0 or 1/2
with the derivative order either even or odd and shown to agree with existing,
even $d$ expressions. The infinite $d$ limits are also derived in these special
cases.
