  Hall viscosity, also known as the Lorentz shear modulus, has been proposed as
a topological property of a quantum Hall fluid. Using a recent formulation of
the composite fermion theory on the torus, we evaluate the Hall viscosities for
a large number of fractional quantum Hall states at filling factors of the form
$\nu=n/(2pn\pm 1)$, where $n$ and $p$ are integers, from the explicit wave
functions for these states. The calculated Hall viscosities $\eta^A$ agree with
the expression $\eta^A=(\hbar/4) {\cal S}\rho$, where $\rho$ is the density and
${\cal S}=2p\pm n$ is the "shift" in the spherical geometry. We discuss the
role of modular invariance of the wave functions, of the center-of-mass
momentum, and also of the lowest-Landau-level projection. Finally, we show that
the Hall viscosity for $\nu={n\over 2pn+1}$ may be derived analytically from
the microscopic wave functions, provided that the overall normalization factor
satisfies a certain behavior in the thermodynamic limit. This derivation should
be applicable to a class of states in the parton construction, which are
products of integer quantum Hall states with magnetic fields pointing in the
same direction.
