  A (2+1)D topological ordered phase with U(1) symmetry may or may not have a
symmetric gapped edge state, even if both thermal and electric Hall
conductivity are vanishing. It is recently discovered that there are "higher"
versions of Hall conductivity valid for fermionic fractional quantum Hall (FQH)
states, which obstructs symmetry-preserving gapped edge state beyond thermal
and electric Hall conductivity. In this paper, we show that one can extract
higher Hall conductivity from a single wave function of an FQH state, by
evaluating the expectation value of the "partial rotation" unitary which is a
combination of partial spatial rotation and a U(1) phase rotation. This result
is verified numerically with the fermionic Laughlin state with $\nu=1/3$,
$1/5$, as well as the non-Abelian Moore-Read state. Together with topological
entanglement entropy, we prove that the expectation values of the partial
rotation completely determines if a bosonic/fermionic Abelian topological order
with U(1) symmetry has a symmetry-preserving gappable edge state or not. We
also show that thermal and electric Hall conductivity of Abelian topological
order can be extracted by partial rotations. Even in non-Abelian FQH states,
partial rotation provides the Lieb-Schultz-Mattis type theorem constraining the
low-energy spectrum of the bulk-boundary system. The generalization of higher
Hall conductivity to the case with Lie group symmetry is also presented.
