  We apply the coverings in the motivic Milnor fibre construction of Denef and
Loeser to compute the motivic Euler characteristic of Ayoub's nearby cycles,
for a scheme over a discrete valuation ring of characteristic zero whose
special fibre has isolated quasi-homogeneous singularities resolved by a
blow-up. This allows to compare the local picture at the singularities with the
global conductor formula for hypersurfaces developed by Levine, Pepin Lehalleur
and Srinivas, revealing that the formula is local in nature, thus extending it
to the more general setting considered in this paper.
