  The analytic moduli of equisingular plane branches has the semimodule of
differential values as the most relevant system of discrete invariants.
Focusing in the case of cusps, the minimal system of generators of this
semimodule is reached by the differential values attached to the differential
$1$-forms of the so-called standard bases. We can complete a standard basis to
an enlarged one by adding a last differential $1$-form that has the considered
cusp as invariant branch and the ``correct'' divisorial order. The elements of
such enlarged standard bases have the ``cuspidal'' divisor as a ``totally
dicritical divisor'' and hence they define packages of plane branches that are
equisingular to the initial one. These are the analytic semiroots. In this
paper we prove that the enlarged standard bases are well structured from this
geometrical and foliated viewpoint, in the sense that the semimodules of
differential values of the branches in the dicritical packages are described
just by a truncation of the list of generators of the initial semimodule at the
corresponding differential value. In particular they have all the same
semimodule of differential values.
