  Satellites (topological powers) of the famous figure-eight orbit are special
periodic solutions of the planar three-body problem. In this paper we use a
modified Newton's method based on the Continuous analog of Newton's method and
high precision arithmetic for a purposeful numerical search of new satellites
of the figure-eight orbit. Over 700 new satellites are found, including 76 new
linearly stable ones. 7 of the newly found linearly stable satellites are
choreographies. The linear stability is checked by a high precision computing
of the eigenvalues of the monodromy matrices. The initial conditions of all
found solutions are given with 150 correct decimal digits.
