sln=expression /.Solve[...];
list= SetAccuracy[N[sln],2]]

GatherBy[SortBy[list, Norm], Norm]

SplitBy[SortBy[list, Norm], Norm]

FullForm[list]=     !(
TagBox[
StyleBox[
RowBox[{"List", "[",
RowBox[{
RowBox[{"List", "[",
RowBox[{"0``2.", ",", "0``2."}], "]"}], ",",
RowBox[{"List", "[",
RowBox[{"0.5`1.6989700043360187", ",",
        "0.86602540378443859658830206171842291951`1.93753063169585"}],
        "]"}], ",",
RowBox[{"List", "[",
RowBox[{"0.5`1.6989700043360187", ",",
RowBox[{"-",
         "0.86602540378443859658830206171842291951`1.93753063169585"}]
}], "]"}], ",",
RowBox[{"List", "[",
RowBox[{
RowBox[{"-", "1.`2."}], ",", "0``2."}], "]"}]}], "]"}],
ShowSpecialCharacters->False,
ShowStringCharacters->True,
NumberMarks->True],
FullForm])

GatherBy[SortBy[a, Norm], Norm] == SplitBy[SortBy[a, Norm], Norm]