# Plotting Triplet Points with Unique Colors for Each Point

I have a set of eigenvalue triplets from some 3x3 matrices and I would like to plot them on the complex plane. My goal is to plot them such that each triplet has a unique color that identifies the points with one another. I believe that Mathematica does this automatically if the points are separated in such a way that

{{x1,x2,x3},{y1,y2,y3},{z1,z2,z3}}


however, I have 125 triplets that I would like to plot -- so it seems Mathematica starts to repeat colors after a handful of them. In theory, I would like to just extend what ComplexListPlot already does, just to a larger number of points.

Below is some sample code where I have provided a list of five eigenvalue triplets, however as mentioned I have 125 in the actual problem. So, my first thought was to attempt to do some sort of color gradient for the points. When I tried this with the below code, it seems to apply the color gradient to the location of the point on the plot instead of the triplet of points.

ComplexListPlot[eigsol, PlotRange -> {{-0.2, 0.2}, {-0.1, 0.1}},
AxesOrigin -> {0, 0}, Frame -> True,
FrameTicks -> {{Automatic, None}, {Automatic, None}},
ColorFunction -> "DarkRainbow"]


This produces the attached result, which is clearly not what I am looking for. So, is there any way to color a large list of triplets in such a way that it is easy to identify the points with one another?

Example Data:

eigsol = {{-0.150398 + 0. I, 0.0607001 + 0.0346517 I,
0.0607001 - 0.0346517 I}, {-0.150368 + 0. I, 0.056947 + 0.0321297 I,
0.056947 - 0.0321297 I}, {-0.150341 + 0. I,
0.0537149 + 0.0294061 I,
0.0537149 - 0.0294061 I}, {-0.150314 + 0. I, 0.0508797 + 0.026467 I,
0.0508797 - 0.026467 I}, {-0.15029 + 0. I, 0.0483519 + 0.0232498 I,
0.0483519 - 0.0232498 I}}


I would welcome anyway to color them uniquely, it doesn't need to be a gradient as I tried (and failed) to do. Thanks so much!

You can use PlotStyle to color each set:
ComplexListPlot[