A bit unsure if my use/mention of proprietary software might be inappropriate or even frowned upon here. If this is the case, or if this kind of experimental question is not welcome, please let me know and I'll remove it quickly.

I was experimenting on the distribution of eigenvalues of random matrices via the following Mathematica code

dim = 301; decomplex = {z_Complex -> {Re[z], Im[z]}, A_Real -> {A, 0}}; b = Eigenvalues[ SparseArray[{i_, i_} -> 1, {dim, dim}] + Table[RandomReal[{-.9, 1.}], {i, 1, dim}, {j, 1, dim}]] /. decomplex; ListPlot[b, PlotStyle -> PointSize[0.015], AspectRatio -> Automatic]

This simply draws (or should draw) a picture of the complex eigenvalues of a 301 x 301 matrix, with entries uniformly distributed in the real interval [-0.9, 1]. If you try the code you will notice a disk of random eigenvalues, which is expected, plus a single positive eigenvalue at some distance of the disk. Decreasing the lower bound on the entries to -1 makes this phenomenon disappear, while increasing the lower bound makes it more evident.

Question: is this an artifact, a real phenomenon, or maybe even a well known and simple to explain phenomenon?