Numerical range and spectrum of random Ginibre matrix

Let $G$ be a matrix of $ \mathrm{dim}\ G=1000 $ drawn from Ginibre ensemble and let $ G_d $ be a family of matrices such that $ G_d=P_d(T) $, where $ T $ is upper triangular matrix obtained by Schur decomposition of $ G $ such that $ G=UTU^\dagger $. $ P_d $ are orthogonal projections $P_d(\cdot)=\sum_{i=1}^d \ketbra{i}{l_i} \cdot \ketbra{l_i}{i}$, where $l_i$ is a sequence of integers from $ 1 $ to $ 1000 $. $ G_d $ are normalized so $\tr G_d G_d^\dagger=\mathrm{dim} G_d$.

In the figure red dots indicate spectrum of $ G_d $, gray area is numerical range $ W(G_d) $, green circle has radius $ 1 $ outer circle has radius $ \sqrt{2} $.