(Python)
from itertools import product
from sympy.matrices import Matrix
def a(n):
eigset = set()
for e in product([0, 1, 2], repeat=n*n):
if n > 1 and e[1] > e[n]: continue
M = Matrix([list(e[n*r:n*(r+1)]) for r in range(n)])
eigset |= set(eig for eig in M.eigenvals().keys())
return len(eigset)
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