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I tried the following on sagecell, the answer came immediately

a = random_matrix(RDF,30,30)
a = a+a.transpose()
a.eigenvalues()

You can check at http://sagecell.sagemath.org/?z=eJxLVLBVKErMS8nPjc9NLCnKrNAIcnHTMTYAIk1erkSgbKJ2ol4JUElxQX5xqgZIUC81Mz01rywxpzS1GCQAAM2AFIU=&lang=sage