Mathematica: Sampling orthogonal matrices with eigenvalues in given range?

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Sampling orthogonal matrices with eigenvalues in given range?
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Thanks to all those great people for their contributions!

(mathematica.stackexchange.com/users/217/yaroslav-bulatov)Yaroslav Bulatov
(mathematica.stackexchange.com/users/62063/a-kato)A. Kato
A special thanks goes out to the (mathematica.stackexchange.com/questions/306231/sampling-orthogonal-matrices-with-eigenvalues-in-given-range)Stackexchange community

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If anything is off, please write me at peter D.O.T schneider A.T ois42.de

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