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[Lapack] What is the biggest size of a real symmetric tridiagonal matrix

Dear Specialist:

I need to diagonalize a real symmetric tridiagonal matrix, which should be
as big as possible.
So my questions regarding this subject  are:
(1) What is the biggest size of a matrix that LAPACK is able to diagonalize?
(2) Which subroutine should I use?

Thanks very much in advance.
Best Regards,

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