Numerically find energy eigenvalues of a large symbolic matrix in Mathematica for a given range -


i have 136x136 hamiltonian (matrix) , need find eigenvalues.

it cannot solved analytically eigenvalues[h] required solve 136th order polynomial.

i need solve numerically replacing symbolic terms values before computing eigenvalues. however, needs plotted range of values of symbolic term example -1 < x < 1.

is there method numerically solve , plot range of values?

{  {10.1358 - 6.72029 x, 0., 0.},...  {0., 10.1358 - 6.72029 x, 0.},  {0., 0., 10.1358 - 6.72029 x},  {0., 0., 0.},  {0., 0., 0.},  {0., 0., 0.},  {0., 0., 0.},  {0., 0., 0.},  {0., 0.204252, 0.},  {0., 0., 0.267429} ...

corner of matrix example. matrix real , symmetric.


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