## 8139 Regular Pentagon Dirichlet Eigenvalues (60 digits)

Robert S Jones

rsjones7 at yahoo dot com

April 13, 2015, Finished 60-digit results.

Note, I inadvertently missed one eigenvalue in this calculation. Can you identify it?

I am currently extending these calculations by a factor of 20, so I won't fix it here yet.

The lowest 8139 Dirichlet eigenvalues of the unit-edged, regular pentagon, correctly rounded to sixty digits, are shown on this page. They are divided by symmetry.

This list [hopefully] includes all eigenvalues below 100,000, and the first one above 100,000 (which is in the S-symmetry tower).

[md5sum.txt][sha256sum.txt]

- pentagon.DS.nom.dat Non-degenerate Symmetric

- pentagon.DA.nom.dat Non-degenerate Antisymmetric

- pentagon.DB.nom.dat Doubly Degenerate Mixed Modes B

- pentagon.DC.nom.dat Doubly Degenerate Mixed Modes C
Note, to number the lines, I used "$ nl -w 4 pentagon.DS.nom.dat > nl.pentagon.DS.nom.dat". The above files do not have numbered lines.

Dirichlet - S-symmetry(1396 eigenvalues)

Dirichlet - A-symmetry(1318 eigenvalues)

Dirichlet - B-symmetry(2712 eigenvalues)

Dirichlet - C-symmetry(2713 eigenvalues)

Notes:

- I used the GSVD method to sweep the interval λ∈[0,100002] using an increment of δλ=1. I then carefully looked for nearby eigenvalues (within that δλ). The sweep output is posted here (browser warning, more than 400,000 lines).

- I intend to post the programs and other details as I did for the L-shape.