Is there anything preventing using,
AppendTo[ee0, e0];(*And similarly for the other results.*)
Thanks man ...... You are awesome Isaac ...... My issue is solved now ..... My workload is reduced to 1/20 and now I can find out 500 eigenvalues in just 5 mins .... which previously took me more than a day ......... I just need to do a small trick of commenting the list ee0 and run the code 500 times then I copy the complete output to the ee0 list in the code .... Thanks again man .......