Euler RE(e^(318310*i*pi)) ≠ 1

[Gil]

Euler

From integer n=0 to n=159154
RE(e^(2*n*i*pi)) = 1

And then, suddenly,
starting from n=159155:
RE(e^(318310*i*pi)) ≠ 1
RE(e^(318312*i*pi)) = 1
RE(e^(318314*i*pi)) ≠ 1
RE(e^(318316*i*pi)) = 1
RE(e^(318318*i*pi)) ≠ 1
RE(e^(318320*i*pi)) = 1
...

the above unexpected series of results seem to repeat itself forever.

Somewhat ennoying.

Of course we should simplify such expressions with n big.
Nethertheless...

Besides all
IM(e^(2*n*i*pi)), with n=integer≠0, never gives 0.

Could that issues be fixed up?

Note that these very same "behaviours" were already to be met with the HP50G.

[parisse]

I just checked with my devel version, it works in CAS. In home, since computations are done in approx. mode, you can not expect exact value for exp(2*i*n*pi) for n integer.