ContinuedFraction[Re[N[Exp[-ZetaZero[1]

ContinuedFraction[Re[N[Exp[-ZetaZero[1]/Im[ZetaZero[1]]*Pi/4], 250]]]

{0, 1, 2, 4, 1, 16, 32, 1, 3, 4, 5, 2, 1, 1, 1, 1, 3, 1, 3, 5, 75, 1, \
3, 8, 1, 1, 1, 1, 3, 2, 2, 1, 51, 6, 1, 2, 4, 11, 1, 2, 1, 2, 7, 79, \
1, 1, 2, 2, 1, 1, 3, 4, 2, 1, 2, 1, 1, 1, 2, 2, 156, 1, 1, 1, 12, 1, \
5, 1, 17, 1, 1, 1, 3, 2, 1, 4, 2, 2, 8, 2, 1, 3, 17, 1, 1, 2, 11, 5, \
2, 8, 2, 1, 3, 1, 7, 1, 8, 1, 7, 4, 1, 1, 15, 1, 1, 4, 99, 1, 1, 1, \
3, 1, 1, 1, 3, 3, 6, 1, 3, 20, 3, 1, 7, 1, 1, 5, 2, 3, 1, 1, 1, 1, 7, \
1, 3, 3, 3, 10, 1, 3, 2, 2, 5, 4, 3, 1, 57, 2, 10, 1, 2, 1, 3, 4, 1, \
16, 1, 4, 1, 91, 1, 3, 2, 1, 4, 25, 1, 1, 8, 1, 8, 1, 44, 1, 1, 6, 4, \
1, 2, 1, 1, 1, 10, 1, 7, 1, 1, 1, 1, 19, 5, 1, 3, 1, 15, 1, 9, 2, 1, \
6, 1, 1, 9, 3, 1, 9, 12, 5, 1, 1, 1, 6, 6, 2, 3, 5, 63, 3, 2, 2, 25, \
1, 4, 1, 1, 2, 9, 3, 1, 5, 1, 12, 1, 2, 18, 3, 8, 1, 18, 3, 3, 3, 3, \
1, 12, 8, 1, 1}