# fixed points of jacobi theta functions for nome = exp(-π)

$z = \theta_{3}(z,e^{-\pi})$ when z is about

mpf(‘0.9689712661757769948280586784850756576401598764754095021’)

$z = \theta_{2}(z,e^{-\pi})$ when z is about:

0.6978516538298066655533072405894043384577095171253148733686

$0 = \theta_{1}(0,e^{-\pi})$ is trivial and uninteresting

$z = \theta_{4}(z,e^{-\pi})$ is about

1.042506133187905661390294579173518574659905922706361693502