  The ABC flow is a prototype for fast dynamo action, essential to the origin
of magnetic field in large astrophysical objects. Probably the most studied
configuration is the classical 1:1:1 flow. We investigate its dynamo properties
varying the magnetic Reynolds number Rm. We identify two kinks in the growth
rate, which correspond respectively to an eigenvalue crossing and to an
eigenvalue coalescence. The dominant eigenvalue becomes purely real for a
finite value of the control parameter. Finally we show that even for Rm =
25000, the dominant eigenvalue has not yet reached an asymptotic behaviour. Its
still varies very significantly with the controlling parameter. Even at these
very large values of Rm the fast dynamo property of this flow cannot yet be
established.
