The transition to phase and amplitude turbulent states in the one-dime
nsional complex Ginzburg-Landau equation is investigated by a numerica
l simulation. In order to describe existing attractors quantitatively,
the largest Lyapunov exponent is estimated. The largest Lyapunov expo
nent is positive but small for the phase turbulence and it is much lar
ger for the amplitude turbulence. Moreover, it seems independent on th
e system size.