  We calculate 800 coefficients of the high-temperature expansion of the
magnetic susceptibility of Dyson's hierarchical model with a Landau-Ginzburg
measure. Log-periodic corrections to the scaling laws appear as in the case of
a Ising measure. The period of oscillation appears to be a universal quantity
given in good approximation by the logarithm of the largest eigenvalue of the
linearized RG transformation, in agreement with a possibility suggested by K.
Wilson and developed by Niemeijer and van Leeuwen. We estimate $\gamma $ to be
1.300 (with a systematic error of the order of 0.002) in good agreement with
the results obtained with other methods such as the $\epsilon $-expansion. We
briefly discuss the relationship between the oscillations and the zeros of the
partition function near the critical point in the complex temperature plane.
