We use a nearly complete sample of Gamma Ray Bursts (GRBs) detected by the Swift satellite to study the correlations between the spectral peak energy Ep of the prompt emission, the isotropic energetics Eiso and the isotropic luminosity Liso. This GRB sample is characterized by a high level of completeness in redshift (90%). This allows us to probe in an unbiased way the issue related to the physical origin of these correlations against selection effects. We find that one burst, GRB 061021, is an outlier to the Ep-Eiso correlation. Despite this case, we find strong Ep-Eiso and Ep-Liso correlations for the bursts of the complete sample. Their slopes, normalisations and dispersions are consistent with those found with the whole sample of bursts with measured redshift and Ep. This means that the biases present in the total sample commonly used to study these correlations do not affect their properties. Finally, we also find no evolution with redshift of the Ep-Eiso and Ep-Liso correlations.
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