1 INTRODUCTION  
2 THE FITTING PROCEDURE  
2.1 The observational sample  
2.2 The method  
2.3 Monte Carlo simulations  
3 RESULTS  
3.1 Implicit fit of the PLZ/PWZ relations  
3.2 The distance of the LMC and the global Gaia EDR3 ZP parallax offset  
4 DISCUSSION  
4.1 Comparison with other PLZ/PWZ coefficients  
4.2 Comparison with other ZP parallax offsets  
5 CONCLUSIONS