Dirichlet distribution and correlation

I have the following variables that follow a beta distribution:

               Alpha1     Alpha2     Beta(Alpha1,Alpha2) 
Variable 1     3.18       2.81       0.53
Variable 2     2.33       3.666      0.38
Variable 3     1.44       4.55       0.24
Variable 4     1.8        4.2        0.3
Variable 5     2.61       3.38       0.436

From the distribution I have generated random values in order to obtain the pearson correlation matrix. The problem is, in general, random numbers of univariate variables, the correlation is very low. My question is this:

From the beta functions that I show above how you could generate a multivariable Dirichlet function in python and how you could obtain its correlation matrix.