How to mean center first and z-score data?

I was reading a paper and found that the authors calculated a score of a gene list for each sample separately based on the following steps: 1) mean center, 2) average over genes, 3) Z-score. The description seems a little bit confusing to me and I want a specific example.

Here is a dataframe. How can I calculate the signature score for these two samples based on the method described above? (R code is welcome)

                                 Sample1         Sample2
Gene_A                 0.3019117       0.3649211
Gene_B                0.2861431       0.3072168
Gene_C                0.3794475       0.6505417
Gene_D                0.2794465       0.3906110
Gene_E                0.3334156       0.5845917
Gene_F                 0.3513268       0.6560779


can you provide the paper? centre=?