Thanks Riccardo,
I can nevertheless see that the "byhand" calculation is consistent with theory.
By running your script i get the following:
PC1 PC2 fac1 fac2
1 -2.709256 0.285568 -854.063 -0.26550
2 -2.066726 0.463805 -662.994 -2.01606
3 -1.980962 0.517025 -616.468 -2.60151
4 -0.078544 -0.938229 -335.217 -13.89559
5 -1.666011 0.657474 -318.786 34.83377
6 -0.451584 -0.754696 -162.769 2.05259
7 0.432158 -0.885727 -114.351 16.87650
8 0.087436 -0.349262 -33.981 -52.69935
9 0.327963 -0.744697 20.738 25.60055
10 -0.276806 -0.689980 32.923 32.34589
11 1.754006 -0.244259 349.105 -19.51842
12 1.454298 2.304822 708.354 -90.62917
13 2.519187 0.173682 895.401 16.20702
14 2.654839 0.204476 1092.108 53.70929
Quite different