Symmetric	Expectation Value	Variance
R (1, 1)	r	$1 + r^{2}$
R (2, 2)	$1 + 2 r^{2}$	$4 (2 + 17 r^{2} + 5 r^{4})$
R (3, 3)	$9 r + 6 r^{3}$	$9 (25 + 441 r^{2} + 588 r^{4} + 76 r^{6})$
R (4, 4)	$9 + 72 r^{2} + 24 r^{4}$	$12^{2} (76 + 2441 r^{2} + 7311 r^{4} + 3896 r^{6} + 276 r^{8})$
R (5, 5)	$225 r + 600 r^{3} + 120 r^{5}$	$\begin{array}{l} 15^{2} (3969 + 198225 r^{2} + 1057200 r^{4} \\ + 1268240 r^{6} + 362240 r^{8} + 16064 r^{10}) \end{array}$
R (6, 6)	$225 + 4050 r^{2} + 5400 r^{4} + 720 r^{6}$	$\begin{array}{l} 90^{2} (13334 + 960273 r^{2} + 8001825 r^{4} + 17070080 r^{6} \\ + 10972800 r^{8} + 1950528 r^{10} + 59072 r^{12}) \end{array}$
Asymmetric
R (2, 1)	0	$3 + 12 r^{2}$
R (3, 1)	3r	$15 + 81 r^{2}$
R (4, 1)	0	$105 + 840 r^{2}$
R (5, 1)	15r	$3^{2} (105 + 1025 r^{2})$
R (6, 1)	0	$3^{2} (1155 + 13860 r^{2})$
R (3, 2)	0	$3^{2} (5 + 60 r^{2} + 40 r^{4})$
R (4, 2)	$3 + 12 r^{2}$	$3^{2} (34 + 552 r^{2} + 544 r^{4})$
R (4, 3)	0	$3^{2} (175 + 4200 r^{2} + 8400 r^{4} + 2240 r^{6})$
R (5, 3)	$45 r + 60 r^{3}$	$15^{2} (63 + 1881 r^{2} + 5016 r^{4} + 2000 r^{6})$
R (6, 4)	$45 + 540 r^{2} + 360 r^{4}$	$45^{2} (538 + 25848 r^{2} + 129200 r^{4} + 137792 r^{6} + 29504 r^{8})$