(p, x, z, y) (p, x, z, y) 
[ p 0 0 0] [x 1 0 z] [ 0 0 1 x] [ 0 0 0 p] [ p 0 0 0] [x 1 0 z] [ 0 0 1 x] [ 0 0 0 p] 
[ 0 0 1 0] [ 0 0 0 1] [ 1 0 0 0] [ 0 1 0 0] [ 0 0 1 0] [ 0 0 0 1] [ 1 0 0 0] [ 0 1 0 0] 
[ 0 0 p 0] [ 0 0 0 p] [ p 0 0 0] [ 0 p 0 0] [ 0 0 p 0] [ 0 0 0 p] [ p 0 0 0] [ 0 p 0 0] 
This gives $\mu(b_2) = p$, as expected. Thus, the new coset representative $b_2^{*} = \mu(b_2) b_2^{1}$ is given by:
[ 1 0 0 0] [ x p 0 z] [ 0 0 p x] [ 0 0 0 1] [ 1 0 0 0] [ x p 0 z] [ 0 0 p x] [ 0 0 0 1] 
[1 0 x y] [0 1 y z] [0 0 p 0] [0 0 0 p] [1 0 x y] [0 1 y z] [0 0 p 0] [0 0 0 p] 
[ 0 0 p 0] [ 0 0 0 p] [ p 0 0 0] [ 0 p 0 0] [ 0 0 p 0] [ 0 0 0 p] [ p 0 0 0] [ 0 p 0 0] 
This gives $\mu(b_1) = p$, as expected. Thus, the new coset representative $b_1^{*} = \mu(b_1) b_1^{1}$ is given by:
[ p 0 x y] [ 0 p y z] [ 0 0 1 0] [ 0 0 0 1] [ p 0 x y] [ 0 p y z] [ 0 0 1 0] [ 0 0 0 1] 
[1 0 x 0] [0 p 0 0] [0 0 p 0] [0 0 0 1] [1 0 x 0] [0 p 0 0] [0 0 p 0] [0 0 0 1] 
[ 0 0 p 0] [ 0 0 0 p] [ p 0 0 0] [ 0 p 0 0] [ 0 0 p 0] [ 0 0 0 p] [ p 0 0 0] [ 0 p 0 0] 
This gives $\mu(b_3) = p$, as expected. Thus, the new coset representative $b_3^{*} = \mu(b_3) b_3^{1}$ is given by:
[ p 0 x 0] [ 0 1 0 0] [ 0 0 1 0] [ 0 0 0 p] [ p 0 x 0] [ 0 1 0 0] [ 0 0 1 0] [ 0 0 0 p] 
[p 0 0 0] [0 p 0 0] [0 0 1 0] [0 0 0 1] [p 0 0 0] [0 p 0 0] [0 0 1 0] [0 0 0 1] 
[ 0 0 p 0] [ 0 0 0 p] [ p 0 0 0] [ 0 p 0 0] [ 0 0 p 0] [ 0 0 0 p] [ p 0 0 0] [ 0 p 0 0] 
This gives $\mu(b_4) = p$, as expected. Thus, the new coset representative $b_4^{*} = \mu(b_4) b_4^{1}$ is given by:
[1 0 0 0] [0 1 0 0] [0 0 p 0] [0 0 0 p] [1 0 0 0] [0 1 0 0] [0 0 p 0] [0 0 0 p] 
