If the components of U are ordered U = [d,D*Vx,d*Vy,d*Vz,E,By,Bz], and d=1, P=1/gamma, bx=1, by=sqrt(2), bz=0.5, gamma=5/3, then the right eigenvectors are as follows:

For a left going fast magnetosonic wave:
4.472135954999580e-01
-8.944271909999160e-01
4.216370213557840e-01
1.490711984999860e-01
2.012457825664615e+00
8.432740427115680e-01
2.981423969999720e-01

For a left going Alfven wave:
0.000000000000000e+00
0.000000000000000e+00
-3.333333333333333e-01
9.428090415820634e-01
0.000000000000000e+00
-3.333333333333333e-01
9.428090415820634e-01

For a left going slow magnetosonic wave:
8.944271909999159e-01
-4.472135954999579e-01
-8.432740427115680e-01
-2.981423969999720e-01
6.708136850795449e-01
-4.216370213557841e-01
-1.490711984999860e-01