12 TABLE III: Scattering matrix for non-azimuthal modes with m = 2. Late–time power law indices ℓ ′ n$_{ℓ}$ for the ℓ –projections of the fields for pure m = 2 mode initial data sets, ℓ ′ = 2 , 3 , 4. This table includes both “down” and “up” excitations. Asterisks relate to kinematically disallowed states. All figures are significant. TABLE IV: Presentation of the data in Tables I,II, and III in a form that emphasizes the independence of the decay rate on m . Late–time power law indices ℓ ′ $_{,m}$n$_{ℓ,m}$ for the ℓ –projections of the fields for pure m = 0 , 1 , 2 mode initial data sets, ℓ = 2 , 3 , 4. This table includes both “down” and “up” excitations. Asterisks relate to kinematically disallowed states. All figures are significant. Acknowledgments We are indebted to Richard Price and Jorge Pullin for discussions. Most of the numerical simulations were executed on Alabama Supercomputer Center (ASC), Louisiana Optical Network Initiative (LONI), and Playstation 3 clusters. LMB was supported in part by a Theodore Dunham, Jr. Grant of the F.A.R., by a NASA EPSCoR RID grant, and by NSF grants PHY–0757344 and DUE–0941327. GK was supported in part by NSF grants PHY–0831631, PHY–0902026, and PHY–1016906. Initial Projected Projected Projected Projected ℓ ′ mode ℓ = 2 ℓ = 3 ℓ = 4 ℓ = 5 2 7.0003 * 8.995 * 3 * 9.0006 * 11.001 4 7.0001 * 11.003 * Initial Projected Projected Projected Projected ℓ $^{′}$, m mode ℓ = 2 ℓ = 3 ℓ = 4 ℓ = 5 2,0 7.009 * 9.01 * 2,1 6.997 * 8.995 * 2,2 7.0003 * 8.995 * 3,0 * 9.009 * 11.008 3,1 * 9.009 * 11.005 3,2 * 9.0006 * 11.001 4,0 7.002 * 11.008 * 4,1 7.0001 * 11.006 * 4,2 7.0001 * 11.003 * [1] L.M. Burko and G. Khanna, Phys. Rev. D 67 , 081502(R) (2003). [2] S. Hod, Phys. Rev. D 61 , 024033 (1999); 61 , 064018 (2000). [3] E. Poisson, Phys. Rev. D 66 , 044088 (2002). [4] W. Krivan, Phys. Rev. D 60 , 101501(R) (1999). [5] R.J. Gleiser, R.H. Price, and J. Pullin, Class. Quantum Grav. 25 , 072001 (2008). [6] M. Tiglio, L. Kidder, and S. Teukolsky, Class. Quantum Grav. 25 , 105022 (2008). [7] L.M. Burko and G. Khanna, Class. Quantum Grav. 26 , 015014 (2009). [8] L. Barack and A. Ori, Phys. Rev. Lett. 82 , 4388 (1999). [9] W. Krivan, P. Laguna, P. Papadopoulos, and N. Andersson, Phys. Rev. D 56 , 3395 (1997). [10] R. Ginjupalli and G. Khanna, High-Precision Numerical Simulations of Rotating Black Holes Accelerated by CUDA , Pro- ceedings of the International Conference on High Performance Computing Systems (HPCS), Orlando, FL (2010).