This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree . Some of these formulas are expressed in terms of the Cartesian expansion of the spherical harmonics into polynomials in x, y, z, and r. For purposes of this table, it is useful to express the usual spherical to Cartesian transformations that relate these Cartesian components to and as Complex spherical harmonics For ℓ = 0, …, 5, see. ℓ = 0 ℓ = 1 ℓ = 2 ℓ = 3 ℓ = 4 ℓ = 5 ℓ = 6 ℓ = 7 ℓ = 8 ℓ = 9 ℓ = 10 Visualization of complex spherical harmonics 2D polar/azimuthal angle maps Below the complex spherical harmonics are represented on 2D plots with the azimuthal angle, , on the horizontal axis and the polar angle, , on the vertical axis. The saturation of the color at any point represents the magnitude of the spherical harmonic and the hue represents the phase. Polar plots Below the complex spherical harmonics are represented on polar plots. The magnitude of the spherical harmonic at particular polar and azimuthal angles is represented by the saturation of the color at that point and the phase is represented by the hue at that point. Polar plots with magnitude as radius Below the complex spherical harmonics are represented on polar plots. The magnitude of the spherical harmonic at particular polar and azimuthal angles is represented by the radius of the plot at that point and the phase is represented by the hue at that point. Real spherical harmonics For each real spherical harmonic, the corresponding atomic orbital symbol (s, p, d, f) is reported as well. For ℓ = 0, …, 3, see. ℓ = 0 ℓ = 1 ℓ = 2 ℓ = 3 ℓ = 4 Visualization of real spherical harmonics 2D polar/azimuthal angle maps Below the real spherical harmonics are represented on 2D plots with the azimuthal angle, , on the horizontal axis and the polar angle, , on the vertical axis. The saturation of the color at any point represents the magnitude of the spherical harmonic and the hue represents the phase. Polar plots Below the real spherical harmonics are represented on polar plots. The magnitude of the spherical harmonic at particular polar and azimuthal angles is represented by the saturation of the color at that point and the