The following table contains the normalized complex spherical harmonics of orders 0 to 4 (s to g).
| l | ml | Yl,ml( θ,φ) | Yl,ml(x,y,z) | ||
| 0 | 0 | √((1/2π)(1/2)) | √(1/4π) | ||
| 1 | 0 | √((1/2π)(3/2))cos(θ) | √(3/4π)(z/r) | ||
| ±1 | ±√((1/2π)(3/4))sin(θ)e±iφ | ±√(3/8π)(x±iy)/r | |||
| 2 | 0 | √((1/2π)(5/8))(2cos2(θ) -sin2(θ)) | √((5/4π)(1/4))(3z2-r2)/r2 | ||
| ±1 | ±√((1/2π)(15/4))(cos(θ)sin(θ))e±iφ | ±√((5/4π)(3/2))z(x±iy)/r2 | |||
| ±2 | √((1/2π)(15/16))sin2(θ)e±i2φ | √((5/4π)(3/8))(x±iy)2/r2 | |||
| 3 | 0 | √((1/2π)(7/8))(2cos3(θ) -3cos(θ)sin2(θ)) | √((7/4π)(1/4))z(5z2-3r2)/r3 | ||
| ±1 | ±√((1/2π)(21/32))(4cos2(θ)sin(θ) -sin3(θ))e±iφ | ±√((7/4π)(3/16))(x±iy)(5z2-r2)/r3 | |||
| ±2 | √((1/2π)(105/16))(cos(θ)sin2(θ))e±i2φ | √((7/4π)(15/8))z(x±iy)2/r3 | |||
| ±3 | ±√((1/2π)(35/32))sin3(θ)e±i3φ | ±√((7/4π)(5/16))(x±iy)3/r3 | |||
| 4 | 0 | √((1/2π)(9/128))(35cos4(θ) -30cos2(θ) +3) | √((9/4π)(1/64))(35z4-30z2r2+3r4)/r4 | ||
| ±1 | ±√((1/2π)(45/32))sin(θ)(7cos3(θ) -3cos(θ))e±iφ | ±√((9/4π)(5/16))(x±iy)(7z3-3zr2)/r4 | |||
| ±2 | √((1/2π)(45/64))sin2(θ)(7cos2(θ) -1)e±i2φ | √((9/4π)(5/32))(x±iy)2(7z2-r2)/r4 | |||
| ±3 | ±√((1/2π)(315/32))sin3(θ)cos(θ)e±i3φ | ±√((9/4π)(35/16))z(x±iy)3/r4 | |||
| ±4 | √((1/2π)(315/256))sin4(θ)e±i4φ | √((9/4π)(35/128))(x±iy)4/r4 |