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Shim Function Table:

Shim Function Gradient Order Interaction Order
 
Z0 1 0 0
Z1 z 1 0
Z2 2z2-(x2+ y2) 2 1
Z3 z [2z2-3(x2+ y2)] 3 2
Z4 8z2 [z2-3(x2+ y2)]+ 3(x2+ y2)2 4 2
Z5 48z3 [z2-5(x2+ y2)]+ 90z(x2+ y2)]2 5 2
X x 1 0
Y y 1 0
ZX zx 2 2
ZY zy 2 2
XY xy 2 1
X2-Y2 x2-y2 2 1
Z2X x [4z2- (x2+ y2)] 3 2
Z2Y y [4z2- (x2+ y2)]  3 2
ZXY zxy 3 2
Z(X2-Y2) z (x2- y2) 3 2
X3 x (x2- 3y2) 3 1
Y3 y (3x2- y2) 3 1