Table 3.

η_lm solutions as a function of projection polynomial coefficients ($a_j^l$) for FASTMAP optimization (using the six projections specified in Table 2)

l	1	2	3
m
0	$\frac{1}{2\sqrt{2}}(a_1^3-a_1^4+a_1^5-a_1^6)$	$\frac{2}{3}(-a_2^1-a_2^2+\frac{1}{2}(a_2^3+a_2^4+a_2^5+a_2^6\left)\right)$	$\frac{2}{\sqrt{2}}(-a_3^3+a_3^4-a_3^5+a_3^6)$
1	$\frac{1}{2\sqrt{2}}(a_1^1+a_1^2+a_1^3+a_1^4)$	$a_2^3-a_2^4$	$\frac{8}{11\sqrt{2}}(-a_3^1-a_3^2+\frac{3}{2}(a_3^3+a_3^4\left)\right)$
−l	$\frac{1}{2\sqrt{2}}(a_1^1-a_1^2-a_1^5-a_1^6)$	$-a_2^5+a_2^6$	$\frac{8}{11\sqrt{2}}(-a_3^1+a_3^2-\frac{3}{2}(a_3^5+a_3^6\left)\right)$
2	NA	$\frac{1}{2}(a_2^3+a_2^4-a_2^5-a_2^6)$	$\frac{1}{\sqrt{2}}(a_3^3-a_3^4-a_3^5+a_3^6)$
−2	NA	$\frac{1}{2}(a_2^1+a_2^2)$	Undetermined
3	NA	NA	$\frac{4}{5\sqrt{2}}(-a_3^1-a_3^2+\frac{1}{2}(a_3^3+a_3^4\left)\right)$
−3	NA	NA	$\frac{4}{5\sqrt{2}}(a_3^1-a_3^2+\frac{1}{2}(a_3^5+a_3^6\left)\right)$