Until recently it was believed there are no compact, graded, embedded Lagrangians in ${\mathbin{\mathbb{C}}}^{m}$. However, Ekholm, Eliashberg, Murphy and Smith [15, Cor. 1.6] found an example of a compact, graded, embedded Lagrangian ${\mathbin{\cal S}}^{1}\times{\mathbin{\cal S}}^{2}$ in ${\mathbin{\mathbb{C}}}^{3}$, and products give Lagrangian $({\mathbin{\cal S}}^{1}\times{\mathbin{\cal S}}^{2})^{n}$’s in ${\mathbin{\mathbb{C}}}^{3n}$. These all have $HF^{*}$ obstructed, as they are not strictly immersed.