Is the following equation solvable by Mathematica?

I want to solve and plot the solutions of the following equation, where Mathematica is still running and doesn’t return anything:

Solve(Rationalize(E^(-b (1.365)) + E^(-b (-0.350)) + E^(-b (-0.409)), 0) == 0, b)
ListPlot(ReIm(b /. % /. C(1) -> 0), ImageSize -> Large, PlotRange -> {{-0.8, 1.9}, {-500, 500}})

where $b$ is complex. Is there any other method to try here?