The first five eigenfunctions of an arbitrary-shaped QD. (a) The sign distribution of the eigenmodes are plotted below the amplitudes (by convention, we attribute the color black to the sign ‘+’ and the color red to the sign ‘-’). The small blue arrows indicate the position where the leads will be connected. Transmittance amplitude (b) (which is proportional to the conductance) and phase (c), respectively, for the same QD with the leads connected as mentioned. The conductance is in units 2e2/h and the phase is in Π units. (d) The corresponding Fano lines which would result by inserting the same QD in an interferometer. Near each Fano resonance we wrote the sign of the Fano parameter.