  The electron wave function experiences a phase modification at coherent
transmission through a quantum dot. This transmission phase undergoes a
characteristic shift of $\pi$ when scanning through a Coulomb-blockade
resonance. Between successive resonances either a transmission phase lapse of
$\pi$ or a phase plateau is theoretically expected to occur depending on the
parity of the corresponding quantum dot states. Despite considerable
experimental effort, this transmission phase behaviour has remained elusive for
a large quantum dot. Here we report on transmission phase measurements across
such a large quantum dot hosting hundreds of electrons. Using an original
electron two-path interferometer to scan the transmission phase along fourteen
successive resonances, we observe both phase lapses and plateaus. Additionally,
we demonstrate that quantum dot deformation alters the sequence of transmission
phase lapses and plateaus via parity modifications of the involved quantum dot
states. Our findings set a milestone towards a comprehensive understanding of
the transmission phase of quantum dots.
