  We present the first broadband lambda = 1 mm spectrum toward the z=2.56
Cloverleaf Quasar, obtained with Z-Spec, a 1-mm grating spectrograph on the
10.4-meter Caltech Submillimeter Observatory. The 190-305 GHz observation band
corresponds to rest-frame 272 to 444 microns, and we measure the dust continuum
as well as all four transitions of carbon monoxide (CO) lying in this range.
The power-law dust emission, F_nu = 14 mJy (nu/240GHz)^3.9 is consistent with
the published continuum measurements. The CO J=6->5, J=8->7, and J=9->8
measurements are the first, and now provide the highest-J CO information in
this source. Our measured CO intensities are very close to the
previously-published interferometric measurements of J=7->6, and we use all
available transitions and our 13CO upper limits to constrain the physical
conditions in the Cloverleaf molecular gas disk. We find a large mass
(2-50x10^9 Msun) of highly-excited gas with thermal pressure nT > 10^6 Kcm^-3.
The ratio of the total CO cooling to the far-IR dust emission exceeds that in
the local dusty galaxies, and we investigate the potential heating sources for
this bulk of warm molecular gas. We conclude that both UV photons and X-rays
likely contribute, and discuss implications for a top-heavy stellar initial
mass function arising in the X-ray-irradiated starburst. Finally we present
tentative identifications of other species in the spectrum, including a
possible detection of the H20 2_0,2->1_1,1 transition at lambda_rest = 303
microns.
