  We present measurements of the CO luminosity functions (LFs) and the
evolution of the cosmic molecular gas density out to z~6 based on an 8.5
arcmin^2 spectral scan survey at 3mm of the iconic Hubble Deep Field North
(HDF-N) observed with the NOrthern Extended Millimeter Array (NOEMA). We use
matched filtering to search for line emission from galaxies and determine their
redshift probability distributions exploiting the extensive multi-wavelength
data for the HDF-N. We identify the 7 highest-fidelity sources as CO emitters
at 1<z<6, including the well-known submillimeter galaxy HDF850.1 at z=5.18.
Four high-fidelity 3mm continuum sources are all found to be radio galaxies at
z<=1, plus HDF850.1. We constrain the CO LFs in the HDF-N out to z~6, including
a first measurement of the CO(5-4) LF at <z>=5.0. The relatively large area and
depth of the NOEMA HDF-N survey extends the existing luminosity functions at
1<z<4 above the knee, yielding a somewhat lower density by 0.15-0.4 dex at the
overlap region for the CO(2-1) and CO(3-2) transitions, attributed to cosmic
variance. We perform a joint analysis of the CO LFs in the HDF-N and Hubble
Ultra Deep Field from ASPECS, finding that they can be well described by a
single Schechter function. The evolution of the cosmic molecular gas density
from a joint analysis is in good agreement with earlier determinations. This
implies that the impact of cosmic field-to-field variance on the measurements
is consistent with previous estimates, adding to the challenges for simulations
that model galaxies from first principles.
