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[en] We present the results of a blind millimeter line emitter search using ALMA Band 6 data with a single-frequency tuning toward four gravitational lensing clusters (RXJ1347.5−1145, Abell S0592, MACS J0416.1−2403, and Abell 2744). We construct 3D signal-to-noise ratio (S/N) cubes with 60 and 100 MHz binning, and search for millimeter line emitters. We do not detect any line emitters with a peak S/N > 5, although we do find a line emitter candidate with a peak S/N ≃ 4.5. These results provide upper limits to the CO(3−2), CO(4−3), CO(5−4), and [C ii] luminosity functions at z ≃ 0.3, 0.7, 1.2, and 6, respectively. Because of the magnification effect of gravitational lensing clusters, the new data provide the first constraints on the CO and [C ii] luminosity functions at unprecedentedly low luminosity levels, i.e., down to ≲10−3 – 10−1 Mpc−3 dex−1 at K km s−1 pc2 and ≲10−3–10−2 Mpc−3 dex−1 at , respectively. Although the constraints to date are not yet stringent, we find that the evolution of the CO and [C ii] luminosity functions are broadly consistent with the predictions of semi-analytical models. This study demonstrates that the wide observations with a single-frequency tuning toward gravitational lensing clusters are promising for constraining the CO and [C ii] luminosity functions.