We observe 1.3~mm spectral lines at 2000~AU resolution toward four massive molecular clouds in the Central Molecular Zone of the Galaxy to investigate their star formation activities. We focus on several potential shock tracers that are usually abundant in protostellar outflows, including SiO, SO, CH$_3$OH, H$_2$CO, HC$_3$N, and HNCO. We identify 43 protostellar outflows, including 37 highly likely ones and 6 candidates. The outflows are found toward both known high-mass star forming cores and less massive, seemingly quiescent cores, while 791 out of the 834 cores identified based on the continuum do not have detected outflows. The outflow masses range from less than 1~$M_odot$ to a few tens of $M_odot$, with typical uncertainties of a factor of 70. We do not find evidence of disagreement between relative molecular abundances in these outflows and in nearby analogs such as the well-studied L1157 and NGC7538S outflows. The results suggest that i) protostellar accretion disks driving outflows ubiquitously exist in the CMZ environment, ii) the large fraction of candidate starless cores is expected if these clouds are at very early evolutionary phases, with a caveat on the potential incompleteness of the outflows, iii) high-mass and low-mass star formation is ongoing simultaneously in these clouds, and iv) current data do not show evidence of difference between the shock chemistry in the outflows that determines the molecular abundances in the CMZ environment and in nearby clouds.
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