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Drosophila melanogaster hemocytes are highly motile cells that are crucial for successful embryogenesis and have important roles in the organism's immunological response. Hemocyte motion was measured using selective plane illumination microscopy. Every hemocyte cell in one half of an embryo was tracked during embryogenesis and analysed using a deep learning neural network. The anomalous transport of the cells was well described by fractional Brownian motion that was heterogeneous in both time and space. Hemocyte motion became less persistent over time. LanB1 and SCAR mutants disrupted the collective cellular motion and reduced its persistence due to the modification of viscoelasticity and actin-based motility respectively. The anomalous motility of the hemocytes oscillated in time with alternating epoques of varying persistent motion. Touching hemocytes experience synchronised contact inhibition of locomotion; an anomalous tango. A quantitative statistical framework is presented for hemocyte motility which provides new biological insights., Comment: 13 pages, 7 figures