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tokens: This work has made use of the HPC resources of CINES (Jade and Occigen supercomputer) under the time allocations 2013047012, 2014047012 and 2015047012 made by GENCI. This work is partially supported by the Spin(e) grants ANR-13-BS05-0005 ( http://cosmicorigin.org ) of the French Agence Nationale de la Recherche and by the ILP LABEX (under reference ANR-10-LABX-63 and ANR-11-IDEX-0004-02). Part of the analysis of the simulation was performed on the DiRAC facility jointly funded by STFC, BIS and the University of Oxford. NEC is supported by a Beecroft Postdoctoral Research Fellowship. We thank S. Rouberol for running smoothly the Horizon cluster for us. NEC thanks Rachel Mandelbaum for useful discussion regarding the grid-locking effect.