  We present nuclear magnetic resonance (NMR) measurements on the three
distinct In sites of CeCoIn$_5$ with magnetic field applied in the [100]
direction. We identify the microscopic nature of the long range magnetic order
(LRO) stabilized at low temperatures in fields above 10.2 T while still in the
superconducting (SC) state. We infer that the ordered moment is oriented along
the $\hat c$-axis and map its field evolution. The study of the field
dependence of the NMR shift for the different In sites indicates that the LRO
likely coexists with a modulated SC phase, possibly that predicted by Fulde,
Ferrell, Larkin, and Ovchinnikov. Furthermore, we discern a field region
dominated by strong spin fluctuations where static LRO is absent and propose a
revised phase diagram.
