Magnet-superconductor hybrid (MSH) systems represent promising platforms to host Majorana zero modes (MZMs), the elemental building blocks for fault-tolerant quantum computers. Theoretical description of such MSH structures is mostly based on simplified models, not accounting for the complexity of real materials. Here, based on density functional theory, we derive an effective superconducting 80-band model to study an MSH system consisting of a magnetic manganese chain on the $s$ wave superconductor niobium. For a wide range of values of the superconducting order parameter, the system is a topological superconductor, with MZMs exhibiting non-universal spatial patterns and a drastic accumulation of spectral weight on both sides along the magnetic chain. Performing scanning tunneling spectroscopy experiments on the same system, we observe a spatial structure in the low-energy local density of states that is consistent with the theoretical results. Our results open a first-principle approach to the discovery of topological superconductors.
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