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We compute the $E_2$ pages of the momentum-space and real-spaceAtiyah-Hirzebruch spectral sequence (AHSS) for topological crystallineinsulators and superconductors up to three spatial dimensions, considering thecell decomposition in which if a group action fixes a cell setwise then itsgroup action fixes the same cell pointwise. We provide a detailed descriptionof the implementation for computing the $E_2$ pages of AHSS. Under a physicallyreasonable assumption, we enumerate all possible $K$-groups that are compatiblewith the $E_2$ pages for both momentum and real-space AHSS. As a result, wedetermine the $K$-groups for approximately 59\% of symmetry settings in threespatial dimensions. All the results can be found at this http\href{https://www2.yukawa.kyoto-u.ac.jp/~ken.shiozaki/ahss/e2.html}{URL}.

Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups