Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: E 2 pages for 1651 magnetic space groups

We compute the E₂ pages of the momentum-space and real-space Atiyah-Hirzebruch spectral sequence (AHSS) for topological crystalline insulators and superconductors up to three spatial dimensions, considering the cell decomposition in which if a group action fixes a cell setwise then its group action fixes the same cell pointwise. We provide a detailed description of the implementation for computing the E₂ pages of AHSS. Under a physically reasonable assumption, we enumerate all possible K-groups that are compatible with the E₂ pages for both momentum and real-space AHSS. As a result, we determine the K-groups for approximately 59\% of symmetry settings in three spatial dimensions. All the results can be found at this http https: //www2. yukawa. kyoto-u. ac. jp/~ken. shiozaki/ahss/e2. htmlURL.