{
  "levels": [
    {
      "level": 163,
      "dim_S": 13,
      "dim_Q": 3,
      "status": "canonical",
      "indep": true,
      "E_idempotent": true,
      "N_nilpotent": true,
      "orthogonal": true,
      "E_minpoly": "x^2 + 2*x",
      "N_minpoly": "x^2",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        1,
        0
      ],
      "matches_I_plus_E": true
    },
    {
      "level": 577,
      "dim_S": 47,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": true,
      "N_nilpotent": true,
      "orthogonal": true,
      "E_minpoly": "x^2 + 2*x",
      "N_minpoly": "x",
      "W_minpoly": "x + 1",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 773,
      "dim_S": 64,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": true,
      "orthogonal": true,
      "E_minpoly": "x^3 + x",
      "N_minpoly": "x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          2,
          1,
          1
        ],
        [
          2,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 811,
      "dim_S": 67,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x^2",
      "N_minpoly": "x^3 + x^2 + x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          1,
          1,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          2,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        0,
        2,
        1
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 829,
      "dim_S": 68,
      "dim_Q": 3,
      "status": "canonical",
      "indep": true,
      "E_idempotent": true,
      "N_nilpotent": true,
      "orthogonal": true,
      "E_minpoly": "x^2 + 2*x",
      "N_minpoly": "x^2",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          2,
          2,
          1
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        1,
        0
      ],
      "matches_I_plus_E": true
    },
    {
      "level": 883,
      "dim_S": 73,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": true,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x + 2",
      "N_minpoly": "x^3 + x^2 + 2*x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          2,
          0,
          2
        ],
        [
          2,
          2,
          0
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 1009,
      "dim_S": 83,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x^2",
      "N_minpoly": "x^3 + 2*x^2 + x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          0,
          1
        ],
        [
          0,
          1,
          0
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 1093,
      "dim_S": 90,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x^2 + x + 1",
      "N_minpoly": "x^3 + 2*x^2 + 2*x + 2",
      "W_minpoly": "x + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        0,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 1697,
      "dim_S": 141,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^2 + 2",
      "N_minpoly": "x^2 + 2*x",
      "W_minpoly": "x + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 1783,
      "dim_S": 148,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": true,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x + 2",
      "N_minpoly": "x^3 + x^2 + 2*x",
      "W_minpoly": "x + 1",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 1949,
      "dim_S": 162,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2",
      "N_minpoly": "x^3",
      "W_minpoly": "x + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        0,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 1999,
      "dim_S": 166,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": true,
      "orthogonal": false,
      "E_minpoly": "x^3 + x^2 + x",
      "N_minpoly": "x^2",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          2,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        1,
        1
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 2053,
      "dim_S": 170,
      "dim_Q": 3,
      "status": "canonical",
      "indep": true,
      "E_idempotent": true,
      "N_nilpotent": true,
      "orthogonal": true,
      "E_minpoly": "x^2 + 2*x",
      "N_minpoly": "x^2",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          2,
          2,
          1
        ],
        [
          2,
          2,
          2
        ],
        [
          2,
          1,
          0
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        1,
        0
      ],
      "matches_I_plus_E": true
    },
    {
      "level": 2179,
      "dim_S": 181,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": true,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x + 2",
      "N_minpoly": "x^3 + x",
      "W_minpoly": "x + 1",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 2237,
      "dim_S": 186,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": true,
      "orthogonal": true,
      "E_minpoly": "x^3 + 2*x^2 + x + 2",
      "N_minpoly": "x",
      "W_minpoly": "x + 1",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 2341,
      "dim_S": 194,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x^2 + x + 2",
      "N_minpoly": "x^3 + x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          1,
          0,
          1
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        1,
        1
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 2351,
      "dim_S": 196,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^2 + 2",
      "N_minpoly": "x^3 + 2*x",
      "W_minpoly": "x + 1",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        2,
        0,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 2371,
      "dim_S": 197,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x + 1",
      "N_minpoly": "x^2 + x",
      "W_minpoly": "x + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 2503,
      "dim_S": 208,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": true,
      "orthogonal": true,
      "E_minpoly": "x^2 + 2",
      "N_minpoly": "x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          1,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 2521,
      "dim_S": 209,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": true,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x + 2",
      "N_minpoly": "x^3 + 2*x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          0,
          2,
          2
        ],
        [
          2,
          0,
          2
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 2683,
      "dim_S": 223,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x^2",
      "N_minpoly": "x^3 + x^2 + x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          2,
          0,
          2
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 2693,
      "dim_S": 224,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x^2 + 1",
      "N_minpoly": "x^3 + 2*x^2 + 2*x + 2",
      "W_minpoly": "x + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        0,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 2719,
      "dim_S": 226,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + x^2 + 1",
      "N_minpoly": "x^3 + 2*x^2 + 2*x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          0,
          1,
          1
        ],
        [
          1,
          0,
          2
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        1,
        2
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 2861,
      "dim_S": 238,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": true,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^2 + 2*x",
      "N_minpoly": "x + 1",
      "W_minpoly": "x + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 2953,
      "dim_S": 245,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x^2",
      "N_minpoly": "x^2 + 2*x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          1,
          2,
          2
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          1,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        2,
        0,
        2
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 2971,
      "dim_S": 247,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x^2 + x + 2",
      "N_minpoly": "x^3 + x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          0,
          1,
          0
        ],
        [
          1,
          0,
          0
        ],
        [
          1,
          2,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        1,
        1
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 3041,
      "dim_S": 253,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": true,
      "orthogonal": true,
      "E_minpoly": "x^2 + x + 1",
      "N_minpoly": "x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          1,
          2,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          1,
          1
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 3169,
      "dim_S": 263,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x^2",
      "N_minpoly": "x^2 + x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          2,
          1,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        2,
        0,
        1
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 3251,
      "dim_S": 271,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + x + 2",
      "N_minpoly": "x + 2",
      "W_minpoly": "x + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 3329,
      "dim_S": 277,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x^2 + 1",
      "N_minpoly": "x^3 + x^2 + 2*x + 1",
      "W_minpoly": "x + 1",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 3331,
      "dim_S": 277,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": true,
      "orthogonal": true,
      "E_minpoly": "x^2 + 2",
      "N_minpoly": "x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          0,
          0,
          2
        ],
        [
          0,
          1,
          0
        ],
        [
          2,
          0,
          0
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 3371,
      "dim_S": 281,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^2 + 2",
      "N_minpoly": "x^3 + x",
      "W_minpoly": "x + 1",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        2,
        0,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 3581,
      "dim_S": 298,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^2 + 2*x + 1",
      "N_minpoly": "x^3 + 2*x^2 + 2*x + 1",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          1,
          1,
          0
        ],
        [
          2,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        2,
        2,
        1
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 3709,
      "dim_S": 308,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^2 + 2",
      "N_minpoly": "x^3 + x^2 + 2*x",
      "W_minpoly": "x + 1",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        2,
        0,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 3767,
      "dim_S": 314,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + x^2 + x + 2",
      "N_minpoly": "x^3 + 2*x^2 + 1",
      "W_minpoly": "x + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        0,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 3823,
      "dim_S": 318,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x + 1",
      "N_minpoly": "x^3 + x^2 + x + 2",
      "W_minpoly": "x + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        0,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 3853,
      "dim_S": 320,
      "dim_Q": 3,
      "status": "T3_partial",
      "indep": true,
      "E_idempotent": true,
      "N_nilpotent": false,
      "orthogonal": true,
      "E_minpoly": "x^2 + 2*x",
      "N_minpoly": "x^3 + 2*x^2 + x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          1,
          2,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        1,
        0
      ],
      "matches_I_plus_E": true
    },
    {
      "level": 3923,
      "dim_S": 327,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + x",
      "N_minpoly": "x^3 + x",
      "W_minpoly": "x + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 4051,
      "dim_S": 337,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2*x^2",
      "N_minpoly": "x^2 + x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          0,
          2,
          0
        ],
        [
          2,
          0,
          0
        ],
        [
          1,
          1,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        2,
        0,
        1
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 4057,
      "dim_S": 337,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + x + 1",
      "N_minpoly": "x^3 + x^2 + 2*x",
      "W_minpoly": "x + 1",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        2,
        0,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 4099,
      "dim_S": 341,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + x^2 + 1",
      "N_minpoly": "x^3 + 2*x^2 + 2*x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          2,
          1,
          1
        ],
        [
          2,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        1,
        2
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 4159,
      "dim_S": 346,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + x^2 + x",
      "N_minpoly": "x^3 + x^2",
      "W_minpoly": "x + 1",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        2,
        0,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 4447,
      "dim_S": 370,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^2 + 2",
      "N_minpoly": "x^3 + x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": [
        0,
        2,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 4519,
      "dim_S": 376,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^3 + 2",
      "N_minpoly": "x^3",
      "W_minpoly": "x + 1",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        2,
        0,
        0
      ],
      "matches_I_plus_E": false
    },
    {
      "level": 4799,
      "dim_S": 400,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^2 + 2",
      "N_minpoly": "x^2 + x",
      "W_minpoly": "x + 2",
      "W_matrix": [
        [
          1,
          0,
          0
        ],
        [
          0,
          1,
          0
        ],
        [
          0,
          0,
          1
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    },
    {
      "level": 4933,
      "dim_S": 410,
      "dim_Q": 3,
      "status": "misaligned",
      "indep": true,
      "E_idempotent": true,
      "N_nilpotent": true,
      "orthogonal": false,
      "E_minpoly": "x^2 + 2*x",
      "N_minpoly": "x^2",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          2,
          1,
          1
        ],
        [
          0,
          0,
          2
        ]
      ],
      "W_coords_in_I_E_N": [
        1,
        1,
        0
      ],
      "matches_I_plus_E": true
    },
    {
      "level": 4999,
      "dim_S": 416,
      "dim_Q": 3,
      "status": "degenerate",
      "indep": false,
      "E_idempotent": false,
      "N_nilpotent": false,
      "orthogonal": false,
      "E_minpoly": "x^2 + 2",
      "N_minpoly": "x^2 + 2*x",
      "W_minpoly": "x^2 + 2",
      "W_matrix": [
        [
          2,
          0,
          0
        ],
        [
          0,
          2,
          0
        ],
        [
          1,
          2,
          1
        ]
      ],
      "W_coords_in_I_E_N": null,
      "matches_I_plus_E": null
    }
  ],
  "summary": {
    "all_qdim3_levels": [
      163,
      577,
      773,
      811,
      829,
      883,
      1009,
      1093,
      1697,
      1783,
      1949,
      1999,
      2053,
      2179,
      2237,
      2341,
      2351,
      2371,
      2503,
      2521,
      2683,
      2693,
      2719,
      2861,
      2953,
      2971,
      3041,
      3169,
      3251,
      3329,
      3331,
      3371,
      3581,
      3709,
      3767,
      3823,
      3853,
      3923,
      4051,
      4057,
      4099,
      4159,
      4447,
      4519,
      4799,
      4933,
      4999
    ],
    "indep_qdim3_levels": [
      163,
      811,
      829,
      1093,
      1949,
      1999,
      2053,
      2341,
      2351,
      2693,
      2719,
      2953,
      2971,
      3169,
      3371,
      3581,
      3709,
      3767,
      3823,
      3853,
      4051,
      4057,
      4099,
      4159,
      4447,
      4519,
      4933
    ],
    "match_counts_by_status": {
      "T3_partial": {
        "total": 1,
        "matches_I_plus_E": 1
      },
      "canonical": {
        "total": 3,
        "matches_I_plus_E": 3
      },
      "misaligned": {
        "total": 23,
        "matches_I_plus_E": 1
      }
    }
  }
}