character-data.json

back to table · edit · history · where entries came from · files · download

108707 bytes, as of the version from 2026-11-02 02:56 (current). Recorded here, not run.

[
  {
    "N": 3,
    "a": 1,
    "b": 1,
    "genus": 1,
    "gcd": 1,
    "d": 3,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        2,
        2
      ]
    ]
  },
  {
    "N": 4,
    "a": 1,
    "b": 1,
    "genus": 3,
    "gcd": 1,
    "d": 4,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        3,
        3
      ]
    ]
  },
  {
    "N": 4,
    "a": 1,
    "b": 2,
    "genus": 3,
    "gcd": 1,
    "d": 4,
    "reduced_pair": [
      1,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        3,
        2
      ]
    ]
  },
  {
    "N": 4,
    "a": 2,
    "b": 1,
    "genus": 3,
    "gcd": 1,
    "d": 4,
    "reduced_pair": [
      2,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          2,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        1
      ],
      [
        2,
        3
      ]
    ]
  },
  {
    "N": 5,
    "a": 1,
    "b": 1,
    "genus": 6,
    "gcd": 1,
    "d": 5,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          4,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        2,
        2
      ],
      [
        3,
        3
      ],
      [
        4,
        4
      ]
    ]
  },
  {
    "N": 5,
    "a": 1,
    "b": 2,
    "genus": 6,
    "gcd": 1,
    "d": 5,
    "reduced_pair": [
      1,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          4,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        2,
        4
      ],
      [
        3,
        1
      ],
      [
        4,
        3
      ]
    ]
  },
  {
    "N": 5,
    "a": 1,
    "b": 3,
    "genus": 6,
    "gcd": 1,
    "d": 5,
    "reduced_pair": [
      1,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          4,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        2,
        1
      ],
      [
        3,
        4
      ],
      [
        4,
        2
      ]
    ]
  },
  {
    "N": 5,
    "a": 2,
    "b": 1,
    "genus": 6,
    "gcd": 1,
    "d": 5,
    "reduced_pair": [
      2,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          2
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          3,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        2,
        1
      ],
      [
        3,
        4
      ],
      [
        4,
        2
      ]
    ]
  },
  {
    "N": 5,
    "a": 2,
    "b": 2,
    "genus": 6,
    "gcd": 1,
    "d": 5,
    "reduced_pair": [
      2,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          3,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        2,
        2
      ],
      [
        3,
        3
      ],
      [
        4,
        4
      ]
    ]
  },
  {
    "N": 5,
    "a": 3,
    "b": 1,
    "genus": 6,
    "gcd": 1,
    "d": 5,
    "reduced_pair": [
      3,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          4,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          2,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        2,
        4
      ],
      [
        3,
        1
      ],
      [
        4,
        3
      ]
    ]
  },
  {
    "N": 6,
    "a": 1,
    "b": 1,
    "genus": 10,
    "gcd": 1,
    "d": 6,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        5,
        5
      ]
    ]
  },
  {
    "N": 6,
    "a": 1,
    "b": 2,
    "genus": 10,
    "gcd": 1,
    "d": 6,
    "reduced_pair": [
      1,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        5,
        4
      ]
    ]
  },
  {
    "N": 6,
    "a": 1,
    "b": 3,
    "genus": 10,
    "gcd": 1,
    "d": 6,
    "reduced_pair": [
      1,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        5,
        3
      ]
    ]
  },
  {
    "N": 6,
    "a": 1,
    "b": 4,
    "genus": 10,
    "gcd": 1,
    "d": 6,
    "reduced_pair": [
      1,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        4
      ],
      [
        5,
        2
      ]
    ]
  },
  {
    "N": 6,
    "a": 2,
    "b": 1,
    "genus": 10,
    "gcd": 1,
    "d": 6,
    "reduced_pair": [
      2,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          4,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        1
      ],
      [
        4,
        5
      ]
    ]
  },
  {
    "N": 6,
    "a": 2,
    "b": 2,
    "genus": 10,
    "gcd": 2,
    "d": 3,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        2
      ],
      [
        4,
        4
      ]
    ]
  },
  {
    "N": 6,
    "a": 2,
    "b": 3,
    "genus": 10,
    "gcd": 1,
    "d": 6,
    "reduced_pair": [
      2,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          4,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        3
      ],
      [
        4,
        3
      ]
    ]
  },
  {
    "N": 6,
    "a": 3,
    "b": 1,
    "genus": 10,
    "gcd": 1,
    "d": 6,
    "reduced_pair": [
      3,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          3,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        3,
        1
      ],
      [
        3,
        5
      ]
    ]
  },
  {
    "N": 6,
    "a": 3,
    "b": 2,
    "genus": 10,
    "gcd": 1,
    "d": 6,
    "reduced_pair": [
      3,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          3,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        3,
        2
      ],
      [
        3,
        4
      ]
    ]
  },
  {
    "N": 6,
    "a": 4,
    "b": 1,
    "genus": 10,
    "gcd": 1,
    "d": 6,
    "reduced_pair": [
      4,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          2,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        5
      ],
      [
        4,
        1
      ]
    ]
  },
  {
    "N": 7,
    "a": 1,
    "b": 1,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          4,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          5,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 6,
        "pair": [
          6,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        2,
        2
      ],
      [
        3,
        3
      ],
      [
        4,
        4
      ],
      [
        5,
        5
      ],
      [
        6,
        6
      ]
    ]
  },
  {
    "N": 7,
    "a": 1,
    "b": 2,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      1,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          4,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 6,
        "pair": [
          6,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        2,
        4
      ],
      [
        3,
        6
      ],
      [
        4,
        1
      ],
      [
        5,
        3
      ],
      [
        6,
        5
      ]
    ]
  },
  {
    "N": 7,
    "a": 1,
    "b": 3,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      1,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          3,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          4,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          5,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 6,
        "pair": [
          6,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        2,
        6
      ],
      [
        3,
        2
      ],
      [
        4,
        5
      ],
      [
        5,
        1
      ],
      [
        6,
        4
      ]
    ]
  },
  {
    "N": 7,
    "a": 1,
    "b": 4,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      1,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          4,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 6,
        "pair": [
          6,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        4
      ],
      [
        2,
        1
      ],
      [
        3,
        5
      ],
      [
        4,
        2
      ],
      [
        5,
        6
      ],
      [
        6,
        3
      ]
    ]
  },
  {
    "N": 7,
    "a": 1,
    "b": 5,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      1,
      5
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          4,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          5,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 6,
        "pair": [
          6,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        5
      ],
      [
        2,
        3
      ],
      [
        3,
        1
      ],
      [
        4,
        6
      ],
      [
        5,
        4
      ],
      [
        6,
        2
      ]
    ]
  },
  {
    "N": 7,
    "a": 2,
    "b": 1,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      2,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          6,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          1,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          3,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 6,
        "pair": [
          5,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        4
      ],
      [
        2,
        1
      ],
      [
        3,
        5
      ],
      [
        4,
        2
      ],
      [
        5,
        6
      ],
      [
        6,
        3
      ]
    ]
  },
  {
    "N": 7,
    "a": 2,
    "b": 2,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      2,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          6,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          3,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 6,
        "pair": [
          5,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        2,
        2
      ],
      [
        3,
        3
      ],
      [
        4,
        4
      ],
      [
        5,
        5
      ],
      [
        6,
        6
      ]
    ]
  },
  {
    "N": 7,
    "a": 2,
    "b": 3,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      2,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          6,
          2
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          1,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 6,
        "pair": [
          5,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        5
      ],
      [
        2,
        3
      ],
      [
        3,
        1
      ],
      [
        4,
        6
      ],
      [
        5,
        4
      ],
      [
        6,
        2
      ]
    ]
  },
  {
    "N": 7,
    "a": 2,
    "b": 4,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      2,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          6,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          3,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 6,
        "pair": [
          5,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        2,
        4
      ],
      [
        3,
        6
      ],
      [
        4,
        1
      ],
      [
        5,
        3
      ],
      [
        6,
        5
      ]
    ]
  },
  {
    "N": 7,
    "a": 3,
    "b": 1,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      3,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          6,
          2
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          2,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          5,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          1,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 6,
        "pair": [
          4,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        5
      ],
      [
        2,
        3
      ],
      [
        3,
        1
      ],
      [
        4,
        6
      ],
      [
        5,
        4
      ],
      [
        6,
        2
      ]
    ]
  },
  {
    "N": 7,
    "a": 3,
    "b": 2,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      3,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          6,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          2,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          5,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 6,
        "pair": [
          4,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        2,
        6
      ],
      [
        3,
        2
      ],
      [
        4,
        5
      ],
      [
        5,
        1
      ],
      [
        6,
        4
      ]
    ]
  },
  {
    "N": 7,
    "a": 3,
    "b": 3,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      3,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          6,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          2,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          5,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 6,
        "pair": [
          4,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        2,
        2
      ],
      [
        3,
        3
      ],
      [
        4,
        4
      ],
      [
        5,
        5
      ],
      [
        6,
        6
      ]
    ]
  },
  {
    "N": 7,
    "a": 4,
    "b": 1,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      4,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          5,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          2,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          6,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 6,
        "pair": [
          3,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        2,
        4
      ],
      [
        3,
        6
      ],
      [
        4,
        1
      ],
      [
        5,
        3
      ],
      [
        6,
        5
      ]
    ]
  },
  {
    "N": 7,
    "a": 4,
    "b": 2,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      4,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          1,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          5,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          6,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 6,
        "pair": [
          3,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        4
      ],
      [
        2,
        1
      ],
      [
        3,
        5
      ],
      [
        4,
        2
      ],
      [
        5,
        6
      ],
      [
        6,
        3
      ]
    ]
  },
  {
    "N": 7,
    "a": 5,
    "b": 1,
    "genus": 15,
    "gcd": 1,
    "d": 7,
    "reduced_pair": [
      5,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          5,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          3,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          6,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          4,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 6,
        "pair": [
          2,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        2,
        6
      ],
      [
        3,
        2
      ],
      [
        4,
        5
      ],
      [
        5,
        1
      ],
      [
        6,
        4
      ]
    ]
  },
  {
    "N": 8,
    "a": 1,
    "b": 1,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          7,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        3,
        3
      ],
      [
        5,
        5
      ],
      [
        7,
        7
      ]
    ]
  },
  {
    "N": 8,
    "a": 1,
    "b": 2,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      1,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          5,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          7,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        3,
        6
      ],
      [
        5,
        2
      ],
      [
        7,
        6
      ]
    ]
  },
  {
    "N": 8,
    "a": 1,
    "b": 3,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      1,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          7,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        3,
        1
      ],
      [
        5,
        7
      ],
      [
        7,
        5
      ]
    ]
  },
  {
    "N": 8,
    "a": 1,
    "b": 4,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      1,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          7,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        4
      ],
      [
        3,
        4
      ],
      [
        5,
        4
      ],
      [
        7,
        4
      ]
    ]
  },
  {
    "N": 8,
    "a": 1,
    "b": 5,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      1,
      5
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          5,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          7,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        5
      ],
      [
        3,
        7
      ],
      [
        5,
        1
      ],
      [
        7,
        3
      ]
    ]
  },
  {
    "N": 8,
    "a": 1,
    "b": 6,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      1,
      6
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          7,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        6
      ],
      [
        3,
        2
      ],
      [
        5,
        6
      ],
      [
        7,
        2
      ]
    ]
  },
  {
    "N": 8,
    "a": 2,
    "b": 1,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      2,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          6,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          2,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          6,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        1
      ],
      [
        2,
        5
      ],
      [
        6,
        3
      ],
      [
        6,
        7
      ]
    ]
  },
  {
    "N": 8,
    "a": 2,
    "b": 2,
    "genus": 21,
    "gcd": 2,
    "d": 4,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        2
      ],
      [
        6,
        6
      ]
    ]
  },
  {
    "N": 8,
    "a": 2,
    "b": 3,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      2,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          6,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          2,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          6,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        3
      ],
      [
        2,
        7
      ],
      [
        6,
        1
      ],
      [
        6,
        5
      ]
    ]
  },
  {
    "N": 8,
    "a": 2,
    "b": 4,
    "genus": 21,
    "gcd": 2,
    "d": 4,
    "reduced_pair": [
      1,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        4
      ],
      [
        6,
        4
      ]
    ]
  },
  {
    "N": 8,
    "a": 2,
    "b": 5,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      2,
      5
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          6,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          6,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        1
      ],
      [
        2,
        5
      ],
      [
        6,
        3
      ],
      [
        6,
        7
      ]
    ]
  },
  {
    "N": 8,
    "a": 3,
    "b": 1,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      3,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          7,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          5,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        3,
        1
      ],
      [
        5,
        7
      ],
      [
        7,
        5
      ]
    ]
  },
  {
    "N": 8,
    "a": 3,
    "b": 2,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      3,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          1,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          7,
          2
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          5,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        6
      ],
      [
        3,
        2
      ],
      [
        5,
        6
      ],
      [
        7,
        2
      ]
    ]
  },
  {
    "N": 8,
    "a": 3,
    "b": 3,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      3,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          7,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          5,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        3,
        3
      ],
      [
        5,
        5
      ],
      [
        7,
        7
      ]
    ]
  },
  {
    "N": 8,
    "a": 3,
    "b": 4,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      3,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          1,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          7,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          5,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        4
      ],
      [
        3,
        4
      ],
      [
        5,
        4
      ],
      [
        7,
        4
      ]
    ]
  },
  {
    "N": 8,
    "a": 4,
    "b": 1,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      4,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          4,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          4,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          4,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        4,
        1
      ],
      [
        4,
        3
      ],
      [
        4,
        5
      ],
      [
        4,
        7
      ]
    ]
  },
  {
    "N": 8,
    "a": 4,
    "b": 2,
    "genus": 21,
    "gcd": 2,
    "d": 4,
    "reduced_pair": [
      2,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          2,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        4,
        2
      ],
      [
        4,
        6
      ]
    ]
  },
  {
    "N": 8,
    "a": 4,
    "b": 3,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      4,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          4,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          4,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          4,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        4,
        1
      ],
      [
        4,
        3
      ],
      [
        4,
        5
      ],
      [
        4,
        7
      ]
    ]
  },
  {
    "N": 8,
    "a": 5,
    "b": 1,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      5,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          5,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          7,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          1,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          3,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        5
      ],
      [
        3,
        7
      ],
      [
        5,
        1
      ],
      [
        7,
        3
      ]
    ]
  },
  {
    "N": 8,
    "a": 5,
    "b": 2,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      5,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          5,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          7,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          3,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        3,
        6
      ],
      [
        5,
        2
      ],
      [
        7,
        6
      ]
    ]
  },
  {
    "N": 8,
    "a": 6,
    "b": 1,
    "genus": 21,
    "gcd": 1,
    "d": 8,
    "reduced_pair": [
      6,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          6,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          2,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          6,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          2,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        3
      ],
      [
        2,
        7
      ],
      [
        6,
        1
      ],
      [
        6,
        5
      ]
    ]
  },
  {
    "N": 9,
    "a": 1,
    "b": 1,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          4,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          7,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          8,
          8
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        2,
        2
      ],
      [
        4,
        4
      ],
      [
        5,
        5
      ],
      [
        7,
        7
      ],
      [
        8,
        8
      ]
    ]
  },
  {
    "N": 9,
    "a": 1,
    "b": 2,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      1,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          4,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          5,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          7,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          8,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        2,
        4
      ],
      [
        4,
        8
      ],
      [
        5,
        1
      ],
      [
        7,
        5
      ],
      [
        8,
        7
      ]
    ]
  },
  {
    "N": 9,
    "a": 1,
    "b": 3,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      1,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          4,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          7,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          8,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        2,
        6
      ],
      [
        4,
        3
      ],
      [
        5,
        6
      ],
      [
        7,
        3
      ],
      [
        8,
        6
      ]
    ]
  },
  {
    "N": 9,
    "a": 1,
    "b": 4,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      1,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          4,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          5,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          7,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 8,
        "pair": [
          8,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        4
      ],
      [
        2,
        8
      ],
      [
        4,
        7
      ],
      [
        5,
        2
      ],
      [
        7,
        1
      ],
      [
        8,
        5
      ]
    ]
  },
  {
    "N": 9,
    "a": 1,
    "b": 5,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      1,
      5
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          4,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          7,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          8,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        5
      ],
      [
        2,
        1
      ],
      [
        4,
        2
      ],
      [
        5,
        7
      ],
      [
        7,
        8
      ],
      [
        8,
        4
      ]
    ]
  },
  {
    "N": 9,
    "a": 1,
    "b": 6,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      1,
      6
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          4,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          5,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          7,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          8,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        6
      ],
      [
        2,
        3
      ],
      [
        4,
        6
      ],
      [
        5,
        3
      ],
      [
        7,
        6
      ],
      [
        8,
        3
      ]
    ]
  },
  {
    "N": 9,
    "a": 1,
    "b": 7,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      1,
      7
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          7
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          4,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          5,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          7,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          8,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        7
      ],
      [
        2,
        5
      ],
      [
        4,
        1
      ],
      [
        5,
        8
      ],
      [
        7,
        4
      ],
      [
        8,
        2
      ]
    ]
  },
  {
    "N": 9,
    "a": 2,
    "b": 1,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      2,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          8,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          1,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          5,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          7,
          8
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        5
      ],
      [
        2,
        1
      ],
      [
        4,
        2
      ],
      [
        5,
        7
      ],
      [
        7,
        8
      ],
      [
        8,
        4
      ]
    ]
  },
  {
    "N": 9,
    "a": 2,
    "b": 2,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      2,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          8,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          5,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          7,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        2,
        2
      ],
      [
        4,
        4
      ],
      [
        5,
        5
      ],
      [
        7,
        7
      ],
      [
        8,
        8
      ]
    ]
  },
  {
    "N": 9,
    "a": 2,
    "b": 3,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      2,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          8,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          1,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          5,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 8,
        "pair": [
          7,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        6
      ],
      [
        2,
        3
      ],
      [
        4,
        6
      ],
      [
        5,
        3
      ],
      [
        7,
        6
      ],
      [
        8,
        3
      ]
    ]
  },
  {
    "N": 9,
    "a": 2,
    "b": 4,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      2,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          8,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          5,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 8,
        "pair": [
          7,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        2,
        4
      ],
      [
        4,
        8
      ],
      [
        5,
        1
      ],
      [
        7,
        5
      ],
      [
        8,
        7
      ]
    ]
  },
  {
    "N": 9,
    "a": 2,
    "b": 5,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      2,
      5
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          8,
          2
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          1,
          7
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          5,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          7,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        7
      ],
      [
        2,
        5
      ],
      [
        4,
        1
      ],
      [
        5,
        8
      ],
      [
        7,
        4
      ],
      [
        8,
        2
      ]
    ]
  },
  {
    "N": 9,
    "a": 2,
    "b": 6,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      2,
      6
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          8,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          5,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          7,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        2,
        6
      ],
      [
        4,
        3
      ],
      [
        5,
        6
      ],
      [
        7,
        3
      ],
      [
        8,
        6
      ]
    ]
  },
  {
    "N": 9,
    "a": 3,
    "b": 1,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      3,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          6,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          3,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          6,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          3,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          6,
          8
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        3,
        1
      ],
      [
        3,
        4
      ],
      [
        3,
        7
      ],
      [
        6,
        2
      ],
      [
        6,
        5
      ],
      [
        6,
        8
      ]
    ]
  },
  {
    "N": 9,
    "a": 3,
    "b": 2,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      3,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          6,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          3,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          6,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          3,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 8,
        "pair": [
          6,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        3,
        2
      ],
      [
        3,
        5
      ],
      [
        3,
        8
      ],
      [
        6,
        1
      ],
      [
        6,
        4
      ],
      [
        6,
        7
      ]
    ]
  },
  {
    "N": 9,
    "a": 3,
    "b": 3,
    "genus": 28,
    "gcd": 3,
    "d": 3,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        3,
        3
      ],
      [
        6,
        6
      ]
    ]
  },
  {
    "N": 9,
    "a": 3,
    "b": 4,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      3,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          6,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          3,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          6,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 8,
        "pair": [
          6,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        3,
        1
      ],
      [
        3,
        4
      ],
      [
        3,
        7
      ],
      [
        6,
        2
      ],
      [
        6,
        5
      ],
      [
        6,
        8
      ]
    ]
  },
  {
    "N": 9,
    "a": 3,
    "b": 5,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      3,
      5
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          6,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          3,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          6,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          3,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          6,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        3,
        2
      ],
      [
        3,
        5
      ],
      [
        3,
        8
      ],
      [
        6,
        1
      ],
      [
        6,
        4
      ],
      [
        6,
        7
      ]
    ]
  },
  {
    "N": 9,
    "a": 4,
    "b": 1,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      4,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          8,
          2
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          7,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          2,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          1,
          7
        ],
        "holomorphic": true
      },
      {
        "u": 8,
        "pair": [
          5,
          8
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        7
      ],
      [
        2,
        5
      ],
      [
        4,
        1
      ],
      [
        5,
        8
      ],
      [
        7,
        4
      ],
      [
        8,
        2
      ]
    ]
  },
  {
    "N": 9,
    "a": 4,
    "b": 2,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      4,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          8,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          7,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          1,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 8,
        "pair": [
          5,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        5
      ],
      [
        2,
        1
      ],
      [
        4,
        2
      ],
      [
        5,
        7
      ],
      [
        7,
        8
      ],
      [
        8,
        4
      ]
    ]
  },
  {
    "N": 9,
    "a": 4,
    "b": 3,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      4,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          8,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          7,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          2,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 8,
        "pair": [
          5,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        2,
        6
      ],
      [
        4,
        3
      ],
      [
        5,
        6
      ],
      [
        7,
        3
      ],
      [
        8,
        6
      ]
    ]
  },
  {
    "N": 9,
    "a": 4,
    "b": 4,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      4,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          8,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          7,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          2,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 8,
        "pair": [
          5,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        2,
        2
      ],
      [
        4,
        4
      ],
      [
        5,
        5
      ],
      [
        7,
        7
      ],
      [
        8,
        8
      ]
    ]
  },
  {
    "N": 9,
    "a": 5,
    "b": 1,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      5,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          5,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          2,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          7,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          8,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          4,
          8
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        2,
        4
      ],
      [
        4,
        8
      ],
      [
        5,
        1
      ],
      [
        7,
        5
      ],
      [
        8,
        7
      ]
    ]
  },
  {
    "N": 9,
    "a": 5,
    "b": 2,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      5,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          5,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          1,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          2,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          7,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          8,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          4,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        4
      ],
      [
        2,
        8
      ],
      [
        4,
        7
      ],
      [
        5,
        2
      ],
      [
        7,
        1
      ],
      [
        8,
        5
      ]
    ]
  },
  {
    "N": 9,
    "a": 5,
    "b": 3,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      5,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          5,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          1,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          2,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          7,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          8,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          4,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        6
      ],
      [
        2,
        3
      ],
      [
        4,
        6
      ],
      [
        5,
        3
      ],
      [
        7,
        6
      ],
      [
        8,
        3
      ]
    ]
  },
  {
    "N": 9,
    "a": 6,
    "b": 1,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      6,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          6,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          3,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          6,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          3,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          6,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          3,
          8
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        3,
        2
      ],
      [
        3,
        5
      ],
      [
        3,
        8
      ],
      [
        6,
        1
      ],
      [
        6,
        4
      ],
      [
        6,
        7
      ]
    ]
  },
  {
    "N": 9,
    "a": 6,
    "b": 2,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      6,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          6,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          3,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          6,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 5,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          6,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          3,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        3,
        1
      ],
      [
        3,
        4
      ],
      [
        3,
        7
      ],
      [
        6,
        2
      ],
      [
        6,
        5
      ],
      [
        6,
        8
      ]
    ]
  },
  {
    "N": 9,
    "a": 7,
    "b": 1,
    "genus": 28,
    "gcd": 1,
    "d": 9,
    "reduced_pair": [
      7,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          7,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          5,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          1,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 5,
        "pair": [
          8,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          4,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 8,
        "pair": [
          2,
          8
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        4
      ],
      [
        2,
        8
      ],
      [
        4,
        7
      ],
      [
        5,
        2
      ],
      [
        7,
        1
      ],
      [
        8,
        5
      ]
    ]
  },
  {
    "N": 10,
    "a": 1,
    "b": 1,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          7,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          9,
          9
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        3,
        3
      ],
      [
        7,
        7
      ],
      [
        9,
        9
      ]
    ]
  },
  {
    "N": 10,
    "a": 1,
    "b": 2,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      1,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          7,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          9,
          8
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        3,
        6
      ],
      [
        7,
        4
      ],
      [
        9,
        8
      ]
    ]
  },
  {
    "N": 10,
    "a": 1,
    "b": 3,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      1,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          9
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          7,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          9,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        3,
        9
      ],
      [
        7,
        1
      ],
      [
        9,
        7
      ]
    ]
  },
  {
    "N": 10,
    "a": 1,
    "b": 4,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      1,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          7,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          9,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        4
      ],
      [
        3,
        2
      ],
      [
        7,
        8
      ],
      [
        9,
        6
      ]
    ]
  },
  {
    "N": 10,
    "a": 1,
    "b": 5,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      1,
      5
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          7,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          9,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        5
      ],
      [
        3,
        5
      ],
      [
        7,
        5
      ],
      [
        9,
        5
      ]
    ]
  },
  {
    "N": 10,
    "a": 1,
    "b": 6,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      1,
      6
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          7,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          9,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        6
      ],
      [
        3,
        8
      ],
      [
        7,
        2
      ],
      [
        9,
        4
      ]
    ]
  },
  {
    "N": 10,
    "a": 1,
    "b": 7,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      1,
      7
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          7
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          7,
          9
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          9,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        7
      ],
      [
        3,
        1
      ],
      [
        7,
        9
      ],
      [
        9,
        3
      ]
    ]
  },
  {
    "N": 10,
    "a": 1,
    "b": 8,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      1,
      8
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          8
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          7,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          9,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        8
      ],
      [
        3,
        4
      ],
      [
        7,
        6
      ],
      [
        9,
        2
      ]
    ]
  },
  {
    "N": 10,
    "a": 2,
    "b": 1,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      2,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          6,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          4,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          8,
          9
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        1
      ],
      [
        4,
        7
      ],
      [
        6,
        3
      ],
      [
        8,
        9
      ]
    ]
  },
  {
    "N": 10,
    "a": 2,
    "b": 2,
    "genus": 36,
    "gcd": 2,
    "d": 5,
    "reduced_pair": [
      1,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          4,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        2
      ],
      [
        4,
        4
      ],
      [
        6,
        6
      ],
      [
        8,
        8
      ]
    ]
  },
  {
    "N": 10,
    "a": 2,
    "b": 3,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      2,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          6,
          9
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          4,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          8,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        3
      ],
      [
        4,
        1
      ],
      [
        6,
        9
      ],
      [
        8,
        7
      ]
    ]
  },
  {
    "N": 10,
    "a": 2,
    "b": 4,
    "genus": 36,
    "gcd": 2,
    "d": 5,
    "reduced_pair": [
      1,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          4,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        4
      ],
      [
        4,
        8
      ],
      [
        6,
        2
      ],
      [
        8,
        6
      ]
    ]
  },
  {
    "N": 10,
    "a": 2,
    "b": 5,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      2,
      5
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          6,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          4,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          8,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        5
      ],
      [
        4,
        5
      ],
      [
        6,
        5
      ],
      [
        8,
        5
      ]
    ]
  },
  {
    "N": 10,
    "a": 2,
    "b": 6,
    "genus": 36,
    "gcd": 2,
    "d": 5,
    "reduced_pair": [
      1,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          3,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          4,
          2
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        6
      ],
      [
        4,
        2
      ],
      [
        6,
        8
      ],
      [
        8,
        4
      ]
    ]
  },
  {
    "N": 10,
    "a": 2,
    "b": 7,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      2,
      7
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          7
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          6,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          4,
          9
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          8,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        7
      ],
      [
        4,
        9
      ],
      [
        6,
        1
      ],
      [
        8,
        3
      ]
    ]
  },
  {
    "N": 10,
    "a": 3,
    "b": 1,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      3,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          9,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          1,
          7
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          7,
          9
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        7
      ],
      [
        3,
        1
      ],
      [
        7,
        9
      ],
      [
        9,
        3
      ]
    ]
  },
  {
    "N": 10,
    "a": 3,
    "b": 2,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      3,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          9,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          1,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          7,
          8
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        4
      ],
      [
        3,
        2
      ],
      [
        7,
        8
      ],
      [
        9,
        6
      ]
    ]
  },
  {
    "N": 10,
    "a": 3,
    "b": 3,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      3,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          9,
          9
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          7,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        1
      ],
      [
        3,
        3
      ],
      [
        7,
        7
      ],
      [
        9,
        9
      ]
    ]
  },
  {
    "N": 10,
    "a": 3,
    "b": 4,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      3,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          9,
          2
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          1,
          8
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          7,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        8
      ],
      [
        3,
        4
      ],
      [
        7,
        6
      ],
      [
        9,
        2
      ]
    ]
  },
  {
    "N": 10,
    "a": 3,
    "b": 5,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      3,
      5
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          9,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          1,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          7,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        5
      ],
      [
        3,
        5
      ],
      [
        7,
        5
      ],
      [
        9,
        5
      ]
    ]
  },
  {
    "N": 10,
    "a": 3,
    "b": 6,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      3,
      6
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          9,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          7,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        2
      ],
      [
        3,
        6
      ],
      [
        7,
        4
      ],
      [
        9,
        8
      ]
    ]
  },
  {
    "N": 10,
    "a": 4,
    "b": 1,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      4,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          2,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          8,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          6,
          9
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        3
      ],
      [
        4,
        1
      ],
      [
        6,
        9
      ],
      [
        8,
        7
      ]
    ]
  },
  {
    "N": 10,
    "a": 4,
    "b": 2,
    "genus": 36,
    "gcd": 2,
    "d": 5,
    "reduced_pair": [
      2,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          2
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          3,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        6
      ],
      [
        4,
        2
      ],
      [
        6,
        8
      ],
      [
        8,
        4
      ]
    ]
  },
  {
    "N": 10,
    "a": 4,
    "b": 3,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      4,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          2,
          9
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          8,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          6,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        9
      ],
      [
        4,
        3
      ],
      [
        6,
        7
      ],
      [
        8,
        1
      ]
    ]
  },
  {
    "N": 10,
    "a": 4,
    "b": 4,
    "genus": 36,
    "gcd": 2,
    "d": 5,
    "reduced_pair": [
      2,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          2,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          4,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 3,
        "pair": [
          1,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 4,
        "pair": [
          3,
          3
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        2
      ],
      [
        4,
        4
      ],
      [
        6,
        6
      ],
      [
        8,
        8
      ]
    ]
  },
  {
    "N": 10,
    "a": 4,
    "b": 5,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      4,
      5
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          4,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          2,
          5
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          8,
          5
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          6,
          5
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        5
      ],
      [
        4,
        5
      ],
      [
        6,
        5
      ],
      [
        8,
        5
      ]
    ]
  },
  {
    "N": 10,
    "a": 5,
    "b": 1,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      5,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          5,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          5,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          5,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          5,
          9
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        5,
        1
      ],
      [
        5,
        3
      ],
      [
        5,
        7
      ],
      [
        5,
        9
      ]
    ]
  },
  {
    "N": 10,
    "a": 5,
    "b": 2,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      5,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          5,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          5,
          6
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          5,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          5,
          8
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        5,
        2
      ],
      [
        5,
        4
      ],
      [
        5,
        6
      ],
      [
        5,
        8
      ]
    ]
  },
  {
    "N": 10,
    "a": 5,
    "b": 3,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      5,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          5,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          5,
          9
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          5,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          5,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        5,
        1
      ],
      [
        5,
        3
      ],
      [
        5,
        7
      ],
      [
        5,
        9
      ]
    ]
  },
  {
    "N": 10,
    "a": 5,
    "b": 4,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      5,
      4
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          5,
          4
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          5,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          5,
          8
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          5,
          6
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        5,
        2
      ],
      [
        5,
        4
      ],
      [
        5,
        6
      ],
      [
        5,
        8
      ]
    ]
  },
  {
    "N": 10,
    "a": 6,
    "b": 1,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      6,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          6,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          8,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          2,
          7
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          4,
          9
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        7
      ],
      [
        4,
        9
      ],
      [
        6,
        1
      ],
      [
        8,
        3
      ]
    ]
  },
  {
    "N": 10,
    "a": 6,
    "b": 2,
    "genus": 36,
    "gcd": 2,
    "d": 5,
    "reduced_pair": [
      3,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          3,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 2,
        "pair": [
          1,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          4,
          3
        ],
        "holomorphic": false
      },
      {
        "u": 4,
        "pair": [
          2,
          4
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        4
      ],
      [
        4,
        8
      ],
      [
        6,
        2
      ],
      [
        8,
        6
      ]
    ]
  },
  {
    "N": 10,
    "a": 6,
    "b": 3,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      6,
      3
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          6,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          8,
          9
        ],
        "holomorphic": false
      },
      {
        "u": 7,
        "pair": [
          2,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 9,
        "pair": [
          4,
          7
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        1
      ],
      [
        4,
        7
      ],
      [
        6,
        3
      ],
      [
        8,
        9
      ]
    ]
  },
  {
    "N": 10,
    "a": 7,
    "b": 1,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      7,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          7,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          1,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          9,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          3,
          9
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        3
      ],
      [
        3,
        9
      ],
      [
        7,
        1
      ],
      [
        9,
        7
      ]
    ]
  },
  {
    "N": 10,
    "a": 7,
    "b": 2,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      7,
      2
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          7,
          2
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          1,
          6
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          9,
          4
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          3,
          8
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        1,
        6
      ],
      [
        3,
        8
      ],
      [
        7,
        2
      ],
      [
        9,
        4
      ]
    ]
  },
  {
    "N": 10,
    "a": 8,
    "b": 1,
    "genus": 36,
    "gcd": 1,
    "d": 10,
    "reduced_pair": [
      8,
      1
    ],
    "embedding": "zeta_d=exp(2*pi*i/d)",
    "galois_embeddings": [
      {
        "u": 1,
        "pair": [
          8,
          1
        ],
        "holomorphic": true
      },
      {
        "u": 3,
        "pair": [
          4,
          3
        ],
        "holomorphic": true
      },
      {
        "u": 7,
        "pair": [
          6,
          7
        ],
        "holomorphic": false
      },
      {
        "u": 9,
        "pair": [
          2,
          9
        ],
        "holomorphic": false
      }
    ],
    "orbit_N": [
      [
        2,
        9
      ],
      [
        4,
        3
      ],
      [
        6,
        7
      ],
      [
        8,
        1
      ]
    ]
  }
]