{
  "root_system": "A2",
  "w": "s1 s2 (right reflection acts first)",
  "euclidean_simple_roots": [
    [
      1,
      0
    ],
    [
      -0.5,
      "sqrt(3)/2"
    ]
  ],
  "w_rho_simple_root_coefficients": [
    -1,
    0
  ],
  "Sigma_w_simple_root_coefficients": [
    [
      1,
      0
    ],
    [
      1,
      1
    ]
  ],
  "Gamma_w_simple_root_coefficients": [
    [
      0,
      -1
    ]
  ],
  "mu_w_simple_root_coefficients": [
    0,
    -1
  ],
  "weight_sample": [
    {
      "a": 0,
      "b": 0,
      "weight_simple_root_coefficients": [
        0,
        -1
      ],
      "multiplicity": 1,
      "basis_exponents": [
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 0,
      "b": 1,
      "weight_simple_root_coefficients": [
        0,
        -2
      ],
      "multiplicity": 1,
      "basis_exponents": [
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 1
        }
      ]
    },
    {
      "a": 0,
      "b": 2,
      "weight_simple_root_coefficients": [
        0,
        -3
      ],
      "multiplicity": 1,
      "basis_exponents": [
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 2
        }
      ]
    },
    {
      "a": 0,
      "b": 3,
      "weight_simple_root_coefficients": [
        0,
        -4
      ],
      "multiplicity": 1,
      "basis_exponents": [
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 3
        }
      ]
    },
    {
      "a": 0,
      "b": 4,
      "weight_simple_root_coefficients": [
        0,
        -5
      ],
      "multiplicity": 1,
      "basis_exponents": [
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 4
        }
      ]
    },
    {
      "a": 1,
      "b": 0,
      "weight_simple_root_coefficients": [
        -1,
        -1
      ],
      "multiplicity": 1,
      "basis_exponents": [
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 1,
      "b": 1,
      "weight_simple_root_coefficients": [
        -1,
        -2
      ],
      "multiplicity": 2,
      "basis_exponents": [
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 1
        },
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 1,
      "b": 2,
      "weight_simple_root_coefficients": [
        -1,
        -3
      ],
      "multiplicity": 2,
      "basis_exponents": [
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 2
        },
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 1
        }
      ]
    },
    {
      "a": 1,
      "b": 3,
      "weight_simple_root_coefficients": [
        -1,
        -4
      ],
      "multiplicity": 2,
      "basis_exponents": [
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 3
        },
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 2
        }
      ]
    },
    {
      "a": 1,
      "b": 4,
      "weight_simple_root_coefficients": [
        -1,
        -5
      ],
      "multiplicity": 2,
      "basis_exponents": [
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 4
        },
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 3
        }
      ]
    },
    {
      "a": 2,
      "b": 0,
      "weight_simple_root_coefficients": [
        -2,
        -1
      ],
      "multiplicity": 1,
      "basis_exponents": [
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 2,
      "b": 1,
      "weight_simple_root_coefficients": [
        -2,
        -2
      ],
      "multiplicity": 2,
      "basis_exponents": [
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 1
        },
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 2,
      "b": 2,
      "weight_simple_root_coefficients": [
        -2,
        -3
      ],
      "multiplicity": 3,
      "basis_exponents": [
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 2
        },
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 1
        },
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 2,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 2,
      "b": 3,
      "weight_simple_root_coefficients": [
        -2,
        -4
      ],
      "multiplicity": 3,
      "basis_exponents": [
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 3
        },
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 2
        },
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 2,
          "normal_derivative_minus_alpha2": 1
        }
      ]
    },
    {
      "a": 2,
      "b": 4,
      "weight_simple_root_coefficients": [
        -2,
        -5
      ],
      "multiplicity": 3,
      "basis_exponents": [
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 4
        },
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 3
        },
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 2,
          "normal_derivative_minus_alpha2": 2
        }
      ]
    },
    {
      "a": 3,
      "b": 0,
      "weight_simple_root_coefficients": [
        -3,
        -1
      ],
      "multiplicity": 1,
      "basis_exponents": [
        {
          "z_alpha1": 3,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 3,
      "b": 1,
      "weight_simple_root_coefficients": [
        -3,
        -2
      ],
      "multiplicity": 2,
      "basis_exponents": [
        {
          "z_alpha1": 3,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 1
        },
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 3,
      "b": 2,
      "weight_simple_root_coefficients": [
        -3,
        -3
      ],
      "multiplicity": 3,
      "basis_exponents": [
        {
          "z_alpha1": 3,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 2
        },
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 1
        },
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 2,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 3,
      "b": 3,
      "weight_simple_root_coefficients": [
        -3,
        -4
      ],
      "multiplicity": 4,
      "basis_exponents": [
        {
          "z_alpha1": 3,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 3
        },
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 2
        },
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 2,
          "normal_derivative_minus_alpha2": 1
        },
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 3,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 3,
      "b": 4,
      "weight_simple_root_coefficients": [
        -3,
        -5
      ],
      "multiplicity": 4,
      "basis_exponents": [
        {
          "z_alpha1": 3,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 4
        },
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 3
        },
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 2,
          "normal_derivative_minus_alpha2": 2
        },
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 3,
          "normal_derivative_minus_alpha2": 1
        }
      ]
    },
    {
      "a": 4,
      "b": 0,
      "weight_simple_root_coefficients": [
        -4,
        -1
      ],
      "multiplicity": 1,
      "basis_exponents": [
        {
          "z_alpha1": 4,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 4,
      "b": 1,
      "weight_simple_root_coefficients": [
        -4,
        -2
      ],
      "multiplicity": 2,
      "basis_exponents": [
        {
          "z_alpha1": 4,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 1
        },
        {
          "z_alpha1": 3,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 4,
      "b": 2,
      "weight_simple_root_coefficients": [
        -4,
        -3
      ],
      "multiplicity": 3,
      "basis_exponents": [
        {
          "z_alpha1": 4,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 2
        },
        {
          "z_alpha1": 3,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 1
        },
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 2,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 4,
      "b": 3,
      "weight_simple_root_coefficients": [
        -4,
        -4
      ],
      "multiplicity": 4,
      "basis_exponents": [
        {
          "z_alpha1": 4,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 3
        },
        {
          "z_alpha1": 3,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 2
        },
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 2,
          "normal_derivative_minus_alpha2": 1
        },
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 3,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    },
    {
      "a": 4,
      "b": 4,
      "weight_simple_root_coefficients": [
        -4,
        -5
      ],
      "multiplicity": 5,
      "basis_exponents": [
        {
          "z_alpha1": 4,
          "z_alpha1_plus_alpha2": 0,
          "normal_derivative_minus_alpha2": 4
        },
        {
          "z_alpha1": 3,
          "z_alpha1_plus_alpha2": 1,
          "normal_derivative_minus_alpha2": 3
        },
        {
          "z_alpha1": 2,
          "z_alpha1_plus_alpha2": 2,
          "normal_derivative_minus_alpha2": 2
        },
        {
          "z_alpha1": 1,
          "z_alpha1_plus_alpha2": 3,
          "normal_derivative_minus_alpha2": 1
        },
        {
          "z_alpha1": 0,
          "z_alpha1_plus_alpha2": 4,
          "normal_derivative_minus_alpha2": 0
        }
      ]
    }
  ],
  "proof_locators": [
    "O.15-O.22",
    "O.33-O.34"
  ],
  "status": "Finite displayed portion of an infinite module; all data exact"
}