{
  "method": "Direct centered root traces, independent of JS change-of-basis implementation",
  "weights": [
    [
      1,
      -1,
      0,
      0,
      0
    ],
    [
      0,
      0,
      1,
      -1,
      0
    ],
    [
      1,
      0,
      -1,
      0,
      0
    ],
    [
      2,
      -1,
      1,
      -3,
      1
    ],
    [
      -2,
      3,
      1,
      -1,
      -1
    ]
  ],
  "cases": [
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "-1",
        "gamma": "-19/12"
      },
      "status": "passes",
      "periods": [
        "1",
        "1",
        "-1",
        "6",
        "6"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "-1",
        "gamma": "-14/9"
      },
      "status": "fails",
      "periods": [
        "1",
        "1",
        "-35/36",
        "217/36",
        "217/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "-1",
        "gamma": "-13/12"
      },
      "status": "fails",
      "periods": [
        "1",
        "1",
        "-1/2",
        "13/2",
        "13/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "-1",
        "gamma": "-7/12"
      },
      "status": "passes",
      "periods": [
        "1",
        "1",
        "0",
        "7",
        "7"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "-1",
        "gamma": "-5/9"
      },
      "status": "fails",
      "periods": [
        "1",
        "1",
        "1/36",
        "253/36",
        "253/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "-1",
        "gamma": "-1/12"
      },
      "status": "fails",
      "periods": [
        "1",
        "1",
        "1/2",
        "15/2",
        "15/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "-1",
        "gamma": "5/12"
      },
      "status": "passes",
      "periods": [
        "1",
        "1",
        "1",
        "8",
        "8"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "-1",
        "gamma": "4/9"
      },
      "status": "fails",
      "periods": [
        "1",
        "1",
        "37/36",
        "289/36",
        "289/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "-1",
        "gamma": "11/12"
      },
      "status": "fails",
      "periods": [
        "1",
        "1",
        "3/2",
        "17/2",
        "17/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "0",
        "gamma": "-5/4"
      },
      "status": "passes",
      "periods": [
        "1",
        "0",
        "-1",
        "1",
        "5"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "0",
        "gamma": "-11/9"
      },
      "status": "fails",
      "periods": [
        "1",
        "0",
        "-35/36",
        "37/36",
        "181/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "0",
        "gamma": "-3/4"
      },
      "status": "fails",
      "periods": [
        "1",
        "0",
        "-1/2",
        "3/2",
        "11/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "0",
        "gamma": "-1/4"
      },
      "status": "passes",
      "periods": [
        "1",
        "0",
        "0",
        "2",
        "6"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "0",
        "gamma": "-2/9"
      },
      "status": "fails",
      "periods": [
        "1",
        "0",
        "1/36",
        "73/36",
        "217/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "0",
        "gamma": "1/4"
      },
      "status": "fails",
      "periods": [
        "1",
        "0",
        "1/2",
        "5/2",
        "13/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "0",
        "gamma": "3/4"
      },
      "status": "passes",
      "periods": [
        "1",
        "0",
        "1",
        "3",
        "7"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "0",
        "gamma": "7/9"
      },
      "status": "fails",
      "periods": [
        "1",
        "0",
        "37/36",
        "109/36",
        "253/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "0",
        "gamma": "5/4"
      },
      "status": "fails",
      "periods": [
        "1",
        "0",
        "3/2",
        "7/2",
        "15/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "1",
        "gamma": "-11/12"
      },
      "status": "passes",
      "periods": [
        "1",
        "-1",
        "-1",
        "-4",
        "4"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "1",
        "gamma": "-8/9"
      },
      "status": "fails",
      "periods": [
        "1",
        "-1",
        "-35/36",
        "-143/36",
        "145/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "1",
        "gamma": "-5/12"
      },
      "status": "fails",
      "periods": [
        "1",
        "-1",
        "-1/2",
        "-7/2",
        "9/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "1",
        "gamma": "1/12"
      },
      "status": "passes",
      "periods": [
        "1",
        "-1",
        "0",
        "-3",
        "5"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "1",
        "gamma": "1/9"
      },
      "status": "fails",
      "periods": [
        "1",
        "-1",
        "1/36",
        "-107/36",
        "181/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "1",
        "gamma": "7/12"
      },
      "status": "fails",
      "periods": [
        "1",
        "-1",
        "1/2",
        "-5/2",
        "11/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "1",
        "gamma": "13/12"
      },
      "status": "passes",
      "periods": [
        "1",
        "-1",
        "1",
        "-2",
        "6"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "1",
        "gamma": "10/9"
      },
      "status": "fails",
      "periods": [
        "1",
        "-1",
        "37/36",
        "-71/36",
        "217/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "-1",
        "beta": "1",
        "gamma": "19/12"
      },
      "status": "fails",
      "periods": [
        "1",
        "-1",
        "3/2",
        "-3/2",
        "13/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "-1",
        "gamma": "-4/3"
      },
      "status": "passes",
      "periods": [
        "0",
        "1",
        "-1",
        "4",
        "0"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "-1",
        "gamma": "-47/36"
      },
      "status": "fails",
      "periods": [
        "0",
        "1",
        "-35/36",
        "145/36",
        "1/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "-1",
        "gamma": "-5/6"
      },
      "status": "fails",
      "periods": [
        "0",
        "1",
        "-1/2",
        "9/2",
        "1/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "-1",
        "gamma": "-1/3"
      },
      "status": "passes",
      "periods": [
        "0",
        "1",
        "0",
        "5",
        "1"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "-1",
        "gamma": "-11/36"
      },
      "status": "fails",
      "periods": [
        "0",
        "1",
        "1/36",
        "181/36",
        "37/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "-1",
        "gamma": "1/6"
      },
      "status": "fails",
      "periods": [
        "0",
        "1",
        "1/2",
        "11/2",
        "3/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "-1",
        "gamma": "2/3"
      },
      "status": "passes",
      "periods": [
        "0",
        "1",
        "1",
        "6",
        "2"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "-1",
        "gamma": "25/36"
      },
      "status": "fails",
      "periods": [
        "0",
        "1",
        "37/36",
        "217/36",
        "73/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "-1",
        "gamma": "7/6"
      },
      "status": "fails",
      "periods": [
        "0",
        "1",
        "3/2",
        "13/2",
        "5/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "0",
        "gamma": "-1"
      },
      "status": "passes",
      "periods": [
        "0",
        "0",
        "-1",
        "-1",
        "-1"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "0",
        "gamma": "-35/36"
      },
      "status": "fails",
      "periods": [
        "0",
        "0",
        "-35/36",
        "-35/36",
        "-35/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "0",
        "gamma": "-1/2"
      },
      "status": "fails",
      "periods": [
        "0",
        "0",
        "-1/2",
        "-1/2",
        "-1/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "0",
        "gamma": "0"
      },
      "status": "passes",
      "periods": [
        "0",
        "0",
        "0",
        "0",
        "0"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "0",
        "gamma": "1/36"
      },
      "status": "fails",
      "periods": [
        "0",
        "0",
        "1/36",
        "1/36",
        "1/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "0",
        "gamma": "1/2"
      },
      "status": "fails",
      "periods": [
        "0",
        "0",
        "1/2",
        "1/2",
        "1/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "0",
        "gamma": "1"
      },
      "status": "passes",
      "periods": [
        "0",
        "0",
        "1",
        "1",
        "1"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "0",
        "gamma": "37/36"
      },
      "status": "fails",
      "periods": [
        "0",
        "0",
        "37/36",
        "37/36",
        "37/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "0",
        "gamma": "3/2"
      },
      "status": "fails",
      "periods": [
        "0",
        "0",
        "3/2",
        "3/2",
        "3/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "1",
        "gamma": "-2/3"
      },
      "status": "passes",
      "periods": [
        "0",
        "-1",
        "-1",
        "-6",
        "-2"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "1",
        "gamma": "-23/36"
      },
      "status": "fails",
      "periods": [
        "0",
        "-1",
        "-35/36",
        "-215/36",
        "-71/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "1",
        "gamma": "-1/6"
      },
      "status": "fails",
      "periods": [
        "0",
        "-1",
        "-1/2",
        "-11/2",
        "-3/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "1",
        "gamma": "1/3"
      },
      "status": "passes",
      "periods": [
        "0",
        "-1",
        "0",
        "-5",
        "-1"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "1",
        "gamma": "13/36"
      },
      "status": "fails",
      "periods": [
        "0",
        "-1",
        "1/36",
        "-179/36",
        "-35/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "1",
        "gamma": "5/6"
      },
      "status": "fails",
      "periods": [
        "0",
        "-1",
        "1/2",
        "-9/2",
        "-1/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "1",
        "gamma": "4/3"
      },
      "status": "passes",
      "periods": [
        "0",
        "-1",
        "1",
        "-4",
        "0"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "1",
        "gamma": "49/36"
      },
      "status": "fails",
      "periods": [
        "0",
        "-1",
        "37/36",
        "-143/36",
        "1/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "0",
        "beta": "1",
        "gamma": "11/6"
      },
      "status": "fails",
      "periods": [
        "0",
        "-1",
        "3/2",
        "-7/2",
        "1/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "-1",
        "gamma": "-13/12"
      },
      "status": "passes",
      "periods": [
        "-1",
        "1",
        "-1",
        "2",
        "-6"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "-1",
        "gamma": "-19/18"
      },
      "status": "fails",
      "periods": [
        "-1",
        "1",
        "-35/36",
        "73/36",
        "-215/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "-1",
        "gamma": "-7/12"
      },
      "status": "fails",
      "periods": [
        "-1",
        "1",
        "-1/2",
        "5/2",
        "-11/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "-1",
        "gamma": "-1/12"
      },
      "status": "passes",
      "periods": [
        "-1",
        "1",
        "0",
        "3",
        "-5"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "-1",
        "gamma": "-1/18"
      },
      "status": "fails",
      "periods": [
        "-1",
        "1",
        "1/36",
        "109/36",
        "-179/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "-1",
        "gamma": "5/12"
      },
      "status": "fails",
      "periods": [
        "-1",
        "1",
        "1/2",
        "7/2",
        "-9/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "-1",
        "gamma": "11/12"
      },
      "status": "passes",
      "periods": [
        "-1",
        "1",
        "1",
        "4",
        "-4"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "-1",
        "gamma": "17/18"
      },
      "status": "fails",
      "periods": [
        "-1",
        "1",
        "37/36",
        "145/36",
        "-143/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "-1",
        "gamma": "17/12"
      },
      "status": "fails",
      "periods": [
        "-1",
        "1",
        "3/2",
        "9/2",
        "-7/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "0",
        "gamma": "-3/4"
      },
      "status": "passes",
      "periods": [
        "-1",
        "0",
        "-1",
        "-3",
        "-7"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "0",
        "gamma": "-13/18"
      },
      "status": "fails",
      "periods": [
        "-1",
        "0",
        "-35/36",
        "-107/36",
        "-251/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "0",
        "gamma": "-1/4"
      },
      "status": "fails",
      "periods": [
        "-1",
        "0",
        "-1/2",
        "-5/2",
        "-13/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "0",
        "gamma": "1/4"
      },
      "status": "passes",
      "periods": [
        "-1",
        "0",
        "0",
        "-2",
        "-6"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "0",
        "gamma": "5/18"
      },
      "status": "fails",
      "periods": [
        "-1",
        "0",
        "1/36",
        "-71/36",
        "-215/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "0",
        "gamma": "3/4"
      },
      "status": "fails",
      "periods": [
        "-1",
        "0",
        "1/2",
        "-3/2",
        "-11/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "0",
        "gamma": "5/4"
      },
      "status": "passes",
      "periods": [
        "-1",
        "0",
        "1",
        "-1",
        "-5"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "0",
        "gamma": "23/18"
      },
      "status": "fails",
      "periods": [
        "-1",
        "0",
        "37/36",
        "-35/36",
        "-179/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "0",
        "gamma": "7/4"
      },
      "status": "fails",
      "periods": [
        "-1",
        "0",
        "3/2",
        "-1/2",
        "-9/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "1",
        "gamma": "-5/12"
      },
      "status": "passes",
      "periods": [
        "-1",
        "-1",
        "-1",
        "-8",
        "-8"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "1",
        "gamma": "-7/18"
      },
      "status": "fails",
      "periods": [
        "-1",
        "-1",
        "-35/36",
        "-287/36",
        "-287/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "1",
        "gamma": "1/12"
      },
      "status": "fails",
      "periods": [
        "-1",
        "-1",
        "-1/2",
        "-15/2",
        "-15/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "1",
        "gamma": "7/12"
      },
      "status": "passes",
      "periods": [
        "-1",
        "-1",
        "0",
        "-7",
        "-7"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "1",
        "gamma": "11/18"
      },
      "status": "fails",
      "periods": [
        "-1",
        "-1",
        "1/36",
        "-251/36",
        "-251/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "1",
        "gamma": "13/12"
      },
      "status": "fails",
      "periods": [
        "-1",
        "-1",
        "1/2",
        "-13/2",
        "-13/2"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "1",
        "gamma": "19/12"
      },
      "status": "passes",
      "periods": [
        "-1",
        "-1",
        "1",
        "-6",
        "-6"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "1",
        "gamma": "29/18"
      },
      "status": "fails",
      "periods": [
        "-1",
        "-1",
        "37/36",
        "-215/36",
        "-215/36"
      ]
    },
    {
      "coefficients": {
        "alpha": "1",
        "beta": "1",
        "gamma": "25/12"
      },
      "status": "fails",
      "periods": [
        "-1",
        "-1",
        "3/2",
        "-11/2",
        "-11/2"
      ]
    }
  ]
}
