{
  "raw_polynomial": "96196864*u**7/11594025 - 1407352736*u**6/11594025 + 2488108196*u**5/3864675 - 33158293823*u**4/23188050 + 10041909623*u**3/11594025 + 902890514*u**2/772935 - 78233027*u/51529 + 173985/454",
  "degree": 7,
  "isolating_intervals": [
    {
      "lower": "-1",
      "upper": "-1",
      "multiplicity": 1
    },
    {
      "lower": "3/8",
      "upper": "3/8",
      "multiplicity": 1
    },
    {
      "lower": "1",
      "upper": "1",
      "multiplicity": 1
    },
    {
      "lower": "15/8",
      "upper": "15/8",
      "multiplicity": 1
    },
    {
      "lower": "3",
      "upper": "3",
      "multiplicity": 1
    },
    {
      "lower": "35/8",
      "upper": "35/8",
      "multiplicity": 1
    },
    {
      "lower": "1880695/375769",
      "upper": "1880695/375769",
      "multiplicity": 1
    }
  ],
  "candidates": [
    {
      "ratio": "-1",
      "ratio_numerical": -1.0,
      "multiplicity": 1,
      "status": "rejected_nonpositive_ratio"
    },
    {
      "ratio": "3/8",
      "ratio_numerical": 0.375,
      "multiplicity": 1,
      "status": "positive_regular_equilibrium",
      "state": [
        "227/1533",
        "72407/61320",
        "7881/16352",
        "1839/81760",
        "1/2",
        "4/3",
        "1657/292",
        "44119/11680",
        "561/11680",
        "227/3066",
        "34501/61320",
        "613/20440"
      ]
    },
    {
      "ratio": "1",
      "ratio_numerical": 1.0,
      "multiplicity": 1,
      "status": "positive_regular_equilibrium",
      "state": [
        "227/5481",
        "72407/82215",
        "5254/5481",
        "9808/82215",
        "1",
        "1",
        "1657/522",
        "44119/7830",
        "748/3915",
        "227/5481",
        "69002/82215",
        "9808/82215"
      ]
    },
    {
      "ratio": "15/8",
      "ratio_numerical": 1.875,
      "multiplicity": 1,
      "status": "positive_regular_equilibrium",
      "state": [
        "908/55755",
        "72407/111510",
        "13135/9912",
        "3065/9912",
        "3/2",
        "4/5",
        "1657/885",
        "44119/7080",
        "187/472",
        "454/18585",
        "34501/37170",
        "613/2478"
      ]
    },
    {
      "ratio": "3",
      "ratio_numerical": 3.0,
      "multiplicity": 1,
      "status": "positive_regular_equilibrium",
      "state": [
        "2270/298683",
        "144814/298683",
        "52540/33187",
        "19616/33187",
        "2",
        "2/3",
        "16570/14223",
        "88238/14223",
        "272/431",
        "4540/298683",
        "276008/298683",
        "39232/99561"
      ]
    },
    {
      "ratio": "35/8",
      "ratio_numerical": 4.375,
      "multiplicity": 1,
      "status": "positive_regular_equilibrium",
      "state": [
        "227/57519",
        "72407/197208",
        "459725/262944",
        "750925/788832",
        "5/2",
        "4/7",
        "8285/10956",
        "1544165/262944",
        "20825/23904",
        "1135/115038",
        "172505/197208",
        "107275/197208"
      ]
    },
    {
      "ratio": "1880695/375769",
      "ratio_numerical": 5.004923237414475,
      "multiplicity": 1,
      "status": "rejected_negative_concentration"
    }
  ],
  "exceptional": {
    "status": "absent",
    "reason": "B(r) differs from r D(r)"
  },
  "positive_count": 5
}