balanced-root-checks.json

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

72516 bytes, as of the version from 2026-10-27 01:12 (current). Recorded here, not run.

{
  "tid": "T512",
  "all_passed": true,
  "count": 336,
  "controls": [
    "pi",
    "displaced_value_rejected",
    "nan_rejected",
    "wide_ball_rejected",
    "integral_t_equals_half",
    "Q0_logarithm",
    "F0_free_sine",
    "G0_free_cosine"
  ],
  "numbers_sha256": "e27094c7ce3bf179a39693107ac45d546e6731b042ae860387f4d3a41adf8b15",
  "new_roots": 0,
  "all_existing_numbers_and_annotations_unchanged": true,
  "independent_free_checks": 48,
  "limitations": "No extension of zero depth or coupling range; fresh endpoint and index checks validate retained roots rather than claim new values.",
  "records": [
    {
      "ell": "0",
      "eta": "0",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "49/16",
        "53/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "0",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "97/16",
        "101/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "0",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "149/16",
        "153/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "0",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "201/16",
        "205/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "0",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "249/16",
        "253/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "0",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "301/16",
        "305/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "0",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "349/16",
        "353/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "0",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "401/16",
        "405/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "0",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "449/16",
        "453/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "0",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "501/16",
        "505/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "0",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "549/16",
        "553/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "0",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "601/16",
        "605/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "69/16",
        "73/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "125/16",
        "129/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "177/16",
        "181/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "229/16",
        "233/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "281/16",
        "285/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "333/16",
        "337/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "385/16",
        "389/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "437/16",
        "441/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "489/16",
        "493/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "537/16",
        "541/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "589/16",
        "593/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1/2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "641/16",
        "645/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "33/16",
        "37/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "77/16",
        "81/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "121/16",
        "125/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "169/16",
        "173/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "217/16",
        "221/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "269/16",
        "273/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "317/16",
        "321/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "365/16",
        "369/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "413/16",
        "417/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "465/16",
        "469/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "513/16",
        "517/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1/2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "565/16",
        "569/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "93/16",
        "97/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "149/16",
        "153/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "205/16",
        "209/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "261/16",
        "265/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "313/16",
        "317/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "365/16",
        "369/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "417/16",
        "421/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "469/16",
        "473/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "521/16",
        "525/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "573/16",
        "577/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "625/16",
        "629/16"
      ]
    },
    {
      "ell": "0",
      "eta": "1",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "677/16",
        "681/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "21/16",
        "25/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "61/16",
        "65/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "101/16",
        "105/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "145/16",
        "149/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "193/16",
        "197/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "241/16",
        "245/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "289/16",
        "293/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "337/16",
        "341/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "385/16",
        "389/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "433/16",
        "437/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "481/16",
        "485/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-1",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "529/16",
        "533/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "133/16",
        "137/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "197/16",
        "201/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "257/16",
        "261/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "313/16",
        "317/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "369/16",
        "373/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "425/16",
        "429/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "477/16",
        "481/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "533/16",
        "537/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "585/16",
        "589/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "637/16",
        "641/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "689/16",
        "693/16"
      ]
    },
    {
      "ell": "0",
      "eta": "2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "745/16",
        "749/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "13/16",
        "17/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "37/16",
        "41/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "73/16",
        "77/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "113/16",
        "117/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "153/16",
        "157/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "197/16",
        "201/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "241/16",
        "245/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "285/16",
        "289/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "333/16",
        "337/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "377/16",
        "381/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "425/16",
        "429/16"
      ]
    },
    {
      "ell": "0",
      "eta": "-2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "473/16",
        "477/16"
      ]
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "69/16",
        "73/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "121/16",
        "125/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "173/16",
        "177/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "225/16",
        "229/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "273/16",
        "277/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "325/16",
        "329/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "373/16",
        "377/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "425/16",
        "429/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "473/16",
        "477/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "525/16",
        "529/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "577/16",
        "581/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "0",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "625/16",
        "629/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "85/16",
        "89/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "141/16",
        "145/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "193/16",
        "197/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "249/16",
        "253/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "301/16",
        "305/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "349/16",
        "353/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "401/16",
        "405/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "453/16",
        "457/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "505/16",
        "509/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "557/16",
        "561/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "605/16",
        "609/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1/2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "657/16",
        "661/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "57/16",
        "61/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "105/16",
        "109/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "153/16",
        "157/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "201/16",
        "205/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "249/16",
        "253/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "297/16",
        "301/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "349/16",
        "353/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "397/16",
        "401/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "445/16",
        "449/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "497/16",
        "501/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "545/16",
        "549/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1/2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "593/16",
        "597/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "105/16",
        "109/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "161/16",
        "165/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "217/16",
        "221/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "273/16",
        "277/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "325/16",
        "329/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "377/16",
        "381/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "429/16",
        "433/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "481/16",
        "485/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "533/16",
        "537/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "585/16",
        "589/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "637/16",
        "641/16"
      ]
    },
    {
      "ell": "1",
      "eta": "1",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "689/16",
        "693/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "45/16",
        "49/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "89/16",
        "93/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "133/16",
        "137/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "181/16",
        "185/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "225/16",
        "229/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "273/16",
        "277/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "321/16",
        "325/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "369/16",
        "373/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "417/16",
        "421/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "469/16",
        "473/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "517/16",
        "521/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-1",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "565/16",
        "569/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "141/16",
        "145/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "205/16",
        "209/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "265/16",
        "269/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "321/16",
        "325/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "377/16",
        "381/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "429/16",
        "433/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "485/16",
        "489/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "537/16",
        "541/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "593/16",
        "597/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "645/16",
        "649/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "697/16",
        "701/16"
      ]
    },
    {
      "ell": "1",
      "eta": "2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "749/16",
        "753/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "29/16",
        "33/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "65/16",
        "69/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "105/16",
        "109/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "145/16",
        "149/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "189/16",
        "193/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "233/16",
        "237/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "277/16",
        "281/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "325/16",
        "329/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "369/16",
        "373/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "417/16",
        "421/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "465/16",
        "469/16"
      ]
    },
    {
      "ell": "1",
      "eta": "-2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "513/16",
        "517/16"
      ]
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "89/16",
        "93/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "145/16",
        "149/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "197/16",
        "201/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "245/16",
        "249/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "297/16",
        "301/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "349/16",
        "353/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "397/16",
        "401/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "449/16",
        "453/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "501/16",
        "505/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "549/16",
        "553/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "601/16",
        "605/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "0",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "649/16",
        "653/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "105/16",
        "109/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "161/16",
        "165/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "213/16",
        "217/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "269/16",
        "273/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "321/16",
        "325/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "369/16",
        "373/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "421/16",
        "425/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "473/16",
        "477/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "525/16",
        "529/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "577/16",
        "581/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "629/16",
        "633/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1/2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "677/16",
        "681/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "77/16",
        "81/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "129/16",
        "133/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "177/16",
        "181/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "225/16",
        "229/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "277/16",
        "281/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "325/16",
        "329/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "373/16",
        "377/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "425/16",
        "429/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "473/16",
        "477/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "525/16",
        "529/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "573/16",
        "577/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1/2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "621/16",
        "625/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "121/16",
        "125/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "177/16",
        "181/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "233/16",
        "237/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "289/16",
        "293/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "341/16",
        "345/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "393/16",
        "397/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "449/16",
        "453/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "501/16",
        "505/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "553/16",
        "557/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "605/16",
        "609/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "657/16",
        "661/16"
      ]
    },
    {
      "ell": "2",
      "eta": "1",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "705/16",
        "709/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "69/16",
        "73/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "113/16",
        "117/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "161/16",
        "165/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "209/16",
        "213/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "257/16",
        "261/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "305/16",
        "309/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "353/16",
        "357/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "401/16",
        "405/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "449/16",
        "453/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "497/16",
        "501/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "549/16",
        "553/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-1",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "597/16",
        "601/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "153/16",
        "157/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "217/16",
        "221/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "277/16",
        "281/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "333/16",
        "337/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "389/16",
        "393/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "445/16",
        "449/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "497/16",
        "501/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "553/16",
        "557/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "605/16",
        "609/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "657/16",
        "661/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "709/16",
        "713/16"
      ]
    },
    {
      "ell": "2",
      "eta": "2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "765/16",
        "769/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "49/16",
        "53/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "89/16",
        "93/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "133/16",
        "137/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "177/16",
        "181/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "221/16",
        "225/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "265/16",
        "269/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "313/16",
        "317/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "357/16",
        "361/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "405/16",
        "409/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "453/16",
        "457/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "497/16",
        "501/16"
      ]
    },
    {
      "ell": "2",
      "eta": "-2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "545/16",
        "549/16"
      ]
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "109/16",
        "113/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "165/16",
        "169/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "217/16",
        "221/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "269/16",
        "273/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "321/16",
        "325/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "369/16",
        "373/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "421/16",
        "425/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "473/16",
        "477/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "521/16",
        "525/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "573/16",
        "577/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "625/16",
        "629/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "0",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "673/16",
        "677/16"
      ],
      "independent_free_bessel_zero_150_digits": true
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "121/16",
        "125/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "181/16",
        "185/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "233/16",
        "237/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "289/16",
        "293/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "341/16",
        "345/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "393/16",
        "397/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "445/16",
        "449/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "497/16",
        "501/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "545/16",
        "549/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "597/16",
        "601/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "649/16",
        "653/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1/2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "701/16",
        "705/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "97/16",
        "101/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "149/16",
        "153/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "201/16",
        "205/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "249/16",
        "253/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "301/16",
        "305/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "349/16",
        "353/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "401/16",
        "405/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "449/16",
        "453/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "501/16",
        "505/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "549/16",
        "553/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "601/16",
        "605/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1/2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "649/16",
        "653/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "137/16",
        "141/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "197/16",
        "201/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "253/16",
        "257/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "309/16",
        "313/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "361/16",
        "365/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "413/16",
        "417/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "465/16",
        "469/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "517/16",
        "521/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "569/16",
        "573/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "621/16",
        "625/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "673/16",
        "677/16"
      ]
    },
    {
      "ell": "3",
      "eta": "1",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "725/16",
        "729/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "89/16",
        "93/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "137/16",
        "141/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "185/16",
        "189/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "233/16",
        "237/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "281/16",
        "285/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "329/16",
        "333/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "381/16",
        "385/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "429/16",
        "433/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "477/16",
        "481/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "525/16",
        "529/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "577/16",
        "581/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-1",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "625/16",
        "629/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "165/16",
        "169/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "229/16",
        "233/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "289/16",
        "293/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "349/16",
        "353/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "405/16",
        "409/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "457/16",
        "461/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "513/16",
        "517/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "565/16",
        "569/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "621/16",
        "625/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "673/16",
        "677/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "725/16",
        "729/16"
      ]
    },
    {
      "ell": "3",
      "eta": "2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "777/16",
        "781/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "1",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "69/16",
        "73/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "2",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "113/16",
        "117/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "3",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "157/16",
        "161/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "4",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "205/16",
        "209/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "5",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "249/16",
        "253/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "6",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "293/16",
        "297/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "7",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "341/16",
        "345/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "8",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "389/16",
        "393/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "9",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "433/16",
        "437/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "10",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "481/16",
        "485/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "11",
      "decimal_endpoint_signs": [
        1,
        -1
      ],
      "indexed_scan_bracket": [
        "529/16",
        "533/16"
      ]
    },
    {
      "ell": "3",
      "eta": "-2",
      "n": "12",
      "decimal_endpoint_signs": [
        -1,
        1
      ],
      "indexed_scan_bracket": [
        "577/16",
        "581/16"
      ]
    }
  ]
}