{
  "tid": "T25",
  "working_bits": 640,
  "mpmath_digits": [
    150,
    200
  ],
  "checked": 774,
  "reference_branches": [],
  "failures": [],
  "records": [
    {
      "parameters": [
        "0"
      ],
      "accuracy_bits": 639,
      "independent_ball": false,
      "mpmath_error_ulps": "0.991074043256641"
    },
    {
      "parameters": [
        "1/2"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.27777187103746"
    },
    {
      "parameters": [
        "1/3"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.682920978176568"
    },
    {
      "parameters": [
        "2/3"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.647285930012124"
    },
    {
      "parameters": [
        "1/4"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.334789378363785"
    },
    {
      "parameters": [
        "3/4"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.551774761119037"
    },
    {
      "parameters": [
        "1/5"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.875296622692873"
    },
    {
      "parameters": [
        "2/5"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.224714815154352"
    },
    {
      "parameters": [
        "3/5"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.127588818972208"
    },
    {
      "parameters": [
        "4/5"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.425613660688722"
    },
    {
      "parameters": [
        "1/6"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.819094079866836"
    },
    {
      "parameters": [
        "5/6"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.37208312092349"
    },
    {
      "parameters": [
        "1/7"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.811940145436497"
    },
    {
      "parameters": [
        "2/7"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.506362792127529"
    },
    {
      "parameters": [
        "3/7"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.216562706400117"
    },
    {
      "parameters": [
        "4/7"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.565036283676371"
    },
    {
      "parameters": [
        "5/7"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.995087702937539"
    },
    {
      "parameters": [
        "6/7"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.70391713642926"
    },
    {
      "parameters": [
        "1/8"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.022098996320096"
    },
    {
      "parameters": [
        "3/8"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0143904226663764"
    },
    {
      "parameters": [
        "5/8"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.444602183294925"
    },
    {
      "parameters": [
        "7/8"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.448314732362723"
    },
    {
      "parameters": [
        "1/9"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.913831070839278"
    },
    {
      "parameters": [
        "2/9"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.616337250068135"
    },
    {
      "parameters": [
        "4/9"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.809963903834011"
    },
    {
      "parameters": [
        "5/9"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.583727864620508"
    },
    {
      "parameters": [
        "7/9"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.902443594080309"
    },
    {
      "parameters": [
        "8/9"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.502184067545677"
    },
    {
      "parameters": [
        "1/10"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0977842851969861"
    },
    {
      "parameters": [
        "3/10"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.466982037667278"
    },
    {
      "parameters": [
        "7/10"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.667049257606637"
    },
    {
      "parameters": [
        "9/10"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.829455043937663"
    },
    {
      "parameters": [
        "1/11"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.979845964162164"
    },
    {
      "parameters": [
        "2/11"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.675258612938704"
    },
    {
      "parameters": [
        "3/11"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.983314876687207"
    },
    {
      "parameters": [
        "4/11"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0427736156856645"
    },
    {
      "parameters": [
        "5/11"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.68176734643287"
    },
    {
      "parameters": [
        "6/11"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.489578714639255"
    },
    {
      "parameters": [
        "7/11"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.839917230702204"
    },
    {
      "parameters": [
        "8/11"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0469659660980192"
    },
    {
      "parameters": [
        "9/11"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.633558241408963"
    },
    {
      "parameters": [
        "10/11"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.994807865257452"
    },
    {
      "parameters": [
        "1/12"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.976451270245889"
    },
    {
      "parameters": [
        "5/12"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.571453107318096"
    },
    {
      "parameters": [
        "7/12"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.418137360839524"
    },
    {
      "parameters": [
        "11/12"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.729776160554294"
    },
    {
      "parameters": [
        "1/13"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.409698437110797"
    },
    {
      "parameters": [
        "2/13"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.071634050125819"
    },
    {
      "parameters": [
        "3/13"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.850835563379597"
    },
    {
      "parameters": [
        "4/13"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.11826993265264"
    },
    {
      "parameters": [
        "5/13"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.874109192451962"
    },
    {
      "parameters": [
        "6/13"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.537694011768791"
    },
    {
      "parameters": [
        "7/13"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.471855150378513"
    },
    {
      "parameters": [
        "8/13"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.293571911000481"
    },
    {
      "parameters": [
        "9/13"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.874770399207234"
    },
    {
      "parameters": [
        "10/13"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.690093182613701"
    },
    {
      "parameters": [
        "11/13"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.917180857989471"
    },
    {
      "parameters": [
        "12/13"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.595695705380473"
    },
    {
      "parameters": [
        "1/14"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.477230979716086"
    },
    {
      "parameters": [
        "3/14"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.918072690081765"
    },
    {
      "parameters": [
        "5/14"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.194238629310569"
    },
    {
      "parameters": [
        "9/14"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.773823484033662"
    },
    {
      "parameters": [
        "11/14"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.95440085340365"
    },
    {
      "parameters": [
        "13/14"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.416704728796865"
    },
    {
      "parameters": [
        "1/15"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.192057468880554"
    },
    {
      "parameters": [
        "2/15"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.841919527281808"
    },
    {
      "parameters": [
        "4/15"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.155836416323444"
    },
    {
      "parameters": [
        "7/15"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.925201098550515"
    },
    {
      "parameters": [
        "8/15"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.255821587015999"
    },
    {
      "parameters": [
        "11/15"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.650303049923801"
    },
    {
      "parameters": [
        "13/15"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.187098535234635"
    },
    {
      "parameters": [
        "14/15"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.376700544627779"
    },
    {
      "parameters": [
        "1/16"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.91952629940943"
    },
    {
      "parameters": [
        "3/16"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.317195794289866"
    },
    {
      "parameters": [
        "5/16"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.681443495480939"
    },
    {
      "parameters": [
        "7/16"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.648144051358271"
    },
    {
      "parameters": [
        "9/16"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.804906325401352"
    },
    {
      "parameters": [
        "11/16"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.521501751550797"
    },
    {
      "parameters": [
        "13/16"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.33135001317803"
    },
    {
      "parameters": [
        "15/16"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.215285535660101"
    },
    {
      "parameters": [
        "1/17"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.706492563103101"
    },
    {
      "parameters": [
        "2/17"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.676918247143829"
    },
    {
      "parameters": [
        "3/17"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.364704484035045"
    },
    {
      "parameters": [
        "4/17"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.990320751183404"
    },
    {
      "parameters": [
        "5/17"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.258225458975743"
    },
    {
      "parameters": [
        "6/17"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.185582679677004"
    },
    {
      "parameters": [
        "7/17"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.354722489833897"
    },
    {
      "parameters": [
        "8/17"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.00453106171096563"
    },
    {
      "parameters": [
        "9/17"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.383509640491698"
    },
    {
      "parameters": [
        "10/17"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0242635105046764"
    },
    {
      "parameters": [
        "11/17"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.263349171961204"
    },
    {
      "parameters": [
        "12/17"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.930697614335713"
    },
    {
      "parameters": [
        "13/17"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.961376679247476"
    },
    {
      "parameters": [
        "14/17"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.667409837039002"
    },
    {
      "parameters": [
        "15/17"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.413503514297766"
    },
    {
      "parameters": [
        "16/17"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.376504661103563"
    },
    {
      "parameters": [
        "1/18"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.897696170376986"
    },
    {
      "parameters": [
        "5/18"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.107016006777913"
    },
    {
      "parameters": [
        "7/18"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.743456110596951"
    },
    {
      "parameters": [
        "11/18"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.108877174968538"
    },
    {
      "parameters": [
        "13/18"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.175101692957306"
    },
    {
      "parameters": [
        "17/18"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.560722573807862"
    },
    {
      "parameters": [
        "1/19"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.403736687448099"
    },
    {
      "parameters": [
        "2/19"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.208074666664651"
    },
    {
      "parameters": [
        "3/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.932477282989743"
    },
    {
      "parameters": [
        "4/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.369728475241653"
    },
    {
      "parameters": [
        "5/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.101489423632611"
    },
    {
      "parameters": [
        "6/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.902760777788118"
    },
    {
      "parameters": [
        "7/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.67576669621036"
    },
    {
      "parameters": [
        "8/19"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.384643819473527"
    },
    {
      "parameters": [
        "9/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.06349471081626"
    },
    {
      "parameters": [
        "10/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.215944538883704"
    },
    {
      "parameters": [
        "11/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.76265081970602"
    },
    {
      "parameters": [
        "12/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.496529337893212"
    },
    {
      "parameters": [
        "13/19"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.155151185800257"
    },
    {
      "parameters": [
        "14/19"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.504229004106237"
    },
    {
      "parameters": [
        "15/19"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0277742007734967"
    },
    {
      "parameters": [
        "16/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.07011499097553"
    },
    {
      "parameters": [
        "17/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.197244575539528"
    },
    {
      "parameters": [
        "18/19"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.301030370499778"
    },
    {
      "parameters": [
        "1/20"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.195390362404479"
    },
    {
      "parameters": [
        "3/20"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.792034992312456"
    },
    {
      "parameters": [
        "7/20"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.580040200902723"
    },
    {
      "parameters": [
        "9/20"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.477838766832458"
    },
    {
      "parameters": [
        "11/20"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.145323298397141"
    },
    {
      "parameters": [
        "13/20"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.312852732472792"
    },
    {
      "parameters": [
        "17/20"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.428928818577147"
    },
    {
      "parameters": [
        "19/20"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.227961007185441"
    },
    {
      "parameters": [
        "1/21"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.634827162280108"
    },
    {
      "parameters": [
        "2/21"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.150785933194577"
    },
    {
      "parameters": [
        "4/21"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.486638045900299"
    },
    {
      "parameters": [
        "5/21"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.920760123876204"
    },
    {
      "parameters": [
        "8/21"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.881682984032269"
    },
    {
      "parameters": [
        "10/21"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.518435348535511"
    },
    {
      "parameters": [
        "11/21"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.483235323270799"
    },
    {
      "parameters": [
        "13/21"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.253468452186053"
    },
    {
      "parameters": [
        "16/21"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.387051862384127"
    },
    {
      "parameters": [
        "17/21"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0471370630405032"
    },
    {
      "parameters": [
        "19/21"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.726362460505909"
    },
    {
      "parameters": [
        "20/21"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.559559907320429"
    },
    {
      "parameters": [
        "1/22"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.702021546159641"
    },
    {
      "parameters": [
        "3/22"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.468649621328388"
    },
    {
      "parameters": [
        "5/22"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0746192892923075"
    },
    {
      "parameters": [
        "7/22"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.19069140955358"
    },
    {
      "parameters": [
        "9/22"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.18371067267302"
    },
    {
      "parameters": [
        "13/22"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.333822156281837"
    },
    {
      "parameters": [
        "15/22"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.309361740853511"
    },
    {
      "parameters": [
        "17/22"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.49292305419789"
    },
    {
      "parameters": [
        "19/22"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.36041354060758"
    },
    {
      "parameters": [
        "21/22"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.287509714904486"
    },
    {
      "parameters": [
        "1/23"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.179639826034581"
    },
    {
      "parameters": [
        "2/23"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0840280721799663"
    },
    {
      "parameters": [
        "3/23"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0900097629590793"
    },
    {
      "parameters": [
        "4/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.958514625322436"
    },
    {
      "parameters": [
        "5/23"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.484550489747452"
    },
    {
      "parameters": [
        "6/23"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.795895050391827"
    },
    {
      "parameters": [
        "7/23"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0990171586862092"
    },
    {
      "parameters": [
        "8/23"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.207202654910212"
    },
    {
      "parameters": [
        "9/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.601669588855723"
    },
    {
      "parameters": [
        "10/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.706100465996296"
    },
    {
      "parameters": [
        "11/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.692093679871042"
    },
    {
      "parameters": [
        "12/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.143614289944332"
    },
    {
      "parameters": [
        "13/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.674622313309348"
    },
    {
      "parameters": [
        "14/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.119832746757404"
    },
    {
      "parameters": [
        "15/23"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.886150012603925"
    },
    {
      "parameters": [
        "16/23"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.687947094937494"
    },
    {
      "parameters": [
        "17/23"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.622032373973864"
    },
    {
      "parameters": [
        "18/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.434773445850407"
    },
    {
      "parameters": [
        "19/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.209870139272772"
    },
    {
      "parameters": [
        "20/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.920723709091592"
    },
    {
      "parameters": [
        "21/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0257948667980263"
    },
    {
      "parameters": [
        "22/23"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.542014747661936"
    },
    {
      "parameters": [
        "1/24"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.243866784863509"
    },
    {
      "parameters": [
        "5/24"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.135681544645316"
    },
    {
      "parameters": [
        "7/24"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.123847059331222"
    },
    {
      "parameters": [
        "11/24"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.154847063962427"
    },
    {
      "parameters": [
        "13/24"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.810028445874645"
    },
    {
      "parameters": [
        "17/24"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.421982513393417"
    },
    {
      "parameters": [
        "19/24"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.609915768090911"
    },
    {
      "parameters": [
        "23/24"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.808305381912666"
    },
    {
      "parameters": [
        "1/25"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.986439887183757"
    },
    {
      "parameters": [
        "2/25"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.149791790846387"
    },
    {
      "parameters": [
        "3/25"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.17989799818379"
    },
    {
      "parameters": [
        "4/25"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.712642723721418"
    },
    {
      "parameters": [
        "6/25"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.245288597942663"
    },
    {
      "parameters": [
        "7/25"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0226171386358805"
    },
    {
      "parameters": [
        "8/25"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.111289086267154"
    },
    {
      "parameters": [
        "9/25"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.884553459787563"
    },
    {
      "parameters": [
        "11/25"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.42289275347257"
    },
    {
      "parameters": [
        "12/25"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.875196705478696"
    },
    {
      "parameters": [
        "13/25"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.303734488006268"
    },
    {
      "parameters": [
        "14/25"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0739968295229274"
    },
    {
      "parameters": [
        "16/25"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.149407874261788"
    },
    {
      "parameters": [
        "17/25"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.287341490185853"
    },
    {
      "parameters": [
        "18/25"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.395048615883197"
    },
    {
      "parameters": [
        "19/25"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.447774466903769"
    },
    {
      "parameters": [
        "21/25"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.829228072112691"
    },
    {
      "parameters": [
        "22/25"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.477770321282867"
    },
    {
      "parameters": [
        "23/25"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.340099596892858"
    },
    {
      "parameters": [
        "24/25"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.683273173056685"
    },
    {
      "parameters": [
        "1/26"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.707582176006086"
    },
    {
      "parameters": [
        "3/26"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.571870678279231"
    },
    {
      "parameters": [
        "5/26"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.381053386064818"
    },
    {
      "parameters": [
        "7/26"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.449941424761062"
    },
    {
      "parameters": [
        "9/26"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.278681202166615"
    },
    {
      "parameters": [
        "11/26"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.865785454918105"
    },
    {
      "parameters": [
        "15/26"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.876901658024955"
    },
    {
      "parameters": [
        "17/26"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.202277873497146"
    },
    {
      "parameters": [
        "19/26"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.597928752961076"
    },
    {
      "parameters": [
        "21/26"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.980977439272449"
    },
    {
      "parameters": [
        "23/26"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.722795829803983"
    },
    {
      "parameters": [
        "25/26"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.826061981926078"
    },
    {
      "parameters": [
        "1/27"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.241065343560445"
    },
    {
      "parameters": [
        "2/27"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.147274689035213"
    },
    {
      "parameters": [
        "4/27"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.732235103278963"
    },
    {
      "parameters": [
        "5/27"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.145062934727657"
    },
    {
      "parameters": [
        "7/27"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.402646947915053"
    },
    {
      "parameters": [
        "8/27"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.530951363146738"
    },
    {
      "parameters": [
        "10/27"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.94629612529379"
    },
    {
      "parameters": [
        "11/27"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.639159347096202"
    },
    {
      "parameters": [
        "13/27"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.933112972840799"
    },
    {
      "parameters": [
        "14/27"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.75717041091152"
    },
    {
      "parameters": [
        "16/27"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.598849950253768"
    },
    {
      "parameters": [
        "17/27"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0913039925397457"
    },
    {
      "parameters": [
        "19/27"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.471523672391708"
    },
    {
      "parameters": [
        "20/27"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.626290606437516"
    },
    {
      "parameters": [
        "22/27"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.352513222628206"
    },
    {
      "parameters": [
        "23/27"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.213959276416817"
    },
    {
      "parameters": [
        "25/27"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.18704396044798"
    },
    {
      "parameters": [
        "26/27"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.574004951669655"
    },
    {
      "parameters": [
        "1/28"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.482144138710857"
    },
    {
      "parameters": [
        "3/28"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.00633211998511525"
    },
    {
      "parameters": [
        "5/28"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.129331661612354"
    },
    {
      "parameters": [
        "9/28"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.952175986524552"
    },
    {
      "parameters": [
        "11/28"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.987677939040012"
    },
    {
      "parameters": [
        "13/28"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.874450426510546"
    },
    {
      "parameters": [
        "15/28"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.833767507458046"
    },
    {
      "parameters": [
        "17/28"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.683252188790724"
    },
    {
      "parameters": [
        "19/28"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.405794380779632"
    },
    {
      "parameters": [
        "23/28"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.979842192015169"
    },
    {
      "parameters": [
        "25/28"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.356918611742654"
    },
    {
      "parameters": [
        "27/28"
      ],
      "accuracy_bits": 634,
      "independent_ball": false,
      "mpmath_error_ulps": "0.910913189516307"
    },
    {
      "parameters": [
        "1/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0903812259692766"
    },
    {
      "parameters": [
        "2/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.184810037591516"
    },
    {
      "parameters": [
        "3/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.876154644437249"
    },
    {
      "parameters": [
        "4/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.070313504278694"
    },
    {
      "parameters": [
        "5/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.391264496760977"
    },
    {
      "parameters": [
        "6/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0581708376126437"
    },
    {
      "parameters": [
        "7/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.107426683545486"
    },
    {
      "parameters": [
        "8/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.955304295636241"
    },
    {
      "parameters": [
        "9/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.332439377809862"
    },
    {
      "parameters": [
        "10/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.318427609773975"
    },
    {
      "parameters": [
        "11/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.319282565553524"
    },
    {
      "parameters": [
        "12/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.962827758958818"
    },
    {
      "parameters": [
        "13/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.117468194827291"
    },
    {
      "parameters": [
        "14/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0100820652595065"
    },
    {
      "parameters": [
        "15/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.524031327502837"
    },
    {
      "parameters": [
        "16/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.323540053420413"
    },
    {
      "parameters": [
        "17/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.885019847647798"
    },
    {
      "parameters": [
        "18/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.966623034093381"
    },
    {
      "parameters": [
        "19/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.960442407191752"
    },
    {
      "parameters": [
        "20/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.405193840341352"
    },
    {
      "parameters": [
        "21/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.216199253715867"
    },
    {
      "parameters": [
        "22/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.948842519706698"
    },
    {
      "parameters": [
        "23/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.524629093950139"
    },
    {
      "parameters": [
        "24/29"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.464093077707069"
    },
    {
      "parameters": [
        "25/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.131246937244367"
    },
    {
      "parameters": [
        "26/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.134172989219068"
    },
    {
      "parameters": [
        "27/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.00150588579194778"
    },
    {
      "parameters": [
        "28/29"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.162168997962589"
    },
    {
      "parameters": [
        "1/30"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.550871694966234"
    },
    {
      "parameters": [
        "7/30"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.410476694637265"
    },
    {
      "parameters": [
        "11/30"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.269955354737252"
    },
    {
      "parameters": [
        "13/30"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.369464370487073"
    },
    {
      "parameters": [
        "17/30"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.312929086854428"
    },
    {
      "parameters": [
        "19/30"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.744969672546779"
    },
    {
      "parameters": [
        "23/30"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0979412567228908"
    },
    {
      "parameters": [
        "29/30"
      ],
      "accuracy_bits": 634,
      "independent_ball": false,
      "mpmath_error_ulps": "0.311493883439034"
    },
    {
      "parameters": [
        "1/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0710316551508565"
    },
    {
      "parameters": [
        "2/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.862702112619189"
    },
    {
      "parameters": [
        "3/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0203983218275163"
    },
    {
      "parameters": [
        "4/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.351190677720549"
    },
    {
      "parameters": [
        "5/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.35954593172588"
    },
    {
      "parameters": [
        "6/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0162037193754209"
    },
    {
      "parameters": [
        "7/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.551699616871529"
    },
    {
      "parameters": [
        "8/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.615079120288894"
    },
    {
      "parameters": [
        "9/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.960228415911671"
    },
    {
      "parameters": [
        "10/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0810432463274678"
    },
    {
      "parameters": [
        "11/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.117070840805542"
    },
    {
      "parameters": [
        "12/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.835300777749106"
    },
    {
      "parameters": [
        "13/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.96003269127237"
    },
    {
      "parameters": [
        "14/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.39421112409424"
    },
    {
      "parameters": [
        "15/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.591569455003926"
    },
    {
      "parameters": [
        "16/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.90900218230278"
    },
    {
      "parameters": [
        "17/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.88622812421181"
    },
    {
      "parameters": [
        "18/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.776622741226016"
    },
    {
      "parameters": [
        "19/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.49231594876027"
    },
    {
      "parameters": [
        "20/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0615639032280473"
    },
    {
      "parameters": [
        "21/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0389977375477284"
    },
    {
      "parameters": [
        "22/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.978562056144521"
    },
    {
      "parameters": [
        "23/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.885557853515889"
    },
    {
      "parameters": [
        "24/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.970318988211801"
    },
    {
      "parameters": [
        "25/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.375835684300222"
    },
    {
      "parameters": [
        "26/31"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.37884514482271"
    },
    {
      "parameters": [
        "27/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.149988707788714"
    },
    {
      "parameters": [
        "28/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.289762027228812"
    },
    {
      "parameters": [
        "29/31"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.317825692010433"
    },
    {
      "parameters": [
        "30/31"
      ],
      "accuracy_bits": 634,
      "independent_ball": false,
      "mpmath_error_ulps": "0.935917211044121"
    },
    {
      "parameters": [
        "1/32"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.741143642207777"
    },
    {
      "parameters": [
        "3/32"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.091816722276849"
    },
    {
      "parameters": [
        "5/32"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.33564488225318"
    },
    {
      "parameters": [
        "7/32"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.736161376887705"
    },
    {
      "parameters": [
        "9/32"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.302534136033747"
    },
    {
      "parameters": [
        "11/32"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.624294396729974"
    },
    {
      "parameters": [
        "13/32"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.425430255700527"
    },
    {
      "parameters": [
        "15/32"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.940025346938538"
    },
    {
      "parameters": [
        "17/32"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0646619833134106"
    },
    {
      "parameters": [
        "19/32"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.425924128185274"
    },
    {
      "parameters": [
        "21/32"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.286613920826561"
    },
    {
      "parameters": [
        "23/32"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.254595248766593"
    },
    {
      "parameters": [
        "25/32"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.71042569759639"
    },
    {
      "parameters": [
        "27/32"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.672850984773956"
    },
    {
      "parameters": [
        "29/32"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.955215748135468"
    },
    {
      "parameters": [
        "31/32"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.67873505686534"
    },
    {
      "parameters": [
        "1/33"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.4392019359667"
    },
    {
      "parameters": [
        "2/33"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.536085245955961"
    },
    {
      "parameters": [
        "4/33"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.976121704176095"
    },
    {
      "parameters": [
        "5/33"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.402513282037199"
    },
    {
      "parameters": [
        "7/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.11477704821925"
    },
    {
      "parameters": [
        "8/33"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.948809209283909"
    },
    {
      "parameters": [
        "10/33"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.482415388947394"
    },
    {
      "parameters": [
        "13/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.663527432757337"
    },
    {
      "parameters": [
        "14/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.283112535494043"
    },
    {
      "parameters": [
        "16/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.34287785493013"
    },
    {
      "parameters": [
        "17/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.152235462502158"
    },
    {
      "parameters": [
        "19/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.609009061387837"
    },
    {
      "parameters": [
        "20/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.41758678758622"
    },
    {
      "parameters": [
        "23/33"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.964327137459329"
    },
    {
      "parameters": [
        "25/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.599184642889921"
    },
    {
      "parameters": [
        "26/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.157479744001859"
    },
    {
      "parameters": [
        "28/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.702047753731269"
    },
    {
      "parameters": [
        "29/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.446234863618402"
    },
    {
      "parameters": [
        "31/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.855438218642801"
    },
    {
      "parameters": [
        "32/33"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.627709983253823"
    },
    {
      "parameters": [
        "1/34"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0235443966095509"
    },
    {
      "parameters": [
        "3/34"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.700017416687505"
    },
    {
      "parameters": [
        "5/34"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.774938149013809"
    },
    {
      "parameters": [
        "7/34"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.569090520238504"
    },
    {
      "parameters": [
        "9/34"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.684529696499876"
    },
    {
      "parameters": [
        "11/34"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.789360008642998"
    },
    {
      "parameters": [
        "13/34"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.56219182022859"
    },
    {
      "parameters": [
        "15/34"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.84073932318297"
    },
    {
      "parameters": [
        "19/34"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.306291217739736"
    },
    {
      "parameters": [
        "21/34"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.751998179815467"
    },
    {
      "parameters": [
        "23/34"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.257867535362421"
    },
    {
      "parameters": [
        "25/34"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.864929801231428"
    },
    {
      "parameters": [
        "27/34"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0669787435531799"
    },
    {
      "parameters": [
        "29/34"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.655013786302352"
    },
    {
      "parameters": [
        "31/34"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0871324318360825"
    },
    {
      "parameters": [
        "33/34"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.566398785709771"
    },
    {
      "parameters": [
        "1/35"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.351814333838928"
    },
    {
      "parameters": [
        "2/35"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.31177564098957"
    },
    {
      "parameters": [
        "3/35"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0747554722745046"
    },
    {
      "parameters": [
        "4/35"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.610535049349469"
    },
    {
      "parameters": [
        "6/35"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.196093266869333"
    },
    {
      "parameters": [
        "8/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.941270265053129"
    },
    {
      "parameters": [
        "9/35"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.677630715556286"
    },
    {
      "parameters": [
        "11/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.935905140872468"
    },
    {
      "parameters": [
        "12/35"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.943205171457225"
    },
    {
      "parameters": [
        "13/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.25758179327618"
    },
    {
      "parameters": [
        "16/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.776938379312476"
    },
    {
      "parameters": [
        "17/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0575275341058531"
    },
    {
      "parameters": [
        "18/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.950057161316023"
    },
    {
      "parameters": [
        "19/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.159415474359374"
    },
    {
      "parameters": [
        "22/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0660926858514096"
    },
    {
      "parameters": [
        "23/35"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.709565940451936"
    },
    {
      "parameters": [
        "24/35"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.34141632505929"
    },
    {
      "parameters": [
        "26/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.197120603128999"
    },
    {
      "parameters": [
        "27/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0183271681669423"
    },
    {
      "parameters": [
        "29/35"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.810215983407493"
    },
    {
      "parameters": [
        "31/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.82287436894479"
    },
    {
      "parameters": [
        "32/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.557206038926982"
    },
    {
      "parameters": [
        "33/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.530206163315487"
    },
    {
      "parameters": [
        "34/35"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0825758879786751"
    },
    {
      "parameters": [
        "1/36"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.909063329218534"
    },
    {
      "parameters": [
        "5/36"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.359267923256252"
    },
    {
      "parameters": [
        "7/36"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.749186307038736"
    },
    {
      "parameters": [
        "11/36"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.522351915490485"
    },
    {
      "parameters": [
        "13/36"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.118207310614197"
    },
    {
      "parameters": [
        "17/36"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.901863817811818"
    },
    {
      "parameters": [
        "19/36"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.423148676139299"
    },
    {
      "parameters": [
        "23/36"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.634399777297224"
    },
    {
      "parameters": [
        "25/36"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0253693498256075"
    },
    {
      "parameters": [
        "29/36"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0947917261503204"
    },
    {
      "parameters": [
        "31/36"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.978414854021882"
    },
    {
      "parameters": [
        "35/36"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0792226377503333"
    },
    {
      "parameters": [
        "1/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.715550540459977"
    },
    {
      "parameters": [
        "2/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.228906483120327"
    },
    {
      "parameters": [
        "3/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.25099306150496"
    },
    {
      "parameters": [
        "4/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.645651914895434"
    },
    {
      "parameters": [
        "5/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.607231973626044"
    },
    {
      "parameters": [
        "6/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.234382526566712"
    },
    {
      "parameters": [
        "7/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.473270273836233"
    },
    {
      "parameters": [
        "8/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.623832859567306"
    },
    {
      "parameters": [
        "9/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.994567151770335"
    },
    {
      "parameters": [
        "10/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.728391459093765"
    },
    {
      "parameters": [
        "11/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.128196233873953"
    },
    {
      "parameters": [
        "12/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.286781386840175"
    },
    {
      "parameters": [
        "13/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.340097921561302"
    },
    {
      "parameters": [
        "14/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.839511473729852"
    },
    {
      "parameters": [
        "15/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.107165669274869"
    },
    {
      "parameters": [
        "16/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.209832586864442"
    },
    {
      "parameters": [
        "17/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.987310808799368"
    },
    {
      "parameters": [
        "18/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0437303722025467"
    },
    {
      "parameters": [
        "19/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.678377386799599"
    },
    {
      "parameters": [
        "20/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.191391027089594"
    },
    {
      "parameters": [
        "21/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0920398817535329"
    },
    {
      "parameters": [
        "22/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.836003521563571"
    },
    {
      "parameters": [
        "23/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.779722161150711"
    },
    {
      "parameters": [
        "24/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.92173103260801"
    },
    {
      "parameters": [
        "25/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.325859586523708"
    },
    {
      "parameters": [
        "26/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.168982531086049"
    },
    {
      "parameters": [
        "27/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0216825045573244"
    },
    {
      "parameters": [
        "28/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.495452921690507"
    },
    {
      "parameters": [
        "29/37"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.969581799092252"
    },
    {
      "parameters": [
        "30/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.465070704147287"
    },
    {
      "parameters": [
        "31/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.957918164678882"
    },
    {
      "parameters": [
        "32/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.468307577984151"
    },
    {
      "parameters": [
        "33/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.587486679417179"
    },
    {
      "parameters": [
        "34/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.230384289197715"
    },
    {
      "parameters": [
        "35/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.780539840138617"
    },
    {
      "parameters": [
        "36/37"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.689847857922943"
    },
    {
      "parameters": [
        "1/38"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.522375123569001"
    },
    {
      "parameters": [
        "3/38"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.64803049657395"
    },
    {
      "parameters": [
        "5/38"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.067217393044875"
    },
    {
      "parameters": [
        "7/38"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.165196759440941"
    },
    {
      "parameters": [
        "9/38"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.789664577926179"
    },
    {
      "parameters": [
        "11/38"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.139420408519854"
    },
    {
      "parameters": [
        "13/38"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.408629043281862"
    },
    {
      "parameters": [
        "15/38"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.471426837205368"
    },
    {
      "parameters": [
        "17/38"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0647098185608726"
    },
    {
      "parameters": [
        "21/38"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.751484820418151"
    },
    {
      "parameters": [
        "23/38"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.122100362897133"
    },
    {
      "parameters": [
        "25/38"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.157006080541843"
    },
    {
      "parameters": [
        "27/38"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.918916970156249"
    },
    {
      "parameters": [
        "29/38"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.728136526134457"
    },
    {
      "parameters": [
        "31/38"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.816212603184778"
    },
    {
      "parameters": [
        "33/38"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.228549634429314"
    },
    {
      "parameters": [
        "35/38"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.601966754758906"
    },
    {
      "parameters": [
        "37/38"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.14537775327289"
    },
    {
      "parameters": [
        "1/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.315823395457934"
    },
    {
      "parameters": [
        "2/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0746935699818468"
    },
    {
      "parameters": [
        "4/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.488424958179064"
    },
    {
      "parameters": [
        "5/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.676221325394064"
    },
    {
      "parameters": [
        "7/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.591735730928865"
    },
    {
      "parameters": [
        "8/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.619290392399079"
    },
    {
      "parameters": [
        "10/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.879352925241392"
    },
    {
      "parameters": [
        "11/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.40754619109946"
    },
    {
      "parameters": [
        "14/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0825598170594853"
    },
    {
      "parameters": [
        "16/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.968050059089548"
    },
    {
      "parameters": [
        "17/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.503942783838761"
    },
    {
      "parameters": [
        "19/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.532054718509478"
    },
    {
      "parameters": [
        "20/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.159204805798093"
    },
    {
      "parameters": [
        "22/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.317477243702393"
    },
    {
      "parameters": [
        "23/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.419414069204185"
    },
    {
      "parameters": [
        "25/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.514414898672345"
    },
    {
      "parameters": [
        "28/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0954002657091522"
    },
    {
      "parameters": [
        "29/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.425597332012013"
    },
    {
      "parameters": [
        "31/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.527219795089734"
    },
    {
      "parameters": [
        "32/39"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.57044312220379"
    },
    {
      "parameters": [
        "34/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.632906174185392"
    },
    {
      "parameters": [
        "35/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.68534405919658"
    },
    {
      "parameters": [
        "37/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.00140182109051564"
    },
    {
      "parameters": [
        "38/39"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.249563834479236"
    },
    {
      "parameters": [
        "1/40"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.963707026022967"
    },
    {
      "parameters": [
        "3/40"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.591592049651633"
    },
    {
      "parameters": [
        "7/40"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.699636462453531"
    },
    {
      "parameters": [
        "9/40"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.805407747141528"
    },
    {
      "parameters": [
        "11/40"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.476897650404978"
    },
    {
      "parameters": [
        "13/40"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.183527513449397"
    },
    {
      "parameters": [
        "17/40"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.431214539087517"
    },
    {
      "parameters": [
        "19/40"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.181520341273884"
    },
    {
      "parameters": [
        "21/40"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.373242954807056"
    },
    {
      "parameters": [
        "23/40"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.152038460172253"
    },
    {
      "parameters": [
        "27/40"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.384339095703845"
    },
    {
      "parameters": [
        "29/40"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0927445381467001"
    },
    {
      "parameters": [
        "31/40"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.688846189692625"
    },
    {
      "parameters": [
        "33/40"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.172938671111713"
    },
    {
      "parameters": [
        "37/40"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.368270074963971"
    },
    {
      "parameters": [
        "39/40"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.143303779310422"
    },
    {
      "parameters": [
        "1/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.24398563162484"
    },
    {
      "parameters": [
        "2/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.389407203842576"
    },
    {
      "parameters": [
        "3/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.791213582368566"
    },
    {
      "parameters": [
        "4/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.684824921957314"
    },
    {
      "parameters": [
        "5/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.467477149091479"
    },
    {
      "parameters": [
        "6/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.379028095013354"
    },
    {
      "parameters": [
        "7/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.632591009921813"
    },
    {
      "parameters": [
        "8/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.857666949348424"
    },
    {
      "parameters": [
        "9/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.131290527142952"
    },
    {
      "parameters": [
        "10/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.18766738993871"
    },
    {
      "parameters": [
        "11/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.416052753119532"
    },
    {
      "parameters": [
        "12/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.759372388382251"
    },
    {
      "parameters": [
        "13/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.902922048249996"
    },
    {
      "parameters": [
        "14/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.309601033522296"
    },
    {
      "parameters": [
        "15/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.694332246158321"
    },
    {
      "parameters": [
        "16/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.87362777547613"
    },
    {
      "parameters": [
        "17/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.126643514169895"
    },
    {
      "parameters": [
        "18/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.210389100816314"
    },
    {
      "parameters": [
        "19/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.819633721952153"
    },
    {
      "parameters": [
        "20/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.546655182442427"
    },
    {
      "parameters": [
        "21/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.4925735867557"
    },
    {
      "parameters": [
        "22/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.161570366986112"
    },
    {
      "parameters": [
        "23/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.781657478688128"
    },
    {
      "parameters": [
        "24/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.774197988055735"
    },
    {
      "parameters": [
        "25/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.717071353257499"
    },
    {
      "parameters": [
        "26/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.883706440963444"
    },
    {
      "parameters": [
        "27/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.394679238854356"
    },
    {
      "parameters": [
        "28/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.314906970034396"
    },
    {
      "parameters": [
        "29/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.973118852713353"
    },
    {
      "parameters": [
        "30/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0365554643721385"
    },
    {
      "parameters": [
        "31/41"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.64206155420022"
    },
    {
      "parameters": [
        "32/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.772480275459631"
    },
    {
      "parameters": [
        "33/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.676694971174"
    },
    {
      "parameters": [
        "34/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.28997614727803"
    },
    {
      "parameters": [
        "35/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.319542280077221"
    },
    {
      "parameters": [
        "36/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.726741364814699"
    },
    {
      "parameters": [
        "37/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.725937693775287"
    },
    {
      "parameters": [
        "38/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.208993615348293"
    },
    {
      "parameters": [
        "39/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.050767988492116"
    },
    {
      "parameters": [
        "40/41"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.726470229792901"
    },
    {
      "parameters": [
        "1/42"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.150260534743041"
    },
    {
      "parameters": [
        "5/42"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.177679067916906"
    },
    {
      "parameters": [
        "11/42"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.619341076367865"
    },
    {
      "parameters": [
        "13/42"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.793553647082381"
    },
    {
      "parameters": [
        "17/42"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.70371115528041"
    },
    {
      "parameters": [
        "19/42"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.480580323503254"
    },
    {
      "parameters": [
        "23/42"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.252202902952017"
    },
    {
      "parameters": [
        "25/42"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.903737669396953"
    },
    {
      "parameters": [
        "29/42"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.940015267366779"
    },
    {
      "parameters": [
        "31/42"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.676158695927498"
    },
    {
      "parameters": [
        "37/42"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0667252147556065"
    },
    {
      "parameters": [
        "41/42"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.990444985287155"
    },
    {
      "parameters": [
        "1/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.602673507722449"
    },
    {
      "parameters": [
        "2/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.751796816163846"
    },
    {
      "parameters": [
        "3/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.633437099607037"
    },
    {
      "parameters": [
        "4/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.405357137981978"
    },
    {
      "parameters": [
        "5/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.144210884848399"
    },
    {
      "parameters": [
        "6/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.784335306659995"
    },
    {
      "parameters": [
        "7/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.128342315949418"
    },
    {
      "parameters": [
        "8/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.136029268735835"
    },
    {
      "parameters": [
        "9/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0535553280915627"
    },
    {
      "parameters": [
        "10/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.799416605201757"
    },
    {
      "parameters": [
        "11/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.503881272584008"
    },
    {
      "parameters": [
        "12/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.522263218832569"
    },
    {
      "parameters": [
        "13/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.802976859429128"
    },
    {
      "parameters": [
        "14/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.892822424458959"
    },
    {
      "parameters": [
        "15/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.69892344340669"
    },
    {
      "parameters": [
        "16/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.840506001263434"
    },
    {
      "parameters": [
        "17/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.746916187357011"
    },
    {
      "parameters": [
        "18/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.342967626079531"
    },
    {
      "parameters": [
        "19/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.16032485132994"
    },
    {
      "parameters": [
        "20/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.133924091407605"
    },
    {
      "parameters": [
        "21/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.815549923155012"
    },
    {
      "parameters": [
        "22/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.835365790527344"
    },
    {
      "parameters": [
        "23/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.564376398116322"
    },
    {
      "parameters": [
        "24/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.995840545283865"
    },
    {
      "parameters": [
        "25/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.33297849466174"
    },
    {
      "parameters": [
        "26/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0954653354246577"
    },
    {
      "parameters": [
        "27/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.963546748702831"
    },
    {
      "parameters": [
        "28/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.693942776845891"
    },
    {
      "parameters": [
        "29/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.154919390530133"
    },
    {
      "parameters": [
        "30/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.571459817508048"
    },
    {
      "parameters": [
        "31/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.219663499245259"
    },
    {
      "parameters": [
        "32/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.206155158027005"
    },
    {
      "parameters": [
        "33/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.90170465649821"
    },
    {
      "parameters": [
        "34/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.607788432363186"
    },
    {
      "parameters": [
        "35/43"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.275210461694516"
    },
    {
      "parameters": [
        "36/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.627281636578374"
    },
    {
      "parameters": [
        "37/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.337751847405298"
    },
    {
      "parameters": [
        "38/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.105950951737723"
    },
    {
      "parameters": [
        "39/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.524001999852491"
    },
    {
      "parameters": [
        "40/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.32996594443497"
    },
    {
      "parameters": [
        "41/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0285122752607685"
    },
    {
      "parameters": [
        "42/43"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.51760216377404"
    },
    {
      "parameters": [
        "1/44"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.820311387785621"
    },
    {
      "parameters": [
        "3/44"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.242987206088757"
    },
    {
      "parameters": [
        "5/44"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.980308602135276"
    },
    {
      "parameters": [
        "7/44"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0686416052235244"
    },
    {
      "parameters": [
        "9/44"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0453531189786964"
    },
    {
      "parameters": [
        "13/44"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.607410890541068"
    },
    {
      "parameters": [
        "15/44"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.501924542802108"
    },
    {
      "parameters": [
        "17/44"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.724059357662415"
    },
    {
      "parameters": [
        "19/44"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.760215848294804"
    },
    {
      "parameters": [
        "21/44"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.583581378993412"
    },
    {
      "parameters": [
        "23/44"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.539204205634842"
    },
    {
      "parameters": [
        "25/44"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.644839513497967"
    },
    {
      "parameters": [
        "27/44"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.591139730101847"
    },
    {
      "parameters": [
        "29/44"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.262691226620834"
    },
    {
      "parameters": [
        "31/44"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.863249935373951"
    },
    {
      "parameters": [
        "35/44"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0802982184241887"
    },
    {
      "parameters": [
        "37/44"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.791689111060935"
    },
    {
      "parameters": [
        "39/44"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.358335642902349"
    },
    {
      "parameters": [
        "41/44"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.125031315305151"
    },
    {
      "parameters": [
        "43/44"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.585899160362786"
    },
    {
      "parameters": [
        "1/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.172526681978499"
    },
    {
      "parameters": [
        "2/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0677868332341579"
    },
    {
      "parameters": [
        "4/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.231427775661541"
    },
    {
      "parameters": [
        "7/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.681020532964884"
    },
    {
      "parameters": [
        "8/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.942943151128085"
    },
    {
      "parameters": [
        "11/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.721306480300104"
    },
    {
      "parameters": [
        "13/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.310273793155174"
    },
    {
      "parameters": [
        "14/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.785652659185536"
    },
    {
      "parameters": [
        "16/45"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.138178534523201"
    },
    {
      "parameters": [
        "17/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.89276487699445"
    },
    {
      "parameters": [
        "19/45"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.319601050569803"
    },
    {
      "parameters": [
        "22/45"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.398619053155964"
    },
    {
      "parameters": [
        "23/45"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.171222980962348"
    },
    {
      "parameters": [
        "26/45"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0389251687521869"
    },
    {
      "parameters": [
        "28/45"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.590314331084433"
    },
    {
      "parameters": [
        "29/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.468776852498842"
    },
    {
      "parameters": [
        "31/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.619564103168298"
    },
    {
      "parameters": [
        "32/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.517877593244689"
    },
    {
      "parameters": [
        "34/45"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.42568184920725"
    },
    {
      "parameters": [
        "37/45"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.776909682935267"
    },
    {
      "parameters": [
        "38/45"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.593784807195629"
    },
    {
      "parameters": [
        "41/45"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.826105916793692"
    },
    {
      "parameters": [
        "43/45"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.785559781618927"
    },
    {
      "parameters": [
        "44/45"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.209085759995018"
    },
    {
      "parameters": [
        "1/46"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.507938522095739"
    },
    {
      "parameters": [
        "3/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.684731775099749"
    },
    {
      "parameters": [
        "5/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.411697016564994"
    },
    {
      "parameters": [
        "7/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.287401734300472"
    },
    {
      "parameters": [
        "9/46"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.501745511198561"
    },
    {
      "parameters": [
        "11/46"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0432813426600509"
    },
    {
      "parameters": [
        "13/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0892610972261831"
    },
    {
      "parameters": [
        "15/46"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.190670045180254"
    },
    {
      "parameters": [
        "17/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.540200676566125"
    },
    {
      "parameters": [
        "19/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.146905082373672"
    },
    {
      "parameters": [
        "21/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.46314244108732"
    },
    {
      "parameters": [
        "25/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.332023916413542"
    },
    {
      "parameters": [
        "27/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0251787302574906"
    },
    {
      "parameters": [
        "29/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.164612919606012"
    },
    {
      "parameters": [
        "31/46"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.451974670674056"
    },
    {
      "parameters": [
        "33/46"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.000838004116088608"
    },
    {
      "parameters": [
        "35/46"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.28692258091989"
    },
    {
      "parameters": [
        "37/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.470806758642288"
    },
    {
      "parameters": [
        "39/46"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.644977124929821"
    },
    {
      "parameters": [
        "41/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.830736333953478"
    },
    {
      "parameters": [
        "43/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.566137341838107"
    },
    {
      "parameters": [
        "45/46"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.333666345689992"
    },
    {
      "parameters": [
        "1/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.5937583593651"
    },
    {
      "parameters": [
        "2/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.506884634266694"
    },
    {
      "parameters": [
        "3/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.834810950714466"
    },
    {
      "parameters": [
        "4/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0154298164980517"
    },
    {
      "parameters": [
        "5/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.841109306873018"
    },
    {
      "parameters": [
        "6/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.401262008251075"
    },
    {
      "parameters": [
        "7/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.652352167604808"
    },
    {
      "parameters": [
        "8/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.161624108048531"
    },
    {
      "parameters": [
        "9/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.942414735909067"
    },
    {
      "parameters": [
        "10/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.886059096473112"
    },
    {
      "parameters": [
        "11/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.623609699974799"
    },
    {
      "parameters": [
        "12/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.207952481685228"
    },
    {
      "parameters": [
        "13/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.416570369246362"
    },
    {
      "parameters": [
        "14/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.737228787006734"
    },
    {
      "parameters": [
        "15/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.824203196761521"
    },
    {
      "parameters": [
        "16/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.629276655906172"
    },
    {
      "parameters": [
        "17/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.113210155404785"
    },
    {
      "parameters": [
        "18/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.943361165811369"
    },
    {
      "parameters": [
        "19/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.17128051053986"
    },
    {
      "parameters": [
        "20/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.519258084051004"
    },
    {
      "parameters": [
        "21/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.658318691956264"
    },
    {
      "parameters": [
        "22/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0353282827948804"
    },
    {
      "parameters": [
        "23/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.31725052703844"
    },
    {
      "parameters": [
        "24/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.414289799206949"
    },
    {
      "parameters": [
        "25/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.470687435261458"
    },
    {
      "parameters": [
        "26/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.292456902440772"
    },
    {
      "parameters": [
        "27/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.844487648164908"
    },
    {
      "parameters": [
        "28/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.448761272028503"
    },
    {
      "parameters": [
        "29/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.856294762399897"
    },
    {
      "parameters": [
        "30/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.917003360586265"
    },
    {
      "parameters": [
        "31/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.738659628035947"
    },
    {
      "parameters": [
        "32/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.553880360931963"
    },
    {
      "parameters": [
        "33/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.68351421141298"
    },
    {
      "parameters": [
        "34/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.262024567273985"
    },
    {
      "parameters": [
        "35/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0197612669026072"
    },
    {
      "parameters": [
        "36/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.947339930859762"
    },
    {
      "parameters": [
        "37/47"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.652109083847433"
    },
    {
      "parameters": [
        "38/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.740919089271831"
    },
    {
      "parameters": [
        "39/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.577054105407631"
    },
    {
      "parameters": [
        "40/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.973691046263632"
    },
    {
      "parameters": [
        "41/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.171240889790596"
    },
    {
      "parameters": [
        "42/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.79107993342689"
    },
    {
      "parameters": [
        "43/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0169554682146325"
    },
    {
      "parameters": [
        "44/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.386866567020852"
    },
    {
      "parameters": [
        "45/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.211169370152024"
    },
    {
      "parameters": [
        "46/47"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0606962755579388"
    },
    {
      "parameters": [
        "1/48"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.771380787102691"
    },
    {
      "parameters": [
        "5/48"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.697952289576659"
    },
    {
      "parameters": [
        "7/48"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.59917535524086"
    },
    {
      "parameters": [
        "11/48"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.751034711304026"
    },
    {
      "parameters": [
        "13/48"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.955251133434591"
    },
    {
      "parameters": [
        "17/48"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.552169774538539"
    },
    {
      "parameters": [
        "19/48"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.354117279622763"
    },
    {
      "parameters": [
        "23/48"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.647277125258442"
    },
    {
      "parameters": [
        "25/48"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.439153788999325"
    },
    {
      "parameters": [
        "29/48"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.354479619204484"
    },
    {
      "parameters": [
        "31/48"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.803622072159981"
    },
    {
      "parameters": [
        "35/48"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.670579114026569"
    },
    {
      "parameters": [
        "37/48"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.619005501203906"
    },
    {
      "parameters": [
        "41/48"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.141033301328746"
    },
    {
      "parameters": [
        "43/48"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.433738987651174"
    },
    {
      "parameters": [
        "47/48"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.73841346510303"
    },
    {
      "parameters": [
        "1/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.317126044938487"
    },
    {
      "parameters": [
        "2/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.905944966428528"
    },
    {
      "parameters": [
        "3/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.899092335384272"
    },
    {
      "parameters": [
        "4/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.747610513644673"
    },
    {
      "parameters": [
        "5/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.845961120375951"
    },
    {
      "parameters": [
        "6/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.316110242136661"
    },
    {
      "parameters": [
        "8/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.276957516080522"
    },
    {
      "parameters": [
        "9/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.580459650478884"
    },
    {
      "parameters": [
        "10/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.542893055608959"
    },
    {
      "parameters": [
        "11/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.443368381113262"
    },
    {
      "parameters": [
        "12/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.512087257894161"
    },
    {
      "parameters": [
        "13/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.18340280560684"
    },
    {
      "parameters": [
        "15/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.902608522523686"
    },
    {
      "parameters": [
        "16/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.118460281420115"
    },
    {
      "parameters": [
        "17/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.250078573688496"
    },
    {
      "parameters": [
        "18/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.818460963550228"
    },
    {
      "parameters": [
        "19/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.754102582508657"
    },
    {
      "parameters": [
        "20/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.782485844098701"
    },
    {
      "parameters": [
        "22/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.681657737288966"
    },
    {
      "parameters": [
        "23/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.099888357800721"
    },
    {
      "parameters": [
        "24/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.393907217421623"
    },
    {
      "parameters": [
        "25/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.462879872021028"
    },
    {
      "parameters": [
        "26/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.214128514910072"
    },
    {
      "parameters": [
        "27/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.562177644479379"
    },
    {
      "parameters": [
        "29/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.325549685007406"
    },
    {
      "parameters": [
        "30/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.844469976040784"
    },
    {
      "parameters": [
        "31/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0731557193448554"
    },
    {
      "parameters": [
        "32/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0163707201282564"
    },
    {
      "parameters": [
        "33/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.310357516365198"
    },
    {
      "parameters": [
        "34/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.168253019635137"
    },
    {
      "parameters": [
        "36/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.886546753855967"
    },
    {
      "parameters": [
        "37/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.164008745008881"
    },
    {
      "parameters": [
        "38/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.753415903599026"
    },
    {
      "parameters": [
        "39/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.74554775338121"
    },
    {
      "parameters": [
        "40/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.597699813209985"
    },
    {
      "parameters": [
        "41/49"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.217668758031586"
    },
    {
      "parameters": [
        "43/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.584180902988888"
    },
    {
      "parameters": [
        "44/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.619357360231022"
    },
    {
      "parameters": [
        "45/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.0900684274650592"
    },
    {
      "parameters": [
        "46/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.901529769840158"
    },
    {
      "parameters": [
        "47/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.800336450737087"
    },
    {
      "parameters": [
        "48/49"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.408586069452366"
    },
    {
      "parameters": [
        "1/50"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.910368294206032"
    },
    {
      "parameters": [
        "3/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.591604471486274"
    },
    {
      "parameters": [
        "7/50"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.595846920545046"
    },
    {
      "parameters": [
        "9/50"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.457073517737589"
    },
    {
      "parameters": [
        "11/50"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.531207312344357"
    },
    {
      "parameters": [
        "13/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.741106937308519"
    },
    {
      "parameters": [
        "17/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.93733492962754"
    },
    {
      "parameters": [
        "19/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.513066756880261"
    },
    {
      "parameters": [
        "21/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.938205846599605"
    },
    {
      "parameters": [
        "23/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.297306338677286"
    },
    {
      "parameters": [
        "27/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.62790791820423"
    },
    {
      "parameters": [
        "29/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.15606246120232"
    },
    {
      "parameters": [
        "31/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.320718008856523"
    },
    {
      "parameters": [
        "33/50"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.656699697276895"
    },
    {
      "parameters": [
        "37/50"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.867830246215745"
    },
    {
      "parameters": [
        "39/50"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.43610869080722"
    },
    {
      "parameters": [
        "41/50"
      ],
      "accuracy_bits": 636,
      "independent_ball": false,
      "mpmath_error_ulps": "0.306555772984655"
    },
    {
      "parameters": [
        "43/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.570366504362935"
    },
    {
      "parameters": [
        "47/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.638964586972233"
    },
    {
      "parameters": [
        "49/50"
      ],
      "accuracy_bits": 635,
      "independent_ball": false,
      "mpmath_error_ulps": "0.652295956616783"
    }
  ]
}
