{
  "schema": "AN02-original-L137-figures/v1",
  "license": "CC0-1.0",
  "author": "GPT-6.1 Sol (OpenAI)",
  "human_source_credit": "Lars Hormander, The Analysis of Linear Partial Differential Operators II (1983; second revised printing 1990; reprint 2005), Theorem 16.1.9, printed page 313; original illustrations and examples",
  "measure": {
    "a": -1.0,
    "b": 2.0,
    "width": 3.0,
    "formula": "delta_a + c delta_b",
    "c": "exp(-3/2) exp(i*pi/4)",
    "argument": "pi/4"
  },
  "zeros": {
    "formula": "(pi/4+(2*k+1)*pi)/3 + i/2, k in Z",
    "height": 0.5,
    "spacing": "2*pi/3",
    "multiplicity": 1
  },
  "scaled_zero_measures": {
    "domain": "open unit disk in the Euclidean complex plane",
    "metric": "identical horizontal and vertical scales",
    "mass_per_dot": "1/R",
    "displayed_dot_area": "100*pi/R square drawing points",
    "panels": [
      {
        "R": 4.0,
        "zeros_in_open_disk": 4,
        "restricted_mass": 1.0,
        "scaled_points": [
          [
            -0.7199483164476609,
            0.125
          ],
          [
            -0.19634954084936207,
            0.125
          ],
          [
            0.3272492347489368,
            0.125
          ],
          [
            0.8508480103472357,
            0.125
          ]
        ],
        "marker_radius_points": 5.0
      },
      {
        "R": 12.0,
        "zeros_in_open_disk": 12,
        "restricted_mass": 1.0,
        "scaled_points": [
          [
            -0.938114472946952,
            0.041666666666666664
          ],
          [
            -0.7635815477475192,
            0.041666666666666664
          ],
          [
            -0.5890486225480862,
            0.041666666666666664
          ],
          [
            -0.41451569734865323,
            0.041666666666666664
          ],
          [
            -0.23998277214922029,
            0.041666666666666664
          ],
          [
            -0.06544984694978735,
            0.041666666666666664
          ],
          [
            0.1090830782496456,
            0.041666666666666664
          ],
          [
            0.28361600344907856,
            0.041666666666666664
          ],
          [
            0.4581489286485115,
            0.041666666666666664
          ],
          [
            0.6326818538479445,
            0.041666666666666664
          ],
          [
            0.8072147790473774,
            0.041666666666666664
          ],
          [
            0.9817477042468101,
            0.041666666666666664
          ]
        ],
        "marker_radius_points": 2.886751345948129
      },
      {
        "R": 30.0,
        "zeros_in_open_disk": 28,
        "restricted_mass": 0.9333333333333333,
        "scaled_points": [
          [
            -0.9337511498169663,
            0.016666666666666666
          ],
          [
            -0.8639379797371931,
            0.016666666666666666
          ],
          [
            -0.7941248096574199,
            0.016666666666666666
          ],
          [
            -0.7243116395776468,
            0.016666666666666666
          ],
          [
            -0.6544984694978736,
            0.016666666666666666
          ],
          [
            -0.5846852994181005,
            0.016666666666666666
          ],
          [
            -0.5148721293383273,
            0.016666666666666666
          ],
          [
            -0.4450589592585541,
            0.016666666666666666
          ],
          [
            -0.3752457891787808,
            0.016666666666666666
          ],
          [
            -0.30543261909900765,
            0.016666666666666666
          ],
          [
            -0.23561944901923448,
            0.016666666666666666
          ],
          [
            -0.1658062789394613,
            0.016666666666666666
          ],
          [
            -0.09599310885968812,
            0.016666666666666666
          ],
          [
            -0.02617993877991494,
            0.016666666666666666
          ],
          [
            0.04363323129985824,
            0.016666666666666666
          ],
          [
            0.11344640137963143,
            0.016666666666666666
          ],
          [
            0.1832595714594046,
            0.016666666666666666
          ],
          [
            0.2530727415391778,
            0.016666666666666666
          ],
          [
            0.32288591161895097,
            0.016666666666666666
          ],
          [
            0.39269908169872403,
            0.016666666666666666
          ],
          [
            0.4625122517784973,
            0.016666666666666666
          ],
          [
            0.5323254218582705,
            0.016666666666666666
          ],
          [
            0.6021385919380436,
            0.016666666666666666
          ],
          [
            0.6719517620178167,
            0.016666666666666666
          ],
          [
            0.7417649320975901,
            0.016666666666666666
          ],
          [
            0.8115781021773631,
            0.016666666666666666
          ],
          [
            0.8813912722571364,
            0.016666666666666666
          ],
          [
            0.9512044423369095,
            0.016666666666666666
          ]
        ],
        "marker_radius_points": 1.8257418583505538
      }
    ],
    "limit_density": "3/(2*pi) length on embedded real axis",
    "limit_disk_mass": "3/pi",
    "limit_boundary_mass": 0,
    "proof_locators": "Lemma Z2 and sections 3-5, (Z17)-(Z22)"
  },
  "zero_count_density": {
    "domain": "R from 2 to 80",
    "sample_radii": [
      2.0,
      2.0325,
      2.065,
      2.0975,
      2.13,
      2.1625,
      2.195,
      2.2275,
      2.26,
      2.2925,
      2.325,
      2.3575,
      2.39,
      2.4225,
      2.455,
      2.4875,
      2.52,
      2.5525,
      2.585,
      2.6175,
      2.65,
      2.6825,
      2.715,
      2.7475,
      2.7800000000000002,
      2.8125,
      2.8449999999999998,
      2.8775,
      2.91,
      2.9425,
      2.975,
      3.0075000000000003,
      3.04,
      3.0725,
      3.105,
      3.1375,
      3.17,
      3.2025,
      3.2350000000000003,
      3.2675,
      3.3,
      3.3325,
      3.365,
      3.3975,
      3.43,
      3.4625000000000004,
      3.495,
      3.5275,
      3.56,
      3.5925000000000002,
      3.625,
      3.6574999999999998,
      3.69,
      3.7225,
      3.755,
      3.7875,
      3.8200000000000003,
      3.8525,
      3.885,
      3.9175,
      3.95,
      3.9825,
      4.015000000000001,
      4.047499999999999,
      4.08,
      4.112500000000001,
      4.145,
      4.1775,
      4.21,
      4.2425,
      4.275,
      4.3075,
      4.34,
      4.3725000000000005,
      4.405,
      4.4375,
      4.470000000000001,
      4.5024999999999995,
      4.535,
      4.5675,
      4.6,
      4.6325,
      4.665,
      4.6975,
      4.73,
      4.7625,
      4.795,
      4.827500000000001,
      4.86,
      4.8925,
      4.925000000000001,
      4.9575,
      4.99,
      5.0225,
      5.055,
      5.0875,
      5.12,
      5.1525,
      5.1850000000000005,
      5.2175,
      5.25,
      5.282500000000001,
      5.3149999999999995,
      5.3475,
      5.38,
      5.4125,
      5.445,
      5.4775,
      5.51,
      5.5425,
      5.575,
      5.6075,
      5.640000000000001,
      5.6725,
      5.705,
      5.737500000000001,
      5.77,
      5.8025,
      5.835,
      5.8675,
      5.9,
      5.9325,
      5.965,
      5.9975000000000005,
      6.03,
      6.0625,
      6.095,
      6.1275,
      6.16,
      6.1925,
      6.2250000000000005,
      6.2575,
      6.29,
      6.3225,
      6.355,
      6.3875,
      6.42,
      6.452500000000001,
      6.485,
      6.5175,
      6.55,
      6.5825000000000005,
      6.615,
      6.6475,
      6.68,
      6.7125,
      6.745,
      6.7775,
      6.8100000000000005,
      6.8425,
      6.875,
      6.9075,
      6.94,
      6.9725,
      7.005,
      7.0375000000000005,
      7.07,
      7.1025,
      7.135,
      7.1675,
      7.2,
      7.2325,
      7.265000000000001,
      7.2975,
      7.33,
      7.3625,
      7.3950000000000005,
      7.4275,
      7.46,
      7.492500000000001,
      7.525,
      7.5575,
      7.59,
      7.6225000000000005,
      7.655,
      7.6875,
      7.720000000000001,
      7.7525,
      7.785,
      7.8175,
      7.8500000000000005,
      7.8825,
      7.915,
      7.9475,
      7.98,
      8.0125,
      8.045,
      8.0775,
      8.11,
      8.1425,
      8.175,
      8.2075,
      8.24,
      8.2725,
      8.305,
      8.3375,
      8.370000000000001,
      8.4025,
      8.435,
      8.467500000000001,
      8.5,
      8.5325,
      8.565000000000001,
      8.5975,
      8.629999999999999,
      8.662500000000001,
      8.695,
      8.7275,
      8.76,
      8.7925,
      8.825,
      8.8575,
      8.89,
      8.9225,
      8.955,
      8.9875,
      9.02,
      9.0525,
      9.085,
      9.1175,
      9.15,
      9.182500000000001,
      9.215,
      9.2475,
      9.280000000000001,
      9.3125,
      9.345,
      9.377500000000001,
      9.41,
      9.442499999999999,
      9.475000000000001,
      9.5075,
      9.54,
      9.572500000000002,
      9.605,
      9.6375,
      9.67,
      9.7025,
      9.735,
      9.7675,
      9.8,
      9.8325,
      9.865,
      9.8975,
      9.93,
      9.9625,
      9.995000000000001,
      10.0275,
      10.06,
      10.092500000000001,
      10.125,
      10.1575,
      10.19,
      10.2225,
      10.255,
      10.2875,
      10.32,
      10.352500000000001,
      10.385,
      10.4175,
      10.450000000000001,
      10.4825,
      10.515,
      10.5475,
      10.58,
      10.6125,
      10.645,
      10.6775,
      10.71,
      10.7425,
      10.775,
      10.807500000000001,
      10.84,
      10.8725,
      10.905000000000001,
      10.9375,
      10.97,
      11.0025,
      11.035,
      11.0675,
      11.1,
      11.1325,
      11.165000000000001,
      11.1975,
      11.23,
      11.262500000000001,
      11.295,
      11.3275,
      11.36,
      11.3925,
      11.425,
      11.4575,
      11.49,
      11.5225,
      11.555,
      11.5875,
      11.620000000000001,
      11.6525,
      11.685,
      11.717500000000001,
      11.75,
      11.7825,
      11.815,
      11.8475,
      11.88,
      11.9125,
      11.945,
      11.977500000000001,
      12.01,
      12.0425,
      12.075000000000001,
      12.1075,
      12.14,
      12.172500000000001,
      12.205,
      12.2375,
      12.27,
      12.3025,
      12.335,
      12.3675,
      12.4,
      12.432500000000001,
      12.465,
      12.4975,
      12.530000000000001,
      12.5625,
      12.595,
      12.6275,
      12.66,
      12.6925,
      12.725,
      12.7575,
      12.790000000000001,
      12.8225,
      12.855,
      12.887500000000001,
      12.92,
      12.9525,
      12.985000000000001,
      13.0175,
      13.05,
      13.0825,
      13.115,
      13.1475,
      13.18,
      13.2125,
      13.245000000000001,
      13.2775,
      13.31,
      13.342500000000001,
      13.375,
      13.4075,
      13.440000000000001,
      13.4725,
      13.505,
      13.5375,
      13.57,
      13.602500000000001,
      13.635,
      13.6675,
      13.700000000000001,
      13.7325,
      13.765,
      13.797500000000001,
      13.83,
      13.8625,
      13.895,
      13.9275,
      13.96,
      13.9925,
      14.025,
      14.057500000000001,
      14.09,
      14.1225,
      14.155000000000001,
      14.1875,
      14.22,
      14.252500000000001,
      14.285,
      14.3175,
      14.35,
      14.3825,
      14.415000000000001,
      14.4475,
      14.48,
      14.512500000000001,
      14.545,
      14.5775,
      14.610000000000001,
      14.6425,
      14.675,
      14.7075,
      14.74,
      14.7725,
      14.805,
      14.8375,
      14.870000000000001,
      14.9025,
      14.935,
      14.967500000000001,
      15.0,
      15.0325,
      15.065000000000001,
      15.0975,
      15.13,
      15.1625,
      15.195,
      15.227500000000001,
      15.26,
      15.2925,
      15.325000000000001,
      15.3575,
      15.39,
      15.422500000000001,
      15.455,
      15.4875,
      15.52,
      15.5525,
      15.585,
      15.6175,
      15.65,
      15.682500000000001,
      15.715,
      15.7475,
      15.780000000000001,
      15.8125,
      15.845,
      15.877500000000001,
      15.91,
      15.9425,
      15.975,
      16.0075,
      16.04,
      16.072499999999998,
      16.105,
      16.137500000000003,
      16.17,
      16.2025,
      16.235,
      16.2675,
      16.3,
      16.332500000000003,
      16.365000000000002,
      16.3975,
      16.43,
      16.4625,
      16.495,
      16.5275,
      16.560000000000002,
      16.5925,
      16.625,
      16.6575,
      16.69,
      16.7225,
      16.755000000000003,
      16.7875,
      16.82,
      16.8525,
      16.884999999999998,
      16.9175,
      16.950000000000003,
      16.9825,
      17.015,
      17.0475,
      17.08,
      17.1125,
      17.145000000000003,
      17.177500000000002,
      17.21,
      17.2425,
      17.275,
      17.3075,
      17.34,
      17.372500000000002,
      17.405,
      17.4375,
      17.47,
      17.5025,
      17.535,
      17.567500000000003,
      17.6,
      17.6325,
      17.665,
      17.697499999999998,
      17.73,
      17.762500000000003,
      17.795,
      17.8275,
      17.86,
      17.8925,
      17.925,
      17.957500000000003,
      17.990000000000002,
      18.0225,
      18.055,
      18.087500000000002,
      18.12,
      18.1525,
      18.185000000000002,
      18.2175,
      18.25,
      18.2825,
      18.315,
      18.3475,
      18.38,
      18.4125,
      18.445,
      18.4775,
      18.51,
      18.5425,
      18.575,
      18.6075,
      18.64,
      18.6725,
      18.705000000000002,
      18.7375,
      18.77,
      18.802500000000002,
      18.835,
      18.8675,
      18.900000000000002,
      18.9325,
      18.965,
      18.997500000000002,
      19.03,
      19.0625,
      19.095,
      19.1275,
      19.16,
      19.1925,
      19.225,
      19.2575,
      19.29,
      19.3225,
      19.355,
      19.3875,
      19.42,
      19.4525,
      19.485,
      19.517500000000002,
      19.55,
      19.5825,
      19.615000000000002,
      19.6475,
      19.68,
      19.712500000000002,
      19.745,
      19.7775,
      19.810000000000002,
      19.8425,
      19.875,
      19.9075,
      19.94,
      19.9725,
      20.005,
      20.0375,
      20.07,
      20.1025,
      20.135,
      20.1675,
      20.2,
      20.2325,
      20.265,
      20.2975,
      20.330000000000002,
      20.3625,
      20.395,
      20.427500000000002,
      20.46,
      20.4925,
      20.525000000000002,
      20.5575,
      20.59,
      20.622500000000002,
      20.655,
      20.6875,
      20.72,
      20.7525,
      20.785,
      20.8175,
      20.85,
      20.8825,
      20.915,
      20.9475,
      20.98,
      21.0125,
      21.045,
      21.0775,
      21.11,
      21.142500000000002,
      21.175,
      21.2075,
      21.240000000000002,
      21.2725,
      21.305,
      21.337500000000002,
      21.37,
      21.4025,
      21.435000000000002,
      21.4675,
      21.5,
      21.532500000000002,
      21.565,
      21.5975,
      21.63,
      21.6625,
      21.695,
      21.7275,
      21.76,
      21.7925,
      21.825,
      21.8575,
      21.89,
      21.9225,
      21.955000000000002,
      21.9875,
      22.02,
      22.052500000000002,
      22.085,
      22.1175,
      22.150000000000002,
      22.1825,
      22.215,
      22.247500000000002,
      22.28,
      22.3125,
      22.345000000000002,
      22.3775,
      22.41,
      22.4425,
      22.475,
      22.5075,
      22.54,
      22.5725,
      22.605,
      22.6375,
      22.67,
      22.7025,
      22.735,
      22.767500000000002,
      22.8,
      22.8325,
      22.865000000000002,
      22.8975,
      22.93,
      22.962500000000002,
      22.995,
      23.0275,
      23.060000000000002,
      23.0925,
      23.125,
      23.157500000000002,
      23.19,
      23.2225,
      23.255,
      23.2875,
      23.32,
      23.3525,
      23.385,
      23.4175,
      23.45,
      23.4825,
      23.515,
      23.5475,
      23.580000000000002,
      23.6125,
      23.645,
      23.677500000000002,
      23.71,
      23.7425,
      23.775000000000002,
      23.8075,
      23.84,
      23.872500000000002,
      23.905,
      23.9375,
      23.970000000000002,
      24.0025,
      24.035,
      24.0675,
      24.1,
      24.1325,
      24.165,
      24.1975,
      24.23,
      24.2625,
      24.295,
      24.3275,
      24.36,
      24.392500000000002,
      24.425,
      24.4575,
      24.490000000000002,
      24.5225,
      24.555,
      24.587500000000002,
      24.62,
      24.6525,
      24.685000000000002,
      24.7175,
      24.75,
      24.782500000000002,
      24.815,
      24.8475,
      24.880000000000003,
      24.9125,
      24.945,
      24.9775,
      25.01,
      25.0425,
      25.075,
      25.1075,
      25.14,
      25.1725,
      25.205000000000002,
      25.2375,
      25.27,
      25.302500000000002,
      25.335,
      25.3675,
      25.400000000000002,
      25.4325,
      25.465,
      25.497500000000002,
      25.53,
      25.5625,
      25.595000000000002,
      25.6275,
      25.66,
      25.692500000000003,
      25.725,
      25.7575,
      25.79,
      25.8225,
      25.855,
      25.8875,
      25.92,
      25.9525,
      25.985,
      26.017500000000002,
      26.05,
      26.0825,
      26.115000000000002,
      26.1475,
      26.18,
      26.212500000000002,
      26.245,
      26.2775,
      26.310000000000002,
      26.3425,
      26.375,
      26.407500000000002,
      26.44,
      26.4725,
      26.505000000000003,
      26.5375,
      26.57,
      26.6025,
      26.635,
      26.6675,
      26.7,
      26.7325,
      26.765,
      26.7975,
      26.830000000000002,
      26.8625,
      26.895,
      26.927500000000002,
      26.96,
      26.9925,
      27.025000000000002,
      27.0575,
      27.09,
      27.122500000000002,
      27.155,
      27.1875,
      27.220000000000002,
      27.2525,
      27.285,
      27.317500000000003,
      27.35,
      27.3825,
      27.415,
      27.4475,
      27.48,
      27.5125,
      27.545,
      27.5775,
      27.61,
      27.642500000000002,
      27.675,
      27.7075,
      27.740000000000002,
      27.7725,
      27.805,
      27.837500000000002,
      27.87,
      27.9025,
      27.935000000000002,
      27.9675,
      28.0,
      28.032500000000002,
      28.065,
      28.0975,
      28.130000000000003,
      28.1625,
      28.195,
      28.2275,
      28.26,
      28.2925,
      28.325,
      28.3575,
      28.39,
      28.4225,
      28.455000000000002,
      28.4875,
      28.52,
      28.552500000000002,
      28.585,
      28.6175,
      28.650000000000002,
      28.6825,
      28.715,
      28.747500000000002,
      28.78,
      28.8125,
      28.845000000000002,
      28.8775,
      28.91,
      28.942500000000003,
      28.975,
      29.0075,
      29.04,
      29.0725,
      29.105,
      29.1375,
      29.17,
      29.2025,
      29.235,
      29.267500000000002,
      29.3,
      29.3325,
      29.365000000000002,
      29.3975,
      29.43,
      29.462500000000002,
      29.495,
      29.5275,
      29.560000000000002,
      29.5925,
      29.625,
      29.657500000000002,
      29.69,
      29.7225,
      29.755000000000003,
      29.7875,
      29.82,
      29.852500000000003,
      29.885,
      29.9175,
      29.95,
      29.9825,
      30.015,
      30.0475,
      30.080000000000002,
      30.1125,
      30.145,
      30.177500000000002,
      30.21,
      30.2425,
      30.275000000000002,
      30.3075,
      30.34,
      30.372500000000002,
      30.405,
      30.4375,
      30.470000000000002,
      30.5025,
      30.535,
      30.567500000000003,
      30.6,
      30.6325,
      30.665000000000003,
      30.6975,
      30.73,
      30.7625,
      30.795,
      30.8275,
      30.86,
      30.892500000000002,
      30.925,
      30.9575,
      30.990000000000002,
      31.0225,
      31.055,
      31.087500000000002,
      31.12,
      31.1525,
      31.185000000000002,
      31.2175,
      31.25,
      31.282500000000002,
      31.315,
      31.3475,
      31.380000000000003,
      31.4125,
      31.445,
      31.477500000000003,
      31.51,
      31.5425,
      31.575,
      31.6075,
      31.64,
      31.6725,
      31.705000000000002,
      31.7375,
      31.77,
      31.802500000000002,
      31.835,
      31.8675,
      31.900000000000002,
      31.9325,
      31.965,
      31.997500000000002,
      32.03,
      32.0625,
      32.095,
      32.1275,
      32.16,
      32.1925,
      32.225,
      32.2575,
      32.290000000000006,
      32.322500000000005,
      32.355000000000004,
      32.3875,
      32.42,
      32.4525,
      32.485,
      32.5175,
      32.55,
      32.582499999999996,
      32.615,
      32.6475,
      32.68,
      32.712500000000006,
      32.745000000000005,
      32.7775,
      32.81,
      32.8425,
      32.875,
      32.9075,
      32.94,
      32.9725,
      33.005,
      33.0375,
      33.07,
      33.102500000000006,
      33.135000000000005,
      33.167500000000004,
      33.2,
      33.2325,
      33.265,
      33.2975,
      33.33,
      33.3625,
      33.394999999999996,
      33.4275,
      33.46,
      33.4925,
      33.525000000000006,
      33.557500000000005,
      33.59,
      33.6225,
      33.655,
      33.6875,
      33.72,
      33.7525,
      33.785,
      33.8175,
      33.85,
      33.8825,
      33.915000000000006,
      33.947500000000005,
      33.980000000000004,
      34.0125,
      34.045,
      34.0775,
      34.11,
      34.1425,
      34.175000000000004,
      34.2075,
      34.24,
      34.2725,
      34.305,
      34.3375,
      34.370000000000005,
      34.4025,
      34.435,
      34.4675,
      34.5,
      34.5325,
      34.565,
      34.597500000000004,
      34.63,
      34.6625,
      34.695,
      34.7275,
      34.76,
      34.792500000000004,
      34.825,
      34.8575,
      34.89,
      34.9225,
      34.955,
      34.987500000000004,
      35.02,
      35.0525,
      35.085,
      35.1175,
      35.15,
      35.182500000000005,
      35.215,
      35.2475,
      35.28,
      35.3125,
      35.345,
      35.3775,
      35.410000000000004,
      35.4425,
      35.475,
      35.5075,
      35.54,
      35.5725,
      35.605000000000004,
      35.6375,
      35.67,
      35.7025,
      35.735,
      35.7675,
      35.800000000000004,
      35.8325,
      35.865,
      35.8975,
      35.93,
      35.9625,
      35.995000000000005,
      36.0275,
      36.06,
      36.0925,
      36.125,
      36.1575,
      36.19,
      36.222500000000004,
      36.255,
      36.2875,
      36.32,
      36.3525,
      36.385,
      36.417500000000004,
      36.45,
      36.4825,
      36.515,
      36.5475,
      36.58,
      36.612500000000004,
      36.645,
      36.6775,
      36.71,
      36.7425,
      36.775,
      36.807500000000005,
      36.84,
      36.8725,
      36.905,
      36.9375,
      36.97,
      37.0025,
      37.035000000000004,
      37.0675,
      37.1,
      37.1325,
      37.165,
      37.1975,
      37.230000000000004,
      37.2625,
      37.295,
      37.3275,
      37.36,
      37.3925,
      37.425000000000004,
      37.4575,
      37.49,
      37.5225,
      37.555,
      37.5875,
      37.620000000000005,
      37.6525,
      37.685,
      37.7175,
      37.75,
      37.7825,
      37.815,
      37.847500000000004,
      37.88,
      37.9125,
      37.945,
      37.9775,
      38.01,
      38.042500000000004,
      38.075,
      38.1075,
      38.14,
      38.1725,
      38.205,
      38.237500000000004,
      38.27,
      38.3025,
      38.335,
      38.3675,
      38.4,
      38.432500000000005,
      38.465,
      38.4975,
      38.53,
      38.5625,
      38.595,
      38.6275,
      38.660000000000004,
      38.6925,
      38.725,
      38.7575,
      38.79,
      38.8225,
      38.855000000000004,
      38.8875,
      38.92,
      38.9525,
      38.985,
      39.0175,
      39.050000000000004,
      39.0825,
      39.115,
      39.1475,
      39.18,
      39.2125,
      39.245000000000005,
      39.2775,
      39.31,
      39.3425,
      39.375,
      39.4075,
      39.44,
      39.472500000000004,
      39.505,
      39.5375,
      39.57,
      39.6025,
      39.635,
      39.667500000000004,
      39.7,
      39.7325,
      39.765,
      39.7975,
      39.83,
      39.862500000000004,
      39.895,
      39.9275,
      39.96,
      39.9925,
      40.025,
      40.057500000000005,
      40.09,
      40.1225,
      40.155,
      40.1875,
      40.22,
      40.252500000000005,
      40.285000000000004,
      40.3175,
      40.35,
      40.3825,
      40.415,
      40.4475,
      40.480000000000004,
      40.5125,
      40.545,
      40.5775,
      40.61,
      40.6425,
      40.675000000000004,
      40.7075,
      40.74,
      40.7725,
      40.805,
      40.8375,
      40.870000000000005,
      40.9025,
      40.935,
      40.9675,
      41.0,
      41.0325,
      41.065000000000005,
      41.097500000000004,
      41.13,
      41.1625,
      41.195,
      41.2275,
      41.26,
      41.292500000000004,
      41.325,
      41.3575,
      41.39,
      41.4225,
      41.455,
      41.487500000000004,
      41.52,
      41.5525,
      41.585,
      41.6175,
      41.65,
      41.682500000000005,
      41.715,
      41.7475,
      41.78,
      41.8125,
      41.845,
      41.877500000000005,
      41.910000000000004,
      41.9425,
      41.975,
      42.0075,
      42.04,
      42.0725,
      42.105000000000004,
      42.1375,
      42.17,
      42.2025,
      42.235,
      42.2675,
      42.300000000000004,
      42.3325,
      42.365,
      42.3975,
      42.43,
      42.4625,
      42.495000000000005,
      42.5275,
      42.56,
      42.5925,
      42.625,
      42.6575,
      42.690000000000005,
      42.722500000000004,
      42.755,
      42.7875,
      42.82,
      42.8525,
      42.885,
      42.917500000000004,
      42.95,
      42.9825,
      43.015,
      43.0475,
      43.08,
      43.112500000000004,
      43.145,
      43.1775,
      43.21,
      43.2425,
      43.275,
      43.307500000000005,
      43.34,
      43.3725,
      43.405,
      43.4375,
      43.47,
      43.502500000000005,
      43.535000000000004,
      43.5675,
      43.6,
      43.6325,
      43.665,
      43.6975,
      43.730000000000004,
      43.7625,
      43.795,
      43.8275,
      43.86,
      43.8925,
      43.925000000000004,
      43.9575,
      43.99,
      44.0225,
      44.055,
      44.0875,
      44.120000000000005,
      44.1525,
      44.185,
      44.2175,
      44.25,
      44.2825,
      44.315000000000005,
      44.347500000000004,
      44.38,
      44.4125,
      44.445,
      44.4775,
      44.51,
      44.542500000000004,
      44.575,
      44.6075,
      44.64,
      44.6725,
      44.705,
      44.737500000000004,
      44.77,
      44.8025,
      44.835,
      44.8675,
      44.9,
      44.932500000000005,
      44.965,
      44.9975,
      45.03,
      45.0625,
      45.095,
      45.127500000000005,
      45.160000000000004,
      45.1925,
      45.225,
      45.2575,
      45.29,
      45.3225,
      45.355000000000004,
      45.3875,
      45.42,
      45.4525,
      45.485,
      45.5175,
      45.550000000000004,
      45.5825,
      45.615,
      45.6475,
      45.68,
      45.7125,
      45.745000000000005,
      45.7775,
      45.81,
      45.8425,
      45.875,
      45.9075,
      45.940000000000005,
      45.972500000000004,
      46.005,
      46.0375,
      46.07,
      46.1025,
      46.135,
      46.167500000000004,
      46.2,
      46.2325,
      46.265,
      46.2975,
      46.33,
      46.362500000000004,
      46.395,
      46.4275,
      46.46,
      46.4925,
      46.525,
      46.557500000000005,
      46.59,
      46.6225,
      46.655,
      46.6875,
      46.72,
      46.752500000000005,
      46.785000000000004,
      46.8175,
      46.85,
      46.8825,
      46.915,
      46.9475,
      46.980000000000004,
      47.0125,
      47.045,
      47.0775,
      47.11,
      47.1425,
      47.175000000000004,
      47.2075,
      47.24,
      47.2725,
      47.305,
      47.3375,
      47.370000000000005,
      47.4025,
      47.435,
      47.4675,
      47.5,
      47.5325,
      47.565000000000005,
      47.597500000000004,
      47.63,
      47.6625,
      47.695,
      47.7275,
      47.760000000000005,
      47.792500000000004,
      47.825,
      47.8575,
      47.89,
      47.9225,
      47.955,
      47.987500000000004,
      48.02,
      48.0525,
      48.085,
      48.1175,
      48.15,
      48.182500000000005,
      48.215,
      48.2475,
      48.28,
      48.3125,
      48.345,
      48.377500000000005,
      48.410000000000004,
      48.4425,
      48.475,
      48.5075,
      48.54,
      48.572500000000005,
      48.605000000000004,
      48.6375,
      48.67,
      48.7025,
      48.735,
      48.7675,
      48.800000000000004,
      48.8325,
      48.865,
      48.8975,
      48.93,
      48.9625,
      48.995000000000005,
      49.0275,
      49.06,
      49.0925,
      49.125,
      49.1575,
      49.190000000000005,
      49.222500000000004,
      49.255,
      49.2875,
      49.32,
      49.3525,
      49.385000000000005,
      49.417500000000004,
      49.45,
      49.4825,
      49.515,
      49.5475,
      49.58,
      49.612500000000004,
      49.645,
      49.6775,
      49.71,
      49.7425,
      49.775,
      49.807500000000005,
      49.84,
      49.8725,
      49.905,
      49.9375,
      49.97,
      50.002500000000005,
      50.035000000000004,
      50.0675,
      50.1,
      50.1325,
      50.165,
      50.197500000000005,
      50.230000000000004,
      50.2625,
      50.295,
      50.3275,
      50.36,
      50.3925,
      50.425000000000004,
      50.4575,
      50.49,
      50.5225,
      50.555,
      50.5875,
      50.620000000000005,
      50.6525,
      50.685,
      50.7175,
      50.75,
      50.7825,
      50.815000000000005,
      50.847500000000004,
      50.88,
      50.9125,
      50.945,
      50.9775,
      51.010000000000005,
      51.042500000000004,
      51.075,
      51.1075,
      51.14,
      51.1725,
      51.205,
      51.237500000000004,
      51.27,
      51.3025,
      51.335,
      51.3675,
      51.4,
      51.432500000000005,
      51.465,
      51.4975,
      51.53,
      51.5625,
      51.595,
      51.627500000000005,
      51.660000000000004,
      51.6925,
      51.725,
      51.7575,
      51.79,
      51.822500000000005,
      51.855000000000004,
      51.8875,
      51.92,
      51.9525,
      51.985,
      52.0175,
      52.050000000000004,
      52.0825,
      52.115,
      52.1475,
      52.18,
      52.2125,
      52.245000000000005,
      52.2775,
      52.31,
      52.3425,
      52.375,
      52.4075,
      52.440000000000005,
      52.472500000000004,
      52.505,
      52.5375,
      52.57,
      52.6025,
      52.635000000000005,
      52.667500000000004,
      52.7,
      52.7325,
      52.765,
      52.7975,
      52.83,
      52.862500000000004,
      52.895,
      52.9275,
      52.96,
      52.9925,
      53.025,
      53.057500000000005,
      53.09,
      53.1225,
      53.155,
      53.1875,
      53.22,
      53.252500000000005,
      53.285000000000004,
      53.3175,
      53.35,
      53.3825,
      53.415,
      53.447500000000005,
      53.480000000000004,
      53.5125,
      53.545,
      53.5775,
      53.61,
      53.6425,
      53.675000000000004,
      53.7075,
      53.74,
      53.7725,
      53.805,
      53.8375,
      53.870000000000005,
      53.9025,
      53.935,
      53.9675,
      54.0,
      54.0325,
      54.065000000000005,
      54.097500000000004,
      54.13,
      54.1625,
      54.195,
      54.2275,
      54.260000000000005,
      54.292500000000004,
      54.325,
      54.3575,
      54.39,
      54.4225,
      54.455,
      54.487500000000004,
      54.52,
      54.5525,
      54.585,
      54.6175,
      54.65,
      54.682500000000005,
      54.715,
      54.7475,
      54.78,
      54.8125,
      54.845,
      54.877500000000005,
      54.910000000000004,
      54.9425,
      54.975,
      55.0075,
      55.04,
      55.072500000000005,
      55.105000000000004,
      55.1375,
      55.17,
      55.2025,
      55.235,
      55.2675,
      55.300000000000004,
      55.3325,
      55.365,
      55.3975,
      55.43,
      55.4625,
      55.495000000000005,
      55.5275,
      55.56,
      55.5925,
      55.625,
      55.6575,
      55.690000000000005,
      55.722500000000004,
      55.755,
      55.7875,
      55.82,
      55.8525,
      55.885000000000005,
      55.917500000000004,
      55.95,
      55.9825,
      56.015,
      56.0475,
      56.08,
      56.112500000000004,
      56.145,
      56.1775,
      56.21,
      56.2425,
      56.275,
      56.307500000000005,
      56.34,
      56.3725,
      56.405,
      56.4375,
      56.47,
      56.502500000000005,
      56.535000000000004,
      56.5675,
      56.6,
      56.6325,
      56.665,
      56.697500000000005,
      56.730000000000004,
      56.7625,
      56.795,
      56.8275,
      56.86,
      56.892500000000005,
      56.925000000000004,
      56.9575,
      56.99,
      57.0225,
      57.055,
      57.0875,
      57.120000000000005,
      57.1525,
      57.185,
      57.2175,
      57.25,
      57.2825,
      57.315000000000005,
      57.347500000000004,
      57.38,
      57.4125,
      57.445,
      57.4775,
      57.510000000000005,
      57.542500000000004,
      57.575,
      57.6075,
      57.64,
      57.6725,
      57.705000000000005,
      57.737500000000004,
      57.77,
      57.8025,
      57.835,
      57.8675,
      57.9,
      57.932500000000005,
      57.965,
      57.9975,
      58.03,
      58.0625,
      58.095,
      58.127500000000005,
      58.160000000000004,
      58.1925,
      58.225,
      58.2575,
      58.29,
      58.322500000000005,
      58.355000000000004,
      58.3875,
      58.42,
      58.4525,
      58.485,
      58.517500000000005,
      58.550000000000004,
      58.5825,
      58.615,
      58.6475,
      58.68,
      58.7125,
      58.745000000000005,
      58.7775,
      58.81,
      58.8425,
      58.875,
      58.9075,
      58.940000000000005,
      58.972500000000004,
      59.005,
      59.0375,
      59.07,
      59.1025,
      59.135000000000005,
      59.167500000000004,
      59.2,
      59.2325,
      59.265,
      59.2975,
      59.330000000000005,
      59.362500000000004,
      59.395,
      59.4275,
      59.46,
      59.4925,
      59.525,
      59.557500000000005,
      59.59,
      59.6225,
      59.655,
      59.6875,
      59.72,
      59.752500000000005,
      59.785000000000004,
      59.8175,
      59.85,
      59.8825,
      59.915,
      59.947500000000005,
      59.980000000000004,
      60.0125,
      60.045,
      60.0775,
      60.11,
      60.142500000000005,
      60.175000000000004,
      60.2075,
      60.24,
      60.2725,
      60.305,
      60.3375,
      60.370000000000005,
      60.4025,
      60.435,
      60.4675,
      60.5,
      60.5325,
      60.565000000000005,
      60.597500000000004,
      60.63,
      60.6625,
      60.695,
      60.7275,
      60.760000000000005,
      60.792500000000004,
      60.825,
      60.8575,
      60.89,
      60.9225,
      60.955000000000005,
      60.987500000000004,
      61.02,
      61.0525,
      61.085,
      61.1175,
      61.15,
      61.182500000000005,
      61.215,
      61.2475,
      61.28,
      61.3125,
      61.345,
      61.377500000000005,
      61.410000000000004,
      61.4425,
      61.475,
      61.5075,
      61.54,
      61.572500000000005,
      61.605000000000004,
      61.6375,
      61.67,
      61.7025,
      61.735,
      61.767500000000005,
      61.800000000000004,
      61.8325,
      61.865,
      61.8975,
      61.93,
      61.9625,
      61.995000000000005,
      62.0275,
      62.06,
      62.0925,
      62.125,
      62.1575,
      62.190000000000005,
      62.222500000000004,
      62.255,
      62.2875,
      62.32,
      62.3525,
      62.385000000000005,
      62.417500000000004,
      62.45,
      62.4825,
      62.515,
      62.5475,
      62.580000000000005,
      62.612500000000004,
      62.645,
      62.6775,
      62.71,
      62.7425,
      62.775,
      62.807500000000005,
      62.84,
      62.8725,
      62.905,
      62.9375,
      62.97,
      63.002500000000005,
      63.035000000000004,
      63.0675,
      63.1,
      63.1325,
      63.165,
      63.197500000000005,
      63.230000000000004,
      63.2625,
      63.295,
      63.3275,
      63.36,
      63.392500000000005,
      63.425000000000004,
      63.4575,
      63.49,
      63.5225,
      63.555,
      63.5875,
      63.620000000000005,
      63.6525,
      63.685,
      63.7175,
      63.75,
      63.7825,
      63.815000000000005,
      63.847500000000004,
      63.88,
      63.9125,
      63.945,
      63.9775,
      64.01,
      64.0425,
      64.075,
      64.1075,
      64.14,
      64.1725,
      64.20500000000001,
      64.23750000000001,
      64.27000000000001,
      64.30250000000001,
      64.33500000000001,
      64.3675,
      64.4,
      64.4325,
      64.465,
      64.4975,
      64.53,
      64.5625,
      64.595,
      64.6275,
      64.66,
      64.6925,
      64.725,
      64.7575,
      64.78999999999999,
      64.8225,
      64.855,
      64.8875,
      64.92,
      64.9525,
      64.985,
      65.01750000000001,
      65.05000000000001,
      65.08250000000001,
      65.11500000000001,
      65.14750000000001,
      65.18,
      65.2125,
      65.245,
      65.2775,
      65.31,
      65.3425,
      65.375,
      65.4075,
      65.44,
      65.4725,
      65.505,
      65.5375,
      65.57,
      65.60249999999999,
      65.635,
      65.6675,
      65.7,
      65.7325,
      65.765,
      65.7975,
      65.83000000000001,
      65.86250000000001,
      65.89500000000001,
      65.92750000000001,
      65.96000000000001,
      65.9925,
      66.025,
      66.0575,
      66.09,
      66.1225,
      66.155,
      66.1875,
      66.22,
      66.2525,
      66.285,
      66.3175,
      66.35000000000001,
      66.38250000000001,
      66.415,
      66.4475,
      66.48,
      66.5125,
      66.545,
      66.5775,
      66.61,
      66.6425,
      66.675,
      66.7075,
      66.74000000000001,
      66.77250000000001,
      66.805,
      66.8375,
      66.87,
      66.9025,
      66.935,
      66.9675,
      67.0,
      67.0325,
      67.065,
      67.0975,
      67.13,
      67.16250000000001,
      67.19500000000001,
      67.2275,
      67.26,
      67.2925,
      67.325,
      67.3575,
      67.39,
      67.4225,
      67.455,
      67.4875,
      67.52,
      67.55250000000001,
      67.58500000000001,
      67.6175,
      67.65,
      67.6825,
      67.715,
      67.7475,
      67.78,
      67.8125,
      67.845,
      67.8775,
      67.91,
      67.9425,
      67.97500000000001,
      68.00750000000001,
      68.04,
      68.0725,
      68.105,
      68.1375,
      68.17,
      68.2025,
      68.235,
      68.2675,
      68.3,
      68.3325,
      68.36500000000001,
      68.39750000000001,
      68.43,
      68.4625,
      68.495,
      68.5275,
      68.56,
      68.5925,
      68.625,
      68.6575,
      68.69,
      68.7225,
      68.755,
      68.78750000000001,
      68.82000000000001,
      68.8525,
      68.885,
      68.9175,
      68.95,
      68.9825,
      69.015,
      69.0475,
      69.08,
      69.1125,
      69.145,
      69.17750000000001,
      69.21000000000001,
      69.2425,
      69.275,
      69.3075,
      69.34,
      69.3725,
      69.405,
      69.4375,
      69.47,
      69.5025,
      69.535,
      69.5675,
      69.60000000000001,
      69.63250000000001,
      69.665,
      69.6975,
      69.73,
      69.7625,
      69.795,
      69.8275,
      69.86,
      69.8925,
      69.925,
      69.9575,
      69.99000000000001,
      70.02250000000001,
      70.055,
      70.0875,
      70.12,
      70.1525,
      70.185,
      70.2175,
      70.25,
      70.2825,
      70.315,
      70.3475,
      70.38,
      70.41250000000001,
      70.44500000000001,
      70.4775,
      70.51,
      70.5425,
      70.575,
      70.6075,
      70.64,
      70.6725,
      70.705,
      70.7375,
      70.77,
      70.80250000000001,
      70.83500000000001,
      70.8675,
      70.9,
      70.9325,
      70.965,
      70.9975,
      71.03,
      71.0625,
      71.095,
      71.1275,
      71.16,
      71.1925,
      71.22500000000001,
      71.25750000000001,
      71.29,
      71.3225,
      71.355,
      71.3875,
      71.42,
      71.4525,
      71.485,
      71.5175,
      71.55,
      71.5825,
      71.61500000000001,
      71.64750000000001,
      71.68,
      71.7125,
      71.745,
      71.7775,
      71.81,
      71.8425,
      71.875,
      71.9075,
      71.94,
      71.9725,
      72.005,
      72.03750000000001,
      72.07000000000001,
      72.1025,
      72.135,
      72.1675,
      72.2,
      72.2325,
      72.265,
      72.2975,
      72.33,
      72.3625,
      72.395,
      72.42750000000001,
      72.46000000000001,
      72.4925,
      72.525,
      72.5575,
      72.59,
      72.6225,
      72.655,
      72.6875,
      72.72,
      72.7525,
      72.785,
      72.8175,
      72.85000000000001,
      72.88250000000001,
      72.915,
      72.9475,
      72.98,
      73.0125,
      73.045,
      73.0775,
      73.11,
      73.1425,
      73.175,
      73.2075,
      73.24000000000001,
      73.27250000000001,
      73.305,
      73.3375,
      73.37,
      73.4025,
      73.435,
      73.4675,
      73.5,
      73.5325,
      73.565,
      73.5975,
      73.63,
      73.66250000000001,
      73.69500000000001,
      73.7275,
      73.76,
      73.7925,
      73.825,
      73.8575,
      73.89,
      73.9225,
      73.955,
      73.9875,
      74.02,
      74.05250000000001,
      74.08500000000001,
      74.1175,
      74.15,
      74.1825,
      74.215,
      74.2475,
      74.28,
      74.3125,
      74.345,
      74.3775,
      74.41,
      74.4425,
      74.47500000000001,
      74.50750000000001,
      74.54,
      74.5725,
      74.605,
      74.6375,
      74.67,
      74.7025,
      74.735,
      74.7675,
      74.8,
      74.8325,
      74.86500000000001,
      74.89750000000001,
      74.93,
      74.9625,
      74.995,
      75.0275,
      75.06,
      75.0925,
      75.125,
      75.1575,
      75.19,
      75.2225,
      75.255,
      75.28750000000001,
      75.32000000000001,
      75.3525,
      75.385,
      75.4175,
      75.45,
      75.4825,
      75.515,
      75.5475,
      75.58,
      75.6125,
      75.645,
      75.67750000000001,
      75.71000000000001,
      75.7425,
      75.775,
      75.8075,
      75.84,
      75.8725,
      75.905,
      75.9375,
      75.97,
      76.0025,
      76.035,
      76.0675,
      76.10000000000001,
      76.13250000000001,
      76.165,
      76.1975,
      76.23,
      76.2625,
      76.295,
      76.3275,
      76.36,
      76.3925,
      76.425,
      76.4575,
      76.49000000000001,
      76.52250000000001,
      76.555,
      76.5875,
      76.62,
      76.6525,
      76.685,
      76.7175,
      76.75,
      76.7825,
      76.815,
      76.8475,
      76.88,
      76.91250000000001,
      76.94500000000001,
      76.9775,
      77.01,
      77.0425,
      77.075,
      77.1075,
      77.14,
      77.1725,
      77.205,
      77.2375,
      77.27,
      77.30250000000001,
      77.33500000000001,
      77.3675,
      77.4,
      77.4325,
      77.465,
      77.4975,
      77.53,
      77.5625,
      77.595,
      77.6275,
      77.66,
      77.69250000000001,
      77.72500000000001,
      77.75750000000001,
      77.79,
      77.8225,
      77.855,
      77.8875,
      77.92,
      77.9525,
      77.985,
      78.0175,
      78.05,
      78.0825,
      78.11500000000001,
      78.14750000000001,
      78.18,
      78.2125,
      78.245,
      78.2775,
      78.31,
      78.3425,
      78.375,
      78.4075,
      78.44,
      78.4725,
      78.50500000000001,
      78.53750000000001,
      78.57000000000001,
      78.6025,
      78.635,
      78.6675,
      78.7,
      78.7325,
      78.765,
      78.7975,
      78.83,
      78.8625,
      78.895,
      78.92750000000001,
      78.96000000000001,
      78.9925,
      79.025,
      79.0575,
      79.09,
      79.1225,
      79.155,
      79.1875,
      79.22,
      79.2525,
      79.285,
      79.31750000000001,
      79.35000000000001,
      79.38250000000001,
      79.415,
      79.4475,
      79.48,
      79.5125,
      79.545,
      79.5775,
      79.61,
      79.6425,
      79.675,
      79.7075,
      79.74000000000001,
      79.77250000000001,
      79.805,
      79.8375,
      79.87,
      79.9025,
      79.935,
      79.9675,
      80.0
    ],
    "simple_counts": [
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      2,
      3,
      3,
      3,
      3,
      3,
      3,
      3,
      3,
      3,
      3,
      3,
      3,
      3,
      3,
      3,
      3,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      4,
      5,
      5,
      5,
      5,
      5,
      5,
      5,
      5,
      5,
      5,
      5,
      5,
      5,
      5,
      5,
      5,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      6,
      7,
      7,
      7,
      7,
      7,
      7,
      7,
      7,
      7,
      7,
      7,
      7,
      7,
      7,
      7,
      7,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      8,
      9,
      9,
      9,
      9,
      9,
      9,
      9,
      9,
      9,
      9,
      9,
      9,
      9,
      9,
      9,
      9,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      10,
      11,
      11,
      11,
      11,
      11,
      11,
      11,
      11,
      11,
      11,
      11,
      11,
      11,
      11,
      11,
      11,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      12,
      13,
      13,
      13,
      13,
      13,
      13,
      13,
      13,
      13,
      13,
      13,
      13,
      13,
      13,
      13,
      13,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      14,
      15,
      15,
      15,
      15,
      15,
      15,
      15,
      15,
      15,
      15,
      15,
      15,
      15,
      15,
      15,
      15,
      15,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      16,
      17,
      17,
      17,
      17,
      17,
      17,
      17,
      17,
      17,
      17,
      17,
      17,
      17,
      17,
      17,
      17,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      18,
      19,
      19,
      19,
      19,
      19,
      19,
      19,
      19,
      19,
      19,
      19,
      19,
      19,
      19,
      19,
      19,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      20,
      21,
      21,
      21,
      21,
      21,
      21,
      21,
      21,
      21,
      21,
      21,
      21,
      21,
      21,
      21,
      21,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      22,
      23,
      23,
      23,
      23,
      23,
      23,
      23,
      23,
      23,
      23,
      23,
      23,
      23,
      23,
      23,
      23,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      24,
      25,
      25,
      25,
      25,
      25,
      25,
      25,
      25,
      25,
      25,
      25,
      25,
      25,
      25,
      25,
      25,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      26,
      27,
      27,
      27,
      27,
      27,
      27,
      27,
      27,
      27,
      27,
      27,
      27,
      27,
      27,
      27,
      27,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      28,
      29,
      29,
      29,
      29,
      29,
      29,
      29,
      29,
      29,
      29,
      29,
      29,
      29,
      29,
      29,
      29,
      29,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      30,
      31,
      31,
      31,
      31,
      31,
      31,
      31,
      31,
      31,
      31,
      31,
      31,
      31,
      31,
      31,
      31,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      32,
      33,
      33,
      33,
      33,
      33,
      33,
      33,
      33,
      33,
      33,
      33,
      33,
      33,
      33,
      33,
      33,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      34,
      35,
      35,
      35,
      35,
      35,
      35,
      35,
      35,
      35,
      35,
      35,
      35,
      35,
      35,
      35,
      35,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      36,
      37,
      37,
      37,
      37,
      37,
      37,
      37,
      37,
      37,
      37,
      37,
      37,
      37,
      37,
      37,
      37,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      38,
      39,
      39,
      39,
      39,
      39,
      39,
      39,
      39,
      39,
      39,
      39,
      39,
      39,
      39,
      39,
      39,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      40,
      41,
      41,
      41,
      41,
      41,
      41,
      41,
      41,
      41,
      41,
      41,
      41,
      41,
      41,
      41,
      41,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      42,
      43,
      43,
      43,
      43,
      43,
      43,
      43,
      43,
      43,
      43,
      43,
      43,
      43,
      43,
      43,
      43,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      44,
      45,
      45,
      45,
      45,
      45,
      45,
      45,
      45,
      45,
      45,
      45,
      45,
      45,
      45,
      45,
      45,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      46,
      47,
      47,
      47,
      47,
      47,
      47,
      47,
      47,
      47,
      47,
      47,
      47,
      47,
      47,
      47,
      47,
      47,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      48,
      49,
      49,
      49,
      49,
      49,
      49,
      49,
      49,
      49,
      49,
      49,
      49,
      49,
      49,
      49,
      49,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      50,
      51,
      51,
      51,
      51,
      51,
      51,
      51,
      51,
      51,
      51,
      51,
      51,
      51,
      51,
      51,
      51,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      52,
      53,
      53,
      53,
      53,
      53,
      53,
      53,
      53,
      53,
      53,
      53,
      53,
      53,
      53,
      53,
      53,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      54,
      55,
      55,
      55,
      55,
      55,
      55,
      55,
      55,
      55,
      55,
      55,
      55,
      55,
      55,
      55,
      55,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      56,
      57,
      57,
      57,
      57,
      57,
      57,
      57,
      57,
      57,
      57,
      57,
      57,
      57,
      57,
      57,
      57,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      58,
      59,
      59,
      59,
      59,
      59,
      59,
      59,
      59,
      59,
      59,
      59,
      59,
      59,
      59,
      59,
      59,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      60,
      61,
      61,
      61,
      61,
      61,
      61,
      61,
      61,
      61,
      61,
      61,
      61,
      61,
      61,
      61,
      61,
      61,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      62,
      63,
      63,
      63,
      63,
      63,
      63,
      63,
      63,
      63,
      63,
      63,
      63,
      63,
      63,
      63,
      63,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      64,
      65,
      65,
      65,
      65,
      65,
      65,
      65,
      65,
      65,
      65,
      65,
      65,
      65,
      65,
      65,
      65,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      66,
      67,
      67,
      67,
      67,
      67,
      67,
      67,
      67,
      67,
      67,
      67,
      67,
      67,
      67,
      67,
      67,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      68,
      69,
      69,
      69,
      69,
      69,
      69,
      69,
      69,
      69,
      69,
      69,
      69,
      69,
      69,
      69,
      69,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      70,
      71,
      71,
      71,
      71,
      71,
      71,
      71,
      71,
      71,
      71,
      71,
      71,
      71,
      71,
      71,
      71,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      72,
      73,
      73,
      73,
      73,
      73,
      73,
      73,
      73,
      73,
      73,
      73,
      73,
      73,
      73,
      73,
      73,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      74,
      75,
      75,
      75,
      75,
      75,
      75,
      75,
      75,
      75,
      75,
      75,
      75,
      75,
      75,
      75,
      75,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76,
      76
    ],
    "method": "bisect_left on exact-formula zero radii; strict open disk",
    "floating_point_scope": "illustrative evaluation only",
    "convolution_power": 3,
    "convolution_support_hull": [
      -3,
      6
    ],
    "simple_limit": "3/pi",
    "triple_limit": "9/pi",
    "point_limit": 0,
    "proof_locators": "Examples A-D, (Z24)-(Z27); section 5"
  },
  "output": {
    "svg": "vector figure",
    "pdf": "original one-page vector figure",
    "png": "rendered from own PDF at scale 1.7"
  }
}