{
  "table": "T519",
  "versions": {
    "python": "3.12.3",
    "sage": "10.9",
    "sympy": "1.14.0",
    "numberdb": "0.1.10",
    "numpy": "2.4.4",
    "scipy": "1.17.1",
    "mpmath": "1.4.1"
  },
  "exact_checks": {
    "kernel_commutator": "0",
    "endpoint_boundary_factors_zero": true,
    "diagonal_limit": "c/pi",
    "trace": "2*c/pi"
  },
  "constant_kernel_max_error": 6.661338147750939e-16,
  "moment_max_error": 3.5860203695392556e-14,
  "all_stored_values_consistency_checked": 48,
  "independent_values_compared": 34,
  "maximum_absolute_error": 5.3013149425851225e-14,
  "rows": [
    {
      "S": 1,
      "n": 0,
      "absolute_error": 7.438494264988549e-15
    },
    {
      "S": 1,
      "n": 1,
      "absolute_error": 5.995204332975845e-15
    },
    {
      "S": 1,
      "n": 2,
      "absolute_error": 8.760353553682876e-16
    },
    {
      "S": 1,
      "n": 3,
      "absolute_error": 2.4259023609363162e-17
    },
    {
      "S": 1,
      "n": 4,
      "absolute_error": 2.549569171235444e-18
    },
    {
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      "absolute_error": 1.8096635301390052e-14
    },
    {
      "S": 2,
      "n": 1,
      "absolute_error": 2.220446049250313e-15
    },
    {
      "S": 2,
      "n": 2,
      "absolute_error": 1.3128387266192476e-14
    },
    {
      "S": 2,
      "n": 3,
      "absolute_error": 2.796374243274613e-15
    },
    {
      "S": 2,
      "n": 4,
      "absolute_error": 1.6479873021779667e-16
    },
    {
      "S": 2,
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      "absolute_error": 1.2054972905323202e-17
    },
    {
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      "absolute_error": 1.3526057376467109e-18
    },
    {
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      "absolute_error": 2.1316282072803006e-14
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    {
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      "absolute_error": 1.1546319456101628e-14
    },
    {
      "S": 4,
      "n": 3,
      "absolute_error": 1.7319479184152442e-14
    },
    {
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      "absolute_error": 2.6922908347160046e-14
    },
    {
      "S": 4,
      "n": 5,
      "absolute_error": 7.563394355258879e-15
    },
    {
      "S": 4,
      "n": 6,
      "absolute_error": 8.261620554339544e-16
    },
    {
      "S": 4,
      "n": 7,
      "absolute_error": 6.358845741627484e-17
    },
    {
      "S": 4,
      "n": 8,
      "absolute_error": 2.2683542327470163e-18
    },
    {
      "S": 4,
      "n": 9,
      "absolute_error": 3.8782726979018226e-18
    },
    {
      "S": 8,
      "n": 0,
      "absolute_error": 2.120525977034049e-14
    },
    {
      "S": 8,
      "n": 1,
      "absolute_error": 2.142730437526552e-14
    },
    {
      "S": 8,
      "n": 2,
      "absolute_error": 1.9206858326015208e-14
    },
    {
      "S": 8,
      "n": 3,
      "absolute_error": 2.0095036745715333e-14
    },
    {
      "S": 8,
      "n": 4,
      "absolute_error": 2.0539125955565396e-14
    },
    {
      "S": 8,
      "n": 5,
      "absolute_error": 1.6542323066914832e-14
    },
    {
      "S": 8,
      "n": 6,
      "absolute_error": 1.4432899320127035e-15
    },
    {
      "S": 8,
      "n": 7,
      "absolute_error": 4.39648317751562e-14
    },
    {
      "S": 8,
      "n": 8,
      "absolute_error": 5.3013149425851225e-14
    },
    {
      "S": 8,
      "n": 9,
      "absolute_error": 1.815214645262131e-14
    },
    {
      "S": 8,
      "n": 10,
      "absolute_error": 2.6419838539126772e-15
    },
    {
      "S": 8,
      "n": 11,
      "absolute_error": 2.391749992503023e-16
    }
  ],
  "bandwidth_checks": {
    "1": {
      "ordered_and_in_unit_interval": true,
      "partial_trace_deficit": "1.87043328323941798759044252775e-27",
      "modes_compared": 5
    },
    "2": {
      "ordered_and_in_unit_interval": true,
      "partial_trace_deficit": "6.2856548788748754355156963216e-20",
      "modes_compared": 7
    },
    "4": {
      "ordered_and_in_unit_interval": true,
      "partial_trace_deficit": "2.10290402957502532817685095291e-12",
      "modes_compared": 10
    },
    "8": {
      "ordered_and_in_unit_interval": true,
      "partial_trace_deficit": "0.0000599438605607974844938504392999",
      "modes_compared": 12
    }
  },
  "displayed_program_value": 0.9810462777518827,
  "precision_limitation": "Independent comparisons use double precision; final stored digits are not re-certified by this repair."
}