{
  "schema_version": 2,
  "source_sha256": "0b7eb57db60a80b656c8ba3223b4e71ac158ee2f5baf043ad0f0f20333d1d871",
  "runtime": {
    "python": "3.9.6",
    "numpy": "2.0.2",
    "mpmath": "1.3.0"
  },
  "scope": "Only the s=-2, ell=m=2 branch on the five stated straight continuation paths; no QNM or arbitrary-complex-c claim.",
  "conventions": {
    "s": -2,
    "ell": 2,
    "m": 2,
    "angular_eigenvalue": "A(0)=ell(ell+1)-s(s+1)",
    "polar_normalization": "integral_-1^1 |S|^2 dx = 1",
    "full_sphere_harmonic": "S(cos(theta);c) exp(i m phi)/sqrt(2 pi)",
    "phase": "continuous overlap phase, then b_2 real positive; real S(x;0)=sqrt(5/32)(1+x)^2"
  },
  "primary_source": "https://arxiv.org/abs/gr-qc/0511111 (v4), printed pp. 3-6, Eq. (2.1), Eqs. (2.5)-(2.10), (2.13), (2.16a)-(2.16b)",
  "projection_checks": {
    "jmax": 8,
    "nonzero_correction_entry": [
      8,
      8
    ],
    "PX2P_minus_PXP_squared_last_diagonal": 0.22661774261361467,
    "expected_C_jmax_plus_1_squared": 0.22661774261361464,
    "projection_identity_max_error": 2.7755575615628914e-17,
    "jacobi_quadrature_basis_gram_error": 2.0704900953025116e-12,
    "jacobi_quadrature_X_squared_max_error": 1.4788170688007085e-13,
    "c_2_wrong_truncation_eigenvalue_minus_correct": 4.4291148526554025e-09
  },
  "cases": [
    {
      "c": {
        "real": "0",
        "imag": "0"
      },
      "matrix": {
        "jmax": 24,
        "steps": 1,
        "maximum_step": 0.05,
        "A": {
          "real": 4.0,
          "imag": 0.0
        },
        "right_residual_l2": 0.0,
        "left_residual_l2": 0.0,
        "scaled_right_residual": 0.0,
        "scaled_left_residual": 0.0,
        "extended_residual_l2": 0.0,
        "left_right_condition_number": 1.0,
        "tail_last_four_l2": 0.0,
        "tail_last_four_max": 0.0,
        "coefficient_norm_error": 0.0,
        "minimum_step_overlap": 1.0,
        "largest_competing_step_overlap": 0.0,
        "real_c_basis_orthogonality_error": 0.0
      },
      "matrix_jmax_sweep": [
        {
          "jmax": 8,
          "steps": 1,
          "maximum_step": 0.05,
          "A": {
            "real": 4.0,
            "imag": 0.0
          },
          "right_residual_l2": 0.0,
          "left_residual_l2": 0.0,
          "scaled_right_residual": 0.0,
          "scaled_left_residual": 0.0,
          "extended_residual_l2": 0.0,
          "left_right_condition_number": 1.0,
          "tail_last_four_l2": 0.0,
          "tail_last_four_max": 0.0,
          "coefficient_norm_error": 0.0,
          "minimum_step_overlap": 1.0,
          "largest_competing_step_overlap": 0.0,
          "real_c_basis_orthogonality_error": 0.0
        },
        {
          "jmax": 12,
          "steps": 1,
          "maximum_step": 0.05,
          "A": {
            "real": 4.0,
            "imag": 0.0
          },
          "right_residual_l2": 0.0,
          "left_residual_l2": 0.0,
          "scaled_right_residual": 0.0,
          "scaled_left_residual": 0.0,
          "extended_residual_l2": 0.0,
          "left_right_condition_number": 1.0,
          "tail_last_four_l2": 0.0,
          "tail_last_four_max": 0.0,
          "coefficient_norm_error": 0.0,
          "minimum_step_overlap": 1.0,
          "largest_competing_step_overlap": 0.0,
          "real_c_basis_orthogonality_error": 0.0
        },
        {
          "jmax": 16,
          "steps": 1,
          "maximum_step": 0.05,
          "A": {
            "real": 4.0,
            "imag": 0.0
          },
          "right_residual_l2": 0.0,
          "left_residual_l2": 0.0,
          "scaled_right_residual": 0.0,
          "scaled_left_residual": 0.0,
          "extended_residual_l2": 0.0,
          "left_right_condition_number": 1.0,
          "tail_last_four_l2": 0.0,
          "tail_last_four_max": 0.0,
          "coefficient_norm_error": 0.0,
          "minimum_step_overlap": 1.0,
          "largest_competing_step_overlap": 0.0,
          "real_c_basis_orthogonality_error": 0.0
        },
        {
          "jmax": 24,
          "steps": 1,
          "maximum_step": 0.05,
          "A": {
            "real": 4.0,
            "imag": 0.0
          },
          "right_residual_l2": 0.0,
          "left_residual_l2": 0.0,
          "scaled_right_residual": 0.0,
          "scaled_left_residual": 0.0,
          "extended_residual_l2": 0.0,
          "left_right_condition_number": 1.0,
          "tail_last_four_l2": 0.0,
          "tail_last_four_max": 0.0,
          "coefficient_norm_error": 0.0,
          "minimum_step_overlap": 1.0,
          "largest_competing_step_overlap": 0.0,
          "real_c_basis_orthogonality_error": 0.0
        }
      ],
      "matrix_A_change_16_to_24": 0.0,
      "continued_fraction": {
        "dps": 80,
        "cutoff": 240,
        "steps": 1,
        "maximum_step": "0.05",
        "A": {
          "real": "4.0",
          "imag": "0.0"
        },
        "absolute_fraction_residual": "0.0",
        "largest_step_eigenvalue_change": "0.0"
      },
      "continued_fraction_sweep": [
        {
          "dps": 50,
          "cutoff": 80,
          "A": {
            "real": "4.0",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "0.0",
          "absolute_fraction_residual": "0.0"
        },
        {
          "dps": 50,
          "cutoff": 160,
          "A": {
            "real": "4.0",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "0.0",
          "absolute_fraction_residual": "0.0"
        },
        {
          "dps": 80,
          "cutoff": 160,
          "A": {
            "real": "4.0",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "0.0",
          "absolute_fraction_residual": "0.0"
        },
        {
          "dps": 80,
          "cutoff": 240,
          "A": {
            "real": "4.0",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "0.0",
          "absolute_fraction_residual": "0.0"
        }
      ],
      "matrix_cf_absolute_difference": 0.0,
      "matrix_step_halving": {
        "eigenvalue_change": 0.0,
        "phase_aligned_vector_change_l2": 0.0,
        "steps": 1
      },
      "cf_step_halving": {
        "eigenvalue_change": "0.0",
        "steps": 1
      },
      "polar_quadrature_norm_error": 1.1546319456101628e-14,
      "leading_mixing_coefficients": [
        {
          "j": 2,
          "b": {
            "real": 1.0,
            "imag": 0.0
          }
        },
        {
          "j": 3,
          "b": {
            "real": 0.0,
            "imag": 0.0
          }
        },
        {
          "j": 4,
          "b": {
            "real": 0.0,
            "imag": 0.0
          }
        },
        {
          "j": 5,
          "b": {
            "real": 0.0,
            "imag": 0.0
          }
        },
        {
          "j": 6,
          "b": {
            "real": 0.0,
            "imag": 0.0
          }
        },
        {
          "j": 7,
          "b": {
            "real": 0.0,
            "imag": 0.0
          }
        },
        {
          "j": 8,
          "b": {
            "real": 0.0,
            "imag": 0.0
          }
        }
      ]
    },
    {
      "c": {
        "real": "0.1",
        "imag": "0"
      },
      "matrix": {
        "jmax": 24,
        "steps": 2,
        "maximum_step": 0.05,
        "A": {
          "real": 3.7259203780062387,
          "imag": 0.0
        },
        "right_residual_l2": 1.249319202733386e-16,
        "left_residual_l2": 4.00885456179158e-16,
        "scaled_right_residual": 2.0762497297413504e-19,
        "scaled_left_residual": 6.662335120024902e-19,
        "extended_residual_l2": 1.249319202733386e-16,
        "left_right_condition_number": 0.9999999999999996,
        "tail_last_four_l2": 3.682298687885691e-44,
        "tail_last_four_max": 3.682288335982994e-44,
        "coefficient_norm_error": 2.220446049250313e-16,
        "minimum_step_overlap": 0.9999555922860719,
        "largest_competing_step_overlap": 0.009424043302254033,
        "real_c_basis_orthogonality_error": 2.6682933994999576e-15
      },
      "matrix_jmax_sweep": [
        {
          "jmax": 8,
          "steps": 2,
          "maximum_step": 0.05,
          "A": {
            "real": 3.7259203780062387,
            "imag": 0.0
          },
          "right_residual_l2": 1.2491894407479396e-16,
          "left_residual_l2": 8.429138382593631e-16,
          "scaled_right_residual": 1.6949328017393244e-18,
          "scaled_left_residual": 1.1436874719741313e-17,
          "extended_residual_l2": 8.615873889545149e-13,
          "left_right_condition_number": 0.9999999999999998,
          "tail_last_four_l2": 3.1968957797137755e-06,
          "tail_last_four_max": 3.1967522628633115e-06,
          "coefficient_norm_error": 2.220446049250313e-16,
          "minimum_step_overlap": 0.9999555922860718,
          "largest_competing_step_overlap": 0.009424043302254036,
          "real_c_basis_orthogonality_error": 7.807026607085115e-16
        },
        {
          "jmax": 12,
          "steps": 2,
          "maximum_step": 0.05,
          "A": {
            "real": 3.7259203780062387,
            "imag": 0.0
          },
          "right_residual_l2": 1.2491893111739479e-16,
          "left_residual_l2": 6.63927598443625e-16,
          "scaled_right_residual": 7.9206747871488e-19,
          "scaled_left_residual": 4.20973389897378e-18,
          "extended_residual_l2": 1.2491893112057572e-16,
          "left_right_condition_number": 0.9999999999999998,
          "tail_last_four_l2": 1.0226593794221247e-14,
          "tail_last_four_max": 1.0226442058769485e-14,
          "coefficient_norm_error": 0.0,
          "minimum_step_overlap": 0.9999555922860718,
          "largest_competing_step_overlap": 0.009424043302254036,
          "real_c_basis_orthogonality_error": 1.6663263308327899e-15
        },
        {
          "jmax": 16,
          "steps": 2,
          "maximum_step": 0.05,
          "A": {
            "real": 3.7259203780062387,
            "imag": 0.0
          },
          "right_residual_l2": 1.2493192689076086e-16,
          "left_residual_l2": 3.567304872446684e-16,
          "scaled_right_residual": 4.564283710609007e-19,
          "scaled_left_residual": 1.3032850709427957e-18,
          "extended_residual_l2": 1.2493192689076086e-16,
          "left_right_condition_number": 0.9999999999999998,
          "tail_last_four_l2": 5.057723180045817e-24,
          "tail_last_four_max": 5.0576865182202836e-24,
          "coefficient_norm_error": 0.0,
          "minimum_step_overlap": 0.999955592286072,
          "largest_competing_step_overlap": 0.009424043302254041,
          "real_c_basis_orthogonality_error": 1.891592496869695e-15
        },
        {
          "jmax": 24,
          "steps": 2,
          "maximum_step": 0.05,
          "A": {
            "real": 3.7259203780062387,
            "imag": 0.0
          },
          "right_residual_l2": 1.249319202733386e-16,
          "left_residual_l2": 4.00885456179158e-16,
          "scaled_right_residual": 2.0762497297413504e-19,
          "scaled_left_residual": 6.662335120024902e-19,
          "extended_residual_l2": 1.249319202733386e-16,
          "left_right_condition_number": 0.9999999999999996,
          "tail_last_four_l2": 3.682298687885691e-44,
          "tail_last_four_max": 3.682288335982994e-44,
          "coefficient_norm_error": 2.220446049250313e-16,
          "minimum_step_overlap": 0.9999555922860719,
          "largest_competing_step_overlap": 0.009424043302254033,
          "real_c_basis_orthogonality_error": 2.6682933994999576e-15
        }
      ],
      "matrix_A_change_16_to_24": 0.0,
      "continued_fraction": {
        "dps": 80,
        "cutoff": 240,
        "steps": 2,
        "maximum_step": "0.05",
        "A": {
          "real": "3.7259203780062382158004998125573388197650706694247495317051768958",
          "imag": "0.0"
        },
        "absolute_fraction_residual": "0.0",
        "largest_step_eigenvalue_change": "0.1389003358405985"
      },
      "continued_fraction_sweep": [
        {
          "dps": 50,
          "cutoff": 80,
          "A": {
            "real": "3.72592037800623821580049981255733881976507067",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "1.8812949e-52",
          "absolute_fraction_residual": "6.6819118e-52"
        },
        {
          "dps": 50,
          "cutoff": 160,
          "A": {
            "real": "3.72592037800623821580049981255733881976507067",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "1.8812949e-52",
          "absolute_fraction_residual": "6.6819118e-52"
        },
        {
          "dps": 80,
          "cutoff": 160,
          "A": {
            "real": "3.7259203780062382158004998125573388197650706694247495317051768958",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "0.0",
          "absolute_fraction_residual": "0.0"
        },
        {
          "dps": 80,
          "cutoff": 240,
          "A": {
            "real": "3.7259203780062382158004998125573388197650706694247495317051768958",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "0.0",
          "absolute_fraction_residual": "0.0"
        }
      ],
      "matrix_cf_absolute_difference": 4.3771162789946237e-16,
      "matrix_step_halving": {
        "eigenvalue_change": 0.0,
        "phase_aligned_vector_change_l2": 0.0,
        "steps": 4
      },
      "cf_step_halving": {
        "eigenvalue_change": "0.0",
        "steps": 4
      },
      "polar_quadrature_norm_error": 1.2656542480726785e-14,
      "leading_mixing_coefficients": [
        {
          "j": 2,
          "b": {
            "real": 0.9998227865911633,
            "imag": 0.0
          }
        },
        {
          "j": 3,
          "b": {
            "real": 0.018823335608927665,
            "imag": 0.0
          }
        },
        {
          "j": 4,
          "b": {
            "real": 0.00027827938294151854,
            "imag": 0.0
          }
        },
        {
          "j": 5,
          "b": {
            "real": 3.1967522628633115e-06,
            "imag": 0.0
          }
        },
        {
          "j": 6,
          "b": {
            "real": 3.0290883110309784e-08,
            "imag": 0.0
          }
        },
        {
          "j": 7,
          "b": {
            "real": 2.4213142918576443e-10,
            "imag": 0.0
          }
        },
        {
          "j": 8,
          "b": {
            "real": 1.6774820557337753e-12,
            "imag": 0.0
          }
        }
      ],
      "independent_series_profile_check": {
        "series_terms_retained": 40,
        "series_finite_tail_derivative_bound": "2.4665181e-67",
        "comparison_grid_points": 161,
        "matrix_series_profile_max_difference": 8.881784197001252e-16,
        "maximum_scaled_ode_residual": "1.0572406e-69",
        "north_pole_boundary_residual": "8.718377e-69",
        "north_pole_value": {
          "real": "1.6166717621044533400361489252132462322787529274602783303152628304",
          "imag": "0.0"
        },
        "finite_tail_bound_meaning": "Uniform bound on discarded finite terms in the unnormalized S second derivative; excludes rounding and uncomputed infinite tail.",
        "south_pole_value": {
          "real": "0.0",
          "imag": "0.0"
        },
        "south_pole_derivative": {
          "real": "0.0",
          "imag": "0.0"
        },
        "south_pole_approach": [
          {
            "epsilon": "0.0001",
            "relative_error_in_quadratic_pole_limit": "6.6408222816535e-6"
          },
          {
            "epsilon": "0.000001",
            "relative_error_in_quadratic_pole_limit": "6.6407964805541e-8"
          }
        ],
        "series_profile_convergence_points": [
          "-1",
          "-0.99",
          "-0.9",
          "-0.5",
          "0",
          "0.5",
          "0.9",
          "0.99",
          "1"
        ],
        "series_profile_convergence_threshold": "1e-30",
        "series_profile_precision_cutoff_sweep": [
          {
            "dps": 50,
            "cutoff": 80,
            "series_terms_retained": 24,
            "finite_tail_derivative_bound": "2.9553679e-36",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "5.5861417e-39"
          },
          {
            "dps": 50,
            "cutoff": 160,
            "series_terms_retained": 24,
            "finite_tail_derivative_bound": "2.9553679e-36",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "5.5861417e-39"
          },
          {
            "dps": 80,
            "cutoff": 80,
            "series_terms_retained": 40,
            "finite_tail_derivative_bound": "2.4665181e-67",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "0.0"
          },
          {
            "dps": 80,
            "cutoff": 160,
            "series_terms_retained": 40,
            "finite_tail_derivative_bound": "2.4665181e-67",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "0.0"
          },
          {
            "dps": 80,
            "cutoff": 240,
            "series_terms_retained": 40,
            "finite_tail_derivative_bound": "2.4665181e-67",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "0.0"
          }
        ],
        "independent_series_norm": "1.0"
      }
    },
    {
      "c": {
        "real": "0.5",
        "imag": "0"
      },
      "matrix": {
        "jmax": 24,
        "steps": 10,
        "maximum_step": 0.05,
        "A": {
          "real": 2.4757027612577653,
          "imag": 0.0
        },
        "right_residual_l2": 7.777928255664555e-16,
        "left_residual_l2": 6.481928592275952e-16,
        "scaled_right_residual": 1.2955449053052565e-18,
        "scaled_left_residual": 1.0796743410637284e-18,
        "extended_residual_l2": 7.777928255664555e-16,
        "left_right_condition_number": 1.0,
        "tail_last_four_l2": 6.466636728265382e-31,
        "tail_last_four_max": 6.466183159156526e-31,
        "coefficient_norm_error": 0.0,
        "minimum_step_overlap": 0.9999552224711541,
        "largest_competing_step_overlap": 0.009460902294313964,
        "real_c_basis_orthogonality_error": 2.74264879001168e-15
      },
      "matrix_jmax_sweep": [
        {
          "jmax": 8,
          "steps": 10,
          "maximum_step": 0.05,
          "A": {
            "real": 2.4757027612577653,
            "imag": 0.0
          },
          "right_residual_l2": 9.15993731374479e-16,
          "left_residual_l2": 4.579455510855384e-16,
          "scaled_right_residual": 1.2667834292110338e-17,
          "scaled_left_residual": 6.333207485225788e-18,
          "extended_residual_l2": 6.44133417838775e-08,
          "left_right_condition_number": 0.9999999999999998,
          "tail_last_four_l2": 0.00038864020892379286,
          "tail_last_four_max": 0.0003882124821951661,
          "coefficient_norm_error": 2.220446049250313e-16,
          "minimum_step_overlap": 0.9999552224711542,
          "largest_competing_step_overlap": 0.009460902294313938,
          "real_c_basis_orthogonality_error": 1.1617125252145958e-15
        },
        {
          "jmax": 12,
          "steps": 10,
          "maximum_step": 0.05,
          "A": {
            "real": 2.4757027612577653,
            "imag": 0.0
          },
          "right_residual_l2": 1.110421483935608e-15,
          "left_residual_l2": 8.754460953261321e-16,
          "scaled_right_residual": 7.102363489699246e-18,
          "scaled_left_residual": 5.599438118404277e-18,
          "extended_residual_l2": 4.086509839583792e-14,
          "left_right_condition_number": 0.9999999999999998,
          "tail_last_four_l2": 7.554074872796788e-10,
          "tail_last_four_max": 7.551296234441009e-10,
          "coefficient_norm_error": 2.220446049250313e-16,
          "minimum_step_overlap": 0.999955222471154,
          "largest_competing_step_overlap": 0.00946090229431395,
          "real_c_basis_orthogonality_error": 2.498183413351102e-15
        },
        {
          "jmax": 16,
          "steps": 10,
          "maximum_step": 0.05,
          "A": {
            "real": 2.4757027612577653,
            "imag": 0.0
          },
          "right_residual_l2": 1.0547373981054365e-15,
          "left_residual_l2": 1.3792427037449773e-15,
          "scaled_right_residual": 3.872652197624292e-18,
          "scaled_left_residual": 5.064129988478244e-18,
          "extended_residual_l2": 1.0547373981222512e-15,
          "left_right_condition_number": 0.9999999999999998,
          "tail_last_four_l2": 2.303650246443969e-16,
          "tail_last_four_max": 2.3032347145772974e-16,
          "coefficient_norm_error": 2.220446049250313e-16,
          "minimum_step_overlap": 0.9999552224711542,
          "largest_competing_step_overlap": 0.00946090229431395,
          "real_c_basis_orthogonality_error": 2.1250705028917065e-15
        },
        {
          "jmax": 24,
          "steps": 10,
          "maximum_step": 0.05,
          "A": {
            "real": 2.4757027612577653,
            "imag": 0.0
          },
          "right_residual_l2": 7.777928255664555e-16,
          "left_residual_l2": 6.481928592275952e-16,
          "scaled_right_residual": 1.2955449053052565e-18,
          "scaled_left_residual": 1.0796743410637284e-18,
          "extended_residual_l2": 7.777928255664555e-16,
          "left_right_condition_number": 1.0,
          "tail_last_four_l2": 6.466636728265382e-31,
          "tail_last_four_max": 6.466183159156526e-31,
          "coefficient_norm_error": 0.0,
          "minimum_step_overlap": 0.9999552224711541,
          "largest_competing_step_overlap": 0.009460902294313964,
          "real_c_basis_orthogonality_error": 2.74264879001168e-15
        }
      ],
      "matrix_A_change_16_to_24": 0.0,
      "continued_fraction": {
        "dps": 80,
        "cutoff": 240,
        "steps": 10,
        "maximum_step": "0.05",
        "A": {
          "real": "2.4757027612577651101953063089361461461381021565297732502307397169",
          "imag": "0.0"
        },
        "absolute_fraction_residual": "2.1084396e-81",
        "largest_step_eigenvalue_change": "0.1701706210070999"
      },
      "continued_fraction_sweep": [
        {
          "dps": 50,
          "cutoff": 80,
          "A": {
            "real": "2.47570276125776511019530630893614614613810216",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "1.1977853e-57",
          "absolute_fraction_residual": "2.6727647e-51"
        },
        {
          "dps": 50,
          "cutoff": 160,
          "A": {
            "real": "2.47570276125776511019530630893614614613810216",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "1.1977853e-57",
          "absolute_fraction_residual": "2.6727647e-51"
        },
        {
          "dps": 80,
          "cutoff": 160,
          "A": {
            "real": "2.4757027612577651101953063089361461461381021565297732502307397169",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "0.0",
          "absolute_fraction_residual": "2.1084396e-81"
        },
        {
          "dps": 80,
          "cutoff": 240,
          "A": {
            "real": "2.4757027612577651101953063089361461461381021565297732502307397169",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "0.0",
          "absolute_fraction_residual": "2.1084396e-81"
        }
      ],
      "matrix_cf_absolute_difference": 2.284030404070897e-16,
      "matrix_step_halving": {
        "eigenvalue_change": 0.0,
        "phase_aligned_vector_change_l2": 0.0,
        "steps": 20
      },
      "cf_step_halving": {
        "eigenvalue_change": "0.0",
        "steps": 20
      },
      "polar_quadrature_norm_error": 1.6209256159527285e-14,
      "leading_mixing_coefficients": [
        {
          "j": 2,
          "b": {
            "real": 0.9955517758526888,
            "imag": 0.0
          }
        },
        {
          "j": 3,
          "b": {
            "real": 0.0939676835981867,
            "imag": 0.0
          }
        },
        {
          "j": 4,
          "b": {
            "real": 0.006825320105076595,
            "imag": 0.0
          }
        },
        {
          "j": 5,
          "b": {
            "real": 0.00038821248219879384,
            "imag": 0.0
          }
        },
        {
          "j": 6,
          "b": {
            "real": 1.8214206060618908e-05,
            "imag": 0.0
          }
        },
        {
          "j": 7,
          "b": {
            "real": 7.230088093377389e-07,
            "imag": 0.0
          }
        },
        {
          "j": 8,
          "b": {
            "real": 2.4891446643907698e-08,
            "imag": 0.0
          }
        }
      ],
      "independent_series_profile_check": {
        "series_terms_retained": 59,
        "series_finite_tail_derivative_bound": "4.4355107e-66",
        "comparison_grid_points": 161,
        "matrix_series_profile_max_difference": 6.661338147750939e-16,
        "maximum_scaled_ode_residual": "8.4073105e-69",
        "north_pole_boundary_residual": "9.503591e-68",
        "north_pole_value": {
          "real": "1.765340630552315087996879131793155797242929261976365380764173383",
          "imag": "0.0"
        },
        "finite_tail_bound_meaning": "Uniform bound on discarded finite terms in the unnormalized S second derivative; excludes rounding and uncomputed infinite tail.",
        "south_pole_value": {
          "real": "0.0",
          "imag": "0.0"
        },
        "south_pole_derivative": {
          "real": "0.0",
          "imag": "0.0"
        },
        "south_pole_approach": [
          {
            "epsilon": "0.0001",
            "relative_error_in_quadratic_pole_limit": "3.2743612679687e-5"
          },
          {
            "epsilon": "0.000001",
            "relative_error_in_quadratic_pole_limit": "3.2742978790259e-7"
          }
        ],
        "series_profile_convergence_points": [
          "-1",
          "-0.99",
          "-0.9",
          "-0.5",
          "0",
          "0.5",
          "0.9",
          "0.99",
          "1"
        ],
        "series_profile_convergence_threshold": "1e-30",
        "series_profile_precision_cutoff_sweep": [
          {
            "dps": 50,
            "cutoff": 80,
            "series_terms_retained": 38,
            "finite_tail_derivative_bound": "1.9352319e-36",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "1.3460988e-39"
          },
          {
            "dps": 50,
            "cutoff": 160,
            "series_terms_retained": 38,
            "finite_tail_derivative_bound": "1.9352319e-36",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "1.3460988e-39"
          },
          {
            "dps": 80,
            "cutoff": 80,
            "series_terms_retained": 59,
            "finite_tail_derivative_bound": "4.4355107e-66",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "0.0"
          },
          {
            "dps": 80,
            "cutoff": 160,
            "series_terms_retained": 59,
            "finite_tail_derivative_bound": "4.4355107e-66",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "0.0"
          },
          {
            "dps": 80,
            "cutoff": 240,
            "series_terms_retained": 59,
            "finite_tail_derivative_bound": "4.4355107e-66",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "0.0"
          }
        ],
        "independent_series_norm": "1.0"
      }
    },
    {
      "c": {
        "real": "0.3",
        "imag": "0.1"
      },
      "matrix": {
        "jmax": 24,
        "steps": 7,
        "maximum_step": 0.05,
        "A": {
          "real": 3.140114487179809,
          "imag": -0.31228668195772713
        },
        "right_residual_l2": 4.912046883911147e-15,
        "left_residual_l2": 4.470172665548976e-15,
        "scaled_right_residual": 8.171551636871094e-18,
        "scaled_left_residual": 7.436461341993151e-18,
        "extended_residual_l2": 4.912046883911147e-15,
        "left_right_condition_number": 1.000717180493987,
        "tail_last_four_l2": 1.1209715045240686e-34,
        "tail_last_four_max": 1.1209400221731518e-34,
        "coefficient_norm_error": 2.220446049250313e-16,
        "minimum_step_overlap": 0.9999633785391195,
        "largest_competing_step_overlap": 0.03605474042563659,
        "real_c_basis_orthogonality_error": null
      },
      "matrix_jmax_sweep": [
        {
          "jmax": 8,
          "steps": 7,
          "maximum_step": 0.05,
          "A": {
            "real": 3.1401144871798117,
            "imag": -0.312286681957727
          },
          "right_residual_l2": 2.296437156206496e-15,
          "left_residual_l2": 1.8827423847780152e-15,
          "scaled_right_residual": 3.1426461325678424e-17,
          "scaled_left_residual": 2.5765099028088302e-17,
          "extended_residual_l2": 2.6728350666805935e-09,
          "left_right_condition_number": 1.0007171804939867,
          "tail_last_four_l2": 9.99434284497079e-05,
          "tail_last_four_max": 9.98989908713765e-05,
          "coefficient_norm_error": 4.440892098500626e-16,
          "minimum_step_overlap": 0.9999633785391194,
          "largest_competing_step_overlap": 0.03605474042563642,
          "real_c_basis_orthogonality_error": null
        },
        {
          "jmax": 12,
          "steps": 7,
          "maximum_step": 0.05,
          "A": {
            "real": 3.1401144871798152,
            "imag": -0.3122866819577267
          },
          "right_residual_l2": 1.3991736572660145e-15,
          "left_residual_l2": 1.8301589995886527e-15,
          "scaled_right_residual": 8.906193916870688e-18,
          "scaled_left_residual": 1.1649555338893613e-17,
          "extended_residual_l2": 1.4257353188952615e-15,
          "left_right_condition_number": 1.000717180493987,
          "tail_last_four_l2": 3.1536694909261253e-11,
          "tail_last_four_max": 3.153203491006342e-11,
          "coefficient_norm_error": 2.220446049250313e-16,
          "minimum_step_overlap": 0.9999633785391195,
          "largest_competing_step_overlap": 0.03605474042563656,
          "real_c_basis_orthogonality_error": null
        },
        {
          "jmax": 16,
          "steps": 7,
          "maximum_step": 0.05,
          "A": {
            "real": 3.1401144871798206,
            "imag": -0.3122866819577279
          },
          "right_residual_l2": 6.72345854878053e-15,
          "left_residual_l2": 6.727877336513117e-15,
          "scaled_right_residual": 2.4618124211646466e-17,
          "scaled_left_residual": 2.463430372171208e-17,
          "extended_residual_l2": 6.72345854878053e-15,
          "left_right_condition_number": 1.0007171804939867,
          "tail_last_four_l2": 1.5494820082801491e-18,
          "tail_last_four_max": 1.5493699455938525e-18,
          "coefficient_norm_error": 4.440892098500626e-16,
          "minimum_step_overlap": 0.9999633785391197,
          "largest_competing_step_overlap": 0.0360547404256367,
          "real_c_basis_orthogonality_error": null
        },
        {
          "jmax": 24,
          "steps": 7,
          "maximum_step": 0.05,
          "A": {
            "real": 3.140114487179809,
            "imag": -0.31228668195772713
          },
          "right_residual_l2": 4.912046883911147e-15,
          "left_residual_l2": 4.470172665548976e-15,
          "scaled_right_residual": 8.171551636871094e-18,
          "scaled_left_residual": 7.436461341993151e-18,
          "extended_residual_l2": 4.912046883911147e-15,
          "left_right_condition_number": 1.000717180493987,
          "tail_last_four_l2": 1.1209715045240686e-34,
          "tail_last_four_max": 1.1209400221731518e-34,
          "coefficient_norm_error": 2.220446049250313e-16,
          "minimum_step_overlap": 0.9999633785391195,
          "largest_competing_step_overlap": 0.03605474042563659,
          "real_c_basis_orthogonality_error": null
        }
      ],
      "matrix_A_change_16_to_24": 1.1572444193553531e-14,
      "continued_fraction": {
        "dps": 80,
        "cutoff": 240,
        "steps": 7,
        "maximum_step": "0.05",
        "A": {
          "real": "3.1401144871798136552334367154499995169246219077018461757120458739",
          "imag": "-0.31228668195772709016650407813324768215121701303955307272636708743"
        },
        "absolute_fraction_residual": "2.6355495e-81",
        "largest_step_eigenvalue_change": "0.1396745051831289"
      },
      "continued_fraction_sweep": [
        {
          "dps": 50,
          "cutoff": 80,
          "A": {
            "real": "3.14011448717981365523343671544999951692462191",
            "imag": "-0.312286681957727090166504078133247682151217013"
          },
          "difference_from_80dps_240cutoff": "4.6702589e-52",
          "absolute_fraction_residual": "3.7798601e-51"
        },
        {
          "dps": 50,
          "cutoff": 160,
          "A": {
            "real": "3.14011448717981365523343671544999951692462191",
            "imag": "-0.312286681957727090166504078133247682151217013"
          },
          "difference_from_80dps_240cutoff": "4.6702589e-52",
          "absolute_fraction_residual": "3.7798601e-51"
        },
        {
          "dps": 80,
          "cutoff": 160,
          "A": {
            "real": "3.1401144871798136552334367154499995169246219077018461757120458739",
            "imag": "-0.31228668195772709016650407813324768215121701303955307272636708743"
          },
          "difference_from_80dps_240cutoff": "0.0",
          "absolute_fraction_residual": "2.6355495e-81"
        },
        {
          "dps": 80,
          "cutoff": 240,
          "A": {
            "real": "3.1401144871798136552334367154499995169246219077018461757120458739",
            "imag": "-0.31228668195772709016650407813324768215121701303955307272636708743"
          },
          "difference_from_80dps_240cutoff": "0.0",
          "absolute_fraction_residual": "2.6355495e-81"
        }
      ],
      "matrix_cf_absolute_difference": 4.644608977452136e-15,
      "matrix_step_halving": {
        "eigenvalue_change": 0.0,
        "phase_aligned_vector_change_l2": 6.938897226582551e-18,
        "steps": 13
      },
      "cf_step_halving": {
        "eigenvalue_change": "0.0",
        "steps": 13
      },
      "polar_quadrature_norm_error": 1.4432899320127035e-14,
      "leading_mixing_coefficients": [
        {
          "j": 2,
          "b": {
            "real": 0.9982178609061934,
            "imag": -4.0085890558997517e-23
          }
        },
        {
          "j": 3,
          "b": {
            "real": 0.056539408729126765,
            "imag": 0.01888796324108124
          }
        },
        {
          "j": 4,
          "b": {
            "real": 0.0022162541884171,
            "imag": 0.0016493943469090668
          }
        },
        {
          "j": 5,
          "b": {
            "real": 5.7367741865162205e-05,
            "imag": 8.17847820221307e-05
          }
        },
        {
          "j": 6,
          "b": {
            "real": 8.586572644858963e-07,
            "imag": 2.852645211075338e-06
          }
        },
        {
          "j": 7,
          "b": {
            "real": -2.0759007740376205e-09,
            "imag": 7.502778134275419e-08
          }
        },
        {
          "j": 8,
          "b": {
            "real": -5.588776060284594e-10,
            "imag": 1.5412003703333648e-09
          }
        }
      ]
    },
    {
      "c": {
        "real": "2",
        "imag": "0"
      },
      "matrix": {
        "jmax": 24,
        "steps": 40,
        "maximum_step": 0.05,
        "A": {
          "real": -4.660240022115655,
          "imag": 0.0
        },
        "right_residual_l2": 2.7703055404313956e-16,
        "left_residual_l2": 5.095914073266719e-15,
        "scaled_right_residual": 4.609736755386127e-19,
        "scaled_left_residual": 8.479505983361318e-18,
        "extended_residual_l2": 2.770305540432645e-16,
        "left_right_condition_number": 0.9999999999999996,
        "tail_last_four_l2": 1.0688518898629701e-19,
        "tail_last_four_max": 1.0676632944804719e-19,
        "coefficient_norm_error": 2.220446049250313e-16,
        "minimum_step_overlap": 0.9999552224711541,
        "largest_competing_step_overlap": 0.009460902294313964,
        "real_c_basis_orthogonality_error": 2.2141084919725363e-15
      },
      "matrix_jmax_sweep": [
        {
          "jmax": 8,
          "steps": 40,
          "maximum_step": 0.05,
          "A": {
            "real": -4.6602400157226915,
            "imag": 0.0
          },
          "right_residual_l2": 1.4748865987566276e-15,
          "left_residual_l2": 9.7835684490875e-16,
          "scaled_right_residual": 2.0106428864552717e-17,
          "scaled_left_residual": 1.3337474435586753e-17,
          "extended_residual_l2": 0.0007569368053898006,
          "left_right_condition_number": 1.0,
          "tail_last_four_l2": 0.01950558180316427,
          "tail_last_four_max": 0.019191322058948322,
          "coefficient_norm_error": 1.1102230246251565e-16,
          "minimum_step_overlap": 0.9999552224711542,
          "largest_competing_step_overlap": 0.009460902294313938,
          "real_c_basis_orthogonality_error": 1.077647728530202e-15
        },
        {
          "jmax": 12,
          "steps": 40,
          "maximum_step": 0.05,
          "A": {
            "real": -4.660240022115655,
            "imag": 0.0
          },
          "right_residual_l2": 1.6262048253548776e-15,
          "left_residual_l2": 3.8148586250165835e-15,
          "scaled_right_residual": 1.0344669689830167e-17,
          "scaled_left_residual": 2.4267209009531964e-17,
          "extended_residual_l2": 1.1250179728017432e-07,
          "left_right_condition_number": 0.9999999999999996,
          "tail_last_four_l2": 8.448116782093211e-06,
          "tail_last_four_max": 8.400256179408774e-06,
          "coefficient_norm_error": 2.220446049250313e-16,
          "minimum_step_overlap": 0.999955222471154,
          "largest_competing_step_overlap": 0.00946090229431395,
          "real_c_basis_orthogonality_error": 1.818420898556758e-15
        },
        {
          "jmax": 16,
          "steps": 40,
          "maximum_step": 0.05,
          "A": {
            "real": -4.660240022115656,
            "imag": 0.0
          },
          "right_residual_l2": 1.0209388761708895e-15,
          "left_residual_l2": 2.770463272197435e-15,
          "scaled_right_residual": 3.738403904684988e-18,
          "scaled_left_residual": 1.0144692259554644e-17,
          "extended_residual_l2": 4.003677166466786e-12,
          "left_right_condition_number": 0.9999999999999998,
          "tail_last_four_l2": 6.180965855445492e-10,
          "tail_last_four_max": 6.163497954983682e-10,
          "coefficient_norm_error": 2.220446049250313e-16,
          "minimum_step_overlap": 0.9999552224711542,
          "largest_competing_step_overlap": 0.00946090229431395,
          "real_c_basis_orthogonality_error": 2.477590780390938e-15
        },
        {
          "jmax": 24,
          "steps": 40,
          "maximum_step": 0.05,
          "A": {
            "real": -4.660240022115655,
            "imag": 0.0
          },
          "right_residual_l2": 2.7703055404313956e-16,
          "left_residual_l2": 5.095914073266719e-15,
          "scaled_right_residual": 4.609736755386127e-19,
          "scaled_left_residual": 8.479505983361318e-18,
          "extended_residual_l2": 2.770305540432645e-16,
          "left_right_condition_number": 0.9999999999999996,
          "tail_last_four_l2": 1.0688518898629701e-19,
          "tail_last_four_max": 1.0676632944804719e-19,
          "coefficient_norm_error": 2.220446049250313e-16,
          "minimum_step_overlap": 0.9999552224711541,
          "largest_competing_step_overlap": 0.009460902294313964,
          "real_c_basis_orthogonality_error": 2.2141084919725363e-15
        }
      ],
      "matrix_A_change_16_to_24": 8.881784197001252e-16,
      "continued_fraction": {
        "dps": 80,
        "cutoff": 240,
        "steps": 40,
        "maximum_step": "0.05",
        "A": {
          "real": "-4.660240022115656088827212113898953247705443399823993859687356332",
          "imag": "0.0"
        },
        "absolute_fraction_residual": "3.3735033e-80",
        "largest_step_eigenvalue_change": "0.3044727438895187"
      },
      "continued_fraction_sweep": [
        {
          "dps": 50,
          "cutoff": 80,
          "A": {
            "real": "-4.6602400221156560888272121138989532477054434",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "3.6218003e-52",
          "absolute_fraction_residual": "2.1382118e-50"
        },
        {
          "dps": 50,
          "cutoff": 160,
          "A": {
            "real": "-4.6602400221156560888272121138989532477054434",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "3.417038e-55",
          "absolute_fraction_residual": "2.1382118e-50"
        },
        {
          "dps": 80,
          "cutoff": 160,
          "A": {
            "real": "-4.660240022115656088827212113898953247705443399823993859687356332",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "2.2520564e-85",
          "absolute_fraction_residual": "3.3735033e-80"
        },
        {
          "dps": 80,
          "cutoff": 240,
          "A": {
            "real": "-4.660240022115656088827212113898953247705443399823993859687356332",
            "imag": "0.0"
          },
          "difference_from_80dps_240cutoff": "2.2520564e-85",
          "absolute_fraction_residual": "3.3735033e-80"
        }
      ],
      "matrix_cf_absolute_difference": 1.0657555445851877e-15,
      "matrix_step_halving": {
        "eigenvalue_change": 0.0,
        "phase_aligned_vector_change_l2": 0.0,
        "steps": 80
      },
      "cf_step_halving": {
        "eigenvalue_change": "3.0563623e-85",
        "steps": 80
      },
      "polar_quadrature_norm_error": 3.4861002973229915e-14,
      "leading_mixing_coefficients": [
        {
          "j": 2,
          "b": {
            "real": 0.9392290951021027,
            "imag": 0.0
          }
        },
        {
          "j": 3,
          "b": {
            "real": 0.33097829165374226,
            "imag": 0.0
          }
        },
        {
          "j": 4,
          "b": {
            "real": 0.08900342022519651,
            "imag": 0.0
          }
        },
        {
          "j": 5,
          "b": {
            "real": 0.01919133065763591,
            "imag": 0.0
          }
        },
        {
          "j": 6,
          "b": {
            "real": 0.0034462271964331393,
            "imag": 0.0
          }
        },
        {
          "j": 7,
          "b": {
            "real": 0.0005289746885347559,
            "imag": 0.0
          }
        },
        {
          "j": 8,
          "b": {
            "real": 7.082359112396851e-05,
            "imag": 0.0
          }
        }
      ],
      "independent_series_profile_check": {
        "series_terms_retained": 96,
        "series_finite_tail_derivative_bound": "1.1442788e-66",
        "comparison_grid_points": 161,
        "matrix_series_profile_max_difference": 8.881784197001252e-16,
        "maximum_scaled_ode_residual": "2.6755674e-70",
        "north_pole_boundary_residual": "7.7333108e-69",
        "north_pole_value": {
          "real": "2.3485381437414695719651939449954020685149066255779128606885632127",
          "imag": "0.0"
        },
        "finite_tail_bound_meaning": "Uniform bound on discarded finite terms in the unnormalized S second derivative; excludes rounding and uncomputed infinite tail.",
        "south_pole_value": {
          "real": "0.0",
          "imag": "0.0"
        },
        "south_pole_derivative": {
          "real": "0.0",
          "imag": "0.0"
        },
        "south_pole_approach": [
          {
            "epsilon": "0.0001",
            "relative_error_in_quadratic_pole_limit": "0.000126612244214"
          },
          {
            "epsilon": "0.000001",
            "relative_error_in_quadratic_pole_limit": "1.2660249865584e-6"
          }
        ],
        "series_profile_convergence_points": [
          "-1",
          "-0.99",
          "-0.9",
          "-0.5",
          "0",
          "0.5",
          "0.9",
          "0.99",
          "1"
        ],
        "series_profile_convergence_threshold": "1e-30",
        "series_profile_precision_cutoff_sweep": [
          {
            "dps": 50,
            "cutoff": 80,
            "series_terms_retained": 66,
            "finite_tail_derivative_bound": "5.137968e-36",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "5.811373e-40"
          },
          {
            "dps": 50,
            "cutoff": 160,
            "series_terms_retained": 66,
            "finite_tail_derivative_bound": "5.137968e-36",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "5.811373e-40"
          },
          {
            "dps": 80,
            "cutoff": 80,
            "series_terms_retained": 81,
            "finite_tail_derivative_bound": "0.0",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "1.6763648e-52"
          },
          {
            "dps": 80,
            "cutoff": 160,
            "series_terms_retained": 96,
            "finite_tail_derivative_bound": "1.1442788e-66",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "0.0"
          },
          {
            "dps": 80,
            "cutoff": 240,
            "series_terms_retained": 96,
            "finite_tail_derivative_bound": "1.1442788e-66",
            "maximum_normalized_profile_difference_from_80dps_240cutoff": "0.0"
          }
        ],
        "independent_series_norm": "1.0"
      }
    }
  ],
  "perturbation_checks": {
    "A_first_derivative_at_zero": -2.6666666666666665,
    "S_3_coefficient_in_S_first_derivative": 0.187812056606337,
    "real_c_halving_checks": [
      {
        "c": 0.1,
        "profile_first_order_remainder_l2": 0.00033260962091874707,
        "finite_difference_derivative_error_l2": 0.0033260962091874705,
        "previous_remainder_over_current": null,
        "eigenvalue_first_order_remainder": -0.007412955327094739,
        "previous_eigenvalue_remainder_over_current": null
      },
      {
        "c": 0.05,
        "profile_first_order_remainder_l2": 8.333580344919867e-05,
        "finite_difference_derivative_error_l2": 0.0016667160689839732,
        "previous_remainder_over_current": 3.991197146392249,
        "eigenvalue_first_order_remainder": -0.0018459528198300212,
        "previous_eigenvalue_remainder_over_current": 4.015788078363421
      },
      {
        "c": 0.025,
        "profile_first_order_remainder_l2": 2.085655170971314e-05,
        "finite_difference_derivative_error_l2": 0.0008342620683885255,
        "previous_remainder_over_current": 3.9956654680547317,
        "eigenvalue_first_order_remainder": -0.0004605734207423495,
        "previous_eigenvalue_remainder_over_current": 4.007944741697698
      },
      {
        "c": 0.0125,
        "profile_first_order_remainder_l2": 5.2169427015051516e-06,
        "finite_difference_derivative_error_l2": 0.0004173554161204121,
        "previous_remainder_over_current": 3.997849488301984,
        "eigenvalue_first_order_remainder": -0.00011502876629698733,
        "previous_eigenvalue_remainder_over_current": 4.003984703732428
      }
    ]
  },
  "figure_data": {
    "x": [
      -1.0,
      -0.995,
      -0.99,
      -0.985,
      -0.98,
      -0.975,
      -0.97,
      -0.965,
      -0.96,
      -0.955,
      -0.95,
      -0.945,
      -0.94,
      -0.935,
      -0.9299999999999999,
      -0.925,
      -0.92,
      -0.915,
      -0.91,
      -0.905,
      -0.9,
      -0.895,
      -0.89,
      -0.885,
      -0.88,
      -0.875,
      -0.87,
      -0.865,
      -0.86,
      -0.855,
      -0.85,
      -0.845,
      -0.84,
      -0.835,
      -0.83,
      -0.825,
      -0.8200000000000001,
      -0.815,
      -0.81,
      -0.8049999999999999,
      -0.8,
      -0.7949999999999999,
      -0.79,
      -0.785,
      -0.78,
      -0.775,
      -0.77,
      -0.765,
      -0.76,
      -0.755,
      -0.75,
      -0.745,
      -0.74,
      -0.735,
      -0.73,
      -0.725,
      -0.72,
      -0.715,
      -0.71,
      -0.7050000000000001,
      -0.7,
      -0.6950000000000001,
      -0.69,
      -0.685,
      -0.6799999999999999,
      -0.675,
      -0.6699999999999999,
      -0.665,
      -0.6599999999999999,
      -0.655,
      -0.6499999999999999,
      -0.645,
      -0.64,
      -0.635,
      -0.63,
      -0.625,
      -0.62,
      -0.615,
      -0.61,
      -0.605,
      -0.6,
      -0.595,
      -0.59,
      -0.585,
      -0.5800000000000001,
      -0.575,
      -0.5700000000000001,
      -0.565,
      -0.56,
      -0.5549999999999999,
      -0.55,
      -0.5449999999999999,
      -0.54,
      -0.5349999999999999,
      -0.53,
      -0.5249999999999999,
      -0.52,
      -0.515,
      -0.51,
      -0.505,
      -0.5,
      -0.495,
      -0.49,
      -0.485,
      -0.48,
      -0.475,
      -0.47,
      -0.46499999999999997,
      -0.45999999999999996,
      -0.45499999999999996,
      -0.44999999999999996,
      -0.44499999999999995,
      -0.43999999999999995,
      -0.43499999999999994,
      -0.42999999999999994,
      -0.42499999999999993,
      -0.42000000000000004,
      -0.41500000000000004,
      -0.41000000000000003,
      -0.405,
      -0.4,
      -0.395,
      -0.39,
      -0.385,
      -0.38,
      -0.375,
      -0.37,
      -0.365,
      -0.36,
      -0.355,
      -0.35,
      -0.345,
      -0.33999999999999997,
      -0.33499999999999996,
      -0.32999999999999996,
      -0.32499999999999996,
      -0.31999999999999995,
      -0.31499999999999995,
      -0.30999999999999994,
      -0.30499999999999994,
      -0.29999999999999993,
      -0.29500000000000004,
      -0.29000000000000004,
      -0.28500000000000003,
      -0.28,
      -0.275,
      -0.27,
      -0.265,
      -0.26,
      -0.255,
      -0.25,
      -0.245,
      -0.24,
      -0.235,
      -0.22999999999999998,
      -0.22499999999999998,
      -0.21999999999999997,
      -0.21499999999999997,
      -0.20999999999999996,
      -0.20499999999999996,
      -0.19999999999999996,
      -0.19499999999999995,
      -0.18999999999999995,
      -0.18499999999999994,
      -0.17999999999999994,
      -0.17499999999999993,
      -0.16999999999999993,
      -0.16500000000000004,
      -0.16000000000000003,
      -0.15500000000000003,
      -0.15000000000000002,
      -0.14500000000000002,
      -0.14,
      -0.135,
      -0.13,
      -0.125,
      -0.12,
      -0.11499999999999999,
      -0.10999999999999999,
      -0.10499999999999998,
      -0.09999999999999998,
      -0.09499999999999997,
      -0.08999999999999997,
      -0.08499999999999996,
      -0.07999999999999996,
      -0.07499999999999996,
      -0.06999999999999995,
      -0.06499999999999995,
      -0.05999999999999994,
      -0.05499999999999994,
      -0.04999999999999993,
      -0.04499999999999993,
      -0.040000000000000036,
      -0.03500000000000003,
      -0.030000000000000027,
      -0.025000000000000022,
      -0.020000000000000018,
      -0.015000000000000013,
      -0.010000000000000009,
      -0.0050000000000000044,
      0.0,
      0.0050000000000001155,
      0.010000000000000009,
      0.015000000000000124,
      0.020000000000000018,
      0.02499999999999991,
      0.030000000000000027,
      0.03499999999999992,
      0.040000000000000036,
      0.04499999999999993,
      0.050000000000000044,
      0.05499999999999994,
      0.06000000000000005,
      0.06499999999999995,
      0.07000000000000006,
      0.07499999999999996,
      0.08000000000000007,
      0.08499999999999996,
      0.09000000000000008,
      0.09499999999999997,
      0.10000000000000009,
      0.10499999999999998,
      0.1100000000000001,
      0.11499999999999999,
      0.1200000000000001,
      0.125,
      0.13000000000000012,
      0.135,
      0.14000000000000012,
      0.14500000000000002,
      0.15000000000000013,
      0.15500000000000003,
      0.15999999999999992,
      0.16500000000000004,
      0.16999999999999993,
      0.17500000000000004,
      0.17999999999999994,
      0.18500000000000005,
      0.18999999999999995,
      0.19500000000000006,
      0.19999999999999996,
      0.20500000000000007,
      0.20999999999999996,
      0.21500000000000008,
      0.21999999999999997,
      0.2250000000000001,
      0.22999999999999998,
      0.2350000000000001,
      0.24,
      0.2450000000000001,
      0.25,
      0.2550000000000001,
      0.26,
      0.2650000000000001,
      0.27,
      0.27500000000000013,
      0.28,
      0.2849999999999999,
      0.29000000000000004,
      0.29499999999999993,
      0.30000000000000004,
      0.30499999999999994,
      0.31000000000000005,
      0.31499999999999995,
      0.32000000000000006,
      0.32499999999999996,
      0.33000000000000007,
      0.33499999999999996,
      0.3400000000000001,
      0.345,
      0.3500000000000001,
      0.355,
      0.3600000000000001,
      0.365,
      0.3700000000000001,
      0.375,
      0.3800000000000001,
      0.385,
      0.3900000000000001,
      0.395,
      0.40000000000000013,
      0.405,
      0.4099999999999999,
      0.41500000000000004,
      0.41999999999999993,
      0.42500000000000004,
      0.42999999999999994,
      0.43500000000000005,
      0.43999999999999995,
      0.44500000000000006,
      0.44999999999999996,
      0.45500000000000007,
      0.45999999999999996,
      0.4650000000000001,
      0.47,
      0.4750000000000001,
      0.48,
      0.4850000000000001,
      0.49,
      0.4950000000000001,
      0.5,
      0.5050000000000001,
      0.51,
      0.5150000000000001,
      0.52,
      0.5250000000000001,
      0.53,
      0.5350000000000001,
      0.54,
      0.5449999999999999,
      0.55,
      0.5549999999999999,
      0.56,
      0.565,
      0.5700000000000001,
      0.575,
      0.5800000000000001,
      0.585,
      0.5900000000000001,
      0.595,
      0.6000000000000001,
      0.605,
      0.6100000000000001,
      0.615,
      0.6200000000000001,
      0.625,
      0.6300000000000001,
      0.635,
      0.6400000000000001,
      0.645,
      0.6500000000000001,
      0.655,
      0.6600000000000001,
      0.665,
      0.6699999999999999,
      0.675,
      0.6799999999999999,
      0.685,
      0.69,
      0.6950000000000001,
      0.7,
      0.7050000000000001,
      0.71,
      0.7150000000000001,
      0.72,
      0.7250000000000001,
      0.73,
      0.7350000000000001,
      0.74,
      0.7450000000000001,
      0.75,
      0.7550000000000001,
      0.76,
      0.7650000000000001,
      0.77,
      0.7750000000000001,
      0.78,
      0.7850000000000001,
      0.79,
      0.7949999999999999,
      0.8,
      0.8049999999999999,
      0.81,
      0.815,
      0.8200000000000001,
      0.825,
      0.8300000000000001,
      0.835,
      0.8400000000000001,
      0.845,
      0.8500000000000001,
      0.855,
      0.8600000000000001,
      0.865,
      0.8700000000000001,
      0.875,
      0.8800000000000001,
      0.885,
      0.8900000000000001,
      0.895,
      0.9000000000000001,
      0.905,
      0.9100000000000001,
      0.915,
      0.9199999999999999,
      0.925,
      0.9299999999999999,
      0.935,
      0.94,
      0.9450000000000001,
      0.95,
      0.9550000000000001,
      0.96,
      0.9650000000000001,
      0.97,
      0.9750000000000001,
      0.98,
      0.9850000000000001,
      0.99,
      0.9950000000000001,
      1.0
    ],
    "profiles": [
      {
        "c": "0",
        "S": [
          0.0,
          9.882117688026204e-06,
          3.952847075210482e-05,
          8.893905919223583e-05,
          0.00015811388300841927,
          0.0002470529422006551,
          0.0003557562367689433,
          0.00048422376671328394,
          0.0006324555320336771,
          0.0008004515327301226,
          0.0009882117688026204,
          0.0011957362402511707,
          0.0014230249470757732,
          0.0016700778892764225,
          0.0019368950668531358,
          0.0022234764798058893,
          0.002529822128134701,
          0.002855932011839565,
          0.003201806130920482,
          0.0035674444853774512,
          0.003952847075210472,
          0.004358013900419547,
          0.004782944961004673,
          0.005227640256965851,
          0.005692099788303083,
          0.006176323555016366,
          0.006680311557105702,
          0.0072040637945710905,
          0.007747580267412531,
          0.008310860975630024,
          0.00889390591922357,
          0.009496715098193168,
          0.01011928851253882,
          0.010761626162260523,
          0.011423728047358276,
          0.012105594167832084,
          0.012807224523681928,
          0.013528619114907856,
          0.014269777941509805,
          0.015030701003487839,
          0.01581138830084189,
          0.01661183983357203,
          0.01743205560167819,
          0.018272035605160414,
          0.019131779844018693,
          0.020011288318253023,
          0.020910561027863404,
          0.021829597972849845,
          0.022768399153212333,
          0.023726964568950872,
          0.024705294220065465,
          0.02570338810655611,
          0.02672124622842281,
          0.02775886858566556,
          0.028816255178284362,
          0.029893406006279218,
          0.030990321069650124,
          0.03210700036839709,
          0.0332434439025201,
          0.03439965167201914,
          0.03557562367689428,
          0.036771359917145426,
          0.03798686039277267,
          0.03922212510377592,
          0.04047715405015528,
          0.04175194723191062,
          0.04304650464904209,
          0.04436082630154954,
          0.045694912189433105,
          0.047048762312692664,
          0.048422376671328336,
          0.04981575526534,
          0.05122889809472775,
          0.05266180515949154,
          0.05411447645963139,
          0.055586911995147294,
          0.05707911176603925,
          0.05859107577230725,
          0.06012280401395132,
          0.061674296490971434,
          0.0632455532033676,
          0.06483657415113982,
          0.06644735933428808,
          0.0680779087528124,
          0.06972822240671275,
          0.0713983002959892,
          0.07308814242064166,
          0.07479774878067022,
          0.07652711937607477,
          0.07827625420685544,
          0.08004515327301209,
          0.08183381657454487,
          0.08364224411145361,
          0.08547043588373851,
          0.08731839189139938,
          0.08918611213443636,
          0.09107359661284933,
          0.09298084532663838,
          0.09490785827580349,
          0.09685463546034465,
          0.09882117688026186,
          0.10080748253555512,
          0.10281355242622443,
          0.1048393865522698,
          0.10688498491369124,
          0.10895034751048871,
          0.11103547434266224,
          0.1131403654102118,
          0.11526502071313745,
          0.11740944025143914,
          0.11957362402511687,
          0.12175757203417066,
          0.1239612842786005,
          0.1261847607584064,
          0.12842800147358835,
          0.13069100642414633,
          0.13297377561008036,
          0.13527630903139043,
          0.1375986066880766,
          0.13994066858013882,
          0.14230249470757708,
          0.14468408507039138,
          0.14708543966858176,
          0.14950655850214817,
          0.15194744157109064,
          0.15440808887540916,
          0.15688850041510374,
          0.15938867619017436,
          0.16190861620062105,
          0.16444832044644378,
          0.16700778892764256,
          0.1695870216442174,
          0.17218601859616828,
          0.1748047797834952,
          0.17744330520619822,
          0.18010159486427726,
          0.18277964875773237,
          0.1854774668865635,
          0.1881950492507707,
          0.190932395850354,
          0.1936895066853133,
          0.19646638175564857,
          0.19926302106136,
          0.20207942460244746,
          0.204915592378911,
          0.20777152439075056,
          0.21064722063796615,
          0.21354268112055783,
          0.21645790583852556,
          0.21939289479186935,
          0.22234764798058917,
          0.22532216540468508,
          0.228316447064157,
          0.23133049295900499,
          0.234364303089229,
          0.23741787745482915,
          0.24049121605580528,
          0.24358431889215748,
          0.24669718596388573,
          0.24982981727099005,
          0.2529822128134704,
          0.2561543725913268,
          0.25934629660455927,
          0.2625579848531678,
          0.2657894373371523,
          0.26904065405651295,
          0.2723116350112496,
          0.2756023802013623,
          0.278912889626851,
          0.28224316328771587,
          0.28559320118395676,
          0.2889630033155737,
          0.2923525696825667,
          0.2957619002849357,
          0.2991909951226808,
          0.30263985419580197,
          0.30610847750429915,
          0.3095968650481724,
          0.3131050168274217,
          0.316632932842047,
          0.3201806130920484,
          0.32374805757742586,
          0.3273352662981794,
          0.330942239254309,
          0.33456897644581457,
          0.33821547787269624,
          0.341881743534954,
          0.34556777343258777,
          0.3492735675655976,
          0.3529991259339834,
          0.35674444853774534,
          0.36050953537688335,
          0.36429438645139733,
          0.3680990017612874,
          0.3719233813065535,
          0.3757675250871957,
          0.37963143310321396,
          0.38351510535460825,
          0.3874185418413786,
          0.391341742563525,
          0.39528470752104744,
          0.399247436713946,
          0.40322993014222047,
          0.40723218780587117,
          0.41125420970489773,
          0.41529599583930044,
          0.4193575462090792,
          0.423438860814234,
          0.42753993965476494,
          0.43166078273067177,
          0.43580139004195484,
          0.4399617615886138,
          0.44414189737064896,
          0.44834179738805996,
          0.4525614616408472,
          0.45680089012901043,
          0.4610600828525498,
          0.46533903981146507,
          0.46963776100575655,
          0.4739562464354239,
          0.4782944961004675,
          0.48265251000088694,
          0.48703028813668264,
          0.4914278305078542,
          0.495845137114402,
          0.5002822079563257,
          0.5047390430336256,
          0.5092156423463013,
          0.5137120058943534,
          0.5182281336777813,
          0.5227640256965853,
          0.5273196819507653,
          0.5318951024403215,
          0.5364902871652537,
          0.5411052361255617,
          0.5457399493212463,
          0.5503944267523064,
          0.5550686684187429,
          0.5597626743205553,
          0.5644764444577438,
          0.5692099788303083,
          0.5739632774382489,
          0.5787363402815655,
          0.5835291673602583,
          0.588341758674327,
          0.593174114223772,
          0.5980262340085927,
          0.6028981180287897,
          0.6077897662843625,
          0.6127011787753116,
          0.6176323555016366,
          0.6225832964633379,
          0.627554001660415,
          0.6325444710928683,
          0.6375547047606974,
          0.6425847026639029,
          0.6476344648024842,
          0.6527039911764414,
          0.6577932817857751,
          0.6629023366304845,
          0.6680311557105703,
          0.6731797390260318,
          0.6783480865768696,
          0.6835361983630832,
          0.6887440743846731,
          0.6939717146416389,
          0.6992191191339808,
          0.7044862878616988,
          0.7097732208247929,
          0.7150799180232628,
          0.7204063794571091,
          0.7257526051263311,
          0.7311185950309295,
          0.7365043491709036,
          0.741909867546254,
          0.7473351501569803,
          0.7527801970030829,
          0.7582450080845613,
          0.763729583401416,
          0.7692339229536463,
          0.7747580267412532,
          0.7803018947642357,
          0.7858655270225943,
          0.7914489235163292,
          0.79705208424544,
          0.802675009209927,
          0.8083176984097898,
          0.8139801518450289,
          0.819662369515644,
          0.8253643514216351,
          0.8310860975630022,
          0.8368276079397456,
          0.8425888825518646,
          0.8483699213993602,
          0.8541707244822313,
          0.8599912918004788,
          0.8658316233541022,
          0.8716917191431021,
          0.8775715791674774,
          0.8834712034272292,
          0.8893905919223567,
          0.8953297446528606,
          0.9012886616187403,
          0.9072673428199962,
          0.913265788256628,
          0.9192839979286361,
          0.9253219718360199,
          0.9313797099787801,
          0.937457212356916,
          0.9435544789704282,
          0.9496715098193166,
          0.9558083049035806,
          0.9619648642232211,
          0.9681411877782373,
          0.9743372755686299,
          0.9805531275943983,
          0.9867887438555429,
          0.9930441243520634,
          0.9993192690839602,
          1.0056141780512327,
          1.0119288512538815,
          1.0182632886919063,
          1.0246174903653071,
          1.030991456274084,
          1.037385186418237,
          1.043798680797766,
          1.0502319394126711,
          1.056684962262952,
          1.0631577493486093,
          1.0696503006696423,
          1.0761626162260518,
          1.082694696017837,
          1.0892465400449984,
          1.0958181483075358,
          1.1024095208054492,
          1.1090206575387387,
          1.115651558507404,
          1.122302223711446,
          1.1289726531508635,
          1.1356628468256573,
          1.142372804735827,
          1.149102526881373,
          1.1558520132622947,
          1.1626212638785929,
          1.1694102787302667,
          1.176219057817317,
          1.1830476011397428,
          1.1898959086975451,
          1.1967639804907233,
          1.2036518165192776,
          1.2105594167832079,
          1.2174867812825143,
          1.2244339100171966,
          1.2314008029872552,
          1.2383874601926896,
          1.2453938816335004,
          1.2524200673096868,
          1.2594660172212495,
          1.266531731368188,
          1.2736172097505027,
          1.2807224523681937,
          1.2878474592212605,
          1.2949922303097035,
          1.3021567656335225,
          1.3093410651927175,
          1.3165451289872887,
          1.323768957017236,
          1.3310125492825589,
          1.3382759057832583,
          1.3455590265193333,
          1.352861911490785,
          1.3601845606976122,
          1.367526974139816,
          1.3748891518173953,
          1.382271093730351,
          1.3896727998786824,
          1.3970942702623903,
          1.4045355048814738,
          1.4119965037359337,
          1.4194772668257694,
          1.4269777941509814,
          1.4344980857115692,
          1.4420381415075334,
          1.4495979615388732,
          1.4571775458055893,
          1.4647768943076815,
          1.4723960070451496,
          1.480034884017994,
          1.487693525226214,
          1.4953719306698106,
          1.5030701003487827,
          1.5107880342631315,
          1.5185257324128558,
          1.5262831947979565,
          1.534060421418433,
          1.5418574122742859,
          1.5496741673655143,
          1.5575106866921193,
          1.5653669702541,
          1.573243018051457,
          1.5811388300841898
        ]
      },
      {
        "c": "0.1",
        "S": [
          0.0,
          8.836559764040519e-06,
          3.535797842704909e-05,
          7.958187541367414e-05,
          0.00014152588398052215,
          0.0002212076512255803,
          0.0003186448380976454,
          0.0004338551194057588,
          0.0005668561838286471,
          0.0007176657339241685,
          0.0008863014861387671,
          0.0010727811708169301,
          0.0012771225322106535,
          0.0014993433284889097,
          0.0017394613317471466,
          0.001997494328016717,
          0.0022734601172744386,
          0.002567376513452036,
          0.002879261344445661,
          0.0032091324521253996,
          0.003557007692344783,
          0.003922904934950315,
          0.004306842063790981,
          0.0047088369767277986,
          0.005128907585643342,
          0.005567071816451291,
          0.006023347609105978,
          0.006497752917611954,
          0.006990305710033533,
          0.007501023968504378,
          0.008029925689237064,
          0.008577028882532657,
          0.009142351572790319,
          0.009725911798516873,
          0.010327727612336426,
          0.010947817080999957,
          0.01158619828539493,
          0.012242889320554954,
          0.012917908295669293,
          0.013611273334092669,
          0.014323002573354681,
          0.015053114165169709,
          0.015801626275446266,
          0.01656855708429692,
          0.017353924786047796,
          0.018157747589248274,
          0.01898004371668068,
          0.01982083140536998,
          0.0206801289065934,
          0.021557954485890193,
          0.022454326423071283,
          0.023369263012228997,
          0.024302782561746776,
          0.025254903394308855,
          0.02622564384691002,
          0.027215022270865346,
          0.02822305703181987,
          0.029249766509758413,
          0.030295169099015258,
          0.03135928320828395,
          0.032442127260627056,
          0.03354371969348585,
          0.03466407895869024,
          0.035803223522468314,
          0.03696117186545645,
          0.03813794248270871,
          0.03933355388370705,
          0.04054802459237073,
          0.041781373147066495,
          0.04303361810061799,
          0.044304778020316064,
          0.04559487148792807,
          0.04690391709970816,
          0.04823193346640682,
          0.04957893921328087,
          0.05094495298010324,
          0.0523299934211729,
          0.05373407920532464,
          0.05515722901593903,
          0.05659946155095221,
          0.05806079552286585,
          0.059541249658757046,
          0.061040842700288075,
          0.06255959340371654,
          0.06409752053990503,
          0.06565464289433126,
          0.06723097926709774,
          0.06882654847294205,
          0.07044136934124634,
          0.07207546071604769,
          0.07372884145604776,
          0.07540153043462298,
          0.07709354653983413,
          0.07880490867443696,
          0.08053563575589134,
          0.08228574671637202,
          0.084055260502778,
          0.08584419607674294,
          0.08765257241464498,
          0.08948040850761665,
          0.09132772336155519,
          0.09319453599713219,
          0.0950808654498039,
          0.09698673076982112,
          0.09891215102223934,
          0.10085714528692863,
          0.1028217326585838,
          0.10480593224673447,
          0.1068097631757551,
          0.108833244584875,
          0.1108763956281885,
          0.11293923547466501,
          0.11502178330815899,
          0.11712405832742027,
          0.11924607974610399,
          0.12138786679278063,
          0.12354943871094641,
          0.12573081475903308,
          0.1279320142104184,
          0.13015305635343577,
          0.13239396049138497,
          0.13465474594254181,
          0.13693543204016873,
          0.1392360381325243,
          0.1415565835828742,
          0.14389708776950078,
          0.14625757008571352,
          0.14863804993985905,
          0.15103854675533157,
          0.15345907997058275,
          0.15589966903913224,
          0.15836033342957762,
          0.1608410926256049,
          0.16334196612599824,
          0.16586297344465092,
          0.16840413411057498,
          0.17096546766791149,
          0.17354699367594129,
          0.17614873170909473,
          0.17877070135696216,
          0.18141292222430408,
          0.18407541393106155,
          0.18675819611236666,
          0.18946128841855214,
          0.1921847105151625,
          0.19492848208296357,
          0.19769262281795344,
          0.2004771524313724,
          0.2032820906497134,
          0.2061074572147322,
          0.20895327188345791,
          0.21181955442820352,
          0.2147063246365756,
          0.21761360231148524,
          0.2205414072711582,
          0.22348975934914544,
          0.22645867839433292,
          0.2294481842709529,
          0.2324582968585937,
          0.23548903605221005,
          0.23854042176213378,
          0.24161247391408427,
          0.2447052124491785,
          0.24781865732394176,
          0.25095282851031797,
          0.2541077459956803,
          0.25728342978284124,
          0.2604798998900634,
          0.26369717635106965,
          0.26693527921505433,
          0.2701942285466923,
          0.27347404442615086,
          0.2767747469490994,
          0.28009635622672013,
          0.28343889238571857,
          0.286802375568334,
          0.29018682593235023,
          0.29359226365110563,
          0.297018708913504,
          0.3004661819240249,
          0.30393470290273467,
          0.3074242920852961,
          0.3109349697229796,
          0.31446675608267405,
          0.3180196714468962,
          0.3215937361138026,
          0.3251889703971992,
          0.3288053946265523,
          0.33244302914699925,
          0.33610189431935883,
          0.339782010520142,
          0.34348339814156237,
          0.3472060775915467,
          0.35095006929374606,
          0.3547153936875458,
          0.3585020712280765,
          0.3623101223862249,
          0.3661395676486438,
          0.36999042751776345,
          0.37386272251180186,
          0.37775647316477556,
          0.38167170002651,
          0.3856084236626507,
          0.38956666465467377,
          0.3935464435998962,
          0.3975477811114874,
          0.401570697818479,
          0.4056152143657762,
          0.4096813514141682,
          0.41376912964033874,
          0.417878569736878,
          0.42200969241229125,
          0.42616251839101155,
          0.43033706841340946,
          0.4345333632358043,
          0.43875142363047465,
          0.442991270385669,
          0.4472529243056169,
          0.45153640621053964,
          0.45584173693666075,
          0.4601689373362173,
          0.4645180282774701,
          0.4688890306447153,
          0.4732819653382944,
          0.4776968532746059,
          0.4821337153861151,
          0.48659257262136624,
          0.4910734459449919,
          0.49557635633772545,
          0.5001013247964103,
          0.5046483723340118,
          0.5092175199796286,
          0.513808788778502,
          0.5184221997920276,
          0.5230577740977663,
          0.5277155327894566,
          0.5323954969770216,
          0.5370976877865845,
          0.5418221263604762,
          0.5465688338572483,
          0.5513378314516825,
          0.5561291403348027,
          0.5609427817138852,
          0.5657787768124709,
          0.570637146870374,
          0.5755179131436953,
          0.5804210969048313,
          0.5853467194424875,
          0.5902948020616866,
          0.5952653660837819,
          0.6002584328464667,
          0.6052740237037865,
          0.6103121600261484,
          0.6153728632003348,
          0.6204561546295114,
          0.6255620557332405,
          0.630690587947491,
          0.6358417727246496,
          0.6410156315335325,
          0.6462121858593944,
          0.6514314572039437,
          0.6566734670853484,
          0.6619382370382517,
          0.6672257886137798,
          0.6725361433795563,
          0.6778693229197086,
          0.6832253488348847,
          0.68860424274226,
          0.6940060262755505,
          0.6994307210850225,
          0.704878348837506,
          0.7103489312164031,
          0.7158424899217017,
          0.7213590466699848,
          0.726898623194443,
          0.7324612412448843,
          0.7380469225877475,
          0.7436556890061097,
          0.7492875622997022,
          0.7549425642849176,
          0.7606207167948245,
          0.7663220416791748,
          0.7720465608044188,
          0.7777942960537145,
          0.7835652693269387,
          0.7893595025406983,
          0.7951770176283429,
          0.8010178365399746,
          0.8068819812424599,
          0.8127694737194409,
          0.8186803359713462,
          0.8246145900154032,
          0.8305722578856478,
          0.8365533616329388,
          0.842557923324964,
          0.8485859650462578,
          0.8546375088982071,
          0.8607125769990664,
          0.8668111914839663,
          0.8729333745049277,
          0.8790791482308704,
          0.8852485348476276,
          0.8914415565579531,
          0.8976582355815371,
          0.9038985941550141,
          0.9101626545319771,
          0.9164504389829862,
          0.9227619697955826,
          0.9290972692742986,
          0.9354563597406691,
          0.9418392635332441,
          0.9482460030075975,
          0.9546766005363428,
          0.96113107850914,
          0.9676094593327108,
          0.9741117654308473,
          0.9806380192444254,
          0.9871882432314149,
          0.9937624598668932,
          1.0003606916430523,
          1.0069829610692165,
          1.013629290671849,
          1.0202997029945646,
          1.0269942205981435,
          1.0337128660605401,
          1.0404556619768943,
          1.0472226309595465,
          1.0540137956380453,
          1.0608291786591624,
          1.0676688026869008,
          1.0745326904025085,
          1.0814208645044898,
          1.088333347708618,
          1.0952701627479435,
          1.1022313323728092,
          1.1092168793508599,
          1.1162268264670552,
          1.123261196523681,
          1.1303200123403596,
          1.1374032967540626,
          1.144511072619123,
          1.1516433628072462,
          1.1588001902075213,
          1.165981577726434,
          1.1731875482878766,
          1.1804181248331616,
          1.1876733303210312,
          1.1949531877276716,
          1.2022577200467226,
          1.2095869502892895,
          1.2169409014839576,
          1.2243195966767992,
          1.231723058931389,
          1.2391513113288144,
          1.246604376967689,
          1.2540822789641615,
          1.261585040451928,
          1.2691126845822474,
          1.2766652345239493,
          1.2842427134634464,
          1.2918451446047479,
          1.2994725511694696,
          1.307124956396847,
          1.3148023835437461,
          1.3225048558846764,
          1.3302323967118013,
          1.3379850293349518,
          1.345762777081635,
          1.353565663297052,
          1.3613937113441026,
          1.3692469446034028,
          1.3771253864732917,
          1.3850290603698507,
          1.3929579897269062,
          1.4009121979960497,
          1.4088917086466435,
          1.416896545165838,
          1.4249267310585785,
          1.4329822898476214,
          1.4410632450735439,
          1.449169620294756,
          1.4573014390875128,
          1.4654587250459281,
          1.4736415017819824,
          1.48184979292554,
          1.4900836221243552,
          1.4983430130440907,
          1.5066279893683243,
          1.5149385747985626,
          1.5232747930542558,
          1.5316366678728048,
          1.5400242230095769,
          1.5484374822379166,
          1.5568764693491577,
          1.5653412081526346,
          1.573831722475697,
          1.5823480361637188,
          1.5908901730801117,
          1.5994581571063367,
          1.6080520121419186,
          1.616671762104454
        ]
      },
      {
        "c": "0.5",
        "S": [
          0.0,
          5.530604685577029e-06,
          2.2158683403908645e-05,
          4.9938792887730693e-05,
          8.892570343562066e-05,
          0.00013917439963733082,
          0.0002007400811014359,
          0.0002736781631853015,
          0.00035804427772738044,
          0.00045389427378184354,
          0.0005612842183555554,
          0.0006802703971473952,
          0.0008109093152899388,
          0.0009532576980934966,
          0.0011073724917925448,
          0.0012733108642944816,
          0.0014511302059308528,
          0.0016408881302108793,
          0.0018426424745774511,
          0.002056451301165495,
          0.0022823728975627663,
          0.0025204657775730658,
          0.002770788681981877,
          0.0030334005793244442,
          0.0033083606666563024,
          0.003595728370326235,
          0.003895563346751724,
          0.004207925483196833,
          0.004532874898552587,
          0.004870471944119827,
          0.005220777204394541,
          0.005583851497855717,
          0.0059597558777556665,
          0.006348551632912886,
          0.006750300288507438,
          0.007165063606878837,
          0.0075929035883264715,
          0.008033882471912633,
          0.008488062736267944,
          0.008955507100399544,
          0.009436278524501641,
          0.009930440210768847,
          0.010438055604211816,
          0.010959188393475807,
          0.011493902511661554,
          0.012042262137148893,
          0.012604331694422958,
          0.013180175854903022,
          0.0137698595377739,
          0.014373447910820096,
          0.014991006391262492,
          0.015622600646597725,
          0.016268296595440275,
          0.01692816040836709,
          0.01760225850876509,
          0.018290657573681125,
          0.0189934245346748,
          0.01971062657867392,
          0.02044233114883265,
          0.021188605945392423,
          0.021949518926545602,
          0.022725138309301653,
          0.023515532570356483,
          0.024320770446964006,
          0.025140920937811038,
          0.025976053303894325,
          0.026826237069401074,
          0.027691542022591418,
          0.028572038216684574,
          0.02946779597074698,
          0.030378885870583967,
          0.031305378769633525,
          0.032247345789863636,
          0.03320485832267178,
          0.03417798802978774,
          0.03516680684417904,
          0.036171386970959306,
          0.03719180088829948,
          0.03822812134834194,
          0.03928042137811746,
          0.04034877428046509,
          0.041433253634955,
          0.04253393329881407,
          0.043650887407854555,
          0.044784190377405664,
          0.04593391690324799,
          0.04710014196255101,
          0.048282940814813394,
          0.04948238900280637,
          0.050698562353520174,
          0.05193153697911313,
          0.053181389277864234,
          0.05444819593512813,
          0.05573203392429384,
          0.05703298050774565,
          0.05835111323782784,
          0.05968650995781183,
          0.061039248802866784,
          0.06240940820103313,
          0.06379706687419896,
          0.06520230383907978,
          0.06662519840820129,
          0.0680658301908852,
          0.06952427909423793,
          0.07100062532414299,
          0.07249494938625586,
          0.07400733208700243,
          0.07553785453458034,
          0.07708659813996374,
          0.07865364461791066,
          0.08023907598797424,
          0.08184297457551679,
          0.08346542301272684,
          0.08510650423963982,
          0.08676630150516162,
          0.08844489836809556,
          0.09014237869817245,
          0.0918588266770839,
          0.09359432679951914,
          0.09534896387420451,
          0.09712282302494694,
          0.09891598969168001,
          0.10072854963151404,
          0.10256058891978857,
          0.10441219395112908,
          0.10628345144050634,
          0.10817444842429932,
          0.11008527226136171,
          0.11201601063409104,
          0.11396675154950209,
          0.11593758334030302,
          0.11792859466597502,
          0.11993987451385542,
          0.12197151220022429,
          0.12402359737139411,
          0.12609622000480308,
          0.1281894704101122,
          0.13030343923030493,
          0.13243821744279097,
          0.13459389636051358,
          0.13677056763305973,
          0.13896832324777422,
          0.14118725553087752,
          0.1434274571485861,
          0.14568902110823753,
          0.1479720407594181,
          0.15027660979509486,
          0.15260282225275004,
          0.15495077251552014,
          0.15732055531333836,
          0.15971226572407957,
          0.16212599917471068,
          0.16456185144244267,
          0.1670199186558879,
          0.16950029729621988,
          0.17200308419833707,
          0.17452837655203068,
          0.1770762719031552,
          0.17964686815480374,
          0.18224026356848616,
          0.18485655676531093,
          0.18749584672717168,
          0.1901582327979358,
          0.19284381468463843,
          0.19555269245867882,
          0.19828496655702146,
          0.2010407377834003,
          0.2038201073095268,
          0.2066231766763021,
          0.2094500477950331,
          0.21230082294865102,
          0.21517560479293585,
          0.2180744963577429,
          0.2209976010482336,
          0.22394502264611105,
          0.22691686531085803,
          0.22991323358098004,
          0.23293423237525107,
          0.23597996699396484,
          0.239050543120188,
          0.2421460668210191,
          0.24526664454885003,
          0.2484123831426322,
          0.25158338982914674,
          0.2547797722242773,
          0.25800163833428963,
          0.26124909655711176,
          0.26452225568362076,
          0.2678212248989319,
          0.27114611378369347,
          0.27449703231538314,
          0.2778740908696116,
          0.28127740022142683,
          0.28470707154662545,
          0.2881632164230657,
          0.29164594683198686,
          0.29515537515933027,
          0.2986916141970663,
          0.30225477714452503,
          0.30584497760973073,
          0.30946232961074044,
          0.31310694757698726,
          0.31677894635062714,
          0.32047844118789104,
          0.3242055477604388,
          0.3279603821567211,
          0.3317430608833413,
          0.3355537008664253,
          0.33939241945299253,
          0.34325933441233414,
          0.34715456393739286,
          0.3510782266461486,
          0.35503044158300867,
          0.3590113282202003,
          0.36302100645917046,
          0.3670595966319873,
          0.3711272195027474,
          0.37522399626898695,
          0.3793500485630983,
          0.38350549845374793,
          0.38769046844730376,
          0.39190508148926106,
          0.39614946096567827,
          0.40042373070461335,
          0.40472801497756594,
          0.40906243850092516,
          0.4134271264374196,
          0.41782220439757334,
          0.42224779844116705,
          0.42670403507870075,
          0.43119104127286517,
          0.4357089444400139,
          0.4402578724516433,
          0.4448379536358736,
          0.4494493167789377,
          0.454092091126674,
          0.4587664063860205,
          0.4634723927265198,
          0.46821018078182125,
          0.4729799016511958,
          0.47778168690104733,
          0.48261566856643606,
          0.48748197915260094,
          0.49238075163649125,
          0.49731211946829834,
          0.5022762165729973,
          0.5072731773518883,
          0.5123031366841474,
          0.5173662299283773,
          0.522462592924168,
          0.5275923619936576,
          0.5327556739431021,
          0.537952666064445,
          0.543183476136899,
          0.5484482424285241,
          0.5537471036978181,
          0.5590801991953062,
          0.5644476686651392,
          0.5698496523466977,
          0.5752862909761937,
          0.5807577257882878,
          0.5862640985177027,
          0.591805551400847,
          0.5973822271774412,
          0.6029942690921493,
          0.608641820896217,
          0.6143250268491122,
          0.6200440317201728,
          0.6257989807902595,
          0.6315900198534108,
          0.6374172952185091,
          0.6432809537109433,
          0.6491811426742862,
          0.655118009971969,
          0.6610917039889662,
          0.6671023736334813,
          0.6731501683386446,
          0.6792352380642063,
          0.6853577332982445,
          0.6915178050588712,
          0.6977156048959507,
          0.7039512848928141,
          0.7102249976679879,
          0.7165368963769234,
          0.7228871347137312,
          0.7292758669129232,
          0.7357032477511585,
          0.7421694325489951,
          0.7486745771726465,
          0.7552188380357445,
          0.7618023721011079,
          0.7684253368825141,
          0.7750878904464787,
          0.7817901914140408,
          0.7885323989625499,
          0.7953146728274659,
          0.8021371733041534,
          0.8090000612496943,
          0.8159034980846948,
          0.8228476457951069,
          0.8298326669340476,
          0.8368587246236311,
          0.8439259825567998,
          0.8510346049991668,
          0.8581847567908596,
          0.8653766033483726,
          0.8726103106664228,
          0.8798860453198142,
          0.887203974465304,
          0.8945642658434783,
          0.9019670877806312,
          0.90941260919065,
          0.9169009995769088,
          0.9244324290341615,
          0.9320070682504504,
          0.9396250885090099,
          0.947286661690184,
          0.9549919602733469,
          0.962741157338829,
          0.9705344265698481,
          0.9783719422544503,
          0.9862538792874532,
          0.9941804131723944,
          1.0021517200234908,
          1.010167976567599,
          1.018229360146184,
          1.0263360487172932,
          1.0344882208575366,
          1.0426860557640758,
          1.0509297332566123,
          1.05921943377939,
          1.0675553384031962,
          1.0759376288273765,
          1.0843664873818497,
          1.0928420970291304,
          1.1013646413663605,
          1.1099343046273435,
          1.1185512716845867,
          1.127215728051349,
          1.1359278598836962,
          1.1446878539825618,
          1.1534958977958134,
          1.1623521794203242,
          1.171256887604059,
          1.1802102117481519,
          1.1892123419090055,
          1.198263468800386,
          1.207363783795531,
          1.2165134789292598,
          1.225712746900091,
          1.2349617810723683,
          1.244260775478393,
          1.2536099248205579,
          1.2630094244734968,
          1.2724594704862295,
          1.2819602595843238,
          1.2915119891720575,
          1.3011148573345896,
          1.3107690628401363,
          1.3204748051421578,
          1.3302322843815453,
          1.340041701388821,
          1.3499032576863406,
          1.3598171554905043,
          1.3697835977139763,
          1.3798027879679031,
          1.389874930564155,
          1.400000230517551,
          1.4101788935481163,
          1.420411126083323,
          1.430697135260357,
          1.4410371289283763,
          1.4514313156507899,
          1.4618799047075315,
          1.4723831060973487,
          1.4829411305400955,
          1.4935541894790327,
          1.5042224950831329,
          1.5149462602493973,
          1.525725698605177,
          1.5365610245105,
          1.5474524530604044,
          1.5584002000872887,
          1.5694044821632513,
          1.5804655166024555,
          1.59158352146349,
          1.602758715551739,
          1.6139913184217651,
          1.6252815503796902,
          1.6366296324855918,
          1.6480357865559019,
          1.6595002351658141,
          1.6710232016517006,
          1.682604910113533,
          1.6942455854173109,
          1.705945453197503,
          1.7177047398594865,
          1.7295236725820038,
          1.741402479319618,
          1.7533413888051828,
          1.7653406305523152
        ]
      }
    ],
    "difference_quotient_c": "0.1",
    "difference_quotient": [
      0.0,
      -1.0455579239856852e-05,
      -4.1704923250557256e-05,
      -9.35718377856169e-05,
      -0.0001658799902789712,
      -0.000258452909750748,
      -0.00037111398671297896,
      -0.0005036864730752514,
      -0.0006559934820502997,
      -0.0008278579880595404,
      -0.0010191028266385335,
      -0.0012295506943424059,
      -0.0014590241486511974,
      -0.0017073456078751286,
      -0.001974337351059892,
      -0.002259821517891724,
      -0.0025636201086026234,
      -0.0028855549838752896,
      -0.0032254478647482116,
      -0.0035831203325205167,
      -0.003958393828656891,
      -0.004351089654692324,
      -0.004761028972136922,
      -0.0051880328023805235,
      -0.005631922026597411,
      -0.006092517385650753,
      -0.0065696394799972385,
      -0.007063108769591363,
      -0.007572745573789976,
      -0.008098370071256463,
      -0.008639802299865058,
      -0.009196862156605114,
      -0.009769369397485007,
      -0.010357143637436499,
      -0.010960004350218499,
      -0.01157777086832127,
      -0.012210262382869978,
      -0.012857297943529022,
      -0.013518696458405116,
      -0.014194276693951704,
      -0.014883857274872077,
      -0.015587256684023217,
      -0.016304293262319226,
      -0.017034785208634926,
      -0.017778550579708972,
      -0.018535407290047497,
      -0.01930517311182725,
      -0.020087665674798638,
      -0.020882702466189333,
      -0.02169010083060679,
      -0.02250967796994182,
      -0.023341250943271115,
      -0.02418463666676033,
      -0.02503965191356705,
      -0.025906113313743408,
      -0.026783837354138716,
      -0.027672640378302547,
      -0.028572338586386747,
      -0.029482748035048398,
      -0.030403684637351908,
      -0.031334964162672216,
      -0.03227640223659574,
      -0.033227814340824335,
      -0.03418901581307608,
      -0.035159821846988265,
      -0.03614004749201913,
      -0.03712950765335038,
      -0.038128017091788105,
      -0.03913539042366611,
      -0.040151442120746755,
      -0.04117598651012272,
      -0.04220883777411935,
      -0.04324980995019587,
      -0.044298716930847165,
      -0.045355372463505225,
      -0.046419590150440504,
      -0.047491183448663474,
      -0.04856996566982609,
      -0.04965574998012291,
      -0.050748349400192225,
      -0.051847576805017434,
      -0.052953244923827705,
      -0.054065166340000054,
      -0.05518315349095859,
      -0.05630701866807725,
      -0.05743657401657942,
      -0.05857163153543912,
      -0.05971200307728172,
      -0.06085750034828433,
      -0.06200793490807752,
      -0.06316311816964335,
      -0.06432286139921889,
      -0.0654869757161948,
      -0.06665527209301553,
      -0.06782756135508036,
      -0.06900365418064339,
      -0.07018336110071327,
      -0.07136649249895433,
      -0.07255285861158506,
      -0.07374226952727991,
      -0.07493453518706672,
      -0.07612946538422927,
      -0.0773268697642053,
      -0.07852655782448689,
      -0.07972833891451897,
      -0.08093202223560081,
      -0.08213741684078443,
      -0.08334433163477331,
      -0.08455257537382341,
      -0.08576195666564132,
      -0.08697228396928366,
      -0.08818336559505646,
      -0.08939500970441508,
      -0.09060702430986126,
      -0.0918192172748436,
      -0.09303139631365698,
      -0.09424336899133953,
      -0.09545494272357347,
      -0.0966659247765822,
      -0.09787612226703046,
      -0.09908534216192116,
      -0.10029339127849562,
      -0.10150007628413033,
      -0.10270520369623864,
      -0.10390857988216429,
      -0.10511001105908385,
      -0.1063093032939022,
      -0.1075062625031531,
      -0.10870069445289482,
      -0.10989240475861028,
      -0.1110811988851032,
      -0.1122668821463979,
      -0.11344925970563385,
      -0.11462813657496962,
      -0.11580331761547297,
      -0.11697460753702288,
      -0.1181418108982088,
      -0.11930473210622211,
      -0.12046317541675983,
      -0.12161694493391828,
      -0.1227658446100921,
      -0.12390967824587013,
      -0.12504824948993354,
      -0.12618136183895318,
      -0.1273088186374849,
      -0.1284304230778699,
      -0.1295459782001271,
      -0.13065528689185424,
      -0.13175815188812168,
      -0.13285437577137155,
      -0.1339437609713126,
      -0.1350261097648156,
      -0.1361012242758139,
      -0.13716890647519742,
      -0.13822895818070807,
      -0.139281181056837,
      -0.1403253766147236,
      -0.14136134621204582,
      -0.1423888910529203,
      -0.1434078121877999,
      -0.1444179105133661,
      -0.1454189867724251,
      -0.14641084155380762,
      -0.1473932752922602,
      -0.14836608826834352,
      -0.1493290806083264,
      -0.15028205228408364,
      -0.1512248031129887,
      -0.15215713275781362,
      -0.15307884072661537,
      -0.15398972637264474,
      -0.1548895888942281,
      -0.1557782273346725,
      -0.15665544058215575,
      -0.1575210273696226,
      -0.15837478627467982,
      -0.15921651571948914,
      -0.16004601397066776,
      -0.16086307913917686,
      -0.1616675091802211,
      -0.16245910189313761,
      -0.16323765492129771,
      -0.16400296575199758,
      -0.16475483171634941,
      -0.1654930499891838,
      -0.16621741758893638,
      -0.16692773137754802,
      -0.16762378806035483,
      -0.1683053841859833,
      -0.16897231614624586,
      -0.16962438017603332,
      -0.17026137235320982,
      -0.17088308859850632,
      -0.17148932467541345,
      -0.17207987619007714,
      -0.17265453859119206,
      -0.17321310716989058,
      -0.1737553770596445,
      -0.1742811432361513,
      -0.17479020051723138,
      -0.17528234356271877,
      -0.17575736687436005,
      -0.17621506479569782,
      -0.17665523151197404,
      -0.1770776610500152,
      -0.17748214727813016,
      -0.1778684839060024,
      -0.17823646448457797,
      -0.17858588240596718,
      -0.17891653090333026,
      -0.1792282030507686,
      -0.17952069176322527,
      -0.17979378979637417,
      -0.18004728974650497,
      -0.1802809840504288,
      -0.18049466498535782,
      -0.18068812466880801,
      -0.18086115505848155,
      -0.18101354795216906,
      -0.18114509498763143,
      -0.18125558764250205,
      -0.18134481723416862,
      -0.18141257491967322,
      -0.18145865169559794,
      -0.18148283839796053,
      -0.18148492570210617,
      -0.18146470412259363,
      -0.1814219640130943,
      -0.18135649556627942,
      -0.1812680888137097,
      -0.1811565336257348,
      -0.18102161971136677,
      -0.18086313661819453,
      -0.18068087373226072,
      -0.1804746202779539,
      -0.18024416531789655,
      -0.17998929775284833,
      -0.17970980632158406,
      -0.17940547960079045,
      -0.17907610600495505,
      -0.17872147378625858,
      -0.1783413710344628,
      -0.1779355856768028,
      -0.17750390547787376,
      -0.17704611803952996,
      -0.17656201080076706,
      -0.17605137103761326,
      -0.1755139858630217,
      -0.17494964222675935,
      -0.17435812691529717,
      -0.17373922655169904,
      -0.17309272759551408,
      -0.17241841634266564,
      -0.1717160789253347,
      -0.17098550131185997,
      -0.17022646930662355,
      -0.16943876854993212,
      -0.1686221845179181,
      -0.16777650252242648,
      -0.1669015077109004,
      -0.1659969850662657,
      -0.16506271940683437,
      -0.16409849538617904,
      -0.16310409749303423,
      -0.1620793100511686,
      -0.16102391721930287,
      -0.159937702990961,
      -0.15882045119438803,
      -0.15767194549242358,
      -0.15649196938240295,
      -0.15528030619603062,
      -0.15403673909928028,
      -0.15276105109227722,
      -0.15145302500918723,
      -0.15011244351811004,
      -0.14873908912095946,
      -0.1473327441533534,
      -0.14589319078451624,
      -0.14442021101713776,
      -0.1429135866872877,
      -0.141373099464287,
      -0.1397985308506089,
      -0.13818966218175466,
      -0.136546274626147,
      -0.13486814918501344,
      -0.1331550666922865,
      -0.13140680781446923,
      -0.12962315305054317,
      -0.12780388273184062,
      -0.12594877702194252,
      -0.12405761591656073,
      -0.12213017924342484,
      -0.1201662466621678,
      -0.11816559766421375,
      -0.11612801157267261,
      -0.11405326754221012,
      -0.11194114455895132,
      -0.10979142144035614,
      -0.10760387683511063,
      -0.10537828922301484,
      -0.10311443691486288,
      -0.10081209805233082,
      -0.09847105060787231,
      -0.09609107238459091,
      -0.09367194101613907,
      -0.09121343396659043,
      -0.0887153285303377,
      -0.08617740183197498,
      -0.08359943082617449,
      -0.08098119229759115,
      -0.07832246286072486,
      -0.07562301895983059,
      -0.07288263686878294,
      -0.07010109269097287,
      -0.06727816235919115,
      -0.06441362163550957,
      -0.06150724611117542,
      -0.058558811206484984,
      -0.05556809217067027,
      -0.05253486408180352,
      -0.049458901846650694,
      -0.04633998020057373,
      -0.043177873707425096,
      -0.03997235675940569,
      -0.03672320357696934,
      -0.03343018820871624,
      -0.030093084531246372,
      -0.02671166624906629,
      -0.023285706894469183,
      -0.01981497982741498,
      -0.016299258235432657,
      -0.012738315133471456,
      -0.009131923363805416,
      -0.005479855595922345,
      -0.0017818843263994744,
      0.0019622181212120005,
      0.005752679596511268,
      0.009589728122350039,
      0.013473591894961334,
      0.017404499284052743,
      0.021382678832959634,
      0.02540835925873175,
      0.029481769452266438,
      0.03360313847841079,
      0.0377726955760993,
      0.04199067015844493,
      0.046257291812883405,
      0.05057279030126427,
      0.054937395559992996,
      0.0593513377001198,
      0.06381484700749729,
      0.0683281539428493,
      0.07289148914192412,
      0.07750508341559215,
      0.08216916774999472,
      0.08688397330661068,
      0.09164973142241184,
      0.0964666736099784,
      0.10133503155761225,
      0.10625503712943685,
      0.11122692236554155,
      0.11625091948209043,
      0.12132726087143553,
      0.12645617910223672,
      0.13163790691958832,
      0.13687267724512564,
      0.14216072317715822,
      0.14750227799076088,
      0.152897575137938,
      0.1583468482476924,
      0.16385033112617853,
      0.1694082577567957,
      0.17502086230034797,
      0.1806883790951086,
      0.1864110426569865,
      0.19218908767961063,
      0.1980227490344766,
      0.2039122617710465,
      0.20985786111687776,
      0.2158597824777453,
      0.22191826143774573,
      0.22803353375943525,
      0.23420583538394713,
      0.24043540243109174,
      0.24672247119950752,
      0.25306727816673646,
      0.25947005998941064,
      0.26593105350330326,
      0.27245049572348634,
      0.2790286238444528,
      0.2856656752402209,
      0.292361887464454,
      0.2991174982506073,
      0.305932745512012,
      0.3128078673420154,
      0.3197431020141117,
      0.3267386879820444,
      0.33379486387992374,
      0.34091186852236666,
      0.34808994090461676,
      0.35532932020264196
    ],
    "first_order_derivative": [
      -0.0,
      -1.0947190372180136e-05,
      -4.3656999919546865e-05,
      -9.793178628833968e-05,
      -0.000173573907124798,
      -0.0002703857200751614,
      -0.0003881695827856693,
      -0.000526727852902561,
      -0.0006858628880720762,
      -0.0008653770459404546,
      -0.0010650726841539351,
      -0.0012847521603587579,
      -0.0015242178322011615,
      -0.0017832720573273798,
      -0.002061717193383671,
      -0.002359355598016249,
      -0.0026759896288713722,
      -0.003011421643595275,
      -0.003365453999834196,
      -0.0037378890552343734,
      -0.004128529167442049,
      -0.004537176694103462,
      -0.004963633992864849,
      -0.005407703421372452,
      -0.005869187337272512,
      -0.006347888098211264,
      -0.006843608061834951,
      -0.007356149585789812,
      -0.007885315027722087,
      -0.008430906745278011,
      -0.008992727096103832,
      -0.00957057843784578,
      -0.010164263128150101,
      -0.010773583524663032,
      -0.011398341985030813,
      -0.01203834086689968,
      -0.012693382527915865,
      -0.013363269325725648,
      -0.014047803617975205,
      -0.014746787762310844,
      -0.015460024116378736,
      -0.016187315037825188,
      -0.01692846288429637,
      -0.017683270013438578,
      -0.018451538782898024,
      -0.01923307155032096,
      -0.02002767067335362,
      -0.020835138509642234,
      -0.02165527741683306,
      -0.022487889752572324,
      -0.023332777874506272,
      -0.02418974414028113,
      -0.025058590907543164,
      -0.025939120533938594,
      -0.026831135377113652,
      -0.027734437794714607,
      -0.02864883014438767,
      -0.029574114783779085,
      -0.030510094070535107,
      -0.03145657036230195,
      -0.032413346016725894,
      -0.03338022339145312,
      -0.03435700484412995,
      -0.03534349273240251,
      -0.03633948941391718,
      -0.03734479724632006,
      -0.03835921858725749,
      -0.03938255579437565,
      -0.04041461122532083,
      -0.041455187237739194,
      -0.04250408618927709,
      -0.04356111043758064,
      -0.04462606234029616,
      -0.04569874425506988,
      -0.04677895853954802,
      -0.04786650755137683,
      -0.04896119364820255,
      -0.05006281918767141,
      -0.05117118652742968,
      -0.05228609802512356,
      -0.05340735603839931,
      -0.054534762924903155,
      -0.05566812104228135,
      -0.05680723274818012,
      -0.0579519004002457,
      -0.05910192635612439,
      -0.06025711297346234,
      -0.061417262609905876,
      -0.06258217762310113,
      -0.06375166037069448,
      -0.06492551321033203,
      -0.06610353849966014,
      -0.06728553859632491,
      -0.06847131585797274,
      -0.0696606726422497,
      -0.07085341130680221,
      -0.07204933420927635,
      -0.07324824370731846,
      -0.07444994215857473,
      -0.07565423192069143,
      -0.07686091535131477,
      -0.07806979480809102,
      -0.07928067264866638,
      -0.08049335123068715,
      -0.08170763291179951,
      -0.08292332004964972,
      -0.08414021500188405,
      -0.08535812012614868,
      -0.08657683778008989,
      -0.08779617032135391,
      -0.089015920107587,
      -0.09023588949643535,
      -0.09145588084554525,
      -0.09267569651256291,
      -0.09389513885513458,
      -0.0951140102309065,
      -0.09633211299752487,
      -0.097549249512636,
      -0.09876522213388607,
      -0.09997983321892139,
      -0.10119288512538814,
      -0.10240418021093255,
      -0.1036135208332009,
      -0.10482070934983943,
      -0.10602554811849435,
      -0.1072278394968119,
      -0.10842738584243836,
      -0.1096239895130199,
      -0.11081745286620283,
      -0.11200757825963338,
      -0.11319416805095772,
      -0.11437702459782217,
      -0.11555595025787294,
      -0.11673074738875623,
      -0.11790121834811834,
      -0.1190671654936055,
      -0.12022839118286395,
      -0.12138469777353987,
      -0.12253588762327958,
      -0.1236817630897293,
      -0.12482212653053522,
      -0.1259567803033436,
      -0.1270855267658007,
      -0.12820816827555276,
      -0.12932450719024602,
      -0.13043434586752672,
      -0.1315374866650411,
      -0.13263373194043535,
      -0.1337228840513558,
      -0.1348047453554486,
      -0.13587911821036003,
      -0.13694580497373632,
      -0.13800460800322376,
      -0.13905532965646852,
      -0.14009777229111686,
      -0.1411317382648151,
      -0.14215702993520934,
      -0.14317344965994588,
      -0.14418079979667098,
      -0.14517888270303084,
      -0.14616750073667176,
      -0.14714645625523992,
      -0.1481155516163816,
      -0.149074589177743,
      -0.1500233712969704,
      -0.15096170033171005,
      -0.15188937863960808,
      -0.15280620857831087,
      -0.15371199250546455,
      -0.15460653277871544,
      -0.15548963175570976,
      -0.15636109179409374,
      -0.15722071525151363,
      -0.15806830448561562,
      -0.15890366185404603,
      -0.15972658971445103,
      -0.16053689042447683,
      -0.16133436634176979,
      -0.1621188198239761,
      -0.16289005322874195,
      -0.16364786891371363,
      -0.16439206923653737,
      -0.16512245655485938,
      -0.16583883322632592,
      -0.16654100160858323,
      -0.16722876405927756,
      -0.16790192293605516,
      -0.16856028059656222,
      -0.16920363939844502,
      -0.16983180169934978,
      -0.17044456985692275,
      -0.17104174622881016,
      -0.1716231331726583,
      -0.1721885330461133,
      -0.1727377482068215,
      -0.17327058101242912,
      -0.17378683382058235,
      -0.17428630898892752,
      -0.1747688088751108,
      -0.1752341358367784,
      -0.17568209223157663,
      -0.1761124804171517,
      -0.17652510275114985,
      -0.17691976159121733,
      -0.17729625929500034,
      -0.1776543982201452,
      -0.17799398072429806,
      -0.17831480916510523,
      -0.1786166859002129,
      -0.1788994132872673,
      -0.17916279368391475,
      -0.1794066294478014,
      -0.17963072293657356,
      -0.17983487650787738,
      -0.1800188925193592,
      -0.18018257332866522,
      -0.18032572129344163,
      -0.18044813877133478,
      -0.18054962811999078,
      -0.18062999169705599,
      -0.18068903186017657,
      -0.18072655096699877,
      -0.18074235137516886,
      -0.18073623544233303,
      -0.18070800552613758,
      -0.1806574639842287,
      -0.18058441317425267,
      -0.18048865545385567,
      -0.180369993180684,
      -0.1802282287123839,
      -0.18006316440660156,
      -0.17987460262098326,
      -0.17966234571317521,
      -0.17942619604082372,
      -0.1791659559615749,
      -0.17888142783307512,
      -0.1785724140129705,
      -0.17823871685890738,
      -0.177880138728532,
      -0.17749648197949053,
      -0.17708754896942927,
      -0.17665314205599436,
      -0.17619306359683215,
      -0.17570711594958882,
      -0.1751951014719107,
      -0.1746568225214439,
      -0.17409208145583474,
      -0.17350068063272941,
      -0.17288242240977422,
      -0.17223710914461535,
      -0.17156454319489903,
      -0.17086452691827156,
      -0.17013686267237915,
      -0.169381352814868,
      -0.1685977997033844,
      -0.16778600569557456,
      -0.16694577314908476,
      -0.16607690442156123,
      -0.16517920187065016,
      -0.16425246785399783,
      -0.16329650472925047,
      -0.16231111485405433,
      -0.16129610058605562,
      -0.16025126428290065,
      -0.15917640830223553,
      -0.15807133500170664,
      -0.1569358467389601,
      -0.15576974587164227,
      -0.1545728347573993,
      -0.15334491575387746,
      -0.15208579121872298,
      -0.15079526350958214,
      -0.14947313498410109,
      -0.14811920799992614,
      -0.1467332849147035,
      -0.1453151680860795,
      -0.1438646598717002,
      -0.14238156262921203,
      -0.14086567871626107,
      -0.13931681049049371,
      -0.13773476030955603,
      -0.13611933053109443,
      -0.13447032351275506,
      -0.1327875416121841,
      -0.13107078718702794,
      -0.12931986259493264,
      -0.12753457019354464,
      -0.12571471234051,
      -0.1238600913934751,
      -0.12197050971008604,
      -0.12004576964798923,
      -0.11808567356483073,
      -0.11609002381825691,
      -0.11405862276591391,
      -0.1119912727654481,
      -0.10988777617450558,
      -0.10774793535073272,
      -0.1055715526517756,
      -0.10335843043528066,
      -0.10110837105889392,
      -0.09882117688026185,
      -0.09649665025703047,
      -0.0941345935468462,
      -0.09173480910735508,
      -0.08929709929620361,
      -0.08682126647103776,
      -0.08430711298950401,
      -0.08175444120924837,
      -0.07916305348791733,
      -0.076532752183157,
      -0.07386333965261348,
      -0.07115461825393325,
      -0.06840639034476236,
      -0.06561845828274722,
      -0.06279062442553388,
      -0.059922691130768806,
      -0.05701446075609799,
      -0.05406573565916791,
      -0.05107631819762458,
      -0.04804601072911446,
      -0.04497461561128357,
      -0.041861935201778375,
      -0.038707771858244866,
      -0.03551192793832956,
      -0.03227420579967841,
      -0.02899440779993794,
      -0.0256723362967541,
      -0.022307793647773425,
      -0.018900582210641854,
      -0.015450504343005931,
      -0.011957362402511591,
      -0.00842095874680538,
      -0.004841095733533223,
      -0.0012175757203416804,
      0.002449798935123168,
      0.0061612258752153015,
      0.009916902742288044,
      0.01371702717869549,
      0.017561796826791168,
      0.021451409328929073,
      0.025386062327462728,
      0.029365953464746252,
      0.033391280383132924,
      0.037462240724976996,
      0.04157903213263174,
      0.04574185224845128,
      0.04995089871478912,
      0.0542063691739993,
      0.058508461268435286,
      0.06285737264045124,
      0.06725330093240042,
      0.0716964437866371,
      0.07618699884551451,
      0.08072516375138683,
      0.0853111361466075,
      0.08994511367353063,
      0.09462729397450963,
      0.09935787469189869,
      0.10413705346805102,
      0.10896502794532073,
      0.11384199576606177,
      0.11876815457262735,
      0.12374370200737171,
      0.12876883571264827,
      0.1338437533308111,
      0.1389686525042137,
      0.14414373087521018,
      0.1493691860861538,
      0.15464521577939888,
      0.15997201759729857,
      0.16534978918220714,
      0.17077872817647793,
      0.17625903222246517,
      0.18179089896252218,
      0.1873745260390032,
      0.19301011109426142,
      0.19869785177065125,
      0.2044379457105257,
      0.2102305905562391,
      0.2160759839501449,
      0.22197432353459712,
      0.22792580695194928,
      0.2339306318445555,
      0.23998899585476904,
      0.2461010966249439,
      0.25226713179743415,
      0.2584872990145929,
      0.26476179591877447,
      0.27109082015233227,
      0.2774745693576204,
      0.2839132411769921,
      0.290407033252802,
      0.2969561432274028,
      0.30356076874314925,
      0.31022110744239423,
      0.31693735696749215,
      0.32370971496079626,
      0.3305383790646608,
      0.3374235469214392,
      0.34436541617348565,
      0.35136418446315326
    ],
    "all_axes_dimensionless": true
  },
  "checks_passed": true
}
