From d587a0c30be7bed9f28104730d08eecc7f22c570 Mon Sep 17 00:00:00 2001 From: Peter Kruyt Date: Sun, 13 Apr 2025 14:17:38 +0200 Subject: [PATCH 1/6] add lasers in elements.py --- xtrack/beam_elements/elements.py | 187 +++++++++++++++++++++++++++++++ 1 file changed, 187 insertions(+) diff --git a/xtrack/beam_elements/elements.py b/xtrack/beam_elements/elements.py index c1ea0153f..ee4374a05 100644 --- a/xtrack/beam_elements/elements.py +++ b/xtrack/beam_elements/elements.py @@ -7,6 +7,7 @@ import numpy as np from numbers import Number from scipy.special import factorial +import json import xobjects as xo import xtrack as xt @@ -3312,6 +3313,192 @@ def __init__(self, current = 0, def get_backtrack_element(self, _context=None, _buffer=None, _offset=None): raise NotImplementedError +class CWLaser(BeamElement): + '''Beam element modeling partially stripped ion excitation and emission of photons. Parameters: + Gaussian laser pulse is assumed (en.wikipedia.org/wiki/Gaussian_beam) + - laser_direction_nx,..._ny,..._nz: Laser direction vector n. Default is ``0,0,-1``. + - laser_x,..._y,..._z [m]: Laser pulse center location at t=0. Default is ``0,0,0``. + - laser_waist_shift [m]: How far is the laser waist from the laser pulse center + along the n vector at t=0. Default is ``0``. + - laser_waist_radius [m]: Laser waist radius. + Laser intensity vs radius at waist I(r)=exp(-2r^2/w_0^2), + where w_0 is the laser_waist_radius. Default is ``1e-3``. + - laser_energy [J]: Total laser pulse energy. Default is ``0``. + - laser_duration_sigma [sec]: Laser duration. Default is ``1e-12``. + assuming Fourier-limited pulse so far: sigma_w = 1/sigma_t. + - laser_wavelength [m]: Central wavelength of the laser. Default is ``1034.0e-9``. + - ion_excitation_energy [eV]: Transition energy in the ion. Default is ``68.6e3``. + - ion_excitation_g1,..._g2: Degeneracy factors of the ion levels. Default is ``1,3``. + - ion_excited_lifetime [s]: Lifetime of the exited state. Default is ``3.9e-17``. + ''' + + _xofields={ + 'laser_direction_nx': xo.Float64, + 'laser_direction_ny': xo.Float64, + 'laser_direction_nz': xo.Float64, + 'laser_x': xo.Float64, + 'laser_y': xo.Float64, + 'laser_z': xo.Float64, + 'laser_waist_shift': xo.Float64, + 'laser_waist_radius': xo.Float64, + 'laser_energy': xo.Float64, + 'laser_intensity': xo.Float64, + 'laser_wavelength': xo.Float64, + 'ion_excitation_energy': xo.Float64, + 'ion_excitation_g1': xo.Float64, + 'ion_excitation_g2': xo.Float64, + 'ion_excited_lifetime': xo.Float64, + 'cooling_section_length': xo.Float64, + } + + _depends_on = [RandomUniformAccurate] + + + _extra_c_sources = [ + _pkg_root.joinpath('headers/constants.h'), + _pkg_root.joinpath('beam_elements/elements_src/cw_laser.h')] + + + def __init__(self, laser_direction_nx = 0, + laser_direction_ny = 0, + laser_direction_nz = -1, + laser_x = 0, + laser_y = 0, + laser_z = 0, + laser_waist_radius = 0, + laser_intensity = 0, + laser_wavelength = 0, # m + ion_excitation_energy = 0, + ion_excitation_g1 = 2, + ion_excitation_g2 = 2, + ion_excited_lifetime = 0, + cooling_section_length=0, + **kwargs): + super().__init__(**kwargs) + self.laser_direction_nx = laser_direction_nx + self.laser_direction_ny = laser_direction_ny + self.laser_direction_nz = laser_direction_nz + self.laser_x = laser_x + self.laser_y = laser_y + self.laser_z = laser_z + self.laser_waist_radius = laser_waist_radius + self.laser_intensity = laser_intensity + self.laser_wavelength = laser_wavelength + self.ion_excitation_energy = ion_excitation_energy + self.ion_excitation_g1 = ion_excitation_g1 + self.ion_excitation_g2 = ion_excitation_g2 + self.ion_excited_lifetime = ion_excited_lifetime + self.cooling_section_length = cooling_section_length + +class PulsedLaserRecord(xo.HybridClass): + _xofields = { + '_index': RecordIndex, + 'photon_energy': xo.Float64[:], + 'emission_time': xo.Float64[:], + 'particle_id': xo.Float64[:]} + +class PulsedLaser(BeamElement): + '''Beam element modeling partially stripped ion excitation and emission of photons. Parameters: + Gaussian laser pulse is assumed (en.wikipedia.org/wiki/Gaussian_beam) + - laser_direction_nx,..._ny,..._nz: Laser direction vector n. Default is ``0,0,-1``. + - laser_x,..._y,..._z [m]: Laser pulse center location at t=0. Default is ``0,0,0``. + - laser_waist_shift [m]: How far is the laser waist from the laser pulse center + along the n vector at t=0. Default is ``0``. + - laser_waist_radius [m]: Laser waist radius. + Laser intensity vs radius at waist I(r)=exp(-2r^2/w_0^2), + where w_0 is the laser_waist_radius. Default is ``1e-3``. + - laser_energy [J]: Total laser pulse energy. Default is ``0``. + - laser_duration_sigma [sec]: Laser duration. Default is ``1e-12``. + assuming Fourier-limited pulse so far: sigma_w = 1/sigma_t. + - laser_wavelength [m]: Central wavelength of the laser. Default is ``1034.0e-9``. + - ion_excitation_energy [eV]: Transition energy in the ion. Default is ``68.6e3``. + - ion_excited_lifetime [s]: Lifetime of the exited state. Default is ``3.9e-17``. + ''' + + # Map of Excitation: + fname = _pkg_root.joinpath('beam_elements/elements_src/laser_excitation_maps/pulsed_excitation_map.json') + with open(fname, 'r') as f: + map_data = json.load(f) + excitation_map = np.array(map_data['Excitation probability']) + + _xofields={ + 'laser_direction_nx': xo.Float64, + 'laser_direction_ny': xo.Float64, + 'laser_direction_nz': xo.Float64, + 'laser_x': xo.Float64, + 'laser_y': xo.Float64, + 'laser_z': xo.Float64, + 'laser_waist_shift': xo.Float64, + 'laser_waist_radius': xo.Float64, + 'laser_energy': xo.Float64, + 'laser_duration_sigma': xo.Float64, + 'laser_wavelength': xo.Float64, + 'ion_excitation_energy': xo.Float64, + 'ion_excitation_g1': xo.Float64, + 'ion_excitation_g2': xo.Float64, + 'ion_excited_lifetime': xo.Float64, + 'Map_of_Excitation': xo.Float64[int(excitation_map.size)], + 'N_OmegaRabiTau_values': xo.Int64, + 'N_DeltaDetuningTau_values': xo.Int64, + 'OmegaRabiTau_max': xo.Float64, + 'DeltaDetuningTau_max': xo.Float64, + 'record_flag': xo.Int64, + } + + _depends_on = [RandomUniformAccurate] + + _extra_c_sources = [ + _pkg_root.joinpath('headers/constants.h'), + _pkg_root.joinpath('beam_elements/elements_src/pulsed_laser.h')] + + _internal_record_class = PulsedLaserRecord + + + def __init__(self, laser_direction_nx = 0, + laser_direction_ny = 0, + laser_direction_nz = -1, + laser_x = 0, + laser_y = 0, + laser_z = 0, + laser_waist_shift = 0, + laser_waist_radius = 1e-3, + laser_energy = 0, + laser_duration_sigma = 1e-12, + # assuming Fourier-limited pulse so far: sigma_w = 1/sigma_t + laser_wavelength = 1034.0e-9, # m + ion_excitation_energy = 68.6e3, + ion_excitation_g1 = 2, + ion_excitation_g2 = 2, + ion_excited_lifetime = 3.9e-17, + record_flag = 0, + **kwargs): + super().__init__(**kwargs) + self.laser_direction_nx = laser_direction_nx + self.laser_direction_ny = laser_direction_ny + self.laser_direction_nz = laser_direction_nz + self.laser_x = laser_x + self.laser_y = laser_y + self.laser_z = laser_z + self.laser_waist_shift = laser_waist_shift + self.laser_energy = laser_energy + self.laser_waist_radius = laser_waist_radius + self.laser_duration_sigma = laser_duration_sigma + self.laser_wavelength = laser_wavelength + self.ion_excitation_energy = ion_excitation_energy + self.ion_excitation_g1 = ion_excitation_g1 + self.ion_excitation_g2 = ion_excitation_g2 + self.ion_excited_lifetime = ion_excited_lifetime + self.record_flag = record_flag + + # Map of Excitation: + fname = _pkg_root.joinpath('beam_elements/elements_src/laser_excitation_maps/pulsed_excitation_map.json') + with open(fname, 'r') as f: + map_data = json.load(f) + self.Excitation = np.array(map_data['Excitation probability']) + self.N_OmegaRabiTau_values, self.N_DeltaDetuningTau_values = np.shape(self.Excitation) + self.OmegaRabiTau_max = map_data['OmegaRabi*tau_pulse max'] + self.DeltaDetuningTau_max = map_data['Delta_detuning*tau_pulse max'] + self.Map_of_Excitation = self.Excitation.flatten() class ThinSliceNotNeededError(Exception): pass From 4eca0488e623cfbe9fe67980f907d7ef5a48a9e7 Mon Sep 17 00:00:00 2001 From: Peter Kruyt Date: Sun, 13 Apr 2025 14:18:23 +0200 Subject: [PATCH 2/6] add laser cooler test --- tests/test_laser_cooler.py | 211 +++++++++++++++++++++++++++++++++++++ 1 file changed, 211 insertions(+) create mode 100644 tests/test_laser_cooler.py diff --git a/tests/test_laser_cooler.py b/tests/test_laser_cooler.py new file mode 100644 index 000000000..654ccd3ed --- /dev/null +++ b/tests/test_laser_cooler.py @@ -0,0 +1,211 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2021. # +# ######################################### # + +import numpy as np +import pytest +import pathlib +from cpymad.madx import Madx +from scipy.stats import linregress +from scipy import constants as cst +import ducktrack as dtk +import xobjects as xo +import xpart as xp +import xtrack as xt +from xobjects.test_helpers import for_all_test_contexts, fix_random_seed +from xtrack.beam_elements.elements import _angle_from_trig +from scipy.optimize import curve_fit + +# test_data_folder = pathlib.Path( +# __file__).parent.joinpath('../test_data').absolute() + + +@for_all_test_contexts +def test_pulsed_laser(test_context): + """Test the decay of horizontal emittance with expected value. + """ + qx=26.299364685601024 + qy=26.249362950069248 + + circumference=6911.5038 + + voltage_rf=7*1e6 + frequency=201.8251348335775*1e6 + lag_rf=180 + momentum_compaction_factor=0.001901471346864482 + + + beta_x = 54.614389 # m + beta_y = 44.332517 # m + alpha_x = -1.535235 + alpha_y = 1.314101 + + Dx = 2.444732 # m + Dpx = 0.097522 + + Dy = 0.0 # m + Dpy = 0.0 + + #index of gamma factory along SPS line: 16675 + + arc = xt.LineSegmentMap( + qx=qx, qy=qy, + length=circumference, + alfx=alpha_x, + alfy=alpha_y, + betx=beta_x, + bety=beta_y, + + dx=Dx, + dpx=Dpx, + dy=Dy, + dpy=Dpy, + + voltage_rf=voltage_rf, + lag_rf=lag_rf, + frequency_rf=frequency, + momentum_compaction_factor=momentum_compaction_factor, + longitudinal_mode = 'nonlinear' + ) + + q0 = 17 + mass0 = 37261297096.799995 + + gamma0= 205.0686404689884 + beta0= 0.9999881125888904 + p0c = mass0*gamma0*beta0 #eV/c + + bunch_intensity = 4000000000.0 + + particle_ref = xp.Particles(p0c=p0c, mass0=mass0, q0=q0, gamma0=gamma0) + + nemitt = 1.5e-6 # m*rad (normalized emittance) + sigma_z = 0.095 + + num_particles=int(1e3) + + line_arc=xt.Line( + elements=[arc]) + line_arc.build_tracker() + + particles = xp.generate_matched_gaussian_bunch( + num_particles=num_particles, + total_intensity_particles=bunch_intensity, + nemitt_x=nemitt, nemitt_y=nemitt, sigma_z=sigma_z, + particle_ref=particle_ref, + line=line_arc, + ) + particles._init_random_number_generator() + + particles0=particles.copy() + + sigma_dp=2e-4 + ################## + # Laser Cooler # + ################## + + #laser-ion beam collision angle + theta_l = 2.6*np.pi/180 # rad + nx = 0; ny = -np.sin(theta_l); nz = -np.cos(theta_l) + + # Ion excitation energy: + ion_excited_lifetime=4.2789999999999997e-13 + hw0 = 661.89 # eV + clight=cst.c + hc=cst.hbar*clight/cst.e # eV*m (ħc) + lambda_0 = 2*np.pi*hc/hw0 # m -- ion excitation wavelength + lambda_l = 7.680000000000001e-07 + + # Shift laser wavelength for fast longitudinal cooling: + #lambda_l = lambda_l*(1+1*sigma_dp) # m + + laser_frequency = clight/lambda_l # Hz + sigma_w = 2*np.pi*laser_frequency*sigma_dp + #sigma_w = 2*np.pi*laser_frequency*sigma_dp/2 # for fast longitudinal cooling + sigma_t = 1/sigma_w # sec -- Fourier-limited laser pulse + + laser_waist_radius = 1.3e-3 #m + laser_energy = 5e-3 + + laser_x = -0.0015771812080536912 + + GF_IP = xt.PulsedLaser( + laser_x=laser_x, + laser_y=0, + laser_z=0, + + laser_direction_nx = 0, + laser_direction_ny = ny, + laser_direction_nz = nz, + laser_energy = laser_energy, # J + laser_duration_sigma = sigma_t, # sec + laser_wavelength = lambda_l, # m + laser_waist_radius = laser_waist_radius, # m + laser_waist_shift = 0, # m + ion_excitation_energy = hw0, # eV + ion_excited_lifetime = ion_excited_lifetime, # sec, + record_flag=1 + ) + + # simulation parameters: simulate 10 s of cooling, and take data once every 100 ms + max_time_s = 1 + int_time_s = 0.01 + T_per_turn = circumference/(clight*beta0) + num_turns = int(max_time_s/T_per_turn) + save_interval = int(int_time_s/T_per_turn) + + # create a monitor object, to reduce holded data + monitor = xt.ParticlesMonitor(start_at_turn=0, stop_at_turn=1, + n_repetitions=int(num_turns/save_interval), + repetition_period=save_interval, + num_particles=num_particles) + + line = xt.Line( + elements=[monitor,GF_IP,arc]) + + line.build_tracker(_context=test_context) + + # Start internal logging for the electron cooler + record = line.start_internal_logging_for_elements_of_type( + xt.PulsedLaser, capacity=num_particles*100) + + line.track(particles, num_turns=num_turns, + turn_by_turn_monitor=False,with_progress=True) + + # extract relevant values + x = monitor.x[:,:,0] + px = monitor.px[:,:,0] + y = monitor.y[:,:,0] + py = monitor.py[:,:,0] + delta = monitor.delta[:,:,0] + zeta = monitor.zeta[:,:,0] + state = monitor.state[:,:,0] + time = monitor.at_turn[:, 0, 0] * T_per_turn + + gamma_x=(1+alpha_x**2)/beta_x + gamma_y=(1+alpha_y**2)/beta_y + + action_x = (gamma_x*(x-Dx*delta)**2 + 2*alpha_x*(x-Dx*delta)*(px-Dpx*delta)+ beta_x*(px-Dpx*delta)**2) + action_y = (gamma_y*(y-Dy*delta)**2 + 2*alpha_y*(y-Dy*delta)*(py-Dpy*delta)+ beta_y*(py-Dpy*delta)**2) + + emittance_x_twiss=np.mean(action_x,axis=1)*beta0*gamma0/2 + rms_dp_p=np.std(delta,axis=1) + + # Define the exponential decay function + def exp_decay(t, A, tau ): + return A * np.exp(-t / tau) + + A0 = emittance_x_twiss[0] + tau0 = (time[-1] - time[0]) / 5.0 + C0 = emittance_x_twiss[-1] + initial_guess = (A0, tau0) + + popt, pcov = curve_fit(exp_decay, time, emittance_x_twiss, p0=initial_guess) + + time_fit = np.linspace(np.min(time), np.max(time), 100) + emittance_fit = exp_decay(time_fit, *popt) + tau=popt[1] + + xo.assert_allclose(tau, 7, rtol=0, atol=1) + From 52dfb25d5196790bd5d7812b00ca1559839204f4 Mon Sep 17 00:00:00 2001 From: Peter Kruyt Date: Sun, 13 Apr 2025 14:19:05 +0200 Subject: [PATCH 3/6] add cw laser in c --- xtrack/beam_elements/elements_src/cw_laser.h | 140 +++++++++++++++++++ 1 file changed, 140 insertions(+) create mode 100644 xtrack/beam_elements/elements_src/cw_laser.h diff --git a/xtrack/beam_elements/elements_src/cw_laser.h b/xtrack/beam_elements/elements_src/cw_laser.h new file mode 100644 index 000000000..b0a87c910 --- /dev/null +++ b/xtrack/beam_elements/elements_src/cw_laser.h @@ -0,0 +1,140 @@ +// copyright ############################### // +// This file is part of the Xtrack Package. // +// Copyright (c) CERN, 2021. // +// ######################################### // +#define POW2(X) ((X)*(X)) +#define POW3(X) ((X)*(X)*(X)) +#define POW4(X) ((X)*(X)*(X)*(X)) +#ifndef XTRACK_IONLASERIP_H +#define XTRACK_IONLASERIP_H + +/*gpufun*/ +void CWLaser_track_local_particle(CWLaserData el, LocalParticle* part0){ + + //The algorithm is partially from https://anaconda.org/petrenko/psi_beam_vs_laser + + double nx = CWLaserData_get_laser_direction_nx(el); + double ny = CWLaserData_get_laser_direction_ny(el); + double nz = CWLaserData_get_laser_direction_nz(el); + + double laser_x = CWLaserData_get_laser_x(el); + double laser_y = CWLaserData_get_laser_y(el); + double laser_z = CWLaserData_get_laser_z(el); + double w0 = CWLaserData_get_laser_waist_radius(el); + + double laser_intensity = CWLaserData_get_laser_intensity(el); // W/m^2 + double laser_wavelength = CWLaserData_get_laser_wavelength(el); // Hz + + double ion_excited_lifetime = CWLaserData_get_ion_excited_lifetime(el); // sec + double ion_excitation_energy = CWLaserData_get_ion_excitation_energy(el); // eV + + double cooling_section_length = CWLaserData_get_cooling_section_length(el); // m + + double p0c = LocalParticle_get_p0c(part0); // eV + double m0 = LocalParticle_get_mass0(part0); // eV/c^2 + double hbar = 1.054571817e-34; // J*sec + + double gamma0 = sqrt(1.0 + POW2(p0c)/POW2(m0)); + double beta0 = sqrt(1.0 - 1.0/POW2(gamma0)); + double OmegaTransition = ion_excitation_energy*QELEM/hbar; // rad/sec + + //number of excitations that will occur over the entire cooling section: + double number_of_excitations = cooling_section_length/(beta0*gamma0*C_LIGHT*ion_excited_lifetime); + + //start_per_particle_block (part0->part) + + double state = LocalParticle_get_state(part); + double delta = LocalParticle_get_delta(part); + double z = LocalParticle_get_zeta(part); + double x = LocalParticle_get_x(part); + double y = LocalParticle_get_y(part); + double px = LocalParticle_get_px(part); + double py = LocalParticle_get_py(part); + + double pc = p0c*(1.0+delta); // eV + double gamma = sqrt(1.0 + POW2(pc)/POW2(m0)); + double beta = sqrt(1.0 - 1.0/POW2(gamma)); + double beta_x = px*p0c/m0/gamma; + double beta_y = py*p0c/m0/gamma; + double beta_z = sqrt(POW2(beta) - POW2(beta_x) -POW2(beta_y)); + + double vx = C_LIGHT*beta_x; // m/sec + double vy = C_LIGHT*beta_y; // m/sec + double vz = C_LIGHT*beta_z; // m/sec + + // Collision of ion with the laser pulse: + // The position of the laser beam center is rl=rl0+ct*n. We can find the moment + // when a particle with a position r=r0+vt collides with the laser as the moment + // when r-rl is perpendicular to n. Then (r-rl,n)=0, which yields the equation + // (r0,n)+(v,n)t-(rl0,n)-ct(n,n)=0. Hence + // tcol=(r0-rl0,n)/[c-(v,n)] + + double tcol = ( (x-laser_x)*nx + (y-laser_y)*ny + (z-laser_z)*nz ) / (C_LIGHT - (vx*nx+vy*ny+vz*nz)); // sec + + double xcol = x + vx*tcol; // m + double ycol = y + vy*tcol; // m + double zcol = z + vz*tcol; // m + + // r^2 to the laser center = |r-rl| at the moment tcol: + double r2 = (\ + POW2(xcol - (laser_x+C_LIGHT*nx*tcol)) + \ + POW2(ycol - (laser_y+C_LIGHT*ny*tcol)) + \ + POW2(zcol - (laser_z+C_LIGHT*nz*tcol)) \ + ); // m + double cos_theta = -(nx*vx + ny*vy + nz*vz)/(beta*C_LIGHT); + double doppler_factor = gamma * (1.0 + beta * cos_theta); + // Max. laser intensity experienced by the ion (in the ion rest frame): + double I = POW2(doppler_factor) * laser_intensity; // W/m^2 + + // Alexey's expression for Rabi frequency + //double OmegaRabi = (hbar * C_LIGHT / (ion_excitation_energy * QELEM)) * \ + // sqrt(I * 2 * PI / (ion_excitation_energy * QELEM * ion_excited_lifetime)); // rad/sec + + // This Rabi frequency is equivalent to the one of Alexey + // This one is clearer because it follows the notation from the ShortPulse mathematica notebook + double OmegaRabi = C_LIGHT*sqrt(2*PI)*sqrt(I)/sqrt(hbar*ion_excited_lifetime*POW3(OmegaTransition)); + + // Detuning from the ion transition resonance in the ion rest frame: + double laser_omega_ion_frame = (2.0*PI*C_LIGHT/laser_wavelength)*doppler_factor; + double DeltaDetuning = (OmegaTransition - laser_omega_ion_frame); + + double gamma_decay=1/ion_excited_lifetime; + //compute saturation parameter and normalized detuning: + double k1=OmegaRabi*OmegaRabi/(POW2(gamma_decay)); + double ratio_detuning_gamma = DeltaDetuning/gamma_decay; + + //1. only apply laser cooling to particles that are within the laser radius + //2. only apply laser cooling to particles that have not been lost. In Xsuite, this means positive state + if (r2 < POW2(w0)) + { + if (state > 0) + { + double excitation_probability = 0.5*k1 / (4*ratio_detuning_gamma * ratio_detuning_gamma + k1 + 1); + + double rnd = RandomUniformAccurate_generate(part); //between 0 and 1 + //printf("rnd : %f\n", rnd); + if ( rnd < excitation_probability ) + { + LocalParticle_set_state(part, 2); // Excited particle + // photon recoil (from emitted photon!): + double rnd = RandomUniformAccurate_generate(part); //between 0 and 1 + + // If particle is excited, reduce its energy by, on average, the excitation energy with Lorentz boost + // 2.0*rnd ensures that the average energy lost is the excitation energy + // gamma is the Lorentz boost + LocalParticle_add_to_energy(part,-number_of_excitations*gamma*ion_excitation_energy*2.0*rnd, 0); // eV + } + else + { + LocalParticle_set_state(part, 1); // Still particle + } + + + } + } + //end_per_particle_block + +} + +#endif + From bcde3a06251d59749e7982af9808365b0d8704b8 Mon Sep 17 00:00:00 2001 From: Peter Kruyt Date: Sun, 13 Apr 2025 14:19:36 +0200 Subject: [PATCH 4/6] add pulsed laser in c --- .../beam_elements/elements_src/pulsed_laser.h | 211 ++++++++++++++++++ 1 file changed, 211 insertions(+) create mode 100644 xtrack/beam_elements/elements_src/pulsed_laser.h diff --git a/xtrack/beam_elements/elements_src/pulsed_laser.h b/xtrack/beam_elements/elements_src/pulsed_laser.h new file mode 100644 index 000000000..1fe70929d --- /dev/null +++ b/xtrack/beam_elements/elements_src/pulsed_laser.h @@ -0,0 +1,211 @@ +// copyright ############################### // +// This file is part of the Xtrack Package. // +// Copyright (c) CERN, 2021. // +// ######################################### // +#define POW2(X) ((X)*(X)) +#define POW3(X) ((X)*(X)*(X)) +#define POW4(X) ((X)*(X)*(X)*(X)) +#ifndef XTRACK_PulsedLaser_H +#define XTRACK_PulsedLaser_H + + +/*gpufun*/ +void PulsedLaser_track_local_particle(PulsedLaserData el, LocalParticle* part0){ + + int64_t record_flag = PulsedLaserData_get_record_flag(el); + PulsedLaserRecordData record = PulsedLaserData_getp_internal_record(el, part0); + RecordIndex record_index = NULL; + + double nx = PulsedLaserData_get_laser_direction_nx(el); + double ny = PulsedLaserData_get_laser_direction_ny(el); + double nz = PulsedLaserData_get_laser_direction_nz(el); + + double laser_x = PulsedLaserData_get_laser_x(el); + double laser_y = PulsedLaserData_get_laser_y(el); + double laser_z = PulsedLaserData_get_laser_z(el); + double w0 = PulsedLaserData_get_laser_waist_radius(el); + + double laser_energy = PulsedLaserData_get_laser_energy(el); + double laser_waist_shift = PulsedLaserData_get_laser_waist_shift(el); + + double laser_sigma_t = PulsedLaserData_get_laser_duration_sigma(el); + //double laser_sigma_w = 1/laser_sigma_t; // rad/sec -- assuming Fourier-limited pulse + + double laser_wavelength = PulsedLaserData_get_laser_wavelength(el); // Hz + + double ion_excited_lifetime = PulsedLaserData_get_ion_excited_lifetime(el); // sec + double ion_excitation_energy = PulsedLaserData_get_ion_excitation_energy(el); // eV + + // constants for the Map_of_Excitation vs OmegaRabi and Detuning: + int64_t N_OmegaRabiTau_values = PulsedLaserData_get_N_OmegaRabiTau_values(el); + int64_t N_DeltaDetuningTau_values = PulsedLaserData_get_N_DeltaDetuningTau_values(el); + double OmegaRabiTau_max = PulsedLaserData_get_OmegaRabiTau_max(el); + double DeltaDetuningTau_max = PulsedLaserData_get_DeltaDetuningTau_max(el); + double dOmegaRabiTau = OmegaRabiTau_max/(N_OmegaRabiTau_values-1.0); + double dDeltaDetuningTau = DeltaDetuningTau_max/(N_DeltaDetuningTau_values-1.0); + + double laser_Rayleigh_length = PI*POW2(w0)/laser_wavelength; + + double p0c = LocalParticle_get_p0c(part0); // eV + double m0 = LocalParticle_get_mass0(part0); // eV/c^2 + double hbar = 1.054571817e-34; // J*sec + + double OmegaTransition = ion_excitation_energy*QELEM/hbar; // rad/sec + + // Maximum laser intensity (at the focal point) + double I0 = sqrt(2/PI)*(laser_energy/laser_sigma_t)/(PI*POW2(w0)); // W/m^2 + + //start_per_particle_block (part0->part) + + double state = LocalParticle_get_state(part); + double delta = LocalParticle_get_delta(part); + double z = LocalParticle_get_zeta(part); + double x = LocalParticle_get_x(part); + double y = LocalParticle_get_y(part); + double px = LocalParticle_get_px(part); + double py = LocalParticle_get_py(part); + + double pc = p0c*(1.0+delta); // eV + double gamma = sqrt(1.0 + POW2(pc)/POW2(m0)); + double beta = sqrt(1.0 - 1.0/POW2(gamma)); + double beta_x = px*p0c/m0/gamma; + double beta_y = py*p0c/m0/gamma; + double beta_z = sqrt(POW2(beta) - POW2(beta_x) -POW2(beta_y)); + + double vx = C_LIGHT*beta_x; // m/sec + double vy = C_LIGHT*beta_y; // m/sec + double vz = C_LIGHT*beta_z; // m/sec + + // Collision of ion with the laser pulse: + // The position of the laser beam center is rl=rl0+ct*n. We can find the moment + // when a particle with a position r=r0+vt collides with the laser as the moment + // when r-rl is perpendicular to n. Then (r-rl,n)=0, which yields the equation + // (r0,n)+(v,n)t-(rl0,n)-ct(n,n)=0. Hence + // tcol=(r0-rl0,n)/[c-(v,n)] + + double tcol = ( (x-laser_x)*nx + (y-laser_y)*ny + (z-laser_z)*nz ) / (C_LIGHT - (vx*nx+vy*ny+vz*nz)); // sec + + double xcol = x + vx*tcol; // m + double ycol = y + vy*tcol; // m + double zcol = z + vz*tcol; // m + + // r^2 to the laser center = |r-rl| at the moment tcol: + double r2 = (\ + POW2(xcol - (laser_x+C_LIGHT*nx*tcol)) + \ + POW2(ycol - (laser_y+C_LIGHT*ny*tcol)) + \ + POW2(zcol - (laser_z+C_LIGHT*nz*tcol)) \ + ); // m + + double Z_to_laser_focus = laser_waist_shift - tcol*C_LIGHT; // m + double cos_theta = -(nx*vx + ny*vy + nz*vz)/(beta*C_LIGHT); + + // Laser beam size at the point of collision: + double w = w0*sqrt(1.0+POW2(Z_to_laser_focus/laser_Rayleigh_length)); + double doppler_factor = gamma * (1.0 + beta * cos_theta); + // Max. laser intensity experienced by the ion (in the ion rest frame): + double I = POW2(doppler_factor) * I0*POW2(w0/w)*exp(-2.0*r2/POW2(w)); // W/m^2 + + // Alexey's expression for Rabi frequency + //double OmegaRabi = (hbar * C_LIGHT / (ion_excitation_energy * QELEM)) * \ + // sqrt(I * 2 * PI / (ion_excitation_energy * QELEM * ion_excited_lifetime)); // rad/sec + + // This Rabi frequency is equivalent to the one of Alexey + // This one is clearer because it follows the notation from the ShortPulse mathematica notebook + double OmegaRabi = C_LIGHT*sqrt(2*PI)*sqrt(I)/sqrt(hbar*ion_excited_lifetime*POW3(OmegaTransition)); + double OmegaRabiTau = OmegaRabi * laser_sigma_t / (doppler_factor); // in the ion rest frame + + + // Detuning from the ion transition resonance in the ion rest frame: + double laser_omega_ion_frame = (2.0*PI*C_LIGHT/laser_wavelength)*doppler_factor; + double DeltaDetuningTau = fabs( + (OmegaTransition - laser_omega_ion_frame) * laser_sigma_t / (doppler_factor) + ); + + + //only apply laser cooling to particles that have not been lost. In Xsuite, this means positive state + if (state > 0) + { + + if (DeltaDetuningTau < DeltaDetuningTau_max && OmegaRabiTau > OmegaRabiTau_max) + { + // In case of a very high laser field: + LocalParticle_set_state(part, 2); // Excited particle + double rnd = RandomUniformAccurate_generate(part); //between 0 and 1 + // If particle is excited, reduce its energy by, on average, the excitation energy with Lorentz boost + // 2.0*rnd ensures that the average energy lost is the excitation energy + // gamma is for the Doppler boost + LocalParticle_add_to_energy(part,-gamma*ion_excitation_energy*2.0*rnd, 0); // eV + // ---- Record the emitted photon event ---- + if (record_flag && record) { + record_index = PulsedLaserRecordData_getp__index(record); + int64_t i_slot = RecordIndex_get_slot(record_index); + if (i_slot >= 0) { + // Record photon properties. + // Here we record the photon energy, the time of collision (as an approximation for emission time), + // and the particle ID; you can extend this to record position (xcol,ycol,zcol) or other details. + PulsedLaserRecordData_set_photon_energy(record, i_slot, gamma*ion_excitation_energy*2.0*rnd); + PulsedLaserRecordData_set_emission_time(record, i_slot, tcol); + PulsedLaserRecordData_set_particle_id(record, i_slot, LocalParticle_get_particle_id(part)); + } + } + } + + else if (DeltaDetuningTau < DeltaDetuningTau_max && + OmegaRabiTau > dOmegaRabiTau/10.0) + { + // N_OmegaRabiTau_values N_DeltaDetuningTau_values + // OmegaRabiTau_max DeltaDetuningTau_max + int64_t row = (int)floor(OmegaRabiTau/dOmegaRabiTau); + int64_t col = (int)floor(DeltaDetuningTau/dDeltaDetuningTau); + int64_t idx = row*N_DeltaDetuningTau_values + col; + + double excitation_probability = PulsedLaserData_get_Map_of_Excitation(el, idx); + double rnd = RandomUniformAccurate_generate(part); //between 0 and 1 + + if ( rnd < excitation_probability ) + { + LocalParticle_set_state(part, 2); // Excited particle + // photon recoil (from emitted photon!): + double rnd = RandomUniformAccurate_generate(part); //between 0 and 1 + LocalParticle_add_to_energy(part,-gamma*ion_excitation_energy*2.0*rnd, 0); // eV + + // ---- Record the emitted photon event ---- + if (record_flag && record) { + record_index = PulsedLaserRecordData_getp__index(record); + int64_t i_slot = RecordIndex_get_slot(record_index); + if (i_slot >= 0) { + PulsedLaserRecordData_set_photon_energy(record, i_slot, gamma*ion_excitation_energy*2.0*rnd); + PulsedLaserRecordData_set_emission_time(record, i_slot, tcol); + PulsedLaserRecordData_set_particle_id(record, i_slot, LocalParticle_get_particle_id(part)); + } + } + + // One can also add transverse emission. This doesnt have a Lorentz boost + // double rnd_x = ((double)rand() / (RAND_MAX)) * 2.0 - 1.0;//between -1 and +1 + // LocalParticle_add_to_px(part,2*rnd_x*ion_excitation_energy/p0c); + // double rnd_y = ((double)rand() / (RAND_MAX)) * 2.0 - 1.0;//between -1 and +1 + // LocalParticle_add_to_py(part,2*rnd_y*ion_excitation_energy/p0c); + } + else + { + LocalParticle_set_state(part, 1); // Still particle + if (record_flag && record) { + record_index = PulsedLaserRecordData_getp__index(record); + int64_t i_slot = RecordIndex_get_slot(record_index); + if (i_slot >= 0) { + PulsedLaserRecordData_set_photon_energy(record, i_slot, 0); + PulsedLaserRecordData_set_emission_time(record, i_slot, 0); + PulsedLaserRecordData_set_particle_id(record, i_slot, LocalParticle_get_particle_id(part)); + } + } + } + + } + } + + //end_per_particle_block + +} + +#endif + From 4dd9c59f664579d7c5933e2dcd9cc3faf62c3b84 Mon Sep 17 00:00:00 2001 From: Peter Kruyt Date: Sun, 13 Apr 2025 14:44:58 +0200 Subject: [PATCH 5/6] add excitation maps --- .../generate_pulsed_excitation_map.py | 61 + .../pulsed_excitation_map.json | 9926 +++++++++++++++++ 2 files changed, 9987 insertions(+) create mode 100644 xtrack/beam_elements/elements_src/laser_excitation_maps/generate_pulsed_excitation_map.py create mode 100644 xtrack/beam_elements/elements_src/laser_excitation_maps/pulsed_excitation_map.json diff --git a/xtrack/beam_elements/elements_src/laser_excitation_maps/generate_pulsed_excitation_map.py b/xtrack/beam_elements/elements_src/laser_excitation_maps/generate_pulsed_excitation_map.py new file mode 100644 index 000000000..6ecb3afff --- /dev/null +++ b/xtrack/beam_elements/elements_src/laser_excitation_maps/generate_pulsed_excitation_map.py @@ -0,0 +1,61 @@ +import numpy as np +from scipy.integrate import solve_ivp +import json + +# Initial values: +rhoRe1100 = 1 +rhoRe1210 = 0 +rhoIm1210 = 0 +rhoRe2200 = 0 +rho0 = np.array([rhoRe1100, rhoRe1210, rhoIm1210, rhoRe2200]) + +Delta = 0 +Omega0 = 5 + +def F(t, rho): + rhoRe1100 = rho[0] + rhoRe1210 = rho[1] + rhoIm1210 = rho[2] + rhoRe2200 = rho[3] + Exp = np.exp(-(1 / 4) * (-5 + t) ** 2) + return np.array([ + Exp * Omega0 * rhoIm1210, + Delta * rhoIm1210, + -Delta * rhoRe1210 + 0.5 * Exp * Omega0 * (-rhoRe1100 + rhoRe2200), + -Exp * Omega0 * rhoIm1210 + ]) + +t_span = (0, 10) # sec +t_eval = np.linspace(t_span[0], t_span[1], 500) # points of output + +sol = solve_ivp(F, t_span, rho0, t_eval=t_eval, rtol=1e-4) + +# Map of resulting excitation as a function of Δd and Ω0 +def excite_ion(newDelta, newOmega0): + global Delta + Delta = newDelta + global Omega0 + Omega0 = newOmega0 + sol = solve_ivp(F, t_span, rho0, rtol=1e-4) + rhoRe1100, rhoRe1210, rhoIm1210, rhoRe2200 = sol.y + return rhoRe2200[-1] + + +Delta_range = np.linspace(0, +3, 30) +Omega0_range = np.linspace(0, +8, 80) +Delta_range = np.linspace(0, +3, 60) +Omega0_range = np.linspace(0, +8, 160) +Delta_range = np.linspace(0, +3, 60) +Omega0_range = np.linspace(0, +8, 160) + +Deltas, Omega0s = np.meshgrid(Delta_range, Omega0_range) + +Excitation = np.vectorize(excite_ion)(Deltas, Omega0s) + + +with open('pulsed_excitation_map.json', "w") as f: + json.dump({ + 'Delta_detuning*tau_pulse max': Delta_range[-1], + 'OmegaRabi*tau_pulse max': Omega0_range[-1], + 'Excitation probability': Excitation.tolist() + }, f, indent=1) \ No newline at end of file diff --git a/xtrack/beam_elements/elements_src/laser_excitation_maps/pulsed_excitation_map.json b/xtrack/beam_elements/elements_src/laser_excitation_maps/pulsed_excitation_map.json new file mode 100644 index 000000000..c8a008b76 --- /dev/null +++ b/xtrack/beam_elements/elements_src/laser_excitation_maps/pulsed_excitation_map.json @@ -0,0 +1,9926 @@ +{ + "Delta_detuning*tau_pulse max": 3.0, + "OmegaRabi*tau_pulse max": 8.0, + "Excitation probability": [ + [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], + [ + 0.007923745499711672, + 0.007883871303114479, + 0.007763701583874302, + 0.007566741665403279, + 0.007299095469467044, + 0.006968819557973702, + 0.006584775019108, + 0.0061580834422359865, + 0.005699751267413286, + 0.005221227472216206, + 0.004733384651589656, + 0.004246735042902995, + 0.0037706523553575565, + 0.0033132825754673694, + 0.002881144380118838, + 0.0024793255880374548, + 0.00211136371776483, + 0.0017793236140434083, + 0.0014839312576049766, + 0.0012247488599510848, + 0.0010003817800150936, + 0.0008086954768220681, + 0.0006470303301642589, + 0.0005123961225990102, + 0.0004016560727807059, + 0.0003116708503842432, + 0.0002394225401679027, + 0.00018209337495717952, + 0.00013711971862902152, + 0.00010223637178933069, + 7.547785240865859e-05, + 5.517412939106681e-05, + 3.9932380386715944e-05, + 2.8610987433177896e-05, + 2.0289343987079034e-05, + 1.4236351372317346e-05, + 9.879729904260742e-06, + 6.777612279609615e-06, + 4.593139440495998e-06, + 3.0725916465427275e-06, + 2.0269610366696515e-06, + 1.317775375963304e-06, + 8.437681551681755e-07, + 5.319902549599719e-07, + 3.305013078899456e-07, + 2.027599466205796e-07, + 1.2344608739201506e-07, + 7.522485840481262e-08, + 4.653284140815867e-08, + 2.978751050169318e-08, + 2.015558107861784e-08, + 1.4650418848756543e-08, + 1.1499020010758186e-08, + 9.640548293607227e-09, + 8.51259154631094e-09, + 7.38936840856595e-09, + 7.2107801976486525e-09, + 6.405218867332212e-09, + 5.955476952766655e-09, + 5.494972659009183e-09 + ], + [ + 0.031447568035490724, + 0.03128894518882016, + 0.030809329588392987, + 0.030026532585867904, + 0.028963151980047702, + 0.027650522713270315, + 0.026126164216475255, + 0.024431788965528625, + 0.02261198957831339, + 0.020711754954400603, + 0.01877504050825195, + 0.01684316817314694, + 0.014953346959194862, + 0.013137821563210483, + 0.011422604058972998, + 0.009827960949589199, + 0.008367914549402049, + 0.007050625265869996, + 0.005878930636991521, + 0.004851054009313377, + 0.00396141673324955, + 0.0032015178023596996, + 0.0025607778638170845, + 0.0020273170860772927, + 0.0015886507921065887, + 0.0012323073711644663, + 0.000946285623789249, + 0.0007193910818819539, + 0.0005414637619104349, + 0.0004035149470383542, + 0.0002977375192266037, + 0.00021751202655626587, + 0.00015731458871697874, + 0.00011262353437941288, + 7.97916233935677e-05, + 5.592728101448666e-05, + 3.8767033852696095e-05, + 2.6556970624187725e-05, + 1.7967825458431015e-05, + 1.1993202881467304e-05, + 7.895713120053514e-06, + 5.120994444471228e-06, + 3.2696342609275042e-06, + 2.0542279519940847e-06, + 1.2703562926700164e-06, + 7.745015833406055e-07, + 4.6730314679565996e-07, + 2.8108254736896157e-07, + 1.705914744528288e-07, + 1.0631586904331447e-07, + 6.947681085092208e-08, + 4.856957657911702e-08, + 3.664829087041384e-08, + 2.9773817666185666e-08, + 2.558687170053158e-08, + 2.2451697984399755e-08, + 1.9773052989715404e-08, + 1.8598801822295945e-08, + 1.6612973734706677e-08, + 1.5075991602593598e-08 + ], + [ + 0.06982893447053629, + 0.06946989048731698, + 0.06840396244291871, + 0.06666292031323831, + 0.06429895359525964, + 0.06138071169686159, + 0.057992237096984166, + 0.054226347941339424, + 0.050181692834718086, + 0.045958577065536264, + 0.04165480062271079, + 0.037362319896401534, + 0.03316388519852699, + 0.02913082500626517, + 0.02532177595459763, + 0.02178109692160964, + 0.018540004310813558, + 0.015616517654854924, + 0.01301684102346449, + 0.010736920430310042, + 0.008764236535922464, + 0.0070798523707794585, + 0.005660145146104358, + 0.004478619489713103, + 0.003507471450079956, + 0.0027189503768957454, + 0.0020863889092570197, + 0.0015848820978996078, + 0.001191866259788993, + 0.0008873554666960925, + 0.0006540447331240347, + 0.00047722539263785524, + 0.00034469257106593896, + 0.0002464095964630489, + 0.00017429475780871223, + 0.0001219431000915292, + 8.43455977426196e-05, + 5.764232882363103e-05, + 3.889351909703412e-05, + 2.5887271154276093e-05, + 1.6980440524450157e-05, + 1.0966191078360128e-05, + 6.965767867944703e-06, + 4.349465500849497e-06, + 2.668397918228854e-06, + 1.6100451086169193e-06, + 9.592012952481415e-07, + 5.676931734825063e-07, + 3.376744016159708e-07, + 2.064386647994278e-07, + 1.3169444587226848e-07, + 8.999084510988085e-08, + 6.632874103947333e-08, + 5.316248908468957e-08, + 4.457133297657443e-08, + 4.02126006726259e-08, + 3.6508268079655115e-08, + 3.3499726136110976e-08, + 3.066073850676606e-08, + 2.8312075646237107e-08 + ], + [ + 0.12184019650778478, + 0.12121724332860957, + 0.11935416720028041, + 0.11631018579503076, + 0.1121761901700366, + 0.10707588615243988, + 0.10115363563815112, + 0.09457199672419447, + 0.08750375592815482, + 0.0801245576069912, + 0.0726058150897413, + 0.0651081429692341, + 0.057776317414195685, + 0.05073496868938162, + 0.04408628520442521, + 0.037907943008673825, + 0.0322541025925072, + 0.027156039455137754, + 0.022624344295123902, + 0.01865159653506764, + 0.015215888404141857, + 0.01228367749164156, + 0.009813549926602372, + 0.007758989060804358, + 0.006071366962834107, + 0.004702088929054275, + 0.0036044454493093896, + 0.002734890868347459, + 0.0020541663989168623, + 0.0015272488901302917, + 0.0011239752283159993, + 0.0008187676762472539, + 0.0005902882295548934, + 0.0004210965985011471, + 0.0002971530763146605, + 0.0002073461323879388, + 0.00014298581628957395, + 9.738232596241873e-05, + 6.544786341718436e-05, + 4.3363374911756396e-05, + 2.8291555699284813e-05, + 1.8153164531980922e-05, + 1.1443336334940117e-05, + 7.079725107227498e-06, + 4.296978557885792e-06, + 2.561919946051475e-06, + 1.5074843570128246e-06, + 8.779261862103867e-07, + 5.116655128982492e-07, + 3.0523426679818403e-07, + 1.909494391727937e-07, + 1.2909816023297787e-07, + 9.4828372940806e-08, + 7.5858301425736e-08, + 6.507606050765681e-08, + 5.426563613574049e-08, + 4.96913108962278e-08, + 4.599298584803452e-08, + 4.2398968015950455e-08, + 3.8526378233353625e-08 + ], + [ + 0.18584913597166447, + 0.1848917669615319, + 0.18203993810633917, + 0.17738415009838668, + 0.17106521350415743, + 0.16326804243288168, + 0.1542147511747079, + 0.14415440987308903, + 0.1333516805370832, + 0.12207628250269091, + 0.11059000322222011, + 0.09913919484717383, + 0.08794438754768877, + 0.07719635711573732, + 0.06705095278647809, + 0.057626761574075314, + 0.049006104135711194, + 0.04123631316071604, + 0.03433290490194663, + 0.028284480450028314, + 0.023056635601538925, + 0.018597778424000493, + 0.01484418319738919, + 0.011724530237418878, + 0.009164107810240471, + 0.007088597364195471, + 0.005426521064822607, + 0.004111430138340715, + 0.003082984951812741, + 0.002288000757977756, + 0.001680500842425653, + 0.0012214457537084627, + 0.0008784019146561574, + 0.000624867169885803, + 0.00043956501920428464, + 0.0003056268983876749, + 0.00020990819491282364, + 0.00014230048808550852, + 9.512472826441864e-05, + 6.263277992053475e-05, + 4.0565297434096824e-05, + 2.5803645721399013e-05, + 1.6100716142568747e-05, + 9.841500117810081e-06, + 5.883630845341111e-06, + 3.4430347218727675e-06, + 1.976401632800269e-06, + 1.1199518784171127e-06, + 6.348611498340568e-07, + 3.656142532637007e-07, + 2.2564483384350684e-07, + 1.475405050061593e-07, + 1.0697644006131568e-07, + 8.563247468335957e-08, + 7.422060202916134e-08, + 6.701637275700193e-08, + 6.314595163810423e-08, + 6.124032635598986e-08, + 5.5733712797283336e-08, + 5.4539771893473197e-08 + ], + [ + 0.2598174034124492, + 0.2584687118954439, + 0.2544703047971543, + 0.24794297406098476, + 0.239083189491364, + 0.2281511753059839, + 0.21545934180234014, + 0.20135750856959286, + 0.18621921781015968, + 0.1704222798761182, + 0.15433488088836606, + 0.13830043442114223, + 0.12263025699841558, + 0.10759104987200035, + 0.0934004911774501, + 0.08022538510908286, + 0.06817933875386253, + 0.05732820612880023, + 0.04769289641418411, + 0.03925654842875815, + 0.031970036811080293, + 0.0257602400979113, + 0.020537299733944612, + 0.016200524153189046, + 0.012644972217387748, + 0.009766091351471648, + 0.007463650007973497, + 0.005644217542886037, + 0.004223628577211686, + 0.0031273942040006167, + 0.0022911840932353165, + 0.0016605799939050372, + 0.0011903988815797596, + 0.0008438065788437738, + 0.0005911919362742009, + 0.0004091925295364531, + 0.0002795707286473826, + 0.0001883877938853909, + 0.00012504059275567542, + 8.166293573260576e-05, + 5.238471281183247e-05, + 3.2946649841361656e-05, + 2.0271067023821947e-05, + 1.217934892901454e-05, + 7.132884854596646e-06, + 4.068973542472868e-06, + 2.2607897765697277e-06, + 1.2333806787901705e-06, + 6.689307150458071e-07, + 3.712194687434761e-07, + 2.1893241698178627e-07, + 1.4403095693580917e-07, + 1.0774874818566603e-07, + 9.011145232510043e-08, + 8.141773233573403e-08, + 8.34320672469783e-08, + 7.69004597455366e-08, + 7.157411886155532e-08, + 6.410697041434451e-08, + 5.860812728705847e-08 + ], + [ + 0.34139745672267013, + 0.33961977222568407, + 0.334346668127101, + 0.32573857492870034, + 0.31405464257918414, + 0.2996392226978931, + 0.282905061923253, + 0.26431775790555856, + 0.24436936047883775, + 0.22355848508089848, + 0.20237090083611542, + 0.18126161912171593, + 0.16063949503969235, + 0.14085650051499893, + 0.12219912959777028, + 0.10488626163613503, + 0.0890666097722769, + 0.0748256887403519, + 0.0621899154451437, + 0.051135012993315, + 0.04159523062179474, + 0.03347313849782008, + 0.02664870584003882, + 0.02098890605227421, + 0.01635458733171816, + 0.012607552144528517, + 0.00961519978342105, + 0.0072546641334892865, + 0.005415024550396461, + 0.003998278862010724, + 0.0029200022417983874, + 0.002108880948721358, + 0.0015058410658515989, + 0.0010627027032652078, + 0.0007408264464949397, + 0.000509803790513166, + 0.0003459879166466393, + 0.00023137272958071808, + 0.0001522319569587741, + 9.838006599042042e-05, + 6.231767532642567e-05, + 3.860071570424037e-05, + 2.331546381631184e-05, + 1.3691281517214727e-05, + 7.787273454253958e-06, + 4.283192609433718e-06, + 2.2757380445316043e-06, + 1.1739450729994547e-06, + 5.989710290552117e-07, + 3.1583076989271754e-07, + 1.8454364505331127e-07, + 1.269650662997515e-07, + 1.0250264533828268e-07, + 9.083615401126335e-08, + 9.492792369834187e-08, + 8.189481696294275e-08, + 7.451152919100389e-08, + 7.186958543520019e-08, + 6.924537657229228e-08, + 6.599501825899937e-08 + ], + [ + 0.42800726468203265, + 0.42577034366883243, + 0.4191306474873485, + 0.40829154852234945, + 0.3935802709556539, + 0.37543148242494123, + 0.35437088168435704, + 0.330983745412107, + 0.3058905171343219, + 0.27972028410398453, + 0.25308608236030605, + 0.22656134664984406, + 0.2006614351338949, + 0.1758280885652401, + 0.1524214186185368, + 0.13071535302715157, + 0.11089569994923144, + 0.09306795568259847, + 0.07726330208108166, + 0.06344906937227421, + 0.051540474842695215, + 0.041413330245582324, + 0.032914816987462944, + 0.025876302953278026, + 0.020121829300247966, + 0.015476817569107917, + 0.011774070298114411, + 0.0088591687943869, + 0.006592431892926384, + 0.00485102678378826, + 0.0035292863486857213, + 0.002538038667905722, + 0.0018036146405957176, + 0.0012659047230951929, + 0.0008769336636043446, + 0.0005991800919449246, + 0.0004033568182768136, + 0.0002671550934272661, + 0.00017379281222037397, + 0.00011080046119142485, + 6.904873824690329e-05, + 4.1921743016364913e-05, + 2.4692524257089224e-05, + 1.4046415653741019e-05, + 7.67366797306083e-06, + 4.002029307415473e-06, + 1.9864056511547665e-06, + 9.442760821457755e-07, + 4.428370576988997e-07, + 2.2581202411081326e-07, + 1.4309327038152828e-07, + 1.1583466157359527e-07, + 1.1822372790536931e-07, + 1.0695136191931412e-07, + 9.808588621755666e-08, + 8.594290718300466e-08, + 7.89954798058354e-08, + 7.720914094658321e-08, + 7.28608971767618e-08, + 6.885200881393642e-08 + ], + [ + 0.5169022655098002, + 0.5141869524132501, + 0.5061268234992344, + 0.49296902640623963, + 0.4751140190039043, + 0.4530937618662518, + 0.42754536852926, + 0.3991818041926663, + 0.3687584652037468, + 0.3370408702891306, + 0.30477510023911425, + 0.2726582495431597, + 0.24131387366187482, + 0.211279158342363, + 0.18298910048816303, + 0.15677397184640499, + 0.1328571409607659, + 0.11136366323852726, + 0.09232840453444346, + 0.07570874864218122, + 0.06139933305353963, + 0.0492466812751377, + 0.03906340885093326, + 0.03064323907477728, + 0.023771448967840537, + 0.018235053552480427, + 0.01383155989538661, + 0.01037318877462819, + 0.007690838454512855, + 0.005636171927381904, + 0.0040816906418562, + 0.0029202035671588356, + 0.002063098867370055, + 0.001438304491574013, + 0.000988860119539532, + 0.0006697352036169879, + 0.00044624090569672534, + 0.00029199741008812633, + 0.00018722133684917602, + 0.00011729600859123694, + 7.154403603728735e-05, + 4.2278995052832466e-05, + 2.406529491824927e-05, + 1.3088335826013656e-05, + 6.733828783372194e-06, + 3.239941059535895e-06, + 1.4451353221546432e-06, + 6.036732870508207e-07, + 2.6484480753643645e-07, + 1.602456245592525e-07, + 1.6359192010490458e-07, + 1.609671422558082e-07, + 1.5651426244625107e-07, + 1.3902728832362824e-07, + 1.2105864088337954e-07, + 1.0869279368081825e-07, + 9.539808955185721e-08, + 8.673202116595033e-08, + 8.157644848621434e-08, + 7.83455144607329e-08 + ], + [ + 0.6052613186100604, + 0.6020628966443551, + 0.5925693370777095, + 0.5770746577982908, + 0.5560513887999056, + 0.5301281269736748, + 0.5000587474241114, + 0.4666860078263821, + 0.4309021289097148, + 0.39361285109205035, + 0.3556978789631817, + 0.3179785092700767, + 0.2811901321460969, + 0.24596333504816614, + 0.2128085862596521, + 0.18211123884422656, + 0.15413347873542688, + 0.12901634534440234, + 0.10679759287925664, + 0.0874234198081707, + 0.07076578844895658, + 0.05664073439053181, + 0.04482496723180665, + 0.03507318756872374, + 0.027131130051326127, + 0.020747091608913696, + 0.015682248741572025, + 0.011715445792153474, + 0.008648289054039233, + 0.0063069078872189, + 0.004542436818721374, + 0.003229759629708341, + 0.0022654844683266256, + 0.0015667455515163227, + 0.0010671011931779053, + 0.0007148658014424152, + 0.0004702016937396028, + 0.00030297663413643585, + 0.00019068254354912527, + 0.00011675892794689112, + 6.918906064271382e-05, + 3.9404784089562305e-05, + 2.1356530241004086e-05, + 1.0865206604143414e-05, + 5.091216997229412e-06, + 2.143905842641932e-06, + 7.975008648187079e-07, + 2.98050164203046e-07, + 1.903056931658653e-07, + 2.423604530730278e-07, + 2.8541789212582e-07, + 3.151100923476693e-07, + 3.020361244110561e-07, + 2.580168680155149e-07, + 2.111493354386567e-07, + 1.7101826925495033e-07, + 1.400316649501346e-07, + 1.1921004296587504e-07, + 1.0385983166678317e-07, + 9.640543203300799e-08 + ], + [ + 0.6902871937153244, + 0.686614702548723, + 0.6757159854632104, + 0.6579285527125462, + 0.6337997390864659, + 0.6040539407925389, + 0.5695604426381969, + 0.5312900198809236, + 0.490273018817948, + 0.4475515010222864, + 0.40413738429400586, + 0.3609743703654484, + 0.3189072143709259, + 0.27865770296050013, + 0.24080947502132713, + 0.2058011123257054, + 0.17392894891814825, + 0.14535024874761568, + 0.1201030180164829, + 0.09812043283685076, + 0.07925070293366292, + 0.0632784911962898, + 0.04994373916568568, + 0.038962418113226635, + 0.03003990854639147, + 0.02288725916194305, + 0.017229096378116447, + 0.012811991446758025, + 0.009409077878048002, + 0.006821935327405915, + 0.004881223491006895, + 0.003444417665125553, + 0.0023955190869206187, + 0.001640248185142121, + 0.0011043009970115962, + 0.0007297354025929197, + 0.0004722088250283689, + 0.0002983085598787659, + 0.00018321896119025943, + 0.00010877960991136543, + 6.195106588099867e-05, + 3.3454859789389955e-05, + 1.684298508504392e-05, + 7.701393623772543e-06, + 3.072352860965922e-06, + 1.0178117453249082e-06, + 3.225908631920579e-07, + 2.885712042804471e-07, + 4.3375487230462303e-07, + 5.97961080822568e-07, + 6.770354467289775e-07, + 6.689010045257067e-07, + 6.019098580209889e-07, + 5.088299479586745e-07, + 3.9968938676412007e-07, + 3.0964401103693466e-07, + 2.3621142421274442e-07, + 1.8664211618064646e-07, + 1.5140260150346419e-07, + 1.3119161483833723e-07 + ], + [ + 0.7692809858901566, + 0.7651569603973722, + 0.7529198940674784, + 0.7329509512923813, + 0.7058682804920574, + 0.6724895182607294, + 0.6337951410201131, + 0.5908823703337387, + 0.5449117223680426, + 0.4970571587427411, + 0.4484569457402506, + 0.40017288140185825, + 0.35315308010585195, + 0.3082054701676551, + 0.2659822638262224, + 0.2269710272226213, + 0.19149859414154483, + 0.159735412877054, + 0.13171778073871074, + 0.10736389840794304, + 0.08649739374361476, + 0.06887096546964618, + 0.05418885124051136, + 0.0421279862055934, + 0.03235549086129528, + 0.024545540159809046, + 0.018388404094726616, + 0.013600041268651861, + 0.009926720289535203, + 0.007147514366120654, + 0.005073857731718207, + 0.0035479548405520666, + 0.0024416722518604893, + 0.0016514755615297558, + 0.0010958667404864881, + 0.0007117169044866953, + 0.0004509676291189177, + 0.0002775819333442793, + 0.00016497528346374037, + 9.38449786567979e-05, + 5.045743809608914e-05, + 2.5115586695555798e-05, + 1.1211967539216499e-05, + 4.227226996736936e-06, + 1.2308651061905153e-06, + 3.413806679860528e-07, + 4.5891340959327924e-07, + 8.491745712490829e-07, + 1.2304592266721679e-06, + 1.4427641140496766e-06, + 1.474418885845401e-06, + 1.3705935932864426e-06, + 1.1870508572804644e-06, + 9.654756125071766e-07, + 7.508552936964005e-07, + 5.602292866905814e-07, + 4.2163315000317906e-07, + 3.1058229273847696e-07, + 2.425910667027537e-07, + 2.1454563673198493e-07 + ], + [ + 0.8397368989390875, + 0.8351967371162753, + 0.8217239538032682, + 0.7997485316536157, + 0.7699472665420829, + 0.7332288871366361, + 0.6906797453982302, + 0.6435129995082937, + 0.5930123037382317, + 0.5404738956544122, + 0.4871554699047853, + 0.43422698521319586, + 0.3827314871519242, + 0.33355606829933515, + 0.28741414944442584, + 0.2448365321406455, + 0.20617563850420642, + 0.17161185306026738, + 0.14117658637082886, + 0.11477187468071819, + 0.09219613906306853, + 0.07317067313367262, + 0.057364272567854264, + 0.04441705861328697, + 0.033960296169783535, + 0.025633105977690505, + 0.019094120706708205, + 0.014031422500425566, + 0.010167054302203188, + 0.007259764664885736, + 0.005104083821251084, + 0.003529896528613631, + 0.002397907431884233, + 0.0015971797637853785, + 0.0010405301037299686, + 0.0006608229414196482, + 0.00040726752415182644, + 0.00024200456032129466, + 0.00013732889648166718, + 7.340917398400398e-05, + 3.608800564749861e-05, + 1.566086321156906e-05, + 5.553833780593161e-06, + 1.3934364162823076e-06, + 3.790957211153545e-07, + 8.365180928665583e-07, + 1.6452315166876865e-06, + 2.460308016211591e-06, + 2.9256106864986614e-06, + 3.0477265530887353e-06, + 2.908891597980235e-06, + 2.5849636158142897e-06, + 2.162831464398947e-06, + 1.720059033660828e-06, + 1.3173271945441537e-06, + 9.810655193920843e-07, + 7.11440573167338e-07, + 5.243695863772545e-07, + 4.1351655526810627e-07, + 3.227806432877691e-07 + ], + [ + 0.8994211707580555, + 0.8945095249954726, + 0.8799458726721312, + 0.8561906560018554, + 0.8239840341946619, + 0.7843151257083492, + 0.7383661883581998, + 0.6874565854536022, + 0.6329803054269871, + 0.5763461959457428, + 0.5189176403591919, + 0.46196153083834446, + 0.4066039978377404, + 0.353802202130442, + 0.30432166161880786, + 0.25872910566479174, + 0.21739672659559436, + 0.18051036905680545, + 0.14809394160286218, + 0.12003183701436218, + 0.09609730531019076, + 0.0759806703464184, + 0.05931759604349175, + 0.045714068279852915, + 0.03476793477276465, + 0.02608686308801322, + 0.01930151057475345, + 0.014075344970197967, + 0.010109951726880199, + 0.007146630286361245, + 0.004965897570630802, + 0.0033874422589037687, + 0.002264045172759038, + 0.0014788490034056381, + 0.000940730145982415, + 0.0005799742814741393, + 0.00034419620865342647, + 0.00019457958663451625, + 0.00010313170269510893, + 4.9877301232251e-05, + 2.0971754721468724e-05, + 6.9277274712170285e-06, + 1.4433159704822541e-06, + 4.983885493062368e-07, + 1.6313237547295814e-06, + 3.2170103664321223e-06, + 4.729145100952459e-06, + 5.6273507607453405e-06, + 5.935794209530517e-06, + 5.76207410926227e-06, + 5.23060196739684e-06, + 4.484306840919149e-06, + 3.6688881052058727e-06, + 2.8815263218450292e-06, + 2.1898709939055275e-06, + 1.6195256217852154e-06, + 1.1677568723782285e-06, + 8.701938897559977e-07, + 6.453685664520527e-07, + 4.983394744629702e-07 + ], + [ + 0.9464386819727904, + 0.9412180298988818, + 0.9257318188145823, + 0.9004745688010692, + 0.8662435696802921, + 0.8240969217699721, + 0.7752999339688255, + 0.7212659976214392, + 0.6634864032754979, + 0.6034666317260972, + 0.5426587074299888, + 0.48241257819424527, + 0.42392587251064007, + 0.368212120999208, + 0.31607909832628894, + 0.2681208640117639, + 0.22472283537488283, + 0.18607123638246512, + 0.1521796872176279, + 0.12291382326103265, + 0.09802158667247893, + 0.07716454679055006, + 0.05994760119689484, + 0.04594560739152813, + 0.034727360556435424, + 0.0258731095345921, + 0.018990018431859296, + 0.013721147090504987, + 0.00975129896316154, + 0.006808374637863393, + 0.004662603412752999, + 0.003126119352404149, + 0.0020463939420444052, + 0.0013030864014495918, + 0.0008029363807341587, + 0.00047519412893781547, + 0.0002670662373930082, + 0.00013999404787505792, + 6.634729010354396e-05, + 2.6798734433239268e-05, + 8.077171959744891e-06, + 1.3451194344535567e-06, + 8.73537024986031e-07, + 3.1544034199324406e-06, + 6.10315593820262e-06, + 8.703568147492382e-06, + 1.0339307897071195e-05, + 1.0986907257585952e-05, + 1.0767941488800696e-05, + 9.934061812443542e-06, + 8.700046314821901e-06, + 7.286498294114402e-06, + 5.865584120112264e-06, + 4.559533588672448e-06, + 3.4401667120251675e-06, + 2.5258545160296076e-06, + 1.8367639735681022e-06, + 1.3455890782358854e-06, + 9.942155583062196e-07, + 7.564400052396024e-07 + ], + [ + 0.9793038538108773, + 0.9738379291186573, + 0.9576255859877291, + 0.9311893291755294, + 0.8953718132534683, + 0.8512896397859321, + 0.8002798028850712, + 0.7438314243586915, + 0.6835159041309937, + 0.6209166922003431, + 0.5575607286870153, + 0.4948622379282153, + 0.4340750215626494, + 0.3762555286368926, + 0.322241538217282, + 0.272644905703886, + 0.2278566922442852, + 0.18805867374777938, + 0.15325116852285672, + 0.12328015974254547, + 0.09786908162800485, + 0.07665281829635581, + 0.05920894551502806, + 0.04508544485569103, + 0.033826590314774176, + 0.02499028100835885, + 0.01816504812819709, + 0.012978958642834798, + 0.009104032744119767, + 0.006258906394820429, + 0.004208570150497382, + 0.0027598092543890274, + 0.0017579328895237533, + 0.0010815561814594508, + 0.0006374633141345174, + 0.00035542508683257193, + 0.0001836682617663979, + 8.484884060426316e-05, + 3.254176043060564e-05, + 8.678917887733006e-06, + 1.0851524882322713e-06, + 1.9013934175714737e-06, + 6.247461288226632e-06, + 1.1269033887856043e-05, + 1.548299100788797e-05, + 1.829579098708055e-05, + 1.9448949762305753e-05, + 1.920694440006563e-05, + 1.7930948267537727e-05, + 1.595718859433313e-05, + 1.3623505521745878e-05, + 1.1204439613828513e-05, + 8.905154354881834e-06, + 6.865436436997796e-06, + 5.14904907374461e-06, + 3.788246813722354e-06, + 2.7542343982951307e-06, + 2.019410920814047e-06, + 1.4715612650599365e-06, + 1.112602667905787e-06 + ], + [ + 0.9969706707680043, + 0.9913325667584144, + 0.9746111438113213, + 0.9473510564038204, + 0.9104301127675238, + 0.865011355730207, + 0.8124860575626852, + 0.7544025075999219, + 0.6923930967258695, + 0.6280976300014645, + 0.5631003941505426, + 0.4988631043912947, + 0.43667612402767025, + 0.3776239863556766, + 0.322562075090811, + 0.2721094776361238, + 0.22665506369899402, + 0.18637109014045097, + 0.15124194340365626, + 0.12109274628530703, + 0.0956242920148441, + 0.07444727296564436, + 0.05711623018123718, + 0.043157085714548606, + 0.032094351870387484, + 0.02346983270848802, + 0.016859492802614773, + 0.011880663088825506, + 0.008198474282600343, + 0.005527432026037251, + 0.0036294976550164783, + 0.0023108800124435926, + 0.001418140926266113, + 0.0008311051394466782, + 0.0004585881554697252, + 0.0002326791538392575, + 0.0001039532983506623, + 3.725838091377472e-05, + 8.356932919286093e-06, + 9.008040771836582e-07, + 4.306990507197301e-06, + 1.202066903666956e-05, + 2.0224077821193854e-05, + 2.691875297722726e-05, + 3.137983260406278e-05, + 3.328182279869362e-05, + 3.2986964446366776e-05, + 3.104804264242553e-05, + 2.795927273253008e-05, + 2.423839642445411e-05, + 2.029316532006825e-05, + 1.6447587797643292e-05, + 1.2947945330197309e-05, + 9.915767904044662e-06, + 7.4220867480272535e-06, + 5.456768695694381e-06, + 3.990987253975998e-06, + 2.892815662393958e-06, + 2.1203398326893877e-06, + 1.582253855950369e-06 + ], + [ + 0.9988795982851885, + 0.99314767018651, + 0.9761486331081902, + 0.9484429479517303, + 0.9109331112829658, + 0.8648140954483985, + 0.8115146052513237, + 0.7526209748070929, + 0.6898061211354793, + 0.6247508324823816, + 0.5590709181585077, + 0.49425498234880066, + 0.4316158683627686, + 0.37224273816592973, + 0.3170019161118806, + 0.26650660974265333, + 0.22113485449807363, + 0.18104660883141122, + 0.14620532616861306, + 0.11641612847991524, + 0.09135849405531317, + 0.07062235160551555, + 0.05374459817752233, + 0.04023354348651204, + 0.029600391480823524, + 0.021377132354773214, + 0.015132529408029166, + 0.010479552034755221, + 0.0070818770011214635, + 0.0046540944259090425, + 0.0029602279167048806, + 0.0018096922757279384, + 0.0010526531654810216, + 0.000573117963201154, + 0.00028404725700047483, + 0.00012151098371444837, + 3.975107517224945e-05, + 6.857984530838264e-06, + 1.4504158754677665e-06, + 9.547986179373734e-06, + 2.2539463752786006e-05, + 3.545324542781071e-05, + 4.572091766336855e-05, + 5.23603533458704e-05, + 5.5363961828389664e-05, + 5.496955281644966e-05, + 5.196719193495123e-05, + 4.7176998394345906e-05, + 4.140108789202765e-05, + 3.5165218641646136e-05, + 2.8975814435888965e-05, + 2.3233767768288967e-05, + 1.8148127049793805e-05, + 1.3827458841033836e-05, + 1.0321491297852915e-05, + 7.578977996601097e-06, + 5.526385461751625e-06, + 4.0072244874949806e-06, + 2.929755212319644e-06, + 2.186669996087714e-06 + ], + [ + 0.9849705337193924, + 0.9792253548004288, + 0.9621874600749706, + 0.9344261385941126, + 0.8968575526265319, + 0.8506935244344249, + 0.7973795141522995, + 0.7385273222380678, + 0.675825203631681, + 0.6109688265631699, + 0.5455863894349444, + 0.48117240248364973, + 0.41904165867416876, + 0.3602794624779896, + 0.3057381625686699, + 0.25601886676493424, + 0.21148220322097971, + 0.17226369039078343, + 0.13831530638708897, + 0.10941691431486826, + 0.08522868494099502, + 0.06532527921032752, + 0.04922861363158429, + 0.036436838170867174, + 0.026453753585935796, + 0.018808663574534885, + 0.013068747848756937, + 0.00884907599684361, + 0.005817003921291556, + 0.003692555753535143, + 0.0022460604971236836, + 0.0012937267607126442, + 0.0006924630047566134, + 0.00033300477166653045, + 0.00013450275917790752, + 3.8595272970394876e-05, + 4.420969324645119e-06, + 4.233552694117531e-06, + 2.0195116514282423e-05, + 4.1177842012609473e-05, + 6.087761454922645e-05, + 7.612735624209261e-05, + 8.576858373122412e-05, + 8.999422055298284e-05, + 8.9231229760251e-05, + 8.464805602433992e-05, + 7.731001229688643e-05, + 6.83536797433202e-05, + 5.875006474120433e-05, + 4.9099181110045545e-05, + 3.99637800176322e-05, + 3.1742295504205756e-05, + 2.4613386851254186e-05, + 1.8676477525874202e-05, + 1.3908300252221259e-05, + 1.0225628016312717e-05, + 7.421039355298614e-06, + 5.379220068432494e-06, + 3.934104111204155e-06, + 2.9388037191833028e-06 + ], + [ + 0.9556829028617344, + 0.9500059070260606, + 0.9331693755554862, + 0.9057445934302121, + 0.8686494978337483, + 0.8230978343303907, + 0.7705376951659644, + 0.7125760327021741, + 0.6509001589689173, + 0.5871986152667031, + 0.5230860152354779, + 0.46004436357981143, + 0.39936681925697726, + 0.34212467251152706, + 0.2891431679699824, + 0.2409985558322096, + 0.1980264577371278, + 0.1603370607245586, + 0.12786166674224897, + 0.10035918808675735, + 0.07747506432510225, + 0.05877006788462352, + 0.04375882058698155, + 0.03193416519193119, + 0.022800671653645452, + 0.015890287958840944, + 0.01077574510067483, + 0.007080381325645249, + 0.004480565038798084, + 0.0027068330582208327, + 0.0015398767460891906, + 0.0008063367649595727, + 0.00037286800990982675, + 0.0001392709945945243, + 3.2807097819731156e-05, + 2.110681066559099e-06, + 1.2315517625266934e-05, + 4.063160741155541e-05, + 7.333682033410496e-05, + 0.00010254051019711766, + 0.00012448863895437635, + 0.00013796305225920617, + 0.00014330418234527502, + 0.00014177144781219833, + 0.0001345965117289953, + 0.00012343464827684297, + 0.00010989311425600861, + 9.521953228866833e-05, + 8.043733805863037e-05, + 6.631994995065988e-05, + 5.34403745814835e-05, + 4.210438110717894e-05, + 3.244933267543271e-05, + 2.452980644493147e-05, + 1.8216656829146367e-05, + 1.3361239971299425e-05, + 9.697185134633002e-06, + 7.0284187259812135e-06, + 5.13984618898415e-06, + 3.828304707262911e-06 + ], + [ + 0.9119532307376337, + 0.9064227606436422, + 0.8900215081297262, + 0.8633153288864104, + 0.8272118676775136, + 0.7829127265266004, + 0.7318478758806275, + 0.675602676856545, + 0.6158369443821013, + 0.5542084968022692, + 0.49230292706638973, + 0.4315659338572501, + 0.37325457744499374, + 0.318400896411734, + 0.26779580851987417, + 0.2219799116463556, + 0.1812566965264144, + 0.14570719069007815, + 0.11524085431672279, + 0.08959855141192895, + 0.06841119871737317, + 0.05123346693126955, + 0.03757483798552711, + 0.02693275835822609, + 0.018818460129295007, + 0.012772673000546917, + 0.008380674833766233, + 0.005279517911668605, + 0.0031606498222333597, + 0.001769230275532687, + 0.0009006005430569134, + 0.0003952822791498836, + 0.0001321802026884677, + 2.247111226471724e-05, + 3.1025022591173786e-06, + 3.1001082355393836e-05, + 7.80834468221095e-05, + 0.00012743931796978193, + 0.0001696047694386592, + 0.00020027062040771547, + 0.00021836605373458138, + 0.00022468732035429048, + 0.00022106126369268633, + 0.00020979640210825836, + 0.0001929739124475861, + 0.0001724782661376614, + 0.000150409520030043, + 0.00012816457950457687, + 0.0001067550915817706, + 8.707433979429895e-05, + 6.953454348585765e-05, + 5.4376212138714184e-05, + 4.170038871334831e-05, + 3.140121021250671e-05, + 2.3290423381049216e-05, + 1.7028255040468884e-05, + 1.235011624862507e-05, + 8.948975321214574e-06, + 6.531587939078009e-06, + 4.848281094785945e-06 + ], + [ + 0.855162620604994, + 0.849853422721743, + 0.8341095027172591, + 0.8084843782476498, + 0.7738655262130524, + 0.7314246912706226, + 0.6825562436072318, + 0.6288024485115427, + 0.5717766215361629, + 0.5130870845940405, + 0.4542643521644756, + 0.39669966954352964, + 0.34159532114354935, + 0.28993127855441186, + 0.24245015338795303, + 0.19964843310638195, + 0.16179139609917065, + 0.12893327506527705, + 0.1009457194706263, + 0.0775677577700774, + 0.0584156947531368, + 0.043041728257222474, + 0.03095888954038043, + 0.021673765172128816, + 0.014710640500274461, + 0.00962658205083433, + 0.006025407005150036, + 0.0035639143753658548, + 0.0019531449268150518, + 0.0009576202518674436, + 0.00039107097215790104, + 0.00011069727972131965, + 1.0187216542046424e-05, + 1.387233601814181e-05, + 6.97947055791604e-05, + 0.00014413875136152376, + 0.0002163696118375766, + 0.0002756698626355868, + 0.0003172851053217184, + 0.0003405319265397434, + 0.0003470382728675444, + 0.00033958639913622864, + 0.0003215678611656464, + 0.0002957382390644686, + 0.00026537261491051264, + 0.00023248555761910117, + 0.00019936458781269852, + 0.00016750082384128594, + 0.00013794356727463242, + 0.00011143210392320309, + 8.827592728181778e-05, + 6.860262161755919e-05, + 5.2356779418088296e-05, + 3.927979776142506e-05, + 2.9045126922490598e-05, + 2.1200094187776024e-05, + 1.5360024864402518e-05, + 1.111598407488841e-05, + 8.097611372027374e-06, + 5.998899970238319e-06 + ], + [ + 0.7871161262983364, + 0.7820923650758252, + 0.7672097700342903, + 0.7429981363199726, + 0.7103134385105048, + 0.6702839744716153, + 0.6242513395162886, + 0.5736968520782266, + 0.5201667664398663, + 0.4651976783408458, + 0.4102465849605002, + 0.3566306806635462, + 0.30548255679588127, + 0.2577158293316544, + 0.21401434560289798, + 0.17482213529523075, + 0.1403617884433519, + 0.11065398806632468, + 0.08555101195510618, + 0.06476432333943426, + 0.047919022524233905, + 0.03456551513229459, + 0.024225354319424994, + 0.01642229370484648, + 0.010699287343539542, + 0.006636353978100004, + 0.003861926379526691, + 0.00205736271296541, + 0.000958368670986611, + 0.00035257796140287037, + 7.53323062059008e-05, + 3.1775471373259436e-06, + 4.645536965659204e-05, + 0.00014414837591709777, + 0.0002564367302534885, + 0.00035945218247475087, + 0.00044059767550559415, + 0.0004953601086563308, + 0.0005237535536439851, + 0.0005286708848845998, + 0.0005143213174246769, + 0.0004853232629644741, + 0.00044631092518933167, + 0.00040088289676578975, + 0.0003524307758256139, + 0.0003038721612569369, + 0.00025695782767672386, + 0.0002133914630006766, + 0.00017402096046859175, + 0.00013933820699967164, + 0.00010961569584294384, + 8.469482989424475e-05, + 6.433705229960412e-05, + 4.8119692568690776e-05, + 3.545223532493835e-05, + 2.582480577193005e-05, + 1.8681489755966325e-05, + 1.3503192479643992e-05, + 9.816911557778293e-06, + 7.2607791355714044e-06 + ], + [ + 0.7099666040041819, + 0.7052983574728326, + 0.6914553461764636, + 0.6689508166605896, + 0.638589677231257, + 0.601459227355426, + 0.5588240505023877, + 0.5120874338942382, + 0.4627100589702404, + 0.4121378064964836, + 0.36173576074232067, + 0.31273242585899386, + 0.266175021671391, + 0.2229008214007386, + 0.18352051421558102, + 0.14842461339247182, + 0.11779092305080877, + 0.09159487841355936, + 0.06967673574625888, + 0.05173709143063729, + 0.03738879245388594, + 0.026201819360610494, + 0.017710292884058, + 0.011459013420307506, + 0.007018549647473037, + 0.0039933846992514545, + 0.0020459104910264645, + 0.0008856864311997345, + 0.00027695457066502266, + 3.391176899787594e-05, + 1.6090732121003365e-05, + 0.00012148799563400491, + 0.000278529441808762, + 0.00044192035939456033, + 0.0005845993470659619, + 0.0006929807665148068, + 0.0007625398654727998, + 0.0007950122462094289, + 0.000795038060458318, + 0.0007688580772983496, + 0.0007230223836815038, + 0.0006637213871021306, + 0.0005966296140133694, + 0.0005256973802429093, + 0.000454715553613081, + 0.0003866242682650034, + 0.0003231669161058677, + 0.000265633703181582, + 0.00021470276656704396, + 0.0001706146626224827, + 0.00013333274500561672, + 0.00010247726404936075, + 7.74930502912012e-05, + 5.7732071494293134e-05, + 4.240793488284461e-05, + 3.082037720879832e-05, + 2.2254357816371948e-05, + 1.6045157524334796e-05, + 1.166237822035065e-05, + 8.599225166487947e-06 + ], + [ + 0.6261606437503644, + 0.6218936764830316, + 0.6092462848448178, + 0.5886958854822415, + 0.561003220077079, + 0.5271781747269388, + 0.4883994374505258, + 0.4459938604401059, + 0.4013093633191123, + 0.35568517547159256, + 0.31038078896967775, + 0.2665208467246438, + 0.22505559459165206, + 0.18673394654209932, + 0.1520947152124757, + 0.12145778343293079, + 0.09495212204286968, + 0.07252551149818028, + 0.053994387522797026, + 0.039051369544841535, + 0.027313071151431383, + 0.018363319833134363, + 0.011757953762771323, + 0.007071095288012568, + 0.003899837807065772, + 0.001889080091135139, + 0.0007314834456498804, + 0.00017140361243716455, + 5.733524837923295e-06, + 7.72351740751959e-05, + 0.00027181614560577085, + 0.0005103070880772513, + 0.0007401456082827591, + 0.0009322981870904861, + 0.0010726865732217994, + 0.0011579870461093742, + 0.0011915435754793174, + 0.0011810427022721096, + 0.0011353817091172063, + 0.0010637596887091948, + 0.0009746166980670018, + 0.0008755512723923199, + 0.0007725962133455016, + 0.0006701181383842607, + 0.0005718884249936778, + 0.0004804650941850986, + 0.00039750440735890374, + 0.00032376988233135014, + 0.0002596350481147568, + 0.00020487916356043618, + 0.00015914398691442422, + 0.00012167850842472486, + 9.159628761107746e-05, + 6.796879543645993e-05, + 4.9770888218073e-05, + 3.6076016363609454e-05, + 2.5982774400104503e-05, + 1.870737052460074e-05, + 1.3560696886068552e-05, + 9.98117675739138e-06 + ], + [ + 0.5383536674434575, + 0.534529138665905, + 0.5231946856787346, + 0.5047921890424502, + 0.48002656349982986, + 0.4498210659338308, + 0.4152775723485192, + 0.377593305312155, + 0.338001725416104, + 0.29773987138961255, + 0.25793766579631494, + 0.21960512117230604, + 0.1835855395505498, + 0.15053250092082393, + 0.12090389247269288, + 0.09495302854265789, + 0.07275936437015433, + 0.054240658180174796, + 0.039185241656362765, + 0.027291984896944097, + 0.018186838554671056, + 0.011460658803622214, + 0.006708862627212481, + 0.0035342943205171197, + 0.0015716445102120832, + 0.0005040622786459376, + 6.254340479179518e-05, + 2.876383379333778e-05, + 0.00023330651418244306, + 0.0005505739392617808, + 0.0008939977585264977, + 0.0012080229074365916, + 0.0014594325732519866, + 0.0016354853292480864, + 0.0017348592329496952, + 0.0017640893860264267, + 0.0017338640377379726, + 0.001657263329140579, + 0.0015468145076278268, + 0.001414133448850518, + 0.0012692724479412695, + 0.001120263078471175, + 0.000973541428731363, + 0.0008332876441374531, + 0.0007029058769304483, + 0.0005845019772055413, + 0.00047913951370141074, + 0.000387084174438656, + 0.0003081544430093455, + 0.00024165165427649616, + 0.00018657272541870284, + 0.00014191814251070012, + 0.00010635443079743783, + 7.859806509882433e-05, + 5.7356047972262065e-05, + 4.144037145024229e-05, + 2.9769407210674068e-05, + 2.1378219283102992e-05, + 1.5461424159318535e-05, + 1.1345169319274043e-05 + ], + [ + 0.4493307407496247, + 0.44597703904070235, + 0.4360394933818782, + 0.4199205673848396, + 0.3982604689115503, + 0.3718985570639639, + 0.34182365040142443, + 0.3091237649321579, + 0.27491084837498775, + 0.24026506628660524, + 0.20621446450260938, + 0.17363519372636316, + 0.14325691918924016, + 0.11563788401772034, + 0.09113874195600744, + 0.06995823071691637, + 0.05212274375280265, + 0.03751907482908896, + 0.025920601400695686, + 0.017026794597521714, + 0.01047735690359704, + 0.005888234531051345, + 0.0028877559563992234, + 0.0011128150837845206, + 0.0002442959485000012, + 5.935232795446819e-06, + 0.0001700543700729973, + 0.0005578074087641202, + 0.0010353989103781323, + 0.001511016093353247, + 0.001924478147507623, + 0.0022446189549898614, + 0.0024572630107573905, + 0.0025654824903502647, + 0.0025800232536300895, + 0.0025164805478913263, + 0.0023920328131867316, + 0.002224402435338185, + 0.002029021373444875, + 0.0018190836547841377, + 0.0016054563224105394, + 0.0013963097619325493, + 0.0011977960116348906, + 0.0010135629363481698, + 0.0008462577796617389, + 0.000697258507148604, + 0.0005668322035288369, + 0.00045449737201818367, + 0.0003593860649764719, + 0.0002800695047419099, + 0.00021502745526525343, + 0.0001627344881427547, + 0.00012140536444314429, + 8.932856480371329e-05, + 6.493969816119255e-05, + 4.675609204741087e-05, + 3.3479453341366104e-05, + 2.397230744825776e-05, + 1.727531393272187e-05, + 1.2633645428094773e-05 + ], + [ + 0.36191510829277235, + 0.35904759974489486, + 0.3505535967048113, + 0.3367925725158283, + 0.3183355667885913, + 0.2959290170189278, + 0.27045356910048063, + 0.24286456504387113, + 0.21413837477218217, + 0.18523336546863667, + 0.15701559822525604, + 0.1302508129691698, + 0.10554674754375902, + 0.08335480347636912, + 0.06396005080696734, + 0.0474872421053871, + 0.033919660489285644, + 0.023115219253375063, + 0.014839343498738868, + 0.008789793776462829, + 0.004631504043253796, + 0.002010123905673784, + 0.0005849514886300187, + 4.124114882697675e-05, + 0.00010265945085455799, + 0.0005381820172995677, + 0.0011636102635243107, + 0.0018409924206977272, + 0.0024733221600311594, + 0.003001655747567149, + 0.003393053692639054, + 0.003639784005340355, + 0.003745796766621589, + 0.003728966173588074, + 0.0036109348331152904, + 0.0034152701620240957, + 0.003164564620283624, + 0.0028799395427427364, + 0.0025787994188267802, + 0.002275090810959125, + 0.0019797544857868784, + 0.0017004192467257927, + 0.0014423815536518164, + 0.0012082416005414034, + 0.00099965638207044, + 0.0008168519234911702, + 0.0006590161337925725, + 0.0005247613366361286, + 0.0004122117675615157, + 0.00031932021624365075, + 0.00024378191948085833, + 0.0001835600590194387, + 0.0001362734134060959, + 9.982416123293386e-05, + 7.225693777475304e-05, + 5.182402486968147e-05, + 3.6971751725443865e-05, + 2.6368714217298427e-05, + 1.8931731873064108e-05, + 1.379332265736242e-05 + ], + [ + 0.27887713358172367, + 0.27649874475110364, + 0.26945670355849427, + 0.2580654468885174, + 0.24282348840961757, + 0.22438078038250925, + 0.20350142064899218, + 0.1810101267099216, + 0.15774784513196047, + 0.13452322100814662, + 0.11207070748621618, + 0.0910101583584737, + 0.07185006532816608, + 0.054931551717234975, + 0.04045679757925596, + 0.02848730692717927, + 0.018963259881427132, + 0.011719462060491348, + 0.006515616631268395, + 0.0030617101816357564, + 0.0010416340178427323, + 0.00013937897187011353, + 5.388027468639728e-05, + 0.0005163863663068428, + 0.0012978848424045483, + 0.0022145529928889077, + 0.003126750028686069, + 0.0039378583175484, + 0.004587484264627721, + 0.005048924072669096, + 0.005315392872054018, + 0.005401315772558338, + 0.005327247776633476, + 0.0051243863832329045, + 0.004823720740322963, + 0.00445516164700407, + 0.004045354464653527, + 0.003617563051028377, + 0.0031900220983605435, + 0.0027764709058215606, + 0.0023869973798434693, + 0.0020279541386473993, + 0.0017032493675456259, + 0.0014139534764045212, + 0.0011602348334810288, + 0.0009408012788573368, + 0.0007536329139165396, + 0.0005960886193442264, + 0.0004653002345998321, + 0.0003583577776002617, + 0.00027215247340700035, + 0.00020375021503513037, + 0.00015049681858267142, + 0.00010971298775879965, + 7.904475710154343e-05, + 5.6439379783999794e-05, + 4.008083430517611e-05, + 2.8461158607755928e-05, + 2.0346723850484917e-05, + 1.4761771796094978e-05 + ], + [ + 0.20284942344109122, + 0.20095054587604033, + 0.1953308486697963, + 0.1862590327167732, + 0.17415967717005446, + 0.15958421448690063, + 0.1431788325347427, + 0.12563574437342778, + 0.1076553973948365, + 0.08990386153630203, + 0.0729765669121568, + 0.05736406242439783, + 0.04345771840475864, + 0.03150080423111063, + 0.02161600141207127, + 0.013806239639245144, + 0.00797364580105921, + 0.003935464020634988, + 0.0014512265427612486, + 0.00024616817252829764, + 3.3612348247790634e-05, + 0.0005351736163129527, + 0.0014933370030722447, + 0.002688356153476741, + 0.003940238166866437, + 0.00511324665228425, + 0.006112344116600001, + 0.006881683075006297, + 0.007396347288738671, + 0.0076595791719336614, + 0.007691417649338082, + 0.007523931307527472, + 0.00719318301614776, + 0.006741442783626131, + 0.006207199718422886, + 0.0056249390335765094, + 0.005023652104142981, + 0.004427317156499362, + 0.0038536941094210833, + 0.0033151853590235474, + 0.0028201707334395048, + 0.0023729957811640615, + 0.0019753816466328506, + 0.0016264378812110502, + 0.0013244285430688632, + 0.001066268552333979, + 0.0008483584340240192, + 0.0006667194522935817, + 0.0005172885688205736, + 0.0003960070181731019, + 0.0002990320179251632, + 0.00022261188969628285, + 0.00016354579000307201, + 0.00011859050173155839, + 8.5002944435283e-05, + 6.037757409870978e-05, + 4.2656947195908546e-05, + 3.013625258575479e-05, + 2.143684773286748e-05, + 1.5477738649517048e-05 + ], + [ + 0.13624256161514084, + 0.1348009540475825, + 0.13053729212560058, + 0.1236744880558227, + 0.11456350450505436, + 0.10365773987409418, + 0.09148654092555765, + 0.07861086183130754, + 0.06559261134752664, + 0.05295798905540311, + 0.04116737964123151, + 0.030592168080516704, + 0.021495933885577443, + 0.014044608300113646, + 0.008282724742938254, + 0.004161305255310559, + 0.001550883836245661, + 0.0002573745604362296, + 4.617734922566557e-05, + 0.0006628033621747689, + 0.0018542001408013448, + 0.0033841152933694724, + 0.005038768367150761, + 0.00665315040896221, + 0.008093149263082803, + 0.009272213971878693, + 0.010138924901939012, + 0.010676688166369087, + 0.010894100843068463, + 0.010822525564437984, + 0.010504350331405926, + 0.009988658323968492, + 0.009323762358043093, + 0.008560637694329694, + 0.007742898201388436, + 0.006907401975581538, + 0.0060840859832323735, + 0.005295706693958635, + 0.00455790007046216, + 0.003881098623671194, + 0.003270667824589051, + 0.0027282029476679943, + 0.0022526771184159977, + 0.0018406947259426763, + 0.0014881629618617054, + 0.0011899351302639132, + 0.0009405261561184938, + 0.0007345042660842235, + 0.0005663626477389082, + 0.00043101385563349136, + 0.00032354950788044567, + 0.0002395474408578261, + 0.00017487585697280967, + 0.0001260745167951265, + 8.984046579225674e-05, + 6.343318628085715e-05, + 4.4548184513144436e-05, + 3.128498760331726e-05, + 2.212376074535561e-05, + 1.5874055200826695e-05 + ], + [ + 0.08116929963638046, + 0.08015074741783638, + 0.07714215042923649, + 0.07232171269895225, + 0.06596851611417147, + 0.058440924586578125, + 0.05015420172630041, + 0.04154307117800872, + 0.03303624360951062, + 0.025026189926362567, + 0.01784492298273816, + 0.011746023736496788, + 0.006893859690249231, + 0.0033590427619796396, + 0.0011305012001401537, + 0.00011277645454577478, + 0.00015218160166507062, + 0.0010503932602528134, + 0.002584742225268933, + 0.004526230819173381, + 0.006659424408458088, + 0.008793131814773533, + 0.0107593274236754, + 0.012446894499658332, + 0.013768787345409579, + 0.014685790505470383, + 0.01518831647759096, + 0.015296384879553466, + 0.015049260327437659, + 0.014503289871848582, + 0.013720005241672365, + 0.012760652088415085, + 0.011687851994851393, + 0.010553369479653154, + 0.009404944697313896, + 0.008280010440451766, + 0.00720676598537987, + 0.006205370746881519, + 0.005288195570204821, + 0.004461937790698556, + 0.003728247004370261, + 0.0030851478956308706, + 0.002528223021198608, + 0.0020511026369825864, + 0.0016469289070658965, + 0.0013081880708862605, + 0.0010273927921078784, + 0.0007972992372906294, + 0.0006109992049682792, + 0.0004619624783700223, + 0.00034473024964566326, + 0.00025362959879303215, + 0.00018402753643712738, + 0.000131767559076286, + 9.327481688224341e-05, + 6.540982248980329e-05, + 4.561684661899417e-05, + 3.18113254648436e-05, + 2.2341720242183533e-05, + 1.5924521462911167e-05 + ], + [ + 0.03938817844064645, + 0.03873471995721286, + 0.036849360568351294, + 0.03385404580909959, + 0.02995942281087755, + 0.025433680836981762, + 0.02058390974740583, + 0.015725838676758058, + 0.01116351058257495, + 0.007164569717885529, + 0.0039423643681523145, + 0.0016429258597367635, + 0.00033821020857265413, + 2.5674452401368342e-05, + 0.0006364349123217682, + 0.002042178411822101, + 0.004073453798099441, + 0.006535152357615029, + 0.00922278048323789, + 0.011937811782699358, + 0.014505844337667278, + 0.01677939198081402, + 0.01864754004467304, + 0.020042152692410994, + 0.0209253024502377, + 0.02130295995854074, + 0.021204314742497114, + 0.020682746099918485, + 0.019804469205555376, + 0.0186469304250906, + 0.017287089719905783, + 0.01579625548666449, + 0.01424331646729285, + 0.012682193255191822, + 0.011161069604903486, + 0.009714770274573615, + 0.008367799550524286, + 0.007136233313451082, + 0.006027646304853457, + 0.0050436842711098296, + 0.004181391069496236, + 0.0034344521519626423, + 0.002794459625114965, + 0.0022515810726786226, + 0.0017959250789455496, + 0.0014173106576757465, + 0.0011059952793073954, + 0.0008527788579506376, + 0.0006493789641231143, + 0.00048783308110597465, + 0.00036162088028851233, + 0.00026424900248521677, + 0.00019038327859170816, + 0.00013531535971986831, + 9.506329284008474e-05, + 6.613856212040786e-05, + 4.5748925025253034e-05, + 3.1639605377086405e-05, + 2.202665309510933e-05, + 1.559859485719034e-05 + ], + [ + 0.012192505880752045, + 0.011868789525821327, + 0.01094817681809051, + 0.009517109086490718, + 0.007722750698332452, + 0.0057495546760301715, + 0.003805399434832375, + 0.0020964802759686043, + 0.0008125514386224083, + 0.0001087693993087244, + 9.256036897824993e-05, + 0.0008151022094002555, + 0.0022684797098997404, + 0.004388233231936358, + 0.0070622061478156665, + 0.010136212835659875, + 0.01343627425169825, + 0.016777252331608036, + 0.01997931715771678, + 0.022879059880239278, + 0.025345900213431284, + 0.02727998982014429, + 0.028619779857814963, + 0.029346393445799066, + 0.029466114182592523, + 0.029026886118528314, + 0.028092889664483534, + 0.026746678691331786, + 0.025076975048454377, + 0.02317803831488677, + 0.02113689194486213, + 0.019033935896444015, + 0.016937714110410625, + 0.014902386416050068, + 0.01297269194011166, + 0.0111789208506505, + 0.009539975525214165, + 0.00806570418881965, + 0.006757515109448411, + 0.005610996011919087, + 0.004617664210539884, + 0.003766071576285478, + 0.0030434156292573128, + 0.002435910963403503, + 0.0019302729557860406, + 0.0015134639099376658, + 0.0011733933997567787, + 0.0008988573335139337, + 0.0006798969507790324, + 0.0005073380317794579, + 0.0003732288303926889, + 0.0002707784868775319, + 0.00019355458829042497, + 0.00013640887389404423, + 9.500581290193598e-05, + 6.549082723471978e-05, + 4.4864332818038546e-05, + 3.072192140160639e-05, + 2.1188795297022653e-05, + 1.4856227740830126e-05 + ], + [ + 0.00046525921158669563, + 0.0004089765154704004, + 0.00027250744888956583, + 0.00010885859882249336, + 7.88858070504872e-06, + 7.899080323349645e-05, + 0.0004407130097758397, + 0.0012020916056002316, + 0.002452310738740164, + 0.004248088643016379, + 0.00660544720401096, + 0.009495575997975606, + 0.012845196279716815, + 0.01654129726701592, + 0.0204424406034493, + 0.02437830511547595, + 0.028180561821788165, + 0.03168172889498056, + 0.03473264966684244, + 0.037209088979321576, + 0.03902647757224051, + 0.04013311683529524, + 0.0405158711197305, + 0.040199139237407575, + 0.03924082471263672, + 0.03771629368502598, + 0.035723560511773195, + 0.03336947487581365, + 0.030760478022200735, + 0.028002450050538873, + 0.02518902931167889, + 0.022402707785988404, + 0.019710255772614243, + 0.01716178253330278, + 0.014796018247879435, + 0.01263604452290263, + 0.010693107426887156, + 0.008968908933555118, + 0.007457619485730631, + 0.00614758879377186, + 0.005024032612885456, + 0.0040698022149385565, + 0.0032669437264938005, + 0.0025977391966486123, + 0.0020450682924546986, + 0.001592957880188052, + 0.0012267786797571542, + 0.0009333737850739315, + 0.000701015021359728, + 0.000519262065388002, + 0.00037904066919600924, + 0.00027270091262765245, + 0.00019319448522592982, + 0.00013491790054786235, + 9.296658731510215e-05, + 6.339124394163531e-05, + 4.2926277855206876e-05, + 2.9029337319486196e-05, + 1.978939752100704e-05, + 1.3719478179340352e-05 + ], + [ + 0.004575137876206896, + 0.004723790905366815, + 0.0051707906918865764, + 0.005951154869030193, + 0.007101166318098754, + 0.008664977446534132, + 0.010683818837759646, + 0.013183493522684966, + 0.016167879902995643, + 0.019611493689856204, + 0.023455635996722, + 0.027607992614863082, + 0.031945796672130884, + 0.03632227025080112, + 0.040575813932014176, + 0.04454477201803519, + 0.04806304866248443, + 0.05099272997156935, + 0.0532209863355377, + 0.05466606555139205, + 0.05529096341698464, + 0.055092365007159166, + 0.054101860408580935, + 0.05238873124724499, + 0.05004909293412104, + 0.04718925703311752, + 0.04393308307757329, + 0.04040627248905429, + 0.03672770162066061, + 0.033009681157935025, + 0.02934748046271128, + 0.02582121041872805, + 0.022492230857677695, + 0.019403031558533228, + 0.016583440181744857, + 0.014046917742471151, + 0.011795004346578052, + 0.009819883165406811, + 0.0081071221852082, + 0.006637007291710592, + 0.005387507344311932, + 0.004335334160391434, + 0.0034571886089532714, + 0.0027309636775606893, + 0.0021356810226437328, + 0.0016522997563542736, + 0.0012636274911419143, + 0.000954481985909984, + 0.0007114142035066728, + 0.0005227463201541465, + 0.00037836231634758927, + 0.0002694516106191144, + 0.0001890783754424401, + 0.00013058384207090317, + 8.888871273106342e-05, + 5.982959618307862e-05, + 3.995038305288968e-05, + 2.6630117196962886e-05, + 1.7878412938469565e-05, + 1.2224127250344998e-05 + ], + [ + 0.024391257517780283, + 0.02466872232701212, + 0.025498439694641918, + 0.026882493688257243, + 0.028818502489925464, + 0.03129639034545103, + 0.03429346413875575, + 0.037767768718504145, + 0.04165469144076119, + 0.045864200039831035, + 0.050280826629714816, + 0.05476640431372167, + 0.05916550490050777, + 0.06331328743620508, + 0.06704451301720468, + 0.07020929972547348, + 0.0726621796731565, + 0.07429892824076759, + 0.07504811902546794, + 0.07487313408676191, + 0.07378523532656822, + 0.07182780927641022, + 0.06907574539782614, + 0.06563791516795525, + 0.06164393928560999, + 0.05722607775490784, + 0.05252818262667343, + 0.04768885188605462, + 0.04283342119940476, + 0.03807543323168806, + 0.03350684060286582, + 0.029200961464781437, + 0.025209807733317532, + 0.02156504074550005, + 0.01828489724672734, + 0.01537082491418863, + 0.012812935004826479, + 0.010592675744516812, + 0.008685384531371887, + 0.007062871775642785, + 0.005695317996117619, + 0.00455289053767349, + 0.003606627560888801, + 0.002829960001130341, + 0.0021979235571422204, + 0.0016884465817990923, + 0.001281784060141039, + 0.0009606628446969225, + 0.0007101090617468269, + 0.0005171491802210953, + 0.0003707064375858257, + 0.00026126012216097185, + 0.00018113333105136686, + 0.0001234961312011995, + 8.283754125264734e-05, + 5.487113610286626e-05, + 3.600919053467502e-05, + 2.3561865131193687e-05, + 1.552564287799669e-05, + 1.043117693634524e-05 + ], + [ + 0.059285366785320925, + 0.059620300565503714, + 0.06061789757652594, + 0.06226165492021686, + 0.06450993647653565, + 0.06731353395764418, + 0.07060009147393032, + 0.07427637884453872, + 0.0782271614983255, + 0.08231651186355474, + 0.08639097739855668, + 0.09028501053711452, + 0.09382795837303425, + 0.09685234168438989, + 0.0992032164271379, + 0.10074729255468638, + 0.10138885888764812, + 0.10104406546584305, + 0.09969374118353226, + 0.09734835285132619, + 0.09406701106016542, + 0.0899314762298286, + 0.0850755970732415, + 0.07962395187800392, + 0.07374043726202166, + 0.06757741703693909, + 0.06129246592989234, + 0.05503092877503394, + 0.04891904270359797, + 0.04306572866047405, + 0.03755483873188907, + 0.03244948652822886, + 0.02778632556058519, + 0.023585423667314934, + 0.019849917878531045, + 0.016567437946201725, + 0.013714805811123292, + 0.011261560407095387, + 0.0091723799466738, + 0.0074096908522067765, + 0.005935623565277886, + 0.0047135007018256, + 0.0037086286073134463, + 0.002889818029870445, + 0.002228363332045495, + 0.0016990004169225624, + 0.0012795767245843467, + 0.0009508814574192636, + 0.0006964368994993696, + 0.0005022165637288433, + 0.00035605308803012903, + 0.0002478208833730035, + 0.0001693693750508544, + 0.00011372508859744428, + 7.498771026780423e-05, + 4.8681293553157155e-05, + 3.12447664252785e-05, + 1.9965301410816834e-05, + 1.2840492331513134e-05, + 8.43269040624444e-06 + ], + [ + 0.10815126020817092, + 0.1084732360608667, + 0.1094285040912946, + 0.11098167312291761, + 0.11307962802620893, + 0.11562801086393266, + 0.11852549249861041, + 0.12164474417533802, + 0.12483827956601268, + 0.12794355596920085, + 0.13078853534439477, + 0.13319847075685404, + 0.1350044735516712, + 0.13605220113888228, + 0.1362103508664272, + 0.13537863884524193, + 0.13349611658836483, + 0.13054269585254763, + 0.1265281701865155, + 0.1215182070343436, + 0.11561839669166843, + 0.1089521477019701, + 0.10168992623518198, + 0.09398488282677166, + 0.08602295957495677, + 0.07797045456437833, + 0.06999223891493263, + 0.06223410669111541, + 0.05481741920820531, + 0.04784109722805809, + 0.04137626407826718, + 0.03546951403894407, + 0.030143937274084334, + 0.025401939230785528, + 0.021228673079735336, + 0.01759697598747834, + 0.01446945310841813, + 0.011802535161236747, + 0.009549664926321408, + 0.007663518235859651, + 0.006097995187451091, + 0.00480944715482011, + 0.003757637841558646, + 0.002906745510631447, + 0.0022243370290593004, + 0.001682229349928933, + 0.00125596694996688, + 0.0009245830893634633, + 0.0006702082132451313, + 0.00047781406167063167, + 0.0003344318771026954, + 0.00022939704406617673, + 0.0001542270598405726, + 0.00010149902869059748, + 6.550934159790403e-05, + 4.1464868440839716e-05, + 2.5869539979330766e-05, + 1.6019879598664176e-05, + 9.972605714806585e-06, + 6.35192121452023e-06 + ], + [ + 0.16944005623997174, + 0.16968104538965104, + 0.17039160786317667, + 0.17152647494722825, + 0.17301198355303596, + 0.1747471149458297, + 0.1766161297821569, + 0.178455294483935, + 0.18011270970384713, + 0.18141802137597474, + 0.18219910468398579, + 0.18229043102359294, + 0.18154176138656153, + 0.1798266728736677, + 0.1770501396686668, + 0.17315492738047725, + 0.16812577057144118, + 0.16200051934875892, + 0.15483105802953054, + 0.14673486360603658, + 0.13786128110126736, + 0.1283726035830447, + 0.11847027083735866, + 0.10833064699716974, + 0.09815214591644343, + 0.08811757784636326, + 0.07838385573176075, + 0.06909379584006324, + 0.060358276169277386, + 0.05226106496820997, + 0.04485611164059416, + 0.03817126788127462, + 0.03220983073728983, + 0.02695520374618284, + 0.0223744561846499, + 0.018423217718897066, + 0.015048787367930482, + 0.012194141217250248, + 0.009801172831487555, + 0.007812563220775604, + 0.006173860871919459, + 0.004834863011871777, + 0.00374954428272195, + 0.0028780624217038353, + 0.0021842533005866117, + 0.0016372906771330226, + 0.0012106850064034175, + 0.0008818568478160935, + 0.0006318200033573531, + 0.00044442048839112816, + 0.00030637889111466204, + 0.00020650478982405277, + 0.000136047097917597, + 8.74489215703887e-05, + 5.484118620418788e-05, + 3.3582467502429386e-05, + 2.0158540427731977e-05, + 1.195842330866871e-05, + 7.111966176918001e-06, + 4.34151963649191e-06 + ], + [ + 0.24120894925658817, + 0.24130594127750904, + 0.2415822737202031, + 0.24199046235984548, + 0.242450797350264, + 0.24285668801561963, + 0.24307987351408142, + 0.24298327444099393, + 0.24238948945963176, + 0.2411496222599181, + 0.23910986690010644, + 0.23613105212483654, + 0.23209733086912018, + 0.2269239784092981, + 0.22056373119878533, + 0.21301123084596926, + 0.2043053801253055, + 0.19453864924042769, + 0.18381341978774285, + 0.17229830727582066, + 0.16017534713289858, + 0.14764966708043686, + 0.13494499499536255, + 0.12225515804371813, + 0.10978800162621236, + 0.09772424558666869, + 0.08622234437686191, + 0.07540657735200293, + 0.06537404537409668, + 0.0561889519985461, + 0.04788413123271625, + 0.0404652691113919, + 0.0339132819770805, + 0.02819070500372541, + 0.0232451627347914, + 0.019014041170209453, + 0.0154288569960291, + 0.012418864753289688, + 0.009914217785119184, + 0.007847814612576375, + 0.006157275010698018, + 0.004785730949817032, + 0.003682101511587825, + 0.002802564023361131, + 0.0021077195955161877, + 0.001564389522872002, + 0.0011442377723771527, + 0.000823381716754391, + 0.0005818655077520494, + 0.0004028835713655513, + 0.0002727002125585713, + 0.00018000845521306194, + 0.00011553365691982205, + 7.197348108339627e-05, + 4.3475630216430216e-05, + 2.5443127841834253e-05, + 1.4471832765695423e-05, + 8.065059904448496e-06, + 4.486192471232188e-06, + 2.584130353741024e-06 + ], + [ + 0.32118246329512884, + 0.32107795812595435, + 0.32075025042345845, + 0.32015457417806903, + 0.3192141736170192, + 0.3178287397301723, + 0.3158800843627964, + 0.31324812795392465, + 0.3097728032149199, + 0.3053353488952022, + 0.29981719443300714, + 0.29312148303220753, + 0.28518118255027364, + 0.2759656406085943, + 0.2654851946309276, + 0.25379381370253584, + 0.24098939817010767, + 0.22721314693206535, + 0.21264246014766836, + 0.19746798856479209, + 0.1819177001484862, + 0.16622569615893115, + 0.15063469372613944, + 0.1353506753658241, + 0.12058247556965512, + 0.10650657401933016, + 0.09326867089883213, + 0.0809763585424999, + 0.06970534448860415, + 0.05949687249316108, + 0.0503587880379121, + 0.042271759362184406, + 0.03519260264342211, + 0.02906113574055605, + 0.023805068228268812, + 0.01934314815633803, + 0.0155906509471518, + 0.01246330130398812, + 0.009879734306983764, + 0.007763587749991119, + 0.006044727361011052, + 0.004660376064133594, + 0.0035548476900097315, + 0.0026806575962490834, + 0.00199572577195784, + 0.001464742251831326, + 0.0010580072781492644, + 0.0007505849496741561, + 0.0005218252462107429, + 0.00035447922016958465, + 0.00023457788574018646, + 0.00015067223412543125, + 9.35202315688202e-05, + 5.5911139287833614e-05, + 3.20476167249778e-05, + 1.756169476117717e-05, + 9.222277975171567e-06, + 4.67121719518772e-06, + 2.3580109474308866e-06, + 1.2840381078611455e-06 + ], + [ + 0.4068246603725582, + 0.4064691918671771, + 0.40539075444815326, + 0.4035527974236193, + 0.4008895773036152, + 0.3973183619663221, + 0.3927436353537017, + 0.38706387373440887, + 0.38019242564473926, + 0.372015931314005, + 0.36247985660660675, + 0.35154410800442565, + 0.3392028753154472, + 0.325489925815113, + 0.3104814735405614, + 0.29429666451076075, + 0.27709551555572826, + 0.2590768198658, + 0.2404681876964982, + 0.22150333834632288, + 0.20244372734603194, + 0.1835469287310566, + 0.16506392134169773, + 0.14721918148138533, + 0.13020432616057245, + 0.11418816958276833, + 0.09929880978357208, + 0.08562204671425, + 0.07320820448557176, + 0.06207109949418173, + 0.05219116951500404, + 0.04352262072605267, + 0.03599606856252492, + 0.029528586075523958, + 0.0240269494232247, + 0.019391375003140858, + 0.015521181246390644, + 0.01231935625369923, + 0.009693148279005139, + 0.007557728360426559, + 0.005836034199661243, + 0.0044599635919076635, + 0.0033695470040490186, + 0.0025144949314639294, + 0.0018505996690240307, + 0.001340790287152716, + 0.0009543288915646996, + 0.0006656347634038589, + 0.00045354034274250506, + 0.00030094713263909586, + 0.00019348945667209202, + 0.00011990862255264262, + 7.1116139226309e-05, + 4.008635475871957e-05, + 2.1262166434551122e-05, + 1.0529694691627543e-05, + 4.838610004537424e-06, + 2.1219285977673338e-06, + 1.0152566192448433e-06, + 6.650345252413061e-07 + ], + [ + 0.49542009174303464, + 0.49477169416986894, + 0.4928261753356109, + 0.4895525437938212, + 0.4849063564392208, + 0.47883202485036946, + 0.471269386439672, + 0.4621599389463134, + 0.45145553432272023, + 0.4391380998157877, + 0.4251781986874951, + 0.40961754157675184, + 0.39252205690789893, + 0.3739984757719482, + 0.3541951008573287, + 0.33330003703148564, + 0.3115372863403708, + 0.2891568922203528, + 0.2664512705974285, + 0.24367672530902162, + 0.22112862670317507, + 0.19908204888991646, + 0.17779453497303815, + 0.157488474400532, + 0.13834644428327303, + 0.12051911446892312, + 0.10411175128054428, + 0.08918411197293614, + 0.07575758454676652, + 0.06381548576346663, + 0.05330928888840906, + 0.04416420911799869, + 0.036285278009881336, + 0.02956619992255772, + 0.02389297376836628, + 0.019147783393588212, + 0.015214822108767484, + 0.01198477358920301, + 0.009354829928041016, + 0.0072323214956399534, + 0.005534274310389557, + 0.004187974571297992, + 0.0031301097216285914, + 0.0023081662627914973, + 0.0016762493843057171, + 0.0011960965767585934, + 0.0008364172417794714, + 0.0005713816736960481, + 0.00037975768021762327, + 0.0002443536200588416, + 0.00015125371443828898, + 8.923189603443031e-05, + 4.9568866767955225e-05, + 2.5544784525554646e-05, + 1.193617413269109e-05, + 4.962174398319245e-06, + 1.8819976434265471e-06, + 8.634993739803178e-07, + 7.673036115348845e-07, + 9.972333801019403e-07 + ], + [ + 0.5841612101835316, + 0.5831914720698348, + 0.5802882659187295, + 0.5754358238857805, + 0.5686155184750998, + 0.559807550259009, + 0.548997177581466, + 0.5361802877764382, + 0.5213711506139147, + 0.5046090653172423, + 0.4859752807335726, + 0.4655533197367397, + 0.443501151627307, + 0.4200045540060336, + 0.39528788273358184, + 0.3696103502723539, + 0.3432597880530219, + 0.31654119629961713, + 0.2897866003626874, + 0.26330069609736934, + 0.23738849077950627, + 0.21234047367547285, + 0.18841436621613808, + 0.16582422170297137, + 0.14473829690937695, + 0.12528346172246674, + 0.10753774696181409, + 0.09153146262132912, + 0.07725389149220323, + 0.06465650334250406, + 0.05365961805553692, + 0.0441599828576877, + 0.036036095139089695, + 0.029160200541308728, + 0.023396580411027053, + 0.018610368431647286, + 0.014673199383466153, + 0.011463663387402661, + 0.008870266398824522, + 0.006793662268770722, + 0.005146075936018765, + 0.003850998968505844, + 0.0028432939825326973, + 0.0020673578006356005, + 0.0014778085002080598, + 0.0010352878261305572, + 0.0007084083504087215, + 0.00047140115231914144, + 0.00030348905301550236, + 0.00018741791819022678, + 0.00010994366885802118, + 6.038617884264485e-05, + 3.0305070947541813e-05, + 1.3402864304970265e-05, + 4.965166783147908e-06, + 1.5638597630208785e-06, + 8.449862305792461e-07, + 1.245831926603956e-06, + 1.9045926494431933e-06, + 2.4560774940079794e-06 + ], + [ + 0.6702338385969312, + 0.6689231523108982, + 0.6650067985318896, + 0.658485871162895, + 0.6493735738623294, + 0.6376930017689036, + 0.6234831909951777, + 0.6068035403436453, + 0.5877400666226739, + 0.5664103864892073, + 0.5429785802187119, + 0.5176134416054818, + 0.49055812059646103, + 0.4620811718883248, + 0.4324849246237753, + 0.4020994109914824, + 0.37127452305314895, + 0.34036705428813147, + 0.30974820918825424, + 0.27975166635016036, + 0.25070061093156293, + 0.22288971745468272, + 0.19657034919379965, + 0.17194250803372926, + 0.14915497945143935, + 0.12830669484968754, + 0.1094446884155108, + 0.09256591267471982, + 0.0776272160178645, + 0.06454593289032165, + 0.05321174920283807, + 0.043492401513587096, + 0.035242316374726294, + 0.028310444619783444, + 0.022541422387305433, + 0.017787279077207258, + 0.013906043082375098, + 0.01076673085631033, + 0.008250480216647219, + 0.006252609032612436, + 0.0046815474335892, + 0.003458500288837615, + 0.0025165695692547065, + 0.0017995614127279838, + 0.001261838636256005, + 0.0008640253869240604, + 0.0005751222546055054, + 0.0003698433423132406, + 0.00022787796406290283, + 0.00013282051329768454, + 7.195978498063648e-05, + 3.519411733234092e-05, + 1.4757767842036599e-05, + 4.882016247494923e-06, + 1.3101664712886049e-06, + 1.0591623833391518e-06, + 2.3028846078699593e-06, + 3.7577420350945354e-06, + 4.7987171246707105e-06, + 5.313136882724788e-06 + ], + [ + 0.750909213336556, + 0.7492499233112583, + 0.7442968170659655, + 0.7360736689524648, + 0.7246272105128077, + 0.7100296530615845, + 0.6923796372785188, + 0.6718071803624356, + 0.6484767364711265, + 0.6225905016877876, + 0.5943903741849814, + 0.5641664262894084, + 0.5322181032307448, + 0.4989082447079957, + 0.46461658115681964, + 0.4297419588803498, + 0.39469265040453827, + 0.35987281101353874, + 0.3256847615348537, + 0.2924917327325646, + 0.26062229733702014, + 0.23037116802492988, + 0.20197708453410954, + 0.17562080235926145, + 0.15142741052316414, + 0.12946333598532905, + 0.1097432179290324, + 0.09222763497751744, + 0.07684037181780655, + 0.06346458181146253, + 0.051959498978627755, + 0.042165886694054466, + 0.03391381850305561, + 0.02703143423376857, + 0.021346023704551454, + 0.01669620964932327, + 0.01293134882867239, + 0.009911376346775906, + 0.00751180095007635, + 0.005624046017439545, + 0.004154289400905377, + 0.0030224911379066934, + 0.002161028617203199, + 0.0015140071778647506, + 0.0010361931069595531, + 0.0006889545503526164, + 0.0004420717215741469, + 0.0002711890931692878, + 0.00015685450437348067, + 8.367682602526597e-05, + 3.9724907468676695e-05, + 1.568258091560239e-05, + 4.527605360786285e-06, + 1.1291566497311657e-06, + 1.8313418786813993e-06, + 4.211783381178946e-06, + 6.792278333052011e-06, + 8.714343672802837e-06, + 9.711918521795775e-06, + 9.792077360137192e-06 + ], + [ + 0.8236286491110174, + 0.8216254336327586, + 0.8156474220680047, + 0.805741827659766, + 0.7919941679102146, + 0.7745288044638611, + 0.7535083700579024, + 0.7291375175625256, + 0.7016634000764125, + 0.6713763605367488, + 0.6386089227617593, + 0.6037330169530292, + 0.5671620541734474, + 0.5293160889709182, + 0.49065768873628607, + 0.45165025596427255, + 0.41275561341313577, + 0.37442114294688017, + 0.3370712615858877, + 0.30108768253311174, + 0.26680723843774423, + 0.234513776331034, + 0.2044279749499834, + 0.17670873818671048, + 0.1514487841562508, + 0.1286839600104796, + 0.10839248665740281, + 0.09049858051619125, + 0.07489222419684914, + 0.0614234915415341, + 0.049922515092887386, + 0.040204028024642055, + 0.03207669519934665, + 0.02535012986415901, + 0.019836807768588142, + 0.015364938583547118, + 0.011775081136147884, + 0.00892144434213747, + 0.006675634279528334, + 0.004927209931192619, + 0.0035811606600588573, + 0.002557419077046659, + 0.0017893114259404396, + 0.0012212843567100734, + 0.0008098645868300154, + 0.0005175276293530563, + 0.0003154195526864869, + 0.00018050138239382837, + 9.452974360202772e-05, + 4.32959795803819e-05, + 1.583565721349731e-05, + 3.863656239827317e-06, + 1.1821555028299102e-06, + 3.3850562741856946e-06, + 7.483102940562386e-06, + 1.1622848720878382e-05, + 1.4783201853916107e-05, + 1.6598775026379255e-05, + 1.69362627157534e-05, + 1.6025926053588976e-05 + ], + [ + 0.886087561157041, + 0.8837553667407865, + 0.8767964730805103, + 0.8652828584716188, + 0.8493407237825039, + 0.8291479878227991, + 0.8049336947441924, + 0.7769788301927781, + 0.7456144474533727, + 0.7112195237072615, + 0.6742170318886656, + 0.6350682059650662, + 0.5942648137442982, + 0.552324903259051, + 0.5097621775526435, + 0.4671049524736344, + 0.42486162567290453, + 0.383513806071273, + 0.34350727507101936, + 0.3052310012276963, + 0.26901906742263176, + 0.23514497706619666, + 0.20380492724767021, + 0.1751303076629479, + 0.14918041887980646, + 0.1259575008127015, + 0.10540301280185782, + 0.08740407530190918, + 0.0718186611626248, + 0.05846517521495695, + 0.04714643969338466, + 0.037654521992736105, + 0.029777717211931648, + 0.023312479333762376, + 0.018056716837553232, + 0.01383154688037961, + 0.010470955264136538, + 0.00782682050910144, + 0.005768367819993121, + 0.004184806396651601, + 0.0029816355436450806, + 0.002080084517118155, + 0.0014152905396901969, + 0.0009333635808107503, + 0.0005925769035167709, + 0.00035777808237118046, + 0.0002017508876863477, + 0.00010308547897228179, + 4.50947082713278e-05, + 1.4946583151306709e-05, + 2.9237439747221863e-06, + 1.738158719692028e-06, + 6.253062771393975e-06, + 1.2797481420332364e-05, + 1.9119962365165356e-05, + 2.395276788721162e-05, + 2.6765521798267703e-05, + 2.757107624333276e-05, + 2.6608118501161063e-05, + 2.4234855161626196e-05 + ], + [ + 0.9363053011612257, + 0.9336694448805652, + 0.9258053056822454, + 0.9128092942583331, + 0.8948480434246655, + 0.8721537862022875, + 0.8450220197763553, + 0.8138088768348605, + 0.7789285734672922, + 0.7408460030469906, + 0.7000712518517346, + 0.6571506530063478, + 0.6126561704294832, + 0.5671772892918213, + 0.5212924387074052, + 0.47558007200700697, + 0.4305875856019732, + 0.3868224390400946, + 0.344744371600755, + 0.3047422218013204, + 0.26714149159928136, + 0.2321996226785367, + 0.20008335025956206, + 0.1708939801294917, + 0.14465517328716074, + 0.12133476771288729, + 0.10083724856351249, + 0.08301432073164171, + 0.06769316095381978, + 0.054663180984520957, + 0.0437035076545001, + 0.03458516303388992, + 0.027081625786119536, + 0.020974590451651343, + 0.016056097659112797, + 0.012140705348784439, + 0.009059496963470793, + 0.006662701617194431, + 0.004820301518784087, + 0.0034227173640013976, + 0.0023776095832260644, + 0.0016090015792274406, + 0.001054131691961962, + 0.0006625101221013687, + 0.0003946513155226539, + 0.00021810099426978975, + 0.00010776653169886537, + 4.429069560283329e-05, + 1.2760018430957574e-05, + 1.931389855292097e-06, + 3.4725799295419515e-06, + 1.1231586013989125e-05, + 2.116613826195769e-05, + 3.0415090713507197e-05, + 3.749754949367195e-05, + 4.1742905686881375e-05, + 4.309995732794068e-05, + 4.198709808018073e-05, + 3.9025428700815136e-05, + 3.456791770113238e-05 + ], + [ + 0.9726907715696713, + 0.9697840399231485, + 0.9611165757456339, + 0.9468092651823017, + 0.9270675683021755, + 0.9021761313782053, + 0.8724932381569535, + 0.8384484910742825, + 0.8005341023096139, + 0.7592969962495297, + 0.7153282848448568, + 0.6692527934720653, + 0.6217147515689617, + 0.5733640076537944, + 0.524841117423964, + 0.4767632862769966, + 0.42970523546190054, + 0.38419330133381346, + 0.3406935021900947, + 0.29958715119025664, + 0.26118832769462463, + 0.22572338313403914, + 0.1933362408913801, + 0.16409227371472662, + 0.13797849936876921, + 0.11492839596268982, + 0.09481057215725043, + 0.0774433589464975, + 0.0626254978104121, + 0.05012191790040561, + 0.03968976232737014, + 0.0310839961008303, + 0.024065701721046235, + 0.018408129245791025, + 0.013897972021345179, + 0.01034749769813702, + 0.007587757922891001, + 0.005469048277653364, + 0.0038654512835771745, + 0.002669498169609504, + 0.0017929476763139766, + 0.0011633082132142631, + 0.0007219998998473187, + 0.00042195166817838957, + 0.00022667085580448524, + 0.00010690902251880648, + 4.0158688666606906e-05, + 9.358807582129446e-06, + 1.586616328729041e-06, + 7.3509748341991345e-06, + 1.977699206265243e-05, + 3.407150304633762e-05, + 4.717047732949784e-05, + 5.712721050173606e-05, + 6.32210542742012e-05, + 6.539815584302822e-05, + 6.407155800957514e-05, + 6.000085506734406e-05, + 5.4079302836319635e-05, + 4.692004083505514e-05 + ], + [ + 0.994090476486552, + 0.9909568568990795, + 0.9816141960301841, + 0.966206642384659, + 0.944975951142184, + 0.918256598447619, + 0.8864664599499615, + 0.8501021373235305, + 0.8097278745997577, + 0.7659646331297768, + 0.7194769692726738, + 0.6709577202032743, + 0.6211153565445452, + 0.5706529306936639, + 0.5202546157392085, + 0.47056845619615917, + 0.4221915191075183, + 0.37565980080489175, + 0.33143089611274407, + 0.28987883359659455, + 0.2512930722497522, + 0.2158747278570524, + 0.18373405438485546, + 0.15490142099276488, + 0.12932710657136046, + 0.10691143219416041, + 0.08748840686982857, + 0.07084682258095833, + 0.05676053581342894, + 0.044972828296807155, + 0.03522405817360032, + 0.0272567793538732, + 0.0208244873576023, + 0.015694156002002732, + 0.01165251624960227, + 0.008512009176475177, + 0.006106128773488474, + 0.004289019514341823, + 0.002939347933977162, + 0.00195473282088618, + 0.0012518798585911934, + 0.000763354631352831, + 0.0004352054356077724, + 0.00022472526303335516, + 9.906401825424132e-05, + 3.2445778883249325e-05, + 5.349161441943193e-06, + 3.2248479739135804e-06, + 1.5317134904962936e-05, + 3.4004508722561874e-05, + 5.396657085185017e-05, + 7.166998920138092e-05, + 8.530415409137885e-05, + 9.362777906313244e-05, + 9.67602028801747e-05, + 9.519674898707125e-05, + 8.981695387075077e-05, + 8.170268734947782e-05, + 7.196541507006365e-05, + 6.146669743945348e-05 + ], + [ + 0.9998232179086595, + 0.9965142155788919, + 0.9866439436346983, + 0.9703799635975398, + 0.9479975451880308, + 0.919876015715645, + 0.8864858646483125, + 0.8483833933351582, + 0.806195934951841, + 0.7606101243432415, + 0.7123530357523388, + 0.662176149267773, + 0.6108351605290433, + 0.5590807869920487, + 0.5076263094196429, + 0.4571415859036111, + 0.4082340575376925, + 0.36143740760059634, + 0.3171984424101819, + 0.2758731967228354, + 0.23772587436177198, + 0.20292220172388103, + 0.1715416738914442, + 0.1435781976535442, + 0.11894558722586444, + 0.09751257876533789, + 0.07908202729946705, + 0.0634210266642975, + 0.05027253626137992, + 0.039372297651445634, + 0.030444510332363086, + 0.02322444003523685, + 0.017461783058203933, + 0.012922837732390623, + 0.009396567266263763, + 0.006699213447208828, + 0.00466943112973699, + 0.003167998147679371, + 0.002079792434840285, + 0.0013092903730456981, + 0.0007795883185027121, + 0.0004292721823136248, + 0.00020988568610823881, + 8.362424088440031e-05, + 2.1782465161841848e-05, + 2.441912384142937e-06, + 9.234974773958013e-06, + 3.032917916844649e-05, + 5.7232109043524275e-05, + 8.425460844003643e-05, + 0.00010767208964215918, + 0.0001252554599990281, + 0.00013629667777681826, + 0.00014037376418333313, + 0.0001383418286439627, + 0.00013123292687512123, + 0.00012035544991277122, + 0.00010702688773008318, + 9.25542365802438e-05, + 7.795607959744727e-05 + ], + [ + 0.989712236192532, + 0.9862800134683641, + 0.9760454626451498, + 0.9591942499640901, + 0.9360299807751596, + 0.9069707921025499, + 0.8725328388622992, + 0.8333235926797294, + 0.7900240257718282, + 0.7433724198409958, + 0.6941463091107042, + 0.6431428823221988, + 0.5911584773421904, + 0.5389679968322051, + 0.48730740932069583, + 0.43685686355397185, + 0.38822358505732474, + 0.34192730702784163, + 0.2984001133403933, + 0.2579718788085403, + 0.22087196732457334, + 0.18723975215605593, + 0.15711210401143366, + 0.13045256509869593, + 0.10713916516004038, + 0.08701184123380913, + 0.06984676506451434, + 0.055388338970102396, + 0.04336389633484735, + 0.03349710802206407, + 0.025504993683981507, + 0.019119838056427415, + 0.014091733852948807, + 0.010190870106281903, + 0.007211492542487556, + 0.004978040614743332, + 0.0033341786589695583, + 0.0021521731948084214, + 0.0013244383750040851, + 0.0007636452220302415, + 0.000400517854775803, + 0.00018050813418695307, + 6.127684112374903e-05, + 1.0556785883179917e-05, + 3.981037022024434e-06, + 2.3804546868316518e-05, + 5.6959757770061226e-05, + 9.441903831277585e-05, + 0.00012999607388925052, + 0.00015994802037923802, + 0.00018209803261089923, + 0.00019551861933311612, + 0.00020055131677153892, + 0.00019751479221322973, + 0.0001879649318554708, + 0.00017339118127412145, + 0.00015553463953363374, + 0.00013582715946480514, + 0.00011571234796454966, + 9.64356473105542e-05 + ], + [ + 0.9640760971171802, + 0.9605787037538718, + 0.9501530180178366, + 0.9329994669701958, + 0.9094454381093489, + 0.8799396108016804, + 0.8450356941525355, + 0.8053810624728421, + 0.7616982520988475, + 0.7147659379979356, + 0.6653983754179568, + 0.6144238657598456, + 0.5626627134079144, + 0.510906165865324, + 0.45989696974118716, + 0.4103116182382703, + 0.36274567527883217, + 0.31770249401881523, + 0.2755863713910896, + 0.2366980541221229, + 0.20123140729221006, + 0.1692908502693616, + 0.14087721049672275, + 0.11592035825659446, + 0.09426714053757891, + 0.0757318890098935, + 0.0600685511683985, + 0.0470044546398998, + 0.036255722231350616, + 0.027539433098075543, + 0.020570608192726207, + 0.015083696821003642, + 0.010833604918858366, + 0.007597863304941187, + 0.005180135547208068, + 0.0034147740650312557, + 0.002156185754270734, + 0.0012869426439398159, + 0.0007098362059967712, + 0.0003470046249927503, + 0.00013769927081409516, + 3.50086389702313e-05, + 3.272272437397536e-06, + 1.6038047101110177e-05, + 5.356030723846523e-05, + 0.00010234496529037248, + 0.000152677606540475, + 0.00019837467186528416, + 0.00023552486855598425, + 0.00026225229187990136, + 0.00027789462555575335, + 0.0002827299591965599, + 0.000278058144643061, + 0.00026489315031842745, + 0.00024537294704543274, + 0.00022148613614532888, + 0.0001950541358471555, + 0.00016778855151641092, + 0.0001411578545201035, + 0.00011643623574441433 + ], + [ + 0.9237272911777451, + 0.9202243712319583, + 0.9097852505525786, + 0.8926207034377232, + 0.8690788227563989, + 0.8396289787892054, + 0.8048511461835703, + 0.7654224948800685, + 0.7220939990754064, + 0.6756706145920004, + 0.626988852831083, + 0.5768933488311861, + 0.5262139436345944, + 0.475743707159336, + 0.42621908151913185, + 0.37830260420718725, + 0.33256861418195266, + 0.28949291866205273, + 0.24944685209120468, + 0.21269739517351088, + 0.17940047503644957, + 0.14962464619222948, + 0.12333739470675492, + 0.10043107742269856, + 0.08073848007728102, + 0.06402924265635114, + 0.050061080754719024, + 0.03854241266807569, + 0.029184086051829563, + 0.021701122591256332, + 0.01581328358990081, + 0.011260748705499953, + 0.007807908874529681, + 0.005243827783903356, + 0.0033846854749772365, + 0.0020772745049128173, + 0.0011893671378974673, + 0.0006155708477536926, + 0.000270230475449296, + 8.614079383295449e-05, + 1.1877290023732852e-05, + 8.661003258415992e-06, + 4.780437633132133e-05, + 0.000108887620221228, + 0.00017685576973730315, + 0.00024247836485262234, + 0.0002993557831290996, + 0.0003440504818497482, + 0.0003748333962894687, + 0.0003915897470392751, + 0.0003950816224421644, + 0.00038671368016198073, + 0.0003684075786004202, + 0.00034200365480514935, + 0.0003100468078851359, + 0.0002748846635969418, + 0.0002384194862299311, + 0.00020247675667175603, + 0.00016851103918617006, + 0.00013767569790710925 + ], + [ + 0.8699449903696022, + 0.8664959151498907, + 0.8562201500595364, + 0.8393358246658892, + 0.8162028317088539, + 0.7873048207419637, + 0.7532388065075644, + 0.7146973741443011, + 0.672445814890041, + 0.6273011606980703, + 0.5801071321084437, + 0.5317095334899805, + 0.4829337223614693, + 0.43456064717933374, + 0.387307770995409, + 0.34181213678990163, + 0.2986173683156211, + 0.25816412737465944, + 0.22078526321853864, + 0.1867102612411261, + 0.15605567023400613, + 0.12885410946999026, + 0.10503972271249123, + 0.08447818836851803, + 0.0669738289687302, + 0.0522870128309065, + 0.04015433091536322, + 0.030287404017928506, + 0.02239118935633127, + 0.01618812580021031, + 0.011405346261623327, + 0.007794424961164057, + 0.0051331805038304186, + 0.003225604050838894, + 0.001904417840156229, + 0.0010286595690894964, + 0.0004838988303697461, + 0.00017736847248674787, + 3.6246760127784336e-05, + 4.518503900954849e-06, + 4.075283855598671e-05, + 0.00011454637929543086, + 0.00020433111988649207, + 0.0002953130937419525, + 0.0003783047266155136, + 0.00044683763895092847, + 0.0004985466889841241, + 0.0005320951747403959, + 0.0005479490489126123, + 0.0005475684398681769, + 0.0005330101941529142, + 0.0005065072682391565, + 0.00047074619460011263, + 0.0004280072508107704, + 0.0003812007232211185, + 0.00033287852525910335, + 0.0002849763489701549, + 0.00023932719901938868, + 0.0001972927161431752, + 0.0001598247739009266 + ], + [ + 0.8044346106498169, + 0.8010965099616137, + 0.7911546297611405, + 0.7748298266066808, + 0.7524877711612441, + 0.724617310725678, + 0.691820781258826, + 0.6547943795925656, + 0.6143049011373974, + 0.5711657565390535, + 0.5262124218368429, + 0.4802775611844248, + 0.434166753667139, + 0.3886356205386111, + 0.34437062922592115, + 0.30197305656038415, + 0.2619470658581015, + 0.22469173386481353, + 0.19049679003642891, + 0.1595518287443016, + 0.13193341757781044, + 0.10763912511395861, + 0.08657253330281893, + 0.06857456078966713, + 0.05343128274492846, + 0.04089125012599483, + 0.030684869678626443, + 0.02252338393357247, + 0.016119487729764778, + 0.011202778386135289, + 0.007514768145760274, + 0.004822758920549638, + 0.002921672171434111, + 0.0016337290653026851, + 0.00080955977232805, + 0.00032579290861652467, + 8.405806230714873e-05, + 6.3605846627281165e-06, + 3.331963145241637e-05, + 0.00012103875123139112, + 0.00023815815460408543, + 0.0003623895141491076, + 0.00047939585380170753, + 0.0005801425181999699, + 0.0006602094355264661, + 0.0007166843186470211, + 0.0007502631214614397, + 0.0007618814873587801, + 0.0007538564685195472, + 0.0007289663124774814, + 0.000690313830442363, + 0.0006408256928605504, + 0.0005837530400942843, + 0.0005216360866003599, + 0.00045767153042096127, + 0.00039446730103939867, + 0.0003338718545859147, + 0.00027763971267512864, + 0.00022691639070951386, + 0.00018239823490880748 + ], + [ + 0.7292722684052673, + 0.7260986279770204, + 0.7166494635781364, + 0.7011451627614239, + 0.6799489336131972, + 0.6535464805518192, + 0.6225350549632209, + 0.5876016509065425, + 0.5495002658335286, + 0.5090270620670589, + 0.466995121167819, + 0.4242087801630119, + 0.38144007788706, + 0.3394066663449298, + 0.2987530146166917, + 0.26003534927165617, + 0.2237106492842623, + 0.19012975176982522, + 0.15954090000738522, + 0.1320872607999037, + 0.10781338974223764, + 0.08666640307574817, + 0.06854004597877537, + 0.05324926336759273, + 0.04056787612717271, + 0.03023927508105648, + 0.02198499204808366, + 0.015532619417806703, + 0.010603967633158221, + 0.006937955054366214, + 0.004299363964050245, + 0.0024734668855513407, + 0.0012757737449768359, + 0.0005491639889746366, + 0.00016444110527731343, + 1.7420723663157406e-05, + 2.6755120793540752e-05, + 0.0001297526440992913, + 0.0002815411473798545, + 0.0004498624125360183, + 0.0006131857363418463, + 0.0007580365097220329, + 0.000876218021026073, + 0.0009643630038525988, + 0.001022482695642703, + 0.0010508589690981045, + 0.0010527085860071582, + 0.0010314817690406314, + 0.000990441889952913, + 0.0009336416156838076, + 0.0008649044924080685, + 0.0007877182255974791, + 0.0007053746489117554, + 0.0006214026607742622, + 0.000538158281870729, + 0.00045854954141695623, + 0.0003841774475804072, + 0.0003165856426376296, + 0.0002566394180724774, + 0.00020494248491959455 + ], + [ + 0.6468412219979218, + 0.6438799748941347, + 0.6350659552292517, + 0.6206150348320474, + 0.6008820823238591, + 0.5763406242751039, + 0.547571639413378, + 0.515241220708441, + 0.4800775583917911, + 0.4428455983420999, + 0.4043220960861745, + 0.36527016086594527, + 0.3264158368674882, + 0.28842722943800053, + 0.2519006934657315, + 0.21733086363421192, + 0.1851234279117081, + 0.1555851167616789, + 0.1289117195612227, + 0.105204939058132, + 0.08447149209344036, + 0.06662893945798114, + 0.0515462918927916, + 0.03902313353298894, + 0.02882751907301432, + 0.020701133061218468, + 0.014371952204472198, + 0.00957815441687104, + 0.006057937577314974, + 0.0035703918216564647, + 0.0019013429463284103, + 0.000859626797759252, + 0.00028394016256466827, + 4.0264736225395006e-05, + 2.0927207056155656e-05, + 0.00014202717914737562, + 0.0003395690675757296, + 0.0005672516597832682, + 0.0007939017440843127, + 0.0009989546624174178, + 0.0011705503534179095, + 0.001303032755353749, + 0.0013943697748077162, + 0.0014462364501277582, + 0.0014625032248073335, + 0.001446253795345958, + 0.0014028829092612776, + 0.0013373311888419403, + 0.0012544238174183018, + 0.0011584943291881482, + 0.0010539025961599836, + 0.0009446038781095444, + 0.0008339200359123034, + 0.0007253785858267687, + 0.0006210821923893668, + 0.0005236317484825084, + 0.0004347152003437227, + 0.0003552940752437611, + 0.00028589793294152814, + 0.00022679407765036004 + ], + [ + 0.5597550152758627, + 0.5570471757329625, + 0.5489901011644337, + 0.5357914598722008, + 0.5177915090108447, + 0.49544362860908303, + 0.46930277426945766, + 0.4400027761269692, + 0.40823361832978056, + 0.3747163685470228, + 0.34017831242572877, + 0.3053297025420085, + 0.2708444034616355, + 0.23732149549590728, + 0.2052982474494534, + 0.17521822126270775, + 0.14742868430376999, + 0.12217744703062408, + 0.09961367737537766, + 0.07978861389325265, + 0.06268691319516008, + 0.04820047499057875, + 0.03617195723833752, + 0.0263945502024792, + 0.01863226670623276, + 0.012633152867015789, + 0.008137592017827808, + 0.0048989263033834265, + 0.002676716431110995, + 0.0012543618868925623, + 0.00044206259342950265, + 7.516985680761227e-05, + 1.7666354368968648e-05, + 0.0001600820309565104, + 0.00041730437050706753, + 0.0007262315098419057, + 0.0010403642388834564, + 0.001329458453201156, + 0.0015757649696920525, + 0.00176985230810312, + 0.0019088571801022332, + 0.0019942902314473822, + 0.0020296047746149954, + 0.0020208105590430693, + 0.001975058367403666, + 0.0018976835000609957, + 0.0017955555119139044, + 0.001674917227577677, + 0.0015413627083883232, + 0.001399528735658868, + 0.001253957988805368, + 0.0011086128331937613, + 0.0009666057675828984, + 0.000831298667422371, + 0.000704561637715687, + 0.0005884629126797228, + 0.0004843523815188796, + 0.0003927601317613395, + 0.0003138275321319695, + 0.00024736321819505616 + ], + [ + 0.4707748705774245, + 0.4683533422979049, + 0.4611508903236549, + 0.4493634136478546, + 0.4333112513578708, + 0.41342003065982336, + 0.39020954878358316, + 0.36427116957091665, + 0.3362457418308951, + 0.3067996662549274, + 0.276600859715898, + 0.2462997335112049, + 0.21648944866552797, + 0.18771685313460496, + 0.16044772328658224, + 0.13506147096573493, + 0.11184516676960465, + 0.09099171018193682, + 0.07260247498028202, + 0.056689295304114685, + 0.04320473864244587, + 0.03201881252083979, + 0.02296088698524769, + 0.015819812036006096, + 0.010363356528869777, + 0.00635080925476795, + 0.0035385783492614753, + 0.0017005841137975684, + 0.0006228999760477225, + 0.00011609793032460709, + 1.7633264186672168e-05, + 0.0001914669476551823, + 0.0005282424467020339, + 0.0009440255990329182, + 0.001376547975719484, + 0.0017834279951281081, + 0.002135246810934464, + 0.0024172618049270347, + 0.0026242860464887256, + 0.0027571289623426498, + 0.002821099943972402, + 0.002823919586322336, + 0.002773674775587467, + 0.0026798993515571913, + 0.0025522420920696624, + 0.002397589440800544, + 0.0022239196063669462, + 0.0020381384268037513, + 0.0018459699442317998, + 0.001652123335472944, + 0.0014609748888573934, + 0.0012761442312194773, + 0.0011005029333481804, + 0.0009368095577875993, + 0.0007865977240610834, + 0.0006512913565954506, + 0.000531668985554444, + 0.0004279924629550873, + 0.00033963946858991116, + 0.00026604402684046773 + ], + [ + 0.3827216258451653, + 0.3806102609398142, + 0.3743333847840062, + 0.36407191932190824, + 0.350121123448244, + 0.3328726389403931, + 0.3128033798635599, + 0.2904534210262607, + 0.26640525365494055, + 0.24126110389874122, + 0.215624740859389, + 0.1900600680445726, + 0.16510163362328156, + 0.14121799199070653, + 0.11880402789140902, + 0.09817217092952928, + 0.07954801822315033, + 0.06307056762749583, + 0.04879488529885012, + 0.03669720394859456, + 0.02670226482555216, + 0.018661657941380593, + 0.012398636342805231, + 0.007702831301214786, + 0.004351588599418191, + 0.0021191466480085094, + 0.000785339883800253, + 0.00014799725427089663, + 2.2100768171119083e-05, + 0.00024850508299786167, + 0.000694833922329706, + 0.0012540851944466225, + 0.001844599311879515, + 0.0024080975719627065, + 0.002904535505748029, + 0.0033127360627254725, + 0.003618330230282045, + 0.0038213904582539053, + 0.00392808519812923, + 0.0039484814149800575, + 0.003894628287986209, + 0.0037790708498413304, + 0.0036146515782843076, + 0.0034123688821450227, + 0.003183847546101382, + 0.002936828622950908, + 0.0026797906301505897, + 0.002419618589178002, + 0.0021619078324620258, + 0.0019107898942432367, + 0.0016703035126135245, + 0.0014434200818859587, + 0.0012323892343927985, + 0.0010393012204720354, + 0.0008650269629942754, + 0.0007104063590304081, + 0.0005754800967459355, + 0.0004599144253511415, + 0.0003625266701082118, + 0.00028218447917039086 + ], + [ + 0.2983867353556193, + 0.29659996319328885, + 0.2912907792308671, + 0.28262273822185424, + 0.2708618594961058, + 0.25636035964429355, + 0.23954591564666358, + 0.22090031539294425, + 0.20094038817628682, + 0.18020139842502755, + 0.159196987578549, + 0.1384276002345632, + 0.11834419945800603, + 0.09933854689307015, + 0.0817323207425653, + 0.06577025502989747, + 0.05161742941663666, + 0.039360565373011414, + 0.029011999900256782, + 0.020516821660493973, + 0.013774508035147149, + 0.008627897441641637, + 0.004896612586048851, + 0.0023776847161859262, + 0.0008628887937420044, + 0.0001473649839573218, + 3.754835039928421e-05, + 0.0003589178407567852, + 0.000957587502191423, + 0.0017082135769063895, + 0.002508105646177739, + 0.0032805337416995832, + 0.0039714097420444116, + 0.004547571230385211, + 0.004990560802346824, + 0.005298444973578044, + 0.005471269396496318, + 0.0055222075039767235, + 0.005467375616175519, + 0.005324399282148007, + 0.005110857128935826, + 0.004843168289215861, + 0.00453669054078769, + 0.004203893632626887, + 0.0038571226405353276, + 0.0035040704414142235, + 0.0031533892834165788, + 0.002811004434893304, + 0.0024819341851130003, + 0.0021694078391615006, + 0.0018769315911830436, + 0.0016061887445111627, + 0.0013588978551577315, + 0.0011360365671987378, + 0.0009377809215592967, + 0.0007641300425412481, + 0.0006144077589973955, + 0.00048745113274393343, + 0.0003816991593317316, + 0.00029521506740965206 + ], + [ + 0.2204441254455215, + 0.21898606942287346, + 0.21465695490109848, + 0.20760082895547463, + 0.19805110490723868, + 0.18631659678666695, + 0.17277085242604093, + 0.1578321025546006, + 0.14194627365438015, + 0.1255710190670412, + 0.10914129583678085, + 0.09307496167946291, + 0.07774184710571926, + 0.0634553931967755, + 0.05046390082518198, + 0.03894551754066968, + 0.029007100344542323, + 0.02068673897521641, + 0.013958457917071197, + 0.008743518056428359, + 0.00491546115364862, + 0.0023217145944138306, + 0.0007776770254596229, + 9.743432894302722e-05, + 9.070917146976387e-05, + 0.0005778341171211489, + 0.001395291828334744, + 0.002398876375612403, + 0.0034691688565435695, + 0.004511469377218368, + 0.005456916371218406, + 0.006258694268815388, + 0.0068881040493591365, + 0.00733585312285395, + 0.007605188270467575, + 0.00770940592362736, + 0.007662870622917279, + 0.0074900234548012905, + 0.007213946065472884, + 0.006858718795936041, + 0.006445905482229802, + 0.005994344322658948, + 0.005520631971003235, + 0.005037645988950676, + 0.004557358993233533, + 0.004086874127557688, + 0.0036338579746038814, + 0.0032030936253232374, + 0.0027982919786898558, + 0.0024217559989616337, + 0.002075503419881123, + 0.0017603042317769328, + 0.001476570969750298, + 0.0012242613410265682, + 0.0010026603818369367, + 0.000810796330169735, + 0.0006471516266105808, + 0.0005097906834357581, + 0.00039654591636729405, + 0.0003046131899097139 + ], + [ + 0.15136453257118238, + 0.1502300603086559, + 0.14686331825746257, + 0.14138799930070495, + 0.1340035935828159, + 0.1249722625450835, + 0.11461001952281862, + 0.10326841414890175, + 0.091322265036699, + 0.07913976316676766, + 0.06708432326816889, + 0.05548677284150613, + 0.044635566957083685, + 0.03476673741208812, + 0.02605722280587963, + 0.018621617637884866, + 0.012512580552111624, + 0.007724517145561577, + 0.004198959426168416, + 0.0018353960855935856, + 0.0004978539167829044, + 3.184180186751698e-05, + 0.00026430427899909426, + 0.0010245328968822092, + 0.0021469787088508434, + 0.003480722355645285, + 0.004895055856553625, + 0.006277837983266847, + 0.0075442114626396726, + 0.008633044446095027, + 0.009506396396524756, + 0.010145257684312866, + 0.010548765852864933, + 0.010726639197586362, + 0.010701478218033413, + 0.010501359325025567, + 0.01015147103816313, + 0.009685363605998611, + 0.009131814576416455, + 0.00851902428372452, + 0.007870940427819986, + 0.007207205246858485, + 0.006544288314570401, + 0.005894349496296903, + 0.005268106547944788, + 0.004671122143744389, + 0.004109406881091653, + 0.003586034598912836, + 0.0031030312921876586, + 0.002661163494720283, + 0.002260764745118707, + 0.0019013358884768603, + 0.0015819037715127959, + 0.0013012662236741989, + 0.0010575919249631754, + 0.0008488095924440704, + 0.000672548936193724, + 0.000525994374736402, + 0.0004061797916223165, + 0.00030993725730076206 + ], + [ + 0.09333966170313805, + 0.0925125204632357, + 0.0900618074714514, + 0.08608943651970917, + 0.08075888036146435, + 0.07428488968900712, + 0.06692519352871146, + 0.05896531683689264, + 0.050697136902942704, + 0.04241771697530063, + 0.03440512215644096, + 0.02690822765007367, + 0.02013621162652459, + 0.01425079982143529, + 0.009361616846297613, + 0.005524713728653629, + 0.0027442164950176075, + 0.000976640744006476, + 0.00013824391290945793, + 0.00011216170153358417, + 0.0007603522945568261, + 0.0019313439596767381, + 0.003469539164669219, + 0.005223786489632359, + 0.0070571670669995834, + 0.008850257705949355, + 0.010507043612452534, + 0.011946965142410304, + 0.013123941538782689, + 0.014004866476220157, + 0.014583180210881907, + 0.014869817190340992, + 0.014882504011304894, + 0.014651584570431577, + 0.014215675774598393, + 0.013614975321487262, + 0.012883012498485504, + 0.012059959913412795, + 0.011178049774682014, + 0.010267651647971108, + 0.009353070785338657, + 0.008453293368762951, + 0.007583280366620337, + 0.006753309759747939, + 0.005971885212962155, + 0.005242135765980093, + 0.004567740136270183, + 0.003949719408778214, + 0.0033878787609722904, + 0.002880908076699209, + 0.0024273694696789637, + 0.0020251355937307342, + 0.0016717763820011805, + 0.0013645780738698998, + 0.001100640721463332, + 0.0008767668365236604, + 0.0006895516094601951, + 0.0005353175050892107, + 0.00041034302482705905, + 0.0003109194361829411 + ], + [ + 0.048207603593096636, + 0.04766321858622278, + 0.04605490189968163, + 0.043462844751600234, + 0.04001439770299757, + 0.03587711445629743, + 0.03125012030859452, + 0.02635039883584665, + 0.021398728221137437, + 0.016612904933615533, + 0.012191613127437849, + 0.008305394538286692, + 0.005088597889668957, + 0.0026338780249148055, + 0.000989493940268055, + 0.00015947437566909254, + 0.00010634862613888963, + 0.0007558665533809713, + 0.002005846004281905, + 0.003731678113431193, + 0.005797856358045737, + 0.0080623458356869, + 0.010391626936906893, + 0.01265854013553208, + 0.014757718732033565, + 0.016603180624264243, + 0.018130723805295058, + 0.01930384801930037, + 0.02009995604449537, + 0.020518611395384564, + 0.02058505679359959, + 0.020330959707663007, + 0.0197950446642892, + 0.019023628920789803, + 0.01806851592700022, + 0.016976554102438243, + 0.015794035340708147, + 0.014556053220761849, + 0.013303751456447296, + 0.012062204791625392, + 0.010855875289416877, + 0.009701522209583265, + 0.008611068228238296, + 0.007592381185551457, + 0.006649539895255396, + 0.005784544250659308, + 0.004996542954968406, + 0.004284117355313799, + 0.0036446227930091724, + 0.003074481263147845, + 0.0025701645980556313, + 0.00212768480110688, + 0.0017430210511356205, + 0.001411885382535644, + 0.001130180540515947, + 0.0008934661405104278, + 0.0006973071811531588, + 0.0005371758704575759, + 0.000408579047837755, + 0.00030717141392416704 + ], + [ + 0.017398454719230134, + 0.017104322908857005, + 0.016240065832008783, + 0.01486512992134408, + 0.013071859508735897, + 0.010982021519783326, + 0.00873777278447101, + 0.0064911975962140345, + 0.00439463205802981, + 0.002591026112922552, + 0.0012046756196916477, + 0.0003335742927767084, + 4.376551873374738e-05, + 0.00036606462389294646, + 0.0012950644563304782, + 0.0027907590801478028, + 0.004782265133531491, + 0.007172512049734898, + 0.009849063020309193, + 0.012685534082142794, + 0.015556492761196418, + 0.018334478338053687, + 0.02091203547091592, + 0.02318988743394204, + 0.02509624649741395, + 0.02657965591486046, + 0.027610639253008388, + 0.028187219580275865, + 0.028317286274523575, + 0.028028868706838544, + 0.027372878864227384, + 0.026401743450613472, + 0.025170767043297865, + 0.02373897086663188, + 0.02216748791877111, + 0.02050899196974364, + 0.018812932329084292, + 0.017115235399745382, + 0.015455623189414128, + 0.013857048523182357, + 0.012340629689977133, + 0.010919305939188089, + 0.009600859776754483, + 0.008388870723149712, + 0.007283678124788559, + 0.006283338024633024, + 0.005383422072863792, + 0.00457931035510077, + 0.003865445091990892, + 0.0032357818791093748, + 0.002684435629592013, + 0.0022054524333179407, + 0.0017929959550582924, + 0.0014412813572745775, + 0.0011448223346680877, + 0.0008979591983480209, + 0.0006952332614902506, + 0.0005312218910980172, + 0.0004006766051669934, + 0.00029866620671621663 + ], + [ + 0.0018910155509139015, + 0.00180699276454816, + 0.0015676824306259988, + 0.001210879555295058, + 0.0007985960557402057, + 0.000406435411624542, + 0.0001273823918064586, + 5.166190111391424e-05, + 0.0002667753476295928, + 0.0008482963801777295, + 0.0018532452093652783, + 0.0033149271889874035, + 0.005239541466558853, + 0.007604924848977047, + 0.010361139706297314, + 0.013433377177562085, + 0.016726379433243264, + 0.020128964894958835, + 0.023526295538003228, + 0.02679745604528774, + 0.02982993861359589, + 0.032525689201852725, + 0.03479732850529083, + 0.03657931995702284, + 0.03783470411557301, + 0.03854683726590333, + 0.038720118948355205, + 0.03838521126842699, + 0.03757805752858045, + 0.036352279218628096, + 0.034780573677475425, + 0.03293247407469901, + 0.03087607429387206, + 0.02867928332018223, + 0.026408899098439267, + 0.02412007223700368, + 0.02186213491994675, + 0.01966918134062011, + 0.017577020884565274, + 0.015604412140121702, + 0.01376730907256006, + 0.012073334949950183, + 0.010524923404785435, + 0.009120473291719762, + 0.007855566892237317, + 0.006723722938026444, + 0.005716644892978111, + 0.0048260381956706355, + 0.0040432081398664626, + 0.0033593153569462966, + 0.0027660697701676947, + 0.002255402768809586, + 0.0018195948211653797, + 0.001451253933413778, + 0.0011435737591154412, + 0.0008896525729559593, + 0.0006829765389403957, + 0.0005173008494213187, + 0.00038663752605031334, + 0.0002854005428997645 + ], + [ + 0.0021752906310880276, + 0.0022554929086246343, + 0.0025039828851804256, + 0.002939557964052915, + 0.003595408990293154, + 0.004505750938039911, + 0.005719154818040305, + 0.007270631326564669, + 0.009189905934102422, + 0.011493310054280078, + 0.014179536178032647, + 0.01722678245247004, + 0.02059148809573404, + 0.024208824363463232, + 0.027994712664169672, + 0.03184967068157399, + 0.03566376719945799, + 0.03932063176149367, + 0.0427084161283855, + 0.04572667123752534, + 0.048275754564407816, + 0.050287635697715154, + 0.05170017352164033, + 0.05249415576185871, + 0.05265503601096623, + 0.05220455668807882, + 0.05117923877175841, + 0.04963968222388023, + 0.047644518417294245, + 0.04527604540567853, + 0.04261776127780154, + 0.03975435485406736, + 0.03676259661753153, + 0.03371523852769602, + 0.030680909228850473, + 0.027713770567689075, + 0.02485985018336981, + 0.022148762066558737, + 0.019609933668334738, + 0.017255936733515262, + 0.015095821847195202, + 0.013130684465439675, + 0.011356333927290914, + 0.0097654012241446, + 0.008347761324217492, + 0.007091947660402737, + 0.005985452721698833, + 0.005016028703551989, + 0.004171623609182181, + 0.0034403972456139636, + 0.0028116620302118143, + 0.0022751313192880245, + 0.0018211730168502956, + 0.0014409700142371485, + 0.0011258872161484428, + 0.0008683012199682042, + 0.0006604728389114065, + 0.0004955377492401289, + 0.00036666344108898395, + 0.0002677980120972214 + ], + [ + 0.018242156051654995, + 0.018436424361260743, + 0.019022844866900146, + 0.020003518460509243, + 0.021385530488866485, + 0.0231695048575534, + 0.025363343833147308, + 0.02795536047148976, + 0.03092635652624337, + 0.03424314403054951, + 0.03785657113925283, + 0.04170078718417822, + 0.045693828317288646, + 0.04973961532029557, + 0.05373112252030223, + 0.057554963860379275, + 0.06109455127335628, + 0.06424335098505483, + 0.06689664838718888, + 0.06897654064220995, + 0.0704079614572912, + 0.07115440188477923, + 0.07118475632888613, + 0.0705166057196863, + 0.06916780993421245, + 0.06719339765433228, + 0.06465949789011895, + 0.06165319852977489, + 0.05825424560926101, + 0.054563177448407045, + 0.05067524011424377, + 0.04668439625216205, + 0.04267154868282872, + 0.03871018291611933, + 0.034866629178163966, + 0.03119110681332622, + 0.027722787707813373, + 0.024484356682357607, + 0.02149661302862921, + 0.018764054731203277, + 0.01628761333522546, + 0.014060098858522154, + 0.012070327772788334, + 0.01030381384867355, + 0.008744685992569654, + 0.007375970116419452, + 0.006180677307817362, + 0.005142420000202192, + 0.0042455546277556724, + 0.0034755935375221586, + 0.002818837905119582, + 0.0022631410439411547, + 0.0017968884461422542, + 0.0014097172340964011, + 0.0010916757418581691, + 0.0008340485548500198, + 0.0006281944292311283, + 0.00046630195680916827, + 0.0003411509354961402, + 0.0002461799526890711 + ], + [ + 0.04958204554980531, + 0.049837454037915827, + 0.05060380531000028, + 0.05186911935073851, + 0.053619392381642234, + 0.055825926072120675, + 0.05846507899577984, + 0.06148674722615608, + 0.06483282255202108, + 0.06843158129704632, + 0.07219775114962176, + 0.0760335719258817, + 0.07983097387787272, + 0.08347480596580538, + 0.08684685625960538, + 0.08983085846234472, + 0.09231528720508203, + 0.09420753318360134, + 0.09542226971902083, + 0.09590850688148808, + 0.09562039717539544, + 0.09455570902119176, + 0.09271603692812837, + 0.09015548146413258, + 0.0869231664706652, + 0.08310500131958617, + 0.0787933358630515, + 0.07409770517202226, + 0.06911464943290888, + 0.0639580304508349, + 0.058730918657678766, + 0.053530779897453785, + 0.048438555350312024, + 0.04352436085232241, + 0.038848436995245136, + 0.034453093827019596, + 0.030367489805064415, + 0.026607987321495375, + 0.02318138925319446, + 0.020083882659905312, + 0.017306312805816574, + 0.014832798872678042, + 0.012643903295053426, + 0.010717909989753856, + 0.009032689852745792, + 0.007565471627605409, + 0.006294713397051156, + 0.005199762644004956, + 0.004261488643967569, + 0.0034623235803227606, + 0.002786140832908657, + 0.0022187055318993844, + 0.0017465582484360084, + 0.00135788277360573, + 0.0010414220157685674, + 0.0007875035561570923, + 0.0005866028630963705, + 0.00043024905430537954, + 0.0003107393140249028, + 0.00022110343084584156 + ], + [ + 0.09520170555916818, + 0.09546423440933746, + 0.09624898535320303, + 0.09753369007734958, + 0.09928766860654467, + 0.10145842634065239, + 0.10400254647485695, + 0.10683771254886869, + 0.10987908368933835, + 0.11302831813255265, + 0.11617652876448493, + 0.11920689844173497, + 0.12199813123511354, + 0.12442853902687906, + 0.12638063896141669, + 0.12774626405148112, + 0.12842882728847713, + 0.12835805893837393, + 0.12747491482401122, + 0.12576055795655305, + 0.12320203051219239, + 0.11983343731048071, + 0.11568983485920575, + 0.11086041203937698, + 0.10542392077376814, + 0.09949383272371368, + 0.09318476655586817, + 0.08662406718268399, + 0.07992082081328705, + 0.07319637478711874, + 0.06655684000009213, + 0.060098769500903516, + 0.05389739486101004, + 0.04801879749418202, + 0.04251030845411134, + 0.03740421190319053, + 0.032718064127315385, + 0.02845617692278562, + 0.02461312059785289, + 0.021174318953947748, + 0.01811948081938156, + 0.01542325307229602, + 0.013057545973185543, + 0.010993189325223907, + 0.009200856193115023, + 0.007652629220938335, + 0.006322144844160862, + 0.005184479745865994, + 0.004217114374297463, + 0.0033995667420539458, + 0.002713284780321189, + 0.0021421468394799245, + 0.0016708868963600536, + 0.0012862596896400745, + 0.000976100295273916, + 0.0007296804307276583, + 0.0005367596848152362, + 0.0003883014447743399, + 0.00027623572968772566, + 0.00019333722436147915 + ], + [ + 0.15365492277490506, + 0.15387111154640956, + 0.15451497087526067, + 0.1555567854910031, + 0.15695486055153623, + 0.15864289585684796, + 0.16055852123399716, + 0.16260507898339133, + 0.16468006117229117, + 0.16667091821333957, + 0.16845812484363928, + 0.16991897990074556, + 0.17093198337727541, + 0.171381440329006, + 0.1711623355044159, + 0.17018522964003366, + 0.16837780516597153, + 0.16569965247392163, + 0.16212449787147973, + 0.15766965024864177, + 0.15235799474226885, + 0.1462609183746622, + 0.1394469405414389, + 0.13203814712039605, + 0.12414027427755901, + 0.11589052024773353, + 0.10742129017125267, + 0.09887260032221339, + 0.09036121624552507, + 0.08201096099993517, + 0.07392627950806326, + 0.06619707724935021, + 0.05889013510192032, + 0.05206066948796999, + 0.045742853061546976, + 0.03995506006260958, + 0.0347008568917546, + 0.02997078896892377, + 0.025745786755462973, + 0.021999369867320727, + 0.018699332838622094, + 0.0158105663344661, + 0.013295736245489695, + 0.011118005379417255, + 0.009241365400772937, + 0.0076322759325565545, + 0.0062598508256098305, + 0.005095041877143557, + 0.004112120982355731, + 0.0032877525077985733, + 0.0026014406746596667, + 0.002034755507331013, + 0.0015713336774194557, + 0.001196533182515177, + 0.0008972763285907313, + 0.0006620578750160159, + 0.00048002025978316373, + 0.00034168033205764974, + 0.0002387166292211886, + 0.00016370484621992015 + ], + [ + 0.22308853691045352, + 0.2232071767578352, + 0.2235575693233189, + 0.22410609956608782, + 0.2248052523724739, + 0.2255808954617544, + 0.22636478256771456, + 0.22705324206848163, + 0.22753867011139017, + 0.22770679276239889, + 0.22744048649838225, + 0.226624254665098, + 0.22514916013157274, + 0.22291765926004828, + 0.21984849242031215, + 0.21588071164163425, + 0.21097485726401843, + 0.2051270519822115, + 0.1983492016764776, + 0.19069378199491066, + 0.18223359374511505, + 0.17306508863368114, + 0.1632934826536221, + 0.15307058848838842, + 0.1425262116312311, + 0.13181621659663878, + 0.12108648997824463, + 0.11048413146033814, + 0.10012873802219756, + 0.09014139517484342, + 0.08061938608453657, + 0.07164107328024372, + 0.06326467786993312, + 0.05552645135977994, + 0.048445893196386876, + 0.042025332467431176, + 0.036252307629894544, + 0.031102087095751973, + 0.0265413105918363, + 0.022529973730522897, + 0.01902454312698173, + 0.015979105086848026, + 0.013347582638210303, + 0.01108534695581822, + 0.009149901860877283, + 0.007502265680015834, + 0.006107291795314187, + 0.004932096663600194, + 0.003947821450685931, + 0.0031287904276967107, + 0.0024524796727810718, + 0.0018988425563626894, + 0.0014502076896513484, + 0.0010909139585844755, + 0.0008070247008659772, + 0.0005865168400705781, + 0.0004180464808523187, + 0.000291836846138073, + 0.0001994142657751134, + 0.00013331424912834455 + ], + [ + 0.30130115684444575, + 0.301274869816389, + 0.3011907372756114, + 0.3010146517496047, + 0.30068992079250056, + 0.30016880830279913, + 0.29935909282925993, + 0.2981692388280361, + 0.2964989272219584, + 0.29424453374022913, + 0.2913038693611994, + 0.287581162251534, + 0.2829921767052604, + 0.2774689211008661, + 0.2709638106718199, + 0.263451028808446, + 0.25493926491761204, + 0.24545891994601646, + 0.23506693581227112, + 0.2238567842931566, + 0.2119404987255303, + 0.19944396495783073, + 0.18652208524762806, + 0.17332952443539093, + 0.1600359894512065, + 0.14679772904639743, + 0.13377339378382905, + 0.12110780786572282, + 0.10893020767970275, + 0.09734178679597516, + 0.08643284683242786, + 0.07626660738082734, + 0.06688481485276554, + 0.05830655661315266, + 0.05053253097650014, + 0.04354692314262482, + 0.03731985929900733, + 0.03181032378656569, + 0.026969984529316607, + 0.0227448493168496, + 0.01908046860307832, + 0.015919551484484002, + 0.013207664349215355, + 0.010892815563932555, + 0.008926240429332927, + 0.0072639329483415085, + 0.005866861241538511, + 0.004698558579511523, + 0.0037277102984478363, + 0.0029261743221781302, + 0.0022701314366819904, + 0.0017378344878777102, + 0.001310715662468026, + 0.0009722710429168645, + 0.0007079264520828259, + 0.0005053381169133032, + 0.0003528108415073109, + 0.00024045668994831856, + 0.0001597226128319527, + 0.00010329412236209602 + ], + [ + 0.38581437047866346, + 0.3855993908408181, + 0.3849556010533166, + 0.38384980308880784, + 0.3822300029507766, + 0.3800569538846506, + 0.37724811402038755, + 0.37372624986215003, + 0.3694090436976256, + 0.36421523728679567, + 0.3580695915874842, + 0.3509078587752655, + 0.3426817700376948, + 0.3333629367197147, + 0.32294683818187414, + 0.3114530107669622, + 0.29893659468841977, + 0.2854744029162915, + 0.2711687996078971, + 0.25615522604047203, + 0.24058441357384597, + 0.22461639908914952, + 0.20843654623312777, + 0.19221412469659924, + 0.17614161036277065, + 0.1603820424996007, + 0.14509690316307003, + 0.13042773805328173, + 0.11649525415394667, + 0.10338950950566213, + 0.09118456483235352, + 0.07992537774240648, + 0.06963385058249351, + 0.060309216896065984, + 0.0519320589240671, + 0.04446631954422963, + 0.03786401192583759, + 0.03206723667765897, + 0.02701237180982375, + 0.02263193824893884, + 0.018859934990596277, + 0.015628973577769045, + 0.012876011795700753, + 0.010542445288703491, + 0.00857389904688737, + 0.006921751891712272, + 0.005543565824592034, + 0.004399806593937749, + 0.003456960255394964, + 0.0026850932243331037, + 0.0020590683280863036, + 0.0015560454998619889, + 0.0011567442476591572, + 0.0008440728169570938, + 0.0006030464254331196, + 0.0004211219572629179, + 0.0002865236047444057, + 0.00018936556772313113, + 0.0001211635070362656, + 7.488178255521203e-05 + ], + [ + 0.47394551771840104, + 0.47350973248704653, + 0.4721986740950061, + 0.46999021385371126, + 0.4668407259441244, + 0.4627259182577826, + 0.457580819502309, + 0.45135227807917716, + 0.443986268880099, + 0.4354346093704612, + 0.4256597793248634, + 0.41463960288260365, + 0.402371533406097, + 0.3888759054049499, + 0.3741988828227728, + 0.3584116865673704, + 0.34162041716466884, + 0.3239512450023705, + 0.3055538867749792, + 0.2866051560996454, + 0.2672931467088079, + 0.24780955404839494, + 0.2283636008501122, + 0.20914294245802506, + 0.19034965248216765, + 0.17215123276961608, + 0.1547066700362756, + 0.13814908016827987, + 0.12258583632276684, + 0.10809176294021028, + 0.09472082886630974, + 0.08249664525019507, + 0.07141861419860691, + 0.06146439892620797, + 0.052592726510399965, + 0.044746881264334314, + 0.037859844319067304, + 0.03185737345177102, + 0.026660508299175857, + 0.022188285504819206, + 0.01836399291002223, + 0.015111029970174881, + 0.012358462061672579, + 0.010041329003901773, + 0.008100534283216646, + 0.006484411823298452, + 0.005145223458179957, + 0.0040433013946584336, + 0.0031425537937249397, + 0.0024119463896895574, + 0.0018251742264716157, + 0.0013587836107975435, + 0.0009929337957948932, + 0.0007103188976906927, + 0.0004958140169262481, + 0.00033674180456068104, + 0.00022155892603540473, + 0.00014050686344440675, + 8.537537377063353e-05, + 4.940131308062218e-05 + ], + [ + 0.5629027237187871, + 0.5622163408904358, + 0.5601565270094317, + 0.5566994988070805, + 0.5518478804206662, + 0.5455660468658217, + 0.5378258871119176, + 0.5286061922896387, + 0.5178904639845469, + 0.5056730694842407, + 0.4919636076266665, + 0.4767909634198985, + 0.46020652696840925, + 0.4422866551850789, + 0.42313423747986456, + 0.4028769182556888, + 0.38167462005866304, + 0.3597045173359666, + 0.3371639901314092, + 0.3142695898632523, + 0.2912443289970352, + 0.2683083433099892, + 0.24568999075090617, + 0.22359096660922076, + 0.2022173437178831, + 0.181736128035799, + 0.16229867886884453, + 0.14402482350594537, + 0.12700424479166758, + 0.11129295460637645, + 0.09692159686735587, + 0.08389010538164905, + 0.0721731967013342, + 0.06172531793393529, + 0.052483970265628, + 0.04437017148339037, + 0.03729902194648695, + 0.031179348953497905, + 0.025917897328893467, + 0.021421149185706877, + 0.01760263562431483, + 0.014376796608362233, + 0.01166659909974214, + 0.00940141590278607, + 0.007518461454610249, + 0.005961586755158458, + 0.004682284637197059, + 0.0036386853277941755, + 0.002793415869559352, + 0.002114632665125736, + 0.001575352303852847, + 0.0011520150651993858, + 0.0008244918492973348, + 0.0005754787675564666, + 0.00038990083071261723, + 0.00025531459331101845, + 0.00016048125892104503, + 9.596925325892243e-05, + 5.394035061423143e-05, + 2.8081748795621294e-05 + ], + [ + 0.6498612394467385, + 0.6489087449797646, + 0.6460381425546262, + 0.6412535080718917, + 0.6345624077704187, + 0.6259550437840771, + 0.6154515070918799, + 0.603054535030007, + 0.5887977740147168, + 0.5727260657832706, + 0.5549039676329679, + 0.5354185607366359, + 0.5143816523243196, + 0.4919309853265764, + 0.46823034521337337, + 0.44346683790007413, + 0.4178553128350659, + 0.39162417405948674, + 0.3650173940439503, + 0.3382884768099537, + 0.31169191343770486, + 0.285472346444682, + 0.2598721386952315, + 0.23510236349207803, + 0.21136734285056305, + 0.1888287618763502, + 0.1676257514986254, + 0.14786018342186397, + 0.1296002939506701, + 0.11288027289615127, + 0.09770528887337844, + 0.08404907561028604, + 0.07186121351594352, + 0.06107284304661855, + 0.05159766353075627, + 0.04333788431675178, + 0.03618930002153184, + 0.030045635980110175, + 0.024800008405106273, + 0.020347722403000746, + 0.016593692719768904, + 0.01344470353907425, + 0.010818033196395923, + 0.008639219946414043, + 0.0068421733414516725, + 0.005368311718907624, + 0.004167674410250076, + 0.0031975386765796033, + 0.0024197426759980756, + 0.0018020514615377777, + 0.0013174771056117952, + 0.0009424266821656414, + 0.0006570620773419391, + 0.00044423839849560084, + 0.00028926838862790635, + 0.00018009975880302193, + 0.00010589376332176137, + 5.782769779362839e-05, + 2.8529155009121845e-05, + 1.223599545043172e-05 + ], + [ + 0.7320728103321231, + 0.730835233239773, + 0.7271244347829081, + 0.7209631660108851, + 0.7123668881500028, + 0.701362723332969, + 0.6880039682686705, + 0.6723470302227128, + 0.6544751238779596, + 0.6344847963302698, + 0.6125039915706968, + 0.588683244150522, + 0.5631993103875639, + 0.5362546910040055, + 0.5080750574717839, + 0.4789118387052498, + 0.44903056892594356, + 0.41871073914188484, + 0.38824051429755224, + 0.3579065142443372, + 0.32799049022150767, + 0.2987569531076877, + 0.27045681253964315, + 0.2433056027721077, + 0.2175004276580272, + 0.1931931960495824, + 0.17050593005794148, + 0.14951922785744523, + 0.13027713187757023, + 0.11278833052930526, + 0.0970314848520196, + 0.082953688342777, + 0.07047873890201443, + 0.05951307768197156, + 0.04994974633728224, + 0.041671209478866766, + 0.03455569127081978, + 0.02848316299765738, + 0.02333454974591531, + 0.0189954206358946, + 0.015363458584150148, + 0.012339357386401463, + 0.009836065154126068, + 0.007776014692219573, + 0.006091161100286184, + 0.004721723501844101, + 0.003616690388581235, + 0.0027331625191613054, + 0.002033048254845014, + 0.0014841936619202295, + 0.001059932281980754, + 0.0007371688105140922, + 0.0004965648095664471, + 0.0003215226024600085, + 0.0001979131154257987, + 0.00011426851407963083, + 6.038376021227912e-05, + 2.8115118227409553e-05, + 1.0715239146350663e-05, + 3.05959336022603e-06 + ], + [ + 0.8069256147316811, + 0.8054055565011637, + 0.8008528638661877, + 0.7933030392068453, + 0.7827945121214505, + 0.7693974252430729, + 0.7531964049253773, + 0.7343011846001313, + 0.7128502690697669, + 0.6890023938940906, + 0.6629492966790825, + 0.6349082740491986, + 0.6051233549422685, + 0.5738631834311777, + 0.5414173898848135, + 0.5080954746390126, + 0.47421691403557115, + 0.4401080209452283, + 0.40609633342398493, + 0.37249807049320083, + 0.33961679495289043, + 0.307731619173359, + 0.27709542143747096, + 0.2479266087862646, + 0.22040637910435149, + 0.19467372862961438, + 0.17082988646967348, + 0.1489309349331588, + 0.12899468212103077, + 0.11100199773302147, + 0.0949046068562202, + 0.0806224939198231, + 0.06805333363003259, + 0.05708244861629575, + 0.047579750663216784, + 0.039411608679486836, + 0.03244003046436261, + 0.026532772965288564, + 0.02156048063181573, + 0.017400840185429072, + 0.013945877223542154, + 0.011091656643219708, + 0.008748429271283638, + 0.006836863165456913, + 0.005287803770283928, + 0.004041246046319398, + 0.0030462621056237815, + 0.002260289119707211, + 0.0016458191591995582, + 0.0011716503499698643, + 0.0008116691733935526, + 0.0005436811442097392, + 0.00034916575199219185, + 0.00021231144139908397, + 0.00011992992862884386, + 6.100543807488121e-05, + 2.644265667090839e-05, + 8.747636994868712e-06, + 1.9869952234171747e-06, + 1.6375508364452934e-06 + ], + [ + 0.8720442032409789, + 0.8702491708986119, + 0.8648808555359625, + 0.8559815222832873, + 0.8436210159733772, + 0.8279045426446053, + 0.8089614883601365, + 0.7869538808260422, + 0.7620764660161975, + 0.7345558458425017, + 0.7046457817654705, + 0.6726328908364633, + 0.6388283812734402, + 0.6035663502773387, + 0.5671985598458504, + 0.5300903118242121, + 0.4926112437198728, + 0.4551294358229652, + 0.41800905526045995, + 0.38158823051904806, + 0.3461872848277818, + 0.31209469757113806, + 0.2795616428886186, + 0.24879854053963832, + 0.2199717389718078, + 0.19320157698190846, + 0.16856533332674695, + 0.14609218978139057, + 0.125772150856407, + 0.1075570034905609, + 0.09137230343633383, + 0.07711085708705324, + 0.06464615768629067, + 0.05384261972367233, + 0.04455009117220875, + 0.036619730636735265, + 0.029899968963140143, + 0.024248525366431437, + 0.019527607909675636, + 0.015611323904385022, + 0.012381694265057098, + 0.00973825323194534, + 0.007587562450315985, + 0.005850008268725359, + 0.0044566455966759165, + 0.003348120110117935, + 0.002474502972700748, + 0.0017945123618450403, + 0.001271345101066136, + 0.0008754798926251378, + 0.000581805752530133, + 0.000369434811572513, + 0.0002208918308617226, + 0.0001214579101494229, + 5.8948586475320055e-05, + 2.3300838278301534e-05, + 6.337746373522589e-06, + 1.4319954320734767e-06, + 3.551458187168369e-06, + 8.897517501854965e-06 + ], + [ + 0.925372188174972, + 0.9233182516295043, + 0.9171788129313488, + 0.9070127871909831, + 0.8929160746068009, + 0.8750310707082279, + 0.853532618429466, + 0.8286365805645033, + 0.8005961051412964, + 0.7697003833091475, + 0.7362704559879133, + 0.7006586699508142, + 0.6632418159561544, + 0.624416651604133, + 0.5845936269269951, + 0.5441890720378023, + 0.5036178945954981, + 0.46328452407666026, + 0.42358360998565386, + 0.3848691217389193, + 0.34747332806853515, + 0.3116849334100206, + 0.2777512889243914, + 0.24586838491360416, + 0.2161847653268677, + 0.18879815802963668, + 0.1637593052385646, + 0.14106919702410234, + 0.12068942946931516, + 0.1025417497297331, + 0.08652756566295877, + 0.07251377260189576, + 0.060350361184438324, + 0.04988326397808134, + 0.04094515791881047, + 0.03337428227913982, + 0.02700790594197972, + 0.021696106128785336, + 0.017295175205549674, + 0.013675874806928043, + 0.010717836396476627, + 0.00832003162309564, + 0.006389081323512155, + 0.0048463110899276095, + 0.0036241693174644363, + 0.002664962550534139, + 0.0019206327399778822, + 0.0013515115706612376, + 0.000922784008620368, + 0.0006065997117551083, + 0.00037935200571961267, + 0.0002217108829521827, + 0.00011757261587016555, + 5.3545296309844936e-05, + 1.8624416325106547e-05, + 3.860966998049319e-06, + 2.0855351325888723e-06, + 7.660772928336561e-06, + 1.6448252972686875e-05, + 2.5570769604655395e-05 + ], + [ + 0.9652127445595656, + 0.9629245962898885, + 0.956087113259117, + 0.9447758228113123, + 0.9291155993019047, + 0.9092826524776363, + 0.8854962646171737, + 0.8580266578991509, + 0.827184050452218, + 0.7933186319995388, + 0.7568151576733952, + 0.7180896587759813, + 0.6775800934628461, + 0.6357418095156385, + 0.5930366834585521, + 0.5499278750281089, + 0.5068685834248422, + 0.4642929486909112, + 0.422619454273174, + 0.38221123171866905, + 0.3434058613872746, + 0.30648741110717126, + 0.27169329199007924, + 0.23920119905713552, + 0.20913936000983702, + 0.18157624704024405, + 0.1565380301672909, + 0.13399660046993533, + 0.11388479809734073, + 0.0960953628057041, + 0.08050609504205358, + 0.0669603473575163, + 0.05528976573126374, + 0.045317849182741766, + 0.0368701353663099, + 0.029769604809606554, + 0.023848923695951874, + 0.018951463978214067, + 0.014930328982805519, + 0.011655199365008306, + 0.009005525268201534, + 0.006881389307456359, + 0.005191110578165851, + 0.0038583119496691043, + 0.002817957066524816, + 0.002015029944942001, + 0.0014039583700192816, + 0.0009475336192530776, + 0.0006134403560607226, + 0.0003757495705648995, + 0.00021293753638839094, + 0.00010738244985780519, + 4.4591471126685936e-05, + 1.2734126784184388e-05, + 2.098900808665008e-06, + 5.0025318646316e-06, + 1.5356244290125695e-05, + 2.865067441024733e-05, + 4.153573824505412e-05, + 5.21495245616232e-05 + ], + [ + 0.9903051726549544, + 0.9878146008912376, + 0.9803738216269662, + 0.9680751049105082, + 0.9510702469680848, + 0.9295689899261917, + 0.9038348141117537, + 0.8741870606134716, + 0.8409910971381556, + 0.804654247353019, + 0.7656184685274138, + 0.7243608111604424, + 0.6813737813588636, + 0.6371649356261393, + 0.5922403589391764, + 0.5471023875299502, + 0.5022357416063644, + 0.45809623494704227, + 0.4151188385663251, + 0.37366926270131495, + 0.3340837739151948, + 0.29663617406169107, + 0.26154903738142904, + 0.22897808564722602, + 0.19902726071171586, + 0.17173683359924108, + 0.14710617392421654, + 0.12507635319731739, + 0.10555254458894289, + 0.08840266761712871, + 0.0734813661394295, + 0.060612170225094644, + 0.04960888815828901, + 0.04028120683432603, + 0.032444513508621035, + 0.025914451487786313, + 0.0205185610485743, + 0.016098429106914898, + 0.012506212886735407, + 0.009612704968484685, + 0.00729926697397975, + 0.005468870573115779, + 0.004033154171641625, + 0.0029193021863288607, + 0.0020659333011774574, + 0.001421119085017392, + 0.0009436954047184454, + 0.0005983366513226313, + 0.00035590865047930523, + 0.0001930496328574306, + 9.049392005654052e-05, + 3.2609726211807634e-05, + 6.726575686447048e-06, + 2.5899538204994686e-06, + 1.1971975798108292e-05, + 2.8570147918526947e-05, + 4.740202936342815e-05, + 6.509452839706312e-05, + 7.924087936578288e-05, + 8.877036702401515e-05 + ], + [ + 0.9998523195585817, + 0.997197304460724, + 0.9892674563965319, + 0.9761705238316257, + 0.958082902992081, + 0.9352454083213692, + 0.9079619520671961, + 0.8765986752437085, + 0.8415694651789003, + 0.8033341303399674, + 0.7623893553081568, + 0.7192576742764364, + 0.6744842598192644, + 0.628619195674221, + 0.5822052893526662, + 0.5357756586799839, + 0.4898375135605981, + 0.44486070615554113, + 0.4012883177238921, + 0.359482071419449, + 0.3197703670866477, + 0.28241147824265567, + 0.24760887834532225, + 0.21549302595279246, + 0.18614155882842398, + 0.159565375776332, + 0.13573652832209493, + 0.11456746479736549, + 0.09593747636020276, + 0.0796906614608501, + 0.06566248523015261, + 0.05365900437710052, + 0.04348012777708049, + 0.03492568115839189, + 0.027804064756336348, + 0.021927176196579464, + 0.01712072428544822, + 0.013227939895412008, + 0.010101504887572468, + 0.007614425137091731, + 0.00565514420164583, + 0.004129790511799002, + 0.0029548861938336556, + 0.002062408135555041, + 0.001395396610231123, + 0.0009063953801443067, + 0.0005579839332480669, + 0.00031844642355941444, + 0.00016184751335688913, + 6.765312356619716e-05, + 1.9105853207870472e-05, + 2.7415673039275873e-06, + 7.884757511326169e-06, + 2.58977364291866e-05, + 5.021919236249548e-05, + 7.583834682452619e-05, + 9.897634582277762e-05, + 0.00011740171307301289, + 0.0001296849493624406, + 0.00013551202964533413 + ], + [ + 0.9935520874192734, + 0.9907757963905761, + 0.982485744619407, + 0.9688060805080517, + 0.9499278191172859, + 0.9261272720728866, + 0.8977416164107705, + 0.8651767248738432, + 0.8288906112661697, + 0.7893877355659378, + 0.7472095176326113, + 0.7029227252300956, + 0.6571084348333822, + 0.6103503795658343, + 0.5632227929336843, + 0.5162780888227254, + 0.47003667911285446, + 0.42497434176936605, + 0.3815340549092338, + 0.34006676668903113, + 0.30088701397887485, + 0.2642327682423197, + 0.2302844934065917, + 0.19914602829232367, + 0.17086420046144316, + 0.1454273051971487, + 0.12276866641695518, + 0.10278488456733426, + 0.08532822148500857, + 0.07022218237687579, + 0.05728644338637502, + 0.046312587654289014, + 0.037091575521983854, + 0.029416890283193935, + 0.02309356827834589, + 0.01793428247939039, + 0.013764573990184433, + 0.010430919345579005, + 0.0077925784145552335, + 0.005727072068169946, + 0.0041291902615158155, + 0.002910960347420791, + 0.001995064953509107, + 0.001319302499516562, + 0.0008321967041751134, + 0.0004914198363243081, + 0.00026353688595347983, + 0.00012109635617031546, + 4.1513650615416963e-05, + 7.412349728500347e-06, + 4.670803196053627e-06, + 2.205963384594404e-05, + 5.1029227728110304e-05, + 8.470256258665196e-05, + 0.0001180683384734121, + 0.00014744518017419035, + 0.0001703043967570327, + 0.000185513709672511, + 0.00019270346556283182, + 0.00019196286953761317 + ], + [ + 0.9716047762488385, + 0.9687539303420271, + 0.9602434071521103, + 0.9462099462186172, + 0.9268603779708855, + 0.9024977690529816, + 0.8734890393966207, + 0.8402740936912305, + 0.8033451067325628, + 0.7632424904984721, + 0.7205445624634073, + 0.6758507585935088, + 0.6297708832650091, + 0.5829123314924598, + 0.5358669304279642, + 0.48919829877024223, + 0.44343015714750605, + 0.3990360375157482, + 0.3564440623873969, + 0.31600725563121207, + 0.27800164225774104, + 0.24264690065540928, + 0.21009746334426366, + 0.18042561873941715, + 0.15365761854164753, + 0.1297436550302283, + 0.10859605310728603, + 0.09008765649501897, + 0.0740494355549512, + 0.06028835335612002, + 0.0486115239211584, + 0.03880135034797256, + 0.030643338021714744, + 0.02392901442334901, + 0.01846389474917131, + 0.014063551949031625, + 0.01055927978135766, + 0.007801527485178056, + 0.005659255342177758, + 0.004016334035586085, + 0.002775627755348874, + 0.0018568661604797425, + 0.0011899669395777825, + 0.0007195534682963326, + 0.0004000360007380149, + 0.00019470033899799747, + 7.498181335815811e-05, + 1.7395488972384923e-05, + 3.389778040558911e-06, + 1.8504345429745474e-05, + 5.159902524936836e-05, + 9.357095274119562e-05, + 0.00013806978554794724, + 0.00018010910762596773, + 0.00021579530836627226, + 0.00024337858174646685, + 0.00026102493656669133, + 0.0002688889321941758, + 0.0002673815317899877, + 0.00025736843689491993 + ], + [ + 0.9347054186008733, + 0.9318288430305827, + 0.9232442600584697, + 0.9090973073026741, + 0.8896086163407225, + 0.8651008894108343, + 0.8359664869074374, + 0.802667661701062, + 0.7657272950233922, + 0.7257121398417259, + 0.683222216389176, + 0.638881155781874, + 0.5933170094535384, + 0.5471496878897995, + 0.5009777770590779, + 0.4553656988818086, + 0.4108318333688581, + 0.3678382647441571, + 0.3267960294032315, + 0.2880374516625019, + 0.2518122576293447, + 0.21831247933461023, + 0.1876640027797455, + 0.15991252702328432, + 0.1350469589096767, + 0.11299939935042037, + 0.09365547913034783, + 0.07686741788294199, + 0.062450885784687125, + 0.05019895637868777, + 0.0399105126331456, + 0.031363441525398515, + 0.024342230068915498, + 0.018639894833152308, + 0.01406644681448842, + 0.01044418671813373, + 0.0076123264869544845, + 0.005430176807579555, + 0.0037759959799523383, + 0.0025435945324376935, + 0.0016450723067852075, + 0.0010086561356119263, + 0.0005726828657805717, + 0.0002890911103186568, + 0.00011918445083117373, + 3.228153853259081e-05, + 4.223846610286388e-06, + 1.631855290992388e-05, + 5.374357170409571e-05, + 0.00010531299240575394, + 0.00016267466010720565, + 0.00021884738439686375, + 0.0002697043140701653, + 0.0003119245859864581, + 0.0003430989441875331, + 0.00036281687026596635, + 0.00037016597908138616, + 0.0003664780532198598, + 0.00035282476127221644, + 0.0003307242160238096 + ], + [ + 0.8840250878334367, + 0.8811722001142047, + 0.8726603421462182, + 0.858642778078253, + 0.839349014891219, + 0.8151190778085249, + 0.7863542028385327, + 0.753541853067339, + 0.7172176076073887, + 0.677967554922504, + 0.6364061144424675, + 0.5931652727504544, + 0.548879730715132, + 0.5041714630809715, + 0.45963543263697965, + 0.4158265007233806, + 0.37324823888293435, + 0.3323432808611656, + 0.29349837352384595, + 0.2570194862692803, + 0.22312623878300208, + 0.19198120914421216, + 0.16367819331390604, + 0.13823422590135637, + 0.11560930245167925, + 0.0957143636704059, + 0.07841250241587126, + 0.06354003934075059, + 0.05089874570079754, + 0.04027483197299163, + 0.031462847464561496, + 0.024239897175467037, + 0.01839417979516873, + 0.013724651844143081, + 0.010049217809448526, + 0.00720021538247045, + 0.005027515268082418, + 0.003401909838136166, + 0.0022126471266801532, + 0.0013655608606266086, + 0.0007828752820051278, + 0.00040217376711080486, + 0.00017126674049240822, + 4.9937700502181766e-05, + 6.4397232314886224e-06, + 1.613720031260545e-05, + 6.003617484238667e-05, + 0.00012398920383316868, + 0.00019665611807962875, + 0.00027012536091323297, + 0.00033874878313440866, + 0.0003979514708155257, + 0.00044526502130395884, + 0.0004791593546651981, + 0.0004985372031808242, + 0.000504195231588023, + 0.0004962600744337799, + 0.0004767735644099285, + 0.0004476125381090133, + 0.0004108150647414377 + ], + [ + 0.821170051545456, + 0.818389289938047, + 0.810100647259053, + 0.7964439370929222, + 0.7776741985851241, + 0.7541265745409804, + 0.7262187157862047, + 0.694443328147795, + 0.6593424605284989, + 0.6215100896555507, + 0.5815628544193864, + 0.5401319747105742, + 0.49784649743699794, + 0.45531841569223724, + 0.4131281940707393, + 0.37181146037581575, + 0.3318483699763412, + 0.29365439188010967, + 0.25758597253874826, + 0.22391763141366475, + 0.1928359154835871, + 0.16447112179894752, + 0.13888624535876326, + 0.11606960822142647, + 0.09595582334400067, + 0.07843429677114373, + 0.06335103624490704, + 0.050528689759621555, + 0.03976429073156567, + 0.030842532749291156, + 0.023544441817368433, + 0.017666166853003096, + 0.01299870727297078, + 0.009350948618495612, + 0.006552884854856642, + 0.004447110445376126, + 0.0028995921631562783, + 0.0017936117747628362, + 0.0010314702940381192, + 0.0005314029906593802, + 0.00022786714658823705, + 6.740331253021063e-05, + 8.579786087504606e-06, + 1.898811060333542e-05, + 7.395926707206855e-05, + 0.00015479836018347315, + 0.00024810191455610004, + 0.0003435385773563693, + 0.0004334770805028951, + 0.0005130048367912538, + 0.0005789884534330453, + 0.0006293027955119843, + 0.000662759763564106, + 0.0006796063381302035, + 0.0006798237200170351, + 0.0006653388069650906, + 0.0006370847138222104, + 0.0005977867365471237, + 0.0005499543317850922, + 0.0004962348390676047 + ], + [ + 0.7481330878261854, + 0.7454702751069806, + 0.7375363179633316, + 0.7244711255789902, + 0.706531687036316, + 0.6840543626306224, + 0.6574583874595568, + 0.6272358003207524, + 0.5939266380748742, + 0.5581173539611425, + 0.520418101340082, + 0.48144760034661904, + 0.4418182936535474, + 0.402121304071299, + 0.36291214222583945, + 0.3246979510088559, + 0.28792744412147225, + 0.25298209998142146, + 0.22018306102538626, + 0.18976883139358236, + 0.16189155481391782, + 0.1366479698848881, + 0.11407059852906859, + 0.09412066759833834, + 0.07671030712465986, + 0.06170895252873954, + 0.04895460239102772, + 0.038256887690466396, + 0.02941100272938338, + 0.02220323613268021, + 0.016420180208438436, + 0.011865547484412776, + 0.008342479317467568, + 0.005673411565368209, + 0.0037024600191071805, + 0.0022880715580319458, + 0.0013115073239842387, + 0.0006712594086896885, + 0.0002839547223661937, + 8.12870897956037e-05, + 9.572559065053497e-06, + 2.692240710660139e-05, + 0.000100813851014221, + 0.00020736449235154514, + 0.00032889330057710197, + 0.0004525261505186201, + 0.0005699938694182688, + 0.0006748819741136183, + 0.0007627870923865291, + 0.0008316621843432035, + 0.0008807018440024662, + 0.0009097063734367997, + 0.0009190027234073852, + 0.0009099610495704477, + 0.0008837580167681146, + 0.0008432668505536732, + 0.0007899472748241385, + 0.0007271297472535661, + 0.0006577178782081283, + 0.0005845858614638742 + ], + [ + 0.6672372250990103, + 0.6647265312395082, + 0.6572722384537597, + 0.6450040564017782, + 0.6281764924512879, + 0.6071200571497666, + 0.5822482061946469, + 0.554043334716837, + 0.5230332623048365, + 0.4897892376667877, + 0.4548998426875716, + 0.4189611338614715, + 0.38255909486883183, + 0.3462537929071217, + 0.31056658672042, + 0.27596755125122424, + 0.2428669693673398, + 0.2116067516223116, + 0.18246800476295388, + 0.15565193325525145, + 0.13127301177555, + 0.10939429367723542, + 0.09002128193474815, + 0.07308948557947076, + 0.05849163486264859, + 0.04608311543199059, + 0.03569323235393178, + 0.02712805889934607, + 0.020184202319696344, + 0.014654358928172528, + 0.01033518953138102, + 0.007041735965677151, + 0.004593146419076295, + 0.0028285548630783202, + 0.0016087665462219192, + 0.0008104656687663982, + 0.00033178914952691416, + 8.777783779269722e-05, + 1.0080321811562168e-05, + 4.4619864525805945e-05, + 0.0001496286676468194, + 0.00029499623642035503, + 0.00045694604898086934, + 0.0006199428064466352, + 0.0007729785211845511, + 0.0009086616636672382, + 0.0010237369718912584, + 0.0011145481779801713, + 0.001180386335659257, + 0.0012214643607256286, + 0.0012390247085399375, + 0.0012343389920781054, + 0.0012091826126692932, + 0.0011658969203549605, + 0.001106411057101991, + 0.001034054907684979, + 0.000951555588860261, + 0.0008619747514153561, + 0.0007684422815161093, + 0.0006742458866758378 + ], + [ + 0.5810319625703951, + 0.57872597529831, + 0.5718527114741859, + 0.5605643605804744, + 0.5450902108207756, + 0.5257595924386012, + 0.5029686739247063, + 0.4771813955130338, + 0.44890410310853, + 0.4186822367352162, + 0.3870751322122656, + 0.3546446794915498, + 0.32193900804459014, + 0.28947920962141205, + 0.25774388123567205, + 0.22715936310751988, + 0.1980914660219597, + 0.17083845808510884, + 0.1456349686282525, + 0.12264975064238912, + 0.10195483158496035, + 0.08358218478072671, + 0.06751243166029788, + 0.053657155995438875, + 0.04189430867557453, + 0.0320695637853986, + 0.024008080345551575, + 0.01751731317308125, + 0.012399903960386937, + 0.008459464178664288, + 0.0055068634324272605, + 0.003372109080850491, + 0.0018936274923183954, + 0.0009300521486975869, + 0.0003608753897045791, + 8.286528129477186e-05, + 1.2009223714986567e-05, + 8.083592133506891e-05, + 0.0002364115238238545, + 0.00043864994422061526, + 0.0006587702868264382, + 0.0008769669262663453, + 0.001078232835251445, + 0.0012550050193865902, + 0.0014023318039341507, + 0.001517821236573061, + 0.0016025496908999575, + 0.0016557092168824488, + 0.001679047210814147, + 0.001675485691601669, + 0.0016472573161006373, + 0.0015970650016365647, + 0.0015276524491041462, + 0.0014420181389807561, + 0.0013429257622595361, + 0.0012340415825244234, + 0.0011183820486898915, + 0.0009990733401625065, + 0.0008796705427689878, + 0.0007629714300489169 + ], + [ + 0.4922580695642674, + 0.49017941138684523, + 0.48399019944793514, + 0.47382175852563274, + 0.4599058117896175, + 0.44255015660433134, + 0.4221302792112559, + 0.3990836878466239, + 0.3738862009755928, + 0.34704858959688145, + 0.31909109196643465, + 0.2905331444039211, + 0.26187733253074347, + 0.23359603482961455, + 0.20611899464273842, + 0.17982292166437633, + 0.15502476783363453, + 0.1319760032778839, + 0.11086586460378386, + 0.09182072230777481, + 0.07488260012069355, + 0.06004957799005577, + 0.04727796396473411, + 0.0364628636994132, + 0.02746920204573232, + 0.0201390819020169, + 0.014297582186269798, + 0.009757907716700487, + 0.006334214321425098, + 0.0038443182289969874, + 0.002117562478878499, + 0.0010017821383174522, + 0.00035742333509654274, + 6.48972958168631e-05, + 2.404122323521531e-05, + 0.00015230131571737006, + 0.00038473431169777904, + 0.0006714712944381475, + 0.0009749460469223014, + 0.0012690218950989621, + 0.00153679928006321, + 0.0017688866362085718, + 0.001958011963597652, + 0.002104022948780582, + 0.0022073197294291106, + 0.002269766258924749, + 0.0022963126649735914, + 0.0022882388970209273, + 0.002249448546723572, + 0.0021845578772026228, + 0.0020968944983575434, + 0.0019900362488943133, + 0.001867367590784877, + 0.0017323403159304502, + 0.0015880674892178573, + 0.0014382964085334572, + 0.0012864568597999305, + 0.0011353363026656207, + 0.0009884581793978752, + 0.0008485122501247231 + ], + [ + 0.40373358997584896, + 0.40190538731364084, + 0.3964609036082745, + 0.3875295002974117, + 0.37532341246077794, + 0.3601292231436083, + 0.34229516461198506, + 0.3222251597924211, + 0.30035751858203513, + 0.27715956250328566, + 0.25310466595964753, + 0.22866193457221712, + 0.2042813395475727, + 0.18038102036151302, + 0.15733579057153935, + 0.13546857595123363, + 0.1150444731410199, + 0.09626525755248985, + 0.07927813884207073, + 0.06416499780947055, + 0.0509378631478481, + 0.03957076041885774, + 0.02998771898310556, + 0.02208091497190696, + 0.015705803637620776, + 0.010703339429124914, + 0.006903868739816273, + 0.00413134882064953, + 0.002214190294616098, + 0.0009897099734882489, + 0.0003083703994916127, + 3.8419315296878666e-05, + 6.440097711372844e-05, + 0.0002897067493924505, + 0.0006364541302013796, + 0.0010424784063357328, + 0.001461797508882532, + 0.0018626991836170558, + 0.0022224067321164535, + 0.002528069502541623, + 0.0027723998807205547, + 0.0029571470007019774, + 0.0030815894498406973, + 0.0031517259285003397, + 0.0031726647923437314, + 0.00314986087852856, + 0.0030908256661565554, + 0.0029988150308933328, + 0.0028791097612678503, + 0.002737551296015534, + 0.0025778253115454463, + 0.0024042558900099265, + 0.0022204124731323013, + 0.0020298521539467637, + 0.001835794363339881, + 0.0016419469610691718, + 0.0014515251897165504, + 0.0012671406160138473, + 0.0010920326850015513, + 0.0009285524308464452 + ], + [ + 0.3182575309669678, + 0.31669512001708444, + 0.31204442263854976, + 0.3044234228206685, + 0.29402542138811905, + 0.28111055944383445, + 0.26599561199017674, + 0.24904459672632226, + 0.2306516448956794, + 0.21123441807847657, + 0.1912131023019363, + 0.17100022720630292, + 0.1509874030821996, + 0.1315336951422288, + 0.1129557499678321, + 0.09552007958615398, + 0.07943860131888363, + 0.06486455071300726, + 0.05189962003742186, + 0.040587371226074545, + 0.030911800965120455, + 0.022822131708873608, + 0.01622636737607764, + 0.011006158469777325, + 0.007016490850216401, + 0.004101665100522834, + 0.002102144689947826, + 0.0008558049776189127, + 0.0002101823895115292, + 2.4850344214964076e-05, + 0.00017400267681941668, + 0.0005482510561084348, + 0.0010576221793547542, + 0.0016293746532762036, + 0.002208308524379329, + 0.002752511844455629, + 0.0032346364410606085, + 0.0036400787559935075, + 0.003959972430973929, + 0.004192968744323175, + 0.004343019403427464, + 0.004418957360261965, + 0.004426358824998226, + 0.004376470098901678, + 0.004277939346982891, + 0.00413880516063652, + 0.003968575082460028, + 0.0037714907965238752, + 0.0035537036083498064, + 0.003321505386626161, + 0.0030787749576284508, + 0.0028298734347311375, + 0.002578264142112072, + 0.0023271413899754816, + 0.002079946773067872, + 0.0018396122519305424, + 0.0016092514172495983, + 0.0013909381348632013, + 0.001187498052715989, + 0.0010007776929274704 + ], + [ + 0.23854328062402222, + 0.23725410999566038, + 0.23341720504064647, + 0.22713899410903854, + 0.21859035608335337, + 0.20800189303144317, + 0.19565390471344138, + 0.18186649851020875, + 0.16698497732506046, + 0.15137319748493672, + 0.1353899151154594, + 0.11938789328639639, + 0.10369938075760152, + 0.08862022026945687, + 0.07440672337825463, + 0.061268260823511646, + 0.04936376289791397, + 0.03879939684905962, + 0.029632877465322737, + 0.02187281525335382, + 0.015479119661348704, + 0.010380636598405534, + 0.006473993278586254, + 0.003634728998584357, + 0.0017224996693082574, + 0.0005895586277345865, + 8.893575278712512e-05, + 8.015888902686775e-05, + 0.00042954673035463907, + 0.0010225228256850233, + 0.0017589915495837658, + 0.002553233355190768, + 0.0033413876181774133, + 0.004074762210940121, + 0.004720492345624109, + 0.005256315981715919, + 0.005672463007108292, + 0.005970243322872536, + 0.006152684155351735, + 0.0062298351380473144, + 0.006215245243622136, + 0.00612240434980815, + 0.005962374862355358, + 0.005750431637335636, + 0.0054975966980176216, + 0.005213515655022876, + 0.004908738269990769, + 0.004587730192713303, + 0.0042567900845524335, + 0.003922141689573107, + 0.0035872694412344037, + 0.003256146735715116, + 0.002931636624414679, + 0.0026167363378604117, + 0.0023140556587835127, + 0.0020260716687659007, + 0.0017551855182259728, + 0.0015032451706952566, + 0.0012720919881302937, + 0.0010630479876238283 + ], + [ + 0.16711967574463626, + 0.1661014347990395, + 0.1630735596544258, + 0.15812731773171187, + 0.15141188125669328, + 0.1431243939081126, + 0.13350568742774538, + 0.12282839712885729, + 0.11138522721212891, + 0.09948202800351622, + 0.08741724445943874, + 0.07548107297194175, + 0.06393892304033641, + 0.053026807867921036, + 0.042940020914235204, + 0.03383162241092017, + 0.02580935546587426, + 0.018934964171456833, + 0.013225769286408362, + 0.00865944145780811, + 0.005176353580206649, + 0.002689800079301391, + 0.0010903736821946265, + 0.00025164085405816845, + 4.296142181827456e-05, + 0.0003291080557789576, + 0.0009792585029624397, + 0.0018777486646898826, + 0.002912283655114542, + 0.003995955858011789, + 0.00505560316417117, + 0.006029683060038328, + 0.006880363147475995, + 0.007582521010187002, + 0.008124692840411242, + 0.00850298237106538, + 0.008723610349622195, + 0.00880225241618482, + 0.008752447729979101, + 0.008593477620958597, + 0.00834564065047022, + 0.008027388358219109, + 0.007652992780344777, + 0.007240456829328282, + 0.006801963887121045, + 0.0063475508421373195, + 0.005887963734836791, + 0.005427043842399575, + 0.004970588836705004, + 0.004524077519745549, + 0.004090139104538166, + 0.003671898357885173, + 0.003271269424993463, + 0.0028906233328585083, + 0.0025316982834488557, + 0.0021960641528834305, + 0.0018853879307623121, + 0.0016007283973602882, + 0.001343214664229544, + 0.0011133587967570601 + ], + [ + 0.1062498438567482, + 0.10549261128411382, + 0.10324375624237146, + 0.09957950582164937, + 0.09462330578466448, + 0.08853932998935676, + 0.08152822583018725, + 0.07381137987999203, + 0.06562934088079264, + 0.057224371765102186, + 0.04883710844394885, + 0.040692742812300974, + 0.032993684897472425, + 0.02591313767785493, + 0.019588446440400007, + 0.014119018552615749, + 0.009564801946044492, + 0.005947025405914353, + 0.0032474473048547453, + 0.0014175820232672507, + 0.0003839795614187288, + 4.791278568717197e-05, + 0.0003016187751036742, + 0.0010200386311688564, + 0.0020868576902012986, + 0.0033833864448922606, + 0.00479825574677343, + 0.006243109265424506, + 0.007628972246816939, + 0.00889753321439098, + 0.01000308765774092, + 0.010906504142290583, + 0.011599877206300185, + 0.012075791776405888, + 0.012344166835432218, + 0.012417663097346508, + 0.012316482932025478, + 0.012068671027125175, + 0.011696180616090257, + 0.011225457684726402, + 0.010681732525576694, + 0.010084727723063375, + 0.009456039193097378, + 0.008809108303705883, + 0.008157860823723124, + 0.007512290427513179, + 0.006880974403523835, + 0.006267599744750765, + 0.005676306662076776, + 0.005111360198029563, + 0.004573858692597937, + 0.004066030134186554, + 0.0035878655224480032, + 0.0031412514309193127, + 0.0027266500612816522, + 0.002344638599437194, + 0.001995822214570491, + 0.0016803894471638752, + 0.0013986200994141646, + 0.0011500446692196825 + ], + [ + 0.057862956596603204, + 0.05734853849897705, + 0.055825156214092134, + 0.05335293328528392, + 0.050029631991742936, + 0.04598540948798792, + 0.041378149171143956, + 0.03638218943831185, + 0.03118065294649051, + 0.025959248723467995, + 0.02089628404148784, + 0.0161549686939039, + 0.0118764983414959, + 0.008175049591923628, + 0.005132802535933278, + 0.002799581451942013, + 0.001193472691370153, + 0.00029916196907813874, + 6.889589352843935e-05, + 0.0004337969287342621, + 0.001311959716693637, + 0.0025988940576403318, + 0.004192848055648781, + 0.005975353785714287, + 0.007849153862823772, + 0.009713128407276977, + 0.011480489643104093, + 0.01309107633334969, + 0.014480502750696381, + 0.01561919160986808, + 0.01648863513985826, + 0.01707240767663241, + 0.017387523658855125, + 0.017445919846410137, + 0.01727557358654581, + 0.0169034670094052, + 0.016361324803671723, + 0.015687211393833327, + 0.014909149625911167, + 0.014058729406581658, + 0.01316367545272082, + 0.012244915529961155, + 0.01132455764549815, + 0.01041526023280488, + 0.009529681737005894, + 0.008676149775206699, + 0.007861292767279912, + 0.007086026819758633, + 0.006354896071884403, + 0.005667852729694889, + 0.005025060243073039, + 0.004427054724791228, + 0.0038723950732885283, + 0.0033613458745276863, + 0.0028931314332736277, + 0.002467244205620741, + 0.0020830095975322618, + 0.0017396493852412911, + 0.0014363240313551402, + 0.0011716945457327357 + ], + [ + 0.023494561195482294, + 0.023198329001719517, + 0.022322928697106288, + 0.02091494162951542, + 0.019048388563700395, + 0.016817951443868846, + 0.01434051833364658, + 0.011740902848821701, + 0.009151579326359845, + 0.006700566087561618, + 0.004507746674725499, + 0.0026775162496407135, + 0.0012936013041518746, + 0.0004155615454199504, + 7.714137781247302e-05, + 0.0002824689544600415, + 0.001014236009121768, + 0.0022270164668121754, + 0.00385008302227085, + 0.005800446096345113, + 0.007993543915232323, + 0.010324970389397904, + 0.012703781696055147, + 0.015022863265935674, + 0.017202415376689616, + 0.019176756625194018, + 0.020870808799058293, + 0.022254453067660013, + 0.023300265304936955, + 0.023995032394849854, + 0.02435016912692558, + 0.024370724003887886, + 0.0240960157155228, + 0.023555240834641986, + 0.022791667778222537, + 0.02184147915642825, + 0.020752832058045043, + 0.01956318223634516, + 0.018306893510706676, + 0.017018232155677795, + 0.015725381598838545, + 0.014448494615776594, + 0.013208405890034044, + 0.012015601563543483, + 0.010880176760067512, + 0.00980768302284138, + 0.008800747364749902, + 0.00786124944214643, + 0.006987320753911674, + 0.0061779074338889, + 0.0054309213081497375, + 0.004744545031668922, + 0.004116359959864485, + 0.0035441745876604123, + 0.003025987246647923, + 0.002559887436680661, + 0.0021439689010657606, + 0.0017763065453683068, + 0.001454875452886765, + 0.0011772952318278673 + ], + [ + 0.00423377416527356, + 0.004123225605457359, + 0.0038019304076677436, + 0.0033000095871061983, + 0.002668145806835767, + 0.0019701091541871225, + 0.0012832053491440613, + 0.0006851932140757318, + 0.0002612076807731899, + 8.459732499292541e-05, + 0.0002216258095263685, + 0.0007230794945176907, + 0.0016209117723484422, + 0.002926601881290168, + 0.00463016028469997, + 0.006700910178819449, + 0.009089877315424827, + 0.011729580642923908, + 0.014533640391807616, + 0.01741155937689171, + 0.020282092731651578, + 0.023046551046366624, + 0.025629430485877947, + 0.027939371537059946, + 0.02992044499891919, + 0.031528646816780345, + 0.03272801588982468, + 0.033503109183555896, + 0.0338583682787008, + 0.033805518969418656, + 0.03338066828863072, + 0.03260836850627435, + 0.03154728137399651, + 0.030240994304303596, + 0.028744964290962436, + 0.027103965113455055, + 0.025372572068305985, + 0.02359170810043258, + 0.02179717903001979, + 0.020023373136601276, + 0.018296759900907993, + 0.016634867148951408, + 0.015055529568562572, + 0.01356567091068928, + 0.012171612006982942, + 0.010875117516463714, + 0.009675203613084571, + 0.008570239364040609, + 0.007555252378875516, + 0.00662651967316793, + 0.005779289165653173, + 0.005009324053478235, + 0.004312194074414637, + 0.003683889689480012, + 0.00312075463687313, + 0.002619366122421887, + 0.002176326088919987, + 0.0017887519114885935, + 0.0014532332020009376, + 0.0011662943161737137 + ], + [ + 0.0006905068919381993, + 0.000728341957652271, + 0.0008487722741048317, + 0.001067671637913996, + 0.0014144225584362105, + 0.0019227772643257458, + 0.002634124793792399, + 0.0035837430179260564, + 0.0048135260029154225, + 0.006348198401780844, + 0.008206216779260379, + 0.010391338279543298, + 0.012890953665397331, + 0.01567602496418611, + 0.018701420835411556, + 0.021907623829252845, + 0.025224071289241787, + 0.028568058855810163, + 0.03184537148234428, + 0.03496486669616551, + 0.03785432104900721, + 0.04042927510287932, + 0.042625150872734476, + 0.04438021015719414, + 0.0456590025791578, + 0.04644485028272008, + 0.046731412883853705, + 0.04652887682386931, + 0.045867975640992875, + 0.04478353351407855, + 0.043328976744965914, + 0.041560089133543594, + 0.039537084706209154, + 0.037319516537370125, + 0.03497162655766323, + 0.03254341416923363, + 0.030092736841583426, + 0.027661010380920833, + 0.02528282137685916, + 0.022990244809440362, + 0.020804761229369913, + 0.018742385633201766, + 0.016813668735131484, + 0.0150213625857347, + 0.013366975449162481, + 0.011847583799116098, + 0.010457899836219533, + 0.009192131734108603, + 0.008041863047911392, + 0.007000185237690998, + 0.006059379873078805, + 0.005212696650588987, + 0.004453466769451445, + 0.0037756993608806335, + 0.003173951215325555, + 0.0026432271298544342, + 0.0021786081647950464, + 0.0017761193997319843, + 0.0014309033958599924, + 0.0011385897120492652 + ], + [ + 0.01297706270764606, + 0.01312162734034835, + 0.013559135839743552, + 0.014292797674844829, + 0.01533297101896907, + 0.016686874605883837, + 0.018361716930151813, + 0.0203630997150902, + 0.022688103935447217, + 0.025321919164433156, + 0.02824277360350108, + 0.03141537344343823, + 0.03479104070428405, + 0.03830905341371717, + 0.041897991743201454, + 0.04547828349496724, + 0.04896620122161966, + 0.05227206011536525, + 0.05530156287005946, + 0.05796982052846403, + 0.060219196264617005, + 0.06198205135094309, + 0.06321622575089852, + 0.06388352122513372, + 0.06397597827801911, + 0.06350452367525619, + 0.06248975216855633, + 0.06096881455625245, + 0.05899327063250875, + 0.05662197140809592, + 0.05392564372549784, + 0.05097500839435839, + 0.04784121025175651, + 0.04459183415972654, + 0.04129620173660291, + 0.03800623384481555, + 0.034779641008890125, + 0.03165557387008368, + 0.028664561473218574, + 0.025833833196302326, + 0.023179117809924987, + 0.020710483999638894, + 0.01843175930538339, + 0.01634011306619415, + 0.014431027812169732, + 0.012696228511862338, + 0.011125284566874874, + 0.009707870791051466, + 0.00843194708690173, + 0.007286933209624005, + 0.006262019931782512, + 0.005347741388830539, + 0.0045350871488188515, + 0.0038159986246819218, + 0.0031831813882510773, + 0.002630051040590608, + 0.0021502986342986107, + 0.0017381687992760382, + 0.0013881320739609455, + 0.0010945318953236305 + ], + [ + 0.040703594691440505, + 0.04091028024004122, + 0.04153157437397584, + 0.04255979729847506, + 0.04398917360478345, + 0.04580483594130985, + 0.047986341593418774, + 0.0505107247363151, + 0.0533427391040046, + 0.05643406025732785, + 0.059731335815760116, + 0.06316927294961057, + 0.0666726074125704, + 0.07015856433124269, + 0.07353900899545361, + 0.07672364252068786, + 0.07962427181982197, + 0.08215293664536269, + 0.08422273598058683, + 0.0857618347775088, + 0.08673213934628252, + 0.08708751990492224, + 0.08681137835219585, + 0.08589145423864405, + 0.08434818029260954, + 0.08221970420705281, + 0.07955218703979185, + 0.07640818821423186, + 0.07285938285786145, + 0.06898265626538241, + 0.06486351890504234, + 0.06058379427372524, + 0.056221932545896434, + 0.051849411474850816, + 0.047537149541114355, + 0.043335416496074336, + 0.039298326658349855, + 0.03545974259144365, + 0.031844103533222076, + 0.02847123155412699, + 0.025349828330736568, + 0.022481052091974672, + 0.019861948615099424, + 0.017482610965243846, + 0.015331787670954698, + 0.0133949795770925, + 0.01165672293267576, + 0.010101403620615162, + 0.008712969233272572, + 0.007477170126307451, + 0.006380209763555449, + 0.005409481462761166, + 0.0045537066939769725, + 0.0038027172665778745, + 0.0031473597846911295, + 0.002579382539205387, + 0.002091201647043606, + 0.0016754212768537464, + 0.0013256531997306855, + 0.0010351011517409135 + ], + [ + 0.08299141716294343, + 0.08321407441980326, + 0.08387944061753734, + 0.08497509931906308, + 0.08648174850242235, + 0.08836437092349315, + 0.09058226189753699, + 0.09309085340253404, + 0.09583037475551065, + 0.09872836709644645, + 0.10170897831160915, + 0.10468680688500312, + 0.10757019893824357, + 0.11026450280908867, + 0.11267490076221977, + 0.11470989952043996, + 0.11628583283056149, + 0.11732442996948042, + 0.11775403945539942, + 0.11752193323219746, + 0.1166139946739866, + 0.11500976016225152, + 0.11272052643433478, + 0.10976162598840995, + 0.10618186380497695, + 0.10204568527405289, + 0.09742476054068427, + 0.09239945286873513, + 0.08706264916487742, + 0.08150646309107659, + 0.0758246660307672, + 0.07010717888559194, + 0.06443511488210678, + 0.05888078656489612, + 0.053508767532034124, + 0.048374778761039405, + 0.04351585779908682, + 0.038961476423497676, + 0.03472749233625256, + 0.030824150501353963, + 0.027251096994755412, + 0.024000589262820306, + 0.021060474986246653, + 0.018413596478888072, + 0.01604102383890775, + 0.013921896064081183, + 0.012034972207074066, + 0.010359428473309423, + 0.008874999681974433, + 0.007564019915728936, + 0.006409015623672137, + 0.005394769517473247, + 0.0045075517001988774, + 0.0037351497385064445, + 0.0030665820556684546, + 0.002491986434847425, + 0.002002391757400029, + 0.0015891973749905172, + 0.0012448702651814778, + 0.0009616862423606665 + ], + [ + 0.13849761057737145, + 0.13869223917729698, + 0.1392651856224688, + 0.14020079283389744, + 0.14146920064783144, + 0.14302439041837486, + 0.14481388098440626, + 0.14677306887703995, + 0.14882834003470624, + 0.15089308019249564, + 0.1528792777554331, + 0.15469123002263616, + 0.1562313390215686, + 0.15740361874281816, + 0.15811666874399963, + 0.1582873637240836, + 0.1578452231890916, + 0.15672955998195637, + 0.15489095346832538, + 0.1523014819497484, + 0.14897470676195734, + 0.14491911020817394, + 0.1401755125280508, + 0.13478763239327998, + 0.12883191959320237, + 0.12239738729925742, + 0.1155776595561078, + 0.1084715442864874, + 0.10118630001312653, + 0.09382448910911417, + 0.08648606054449277, + 0.07926522035393153, + 0.07223811102593454, + 0.0654774899665644, + 0.05904052579579371, + 0.052974057461367643, + 0.047306075223486364, + 0.04205538970710464, + 0.037227244339563224, + 0.03282077326038992, + 0.028824972171358394, + 0.02522184394681304, + 0.021989749303929725, + 0.01910321882758162, + 0.016535573100729877, + 0.014259111296203964, + 0.012246745312586306, + 0.010472352305845757, + 0.008911505680441726, + 0.007543110798300055, + 0.006346110095609861, + 0.0053026740264018974, + 0.004396765015910914, + 0.003614215742286686, + 0.002942296938796114, + 0.002369638785509048, + 0.0018859801575283933, + 0.001481521933721583, + 0.0011478267931186933, + 0.0008762666282789275 + ], + [ + 0.2054665097061255, + 0.2055839589652688, + 0.2059332826782499, + 0.20649098200321409, + 0.2072175012249374, + 0.2080666425053253, + 0.20897629846715776, + 0.2098744029532506, + 0.21068068740796253, + 0.21130377501477365, + 0.21165319149246437, + 0.2116346419913157, + 0.2111550678176785, + 0.2101269764870531, + 0.20847231650957382, + 0.2061274892912031, + 0.20304114280795094, + 0.19917289078341183, + 0.1945101170782563, + 0.18905119987111976, + 0.18284037662831087, + 0.17591741476447803, + 0.16835343718744103, + 0.1602205913929253, + 0.15162148127459574, + 0.1426672769235147, + 0.13347051212765512, + 0.12414331692354795, + 0.11480816875234356, + 0.10556887385291905, + 0.09652893417966645, + 0.08778073400595132, + 0.0793965454926807, + 0.07144087268035602, + 0.06396166640873581, + 0.05699361519169941, + 0.05055318847753517, + 0.04464484244764124, + 0.039266057005448426, + 0.03439866355396664, + 0.03002136155105376, + 0.026105375843640206, + 0.0226191095473421, + 0.019528137133286234, + 0.01679809080472144, + 0.01439414114167531, + 0.012283368498782365, + 0.01043472068462379, + 0.008819520767078962, + 0.007413306420498381, + 0.00619174587817442, + 0.005134526349510766, + 0.004223435683552653, + 0.0034424993157144046, + 0.0027773799441909506, + 0.002215327678458016, + 0.0017448508979052873, + 0.00135527162834962, + 0.0010371217901808563, + 0.0007811257608756224 + ], + [ + 0.28177291527294335, + 0.281773324849266, + 0.2817717315216104, + 0.281743401276682, + 0.28164872148566966, + 0.28143663634523264, + 0.2810487988487902, + 0.2804121039113269, + 0.27944855279578307, + 0.27807181183444674, + 0.27619922003380964, + 0.2737476607301899, + 0.2706392257945569, + 0.2668053923520026, + 0.26219054062276775, + 0.2567569873184205, + 0.25048217135944034, + 0.2433575239283181, + 0.2354038796570524, + 0.22666302452954185, + 0.21718323511201382, + 0.2070656469328969, + 0.1963974791373237, + 0.1852922334383444, + 0.173862752256286, + 0.16224483870314169, + 0.1505636528031598, + 0.1389453026715221, + 0.1275169830805152, + 0.11638458227867687, + 0.10564909727213428, + 0.0953970500801184, + 0.0856926046979591, + 0.0765888373503187, + 0.0681213055559694, + 0.0603090694697636, + 0.05315595864646159, + 0.04665182968627145, + 0.040778901874686135, + 0.035506643310484844, + 0.030800848950361417, + 0.02662154687570587, + 0.022926276327822216, + 0.019672786070535634, + 0.016817719285686004, + 0.014320147912382382, + 0.012141485964301587, + 0.010245340775012482, + 0.008600499326841848, + 0.0071766333542847794, + 0.00594891557489064, + 0.004893946801706262, + 0.003991537418841493, + 0.003224115193837691, + 0.002575908628316124, + 0.002033011781586767, + 0.0015827611963066361, + 0.0012137738915324707, + 0.0009158536790642701, + 0.0006790826977863567 + ], + [ + 0.3649975464760929, + 0.36484308806255383, + 0.36437747402713905, + 0.36357769621001546, + 0.36240680351971816, + 0.3608179487914169, + 0.3587590676699804, + 0.356165990440439, + 0.35297212412874684, + 0.34910492872734444, + 0.3444992951696443, + 0.3390932897392625, + 0.33283377418908805, + 0.32568036423933444, + 0.3176085932146083, + 0.30861432616269197, + 0.29871020505106416, + 0.2879229930717016, + 0.27631791326173494, + 0.26396577348165606, + 0.2509535349932059, + 0.2374130374339847, + 0.2234618592778824, + 0.20923872201444815, + 0.19487838280324352, + 0.18053179637020603, + 0.1663362966039784, + 0.15242441374539759, + 0.13892457582008075, + 0.12594052611150303, + 0.11356654980787424, + 0.10187913686936674, + 0.09093102276717008, + 0.08076058981483812, + 0.07138789461111424, + 0.06281557384898487, + 0.055030836554190846, + 0.04800892662256923, + 0.04171535966054861, + 0.03610683884771154, + 0.031135676416488754, + 0.026750522797338104, + 0.022899598644756356, + 0.01952925724119691, + 0.016590970194891894, + 0.014036714138899162, + 0.011822673674029761, + 0.009907592656396362, + 0.00825762573592666, + 0.00683856926223054, + 0.005623517563977388, + 0.004586979773609843, + 0.0037070613843246925, + 0.0029648344755772403, + 0.0023433373863806584, + 0.001827644871634583, + 0.001404296542081102, + 0.0010611840577350487, + 0.0007876231213763338, + 0.000573186331578731 + ], + [ + 0.45250228911604556, + 0.4521602420996912, + 0.4511331301507734, + 0.4494023126562241, + 0.4469379042402598, + 0.44370193932358415, + 0.43965530594450536, + 0.4347499603515186, + 0.42893863084452594, + 0.422172807617931, + 0.4144132546129381, + 0.4056281592285662, + 0.3957979486472448, + 0.3849186456842437, + 0.37300448643094697, + 0.3600913059629933, + 0.34623258494836956, + 0.3314971648418394, + 0.3159901516368037, + 0.29982054371945777, + 0.2831123339326859, + 0.26602683449130554, + 0.24871043075011706, + 0.23132460530106108, + 0.21402271502096662, + 0.1969671263268043, + 0.18030304122290564, + 0.1641651092156806, + 0.14867833021768082, + 0.13394021055766703, + 0.1200345143197691, + 0.10702396619089019, + 0.09494657161243525, + 0.08382327813757907, + 0.07365646614840517, + 0.06443003912181852, + 0.05611498680095273, + 0.0486691457079754, + 0.04204150463607623, + 0.03617582562916678, + 0.031010982263543437, + 0.026484192134090503, + 0.02253412426472072, + 0.019098239323399803, + 0.01612139435966473, + 0.013549407691803694, + 0.011334091391708583, + 0.00942966342887544, + 0.007799911394768927, + 0.0064075820148994, + 0.0052239042048980696, + 0.004221677411190219, + 0.003377618190645085, + 0.0026717516208855825, + 0.0020861618338801277, + 0.0016051746631471602, + 0.001214677532089168, + 0.0009019496179264066, + 0.0006563717267141935, + 0.00046684986631950276 + ], + [ + 0.5415125766024494, + 0.5409565894446381, + 0.5392896026829028, + 0.5364993831540842, + 0.5325667486907263, + 0.5274680280019404, + 0.5211825398228664, + 0.5136854170354891, + 0.504956229800178, + 0.4949778792685461, + 0.4837459903759283, + 0.4712668347766522, + 0.45756171274873614, + 0.4426700903434469, + 0.4266509899594227, + 0.4095854907637832, + 0.3915721654921319, + 0.37272134800342566, + 0.353190606271275, + 0.3331151778720759, + 0.31266418789364947, + 0.29202159151147833, + 0.27136193872283, + 0.25086604090669457, + 0.2307025609540212, + 0.21104061027557947, + 0.19202917215497525, + 0.17380068959520348, + 0.15647227908983624, + 0.140131519209838, + 0.12484744700372133, + 0.11066640944634862, + 0.09760864271259144, + 0.08567576517650681, + 0.07485041760357246, + 0.06509682383598615, + 0.05636838681029155, + 0.048606349980002427, + 0.041741845077348814, + 0.03570637999342974, + 0.030426328264602464, + 0.025826079861778685, + 0.021837271686657386, + 0.018388801395938667, + 0.015419753502228175, + 0.012870145127800435, + 0.010687991722376828, + 0.008823725061553671, + 0.0072394173172860175, + 0.0058952246852303014, + 0.004760955073000036, + 0.00380814155221349, + 0.003012474821459275, + 0.0023532429712815072, + 0.0018118534076929894, + 0.0013721512090924886, + 0.0010196527412784787, + 0.0007413222232945901, + 0.0005264949584470738, + 0.0003636082888765968 + ], + [ + 0.6292064890024925, + 0.628417299037685, + 0.6260529692474762, + 0.6221098900836053, + 0.6165825959716507, + 0.6094667178512573, + 0.6007645203236677, + 0.590480589783234, + 0.5786280538805267, + 0.5652280997743866, + 0.5503176993902386, + 0.5339481640936723, + 0.5161881600074895, + 0.4971260566391105, + 0.476870246704869, + 0.4555507087809781, + 0.4333121966916145, + 0.41031821648637345, + 0.38676014656988394, + 0.3628160760876412, + 0.3386886206614074, + 0.3145873048428754, + 0.2907098682661205, + 0.267252588798497, + 0.24439601079221387, + 0.22231033507237286, + 0.20114463176481528, + 0.18102576290080472, + 0.16205760405062317, + 0.1443146357075236, + 0.12784874136327679, + 0.11268546730636933, + 0.09882662464007475, + 0.0862525127575982, + 0.07492451787827883, + 0.06478753926975415, + 0.05577704201536471, + 0.04781540560551465, + 0.040819073197276005, + 0.034706937075141886, + 0.029393194086869783, + 0.02479153026191876, + 0.020826565571153064, + 0.01741946368605109, + 0.014504197343346712, + 0.012016771486752157, + 0.00990164355812724, + 0.008106352052695604, + 0.006591523535855595, + 0.005315822162362022, + 0.004247807984793126, + 0.003358294409837598, + 0.002622428981205951, + 0.0020187674945263863, + 0.0015287276980108112, + 0.0011358229388013217, + 0.0008253820420939021, + 0.0005843465331011746, + 0.00040204283280013725, + 0.00026704622997361974 + ], + [ + 0.7128035925068799, + 0.7117703838279865, + 0.7086735391928739, + 0.7035217726544248, + 0.6963251786333522, + 0.687102494422985, + 0.6758843805381097, + 0.6627092392821554, + 0.6476289054936345, + 0.6307083881623404, + 0.6120317166621717, + 0.591700308349679, + 0.5698349046605828, + 0.546576698722353, + 0.5220867706420277, + 0.4965460334492029, + 0.47014904705398153, + 0.4431058096152621, + 0.41564636513683767, + 0.38799070624227305, + 0.3603694945993648, + 0.33301533673838, + 0.30614539898632076, + 0.27996725938047784, + 0.25466829004804586, + 0.23041724916276698, + 0.2073579810109174, + 0.18560611786384223, + 0.1652507107220382, + 0.14634989584839653, + 0.12893455559704706, + 0.11300840559709105, + 0.09855283856929557, + 0.0855261108064794, + 0.07386793766516436, + 0.06350319832841445, + 0.05435022691097225, + 0.046313688098800924, + 0.03929511787070384, + 0.03320228307341039, + 0.02793852921821702, + 0.023408921613482275, + 0.019528887255179372, + 0.016216345308843298, + 0.013400267995174842, + 0.011013192434998612, + 0.008996613004524704, + 0.007297850088091612, + 0.005875055268525487, + 0.004686030359811274, + 0.003699452682131346, + 0.002885423568722936, + 0.002218945385161108, + 0.0016785620738366223, + 0.001245607640234245, + 0.0009036909466553826, + 0.0006382506911267636, + 0.0004363364794853912, + 0.000287529428199121, + 0.00018074056713106068 + ], + [ + 0.7896531550368023, + 0.7883709953389649, + 0.7845315692333558, + 0.7781547195278302, + 0.7692689568898752, + 0.7579184132211233, + 0.7441659078318764, + 0.7280876520027187, + 0.7097787479036578, + 0.6893516976203082, + 0.6669412366396471, + 0.6427027536025494, + 0.6168119479381736, + 0.5894651188138459, + 0.5608775236545291, + 0.5312815132114617, + 0.500921288066203, + 0.4700519444869481, + 0.43894140095423817, + 0.4078448032165806, + 0.37702138382278444, + 0.3467213934489429, + 0.3171771230915171, + 0.28860295179592627, + 0.2611886575433551, + 0.23509695625925195, + 0.21046282318404616, + 0.18738692773246132, + 0.16594041891836592, + 0.14616151583002143, + 0.1280592320242734, + 0.11161358395408388, + 0.09678479452307279, + 0.0835087494973767, + 0.07170363125803703, + 0.061274758317619804, + 0.05212428379367646, + 0.04414020005542793, + 0.03721060664843486, + 0.031233453572794594, + 0.026102287620000452, + 0.021714630646928135, + 0.017980435157272493, + 0.014813405744858866, + 0.01213912305534313, + 0.009888047961875441, + 0.008000134669378023, + 0.006423688909890344, + 0.005111003946214899, + 0.004024817399391713, + 0.0031323791385460074, + 0.0024040283686593013, + 0.001814739127758554, + 0.0013433623487487752, + 0.0009716293054535225, + 0.0006834532523279614, + 0.0004646634794924988, + 0.00030258997361105037, + 0.00018725662313394528, + 0.00010811526992152918 + ], + [ + 0.8573197205503741, + 0.8557924570216863, + 0.8512233992018703, + 0.8436435710519755, + 0.833102944078497, + 0.8196714603492092, + 0.8034472242244058, + 0.7845475728512877, + 0.763111673681884, + 0.7393035435477132, + 0.7133109296780964, + 0.6853442630990388, + 0.6556355962559621, + 0.6244368830473768, + 0.5920172317816743, + 0.5586594293354583, + 0.5246555253481993, + 0.49030301826390554, + 0.45590439478469946, + 0.4217461704341959, + 0.38811179101635745, + 0.35526462697603733, + 0.32344734781841283, + 0.2928764273372802, + 0.2637396289186492, + 0.23618963575961197, + 0.21034845592604812, + 0.18629826007745595, + 0.1640906426442469, + 0.14374160023564267, + 0.125236789917023, + 0.10853538125554626, + 0.09356727296783003, + 0.08025222375956663, + 0.06848882161176, + 0.05816235028003675, + 0.0491602890306696, + 0.04135529388501564, + 0.03462392207335104, + 0.028855895352915047, + 0.02393663410205629, + 0.019758005173670202, + 0.01622617919762018, + 0.013251328087977953, + 0.0107578472880631, + 0.008674641690098128, + 0.006941397357664119, + 0.005506417626132101, + 0.004322271005715928, + 0.003352441483162653, + 0.0025642933040641008, + 0.0019291708259291111, + 0.001422676658465063, + 0.0010241461538431109, + 0.0007160034250527689, + 0.0004827503876954144, + 0.00031084667351430583, + 0.00018835856216492216, + 0.00010526274764715451, + 5.233285099016027e-05 + ], + [ + 0.9136578794279929, + 0.9118981617853051, + 0.9066357512711962, + 0.8979131356128844, + 0.8858032323365265, + 0.8704054896108608, + 0.8518519455561713, + 0.8303013978053858, + 0.80593954881625, + 0.7789830643101303, + 0.7496728156000935, + 0.7182745786879872, + 0.6850759257939029, + 0.6503832163674141, + 0.6145175186503061, + 0.5778095166294362, + 0.5405956249882238, + 0.5032117487920196, + 0.4659906610946226, + 0.42924553955373007, + 0.393278947753135, + 0.35836253742044494, + 0.32474429050956, + 0.29263809228430465, + 0.26222535170504796, + 0.23364483280393133, + 0.20700231155128013, + 0.182359070457465, + 0.15974467086275668, + 0.13915186632530652, + 0.12054229973543279, + 0.10385174989640208, + 0.08898688857209429, + 0.07584799828202288, + 0.06431459177543172, + 0.05425548001513051, + 0.04554298446678773, + 0.038039091197047153, + 0.03160993352467447, + 0.02613882126391848, + 0.02150524888459166, + 0.017596216172200016, + 0.014317859689101287, + 0.011576766667060189, + 0.009297746546267593, + 0.007409551965722181, + 0.005852559299677877, + 0.004575862637359387, + 0.003533412564989778, + 0.0026898650773884173, + 0.0020134076091896627, + 0.0014763556225806792, + 0.001055735406289628, + 0.0007318080237944852, + 0.00048774748459227307, + 0.00030895601571658525, + 0.00018272030937772083, + 9.791654212612659e-05, + 4.521534940334081e-05, + 1.6197576808247986e-05 + ], + [ + 0.9568792895434172, + 0.9549067010642858, + 0.9490094299215415, + 0.9392436393139257, + 0.9257004219383662, + 0.9085124303424055, + 0.8878443499452368, + 0.8638970939441054, + 0.8369043875381428, + 0.8071316979000527, + 0.7748729080359638, + 0.7404475585754302, + 0.7041963353152368, + 0.666477105633875, + 0.6276592448839636, + 0.5881170327846039, + 0.5482271056247623, + 0.5083582055216416, + 0.4688681644728869, + 0.4300914624903183, + 0.39234411054325347, + 0.3559008111154973, + 0.3210097987849889, + 0.2878777552403987, + 0.2566756042446697, + 0.22752484784201693, + 0.20051218771166485, + 0.17567604391663882, + 0.1530226315675285, + 0.1325202297720077, + 0.11410861619632333, + 0.09769879357773491, + 0.08317625216838694, + 0.07042315577429112, + 0.059302049360354124, + 0.04967096436236171, + 0.04137859933452043, + 0.034286860506808445, + 0.02825790835513378, + 0.02316308995648737, + 0.018880670766127972, + 0.01529545125872475, + 0.01231317892208613, + 0.009840599305327503, + 0.007803548278826974, + 0.006131828431126946, + 0.004767555462789492, + 0.003661614699528465, + 0.0027698685588294146, + 0.002058602504598455, + 0.0014977164855147977, + 0.0010609302108772986, + 0.0007267130187594872, + 0.0004767121842137601, + 0.0002953047843783068, + 0.00016883764101399123, + 8.566395211254166e-05, + 3.56523281769657e-05, + 1.0269734579191057e-05, + 2.0454520969030252e-06 + ], + [ + 0.9856161568693496, + 0.9834568303951562, + 0.977002666975467, + 0.9663221011590329, + 0.9515298908859661, + 0.9327838799764709, + 0.910283118443375, + 0.8842692821129124, + 0.855021369080477, + 0.8228528275801404, + 0.7881077596386575, + 0.7511548888209769, + 0.7123837384898171, + 0.6721998614911875, + 0.6310157493931795, + 0.589243581530503, + 0.547294610157528, + 0.5055645419850247, + 0.464429531849438, + 0.424239599206698, + 0.3853183247389804, + 0.3479380047657059, + 0.3123423429938582, + 0.2787259421951832, + 0.2472460011964128, + 0.21800541283490935, + 0.191064282822286, + 0.16644221841530865, + 0.14412156656208439, + 0.12404142290758804, + 0.10612422185027917, + 0.09025743906345249, + 0.07630670578456678, + 0.06413901877145058, + 0.05360101133666568, + 0.04453819020129508, + 0.036791562293397015, + 0.03021603203228753, + 0.024668853012952095, + 0.02001877883144337, + 0.016141118446950316, + 0.012925503177051177, + 0.01027390800666211, + 0.008096748891406814, + 0.0063219885005739405, + 0.004881802956944933, + 0.003721007519308589, + 0.002793137517480884, + 0.0020564703339003704, + 0.0014802518764050032, + 0.00103476427268747, + 0.0006972799194204542, + 0.00044754233872298737, + 0.0002685942103075745, + 0.00014636376443875006, + 6.845016964376633e-05, + 2.4331034759514197e-05, + 5.033516230042751e-06, + 2.966483565814343e-06, + 1.1651165792704424e-05 + ], + [ + 0.9989572049764809, + 0.9966431283817676, + 0.9897280205956135, + 0.9782916851876845, + 0.9624700069101073, + 0.9424466376444991, + 0.918452846365059, + 0.8907684801677254, + 0.8597122112015703, + 0.8256426804458376, + 0.7889498467697753, + 0.7500470784452802, + 0.7093681338299903, + 0.6673583264501476, + 0.6244672375472489, + 0.5811407702618024, + 0.537811040133735, + 0.49490094865692286, + 0.4527960963829482, + 0.41185510545151777, + 0.37240315504299026, + 0.3347050036176573, + 0.29899473328780385, + 0.26545111042110553, + 0.23421414733861584, + 0.20536448952525727, + 0.1789382632842834, + 0.1549316182173498, + 0.13330293063882473, + 0.11396770498250944, + 0.09682769710552382, + 0.08175087870391295, + 0.06858468716944612, + 0.05718386532238137, + 0.04738213202076284, + 0.039016511836381954, + 0.03192188122525471, + 0.02594895141500616, + 0.020953247591694094, + 0.016803152645699274, + 0.01337497268734335, + 0.010560365940425583, + 0.008264249782998076, + 0.006400484070017651, + 0.004900485131417625, + 0.0036999094868481537, + 0.0027472556819610845, + 0.0019992452381593145, + 0.001417494405730545, + 0.0009737942826789031, + 0.0006411176182248753, + 0.0003989021974364715, + 0.00022892310037077242, + 0.00011606255757331926, + 4.765716402051231e-05, + 1.2881872256662563e-05, + 2.4771429923532924e-06, + 8.713510671224076e-06, + 2.511849391237832e-05, + 4.6175582326546546e-05 + ], + [ + 0.9964790522670987, + 0.9940470040288114, + 0.9867810027685164, + 0.9747735196115752, + 0.9581737662495857, + 0.937193830829768, + 0.9120924216582267, + 0.8831829367061355, + 0.850822563303855, + 0.8154055106072523, + 0.7773639439159142, + 0.7371491158106378, + 0.695231701164531, + 0.6520905410880183, + 0.6082043360197139, + 0.564043628014008, + 0.5200581312612472, + 0.4766853106042986, + 0.43431525865177584, + 0.3933086134801768, + 0.3539853060486763, + 0.31659862384971343, + 0.28136776775828815, + 0.24845214413077904, + 0.21797200440914097, + 0.18998425208807582, + 0.16449990538888656, + 0.1414915671060031, + 0.12089426169637103, + 0.10260393147605744, + 0.08650130226698828, + 0.07243715601178845, + 0.06024574342151662, + 0.04977107443351636, + 0.04083661122350429, + 0.033275790328447324, + 0.026919657379954685, + 0.021617892946601817, + 0.017226823430831394, + 0.013616951493448166, + 0.010667897129799141, + 0.008275346616859648, + 0.006348652815327596, + 0.004808414868339055, + 0.0035856626673026726, + 0.0026255628524483056, + 0.0018792037843319038, + 0.0013073591269389543, + 0.0008754786407914811, + 0.0005582409741267033, + 0.00033173811700371985, + 0.00017771471739958184, + 8.025850437046869e-05, + 2.6199514736588745e-05, + 4.573130378055742e-06, + 6.058376968982603e-06, + 2.2817259889720698e-05, + 4.846374287674309e-05, + 7.777889135903302e-05, + 0.00010607142256306664 + ], + [ + 0.9782609361229391, + 0.9757513827216401, + 0.9682554973432429, + 0.9558754288699389, + 0.9387748760863216, + 0.9171888637268788, + 0.8913996671826164, + 0.8617482315019416, + 0.8286247957046083, + 0.7924578311074209, + 0.7537074520561557, + 0.7128576204667512, + 0.6704089376549789, + 0.6268650668691786, + 0.5827253955516362, + 0.53847698392082, + 0.49457819634207834, + 0.4514737372975289, + 0.4095507963367141, + 0.3691655104875643, + 0.33062647156874464, + 0.2941702291027152, + 0.2599979224449494, + 0.2282472598289826, + 0.19901478321569124, + 0.1723330976428504, + 0.14818920128274118, + 0.12653292755217566, + 0.10727713070204546, + 0.09029855762721466, + 0.07546144159495674, + 0.0626029199390516, + 0.05154724299517183, + 0.04212936786724391, + 0.03416771081858771, + 0.02749512180135878, + 0.021941548133682303, + 0.017359206721015423, + 0.01360780219139759, + 0.0105620116069649, + 0.008107172947859537, + 0.006144736603693998, + 0.004590091035045849, + 0.0033703595290191105, + 0.0024220541330892942, + 0.0016956271284216402, + 0.0011473823001665238, + 0.0007424591345714852, + 0.00045070732667143194, + 0.00024987772752001826, + 0.0001194481582464459, + 4.368053783043357e-05, + 9.094589855214438e-06, + 4.601368572702346e-06, + 2.0984879455415787e-05, + 5.054649933277493e-05, + 8.693245078331577e-05, + 0.00012504773151850133, + 0.00016106157133165884, + 0.00019094758722557254 + ], + [ + 0.9448805247701795, + 0.9423361762536234, + 0.9347379436847052, + 0.9221964332641303, + 0.90488649123894, + 0.8830619909941355, + 0.8570243422485198, + 0.8271383917636366, + 0.7938163229453855, + 0.7575142191820448, + 0.7187173515161264, + 0.6779301853499157, + 0.6356721945540931, + 0.5924652724908193, + 0.5488202055354301, + 0.5052312215558855, + 0.4621583740333706, + 0.42004413417473874, + 0.379266153492995, + 0.34016909146645014, + 0.3030454758520396, + 0.2681104490202701, + 0.23554321381628116, + 0.20545688333062115, + 0.17792470223152848, + 0.15295413688559745, + 0.13050844180839966, + 0.11051608287164459, + 0.0928703192581148, + 0.07743187803233638, + 0.06405054134323686, + 0.05255408620406557, + 0.042759786083661, + 0.034497914099160545, + 0.02758590093614747, + 0.02185717412267785, + 0.017146666635807297, + 0.013309874654159514, + 0.010213047853152279, + 0.007737967409388264, + 0.005777056687544334, + 0.0042395438019218355, + 0.0030484199109431314, + 0.00213730613536816, + 0.0014503489026227625, + 0.0009435458791374532, + 0.0005790114467157469, + 0.00032637966976895304, + 0.00016048557773605602, + 6.212660823326236e-05, + 1.4514819704533783e-05, + 4.423827039043575e-06, + 2.0885356324114214e-05, + 5.495068842581916e-05, + 9.91781703659201e-05, + 0.00014754552461882748, + 0.00019514638876382668, + 0.00023817793328130524, + 0.00027410253217662923, + 0.0002999922787415758 + ], + [ + 0.8973958563865511, + 0.8948604081439057, + 0.8872903389080399, + 0.8748025777001559, + 0.8575808729387406, + 0.835892998718238, + 0.8100520292068546, + 0.7804409702110467, + 0.7474928611364605, + 0.7116748092692002, + 0.6734907238978148, + 0.6334585332285463, + 0.5921075045533976, + 0.5499652347610887, + 0.5075458166815597, + 0.46534194738455914, + 0.4238068610742872, + 0.3833728901189904, + 0.3444041511603112, + 0.307221989036461, + 0.27209731485676647, + 0.23922649633970688, + 0.2087611680702416, + 0.1807912279767466, + 0.15535696425567805, + 0.13244985629825948, + 0.11200803911082893, + 0.09394068591397559, + 0.07812435947179136, + 0.06440731708219334, + 0.0526273136470601, + 0.04260754311786528, + 0.034161822106158014, + 0.027119727432766732, + 0.021301232039859737, + 0.01654401026481201, + 0.012690001807549119, + 0.009602019125727813, + 0.007158129073816566, + 0.005239017038061342, + 0.003756472699914033, + 0.002625303596408706, + 0.0017770155903301095, + 0.001153511100359679, + 0.000706611938511098, + 0.0003982516103449855, + 0.00019671177651089876, + 7.690410440202065e-05, + 1.830948815481909e-05, + 5.139863073314017e-06, + 2.4201504050172685e-05, + 6.485452042304452e-05, + 0.00011875774541676908, + 0.00017891288313815097, + 0.00023970403444493674, + 0.0002967164311925548, + 0.00034649354178598925, + 0.00038651524989442555, + 0.0004154882380283171, + 0.00043133496810914603 + ], + [ + 0.8373124370877976, + 0.8348291510407144, + 0.827416385395279, + 0.8151952901769492, + 0.7983567960050247, + 0.7771724416171979, + 0.7519672625049684, + 0.7231336367083049, + 0.6911130896927021, + 0.6563836746496776, + 0.6194512438749337, + 0.5808400566190364, + 0.5410801914678852, + 0.5006957300768886, + 0.4601937115894056, + 0.42005625807836683, + 0.3807218790656306, + 0.34260477655408067, + 0.3060470099408584, + 0.2713460503377412, + 0.23874679801495913, + 0.2084190417732844, + 0.18048713555450976, + 0.1550144166139278, + 0.1320162541738429, + 0.11146124293067002, + 0.09326731176328182, + 0.07732698516197477, + 0.06350326985496363, + 0.051634998666067244, + 0.0415545669307032, + 0.033080754632705565, + 0.026028750702060892, + 0.02023259229527688, + 0.015518809959042337, + 0.011729106126541046, + 0.008718916218745171, + 0.006360071834000795, + 0.004539309104168634, + 0.0031511648782623324, + 0.0021161936833338883, + 0.0013598773864244899, + 0.0008235128337393195, + 0.0004566450401428709, + 0.0002202569365658533, + 8.26578709192049e-05, + 1.832063404026364e-05, + 7.2834374761381456e-06, + 3.3803172774255916e-05, + 8.543783404636111e-05, + 0.00015265349809012984, + 0.00022724977878934487, + 0.00030328494757798257, + 0.00037604521035668133, + 0.0004412471587873453, + 0.000496173744210954, + 0.0005387231708027124, + 0.000567561689988026, + 0.0005827117205116779, + 0.0005826352911851721 + ], + [ + 0.7665354875386753, + 0.7641457543998419, + 0.757013917782857, + 0.7452631539151198, + 0.7290864501145314, + 0.708758502895443, + 0.6846073374694843, + 0.6570259635929789, + 0.6264589825806693, + 0.59338441387622, + 0.5583023228849952, + 0.5217321671752525, + 0.48419607927380587, + 0.44620533846814897, + 0.4082507645108166, + 0.3707951731023321, + 0.3342641271487049, + 0.29901758479563084, + 0.2653990879299095, + 0.23366785195744347, + 0.20403915720102306, + 0.1766540334596041, + 0.15160832494173349, + 0.12893879937985392, + 0.10863681102180105, + 0.090649796485417, + 0.07487839302178767, + 0.06120148192635171, + 0.04947206232589312, + 0.039523419162967366, + 0.031185847290940844, + 0.02427955495208185, + 0.018624947032537954, + 0.014062188073152704, + 0.010427617802408088, + 0.007573629355883244, + 0.005367998765767262, + 0.0036945127483735867, + 0.002452161662831195, + 0.0015492538873136748, + 0.0009166618368029677, + 0.0004919498315375708, + 0.00022489054300591716, + 7.61014746375957e-05, + 1.4011564990307721e-05, + 1.3654653058361727e-05, + 5.583522187986382e-05, + 0.00012550452552194085, + 0.00021197320881620376, + 0.00030561527320270847, + 0.00040052544873891657, + 0.0004907986165728333, + 0.0005727725856539002, + 0.0006434733881452157, + 0.0007004979335434225, + 0.0007424864873415185, + 0.000768280311963478, + 0.0007777956719345566, + 0.000772019697460612, + 0.000750314879696359 + ], + [ + 0.687308235396994, + 0.6850505299854769, + 0.6783192689813243, + 0.6672223619905004, + 0.6519657579212694, + 0.6328176959753335, + 0.6101026467661899, + 0.5842088003164115, + 0.5555731865963093, + 0.524665009498571, + 0.49197302115026376, + 0.457999793439623, + 0.42324875657833, + 0.3882109723757915, + 0.35335509366296075, + 0.3191088580187515, + 0.2858758178419353, + 0.2539823822616436, + 0.22373929083054356, + 0.19537338172474636, + 0.16906754197247156, + 0.14493292178837844, + 0.12303628468142687, + 0.10339052498543314, + 0.08596184245965242, + 0.07067724464722802, + 0.057427555890973606, + 0.04608103178764559, + 0.03648259164969633, + 0.028464365317860604, + 0.021859142770101595, + 0.016493665605724708, + 0.012195667431510742, + 0.00881515018268133, + 0.006201420669508787, + 0.004220280492089146, + 0.002755067265613273, + 0.0017019210666432735, + 0.0009736717460752856, + 0.0004946045816161778, + 0.00020604129910570848, + 5.743908277128546e-05, + 9.824461539973127e-06, + 3.2592428420110635e-05, + 0.00010240170010866067, + 0.00020086720812319923, + 0.0003149739520053711, + 0.0004344078928921141, + 0.0005534680873991943, + 0.0006641537690525008, + 0.0007649523367433782, + 0.000851660132597309, + 0.000922661848162261, + 0.0009766763779180045, + 0.0010127858360088127, + 0.001030739326841926, + 0.001030396156713639, + 0.0010127231274716997, + 0.0009795379268794345, + 0.0009308602203405677 + ], + [ + 0.6021427991407771, + 0.6000512415457729, + 0.5938172518485029, + 0.5835458514662032, + 0.5694383234019998, + 0.5517553766633333, + 0.5308125130353293, + 0.5069864573393411, + 0.4806981795354899, + 0.45239944341777166, + 0.42255837146074504, + 0.39165400590998317, + 0.3601620584966143, + 0.32854296797322413, + 0.2972355222132219, + 0.2666286325572567, + 0.2370941378405438, + 0.2089212180750641, + 0.18238375412110813, + 0.15767557082085243, + 0.13493907310559997, + 0.11426127833098239, + 0.09567870624375653, + 0.07917982695048482, + 0.06471083119393133, + 0.052183088302080884, + 0.04147670961031808, + 0.03245397816373973, + 0.024956474705495037, + 0.018820785146317232, + 0.013884494305899402, + 0.009983502160761602, + 0.0069594464213936745, + 0.004671962022303785, + 0.0029884832000216855, + 0.0017901786542185848, + 0.0009759181018521762, + 0.0004578011448280952, + 0.0001635121450799012, + 3.273132380759071e-05, + 1.8306386873425216e-05, + 8.16544800826789e-05, + 0.00019519273345834496, + 0.00033685946336404435, + 0.0004913360012863152, + 0.0006464059351796922, + 0.0007949321435688338, + 0.000930940922022801, + 0.0010530647251287544, + 0.0011553240704785745, + 0.0012394819790683756, + 0.0013030056256059512, + 0.001346024890711426, + 0.0013686598186905903, + 0.0013713235560739077, + 0.0013544090335737727, + 0.0013191853140756694, + 0.0012669609037504266, + 0.0012003935387066174, + 0.0011199142478197906 + ], + [ + 0.5137393541722277, + 0.5118426720419995, + 0.5061914000503444, + 0.4968885022896228, + 0.48411921056078083, + 0.46813988072963, + 0.449248446805286, + 0.4278037224827043, + 0.40420399448890976, + 0.3788750609925317, + 0.3522559864616651, + 0.3247943862372372, + 0.2969310511131001, + 0.2690888945994948, + 0.24166688277116374, + 0.215015057257808, + 0.18946327987785747, + 0.16526220664358102, + 0.1426445864226208, + 0.12176843478745618, + 0.10273970629755226, + 0.08561744115680815, + 0.07041052745327005, + 0.057085387505776845, + 0.04557106363553699, + 0.03576666476095382, + 0.027545554708759697, + 0.020767212183794324, + 0.015276437043481526, + 0.010916890751054818, + 0.007531357639149695, + 0.004973015824425759, + 0.003099455643966428, + 0.0017815274612745732, + 0.000907737255231011, + 0.00037644299154766163, + 0.00010333393481882765, + 1.7344150923343547e-05, + 6.196247647951586e-05, + 0.00019163023568871502, + 0.00037148154449697464, + 0.0005755799135839963, + 0.0007860370563974288, + 0.0009893352397809317, + 0.0011777270776178468, + 0.0013446549280654006, + 0.0014882512792746953, + 0.0016064034237370298, + 0.0017015561301387157, + 0.00176930318986429, + 0.0018136223510302788, + 0.0018351438942314161, + 0.0018335370050298434, + 0.0018106880036263826, + 0.001767791929801649, + 0.001706178918409518, + 0.0016277433849864183, + 0.0015343133521432408, + 0.0014286170480313995, + 0.0013129664157246616 + ], + [ + 0.42490521775362, + 0.4232260533852611, + 0.4182196497673605, + 0.4099920992311325, + 0.39871273006623575, + 0.38462096952486136, + 0.36799520054419393, + 0.3491697850396372, + 0.32851523849208747, + 0.30642058325798366, + 0.28329337651574343, + 0.2595399980088836, + 0.23556012126866915, + 0.21173328834304703, + 0.1884134980938855, + 0.16591528156625193, + 0.144496998361243, + 0.12439451973501624, + 0.10578820204919126, + 0.08879943280282597, + 0.07350256543447303, + 0.05992167368145426, + 0.04804681116482948, + 0.037823314154104795, + 0.02916641419349697, + 0.021966892000948646, + 0.01609568093341034, + 0.011412556555683366, + 0.007769499073349628, + 0.0050206092578742485, + 0.003022633909267322, + 0.0016428072098755798, + 0.0007572655816512469, + 0.0002558167598800857, + 4.4884177147209844e-05, + 4.259057563701419e-05, + 0.00018276133296332966, + 0.00041110814029359324, + 0.000687391026775183, + 0.0009810885481134667, + 0.00126870138326775, + 0.001536680687877809, + 0.001775172678180901, + 0.0019798786141610207, + 0.0021494622356284525, + 0.00228219397586307, + 0.002380841654075004, + 0.0024464458986076516, + 0.0024828194536837306, + 0.0024923475179067173, + 0.0024753802331450633, + 0.002435686724535598, + 0.002373659172862503, + 0.0022920811970944784, + 0.0021927255678010835, + 0.002077431653214907, + 0.0019485649954314175, + 0.0018081926522266502, + 0.0016594115929899518, + 0.0015048361373459483 + ], + [ + 0.3384476847463157, + 0.3370015012939147, + 0.33269371454245655, + 0.325614521597464, + 0.31592631058788934, + 0.3038463776439096, + 0.2896287602684966, + 0.27357767718878306, + 0.25602921188706096, + 0.2373340478212276, + 0.21785739429036238, + 0.19796159915782452, + 0.17799860622930458, + 0.15829959254819184, + 0.13916972510136078, + 0.12087518297512558, + 0.10362988758108634, + 0.08762417049252987, + 0.07299559040580586, + 0.05982913178163059, + 0.048166792786988134, + 0.03800691856388512, + 0.029316498675400326, + 0.022025684065730133, + 0.016039756223098754, + 0.011245329170254724, + 0.00751388134303126, + 0.004710872429376574, + 0.0026995567686093473, + 0.0013466014025614833, + 0.0005263140970052548, + 0.00012266991025853362, + 3.220683774079179e-05, + 0.00016611159495590023, + 0.00044902052612925193, + 0.0008198332887056071, + 0.0012290836174906647, + 0.0016450514633892881, + 0.0020372664955351015, + 0.00239164355226223, + 0.002695882018799769, + 0.0029466531204161506, + 0.0031440321661942495, + 0.003287986621289814, + 0.0033854729174034328, + 0.003438051674138766, + 0.0034522585459361927, + 0.003432649599566942, + 0.0033820156688620503, + 0.0033070800178881714, + 0.00320812913628021, + 0.0030896894451007163, + 0.0029529544916070535, + 0.002800739568962696, + 0.0026352547979004914, + 0.00245855404556048, + 0.0022730475873046566, + 0.002081393246389363, + 0.0018862453937577746, + 0.0016904798463337207 + ], + [ + 0.25711464844529236, + 0.2559095272799505, + 0.25231980793158487, + 0.24643082649184422, + 0.23838566292302787, + 0.22837760078837233, + 0.216634812223651, + 0.20342752919573093, + 0.1890480034339511, + 0.17380919312128584, + 0.15802771431667573, + 0.14201675762616459, + 0.126077505180317, + 0.11048983054131914, + 0.09550666798851591, + 0.08134424154913739, + 0.06817235448526429, + 0.056133651123778626, + 0.04532509234099988, + 0.03579663838708113, + 0.02756038855270995, + 0.02059203866449755, + 0.014839085957805837, + 0.010220399919588992, + 0.0066353810577668235, + 0.00397010005214013, + 0.002101686237939751, + 0.0009046458327472536, + 0.0002566430655784789, + 4.035154788399604e-05, + 0.0001497680466899056, + 0.0004883531440435553, + 0.00097335310609725, + 0.0015401530624597705, + 0.002130897352274421, + 0.002705744170406018, + 0.0032334344027824258, + 0.003698374667296017, + 0.004086303204429913, + 0.004394749917232846, + 0.0046220319149898525, + 0.004774523586953052, + 0.004858928123220855, + 0.004883039157405509, + 0.0048564707099938145, + 0.004784420259408299, + 0.004676429849109012, + 0.0045386208352759805, + 0.004375000294243062, + 0.004193129872331983, + 0.0039934361769756255, + 0.0037808454905179953, + 0.0035566243725807366, + 0.0033235973382576885, + 0.003083930996411361, + 0.002839611662616908, + 0.0025929757579031235, + 0.0023465476752729895, + 0.0021029124758868683, + 0.0018649061753225685 + ], + [ + 0.1834791093279009, + 0.18251600201594032, + 0.1796485386642006, + 0.17495188820319585, + 0.16854989463015715, + 0.16060979469641343, + 0.15132977839958311, + 0.1409433486849359, + 0.12970004973312493, + 0.1178660170137226, + 0.10570858442553703, + 0.09348900304522224, + 0.081455048751088, + 0.06983346385576021, + 0.05882594380271692, + 0.0485939420982297, + 0.03926785575044144, + 0.030943690813198674, + 0.0236783696413586, + 0.01749019121852486, + 0.012364878829785871, + 0.008259080922613344, + 0.005104856054223765, + 0.0028139250887083186, + 0.0012843478701861045, + 0.0004055509951115582, + 6.410420312426319e-05, + 0.0001478115813578887, + 0.0005509412698770781, + 0.0011749692427050127, + 0.00193529309160888, + 0.0027573787264265144, + 0.003579420413541209, + 0.0043604203716311385, + 0.005061559530687619, + 0.005663206278212145, + 0.006151637907826006, + 0.006526757841898092, + 0.006787447146367865, + 0.006943157715283643, + 0.007001287509504632, + 0.006975606533325205, + 0.006879442133247521, + 0.00672507139289112, + 0.00652343673734274, + 0.006286945951881387, + 0.006021910447747882, + 0.0057368402872106684, + 0.005436036858144755, + 0.005127295682699107, + 0.004810605659695165, + 0.004490759463632144, + 0.004168625485094999, + 0.0038466447326292153, + 0.003526640525407326, + 0.0032102251850637292, + 0.002899411317906113, + 0.002596395184869642, + 0.002303346138468961, + 0.002022802934277952 + ], + [ + 0.11987983134575547, + 0.11915182720689244, + 0.11698574676597152, + 0.11344483436125667, + 0.10863430693918229, + 0.10269360218278688, + 0.0957886763245964, + 0.08811290734130002, + 0.07987356740349857, + 0.07128835563915185, + 0.0625703354788418, + 0.053929431418076434, + 0.045560933631773666, + 0.03763724679601165, + 0.030307016878202277, + 0.023685173170670676, + 0.017858164994331873, + 0.012879934714775878, + 0.0087710324336795, + 0.00552159662519873, + 0.0030952090983121985, + 0.0014336615080655815, + 0.0004581696363723723, + 7.732498800481401e-05, + 0.00019350767906639056, + 0.0007020719302502952, + 0.0015028782799163707, + 0.0025006567550634852, + 0.0036084666061512757, + 0.004748673543158785, + 0.005859682229917944, + 0.006889068598993259, + 0.00779693163104885, + 0.008564238493335001, + 0.009174431586048134, + 0.009622799524832382, + 0.009913062323051317, + 0.010059697040333876, + 0.010072917364900085, + 0.009972204950300101, + 0.009772182485638497, + 0.009493077862228628, + 0.009152469810415871, + 0.008765935034019425, + 0.008345693525454475, + 0.007905967228122908, + 0.007453007231788306, + 0.006995370152980832, + 0.006536719396837774, + 0.006084497893958542, + 0.005637613290958669, + 0.005200169153845374, + 0.004772258160199096, + 0.00435554533928465, + 0.003951159316855492, + 0.003560081237655774, + 0.003183738143365072, + 0.002823672190235903, + 0.0024817120605718506, + 0.0021597257289554905 + ], + [ + 0.06833232165521998, + 0.06782492273971039, + 0.06631762813526733, + 0.06386177476442458, + 0.060541318858765236, + 0.05646820236131471, + 0.05177706288322477, + 0.046618893807596956, + 0.04115698538804028, + 0.03555990444431568, + 0.029991745472070293, + 0.024608553110129373, + 0.019551902650546262, + 0.014943019872055745, + 0.010880262899839422, + 0.007434407442707102, + 0.004651648683634613, + 0.002547279464747867, + 0.001109444989325151, + 0.0003065577228361772, + 8.309669695775967e-05, + 0.0003703212789050034, + 0.0010853375028185542, + 0.0021382777903758907, + 0.0034373458789339127, + 0.004889766776896344, + 0.006412080622807308, + 0.007927225654869467, + 0.009369635820635092, + 0.01068394790120189, + 0.011832297454410052, + 0.012784474894000562, + 0.013522225369664659, + 0.014048480027879076, + 0.014364441357104761, + 0.014482143871024793, + 0.014420288541321245, + 0.014204735607448435, + 0.01385477786862223, + 0.013401485639791696, + 0.012861029023718442, + 0.012259471202474274, + 0.011616867029061617, + 0.010950514151558642, + 0.010272559353874956, + 0.009597474432884365, + 0.00893069032057727, + 0.008279788569552776, + 0.007646964223902285, + 0.007038357168611012, + 0.006451572919599628, + 0.005889396908339276, + 0.0053506841063638115, + 0.004836000124280983, + 0.004345468991232427, + 0.0038791775705663656, + 0.0034377331114776744, + 0.0030219066754350976, + 0.002632726075716713, + 0.0022714960025525884 + ], + [ + 0.03046983554423975, + 0.03016186705034865, + 0.02925048793512139, + 0.027775114824008622, + 0.02579874854836949, + 0.023404597263690295, + 0.02069538761734734, + 0.01778431675993348, + 0.01478851416226454, + 0.01182992958397988, + 0.0090233742319237, + 0.006474262272438296, + 0.0042746855226644415, + 0.0024953516752964067, + 0.001189863741532355, + 0.00038798139208917284, + 0.00010056953753765444, + 0.0003093651375331661, + 0.0009753847564532051, + 0.00205043551765405, + 0.003465494439639892, + 0.0051466158559724945, + 0.007011022132437783, + 0.008974675121845747, + 0.010956958856051182, + 0.012879336605706275, + 0.014677511638269303, + 0.016295540359626784, + 0.017690241966752188, + 0.018829205566554208, + 0.019698321675224513, + 0.02028903275362038, + 0.020601803922186523, + 0.020665810837862498, + 0.020492478340396924, + 0.020110350117463628, + 0.01955065890915911, + 0.018849115346879223, + 0.018032256863805763, + 0.017137292789786197, + 0.016183208078210554, + 0.015198945748707116, + 0.01420514176119183, + 0.013218538460845376, + 0.0122506478847123, + 0.011314597678302958, + 0.010413955502355094, + 0.009554238580674177, + 0.008735685204507689, + 0.007962174463931177, + 0.007229599557663473, + 0.006538836131396777, + 0.0058873475657138675, + 0.005274150852829613, + 0.004698090178540311, + 0.0041581160861478995, + 0.0036538069451333734, + 0.0031850213897898923, + 0.0027517823099499107, + 0.002354507538154373 + ], + [ + 0.007494083446024579, + 0.00735896931672804, + 0.0069618425178189424, + 0.006330795286093396, + 0.005508418880205302, + 0.0045562918356451525, + 0.0035382167521506667, + 0.0025333109482090894, + 0.0016159571386021186, + 0.0008653889189123326, + 0.0003487562257646071, + 0.0001241010721764456, + 0.00023739416538112604, + 0.0007170426034271783, + 0.001574293259742592, + 0.0028034639718768875, + 0.004386130618494759, + 0.006276413877238014, + 0.008414343395286673, + 0.010740891560309936, + 0.013179346181141898, + 0.015655692292410227, + 0.01809220957211822, + 0.020415012441201613, + 0.02255826861031029, + 0.0244590568863356, + 0.02607944770066907, + 0.027380988661094757, + 0.028345223867543942, + 0.0289627612925197, + 0.02924267318325308, + 0.029196628764154086, + 0.028844196297148933, + 0.02823332573694359, + 0.027388630552229114, + 0.02635097624015431, + 0.025161535567735042, + 0.023863241070147583, + 0.022487433791868464, + 0.021074894929240785, + 0.019645433331499724, + 0.018228458350786503, + 0.016843612629657667, + 0.015504285645566487, + 0.014223944391379318, + 0.013008625592432186, + 0.011860561616294724, + 0.010782352271797833, + 0.009771691434902668, + 0.008829384301443846, + 0.007949259011042526, + 0.0071297683916088294, + 0.006366688877300629, + 0.005657196671922152, + 0.004998618612931273, + 0.004388565127688757, + 0.0038253988029099233, + 0.0033078242498973736, + 0.0028349552679758356, + 0.002406013785095823 + ], + [ + 0.00013319766902115992, + 0.00013819731954621905, + 0.00015867655443862696, + 0.000212109794144177, + 0.00032057787569576726, + 0.0005252714817501687, + 0.0008561387845258277, + 0.0013605103905359125, + 0.0020718562831503317, + 0.003031441909178981, + 0.004263037514918587, + 0.005783017351867975, + 0.007597179769082111, + 0.009693503163587261, + 0.012055146926974987, + 0.014641024357065076, + 0.01741430733422864, + 0.020300895196215432, + 0.023234081259423035, + 0.026147480434889653, + 0.028962755008206383, + 0.03161095716950931, + 0.03402421610180946, + 0.03614278394207669, + 0.03791889467950973, + 0.03930893080412665, + 0.04029889680433365, + 0.040872602503513954, + 0.04103505439921559, + 0.0407992176060444, + 0.04019596667186414, + 0.03925550782265912, + 0.03801449359154578, + 0.036536552502545575, + 0.03485717331782967, + 0.03302677107116241, + 0.031093296615253677, + 0.029104316046522062, + 0.027093272649858353, + 0.025101897057003133, + 0.023148737186967316, + 0.021261495693721984, + 0.01945700821156737, + 0.01774507949431335, + 0.01613566963426441, + 0.014630694392114545, + 0.013228734272290961, + 0.011928168665293823, + 0.01072481208890224, + 0.009614597536847553, + 0.008589307437710605, + 0.007644622924585812, + 0.006774309519364446, + 0.005973489112274279, + 0.005237765166166728, + 0.004563251436231297, + 0.003946940231391617, + 0.0033863044923995093, + 0.00287926195037456, + 0.0024240107865130577 + ], + [ + 0.008619746969698075, + 0.008728382444803576, + 0.009057173298290769, + 0.009613974417301021, + 0.010403776559700656, + 0.01144615909422107, + 0.012743663592352, + 0.014314579903378047, + 0.01615645906795568, + 0.01827753417484358, + 0.020664180730632094, + 0.023297200047918562, + 0.02614892544282641, + 0.029175661632019994, + 0.032335593172283, + 0.03556373152767273, + 0.03880870485734886, + 0.04198144590560276, + 0.04500970796488609, + 0.04782796800941646, + 0.0503622615132977, + 0.052553711419495025, + 0.05434875848407332, + 0.0557054547601226, + 0.05659672094774861, + 0.05700016822899403, + 0.056926459268568, + 0.05638189186256615, + 0.05539189532459021, + 0.053997747374099125, + 0.0522427295000466, + 0.05017496208381037, + 0.04784841266292628, + 0.045336106402141356, + 0.042682715234288356, + 0.03994480948064274, + 0.03717463650961221, + 0.03442062930418903, + 0.0317162971178998, + 0.02910143634733466, + 0.02659130104237978, + 0.024209780866437196, + 0.021969137368197344, + 0.019874220207107874, + 0.017929793536235736, + 0.016133142900807664, + 0.014478117509164758, + 0.012958695372221801, + 0.011566661269196905, + 0.010294340276470594, + 0.009130481384800476, + 0.008067726119120244, + 0.007097649063099326, + 0.0062131227087392086, + 0.005407871243456049, + 0.004676404689449541, + 0.004014234284116154, + 0.003417503419613568, + 0.002882910055181541, + 0.0024074107827192553 + ], + [ + 0.032684480808807946, + 0.03285722782247966, + 0.033376137010645124, + 0.034240798455364166, + 0.03544044004461454, + 0.03697479605106591, + 0.03883304139329912, + 0.04099717293088477, + 0.04343897327217809, + 0.04613946809974683, + 0.04905502314409554, + 0.05213785686037775, + 0.055329623238563816, + 0.05857813936609576, + 0.0618057441022246, + 0.06494777582410939, + 0.0679347131931151, + 0.07067159986997221, + 0.07309605572583315, + 0.07514111801324856, + 0.07674595623905073, + 0.07786647106658363, + 0.07846770024007278, + 0.0785261510475372, + 0.07804146220962532, + 0.07701359810489089, + 0.07547466686859071, + 0.07345449492939371, + 0.07099994184756728, + 0.06817189038031826, + 0.06503038758595966, + 0.061637234090448904, + 0.058058114765102316, + 0.05437439179592121, + 0.050636008441495683, + 0.046902594633772464, + 0.04322721544162175, + 0.039656384554484135, + 0.036220900664965444, + 0.0329558287420119, + 0.029871631096583768, + 0.026986185122031717, + 0.02430563829932975, + 0.021828503458540153, + 0.019553166057111295, + 0.01747114096798601, + 0.015571256630808397, + 0.013842361708937207, + 0.012271857077886219, + 0.010847807862245838, + 0.009555947501215231, + 0.008385832033019607, + 0.0073263937148687775, + 0.006368229922350644, + 0.005503172748051809, + 0.004723978547778559, + 0.004024571671413488, + 0.003399824328100048, + 0.0028451373141813153, + 0.002356159558805296 + ], + [ + 0.07156440514000363, + 0.07175997766982256, + 0.07234567863136515, + 0.07331435078807433, + 0.07464240689635478, + 0.07631645959000107, + 0.07830679059396804, + 0.08057532119971828, + 0.08307079018678155, + 0.0857539341367195, + 0.08855883896374422, + 0.09141763161685754, + 0.09425367375152378, + 0.09700245581027186, + 0.0995746099098832, + 0.10190081888186546, + 0.10391042043133868, + 0.10551028577306212, + 0.10664709691108312, + 0.10726614644885718, + 0.10732274908194972, + 0.10679181816879728, + 0.10566021930865847, + 0.10392743093718089, + 0.10161768876476462, + 0.09875406789881201, + 0.09539236032764968, + 0.09158364114387478, + 0.08739406933534286, + 0.08290153623539341, + 0.07817998043614251, + 0.07330278104128472, + 0.06834111847044805, + 0.0633810209870859, + 0.05848132892329082, + 0.05369366981409751, + 0.049071184649582364, + 0.04465575593991709, + 0.04047283960979586, + 0.03655033299862164, + 0.03289196873970597, + 0.029507808828128642, + 0.026396278744256006, + 0.023549032071330217, + 0.020956486271823734, + 0.018603914735877636, + 0.01647461542651307, + 0.014551851165299303, + 0.012818377670123067, + 0.01125748797098751, + 0.009852287502765846, + 0.008588599404722942, + 0.007452692866884097, + 0.006433256927272895, + 0.005519834304742165, + 0.004703601144933236, + 0.003976878107343363, + 0.0033330926693558847, + 0.002766408183364645, + 0.00227118256087047 + ], + [ + 0.12402560289557368, + 0.12420235942558659, + 0.1247302170613829, + 0.1255974212008375, + 0.1267714478703604, + 0.12822746831441154, + 0.1299231894038243, + 0.13180224645785904, + 0.13381167978165978, + 0.13588479665890624, + 0.13794613712773954, + 0.13991774452766362, + 0.14171296550910328, + 0.14326361808985988, + 0.14447772993066016, + 0.14528971965193743, + 0.14563556986884035, + 0.1454322791451263, + 0.14464195456980475, + 0.14322788658077093, + 0.1411664323426571, + 0.13845528694551648, + 0.1351041359636952, + 0.13114259158969127, + 0.12661226513849808, + 0.12156851471331412, + 0.11608199789101778, + 0.110223207560478, + 0.10408301264776917, + 0.09774563108108847, + 0.09129494499420349, + 0.08482042434139227, + 0.07838949107123935, + 0.0720912464417073, + 0.06598337164486895, + 0.060114151776479954, + 0.054530972040590986, + 0.0492683472682673, + 0.044343868662831416, + 0.03977336958241223, + 0.03556070225206093, + 0.031697942718591096, + 0.02817750700307511, + 0.024982971460527137, + 0.022096586821172864, + 0.0194964392588, + 0.017160092610785382, + 0.015064880766844466, + 0.013188661593487616, + 0.011510068462765921, + 0.010009368629219882, + 0.008668720874231607, + 0.007471790859611091, + 0.006405261979552179, + 0.005456535382388836, + 0.004615110137471745, + 0.0038717553556503097, + 0.00321856105552778, + 0.0026484646126578738, + 0.0021545400308027023 + ], + [ + 0.18840789672316446, + 0.188524927767522, + 0.18887296326292874, + 0.18943731095495367, + 0.1901791568975991, + 0.19106894785360384, + 0.19205582040262822, + 0.193075314143059, + 0.19406870808677487, + 0.19496199915178702, + 0.19567461995131238, + 0.19612333773448207, + 0.1962317188189485, + 0.19592676600896403, + 0.19512583185710836, + 0.19377542978499723, + 0.19182580161434937, + 0.18921154724916267, + 0.18591630098119824, + 0.18192657172732907, + 0.17724410802476565, + 0.17189229674863676, + 0.1659075859583396, + 0.15934552626046009, + 0.15227209655990537, + 0.1447658347338406, + 0.13691743578946086, + 0.1288147629072397, + 0.12056252791569932, + 0.11225556044048265, + 0.1039848112745649, + 0.0958431231130212, + 0.08789936321566211, + 0.08023891593806673, + 0.07291489296959638, + 0.06596927781733956, + 0.05944080269691854, + 0.05335357809009113, + 0.0477161833263548, + 0.0425321317543648, + 0.037795568989768984, + 0.033488759470019995, + 0.02959331791620653, + 0.026085396550611012, + 0.022937300910026014, + 0.020120226352252694, + 0.017605406927312675, + 0.015364369332012653, + 0.013369993287739183, + 0.011596430526751701, + 0.010021015970760768, + 0.008622497962174566, + 0.007381827600180107, + 0.006283937081283293, + 0.005314066221184914, + 0.004460170390648442, + 0.0037115280257869715, + 0.003058902671581144, + 0.00249421823083452, + 0.002009767822011909 + ], + [ + 0.2626686830653321, + 0.26268731825398695, + 0.2627401444140118, + 0.2628114748732222, + 0.2628597177106005, + 0.2628551251738213, + 0.2627439209639931, + 0.2624605448252016, + 0.26194665495730174, + 0.26113090826020113, + 0.2599354348058002, + 0.2582840734363807, + 0.2561097321281741, + 0.25335255206876617, + 0.24994585455340507, + 0.2458551314291105, + 0.24105231544675257, + 0.23549657659174136, + 0.22919845884487458, + 0.22217216109184795, + 0.21444813237649252, + 0.2060779182789071, + 0.19712592718236271, + 0.18767368238550958, + 0.17781128007794, + 0.16763834246070541, + 0.15726345132606842, + 0.14678917524110893, + 0.13633048847852794, + 0.12598913767777314, + 0.11585979500535988, + 0.1060346322301997, + 0.0965803005508586, + 0.08757493726066841, + 0.07906364597936641, + 0.07107938059095563, + 0.06364936916326505, + 0.05678531423714047, + 0.05048431769527099, + 0.044737535559716206, + 0.039526625566379925, + 0.034823718312551134, + 0.030599532593245334, + 0.026820705465916146, + 0.023450978045903643, + 0.020454152908274653, + 0.01779499770584573, + 0.015439326809186273, + 0.013355059285013389, + 0.011511853649770814, + 0.009885369359257414, + 0.008449874975579268, + 0.007184225326283282, + 0.006071754231822524, + 0.0050956690958640785, + 0.004242511064166716, + 0.0035001845275459526, + 0.0028583443380804973, + 0.002307736773267868, + 0.0018396874294299799 + ], + [ + 0.34445345065399624, + 0.34433840993777465, + 0.34399081692993383, + 0.3433960099982468, + 0.34251320664682205, + 0.34131613478412637, + 0.3397550089590775, + 0.3377692801152529, + 0.3353084755361113, + 0.33231047021843785, + 0.3287077931312395, + 0.32444866391761434, + 0.3194710155190602, + 0.31374834699278276, + 0.3072294236985044, + 0.29990882481493425, + 0.2917865554017563, + 0.2828526851907367, + 0.2731491050575619, + 0.2627211111451064, + 0.2516306860475594, + 0.23995716326649214, + 0.22779843628293872, + 0.2152546639175999, + 0.2024452035248353, + 0.1894838031881008, + 0.17649562445597902, + 0.16359484877486166, + 0.15090290708247223, + 0.13852485063071854, + 0.1265552128317391, + 0.11508135933121352, + 0.10416503851440763, + 0.09387270700321367, + 0.08423912819223214, + 0.07528561253162708, + 0.0670253649779352, + 0.05945487697296434, + 0.05256122130519797, + 0.0463193855529011, + 0.04069817512909629, + 0.03565938824991956, + 0.031162448395758168, + 0.02716413282905655, + 0.023619884819491423, + 0.0204857700600363, + 0.01772083829361163, + 0.015285359726379125, + 0.013142601614065604, + 0.01125789158231879, + 0.00960485301910695, + 0.008154561659230466, + 0.006883653188603179, + 0.005773961022307979, + 0.004806924670253916, + 0.003967846946022226, + 0.0032434164408848163, + 0.002622258980239314, + 0.0020941818961839765, + 0.0016496251967694116 + ], + [ + 0.4311692083903133, + 0.4308897259630736, + 0.4300498556727055, + 0.42863905173675976, + 0.4266178837456579, + 0.4239705929330715, + 0.4206552995359306, + 0.4166242996119813, + 0.4118409897039116, + 0.4062604923455225, + 0.39983598461174624, + 0.3925317990612729, + 0.3843351757408392, + 0.37522395628416905, + 0.36518666205000583, + 0.35425023088931706, + 0.34244810591317065, + 0.3298069251794422, + 0.3164030072548204, + 0.30231556323093023, + 0.28763690571733236, + 0.27248497307064024, + 0.25697641650190844, + 0.24123852573997137, + 0.22541289416511506, + 0.20962746101457255, + 0.19401816155719923, + 0.17871241696084364, + 0.1638291057109032, + 0.1494744613746476, + 0.13573906767658664, + 0.1227001864296081, + 0.1104170800177635, + 0.0989351637102072, + 0.08827862746045338, + 0.07845513528314536, + 0.06946142916324513, + 0.06127939087120541, + 0.0538799472461908, + 0.04722549283998533, + 0.04127083174562392, + 0.035966757186107, + 0.031261485795758284, + 0.027101851105602023, + 0.02343571198585182, + 0.020212531604538207, + 0.017383326196944538, + 0.014905169213809261, + 0.012737055620022931, + 0.010841796334402218, + 0.009186531573758074, + 0.007744220551462496, + 0.006488122791590283, + 0.0053984896490413044, + 0.00445562447387185, + 0.0036437077918156802, + 0.0029483427198737054, + 0.0023572843782146006, + 0.0018596390695889136, + 0.0014450713026635173 + ], + [ + 0.5200670004615636, + 0.5195976773163834, + 0.5181899634404028, + 0.515838058890306, + 0.5125106386422618, + 0.508202960566913, + 0.5028873093609771, + 0.49653478825188174, + 0.48912924938688235, + 0.4806512229107663, + 0.4710783749333533, + 0.46040935190765686, + 0.44866238752434295, + 0.4358493366513886, + 0.4220023834177303, + 0.40717967565043683, + 0.3914565779938275, + 0.37489428308627, + 0.3576121098400676, + 0.33972266128409245, + 0.32135236409234313, + 0.30264793282222907, + 0.28375080072465997, + 0.2648179490628927, + 0.24600068507710587, + 0.22744324819317582, + 0.20928976885587797, + 0.1916713120762933, + 0.17470603979740165, + 0.15849586132308982, + 0.14312379397875374, + 0.12865603989634858, + 0.11513899022689003, + 0.10260189621682056, + 0.09105336076883569, + 0.08048544579672365, + 0.07087784709346223, + 0.062196536826360865, + 0.0543953776922952, + 0.04742434595691666, + 0.0412232885389783, + 0.035732995057714816, + 0.030890339483209094, + 0.026633009662844084, + 0.022901360346061973, + 0.01963842907753049, + 0.01678977334237331, + 0.014308040880394206, + 0.012148711520337778, + 0.010271638003309057, + 0.008641508495476041, + 0.0072299038777563635, + 0.006008232206584617, + 0.0049557074440179285, + 0.0040516174326670935, + 0.0032792358255195535, + 0.0026237058532727247, + 0.002071149284792968, + 0.0016110458554457817, + 0.0012321191039928665 + ], + [ + 0.608328229726827, + 0.6076499468425972, + 0.6056201478906492, + 0.602230992922614, + 0.5974713621708592, + 0.5913471707776793, + 0.583850138994367, + 0.5749751257568142, + 0.564732654793265, + 0.5531331345124983, + 0.5401893954143335, + 0.5259363363146558, + 0.5104301314359777, + 0.4937200317213537, + 0.475893730513213, + 0.4570378454145052, + 0.4372724665574777, + 0.4167038317070652, + 0.39548782887550066, + 0.3737724364246754, + 0.35172089147871155, + 0.3295042331882894, + 0.30729054985608, + 0.2852547295188036, + 0.26356507272430535, + 0.24237374357168412, + 0.22182999603041129, + 0.2020645564976951, + 0.18319141382558865, + 0.16530400969208098, + 0.14847493401835513, + 0.1327562338328809, + 0.11817877396734607, + 0.10475340084047229, + 0.09247159311940617, + 0.08130870830094714, + 0.07122580323778384, + 0.06217298987573375, + 0.05408695444176328, + 0.04690488969659481, + 0.04055254975445562, + 0.03496115403255012, + 0.030056726536394473, + 0.025768532703619455, + 0.022030867745320527, + 0.018779213340735006, + 0.015956176166716025, + 0.013510152458410666, + 0.011392839850228991, + 0.009564369429691825, + 0.00798496193064666, + 0.006626059015202093, + 0.005457671097434843, + 0.004458369031297539, + 0.0036066086944617545, + 0.0028851174000889316, + 0.0022785182883478115, + 0.0017723831021544587, + 0.0013558923172935248, + 0.0010173560123733756 + ], + [ + 0.6931551118608545, + 0.6922555695366732, + 0.6895637062111859, + 0.6850803387059847, + 0.6788082114693208, + 0.6707708446241587, + 0.6609819245746946, + 0.649465135245534, + 0.636262137982774, + 0.6214191110985193, + 0.6049886637609295, + 0.5870471398643046, + 0.5676929160384516, + 0.5470221048526684, + 0.5251661675406412, + 0.5022570925133458, + 0.4784595166135866, + 0.4539234001816158, + 0.4288419136634839, + 0.40339918365522476, + 0.37778994190820975, + 0.3522106144109192, + 0.32685399847124386, + 0.301908461586197, + 0.2775531595348496, + 0.2539480463114434, + 0.23124219149046416, + 0.20956225732928266, + 0.18901431358034598, + 0.16968027030420546, + 0.15161912468488536, + 0.13486633883257199, + 0.11943520888597953, + 0.10531604328008559, + 0.09248273848834154, + 0.0808927440951735, + 0.07048834910769229, + 0.06120356543960617, + 0.05295853571425614, + 0.0456782251865845, + 0.03927486961462793, + 0.03367091450279044, + 0.028782628192066794, + 0.02453166086940993, + 0.020846752817431577, + 0.017658504371592602, + 0.014905690526166828, + 0.012533863372399773, + 0.010492435589037494, + 0.00874016951094678, + 0.007235671739064815, + 0.005950095446058465, + 0.004852447274708324, + 0.0039209636418562335, + 0.0031337087228380657, + 0.0024730691728960972, + 0.0019234444787028283, + 0.001470082245203237, + 0.0011020930837582945, + 0.0008073473323449423 + ], + [ + 0.7718571010040236, + 0.7707309070017615, + 0.7673620764066228, + 0.7617605915102392, + 0.7539448788063549, + 0.7439582170694448, + 0.7318412819888519, + 0.717648201066794, + 0.7014562806484704, + 0.6833510393036138, + 0.6634296564113858, + 0.641812931486516, + 0.6186445466453998, + 0.5940702598174729, + 0.5682662876748089, + 0.541415612138243, + 0.5137208841041383, + 0.4853811770704165, + 0.4566241792226948, + 0.4276684883377342, + 0.39873790204198484, + 0.3700518449461954, + 0.34182300551305167, + 0.3142507074478057, + 0.28752091121872797, + 0.2617969146021488, + 0.2372243682080146, + 0.21392224400454268, + 0.1919848712139226, + 0.17148000459839063, + 0.15245001663996677, + 0.1349125364804872, + 0.11886086731043373, + 0.10426511813608826, + 0.09107885811900321, + 0.07924338851234365, + 0.06868175490447558, + 0.05931267689340494, + 0.051039584721532305, + 0.043777226875045865, + 0.037425192430742625, + 0.03189811684773007, + 0.027103662262529547, + 0.02295737479432185, + 0.019383872070463503, + 0.016308390434758277, + 0.013668568200505814, + 0.011407428483040162, + 0.009472956313476255, + 0.007823170357178222, + 0.006415657221015709, + 0.0052218724152387885, + 0.004210537325157363, + 0.003359629234778336, + 0.002647184899050597, + 0.0020556360791351234, + 0.0015694556127141231, + 0.0011737166764568187, + 0.0008577036936412989, + 0.0006092988419715838 + ], + [ + 0.8419396898788761, + 0.8405890670904744, + 0.8365492660726555, + 0.8298419315505657, + 0.8205008838610313, + 0.8085907333413825, + 0.7941828452276843, + 0.7773662171774913, + 0.7582530117978407, + 0.7369684784533248, + 0.7136648930138194, + 0.6885030374786063, + 0.6616752437750102, + 0.6333785087663453, + 0.60383520907071, + 0.5732754441094555, + 0.541942805192911, + 0.5100831040293224, + 0.4779560416837243, + 0.4458119785988276, + 0.4139006935857204, + 0.3824610246439065, + 0.35171997415143963, + 0.3218861804333938, + 0.293146899054788, + 0.26566562926426973, + 0.23958018701712946, + 0.2149981096423496, + 0.19200039999605586, + 0.17063808347567785, + 0.1509327504548548, + 0.1328843090908846, + 0.11646497620378535, + 0.101625262864766, + 0.08829583708035159, + 0.07640468489180745, + 0.06585547191899785, + 0.05655198292665854, + 0.04838414223605525, + 0.04125593036187837, + 0.035056387245499816, + 0.029693683003611603, + 0.025068413457616855, + 0.02109134569833104, + 0.017683903099391197, + 0.014768317581024875, + 0.012281102572036766, + 0.01016400591898541, + 0.008364988636419437, + 0.0068403147944002185, + 0.005549549490491515, + 0.004463610986391355, + 0.0035513762852429943, + 0.0027914629127215903, + 0.0021620602224505705, + 0.0016458741967044148, + 0.0012276948311634706, + 0.0008928380816574025, + 0.0006307575672757803, + 0.0004296613566019789 + ], + [ + 0.9011817502945029, + 0.899615965834984, + 0.8949325317313656, + 0.8871646616340856, + 0.8763665371860785, + 0.8626230539925931, + 0.8460343148552492, + 0.8267269127870063, + 0.8048522262132087, + 0.7805792745391783, + 0.7541044980487404, + 0.7256398981469445, + 0.6954232569779982, + 0.6637026212966735, + 0.6307453530673864, + 0.5968271288743466, + 0.562230282224359, + 0.5272447483671641, + 0.49215878675789765, + 0.45725084158524126, + 0.4227920340496154, + 0.3890380926734743, + 0.35622474565498574, + 0.3245647100345624, + 0.29424429981956396, + 0.26542162740478625, + 0.23822443521670944, + 0.21274560273758364, + 0.1890493743680396, + 0.16716850667773128, + 0.14710343727593517, + 0.12883463317907756, + 0.1123133739410465, + 0.09746865183094688, + 0.08421628316997419, + 0.07245769079431291, + 0.06209081207785465, + 0.05300238243034296, + 0.04506939180112737, + 0.03818794196295487, + 0.032238032208098545, + 0.0271225889905386, + 0.02273691937887949, + 0.018988936185560457, + 0.015797801275821036, + 0.013084429437542445, + 0.010784984179620243, + 0.008841069859299581, + 0.00720109625720965, + 0.005821895094522579, + 0.004663683982751525, + 0.0036983337388688114, + 0.002896304148545236, + 0.0022342145282212796, + 0.0016936274673316973, + 0.0012568601257761296, + 0.000909283445805092, + 0.0006367762561748213, + 0.00042902562841163965, + 0.0002747613843775679 + ], + [ + 0.9477039139136432, + 0.9459388846257604, + 0.9406611299819, + 0.9319128210713067, + 0.9197702179130122, + 0.9043396823712699, + 0.8857516100526425, + 0.8641668719737198, + 0.8397774964513414, + 0.812797430687146, + 0.7834664000847811, + 0.7520459397536448, + 0.7188178913456613, + 0.6840797745669536, + 0.6481412216759482, + 0.6113207151304146, + 0.5739358089452549, + 0.5363166216725005, + 0.49877624372983614, + 0.4616148129467529, + 0.4251218805269394, + 0.38956462895359967, + 0.3551831935545768, + 0.3221899121270022, + 0.2907669004383356, + 0.26106013035746306, + 0.23318729386880332, + 0.20722296042905267, + 0.18321232438750681, + 0.1611690068312373, + 0.14107112540807668, + 0.12288003927294162, + 0.10652567249401894, + 0.09191721527555297, + 0.07895298074567339, + 0.06751877386951018, + 0.05749909990762151, + 0.04876885100028245, + 0.041194356106816946, + 0.03466514916035388, + 0.029054168127810497, + 0.024261004165490086, + 0.020179521191240557, + 0.016713370546457714, + 0.013782588495398158, + 0.011307653642181394, + 0.009225635159549841, + 0.0074789929292406535, + 0.0060174903310713295, + 0.004799076202480821, + 0.0037855243337892603, + 0.0029500208776843022, + 0.002264104916286042, + 0.0017055885782035608, + 0.001256978432237583, + 0.0009013459848129699, + 0.000624925466943992, + 0.0004143153245583298, + 0.00025964675417002806, + 0.0001503527595571125 + ], + [ + 0.9800314535795, + 0.9780896768327519, + 0.9722837142744232, + 0.9626693524198434, + 0.9493385509272577, + 0.9324193151786514, + 0.9120735382200643, + 0.8884985889779661, + 0.8619212840453886, + 0.8326005787024436, + 0.800817296591933, + 0.7668805851178645, + 0.7311136123222115, + 0.6938591071830834, + 0.6554658605394638, + 0.6162900963888901, + 0.5766806062135307, + 0.5370032298113177, + 0.4975876285991179, + 0.458754252723825, + 0.42080422694782116, + 0.38401114975534906, + 0.3486148941404007, + 0.3148230211591587, + 0.2828089071609925, + 0.2527048553410178, + 0.22461393825309914, + 0.19859097511572849, + 0.1746609848212454, + 0.15281708775184688, + 0.13301859840263983, + 0.1151980455279375, + 0.09927511211813288, + 0.08513723732979821, + 0.07266688387097299, + 0.06173579159022083, + 0.052218150608177256, + 0.04397886812987959, + 0.03687571851405596, + 0.030793865385635704, + 0.025601672206975894, + 0.02119758598231189, + 0.017473105685123082, + 0.014334382017575985, + 0.011700039919789424, + 0.009492636297717304, + 0.007651207384474716, + 0.006120002144559834, + 0.004850980613943444, + 0.003803924823592879, + 0.002942851354115961, + 0.002242472613827795, + 0.0016760513295746135, + 0.0012228886343913453, + 0.0008668444518491707, + 0.0005914435554938584, + 0.0003843799338496921, + 0.00023369873226103443, + 0.00012904121892650695, + 6.144771209315633e-05 + ], + [ + 0.9971405326811051, + 0.9950499466050804, + 0.9887994355528708, + 0.9784579306834811, + 0.9641304914358964, + 0.9459706482227513, + 0.9241657467156174, + 0.8989475510314785, + 0.8705788248910721, + 0.8393581610294512, + 0.8056056770553012, + 0.7696687371162816, + 0.7319140901455037, + 0.6927230524059876, + 0.652477917045628, + 0.6115679375813224, + 0.5703683963982936, + 0.5292690685680993, + 0.4886180293860669, + 0.4487462501353581, + 0.40996301766648846, + 0.37253856685062336, + 0.33671263412762853, + 0.30268174650314494, + 0.270607320534874, + 0.240604955236743, + 0.21276076701796703, + 0.18710835868121614, + 0.1636518912741396, + 0.14236437372955457, + 0.12318221842013051, + 0.1060201800502424, + 0.09078052425112164, + 0.0773336240888895, + 0.06554827008612701, + 0.05528494552934289, + 0.04640915645083468, + 0.03877851189913215, + 0.03224535652768178, + 0.02669254415319823, + 0.021986284062426472, + 0.018025777493777633, + 0.014702865428060867, + 0.011925491313951656, + 0.009614791392035634, + 0.007695999989955741, + 0.006111020109382935, + 0.00480690808511717, + 0.0037385675281593196, + 0.0028683266272810834, + 0.002162796162477797, + 0.0015988384750130948, + 0.0011516970845293377, + 0.0008024296506996898, + 0.0005362724643547789, + 0.00033829391023241134, + 0.00019683848754359167, + 0.00010146170500665577, + 4.261692613098583e-05, + 1.2128039587575019e-05 + ], + [ + 0.9984878103897655, + 0.9962809897121406, + 0.9896836589549751, + 0.9787769524472264, + 0.963679882404573, + 0.944561889764362, + 0.9216426946740608, + 0.8951809508634399, + 0.8654714589536397, + 0.8328494763700433, + 0.7976715499647724, + 0.7603152998553087, + 0.7211862018648151, + 0.6806985070470831, + 0.6392618508634401, + 0.5972918656298631, + 0.5551832946958792, + 0.5133461348483621, + 0.47213692433701876, + 0.43189249029228083, + 0.3929217420488852, + 0.3554961272207555, + 0.31983683912639455, + 0.2861345056481662, + 0.25453247994814276, + 0.2251279620618935, + 0.19798809228871656, + 0.17312440214419406, + 0.15052014902317903, + 0.13012805425591809, + 0.11186460378642014, + 0.09562610456284669, + 0.08130157510975285, + 0.06874524473392593, + 0.05781533883976775, + 0.04836404878728864, + 0.04025056402293704, + 0.03332800199457393, + 0.027446380060715116, + 0.02248833532536841, + 0.018320380006382683, + 0.01484440253318266, + 0.01195460807848289, + 0.009562384522270958, + 0.007592558038074911, + 0.005974647889023785, + 0.004654165906266812, + 0.003581834886846868, + 0.002716219528115237, + 0.0020227767235521834, + 0.0014712477602827404, + 0.0010407304264972096, + 0.0007089236432916741, + 0.00045893909718692995, + 0.0002774162726637052, + 0.0001511083236867918, + 6.958531610296274e-05, + 2.3570817640678338e-05, + 4.611129312156844e-06, + 5.410668932023349e-06 + ] + ] +} \ No newline at end of file From 39ea38b202c51ca9f6dcb093cd75d8c4d2c7ad67 Mon Sep 17 00:00:00 2001 From: Peter Kruyt Date: Sun, 13 Apr 2025 16:30:29 +0200 Subject: [PATCH 6/6] add cw laser test based on Lanzhou --- ..._laser_cooler.py => test_laser_coolers.py} | 182 ++++++++++++++++++ 1 file changed, 182 insertions(+) rename tests/{test_laser_cooler.py => test_laser_coolers.py} (54%) diff --git a/tests/test_laser_cooler.py b/tests/test_laser_coolers.py similarity index 54% rename from tests/test_laser_cooler.py rename to tests/test_laser_coolers.py index 654ccd3ed..61610c53c 100644 --- a/tests/test_laser_cooler.py +++ b/tests/test_laser_coolers.py @@ -209,3 +209,185 @@ def exp_decay(t, A, tau ): xo.assert_allclose(tau, 7, rtol=0, atol=1) + +@for_all_test_contexts +def test_cw_laser(test_context): + """Test phase space acumulation for Lanzhou experiment + https://www.sciencedirect.com/science/article/pii/S0168900222011445?ref=pdf_download&fr=RR-2&rr=80ca25af8a5ace93 + """ + # Ion properties: + m_u = 931.49410242e6 # eV/c^2 -- atomic mass unit + A = 16 # Weight of O + + m_p = 938.272088e6 # eV/c^2 -- proton mass + clight = 299792458.0 # m/s + + q0=5 + + mass0 = A*m_u #+ Ne*m_e # eV/c^2 + + beta_rel = 0.64 + gamma_rel = 1.30 + + p0c = mass0*beta_rel*gamma_rel #eV/c + + + circumference = 128.80 #m + T = circumference/(clight*beta_rel) + s_per_turn = T + + beta_x = 6 + beta_y = 2 + + disp_x = 0 + Q_x = 2.2 + Q_y = 2.4 + + arc = xt.LineSegmentMap( + qx=Q_x, qy=Q_y, + length=circumference, + betx=beta_x, + bety=beta_y + ) + + emittance_x=10*1e-6 #inital emittance + emittance_y=15*1e-6 #inital emittance + num_particles = int(1e4) + + sigma_x = np.sqrt(beta_x*emittance_x) + sigma_px = np.sqrt(emittance_x*1/beta_x) + sigma_y = np.sqrt(beta_y*emittance_y) + sigma_py = np.sqrt(emittance_y*1/beta_y) + + + delta = np.linspace(0, 1e-5, num_particles) + + # delta = np.random.normal(loc=0, scale=sigma_p, size=num_particles) + x = np.random.normal(loc=0.0, scale=sigma_x, size=num_particles) + disp_x * delta + px = np.random.normal(loc=0.0, scale=sigma_px, size=num_particles) + y = np.random.normal(loc=0.0, scale=sigma_y, size=num_particles) + py = np.random.normal(loc=0.0, scale=sigma_py, size=num_particles) + + particles = xp.Particles( + mass0=mass0, + p0c=p0c, + q0=q0, + x=x*0, + px=px*0, + y=y*0, + py=py*0, + delta=delta, + zeta=0 + ) + particles._init_random_number_generator() + + ################## + # Laser Cooler # + ################## + + theta_l = 0 + nx = 0; ny = -np.sin(theta_l); nz = -np.cos(theta_l) + + # Ion excitation energy: + # hw0 = 230.823 # eV + hc=cst.hbar*clight/cst.e # eV*m (ħc) + lambda_0 = 103.76*1e-9 # m -- ion excitation wavelength + hw0 = 2*np.pi*hc/lambda_0 # eV -- ion excitation energy + ion_excited_lifetime=2.44e-9 + + + lambda_l = 2.2130563056305633e-07 + #lambda_l = lambda_l*(1+1*sigma_p) # m + + laser_frequency = clight/lambda_l # Hz + + laser_power=40*1e-3 #W + laser_waist_radius = 5*1e-3 + laser_area=np.pi*(laser_waist_radius*laser_waist_radius) + + laser_intensity=laser_power/laser_area + + cooling_section_length=25 + CW_laser = xt.CWLaser( + laser_x=0, + laser_y=0, + laser_z=0, + + laser_direction_nx = 0, + laser_direction_ny = 0, + laser_direction_nz = -1, + laser_wavelength = lambda_l, # m + laser_waist_radius = laser_waist_radius, # m + laser_intensity=laser_intensity, + ion_excitation_energy = hw0, # eV + ion_excited_lifetime = ion_excited_lifetime, # sec + cooling_section_length=cooling_section_length + + ) + + # ################## + # # Tracking # + # ################## + + # simulation parameters: simulate 10 s of cooling, and take data once every 100 ms + T_per_turn = circumference/(clight*beta_rel) + + + num_turns = int(1e5) # 0 emittance + save_interval=num_turns/100 + + # create a monitor object, to reduce holded data + monitor = xt.ParticlesMonitor(start_at_turn=0, stop_at_turn=1, + n_repetitions=int(num_turns/save_interval), + repetition_period=save_interval, + num_particles=num_particles) + + line = xt.Line( + elements=[monitor,CW_laser, arc]) + + particle_ref = xp.Particles(mass0=mass0, q0=q0, p0c=p0c) + + line.particle_ref = particle_ref + line.build_tracker(_context=test_context) + + line.track(particles, num_turns=num_turns, + turn_by_turn_monitor=False,with_progress=True) + + # extract relevant values + x = monitor.x[:,:,0] + px = monitor.px[:,:,0] + y = monitor.y[:,:,0] + py = monitor.py[:,:,0] + delta = monitor.delta[:,:,0] + zeta = monitor.zeta[:,:,0] + accumulated_length=monitor.s[:,:,0] + state = monitor.state[:,:,0] + time = monitor.at_turn[:, 0, 0] * T_per_turn + + excited=particles.state==2 + excited = excited.astype(int) + fraction_excitation = sum(excited)/len(excited) + time = np.arange(0, num_turns, save_interval) * s_per_turn + + delta_first_turn = delta[0, :] + delta_final_turn = delta[-1, :] + + bins = np.linspace(0, 1e-5, 51) # 50 bins between 0 and 1e-5 + + hist_before, bin_edges = np.histogram(delta_first_turn, bins=bins) + hist_after, _ = np.histogram(delta_final_turn, bins=bins) + + bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2 + + max_bin_height_before = np.max(hist_before) + max_bin_height_after = np.max(hist_after) + + min_index_after = np.argmin(hist_after) + min_bin_center_after = bin_centers[min_index_after] + min_bin_count_after = hist_after[min_index_after] + + + assert max_bin_height_after > 1.5* max_bin_height_before + + xo.assert_allclose(min_bin_center_after, 4.10e-06, rtol=0.1, atol=0) +