function [Fsw,ecc,obliquity,long_perh] = daily_insolation(kyear,lat,day,day_type)

% Usage:
%   Fsw = daily_insolation(kyear,lat,day)
%
% Optional inputs/outputs:
%   [Fsw, ecc, obliquity, long_perh] = daily_insolation(kyear,lat,day,day_type)
%
% Description:
%   Computes daily average insolation as a function of day and latitude at
%   any point during the past 5 million years.
%
% Inputs:
%   kyear:    Thousands of years before 1950 AD (0 to 5000).
%   lat:      Latitude in degrees (-90 to 90).
%   day:      Indicator of time of year; calendar day by default.
%   day_type: Convention for specifying time of year (+/- 1,2) [optional].
%     day_type=1 (default): day input is calendar day (1-365.24), where day 1 
%       is January first.  The calendar is referenced to the vernal equinox 
%       which always occurs at day 80.
%     day_type=2: day input is solar longitude (0-360 degrees). Solar
%       longitude is the angle of the Earth's orbit measured from spring
%       equinox (21 March). Note that calendar days and solar longitude are
%       not linearly related because, by Kepler's Second Law, Earth's
%       angular velocity varies according to its distance from the sun.
%     If day_type is negative, kyear is taken to be a 3 element array
%       containing [eccentricity, obliquity, and longitude of perihelion].
%
% Output:
%   Fsw = Daily average solar radiation in W/m^2.
%   Can also output orbital parameters.
%
% This script contains orbital parameter data for the past 50000 years 
%   from Berger and Loutre (1991).
%
% Detailed description of calculation:
%   Values for eccentricity, obliquity, and longitude of perihelion for the
%   past 5 Myr are taken from Berger and Loutre 1991 (data from
%   ncdc.noaa.gov). If using calendar days, solar longitude is found using an
%   approximate solution to the differential equation representing conservation
%   of angular momentum (Kepler's Second Law).  Given the orbital parameters
%   and solar longitude, daily average insolation is calculated exactly
%   following Berger 1978.
%
% References: 
%   Berger A. and Loutre M.F. (1991). Insolation values for the climate of
%     the last 10 million years. Quaternary Science Reviews, 10(4), 297-317.
%   Berger A. (1978). Long-term variations of daily insolation and
%     Quaternary climatic changes. Journal of Atmospheric Science, 35(12),
%     2362-2367.
%
% Authors:
%   Ian Eisenman and Peter Huybers, Harvard University, 2006
%   eisenman@post.harvard.edu
%
% Suggested citation: 
%   P. Huybers and I. Eisenman, 2006. Integrated summer insolation 
%   calculations. NOAA/NCDC Paleoclimatology Program Data 
%   Contribution #2006-079.
%
% For function syntax, enter daily_insolation with no arguments.
% For examples, enter daily_insolation('examples')

% === Examples ===
if nargin==1
    if isstr(kyear)
        if kyear=='examples'
disp(' ')
disp(' Example 1: Summer solstice insolation at 65 N')
disp('   Fsw=daily_insolation(0:1000,65,90,2);')
disp('   plot(0:1000,Fsw)')
disp(' ')
disp(' Example 2: Difference between June 20 (calendar day) and summer solstice insolation at 65 N')
disp('   june20=datenum(0,6,20)-1; % year 0 is leap-year for datenum')
disp('   Fsw1=daily_insolation(0:1000,65,june20);   % June 20')
disp('   Fsw2=daily_insolation(0:1000,65,90,2); % solstice')
disp('   plot(0:1000,Fsw1-Fsw2)')
disp(' ')
disp(' Example 3: Insolation for the current orbital configuration as a function of day and latitude')
disp('   [day lat]=meshgrid(1:5:365, -90:90);')
disp('   [Fsw,ecc,obl,omega]=daily_insolation(0,lat,day);')
disp('   [c,h]=contour(day,lat,Fsw,[0:50:500]);')
disp('   clabel(c,h)')
disp('   disp([ecc,obl,omega])')
disp(' ')
disp(' Example 4: Annual average insolation by explicitly specifying orbital parameters')
disp('   ecc=0.017236; obl=23.446; omega=101.37+180;')
disp('   [day lat]=meshgrid(1:5:365, -90:90);')
disp('   Fsw=daily_insolation([ecc,obl,omega],lat,day,-1);')
disp('   plot(-90:90,mean(Fsw''))')
disp(' ')
disp(' Example 5: Compare calculated insolation with example values given by Berger (1991); requires file ORBIT91 from ncdc.noaa.gov')
disp('   m=dlmread(''ORBIT91'','' '',3,0); % Matlab 6.5')
disp('   m=dlmread(''ORBIT91'','''',3,0);  % Matlab 7')
disp('   Fsw=daily_insolation(0:5000,65,(7-3)*30,2)*1360/1365; % July 65N; Berger uses So=1360')
disp('   plot(m(:,1),1-m(:,6)./Fsw'') % values agree within 3e-5')
disp(' ')
disp(' Example 6: Plot 65N integrated summer insolation as in Huybers (2006), Science 313 508-511')
disp('   [kyear day]=meshgrid(1000:1:2000,1:1:365);')
disp('   Fsw = daily_insolation(kyear,65,day);')
disp('   Fsw(Fsw<275)=0;')
disp('   plot(-(1000:1:2000),sum(Fsw,1)*86400*10^-9)')
disp('   title(''As in Huybers (2006) Fig. 2C'')')
return
        end
    end
end

% === Check input arguments ===
if nargin<3, disp('Fsw = daily_insolation(kyear,lat,day,[day_type])');
    disp('  for examples, enter daily_insolation(''examples'')'); return; end
if nargin<4, day_type=1; end

% === Get orbital parameters ===
if day_type>=0
    [ecc,epsilon,omega]=orbital_parameters(kyear); % function is below in this file
else
    if length(kyear)~=3
        disp('Error: expect 3-element kyear argument for day_type<0'), Fsw=nan; daily_insolation; return
    end
    ecc=kyear(1);
    epsilon=kyear(2) * pi/180;
    omega=kyear(3) * pi/180;
end
% For output of orbital parameters
obliquity=epsilon*180/pi;
long_perh=omega*180/pi;

% === Calculate insolation ===
lat=lat*pi/180; % latitude
% lambda (or solar longitude) is the angular distance along Earth's orbit measured from spring equinox (21 March)
if abs(day_type)==1 % calendar days
    % estimate lambda from calendar day using an approximation from Berger 1978 section 3
    delta_lambda_m=(day-80)*2*pi/365.2422;
    beta=(1-ecc.^2).^(1/2);
    lambda_m0=-2*( (1/2*ecc+1/8*ecc.^3).*(1+beta).*sin(-omega)-...
        1/4*ecc.^2.*(1/2+beta).*sin(-2*omega)+1/8*ecc.^3.*(1/3+beta).*(sin(-3*omega)) );
    lambda_m=lambda_m0+delta_lambda_m;
    lambda=lambda_m+(2*ecc-1/4*ecc.^3).*sin(lambda_m-omega)+...
        (5/4)*ecc.^2.*sin(2*(lambda_m-omega))+(13/12)*ecc.^3.*sin(3*(lambda_m-omega));
elseif abs(day_type)==2 %solar longitude (1-360)
    lambda=day*2*pi/360; % lambda=0 for spring equinox
else
    disp('Error: invalid day_type'); Fsw=nan; daily_insolation; return
end
So=1365; % solar constant (W/m^2)
delta=asin(sin(epsilon).*sin(lambda)); % declination of the sun
Ho=acos(-tan(lat).*tan(delta)); % hour angle at sunrise/sunset
% no sunrise or no sunset: Berger 1978 eqn (8),(9)
Ho( ( abs(lat) >= pi/2 - abs(delta) ) & ( lat.*delta > 0 ) )=pi;
Ho( ( abs(lat) >= pi/2 - abs(delta) ) & ( lat.*delta <= 0 ) )=0;

% Insolation: Berger 1978 eq (10)
Fsw=So/pi*(1+ecc.*cos(lambda-omega)).^2 ./ ...
    (1-ecc.^2).^2 .* ...
    ( Ho.*sin(lat).*sin(delta) + cos(lat).*cos(delta).*sin(Ho) );


% === Calculate orbital parameters ===

function [ecc,epsilon,omega] = orbital_parameters(kyear)

% === Load orbital parameters (given each kyr for 0-5Mya) ===
% This matrix contains data from Berger and Loutre (1991), 
%   downloaded as ORBIT91 from ncdc.noaa.gov
% Search for "===" to find end of matrix.

% ===
m=[0 0.017236 101.37 23.446
   -1 0.017644  84.26 23.573
   -2 0.018024  67.23 23.697
   -3 0.018376  50.30 23.815
   -4 0.018697  33.45 23.923
   -5 0.018988  16.68 24.019
   -6 0.019249 359.99 24.100
   -7 0.019477 343.37 24.163
   -8 0.019674 326.82 24.206
   -9 0.019839 310.32 24.229
  -10 0.019971 293.86 24.229
  -11 0.020071 277.45 24.207
  -12 0.020139 261.07 24.161
  -13 0.020175 244.71 24.093
  -14 0.020180 228.37 24.004
  -15 0.020154 212.04 23.895
  -16 0.020098 195.71 23.769
  -17 0.020012 179.38 23.627
  -18 0.019898 163.04 23.475
  -19 0.019756 146.69 23.315
  -20 0.019589 130.34 23.151
  -21 0.019398 113.98 22.989
  -22 0.019183  97.61 22.832
  -23 0.018948  81.26 22.685
  -24 0.018693  64.91 22.553
  -25 0.018422  48.60 22.439
  -26 0.018136  32.33 22.348
  -27 0.017839  16.13 22.282
  -28 0.017532   0.00 22.244
  -29 0.017218 343.99 22.235
  -30 0.016902 328.11 22.255
  -31 0.016585 312.37 22.305
  -32 0.016272 296.80 22.382
  -33 0.015966 281.42 22.485
  -34 0.015671 266.24 22.610
  -35 0.015390 251.28 22.754
  -36 0.015127 236.54 22.913
  -37 0.014886 222.02 23.082
  -38 0.014672 207.73 23.257
  -39 0.014486 193.65 23.433
  -40 0.014333 179.77 23.605
  -41 0.014215 166.06 23.769
  -42 0.014134 152.51 23.922
  -43 0.014093 139.09 24.059
  -44 0.014093 125.77 24.178
  -45 0.014133 112.50 24.277
  -46 0.014215  99.27 24.353
  -47 0.014337  86.04 24.405
  -48 0.014498  72.79 24.433
  -49 0.014697  59.47 24.437
  -50 0.014931  46.07 24.416
  -51 0.015198  32.57 24.371
  -52 0.015495  18.95 24.305
  -53 0.015819   5.20 24.218
  -54 0.016168 351.31 24.113
  -55 0.016540 337.27 23.992
  -56 0.016931 323.07 23.859
  -57 0.017339 308.72 23.715
  -58 0.017762 294.21 23.565
  -59 0.018198 279.55 23.411
  -60 0.018646 264.74 23.258
  -61 0.019103 249.78 23.108
  -62 0.019569 234.69 22.965
  -63 0.020043 219.48 22.831
  -64 0.020522 204.14 22.710
  -65 0.021008 188.71 22.603
  -66 0.021498 173.17 22.514
  -67 0.021993 157.56 22.442
  -68 0.022493 141.88 22.391
  -69 0.022997 126.14 22.360
  -70 0.023505 110.35 22.350
  -71 0.024017  94.54 22.360
  -72 0.024534  78.70 22.390
  -73 0.025055  62.85 22.440
  -74 0.025581  47.00 22.507
  -75 0.026111  31.16 22.590
  -76 0.026646  15.33 22.687
  -77 0.027186 359.52 22.797
  -78 0.027731 343.74 22.916
  -79 0.028281 327.98 23.043
  -80 0.028836 312.25 23.175
  -81 0.029395 296.54 23.310
  -82 0.029958 280.87 23.444
  -83 0.030526 265.23 23.576
  -84 0.031097 249.61 23.703
  -85 0.031671 234.01 23.822
  -86 0.032247 218.43 23.932
  -87 0.032825 202.87 24.030
  -88 0.033403 187.31 24.115
  -89 0.033980 171.75 24.184
  -90 0.034556 156.19 24.236
  -91 0.035128 140.61 24.270
  -92 0.035697 125.02 24.285
  -93 0.036260 109.41 24.281
  -94 0.036816  93.75 24.256
  -95 0.037363  78.06 24.212
  -96 0.037900  62.32 24.147
  -97 0.038424  46.53 24.065
  -98 0.038936  30.67 23.964
  -99 0.039432  14.74 23.849
 -100 0.039911 358.73 23.719
 -101 0.040372 342.64 23.579
 -102 0.040812 326.47 23.432
 -103 0.041230 310.20 23.280
 -104 0.041624 293.85 23.127
 -105 0.041993 277.40 22.978
 -106 0.042335 260.86 22.836
 -107 0.042649 244.24 22.706
 -108 0.042933 227.54 22.591
 -109 0.043185 210.78 22.494
 -110 0.043406 193.96 22.420
 -111 0.043592 177.10 22.370
 -112 0.043744 160.21 22.346
 -113 0.043860 143.31 22.349
 -114 0.043940 126.41 22.380
 -115 0.043983 109.54 22.438
 -116 0.043988  92.71 22.520
 -117 0.043954  75.93 22.625
 -118 0.043882  59.22 22.750
 -119 0.043771  42.59 22.891
 -120 0.043622  26.04 23.043
 -121 0.043434   9.59 23.202
 -122 0.043208 353.23 23.364
 -123 0.042945 336.98 23.523
 -124 0.042644 320.82 23.676
 -125 0.042308 304.76 23.818
 -126 0.041936 288.80 23.945
 -127 0.041531 272.92 24.054
 -128 0.041094 257.12 24.142
 -129 0.040626 241.39 24.207
 -130 0.040129 225.73 24.247
 -131 0.039605 210.14 24.262
 -132 0.039058 194.59 24.251
 -133 0.038488 179.08 24.214
 -134 0.037900 163.62 24.154
 -135 0.037295 148.18 24.071
 -136 0.036677 132.77 23.967
 -137 0.036051 117.39 23.847
 -138 0.035418 102.02 23.712
 -139 0.034783  86.66 23.568
 -140 0.034151  71.32 23.417
 -141 0.033525  56.00 23.265
 -142 0.032910  40.69 23.116
 -143 0.032311  25.41 22.974
 -144 0.031732  10.16 22.844
 -145 0.031178 354.95 22.729
 -146 0.030655 339.78 22.632
 -147 0.030166 324.67 22.557
 -148 0.029717 309.63 22.505
 -149 0.029312 294.66 22.478
 -150 0.028955 279.76 22.476
 -151 0.028650 264.96 22.498
 -152 0.028400 250.23 22.544
 -153 0.028208 235.59 22.611
 -154 0.028075 221.04 22.698
 -155 0.028003 206.56 22.800
 -156 0.027993 192.14 22.915
 -157 0.028043 177.79 23.039
 -158 0.028152 163.47 23.169
 -159 0.028319 149.18 23.301
 -160 0.028542 134.91 23.432
 -161 0.028816 120.64 23.557
 -162 0.029139 106.36 23.676
 -163 0.029506  92.06 23.783
 -164 0.029913  77.72 23.879
 -165 0.030356  63.33 23.960
 -166 0.030831  48.89 24.026
 -167 0.031333  34.38 24.075
 -168 0.031859  19.80 24.107
 -169 0.032403   5.15 24.122
 -170 0.032963 350.42 24.119
 -171 0.033534 335.60 24.100
 -172 0.034113 320.70 24.064
 -173 0.034697 305.71 24.014
 -174 0.035284 290.63 23.950
 -175 0.035870 275.45 23.873
 -176 0.036453 260.19 23.784
 -177 0.037030 244.83 23.687
 -178 0.037602 229.39 23.582
 -179 0.038164 213.85 23.471
 -180 0.038717 198.22 23.356
 -181 0.039259 182.51 23.240
 -182 0.039789 166.71 23.124
 -183 0.040306 150.84 23.011
 -184 0.040810 134.88 22.902
 -185 0.041300 118.85 22.800
 -186 0.041775 102.75 22.707
 -187 0.042236  86.59 22.626
 -188 0.042682  70.37 22.557
 -189 0.043114  54.10 22.502
 -190 0.043530  37.79 22.464
 -191 0.043933  21.45 22.444
 -192 0.044321   5.08 22.442
 -193 0.044694 348.70 22.459
 -194 0.045053 332.32 22.496
 -195 0.045399 315.94 22.552
 -196 0.045731 299.58 22.627
 -197 0.046049 283.23 22.719
 -198 0.046353 266.93 22.828
 -199 0.046645 250.66 22.951
 -200 0.046922 234.44 23.086
 -201 0.047187 218.27 23.230
 -202 0.047438 202.16 23.380
 -203 0.047675 186.10 23.533
 -204 0.047898 170.10 23.685
 -205 0.048107 154.16 23.833
 -206 0.048302 138.27 23.973
 -207 0.048481 122.43 24.102
 -208 0.048645 106.64 24.216
 -209 0.048793  90.87 24.313
 -210 0.048923  75.14 24.390
 -211 0.049036  59.42 24.444
 -212 0.049131  43.72 24.475
 -213 0.049206  28.01 24.480
 -214 0.049260  12.29 24.459
 -215 0.049294 356.55 24.412
 -216 0.049305 340.77 24.338
 -217 0.049292 324.95 24.240
 -218 0.049256 309.07 24.118
 -219 0.049194 293.12 23.975
 -220 0.049105 277.10 23.813
 -221 0.048990 261.00 23.637
 -222 0.048846 244.80 23.450
 -223 0.048672 228.50 23.258
 -224 0.048469 212.10 23.064
 -225 0.048234 195.60 22.875
 -226 0.047967 179.00 22.695
 -227 0.047668 162.30 22.530
 -228 0.047336 145.53 22.385
 -229 0.046971 128.68 22.264
 -230 0.046571 111.77 22.171
 -231 0.046137  94.83 22.109
 -232 0.045669  77.86 22.079
 -233 0.045166  60.89 22.084
 -234 0.044629  43.95 22.122
 -235 0.044057  27.04 22.191
 -236 0.043452  10.20 22.291
 -237 0.042814 353.43 22.417
 -238 0.042143 336.75 22.566
 -239 0.041440 320.19 22.733
 -240 0.040707 303.74 22.912
 -241 0.039945 287.41 23.099
 -242 0.039155 271.21 23.288
 -243 0.038338 255.14 23.475
 -244 0.037498 239.21 23.654
 -245 0.036635 223.40 23.820
 -246 0.035753 207.73 23.971
 -247 0.034853 192.17 24.103
 -248 0.033939 176.74 24.213
 -249 0.033014 161.43 24.299
 -250 0.032082 146.23 24.360
 -251 0.031146 131.15 24.396
 -252 0.030210 116.18 24.406
 -253 0.029280 101.32 24.391
 -254 0.028360  86.58 24.351
 -255 0.027455  71.95 24.290
 -256 0.026572  57.43 24.208
 -257 0.025716  43.04 24.108
 -258 0.024895  28.76 23.994
 -259 0.024115  14.61 23.867
 -260 0.023384   0.59 23.732
 -261 0.022709 346.68 23.591
 -262 0.022098 332.90 23.449
 -263 0.021559 319.23 23.309
 -264 0.021097 305.65 23.174
 -265 0.020719 292.15 23.046
 -266 0.020429 278.71 22.930
 -267 0.020232 265.30 22.826
 -268 0.020128 251.87 22.737
 -269 0.020117 238.41 22.665
 -270 0.020198 224.88 22.611
 -271 0.020366 211.25 22.574
 -272 0.020616 197.49 22.556
 -273 0.020942 183.58 22.555
 -274 0.021336 169.52 22.571
 -275 0.021789 155.30 22.604
 -276 0.022294 140.91 22.651
 -277 0.022843 126.36 22.711
 -278 0.023428 111.66 22.783
 -279 0.024041  96.82 22.865
 -280 0.024675  81.85 22.954
 -281 0.025323  66.76 23.048
 -282 0.025980  51.57 23.147
 -283 0.026641  36.27 23.248
 -284 0.027300  20.90 23.348
 -285 0.027953   5.45 23.447
 -286 0.028596 349.93 23.542
 -287 0.029226 334.35 23.632
 -288 0.029839 318.72 23.714
 -289 0.030434 303.05 23.789
 -290 0.031007 287.32 23.854
 -291 0.031557 271.56 23.907
 -292 0.032082 255.76 23.949
 -293 0.032581 239.92 23.978
 -294 0.033052 224.04 23.993
 -295 0.033494 208.13 23.993
 -296 0.033907 192.17 23.979
 -297 0.034289 176.17 23.949
 -298 0.034642 160.13 23.906
 -299 0.034963 144.04 23.847
 -300 0.035254 127.90 23.776
 -301 0.035514 111.70 23.692
 -302 0.035744  95.45 23.598
 -303 0.035943  79.13 23.494
 -304 0.036112  62.75 23.384
 -305 0.036252  46.31 23.270
 -306 0.036362  29.79 23.154
 -307 0.036444  13.21 23.041
 -308 0.036499 356.57 22.931
 -309 0.036526 339.86 22.830
 -310 0.036527 323.09 22.740
 -311 0.036502 306.27 22.664
 -312 0.036452 289.41 22.605
 -313 0.036379 272.51 22.565
 -314 0.036281 255.58 22.546
 -315 0.036162 238.64 22.549
 -316 0.036020 221.69 22.575
 -317 0.035857 204.76 22.624
 -318 0.035674 187.85 22.694
 -319 0.035471 170.97 22.784
 -320 0.035248 154.13 22.891
 -321 0.035007 137.34 23.014
 -322 0.034748 120.60 23.148
 -323 0.034471 103.93 23.289
 -324 0.034177  87.31 23.435
 -325 0.033865  70.76 23.579
 -326 0.033537  54.26 23.719
 -327 0.033193  37.82 23.851
 -328 0.032832  21.42 23.970
 -329 0.032454   5.07 24.074
 -330 0.032061 348.74 24.159
 -331 0.031652 332.43 24.223
 -332 0.031226 316.12 24.264
 -333 0.030785 299.81 24.280
 -334 0.030327 283.48 24.272
 -335 0.029853 267.12 24.238
 -336 0.029362 250.72 24.180
 -337 0.028855 234.27 24.099
 -338 0.028331 217.74 23.996
 -339 0.027791 201.14 23.874
 -340 0.027233 184.45 23.735
 -341 0.026659 167.66 23.585
 -342 0.026068 150.75 23.425
 -343 0.025460 133.74 23.261
 -344 0.024835 116.60 23.096
 -345 0.024193  99.35 22.937
 -346 0.023534  81.97 22.787
 -347 0.022859  64.47 22.650
 -348 0.022168  46.86 22.531
 -349 0.021461  29.13 22.433
 -350 0.020738  11.31 22.359
 -351 0.020001 353.38 22.312
 -352 0.019250 335.38 22.291
 -353 0.018485 317.29 22.298
 -354 0.017708 299.14 22.333
 -355 0.016919 280.92 22.393
 -356 0.016120 262.63 22.478
 -357 0.015313 244.28 22.583
 -358 0.014498 225.85 22.707
 -359 0.013678 207.34 22.844
 -360 0.012854 188.71 22.993
 -361 0.012030 169.94 23.147
 -362 0.011209 151.00 23.304
 -363 0.010393 131.81 23.459
 -364 0.009588 112.32 23.608
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-1906 0.017353 261.08 23.626
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-1908 0.019570 231.70 23.540
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-1912 0.023991 169.55 23.308
-1913 0.025058 153.50 23.245
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-1915 0.027120 120.94 23.121
-1916 0.028107 104.46 23.064
-1917 0.029061  87.86 23.011
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-1919 0.030861  54.38 22.924
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-1921 0.032504  20.59 22.871
-1922 0.033262   3.60 22.859
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-1924 0.034643 329.48 22.868
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-1926 0.035839 295.24 22.922
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-1928 0.036842 260.95 23.018
-1929 0.037269 243.81 23.080
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-1931 0.037975 209.54 23.227
-1932 0.038252 192.43 23.309
-1933 0.038479 175.35 23.393
-1934 0.038656 158.28 23.479
-1935 0.038783 141.25 23.564
-1936 0.038861 124.24 23.646
-1937 0.038890 107.25 23.724
-1938 0.038870  90.29 23.794
-1939 0.038803  73.35 23.856
-1940 0.038689  56.43 23.908
-1941 0.038528  39.52 23.948
-1942 0.038323  22.63 23.975
-1943 0.038073   5.73 23.988
-1944 0.037781 348.84 23.986
-1945 0.037447 331.93 23.969
-1946 0.037072 315.02 23.937
-1947 0.036659 298.08 23.890
-1948 0.036207 281.11 23.829
-1949 0.035719 264.10 23.755
-1950 0.035196 247.06 23.669
-1951 0.034640 229.97 23.572
-1952 0.034053 212.82 23.468
-1953 0.033435 195.62 23.358
-1954 0.032788 178.35 23.245
-1955 0.032115 161.02 23.131
-1956 0.031416 143.63 23.020
-1957 0.030693 126.16 22.913
-1958 0.029949 108.63 22.815
-1959 0.029184  91.03 22.728
-1960 0.028401  73.37 22.653
-1961 0.027600  55.65 22.594
-1962 0.026785  37.88 22.552
-1963 0.025955  20.06 22.528
-1964 0.025113   2.19 22.523
-1965 0.024261 344.28 22.537
-1966 0.023401 326.34 22.571
-1967 0.022533 308.37 22.622
-1968 0.021660 290.36 22.691
-1969 0.020784 272.32 22.774
-1970 0.019906 254.24 22.870
-1971 0.019028 236.11 22.977
-1972 0.018152 217.93 23.091
-1973 0.017281 199.69 23.211
-1974 0.016417 181.35 23.332
-1975 0.015563 162.90 23.453
-1976 0.014721 144.31 23.570
-1977 0.013895 125.54 23.681
-1978 0.013089 106.56 23.783
-1979 0.012309  87.31 23.875
-1980 0.011559  67.74 23.954
-1981 0.010846  47.79 24.020
-1982 0.010180  27.40 24.070
-1983 0.009568   6.51 24.105
-1984 0.009023 345.06 24.124
-1985 0.008556 323.04 24.127
-1986 0.008181 300.46 24.113
-1987 0.007907 277.38 24.084
-1988 0.007747 253.94 24.040
-1989 0.007704 230.33 23.983
-1990 0.007778 206.75 23.913
-1991 0.007965 183.41 23.833
-1992 0.008254 160.46 23.743
-1993 0.008633 137.99 23.647
-1994 0.009087 116.06 23.544
-1995 0.009603  94.63 23.439
-1996 0.010169  73.69 23.332
-1997 0.010774  53.18 23.226
-1998 0.011408  33.04 23.123
-1999 0.012063  13.22 23.025
-2000 0.012734 353.67 22.934
-2001 0.013414 334.36 22.851
-2002 0.014099 315.24 22.778
-2003 0.014784 296.29 22.716
-2004 0.015466 277.48 22.667
-2005 0.016142 258.81 22.631
-2006 0.016808 240.24 22.609
-2007 0.017463 221.77 22.602
-2008 0.018104 203.40 22.609
-2009 0.018728 185.11 22.630
-2010 0.019333 166.90 22.666
-2011 0.019919 148.77 22.714
-2012 0.020482 130.71 22.775
-2013 0.021021 112.73 22.846
-2014 0.021534  94.82 22.928
-2015 0.022019  76.98 23.017
-2016 0.022476  59.21 23.113
-2017 0.022902  41.51 23.214
-2018 0.023296  23.87 23.316
-2019 0.023657   6.30 23.420
-2020 0.023983 348.79 23.521
-2021 0.024274 331.33 23.619
-2022 0.024527 313.93 23.712
-2023 0.024742 296.57 23.796
-2024 0.024918 279.26 23.871
-2025 0.025054 261.98 23.935
-2026 0.025148 244.74 23.987
-2027 0.025201 227.51 24.024
-2028 0.025212 210.31 24.047
-2029 0.025179 193.11 24.054
-2030 0.025103 175.92 24.045
-2031 0.024983 158.71 24.020
-2032 0.024818 141.50 23.979
-2033 0.024609 124.26 23.923
-2034 0.024355 106.99 23.853
-2035 0.024057  89.69 23.770
-2036 0.023713  72.34 23.676
-2037 0.023326  54.94 23.572
-2038 0.022894  37.48 23.462
-2039 0.022418  19.96 23.348
-2040 0.021900   2.38 23.233
-2041 0.021338 344.72 23.120
-2042 0.020735 327.00 23.011
-2043 0.020090 309.21 22.911
-2044 0.019406 291.35 22.821
-2045 0.018682 273.42 22.745
-2046 0.017921 255.42 22.685
-2047 0.017123 237.37 22.643
-2048 0.016289 219.25 22.619
-2049 0.015422 201.07 22.616
-2050 0.014523 182.82 22.633
-2051 0.013594 164.51 22.669
-2052 0.012636 146.12 22.724
-2053 0.011652 127.61 22.796
-2054 0.010645 108.97 22.883
-2055 0.009617  90.13 22.982
-2056 0.008573  71.00 23.090
-2057 0.007517  51.42 23.204
-2058 0.006456  31.14 23.321
-2059 0.005403   9.71 23.436
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-2062 0.002640 285.15 23.746
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-2067 0.005111 103.55 23.990
-2068 0.006227  81.79 23.985
-2069 0.007374  61.52 23.962
-2070 0.008536  42.17 23.921
-2071 0.009706  23.41 23.864
-2072 0.010878   5.03 23.792
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-2074 0.013212 328.98 23.612
-2075 0.014369 311.17 23.510
-2076 0.015515 293.45 23.403
-2077 0.016649 275.79 23.294
-2078 0.017769 258.16 23.187
-2079 0.018873 240.56 23.085
-2080 0.019961 222.98 22.990
-2081 0.021030 205.41 22.906
-2082 0.022080 187.85 22.833
-2083 0.023110 170.30 22.775
-2084 0.024118 152.78 22.733
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-2087 0.027004 100.36 22.708
-2088 0.027918  82.96 22.733
-2089 0.028807  65.60 22.774
-2090 0.029671  48.30 22.828
-2091 0.030508  31.06 22.894
-2092 0.031320  13.88 22.971
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-2094 0.032863 339.71 23.146
-2095 0.033595 322.73 23.239
-2096 0.034299 305.81 23.334
-2097 0.034978 288.95 23.427
-2098 0.035629 272.15 23.518
-2099 0.036253 255.41 23.603
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-2101 0.037422 222.09 23.753
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-2109 0.041044  90.13 23.934
-2110 0.041380  73.70 23.905
-2111 0.041689  57.27 23.864
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-2113 0.042230  24.38 23.752
-2114 0.042461   7.92 23.681
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-2129 0.042524 117.34 22.497
-2130 0.042281 100.43 22.493
-2131 0.042004  83.53 22.509
-2132 0.041693  66.66 22.545
-2133 0.041347  49.81 22.600
-2134 0.040967  33.00 22.674
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-2224 0.051446  85.74 23.453
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-2228 0.050409  20.63 23.801
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-4521 0.019053 182.75 23.291
-4522 0.019004 168.13 23.365
-4523 0.018987 153.57 23.443
-4524 0.019003 139.07 23.522
-4525 0.019052 124.62 23.599
-4526 0.019132 110.19 23.673
-4527 0.019243  95.78 23.742
-4528 0.019383  81.37 23.803
-4529 0.019552  66.95 23.855
-4530 0.019746  52.52 23.895
-4531 0.019963  38.05 23.923
-4532 0.020202  23.55 23.937
-4533 0.020460   8.99 23.935
-4534 0.020734 354.37 23.918
-4535 0.021022 339.69 23.886
-4536 0.021322 324.94 23.837
-4537 0.021631 310.10 23.774
-4538 0.021948 295.18 23.697
-4539 0.022270 280.18 23.608
-4540 0.022596 265.08 23.508
-4541 0.022923 249.88 23.399
-4542 0.023251 234.60 23.286
-4543 0.023577 219.22 23.169
-4544 0.023902 203.74 23.053
-4545 0.024224 188.18 22.941
-4546 0.024542 172.54 22.835
-4547 0.024855 156.82 22.740
-4548 0.025165 141.03 22.657
-4549 0.025469 125.18 22.590
-4550 0.025768 109.28 22.541
-4551 0.026062  93.35 22.511
-4552 0.026352  77.39 22.503
-4553 0.026638  61.43 22.515
-4554 0.026919  45.47 22.549
-4555 0.027198  29.52 22.603
-4556 0.027473  13.60 22.677
-4557 0.027746 357.72 22.768
-4558 0.028018 341.88 22.874
-4559 0.028290 326.09 22.992
-4560 0.028561 310.36 23.118
-4561 0.028832 294.69 23.251
-4562 0.029105 279.08 23.385
-4563 0.029380 263.53 23.519
-4564 0.029657 248.03 23.648
-4565 0.029938 232.58 23.769
-4566 0.030221 217.18 23.880
-4567 0.030508 201.81 23.978
-4568 0.030799 186.47 24.060
-4569 0.031093 171.15 24.126
-4570 0.031391 155.84 24.174
-4571 0.031693 140.53 24.202
-4572 0.031997 125.21 24.212
-4573 0.032304 109.88 24.201
-4574 0.032613  94.51 24.172
-4575 0.032923  79.11 24.124
-4576 0.033233  63.66 24.059
-4577 0.033543  48.16 23.979
-4578 0.033851  32.59 23.885
-4579 0.034156  16.97 23.779
-4580 0.034457   1.26 23.664
-4581 0.034752 345.49 23.544
-4582 0.035041 329.63 23.419
-4583 0.035321 313.70 23.293
-4584 0.035592 297.69 23.170
-4585 0.035852 281.60 23.051
-4586 0.036099 265.44 22.940
-4587 0.036332 249.21 22.839
-4588 0.036550 232.92 22.750
-4589 0.036751 216.58 22.675
-4590 0.036935 200.19 22.615
-4591 0.037099 183.77 22.572
-4592 0.037242 167.32 22.546
-4593 0.037365 150.85 22.538
-4594 0.037464 134.38 22.547
-4595 0.037541 117.91 22.572
-4596 0.037594 101.45 22.614
-4597 0.037621  85.02 22.670
-4598 0.037624  68.62 22.739
-4599 0.037601  52.26 22.820
-4600 0.037553  35.95 22.910
-4601 0.037479  19.69 23.006
-4602 0.037379   3.48 23.108
-4603 0.037254 347.33 23.213
-4604 0.037103 331.25 23.318
-4605 0.036929 315.23 23.422
-4606 0.036731 299.27 23.522
-4607 0.036510 283.38 23.616
-4608 0.036268 267.56 23.704
-4609 0.036005 251.80 23.783
-4610 0.035724 236.10 23.851
-4611 0.035426 220.47 23.909
-4612 0.035113 204.89 23.954
-4613 0.034787 189.38 23.986
-4614 0.034450 173.92 24.005
-4615 0.034105 158.51 24.010
-4616 0.033754 143.15 24.002
-4617 0.033399 127.83 23.980
-4618 0.033044 112.56 23.945
-4619 0.032691  97.33 23.897
-4620 0.032344  82.13 23.838
-4621 0.032005  66.96 23.768
-4622 0.031677  51.82 23.689
-4623 0.031364  36.70 23.603
-4624 0.031069  21.60 23.510
-4625 0.030793   6.51 23.414
-4626 0.030541 351.42 23.316
-4627 0.030314 336.34 23.218
-4628 0.030115 321.25 23.123
-4629 0.029945 306.16 23.032
-4630 0.029807 291.05 22.948
-4631 0.029702 275.93 22.873
-4632 0.029631 260.79 22.809
-4633 0.029594 245.63 22.758
-4634 0.029592 230.45 22.720
-4635 0.029623 215.25 22.698
-4636 0.029687 200.02 22.691
-4637 0.029784 184.77 22.700
-4638 0.029911 169.50 22.725
-4639 0.030066 154.21 22.766
-4640 0.030248 138.90 22.821
-4641 0.030453 123.57 22.889
-4642 0.030680 108.24 22.969
-4643 0.030925  92.89 23.058
-4644 0.031185  77.54 23.154
-4645 0.031457  62.17 23.255
-4646 0.031740  46.81 23.358
-4647 0.032028  31.43 23.460
-4648 0.032320  16.05 23.558
-4649 0.032612   0.66 23.651
-4650 0.032902 345.27 23.735
-4651 0.033187 329.86 23.809
-4652 0.033465 314.43 23.870
-4653 0.033734 298.99 23.916
-4654 0.033990 283.53 23.948
-4655 0.034232 268.03 23.962
-4656 0.034459 252.51 23.960
-4657 0.034669 236.95 23.940
-4658 0.034860 221.35 23.904
-4659 0.035032 205.70 23.851
-4660 0.035182 190.00 23.784
-4661 0.035311 174.25 23.703
-4662 0.035417 158.44 23.610
-4663 0.035500 142.58 23.509
-4664 0.035560 126.65 23.400
-4665 0.035597 110.66 23.288
-4666 0.035610  94.61 23.176
-4667 0.035601  78.49 23.066
-4668 0.035568  62.33 22.963
-4669 0.035514  46.11 22.868
-4670 0.035438  29.86 22.785
-4671 0.035341  13.57 22.717
-4672 0.035224 357.25 22.665
-4673 0.035088 340.92 22.633
-4674 0.034934 324.59 22.620
-4675 0.034764 308.28 22.628
-4676 0.034578 291.99 22.657
-4677 0.034378 275.73 22.705
-4678 0.034166 259.52 22.772
-4679 0.033942 243.37 22.856
-4680 0.033708 227.29 22.954
-4681 0.033466 211.28 23.065
-4682 0.033217 195.35 23.183
-4683 0.032962 179.50 23.308
-4684 0.032703 163.74 23.434
-4685 0.032441 148.06 23.558
-4686 0.032178 132.46 23.678
-4687 0.031914 116.93 23.789
-4688 0.031651 101.48 23.890
-4689 0.031389  86.09 23.976
-4690 0.031130  70.75 24.048
-4691 0.030873  55.46 24.101
-4692 0.030621  40.21 24.135
-4693 0.030372  24.98 24.150
-4694 0.030128   9.76 24.144
-4695 0.029889 354.55 24.118
-4696 0.029654 339.33 24.072
-4697 0.029423 324.09 24.007
-4698 0.029196 308.83 23.925
-4699 0.028973 293.53 23.827
-4700 0.028753 278.18 23.716
-4701 0.028536 262.78 23.595
-4702 0.028321 247.32 23.466
-4703 0.028106 231.80 23.332
-4704 0.027892 216.21 23.197
-4705 0.027676 200.55 23.065
-4706 0.027460 184.83 22.938
-4707 0.027240 169.04 22.820
-4708 0.027017 153.19 22.713
-4709 0.026790 137.29 22.622
-4710 0.026558 121.35 22.547
-4711 0.026320 105.38 22.491
-4712 0.026075  89.38 22.456
-4713 0.025823  73.37 22.441
-4714 0.025564  57.37 22.448
-4715 0.025296  41.39 22.476
-4716 0.025021  25.43 22.523
-4717 0.024738   9.51 22.590
-4718 0.024446 353.65 22.673
-4719 0.024147 337.86 22.771
-4720 0.023841 322.13 22.881
-4721 0.023528 306.49 23.000
-4722 0.023209 290.94 23.126
-4723 0.022886 275.47 23.255
-4724 0.022559 260.11 23.385
-4725 0.022230 244.85 23.513
-4726 0.021901 229.69 23.637
-4727 0.021572 214.63 23.753
-4728 0.021247 199.67 23.860
-4729 0.020927 184.81 23.955
-4730 0.020614 170.05 24.038
-4731 0.020311 155.38 24.106
-4732 0.020020 140.80 24.159
-4733 0.019743 126.29 24.196
-4734 0.019484 111.86 24.216
-4735 0.019243  97.49 24.219
-4736 0.019024  83.17 24.205
-4737 0.018829  68.89 24.174
-4738 0.018659  54.64 24.127
-4739 0.018516  40.41 24.065
-4740 0.018402  26.16 23.988
-4741 0.018318  11.90 23.898
-4742 0.018263 357.61 23.796
-4743 0.018239 343.25 23.685
-4744 0.018244 328.83 23.565
-4745 0.018279 314.33 23.440
-4746 0.018341 299.72 23.311
-4747 0.018430 285.00 23.181
-4748 0.018543 270.15 23.053
-4749 0.018678 255.18 22.928
-4750 0.018832 240.06 22.811
-4751 0.019003 224.81 22.703
-4752 0.019188 209.41 22.607
-4753 0.019383 193.88 22.526
-4754 0.019586 178.22 22.461
-4755 0.019794 162.43 22.414
-4756 0.020004 146.53 22.388
-4757 0.020212 130.52 22.382
-4758 0.020416 114.42 22.397
-4759 0.020613  98.24 22.434
-4760 0.020800  81.99 22.491
-4761 0.020975  65.69 22.569
-4762 0.021136  49.36 22.664
-4763 0.021281  32.99 22.776
-4764 0.021406  16.61 22.901
-4765 0.021512   0.22 23.037
-4766 0.021595 343.83 23.181
-4767 0.021654 327.45 23.329
-4768 0.021689 311.08 23.478
-4769 0.021698 294.72 23.624
-4770 0.021679 278.37 23.764
-4771 0.021632 262.04 23.894
-4772 0.021557 245.72 24.012
-4773 0.021453 229.40 24.114
-4774 0.021319 213.08 24.199
-4775 0.021155 196.75 24.263
-4776 0.020961 180.41 24.306
-4777 0.020737 164.06 24.326
-4778 0.020483 147.67 24.323
-4779 0.020200 131.25 24.296
-4780 0.019887 114.79 24.246
-4781 0.019546  98.27 24.174
-4782 0.019177  81.69 24.081
-4783 0.018781  65.04 23.970
-4784 0.018358  48.32 23.842
-4785 0.017910  31.51 23.702
-4786 0.017437  14.60 23.552
-4787 0.016941 357.61 23.396
-4788 0.016422 340.51 23.238
-4789 0.015883 323.32 23.084
-4790 0.015324 306.03 22.936
-4791 0.014747 288.64 22.799
-4792 0.014153 271.16 22.678
-4793 0.013543 253.59 22.575
-4794 0.012920 235.95 22.494
-4795 0.012284 218.23 22.437
-4796 0.011638 200.46 22.406
-4797 0.010983 182.62 22.402
-4798 0.010320 164.74 22.424
-4799 0.009652 146.82 22.471
-4800 0.008979 128.84 22.542
-4801 0.008305 110.81 22.635
-4802 0.007630  92.70 22.746
-4803 0.006957  74.49 22.871
-4804 0.006287  56.13 23.008
-4805 0.005624  37.55 23.150
-4806 0.004971  18.63 23.295
-4807 0.004330 359.19 23.438
-4808 0.003707 338.96 23.575
-4809 0.003111 317.47 23.702
-4810 0.002554 293.91 23.816
-4811 0.002063 266.97 23.915
-4812 0.001686 234.82 23.996
-4813 0.001497 196.89 24.058
-4814 0.001552 157.50 24.098
-4815 0.001817 122.79 24.117
-4816 0.002208  94.00 24.115
-4817 0.002661  69.46 24.092
-4818 0.003142  47.56 24.048
-4819 0.003632  27.31 23.986
-4820 0.004123   8.10 23.908
-4821 0.004609 349.60 23.815
-4822 0.005088 331.56 23.711
-4823 0.005557 313.87 23.597
-4824 0.006015 296.41 23.478
-4825 0.006461 279.12 23.357
-4826 0.006896 261.96 23.237
-4827 0.007319 244.90 23.121
-4828 0.007730 227.90 23.011
-4829 0.008129 210.97 22.912
-4830 0.008517 194.08 22.825
-4831 0.008894 177.24 22.753
-4832 0.009261 160.43 22.697
-4833 0.009617 143.66 22.658
-4834 0.009964 126.94 22.637
-4835 0.010302 110.26 22.634
-4836 0.010630  93.62 22.650
-4837 0.010951  77.04 22.682
-4838 0.011263  60.50 22.730
-4839 0.011567  44.03 22.792
-4840 0.011864  27.60 22.867
-4841 0.012153  11.24 22.953
-4842 0.012434 354.93 23.046
-4843 0.012709 338.67 23.146
-4844 0.012975 322.47 23.249
-4845 0.013234 306.32 23.354
-4846 0.013484 290.22 23.457
-4847 0.013726 274.17 23.558
-4848 0.013959 258.15 23.653
-4849 0.014182 242.16 23.742
-4850 0.014395 226.21 23.822
-4851 0.014597 210.28 23.892
-4852 0.014787 194.37 23.951
-4853 0.014964 178.47 23.997
-4854 0.015128 162.59 24.030
-4855 0.015276 146.70 24.049
-4856 0.015409 130.81 24.054
-4857 0.015525 114.92 24.044
-4858 0.015624  99.01 24.020
-4859 0.015703  83.09 23.981
-4860 0.015763  67.15 23.927
-4861 0.015802  51.19 23.860
-4862 0.015819  35.20 23.780
-4863 0.015813  19.19 23.689
-4864 0.015784   3.14 23.587
-4865 0.015730 347.06 23.477
-4866 0.015652 330.95 23.360
-4867 0.015547 314.81 23.239
-4868 0.015417 298.64 23.115
-4869 0.015260 282.45 22.993
-4870 0.015077 266.24 22.874
-4871 0.014866 250.02 22.761
-4872 0.014630 233.81 22.658
-4873 0.014367 217.62 22.567
-4874 0.014078 201.46 22.491
-4875 0.013765 185.36 22.433
-4876 0.013429 169.34 22.394
-4877 0.013071 153.42 22.377
-4878 0.012693 137.65 22.382
-4879 0.012298 122.06 22.410
-4880 0.011889 106.69 22.462
-4881 0.011470  91.57 22.536
-4882 0.011046  76.77 22.632
-4883 0.010623  62.32 22.748
-4884 0.010207  48.28 22.880
-4885 0.009807  34.71 23.027
-4886 0.009434  21.64 23.184
-4887 0.009098   9.11 23.347
-4888 0.008812 357.14 23.514
-4889 0.008591 345.70 23.679
-4890 0.008447 334.74 23.838
-4891 0.008393 324.15 23.988
-4892 0.008439 313.78 24.125
-4893 0.008590 303.46 24.246
-4894 0.008848 293.03 24.346
-4895 0.009210 282.32 24.425
-4896 0.009670 271.23 24.479
-4897 0.010217 259.70 24.508
-4898 0.010843 247.69 24.509
-4899 0.011537 235.20 24.483
-4900 0.012289 222.26 24.430
-4901 0.013090 208.88 24.351
-4902 0.013932 195.11 24.247
-4903 0.014808 180.96 24.120
-4904 0.015711 166.48 23.973
-4905 0.016636 151.68 23.809
-4906 0.017577 136.60 23.631
-4907 0.018530 121.25 23.444
-4908 0.019491 105.65 23.254
-4909 0.020456  89.81 23.063
-4910 0.021422  73.77 22.879
-4911 0.022385  57.53 22.705
-4912 0.023342  41.11 22.547
-4913 0.024291  24.54 22.409
-4914 0.025230   7.83 22.295
-4915 0.026155 351.01 22.209
-4916 0.027065 334.10 22.152
-4917 0.027957 317.13 22.126
-4918 0.028831 300.11 22.132
-4919 0.029682 283.07 22.170
-4920 0.030512 266.04 22.237
-4921 0.031316 249.02 22.332
-4922 0.032095 232.04 22.451
-4923 0.032847 215.12 22.590
-4924 0.033571 198.26 22.746
-4925 0.034266 181.47 22.914
-4926 0.034930 164.76 23.089
-4927 0.035564 148.13 23.265
-4928 0.036166 131.58 23.439
-4929 0.036736 115.11 23.607
-4930 0.037274  98.71 23.763
-4931 0.037779  82.38 23.906
-4932 0.038251  66.12 24.031
-4933 0.038690  49.91 24.136
-4934 0.039095  33.75 24.221
-4935 0.039468  17.62 24.282
-4936 0.039809   1.52 24.321
-4937 0.040117 345.44 24.336
-4938 0.040393 329.37 24.327
-4939 0.040638 313.31 24.297
-4940 0.040852 297.24 24.246
-4941 0.041036 281.16 24.176
-4942 0.041191 265.06 24.088
-4943 0.041318 248.93 23.986
-4944 0.041417 232.77 23.872
-4945 0.041489 216.58 23.749
-4946 0.041536 200.36 23.620
-4947 0.041557 184.09 23.488
-4948 0.041556 167.79 23.356
-4949 0.041531 151.45 23.227
-4950 0.041485 135.08 23.104
-4951 0.041418 118.68 22.989
-4952 0.041332 102.25 22.886
-4953 0.041226  85.80 22.795
-4954 0.041103  69.34 22.719
-4955 0.040963  52.87 22.659
-4956 0.040808  36.40 22.616
-4957 0.040636  19.95 22.590
-4958 0.040451   3.51 22.581
-4959 0.040251 347.11 22.589
-4960 0.040039 330.73 22.613
-4961 0.039814 314.40 22.653
-4962 0.039576 298.11 22.706
-4963 0.039327 281.87 22.772
-4964 0.039067 265.70 22.849
-4965 0.038795 249.58 22.934
-4966 0.038512 233.53 23.026
-4967 0.038219 217.54 23.124
-4968 0.037915 201.62 23.224
-4969 0.037601 185.77 23.325
-4970 0.037276 169.99 23.426
-4971 0.036941 154.28 23.523
-4972 0.036596 138.63 23.616
-4973 0.036241 123.05 23.701
-4974 0.035876 107.54 23.779
-4975 0.035501  92.08 23.847
-4976 0.035117  76.69 23.904
-4977 0.034723  61.35 23.948
-4978 0.034321  46.07 23.979
-4979 0.033911  30.83 23.996
-4980 0.033494  15.65 23.998
-4981 0.033070   0.51 23.985
-4982 0.032641 345.42 23.956
-4983 0.032209 330.37 23.913
-4984 0.031774 315.35 23.855
-4985 0.031338 300.37 23.783
-4986 0.030905 285.43 23.699
-4987 0.030475 270.51 23.603
-4988 0.030052 255.63 23.499
-4989 0.029639 240.77 23.387
-4990 0.029238 225.95 23.271
-4991 0.028855 211.15 23.154
-4992 0.028492 196.38 23.037
-4993 0.028154 181.64 22.926
-4994 0.027844 166.93 22.822
-4995 0.027569 152.25 22.730
-4996 0.027331 137.61 22.651
-4997 0.027136 123.01 22.589
-4998 0.026988 108.44 22.546
-4999 0.026892  93.92 22.525
-5000 0.026851  79.43 22.525];
% ===

kyear0=-m(:,1); % kyears before present for data (kyear0>=0);
ecc0=m(:,2); % eccentricity
% add 180 degrees to omega (see lambda definition, Berger 1978 Appendix)
omega0=m(:,3)+180; % longitude of perihelion (precession angle)
omega0=unwrap(omega0*pi/180)*180/pi; % remove discontinuities (360 degree jumps)
epsilon0=m(:,4); % obliquity angle

% Interpolate to requested dates
ecc=spline(kyear0,ecc0,kyear); % eccs means array of ecc values
omega=spline(kyear0,omega0,kyear) * pi/180;
epsilon=spline(kyear0,epsilon0,kyear) * pi/180;
