Use the StMoMo (“Stochastic Mortality Modelling”) package by Villegas, Millossovich, Kaishev to fit mortality data. The R Code is taken from a presentation by the creator of this package at R Consortium: https://www.youtube.com/watch?v=prk-0G689GU

# Install the StMoMo package
install.packages("StMoMo")
Error in install.packages : Updating loaded packages
library(StMoMo)

# There are packages that link to Human Mortality Database
install.packages("demography")
Error in install.packages : Updating loaded packages
library(demography)

# Load mortality data with login details of Human Mortality Database 
download_data <- hmd.mx(country = "PRT", username = "f.hagelstein@student.maastrichtuniversity.nl", password = "Life_In$urance_2")
install.packages("demography")
WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:

https://cran.rstudio.com/bin/windows/Rtools/
Warning in install.packages :
  package ‘demography’ is in use and will not be installed
install.packages("StMoMo")
Error in install.packages : Updating loaded packages
PT_data_total <- download_data

# Plot the data to check if it loaded properly
plot(PT_data_total, series = "male") # male death rates in Portugal between 1940 - 2021

plot(PT_data_total, series = "female") # female death rates in Portugal between 1940 - 2021

plot(PT_data_total, series = "total") # total death rates in Portugal between 1940 - 2021

Model fitting


# Model fitting
PRTmale <- StMoMoData(PT_data_total, series = "female")
ages.fit <- 50:89 # age interval
years.fit <- 1940:2021 # time interval

# Fit Lee-Carter model
LC <- lc()
LCfit <- fit(LC, data = PRTmale, ages.fit = ages.fit, years.fit = years.fit)
StMoMo: Start fitting with gnm
Initialising
Running start-up iterations..
Running main iterations........
Done
StMoMo: Finish fitting with gnm
install.packages("StMoMo")
WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:

https://cran.rstudio.com/bin/windows/Rtools/
Warning in install.packages :
  package ‘StMoMo’ is in use and will not be installed
plot(LCfit)


# Fit CBD model from paper
CBD <- cbd(link = "log")
CBDfit <- fit(CBD, data = PRTmale, ages.fit = ages.fit, years.fit = years.fit)
StMoMo: Start fitting with gnm
Warning: non-integer x = 367.562096Warning: non-integer x = 365.571281Warning: non-integer x = 417.540403Warning: non-integer x = 375.416915Warning: non-integer x = 355.640446Warning: non-integer x = 356.797149Warning: non-integer x = 332.696696Warning: non-integer x = 303.581007Warning: non-integer x = 343.500365Warning: non-integer x = 363.563929Warning: non-integer x = 328.371257Warning: non-integer x = 306.378115Warning: non-integer x = 262.353462Warning: non-integer x = 256.289518Warning: non-integer x = 257.195134Warning: non-integer x = 319.294113Warning: non-integer x = 292.127611Warning: non-integer x = 261.078902Warning: non-integer x = 247.100126Warning: non-integer x = 251.073349Warning: non-integer x = 286.137209Warning: non-integer x = 245.061565Warning: non-integer x = 219.044606Warning: non-integer x = 252.182540Warning: non-integer x = 226.155121Warning: non-integer x = 205.064245Warning: non-integer x = 257.143112Warning: non-integer x = 212.094366Warning: non-integer x = 211.050357Warning: non-integer x = 201.147375Warning: non-integer x = 233.122982Warning: non-integer x = 225.093876Warning: non-integer x = 202.137191Warning: non-integer x = 248.985323Warning: non-integer x = 257.979644Warning: non-integer x = 240.997601Warning: non-integer x = 255.990902Warning: non-integer x = 243.998634Warning: non-integer x = 219.990012Warning: non-integer x = 218.994037Warning: non-integer x = 191.017736Warning: non-integer x = 228.994777Warning: non-integer x = 209.986475Warning: non-integer x = 232.989537Warning: non-integer x = 209.972681Warning: non-integer x = 233.993445Warning: non-integer x = 198.992995Warning: non-integer x = 197.983628Warning: non-integer x = 186.028056Warning: non-integer x = 174.982889Warning: non-integer x = 186.027144Warning: non-integer x = 186.020364Warning: non-integer x = 156.004956Warning: non-integer x = 198.018827Warning: non-integer x = 184.970421Warning: non-integer x = 168.016534Warning: non-integer x = 171.030790Warning: non-integer x = 169.974987Warning: non-integer x = 180.980300Warning: non-integer x = 171.971024Warning: non-integer x = 146.975282Warning: non-integer x = 164.007131Warning: non-integer x = 149.978088Warning: non-integer x = 173.966544Warning: non-integer x = 157.965715Warning: non-integer x = 161.028466Warning: non-integer x = 170.026022Warning: non-integer x = 144.998482Warning: non-integer x = 148.037254Warning: non-integer x = 174.039041Warning: non-integer x = 161.041418Warning: non-integer x = 154.007336Warning: non-integer x = 152.990918Warning: non-integer x = 176.008441Warning: non-integer x = 158.960126Warning: non-integer x = 126.001249Warning: non-integer x = 160.043283Warning: non-integer x = 141.987414Warning: non-integer x = 145.975935Warning: non-integer x = 142.027289Warning: non-integer x = 151.983668Warning: non-integer x = 142.973587Warning: non-integer x = 283.445820Warning: non-integer x = 293.473995Warning: non-integer x = 285.398069Warning: non-integer x = 274.291047Warning: non-integer x = 256.432702Warning: non-integer x = 267.585440Warning: non-integer x = 244.526886Warning: non-integer x = 237.464180Warning: non-integer x = 292.437586Warning: non-integer x = 270.412015Warning: non-integer x = 246.261483Warning: non-integer x = 275.330178Warning: non-integer x = 259.355224Warning: non-integer x = 232.228237Warning: non-integer x = 248.222240Warning: non-integer x = 278.216550Warning: non-integer x = 289.150192Warning: non-integer x = 252.077544Warning: non-integer x = 241.084423Warning: non-integer x = 206.049266Warning: non-integer x = 250.120241Warning: non-integer x = 271.094740Warning: non-integer x = 237.092808Warning: non-integer x = 255.156915Warning: non-integer x = 272.148305Warning: non-integer x = 207.088941Warning: non-integer x = 256.119080Warning: non-integer x = 216.108125Warning: non-integer x = 201.084567Warning: non-integer x = 191.122268Warning: non-integer x = 173.102507Warning: non-integer x = 243.097689Warning: non-integer x = 224.192424Warning: non-integer x = 235.023705Warning: non-integer x = 246.976053Warning: non-integer x = 242.998350Warning: non-integer x = 280.009638Warning: non-integer x = 256.018752Warning: non-integer x = 204.011092Warning: non-integer x = 216.001890Warning: non-integer x = 239.972161Warning: non-integer x = 182.018910Warning: non-integer x = 222.024865Warning: non-integer x = 248.970563Warning: non-integer x = 232.989871Warning: non-integer x = 216.000953Warning: non-integer x = 220.999957Warning: non-integer x = 224.979895Warning: non-integer x = 203.979852Warning: non-integer x = 191.979100Warning: non-integer x = 201.006925Warning: non-integer x = 200.980082Warning: non-integer x = 168.022553Warning: non-integer x = 181.023051Warning: non-integer x = 170.019709Warning: non-integer x = 187.023985Warning: non-integer x = 207.988630Warning: non-integer x = 189.977049Warning: non-integer x = 185.973314Warning: non-integer x = 186.019340Warning: non-integer x = 201.001966Warning: non-integer x = 183.989791Warning: non-integer x = 182.974733Warning: non-integer x = 175.005882Warning: non-integer x = 167.965962Warning: non-integer x = 178.030647Warning: non-integer x = 167.004290Warning: non-integer x = 170.998666Warning: non-integer x = 163.021548Warning: non-integer x = 204.008229Warning: non-integer x = 183.006994Warning: non-integer x = 165.984761Warning: non-integer x = 167.031889Warning: non-integer x = 153.046734Warning: non-integer x = 153.015240Warning: non-integer x = 156.005863Warning: non-integer x = 153.972801Warning: non-integer x = 173.009423Warning: non-integer x = 149.967614Warning: non-integer x = 121.986326Warning: non-integer x = 179.000082Warning: non-integer x = 133.006820Warning: non-integer x = 352.543020Warning: non-integer x = 421.681236Warning: non-integer x = 414.557365Warning: non-integer x = 403.452752Warning: non-integer x = 311.562739Warning: non-integer x = 355.764058Warning: non-integer x = 331.679252Warning: non-integer x = 315.582005Warning: non-integer x = 295.422976Warning: non-integer x = 326.519923Warning: non-integer x = 279.284406Warning: non-integer x = 332.406017Warning: non-integer x = 302.380980Warning: non-integer x = 312.362689Warning: non-integer x = 277.229663Warning: non-integer x = 325.302189Warning: non-integer x = 357.171303Warning: non-integer x = 305.107745Warning: non-integer x = 261.059354Warning: non-integer x = 274.088675Warning: non-integer x = 295.143727Warning: non-integer x = 285.098881Warning: non-integer x = 295.121213Warning: non-integer x = 296.196663Warning: non-integer x = 304.158485Warning: non-integer x = 265.106334Warning: non-integer x = 301.177392Warning: non-integer x = 260.133611Warning: non-integer x = 239.072446Warning: non-integer x = 261.159551Warning: non-integer x = 212.095426Warning: non-integer x = 205.075798Warning: non-integer x = 254.217673Warning: non-integer x = 255.025770Warning: non-integer x = 274.990675Warning: non-integer x = 278.979179Warning: non-integer x = 280.008609Warning: non-integer x = 258.995174Warning: non-integer x = 241.992367Warning: non-integer x = 267.018540Warning: non-integer x = 240.001628Warning: non-integer x = 285.008662Warning: non-integer x = 253.023079Warning: non-integer x = 257.000597Warning: non-integer x = 246.996407Warning: non-integer x = 203.975809Warning: non-integer x = 231.007408Warning: non-integer x = 228.999918Warning: non-integer x = 236.026310Warning: non-integer x = 187.977191Warning: non-integer x = 218.977219Warning: non-integer x = 222.022210Warning: non-integer x = 222.979673Warning: non-integer x = 197.007566Warning: non-integer x = 161.974877Warning: non-integer x = 209.007894Warning: non-integer x = 219.013406Warning: non-integer x = 190.981744Warning: non-integer x = 187.983559Warning: non-integer x = 166.984437Warning: non-integer x = 222.979196Warning: non-integer x = 223.032353Warning: non-integer x = 184.980678Warning: non-integer x = 210.967455Warning: non-integer x = 190.976931Warning: non-integer x = 204.006460Warning: non-integer x = 146.995719Warning: non-integer x = 180.040715Warning: non-integer x = 173.011505Warning: non-integer x = 185.047462Warning: non-integer x = 164.041064Warning: non-integer x = 186.962607Warning: non-integer x = 155.010944Warning: non-integer x = 146.045420Warning: non-integer x = 168.008525Warning: non-integer x = 195.991017Warning: non-integer x = 172.024351Warning: non-integer x = 191.996387Warning: non-integer x = 186.035216Warning: non-integer x = 168.011601Warning: non-integer x = 167.027953Warning: non-integer x = 334.515538Warning: non-integer x = 380.599836Warning: non-integer x = 344.470253Warning: non-integer x = 363.422687Warning: non-integer x = 319.585174Warning: non-integer x = 353.766799Warning: non-integer x = 354.743032Warning: non-integer x = 324.610240Warning: non-integer x = 337.482817Warning: non-integer x = 315.513605Warning: non-integer x = 300.323584Warning: non-integer x = 300.374329Warning: non-integer x = 283.356504Warning: non-integer x = 320.359437Warning: non-integer x = 306.226488Warning: non-integer x = 259.205728Warning: non-integer x = 348.154750Warning: non-integer x = 302.103527Warning: non-integer x = 270.099392Warning: non-integer x = 322.065017Warning: non-integer x = 288.152738Warning: non-integer x = 289.098800Warning: non-integer x = 283.099800Warning: non-integer x = 340.200356Warning: non-integer x = 293.201716Warning: non-integer x = 279.113296Warning: non-integer x = 324.177832Warning: non-integer x = 271.131503Warning: non-integer x = 247.073200Warning: non-integer x = 285.169272Warning: non-integer x = 253.134816Warning: non-integer x = 239.117307Warning: non-integer x = 226.194860Warning: non-integer x = 267.983745Warning: non-integer x = 285.989888Warning: non-integer x = 293.025915Warning: non-integer x = 300.978637Warning: non-integer x = 290.016474Warning: non-integer x = 258.992403Warning: non-integer x = 274.999063Warning: non-integer x = 275.026441Warning: non-integer x = 291.981365Warning: non-integer x = 251.987887Warning: non-integer x = 232.970858Warning: non-integer x = 271.007890Warning: non-integer x = 269.996853Warning: non-integer x = 257.030510Warning: non-integer x = 230.975095Warning: non-integer x = 231.971448Warning: non-integer x = 201.011217Warning: non-integer x = 239.979460Warning: non-integer x = 224.017693Warning: non-integer x = 220.003023Warning: non-integer x = 228.971906Warning: non-integer x = 235.008046Warning: non-integer x = 172.982923Warning: non-integer x = 212.019048Warning: non-integer x = 199.012426Warning: non-integer x = 208.985954Warning: non-integer x = 225.973888Warning: non-integer x = 187.980881Warning: non-integer x = 200.982192Warning: non-integer x = 218.010728Warning: non-integer x = 197.003348Warning: non-integer x = 202.971336Warning: non-integer x = 199.012531Warning: non-integer x = 189.007124Warning: non-integer x = 169.988884Warning: non-integer x = 163.001412Warning: non-integer x = 187.013150Warning: non-integer x = 181.070049Warning: non-integer x = 197.970927Warning: non-integer x = 178.005765Warning: non-integer x = 195.036418Warning: non-integer x = 188.024256Warning: non-integer x = 192.004046Warning: non-integer x = 188.032451Warning: non-integer x = 202.035501Warning: non-integer x = 161.034702Warning: non-integer x = 176.970449Warning: non-integer x = 192.038678Warning: non-integer x = 198.006462Warning: non-integer x = 332.509893Warning: non-integer x = 401.650579Warning: non-integer x = 418.546315Warning: non-integer x = 359.419632Warning: non-integer x = 331.566567Warning: non-integer x = 350.777956Warning: non-integer x = 371.751237Warning: non-integer x = 307.586673Warning: non-integer x = 344.499366Warning: non-integer x = 332.533845Warning: non-integer x = 307.341863Warning: non-integer x = 322.409789Warning: non-integer x = 302.380306Warning: non-integer x = 275.311211Warning: non-integer x = 321.278322Warning: non-integer x = 380.336946Warning: non-integer x = 336.183798Warning: non-integer x = 319.113034Warning: non-integer x = 280.084850Warning: non-integer x = 272.069868Warning: non-integer x = 311.160859Warning: non-integer x = 317.114027Warning: non-integer x = 315.109160Warning: non-integer x = 288.159352Warning: non-integer x = 344.190051Warning: non-integer x = 312.080874Warning: non-integer x = 326.170180Warning: non-integer x = 302.127079Warning: non-integer x = 293.092739Warning: non-integer x = 324.200526Warning: non-integer x = 242.138514Warning: non-integer x = 272.128204Warning: non-integer x = 239.220117Warning: non-integer x = 236.012476Warning: non-integer x = 277.984181Warning: non-integer x = 304.017353Warning: non-integer x = 322.016483Warning: non-integer x = 294.027252Warning: non-integer x = 279.016298Warning: non-integer x = 266.011132Warning: non-integer x = 302.995608Warning: non-integer x = 262.012672Warning: non-integer x = 280.016627Warning: non-integer x = 280.020388Warning: non-integer x = 286.005794Warning: non-integer x = 292.018175Warning: non-integer x = 272.002089Warning: non-integer x = 248.991683Warning: non-integer x = 270.985290Warning: non-integer x = 208.989528Warning: non-integer x = 235.994749Warning: non-integer x = 244.029578Warning: non-integer x = 229.984573Warning: non-integer x = 238.980002Warning: non-integer x = 193.022816Warning: non-integer x = 207.973079Warning: non-integer x = 188.972663Warning: non-integer x = 218.994575Warning: non-integer x = 190.022798Warning: non-integer x = 225.991962Warning: non-integer x = 239.996033Warning: non-integer x = 191.984321Warning: non-integer x = 233.996216Warning: non-integer x = 209.995465Warning: non-integer x = 196.980222Warning: non-integer x = 208.015209Warning: non-integer x = 172.026680Warning: non-integer x = 206.046271Warning: non-integer x = 197.063518Warning: non-integer x = 208.047902Warning: non-integer x = 213.075725Warning: non-integer x = 181.000438Warning: non-integer x = 189.001933Warning: non-integer x = 196.997830Warning: non-integer x = 177.985444Warning: non-integer x = 184.015264Warning: non-integer x = 178.022629Warning: non-integer x = 217.037986Warning: non-integer x = 173.006261Warning: non-integer x = 181.985718Warning: non-integer x = 205.011581Warning: non-integer x = 167.961259Warning: non-integer x = 413.640359Warning: non-integer x = 453.727348Warning: non-integer x = 433.567100Warning: non-integer x = 406.475429Warning: non-integer x = 401.720005Warning: non-integer x = 435.964364Warning: non-integer x = 436.881028Warning: non-integer x = 393.741492Warning: non-integer x = 358.527569Warning: non-integer x = 338.552760Warning: non-integer x = 327.342592Warning: non-integer x = 358.463422Warning: non-integer x = 319.405494Warning: non-integer x = 332.363775Warning: non-integer x = 322.260913Warning: non-integer x = 341.280893Warning: non-integer x = 396.176094Warning: non-integer x = 339.150170Warning: non-integer x = 322.110754Warning: non-integer x = 320.056989Warning: non-integer x = 279.136741Warning: non-integer x = 293.086409Warning: non-integer x = 313.133462Warning: non-integer x = 317.203711Warning: non-integer x = 323.193928Warning: non-integer x = 337.134904Warning: non-integer x = 360.172698Warning: non-integer x = 344.165897Warning: non-integer x = 337.140626Warning: non-integer x = 318.202535Warning: non-integer x = 281.140596Warning: non-integer x = 312.131765Warning: non-integer x = 274.235870Warning: non-integer x = 276.992978Warning: non-integer x = 256.019017Warning: non-integer x = 315.024178Warning: non-integer x = 322.017152Warning: non-integer x = 319.999026Warning: non-integer x = 301.003057Warning: non-integer x = 294.974402Warning: non-integer x = 288.001268Warning: non-integer x = 315.025650Warning: non-integer x = 283.996380Warning: non-integer x = 291.000085Warning: non-integer x = 285.990265Warning: non-integer x = 289.005870Warning: non-integer x = 306.003932Warning: non-integer x = 305.029059Warning: non-integer x = 256.015284Warning: non-integer x = 247.016587Warning: non-integer x = 269.006422Warning: non-integer x = 277.977954Warning: non-integer x = 258.013868Warning: non-integer x = 279.025297Warning: non-integer x = 232.991802Warning: non-integer x = 227.991235Warning: non-integer x = 211.976622Warning: non-integer x = 213.022157Warning: non-integer x = 206.015079Warning: non-integer x = 222.995474Warning: non-integer x = 253.976414Warning: non-integer x = 223.980855Warning: non-integer x = 224.997132Warning: non-integer x = 244.973668Warning: non-integer x = 214.024608Warning: non-integer x = 210.026470Warning: non-integer x = 193.978226Warning: non-integer x = 217.048493Warning: non-integer x = 200.043575Warning: non-integer x = 210.032102Warning: non-integer x = 198.041245Warning: non-integer x = 222.025110Warning: non-integer x = 192.969304Warning: non-integer x = 206.986399Warning: non-integer x = 217.978340Warning: non-integer x = 174.987124Warning: non-integer x = 231.036998Warning: non-integer x = 218.981323Warning: non-integer x = 206.993106Warning: non-integer x = 235.046049Warning: non-integer x = 226.036718Warning: non-integer x = 208.033722Warning: non-integer x = 397.602131Warning: non-integer x = 451.702875Warning: non-integer x = 418.568162Warning: non-integer x = 387.431004Warning: non-integer x = 413.706274Warning: non-integer x = 396.884771Warning: non-integer x = 426.893323Warning: non-integer x = 378.694092Warning: non-integer x = 367.542733Warning: non-integer x = 415.642758Warning: non-integer x = 350.382626Warning: non-integer x = 377.489338Warning: non-integer x = 350.460276Warning: non-integer x = 317.348333Warning: non-integer x = 330.274959Warning: non-integer x = 352.282641Warning: non-integer x = 447.204510Warning: non-integer x = 439.169712Warning: non-integer x = 347.129510Warning: non-integer x = 352.105064Warning: non-integer x = 343.169174Warning: non-integer x = 334.106835Warning: non-integer x = 344.097579Warning: non-integer x = 378.269540Warning: non-integer x = 333.198490Warning: non-integer x = 346.091849Warning: non-integer x = 383.184331Warning: non-integer x = 406.161931Warning: non-integer x = 320.094109Warning: non-integer x = 380.216627Warning: non-integer x = 295.149886Warning: non-integer x = 330.156861Warning: non-integer x = 300.244041Warning: non-integer x = 333.987683Warning: non-integer x = 267.022717Warning: non-integer x = 300.011119Warning: non-integer x = 331.004683Warning: non-integer x = 382.024089Warning: non-integer x = 309.979249Warning: non-integer x = 342.012396Warning: non-integer x = 296.023885Warning: non-integer x = 347.994629Warning: non-integer x = 315.019200Warning: non-integer x = 341.977828Warning: non-integer x = 331.998244Warning: non-integer x = 313.019573Warning: non-integer x = 338.979085Warning: non-integer x = 291.974365Warning: non-integer x = 316.016883Warning: non-integer x = 297.995630Warning: non-integer x = 316.022640Warning: non-integer x = 309.999175Warning: non-integer x = 282.985666Warning: non-integer x = 287.989020Warning: non-integer x = 260.977230Warning: non-integer x = 249.016326Warning: non-integer x = 224.017144Warning: non-integer x = 253.993629Warning: non-integer x = 213.987726Warning: non-integer x = 232.984150Warning: non-integer x = 215.973483Warning: non-integer x = 209.981271Warning: non-integer x = 230.024060Warning: non-integer x = 221.977203Warning: non-integer x = 262.982169Warning: non-integer x = 245.011446Warning: non-integer x = 228.984331Warning: non-integer x = 204.041594Warning: non-integer x = 218.055403Warning: non-integer x = 219.009520Warning: non-integer x = 193.044748Warning: non-integer x = 227.012283Warning: non-integer x = 231.965808Warning: non-integer x = 201.047442Warning: non-integer x = 235.015765Warning: non-integer x = 226.001328Warning: non-integer x = 186.000711Warning: non-integer x = 202.995276Warning: non-integer x = 212.024166Warning: non-integer x = 244.016469Warning: non-integer x = 221.971430Warning: non-integer x = 243.015323Warning: non-integer x = 405.613350Warning: non-integer x = 415.653740Warning: non-integer x = 419.556557Warning: non-integer x = 345.393776Warning: non-integer x = 379.673500Warning: non-integer x = 401.883006Warning: non-integer x = 406.843138Warning: non-integer x = 373.691102Warning: non-integer x = 363.551480Warning: non-integer x = 356.566247Warning: non-integer x = 397.419590Warning: non-integer x = 334.434510Warning: non-integer x = 333.456599Warning: non-integer x = 342.378648Warning: non-integer x = 338.279352Warning: non-integer x = 363.306674Warning: non-integer x = 397.205710Warning: non-integer x = 413.138275Warning: non-integer x = 385.089349Warning: non-integer x = 319.068768Warning: non-integer x = 415.210011Warning: non-integer x = 358.114482Warning: non-integer x = 395.146679Warning: non-integer x = 365.225035Warning: non-integer x = 367.223308Warning: non-integer x = 376.103674Warning: non-integer x = 347.191975Warning: non-integer x = 385.182775Warning: non-integer x = 397.139930Warning: non-integer x = 377.232800Warning: non-integer x = 331.191757Warning: non-integer x = 355.146409Warning: non-integer x = 337.257102Warning: non-integer x = 327.009646Warning: non-integer x = 309.010172Warning: non-integer x = 297.981451Warning: non-integer x = 307.996843Warning: non-integer x = 333.984414Warning: non-integer x = 358.022566Warning: non-integer x = 324.982996Warning: non-integer x = 334.020892Warning: non-integer x = 343.020954Warning: non-integer x = 334.013282Warning: non-integer x = 328.000079Warning: non-integer x = 355.017161Warning: non-integer x = 334.979950Warning: non-integer x = 352.975325Warning: non-integer x = 336.988623Warning: non-integer x = 294.020947Warning: non-integer x = 296.002284Warning: non-integer x = 313.017805Warning: non-integer x = 324.008875Warning: non-integer x = 308.984739Warning: non-integer x = 304.003348Warning: non-integer x = 236.985982Warning: non-integer x = 292.002898Warning: non-integer x = 276.024916Warning: non-integer x = 262.000139Warning: non-integer x = 249.020327Warning: non-integer x = 247.002757Warning: non-integer x = 228.010974Warning: non-integer x = 247.005896Warning: non-integer x = 236.995296Warning: non-integer x = 266.023832Warning: non-integer x = 211.020789Warning: non-integer x = 250.978075Warning: non-integer x = 263.016861Warning: non-integer x = 238.002288Warning: non-integer x = 244.035557Warning: non-integer x = 225.017979Warning: non-integer x = 243.067306Warning: non-integer x = 242.014434Warning: non-integer x = 230.034816Warning: non-integer x = 228.031326Warning: non-integer x = 203.005944Warning: non-integer x = 201.002043Warning: non-integer x = 258.056715Warning: non-integer x = 207.002756Warning: non-integer x = 238.973037Warning: non-integer x = 256.023415Warning: non-integer x = 247.021414Warning: non-integer x = 223.974631Warning: non-integer x = 462.685584Warning: non-integer x = 489.764399Warning: non-integer x = 470.629901Warning: non-integer x = 475.534924Warning: non-integer x = 458.795124Warning: non-integer x = 432.957683Warning: non-integer x = 452.943239Warning: non-integer x = 417.803398Warning: non-integer x = 422.652252Warning: non-integer x = 449.722946Warning: non-integer x = 436.459227Warning: non-integer x = 435.533335Warning: non-integer x = 363.483587Warning: non-integer x = 343.383026Warning: non-integer x = 407.322991Warning: non-integer x = 359.292184Warning: non-integer x = 471.239250Warning: non-integer x = 391.140991Warning: non-integer x = 389.129178Warning: non-integer x = 390.108965Warning: non-integer x = 349.193826Warning: non-integer x = 421.180515Warning: non-integer x = 373.144368Warning: non-integer x = 396.250261Warning: non-integer x = 439.271701Warning: non-integer x = 422.150839Warning: non-integer x = 422.206087Warning: non-integer x = 420.187561Warning: non-integer x = 451.185537Warning: non-integer x = 446.282727Warning: non-integer x = 382.219229Warning: non-integer x = 440.207765Warning: non-integer x = 391.305546Warning: non-integer x = 384.984994Warning: non-integer x = 341.012859Warning: non-integer x = 354.984973Warning: non-integer x = 350.999327Warning: non-integer x = 311.982745Warning: non-integer x = 382.022234Warning: non-integer x = 389.985061Warning: non-integer x = 388.016574Warning: non-integer x = 408.006096Warning: non-integer x = 412.008261Warning: non-integer x = 406.003246Warning: non-integer x = 351.975576Warning: non-integer x = 382.971876Warning: non-integer x = 365.987144Warning: non-integer x = 343.018198Warning: non-integer x = 343.973884Warning: non-integer x = 362.006956Warning: non-integer x = 379.018717Warning: non-integer x = 356.015629Warning: non-integer x = 311.007163Warning: non-integer x = 310.015524Warning: non-integer x = 312.989070Warning: non-integer x = 302.988416Warning: non-integer x = 275.979493Warning: non-integer x = 288.984257Warning: non-integer x = 264.978977Warning: non-integer x = 262.006040Warning: non-integer x = 245.027250Warning: non-integer x = 269.006932Warning: non-integer x = 280.006839Warning: non-integer x = 284.028583Warning: non-integer x = 256.029412Warning: non-integer x = 253.004507Warning: non-integer x = 241.030315Warning: non-integer x = 281.008347Warning: non-integer x = 292.068520Warning: non-integer x = 257.032835Warning: non-integer x = 240.056139Warning: non-integer x = 239.048096Warning: non-integer x = 230.033354Warning: non-integer x = 247.055710Warning: non-integer x = 254.966532Warning: non-integer x = 212.007243Warning: non-integer x = 246.996453Warning: non-integer x = 237.985986Warning: non-integer x = 245.034400Warning: non-integer x = 236.030728Warning: non-integer x = 236.966514Warning: non-integer x = 249.980352Warning: non-integer x = 406.636507Warning: non-integer x = 443.713238Warning: non-integer x = 430.584755Warning: non-integer x = 395.437185Warning: non-integer x = 398.725528Warning: non-integer x = 381.831805Warning: non-integer x = 390.812659Warning: non-integer x = 383.721565Warning: non-integer x = 389.594895Warning: non-integer x = 430.678267Warning: non-integer x = 376.400832Warning: non-integer x = 413.512693Warning: non-integer x = 377.489747Warning: non-integer x = 370.407523Warning: non-integer x = 397.329390Warning: non-integer x = 383.303983Warning: non-integer x = 395.193731Warning: non-integer x = 376.129163Warning: non-integer x = 387.118680Warning: non-integer x = 393.109503Warning: non-integer x = 375.202856Warning: non-integer x = 416.165284Warning: non-integer x = 436.163130Warning: non-integer x = 431.262702Warning: non-integer x = 396.223825Warning: non-integer x = 419.111784Warning: non-integer x = 487.239524Warning: non-integer x = 405.161411Warning: non-integer x = 410.128688Warning: non-integer x = 457.295629Warning: non-integer x = 426.223310Warning: non-integer x = 418.191502Warning: non-integer x = 403.324440Warning: non-integer x = 397.984674Warning: non-integer x = 440.989240Warning: non-integer x = 425.983255Warning: non-integer x = 359.999494Warning: non-integer x = 364.004801Warning: non-integer x = 327.017138Warning: non-integer x = 372.016729Warning: non-integer x = 433.010367Warning: non-integer x = 414.987070Warning: non-integer x = 375.974375Warning: non-integer x = 390.990960Warning: non-integer x = 404.977186Warning: non-integer x = 393.998293Warning: non-integer x = 436.982584Warning: non-integer x = 344.021193Warning: non-integer x = 373.973320Warning: non-integer x = 353.986725Warning: non-integer x = 338.970881Warning: non-integer x = 368.990914Warning: non-integer x = 371.021501Warning: non-integer x = 393.976155Warning: non-integer x = 323.996348Warning: non-integer x = 343.021327Warning: non-integer x = 308.027740Warning: non-integer x = 317.003332Warning: non-integer x = 339.993393Warning: non-integer x = 299.025409Warning: non-integer x = 275.997380Warning: non-integer x = 278.996650Warning: non-integer x = 295.983598Warning: non-integer x = 298.010921Warning: non-integer x = 311.001729Warning: non-integer x = 279.978742Warning: non-integer x = 238.025274Warning: non-integer x = 255.999217Warning: non-integer x = 281.055802Warning: non-integer x = 234.033419Warning: non-integer x = 246.084021Warning: non-integer x = 281.004856Warning: non-integer x = 265.991563Warning: non-integer x = 224.044539Warning: non-integer x = 236.980815Warning: non-integer x = 234.031051Warning: non-integer x = 250.995954Warning: non-integer x = 258.018367Warning: non-integer x = 264.025463Warning: non-integer x = 275.050166Warning: non-integer x = 278.007265Warning: non-integer x = 320.007974Warning: non-integer x = 772.194368Warning: non-integer x = 778.249261Warning: non-integer x = 811.081434Warning: non-integer x = 713.817488Warning: non-integer x = 664.160346Warning: non-integer x = 611.324500Warning: non-integer x = 666.382176Warning: non-integer x = 610.151698Warning: non-integer x = 524.775452Warning: non-integer x = 572.912162Warning: non-integer x = 548.590423Warning: non-integer x = 550.697871Warning: non-integer x = 554.743543Warning: non-integer x = 525.566622Warning: non-integer x = 514.401359Warning: non-integer x = 490.401770Warning: non-integer x = 517.242463Warning: non-integer x = 467.163544Warning: non-integer x = 448.122892Warning: non-integer x = 424.115449Warning: non-integer x = 477.270757Warning: non-integer x = 493.172279Warning: non-integer x = 454.173173Warning: non-integer x = 455.296550Warning: non-integer x = 531.305021Warning: non-integer x = 461.167241Warning: non-integer x = 493.285373Warning: non-integer x = 489.197812Warning: non-integer x = 566.196616Warning: non-integer x = 563.331181Warning: non-integer x = 517.280887Warning: non-integer x = 518.204686Warning: non-integer x = 455.374634Warning: non-integer x = 470.004112Warning: non-integer x = 462.990967Warning: non-integer x = 486.010908Warning: non-integer x = 461.984157Warning: non-integer x = 397.001971Warning: non-integer x = 386.014344Warning: non-integer x = 337.012613Warning: non-integer x = 400.984246Warning: non-integer x = 450.978815Warning: non-integer x = 432.995890Warning: non-integer x = 454.981010Warning: non-integer x = 436.004022Warning: non-integer x = 436.980064Warning: non-integer x = 428.993229Warning: non-integer x = 453.024753Warning: non-integer x = 398.993611Warning: non-integer x = 355.974561Warning: non-integer x = 409.988214Warning: non-integer x = 399.005338Warning: non-integer x = 413.996854Warning: non-integer x = 395.014186Warning: non-integer x = 362.984948Warning: non-integer x = 370.990841Warning: non-integer x = 362.026292Warning: non-integer x = 339.002172Warning: non-integer x = 379.024699Warning: non-integer x = 351.027208Warning: non-integer x = 321.994803Warning: non-integer x = 292.001845Warning: non-integer x = 296.974128Warning: non-integer x = 301.020113Warning: non-integer x = 285.021289Warning: non-integer x = 285.987296Warning: non-integer x = 343.012413Warning: non-integer x = 270.015619Warning: non-integer x = 270.059242Warning: non-integer x = 312.030468Warning: non-integer x = 269.058109Warning: non-integer x = 287.036458Warning: non-integer x = 269.020870Warning: non-integer x = 270.015202Warning: non-integer x = 270.981326Warning: non-integer x = 295.025210Warning: non-integer x = 287.987084Warning: non-integer x = 280.014171Warning: non-integer x = 273.987716Warning: non-integer x = 303.998534Warning: non-integer x = 266.998979Warning: non-integer x = 312.035177Warning: non-integer x = 432.648604Warning: non-integer x = 417.646064Warning: non-integer x = 452.611864Warning: non-integer x = 373.432329Warning: non-integer x = 365.639286Warning: non-integer x = 389.850688Warning: non-integer x = 406.839544Warning: non-integer x = 367.700296Warning: non-integer x = 414.607156Warning: non-integer x = 472.748444Warning: non-integer x = 459.489891Warning: non-integer x = 456.566865Warning: non-integer x = 385.528300Warning: non-integer x = 390.422146Warning: non-integer x = 375.305894Warning: non-integer x = 405.342610Warning: non-integer x = 498.240140Warning: non-integer x = 395.142583Warning: non-integer x = 373.107199Warning: non-integer x = 399.118091Warning: non-integer x = 397.203264Warning: non-integer x = 498.184717Warning: non-integer x = 480.167519Warning: non-integer x = 493.334676Warning: non-integer x = 504.314337Warning: non-integer x = 470.163745Warning: non-integer x = 522.273643Warning: non-integer x = 488.215305Warning: non-integer x = 487.178489Warning: non-integer x = 482.291068Warning: non-integer x = 510.287043Warning: non-integer x = 522.203906Warning: non-integer x = 528.434714Warning: non-integer x = 509.017032Warning: non-integer x = 528.015388Warning: non-integer x = 483.006442Warning: non-integer x = 516.011749Warning: non-integer x = 453.008685Warning: non-integer x = 418.984630Warning: non-integer x = 358.007271Warning: non-integer x = 385.992688Warning: non-integer x = 430.017904Warning: non-integer x = 446.980065Warning: non-integer x = 423.002622Warning: non-integer x = 447.985872Warning: non-integer x = 465.981476Warning: non-integer x = 440.017655Warning: non-integer x = 446.025577Warning: non-integer x = 458.978107Warning: non-integer x = 389.028781Warning: non-integer x = 398.996674Warning: non-integer x = 459.977845Warning: non-integer x = 392.021330Warning: non-integer x = 414.998634Warning: non-integer x = 429.000401Warning: non-integer x = 395.983032Warning: non-integer x = 406.997019Warning: non-integer x = 413.976790Warning: non-integer x = 350.980552Warning: non-integer x = 395.007927Warning: non-integer x = 343.023028Warning: non-integer x = 341.991602Warning: non-integer x = 315.977745Warning: non-integer x = 300.986668Warning: non-integer x = 323.978325Warning: non-integer x = 302.986188Warning: non-integer x = 358.003034Warning: non-integer x = 277.995558Warning: non-integer x = 290.036360Warning: non-integer x = 309.033780Warning: non-integer x = 311.085875Warning: non-integer x = 285.009486Warning: non-integer x = 339.017455Warning: non-integer x = 316.019940Warning: non-integer x = 265.021816Warning: non-integer x = 310.048072Warning: non-integer x = 275.040661Warning: non-integer x = 302.021087Warning: non-integer x = 312.020699Warning: non-integer x = 302.010672Warning: non-integer x = 304.963766Warning: non-integer x = 336.012341Warning: non-integer x = 563.883222Warning: non-integer x = 689.094539Warning: non-integer x = 627.824673Warning: non-integer x = 548.603827Warning: non-integer x = 559.986292Warning: non-integer x = 541.172186Warning: non-integer x = 568.159395Warning: non-integer x = 578.107133Warning: non-integer x = 532.795006Warning: non-integer x = 610.985690Warning: non-integer x = 611.661810Warning: non-integer x = 616.782132Warning: non-integer x = 523.699174Warning: non-integer x = 544.575603Warning: non-integer x = 527.416715Warning: non-integer x = 537.464475Warning: non-integer x = 533.275779Warning: non-integer x = 537.225512Warning: non-integer x = 477.153943Warning: non-integer x = 482.107309Warning: non-integer x = 460.235271Warning: non-integer x = 494.179736Warning: non-integer x = 508.183551Warning: non-integer x = 549.328365Warning: non-integer x = 533.319271Warning: non-integer x = 507.160285Warning: non-integer x = 585.332829Warning: non-integer x = 589.263130Warning: non-integer x = 554.217359Warning: non-integer x = 583.383277Warning: non-integer x = 514.284063Warning: non-integer x = 575.235308Warning: non-integer x = 546.462373Warning: non-integer x = 580.024819Warning: non-integer x = 579.007475Warning: non-integer x = 492.018590Warning: non-integer x = 558.994307Warning: non-integer x = 545.996060Warning: non-integer x = 540.021970Warning: non-integer x = 475.012440Warning: non-integer x = 455.993701Warning: non-integer x = 405.018714Warning: non-integer x = 454.004479Warning: non-integer x = 461.988616Warning: non-integer x = 480.984930Warning: non-integer x = 528.989916Warning: non-integer x = 506.021588Warning: non-integer x = 463.007351Warning: non-integer x = 434.975900Warning: non-integer x = 493.017195Warning: non-integer x = 429.986025Warning: non-integer x = 488.008686Warning: non-integer x = 441.024448Warning: non-integer x = 484.004995Warning: non-integer x = 389.988614Warning: non-integer x = 430.017665Warning: non-integer x = 416.016815Warning: non-integer x = 370.028704Warning: non-integer x = 429.991802Warning: non-integer x = 427.980714Warning: non-integer x = 384.971106Warning: non-integer x = 405.980113Warning: non-integer x = 377.016558Warning: non-integer x = 370.981196Warning: non-integer x = 302.018885Warning: non-integer x = 346.004592Warning: non-integer x = 305.032717Warning: non-integer x = 310.019476Warning: non-integer x = 315.064771Warning: non-integer x = 323.065220Warning: non-integer x = 318.080346Warning: non-integer x = 326.006786Warning: non-integer x = 311.010570Warning: non-integer x = 319.005645Warning: non-integer x = 286.971076Warning: non-integer x = 340.035165Warning: non-integer x = 305.044016Warning: non-integer x = 291.017906Warning: non-integer x = 311.031655Warning: non-integer x = 314.025961Warning: non-integer x = 306.980310Warning: non-integer x = 352.994200Warning: non-integer x = 634.969783Warning: non-integer x = 650.034428Warning: non-integer x = 663.879145Warning: non-integer x = 624.700243Warning: non-integer x = 590.053989Warning: non-integer x = 586.285992Warning: non-integer x = 604.231540Warning: non-integer x = 555.048514Warning: non-integer x = 592.886797Warning: non-integer x = 623.000544Warning: non-integer x = 585.614931Warning: non-integer x = 591.743744Warning: non-integer x = 530.708630Warning: non-integer x = 573.632173Warning: non-integer x = 531.422247Warning: non-integer x = 523.445863Warning: non-integer x = 657.325498Warning: non-integer x = 497.185276Warning: non-integer x = 533.175923Warning: non-integer x = 469.127772Warning: non-integer x = 536.283633Warning: non-integer x = 500.185082Warning: non-integer x = 539.182512Warning: non-integer x = 528.354918Warning: non-integer x = 582.330308Warning: non-integer x = 578.185278Warning: non-integer x = 626.348730Warning: non-integer x = 637.295814Warning: non-integer x = 570.190819Warning: non-integer x = 671.417677Warning: non-integer x = 611.344961Warning: non-integer x = 625.239533Warning: non-integer x = 602.501265Warning: non-integer x = 622.012492Warning: non-integer x = 663.993608Warning: non-integer x = 637.019715Warning: non-integer x = 636.011738Warning: non-integer x = 556.022036Warning: non-integer x = 546.017062Warning: non-integer x = 467.995427Warning: non-integer x = 512.001270Warning: non-integer x = 487.011411Warning: non-integer x = 427.020763Warning: non-integer x = 524.991452Warning: non-integer x = 524.994576Warning: non-integer x = 535.982061Warning: non-integer x = 536.973991Warning: non-integer x = 522.994855Warning: non-integer x = 554.976726Warning: non-integer x = 491.976160Warning: non-integer x = 518.020453Warning: non-integer x = 528.017601Warning: non-integer x = 497.006394Warning: non-integer x = 483.004356Warning: non-integer x = 465.005338Warning: non-integer x = 479.019223Warning: non-integer x = 459.983729Warning: non-integer x = 468.024717Warning: non-integer x = 473.990489Warning: non-integer x = 424.973283Warning: non-integer x = 411.016521Warning: non-integer x = 390.017998Warning: non-integer x = 388.026497Warning: non-integer x = 392.004058Warning: non-integer x = 331.003201Warning: non-integer x = 321.978409Warning: non-integer x = 363.032424Warning: non-integer x = 329.000094Warning: non-integer x = 319.069329Warning: non-integer x = 384.060256Warning: non-integer x = 297.058097Warning: non-integer x = 356.049921Warning: non-integer x = 370.021730Warning: non-integer x = 332.058970Warning: non-integer x = 298.008358Warning: non-integer x = 330.035064Warning: non-integer x = 362.010574Warning: non-integer x = 347.011793Warning: non-integer x = 337.023885Warning: non-integer x = 320.994921Warning: non-integer x = 380.026495Warning: non-integer x = 400.972238Warning: non-integer x = 636.965705Warning: non-integer x = 675.081179Warning: non-integer x = 628.837532Warning: non-integer x = 576.643348Warning: non-integer x = 626.089065Warning: non-integer x = 604.308580Warning: non-integer x = 665.378123Warning: non-integer x = 654.230177Warning: non-integer x = 627.931993Warning: non-integer x = 644.010193Warning: non-integer x = 567.606948Warning: non-integer x = 650.820146Warning: non-integer x = 585.765095Warning: non-integer x = 595.649021Warning: non-integer x = 620.513365Warning: non-integer x = 612.510644Warning: non-integer x = 662.325297Warning: non-integer x = 654.240161Warning: non-integer x = 558.160776Warning: non-integer x = 554.143108Warning: non-integer x = 561.297571Warning: non-integer x = 574.197507Warning: non-integer x = 590.221080Warning: non-integer x = 575.372773Warning: non-integer x = 614.371407Warning: non-integer x = 616.219864Warning: non-integer x = 668.358898Warning: non-integer x = 633.279717Warning: non-integer x = 648.222089Warning: non-integer x = 674.409404Warning: non-integer x = 615.339177Warning: non-integer x = 711.294418Warning: non-integer x = 644.549793Warning: non-integer x = 666.986562Warning: non-integer x = 714.982460Warning: non-integer x = 674.979087Warning: non-integer x = 643.996070Warning: non-integer x = 661.988447Warning: non-integer x = 642.982607Warning: non-integer x = 589.014774Warning: non-integer x = 523.994903Warning: non-integer x = 528.012918Warning: non-integer x = 484.015752Warning: non-integer x = 499.016847Warning: non-integer x = 557.004148Warning: non-integer x = 556.015223Warning: non-integer x = 574.017700Warning: non-integer x = 571.013604Warning: non-integer x = 576.020179Warning: non-integer x = 556.982961Warning: non-integer x = 593.986235Warning: non-integer x = 601.972428Warning: non-integer x = 534.972455Warning: non-integer x = 567.009282Warning: non-integer x = 528.993708Warning: non-integer x = 539.009663Warning: non-integer x = 537.997697Warning: non-integer x = 497.974234Warning: non-integer x = 457.986064Warning: non-integer x = 470.977718Warning: non-integer x = 465.002636Warning: non-integer x = 467.992853Warning: non-integer x = 462.986105Warning: non-integer x = 411.972300Warning: non-integer x = 396.028181Warning: non-integer x = 399.997921Warning: non-integer x = 326.038878Warning: non-integer x = 380.020535Warning: non-integer x = 382.079327Warning: non-integer x = 375.046034Warning: non-integer x = 372.078441Warning: non-integer x = 378.011124Warning: non-integer x = 338.010894Warning: non-integer x = 405.008928Warning: non-integer x = 361.009437Warning: non-integer x = 342.986494Warning: non-integer x = 371.011417Warning: non-integer x = 374.007756Warning: non-integer x = 344.979791Warning: non-integer x = 357.023248Warning: non-integer x = 375.004414Warning: non-integer x = 421.022147Warning: non-integer x = 812.233241Warning: non-integer x = 888.416381Warning: non-integer x = 891.183894Warning: non-integer x = 800.901703Warning: non-integer x = 762.349956Warning: non-integer x = 713.569522Warning: non-integer x = 843.734220Warning: non-integer x = 762.453503Warning: non-integer x = 711.063201Warning: non-integer x = 769.234758Warning: non-integer x = 703.736401Warning: non-integer x = 710.900894Warning: non-integer x = 702.917171Warning: non-integer x = 637.691968Warning: non-integer x = 665.545041Warning: non-integer x = 684.585659Warning: non-integer x = 713.356934Warning: non-integer x = 654.251362Warning: non-integer x = 597.191519Warning: non-integer x = 586.138679Warning: non-integer x = 579.314703Warning: non-integer x = 608.215574Warning: non-integer x = 597.207340Warning: non-integer x = 613.377309Warning: non-integer x = 620.378136Warning: non-integer x = 698.206227Warning: non-integer x = 716.383244Warning: non-integer x = 666.310288Warning: non-integer x = 681.265285Warning: non-integer x = 819.506391Warning: non-integer x = 662.345579Warning: non-integer x = 788.306062Warning: non-integer x = 726.608756Warning: non-integer x = 708.008590Warning: non-integer x = 712.984507Warning: non-integer x = 715.002897Warning: non-integer x = 727.023867Warning: non-integer x = 656.001797Warning: non-integer x = 725.982693Warning: non-integer x = 590.015829Warning: non-integer x = 629.004872Warning: non-integer x = 628.995234Warning: non-integer x = 553.983440Warning: non-integer x = 528.993009Warning: non-integer x = 495.997628Warning: non-integer x = 622.983523Warning: non-integer x = 582.997782Warning: non-integer x = 571.021508Warning: non-integer x = 604.006053Warning: non-integer x = 583.006875Warning: non-integer x = 657.979427Warning: non-integer x = 613.004851Warning: non-integer x = 636.991538Warning: non-integer x = 617.985412Warning: non-integer x = 576.009347Warning: non-integer x = 568.010166Warning: non-integer x = 601.019433Warning: non-integer x = 561.028406Warning: non-integer x = 541.025625Warning: non-integer x = 561.012203Warning: non-integer x = 489.009646Warning: non-integer x = 500.025160Warning: non-integer x = 441.975810Warning: non-integer x = 497.022992Warning: non-integer x = 447.976109Warning: non-integer x = 431.993975Warning: non-integer x = 409.020996Warning: non-integer x = 438.042375Warning: non-integer x = 372.086929Warning: non-integer x = 438.071676Warning: non-integer x = 373.127804Warning: non-integer x = 412.999410Warning: non-integer x = 367.004068Warning: non-integer x = 394.023698Warning: non-integer x = 402.018486Warning: non-integer x = 391.033760Warning: non-integer x = 370.995210Warning: non-integer x = 400.048307Warning: non-integer x = 376.023296Warning: non-integer x = 422.996242Warning: non-integer x = 425.010536Warning: non-integer x = 461.032375Warning: non-integer x = 716.096794Warning: non-integer x = 807.279322Warning: non-integer x = 797.071622Warning: non-integer x = 718.811384Warning: non-integer x = 689.209521Warning: non-integer x = 699.538338Warning: non-integer x = 737.497426Warning: non-integer x = 745.395256Warning: non-integer x = 660.992930Warning: non-integer x = 728.170977Warning: non-integer x = 655.707044Warning: non-integer x = 732.903121Warning: non-integer x = 646.857595Warning: non-integer x = 659.716485Warning: non-integer x = 728.576745Warning: non-integer x = 727.629783Warning: non-integer x = 786.390068Warning: non-integer x = 790.302725Warning: non-integer x = 658.218243Warning: non-integer x = 635.147331Warning: non-integer x = 632.355239Warning: non-integer x = 656.225010Warning: non-integer x = 672.240755Warning: non-integer x = 631.399043Warning: non-integer x = 676.410055Warning: non-integer x = 679.209000Warning: non-integer x = 767.434890Warning: non-integer x = 760.332113Warning: non-integer x = 716.257526Warning: non-integer x = 863.541711Warning: non-integer x = 766.425265Warning: non-integer x = 780.323833Warning: non-integer x = 742.603816Warning: non-integer x = 788.983255Warning: non-integer x = 767.994256Warning: non-integer x = 711.017748Warning: non-integer x = 835.992475Warning: non-integer x = 785.010455Warning: non-integer x = 770.979544Warning: non-integer x = 733.011892Warning: non-integer x = 706.000374Warning: non-integer x = 660.980583Warning: non-integer x = 635.014097Warning: non-integer x = 637.992311Warning: non-integer x = 599.004584Warning: non-integer x = 552.017472Warning: non-integer x = 627.976554Warning: non-integer x = 644.013735Warning: non-integer x = 714.006374Warning: non-integer x = 606.009059Warning: non-integer x = 705.005372Warning: non-integer x = 692.003810Warning: non-integer x = 640.990650Warning: non-integer x = 623.026832Warning: non-integer x = 595.020835Warning: non-integer x = 611.994482Warning: non-integer x = 636.997454Warning: non-integer x = 607.016266Warning: non-integer x = 587.983114Warning: non-integer x = 608.986237Warning: non-integer x = 508.988698Warning: non-integer x = 530.983555Warning: non-integer x = 550.025265Warning: non-integer x = 518.981993Warning: non-integer x = 496.018914Warning: non-integer x = 561.994476Warning: non-integer x = 436.011703Warning: non-integer x = 403.022985Warning: non-integer x = 396.073345Warning: non-integer x = 413.025381Warning: non-integer x = 441.119949Warning: non-integer x = 437.997965Warning: non-integer x = 396.018394Warning: non-integer x = 416.040093Warning: non-integer x = 424.004568Warning: non-integer x = 447.988870Warning: non-integer x = 417.048888Warning: non-integer x = 420.995619Warning: non-integer x = 418.995424Warning: non-integer x = 368.987189Warning: non-integer x = 458.977043Warning: non-integer x = 476.970517Warning: non-integer x = 661.018782Warning: non-integer x = 816.301781Warning: non-integer x = 733.969379Warning: non-integer x = 730.832955Warning: non-integer x = 680.179594Warning: non-integer x = 719.574480Warning: non-integer x = 717.466780Warning: non-integer x = 712.358768Warning: non-integer x = 672.002309Warning: non-integer x = 753.197800Warning: non-integer x = 702.743052Warning: non-integer x = 724.899355Warning: non-integer x = 712.921363Warning: non-integer x = 711.776394Warning: non-integer x = 745.619649Warning: non-integer x = 725.631590Warning: non-integer x = 796.393810Warning: non-integer x = 776.284777Warning: non-integer x = 719.215603Warning: non-integer x = 688.171754Warning: non-integer x = 750.391181Warning: non-integer x = 665.255038Warning: non-integer x = 740.262191Warning: non-integer x = 703.456598Warning: non-integer x = 711.416639Warning: non-integer x = 696.233913Warning: non-integer x = 757.423813Warning: non-integer x = 853.371015Warning: non-integer x = 755.275597Warning: non-integer x = 835.527276Warning: non-integer x = 779.416349Warning: non-integer x = 893.382196Warning: non-integer x = 812.648061Warning: non-integer x = 824.988571Warning: non-integer x = 846.012543Warning: non-integer x = 832.998211Warning: non-integer x = 854.996322Warning: non-integer x = 864.010369Warning: non-integer x = 829.017622Warning: non-integer x = 820.009847Warning: non-integer x = 827.010316Warning: non-integer x = 749.997769Warning: non-integer x = 699.012163Warning: non-integer x = 676.012927Warning: non-integer x = 735.017419Warning: non-integer x = 561.019408Warning: non-integer x = 572.981043Warning: non-integer x = 666.992786Warning: non-integer x = 766.990015Warning: non-integer x = 656.012600Warning: non-integer x = 714.009588Warning: non-integer x = 744.979976Warning: non-integer x = 652.993481Warning: non-integer x = 728.005883Warning: non-integer x = 721.008273Warning: non-integer x = 644.978877Warning: non-integer x = 713.020338Warning: non-integer x = 635.027306Warning: non-integer x = 634.006838Warning: non-integer x = 662.996421Warning: non-integer x = 646.004380Warning: non-integer x = 608.996388Warning: non-integer x = 614.003651Warning: non-integer x = 578.991961Warning: non-integer x = 583.017273Warning: non-integer x = 568.992498Warning: non-integer x = 499.008026Warning: non-integer x = 466.031633Warning: non-integer x = 434.069951Warning: non-integer x = 450.074832Warning: non-integer x = 461.100635Warning: non-integer x = 404.040261Warning: non-integer x = 481.974909Warning: non-integer x = 468.080379Warning: non-integer x = 452.973706Warning: non-integer x = 421.016983Warning: non-integer x = 465.039082Warning: non-integer x = 465.011064Warning: non-integer x = 467.025501Warning: non-integer x = 435.039674Warning: non-integer x = 504.992738Warning: non-integer x = 494.969463Warning: non-integer x = 816.255152Warning: non-integer x = 908.450924Warning: non-integer x = 868.152944Warning: non-integer x = 840.969473Warning: non-integer x = 838.481917Warning: non-integer x = 779.712586Warning: non-integer x = 932.924101Warning: non-integer x = 794.506925Warning: non-integer x = 826.249711Warning: non-integer x = 857.381425Warning: non-integer x = 776.833050Warning: non-integer x = 819.012111Warning: non-integer x = 810.067786Warning: non-integer x = 765.826680Warning: non-integer x = 809.665979Warning: non-integer x = 824.703915Warning: non-integer x = 917.456846Warning: non-integer x = 899.334422Warning: non-integer x = 718.209665Warning: non-integer x = 787.186705Warning: non-integer x = 798.430155Warning: non-integer x = 821.303227Warning: non-integer x = 765.277854Warning: non-integer x = 767.507135Warning: non-integer x = 807.478704Warning: non-integer x = 848.277686Warning: non-integer x = 827.447578Warning: non-integer x = 821.375024Warning: non-integer x = 922.333236Warning: non-integer x = 997.633253Warning: non-integer x = 841.471844Warning: non-integer x = 949.405604Warning: non-integer x = 885.715297Warning: non-integer x = 879.993114Warning: non-integer x = 943.987820Warning: non-integer x = 969.017195Warning: non-integer x = 967.995195Warning: non-integer x = 899.982415Warning: non-integer x = 877.012983Warning: non-integer x = 889.020976Warning: non-integer x = 869.992948Warning: non-integer x = 911.001402Warning: non-integer x = 806.004838Warning: non-integer x = 861.982112Warning: non-integer x = 783.013506Warning: non-integer x = 744.992030Warning: non-integer x = 669.003451Warning: non-integer x = 611.001892Warning: non-integer x = 679.016456Warning: non-integer x = 752.980488Warning: non-integer x = 820.996553Warning: non-integer x = 804.993080Warning: non-integer x = 785.007835Warning: non-integer x = 783.021679Warning: non-integer x = 723.008488Warning: non-integer x = 747.992522Warning: non-integer x = 710.980374Warning: non-integer x = 780.015509Warning: non-integer x = 691.986138Warning: non-integer x = 698.025171Warning: non-integer x = 658.997908Warning: non-integer x = 650.977136Warning: non-integer x = 645.022610Warning: non-integer x = 650.998695Warning: non-integer x = 645.009858Warning: non-integer x = 576.027108Warning: non-integer x = 549.047602Warning: non-integer x = 571.046019Warning: non-integer x = 561.097297Warning: non-integer x = 513.061236Warning: non-integer x = 487.127688Warning: non-integer x = 493.034210Warning: non-integer x = 492.986686Warning: non-integer x = 508.088981Warning: non-integer x = 532.017795Warning: non-integer x = 469.033470Warning: non-integer x = 515.056449Warning: non-integer x = 530.025537Warning: non-integer x = 446.012636Warning: non-integer x = 472.018703Warning: non-integer x = 514.986856Warning: non-integer x = 540.029724Warning: non-integer x = 618.952522Warning: non-integer x = 627.000288Warning: non-integer x = 674.905752Warning: non-integer x = 683.783628Warning: non-integer x = 667.165763Warning: non-integer x = 623.363303Warning: non-integer x = 729.495989Warning: non-integer x = 675.286689Warning: non-integer x = 682.029504Warning: non-integer x = 746.198152Warning: non-integer x = 613.652351Warning: non-integer x = 719.895492Warning: non-integer x = 654.871260Warning: non-integer x = 685.738648Warning: non-integer x = 731.589726Warning: non-integer x = 797.675985Warning: non-integer x = 872.422025Warning: non-integer x = 804.321193Warning: non-integer x = 749.221460Warning: non-integer x = 798.189695Warning: non-integer x = 870.452841Warning: non-integer x = 764.286012Warning: non-integer x = 802.265722Warning: non-integer x = 804.519476Warning: non-integer x = 838.495111Warning: non-integer x = 762.239076Warning: non-integer x = 889.472887Warning: non-integer x = 884.387773Warning: non-integer x = 861.331917Warning: non-integer x = 1050.645625Warning: non-integer x = 969.532209Warning: non-integer x = 1021.421302Warning: non-integer x = 997.812020Warning: non-integer x = 1036.991187Warning: non-integer x = 1008.987031Warning: non-integer x = 1090.990943Warning: non-integer x = 1033.011496Warning: non-integer x = 939.983642Warning: non-integer x = 952.011172Warning: non-integer x = 908.997295Warning: non-integer x = 986.999141Warning: non-integer x = 951.980663Warning: non-integer x = 870.018450Warning: non-integer x = 837.995851Warning: non-integer x = 864.005173Warning: non-integer x = 787.017241Warning: non-integer x = 784.017445Warning: non-integer x = 735.980612Warning: non-integer x = 696.984319Warning: non-integer x = 770.003774Warning: non-integer x = 829.999188Warning: non-integer x = 825.994106Warning: non-integer x = 810.994400Warning: non-integer x = 968.021236Warning: non-integer x = 765.973971Warning: non-integer x = 792.973738Warning: non-integer x = 816.981645Warning: non-integer x = 815.022181Warning: non-integer x = 770.019137Warning: non-integer x = 812.016681Warning: non-integer x = 832.001950Warning: non-integer x = 771.973852Warning: non-integer x = 703.016434Warning: non-integer x = 740.977886Warning: non-integer x = 679.018860Warning: non-integer x = 732.989180Warning: non-integer x = 578.014622Warning: non-integer x = 603.047065Warning: non-integer x = 631.073115Warning: non-integer x = 538.084370Warning: non-integer x = 472.124275Warning: non-integer x = 477.032830Warning: non-integer x = 541.016867Warning: non-integer x = 534.077196Warning: non-integer x = 542.005676Warning: non-integer x = 571.032812Warning: non-integer x = 554.037954Warning: non-integer x = 530.013305Warning: non-integer x = 575.997670Warning: non-integer x = 526.034998Warning: non-integer x = 575.027625Warning: non-integer x = 576.021624Warning: non-integer x = 1332.026642Warning: non-integer x = 1455.320384Warning: non-integer x = 1348.811833Warning: non-integer x = 1288.455424Warning: non-integer x = 1171.068700Warning: non-integer x = 1082.353957Warning: non-integer x = 1333.757947Warning: non-integer x = 1226.317722Warning: non-integer x = 1013.523405Warning: non-integer x = 1140.827529Warning: non-integer x = 1061.146726Warning: non-integer x = 1140.418349Warning: non-integer x = 977.277041Warning: non-integer x = 949.027621Warning: non-integer x = 1017.817357Warning: non-integer x = 1009.847953Warning: non-integer x = 1193.571193Warning: non-integer x = 1087.405373Warning: non-integer x = 861.260550Warning: non-integer x = 923.219027Warning: non-integer x = 965.515430Warning: non-integer x = 883.324252Warning: non-integer x = 956.342314Warning: non-integer x = 996.637571Warning: non-integer x = 939.541793Warning: non-integer x = 946.297382Warning: non-integer x = 959.500052Warning: non-integer x = 961.420114Warning: non-integer x = 985.347980Warning: non-integer x = 1045.650713Warning: non-integer x = 1035.571821Warning: non-integer x = 1143.491063Warning: non-integer x = 1020.833006Warning: non-integer x = 1071.000731Warning: non-integer x = 1091.015227Warning: non-integer x = 1073.012440Warning: non-integer x = 1154.982196Warning: non-integer x = 1109.995160Warning: non-integer x = 1123.006024Warning: non-integer x = 1094.989905Warning: non-integer x = 1039.993844Warning: non-integer x = 1042.013951Warning: non-integer x = 1039.994894Warning: non-integer x = 1069.987772Warning: non-integer x = 930.978722Warning: non-integer x = 971.987386Warning: non-integer x = 907.987673Warning: non-integer x = 869.014337Warning: non-integer x = 811.996826Warning: non-integer x = 675.008317Warning: non-integer x = 899.003422Warning: non-integer x = 933.986118Warning: non-integer x = 910.998251Warning: non-integer x = 980.984829Warning: non-integer x = 887.990359Warning: non-integer x = 949.007507Warning: non-integer x = 941.997495Warning: non-integer x = 873.009890Warning: non-integer x = 931.983768Warning: non-integer x = 863.978257Warning: non-integer x = 859.006528Warning: non-integer x = 894.012285Warning: non-integer x = 811.996180Warning: non-integer x = 825.994938Warning: non-integer x = 764.000783Warning: non-integer x = 768.986073Warning: non-integer x = 722.038431Warning: non-integer x = 685.021870Warning: non-integer x = 672.122129Warning: non-integer x = 625.059288Warning: non-integer x = 630.165264Warning: non-integer x = 585.025790Warning: non-integer x = 546.001814Warning: non-integer x = 504.076343Warning: non-integer x = 582.045710Warning: non-integer x = 584.992290Warning: non-integer x = 599.034160Warning: non-integer x = 570.038239Warning: non-integer x = 598.020689Warning: non-integer x = 602.030170Warning: non-integer x = 596.981146Warning: non-integer x = 667.023498Warning: non-integer x = 643.978172Warning: non-integer x = 754.195275Warning: non-integer x = 709.948544Warning: non-integer x = 659.755165Warning: non-integer x = 609.071509Warning: non-integer x = 626.373551Warning: non-integer x = 743.547079Warning: non-integer x = 697.311330Warning: non-integer x = 672.010470Warning: non-integer x = 783.251418Warning: non-integer x = 683.722257Warning: non-integer x = 835.034591Warning: non-integer x = 774.012828Warning: non-integer x = 683.749449Warning: non-integer x = 762.629364Warning: non-integer x = 801.686439Warning: non-integer x = 978.472973Warning: non-integer x = 902.358325Warning: non-integer x = 832.250486Warning: non-integer x = 838.209678Warning: non-integer x = 925.495392Warning: non-integer x = 909.332346Warning: non-integer x = 906.333198Warning: non-integer x = 943.619944Warning: non-integer x = 903.518163Warning: non-integer x = 988.325088Warning: non-integer x = 1010.540819Warning: non-integer x = 904.396235Warning: non-integer x = 969.359650Warning: non-integer x = 1088.689172Warning: non-integer x = 1051.577714Warning: non-integer x = 1150.483702Warning: non-integer x = 1131.934736Warning: non-integer x = 1126.997987Warning: non-integer x = 1159.004733Warning: non-integer x = 1154.996491Warning: non-integer x = 1149.013988Warning: non-integer x = 1170.008673Warning: non-integer x = 1180.984804Warning: non-integer x = 1103.010293Warning: non-integer x = 1059.018277Warning: non-integer x = 1119.019046Warning: non-integer x = 1102.990856Warning: non-integer x = 1022.010915Warning: non-integer x = 1073.979960Warning: non-integer x = 1007.997654Warning: non-integer x = 1003.004632Warning: non-integer x = 896.015822Warning: non-integer x = 893.016869Warning: non-integer x = 797.016856Warning: non-integer x = 854.993441Warning: non-integer x = 930.988866Warning: non-integer x = 1015.984255Warning: non-integer x = 1039.988510Warning: non-integer x = 1014.012175Warning: non-integer x = 1010.989267Warning: non-integer x = 1074.000140Warning: non-integer x = 983.011958Warning: non-integer x = 995.978081Warning: non-integer x = 886.022706Warning: non-integer x = 981.010418Warning: non-integer x = 997.003252Warning: non-integer x = 876.986751Warning: non-integer x = 928.002749Warning: non-integer x = 878.988459Warning: non-integer x = 781.000296Warning: non-integer x = 780.052273Warning: non-integer x = 757.019065Warning: non-integer x = 754.112333Warning: non-integer x = 716.078334Warning: non-integer x = 714.188949Warning: non-integer x = 665.045923Warning: non-integer x = 611.003558Warning: non-integer x = 626.054570Warning: non-integer x = 584.000230Warning: non-integer x = 639.022663Warning: non-integer x = 695.049864Warning: non-integer x = 616.042232Warning: non-integer x = 575.029231Warning: non-integer x = 657.015698Warning: non-integer x = 671.030384Warning: non-integer x = 733.026768Warning: non-integer x = 1003.528890Warning: non-integer x = 1012.626123Warning: non-integer x = 1086.453134Warning: non-integer x = 975.093502Warning: non-integer x = 926.632597Warning: non-integer x = 913.997105Warning: non-integer x = 1039.135194Warning: non-integer x = 994.887176Warning: non-integer x = 971.455443Warning: non-integer x = 1051.688579Warning: non-integer x = 1005.075846Warning: non-integer x = 1078.341922Warning: non-integer x = 985.279556Warning: non-integer x = 1024.116700Warning: non-integer x = 993.817885Warning: non-integer x = 950.806001Warning: non-integer x = 1137.543988Warning: non-integer x = 1122.425000Warning: non-integer x = 958.295514Warning: non-integer x = 1033.249984Warning: non-integer x = 1112.602260Warning: non-integer x = 1093.408903Warning: non-integer x = 1067.396501Warning: non-integer x = 1080.712884Warning: non-integer x = 1114.651775Warning: non-integer x = 1085.366172Warning: non-integer x = 1153.626638Warning: non-integer x = 1106.502502Warning: non-integer x = 1131.415058Warning: non-integer x = 1254.794721Warning: non-integer x = 1112.603497Warning: non-integer x = 1187.491656Warning: non-integer x = 1127.906691Warning: non-integer x = 1281.002818Warning: non-integer x = 1232.990882Warning: non-integer x = 1244.006896Warning: non-integer x = 1302.012656Warning: non-integer x = 1198.003996Warning: non-integer x = 1280.993537Warning: non-integer x = 1221.012356Warning: non-integer x = 1219.992663Warning: non-integer x = 1252.013445Warning: non-integer x = 1151.001619Warning: non-integer x = 1166.002979Warning: non-integer x = 1173.993578Warning: non-integer x = 1142.984273Warning: non-integer x = 1133.989937Warning: non-integer x = 1054.013011Warning: non-integer x = 1015.014536Warning: non-integer x = 985.981581Warning: non-integer x = 946.988017Warning: non-integer x = 902.999014Warning: non-integer x = 1000.004538Warning: non-integer x = 1154.986185Warning: non-integer x = 1011.020672Warning: non-integer x = 1092.020720Warning: non-integer x = 1093.001177Warning: non-integer x = 1047.985541Warning: non-integer x = 1140.025073Warning: non-integer x = 1029.981792Warning: non-integer x = 1028.981910Warning: non-integer x = 1016.985702Warning: non-integer x = 1021.996697Warning: non-integer x = 1011.013778Warning: non-integer x = 932.024911Warning: non-integer x = 955.979284Warning: non-integer x = 846.028427Warning: non-integer x = 852.042054Warning: non-integer x = 882.160965Warning: non-integer x = 781.110073Warning: non-integer x = 798.200836Warning: non-integer x = 757.062027Warning: non-integer x = 712.989573Warning: non-integer x = 654.069272Warning: non-integer x = 629.040125Warning: non-integer x = 697.999684Warning: non-integer x = 721.056160Warning: non-integer x = 704.013177Warning: non-integer x = 696.034131Warning: non-integer x = 691.061085Warning: non-integer x = 813.992219Warning: non-integer x = 793.992029Warning: non-integer x = 925.418872Warning: non-integer x = 1022.630551Warning: non-integer x = 919.234624Warning: non-integer x = 920.035227Warning: non-integer x = 875.531159Warning: non-integer x = 830.806039Warning: non-integer x = 887.827291Warning: non-integer x = 1002.898780Warning: non-integer x = 890.326222Warning: non-integer x = 1015.616642Warning: non-integer x = 1022.096869Warning: non-integer x = 1075.332001Warning: non-integer x = 932.212385Warning: non-integer x = 989.079622Warning: non-integer x = 1004.830783Warning: non-integer x = 997.867775Warning: non-integer x = 1152.564725Warning: non-integer x = 1082.400103Warning: non-integer x = 972.308020Warning: non-integer x = 1095.286977Warning: non-integer x = 1063.561060Warning: non-integer x = 1093.418799Warning: non-integer x = 1128.408298Warning: non-integer x = 1192.773657Warning: non-integer x = 1124.667277Warning: non-integer x = 1190.401080Warning: non-integer x = 1278.670205Warning: non-integer x = 1173.537131Warning: non-integer x = 1147.423816Warning: non-integer x = 1266.787916Warning: non-integer x = 1190.653652Warning: non-integer x = 1238.505838Warning: non-integer x = 1182.959337Warning: non-integer x = 1269.997171Warning: non-integer x = 1416.992836Warning: non-integer x = 1270.986780Warning: non-integer x = 1451.993550Warning: non-integer x = 1393.013863Warning: non-integer x = 1275.985101Warning: non-integer x = 1329.006764Warning: non-integer x = 1281.999696Warning: non-integer x = 1272.998658Warning: non-integer x = 1207.984906Warning: non-integer x = 1275.010136Warning: non-integer x = 1274.996556Warning: non-integer x = 1228.010465Warning: non-integer x = 1191.981004Warning: non-integer x = 1157.997997Warning: non-integer x = 1116.014493Warning: non-integer x = 1091.017848Warning: non-integer x = 1120.986657Warning: non-integer x = 1081.018233Warning: non-integer x = 944.997064Warning: non-integer x = 1068.992751Warning: non-integer x = 1099.997250Warning: non-integer x = 1176.988755Warning: non-integer x = 1203.993802Warning: non-integer x = 1163.977405Warning: non-integer x = 1157.987013Warning: non-integer x = 1238.012771Warning: non-integer x = 1163.990597Warning: non-integer x = 1058.010992Warning: non-integer x = 1097.998152Warning: non-integer x = 1093.020906Warning: non-integer x = 1036.016319Warning: non-integer x = 1092.998735Warning: non-integer x = 1027.050830Warning: non-integer x = 967.038473Warning: non-integer x = 922.142843Warning: non-integer x = 925.074658Warning: non-integer x = 865.242489Warning: non-integer x = 832.061094Warning: non-integer x = 810.026597Warning: non-integer x = 779.068998Warning: non-integer x = 691.027414Warning: non-integer x = 699.007250Warning: non-integer x = 751.085430Warning: non-integer x = 756.052786Warning: non-integer x = 785.017456Warning: non-integer x = 751.043448Warning: non-integer x = 856.016274Warning: non-integer x = 814.026159Warning: non-integer x = 931.413217Warning: non-integer x = 998.605877Warning: non-integer x = 974.305445Warning: non-integer x = 872.993922Warning: non-integer x = 925.634577Warning: non-integer x = 912.995599Warning: non-integer x = 949.952874Warning: non-integer x = 921.745690Warning: non-integer x = 964.456292Warning: non-integer x = 1080.722176Warning: non-integer x = 949.008254Warning: non-integer x = 1117.396726Warning: non-integer x = 1001.313570Warning: non-integer x = 1044.128736Warning: non-integer x = 1052.869133Warning: non-integer x = 1105.942397Warning: non-integer x = 1249.602739Warning: non-integer x = 1181.458781Warning: non-integer x = 1001.301117Warning: non-integer x = 1172.288011Warning: non-integer x = 1135.599775Warning: non-integer x = 1189.431799Warning: non-integer x = 1184.425951Warning: non-integer x = 1236.805414Warning: non-integer x = 1235.736652Warning: non-integer x = 1242.396450Warning: non-integer x = 1388.741638Warning: non-integer x = 1209.542914Warning: non-integer x = 1305.487764Warning: non-integer x = 1409.887230Warning: non-integer x = 1268.689763Warning: non-integer x = 1356.569571Warning: non-integer x = 1303.061018Warning: non-integer x = 1354.998892Warning: non-integer x = 1438.014042Warning: non-integer x = 1436.008006Warning: non-integer x = 1452.989944Warning: non-integer x = 1498.997298Warning: non-integer x = 1487.992569Warning: non-integer x = 1398.988565Warning: non-integer x = 1447.003449Warning: non-integer x = 1397.989658Warning: non-integer x = 1391.991372Warning: non-integer x = 1407.017542Warning: non-integer x = 1425.993847Warning: non-integer x = 1370.006014Warning: non-integer x = 1325.003782Warning: non-integer x = 1227.994097Warning: non-integer x = 1296.989038Warning: non-integer x = 1286.993119Warning: non-integer x = 1350.007279Warning: non-integer x = 1187.005022Warning: non-integer x = 1173.013790Warning: non-integer x = 1091.004494Warning: non-integer x = 1166.004526Warning: non-integer x = 1291.011336Warning: non-integer x = 1243.001130Warning: non-integer x = 1295.011951Warning: non-integer x = 1339.977553Warning: non-integer x = 1289.986148Warning: non-integer x = 1292.999615Warning: non-integer x = 1262.019458Warning: non-integer x = 1173.985734Warning: non-integer x = 1291.996094Warning: non-integer x = 1119.990952Warning: non-integer x = 1166.974289Warning: non-integer x = 1092.044493Warning: non-integer x = 1119.055239Warning: non-integer x = 1011.172695Warning: non-integer x = 1032.136385Warning: non-integer x = 1000.231832Warning: non-integer x = 957.063287Warning: non-integer x = 922.987849Warning: non-integer x = 930.097246Warning: non-integer x = 836.018461Warning: non-integer x = 808.036617Warning: non-integer x = 800.068801Warning: non-integer x = 826.026328Warning: non-integer x = 865.029164Warning: non-integer x = 870.039399Warning: non-integer x = 927.008210Warning: non-integer x = 872.047453Warning: non-integer x = 1213.843509Warning: non-integer x = 1381.216708Warning: non-integer x = 1257.677794Warning: non-integer x = 1176.323534Warning: non-integer x = 1101.929639Warning: non-integer x = 1159.532377Warning: non-integer x = 1297.686564Warning: non-integer x = 1181.241449Warning: non-integer x = 1071.593345Warning: non-integer x = 1169.868538Warning: non-integer x = 1216.306195Warning: non-integer x = 1244.547199Warning: non-integer x = 1127.466133Warning: non-integer x = 1153.246769Warning: non-integer x = 1229.002844Warning: non-integer x = 1202.025941Warning: non-integer x = 1457.700580Warning: non-integer x = 1206.460754Warning: non-integer x = 1138.347020Warning: non-integer x = 1194.302992Warning: non-integer x = 1174.620926Warning: non-integer x = 1225.457834Warning: non-integer x = 1225.442235Warning: non-integer x = 1304.849454Warning: non-integer x = 1277.740498Warning: non-integer x = 1299.426122Warning: non-integer x = 1390.742907Warning: non-integer x = 1331.599157Warning: non-integer x = 1341.485863Warning: non-integer x = 1474.928748Warning: non-integer x = 1367.752415Warning: non-integer x = 1448.604360Warning: non-integer x = 1371.115694Warning: non-integer x = 1426.006700Warning: non-integer x = 1592.009223Warning: non-integer x = 1450.999609Warning: non-integer x = 1618.995090Warning: non-integer x = 1413.988014Warning: non-integer x = 1581.008733Warning: non-integer x = 1505.989863Warning: non-integer x = 1399.003101Warning: non-integer x = 1456.005259Warning: non-integer x = 1483.007575Warning: non-integer x = 1585.013442Warning: non-integer x = 1409.012397Warning: non-integer x = 1552.002210Warning: non-integer x = 1464.990519Warning: non-integer x = 1411.989834Warning: non-integer x = 1419.002948Warning: non-integer x = 1323.004793Warning: non-integer x = 1371.997520Warning: non-integer x = 1378.007686Warning: non-integer x = 1287.004616Warning: non-integer x = 1286.007774Warning: non-integer x = 1066.989800Warning: non-integer x = 1324.019890Warning: non-integer x = 1374.991880Warning: non-integer x = 1315.003092Warning: non-integer x = 1490.990675Warning: non-integer x = 1394.978763Warning: non-integer x = 1349.017891Warning: non-integer x = 1349.005100Warning: non-integer x = 1339.004295Warning: non-integer x = 1248.987156Warning: non-integer x = 1300.993921Warning: non-integer x = 1131.054021Warning: non-integer x = 1218.093495Warning: non-integer x = 1138.155448Warning: non-integer x = 1145.118160Warning: non-integer x = 1079.258356Warning: non-integer x = 1069.050715Warning: non-integer x = 990.020564Warning: non-integer x = 1022.129683Warning: non-integer x = 981.029014Warning: non-integer x = 902.026195Warning: non-integer x = 850.066918Warning: non-integer x = 856.029180Warning: non-integer x = 933.025461Warning: non-integer x = 891.022131Warning: non-integer x = 1049.048002Warning: non-integer x = 1035.020621Warning: non-integer x = 1037.592045Warning: non-integer x = 1141.825877Warning: non-integer x = 970.299955Warning: non-integer x = 946.065654Warning: non-integer x = 958.695183Warning: non-integer x = 861.875376Warning: non-integer x = 1004.074042Warning: non-integer x = 990.887212Warning: non-integer x = 915.370982Warning: non-integer x = 1121.788661Warning: non-integer x = 998.071376Warning: non-integer x = 1200.497602Warning: non-integer x = 1060.383548Warning: non-integer x = 1057.139486Warning: non-integer x = 1196.977535Warning: non-integer x = 1214.030883Warning: non-integer x = 1381.662373Warning: non-integer x = 1245.475014Warning: non-integer x = 1093.333501Warning: non-integer x = 1221.304684Warning: non-integer x = 1187.632195Warning: non-integer x = 1240.457648Warning: non-integer x = 1281.464392Warning: non-integer x = 1392.907900Warning: non-integer x = 1325.784861Warning: non-integer x = 1360.454754Warning: non-integer x = 1403.749673Warning: non-integer x = 1447.643069Warning: non-integer x = 1327.498942Warning: non-integer x = 1590.990423Warning: non-integer x = 1325.717590Warning: non-integer x = 1466.609441Warning: non-integer x = 1310.062162Warning: non-integer x = 1476.992009Warning: non-integer x = 1549.006686Warning: non-integer x = 1476.001460Warning: non-integer x = 1680.987704Warning: non-integer x = 1526.010477Warning: non-integer x = 1552.009700Warning: non-integer x = 1581.007088Warning: non-integer x = 1614.986949Warning: non-integer x = 1537.991865Warning: non-integer x = 1549.993451Warning: non-integer x = 1564.994323Warning: non-integer x = 1604.004516Warning: non-integer x = 1551.983934Warning: non-integer x = 1591.015509Warning: non-integer x = 1483.015438Warning: non-integer x = 1574.005755Warning: non-integer x = 1488.995681Warning: non-integer x = 1473.996003Warning: non-integer x = 1553.010675Warning: non-integer x = 1409.997195Warning: non-integer x = 1443.009123Warning: non-integer x = 1274.995959Warning: non-integer x = 1186.013352Warning: non-integer x = 1436.004396Warning: non-integer x = 1506.012392Warning: non-integer x = 1496.016739Warning: non-integer x = 1493.019612Warning: non-integer x = 1461.010153Warning: non-integer x = 1485.986076Warning: non-integer x = 1463.004108Warning: non-integer x = 1525.022525Warning: non-integer x = 1373.018153Warning: non-integer x = 1450.006729Warning: non-integer x = 1218.066052Warning: non-integer x = 1267.104780Warning: non-integer x = 1355.234498Warning: non-integer x = 1247.154928Warning: non-integer x = 1220.332817Warning: non-integer x = 1202.035082Warning: non-integer x = 1237.984875Warning: non-integer x = 1169.136499Warning: non-integer x = 1060.023970Warning: non-integer x = 1090.020933Warning: non-integer x = 1048.084615Warning: non-integer x = 928.065306Warning: non-integer x = 987.006820Warning: non-integer x = 1008.063144Warning: non-integer x = 1139.994647Warning: non-integer x = 1131.993870Warning: non-integer x = 968.480377Warning: non-integer x = 1134.818926Warning: non-integer x = 991.319503Warning: non-integer x = 895.014983Warning: non-integer x = 954.682273Warning: non-integer x = 982.141875Warning: non-integer x = 1011.077529Warning: non-integer x = 1060.014012Warning: non-integer x = 982.486367Warning: non-integer x = 1063.702867Warning: non-integer x = 947.014166Warning: non-integer x = 1126.414102Warning: non-integer x = 1098.440285Warning: non-integer x = 1127.212180Warning: non-integer x = 1084.878871Warning: non-integer x = 1195.019368Warning: non-integer x = 1323.644170Warning: non-integer x = 1212.466301Warning: non-integer x = 1118.348444Warning: non-integer x = 1172.291490Warning: non-integer x = 1259.687446Warning: non-integer x = 1246.461636Warning: non-integer x = 1286.472121Warning: non-integer x = 1367.883385Warning: non-integer x = 1365.808583Warning: non-integer x = 1351.442798Warning: non-integer x = 1465.794198Warning: non-integer x = 1383.628712Warning: non-integer x = 1419.532478Warning: non-integer x = 1535.959450Warning: non-integer x = 1475.808728Warning: non-integer x = 1484.623966Warning: non-integer x = 1381.114047Warning: non-integer x = 1444.991500Warning: non-integer x = 1456.994364Warning: non-integer x = 1491.000786Warning: non-integer x = 1563.995451Warning: non-integer x = 1499.989838Warning: non-integer x = 1651.989736Warning: non-integer x = 1539.991523Warning: non-integer x = 1719.011607Warning: non-integer x = 1606.007820Warning: non-integer x = 1549.996026Warning: non-integer x = 1615.994898Warning: non-integer x = 1659.998213Warning: non-integer x = 1697.987295Warning: non-integer x = 1594.000164Warning: non-integer x = 1619.014345Warning: non-integer x = 1699.008722Warning: non-integer x = 1636.012152Warning: non-integer x = 1768.009102Warning: non-integer x = 1652.986018Warning: non-integer x = 1526.004935Warning: non-integer x = 1634.005693Warning: non-integer x = 1384.996469Warning: non-integer x = 1377.984656Warning: non-integer x = 1306.987166Warning: non-integer x = 1533.999443Warning: non-integer x = 1672.016162Warning: non-integer x = 1632.997715Warning: non-integer x = 1618.017526Warning: non-integer x = 1629.980884Warning: non-integer x = 1577.016302Warning: non-integer x = 1652.012587Warning: non-integer x = 1404.020815Warning: non-integer x = 1566.995238Warning: non-integer x = 1415.047231Warning: non-integer x = 1456.108022Warning: non-integer x = 1472.215310Warning: non-integer x = 1378.180584Warning: non-integer x = 1379.360900Warning: non-integer x = 1305.063813Warning: non-integer x = 1279.980662Warning: non-integer x = 1304.150758Warning: non-integer x = 1178.996623Warning: non-integer x = 1141.029798Warning: non-integer x = 1167.078949Warning: non-integer x = 1109.079518Warning: non-integer x = 1134.035879Warning: non-integer x = 1034.047944Warning: non-integer x = 1247.031878Warning: non-integer x = 1294.040088Warning: non-integer x = 1172.786978Warning: non-integer x = 1327.120912Warning: non-integer x = 1240.661366Warning: non-integer x = 1135.290470Warning: non-integer x = 1043.835375Warning: non-integer x = 1063.321322Warning: non-integer x = 1179.432337Warning: non-integer x = 1197.268687Warning: non-integer x = 1032.546392Warning: non-integer x = 1173.867730Warning: non-integer x = 1052.133150Warning: non-integer x = 1243.547151Warning: non-integer x = 1181.546747Warning: non-integer x = 1295.406159Warning: non-integer x = 1164.947093Warning: non-integer x = 1255.077329Warning: non-integer x = 1470.722176Warning: non-integer x = 1322.501418Warning: non-integer x = 1268.393890Warning: non-integer x = 1292.335849Warning: non-integer x = 1367.725328Warning: non-integer x = 1331.489827Warning: non-integer x = 1311.472172Warning: non-integer x = 1392.904653Warning: non-integer x = 1411.828898Warning: non-integer x = 1397.448550Warning: non-integer x = 1540.817040Warning: non-integer x = 1455.655694Warning: non-integer x = 1505.560834Warning: non-integer x = 1686.060108Warning: non-integer x = 1518.828603Warning: non-integer x = 1609.662610Warning: non-integer x = 1460.177252Warning: non-integer x = 1593.008256Warning: non-integer x = 1533.005600Warning: non-integer x = 1573.995704Warning: non-integer x = 1694.006583Warning: non-integer x = 1591.009620Warning: non-integer x = 1676.994530Warning: non-integer x = 1627.004542Warning: non-integer x = 1755.002813Warning: non-integer x = 1712.990188Warning: non-integer x = 1713.994999Warning: non-integer x = 1651.994525Warning: non-integer x = 1755.991952Warning: non-integer x = 1745.999560Warning: non-integer x = 1779.994666Warning: non-integer x = 1651.003562Warning: non-integer x = 1780.014716Warning: non-integer x = 1699.015910Warning: non-integer x = 1901.991487Warning: non-integer x = 1844.984760Warning: non-integer x = 1669.991269Warning: non-integer x = 1686.984987Warning: non-integer x = 1562.991703Warning: non-integer x = 1625.985563Warning: non-integer x = 1485.014235Warning: non-integer x = 1324.986750Warning: non-integer x = 1637.017173Warning: non-integer x = 1741.017687Warning: non-integer x = 1648.009679Warning: non-integer x = 1683.001757Warning: non-integer x = 1750.984995Warning: non-integer x = 1740.005858Warning: non-integer x = 1668.981120Warning: non-integer x = 1719.988366Warning: non-integer x = 1482.064650Warning: non-integer x = 1467.093687Warning: non-integer x = 1482.250552Warning: non-integer x = 1510.157152Warning: non-integer x = 1491.356650Warning: non-integer x = 1547.075926Warning: non-integer x = 1465.988401Warning: non-integer x = 1423.156375Warning: non-integer x = 1395.025343Warning: non-integer x = 1339.055848Warning: non-integer x = 1364.115402Warning: non-integer x = 1337.068276Warning: non-integer x = 1231.014115Warning: non-integer x = 1159.036787Warning: non-integer x = 1315.003521Warning: non-integer x = 1380.035215Warning: non-integer x = 809.230277Warning: non-integer x = 902.443727Warning: non-integer x = 832.110880Warning: non-integer x = 777.890893Warning: non-integer x = 764.354354Warning: non-integer x = 745.626447Warning: non-integer x = 828.708664Warning: non-integer x = 859.626859Warning: non-integer x = 805.201477Warning: non-integer x = 872.395824Warning: non-integer x = 834.890168Warning: non-integer x = 929.163751Warning: non-integer x = 894.174902Warning: non-integer x = 973.054197Warning: non-integer x = 1080.879660Warning: non-integer x = 1153.989433Warning: non-integer x = 1267.617001Warning: non-integer x = 1193.463652Warning: non-integer x = 1032.317865Warning: non-integer x = 1153.296713Warning: non-integer x = 1278.691793Warning: non-integer x = 1224.453640Warning: non-integer x = 1195.435252Warning: non-integer x = 1345.874628Warning: non-integer x = 1317.773675Warning: non-integer x = 1365.449351Warning: non-integer x = 1458.783788Warning: non-integer x = 1452.657888Warning: non-integer x = 1461.534884Warning: non-integer x = 1677.050061Warning: non-integer x = 1524.836988Warning: non-integer x = 1495.622460Warning: non-integer x = 1542.252960Warning: non-integer x = 1643.994971Warning: non-integer x = 1564.003287Warning: non-integer x = 1559.996077Warning: non-integer x = 1751.006533Warning: non-integer x = 1601.002613Warning: non-integer x = 1645.992063Warning: non-integer x = 1647.992651Warning: non-integer x = 1701.004339Warning: non-integer x = 1768.996648Warning: non-integer x = 1733.998488Warning: non-integer x = 1804.997928Warning: non-integer x = 1723.001045Warning: non-integer x = 1810.005737Warning: non-integer x = 1813.009736Warning: non-integer x = 1765.993092Warning: non-integer x = 1752.011901Warning: non-integer x = 1863.994587Warning: non-integer x = 1921.991941Warning: non-integer x = 1879.995025Warning: non-integer x = 1801.001629Warning: non-integer x = 1835.999290Warning: non-integer x = 1746.001488Warning: non-integer x = 1828.006820Warning: non-integer x = 1724.997299Warning: non-integer x = 1591.990384Warning: non-integer x = 1436.000356Warning: non-integer x = 1730.002366Warning: non-integer x = 1830.013391Warning: non-integer x = 1774.984564Warning: non-integer x = 1817.984082Warning: non-integer x = 1978.989251Warning: non-integer x = 1723.014508Warning: non-integer x = 1813.998790Warning: non-integer x = 1791.092969Warning: non-integer x = 1737.103068Warning: non-integer x = 1688.261414Warning: non-integer x = 1665.194990Warning: non-integer x = 1606.417772Warning: non-integer x = 1583.063718Warning: non-integer x = 1711.994252Warning: non-integer x = 1533.149046Warning: non-integer x = 1468.004092Warning: non-integer x = 1599.035609Warning: non-integer x = 1558.125283Warning: non-integer x = 1449.099028Warning: non-integer x = 1499.012427Warning: non-integer x = 1426.063704Warning: non-integer x = 1483.018179Warning: non-integer x = 1419.001112Warning: non-integer x = 1638.511410Warning: non-integer x = 1673.683528Warning: non-integer x = 1593.127670Warning: non-integer x = 1507.707322Warning: non-integer x = 1364.401868Warning: non-integer x = 1316.878904Warning: non-integer x = 1480.048897Warning: non-integer x = 1403.663800Warning: non-integer x = 1218.833054Warning: non-integer x = 1399.236045Warning: non-integer x = 1243.327523Warning: non-integer x = 1304.633867Warning: non-integer x = 1255.646550Warning: non-integer x = 1280.379786Warning: non-integer x = 1306.058467Warning: non-integer x = 1333.138314Warning: non-integer x = 1688.834538Warning: non-integer x = 1373.520466Warning: non-integer x = 1328.403856Warning: non-integer x = 1303.324521Warning: non-integer x = 1378.735736Warning: non-integer x = 1382.515702Warning: non-integer x = 1297.468965Warning: non-integer x = 1361.886950Warning: non-integer x = 1376.821420Warning: non-integer x = 1466.474625Warning: non-integer x = 1549.828344Warning: non-integer x = 1546.685307Warning: non-integer x = 1480.532777Warning: non-integer x = 1662.057441Warning: non-integer x = 1498.820427Warning: non-integer x = 1664.692114Warning: non-integer x = 1515.225740Warning: non-integer x = 1693.001694Warning: non-integer x = 1668.997063Warning: non-integer x = 1629.998884Warning: non-integer x = 1666.008010Warning: non-integer x = 1569.997737Warning: non-integer x = 1663.999506Warning: non-integer x = 1690.999309Warning: non-integer x = 1719.994069Warning: non-integer x = 1801.996178Warning: non-integer x = 1712.001272Warning: non-integer x = 1835.004503Warning: non-integer x = 1885.998430Warning: non-integer x = 1841.988358Warning: non-integer x = 1878.991213Warning: non-integer x = 1940.006829Warning: non-integer x = 1946.989392Warning: non-integer x = 1789.992375Warning: non-integer x = 2033.001479Warning: non-integer x = 2106.002566Warning: non-integer x = 1989.988660Warning: non-integer x = 2055.013977Warning: non-integer x = 1782.005550Warning: non-integer x = 1912.009807Warning: non-integer x = 1844.992980Warning: non-integer x = 1785.991508Warning: non-integer x = 1655.998986Warning: non-integer x = 1582.005524Warning: non-integer x = 1835.016033Warning: non-integer x = 1862.987497Warning: non-integer x = 1933.012604Warning: non-integer x = 2069.003226Warning: non-integer x = 1888.003374Warning: non-integer x = 1971.980819Warning: non-integer x = 1841.060405Warning: non-integer x = 1840.100479Warning: non-integer x = 1790.274056Warning: non-integer x = 1932.229521Warning: non-integer x = 1850.456848Warning: non-integer x = 1710.072427Warning: non-integer x = 1814.001795Warning: non-integer x = 1731.201052Warning: non-integer x = 1677.051367Warning: non-integer x = 1712.073130Warning: non-integer x = 1698.136337Warning: non-integer x = 1611.063864Warning: non-integer x = 1604.010534Warning: non-integer x = 1641.089237Warning: non-integer x = 1629.038366Warning: non-integer x = 1634.041777Warning: non-integer x = 707.079588Warning: non-integer x = 880.401580Warning: non-integer x = 747.994262Warning: non-integer x = 709.803614Warning: non-integer x = 631.107267Warning: non-integer x = 708.544316Warning: non-integer x = 734.510674Warning: non-integer x = 726.376760Warning: non-integer x = 732.098678Warning: non-integer x = 801.273164Warning: non-integer x = 747.803199Warning: non-integer x = 906.126642Warning: non-integer x = 855.121066Warning: non-integer x = 889.955852Warning: non-integer x = 868.696668Warning: non-integer x = 1010.867717Warning: non-integer x = 1285.634027Warning: non-integer x = 1050.394730Warning: non-integer x = 951.295452Warning: non-integer x = 1129.286017Warning: non-integer x = 1239.673137Warning: non-integer x = 1170.428327Warning: non-integer x = 1174.415913Warning: non-integer x = 1309.834185Warning: non-integer x = 1323.781190Warning: non-integer x = 1322.425244Warning: non-integer x = 1350.725160Warning: non-integer x = 1374.623516Warning: non-integer x = 1440.534611Warning: non-integer x = 1607.005826Warning: non-integer x = 1488.817843Warning: non-integer x = 1560.644301Warning: non-integer x = 1422.158179Warning: non-integer x = 1567.007531Warning: non-integer x = 1678.005857Warning: non-integer x = 1495.992191Warning: non-integer x = 1667.004062Warning: non-integer x = 1574.001540Warning: non-integer x = 1603.999402Warning: non-integer x = 1655.997478Warning: non-integer x = 1677.004410Warning: non-integer x = 1858.010317Warning: non-integer x = 1925.007329Warning: non-integer x = 1912.998962Warning: non-integer x = 1788.994999Warning: non-integer x = 1938.995065Warning: non-integer x = 1850.992278Warning: non-integer x = 1982.998031Warning: non-integer x = 1969.999156Warning: non-integer x = 2070.987675Warning: non-integer x = 2072.008907Warning: non-integer x = 2038.990644Warning: non-integer x = 2013.987197Warning: non-integer x = 1918.003744Warning: non-integer x = 1996.002237Warning: non-integer x = 1897.012625Warning: non-integer x = 1826.998470Warning: non-integer x = 1848.009046Warning: non-integer x = 1630.006960Warning: non-integer x = 1912.014217Warning: non-integer x = 2071.011486Warning: non-integer x = 2071.992943Warning: non-integer x = 1949.005508Warning: non-integer x = 2142.002636Warning: non-integer x = 1955.074660Warning: non-integer x = 2077.122725Warning: non-integer x = 1986.316574Warning: non-integer x = 1945.243838Warning: non-integer x = 2017.496738Warning: non-integer x = 1801.078700Warning: non-integer x = 1968.000647Warning: non-integer x = 1887.215865Warning: non-integer x = 1874.040837Warning: non-integer x = 1851.059613Warning: non-integer x = 1815.149924Warning: non-integer x = 1756.110811Warning: non-integer x = 1840.034558Warning: non-integer x = 1698.082822Warning: non-integer x = 2018.038626Warning: non-integer x = 1851.018044Warning: non-integer x = 950.452388Warning: non-integer x = 1043.658206Warning: non-integer x = 990.317892Warning: non-integer x = 855.970874Warning: non-integer x = 815.431442Warning: non-integer x = 873.913793Warning: non-integer x = 974.008582Warning: non-integer x = 982.857940Warning: non-integer x = 914.380289Warning: non-integer x = 1039.657525Warning: non-integer x = 937.007896Warning: non-integer x = 1042.309736Warning: non-integer x = 996.309439Warning: non-integer x = 1051.142712Warning: non-integer x = 1009.808966Warning: non-integer x = 1140.984001Warning: non-integer x = 1382.682413Warning: non-integer x = 1189.450556Warning: non-integer x = 1110.348410Warning: non-integer x = 1245.323452Warning: non-integer x = 1227.648014Warning: non-integer x = 1246.456831Warning: non-integer x = 1206.429211Warning: non-integer x = 1356.866190Warning: non-integer x = 1320.781424Warning: non-integer x = 1314.420758Warning: non-integer x = 1451.775349Warning: non-integer x = 1289.574249Warning: non-integer x = 1499.548345Warning: non-integer x = 1535.966343Warning: non-integer x = 1444.784806Warning: non-integer x = 1551.644782Warning: non-integer x = 1546.256973Warning: non-integer x = 1585.005406Warning: non-integer x = 1650.000986Warning: non-integer x = 1607.996134Warning: non-integer x = 1655.006906Warning: non-integer x = 1561.002622Warning: non-integer x = 1598.997476Warning: non-integer x = 1571.999568Warning: non-integer x = 1648.002363Warning: non-integer x = 1719.993489Warning: non-integer x = 1583.992924Warning: non-integer x = 1857.991024Warning: non-integer x = 1801.005336Warning: non-integer x = 1863.006836Warning: non-integer x = 1826.009657Warning: non-integer x = 1847.000260Warning: non-integer x = 1859.998081Warning: non-integer x = 1934.005429Warning: non-integer x = 2095.994653Warning: non-integer x = 2062.997251Warning: non-integer x = 2025.005979Warning: non-integer x = 2196.988319Warning: non-integer x = 2002.995081Warning: non-integer x = 2204.008718Warning: non-integer x = 2054.991510Warning: non-integer x = 2012.002392Warning: non-integer x = 1963.011086Warning: non-integer x = 1987.011214Warning: non-integer x = 1810.012140Warning: non-integer x = 1659.006364Warning: non-integer x = 1994.013544Warning: non-integer x = 2222.999238Warning: non-integer x = 2068.004695Warning: non-integer x = 2180.010634Warning: non-integer x = 2082.087867Warning: non-integer x = 2107.142926Warning: non-integer x = 2066.344457Warning: non-integer x = 2125.248696Warning: non-integer x = 2193.531481Warning: non-integer x = 2046.112210Warning: non-integer x = 2102.992282Warning: non-integer x = 2055.227047Warning: non-integer x = 2000.039279Warning: non-integer x = 2230.099845Warning: non-integer x = 2118.160453Warning: non-integer x = 1974.127881Warning: non-integer x = 2069.060838Warning: non-integer x = 1957.089835Warning: non-integer x = 2120.027283Warning: non-integer x = 2156.054770Warning: non-integer x = 805.232029Warning: non-integer x = 836.332470Warning: non-integer x = 794.060566Warning: non-integer x = 786.890045Warning: non-integer x = 801.407300Warning: non-integer x = 750.640387Warning: non-integer x = 843.741500Warning: non-integer x = 840.589583Warning: non-integer x = 741.107172Warning: non-integer x = 927.482291Warning: non-integer x = 809.857390Warning: non-integer x = 903.117533Warning: non-integer x = 826.079588Warning: non-integer x = 888.962392Warning: non-integer x = 913.738589Warning: non-integer x = 950.807900Warning: non-integer x = 1153.556205Warning: non-integer x = 1069.409687Warning: non-integer x = 986.300928Warning: non-integer x = 1119.279272Warning: non-integer x = 1131.599440Warning: non-integer x = 1127.421353Warning: non-integer x = 1147.418292Warning: non-integer x = 1271.817479Warning: non-integer x = 1254.740236Warning: non-integer x = 1269.417791Warning: non-integer x = 1321.704867Warning: non-integer x = 1348.602341Warning: non-integer x = 1343.495386Warning: non-integer x = 1423.889250Warning: non-integer x = 1427.783154Warning: non-integer x = 1478.604545Warning: non-integer x = 1355.101139Warning: non-integer x = 1515.003236Warning: non-integer x = 1575.994770Warning: non-integer x = 1509.004446Warning: non-integer x = 1590.999066Warning: non-integer x = 1478.003570Warning: non-integer x = 1540.998828Warning: non-integer x = 1498.001806Warning: non-integer x = 1543.996299Warning: non-integer x = 1613.996796Warning: non-integer x = 1611.006221Warning: non-integer x = 1685.997629Warning: non-integer x = 1784.993247Warning: non-integer x = 1781.998323Warning: non-integer x = 1874.002290Warning: non-integer x = 1903.995674Warning: non-integer x = 1914.997557Warning: non-integer x = 1880.004734Warning: non-integer x = 2151.996759Warning: non-integer x = 2095.989875Warning: non-integer x = 1911.996009Warning: non-integer x = 2155.994444Warning: non-integer x = 2117.010957Warning: non-integer x = 2044.009064Warning: non-integer x = 2150.008588Warning: non-integer x = 2134.993896Warning: non-integer x = 2084.001512Warning: non-integer x = 1898.994567Warning: non-integer x = 1837.007724Warning: non-integer x = 1713.008252Warning: non-integer x = 2107.000539Warning: non-integer x = 2073.999623Warning: non-integer x = 2222.988117Warning: non-integer x = 2085.088496Warning: non-integer x = 2196.120655Warning: non-integer x = 2207.343330Warning: non-integer x = 2323.263087Warning: non-integer x = 2314.600865Warning: non-integer x = 2121.093582Warning: non-integer x = 2313.984362Warning: non-integer x = 2191.263614Warning: non-integer x = 2090.036463Warning: non-integer x = 2338.103496Warning: non-integer x = 2213.166976Warning: non-integer x = 2107.136250Warning: non-integer x = 2151.027081Warning: non-integer x = 2148.119222Warning: non-integer x = 2325.039172Warning: non-integer x = 2342.056894Warning: non-integer x = 786.200177Warning: non-integer x = 791.261084Warning: non-integer x = 818.087814Warning: non-integer x = 770.880722Warning: non-integer x = 880.552136Warning: non-integer x = 755.652382Warning: non-integer x = 903.857881Warning: non-integer x = 785.478209Warning: non-integer x = 709.060792Warning: non-integer x = 899.427698Warning: non-integer x = 807.859957Warning: non-integer x = 981.229059Warning: non-integer x = 864.128325Warning: non-integer x = 891.963448Warning: non-integer x = 999.807978Warning: non-integer x = 944.810197Warning: non-integer x = 1133.551726Warning: non-integer x = 1024.388528Warning: non-integer x = 963.301343Warning: non-integer x = 1058.260205Warning: non-integer x = 1159.619737Warning: non-integer x = 1110.407384Warning: non-integer x = 1137.408536Warning: non-integer x = 1149.746906Warning: non-integer x = 1103.649244Warning: non-integer x = 1199.391360Warning: non-integer x = 1295.690215Warning: non-integer x = 1240.559791Warning: non-integer x = 1237.457728Warning: non-integer x = 1434.896134Warning: non-integer x = 1282.701535Warning: non-integer x = 1465.604374Warning: non-integer x = 1345.086008Warning: non-integer x = 1426.997009Warning: non-integer x = 1500.004687Warning: non-integer x = 1443.002222Warning: non-integer x = 1513.994968Warning: non-integer x = 1504.001752Warning: non-integer x = 1481.998066Warning: non-integer x = 1451.004264Warning: non-integer x = 1387.000256Warning: non-integer x = 1478.996416Warning: non-integer x = 1510.003731Warning: non-integer x = 1592.999227Warning: non-integer x = 1638.006789Warning: non-integer x = 1726.994370Warning: non-integer x = 1729.994202Warning: non-integer x = 1844.004758Warning: non-integer x = 1909.992255Warning: non-integer x = 1755.996807Warning: non-integer x = 2067.992853Warning: non-integer x = 2117.992180Warning: non-integer x = 2024.008286Warning: non-integer x = 2118.992252Warning: non-integer x = 1985.006320Warning: non-integer x = 2134.993212Warning: non-integer x = 2209.007626Warning: non-integer x = 2200.998137Warning: non-integer x = 2124.990785Warning: non-integer x = 2168.994200Warning: non-integer x = 2003.009052Warning: non-integer x = 2011.995920Warning: non-integer x = 1932.993109Warning: non-integer x = 1843.001820Warning: non-integer x = 2030.005227Warning: non-integer x = 2362.997336Warning: non-integer x = 2108.097387Warning: non-integer x = 2230.151755Warning: non-integer x = 2373.362249Warning: non-integer x = 2328.264651Warning: non-integer x = 2307.584205Warning: non-integer x = 2288.109425Warning: non-integer x = 2315.010134Warning: non-integer x = 2267.270558Warning: non-integer x = 2297.029429Warning: non-integer x = 2305.101447Warning: non-integer x = 2271.183976Warning: non-integer x = 2296.115112Warning: non-integer x = 2331.038402Warning: non-integer x = 2294.138428Warning: non-integer x = 2636.052237Warning: non-integer x = 2502.056242Warning: non-integer x = 876.340020Warning: non-integer x = 979.567454Warning: non-integer x = 949.267259Warning: non-integer x = 839.949008Warning: non-integer x = 843.481311Warning: non-integer x = 874.909299Warning: non-integer x = 968.991017Warning: non-integer x = 842.598772Warning: non-integer x = 752.126959Warning: non-integer x = 908.450210Warning: non-integer x = 818.880351Warning: non-integer x = 875.090062Warning: non-integer x = 868.141880Warning: non-integer x = 853.920567Warning: non-integer x = 844.689146Warning: non-integer x = 959.829286Warning: non-integer x = 1071.519729Warning: non-integer x = 917.349169Warning: non-integer x = 847.272528Warning: non-integer x = 1030.259926Warning: non-integer x = 1077.569162Warning: non-integer x = 1025.370805Warning: non-integer x = 1047.381535Warning: non-integer x = 1135.740474Warning: non-integer x = 1098.649325Warning: non-integer x = 1106.351924Warning: non-integer x = 1166.629893Warning: non-integer x = 1088.486074Warning: non-integer x = 1148.427414Warning: non-integer x = 1323.832982Warning: non-integer x = 1172.636433Warning: non-integer x = 1294.537556Warning: non-integer x = 1230.002626Warning: non-integer x = 1313.000167Warning: non-integer x = 1411.996094Warning: non-integer x = 1346.002242Warning: non-integer x = 1301.004337Warning: non-integer x = 1277.001088Warning: non-integer x = 1399.998202Warning: non-integer x = 1368.998871Warning: non-integer x = 1301.997885Warning: non-integer x = 1416.998259Warning: non-integer x = 1345.998277Warning: non-integer x = 1584.000181Warning: non-integer x = 1612.003891Warning: non-integer x = 1635.001476Warning: non-integer x = 1652.003764Warning: non-integer x = 1767.005199Warning: non-integer x = 1817.002989Warning: non-integer x = 1928.999489Warning: non-integer x = 1968.002761Warning: non-integer x = 1830.995990Warning: non-integer x = 2085.003518Warning: non-integer x = 1949.002479Warning: non-integer x = 2174.009343Warning: non-integer x = 2171.991997Warning: non-integer x = 2178.993717Warning: non-integer x = 2238.007958Warning: non-integer x = 2258.007660Warning: non-integer x = 2058.007695Warning: non-integer x = 1980.992797Warning: non-integer x = 1959.003635Warning: non-integer x = 1712.007961Warning: non-integer x = 2253.000873Warning: non-integer x = 2230.099155Warning: non-integer x = 2217.138940Warning: non-integer x = 2355.380689Warning: non-integer x = 2374.289861Warning: non-integer x = 2454.623294Warning: non-integer x = 2329.111598Warning: non-integer x = 2473.991040Warning: non-integer x = 2465.285902Warning: non-integer x = 2390.048833Warning: non-integer x = 2496.104581Warning: non-integer x = 2509.171866Warning: non-integer x = 2524.136963Warning: non-integer x = 2558.052700Warning: non-integer x = 2481.143631Warning: non-integer x = 2614.054775Warning: non-integer x = 2730.028404Warning: non-integer x = 682.037656Warning: non-integer x = 672.068569Warning: non-integer x = 604.799706Warning: non-integer x = 562.630078Warning: non-integer x = 601.048591Warning: non-integer x = 576.260188Warning: non-integer x = 697.439078Warning: non-integer x = 642.220223Warning: non-integer x = 684.020476Warning: non-integer x = 709.131385Warning: non-integer x = 746.801764Warning: non-integer x = 722.910429Warning: non-integer x = 680.901889Warning: non-integer x = 749.810305Warning: non-integer x = 753.611963Warning: non-integer x = 742.629744Warning: non-integer x = 892.442012Warning: non-integer x = 821.308379Warning: non-integer x = 757.240961Warning: non-integer x = 888.228479Warning: non-integer x = 916.491496Warning: non-integer x = 883.319238Warning: non-integer x = 931.342548Warning: non-integer x = 1087.710456Warning: non-integer x = 984.581554Warning: non-integer x = 999.319195Warning: non-integer x = 1062.571200Warning: non-integer x = 1028.463293Warning: non-integer x = 1025.378676Warning: non-integer x = 1122.698672Warning: non-integer x = 1091.589877Warning: non-integer x = 1172.491714Warning: non-integer x = 1140.927355Warning: non-integer x = 1230.001379Warning: non-integer x = 1283.998901Warning: non-integer x = 1263.000879Warning: non-integer x = 1300.002133Warning: non-integer x = 1259.998460Warning: non-integer x = 1375.003145Warning: non-integer x = 1298.998764Warning: non-integer x = 1263.000437Warning: non-integer x = 1287.003724Warning: non-integer x = 1223.001489Warning: non-integer x = 1344.996891Warning: non-integer x = 1447.001573Warning: non-integer x = 1498.001886Warning: non-integer x = 1481.999582Warning: non-integer x = 1484.997908Warning: non-integer x = 1679.997894Warning: non-integer x = 1769.004908Warning: non-integer x = 1891.996987Warning: non-integer x = 1853.996169Warning: non-integer x = 1788.998420Warning: non-integer x = 1955.997092Warning: non-integer x = 1919.993811Warning: non-integer x = 1974.995901Warning: non-integer x = 2067.004506Warning: non-integer x = 2055.006385Warning: non-integer x = 2158.001105Warning: non-integer x = 2217.001809Warning: non-integer x = 2109.994891Warning: non-integer x = 2125.001989Warning: non-integer x = 2042.992343Warning: non-integer x = 2148.993026Warning: non-integer x = 1793.005365Warning: non-integer x = 1811.994512Warning: non-integer x = 2061.091589Warning: non-integer x = 2362.141165Warning: non-integer x = 2280.364876Warning: non-integer x = 2255.272142Warning: non-integer x = 2490.637065Warning: non-integer x = 2341.092213Warning: non-integer x = 2608.002201Warning: non-integer x = 2491.293022Warning: non-integer x = 2321.029827Warning: non-integer x = 2612.106535Warning: non-integer x = 2542.189318Warning: non-integer x = 2597.146964Warning: non-integer x = 2639.049803Warning: non-integer x = 2658.146527Warning: non-integer x = 2786.032203Warning: non-integer x = 2752.025868Warning: non-integer x = 550.851174Warning: non-integer x = 576.918975Warning: non-integer x = 546.729350Warning: non-integer x = 507.570428Warning: non-integer x = 527.930260Warning: non-integer x = 498.081313Warning: non-integer x = 570.171728Warning: non-integer x = 584.111765Warning: non-integer x = 522.782058Warning: non-integer x = 620.989903Warning: non-integer x = 543.580594Warning: non-integer x = 642.811513Warning: non-integer x = 596.779235Warning: non-integer x = 659.709397Warning: non-integer x = 637.519492Warning: non-integer x = 670.570790Warning: non-integer x = 767.378718Warning: non-integer x = 699.270692Warning: non-integer x = 626.188052Warning: non-integer x = 716.181426Warning: non-integer x = 795.429371Warning: non-integer x = 757.278449Warning: non-integer x = 775.279678Warning: non-integer x = 834.540689Warning: non-integer x = 819.489374Warning: non-integer x = 870.279294Warning: non-integer x = 936.497408Warning: non-integer x = 897.410636Warning: non-integer x = 968.361936Warning: non-integer x = 956.599892Warning: non-integer x = 926.509344Warning: non-integer x = 1038.431990Warning: non-integer x = 985.799546Warning: non-integer x = 1062.001670Warning: non-integer x = 1142.002961Warning: non-integer x = 1119.000244Warning: non-integer x = 1164.001719Warning: non-integer x = 1092.998341Warning: non-integer x = 1251.000759Warning: non-integer x = 1075.999539Warning: non-integer x = 1184.000279Warning: non-integer x = 1184.996667Warning: non-integer x = 1105.002731Warning: non-integer x = 1189.999027Warning: non-integer x = 1272.997817Warning: non-integer x = 1308.002021Warning: non-integer x = 1278.998016Warning: non-integer x = 1356.000525Warning: non-integer x = 1544.000463Warning: non-integer x = 1409.998776Warning: non-integer x = 1705.996598Warning: non-integer x = 1793.997379Warning: non-integer x = 1679.003765Warning: non-integer x = 1797.001622Warning: non-integer x = 1713.003850Warning: non-integer x = 1830.002327Warning: non-integer x = 1937.006612Warning: non-integer x = 1913.993925Warning: non-integer x = 2056.997749Warning: non-integer x = 2130.998192Warning: non-integer x = 2102.996652Warning: non-integer x = 1998.000813Warning: non-integer x = 2175.002715Warning: non-integer x = 2172.995722Warning: non-integer x = 1920.994086Warning: non-integer x = 1960.998994Warning: non-integer x = 1681.074821Warning: non-integer x = 2042.127896Warning: non-integer x = 2303.365141Warning: non-integer x = 2286.278789Warning: non-integer x = 2367.596975Warning: non-integer x = 2392.109848Warning: non-integer x = 2569.993510Warning: non-integer x = 2599.293164Warning: non-integer x = 2459.045638Warning: non-integer x = 2558.104361Warning: non-integer x = 2633.201142Warning: non-integer x = 2630.147757Warning: non-integer x = 2634.031655Warning: non-integer x = 2689.161161Warning: non-integer x = 3029.041655Warning: non-integer x = 2930.025712Warning: non-integer x = 510.781373Warning: non-integer x = 575.920276Warning: non-integer x = 523.699452Warning: non-integer x = 468.530538Warning: non-integer x = 458.808204Warning: non-integer x = 486.068164Warning: non-integer x = 552.130220Warning: non-integer x = 515.979686Warning: non-integer x = 547.819285Warning: non-integer x = 607.971032Warning: non-integer x = 567.609620Warning: non-integer x = 577.719073Warning: non-integer x = 569.751292Warning: non-integer x = 619.669072Warning: non-integer x = 577.470132Warning: non-integer x = 590.498905Warning: non-integer x = 750.358802Warning: non-integer x = 620.228764Warning: non-integer x = 591.179556Warning: non-integer x = 636.162039Warning: non-integer x = 662.350497Warning: non-integer x = 679.252606Warning: non-integer x = 702.260393Warning: non-integer x = 812.528682Warning: non-integer x = 789.468548Warning: non-integer x = 728.240855Warning: non-integer x = 794.420816Warning: non-integer x = 798.361297Warning: non-integer x = 803.292459Warning: non-integer x = 902.562418Warning: non-integer x = 866.469451Warning: non-integer x = 924.381137Warning: non-integer x = 855.690140Warning: non-integer x = 935.001063Warning: non-integer x = 991.999422Warning: non-integer x = 951.997779Warning: non-integer x = 1032.001026Warning: non-integer x = 955.001460Warning: non-integer x = 1004.999400Warning: non-integer x = 992.998708Warning: non-integer x = 1104.001046Warning: non-integer x = 1080.000506Warning: non-integer x = 965.998613Warning: non-integer x = 1131.001025Warning: non-integer x = 1067.001654Warning: non-integer x = 1117.998633Warning: non-integer x = 1241.999152Warning: non-integer x = 1287.998303Warning: non-integer x = 1252.998777Warning: non-integer x = 1253.002677Warning: non-integer x = 1556.000846Warning: non-integer x = 1565.997572Warning: non-integer x = 1625.003164Warning: non-integer x = 1577.000865Warning: non-integer x = 1579.002393Warning: non-integer x = 1703.002284Warning: non-integer x = 1762.002474Warning: non-integer x = 1818.994812Warning: non-integer x = 1998.003421Warning: non-integer x = 1920.006510Warning: non-integer x = 1909.994549Warning: non-integer x = 2007.998850Warning: non-integer x = 1996.001970Warning: non-integer x = 1816.997180Warning: non-integer x = 1973.996734Warning: non-integer x = 1736.065744Warning: non-integer x = 1668.095611Warning: non-integer x = 2010.316872Warning: non-integer x = 2140.251480Warning: non-integer x = 2169.542240Warning: non-integer x = 2256.107829Warning: non-integer x = 2534.993916Warning: non-integer x = 2415.288918Warning: non-integer x = 2550.029809Warning: non-integer x = 2665.095596Warning: non-integer x = 2582.182540Warning: non-integer x = 2611.145550Warning: non-integer x = 2693.049159Warning: non-integer x = 2611.133618Warning: non-integer x = 3112.048741Warning: non-integer x = 3049.051049Warning: non-integer x = 332.509663Warning: non-integer x = 362.580415Warning: non-integer x = 331.441164Warning: non-integer x = 298.328900Warning: non-integer x = 324.568829Warning: non-integer x = 320.699986Warning: non-integer x = 342.699580Warning: non-integer x = 343.649153Warning: non-integer x = 298.450337Warning: non-integer x = 445.709789Warning: non-integer x = 383.410434Warning: non-integer x = 416.519237Warning: non-integer x = 419.551984Warning: non-integer x = 416.448811Warning: non-integer x = 466.380872Warning: non-integer x = 432.371917Warning: non-integer x = 538.259324Warning: non-integer x = 464.180340Warning: non-integer x = 442.141253Warning: non-integer x = 504.131444Warning: non-integer x = 551.289717Warning: non-integer x = 548.209614Warning: non-integer x = 617.219834Warning: non-integer x = 611.400284Warning: non-integer x = 628.379805Warning: non-integer x = 596.187670Warning: non-integer x = 707.379841Warning: non-integer x = 715.322028Warning: non-integer x = 680.250561Warning: non-integer x = 768.480428Warning: non-integer x = 733.409867Warning: non-integer x = 742.310144Warning: non-integer x = 722.580438Warning: non-integer x = 751.001428Warning: non-integer x = 814.999651Warning: non-integer x = 763.997932Warning: non-integer x = 919.999430Warning: non-integer x = 782.999364Warning: non-integer x = 914.000340Warning: non-integer x = 916.000157Warning: non-integer x = 949.001749Warning: non-integer x = 885.998028Warning: non-integer x = 967.001694Warning: non-integer x = 931.998245Warning: non-integer x = 976.000611Warning: non-integer x = 973.002236Warning: non-integer x = 1019.002233Warning: non-integer x = 1123.001347Warning: non-integer x = 1388.998388Warning: non-integer x = 1377.998780Warning: non-integer x = 1360.002844Warning: non-integer x = 1473.998382Warning: non-integer x = 1343.997034Warning: non-integer x = 1525.003012Warning: non-integer x = 1702.996431Warning: non-integer x = 1655.997437Warning: non-integer x = 1661.995739Warning: non-integer x = 1832.004299Warning: non-integer x = 1928.003514Warning: non-integer x = 1845.000912Warning: non-integer x = 1836.997912Warning: non-integer x = 1842.001373Warning: non-integer x = 1828.003593Warning: non-integer x = 1839.997141Warning: non-integer x = 1660.064944Warning: non-integer x = 1802.097452Warning: non-integer x = 1678.253996Warning: non-integer x = 2037.235571Warning: non-integer x = 2216.558001Warning: non-integer x = 2104.103462Warning: non-integer x = 2451.003457Warning: non-integer x = 2414.277381Warning: non-integer x = 2465.031788Warning: non-integer x = 2556.081508Warning: non-integer x = 2589.198062Warning: non-integer x = 2461.137408Warning: non-integer x = 2723.050527Warning: non-integer x = 2589.150714Warning: non-integer x = 2978.051068Warning: non-integer x = 3065.056784
StMoMo: Finish fitting with gnm
plot(CBDfit)

Inspect goodness-of-fit

# Calculate residuals
LCres <- residuals(LCfit)
CBDres <- residuals(CBDfit)

# Plot in residual heatmaps
plot(LCres, type = "colourmap", reslim = c(-3.5, 3.5))

plot(CBDres, type = "colourmap", reslim = c(-3.5, 3.5))

Forecasting Forecasting depends on random variable kappa and cohort-specific effects

# ARIMA(p,q,d) to forecast cohort-specific effects
pqd <- c(1,0,0) #choose ARIMA

# Forecast 50 years ahead
LCfor  <- forecast(LCfit, h = 50)
CBDfor <- forecast(CBDfit, h = 50)

# Forecast with more functions
# Research what gc.order and gc.include.constant are for
# Since Lee-Carter and CBD do not have cohort effect in model, they are not relevant?
LCfor1 <- forecast(LCfit, h = 50, gc.order = pqd, gc.include.constant = FALSE)
CBDfor1 <- forecast(CBDfit, h = 50, gc.order = pqd, gc.include.constant = FALSE)

# Plot forecasts
plot(LCfor, parametricbx = FALSE)

plot(CBDfor, parametricbx = FALSE)

Simulations Simulate trajectories data based on fitted models

# Simulate 1000 cases 50 years ahead
LCsim <- simulate(LCfit, nsim = 1000, h = 50)
CBDsim <- simulate(CBDfit, nsim = 1000, h = 50)

# Plot period index trajectories for the Lee-Carter model
plot(LCfit$years, LCfit$kt[1,], type = "l", xlim = c(1960, 2060), ylim = c(-80, 20), xlab = "year", ylab = "kappa_t", main = "Period index (Lee-Carter)")
matlines(LCsim$kt.s$years, LCsim$kt.s$sim[1,,1:20], type = "l", lty = 1)


# Display fancharts to show confidence intervals of projections
install.packages("fanplot")
Error in install.packages : Updating loaded packages
library(fanplot)
mxt <- LCfit$Dxt/LCfit$Ext
plot(LCfit$years, mxt["65",], xlim = c(1970,2041), ylim = c(0.002, 0.045), pch = 20, log = "y", xlab = "year", ylab = "m(65,t) (log scale)")
fan(t(LCsim$rates["65",,]), start = 2015, probs = c(2.5, 10, 25, 50, 75, 90, 97.5), n.fan = 4, ln = NULL, fan.col = colorRampPalette(c("black","white")))

Bootstrapping StMoMo implements: -> Semiparametric bootstrapping (Brouhns et al., 2005) -> Residuals bootstrapping (Koissi et al., 2006)

LCboot <- bootstrap(LCfit, nBoot = 500)
install.packages("fanplot")
WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:

https://cran.rstudio.com/bin/windows/Rtools/
Warning in install.packages :
  package ‘fanplot’ is in use and will not be installed
plot(LCboot, nCol = 3)

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dGUoYygiYmxhY2siLCJ3aGl0ZSIpKSkNCg0KYGBgDQoNCkJvb3RzdHJhcHBpbmcNClN0TW9NbyBpbXBsZW1lbnRzOg0KLT4gU2VtaXBhcmFtZXRyaWMgYm9vdHN0cmFwcGluZyAoQnJvdWhucyBldCBhbC4sIDIwMDUpDQotPiBSZXNpZHVhbHMgYm9vdHN0cmFwcGluZyAoS29pc3NpIGV0IGFsLiwgMjAwNikNCmBgYHtyfQ0KTENib290IDwtIGJvb3RzdHJhcChMQ2ZpdCwgbkJvb3QgPSA1MDApDQpwbG90KExDYm9vdCwgbkNvbCA9IDMpDQpgYGANCg0K