Life Insurance 2 Paper Code

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)

Loading required package: gnm
Loading required package: forecast

# There are packages that link to Human Mortality Database
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/
Installing package into ‘C:/Users/Frederick/AppData/Local/R/win-library/4.3’
(as ‘lib’ is unspecified)
trying URL 'https://cloud.r-project.org/bin/windows/contrib/4.3/demography_2.0.zip'
Content type 'application/zip' length 3601084 bytes (3.4 MB)
downloaded 3.4 MB

package ‘demography’ successfully unpacked and MD5 sums checked

The downloaded binary packages are in
    C:\Users\Frederick\AppData\Local\Temp\Rtmp6dQCra\downloaded_packages

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

library(demography)

Registered S3 method overwritten by 'htmlwidgets':
  method           from         
  print.htmlwidget tools:rstudio
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     
Registered S3 methods overwritten by 'demography':
  method      from 
  print.lca   e1071
  summary.lca e1071
This is demography 2.0 

# 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")
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 = "male")
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

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 = 512.123053Warning: non-integer x = 529.130450Warning: non-integer x = 461.879779Warning: non-integer x = 504.188399Warning: non-integer x = 492.515161Warning: non-integer x = 492.732846Warning: non-integer x = 526.716804Warning: non-integer x = 454.364485Warning: non-integer x = 498.184328Warning: non-integer x = 442.881615Warning: non-integer x = 438.634836Warning: non-integer x = 491.758997Warning: non-integer x = 398.584587Warning: non-integer x = 403.596456Warning: non-integer x = 391.735094Warning: non-integer x = 401.760047Warning: non-integer x = 480.590448Warning: non-integer x = 472.440221Warning: non-integer x = 355.406263Warning: non-integer x = 399.297496Warning: non-integer x = 409.509954Warning: non-integer x = 423.333747Warning: non-integer x = 393.273017Warning: non-integer x = 409.385462Warning: non-integer x = 378.408755Warning: non-integer x = 415.348470Warning: non-integer x = 452.352423Warning: non-integer x = 407.412570Warning: non-integer x = 342.313898Warning: non-integer x = 359.365996Warning: non-integer x = 354.309780Warning: non-integer x = 415.498486Warning: non-integer x = 385.687916Warning: non-integer x = 414.018661Warning: non-integer x = 437.019825Warning: non-integer x = 474.012371Warning: non-integer x = 495.018716Warning: non-integer x = 426.024895Warning: non-integer x = 391.996033Warning: non-integer x = 423.002036Warning: non-integer x = 419.999207Warning: non-integer x = 465.994557Warning: non-integer x = 423.023211Warning: non-integer x = 410.012301Warning: non-integer x = 435.004976Warning: non-integer x = 419.988681Warning: non-integer x = 417.987734Warning: non-integer x = 386.972926Warning: non-integer x = 363.004372Warning: non-integer x = 350.981064Warning: non-integer x = 337.007727Warning: non-integer x = 346.013989Warning: non-integer x = 313.985385Warning: non-integer x = 355.023957Warning: non-integer x = 310.979926Warning: non-integer x = 358.995494Warning: non-integer x = 326.028474Warning: non-integer x = 350.984966Warning: non-integer x = 363.014809Warning: non-integer x = 353.996588Warning: non-integer x = 364.021685Warning: non-integer x = 336.981039Warning: non-integer x = 367.023444Warning: non-integer x = 384.008390Warning: non-integer x = 371.969998Warning: non-integer x = 426.982395Warning: non-integer x = 369.140806Warning: non-integer x = 357.094257Warning: non-integer x = 405.099789Warning: non-integer x = 383.153996Warning: non-integer x = 355.100430Warning: non-integer x = 373.064230Warning: non-integer x = 345.032777Warning: non-integer x = 379.146666Warning: non-integer x = 327.076924Warning: non-integer x = 321.052298Warning: non-integer x = 339.064440Warning: non-integer x = 310.044981Warning: non-integer x = 291.035386Warning: non-integer x = 265.103325Warning: non-integer x = 297.121035Warning: non-integer x = 304.048054Warning: non-integer x = 404.861566Warning: non-integer x = 371.783667Warning: non-integer x = 359.695320Warning: non-integer x = 344.825747Warning: non-integer x = 402.228904Warning: non-integer x = 365.264680Warning: non-integer x = 411.335878Warning: non-integer x = 352.066871Warning: non-integer x = 400.935923Warning: non-integer x = 371.729889Warning: non-integer x = 361.543927Warning: non-integer x = 424.659825Warning: non-integer x = 381.570922Warning: non-integer x = 315.487124Warning: non-integer x = 389.709691Warning: non-integer x = 380.704769Warning: non-integer x = 405.501580Warning: non-integer x = 429.409211Warning: non-integer x = 384.435684Warning: non-integer x = 369.260911Warning: non-integer x = 378.470881Warning: non-integer x = 412.318927Warning: non-integer x = 423.287064Warning: non-integer x = 420.393619Warning: non-integer x = 466.459741Warning: non-integer x = 425.325088Warning: non-integer x = 422.317232Warning: non-integer x = 401.384475Warning: non-integer x = 371.332391Warning: non-integer x = 372.379512Warning: non-integer x = 309.283226Warning: non-integer x = 404.474094Warning: non-integer x = 417.719021Warning: non-integer x = 397.019623Warning: non-integer x = 387.008922Warning: non-integer x = 454.994749Warning: non-integer x = 483.013373Warning: non-integer x = 449.013062Warning: non-integer x = 465.985755Warning: non-integer x = 433.013648Warning: non-integer x = 505.009886Warning: non-integer x = 477.017136Warning: non-integer x = 479.002715Warning: non-integer x = 495.974444Warning: non-integer x = 436.997980Warning: non-integer x = 408.977126Warning: non-integer x = 442.002009Warning: non-integer x = 412.993184Warning: non-integer x = 423.987559Warning: non-integer x = 402.024315Warning: non-integer x = 372.990189Warning: non-integer x = 363.983278Warning: non-integer x = 343.004427Warning: non-integer x = 314.997977Warning: non-integer x = 341.009204Warning: non-integer x = 334.979755Warning: non-integer x = 352.994817Warning: non-integer x = 368.985298Warning: non-integer x = 380.998814Warning: non-integer x = 382.996173Warning: non-integer x = 358.013859Warning: non-integer x = 341.004550Warning: non-integer x = 403.973618Warning: non-integer x = 388.973706Warning: non-integer x = 383.031457Warning: non-integer x = 430.993483Warning: non-integer x = 384.155402Warning: non-integer x = 411.092375Warning: non-integer x = 410.072417Warning: non-integer x = 376.166859Warning: non-integer x = 378.166560Warning: non-integer x = 423.130324Warning: non-integer x = 386.046904Warning: non-integer x = 384.144161Warning: non-integer x = 392.100145Warning: non-integer x = 332.079336Warning: non-integer x = 360.023970Warning: non-integer x = 386.060748Warning: non-integer x = 347.011382Warning: non-integer x = 330.092945Warning: non-integer x = 308.079444Warning: non-integer x = 345.063581Warning: non-integer x = 450.987015Warning: non-integer x = 527.119070Warning: non-integer x = 480.930757Warning: non-integer x = 479.113221Warning: non-integer x = 484.480078Warning: non-integer x = 522.834485Warning: non-integer x = 497.635197Warning: non-integer x = 450.373453Warning: non-integer x = 475.108592Warning: non-integer x = 506.006172Warning: non-integer x = 408.588986Warning: non-integer x = 466.744484Warning: non-integer x = 442.668568Warning: non-integer x = 407.599972Warning: non-integer x = 397.767067Warning: non-integer x = 485.948138Warning: non-integer x = 496.626821Warning: non-integer x = 505.494583Warning: non-integer x = 424.500502Warning: non-integer x = 440.322376Warning: non-integer x = 437.550963Warning: non-integer x = 444.309721Warning: non-integer x = 462.326723Warning: non-integer x = 467.408611Warning: non-integer x = 449.457914Warning: non-integer x = 470.374494Warning: non-integer x = 479.363544Warning: non-integer x = 504.487329Warning: non-integer x = 446.401876Warning: non-integer x = 427.422544Warning: non-integer x = 373.326209Warning: non-integer x = 398.466711Warning: non-integer x = 425.732999Warning: non-integer x = 467.030117Warning: non-integer x = 507.003094Warning: non-integer x = 512.979939Warning: non-integer x = 541.012426Warning: non-integer x = 513.976119Warning: non-integer x = 475.001244Warning: non-integer x = 487.979260Warning: non-integer x = 499.006209Warning: non-integer x = 518.002667Warning: non-integer x = 474.006626Warning: non-integer x = 464.020663Warning: non-integer x = 496.987664Warning: non-integer x = 432.993999Warning: non-integer x = 447.999693Warning: non-integer x = 432.021699Warning: non-integer x = 434.013160Warning: non-integer x = 342.026516Warning: non-integer x = 394.974771Warning: non-integer x = 388.009113Warning: non-integer x = 383.985865Warning: non-integer x = 360.983552Warning: non-integer x = 369.005675Warning: non-integer x = 364.985352Warning: non-integer x = 417.992374Warning: non-integer x = 369.006150Warning: non-integer x = 400.020535Warning: non-integer x = 364.980865Warning: non-integer x = 361.972660Warning: non-integer x = 426.980552Warning: non-integer x = 399.026960Warning: non-integer x = 397.010084Warning: non-integer x = 411.015294Warning: non-integer x = 381.995688Warning: non-integer x = 418.188900Warning: non-integer x = 464.117210Warning: non-integer x = 405.076313Warning: non-integer x = 414.177083Warning: non-integer x = 411.177608Warning: non-integer x = 453.086839Warning: non-integer x = 383.091881Warning: non-integer x = 459.154456Warning: non-integer x = 452.143647Warning: non-integer x = 386.062479Warning: non-integer x = 420.033116Warning: non-integer x = 399.097110Warning: non-integer x = 367.046627Warning: non-integer x = 366.113380Warning: non-integer x = 368.068255Warning: non-integer x = 372.029255Warning: non-integer x = 417.895374Warning: non-integer x = 496.073798Warning: non-integer x = 484.945402Warning: non-integer x = 491.140016Warning: non-integer x = 501.516394Warning: non-integer x = 486.705076Warning: non-integer x = 510.691875Warning: non-integer x = 451.354674Warning: non-integer x = 454.085044Warning: non-integer x = 483.945579Warning: non-integer x = 420.625351Warning: non-integer x = 481.775584Warning: non-integer x = 421.639750Warning: non-integer x = 470.685259Warning: non-integer x = 450.840379Warning: non-integer x = 399.750807Warning: non-integer x = 518.639748Warning: non-integer x = 486.485846Warning: non-integer x = 438.499677Warning: non-integer x = 442.326717Warning: non-integer x = 477.572648Warning: non-integer x = 464.343262Warning: non-integer x = 474.298797Warning: non-integer x = 497.479647Warning: non-integer x = 524.542456Warning: non-integer x = 520.413151Warning: non-integer x = 586.481017Warning: non-integer x = 497.505591Warning: non-integer x = 479.452456Warning: non-integer x = 487.461472Warning: non-integer x = 453.401836Warning: non-integer x = 431.518206Warning: non-integer x = 389.669916Warning: non-integer x = 501.023494Warning: non-integer x = 494.021166Warning: non-integer x = 535.981481Warning: non-integer x = 576.997091Warning: non-integer x = 559.980547Warning: non-integer x = 541.001259Warning: non-integer x = 522.003155Warning: non-integer x = 487.977897Warning: non-integer x = 535.995608Warning: non-integer x = 485.988635Warning: non-integer x = 508.001823Warning: non-integer x = 507.010506Warning: non-integer x = 548.000235Warning: non-integer x = 465.992750Warning: non-integer x = 480.996461Warning: non-integer x = 459.011442Warning: non-integer x = 484.988174Warning: non-integer x = 475.004430Warning: non-integer x = 466.993618Warning: non-integer x = 445.002942Warning: non-integer x = 446.983038Warning: non-integer x = 392.986697Warning: non-integer x = 338.007127Warning: non-integer x = 435.024247Warning: non-integer x = 421.008414Warning: non-integer x = 425.982309Warning: non-integer x = 419.989940Warning: non-integer x = 393.987105Warning: non-integer x = 399.974150Warning: non-integer x = 467.017242Warning: non-integer x = 439.008746Warning: non-integer x = 427.992970Warning: non-integer x = 420.019764Warning: non-integer x = 428.208795Warning: non-integer x = 434.149811Warning: non-integer x = 444.110305Warning: non-integer x = 499.199701Warning: non-integer x = 455.195094Warning: non-integer x = 485.128804Warning: non-integer x = 496.051421Warning: non-integer x = 428.172903Warning: non-integer x = 426.098856Warning: non-integer x = 407.086122Warning: non-integer x = 402.057754Warning: non-integer x = 432.110555Warning: non-integer x = 425.033677Warning: non-integer x = 432.147452Warning: non-integer x = 450.093020Warning: non-integer x = 381.029433Warning: non-integer x = 500.090131Warning: non-integer x = 500.062749Warning: non-integer x = 490.952914Warning: non-integer x = 447.031106Warning: non-integer x = 549.687076Warning: non-integer x = 518.808598Warning: non-integer x = 532.739757Warning: non-integer x = 455.362057Warning: non-integer x = 470.132180Warning: non-integer x = 543.071665Warning: non-integer x = 456.667539Warning: non-integer x = 461.731239Warning: non-integer x = 420.632468Warning: non-integer x = 387.586438Warning: non-integer x = 481.897759Warning: non-integer x = 548.054228Warning: non-integer x = 523.660312Warning: non-integer x = 511.494721Warning: non-integer x = 461.536806Warning: non-integer x = 491.340946Warning: non-integer x = 445.549049Warning: non-integer x = 481.375758Warning: non-integer x = 514.344270Warning: non-integer x = 502.444769Warning: non-integer x = 546.556383Warning: non-integer x = 519.410216Warning: non-integer x = 573.456654Warning: non-integer x = 608.593699Warning: non-integer x = 549.502497Warning: non-integer x = 573.571648Warning: non-integer x = 467.421228Warning: non-integer x = 477.584939Warning: non-integer x = 462.788470Warning: non-integer x = 360.999294Warning: non-integer x = 504.979534Warning: non-integer x = 622.991534Warning: non-integer x = 590.999379Warning: non-integer x = 578.981426Warning: non-integer x = 521.008182Warning: non-integer x = 534.010217Warning: non-integer x = 560.016190Warning: non-integer x = 534.004289Warning: non-integer x = 555.021262Warning: non-integer x = 564.996644Warning: non-integer x = 574.016465Warning: non-integer x = 581.991724Warning: non-integer x = 530.026236Warning: non-integer x = 546.007129Warning: non-integer x = 528.991398Warning: non-integer x = 500.989866Warning: non-integer x = 520.018243Warning: non-integer x = 467.999757Warning: non-integer x = 486.010185Warning: non-integer x = 486.012065Warning: non-integer x = 419.990063Warning: non-integer x = 371.020705Warning: non-integer x = 409.996184Warning: non-integer x = 387.020931Warning: non-integer x = 413.006986Warning: non-integer x = 427.016281Warning: non-integer x = 430.992094Warning: non-integer x = 421.006414Warning: non-integer x = 411.978195Warning: non-integer x = 467.982759Warning: non-integer x = 450.999608Warning: non-integer x = 438.985184Warning: non-integer x = 451.171337Warning: non-integer x = 469.127959Warning: non-integer x = 474.090485Warning: non-integer x = 459.194102Warning: non-integer x = 488.200391Warning: non-integer x = 470.104432Warning: non-integer x = 489.094545Warning: non-integer x = 447.152814Warning: non-integer x = 459.143537Warning: non-integer x = 432.067880Warning: non-integer x = 466.082405Warning: non-integer x = 422.128650Warning: non-integer x = 430.026325Warning: non-integer x = 414.122870Warning: non-integer x = 439.125295Warning: non-integer x = 470.085715Warning: non-integer x = 546.184082Warning: non-integer x = 610.296357Warning: non-integer x = 527.022038Warning: non-integer x = 535.249845Warning: non-integer x = 582.772511Warning: non-integer x = 605.116058Warning: non-integer x = 558.829484Warning: non-integer x = 518.548445Warning: non-integer x = 499.175801Warning: non-integer x = 506.010947Warning: non-integer x = 458.678128Warning: non-integer x = 470.762549Warning: non-integer x = 452.663977Warning: non-integer x = 449.664305Warning: non-integer x = 439.808175Warning: non-integer x = 579.091879Warning: non-integer x = 625.796859Warning: non-integer x = 539.516914Warning: non-integer x = 445.514162Warning: non-integer x = 462.340188Warning: non-integer x = 505.594545Warning: non-integer x = 491.364808Warning: non-integer x = 511.350316Warning: non-integer x = 528.461003Warning: non-integer x = 544.546941Warning: non-integer x = 579.443153Warning: non-integer x = 655.505164Warning: non-integer x = 605.609189Warning: non-integer x = 564.537710Warning: non-integer x = 590.581642Warning: non-integer x = 523.460457Warning: non-integer x = 538.620581Warning: non-integer x = 482.822258Warning: non-integer x = 442.001935Warning: non-integer x = 438.993519Warning: non-integer x = 587.992262Warning: non-integer x = 643.977305Warning: non-integer x = 564.005081Warning: non-integer x = 577.986086Warning: non-integer x = 567.986288Warning: non-integer x = 630.987731Warning: non-integer x = 581.975987Warning: non-integer x = 552.002801Warning: non-integer x = 565.982127Warning: non-integer x = 617.004093Warning: non-integer x = 581.023872Warning: non-integer x = 642.003885Warning: non-integer x = 546.976475Warning: non-integer x = 590.997714Warning: non-integer x = 520.002885Warning: non-integer x = 520.982150Warning: non-integer x = 562.023808Warning: non-integer x = 555.011524Warning: non-integer x = 554.025981Warning: non-integer x = 456.993174Warning: non-integer x = 449.999211Warning: non-integer x = 460.991113Warning: non-integer x = 424.982192Warning: non-integer x = 466.002817Warning: non-integer x = 464.012612Warning: non-integer x = 437.995255Warning: non-integer x = 506.995783Warning: non-integer x = 421.020159Warning: non-integer x = 444.972676Warning: non-integer x = 472.005803Warning: non-integer x = 501.999152Warning: non-integer x = 494.202295Warning: non-integer x = 467.126298Warning: non-integer x = 492.080091Warning: non-integer x = 453.239916Warning: non-integer x = 511.221438Warning: non-integer x = 511.136665Warning: non-integer x = 487.045960Warning: non-integer x = 493.144879Warning: non-integer x = 481.103578Warning: non-integer x = 522.139839Warning: non-integer x = 468.056905Warning: non-integer x = 466.103622Warning: non-integer x = 488.090742Warning: non-integer x = 471.141053Warning: non-integer x = 486.132467Warning: non-integer x = 504.094496Warning: non-integer x = 530.146500Warning: non-integer x = 515.096323Warning: non-integer x = 584.143651Warning: non-integer x = 520.223098Warning: non-integer x = 593.810278Warning: non-integer x = 543.899767Warning: non-integer x = 592.957898Warning: non-integer x = 520.581466Warning: non-integer x = 512.205519Warning: non-integer x = 570.117867Warning: non-integer x = 486.720875Warning: non-integer x = 542.870047Warning: non-integer x = 478.697077Warning: non-integer x = 527.807773Warning: non-integer x = 516.946815Warning: non-integer x = 499.975082Warning: non-integer x = 598.747823Warning: non-integer x = 632.605496Warning: non-integer x = 457.503291Warning: non-integer x = 500.358260Warning: non-integer x = 536.666658Warning: non-integer x = 583.434192Warning: non-integer x = 524.361421Warning: non-integer x = 581.521803Warning: non-integer x = 599.601269Warning: non-integer x = 589.464828Warning: non-integer x = 684.568814Warning: non-integer x = 634.598172Warning: non-integer x = 552.533808Warning: non-integer x = 686.670868Warning: non-integer x = 593.518487Warning: non-integer x = 626.751286Warning: non-integer x = 502.882273Warning: non-integer x = 520.998226Warning: non-integer x = 470.008620Warning: non-integer x = 502.991144Warning: non-integer x = 625.989921Warning: non-integer x = 680.008524Warning: non-integer x = 621.014200Warning: non-integer x = 602.004481Warning: non-integer x = 586.020396Warning: non-integer x = 634.997450Warning: non-integer x = 664.983887Warning: non-integer x = 683.024793Warning: non-integer x = 613.985060Warning: non-integer x = 619.012853Warning: non-integer x = 633.990152Warning: non-integer x = 594.010951Warning: non-integer x = 585.011949Warning: non-integer x = 568.975316Warning: non-integer x = 575.992884Warning: non-integer x = 567.994891Warning: non-integer x = 587.010273Warning: non-integer x = 583.983318Warning: non-integer x = 524.996853Warning: non-integer x = 504.997520Warning: non-integer x = 500.000363Warning: non-integer x = 467.999548Warning: non-integer x = 437.004682Warning: non-integer x = 483.023112Warning: non-integer x = 440.012824Warning: non-integer x = 483.999063Warning: non-integer x = 473.976096Warning: non-integer x = 488.993749Warning: non-integer x = 486.026092Warning: non-integer x = 531.986352Warning: non-integer x = 468.238103Warning: non-integer x = 516.164172Warning: non-integer x = 461.131398Warning: non-integer x = 493.190602Warning: non-integer x = 494.208661Warning: non-integer x = 473.101448Warning: non-integer x = 529.080049Warning: non-integer x = 519.176895Warning: non-integer x = 537.133837Warning: non-integer x = 499.089894Warning: non-integer x = 533.075179Warning: non-integer x = 512.094125Warning: non-integer x = 495.038763Warning: non-integer x = 476.171266Warning: non-integer x = 495.154063Warning: non-integer x = 543.062984Warning: non-integer x = 507.097211Warning: non-integer x = 502.064989Warning: non-integer x = 521.014760Warning: non-integer x = 497.170536Warning: non-integer x = 530.630305Warning: non-integer x = 501.766643Warning: non-integer x = 544.800274Warning: non-integer x = 473.406622Warning: non-integer x = 497.169326Warning: non-integer x = 545.104071Warning: non-integer x = 500.742552Warning: non-integer x = 520.826192Warning: non-integer x = 501.751227Warning: non-integer x = 503.753526Warning: non-integer x = 513.954251Warning: non-integer x = 504.965525Warning: non-integer x = 579.708883Warning: non-integer x = 597.553070Warning: non-integer x = 547.636336Warning: non-integer x = 520.369398Warning: non-integer x = 574.703693Warning: non-integer x = 584.443023Warning: non-integer x = 571.398441Warning: non-integer x = 611.576993Warning: non-integer x = 655.671206Warning: non-integer x = 619.495570Warning: non-integer x = 686.552810Warning: non-integer x = 653.650982Warning: non-integer x = 703.658515Warning: non-integer x = 643.647914Warning: non-integer x = 634.585925Warning: non-integer x = 634.763605Warning: non-integer x = 624.075507Warning: non-integer x = 596.998091Warning: non-integer x = 578.998658Warning: non-integer x = 604.003326Warning: non-integer x = 562.996730Warning: non-integer x = 644.010680Warning: non-integer x = 675.990904Warning: non-integer x = 616.016119Warning: non-integer x = 672.995949Warning: non-integer x = 725.987936Warning: non-integer x = 656.019792Warning: non-integer x = 739.000197Warning: non-integer x = 671.984277Warning: non-integer x = 614.984984Warning: non-integer x = 695.004034Warning: non-integer x = 681.003252Warning: non-integer x = 632.008963Warning: non-integer x = 626.990370Warning: non-integer x = 652.025751Warning: non-integer x = 579.994564Warning: non-integer x = 614.997874Warning: non-integer x = 644.027101Warning: non-integer x = 554.999225Warning: non-integer x = 583.974162Warning: non-integer x = 604.973473Warning: non-integer x = 496.006055Warning: non-integer x = 486.009577Warning: non-integer x = 490.003999Warning: non-integer x = 502.988054Warning: non-integer x = 475.013492Warning: non-integer x = 499.995862Warning: non-integer x = 529.027478Warning: non-integer x = 485.013975Warning: non-integer x = 528.993353Warning: non-integer x = 590.265576Warning: non-integer x = 525.137639Warning: non-integer x = 522.114035Warning: non-integer x = 546.254154Warning: non-integer x = 541.230431Warning: non-integer x = 552.118693Warning: non-integer x = 545.062936Warning: non-integer x = 568.160537Warning: non-integer x = 550.116311Warning: non-integer x = 497.088584Warning: non-integer x = 564.071622Warning: non-integer x = 538.104472Warning: non-integer x = 557.054684Warning: non-integer x = 499.194513Warning: non-integer x = 556.176734Warning: non-integer x = 589.076261Warning: non-integer x = 573.234591Warning: non-integer x = 607.291413Warning: non-integer x = 536.023755Warning: non-integer x = 576.345724Warning: non-integer x = 630.939042Warning: non-integer x = 600.104948Warning: non-integer x = 650.140127Warning: non-integer x = 571.710425Warning: non-integer x = 557.308680Warning: non-integer x = 612.214081Warning: non-integer x = 526.776791Warning: non-integer x = 582.925478Warning: non-integer x = 547.806870Warning: non-integer x = 490.740074Warning: non-integer x = 527.998661Warning: non-integer x = 568.090751Warning: non-integer x = 647.811648Warning: non-integer x = 547.518386Warning: non-integer x = 604.676638Warning: non-integer x = 606.423191Warning: non-integer x = 565.682706Warning: non-integer x = 613.448346Warning: non-integer x = 555.381083Warning: non-integer x = 655.599150Warning: non-integer x = 661.664594Warning: non-integer x = 662.545971Warning: non-integer x = 746.571771Warning: non-integer x = 674.656155Warning: non-integer x = 711.677321Warning: non-integer x = 831.815707Warning: non-integer x = 634.547187Warning: non-integer x = 734.855132Warning: non-integer x = 633.112804Warning: non-integer x = 676.995269Warning: non-integer x = 649.008192Warning: non-integer x = 669.018636Warning: non-integer x = 688.985843Warning: non-integer x = 535.017971Warning: non-integer x = 679.993554Warning: non-integer x = 662.003233Warning: non-integer x = 728.003668Warning: non-integer x = 707.993888Warning: non-integer x = 668.992646Warning: non-integer x = 701.013153Warning: non-integer x = 779.999608Warning: non-integer x = 716.023582Warning: non-integer x = 665.025057Warning: non-integer x = 671.986044Warning: non-integer x = 721.980240Warning: non-integer x = 670.025949Warning: non-integer x = 721.007742Warning: non-integer x = 708.001684Warning: non-integer x = 647.999134Warning: non-integer x = 658.975306Warning: non-integer x = 607.004685Warning: non-integer x = 577.015575Warning: non-integer x = 604.979957Warning: non-integer x = 597.979638Warning: non-integer x = 531.999655Warning: non-integer x = 495.993272Warning: non-integer x = 507.022606Warning: non-integer x = 508.010281Warning: non-integer x = 553.978003Warning: non-integer x = 515.021661Warning: non-integer x = 525.981930Warning: non-integer x = 540.019021Warning: non-integer x = 583.278742Warning: non-integer x = 551.201181Warning: non-integer x = 587.120436Warning: non-integer x = 556.228002Warning: non-integer x = 594.198511Warning: non-integer x = 585.123179Warning: non-integer x = 521.078743Warning: non-integer x = 581.216824Warning: non-integer x = 554.111904Warning: non-integer x = 590.107648Warning: non-integer x = 577.089173Warning: non-integer x = 582.144253Warning: non-integer x = 586.096379Warning: non-integer x = 547.148241Warning: non-integer x = 626.195009Warning: non-integer x = 577.085636Warning: non-integer x = 555.199230Warning: non-integer x = 549.175729Warning: non-integer x = 557.085383Warning: non-integer x = 478.130455Warning: non-integer x = 540.665118Warning: non-integer x = 562.968076Warning: non-integer x = 584.917613Warning: non-integer x = 529.596501Warning: non-integer x = 534.281522Warning: non-integer x = 586.160242Warning: non-integer x = 513.764411Warning: non-integer x = 554.889123Warning: non-integer x = 547.822607Warning: non-integer x = 545.821053Warning: non-integer x = 531.986896Warning: non-integer x = 517.990329Warning: non-integer x = 582.732907Warning: non-integer x = 601.572160Warning: non-integer x = 570.642251Warning: non-integer x = 593.439384Warning: non-integer x = 642.752293Warning: non-integer x = 615.475336Warning: non-integer x = 675.449578Warning: non-integer x = 659.597629Warning: non-integer x = 690.717744Warning: non-integer x = 747.592407Warning: non-integer x = 785.609346Warning: non-integer x = 774.767156Warning: non-integer x = 720.680621Warning: non-integer x = 779.781542Warning: non-integer x = 718.627415Warning: non-integer x = 781.935482Warning: non-integer x = 748.289586Warning: non-integer x = 715.028256Warning: non-integer x = 708.004392Warning: non-integer x = 741.020214Warning: non-integer x = 731.983003Warning: non-integer x = 663.002078Warning: non-integer x = 587.997807Warning: non-integer x = 658.989096Warning: non-integer x = 728.022377Warning: non-integer x = 711.988069Warning: non-integer x = 727.986641Warning: non-integer x = 782.975517Warning: non-integer x = 799.013820Warning: non-integer x = 806.983608Warning: non-integer x = 753.006817Warning: non-integer x = 716.996506Warning: non-integer x = 717.987356Warning: non-integer x = 678.020457Warning: non-integer x = 755.016456Warning: non-integer x = 788.989626Warning: non-integer x = 680.977710Warning: non-integer x = 746.982709Warning: non-integer x = 689.011352Warning: non-integer x = 705.025428Warning: non-integer x = 703.974812Warning: non-integer x = 670.978783Warning: non-integer x = 624.998101Warning: non-integer x = 592.008283Warning: non-integer x = 600.978618Warning: non-integer x = 533.991725Warning: non-integer x = 590.003196Warning: non-integer x = 589.991275Warning: non-integer x = 498.002119Warning: non-integer x = 613.985844Warning: non-integer x = 547.261785Warning: non-integer x = 545.168935Warning: non-integer x = 552.135625Warning: non-integer x = 557.250443Warning: non-integer x = 591.240829Warning: non-integer x = 549.123798Warning: non-integer x = 582.094462Warning: non-integer x = 575.191101Warning: non-integer x = 611.165797Warning: non-integer x = 561.108211Warning: non-integer x = 611.099541Warning: non-integer x = 643.120658Warning: non-integer x = 608.080229Warning: non-integer x = 618.232106Warning: non-integer x = 664.176436Warning: non-integer x = 660.093619Warning: non-integer x = 764.652114Warning: non-integer x = 890.907797Warning: non-integer x = 794.549409Warning: non-integer x = 732.713520Warning: non-integer x = 721.208127Warning: non-integer x = 739.603139Warning: non-integer x = 804.632094Warning: non-integer x = 684.071365Warning: non-integer x = 622.471138Warning: non-integer x = 666.320431Warning: non-integer x = 665.968681Warning: non-integer x = 674.074040Warning: non-integer x = 616.919942Warning: non-integer x = 625.951172Warning: non-integer x = 583.087731Warning: non-integer x = 631.189918Warning: non-integer x = 706.877984Warning: non-integer x = 688.660261Warning: non-integer x = 576.654424Warning: non-integer x = 649.482787Warning: non-integer x = 670.791247Warning: non-integer x = 731.527166Warning: non-integer x = 671.458578Warning: non-integer x = 730.673473Warning: non-integer x = 692.716266Warning: non-integer x = 731.597682Warning: non-integer x = 830.642284Warning: non-integer x = 760.755972Warning: non-integer x = 767.713375Warning: non-integer x = 872.866138Warning: non-integer x = 779.680328Warning: non-integer x = 891.076895Warning: non-integer x = 796.398984Warning: non-integer x = 781.012170Warning: non-integer x = 784.014273Warning: non-integer x = 893.014432Warning: non-integer x = 843.984853Warning: non-integer x = 785.003135Warning: non-integer x = 636.013933Warning: non-integer x = 617.007737Warning: non-integer x = 772.978335Warning: non-integer x = 863.998367Warning: non-integer x = 794.022438Warning: non-integer x = 801.995682Warning: non-integer x = 831.005323Warning: non-integer x = 807.022078Warning: non-integer x = 820.988812Warning: non-integer x = 778.022544Warning: non-integer x = 756.976224Warning: non-integer x = 771.016369Warning: non-integer x = 771.011411Warning: non-integer x = 804.993221Warning: non-integer x = 807.002806Warning: non-integer x = 823.985709Warning: non-integer x = 767.987053Warning: non-integer x = 693.020775Warning: non-integer x = 746.993154Warning: non-integer x = 727.020168Warning: non-integer x = 660.024758Warning: non-integer x = 663.977645Warning: non-integer x = 626.022455Warning: non-integer x = 608.020377Warning: non-integer x = 543.990384Warning: non-integer x = 593.007534Warning: non-integer x = 579.975933Warning: non-integer x = 619.995289Warning: non-integer x = 622.286257Warning: non-integer x = 628.180150Warning: non-integer x = 622.133595Warning: non-integer x = 634.283650Warning: non-integer x = 601.237011Warning: non-integer x = 584.131766Warning: non-integer x = 611.091894Warning: non-integer x = 646.215008Warning: non-integer x = 560.177471Warning: non-integer x = 663.167525Warning: non-integer x = 605.052817Warning: non-integer x = 659.159703Warning: non-integer x = 659.092374Warning: non-integer x = 656.216232Warning: non-integer x = 701.223889Warning: non-integer x = 740.087937Warning: non-integer x = 514.105447Warning: non-integer x = 597.276631Warning: non-integer x = 561.095288Warning: non-integer x = 509.196637Warning: non-integer x = 530.612387Warning: non-integer x = 506.785578Warning: non-integer x = 536.781407Warning: non-integer x = 528.599096Warning: non-integer x = 517.214793Warning: non-integer x = 551.091483Warning: non-integer x = 513.770776Warning: non-integer x = 522.829533Warning: non-integer x = 516.768550Warning: non-integer x = 537.809860Warning: non-integer x = 586.078550Warning: non-integer x = 593.124435Warning: non-integer x = 654.806218Warning: non-integer x = 597.551960Warning: non-integer x = 579.638061Warning: non-integer x = 623.445840Warning: non-integer x = 629.770651Warning: non-integer x = 674.500504Warning: non-integer x = 707.462653Warning: non-integer x = 689.627690Warning: non-integer x = 705.724735Warning: non-integer x = 738.595511Warning: non-integer x = 799.636079Warning: non-integer x = 799.771734Warning: non-integer x = 808.764177Warning: non-integer x = 862.867247Warning: non-integer x = 768.677175Warning: non-integer x = 838.010463Warning: non-integer x = 839.457011Warning: non-integer x = 779.018629Warning: non-integer x = 858.996976Warning: non-integer x = 897.986460Warning: non-integer x = 954.000404Warning: non-integer x = 809.014846Warning: non-integer x = 754.988175Warning: non-integer x = 691.002397Warning: non-integer x = 651.994043Warning: non-integer x = 794.015114Warning: non-integer x = 862.016142Warning: non-integer x = 815.013422Warning: non-integer x = 901.016004Warning: non-integer x = 869.993175Warning: non-integer x = 865.007161Warning: non-integer x = 814.991706Warning: non-integer x = 931.016038Warning: non-integer x = 804.999232Warning: non-integer x = 847.997586Warning: non-integer x = 883.977895Warning: non-integer x = 830.979239Warning: non-integer x = 848.024824Warning: non-integer x = 753.011107Warning: non-integer x = 812.975313Warning: non-integer x = 786.013779Warning: non-integer x = 801.998698Warning: non-integer x = 746.997770Warning: non-integer x = 692.975725Warning: non-integer x = 689.986614Warning: non-integer x = 671.991943Warning: non-integer x = 614.990109Warning: non-integer x = 653.010304Warning: non-integer x = 622.020119Warning: non-integer x = 630.007930Warning: non-integer x = 588.284977Warning: non-integer x = 622.194032Warning: non-integer x = 621.128154Warning: non-integer x = 672.312987Warning: non-integer x = 685.228018Warning: non-integer x = 649.161428Warning: non-integer x = 641.105945Warning: non-integer x = 673.243534Warning: non-integer x = 644.175692Warning: non-integer x = 679.169341Warning: non-integer x = 696.103214Warning: non-integer x = 647.152559Warning: non-integer x = 724.100400Warning: non-integer x = 696.205564Warning: non-integer x = 771.178680Warning: non-integer x = 781.122407Warning: non-integer x = 681.480306Warning: non-integer x = 775.657866Warning: non-integer x = 794.538471Warning: non-integer x = 680.587692Warning: non-integer x = 680.078105Warning: non-integer x = 628.218655Warning: non-integer x = 702.314821Warning: non-integer x = 660.985335Warning: non-integer x = 677.601057Warning: non-integer x = 678.359216Warning: non-integer x = 597.874879Warning: non-integer x = 706.125644Warning: non-integer x = 672.987461Warning: non-integer x = 641.947031Warning: non-integer x = 653.218293Warning: non-integer x = 733.382126Warning: non-integer x = 728.916189Warning: non-integer x = 664.626930Warning: non-integer x = 668.770670Warning: non-integer x = 678.489839Warning: non-integer x = 668.816295Warning: non-integer x = 702.532265Warning: non-integer x = 797.522352Warning: non-integer x = 835.756299Warning: non-integer x = 751.756050Warning: non-integer x = 810.645336Warning: non-integer x = 898.711940Warning: non-integer x = 809.805018Warning: non-integer x = 794.755229Warning: non-integer x = 929.931919Warning: non-integer x = 839.763043Warning: non-integer x = 923.087251Warning: non-integer x = 927.595067Warning: non-integer x = 907.020947Warning: non-integer x = 944.990954Warning: non-integer x = 1044.008406Warning: non-integer x = 975.014365Warning: non-integer x = 929.018195Warning: non-integer x = 870.013169Warning: non-integer x = 807.005131Warning: non-integer x = 820.011583Warning: non-integer x = 786.010443Warning: non-integer x = 844.993247Warning: non-integer x = 831.005313Warning: non-integer x = 892.000106Warning: non-integer x = 860.010289Warning: non-integer x = 912.009905Warning: non-integer x = 883.013861Warning: non-integer x = 902.990936Warning: non-integer x = 873.005405Warning: non-integer x = 853.995541Warning: non-integer x = 898.014878Warning: non-integer x = 857.008328Warning: non-integer x = 918.982300Warning: non-integer x = 837.015240Warning: non-integer x = 845.995193Warning: non-integer x = 873.988116Warning: non-integer x = 839.989968Warning: non-integer x = 805.979783Warning: non-integer x = 810.014669Warning: non-integer x = 744.015488Warning: non-integer x = 705.979615Warning: non-integer x = 690.003956Warning: non-integer x = 660.021362Warning: non-integer x = 667.011513Warning: non-integer x = 651.007506Warning: non-integer x = 650.316993Warning: non-integer x = 713.193065Warning: non-integer x = 624.163070Warning: non-integer x = 640.305933Warning: non-integer x = 709.233506Warning: non-integer x = 708.152166Warning: non-integer x = 682.101370Warning: non-integer x = 716.229796Warning: non-integer x = 678.180872Warning: non-integer x = 656.112781Warning: non-integer x = 735.086729Warning: non-integer x = 710.174498Warning: non-integer x = 758.061805Warning: non-integer x = 740.215976Warning: non-integer x = 820.217616Warning: non-integer x = 827.139913Warning: non-integer x = 736.605889Warning: non-integer x = 796.693033Warning: non-integer x = 679.303598Warning: non-integer x = 707.668236Warning: non-integer x = 731.243874Warning: non-integer x = 769.712484Warning: non-integer x = 719.351632Warning: non-integer x = 683.061875Warning: non-integer x = 660.563068Warning: non-integer x = 734.449844Warning: non-integer x = 694.023846Warning: non-integer x = 684.073062Warning: non-integer x = 682.020322Warning: non-integer x = 695.042331Warning: non-integer x = 679.266131Warning: non-integer x = 681.293169Warning: non-integer x = 824.027765Warning: non-integer x = 724.698113Warning: non-integer x = 670.758351Warning: non-integer x = 710.500479Warning: non-integer x = 724.870615Warning: non-integer x = 749.569506Warning: non-integer x = 777.514607Warning: non-integer x = 782.716479Warning: non-integer x = 843.871448Warning: non-integer x = 795.643871Warning: non-integer x = 903.707775Warning: non-integer x = 919.900120Warning: non-integer x = 867.841747Warning: non-integer x = 966.976531Warning: non-integer x = 949.853287Warning: non-integer x = 991.180573Warning: non-integer x = 908.583781Warning: non-integer x = 977.022403Warning: non-integer x = 988.996336Warning: non-integer x = 1059.006620Warning: non-integer x = 1062.019566Warning: non-integer x = 1037.000239Warning: non-integer x = 939.009635Warning: non-integer x = 894.005429Warning: non-integer x = 869.986802Warning: non-integer x = 826.992527Warning: non-integer x = 741.982181Warning: non-integer x = 912.017284Warning: non-integer x = 997.989558Warning: non-integer x = 935.978393Warning: non-integer x = 939.983534Warning: non-integer x = 1032.999037Warning: non-integer x = 943.996227Warning: non-integer x = 925.992012Warning: non-integer x = 996.980041Warning: non-integer x = 1005.018885Warning: non-integer x = 936.013769Warning: non-integer x = 1004.000463Warning: non-integer x = 947.983482Warning: non-integer x = 958.005696Warning: non-integer x = 927.978408Warning: non-integer x = 853.979139Warning: non-integer x = 883.981195Warning: non-integer x = 867.983292Warning: non-integer x = 796.017787Warning: non-integer x = 835.004467Warning: non-integer x = 761.987617Warning: non-integer x = 722.006048Warning: non-integer x = 708.019013Warning: non-integer x = 648.981951Warning: non-integer x = 668.294979Warning: non-integer x = 696.214144Warning: non-integer x = 690.143845Warning: non-integer x = 685.314697Warning: non-integer x = 695.284611Warning: non-integer x = 717.144395Warning: non-integer x = 726.086698Warning: non-integer x = 695.219219Warning: non-integer x = 716.151580Warning: non-integer x = 756.156380Warning: non-integer x = 778.090091Warning: non-integer x = 719.192355Warning: non-integer x = 731.065513Warning: non-integer x = 794.256048Warning: non-integer x = 843.226648Warning: non-integer x = 871.155190Warning: non-integer x = 778.696917Warning: non-integer x = 802.702584Warning: non-integer x = 818.589390Warning: non-integer x = 665.559977Warning: non-integer x = 803.463827Warning: non-integer x = 725.558260Warning: non-integer x = 762.504648Warning: non-integer x = 733.201725Warning: non-integer x = 676.601231Warning: non-integer x = 748.489029Warning: non-integer x = 733.085656Warning: non-integer x = 786.241463Warning: non-integer x = 667.995238Warning: non-integer x = 690.048666Warning: non-integer x = 764.408969Warning: non-integer x = 750.433806Warning: non-integer x = 804.018510Warning: non-integer x = 796.758461Warning: non-integer x = 657.744439Warning: non-integer x = 714.527461Warning: non-integer x = 748.908946Warning: non-integer x = 741.562744Warning: non-integer x = 784.542727Warning: non-integer x = 749.690393Warning: non-integer x = 849.868229Warning: non-integer x = 924.718214Warning: non-integer x = 956.773123Warning: non-integer x = 935.923824Warning: non-integer x = 910.884738Warning: non-integer x = 1025.026455Warning: non-integer x = 972.849560Warning: non-integer x = 981.160639Warning: non-integer x = 985.715024Warning: non-integer x = 953.016909Warning: non-integer x = 1047.996073Warning: non-integer x = 1096.997484Warning: non-integer x = 1132.016189Warning: non-integer x = 1065.990103Warning: non-integer x = 977.007687Warning: non-integer x = 940.993439Warning: non-integer x = 971.988128Warning: non-integer x = 970.981767Warning: non-integer x = 846.987974Warning: non-integer x = 807.006489Warning: non-integer x = 940.992266Warning: non-integer x = 980.993005Warning: non-integer x = 976.010761Warning: non-integer x = 949.006965Warning: non-integer x = 1015.012138Warning: non-integer x = 984.010074Warning: non-integer x = 1069.983553Warning: non-integer x = 1081.006525Warning: non-integer x = 975.997328Warning: non-integer x = 1081.015069Warning: non-integer x = 974.019529Warning: non-integer x = 992.980288Warning: non-integer x = 997.012602Warning: non-integer x = 952.020108Warning: non-integer x = 902.019593Warning: non-integer x = 906.976488Warning: non-integer x = 880.020676Warning: non-integer x = 827.024395Warning: non-integer x = 873.005652Warning: non-integer x = 818.008207Warning: non-integer x = 728.023626Warning: non-integer x = 704.000174Warning: non-integer x = 709.294462Warning: non-integer x = 690.231035Warning: non-integer x = 719.151688Warning: non-integer x = 761.328016Warning: non-integer x = 713.279712Warning: non-integer x = 728.180650Warning: non-integer x = 699.127155Warning: non-integer x = 841.308033Warning: non-integer x = 747.203665Warning: non-integer x = 714.151551Warning: non-integer x = 780.105225Warning: non-integer x = 770.174474Warning: non-integer x = 802.097210Warning: non-integer x = 829.278141Warning: non-integer x = 904.223191Warning: non-integer x = 837.162479Warning: non-integer x = 858.852723Warning: non-integer x = 946.009247Warning: non-integer x = 889.723322Warning: non-integer x = 847.988544Warning: non-integer x = 879.683636Warning: non-integer x = 835.943269Warning: non-integer x = 894.940711Warning: non-integer x = 724.180115Warning: non-integer x = 735.746106Warning: non-integer x = 811.622143Warning: non-integer x = 743.098292Warning: non-integer x = 780.259108Warning: non-integer x = 689.018992Warning: non-integer x = 707.068236Warning: non-integer x = 750.391530Warning: non-integer x = 728.396490Warning: non-integer x = 848.067280Warning: non-integer x = 758.730770Warning: non-integer x = 763.864314Warning: non-integer x = 760.552262Warning: non-integer x = 751.911353Warning: non-integer x = 781.575006Warning: non-integer x = 814.547951Warning: non-integer x = 850.771882Warning: non-integer x = 838.838272Warning: non-integer x = 896.696595Warning: non-integer x = 1003.797128Warning: non-integer x = 885.859487Warning: non-integer x = 961.913488Warning: non-integer x = 1083.073699Warning: non-integer x = 948.827938Warning: non-integer x = 1046.224707Warning: non-integer x = 969.678237Warning: non-integer x = 1027.021959Warning: non-integer x = 1112.010613Warning: non-integer x = 1185.008779Warning: non-integer x = 1287.007039Warning: non-integer x = 1079.005246Warning: non-integer x = 1179.985785Warning: non-integer x = 985.988397Warning: non-integer x = 1049.008241Warning: non-integer x = 1027.985805Warning: non-integer x = 895.006110Warning: non-integer x = 928.986708Warning: non-integer x = 848.000798Warning: non-integer x = 1054.998959Warning: non-integer x = 1070.988321Warning: non-integer x = 1026.016892Warning: non-integer x = 1062.988335Warning: non-integer x = 1058.018621Warning: non-integer x = 1189.006804Warning: non-integer x = 1164.985387Warning: non-integer x = 976.995709Warning: non-integer x = 1112.010251Warning: non-integer x = 1053.005231Warning: non-integer x = 1061.980909Warning: non-integer x = 1074.976889Warning: non-integer x = 1044.998351Warning: non-integer x = 1052.010710Warning: non-integer x = 1001.012126Warning: non-integer x = 1005.980455Warning: non-integer x = 979.021361Warning: non-integer x = 948.018646Warning: non-integer x = 930.009142Warning: non-integer x = 840.003132Warning: non-integer x = 860.993276Warning: non-integer x = 731.352920Warning: non-integer x = 794.250703Warning: non-integer x = 747.154551Warning: non-integer x = 848.400516Warning: non-integer x = 742.285212Warning: non-integer x = 792.159520Warning: non-integer x = 790.112000Warning: non-integer x = 798.249399Warning: non-integer x = 777.196724Warning: non-integer x = 798.164483Warning: non-integer x = 820.144910Warning: non-integer x = 793.195671Warning: non-integer x = 846.084642Warning: non-integer x = 831.257388Warning: non-integer x = 911.256471Warning: non-integer x = 947.153698Warning: non-integer x = 719.543010Warning: non-integer x = 921.962045Warning: non-integer x = 911.750685Warning: non-integer x = 819.913588Warning: non-integer x = 829.529471Warning: non-integer x = 757.656356Warning: non-integer x = 941.095964Warning: non-integer x = 899.712786Warning: non-integer x = 738.731751Warning: non-integer x = 827.646159Warning: non-integer x = 709.036154Warning: non-integer x = 781.235415Warning: non-integer x = 763.131849Warning: non-integer x = 783.164444Warning: non-integer x = 761.413395Warning: non-integer x = 869.657685Warning: non-integer x = 924.155398Warning: non-integer x = 811.778644Warning: non-integer x = 764.851607Warning: non-integer x = 822.594154Warning: non-integer x = 847.011367Warning: non-integer x = 803.598238Warning: non-integer x = 798.540250Warning: non-integer x = 871.806001Warning: non-integer x = 892.893321Warning: non-integer x = 884.712125Warning: non-integer x = 1000.811263Warning: non-integer x = 1052.005635Warning: non-integer x = 902.869391Warning: non-integer x = 1142.139736Warning: non-integer x = 923.832986Warning: non-integer x = 1044.241003Warning: non-integer x = 1003.751179Warning: non-integer x = 1073.034787Warning: non-integer x = 1126.989936Warning: non-integer x = 1170.987249Warning: non-integer x = 1213.993994Warning: non-integer x = 1221.998032Warning: non-integer x = 1220.002737Warning: non-integer x = 1149.989079Warning: non-integer x = 1125.999186Warning: non-integer x = 1063.003818Warning: non-integer x = 1007.017237Warning: non-integer x = 1023.987555Warning: non-integer x = 972.990587Warning: non-integer x = 911.005176Warning: non-integer x = 1053.997051Warning: non-integer x = 1054.992738Warning: non-integer x = 1180.989470Warning: non-integer x = 1081.986780Warning: non-integer x = 1167.013631Warning: non-integer x = 1211.008132Warning: non-integer x = 1176.019671Warning: non-integer x = 1159.008075Warning: non-integer x = 1032.995906Warning: non-integer x = 1106.997092Warning: non-integer x = 1117.001651Warning: non-integer x = 1127.003929Warning: non-integer x = 1127.011705Warning: non-integer x = 1075.004437Warning: non-integer x = 1030.976554Warning: non-integer x = 1045.017005Warning: non-integer x = 1025.013761Warning: non-integer x = 1022.990713Warning: non-integer x = 909.019928Warning: non-integer x = 931.977405Warning: non-integer x = 905.376650Warning: non-integer x = 740.220405Warning: non-integer x = 788.170850Warning: non-integer x = 772.345766Warning: non-integer x = 856.322644Warning: non-integer x = 767.144058Warning: non-integer x = 827.146254Warning: non-integer x = 809.290710Warning: non-integer x = 790.215137Warning: non-integer x = 828.163345Warning: non-integer x = 893.104557Warning: non-integer x = 826.162613Warning: non-integer x = 785.092334Warning: non-integer x = 936.286136Warning: non-integer x = 919.254129Warning: non-integer x = 1044.149617Warning: non-integer x = 723.552921Warning: non-integer x = 841.785603Warning: non-integer x = 815.580541Warning: non-integer x = 749.757206Warning: non-integer x = 806.470582Warning: non-integer x = 789.782544Warning: non-integer x = 837.756838Warning: non-integer x = 821.478762Warning: non-integer x = 739.756228Warning: non-integer x = 780.543904Warning: non-integer x = 748.104969Warning: non-integer x = 795.264871Warning: non-integer x = 808.195088Warning: non-integer x = 759.144301Warning: non-integer x = 774.445813Warning: non-integer x = 813.547060Warning: non-integer x = 861.064636Warning: non-integer x = 874.825040Warning: non-integer x = 784.883395Warning: non-integer x = 812.572905Warning: non-integer x = 866.058093Warning: non-integer x = 822.630312Warning: non-integer x = 875.587169Warning: non-integer x = 926.840940Warning: non-integer x = 844.842329Warning: non-integer x = 954.754612Warning: non-integer x = 1044.826271Warning: non-integer x = 1027.006460Warning: non-integer x = 1061.996196Warning: non-integer x = 1115.109773Warning: non-integer x = 1067.952143Warning: non-integer x = 1173.400077Warning: non-integer x = 1053.817245Warning: non-integer x = 1114.020100Warning: non-integer x = 1177.000319Warning: non-integer x = 1207.989807Warning: non-integer x = 1272.011845Warning: non-integer x = 1265.998974Warning: non-integer x = 1250.985371Warning: non-integer x = 1160.002955Warning: non-integer x = 1229.003835Warning: non-integer x = 1180.982857Warning: non-integer x = 1168.009809Warning: non-integer x = 1123.987465Warning: non-integer x = 1116.010432Warning: non-integer x = 988.012738Warning: non-integer x = 942.998630Warning: non-integer x = 1075.005419Warning: non-integer x = 1164.983094Warning: non-integer x = 1160.985212Warning: non-integer x = 1216.999532Warning: non-integer x = 1209.996882Warning: non-integer x = 1203.000240Warning: non-integer x = 1342.014114Warning: non-integer x = 1201.005753Warning: non-integer x = 1184.987833Warning: non-integer x = 1214.998833Warning: non-integer x = 1215.020330Warning: non-integer x = 1191.002909Warning: non-integer x = 1168.005370Warning: non-integer x = 1127.980437Warning: non-integer x = 1068.991024Warning: non-integer x = 1135.983865Warning: non-integer x = 1073.991285Warning: non-integer x = 971.983804Warning: non-integer x = 978.019420Warning: non-integer x = 971.439974Warning: non-integer x = 890.253021Warning: non-integer x = 808.159646Warning: non-integer x = 802.360220Warning: non-integer x = 882.337515Warning: non-integer x = 867.219876Warning: non-integer x = 906.138343Warning: non-integer x = 854.296619Warning: non-integer x = 763.224974Warning: non-integer x = 857.167149Warning: non-integer x = 964.115326Warning: non-integer x = 864.209718Warning: non-integer x = 938.113204Warning: non-integer x = 941.325391Warning: non-integer x = 1041.292212Warning: non-integer x = 1022.168396Warning: non-integer x = 849.834477Warning: non-integer x = 959.049527Warning: non-integer x = 947.822568Warning: non-integer x = 875.052352Warning: non-integer x = 917.799254Warning: non-integer x = 862.026766Warning: non-integer x = 990.242225Warning: non-integer x = 829.494080Warning: non-integer x = 852.016446Warning: non-integer x = 891.778132Warning: non-integer x = 786.157037Warning: non-integer x = 870.386610Warning: non-integer x = 782.155370Warning: non-integer x = 817.239532Warning: non-integer x = 828.536092Warning: non-integer x = 917.741759Warning: non-integer x = 1002.245237Warning: non-integer x = 939.886189Warning: non-integer x = 844.969857Warning: non-integer x = 916.663552Warning: non-integer x = 877.057327Warning: non-integer x = 918.691805Warning: non-integer x = 902.608799Warning: non-integer x = 944.854958Warning: non-integer x = 932.948844Warning: non-integer x = 956.757353Warning: non-integer x = 1053.824861Warning: non-integer x = 1008.981618Warning: non-integer x = 1063.030573Warning: non-integer x = 1234.213702Warning: non-integer x = 1113.973579Warning: non-integer x = 1294.536520Warning: non-integer x = 1140.971974Warning: non-integer x = 1177.027137Warning: non-integer x = 1222.995514Warning: non-integer x = 1270.004157Warning: non-integer x = 1376.986337Warning: non-integer x = 1337.992610Warning: non-integer x = 1318.988378Warning: non-integer x = 1292.007779Warning: non-integer x = 1268.017147Warning: non-integer x = 1303.995893Warning: non-integer x = 1168.987491Warning: non-integer x = 1230.017136Warning: non-integer x = 1143.997455Warning: non-integer x = 1097.998214Warning: non-integer x = 1115.984184Warning: non-integer x = 934.985466Warning: non-integer x = 1206.006445Warning: non-integer x = 1215.998456Warning: non-integer x = 1252.985187Warning: non-integer x = 1318.000948Warning: non-integer x = 1320.999286Warning: non-integer x = 1218.005210Warning: non-integer x = 1274.984812Warning: non-integer x = 1277.991768Warning: non-integer x = 1226.007079Warning: non-integer x = 1269.013577Warning: non-integer x = 1275.977829Warning: non-integer x = 1213.016861Warning: non-integer x = 1176.981590Warning: non-integer x = 1161.994807Warning: non-integer x = 1135.984689Warning: non-integer x = 1110.002578Warning: non-integer x = 1073.997004Warning: non-integer x = 993.427861Warning: non-integer x = 972.291571Warning: non-integer x = 921.215991Warning: non-integer x = 833.396592Warning: non-integer x = 860.302076Warning: non-integer x = 896.177206Warning: non-integer x = 920.142734Warning: non-integer x = 948.318029Warning: non-integer x = 896.258036Warning: non-integer x = 919.196241Warning: non-integer x = 977.166497Warning: non-integer x = 989.223225Warning: non-integer x = 997.105236Warning: non-integer x = 954.334527Warning: non-integer x = 1007.290720Warning: non-integer x = 1113.190292Warning: non-integer x = 690.496046Warning: non-integer x = 756.614337Warning: non-integer x = 688.324222Warning: non-integer x = 726.702739Warning: non-integer x = 752.299333Warning: non-integer x = 699.461322Warning: non-integer x = 802.645291Warning: non-integer x = 788.375303Warning: non-integer x = 749.778785Warning: non-integer x = 828.631776Warning: non-integer x = 748.096818Warning: non-integer x = 777.232463Warning: non-integer x = 755.105108Warning: non-integer x = 764.135324Warning: non-integer x = 868.626160Warning: non-integer x = 829.580349Warning: non-integer x = 974.203352Warning: non-integer x = 919.866778Warning: non-integer x = 833.942541Warning: non-integer x = 887.642606Warning: non-integer x = 838.003539Warning: non-integer x = 896.682016Warning: non-integer x = 964.636985Warning: non-integer x = 979.896743Warning: non-integer x = 908.924929Warning: non-integer x = 957.767580Warning: non-integer x = 998.790998Warning: non-integer x = 1042.018589Warning: non-integer x = 1081.036070Warning: non-integer x = 1265.239530Warning: non-integer x = 1207.057619Warning: non-integer x = 1189.400077Warning: non-integer x = 1168.037292Warning: non-integer x = 1283.025051Warning: non-integer x = 1267.000450Warning: non-integer x = 1343.993200Warning: non-integer x = 1360.990800Warning: non-integer x = 1377.013994Warning: non-integer x = 1269.988999Warning: non-integer x = 1339.984115Warning: non-integer x = 1376.990886Warning: non-integer x = 1290.011155Warning: non-integer x = 1308.015225Warning: non-integer x = 1326.006946Warning: non-integer x = 1285.992801Warning: non-integer x = 1246.001353Warning: non-integer x = 1139.006433Warning: non-integer x = 1084.996649Warning: non-integer x = 1020.004802Warning: non-integer x = 1209.989554Warning: non-integer x = 1323.994014Warning: non-integer x = 1355.018922Warning: non-integer x = 1359.006797Warning: non-integer x = 1458.982357Warning: non-integer x = 1312.002923Warning: non-integer x = 1380.989085Warning: non-integer x = 1388.989676Warning: non-integer x = 1314.979488Warning: non-integer x = 1303.009781Warning: non-integer x = 1359.985094Warning: non-integer x = 1292.021260Warning: non-integer x = 1225.997256Warning: non-integer x = 1244.003633Warning: non-integer x = 1229.018949Warning: non-integer x = 1126.987359Warning: non-integer x = 1180.003355Warning: non-integer x = 1118.492644Warning: non-integer x = 1044.341461Warning: non-integer x = 1048.238876Warning: non-integer x = 978.427963Warning: non-integer x = 935.359639Warning: non-integer x = 901.207478Warning: non-integer x = 910.131097Warning: non-integer x = 936.332995Warning: non-integer x = 988.282620Warning: non-integer x = 988.195350Warning: non-integer x = 947.112823Warning: non-integer x = 1007.254093Warning: non-integer x = 1028.101550Warning: non-integer x = 1019.307351Warning: non-integer x = 1097.321857Warning: non-integer x = 1172.216695Warning: non-integer x = 1146.473636Warning: non-integer x = 1220.592931Warning: non-integer x = 1165.252269Warning: non-integer x = 1027.411294Warning: non-integer x = 1110.397453Warning: non-integer x = 993.490248Warning: non-integer x = 1151.786287Warning: non-integer x = 962.914825Warning: non-integer x = 921.182038Warning: non-integer x = 1027.037510Warning: non-integer x = 1013.491970Warning: non-integer x = 1049.668756Warning: non-integer x = 846.247172Warning: non-integer x = 864.296588Warning: non-integer x = 926.727522Warning: non-integer x = 967.846478Warning: non-integer x = 1099.361537Warning: non-integer x = 1054.992086Warning: non-integer x = 928.053276Warning: non-integer x = 960.709010Warning: non-integer x = 1033.238037Warning: non-integer x = 984.746661Warning: non-integer x = 976.645827Warning: non-integer x = 1157.050347Warning: non-integer x = 1067.082684Warning: non-integer x = 1008.808997Warning: non-integer x = 1103.881838Warning: non-integer x = 1096.061324Warning: non-integer x = 1122.067728Warning: non-integer x = 1300.290102Warning: non-integer x = 1179.040761Warning: non-integer x = 1282.508122Warning: non-integer x = 1184.064226Warning: non-integer x = 1292.035538Warning: non-integer x = 1403.006993Warning: non-integer x = 1346.991527Warning: non-integer x = 1498.000604Warning: non-integer x = 1424.012419Warning: non-integer x = 1344.991287Warning: non-integer x = 1331.002084Warning: non-integer x = 1436.014644Warning: non-integer x = 1450.013210Warning: non-integer x = 1362.012612Warning: non-integer x = 1406.994738Warning: non-integer x = 1432.983762Warning: non-integer x = 1406.990589Warning: non-integer x = 1284.001808Warning: non-integer x = 1141.015160Warning: non-integer x = 1052.992926Warning: non-integer x = 1328.995935Warning: non-integer x = 1434.014217Warning: non-integer x = 1387.983213Warning: non-integer x = 1478.990242Warning: non-integer x = 1430.992435Warning: non-integer x = 1418.987439Warning: non-integer x = 1468.992425Warning: non-integer x = 1378.985050Warning: non-integer x = 1348.999161Warning: non-integer x = 1393.011526Warning: non-integer x = 1348.004475Warning: non-integer x = 1353.977697Warning: non-integer x = 1359.010024Warning: non-integer x = 1377.981495Warning: non-integer x = 1223.996346Warning: non-integer x = 1216.009284Warning: non-integer x = 1170.537643Warning: non-integer x = 1109.315518Warning: non-integer x = 1086.254529Warning: non-integer x = 1101.503544Warning: non-integer x = 1056.397001Warning: non-integer x = 983.193408Warning: non-integer x = 992.138450Warning: non-integer x = 962.335438Warning: non-integer x = 1075.295299Warning: non-integer x = 1050.213259Warning: non-integer x = 1026.146344Warning: non-integer x = 957.236570Warning: non-integer x = 1085.140678Warning: non-integer x = 1156.394963Warning: non-integer x = 1131.320638Warning: non-integer x = 1235.206311Warning: non-integer x = 701.519210Warning: non-integer x = 798.711815Warning: non-integer x = 687.325440Warning: non-integer x = 645.525624Warning: non-integer x = 685.088585Warning: non-integer x = 700.462704Warning: non-integer x = 789.594759Warning: non-integer x = 717.162468Warning: non-integer x = 729.729140Warning: non-integer x = 795.579080Warning: non-integer x = 778.136024Warning: non-integer x = 825.312140Warning: non-integer x = 779.149499Warning: non-integer x = 709.064544Warning: non-integer x = 808.507187Warning: non-integer x = 820.558805Warning: non-integer x = 949.182356Warning: non-integer x = 932.883507Warning: non-integer x = 890.013174Warning: non-integer x = 923.655320Warning: non-integer x = 993.197388Warning: non-integer x = 966.727338Warning: non-integer x = 960.631304Warning: non-integer x = 1074.993400Warning: non-integer x = 1010.025414Warning: non-integer x = 1056.848457Warning: non-integer x = 1034.820653Warning: non-integer x = 1055.038461Warning: non-integer x = 1118.056544Warning: non-integer x = 1255.238660Warning: non-integer x = 1136.018276Warning: non-integer x = 1277.519774Warning: non-integer x = 1214.115902Warning: non-integer x = 1248.022585Warning: non-integer x = 1365.007739Warning: non-integer x = 1334.007255Warning: non-integer x = 1395.991416Warning: non-integer x = 1411.995238Warning: non-integer x = 1372.999348Warning: non-integer x = 1382.010002Warning: non-integer x = 1514.010013Warning: non-integer x = 1397.014405Warning: non-integer x = 1433.014011Warning: non-integer x = 1470.006498Warning: non-integer x = 1418.006927Warning: non-integer x = 1347.009697Warning: non-integer x = 1328.985085Warning: non-integer x = 1305.995108Warning: non-integer x = 1238.014011Warning: non-integer x = 1162.012798Warning: non-integer x = 1399.001577Warning: non-integer x = 1452.988540Warning: non-integer x = 1534.014253Warning: non-integer x = 1477.014912Warning: non-integer x = 1444.007211Warning: non-integer x = 1530.996631Warning: non-integer x = 1524.990131Warning: non-integer x = 1529.994747Warning: non-integer x = 1428.999695Warning: non-integer x = 1447.000669Warning: non-integer x = 1397.010900Warning: non-integer x = 1390.981794Warning: non-integer x = 1462.989135Warning: non-integer x = 1425.000233Warning: non-integer x = 1358.006883Warning: non-integer x = 1271.559740Warning: non-integer x = 1256.362108Warning: non-integer x = 1219.284098Warning: non-integer x = 1119.490053Warning: non-integer x = 1230.473771Warning: non-integer x = 1067.219478Warning: non-integer x = 1001.143818Warning: non-integer x = 941.306724Warning: non-integer x = 1027.265918Warning: non-integer x = 1051.246299Warning: non-integer x = 1022.117380Warning: non-integer x = 1031.247906Warning: non-integer x = 1115.148782Warning: non-integer x = 1143.386866Warning: non-integer x = 1284.373205Warning: non-integer x = 1224.214039Warning: non-integer x = 898.947870Warning: non-integer x = 1003.132255Warning: non-integer x = 976.879884Warning: non-integer x = 972.277538Warning: non-integer x = 960.945266Warning: non-integer x = 922.251018Warning: non-integer x = 1011.321056Warning: non-integer x = 979.961036Warning: non-integer x = 923.181198Warning: non-integer x = 1017.023726Warning: non-integer x = 975.427026Warning: non-integer x = 994.584496Warning: non-integer x = 1002.474190Warning: non-integer x = 962.440368Warning: non-integer x = 992.856221Warning: non-integer x = 970.856456Warning: non-integer x = 1132.404892Warning: non-integer x = 1033.986403Warning: non-integer x = 943.075683Warning: non-integer x = 986.711449Warning: non-integer x = 1012.211812Warning: non-integer x = 1016.758011Warning: non-integer x = 1050.693696Warning: non-integer x = 1117.024262Warning: non-integer x = 1088.096062Warning: non-integer x = 1150.920752Warning: non-integer x = 1196.951183Warning: non-integer x = 1130.095699Warning: non-integer x = 1126.074980Warning: non-integer x = 1261.249753Warning: non-integer x = 1218.073594Warning: non-integer x = 1301.552792Warning: non-integer x = 1238.141412Warning: non-integer x = 1380.023970Warning: non-integer x = 1334.998421Warning: non-integer x = 1423.990390Warning: non-integer x = 1552.000432Warning: non-integer x = 1439.990110Warning: non-integer x = 1471.990545Warning: non-integer x = 1452.001624Warning: non-integer x = 1474.988682Warning: non-integer x = 1427.994681Warning: non-integer x = 1416.011656Warning: non-integer x = 1559.008505Warning: non-integer x = 1583.987306Warning: non-integer x = 1574.991107Warning: non-integer x = 1490.998777Warning: non-integer x = 1385.003697Warning: non-integer x = 1426.998102Warning: non-integer x = 1296.992831Warning: non-integer x = 1339.009976Warning: non-integer x = 1307.991367Warning: non-integer x = 1441.995895Warning: non-integer x = 1510.003415Warning: non-integer x = 1509.983718Warning: non-integer x = 1501.986000Warning: non-integer x = 1564.983836Warning: non-integer x = 1567.008272Warning: non-integer x = 1585.008531Warning: non-integer x = 1563.993201Warning: non-integer x = 1527.981404Warning: non-integer x = 1551.986872Warning: non-integer x = 1410.982578Warning: non-integer x = 1432.016785Warning: non-integer x = 1395.016419Warning: non-integer x = 1427.006693Warning: non-integer x = 1377.620849Warning: non-integer x = 1365.429895Warning: non-integer x = 1341.309347Warning: non-integer x = 1253.557720Warning: non-integer x = 1198.443125Warning: non-integer x = 1201.259042Warning: non-integer x = 1118.157924Warning: non-integer x = 1086.379145Warning: non-integer x = 965.257443Warning: non-integer x = 1119.269404Warning: non-integer x = 1156.146220Warning: non-integer x = 1127.252166Warning: non-integer x = 1192.126492Warning: non-integer x = 1113.373328Warning: non-integer x = 1277.370491Warning: non-integer x = 1412.235154Warning: non-integer x = 940.033850Warning: non-integer x = 933.994309Warning: non-integer x = 854.646221Warning: non-integer x = 855.007414Warning: non-integer x = 879.685908Warning: non-integer x = 833.927820Warning: non-integer x = 903.981004Warning: non-integer x = 890.681273Warning: non-integer x = 876.085843Warning: non-integer x = 936.854601Warning: non-integer x = 931.371423Warning: non-integer x = 979.558774Warning: non-integer x = 881.296109Warning: non-integer x = 960.434127Warning: non-integer x = 987.840858Warning: non-integer x = 930.775081Warning: non-integer x = 1108.376693Warning: non-integer x = 1028.967832Warning: non-integer x = 922.032999Warning: non-integer x = 1080.780441Warning: non-integer x = 1099.313126Warning: non-integer x = 1009.746045Warning: non-integer x = 1047.697340Warning: non-integer x = 1174.082106Warning: non-integer x = 1109.125493Warning: non-integer x = 1089.871723Warning: non-integer x = 1225.970122Warning: non-integer x = 1168.135539Warning: non-integer x = 1106.056528Warning: non-integer x = 1246.232538Warning: non-integer x = 1186.057095Warning: non-integer x = 1282.522362Warning: non-integer x = 1234.144899Warning: non-integer x = 1267.027223Warning: non-integer x = 1438.993392Warning: non-integer x = 1324.996419Warning: non-integer x = 1639.993712Warning: non-integer x = 1475.990390Warning: non-integer x = 1463.002170Warning: non-integer x = 1460.993659Warning: non-integer x = 1466.988036Warning: non-integer x = 1540.006388Warning: non-integer x = 1512.997654Warning: non-integer x = 1539.012686Warning: non-integer x = 1615.999691Warning: non-integer x = 1634.007991Warning: non-integer x = 1543.988007Warning: non-integer x = 1466.011670Warning: non-integer x = 1475.994922Warning: non-integer x = 1437.988832Warning: non-integer x = 1443.986849Warning: non-integer x = 1373.003530Warning: non-integer x = 1263.997642Warning: non-integer x = 1522.002198Warning: non-integer x = 1546.999301Warning: non-integer x = 1570.985176Warning: non-integer x = 1671.988299Warning: non-integer x = 1670.998101Warning: non-integer x = 1706.005728Warning: non-integer x = 1698.983614Warning: non-integer x = 1554.002150Warning: non-integer x = 1497.990202Warning: non-integer x = 1613.993025Warning: non-integer x = 1577.980928Warning: non-integer x = 1492.016601Warning: non-integer x = 1588.002194Warning: non-integer x = 1441.632850Warning: non-integer x = 1452.454768Warning: non-integer x = 1359.299815Warning: non-integer x = 1420.657944Warning: non-integer x = 1347.487985Warning: non-integer x = 1251.263029Warning: non-integer x = 1313.180660Warning: non-integer x = 1204.405962Warning: non-integer x = 1079.307960Warning: non-integer x = 1087.242915Warning: non-integer x = 1175.164305Warning: non-integer x = 1226.268728Warning: non-integer x = 1225.149254Warning: non-integer x = 1213.388627Warning: non-integer x = 1298.355302Warning: non-integer x = 1387.241136Warning: non-integer x = 932.023605Warning: non-integer x = 957.039401Warning: non-integer x = 910.761684Warning: non-integer x = 784.843699Warning: non-integer x = 906.766717Warning: non-integer x = 832.931320Warning: non-integer x = 890.932035Warning: non-integer x = 854.582102Warning: non-integer x = 827.964451Warning: non-integer x = 1052.083816Warning: non-integer x = 886.296918Warning: non-integer x = 1003.602184Warning: non-integer x = 932.381562Warning: non-integer x = 966.445370Warning: non-integer x = 979.829899Warning: non-integer x = 1026.950118Warning: non-integer x = 1155.434912Warning: non-integer x = 1014.963415Warning: non-integer x = 930.049414Warning: non-integer x = 1022.741975Warning: non-integer x = 1041.249157Warning: non-integer x = 1049.779034Warning: non-integer x = 1073.713283Warning: non-integer x = 1165.070088Warning: non-integer x = 1190.198718Warning: non-integer x = 1166.927873Warning: non-integer x = 1194.953790Warning: non-integer x = 1226.193797Warning: non-integer x = 1182.117892Warning: non-integer x = 1325.309017Warning: non-integer x = 1159.033688Warning: non-integer x = 1302.550014Warning: non-integer x = 1201.095885Warning: non-integer x = 1353.027847Warning: non-integer x = 1421.995405Warning: non-integer x = 1402.009693Warning: non-integer x = 1551.006015Warning: non-integer x = 1468.002784Warning: non-integer x = 1501.989839Warning: non-integer x = 1371.004952Warning: non-integer x = 1441.994781Warning: non-integer x = 1452.991840Warning: non-integer x = 1536.011080Warning: non-integer x = 1604.989790Warning: non-integer x = 1652.008556Warning: non-integer x = 1669.000780Warning: non-integer x = 1624.990990Warning: non-integer x = 1591.989116Warning: non-integer x = 1557.998996Warning: non-integer x = 1524.006252Warning: non-integer x = 1615.001383Warning: non-integer x = 1531.995026Warning: non-integer x = 1404.996300Warning: non-integer x = 1322.993707Warning: non-integer x = 1474.006577Warning: non-integer x = 1745.987548Warning: non-integer x = 1725.998091Warning: non-integer x = 1681.015207Warning: non-integer x = 1720.996446Warning: non-integer x = 1741.998910Warning: non-integer x = 1687.986397Warning: non-integer x = 1734.001266Warning: non-integer x = 1640.017216Warning: non-integer x = 1639.984441Warning: non-integer x = 1584.998846Warning: non-integer x = 1599.985921Warning: non-integer x = 1606.719298Warning: non-integer x = 1562.450509Warning: non-integer x = 1484.320824Warning: non-integer x = 1399.645621Warning: non-integer x = 1445.534786Warning: non-integer x = 1326.283182Warning: non-integer x = 1358.184624Warning: non-integer x = 1365.461497Warning: non-integer x = 1249.335771Warning: non-integer x = 1203.287494Warning: non-integer x = 1205.187295Warning: non-integer x = 1204.288554Warning: non-integer x = 1312.165667Warning: non-integer x = 1240.408982Warning: non-integer x = 1416.391304Warning: non-integer x = 1401.200278Warning: non-integer x = 1061.302081Warning: non-integer x = 1089.317265Warning: non-integer x = 1040.009113Warning: non-integer x = 922.157716Warning: non-integer x = 960.926698Warning: non-integer x = 977.437795Warning: non-integer x = 1022.360714Warning: non-integer x = 934.815373Warning: non-integer x = 809.910443Warning: non-integer x = 999.989547Warning: non-integer x = 992.460392Warning: non-integer x = 1033.644115Warning: non-integer x = 949.397554Warning: non-integer x = 976.470923Warning: non-integer x = 1027.916827Warning: non-integer x = 1004.910956Warning: non-integer x = 1226.535359Warning: non-integer x = 1027.984705Warning: non-integer x = 913.045862Warning: non-integer x = 1049.755958Warning: non-integer x = 1026.233963Warning: non-integer x = 1076.803137Warning: non-integer x = 1062.700000Warning: non-integer x = 1193.093693Warning: non-integer x = 1173.188754Warning: non-integer x = 1148.925913Warning: non-integer x = 1281.018839Warning: non-integer x = 1204.174333Warning: non-integer x = 1177.120375Warning: non-integer x = 1300.284654Warning: non-integer x = 1213.075097Warning: non-integer x = 1307.544115Warning: non-integer x = 1259.185832Warning: non-integer x = 1321.015251Warning: non-integer x = 1403.000844Warning: non-integer x = 1556.993131Warning: non-integer x = 1444.997858Warning: non-integer x = 1472.006900Warning: non-integer x = 1455.990738Warning: non-integer x = 1428.003817Warning: non-integer x = 1497.996155Warning: non-integer x = 1485.996715Warning: non-integer x = 1525.011265Warning: non-integer x = 1679.009826Warning: non-integer x = 1700.008794Warning: non-integer x = 1631.991133Warning: non-integer x = 1687.007657Warning: non-integer x = 1678.003753Warning: non-integer x = 1510.001474Warning: non-integer x = 1654.009434Warning: non-integer x = 1643.989782Warning: non-integer x = 1519.990975Warning: non-integer x = 1496.991797Warning: non-integer x = 1316.008333Warning: non-integer x = 1671.995932Warning: non-integer x = 1756.004454Warning: non-integer x = 1681.013835Warning: non-integer x = 1820.996401Warning: non-integer x = 1716.012937Warning: non-integer x = 1732.015253Warning: non-integer x = 1724.008866Warning: non-integer x = 1619.982769Warning: non-integer x = 1668.992601Warning: non-integer x = 1664.766145Warning: non-integer x = 1654.513836Warning: non-integer x = 1556.340899Warning: non-integer x = 1520.668912Warning: non-integer x = 1557.567332Warning: non-integer x = 1525.346454Warning: non-integer x = 1499.219404Warning: non-integer x = 1446.462915Warning: non-integer x = 1452.385057Warning: non-integer x = 1295.276660Warning: non-integer x = 1321.200948Warning: non-integer x = 1252.272486Warning: non-integer x = 1325.163360Warning: non-integer x = 1343.422598Warning: non-integer x = 1486.417900Warning: non-integer x = 1583.268197Warning: non-integer x = 829.802937Warning: non-integer x = 885.892699Warning: non-integer x = 879.701257Warning: non-integer x = 802.881758Warning: non-integer x = 836.560564Warning: non-integer x = 805.832762Warning: non-integer x = 968.180991Warning: non-integer x = 772.316352Warning: non-integer x = 778.838337Warning: non-integer x = 867.723172Warning: non-integer x = 804.191958Warning: non-integer x = 1010.613839Warning: non-integer x = 928.368486Warning: non-integer x = 895.340904Warning: non-integer x = 1009.894978Warning: non-integer x = 997.897619Warning: non-integer x = 1088.364596Warning: non-integer x = 1078.015875Warning: non-integer x = 861.976228Warning: non-integer x = 986.710744Warning: non-integer x = 1053.266947Warning: non-integer x = 1068.797646Warning: non-integer x = 1060.708896Warning: non-integer x = 1110.011133Warning: non-integer x = 1122.124702Warning: non-integer x = 1178.936573Warning: non-integer x = 1188.943864Warning: non-integer x = 1169.141027Warning: non-integer x = 1169.108149Warning: non-integer x = 1361.341997Warning: non-integer x = 1152.023375Warning: non-integer x = 1275.525645Warning: non-integer x = 1084.886673Warning: non-integer x = 1234.015687Warning: non-integer x = 1405.005850Warning: non-integer x = 1396.000387Warning: non-integer x = 1448.002904Warning: non-integer x = 1502.006387Warning: non-integer x = 1460.994616Warning: non-integer x = 1544.996963Warning: non-integer x = 1470.991848Warning: non-integer x = 1561.996845Warning: non-integer x = 1530.994080Warning: non-integer x = 1626.995465Warning: non-integer x = 1683.007363Warning: non-integer x = 1674.009530Warning: non-integer x = 1656.991105Warning: non-integer x = 1720.999551Warning: non-integer x = 1682.008781Warning: non-integer x = 1684.000422Warning: non-integer x = 1644.009674Warning: non-integer x = 1726.992600Warning: non-integer x = 1663.002006Warning: non-integer x = 1691.994525Warning: non-integer x = 1487.990347Warning: non-integer x = 1384.995045Warning: non-integer x = 1693.001263Warning: non-integer x = 1725.992425Warning: non-integer x = 1766.011625Warning: non-integer x = 1871.011290Warning: non-integer x = 1856.992845Warning: non-integer x = 1810.999483Warning: non-integer x = 1828.005651Warning: non-integer x = 1834.014536Warning: non-integer x = 1661.987214Warning: non-integer x = 1840.990080Warning: non-integer x = 1715.779166Warning: non-integer x = 1712.516137Warning: non-integer x = 1744.373066Warning: non-integer x = 1649.752343Warning: non-integer x = 1610.602349Warning: non-integer x = 1492.328988Warning: non-integer x = 1534.223039Warning: non-integer x = 1518.506102Warning: non-integer x = 1429.376629Warning: non-integer x = 1431.307908Warning: non-integer x = 1434.220181Warning: non-integer x = 1332.337635Warning: non-integer x = 1296.148597Warning: non-integer x = 1413.459353Warning: non-integer x = 1525.405582Warning: non-integer x = 1557.228147Warning: non-integer x = 789.709513Warning: non-integer x = 934.992126Warning: non-integer x = 852.650865Warning: non-integer x = 834.947996Warning: non-integer x = 821.523300Warning: non-integer x = 765.693342Warning: non-integer x = 880.888851Warning: non-integer x = 885.667796Warning: non-integer x = 821.937271Warning: non-integer x = 895.783939Warning: non-integer x = 819.199910Warning: non-integer x = 937.498424Warning: non-integer x = 934.369280Warning: non-integer x = 916.372705Warning: non-integer x = 943.761445Warning: non-integer x = 1035.973446Warning: non-integer x = 1162.452541Warning: non-integer x = 1048.990603Warning: non-integer x = 1003.135757Warning: non-integer x = 1009.727242Warning: non-integer x = 1001.200198Warning: non-integer x = 1023.770764Warning: non-integer x = 969.637233Warning: non-integer x = 1037.949353Warning: non-integer x = 1145.157682Warning: non-integer x = 1175.932194Warning: non-integer x = 1257.002065Warning: non-integer x = 1130.095648Warning: non-integer x = 1188.128628Warning: non-integer x = 1269.256492Warning: non-integer x = 1254.106318Warning: non-integer x = 1308.556399Warning: non-integer x = 1150.995597Warning: non-integer x = 1281.031193Warning: non-integer x = 1360.005668Warning: non-integer x = 1275.996969Warning: non-integer x = 1428.999142Warning: non-integer x = 1430.998992Warning: non-integer x = 1463.004356Warning: non-integer x = 1450.004895Warning: non-integer x = 1545.001108Warning: non-integer x = 1537.000495Warning: non-integer x = 1418.993515Warning: non-integer x = 1525.997425Warning: non-integer x = 1581.009030Warning: non-integer x = 1678.993761Warning: non-integer x = 1604.002266Warning: non-integer x = 1746.003738Warning: non-integer x = 1728.998078Warning: non-integer x = 1719.996955Warning: non-integer x = 1750.010301Warning: non-integer x = 1727.006250Warning: non-integer x = 1721.995258Warning: non-integer x = 1741.010802Warning: non-integer x = 1600.008324Warning: non-integer x = 1498.008928Warning: non-integer x = 1477.990779Warning: non-integer x = 1700.989331Warning: non-integer x = 1769.988530Warning: non-integer x = 1863.010966Warning: non-integer x = 1833.995336Warning: non-integer x = 1840.004563Warning: non-integer x = 1900.985839Warning: non-integer x = 1938.013119Warning: non-integer x = 1737.007881Warning: non-integer x = 1844.989357Warning: non-integer x = 1744.791954Warning: non-integer x = 1682.494935Warning: non-integer x = 1730.403689Warning: non-integer x = 1757.788714Warning: non-integer x = 1711.648025Warning: non-integer x = 1607.356298Warning: non-integer x = 1742.271785Warning: non-integer x = 1641.558666Warning: non-integer x = 1569.406513Warning: non-integer x = 1610.362315Warning: non-integer x = 1604.234228Warning: non-integer x = 1482.333246Warning: non-integer x = 1437.192991Warning: non-integer x = 1357.444324Warning: non-integer x = 1633.459184Warning: non-integer x = 1667.288011Warning: non-integer x = 884.920947Warning: non-integer x = 1024.176958Warning: non-integer x = 960.857360Warning: non-integer x = 858.007859Warning: non-integer x = 946.891948Warning: non-integer x = 846.978194Warning: non-integer x = 991.262949Warning: non-integer x = 828.488748Warning: non-integer x = 779.838035Warning: non-integer x = 943.870638Warning: non-integer x = 821.212103Warning: non-integer x = 910.451993Warning: non-integer x = 887.312427Warning: non-integer x = 892.339137Warning: non-integer x = 988.846623Warning: non-integer x = 1046.992209Warning: non-integer x = 1197.496366Warning: non-integer x = 985.940908Warning: non-integer x = 955.078118Warning: non-integer x = 985.717829Warning: non-integer x = 979.182045Warning: non-integer x = 1000.751973Warning: non-integer x = 1049.699123Warning: non-integer x = 1111.022439Warning: non-integer x = 1070.093197Warning: non-integer x = 1116.889718Warning: non-integer x = 1274.022311Warning: non-integer x = 1163.133183Warning: non-integer x = 1102.051030Warning: non-integer x = 1330.323692Warning: non-integer x = 1159.026228Warning: non-integer x = 1337.588874Warning: non-integer x = 1231.135465Warning: non-integer x = 1190.030774Warning: non-integer x = 1234.997897Warning: non-integer x = 1244.005691Warning: non-integer x = 1403.002982Warning: non-integer x = 1365.000252Warning: non-integer x = 1464.005402Warning: non-integer x = 1381.000504Warning: non-integer x = 1443.003007Warning: non-integer x = 1491.999324Warning: non-integer x = 1497.994160Warning: non-integer x = 1468.994573Warning: non-integer x = 1519.993361Warning: non-integer x = 1686.003585Warning: non-integer x = 1592.004778Warning: non-integer x = 1626.000354Warning: non-integer x = 1783.003899Warning: non-integer x = 1712.995232Warning: non-integer x = 1810.007416Warning: non-integer x = 1808.994805Warning: non-integer x = 1778.010280Warning: non-integer x = 1784.004413Warning: non-integer x = 1680.991592Warning: non-integer x = 1636.007490Warning: non-integer x = 1560.004101Warning: non-integer x = 1439.001890Warning: non-integer x = 1773.988431Warning: non-integer x = 1926.000361Warning: non-integer x = 1871.996625Warning: non-integer x = 1818.010916Warning: non-integer x = 1865.011815Warning: non-integer x = 1913.988541Warning: non-integer x = 1900.008960Warning: non-integer x = 1871.994859Warning: non-integer x = 1774.792238Warning: non-integer x = 1798.535396Warning: non-integer x = 1824.400567Warning: non-integer x = 1789.794176Warning: non-integer x = 1916.695708Warning: non-integer x = 1748.382324Warning: non-integer x = 1765.248719Warning: non-integer x = 1738.578308Warning: non-integer x = 1678.444164Warning: non-integer x = 1675.355007Warning: non-integer x = 1683.231251Warning: non-integer x = 1618.388822Warning: non-integer x = 1582.201210Warning: non-integer x = 1397.453072Warning: non-integer x = 1606.443812Warning: non-integer x = 1786.271993Warning: non-integer x = 625.351709Warning: non-integer x = 697.482082Warning: non-integer x = 609.178931Warning: non-integer x = 647.517669Warning: non-integer x = 641.962187Warning: non-integer x = 608.141962Warning: non-integer x = 670.210447Warning: non-integer x = 632.908610Warning: non-integer x = 591.401000Warning: non-integer x = 769.527590Warning: non-integer x = 671.988688Warning: non-integer x = 713.131688Warning: non-integer x = 639.940368Warning: non-integer x = 750.128041Warning: non-integer x = 872.627217Warning: non-integer x = 881.678544Warning: non-integer x = 955.188443Warning: non-integer x = 894.850640Warning: non-integer x = 839.951875Warning: non-integer x = 956.691550Warning: non-integer x = 986.182774Warning: non-integer x = 1000.751703Warning: non-integer x = 980.648359Warning: non-integer x = 1034.947313Warning: non-integer x = 1001.006150Warning: non-integer x = 1048.835955Warning: non-integer x = 1097.876851Warning: non-integer x = 1085.059881Warning: non-integer x = 1109.052454Warning: non-integer x = 1200.187940Warning: non-integer x = 1229.464147Warning: non-integer x = 1139.980268Warning: non-integer x = 1241.027165Warning: non-integer x = 1215.999547Warning: non-integer x = 1187.000319Warning: non-integer x = 1318.000276Warning: non-integer x = 1261.003458Warning: non-integer x = 1352.995872Warning: non-integer x = 1253.004198Warning: non-integer x = 1446.999018Warning: non-integer x = 1387.998630Warning: non-integer x = 1491.994724Warning: non-integer x = 1527.004109Warning: non-integer x = 1442.996804Warning: non-integer x = 1504.005593Warning: non-integer x = 1451.993395Warning: non-integer x = 1637.992424Warning: non-integer x = 1718.000829Warning: non-integer x = 1872.006996Warning: non-integer x = 1817.003699Warning: non-integer x = 1761.005453Warning: non-integer x = 1774.994817Warning: non-integer x = 1720.995710Warning: non-integer x = 1662.002872Warning: non-integer x = 1738.006439Warning: non-integer x = 1591.002356Warning: non-integer x = 1471.998005Warning: non-integer x = 1846.003549Warning: non-integer x = 1937.995913Warning: non-integer x = 1849.990061Warning: non-integer x = 1958.011767Warning: non-integer x = 1989.000736Warning: non-integer x = 1953.000672Warning: non-integer x = 1975.006312Warning: non-integer x = 1896.851956Warning: non-integer x = 1756.518667Warning: non-integer x = 1966.433248Warning: non-integer x = 1876.842818Warning: non-integer x = 1813.656310Warning: non-integer x = 1823.389064Warning: non-integer x = 1828.266279Warning: non-integer x = 1720.581313Warning: non-integer x = 1714.437677Warning: non-integer x = 1794.404508Warning: non-integer x = 1818.269287Warning: non-integer x = 1681.396757Warning: non-integer x = 1828.225352Warning: non-integer x = 1624.529203Warning: non-integer x = 1666.456071Warning: non-integer x = 1658.273642Warning: non-integer x = 995.160428Warning: non-integer x = 1044.228986Warning: non-integer x = 975.890150Warning: non-integer x = 894.089569Warning: non-integer x = 903.758373Warning: non-integer x = 822.888764Warning: non-integer x = 903.970632Warning: non-integer x = 840.537637Warning: non-integer x = 702.660376Warning: non-integer x = 814.622324Warning: non-integer x = 781.148154Warning: non-integer x = 832.330985Warning: non-integer x = 755.112314Warning: non-integer x = 831.250313Warning: non-integer x = 844.578089Warning: non-integer x = 870.649318Warning: non-integer x = 1082.349926Warning: non-integer x = 926.879427Warning: non-integer x = 809.922117Warning: non-integer x = 862.617726Warning: non-integer x = 981.181539Warning: non-integer x = 950.707829Warning: non-integer x = 909.599252Warning: non-integer x = 1095.008675Warning: non-integer x = 961.979137Warning: non-integer x = 1014.811913Warning: non-integer x = 1051.837862Warning: non-integer x = 1098.071155Warning: non-integer x = 1063.012851Warning: non-integer x = 1236.216826Warning: non-integer x = 1119.003482Warning: non-integer x = 1209.440852Warning: non-integer x = 1110.930978Warning: non-integer x = 1211.029858Warning: non-integer x = 1221.000466Warning: non-integer x = 1187.997418Warning: non-integer x = 1174.003924Warning: non-integer x = 1175.997624Warning: non-integer x = 1264.998033Warning: non-integer x = 1218.995309Warning: non-integer x = 1293.995190Warning: non-integer x = 1430.993766Warning: non-integer x = 1374.002917Warning: non-integer x = 1353.001699Warning: non-integer x = 1514.995637Warning: non-integer x = 1426.997115Warning: non-integer x = 1464.998030Warning: non-integer x = 1502.996892Warning: non-integer x = 1648.993482Warning: non-integer x = 1595.995442Warning: non-integer x = 1788.997694Warning: non-integer x = 1849.001198Warning: non-integer x = 1805.998618Warning: non-integer x = 1868.005550Warning: non-integer x = 1691.000549Warning: non-integer x = 1885.003537Warning: non-integer x = 1720.991616Warning: non-integer x = 1674.991129Warning: non-integer x = 1626.999507Warning: non-integer x = 1555.001000Warning: non-integer x = 1763.998083Warning: non-integer x = 1835.008726Warning: non-integer x = 1893.002703Warning: non-integer x = 1884.997560Warning: non-integer x = 1916.004080Warning: non-integer x = 1980.012210Warning: non-integer x = 1886.840076Warning: non-integer x = 1908.563668Warning: non-integer x = 1893.440746Warning: non-integer x = 1890.855456Warning: non-integer x = 1865.677625Warning: non-integer x = 1813.407788Warning: non-integer x = 1952.285887Warning: non-integer x = 1943.637199Warning: non-integer x = 1827.498692Warning: non-integer x = 1874.404833Warning: non-integer x = 1880.276228Warning: non-integer x = 1784.426477Warning: non-integer x = 1774.214495Warning: non-integer x = 1794.572365Warning: non-integer x = 1918.538764Warning: non-integer x = 1768.287110Warning: non-integer x = 521.130839Warning: non-integer x = 573.218851Warning: non-integer x = 521.010143Warning: non-integer x = 500.171400Warning: non-integer x = 515.578430Warning: non-integer x = 520.830851Warning: non-integer x = 541.780733Warning: non-integer x = 527.589315Warning: non-integer x = 481.140155Warning: non-integer x = 550.091404Warning: non-integer x = 534.789225Warning: non-integer x = 637.021977Warning: non-integer x = 599.890247Warning: non-integer x = 616.930368Warning: non-integer x = 632.180833Warning: non-integer x = 720.380926Warning: non-integer x = 857.070220Warning: non-integer x = 784.749547Warning: non-integer x = 681.771079Warning: non-integer x = 755.538501Warning: non-integer x = 805.970351Warning: non-integer x = 857.638892Warning: non-integer x = 936.619005Warning: non-integer x = 919.840784Warning: non-integer x = 918.930027Warning: non-integer x = 887.709267Warning: non-integer x = 1009.810882Warning: non-integer x = 981.962728Warning: non-integer x = 949.902430Warning: non-integer x = 1100.092378Warning: non-integer x = 1034.918893Warning: non-integer x = 1076.277970Warning: non-integer x = 1079.880501Warning: non-integer x = 1099.022462Warning: non-integer x = 1183.002171Warning: non-integer x = 1111.996881Warning: non-integer x = 1130.998005Warning: non-integer x = 1071.002971Warning: non-integer x = 1104.998374Warning: non-integer x = 1155.997737Warning: non-integer x = 1184.002479Warning: non-integer x = 1202.998118Warning: non-integer x = 1239.994968Warning: non-integer x = 1286.002905Warning: non-integer x = 1410.000333Warning: non-integer x = 1404.003943Warning: non-integer x = 1411.996860Warning: non-integer x = 1363.998129Warning: non-integer x = 1553.006307Warning: non-integer x = 1570.002096Warning: non-integer x = 1661.006909Warning: non-integer x = 1722.006990Warning: non-integer x = 1682.998215Warning: non-integer x = 1813.993862Warning: non-integer x = 1664.003291Warning: non-integer x = 1711.003350Warning: non-integer x = 1850.995995Warning: non-integer x = 1630.002398Warning: non-integer x = 1753.998967Warning: non-integer x = 1597.996844Warning: non-integer x = 1479.001534Warning: non-integer x = 1726.002687Warning: non-integer x = 1911.995571Warning: non-integer x = 2002.002463Warning: non-integer x = 1914.991990Warning: non-integer x = 2020.997775Warning: non-integer x = 1966.888607Warning: non-integer x = 1959.600665Warning: non-integer x = 2027.469651Warning: non-integer x = 1882.858926Warning: non-integer x = 1877.704620Warning: non-integer x = 1862.407617Warning: non-integer x = 1969.279980Warning: non-integer x = 1975.654032Warning: non-integer x = 1903.500322Warning: non-integer x = 1882.414068Warning: non-integer x = 1913.271289Warning: non-integer x = 1926.461001Warning: non-integer x = 1975.250955Warning: non-integer x = 1812.579251Warning: non-integer x = 2007.559979Warning: non-integer x = 1939.295414Warning: non-integer x = 647.409910Warning: non-integer x = 683.459278Warning: non-integer x = 610.179442Warning: non-integer x = 610.431260Warning: non-integer x = 621.900645Warning: non-integer x = 588.058894Warning: non-integer x = 675.220772Warning: non-integer x = 548.650202Warning: non-integer x = 563.329339Warning: non-integer x = 615.220910Warning: non-integer x = 585.859168Warning: non-integer x = 667.072733Warning: non-integer x = 606.900676Warning: non-integer x = 644.968796Warning: non-integer x = 690.290982Warning: non-integer x = 674.279725Warning: non-integer x = 871.091661Warning: non-integer x = 832.790539Warning: non-integer x = 705.802743Warning: non-integer x = 821.591196Warning: non-integer x = 829.992022Warning: non-integer x = 736.548867Warning: non-integer x = 823.538728Warning: non-integer x = 922.847965Warning: non-integer x = 826.839680Warning: non-integer x = 843.679515Warning: non-integer x = 957.760508Warning: non-integer x = 890.868474Warning: non-integer x = 918.870586Warning: non-integer x = 1054.039625Warning: non-integer x = 972.870630Warning: non-integer x = 1034.231811Warning: non-integer x = 976.701796Warning: non-integer x = 1071.019374Warning: non-integer x = 1095.998754Warning: non-integer x = 1040.998395Warning: non-integer x = 1117.002556Warning: non-integer x = 1059.999167Warning: non-integer x = 1087.001849Warning: non-integer x = 1024.002832Warning: non-integer x = 1106.000627Warning: non-integer x = 1113.000864Warning: non-integer x = 1308.997359Warning: non-integer x = 1296.000727Warning: non-integer x = 1259.002624Warning: non-integer x = 1303.004667Warning: non-integer x = 1400.003357Warning: non-integer x = 1376.995448Warning: non-integer x = 1565.997821Warning: non-integer x = 1549.006158Warning: non-integer x = 1591.004873Warning: non-integer x = 1790.003184Warning: non-integer x = 1644.994308Warning: non-integer x = 1684.006511Warning: non-integer x = 1814.002214Warning: non-integer x = 1694.003706Warning: non-integer x = 1686.001190Warning: non-integer x = 1606.996215Warning: non-integer x = 1568.994907Warning: non-integer x = 1459.994180Warning: non-integer x = 1976.005218Warning: non-integer x = 1806.007570Warning: non-integer x = 1957.007195Warning: non-integer x = 1846.827359Warning: non-integer x = 1943.590370Warning: non-integer x = 1937.434278Warning: non-integer x = 1933.874910Warning: non-integer x = 1935.711019Warning: non-integer x = 1906.412433Warning: non-integer x = 1960.279230Warning: non-integer x = 2001.667142Warning: non-integer x = 1996.526903Warning: non-integer x = 2011.427669Warning: non-integer x = 2017.282599Warning: non-integer x = 2039.470627Warning: non-integer x = 2099.250976Warning: non-integer x = 1967.632937Warning: non-integer x = 2183.618486Warning: non-integer x = 2175.337060Warning: non-integer x = 450.969793Warning: non-integer x = 558.190507Warning: non-integer x = 498.960727Warning: non-integer x = 540.269325Warning: non-integer x = 493.509030Warning: non-integer x = 527.849789Warning: non-integer x = 567.861011Warning: non-integer x = 577.740081Warning: non-integer x = 470.110793Warning: non-integer x = 523.040253Warning: non-integer x = 506.750468Warning: non-integer x = 572.909680Warning: non-integer x = 507.751189Warning: non-integer x = 612.920677Warning: non-integer x = 603.121531Warning: non-integer x = 612.170026Warning: non-integer x = 764.947833Warning: non-integer x = 627.600023Warning: non-integer x = 646.740086Warning: non-integer x = 674.492448Warning: non-integer x = 731.880604Warning: non-integer x = 710.528569Warning: non-integer x = 761.511342Warning: non-integer x = 735.669475Warning: non-integer x = 742.751423Warning: non-integer x = 774.610527Warning: non-integer x = 843.669011Warning: non-integer x = 833.810646Warning: non-integer x = 864.833012Warning: non-integer x = 923.911823Warning: non-integer x = 862.768923Warning: non-integer x = 920.090070Warning: non-integer x = 866.502830Warning: non-integer x = 956.020280Warning: non-integer x = 1019.997293Warning: non-integer x = 938.999739Warning: non-integer x = 1062.999837Warning: non-integer x = 977.997081Warning: non-integer x = 934.000217Warning: non-integer x = 918.998835Warning: non-integer x = 1053.001988Warning: non-integer x = 1001.002970Warning: non-integer x = 965.997332Warning: non-integer x = 1154.001368Warning: non-integer x = 1191.002504Warning: non-integer x = 1208.998151Warning: non-integer x = 1245.001571Warning: non-integer x = 1228.002445Warning: non-integer x = 1287.004169Warning: non-integer x = 1324.995378Warning: non-integer x = 1437.996188Warning: non-integer x = 1446.003267Warning: non-integer x = 1701.000934Warning: non-integer x = 1576.994603Warning: non-integer x = 1626.001699Warning: non-integer x = 1742.999701Warning: non-integer x = 1670.005898Warning: non-integer x = 1731.000601Warning: non-integer x = 1698.993383Warning: non-integer x = 1616.996062Warning: non-integer x = 1394.995716Warning: non-integer x = 1436.005522Warning: non-integer x = 1752.002993Warning: non-integer x = 1739.992833Warning: non-integer x = 1892.993868Warning: non-integer x = 1809.812348Warning: non-integer x = 1958.595233Warning: non-integer x = 1919.434388Warning: non-integer x = 1944.877386Warning: non-integer x = 1928.711575Warning: non-integer x = 1849.402111Warning: non-integer x = 1985.280476Warning: non-integer x = 2061.681705Warning: non-integer x = 1988.522676Warning: non-integer x = 2125.461610Warning: non-integer x = 2196.309122Warning: non-integer x = 2033.490559Warning: non-integer x = 2107.262371Warning: non-integer x = 2077.677262Warning: non-integer x = 2167.590842Warning: non-integer x = 2187.332016Warning: non-integer x = 508.101533Warning: non-integer x = 533.130244Warning: non-integer x = 525.009355Warning: non-integer x = 481.129785Warning: non-integer x = 500.529528Warning: non-integer x = 486.710778Warning: non-integer x = 512.690266Warning: non-integer x = 510.530404Warning: non-integer x = 450.059677Warning: non-integer x = 587.168721Warning: non-integer x = 520.760754Warning: non-integer x = 528.838358Warning: non-integer x = 495.729660Warning: non-integer x = 576.868895Warning: non-integer x = 590.100154Warning: non-integer x = 580.108253Warning: non-integer x = 693.870116Warning: non-integer x = 530.498591Warning: non-integer x = 554.630805Warning: non-integer x = 634.460852Warning: non-integer x = 648.780822Warning: non-integer x = 629.469196Warning: non-integer x = 658.439791Warning: non-integer x = 728.671971Warning: non-integer x = 634.641173Warning: non-integer x = 760.609470Warning: non-integer x = 740.591127Warning: non-integer x = 707.688811Warning: non-integer x = 693.659075Warning: non-integer x = 775.772238Warning: non-integer x = 787.699252Warning: non-integer x = 839.998926Warning: non-integer x = 763.329128Warning: non-integer x = 900.017831Warning: non-integer x = 911.000860Warning: non-integer x = 892.000195Warning: non-integer x = 927.998881Warning: non-integer x = 947.999396Warning: non-integer x = 862.997059Warning: non-integer x = 805.000970Warning: non-integer x = 826.002469Warning: non-integer x = 958.003288Warning: non-integer x = 867.001298Warning: non-integer x = 971.998443Warning: non-integer x = 1044.999539Warning: non-integer x = 1068.996536Warning: non-integer x = 1034.003566Warning: non-integer x = 1115.997191Warning: non-integer x = 1167.003452Warning: non-integer x = 1194.003025Warning: non-integer x = 1329.996808Warning: non-integer x = 1326.998428Warning: non-integer x = 1335.995829Warning: non-integer x = 1506.003793Warning: non-integer x = 1463.997124Warning: non-integer x = 1491.004969Warning: non-integer x = 1646.004064Warning: non-integer x = 1644.004444Warning: non-integer x = 1587.997389Warning: non-integer x = 1632.997607Warning: non-integer x = 1595.005645Warning: non-integer x = 1529.001199Warning: non-integer x = 1484.996287Warning: non-integer x = 1412.994937Warning: non-integer x = 1588.999718Warning: non-integer x = 1844.006568Warning: non-integer x = 1762.791199Warning: non-integer x = 1793.546952Warning: non-integer x = 1861.415636Warning: non-integer x = 1873.845344Warning: non-integer x = 1966.730210Warning: non-integer x = 1843.410709Warning: non-integer x = 1957.294459Warning: non-integer x = 1947.641664Warning: non-integer x = 1962.517294Warning: non-integer x = 2003.447366Warning: non-integer x = 2047.288475Warning: non-integer x = 2109.496129Warning: non-integer x = 2058.264215Warning: non-integer x = 2139.681843Warning: non-integer x = 2400.678543Warning: non-integer x = 2290.359232Warning: non-integer x = 523.130721Warning: non-integer x = 521.109660Warning: non-integer x = 479.929612Warning: non-integer x = 411.970058Warning: non-integer x = 472.439472Warning: non-integer x = 451.580618Warning: non-integer x = 533.751318Warning: non-integer x = 447.351076Warning: non-integer x = 394.940791Warning: non-integer x = 473.939463Warning: non-integer x = 409.599386Warning: non-integer x = 461.730422Warning: non-integer x = 465.689681Warning: non-integer x = 428.640024Warning: non-integer x = 427.800280Warning: non-integer x = 504.959828Warning: non-integer x = 604.760974Warning: non-integer x = 519.500950Warning: non-integer x = 450.510294Warning: non-integer x = 541.390195Warning: non-integer x = 615.739151Warning: non-integer x = 559.408272Warning: non-integer x = 604.398560Warning: non-integer x = 613.571265Warning: non-integer x = 610.621012Warning: non-integer x = 629.499548Warning: non-integer x = 660.530996Warning: non-integer x = 613.600144Warning: non-integer x = 667.640237Warning: non-integer x = 666.658066Warning: non-integer x = 657.579340Warning: non-integer x = 706.838231Warning: non-integer x = 653.130546Warning: non-integer x = 731.019601Warning: non-integer x = 806.001887Warning: non-integer x = 706.001001Warning: non-integer x = 795.999761Warning: non-integer x = 765.000397Warning: non-integer x = 815.000889Warning: non-integer x = 759.000305Warning: non-integer x = 742.002333Warning: non-integer x = 789.000271Warning: non-integer x = 728.999414Warning: non-integer x = 858.000504Warning: non-integer x = 894.002142Warning: non-integer x = 978.001973Warning: non-integer x = 943.001922Warning: non-integer x = 1010.997637Warning: non-integer x = 1122.002584Warning: non-integer x = 1100.997926Warning: non-integer x = 1116.997543Warning: non-integer x = 1189.998398Warning: non-integer x = 1264.004362Warning: non-integer x = 1372.000600Warning: non-integer x = 1256.999174Warning: non-integer x = 1364.000291Warning: non-integer x = 1466.998931Warning: non-integer x = 1472.002452Warning: non-integer x = 1536.999345Warning: non-integer x = 1546.997626Warning: non-integer x = 1420.998445Warning: non-integer x = 1515.997511Warning: non-integer x = 1496.998312Warning: non-integer x = 1448.002555Warning: non-integer x = 1365.000833Warning: non-integer x = 1516.004110Warning: non-integer x = 1600.719276Warning: non-integer x = 1657.501559Warning: non-integer x = 1740.393432Warning: non-integer x = 1827.827001Warning: non-integer x = 1859.674577Warning: non-integer x = 1782.396109Warning: non-integer x = 1950.272376Warning: non-integer x = 1921.636561Warning: non-integer x = 1916.496601Warning: non-integer x = 1996.441277Warning: non-integer x = 2080.305281Warning: non-integer x = 2014.467287Warning: non-integer x = 2177.261024Warning: non-integer x = 2059.665995Warning: non-integer x = 2304.636558Warning: non-integer x = 2419.381543Warning: non-integer x = 363.789931Warning: non-integer x = 383.821701Warning: non-integer x = 360.700179Warning: non-integer x = 334.780681Warning: non-integer x = 335.029686Warning: non-integer x = 339.189856Warning: non-integer x = 393.300768Warning: non-integer x = 396.189917Warning: non-integer x = 308.729943Warning: non-integer x = 377.750069Warning: non-integer x = 321.470265Warning: non-integer x = 379.598594Warning: non-integer x = 346.511590Warning: non-integer x = 343.510746Warning: non-integer x = 381.719083Warning: non-integer x = 399.759074Warning: non-integer x = 487.611652Warning: non-integer x = 384.359779Warning: non-integer x = 395.450577Warning: non-integer x = 405.300624Warning: non-integer x = 460.559110Warning: non-integer x = 463.349883Warning: non-integer x = 480.320279Warning: non-integer x = 530.480764Warning: non-integer x = 503.510189Warning: non-integer x = 526.418982Warning: non-integer x = 507.408817Warning: non-integer x = 551.539028Warning: non-integer x = 572.540712Warning: non-integer x = 590.580425Warning: non-integer x = 519.460014Warning: non-integer x = 601.722375Warning: non-integer x = 565.988749Warning: non-integer x = 604.012215Warning: non-integer x = 634.000296Warning: non-integer x = 659.000598Warning: non-integer x = 708.998731Warning: non-integer x = 665.999313Warning: non-integer x = 696.001929Warning: non-integer x = 686.000900Warning: non-integer x = 685.000197Warning: non-integer x = 688.001003Warning: non-integer x = 649.998977Warning: non-integer x = 712.000473Warning: non-integer x = 761.998777Warning: non-integer x = 843.001152Warning: non-integer x = 868.997376Warning: non-integer x = 909.001679Warning: non-integer x = 956.998630Warning: non-integer x = 1057.999569Warning: non-integer x = 1057.998309Warning: non-integer x = 1012.000199Warning: non-integer x = 1206.997195Warning: non-integer x = 1184.997130Warning: non-integer x = 1139.998466Warning: non-integer x = 1357.998229Warning: non-integer x = 1387.997210Warning: non-integer x = 1367.999274Warning: non-integer x = 1465.997595Warning: non-integer x = 1424.998130Warning: non-integer x = 1424.996358Warning: non-integer x = 1367.003843Warning: non-integer x = 1421.998851Warning: non-integer x = 1270.004111Warning: non-integer x = 1306.003230Warning: non-integer x = 1507.677863Warning: non-integer x = 1590.480846Warning: non-integer x = 1592.349129Warning: non-integer x = 1720.774478Warning: non-integer x = 1883.704055Warning: non-integer x = 1770.392537Warning: non-integer x = 1940.273929Warning: non-integer x = 1904.628755Warning: non-integer x = 1854.486981Warning: non-integer x = 1894.420282Warning: non-integer x = 1994.296867Warning: non-integer x = 2092.499029Warning: non-integer x = 2092.247540Warning: non-integer x = 2144.693212Warning: non-integer x = 2220.602133Warning: non-integer x = 2314.365857Warning: non-integer x = 276.600697Warning: non-integer x = 300.641348Warning: non-integer x = 249.478539Warning: non-integer x = 269.630139Warning: non-integer x = 268.819406Warning: non-integer x = 308.089140Warning: non-integer x = 309.019658Warning: non-integer x = 279.841018Warning: non-integer x = 252.601380Warning: non-integer x = 328.649712Warning: non-integer x = 283.409803Warning: non-integer x = 313.500845Warning: non-integer x = 297.441361Warning: non-integer x = 313.470413Warning: non-integer x = 353.660354Warning: non-integer x = 331.629245Warning: non-integer x = 377.479529Warning: non-integer x = 346.321329Warning: non-integer x = 284.320678Warning: non-integer x = 343.248746Warning: non-integer x = 361.429979Warning: non-integer x = 363.268936Warning: non-integer x = 408.271029Warning: non-integer x = 428.389643Warning: non-integer x = 414.420050Warning: non-integer x = 435.340702Warning: non-integer x = 477.380276Warning: non-integer x = 416.399231Warning: non-integer x = 473.451139Warning: non-integer x = 531.519296Warning: non-integer x = 441.390292Warning: non-integer x = 494.591240Warning: non-integer x = 487.840470Warning: non-integer x = 532.009948Warning: non-integer x = 532.999755Warning: non-integer x = 555.000871Warning: non-integer x = 573.000941Warning: non-integer x = 580.000605Warning: non-integer x = 546.999518Warning: non-integer x = 552.999937Warning: non-integer x = 650.000075Warning: non-integer x = 580.000986Warning: non-integer x = 599.999818Warning: non-integer x = 617.997945Warning: non-integer x = 662.000941Warning: non-integer x = 699.000992Warning: non-integer x = 665.001356Warning: non-integer x = 672.001799Warning: non-integer x = 795.000412Warning: non-integer x = 795.999764Warning: non-integer x = 942.999388Warning: non-integer x = 959.998323Warning: non-integer x = 888.002137Warning: non-integer x = 1009.997856Warning: non-integer x = 1009.001696Warning: non-integer x = 1206.002174Warning: non-integer x = 1173.999563Warning: non-integer x = 1256.999223Warning: non-integer x = 1397.998733Warning: non-integer x = 1312.000392Warning: non-integer x = 1294.001253Warning: non-integer x = 1327.995801Warning: non-integer x = 1323.999683Warning: non-integer x = 1199.998674Warning: non-integer x = 1273.000245Warning: non-integer x = 1105.503417Warning: non-integer x = 1339.400183Warning: non-integer x = 1563.350564Warning: non-integer x = 1468.664553Warning: non-integer x = 1616.595620Warning: non-integer x = 1578.347233Warning: non-integer x = 1744.260268Warning: non-integer x = 1695.564566Warning: non-integer x = 1747.455179Warning: non-integer x = 1751.386156Warning: non-integer x = 1872.275847Warning: non-integer x = 1882.447893Warning: non-integer x = 1997.238418Warning: non-integer x = 1911.608469Warning: non-integer x = 2243.622032Warning: non-integer x = 2266.367207Warning: non-integer x = 275.599692Warning: non-integer x = 317.679678Warning: non-integer x = 218.420252Warning: non-integer x = 241.571000Warning: non-integer x = 253.771676Warning: non-integer x = 269.951290Warning: non-integer x = 282.928666Warning: non-integer x = 254.771195Warning: non-integer x = 268.629967Warning: non-integer x = 277.549679Warning: non-integer x = 254.380976Warning: non-integer x = 288.460707Warning: non-integer x = 270.399896Warning: non-integer x = 292.439595Warning: non-integer x = 262.489382Warning: non-integer x = 290.560768Warning: non-integer x = 310.381779Warning: non-integer x = 293.281659Warning: non-integer x = 260.291635Warning: non-integer x = 311.221565Warning: non-integer x = 304.370709Warning: non-integer x = 307.229331Warning: non-integer x = 280.178960Warning: non-integer x = 375.340898Warning: non-integer x = 358.360151Warning: non-integer x = 364.290538Warning: non-integer x = 405.329923Warning: non-integer x = 356.341455Warning: non-integer x = 411.389821Warning: non-integer x = 421.420845Warning: non-integer x = 374.331412Warning: non-integer x = 413.489674Warning: non-integer x = 408.711307Warning: non-integer x = 410.009824Warning: non-integer x = 413.001320Warning: non-integer x = 445.000730Warning: non-integer x = 464.000211Warning: non-integer x = 461.000180Warning: non-integer x = 470.000842Warning: non-integer x = 440.000467Warning: non-integer x = 477.001573Warning: non-integer x = 506.001428Warning: non-integer x = 482.000596Warning: non-integer x = 536.000893Warning: non-integer x = 534.998929Warning: non-integer x = 571.999251Warning: non-integer x = 588.001090Warning: non-integer x = 569.000338Warning: non-integer x = 688.998891Warning: non-integer x = 713.998895Warning: non-integer x = 797.999322Warning: non-integer x = 762.001435Warning: non-integer x = 886.000141Warning: non-integer x = 814.998563Warning: non-integer x = 886.001406Warning: non-integer x = 996.997741Warning: non-integer x = 1045.001329Warning: non-integer x = 1116.997810Warning: non-integer x = 1148.002010Warning: non-integer x = 1141.999693Warning: non-integer x = 1172.001268Warning: non-integer x = 1223.001022Warning: non-integer x = 1104.000827Warning: non-integer x = 1202.996934Warning: non-integer x = 1075.477793Warning: non-integer x = 1104.329520Warning: non-integer x = 1306.292632Warning: non-integer x = 1394.631436Warning: non-integer x = 1446.525406Warning: non-integer x = 1414.315238Warning: non-integer x = 1594.244104Warning: non-integer x = 1611.540039Warning: non-integer x = 1568.413690Warning: non-integer x = 1724.374384Warning: non-integer x = 1773.256959Warning: non-integer x = 1766.416322Warning: non-integer x = 1811.231202Warning: non-integer x = 1809.593784Warning: non-integer x = 2140.603700Warning: non-integer x = 2178.347748Warning: non-integer x = 218.471256Warning: non-integer x = 181.390997Warning: non-integer x = 158.309679Warning: non-integer x = 158.370969Warning: non-integer x = 177.539234Warning: non-integer x = 140.499352Warning: non-integer x = 153.510644Warning: non-integer x = 173.519577Warning: non-integer x = 163.389072Warning: non-integer x = 163.320715Warning: non-integer x = 194.279358Warning: non-integer x = 155.250230Warning: non-integer x = 166.250283Warning: non-integer x = 202.309632Warning: non-integer x = 184.340942Warning: non-integer x = 187.361134Warning: non-integer x = 240.300639Warning: non-integer x = 207.199280Warning: non-integer x = 177.199422Warning: non-integer x = 231.171629Warning: non-integer x = 248.299170Warning: non-integer x = 220.159034Warning: non-integer x = 226.150220Warning: non-integer x = 265.248316Warning: non-integer x = 254.259261Warning: non-integer x = 266.210608Warning: non-integer x = 304.251915Warning: non-integer x = 305.299693Warning: non-integer x = 288.281723Warning: non-integer x = 359.350686Warning: non-integer x = 293.259848Warning: non-integer x = 358.429408Warning: non-integer x = 337.590105Warning: non-integer x = 369.011645Warning: non-integer x = 346.001289Warning: non-integer x = 348.001603Warning: non-integer x = 395.999601Warning: non-integer x = 331.999422Warning: non-integer x = 376.998825Warning: non-integer x = 403.001136Warning: non-integer x = 374.001930Warning: non-integer x = 441.000311Warning: non-integer x = 439.001120Warning: non-integer x = 430.999887Warning: non-integer x = 467.000800Warning: non-integer x = 450.000059Warning: non-integer x = 496.999925Warning: non-integer x = 522.001296Warning: non-integer x = 526.999550Warning: non-integer x = 625.000865Warning: non-integer x = 637.001203Warning: non-integer x = 679.002234Warning: non-integer x = 753.998362Warning: non-integer x = 673.001464Warning: non-integer x = 725.999780Warning: non-integer x = 837.998344Warning: non-integer x = 819.001633Warning: non-integer x = 887.000840Warning: non-integer x = 911.000213Warning: non-integer x = 960.999295Warning: non-integer x = 1017.000961Warning: non-integer x = 1070.998849Warning: non-integer x = 1073.001903Warning: non-integer x = 980.001563Warning: non-integer x = 1003.002512Warning: non-integer x = 1022.462187Warning: non-integer x = 1000.300342Warning: non-integer x = 975.217559Warning: non-integer x = 1205.549758Warning: non-integer x = 1337.490540Warning: non-integer x = 1311.291466Warning: non-integer x = 1434.210786Warning: non-integer x = 1486.498617Warning: non-integer x = 1598.418784Warning: non-integer x = 1557.336304Warning: non-integer x = 1658.243902Warning: non-integer x = 1614.379635Warning: non-integer x = 1788.215606Warning: non-integer x = 1664.543091Warning: non-integer x = 1954.535337Warning: non-integer x = 2068.326002

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)