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)

# There are packages that link to Human Mortality Database
install.packages("demography")

Error in install.packages : Updating loaded packages

library(demography)

# Load mortality data with login details of Human Mortality Database 
download_data <- hmd.mx(country = "PRT", username = "f.hagelstein@student.maastrichtuniversity.nl", password = "Life_In$urance_2")
install.packages("demography")

WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:

https://cran.rstudio.com/bin/windows/Rtools/

Warning in install.packages :
  package ‘demography’ is in use and will not be installed

install.packages("StMoMo")

Error in install.packages : Updating loaded packages

PT_data_total <- download_data

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

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

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

Model fitting

# Model fitting
PRTmale <- StMoMoData(PT_data_total, series = "total")
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 = 879.654092Warning: non-integer x = 894.705442Warning: non-integer x = 879.448007Warning: non-integer x = 879.599562Warning: non-integer x = 848.160866Warning: non-integer x = 849.539749Warning: non-integer x = 859.401700Warning: non-integer x = 757.978451Warning: non-integer x = 841.715815Warning: non-integer x = 806.472443Warning: non-integer x = 767.018048Warning: non-integer x = 798.120074Warning: non-integer x = 660.899536Warning: non-integer x = 659.869199Warning: non-integer x = 648.933169Warning: non-integer x = 720.994483Warning: non-integer x = 772.701103Warning: non-integer x = 733.506018Warning: non-integer x = 602.453546Warning: non-integer x = 650.356121Warning: non-integer x = 695.624089Warning: non-integer x = 668.424966Warning: non-integer x = 612.287554Warning: non-integer x = 661.553973Warning: non-integer x = 604.499701Warning: non-integer x = 620.393101Warning: non-integer x = 709.458020Warning: non-integer x = 619.497278Warning: non-integer x = 553.430082Warning: non-integer x = 560.481615Warning: non-integer x = 587.463160Warning: non-integer x = 640.572079Warning: non-integer x = 587.835590Warning: non-integer x = 662.992323Warning: non-integer x = 694.970097Warning: non-integer x = 714.962021Warning: non-integer x = 751.035053Warning: non-integer x = 670.026173Warning: non-integer x = 612.042409Warning: non-integer x = 642.050107Warning: non-integer x = 610.965863Warning: non-integer x = 694.988395Warning: non-integer x = 633.058332Warning: non-integer x = 643.010676Warning: non-integer x = 644.968376Warning: non-integer x = 653.950549Warning: non-integer x = 617.032930Warning: non-integer x = 584.986411Warning: non-integer x = 548.961504Warning: non-integer x = 525.982544Warning: non-integer x = 523.040090Warning: non-integer x = 532.052052Warning: non-integer x = 470.010992Warning: non-integer x = 553.007758Warning: non-integer x = 496.033541Warning: non-integer x = 526.998678Warning: non-integer x = 497.031857Warning: non-integer x = 521.002241Warning: non-integer x = 544.051432Warning: non-integer x = 526.029766Warning: non-integer x = 510.990227Warning: non-integer x = 500.968359Warning: non-integer x = 517.048003Warning: non-integer x = 557.934008Warning: non-integer x = 529.934325Warning: non-integer x = 587.952436Warning: non-integer x = 539.167336Warning: non-integer x = 502.158374Warning: non-integer x = 553.064407Warning: non-integer x = 557.193801Warning: non-integer x = 516.240674Warning: non-integer x = 527.143014Warning: non-integer x = 498.031827Warning: non-integer x = 555.158473Warning: non-integer x = 486.021362Warning: non-integer x = 447.065193Warning: non-integer x = 499.081343Warning: non-integer x = 452.022429Warning: non-integer x = 437.032075Warning: non-integer x = 407.130033Warning: non-integer x = 449.092619Warning: non-integer x = 447.055973Warning: non-integer x = 688.313740Warning: non-integer x = 665.242950Warning: non-integer x = 645.082413Warning: non-integer x = 619.111484Warning: non-integer x = 658.676925Warning: non-integer x = 632.862328Warning: non-integer x = 655.888406Warning: non-integer x = 589.527834Warning: non-integer x = 693.360023Warning: non-integer x = 642.186113Warning: non-integer x = 607.765910Warning: non-integer x = 699.997901Warning: non-integer x = 640.878597Warning: non-integer x = 547.735762Warning: non-integer x = 637.905713Warning: non-integer x = 659.001994Warning: non-integer x = 694.646751Warning: non-integer x = 681.503342Warning: non-integer x = 625.475021Warning: non-integer x = 575.333039Warning: non-integer x = 628.641480Warning: non-integer x = 683.438664Warning: non-integer x = 660.402682Warning: non-integer x = 675.560717Warning: non-integer x = 738.607643Warning: non-integer x = 632.392604Warning: non-integer x = 678.424310Warning: non-integer x = 617.464724Warning: non-integer x = 572.446789Warning: non-integer x = 563.522274Warning: non-integer x = 482.321453Warning: non-integer x = 647.538016Warning: non-integer x = 641.957706Warning: non-integer x = 632.031773Warning: non-integer x = 634.050625Warning: non-integer x = 697.955563Warning: non-integer x = 763.033836Warning: non-integer x = 704.978776Warning: non-integer x = 669.953024Warning: non-integer x = 649.039497Warning: non-integer x = 745.021029Warning: non-integer x = 658.985149Warning: non-integer x = 700.959152Warning: non-integer x = 745.030233Warning: non-integer x = 670.042669Warning: non-integer x = 624.981531Warning: non-integer x = 663.013429Warning: non-integer x = 638.034156Warning: non-integer x = 628.045953Warning: non-integer x = 594.039090Warning: non-integer x = 574.034830Warning: non-integer x = 564.950199Warning: non-integer x = 510.952119Warning: non-integer x = 495.971712Warning: non-integer x = 511.009912Warning: non-integer x = 522.029426Warning: non-integer x = 561.055685Warning: non-integer x = 559.042019Warning: non-integer x = 566.978892Warning: non-integer x = 569.008003Warning: non-integer x = 559.047463Warning: non-integer x = 524.950125Warning: non-integer x = 586.952228Warning: non-integer x = 564.021332Warning: non-integer x = 550.937390Warning: non-integer x = 608.971358Warning: non-integer x = 551.216652Warning: non-integer x = 582.155905Warning: non-integer x = 573.124447Warning: non-integer x = 580.170832Warning: non-integer x = 561.119159Warning: non-integer x = 589.132783Warning: non-integer x = 553.045439Warning: non-integer x = 537.082390Warning: non-integer x = 545.106034Warning: non-integer x = 488.101470Warning: non-integer x = 514.041342Warning: non-integer x = 559.042923Warning: non-integer x = 496.995686Warning: non-integer x = 452.045933Warning: non-integer x = 487.126679Warning: non-integer x = 478.027018Warning: non-integer x = 803.528679Warning: non-integer x = 948.820489Warning: non-integer x = 895.510825Warning: non-integer x = 882.608987Warning: non-integer x = 796.034524Warning: non-integer x = 878.596903Warning: non-integer x = 829.316425Warning: non-integer x = 765.937381Warning: non-integer x = 770.529863Warning: non-integer x = 832.488452Warning: non-integer x = 687.917722Warning: non-integer x = 799.177909Warning: non-integer x = 745.015211Warning: non-integer x = 719.914846Warning: non-integer x = 674.985106Warning: non-integer x = 811.182957Warning: non-integer x = 853.764784Warning: non-integer x = 810.624533Warning: non-integer x = 685.574752Warning: non-integer x = 714.428945Warning: non-integer x = 732.710857Warning: non-integer x = 729.467057Warning: non-integer x = 757.388813Warning: non-integer x = 763.669953Warning: non-integer x = 753.607218Warning: non-integer x = 735.485711Warning: non-integer x = 780.494365Warning: non-integer x = 764.598372Warning: non-integer x = 685.464275Warning: non-integer x = 688.571582Warning: non-integer x = 585.487892Warning: non-integer x = 603.517079Warning: non-integer x = 679.991239Warning: non-integer x = 721.965644Warning: non-integer x = 781.969305Warning: non-integer x = 791.972545Warning: non-integer x = 821.004600Warning: non-integer x = 772.969726Warning: non-integer x = 716.979442Warning: non-integer x = 754.981363Warning: non-integer x = 739.012243Warning: non-integer x = 802.951626Warning: non-integer x = 726.987218Warning: non-integer x = 720.997169Warning: non-integer x = 744.001094Warning: non-integer x = 637.053561Warning: non-integer x = 679.055201Warning: non-integer x = 660.985027Warning: non-integer x = 669.959533Warning: non-integer x = 529.955079Warning: non-integer x = 614.033631Warning: non-integer x = 609.950793Warning: non-integer x = 606.987656Warning: non-integer x = 557.976143Warning: non-integer x = 530.968096Warning: non-integer x = 573.994666Warning: non-integer x = 637.045367Warning: non-integer x = 560.002962Warning: non-integer x = 587.983484Warning: non-integer x = 531.973883Warning: non-integer x = 584.977828Warning: non-integer x = 650.055418Warning: non-integer x = 584.057257Warning: non-integer x = 607.974929Warning: non-integer x = 601.940487Warning: non-integer x = 586.026483Warning: non-integer x = 565.150014Warning: non-integer x = 644.192405Warning: non-integer x = 578.185387Warning: non-integer x = 599.184445Warning: non-integer x = 575.198094Warning: non-integer x = 640.127151Warning: non-integer x = 538.009010Warning: non-integer x = 605.145436Warning: non-integer x = 620.134515Warning: non-integer x = 582.076599Warning: non-integer x = 592.021738Warning: non-integer x = 591.147823Warning: non-integer x = 544.105695Warning: non-integer x = 552.065549Warning: non-integer x = 536.043431Warning: non-integer x = 539.050011Warning: non-integer x = 752.430601Warning: non-integer x = 876.681130Warning: non-integer x = 829.376176Warning: non-integer x = 854.601386Warning: non-integer x = 821.101183Warning: non-integer x = 840.445942Warning: non-integer x = 865.377209Warning: non-integer x = 775.936335Warning: non-integer x = 791.571775Warning: non-integer x = 799.468374Warning: non-integer x = 720.947405Warning: non-integer x = 782.103584Warning: non-integer x = 705.009711Warning: non-integer x = 791.072755Warning: non-integer x = 757.055561Warning: non-integer x = 658.998592Warning: non-integer x = 866.852796Warning: non-integer x = 788.610673Warning: non-integer x = 708.572203Warning: non-integer x = 764.422045Warning: non-integer x = 765.723727Warning: non-integer x = 753.504185Warning: non-integer x = 757.438890Warning: non-integer x = 837.708310Warning: non-integer x = 817.740664Warning: non-integer x = 799.491807Warning: non-integer x = 910.681792Warning: non-integer x = 768.642640Warning: non-integer x = 726.568398Warning: non-integer x = 772.692009Warning: non-integer x = 706.527402Warning: non-integer x = 670.598628Warning: non-integer x = 615.850157Warning: non-integer x = 769.001465Warning: non-integer x = 779.966103Warning: non-integer x = 828.980612Warning: non-integer x = 877.980888Warning: non-integer x = 850.044464Warning: non-integer x = 800.027634Warning: non-integer x = 797.035795Warning: non-integer x = 762.996791Warning: non-integer x = 828.024151Warning: non-integer x = 737.987193Warning: non-integer x = 740.981488Warning: non-integer x = 777.965910Warning: non-integer x = 817.952784Warning: non-integer x = 722.963498Warning: non-integer x = 711.978948Warning: non-integer x = 690.968119Warning: non-integer x = 686.051430Warning: non-integer x = 715.049055Warning: non-integer x = 690.970748Warning: non-integer x = 664.974052Warning: non-integer x = 676.012635Warning: non-integer x = 627.956654Warning: non-integer x = 510.980617Warning: non-integer x = 647.011232Warning: non-integer x = 619.945935Warning: non-integer x = 635.025755Warning: non-integer x = 645.993279Warning: non-integer x = 582.008857Warning: non-integer x = 601.013514Warning: non-integer x = 685.005156Warning: non-integer x = 636.001504Warning: non-integer x = 631.044346Warning: non-integer x = 618.999283Warning: non-integer x = 617.239662Warning: non-integer x = 604.091245Warning: non-integer x = 607.054793Warning: non-integer x = 686.289134Warning: non-integer x = 636.274087Warning: non-integer x = 683.153587Warning: non-integer x = 674.130480Warning: non-integer x = 623.193451Warning: non-integer x = 614.106596Warning: non-integer x = 599.149772Warning: non-integer x = 590.023209Warning: non-integer x = 634.129058Warning: non-integer x = 585.997400Warning: non-integer x = 609.202895Warning: non-integer x = 642.052139Warning: non-integer x = 579.073897Warning: non-integer x = 832.593581Warning: non-integer x = 901.739461Warning: non-integer x = 909.497426Warning: non-integer x = 806.472304Warning: non-integer x = 881.275251Warning: non-integer x = 869.612064Warning: non-integer x = 904.519971Warning: non-integer x = 762.942808Warning: non-integer x = 814.654734Warning: non-integer x = 875.585804Warning: non-integer x = 764.003714Warning: non-integer x = 784.113145Warning: non-integer x = 723.016469Warning: non-integer x = 662.859612Warning: non-integer x = 803.131310Warning: non-integer x = 928.397854Warning: non-integer x = 859.787284Warning: non-integer x = 830.585293Warning: non-integer x = 741.607198Warning: non-integer x = 763.408179Warning: non-integer x = 756.705948Warning: non-integer x = 798.471946Warning: non-integer x = 829.441617Warning: non-integer x = 790.673300Warning: non-integer x = 890.747606Warning: non-integer x = 831.541553Warning: non-integer x = 899.687136Warning: non-integer x = 910.743958Warning: non-integer x = 842.579150Warning: non-integer x = 897.766269Warning: non-integer x = 709.591667Warning: non-integer x = 749.709485Warning: non-integer x = 702.019588Warning: non-integer x = 596.974125Warning: non-integer x = 782.978673Warning: non-integer x = 926.999457Warning: non-integer x = 912.970956Warning: non-integer x = 873.018483Warning: non-integer x = 800.023132Warning: non-integer x = 800.001334Warning: non-integer x = 862.999224Warning: non-integer x = 795.949946Warning: non-integer x = 834.999462Warning: non-integer x = 844.976983Warning: non-integer x = 859.983175Warning: non-integer x = 874.020531Warning: non-integer x = 802.046717Warning: non-integer x = 794.974998Warning: non-integer x = 800.029401Warning: non-integer x = 710.004370Warning: non-integer x = 755.943438Warning: non-integer x = 711.995988Warning: non-integer x = 715.962645Warning: non-integer x = 724.980619Warning: non-integer x = 613.000104Warning: non-integer x = 579.003508Warning: non-integer x = 598.994214Warning: non-integer x = 605.951576Warning: non-integer x = 602.967069Warning: non-integer x = 652.997297Warning: non-integer x = 670.946656Warning: non-integer x = 613.024080Warning: non-integer x = 645.982670Warning: non-integer x = 677.954414Warning: non-integer x = 648.031287Warning: non-integer x = 647.010713Warning: non-integer x = 623.157694Warning: non-integer x = 675.223779Warning: non-integer x = 671.154374Warning: non-integer x = 667.283123Warning: non-integer x = 701.223973Warning: non-integer x = 651.048318Warning: non-integer x = 678.133124Warning: non-integer x = 644.139280Warning: non-integer x = 637.124517Warning: non-integer x = 616.113856Warning: non-integer x = 644.088153Warning: non-integer x = 639.097179Warning: non-integer x = 603.106516Warning: non-integer x = 596.079830Warning: non-integer x = 644.096999Warning: non-integer x = 638.026951Warning: non-integer x = 959.802648Warning: non-integer x = 1064.033559Warning: non-integer x = 960.559232Warning: non-integer x = 941.701749Warning: non-integer x = 984.488414Warning: non-integer x = 1041.071646Warning: non-integer x = 995.745719Warning: non-integer x = 912.271046Warning: non-integer x = 857.698452Warning: non-integer x = 844.566006Warning: non-integer x = 786.022153Warning: non-integer x = 829.204590Warning: non-integer x = 772.059891Warning: non-integer x = 782.026654Warning: non-integer x = 762.077089Warning: non-integer x = 920.401436Warning: non-integer x = 1021.931872Warning: non-integer x = 878.668190Warning: non-integer x = 767.584773Warning: non-integer x = 782.398921Warning: non-integer x = 784.752292Warning: non-integer x = 784.499573Warning: non-integer x = 824.463425Warning: non-integer x = 845.720331Warning: non-integer x = 867.769003Warning: non-integer x = 916.526550Warning: non-integer x = 1015.759485Warning: non-integer x = 949.725092Warning: non-integer x = 901.652072Warning: non-integer x = 908.795070Warning: non-integer x = 804.624077Warning: non-integer x = 850.766285Warning: non-integer x = 757.050159Warning: non-integer x = 719.002302Warning: non-integer x = 694.983451Warning: non-integer x = 902.974492Warning: non-integer x = 965.997963Warning: non-integer x = 883.993926Warning: non-integer x = 879.014476Warning: non-integer x = 862.987469Warning: non-integer x = 918.985695Warning: non-integer x = 896.981048Warning: non-integer x = 836.010428Warning: non-integer x = 857.047269Warning: non-integer x = 903.046928Warning: non-integer x = 869.992532Warning: non-integer x = 947.971163Warning: non-integer x = 852.021876Warning: non-integer x = 847.034758Warning: non-integer x = 766.992818Warning: non-integer x = 789.970569Warning: non-integer x = 839.960427Warning: non-integer x = 812.962109Warning: non-integer x = 833.039726Warning: non-integer x = 689.982540Warning: non-integer x = 677.997791Warning: non-integer x = 672.951528Warning: non-integer x = 638.035166Warning: non-integer x = 671.957586Warning: non-integer x = 686.999699Warning: non-integer x = 691.969696Warning: non-integer x = 730.951519Warning: non-integer x = 646.048872Warning: non-integer x = 690.002829Warning: non-integer x = 686.026592Warning: non-integer x = 711.941872Warning: non-integer x = 688.274415Warning: non-integer x = 684.093089Warning: non-integer x = 692.128034Warning: non-integer x = 663.273395Warning: non-integer x = 709.296715Warning: non-integer x = 733.189490Warning: non-integer x = 680.056920Warning: non-integer x = 700.168734Warning: non-integer x = 699.063078Warning: non-integer x = 697.128272Warning: non-integer x = 699.155597Warning: non-integer x = 685.126079Warning: non-integer x = 695.039730Warning: non-integer x = 706.196466Warning: non-integer x = 712.087417Warning: non-integer x = 712.030701Warning: non-integer x = 927.760570Warning: non-integer x = 966.832473Warning: non-integer x = 1002.692738Warning: non-integer x = 907.640256Warning: non-integer x = 1007.538254Warning: non-integer x = 940.808385Warning: non-integer x = 1019.834238Warning: non-integer x = 899.283969Warning: non-integer x = 879.737742Warning: non-integer x = 985.820718Warning: non-integer x = 837.110046Warning: non-integer x = 920.320283Warning: non-integer x = 829.168507Warning: non-integer x = 845.127036Warning: non-integer x = 847.222188Warning: non-integer x = 852.285719Warning: non-integer x = 1046.002437Warning: non-integer x = 1071.786342Warning: non-integer x = 804.607962Warning: non-integer x = 852.462368Warning: non-integer x = 879.821784Warning: non-integer x = 917.572275Warning: non-integer x = 868.493366Warning: non-integer x = 959.783236Warning: non-integer x = 932.800022Warning: non-integer x = 935.569275Warning: non-integer x = 1067.728623Warning: non-integer x = 1040.787923Warning: non-integer x = 872.623445Warning: non-integer x = 1066.896334Warning: non-integer x = 888.695937Warning: non-integer x = 956.894490Warning: non-integer x = 803.089611Warning: non-integer x = 855.033222Warning: non-integer x = 737.037148Warning: non-integer x = 803.024901Warning: non-integer x = 956.984367Warning: non-integer x = 1061.966100Warning: non-integer x = 931.010321Warning: non-integer x = 943.954475Warning: non-integer x = 881.946890Warning: non-integer x = 983.035576Warning: non-integer x = 980.014155Warning: non-integer x = 1025.028081Warning: non-integer x = 945.959830Warning: non-integer x = 932.039882Warning: non-integer x = 973.018175Warning: non-integer x = 886.019034Warning: non-integer x = 901.040671Warning: non-integer x = 867.012818Warning: non-integer x = 891.983711Warning: non-integer x = 878.040158Warning: non-integer x = 869.987137Warning: non-integer x = 871.986889Warning: non-integer x = 786.051367Warning: non-integer x = 753.954897Warning: non-integer x = 724.016076Warning: non-integer x = 722.035989Warning: non-integer x = 650.971208Warning: non-integer x = 715.974973Warning: non-integer x = 656.040679Warning: non-integer x = 693.953096Warning: non-integer x = 704.022803Warning: non-integer x = 711.055325Warning: non-integer x = 749.043013Warning: non-integer x = 776.982143Warning: non-integer x = 697.234183Warning: non-integer x = 720.242881Warning: non-integer x = 679.084392Warning: non-integer x = 712.258845Warning: non-integer x = 687.186210Warning: non-integer x = 700.150991Warning: non-integer x = 761.141215Warning: non-integer x = 720.214759Warning: non-integer x = 772.142199Warning: non-integer x = 725.062893Warning: non-integer x = 719.123640Warning: non-integer x = 715.072639Warning: non-integer x = 707.040712Warning: non-integer x = 720.246675Warning: non-integer x = 717.124794Warning: non-integer x = 786.138721Warning: non-integer x = 912.738906Warning: non-integer x = 917.725351Warning: non-integer x = 940.601424Warning: non-integer x = 842.555395Warning: non-integer x = 910.309906Warning: non-integer x = 903.653541Warning: non-integer x = 951.607090Warning: non-integer x = 847.144378Warning: non-integer x = 860.691033Warning: non-integer x = 901.682447Warning: non-integer x = 898.133712Warning: non-integer x = 855.265841Warning: non-integer x = 835.157278Warning: non-integer x = 846.109032Warning: non-integer x = 852.235023Warning: non-integer x = 868.247937Warning: non-integer x = 976.949327Warning: non-integer x = 1010.711319Warning: non-integer x = 932.728429Warning: non-integer x = 839.420785Warning: non-integer x = 989.946998Warning: non-integer x = 942.539783Warning: non-integer x = 966.536485Warning: non-integer x = 976.780035Warning: non-integer x = 1022.908530Warning: non-integer x = 995.647994Warning: non-integer x = 1033.700575Warning: non-integer x = 1038.809394Warning: non-integer x = 1100.799191Warning: non-integer x = 1020.872535Warning: non-integer x = 965.757103Warning: non-integer x = 989.950268Warning: non-integer x = 961.358359Warning: non-integer x = 923.969935Warning: non-integer x = 887.987125Warning: non-integer x = 902.003725Warning: non-integer x = 871.023172Warning: non-integer x = 977.986925Warning: non-integer x = 1034.007215Warning: non-integer x = 940.983800Warning: non-integer x = 1006.978004Warning: non-integer x = 1068.986790Warning: non-integer x = 990.048461Warning: non-integer x = 1067.033765Warning: non-integer x = 1027.010197Warning: non-integer x = 949.952880Warning: non-integer x = 1048.027836Warning: non-integer x = 1018.010220Warning: non-integer x = 926.029505Warning: non-integer x = 923.046193Warning: non-integer x = 964.981625Warning: non-integer x = 903.955369Warning: non-integer x = 923.949916Warning: non-integer x = 947.957095Warning: non-integer x = 792.019243Warning: non-integer x = 875.980616Warning: non-integer x = 881.025090Warning: non-integer x = 758.040127Warning: non-integer x = 735.017358Warning: non-integer x = 736.979968Warning: non-integer x = 731.049855Warning: non-integer x = 721.982306Warning: non-integer x = 736.967865Warning: non-integer x = 795.053378Warning: non-integer x = 696.042319Warning: non-integer x = 779.974276Warning: non-integer x = 853.341739Warning: non-integer x = 763.227350Warning: non-integer x = 766.115916Warning: non-integer x = 771.309402Warning: non-integer x = 784.214945Warning: non-integer x = 794.112758Warning: non-integer x = 775.097670Warning: non-integer x = 796.243832Warning: non-integer x = 753.153537Warning: non-integer x = 698.089857Warning: non-integer x = 822.116326Warning: non-integer x = 745.110183Warning: non-integer x = 796.006822Warning: non-integer x = 755.159580Warning: non-integer x = 803.153059Warning: non-integer x = 813.123451Warning: non-integer x = 1035.924375Warning: non-integer x = 1097.086175Warning: non-integer x = 1006.670405Warning: non-integer x = 1051.861332Warning: non-integer x = 1089.759051Warning: non-integer x = 1033.037721Warning: non-integer x = 1103.100729Warning: non-integer x = 989.492174Warning: non-integer x = 979.954024Warning: non-integer x = 1061.943330Warning: non-integer x = 963.237987Warning: non-integer x = 1018.466633Warning: non-integer x = 911.290706Warning: non-integer x = 834.102288Warning: non-integer x = 935.334049Warning: non-integer x = 927.373790Warning: non-integer x = 1119.060423Warning: non-integer x = 938.696432Warning: non-integer x = 993.781361Warning: non-integer x = 996.537922Warning: non-integer x = 914.849867Warning: non-integer x = 1034.616919Warning: non-integer x = 928.543113Warning: non-integer x = 1051.864282Warning: non-integer x = 1100.934967Warning: non-integer x = 1084.628457Warning: non-integer x = 1168.837616Warning: non-integer x = 1094.820773Warning: non-integer x = 1162.880833Warning: non-integer x = 1278.155222Warning: non-integer x = 1016.757535Warning: non-integer x = 1175.101072Warning: non-integer x = 1024.429974Warning: non-integer x = 1062.053186Warning: non-integer x = 989.977127Warning: non-integer x = 1023.985331Warning: non-integer x = 1039.990539Warning: non-integer x = 847.024671Warning: non-integer x = 1062.045064Warning: non-integer x = 1052.049670Warning: non-integer x = 1116.010389Warning: non-integer x = 1116.005175Warning: non-integer x = 1080.961518Warning: non-integer x = 1106.969662Warning: non-integer x = 1132.052235Warning: non-integer x = 1098.951554Warning: non-integer x = 1031.037038Warning: non-integer x = 1014.960596Warning: non-integer x = 1065.972408Warning: non-integer x = 1032.051214Warning: non-integer x = 1100.003102Warning: non-integer x = 1064.055582Warning: non-integer x = 958.972019Warning: non-integer x = 969.007287Warning: non-integer x = 919.969081Warning: non-integer x = 879.951318Warning: non-integer x = 881.029324Warning: non-integer x = 887.052776Warning: non-integer x = 796.956394Warning: non-integer x = 757.952170Warning: non-integer x = 752.031680Warning: non-integer x = 777.028854Warning: non-integer x = 833.975233Warning: non-integer x = 798.942788Warning: non-integer x = 781.959147Warning: non-integer x = 793.020443Warning: non-integer x = 824.306612Warning: non-integer x = 832.180497Warning: non-integer x = 879.187375Warning: non-integer x = 813.332736Warning: non-integer x = 834.217021Warning: non-integer x = 824.112335Warning: non-integer x = 751.070455Warning: non-integer x = 828.204095Warning: non-integer x = 809.151789Warning: non-integer x = 802.136996Warning: non-integer x = 824.167181Warning: non-integer x = 820.096091Warning: non-integer x = 831.112555Warning: non-integer x = 783.207107Warning: non-integer x = 863.160962Warning: non-integer x = 827.137025Warning: non-integer x = 961.811822Warning: non-integer x = 992.877643Warning: non-integer x = 987.661696Warning: non-integer x = 873.584086Warning: non-integer x = 939.395830Warning: non-integer x = 944.793583Warning: non-integer x = 975.746102Warning: non-integer x = 913.291784Warning: non-integer x = 923.847864Warning: non-integer x = 1016.823299Warning: non-integer x = 890.194174Warning: non-integer x = 968.409383Warning: non-integer x = 925.293310Warning: non-integer x = 916.229134Warning: non-integer x = 929.318023Warning: non-integer x = 901.279311Warning: non-integer x = 977.951500Warning: non-integer x = 977.733440Warning: non-integer x = 957.748265Warning: non-integer x = 986.539745Warning: non-integer x = 1017.943743Warning: non-integer x = 1031.633182Warning: non-integer x = 1111.581708Warning: non-integer x = 1090.869956Warning: non-integer x = 1086.953274Warning: non-integer x = 1166.693704Warning: non-integer x = 1272.890413Warning: non-integer x = 1179.906194Warning: non-integer x = 1130.814514Warning: non-integer x = 1237.020831Warning: non-integer x = 1144.845816Warning: non-integer x = 1200.067841Warning: non-integer x = 1151.597606Warning: non-integer x = 1113.039351Warning: non-integer x = 1149.022757Warning: non-integer x = 1166.961452Warning: non-integer x = 1091.974279Warning: non-integer x = 1027.021889Warning: non-integer x = 915.011130Warning: non-integer x = 1031.017694Warning: non-integer x = 1160.966053Warning: non-integer x = 1127.050415Warning: non-integer x = 1103.950275Warning: non-integer x = 1174.013405Warning: non-integer x = 1204.000193Warning: non-integer x = 1201.001474Warning: non-integer x = 1190.010277Warning: non-integer x = 1060.957021Warning: non-integer x = 1092.000131Warning: non-integer x = 1032.007648Warning: non-integer x = 1094.016320Warning: non-integer x = 1157.994596Warning: non-integer x = 1051.966555Warning: non-integer x = 1140.948903Warning: non-integer x = 1013.019077Warning: non-integer x = 1047.944555Warning: non-integer x = 1011.972936Warning: non-integer x = 987.988844Warning: non-integer x = 964.970777Warning: non-integer x = 891.028318Warning: non-integer x = 876.947531Warning: non-integer x = 813.045592Warning: non-integer x = 885.973955Warning: non-integer x = 888.017069Warning: non-integer x = 809.008559Warning: non-integer x = 893.940192Warning: non-integer x = 785.218345Warning: non-integer x = 801.222145Warning: non-integer x = 833.231717Warning: non-integer x = 791.294809Warning: non-integer x = 837.232346Warning: non-integer x = 830.092987Warning: non-integer x = 848.077473Warning: non-integer x = 799.231493Warning: non-integer x = 848.203170Warning: non-integer x = 795.134342Warning: non-integer x = 862.088351Warning: non-integer x = 901.131993Warning: non-integer x = 872.079960Warning: non-integer x = 893.231984Warning: non-integer x = 942.218654Warning: non-integer x = 980.055827Warning: non-integer x = 1536.870281Warning: non-integer x = 1669.135819Warning: non-integer x = 1605.643970Warning: non-integer x = 1446.508288Warning: non-integer x = 1385.345788Warning: non-integer x = 1350.953264Warning: non-integer x = 1471.023679Warning: non-integer x = 1294.193352Warning: non-integer x = 1147.259293Warning: non-integer x = 1239.267836Warning: non-integer x = 1214.551295Warning: non-integer x = 1224.789947Warning: non-integer x = 1171.663849Warning: non-integer x = 1151.486236Warning: non-integer x = 1097.513118Warning: non-integer x = 1121.603714Warning: non-integer x = 1224.165750Warning: non-integer x = 1155.843308Warning: non-integer x = 1024.800344Warning: non-integer x = 1073.576523Warning: non-integer x = 1148.036219Warning: non-integer x = 1224.744889Warning: non-integer x = 1125.583752Warning: non-integer x = 1185.968244Warning: non-integer x = 1224.044260Warning: non-integer x = 1192.721264Warning: non-integer x = 1323.954177Warning: non-integer x = 1249.949351Warning: non-integer x = 1333.975424Warning: non-integer x = 1436.228969Warning: non-integer x = 1296.945384Warning: non-integer x = 1409.276381Warning: non-integer x = 1251.736177Warning: non-integer x = 1250.997522Warning: non-integer x = 1247.014811Warning: non-integer x = 1379.019737Warning: non-integer x = 1305.991535Warning: non-integer x = 1182.034682Warning: non-integer x = 1022.020588Warning: non-integer x = 954.015359Warning: non-integer x = 1174.039565Warning: non-integer x = 1314.994422Warning: non-integer x = 1226.986235Warning: non-integer x = 1257.009846Warning: non-integer x = 1267.001580Warning: non-integer x = 1244.002958Warning: non-integer x = 1250.050308Warning: non-integer x = 1230.954892Warning: non-integer x = 1155.960140Warning: non-integer x = 1126.951944Warning: non-integer x = 1180.975660Warning: non-integer x = 1204.052530Warning: non-integer x = 1221.002612Warning: non-integer x = 1219.035864Warning: non-integer x = 1131.028981Warning: non-integer x = 1063.973912Warning: non-integer x = 1109.048556Warning: non-integer x = 1066.040726Warning: non-integer x = 1038.952133Warning: non-integer x = 1014.967000Warning: non-integer x = 948.010373Warning: non-integer x = 900.018926Warning: non-integer x = 841.016366Warning: non-integer x = 894.021356Warning: non-integer x = 865.014625Warning: non-integer x = 905.948346Warning: non-integer x = 965.325410Warning: non-integer x = 898.146704Warning: non-integer x = 892.205147Warning: non-integer x = 946.380872Warning: non-integer x = 870.238418Warning: non-integer x = 871.096393Warning: non-integer x = 880.064674Warning: non-integer x = 916.288403Warning: non-integer x = 831.185248Warning: non-integer x = 958.133681Warning: non-integer x = 893.043466Warning: non-integer x = 939.209362Warning: non-integer x = 933.148081Warning: non-integer x = 960.248679Warning: non-integer x = 968.232899Warning: non-integer x = 1052.163221Warning: non-integer x = 946.776555Warning: non-integer x = 1014.923816Warning: non-integer x = 1013.715108Warning: non-integer x = 882.606839Warning: non-integer x = 896.261809Warning: non-integer x = 896.641594Warning: non-integer x = 943.619764Warning: non-integer x = 896.309645Warning: non-integer x = 931.833108Warning: non-integer x = 1023.836009Warning: non-integer x = 973.248036Warning: non-integer x = 979.405590Warning: non-integer x = 902.296372Warning: non-integer x = 928.229441Warning: non-integer x = 961.403934Warning: non-integer x = 998.480139Warning: non-integer x = 1153.082326Warning: non-integer x = 992.741357Warning: non-integer x = 952.748899Warning: non-integer x = 1022.553105Warning: non-integer x = 1026.970320Warning: non-integer x = 1172.709252Warning: non-integer x = 1187.639210Warning: non-integer x = 1182.942820Warning: non-integer x = 1210.044278Warning: non-integer x = 1208.766250Warning: non-integer x = 1321.922898Warning: non-integer x = 1288.017132Warning: non-integer x = 1295.982994Warning: non-integer x = 1345.180516Warning: non-integer x = 1278.965568Warning: non-integer x = 1360.169683Warning: non-integer x = 1367.879366Warning: non-integer x = 1288.032321Warning: non-integer x = 1386.999203Warning: non-integer x = 1381.015255Warning: non-integer x = 1469.979471Warning: non-integer x = 1261.994266Warning: non-integer x = 1173.983150Warning: non-integer x = 1048.983965Warning: non-integer x = 1037.966974Warning: non-integer x = 1224.019348Warning: non-integer x = 1308.982802Warning: non-integer x = 1237.980619Warning: non-integer x = 1348.997208Warning: non-integer x = 1336.028964Warning: non-integer x = 1305.027447Warning: non-integer x = 1260.986239Warning: non-integer x = 1389.960237Warning: non-integer x = 1193.952085Warning: non-integer x = 1247.038419Warning: non-integer x = 1344.010468Warning: non-integer x = 1222.950165Warning: non-integer x = 1262.996626Warning: non-integer x = 1181.946868Warning: non-integer x = 1209.031564Warning: non-integer x = 1192.947886Warning: non-integer x = 1216.000988Warning: non-integer x = 1098.010348Warning: non-integer x = 1088.016509Warning: non-integer x = 1033.031547Warning: non-integer x = 1014.052422Warning: non-integer x = 931.039096Warning: non-integer x = 954.035635Warning: non-integer x = 945.990188Warning: non-integer x = 933.014080Warning: non-integer x = 946.260544Warning: non-integer x = 900.212821Warning: non-integer x = 911.157822Warning: non-integer x = 981.334761Warning: non-integer x = 996.301540Warning: non-integer x = 934.215880Warning: non-integer x = 980.081674Warning: non-integer x = 989.303399Warning: non-integer x = 909.179600Warning: non-integer x = 989.236643Warning: non-integer x = 971.173969Warning: non-integer x = 949.122118Warning: non-integer x = 1036.118102Warning: non-integer x = 998.233910Warning: non-integer x = 1076.266476Warning: non-integer x = 1117.081181Warning: non-integer x = 1245.359286Warning: non-integer x = 1464.748296Warning: non-integer x = 1422.353211Warning: non-integer x = 1229.200312Warning: non-integer x = 1240.047281Warning: non-integer x = 1169.369458Warning: non-integer x = 1270.503118Warning: non-integer x = 1239.115838Warning: non-integer x = 1210.392639Warning: non-integer x = 1289.314384Warning: non-integer x = 1209.506457Warning: non-integer x = 1322.879872Warning: non-integer x = 1196.680863Warning: non-integer x = 1186.560599Warning: non-integer x = 1180.634518Warning: non-integer x = 1270.862807Warning: non-integer x = 1262.167397Warning: non-integer x = 1201.815340Warning: non-integer x = 1145.888404Warning: non-integer x = 1160.597442Warning: non-integer x = 1129.035412Warning: non-integer x = 1196.687532Warning: non-integer x = 1305.701915Warning: non-integer x = 1385.092498Warning: non-integer x = 1285.115091Warning: non-integer x = 1317.811601Warning: non-integer x = 1484.034024Warning: non-integer x = 1399.030556Warning: non-integer x = 1348.929452Warning: non-integer x = 1513.259925Warning: non-integer x = 1354.042865Warning: non-integer x = 1498.304947Warning: non-integer x = 1474.062715Warning: non-integer x = 1486.996419Warning: non-integer x = 1524.002805Warning: non-integer x = 1535.978282Warning: non-integer x = 1534.042494Warning: non-integer x = 1475.000325Warning: non-integer x = 1410.031971Warning: non-integer x = 1282.039116Warning: non-integer x = 1275.979528Warning: non-integer x = 1191.038840Warning: non-integer x = 1299.020187Warning: non-integer x = 1292.986011Warning: non-integer x = 1372.973462Warning: non-integer x = 1389.030559Warning: non-integer x = 1417.983274Warning: non-integer x = 1345.958482Warning: non-integer x = 1337.949892Warning: non-integer x = 1365.967287Warning: non-integer x = 1283.986368Warning: non-integer x = 1385.969921Warning: non-integer x = 1298.014700Warning: non-integer x = 1403.054682Warning: non-integer x = 1226.952746Warning: non-integer x = 1276.054045Warning: non-integer x = 1290.040426Warning: non-integer x = 1209.955631Warning: non-integer x = 1235.961828Warning: non-integer x = 1238.053045Warning: non-integer x = 1128.986937Warning: non-integer x = 1111.954356Warning: non-integer x = 1066.962600Warning: non-integer x = 1031.002856Warning: non-integer x = 968.991210Warning: non-integer x = 996.961221Warning: non-integer x = 955.299592Warning: non-integer x = 1023.269861Warning: non-integer x = 939.247450Warning: non-integer x = 963.299117Warning: non-integer x = 1027.307676Warning: non-integer x = 1034.223348Warning: non-integer x = 993.075871Warning: non-integer x = 1035.283857Warning: non-integer x = 965.174999Warning: non-integer x = 996.103262Warning: non-integer x = 1040.070888Warning: non-integer x = 1001.166869Warning: non-integer x = 1069.079782Warning: non-integer x = 1054.267746Warning: non-integer x = 1127.239233Warning: non-integer x = 1180.161186Warning: non-integer x = 1371.547669Warning: non-integer x = 1446.758648Warning: non-integer x = 1343.185783Warning: non-integer x = 1332.382531Warning: non-integer x = 1321.280117Warning: non-integer x = 1355.976667Warning: non-integer x = 1323.594812Warning: non-integer x = 1238.089556Warning: non-integer x = 1253.452848Warning: non-integer x = 1357.424456Warning: non-integer x = 1279.623781Warning: non-integer x = 1275.846053Warning: non-integer x = 1212.701443Warning: non-integer x = 1268.660125Warning: non-integer x = 1210.705290Warning: non-integer x = 1204.761276Warning: non-integer x = 1481.353843Warning: non-integer x = 1221.898856Warning: non-integer x = 1203.908935Warning: non-integer x = 1179.640433Warning: non-integer x = 1261.122610Warning: non-integer x = 1249.776773Warning: non-integer x = 1316.717052Warning: non-integer x = 1311.061660Warning: non-integer x = 1426.248062Warning: non-integer x = 1373.807748Warning: non-integer x = 1530.071876Warning: non-integer x = 1557.164965Warning: non-integer x = 1438.056783Warning: non-integer x = 1638.417958Warning: non-integer x = 1561.189712Warning: non-integer x = 1616.447797Warning: non-integer x = 1511.102593Warning: non-integer x = 1599.034668Warning: non-integer x = 1653.013540Warning: non-integer x = 1696.025824Warning: non-integer x = 1697.972557Warning: non-integer x = 1593.041186Warning: non-integer x = 1484.958488Warning: non-integer x = 1361.970760Warning: non-integer x = 1381.992640Warning: non-integer x = 1314.039888Warning: non-integer x = 1168.988647Warning: non-integer x = 1436.958470Warning: non-integer x = 1522.981639Warning: non-integer x = 1471.993341Warning: non-integer x = 1477.045325Warning: non-integer x = 1555.985255Warning: non-integer x = 1498.964507Warning: non-integer x = 1418.014981Warning: non-integer x = 1514.958506Warning: non-integer x = 1533.016448Warning: non-integer x = 1433.037337Warning: non-integer x = 1486.967993Warning: non-integer x = 1413.019090Warning: non-integer x = 1436.980480Warning: non-integer x = 1387.998428Warning: non-integer x = 1321.954793Warning: non-integer x = 1358.043116Warning: non-integer x = 1292.960439Warning: non-integer x = 1207.003487Warning: non-integer x = 1225.042172Warning: non-integer x = 1150.054673Warning: non-integer x = 1113.975815Warning: non-integer x = 1038.966475Warning: non-integer x = 970.993077Warning: non-integer x = 1031.358046Warning: non-integer x = 1025.192442Warning: non-integer x = 1009.228911Warning: non-integer x = 1069.347856Warning: non-integer x = 992.324186Warning: non-integer x = 1073.175121Warning: non-integer x = 1096.091949Warning: non-integer x = 1027.301548Warning: non-integer x = 1014.194463Warning: non-integer x = 1086.212790Warning: non-integer x = 1140.138885Warning: non-integer x = 1066.215749Warning: non-integer x = 1068.142069Warning: non-integer x = 1115.242550Warning: non-integer x = 1223.218449Warning: non-integer x = 1272.132241Warning: non-integer x = 1415.679685Warning: non-integer x = 1477.781630Warning: non-integer x = 1447.400398Warning: non-integer x = 1242.225116Warning: non-integer x = 1429.551454Warning: non-integer x = 1329.875009Warning: non-integer x = 1427.896863Warning: non-integer x = 1387.453662Warning: non-integer x = 1304.519348Warning: non-integer x = 1392.510658Warning: non-integer x = 1300.702420Warning: non-integer x = 1437.075173Warning: non-integer x = 1253.762751Warning: non-integer x = 1285.660476Warning: non-integer x = 1384.905563Warning: non-integer x = 1362.963571Warning: non-integer x = 1466.331152Warning: non-integer x = 1451.017189Warning: non-integer x = 1215.930519Warning: non-integer x = 1268.683115Warning: non-integer x = 1310.177645Warning: non-integer x = 1315.781979Warning: non-integer x = 1374.740132Warning: non-integer x = 1325.059035Warning: non-integer x = 1464.249566Warning: non-integer x = 1540.900502Warning: non-integer x = 1625.133113Warning: non-integer x = 1569.205679Warning: non-integer x = 1559.096754Warning: non-integer x = 1699.451882Warning: non-integer x = 1588.228920Warning: non-integer x = 1692.446386Warning: non-integer x = 1630.261456Warning: non-integer x = 1620.004700Warning: non-integer x = 1763.023950Warning: non-integer x = 1772.028830Warning: non-integer x = 1776.015251Warning: non-integer x = 1727.983730Warning: non-integer x = 1620.008708Warning: non-integer x = 1529.999200Warning: non-integer x = 1495.975178Warning: non-integer x = 1498.981582Warning: non-integer x = 1330.969552Warning: non-integer x = 1306.028411Warning: non-integer x = 1497.955437Warning: non-integer x = 1536.978110Warning: non-integer x = 1550.000431Warning: non-integer x = 1519.991592Warning: non-integer x = 1590.957343Warning: non-integer x = 1540.984930Warning: non-integer x = 1663.958095Warning: non-integer x = 1682.963866Warning: non-integer x = 1511.001005Warning: non-integer x = 1647.964129Warning: non-integer x = 1503.033822Warning: non-integer x = 1531.979387Warning: non-integer x = 1535.024003Warning: non-integer x = 1450.048064Warning: non-integer x = 1360.029078Warning: non-integer x = 1377.991629Warning: non-integer x = 1345.043373Warning: non-integer x = 1294.949723Warning: non-integer x = 1336.046960Warning: non-integer x = 1229.959656Warning: non-integer x = 1123.955681Warning: non-integer x = 1103.953594Warning: non-integer x = 1035.323945Warning: non-integer x = 1070.213068Warning: non-integer x = 1101.195580Warning: non-integer x = 1136.406171Warning: non-integer x = 1085.389140Warning: non-integer x = 1106.208547Warning: non-integer x = 1037.127183Warning: non-integer x = 1246.373179Warning: non-integer x = 1108.146561Warning: non-integer x = 1057.184390Warning: non-integer x = 1151.107643Warning: non-integer x = 1144.145374Warning: non-integer x = 1147.057705Warning: non-integer x = 1186.340286Warning: non-integer x = 1279.310490Warning: non-integer x = 1258.148402Warning: non-integer x = 1671.115693Warning: non-integer x = 1834.451012Warning: non-integer x = 1780.917320Warning: non-integer x = 1648.891334Warning: non-integer x = 1642.017602Warning: non-integer x = 1549.476461Warning: non-integer x = 1738.702832Warning: non-integer x = 1486.649198Warning: non-integer x = 1446.809973Warning: non-integer x = 1580.872583Warning: non-integer x = 1446.863896Warning: non-integer x = 1491.123177Warning: non-integer x = 1391.952282Warning: non-integer x = 1344.784889Warning: non-integer x = 1415.932541Warning: non-integer x = 1412.991319Warning: non-integer x = 1561.377391Warning: non-integer x = 1412.986954Warning: non-integer x = 1361.040203Warning: non-integer x = 1346.700365Warning: non-integer x = 1331.212749Warning: non-integer x = 1389.826724Warning: non-integer x = 1411.782651Warning: non-integer x = 1464.159591Warning: non-integer x = 1459.183439Warning: non-integer x = 1594.925799Warning: non-integer x = 1720.184780Warning: non-integer x = 1552.141469Warning: non-integer x = 1643.175949Warning: non-integer x = 1902.608766Warning: non-integer x = 1611.204910Warning: non-integer x = 1834.591110Warning: non-integer x = 1696.243215Warning: non-integer x = 1735.040979Warning: non-integer x = 1824.973887Warning: non-integer x = 1900.005528Warning: non-integer x = 2014.020098Warning: non-integer x = 1734.975811Warning: non-integer x = 1905.959903Warning: non-integer x = 1575.960357Warning: non-integer x = 1677.963252Warning: non-integer x = 1657.037109Warning: non-integer x = 1448.991668Warning: non-integer x = 1457.968473Warning: non-integer x = 1344.022955Warning: non-integer x = 1677.991927Warning: non-integer x = 1654.043134Warning: non-integer x = 1597.017581Warning: non-integer x = 1667.021181Warning: non-integer x = 1640.983864Warning: non-integer x = 1846.970530Warning: non-integer x = 1778.026486Warning: non-integer x = 1614.037001Warning: non-integer x = 1730.043499Warning: non-integer x = 1629.047359Warning: non-integer x = 1629.987144Warning: non-integer x = 1676.037223Warning: non-integer x = 1605.963442Warning: non-integer x = 1592.997253Warning: non-integer x = 1561.980368Warning: non-integer x = 1494.994436Warning: non-integer x = 1478.962191Warning: non-integer x = 1390.025946Warning: non-integer x = 1426.975850Warning: non-integer x = 1287.988342Warning: non-integer x = 1293.030511Warning: non-integer x = 1140.390318Warning: non-integer x = 1232.214439Warning: non-integer x = 1119.273504Warning: non-integer x = 1286.425038Warning: non-integer x = 1115.329104Warning: non-integer x = 1205.141576Warning: non-integer x = 1157.166050Warning: non-integer x = 1192.250894Warning: non-integer x = 1179.209774Warning: non-integer x = 1189.168658Warning: non-integer x = 1191.151347Warning: non-integer x = 1193.168804Warning: non-integer x = 1222.117805Warning: non-integer x = 1254.233574Warning: non-integer x = 1336.235026Warning: non-integer x = 1408.091854Warning: non-integer x = 1435.636196Warning: non-integer x = 1729.243749Warning: non-integer x = 1708.848682Warning: non-integer x = 1538.745354Warning: non-integer x = 1518.757316Warning: non-integer x = 1457.208465Warning: non-integer x = 1678.615434Warning: non-integer x = 1645.134070Warning: non-integer x = 1399.729164Warning: non-integer x = 1555.791484Warning: non-integer x = 1364.755185Warning: non-integer x = 1514.173250Warning: non-integer x = 1409.957627Warning: non-integer x = 1442.880227Warning: non-integer x = 1490.013539Warning: non-integer x = 1597.288109Warning: non-integer x = 1710.509138Warning: non-integer x = 1602.094848Warning: non-integer x = 1423.080164Warning: non-integer x = 1457.723344Warning: non-integer x = 1479.363401Warning: non-integer x = 1459.825765Warning: non-integer x = 1470.790257Warning: non-integer x = 1503.193981Warning: non-integer x = 1569.279215Warning: non-integer x = 1563.954685Warning: non-integer x = 1768.196890Warning: non-integer x = 1812.377257Warning: non-integer x = 1619.104288Warning: non-integer x = 2005.663237Warning: non-integer x = 1690.241527Warning: non-integer x = 1824.566145Warning: non-integer x = 1746.359734Warning: non-integer x = 1862.019663Warning: non-integer x = 1895.017701Warning: non-integer x = 1881.981942Warning: non-integer x = 2050.005619Warning: non-integer x = 2007.012530Warning: non-integer x = 1990.990625Warning: non-integer x = 1882.983694Warning: non-integer x = 1832.029362Warning: non-integer x = 1723.992042Warning: non-integer x = 1642.027077Warning: non-integer x = 1661.991746Warning: non-integer x = 1572.010924Warning: non-integer x = 1463.007695Warning: non-integer x = 1681.956546Warning: non-integer x = 1699.017952Warning: non-integer x = 1895.028811Warning: non-integer x = 1687.976029Warning: non-integer x = 1872.015692Warning: non-integer x = 1902.986125Warning: non-integer x = 1817.047987Warning: non-integer x = 1781.997448Warning: non-integer x = 1628.005960Warning: non-integer x = 1718.992082Warning: non-integer x = 1754.030305Warning: non-integer x = 1733.967368Warning: non-integer x = 1714.946810Warning: non-integer x = 1684.048389Warning: non-integer x = 1539.958005Warning: non-integer x = 1576.035482Warning: non-integer x = 1575.028126Warning: non-integer x = 1542.026408Warning: non-integer x = 1404.985361Warning: non-integer x = 1493.947583Warning: non-integer x = 1341.414105Warning: non-integer x = 1143.253564Warning: non-integer x = 1184.202176Warning: non-integer x = 1185.351024Warning: non-integer x = 1297.381788Warning: non-integer x = 1205.151549Warning: non-integer x = 1223.082545Warning: non-integer x = 1225.285242Warning: non-integer x = 1214.179302Warning: non-integer x = 1276.157938Warning: non-integer x = 1310.092679Warning: non-integer x = 1247.166504Warning: non-integer x = 1204.140179Warning: non-integer x = 1305.353609Warning: non-integer x = 1378.264151Warning: non-integer x = 1521.225134Warning: non-integer x = 1384.558771Warning: non-integer x = 1658.091207Warning: non-integer x = 1549.572348Warning: non-integer x = 1480.598327Warning: non-integer x = 1486.658198Warning: non-integer x = 1509.338231Warning: non-integer x = 1555.232918Warning: non-integer x = 1533.832059Warning: non-integer x = 1411.754428Warning: non-integer x = 1533.767973Warning: non-integer x = 1450.834004Warning: non-integer x = 1520.201819Warning: non-integer x = 1521.119033Warning: non-integer x = 1470.904952Warning: non-integer x = 1520.069850Warning: non-integer x = 1539.161659Warning: non-integer x = 1657.441399Warning: non-integer x = 1651.132024Warning: non-integer x = 1504.100930Warning: non-integer x = 1500.735365Warning: non-integer x = 1616.440800Warning: non-integer x = 1487.864371Warning: non-integer x = 1615.873406Warning: non-integer x = 1630.295271Warning: non-integer x = 1556.281923Warning: non-integer x = 1650.975103Warning: non-integer x = 1802.224142Warning: non-integer x = 1880.350858Warning: non-integer x = 1817.248126Warning: non-integer x = 1950.605124Warning: non-integer x = 1847.397137Warning: non-integer x = 2066.775861Warning: non-integer x = 1866.488581Warning: non-integer x = 1939.009018Warning: non-integer x = 2022.987179Warning: non-integer x = 2041.016948Warning: non-integer x = 2126.968964Warning: non-integer x = 2130.003296Warning: non-integer x = 2079.963921Warning: non-integer x = 1979.962145Warning: non-integer x = 2056.000483Warning: non-integer x = 1930.969703Warning: non-integer x = 1867.009831Warning: non-integer x = 1800.036746Warning: non-integer x = 1851.030872Warning: non-integer x = 1549.015038Warning: non-integer x = 1516.033357Warning: non-integer x = 1742.004995Warning: non-integer x = 1932.018253Warning: non-integer x = 1816.974810Warning: non-integer x = 1930.972261Warning: non-integer x = 1955.020369Warning: non-integer x = 1855.951779Warning: non-integer x = 2069.979035Warning: non-integer x = 1921.987049Warning: non-integer x = 1829.974443Warning: non-integer x = 1927.955356Warning: non-integer x = 1850.045427Warning: non-integer x = 1825.038722Warning: non-integer x = 1830.985756Warning: non-integer x = 1774.012492Warning: non-integer x = 1677.967096Warning: non-integer x = 1749.952924Warning: non-integer x = 1652.968060Warning: non-integer x = 1554.988600Warning: non-integer x = 1547.007842Warning: non-integer x = 1470.475774Warning: non-integer x = 1356.299095Warning: non-integer x = 1242.273766Warning: non-integer x = 1252.455620Warning: non-integer x = 1343.428116Warning: non-integer x = 1271.212718Warning: non-integer x = 1388.122216Warning: non-integer x = 1322.342187Warning: non-integer x = 1216.204003Warning: non-integer x = 1278.151168Warning: non-integer x = 1429.184138Warning: non-integer x = 1329.223675Warning: non-integer x = 1405.057280Warning: non-integer x = 1376.331547Warning: non-integer x = 1546.336814Warning: non-integer x = 1517.168517Warning: non-integer x = 1666.075681Warning: non-integer x = 1867.505232Warning: non-integer x = 1815.978588Warning: non-integer x = 1716.002614Warning: non-integer x = 1756.258652Warning: non-integer x = 1641.753354Warning: non-integer x = 1923.186621Warning: non-integer x = 1624.019366Warning: non-integer x = 1678.265237Warning: non-integer x = 1749.128580Warning: non-integer x = 1562.979898Warning: non-integer x = 1689.401656Warning: non-integer x = 1592.241553Warning: non-integer x = 1583.084307Warning: non-integer x = 1638.209888Warning: non-integer x = 1742.458954Warning: non-integer x = 1919.703813Warning: non-integer x = 1839.217858Warning: non-integer x = 1563.174552Warning: non-integer x = 1703.865873Warning: non-integer x = 1675.484992Warning: non-integer x = 1739.969123Warning: non-integer x = 1667.876511Warning: non-integer x = 1712.380845Warning: non-integer x = 1740.436740Warning: non-integer x = 1805.038591Warning: non-integer x = 1881.257100Warning: non-integer x = 1830.359332Warning: non-integer x = 1985.359740Warning: non-integer x = 2231.877172Warning: non-integer x = 1955.451030Warning: non-integer x = 2243.923148Warning: non-integer x = 2026.705386Warning: non-integer x = 2057.005274Warning: non-integer x = 2167.001328Warning: non-integer x = 2238.984013Warning: non-integer x = 2345.023124Warning: non-integer x = 2238.001962Warning: non-integer x = 2195.985041Warning: non-integer x = 2180.994536Warning: non-integer x = 2138.002792Warning: non-integer x = 2214.984653Warning: non-integer x = 1975.023293Warning: non-integer x = 2092.004420Warning: non-integer x = 1927.036768Warning: non-integer x = 1843.023822Warning: non-integer x = 1784.989419Warning: non-integer x = 1545.976818Warning: non-integer x = 1968.994831Warning: non-integer x = 2074.001233Warning: non-integer x = 2136.984199Warning: non-integer x = 2103.005600Warning: non-integer x = 2103.984772Warning: non-integer x = 1941.003917Warning: non-integer x = 2023.035430Warning: non-integer x = 1988.969472Warning: non-integer x = 2006.005195Warning: non-integer x = 1961.040559Warning: non-integer x = 1973.949167Warning: non-integer x = 1872.004737Warning: non-integer x = 1828.008081Warning: non-integer x = 1807.004388Warning: non-integer x = 1786.988389Warning: non-integer x = 1755.051555Warning: non-integer x = 1649.965338Warning: non-integer x = 1542.444476Warning: non-integer x = 1543.340363Warning: non-integer x = 1482.287491Warning: non-integer x = 1346.442119Warning: non-integer x = 1347.431071Warning: non-integer x = 1389.206383Warning: non-integer x = 1413.170321Warning: non-integer x = 1456.395543Warning: non-integer x = 1428.211516Warning: non-integer x = 1388.243996Warning: non-integer x = 1492.161935Warning: non-integer x = 1519.237025Warning: non-integer x = 1443.135656Warning: non-integer x = 1426.269330Warning: non-integer x = 1522.219779Warning: non-integer x = 1653.155358Warning: non-integer x = 1309.428457Warning: non-integer x = 1383.605055Warning: non-integer x = 1363.227963Warning: non-integer x = 1410.490067Warning: non-integer x = 1419.467392Warning: non-integer x = 1322.829138Warning: non-integer x = 1532.155024Warning: non-integer x = 1463.673058Warning: non-integer x = 1431.794270Warning: non-integer x = 1574.837223Warning: non-integer x = 1361.740167Warning: non-integer x = 1497.133057Warning: non-integer x = 1409.961266Warning: non-integer x = 1449.863089Warning: non-integer x = 1600.205355Warning: non-integer x = 1627.246753Warning: non-integer x = 1846.626983Warning: non-integer x = 1724.184683Warning: non-integer x = 1583.179444Warning: non-integer x = 1685.838148Warning: non-integer x = 1708.481791Warning: non-integer x = 1660.968339Warning: non-integer x = 1766.904686Warning: non-integer x = 1784.439867Warning: non-integer x = 1747.426637Warning: non-integer x = 1719.998121Warning: non-integer x = 1888.257515Warning: non-integer x = 1926.443447Warning: non-integer x = 1942.372074Warning: non-integer x = 2315.880962Warning: non-integer x = 2176.570013Warning: non-integer x = 2210.817236Warning: non-integer x = 2165.828343Warning: non-integer x = 2320.009335Warning: non-integer x = 2276.029048Warning: non-integer x = 2435.013764Warning: non-integer x = 2393.977213Warning: non-integer x = 2316.985964Warning: non-integer x = 2221.971029Warning: non-integer x = 2248.990395Warning: non-integer x = 2364.002367Warning: non-integer x = 2242.022998Warning: non-integer x = 2178.038968Warning: non-integer x = 2163.986237Warning: non-integer x = 2149.964011Warning: non-integer x = 2032.984776Warning: non-integer x = 1922.966994Warning: non-integer x = 1821.014156Warning: non-integer x = 1717.031880Warning: non-integer x = 1980.023883Warning: non-integer x = 2153.962452Warning: non-integer x = 2180.990098Warning: non-integer x = 2169.992370Warning: non-integer x = 2426.955877Warning: non-integer x = 2077.985729Warning: non-integer x = 2206.037458Warning: non-integer x = 2130.005230Warning: non-integer x = 2072.976009Warning: non-integer x = 2172.019873Warning: non-integer x = 2124.005456Warning: non-integer x = 1998.050667Warning: non-integer x = 1946.996013Warning: non-integer x = 1969.997364Warning: non-integer x = 1805.978553Warning: non-integer x = 1912.976252Warning: non-integer x = 1696.481686Warning: non-integer x = 1647.390864Warning: non-integer x = 1679.282840Warning: non-integer x = 1516.494743Warning: non-integer x = 1407.513837Warning: non-integer x = 1378.254238Warning: non-integer x = 1451.143323Warning: non-integer x = 1470.384316Warning: non-integer x = 1530.270285Warning: non-integer x = 1559.228168Warning: non-integer x = 1501.217180Warning: non-integer x = 1537.260690Warning: non-integer x = 1604.072546Warning: non-integer x = 1545.329049Warning: non-integer x = 1672.328252Warning: non-integer x = 1748.192557Warning: non-integer x = 2478.517712Warning: non-integer x = 2675.924802Warning: non-integer x = 2514.070997Warning: non-integer x = 2315.855408Warning: non-integer x = 2281.444160Warning: non-integer x = 2075.836417Warning: non-integer x = 2485.540147Warning: non-integer x = 2189.232709Warning: non-integer x = 1934.682545Warning: non-integer x = 2167.864371Warning: non-integer x = 2074.638335Warning: non-integer x = 2190.084981Warning: non-integer x = 1823.529906Warning: non-integer x = 1813.302241Warning: non-integer x = 1944.556749Warning: non-integer x = 1977.679546Warning: non-integer x = 2292.949401Warning: non-integer x = 2142.423001Warning: non-integer x = 1789.310143Warning: non-integer x = 1883.926954Warning: non-integer x = 1998.761214Warning: non-integer x = 1868.060984Warning: non-integer x = 1932.969829Warning: non-integer x = 2153.724128Warning: non-integer x = 2006.648166Warning: non-integer x = 1955.090529Warning: non-integer x = 2063.385918Warning: non-integer x = 2057.485651Warning: non-integer x = 2107.424835Warning: non-integer x = 2345.949033Warning: non-integer x = 2214.595327Warning: non-integer x = 2425.984601Warning: non-integer x = 2204.895969Warning: non-integer x = 2363.055576Warning: non-integer x = 2494.021556Warning: non-integer x = 2419.985985Warning: non-integer x = 2653.022652Warning: non-integer x = 2534.010928Warning: non-integer x = 2468.025112Warning: non-integer x = 2426.033459Warning: non-integer x = 2475.980172Warning: non-integer x = 2491.974706Warning: non-integer x = 2402.001089Warning: non-integer x = 2582.018940Warning: non-integer x = 2337.986578Warning: non-integer x = 2405.002265Warning: non-integer x = 2314.983176Warning: non-integer x = 2153.005212Warning: non-integer x = 1953.018932Warning: non-integer x = 1728.007718Warning: non-integer x = 2227.963825Warning: non-integer x = 2367.995983Warning: non-integer x = 2299.015168Warning: non-integer x = 2459.961480Warning: non-integer x = 2318.987432Warning: non-integer x = 2367.967806Warning: non-integer x = 2411.045597Warning: non-integer x = 2252.021712Warning: non-integer x = 2281.008352Warning: non-integer x = 2257.041525Warning: non-integer x = 2206.972566Warning: non-integer x = 2248.007876Warning: non-integer x = 2170.949378Warning: non-integer x = 2203.985249Warning: non-integer x = 1987.978838Warning: non-integer x = 1985.011038Warning: non-integer x = 1892.515033Warning: non-integer x = 1794.404183Warning: non-integer x = 1758.365476Warning: non-integer x = 1726.600578Warning: non-integer x = 1686.528987Warning: non-integer x = 1568.267178Warning: non-integer x = 1538.179669Warning: non-integer x = 1466.390576Warning: non-integer x = 1657.286493Warning: non-integer x = 1635.197190Warning: non-integer x = 1625.235003Warning: non-integer x = 1527.286529Warning: non-integer x = 1683.104979Warning: non-integer x = 1758.370586Warning: non-integer x = 1728.334725Warning: non-integer x = 1902.225942Warning: non-integer x = 1345.507745Warning: non-integer x = 1552.901368Warning: non-integer x = 1397.273224Warning: non-integer x = 1305.280116Warning: non-integer x = 1294.164802Warning: non-integer x = 1326.835351Warning: non-integer x = 1533.115074Warning: non-integer x = 1414.463068Warning: non-integer x = 1401.744024Warning: non-integer x = 1578.815079Warning: non-integer x = 1461.857639Warning: non-integer x = 1660.368390Warning: non-integer x = 1553.179646Warning: non-integer x = 1392.803414Warning: non-integer x = 1571.125930Warning: non-integer x = 1622.240452Warning: non-integer x = 1927.690362Warning: non-integer x = 1835.239494Warning: non-integer x = 1722.260967Warning: non-integer x = 1761.857858Warning: non-integer x = 1918.679787Warning: non-integer x = 1876.072865Warning: non-integer x = 1866.977410Warning: non-integer x = 2018.625547Warning: non-integer x = 1913.552203Warning: non-integer x = 2045.166429Warning: non-integer x = 2045.337418Warning: non-integer x = 1959.415038Warning: non-integer x = 2087.393779Warning: non-integer x = 2343.914307Warning: non-integer x = 2187.576959Warning: non-integer x = 2427.974879Warning: non-integer x = 2346.009373Warning: non-integer x = 2375.023994Warning: non-integer x = 2523.980752Warning: non-integer x = 2488.984770Warning: non-integer x = 2545.012840Warning: non-integer x = 2582.027600Warning: non-integer x = 2554.019524Warning: non-integer x = 2484.978537Warning: non-integer x = 2454.999497Warning: non-integer x = 2633.021854Warning: non-integer x = 2500.030195Warning: non-integer x = 2454.972956Warning: non-integer x = 2544.007987Warning: non-integer x = 2425.980476Warning: non-integer x = 2349.964380Warning: non-integer x = 2225.015436Warning: non-integer x = 2199.023353Warning: non-integer x = 2034.997103Warning: non-integer x = 2017.022323Warning: non-integer x = 2329.962056Warning: non-integer x = 2468.971612Warning: non-integer x = 2573.962715Warning: non-integer x = 2491.025534Warning: non-integer x = 2454.975223Warning: non-integer x = 2604.984697Warning: non-integer x = 2508.016633Warning: non-integer x = 2526.032434Warning: non-integer x = 2315.014859Warning: non-integer x = 2428.031437Warning: non-integer x = 2393.961647Warning: non-integer x = 2267.958347Warning: non-integer x = 2391.024712Warning: non-integer x = 2303.960292Warning: non-integer x = 2139.023957Warning: non-integer x = 2051.634618Warning: non-integer x = 2013.436164Warning: non-integer x = 1973.428890Warning: non-integer x = 1835.564412Warning: non-integer x = 1944.677776Warning: non-integer x = 1732.225068Warning: non-integer x = 1612.160071Warning: non-integer x = 1567.368302Warning: non-integer x = 1611.334078Warning: non-integer x = 1690.261108Warning: non-integer x = 1717.176828Warning: non-integer x = 1647.231970Warning: non-integer x = 1690.135289Warning: non-integer x = 1800.454723Warning: non-integer x = 1955.342072Warning: non-integer x = 1957.219686Warning: non-integer x = 1902.484841Warning: non-integer x = 2015.753564Warning: non-integer x = 2063.325480Warning: non-integer x = 1947.374094Warning: non-integer x = 1887.574329Warning: non-integer x = 1836.264332Warning: non-integer x = 2050.463027Warning: non-integer x = 1974.853038Warning: non-integer x = 1894.626726Warning: non-integer x = 2068.694954Warning: non-integer x = 1980.508293Warning: non-integer x = 2072.930380Warning: non-integer x = 1987.755144Warning: non-integer x = 1986.549244Warning: non-integer x = 1986.668065Warning: non-integer x = 1921.678477Warning: non-integer x = 2269.945839Warning: non-integer x = 2156.426013Warning: non-integer x = 1901.360158Warning: non-integer x = 2019.959334Warning: non-integer x = 2124.795853Warning: non-integer x = 2110.163504Warning: non-integer x = 2118.098474Warning: non-integer x = 2197.746879Warning: non-integer x = 2202.750762Warning: non-integer x = 2236.267268Warning: non-integer x = 2350.568311Warning: non-integer x = 2236.607872Warning: non-integer x = 2257.496606Warning: non-integer x = 2516.054794Warning: non-integer x = 2330.681264Warning: non-integer x = 2489.039881Warning: non-integer x = 2366.091853Warning: non-integer x = 2661.019575Warning: non-integer x = 2568.022025Warning: non-integer x = 2667.986436Warning: non-integer x = 2853.996096Warning: non-integer x = 2637.987041Warning: non-integer x = 2752.975378Warning: non-integer x = 2672.988619Warning: non-integer x = 2694.970195Warning: non-integer x = 2679.999649Warning: non-integer x = 2566.970523Warning: non-integer x = 2725.032659Warning: non-integer x = 2757.994607Warning: non-integer x = 2718.005872Warning: non-integer x = 2624.989129Warning: non-integer x = 2439.013539Warning: non-integer x = 2441.980829Warning: non-integer x = 2283.004469Warning: non-integer x = 2285.973083Warning: non-integer x = 2210.988776Warning: non-integer x = 2442.025732Warning: non-integer x = 2665.032991Warning: non-integer x = 2521.027152Warning: non-integer x = 2594.021970Warning: non-integer x = 2658.014481Warning: non-integer x = 2614.961167Warning: non-integer x = 2724.996261Warning: non-integer x = 2594.042310Warning: non-integer x = 2556.987314Warning: non-integer x = 2568.994185Warning: non-integer x = 2432.997868Warning: non-integer x = 2443.001702Warning: non-integer x = 2327.037832Warning: non-integer x = 2383.029672Warning: non-integer x = 2223.673127Warning: non-integer x = 2217.494494Warning: non-integer x = 2223.450290Warning: non-integer x = 2034.654610Warning: non-integer x = 1996.675789Warning: non-integer x = 1958.327912Warning: non-integer x = 1831.207599Warning: non-integer x = 1740.463478Warning: non-integer x = 1594.302149Warning: non-integer x = 1817.301137Warning: non-integer x = 1877.251138Warning: non-integer x = 1831.254147Warning: non-integer x = 1888.203010Warning: non-integer x = 1804.353003Warning: non-integer x = 2091.380196Warning: non-integer x = 2206.203934Warning: non-integer x = 1865.459111Warning: non-integer x = 1956.615643Warning: non-integer x = 1773.890224Warning: non-integer x = 1775.044806Warning: non-integer x = 1755.230654Warning: non-integer x = 1664.748522Warning: non-integer x = 1791.819097Warning: non-integer x = 1893.567772Warning: non-integer x = 1766.419466Warning: non-integer x = 1952.483752Warning: non-integer x = 1953.482563Warning: non-integer x = 2054.904307Warning: non-integer x = 1813.515569Warning: non-integer x = 1949.497627Warning: non-integer x = 1992.667202Warning: non-integer x = 1928.630339Warning: non-integer x = 2260.951977Warning: non-integer x = 2111.388157Warning: non-integer x = 1894.350631Warning: non-integer x = 2176.042220Warning: non-integer x = 2162.875277Warning: non-integer x = 2103.172120Warning: non-integer x = 2176.114383Warning: non-integer x = 2366.852307Warning: non-integer x = 2233.784761Warning: non-integer x = 2280.255061Warning: non-integer x = 2504.668971Warning: non-integer x = 2341.657369Warning: non-integer x = 2253.460232Warning: non-integer x = 2513.005000Warning: non-integer x = 2376.695706Warning: non-integer x = 2521.020753Warning: non-integer x = 2417.098197Warning: non-integer x = 2537.038827Warning: non-integer x = 2856.000516Warning: non-integer x = 2596.010578Warning: non-integer x = 3092.010316Warning: non-integer x = 2869.024269Warning: non-integer x = 2738.985473Warning: non-integer x = 2790.010804Warning: non-integer x = 2748.987022Warning: non-integer x = 2812.993248Warning: non-integer x = 2721.017232Warning: non-integer x = 2814.011439Warning: non-integer x = 2891.027594Warning: non-integer x = 2861.982837Warning: non-integer x = 2735.994599Warning: non-integer x = 2624.008407Warning: non-integer x = 2591.975818Warning: non-integer x = 2528.969364Warning: non-integer x = 2564.973084Warning: non-integer x = 2453.993525Warning: non-integer x = 2208.997225Warning: non-integer x = 2591.037288Warning: non-integer x = 2647.030565Warning: non-integer x = 2748.010605Warning: non-integer x = 2876.019201Warning: non-integer x = 2835.024610Warning: non-integer x = 2864.029583Warning: non-integer x = 2937.006641Warning: non-integer x = 2718.011478Warning: non-integer x = 2555.992246Warning: non-integer x = 2711.986737Warning: non-integer x = 2671.030869Warning: non-integer x = 2528.012900Warning: non-integer x = 2680.952451Warning: non-integer x = 2468.679839Warning: non-integer x = 2419.495318Warning: non-integer x = 2281.452906Warning: non-integer x = 2345.789587Warning: non-integer x = 2212.710091Warning: non-integer x = 2083.289679Warning: non-integer x = 2123.224927Warning: non-integer x = 1983.534117Warning: non-integer x = 1770.335443Warning: non-integer x = 1786.295435Warning: non-integer x = 1926.190397Warning: non-integer x = 1982.282719Warning: non-integer x = 2010.128738Warning: non-integer x = 1964.387748Warning: non-integer x = 2154.397066Warning: non-integer x = 2201.188953Warning: non-integer x = 1863.431952Warning: non-integer x = 1955.640174Warning: non-integer x = 1885.060386Warning: non-integer x = 1657.836821Warning: non-integer x = 1832.402822Warning: non-integer x = 1745.929586Warning: non-integer x = 1840.891658Warning: non-integer x = 1776.318063Warning: non-integer x = 1792.406209Warning: non-integer x = 2132.820967Warning: non-integer x = 1835.310224Warning: non-integer x = 2121.001802Warning: non-integer x = 1933.696144Warning: non-integer x = 2010.583573Warning: non-integer x = 2032.677555Warning: non-integer x = 2132.901007Warning: non-integer x = 2405.048541Warning: non-integer x = 2196.412642Warning: non-integer x = 1931.362927Warning: non-integer x = 2195.038898Warning: non-integer x = 2176.866595Warning: non-integer x = 2239.233100Warning: non-integer x = 2258.144824Warning: non-integer x = 2401.869554Warning: non-integer x = 2425.928186Warning: non-integer x = 2409.331415Warning: non-integer x = 2583.714866Warning: non-integer x = 2435.738087Warning: non-integer x = 2487.594728Warning: non-integer x = 2735.205760Warning: non-integer x = 2427.724624Warning: non-integer x = 2659.099880Warning: non-integer x = 2504.155452Warning: non-integer x = 2708.046870Warning: non-integer x = 2860.017825Warning: non-integer x = 2837.997780Warning: non-integer x = 3004.016311Warning: non-integer x = 2967.021733Warning: non-integer x = 2990.018779Warning: non-integer x = 2770.021668Warning: non-integer x = 2889.005076Warning: non-integer x = 2850.990515Warning: non-integer x = 2927.979011Warning: non-integer x = 3012.000995Warning: non-integer x = 3077.973095Warning: non-integer x = 3038.967540Warning: non-integer x = 2949.969714Warning: non-integer x = 2820.026296Warning: non-integer x = 2855.016709Warning: non-integer x = 2811.006672Warning: non-integer x = 2965.023721Warning: non-integer x = 2719.002730Warning: non-integer x = 2578.008890Warning: non-integer x = 2413.986708Warning: non-integer x = 2639.989016Warning: non-integer x = 3037.016066Warning: non-integer x = 2969.025149Warning: non-integer x = 2975.973876Warning: non-integer x = 3060.999391Warning: non-integer x = 3032.011437Warning: non-integer x = 2981.011262Warning: non-integer x = 2996.018278Warning: non-integer x = 2813.969146Warning: non-integer x = 2932.033529Warning: non-integer x = 2705.009823Warning: non-integer x = 2767.019520Warning: non-integer x = 2698.762403Warning: non-integer x = 2681.525529Warning: non-integer x = 2495.523843Warning: non-integer x = 2431.757412Warning: non-integer x = 2445.765016Warning: non-integer x = 2283.362037Warning: non-integer x = 2281.184074Warning: non-integer x = 2295.537086Warning: non-integer x = 2085.319772Warning: non-integer x = 2011.314214Warning: non-integer x = 2005.202163Warning: non-integer x = 2030.313474Warning: non-integer x = 2177.139597Warning: non-integer x = 2110.400179Warning: non-integer x = 2343.427968Warning: non-integer x = 2273.208207Warning: non-integer x = 2275.150110Warning: non-integer x = 2470.524100Warning: non-integer x = 2297.688717Warning: non-integer x = 2098.492026Warning: non-integer x = 2062.868404Warning: non-integer x = 2136.981310Warning: non-integer x = 2320.042260Warning: non-integer x = 2116.064835Warning: non-integer x = 1881.497858Warning: non-integer x = 2169.858930Warning: non-integer x = 2208.768828Warning: non-integer x = 2278.197240Warning: non-integer x = 2076.869793Warning: non-integer x = 2129.700354Warning: non-integer x = 2256.911798Warning: non-integer x = 2206.937280Warning: non-integer x = 2684.248827Warning: non-integer x = 2234.444286Warning: non-integer x = 2051.393023Warning: non-integer x = 2244.044884Warning: non-integer x = 2200.850137Warning: non-integer x = 2302.265145Warning: non-integer x = 2288.135805Warning: non-integer x = 2497.934810Warning: non-integer x = 2450.923970Warning: non-integer x = 2448.325884Warning: non-integer x = 2671.760668Warning: non-integer x = 2535.763986Warning: non-integer x = 2518.600952Warning: non-integer x = 2775.204107Warning: non-integer x = 2580.823678Warning: non-integer x = 2756.132125Warning: non-integer x = 2630.296807Warning: non-integer x = 2747.017317Warning: non-integer x = 2970.012055Warning: non-integer x = 2853.987060Warning: non-integer x = 3176.023652Warning: non-integer x = 2858.991715Warning: non-integer x = 3052.996916Warning: non-integer x = 2961.985565Warning: non-integer x = 2826.980041Warning: non-integer x = 2953.992434Warning: non-integer x = 2969.026033Warning: non-integer x = 3109.984346Warning: non-integer x = 3087.984268Warning: non-integer x = 3252.018802Warning: non-integer x = 3096.969101Warning: non-integer x = 3098.990043Warning: non-integer x = 3097.022022Warning: non-integer x = 2832.979387Warning: non-integer x = 3026.030604Warning: non-integer x = 3022.024580Warning: non-integer x = 2806.991303Warning: non-integer x = 2783.010825Warning: non-integer x = 2382.973452Warning: non-integer x = 2996.012770Warning: non-integer x = 3130.998681Warning: non-integer x = 3025.023709Warning: non-integer x = 3135.988102Warning: non-integer x = 3261.035911Warning: non-integer x = 3110.991601Warning: non-integer x = 3152.979546Warning: non-integer x = 3080.993097Warning: non-integer x = 3062.971288Warning: non-integer x = 2869.015016Warning: non-integer x = 2970.006949Warning: non-integer x = 2795.774515Warning: non-integer x = 2872.620012Warning: non-integer x = 2694.485088Warning: non-integer x = 2665.801600Warning: non-integer x = 2636.834331Warning: non-integer x = 2594.364804Warning: non-integer x = 2489.247436Warning: non-integer x = 2468.641721Warning: non-integer x = 2433.394951Warning: non-integer x = 2197.309516Warning: non-integer x = 2171.224597Warning: non-integer x = 2108.333194Warning: non-integer x = 2258.228217Warning: non-integer x = 2234.480248Warning: non-integer x = 2535.441371Warning: non-integer x = 2618.232419Warning: non-integer x = 1867.382662Warning: non-integer x = 2027.704858Warning: non-integer x = 1850.005166Warning: non-integer x = 1748.952959Warning: non-integer x = 1795.251567Warning: non-integer x = 1667.711138Warning: non-integer x = 1972.246495Warning: non-integer x = 1763.208774Warning: non-integer x = 1694.211962Warning: non-integer x = 1989.502511Warning: non-integer x = 1802.254328Warning: non-integer x = 2211.105146Warning: non-integer x = 1988.756847Warning: non-integer x = 1952.486701Warning: non-integer x = 2206.847545Warning: non-integer x = 2211.938950Warning: non-integer x = 2470.023383Warning: non-integer x = 2323.498910Warning: non-integer x = 1955.318051Warning: non-integer x = 2208.023826Warning: non-integer x = 2240.888715Warning: non-integer x = 2309.255830Warning: non-integer x = 2342.184668Warning: non-integer x = 2502.925141Warning: non-integer x = 2447.916614Warning: non-integer x = 2539.377564Warning: non-integer x = 2592.673530Warning: non-integer x = 2616.785216Warning: non-integer x = 2496.584960Warning: non-integer x = 2952.340612Warning: non-integer x = 2477.728257Warning: non-integer x = 2742.120490Warning: non-integer x = 2394.952480Warning: non-integer x = 2711.028271Warning: non-integer x = 2953.983574Warning: non-integer x = 2872.016572Warning: non-integer x = 3129.010738Warning: non-integer x = 3028.011667Warning: non-integer x = 3012.996488Warning: non-integer x = 3126.020307Warning: non-integer x = 3086.016578Warning: non-integer x = 3099.990100Warning: non-integer x = 3192.023264Warning: non-integer x = 3286.991520Warning: non-integer x = 3225.982902Warning: non-integer x = 3248.026789Warning: non-integer x = 3203.970823Warning: non-integer x = 3256.028034Warning: non-integer x = 3172.996547Warning: non-integer x = 3117.978919Warning: non-integer x = 3279.972823Warning: non-integer x = 3072.991467Warning: non-integer x = 3135.009382Warning: non-integer x = 2762.986428Warning: non-integer x = 2570.995302Warning: non-integer x = 3128.995386Warning: non-integer x = 3231.968804Warning: non-integer x = 3261.983874Warning: non-integer x = 3364.032330Warning: non-integer x = 3317.998457Warning: non-integer x = 3296.980029Warning: non-integer x = 3290.995204Warning: non-integer x = 3358.979860Warning: non-integer x = 3035.000639Warning: non-integer x = 3291.001443Warning: non-integer x = 2933.801008Warning: non-integer x = 2979.613342Warning: non-integer x = 3099.597716Warning: non-integer x = 2896.858457Warning: non-integer x = 2830.896911Warning: non-integer x = 2694.428683Warning: non-integer x = 2772.194648Warning: non-integer x = 2687.652088Warning: non-integer x = 2489.424564Warning: non-integer x = 2521.307717Warning: non-integer x = 2482.332781Warning: non-integer x = 2260.339212Warning: non-integer x = 2283.220962Warning: non-integer x = 2421.541609Warning: non-integer x = 2665.427802Warning: non-integer x = 2689.290341Warning: non-integer x = 1758.185594Warning: non-integer x = 2069.814685Warning: non-integer x = 1843.972332Warning: non-integer x = 1729.961628Warning: non-integer x = 1776.203856Warning: non-integer x = 1747.838314Warning: non-integer x = 1891.963339Warning: non-integer x = 1945.682416Warning: non-integer x = 1804.414513Warning: non-integer x = 1959.472779Warning: non-integer x = 1766.220649Warning: non-integer x = 2063.902640Warning: non-integer x = 2032.801091Warning: non-integer x = 2043.574367Warning: non-integer x = 2028.643029Warning: non-integer x = 2230.996250Warning: non-integer x = 2486.082781Warning: non-integer x = 2261.450134Warning: non-integer x = 2121.486566Warning: non-integer x = 2182.011128Warning: non-integer x = 2260.871857Warning: non-integer x = 2270.225848Warning: non-integer x = 2256.120868Warning: non-integer x = 2405.839172Warning: non-integer x = 2510.982412Warning: non-integer x = 2527.358784Warning: non-integer x = 2722.778233Warning: non-integer x = 2513.733434Warning: non-integer x = 2607.653984Warning: non-integer x = 2805.217853Warning: non-integer x = 2729.922009Warning: non-integer x = 2793.189205Warning: non-integer x = 2532.120126Warning: non-integer x = 2726.015580Warning: non-integer x = 2816.996579Warning: non-integer x = 2767.007612Warning: non-integer x = 2992.994909Warning: non-integer x = 2930.996434Warning: non-integer x = 3115.020496Warning: non-integer x = 2989.987092Warning: non-integer x = 3264.014226Warning: non-integer x = 3143.017010Warning: non-integer x = 2969.020873Warning: non-integer x = 3142.009809Warning: non-integer x = 3241.005648Warning: non-integer x = 3377.006356Warning: non-integer x = 3198.002299Warning: non-integer x = 3364.994387Warning: non-integer x = 3427.997792Warning: non-integer x = 3356.022880Warning: non-integer x = 3517.990943Warning: non-integer x = 3379.992456Warning: non-integer x = 3374.980003Warning: non-integer x = 2984.979608Warning: non-integer x = 2875.997328Warning: non-integer x = 2785.009354Warning: non-integer x = 3235.007984Warning: non-integer x = 3442.004009Warning: non-integer x = 3496.032858Warning: non-integer x = 3452.013762Warning: non-integer x = 3478.000528Warning: non-integer x = 3589.976875Warning: non-integer x = 3140.965661Warning: non-integer x = 3412.002518Warning: non-integer x = 3159.813311Warning: non-integer x = 3138.564281Warning: non-integer x = 3202.601047Warning: non-integer x = 3135.913852Warning: non-integer x = 3091.027432Warning: non-integer x = 2912.424439Warning: non-integer x = 3022.221471Warning: non-integer x = 2945.720079Warning: non-integer x = 2748.465924Warning: non-integer x = 2751.374325Warning: non-integer x = 2771.351088Warning: non-integer x = 2591.431004Warning: non-integer x = 2571.217052Warning: non-integer x = 2391.473093Warning: non-integer x = 2880.487527Warning: non-integer x = 2961.311017Warning: non-integer x = 2057.709519Warning: non-integer x = 2351.303735Warning: non-integer x = 2201.517116Warning: non-integer x = 1993.296387Warning: non-integer x = 1990.725598Warning: non-integer x = 1910.294495Warning: non-integer x = 2170.696012Warning: non-integer x = 2025.761365Warning: non-integer x = 1812.396876Warning: non-integer x = 2117.734906Warning: non-integer x = 1873.339537Warning: non-integer x = 2153.990736Warning: non-integer x = 2068.864880Warning: non-integer x = 2187.741178Warning: non-integer x = 2153.803573Warning: non-integer x = 2302.075956Warning: non-integer x = 2668.222646Warning: non-integer x = 2308.436864Warning: non-integer x = 2223.472517Warning: non-integer x = 2278.058441Warning: non-integer x = 2346.918881Warning: non-integer x = 2332.237530Warning: non-integer x = 2361.170461Warning: non-integer x = 2503.922725Warning: non-integer x = 2481.931942Warning: non-integer x = 2514.329500Warning: non-integer x = 2814.829471Warning: non-integer x = 2618.789834Warning: non-integer x = 2607.599097Warning: non-integer x = 3016.373524Warning: non-integer x = 2677.865806Warning: non-integer x = 2947.263119Warning: non-integer x = 2691.325957Warning: non-integer x = 2783.037667Warning: non-integer x = 2767.990025Warning: non-integer x = 2818.011201Warning: non-integer x = 3096.998330Warning: non-integer x = 2955.991538Warning: non-integer x = 3140.986091Warning: non-integer x = 3007.988192Warning: non-integer x = 3197.996892Warning: non-integer x = 3204.985848Warning: non-integer x = 3212.015808Warning: non-integer x = 3121.014393Warning: non-integer x = 3275.984095Warning: non-integer x = 3431.998913Warning: non-integer x = 3371.987109Warning: non-integer x = 3277.015016Warning: non-integer x = 3563.012260Warning: non-integer x = 3412.013897Warning: non-integer x = 3712.024535Warning: non-integer x = 3654.002606Warning: non-integer x = 3448.009591Warning: non-integer x = 3471.011100Warning: non-integer x = 3243.986784Warning: non-integer x = 3262.001297Warning: non-integer x = 3044.984307Warning: non-integer x = 2763.985698Warning: non-integer x = 3410.989283Warning: non-integer x = 3667.026297Warning: non-integer x = 3520.010040Warning: non-integer x = 3501.031307Warning: non-integer x = 3615.969898Warning: non-integer x = 3653.987492Warning: non-integer x = 3568.970857Warning: non-integer x = 3591.975526Warning: non-integer x = 3256.885910Warning: non-integer x = 3265.638505Warning: non-integer x = 3306.645728Warning: non-integer x = 3300.019733Warning: non-integer x = 3408.049384Warning: non-integer x = 3295.449258Warning: non-integer x = 3231.276739Warning: non-integer x = 3161.722672Warning: non-integer x = 3073.454105Warning: non-integer x = 3014.379975Warning: non-integer x = 3047.305197Warning: non-integer x = 2955.433031Warning: non-integer x = 2813.250100Warning: non-integer x = 2556.476614Warning: non-integer x = 2921.486879Warning: non-integer x = 3166.331691Warning: non-integer x = 1434.573992Warning: non-integer x = 1599.925287Warning: non-integer x = 1441.286251Warning: non-integer x = 1425.413861Warning: non-integer x = 1406.313411Warning: non-integer x = 1353.775431Warning: non-integer x = 1498.914019Warning: non-integer x = 1492.546233Warning: non-integer x = 1396.602144Warning: non-integer x = 1641.925552Warning: non-integer x = 1506.878187Warning: non-integer x = 1642.288032Warning: non-integer x = 1534.109375Warning: non-integer x = 1723.183153Warning: non-integer x = 1953.511895Warning: non-integer x = 2035.671820Warning: non-integer x = 2222.818550Warning: non-integer x = 2088.317659Warning: non-integer x = 1872.267369Warning: non-integer x = 2109.974184Warning: non-integer x = 2264.859595Warning: non-integer x = 2225.205577Warning: non-integer x = 2176.075140Warning: non-integer x = 2380.827351Warning: non-integer x = 2318.780121Warning: non-integer x = 2414.284251Warning: non-integer x = 2556.659256Warning: non-integer x = 2537.717093Warning: non-integer x = 2570.590633Warning: non-integer x = 2877.237135Warning: non-integer x = 2648.835006Warning: non-integer x = 2725.080114Warning: non-integer x = 2682.244217Warning: non-integer x = 2885.023641Warning: non-integer x = 2780.005961Warning: non-integer x = 2746.999360Warning: non-integer x = 3068.987885Warning: non-integer x = 2862.001998Warning: non-integer x = 2998.987708Warning: non-integer x = 2900.986292Warning: non-integer x = 3147.993907Warning: non-integer x = 3157.011767Warning: non-integer x = 3226.001369Warning: non-integer x = 3332.000498Warning: non-integer x = 3165.990489Warning: non-integer x = 3313.992204Warning: non-integer x = 3265.001610Warning: non-integer x = 3435.013163Warning: non-integer x = 3389.994140Warning: non-integer x = 3582.010600Warning: non-integer x = 3793.983858Warning: non-integer x = 3696.993700Warning: non-integer x = 3562.004316Warning: non-integer x = 3610.993778Warning: non-integer x = 3467.001074Warning: non-integer x = 3489.996384Warning: non-integer x = 3462.980386Warning: non-integer x = 3182.980043Warning: non-integer x = 2907.998668Warning: non-integer x = 3575.974931Warning: non-integer x = 3767.983009Warning: non-integer x = 3625.011659Warning: non-integer x = 3776.000615Warning: non-integer x = 3968.021485Warning: non-integer x = 3675.973383Warning: non-integer x = 3789.010554Warning: non-integer x = 3687.930203Warning: non-integer x = 3493.624102Warning: non-integer x = 3654.696984Warning: non-integer x = 3542.018870Warning: non-integer x = 3420.077460Warning: non-integer x = 3406.503067Warning: non-integer x = 3540.288792Warning: non-integer x = 3253.766822Warning: non-integer x = 3182.487851Warning: non-integer x = 3393.422198Warning: non-integer x = 3376.339045Warning: non-integer x = 3130.477697Warning: non-integer x = 3327.224029Warning: non-integer x = 3050.641475Warning: non-integer x = 3149.508426Warning: non-integer x = 3077.301349Warning: non-integer x = 2633.670183Warning: non-integer x = 2717.905812Warning: non-integer x = 2569.026184Warning: non-integer x = 2401.794601Warning: non-integer x = 2268.166633Warning: non-integer x = 2139.764863Warning: non-integer x = 2384.014011Warning: non-integer x = 2244.194988Warning: non-integer x = 1921.497243Warning: non-integer x = 2213.860440Warning: non-integer x = 2024.474844Warning: non-integer x = 2136.952241Warning: non-integer x = 2010.755292Warning: non-integer x = 2111.623483Warning: non-integer x = 2150.644909Warning: non-integer x = 2203.798144Warning: non-integer x = 2771.186562Warning: non-integer x = 2300.399652Warning: non-integer x = 2138.332610Warning: non-integer x = 2165.931243Warning: non-integer x = 2359.901784Warning: non-integer x = 2333.222139Warning: non-integer x = 2207.076739Warning: non-integer x = 2456.902063Warning: non-integer x = 2338.795059Warning: non-integer x = 2481.278216Warning: non-integer x = 2601.663222Warning: non-integer x = 2644.749612Warning: non-integer x = 2543.546058Warning: non-integer x = 2898.280712Warning: non-integer x = 2617.815929Warning: non-integer x = 2874.145915Warning: non-integer x = 2626.162332Warning: non-integer x = 2904.027389Warning: non-integer x = 2889.997483Warning: non-integer x = 2817.995599Warning: non-integer x = 2839.996738Warning: non-integer x = 2746.012843Warning: non-integer x = 2928.996288Warning: non-integer x = 2909.991128Warning: non-integer x = 3013.996334Warning: non-integer x = 3233.010202Warning: non-integer x = 3086.014066Warning: non-integer x = 3188.015228Warning: non-integer x = 3400.990649Warning: non-integer x = 3269.007901Warning: non-integer x = 3344.017945Warning: non-integer x = 3443.002402Warning: non-integer x = 3595.983739Warning: non-integer x = 3385.999382Warning: non-integer x = 3955.020380Warning: non-integer x = 3796.003533Warning: non-integer x = 3922.996260Warning: non-integer x = 3472.998771Warning: non-integer x = 3797.019249Warning: non-integer x = 3566.017976Warning: non-integer x = 3460.998517Warning: non-integer x = 3283.016800Warning: non-integer x = 3137.004082Warning: non-integer x = 3598.975546Warning: non-integer x = 3698.005570Warning: non-integer x = 3826.024922Warning: non-integer x = 3953.972867Warning: non-integer x = 3804.025746Warning: non-integer x = 3951.973992Warning: non-integer x = 3727.950644Warning: non-integer x = 3748.689893Warning: non-integer x = 3683.705743Warning: non-integer x = 3823.104330Warning: non-integer x = 3716.130233Warning: non-integer x = 3523.512310Warning: non-integer x = 3766.262695Warning: non-integer x = 3674.887410Warning: non-integer x = 3504.522456Warning: non-integer x = 3586.516216Warning: non-integer x = 3578.388650Warning: non-integer x = 3395.519394Warning: non-integer x = 3378.244854Warning: non-integer x = 3435.647367Warning: non-integer x = 3547.525977Warning: non-integer x = 3402.268060Warning: non-integer x = 1228.206824Warning: non-integer x = 1453.624407Warning: non-integer x = 1268.999685Warning: non-integer x = 1209.966342Warning: non-integer x = 1146.685951Warning: non-integer x = 1229.372252Warning: non-integer x = 1276.292352Warning: non-integer x = 1253.969403Warning: non-integer x = 1213.234641Warning: non-integer x = 1351.361860Warning: non-integer x = 1282.591057Warning: non-integer x = 1543.154684Warning: non-integer x = 1455.012641Warning: non-integer x = 1506.894594Warning: non-integer x = 1500.880961Warning: non-integer x = 1731.248805Warning: non-integer x = 2142.706504Warning: non-integer x = 1835.145554Warning: non-integer x = 1633.053314Warning: non-integer x = 1884.822618Warning: non-integer x = 2045.646493Warning: non-integer x = 2028.076982Warning: non-integer x = 2111.045394Warning: non-integer x = 2229.676427Warning: non-integer x = 2242.704402Warning: non-integer x = 2210.145278Warning: non-integer x = 2360.537975Warning: non-integer x = 2356.585212Warning: non-integer x = 2390.440080Warning: non-integer x = 2707.098122Warning: non-integer x = 2523.741400Warning: non-integer x = 2636.935560Warning: non-integer x = 2502.032047Warning: non-integer x = 2666.028116Warning: non-integer x = 2860.992994Warning: non-integer x = 2607.998565Warning: non-integer x = 2797.992395Warning: non-integer x = 2607.008275Warning: non-integer x = 2679.006752Warning: non-integer x = 2760.005729Warning: non-integer x = 2771.992559Warning: non-integer x = 2858.986824Warning: non-integer x = 2917.015242Warning: non-integer x = 3144.014892Warning: non-integer x = 3334.985189Warning: non-integer x = 3316.987591Warning: non-integer x = 3201.000680Warning: non-integer x = 3302.994583Warning: non-integer x = 3404.007208Warning: non-integer x = 3553.014834Warning: non-integer x = 3630.995197Warning: non-integer x = 3793.020438Warning: non-integer x = 3755.002684Warning: non-integer x = 3852.999009Warning: non-integer x = 3677.993415Warning: non-integer x = 3629.005353Warning: non-integer x = 3847.019937Warning: non-integer x = 3526.998895Warning: non-integer x = 3580.994740Warning: non-integer x = 3446.001657Warning: non-integer x = 3109.017693Warning: non-integer x = 3638.013732Warning: non-integer x = 3982.989560Warning: non-integer x = 4074.017731Warning: non-integer x = 3863.986573Warning: non-integer x = 4163.022566Warning: non-integer x = 3921.947357Warning: non-integer x = 4036.713077Warning: non-integer x = 4013.766660Warning: non-integer x = 3828.101372Warning: non-integer x = 3895.215918Warning: non-integer x = 3663.494738Warning: non-integer x = 3937.292107Warning: non-integer x = 3862.897063Warning: non-integer x = 3777.531247Warning: non-integer x = 3733.519792Warning: non-integer x = 3728.415349Warning: non-integer x = 3682.534907Warning: non-integer x = 3815.284558Warning: non-integer x = 3510.710111Warning: non-integer x = 4025.571226Warning: non-integer x = 3790.345286Warning: non-integer x = 1597.865255Warning: non-integer x = 1727.115530Warning: non-integer x = 1600.504546Warning: non-integer x = 1466.394871Warning: non-integer x = 1437.326208Warning: non-integer x = 1461.965848Warning: non-integer x = 1649.233008Warning: non-integer x = 1531.512662Warning: non-integer x = 1477.710573Warning: non-integer x = 1654.878450Warning: non-integer x = 1522.869006Warning: non-integer x = 1709.382912Warning: non-integer x = 1603.215152Warning: non-integer x = 1696.114516Warning: non-integer x = 1700.099030Warning: non-integer x = 1815.259984Warning: non-integer x = 2253.766792Warning: non-integer x = 2022.245942Warning: non-integer x = 1816.147377Warning: non-integer x = 2066.909887Warning: non-integer x = 2057.633215Warning: non-integer x = 1983.013357Warning: non-integer x = 2029.973372Warning: non-integer x = 2279.720645Warning: non-integer x = 2147.624054Warning: non-integer x = 2158.092583Warning: non-integer x = 2409.541386Warning: non-integer x = 2180.452037Warning: non-integer x = 2418.426641Warning: non-integer x = 2590.003602Warning: non-integer x = 2417.664024Warning: non-integer x = 2585.870902Warning: non-integer x = 2522.964446Warning: non-integer x = 2656.026260Warning: non-integer x = 2746.005914Warning: non-integer x = 2649.009290Warning: non-integer x = 2772.008514Warning: non-integer x = 2620.997000Warning: non-integer x = 2686.008812Warning: non-integer x = 2596.008471Warning: non-integer x = 2753.996944Warning: non-integer x = 2832.993049Warning: non-integer x = 2686.989784Warning: non-integer x = 3109.997808Warning: non-integer x = 3110.002395Warning: non-integer x = 3159.005400Warning: non-integer x = 3085.011122Warning: non-integer x = 3150.000497Warning: non-integer x = 3260.008197Warning: non-integer x = 3311.014099Warning: non-integer x = 3661.992103Warning: non-integer x = 3612.002790Warning: non-integer x = 3616.017872Warning: non-integer x = 3987.013685Warning: non-integer x = 3647.987809Warning: non-integer x = 3888.007495Warning: non-integer x = 3868.993929Warning: non-integer x = 3706.005453Warning: non-integer x = 3648.987449Warning: non-integer x = 3593.988805Warning: non-integer x = 3379.009318Warning: non-integer x = 3118.999627Warning: non-integer x = 3711.006465Warning: non-integer x = 4198.986855Warning: non-integer x = 3874.000551Warning: non-integer x = 4136.983479Warning: non-integer x = 3928.926525Warning: non-integer x = 4050.697206Warning: non-integer x = 4003.778556Warning: non-integer x = 4059.135351Warning: non-integer x = 4129.270304Warning: non-integer x = 3952.524931Warning: non-integer x = 4063.290091Warning: non-integer x = 4056.872922Warning: non-integer x = 3996.555435Warning: non-integer x = 4241.496669Warning: non-integer x = 4135.481769Warning: non-integer x = 4013.594383Warning: non-integer x = 4168.298430Warning: non-integer x = 3924.768396Warning: non-integer x = 4303.618147Warning: non-integer x = 4331.364385Warning: non-integer x = 1256.200378Warning: non-integer x = 1394.521778Warning: non-integer x = 1293.020683Warning: non-integer x = 1327.155749Warning: non-integer x = 1294.917895Warning: non-integer x = 1278.491227Warning: non-integer x = 1411.600272Warning: non-integer x = 1418.328069Warning: non-integer x = 1211.219540Warning: non-integer x = 1450.516346Warning: non-integer x = 1316.612295Warning: non-integer x = 1476.026017Warning: non-integer x = 1333.832431Warning: non-integer x = 1501.881821Warning: non-integer x = 1516.864340Warning: non-integer x = 1562.984992Warning: non-integer x = 1918.509396Warning: non-integer x = 1697.012060Warning: non-integer x = 1633.042330Warning: non-integer x = 1793.775669Warning: non-integer x = 1863.480392Warning: non-integer x = 1837.945857Warning: non-integer x = 1908.926815Warning: non-integer x = 2007.490845Warning: non-integer x = 1997.495944Warning: non-integer x = 2044.025149Warning: non-integer x = 2165.370743Warning: non-integer x = 2182.414066Warning: non-integer x = 2208.313119Warning: non-integer x = 2347.804576Warning: non-integer x = 2290.550970Warning: non-integer x = 2398.701384Warning: non-integer x = 2221.596903Warning: non-integer x = 2471.017590Warning: non-integer x = 2596.001105Warning: non-integer x = 2447.992657Warning: non-integer x = 2653.998079Warning: non-integer x = 2455.992350Warning: non-integer x = 2475.001380Warning: non-integer x = 2417.007094Warning: non-integer x = 2597.003937Warning: non-integer x = 2614.993115Warning: non-integer x = 2576.991474Warning: non-integer x = 2840.001926Warning: non-integer x = 2976.011416Warning: non-integer x = 2991.006050Warning: non-integer x = 3119.011780Warning: non-integer x = 3132.004796Warning: non-integer x = 3202.001844Warning: non-integer x = 3205.006547Warning: non-integer x = 3589.998710Warning: non-integer x = 3581.988436Warning: non-integer x = 3357.985552Warning: non-integer x = 3694.014076Warning: non-integer x = 3669.994711Warning: non-integer x = 4045.010473Warning: non-integer x = 3820.005522Warning: non-integer x = 3865.989109Warning: non-integer x = 3782.981782Warning: non-integer x = 3516.009616Warning: non-integer x = 3232.000899Warning: non-integer x = 3149.004574Warning: non-integer x = 3859.000841Warning: non-integer x = 3814.014777Warning: non-integer x = 4116.021063Warning: non-integer x = 3894.866388Warning: non-integer x = 4154.717703Warning: non-integer x = 4126.803474Warning: non-integer x = 4268.134829Warning: non-integer x = 4243.302604Warning: non-integer x = 3970.492703Warning: non-integer x = 4299.262360Warning: non-integer x = 4252.913330Warning: non-integer x = 4078.544340Warning: non-integer x = 4463.534681Warning: non-integer x = 4409.448873Warning: non-integer x = 4140.624517Warning: non-integer x = 4258.331434Warning: non-integer x = 4225.786766Warning: non-integer x = 4492.632756Warning: non-integer x = 4529.368476Warning: non-integer x = 1294.301115Warning: non-integer x = 1324.388327Warning: non-integer x = 1343.098383Warning: non-integer x = 1252.012059Warning: non-integer x = 1381.079580Warning: non-integer x = 1242.360230Warning: non-integer x = 1416.547298Warning: non-integer x = 1296.010645Warning: non-integer x = 1159.117296Warning: non-integer x = 1486.604500Warning: non-integer x = 1328.619184Warning: non-integer x = 1510.073324Warning: non-integer x = 1359.862877Warning: non-integer x = 1468.833649Warning: non-integer x = 1589.910913Warning: non-integer x = 1524.916873Warning: non-integer x = 1827.421426Warning: non-integer x = 1554.893207Warning: non-integer x = 1517.928331Warning: non-integer x = 1692.721060Warning: non-integer x = 1808.404186Warning: non-integer x = 1739.880091Warning: non-integer x = 1795.849616Warning: non-integer x = 1878.423268Warning: non-integer x = 1738.294107Warning: non-integer x = 1959.996887Warning: non-integer x = 2036.277120Warning: non-integer x = 1948.248410Warning: non-integer x = 1931.121173Warning: non-integer x = 2210.676027Warning: non-integer x = 2070.395559Warning: non-integer x = 2305.605016Warning: non-integer x = 2108.427590Warning: non-integer x = 2327.014132Warning: non-integer x = 2411.004023Warning: non-integer x = 2334.998328Warning: non-integer x = 2441.997630Warning: non-integer x = 2451.993281Warning: non-integer x = 2345.000301Warning: non-integer x = 2256.001790Warning: non-integer x = 2212.996045Warning: non-integer x = 2437.008080Warning: non-integer x = 2377.000562Warning: non-integer x = 2564.998906Warning: non-integer x = 2683.004695Warning: non-integer x = 2764.007412Warning: non-integer x = 2959.991238Warning: non-integer x = 3076.997151Warning: non-integer x = 2949.988417Warning: non-integer x = 3398.006777Warning: non-integer x = 3444.988566Warning: non-integer x = 3360.013056Warning: non-integer x = 3624.989482Warning: non-integer x = 3449.005159Warning: non-integer x = 3625.996929Warning: non-integer x = 3854.990600Warning: non-integer x = 3845.009994Warning: non-integer x = 3712.986347Warning: non-integer x = 3801.988228Warning: non-integer x = 3598.001802Warning: non-integer x = 3541.004818Warning: non-integer x = 3417.984334Warning: non-integer x = 3256.010989Warning: non-integer x = 3619.017407Warning: non-integer x = 4206.982399Warning: non-integer x = 3870.891034Warning: non-integer x = 4023.681045Warning: non-integer x = 4234.814101Warning: non-integer x = 4202.113464Warning: non-integer x = 4274.312628Warning: non-integer x = 4131.522394Warning: non-integer x = 4272.288268Warning: non-integer x = 4214.906891Warning: non-integer x = 4259.537872Warning: non-integer x = 4308.538137Warning: non-integer x = 4318.438872Warning: non-integer x = 4405.610214Warning: non-integer x = 4389.313490Warning: non-integer x = 4433.814994Warning: non-integer x = 5036.694322Warning: non-integer x = 4792.409035Warning: non-integer x = 1399.469446Warning: non-integer x = 1500.677525Warning: non-integer x = 1429.198787Warning: non-integer x = 1251.918445Warning: non-integer x = 1315.919443Warning: non-integer x = 1326.488759Warning: non-integer x = 1502.739565Warning: non-integer x = 1289.950466Warning: non-integer x = 1147.067048Warning: non-integer x = 1382.392402Warning: non-integer x = 1228.479812Warning: non-integer x = 1336.818015Warning: non-integer x = 1333.826651Warning: non-integer x = 1282.557111Warning: non-integer x = 1272.487331Warning: non-integer x = 1464.789019Warning: non-integer x = 1676.278337Warning: non-integer x = 1436.853102Warning: non-integer x = 1297.781526Warning: non-integer x = 1571.647676Warning: non-integer x = 1693.310705Warning: non-integer x = 1584.781871Warning: non-integer x = 1651.776865Warning: non-integer x = 1749.306803Warning: non-integer x = 1709.270560Warning: non-integer x = 1735.844870Warning: non-integer x = 1827.157048Warning: non-integer x = 1702.094229Warning: non-integer x = 1816.064882Warning: non-integer x = 1990.486974Warning: non-integer x = 1830.224046Warning: non-integer x = 2001.379318Warning: non-integer x = 1883.133359Warning: non-integer x = 2044.024979Warning: non-integer x = 2217.997502Warning: non-integer x = 2051.998801Warning: non-integer x = 2097.003504Warning: non-integer x = 2042.005762Warning: non-integer x = 2214.997902Warning: non-integer x = 2127.996473Warning: non-integer x = 2044.003110Warning: non-integer x = 2205.995581Warning: non-integer x = 2074.997132Warning: non-integer x = 2432.003305Warning: non-integer x = 2478.003734Warning: non-integer x = 2590.005931Warning: non-integer x = 2577.996097Warning: non-integer x = 2662.998646Warning: non-integer x = 2888.994036Warning: non-integer x = 2917.995037Warning: non-integer x = 3045.999404Warning: non-integer x = 3158.005420Warning: non-integer x = 3094.991432Warning: non-integer x = 3456.988119Warning: non-integer x = 3206.007511Warning: non-integer x = 3538.004155Warning: non-integer x = 3638.988944Warning: non-integer x = 3650.991426Warning: non-integer x = 3774.985862Warning: non-integer x = 3805.003812Warning: non-integer x = 3581.014874Warning: non-integer x = 3573.996220Warning: non-integer x = 3477.988258Warning: non-integer x = 3406.985638Warning: non-integer x = 3076.987452Warning: non-integer x = 3769.013720Warning: non-integer x = 3830.822197Warning: non-integer x = 3874.627971Warning: non-integer x = 4095.764005Warning: non-integer x = 4202.110170Warning: non-integer x = 4314.283093Warning: non-integer x = 4111.485691Warning: non-integer x = 4424.300423Warning: non-integer x = 4386.897371Warning: non-integer x = 4306.515355Warning: non-integer x = 4492.537987Warning: non-integer x = 4589.500037Warning: non-integer x = 4538.627795Warning: non-integer x = 4735.286582Warning: non-integer x = 4540.775454Warning: non-integer x = 4918.687964Warning: non-integer x = 5149.393516Warning: non-integer x = 1045.831350Warning: non-integer x = 1055.887709Warning: non-integer x = 965.499435Warning: non-integer x = 897.412514Warning: non-integer x = 936.077675Warning: non-integer x = 915.446743Warning: non-integer x = 1090.739844Warning: non-integer x = 1038.408913Warning: non-integer x = 992.752821Warning: non-integer x = 1086.882597Warning: non-integer x = 1068.270894Warning: non-integer x = 1102.507247Warning: non-integer x = 1027.410867Warning: non-integer x = 1093.319207Warning: non-integer x = 1135.330887Warning: non-integer x = 1142.387977Warning: non-integer x = 1380.048161Warning: non-integer x = 1205.666217Warning: non-integer x = 1152.688045Warning: non-integer x = 1293.527328Warning: non-integer x = 1377.047451Warning: non-integer x = 1346.672648Warning: non-integer x = 1411.661225Warning: non-integer x = 1618.188103Warning: non-integer x = 1488.091603Warning: non-integer x = 1525.739270Warning: non-integer x = 1569.977999Warning: non-integer x = 1579.999627Warning: non-integer x = 1597.921482Warning: non-integer x = 1713.276902Warning: non-integer x = 1611.046412Warning: non-integer x = 1774.210197Warning: non-integer x = 1706.923302Warning: non-integer x = 1834.005756Warning: non-integer x = 1918.003037Warning: non-integer x = 1922.003201Warning: non-integer x = 2009.004865Warning: non-integer x = 1925.997700Warning: non-integer x = 2071.001313Warning: non-integer x = 1985.000603Warning: non-integer x = 1948.001907Warning: non-integer x = 1975.002152Warning: non-integer x = 1872.996807Warning: non-integer x = 2057.001739Warning: non-integer x = 2208.996962Warning: non-integer x = 2340.995035Warning: non-integer x = 2351.002669Warning: non-integer x = 2588.993735Warning: non-integer x = 2725.993812Warning: non-integer x = 2949.997858Warning: non-integer x = 2912.008126Warning: non-integer x = 2801.006950Warning: non-integer x = 3162.992388Warning: non-integer x = 3104.992417Warning: non-integer x = 3114.992499Warning: non-integer x = 3442.991740Warning: non-integer x = 3525.996510Warning: non-integer x = 3683.009262Warning: non-integer x = 3534.991358Warning: non-integer x = 3550.000985Warning: non-integer x = 3409.998715Warning: non-integer x = 3571.002631Warning: non-integer x = 3063.010848Warning: non-integer x = 3117.989769Warning: non-integer x = 3568.769294Warning: non-integer x = 3952.630327Warning: non-integer x = 3872.709174Warning: non-integer x = 3976.053592Warning: non-integer x = 4374.349485Warning: non-integer x = 4111.486173Warning: non-integer x = 4548.292978Warning: non-integer x = 4395.928423Warning: non-integer x = 4175.537939Warning: non-integer x = 4506.535248Warning: non-integer x = 4536.457121Warning: non-integer x = 4689.635290Warning: non-integer x = 4731.306258Warning: non-integer x = 4802.840259Warning: non-integer x = 5006.652754Warning: non-integer x = 5066.420652Warning: non-integer x = 827.449470Warning: non-integer x = 877.561710Warning: non-integer x = 796.211836Warning: non-integer x = 777.201577Warning: non-integer x = 796.752501Warning: non-integer x = 806.171449Warning: non-integer x = 879.191313Warning: non-integer x = 863.950085Warning: non-integer x = 775.380732Warning: non-integer x = 949.639945Warning: non-integer x = 826.990754Warning: non-integer x = 956.310916Warning: non-integer x = 894.220220Warning: non-integer x = 973.178690Warning: non-integer x = 991.178688Warning: non-integer x = 1002.201109Warning: non-integer x = 1144.857327Warning: non-integer x = 1045.591216Warning: non-integer x = 910.511560Warning: non-integer x = 1059.431942Warning: non-integer x = 1156.862861Warning: non-integer x = 1120.552336Warning: non-integer x = 1183.547257Warning: non-integer x = 1262.929190Warning: non-integer x = 1233.910934Warning: non-integer x = 1305.620008Warning: non-integer x = 1413.880096Warning: non-integer x = 1313.810792Warning: non-integer x = 1441.812384Warning: non-integer x = 1488.118408Warning: non-integer x = 1367.896712Warning: non-integer x = 1533.020569Warning: non-integer x = 1473.640585Warning: non-integer x = 1594.012852Warning: non-integer x = 1675.002593Warning: non-integer x = 1673.997186Warning: non-integer x = 1736.997440Warning: non-integer x = 1673.000263Warning: non-integer x = 1797.998218Warning: non-integer x = 1629.001587Warning: non-integer x = 1833.998671Warning: non-integer x = 1765.000325Warning: non-integer x = 1704.998123Warning: non-integer x = 1807.995999Warning: non-integer x = 1935.002704Warning: non-integer x = 2006.997147Warning: non-integer x = 1943.997150Warning: non-integer x = 2027.996607Warning: non-integer x = 2338.996823Warning: non-integer x = 2205.992801Warning: non-integer x = 2649.004586Warning: non-integer x = 2754.000680Warning: non-integer x = 2567.006403Warning: non-integer x = 2806.996608Warning: non-integer x = 2721.995456Warning: non-integer x = 2929.991452Warning: non-integer x = 3142.992932Warning: non-integer x = 3088.007229Warning: non-integer x = 3314.001068Warning: non-integer x = 3528.989739Warning: non-integer x = 3415.011826Warning: non-integer x = 3291.995574Warning: non-integer x = 3502.998906Warning: non-integer x = 3496.990827Warning: non-integer x = 3121.009360Warning: non-integer x = 3234.002614Warning: non-integer x = 2786.564506Warning: non-integer x = 3381.530163Warning: non-integer x = 3866.724586Warning: non-integer x = 3754.927497Warning: non-integer x = 3984.201804Warning: non-integer x = 3970.453035Warning: non-integer x = 4314.267170Warning: non-integer x = 4294.854272Warning: non-integer x = 4206.528804Warning: non-integer x = 4309.488970Warning: non-integer x = 4505.446608Warning: non-integer x = 4512.596664Warning: non-integer x = 4631.265668Warning: non-integer x = 4600.766541Warning: non-integer x = 5272.681843Warning: non-integer x = 5196.399375Warning: non-integer x = 786.381918Warning: non-integer x = 893.597505Warning: non-integer x = 742.120893Warning: non-integer x = 710.100880Warning: non-integer x = 712.579100Warning: non-integer x = 756.020431Warning: non-integer x = 835.060985Warning: non-integer x = 770.751904Warning: non-integer x = 816.449184Warning: non-integer x = 885.521251Warning: non-integer x = 821.990013Warning: non-integer x = 866.178780Warning: non-integer x = 840.150312Warning: non-integer x = 912.108288Warning: non-integer x = 839.961409Warning: non-integer x = 881.059816Warning: non-integer x = 1060.739476Warning: non-integer x = 913.509788Warning: non-integer x = 851.468998Warning: non-integer x = 947.381637Warning: non-integer x = 966.719451Warning: non-integer x = 986.479856Warning: non-integer x = 982.438614Warning: non-integer x = 1187.870036Warning: non-integer x = 1147.831690Warning: non-integer x = 1092.531065Warning: non-integer x = 1199.752873Warning: non-integer x = 1154.700887Warning: non-integer x = 1214.681190Warning: non-integer x = 1323.980144Warning: non-integer x = 1240.797813Warning: non-integer x = 1337.869272Warning: non-integer x = 1264.403100Warning: non-integer x = 1345.012408Warning: non-integer x = 1405.001723Warning: non-integer x = 1396.997256Warning: non-integer x = 1496.001008Warning: non-integer x = 1415.998881Warning: non-integer x = 1475.000927Warning: non-integer x = 1433.001979Warning: non-integer x = 1581.001577Warning: non-integer x = 1585.998641Warning: non-integer x = 1448.001598Warning: non-integer x = 1666.995783Warning: non-integer x = 1602.001991Warning: non-integer x = 1690.001300Warning: non-integer x = 1829.998438Warning: non-integer x = 1857.001835Warning: non-integer x = 1942.004805Warning: non-integer x = 1967.000312Warning: non-integer x = 2354.001549Warning: non-integer x = 2354.996616Warning: non-integer x = 2386.997249Warning: non-integer x = 2462.998226Warning: non-integer x = 2393.998627Warning: non-integer x = 2588.994717Warning: non-integer x = 2759.003396Warning: non-integer x = 2864.003355Warning: non-integer x = 3120.995005Warning: non-integer x = 3068.000367Warning: non-integer x = 3051.992952Warning: non-integer x = 3179.992555Warning: non-integer x = 3219.005683Warning: non-integer x = 2921.004095Warning: non-integer x = 3176.995037Warning: non-integer x = 2811.542983Warning: non-integer x = 2772.430093Warning: non-integer x = 3316.617178Warning: non-integer x = 3534.874859Warning: non-integer x = 3616.076687Warning: non-integer x = 3670.420387Warning: non-integer x = 4129.244835Warning: non-integer x = 4026.827059Warning: non-integer x = 4118.463661Warning: non-integer x = 4389.482723Warning: non-integer x = 4355.456858Warning: non-integer x = 4377.563208Warning: non-integer x = 4504.284608Warning: non-integer x = 4420.734356Warning: non-integer x = 5252.650767Warning: non-integer x = 5227.394285Warning: non-integer x = 550.979205Warning: non-integer x = 543.971296Warning: non-integer x = 489.749434Warning: non-integer x = 456.700776Warning: non-integer x = 502.108924Warning: non-integer x = 461.200757Warning: non-integer x = 496.210653Warning: non-integer x = 517.168434Warning: non-integer x = 461.839926Warning: non-integer x = 609.031163Warning: non-integer x = 577.691467Warning: non-integer x = 571.769133Warning: non-integer x = 585.801100Warning: non-integer x = 618.759712Warning: non-integer x = 650.720991Warning: non-integer x = 619.729417Warning: non-integer x = 778.559402Warning: non-integer x = 671.381736Warning: non-integer x = 619.340216Warning: non-integer x = 735.300237Warning: non-integer x = 799.591096Warning: non-integer x = 768.369792Warning: non-integer x = 843.369814Warning: non-integer x = 876.649902Warning: non-integer x = 882.640226Warning: non-integer x = 862.399400Warning: non-integer x = 1011.628865Warning: non-integer x = 1020.620133Warning: non-integer x = 968.528512Warning: non-integer x = 1127.830341Warning: non-integer x = 1026.666944Warning: non-integer x = 1100.740412Warning: non-integer x = 1060.167575Warning: non-integer x = 1120.011553Warning: non-integer x = 1160.999088Warning: non-integer x = 1112.000660Warning: non-integer x = 1316.000757Warning: non-integer x = 1114.999434Warning: non-integer x = 1291.001113Warning: non-integer x = 1318.998348Warning: non-integer x = 1252.001285Warning: non-integer x = 1373.998916Warning: non-integer x = 1327.002651Warning: non-integer x = 1406.003102Warning: non-integer x = 1362.998189Warning: non-integer x = 1442.998534Warning: non-integer x = 1422.998694Warning: non-integer x = 1515.998217Warning: non-integer x = 1645.001304Warning: non-integer x = 1686.997009Warning: non-integer x = 2013.995469Warning: non-integer x = 2015.002537Warning: non-integer x = 2228.003506Warning: non-integer x = 2017.001940Warning: non-integer x = 2250.994233Warning: non-integer x = 2540.995382Warning: non-integer x = 2475.005609Warning: non-integer x = 2548.999594Warning: non-integer x = 2742.998499Warning: non-integer x = 2888.999288Warning: non-integer x = 2861.998461Warning: non-integer x = 2908.003581Warning: non-integer x = 2914.996606Warning: non-integer x = 2807.993922Warning: non-integer x = 2843.001114Warning: non-integer x = 2682.523453Warning: non-integer x = 2802.398342Warning: non-integer x = 2653.482294Warning: non-integer x = 3242.785803Warning: non-integer x = 3554.041403Warning: non-integer x = 3415.384651Warning: non-integer x = 3885.202031Warning: non-integer x = 3900.790499Warning: non-integer x = 4063.454706Warning: non-integer x = 4113.434127Warning: non-integer x = 4247.440429Warning: non-integer x = 4075.516927Warning: non-integer x = 4511.278382Warning: non-integer x = 4253.684375Warning: non-integer x = 4932.588223Warning: non-integer x = 5133.379049

StMoMo: Finish fitting with gnm

install.packages("StMoMo")

WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:

https://cran.rstudio.com/bin/windows/Rtools/

Warning in install.packages :
  package ‘StMoMo’ is in use and will not be installed

plot(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)