adrc.reml.jack: AD model with row and column effects analyzed by MINQUE and...
In qgtools: Generalized Quantitative Genetics Data Analyses
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
Description
An AD model with row and column effects included is used for controlling field variation. This model will be analyzed by MINQUE approach and tested by jackknife technique. The data set can be irregular or missing but the field layout should be rectangular. It can analyze any genetic mating designs and data including F1, F2, or F3 with parents..
Usage
1
adrc.reml.jack(Y, Ped, Row = NULL, Col = NULL, JacNum = NULL, JacRep = NULL)
Arguments
Y
A data matrix for one or more traits
Ped
A pedigree matrix including Environment, Female, Male,Generation is required.
Row
A vector for field rows. It can be default.
Col
A vector for field colums.It can be default.
JacNum
Number of jackknife groups to be used. The default is 10.
JacRep
Repeating times for jackknife process. The default is 1.
Details
A pedigree matrix used for analysis is required in the order of Environment (column 1), Female(column 2), Male(column 3), Generation (column 4). Even though there is only one environment, this first column is needed.If only row or column vector is included, this is equivallent to an AD model with block effects.
Value
Return a list of results: estimated Variance components, estimated proportional variance components, estimated fixed effects, and predicted random effects, and their statistical tests
Author(s)
Jixiang Wu <qgtools@gmail.com>
References
Rao, C.R. 1971. Estimation of variance and covariance components-MINQUE theory. J Multiva Ana 1:19
Wu, J., McCarty Jr., J.C., Jenkins, J.N. 2010. Cotton chromosome substitution lines crossed with cultivars: Genetic model evaluation and seed trait analyses. Theoretical and Applied Genetics 120:1473-1483.
Wu, J., J. N. Jenkins, J. C. McCarty, K. Glover, and W. Berzonsky. 2010. Presentation titled by "Unbalanced Genetic Data Analysis: model evaluation and application" was offered at ASA, CSSA, & SSSA 2010 International Annual Meetings, Long Beach, CA.
Wu, J., J. N. Jenkins, and J.C., McCarty. 2011. A generalized approach and computer tool for quantitative genetics study. Proceedings Applied Statistics in Agriculture, April 25-27, 2010, Manhattan, KS. p.85-106.
Wu, J. 2012. GenMod: An R package for various agricultural data analyses. ASA, CSSA, and SSSA 2012 International Annual Meetings, Cincinnati, OH, p 127
Wu, J., Bondalapati K., Glover K., Berzonsky W., Jenkins J.N., McCarty J.C. 2013. Genetic analysis without replications: model evaluation and application in spring wheat. Euphytica. 190:447-458
Zhu, J. 1989. Estimation of Genetic Variance Components in the General Mixed Model. Ph.D. Dissertation, NC State University, Raleigh, U.S.A
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
library(qgtools)
data(adrcdat)
dat=adrcdat[which(adrcdat$Env==1&adrcdat$Row<=3),]
Ped=dat[,c(1,4,5,6)]
Y=as.matrix(dat[,8])
colnames(Y)=colnames(dat)[8]
Row=dat$Row
Col=dat$Column
##run AD model with field row and column effects
res=adrc.reml.jack(Y,Ped,Row=Row,JacNum=5)
res$Var
res$PVar
res$FixedEffect
res$RandomEffect
Example output
$YIELD
Estimate SE PValue 2.5%LL 97.5%UL
V(A) 5218.355 9646.840 0.6695348 -32795.181 43231.891
V(D) 69063.466 33149.080 0.1502018 -61561.040 199687.973
V(Row) 929.278 1596.716 0.6509346 -5362.609 7221.165
V(e) 9359.428 3839.227 0.1032862 -5769.109 24487.965
$YIELD
Estimate SE PValue 2.5%LL 97.5%UL
V(A)/VP 0.072124955 0.11219156 0.623088755 -0.36996777 0.51421768
V(D)/VP 0.780308538 0.13992566 0.007583356 0.22892912 1.33168796
V(Row)/VP 0.008160273 0.01294601 0.628843325 -0.04285369 0.05917424
V(e)/VP 0.139406234 0.10917256 0.353586942 -0.29079008 0.56960255
NULL
$YIELD
Pre SE PValue 2.5%LL 97.5%UL
A(3) -2.630909 7.916448 0.75954540 -33.82581 28.5639873
A(4) -41.939810 57.496910 0.58329922 -268.50735 184.6277310
A(19) -25.459748 35.124947 0.58540938 -163.87019 112.9506959
A(1) 5.771434 36.053130 0.82465465 -136.29653 147.8393997
A(5) -4.408206 7.960740 0.66375371 -35.77764 26.9612250
A(13) 8.151241 11.162535 0.58292955 -35.83492 52.1373977
A(14) -28.905778 56.742950 0.68367615 -252.50233 194.6907699
A(18) 9.685692 16.764211 0.65286055 -56.37397 75.7453485
A(20) -8.481537 27.461646 0.76900658 -116.69462 99.7315421
A(22) -16.749267 32.367122 0.68007309 -144.29246 110.7939231
A(23) 24.875303 36.679949 0.60686612 -119.66266 169.4132603
A(24) -48.845787 69.835111 0.59708164 -324.03222 226.3406431
A(26) -14.781646 20.242392 0.58292950 -94.54713 64.9838413
A(27) 36.708689 51.766983 0.59263496 -167.27998 240.6973560
A(28) 27.098966 43.452992 0.63191091 -144.12828 198.3262106
A(32) 5.546171 20.038323 0.78165009 -73.41518 84.5075202
A(6) 10.892684 19.121697 0.65654542 -64.45669 86.2420535
A(7) 8.330282 11.593196 0.58829738 -37.35290 54.0134675
A(8) 24.248689 37.686055 0.62282889 -124.25384 172.7512225
A(9) 29.801004 41.928340 0.59187793 -135.41832 195.0203317
A(15) -31.086105 44.613520 0.59830409 -206.88643 144.7142208
A(25) -1.084263 8.909560 0.83767903 -36.19253 34.0240085
A(17) 10.573585 21.430867 0.69081290 -73.87511 95.0222762
A(29) 34.661617 62.419615 0.66304946 -211.30393 280.6271618
A(12) -76.530362 179.049561 0.71967932 -782.07817 629.0174446
A(30) 45.482834 75.171168 0.64041447 -250.73042 341.6960864
A(21) -2.056214 21.076672 0.84556748 -85.10919 80.9967643
A(11) 13.726349 27.074768 0.68476333 -92.96223 120.4149268
A(10) 21.664211 31.821250 0.60565288 -103.72796 147.0563829
A(31) -6.359299 14.219826 0.71110924 -62.39276 49.6741624
A(34) -13.027476 21.374902 0.63839445 -97.25564 71.2006850
A(16) 5.127657 7.043904 0.58397473 -22.62897 32.8842801
D(1*1) -22.879363 80.244172 0.77839271 -339.08287 293.3241468
D(3*3) 174.394463 110.356458 0.25779221 -260.46702 609.2559433
D(4*4) -488.202430 123.648970 0.02505101 -975.44328 -0.9615827
D(5*5) 4.100805 91.799875 0.86201619 -357.63815 365.8397578
D(6*6) 36.992940 26.790256 0.31790578 -68.57451 142.5603933
D(7*7) 88.683124 55.246869 0.25103679 -129.01809 306.3843404
D(8*8) 120.782413 26.305494 0.01506646 17.12517 224.4396526
D(9*9) 190.779548 57.125521 0.04264651 -34.32453 415.8836243
D(10*10) 101.844244 67.882912 0.28059022 -165.64951 369.3379995
D(11*11) 26.795941 32.923173 0.54469361 -102.93838 156.5302578
D(12*12) -450.535310 275.642759 0.24331321 -1536.71024 635.6396157
D(13*13) 58.378209 61.225210 0.48253911 -182.88076 299.6371764
D(14*14) -328.330221 238.838711 0.31993140 -1269.47818 612.8177352
D(15*15) -208.023825 106.192170 0.17167088 -626.47586 210.4282071
D(16*16) 50.972415 49.770810 0.45231582 -145.15030 247.0951276
D(17*17) 45.202333 63.103724 0.58932295 -203.45895 293.8636207
D(18*18) 129.854141 80.489046 0.24887759 -187.31430 447.0225822
D(19*19) -341.399652 119.044195 0.06680610 -810.49530 127.6959990
D(20*20) 25.463462 63.441872 0.73083192 -224.53030 275.4572237
D(21*21) 97.237484 102.317975 0.48391033 -305.94822 500.4231838
D(22*22) -43.145821 59.575803 0.58569267 -277.90527 191.6136306
D(23*23) 110.609711 86.385328 0.35234083 -229.79313 451.0125469
D(24*24) -268.246160 190.804885 0.30975853 -1020.11602 483.6236992
D(25*25) -7.754166 26.806126 0.77676539 -113.38416 97.8758247
D(26*26) -102.593162 48.661946 0.14626018 -294.34638 89.1600527
D(27*27) 225.920833 143.369773 0.25902685 -339.03017 790.8718340
D(28*28) 129.118561 66.146288 0.17295393 -131.53200 389.7691197
D(29*29) 225.894912 110.970457 0.15809390 -211.38604 663.1758636
D(30*30) 207.148058 94.325328 0.13319054 -164.54248 578.8386009
D(31*31) -68.999766 52.790732 0.34293968 -277.02254 139.0230026
D(32*32) 50.643701 50.366413 0.46019337 -147.82600 249.1133982
D(34*34) -31.453284 33.837918 0.49300612 -164.79217 101.8856003
D(1*18) -45.591461 47.926616 0.48350559 -234.44710 143.2641771
D(3*5) -348.046030 206.698344 0.23079459 -1162.54433 466.4522690
D(3*6) 73.985881 53.580511 0.31790578 -137.14903 285.1207865
D(3*7) -166.394813 98.317750 0.22868017 -553.81756 221.0279341
D(3*8) 241.564825 52.610987 0.01506646 34.25035 448.8793051
D(3*9) 67.561130 83.165810 0.54538657 -260.15514 395.2774024
D(3*15) 89.145129 108.344030 0.54065583 -337.78634 516.0766009
D(3*20) -115.077513 101.982287 0.40966788 -516.94043 286.7854053
D(3*25) -110.170391 65.057463 0.22843180 -366.53042 146.1896351
D(5*17) -106.074283 84.954054 0.36383074 -440.83716 228.6885958
D(5*27) 272.315793 175.272280 0.26518476 -418.34757 962.9791589
D(13*29) 153.341984 127.493285 0.38087427 -349.04745 655.7314187
D(1*14) 314.579829 219.300335 0.30066183 -549.57683 1178.7364856
D(12*14) -1125.409465 675.545792 0.23526625 -3787.40902 1536.5900876
D(14*15) -70.112428 99.595789 0.59500046 -462.57131 322.3464544
D(14*29) 11.763392 106.293025 0.84131206 -407.08606 430.6128448
D(14*30) 362.769751 258.974225 0.31139515 -657.72254 1383.2620379
D(14*32) -150.251523 94.442780 0.25488828 -522.40489 221.9018417
D(18*21) 324.535388 196.113977 0.23807756 -448.25504 1097.3258142
D(18*25) -19.235644 35.061804 0.66606878 -157.39727 118.9259834
D(12*20) 224.338844 181.425528 0.36826299 -490.57150 939.2491889
D(20*27) -356.990821 212.575770 0.23190497 -1194.64922 480.6675770
D(20*29) 298.656414 172.400456 0.21908640 -380.69048 978.0033091
D(1*22) -191.409890 130.835752 0.29182175 -706.97037 324.1505897
D(11*22) 53.591882 65.846346 0.54469361 -205.87675 313.0605155
D(22*30) 51.526366 87.580869 0.64804895 -293.58752 396.6402522
D(7*23) 90.315224 59.791728 0.27758536 -145.29509 325.9255340
D(10*23) 203.688487 135.765824 0.28059022 -331.29902 738.6759990
D(13*23) -16.014082 63.152984 0.79058653 -264.86948 232.8413124
D(15*23) 144.135892 89.873935 0.25142760 -210.01386 498.2856430
D(23*31) -137.999533 105.581465 0.34293968 -554.04507 278.0460052
D(23*34) -62.906567 67.675836 0.49300612 -329.58434 203.7712007
D(13*24) -20.571484 88.956047 0.79900925 -371.10429 329.9613165
D(15*24) -622.957177 392.186321 0.25556905 -2168.37397 922.4596178
D(17*24) 107.036341 146.228058 0.58212575 -469.17778 683.2504612
D(15*26) -96.337520 93.027064 0.44751526 -462.91223 270.2371904
D(17*26) 21.211617 49.014313 0.71737568 -171.93011 214.3533400
D(21*26) -130.060421 85.840345 0.27622658 -468.31574 208.1949035
D(1*27) -123.337204 71.730584 0.22214112 -405.99277 159.3183669
D(7*27) 253.445837 153.742655 0.23969383 -352.37968 859.2713527
D(9*27) 190.565528 149.647553 0.35484285 -399.12317 780.2542260
D(16*27) 101.944831 99.541619 0.45231582 -290.30059 494.1902551
D(25*27) 113.897703 82.425244 0.31757868 -210.90036 438.6957631
D(5*28) 190.006130 116.776936 0.24524548 -270.15535 650.1676110
D(17*28) 68.230992 77.697368 0.51574513 -237.93679 374.3987765
D(9*32) 123.432438 87.950463 0.31054342 -223.13784 470.0027170
D(15*32) 140.078453 105.091431 0.33398885 -274.03610 554.1930046
D(29*32) -11.971967 36.738202 0.76216535 -156.73947 132.7955379
Row(1) -18.893618 29.619138 0.62537806 -135.60833 97.8210917
Row(2) 16.657253 16.032480 0.44610132 -46.51900 79.8335085
Row(3) 2.236365 19.737491 0.84044807 -75.53955 80.0122785
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Description Usage Arguments Details Value Author(s) References Examples
Description
An AD model with row and column effects included is used for controlling field variation. This model will be analyzed by MINQUE approach and tested by jackknife technique. The data set can be irregular or missing but the field layout should be rectangular. It can analyze any genetic mating designs and data including F1, F2, or F3 with parents..
Usage
1 | adrc.reml.jack(Y, Ped, Row = NULL, Col = NULL, JacNum = NULL, JacRep = NULL)
|
Arguments
Y |
A data matrix for one or more traits |
Ped |
A pedigree matrix including Environment, Female, Male,Generation is required. |
Row |
A vector for field rows. It can be default. |
Col |
A vector for field colums.It can be default. |
JacNum |
Number of jackknife groups to be used. The default is 10. |
JacRep |
Repeating times for jackknife process. The default is 1. |
Details
A pedigree matrix used for analysis is required in the order of Environment (column 1), Female(column 2), Male(column 3), Generation (column 4). Even though there is only one environment, this first column is needed.If only row or column vector is included, this is equivallent to an AD model with block effects.
Value
Return a list of results: estimated Variance components, estimated proportional variance components, estimated fixed effects, and predicted random effects, and their statistical tests
Author(s)
Jixiang Wu <qgtools@gmail.com>
References
Rao, C.R. 1971. Estimation of variance and covariance components-MINQUE theory. J Multiva Ana 1:19
Wu, J., McCarty Jr., J.C., Jenkins, J.N. 2010. Cotton chromosome substitution lines crossed with cultivars: Genetic model evaluation and seed trait analyses. Theoretical and Applied Genetics 120:1473-1483.
Wu, J., J. N. Jenkins, J. C. McCarty, K. Glover, and W. Berzonsky. 2010. Presentation titled by "Unbalanced Genetic Data Analysis: model evaluation and application" was offered at ASA, CSSA, & SSSA 2010 International Annual Meetings, Long Beach, CA.
Wu, J., J. N. Jenkins, and J.C., McCarty. 2011. A generalized approach and computer tool for quantitative genetics study. Proceedings Applied Statistics in Agriculture, April 25-27, 2010, Manhattan, KS. p.85-106.
Wu, J. 2012. GenMod: An R package for various agricultural data analyses. ASA, CSSA, and SSSA 2012 International Annual Meetings, Cincinnati, OH, p 127
Wu, J., Bondalapati K., Glover K., Berzonsky W., Jenkins J.N., McCarty J.C. 2013. Genetic analysis without replications: model evaluation and application in spring wheat. Euphytica. 190:447-458
Zhu, J. 1989. Estimation of Genetic Variance Components in the General Mixed Model. Ph.D. Dissertation, NC State University, Raleigh, U.S.A
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | library(qgtools)
data(adrcdat)
dat=adrcdat[which(adrcdat$Env==1&adrcdat$Row<=3),]
Ped=dat[,c(1,4,5,6)]
Y=as.matrix(dat[,8])
colnames(Y)=colnames(dat)[8]
Row=dat$Row
Col=dat$Column
##run AD model with field row and column effects
res=adrc.reml.jack(Y,Ped,Row=Row,JacNum=5)
res$Var
res$PVar
res$FixedEffect
res$RandomEffect
|
Example output
$YIELD
Estimate SE PValue 2.5%LL 97.5%UL
V(A) 5218.355 9646.840 0.6695348 -32795.181 43231.891
V(D) 69063.466 33149.080 0.1502018 -61561.040 199687.973
V(Row) 929.278 1596.716 0.6509346 -5362.609 7221.165
V(e) 9359.428 3839.227 0.1032862 -5769.109 24487.965
$YIELD
Estimate SE PValue 2.5%LL 97.5%UL
V(A)/VP 0.072124955 0.11219156 0.623088755 -0.36996777 0.51421768
V(D)/VP 0.780308538 0.13992566 0.007583356 0.22892912 1.33168796
V(Row)/VP 0.008160273 0.01294601 0.628843325 -0.04285369 0.05917424
V(e)/VP 0.139406234 0.10917256 0.353586942 -0.29079008 0.56960255
NULL
$YIELD
Pre SE PValue 2.5%LL 97.5%UL
A(3) -2.630909 7.916448 0.75954540 -33.82581 28.5639873
A(4) -41.939810 57.496910 0.58329922 -268.50735 184.6277310
A(19) -25.459748 35.124947 0.58540938 -163.87019 112.9506959
A(1) 5.771434 36.053130 0.82465465 -136.29653 147.8393997
A(5) -4.408206 7.960740 0.66375371 -35.77764 26.9612250
A(13) 8.151241 11.162535 0.58292955 -35.83492 52.1373977
A(14) -28.905778 56.742950 0.68367615 -252.50233 194.6907699
A(18) 9.685692 16.764211 0.65286055 -56.37397 75.7453485
A(20) -8.481537 27.461646 0.76900658 -116.69462 99.7315421
A(22) -16.749267 32.367122 0.68007309 -144.29246 110.7939231
A(23) 24.875303 36.679949 0.60686612 -119.66266 169.4132603
A(24) -48.845787 69.835111 0.59708164 -324.03222 226.3406431
A(26) -14.781646 20.242392 0.58292950 -94.54713 64.9838413
A(27) 36.708689 51.766983 0.59263496 -167.27998 240.6973560
A(28) 27.098966 43.452992 0.63191091 -144.12828 198.3262106
A(32) 5.546171 20.038323 0.78165009 -73.41518 84.5075202
A(6) 10.892684 19.121697 0.65654542 -64.45669 86.2420535
A(7) 8.330282 11.593196 0.58829738 -37.35290 54.0134675
A(8) 24.248689 37.686055 0.62282889 -124.25384 172.7512225
A(9) 29.801004 41.928340 0.59187793 -135.41832 195.0203317
A(15) -31.086105 44.613520 0.59830409 -206.88643 144.7142208
A(25) -1.084263 8.909560 0.83767903 -36.19253 34.0240085
A(17) 10.573585 21.430867 0.69081290 -73.87511 95.0222762
A(29) 34.661617 62.419615 0.66304946 -211.30393 280.6271618
A(12) -76.530362 179.049561 0.71967932 -782.07817 629.0174446
A(30) 45.482834 75.171168 0.64041447 -250.73042 341.6960864
A(21) -2.056214 21.076672 0.84556748 -85.10919 80.9967643
A(11) 13.726349 27.074768 0.68476333 -92.96223 120.4149268
A(10) 21.664211 31.821250 0.60565288 -103.72796 147.0563829
A(31) -6.359299 14.219826 0.71110924 -62.39276 49.6741624
A(34) -13.027476 21.374902 0.63839445 -97.25564 71.2006850
A(16) 5.127657 7.043904 0.58397473 -22.62897 32.8842801
D(1*1) -22.879363 80.244172 0.77839271 -339.08287 293.3241468
D(3*3) 174.394463 110.356458 0.25779221 -260.46702 609.2559433
D(4*4) -488.202430 123.648970 0.02505101 -975.44328 -0.9615827
D(5*5) 4.100805 91.799875 0.86201619 -357.63815 365.8397578
D(6*6) 36.992940 26.790256 0.31790578 -68.57451 142.5603933
D(7*7) 88.683124 55.246869 0.25103679 -129.01809 306.3843404
D(8*8) 120.782413 26.305494 0.01506646 17.12517 224.4396526
D(9*9) 190.779548 57.125521 0.04264651 -34.32453 415.8836243
D(10*10) 101.844244 67.882912 0.28059022 -165.64951 369.3379995
D(11*11) 26.795941 32.923173 0.54469361 -102.93838 156.5302578
D(12*12) -450.535310 275.642759 0.24331321 -1536.71024 635.6396157
D(13*13) 58.378209 61.225210 0.48253911 -182.88076 299.6371764
D(14*14) -328.330221 238.838711 0.31993140 -1269.47818 612.8177352
D(15*15) -208.023825 106.192170 0.17167088 -626.47586 210.4282071
D(16*16) 50.972415 49.770810 0.45231582 -145.15030 247.0951276
D(17*17) 45.202333 63.103724 0.58932295 -203.45895 293.8636207
D(18*18) 129.854141 80.489046 0.24887759 -187.31430 447.0225822
D(19*19) -341.399652 119.044195 0.06680610 -810.49530 127.6959990
D(20*20) 25.463462 63.441872 0.73083192 -224.53030 275.4572237
D(21*21) 97.237484 102.317975 0.48391033 -305.94822 500.4231838
D(22*22) -43.145821 59.575803 0.58569267 -277.90527 191.6136306
D(23*23) 110.609711 86.385328 0.35234083 -229.79313 451.0125469
D(24*24) -268.246160 190.804885 0.30975853 -1020.11602 483.6236992
D(25*25) -7.754166 26.806126 0.77676539 -113.38416 97.8758247
D(26*26) -102.593162 48.661946 0.14626018 -294.34638 89.1600527
D(27*27) 225.920833 143.369773 0.25902685 -339.03017 790.8718340
D(28*28) 129.118561 66.146288 0.17295393 -131.53200 389.7691197
D(29*29) 225.894912 110.970457 0.15809390 -211.38604 663.1758636
D(30*30) 207.148058 94.325328 0.13319054 -164.54248 578.8386009
D(31*31) -68.999766 52.790732 0.34293968 -277.02254 139.0230026
D(32*32) 50.643701 50.366413 0.46019337 -147.82600 249.1133982
D(34*34) -31.453284 33.837918 0.49300612 -164.79217 101.8856003
D(1*18) -45.591461 47.926616 0.48350559 -234.44710 143.2641771
D(3*5) -348.046030 206.698344 0.23079459 -1162.54433 466.4522690
D(3*6) 73.985881 53.580511 0.31790578 -137.14903 285.1207865
D(3*7) -166.394813 98.317750 0.22868017 -553.81756 221.0279341
D(3*8) 241.564825 52.610987 0.01506646 34.25035 448.8793051
D(3*9) 67.561130 83.165810 0.54538657 -260.15514 395.2774024
D(3*15) 89.145129 108.344030 0.54065583 -337.78634 516.0766009
D(3*20) -115.077513 101.982287 0.40966788 -516.94043 286.7854053
D(3*25) -110.170391 65.057463 0.22843180 -366.53042 146.1896351
D(5*17) -106.074283 84.954054 0.36383074 -440.83716 228.6885958
D(5*27) 272.315793 175.272280 0.26518476 -418.34757 962.9791589
D(13*29) 153.341984 127.493285 0.38087427 -349.04745 655.7314187
D(1*14) 314.579829 219.300335 0.30066183 -549.57683 1178.7364856
D(12*14) -1125.409465 675.545792 0.23526625 -3787.40902 1536.5900876
D(14*15) -70.112428 99.595789 0.59500046 -462.57131 322.3464544
D(14*29) 11.763392 106.293025 0.84131206 -407.08606 430.6128448
D(14*30) 362.769751 258.974225 0.31139515 -657.72254 1383.2620379
D(14*32) -150.251523 94.442780 0.25488828 -522.40489 221.9018417
D(18*21) 324.535388 196.113977 0.23807756 -448.25504 1097.3258142
D(18*25) -19.235644 35.061804 0.66606878 -157.39727 118.9259834
D(12*20) 224.338844 181.425528 0.36826299 -490.57150 939.2491889
D(20*27) -356.990821 212.575770 0.23190497 -1194.64922 480.6675770
D(20*29) 298.656414 172.400456 0.21908640 -380.69048 978.0033091
D(1*22) -191.409890 130.835752 0.29182175 -706.97037 324.1505897
D(11*22) 53.591882 65.846346 0.54469361 -205.87675 313.0605155
D(22*30) 51.526366 87.580869 0.64804895 -293.58752 396.6402522
D(7*23) 90.315224 59.791728 0.27758536 -145.29509 325.9255340
D(10*23) 203.688487 135.765824 0.28059022 -331.29902 738.6759990
D(13*23) -16.014082 63.152984 0.79058653 -264.86948 232.8413124
D(15*23) 144.135892 89.873935 0.25142760 -210.01386 498.2856430
D(23*31) -137.999533 105.581465 0.34293968 -554.04507 278.0460052
D(23*34) -62.906567 67.675836 0.49300612 -329.58434 203.7712007
D(13*24) -20.571484 88.956047 0.79900925 -371.10429 329.9613165
D(15*24) -622.957177 392.186321 0.25556905 -2168.37397 922.4596178
D(17*24) 107.036341 146.228058 0.58212575 -469.17778 683.2504612
D(15*26) -96.337520 93.027064 0.44751526 -462.91223 270.2371904
D(17*26) 21.211617 49.014313 0.71737568 -171.93011 214.3533400
D(21*26) -130.060421 85.840345 0.27622658 -468.31574 208.1949035
D(1*27) -123.337204 71.730584 0.22214112 -405.99277 159.3183669
D(7*27) 253.445837 153.742655 0.23969383 -352.37968 859.2713527
D(9*27) 190.565528 149.647553 0.35484285 -399.12317 780.2542260
D(16*27) 101.944831 99.541619 0.45231582 -290.30059 494.1902551
D(25*27) 113.897703 82.425244 0.31757868 -210.90036 438.6957631
D(5*28) 190.006130 116.776936 0.24524548 -270.15535 650.1676110
D(17*28) 68.230992 77.697368 0.51574513 -237.93679 374.3987765
D(9*32) 123.432438 87.950463 0.31054342 -223.13784 470.0027170
D(15*32) 140.078453 105.091431 0.33398885 -274.03610 554.1930046
D(29*32) -11.971967 36.738202 0.76216535 -156.73947 132.7955379
Row(1) -18.893618 29.619138 0.62537806 -135.60833 97.8210917
Row(2) 16.657253 16.032480 0.44610132 -46.51900 79.8335085
Row(3) 2.236365 19.737491 0.84044807 -75.53955 80.0122785
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