Sim CCS City
I extended the work of (Wu and Plantinga 2003) using R and certain equation modififications to investigate how the addition of a light rail line would influence a city.
Cities have housed most of the human race since 2004 and as a result influence most of the individual, commercial, and industrial energy and GHG patterns. However, city designs, have placed amenities in isolated suburban pockets, the abundance of roads have encouraged sprawl, and zoning laws have discouraged density. Therefore, for this study I will investigate how these choices can positively or negatively influence a city’s environmental footprint.
I extended the work of (Wu and Plantinga 2003) using R and certain equation modififications to investigate how the addition of a light rail line would influence a city. First, I tried to replicate their city without any parks using their parameters. Second, I made some modifications to get the city to a scale that I could represent graphically. Third, I modeled the light rail as an amenity to see the influence it has on the city. Finally, I modeled the light rail so that it reduced travel costs for the citizens close to it instead of providing an amenity value. The parameters I used where nearly identical to the (Wu and Plantinga 2003) parameters; however I did have to make some minor modifications. The given utility produced a much larger area then was graphically tractable, so I increased it to 6,000 for all the models excluding the original monocentric model which uses the original utility value. The transport cost for the rail is set to half of the normal transport costs (t¬¬rail=$500). The original parameters are shown in Table 1.
Wu, Jun Jie, and Andrew J. Plantinga. 2003. “The Influence of Public Open Space on Urban Spatial Structure.” Journal of Environmental Economics and Management 46 (2): 288–309. https://doi.org/10.1016/S0095-0696(03)00023-8.
require(ggplot2)## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 4.0.2require(grid)## Loading required package: gridrequire(gridExtra)## Loading required package: gridExtrarequire(RColorBrewer)## Loading required package: RColorBrewerrequire(viridis)## Loading required package: viridis## Warning: package 'viridis' was built under R version 4.0.2## Loading required package: viridisLite#budget
#median income per capita Austin https://www.deptofnumbers.com/income/texas/austin/
y <- 40000
u <- c(0:150)
v <- c(0:150)
#Loop to give 15 miles worth of u and v
i <- 0
j <- 0
ii <- 1
while(i < 151){
j <- 0
while(j < 151){
u[ii] <- i/5 - 15
v[ii] <- j/5 - 15
j <- j+1
ii <- ii+1
}
i <- i +1
}
#distance from center
x <- sqrt(u^2+v^2)
#transportation cost 50 cents a mile by 320 days
t <- 1000
#housing price per sqft vector
p <- c(0:150)
#housing consumption (sqft) by mile vector
q <- c(0:150)
#general good
g <- c(0:150)
#utility level
V <- 4200
#alpha for Cobb Douglas
al <- .5
#beta for development cobb-douglas
bt <- 4/3
#capital
c0 <- 0
#amentiy
ad <- 0.16
ng <- 1
d <- 0
#gamma for amenity
gm <- 0.5
#z distance to amentiy
z <- sqrt((x-d)^2)
#land rent/acre
r <- c(0:150)
#Housing floor space / acre
s <- c(0:150)
#ag rent
#Ausitn is about 8000 https://heritagelandbank.com/announcements/news-events/how-much-average-price-land-texas
ag <- 8000
#Multiplier values
tm1 <- 1 - 0
tm2 <- 1 - 0
tm3 <- 1 - 0
tm4 <- 1 - 0
im1 <- 1 + 0
im2 <- 1 + 0
im3 <- 1 + 0
im4 <- 1 + 0
am1 <- 1 + 0
am2 <- 1 + 0
am3 <- 1 + 0
am4 <- 1 + 0#monocentric original model parameters, Iterations to determine Utility Value (V) that gives start of about 100k
V <- 4000
i <- 1
NN <- c(1:10)
while(i <= 10){
#finding x for various u,v
x <- sqrt(u^2+v^2)
#z distance to amentiy
z <- sqrt((x-d)^2)
#amentiy distribution
am <- 1 + ad*(exp(-ng*z))
#finding the price for various u,v
p <- (al^al*(1-al)^(1-al)*am^gm*(y-t*x)/V)^(1/al)
#optimal q
q <- al*(y-t*x)/p
#optimal g
g <- (1-al)*(y-t*x)
#theta some funciton of beta
ph <- ((bt-1)^((bt-1)/bt))/bt
#optimal r
r <- (ph*p)^(bt/(bt-1))
r1 <- ((ph*al)^al * (1-al)^(1-al) * (y-t*x)/V)^(bt/(al*(bt-1)))
#optimal s
s <- (p/bt)^(1/(bt-1))
s1 <- (bt-1)^(-1/bt) * (r)^(1/bt)
#population n s(floorspaceperacre/ floorspace per household * (size of square (sqmi)) * acres/sqmi * fraction of housing in area)
n <- s/q * (.2*.2) * 640 * .25
#s <- n*q /(1 * 640 * .25 )
#q <- s/(n*(1 * 640 * .25 ))
#Utility Value
U <- q^al*g^(1-al)
dfsc <- data.frame(u,v,x,p,g,q,s,r,U,n)
#delete values where ag rent exceeds land rent
dfsc1 <- dfsc[(dfsc$r > ag),]
#total population
NN[i] <- sum(dfsc1$n)
print(V)
V <- V + 50
i <- i + 1
}## [1] 4000
## [1] 4050
## [1] 4100
## [1] 4150
## [1] 4200
## [1] 4250
## [1] 4300
## [1] 4350
## [1] 4400
## [1] 4450dfsc1## u v x p g q s r
## 8531 -3.8 -0.2 3.8052595 16.59795 18097.37 1090.3376 1929.067 8004.640
## 8532 -3.8 0.0 3.8000000 16.60309 18100.00 1090.1587 1930.858 8014.550
## 8533 -3.8 0.2 3.8052595 16.59795 18097.37 1090.3376 1929.067 8004.640
## 8677 -3.6 -1.2 3.7947332 16.60823 18102.63 1089.9796 1932.653 8024.487
## 8678 -3.6 -1.0 3.7363083 16.66547 18131.85 1087.9889 1952.704 8135.684
## 8679 -3.6 -0.8 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 8680 -3.6 -0.6 3.6496575 16.75097 18175.17 1085.0221 1982.913 8303.926
## 8681 -3.6 -0.4 3.6221541 16.77826 18188.92 1084.0766 1992.622 8358.184
## 8682 -3.6 -0.2 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 8683 -3.6 0.0 3.6000000 16.80031 18200.00 1083.3134 2000.486 8402.197
## 8684 -3.6 0.2 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 8685 -3.6 0.4 3.6221541 16.77826 18188.92 1084.0766 1992.622 8358.184
## 8686 -3.6 0.6 3.6496575 16.75097 18175.17 1085.0221 1982.913 8303.926
## 8687 -3.6 0.8 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 8688 -3.6 1.0 3.7363083 16.66547 18131.85 1087.9889 1952.704 8135.684
## 8689 -3.6 1.2 3.7947332 16.60823 18102.63 1089.9796 1932.653 8024.487
## 8826 -3.4 -1.6 3.7576588 16.64452 18121.17 1088.7172 1945.348 8094.844
## 8827 -3.4 -1.4 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 8828 -3.4 -1.2 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 8829 -3.4 -1.0 3.5440090 16.85626 18228.00 1081.3786 2020.539 8514.682
## 8830 -3.4 -0.8 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 8831 -3.4 -0.6 3.4525353 16.94842 18273.73 1078.1967 2053.864 8702.437
## 8832 -3.4 -0.4 3.4234486 16.97794 18288.28 1077.1790 2064.612 8763.212
## 8833 -3.4 -0.2 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 8834 -3.4 0.0 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 8835 -3.4 0.2 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 8836 -3.4 0.4 3.4234486 16.97794 18288.28 1077.1790 2064.612 8763.212
## 8837 -3.4 0.6 3.4525353 16.94842 18273.73 1078.1967 2053.864 8702.437
## 8838 -3.4 0.8 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 8839 -3.4 1.0 3.5440090 16.85626 18228.00 1081.3786 2020.539 8514.682
## 8840 -3.4 1.2 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 8841 -3.4 1.4 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 8842 -3.4 1.6 3.7576588 16.64452 18121.17 1088.7172 1945.348 8094.844
## 8975 -3.2 -2.0 3.7735925 16.62891 18113.20 1089.2601 1939.880 8064.520
## 8976 -3.2 -1.8 3.6715120 16.72933 18164.24 1085.7721 1975.240 8261.110
## 8977 -3.2 -1.6 3.5777088 16.82254 18211.15 1082.5442 2008.439 8446.763
## 8978 -3.2 -1.4 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 8979 -3.2 -1.2 3.4176015 16.98388 18291.20 1076.9741 2066.782 8775.493
## 8980 -3.2 -1.0 3.3526109 17.05025 18323.69 1074.6875 2091.107 8913.477
## 8981 -3.2 -0.8 3.2984845 17.10595 18350.76 1072.7704 2111.667 9030.518
## 8982 -3.2 -0.6 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 8983 -3.2 -0.4 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 8984 -3.2 -0.2 3.2062439 17.20180 18396.88 1069.4738 2147.364 9234.634
## 8985 -3.2 0.0 3.2000000 17.20834 18400.00 1069.2492 2149.812 9248.670
## 8986 -3.2 0.2 3.2062439 17.20180 18396.88 1069.4738 2147.364 9234.634
## 8987 -3.2 0.4 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 8988 -3.2 0.6 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 8989 -3.2 0.8 3.2984845 17.10595 18350.76 1072.7704 2111.667 9030.518
## 8990 -3.2 1.0 3.3526109 17.05025 18323.69 1074.6875 2091.107 8913.477
## 8991 -3.2 1.2 3.4176015 16.98388 18291.20 1076.9741 2066.782 8775.493
## 8992 -3.2 1.4 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 8993 -3.2 1.6 3.5777088 16.82254 18211.15 1082.5442 2008.439 8446.763
## 8994 -3.2 1.8 3.6715120 16.72933 18164.24 1085.7721 1975.240 8261.110
## 8995 -3.2 2.0 3.7735925 16.62891 18113.20 1089.2601 1939.880 8064.520
## 9125 -3.0 -2.2 3.7202150 16.68129 18139.89 1087.4392 1958.272 8166.627
## 9126 -3.0 -2.0 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 9127 -3.0 -1.8 3.4985711 16.90192 18250.71 1079.8014 2037.003 8607.315
## 9128 -3.0 -1.6 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 9129 -3.0 -1.4 3.3105891 17.09346 18344.71 1073.2002 2107.045 9004.172
## 9130 -3.0 -1.2 3.2310989 17.17585 18384.45 1070.3660 2137.661 9179.040
## 9131 -3.0 -1.0 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 9132 -3.0 -0.8 3.1048349 17.30864 18447.58 1065.8018 2187.625 9466.205
## 9133 -3.0 -0.6 3.0594117 17.35703 18470.29 1064.1390 2206.023 9572.504
## 9134 -3.0 -0.4 3.0265492 17.39225 18486.73 1062.9286 2219.481 9650.444
## 9135 -3.0 -0.2 3.0066593 17.41366 18496.67 1062.1929 2227.688 9698.051
## 9136 -3.0 0.0 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 9137 -3.0 0.2 3.0066593 17.41366 18496.67 1062.1929 2227.688 9698.051
## 9138 -3.0 0.4 3.0265492 17.39225 18486.73 1062.9286 2219.481 9650.444
## 9139 -3.0 0.6 3.0594117 17.35703 18470.29 1064.1390 2206.023 9572.504
## 9140 -3.0 0.8 3.1048349 17.30864 18447.58 1065.8018 2187.625 9466.205
## 9141 -3.0 1.0 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 9142 -3.0 1.2 3.2310989 17.17585 18384.45 1070.3660 2137.661 9179.040
## 9143 -3.0 1.4 3.3105891 17.09346 18344.71 1073.2002 2107.045 9004.172
## 9144 -3.0 1.6 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 9145 -3.0 1.8 3.4985711 16.90192 18250.71 1079.8014 2037.003 8607.315
## 9146 -3.0 2.0 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 9147 -3.0 2.2 3.7202150 16.68129 18139.89 1087.4392 1958.272 8166.627
## 9275 -2.8 -2.4 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 9276 -2.8 -2.2 3.5608988 16.83934 18219.55 1081.9632 2014.463 8480.560
## 9277 -2.8 -2.0 3.4409301 16.96019 18279.53 1077.7910 2058.143 8726.622
## 9278 -2.8 -1.8 3.3286634 17.07485 18335.67 1073.8408 2100.169 8965.018
## 9279 -2.8 -1.6 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 9280 -2.8 -1.4 3.1304952 17.28146 18434.75 1066.7360 2177.333 9406.871
## 9281 -2.8 -1.2 3.0463092 17.37105 18476.85 1063.6572 2211.374 9603.473
## 9282 -2.8 -1.0 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 9283 -2.8 -0.8 2.9120440 17.51649 18543.98 1058.6583 2267.384 9929.151
## 9284 -2.8 -0.6 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 9285 -2.8 -0.4 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 9286 -2.8 -0.2 2.8071338 17.63253 18596.43 1054.6662 2312.745 10194.884
## 9287 -2.8 0.0 2.8000000 17.64050 18600.00 1054.3917 2315.883 10213.336
## 9288 -2.8 0.2 2.8071338 17.63253 18596.43 1054.6662 2312.745 10194.884
## 9289 -2.8 0.4 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 9290 -2.8 0.6 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 9291 -2.8 0.8 2.9120440 17.51649 18543.98 1058.6583 2267.384 9929.151
## 9292 -2.8 1.0 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 9293 -2.8 1.2 3.0463092 17.37105 18476.85 1063.6572 2211.374 9603.473
## 9294 -2.8 1.4 3.1304952 17.28146 18434.75 1066.7360 2177.333 9406.871
## 9295 -2.8 1.6 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 9296 -2.8 1.8 3.3286634 17.07485 18335.67 1073.8408 2100.169 8965.018
## 9297 -2.8 2.0 3.4409301 16.96019 18279.53 1077.7910 2058.143 8726.622
## 9298 -2.8 2.2 3.5608988 16.83934 18219.55 1081.9632 2014.463 8480.560
## 9299 -2.8 2.4 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 9425 -2.6 -2.6 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 9426 -2.6 -2.4 3.5383612 16.86192 18230.82 1081.1829 2022.576 8526.130
## 9427 -2.6 -2.2 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 9428 -2.6 -2.0 3.2802439 17.12481 18359.88 1072.1215 2118.659 9070.409
## 9429 -2.6 -1.8 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 9430 -2.6 -1.6 3.0528675 17.36403 18473.57 1063.8985 2208.693 9587.954
## 9431 -2.6 -1.4 2.9529646 17.47181 18523.52 1060.1942 2250.079 9828.243
## 9432 -2.6 -1.2 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 9433 -2.6 -1.0 2.7856777 17.65654 18607.16 1053.8394 2322.206 10250.534
## 9434 -2.6 -0.8 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 9435 -2.6 -0.6 2.6683328 17.78969 18665.83 1049.2501 2375.138 10563.243
## 9436 -2.6 -0.4 2.6305893 17.83321 18684.71 1047.7480 2392.611 10666.981
## 9437 -2.6 -0.2 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 9438 -2.6 0.0 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 9439 -2.6 0.2 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 9440 -2.6 0.4 2.6305893 17.83321 18684.71 1047.7480 2392.611 10666.981
## 9441 -2.6 0.6 2.6683328 17.78969 18665.83 1049.2501 2375.138 10563.243
## 9442 -2.6 0.8 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 9443 -2.6 1.0 2.7856777 17.65654 18607.16 1053.8394 2322.206 10250.534
## 9444 -2.6 1.2 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 9445 -2.6 1.4 2.9529646 17.47181 18523.52 1060.1942 2250.079 9828.243
## 9446 -2.6 1.6 3.0528675 17.36403 18473.57 1063.8985 2208.693 9587.954
## 9447 -2.6 1.8 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 9448 -2.6 2.0 3.2802439 17.12481 18359.88 1072.1215 2118.659 9070.409
## 9449 -2.6 2.2 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 9450 -2.6 2.4 3.5383612 16.86192 18230.82 1081.1829 2022.576 8526.130
## 9451 -2.6 2.6 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 9575 -2.4 -2.8 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 9576 -2.4 -2.6 3.5383612 16.86192 18230.82 1081.1829 2022.576 8526.130
## 9577 -2.4 -2.4 3.3941125 17.00781 18302.94 1076.1495 2075.529 8825.049
## 9578 -2.4 -2.2 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 9579 -2.4 -2.0 3.1240999 17.28822 18437.95 1066.5035 2179.891 9421.611
## 9580 -2.4 -1.8 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 9581 -2.4 -1.6 2.8844410 17.54681 18557.78 1057.6158 2279.177 9998.070
## 9582 -2.4 -1.4 2.7784888 17.66461 18610.76 1053.5616 2325.391 10269.282
## 9583 -2.4 -1.2 2.6832816 17.77255 18658.36 1049.8414 2368.280 10522.594
## 9584 -2.4 -1.0 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 9585 -2.4 -0.8 2.5298221 17.95117 18735.09 1043.6695 2440.406 10952.036
## 9586 -2.4 -0.6 2.4738634 18.01787 18763.07 1041.3588 2467.711 11115.723
## 9587 -2.4 -0.4 2.4331050 18.06702 18783.45 1039.6536 2487.962 11237.516
## 9588 -2.4 -0.2 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 9589 -2.4 0.0 2.4000000 18.10732 18800.00 1038.2543 2504.644 11338.097
## 9590 -2.4 0.2 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 9591 -2.4 0.4 2.4331050 18.06702 18783.45 1039.6536 2487.962 11237.516
## 9592 -2.4 0.6 2.4738634 18.01787 18763.07 1041.3588 2467.711 11115.723
## 9593 -2.4 0.8 2.5298221 17.95117 18735.09 1043.6695 2440.406 10952.036
## 9594 -2.4 1.0 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 9595 -2.4 1.2 2.6832816 17.77255 18658.36 1049.8414 2368.280 10522.594
## 9596 -2.4 1.4 2.7784888 17.66461 18610.76 1053.5616 2325.391 10269.282
## 9597 -2.4 1.6 2.8844410 17.54681 18557.78 1057.6158 2279.177 9998.070
## 9598 -2.4 1.8 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 9599 -2.4 2.0 3.1240999 17.28822 18437.95 1066.5035 2179.891 9421.611
## 9600 -2.4 2.2 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 9601 -2.4 2.4 3.3941125 17.00781 18302.94 1076.1495 2075.529 8825.049
## 9602 -2.4 2.6 3.5383612 16.86192 18230.82 1081.1829 2022.576 8526.130
## 9603 -2.4 2.8 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 9725 -2.2 -3.0 3.7202150 16.68129 18139.89 1087.4392 1958.272 8166.627
## 9726 -2.2 -2.8 3.5608988 16.83934 18219.55 1081.9632 2014.463 8480.560
## 9727 -2.2 -2.6 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 9728 -2.2 -2.4 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 9729 -2.2 -2.2 3.1112698 17.30182 18444.37 1066.0364 2185.037 9451.277
## 9730 -2.2 -2.0 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 9731 -2.2 -1.8 2.8425341 17.59312 18578.73 1056.0224 2297.273 10104.053
## 9732 -2.2 -1.6 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 9733 -2.2 -1.4 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 9734 -2.2 -1.2 2.5059928 17.97947 18747.00 1042.6897 2451.964 11021.252
## 9735 -2.2 -1.0 2.4166092 18.08706 18791.70 1038.9580 2496.248 11287.445
## 9736 -2.2 -0.8 2.3409400 18.18006 18829.53 1035.7245 2534.950 11521.384
## 9737 -2.2 -0.6 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 9738 -2.2 -0.4 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 9739 -2.2 -0.2 2.2090722 18.34673 18895.46 1029.9090 2605.313 11949.745
## 9740 -2.2 0.0 2.2000000 18.35843 18900.00 1029.4998 2610.300 11980.251
## 9741 -2.2 0.2 2.2090722 18.34673 18895.46 1029.9090 2605.313 11949.745
## 9742 -2.2 0.4 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 9743 -2.2 0.6 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 9744 -2.2 0.8 2.3409400 18.18006 18829.53 1035.7245 2534.950 11521.384
## 9745 -2.2 1.0 2.4166092 18.08706 18791.70 1038.9580 2496.248 11287.445
## 9746 -2.2 1.2 2.5059928 17.97947 18747.00 1042.6897 2451.964 11021.252
## 9747 -2.2 1.4 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 9748 -2.2 1.6 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 9749 -2.2 1.8 2.8425341 17.59312 18578.73 1056.0224 2297.273 10104.053
## 9750 -2.2 2.0 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 9751 -2.2 2.2 3.1112698 17.30182 18444.37 1066.0364 2185.037 9451.277
## 9752 -2.2 2.4 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 9753 -2.2 2.6 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 9754 -2.2 2.8 3.5608988 16.83934 18219.55 1081.9632 2014.463 8480.560
## 9755 -2.2 3.0 3.7202150 16.68129 18139.89 1087.4392 1958.272 8166.627
## 9875 -2.0 -3.2 3.7735925 16.62891 18113.20 1089.2601 1939.880 8064.520
## 9876 -2.0 -3.0 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 9877 -2.0 -2.8 3.4409301 16.96019 18279.53 1077.7910 2058.143 8726.622
## 9878 -2.0 -2.6 3.2802439 17.12481 18359.88 1072.1215 2118.659 9070.409
## 9879 -2.0 -2.4 3.1240999 17.28822 18437.95 1066.5035 2179.891 9421.611
## 9880 -2.0 -2.2 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 9881 -2.0 -2.0 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 9882 -2.0 -1.8 2.6907248 17.76404 18654.64 1050.1351 2364.878 10502.445
## 9883 -2.0 -1.6 2.5612497 17.91409 18719.38 1044.9525 2425.315 10861.828
## 9884 -2.0 -1.4 2.4413111 18.05709 18779.34 1039.9985 2483.859 11212.816
## 9885 -2.0 -1.2 2.3323808 18.19069 18833.81 1035.3542 2539.402 11548.369
## 9886 -2.0 -1.0 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 9887 -2.0 -0.8 2.1540659 18.41814 18922.97 1027.4091 2635.854 12136.883
## 9888 -2.0 -0.6 2.0880613 18.50542 18955.97 1024.3466 2673.505 12368.585
## 9889 -2.0 -0.4 2.0396078 18.57067 18980.20 1022.0526 2701.881 12543.930
## 9890 -2.0 -0.2 2.0099751 18.61108 18995.01 1020.6295 2719.557 12653.470
## 9891 -2.0 0.0 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 9892 -2.0 0.2 2.0099751 18.61108 18995.01 1020.6295 2719.557 12653.470
## 9893 -2.0 0.4 2.0396078 18.57067 18980.20 1022.0526 2701.881 12543.930
## 9894 -2.0 0.6 2.0880613 18.50542 18955.97 1024.3466 2673.505 12368.585
## 9895 -2.0 0.8 2.1540659 18.41814 18922.97 1027.4091 2635.854 12136.883
## 9896 -2.0 1.0 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 9897 -2.0 1.2 2.3323808 18.19069 18833.81 1035.3542 2539.402 11548.369
## 9898 -2.0 1.4 2.4413111 18.05709 18779.34 1039.9985 2483.859 11212.816
## 9899 -2.0 1.6 2.5612497 17.91409 18719.38 1044.9525 2425.315 10861.828
## 9900 -2.0 1.8 2.6907248 17.76404 18654.64 1050.1351 2364.878 10502.445
## 9901 -2.0 2.0 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 9902 -2.0 2.2 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 9903 -2.0 2.4 3.1240999 17.28822 18437.95 1066.5035 2179.891 9421.611
## 9904 -2.0 2.6 3.2802439 17.12481 18359.88 1072.1215 2118.659 9070.409
## 9905 -2.0 2.8 3.4409301 16.96019 18279.53 1077.7910 2058.143 8726.622
## 9906 -2.0 3.0 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 9907 -2.0 3.2 3.7735925 16.62891 18113.20 1089.2601 1939.880 8064.520
## 10026 -1.8 -3.2 3.6715120 16.72933 18164.24 1085.7721 1975.240 8261.110
## 10027 -1.8 -3.0 3.4985711 16.90192 18250.71 1079.8014 2037.003 8607.315
## 10028 -1.8 -2.8 3.3286634 17.07485 18335.67 1073.8408 2100.169 8965.018
## 10029 -1.8 -2.6 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 10030 -1.8 -2.4 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 10031 -1.8 -2.2 2.8425341 17.59312 18578.73 1056.0224 2297.273 10104.053
## 10032 -1.8 -2.0 2.6907248 17.76404 18654.64 1050.1351 2364.878 10502.445
## 10033 -1.8 -1.8 2.5455844 17.93254 18727.21 1044.3143 2432.816 10906.641
## 10034 -1.8 -1.6 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 10035 -1.8 -1.4 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 10036 -1.8 -1.2 2.1633308 18.40603 18918.33 1027.8334 2630.658 12104.994
## 10037 -1.8 -1.0 2.0591260 18.54426 18970.44 1022.9815 2690.373 12472.744
## 10038 -1.8 -0.8 1.9697716 18.66655 19015.11 1018.6735 2743.946 12805.000
## 10039 -1.8 -0.6 1.8973666 18.76841 19051.32 1015.0737 2789.113 13086.800
## 10040 -1.8 -0.4 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 10041 -1.8 -0.2 1.8110770 18.89333 19094.46 1010.6459 2845.175 13438.704
## 10042 -1.8 0.0 1.8000000 18.90965 19100.00 1010.0661 2852.559 13485.224
## 10043 -1.8 0.2 1.8110770 18.89333 19094.46 1010.6459 2845.175 13438.704
## 10044 -1.8 0.4 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 10045 -1.8 0.6 1.8973666 18.76841 19051.32 1015.0737 2789.113 13086.800
## 10046 -1.8 0.8 1.9697716 18.66655 19015.11 1018.6735 2743.946 12805.000
## 10047 -1.8 1.0 2.0591260 18.54426 18970.44 1022.9815 2690.373 12472.744
## 10048 -1.8 1.2 2.1633308 18.40603 18918.33 1027.8334 2630.658 12104.994
## 10049 -1.8 1.4 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 10050 -1.8 1.6 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 10051 -1.8 1.8 2.5455844 17.93254 18727.21 1044.3143 2432.816 10906.641
## 10052 -1.8 2.0 2.6907248 17.76404 18654.64 1050.1351 2364.878 10502.445
## 10053 -1.8 2.2 2.8425341 17.59312 18578.73 1056.0224 2297.273 10104.053
## 10054 -1.8 2.4 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 10055 -1.8 2.6 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 10056 -1.8 2.8 3.3286634 17.07485 18335.67 1073.8408 2100.169 8965.018
## 10057 -1.8 3.0 3.4985711 16.90192 18250.71 1079.8014 2037.003 8607.315
## 10058 -1.8 3.2 3.6715120 16.72933 18164.24 1085.7721 1975.240 8261.110
## 10176 -1.6 -3.4 3.7576588 16.64452 18121.17 1088.7172 1945.348 8094.844
## 10177 -1.6 -3.2 3.5777088 16.82254 18211.15 1082.5442 2008.439 8446.763
## 10178 -1.6 -3.0 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 10179 -1.6 -2.8 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 10180 -1.6 -2.6 3.0528675 17.36403 18473.57 1063.8985 2208.693 9587.954
## 10181 -1.6 -2.4 2.8844410 17.54681 18557.78 1057.6158 2279.177 9998.070
## 10182 -1.6 -2.2 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 10183 -1.6 -2.0 2.5612497 17.91409 18719.38 1044.9525 2425.315 10861.828
## 10184 -1.6 -1.8 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 10185 -1.6 -1.6 2.2627417 18.27815 18868.63 1032.3051 2576.207 11772.074
## 10186 -1.6 -1.4 2.1260292 18.45500 18936.99 1026.1168 2651.709 12234.324
## 10187 -1.6 -1.2 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 10188 -1.6 -1.0 1.8867962 18.78350 19056.60 1014.5396 2795.846 13128.941
## 10189 -1.6 -0.8 1.7888544 18.92615 19105.57 1009.4799 2860.032 13532.353
## 10190 -1.6 -0.6 1.7088007 19.04680 19145.60 1005.1872 2915.076 13880.715
## 10191 -1.6 -0.4 1.6492423 19.13911 19175.38 1001.8949 2957.666 14151.773
## 10192 -1.6 -0.2 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 10193 -1.6 0.0 1.6000000 19.21719 19200.00 999.1057 2994.010 14384.112
## 10194 -1.6 0.2 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 10195 -1.6 0.4 1.6492423 19.13911 19175.38 1001.8949 2957.666 14151.773
## 10196 -1.6 0.6 1.7088007 19.04680 19145.60 1005.1872 2915.076 13880.715
## 10197 -1.6 0.8 1.7888544 18.92615 19105.57 1009.4799 2860.032 13532.353
## 10198 -1.6 1.0 1.8867962 18.78350 19056.60 1014.5396 2795.846 13128.941
## 10199 -1.6 1.2 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 10200 -1.6 1.4 2.1260292 18.45500 18936.99 1026.1168 2651.709 12234.324
## 10201 -1.6 1.6 2.2627417 18.27815 18868.63 1032.3051 2576.207 11772.074
## 10202 -1.6 1.8 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 10203 -1.6 2.0 2.5612497 17.91409 18719.38 1044.9525 2425.315 10861.828
## 10204 -1.6 2.2 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 10205 -1.6 2.4 2.8844410 17.54681 18557.78 1057.6158 2279.177 9998.070
## 10206 -1.6 2.6 3.0528675 17.36403 18473.57 1063.8985 2208.693 9587.954
## 10207 -1.6 2.8 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 10208 -1.6 3.0 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 10209 -1.6 3.2 3.5777088 16.82254 18211.15 1082.5442 2008.439 8446.763
## 10210 -1.6 3.4 3.7576588 16.64452 18121.17 1088.7172 1945.348 8094.844
## 10327 -1.4 -3.4 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 10328 -1.4 -3.2 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 10329 -1.4 -3.0 3.3105891 17.09346 18344.71 1073.2002 2107.045 9004.172
## 10330 -1.4 -2.8 3.1304952 17.28146 18434.75 1066.7360 2177.333 9406.871
## 10331 -1.4 -2.6 2.9529646 17.47181 18523.52 1060.1942 2250.079 9828.243
## 10332 -1.4 -2.4 2.7784888 17.66461 18610.76 1053.5616 2325.391 10269.282
## 10333 -1.4 -2.2 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 10334 -1.4 -2.0 2.4413111 18.05709 18779.34 1039.9985 2483.859 11212.816
## 10335 -1.4 -1.8 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 10336 -1.4 -1.6 2.1260292 18.45500 18936.99 1026.1168 2651.709 12234.324
## 10337 -1.4 -1.4 1.9798990 18.65250 19010.05 1019.1690 2737.758 12766.506
## 10338 -1.4 -1.2 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 10339 -1.4 -1.0 1.7204651 19.02898 19139.77 1005.8220 2906.902 13828.847
## 10340 -1.4 -0.8 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 10341 -1.4 -0.6 1.5231546 19.34240 19238.42 994.6242 3052.918 14762.692
## 10342 -1.4 -0.4 1.4560220 19.45539 19271.99 990.5733 3106.730 15110.660
## 10343 -1.4 -0.2 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 10344 -1.4 0.0 1.4000000 19.55242 19300.00 987.0901 3153.445 15414.371
## 10345 -1.4 0.2 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 10346 -1.4 0.4 1.4560220 19.45539 19271.99 990.5733 3106.730 15110.660
## 10347 -1.4 0.6 1.5231546 19.34240 19238.42 994.6242 3052.918 14762.692
## 10348 -1.4 0.8 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 10349 -1.4 1.0 1.7204651 19.02898 19139.77 1005.8220 2906.902 13828.847
## 10350 -1.4 1.2 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 10351 -1.4 1.4 1.9798990 18.65250 19010.05 1019.1690 2737.758 12766.506
## 10352 -1.4 1.6 2.1260292 18.45500 18936.99 1026.1168 2651.709 12234.324
## 10353 -1.4 1.8 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 10354 -1.4 2.0 2.4413111 18.05709 18779.34 1039.9985 2483.859 11212.816
## 10355 -1.4 2.2 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 10356 -1.4 2.4 2.7784888 17.66461 18610.76 1053.5616 2325.391 10269.282
## 10357 -1.4 2.6 2.9529646 17.47181 18523.52 1060.1942 2250.079 9828.243
## 10358 -1.4 2.8 3.1304952 17.28146 18434.75 1066.7360 2177.333 9406.871
## 10359 -1.4 3.0 3.3105891 17.09346 18344.71 1073.2002 2107.045 9004.172
## 10360 -1.4 3.2 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 10361 -1.4 3.4 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 10477 -1.2 -3.6 3.7947332 16.60823 18102.63 1089.9796 1932.653 8024.487
## 10478 -1.2 -3.4 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 10479 -1.2 -3.2 3.4176015 16.98388 18291.20 1076.9741 2066.782 8775.493
## 10480 -1.2 -3.0 3.2310989 17.17585 18384.45 1070.3660 2137.661 9179.040
## 10481 -1.2 -2.8 3.0463092 17.37105 18476.85 1063.6572 2211.374 9603.473
## 10482 -1.2 -2.6 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 10483 -1.2 -2.4 2.6832816 17.77255 18658.36 1049.8414 2368.280 10522.594
## 10484 -1.2 -2.2 2.5059928 17.97947 18747.00 1042.6897 2451.964 11021.252
## 10485 -1.2 -2.0 2.3323808 18.19069 18833.81 1035.3542 2539.402 11548.369
## 10486 -1.2 -1.8 2.1633308 18.40603 18918.33 1027.8334 2630.658 12104.994
## 10487 -1.2 -1.6 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 10488 -1.2 -1.4 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 10489 -1.2 -1.2 1.6970563 19.06482 19151.47 1004.5449 2923.360 13933.335
## 10490 -1.2 -1.0 1.5620499 19.27850 19218.98 996.9126 3022.757 14568.551
## 10491 -1.2 -0.8 1.4422205 19.47905 19278.89 989.7241 3118.081 15184.319
## 10492 -1.2 -0.6 1.3416408 19.65632 19329.18 983.3569 3203.986 15744.646
## 10493 -1.2 -0.4 1.2649111 19.79761 19367.54 978.2767 3273.575 16202.244
## 10494 -1.2 -0.2 1.2165525 19.88957 19391.72 974.9696 3319.402 16505.369
## 10495 -1.2 0.0 1.2000000 19.92159 19400.00 973.8181 3335.458 16611.903
## 10496 -1.2 0.2 1.2165525 19.88957 19391.72 974.9696 3319.402 16505.369
## 10497 -1.2 0.4 1.2649111 19.79761 19367.54 978.2767 3273.575 16202.244
## 10498 -1.2 0.6 1.3416408 19.65632 19329.18 983.3569 3203.986 15744.646
## 10499 -1.2 0.8 1.4422205 19.47905 19278.89 989.7241 3118.081 15184.319
## 10500 -1.2 1.0 1.5620499 19.27850 19218.98 996.9126 3022.757 14568.551
## 10501 -1.2 1.2 1.6970563 19.06482 19151.47 1004.5449 2923.360 13933.335
## 10502 -1.2 1.4 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 10503 -1.2 1.6 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 10504 -1.2 1.8 2.1633308 18.40603 18918.33 1027.8334 2630.658 12104.994
## 10505 -1.2 2.0 2.3323808 18.19069 18833.81 1035.3542 2539.402 11548.369
## 10506 -1.2 2.2 2.5059928 17.97947 18747.00 1042.6897 2451.964 11021.252
## 10507 -1.2 2.4 2.6832816 17.77255 18658.36 1049.8414 2368.280 10522.594
## 10508 -1.2 2.6 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 10509 -1.2 2.8 3.0463092 17.37105 18476.85 1063.6572 2211.374 9603.473
## 10510 -1.2 3.0 3.2310989 17.17585 18384.45 1070.3660 2137.661 9179.040
## 10511 -1.2 3.2 3.4176015 16.98388 18291.20 1076.9741 2066.782 8775.493
## 10512 -1.2 3.4 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 10513 -1.2 3.6 3.7947332 16.60823 18102.63 1089.9796 1932.653 8024.487
## 10628 -1.0 -3.6 3.7363083 16.66547 18131.85 1087.9889 1952.704 8135.684
## 10629 -1.0 -3.4 3.5440090 16.85626 18228.00 1081.3786 2020.539 8514.682
## 10630 -1.0 -3.2 3.3526109 17.05025 18323.69 1074.6875 2091.107 8913.477
## 10631 -1.0 -3.0 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 10632 -1.0 -2.8 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 10633 -1.0 -2.6 2.7856777 17.65654 18607.16 1053.8394 2322.206 10250.534
## 10634 -1.0 -2.4 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 10635 -1.0 -2.2 2.4166092 18.08706 18791.70 1038.9580 2496.248 11287.445
## 10636 -1.0 -2.0 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 10637 -1.0 -1.8 2.0591260 18.54426 18970.44 1022.9815 2690.373 12472.744
## 10638 -1.0 -1.6 1.8867962 18.78350 19056.60 1014.5396 2795.846 13128.941
## 10639 -1.0 -1.4 1.7204651 19.02898 19139.77 1005.8220 2906.902 13828.847
## 10640 -1.0 -1.2 1.5620499 19.27850 19218.98 996.9126 3022.757 14568.551
## 10641 -1.0 -1.0 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 10642 -1.0 -0.8 1.2806248 19.76823 19359.69 979.3335 3259.019 16106.259
## 10643 -1.0 -0.6 1.1661904 19.98787 19416.90 971.4344 3368.863 16834.098
## 10644 -1.0 -0.4 1.0770330 20.16866 19461.48 964.9367 3461.108 17451.478
## 10645 -1.0 -0.2 1.0198039 20.28959 19490.10 960.5961 3523.736 17873.788
## 10646 -1.0 0.0 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 10647 -1.0 0.2 1.0198039 20.28959 19490.10 960.5961 3523.736 17873.788
## 10648 -1.0 0.4 1.0770330 20.16866 19461.48 964.9367 3461.108 17451.478
## 10649 -1.0 0.6 1.1661904 19.98787 19416.90 971.4344 3368.863 16834.098
## 10650 -1.0 0.8 1.2806248 19.76823 19359.69 979.3335 3259.019 16106.259
## 10651 -1.0 1.0 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 10652 -1.0 1.2 1.5620499 19.27850 19218.98 996.9126 3022.757 14568.551
## 10653 -1.0 1.4 1.7204651 19.02898 19139.77 1005.8220 2906.902 13828.847
## 10654 -1.0 1.6 1.8867962 18.78350 19056.60 1014.5396 2795.846 13128.941
## 10655 -1.0 1.8 2.0591260 18.54426 18970.44 1022.9815 2690.373 12472.744
## 10656 -1.0 2.0 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 10657 -1.0 2.2 2.4166092 18.08706 18791.70 1038.9580 2496.248 11287.445
## 10658 -1.0 2.4 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 10659 -1.0 2.6 2.7856777 17.65654 18607.16 1053.8394 2322.206 10250.534
## 10660 -1.0 2.8 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 10661 -1.0 3.0 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 10662 -1.0 3.2 3.3526109 17.05025 18323.69 1074.6875 2091.107 8913.477
## 10663 -1.0 3.4 3.5440090 16.85626 18228.00 1081.3786 2020.539 8514.682
## 10664 -1.0 3.6 3.7363083 16.66547 18131.85 1087.9889 1952.704 8135.684
## 10779 -0.8 -3.6 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 10780 -0.8 -3.4 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 10781 -0.8 -3.2 3.2984845 17.10595 18350.76 1072.7704 2111.667 9030.518
## 10782 -0.8 -3.0 3.1048349 17.30864 18447.58 1065.8018 2187.625 9466.205
## 10783 -0.8 -2.8 2.9120440 17.51649 18543.98 1058.6583 2267.384 9929.151
## 10784 -0.8 -2.6 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 10785 -0.8 -2.4 2.5298221 17.95117 18735.09 1043.6695 2440.406 10952.036
## 10786 -0.8 -2.2 2.3409400 18.18006 18829.53 1035.7245 2534.950 11521.384
## 10787 -0.8 -2.0 2.1540659 18.41814 18922.97 1027.4091 2635.854 12136.883
## 10788 -0.8 -1.8 1.9697716 18.66655 19015.11 1018.6735 2743.946 12805.000
## 10789 -0.8 -1.6 1.7888544 18.92615 19105.57 1009.4799 2860.032 13532.353
## 10790 -0.8 -1.4 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 10791 -0.8 -1.2 1.4422205 19.47905 19278.89 989.7241 3118.081 15184.319
## 10792 -0.8 -1.0 1.2806248 19.76823 19359.69 979.3335 3259.019 16106.259
## 10793 -0.8 -0.8 1.1313708 20.05742 19434.31 968.9341 3404.151 17069.619
## 10794 -0.8 -0.6 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 10795 -0.8 -0.4 0.8944272 20.56913 19552.79 950.5888 3671.400 18879.377
## 10796 -0.8 -0.2 0.8246211 20.73427 19587.69 944.7013 3760.537 19492.994
## 10797 -0.8 0.0 0.8000000 20.79426 19600.00 942.5679 3793.272 19719.569
## 10798 -0.8 0.2 0.8246211 20.73427 19587.69 944.7013 3760.537 19492.994
## 10799 -0.8 0.4 0.8944272 20.56913 19552.79 950.5888 3671.400 18879.377
## 10800 -0.8 0.6 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 10801 -0.8 0.8 1.1313708 20.05742 19434.31 968.9341 3404.151 17069.619
## 10802 -0.8 1.0 1.2806248 19.76823 19359.69 979.3335 3259.019 16106.259
## 10803 -0.8 1.2 1.4422205 19.47905 19278.89 989.7241 3118.081 15184.319
## 10804 -0.8 1.4 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 10805 -0.8 1.6 1.7888544 18.92615 19105.57 1009.4799 2860.032 13532.353
## 10806 -0.8 1.8 1.9697716 18.66655 19015.11 1018.6735 2743.946 12805.000
## 10807 -0.8 2.0 2.1540659 18.41814 18922.97 1027.4091 2635.854 12136.883
## 10808 -0.8 2.2 2.3409400 18.18006 18829.53 1035.7245 2534.950 11521.384
## 10809 -0.8 2.4 2.5298221 17.95117 18735.09 1043.6695 2440.406 10952.036
## 10810 -0.8 2.6 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 10811 -0.8 2.8 2.9120440 17.51649 18543.98 1058.6583 2267.384 9929.151
## 10812 -0.8 3.0 3.1048349 17.30864 18447.58 1065.8018 2187.625 9466.205
## 10813 -0.8 3.2 3.2984845 17.10595 18350.76 1072.7704 2111.667 9030.518
## 10814 -0.8 3.4 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 10815 -0.8 3.6 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 10930 -0.6 -3.6 3.6496575 16.75097 18175.17 1085.0221 1982.913 8303.926
## 10931 -0.6 -3.4 3.4525353 16.94842 18273.73 1078.1967 2053.864 8702.437
## 10932 -0.6 -3.2 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 10933 -0.6 -3.0 3.0594117 17.35703 18470.29 1064.1390 2206.023 9572.504
## 10934 -0.6 -2.8 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 10935 -0.6 -2.6 2.6683328 17.78969 18665.83 1049.2501 2375.138 10563.243
## 10936 -0.6 -2.4 2.4738634 18.01787 18763.07 1041.3588 2467.711 11115.723
## 10937 -0.6 -2.2 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 10938 -0.6 -2.0 2.0880613 18.50542 18955.97 1024.3466 2673.505 12368.585
## 10939 -0.6 -1.8 1.8973666 18.76841 19051.32 1015.0737 2789.113 13086.800
## 10940 -0.6 -1.6 1.7088007 19.04680 19145.60 1005.1872 2915.076 13880.715
## 10941 -0.6 -1.4 1.5231546 19.34240 19238.42 994.6242 3052.918 14762.692
## 10942 -0.6 -1.2 1.3416408 19.65632 19329.18 983.3569 3203.986 15744.646
## 10943 -0.6 -1.0 1.1661904 19.98787 19416.90 971.4344 3368.863 16834.098
## 10944 -0.6 -0.8 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 10945 -0.6 -0.6 0.8485281 20.67690 19575.74 946.7442 3729.410 19278.163
## 10946 -0.6 -0.4 0.7211103 20.99298 19639.44 935.5243 3903.069 20484.262
## 10947 -0.6 -0.2 0.6324555 21.22896 19683.77 927.2133 4036.173 21420.936
## 10948 -0.6 0.0 0.6000000 21.31893 19700.00 924.0613 4087.710 21786.401
## 10949 -0.6 0.2 0.6324555 21.22896 19683.77 927.2133 4036.173 21420.936
## 10950 -0.6 0.4 0.7211103 20.99298 19639.44 935.5243 3903.069 20484.262
## 10951 -0.6 0.6 0.8485281 20.67690 19575.74 946.7442 3729.410 19278.163
## 10952 -0.6 0.8 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 10953 -0.6 1.0 1.1661904 19.98787 19416.90 971.4344 3368.863 16834.098
## 10954 -0.6 1.2 1.3416408 19.65632 19329.18 983.3569 3203.986 15744.646
## 10955 -0.6 1.4 1.5231546 19.34240 19238.42 994.6242 3052.918 14762.692
## 10956 -0.6 1.6 1.7088007 19.04680 19145.60 1005.1872 2915.076 13880.715
## 10957 -0.6 1.8 1.8973666 18.76841 19051.32 1015.0737 2789.113 13086.800
## 10958 -0.6 2.0 2.0880613 18.50542 18955.97 1024.3466 2673.505 12368.585
## 10959 -0.6 2.2 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 10960 -0.6 2.4 2.4738634 18.01787 18763.07 1041.3588 2467.711 11115.723
## 10961 -0.6 2.6 2.6683328 17.78969 18665.83 1049.2501 2375.138 10563.243
## 10962 -0.6 2.8 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 10963 -0.6 3.0 3.0594117 17.35703 18470.29 1064.1390 2206.023 9572.504
## 10964 -0.6 3.2 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 10965 -0.6 3.4 3.4525353 16.94842 18273.73 1078.1967 2053.864 8702.437
## 10966 -0.6 3.6 3.6496575 16.75097 18175.17 1085.0221 1982.913 8303.926
## 11081 -0.4 -3.6 3.6221541 16.77826 18188.92 1084.0766 1992.622 8358.184
## 11082 -0.4 -3.4 3.4234486 16.97794 18288.28 1077.1790 2064.612 8763.212
## 11083 -0.4 -3.2 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 11084 -0.4 -3.0 3.0265492 17.39225 18486.73 1062.9286 2219.481 9650.444
## 11085 -0.4 -2.8 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 11086 -0.4 -2.6 2.6305893 17.83321 18684.71 1047.7480 2392.611 10666.981
## 11087 -0.4 -2.4 2.4331050 18.06702 18783.45 1039.6536 2487.962 11237.516
## 11088 -0.4 -2.2 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 11089 -0.4 -2.0 2.0396078 18.57067 18980.20 1022.0526 2701.881 12543.930
## 11090 -0.4 -1.8 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 11091 -0.4 -1.6 1.6492423 19.13911 19175.38 1001.8949 2957.666 14151.773
## 11092 -0.4 -1.4 1.4560220 19.45539 19271.99 990.5733 3106.730 15110.660
## 11093 -0.4 -1.2 1.2649111 19.79761 19367.54 978.2767 3273.575 16202.244
## 11094 -0.4 -1.0 1.0770330 20.16866 19461.48 964.9367 3461.108 17451.478
## 11095 -0.4 -0.8 0.8944272 20.56913 19552.79 950.5888 3671.400 18879.377
## 11096 -0.4 -0.6 0.7211103 20.99298 19639.44 935.5243 3903.069 20484.262
## 11097 -0.4 -0.4 0.5656854 21.41626 19717.16 920.6628 4143.953 22187.000
## 11098 -0.4 -0.2 0.4472136 21.77088 19776.39 908.3874 4353.232 23693.422
## 11099 -0.4 0.0 0.4000000 21.92081 19800.00 903.2515 4443.788 24352.855
## 11100 -0.4 0.2 0.4472136 21.77088 19776.39 908.3874 4353.232 23693.422
## 11101 -0.4 0.4 0.5656854 21.41626 19717.16 920.6628 4143.953 22187.000
## 11102 -0.4 0.6 0.7211103 20.99298 19639.44 935.5243 3903.069 20484.262
## 11103 -0.4 0.8 0.8944272 20.56913 19552.79 950.5888 3671.400 18879.377
## 11104 -0.4 1.0 1.0770330 20.16866 19461.48 964.9367 3461.108 17451.478
## 11105 -0.4 1.2 1.2649111 19.79761 19367.54 978.2767 3273.575 16202.244
## 11106 -0.4 1.4 1.4560220 19.45539 19271.99 990.5733 3106.730 15110.660
## 11107 -0.4 1.6 1.6492423 19.13911 19175.38 1001.8949 2957.666 14151.773
## 11108 -0.4 1.8 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 11109 -0.4 2.0 2.0396078 18.57067 18980.20 1022.0526 2701.881 12543.930
## 11110 -0.4 2.2 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 11111 -0.4 2.4 2.4331050 18.06702 18783.45 1039.6536 2487.962 11237.516
## 11112 -0.4 2.6 2.6305893 17.83321 18684.71 1047.7480 2392.611 10666.981
## 11113 -0.4 2.8 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 11114 -0.4 3.0 3.0265492 17.39225 18486.73 1062.9286 2219.481 9650.444
## 11115 -0.4 3.2 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 11116 -0.4 3.4 3.4234486 16.97794 18288.28 1077.1790 2064.612 8763.212
## 11117 -0.4 3.6 3.6221541 16.77826 18188.92 1084.0766 1992.622 8358.184
## 11231 -0.2 -3.8 3.8052595 16.59795 18097.37 1090.3376 1929.067 8004.640
## 11232 -0.2 -3.6 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 11233 -0.2 -3.4 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 11234 -0.2 -3.2 3.2062439 17.20180 18396.88 1069.4738 2147.364 9234.634
## 11235 -0.2 -3.0 3.0066593 17.41366 18496.67 1062.1929 2227.688 9698.051
## 11236 -0.2 -2.8 2.8071338 17.63253 18596.43 1054.6662 2312.745 10194.884
## 11237 -0.2 -2.6 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 11238 -0.2 -2.4 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 11239 -0.2 -2.2 2.2090722 18.34673 18895.46 1029.9090 2605.313 11949.745
## 11240 -0.2 -2.0 2.0099751 18.61108 18995.01 1020.6295 2719.557 12653.470
## 11241 -0.2 -1.8 1.8110770 18.89333 19094.46 1010.6459 2845.175 13438.704
## 11242 -0.2 -1.6 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 11243 -0.2 -1.4 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 11244 -0.2 -1.2 1.2165525 19.88957 19391.72 974.9696 3319.402 16505.369
## 11245 -0.2 -1.0 1.0198039 20.28959 19490.10 960.5961 3523.736 17873.788
## 11246 -0.2 -0.8 0.8246211 20.73427 19587.69 944.7013 3760.537 19492.994
## 11247 -0.2 -0.6 0.6324555 21.22896 19683.77 927.2133 4036.173 21420.936
## 11248 -0.2 -0.4 0.4472136 21.77088 19776.39 908.3874 4353.232 23693.422
## 11249 -0.2 -0.2 0.2828427 22.31619 19858.58 889.8733 4688.606 26157.954
## 11250 -0.2 0.0 0.2000000 22.61765 19900.00 879.8437 4881.198 27600.313
## 11251 -0.2 0.2 0.2828427 22.31619 19858.58 889.8733 4688.606 26157.954
## 11252 -0.2 0.4 0.4472136 21.77088 19776.39 908.3874 4353.232 23693.422
## 11253 -0.2 0.6 0.6324555 21.22896 19683.77 927.2133 4036.173 21420.936
## 11254 -0.2 0.8 0.8246211 20.73427 19587.69 944.7013 3760.537 19492.994
## 11255 -0.2 1.0 1.0198039 20.28959 19490.10 960.5961 3523.736 17873.788
## 11256 -0.2 1.2 1.2165525 19.88957 19391.72 974.9696 3319.402 16505.369
## 11257 -0.2 1.4 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 11258 -0.2 1.6 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 11259 -0.2 1.8 1.8110770 18.89333 19094.46 1010.6459 2845.175 13438.704
## 11260 -0.2 2.0 2.0099751 18.61108 18995.01 1020.6295 2719.557 12653.470
## 11261 -0.2 2.2 2.2090722 18.34673 18895.46 1029.9090 2605.313 11949.745
## 11262 -0.2 2.4 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 11263 -0.2 2.6 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 11264 -0.2 2.8 2.8071338 17.63253 18596.43 1054.6662 2312.745 10194.884
## 11265 -0.2 3.0 3.0066593 17.41366 18496.67 1062.1929 2227.688 9698.051
## 11266 -0.2 3.2 3.2062439 17.20180 18396.88 1069.4738 2147.364 9234.634
## 11267 -0.2 3.4 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 11268 -0.2 3.6 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 11269 -0.2 3.8 3.8052595 16.59795 18097.37 1090.3376 1929.067 8004.640
## 11382 0.0 -3.8 3.8000000 16.60309 18100.00 1090.1587 1930.858 8014.550
## 11383 0.0 -3.6 3.6000000 16.80031 18200.00 1083.3134 2000.486 8402.197
## 11384 0.0 -3.4 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 11385 0.0 -3.2 3.2000000 17.20834 18400.00 1069.2492 2149.812 9248.670
## 11386 0.0 -3.0 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 11387 0.0 -2.8 2.8000000 17.64050 18600.00 1054.3917 2315.883 10213.336
## 11388 0.0 -2.6 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 11389 0.0 -2.4 2.4000000 18.10732 18800.00 1038.2543 2504.644 11338.097
## 11390 0.0 -2.2 2.2000000 18.35843 18900.00 1029.4998 2610.300 11980.251
## 11391 0.0 -2.0 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 11392 0.0 -1.8 1.8000000 18.90965 19100.00 1010.0661 2852.559 13485.224
## 11393 0.0 -1.6 1.6000000 19.21719 19200.00 999.1057 2994.010 14384.112
## 11394 0.0 -1.4 1.4000000 19.55242 19300.00 987.0901 3153.445 15414.371
## 11395 0.0 -1.2 1.2000000 19.92159 19400.00 973.8181 3335.458 16611.903
## 11396 0.0 -1.0 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 11397 0.0 -0.8 0.8000000 20.79426 19600.00 942.5679 3793.272 19719.569
## 11398 0.0 -0.6 0.6000000 21.31893 19700.00 924.0613 4087.710 21786.401
## 11399 0.0 -0.4 0.4000000 21.92081 19800.00 903.2515 4443.788 24352.855
## 11400 0.0 -0.2 0.2000000 22.61765 19900.00 879.8437 4881.198 27600.313
## 11401 0.0 0.0 0.0000000 23.43138 20000.00 853.5560 5427.223 31791.838
## 11402 0.0 0.2 0.2000000 22.61765 19900.00 879.8437 4881.198 27600.313
## 11403 0.0 0.4 0.4000000 21.92081 19800.00 903.2515 4443.788 24352.855
## 11404 0.0 0.6 0.6000000 21.31893 19700.00 924.0613 4087.710 21786.401
## 11405 0.0 0.8 0.8000000 20.79426 19600.00 942.5679 3793.272 19719.569
## 11406 0.0 1.0 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 11407 0.0 1.2 1.2000000 19.92159 19400.00 973.8181 3335.458 16611.903
## 11408 0.0 1.4 1.4000000 19.55242 19300.00 987.0901 3153.445 15414.371
## 11409 0.0 1.6 1.6000000 19.21719 19200.00 999.1057 2994.010 14384.112
## 11410 0.0 1.8 1.8000000 18.90965 19100.00 1010.0661 2852.559 13485.224
## 11411 0.0 2.0 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 11412 0.0 2.2 2.2000000 18.35843 18900.00 1029.4998 2610.300 11980.251
## 11413 0.0 2.4 2.4000000 18.10732 18800.00 1038.2543 2504.644 11338.097
## 11414 0.0 2.6 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 11415 0.0 2.8 2.8000000 17.64050 18600.00 1054.3917 2315.883 10213.336
## 11416 0.0 3.0 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 11417 0.0 3.2 3.2000000 17.20834 18400.00 1069.2492 2149.812 9248.670
## 11418 0.0 3.4 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 11419 0.0 3.6 3.6000000 16.80031 18200.00 1083.3134 2000.486 8402.197
## 11420 0.0 3.8 3.8000000 16.60309 18100.00 1090.1587 1930.858 8014.550
## 11533 0.2 -3.8 3.8052595 16.59795 18097.37 1090.3376 1929.067 8004.640
## 11534 0.2 -3.6 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 11535 0.2 -3.4 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 11536 0.2 -3.2 3.2062439 17.20180 18396.88 1069.4738 2147.364 9234.634
## 11537 0.2 -3.0 3.0066593 17.41366 18496.67 1062.1929 2227.688 9698.051
## 11538 0.2 -2.8 2.8071338 17.63253 18596.43 1054.6662 2312.745 10194.884
## 11539 0.2 -2.6 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 11540 0.2 -2.4 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 11541 0.2 -2.2 2.2090722 18.34673 18895.46 1029.9090 2605.313 11949.745
## 11542 0.2 -2.0 2.0099751 18.61108 18995.01 1020.6295 2719.557 12653.470
## 11543 0.2 -1.8 1.8110770 18.89333 19094.46 1010.6459 2845.175 13438.704
## 11544 0.2 -1.6 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 11545 0.2 -1.4 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 11546 0.2 -1.2 1.2165525 19.88957 19391.72 974.9696 3319.402 16505.369
## 11547 0.2 -1.0 1.0198039 20.28959 19490.10 960.5961 3523.736 17873.788
## 11548 0.2 -0.8 0.8246211 20.73427 19587.69 944.7013 3760.537 19492.994
## 11549 0.2 -0.6 0.6324555 21.22896 19683.77 927.2133 4036.173 21420.936
## 11550 0.2 -0.4 0.4472136 21.77088 19776.39 908.3874 4353.232 23693.422
## 11551 0.2 -0.2 0.2828427 22.31619 19858.58 889.8733 4688.606 26157.954
## 11552 0.2 0.0 0.2000000 22.61765 19900.00 879.8437 4881.198 27600.313
## 11553 0.2 0.2 0.2828427 22.31619 19858.58 889.8733 4688.606 26157.954
## 11554 0.2 0.4 0.4472136 21.77088 19776.39 908.3874 4353.232 23693.422
## 11555 0.2 0.6 0.6324555 21.22896 19683.77 927.2133 4036.173 21420.936
## 11556 0.2 0.8 0.8246211 20.73427 19587.69 944.7013 3760.537 19492.994
## 11557 0.2 1.0 1.0198039 20.28959 19490.10 960.5961 3523.736 17873.788
## 11558 0.2 1.2 1.2165525 19.88957 19391.72 974.9696 3319.402 16505.369
## 11559 0.2 1.4 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 11560 0.2 1.6 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 11561 0.2 1.8 1.8110770 18.89333 19094.46 1010.6459 2845.175 13438.704
## 11562 0.2 2.0 2.0099751 18.61108 18995.01 1020.6295 2719.557 12653.470
## 11563 0.2 2.2 2.2090722 18.34673 18895.46 1029.9090 2605.313 11949.745
## 11564 0.2 2.4 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 11565 0.2 2.6 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 11566 0.2 2.8 2.8071338 17.63253 18596.43 1054.6662 2312.745 10194.884
## 11567 0.2 3.0 3.0066593 17.41366 18496.67 1062.1929 2227.688 9698.051
## 11568 0.2 3.2 3.2062439 17.20180 18396.88 1069.4738 2147.364 9234.634
## 11569 0.2 3.4 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 11570 0.2 3.6 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 11571 0.2 3.8 3.8052595 16.59795 18097.37 1090.3376 1929.067 8004.640
## 11685 0.4 -3.6 3.6221541 16.77826 18188.92 1084.0766 1992.622 8358.184
## 11686 0.4 -3.4 3.4234486 16.97794 18288.28 1077.1790 2064.612 8763.212
## 11687 0.4 -3.2 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 11688 0.4 -3.0 3.0265492 17.39225 18486.73 1062.9286 2219.481 9650.444
## 11689 0.4 -2.8 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 11690 0.4 -2.6 2.6305893 17.83321 18684.71 1047.7480 2392.611 10666.981
## 11691 0.4 -2.4 2.4331050 18.06702 18783.45 1039.6536 2487.962 11237.516
## 11692 0.4 -2.2 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 11693 0.4 -2.0 2.0396078 18.57067 18980.20 1022.0526 2701.881 12543.930
## 11694 0.4 -1.8 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 11695 0.4 -1.6 1.6492423 19.13911 19175.38 1001.8949 2957.666 14151.773
## 11696 0.4 -1.4 1.4560220 19.45539 19271.99 990.5733 3106.730 15110.660
## 11697 0.4 -1.2 1.2649111 19.79761 19367.54 978.2767 3273.575 16202.244
## 11698 0.4 -1.0 1.0770330 20.16866 19461.48 964.9367 3461.108 17451.478
## 11699 0.4 -0.8 0.8944272 20.56913 19552.79 950.5888 3671.400 18879.377
## 11700 0.4 -0.6 0.7211103 20.99298 19639.44 935.5243 3903.069 20484.262
## 11701 0.4 -0.4 0.5656854 21.41626 19717.16 920.6628 4143.953 22187.000
## 11702 0.4 -0.2 0.4472136 21.77088 19776.39 908.3874 4353.232 23693.422
## 11703 0.4 0.0 0.4000000 21.92081 19800.00 903.2515 4443.788 24352.855
## 11704 0.4 0.2 0.4472136 21.77088 19776.39 908.3874 4353.232 23693.422
## 11705 0.4 0.4 0.5656854 21.41626 19717.16 920.6628 4143.953 22187.000
## 11706 0.4 0.6 0.7211103 20.99298 19639.44 935.5243 3903.069 20484.262
## 11707 0.4 0.8 0.8944272 20.56913 19552.79 950.5888 3671.400 18879.377
## 11708 0.4 1.0 1.0770330 20.16866 19461.48 964.9367 3461.108 17451.478
## 11709 0.4 1.2 1.2649111 19.79761 19367.54 978.2767 3273.575 16202.244
## 11710 0.4 1.4 1.4560220 19.45539 19271.99 990.5733 3106.730 15110.660
## 11711 0.4 1.6 1.6492423 19.13911 19175.38 1001.8949 2957.666 14151.773
## 11712 0.4 1.8 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 11713 0.4 2.0 2.0396078 18.57067 18980.20 1022.0526 2701.881 12543.930
## 11714 0.4 2.2 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 11715 0.4 2.4 2.4331050 18.06702 18783.45 1039.6536 2487.962 11237.516
## 11716 0.4 2.6 2.6305893 17.83321 18684.71 1047.7480 2392.611 10666.981
## 11717 0.4 2.8 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 11718 0.4 3.0 3.0265492 17.39225 18486.73 1062.9286 2219.481 9650.444
## 11719 0.4 3.2 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 11720 0.4 3.4 3.4234486 16.97794 18288.28 1077.1790 2064.612 8763.212
## 11721 0.4 3.6 3.6221541 16.77826 18188.92 1084.0766 1992.622 8358.184
## 11836 0.6 -3.6 3.6496575 16.75097 18175.17 1085.0221 1982.913 8303.926
## 11837 0.6 -3.4 3.4525353 16.94842 18273.73 1078.1967 2053.864 8702.437
## 11838 0.6 -3.2 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 11839 0.6 -3.0 3.0594117 17.35703 18470.29 1064.1390 2206.023 9572.504
## 11840 0.6 -2.8 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 11841 0.6 -2.6 2.6683328 17.78969 18665.83 1049.2501 2375.138 10563.243
## 11842 0.6 -2.4 2.4738634 18.01787 18763.07 1041.3588 2467.711 11115.723
## 11843 0.6 -2.2 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 11844 0.6 -2.0 2.0880613 18.50542 18955.97 1024.3466 2673.505 12368.585
## 11845 0.6 -1.8 1.8973666 18.76841 19051.32 1015.0737 2789.113 13086.800
## 11846 0.6 -1.6 1.7088007 19.04680 19145.60 1005.1872 2915.076 13880.715
## 11847 0.6 -1.4 1.5231546 19.34240 19238.42 994.6242 3052.918 14762.692
## 11848 0.6 -1.2 1.3416408 19.65632 19329.18 983.3569 3203.986 15744.646
## 11849 0.6 -1.0 1.1661904 19.98787 19416.90 971.4344 3368.863 16834.098
## 11850 0.6 -0.8 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 11851 0.6 -0.6 0.8485281 20.67690 19575.74 946.7442 3729.410 19278.163
## 11852 0.6 -0.4 0.7211103 20.99298 19639.44 935.5243 3903.069 20484.262
## 11853 0.6 -0.2 0.6324555 21.22896 19683.77 927.2133 4036.173 21420.936
## 11854 0.6 0.0 0.6000000 21.31893 19700.00 924.0613 4087.710 21786.401
## 11855 0.6 0.2 0.6324555 21.22896 19683.77 927.2133 4036.173 21420.936
## 11856 0.6 0.4 0.7211103 20.99298 19639.44 935.5243 3903.069 20484.262
## 11857 0.6 0.6 0.8485281 20.67690 19575.74 946.7442 3729.410 19278.163
## 11858 0.6 0.8 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 11859 0.6 1.0 1.1661904 19.98787 19416.90 971.4344 3368.863 16834.098
## 11860 0.6 1.2 1.3416408 19.65632 19329.18 983.3569 3203.986 15744.646
## 11861 0.6 1.4 1.5231546 19.34240 19238.42 994.6242 3052.918 14762.692
## 11862 0.6 1.6 1.7088007 19.04680 19145.60 1005.1872 2915.076 13880.715
## 11863 0.6 1.8 1.8973666 18.76841 19051.32 1015.0737 2789.113 13086.800
## 11864 0.6 2.0 2.0880613 18.50542 18955.97 1024.3466 2673.505 12368.585
## 11865 0.6 2.2 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 11866 0.6 2.4 2.4738634 18.01787 18763.07 1041.3588 2467.711 11115.723
## 11867 0.6 2.6 2.6683328 17.78969 18665.83 1049.2501 2375.138 10563.243
## 11868 0.6 2.8 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 11869 0.6 3.0 3.0594117 17.35703 18470.29 1064.1390 2206.023 9572.504
## 11870 0.6 3.2 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 11871 0.6 3.4 3.4525353 16.94842 18273.73 1078.1967 2053.864 8702.437
## 11872 0.6 3.6 3.6496575 16.75097 18175.17 1085.0221 1982.913 8303.926
## 11987 0.8 -3.6 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 11988 0.8 -3.4 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 11989 0.8 -3.2 3.2984845 17.10595 18350.76 1072.7704 2111.667 9030.518
## 11990 0.8 -3.0 3.1048349 17.30864 18447.58 1065.8018 2187.625 9466.205
## 11991 0.8 -2.8 2.9120440 17.51649 18543.98 1058.6583 2267.384 9929.151
## 11992 0.8 -2.6 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 11993 0.8 -2.4 2.5298221 17.95117 18735.09 1043.6695 2440.406 10952.036
## 11994 0.8 -2.2 2.3409400 18.18006 18829.53 1035.7245 2534.950 11521.384
## 11995 0.8 -2.0 2.1540659 18.41814 18922.97 1027.4091 2635.854 12136.883
## 11996 0.8 -1.8 1.9697716 18.66655 19015.11 1018.6735 2743.946 12805.000
## 11997 0.8 -1.6 1.7888544 18.92615 19105.57 1009.4799 2860.032 13532.353
## 11998 0.8 -1.4 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 11999 0.8 -1.2 1.4422205 19.47905 19278.89 989.7241 3118.081 15184.319
## 12000 0.8 -1.0 1.2806248 19.76823 19359.69 979.3335 3259.019 16106.259
## 12001 0.8 -0.8 1.1313708 20.05742 19434.31 968.9341 3404.151 17069.619
## 12002 0.8 -0.6 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 12003 0.8 -0.4 0.8944272 20.56913 19552.79 950.5888 3671.400 18879.377
## 12004 0.8 -0.2 0.8246211 20.73427 19587.69 944.7013 3760.537 19492.994
## 12005 0.8 0.0 0.8000000 20.79426 19600.00 942.5679 3793.272 19719.569
## 12006 0.8 0.2 0.8246211 20.73427 19587.69 944.7013 3760.537 19492.994
## 12007 0.8 0.4 0.8944272 20.56913 19552.79 950.5888 3671.400 18879.377
## 12008 0.8 0.6 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 12009 0.8 0.8 1.1313708 20.05742 19434.31 968.9341 3404.151 17069.619
## 12010 0.8 1.0 1.2806248 19.76823 19359.69 979.3335 3259.019 16106.259
## 12011 0.8 1.2 1.4422205 19.47905 19278.89 989.7241 3118.081 15184.319
## 12012 0.8 1.4 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 12013 0.8 1.6 1.7888544 18.92615 19105.57 1009.4799 2860.032 13532.353
## 12014 0.8 1.8 1.9697716 18.66655 19015.11 1018.6735 2743.946 12805.000
## 12015 0.8 2.0 2.1540659 18.41814 18922.97 1027.4091 2635.854 12136.883
## 12016 0.8 2.2 2.3409400 18.18006 18829.53 1035.7245 2534.950 11521.384
## 12017 0.8 2.4 2.5298221 17.95117 18735.09 1043.6695 2440.406 10952.036
## 12018 0.8 2.6 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 12019 0.8 2.8 2.9120440 17.51649 18543.98 1058.6583 2267.384 9929.151
## 12020 0.8 3.0 3.1048349 17.30864 18447.58 1065.8018 2187.625 9466.205
## 12021 0.8 3.2 3.2984845 17.10595 18350.76 1072.7704 2111.667 9030.518
## 12022 0.8 3.4 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 12023 0.8 3.6 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 12138 1.0 -3.6 3.7363083 16.66547 18131.85 1087.9889 1952.704 8135.684
## 12139 1.0 -3.4 3.5440090 16.85626 18228.00 1081.3786 2020.539 8514.682
## 12140 1.0 -3.2 3.3526109 17.05025 18323.69 1074.6875 2091.107 8913.477
## 12141 1.0 -3.0 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 12142 1.0 -2.8 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 12143 1.0 -2.6 2.7856777 17.65654 18607.16 1053.8394 2322.206 10250.534
## 12144 1.0 -2.4 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 12145 1.0 -2.2 2.4166092 18.08706 18791.70 1038.9580 2496.248 11287.445
## 12146 1.0 -2.0 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 12147 1.0 -1.8 2.0591260 18.54426 18970.44 1022.9815 2690.373 12472.744
## 12148 1.0 -1.6 1.8867962 18.78350 19056.60 1014.5396 2795.846 13128.941
## 12149 1.0 -1.4 1.7204651 19.02898 19139.77 1005.8220 2906.902 13828.847
## 12150 1.0 -1.2 1.5620499 19.27850 19218.98 996.9126 3022.757 14568.551
## 12151 1.0 -1.0 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 12152 1.0 -0.8 1.2806248 19.76823 19359.69 979.3335 3259.019 16106.259
## 12153 1.0 -0.6 1.1661904 19.98787 19416.90 971.4344 3368.863 16834.098
## 12154 1.0 -0.4 1.0770330 20.16866 19461.48 964.9367 3461.108 17451.478
## 12155 1.0 -0.2 1.0198039 20.28959 19490.10 960.5961 3523.736 17873.788
## 12156 1.0 0.0 1.0000000 20.33237 19500.00 959.0618 3546.075 18025.028
## 12157 1.0 0.2 1.0198039 20.28959 19490.10 960.5961 3523.736 17873.788
## 12158 1.0 0.4 1.0770330 20.16866 19461.48 964.9367 3461.108 17451.478
## 12159 1.0 0.6 1.1661904 19.98787 19416.90 971.4344 3368.863 16834.098
## 12160 1.0 0.8 1.2806248 19.76823 19359.69 979.3335 3259.019 16106.259
## 12161 1.0 1.0 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 12162 1.0 1.2 1.5620499 19.27850 19218.98 996.9126 3022.757 14568.551
## 12163 1.0 1.4 1.7204651 19.02898 19139.77 1005.8220 2906.902 13828.847
## 12164 1.0 1.6 1.8867962 18.78350 19056.60 1014.5396 2795.846 13128.941
## 12165 1.0 1.8 2.0591260 18.54426 18970.44 1022.9815 2690.373 12472.744
## 12166 1.0 2.0 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 12167 1.0 2.2 2.4166092 18.08706 18791.70 1038.9580 2496.248 11287.445
## 12168 1.0 2.4 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 12169 1.0 2.6 2.7856777 17.65654 18607.16 1053.8394 2322.206 10250.534
## 12170 1.0 2.8 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 12171 1.0 3.0 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 12172 1.0 3.2 3.3526109 17.05025 18323.69 1074.6875 2091.107 8913.477
## 12173 1.0 3.4 3.5440090 16.85626 18228.00 1081.3786 2020.539 8514.682
## 12174 1.0 3.6 3.7363083 16.66547 18131.85 1087.9889 1952.704 8135.684
## 12289 1.2 -3.6 3.7947332 16.60823 18102.63 1089.9796 1932.653 8024.487
## 12290 1.2 -3.4 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 12291 1.2 -3.2 3.4176015 16.98388 18291.20 1076.9741 2066.782 8775.493
## 12292 1.2 -3.0 3.2310989 17.17585 18384.45 1070.3660 2137.661 9179.040
## 12293 1.2 -2.8 3.0463092 17.37105 18476.85 1063.6572 2211.374 9603.473
## 12294 1.2 -2.6 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 12295 1.2 -2.4 2.6832816 17.77255 18658.36 1049.8414 2368.280 10522.594
## 12296 1.2 -2.2 2.5059928 17.97947 18747.00 1042.6897 2451.964 11021.252
## 12297 1.2 -2.0 2.3323808 18.19069 18833.81 1035.3542 2539.402 11548.369
## 12298 1.2 -1.8 2.1633308 18.40603 18918.33 1027.8334 2630.658 12104.994
## 12299 1.2 -1.6 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 12300 1.2 -1.4 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 12301 1.2 -1.2 1.6970563 19.06482 19151.47 1004.5449 2923.360 13933.335
## 12302 1.2 -1.0 1.5620499 19.27850 19218.98 996.9126 3022.757 14568.551
## 12303 1.2 -0.8 1.4422205 19.47905 19278.89 989.7241 3118.081 15184.319
## 12304 1.2 -0.6 1.3416408 19.65632 19329.18 983.3569 3203.986 15744.646
## 12305 1.2 -0.4 1.2649111 19.79761 19367.54 978.2767 3273.575 16202.244
## 12306 1.2 -0.2 1.2165525 19.88957 19391.72 974.9696 3319.402 16505.369
## 12307 1.2 0.0 1.2000000 19.92159 19400.00 973.8181 3335.458 16611.903
## 12308 1.2 0.2 1.2165525 19.88957 19391.72 974.9696 3319.402 16505.369
## 12309 1.2 0.4 1.2649111 19.79761 19367.54 978.2767 3273.575 16202.244
## 12310 1.2 0.6 1.3416408 19.65632 19329.18 983.3569 3203.986 15744.646
## 12311 1.2 0.8 1.4422205 19.47905 19278.89 989.7241 3118.081 15184.319
## 12312 1.2 1.0 1.5620499 19.27850 19218.98 996.9126 3022.757 14568.551
## 12313 1.2 1.2 1.6970563 19.06482 19151.47 1004.5449 2923.360 13933.335
## 12314 1.2 1.4 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 12315 1.2 1.6 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 12316 1.2 1.8 2.1633308 18.40603 18918.33 1027.8334 2630.658 12104.994
## 12317 1.2 2.0 2.3323808 18.19069 18833.81 1035.3542 2539.402 11548.369
## 12318 1.2 2.2 2.5059928 17.97947 18747.00 1042.6897 2451.964 11021.252
## 12319 1.2 2.4 2.6832816 17.77255 18658.36 1049.8414 2368.280 10522.594
## 12320 1.2 2.6 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 12321 1.2 2.8 3.0463092 17.37105 18476.85 1063.6572 2211.374 9603.473
## 12322 1.2 3.0 3.2310989 17.17585 18384.45 1070.3660 2137.661 9179.040
## 12323 1.2 3.2 3.4176015 16.98388 18291.20 1076.9741 2066.782 8775.493
## 12324 1.2 3.4 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 12325 1.2 3.6 3.7947332 16.60823 18102.63 1089.9796 1932.653 8024.487
## 12441 1.4 -3.4 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 12442 1.4 -3.2 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 12443 1.4 -3.0 3.3105891 17.09346 18344.71 1073.2002 2107.045 9004.172
## 12444 1.4 -2.8 3.1304952 17.28146 18434.75 1066.7360 2177.333 9406.871
## 12445 1.4 -2.6 2.9529646 17.47181 18523.52 1060.1942 2250.079 9828.243
## 12446 1.4 -2.4 2.7784888 17.66461 18610.76 1053.5616 2325.391 10269.282
## 12447 1.4 -2.2 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 12448 1.4 -2.0 2.4413111 18.05709 18779.34 1039.9985 2483.859 11212.816
## 12449 1.4 -1.8 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 12450 1.4 -1.6 2.1260292 18.45500 18936.99 1026.1168 2651.709 12234.324
## 12451 1.4 -1.4 1.9798990 18.65250 19010.05 1019.1690 2737.758 12766.506
## 12452 1.4 -1.2 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 12453 1.4 -1.0 1.7204651 19.02898 19139.77 1005.8220 2906.902 13828.847
## 12454 1.4 -0.8 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 12455 1.4 -0.6 1.5231546 19.34240 19238.42 994.6242 3052.918 14762.692
## 12456 1.4 -0.4 1.4560220 19.45539 19271.99 990.5733 3106.730 15110.660
## 12457 1.4 -0.2 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 12458 1.4 0.0 1.4000000 19.55242 19300.00 987.0901 3153.445 15414.371
## 12459 1.4 0.2 1.4142136 19.52756 19292.89 987.9830 3141.431 15336.115
## 12460 1.4 0.4 1.4560220 19.45539 19271.99 990.5733 3106.730 15110.660
## 12461 1.4 0.6 1.5231546 19.34240 19238.42 994.6242 3052.918 14762.692
## 12462 1.4 0.8 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 12463 1.4 1.0 1.7204651 19.02898 19139.77 1005.8220 2906.902 13828.847
## 12464 1.4 1.2 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 12465 1.4 1.4 1.9798990 18.65250 19010.05 1019.1690 2737.758 12766.506
## 12466 1.4 1.6 2.1260292 18.45500 18936.99 1026.1168 2651.709 12234.324
## 12467 1.4 1.8 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 12468 1.4 2.0 2.4413111 18.05709 18779.34 1039.9985 2483.859 11212.816
## 12469 1.4 2.2 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 12470 1.4 2.4 2.7784888 17.66461 18610.76 1053.5616 2325.391 10269.282
## 12471 1.4 2.6 2.9529646 17.47181 18523.52 1060.1942 2250.079 9828.243
## 12472 1.4 2.8 3.1304952 17.28146 18434.75 1066.7360 2177.333 9406.871
## 12473 1.4 3.0 3.3105891 17.09346 18344.71 1073.2002 2107.045 9004.172
## 12474 1.4 3.2 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 12475 1.4 3.4 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 12592 1.6 -3.4 3.7576588 16.64452 18121.17 1088.7172 1945.348 8094.844
## 12593 1.6 -3.2 3.5777088 16.82254 18211.15 1082.5442 2008.439 8446.763
## 12594 1.6 -3.0 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 12595 1.6 -2.8 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 12596 1.6 -2.6 3.0528675 17.36403 18473.57 1063.8985 2208.693 9587.954
## 12597 1.6 -2.4 2.8844410 17.54681 18557.78 1057.6158 2279.177 9998.070
## 12598 1.6 -2.2 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 12599 1.6 -2.0 2.5612497 17.91409 18719.38 1044.9525 2425.315 10861.828
## 12600 1.6 -1.8 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 12601 1.6 -1.6 2.2627417 18.27815 18868.63 1032.3051 2576.207 11772.074
## 12602 1.6 -1.4 2.1260292 18.45500 18936.99 1026.1168 2651.709 12234.324
## 12603 1.6 -1.2 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 12604 1.6 -1.0 1.8867962 18.78350 19056.60 1014.5396 2795.846 13128.941
## 12605 1.6 -0.8 1.7888544 18.92615 19105.57 1009.4799 2860.032 13532.353
## 12606 1.6 -0.6 1.7088007 19.04680 19145.60 1005.1872 2915.076 13880.715
## 12607 1.6 -0.4 1.6492423 19.13911 19175.38 1001.8949 2957.666 14151.773
## 12608 1.6 -0.2 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 12609 1.6 0.0 1.6000000 19.21719 19200.00 999.1057 2994.010 14384.112
## 12610 1.6 0.2 1.6124515 19.19729 19193.77 999.8169 2984.720 14324.632
## 12611 1.6 0.4 1.6492423 19.13911 19175.38 1001.8949 2957.666 14151.773
## 12612 1.6 0.6 1.7088007 19.04680 19145.60 1005.1872 2915.076 13880.715
## 12613 1.6 0.8 1.7888544 18.92615 19105.57 1009.4799 2860.032 13532.353
## 12614 1.6 1.0 1.8867962 18.78350 19056.60 1014.5396 2795.846 13128.941
## 12615 1.6 1.2 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 12616 1.6 1.4 2.1260292 18.45500 18936.99 1026.1168 2651.709 12234.324
## 12617 1.6 1.6 2.2627417 18.27815 18868.63 1032.3051 2576.207 11772.074
## 12618 1.6 1.8 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 12619 1.6 2.0 2.5612497 17.91409 18719.38 1044.9525 2425.315 10861.828
## 12620 1.6 2.2 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 12621 1.6 2.4 2.8844410 17.54681 18557.78 1057.6158 2279.177 9998.070
## 12622 1.6 2.6 3.0528675 17.36403 18473.57 1063.8985 2208.693 9587.954
## 12623 1.6 2.8 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 12624 1.6 3.0 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 12625 1.6 3.2 3.5777088 16.82254 18211.15 1082.5442 2008.439 8446.763
## 12626 1.6 3.4 3.7576588 16.64452 18121.17 1088.7172 1945.348 8094.844
## 12744 1.8 -3.2 3.6715120 16.72933 18164.24 1085.7721 1975.240 8261.110
## 12745 1.8 -3.0 3.4985711 16.90192 18250.71 1079.8014 2037.003 8607.315
## 12746 1.8 -2.8 3.3286634 17.07485 18335.67 1073.8408 2100.169 8965.018
## 12747 1.8 -2.6 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 12748 1.8 -2.4 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 12749 1.8 -2.2 2.8425341 17.59312 18578.73 1056.0224 2297.273 10104.053
## 12750 1.8 -2.0 2.6907248 17.76404 18654.64 1050.1351 2364.878 10502.445
## 12751 1.8 -1.8 2.5455844 17.93254 18727.21 1044.3143 2432.816 10906.641
## 12752 1.8 -1.6 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 12753 1.8 -1.4 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 12754 1.8 -1.2 2.1633308 18.40603 18918.33 1027.8334 2630.658 12104.994
## 12755 1.8 -1.0 2.0591260 18.54426 18970.44 1022.9815 2690.373 12472.744
## 12756 1.8 -0.8 1.9697716 18.66655 19015.11 1018.6735 2743.946 12805.000
## 12757 1.8 -0.6 1.8973666 18.76841 19051.32 1015.0737 2789.113 13086.800
## 12758 1.8 -0.4 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 12759 1.8 -0.2 1.8110770 18.89333 19094.46 1010.6459 2845.175 13438.704
## 12760 1.8 0.0 1.8000000 18.90965 19100.00 1010.0661 2852.559 13485.224
## 12761 1.8 0.2 1.8110770 18.89333 19094.46 1010.6459 2845.175 13438.704
## 12762 1.8 0.4 1.8439089 18.84533 19078.05 1012.3490 2823.545 13302.655
## 12763 1.8 0.6 1.8973666 18.76841 19051.32 1015.0737 2789.113 13086.800
## 12764 1.8 0.8 1.9697716 18.66655 19015.11 1018.6735 2743.946 12805.000
## 12765 1.8 1.0 2.0591260 18.54426 18970.44 1022.9815 2690.373 12472.744
## 12766 1.8 1.2 2.1633308 18.40603 18918.33 1027.8334 2630.658 12104.994
## 12767 1.8 1.4 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 12768 1.8 1.6 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 12769 1.8 1.8 2.5455844 17.93254 18727.21 1044.3143 2432.816 10906.641
## 12770 1.8 2.0 2.6907248 17.76404 18654.64 1050.1351 2364.878 10502.445
## 12771 1.8 2.2 2.8425341 17.59312 18578.73 1056.0224 2297.273 10104.053
## 12772 1.8 2.4 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 12773 1.8 2.6 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 12774 1.8 2.8 3.3286634 17.07485 18335.67 1073.8408 2100.169 8965.018
## 12775 1.8 3.0 3.4985711 16.90192 18250.71 1079.8014 2037.003 8607.315
## 12776 1.8 3.2 3.6715120 16.72933 18164.24 1085.7721 1975.240 8261.110
## 12895 2.0 -3.2 3.7735925 16.62891 18113.20 1089.2601 1939.880 8064.520
## 12896 2.0 -3.0 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 12897 2.0 -2.8 3.4409301 16.96019 18279.53 1077.7910 2058.143 8726.622
## 12898 2.0 -2.6 3.2802439 17.12481 18359.88 1072.1215 2118.659 9070.409
## 12899 2.0 -2.4 3.1240999 17.28822 18437.95 1066.5035 2179.891 9421.611
## 12900 2.0 -2.2 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 12901 2.0 -2.0 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 12902 2.0 -1.8 2.6907248 17.76404 18654.64 1050.1351 2364.878 10502.445
## 12903 2.0 -1.6 2.5612497 17.91409 18719.38 1044.9525 2425.315 10861.828
## 12904 2.0 -1.4 2.4413111 18.05709 18779.34 1039.9985 2483.859 11212.816
## 12905 2.0 -1.2 2.3323808 18.19069 18833.81 1035.3542 2539.402 11548.369
## 12906 2.0 -1.0 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 12907 2.0 -0.8 2.1540659 18.41814 18922.97 1027.4091 2635.854 12136.883
## 12908 2.0 -0.6 2.0880613 18.50542 18955.97 1024.3466 2673.505 12368.585
## 12909 2.0 -0.4 2.0396078 18.57067 18980.20 1022.0526 2701.881 12543.930
## 12910 2.0 -0.2 2.0099751 18.61108 18995.01 1020.6295 2719.557 12653.470
## 12911 2.0 0.0 2.0000000 18.62477 19000.00 1020.1469 2725.564 12690.750
## 12912 2.0 0.2 2.0099751 18.61108 18995.01 1020.6295 2719.557 12653.470
## 12913 2.0 0.4 2.0396078 18.57067 18980.20 1022.0526 2701.881 12543.930
## 12914 2.0 0.6 2.0880613 18.50542 18955.97 1024.3466 2673.505 12368.585
## 12915 2.0 0.8 2.1540659 18.41814 18922.97 1027.4091 2635.854 12136.883
## 12916 2.0 1.0 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 12917 2.0 1.2 2.3323808 18.19069 18833.81 1035.3542 2539.402 11548.369
## 12918 2.0 1.4 2.4413111 18.05709 18779.34 1039.9985 2483.859 11212.816
## 12919 2.0 1.6 2.5612497 17.91409 18719.38 1044.9525 2425.315 10861.828
## 12920 2.0 1.8 2.6907248 17.76404 18654.64 1050.1351 2364.878 10502.445
## 12921 2.0 2.0 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 12922 2.0 2.2 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 12923 2.0 2.4 3.1240999 17.28822 18437.95 1066.5035 2179.891 9421.611
## 12924 2.0 2.6 3.2802439 17.12481 18359.88 1072.1215 2118.659 9070.409
## 12925 2.0 2.8 3.4409301 16.96019 18279.53 1077.7910 2058.143 8726.622
## 12926 2.0 3.0 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 12927 2.0 3.2 3.7735925 16.62891 18113.20 1089.2601 1939.880 8064.520
## 13047 2.2 -3.0 3.7202150 16.68129 18139.89 1087.4392 1958.272 8166.627
## 13048 2.2 -2.8 3.5608988 16.83934 18219.55 1081.9632 2014.463 8480.560
## 13049 2.2 -2.6 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 13050 2.2 -2.4 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 13051 2.2 -2.2 3.1112698 17.30182 18444.37 1066.0364 2185.037 9451.277
## 13052 2.2 -2.0 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 13053 2.2 -1.8 2.8425341 17.59312 18578.73 1056.0224 2297.273 10104.053
## 13054 2.2 -1.6 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 13055 2.2 -1.4 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 13056 2.2 -1.2 2.5059928 17.97947 18747.00 1042.6897 2451.964 11021.252
## 13057 2.2 -1.0 2.4166092 18.08706 18791.70 1038.9580 2496.248 11287.445
## 13058 2.2 -0.8 2.3409400 18.18006 18829.53 1035.7245 2534.950 11521.384
## 13059 2.2 -0.6 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 13060 2.2 -0.4 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 13061 2.2 -0.2 2.2090722 18.34673 18895.46 1029.9090 2605.313 11949.745
## 13062 2.2 0.0 2.2000000 18.35843 18900.00 1029.4998 2610.300 11980.251
## 13063 2.2 0.2 2.2090722 18.34673 18895.46 1029.9090 2605.313 11949.745
## 13064 2.2 0.4 2.2360680 18.31210 18881.97 1031.1194 2590.589 11859.785
## 13065 2.2 0.6 2.2803509 18.25588 18859.82 1033.0823 2566.800 11714.795
## 13066 2.2 0.8 2.3409400 18.18006 18829.53 1035.7245 2534.950 11521.384
## 13067 2.2 1.0 2.4166092 18.08706 18791.70 1038.9580 2496.248 11287.445
## 13068 2.2 1.2 2.5059928 17.97947 18747.00 1042.6897 2451.964 11021.252
## 13069 2.2 1.4 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 13070 2.2 1.6 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 13071 2.2 1.8 2.8425341 17.59312 18578.73 1056.0224 2297.273 10104.053
## 13072 2.2 2.0 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 13073 2.2 2.2 3.1112698 17.30182 18444.37 1066.0364 2185.037 9451.277
## 13074 2.2 2.4 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 13075 2.2 2.6 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 13076 2.2 2.8 3.5608988 16.83934 18219.55 1081.9632 2014.463 8480.560
## 13077 2.2 3.0 3.7202150 16.68129 18139.89 1087.4392 1958.272 8166.627
## 13199 2.4 -2.8 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 13200 2.4 -2.6 3.5383612 16.86192 18230.82 1081.1829 2022.576 8526.130
## 13201 2.4 -2.4 3.3941125 17.00781 18302.94 1076.1495 2075.529 8825.049
## 13202 2.4 -2.2 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 13203 2.4 -2.0 3.1240999 17.28822 18437.95 1066.5035 2179.891 9421.611
## 13204 2.4 -1.8 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 13205 2.4 -1.6 2.8844410 17.54681 18557.78 1057.6158 2279.177 9998.070
## 13206 2.4 -1.4 2.7784888 17.66461 18610.76 1053.5616 2325.391 10269.282
## 13207 2.4 -1.2 2.6832816 17.77255 18658.36 1049.8414 2368.280 10522.594
## 13208 2.4 -1.0 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 13209 2.4 -0.8 2.5298221 17.95117 18735.09 1043.6695 2440.406 10952.036
## 13210 2.4 -0.6 2.4738634 18.01787 18763.07 1041.3588 2467.711 11115.723
## 13211 2.4 -0.4 2.4331050 18.06702 18783.45 1039.6536 2487.962 11237.516
## 13212 2.4 -0.2 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 13213 2.4 0.0 2.4000000 18.10732 18800.00 1038.2543 2504.644 11338.097
## 13214 2.4 0.2 2.4083189 18.09716 18795.84 1038.6072 2500.432 11312.680
## 13215 2.4 0.4 2.4331050 18.06702 18783.45 1039.6536 2487.962 11237.516
## 13216 2.4 0.6 2.4738634 18.01787 18763.07 1041.3588 2467.711 11115.723
## 13217 2.4 0.8 2.5298221 17.95117 18735.09 1043.6695 2440.406 10952.036
## 13218 2.4 1.0 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 13219 2.4 1.2 2.6832816 17.77255 18658.36 1049.8414 2368.280 10522.594
## 13220 2.4 1.4 2.7784888 17.66461 18610.76 1053.5616 2325.391 10269.282
## 13221 2.4 1.6 2.8844410 17.54681 18557.78 1057.6158 2279.177 9998.070
## 13222 2.4 1.8 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 13223 2.4 2.0 3.1240999 17.28822 18437.95 1066.5035 2179.891 9421.611
## 13224 2.4 2.2 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 13225 2.4 2.4 3.3941125 17.00781 18302.94 1076.1495 2075.529 8825.049
## 13226 2.4 2.6 3.5383612 16.86192 18230.82 1081.1829 2022.576 8526.130
## 13227 2.4 2.8 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 13351 2.6 -2.6 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 13352 2.6 -2.4 3.5383612 16.86192 18230.82 1081.1829 2022.576 8526.130
## 13353 2.6 -2.2 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 13354 2.6 -2.0 3.2802439 17.12481 18359.88 1072.1215 2118.659 9070.409
## 13355 2.6 -1.8 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 13356 2.6 -1.6 3.0528675 17.36403 18473.57 1063.8985 2208.693 9587.954
## 13357 2.6 -1.4 2.9529646 17.47181 18523.52 1060.1942 2250.079 9828.243
## 13358 2.6 -1.2 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 13359 2.6 -1.0 2.7856777 17.65654 18607.16 1053.8394 2322.206 10250.534
## 13360 2.6 -0.8 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 13361 2.6 -0.6 2.6683328 17.78969 18665.83 1049.2501 2375.138 10563.243
## 13362 2.6 -0.4 2.6305893 17.83321 18684.71 1047.7480 2392.611 10666.981
## 13363 2.6 -0.2 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 13364 2.6 0.0 2.6000000 17.86874 18700.00 1046.5206 2406.940 10752.243
## 13365 2.6 0.2 2.6076810 17.85979 18696.16 1046.8296 2403.328 10730.732
## 13366 2.6 0.4 2.6305893 17.83321 18684.71 1047.7480 2392.611 10666.981
## 13367 2.6 0.6 2.6683328 17.78969 18665.83 1049.2501 2375.138 10563.243
## 13368 2.6 0.8 2.7202941 17.73034 18639.85 1051.2969 2351.446 10422.987
## 13369 2.6 1.0 2.7856777 17.65654 18607.16 1053.8394 2322.206 10250.534
## 13370 2.6 1.2 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 13371 2.6 1.4 2.9529646 17.47181 18523.52 1060.1942 2250.079 9828.243
## 13372 2.6 1.6 3.0528675 17.36403 18473.57 1063.8985 2208.693 9587.954
## 13373 2.6 1.8 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 13374 2.6 2.0 3.2802439 17.12481 18359.88 1072.1215 2118.659 9070.409
## 13375 2.6 2.2 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 13376 2.6 2.4 3.5383612 16.86192 18230.82 1081.1829 2022.576 8526.130
## 13377 2.6 2.6 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 13503 2.8 -2.4 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 13504 2.8 -2.2 3.5608988 16.83934 18219.55 1081.9632 2014.463 8480.560
## 13505 2.8 -2.0 3.4409301 16.96019 18279.53 1077.7910 2058.143 8726.622
## 13506 2.8 -1.8 3.3286634 17.07485 18335.67 1073.8408 2100.169 8965.018
## 13507 2.8 -1.6 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 13508 2.8 -1.4 3.1304952 17.28146 18434.75 1066.7360 2177.333 9406.871
## 13509 2.8 -1.2 3.0463092 17.37105 18476.85 1063.6572 2211.374 9603.473
## 13510 2.8 -1.0 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 13511 2.8 -0.8 2.9120440 17.51649 18543.98 1058.6583 2267.384 9929.151
## 13512 2.8 -0.6 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 13513 2.8 -0.4 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 13514 2.8 -0.2 2.8071338 17.63253 18596.43 1054.6662 2312.745 10194.884
## 13515 2.8 0.0 2.8000000 17.64050 18600.00 1054.3917 2315.883 10213.336
## 13516 2.8 0.2 2.8071338 17.63253 18596.43 1054.6662 2312.745 10194.884
## 13517 2.8 0.4 2.8284271 17.60880 18585.79 1055.4831 2303.418 10140.104
## 13518 2.8 0.6 2.8635642 17.56984 18568.22 1056.8236 2288.163 10050.662
## 13519 2.8 0.8 2.9120440 17.51649 18543.98 1058.6583 2267.384 9929.151
## 13520 2.8 1.0 2.9732137 17.44982 18513.39 1060.9501 2241.594 9778.855
## 13521 2.8 1.2 3.0463092 17.37105 18476.85 1063.6572 2211.374 9603.473
## 13522 2.8 1.4 3.1304952 17.28146 18434.75 1066.7360 2177.333 9406.871
## 13523 2.8 1.6 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 13524 2.8 1.8 3.3286634 17.07485 18335.67 1073.8408 2100.169 8965.018
## 13525 2.8 2.0 3.4409301 16.96019 18279.53 1077.7910 2058.143 8726.622
## 13526 2.8 2.2 3.5608988 16.83934 18219.55 1081.9632 2014.463 8480.560
## 13527 2.8 2.4 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 13655 3.0 -2.2 3.7202150 16.68129 18139.89 1087.4392 1958.272 8166.627
## 13656 3.0 -2.0 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 13657 3.0 -1.8 3.4985711 16.90192 18250.71 1079.8014 2037.003 8607.315
## 13658 3.0 -1.6 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 13659 3.0 -1.4 3.3105891 17.09346 18344.71 1073.2002 2107.045 9004.172
## 13660 3.0 -1.2 3.2310989 17.17585 18384.45 1070.3660 2137.661 9179.040
## 13661 3.0 -1.0 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 13662 3.0 -0.8 3.1048349 17.30864 18447.58 1065.8018 2187.625 9466.205
## 13663 3.0 -0.6 3.0594117 17.35703 18470.29 1064.1390 2206.023 9572.504
## 13664 3.0 -0.4 3.0265492 17.39225 18486.73 1062.9286 2219.481 9650.444
## 13665 3.0 -0.2 3.0066593 17.41366 18496.67 1062.1929 2227.688 9698.051
## 13666 3.0 0.0 3.0000000 17.42085 18500.00 1061.9460 2230.446 9714.064
## 13667 3.0 0.2 3.0066593 17.41366 18496.67 1062.1929 2227.688 9698.051
## 13668 3.0 0.4 3.0265492 17.39225 18486.73 1062.9286 2219.481 9650.444
## 13669 3.0 0.6 3.0594117 17.35703 18470.29 1064.1390 2206.023 9572.504
## 13670 3.0 0.8 3.1048349 17.30864 18447.58 1065.8018 2187.625 9466.205
## 13671 3.0 1.0 3.1622777 17.24793 18418.86 1067.8883 2164.685 9334.081
## 13672 3.0 1.2 3.2310989 17.17585 18384.45 1070.3660 2137.661 9179.040
## 13673 3.0 1.4 3.3105891 17.09346 18344.71 1073.2002 2107.045 9004.172
## 13674 3.0 1.6 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 13675 3.0 1.8 3.4985711 16.90192 18250.71 1079.8014 2037.003 8607.315
## 13676 3.0 2.0 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 13677 3.0 2.2 3.7202150 16.68129 18139.89 1087.4392 1958.272 8166.627
## 13807 3.2 -2.0 3.7735925 16.62891 18113.20 1089.2601 1939.880 8064.520
## 13808 3.2 -1.8 3.6715120 16.72933 18164.24 1085.7721 1975.240 8261.110
## 13809 3.2 -1.6 3.5777088 16.82254 18211.15 1082.5442 2008.439 8446.763
## 13810 3.2 -1.4 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 13811 3.2 -1.2 3.4176015 16.98388 18291.20 1076.9741 2066.782 8775.493
## 13812 3.2 -1.0 3.3526109 17.05025 18323.69 1074.6875 2091.107 8913.477
## 13813 3.2 -0.8 3.2984845 17.10595 18350.76 1072.7704 2111.667 9030.518
## 13814 3.2 -0.6 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 13815 3.2 -0.4 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 13816 3.2 -0.2 3.2062439 17.20180 18396.88 1069.4738 2147.364 9234.634
## 13817 3.2 0.0 3.2000000 17.20834 18400.00 1069.2492 2149.812 9248.670
## 13818 3.2 0.2 3.2062439 17.20180 18396.88 1069.4738 2147.364 9234.634
## 13819 3.2 0.4 3.2249031 17.18231 18387.55 1070.1439 2140.074 9192.856
## 13820 3.2 0.6 3.2557641 17.15019 18372.12 1071.2484 2128.094 9124.307
## 13821 3.2 0.8 3.2984845 17.10595 18350.76 1072.7704 2111.667 9030.518
## 13822 3.2 1.0 3.3526109 17.05025 18323.69 1074.6875 2091.107 8913.477
## 13823 3.2 1.2 3.4176015 16.98388 18291.20 1076.9741 2066.782 8775.493
## 13824 3.2 1.4 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 13825 3.2 1.6 3.5777088 16.82254 18211.15 1082.5442 2008.439 8446.763
## 13826 3.2 1.8 3.6715120 16.72933 18164.24 1085.7721 1975.240 8261.110
## 13827 3.2 2.0 3.7735925 16.62891 18113.20 1089.2601 1939.880 8064.520
## 13960 3.4 -1.6 3.7576588 16.64452 18121.17 1088.7172 1945.348 8094.844
## 13961 3.4 -1.4 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 13962 3.4 -1.2 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 13963 3.4 -1.0 3.5440090 16.85626 18228.00 1081.3786 2020.539 8514.682
## 13964 3.4 -0.8 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 13965 3.4 -0.6 3.4525353 16.94842 18273.73 1078.1967 2053.864 8702.437
## 13966 3.4 -0.4 3.4234486 16.97794 18288.28 1077.1790 2064.612 8763.212
## 13967 3.4 -0.2 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 13968 3.4 0.0 3.4000000 17.00180 18300.00 1076.3564 2073.332 8812.595
## 13969 3.4 0.2 3.4058773 16.99581 18297.06 1076.5628 2071.141 8800.184
## 13970 3.4 0.4 3.4234486 16.97794 18288.28 1077.1790 2064.612 8763.212
## 13971 3.4 0.6 3.4525353 16.94842 18273.73 1078.1967 2053.864 8702.437
## 13972 3.4 0.8 3.4928498 16.90768 18253.58 1079.6024 2039.089 8619.067
## 13973 3.4 1.0 3.5440090 16.85626 18228.00 1081.3786 2020.539 8514.682
## 13974 3.4 1.2 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 13975 3.4 1.4 3.6769553 16.72395 18161.52 1085.9587 1973.334 8250.487
## 13976 3.4 1.6 3.7576588 16.64452 18121.17 1088.7172 1945.348 8094.844
## 14113 3.6 -1.2 3.7947332 16.60823 18102.63 1089.9796 1932.653 8024.487
## 14114 3.6 -1.0 3.7363083 16.66547 18131.85 1087.9889 1952.704 8135.684
## 14115 3.6 -0.8 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 14116 3.6 -0.6 3.6496575 16.75097 18175.17 1085.0221 1982.913 8303.926
## 14117 3.6 -0.4 3.6221541 16.77826 18188.92 1084.0766 1992.622 8358.184
## 14118 3.6 -0.2 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 14119 3.6 0.0 3.6000000 16.80031 18200.00 1083.3134 2000.486 8402.197
## 14120 3.6 0.2 3.6055513 16.79478 18197.22 1083.5048 1998.512 8391.142
## 14121 3.6 0.4 3.6221541 16.77826 18188.92 1084.0766 1992.622 8358.184
## 14122 3.6 0.6 3.6496575 16.75097 18175.17 1085.0221 1982.913 8303.926
## 14123 3.6 0.8 3.6878178 16.71322 18156.09 1086.3309 1969.539 8229.335
## 14124 3.6 1.0 3.7363083 16.66547 18131.85 1087.9889 1952.704 8135.684
## 14125 3.6 1.2 3.7947332 16.60823 18102.63 1089.9796 1932.653 8024.487
## 14269 3.8 -0.2 3.8052595 16.59795 18097.37 1090.3376 1929.067 8004.640
## 14270 3.8 0.0 3.8000000 16.60309 18100.00 1090.1587 1930.858 8014.550
## 14271 3.8 0.2 3.8052595 16.59795 18097.37 1090.3376 1929.067 8004.640
## U n
## 8531 4442.099 11.32312
## 8532 4442.057 11.33550
## 8533 4442.099 11.32312
## 8677 4442.015 11.34790
## 8678 4441.536 11.48661
## 8679 4441.117 11.60332
## 8680 4440.773 11.69620
## 8681 4440.516 11.76373
## 8682 4440.358 11.80473
## 8683 4440.305 11.81847
## 8684 4440.358 11.80473
## 8685 4440.516 11.76373
## 8686 4440.773 11.69620
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## 8689 4442.015 11.34790
## 8826 4441.715 11.43568
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## 8828 4440.358 11.80473
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## 8840 4440.358 11.80473
## 8841 4441.020 11.62967
## 8842 4441.715 11.43568
## 8975 4441.845 11.39786
## 8976 4440.972 11.64290
## 8977 4440.087 11.87389
## 8978 4439.212 12.08794
## 8979 4438.372 12.28201
## 8980 4437.595 12.45300
## 8981 4436.908 12.59791
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## 8983 4435.913 12.79872
## 8984 4435.649 12.85037
## 8985 4435.559 12.86772
## 8986 4435.649 12.85037
## 8987 4435.913 12.79872
## 8988 4436.339 12.71395
## 8989 4436.908 12.59791
## 8990 4437.595 12.45300
## 8991 4438.372 12.28201
## 8992 4439.212 12.08794
## 8993 4440.087 11.87389
## 8994 4440.972 11.64290
## 8995 4441.845 11.39786
## 9125 4441.400 11.52519
## 9126 4440.358 11.80473
## 9127 4439.273 12.07335
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## 9129 4437.065 12.56530
## 9130 4435.999 12.78164
## 9131 4435.007 12.97325
## 9132 4434.125 13.13640
## 9133 4433.392 13.26758
## 9134 4432.840 13.36372
## 9135 4432.497 13.42242
## 9136 4432.381 13.44216
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## 9138 4432.840 13.36372
## 9139 4433.392 13.26758
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## 9141 4435.007 12.97325
## 9142 4435.999 12.78164
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## 9144 4438.166 12.32800
## 9145 4439.273 12.07335
## 9146 4440.358 11.80473
## 9147 4441.400 11.52519
## 9275 4441.117 11.60332
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## 9284 4429.823 13.85685
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## 9287 4428.508 14.05707
## 9288 4428.660 14.03436
## 9289 4429.106 13.96695
## 9290 4429.823 13.85685
## 9291 4430.772 13.70721
## 9292 4431.906 13.52203
## 9293 4433.174 13.30578
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## 9295 4435.913 12.79872
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## 9299 4441.117 11.60332
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## 9428 4436.668 12.64728
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## 9430 4433.283 13.28664
## 9431 4431.538 13.58290
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## 9433 4428.201 14.10283
## 9434 4426.739 14.31495
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## 9437 4423.991 14.69322
## 9438 4423.792 14.71965
## 9439 4423.991 14.69322
## 9440 4424.575 14.61488
## 9441 4425.509 14.48738
## 9442 4426.739 14.31495
## 9443 4428.201 14.10283
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## 9585 4421.905 14.96508
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## 9590 4418.314 15.40791
## 9591 4419.081 15.31563
## 9592 4420.304 15.16610
## 9593 4421.905 14.96508
## 9594 4423.792 14.71965
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## 9601 4438.097 12.34344
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## 9738 4412.433 16.07939
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## 9740 4411.071 16.22722
## 9741 4411.418 16.18978
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## 9749 4429.397 13.92257
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## 9887 4409.266 16.41942
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## 9889 4404.402 16.91893
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## 9891 4402.589 17.09912
## 9892 4403.052 17.05336
## 9893 4404.402 16.91893
## 9894 4406.527 16.70375
## 9895 4409.266 16.41942
## 9896 4412.433 16.07939
## 9897 4415.842 15.69721
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## 12771 4429.397 13.92257
## 12772 4432.381 13.44216
## 12773 4435.007 12.97325
## 12774 4437.295 12.51683
## 12775 4439.273 12.07335
## 12776 4440.972 11.64290
## 12895 4441.845 11.39786
## 12896 4440.358 11.80473
## 12897 4438.639 12.22140
## 12898 4436.668 12.64728
## 12899 4434.427 13.08135
## 12900 4431.906 13.52203
## 12901 4429.106 13.96695
## 12902 4426.047 14.41264
## 12903 4422.766 14.85428
## 12904 4419.331 15.28531
## 12905 4415.842 15.69721
## 12906 4412.433 16.07939
## 12907 4409.266 16.41942
## 12908 4406.527 16.70375
## 12909 4404.402 16.91893
## 12910 4403.052 17.05336
## 12911 4402.589 17.09912
## 12912 4403.052 17.05336
## 12913 4404.402 16.91893
## 12914 4406.527 16.70375
## 12915 4409.266 16.41942
## 12916 4412.433 16.07939
## 12917 4415.842 15.69721
## 12918 4419.331 15.28531
## 12919 4422.766 14.85428
## 12920 4426.047 14.41264
## 12921 4429.106 13.96695
## 12922 4431.906 13.52203
## 12923 4434.427 13.08135
## 12924 4436.668 12.64728
## 12925 4438.639 12.22140
## 12926 4440.358 11.80473
## 12927 4441.845 11.39786
## 13047 4441.400 11.52519
## 13048 4439.919 11.91590
## 13049 4438.236 12.31262
## 13050 4436.339 12.71395
## 13051 4434.226 13.11797
## 13052 4431.906 13.52203
## 13053 4429.397 13.92257
## 13054 4426.739 14.31495
## 13055 4423.991 14.69322
## 13056 4421.234 15.05009
## 13057 4418.572 15.37693
## 13058 4416.130 15.66409
## 13059 4414.040 15.90146
## 13060 4412.433 16.07939
## 13061 4411.418 16.18978
## 13062 4411.071 16.22722
## 13063 4411.418 16.18978
## 13064 4412.433 16.07939
## 13065 4414.040 15.90146
## 13066 4416.130 15.66409
## 13067 4418.572 15.37693
## 13068 4421.234 15.05009
## 13069 4423.991 14.69322
## 13070 4426.739 14.31495
## 13071 4429.397 13.92257
## 13072 4431.906 13.52203
## 13073 4434.226 13.11797
## 13074 4436.339 12.71395
## 13075 4438.236 12.31262
## 13076 4439.919 11.91590
## 13077 4441.400 11.52519
## 13199 4441.117 11.60332
## 13200 4439.690 11.97252
## 13201 4438.097 12.34344
## 13202 4436.339 12.71395
## 13203 4434.427 13.08135
## 13204 4432.381 13.44216
## 13205 4430.237 13.79209
## 13206 4428.044 14.12590
## 13207 4425.869 14.43741
## 13208 4423.792 14.71965
## 13209 4421.905 14.96508
## 13210 4420.304 15.16610
## 13211 4419.081 15.31563
## 13212 4418.314 15.40791
## 13213 4418.052 15.43911
## 13214 4418.314 15.40791
## 13215 4419.081 15.31563
## 13216 4420.304 15.16610
## 13217 4421.905 14.96508
## 13218 4423.792 14.71965
## 13219 4425.869 14.43741
## 13220 4428.044 14.12590
## 13221 4430.237 13.79209
## 13222 4432.381 13.44216
## 13223 4434.427 13.08135
## 13224 4436.339 12.71395
## 13225 4438.097 12.34344
## 13226 4439.690 11.97252
## 13227 4441.117 11.60332
## 13351 4441.020 11.62967
## 13352 4439.690 11.97252
## 13353 4438.236 12.31262
## 13354 4436.668 12.64728
## 13355 4435.007 12.97325
## 13356 4433.283 13.28664
## 13357 4431.538 13.58290
## 13358 4429.823 13.85685
## 13359 4428.201 14.10283
## 13360 4426.739 14.31495
## 13361 4425.509 14.48738
## 13362 4424.575 14.61488
## 13363 4423.991 14.69322
## 13364 4423.792 14.71965
## 13365 4423.991 14.69322
## 13366 4424.575 14.61488
## 13367 4425.509 14.48738
## 13368 4426.739 14.31495
## 13369 4428.201 14.10283
## 13370 4429.823 13.85685
## 13371 4431.538 13.58290
## 13372 4433.283 13.28664
## 13373 4435.007 12.97325
## 13374 4436.668 12.64728
## 13375 4438.236 12.31262
## 13376 4439.690 11.97252
## 13377 4441.020 11.62967
## 13503 4441.117 11.60332
## 13504 4439.919 11.91590
## 13505 4438.639 12.22140
## 13506 4437.295 12.51683
## 13507 4435.913 12.79872
## 13508 4434.525 13.06315
## 13509 4433.174 13.30578
## 13510 4431.906 13.52203
## 13511 4430.772 13.70721
## 13512 4429.823 13.85685
## 13513 4429.106 13.96695
## 13514 4428.660 14.03436
## 13515 4428.508 14.05707
## 13516 4428.660 14.03436
## 13517 4429.106 13.96695
## 13518 4429.823 13.85685
## 13519 4430.772 13.70721
## 13520 4431.906 13.52203
## 13521 4433.174 13.30578
## 13522 4434.525 13.06315
## 13523 4435.913 12.79872
## 13524 4437.295 12.51683
## 13525 4438.639 12.22140
## 13526 4439.919 11.91590
## 13527 4441.117 11.60332
## 13655 4441.400 11.52519
## 13656 4440.358 11.80473
## 13657 4439.273 12.07335
## 13658 4438.166 12.32800
## 13659 4437.065 12.56530
## 13660 4435.999 12.78164
## 13661 4435.007 12.97325
## 13662 4434.125 13.13640
## 13663 4433.392 13.26758
## 13664 4432.840 13.36372
## 13665 4432.497 13.42242
## 13666 4432.381 13.44216
## 13667 4432.497 13.42242
## 13668 4432.840 13.36372
## 13669 4433.392 13.26758
## 13670 4434.125 13.13640
## 13671 4435.007 12.97325
## 13672 4435.999 12.78164
## 13673 4437.065 12.56530
## 13674 4438.166 12.32800
## 13675 4439.273 12.07335
## 13676 4440.358 11.80473
## 13677 4441.400 11.52519
## 13807 4441.845 11.39786
## 13808 4440.972 11.64290
## 13809 4440.087 11.87389
## 13810 4439.212 12.08794
## 13811 4438.372 12.28201
## 13812 4437.595 12.45300
## 13813 4436.908 12.59791
## 13814 4436.339 12.71395
## 13815 4435.913 12.79872
## 13816 4435.649 12.85037
## 13817 4435.559 12.86772
## 13818 4435.649 12.85037
## 13819 4435.913 12.79872
## 13820 4436.339 12.71395
## 13821 4436.908 12.59791
## 13822 4437.595 12.45300
## 13823 4438.372 12.28201
## 13824 4439.212 12.08794
## 13825 4440.087 11.87389
## 13826 4440.972 11.64290
## 13827 4441.845 11.39786
## 13960 4441.715 11.43568
## 13961 4441.020 11.62967
## 13962 4440.358 11.80473
## 13963 4439.748 11.95830
## 13964 4439.212 12.08794
## 13965 4438.770 12.19140
## 13966 4438.440 12.26678
## 13967 4438.236 12.31262
## 13968 4438.166 12.32800
## 13969 4438.236 12.31262
## 13970 4438.440 12.26678
## 13971 4438.770 12.19140
## 13972 4439.212 12.08794
## 13973 4439.748 11.95830
## 13974 4440.358 11.80473
## 13975 4441.020 11.62967
## 13976 4441.715 11.43568
## 14113 4442.015 11.34790
## 14114 4441.536 11.48661
## 14115 4441.117 11.60332
## 14116 4440.773 11.69620
## 14117 4440.516 11.76373
## 14118 4440.358 11.80473
## 14119 4440.305 11.81847
## 14120 4440.358 11.80473
## 14121 4440.516 11.76373
## 14122 4440.773 11.69620
## 14123 4441.117 11.60332
## 14124 4441.536 11.48661
## 14125 4442.015 11.34790
## 14269 4442.099 11.32312
## 14270 4442.057 11.33550
## 14271 4442.099 11.32312nrow(dfsc1$n)## NULLsum(dfsc1$n)## [1] 17997.98NN## [1] 99500.53 84673.14 71395.90 60045.24 50182.63 41877.02 34273.63 27997.58
## [9] 22468.26 17997.98#Reseting Parameters for All Cities
V <- 4000
#housing price per sqft vector
p <- c(0:150)
#housing consumption (sqft) by mile vector
q <- c(0:150)
#general good
g <- c(0:150)
#land rent/acre
r <- c(0:150)
#Housing floor space / acre
s <- c(0:150)#City 1
#new t,y,and ad multiplication factors
t <- 1000*tm1
y <- 40000*im1
ad <- 0.16*am1
#finding x for various u,v
x <- sqrt(u^2+v^2)
#finding distance to rail
z <- sqrt((x-d)^2)
#amentiy distribution
am <- 1 + ad*(exp(-ng*z))
#finding the price for various u,v
p <- (al^al*(1-al)^(1-al)*am^gm*(y-t*x)/V)^(1/al)
#optimal q
q <- al*(y-t*x)/p
#optimal g
g <- (1-al)*(y-t*x)
#theta some funciton of beta
ph <- ((bt-1)^((bt-1)/bt))/bt
#optimal r
r <- (ph*p)^(bt/(bt-1))
r1 <- ((ph*al)^al * (1-al)^(1-al) * (y-t*x)/V)^(bt/(al*(bt-1)))
#optimal s
s <- (p/bt)^(1/(bt-1))
s1 <- (bt-1)^(-1/bt) * (r)^(1/bt)
#Utility Value
U <- q^al*g^(1-al)
#population n s(floorspaceperacre/ floorspace per household * (size of square (sqmi)) * acres/sqmi * fraction of housing in area)
n <- s/q * (.2*.2) * 640 * .25
nn <- s/q
dfscm <- data.frame(u,v,t,x,p,g,q,s,r,U,n,nn)
#delete values where ag rent exceeds land rent
dfscm1 <- dfscm[(dfscm$r > ag),]
head(dfscm1)## u v t x p g q s r
## 5812 -7.4 -0.4 1000 7.410803 16.59623 16294.60 981.8255 1928.466 8001.313
## 5813 -7.4 -0.2 1000 7.402702 16.60449 16298.65 981.5807 1931.348 8017.263
## 5814 -7.4 0.0 1000 7.400000 16.60725 16300.00 981.4991 1932.310 8022.590
## 5815 -7.4 0.2 1000 7.402702 16.60449 16298.65 981.5807 1931.348 8017.263
## 5816 -7.4 0.4 1000 7.410803 16.59623 16294.60 981.8255 1928.466 8001.313
## 5957 -7.2 -1.6 1000 7.375636 16.63212 16312.18 980.7637 1941.006 8070.760
## U n nn
## 5812 3999.807 12.57064 1.964163
## 5813 3999.805 12.59257 1.967590
## 5814 3999.804 12.59990 1.968734
## 5815 3999.805 12.59257 1.967590
## 5816 3999.807 12.57064 1.964163
## 5957 3999.800 12.66608 1.979076#Total Land Area of the City
print('Land Area')## [1] "Land Area"nrow(dfscm1)*(.2*.2)## [1] 172.68max(dfscm1$u)## [1] 7.4max(dfscm1$v)## [1] 7.4#Total Population
print('Population')## [1] "Population"round(sum(dfscm1$n),0)## [1] 99501p1<-ggplot(dfscm1, aes(x = u, y = v, color = n)) +
geom_point(size = 2, shape = 7) +
scale_color_viridis(limits = c(5,150), direction = -1) +
lims(x=c(-15,15),y=c(-15,15)) +
coord_fixed() +
theme_minimal()+
geom_vline(xintercept = 0) +
geom_hline(yintercept = 0) +
labs(title = 'City 1')#City 2
#new t,y,and ad multiplication factors
t <- 1000*tm2
y <- 40000*im2
ad <- 0.16*am2
#finding x for various u,v
x <- sqrt(u^2+v^2)
#finding distance to rail
z <- sqrt((x-d)^2)
#amentiy distribution
am <- 1 + ad*(exp(-ng*z))
#finding the price for various u,v
p <- (al^al*(1-al)^(1-al)*am^gm*(y-t*x)/V)^(1/al)
#optimal q
q <- al*(y-t*x)/p
#optimal g
g <- (1-al)*(y-t*x)
#theta some funciton of beta
ph <- ((bt-1)^((bt-1)/bt))/bt
#optimal r
r <- (ph*p)^(bt/(bt-1))
r1 <- ((ph*al)^al * (1-al)^(1-al) * (y-t*x)/V)^(bt/(al*(bt-1)))
#optimal s
s <- (p/bt)^(1/(bt-1))
s1 <- (bt-1)^(-1/bt) * (r)^(1/bt)
#Utility Value
U <- q^al*g^(1-al)
#population n s(floorspaceperacre/ floorspace per household * (size of square (sqmi)) * acres/sqmi * fraction of housing in area)
n <- s/q * (.2*.2) * 640 * .25
nn <- s/q
dfscm <- data.frame(u,v,t,x,p,g,q,s,r,U,n,nn)
#delete values where ag rent exceeds land rent
dfscm2 <- dfscm[(dfscm$r > ag),]
head(dfscm2)## u v t x p g q s r
## 5812 -7.4 -0.4 1000 7.410803 16.59623 16294.60 981.8255 1928.466 8001.313
## 5813 -7.4 -0.2 1000 7.402702 16.60449 16298.65 981.5807 1931.348 8017.263
## 5814 -7.4 0.0 1000 7.400000 16.60725 16300.00 981.4991 1932.310 8022.590
## 5815 -7.4 0.2 1000 7.402702 16.60449 16298.65 981.5807 1931.348 8017.263
## 5816 -7.4 0.4 1000 7.410803 16.59623 16294.60 981.8255 1928.466 8001.313
## 5957 -7.2 -1.6 1000 7.375636 16.63212 16312.18 980.7637 1941.006 8070.760
## U n nn
## 5812 3999.807 12.57064 1.964163
## 5813 3999.805 12.59257 1.967590
## 5814 3999.804 12.59990 1.968734
## 5815 3999.805 12.59257 1.967590
## 5816 3999.807 12.57064 1.964163
## 5957 3999.800 12.66608 1.979076#Total Land Area of the City
print('Land Area')## [1] "Land Area"nrow(dfscm2)*(.2*.2)## [1] 172.68max(dfscm2$u)## [1] 7.4max(dfscm2$v)## [1] 7.4#Total Population
print('Population')## [1] "Population"round(sum(dfscm2$n),0)## [1] 99501p2<-ggplot(dfscm2, aes(x = u, y = v, color = n)) +
geom_point(size = 2, shape = 7) +
scale_color_viridis(limits = c(5,150), direction = -1) +
lims(x=c(-15,15),y=c(-15,15)) +
coord_fixed() +
theme_minimal()+
geom_vline(xintercept = 0) +
geom_hline(yintercept = 0) +
labs(title = 'City 2')#City 3
#new t,y,and ad multiplication factors
t <- 1000*tm3
y <- 40000*im3
ad <- 0.16*am3
#finding x for various u,v
x <- sqrt(u^2+v^2)
#finding distance to rail
z <- sqrt((x-d)^2)
#amentiy distribution
am <- 1 + ad*(exp(-ng*z))
#finding the price for various u,v
p <- (al^al*(1-al)^(1-al)*am^gm*(y-t*x)/V)^(1/al)
#optimal q
q <- al*(y-t*x)/p
#optimal g
g <- (1-al)*(y-t*x)
#theta some funciton of beta
ph <- ((bt-1)^((bt-1)/bt))/bt
#optimal r
r <- (ph*p)^(bt/(bt-1))
r1 <- ((ph*al)^al * (1-al)^(1-al) * (y-t*x)/V)^(bt/(al*(bt-1)))
#optimal s
s <- (p/bt)^(1/(bt-1))
s1 <- (bt-1)^(-1/bt) * (r)^(1/bt)
#Utility Value
U <- q^al*g^(1-al)
#population n s(floorspaceperacre/ floorspace per household * (size of square (sqmi)) * acres/sqmi * fraction of housing in area)
n <- s/q * (.2*.2) * 640 * .25
nn <- s/q
dfscm <- data.frame(u,v,t,x,p,g,q,s,r,U,n,nn)
#delete values where ag rent exceeds land rent
dfscm3 <- dfscm[(dfscm$r > ag),]
head(dfscm3)## u v t x p g q s r
## 5812 -7.4 -0.4 1000 7.410803 16.59623 16294.60 981.8255 1928.466 8001.313
## 5813 -7.4 -0.2 1000 7.402702 16.60449 16298.65 981.5807 1931.348 8017.263
## 5814 -7.4 0.0 1000 7.400000 16.60725 16300.00 981.4991 1932.310 8022.590
## 5815 -7.4 0.2 1000 7.402702 16.60449 16298.65 981.5807 1931.348 8017.263
## 5816 -7.4 0.4 1000 7.410803 16.59623 16294.60 981.8255 1928.466 8001.313
## 5957 -7.2 -1.6 1000 7.375636 16.63212 16312.18 980.7637 1941.006 8070.760
## U n nn
## 5812 3999.807 12.57064 1.964163
## 5813 3999.805 12.59257 1.967590
## 5814 3999.804 12.59990 1.968734
## 5815 3999.805 12.59257 1.967590
## 5816 3999.807 12.57064 1.964163
## 5957 3999.800 12.66608 1.979076#Total Land Area of the City
print('Land Area')## [1] "Land Area"nrow(dfscm3)*(.2*.2)## [1] 172.68max(dfscm3$u)## [1] 7.4max(dfscm3$v)## [1] 7.4#Total Population
print('Population')## [1] "Population"round(sum(dfscm3$n),0)## [1] 99501p3 <- ggplot(dfscm3, aes(x = u, y = v, color = n)) +
geom_point(size = 2, shape = 7) +
scale_color_viridis(limits = c(5,150), direction = -1) +
lims(x=c(-15,15),y=c(-15,15)) +
coord_fixed() +
theme_minimal()+
geom_vline(xintercept = 0) +
geom_hline(yintercept = 0) +
labs(title = 'City 3')#City 4
#new t,y,and ad multiplication factors
t <- 1000*tm4
y <- 40000*im4
ad <- 0.16*am4
#finding x for various u,v
x <- sqrt(u^2+v^2)
#finding distance to rail
z <- sqrt((x-d)^2)
#amentiy distribution
am <- 1 + ad*(exp(-ng*z))
#finding the price for various u,v
p <- (al^al*(1-al)^(1-al)*am^gm*(y-t*x)/V)^(1/al)
#optimal q
q <- al*(y-t*x)/p
#optimal g
g <- (1-al)*(y-t*x)
#theta some funciton of beta
ph <- ((bt-1)^((bt-1)/bt))/bt
#optimal r
r <- (ph*p)^(bt/(bt-1))
r1 <- ((ph*al)^al * (1-al)^(1-al) * (y-t*x)/V)^(bt/(al*(bt-1)))
#optimal s
s <- (p/bt)^(1/(bt-1))
s1 <- (bt-1)^(-1/bt) * (r)^(1/bt)
#Utility Value
U <- q^al*g^(1-al)
#population n s(floorspaceperacre/ floorspace per household * (size of square (sqmi)) * acres/sqmi * fraction of housing in area)
n <- s/q * (.2*.2) * 640 * .25
nn <- s/q
dfscm <- data.frame(u,v,t,x,p,g,q,s,r,U,n,nn)
#delete values where ag rent exceeds land rent
dfscm4 <- dfscm[(dfscm$r > ag),]
head(dfscm4)## u v t x p g q s r
## 5812 -7.4 -0.4 1000 7.410803 16.59623 16294.60 981.8255 1928.466 8001.313
## 5813 -7.4 -0.2 1000 7.402702 16.60449 16298.65 981.5807 1931.348 8017.263
## 5814 -7.4 0.0 1000 7.400000 16.60725 16300.00 981.4991 1932.310 8022.590
## 5815 -7.4 0.2 1000 7.402702 16.60449 16298.65 981.5807 1931.348 8017.263
## 5816 -7.4 0.4 1000 7.410803 16.59623 16294.60 981.8255 1928.466 8001.313
## 5957 -7.2 -1.6 1000 7.375636 16.63212 16312.18 980.7637 1941.006 8070.760
## U n nn
## 5812 3999.807 12.57064 1.964163
## 5813 3999.805 12.59257 1.967590
## 5814 3999.804 12.59990 1.968734
## 5815 3999.805 12.59257 1.967590
## 5816 3999.807 12.57064 1.964163
## 5957 3999.800 12.66608 1.979076#Total Land Area of the City
print('Land Area')## [1] "Land Area"nrow(dfscm4)*(.2*.2)## [1] 172.68max(dfscm4$u)## [1] 7.4max(dfscm4$v)## [1] 7.4#Total Population
print('Population')## [1] "Population"round(sum(dfscm4$n),0)## [1] 99501p4 <- ggplot(dfscm4, aes(x = u, y = v, color = n)) +
geom_point(size = 2, shape = 7) +
scale_color_viridis(limits = c(5,150), direction = -1) +
lims(x=c(-15,15),y=c(-15,15)) +
coord_fixed() +
theme_minimal()+
geom_vline(xintercept = 0) +
geom_hline(yintercept = 0) +
labs(title = 'City 4')# Displaying all graphs and Saving All Graphs
#Population Density Across Urban Areas
pop_den <- grid.arrange(p1,p2,p3,p4, ncol=2, nrow = 2)
#Land and Population Table
lnda <- c(nrow(dfscm1)*(0.2*0.2),nrow(dfscm2)*(0.2*0.2),nrow(dfscm3)*(0.2*0.2),nrow(dfscm4)*(0.2*0.2))
popg <- c(sum(dfscm1$n),sum(dfscm2$n),sum(dfscm3$n),sum(dfscm4$n))
lap <- data.frame(Land_Area = lnda, Population = round(popg), Population_Density = round(popg/lnda))
rownames(lap) <- c('City 1', 'City 2', 'City 3', 'City 4')
lap## Land_Area Population Population_Density
## City 1 172.68 99501 576
## City 2 172.68 99501 576
## City 3 172.68 99501 576
## City 4 172.68 99501 576# Multiplier Table
mtable <- data.frame(Income_Multiplier = c(im1, im2, im3, im4), Traffic_Multiplier = c(tm1, tm2, tm3, tm4), Amenity_Multiplier = c(am1, am2, am3, am4) )
rownames(mtable) <- c('City 1', 'City 2', 'City 3', 'City 4')
mtable## Income_Multiplier Traffic_Multiplier Amenity_Multiplier
## City 1 1 1 1
## City 2 1 1 1
## City 3 1 1 1
## City 4 1 1 1#Saving files as Pdfs
# pdf("land_pop.pdf", height =2, width = 8.5)
# grid.table(lap)
# dev.off()
# ggsave(filename = "pop_den.pdf", pop_den)Add a new chunk by clicking the Insert Chunk button on the toolbar or by pressing Ctrl+Alt+I.
When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the Preview button or press Ctrl+Shift+K to preview the HTML file).
The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike Knit, Preview does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.
Erick Jones
PhD Candidate
Erick Jones is a Ph.D. candidate in Operations Research and Industrial Engineering who develops multi-systems optimization models to analyze how energy systems, water resources, supply chains, urban space, and transportation networks operate in concert to influence economic and environmental well-being.