SECTION 8 STARTS HERE:

library(haven)
library(dplyr)
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library(ggplot2)
library(psych)
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## Attaching package: 'psych'
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##     %+%, alpha
library(knitr)
library(stats)
library(lm.beta)
#install.packages("lavaan")
library(lavaan)
## This is lavaan 0.6-14
## lavaan is FREE software! Please report any bugs.
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## Attaching package: 'lavaan'
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#install.packages("semTools")
library(semTools)
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## ###############################################################################
## This is semTools 0.5-6
## All users of R (or SEM) are invited to submit functions or ideas for functions.
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 8-0 LOAD DATA

here we are using a new dataset from R. mtcar!

dfmtcars <- data.frame(mtcars)

Define the variables in the model. For this example, we will use the variables “mpg”, “wt”, and “qsec” from the mtcars dataset. “mpg” will be the dependent variable, “qsec” will be the mediator variable, and “mpg” will be the dependent variable.

In the “mtcars” dataset, “mpg” represents the number of miles per gallon of fuel consumed by the car. This variable is often used as a measure of fuel efficiency, with higher values indicating better fuel economy. “wt” represents the weight of the car in thousands of pounds. This variable can be used to explore the relationship between a car’s weight and other variables such as fuel efficiency, acceleration time, and engine characteristics. “qsec” is a variable that represents the time taken by a car to accelerate from 0 to 60 miles per hour (in seconds).

8-1 : TOTAL EFFECT

In the subsequent models, we are trying to find the causes of qsec (i.e., accelaretion of the car)

P8-1: What is the total effect of wt on mpg? report b and R-squared and interpret them in plain English.

# Calculate the total effect of mpg on qsec

model_01 <- lm (dfmtcars$mpg ~ dfmtcars$wt)
model_01
## 
## Call:
## lm(formula = dfmtcars$mpg ~ dfmtcars$wt)
## 
## Coefficients:
## (Intercept)  dfmtcars$wt  
##      37.285       -5.344
#-5.34 = direct effect more weight means less 

model_02 <- lm (dfmtcars$mpg ~ dfmtcars$wt +dfmtcars$qsec)
model_02
## 
## Call:
## lm(formula = dfmtcars$mpg ~ dfmtcars$wt + dfmtcars$qsec)
## 
## Coefficients:
##   (Intercept)    dfmtcars$wt  dfmtcars$qsec  
##       19.7462        -5.0480         0.9292
#-5.04 = direct effect more weight means less - the product if .319 and .929 is the indirect

model_03 <- lm (dfmtcars$qsec ~dfmtcars$wt)
model_03
## 
## Call:
## lm(formula = dfmtcars$qsec ~ dfmtcars$wt)
## 
## Coefficients:
## (Intercept)  dfmtcars$wt  
##     18.8753      -0.3191
total_effect <- coef(model_01)["dfmtcars$wt"]
  8-2 MEDIATION EFFECT

P8-2: Now add weight (“qsec”) as the mediator. a. what is the direct effect (wt –> mpg)? # the direct direct effect (wt –> mpg) was 5.34 b. what is the indirect effect (wt –> qsec –> mpg)? .319 and .929
c. what is the sum of direct effect and indirect effect? is it equal to total effect obtained in P8-1? its different d. test whether or not the indirect effect is significant. do this in two ways: the Soble test and bootstrapping (mediate() method) *e. interpret your results in plain English and describe if weight is

# Create a model with "qsec" as a mediator
model <- lm(dfmtcars$mpg ~ dfmtcars$wt +dfmtcars$qsec)
summary(model)
## 
## Call:
## lm(formula = dfmtcars$mpg ~ dfmtcars$wt + dfmtcars$qsec)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.3962 -2.1431 -0.2129  1.4915  5.7486 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    19.7462     5.2521   3.760 0.000765 ***
## dfmtcars$wt    -5.0480     0.4840 -10.430 2.52e-11 ***
## dfmtcars$qsec   0.9292     0.2650   3.506 0.001500 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.596 on 29 degrees of freedom
## Multiple R-squared:  0.8264, Adjusted R-squared:  0.8144 
## F-statistic: 69.03 on 2 and 29 DF,  p-value: 9.395e-12
# Calculate the direct effect of "wt" on "mpg"
direct_effect <- coef(model)["dfmtcars$wt"]
direct_effect # View the direct effect
## dfmtcars$wt 
##   -5.047982
model_m <- lm(dfmtcars$qsec~ dfmtcars$wt)
summary(model_m) # View the model summary
## 
## Call:
## lm(formula = dfmtcars$qsec ~ dfmtcars$wt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3638 -1.0766  0.2051  0.8655  5.0298 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  18.8753     1.1025  17.120   <2e-16 ***
## dfmtcars$wt  -0.3191     0.3283  -0.972    0.339    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.789 on 30 degrees of freedom
## Multiple R-squared:  0.03053,    Adjusted R-squared:  -0.00179 
## F-statistic: 0.9446 on 1 and 30 DF,  p-value: 0.3389
wt_qsec <- coef(model_m)["dfmtcars$wt"]
wt_qsec
## dfmtcars$wt 
##  -0.3190812
qsec_mpg <- coef(model_02)["dfmtcars$qsec"]
qsec_mpg
## dfmtcars$qsec 
##      0.929198
indirect_effect <- wt_qsec*qsec_mpg
indirect_effect
## dfmtcars$wt 
##  -0.2964896
direct_effect+indirect_effect
## dfmtcars$wt 
##   -5.344472
se_qsec <- summary(model)$coef["dfmtcars$qsec",2] #refers to the standard error of "qsec".
se_wt <- summary(model_m)$coef["dfmtcars$wt",2] #refers to the standard error of "wt".
se_indirect <- sqrt((se_wt^2)*(qsec_mpg^2) + (se_qsec^2)*(wt_qsec^2)) #use Sobel test formula
se_indirect
## dfmtcars$qsec 
##     0.3165629
t_val <- indirect_effect/se_indirect
degreef <-  nrow(mtcars) - 3
p_val <- 2*pt(-abs(t_val), df = degreef)
p_val
## dfmtcars$wt 
##   0.3567043

#we can also find the standard error of indirect effect by bootstrapping

x1 <- rnorm(n=10000, mean=wt_qsec,sd=se_wt)
x2 <- rnorm(n=10000, mean=qsec_mpg,sd=se_qsec)
x3 <- x1*x2
sd(x3)
## [1] 0.3277215
percentile <- round(sum(x3 >= 0) / length(x3), 2)
p <- 2*percentile
p
## [1] 0.34
x3
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##   [756] -6.178916e-01 -4.518930e-01 -2.592849e-01 -6.746151e-02 -4.172589e-01
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##   [766] -1.757314e-01 -1.741612e-01 -2.607219e-01 -3.378050e-01  6.930504e-01
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##   [776] -8.554261e-01 -1.110891e-01 -2.589212e-01 -1.201118e-01 -6.690512e-01
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##   [816] -4.613719e-01 -9.797767e-01 -7.717493e-02 -2.673463e-01 -2.329677e-01
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##   [861] -8.042691e-01 -5.012269e-01  7.711958e-02 -1.564253e-01 -4.650554e-01
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##   [871] -3.706772e-01 -9.658974e-02 -2.828383e-01 -6.686547e-01  9.327177e-02
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##  [1336] -1.082816e-01  3.774255e-02 -4.623876e-01  2.769822e-02  5.165588e-02
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##  [1356]  2.099506e-01 -7.049817e-02 -4.969066e-01 -2.031283e-01 -1.006572e+00
##  [1361] -8.222031e-01 -5.533430e-01 -3.643271e-01 -1.078588e+00 -3.530092e-01
##  [1366] -8.921157e-02 -9.450398e-01 -9.721680e-02 -1.161097e-01  2.224148e-01
##  [1371] -3.553952e-01 -9.299570e-03 -5.006793e-01 -9.800213e-01 -5.390516e-01
##  [1376] -2.809311e-02 -3.271751e-01 -3.837317e-01 -1.046562e+00 -2.227553e-04
##  [1381] -4.911485e-01 -3.177771e-01 -2.558063e-01 -1.330864e-01 -1.244013e-01
##  [1386] -9.806889e-02  3.515104e-01 -3.891381e-01 -5.984940e-02 -2.697926e-01
##  [1391] -4.441903e-01 -3.528136e-01 -2.422325e-01 -1.514364e-01 -2.292953e-01
##  [1396] -5.018005e-01 -2.498976e-01 -3.670006e-01 -9.027424e-02 -4.765209e-01
##  [1401] -7.928859e-01 -3.656212e-01 -1.035477e-02 -4.354254e-01 -1.948942e-01
##  [1406] -5.383266e-03 -2.151396e-01 -4.537152e-01 -7.915037e-02  1.473396e-03
##  [1411] -5.515468e-01  1.572742e-01 -5.379907e-01 -8.100904e-01  3.909894e-02
##  [1416]  8.831290e-02  1.080039e-01 -1.248523e-01 -7.065855e-01 -1.798326e-01
##  [1421] -4.191879e-01 -3.774385e-02 -2.827768e-01 -5.227601e-01 -1.095442e+00
##  [1426] -2.229234e-01 -2.748386e-01 -8.225882e-01 -4.105205e-01 -6.858525e-01
##  [1431]  9.181580e-02 -1.997028e-01 -3.157660e-01 -1.021356e+00 -2.830550e-01
##  [1436] -5.202425e-01 -4.804548e-02 -3.765247e-01 -5.351282e-01  1.392503e-01
##  [1441] -4.949407e-01 -3.481338e-01 -4.197572e-01 -2.518874e-01 -4.563178e-01
##  [1446] -8.382440e-03  5.332646e-01 -6.934957e-01 -4.125589e-01 -5.101391e-01
##  [1451] -1.476599e-01  9.726189e-02 -1.271544e-01 -3.246293e-01  2.731214e-02
##  [1456] -3.887435e-01  5.915192e-02  1.143150e-01 -8.672225e-02  1.454571e-01
##  [1461] -3.069567e-01 -7.264625e-02 -7.856511e-02 -5.477450e-01 -8.121542e-02
##  [1466] -7.471198e-01 -4.748371e-01 -1.723021e-01 -5.151876e-01 -2.980225e-02
##  [1471] -6.921248e-02  1.476785e-01  3.579352e-01 -4.772116e-01 -1.743492e-01
##  [1476] -6.150425e-01 -4.822494e-01 -6.082560e-01 -6.205020e-01 -2.779414e-01
##  [1481] -4.048540e-01 -3.253638e-01 -3.431586e-01 -3.976678e-01  2.672880e-01
##  [1486] -4.417154e-01 -2.113079e-01 -1.193497e-01 -5.296570e-01 -9.719979e-01
##  [1491] -4.789066e-01 -2.613978e-01 -9.141915e-01 -6.156955e-01 -9.611646e-01
##  [1496] -5.701205e-01  4.133882e-02 -8.302029e-01 -2.844201e-01 -6.920976e-02
##  [1501] -3.289498e-01 -3.564745e-01 -4.253264e-04 -3.427384e-01 -1.363711e-01
##  [1506] -1.255169e+00 -3.132921e-01 -2.815840e-01 -4.431984e-01 -1.290680e-01
##  [1511] -6.469961e-01 -2.569980e-01  2.468355e-01 -5.968200e-01 -3.114517e-01
##  [1516]  1.866433e-01 -1.367672e-01 -1.398416e-01 -4.150768e-01 -5.230371e-01
##  [1521] -7.862754e-01 -1.152239e-01 -8.930442e-01  2.807925e-02 -4.309265e-01
##  [1526] -6.620130e-01 -7.392669e-01 -2.019263e-01 -8.096321e-01  1.093016e-01
##  [1531] -1.923211e-01 -2.253444e-01 -4.122933e-01  1.742989e-01 -7.694660e-01
##  [1536] -3.959373e-01 -3.999299e-01 -5.709079e-01 -1.608392e-02 -2.602349e-01
##  [1541]  2.234353e-02  2.851637e-02 -5.710683e-01 -8.370242e-01 -2.573919e-01
##  [1546] -1.938483e-01  6.392282e-02 -4.938296e-01 -2.908563e-01 -9.447963e-02
##  [1551] -1.590330e-01 -1.558987e-01 -1.279208e+00  2.630351e-01  7.485473e-02
##  [1556] -5.250536e-01 -8.621224e-01 -3.477118e-01 -2.023119e-01 -3.959627e-01
##  [1561] -1.726917e-01  1.144387e-01 -5.655732e-01 -6.147159e-01 -5.402637e-02
##  [1566] -4.301421e-01 -3.689288e-01  2.028302e-01 -1.717221e-01  8.150150e-02
##  [1571]  2.219780e-01 -7.225965e-01 -2.151979e-01 -2.137579e-01 -6.089829e-01
##  [1576] -3.272563e-01 -3.021542e-01 -2.360450e-01 -9.616199e-01 -3.153961e-01
##  [1581] -2.939604e-01 -3.047498e-02 -5.174223e-01 -3.145185e-01 -3.876147e-01
##  [1586] -3.938897e-01 -8.012253e-01  1.928019e-01 -7.339956e-01 -1.839369e-01
##  [1591] -8.014663e-01 -4.033134e-01 -1.429808e-01 -2.173378e-01 -2.965091e-02
##  [1596]  4.934238e-03 -2.815044e-01  3.869729e-01 -9.410409e-01 -5.022081e-02
##  [1601] -2.106108e-01 -3.265321e-01 -2.352675e-01 -1.306954e-01 -2.160340e-01
##  [1606] -5.114365e-01 -1.089973e-01 -1.248540e-01 -5.372217e-01 -4.164056e-01
##  [1611] -5.495969e-01 -1.381246e-01 -1.524629e-01 -4.379060e-01 -5.646486e-01
##  [1616] -4.413333e-01  1.867857e-01 -1.702530e-01 -3.358096e-01 -5.961447e-01
##  [1621] -8.625471e-01 -1.906143e-01 -8.721142e-02 -2.279371e-01 -5.545996e-01
##  [1626] -5.005666e-01 -2.260392e-01 -2.045486e-01 -2.280254e-01  2.074237e-01
##  [1631] -3.497386e-01 -1.911161e-01 -3.924886e-01 -9.242843e-02 -5.091566e-01
##  [1636] -3.367795e-01 -5.810168e-01 -1.986834e-01 -6.951997e-01 -5.516465e-01
##  [1641] -5.065748e-02 -3.411890e-02 -2.893449e-01 -3.710237e-01 -9.639098e-01
##  [1646] -2.939283e-01 -3.179734e-01 -8.576358e-02  3.452740e-01 -7.416053e-01
##  [1651] -6.829540e-02 -7.218679e-02 -6.330313e-01 -6.705038e-01 -5.954627e-01
##  [1656] -3.068689e-01 -4.993420e-01 -5.274137e-01 -2.139746e-01 -1.755124e-01
##  [1661] -1.777456e-01 -1.783577e-01 -6.127709e-01 -5.696553e-01 -9.419504e-02
##  [1666] -2.226368e-01 -4.959819e-01 -1.016726e-01 -3.468894e-01 -1.074274e-01
##  [1671] -9.547588e-01 -1.942271e-01 -7.175599e-01 -4.830851e-01 -5.241507e-01
##  [1676]  1.978569e-01 -5.666269e-01  2.283641e-01  1.145288e-01 -2.833628e-02
##  [1681] -4.187870e-01  3.074706e-01 -6.570870e-02  2.181637e-01 -6.974501e-01
##  [1686] -6.466891e-01 -5.647009e-01  5.914402e-02 -4.156378e-01 -5.133937e-01
##  [1691] -7.799864e-01  1.058029e-01 -2.765983e-01 -7.275374e-01 -5.162015e-01
##  [1696] -1.236212e+00  6.292353e-02 -4.945139e-01  5.453942e-02 -3.257955e-02
##  [1701]  3.998447e-01 -4.531654e-01 -1.289049e-01 -4.084921e-01 -6.955948e-01
##  [1706] -5.501611e-01 -4.856419e-01 -6.345154e-02 -7.137118e-01 -1.413555e-01
##  [1711] -4.925471e-01  2.688367e-01 -2.334846e-01 -6.277745e-01  3.129023e-01
##  [1716]  1.003670e-02 -3.687810e-01 -2.704747e-01 -5.512722e-01 -7.040029e-02
##  [1721] -2.779882e-01 -8.194628e-01  1.313322e-01  7.436594e-02 -2.071092e-01
##  [1726] -3.797344e-01 -3.689920e-01 -2.856604e-01  1.957759e-01 -2.628173e-01
##  [1731] -3.376506e-01 -2.740304e-01 -3.168345e-01 -1.168030e-01 -1.072928e+00
##  [1736] -9.504247e-02 -8.275434e-01 -9.047122e-01 -4.672897e-01 -5.636672e-01
##  [1741] -9.861882e-01  9.909906e-02 -9.937494e-01 -4.898618e-01 -2.818467e-01
##  [1746] -4.128463e-01 -1.491328e-01 -1.499985e-01 -6.402788e-01 -3.817868e-01
##  [1751] -4.620145e-01 -7.307792e-01 -3.744548e-02 -1.406682e-01 -4.728182e-01
##  [1756] -4.412440e-02 -7.328641e-01 -2.375644e-01 -8.525085e-02  8.972712e-02
##  [1761] -1.644021e-01 -4.907561e-01 -3.592888e-01 -3.571242e-01 -3.968884e-01
##  [1766] -2.004024e-02 -1.712156e-01 -5.332181e-01 -7.393933e-01 -5.749890e-01
##  [1771] -7.450622e-01 -3.423927e-01 -1.497674e-01 -6.629397e-01 -1.142901e-01
##  [1776]  1.100214e-02  1.860315e-01 -4.878722e-01  1.059692e-01 -2.750085e-01
##  [1781]  2.095574e-01 -7.028057e-01 -2.873174e-01 -4.877726e-03 -3.045501e-01
##  [1786] -1.689219e-01 -2.579855e-01 -1.626917e-01 -1.390228e-01 -3.200770e-01
##  [1791] -2.118896e-01 -2.692353e-01 -1.087035e-01 -3.603596e-01 -1.186719e-01
##  [1796] -3.696348e-01 -1.284436e-01 -6.053934e-01 -5.294883e-01 -8.195194e-02
##  [1801] -4.622574e-02 -2.043061e-01 -6.570933e-01 -1.065276e-01 -2.721287e-01
##  [1806] -3.814743e-01 -2.740856e-01 -4.468139e-02 -6.709098e-01 -2.410931e-01
##  [1811] -5.667877e-02  1.890652e-01 -8.914874e-01 -6.469211e-01 -6.749904e-01
##  [1816] -1.638168e-01 -3.548018e-01 -8.073434e-02 -4.703908e-01 -1.447758e-01
##  [1821] -6.425364e-01 -5.378105e-01 -6.370740e-01 -3.388040e-02 -6.952349e-01
##  [1826] -5.502167e-01 -6.380393e-01 -2.504701e-01 -5.716639e-02 -8.790970e-02
##  [1831] -5.759046e-01 -6.089080e-02 -2.335606e-01 -2.288659e-01 -9.754203e-02
##  [1836]  1.228923e-01 -6.897858e-01 -1.639375e-01  2.466527e-01 -6.490725e-02
##  [1841] -1.625872e+00  2.404928e-01  2.189881e-01  1.322749e-01 -2.190449e-01
##  [1846] -2.530613e-01 -6.077019e-01 -1.192337e+00  7.838607e-03 -1.569197e-01
##  [1851] -3.207544e-01 -4.030357e-01 -1.145894e-01 -3.520869e-02 -4.526671e-01
##  [1856] -3.025245e-02 -5.807798e-01 -2.032581e-02 -4.723605e-01 -3.575737e-01
##  [1861] -5.354426e-01 -1.270363e+00 -1.688225e-01 -3.048044e-01 -2.996493e-01
##  [1866] -5.122860e-01 -1.273222e-01 -4.556967e-01 -7.158324e-02 -1.527639e+00
##  [1871] -1.418383e-01 -5.492143e-01 -8.680942e-01 -7.748457e-01  1.560588e-01
##  [1876] -9.166118e-02 -7.783790e-02 -3.853910e-01 -1.795597e-01 -9.260507e-02
##  [1881] -2.818624e-01  4.794031e-02 -5.682730e-01 -3.946163e-01 -1.043812e+00
##  [1886] -3.672624e-01 -3.651680e-01 -2.350265e-01 -5.233322e-01 -3.917495e-01
##  [1891] -1.372980e-01 -8.056672e-02 -9.217485e-02  9.518311e-02 -3.070799e-01
##  [1896] -2.833428e-01 -2.170051e-01 -6.676498e-01 -1.126890e-01  8.630520e-02
##  [1901] -2.224684e-01 -6.138489e-01 -2.229311e-01 -1.849921e-01  3.692128e-01
##  [1906]  1.506969e-01 -1.891266e-01  9.173470e-02 -6.707310e-01  7.839638e-02
##  [1911] -6.393351e-01  4.744564e-02 -1.100679e+00 -6.656670e-01 -7.613695e-01
##  [1916] -4.546227e-01 -1.020983e+00 -3.731644e-02 -6.122435e-01 -1.867107e-01
##  [1921] -5.210024e-02  1.995240e-01 -9.439287e-02 -3.621601e-02 -1.939174e-01
##  [1926] -1.482124e-01 -1.565722e-01 -3.399150e-01 -6.457195e-01  1.315593e-01
##  [1931] -2.034740e-01 -7.575397e-02 -1.043292e-01  1.516723e-02 -7.507300e-01
##  [1936] -6.717642e-03 -5.538574e-01 -6.945679e-01 -2.495742e-01 -1.140825e-01
##  [1941]  1.933052e-01 -3.108624e-01 -1.105496e+00 -2.869005e-01 -6.402404e-01
##  [1946] -2.715838e-01 -2.547738e-01 -2.304893e-01 -2.968163e-01 -2.331669e-01
##  [1951] -3.052645e-01 -6.677401e-02  1.504009e-01 -1.190988e+00 -1.289082e+00
##  [1956] -1.099167e+00  3.570904e-01 -4.555963e-01 -3.830375e-01 -4.776906e-01
##  [1961]  9.599575e-02  2.776941e-01 -2.719671e-01 -1.666223e-02 -5.764747e-01
##  [1966] -4.501609e-02 -4.931222e-02 -4.631622e-01  1.708812e-01 -2.663249e-01
##  [1971] -5.319014e-02 -3.287489e-02 -1.756953e-02 -3.305211e-01  5.562534e-02
##  [1976] -6.959827e-01  2.073701e-01 -3.065628e-01  1.497280e-01  1.229040e-01
##  [1981] -4.806156e-01 -3.910566e-01 -9.468407e-03 -9.699348e-01 -4.012580e-01
##  [1986] -6.207730e-01 -2.127874e-01 -2.130571e-01 -1.160823e-01 -5.032045e-01
##  [1991] -6.423311e-01 -2.972502e-01 -1.148815e+00 -4.370305e-01 -5.983717e-01
##  [1996] -5.837926e-02 -1.037573e+00 -5.038957e-02  1.849892e-01 -5.282079e-01
##  [2001]  8.438464e-02  1.427450e-02 -7.067129e-01 -2.996709e-01 -4.530200e-01
##  [2006] -2.712128e-01 -3.079022e-01 -1.302439e+00 -1.313604e-02 -2.434250e-02
##  [2011] -6.244280e-01 -8.556103e-01  7.592650e-03 -4.137088e-01 -1.722883e-02
##  [2016] -1.069302e-01 -2.217025e-01 -2.111598e-01 -3.168538e-01  2.780911e-01
##  [2021] -6.235589e-01 -2.613499e-01 -2.245758e-02 -7.610595e-01  5.933608e-01
##  [2026] -5.359460e-01 -9.070788e-01 -4.221217e-01 -1.377797e+00 -6.545197e-01
##  [2031] -2.346483e-01 -3.837447e-01 -1.687387e-01 -1.155888e-01 -2.753284e-01
##  [2036]  6.918444e-02  2.421941e-01 -4.983079e-01 -3.216612e-01  1.342678e-01
##  [2041] -4.508615e-01 -9.183369e-01 -1.014730e-02 -1.412503e-01 -3.982565e-01
##  [2046] -4.468596e-01 -7.013112e-01 -1.375631e-01 -2.681967e-01 -5.449947e-02
##  [2051] -1.779752e-01 -9.153238e-02  3.011654e-01 -1.408586e-01 -3.444644e-01
##  [2056] -1.009050e+00 -2.833587e-01 -1.883999e-01 -7.653230e-01 -5.413735e-01
##  [2061] -4.809602e-01 -2.532167e-01 -7.587850e-01 -5.535804e-01 -1.148824e-01
##  [2066] -3.998650e-01 -7.904008e-02  3.618264e-02 -4.165231e-01  3.513326e-01
##  [2071] -7.503830e-01 -2.025931e-01 -2.121958e-02 -7.412326e-01 -4.731678e-01
##  [2076] -3.734958e-01 -8.021874e-01 -2.638923e-01 -2.893340e-01 -3.705144e-01
##  [2081] -2.426317e-01 -6.484148e-01 -3.960539e-03 -3.695196e-01  1.674736e-02
##  [2086] -2.093879e-01 -5.418399e-01 -1.969929e-01  3.715317e-02 -3.029597e-01
##  [2091] -3.524137e-01  3.235942e-02 -1.698801e-01 -8.585643e-01 -2.468987e-01
##  [2096] -4.716350e-03 -3.359952e-02 -6.795656e-01 -3.553660e-01  4.214579e-02
##  [2101] -4.321171e-01 -2.968638e-01 -2.191112e-01 -8.600464e-02 -2.586352e-01
##  [2106] -1.097200e-01  1.066759e-01 -3.217745e-01 -3.435251e-02 -2.028491e-01
##  [2111] -2.189060e-01 -2.917513e-01 -2.629438e-02 -6.934128e-01 -2.338634e-01
##  [2116] -2.645779e-01 -5.233441e-01 -4.960831e-01  5.185533e-01 -3.310159e-01
##  [2121] -2.994922e-01 -5.544875e-01 -8.213721e-01 -3.612050e-01 -5.446112e-01
##  [2126]  8.864192e-02 -1.879822e-01  7.999440e-02 -1.026985e-01 -1.285746e-01
##  [2131] -4.528652e-01 -7.700918e-01 -3.597974e-01 -3.548660e-01 -2.625786e-01
##  [2136] -1.680059e-01 -5.856366e-01  1.754461e-01 -5.835213e-01 -2.257362e-02
##  [2141] -2.295724e-01 -8.350771e-01 -3.332024e-01 -3.504878e-01 -2.981289e-01
##  [2146]  2.457807e-01 -2.008687e-01 -5.378976e-01  6.709602e-01 -7.291109e-03
##  [2151] -1.951607e-01 -8.157100e-01 -1.872708e-01 -3.315821e-01 -4.327848e-01
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##  [4696] -2.231902e-02 -3.958035e-01 -8.999868e-01 -3.956128e-01  1.662524e-02
##  [4701] -4.624697e-01  1.543020e-01 -3.331732e-01 -6.555683e-01  3.570973e-01
##  [4706] -3.041632e-01 -1.686934e-01 -3.146830e-01  9.894376e-02  2.621003e-01
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##  [4756] -5.058708e-01 -1.467231e-01 -2.930763e-02  9.056901e-02 -2.055945e-01
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##  [5261] -3.290757e-02 -7.938044e-01 -4.869752e-01 -1.726648e-01  1.196597e-01
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##  [5281] -5.482925e-01 -7.321438e-01 -6.352182e-01  7.163736e-02 -1.520684e-01
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##  [5291] -1.112422e-01 -4.015622e-01  3.482249e-02 -5.115678e-01 -1.487677e-01
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##  [5476] -8.019316e-01 -1.655668e-01  1.259915e-01 -8.240322e-01 -5.508963e-01
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##  [5486] -7.216467e-02 -4.918927e-01  8.178776e-04 -4.087740e-01 -1.131541e-01
##  [5491]  4.756999e-02 -5.003272e-01 -4.667131e-01 -1.183719e+00 -3.989760e-01
##  [5496] -6.596875e-01  2.558056e-01 -5.674551e-01 -7.674459e-01 -1.901910e-01
##  [5501] -4.932807e-01 -6.655742e-01 -2.023028e-01 -2.504256e-02 -1.503882e-01
##  [5506] -4.368442e-01 -3.751202e-01 -1.141141e+00 -4.991306e-01 -2.337270e-01
##  [5511] -7.179958e-02 -3.447548e-01 -6.748000e-02  1.208575e-01 -2.059838e-01
##  [5516] -7.162406e-01 -1.491714e-01 -1.550624e-01 -4.705677e-02 -7.504398e-02
##  [5521] -2.294843e-01  2.267230e-01 -4.275789e-01 -2.767096e-01 -4.391807e-01
##  [5526] -8.428722e-01 -2.408734e-01 -1.144446e+00  1.463603e-02 -4.069324e-01
##  [5531] -1.173693e+00 -3.615958e-01 -5.840618e-01 -3.694111e-01 -4.339361e-01
##  [5536]  9.096111e-02 -5.785963e-01 -4.427545e-01 -2.040005e-01 -1.957741e-01
##  [5541] -3.518913e-01 -4.550237e-01 -6.552159e-01 -1.693478e-01 -7.106122e-01
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##  [5561] -3.394194e-01 -2.815598e-01 -2.250601e-01 -2.617816e-01 -6.932484e-01
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##  [5576]  4.720268e-02  1.916043e-01  1.717521e-01 -1.953770e-01 -1.079265e+00
##  [5581] -3.276813e-01 -5.239175e-01 -3.290856e-01 -4.801952e-01 -3.623358e-01
##  [5586] -1.676728e-01 -4.661817e-01 -7.135987e-01 -4.755224e-01 -5.638044e-01
##  [5591] -8.277474e-01 -6.358584e-01 -1.161385e-01 -4.530391e-01 -4.417315e-01
##  [5596]  8.670618e-02 -5.441016e-01 -4.307436e-01 -8.310316e-01  1.542390e-01
##  [5601]  1.286290e-01 -1.072786e+00 -1.592386e-01  3.550696e-01 -9.979362e-01
##  [5606] -1.291156e-02 -1.725877e-01 -1.141470e-01 -7.876877e-01 -1.068619e+00
##  [5611] -2.534270e-01  4.630718e-01  3.779886e-01 -1.194804e+00 -3.163797e-01
##  [5616] -1.276296e-01 -3.717946e-01 -3.644268e-01 -2.695306e-01 -1.122189e+00
##  [5621] -2.868908e-01 -2.385511e-01 -9.676313e-02 -1.023892e-02 -5.316544e-01
##  [5626] -3.006645e-01 -2.083377e-01  1.332606e-02 -5.613499e-01 -1.711937e-01
##  [5631] -2.466229e-01 -4.085622e-01 -8.300948e-01 -5.379776e-02 -3.877208e-02
##  [5636] -2.797394e-01 -7.218505e-01 -3.504130e-01 -6.836709e-01 -2.496646e-01
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##  [5646] -1.113718e+00 -7.969732e-01  4.623308e-02 -3.553744e-02 -5.885142e-01
##  [5651] -1.245107e-01 -4.842069e-02 -1.339032e+00 -5.321036e-01 -8.925533e-01
##  [5656] -1.038065e+00  1.497912e-01  4.125533e-01 -1.631893e-01 -9.576418e-01
##  [5661] -1.644518e-01 -8.376431e-01 -8.023551e-01 -6.512939e-01 -1.991107e-02
##  [5666] -7.046702e-01 -1.307903e-01  4.581131e-02 -9.270517e-01 -7.034718e-01
##  [5671] -7.342234e-01 -1.111361e-01 -6.910666e-01  7.990826e-02 -3.274339e-01
##  [5676] -6.203603e-01 -2.014512e-02 -5.954479e-01  1.859104e-03 -4.012183e-01
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##  [5691] -3.337987e-01 -1.283373e-01 -1.744746e-01  1.121863e-01 -6.414657e-02
##  [5696] -1.225247e+00 -3.789630e-01  2.289794e-02 -9.623876e-01  7.371069e-02
##  [5701] -1.081383e-01 -1.389002e-01 -6.793369e-01  6.028040e-02 -1.562018e-01
##  [5706]  1.519176e-01 -3.711459e-01  8.973650e-02 -8.914319e-01 -5.123230e-03
##  [5711] -2.525454e-01 -5.130597e-02 -2.369939e-01 -4.934565e-01 -3.962077e-01
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##  [5906]  3.380783e-01 -5.595816e-01 -1.571824e-01  2.219714e-02 -3.845178e-01
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##  [6001] -4.271647e-01 -1.026969e+00 -8.297742e-01 -9.149409e-01 -1.257850e-02
##  [6006] -9.210114e-01 -4.453634e-03 -7.815924e-01 -4.740418e-02 -7.172576e-01
##  [6011] -3.854401e-01 -2.049785e-01 -1.174961e-01  1.294044e-01 -4.999405e-01
##  [6016] -5.542567e-01 -5.378521e-01 -8.500363e-01 -1.831357e-01 -3.967425e-01
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##  [6026] -5.851202e-01 -2.269616e-01  3.711440e-01 -1.699772e-01 -7.619136e-01
##  [6031] -1.830828e-01 -4.872398e-01 -4.110190e-01 -4.883475e-01 -4.279700e-01
##  [6036] -3.464194e-03 -2.397621e-01 -5.585337e-01 -5.012705e-01 -3.368954e-01
##  [6041]  2.626309e-01 -3.263638e-02 -2.887036e-01  3.907715e-01 -6.264823e-01
##  [6046]  3.029057e-01 -4.031258e-01 -2.466607e-01 -3.570858e-01  3.067583e-02
##  [6051] -1.957194e-01 -1.188819e-01 -5.991827e-01 -7.810004e-01  1.621116e-01
##  [6056] -5.698277e-01 -1.165151e-01 -9.901958e-01 -1.808503e-01 -2.097757e-01
##  [6061] -2.001749e-01 -2.839768e-01  6.211491e-02 -1.579817e-01  1.067607e-01
##  [6066] -2.204042e-01 -1.222228e-01 -3.939878e-01 -9.496615e-01 -4.913580e-01
##  [6071] -9.569219e-01  2.067968e-02 -4.255219e-01 -4.861760e-01 -1.866598e-01
##  [6076] -4.935360e-01 -4.333104e-01 -3.416158e-01 -3.684245e-01  1.411747e-01
##  [6081] -7.586273e-01 -6.640413e-01 -4.562844e-01  1.957815e-01  2.918560e-01
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##  [6201] -3.842125e-02  5.948670e-01 -9.056119e-01  3.250895e-01 -4.642377e-01
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##  [6211] -6.716223e-02 -7.122421e-01  1.201105e-02 -1.105974e-01 -1.913592e-02
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##  [6226] -6.658858e-02 -4.285187e-01 -9.053378e-01 -8.305017e-02 -7.159533e-01
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##  [6236] -3.617745e-02 -6.752845e-02 -2.793826e-01  9.426680e-02 -9.219748e-02
##  [6241] -7.888272e-01 -4.369823e-02  2.182164e-01 -1.979861e-02  9.203064e-02
##  [6246] -1.236952e-01 -1.201212e+00 -2.099596e-01 -1.273448e-01  2.835553e-02
##  [6251] -5.039835e-02 -1.236794e-01 -4.209001e-01 -2.357976e-01 -6.842728e-01
##  [6256] -1.735233e-01 -1.746199e-01 -4.710120e-02  9.678206e-03 -1.804996e-01
##  [6261] -5.388067e-01 -7.349660e-01 -1.838863e-01 -1.552718e-01 -1.709195e+00
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##  [6271] -6.558683e-01 -7.749540e-01  7.282252e-02 -3.489769e-01 -1.071662e+00
##  [6276] -1.526191e-01 -4.283504e-02 -4.714233e-01 -3.563817e-01 -4.750203e-01
##  [6281] -6.432023e-01 -2.635638e-01  2.160995e-01 -8.339615e-01 -4.907584e-01
##  [6286] -3.554896e-01 -1.718244e-01 -3.103753e-01  9.002703e-02 -4.535167e-02
##  [6291] -3.973570e-01  1.139032e-01 -1.622155e-01 -7.240288e-02 -2.796252e-03
##  [6296]  1.585894e-01  2.100083e-01 -4.880903e-01 -3.992161e-01 -2.461850e-01
##  [6301] -2.251350e-01 -6.243750e-01 -4.763640e-01 -4.940536e-01 -7.303646e-02
##  [6306] -9.982999e-02 -1.417836e+00 -4.658867e-01 -9.523964e-01 -1.240710e+00
##  [6311] -1.520205e-01 -6.255206e-01 -4.017357e-01 -5.455725e-01 -1.671522e-01
##  [6316] -1.835358e-01 -2.372451e-01 -2.628095e-01 -7.686330e-01 -5.495830e-02
##  [6321] -4.117707e-01 -7.889765e-01 -1.001400e+00 -2.860606e-01 -2.947547e-01
##  [6326] -3.808071e-02 -5.405342e-01 -4.378631e-01 -2.113811e-01 -2.724076e-01
##  [6331] -5.888836e-01 -5.122715e-02 -1.015557e+00  4.022148e-01 -1.053949e-01
##  [6336]  1.128108e-01 -1.093454e+00 -7.008118e-01  6.049350e-02 -6.494685e-02
##  [6341] -7.407723e-01  2.944499e-01  1.066757e-01 -9.698106e-01 -7.512191e-01
##  [6346] -6.271212e-01 -1.264969e+00 -3.257288e-01 -8.636703e-01 -8.965364e-01
##  [6351]  3.081545e-02 -1.325206e-01 -2.235450e-01 -8.176816e-01  6.183904e-02
##  [6356] -1.489219e-01 -6.296235e-01 -1.983381e-01 -7.972160e-01 -4.291912e-01
##  [6361] -7.984114e-01 -7.618731e-02 -2.383088e-01 -4.251447e-01 -2.634027e-01
##  [6366] -4.696714e-01 -4.839806e-02 -3.735665e-01 -3.036677e-01 -1.108291e+00
##  [6371] -4.087106e-01 -3.800149e-01 -2.653684e-01 -4.982912e-01  3.226704e-03
##  [6376] -8.496148e-01 -1.235267e-01 -1.306025e-01  2.970358e-01 -8.860688e-02
##  [6381] -6.425372e-02 -1.549131e-01 -1.610003e-01  3.173924e-01 -4.891024e-01
##  [6386] -1.467145e-01 -2.492963e-01 -1.179070e-01 -6.775024e-01  1.875434e-01
##  [6391]  5.790127e-02 -1.766838e-01  9.810291e-02 -2.862256e-01 -6.045486e-02
##  [6396] -3.035200e-01 -3.316697e-02 -3.527311e-01 -5.487782e-01 -4.871802e-01
##  [6401] -1.221191e+00 -1.909239e-01 -3.011349e-01 -2.663069e-01 -1.870474e-01
##  [6406] -5.503729e-01 -1.753579e-01 -2.714474e-01  5.571613e-01 -4.171285e-01
##  [6411] -1.107493e-01  7.691323e-02  1.199265e-01 -8.677116e-02  2.666582e-02
##  [6416] -7.496633e-01 -1.838439e-01 -5.459008e-01 -1.395303e-01 -4.048859e-01
##  [6421] -1.024277e-01 -2.326959e-01 -9.506693e-01  1.027883e-01 -4.822935e-01
##  [6426] -3.175933e-01 -6.448186e-02 -5.843627e-01 -6.905206e-01 -2.277892e-01
##  [6431]  7.987111e-02 -1.266663e-01 -1.395858e-01 -1.723537e-01 -2.336798e-01
##  [6436] -7.552088e-02  5.644168e-02  6.542338e-01 -2.390214e-01 -3.705937e-01
##  [6441] -6.605420e-01 -8.113834e-01 -5.288365e-01  9.561203e-02  3.704227e-02
##  [6446] -4.553753e-01 -3.697223e-01 -6.247775e-01  7.416850e-02 -2.873972e-01
##  [6451] -2.596016e-01  1.875783e-01 -7.286692e-01 -1.017983e-01 -3.525731e-01
##  [6456]  1.049550e-01 -2.275892e-01 -2.409633e-01  4.070237e-01 -4.199862e-01
##  [6461] -4.536066e-02 -4.586667e-01 -6.395838e-01 -5.525010e-01 -5.061586e-01
##  [6466] -7.632868e-01 -2.383245e-01 -6.617998e-01 -2.886201e-01 -1.322669e-01
##  [6471] -7.342127e-01 -3.731747e-01 -1.492422e-01 -7.756019e-01 -6.982683e-01
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##  [6481] -7.407201e-01  4.710037e-02 -4.193903e-01 -1.284204e-01 -7.027874e-01
##  [6486] -6.470531e-01 -1.291725e-01  3.222809e-01 -2.798874e-01  3.770938e-02
##  [6491] -6.010902e-01 -2.926007e-01 -4.891050e-01 -9.184108e-02 -2.468345e-01
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##  [6506] -2.267444e-01 -1.315888e-01  1.639906e-02 -6.134629e-01 -3.225504e-01
##  [6511]  1.292846e-01 -3.048807e-01 -1.266059e+00  2.373285e-01 -4.933547e-01
##  [6516] -5.296394e-01 -7.556352e-02 -1.841406e-01 -3.762669e-01 -2.296530e-01
##  [6521] -8.625248e-02 -7.647640e-01 -8.413392e-01  4.931095e-02 -3.207350e-01
##  [6526] -1.580086e-02 -3.974868e-01 -2.778406e-01 -2.386041e-01 -7.862970e-01
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##  [6601]  5.808316e-02 -1.021441e-01  1.099993e-01  3.000876e-02  1.981480e-01
##  [6606]  2.381732e-01  9.452057e-03  3.893471e-02 -5.934705e-01 -1.062534e-01
##  [6611] -8.316351e-01 -1.135104e-01 -2.748118e-01 -3.169119e-01  1.976032e-01
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##  [6626] -5.516222e-01 -5.188740e-01 -4.133687e-01 -1.353059e+00  9.147832e-02
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##  [6646] -3.407418e-02 -1.228267e-01 -5.618970e-01 -4.846275e-01 -1.770115e-01
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##  [6681]  9.759964e-02  1.455925e-01 -3.504336e-01 -4.717822e-01 -1.285686e-01
##  [6686] -5.576547e-01 -4.688593e-01 -5.011554e-01 -9.867985e-01 -1.168418e-01
##  [6691] -5.138606e-01 -6.433427e-01 -5.178924e-01 -6.320788e-01  1.335237e-01
##  [6696] -3.582740e-01  5.581499e-01 -6.113999e-01 -3.773910e-01 -8.575147e-02
##  [6701] -1.296639e+00 -3.272470e-01 -7.599704e-01  3.555093e-02 -4.100846e-01
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##  [6846] -5.578243e-01  3.154275e-02 -1.775029e-01  9.497111e-02 -1.566448e-01
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##  [6856] -3.683750e-01 -5.959830e-01 -1.552682e-01 -1.252548e-01 -1.830238e-01
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##  [6866] -1.150310e-01 -5.033590e-01 -2.470350e-01  3.370858e-01  2.328863e-01
##  [6871] -6.385416e-01 -2.701188e-01 -2.907769e-01 -2.197580e-01 -3.131552e-01
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##  [6906] -6.278985e-01 -4.953737e-01 -1.028853e-01 -5.888458e-02 -5.004277e-01
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##  [6926] -5.635211e-01  6.672295e-02 -3.663883e-01 -4.398437e-01 -9.308628e-01
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##  [7011] -1.562301e-01 -2.922485e-01 -9.195160e-01 -8.475085e-01 -6.507721e-01
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##  [7026] -6.032370e-01 -4.477209e-01 -4.161522e-01 -4.638062e-01  3.185077e-01
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##  [7036] -3.121820e-01 -7.795781e-03 -1.334384e+00 -1.543697e-01 -2.131134e-02
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##  [7046] -2.557807e-01 -3.493185e-01 -1.015939e-01 -6.042088e-01 -2.263150e-02
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##  [7056] -6.483773e-02 -3.213338e-01 -2.975089e-01 -8.802199e-01 -4.199594e-01
##  [7061] -8.047931e-02 -6.152308e-01 -5.518086e-01 -9.230108e-02 -1.144801e-01
##  [7066] -4.831019e-01 -8.662918e-02 -3.037252e-01 -2.156467e-01 -1.892373e-01
##  [7071] -7.248556e-01  4.131983e-01 -2.918052e-01  4.288389e-01 -5.816386e-01
##  [7076] -1.962201e-01 -4.365782e-01 -1.008338e-01 -2.276786e-01 -2.550349e-01
##  [7081] -4.332492e-01 -2.418705e-01 -6.553914e-01 -1.332481e-01 -6.964980e-01
##  [7086] -1.084740e+00  9.416042e-02 -5.751342e-01  1.704258e-02 -3.801006e-01
##  [7091] -2.957538e-01 -4.175827e-01 -4.354412e-01 -3.325192e-01 -1.601057e-01
##  [7096] -4.031657e-01 -7.624982e-01 -3.425554e-01  1.767116e-01  1.614508e-01
##  [7101] -4.633416e-01 -3.249443e-01  4.301151e-02 -1.507214e-01 -6.833985e-01
##  [7106] -8.110989e-01 -2.756135e-01 -1.955247e-01 -3.582327e-02 -1.013118e+00
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##  [7116] -2.918135e-01 -2.887984e-02 -2.747924e-01 -1.487476e-01 -4.174038e-01
##  [7121]  1.221316e-01  2.121220e-02 -6.361229e-01 -9.861478e-01 -4.242168e-01
##  [7126] -5.196921e-01 -4.099837e-01 -6.639976e-01 -1.072424e-01 -8.320291e-01
##  [7131] -4.596865e-01 -2.883340e-01  3.615220e-01 -2.693928e-01 -6.293738e-02
##  [7136] -3.768282e-01  2.677033e-01 -6.249050e-01 -6.889581e-01 -4.073727e-01
##  [7141] -1.418108e-01  2.538042e-01 -7.282413e-01 -7.401111e-01 -5.011363e-01
##  [7146] -4.224514e-01 -3.543693e-01 -3.314098e-01 -3.700144e-01  2.041404e-01
##  [7151] -4.690966e-01 -3.775460e-01 -1.152116e-01 -3.054214e-01 -1.334622e-01
##  [7156] -5.707086e-01 -3.397933e-01 -8.562695e-02  1.310312e-01 -6.360671e-01
##  [7161] -1.372723e-01  3.536190e-02 -4.434338e-01  1.065798e-01 -2.699656e-01
##  [7166] -6.227308e-01 -1.457356e-01 -3.259253e-01  2.020520e-01 -3.966863e-01
##  [7171]  1.754278e-02 -3.420115e-01  7.529528e-01 -2.979271e-01 -3.819825e-01
##  [7176] -2.129426e-01  2.169273e-01 -4.490651e-02 -2.251239e-01 -6.754609e-02
##  [7181] -3.899427e-01 -8.609946e-02 -2.809101e-01 -4.962343e-01 -4.460930e-01
##  [7186] -4.373078e-01 -6.696444e-01 -7.730961e-01  7.577647e-02 -5.044915e-01
##  [7191] -3.343568e-01 -1.135770e-01 -6.177471e-01 -4.671077e-01 -3.543015e-02
##  [7196] -5.184681e-02 -3.367902e-01 -4.771269e-01 -7.262440e-02 -1.225590e-01
##  [7201] -1.049035e-02 -3.549185e-01  1.017175e-01 -3.372050e-01 -6.890281e-01
##  [7206] -2.189926e-01 -2.006472e-01  4.245537e-01 -4.108289e-01 -2.920432e-01
##  [7211] -1.870353e-01 -3.064698e-01 -2.841820e-01  1.022723e-01 -4.707266e-01
##  [7216] -5.210977e-01 -4.226598e-01 -5.275293e-01 -4.747718e-01 -4.932620e-01
##  [7221]  1.554003e-01  3.070329e-01  1.675399e-01 -2.698190e-01 -1.198086e-01
##  [7226] -4.022417e-01 -8.652327e-02 -1.032677e-01  1.442562e-01 -4.952148e-01
##  [7231] -2.616075e-01 -3.099108e-01 -1.672156e-01 -1.538980e-01 -3.308246e-01
##  [7236] -7.376722e-02 -4.924877e-01 -7.637010e-01 -5.872918e-02 -1.523921e-01
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##  [7246] -8.864668e-01 -1.178101e-01 -1.213116e-01 -1.004624e-01 -5.956654e-01
##  [7251] -4.587562e-01  1.674806e-01  4.724235e-01 -2.629637e-01 -6.922746e-02
##  [7256] -3.581549e-01 -7.786314e-02 -5.852641e-02 -4.506741e-01 -8.543721e-02
##  [7261] -4.055022e-02 -1.010479e+00 -5.257027e-01 -3.468173e-01 -1.993461e-01
##  [7266] -1.906722e-01 -4.737675e-01 -2.119936e-01 -1.694015e-02 -1.900118e-01
##  [7271] -5.500285e-01 -7.736773e-01 -3.102283e-01 -1.287332e+00 -4.952990e-01
##  [7276] -2.521959e-01 -5.016363e-01 -2.294199e-01 -9.619702e-01 -4.323183e-01
##  [7281] -2.022678e-01  1.361003e-02 -7.100932e-01 -5.703882e-01  6.427268e-02
##  [7286] -1.840930e-01  3.659039e-01 -2.931980e-01 -1.119259e-01 -5.268748e-01
##  [7291] -1.602799e-02 -7.873265e-02 -8.793275e-02  4.133949e-02  4.253861e-01
##  [7296]  4.675394e-01 -2.399977e-01 -6.476886e-01 -4.700827e-02 -9.772560e-02
##  [7301] -3.279541e-01 -4.447012e-01 -3.289887e-01 -4.132269e-01 -6.248327e-01
##  [7306] -4.261622e-02 -8.014553e-01 -3.490698e-01 -5.788343e-01  1.886109e-02
##  [7311] -6.588644e-01 -2.118919e-01 -5.976607e-01 -2.194056e-01 -6.171086e-01
##  [7316] -1.718898e-01 -1.342272e-01 -5.534327e-01 -5.568146e-01  1.750276e-01
##  [7321] -5.431722e-01 -8.383625e-02 -5.464427e-01 -9.264900e-01  2.373477e-01
##  [7326] -2.279119e-01 -5.259909e-01  3.395761e-01 -1.202818e-01 -5.976963e-01
##  [7331] -8.481387e-01  1.036473e-01 -5.287064e-01 -4.409030e-01 -2.366982e-03
##  [7336] -2.094617e-01 -1.625604e-01 -1.558610e-01 -7.625195e-01 -6.129310e-01
##  [7341] -3.723544e-01 -2.811617e-01  8.603798e-02 -2.223298e-01  1.930970e-02
##  [7346] -5.842129e-01 -6.122222e-01 -5.369428e-01 -2.415110e-01  3.260127e-01
##  [7351] -1.422614e-01 -3.442269e-01 -3.928152e-01 -6.553810e-01  5.140662e-02
##  [7356] -7.708093e-01 -7.031995e-01 -1.304566e-01 -2.483655e-01 -5.103808e-01
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##  [7381] -2.859206e-01 -6.502986e-02 -6.957390e-01 -3.067694e-02 -7.225363e-01
##  [7386] -1.455971e-02  2.152973e-02 -4.394961e-01 -2.732294e-01 -1.080582e-01
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##  [7396] -4.749695e-01 -7.679457e-02  2.109755e-01 -6.560305e-01 -5.681139e-01
##  [7401] -1.214961e-01 -3.604029e-01 -1.225137e-01 -3.980499e-01  2.083299e-01
##  [7406] -5.970795e-01 -4.525912e-01 -3.764870e-01 -3.324756e-01 -5.983762e-02
##  [7411] -2.808836e-01  1.180329e-01 -3.256818e-01  5.295610e-02 -7.576747e-02
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##  [7426]  2.877963e-01 -8.746820e-01 -6.692014e-01  8.311853e-02 -2.379717e-01
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##  [7436] -1.765655e-01 -2.123875e-01 -6.841332e-01 -3.559521e-01 -5.114673e-01
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##  [7486] -5.619163e-03 -1.773964e-01 -1.380313e-01 -7.637844e-03 -4.246542e-01
##  [7491] -3.922780e-01 -2.413404e-01 -1.174504e-01 -2.649337e-01  3.285910e-01
##  [7496] -1.107111e+00 -4.151588e-01 -1.598114e-01 -1.436185e-01 -6.319940e-01
##  [7501] -2.695708e-01 -1.221759e-01 -8.884159e-01 -5.733427e-01 -1.200062e-01
##  [7506] -1.019797e+00  1.113257e-01  1.202917e-01 -1.721757e-01 -2.561557e-01
##  [7511] -4.375223e-01  2.407115e-02  4.342433e-02 -3.861156e-01 -3.607936e-01
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##  [7561] -1.024823e+00 -4.262677e-01  3.255698e-02 -3.854083e-01 -6.580975e-01
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##  [7586] -3.761476e-01 -4.963227e-03 -1.350513e-01 -5.056132e-01 -4.297373e-01
##  [7591] -2.673720e-01 -3.938283e-01  4.935354e-02 -3.435570e-01 -2.972298e-01
##  [7596]  4.080428e-02 -3.875395e-01  2.661552e-01 -1.229467e+00 -3.350203e-01
##  [7601] -1.642750e-01 -3.404902e-01 -1.902423e-01 -2.952178e-01 -4.016682e-01
##  [7606] -2.912966e-01 -8.183659e-02 -2.788108e-01 -3.115229e-01 -4.936887e-02
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##  [7621]  1.328976e-01 -1.407646e-01  2.199773e-01 -2.909012e-01 -4.072088e-01
##  [7626] -2.151698e-01 -2.516849e-01 -2.894274e-01  2.376415e-01 -7.646655e-02
##  [7631] -9.408208e-02 -5.629261e-01 -1.832479e-01  1.290866e-01 -5.646129e-01
##  [7636] -9.543253e-01 -3.898548e-01 -1.076789e+00  3.738723e-02 -9.693611e-01
##  [7641]  3.591648e-01  5.991019e-02 -2.662829e-01 -1.256030e-01 -9.346374e-01
##  [7646] -3.071444e-01  7.186059e-02 -2.662087e-01 -2.341616e-01 -8.260780e-01
##  [7651] -4.873234e-01 -3.082539e-01 -4.844078e-01  3.755710e-02 -1.160494e-01
##  [7656] -8.724577e-02 -3.216211e-01  5.329120e-02 -4.026310e-01 -6.680531e-01
##  [7661] -5.388454e-01  1.983296e-01 -6.240055e-01 -4.649846e-01 -2.247686e-01
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##  [7836] -1.753014e-01  2.198436e-01 -7.798054e-01 -6.979086e-01 -7.504576e-02
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##  [7861] -2.784520e-02 -5.170857e-03  1.210709e-01 -3.195824e-02 -2.809446e-01
##  [7866] -1.755584e-01 -1.599169e-01 -7.304252e-01 -1.198937e-01 -9.573641e-01
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##  [7886] -7.441382e-01 -4.853583e-01 -2.267206e-01 -4.765926e-01  7.724924e-03
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##  [7896] -2.450882e-01  2.666232e-01  1.457743e-01 -8.022655e-02 -7.772137e-01
##  [7901] -1.001298e+00 -4.252130e-01  1.690652e-01 -6.721716e-02  4.904432e-03
##  [7906] -8.792269e-02 -2.190512e-01 -2.590859e-02 -2.303146e-01 -1.222228e+00
##  [7911] -1.163374e-01  1.344584e-02 -2.121463e-01  1.243686e-01  1.435370e-01
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##  [7921] -9.934022e-01 -7.921771e-01 -6.020175e-01 -4.767317e-01 -2.580151e-01
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##  [7936] -3.874905e-01 -1.940541e-01 -1.386134e+00 -6.413857e-01 -3.906163e-01
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##  [7946] -9.148704e-01  2.167629e-02  1.100212e-02 -9.609505e-01 -5.039156e-01
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##  [7971] -6.983667e-03 -3.732702e-01  6.210484e-02 -5.659129e-02  3.323923e-02
##  [7976] -4.825314e-02 -5.098509e-01 -2.536093e-01 -1.961748e-01 -3.227565e-01
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##  [8476] -2.769274e-01 -2.644750e-01 -7.640996e-01 -5.479538e-01 -1.221540e-01
##  [8481] -2.486625e-01 -4.877791e-01  1.157086e-01 -7.772289e-01 -1.085966e-01
##  [8486] -1.564470e-01 -3.844162e-01 -1.192666e-01 -3.131636e-01 -3.343993e-01
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##  [8496] -6.369581e-01 -1.120660e-01 -4.534229e-01 -1.754582e-01 -6.348255e-01
##  [8501] -4.652016e-01 -6.853239e-01 -4.765736e-01  2.172548e-02 -1.575748e-01
##  [8506] -4.682435e-01 -3.460552e-01 -1.537761e-01 -2.472224e-01  3.931019e-02
##  [8511] -5.048070e-02 -1.541392e-01  2.180587e-01 -2.390899e-01  2.600252e-01
##  [8516]  8.495668e-02 -6.305975e-01  2.449425e-01  8.944637e-02 -1.517985e-01
##  [8521] -3.390024e-01 -4.898379e-01 -2.262542e-01 -1.506187e-02 -1.821839e-01
##  [8526] -3.372227e-01 -5.470973e-01 -8.696403e-01 -5.282183e-01 -3.837834e-01
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##  [8536] -3.065740e-01 -9.083502e-01  1.241637e-01 -2.764679e-01 -2.680928e-02
##  [8541] -4.167631e-01  9.856216e-02  1.809217e-01 -1.026769e+00 -5.093709e-02
##  [8546] -3.388039e-01 -4.580829e-01 -2.201043e-03 -3.298318e-01 -4.167765e-01
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##  [8566]  2.733141e-01  5.030284e-01  4.643824e-01 -3.213403e-01 -3.926678e-01
##  [8571] -2.765695e-01 -5.870680e-01 -2.126202e-01 -2.003217e-02  3.151859e-01
##  [8576] -1.935630e-01 -1.257711e-01 -6.139603e-01 -4.329386e-01 -1.374337e-01
##  [8581] -1.109066e+00  1.620378e-01 -6.284327e-02 -4.350909e-01 -7.896826e-01
##  [8586] -7.452596e-01  5.920699e-02 -8.876022e-01  3.657288e-01 -1.623557e-01
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##  [8601] -5.101622e-01 -1.559634e-01 -1.379851e-01 -3.679088e-02  2.697714e-01
##  [8606] -4.304373e-01 -7.510962e-02 -2.468267e-01 -5.468767e-01 -3.013487e-01
##  [8611]  1.156601e-01 -3.280009e-01 -4.347666e-01 -6.597841e-01 -1.750211e-01
##  [8616] -5.246492e-01 -5.008492e-01 -8.369460e-03 -3.284286e-01 -7.255039e-01
##  [8621]  1.765891e-01  2.469626e-02  3.301130e-01 -3.738602e-01  1.064317e-01
##  [8626] -5.490878e-01 -4.236265e-01  8.440992e-02 -2.217577e-01 -2.009651e-01
##  [8631] -4.650355e-01 -4.950770e-01 -3.320484e-01  1.185144e-01 -2.200121e-01
##  [8636] -1.644243e-01 -2.063509e-01  1.744729e-01 -4.844310e-01 -4.528801e-01
##  [8641] -7.613841e-01 -3.555385e-01  1.911522e-01  4.590062e-01 -2.092684e-01
##  [8646] -4.370983e-01  4.545378e-01 -4.207173e-01 -4.693273e-01 -5.016071e-01
##  [8651] -5.944461e-01  1.477504e-01 -6.331951e-01 -6.119887e-01 -2.965298e-01
##  [8656] -2.384582e-01 -6.193647e-02 -2.796728e-01 -7.577040e-01 -5.207746e-01
##  [8661]  1.260939e-02 -1.438270e-01 -1.640853e-01 -1.706343e-01 -7.209781e-01
##  [8666]  6.371842e-02 -5.215044e-01  3.143842e-01 -4.212115e-01 -2.047424e-01
##  [8671] -7.827900e-02 -5.489033e-01 -3.221030e-01  3.032331e-01  8.080697e-02
##  [8676] -2.340207e-01 -4.586611e-01 -6.191082e-01 -6.599255e-01  3.117540e-01
##  [8681] -2.606516e-01 -7.632300e-01 -2.548267e-01 -3.841465e-01 -6.244455e-01
##  [8686] -2.518873e-01 -3.107031e-01 -7.558253e-01 -2.842225e-01 -2.110794e-01
##  [8691] -6.703706e-02 -1.329018e-01 -4.292494e-01 -1.243121e-01 -1.234303e-01
##  [8696] -3.922515e-01 -1.043865e+00 -1.983926e-01 -5.111220e-01 -3.518353e-02
##  [8701] -4.947442e-01  2.311147e-01 -3.455503e-01 -4.666706e-01 -4.317476e-01
##  [8706] -2.553129e-01 -1.792733e-01 -5.115751e-01  1.576114e-01 -1.745775e-01
##  [8711] -2.253627e-01 -1.209388e-01  1.105364e-01  9.824179e-02 -1.846275e-01
##  [8716] -1.458932e-01  6.102510e-02 -3.654328e-01  6.289531e-02 -9.573656e-02
##  [8721] -1.561047e-01 -6.097029e-01 -9.063721e-01  1.994480e-01 -4.191310e-01
##  [8726] -3.237347e-01 -1.481678e-01 -2.387204e-02 -1.972425e-01  2.282019e-02
##  [8731] -7.942597e-01 -5.112770e-01 -1.515755e-01 -4.968061e-01 -9.776295e-02
##  [8736] -5.653603e-01 -9.713005e-02 -4.742133e-01 -2.255603e-01 -3.193620e-01
##  [8741]  4.418198e-02 -5.747455e-01  4.192008e-01 -6.299683e-02 -4.586895e-01
##  [8746] -8.526210e-01 -1.232563e-01 -4.634692e-01 -1.818631e-01 -2.618047e-01
##  [8751] -4.412146e-01 -1.025146e-01 -7.819710e-02  6.524855e-03 -4.325475e-01
##  [8756] -4.046758e-01 -6.786224e-01 -8.505514e-01 -1.409644e-01 -3.628584e-01
##  [8761] -7.306535e-01 -1.916393e-01 -6.057137e-02 -5.683567e-02 -3.014939e-01
##  [8766] -1.095962e-01  5.643246e-01 -3.639220e-01 -1.849468e-01 -9.728517e-01
##  [8771] -1.578883e-01 -3.254943e-01 -1.781294e-01 -1.114420e-01 -8.730458e-01
##  [8776] -1.625977e-01 -2.576940e-01 -2.631596e-01 -2.444923e-01 -1.752684e-01
##  [8781] -5.391394e-01 -3.394338e-01 -7.442041e-01  1.616734e-02 -2.428208e-01
##  [8786] -2.211449e-01  1.296181e-01 -1.100980e-01 -3.387405e-01  1.009317e-01
##  [8791] -1.519634e-01 -3.290499e-01 -3.318696e-01 -2.724824e-01 -4.574538e-01
##  [8796] -7.543107e-01 -7.891604e-02 -3.095215e-01 -4.230432e-01 -6.162533e-01
##  [8801] -2.516913e-01 -5.884010e-01 -6.362451e-01 -4.533981e-02 -5.386097e-01
##  [8806] -3.197046e-01 -2.367032e-01 -4.238639e-01 -2.463774e-02 -2.006234e-01
##  [8811] -2.167431e-02 -9.144980e-02 -2.118496e-01  1.485960e-01 -2.683184e-03
##  [8816] -8.018625e-01 -5.476425e-01 -5.641692e-01  1.319819e-01 -3.662391e-01
##  [8821] -1.737347e-01 -3.438361e-01 -6.582744e-01 -4.165731e-01  1.512743e-01
##  [8826] -1.664541e-01 -3.341452e-01 -3.924809e-01 -5.191877e-01 -2.675107e-01
##  [8831] -1.125087e+00 -2.323642e-01  1.462352e-01 -3.367240e-01 -1.336418e-01
##  [8836] -6.458553e-01 -3.617164e-01 -3.741192e-01 -1.364480e-01 -2.092365e-01
##  [8841] -4.210266e-01 -8.539180e-02 -1.594928e-02 -4.930516e-01 -4.560351e-01
##  [8846] -1.651300e-01 -8.353155e-01 -1.775759e-01 -2.358020e-01 -1.597762e-01
##  [8851] -1.005415e-01 -8.612383e-02 -6.612440e-01 -2.612702e-01 -1.089371e+00
##  [8856] -6.191501e-01  6.933657e-01 -2.835045e-01 -1.089199e-01 -6.178753e-01
##  [8861] -3.215248e-01 -1.980008e-01 -1.097334e-01 -3.393530e-01 -6.790608e-01
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##  [8871] -9.060960e-01 -1.363177e+00 -4.358464e-01  3.734502e-02 -8.412191e-02
##  [8876] -3.078140e-02 -7.756916e-01 -2.274489e-01  5.001601e-02 -4.765738e-01
##  [8881]  9.932162e-02  1.761498e-02  1.002895e-01 -3.371705e-01  6.685047e-03
##  [8886] -1.675090e-01 -6.437995e-01 -9.708792e-01 -8.902380e-01  1.549500e-02
##  [8891] -8.613814e-01 -3.509254e-01 -2.442827e-01 -5.600185e-01 -1.866380e-01
##  [8896] -7.836282e-01 -1.569781e-01 -9.617095e-01 -4.156078e-01  2.479381e-01
##  [8901] -3.623318e-01  1.536655e-01 -8.288069e-02 -4.247845e-01 -4.158193e-01
##  [8906] -1.209867e+00 -3.186487e-01 -4.842572e-03 -5.733886e-01 -2.112094e-01
##  [8911] -8.735294e-01 -2.155664e-01 -3.378505e-01  1.536716e-01 -6.968772e-01
##  [8916] -8.687467e-01 -4.820650e-01  1.291462e-01 -1.823058e-01 -1.230482e-01
##  [8921] -7.386567e-01 -1.032368e-01 -2.200298e-01 -2.955507e-01 -8.901906e-01
##  [8926] -7.062631e-01 -3.002988e-01  7.680927e-03 -2.830107e-01  4.629277e-01
##  [8931] -3.750082e-01 -2.652951e-01 -1.153487e-01 -1.865096e-01 -4.991174e-01
##  [8936] -2.149019e-01 -2.093998e-01  6.090997e-02 -3.555537e-02  4.964445e-02
##  [8941] -6.532085e-01 -1.841714e-01 -3.637285e-01 -2.703351e-01 -9.666994e-01
##  [8946] -1.583856e-01 -8.869397e-03 -2.830701e-01 -3.130314e-01 -3.642423e-01
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##  [8961] -6.222443e-02 -4.384356e-01  1.511673e-02 -3.477713e-01 -2.606086e-02
##  [8966] -2.106025e-01 -2.917400e-01 -5.662562e-01 -4.257306e-01 -7.642006e-01
##  [8971]  5.717955e-01 -3.702858e-01 -5.366213e-01 -1.037069e+00 -2.198827e-01
##  [8976] -5.290815e-01 -4.868301e-01 -4.131077e-01 -3.894164e-01 -1.580941e-01
##  [8981] -4.724645e-01  5.400904e-01 -1.297158e-02 -1.688286e-01  1.491800e-01
##  [8986] -7.798365e-03 -1.540508e-01 -7.914231e-01 -2.948219e-01 -1.053284e+00
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##  [8996] -1.800545e-01 -7.430491e-01 -3.183843e-01 -1.397435e-01 -3.609291e-01
##  [9001] -4.247351e-01 -4.246175e-01 -2.796805e-01 -3.543517e-01 -8.961051e-01
##  [9006] -2.921415e-01  3.840862e-01 -7.991369e-02 -4.936378e-01  1.327878e-01
##  [9011] -4.621146e-02 -2.168926e-01 -4.730005e-01 -2.135626e-02  7.573322e-02
##  [9016] -2.166722e-01 -2.589571e-01 -3.784949e-01 -2.887015e-01 -6.778023e-01
##  [9021] -8.430679e-01  8.432952e-02 -2.430704e-01 -1.395976e-01 -4.087280e-02
##  [9026] -2.651379e-01 -3.415188e-01 -3.866629e-01 -2.290979e-02 -7.424376e-02
##  [9031] -6.941670e-01  3.922362e-01 -8.096537e-01 -3.418161e-01 -5.411776e-01
##  [9036] -8.569820e-01  1.302085e-01 -3.802556e-01 -3.540696e-01  1.010502e-01
##  [9041] -7.089045e-01 -4.886320e-02 -2.077227e-01 -1.125515e+00 -2.859908e-01
##  [9046] -6.238787e-01  1.448789e-01 -4.793341e-01 -3.307701e-01 -6.736805e-01
##  [9051] -6.142052e-01 -3.331368e-01 -4.192518e-01 -1.606944e-01 -3.067015e-01
##  [9056] -4.453654e-01 -5.441283e-01 -4.547445e-01  3.107401e-02 -5.597176e-01
##  [9061] -6.319172e-01 -4.497975e-01 -7.500273e-01 -8.720154e-02 -9.075303e-01
##  [9066] -2.609895e-01 -4.026264e-02 -7.960117e-01 -1.892860e-01 -1.406765e-01
##  [9071] -1.032346e+00 -4.555046e-01 -2.104124e-02 -4.119183e-01 -3.035812e-01
##  [9076] -4.959732e-01 -2.444708e-01 -5.597950e-01 -5.196820e-01 -3.488306e-01
##  [9081] -2.731773e-01 -2.476099e-01 -5.037120e-01 -1.237371e-01  3.329364e-02
##  [9086] -1.812321e-01  7.868146e-02 -2.536657e-01  3.889351e-01 -4.545989e-01
##  [9091] -1.591950e-01 -4.897434e-01  5.700979e-02 -2.468642e-01 -2.368426e-02
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##  [9106] -2.945472e-01 -6.744925e-01 -8.050011e-01 -1.094575e+00 -8.408421e-01
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##  [9136] -1.819397e-01 -2.233283e-01 -7.048740e-02 -1.839086e-01 -7.341242e-01
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##  [9151] -1.847895e-01 -1.537744e-01 -8.492188e-01  3.256113e-01 -2.282729e-01
##  [9156] -1.023722e+00 -4.297304e-01 -4.434748e-01 -6.797011e-01 -2.090305e-01
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##  [9171] -1.876206e-01 -3.224933e-01 -4.888085e-01 -2.437785e-01 -7.554121e-02
##  [9176] -1.373092e-01  1.102412e-01 -3.006564e-01 -3.001093e-01  9.526794e-02
##  [9181] -8.910768e-01 -7.852525e-02 -7.868204e-02 -3.369811e-01  2.438009e-02
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##  [9191] -2.016599e-01 -2.022864e-01  4.518858e-01 -1.007640e-01 -6.318779e-01
##  [9196] -2.843806e-01 -2.943610e-01 -1.384800e-01 -5.600248e-01 -1.848993e-01
##  [9201] -2.684689e-01  1.090049e-01 -3.074003e-03 -5.315498e-01  1.519161e-01
##  [9206] -1.710178e-01 -4.127642e-01 -1.032554e-01  4.028436e-01 -9.035380e-01
##  [9211] -6.623777e-01  2.043169e-01 -8.124326e-02 -1.243679e-02  3.530215e-01
##  [9216] -4.341641e-01 -6.052637e-01 -3.499939e-01 -2.521585e-01 -4.475063e-01
##  [9221]  9.622859e-02 -4.948571e-02 -8.314397e-02 -4.814239e-01 -5.949765e-01
##  [9226] -2.097599e-01 -2.958655e-01 -2.013424e-01 -3.076605e-01  2.019166e-01
##  [9231]  5.344808e-01 -2.169018e-01 -2.018503e-01 -5.600220e-01 -3.061272e-01
##  [9236] -2.031575e-01 -2.267910e-01 -1.971786e-01 -2.759395e-01 -2.205153e-01
##  [9241] -4.575460e-01 -2.441440e-01 -1.904575e-01 -1.159317e+00  2.084658e-02
##  [9246] -2.630079e-01 -5.597048e-01  1.687325e-01  1.173131e-02 -9.952695e-01
##  [9251] -2.817768e-02 -7.841921e-03 -1.847143e-01 -4.839471e-01 -4.644146e-01
##  [9256] -7.102269e-01 -7.045595e-01 -3.245717e-01 -2.948079e-01  2.939816e-01
##  [9261] -3.621776e-01 -3.462332e-01 -3.697454e-01 -3.044465e-01 -1.120769e+00
##  [9266] -1.819929e-01  4.604024e-02 -2.656891e-01  9.892378e-02 -1.382388e-01
##  [9271] -2.675779e-01 -5.276943e-01 -6.007378e-02 -7.704846e-02 -8.126040e-01
##  [9276] -2.362156e-01  1.238950e-01 -4.622160e-01 -5.363123e-01 -4.454137e-02
##  [9281]  8.110203e-01 -1.516046e-01 -5.494822e-01 -6.662302e-01 -1.530089e-01
##  [9286] -2.098024e-01 -2.244033e-02  2.472309e-02 -3.712230e-02 -1.033567e+00
##  [9291] -4.045927e-01 -5.374230e-01 -4.880417e-01 -1.090816e-01 -1.859313e-01
##  [9296] -7.332825e-01 -6.519049e-01 -1.912192e-01 -3.854081e-01 -6.231866e-02
##  [9301] -5.688347e-01  1.510193e-01 -3.102257e-01 -2.753113e-01 -3.214057e-01
##  [9306] -1.202076e-01 -3.263045e-02  5.548547e-02 -5.283433e-01  1.010472e-01
##  [9311] -1.178286e-01 -1.051651e-01 -5.814042e-01 -2.368132e-01 -5.731474e-02
##  [9316] -8.121634e-01 -7.005953e-01 -1.511678e-01  6.789182e-01 -1.627999e-01
##  [9321] -4.654165e-01 -5.479478e-01 -2.368090e-01  2.711562e-01 -2.355351e-02
##  [9326]  5.136853e-02 -3.304193e-01 -6.701678e-01 -6.851732e-03 -4.036740e-01
##  [9331] -6.331119e-01 -1.156696e+00 -1.047515e+00  4.856265e-02 -5.956996e-01
##  [9336] -6.163136e-01 -1.974230e-01 -5.670699e-01 -4.978735e-01 -3.610074e-01
##  [9341] -4.931905e-02 -1.348509e-01 -3.162635e-01 -5.247681e-01 -3.134820e-01
##  [9346] -1.909833e-01 -2.872679e-01  3.641898e-01  1.847253e-01  2.225000e-01
##  [9351]  3.141369e-02 -2.061509e-01 -1.181779e-01 -3.575279e-01 -3.617845e-01
##  [9356]  2.042116e-02 -2.122822e-01 -1.025967e+00 -2.886631e-01 -7.829916e-01
##  [9361] -6.493844e-02 -2.888810e-01  2.063781e-01 -1.600118e-01 -4.640384e-01
##  [9366] -4.667981e-01 -5.031959e-01 -6.326372e-01 -3.266495e-01 -5.657240e-01
##  [9371]  3.296720e-01 -1.725400e-01  3.052994e-01 -7.015034e-01 -7.418144e-02
##  [9376] -3.571091e-01  7.876250e-02 -3.179614e-01 -4.673086e-01 -3.587468e-01
##  [9381] -1.977836e-01 -5.397616e-01  1.141388e-01 -5.571569e-01 -6.266080e-01
##  [9386] -3.936380e-01 -6.793796e-01 -5.904516e-01 -1.986163e-01 -3.620536e-01
##  [9391] -3.851122e-01 -5.213698e-02 -7.266397e-01 -6.959528e-01 -5.747417e-01
##  [9396] -3.908459e-01 -4.822768e-01 -6.638801e-02 -3.795118e-01  5.273054e-02
##  [9401] -8.416577e-01 -3.890234e-02 -3.884693e-01 -2.736244e-01 -1.411911e-01
##  [9406] -2.332892e-01 -3.528161e-01 -1.430924e-01 -1.994664e-01 -3.642613e-01
##  [9411] -5.905614e-02 -6.102318e-01 -2.133819e-01 -3.484252e-01 -1.938054e-02
##  [9416]  7.101536e-02 -6.236037e-01 -7.877757e-01 -3.429664e-01 -4.584314e-01
##  [9421] -4.909798e-01 -5.240493e-01 -1.321361e-01 -8.935454e-01 -4.689885e-01
##  [9426] -1.024255e-02 -4.600173e-01 -3.962402e-01 -1.508957e-01 -2.236512e-01
##  [9431] -4.784330e-01 -3.430717e-01 -4.780781e-01 -2.499416e-01 -8.801873e-01
##  [9436] -2.808880e-01 -1.057870e+00 -3.848857e-01 -7.060673e-01 -1.120508e-01
##  [9441] -5.938823e-01 -9.385197e-01 -4.673047e-01 -1.266891e-01 -1.005978e-01
##  [9446] -4.079643e-01 -6.604611e-01 -5.353752e-01  7.849714e-02 -3.426776e-01
##  [9451] -5.129829e-01 -5.412393e-01 -4.430385e-01 -5.914028e-01 -1.601948e-01
##  [9456] -5.259010e-01  8.212782e-02 -3.841195e-01  2.545700e-02  3.280346e-02
##  [9461] -1.461320e-01 -8.713918e-01 -5.276069e-01  1.023299e-01 -4.211525e-01
##  [9466] -4.213208e-01 -2.960711e-01 -7.099330e-01 -8.132591e-01 -7.952919e-01
##  [9471]  1.199427e-01 -7.042868e-01 -3.276253e-01 -5.924696e-01 -2.403007e-01
##  [9476] -3.345082e-01  9.846335e-03 -2.082082e-01 -3.892711e-03 -1.676235e-01
##  [9481] -6.614162e-01  5.393185e-02  2.844392e-02  1.366997e-02 -1.537504e-01
##  [9486] -2.789607e-01 -4.309729e-01 -5.160580e-01 -3.623613e-01 -7.653746e-02
##  [9491] -8.440409e-02  3.672440e-01  6.343996e-01 -3.947432e-01 -5.150693e-01
##  [9496] -5.394980e-01 -6.217585e-01 -4.056883e-01 -9.139594e-01 -2.116099e-01
##  [9501] -7.911137e-02 -5.103955e-01  3.961275e-01 -4.295641e-01 -1.684461e-01
##  [9506] -3.345823e-01 -1.423435e+00 -7.775454e-01 -5.597545e-01 -1.338531e-01
##  [9511] -6.530109e-01 -5.279316e-01 -9.350923e-03 -4.922364e-01 -1.992596e-01
##  [9516] -4.825215e-01 -1.109177e-01 -2.299140e-01 -7.218206e-01 -4.442456e-01
##  [9521] -2.560934e-02 -2.613176e-01 -8.923221e-01 -4.740198e-01 -4.355492e-01
##  [9526] -6.594866e-01 -5.312944e-01 -2.915026e-01  8.291132e-02 -2.987406e-01
##  [9531] -4.852953e-01 -4.249293e-01 -6.839426e-01 -9.068379e-02 -8.957786e-01
##  [9536] -4.565447e-01 -6.905485e-02 -5.569503e-01 -1.485718e-01 -3.100944e-01
##  [9541] -2.577789e-01 -5.080041e-01 -4.107204e-02  9.285988e-03 -7.127287e-01
##  [9546] -2.160740e-01 -1.344804e+00  7.249819e-03 -3.516429e-01 -4.591939e-01
##  [9551] -3.238992e-01 -4.826795e-01 -1.345338e-01  3.141337e-02  5.697748e-02
##  [9556] -9.984289e-01 -3.699811e-01 -6.200455e-01  5.291329e-01 -5.994910e-01
##  [9561] -6.652000e-01 -7.417453e-01 -1.701320e-01  2.466467e-01  9.640946e-02
##  [9566] -3.976323e-01  6.310315e-01 -3.163931e-01 -2.038386e-01 -5.953857e-01
##  [9571] -8.573208e-01 -7.705523e-01  1.676583e-01 -4.104057e-01  5.010969e-01
##  [9576] -2.724296e-01 -9.707241e-01  1.148485e-01 -4.722217e-01 -5.773774e-02
##  [9581]  1.461369e-01 -3.184180e-01  1.870151e-01 -3.670524e-01  4.216321e-01
##  [9586] -5.811619e-01 -1.420928e-01 -3.782030e-01 -6.105432e-01 -4.446116e-01
##  [9591] -3.646268e-02 -3.539249e-01 -1.729071e-01 -4.484311e-01 -6.074968e-01
##  [9596] -6.160798e-01 -2.474804e-01 -1.171306e-01 -1.468489e-01 -4.424018e-01
##  [9601] -1.656665e-01 -2.573348e-01  2.898367e-01  1.236475e-01  1.938565e-01
##  [9606]  1.138299e-01 -1.303600e-01  4.699428e-01 -3.120026e-01 -2.986941e-01
##  [9611]  2.455175e-01  3.082424e-02 -1.098527e+00 -4.730693e-01  1.818727e-01
##  [9616] -1.064567e+00  5.657306e-01  3.324800e-02 -4.646639e-01 -8.319036e-01
##  [9621] -4.558147e-01 -2.980439e-01 -3.466490e-01 -7.953049e-01 -1.115928e-01
##  [9626] -6.360741e-01 -6.584897e-01 -6.717746e-02  1.761555e-01  2.299430e-01
##  [9631] -1.709872e-01 -5.413535e-01  7.279784e-03  7.946325e-02 -3.294608e-01
##  [9636] -5.013825e-01 -2.072594e-01  8.914688e-02  2.777313e-01 -1.938712e-01
##  [9641] -1.956643e-01 -3.662375e-01 -1.877431e-01 -7.396762e-01 -1.467743e-01
##  [9646] -3.171216e-01 -4.211939e-02 -1.768819e-01 -3.956425e-01  1.074047e-02
##  [9651] -8.094869e-01  1.311640e-01 -9.548785e-01  1.067147e-01 -2.496536e-01
##  [9656] -3.489438e-01 -4.313096e-01 -3.402752e-01 -9.357148e-02 -5.954638e-01
##  [9661] -4.083786e-01  1.476908e-01 -3.600285e-01  1.739387e-02 -1.697644e-01
##  [9666] -2.435884e-01  1.736077e-01 -2.916868e-01  3.644757e-02 -3.244056e-02
##  [9671] -3.433432e-01 -4.398788e-01  8.707347e-02 -2.788587e-01 -4.422588e-02
##  [9676] -4.718067e-01  7.997482e-02 -2.502780e-01 -3.466486e-01 -5.731349e-01
##  [9681] -5.734584e-01 -6.790278e-01  1.368742e-01  3.954361e-03 -2.895291e-01
##  [9686] -4.791135e-01 -2.938019e-01  3.623417e-01 -1.608209e-01 -4.233018e-01
##  [9691] -5.221017e-01  9.992317e-02 -7.209353e-01 -8.094244e-01 -4.030866e-01
##  [9696] -2.310659e-01  5.579814e-02 -2.006636e-01 -5.189528e-01 -3.197258e-02
##  [9701]  2.092670e-01 -7.890485e-01 -5.423994e-01 -2.077735e-01 -4.061153e-01
##  [9706] -7.604178e-01 -2.773573e-01 -5.449118e-01 -2.402532e-01 -6.152620e-01
##  [9711]  3.936394e-01 -9.285852e-02 -6.562372e-01 -1.295050e-01  2.246806e-01
##  [9716] -1.018889e-01 -2.560552e-01 -3.000733e-01 -5.346773e-01 -5.718498e-01
##  [9721] -2.905972e-01 -5.482548e-01 -3.450555e-01  1.862938e-01  7.035647e-02
##  [9726] -5.236140e-01  1.078870e-01 -3.855296e-01 -1.516165e-01 -4.411921e-01
##  [9731] -3.729021e-01 -1.266851e-01  3.593087e-02 -4.177562e-01 -2.255160e-01
##  [9736] -1.795431e-01 -5.945468e-01 -3.076523e-01 -2.238168e-01 -3.063489e-01
##  [9741] -7.188502e-01 -3.180734e-01 -2.663521e-01 -2.023474e-01 -8.714626e-02
##  [9746] -1.900447e-01 -4.130831e-01  1.702080e-02 -4.179396e-01 -4.867669e-01
##  [9751] -2.020263e-01  9.639601e-02  9.542355e-02 -5.092462e-01 -6.505908e-01
##  [9756] -2.166363e-01 -9.261208e-02 -4.690806e-01 -1.441566e-01 -6.821330e-01
##  [9761] -3.648448e-01 -2.063152e-01 -6.717992e-01 -4.440117e-01 -5.257765e-01
##  [9766] -9.309425e-01 -3.699253e-01 -9.019103e-01 -6.316047e-01 -3.139708e-01
##  [9771] -1.141331e-01 -2.833956e-02 -2.883854e-01 -6.859029e-01  2.782328e-02
##  [9776] -2.028468e-01 -4.115983e-01 -4.979795e-01 -2.512724e-01 -1.148149e-01
##  [9781] -2.291937e-01  8.152409e-02 -2.985528e-01  5.957461e-02  2.761604e-02
##  [9786] -3.530296e-01 -2.626034e-02 -3.986005e-01 -1.984040e-01  1.921004e-01
##  [9791] -5.392870e-01 -8.353629e-01 -1.651217e-01 -3.230708e-01 -5.933202e-01
##  [9796] -3.477407e-01 -1.605157e-01 -3.239686e-01 -7.012536e-01 -2.843118e-01
##  [9801]  9.533890e-02 -6.052366e-01 -8.370972e-01 -5.803957e-01  1.235945e-01
##  [9806] -4.529097e-01 -3.548189e-01 -3.206967e-01 -1.327477e-01 -6.662522e-01
##  [9811] -2.064624e-01 -2.490054e-01  2.703034e-01 -7.960803e-01 -6.866941e-01
##  [9816] -1.999831e-01  2.787889e-01 -6.030132e-02 -3.006849e-01 -9.896325e-01
##  [9821]  8.296922e-02 -2.846012e-01 -7.096650e-01 -2.255627e-01 -1.625834e-01
##  [9826] -3.213161e-01  9.682894e-02  2.231738e-02 -3.201696e-01 -4.543179e-01
##  [9831] -5.963478e-01 -4.773411e-01 -3.874358e-01 -6.259391e-01 -1.737167e+00
##  [9836]  1.269807e-01  5.387186e-02  2.182517e-01 -1.310589e-01 -6.486116e-01
##  [9841] -7.479831e-01 -2.663619e-01 -5.156087e-01 -3.460975e-01 -4.566478e-01
##  [9846] -1.445312e+00 -3.385758e-01 -2.573671e-01 -5.947589e-01 -7.337136e-01
##  [9851]  1.892291e-01 -3.890791e-01 -6.396643e-01 -3.357758e-01 -2.108927e-02
##  [9856] -6.291004e-02  2.191567e-02 -2.719660e-01 -6.312707e-01 -3.891277e-01
##  [9861] -5.327680e-01 -6.000188e-01 -1.288496e+00 -7.962290e-01  1.054866e-01
##  [9866] -3.038724e-01 -2.703918e-01 -1.039860e-01 -8.851985e-01  5.947608e-02
##  [9871] -4.656696e-01  5.868075e-02 -4.062523e-02 -3.952358e-01 -2.970697e-01
##  [9876] -6.940202e-01 -4.346737e-01 -2.957591e-01 -5.432097e-01 -4.342869e-01
##  [9881] -8.596021e-01 -3.283861e-01 -8.542074e-01  1.880457e-02 -6.281447e-01
##  [9886] -1.905791e-01 -1.726051e-02 -1.201865e-01 -2.580433e-01 -2.180573e-01
##  [9891] -4.899966e-01 -6.761520e-01 -2.240874e-01 -5.536716e-01 -6.037076e-01
##  [9896] -4.059302e-02 -1.669030e-01  8.526830e-02 -2.415581e-01 -2.377560e-01
##  [9901] -3.921086e-01 -8.322930e-01 -2.894660e-01  1.952857e-01 -9.993700e-02
##  [9906] -6.137321e-01 -2.431689e-01  1.516870e-01 -4.768533e-01 -1.193852e+00
##  [9911] -8.379530e-01  1.332975e-01 -2.083156e-01 -7.089035e-01  1.179213e+00
##  [9916] -4.589753e-01 -3.796217e-02 -7.665077e-01 -3.058692e-01 -7.816347e-01
##  [9921] -7.174558e-01 -2.593869e-01 -2.680157e-01 -4.950459e-01  1.315250e-02
##  [9926] -2.121566e-01 -5.919496e-01 -3.305361e-01 -5.383577e-01 -4.819566e-01
##  [9931] -6.887002e-01 -4.780328e-01 -3.875905e-01 -3.330497e-01 -1.276210e-01
##  [9936] -1.184867e-01 -1.070694e+00 -2.511570e-01 -3.474919e-01 -1.143749e-01
##  [9941] -3.594624e-01  4.499172e-01 -4.091187e-01  1.590633e-01 -8.657877e-01
##  [9946]  2.077913e-01  3.418623e-01 -3.336472e-01 -3.254492e-01  1.963526e-01
##  [9951] -8.040658e-01 -1.865338e-01 -1.129815e+00 -5.058417e-01 -3.319257e-01
##  [9956] -9.424659e-01 -7.627001e-02  2.597468e-02 -3.186423e-01 -2.695140e-01
##  [9961] -3.653348e-01 -2.720012e-01  4.788958e-02 -4.780608e-01 -5.828297e-02
##  [9966] -1.477088e-01 -4.980148e-01 -3.836878e-01 -1.730081e-01  1.425673e-01
##  [9971] -5.210931e-01 -1.271592e-01 -2.385723e-01 -1.544558e-02 -1.943512e-01
##  [9976] -2.208862e-01  4.751507e-01 -8.641340e-02 -1.468751e-01 -5.050898e-01
##  [9981] -4.983859e-01 -5.841567e-01 -6.431031e-01 -5.953288e-02 -4.107195e-01
##  [9986] -2.663734e-01  2.635324e-02 -5.718246e-01 -2.880722e-01 -2.491507e-01
##  [9991] -2.711169e-01 -9.408996e-02 -1.124309e-01 -1.533731e-02 -6.159624e-01
##  [9996]  3.340206e-01 -3.222332e-01 -1.408667e-02 -1.256720e-01 -6.487705e-02
mean(x3)
## [1] -0.2975686
hist(x3, main="Distribution of Data", xlab="Data Values", ylab="Frequency")

you could also use lavaan::sem

model <- ' mpg ~ c*wt + b * qsec
  qsec ~ a*wt'

# Fit the model
fit <- lavaan::sem(model, data=mtcars, std.lv=TRUE)
summary(fit)
## lavaan 0.6.14 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                         5
## 
##   Number of observations                            32
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)
##   mpg ~                                               
##     wt         (c)   -5.048    0.461  -10.956    0.000
##     qsec       (b)    0.929    0.252    3.683    0.000
##   qsec ~                                              
##     wt         (a)   -0.319    0.318   -1.004    0.315
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .mpg               6.108    1.527    4.000    0.000
##    .qsec              2.999    0.750    4.000    0.000