Multilevel Modeling

Null Models

Spring 2026 | CLAS | PSYC 894
Jeffrey M. Girard | Lecture 06a

Roadmap

  1. Overview
    • Fixed, Random, Null Models
  2. Specifications
    • Equations, Formulas, Diagrams
  3. Practicalities
    • ICCs, Estimates, Interpretation

Overview

Random Intercepts

  • The intercept is the expected value of \(y\) when all \(x=0\)
    • If there are no \(x\) variables, it estimates the mean of \(y\)
    • We are used to there being just one intercept per model
  • But with clustered data, we might want intercepts to vary
    • e.g., schools vary in their average math scores
  • Doing so will partition the \(y\) variance and correct our SEs
    • This will create our first, simple multilevel model!

Intercept Distribution

  • In the population of clusters, we assume that all the intercepts are normally distributed, which implies that…
    1. There is an average intercept in the population
    2. Each cluster’s intercept deviates from this average
    3. Smaller deviations are more common than larger ones
  • We can summarize this distribution by its mean and SD
    • The mean is the fixed intercept (average level)
    • The SD is the random intercept SD (spread of levels)

Visualizing the Fixed Effect

Visualizing the Random Effect

Null Models

  • We begin with MLMs that have no predictor variables
    • These are called “empty models” or “null models”
    • They are a nice first step when learning MLM
    • And we will continue using them to estimate ICCs
  • As stated before, intercepts are averages in empty models
    • However, this interpretation isn’t true in many models
    • e.g., when adding dummy codes or uncentered predictors

Specifications

Multilevel Equation

Level One (Observation)

\[ y_{ij} = \beta_{0j} + \color{#e41a1c}{e_{ij}}, \qquad \color{#e41a1c}{e_{ij}} \sim \text{Normal}(0, \color{#e41a1c}{\sigma}) \]

Level Two (Cluster)

\[ \beta_{0j} = \color{#377eb8}{\gamma_{00}} + \color{#4daf4a}{u_{0j}}, \qquad \color{#4daf4a}{u_{0j}} \sim \text{Normal}(0, \color{#4daf4a}{\tau_{00}}) \]

  • \(\color{#377eb8}{\gamma_{00}}\) is the Fixed Intercept (Population Average)
  • \(\color{#4daf4a}{u_{0j}}\) is the Cluster Deviation (Random Effect)
  • \(\color{#e41a1c}{e_{ij}}\) is the Observation Deviation (Residual Error)

Reading the Equation

\[ y_{ij} = \beta_{0j} + \color{#e41a1c}{e_{ij}}, \qquad \color{#e41a1c}{e_{ij}} \sim \text{Normal}(0, \color{#e41a1c}{\sigma}) \]

\(y_{ij}\) is the outcome for observation \(i\) in cluster \(j\) and equals …
…the Cluster Average \((\beta_{0j})\) plus the Observation Deviation \((\color{#e41a1c}{e_{ij}})\).
These deviations are normally distributed with 0 mean and \(\color{#e41a1c}{\sigma}\) SD.

\[ \beta_{0j} = \color{#377eb8}{\gamma_{00}} + \color{#4daf4a}{u_{0j}}, \qquad \color{#4daf4a}{u_{0j}} \sim \text{Normal}(0, \color{#4daf4a}{\tau_{00}}) \]

\(\beta_{0j}\) is the Cluster Average for cluster \(j\) and equals…
…the Population Average \((\color{#377eb8}{\gamma_{00}})\) plus the Cluster Deviation \((\color{#4daf4a}{u_{0j}})\).
These deviations are normally distributed with 0 mean and \(\color{#4daf4a}{\tau_{00}}\) SD.

Notation Cheat Sheet

Symbol Name Meaning
\(\gamma_{00}\) Fixed Intercept The average outcome for the average cluster
\(u_{0j}\) Cluster Deviation How far cluster \(j\) is from the Fixed Intercept
\(\beta_{0j}\) Cluster Intercept The specific intercept for cluster \(j\)
\((\beta_{0j} = \gamma_{00} + u_{0j})\)
\(\tau_{00}\) Random Intercept SD The standard deviation of the \(u_{0j}\) deviations
(Between-cluster variation)
\(\sigma\) Residual SD The standard deviation of the \(e_{ij}\) residuals
(Within-cluster variation)

Parameter Interpretations

  • Manifest (Observed) Variables
    • \(y_{ij}\) is the outcome for observation \(i\) from cluster \(j\)
  • Estimated Parameters
    • \(\sigma\) is the SD of the L1 residuals
    • \(\gamma_{00}\) is the mean of the random intercept distribution
    • \(\tau_{00}\) is the SD of the random intercept distribution
  • Derivable Values
    • We don’t estimate \(\beta_{0j}\) or \(e_{ij}\) or \(u_{0j}\) but can derive them

Students in Schools Example

\[ \begin{align} \text{MATH}_{ij} &= \beta_{0j} + e_{ij} \\ \beta_{0j} &= \gamma_{00} + u_{0j} \end{align} \]

  • Level One: The math score for student \(i\) in school \(j\) is estimated by that student’s deviation \((e_{ij})\) from their school’s average math score \((\beta_{0j})\)

  • Level Two: The average math score for each school is estimated as its deviation \((u_{0j})\) from the average of all schools in the population \((\gamma_{00})\)

Days in Participants Example

\[ \begin{align} \text{STRESS}_{ij} &= \beta_{0j} + e_{ij} \\ \beta_{0j} &= \gamma_{00} + u_{0j} \end{align} \]

  • Level One: The stress reported on day \(i\) by participant \(j\) is estimated by that day’s deviation \((e_{ij})\) from the participant’s average daily stress \((\beta_{0j})\)

  • Level Two: The average daily stress reported by each participant is estimated as their deviation \((u_{0j})\) from the daily average of all participants in the population \((\gamma_{00})\)

Path Diagram

Mixed (or Reduced) Equation

\[ \begin{alignat}{2} &\text{L1:} \quad & y_{ij} &= \beta_{0j} + \color{#e41a1c}{e_{ij}} \\ &\text{L2:} \quad & \beta_{0j} &= \color{#377eb8}{\gamma_{00}} + \color{#4daf4a}{u_{0j}} \end{alignat} \]

Substitute the L2 equation directly into the L1 equation:

\[ y_{ij} = (\color{#377eb8}{\gamma_{00}} + \color{#4daf4a}{u_{0j}}) + \color{#e41a1c}{e_{ij}} \]

Rearrange to group the fixed and random parts:

\[ y_{ij} = \underbrace{\color{#377eb8}{\gamma_{00}}}_{\text{Fixed}} + \underbrace{\color{#4daf4a}{u_{0j}} + \color{#e41a1c}{e_{ij}}}_{\text{Random}} \]

This mixed equation is the basis of the R formula.

Formula

Generic

y ~ 1 + (1 | cluster)

where y is the outcome variable and cluster
is a factor indicating cluster membership,
the first 1 is the fixed intercept \((\gamma_{00})\),
and the (1) is the random intercept \((u_{0j})\)

Examples

math ~ 1 + (1 | school)

stress ~ 1 + (1 | participant)

Practicalities

Setup

library(tidyverse)
library(easystats)
library(lme4)

dat <- 
  read_csv("heck2011.csv") |> 
  mutate(school = factor(school))

glimpse(dat)
Rows: 6,871
Columns: 7
$ school  <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2,…
$ student <dbl> 6701, 6702, 6703, 6704, 6705, 6706, 6707, 6708, 6709, 6710, 67…
$ female  <dbl> 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ ses     <dbl> 0.586, 0.304, -0.544, -0.848, 0.001, -0.106, -0.330, -0.891, 0…
$ math    <dbl> 47.1400, 63.6100, 57.7100, 53.9000, 58.0100, 59.8700, 62.5556,…
$ puniv   <dbl> 0.08333333, 0.08333333, 0.08333333, 0.08333333, 0.08333333, 0.…
$ public  <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…

Fitting an Empty Model

fit_null <- lmer(
  formula = math ~ 1 + (1 | school),
  data = dat,
  REML = TRUE
)
model_parameters(fit_null)
# Fixed Effects

Parameter   | Coefficient |   SE |         95% CI | t(6868) |      p
--------------------------------------------------------------------
(Intercept) |       57.67 | 0.19 | [57.31, 58.04] |  306.34 | < .001

# Random Effects

Parameter              | Coefficient
------------------------------------
SD (Intercept: school) |        3.26
SD (Residual)          |        8.16

Interpreting the Table

  • The fixed intercept \((\gamma_{00}=57.67)\) is…
    • The mean of the distribution of the random intercepts
    • The average math score of the average school
  • The random intercept SD \((\tau_{00}=3.26)\) is…
    • The spread of the distribution of the random intercepts
    • The spread of average math scores between schools
  • The L1 residual SD \((\sigma=8.16)\) is…
    • The spread of the residuals at the lowest model level
    • The spread of students’ math scores within schools

The Cost of Ignoring Clustering

We can compare the fixed intercept point estimates and standard errors (SEs) between our MLM and a standard OLS model that ignores clustering.

# Fit OLS model with a fixed intercept
fit_ols <- lm(math ~ 1, data = dat)

# Compare the point and SE estimates
compare_parameters(fit_ols, fit_null, select = "se")
Parameter    |      fit_ols |     fit_null
------------------------------------------
(Intercept)  | 57.73 (0.11) | 57.67 (0.19)
------------------------------------------
Observations |         6871 |         6871

Note: The point estimates are similar, but the SE is larger in the MLM. The OLS model was too confident because it assumed all students were independent.

Why are the estimates different?

You might notice the intercept point estimates are slightly different.

  • OLS treats all observations as equal
    • Larger clusters dominate the estimate
    • e.g., A school with 100 students pulls the mean more than one with 10
  • MLM treats all clusters as (roughly) equal
    • It is a “precision-weighted” mean of the cluster means
    • Smaller clusters have less influence, but more than in OLS

Key Takeaway: If your clusters are different sizes, OLS is biased toward the larger clusters, while MLM is more representative of the “average cluster.”

Estimating the ICC (Manual)

To calculate the ICC, we first need to extract the Variances (not SDs!)

# Extract variance estimates
vars <- get_variance(fit_null)

tau2 <- vars$var.intercept  # between-school variance
sigma2 <- vars$var.residual # within-school variance

\[\rho = \frac{\tau_{00}^2}{\tau_{00}^2+\sigma^2}\]

# Calculate the ICC manually
tau2 / (tau2 + sigma2)
   school 
0.1378652

Reporting the ICC

In practice, we use convenience functions to estimate and report the ICC with uncertainty intervals.

# Use the performance package for a rigorous estimate
icc(fit_null, ci = 0.95)
# Intraclass Correlation Coefficient

    Adjusted ICC: 0.138 [0.109, 0.161]
  Unadjusted ICC: 0.138 [0.109, 0.161]
  • Interpretation:
    • 14% of the variance in math scores is between schools
    • 86% of the variance is within schools (among students)

Deriving L1 Residuals

What is each observation’s deviation from its cluster mean?

In other words, derive estimates of \(e_{ij}\) for every observation \(ij\)

get_residuals(fit_null)
            1             2             3             4             5 
-11.403679471   5.066320529  -0.833679471  -4.643679471  -0.533679471 
            6             7             8             9            10 
  1.326320529   4.011920529 -11.533679471  13.876320529   7.296320529 
           11            12            13            14            15 
 -1.203679471   4.011920529   0.253287014   8.520487014  -2.919512986 
           16            17            18            19            20 
  3.840487014  -1.929512986   2.370487014   0.253287014   5.130487014 
           21            22            23            24            25 
  7.710487014  -5.189512986  -4.479512986   3.190487014   8.420487014 
           26            27            28            29            30 
 -1.415613204  -5.525613204  10.417286796  -5.185613204   0.724386796 
           31            32            33            34            35 
 -7.235613204   0.494386796 -10.505613204 -12.375613204  -6.075613204 
           36            37            38            39            40 
  7.054386796  -9.205613204 -12.555613204  10.417286796   2.074386796 
           41            42            43            44            45 
 10.417286796  -8.575613204  -9.835613204  -0.809886246  -0.809886246 
           46            47            48            49            50 
 -0.809886246  -0.809886246   5.522213754  15.462213754  -0.809886246 
           51            52            53            54            55 
 -0.809886246  -0.809886246  -0.809886246   9.572213754   7.622213754 
           56            57            58            59            60 
 -0.809886246  -0.809886246  -0.809886246  -0.809886246   8.082213754 
           61            62            63            64            65 
 -0.041499735  11.595200265   0.648500265  -4.841499735  -0.711499735 
           66            67            68            69            70 
  9.658500265  -4.971499735 -10.821499735   8.948500265 -15.591499735 
           71            72            73            74            75 
-13.551499735 -10.591499735  -2.441499735  -0.271499735   3.048500265 
           76            77            78            79            80 
-15.821499735   2.028500265   0.488805454  -1.128094546   0.494105454 
           81            82            83            84            85 
  6.981905454   8.011905454   9.091905454   0.494105454  12.501905454 
           86            87            88            89            90 
  0.494105454   0.494105454   0.494105454   0.494105454   0.494105454 
           91            92            93            94            95 
  0.494105454 -11.158094546 -13.648094546   3.135374915   7.801774915 
           96            97            98            99           100 
  1.301774915   1.051774915   2.071774915  12.121774915 -18.138225085 
          101           102           103           104           105 
  3.135374915  11.981774915   4.651774915  13.971774915  -5.248225085 
          106           107           108           109           110 
  3.135374915 -19.158225085 -14.928225085  -8.238225085  -8.874957031 
          111           112           113           114           115 
 11.815042969  10.085042969  -1.204957031   9.295042969  10.095042969 
          116           117           118           119           120 
 -2.544957031  -3.184957031   3.525042969  -0.374957031 -13.244957031 
          121           122           123           124           125 
-13.774957031   5.685042969  -7.504957031   6.035042969   0.928842969 
          126           127           128           129           130 
-19.404957031  -6.174957031   0.928842969   0.928842969  10.095042969 
          131           132           133           134           135 
 12.965042969  -6.254957031   0.928842969  17.445042969   0.928842969 
          136           137           138           139           140 
  2.654494993   7.434494993   6.786294993 -16.825505007   2.384494993 
          141           142           143           144           145 
  3.574494993  -5.255505007   1.284494993 -18.515505007  -3.085505007 
          146           147           148           149           150 
 -1.625505007   2.374494993  -0.415505007   0.764494993  -6.105505007 
          151           152           153           154           155 
 17.354494993  -5.845505007   7.129319771   5.169319771  14.039319771 
          156           157           158           159           160 
  1.625219771   1.059319771  -4.300680229  -0.730680229   1.625219771 
          161           162           163           164           165 
  1.625219771 -10.430680229  -8.490680229  -6.210680229   4.459319771 
          166           167           168           169           170 
  6.729319771  -1.040680229   6.329319771   1.625219771  -4.940680229 
          171           172           173           174           175 
  1.625219771   1.716519771  14.095455114   5.529255114  -1.624544886 
          176           177           178           179           180 
  2.415455114  -5.984544886 -13.874544886  -7.494544886  -3.734544886 
          181           182           183           184           185 
 10.505455114 -16.114544886 -18.314544886   5.529355114  11.875455114 
          186           187           188           189           190 
  5.529355114   6.745455114   1.195455114  -7.684544886   5.529355114 
          191           192           193           194           195 
  9.014567167   4.670667167   4.670667167  -3.055432833   4.670667167 
          196           197           198           199           200 
-13.575432833   4.670667167 -21.865432833   4.670667167  -5.385432833 
          201           202           203           204           205 
  4.670667167  -4.155432833   2.759756742   2.759756742   2.759756742 
          206           207           208           209           210 
  2.759756742   2.759756742   2.759756742   2.759756742   2.759756742 
          211           212           213           214           215 
  8.155356742  -5.124643258  -1.754643258   2.759756742   2.759756742 
          216           217           218           219           220 
  6.375356742 -20.674643258 -10.694643258   4.448126082   9.050226082 
          221           222           223           224           225 
-11.139773918   6.350226082   2.730226082   4.448126082 -16.599773918 
          226           227           228           229           230 
 -1.749773918   0.830226082   8.620226082   4.448126082   4.448126082 
          231           232           233           234           235 
-19.359773918   4.448126082   0.581337999   0.581337999   1.317937999 
          236           237           238           239           240 
  1.967937999   0.582637999   0.582637999   0.582637999   0.582637999 
          241           242           243           244           245 
  0.582637999   0.582637999   0.582637999   0.582637999   0.582637999 
          246           247           248           249           250 
  0.582637999   3.087937999  12.707937999   0.057937999   0.582637999 
          251           252           253           254           255 
  0.582637999   0.582837999   4.501281441  -4.136418559 -19.516418559 
          256           257           258           259           260 
  4.501281441   4.501281441   4.501281441 -13.696418559   4.501281441 
          261           262           263           264           265 
 -0.916418559   4.501381441   4.501381441   2.203581441  -5.376418559 
          266           267           268           269           270 
  7.342917585  -9.915782415 -20.295782415   7.342917585  -4.555782415 
          271           272           273           274           275 
  7.342917585  -7.865782415   4.384217585 -10.495782415  -4.005782415 
          276           277           278           279           280 
  2.954217585  -7.385782415   7.342917585  -1.395782415  -5.615782415 
          281           282           283           284           285 
  0.364217585   1.444217585  10.234217585   7.342917585   1.558733599 
          286           287           288           289           290 
  1.558733599   1.558733599 -16.139766401   8.950233599   4.030233599 
          291           292           293           294           295 
  1.558733599  -2.479766401  -1.729766401  12.690233599   1.558733599 
          296           297           298           299           300 
  1.558733599   1.558733599   9.060233599  -5.559766401   5.154684760 
          301           302           303           304           305 
  3.337784760  -8.655315240   3.337784760  -9.375315240   3.337784760 
          306           307           308           309           310 
  3.337784760  -7.295315240   3.337784760   4.524684760 -11.855315240 
          311           312           313           314           315 
  3.337784760   1.674684760   3.337784760   2.844684760   3.729723052 
          316           317           318           319           320 
  2.609723052   3.729723052   3.729723052   1.259723052  -7.780276948 
          321           322           323           324           325 
 -8.360276948   2.179723052   3.729723052 -11.570276948   3.729823052 
          326           327           328           329           330 
  3.729823052   6.199723052   3.070468573  12.457968573   3.070468573 
          331           332           333           334           335 
-29.642031427  12.607968573  -9.902031427   3.070468573  -6.922031427 
          336           337           338           339           340 
-16.032031427   3.070468573   3.070468573  14.447968573   5.897968573 
          341           342           343           344           345 
  3.070468573   3.070468573   0.287968573   3.070468573 -12.332031427 
          346           347           348           349           350 
  5.127968573   9.617968573 -10.098122094   4.815477906  -9.008122094 
          351           352           353           354           355 
  4.815477906   2.411877906   3.731877906 -16.178122094  -5.988122094 
          356           357           358           359           360 
  1.731877906   4.815477906   5.341877906   4.815477906   3.003876468 
          361           362           363           364           365 
  3.199876468   3.199876468  -8.766023532 -19.916023532   3.199876468 
          366           367           368           369           370 
  4.833976468  -0.006023532   3.199876468   3.993976468   3.199876468 
          371           372           373           374           375 
  4.723976468   3.199876468   3.199876468 -14.722741174 -14.102741174 
          376           377           378           379           380 
 -4.692741174   2.535558826   2.535558826   2.535558826 -11.902741174 
          381           382           383           384           385 
  2.535558826   2.535558826  13.277258826  -8.132741174  14.887258826 
          386           387           388           389           390 
  2.535558826  10.007258826   2.535558826 -10.396111223   6.546788777 
          391           392           393           394           395 
  6.546788777   6.546788777 -20.136111223   6.546788777 -10.496111223 
          396           397           398           399           400 
  3.873888777   6.546788777 -17.496111223  -9.066111223   6.546788777 
          401           402           403           404           405 
  6.546788777   6.546788777   6.546788777 -20.626111223   6.546788777 
          406           407           408           409           410 
  6.546788777   1.583888777   2.049308553   2.049308553 -11.898491447 
          411           412           413           414           415 
  2.049308553   9.251508553  -8.918491447   2.049308553   2.049308553 
          416           417           418           419           420 
  2.049308553   7.651508553  -4.428491447 -13.088491447   2.049308553 
          421           422           423           424           425 
  2.049308553   2.049308553   2.049308553   2.049308553  14.861508553 
          426           427           428           429           430 
 -3.951924614  -4.361924614   7.674875386   7.674875386 -12.331924614 
          431           432           433           434           435 
  7.674875386  21.378075386  12.508075386 -13.621924614   7.674875386 
          436           437           438           439           440 
 -6.311924614 -17.621924614  -1.841924614  -1.041924614  -8.701924614 
          441           442           443           444           445 
  7.674875386   1.538075386  -3.891924614 -19.331924614  -0.976576565 
          446           447           448           449           450 
  4.663923435  -0.534376565   4.193923435  -1.206076565  -1.296076565 
          451           452           453           454           455 
 -2.906076565  -1.226076565   3.683923435 -11.116076565   2.283923435 
          456           457           458           459           460 
 -0.534376565   3.503923435  -3.956076565  -4.506076565  -1.586076565 
          461           462           463           464           465 
 -1.466076565  -1.966076565  37.113923435  10.833923435  -0.534376565 
          466           467           468           469           470 
  3.254510961 -13.257089039   9.722910961   3.254510961  -0.297089039 
          471           472           473           474           475 
  4.232910961  -8.187089039   1.242910961  -6.257089039   6.082910961 
          476           477           478           479           480 
  3.254510961  -9.817089039  12.682910961   3.112910961   1.122910961 
          481           482           483           484           485 
-14.944917106 -10.864917106  15.265082894 -13.354917106 -16.824917106 
          486           487           488           489           490 
  6.276782894  -4.164917106  -5.334917106   6.276782894   7.015082894 
          491           492           493           494           495 
 -7.734917106   9.345082894  -3.344917106   6.835082894 -15.924917106 
          496           497           498           499           500 
 -3.324917106   9.015082894   6.276782894  12.735082894   6.276782894 
          501           502           503           504           505 
  7.968907449 -16.021092551   5.331407449   5.331407449   5.331407449 
          506           507           508           509           510 
  3.968907449   5.331407449 -21.181092551   5.331407449  -7.811092551 
          511           512           513           514           515 
  5.331407449  13.488907449 -20.021092551   7.358907449   5.331407449 
          516           517           518           519           520 
  8.408907449 -15.651092551  14.068907449 -15.281092551  -5.141092551 
          521           522           523           524           525 
  0.656680525   0.656680525   0.656680525   0.656680525   0.656680525 
          526           527           528           529           530 
  0.656680525   0.656680525   0.656680525   0.656680525   0.656680525 
          531           532           533           534           535 
  0.656680525   0.656680525   0.656680525   0.656680525   0.656680525 
          536           537           538           539           540 
  0.656680525   0.656680525   0.656680525   0.656680525   0.656680525 
          541           542           543           544           545 
  0.656680525   0.656680525   0.656680525   0.656680525   0.656680525 
          546           547           548           549           550 
  0.656680525   0.656680525   0.656680525   0.656680525   0.656680525 
          551           552           553           554           555 
  0.656680525   0.656680525   0.656680525   0.656680525   0.656680525 
          556           557           558           559           560 
  0.656680525 -14.687466936   9.163933064  -3.287466936 -10.137466936 
          561           562           563           564           565 
 -6.007466936  -4.407466936  -3.157466936   9.163933064 -21.327466936 
          566           567           568           569           570 
 -5.037466936   0.282533064   9.163933064  -4.187466936  -8.017466936 
          571           572           573           574           575 
 11.052533064   8.182533064   9.163933064   9.163933064   8.452533064 
          576           577           578           579           580 
 -9.507466936 -11.147466936   7.496003339 -18.673996661   9.456003339 
          581           582           583           584           585 
 -0.373996661  10.576003339 -12.233996661  -6.623996661 -17.393996661 
          586           587           588           589           590 
  3.854803339 -25.693996661   3.854803339  -6.323996661  -1.833996661 
          591           592           593           594           595 
 42.756003339   6.316003339   4.246003339   3.854803339  -6.073996661 
          596           597           598           599           600 
  0.560455828  10.733155828   0.560455828   0.560455828   0.560455828 
          601           602           603           604           605 
  0.560455828  10.263155828   0.560455828   0.560455828   7.053155828 
          606           607           608           609           610 
 -8.376844172   0.560455828  -9.506844172  -5.727619190   8.122380810 
          611           612           613           614           615 
 -8.677619190   6.826480810   7.962380810  -2.727619190   8.122380810 
          616           617           618           619           620 
 -3.427619190  -1.717619190   5.132380810 -16.537619190 -21.717619190 
          621           622           623           624           625 
  0.193049612  12.013549612   7.463549612   8.823549612  -6.916450388 
          626           627           628           629           630 
  0.193049612   5.953549612   5.753549612   0.193049612  -5.576450388 
          631           632           633           634           635 
 -6.406450388   0.193049612   0.193049612  -4.356450388  -0.756450388 
          636           637           638           639           640 
 -4.271546319  -7.121546319  -4.081546319  -6.801546319  -0.201546319 
          641           642           643           644           645 
  5.200153681   5.768453681  -5.231546319  -8.211546319   5.200153681 
          646           647           648           649           650 
  4.008453681   5.158453681   6.050236378  17.710236378   6.330236378 
          651           652           653           654           655 
  4.744836378   0.440236378  -5.679763622  -4.709763622   4.744936378 
          656           657           658           659           660 
 -9.329763622 -15.659763622  -8.429763622   2.020236378  11.850236378 
          661           662           663           664           665 
 -3.169763622  -2.369763622  -6.509763622  10.540236378  -1.629763622 
          666           667           668           669           670 
-17.579763622   9.670236378  -4.186271783   7.247028217   7.247028217 
          671           672           673           674           675 
 -4.466271783  -5.456271783 -14.806271783 -11.436271783  -5.566271783 
          676           677           678           679           680 
  7.247028217   7.247028217 -17.536271783   7.247028217 -18.006271783 
          681           682           683           684           685 
  7.247028217  13.093728217   0.883728217  19.113943347   1.132643347 
          686           687           688           689           690 
  4.243943347   1.132643347   1.132643347   1.132643347 -13.546056653 
          691           692           693           694           695 
  5.693943347   1.132643347   1.132643347  -1.816056653  -0.676056653 
          696           697           698           699           700 
  5.683943347  -3.456056653   1.132643347   1.132643347   5.923943347 
          701           702           703           704           705 
-24.056056653   1.132643347   0.503943347   1.132643347   1.132643347 
          706           707           708           709           710 
  1.132643347   4.911771213 -13.458228787   3.031471213   6.281771213 
          711           712           713           714           715 
 -0.848228787   8.541771213  -2.568228787  13.891771213   4.231771213 
          716           717           718           719           720 
 -5.408228787  -7.138228787  -2.928228787  -8.078228787  -8.898196022 
          721           722           723           724           725 
  3.740203978   2.021803978  10.511803978   8.581803978  11.341803978 
          726           727           728           729           730 
 -6.668196022   1.141803978   2.391803978   3.816703978 -12.258196022 
          731           732           733           734           735 
 -1.888196022   6.621803978 -12.858196022  -2.008196022 -19.421119596 
          736           737           738           739           740 
 -6.751119596  -9.341119596  14.098880404   1.575980404   2.878880404 
          741           742           743           744           745 
  1.628880404   1.575980404   0.268880404   1.575980404   7.878880404 
          746           747           748           749           750 
  2.858880404   4.708880404   1.575980404  -3.391119596   1.575980404 
          751           752           753           754           755 
  1.575980404   1.248880404  13.368880404  19.000461586   0.868961586 
          756           757           758           759           760 
  0.868961586  -4.189538414  -2.909538414  11.020461586   0.868961586 
          761           762           763           764           765 
  0.868961586  15.120461586  -3.819538414   3.080461586 -16.299538414 
          766           767           768           769           770 
 -9.449538414   2.460461586 -11.289538414  -4.149538414  20.130461586 
          771           772           773           774           775 
  1.460461586 -10.789538414   5.387876016 -10.270923984   0.889076016 
          776           777           778           779           780 
 -3.340923984   5.387876016  -6.510923984   5.387876016  -3.640923984 
          781           782           783           784           785 
-10.750923984   6.349076016   5.387876016   5.387876016   1.529076016 
          786           787           788           789           790 
  5.387876016 -10.260923984  -3.660923984  -1.380923984   5.387876016 
          791           792           793           794           795 
-13.263573526 -15.703573526   8.916826474 -19.333573526 -11.653573526 
          796           797           798           799           800 
-18.573573526   8.916826474 -12.863573526   8.916826474   8.916826474 
          801           802           803           804           805 
 -6.083573526  11.456426474   8.916826474   6.186426474   8.916826474 
          806           807           808           809           810 
  3.786010718   3.786010718 -12.805989282   3.786010718  -0.605989282 
          811           812           813           814           815 
 -0.115989282  -6.485989282   3.786010718   3.786010718  -8.915989282 
          816           817           818           819           820 
  3.786010718   3.786010718  -9.273343616  -4.003343616  -5.303343616 
          821           822           823           824           825 
 18.816656384 -14.343343616   2.934356384   2.934356384  -1.743343616 
          826           827           828           829           830 
  9.026656384  -1.473343616  -1.493343616   2.934456384   2.934456384 
          831           832           833           834           835 
  2.934456384   0.226656384  11.666656384   2.934456384 -20.653343616 
          836           837           838           839           840 
 -2.992107067  -5.482107067   4.547892933   2.027892933  -8.982107067 
          841           842           843           844           845 
  8.641892933 -16.022107067   8.337892933 -21.172107067   8.641892933 
          846           847           848           849           850 
  9.297892933 -12.122107067  -8.593330514   8.526669486   2.491369486 
          851           852           853           854           855 
  2.491469486   2.491469486  -2.123330514   2.491469486   2.491469486 
          856           857           858           859           860 
  2.491469486   2.491469486   1.726669486  -4.913330514   0.369871257 
          861           862           863           864           865 
  0.369871257   0.369871257   0.369871257   0.369871257   0.369871257 
          866           867           868           869           870 
  0.369871257   0.369871257  14.540771257   0.369871257   0.369871257 
          871           872           873           874           875 
  0.369871257   0.369871257   5.436255049  10.886255049   2.032355049 
          876           877           878           879           880 
  2.032355049  -6.333744951   2.032355049   8.756255049  -9.333744951 
          881           882           883           884           885 
  2.032355049   2.032355049   2.032355049  -7.513744951   2.032355049 
          886           887           888           889           890 
  2.032355049  13.206255049   2.032355049 -23.423744951   2.032355049 
          891           892           893           894           895 
 -0.505040576   2.716859424   0.156859424  -0.505040576  -0.643140576 
          896           897           898           899           900 
 14.756859424  -0.505040576   6.426859424  -0.505040576  -0.505040576 
          901           902           903           904           905 
 -0.505040576   8.416859424  -0.505040576   2.526859424  -5.763266726 
          906           907           908           909           910 
-11.483266726   2.716733274  -6.863266726  -9.143266726  10.836133274 
          911           912           913           914           915 
  7.246733274   3.936733274 -10.493266726  -6.583266726  -8.623266726 
          916           917           918           919           920 
 -8.613266726 -11.763266726   8.186733274  -4.333266726  -6.503266726 
          921           922           923           924           925 
 10.836133274 -11.315762473   4.446137527  -7.735762473   4.446137527 
          926           927           928           929           930 
  4.446137527   7.284237527   4.446137527   4.446137527  -7.055762473 
          931           932           933           934           935 
-14.435762473  -2.055762473   1.854237527   0.204237527   4.468837527 
          936           937           938           939           940 
  4.194217688   4.194217688   4.194217688   4.194317688 -15.720182312 
          941           942           943           944           945 
-19.890182312   4.194317688   4.194317688   4.194317688   4.194317688 
          946           947           948           949           950 
 -5.400182312   4.194317688   4.194317688   4.194317688  -1.900182312 
          951           952           953           954           955 
  0.746081644   4.204181644   4.204181644   4.204181644  -7.423918356 
          956           957           958           959           960 
  4.204181644   4.204181644   4.204181644   4.204181644  -6.223918356 
          961           962           963           964           965 
  4.204181644   4.204181644  -9.303918356   4.204181644 -16.773918356 
          966           967           968           969           970 
  0.445883318   1.904183318   1.904183318   1.904183318   1.904183318 
          971           972           973           974           975 
  1.904183318   2.165883318  -6.364116682   0.925883318  16.825883318 
          976           977           978           979           980 
  1.904183318  -8.204116682   0.895883318  -8.784116682   1.904183318 
          981           982           983           984           985 
-10.804116682   2.972783318   2.972783318  -9.921033418  -8.461033418 
          986           987           988           989           990 
 -9.981033418   8.145166582 -15.911033418   8.145166582   8.145166582 
          991           992           993           994           995 
 -5.331033418   8.145166582   3.768966582 -14.981033418   8.145166582 
          996           997           998           999          1000 
-10.211033418   8.145166582   2.392882829 -14.326817171   2.392882829 
         1001          1002          1003          1004          1005 
  2.392882829  -0.446817171   2.392882829  -2.956817171  14.843182829 
         1006          1007          1008          1009          1010 
  0.253182829   2.392882829   2.392882829 -22.866817171   0.853182829 
         1011          1012          1013          1014          1015 
 -7.726817171   1.993182829   2.392882829  -6.956817171   3.603182829 
         1016          1017          1018          1019          1020 
 17.593182829   9.163182829  -6.194798027  -7.434798027  13.399401973 
         1021          1022          1023          1024          1025 
 -6.024798027  -7.984798027  -8.534798027   2.175201973   9.755201973 
         1026          1027          1028          1029          1030 
 -8.424798027  -9.444798027  -3.594798027 -13.334798027  13.399401973 
         1031          1032          1033          1034          1035 
 -7.414798027 -13.804798027   3.455835925   3.455835925  16.969035925 
         1036          1037          1038          1039          1040 
  0.129035925   3.549035925 -16.100964075   3.455835925   3.455835925 
         1041          1042          1043          1044          1045 
-15.970964075  -6.140964075   9.629035925   0.899035925   3.455835925 
         1046          1047          1048          1049          1050 
-16.330964075   3.455835925   3.455835925   3.455835925   3.455835925 
         1051          1052          1053          1054          1055 
 12.169679496   4.011979496  -6.450320504   4.011979496   4.011979496 
         1056          1057          1058          1059          1060 
 18.999679496   4.011979496 -10.310320504   4.011979496   1.869679496 
         1061          1062          1063          1064          1065 
-15.560320504  -9.410320504  -2.510320504   4.011979496   4.011979496 
         1066          1067          1068          1069          1070 
-11.590320504  16.479561313  -0.790438687  -7.960438687   0.903961313 
         1071          1072          1073          1074          1075 
  0.903961313   2.669561313   0.903961313  -0.200438687  15.619561313 
         1076          1077          1078          1079          1080 
  0.903961313  -5.690438687   3.389561313  -4.550438687   1.220061313 
         1081          1082          1083          1084          1085 
  6.983394921   6.153394921   6.016794921   6.016794921  22.663394921 
         1086          1087          1088          1089          1090 
  6.016794921 -17.616605079 -16.766605079 -24.926605079   6.016794921 
         1091          1092          1093          1094          1095 
  6.016794921   6.016794921   6.016794921 -22.246605079   6.016794921 
         1096          1097          1098          1099          1100 
  3.863394921 -15.106605079 -11.120592160   1.532807840  15.179407840 
         1101          1102          1103          1104          1105 
 13.869407840   7.269407840  -5.760592160  -3.280592160  -1.550592160 
         1106          1107          1108          1109          1110 
  1.532807840   4.999407840   1.532807840 -14.090592160   1.558107840 
         1111          1112          1113          1114          1115 
  4.980696991   6.414796991   4.980696991   7.704796991   4.980696991 
         1116          1117          1118          1119          1120 
-19.805203009   4.980696991  -1.205203009 -16.245203009   4.980696991 
         1121          1122          1123          1124          1125 
 -3.025203009   6.804796991   4.980696991 -12.335203009 -11.001262765 
         1126          1127          1128          1129          1130 
  2.618737235 -18.461262765   5.538737235  -6.491262765   7.269237235 
         1131          1132          1133          1134          1135 
 -6.161262765   9.058737235   7.269237235   7.269237235  -3.151262765 
         1136          1137          1138          1139          1140 
  7.269237235 -12.581262765  -4.021262765  -8.581262765   0.059388034 
         1141          1142          1143          1144          1145 
  5.550688034  -5.589311966   0.059488034  12.520688034   5.200688034 
         1146          1147          1148          1149          1150 
 -7.729311966  -3.589311966   4.440688034   1.090688034   4.990688034 
         1151          1152          1153          1154          1155 
 -1.809311966  -2.969311966   4.320688034  12.500688034   1.121485240 
         1156          1157          1158          1159          1160 
 -2.728514760   5.989985240  -9.818514760   5.989985240   3.511485240 
         1161          1162          1163          1164          1165 
-11.678514760   5.989985240  -2.048514760  -8.538514760   5.989985240 
         1166          1167          1168          1169          1170 
 -1.558514760   5.989985240  -1.038514760  -9.778514760  10.246591464 
         1171          1172          1173          1174          1175 
 -7.459508536   1.320491464 -17.829508536  -6.249508536 -11.579508536 
         1176          1177          1178          1179          1180 
 10.246591464  -2.069508536  -6.689508536 -10.699508536   8.820491464 
         1181          1182          1183          1184          1185 
 -9.089508536 -19.199508536   4.610491464   7.090491464  10.246591464 
         1186          1187          1188          1189          1190 
 -6.469508536  10.246591464  -0.229508536   9.671905433  -8.998094567 
         1191          1192          1193          1194          1195 
 -5.808094567   4.325005433   4.325005433   4.325005433   4.325005433 
         1196          1197          1198          1199          1200 
 -2.328094567  -5.998094567 -10.738094567   1.431905433  -9.508094567 
         1201          1202          1203          1204          1205 
  4.325005433  -1.798094567  -1.418094567   0.691905433   4.325005433 
         1206          1207          1208          1209          1210 
  6.621905433   5.045059803  -7.554940197   7.175059803  -0.975140197 
         1211          1212          1213          1214          1215 
 13.155059803  -0.975140197  -0.975140197  -0.975040197  -0.975040197 
         1216          1217          1218          1219          1220 
  5.335059803   5.535059803  -2.144940197  -0.975040197  -0.975040197 
         1221          1222          1223          1224          1225 
 -0.975040197  -0.975040197  14.565059803  -2.993753519  -1.703753519 
         1226          1227          1228          1229          1230 
  9.556246481  12.626246481   1.106246481   8.736246481 -18.343753519 
         1231          1232          1233          1234          1235 
  3.646246481  -3.363753519   7.846246481   4.768646481  -8.143753519 
         1236          1237          1238          1239          1240 
  1.576246481  -1.233753519 -19.033753519   5.576246481   3.230829469 
         1241          1242          1243          1244          1245 
  3.230829469   3.230829469 -18.974770531  -5.774770531  -8.254770531 
         1246          1247          1248          1249          1250 
  3.230829469  -1.714770531   3.230829469   3.230829469  14.265229469 
         1251          1252          1253          1254          1255 
  3.230829469   3.230829469  -7.744770531   3.230829469  -1.119358023 
         1256          1257          1258          1259          1260 
 -1.119358023  -1.119358023  11.542241977   9.852241977  -1.119358023 
         1261          1262          1263          1264          1265 
 -1.119358023  -1.119358023  -1.119358023  -1.119358023  -1.119358023 
         1266          1267          1268          1269          1270 
 -1.119358023  -1.119358023  -1.119358023   5.112241977  -1.119358023 
         1271          1272          1273          1274          1275 
  8.192241977  -1.119358023  -1.119358023  -1.119358023  -1.119258023 
         1276          1277          1278          1279          1280 
 -1.119258023  -1.119258023  -1.119258023  15.692241977   0.470841977 
         1281          1282          1283          1284          1285 
 -1.470390099  -0.470390099  -7.110390099   0.919609901 -18.020390099 
         1286          1287          1288          1289          1290 
 -8.790390099   6.126909901  11.059609901   1.359609901  -8.340390099 
         1291          1292          1293          1294          1295 
 13.769609901  -3.670390099  -6.520390099   6.126909901   6.126909901 
         1296          1297          1298          1299          1300 
 -6.289095384   7.289704616   7.289704616 -16.209095384   3.380904616 
         1301          1302          1303          1304          1305 
  2.240904616 -15.109095384   6.870904616   7.289704616   7.289704616 
         1306          1307          1308          1309          1310 
 -7.699095384 -13.199095384   9.517952866  -0.828747134  -0.982047134 
         1311          1312          1313          1314          1315 
 10.397952866  -1.692047134   0.057952866  -0.828747134   0.747952866 
         1316          1317          1318          1319          1320 
  6.007952866  -0.828747134   7.927952866  -1.582047134  -1.652047134 
         1321          1322          1323          1324          1325 
 13.437952866 -10.742047134  -7.782047134   6.777952866  -0.828747134 
         1326          1327          1328          1329          1330 
  6.624647112   6.624647112  19.208247112   6.624647112   6.624647112 
         1331          1332          1333          1334          1335 
-27.601752888 -16.551752888  -1.681752888  -6.701752888 -10.081752888 
         1336          1337          1338          1339          1340 
  8.338247112  -8.151752888   0.138247112 -15.722392116  -4.042392116 
         1341          1342          1343          1344          1345 
 -3.322392116   2.651807884   7.967607884   3.677607884  16.247607884 
         1346          1347          1348          1349          1350 
 15.217607884  -1.132392116   0.047607884 -16.042392116   3.747607884 
         1351          1352          1353          1354          1355 
  2.651907884   5.467607884   4.677607884  -5.982392116  -7.492392116 
         1356          1357          1358          1359          1360 
  0.877607884   6.987607884  -8.052392116 -10.616717896  -5.076717896 
         1361          1362          1363          1364          1365 
 -3.726717896   4.573282104   0.324082104 -17.846717896   0.324082104 
         1366          1367          1368          1369          1370 
  6.593282104  11.673282104  -3.216717896   3.643282104  -2.266717896 
         1371          1372          1373          1374          1375 
  0.324182104   7.893282104 -12.736717896   4.643282104   3.853282104 
         1376          1377          1378          1379          1380 
  8.453282104   6.963282104   4.313282104  -1.656717896 -15.326717896 
         1381          1382          1383          1384          1385 
 15.133282104   6.533282104 -12.886717896   0.324182104  -4.856717896 
         1386          1387          1388          1389          1390 
  6.183282104  15.153282104  -0.726717896   1.503027146   1.503027146 
         1391          1392          1393          1394          1395 
  9.607827146   1.503027146   1.503027146   1.503027146   1.503027146 
         1396          1397          1398          1399          1400 
  4.007827146  -7.082172854   1.503027146   1.503027146   1.503027146 
         1401          1402          1403          1404          1405 
  4.250916148  10.402616148   4.250916148  41.712616148   4.250916148 
         1406          1407          1408          1409          1410 
 -9.097383852   4.250916148  -3.537383852 -10.547383852 -20.337383852 
         1411          1412          1413          1414          1415 
-10.197383852  -7.067383852   4.251016148 -13.127383852   4.251016148 
         1416          1417          1418          1419          1420 
  6.286792443 -11.934407557 -20.574407557  -1.654407557   6.286792443 
         1421          1422          1423          1424          1425 
 15.565592443  -9.544407557   6.286792443  -3.804407557  -4.714407557 
         1426          1427          1428          1429          1430 
 11.185592443   6.286792443 -17.214407557  -8.324407557   3.885592443 
         1431          1432          1433          1434          1435 
  6.815592443   6.286892443  -9.100075445   2.043024555  -5.110075445 
         1436          1437          1438          1439          1440 
 10.759924555   4.569924555  -2.770075445   2.043024555   5.559924555 
         1441          1442          1443          1444          1445 
  2.043024555   2.043024555   2.043024555   2.043024555   2.043024555 
         1446          1447          1448          1449          1450 
 -6.230075445   1.338666332   1.338666332   1.338666332  12.591066332 
         1451          1452          1453          1454          1455 
-20.638933668   1.338666332   6.851066332   1.338666332  -2.078933668 
         1456          1457          1458          1459          1460 
  9.351066332 -11.628933668   1.338666332   1.338666332   1.338666332 
         1461          1462          1463          1464          1465 
 -8.128933668  10.021066332   5.351066332  -5.228933668   1.338666332 
         1466          1467          1468          1469          1470 
  1.338666332  -9.269527480   2.668972520   2.672872520  12.050472520 
         1471          1472          1473          1474          1475 
 -2.089527480 -12.679527480   2.672872520   2.672972520   3.770472520 
         1476          1477          1478          1479          1480 
  2.672972520  -6.219527480   2.672972520  11.913608116  -0.016391884 
         1481          1482          1483          1484          1485 
  1.604708116  10.243608116   1.604708116   6.713608116   1.604708116 
         1486          1487          1488          1489          1490 
-10.146391884  -2.166391884   1.604708116   1.620708116   1.513608116 
         1491          1492          1493          1494          1495 
-18.836391884   1.620708116   1.620708116   3.383608116  -8.486391884 
         1496          1497          1498          1499          1500 
  5.173608116  -2.476391884   1.620708116   4.243608116   6.253608116 
         1501          1502          1503          1504          1505 
  0.230232806   9.780232806 -17.829767194  -0.969767194  -8.739767194 
         1506          1507          1508          1509          1510 
  2.760832806   5.560232806  -7.099767194   5.380232806   2.570232806 
         1511          1512          1513          1514          1515 
  7.500232806  -6.319767194   8.200232806   6.250232806   2.760832806 
         1516          1517          1518          1519          1520 
 -3.579767194  -5.419767194   2.209408911   2.209408911   0.122808911 
         1521          1522          1523          1524          1525 
 11.082808911   2.209408911  12.092808911  -6.817191089   2.209408911 
         1526          1527          1528          1529          1530 
 -1.407191089  -5.737191089   2.209408911  -3.477191089   2.209408911 
         1531          1532          1533          1534          1535 
 -0.487191089  -3.727191089   6.752520364 -10.831179636   6.755920364 
         1536          1537          1538          1539          1540 
 -4.451179636   2.568820364   6.755920364   3.428820364 -15.001179636 
         1541          1542          1543          1544          1545 
  6.755920364 -13.301179636   9.478820364  -9.441179636  -5.601179636 
         1546          1547          1548          1549          1550 
  6.755920364  -4.041179636   6.755920364   6.755920364  -6.441179636 
         1551          1552          1553          1554          1555 
  6.755920364   6.755920364 -19.781179636  11.128820364 -21.311179636 
         1556          1557          1558          1559          1560 
  4.788820364   6.755920364 -15.161179636   6.755920364   6.755920364 
         1561          1562          1563          1564          1565 
  2.017942835   2.018142835   8.033142835  -0.936857165   2.018142835 
         1566          1567          1568          1569          1570 
  2.018142835  -9.396857165  -7.476857165   7.323142835  13.013142835 
         1571          1572          1573          1574          1575 
  2.018142835   2.018142835 -10.456857165  -6.823756796   4.766243204 
         1576          1577          1578          1579          1580 
  0.696243204   8.386243204 -11.543756796  -3.043756796  11.876243204 
         1581          1582          1583          1584          1585 
  3.074843204   3.074843204  -8.713756796   1.226243204   3.074843204 
         1586          1587          1588          1589          1590 
-17.543756796  -2.073756796   3.074843204   3.074843204  -4.243756796 
         1591          1592          1593          1594          1595 
 -4.663756796  12.246243204   3.074843204   2.698636655   2.698636655 
         1596          1597          1598          1599          1600 
  2.698636655  -6.147463345   0.172536655  -2.927463345   2.698636655 
         1601          1602          1603          1604          1605 
  2.698636655   2.698636655   2.698636655  -0.847463345   2.698636655 
         1606          1607          1608          1609          1610 
 -0.635873823   0.833726177   0.843026177   0.843026177   2.564126177 
         1611          1612          1613          1614          1615 
  2.134126177   0.843026177  -9.555873823 -13.985873823   6.614126177 
         1616          1617          1618          1619          1620 
  0.843026177 -10.615873823   0.843026177   0.843026177   3.444126177 
         1621          1622          1623          1624          1625 
  5.784126177   7.634126177   0.843026177   9.764126177  11.204126177 
         1626          1627          1628          1629          1630 
  8.744481202   2.879781202  -3.705518798   2.879781202   2.879781202 
         1631          1632          1633          1634          1635 
  2.879781202   2.879781202   2.879781202   8.014481202 -16.875518798 
         1636          1637          1638          1639          1640 
  2.879781202   0.294481202  -1.315518798 -12.055518798   1.396584297 
         1641          1642          1643          1644          1645 
 -3.893415703  -4.473415703  -1.753415703   0.866584297   3.757684297 
         1646          1647          1648          1649          1650 
  3.757684297   3.757684297  -8.513415703   3.757684297   3.757684297 
         1651          1652          1653          1654          1655 
 -7.613415703   2.072893335  14.790393335   2.079393335   6.350393335 
         1656          1657          1658          1659          1660 
 -4.269606665 -14.459606665   2.079393335   2.079393335  -5.809606665 
         1661          1662          1663          1664          1665 
  2.079393335  15.420393335  -5.579606665   2.079393335   6.080393335 
         1666          1667          1668          1669          1670 
  7.030393335 -12.549606665 -22.579606665   2.079393335   6.250393335 
         1671          1672          1673          1674          1675 
  3.675670876   3.691870876  -4.747029124   3.691970876 -18.427029124 
         1676          1677          1678          1679          1680 
  3.691970876   3.691970876   3.691970876   3.691970876  -3.137029124 
         1681          1682          1683          1684          1685 
-17.747029124  -1.217029124   3.691970876   3.691970876   3.691970876 
         1686          1687          1688          1689          1690 
  4.992970876  12.422970876   3.691970876 -14.407029124  -7.618413299 
         1691          1692          1693          1694          1695 
  4.984186701   8.281586701 -12.328413299 -17.308413299   9.841586701 
         1696          1697          1698          1699          1700 
  7.961586701   3.431586701   4.984186701 -17.888413299   4.984186701 
         1701          1702          1703          1704          1705 
  4.091586701  -2.088413299  -3.588413299   0.851586701  10.621586701 
         1706          1707          1708          1709          1710 
 11.721315896   9.271315896  -1.971984104   5.581315896  -1.971984104 
         1711          1712          1713          1714          1715 
 11.001315896  -3.118684104  -4.028684104   4.701315896  -1.971984104 
         1716          1717          1718          1719          1720 
 -1.971984104   1.991315896  13.381315896  -5.932142579   5.727857421 
         1721          1722          1723          1724          1725 
 -6.912142579   9.297857421  -5.142142579  10.447857421   7.497857421 
         1726          1727          1728          1729          1730 
-13.142142579 -11.572142579  -5.912142579   4.343857421  12.847857421 
         1731          1732          1733          1734          1735 
  1.617816080   1.617816080   0.337916080   1.617816080  -1.802083920 
         1736          1737          1738          1739          1740 
 11.797916080   1.617816080   1.617816080   0.687916080 -13.582083920 
         1741          1742          1743          1744          1745 
  1.617816080 -11.122083920   1.617916080   7.237916080   1.617916080 
         1746          1747          1748          1749          1750 
  1.617916080   2.755474960 -13.494525040  -7.804525040 -11.594525040 
         1751          1752          1753          1754          1755 
-10.524525040   7.944374960  -0.294525040 -10.594525040  -3.694525040 
         1756          1757          1758          1759          1760 
  7.944374960   7.944374960   7.944374960   7.944374960   7.944374960 
         1761          1762          1763          1764          1765 
-10.794525040  -7.094525040   7.944374960  -2.444525040   7.944374960 
         1766          1767          1768          1769          1770 
 -3.364525040 -12.874525040   8.053345900  -0.879254100  -0.879254100 
         1771          1772          1773          1774          1775 
 -0.879254100  10.483345900  12.033345900   3.823345900  -0.879254100 
         1776          1777          1778          1779          1780 
 -0.879254100  11.523345900 -14.226654100  -0.879254100  12.463345900 
         1781          1782          1783          1784          1785 
 -0.879254100  -3.026654100   4.190903655  -5.912796345  -3.732796345 
         1786          1787          1788          1789          1790 
  4.190903655   1.517203655   4.190903655 -16.022796345  -8.202796345 
         1791          1792          1793          1794          1795 
-12.792796345  -4.112796345   4.190903655   4.190903655  15.597203655 
         1796          1797          1798          1799          1800 
  4.190903655   4.190903655   4.190903655   4.190903655  -5.865166406 
         1801          1802          1803          1804          1805 
  1.034033594   1.034033594  11.224833594   1.034033594   1.034033594 
         1806          1807          1808          1809          1810 
  1.034033594   5.744833594   1.034033594  -2.645166406   1.034033594 
         1811          1812          1813          1814          1815 
  1.034033594  -3.515166406  11.894833594   1.034033594   4.955697869 
         1816          1817          1818          1819          1820 
  4.955697869   4.802897869  -4.817102131   4.955697869   4.955697869 
         1821          1822          1823          1824          1825 
-16.067102131   0.982897869   4.955697869 -10.687102131  -4.997102131 
         1826          1827          1828          1829          1830 
  8.562897869 -14.487102131   3.772897869  -1.707102131  -3.241628480 
         1831          1832          1833          1834          1835 
  5.944071520   1.978371520   8.808371520   7.468371520   5.944071520 
         1836          1837          1838          1839          1840 
  5.944071520  12.118371520 -20.711628480  16.258371520  -0.131628480 
         1841          1842          1843          1844          1845 
-10.551628480 -19.181628480  -8.191628480  -9.591628480   3.118371520 
         1846          1847          1848          1849          1850 
 -3.751628480 -12.988644964   2.077855036   9.921355036  -3.798644964 
         1851          1852          1853          1854          1855 
 -3.698644964   2.941355036   2.077955036  -5.938644964   5.461355036 
         1856          1857          1858          1859          1860 
-11.988644964  -5.388644964   2.092855036  -2.428644964   2.092855036 
         1861          1862          1863          1864          1865 
  2.092855036   2.092855036   9.381355036   2.095955036  -0.118644964 
         1866          1867          1868          1869          1870 
 -2.208644964  14.511355036  16.131355866   2.255655866  -5.498644134 
         1871          1872          1873          1874          1875 
  2.255655866   2.255655866   3.881355866  -4.738644134  -3.928644134 
         1876          1877          1878          1879          1880 
 10.761355866  -8.438644134   2.255655866   2.255655866 -12.018644134 
         1881          1882          1883          1884          1885 
 -7.538644134   1.591355866  -5.178644134   2.255655866   2.255655866 
         1886          1887          1888          1889          1890 
 -4.168644134   2.255755866  -5.828644134   2.255755866   2.255755866 
         1891          1892          1893          1894          1895 
  7.441355866   2.255755866  -7.605159356  -5.305159356  -4.575159356 
         1896          1897          1898          1899          1900 
  6.464840644   4.846940644   4.846940644 -10.055159356  -8.895159356 
         1901          1902          1903          1904          1905 
  4.846940644  -2.745159356  -0.685159356   0.104840644   4.846940644 
         1906          1907          1908          1909          1910 
  4.846940644   1.145688301   1.145688301  -0.969611699   1.145688301 
         1911          1912          1913          1914          1915 
  1.145688301   1.145688301   1.740388301  10.410388301   1.145688301 
         1916          1917          1918          1919          1920 
 -3.259611699   1.145688301   3.290388301  13.211917738  -7.407082262 
         1921          1922          1923          1924          1925 
-13.167082262 -13.997082262  13.211917738 -12.097082262  -8.137082262 
         1926          1927          1928          1929          1930 
  4.542917738  13.211917738  -3.187082262 -14.507082262  13.211917738 
         1931          1932          1933          1934          1935 
 -6.507082262  -8.847082262  13.211917738  -8.967082262 -11.607082262 
         1936          1937          1938          1939          1940 
 -9.527082262  -6.597082262 -10.399410596   6.296589404 -18.029410596 
         1941          1942          1943          1944          1945 
  6.296589404  -7.209410596   6.296589404  -5.029410596   6.296589404 
         1946          1947          1948          1949          1950 
  5.770589404  -2.169410596   6.498789404  -9.219410596  -4.556512822 
         1951          1952          1953          1954          1955 
  3.324187178   3.324187178   6.583487178   3.324187178   3.324187178 
         1956          1957          1958          1959          1960 
 -3.716512822   3.324187178  -2.166512822   3.324187178  -4.706512822 
         1961          1962          1963          1964          1965 
  3.324287178 -17.256512822  -7.230864171   0.844435829  -7.390864171 
         1966          1967          1968          1969          1970 
  0.844435829   0.844435829  11.019135829   0.844435829  -3.870864171 
         1971          1972          1973          1974          1975 
 11.099135829  -5.080864171  10.219135829   0.844435829   0.845445825 
         1976          1977          1978          1979          1980 
  0.845445825   0.845445825   0.845445825  -1.270654175   0.845445825 
         1981          1982          1983          1984          1985 
 17.819345825   0.845445825   0.845445825   9.859345825   0.845445825 
         1986          1987          1988          1989          1990 
 -6.510654175   0.845445825   0.845445825  -4.520654175  -0.560654175 
         1991          1992          1993          1994          1995 
  0.845445825   5.244879198  -1.265120802  -2.005120802   7.914879198 
         1996          1997          1998          1999          2000 
  1.414879198 -12.465120802  12.434879198  -8.735120802   4.480579198 
         2001          2002          2003          2004          2005 
 12.174879198  -3.555120802  -2.415120802  -3.495120802   4.480579198 
         2006          2007          2008          2009          2010 
-12.725120802   1.084879198   4.873276160 -16.786723840  -5.376723840 
         2011          2012          2013          2014          2015 
  5.473276160   6.862476160  -5.556723840  -7.036723840   6.862476160 
         2016          2017          2018          2019          2020 
 -3.436723840  -2.176723840   9.363276160 -10.716723840  -4.156723840 
         2021          2022          2023          2024          2025 
  6.059677691  -7.220322309 -11.100322309   2.458977691   2.458977691 
         2026          2027          2028          2029          2030 
  9.279677691   2.467477691   2.467477691 -12.520322309  -5.230322309 
         2031          2032          2033          2034          2035 
 -6.580322309   2.467477691   2.467477691  17.759677691 -12.330322309 
         2036          2037          2038          2039          2040 
  4.949677691   2.467477691   2.467477691   2.841010081  -1.230289919 
         2041          2042          2043          2044          2045 
  2.841010081  10.839710081  -5.450289919   2.841010081   3.749710081 
         2046          2047          2048          2049          2050 
-10.610289919  -3.320289919   9.179710081   1.839710081  -5.380289919 
         2051          2052          2053          2054          2055 
  2.841010081   5.773648229   5.773648229  19.228148229   5.718148229 
         2056          2057          2058          2059          2060 
  5.773648229  -8.131851771 -13.251851771   5.773648229  -0.681851771 
         2061          2062          2063          2064          2065 
  3.248148229   5.773648229  -8.371851771   3.308148229   1.388148229 
         2066          2067          2068          2069          2070 
  2.418148229 -20.991851771 -20.141851771   3.841442987  -2.571257013 
         2071          2072          2073          2074          2075 
  3.841442987 -13.891257013  -2.771257013   3.841442987 -10.711257013 
         2076          2077          2078          2079          2080 
  3.841442987   3.841442987   3.841442987   3.841442987  -9.421257013 
         2081          2082          2083          2084          2085 
  3.841442987  -4.621257013  -3.261257013  -8.391257013   1.978742987 
         2086          2087          2088          2089          2090 
  0.208742987   3.841442987   3.841442987   3.841442987   3.841442987 
         2091          2092          2093          2094          2095 
  3.841442987   0.868742987   0.424242283   3.412442283   0.424242283 
         2096          2097          2098          2099          2100 
  0.424242283   0.424242283   0.424242283   0.052442283   0.424242283 
         2101          2102          2103          2104          2105 
  9.712442283   0.424242283   0.424242283   2.272442283   0.300693974 
         2106          2107          2108          2109          2110 
  2.404893974  12.360693974   2.404893974 -26.309306026   2.404893974 
         2111          2112          2113          2114          2115 
  4.000693974   2.404893974   2.404893974  -2.749306026   4.130693974 
         2116          2117          2118          2119          2120 
 -9.809306026   2.404893974   2.404893974   2.404893974   3.910693974 
         2121          2122          2123          2124          2125 
  4.430693974   2.404893974  -8.689306026  -2.662281159 -12.842281159 
         2126          2127          2128          2129          2130 
  8.557718841 -14.072281159   8.347718841  -2.372281159 -10.912281159 
         2131          2132          2133          2134          2135 
  6.997718841  -1.972281159 -13.082281159   7.344118841  11.597718841 
         2136          2137          2138          2139          2140 
-12.212281159  -2.622281159   7.344118841   1.987718841   6.257718841 
         2141          2142          2143          2144          2145 
 -1.142281159   4.441997360  -6.908202640 -10.348202640   7.411797360 
         2146          2147          2148          2149          2150 
  4.441997360   4.441997360  -6.568202640  -5.058202640 -15.938202640 
         2151          2152          2153          2154          2155 
 -2.698202640   0.781797360 -14.768202640   4.441997360  13.931797360 
         2156          2157          2158          2159          2160 
  6.181797360   6.731797360  -0.603321282  10.936678718  -1.483321282 
         2161          2162          2163          2164          2165 
-14.303321282   5.743778718  -6.863321282   8.416678718 -14.883321282 
         2166          2167          2168          2169          2170 
 10.106678718  -6.423321282  -3.603321282   5.743778718   5.743778718 
         2171          2172          2173          2174          2175 
  4.536678718  -6.533321282  -3.103321282  11.098869167 -20.261130833 
         2176          2177          2178          2179          2180 
  6.256969167 -15.041130833  -4.961130833   6.256969167  -5.551130833 
         2181          2182          2183          2184          2185 
  6.256969167  -7.181130833 -13.181130833  -2.031130833   3.738869167 
         2186          2187          2188          2189          2190 
  7.498869167   6.256969167  11.158755684  -0.253344316  -7.041244316 
         2191          2192          2193          2194          2195 
  0.253255684   0.253255684   0.253255684   0.253255684   0.253255684 
         2196          2197          2198          2199          2200 
  0.253255684   0.253255684   0.253255684   5.708755684   0.253255684 
         2201          2202          2203          2204          2205 
  0.253255684   0.078755684   5.998755684   9.688755684   5.088215077 
         2206          2207          2208          2209          2210 
 -4.711784923   4.556215077  15.198215077  -9.321784923  -1.361784923 
         2211          2212          2213          2214          2215 
  9.848215077   4.238215077 -13.841784923 -19.221784923  13.848215077 
         2216          2217          2218          2219          2220 
 -8.371784923  -1.811784923   1.368215077   4.556215077  -1.411784923 
         2221          2222          2223          2224          2225 
  3.088215077 -15.553847698   2.216152302  -1.043847698   4.686152302 
         2226          2227          2228          2229          2230 
-10.473847698   8.125552302   7.166152302  17.616152302   0.826152302 
         2231          2232          2233          2234          2235 
  0.076152302  -6.623847698   8.125552302   8.125552302   8.476152302 
         2236          2237          2238          2239          2240 
-16.313847698 -12.303847698 -15.533847698   2.226152302 -10.923847698 
         2241          2242          2243          2244          2245 
 -8.413847698   7.199197752  13.499197752 -10.830802248   0.739197752 
         2246          2247          2248          2249          2250 
  0.209197752  -1.680802248 -16.070802248   5.161797752 -14.420802248 
         2251          2252          2253          2254          2255 
  9.749197752   0.009197752  10.589197752   5.161897752 -12.900802248 
         2256          2257          2258          2259          2260 
 -5.688396974   4.631603026  -5.128396974  -9.868396974   2.590403026 
         2261          2262          2263          2264          2265 
 -1.398396974   1.151603026  -0.268396974  11.271603026  -7.298396974 
         2266          2267          2268          2269          2270 
 -1.678396974   8.191603026   2.590403026  -3.558396974   9.661603026 
         2271          2272          2273          2274          2275 
  2.590403026  -9.418396974   2.590403026 -11.115894464   5.100805536 
         2276          2277          2278          2279          2280 
 -3.915894464   5.100805536   5.100805536  -1.975894464   5.100805536 
         2281          2282          2283          2284          2285 
 -2.615894464 -18.635894464   5.100905536   5.100905536   5.100905536 
         2286          2287          2288          2289          2290 
  5.266391668  -9.720108332  11.769891668   4.699891668  11.429891668 
         2291          2292          2293          2294          2295 
 16.479891668   5.851091668   8.699891668  -2.710108332 -24.370108332 
         2296          2297          2298          2299          2300 
-22.560108332  17.759891668 -21.850108332 -14.440108332   5.851191668 
         2301          2302          2303          2304          2305 
 -2.102997602  -2.102997602  -2.102997602  -5.637097602  -2.102997602 
         2306          2307          2308          2309          2310 
 -0.997097602  -2.102997602   4.442902398  36.802902398   5.722902398 
         2311          2312          2313          2314          2315 
 -2.102997602   4.742902398  -2.102997602  -2.102997602   1.402902398 
         2316          2317          2318          2319          2320 
 12.222902398  -2.102997602  -1.867097602  -2.102997602  -1.357097602 
         2321          2322          2323          2324          2325 
 -0.037097602   2.026921222   2.026921222   2.026921222   2.026921222 
         2326          2327          2328          2329          2330 
 -3.296178778   2.026921222   3.553821222   2.026921222   2.026921222 
         2331          2332          2333          2334          2335 
  2.026921222  -1.556178778  -4.336178778  -1.876178778   4.523440015 
         2336          2337          2338          2339          2340 
  9.613440015 -11.726559985   2.165540015   2.165540015  -8.626559985 
         2341          2342          2343          2344          2345 
  2.165540015   9.383440015   2.165540015   2.165540015  -4.216559985 
         2346          2347          2348          2349          2350 
  2.165540015   2.165540015  -2.306559985   2.165540015   2.165540015 
         2351          2352          2353          2354          2355 
  5.963440015  -7.426559985   2.165540015   2.615863695  -0.667336305 
         2356          2357          2358          2359          2360 
  2.615863695   4.922663695   2.615863695   2.615863695  12.852663695 
         2361          2362          2363          2364          2365 
 -9.057336305   2.615863695   2.615863695   2.615863695  -7.167336305 
         2366          2367          2368          2369          2370 
 -7.987336305   2.882663695 -20.154226755  -5.944226755   4.603473245 
         2371          2372          2373          2374          2375 
  3.855773245   4.603473245  -0.344226755   4.603473245   4.603473245 
         2376          2377          2378          2379          2380 
  4.603473245  11.485773245 -20.164226755 -13.254226755   4.603473245 
         2381          2382          2383          2384          2385 
  4.603473245   4.603473245  -6.784415463 -13.784415463   7.115584537 
         2386          2387          2388          2389          2390 
  4.679884537   3.755584537   2.685584537   4.679884537   4.679884537 
         2391          2392          2393          2394          2395 
  4.679884537   4.679884537   3.535584537   4.679884537  -5.904415463 
         2396          2397          2398          2399          2400 
  1.915584537 -11.414415463   4.679884537   2.525584537  -8.044415463 
         2401          2402          2403          2404          2405 
 -8.234415463 -10.855917867  -4.225917867   4.151482133   3.984082133 
         2406          2407          2408          2409          2410 
  2.094082133   4.151482133  11.084082133   4.151582133   4.151582133 
         2411          2412          2413          2414          2415 
 -1.085917867   4.151582133  -7.815917867 -17.695917867   9.524082133 
         2416          2417          2418          2419          2420 
  4.151582133  -6.345917867   4.151582133  -8.765917867  -2.745917867 
         2421          2422          2423          2424          2425 
  4.151582133   4.151582133   8.867469125   2.704669125   2.704669125 
         2426          2427          2428          2429          2430 
-16.682530875   3.717469125   8.387469125  -7.692530875   2.704669125 
         2431          2432          2433          2434          2435 
  2.704669125   0.847469125 -13.092530875  12.637469125   2.704669125 
         2436          2437          2438          2439          2440 
-10.932530875   2.704669125 -16.232530875   2.117469125   4.587469125 
         2441          2442          2443          2444          2445 
  8.607469125   2.173934583   7.033034583   2.453934583   8.763934583 
         2446          2447          2448          2449          2450 
  7.033034583 -12.876065417   7.223934583   4.173934583 -11.456065417 
         2451          2452          2453          2454          2455 
  7.033034583  -2.306065417 -18.646065417 -15.926065417  10.513934583 
         2456          2457          2458          2459          2460 
-18.006065417   5.016910308   5.016910308   3.953310308  -6.656689692 
         2461          2462          2463          2464          2465 
 12.973310308   6.493310308  -2.296689692 -11.286689692  13.083310308 
         2466          2467          2468          2469          2470 
  5.663310308   2.713310308  -2.116689692  -5.396689692   2.813310308 
         2471          2472          2473          2474          2475 
-11.616689692  -4.886689692 -18.016689692   2.623310308  -0.592832730 
         2476          2477          2478          2479          2480 
  8.245867270  -3.134132730  -0.284132730 -14.024132730   9.865867270 
         2481          2482          2483          2484          2485 
 -2.224132730   1.355867270   0.705867270  14.555867270  -3.284132730 
         2486          2487          2488          2489          2490 
  0.294467270   0.294467270   0.294467270  11.225867270   4.435867270 
         2491          2492          2493          2494          2495 
  9.045867270   0.294467270 -13.934132730  -1.945763231   7.552336769 
         2496          2497          2498          2499          2500 
 -2.615763231   5.804236769   7.552336769  10.884236769   7.552336769 
         2501          2502          2503          2504          2505 
 -7.575763231 -22.445763231 -25.845763231  -1.395763231   7.552336769 
         2506          2507          2508          2509          2510 
 -9.845763231 -12.115763231   7.552336769   7.552336769 -15.245763231 
         2511          2512          2513          2514          2515 
 11.664236769   7.552336769  -1.025652039   0.858747961   0.858747961 
         2516          2517          2518          2519          2520 
  0.858747961   0.858747961   0.858747961   0.858747961   2.474347961 
         2521          2522          2523          2524          2525 
  0.858747961   0.858747961   0.858747961   0.858747961  -3.635652039 
         2526          2527          2528          2529          2530 
  8.554347961   5.144347961   0.858747961  -2.323228505   3.582471495 
         2531          2532          2533          2534          2535 
 -2.323228505  -2.323228505  -2.323228505  14.442471495   7.662471495 
         2536          2537          2538          2539          2540 
 13.402471495  -2.323228505  -2.323228505   0.932471495  13.082471495 
         2541          2542          2543          2544          2545 
 -2.323228505  -2.323228505   7.712471495   0.093807364   4.163107364 
         2546          2547          2548          2549          2550 
-11.666192636  -1.646192636  -4.036192636  -7.126192636   4.163107364 
         2551          2552          2553          2554          2555 
  2.423807364   1.253807364   4.163107364   4.163107364  -3.816192636 
         2556          2557          2558          2559          2560 
  7.450605300  -3.635794700 -12.035794700 -13.165794700   7.450605300 
         2561          2562          2563          2564          2565 
 -6.695794700 -14.095794700   2.274205300  12.734205300   7.450605300 
         2566          2567          2568          2569          2570 
  7.450705300  -7.225794700   7.450705300   7.450705300   7.450705300 
         2571          2572          2573          2574          2575 
-18.795794700 -16.775794700   7.450705300  -4.652225655   7.127774345 
         2576          2577          2578          2579          2580 
  0.336274345   7.737774345  -2.252225655   0.336274345   0.336274345 
         2581          2582          2583          2584          2585 
  0.336274345   1.797774345   4.827774345   0.336274345   0.336274345 
         2586          2587          2588          2589          2590 
  0.336274345   7.247774345  14.160286051   1.388086051  -3.139713949 
         2591          2592          2593          2594          2595 
  4.150286051 -10.419713949  12.230286051   1.388086051  -8.549713949 
         2596          2597          2598          2599          2600 
  4.960286051  -6.639713949  -3.019713949   1.388086051   2.990286051 
         2601          2602          2603          2604          2605 
 -7.649713949   7.490286051 -12.261116467  -4.741116467   1.379583533 
         2606          2607          2608          2609          2610 
  1.379583533   1.379583533   0.198883533   1.379583533  -8.611116467 
         2611          2612          2613          2614          2615 
 -1.691116467   1.379583533   1.379583533  20.098883533   1.379583533 
         2616          2617          2618          2619          2620 
  1.379583533   1.379583533   1.379583533   1.379583533   1.379583533 
         2621          2622          2623          2624          2625 
  4.475274971   0.576474971   2.586474971 -12.013525029   4.475274971 
         2626          2627          2628          2629          2630 
  4.475274971   7.036474971  -2.543525029   4.475274971   1.086474971 
         2631          2632          2633          2634          2635 
  4.475274971   4.475274971  10.216474971  -4.543525029 -10.853525029 
         2636          2637          2638          2639          2640 
-16.903525029   8.295661664   9.055661664  -3.404338336   0.805661664 
         2641          2642          2643          2644          2645 
 -0.934338336  -2.494338336  -5.054338336  -1.844338336   3.189261664 
         2646          2647          2648          2649          2650 
 -7.014338336   7.695661664   2.335661664 -11.839876324 -18.429876324 
         2651          2652          2653          2654          2655 
  5.609523676   5.609523676   5.609523676  -8.189876324  10.630123676 
         2656          2657          2658          2659          2660 
 -2.369876324   5.609523676   5.609523676   5.609523676  -2.509876324 
         2661          2662          2663          2664          2665 
-20.529876324   5.609523676   3.867675626   7.363275626   3.867675626 
         2666          2667          2668          2669          2670 
  3.867675626   3.093275626   3.867675626   3.867675626   2.253275626 
         2671          2672          2673          2674          2675 
  3.923275626  -4.236724374 -16.266724374 -22.196724374   3.867675626 
         2676          2677          2678          2679          2680 
 -9.908171774  -4.218171774   5.234028226  -9.848171774  -9.808171774 
         2681          2682          2683          2684          2685 
  5.234028226   5.234028226   5.234028226   1.921828226  -3.478171774 
         2686          2687          2688          2689          2690 
-14.768171774  10.101828226   5.234028226  -0.648171774   4.705397054 
         2691          2692          2693          2694          2695 
  4.705397054  -8.381002946   5.678997054   4.705397054  -7.371002946 
         2696          2697          2698          2699          2700 
  0.868997054   4.705397054  -1.231002946  10.928997054 -12.091002946 
         2701          2702          2703          2704          2705 
  4.705497054  -4.311002946  -1.981002946   0.318997054   4.707697054 
         2706          2707          2708          2709          2710 
 -2.621002946  -7.251002946  -6.679161941  -5.139161941 -13.649161941 
         2711          2712          2713          2714          2715 
 -5.929161941   6.111938059   6.111938059   6.111938059   6.111938059 
         2716          2717          2718          2719          2720 
 -6.679161941   6.111938059  10.290838059 -12.249161941   7.256566478 
         2721          2722          2723          2724          2725 
  7.256566478 -16.056433522 -16.076433522   6.303566478   7.256566478 
         2726          2727          2728          2729          2730 
  1.773566478   7.256566478   7.883566478 -13.746433522  -5.926433522 
         2731          2732          2733          2734          2735 
-13.866433522   4.264552685  -5.316147315  -4.906147315   4.264552685 
         2736          2737          2738          2739          2740 
  5.083852685   4.264552685 -15.306147315  -7.936147315   4.264552685 
         2741          2742          2743          2744          2745 
  4.264552685  -0.366147315   4.264552685   4.264552685  -2.606147315 
         2746          2747          2748          2749          2750 
  4.264652685   2.978328713   9.729028713   2.978328713  -6.830971287 
         2751          2752          2753          2754          2755 
  9.649028713  -6.530971287   2.978328713  -2.790971287 -15.840971287 
         2756          2757          2758          2759          2760 
 -8.530971287   2.978328713   2.978328713   2.169028713   2.978328713 
         2761          2762          2763          2764          2765 
  5.949028713   2.978428713   2.978428713  -0.806049762   4.639350238 
         2766          2767          2768          2769          2770 
-12.336049762   6.493950238  -6.386049762   4.639350238 -11.026049762 
         2771          2772          2773          2774          2775 
 -2.156049762  -0.446049762   4.639350238   3.863950238   4.639350238 
         2776          2777          2778          2779          2780 
-11.654085870   2.593014130  -9.434085870   2.593014130  -8.194085870 
         2781          2782          2783          2784          2785 
  2.593014130   0.795914130   2.593014130   6.275914130   6.045914130 
         2786          2787          2788          2789          2790 
  2.593114130   2.593114130   2.606414130   3.682475972   3.682475972 
         2791          2792          2793          2794          2795 
  3.682475972   3.682475972   9.139575972   3.682475972  19.209575972 
         2796          2797          2798          2799          2800 
  3.682475972 -15.890424028  -6.010424028 -14.370424028   3.619575972 
         2801          2802          2803          2804          2805 
-13.350424028   3.682475972   0.169575972   3.682475972 -18.800424028 
         2806          2807          2808          2809          2810 
  3.682475972   3.682475972   3.682475972   3.682475972   3.682475972 
         2811          2812          2813          2814          2815 
  3.682475972   3.682475972   3.682475972   3.682475972   3.682475972 
         2816          2817          2818          2819          2820 
  3.682475972  -8.830424028   3.682475972 -17.450424028  -9.310424028 
         2821          2822          2823          2824          2825 
  3.682475972   3.682475972   3.682475972  -8.040424028  -9.620424028 
         2826          2827          2828          2829          2830 
 11.174107458   3.484107458   0.834107458   3.744107458  -8.185892542 
         2831          2832          2833          2834          2835 
-12.055892542   4.398907458  -8.895892542   4.418007458  -7.915892542 
         2836          2837          2838          2839          2840 
  4.114107458   4.418007458   1.604107458   1.474469308   7.504469308 
         2841          2842          2843          2844          2845 
 -1.186430692   0.654469308  -1.186430692  -1.186430692  -1.186430692 
         2846          2847          2848          2849          2850 
  7.054469308 -14.655530692  -5.025530692  -1.186430692  38.194469308 
         2851          2852          2853          2854          2855 
 -1.186430692  -1.186430692  -1.186430692  -4.851958463   4.520741537 
         2856          2857          2858          2859          2860 
 -9.221958463   4.527741537   4.527741537   4.527741537  -7.211958463 
         2861          2862          2863          2864          2865 
  3.228041537   4.527741537   4.527741537 -17.021958463  -2.161958463 
         2866          2867          2868          2869          2870 
 -9.282837727   3.757162273   1.827262273   1.827362273   1.827362273 
         2871          2872          2873          2874          2875 
  1.827362273   1.827362273   1.827362273   1.827362273   1.827362273 
         2876          2877          2878          2879          2880 
  1.827362273   1.827362273  -6.002837727 -10.546315587   6.193684413 
         2881          2882          2883          2884          2885 
 -8.056315587   1.643484413   1.643484413   1.643484413   1.643484413 
         2886          2887          2888          2889          2890 
 17.473684413   1.643484413 -11.296315587   1.643484413  14.713684413 
         2891          2892          2893          2894          2895 
-22.756315587   1.643484413   9.143684413   1.643584413 -16.553741750 
         2896          2897          2898          2899          2900 
  3.696258250  10.156258250   3.318358250   7.636258250   3.466258250 
         2901          2902          2903          2904          2905 
 -5.823741750  12.696258250   1.076258250 -14.573741750   2.086258250 
         2906          2907          2908          2909          2910 
-11.353741750  -7.563741750   3.318358250   5.976258250  -0.126242735 
         2911          2912          2913          2914          2915 
  6.138057265  -0.126242735  14.798057265  -0.126242735  -0.126242735 
         2916          2917          2918          2919          2920 
 -0.126242735  -0.126242735  -0.126242735  13.578057265  -0.126242735 
         2921          2922          2923          2924          2925 
 10.694860862   6.858560862  -7.815139138   6.858560862  -1.505139138 
         2926          2927          2928          2929          2930 
 -4.905139138   4.424860862  -7.995139138   6.858560862 -11.145139138 
         2931          2932          2933          2934          2935 
  6.858560862  -0.145139138   1.204860862 -22.445139138  -5.745139138 
         2936          2937          2938          2939          2940 
 -1.605139138   6.858560862   3.037845596  -3.588754404   3.037845596 
         2941          2942          2943          2944          2945 
  3.037845596   3.037845596  12.321245596   3.037845596   3.037845596 
         2946          2947          2948          2949          2950 
  3.037845596 -10.858754404   3.037845596   6.131245596   3.037845596 
         2951          2952          2953          2954          2955 
  3.037845596  -4.008754404 -16.668754404 -11.028754404   3.041745596 
         2956          2957          2958          2959          2960 
  3.584694475  15.993094475   3.947794475   3.947794475  10.043094475 
         2961          2962          2963          2964          2965 
 -3.726905525   3.947794475 -22.146905525   3.947794475   6.463094475 
         2966          2967          2968          2969          2970 
-11.666905525   7.163094475   3.947794475  -4.566905525 -12.246905525 
         2971          2972          2973          2974          2975 
  3.947794475   3.947794475   3.093094475 -11.006905525  -4.656905525 
         2976          2977          2978          2979          2980 
  4.547136978  -1.952863022  12.067136978   1.791036978  -5.252863022 
         2981          2982          2983          2984          2985 
  3.167136978  -1.792863022  -1.522863022  -0.092863022  -6.832863022 
         2986          2987          2988          2989          2990 
  3.217136978  11.187136978  11.577136978   6.767136978   1.791136978 
         2991          2992          2993          2994          2995 
-19.412863022   3.502508893  -1.562291107   3.502608893 -25.162291107 
         2996          2997          2998          2999          3000 
-13.972291107   3.502608893   9.907708893   9.397708893   9.007708893 
         3001          3002          3003          3004          3005 
 11.437708893  -5.572291107   3.502608893 -10.656633675 -22.286633675 
         3006          3007          3008          3009          3010 
  3.295366325   0.453366325   3.295366325 -20.136633675  20.613366325 
         3011          3012          3013          3014          3015 
  3.295366325   3.295366325  -5.016633675 -10.036633675 -12.396633675 
         3016          3017          3018          3019          3020 
  3.295366325   3.295366325  42.673366325   3.295366325  -8.576633675 
         3021          3022          3023          3024          3025 
 -1.900024587  -1.650024587 -10.910024587   1.619975413 -18.300024587 
         3026          3027          3028          3029          3030 
 10.027675413  -1.900024587   1.559975413   1.539975413  -8.680024587 
         3031          3032          3033          3034          3035 
 -9.430024587  -4.070024587   8.109975413  -4.447741139  10.087958861 
         3036          3037          3038          3039          3040 
 10.087958861  -7.737741139   5.082258861  -3.817741139  -9.607741139 
         3041          3042          3043          3044          3045 
-13.857741139  10.087958861  -7.357741139  -8.427741139 -11.097741139 
         3046          3047          3048          3049          3050 
  9.472258861 -11.337741139   0.881201602   5.411501602 -16.028798398 
         3051          3052          3053          3054          3055 
  5.411501602  11.581201602 -19.448798398   2.761201602  -7.318798398 
         3056          3057          3058          3059          3060 
 -9.798798398   5.411501602   8.661201602   5.411501602 -13.328798398 
         3061          3062          3063          3064          3065 
  5.411501602   0.531201602   5.411501602   3.336959957  -0.283040043 
         3066          3067          3068          3069          3070 
  1.507259957  -1.203040043  14.906959957   7.126959957   1.346959957 
         3071          3072          3073          3074          3075 
-17.883040043  -0.833040043  -5.643040043   6.696959957   1.507259957 
         3076          3077          3078          3079          3080 
  9.356959957   7.371661952 -11.792538048   0.517461952   1.497461952 
         3081          3082          3083          3084          3085 
 -5.312538048  -9.742538048   7.371661952 -10.832538048   7.371661952 
         3086          3087          3088          3089          3090 
 15.427461952  -1.262538048   7.371661952  21.337461952   8.627461952 
         3091          3092          3093          3094          3095 
  0.737461952 -11.172538048 -14.482538048   6.867461952  -9.582538048 
         3096          3097          3098          3099          3100 
  7.393561952 -18.182538048   7.393561952 -14.692538048 -10.582538048 
         3101          3102          3103          3104          3105 
 -6.672538048 -11.192372926   4.891827074  10.087627074   4.891827074 
         3106          3107          3108          3109          3110 
-22.682372926 -11.492372926  10.017627074  -8.482372926  -9.772372926 
         3111          3112          3113          3114          3115 
-12.652372926   9.307627074  -7.402372926  43.227627074  -4.512372926 
         3116          3117          3118          3119          3120 
-19.632365142   3.837634858  -4.412365142  -2.552365142   4.942634858 
         3121          3122          3123          3124          3125 
 -6.772365142  -3.462365142   5.777634858   4.942734858   4.942734858 
         3126          3127          3128          3129          3130 
  4.942734858  -8.642365142   4.942734858   4.942734858   0.911277674 
         3131          3132          3133          3134          3135 
  4.069177674   0.911277674  10.429177674   4.999177674   0.911277674 
         3136          3137          3138          3139          3140 
  0.911277674   0.911277674   0.911277674 -23.360822326   0.911277674 
         3141          3142          3143          3144          3145 
  0.911277674   0.911277674  -4.500822326   9.869177674   0.911277674 
         3146          3147          3148          3149          3150 
  0.911277674   0.911277674   8.639177674   0.911277674   0.041229986 
         3151          3152          3153          3154          3155 
  6.335529986  -7.258770014  -9.378770014   6.335529986   1.811229986 
         3156          3157          3158          3159          3160 
 -4.488770014 -15.428770014  -1.598770014   6.335529986   6.335529986 
         3161          3162          3163          3164          3165 
 -3.468770014  -3.928770014  -3.320815482 -14.620815482 -14.300815482 
         3166          3167          3168          3169          3170 
  2.071284518   2.071284518  14.499184518   2.071284518  -1.110815482 
         3171          3172          3173          3174          3175 
  2.071284518   9.099184518   2.071284518  16.699184518   4.188784323 
         3176          3177          3178          3179          3180 
  4.813484323   4.188784323   4.188784323   8.463484323 -17.176515677 
         3181          3182          3183          3184          3185 
 -4.836515677  -8.266515677  -4.076515677   4.188884323  -3.756515677 
         3186          3187          3188          3189          3190 
  4.188884323   4.188884323   3.383484323   4.188884323 -12.486515677 
         3191          3192          3193          3194          3195 
  4.188884323  -7.106515677   8.623484323   1.763484323   0.413484323 
         3196          3197          3198          3199          3200 
-13.429387497  -2.989387497   6.240612503   5.888512503   1.270612503 
         3201          3202          3203          3204          3205 
 11.020612503  -9.499387497   5.888512503 -11.199387497   5.888512503 
         3206          3207          3208          3209          3210 
  5.888512503  -5.889387497 -12.439387497   5.888512503  -2.160398099 
         3211          3212          3213          3214          3215 
-14.380398099   4.989601901  -5.100398099 -12.430398099  -4.030398099 
         3216          3217          3218          3219          3220 
 -9.170398099 -11.460398099  12.092201901 -10.000398099  -1.680398099 
         3221          3222          3223          3224          3225 
 12.118301901  10.619601901 -14.480398099  -0.320398099  -7.160398099 
         3226          3227          3228          3229          3230 
-10.490398099  12.118301901  -4.377741245 -12.697741245   6.409458755 
         3231          3232          3233          3234          3235 
 10.362258755   6.409458755   0.552258755   6.409458755 -19.967741245 
         3236          3237          3238          3239          3240 
-18.237741245   6.409458755  -8.637741245  13.802258755   3.282258755 
         3241          3242          3243          3244          3245 
 -9.517741245  13.122258755   6.409458755 -12.637741245  -6.617741245 
         3246          3247          3248          3249          3250 
  9.162258755  -7.407741245   6.409458755  10.485870290   8.485870290 
         3251          3252          3253          3254          3255 
 11.775870290   4.371970290 -18.874129710  -8.404129710   0.035870290 
         3256          3257          3258          3259          3260 
  4.245870290   6.855870290 -10.324129710   7.435870290   3.645870290 
         3261          3262          3263          3264          3265 
  4.372070290   0.855870290 -14.114129710   3.005870290 -15.164129710 
         3266          3267          3268          3269          3270 
 -1.194129710  11.114926678 -19.345073322  -8.345073322   7.435626678 
         3271          3272          3273          3274          3275 
  1.534926678   7.435626678  -6.085073322   7.435626678 -11.415073322 
         3276          3277          3278          3279          3280 
  0.164926678   7.435626678  -0.135073322  -2.955073322 -13.325073322 
         3281          3282          3283          3284          3285 
  7.435626678 -13.515073322   7.435626678 -15.643507550   3.925192450 
         3286          3287          3288          3289          3290 
  3.925192450   3.925192450  18.596492450   3.925192450   5.026492450 
         3291          3292          3293          3294          3295 
  0.616492450 -11.003507550  -7.193507550   8.646492450 -14.543507550 
         3296          3297          3298          3299          3300 
 -8.413507550  13.146492450   7.950990804   0.409990804  15.160990804 
         3301          3302          3303          3304          3305 
 13.940990804   0.409990804   8.000990804  -8.279009196  -7.409009196 
         3306          3307          3308          3309          3310 
  8.650990804  11.690990804  -7.649009196  -8.609009196   0.409990804 
         3311          3312          3313          3314          3315 
  0.420990804  -0.439009196   0.420990804   0.420990804  17.210990804 
         3316          3317          3318          3319          3320 
  0.420990804 -20.419009196   0.420990804   0.420990804  13.980990804 
         3321          3322          3323          3324          3325 
-23.079009196   2.320990804   4.680990804   3.740990804   0.420990804 
         3326          3327          3328          3329          3330 
-23.059009196   0.420990804   5.740990804   2.192263228   0.152263228 
         3331          3332          3333          3334          3335 
  3.061763228   3.061763228  -3.097736772 -22.917736772   3.061763228 
         3336          3337          3338          3339          3340 
-10.357736772   8.442263228   3.061763228   3.061763228   6.362263228 
         3341          3342          3343          3344          3345 
  3.061763228  -3.670314633  13.209685367   3.396685367   6.839685367 
         3346          3347          3348          3349          3350 
 -2.460314633   3.396685367   8.359685367 -19.370314633   3.396685367 
         3351          3352          3353          3354          3355 
  3.396685367   3.396685367  -2.770314633 -12.610314633  -0.440314633 
         3356          3357          3358          3359          3360 
  5.979685367  -6.510314633 -11.032711179 -16.062711179  -2.952711179 
         3361          3362          3363          3364          3365 
-10.592711179   5.935988821   8.997288821   3.317288821   5.935988821 
         3366          3367          3368          3369          3370 
  5.935988821   5.935988821   5.935988821   5.935988821   5.935988821 
         3371          3372          3373          3374          3375 
  5.935988821 -14.052711179  -5.692711179  -8.072711179  13.527288821 
         3376          3377          3378          3379          3380 
 -3.562711179  -5.542711179  -7.462711179   5.935988821 -13.482711179 
         3381          3382          3383          3384          3385 
 -2.522711179   5.935988821   5.153052224  -9.845247776  -2.645247776 
         3386          3387          3388          3389          3390 
 11.654752224   5.153052224  -7.335247776   5.153052224   4.964752224 
         3391          3392          3393          3394          3395 
 -2.845247776  -0.695247776 -16.235247776   5.153052224  -3.235247776 
         3396          3397          3398          3399          3400 
-10.485247776   5.153052224   1.014050467   2.714050467  -9.805949533 
         3401          3402          3403          3404          3405 
 -7.755949533   4.277550467  -0.235949533   4.277550467  -8.965949533 
         3406          3407          3408          3409          3410 
 -1.905949533   4.277650467   3.024050467   4.277650467   4.277650467 
         3411          3412          3413          3414          3415 
  4.277650467  -5.675949533  -4.795948689   1.124051311  -6.055948689 
         3416          3417          3418          3419          3420 
 -3.275948689 -24.195948689   5.866251311  -8.315948689   5.866251311 
         3421          3422          3423          3424          3425 
 15.214051311 -15.305948689   5.866251311  -2.515948689  -1.355948689 
         3426          3427          3428          3429          3430 
  1.404051311  11.184051311   5.866251311   5.866251311  -7.725948689 
         3431          3432          3433          3434          3435 
  5.866251311   5.866251311 -14.945948689   1.063569057  -2.753930943 
         3436          3437          3438          3439          3440 
  1.063569057   2.506069057   6.076069057  -5.343930943   1.076069057 
         3441          3442          3443          3444          3445 
  1.076069057   3.216069057  -5.713930943   5.656069057   1.076169057 
         3446          3447          3448          3449          3450 
 -0.963930943   1.076169057  10.216069057  -1.603930943   6.596069057 
         3451          3452          3453          3454          3455 
 -7.323930943   1.076169057  -7.902452463   8.729947537  -8.802452463 
         3456          3457          3458          3459          3460 
  8.729947537   1.947547537  -1.902452463  -9.772452463   8.027547537 
         3461          3462          3463          3464          3465 
-13.232452463  -6.052452463   0.727547537   8.729947537   3.197547537 
         3466          3467          3468          3469          3470 
  8.729947537  -2.992452463 -11.692452463   1.137547537 -10.942452463 
         3471          3472          3473          3474          3475 
 -6.682452463   8.729947537  -2.862452463 -13.014890363 -16.264890363 
         3476          3477          3478          3479          3480 
 -0.254890363   5.478809637  -6.614890363   5.478809637   5.478809637 
         3481          3482          3483          3484          3485 
 -4.514890363   5.478809637   7.525109637   5.478809637   5.478809637 
         3486          3487          3488          3489          3490 
-10.604890363  13.065109637 -11.694890363   7.252493281 -10.317506719 
         3491          3492          3493          3494          3495 
 16.702493281  -0.157506719   6.152493281 -11.057506719  -5.757506719 
         3496          3497          3498          3499          3500 
 -3.877506719   2.382493281 -10.017506719   2.572493281  -8.567506719 
         3501          3502          3503          3504          3505 
 -9.557506719 -13.477506719   9.352493281   0.172493281   6.395993281 
         3506          3507          3508          3509          3510 
-18.914659480  -3.874659480   5.295340520   4.755340520   8.735340520 
         3511          3512          3513          3514          3515 
  4.475340520   5.605340520   2.101940520   2.101940520  -5.474659480 
         3516          3517          3518          3519          3520 
  1.425340520  -5.124659480   6.835340520   1.745340520   2.101940520 
         3521          3522          3523          3524          3525 
  2.101940520   2.101940520   0.205340520 -13.095421653   3.374578347 
         3526          3527          3528          3529          3530 
 -8.675421653   7.033178347   7.033178347 -12.965421653   0.884578347 
         3531          3532          3533          3534          3535 
 -5.545421653   7.033878347  -3.285421653 -13.275421653   7.033878347 
         3536          3537          3538          3539          3540 
 -6.035421653   7.854578347 -24.573325299  11.586674701   5.006674701 
         3541          3542          3543          3544          3545 
  0.046674701  11.646674701   0.446674701   2.278074701   2.278074701 
         3546          3547          3548          3549          3550 
  1.356674701 -11.623325299   0.276674701  15.076674701  -8.783325299 
         3551          3552          3553          3554          3555 
  2.278074701  -4.833325299  -0.683325299   2.278074701  15.123990427 
         3556          3557          3558          3559          3560 
  2.388790427   5.463990427 -14.206009573  -8.846009573  -1.976009573 
         3561          3562          3563          3564          3565 
  3.053990427   2.388790427  -8.136009573   5.453990427   3.060690427 
         3566          3567          3568          3569          3570 
  3.060690427   3.060690427  -0.110273039  -0.110273039  -0.110273039 
         3571          3572          3573          3574          3575 
 -0.110273039  -0.110273039  -0.110273039  -0.110273039  -0.110273039 
         3576          3577          3578          3579          3580 
 -0.110273039  -0.110273039   6.145426961  14.065426961  -0.110273039 
         3581          3582          3583          3584          3585 
 -0.110273039   5.826863615 -13.211836385  -1.461836385  -4.101836385 
         3586          3587          3588          3589          3590 
-13.941836385   5.826863615   5.826863615   5.826863615   5.826863615 
         3591          3592          3593          3594          3595 
-15.971836385   5.833463615   5.833463615   5.833463615 -21.651836385 
         3596          3597          3598          3599          3600 
  5.833463615   5.833463615   5.833463615 -19.429217964  -5.579217964 
         3601          3602          3603          3604          3605 
 -8.329217964   4.340782036   4.369182036   4.369182036   4.369182036 
         3606          3607          3608          3609          3610 
  4.369182036  13.180782036   4.369182036   4.369182036 -12.869217964 
         3611          3612          3613          3614          3615 
 -8.650734757   8.394465243  -8.710734757   4.849265243  -2.710734757 
         3616          3617          3618          3619          3620 
-12.640734757  -2.290734757   8.394565243  -2.780734757  -1.620734757 
         3621          3622          3623          3624          3625 
 -7.130734757  -9.330734757   0.751105783   0.751105783   5.996005783 
         3626          3627          3628          3629          3630 
  6.786005783  13.416005783  -5.963994217   0.751105783   0.751105783 
         3631          3632          3633          3634          3635 
  7.126005783  -2.143994217   4.806005783 -10.643994217   0.751105783 
         3636          3637          3638          3639          3640 
 -3.123994217   6.702570178  -9.753129822  -2.843129822 -10.023129822 
         3641          3642          3643          3644          3645 
-17.283129822   6.702570178   8.106870178 -15.373129822  -1.853129822 
         3646          3647          3648          3649          3650 
  6.702570178   9.876870178   6.702570178   3.146870178  -3.083129822 
         3651          3652          3653          3654          3655 
-15.633129822   0.126870178   6.702570178  -4.443129822  -1.953129822 
         3656          3657          3658          3659          3660 
  6.702570178   9.145233253 -13.489266747 -11.259266747 -11.479266747 
         3661          3662          3663          3664          3665 
  9.145233253  -9.599266747   9.145233253  -0.019266747  -5.479266747 
         3666          3667          3668          3669          3670 
 -7.879266747   5.430733253  -0.589266747 -21.969266747   9.145233253 
         3671          3672          3673          3674          3675 
  3.700733253   1.643688393   1.643688393   1.643688393   1.643688393 
         3676          3677          3678          3679          3680 
 -0.950711607   1.643688393   2.859288393  -6.140711607   1.643688393 
         3681          3682          3683          3684          3685 
  1.643688393   1.643688393 -12.250711607   1.643788393   8.859288393 
         3686          3687          3688          3689          3690 
  0.589288393   1.643788393   1.643788393 -16.874968662  -4.464968662 
         3691          3692          3693          3694          3695 
  8.208331338   8.208331338  -7.614968662   2.775031338  -4.954968662 
         3696          3697          3698          3699          3700 
  0.285031338  -5.914968662   8.208331338  -3.554968662  -0.334968662 
         3701          3702          3703          3704          3705 
-10.024968662   5.365031338  -2.784968662   8.208331338   8.208331338 
         3706          3707          3708          3709          3710 
-15.574968662   2.126278169   0.925578169   0.925578169   0.925578169 
         3711          3712          3713          3714          3715 
  0.925578169   0.925578169   0.925578169   0.925578169   0.925578169 
         3716          3717          3718          3719          3720 
  0.925578169   9.576278169   0.925578169   0.925578169  -4.462520614 
         3721          3722          3723          3724          3725 
 -9.872520614   4.447379386   4.447379386   1.237479386   4.447379386 
         3726          3727          3728          3729          3730 
 -0.552520614   4.447379386   4.447379386   2.557479386   4.447379386 
         3731          3732          3733          3734          3735 
-17.592520614  -4.572520614  -7.452520614   4.447379386  -4.997641712 
         3736          3737          3738          3739          3740 
  2.891258288   2.202358288   0.902358288   6.672358288   6.712358288 
         3741          3742          3743          3744          3745 
  2.891358288   2.891358288   4.432358288   2.891358288 -21.807641712 
         3746          3747          3748          3749          3750 
  6.192358288  -2.907641712  -8.757641712   2.443183801   2.443183801 
         3751          3752          3753          3754          3755 
  2.443183801   4.148783801  -0.241216199 -15.781216199   2.443183801 
         3756          3757          3758          3759          3760 
  5.998783801  -5.051216199  -5.061216199 -15.991216199   6.728783801 
         3761          3762          3763          3764          3765 
 10.968783801   2.443183801  -5.591216199  15.128783801   2.443183801 
         3766          3767          3768          3769          3770 
  5.198783801   3.115236169   3.115236169  -3.826063831   3.115336169 
         3771          3772          3773          3774          3775 
  3.115336169   7.153936169   2.963936169   6.603936169 -14.176063831 
         3776          3777          3778          3779          3780 
  3.115336169  15.813936169 -20.906063831  -1.256187500 -13.646187500 
         3781          3782          3783          3784          3785 
 -5.836187500  -2.156187500  -3.456187500  -6.256187500   7.237812500 
         3786          3787          3788          3789          3790 
  7.237812500   0.303812500  -5.196187500   5.603812500   1.313812500 
         3791          3792          3793          3794          3795 
 -0.396187500   1.443812500   4.018256899   4.018256899   4.018256899 
         3796          3797          3798          3799          3800 
 -4.126843101  -1.426843101   0.793156899   4.018256899  -3.206843101 
         3801          3802          3803          3804          3805 
  4.693156899 -15.486843101   6.663156899   4.018256899  -4.926843101 
         3806          3807          3808          3809          3810 
  4.018256899   0.693156899  -8.136843101   4.017507902   2.551207902 
         3811          3812          3813          3814          3815 
 -6.818792098   4.017507902   4.331207902  -2.338792098   4.017507902 
         3816          3817          3818          3819          3820 
  8.521207902   5.491207902  -7.468792098 -11.358792098  -0.618792098 
         3821          3822          3823          3824          3825 
 10.897820919  -5.212179081 -10.122179081   0.917820919  -0.762179081 
         3826          3827          3828          3829          3830 
  1.909720919   1.909720919   1.909720919   1.909720919   1.909720919 
         3831          3832          3833          3834          3835 
  1.909720919   3.757820919   0.127820919   1.909720919  -6.732179081 
         3836          3837          3838          3839          3840 
  0.476436489 -12.083563511  -0.096563511  -0.096563511  11.056436489 
         3841          3842          3843          3844          3845 
 -0.096563511  -0.096563511  -4.343563511  18.646436489  -0.096563511 
         3846          3847          3848          3849          3850 
 -0.096563511  -0.096563511  -0.096563511  -4.033563511   7.936436489 
         3851          3852          3853          3854          3855 
  6.536436489  -0.096563511   6.946436489 -11.353563511  -0.096563511 
         3856          3857          3858          3859          3860 
  3.437245120 -18.692554880   3.437245120   7.847445120   7.727445120 
         3861          3862          3863          3864          3865 
 12.667445120   3.437245120   3.437245120  -1.902554880   3.437245120 
         3866          3867          3868          3869          3870 
  2.027445120 -13.852554880  -9.502554880 -11.152554880   3.437245120 
         3871          3872          3873          3874          3875 
 -2.552554880   3.437245120   9.885770369   4.535770369 -12.784229631 
         3876          3877          3878          3879          3880 
 -1.094229631  -1.154229631  -0.934229631   5.427370369  11.365770369 
         3881          3882          3883          3884          3885 
-11.374229631  -8.134229631  11.095770369   5.045770369  -5.444229631 
         3886          3887          3888          3889          3890 
-13.864229631   4.235770369   0.025770369   0.265770369  -6.694229631 
         3891          3892          3893          3894          3895 
  2.765770369 -13.044229631   5.427470369  -6.459456043  -4.519456043 
         3896          3897          3898          3899          3900 
  2.411543957   7.410543957  -8.749456043  -5.269456043  -6.829456043 
         3901          3902          3903          3904          3905 
  2.411543957  -1.399456043  12.960543957   9.030543957   2.411543957 
         3906          3907          3908          3909          3910 
 -8.609642101  -6.479642101  -7.559642101   5.770357899   8.260357899 
         3911          3912          3913          3914          3915 
 -2.479642101   0.980357899   1.530357899   6.352157899  -6.069642101 
         3916          3917          3918          3919          3920 
 -7.589642101   6.352157899  12.230357899   1.680357899  -6.229642101 
         3921          3922          3923          3924          3925 
 -3.269642101  -7.839642101   6.352157899 -11.439642101   0.170357899 
         3926          3927          3928          3929          3930 
  8.260357899   8.210357899 -12.219642101  -4.089642101  15.747766405 
         3931          3932          3933          3934          3935 
  1.453166405   1.453166405  11.937766405   1.453166405  -0.422233595 
         3936          3937          3938          3939          3940 
  3.877766405   1.453166405   1.453166405   1.453166405  -9.262233595 
         3941          3942          3943          3944          3945 
 -4.542233595  -6.432233595  -4.379684379  -0.767284379  -7.619684379 
         3946          3947          3948          3949          3950 
 -6.059684379  -7.529684379   6.530315621   0.970315621  13.240315621 
         3951          3952          3953          3954          3955 
 -0.767284379   9.130315621   1.070315621  13.010315621   9.970315621 
         3956          3957          3958          3959          3960 
  4.553355910   5.391455910  -5.776644090   8.373355910  -7.446644090 
         3961          3962          3963          3964          3965 
  5.391555910  -7.226644090  11.233355910  -6.626644090  -0.776644090 
         3966          3967          3968          3969          3970 
 -3.866644090   1.343355910  -5.016644090   5.391555910  -9.866644090 
         3971          3972          3973          3974          3975 
-15.358613972  -3.598613972 -12.498613972   8.515486028   8.515486028 
         3976          3977          3978          3979          3980 
-18.168613972   8.515486028 -15.738613972 -11.098613972   8.515486028 
         3981          3982          3983          3984          3985 
  1.831386028   8.515486028   2.255698409   3.384098409 -23.614301591 
         3986          3987          3988          3989          3990 
  3.384198409  -9.694301591   3.384198409   3.384198409   3.384198409 
         3991          3992          3993          3994          3995 
  3.384198409   3.384198409   3.384198409   9.725698409   3.384198409 
         3996          3997          3998          3999          4000 
  4.946353217  15.546353217   5.446353217  -6.413646783   0.636953217 
         4001          4002          4003          4004          4005 
 -8.633646783   9.026353217   7.896353217   0.636953217  12.596353217 
         4006          4007          4008          4009          4010 
 -2.583646783   0.636953217  11.546353217  -0.263646783 -18.693646783 
         4011          4012          4013          4014          4015 
-13.473646783  -5.173646783   0.636953217   7.696836808 -12.153163192 
         4016          4017          4018          4019          4020 
 -1.663163192  -6.253163192   0.606836808  -0.823163192  11.160736808 
         4021          4022          4023          4024          4025 
  1.086836808  -0.503163192 -10.843163192 -11.543163192 -17.173163192 
         4026          4027          4028          4029          4030 
  4.322424531   4.322424531   4.322424531   4.322424531 -16.161475469 
         4031          4032          4033          4034          4035 
  4.322424531  -4.701475469 -18.801475469 -18.621475469   6.218524531 
         4036          4037          4038          4039          4040 
-12.131475469   4.322424531   4.322424531  -1.951475469   4.322424531 
         4041          4042          4043          4044          4045 
  2.248524531   6.948524531   4.322424531   3.568524531  -2.871475469 
         4046          4047          4048          4049          4050 
  4.322424531   4.322424531   8.129360288   2.476060288   2.476060288 
         4051          4052          4053          4054          4055 
 10.469360288   0.169360288  -1.240639712   2.476060288  -0.610639712 
         4056          4057          4058          4059          4060 
-20.750639712   2.476060288 -11.460639712  12.209360288   2.476060288 
         4061          4062          4063          4064          4065 
 -5.910085082  -9.030085082  -0.530085082 -16.840085082   9.439914918 
         4066          4067          4068          4069          4070 
  0.679914918   8.779914918  -5.420085082  -6.290085082  -6.210085082 
         4071          4072          4073          4074          4075 
-18.320085082   7.246714918  18.239914918   4.815960320   0.265960320 
         4076          4077          4078          4079          4080 
  7.026060320  -3.554039680   7.545960320 -13.334039680   1.935960320 
         4081          4082          4083          4084          4085 
 -3.124039680  -1.214039680  12.055960320   4.565960320  -2.514039680 
         4086          4087          4088          4089          4090 
  7.026060320 -21.744039680 -10.334039680 -14.024039680  -3.494039680 
         4091          4092          4093          4094          4095 
  7.026060320   7.705960320   7.026060320  -7.764039680   7.026060320 
         4096          4097          4098          4099          4100 
  7.026060320   4.945960320   7.026060320   7.026060320  -8.124039680 
         4101          4102          4103          4104          4105 
-19.554039680  -9.924039680   3.045960320  -3.074039680   7.026060320 
         4106          4107          4108          4109          4110 
-18.194039680   7.026060320   2.036223864  -9.959176136  12.980823864 
         4111          4112          4113          4114          4115 
-10.119176136  11.900823864 -11.489176136   4.050823864   2.036223864 
         4116          4117          4118          4119          4120 
  2.036223864   2.036223864  -6.699176136   2.036223864   9.640823864 
         4121          4122          4123          4124          4125 
  2.036223864   2.036223864   2.042423864   7.715967181  -0.384032819 
         4126          4127          4128          4129          4130 
  8.295967181  -6.424032819   1.855967181   9.665967181   2.305967181 
         4131          4132          4133          4134          4135 
 -0.504032819  -9.284032819   3.965967181  -1.104032819  13.385967181 
         4136          4137          4138          4139          4140 
 12.665967181  -7.854032819  -8.564032819  -0.394032819   2.105967181 
         4141          4142          4143          4144          4145 
-15.033208072  -7.363208072   6.342091928  -7.253208072 -10.233208072 
         4146          4147          4148          4149          4150 
 -7.643208072  -4.473208072  -5.703208072   6.342091928   6.342091928 
         4151          4152          4153          4154          4155 
  6.342091928   2.626791928  -2.093208072   6.342091928   1.886791928 
         4156          4157          4158          4159          4160 
  6.342091928   6.342091928 -12.209786751   5.449113249 -15.319786751 
         4161          4162          4163          4164          4165 
  5.449213249   5.449213249  -2.539786751 -17.119786751   5.449213249 
         4166          4167          4168          4169          4170 
 -2.909786751  17.150213249 -11.659786751   9.450213249   5.449213249 
         4171          4172          4173          4174          4175 
 -5.679786751   5.449213249   1.900213249  -6.729786751  -5.755225522 
         4176          4177          4178          4179          4180 
  5.794774478   8.924774478  -8.615225522   4.071474478  -2.025225522 
         4181          4182          4183          4184          4185 
-18.985225522   4.071474478  11.754774478   2.104774478  -4.695225522 
         4186          4187          4188          4189          4190 
 -1.025225522   7.574774478   8.305740029  -6.814259971   3.050640029 
         4191          4192          4193          4194          4195 
-11.354259971   3.050640029   3.050640029 -19.034259971  10.925740029 
         4196          4197          4198          4199          4200 
  3.050640029   3.050640029   5.295740029   3.050640029  -1.421975185 
         4201          4202          4203          4204          4205 
  0.972924815   4.842924815  -1.421975185   5.872924815  -1.421975185 
         4206          4207          4208          4209          4210 
 11.612924815   9.492924815  -1.421975185   1.872924815  -1.421975185 
         4211          4212          4213          4214          4215 
 -1.421975185  -1.421975185   5.952924815   8.542924815  -1.421975185 
         4216          4217          4218          4219          4220 
 -1.187075185   3.843616061  -4.862183939  -7.902183939 -12.352183939 
         4221          4222          4223          4224          4225 
 -0.342183939   3.843616061   3.843616061  14.807816061   8.157816061 
         4226          4227          4228          4229          4230 
-10.232183939  -1.842183939   3.843616061   3.247816061   1.247816061 
         4231          4232          4233          4234          4235 
 -9.258185671   7.359814329  -7.238185671   7.359814329   7.359814329 
         4236          4237          4238          4239          4240 
  7.359814329 -16.618185671  -0.348185671 -16.178185671  -5.868185671 
         4241          4242          4243          4244          4245 
-14.718185671   7.359814329   1.141814329   7.359814329  18.357985048 
         4246          4247          4248          4249          4250 
 -8.362014952   3.627985048   4.849585048   2.307985048 -11.552014952 
         4251          4252          4253          4254          4255 
 -4.402014952  -7.242014952  -3.892014952   4.849585048  -5.852014952 
         4256          4257          4258          4259          4260 
 -6.622014952   4.849585048   7.654484583   0.364484583  19.634484583 
         4261          4262          4263          4264          4265 
-11.435515417 -15.835515417   5.241284583 -13.335515417   5.241284583 
         4266          4267          4268          4269          4270 
-16.565515417   5.241284583   5.241284583   5.241284583   5.241284583 
         4271          4272          4273          4274          4275 
 -9.925515417  -4.186189269   1.443710731  -8.076189269   1.443710731 
         4276          4277          4278          4279          4280 
  5.233810731   1.443710731  15.713810731   3.603810731   1.443710731 
         4281          4282          4283          4284          4285 
  1.443710731  15.953810731   1.443710731 -11.416189269   9.663810731 
         4286          4287          4288          4289          4290 
  1.443710731   0.593810731 -11.716189269  -5.456189269   1.443710731 
         4291          4292          4293          4294          4295 
  3.740668750  10.556468750  -3.073531250   8.516468750   1.446468750 
         4296          4297          4298          4299          4300 
  3.740668750   3.740668750   3.740668750 -11.963531250   3.740668750 
         4301          4302          4303          4304          4305 
-13.973531250   3.740668750 -11.783531250   3.740668750 -18.523531250 
         4306          4307          4308          4309          4310 
  3.740668750   3.740668750  -9.674734219  13.025265781   6.877165781 
         4311          4312          4313          4314          4315 
 -3.214734219   5.885265781   6.877165781 -14.554734219  -1.874734219 
         4316          4317          4318          4319          4320 
-20.204734219 -19.054734219   6.605265781  -2.424734219   0.095265781 
         4321          4322          4323          4324          4325 
  6.877165781   5.288857109 -14.300142891  -5.900142891  -4.560142891 
         4326          4327          4328          4329          4330 
  5.288857109 -12.000142891   0.599857109  -1.750142891   5.288857109 
         4331          4332          4333          4334          4335 
  5.288857109  -0.010142891  11.099857109   7.529857109  12.939857109 
         4336          4337          4338          4339          4340 
-17.030142891 -12.620142891   7.742110058 -23.959989942   7.742110058 
         4341          4342          4343          4344          4345 
 -1.589989942  -1.249989942  17.700010058 -18.379989942   7.742110058 
         4346          4347          4348          4349          4350 
  1.310010058   7.742110058  -6.509989942   5.960010058   2.780010058 
         4351          4352          4353          4354          4355 
 -3.949989942 -24.419989942   3.430010058 -12.859151988   3.924248012 
         4356          4357          4358          4359          4360 
  3.924248012  -1.969151988   5.260848012 -21.529151988   3.900848012 
         4361          4362          4363          4364          4365 
  3.924248012   7.870848012   3.924248012   3.924248012   3.924248012 
         4366          4367          4368          4369          4370 
  2.239702993   2.410102993 -19.189397007  10.380602993   3.020602993 
         4371          4372          4373          4374          4375 
  1.730602993  -1.849397007   2.410102993   0.670602993  -1.679397007 
         4376          4377          4378          4379          4380 
  2.410102993  11.110602993 -17.439730286  -9.139730286   5.468769714 
         4381          4382          4383          4384          4385 
  7.450269714   5.468769714  20.730269714 -20.979730286  -8.789730286 
         4386          4387          4388          4389          4390 
  5.468769714   5.468769714   5.468769714  -9.549730286   5.468769714 
         4391          4392          4393          4394          4395 
 -7.879730286   1.277837208  11.210837208 -12.249162792   9.880837208 
         4396          4397          4398          4399          4400 
  2.560237208   2.560237208 -25.679162792  12.640837208  -7.029162792 
         4401          4402          4403          4404          4405 
  2.560237208 -18.689162792   7.180837208   7.540837208  -4.739162792 
         4406          4407          4408          4409          4410 
  7.950837208   6.860837208   2.560237208  -5.389162792   2.560237208 
         4411          4412          4413          4414          4415 
  0.490837208  -1.839162792  11.500837208  11.380837208  -3.809162792 
         4416          4417          4418          4419          4420 
 -6.399162792  -1.419162792 -26.295615914   8.164384086   2.174384086 
         4421          4422          4423          4424          4425 
  2.475484086 -11.615615914  -4.245615914   2.475484086   2.475484086 
         4426          4427          4428          4429          4430 
  2.475484086   5.804384086   2.475584086   6.524384086  16.124384086 
         4431          4432          4433          4434          4435 
  4.514384086   2.475584086   2.954384086  -5.065615914  13.210431406 
         4436          4437          4438          4439          4440 
 -8.449568594  -6.319568594   4.883431406   0.410431406   4.883431406 
         4441          4442          4443          4444          4445 
-17.099568594  -9.179568594   4.883431406   4.883431406   4.883431406 
         4446          4447          4448          4449          4450 
 -2.709568594   3.103618556 -17.606181444   3.103618556  -2.016181444 
         4451          4452          4453          4454          4455 
  3.103618556   3.103618556  -9.486181444   3.103618556   3.103618556 
         4456          4457          4458          4459          4460 
  3.103618556   3.103618556   3.103618556   1.450844614   1.450844614 
         4461          4462          4463          4464          4465 
 18.932744614   2.742744614  -5.247255386  -5.957255386   1.492744614 
         4466          4467          4468          4469          4470 
  1.450844614   1.450844614   1.450844614   3.752744614  -3.597255386 
         4471          4472          4473          4474          4475 
 -2.027255386  -1.157255386   6.532744614   2.872744614  -6.097255386 
         4476          4477          4478          4479          4480 
  9.352744614  -8.507255386  -0.227983674  -0.227983674   0.923416326 
         4481          4482          4483          4484          4485 
 -0.227983674  -0.227983674  -0.227983674  -0.227983674  -0.227983674 
         4486          4487          4488          4489          4490 
  3.513416326   9.183416326  -0.227983674   3.223416326  -0.227983674 
         4491          4492          4493          4494          4495 
 -0.227983674  -0.227983674  -0.227983674  -0.227983674  15.213416326 
         4496          4497          4498          4499          4500 
-10.756671360  -6.156671360   4.997228640   7.123328640  -7.076671360 
         4501          4502          4503          4504          4505 
 -7.806671360  -0.816671360  -4.366671360   4.997228640  -8.406671360 
         4506          4507          4508          4509          4510 
 16.783328640   4.997228640  -6.850171030   0.069828970 -17.900171030 
         4511          4512          4513          4514          4515 
-10.240171030   5.929828970  11.239828970  11.309828970   3.399828970 
         4516          4517          4518          4519          4520 
  4.922328970   4.129828970  -7.500171030  -6.820171030   9.809828970 
         4521          4522          4523          4524          4525 
  4.922328970   4.409828970  -7.600171030  -0.710171030  -2.860171030 
         4526          4527          4528          4529          4530 
 -9.814131738  -4.504131738  -5.704131738   3.033268262   3.033268262 
         4531          4532          4533          4534          4535 
  3.033268262   3.033268262   3.033268262   3.033268262  -7.914131738 
         4536          4537          4538          4539          4540 
  3.033268262 -23.784131738   3.033268262  -1.584131738  -5.864131738 
         4541          4542          4543          4544          4545 
  0.805868262   3.033268262  40.755868262   3.374047040   0.166947040 
         4546          4547          4548          4549          4550 
 11.996947040 -27.253052960   3.374047040   3.374047040   3.374047040 
         4551          4552          4553          4554          4555 
  3.374047040   3.374047040   3.374047040   3.374047040   3.374047040 
         4556          4557          4558          4559          4560 
-11.683052960  -5.823052960   3.374147040   3.374147040   3.374147040 
         4561          4562          4563          4564          4565 
  3.374147040  -7.523052960   3.415771713   3.415771713   3.415771713 
         4566          4567          4568          4569          4570 
-11.769228287   3.415771713   3.415771713   3.415771713   3.415771713 
         4571          4572          4573          4574          4575 
  3.415771713  -3.939228287   3.415771713   3.415771713   3.415771713 
         4576          4577          4578          4579          4580 
  3.415771713   3.439471713   3.439471713  -2.749228287  -6.759228287 
         4581          4582          4583          4584          4585 
 -8.959228287  -3.059228287   3.439471713 -13.069228287 -10.939228287 
         4586          4587          4588          4589          4590 
  7.450771713 -12.429228287  14.820771713  -1.239419798  -1.239419798 
         4591          4592          4593          4594          4595 
 -1.239419798   1.614880202  10.604880202   5.994880202   7.754880202 
         4596          4597          4598          4599          4600 
  8.674880202  -0.635119798   3.204880202  -1.239419798   8.324880202 
         4601          4602          4603          4604          4605 
 -1.239419798  -1.239419798  -1.239419798   1.624880202  -4.725119798 
         4606          4607          4608          4609          4610 
 -1.239319798  -1.809976282  -1.809976282  -1.809976282  -1.809976282 
         4611          4612          4613          4614          4615 
 -1.809976282  14.046423718  -1.153576282   0.936423718  -1.809976282 
         4616          4617          4618          4619          4620 
 -1.809976282  -0.273576282  -1.809976282   8.946423718  -1.809976282 
         4621          4622          4623          4624          4625 
 -1.809976282  -1.809976282   7.216423718  -1.809976282  -1.809976282 
         4626          4627          4628          4629          4630 
 -1.809976282  -1.804076282  -1.804076282   9.176423718  -1.804076282 
         4631          4632          4633          4634          4635 
  7.386423718  -1.804076282   7.756423718   6.076423718   9.746423718 
         4636          4637          4638          4639          4640 
  3.486423718  -1.804076282  -1.804076282  -0.043576282   2.306423718 
         4641          4642          4643          4644          4645 
 -1.804076282  17.435262264   2.285262264  15.135262264   6.456362264 
         4646          4647          4648          4649          4650 
 -1.074737736   6.456362264   9.415262264 -17.644737736  -1.894737736 
         4651          4652          4653          4654          4655 
 -9.464737736 -13.054737736 -15.844737736   6.175262264 -20.034737736 
         4656          4657          4658          4659          4660 
  7.675262264 -13.574737736   2.085262264   8.215262264  -4.677033845 
         4661          4662          4663          4664          4665 
 11.962966155   1.296766155   1.296766155  11.452966155  -5.077033845 
         4666          4667          4668          4669          4670 
  1.562966155   1.296766155  -1.477033845 -13.117033845   1.762966155 
         4671          4672          4673          4674          4675 
-13.297033845   1.296766155   6.362966155 -12.157033845   1.296766155 
         4676          4677          4678          4679          4680 
  1.296766155   1.296766155  -5.037033845   3.212966155   8.032966155 
         4681          4682          4683          4684          4685 
  9.642966155 -10.477033845   5.162966155   3.152966155  -7.277033845 
         4686          4687          4688          4689          4690 
 16.732966155  -0.457033845  -2.587033845  -2.397033845   6.371364822 
         4691          4692          4693          4694          4695 
  1.649864822   6.371364822   8.389864822   6.371364822  -4.940135178 
         4696          4697          4698          4699          4700 
 -3.840135178   6.371364822   6.371364822 -10.990135178 -17.680135178 
         4701          4702          4703          4704          4705 
  0.559864822 -16.100135178  -6.044392776  -8.994392776  -8.064392776 
         4706          4707          4708          4709          4710 
-13.124392776   8.855607224  -6.584392776  -8.124392776   6.293907224 
         4711          4712          4713          4714          4715 
  6.293907224   6.293907224   6.293907224   6.293907224 -18.744392776 
         4716          4717          4718          4719          4720 
  6.685607224   6.293907224  -1.554392776   6.293907224   4.835607224 
         4721          4722          4723          4724          4725 
  6.293907224  -8.434392776  -9.304962446  -2.764962446   8.823137554 
         4726          4727          4728          4729          4730 
 -5.714962446   8.823137554 -12.534962446   2.175037554  -7.994962446 
         4731          4732          4733          4734          4735 
-11.924962446   8.823237554   4.465037554   1.575037554  -2.564962446 
         4736          4737          4738          4739          4740 
-19.654962446  -1.634962446   7.765037554   8.823237554  -0.314962446 
         4741          4742          4743          4744          4745 
 -1.684962446  -9.007565306   1.059534694   0.922434694   4.792434694 
         4746          4747          4748          4749          4750 
-12.177565306  -5.767565306   9.532434694   1.059534694   1.059534694 
         4751          4752          4753          4754          4755 
  1.059534694   1.059534694  10.692434694   3.672434694   6.912434694 
         4756          4757          4758          4759          4760 
 10.172434694  -2.317565306   1.059534694   5.638147263 -14.484052737 
         4761          4762          4763          4764          4765 
  5.638147263   5.638147263  -1.194052737  -0.314052737 -14.754052737 
         4766          4767          4768          4769          4770 
  4.945947263   5.638147263   5.638147263  -2.134052737   5.638247263 
         4771          4772          4773          4774          4775 
-11.774052737 -15.364992121  11.005007879 -11.794992121   0.135007879 
         4776          4777          4778          4779          4780 
  7.229307879 -11.024992121   0.935007879 -17.604992121   7.229307879 
         4781          4782          4783          4784          4785 
-14.664992121 -11.624992121   7.229307879   7.229307879   7.315007879 
         4786          4787          4788          4789          4790 
  0.635007879  -6.644992121   9.445007879   7.229307879   7.229307879 
         4791          4792          4793          4794          4795 
-10.954384413   4.050315587 -20.984384413   4.050315587   4.050315587 
         4796          4797          4798          4799          4800 
  4.050315587   4.050315587   4.050315587 -10.144384413   4.050315587 
         4801          4802          4803          4804          4805 
  4.050315587   2.505615587   4.050315587   5.122115587  -0.034384413 
         4806          4807          4808          4809          4810 
 -9.904384413  -1.254384413  -3.054384413   5.122115587  -7.711059491 
         4811          4812          4813          4814          4815 
  5.962140509 -12.451059491  -5.441059491 -14.981059491   5.962140509 
         4816          4817          4818          4819          4820 
  5.962140509   5.962140509   5.962140509   5.962140509   5.962140509 
         4821          4822          4823          4824          4825 
-12.111059491   5.962140509   5.962140509  -9.551059491   9.561350223 
         4826          4827          4828          4829          4830 
  7.311350223 -12.948649777  -1.018649777   5.861350223   6.640050223 
         4831          4832          4833          4834          4835 
-13.368649777   1.351350223   6.640050223   6.640050223   6.640050223 
         4836          4837          4838          4839          4840 
-12.758649777   6.640050223  -6.018649777  -2.958649777  -9.258649777 
         4841          4842          4843          4844          4845 
-10.058649777  11.332450456 -11.217549544  12.862450456   7.622450456 
         4846          4847          4848          4849          4850 
 -2.897549544  -1.007549544  -0.367549544  -7.797549544   9.532450456 
         4851          4852          4853          4854          4855 
-10.617549544  -6.117549544   5.322450456   8.087598633   8.553998633 
         4856          4857          4858          4859          4860 
  8.553998633   8.553998633 -12.251901367  -4.621901367  -3.211901367 
         4861          4862          4863          4864          4865 
 -1.611901367 -18.021901367  -7.031901367  -4.121901367  -6.641901367 
         4866          4867          4868          4869          4870 
 -8.641901367   5.417061055 -16.522938945   3.046261055   3.046261055 
         4871          4872          4873          4874          4875 
  1.567061055  -0.432938945  -8.362938945   3.046361055  10.567061055 
         4876          4877          4878          4879          4880 
  3.046361055   3.046361055  -6.292938945   3.046361055   3.046361055 
         4881          4882          4883          4884          4885 
  3.046361055  -3.292407600 -17.632407600  -4.322407600  -5.702407600 
         4886          4887          4888          4889          4890 
 -4.042407600 -10.022407600   9.968292400   9.968292400 -15.752407600 
         4891          4892          4893          4894          4895 
-15.512407600   9.968292400   7.397592400  -2.182407600  -0.446643304 
         4896          4897          4898          4899          4900 
  2.560056696   2.560056696  -2.276643304 -15.686643304   2.560056696 
         4901          4902          4903          4904          4905 
  2.560056696  -7.866643304   7.873356696  12.003356696   2.560056696 
         4906          4907          4908          4909          4910 
 -4.196643304   3.315788298 -17.944211702   6.725788298   2.495788298 
         4911          4912          4913          4914          4915 
 -3.384211702  11.325788298   3.768088298   3.768088298   0.745788298 
         4916          4917          4918          4919          4920 
  8.425788298  -0.934211702   3.768088298 -20.654211702   3.768088298 
         4921          4922          4923          4924          4925 
-22.104240636   4.885759364  -7.614240636  -0.314240636  10.275759364 
         4926          4927          4928          4929          4930 
-14.024240636   8.835759364  10.215759364   3.625459364 -12.424240636 
         4931          4932          4933          4934          4935 
 -4.344240636   3.625459364  -8.624240636   3.625459364   3.475759364 
         4936          4937          4938          4939          4940 
 -8.794240636   9.795759364   0.685759364 -19.734240636  -2.274240636 
         4941          4942          4943          4944          4945 
 12.005759364   1.755759364   9.235759364   3.625459364   3.625459364 
         4946          4947          4948          4949          4950 
  7.705759364  -6.027563232 -15.757563232 -10.937563232   6.068036768 
         4951          4952          4953          4954          4955 
  6.068036768   6.068036768   6.068036768   4.902436768  10.452436768 
         4956          4957          4958          4959          4960 
  7.622436768  -9.627563232 -16.647563232  -4.927563232   7.971092636 
         4961          4962          4963          4964          4965 
  7.971092636  -6.968307364 -23.348307364  -2.388307364  -2.318307364 
         4966          4967          4968          4969          4970 
 -9.938307364   7.971092636   3.711692636   0.181692636 -13.388307364 
         4971          4972          4973          4974          4975 
  2.961692636   7.971092636   0.450537603   0.450537603   0.450537603 
         4976          4977          4978          4979          4980 
  0.450537603   0.450537603   0.450537603   0.450537603  10.171937603 
         4981          4982          4983          4984          4985 
  0.450537603   5.461937603   0.450537603   7.561937603   0.450537603 
         4986          4987          4988          4989          4990 
  0.450537603   0.450537603   2.310302604   2.312602604   1.090802604 
         4991          4992          4993          4994          4995 
  2.312602604   2.312602604  -2.519197396 -10.339197396  17.310802604 
         4996          4997          4998          4999          5000 
  2.312602604 -10.739197396   2.312602604   6.940802604  -1.329197396 
         5001          5002          5003          5004          5005 
  4.661696258   8.419496258  -1.550503742 -15.620503742  -8.590503742 
         5006          5007          5008          5009          5010 
  7.809496258  -1.510503742 -12.000503742   7.899496258   7.349496258 
         5011          5012          5013          5014          5015 
  7.799496258   3.619496258 -19.190503742  -7.298621176 -16.298621176 
         5016          5017          5018          5019          5020 
  2.911378824   6.041678824   6.041678824   6.041678824   6.041678824 
         5021          5022          5023          5024          5025 
 20.541378824   4.881378824   6.041678824 -13.338621176 -23.278621176 
         5026          5027          5028          5029          5030 
  2.551378824   6.041678824 -10.498621176   6.041678824  -0.628621176 
         5031          5032          5033          5034          5035 
 -9.618621176  -8.698621176   1.261039513  -5.183160487   1.261039513 
         5036          5037          5038          5039          5040 
  1.261039513   1.261039513   1.261039513   1.261039513   1.261039513 
         5041          5042          5043          5044          5045 
  0.966839513   1.261039513   1.261039513   1.261039513   1.261039513 
         5046          5047          5048          5049          5050 
  1.261039513   1.261039513   1.261039513  -7.589443323   5.740556677 
         5051          5052          5053          5054          5055 
  3.381056677   3.381056677   3.381056677   4.130556677   3.381056677 
         5056          5057          5058          5059          5060 
-10.499443323   9.660556677  -5.299443323   3.381056677   3.381056677 
         5061          5062          5063          5064          5065 
 -7.079443323  -2.478192889 -13.818192889  -3.098192889   1.903307111 
         5066          5067          5068          5069          5070 
  1.903307111   3.631807111   1.903307111   1.903307111  12.381807111 
         5071          5072          5073          5074          5075 
  7.651807111  -2.178192889 -10.898192889   2.531807111  -1.798192889 
         5076          5077          5078          5079          5080 
  0.291807111   4.541807111   1.903307111  -6.542524553  -7.562524553 
         5081          5082          5083          5084          5085 
 -6.022524553   7.077475447  -3.012524553   4.487475447  -0.842524553 
         5086          5087          5088          5089          5090 
  6.138075447  -3.882524553   6.138075447  -6.622524553   6.138075447 
         5091          5092          5093          5094          5095 
 -5.132524553  -0.841870762  -0.841870762   4.780129238  -9.459870762 
         5096          5097          5098          5099          5100 
 -0.841870762  -0.841870762  -0.841870762  -0.841870762  13.260129238 
         5101          5102          5103          5104          5105 
  7.060129238   3.730129238   0.790129238  13.690129238  -0.841870762 
         5106          5107          5108          5109          5110 
  0.930129238  -0.841870762  -0.841870762  -0.841870762   0.055070993 
         5111          5112          5113          5114          5115 
  4.152870993   4.152870993 -15.414929007  -6.844929007   7.025070993 
         5116          5117          5118          5119          5120 
  4.152870993   6.265070993   4.165070993 -13.074929007  -3.484929007 
         5121          5122          5123          5124          5125 
  4.165070993   7.384321656   7.384321656 -15.030978344   7.384321656 
         5126          5127          5128          5129          5130 
  7.384321656 -13.790978344   7.384321656  -0.580978344   6.339021656 
         5131          5132          5133          5134          5135 
-10.310978344   0.529021656 -10.370978344 -14.110978344  -1.000978344 
         5136          5137          5138          5139          5140 
 -2.704028209  12.745971791   6.355971791  -1.184028209 -19.364028209 
         5141          5142          5143          5144          5145 
  4.612271791 -13.894028209   2.335971791  -8.074028209   6.845971791 
         5146          5147          5148          5149          5150 
  4.612271791   3.705971791   5.165971791   4.612271791  -7.074028209 
         5151          5152          5153          5154          5155 
 -7.424028209   4.612271791   4.612271791   2.306718904   9.716618904 
         5156          5157          5158          5159          5160 
  2.306718904   2.306718904 -17.993381096   2.306718904   2.306718904 
         5161          5162          5163          5164          5165 
 21.456618904   2.306718904   2.306718904  -1.333381096 -13.493381096 
         5166          5167          5168          5169          5170 
-10.753381096   7.294646381  -8.735253619 -10.625253619   7.294646381 
         5171          5172          5173          5174          5175 
-17.745253619   7.294646381  -8.005253619  -6.185253619   7.294646381 
         5176          5177          5178          5179          5180 
 -0.915253619   7.294646381  -4.275253619  -7.185253619   7.294646381 
         5181          5182          5183          5184          5185 
 -9.965253619   5.424746381  -5.709627494  -6.469627494 -10.019627494 
         5186          5187          5188          5189          5190 
  4.029772506   4.029772506   4.029772506 -14.469627494  13.630372506 
         5191          5192          5193          5194          5195 
  4.029772506   4.029772506   4.029772506   4.029772506  -3.619627494 
         5196          5197          5198          5199          5200 
  2.610372506   3.152650700  -9.374549300   9.245450700   3.152650700 
         5201          5202          5203          5204          5205 
-11.164549300   6.785450700   3.152650700 -17.304549300   1.335450700 
         5206          5207          5208          5209          5210 
  3.152650700   3.152650700   3.152650700   5.189616851 -22.124883149 
         5211          5212          5213          5214          5215 
  5.189616851  -1.864883149   3.675116851   5.189616851   3.415116851 
         5216          5217          5218          5219          5220 
-17.164883149   0.625116851  -3.074883149   3.685116851   8.385116851 
         5221          5222          5223          5224          5225 
  5.189616851   7.274252238  -3.145747762   1.168252238   1.168252238 
         5226          5227          5228          5229          5230 
  6.234252238  -3.655747762   1.168252238  -4.645747762   1.154252238 
         5231          5232          5233          5234          5235 
 -5.765747762  -1.905747762  11.904252238   2.438183326   2.438183326 
         5236          5237          5238          5239          5240 
  2.438183326   2.438183326  -2.068416674   2.438183326   2.438183326 
         5241          5242          5243          5244          5245 
-11.148416674   2.438183326 -14.428416674   2.438183326   2.438183326 
         5246          5247          5248          5249          5250 
 -4.728416674   2.438183326   2.438183326 -13.958416674   2.438183326 
         5251          5252          5253          5254          5255 
  2.438183326   8.031583326   2.438283326   2.438283326   2.438283326 
         5256          5257          5258          5259          5260 
  2.438283326   2.438283326   2.438283326   2.438283326  -9.248416674 
         5261          5262          5263          5264          5265 
  2.438283326   2.438283326   5.395875596  -0.888324404   5.395875596 
         5266          5267          5268          5269          5270 
 -0.998324404 -12.478324404   5.395875596  -6.028324404 -16.488324404 
         5271          5272          5273          5274          5275 
  7.571675596  -5.038324404  -2.848324404   5.395875596   5.395875596 
         5276          5277          5278          5279          5280 
 -0.538324404   4.881675596   4.711675596   8.321675596   5.395875596 
         5281          5282          5283          5284          5285 
 -7.398324404  -8.508324404   1.769541373   1.769541373   1.769541373 
         5286          5287          5288          5289          5290 
  1.769541373 -16.867158627   1.769541373   1.769541373   5.432841373 
         5291          5292          5293          5294          5295 
  1.769541373   1.769541373 -10.697158627   1.769541373  13.352841373 
         5296          5297          5298          5299          5300 
 11.840807755   4.700807755   2.190807755   8.940807755 -24.169192245 
         5301          5302          5303          5304          5305 
  4.440807755  -0.859192245   3.310707755   3.440807755  -4.769192245 
         5306          5307          5308          5309          5310 
  3.310707755   7.620807755   5.000807755 -16.699192245  10.510807755 
         5311          5312          5313          5314          5315 
 -8.379192245   3.310707755 -15.539192245   7.210807755   3.370807755 
         5316          5317          5318          5319          5320 
 -2.532219217 -17.972219217   6.017780783   1.600280783   1.600280783 
         5321          5322          5323          5324          5325 
 11.137780783   1.600280783   6.217780783   8.507780783   1.600380783 
         5326          5327          5328          5329          5330 
  1.600380783   1.600380783  -3.372219217   0.447780783  -1.712219217 
         5331          5332          5333          5334          5335 
 16.507780783  -0.402219217 -11.672219217  -1.402219217   6.995558718 
         5336          5337          5338          5339          5340 
  3.436558718  -4.394441282  -8.104441282  -7.304441282   3.436558718 
         5341          5342          5343          5344          5345 
  8.045558718 -13.814441282  -2.164441282   3.436558718   3.436558718 
         5346          5347          5348          5349          5350 
  3.436558718  -1.454441282  -9.344441282  23.515558718   7.525558718 
         5351          5352          5353          5354          5355 
-19.934441282   6.377316136   1.493316136   3.247316136   6.027316136 
         5356          5357          5358          5359          5360 
  2.457316136   7.747316136  -5.602683864   3.247316136  -0.862683864 
         5361          5362          5363          5364          5365 
 -2.712683864  -3.742683864   0.047316136   1.777316136   0.903131652 
         5366          5367          5368          5369          5370 
  0.903131652   0.903131652   0.903131652   0.903131652   0.903131652 
         5371          5372          5373          5374          5375 
  3.452931652   0.903131652   0.903131652   0.903131652  12.252931652 
         5376          5377          5378          5379          5380 
  0.903131652   0.903131652   0.903131652   0.903131652   0.903131652 
         5381          5382          5383          5384          5385 
  0.903131652   0.903131652  -5.437068348  11.239832490   3.779832490 
         5386          5387          5388          5389          5390 
 -0.841967510   7.229832490  -0.841967510  -0.841967510  -0.841967510 
         5391          5392          5393          5394          5395 
-18.700167510  -0.841967510  -9.170167510  -0.841967510  17.339832490 
         5396          5397          5398          5399          5400 
 -0.841967510  17.599832490  19.240080239  -7.939919761   8.172880239 
         5401          5402          5403          5404          5405 
 -4.069919761 -15.749919761   8.172880239   8.172880239  -2.319919761 
         5406          5407          5408          5409          5410 
-12.389919761   8.172880239   6.350080239   8.172880239 -17.379919761 
         5411          5412          5413          5414          5415 
-15.879919761   8.172880239 -15.699919761  -5.549919761  -3.556183456 
         5416          5417          5418          5419          5420 
 -3.376183456   3.110016544  -5.816183456  -3.956183456   3.110016544 
         5421          5422          5423          5424          5425 
 13.413816544   1.553816544   3.110016544   0.633816544   3.110016544 
         5426          5427          5428          5429          5430 
  6.123816544  -7.466183456  -8.106183456   3.809004047   2.169004047 
         5431          5432          5433          5434          5435 
  2.818504047   2.409004047  -8.250995953   8.719004047  -4.720995953 
         5436          5437          5438          5439          5440 
 -4.290995953 -16.390995953   2.818504047  -4.260995953   2.818504047 
         5441          5442          5443          5444          5445 
 -1.520995953   7.209004047   9.909004047  -2.700995953   1.520089071 
         5446          5447          5448          5449          5450 
  0.270089071   7.820089071   7.270089071   2.358489071  -9.869910929 
         5451          5452          5453          5454          5455 
 -3.819910929   0.920089071 -11.139910929   5.730089071  -8.959910929 
         5456          5457          5458          5459          5460 
 -4.619910929   5.900089071   2.358489071   2.460089071   2.358489071 
         5461          5462          5463          5464          5465 
  4.640089071   2.358489071   1.090089071   2.358489071  -5.049910929 
         5466          5467          5468          5469          5470 
  7.950089071  -3.539910929   2.910089071   2.520089071   4.454331690 
         5471          5472          5473          5474          5475 
  1.551931690  -6.275668310   1.551931690  -3.155668310  -4.675668310 
         5476          5477          5478          5479          5480 
  1.551931690  14.774331690   1.557931690   6.234331690   1.573231690 
         5481          5482          5483          5484          5485 
 -4.125668310  -0.714489885   0.344910115   7.665510115   0.349610115 
         5486          5487          5488          5489          5490 
  8.725510115  -7.824489885  11.155510115   3.155510115   4.795510115 
         5491          5492          5493          5494          5495 
-11.904489885   0.349610115  -1.284489885   0.349710115  -6.954489885 
         5496          5497          5498          5499          5500 
  0.349710115  18.645510115  -0.083654658   5.335145342  -2.613654658 
         5501          5502          5503          5504          5505 
 10.056345342  -0.113654658   5.335145342   2.966345342   4.476345342 
         5506          5507          5508          5509          5510 
  5.335145342   5.335145342  -1.383654658  10.106345342   1.716345342 
         5511          5512          5513          5514          5515 
 -5.963654658  -6.983654658  -5.013654658  -8.133654658  -9.703654658 
         5516          5517          5518          5519          5520 
-10.643654658   5.335145342  -8.303654658  12.629897081   3.136497081 
         5521          5522          5523          5524          5525 
-22.730102919  -9.530102919 -16.010102919   3.136497081   3.136497081 
         5526          5527          5528          5529          5530 
-16.780102919   5.799897081   3.579897081   0.689897081 -12.660102919 
         5531          5532          5533          5534          5535 
 10.039897081  -4.640102919  -3.000102919   3.136497081   3.136497081 
         5536          5537          5538          5539          5540 
 16.509897081   9.779897081   9.299897081   4.733876064  -8.670123936 
         5541          5542          5543          5544          5545 
  7.419876064  17.799876064   4.733876064   4.733876064 -10.090123936 
         5546          5547          5548          5549          5550 
-10.970123936   4.733876064  -7.780123936 -16.940123936   4.733876064 
         5551          5552          5553          5554          5555 
  4.733876064  -7.390123936  -7.414400998   8.061199002 -19.384400998 
         5556          5557          5558          5559          5560 
  8.061299002   8.061299002 -11.694400998   8.061299002   8.061299002 
         5561          5562          5563          5564          5565 
  8.061299002 -14.934400998   5.755599002 -21.034400998   0.115599002 
         5566          5567          5568          5569          5570 
 -4.464400998   2.585599002   8.061299002 -14.974400998   7.126685975 
         5571          5572          5573          5574          5575 
-17.948614025  -4.898614025  -3.558614025   7.126785975   7.126785975 
         5576          5577          5578          5579          5580 
 -9.698614025 -14.268614025 -11.498614025  -7.188614025   7.126785975 
         5581          5582          5583          5584          5585 
  7.126785975   7.126785975   4.081566084  13.591566084 -13.468433916 
         5586          5587          5588          5589          5590 
 -8.408433916   4.261566084   2.881566084  18.011566084  10.241566084 
         5591          5592          5593          5594          5595 
 -5.568433916   0.673266084   0.673266084   5.781566084   0.673266084 
         5596          5597          5598          5599          5600 
  0.673266084   1.821566084 -14.818433916 -13.738433916  -9.098433916 
         5601          5602          5603          5604          5605 
 15.831566084 -18.908562217 -13.128562217  11.101437783  -8.388562217 
         5606          5607          5608          5609          5610 
 -1.728562217   3.601437783  -5.508562217   7.515337783  11.361437783 
         5611          5612          5613          5614          5615 
  9.011437783   1.981437783 -10.808562217   7.515337783 -10.098562217 
         5616          5617          5618          5619          5620 
  2.316648507   2.316648507   2.316648507   2.316648507   2.316648507 
         5621          5622          5623          5624          5625 
  2.316648507   2.316648507   2.316648507  10.200848507 -24.299151493 
         5626          5627          5628          5629          5630 
  2.316648507  -3.079151493   6.670848507   2.316648507   2.316648507 
         5631          5632          5633          5634          5635 
 -7.632226559  -4.962226559   5.236473441   4.117773441   5.236473441 
         5636          5637          5638          5639          5640 
  6.087773441 -20.612226559   4.987773441  -0.422226559   5.236473441 
         5641          5642          5643          5644          5645 
  1.027773441 -13.272226559   5.236473441  -4.902226559   5.236473441 
         5646          5647          5648          5649          5650 
 19.027773441 -12.892226559   4.207644474   4.207644474   4.207644474 
         5651          5652          5653          5654          5655 
  4.207644474 -12.912555526 -10.682555526   4.207644474   0.917444474 
         5656          5657          5658          5659          5660 
 -3.762555526  -5.072555526   4.207644474   4.207644474  -3.312555526 
         5661          5662          5663          5664          5665 
  4.207644474  -3.202555526   2.587444474   4.207644474   4.719222716 
         5666          5667          5668          5669          5670 
 17.139222716  10.099222716   2.912822716   2.912822716   2.912822716 
         5671          5672          5673          5674          5675 
-20.100777284  -8.390777284   2.912822716  -9.760777284  -6.350777284 
         5676          5677          5678          5679          5680 
 -8.570777284  -0.990777284   2.912822716   2.912822716   2.912822716 
         5681          5682          5683          5684          5685 
  8.299222716   2.364850778  -2.755149222   4.686550778   3.984850778 
         5686          5687          5688          5689          5690 
 -9.565149222  -7.575149222   4.686550778   4.686650778  10.744850778 
         5691          5692          5693          5694          5695 
 -6.465149222 -10.085149222   4.964850778   0.394850778   5.272096488 
         5696          5697          5698          5699          5700 
  9.342096488   6.122096488  -9.367903512  13.772096488   0.470896488 
         5701          5702          5703          5704          5705 
  0.470896488   0.470896488   0.470996488  -1.377903512   7.502096488 
         5706          5707          5708          5709          5710 
 -1.177903512  -2.257903512  -2.707903512   0.470996488   3.193293487 
         5711          5712          5713          5714          5715 
 20.241593487   2.621593487 -11.298406513 -14.538406513 -17.168406513 
         5716          5717          5718          5719          5720 
  3.193293487   3.193293487   2.321593487   3.193293487   3.193293487 
         5721          5722          5723          5724          5725 
  3.193293487  10.296994095   3.186994095   5.606994095 -15.013005905 
         5726          5727          5728          5729          5730 
  2.906994095   3.266994095   7.896994095   7.456994095 -17.263005905 
         5731          5732          5733          5734          5735 
 -0.023005905   8.926994095   3.466994095  -4.873005905   4.038394095 
         5736          5737          5738          5739          5740 
 -8.693005905 -14.393005905   8.576994095   3.425818701   3.425818701 
         5741          5742          5743          5744          5745 
 -5.028381299   3.425818701  -1.198381299 -18.288381299 -22.858381299 
         5746          5747          5748          5749          5750 
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         5761          5762          5763          5764          5765 
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         5766          5767          5768          5769          5770 
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         5771          5772          5773          5774          5775 
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         5776          5777          5778          5779          5780 
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         5781          5782          5783          5784          5785 
 11.604410396   1.073310396   1.073310396   1.073310396   1.073310396 
         5786          5787          5788          5789          5790 
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         5791          5792          5793          5794          5795 
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         5796          5797          5798          5799          5800 
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         5801          5802          5803          5804          5805 
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         5806          5807          5808          5809          5810 
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         5811          5812          5813          5814          5815 
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         5816          5817          5818          5819          5820 
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         5821          5822          5823          5824          5825 
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         5826          5827          5828          5829          5830 
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         5831          5832          5833          5834          5835 
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         5836          5837          5838          5839          5840 
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         5841          5842          5843          5844          5845 
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         5866          5867          5868          5869          5870 
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         5881          5882          5883          5884          5885 
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         5901          5902          5903          5904          5905 
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         5911          5912          5913          5914          5915 
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         5916          5917          5918          5919          5920 
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         5921          5922          5923          5924          5925 
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         5926          5927          5928          5929          5930 
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         5931          5932          5933          5934          5935 
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         5936          5937          5938          5939          5940 
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         5941          5942          5943          5944          5945 
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         5946          5947          5948          5949          5950 
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         5961          5962          5963          5964          5965 
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         5966          5967          5968          5969          5970 
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         5971          5972          5973          5974          5975 
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         5976          5977          5978          5979          5980 
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         5981          5982          5983          5984          5985 
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         5986          5987          5988          5989          5990 
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         5991          5992          5993          5994          5995 
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         6001          6002          6003          6004          6005 
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         6006          6007          6008          6009          6010 
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         6011          6012          6013          6014          6015 
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         6021          6022          6023          6024          6025 
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         6026          6027          6028          6029          6030 
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         6031          6032          6033          6034          6035 
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         6036          6037          6038          6039          6040 
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         6041          6042          6043          6044          6045 
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         6046          6047          6048          6049          6050 
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         6056          6057          6058          6059          6060 
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         6076          6077          6078          6079          6080 
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         6081          6082          6083          6084          6085 
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         6086          6087          6088          6089          6090 
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         6091          6092          6093          6094          6095 
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         6096          6097          6098          6099          6100 
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         6101          6102          6103          6104          6105 
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         6106          6107          6108          6109          6110 
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         6111          6112          6113          6114          6115 
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         6126          6127          6128          6129          6130 
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         6136          6137          6138          6139          6140 
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         6151          6152          6153          6154          6155 
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         6161          6162          6163          6164          6165 
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         6166          6167          6168          6169          6170 
 10.351629892   5.767029892  -5.688370108  -1.668370108  -1.958370108 
         6171          6172          6173          6174          6175 
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         6191          6192          6193          6194          6195 
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         6196          6197          6198          6199          6200 
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         6201          6202          6203          6204          6205 
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         6206          6207          6208          6209          6210 
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         6211          6212          6213          6214          6215 
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         6216          6217          6218          6219          6220 
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         6221          6222          6223          6224          6225 
 13.723184866   4.008984866   2.763184866   8.738519442   0.458519442 
         6226          6227          6228          6229          6230 
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         6231          6232          6233          6234          6235 
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         6236          6237          6238          6239          6240 
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         6241          6242          6243          6244          6245 
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         6246          6247          6248          6249          6250 
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         6251          6252          6253          6254          6255 
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         6256          6257          6258          6259          6260 
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         6266          6267          6268          6269          6270 
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         6276          6277          6278          6279          6280 
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         6281          6282          6283          6284          6285 
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         6286          6287          6288          6289          6290 
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         6291          6292          6293          6294          6295 
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         6301          6302          6303          6304          6305 
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         6306          6307          6308          6309          6310 
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         6311          6312          6313          6314          6315 
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         6316          6317          6318          6319          6320 
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         6321          6322          6323          6324          6325 
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         6326          6327          6328          6329          6330 
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         6331          6332          6333          6334          6335 
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         6336          6337          6338          6339          6340 
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         6341          6342          6343          6344          6345 
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         6346          6347          6348          6349          6350 
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         6356          6357          6358          6359          6360 
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         6366          6367          6368          6369          6370 
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         6371          6372          6373          6374          6375 
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         6376          6377          6378          6379          6380 
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         6381          6382          6383          6384          6385 
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         6386          6387          6388          6389          6390 
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         6401          6402          6403          6404          6405 
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         6411          6412          6413          6414          6415 
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         6416          6417          6418          6419          6420 
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         6421          6422          6423          6424          6425 
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         6426          6427          6428          6429          6430 
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         6431          6432          6433          6434          6435 
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         6436          6437          6438          6439          6440 
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         6441          6442          6443          6444          6445 
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         6446          6447          6448          6449          6450 
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         6451          6452          6453          6454          6455 
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         6456          6457          6458          6459          6460 
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         6461          6462          6463          6464          6465 
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         6466          6467          6468          6469          6470 
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         6471          6472          6473          6474          6475 
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         6476          6477          6478          6479          6480 
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         6481          6482          6483          6484          6485 
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         6486          6487          6488          6489          6490 
 -6.985874199   6.727725801  -0.855874199 -12.525874199   6.727725801 
         6491          6492          6493          6494          6495 
 13.344125801   6.727725801  -7.221309220   8.778690780  -0.781309220 
         6496          6497          6498          6499          6500 
  4.234590780   4.088690780  -6.511309220  -0.951309220   4.234590780 
         6501          6502          6503          6504          6505 
  4.234590780 -14.841309220   4.234590780   4.234590780   1.006529917 
         6506          6507          6508          6509          6510 
 12.666529917   8.646529917   2.796529917  -1.723470083   0.506529917 
         6511          6512          6513          6514          6515 
  4.706529917  -2.673470083   2.528929917  -6.893470083  -8.743470083 
         6516          6517          6518          6519          6520 
  6.486529917  -1.533470083  -6.083470083  -2.443470083  -0.528269007 
         6521          6522          6523          6524          6525 
  8.187730993 -14.228269007 -16.888269007 -10.898269007  -3.608269007 
         6526          6527          6528          6529          6530 
  1.271730993  -9.408269007   8.187730993   8.581730993   3.811730993 
         6531          6532          6533          6534          6535 
  3.031730993   8.323465689   8.693465689   5.893465689  -5.626534311 
         6536          6537          6538          6539          6540 
-13.046534311   3.803465689 -12.936534311   3.444065689   4.623465689 
         6541          6542          6543          6544          6545 
-11.646534311  -5.536534311  -9.236534311  -3.796534311  -2.366534311 
         6546          6547          6548          6549          6550 
 -2.956534311   6.653465689  12.023465689 -11.886534311  20.153465689 
         6551          6552          6553          6554          6555 
  1.873465689   2.022946670   2.022946670   2.022946670  -5.613053330 
         6556          6557          6558          6559          6560 
  2.022946670  -7.493053330   2.022946670   2.022946670   3.046946670 
         6561          6562          6563          6564          6565 
  2.022946670  -2.523053330   2.022946670   2.022946670   1.796946670 
         6566          6567          6568          6569          6570 
 -1.863053330  -4.621458646   6.602441354   6.602441354  -8.251458646 
         6571          6572          6573          6574          6575 
-11.791458646  -3.711458646  -4.091458646   6.602441354   5.728541354 
         6576          6577          6578          6579          6580 
-11.981458646   0.498541354   6.602441354  -8.091458646   5.746064069 
         6581          6582          6583          6584          6585 
  2.178964069   2.178964069  -4.623935931   5.286064069  11.466064069 
         6586          6587          6588          6589          6590 
 -0.443935931 -12.143935931   2.178964069   2.178964069  -0.233935931 
         6591          6592          6593          6594          6595 
 -3.753935931   2.178964069   3.626064069   1.563659139   1.981059139 
         6596          6597          6598          6599          6600 
-13.776340861  12.643659139   1.981059139 -11.176340861  -3.546340861 
         6601          6602          6603          6604          6605 
  1.981059139   3.223659139   1.981059139  -3.346340861   1.981059139 
         6606          6607          6608          6609          6610 
 11.483659139   1.981059139   3.479281534   3.479281534 -10.333418466 
         6611          6612          6613          6614          6615 
 -2.303418466  -6.773418466   3.479281534   3.479281534   3.479281534 
         6616          6617          6618          6619          6620 
  3.479281534  -5.113418466   3.479281534  -3.753418466   3.479281534 
         6621          6622          6623          6624          6625 
  9.978381415   2.651281415   2.651281415  11.158381415 -12.481618585 
         6626          6627          6628          6629          6630 
-11.271618585   5.718381415   2.651281415  -2.491618585   2.651281415 
         6631          6632          6633          6634          6635 
  2.651281415  -9.831618585   3.148381415 -17.901618585  -3.041618585 
         6636          6637          6638          6639          6640 
  2.651281415   6.258381415   2.651281415   3.808381415   5.337374823 
         6641          6642          6643          6644          6645 
 13.579374823 -18.800625177  -1.060625177  -8.630625177   5.337374823 
         6646          6647          6648          6649          6650 
  5.337374823   5.337374823   5.337374823  -7.880625177  -7.880625177 
         6651          6652          6653          6654          6655 
  5.337374823  -6.000625177   6.834417708  -3.964282292 -11.154282292 
         6656          6657          6658          6659          6660 
  6.215717708   6.834417708 -15.464282292  -9.614282292  -3.464282292 
         6661          6662          6663          6664          6665 
 -6.524282292   6.834417708   4.425717708   7.005717708  -1.284282292 
         6666          6667          6668          6669          6670 
  8.720346889 -12.589653111  10.568146889   6.760346889  -1.169653111 
         6671          6672          6673          6674          6675 
-10.939653111   0.520346889 -14.689653111  -4.129653111 -12.349653111 
         6676          6677          6678          6679          6680 
 10.568146889   0.040346889 -19.259653111  -9.229653111  10.568146889 
         6681          6682          6683          6684          6685 
-12.224220416 -11.494220416   5.671479584   5.671479584   5.671479584 
         6686          6687          6688          6689          6690 
  5.671479584  18.195779584   5.671479584  -8.334220416  -2.664220416 
         6691          6692          6693          6694          6695 
  5.671479584 -13.994220416  -5.164220416   5.671479584 -10.024220416 
         6696          6697          6698          6699          6700 
  5.410724069  13.710724069 -11.929275931   4.250724069   2.351824069 
         6701          6702          6703          6704          6705 
-15.529275931   2.351824069   2.351824069   2.351824069  10.980724069 
         6706          6707          6708          6709          6710 
-21.639275931  -2.959275931  -1.059275931   9.230724069   9.100724069 
         6711          6712          6713          6714          6715 
  9.630724069  -4.329275931   1.820724069  -2.839275931 -12.299275931 
         6716          6717          6718          6719          6720 
  9.140724069 -14.183453027   9.276546973   3.479746973  -7.653453027 
         6721          6722          6723          6724          6725 
-13.543453027   4.476546973  -4.823453027  -3.533453027  13.576546973 
         6726          6727          6728          6729          6730 
  8.256546973  -6.053453027   0.316546973  13.056546973  -1.253453027 
         6731          6732          6733          6734          6735 
 11.686546973 -12.263453027  -1.363453027   3.479746973   6.443309930 
         6736          6737          6738          6739          6740 
-14.576690070   3.063309930 -17.786690070  -0.756690070   2.123309930 
         6741          6742          6743          6744          6745 
  7.143309930   0.223309930   7.893309930  -8.226690070   1.589609930 
         6746          6747          6748          6749          6750 
  1.589609930  -6.566690070   6.813309930   7.213309930  10.293309930 
         6751          6752          6753          6754          6755 
  1.589609930  -0.196690070   1.589609930   3.355427912 -15.945572088 
         6756          6757          6758          6759          6760 
-15.535572088  14.794427912   4.014427912   3.355427912  -2.715572088 
         6761          6762          6763          6764          6765 
 11.284427912   3.355427912 -13.805572088   3.355427912  -3.485572088 
         6766          6767          6768          6769          6770 
  3.355427912 -10.215572088   3.355427912   8.734427912  -0.258004850 
         6771          6772          6773          6774          6775 
  0.533495150   0.533495150   4.540395150   0.533495150   0.533495150 
         6776          6777          6778          6779          6780 
  2.510395150   4.050395150   0.533495150   0.670395150   0.533495150 
         6781          6782          6783          6784          6785 
  0.533495150   0.533495150   0.533495150   0.533495150  -6.399604850 
         6786          6787          6788          6789          6790 
  0.533495150   0.533495150   0.533495150   0.533495150   6.070395150 
         6791          6792          6793          6794          6795 
  0.533495150   0.533495150   0.533495150   0.533495150   0.533495150 
         6796          6797          6798          6799          6800 
  0.533495150   0.533495150   0.533495150   3.734838803   3.879238803 
         6801          6802          6803          6804          6805 
  3.734838803   3.734838803 -20.020761197   3.734838803   8.119238803 
         6806          6807          6808          6809          6810 
 -6.220761197   3.734838803   3.734838803  -1.170761197   3.734838803 
         6811          6812          6813          6814          6815 
  3.734838803  -8.420761197 -12.527541954  -7.417541954  10.867958046 
         6816          6817          6818          6819          6820 
 -5.717541954  10.867958046 -16.187541954  10.867958046 -11.587541954 
         6821          6822          6823          6824          6825 
-12.037541954  10.482458046 -11.657541954  10.867958046  -4.347541954 
         6826          6827          6828          6829          6830 
-11.787541954   5.640559113 -19.712240887   8.357759113  14.517759113 
         6831          6832          6833          6834          6835 
  1.557759113  -4.482240887   2.027759113  -8.072240887 -14.622240887 
         6836          6837          6838          6839          6840 
 -5.692240887 -14.962240887   5.640559113 -10.662240887   7.117759113 
         6841          6842          6843          6844          6845 
-14.732240887 -14.102240887  -3.722240887  -6.132240887  12.607759113 
         6846          6847          6848          6849          6850 
 16.917759113   6.397759113   8.737759113   6.527759113  15.017759113 
         6851          6852          6853          6854          6855 
  0.033877735  -8.896122265 -13.086122265 -12.636122265   6.973877735 
         6856          6857          6858          6859          6860 
 -5.666122265 -17.726122265   6.374577735   6.374577735   6.374577735 
         6861          6862          6863          6864          6865 
  6.374577735  -5.146122265 -15.526122265   6.723877735   6.374577735 
         6866          6867          6868          6869          6870 
  6.374577735   6.374577735 -13.916122265   6.374577735   6.374577735 
         6871 
  6.374577735

Deriving Cluster Deviations

What is each cluster’s deviation from the fixed intercept?

In other words, derive estimates of \(u_{0j}\) for every cluster \(j\)

estimate_grouplevel(fit_null, type = "random")
Group  | Level | Parameter   | Coefficient |   SE |          95% CI
-------------------------------------------------------------------
school | 1     | (Intercept) |        0.87 | 1.91 | [ -2.87,  4.61]
school | 2     | (Intercept) |        4.03 | 1.86 | [  0.38,  7.67]
school | 3     | (Intercept) |       -7.50 | 1.66 | [-10.75, -4.25]
school | 4     | (Intercept) |        5.84 | 1.69 | [  2.53,  9.16]
school | 5     | (Intercept) |       -6.99 | 1.69 | [-10.31, -3.68]
school | 6     | (Intercept) |        2.41 | 1.73 | [ -0.98,  5.80]
school | 7     | (Intercept) |       -0.22 | 1.73 | [ -3.61,  3.17]
school | 8     | (Intercept) |        3.06 | 1.44 | [  0.25,  5.88]
school | 9     | (Intercept) |       -2.09 | 1.69 | [ -5.40,  1.23]
school | 10    | (Intercept) |        2.98 | 1.59 | [ -0.14,  6.10]
school | 11    | (Intercept) |       -0.94 | 1.66 | [ -4.19,  2.31]
school | 12    | (Intercept) |       -1.76 | 1.91 | [ -5.50,  1.98]
school | 13    | (Intercept) |        0.62 | 1.73 | [ -2.77,  4.01]
school | 14    | (Intercept) |        0.16 | 1.81 | [ -3.40,  3.71]
school | 15    | (Intercept) |        4.46 | 1.59 | [  1.34,  7.58]
school | 16    | (Intercept) |       -1.59 | 1.86 | [ -5.23,  2.06]
school | 17    | (Intercept) |       -2.47 | 1.62 | [ -5.65,  0.71]
school | 18    | (Intercept) |        3.16 | 1.77 | [ -0.31,  6.62]
school | 19    | (Intercept) |        0.06 | 1.77 | [ -3.41,  3.53]
school | 20    | (Intercept) |        1.11 | 1.86 | [ -2.54,  4.75]
school | 21    | (Intercept) |        1.63 | 1.59 | [ -1.49,  4.75]
school | 22    | (Intercept) |       -1.41 | 1.91 | [ -5.15,  2.34]
school | 23    | (Intercept) |        1.64 | 1.81 | [ -1.91,  5.19]
school | 24    | (Intercept) |        0.38 | 1.77 | [ -3.09,  3.85]
school | 25    | (Intercept) |       -1.72 | 1.62 | [ -4.90,  1.46]
school | 26    | (Intercept) |        2.55 | 1.66 | [ -0.69,  5.80]
school | 27    | (Intercept) |       -3.07 | 1.62 | [ -6.25,  0.11]
school | 28    | (Intercept) |        5.19 | 1.56 | [  2.13,  8.25]
school | 29    | (Intercept) |        1.62 | 1.77 | [ -1.85,  5.09]
school | 30    | (Intercept) |       -1.68 | 1.59 | [ -4.80,  1.44]
school | 31    | (Intercept) |       -1.36 | 1.59 | [ -4.48,  1.76]
school | 32    | (Intercept) |        3.78 | 1.26 | [  1.32,  6.24]
school | 33    | (Intercept) |       -4.34 | 1.56 | [ -7.40, -1.27]
school | 34    | (Intercept) |       -0.45 | 1.66 | [ -3.70,  2.80]
school | 35    | (Intercept) |        2.34 | 1.86 | [ -1.30,  5.99]
school | 36    | (Intercept) |       -3.90 | 1.91 | [ -7.64, -0.15]
school | 37    | (Intercept) |        2.71 | 1.77 | [ -0.76,  6.18]
school | 38    | (Intercept) |       -1.69 | 1.91 | [ -5.44,  2.05]
school | 39    | (Intercept) |       -0.15 | 1.59 | [ -3.28,  2.97]
school | 40    | (Intercept) |       -3.84 | 1.73 | [ -7.23, -0.45]
school | 41    | (Intercept) |        1.79 | 1.51 | [ -1.16,  4.75]
school | 42    | (Intercept) |        0.07 | 1.86 | [ -3.57,  3.72]
school | 43    | (Intercept) |        0.89 | 1.77 | [ -2.57,  4.36]
school | 44    | (Intercept) |        3.12 | 1.62 | [ -0.06,  6.30]
school | 45    | (Intercept) |        2.06 | 1.62 | [ -1.13,  5.24]
school | 46    | (Intercept) |       -0.53 | 1.66 | [ -3.78,  2.71]
school | 47    | (Intercept) |       -4.21 | 1.77 | [ -7.68, -0.74]
school | 48    | (Intercept) |       -0.39 | 1.91 | [ -4.13,  3.35]
school | 49    | (Intercept) |       -0.15 | 1.66 | [ -3.40,  3.10]
school | 50    | (Intercept) |       -4.04 | 1.91 | [ -7.78, -0.30]
school | 51    | (Intercept) |        1.93 | 1.91 | [ -1.81,  5.67]
school | 52    | (Intercept) |        3.03 | 1.86 | [ -0.61,  6.68]
school | 53    | (Intercept) |        1.92 | 1.66 | [ -1.33,  5.17]
school | 54    | (Intercept) |        4.93 | 1.81 | [  1.38,  8.48]
school | 55    | (Intercept) |       -7.42 | 1.69 | [-10.74, -4.11]
school | 56    | (Intercept) |       -1.05 | 1.81 | [ -4.60,  2.50]
school | 57    | (Intercept) |        0.52 | 1.77 | [ -2.95,  3.98]
school | 58    | (Intercept) |        0.49 | 1.77 | [ -2.98,  3.96]
school | 59    | (Intercept) |        1.02 | 1.66 | [ -2.23,  4.27]
school | 60    | (Intercept) |       -3.54 | 1.81 | [ -7.10,  0.01]
school | 61    | (Intercept) |        1.56 | 1.59 | [ -1.56,  4.68]
school | 62    | (Intercept) |       -8.55 | 1.77 | [-12.02, -5.08]
school | 63    | (Intercept) |        1.24 | 1.66 | [ -2.01,  4.48]
school | 64    | (Intercept) |        0.85 | 1.73 | [ -2.54,  4.24]
school | 65    | (Intercept) |        3.81 | 1.81 | [  0.25,  7.36]
school | 66    | (Intercept) |       -1.42 | 1.69 | [ -4.73,  1.90]
school | 67    | (Intercept) |        1.87 | 1.86 | [ -1.78,  5.51]
school | 68    | (Intercept) |       -0.29 | 1.81 | [ -3.84,  3.26]
school | 69    | (Intercept) |       -3.86 | 1.77 | [ -7.33, -0.39]
school | 70    | (Intercept) |        4.65 | 1.77 | [  1.18,  8.11]
school | 71    | (Intercept) |       -2.02 | 1.77 | [ -5.48,  1.45]
school | 72    | (Intercept) |       -5.55 | 1.62 | [ -8.74, -2.37]
school | 73    | (Intercept) |       -0.36 | 1.66 | [ -3.60,  2.89]
school | 74    | (Intercept) |        5.17 | 1.69 | [  1.85,  8.49]
school | 75    | (Intercept) |        0.10 | 1.73 | [ -3.29,  3.49]
school | 76    | (Intercept) |        0.14 | 1.77 | [ -3.33,  3.61]
school | 77    | (Intercept) |        4.55 | 1.44 | [  1.74,  7.37]
school | 78    | (Intercept) |       -1.42 | 1.77 | [ -4.89,  2.04]
school | 79    | (Intercept) |       -2.70 | 1.91 | [ -6.44,  1.05]
school | 80    | (Intercept) |        4.34 | 1.66 | [  1.09,  7.58]
school | 81    | (Intercept) |       -2.65 | 1.86 | [ -6.30,  0.99]
school | 82    | (Intercept) |        1.35 | 1.59 | [ -1.77,  4.47]
school | 83    | (Intercept) |        2.55 | 1.35 | [ -0.10,  5.21]
school | 84    | (Intercept) |        3.21 | 1.91 | [ -0.53,  6.95]
school | 85    | (Intercept) |        0.59 | 1.77 | [ -2.88,  4.06]
school | 86    | (Intercept) |       -1.42 | 1.69 | [ -4.74,  1.90]
school | 87    | (Intercept) |        1.92 | 1.81 | [ -1.64,  5.47]
school | 88    | (Intercept) |        1.57 | 1.59 | [ -1.55,  4.70]
school | 89    | (Intercept) |        0.26 | 1.91 | [ -3.49,  4.00]
school | 90    | (Intercept) |        3.23 | 1.53 | [  0.22,  6.24]
school | 91    | (Intercept) |        0.17 | 1.69 | [ -3.15,  3.48]
school | 92    | (Intercept) |        2.38 | 1.77 | [ -1.09,  5.85]
school | 93    | (Intercept) |       -2.06 | 1.39 | [ -4.79,  0.67]
school | 94    | (Intercept) |        1.95 | 1.86 | [ -1.69,  5.60]
school | 95    | (Intercept) |       -0.16 | 1.59 | [ -3.28,  2.96]
school | 96    | (Intercept) |        1.89 | 1.91 | [ -1.85,  5.64]
school | 97    | (Intercept) |        3.37 | 1.59 | [  0.25,  6.49]
school | 98    | (Intercept) |        0.52 | 1.81 | [ -3.03,  4.07]
school | 99    | (Intercept) |       -0.83 | 1.91 | [ -4.57,  2.91]
school | 100   | (Intercept) |        0.84 | 1.62 | [ -2.35,  4.02]
school | 101   | (Intercept) |       -0.27 | 1.62 | [ -3.45,  2.91]
school | 102   | (Intercept) |       -0.13 | 1.73 | [ -3.52,  3.26]
school | 103   | (Intercept) |        6.81 | 1.86 | [  3.17, 10.46]
school | 104   | (Intercept) |        0.25 | 1.91 | [ -3.49,  3.99]
school | 105   | (Intercept) |        1.30 | 1.73 | [ -2.09,  4.69]
school | 106   | (Intercept) |       -4.52 | 1.56 | [ -7.58, -1.46]
school | 107   | (Intercept) |        5.59 | 1.77 | [  2.12,  9.06]
school | 108   | (Intercept) |        0.65 | 1.69 | [ -2.67,  3.96]
school | 109   | (Intercept) |        4.18 | 1.77 | [  0.71,  7.65]
school | 110   | (Intercept) |       -1.58 | 1.77 | [ -5.05,  1.89]
school | 111   | (Intercept) |       -1.24 | 1.69 | [ -4.56,  2.07]
school | 112   | (Intercept) |        1.32 | 1.56 | [ -1.74,  4.39]
school | 113   | (Intercept) |        1.16 | 1.46 | [ -1.70,  4.02]
school | 114   | (Intercept) |       -1.45 | 1.81 | [ -5.00,  2.10]
school | 115   | (Intercept) |        3.08 | 1.91 | [ -0.67,  6.82]
school | 116   | (Intercept) |       -8.63 | 1.62 | [-11.81, -5.45]
school | 117   | (Intercept) |       -2.33 | 1.91 | [ -6.08,  1.41]
school | 118   | (Intercept) |       -0.41 | 1.86 | [ -4.05,  3.24]
school | 119   | (Intercept) |        2.08 | 1.91 | [ -1.67,  5.82]
school | 120   | (Intercept) |        3.86 | 1.69 | [  0.54,  7.17]
school | 121   | (Intercept) |        0.41 | 1.73 | [ -2.98,  3.80]
school | 122   | (Intercept) |       -3.49 | 1.86 | [ -7.13,  0.16]
school | 123   | (Intercept) |        0.45 | 1.66 | [ -2.80,  3.69]
school | 124   | (Intercept) |        1.76 | 1.86 | [ -1.89,  5.40]
school | 125   | (Intercept) |       -1.18 | 1.69 | [ -4.50,  2.13]
school | 126   | (Intercept) |       -0.42 | 1.48 | [ -3.33,  2.48]
school | 127   | (Intercept) |        3.01 | 1.91 | [ -0.73,  6.76]
school | 128   | (Intercept) |        0.52 | 1.62 | [ -2.67,  3.70]
school | 129   | (Intercept) |       -2.47 | 1.66 | [ -5.72,  0.77]
school | 130   | (Intercept) |       -1.52 | 1.73 | [ -4.91,  1.87]
school | 131   | (Intercept) |       -1.05 | 1.73 | [ -4.44,  2.34]
school | 132   | (Intercept) |       -3.33 | 1.81 | [ -6.89,  0.22]
school | 133   | (Intercept) |        4.46 | 1.69 | [  1.14,  7.77]
school | 134   | (Intercept) |        0.28 | 1.69 | [ -3.04,  3.59]
school | 135   | (Intercept) |       -4.72 | 1.59 | [ -7.84, -1.60]
school | 136   | (Intercept) |       -0.57 | 1.81 | [ -4.13,  2.98]
school | 137   | (Intercept) |        0.15 | 1.66 | [ -3.09,  3.40]
school | 138   | (Intercept) |       -0.41 | 1.91 | [ -4.15,  3.33]
school | 139   | (Intercept) |       -1.25 | 1.77 | [ -4.72,  2.21]
school | 140   | (Intercept) |        5.50 | 1.56 | [  2.44,  8.57]
school | 141   | (Intercept) |        1.39 | 1.86 | [ -2.25,  5.04]
school | 142   | (Intercept) |        2.69 | 1.62 | [ -0.49,  5.87]
school | 143   | (Intercept) |        2.25 | 1.81 | [ -1.30,  5.81]
school | 144   | (Intercept) |       -1.23 | 1.77 | [ -4.70,  2.24]
school | 145   | (Intercept) |        0.02 | 1.62 | [ -3.16,  3.20]
school | 146   | (Intercept) |        0.72 | 1.56 | [ -2.34,  3.78]
school | 147   | (Intercept) |        0.22 | 1.62 | [ -2.96,  3.40]
school | 148   | (Intercept) |       -3.65 | 1.77 | [ -7.12, -0.18]
school | 149   | (Intercept) |       -0.31 | 1.66 | [ -3.55,  2.94]
school | 150   | (Intercept) |        3.70 | 1.62 | [  0.52,  6.88]
school | 151   | (Intercept) |       -2.85 | 1.62 | [ -6.03,  0.33]
school | 152   | (Intercept) |        3.35 | 1.73 | [ -0.04,  6.74]
school | 153   | (Intercept) |        6.75 | 1.77 | [  3.29, 10.22]
school | 154   | (Intercept) |       -1.26 | 1.91 | [ -5.00,  2.48]
school | 155   | (Intercept) |       -2.85 | 1.66 | [ -6.10,  0.40]
school | 156   | (Intercept) |        3.87 | 1.81 | [  0.32,  7.42]
school | 157   | (Intercept) |        1.72 | 1.77 | [ -1.75,  5.18]
school | 158   | (Intercept) |        1.53 | 1.66 | [ -1.72,  4.77]
school | 159   | (Intercept) |        0.24 | 1.73 | [ -3.15,  3.63]
school | 160   | (Intercept) |        1.70 | 1.91 | [ -2.04,  5.44]
school | 161   | (Intercept) |       -2.23 | 1.81 | [ -5.79,  1.32]
school | 162   | (Intercept) |       -0.46 | 1.86 | [ -4.10,  3.19]
school | 163   | (Intercept) |       -2.32 | 1.81 | [ -5.87,  1.24]
school | 164   | (Intercept) |        0.13 | 1.66 | [ -3.12,  3.37]
school | 165   | (Intercept) |       -1.52 | 1.91 | [ -5.26,  2.23]
school | 166   | (Intercept) |       -3.31 | 1.91 | [ -7.05,  0.43]
school | 167   | (Intercept) |        0.44 | 1.77 | [ -3.03,  3.91]
school | 168   | (Intercept) |        1.73 | 1.69 | [ -1.59,  5.04]
school | 169   | (Intercept) |       -0.68 | 1.91 | [ -4.42,  3.06]
school | 170   | (Intercept) |        0.32 | 1.86 | [ -3.32,  3.96]
school | 171   | (Intercept) |       -0.77 | 1.24 | [ -3.20,  1.66]
school | 172   | (Intercept) |        0.18 | 1.86 | [ -3.46,  3.83]
school | 173   | (Intercept) |        4.11 | 1.77 | [  0.64,  7.58]
school | 174   | (Intercept) |       -1.61 | 1.91 | [ -5.35,  2.13]
school | 175   | (Intercept) |        1.08 | 1.86 | [ -2.57,  4.72]
school | 176   | (Intercept) |        1.28 | 1.73 | [ -2.11,  4.67]
school | 177   | (Intercept) |       -0.39 | 1.77 | [ -3.86,  3.08]
school | 178   | (Intercept) |        5.36 | 1.96 | [  1.51,  9.21]
school | 179   | (Intercept) |       -2.03 | 1.69 | [ -5.34,  1.29]
school | 180   | (Intercept) |        0.91 | 1.66 | [ -2.33,  4.16]
school | 181   | (Intercept) |        0.63 | 1.59 | [ -2.49,  3.75]
school | 182   | (Intercept) |        3.08 | 1.73 | [ -0.31,  6.47]
school | 183   | (Intercept) |        1.20 | 1.91 | [ -2.54,  4.94]
school | 184   | (Intercept) |       -0.37 | 1.69 | [ -3.68,  2.95]
school | 185   | (Intercept) |       -5.43 | 1.86 | [ -9.08, -1.79]
school | 186   | (Intercept) |       -5.26 | 1.81 | [ -8.81, -1.70]
school | 187   | (Intercept) |       -1.45 | 1.73 | [ -4.83,  1.94]
school | 188   | (Intercept) |        3.19 | 1.86 | [ -0.46,  6.83]
school | 189   | (Intercept) |       -4.00 | 1.46 | [ -6.86, -1.14]
school | 190   | (Intercept) |       -0.92 | 1.81 | [ -4.47,  2.63]
school | 191   | (Intercept) |       -0.99 | 1.81 | [ -4.54,  2.56]
school | 192   | (Intercept) |        3.52 | 1.59 | [  0.40,  6.64]
school | 193   | (Intercept) |       -2.94 | 1.86 | [ -6.58,  0.71]
school | 194   | (Intercept) |        2.77 | 1.91 | [ -0.98,  6.51]
school | 195   | (Intercept) |        0.52 | 1.56 | [ -2.54,  3.59]
school | 196   | (Intercept) |       -1.19 | 1.81 | [ -4.75,  2.36]
school | 197   | (Intercept) |       -8.14 | 1.66 | [-11.39, -4.90]
school | 198   | (Intercept) |       -1.82 | 1.56 | [ -4.88,  1.25]
school | 199   | (Intercept) |       -0.40 | 1.66 | [ -3.65,  2.85]
school | 200   | (Intercept) |       -2.83 | 1.69 | [ -6.14,  0.49]
school | 201   | (Intercept) |        0.79 | 1.81 | [ -2.76,  4.34]
school | 202   | (Intercept) |        2.99 | 1.34 | [  0.38,  5.61]
school | 203   | (Intercept) |       -0.14 | 1.86 | [ -3.78,  3.51]
school | 204   | (Intercept) |        0.57 | 1.73 | [ -2.82,  3.96]
school | 205   | (Intercept) |       -2.53 | 1.46 | [ -5.39,  0.33]
school | 206   | (Intercept) |       -1.75 | 1.77 | [ -5.22,  1.72]
school | 207   | (Intercept) |       -0.31 | 1.77 | [ -3.78,  3.16]
school | 208   | (Intercept) |       -2.96 | 1.56 | [ -6.02,  0.10]
school | 209   | (Intercept) |        2.89 | 1.62 | [ -0.29,  6.07]
school | 210   | (Intercept) |       -3.86 | 1.56 | [ -6.92, -0.80]
school | 211   | (Intercept) |       -1.52 | 1.77 | [ -4.99,  1.95]
school | 212   | (Intercept) |       -3.49 | 1.69 | [ -6.80, -0.17]
school | 213   | (Intercept) |        2.59 | 1.66 | [ -0.66,  5.84]
school | 214   | (Intercept) |       -3.62 | 1.81 | [ -7.17, -0.07]
school | 215   | (Intercept) |        0.65 | 1.69 | [ -2.67,  3.96]
school | 216   | (Intercept) |        1.58 | 1.86 | [ -2.06,  5.23]
school | 217   | (Intercept) |        3.02 | 1.81 | [ -0.53,  6.57]
school | 218   | (Intercept) |       -0.99 | 1.69 | [ -4.31,  2.32]
school | 219   | (Intercept) |       -0.40 | 1.91 | [ -4.14,  3.35]
school | 220   | (Intercept) |       -5.47 | 1.91 | [ -9.22, -1.73]
school | 221   | (Intercept) |        3.20 | 1.81 | [ -0.35,  6.75]
school | 222   | (Intercept) |       -3.32 | 1.59 | [ -6.44, -0.20]
school | 223   | (Intercept) |       -5.76 | 1.77 | [ -9.23, -2.30]
school | 224   | (Intercept) |        1.77 | 1.69 | [ -1.55,  5.08]
school | 225   | (Intercept) |       -3.62 | 1.66 | [ -6.87, -0.37]
school | 226   | (Intercept) |        3.50 | 1.86 | [ -0.14,  7.14]
school | 227   | (Intercept) |       -1.53 | 1.77 | [ -5.00,  1.94]
school | 228   | (Intercept) |        0.03 | 1.81 | [ -3.52,  3.59]
school | 229   | (Intercept) |        2.42 | 1.66 | [ -0.83,  5.66]
school | 230   | (Intercept) |        1.47 | 1.91 | [ -2.27,  5.21]
school | 231   | (Intercept) |       -2.41 | 1.81 | [ -5.96,  1.14]
school | 232   | (Intercept) |       -0.06 | 1.73 | [ -3.45,  3.33]
school | 233   | (Intercept) |        0.69 | 1.91 | [ -3.05,  4.44]
school | 234   | (Intercept) |        1.00 | 1.77 | [ -2.47,  4.47]
school | 235   | (Intercept) |        3.01 | 1.59 | [ -0.11,  6.13]
school | 236   | (Intercept) |       -0.53 | 1.69 | [ -3.85,  2.78]
school | 237   | (Intercept) |       -2.31 | 1.56 | [ -5.37,  0.75]
school | 238   | (Intercept) |        0.55 | 1.91 | [ -3.20,  4.29]
school | 239   | (Intercept) |       -2.83 | 1.48 | [ -5.74,  0.07]
school | 240   | (Intercept) |        3.14 | 1.86 | [ -0.51,  6.78]
school | 241   | (Intercept) |        4.29 | 1.86 | [  0.64,  7.93]
school | 242   | (Intercept) |       -0.79 | 1.77 | [ -4.26,  2.68]
school | 243   | (Intercept) |       -5.13 | 1.91 | [ -8.87, -1.38]
school | 244   | (Intercept) |        1.46 | 1.86 | [ -2.18,  5.10]
school | 245   | (Intercept) |        2.29 | 1.66 | [ -0.96,  5.54]
school | 246   | (Intercept) |       -6.46 | 1.91 | [-10.20, -2.72]
school | 247   | (Intercept) |       -1.39 | 1.53 | [ -4.40,  1.62]
school | 248   | (Intercept) |        1.49 | 1.86 | [ -2.16,  5.13]
school | 249   | (Intercept) |       -3.86 | 1.86 | [ -7.51, -0.22]
school | 250   | (Intercept) |       -3.65 | 1.29 | [ -6.17, -1.13]
school | 251   | (Intercept) |        2.65 | 1.73 | [ -0.73,  6.04]
school | 252   | (Intercept) |        4.39 | 1.69 | [  1.07,  7.71]
school | 253   | (Intercept) |       -1.74 | 1.69 | [ -5.06,  1.57]
school | 254   | (Intercept) |       -2.07 | 1.69 | [ -5.39,  1.24]
school | 255   | (Intercept) |        0.51 | 1.86 | [ -3.13,  4.15]
school | 256   | (Intercept) |        0.90 | 1.91 | [ -2.84,  4.64]
school | 257   | (Intercept) |        5.85 | 1.69 | [  2.54,  9.17]
school | 258   | (Intercept) |        0.85 | 1.81 | [ -2.70,  4.40]
school | 259   | (Intercept) |       -3.99 | 1.81 | [ -7.54, -0.43]
school | 260   | (Intercept) |       -1.45 | 1.86 | [ -5.10,  2.19]
school | 261   | (Intercept) |       -1.28 | 1.81 | [ -4.83,  2.27]
school | 262   | (Intercept) |        3.43 | 1.62 | [  0.25,  6.61]
school | 263   | (Intercept) |       -0.82 | 1.69 | [ -4.14,  2.50]
school | 264   | (Intercept) |       -3.96 | 1.81 | [ -7.51, -0.41]
school | 265   | (Intercept) |       -2.37 | 1.73 | [ -5.76,  1.02]
school | 266   | (Intercept) |       -2.86 | 1.73 | [ -6.25,  0.53]
school | 267   | (Intercept) |        0.67 | 1.91 | [ -3.07,  4.42]
school | 268   | (Intercept) |        2.19 | 1.91 | [ -1.56,  5.93]
school | 269   | (Intercept) |       -2.04 | 1.81 | [ -5.60,  1.51]
school | 270   | (Intercept) |        2.15 | 1.44 | [ -0.66,  4.97]
school | 271   | (Intercept) |        2.22 | 1.69 | [ -1.09,  5.54]
school | 272   | (Intercept) |       -0.91 | 1.91 | [ -4.66,  2.83]
school | 273   | (Intercept) |       -0.19 | 1.91 | [ -3.93,  3.55]
school | 274   | (Intercept) |        3.25 | 1.62 | [  0.07,  6.43]
school | 275   | (Intercept) |        4.65 | 1.66 | [  1.41,  7.90]
school | 276   | (Intercept) |       -1.04 | 1.91 | [ -4.78,  2.70]
school | 277   | (Intercept) |       -0.05 | 1.66 | [ -3.30,  3.19]
school | 278   | (Intercept) |        1.55 | 1.66 | [ -1.70,  4.80]
school | 279   | (Intercept) |        0.60 | 1.62 | [ -2.58,  3.78]
school | 280   | (Intercept) |       -0.02 | 1.44 | [ -2.83,  2.80]
school | 281   | (Intercept) |        5.20 | 1.66 | [  1.95,  8.45]
school | 282   | (Intercept) |        6.02 | 1.27 | [  3.53,  8.51]
school | 283   | (Intercept) |       -1.80 | 1.66 | [ -5.05,  1.45]
school | 284   | (Intercept) |        1.61 | 1.35 | [ -1.04,  4.27]
school | 285   | (Intercept) |       -1.77 | 1.86 | [ -5.42,  1.87]
school | 286   | (Intercept) |       -1.43 | 1.59 | [ -4.55,  1.69]
school | 287   | (Intercept) |       -3.97 | 1.62 | [ -7.15, -0.79]
school | 288   | (Intercept) |        3.80 | 1.69 | [  0.49,  7.12]
school | 289   | (Intercept) |       -0.94 | 1.86 | [ -4.58,  2.70]
school | 290   | (Intercept) |       -2.54 | 1.62 | [ -5.72,  0.64]
school | 291   | (Intercept) |       -1.14 | 1.62 | [ -4.32,  2.04]
school | 292   | (Intercept) |       -1.37 | 1.77 | [ -4.84,  2.10]
school | 293   | (Intercept) |       -1.78 | 1.69 | [ -5.09,  1.54]
school | 294   | (Intercept) |        1.06 | 1.91 | [ -2.68,  4.81]
school | 295   | (Intercept) |       -5.18 | 1.86 | [ -8.83, -1.54]
school | 296   | (Intercept) |        1.65 | 1.77 | [ -1.82,  5.12]
school | 297   | (Intercept) |       -6.58 | 1.86 | [-10.23, -2.94]
school | 298   | (Intercept) |        0.35 | 1.91 | [ -3.39,  4.09]
school | 299   | (Intercept) |        0.83 | 1.81 | [ -2.72,  4.38]
school | 300   | (Intercept) |       -0.52 | 1.44 | [ -3.34,  2.30]
school | 301   | (Intercept) |       -2.67 | 1.86 | [ -6.31,  0.98]
school | 302   | (Intercept) |       -3.14 | 1.86 | [ -6.78,  0.51]
school | 303   | (Intercept) |        4.57 | 1.77 | [  1.11,  8.04]
school | 304   | (Intercept) |        2.28 | 1.86 | [ -1.36,  5.93]
school | 305   | (Intercept) |       -1.74 | 1.86 | [ -5.39,  1.90]
school | 306   | (Intercept) |       -2.64 | 1.62 | [ -5.82,  0.55]
school | 307   | (Intercept) |        2.15 | 1.73 | [ -1.24,  5.54]
school | 308   | (Intercept) |        1.50 | 1.86 | [ -2.15,  5.14]
school | 309   | (Intercept) |        1.00 | 1.69 | [ -2.31,  4.32]
school | 310   | (Intercept) |       -1.54 | 1.86 | [ -5.19,  2.10]
school | 311   | (Intercept) |        4.22 | 1.66 | [  0.97,  7.46]
school | 312   | (Intercept) |       -0.75 | 1.91 | [ -4.49,  2.99]
school | 313   | (Intercept) |       -3.42 | 1.81 | [ -6.98,  0.13]
school | 314   | (Intercept) |        0.08 | 1.66 | [ -3.17,  3.33]
school | 315   | (Intercept) |        0.60 | 1.86 | [ -3.04,  4.24]
school | 316   | (Intercept) |       -3.91 | 1.73 | [ -7.30, -0.52]
school | 317   | (Intercept) |        0.67 | 1.81 | [ -2.89,  4.22]
school | 318   | (Intercept) |       -0.25 | 1.91 | [ -3.99,  3.49]
school | 319   | (Intercept) |       -0.59 | 1.86 | [ -4.23,  3.05]
school | 320   | (Intercept) |        1.75 | 1.91 | [ -1.99,  5.49]
school | 321   | (Intercept) |        0.97 | 1.37 | [ -1.72,  3.67]
school | 322   | (Intercept) |       -0.54 | 1.59 | [ -3.66,  2.58]
school | 323   | (Intercept) |        1.14 | 1.86 | [ -2.50,  4.79]
school | 324   | (Intercept) |        1.40 | 1.59 | [ -1.72,  4.53]
school | 325   | (Intercept) |        3.10 | 1.62 | [ -0.08,  6.28]
school | 326   | (Intercept) |       -0.52 | 1.69 | [ -3.84,  2.80]
school | 327   | (Intercept) |        3.12 | 1.86 | [ -0.53,  6.76]
school | 328   | (Intercept) |        3.95 | 1.62 | [  0.77,  7.13]
school | 329   | (Intercept) |        3.75 | 1.81 | [  0.19,  7.30]
school | 330   | (Intercept) |       -3.57 | 1.69 | [ -6.89, -0.26]
school | 331   | (Intercept) |        0.30 | 1.81 | [ -3.25,  3.85]
school | 332   | (Intercept) |        0.09 | 1.73 | [ -3.30,  3.48]
school | 333   | (Intercept) |        2.53 | 1.46 | [ -0.33,  5.39]
school | 334   | (Intercept) |        2.40 | 1.91 | [ -1.34,  6.14]
school | 335   | (Intercept) |        4.35 | 1.73 | [  0.96,  7.74]
school | 336   | (Intercept) |       -0.47 | 1.56 | [ -3.53,  2.59]
school | 337   | (Intercept) |       -0.21 | 1.59 | [ -3.33,  2.91]
school | 338   | (Intercept) |       -1.31 | 1.81 | [ -4.87,  2.24]
school | 339   | (Intercept) |       -4.64 | 1.69 | [ -7.96, -1.32]
school | 340   | (Intercept) |       -4.21 | 1.86 | [ -7.85, -0.56]
school | 341   | (Intercept) |        2.25 | 1.62 | [ -0.93,  5.44]
school | 342   | (Intercept) |       -2.64 | 1.81 | [ -6.19,  0.92]
school | 343   | (Intercept) |        2.39 | 1.77 | [ -1.07,  5.86]
school | 344   | (Intercept) |       -0.52 | 1.69 | [ -3.84,  2.79]
school | 345   | (Intercept) |        0.39 | 1.69 | [ -2.93,  3.70]
school | 346   | (Intercept) |        1.04 | 1.69 | [ -2.28,  4.35]
school | 347   | (Intercept) |        0.01 | 1.86 | [ -3.63,  3.65]
school | 348   | (Intercept) |        4.39 | 1.77 | [  0.93,  7.86]
school | 349   | (Intercept) |        0.21 | 1.91 | [ -3.53,  3.96]
school | 350   | (Intercept) |        0.86 | 1.69 | [ -2.46,  4.17]
school | 351   | (Intercept) |        1.26 | 1.73 | [ -2.13,  4.65]
school | 352   | (Intercept) |        3.31 | 1.91 | [ -0.43,  7.06]
school | 353   | (Intercept) |        1.45 | 1.81 | [ -2.10,  5.00]
school | 354   | (Intercept) |        3.12 | 1.41 | [  0.35,  5.89]
school | 355   | (Intercept) |       -0.19 | 1.48 | [ -3.09,  2.72]
school | 356   | (Intercept) |        1.61 | 1.81 | [ -1.95,  5.16]
school | 357   | (Intercept) |        0.32 | 1.62 | [ -2.86,  3.50]
school | 358   | (Intercept) |       -0.22 | 1.91 | [ -3.97,  3.52]
school | 359   | (Intercept) |       -0.05 | 1.86 | [ -3.69,  3.59]
school | 360   | (Intercept) |       -2.74 | 1.73 | [ -6.13,  0.65]
school | 361   | (Intercept) |       -1.43 | 1.69 | [ -4.75,  1.88]
school | 362   | (Intercept) |       -6.18 | 1.66 | [ -9.42, -2.93]
school | 363   | (Intercept) |       -4.28 | 1.91 | [ -8.02, -0.54]
school | 364   | (Intercept) |       -2.87 | 1.91 | [ -6.61,  0.88]
school | 365   | (Intercept) |        2.84 | 1.91 | [ -0.90,  6.58]
school | 366   | (Intercept) |        2.27 | 1.59 | [ -0.85,  5.39]
school | 367   | (Intercept) |        1.84 | 1.59 | [ -1.28,  4.96]
school | 368   | (Intercept) |        4.61 | 1.77 | [  1.14,  8.08]
school | 369   | (Intercept) |        4.56 | 1.86 | [  0.92,  8.20]
school | 370   | (Intercept) |       -2.08 | 1.69 | [ -5.39,  1.24]
school | 371   | (Intercept) |       -3.84 | 1.77 | [ -7.31, -0.38]
school | 372   | (Intercept) |       -0.92 | 1.81 | [ -4.47,  2.64]
school | 373   | (Intercept) |        1.09 | 1.62 | [ -2.09,  4.27]
school | 374   | (Intercept) |        1.25 | 1.66 | [ -1.99,  4.50]
school | 375   | (Intercept) |       -3.11 | 1.81 | [ -6.66,  0.44]
school | 376   | (Intercept) |        1.17 | 1.81 | [ -2.38,  4.73]
school | 377   | (Intercept) |       -2.38 | 1.56 | [ -5.44,  0.69]
school | 378   | (Intercept) |       -1.93 | 1.91 | [ -5.67,  1.81]
school | 379   | (Intercept) |        0.36 | 1.77 | [ -3.11,  3.83]
school | 380   | (Intercept) |        0.68 | 1.59 | [ -2.44,  3.80]
school | 381   | (Intercept) |        2.74 | 1.62 | [ -0.44,  5.92]
school | 382   | (Intercept) |       -3.81 | 1.53 | [ -6.82, -0.80]
school | 383   | (Intercept) |       -5.82 | 1.91 | [ -9.56, -2.07]
school | 384   | (Intercept) |        0.12 | 1.73 | [ -3.27,  3.51]
school | 385   | (Intercept) |       -3.39 | 1.69 | [ -6.71, -0.07]
school | 386   | (Intercept) |        1.07 | 1.69 | [ -2.25,  4.38]
school | 387   | (Intercept) |       -3.95 | 1.73 | [ -7.34, -0.56]
school | 388   | (Intercept) |        0.71 | 1.62 | [ -2.47,  3.89]
school | 389   | (Intercept) |       -0.48 | 1.81 | [ -4.04,  3.07]
school | 390   | (Intercept) |        4.39 | 1.77 | [  0.92,  7.86]
school | 391   | (Intercept) |       -1.94 | 1.59 | [ -5.06,  1.18]
school | 392   | (Intercept) |        2.46 | 1.73 | [ -0.93,  5.85]
school | 393   | (Intercept) |       -1.32 | 1.69 | [ -4.63,  2.00]
school | 394   | (Intercept) |       -3.19 | 1.77 | [ -6.66,  0.28]
school | 395   | (Intercept) |        3.17 | 1.81 | [ -0.38,  6.72]
school | 396   | (Intercept) |       -1.89 | 1.59 | [ -5.01,  1.23]
school | 397   | (Intercept) |        0.60 | 1.91 | [ -3.15,  4.34]
school | 398   | (Intercept) |        1.48 | 1.77 | [ -1.99,  4.95]
school | 399   | (Intercept) |       -3.60 | 1.91 | [ -7.34,  0.15]
school | 400   | (Intercept) |       -0.57 | 1.59 | [ -3.69,  2.55]
school | 401   | (Intercept) |        0.89 | 1.77 | [ -2.58,  4.36]
school | 402   | (Intercept) |       -3.18 | 1.86 | [ -6.83,  0.46]
school | 403   | (Intercept) |        2.53 | 1.81 | [ -1.02,  6.08]
school | 404   | (Intercept) |        1.43 | 1.81 | [ -2.12,  4.98]
school | 405   | (Intercept) |       -0.07 | 1.86 | [ -3.71,  3.57]
school | 406   | (Intercept) |        0.26 | 1.62 | [ -2.92,  3.44]
school | 407   | (Intercept) |       -0.74 | 1.86 | [ -4.39,  2.90]
school | 408   | (Intercept) |       -2.13 | 1.86 | [ -5.77,  1.51]
school | 409   | (Intercept) |       -5.85 | 1.77 | [ -9.32, -2.39]
school | 410   | (Intercept) |       -0.96 | 1.77 | [ -4.43,  2.51]
school | 411   | (Intercept) |        1.62 | 1.56 | [ -1.45,  4.68]
school | 412   | (Intercept) |        0.47 | 1.66 | [ -2.78,  3.72]
school | 413   | (Intercept) |        1.51 | 1.62 | [ -1.67,  4.69]
school | 414   | (Intercept) |       -0.44 | 1.73 | [ -3.83,  2.95]
school | 415   | (Intercept) |        3.67 | 1.37 | [  0.97,  6.36]
school | 416   | (Intercept) |        0.97 | 1.81 | [ -2.59,  4.52]
school | 417   | (Intercept) |       -6.29 | 1.81 | [ -9.84, -2.73]
school | 418   | (Intercept) |       -0.93 | 1.48 | [ -3.84,  1.97]
school | 419   | (Intercept) |       -2.42 | 1.56 | [ -5.48,  0.64]

Deriving Cluster Intercepts

What is each cluster’s intercept (best linear unbiased prediction)?

In other words, derive predictions of \(\beta_{0j}\) for every cluster \(j\)

estimate_grouplevel(fit_null, type = "total")
Group  | Level | Parameter   | Coefficient
------------------------------------------
school | 1     | (Intercept) |       58.54
school | 2     | (Intercept) |       61.70
school | 3     | (Intercept) |       50.18
school | 4     | (Intercept) |       63.52
school | 5     | (Intercept) |       50.68
school | 6     | (Intercept) |       60.09
school | 7     | (Intercept) |       57.46
school | 8     | (Intercept) |       60.73
school | 9     | (Intercept) |       55.59
school | 10    | (Intercept) |       60.65
school | 11    | (Intercept) |       56.73
school | 12    | (Intercept) |       55.92
school | 13    | (Intercept) |       58.29
school | 14    | (Intercept) |       57.83
school | 15    | (Intercept) |       62.13
school | 16    | (Intercept) |       56.09
school | 17    | (Intercept) |       55.21
school | 18    | (Intercept) |       60.83
school | 19    | (Intercept) |       57.74
school | 20    | (Intercept) |       58.78
school | 21    | (Intercept) |       59.30
school | 22    | (Intercept) |       56.27
school | 23    | (Intercept) |       59.32
school | 24    | (Intercept) |       58.05
school | 25    | (Intercept) |       55.96
school | 26    | (Intercept) |       60.23
school | 27    | (Intercept) |       54.60
school | 28    | (Intercept) |       62.87
school | 29    | (Intercept) |       59.30
school | 30    | (Intercept) |       55.99
school | 31    | (Intercept) |       56.31
school | 32    | (Intercept) |       61.45
school | 33    | (Intercept) |       53.34
school | 34    | (Intercept) |       57.22
school | 35    | (Intercept) |       60.02
school | 36    | (Intercept) |       53.78
school | 37    | (Intercept) |       60.39
school | 38    | (Intercept) |       55.98
school | 39    | (Intercept) |       57.52
school | 40    | (Intercept) |       53.84
school | 41    | (Intercept) |       59.47
school | 42    | (Intercept) |       57.75
school | 43    | (Intercept) |       58.57
school | 44    | (Intercept) |       60.79
school | 45    | (Intercept) |       59.73
school | 46    | (Intercept) |       57.14
school | 47    | (Intercept) |       53.46
school | 48    | (Intercept) |       57.29
school | 49    | (Intercept) |       57.52
school | 50    | (Intercept) |       53.63
school | 51    | (Intercept) |       59.60
school | 52    | (Intercept) |       60.71
school | 53    | (Intercept) |       59.59
school | 54    | (Intercept) |       62.60
school | 55    | (Intercept) |       50.25
school | 56    | (Intercept) |       56.63
school | 57    | (Intercept) |       58.19
school | 58    | (Intercept) |       58.16
school | 59    | (Intercept) |       58.69
school | 60    | (Intercept) |       54.13
school | 61    | (Intercept) |       59.24
school | 62    | (Intercept) |       49.12
school | 63    | (Intercept) |       58.91
school | 64    | (Intercept) |       58.52
school | 65    | (Intercept) |       61.48
school | 66    | (Intercept) |       56.26
school | 67    | (Intercept) |       59.54
school | 68    | (Intercept) |       57.39
school | 69    | (Intercept) |       53.81
school | 70    | (Intercept) |       62.32
school | 71    | (Intercept) |       55.66
school | 72    | (Intercept) |       52.12
school | 73    | (Intercept) |       57.32
school | 74    | (Intercept) |       62.84
school | 75    | (Intercept) |       57.77
school | 76    | (Intercept) |       57.81
school | 77    | (Intercept) |       62.23
school | 78    | (Intercept) |       56.25
school | 79    | (Intercept) |       54.98
school | 80    | (Intercept) |       62.01
school | 81    | (Intercept) |       55.02
school | 82    | (Intercept) |       59.02
school | 83    | (Intercept) |       60.23
school | 84    | (Intercept) |       60.88
school | 85    | (Intercept) |       58.27
school | 86    | (Intercept) |       56.25
school | 87    | (Intercept) |       59.59
school | 88    | (Intercept) |       59.25
school | 89    | (Intercept) |       57.93
school | 90    | (Intercept) |       60.91
school | 91    | (Intercept) |       57.84
school | 92    | (Intercept) |       60.06
school | 93    | (Intercept) |       55.61
school | 94    | (Intercept) |       59.63
school | 95    | (Intercept) |       57.51
school | 96    | (Intercept) |       59.57
school | 97    | (Intercept) |       61.05
school | 98    | (Intercept) |       58.20
school | 99    | (Intercept) |       56.84
school | 100   | (Intercept) |       58.51
school | 101   | (Intercept) |       57.41
school | 102   | (Intercept) |       57.55
school | 103   | (Intercept) |       64.49
school | 104   | (Intercept) |       57.92
school | 105   | (Intercept) |       58.97
school | 106   | (Intercept) |       53.15
school | 107   | (Intercept) |       63.27
school | 108   | (Intercept) |       58.32
school | 109   | (Intercept) |       61.86
school | 110   | (Intercept) |       56.10
school | 111   | (Intercept) |       56.43
school | 112   | (Intercept) |       59.00
school | 113   | (Intercept) |       58.84
school | 114   | (Intercept) |       56.23
school | 115   | (Intercept) |       60.75
school | 116   | (Intercept) |       49.05
school | 117   | (Intercept) |       55.34
school | 118   | (Intercept) |       57.27
school | 119   | (Intercept) |       59.75
school | 120   | (Intercept) |       61.53
school | 121   | (Intercept) |       58.09
school | 122   | (Intercept) |       54.19
school | 123   | (Intercept) |       58.12
school | 124   | (Intercept) |       59.43
school | 125   | (Intercept) |       56.49
school | 126   | (Intercept) |       57.25
school | 127   | (Intercept) |       60.69
school | 128   | (Intercept) |       58.19
school | 129   | (Intercept) |       55.20
school | 130   | (Intercept) |       56.16
school | 131   | (Intercept) |       56.62
school | 132   | (Intercept) |       54.34
school | 133   | (Intercept) |       62.13
school | 134   | (Intercept) |       57.95
school | 135   | (Intercept) |       52.95
school | 136   | (Intercept) |       57.10
school | 137   | (Intercept) |       57.83
school | 138   | (Intercept) |       57.27
school | 139   | (Intercept) |       56.42
school | 140   | (Intercept) |       63.18
school | 141   | (Intercept) |       59.07
school | 142   | (Intercept) |       60.37
school | 143   | (Intercept) |       59.93
school | 144   | (Intercept) |       56.44
school | 145   | (Intercept) |       57.69
school | 146   | (Intercept) |       58.40
school | 147   | (Intercept) |       57.89
school | 148   | (Intercept) |       54.03
school | 149   | (Intercept) |       57.37
school | 150   | (Intercept) |       61.37
school | 151   | (Intercept) |       54.83
school | 152   | (Intercept) |       61.03
school | 153   | (Intercept) |       64.43
school | 154   | (Intercept) |       56.42
school | 155   | (Intercept) |       54.83
school | 156   | (Intercept) |       61.54
school | 157   | (Intercept) |       59.39
school | 158   | (Intercept) |       59.20
school | 159   | (Intercept) |       57.91
school | 160   | (Intercept) |       59.37
school | 161   | (Intercept) |       55.44
school | 162   | (Intercept) |       57.22
school | 163   | (Intercept) |       55.36
school | 164   | (Intercept) |       57.80
school | 165   | (Intercept) |       56.16
school | 166   | (Intercept) |       54.37
school | 167   | (Intercept) |       58.12
school | 168   | (Intercept) |       59.40
school | 169   | (Intercept) |       57.00
school | 170   | (Intercept) |       57.99
school | 171   | (Intercept) |       56.90
school | 172   | (Intercept) |       57.86
school | 173   | (Intercept) |       61.79
school | 174   | (Intercept) |       56.06
school | 175   | (Intercept) |       58.75
school | 176   | (Intercept) |       58.96
school | 177   | (Intercept) |       57.28
school | 178   | (Intercept) |       63.03
school | 179   | (Intercept) |       55.65
school | 180   | (Intercept) |       58.59
school | 181   | (Intercept) |       58.31
school | 182   | (Intercept) |       60.75
school | 183   | (Intercept) |       58.87
school | 184   | (Intercept) |       57.31
school | 185   | (Intercept) |       52.24
school | 186   | (Intercept) |       52.42
school | 187   | (Intercept) |       56.23
school | 188   | (Intercept) |       60.86
school | 189   | (Intercept) |       53.67
school | 190   | (Intercept) |       56.75
school | 191   | (Intercept) |       56.68
school | 192   | (Intercept) |       61.19
school | 193   | (Intercept) |       54.74
school | 194   | (Intercept) |       60.44
school | 195   | (Intercept) |       58.20
school | 196   | (Intercept) |       56.48
school | 197   | (Intercept) |       49.53
school | 198   | (Intercept) |       55.86
school | 199   | (Intercept) |       57.27
school | 200   | (Intercept) |       54.85
school | 201   | (Intercept) |       58.46
school | 202   | (Intercept) |       60.67
school | 203   | (Intercept) |       57.54
school | 204   | (Intercept) |       58.24
school | 205   | (Intercept) |       55.14
school | 206   | (Intercept) |       55.93
school | 207   | (Intercept) |       57.37
school | 208   | (Intercept) |       54.72
school | 209   | (Intercept) |       60.56
school | 210   | (Intercept) |       53.81
school | 211   | (Intercept) |       56.15
school | 212   | (Intercept) |       54.19
school | 213   | (Intercept) |       60.26
school | 214   | (Intercept) |       54.06
school | 215   | (Intercept) |       58.32
school | 216   | (Intercept) |       59.26
school | 217   | (Intercept) |       60.69
school | 218   | (Intercept) |       56.68
school | 219   | (Intercept) |       57.28
school | 220   | (Intercept) |       52.20
school | 221   | (Intercept) |       60.87
school | 222   | (Intercept) |       54.35
school | 223   | (Intercept) |       51.91
school | 224   | (Intercept) |       59.44
school | 225   | (Intercept) |       54.05
school | 226   | (Intercept) |       61.17
school | 227   | (Intercept) |       56.14
school | 228   | (Intercept) |       57.71
school | 229   | (Intercept) |       60.09
school | 230   | (Intercept) |       59.15
school | 231   | (Intercept) |       55.27
school | 232   | (Intercept) |       57.62
school | 233   | (Intercept) |       58.37
school | 234   | (Intercept) |       58.67
school | 235   | (Intercept) |       60.68
school | 236   | (Intercept) |       57.14
school | 237   | (Intercept) |       55.36
school | 238   | (Intercept) |       58.22
school | 239   | (Intercept) |       54.84
school | 240   | (Intercept) |       60.81
school | 241   | (Intercept) |       61.96
school | 242   | (Intercept) |       56.89
school | 243   | (Intercept) |       52.55
school | 244   | (Intercept) |       59.13
school | 245   | (Intercept) |       59.96
school | 246   | (Intercept) |       51.21
school | 247   | (Intercept) |       56.28
school | 248   | (Intercept) |       59.16
school | 249   | (Intercept) |       53.81
school | 250   | (Intercept) |       54.02
school | 251   | (Intercept) |       60.33
school | 252   | (Intercept) |       62.06
school | 253   | (Intercept) |       55.93
school | 254   | (Intercept) |       55.60
school | 255   | (Intercept) |       58.19
school | 256   | (Intercept) |       58.57
school | 257   | (Intercept) |       63.53
school | 258   | (Intercept) |       58.52
school | 259   | (Intercept) |       53.69
school | 260   | (Intercept) |       56.22
school | 261   | (Intercept) |       56.40
school | 262   | (Intercept) |       61.11
school | 263   | (Intercept) |       56.85
school | 264   | (Intercept) |       53.71
school | 265   | (Intercept) |       55.30
school | 266   | (Intercept) |       54.81
school | 267   | (Intercept) |       58.35
school | 268   | (Intercept) |       59.86
school | 269   | (Intercept) |       55.63
school | 270   | (Intercept) |       59.83
school | 271   | (Intercept) |       59.90
school | 272   | (Intercept) |       56.76
school | 273   | (Intercept) |       57.49
school | 274   | (Intercept) |       60.93
school | 275   | (Intercept) |       62.33
school | 276   | (Intercept) |       56.64
school | 277   | (Intercept) |       57.62
school | 278   | (Intercept) |       59.22
school | 279   | (Intercept) |       58.27
school | 280   | (Intercept) |       57.66
school | 281   | (Intercept) |       62.88
school | 282   | (Intercept) |       63.69
school | 283   | (Intercept) |       55.87
school | 284   | (Intercept) |       59.29
school | 285   | (Intercept) |       55.90
school | 286   | (Intercept) |       56.24
school | 287   | (Intercept) |       53.70
school | 288   | (Intercept) |       61.48
school | 289   | (Intercept) |       56.73
school | 290   | (Intercept) |       55.13
school | 291   | (Intercept) |       56.53
school | 292   | (Intercept) |       56.30
school | 293   | (Intercept) |       55.90
school | 294   | (Intercept) |       58.74
school | 295   | (Intercept) |       52.49
school | 296   | (Intercept) |       59.32
school | 297   | (Intercept) |       51.09
school | 298   | (Intercept) |       58.03
school | 299   | (Intercept) |       58.50
school | 300   | (Intercept) |       57.15
school | 301   | (Intercept) |       55.01
school | 302   | (Intercept) |       54.54
school | 303   | (Intercept) |       62.25
school | 304   | (Intercept) |       59.96
school | 305   | (Intercept) |       55.93
school | 306   | (Intercept) |       55.04
school | 307   | (Intercept) |       59.82
school | 308   | (Intercept) |       59.17
school | 309   | (Intercept) |       58.68
school | 310   | (Intercept) |       56.13
school | 311   | (Intercept) |       61.89
school | 312   | (Intercept) |       56.92
school | 313   | (Intercept) |       54.25
school | 314   | (Intercept) |       57.75
school | 315   | (Intercept) |       58.27
school | 316   | (Intercept) |       53.77
school | 317   | (Intercept) |       58.34
school | 318   | (Intercept) |       57.42
school | 319   | (Intercept) |       57.08
school | 320   | (Intercept) |       59.43
school | 321   | (Intercept) |       58.65
school | 322   | (Intercept) |       57.14
school | 323   | (Intercept) |       58.82
school | 324   | (Intercept) |       59.08
school | 325   | (Intercept) |       60.77
school | 326   | (Intercept) |       57.15
school | 327   | (Intercept) |       60.79
school | 328   | (Intercept) |       61.63
school | 329   | (Intercept) |       61.42
school | 330   | (Intercept) |       54.10
school | 331   | (Intercept) |       57.98
school | 332   | (Intercept) |       57.76
school | 333   | (Intercept) |       60.20
school | 334   | (Intercept) |       60.08
school | 335   | (Intercept) |       62.02
school | 336   | (Intercept) |       57.20
school | 337   | (Intercept) |       57.46
school | 338   | (Intercept) |       56.36
school | 339   | (Intercept) |       53.03
school | 340   | (Intercept) |       53.47
school | 341   | (Intercept) |       59.93
school | 342   | (Intercept) |       55.04
school | 343   | (Intercept) |       60.07
school | 344   | (Intercept) |       57.15
school | 345   | (Intercept) |       58.06
school | 346   | (Intercept) |       58.71
school | 347   | (Intercept) |       57.69
school | 348   | (Intercept) |       62.07
school | 349   | (Intercept) |       57.89
school | 350   | (Intercept) |       58.53
school | 351   | (Intercept) |       58.94
school | 352   | (Intercept) |       60.99
school | 353   | (Intercept) |       59.12
school | 354   | (Intercept) |       60.80
school | 355   | (Intercept) |       57.49
school | 356   | (Intercept) |       59.28
school | 357   | (Intercept) |       57.99
school | 358   | (Intercept) |       57.45
school | 359   | (Intercept) |       57.62
school | 360   | (Intercept) |       54.93
school | 361   | (Intercept) |       56.24
school | 362   | (Intercept) |       51.50
school | 363   | (Intercept) |       53.40
school | 364   | (Intercept) |       54.81
school | 365   | (Intercept) |       60.51
school | 366   | (Intercept) |       59.95
school | 367   | (Intercept) |       59.51
school | 368   | (Intercept) |       62.28
school | 369   | (Intercept) |       62.23
school | 370   | (Intercept) |       55.60
school | 371   | (Intercept) |       53.83
school | 372   | (Intercept) |       56.76
school | 373   | (Intercept) |       58.77
school | 374   | (Intercept) |       58.93
school | 375   | (Intercept) |       54.56
school | 376   | (Intercept) |       58.85
school | 377   | (Intercept) |       55.30
school | 378   | (Intercept) |       55.75
school | 379   | (Intercept) |       58.04
school | 380   | (Intercept) |       58.36
school | 381   | (Intercept) |       60.41
school | 382   | (Intercept) |       53.86
school | 383   | (Intercept) |       51.86
school | 384   | (Intercept) |       57.79
school | 385   | (Intercept) |       54.28
school | 386   | (Intercept) |       58.74
school | 387   | (Intercept) |       53.72
school | 388   | (Intercept) |       58.38
school | 389   | (Intercept) |       57.19
school | 390   | (Intercept) |       62.06
school | 391   | (Intercept) |       55.74
school | 392   | (Intercept) |       60.14
school | 393   | (Intercept) |       56.36
school | 394   | (Intercept) |       54.48
school | 395   | (Intercept) |       60.85
school | 396   | (Intercept) |       55.79
school | 397   | (Intercept) |       58.27
school | 398   | (Intercept) |       59.15
school | 399   | (Intercept) |       54.08
school | 400   | (Intercept) |       57.11
school | 401   | (Intercept) |       58.56
school | 402   | (Intercept) |       54.49
school | 403   | (Intercept) |       60.20
school | 404   | (Intercept) |       59.11
school | 405   | (Intercept) |       57.60
school | 406   | (Intercept) |       57.93
school | 407   | (Intercept) |       56.93
school | 408   | (Intercept) |       55.54
school | 409   | (Intercept) |       51.82
school | 410   | (Intercept) |       56.71
school | 411   | (Intercept) |       59.29
school | 412   | (Intercept) |       58.14
school | 413   | (Intercept) |       59.19
school | 414   | (Intercept) |       57.24
school | 415   | (Intercept) |       61.34
school | 416   | (Intercept) |       58.64
school | 417   | (Intercept) |       51.39
school | 418   | (Intercept) |       56.74
school | 419   | (Intercept) |       55.26

Visualizing the Distribution

Sample-based intercept distribution (blue)
Population-level intercept estimate (red)