Meetup 12: Hierarchical Clustering

George I. Hagstrom

Week Summary

• Entering home stretch
  • This week finish clustering
  • Talk about making plots interactive
• Finish with Shiny Apps

Reading

1. Wikipedia article on Hierarchical Clustering
2. ggdendro introduction and reference
3. tidy_heatmaps documentation
4. Bioinformatics Training and Education Program Tutorial on Hierarchical Clustering
5. For Python: Seaborn Clustermap
6. For Python: Scipy Clusters

Tree of Life

• Lots of data has a hierarchical structure

Jonathan Eisen

Statistics of US States

US_state_stats |> head(n=15)

# A tibble: 15 × 20
   state       homeownership multiunit income med_income poverty fed_spend smoke
   <chr>               <dbl>     <dbl>  <dbl>      <dbl>   <dbl>     <dbl> <dbl>
 1 Alabama              71.1      15.5  22984      42081    17.1     11.7   24.8
 2 Alaska               64.7      24.6  30726      66521     9.5     16.8   25  
 3 Arizona              67.4      20.7  25680      50448    15.3      9.85  20.4
 4 Arkansas             67.7      15.2  21274      39267    18        9.61  23.5
 5 California           57.4      30.7  29188      60883    13.7      8.89  15.2
 6 Colorado             67.6      25.6  30151      56456    12.2      9.15  19.9
 7 Connecticut          69.2      34.6  36775      67740     9.2     14.8   16.5
 8 Delaware             73.6      17.7  29007      57599    11        8.89  20.7
 9 Florida              69.7      30    26551      47661    13.8      9.62  21.6
10 Georgia              67.2      20.5  25134      49347    15.7      8.88  22.2
11 Hawaii               59.3      39.2  28882      66420     9.6     14.0   17.1
12 Idaho                71        14.9  22518      46423    13.6      8.82  17.9
13 Illinois             69.2      33    28782      55735    12.6      8.52  19.9
14 Indiana              71.5      18.6  24058      47697    13.5      9.45  27.3
15 Iowa                 73.2      18.6  25335      48872    11.6      9.50  20.4
# ℹ 12 more variables: murder <dbl>, robbery <dbl>, agg_assault <dbl>,
#   larceny <dbl>, motor_theft <dbl>, soc_sec <dbl>, nuclear <dbl>, coal <dbl>,
#   tr_deaths <dbl>, tr_deaths_no_alc <dbl>, unempl <dbl>, popdens2010 <dbl>

Could Cluster Them

Different Levels and Meaning

Hierarchical Clustering is Bottom-Up

Dendrogram Clusters

Dendrogram Cuts

Dendrogram Cuts

Dendrogram Cuts

Why Hierarchical Clustering?

• You care about fine details
  • Can find clusters of small numbers of points
  • Biological Species
• You want to explore multiple different clustering scales
• You want robustness to outliers

How does it work?

• Needs two basic ingredients:
  1. Distance function between the points
  2. Rule for applying the distance to clusters

Agglomerative Clustering

• Begin with points

Agglomerative Clustering

• Begin with points
• Distance Matrix

Agglomerative Clustering

• Begin with points
• Distance Matrix
• Group Closest

Agglomerative Clustering

• Begin with points
• Distance Matrix
• Group Closest
• Recalculate Distances

Agglomerative Clustering

• Begin with points
• Distance Matrix
• Group Closest
• Recalculate Distances
• Rinse and Repeat

Agglomerative Clustering

• Begin with points
• Distance Matrix
• Group Closest
• Recalculate Distances
• Rinse and Repeat

Agglomerative Clustering

• Begin with points
• Distance Matrix
• Group Closest
• Recalculate Distances
• Rinse and Repeat

Agglomerative Clustering

• Begin with points
• Distance Matrix
• Group Closest
• Recalculate Distances
• Rinse and Repeat

Agglomerative Clustering

• Begin with points
• Distance Matrix
• Group Closest
• Recalculate Distances
• Rinse and Repeat

Agglomerative Clustering

• Begin with points
• Distance Matrix
• Group Closest
• Recalculate Distances
• Rinse and Repeat
• Form Dendrogram

Distance Metrics

• Euclidean Distance (Most Common)
• Correlation Distance (Common in Bio)
• Manhattan, Maximum (Other Metrics)
• Categorical Metrics:
  • Gower’s (Mixed categorical and numerical)
  • Jaccard, Hamming, many more

Linkage Methods

• How to determine the distance between clusters?
• Many on wikipedia
  • Max or Min distance between points
  • UPGMA (unweighted average distance between pairs)
  • Ward’s Linkage (minimize increase in within cluster variance)

Implementing Hierarchical Clustering

• Demonstrate it on a Kaggle Customer Segmentation Dataset

mall_customers = read_csv("Mall_Customers.csv")
mall_customers

# A tibble: 200 × 5
   CustomerID Gender   Age `Annual Income (k$)` `Spending Score (1-100)`
        <dbl> <chr>  <dbl>                <dbl>                    <dbl>
 1          1 Male      19                   15                       39
 2          2 Male      21                   15                       81
 3          3 Female    20                   16                        6
 4          4 Female    23                   16                       77
 5          5 Female    31                   17                       40
 6          6 Female    22                   17                       76
 7          7 Female    35                   18                        6
 8          8 Female    23                   18                       94
 9          9 Male      64                   19                        3
10         10 Female    30                   19                       72
# ℹ 190 more rows

Calculate Distance Matrix

• Ignore Categorical

mall_customers |> 
  select(-Gender) |> 
  column_to_rownames(var = "CustomerID")  |> 
  scale()  |> 
  dist(method = "euclidean")

             1          2          3          4          5          6
2   1.63271382                                                       
3   1.28047443 2.90546048                                            
4   1.49961180 0.21434013 2.75780621                                 
5   0.86328190 1.74328990 1.53461759 1.54348731                      
6   1.45080775 0.22002872 2.71475242 0.08985491 1.53575852           
7   1.71988710 3.07451056 1.07650230 2.88151502 1.34794551 2.86626187
8   2.15203749 0.53569963 3.41535546 0.66270395 2.16845573 0.70173898
9   3.51342790 4.31534552 3.15404067 4.10357961 2.76396907 4.12759374
10  1.50874907 0.74817170 2.65662924 0.54922364 1.24357994 0.59814119
11  3.57319907 4.19507763 3.38075346 3.98576234 2.76787491 4.01842070
12  2.59491799 1.23024367 3.75978131 1.21523657 2.30387170 1.29040710
13  2.94867334 3.68566467 2.74676800 3.47351925 2.16476168 3.49779854
14  1.52635147 0.32612286 2.76849453 0.16828143 1.52219560 0.18720306
15  1.64631705 2.87788357 1.25607051 2.67766834 1.13610226 2.66794498
16  1.57533732 0.21763166 2.83459767 0.18524835 1.64590579 0.16291958
17  1.17817834 2.05663212 1.56538952 1.84917650 0.37772830 1.84663472
18  1.07261523 0.62826436 2.33124888 0.51362614 1.28724435 0.44005745
19  2.41320073 3.01205521 2.47224727 2.79927427 1.57912330 2.82435640
20  2.57385535 1.23717260 3.73048501 1.21256048 2.27568936 1.28220799
21  1.20554433 2.07243061 1.58334442 1.86440042 0.43648156 1.85954222
22  1.42668176 0.54349569 2.63675919 0.37049669 1.37424935 0.36145535
23  2.36946925 3.46546758 1.89293945 3.25610210 1.75579541 3.25637510
24  1.61753882 0.86798941 2.73296804 0.68512311 1.31370323 0.72206168
25  2.73129756 3.54364161 2.49577200 3.32947630 1.97486406 3.34476911
26  1.87887631 0.75793578 3.04719693 0.65629585 1.68557365 0.69318071
27  1.94493345 2.60716380 2.10366372 2.39285359 1.12952175 2.40614969
28  1.51086276 1.35987477 2.42858551 1.15351417 0.95849533 1.17425908
29  1.62483654 2.42550806 1.79780543 2.21339849 0.86331475 2.21490303
30  1.95477587 0.59883997 3.18274089 0.62844548 1.96196187 0.62874402
31  3.28295258 4.12454115 2.91370086 3.91038344 2.54917954 3.92668728
32  1.44228141 0.64972123 2.64968980 0.57325190 1.54612319 0.51342655
33  2.86894052 3.82209021 2.45066174 3.60865994 2.18972908 3.61521193
34  2.16497493 0.83501403 3.39563222 0.94045898 2.30044280 0.91487167
35  2.45339526 3.34948532 2.19654062 3.13609094 1.74505651 3.14187700
36  1.77071499 0.68532995 2.97643938 0.68075875 1.84509190 0.64320843
37  1.98999449 2.98757088 1.76959982 2.77816066 1.35362718 2.77287822
38  1.69614700 1.01704830 2.77736446 0.86300693 1.43426133 0.87201936
39  1.56079628 2.52802268 1.59719710 2.32502912 1.00094118 2.30937992
40  1.62794173 0.87219607 2.78904530 0.83150672 1.74267632 0.77578781
41  3.41097045 3.72308827 3.51287491 3.51949606 2.56922785 3.55466648
42  2.25992957 0.99720644 3.44593829 1.02183473 2.22379232 1.02160343
43  2.27120124 2.75817645 2.47673953 2.54766186 1.48547958 2.56227285
44  1.51615795 1.39545094 2.43375476 1.21602735 1.16744609 1.20587008
45  2.37248086 3.01082468 2.40884255 2.79850622 1.60560277 2.80936905
46  1.40599216 1.12472036 2.46350883 0.99393830 1.37475936 0.95055995
47  2.49293941 2.49591767 3.00794004 2.30145337 1.71879991 2.33365216
48  1.15324201 1.68048046 1.89917950 1.50552219 0.96037702 1.46837057
49  1.19665356 1.87479393 1.78704668 1.69010474 0.89070003 1.65875620
50  1.28742642 1.92336728 1.84350862 1.73203516 0.87911758 1.70747261
51  2.43360579 2.51707921 2.90911121 2.31980189 1.66803981 2.34641859
52  1.65000901 1.56717741 2.49374986 1.38772917 1.23545256 1.38202544
53  1.48723412 1.65594856 2.26536766 1.47581553 1.12865449 1.45631060
54  3.16185789 3.03280255 3.63651207 2.85162583 2.36591292 2.89474652
55  2.47291922 2.71842474 2.81955078 2.51560166 1.69335518 2.53748048
56  2.27162279 2.64577558 2.57481395 2.43968379 1.51438695 2.45354185
57  2.57842557 2.69674998 2.99408211 2.49949278 1.80460897 2.52593856
58  3.75557906 3.85531264 3.97998057 3.66353298 2.91733321 3.70497883
59  1.39176362 1.71090479 2.14299201 1.54931234 1.21761049 1.51145128
60  2.71858868 2.91166053 3.04709497 2.71256117 1.93738828 2.73744283
61  3.89304797 3.82553782 4.22674430 3.64505788 3.06556684 3.69137964
62  1.33303322 1.55797919 2.21591295 1.45342690 1.51475864 1.38800841
63  3.68037522 3.68638489 3.98580820 3.50025022 2.85695926 3.54202544
64  2.89171352 2.79123838 3.39552054 2.60840771 2.13470737 2.64305413
65  3.42286518 3.45951408 3.74120803 3.27072701 2.61194045 3.30831554
66  1.47769853 1.53315203 2.39107197 1.44858297 1.67347198 1.38146984
67  2.17069490 2.34522685 2.66431303 2.15115928 1.51029831 2.16027670
68  3.74226144 3.81210596 3.99211581 3.62257993 2.91629566 3.66232597
69  1.47596350 1.52477265 2.38785490 1.43257470 1.63474488 1.36842463
70  1.59395272 1.98298729 2.17787968 1.80253517 1.21313215 1.77952276
71  3.92288319 3.87219501 4.24156663 3.69119319 3.10104720 3.73537776
72  2.38893845 2.72413669 2.69406764 2.52338076 1.67401750 2.53394254
73  3.24659408 3.33257113 3.55640410 3.14120241 2.45152609 3.17362633
74  3.28995340 3.24155807 3.69110219 3.05823435 2.50447725 3.09492212
75  3.24042821 3.36726300 3.52260132 3.17560875 2.46490959 3.20334165
76  1.67134343 1.85099520 2.39432027 1.71249863 1.55131099 1.67102421
77  2.44194419 2.51642062 2.93406905 2.33181620 1.80066705 2.34281387
78  2.14157282 2.38493865 2.60545394 2.19896280 1.57974840 2.19558753
79  1.59383098 1.86722178 2.30488218 1.74082988 1.59011045 1.68920470
80  2.61354249 2.91607621 2.88904531 2.71928968 1.91074168 2.73019291
81  3.13382947 3.19313509 3.48505662 3.00518330 2.37282125 3.03307292
82  2.10684216 2.16786251 2.71185247 1.99301453 1.60407185 1.98941433
83  3.74408773 3.93040390 3.90521572 3.73605879 2.93728594 3.76816168
84  2.44505071 2.73143487 2.77901853 2.53717600 1.77808404 2.54399864
85  1.64658292 1.75175060 2.44924060 1.64729550 1.71183511 1.59091271
86  2.56675473 2.78886475 2.91724979 2.59562860 1.87604786 2.60738412
87  3.12091285 3.04541744 3.57343472 2.86807577 2.39939303 2.89586961
88  1.72833602 1.89102367 2.46125947 1.77981264 1.75268350 1.72647247
89  2.12007582 2.05127716 2.81679655 1.90015749 1.75578077 1.88644165
90  2.77104134 2.97106197 3.09333005 2.78103143 2.08346251 2.79360016
91  3.93634039 3.89109945 4.25301740 3.71263696 3.14805621 3.74997623
92  1.67856751 2.29170527 2.13021847 2.17988981 1.85059609 2.11568179
93  2.71943325 2.86477927 3.09789520 2.68049919 2.06950587 2.69032379
94  2.27968787 2.70301525 2.56707231 2.51802066 1.75938910 2.50683197
95  1.95321620 2.41587037 2.34262173 2.24912207 1.64057059 2.21953409
96  1.82127110 2.05979357 2.46202523 1.93618874 1.77409094 1.88801605
97  2.65503751 2.85189326 3.01050939 2.66606759 2.01637119 2.67290757
98  1.85604747 2.13566523 2.44146666 1.99540811 1.70654679 1.95503995
99  2.71859727 3.01399503 2.98273436 2.82407615 2.07207723 2.82918344
100 1.79512677 2.14664627 2.38918435 2.03893934 1.88361913 1.97993865
101 1.81389248 2.37108329 2.22497259 2.23849295 1.80692082 2.18576986
102 2.81707527 2.97540281 3.16583804 2.79156651 2.16607010 2.80126071
103 3.95086888 3.84342098 4.31279336 3.67078883 3.18095081 3.70761227
104 1.95888103 2.08423720 2.61770392 1.95941719 1.84418134 1.91801754
105 2.87190273 2.85608433 3.33559888 2.68197919 2.23154177 2.69652065
106 1.79894618 2.34159571 2.23963734 2.21920695 1.85848082 2.16197109
107 3.85251212 3.89339817 4.11694937 3.71092780 3.08141519 3.74199707
108 3.11306438 3.27989537 3.39495164 3.09324243 2.41502621 3.10881267
109 3.95832507 4.10192532 4.13067259 3.91321518 3.17751720 3.94262791
110 3.84471930 3.91797082 4.08550422 3.73348870 3.07264296 3.76357497
111 3.79963574 3.81083996 4.09302430 3.63034833 3.03438566 3.66152085
112 1.91763692 2.11035957 2.58115571 2.01927819 2.02466602 1.95941719
113 2.31172109 2.69117773 2.63510607 2.51594279 1.85992506 2.49952978
114 1.88521056 2.31041585 2.39674276 2.20522472 1.99853815 2.14428424
115 1.93665756 2.30287099 2.47917203 2.20676285 2.07412018 2.14419933
116 1.95076932 2.25513753 2.52761691 2.15771342 2.05617161 2.09756130
117 3.68367683 3.85089899 3.87415052 3.66245552 2.93276677 3.68613573
118 2.97256087 2.89268333 3.46449584 2.72593171 2.35407700 2.74029463
119 3.03174311 3.27068803 3.27844901 3.08573248 2.38483341 3.09305185
120 3.05458342 3.01552796 3.50472552 2.84713982 2.43052437 2.86062384
121 2.16359281 2.24532855 2.78756512 2.12456416 2.02235982 2.08614497
122 2.40235153 2.81453462 2.67663603 2.64129603 1.96854326 2.62286669
123 2.65111995 2.62114282 3.19009811 2.46867826 2.19561815 2.46293371
124 3.21431725 2.45712365 4.09346486 2.38281907 2.85449789 2.39545811
125 2.14873358 2.90868710 2.25088724 2.77166412 2.14042400 2.71839610
126 2.69971316 2.21846044 3.52229419 2.13426226 2.47485497 2.11862822
127 2.74259629 3.19366174 2.89088519 3.01334377 2.23663615 3.00131304
128 3.39244492 2.58649314 4.27938576 2.52031864 3.02959054 2.53551700
129 3.73111360 4.39249562 3.49532107 4.19033209 3.08318154 4.19267613
130 2.88781623 2.46597557 3.63111531 2.35460399 2.51300375 2.35383058
131 3.14855524 3.97292387 2.85210613 3.77769532 2.64199041 3.76319556
132 2.92221596 2.50207917 3.65713173 2.38810088 2.52825205 2.38948398
133 2.22076492 2.84681947 2.41863549 2.70910121 2.15025048 2.66016557
134 2.64260164 2.31781067 3.39143292 2.21990468 2.41375172 2.19947573
135 2.57199558 3.68011028 2.17055697 3.53973907 2.64633392 3.48222377
136 2.99824644 2.29738652 3.89975405 2.25294392 2.83223187 2.23898652
137 3.10081169 3.97481858 2.76823913 3.78387966 2.65426572 3.76375599
138 2.73424793 2.36486505 3.48989702 2.26912149 2.48680035 2.25210514
139 2.51142890 3.55330854 2.21486846 3.41908253 2.60718157 3.35977709
140 2.82685250 2.48435869 3.54425520 2.37738751 2.51542862 2.36640792
141 3.78843262 4.53010107 3.47323356 4.32944591 3.19026775 4.32592895
142 3.23380265 2.46062258 4.13937115 2.41766894 3.01561995 2.41295938
143 2.41052685 2.85761092 2.69817127 2.72023433 2.25660195 2.67844591
144 3.11691224 2.46335405 3.97433312 2.40493114 2.89202741 2.39584004
145 2.61725507 3.57684617 2.36138549 3.42786448 2.56491587 3.37742931
146 3.32144907 2.49145437 4.25911090 2.47426511 3.18384770 2.46260800
147 3.14574567 3.51353072 3.28046159 3.33433210 2.59300366 3.32900294
148 2.87669961 2.50318018 3.61469850 2.41301395 2.63766407 2.39522519
149 2.70924006 3.44087942 2.63830942 3.27546259 2.43434275 3.24110568
150 3.28740111 2.59636014 4.14219833 2.53886990 3.03135388 2.53493863
151 3.07102117 3.79159253 2.90942614 3.60842145 2.63159141 3.58804475
152 3.37696816 2.73631665 4.18396027 2.65814143 3.02936427 2.66289656
153 3.08185553 3.74759175 2.96952689 3.56433253 2.61914975 3.54641693
154 3.10748868 2.69667838 3.81846555 2.59362693 2.75474185 2.58958753
155 3.25032164 3.94380057 3.07542037 3.75554290 2.75131251 3.74105075
156 3.13535821 2.45642165 4.01920960 2.42286542 3.01272652 2.40324474
157 3.09505091 4.08200549 2.66286907 3.90363256 2.80345974 3.87068780
158 2.94185187 2.48639142 3.72271746 2.41349383 2.75037349 2.39332790
159 3.01197515 4.02702364 2.57182310 3.85408800 2.77867225 3.81669004
160 2.84730513 2.50292211 3.58000259 2.41814933 2.65183034 2.39489380
161 3.60241055 3.92282016 3.69544427 3.73893097 2.96863145 3.74396748
162 3.05831659 2.50432151 3.88067573 2.44786012 2.89232794 2.42835999
163 2.83691036 3.87254562 2.47614058 3.73904474 2.91763388 3.68010080
164 3.38012947 2.65385719 4.25382689 2.61467416 3.18590041 2.60501938
165 3.50448463 3.99365029 3.48047565 3.81286733 2.97438776 3.80391386
166 3.24463170 2.88273923 3.91829811 2.78813883 2.94417174 2.77650651
167 3.24959310 3.89197422 3.14283576 3.71823742 2.84983599 3.69515946
168 3.60758331 2.88780424 4.45503923 2.84630914 3.38502096 2.83955659
169 3.03509692 3.61118573 3.04643676 3.45290583 2.73581582 3.42170586
170 3.04050429 2.93611765 3.59410976 2.83135248 2.81096841 2.80518112
171 3.28459192 4.03718981 3.07097703 3.86404579 2.93452473 3.83606199
172 3.14219485 2.79641370 3.84382758 2.72793959 2.99770701 2.69983905
173 3.20265814 4.02830804 2.93997556 3.86072782 2.92931387 3.82619210
174 3.63430718 2.97478434 4.43963309 2.91736503 3.35948188 2.91401375
175 3.78411789 4.42537229 3.58273805 4.23874781 3.26507671 4.22748134
176 3.41433543 2.85965379 4.19816674 2.80845342 3.23817390 2.79024683
177 4.04764909 4.61225680 3.87767646 4.42232702 3.46131261 4.41917260
178 3.06637091 2.85051887 3.70375079 2.77359018 2.94120364 2.74028017
179 4.23748250 4.79073828 4.06022804 4.60306909 3.66121476 4.59925096
180 3.74590709 3.15363299 4.50875624 3.09615697 3.49341524 3.08755603
181 3.38838223 3.82879376 3.46492665 3.68131088 3.09160727 3.65154965
182 3.73174132 3.22565172 4.45490953 3.16978375 3.52927824 3.15277678
183 3.81917594 4.44089410 3.65144039 4.26879342 3.40606181 4.24767256
184 3.75491611 3.22302624 4.49950152 3.18012399 3.60367709 3.15879911
185 3.56495186 3.86311560 3.72551650 3.71648125 3.20331397 3.69461652
186 3.98662691 3.32077061 4.78716134 3.29201753 3.82419977 3.27666680
187 4.16372005 4.60155719 4.10895766 4.42839326 3.65012130 4.41939834
188 3.52102849 3.35051260 4.07011907 3.27461352 3.38383153 3.24175674
189 3.79894941 4.40658793 3.66246145 4.24630018 3.46801712 4.21799065
190 3.98497307 3.52177731 4.65220064 3.45459520 3.72641363 3.44199121
191 3.57250810 4.13962789 3.52278301 3.99562744 3.34677394 3.95874571
192 3.66627316 3.47302347 4.20261377 3.38869502 3.46232079 3.36263963
193 4.04570079 4.75934522 3.80940358 4.61426522 3.86209425 4.57316557
194 4.45275597 3.94374895 5.11217544 3.88412900 4.18464075 3.87414957
195 4.55994683 5.07760645 4.42323034 4.92045309 4.18983395 4.89698364
196 4.43771548 4.12219721 4.98230955 4.05253679 4.21211117 4.03219524
197 4.63751309 5.00249166 4.63348123 4.86017035 4.29456938 4.83621149
198 4.53473661 4.30747566 5.02119686 4.23898679 4.35448982 4.21205574
199 4.80661472 5.30547551 4.70933062 5.18256985 4.64816737 5.14116625
200 5.00993297 4.69012317 5.53419973 4.63993464 4.86337166 4.61259146
             7          8          9         10         11         12
2                                                                    
3                                                                    
4                                                                    
5                                                                    
6                                                                    
7                                                                    
8   3.51435480                                                       
9   2.07962091 4.58629316                                            
10  2.58103256 0.98911877 3.61436722                                 
11  2.31195177 4.41816462 0.47704433 3.47279458                      
12  3.60156908 0.88141741 4.25793239 1.10512895 4.01025554           
13  1.68470576 3.95505108 0.63393868 2.98183629 0.64656813 3.64601717
14  2.86098944 0.66655925 4.05125506 0.47268221 3.92795814 1.16074749
15  0.31587439 3.29377778 1.97162819 2.33935701 2.14829796 3.33359077
16  2.97710008 0.59019339 4.20749244 0.63475199 4.08836095 1.21134473
17  1.12880100 2.44357018 2.41893440 1.47879627 2.43203840 2.47953020
18  2.56214483 1.11123269 3.98485299 0.75647461 3.92187860 1.67089726
19  1.52005170 3.26830765 1.33224106 2.29701352 1.23030797 2.97525899
20  3.56772600 0.89341556 4.22690936 1.07936384 3.98144631 0.15714169
21  1.14600674 2.45156582 2.42521869 1.48905354 2.43828891 2.48566129
22  2.70115949 0.85673746 3.89600433 0.40725635 3.78103848 1.24997032
23  0.83223816 3.82885858 1.31094974 2.84529728 1.56001515 3.73129294
24  2.62385830 1.02972155 3.60290478 0.24250904 3.45164246 1.07139926
25  1.44601305 3.82976543 0.90074345 2.84847855 0.99171292 3.57797276
26  2.99850197 0.73850573 3.96913716 0.52201704 3.80151847 0.85748862
27  1.29272865 2.89649743 1.79682583 1.91567294 1.75602961 2.71320761
28  2.16360476 1.58617783 3.07764147 0.65344155 2.94579115 1.51089706
29  1.11389318 2.75830910 2.06699337 1.78275721 2.07707737 2.68460955
30  3.27903843 0.49888219 4.39779654 0.85643313 4.24942856 1.04826471
31  1.84869809 4.40125539 0.50882117 3.42369504 0.75925785 4.11242466
32  2.81865098 0.94369387 4.12297426 0.76941851 4.02980296 1.48106756
33  1.41158335 4.13339829 0.95169040 3.15105436 1.19938557 3.93423713
34  3.59139019 0.67843985 4.79647369 1.27354406 4.65961115 1.35596640
35  1.19439522 3.65892946 1.27225522 2.67931423 1.39446414 3.48181261
36  3.12501732 0.77465617 4.34547335 0.90592088 4.22606296 1.33207778
37  0.89647221 3.33348460 1.76080647 2.36650496 1.88218006 3.26503258
38  2.68901957 1.13292868 3.68758138 0.57241965 3.54427955 1.21160928
39  1.06220008 2.88503675 2.29798237 1.95634189 2.36864061 2.90964827
40  2.96915185 1.05393696 4.26203230 0.99781957 4.16774295 1.57686169
41  2.54032052 3.85225386 1.43666478 2.97556710 1.09778223 3.35824650
42  3.50582610 0.76874660 4.53883237 1.14351813 4.37290820 1.10312365
43  1.68966807 2.98107432 1.87744863 2.04541096 1.77641852 2.71988026
44  2.29292423 1.61254593 3.34742184 0.87545529 3.24561772 1.68143815
45  1.53932479 3.26124907 1.63405731 2.30933974 1.59190772 3.02384909
46  2.54546718 1.38041754 3.81362753 0.91532346 3.73575041 1.71273169
47  2.33562882 2.59198474 2.38717071 1.76707187 2.15432432 2.16691590
48  1.88424740 2.02390207 3.24933648 1.27382941 3.23602410 2.24100934
49  1.68212929 2.22282811 3.03280483 1.41210045 3.03562623 2.38660871
50  1.65138271 2.25487395 2.91563804 1.41210045 2.90801826 2.36503848
51  2.23886822 2.63524915 2.34955207 1.79351590 2.14304564 2.25474156
52  2.28653665 1.75526759 3.25020312 1.01435249 3.14071902 1.75162963
53  2.10785104 1.90612669 3.21188235 1.15150752 3.14259839 1.98837178
54  2.86890446 3.04649691 2.41562169 2.31533974 2.08232317 2.46326411
55  2.08324984 2.87095978 2.11770618 1.99450649 1.93832813 2.52206459
56  1.86573140 2.84080235 2.11693460 1.93832813 1.99450649 2.57245400
57  2.27926551 2.81085321 2.25491819 1.97276554 2.03994870 2.41214104
58  3.05015212 3.90881672 1.95111516 3.11679398 1.56910156 3.32302379
59  2.12158651 1.99780323 3.39522062 1.32823560 3.36291906 2.19995055
60  2.27952453 3.03377081 2.10940339 2.18665440 1.89651884 2.63239297
61  3.34113931 3.82392046 2.33528961 3.10486622 1.93601434 3.17919133
62  2.45945402 1.87065661 3.93562715 1.45266685 3.92235714 2.29605775
63  3.10482472 3.71292559 2.18703266 2.95838734 1.81711126 3.11396354
64  2.69841887 2.82505860 2.52024798 2.08368945 2.24482146 2.32074259
65  2.89120620 3.50384178 2.16316516 2.73152874 1.83140620 2.94820757
66  2.64537582 1.80824761 4.09459210 1.48678087 4.06942187 2.25820632
67  2.12974714 2.50154431 2.60608788 1.67660433 2.47273422 2.26883209
68  3.08718619 3.85425665 2.08273182 3.07944195 1.71981626 3.27113707
69  2.61321601 1.79544899 4.03724365 1.44659916 4.00787948 2.22044601
70  1.96763099 2.24328502 3.06104762 1.47542067 3.02157835 2.30653688
71  3.35728113 3.87226266 2.35457152 3.15239044 1.96763099 3.23814853
72  2.01853815 2.89823651 2.25090132 2.03354833 2.12842901 2.62959032
73  2.73131330 3.39658342 2.15596566 2.60741199 1.86579185 2.88876644
74  2.90453053 3.26581140 2.38482609 2.52768916 2.07109917 2.71454347
75  2.71133353 3.43989748 2.19250682 2.65007529 1.93308227 2.96352404
76  2.39767334 2.07946044 3.61611152 1.53089648 3.57627462 2.28637969
77  2.38825185 2.62294808 2.71564894 1.86284510 2.55675597 2.33695594
78  2.15686852 2.55594513 2.78644241 1.77539093 2.69169239 2.40921263
79  2.40619476 2.12696125 3.74044144 1.62071813 3.72325206 2.41377523
80  2.19695333 3.06559429 2.28247724 2.23056593 2.14752397 2.76628934
81  2.71950574 3.25201288 2.34135084 2.48455422 2.08354945 2.77689947
82  2.35059943 2.30491332 3.04876127 1.59284170 2.93367575 2.17372741
83  2.99389212 4.00155632 1.99682209 3.19884381 1.69380573 3.47391196
84  2.15967325 2.88766736 2.44069266 2.06479520 2.32064663 2.63288783
85  2.60452553 1.98799640 3.95273770 1.59006027 3.92331263 2.32926670
86  2.26806274 2.92175926 2.42083246 2.10947974 2.27186532 2.61804800
87  2.88264017 3.06529358 2.65416221 2.36434148 2.39465927 2.58145797
88  2.58291216 2.11916401 3.89719024 1.68955959 3.87189509 2.42126221
89  2.58791179 2.16171108 3.41895263 1.58202647 3.31040549 2.11916401
90  2.42317495 3.08388250 2.44581995 2.29531483 2.28505601 2.75140811
91  3.40853394 3.88525408 2.54091470 3.18635309 2.20120617 3.28684964
92  2.39892382 2.60331420 3.91518335 2.12095387 3.96446761 2.97405675
93  2.48916172 2.96592607 2.63093980 2.21144611 2.47463417 2.65552872
94  2.10208489 2.90016214 2.72792324 2.11774668 2.68075317 2.79015434
95  2.13230076 2.65086612 3.15679729 1.95113597 3.14487613 2.71202210
96  2.51998562 2.28199724 3.77317215 1.79475156 3.75203726 2.52378084
97  2.41161342 2.97010593 2.61171121 2.20342658 2.47380985 2.68879696
98  2.40588762 2.35421099 3.57282831 1.79129301 3.54680059 2.52295075
99  2.34304869 3.15248294 2.47990198 2.35948212 2.36279896 2.88016237
100 2.57023877 2.40064922 3.95621889 1.96542067 3.96416303 2.73114167
101 2.31978588 2.64929811 3.66883761 2.09106525 3.70067169 2.90910413
102 2.54089821 3.07308864 2.62107860 2.32252545 2.46460252 2.75412300
103 3.50235333 3.81639603 2.72564632 3.15428269 2.39102370 3.21362289
104 2.61190616 2.26571101 3.75969181 1.78765830 3.71695700 2.44921069
105 2.74951871 2.90450639 2.83649823 2.21681291 2.64310594 2.54116329
106 2.39882497 2.62332301 3.79957727 2.10833351 3.83404418 2.92522137
107 3.28077843 3.91334199 2.47780800 3.18965200 2.18060626 3.36627310
108 2.68045250 3.36382993 2.46812807 2.60230877 2.28212817 2.97805291
109 3.25103194 4.14890504 2.29951864 3.38639715 2.01810200 3.61800314
110 3.24123120 3.94767901 2.42148924 3.21120555 2.13192466 3.41052931
111 3.27426695 3.82370477 2.53220800 3.11192244 2.23435792 3.27586150
112 2.77532601 2.32740246 4.13332757 1.97798344 4.12469539 2.67488989
113 2.24877145 2.87668477 2.94629278 2.14780899 2.90190085 2.80245132
114 2.60358350 2.56990673 4.01070198 2.13758888 4.03464637 2.90856001
115 2.70712169 2.55018373 4.11678513 2.16081284 4.13585875 2.90668882
116 2.72347571 2.48744661 4.09359182 2.10078146 4.10099647 2.82485557
117 3.04514428 3.91179543 2.33919797 3.14791152 2.10012809 3.43334288
118 2.90154601 2.91607549 2.98716136 2.27394920 2.78647585 2.54384840
119 2.61636894 3.37619772 2.57008295 2.61936376 2.43166528 3.05851721
120 2.92130119 3.04456435 2.95247998 2.39315974 2.75566434 2.67174861
121 2.74908452 2.39330848 3.81680006 1.94163350 3.76625950 2.53783908
122 2.29350693 3.00106110 2.97609635 2.28111274 2.94338552 2.93361206
123 2.82018444 2.68234164 3.33348253 2.10486100 3.20361441 2.50458784
124 3.83235047 2.25740659 4.29415009 2.14021046 4.06605695 1.94987699
125 2.33473960 3.20241967 3.66043827 2.60658666 3.74557052 3.44330561
126 3.40016803 2.16359281 4.19081819 1.95271039 4.04523264 2.13968566
127 2.37930895 3.36777346 2.77764966 2.61510462 2.74461634 3.22335653
128 4.00977055 2.35680383 4.42312483 2.28594006 4.18263269 2.01789135
129 2.65731154 4.58739534 2.03564861 3.71612455 2.06428002 4.29934147
130 3.35523443 2.40133113 3.89331323 2.06428002 3.71612455 2.19764736
131 2.19623282 4.22590420 2.33555118 3.36936784 2.45094803 4.09930654
132 3.36057599 2.43418509 3.85960204 2.08527504 3.67661168 2.20579393
133 2.43212540 3.10581292 3.64797975 2.52299289 3.70294429 3.30456842
134 3.26263798 2.31265046 4.07269417 2.01955666 3.94787690 2.30860331
135 2.35364849 4.03848767 3.76224964 3.38691164 3.95841312 4.31629752
136 3.82789170 2.15025048 4.61944905 2.14851365 4.45408331 2.14313615
137 2.19127899 4.24209900 2.51017324 3.40106654 2.64793179 4.16348696
138 3.34108230 2.33698908 4.10155152 2.06133273 3.96546208 2.29933280
139 2.42526878 3.89987545 3.85176723 3.28170232 4.02696133 4.19227682
140 3.32838889 2.45148203 3.97925509 2.12443417 3.83110711 2.34057584
141 2.68172985 4.74469545 2.19160208 3.87472925 2.27594973 4.50295898
142 4.01325881 2.26415960 4.68404644 2.28644343 4.49250947 2.15548555
143 2.61937914 3.06225594 3.66119633 2.50317492 3.67671181 3.19076160
144 3.84205388 2.31626959 4.53194647 2.25116011 4.35647029 2.22977119
145 2.36908956 3.89227329 3.57668382 3.22538724 3.73128706 4.09136907
146 4.20894833 2.27766192 4.97678751 2.41542117 4.79601858 2.26575225
147 2.69477743 3.64604598 2.79669258 2.91210955 2.72989721 3.41971120
148 3.46789577 2.46192249 4.20518674 2.21427674 4.06850948 2.42071951
149 2.36804805 3.68951713 3.19369888 2.97944127 3.27458505 3.73393261
150 3.97552286 2.42130491 4.58352166 2.36938569 4.39186712 2.27436156
151 2.39333762 4.01988993 2.75681744 3.23240293 2.83045165 3.93157394
152 3.92221783 2.56603669 4.36846907 2.41766894 4.15639125 2.30425134
153 2.43467725 3.96110075 2.74397344 3.17890409 2.79483166 3.84968797
154 3.55143484 2.61869373 4.06222625 2.32338210 3.88849394 2.42601095
155 2.47114351 4.15859325 2.60395825 3.35109631 2.66495975 4.01430946
156 3.98462155 2.31043710 4.81172845 2.35066595 4.65626299 2.35033379
157 2.29709015 4.38097333 2.96446261 3.58561198 3.14830011 4.41232093
158 3.62223203 2.41942915 4.40515786 2.25834338 4.26662903 2.41569069
159 2.29374127 4.33688534 3.10875590 3.56195143 3.29853951 4.41057841
160 3.47539324 2.47609760 4.27997918 2.24669303 4.15714840 2.48756153
161 2.98582973 4.02428556 2.66123729 3.27656193 2.54951723 3.69065055
162 3.80388307 2.39999527 4.59278764 2.32491043 4.44501974 2.40562180
163 2.65837716 4.20876438 3.99447984 3.59500172 4.18343514 4.48715257
164 4.14558152 2.46637906 4.82697923 2.49775518 4.64465574 2.38920958
165 2.87406292 4.14455145 2.84820421 3.39669508 2.83046415 3.93177544
166 3.69485634 2.81332022 4.25512981 2.55196665 4.10113642 2.68019213
167 2.69222481 4.09447853 3.06937832 3.36157170 3.12478375 4.01463880
168 4.31296914 2.68645057 4.91168179 2.71048831 4.71913536 2.55965619
169 2.75101494 3.80779799 3.40361170 3.15026688 3.44692866 3.80552016
170 3.43800755 2.95936483 4.16524018 2.61629723 4.07201394 2.94832529
171 2.66519072 4.26865503 3.13126727 3.52640726 3.23116951 4.23344342
172 3.78050871 2.75156499 4.59548444 2.59558117 4.48080945 2.79605330
173 2.63263415 4.28354319 3.28546724 3.55695288 3.41348528 4.31118646
174 4.24236352 2.78813883 4.75383772 2.73630539 4.55536180 2.60416025
175 2.94239037 4.60996209 2.79097832 3.82126067 2.83834510 4.41288607
176 4.10226264 2.72951011 4.81210941 2.68245445 4.65737896 2.69873877
177 3.15207502 4.76862375 2.70223486 3.97385740 2.70522556 4.49373299
178 3.65827120 2.84997780 4.52211546 2.63842058 4.43141025 2.92903499
179 3.34692700 4.93893050 2.87187919 4.15843495 2.87508341 4.66094464
180 4.32841073 2.98597854 4.85780884 2.92439813 4.67411857 2.83894158
181 3.17510582 3.97692136 3.71706178 3.38672826 3.73062878 3.94608634
182 4.32325167 3.09162700 4.93941132 3.02223577 4.78237070 3.01977548
183 3.16530066 4.62032560 3.30506085 3.90270892 3.36282293 4.49979946
184 4.42099819 3.08480912 5.11461618 3.07182357 4.96576754 3.06806482
185 3.36578251 3.96328022 3.73255883 3.39568887 3.69852812 3.85493753
186 4.69649712 3.12659061 5.33404198 3.19606154 5.15983408 3.06784762
187 3.51031617 4.71796692 3.30469888 4.01921738 3.28074431 4.47575638
188 4.00024076 3.33590618 4.76703111 3.12917598 4.68131357 3.38222638
189 3.29233179 4.58529310 3.63777553 3.92235098 3.70220494 4.52727029
190 4.45393100 3.38541745 4.93248983 3.26595199 4.76578840 3.24462114
191 3.30333362 4.31890870 3.92945167 3.72974616 3.99133993 4.34686227
192 4.05850437 3.43887302 4.69130947 3.20351672 4.58721179 3.40943792
193 3.62068016 4.96851861 4.21558783 4.35858271 4.33439658 5.02467448
194 4.89524271 3.77483544 5.28070851 3.69840211 5.09997301 3.59874210
195 3.99621948 5.21124915 4.06473250 4.57944301 4.10407873 5.08489255
196 4.80344730 4.01960414 5.26868310 3.87158607 5.13526993 3.92267931
197 4.25988771 5.09125684 4.40272227 4.54455171 4.40124792 4.96674459
198 4.88759123 4.23359296 5.42252521 4.07715656 5.31723175 4.19285906
199 4.55962078 5.44102415 5.07637897 4.95759904 5.14648204 5.48355484
200 5.43573323 4.57827911 5.97544799 4.51286704 5.86001132 4.54934386
            13         14         15         16         17         18
2                                                                    
3                                                                    
4                                                                    
5                                                                    
6                                                                    
7                                                                    
8                                                                    
9                                                                    
10                                                                   
11                                                                   
12                                                                   
13                                                                   
14  3.41885030                                                       
15  1.50532170 2.64732823                                            
16  3.57545659 0.16277940 2.77222303                                 
17  1.81995879 1.80742762 0.86472204 1.94183106                      
18  3.36183383 0.51467839 2.38637887 0.52476388 1.61063751           
19  0.70103728 2.73602694 1.24498887 2.89382559 1.24129898 2.70303888
20  3.61311620 1.13773892 3.29666445 1.19183450 2.44082437 1.64147041
21  1.82592287 1.81343290 0.87720494 1.94742193 0.11422166 1.61468256
22  3.26321599 0.22871792 2.48186066 0.35114255 1.64039866 0.46329639
23  0.96133028 3.20786695 0.73980717 3.34660425 1.41170234 3.01121646
24  2.96929810 0.55798238 2.37048745 0.71086319 1.50684434 0.84661834
25  0.41984592 3.26448093 1.25511561 3.41704422 1.60697355 3.17018136
26  3.33680367 0.50831370 2.74959047 0.59781477 1.88893849 0.93275106
27  1.17992754 2.32151164 0.98086928 2.47311802 0.77265656 2.23774094
28  2.44476011 1.04726170 1.88899505 1.20196266 1.04151148 1.12320060
29  1.47027746 2.14533236 0.80585663 2.28754270 0.49486020 1.99490375
30  3.76417267 0.52201704 3.05508604 0.46745800 2.21033759 0.89454568
31  0.58899053 3.84419453 1.72551357 3.99751961 2.18207577 3.75250928
32  3.49360334 0.46376468 2.61827567 0.45174284 1.81307810 0.44274520
33  0.74468281 3.54204946 1.29552164 3.68848941 1.81940771 3.39910687
34  4.16359372 0.87571706 3.38435680 0.76184637 2.56162336 1.11488069
35  0.81337976 3.06590149 0.99219105 3.21194852 1.36912438 2.92805082
36  3.71387527 0.56133903 2.91392505 0.50607206 2.09434828 0.74247906
37  1.26572058 2.70979908 0.66048207 2.84576628 0.99093883 2.51512031
38  3.05720055 0.70186061 2.43592222 0.81614437 1.59326526 0.91155679
39  1.75520563 2.24884424 0.82310011 2.37396236 0.70547392 2.02048319
40  3.63558742 0.71199298 2.76845772 0.68075875 1.98077926 0.70183242
41  1.14918184 3.42484490 2.28325250 3.58447214 2.24302816 3.49822290
42  3.90958241 0.89837753 3.27026279 0.86232514 2.43128746 1.23071135
43  1.30272697 2.44865965 1.39164623 2.60006418 1.15639610 2.41600216
44  2.72623008 1.07625074 2.04030151 1.19343099 1.25115433 1.06172310
45  1.09171559 2.70679530 1.26438750 2.85650587 1.24402521 2.63532637
46  3.19318299 0.85979785 2.33329108 0.91527549 1.56185361 0.74375534
47  1.81855830 2.18402037 2.02266635 2.33695835 1.50870906 2.30586144
48  2.65334848 1.40555714 1.68102083 1.49784306 1.03306993 1.14707076
49  2.44600040 1.59528963 1.47274389 1.69819939 0.88390148 1.34244969
50  2.32571515 1.63338359 1.42319458 1.74581550 0.82388574 1.41674253
51  1.78034825 2.20040761 1.92884219 2.35174810 1.44121584 2.28977670
52  2.63461626 1.24502837 2.02390207 1.36493717 1.26373172 1.24873648
53  2.60453793 1.34582196 1.86336508 1.45574270 1.15106881 1.24001817
54  1.95156849 2.73459168 2.56120570 2.88512025 2.14258794 2.92408589
55  1.56347394 2.40139921 1.78002598 2.55306300 1.41585063 2.44441512
56  1.54940424 2.32836245 1.56684049 2.47692974 1.22211246 2.31835351
57  1.70970033 2.37993366 1.97290297 2.53100849 1.55440633 2.46486984
58  1.70181239 3.55719055 2.77771856 3.71328647 2.62153731 3.69744485
59  2.80147081 1.42820893 1.91253885 1.51120166 1.27196152 1.22250915
60  1.59660758 2.59440078 1.98113824 2.74551016 1.65766900 2.66207597
61  2.05880836 3.53343095 3.05507244 3.68517867 2.80090897 3.72394071
62  3.34274520 1.35419978 2.29904411 1.37470831 1.67862110 1.04526869
63  1.87744427 3.38667834 2.81955078 3.53942008 2.58089521 3.54884986
64  2.01046061 2.48090140 2.38975323 2.62760407 1.92190511 2.64151140
65  1.79110956 3.15355267 2.60119093 3.30557132 2.33632930 3.29693176
66  3.49845887 1.34419321 2.48185988 1.34845437 1.84433467 1.07273096
67  2.03138979 2.01983013 1.83682182 2.15815730 1.31231085 2.03755607
68  1.81163288 3.50985435 2.81039636 3.66353298 2.62507266 3.65375946
69  3.44011086 1.32305843 2.44336128 1.33508661 1.79790297 1.06554098
70  2.47717005 1.67752915 1.73151163 1.78452827 1.14840548 1.52842363
71  2.08720231 3.57614368 3.07330294 3.72695712 2.83091824 3.75895135
72  1.71242892 2.40147524 1.72995570 2.54460101 1.39568607 2.39503025
73  1.74890529 3.02025597 2.44112290 3.17086007 2.17163286 3.13879561
74  1.96110891 2.93386961 2.60544577 3.08188419 2.25463653 3.09331822
75  1.79344758 3.05010591 2.42685625 3.19797612 2.17862494 3.14875558
76  3.03386193 1.57782674 2.19468486 1.64164344 1.59219529 1.40679269
77  2.16961460 2.19077924 2.09834878 2.32388588 1.60529464 2.24388205
78  2.22917174 2.06126935 1.88649597 2.18569455 1.40006549 2.02839407
79  3.16329703 1.61806137 2.22734417 1.66555658 1.65830416 1.38516305
80  1.78439210 2.59146399 1.91699357 2.73214096 1.62989528 2.59851328
81  1.90376980 2.87580956 2.42714533 3.02145577 2.10781557 2.98860567
82  2.47486740 1.84553506 2.07993797 1.96250941 1.49150615 1.84945683
83  1.76198113 3.61867312 2.73197103 3.77076661 2.62303646 3.71972414
84  1.91699357 2.40606723 1.87935022 2.54255286 1.52321772 2.40181883
85  3.36700743 1.52371756 2.42711130 1.55134848 1.81903136 1.30584362
86  1.90507917 2.46347041 1.98214315 2.60251858 1.62054349 2.48922424
87  2.19165986 2.72960079 2.58487541 2.86821356 2.17298585 2.87270704
88  3.32046291 1.65252094 2.40475471 1.68768712 1.82882885 1.44244803
89  2.84283806 1.74330176 2.33493953 1.83645247 1.71081613 1.74440762
90  1.96528065 2.64549575 2.14298113 2.78281547 1.82182286 2.68264738
91  2.26200544 3.58498239 3.12649497 3.72994731 2.87643666 3.75260213
92  3.37907039 2.08154167 2.28704199 2.11003772 1.90480369 1.74670762
93  2.13667405 2.53907321 2.20973658 2.67082653 1.83435704 2.57992642
94  2.21743863 2.38416446 1.85976020 2.50213029 1.53963642 2.29531483
95  2.62238184 2.11763016 1.92578712 2.21015522 1.52462287 1.95104786
96  3.20881210 1.80461340 2.33801767 1.85285846 1.80508743 1.60648243
97  2.11543152 2.52586276 2.13667405 2.65667124 1.77729290 2.54600298
98  3.01350598 1.85976020 2.21015522 1.92578712 1.69418400 1.68519310
99  2.01059083 2.68805245 2.07799110 2.82029001 1.80525561 2.68345287
100 3.40152898 1.92210224 2.42101333 1.95113597 1.94071360 1.65914777
101 3.13824951 2.12266552 2.17652074 2.17431516 1.79687366 1.84937048
102 2.14598991 2.64975793 2.26540763 2.78103143 1.92215595 2.68934065
103 2.42392559 3.53815980 3.21597156 3.67892523 2.92374210 3.71897382
104 3.19439420 1.81753285 2.41298074 1.87159913 1.85788722 1.67414184
105 2.34371988 2.53404536 2.46329219 2.66201392 2.02547988 2.62614692
106 3.26589118 2.10718687 2.26499466 2.14829655 1.87476243 1.81815681
107 2.20120718 3.57959797 3.00718281 3.72329474 2.79631509 3.71280215
108 2.05022892 2.95527972 2.40716206 3.09210085 2.14210147 3.01348997
109 2.09009295 3.78619741 2.99245902 3.93289699 2.86947875 3.89329285
110 2.15438401 3.60298132 2.97106197 3.74738216 2.78125902 3.72650924
111 2.23257289 3.49745836 2.99649397 3.63993429 2.75730739 3.63711107
112 3.57153804 1.89782593 2.61945492 1.91408136 2.10009603 1.66679184
113 2.43916798 2.37652923 2.01810200 2.48421270 1.67330527 2.28133960
114 3.47019269 2.09181212 2.46979977 2.11793028 2.04296901 1.81254097
115 3.57324101 2.09311171 2.57341871 2.11153306 2.13094684 1.82011757
116 3.54501653 2.03882126 2.57852845 2.05979357 2.11087553 1.78759127
117 2.05894850 3.53039251 2.78377499 3.67335883 2.63062881 3.61598161
118 2.50075314 2.57376889 2.61659068 2.69652065 2.16209738 2.68138443
119 2.15150925 2.94476396 2.35717518 3.07498662 2.11548935 2.96403717
120 2.48504509 2.69561578 2.64035425 2.81882550 2.22401711 2.79304464
121 3.26310357 1.97728313 2.54703801 2.03066658 2.01412330 1.86238180
122 2.48783657 2.50191465 2.07377178 2.60672114 1.77510828 2.39614626
123 2.81312350 2.30950466 2.56189526 2.40878766 2.06429666 2.34217452
124 3.74060433 2.21980079 3.55309315 2.27541615 2.85036809 2.47531437
125 3.19307586 2.66161688 2.23883591 2.71626982 2.06699829 2.36211434
126 3.62275312 1.96854326 3.15449091 2.01125619 2.49154378 2.06931820
127 2.35018162 2.87501965 2.16350384 2.98891984 1.98797212 2.78856874
128 3.87661805 2.35971430 3.72823666 2.41138139 3.02500421 2.63345387
129 1.94925156 4.07190246 2.50136352 4.20954085 2.72757021 3.99436509
130 3.34945170 2.18652790 3.08868358 2.25973041 2.46363535 2.32506395
131 2.10820726 3.66271506 2.07531383 3.78435422 2.31856083 3.49744067
132 3.31948237 2.22025240 3.09117136 2.29684497 2.47090512 2.36548863
133 3.16889989 2.58797586 2.30630573 2.64623175 2.06988739 2.33112617
134 3.51544614 2.05544886 3.02470568 2.10495814 2.40747006 2.10429145
135 3.40910799 3.45366363 2.37676202 3.50773044 2.53425602 3.08215905
136 4.04637039 2.09321556 3.58260970 2.10821280 2.88384789 2.24959364
137 2.27429112 3.67012251 2.09214727 3.78499071 2.34745499 3.47730298
138 3.54695167 2.10332100 3.09815805 2.15370383 2.47614370 2.17513483
139 3.47264463 3.32968731 2.42919637 3.37826990 2.51418887 2.96307039
140 3.43659605 2.21012965 3.07695046 2.27302635 2.47485497 2.29761362
141 2.13077108 4.21185464 2.55557392 4.34448573 2.83849818 4.10155407
142 4.11981024 2.25764834 3.75639718 2.27848431 3.05250668 2.46135008
143 3.17733882 2.58474919 2.46054960 2.64789697 2.16187486 2.39307309
144 3.97292387 2.24141691 3.58968211 2.27034234 2.91308843 2.40507264
145 3.21000287 3.32425326 2.33436825 3.38932825 2.41904075 3.00780617
146 4.40513512 2.32199149 3.96307223 2.31951948 3.24984603 2.51298357
147 2.42561382 3.19099341 2.47450684 3.30860070 2.32671133 3.14855524
148 3.65980189 2.24750869 3.22767182 2.29342058 2.62163905 2.31947007
149 2.81102010 3.15043146 2.24591018 3.23830371 2.22898438 2.93554820
150 4.03280064 2.37537862 3.71667119 2.40747396 3.04157297 2.56476454
151 2.45674203 3.48210050 2.25499601 3.59178192 2.35024730 3.31983041
152 3.83637775 2.49219422 3.65132161 2.54539389 3.00068790 2.69919106
153 2.43278772 3.43489963 2.28059515 3.54639434 2.33716156 3.29161896
154 3.53642988 2.42537960 3.29142434 2.49037049 2.69754165 2.55346438
155 2.34480560 3.62869444 2.32432595 3.74583641 2.44726852 3.49208724
156 4.24417901 2.26684493 3.74840733 2.27037437 3.06766501 2.39879247
157 2.72588275 3.79528157 2.25664875 3.89268746 2.54240614 3.53929017
158 3.85306612 2.25000296 3.38575723 2.28166717 2.75874162 2.33200080
159 2.84996000 3.74840733 2.26684493 3.83899916 2.53938080 3.47130773
160 3.73348013 2.25499601 3.24439760 2.29313984 2.64637984 2.30125354
161 2.38043274 3.59709383 2.76078692 3.72471107 2.67142649 3.59989404
162 4.03609415 2.28653284 3.56679736 2.30677997 2.91822574 2.39269796
163 3.65221492 3.64636381 2.67402628 3.69484107 2.80716577 3.28689661
164 4.27239767 2.45541066 3.89561646 2.47043669 3.21639714 2.63285332
165 2.57567039 3.67278520 2.69149620 3.78876386 2.68554861 3.59850059
166 3.74212321 2.62080212 3.44878971 2.67452489 2.88826874 2.71496541
167 2.76838622 3.58428259 2.55267412 3.68571044 2.59097732 3.43192546
168 4.37204624 2.68617062 4.05952042 2.70527809 3.39759143 2.87260652
169 3.03375088 3.31575789 2.60890585 3.40097765 2.53291253 3.14759129
170 3.66424295 2.67006483 3.22248513 2.72097598 2.74523946 2.65819525
171 2.85897720 3.73651494 2.55997463 3.83404670 2.67739829 3.54637068
172 4.06424206 2.56813967 3.56185721 2.59149193 2.99415824 2.60076819
173 3.00419617 3.73857072 2.55459755 3.82769917 2.69386510 3.51128885
174 4.22832156 2.75367217 3.98388489 2.78661420 3.34541505 2.93941959
175 2.62555409 4.10646894 2.80287447 4.22462345 2.95197957 3.99591801
176 4.27553370 2.64745194 3.86592917 2.66542811 3.24590015 2.76037126
177 2.58902425 4.28854100 2.99483555 4.41440102 3.13339243 4.21993185
178 4.00008225 2.61632221 3.45227371 2.64218130 2.92725829 2.60229793
179 2.78058510 4.46705927 3.19482179 4.59091147 3.33586248 4.40049658
180 4.34409078 2.93232796 4.07878978 2.96184966 3.47146333 3.08733702
181 3.35978792 3.53518350 3.02260639 3.61392145 2.89948353 3.40405079
182 4.42927481 3.00736574 4.08829678 3.02997551 3.50991944 3.11621541
183 3.09151266 4.13088710 3.03983427 4.23244549 3.13284571 3.99493492
184 4.59571773 3.02143335 4.19316114 3.03184256 3.60438701 3.12020810
185 3.37518595 3.56279580 3.18477525 3.64642659 3.00465898 3.48893686
186 4.81123841 3.13550698 4.45861149 3.14021143 3.83562100 3.28223368
187 3.11679694 4.28199855 3.34267122 4.39259421 3.36289172 4.22456959
188 4.28199855 3.11679694 3.80293133 3.14275363 3.34091666 3.10025040
189 3.38725196 4.10681852 3.17685791 4.19533481 3.22763116 3.95066224
190 4.45137365 3.28943282 4.21489914 3.32338152 3.67441423 3.40595398
191 3.61029653 3.85638142 3.19100577 3.92773114 3.15726372 3.67755520
192 4.22178967 3.22651388 3.84931578 3.26326003 3.39512662 3.24017037
193 3.97670599 4.48245048 3.55770361 4.55161865 3.65831677 4.26382998
194 4.82174398 3.71969486 4.65471026 3.75041786 4.12533507 3.85580488
195 3.88816112 4.77358428 3.87584503 4.86322671 3.93535750 4.65753032
196 4.83212672 3.88873960 4.58790460 3.91947486 4.13653435 3.95148337
197 4.17222281 4.70621091 4.11744162 4.78532244 4.07038317 4.62064940
198 4.99722635 4.07791817 4.68998792 4.10340094 4.27890755 4.10073163
199 4.82925006 5.03903476 4.47319418 5.09276540 4.47052545 4.86817037
200 5.54938527 4.48133164 5.23859732 4.49397747 4.80512672 4.52238278
            19         20         21         22         23         24
2                                                                    
3                                                                    
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5                                                                    
6                                                                    
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8                                                                    
9                                                                    
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11                                                                   
12                                                                   
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14                                                                   
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16                                                                   
17                                                                   
18                                                                   
19                                                                   
20  2.93607404                                                       
21  1.23954601 2.43993335                                            
22  2.57692509 1.20463954 1.63641718                                 
23  1.02666685 3.68723989 1.40397977 3.03240720                      
24  2.27353835 1.01243767 1.49961180 0.43120647 2.84378400           
25  0.62780920 3.53090380 1.59201963 3.09080932 0.68006879 2.81851855
26  2.63809104 0.77757436 1.87623323 0.47608302 3.22258972 0.39371465
27  0.54849548 2.66099096 0.74105376 2.14333076 1.05421234 1.88103150
28  1.74724019 1.44539365 1.01828712 0.86695081 2.30993779 0.55765680
29  0.89226804 2.62905110 0.43399471 1.95820194 1.10516879 1.75600418
30  3.06702528 0.98569411 2.19751156 0.59216267 3.58012928 0.80317643
31  1.15596229 4.06500229 2.16707677 3.67007376 1.02087334 3.38904245
32  2.81052600 1.41870009 1.79499840 0.36630812 3.18955015 0.74075034
33  1.04274783 3.88015952 1.79413442 3.35777892 0.58769539 3.11650831
34  3.46712369 1.29614303 2.54373507 0.95387500 3.93202883 1.22482595
35  0.72697282 3.42497106 1.33535593 2.87911109 0.51025866 2.64068388
36  3.02070571 1.25808680 2.07243061 0.54349569 3.45792990 0.83738836
37  0.95069127 3.20394226 0.93911443 2.51568650 0.64447948 2.33242048
38  2.35774142 1.11389318 1.56156023 0.52257030 2.89195308 0.35006284
39  1.26867903 2.83955327 0.60957070 2.04392835 1.17581029 1.91034836
40  2.95041203 1.49347286 1.94868403 0.61571248 3.31978592 0.91369200
41  1.11634435 3.30003405 2.21277215 3.26328746 1.85597004 2.88695966
42  3.20870050 1.00011942 2.40340258 0.91137152 3.75175283 1.01855002
43  0.72565662 2.64604535 1.09258385 2.25611528 1.32125659 1.95399280
44  2.04124127 1.58304154 1.19242388 0.85240443 2.47787430 0.70715268
45  0.64708952 2.95355336 1.18494146 2.51289484 1.05996452 2.23185477
46  2.51641116 1.61994837 1.51521426 0.65365310 2.85709012 0.79448678
47  1.20546836 2.08439892 1.45739248 2.01492112 2.03889798 1.63157796
48  2.02675716 2.15576528 0.95656851 1.18546045 2.19577753 1.19242388
49  1.83938530 2.30349874 0.79314037 1.37629673 1.96472055 1.33707067
50  1.71241473 2.28114277 0.72565662 1.41304168 1.87940036 1.32938299
51  1.16735266 2.16814724 1.38112181 2.02059926 1.94361276 1.65549355
52  1.95305562 1.64596554 1.19474358 1.02522533 2.41272442 0.83238688
53  1.94347104 1.88812781 1.07082027 1.11765387 2.28543708 1.00549729
54  1.50733319 2.38685343 2.10056652 2.58860992 2.42321601 2.17735502
55  0.99208826 2.43828253 1.35141764 2.21402872 1.71784669 1.86958952
56  0.96119987 2.48795797 1.14684589 2.13054886 1.55507393 1.82130986
57  1.14268166 2.32513120 1.49304319 2.19941492 1.92043646 1.83479483
58  1.59803025 3.25857349 2.58562502 3.40506541 2.39897331 3.00276209
59  2.16693010 2.09938047 1.18890268 1.20329175 2.37958158 1.20294381
60  1.09788531 2.54599939 1.59482600 2.41092885 1.84693908 2.05251859
61  1.87628525 3.11285547 2.76418063 3.39301091 2.73706330 2.97780755
62  2.71318418 2.20261066 1.61659280 1.17131086 2.85028737 1.36495554
63  1.66772812 3.04233250 2.53927664 3.23545109 2.50483121 2.82923110
64  1.48495812 2.22842061 1.86564332 2.31746499 2.32429927 1.92522802
65  1.50063257 2.86990416 2.28837117 2.99346823 2.32830332 2.59621716
66  2.86003369 2.16053489 1.78319331 1.17473803 3.02611764 1.38810731
67  1.40798723 2.16541494 1.22489501 1.81346710 1.96204414 1.51594319
68  1.66110965 3.19933778 2.58248224 3.35377373 2.45355387 2.95293201
69  2.79936376 2.12103648 1.73512625 1.14603153 2.97918263 1.34116527
70  1.85519769 2.20284764 1.04739828 1.44907104 2.10155830 1.33629669
71  1.91156035 3.16708503 2.78991190 3.43065662 2.74513332 3.01919225
72  1.16682903 2.53388592 1.31051513 2.19714927 1.70089052 1.89420185
73  1.40875332 2.80360505 2.11584542 2.84981838 2.19400052 2.46569406
74  1.57414964 2.62773098 2.20095399 2.77328071 2.41057206 2.37681895
75  1.45947231 2.87146623 2.11481165 2.87098118 2.17496251 2.50012298
76  2.40720226 2.17056899 1.50369795 1.36056278 2.62097312 1.37426212
77  1.58365182 2.22310629 1.51756138 1.98856031 2.16316516 1.68029895
78  1.63474488 2.29568034 1.29853958 1.84254001 2.04360961 1.60357990
79  2.54877218 2.30307408 1.57352926 1.40942238 2.69122056 1.48607743
80  1.30101369 2.66462089 1.54356092 2.38696115 1.82158605 2.07861255
81  1.49899933 2.68067358 2.04179042 2.69780519 2.23882280 2.32577465
82  1.84695495 2.05229814 1.39664321 1.62990712 2.30131642 1.39860821
83  1.66195173 3.39306836 2.57028051 3.44676762 2.32864323 3.06534129
84  1.38382804 2.52704262 1.43045933 2.19677011 1.87082582 1.90613088
85  2.73744346 2.21772823 1.74209550 1.33061864 2.91151695 1.45447365
86  1.38146984 2.51277133 1.53368278 2.26026996 1.93918038 1.94765586
87  1.72714478 2.47486740 2.10280670 2.55504932 2.47221105 2.18486775
88  2.70216789 2.30533221 1.74486202 1.45279822 2.86097659 1.54446629
89  2.20845750 1.98652985 1.61806137 1.53110792 2.61778878 1.37047002
90  1.49320539 2.64266970 1.73501277 2.44374608 2.04485280 2.12646375
91  2.05045065 3.19878610 2.82071284 3.42596397 2.81159458 3.02941359
92  2.83174986 2.86912485 1.81956318 1.88744905 2.76350933 2.01925846
93  1.63289845 2.53990017 1.74318704 2.33525902 2.16782548 2.02992174
94  1.70409430 2.67529978 1.42979566 2.15981660 1.94865542 1.95548640
95  2.07071044 2.59486606 1.41361601 1.88968611 2.19844264 1.79499433
96  2.60683270 2.40369035 1.71235976 1.59535174 2.75112899 1.63957615
97  1.61199001 2.57349779 1.68303457 2.31792595 2.10384548 2.02519747
98  2.41842628 2.40157027 1.59502187 1.64087908 2.58117214 1.62820684
99  1.55842112 2.76803257 1.70999574 2.47721507 1.98799640 2.19108259
100 2.81793932 2.61663868 1.85243269 1.72522620 2.87161844 1.83372704
101 2.59435729 2.79552495 1.69858613 1.91031912 2.57661661 1.96165234
102 1.67103059 2.63785150 1.83060738 2.44587797 2.19165986 2.14060078
103 2.16968942 3.11984451 2.86438610 3.38040680 2.93552303 2.98664803
104 2.58512840 2.32221750 1.76300447 1.60755728 2.78986704 1.61199001
105 1.82871210 2.41962210 1.93881629 2.34061121 2.43537587 2.01948347
106 2.71719412 2.81282636 1.78077905 1.90166826 2.69079804 1.98446363
107 1.99628391 3.27097278 2.73260320 3.40775291 2.67951116 3.02725839
108 1.66531383 2.86779896 2.05823731 2.75824997 2.22306640 2.42845918
109 1.98122062 3.52653101 2.80742773 3.60971936 2.59595850 3.23397502
110 1.96600692 3.31559651 2.71719412 3.42881020 2.62980120 3.05094295
111 1.99467924 3.17879462 2.69267268 3.32651708 2.69366645 2.94596773
112 2.97278216 2.55626698 2.01448393 1.71193174 3.07077344 1.83645247
113 1.92215595 2.68059910 1.56172819 2.15094467 2.14144266 1.97410189
114 2.90705948 2.79349174 1.95263074 1.89659564 2.90887850 2.00898561
115 3.00377067 2.79054045 2.04237145 1.90398513 3.01825812 2.03044447
116 2.96635285 2.70630438 2.02142084 1.84785787 3.01528589 1.96230161
117 1.86309896 3.33333521 2.55940513 3.34462366 2.44250359 2.98608638
118 1.98818350 2.41711222 2.07485223 2.38381211 2.59582070 2.06729658
119 1.76224512 2.94187252 2.02194126 2.73756643 2.20241671 2.44062153
120 2.00065835 2.54564633 2.13522911 2.50343399 2.58727372 2.18884484
121 2.66507019 2.40410121 1.91563146 1.77037446 2.88228246 1.75285607
122 1.99808835 2.81019014 1.66251636 2.27584370 2.17303826 2.10743496
123 2.25088878 2.36534142 1.96389320 2.10379322 2.68389081 1.88652380
124 3.11413723 1.79523598 2.77851652 2.10375561 3.76144326 1.90271130
125 2.74081915 3.32861245 1.96452030 2.44766817 2.55151097 2.48327330
126 2.98617400 1.98633369 2.40720761 1.80993929 3.44417671 1.72031258
127 1.95166910 3.10156937 1.87888091 2.65103896 2.11261453 2.44351096
128 3.25730651 1.86588857 2.95445609 2.25412218 3.92408829 2.05141281
129 2.01913352 4.20024554 2.64911299 3.85885342 1.99686195 3.58462614
130 2.74180153 2.04433985 2.37648049 2.01848604 3.27769904 1.82332292
131 2.01689741 3.99450138 2.22573239 3.43872670 1.75969189 3.24370062
132 2.71645147 2.05309483 2.38401603 2.05247483 3.26595169 1.84428226
133 2.69331381 3.18359570 1.96313434 2.37081937 2.59294284 2.38066375
134 2.89582290 2.15771342 2.31632785 1.87893960 3.29961102 1.79114786
135 3.12017745 4.21271420 2.44606183 3.24695332 2.60849137 3.30061576
136 3.39927231 1.98959775 2.80666057 1.97482654 3.89250036 1.92297431
137 2.16282891 4.05674237 2.25195689 3.44422996 1.83478158 3.27691369
138 2.92867158 2.14648797 2.38580228 1.93174794 3.35833549 1.82894806
139 3.14525287 4.08596627 2.42347124 3.12415853 2.69331381 3.18909427
140 2.83270600 2.18727649 2.38264019 2.03421290 3.29123602 1.88786504
141 2.21622409 4.40113420 2.75688979 3.99402188 2.06013139 3.74464973
142 3.48021958 2.00084643 2.97677115 2.14974544 4.03004049 2.05645518
143 2.68426230 3.06066591 2.05143234 2.36620739 2.69589527 2.33444351
144 3.34162347 2.07353710 2.83209391 2.11300793 3.85461652 2.01730159
145 2.89765122 3.97874902 2.31899378 3.10675306 2.50064973 3.11194373
146 3.75672375 2.11653122 3.17607828 2.23200898 4.27464706 2.19764736
147 2.09345859 3.29507926 2.22251201 2.97252019 2.31977756 2.73015326
148 3.05182272 2.26648925 2.52961762 2.07956605 3.47328487 1.98151430
149 2.47365859 3.61272614 2.11793476 2.92277228 2.28982979 2.83169729
150 3.40960954 2.11806530 2.96115559 2.25290333 3.95529942 2.13342101
151 2.23967482 3.81468418 2.24520348 3.25425498 2.08183727 3.08425340
152 3.23592478 2.14873358 2.91914442 2.35986050 3.82801362 2.17655026
153 2.19876099 3.73143895 2.23150183 3.20771376 2.10473008 3.02495862
154 2.94993441 2.27090753 2.60653165 2.25979328 3.45822768 2.08244846
155 2.18326573 3.89951574 2.34657186 3.40287829 2.06362750 3.20250501
156 3.60368210 2.19876099 2.98794994 2.15208853 4.06239165 2.13022817
157 2.59110610 4.30292124 2.44562983 3.56915455 2.12393013 3.46847036
158 3.23511161 2.26120582 2.66981865 2.09587722 3.65720667 2.02844743
159 2.68722471 4.30113440 2.44248462 3.52363559 2.19862131 3.44846626
160 3.12548290 2.33462134 2.55354705 2.08691444 3.50969488 2.01918536
161 2.16379087 3.57181061 2.57780876 3.38752646 2.46762740 3.09764843
162 3.41024185 2.25120085 2.83277603 2.14873358 3.85117732 2.09703383
163 3.36468209 4.37701944 2.71502537 3.43923772 2.87783271 3.49542803
164 3.64400755 2.23517541 3.13630255 2.34395789 4.16074532 2.26844485
165 2.36777055 3.80778327 2.58235620 3.45102126 2.44170925 3.22199028
166 3.17133631 2.52403324 2.79257739 2.45359464 3.61649522 2.31360127
167 2.52734669 3.88948430 2.48210756 3.35644110 2.41110749 3.19788101
168 3.75975071 2.40573065 3.31531627 2.57412495 4.29030256 2.47796965
169 2.69361647 3.67452640 2.41963688 3.08978015 2.60971428 2.97885331
170 3.11785842 2.79656078 2.64108623 2.48084931 3.40901232 2.39320389
171 2.65697127 4.11098717 2.57049768 3.50786039 2.41925706 3.37430353
172 3.47312312 2.64235390 2.89896194 2.40949489 3.81846555 2.37159503
173 2.79122178 4.18992883 2.58764486 3.51076337 2.47432866 3.41354436
174 3.63337261 2.44882754 3.26049055 2.62963533 4.17553815 2.49836099
175 2.55118401 4.29419828 2.85385396 3.88227226 2.45642165 3.66224260
176 3.67112166 2.54336485 3.15692363 2.51380053 4.11147186 2.45195806
177 2.56964094 4.37792302 3.04112597 4.06977044 2.57710309 3.81235303
178 3.42445815 2.77736820 2.82827511 2.44584113 3.70753761 2.42064733
179 2.77338377 4.54268584 3.24265152 4.24803898 2.77319087 3.99259899
180 3.76352382 2.68311664 3.38199173 2.80133775 4.26117203 2.68671173
181 3.01739597 3.80667625 2.78550251 3.31417825 3.00385215 3.19689134
182 3.85488451 2.86359653 3.41636561 2.86872245 4.28462458 2.78807955
183 2.93811567 4.37090371 3.02622604 3.90418993 2.80624073 3.73130920
184 4.01062554 2.91351406 3.51211154 2.89093823 4.42002964 2.84304996
185 3.02374881 3.71180955 2.89181597 3.34657344 3.13045576 3.19125464
186 4.21751300 2.91592643 3.74788107 3.02423404 4.68427970 2.96765987
187 2.97951023 4.34525037 3.25979590 4.06265502 3.04012147 3.83203154
188 3.74862394 3.22803713 3.23712105 2.94591471 3.99815450 2.90802708
189 3.18018894 4.39326687 3.11728023 3.88093863 3.02713558 3.74628351
190 3.91052098 3.08806193 3.57786991 3.14374172 4.35077726 3.02713558
191 3.31541287 4.20925458 3.04436321 3.63471176 3.16911877 3.55169823
192 3.70496695 3.25343519 3.29039784 3.05322571 3.99577361 2.97466147
193 3.77534913 4.88968395 3.54910376 4.25982917 3.47928655 4.19309902
194 4.30241195 3.44405722 4.02880197 3.58251097 4.75864724 3.45873348
195 3.74446637 4.94576609 3.82609599 4.55106489 3.64271895 4.38940557
196 4.34389997 3.76574425 4.03272715 3.73177714 4.68130390 3.63576784
197 3.95368653 4.82072918 3.95825778 4.49092222 3.94790871 4.33920148
198 4.52388712 4.03595172 4.17238964 3.91592453 4.78868614 3.84632370
199 4.59027265 5.33691798 4.35771825 4.82675274 4.40929861 4.76711563
200 5.06876699 4.39372218 4.70035672 4.33454535 5.34971032 4.28242055
            25         26         27         28         29         30
2                                                                    
3                                                                    
4                                                                    
5                                                                    
6                                                                    
7                                                                    
8                                                                    
9                                                                    
10                                                                   
11                                                                   
12                                                                   
13                                                                   
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16                                                                   
17                                                                   
18                                                                   
19                                                                   
20                                                                   
21                                                                   
22                                                                   
23                                                                   
24                                                                   
25                                                                   
26  3.18386395                                                       
27  0.94919145 2.24963766                                            
28  2.27213259 0.91967565 1.33177162                                 
29  1.19969577 2.12648569 0.36203154 1.21621851                      
30  3.59409833 0.47268221 2.64915657 1.32405511 2.48670797           
31  0.58330582 3.74887624 1.52791569 2.84268682 1.77328062 4.16506474
32  3.28734449 0.67471879 2.34060237 1.10733012 2.12054802 0.56201933
33  0.43740488 3.48015854 1.24092338 2.56296197 1.40799912 3.86859429
34  3.97508382 0.89793523 3.02830508 1.71999269 2.84314635 0.43451239
35  0.40541110 3.00336002 0.77723811 2.08644449 0.93363436 3.38802982
36  3.51406466 0.60474891 2.56681859 1.28082551 2.37110894 0.31253410
37  0.89645978 2.69332112 0.66008617 1.79066466 0.59216267 3.03878124
38  2.86776006 0.42282014 1.93029420 0.62947853 1.78716722 0.76240959
39  1.41200676 2.25193394 0.76583630 1.39983108 0.46071734 2.55710397
40  3.40903338 0.77845986 2.46841648 1.25075789 2.24629494 0.59568223
41  1.19430538 3.17791570 1.48604861 2.40227220 1.82875735 3.63486707
42  3.72567170 0.65041334 2.79346344 1.48531004 2.64750329 0.40004180
43  1.04196414 2.28002848 0.49549946 1.40666826 0.71444571 2.69226770
44  2.48976728 0.92586005 1.56236727 0.50734545 1.38191296 1.21928584
45  0.77294181 2.56866809 0.53046456 1.67716631 0.75733706 2.97141280
46  2.94754838 0.85842868 2.01703735 0.90525506 1.78616876 0.93588597
47  1.67676215 1.88730837 1.06308033 1.18986929 1.24564505 2.33385567
48  2.36171466 1.43743775 1.48544775 0.91139664 1.19388915 1.62994608
49  2.14181126 1.61495208 1.29252768 0.96673805 0.98840397 1.84297015
50  2.02370545 1.62128623 1.16753821 0.91218877 0.87860924 1.88149694
51  1.60550115 1.91927801 0.98282866 1.18744843 1.14952206 2.35505199
52  2.39107253 1.04494819 1.48248184 0.55328481 1.32560989 1.36038554
53  2.33162147 1.23382846 1.43401628 0.69400237 1.22168064 1.49838155
54  1.90457066 2.37995701 1.58312227 1.81093749 1.84263112 2.83177265
55  1.35987295 2.15385285 0.84125561 1.36495984 1.04427655 2.58172260
56  1.29246571 2.12305438 0.68419977 1.28994320 0.82776449 2.53161274
57  1.53644992 2.09452339 1.02051732 1.36545833 1.21967278 2.52920067
58  1.74920826 3.24254295 1.90180192 2.57539657 2.23012265 3.70011244
59  2.50170136 1.38970156 1.63445078 0.97345575 1.37289724 1.56345412
60  1.41787507 2.31623846 1.04478494 1.57082359 1.27374279 2.74808405
61  2.10400982 3.17773846 2.12987675 2.60478997 2.44303327 3.63049711
62  3.04437710 1.44060406 2.17422510 1.35483820 1.88220415 1.42706117
63  1.88541215 3.04516141 1.89828916 2.42744255 2.20610546 3.49686859
64  1.88678525 2.12591881 1.42534439 1.54250773 1.62781712 2.56323784
65  1.74581550 2.81870578 1.66781310 2.17889311 1.95808925 3.26592941
66  3.20282876 1.41181247 2.32571515 1.43766704 2.04434334 1.35170259
67  1.77296102 1.76631211 1.04221419 1.04368501 1.05393696 2.15084113
68  1.82148367 3.17931400 1.91695318 2.53260365 2.23034980 3.63066107
69  3.14551394 1.37316992 2.26657044 1.37759618 1.98971791 1.33453271
70  2.16639013 1.56938005 1.33541327 0.95910790 1.11138932 1.82694802
71  2.11470991 3.21669163 2.15302124 2.64027115 2.46086167 3.66550004
72  1.43738043 2.16772050 0.89985521 1.38513105 1.00618479 2.56287419
73  1.65017845 2.69434572 1.51263123 2.02990064 1.78186089 3.13375098
74  1.87919171 2.57685334 1.64876685 1.98545885 1.90431122 3.01597397
75  1.65562730 2.72564885 1.52374243 2.05564863 1.77198297 3.15387953
76  2.71974954 1.48382451 1.88567179 1.21182677 1.64430290 1.60784819
77  1.91726444 1.88494386 1.28111575 1.26031234 1.32662217 2.26271576
78  1.92818518 1.82579988 1.22145539 1.16682903 1.15732063 2.16053489
79  2.84080556 1.58557663 2.01497700 1.35623267 1.74595727 1.65619928
80  1.51120166 2.33005379 1.10086182 1.58925567 1.22579080 2.72157296
81  1.75470462 2.53748048 1.50307981 1.90006813 1.72826042 2.96203066
82  2.19377731 1.57741471 1.42278986 1.03925493 1.33800925 1.89595348
83  1.71441280 3.30163732 1.89255566 2.61294341 2.18903656 3.74173086
84  1.63019785 2.15090078 1.09590492 1.42597723 1.15928041 2.52778597
85  3.05507244 1.49838615 2.20658339 1.41717295 1.94158348 1.50868553
86  1.64316796 2.18481474 1.14890526 1.47764134 1.25355463 2.57482903
87  2.03160991 2.35524710 1.65689963 1.81176971 1.83922641 2.76502192
88  2.99793598 1.60107277 2.17333316 1.46259739 1.91328623 1.63621371
89  2.55492622 1.46920799 1.76080017 1.14511266 1.63241098 1.71242892
90  1.70945076 2.34693565 1.31403715 1.67186199 1.43840422 2.73419677
91  2.21772823 3.20639283 2.21299154 2.65101389 2.48720420 3.63562308
92  3.02124084 2.12931106 2.29138859 1.86385532 1.98367688 2.14613220
93  1.87240064 2.22878236 1.40139648 1.60200691 1.48557397 2.60027251
94  1.87151508 2.17939365 1.30709691 1.50792680 1.23067112 2.48730643
95  2.26725347 1.98238716 1.58127946 1.43940325 1.37931710 2.20109795
96  2.87437598 1.72108964 2.08428357 1.49196745 1.83475450 1.79866432
97  1.83536446 2.23199447 1.35731926 1.58628074 1.42410959 2.59696761
98  2.67652294 1.74369676 1.90543421 1.41203463 1.67347198 1.87829794
99  1.71429157 2.41412107 1.33218512 1.72802197 1.41203463 2.77920817
100 3.05610530 1.90441031 2.28362782 1.71686779 2.00503296 1.92247879
101 2.77376927 2.09309380 2.06823231 1.73595807 1.79154535 2.17984956
102 1.88079543 2.33648368 1.46343736 1.71278504 1.55792048 2.70625130
103 2.36188110 3.14151446 2.29113759 2.63238643 2.54759033 3.56029998
104 2.86606374 1.67781893 2.07823412 1.46452982 1.85656571 1.77773093
105 2.10929725 2.17700679 1.61910897 1.64854280 1.71200889 2.54637633
106 2.90383110 2.09834878 2.18576069 1.79486812 1.90002754 2.15308647
107 2.11120728 3.21357669 2.12641573 2.62337118 2.38357089 3.63376724
108 1.81971244 2.63100351 1.57632608 1.99078105 1.73712664 3.02016460
109 2.01031660 3.44257471 2.16060260 2.80043800 2.43094014 3.86735998
110 2.06088700 3.24422863 2.10230173 2.63705444 2.36081354 3.66499661
111 2.13571194 3.12522383 2.10368697 2.55136948 2.35372395 3.54298252
112 3.23309055 1.86116232 2.44251553 1.77797340 2.17463411 1.84141179
113 2.08956989 2.16636435 1.50989302 1.57040713 1.40631904 2.44243519
114 3.11320424 2.08197795 2.37422129 1.87830727 2.09121631 2.09250362
115 3.21864278 2.08281838 2.47069487 1.92847075 2.18916515 2.07067244
116 3.19464367 2.00812582 2.43612295 1.86491405 2.16334263 2.00340364
117 1.91331574 3.19210722 1.95611461 2.54718732 2.19217175 3.60297381
118 2.26920558 2.19720045 1.77755971 1.73059858 1.86265371 2.55317030
119 1.87407062 2.63933492 1.60337506 2.00066517 1.71151425 3.00236649
120 2.24935285 2.32424280 1.80837693 1.83900114 1.90248199 2.67932509
121 2.93019438 1.79974631 2.17463439 1.60322919 1.97397161 1.90166826
122 2.12850007 2.29460889 1.59748452 1.70654900 1.49506424 2.56103084
123 2.51881676 1.98006537 1.89173067 1.60574792 1.84731850 2.24979516
124 3.53282738 1.75235525 2.80023803 1.96683198 2.77902839 1.91188680
125 2.79631509 2.63703150 2.24743959 2.19787546 1.98087121 2.73521352
126 3.34961571 1.61713307 2.56869983 1.73868293 2.45459177 1.70726433
127 1.99041506 2.64525215 1.64752659 2.00550361 1.62087837 2.94310588
128 3.67743422 1.88517026 2.95977898 2.13119184 2.94947497 2.03325944
129 1.67986984 3.85382362 2.08473140 3.06286210 2.23762842 4.22614623
130 3.09389774 1.78014868 2.38834235 1.73792649 2.34111361 1.98144620
131 1.72306380 3.51169541 1.86925772 2.73370909 1.87990356 3.82523124
132 3.06811625 1.80729044 2.37435423 1.74821664 2.33782780 2.02113704
133 2.77780027 2.51862837 2.20507287 2.10050679 1.96135254 2.62928931
134 3.22328466 1.73447791 2.46815038 1.74310612 2.34409360 1.84179857
135 2.99684959 3.49879712 2.68916630 2.96499873 2.42282124 3.59663047
136 3.78815419 1.72900750 2.99166899 2.05259930 2.88074368 1.72987134
137 1.87654789 3.53887936 1.96922398 2.77909207 1.93706429 3.82932895
138 3.26126825 1.76155337 2.51442796 1.78816769 2.40410121 1.87496248
139 3.06090755 3.36952230 2.69397369 2.87745106 2.42008081 3.45086589
140 3.15626309 1.84440907 2.44523884 1.80245570 2.36313148 2.00270935
141 1.83570164 4.01384846 2.24351561 3.22261484 2.35842155 4.36746146
142 3.87832904 1.85196750 3.10615797 2.18721343 3.02650898 1.88055406
143 2.79605829 2.44751029 2.21741723 2.06212288 2.01535003 2.57738197
144 3.71638735 1.85028055 2.95672539 2.09756130 2.86929784 1.90192363
145 2.79220614 3.30309961 2.47593476 2.75563003 2.24373187 3.43446523
146 4.15637262 1.95526706 3.36114512 2.38224751 3.25730651 1.90210456
147 2.09542948 2.91610447 1.88431821 2.29866287 1.92494076 3.23160481
148 3.37036761 1.90332206 2.64421451 1.94424550 2.53783908 2.00211292
149 2.40206311 3.02500421 2.09621067 2.43105632 1.94589176 3.23053339
150 3.78622460 1.96166833 3.04774044 2.21140720 2.98078177 2.02833062
151 2.06340436 3.31122505 1.99548387 2.61824677 1.95463019 3.58864236
152 3.60399777 2.04707287 2.91739919 2.19071670 2.89098481 2.18951221
153 2.04707287 3.24676587 1.96089672 2.56123872 1.93493766 3.53159175
154 3.27113963 2.02315050 2.60352561 2.00189395 2.55688948 2.19432158
155 1.97006621 3.43753085 2.00709810 2.72004688 2.01718991 3.74055378
156 3.97430353 1.92821942 3.18693983 2.26444304 3.06450570 1.88905615
157 2.31484785 3.71359185 2.32231083 3.00716339 2.20823053 3.94662650
158 3.56625207 1.91132675 2.81961306 2.04586111 2.70288326 1.96293554
159 2.43461760 3.68658391 2.38437325 3.00460605 2.23934123 3.89762849
160 3.43451793 1.93665756 2.70146282 1.99201126 2.57648320 2.00638167
161 2.11004180 3.28921598 2.09858268 2.65408620 2.22709897 3.64138918
162 3.75671339 1.94215429 2.99713041 2.16350384 2.88079855 1.95768604
163 3.23592565 3.67089272 2.93759733 3.17593861 2.68206720 3.75298980
164 4.01768843 2.06734917 3.26440758 2.38527734 3.17793229 2.07406379
165 2.23780082 3.41650256 2.21176862 2.77486211 2.25742571 3.72315066
166 3.45689923 2.24374862 2.81027380 2.23804825 2.74430121 2.37234594
167 2.38085421 3.39219360 2.26684493 2.76557870 2.21625038 3.64574304
168 4.12010325 2.28296919 3.40092738 2.57498259 3.33214646 2.30613562
169 2.63817423 3.13583546 2.34493509 2.60475851 2.23215432 3.33782570
170 3.33571195 2.37352059 2.71169683 2.25793061 2.59616513 2.48100432
171 2.46009590 3.57850671 2.39073112 2.93756283 2.31568297 3.81696914
172 3.75371292 2.26378754 3.04957204 2.36456293 2.91850389 2.28485913
173 2.59432608 3.61539112 2.48737349 2.99193200 2.37061881 3.82538855
174 3.97868913 2.33392338 3.29540771 2.54800886 3.24629780 2.40418157
175 2.28924295 3.88189322 2.45175307 3.18664439 2.50398699 4.19138360
176 3.99302863 2.29079742 3.27787478 2.50678854 3.17723528 2.30189925
177 2.30263539 4.03238364 2.55305467 3.33207310 2.66278548 4.37009228
178 3.67297817 2.34362164 2.98863878 2.37541344 2.84211116 2.36938569
179 2.50055304 4.20368071 2.75952050 3.51980767 2.86723621 4.53547310
180 4.07875338 2.53083193 3.41785003 2.71768154 3.35943380 2.58632956
181 2.97801071 3.31339264 2.68879634 2.86064478 2.59820486 3.49910164
182 4.14195780 2.64040910 3.48432049 2.80802479 3.40106618 2.66826672
183 2.72628367 3.91353899 2.74620550 3.30096021 2.73313483 4.16970337
184 4.30322809 2.67528068 3.62184251 2.89496523 3.52049186 2.66226099
185 3.01841845 3.28910562 2.73185158 2.86667466 2.68407146 3.49550772
186 4.53761630 2.76587566 3.84659775 3.06253313 3.76135272 2.73938137
187 2.80624073 3.99656735 2.86986121 3.40998097 2.93134027 4.28853137
188 3.94488271 2.83267916 3.33909003 2.83718507 3.21025141 2.86082147
189 3.00560949 3.90228031 2.92805692 3.35287778 2.87004625 4.11660786
190 4.16820037 2.90150371 3.57512696 3.00383066 3.52035343 2.96819760
191 3.21332616 3.67454292 2.98256134 3.21319659 2.86680761 3.83412107
192 3.89495801 2.90751922 3.32762896 2.88031462 3.22978254 2.97306036
193 3.57596003 4.33211204 3.47494241 3.83488249 3.35751570 4.48328688
194 4.54713458 3.31814364 3.99307549 3.44517820 3.95569261 3.37721428
195 3.53930774 4.52351156 3.56005354 4.00552038 3.54863712 4.74505141
196 4.52275648 3.53094549 4.01181116 3.57147780 3.94809513 3.58304904
197 3.82507210 4.42796253 3.73445463 4.00844972 3.71228985 4.61950978
198 4.66915371 3.75023379 4.17534298 3.77116814 4.09147687 3.78259328
199 4.44154200 4.83852649 4.28753276 4.47680542 4.18207924 4.94600536
200 5.22630519 4.15085160 4.71978875 4.25168885 4.63418887 4.14529622
            31         32         33         34         35         36
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24                                                                   
25                                                                   
26                                                                   
27                                                                   
28                                                                   
29                                                                   
30                                                                   
31                                                                   
32  3.86447511                                                       
33  0.51396221 3.52139686                                            
34  4.54596075 0.77493006 4.22971586                                 
35  0.88492584 3.04152046 0.48161508 3.74810279                      
36  4.08640693 0.33018113 3.76014580 0.47704433 3.27862391           
37  1.39177124 2.64307882 0.93539706 3.37467128 0.51580654 2.89891639
38  3.43146029 0.66203858 3.13877519 1.13170441 2.65922909 0.71590764
39  1.93614501 2.12994318 1.49332835 2.86631476 1.05128892 2.39007869
40  3.97868482 0.28662595 3.62813601 0.69070312 3.14849186 0.28688577
41  1.28918107 3.48992781 1.48838589 4.02850392 1.41756094 3.62364145
42  4.28335454 0.82477011 3.99485293 0.46981903 3.51605091 0.51362614
43  1.54626801 2.43027814 1.30991292 3.06057150 0.88493322 2.61242073
44  3.04949595 0.91968966 2.72115283 1.53601954 2.24168658 1.07911450
45  1.26541123 2.67802797 0.99896875 3.33456141 0.58830574 2.87789334
46  3.51268663 0.50942578 3.15309267 1.15319908 2.67498218 0.69440670
47  2.13490867 2.22276914 2.00438424 2.71507865 1.61150450 2.32263287
48  2.91521630 1.15895048 2.51158357 1.87690650 2.04558777 1.41033081
49  2.68983172 1.38348751 2.27777356 2.10714636 1.81564940 1.63703107
50  2.57298076 1.44862938 2.17181480 2.16472900 1.70502350 1.69244206
51  2.06974938 2.21084336 1.91165957 2.72792706 1.51089706 2.32300096
52  2.94063468 1.09550521 2.62106431 1.67512563 2.14533236 1.23154000
53  2.88163291 1.13965088 2.52473059 1.78225361 2.05053443 1.32311186
54  2.22548585 2.81042511 2.24324054 3.20860715 1.95717646 2.86467287
55  1.81059302 2.39385304 1.64677717 2.95046239 1.26142033 2.52948463
56  1.77875896 2.29016477 1.54349401 2.89054351 1.12189717 2.45124209
57  1.96782466 2.38529607 1.83548631 2.89852790 1.46265377 2.49574307
58  1.82879261 3.63106588 2.03287587 4.08385481 1.93929219 3.71748686
59  3.04376001 1.13198413 2.64987823 1.78350152 2.18592444 1.33382739
60  1.80761420 2.59075157 1.70007103 3.11381714 1.36475239 2.70733584
61  2.22225840 3.62062132 2.40434705 4.00570126 2.26941328 3.67241610
62  3.58972634 0.93673103 3.17325508 1.51757468 2.71624952 1.13101701
63  2.03102898 3.45313351 2.17797972 3.87141683 2.02729398 3.51982209
64  2.26708034 2.50871719 2.19669612 2.92554002 1.85711841 2.56724087
65  1.95662140 3.19928950 2.03745013 3.63654834 1.83943721 3.27349436
66  3.74778348 0.89984264 3.33768667 1.39971609 2.87882825 1.04789445
67  2.26358655 1.93476390 2.00293342 2.48482619 1.56655902 2.06097467
68  1.92375708 3.56754646 2.09341979 4.00513562 1.97729500 3.64412946
69  3.69060029 0.88549040 3.28428800 1.40154552 2.82401223 1.03559609
70  2.69446951 1.45033832 2.31492538 2.08979722 1.85478975 1.63699915
71  2.22175292 3.64877982 2.39844641 4.03500047 2.26977723 3.69989668
72  1.88541215 2.32995890 1.64954023 2.90343335 1.25190691 2.47310775
73  1.90170812 3.03945427 1.92527828 3.49737624 1.69588114 3.12236854
74  2.15283702 2.96781121 2.17368579 3.37674013 1.91944924 3.02503780
75  1.90074354 3.04117921 1.89644191 3.50578923 1.66877014 3.12615893
76  3.24161782 1.22655896 2.85028737 1.76993067 2.39782751 1.36403547
77  2.36400658 2.09443146 2.13722968 2.57993240 1.73266737 2.18329619
78  2.40583598 1.90321741 2.09965259 2.45414409 1.66969940 2.03035511
79  3.36239960 1.23158203 2.95068558 1.77952949 2.50379199 1.38597500
80  1.90275106 2.50875370 1.69901992 3.05173225 1.34720152 2.63399127
81  2.04784564 2.86398247 2.00844365 3.30979613 1.73786830 2.93777488
82  2.68621321 1.67388313 2.38594717 2.17763341 1.94426407 1.77032127
83  1.77172640 3.63516522 1.92266672 4.10415679 1.84197712 3.72592060
84  2.05882215 2.30197037 1.81375802 2.84817127 1.42654314 2.42799217
85  3.58356990 1.10402606 3.17793892 1.58820281 2.72576074 1.22598520
86  2.05382443 2.37993366 1.84733755 2.90252041 1.47647396 2.49242374
87  2.35746912 2.70524271 2.28653665 3.09583842 1.98056911 2.74816627
88  3.51528813 1.24409065 3.10809040 1.72333954 2.66302131 1.36155096
89  3.05016069 1.50200087 2.73106358 1.93739657 2.28739564 1.55993658
90  2.07225212 2.55725876 1.89667893 3.05398403 1.56419487 2.65572464
91  2.33399114 3.60908142 2.45629900 3.98053132 2.31316946 3.64885362
92  3.50885078 1.67356545 3.05133252 2.20915053 2.64536916 1.85078114
93  2.25372176 2.42988188 2.05463784 2.90546523 1.70261015 2.51560166
94  2.30173717 2.18808543 1.96629140 2.75535659 1.57657522 2.32971734
95  2.73638785 1.83462327 2.34140114 2.41042752 1.92703985 1.98940219
96  3.37658181 1.41848333 2.97013107 1.90803243 2.53477911 1.53754383
97  2.22338788 2.40471918 2.00349262 2.89884396 1.64630278 2.50091716
98  3.17152487 1.51076963 2.77383877 2.02907129 2.34106474 1.63779041
99  2.07278407 2.56321874 1.85202888 3.08183105 1.52226692 2.67455999
100 3.55376699 1.50398378 3.12313183 1.98235246 2.69877066 1.63621371
101 3.24854672 1.74369676 2.80789749 2.29077522 2.40346091 1.90760445
102 2.23778553 2.53760064 2.05044127 3.00784908 1.71832572 2.62105716
103 2.50434537 3.55277437 2.59996093 3.89314646 2.43232011 3.57614368
104 3.36288174 1.44858297 2.97580977 1.89737570 2.53986041 1.53654270
105 2.48180579 2.43630023 2.31430018 2.84384003 1.96580434 2.48478096
106 3.38296901 1.71041111 2.93806401 2.23924060 2.53230514 1.87082582
107 2.22176360 3.57063613 2.31167493 3.96953847 2.17466128 3.62260704
108 2.09961474 2.87273975 1.98872799 3.33457404 1.72288834 2.95337875
109 2.04633241 3.77474921 2.17682696 4.20914589 2.10138585 3.84584499
110 2.16016422 3.59073834 2.25253567 4.00189494 2.12584354 3.64900366
111 2.27195564 3.48731712 2.34470553 3.87613956 2.18677250 3.53372800
112 3.73392715 1.46303914 3.31327078 1.86418188 2.88378544 1.55510447
113 2.51426127 2.14427050 2.17060705 2.68177419 1.78573349 2.27045890
114 3.59661607 1.67016551 3.15634293 2.13806393 2.74606780 1.80293302
115 3.70390995 1.66106715 3.26578611 2.09465862 2.85355319 1.77864400
116 3.68286878 1.60921132 3.25294917 2.03341880 2.83550696 1.71639302
117 2.02552857 3.48789136 2.06826990 3.93222927 1.93649143 3.56227214
118 2.63288783 2.46728025 2.47035027 2.83589388 2.12627777 2.49559142
119 2.16344405 2.81893348 1.99427145 3.29500420 1.71971090 2.90747093
120 2.59023475 2.58424073 2.43602106 2.95980457 2.11035686 2.61713505
121 3.40884057 1.61319506 3.03231289 2.00856065 2.60794453 1.67256907
122 2.53147021 2.25801045 2.18455338 2.78935526 1.81922119 2.38276985
123 2.93726486 2.09578075 2.66787429 2.46831484 2.27969136 2.12650041
124 3.97682968 2.08593890 3.77272538 2.03474894 3.35889522 1.92069543
125 3.20505090 2.28977622 2.74481366 2.83980169 2.40545979 2.46168410
126 3.82367909 1.68992813 3.52932565 1.78550025 3.09786387 1.58776405
127 2.31493993 2.66130807 2.01167031 3.18878069 1.71436744 2.78329246
128 4.11153259 2.23888968 3.92139429 2.14175304 3.51384190 2.05844320
129 1.58600649 3.94984368 1.53336921 4.53283726 1.61840019 4.10381035
130 3.53221499 1.98087121 3.28720001 2.13927854 2.87980408 1.90480369
131 1.82766989 3.47035805 1.52158841 4.09068730 1.46671084 3.65121428
132 3.50088280 2.02563951 3.26451642 2.18783582 2.86105798 1.95131797
133 3.19131877 2.21810381 2.75177443 2.73871580 2.39927797 2.36631282
134 3.68762987 1.75373885 3.37888093 1.93190640 2.95591048 1.69331083
135 3.29869325 3.10153547 2.81099575 3.70002676 2.59821792 3.31452569
136 4.26452966 1.82913506 3.98148792 1.72147492 3.54696555 1.64950106
137 2.00144189 3.45303922 1.65770643 4.07653594 1.58776265 3.63896299
138 3.71989366 1.81671082 3.42328487 1.96600692 3.00340876 1.74225590
139 3.38748883 2.96290226 2.90085451 3.53908177 2.65951889 3.16491455
140 3.59770142 1.95253879 3.32133495 2.12548433 2.91304570 1.88751706
141 1.72716648 4.06339133 1.62500029 4.65855278 1.73394869 4.22614623
142 4.33951709 2.03848048 4.08598625 1.88761038 3.66019635 1.84205312
143 3.20289698 2.22520755 2.79763165 2.69215125 2.44009399 2.33500536
144 4.17321933 1.99534565 3.90780461 1.92932127 3.48606367 1.83150840
145 3.09450311 2.97727012 2.63062881 3.55736921 2.40089452 3.16669418
146 4.62814876 2.07775837 4.35651890 1.83205509 3.92390798 1.85511951
147 2.34002945 2.99850711 2.11427325 3.48157686 1.88079407 3.09499945
148 3.81679364 1.95545424 3.52340648 2.07286551 3.11223177 1.87083793
149 2.70001676 2.84717473 2.29594513 3.40519294 2.04560843 3.00359591
150 4.23026077 2.15392191 3.98451750 2.06237849 3.57072870 1.98066230
151 2.25264175 3.24391128 1.92389744 3.81753184 1.77016036 3.39972221
152 4.02255439 2.31035407 3.81063601 2.28461604 3.41462177 2.16087158
153 2.24404610 3.20362453 1.93247904 3.76478358 1.76566830 3.35057921
154 3.68701724 2.19874109 3.44417671 2.31716557 3.05285921 2.11045290
155 2.10284112 3.41706836 1.82644757 3.98834828 1.72104016 3.56868324
156 4.44468015 1.97694403 4.15141351 1.83414270 3.72168858 1.79330547
157 2.46259857 3.52500543 2.06419546 4.14771097 1.98163276 3.72084748
158 4.02042913 1.94743855 3.72265234 1.99182253 3.30571812 1.83414270
159 2.61107706 3.46118678 2.19066131 4.08232926 2.08373931 3.66044486
160 3.88479757 1.93778932 3.57574359 2.05299473 3.16315220 1.85649030
161 2.23687936 3.45307028 2.13415426 3.91658030 1.99494914 3.53811657
162 4.21476545 1.98959254 3.92149134 1.95165386 3.50096711 1.84428226
163 3.51945921 3.27490629 3.04394241 3.83345236 2.84141286 3.46727382
164 4.46749352 2.20969804 4.20695153 2.05121942 3.78935314 2.01701167
165 2.37136442 3.46519091 2.16603156 3.96227647 2.03490505 3.57293652
166 3.85957329 2.35460399 3.60002601 2.45225554 3.21959308 2.26424782
167 2.56715939 3.31938557 2.25299049 3.84676846 2.09214727 3.45136345
168 4.54971720 2.45148203 4.30579522 2.28878565 3.90162027 2.25917235
169 2.90773539 3.00599131 2.54978644 3.49617161 2.31227121 3.12296693
170 3.73465100 2.34091118 3.42156695 2.54807410 3.05100326 2.30933906
171 2.62319766 3.45808003 2.28355759 4.00828118 2.15492342 3.60709878
172 4.18531828 2.22866033 3.87161567 2.27441044 3.47376152 2.12889399
173 2.77770285 3.43725207 2.40044140 3.99633098 2.26211466 3.59715522
174 4.39025972 2.53065690 4.16183448 2.42641687 3.77049096 2.35830488
175 2.30780661 3.89869813 2.12407472 4.43487641 2.10540372 4.03038380
176 4.42401648 2.35479387 4.14478403 2.27531213 3.74285105 2.19947573
177 2.25354657 4.11543759 2.16671860 4.63418058 2.19127899 4.23473570
178 4.09793188 2.25499601 3.76631397 2.36505408 3.37663795 2.18758578
179 2.43076684 4.28644966 2.35649784 4.79131478 2.39397273 4.39889932
180 4.47742837 2.68167210 4.23909405 2.58953144 3.85806165 2.51883762
181 3.22397055 3.21559683 2.90262649 3.63127337 2.67609186 3.29394265
182 4.53963428 2.71677489 4.27560574 2.64500924 3.89775564 2.56811713
183 2.80872529 3.86659642 2.56070447 4.36273022 2.48440532 3.98243024
184 4.71263312 2.71448573 4.43367800 2.60167840 4.04798953 2.55462489
185 3.25402003 3.26879779 2.98152458 3.63838316 2.75313741 3.31808469
186 4.94810365 2.86015781 4.68992192 2.66270449 4.30059993 2.66712229
187 2.84461931 4.06064397 2.70333174 4.50318926 2.64218130 4.14197776
188 4.32406156 2.75610930 4.00602783 2.84240638 3.65182299 2.68469473
189 3.13504012 3.80494258 2.84508843 4.27191261 2.72848296 3.91092005
190 4.52941397 3.01563048 4.29219211 2.97271354 3.94063318 2.87753260
191 3.42500770 3.51284066 3.08131599 3.94392665 2.89441988 3.60746414
192 4.25188375 2.89294173 3.96217795 2.98343107 3.62221000 2.81765337
193 3.70760586 4.13038888 3.36919108 4.58384710 3.26243506 4.24343987
194 4.88027674 3.45736038 4.66700523 3.36585128 4.33458885 3.30281256
195 3.58105332 4.48088811 3.37232982 4.89322181 3.31642533 4.55765266
196 4.83528651 3.57775845 4.58995759 3.56463860 4.27929190 3.46159218
197 3.92129072 4.39865674 3.70533512 4.73454877 3.59356130 4.43868395
198 4.97246484 3.73915688 4.70592155 3.74540730 4.40650553 3.63749075
199 4.57256983 4.66401344 4.27001299 4.98951200 4.14537473 4.71709794
200 5.52881631 4.14267636 5.26772570 4.06675816 4.96675026 4.01250520
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38  2.33251671                                                       
39  0.56480245 1.87352710                                            
40  2.74553901 0.72905106 2.21639604                                 
41  1.79444320 2.90969908 2.10541985 3.57467523                      
42  3.18099431 0.86546576 2.69658469 0.71890399 3.67243228           
43  0.87297055 1.93637997 0.94536441 2.51086155 1.21819090 2.76693993
44  1.88666714 0.50725187 1.40388717 0.95906472 2.63425964 1.30140488
45  0.68468973 2.21876196 0.93694825 2.76192751 1.17764746 3.05723111
46  2.26972968 0.56276364 1.73914181 0.48759776 3.15684965 1.04625140
47  1.59548054 1.60870501 1.50951448 2.28585054 1.32615550 2.35011099
48  1.59839460 1.05452522 1.04377279 1.19992763 2.76076301 1.75743173
49  1.36216659 1.22409375 0.80501498 1.43568387 2.59246911 1.97049769
50  1.26866543 1.22409375 0.72460761 1.50538248 2.45019128 2.00146298
51  1.47677668 1.61372498 1.38420753 2.26702329 1.32984833 2.37180515
52  1.81124173 0.62635993 1.34754408 1.11342750 2.49161164 1.40494233
53  1.67045830 0.81479547 1.16446260 1.15481150 2.54985248 1.56612315
54  2.09073645 2.16349838 2.12053477 2.86081604 1.07608837 2.80170887
55  1.27321231 1.82837923 1.26411087 2.45235427 1.15726274 2.61019333
56  1.05323020 1.77031834 1.00482872 2.34981038 1.32311371 2.57829636
57  1.48091312 1.78836069 1.44493843 2.43579753 1.18069203 2.53640538
58  2.26760170 3.00546693 2.50033335 3.69277597 0.56181009 3.68820037
59  1.75935110 0.99028455 1.21233522 1.11008413 2.80655347 1.63085521
60  1.44567626 2.00322414 1.48266327 2.63806153 1.00607269 2.75240987
61  2.55095524 2.97349158 2.71867596 3.67022214 0.93925889 3.58888640
62  2.25501779 1.14660282 1.69103645 0.84992658 3.39653996 1.50791766
63  2.29889319 2.81460860 2.46647902 3.50124452 0.75584135 3.46299357
64  1.90478322 1.86835049 1.85429423 2.54027824 1.26541123 2.52243823
65  2.06824393 2.56724087 2.20194247 3.24264421 0.74118343 3.23425876
66  2.42512095 1.14717067 1.86248467 0.76144265 3.51129511 1.40088969
67  1.38646703 1.39408668 1.13590124 1.95540522 1.72125668 2.15412079
68  2.27805203 2.93622830 2.47969721 3.61606386 0.66671817 3.60132960
69  2.37494220 1.09459231 1.81369359 0.75127944 3.44275990 1.38062311
70  1.46499707 1.14818955 0.95849533 1.44534801 2.43756140 1.87338963
71  2.55133777 3.00192550 2.71920025 3.69057451 0.95044882 3.61555019
72  1.17962645 1.80230381 1.10123872 2.36171466 1.38176988 2.57591116
73  1.88867027 2.41807667 1.99752172 3.07542345 0.79421680 3.10210951
74  2.07662362 2.32738391 2.13223743 2.99764279 0.99908805 2.96543703
75  1.84675618 2.42969964 1.94710644 3.06419428 0.87836869 3.11215562
76  1.98612568 1.09690076 1.45157849 1.12460825 2.95078423 1.59905985
77  1.60294222 1.52733043 1.38824851 2.08510841 1.70494821 2.21629334
78  1.42879026 1.42462455 1.10757910 1.88733011 1.95639273 2.14154396
79  2.06563551 1.22158618 1.51615645 1.12175734 3.13758847 1.66599893
80  1.32973499 1.96747591 1.29186207 2.52227242 1.32533273 2.70610215
81  1.86183222 2.24534059 1.90162346 2.88069768 1.04066135 2.91078989
82  1.68143815 1.18054765 1.30406454 1.63681892 2.16952631 1.85161213
83  2.15558488 3.02177729 2.38352416 3.67054859 0.66752270 3.70770626
84  1.32477771 1.77564580 1.19049327 2.30745222 1.53055134 2.51127221
85  2.28892294 1.17424079 1.73582649 0.95390167 3.31938676 1.50140212
86  1.42319458 1.82577251 1.32541661 2.38701793 1.42604058 2.54873308
87  2.03806655 2.07537837 1.99133997 2.70018343 1.35242760 2.67986329
88  2.23206681 1.25725647 1.68684193 1.09552651 3.25556826 1.61143856
89  1.98385545 1.08185283 1.54702740 1.40752623 2.53809506 1.62107580
90  1.55695467 1.99450649 1.49785054 2.55199193 1.38360254 2.68649517
91  2.55650240 2.96512242 2.68522996 3.62060341 1.13368264 3.55156794
92  2.17292436 1.78312604 1.64299303 1.56704418 3.46608453 2.17351664
93  1.64316796 1.87192552 1.51594319 2.40797284 1.57371333 2.53498847
94  1.33929804 1.76789554 1.06900046 2.15724701 1.98545885 2.46341227
95  1.55873361 1.56254182 1.11028675 1.77139703 2.52109104 2.18598779
96  2.11597053 1.35120204 1.58698510 1.28145287 3.12243885 1.76094897
97  1.56769943 1.86405426 1.43117178 2.38294541 1.60560277 2.53953364
98  1.94062950 1.34883015 1.43028231 1.39828331 2.90501225 1.84200826
99  1.47597399 2.03918430 1.39886780 2.54672164 1.52360382 2.73269551
100 2.25226528 1.55980801 1.71469617 1.35966772 3.38205488 1.90304084
101 1.96221261 1.70973131 1.45240947 1.63879453 3.15102314 2.17727093
102 1.68187626 1.98084770 1.58046954 2.51178874 1.54930141 2.63459779
103 2.64285815 2.90622466 2.73201307 3.55110959 1.31119691 3.45595174
104 2.14797997 1.30551188 1.63695713 1.30012830 3.03800754 1.70540397
105 1.91532541 1.84929701 1.76683571 2.39942450 1.67577447 2.44568510
106 2.08176225 1.72994171 1.56299830 1.59504801 3.29087992 2.15175485
107 2.40914962 2.94177262 2.54085330 3.57226212 1.11738210 3.54841500
108 1.79394364 2.29437438 1.80004984 2.85748986 1.30673306 2.94811041
109 2.38686965 3.15734477 2.58089521 3.78455188 1.02377162 3.79841145
110 2.36897782 2.96613985 2.51355810 3.59402459 1.07915077 3.58457479
111 2.40147524 2.85625790 2.51068431 3.48579245 1.15732063 3.45253062
112 2.44602178 1.54290898 1.90700097 1.28311428 3.50588611 1.78872057
113 1.52443113 1.75320687 1.20878631 2.08571776 2.18845454 2.39443750
114 2.29712277 1.73722205 1.77133979 1.52415333 3.46486210 2.06909844
115 2.40541273 1.75165049 1.87688653 1.50006463 3.55396632 2.03579124
116 2.39522342 1.67524676 1.86582408 1.44182650 3.49829321 1.95707609
117 2.16027670 2.88504940 2.30343027 3.48534804 1.08316452 3.52873028
118 2.07109917 1.88069709 1.90672976 2.41459561 1.79790297 2.42749973
119 1.73420095 2.27777355 1.70032217 2.78658726 1.52300570 2.92498345
120 2.07507663 2.00310040 1.93654214 2.53036695 1.76010953 2.55351034
121 2.23887336 1.43462101 1.75196463 1.44814258 3.04639454 1.79128628
122 1.56649580 1.88139806 1.27242871 2.19135719 2.23439719 2.50568001
123 2.07775719 1.62038917 1.76124242 1.99190158 2.32148730 2.10678009
124 3.16758536 1.63607759 2.80468378 1.92829519 3.09193517 1.59613405
125 1.98611844 2.24343534 1.56786749 2.19040326 3.25244169 2.72788591
126 2.81020973 1.38124093 2.36794364 1.48483155 3.17077700 1.43976641
127 1.57337817 2.23964210 1.43120160 2.60500588 2.01469464 2.88110824
128 3.33593500 1.79521508 2.98282548 2.07977764 3.19062044 1.70412964
129 1.87604786 3.47257628 2.17350774 3.95129221 1.62076629 4.20655828
130 2.66666582 1.52266554 2.30146633 1.82651751 2.77738585 1.73679514
131 1.48614316 3.09965196 1.65203785 3.45598520 2.06222122 3.82363690
132 2.65993113 1.55100945 2.30702640 1.87770613 2.72805109 1.77906543
133 2.00191667 2.12184547 1.57855878 2.10349560 3.14273606 2.59335049
134 2.66197507 1.45064656 2.22273448 1.55559252 3.08923522 1.60878405
135 2.21385860 3.10666903 1.96263778 3.03753861 3.67463389 3.63429315
136 3.26041733 1.59605858 2.80966136 1.59600701 3.55383151 1.38848708
137 1.54121052 3.12113398 1.65772053 3.42995446 2.28285999 3.82885345
138 2.72397144 1.49176810 2.29636052 1.61946425 3.08577063 1.62638073
139 2.25916838 2.98182960 1.96200477 2.88537219 3.69591958 3.47706611
140 2.66584458 1.56493146 2.27217135 1.77512980 2.92298918 1.76029234
141 1.95084867 3.62032755 2.23932165 4.05671128 1.91366983 4.34921154
142 3.40746910 1.74846864 2.98443519 1.82128342 3.55104429 1.52118756
143 2.08682777 2.05199180 1.68130059 2.09041561 3.02431210 2.49601816
144 3.22762047 1.69456401 2.80478133 1.77729290 3.42475044 1.56803158
145 2.04911644 2.89627282 1.79816571 2.89816080 3.34629328 3.43617479
146 3.64446023 1.88801605 3.19480002 1.83661923 3.87104287 1.52458452
147 1.84558552 2.52857187 1.79089605 2.93564652 1.92026370 3.13996500
148 2.83988527 1.64388176 2.42000337 1.74895696 3.17278043 1.73744573
149 1.78099311 2.60554477 1.57521574 2.76650853 2.73818624 3.19057927
150 3.33552068 1.82259134 2.93250454 1.94387754 3.43226728 1.68459554
151 1.67677982 2.89399684 1.67612319 3.19254791 2.29904632 3.55028706
152 3.22675703 1.88652380 2.87181350 2.13078857 3.16164653 1.86987841
153 1.68536669 2.83252939 1.67892183 3.15037559 2.21738437 3.48469337
154 2.84754143 1.77424441 2.49123592 2.02452876 2.92849692 1.92554603
155 1.71350024 3.02648884 1.79077071 3.37531538 2.12629855 3.70026013
156 3.42539589 1.79902201 2.96710951 1.72680063 3.75396290 1.54240456
157 1.82166832 3.29110754 1.83825284 3.48274915 2.84089326 3.95012329
158 3.02065444 1.68640307 2.58382679 1.72127258 3.37192485 1.67266254
159 1.87572359 3.26531370 1.84242982 3.41364087 2.99628894 3.90510810
160 2.87177647 1.67525098 2.43595357 1.71909320 3.28063227 1.74505883
161 2.10375561 2.92663179 2.17450663 3.40559454 1.68876100 3.54353494
162 3.21461026 1.75800018 2.77134816 1.75162930 3.54026250 1.63902288
163 2.47570611 3.27968755 2.22459426 3.18740064 3.85666252 3.76281443
164 3.53325123 1.95119662 3.10904956 1.97798344 3.69446732 1.71258839
165 2.05424211 3.02207109 2.08431490 3.39891866 2.11583007 3.63299808
166 2.99992225 1.99021391 2.63446638 2.15681499 3.14823990 2.09130294
167 1.98324755 2.97826239 1.92847446 3.23992599 2.52750876 3.57409335
168 3.66855672 2.16603156 3.26590765 2.22406069 3.73980020 1.94126857
169 2.09915031 2.72572583 1.90408812 2.89672303 2.80827168 3.24872501
170 2.78524010 2.05971878 2.39978532 2.13961417 3.19953324 2.25159183
171 2.02891027 3.15957848 1.98984320 3.38205737 2.72199857 3.76182542
172 3.18135309 2.02447078 2.74818484 1.98797212 3.59104248 1.99897795
173 2.08085404 3.19504293 2.00198501 3.35733431 2.95426016 3.78175351
174 3.56252726 2.19039309 3.18688152 2.31718679 3.55844710 2.05389803
175 2.18255768 3.47935806 2.30993874 3.84480688 2.28383952 4.12318899
176 3.47915834 2.11672458 3.05833842 2.11290870 3.71513372 1.96533107
177 2.35478601 3.64546893 2.53619204 4.07050601 2.11541811 4.29409007
178 3.07164645 2.07297126 2.63785606 2.01880139 3.57178371 2.11268812
179 2.55747259 3.81785782 2.73366407 4.23327504 2.28711745 4.44817937
180 3.64533836 2.36804258 3.27007753 2.45692381 3.67879889 2.23856887
181 2.49380585 2.91983666 2.29733419 3.07772554 3.01287160 3.36313634
182 3.66135308 2.45509113 3.27094955 2.47750709 3.81147434 2.32982745
183 2.45471798 3.50630173 2.46737887 3.77582053 2.76920291 4.07308118
184 3.78986738 2.50602804 3.37779920 2.46222842 4.00906071 2.31748695
185 2.61831402 2.91174336 2.44005915 3.12662606 2.89307148 3.32977379
186 4.05708081 2.64355912 3.64913750 2.60971428 4.17566534 2.36981388
187 2.70532524 3.61381584 2.75754414 3.97016482 2.56028968 4.15930626
188 3.37819366 2.56229117 2.98511031 2.51775838 3.79503718 2.58830005
189 2.62807331 3.49634246 2.56205614 3.69040970 3.09230359 4.00509851
190 3.74435344 2.70223486 3.39625960 2.78862521 3.76609482 2.63364477
191 2.69881651 3.27606241 2.51963156 3.37251381 3.35640120 3.71168551
192 3.38658738 2.63555244 3.02807913 2.66580018 3.66591930 2.69182202
193 3.09574714 3.92796675 2.98412388 3.99633465 3.80723098 4.37609878
194 4.16422476 3.14021143 3.83786733 3.22758521 4.07341428 3.02655891
195 3.29408753 4.13213797 3.27970804 4.35228434 3.45673292 4.59562640
196 4.09107368 3.30204450 3.76880313 3.34118088 4.15483672 3.25895202
197 3.53513249 4.05700562 3.45015156 4.24239968 3.65365912 4.43036455
198 4.20168894 3.50593623 3.87549601 3.49598391 4.36892731 3.46982822
199 3.98660221 4.46494673 3.83068874 4.48400429 4.49687844 4.76942384
200 4.75911194 3.94068330 4.42185779 3.88647031 4.89290561 3.80968354
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43                                                                   
44  1.55508075                                                       
45  0.31795864 1.81478512                                            
46  2.05255340 0.52450340 2.29256695                                 
47  0.75053055 1.38038151 1.04869762 1.90150159                      
48  1.56297590 0.61429813 1.73872215 0.73036651 1.67539314           
49  1.38038151 0.75053055 1.53142061 0.96064771 1.58537812 0.24080754
50  1.23954601 0.73674777 1.39848900 1.02266170 1.45032664 0.34566564
51  0.63408459 1.33974512 0.93637787 1.86263689 0.15626705 1.58859856
52  1.42473234 0.18720306 1.69131282 0.68237613 1.23463671 0.66612053
53  1.41070801 0.31092323 1.64234991 0.67509513 1.36549069 0.41051333
54  1.22761567 2.01058762 1.43917767 2.51762737 0.68237613 2.34822777
55  0.40639706 1.50236632 0.67948266 2.02171364 0.40373802 1.65227543
56  0.25653087 1.39102471 0.54508847 1.89681840 0.59421059 1.45496171
57  0.61341679 1.50584582 0.88461014 2.02720395 0.25653087 1.72873378
58  1.56403115 2.78813921 1.60374124 3.30985147 1.41233085 3.01075969
59  1.63353346 0.55044028 1.82884270 0.64114823 1.66947560 0.27600652
60  0.59085265 1.69964523 0.79930594 2.21861587 0.46880115 1.87562971
61  1.77516762 2.81126268 1.87261734 3.32210385 1.45036827 3.10632139
62  2.21861587 0.92896384 2.40342645 0.59085265 2.23092543 0.69002934
63  1.52534795 2.61836969 1.61769504 3.13397269 1.25122640 2.88236875
64  1.03466994 1.67622887 1.28918107 2.18151219 0.42073739 2.00571208
65  1.26802329 2.34841978 1.38388523 2.86461404 0.99138499 2.59968984
66  2.35009169 0.99473254 2.54624345 0.59656809 2.31613198 0.85077383
67  0.73447547 1.01824644 1.01375758 1.51817094 0.61755627 1.19088057
68  1.54377482 2.71782445 1.60227000 3.23608206 1.35153972 2.95108542
69  2.28485740 0.92810300 2.48409917 0.54728578 2.24535318 0.79793240
70  1.26917013 0.64533811 1.46280786 0.96502006 1.35983576 0.46999294
71  1.77951319 2.82729975 1.87033408 3.33748358 1.47217576 3.11271147
72  0.45174284 1.41358917 0.67777444 1.91029004 0.64573239 1.48485384
73  1.08018072 2.16822984 1.20698276 2.68345195 0.84345565 2.39411041
74  1.23011906 2.12668071 1.40398100 2.63410102 0.81174639 2.41810507
75  1.06193360 2.15356705 1.17472673 2.66266636 0.89173977 2.35198301
76  1.81449315 0.72647205 2.01267201 0.72671345 1.79929308 0.60227046
77  0.89758848 1.19439522 1.15991216 1.67394714 0.64671603 1.41368846
78  0.93278350 0.99734372 1.15805744 1.43925930 0.93277840 1.07317309
79  1.97812981 0.88068817 2.15736471 0.76466860 2.00836554 0.63530340
80  0.62070459 1.58994242 0.78745284 2.07903400 0.73666754 1.67390937
81  1.03859081 1.98504997 1.20308877 2.49015787 0.74781648 2.21818706
82  1.17472673 0.79451876 1.42809188 1.21678459 1.01098134 1.00009401
83  1.48784166 2.75092969 1.49666226 3.26580802 1.43495047 2.92192389
84  0.66530932 1.38296835 0.86958553 1.86221267 0.73997966 1.46548304
85  2.17333588 0.92877795 2.36750478 0.68429527 2.14476136 0.78649404
86  0.69001629 1.46444857 0.90396497 1.95431387 0.65275594 1.59550003
87  1.20273998 1.85337629 1.41555174 2.33837516 0.74870171 2.14899010
88  2.11549656 0.96889787 2.30190786 0.80008360 2.10634980 0.80189216
89  1.54645152 0.75560243 1.79218853 1.03598895 1.34873689 0.98702401
90  0.83292841 1.64643154 1.00712516 2.12813572 0.76885822 1.78385703
91  1.78075213 2.76578287 1.87698145 3.26362312 1.47774073 3.03873592
92  2.28682590 1.43029883 2.39960808 1.27596812 2.46270761 0.99619228
93  0.94483409 1.52848352 1.14268166 1.99374148 0.80890787 1.68696228
94  0.99561899 1.30984649 1.12708613 1.69954218 1.19571063 1.23264061
95  1.41604808 1.08892384 1.55378246 1.32685368 1.57913950 0.86339759
96  1.99374148 1.00591210 2.16932723 0.94483409 2.01435980 0.81453061
97  0.90876643 1.49837400 1.09596043 1.95860033 0.84967268 1.62164438
98  1.78695136 0.95011946 1.96097832 1.01134078 1.82436481 0.77028860
99  0.86925329 1.65045570 1.00032918 2.10872558 0.95562036 1.71369989
100 2.22998077 1.24001817 2.38176566 1.08051086 2.30336764 0.94677962
101 2.00181911 1.30179175 2.11768245 1.27895701 2.17518828 0.91520302
102 0.99393830 1.63727904 1.16905116 2.09837279 0.88330091 1.78422910
103 1.84665775 2.72295170 1.96681174 3.20880267 1.48547958 3.01945101
104 1.94642095 0.97414159 2.13799227 0.96814566 1.91139918 0.89594317
105 1.17124093 1.56995013 1.39374264 2.02268538 0.84157041 1.81753672
106 2.13465325 1.34932117 2.25356069 1.26737860 2.29454188 0.96103866
107 1.67012079 2.70077669 1.74408062 3.19567944 1.45473828 2.92831395
108 1.08140130 1.97062321 1.20372858 2.44715430 0.98504340 2.12232402
109 1.71998345 2.88731131 1.73850663 3.38854056 1.62579002 3.06683428
110 1.64661027 2.71406972 1.70758679 3.21066038 1.46705600 2.92626485
111 1.64314133 2.62309110 1.73512625 3.11497033 1.39046910 2.86433475
112 2.37291427 1.28312840 2.54183619 1.06983557 2.38604085 1.08088384
113 1.21345307 1.30325409 1.34908104 1.64430290 1.35143178 1.22170389
114 2.31643003 1.40761345 2.45032879 1.25518058 2.42513697 1.07910255
115 2.41000369 1.44894705 2.55041503 1.26404553 2.49543397 1.15004944
116 2.36299349 1.37816914 2.51355810 1.20227549 2.42246659 1.11691107
117 1.48542307 2.59104329 1.52374243 3.08227455 1.40997427 2.75165850
118 1.33354607 1.62675952 1.55596855 2.05836571 0.96702169 1.89797515
119 1.12076062 1.91631108 1.22245923 2.36605341 1.13041475 2.00813275
120 1.34844927 1.73508346 1.55008791 2.16720479 1.03090828 1.97931820
121 1.99908204 1.12070846 2.18918462 1.14196798 1.94145366 1.08546736
122 1.29343206 1.43140741 1.40446833 1.75447463 1.46018362 1.32300501
123 1.53571990 1.31653183 1.75196463 1.64014104 1.32102151 1.50554151
124 2.50119638 1.72692214 2.78728441 1.86317798 1.94490965 2.20460239
125 2.16090394 1.80461481 2.20428811 1.82802171 2.46054541 1.36839953
126 2.32269587 1.33303322 2.57953037 1.36386780 1.96989166 1.65416874
127 1.27044438 1.79891190 1.31999258 2.16426675 1.49800780 1.70907853
128 2.65187177 1.90604958 2.93787653 2.03616220 2.07482070 2.39043689
129 1.74405771 3.04156634 1.55892921 3.48352485 2.17056899 2.92988687
130 2.06826990 1.42458399 2.32745975 1.62444199 1.65253574 1.78573349
131 1.60708704 2.61747879 1.43047481 2.98296120 2.14763009 2.36819729
132 2.04459556 1.45131324 2.30422439 1.66955929 1.61647955 1.81843678
133 2.07258403 1.69006474 2.14113339 1.73921138 2.31271842 1.32602383
134 2.21283980 1.31476038 2.45188934 1.37249132 1.92829519 1.55889830
135 2.67107192 2.64547305 2.60363509 2.67511453 3.15274753 2.11542034
136 2.75329607 1.67016551 3.02061660 1.61156943 2.33916066 2.02976021
137 1.73749879 2.62956391 1.57009337 2.96145644 2.28432795 2.33645067
138 2.24512996 1.37725291 2.48866369 1.44903961 1.93000127 1.64938456
139 2.66446571 2.53261633 2.62180923 2.53774045 3.10439190 2.01411645
140 2.14133458 1.42801600 2.38399051 1.57141788 1.80615570 1.71492829
141 1.93259001 3.16949303 1.73204113 3.58580446 2.40329796 3.00554088
142 2.83950033 1.84916228 3.11375425 1.83911904 2.36676587 2.25322218
143 2.01454866 1.64072152 2.11198135 1.73313658 2.16713429 1.39903988
144 2.68269601 1.73302346 2.94713451 1.74307423 2.25270526 2.09908337
145 2.38075168 2.42450585 2.33001604 2.51210903 2.82138114 1.96010529
146 3.11818287 2.02060087 3.39009416 1.92634774 2.66648531 2.39553764
147 1.44680767 2.12403591 1.48133390 2.51122040 1.59573724 2.10380011
148 2.36020501 1.53355985 2.59757567 1.59458440 2.04604084 1.79048621
149 1.87169249 2.12881510 1.84713745 2.34308846 2.24459740 1.81151849
150 2.75355860 1.87407062 3.02031618 1.91169559 2.28957640 2.26209698
151 1.69538743 2.41785315 1.60337506 2.74042326 2.12361805 2.18054976
152 2.58356988 1.90421815 2.84882864 2.03745153 2.08479789 2.31343914
153 1.63424615 2.36468583 1.55851335 2.70025941 2.02847847 2.16043622
154 2.26200544 1.67134343 2.50599089 1.84140285 1.86882956 1.99361152
155 1.67625450 2.55996939 1.56246961 2.91827504 2.10243500 2.36309735
156 2.94570585 1.86078953 3.20392891 1.76486615 2.55689925 2.17681144
157 2.15915392 2.79067079 2.00898561 3.03532864 2.70778454 2.40391972
158 2.55157469 1.62584624 2.79353484 1.62566642 2.22180363 1.89221279
159 2.24639680 2.76576868 2.10976879 2.97651059 2.78889700 2.34892956
160 2.43273511 1.55754203 2.66299406 1.57649473 2.15151061 1.77569409
161 1.62753618 2.55656976 1.62603295 2.98608638 1.72892852 2.59435729
162 2.73532078 1.75091058 2.98420826 1.71270960 2.37498158 2.04177010
163 2.88237798 2.82803206 2.82181551 2.84319003 3.33325659 2.32595127
164 2.98501255 2.02304201 3.24857703 1.99597365 2.54012241 2.38577344
165 1.79940385 2.59892273 1.75457135 2.96859506 2.04856711 2.51152647
166 2.46702520 1.86800228 2.69184707 1.98879687 2.13067022 2.12749910
167 1.94180167 2.51854965 1.88395751 2.81056264 2.28743564 2.30513529
168 3.09439851 2.22625770 3.35346725 2.22866186 2.63586083 2.58977117
169 2.04923150 2.28069203 2.05121942 2.49865455 2.31998357 2.05356877
170 2.39688199 1.83058716 2.58030023 1.91674353 2.22678915 1.92723168
171 2.11215156 2.68515459 2.02297615 2.95071345 2.52189185 2.40869254
172 2.76959684 1.91832374 2.98537925 1.88994164 2.50647182 2.09356304
173 2.25645710 2.71448823 2.16607129 2.93497996 2.69133797 2.38122569
174 2.96320106 2.21565756 3.21687318 2.27400006 2.50191465 2.57952688
175 2.08705812 3.03241857 1.96572301 3.39899508 2.45064905 2.87686972
176 2.98159171 2.10306930 3.22104620 2.07998626 2.61359962 2.38052658
177 2.15738823 3.22328356 2.03692645 3.62679529 2.46317524 3.13054886
178 2.71543276 1.91272262 2.91233370 1.88431821 2.51889118 2.01636358
179 2.36071586 3.39962221 2.24354231 3.79542630 2.64723943 3.30948994
180 3.07667661 2.36013445 3.31600880 2.40508209 2.65744739 2.67818702
181 2.34959719 2.51439036 2.37454737 2.71581296 2.52372145 2.35790025
182 3.15236324 2.41223658 3.37670618 2.42194538 2.79487334 2.66810677
183 2.39331208 3.06142055 2.31207289 3.35789107 2.71253469 2.87438879
184 3.30923067 2.48189871 3.53475501 2.44285169 2.96134428 2.72356638
185 2.34163226 2.54104332 2.39333762 2.77729895 2.41766894 2.47922271
186 3.52972651 2.67716504 3.76936924 2.63413974 3.12110041 2.97341510
187 2.44392532 3.21500137 2.39258296 3.56445899 2.63004349 3.15011524
188 3.02618446 2.38577954 3.19869696 2.38072128 2.85093408 2.46180373
189 2.59424459 3.05831659 2.53910946 3.29753156 2.88687317 2.84738607
190 3.20563428 2.63239840 3.41699443 2.69730154 2.84738607 2.88687317
191 2.68244622 2.85467332 2.66986797 3.01585360 2.93275253 2.62076562
192 2.98037109 2.45738570 3.15269366 2.50791172 2.77630452 2.57049768
193 3.20419278 3.48868699 3.13845173 3.63666792 3.53816858 3.19223695
194 3.60372273 3.08850356 3.80920437 3.15535743 3.22590141 3.35384878
195 3.18055309 3.72283925 3.12208265 3.97774032 3.40654570 3.57331075
196 3.62625937 3.17471583 3.79681534 3.22877201 3.36071254 3.33783195
197 3.33380791 3.68912761 3.32478196 3.90961599 3.45582196 3.59487797
198 3.80124914 3.35122861 3.95301489 3.37958974 3.59487797 3.45582196
199 3.96483871 4.08656366 3.94374895 4.19078836 4.16567029 3.87669251
200 4.34685294 3.82793398 4.50648425 3.82001450 4.10670591 3.95336028
            49         50         51         52         53         54
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47                                                                   
48                                                                   
49                                                                   
50  0.14317410                                                       
51  1.48513921 1.34765012                                            
52  0.75740151 0.71565395 1.18654860                                 
53  0.49948438 0.47852463 1.29145364 0.27555989                      
54  2.26078411 2.12524797 0.78095657 1.86165263 2.01785874           
55  1.51213025 1.36987644 0.28293753 1.34903467 1.40409561 0.86747115
56  1.29419888 1.15172512 0.45099599 1.24388084 1.25114079 1.13106377
57  1.61230406 1.47276920 0.17970981 1.34765012 1.44059885 0.69237892
58  2.87170958 2.72896718 1.45246875 2.63464116 2.73815582 0.89879778
59  0.44062568 0.50561592 1.58273528 0.57371521 0.32945117 2.31995922
60  1.74011780 1.59891746 0.39896620 1.53850363 1.60915413 0.70103728
61  2.99344843 2.85320533 1.51894117 2.65761339 2.79530354 0.81063506
62  0.90448083 1.02155402 2.15613660 1.03204925 0.86746974 2.87229260
63  2.76062745 2.61965790 1.30255330 2.46096994 2.58279123 0.66869131
64  1.92544810 1.79314769 0.48768584 1.51582822 1.66482809 0.39091066
65  2.47757968 2.33707936 1.02865358 2.18766704 2.30161576 0.48959333
66  1.07062745 1.17992754 2.24733345 1.09851930 0.96943550 2.94149111
67  1.09233282 0.96265586 0.49261959 0.84534886 0.89341556 1.22397832
68  2.81805563 2.67628143 1.38787545 2.55849365 2.66569824 0.81687263
69  1.01912920 1.12432707 2.17667191 1.02865358 0.90093704 2.87006426
70  0.41998515 0.36795365 1.25328196 0.55744034 0.33888722 2.00638468
71  2.99757866 2.85753827 1.53118344 2.66912769 2.80149298 0.84247561
72  1.33335061 1.19555171 0.49141433 1.24953470 1.25700047 1.12960489
73  2.26788081 2.12798466 0.85226832 2.00253213 2.10199861 0.50754809
74  2.31597092 2.17916421 0.85840453 1.96282431 2.09449445 0.31646386
75  2.22122715 2.08311886 0.87103696 1.98153349 2.06558769 0.65485327
76  0.73904483 0.79257968 1.71047154 0.71682688 0.55092808 2.41043423
77  1.33322887 1.21244253 0.54059251 1.01004074 1.08689740 1.11952030
78  0.97887683 0.86787766 0.80488495 0.82206763 0.80280139 1.49711790
79  0.78649404 0.87296313 1.91651931 0.90398503 0.71371113 2.62925757
80  1.52774601 1.39446414 0.59891835 1.41652154 1.43239238 1.08339187
81  2.10317868 1.96720421 0.73363896 1.81164057 1.91133493 0.56335491
82  0.97604073 0.88806809 0.91778590 0.61184351 0.65422799 1.57254211
83  2.77230949 2.63196572 1.43199124 2.58345748 2.65903198 1.02212178
84  1.33085081 1.20132540 0.59231810 1.20777174 1.21590322 1.19388915
85  0.97442900 1.06489496 2.06494647 0.97989754 0.83747887 2.75480943
86  1.46906011 1.33759441 0.51754701 1.28674839 1.32378888 1.04374842
87  2.06570406 1.93769521 0.75142457 1.67705708 1.80553296 0.61001580
88  0.96097849 1.04281841 2.01880439 0.99183844 0.83709402 2.70875191
89  1.04098898 1.00083104 1.27284510 0.61337397 0.65289497 1.87859138
90  1.65941721 1.53091119 0.65590581 1.46494372 1.50736735 1.01743949
91  2.92769855 2.79149844 1.51077969 2.59503257 2.71814721 0.90757563
92  1.07000096 1.17935911 2.35058105 1.45373546 1.22090410 3.08659691
93  1.58219667 1.46094747 0.69878326 1.34319947 1.39193022 1.10475278
94  1.09815117 1.00047377 1.04915085 1.14918184 1.06205407 1.69375036
95  0.79118308 0.76483529 1.44937049 0.98013526 0.80000272 2.15423164
96  0.92624174 0.99041238 1.91640759 0.99032887 0.82222217 2.60627658
97  1.50921912 1.38897889 0.72640582 1.31436224 1.34325885 1.18757176
98  0.83445799 0.87052662 1.71931175 0.89672980 0.72451980 2.41176214
99  1.57775202 1.45613277 0.82364775 1.47045405 1.47195661 1.25524092
100 1.06200906 1.15449186 2.20151916 1.25333047 1.06172310 2.90616639
101 0.94212814 1.01542956 2.05562597 1.27814965 1.05105801 2.77601856
102 1.67495775 1.55435062 0.77707243 1.45179618 1.49589521 1.11880422
103 2.92148407 2.78865788 1.52109573 2.55058962 2.68373263 0.92346837
104 1.00058358 1.04075107 1.81777713 0.93190576 0.80804104 2.47822654
105 1.74511201 1.62970498 0.77707243 1.38411205 1.47976890 1.02945466
106 1.01469090 1.10185617 2.17889311 1.34300751 1.11880422 2.89987087
107 2.80687445 2.67218760 1.45819099 2.52389477 2.62328149 0.99041238
108 1.99844529 1.87131286 0.90630305 1.78695136 1.84032348 1.00094118
109 2.92626485 2.78999476 1.61578689 2.71116672 2.78873072 1.19512656
110 2.79938493 2.66431950 1.46434828 2.53693245 2.62899169 1.02318039
111 2.74925908 2.61552418 1.39685624 2.44600780 2.55147137 0.92752936
112 1.22280791 1.31177217 2.29292739 1.30296195 1.14795727 2.97209722
113 1.11807098 1.04215745 1.21312144 1.14699493 1.05182345 1.83987531
114 1.17108726 1.26369791 2.31685912 1.41420509 1.21376001 3.02204050
115 1.25701518 1.35132270 2.39074980 1.46145385 1.27345063 3.08742378
116 1.23063258 1.31906921 2.32057808 1.38609144 1.20977986 3.00850511
117 2.61374675 2.48096976 1.37577523 2.41090488 2.47603792 1.10317261
118 1.84099789 1.73199180 0.91669446 1.44231535 1.54903534 1.10253643
119 1.88112482 1.76299612 1.02370779 1.73199180 1.75108900 1.26346380
120 1.91158932 1.80116553 0.97397492 1.54937054 1.64271009 1.12409026
121 1.17097808 1.19694868 1.84671700 1.05569676 0.96071597 2.47116839
122 1.21567801 1.14624711 1.31986423 1.27826517 1.17473803 1.92218831
123 1.49101054 1.42060698 1.23525686 1.14624711 1.19123383 1.68403107
124 2.30913153 2.26883209 1.96216774 1.63779041 1.83326133 2.11445509
125 1.32006697 1.37334211 2.32251595 1.75785884 1.52380805 3.02315833
126 1.77824087 1.77246771 1.93239321 1.26110252 1.36016555 2.34689597
127 1.57194376 1.48476345 1.35535919 1.63365783 1.55428696 1.84001727
128 2.49509310 2.45367100 2.09927415 1.81857766 2.01801746 2.19624781
129 2.72881201 2.61762280 2.06213294 2.87817977 2.81549135 2.17646261
130 1.85505449 1.81031395 1.62249722 1.29794213 1.43140741 1.93233094
131 2.16483963 2.08279875 2.00308503 2.47466680 2.34202322 2.40309440
132 1.88111578 1.83142218 1.58898660 1.31947927 1.45801158 1.87717605
133 1.28933315 1.32848564 2.17769427 1.62676200 1.41543339 2.85604715
134 1.66314630 1.65697218 1.87254131 1.22743899 1.28549957 2.32773476
135 2.01163130 2.06195264 3.00258733 2.60679579 2.35058182 3.69263581
136 2.17984956 2.18454639 2.32086640 1.62811241 1.74890529 2.66318659
137 2.13744680 2.06922578 2.13491187 2.49509310 2.34164510 2.58264052
138 1.75095798 1.73921138 1.88027641 1.28516107 1.36056278 2.30086890
139 1.92971502 1.98728134 2.95667080 2.49755861 2.24370814 3.65260994
140 1.79161135 1.76277541 1.75746555 1.31181163 1.40033715 2.13561587
141 2.80115634 2.70055710 2.28455379 3.01109463 2.92390140 2.45787184
142 2.39213508 2.38355041 2.36230133 1.79354459 1.94175038 2.61789275
143 1.37471145 1.38954281 2.03757110 1.55039043 1.38516305 2.66520359
144 2.22743717 2.21821521 2.23467773 1.66555658 1.79354459 2.53135136
145 1.84828200 1.87580395 2.66963305 2.35770956 2.12261788 3.32489833
146 2.55458001 2.56259179 2.65940333 1.98917707 2.12004805 2.94168759
147 1.97193670 1.87604786 1.47132666 1.94746018 1.90857664 1.77752860
148 1.88844410 1.87755784 1.99565055 1.44042614 1.51020447 2.38863752
149 1.67964320 1.65505468 2.09317641 2.01226835 1.83234159 2.67284811
150 2.38251921 2.36524893 2.27972760 1.79818060 1.94045379 2.51562052
151 2.00871376 1.94124864 1.97488759 2.27242136 2.13697575 2.42083246
152 2.40391972 2.36523585 2.08197795 1.79968528 1.95889734 2.23636688
153 1.99301453 1.91966753 1.88212488 2.21317029 2.09173920 2.30828270
154 2.05957902 2.01937495 1.83372704 1.54619474 1.65912380 2.10230173
155 2.18343118 2.10211602 1.96027051 2.40547996 2.29196438 2.32742907
156 2.32944609 2.34260870 2.53219041 1.82327811 1.92217684 2.87830314
157 2.22306640 2.19055529 2.55285498 2.67968933 2.48446966 3.07833948
158 2.01043036 2.01043036 2.17771485 1.55264103 1.62624325 2.56349879
159 2.17765027 2.15874163 2.63290138 2.66530754 2.45646544 3.19354935
160 1.88134835 1.88134835 2.09524250 1.47589281 1.52389561 2.51775524
161 2.45239940 2.34121624 1.63371340 2.37333864 2.37128596 1.69176451
162 2.17385921 2.17856895 2.33998024 1.69109518 1.77773802 2.69892946
163 2.23656107 2.28641476 3.18271519 2.78308084 2.53607902 3.85084467
164 2.52145073 2.51738256 2.52706716 1.96428422 2.09143744 2.78281547
165 2.36206884 2.27362986 1.92332740 2.42794170 2.36279896 2.16927278
166 2.19536629 2.16717332 2.08319486 1.75039317 1.82936126 2.36759484
167 2.15853390 2.10078146 2.14316222 2.37084201 2.24364667 2.56138899
168 2.71324667 2.70189027 2.62509242 2.15486634 2.28509044 2.82517837
169 1.94697919 1.91513316 2.17687703 2.14817246 2.00693195 2.67403730
170 1.97728313 1.96688865 2.14428798 1.71875042 1.71261682 2.56044378
171 2.25465004 2.20872329 2.37306582 2.54934511 2.39632169 2.82295100
172 2.20008579 2.20938343 2.44719308 1.84418134 1.87454051 2.84054799
173 2.23358250 2.20587802 2.53905749 2.59433026 2.41614704 3.04407294
174 2.68370414 2.66069070 2.49015705 2.12536405 2.25831223 2.65574903
175 2.70407851 2.61936376 2.32258005 2.86879489 2.77781710 2.54934511
176 2.49964678 2.49964678 2.57893940 2.03155967 2.11569721 2.87386049
177 2.95685576 2.85815132 2.35274755 3.05073499 2.99203117 2.44484198
178 2.11035957 2.12487975 2.44563552 1.83666895 1.83163382 2.88177833
179 3.14004600 3.04391574 2.53935521 3.22612332 3.16877672 2.60713618
180 2.77695912 2.75844301 2.63444427 2.26728532 2.37686777 2.81522691
181 2.27766480 2.24594416 2.39225661 2.37545098 2.26657879 2.80768959
182 2.76751212 2.76009523 2.75674717 2.32463811 2.40162171 2.99611736
183 2.72960741 2.66885284 2.57780051 2.90667018 2.79625102 2.87885804
184 2.83718724 2.84079747 2.92221596 2.40908183 2.47772353 3.18951516
185 2.40781722 2.36052891 2.30026690 2.38728151 2.32290474 2.62063528
186 3.09636532 3.09636532 3.09781893 2.60937974 2.70626223 3.30284883
187 3.01377557 2.93101884 2.51990412 3.04131192 2.98950059 2.63592395
188 2.53236617 2.54044801 2.77308800 2.29569611 2.28397986 3.14600370
189 2.72557128 2.68388743 2.74936414 2.91457370 2.78998704 3.10672805
190 2.96266354 2.94183316 2.80947587 2.52535098 2.60534968 2.97772402
191 2.53436585 2.51813720 2.79432332 2.72985091 2.58956593 3.23643292
192 2.62542561 2.61760616 2.70341578 2.34960199 2.35821217 3.01264186
193 3.08877592 3.07880500 3.39450233 3.37081553 3.20885459 3.82391184
194 3.42645840 3.40244421 3.19507213 2.97938761 3.06711180 3.28697908
195 3.45712198 3.40634884 3.28381559 3.56750869 3.47449521 3.49799118
196 3.39337366 3.37823781 3.30410768 3.06289722 3.10065046 3.47677720
197 3.51101656 3.46695183 3.34279472 3.53582378 3.46476474 3.53927222
198 3.50757546 3.50172643 3.52638058 3.24462114 3.25444213 3.74383029
199 3.81436251 3.80898460 4.03700133 3.96651081 3.84153969 4.38064096
200 4.02062152 4.02062152 4.04647264 3.73125003 3.75168218 4.23225748
            55         56         57         58         59         60
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54                                                                   
55                                                                   
56  0.26479350                                                       
57  0.20991374 0.45267066                                            
58  1.36123762 1.58722919 1.29784353                                 
59  1.66673351 1.48757742 1.72021173 3.01384611                      
60  0.24630979 0.48479422 0.22425555 1.14792120 1.87130712           
61  1.49812473 1.74969164 1.38195585 0.40109973 3.08432648 1.27710519
62  2.25562549 2.07959923 2.30021441 3.59708604 0.59327430 2.45878534
63  1.25607051 1.50150759 1.15367651 0.29585506 2.86399685 1.02950313
64  0.63174877 0.87187601 0.42501148 1.19144198 1.95788991 0.50990490
65  0.97790621 1.22397832 0.87329897 0.49514925 2.57825847 0.74549211
66  2.36174855 2.19817676 2.39279418 3.68862868 0.71893854 2.55675407
67  0.56994784 0.48959333 0.59260027 1.87389649 1.14857419 0.73638460
68  1.30772371 1.53938785 1.22891502 0.18524835 2.93835406 1.07928473
69  2.29237862 2.13069774 2.32214516 3.61778748 0.65555520 2.48664165
70  1.30485379 1.11502648 1.37357519 2.65337809 0.39737812 1.50575336
71  1.50067529 1.74844869 1.38699266 0.40352329 3.08425359 1.27104378
72  0.33437240 0.23170224 0.46282697 1.59392321 1.47796975 0.47066892
73  0.77941979 1.01640525 0.68468027 0.69338567 2.36854312 0.53647060
74  0.87461472 1.12894273 0.72199190 0.78564960 2.37518160 0.65135421
75  0.77233644 0.98353775 0.69745210 0.81174639 2.31613198 0.52798173
76  1.80241512 1.63976459 1.83627238 3.11713257 0.33376135 1.98107521
77  0.63205597 0.64174931 0.58561735 1.78052569 1.32634031 0.70301935
78  0.83747887 0.70710254 0.87809439 2.11206953 0.98607665 0.98226741
79  1.99619481 1.81897867 2.04174667 3.32307443 0.41984592 2.18151219
80  0.44048272 0.44430003 0.51130607 1.48957629 1.64152338 0.44582986
81  0.69318071 0.91533189 0.57528346 0.95937955 2.16910365 0.46071734
82  1.03117385 0.94043742 1.02397595 2.27843583 0.85840453 1.16931616
83  1.29631680 1.49173935 1.25632500 0.45050011 2.90555714 1.06522648
84  0.50882117 0.44048272 0.57189555 1.69172385 1.41995554 0.59151045
85  2.16822984 2.00589057 2.19787996 3.48335074 0.57554317 2.34987724
86  0.44430003 0.46692427 0.46376468 1.55079244 1.54604666 0.46999294
87  0.81588724 1.02248955 0.65034929 1.21052361 2.06558769 0.64174931
88  2.10994136 1.94447522 2.14297752 3.41861464 0.57228926 2.28510654
89  1.40552280 1.31665772 1.38387982 2.61835963 0.76244461 1.53384528
90  0.57241965 0.64013786 0.55968172 1.46087109 1.71965230 0.50484428
91  1.47697843 1.71026762 1.35819513 0.67287087 2.98053838 1.23268425
92  2.37545671 2.16355731 2.45528710 3.70040714 0.90002492 2.56129646
93  0.68075875 0.72113668 0.64708952 1.62622084 1.59690923 0.65248718
94  0.98432739 0.81948188 1.06824627 2.17599748 1.15397133 1.09735396
95  1.44666554 1.25439177 1.52220057 2.72228175 0.73055399 1.60253363
96  1.98915073 1.81971386 2.02805609 3.28673338 0.57597535 2.15591924
97  0.68633889 0.68769559 0.68307717 1.68907073 1.53557843 0.68564907
98  1.77971881 1.60943730 1.82289146 3.07165698 0.53443920 1.94227182
99  0.70969864 0.69014594 0.74902320 1.64405863 1.64548643 0.69157470
100 2.25962503 2.07402035 2.31198658 3.56887299 0.76372348 2.43320059
101 2.06959335 1.86417366 2.14683768 3.36913095 0.77656681 2.24072026
102 0.73616168 0.78567885 0.70439639 1.58920031 1.69261826 0.67756662
103 1.51600471 1.74901646 1.37951715 0.86232514 2.94390976 1.27631261
104 1.90396987 1.75420224 1.92616393 3.17281001 0.63263013 2.05632658
105 0.84254777 0.93873158 0.73767253 1.63386570 1.69969109 0.77656681
106 2.20151916 1.99727654 2.27549666 3.50727697 0.82283543 2.37545671
107 1.38897889 1.59728921 1.29474779 0.77034324 2.86620254 1.14411926
108 0.81445883 0.93190576 0.77034324 1.29474779 2.04752049 0.65120282
109 1.49874988 1.68696228 1.44146880 0.73616168 3.02151341 1.25916454
110 1.38031486 1.58219667 1.29706212 0.75857351 2.86829455 1.13622795
111 1.34401874 1.55618181 1.23844810 0.81196872 2.79651831 1.10040120
112 2.37195196 2.20250904 2.40728161 3.66483966 0.87201936 2.53753284
113 1.17929494 1.02756192 1.24173126 2.35131527 1.10056000 1.28324944
114 2.35915754 2.16668902 2.41899565 3.65945515 0.91386418 2.52860370
115 2.44188678 2.25498849 2.49521248 3.73826698 0.97565898 2.60903729
116 2.37990501 2.20019348 2.42631019 3.67083637 0.92346837 2.54390760
117 1.25446801 1.42110498 1.20445825 0.91502370 2.69460653 1.02434362
118 1.00032918 1.09908078 0.88388201 1.71539897 1.76058046 0.92668068
119 0.91983944 0.96071597 0.91669446 1.56229004 1.92017867 0.82053507
120 1.02514429 1.12472036 0.91948542 1.67281709 1.84505739 0.93104998
121 1.93064748 1.79506791 1.94233482 3.15543779 0.82266167 2.06241156
122 1.26902664 1.11874139 1.33524620 2.39701401 1.20034206 1.35879590
123 1.32130348 1.29012878 1.27360722 2.33062857 1.30629397 1.35972933
124 2.18475172 2.24874850 2.04077466 2.92487493 1.97588760 2.19270088
125 2.27520896 2.05536934 2.37887087 3.50102820 1.28170692 2.42499372
126 2.10769071 2.07657200 2.03052166 3.13386547 1.38949329 2.18092492
127 1.23998834 1.12804379 1.31231085 2.16853024 1.61301877 1.26488438
128 2.32334205 2.40007974 2.17106158 2.99451793 2.16223755 2.31788158
129 1.81248890 1.79557247 1.91457903 1.84559670 2.92455744 1.71098961
130 1.79557247 1.81248890 1.69117859 2.69123775 1.54591697 1.82214622
131 1.76807187 1.63464693 1.91299751 2.36432935 2.36667505 1.77297058
132 1.76244497 1.78829417 1.65286642 2.63251849 1.58358060 1.78089875
133 2.14558173 1.94241289 2.23264318 3.35765866 1.19742245 2.28334228
134 2.02060993 1.96994312 1.96155520 3.07795608 1.28909664 2.09703060
135 2.88378544 2.64273005 3.02995355 4.00553861 2.11683518 3.02627964
136 2.51741406 2.50552013 2.42175126 3.47331476 1.76923562 2.57950761
137 1.91168480 1.75621560 2.05984499 2.58900177 2.33259436 1.93719716
138 2.03487898 1.99832063 1.96530571 3.05418487 1.38227600 2.09999072
139 2.85568041 2.61762280 2.99193615 4.00747744 1.99631523 3.00068581
140 1.90770456 1.89000996 1.82821746 2.87098118 1.45801158 1.95208145
141 2.03343234 1.98502779 2.14807366 2.15681103 3.00074542 1.95497238
142 2.56901615 2.58695368 2.45271767 3.42364939 1.99812520 2.60608788
143 2.02397726 1.85206784 2.08454760 3.18638139 1.22116025 2.13578661
144 2.42575704 2.42998001 2.32106714 3.31977772 1.83745189 2.46686936
145 2.55181171 2.32750171 2.68483306 3.63779865 1.92209328 2.67289484
146 2.86548042 2.86852871 2.75720403 3.75415361 2.13806393 2.91486344
147 1.34823080 1.31086834 1.38516305 1.99714545 1.99762002 1.29273393
148 2.14413416 2.11231172 2.07181386 3.12570440 1.52134151 2.19744166
149 1.97002204 1.78415480 2.08145879 2.96939097 1.73108849 2.04894785
150 2.47474353 2.49846903 2.35714368 3.29495203 2.00409092 2.49752145
151 1.78957123 1.64970837 1.90703520 2.53006080 2.12834407 1.80500065
152 2.27345433 2.32730197 2.13988548 2.98885466 2.06767782 2.26585736
153 1.70220772 1.57582414 1.81010840 2.42743018 2.09917747 1.70681797
154 1.98867733 2.00695533 1.88561703 2.81961412 1.74405771 1.99677005
155 1.75586245 1.64712529 1.86849381 2.34643118 2.31760155 1.73738922
156 2.71844398 2.69827637 2.62839307 3.67266413 1.91044559 2.77874654
157 2.35479165 2.16508218 2.50613062 3.15596348 2.39704553 2.41515667
158 2.33638783 2.30428897 2.26084628 3.31753018 1.61979209 2.39394001
159 2.44763010 2.24525845 2.59947847 3.31514273 2.34189395 2.52409901
160 2.23636688 2.18915354 2.17463411 3.25017400 1.50210845 2.29968982
161 1.48766789 1.53225145 1.49709992 1.68027070 2.50447725 1.34395251
162 2.51079555 2.48683910 2.42676397 3.46817481 1.77050946 2.56581170
163 3.06878138 2.83804063 3.20450850 4.16138020 2.29714468 3.19698852
164 2.71998140 2.73130664 2.60904825 3.56330933 2.12203590 2.75112899
165 1.76024963 1.71483483 1.81815681 2.21057966 2.41931368 1.68843916
166 2.21612129 2.21601729 2.12770006 3.04610602 1.86647564 2.22419833
167 1.98634495 1.86273465 2.07890655 2.70310120 2.21665209 1.98826491
168 2.81253156 2.83858426 2.69335871 3.57760201 2.32530981 2.82307674
169 2.07286551 1.92885264 2.15097288 2.96690087 1.92760749 2.11168182
170 2.22547382 2.16456008 2.18718911 3.18267948 1.66759390 2.26499133
171 2.20329396 2.05748526 2.31373302 2.93653990 2.33843504 2.22169490
172 2.57612956 2.52784428 2.51566180 3.54346213 1.81815681 2.62695614
173 2.37652923 2.20627507 2.49654409 3.19446493 2.31790947 2.42101333
174 2.66898407 2.70683535 2.54532182 3.38145829 2.31790947 2.66288556
175 2.11932744 2.05894850 2.20556407 2.43321725 2.81521982 2.04824223
176 2.73973629 2.73004898 2.64762423 3.60561613 2.10718687 2.76901157
177 2.14780899 2.13758888 2.21236513 2.20627507 3.07008569 2.03134024
178 2.55151097 2.48214292 2.50990914 3.55523882 1.74441806 2.61049971
179 2.34099287 2.33563737 2.39832729 2.35129283 3.24080746 2.21861885
180 2.79530968 2.82178957 2.68175110 3.50825912 2.41061230 2.78671849
181 2.31227121 2.20477450 2.35845084 3.10058067 2.19642480 2.31868618
182 2.89970506 2.90117191 2.80454213 3.67246939 2.39490384 2.90340896
183 2.41178739 2.32463811 2.48841213 2.89467751 2.77727320 2.36896173
184 3.06884632 3.05909714 2.97873166 3.88225174 2.44810044 3.08494094
185 2.23944117 2.17634982 2.25366865 2.91141741 2.30051436 2.20984654
186 3.26354898 3.27562625 3.15557694 4.01001026 2.70022485 3.26854041
187 2.37061881 2.35818001 2.40201063 2.56684095 3.03549099 2.26186281
188 2.85484826 2.79637898 2.81187667 3.74836546 2.19627085 2.88337295
189 2.60948370 2.50337396 2.68172351 3.21326068 2.72906072 2.59015842
190 2.93639268 2.95667165 2.83481424 3.59274163 2.61886069 2.91062124
191 2.69376228 2.56331297 2.76050036 3.48097270 2.47721571 2.71166248
192 2.78258807 2.74724639 2.72717735 3.58540493 2.30733588 2.78623219
193 3.26145735 3.12099738 3.34773129 3.96341438 3.07645200 3.27454128
194 3.31876582 3.35666323 3.20757080 3.85527328 3.08654531 3.27063479
195 3.14675534 3.08739987 3.19194567 3.49327745 3.43874813 3.07769932
196 3.38841742 3.39089220 3.30848597 3.99126668 3.07274695 3.35135323
197 3.24775820 3.20318048 3.26458809 3.63110780 3.42509189 3.17669916
198 3.59276876 3.57386861 3.53001782 4.23540331 3.19358224 3.56556270
199 3.94492665 3.84124783 3.99040810 4.55292886 3.71018435 3.92937324
200 4.12602983 4.11523327 4.05349304 4.73131795 3.68591916 4.09489942
            61         62         63         64         65         66
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62  3.65114482                                                       
63  0.26751676 3.43835240                                            
64  1.15189862 2.51061886 0.96930622                                 
65  0.54258502 3.15455567 0.29145237 0.71590764                      
66  3.72511721 0.18685940 3.51842959 2.57741496 3.23627897           
67  1.94825398 1.73064100 1.72025529 0.86197726 1.43226456 1.82329557
68  0.34967170 3.51904754 0.17483585 1.08965170 0.37631614 3.60460991
69  3.65358093 0.17260281 3.44706401 2.50583595 3.16502808 0.07158705
70  2.74359964 0.98379200 2.51330525 1.64248175 2.22459776 1.10470879
71  0.12060748 3.65272576 0.25576754 1.15832479 0.52588348 3.72594235
72  1.73721992 2.06984162 1.48513921 0.83083518 1.19784809 2.17823437
73  0.78047665 2.94818734 0.52692823 0.58948603 0.24066397 3.03244731
74  0.73189103 2.93927259 0.53679643 0.45938240 0.29901552 3.00986297
75  0.91341716 2.89625231 0.66068299 0.64427346 0.39771206 2.98039518
76  3.16547055 0.58769539 2.94816207 2.03132714 2.66109081 0.64626384
77  1.81912420 1.88761091 1.59777609 0.73492678 1.31094974 1.96012281
78  2.19111470 1.55764250 1.95727743 1.12112561 1.66632882 1.64742002
79  3.38189937 0.43389771 3.16108544 2.25152230 2.87284087 0.50376910
80  1.62686451 2.22675534 1.37163909 0.79531572 1.08540059 2.32602802
81  0.99816852 2.74168628 0.76485394 0.46165654 0.48649331 2.81830381
82  2.31127101 1.39384160 2.09628360 1.18614892 1.81083420 1.45810212
83  0.69014718 3.49199290 0.50247424 1.19288303 0.53304731 3.58363885
84  1.80569801 2.00253213 1.55788302 0.85814778 1.26755889 2.09937145
85  3.52117780 0.34535904 3.30944068 2.37862018 3.02426050 0.32296596
86  1.65017907 2.12699761 1.40535935 0.71340697 1.11478004 2.21762259
87  1.15518880 2.61352608 0.96793826 0.38934093 0.72033309 2.67107481
88  3.46182395 0.47066598 3.24591849 2.32737056 2.95906107 0.47266036
89  2.62189949 1.18291740 2.41912822 1.49224190 2.13923005 1.20763664
90  1.55196178 2.29239027 1.30783363 0.71472238 1.02397595 2.37615007
91  0.51670525 3.54251376 0.47682943 1.11228634 0.57228926 3.60709870
92  3.79994665 0.73758248 3.56294992 2.70854702 3.27152724 0.81318349
93  1.68462531 2.15591924 1.45206776 0.76120504 1.16953086 2.22956007
94  2.29788001 1.69750577 2.04861793 1.33819873 1.76101207 1.79734540
95  2.82455619 1.18474874 2.58315851 1.77727921 2.29239027 1.28318577
96  3.33946039 0.65248718 3.11778227 2.22051799 2.82929708 0.68316478
97  1.76537834 2.09710938 1.52720580 0.84382209 1.24284482 2.17590485
98  3.13268110 0.80597536 2.90697660 2.02542885 2.61760640 0.86331475
99  1.76080647 2.21121475 1.51132463 0.94973318 1.23268425 2.30013019
100 3.63475001 0.62070459 3.40853286 2.52155567 3.11874408 0.64454832
101 3.46828233 0.86430058 3.22940295 2.39517638 2.93830091 0.94768486
102 1.65138458 2.24873679 1.41794305 0.79732757 1.14108025 2.32172706
103 0.65629374 3.49319589 0.63217403 1.09189739 0.67977493 3.54803375
104 3.20843143 0.78880510 2.99237210 2.08995861 2.70625954 0.79755882
105 1.62206598 2.23267495 1.41794305 0.68394336 1.15154566 2.28527106
106 3.60131060 0.80313786 3.36452065 2.51800456 3.07336492 0.87385701
107 0.74492987 3.43174944 0.61824424 1.10929091 0.61138090 3.50070734
108 1.37143093 2.61116266 1.13629352 0.79027312 0.88247112 2.68723122
109 0.83238688 3.59712350 0.70547392 1.32643777 0.74179196 3.67720278
110 0.77259866 3.43698910 0.63263013 1.13600592 0.62111451 3.50926417
111 0.75567936 3.35802224 0.62578091 1.03182925 0.59005345 3.42346584
112 3.70867869 0.64841344 3.49061923 2.58579902 3.20329372 0.60727163
113 2.45179380 1.60409616 2.20879503 1.47113665 1.92237084 1.68948606
114 3.73483518 0.76885822 3.50431828 2.63631054 3.21403518 0.79350886
115 3.80479824 0.77583319 3.57744157 2.70050817 3.28785115 0.77484795
116 3.72916302 0.74886752 3.50471066 2.62086000 3.21587776 0.73860066
117 1.01383054 3.26507000 0.82045003 1.12635263 0.71757467 3.34370467
118 1.67236492 2.27146236 1.48443963 0.77317189 1.23262146 2.31166225
119 1.65611899 2.47040895 1.41888644 1.00491922 1.16500802 2.54715711
120 1.64032452 2.36011081 1.44857780 0.81721596 1.20140465 2.40354110
121 3.18038727 0.98425784 2.96704740 2.08068614 2.68373263 0.97565898
122 2.50417115 1.68128121 2.25957183 1.55984633 1.97679108 1.76480677
123 2.32057808 1.74365728 2.11931865 1.30673575 1.85033275 1.76667478
124 2.74384300 2.18178475 2.64579736 1.84126127 2.44753711 2.10590735
125 3.63986927 1.38949329 3.38844447 2.65354698 3.10273121 1.47626363
126 3.04810966 1.51615795 2.88889320 1.99089976 2.63875531 1.43302302
127 2.30287585 2.11132057 2.05431010 1.52276980 1.78902866 2.19853298
128 2.79268796 2.35909578 2.70990989 1.94496194 2.52606445 2.27830199
129 2.13605895 3.46536070 1.91931065 2.10193410 1.80226788 3.58280714
130 2.58748122 1.83190144 2.43682901 1.59084825 2.19853298 1.78902866
131 2.63240385 2.84550332 2.37856753 2.19887179 2.17348329 2.97080321
132 2.52432221 1.88566338 2.37613708 1.54010788 2.14066267 1.84681793
133 3.47609953 1.35120204 3.22983849 2.48054965 2.94422049 1.42243749
134 3.01861321 1.44975626 2.84411303 1.95778482 2.58505535 1.38455626
135 4.21532200 2.19336346 3.95132710 3.35810551 3.68167088 2.30201679
136 3.34768148 1.78949282 3.21301594 2.33324445 2.98045211 1.66950516
137 2.84983530 2.77754248 2.59375371 2.35526498 2.37891040 2.90261482
138 2.98164825 1.55200260 2.81407565 1.93758055 2.56059577 1.48471295
139 4.19987722 2.04282847 3.93819128 3.30681486 3.66362717 2.14139094
140 2.79251837 1.69758810 2.62760407 1.77770102 2.37887087 1.64754733
141 2.44655037 3.51683818 2.22745170 2.35698844 2.10104022 3.63651207
142 3.26682232 2.06169759 3.15199263 2.31308718 2.93715357 1.94800616
143 3.27544365 1.43428202 3.03804992 2.28577769 2.75603262 1.47997328
144 3.18525162 1.92517579 3.05513966 2.20797593 2.82927513 1.82115736
145 3.83063926 2.08573601 3.56986890 2.98782594 3.30152448 2.18696353
146 3.59914666 2.11031806 3.48367352 2.63331545 3.26649695 1.97408011
147 2.11501164 2.49886185 1.88110854 1.51076963 1.64608471 2.57383814
148 3.04614897 1.67347198 2.88239807 2.03037465 2.63386594 1.60030572
149 3.13999079 2.06652144 2.88504940 2.34433147 2.62215200 2.16090389
150 3.13999079 2.11529040 3.02312429 2.20999146 2.80987440 2.01436784
151 2.73882824 2.56936426 2.48634249 2.15833977 2.25567131 2.67448224
152 2.81865598 2.27317714 2.71188270 1.95122767 2.51185417 2.19677011
153 2.62529345 2.55427792 2.37478897 2.04607289 2.14377514 2.65514929
154 2.70775577 1.99893578 2.56256118 1.77154967 2.33341721 1.94625768
155 2.56801591 2.78980984 2.32086640 2.10164600 2.11034745 2.89607592
156 3.54866630 1.88305736 3.41255573 2.54531257 3.17988485 1.75196463
157 3.40608858 2.74182161 3.14733584 2.81401952 2.91854495 2.86343462
158 3.22641228 1.70228606 3.06961269 2.21048945 2.82465136 1.60747129
159 3.55840603 2.64768576 3.29761918 2.91333970 3.05998056 2.76788073
160 3.18077325 1.60946088 3.01166420 2.15379507 2.75885098 1.52857240
161 1.80121993 3.03219228 1.59307222 1.53904758 1.42410959 3.10755808
162 3.35953260 1.80742268 3.21334418 2.35607927 2.97536770 1.69615208
163 4.35953516 2.35047453 4.09824973 3.51088241 3.83055791 2.44060059
164 3.40930855 2.16313053 3.29213769 2.47391249 3.07759501 2.04407056
165 2.36735625 2.89669817 2.14196336 1.95148358 1.94623800 2.97746028
166 2.94455097 2.07020393 2.79488303 2.03409660 2.56596923 2.00719391
167 2.87760585 2.62056206 2.63502980 2.28553910 2.40714395 2.70664754
168 3.40822141 2.39231276 3.30178020 2.53146626 3.09978554 2.27810541
169 3.10195377 2.25688316 2.86032716 2.34848158 2.60855141 2.32397196
170 3.14807347 1.84359995 2.96287131 2.19630234 2.71028678 1.79814036
171 3.13396988 2.70962419 2.88724119 2.54891008 2.66105864 2.80327268
172 3.46671900 1.85788722 3.30262729 2.48346253 3.05718733 1.76103258
173 3.39618597 2.63713820 3.14475608 2.75323167 2.90887850 2.73235514
174 3.21005065 2.44351688 3.10540819 2.36914295 2.90887850 2.34484930
175 2.64390911 3.28377693 2.42295882 2.37285028 2.25939666 3.37885481
176 3.47940800 2.14902650 3.34455475 2.54594487 3.12044557 2.03728820
177 2.41161342 3.57087285 2.21468643 2.32851688 2.09546272 3.66361912
178 3.50515908 1.78298332 3.32711877 2.51449411 3.07357688 1.69836752
179 2.54313926 3.73129089 2.35812837 2.49642959 2.25175480 3.81926138
180 3.34865476 2.52014285 3.23735797 2.52160876 3.03876773 2.42025132
181 3.19609525 2.49482365 2.97256087 2.48963536 2.73608993 2.53451190
182 3.53838361 2.46528566 3.41105971 2.68283466 3.20036944 2.36181586
183 3.06470155 3.17096353 2.84312875 2.64605893 2.65490960 3.24730721
184 3.75099619 2.46278006 3.62132455 2.86959051 3.40604372 2.34633469
185 2.96904701 2.63367314 2.76360348 2.32070702 2.54298257 2.66106446
186 3.84607647 2.70875059 3.73793283 3.00615961 3.53897937 2.58337220
187 2.68934851 3.47907481 2.50376489 2.46253473 2.36226127 3.54268064
188 3.69337550 2.24802863 3.52216740 2.79514954 3.28376720 2.16931353
189 3.36162958 3.05868698 3.13803996 2.83854569 2.93240047 3.12111001
190 3.44893064 2.74599309 3.33225047 2.68702998 3.13919183 2.65691968
191 3.60339794 2.72000819 3.37460519 2.92221596 3.14175896 2.76414193
192 3.51615149 2.42276918 3.35516811 2.67886656 3.12982558 2.35361488
193 4.12044867 3.29003919 3.89125824 3.53198892 3.67554112 3.34336791
194 3.68673693 3.20948898 3.59239247 3.02688630 3.42445815 3.11610300
195 3.61225933 3.77316190 3.42320968 3.27854534 3.26553853 3.82065848
196 3.87416629 3.18022091 3.75045597 3.18980863 3.56486640 3.09769354
197 3.69542733 3.71955190 3.52011332 3.30201136 3.35755480 3.74118934
198 4.14288680 3.26879121 4.00632542 3.44453856 3.81282200 3.18768572
199 4.64432720 3.86306968 4.44445776 4.09183046 4.24739081 3.87397460
200 4.61487063 3.71484432 4.49430136 3.94430168 4.31263475 3.61720346
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67                                                                   
68  1.79135123                                                       
69  1.75308190 3.53353460                                            
70  0.79598088 2.57742465 1.04019924                                 
71  1.94289715 0.30891385 3.65442222 2.73815582                      
72  0.42357750 1.52165355 2.11011771 1.09178652 1.72174268           
73  1.21997456 0.57903300 2.96148378 2.00737786 0.75359470 0.97005369
74  1.24129898 0.65555520 2.93835406 2.03593551 0.71792740 1.07770225
75  1.17371511 0.68468027 2.90992342 1.94630332 0.86735395 0.90093704
76  1.24788600 3.02426050 0.58376910 0.55691567 3.15581525 1.58498418
77  0.29356664 1.67351277 1.88956928 0.98602555 1.80143824 0.48804537
78  0.32296596 2.01741305 1.57912330 0.61779210 2.17300593 0.58423959
79  1.45191833 3.23321947 0.45569832 0.71047656 3.37197436 1.77144818
80  0.57675709 1.39863856 2.25783066 1.25328196 1.59676683 0.23820021
81  1.02865358 0.82811347 2.74740496 1.81083420 0.96244947 0.81864332
82  0.46668344 2.17667191 1.38787545 0.57675709 2.29868199 0.83950601
83  1.76790342 0.36164952 3.51359801 2.52664508 0.61341679 1.44486064
84  0.39024801 1.59891746 2.03113310 1.03446838 1.78031452 0.21763166
85  1.61431816 3.39029888 0.28050576 0.90677092 3.51378096 1.95906775
86  0.45199251 1.45191833 2.14836969 1.16859340 1.62421174 0.25565303
87  0.97537165 1.06463717 2.60010329 1.73488830 1.12219903 0.89702221
88  1.55399609 3.32186324 0.43305298 0.85197583 3.44965174 1.88391755
89  0.84262745 2.50700236 1.13996508 0.64721680 2.60701496 1.21217069
90  0.64812491 1.34586959 2.30721319 1.34419724 1.51286724 0.43305298
91  1.84819763 0.49888219 3.53607341 2.62925757 0.40676886 1.63045572
92  1.87077814 3.61395173 0.81632842 1.11077954 3.78101612 2.11100425
93  0.58168944 1.50337193 2.16068982 1.23558420 1.64613073 0.50399221
94  0.63625902 2.07905927 1.73496057 0.78115675 2.26385602 0.65765720
95  0.96166925 2.62761270 1.22808740 0.49622056 2.79801849 1.15258963
96  1.43692810 3.18656059 0.64057970 0.75777041 3.32156244 1.74250713
97  0.55157673 1.57169974 2.10771291 1.16696363 1.72694710 0.46140391
98  1.23315449 2.97142619 0.81129055 0.59191151 3.11263136 1.52356795
99  0.68489163 1.53259679 2.23343709 1.26269551 1.71538087 0.46246092
100 1.71972518 3.47185928 0.63250962 0.99445554 3.61586696 2.00452862
101 1.56699511 3.27645137 0.92302992 0.86787766 3.44374470 1.78838358
102 0.68892190 1.46087109 2.25339955 1.32915956 1.60575849 0.56521637
103 1.83232689 0.68607530 3.47727581 2.60342641 0.56133903 1.65174034
104 1.34262988 3.06554814 0.74781648 0.75139075 3.18848172 1.66084608
105 0.72291070 1.49335774 2.21581967 1.37354700 1.58318685 0.74793183
106 1.69128830 3.41446699 0.85907074 0.97041460 3.57810458 1.92595088
107 1.74273746 0.59385336 3.43046715 2.50276255 0.63530340 1.49335774
108 0.98501131 1.15611646 2.61865568 1.67571528 1.31054038 0.74781648
109 1.89804766 0.60303742 3.60755796 2.64419670 0.72150103 1.59550003
110 1.74445756 0.58878137 3.43919874 2.50036473 0.66302359 1.47923262
111 1.67705708 0.62950796 3.35313596 2.43812600 0.65248718 1.44723462
112 1.81713738 3.56154002 0.60303742 1.12504188 3.68984880 2.12551970
113 0.77148788 2.24439806 1.62926353 0.77011802 2.41397841 0.86096796
114 1.82946072 3.56111205 0.79027312 1.11295899 3.71173671 2.08995861
115 1.90469936 3.63740348 0.77814784 1.19368432 3.78177019 2.17599748
116 1.83596589 3.56782238 0.73512327 1.13952263 3.70647424 2.11774526
117 1.59445976 0.76455706 3.27479192 2.31684605 0.91550681 1.29789333
118 0.85140803 1.56537792 2.24302816 1.45462006 1.62944508 0.90828398
119 0.96165149 1.42893052 2.48090779 1.54832975 1.59236775 0.74375534
120 0.92081648 1.51828307 2.33541289 1.52763722 1.58920031 0.92369072
121 1.37448991 3.03873592 0.92994111 0.87914536 3.15384798 1.67734213
122 0.89520307 2.28725185 1.70724323 0.88390148 2.46064637 0.94380962
123 0.88395595 2.19248937 1.70316689 1.07178023 2.28157389 1.10220273
124 1.80057454 2.77882705 2.05541549 1.94771054 2.72912868 2.12327960
125 1.84737992 3.40888437 1.46055878 1.26593084 3.60187061 1.96075032
126 1.59146675 2.99641174 1.38760129 1.43400188 3.02650880 1.94632742
127 1.05083512 2.05504720 2.14066267 1.26604818 2.24440592 0.92579213
128 1.96204414 2.84555553 2.22941643 2.13303968 2.77726056 2.27267280
129 2.08797322 1.79857522 3.52440149 2.53893930 2.05545344 1.69725323
130 1.35358904 2.54406696 1.73227020 1.45842653 2.55912994 1.65823945
131 1.83565665 2.30384519 2.92122637 2.02121220 2.56626045 1.52795841
132 1.33644339 2.48393218 1.78902866 1.48109052 2.49525342 1.63175919
133 1.69684357 3.25645194 1.39882352 1.15737670 3.43594119 1.82843645
134 1.49474181 2.94006465 1.33748959 1.30532112 2.99088923 1.82754456
135 2.57946267 3.93523241 2.29867509 2.07104471 4.17081410 2.57367717
136 2.01887244 3.33166847 1.63695713 1.86357881 3.32906172 2.38085976
137 1.91933776 2.52559577 2.85723867 2.01079472 2.78465621 1.64866218
138 1.52295080 2.91287959 1.43736061 1.38554240 2.95312030 1.85179231
139 2.51616749 3.93061727 2.14019402 1.97457367 4.15596167 2.54152512
140 1.42608575 2.72479446 1.59539868 1.40117888 2.75991942 1.73019964
141 2.25784439 2.10940339 3.58184557 2.62773098 2.36536760 1.88290640
142 2.10940339 3.27643668 1.91216133 2.05666736 3.24736955 2.45629900
143 1.56189604 3.07115686 1.44670367 1.13665180 3.23019489 1.70668994
144 1.95179772 3.17158937 1.78276389 1.88037962 3.16107832 2.29051910
145 2.24609134 3.55501963 2.17167868 1.81857766 3.77978187 2.22856015
146 2.38427298 3.60820546 1.94926214 2.24723639 3.58074556 2.74276227
147 1.28108002 1.86680275 2.51441547 1.64696831 2.03916841 1.09344054
148 1.64407341 2.97900388 1.55647402 1.52063258 3.01295952 1.95579378
149 1.70159602 2.87098118 2.12382667 1.50412559 3.08119941 1.63860841
150 2.02955283 3.14230391 1.97454094 2.02432144 3.11411824 2.35377018
151 1.71397175 2.43899448 2.62711718 1.80952156 2.66841376 1.49611585
152 1.88468688 2.83087633 2.14841477 2.01904926 2.78872973 2.17260657
153 1.63076780 2.33069908 2.60546690 1.77082147 2.55351034 1.41104543
154 1.56412630 2.66318659 1.89421631 1.65840080 2.66985831 1.83514152
155 1.76639921 2.25836704 2.84519727 1.97454094 2.49217945 1.49427100
156 2.21301637 3.52704965 1.72692214 2.01941377 3.52536858 2.56545924
157 2.25602192 3.08902387 2.83013139 2.14613220 3.34255962 2.06213294
158 1.82931766 3.17086007 1.57038076 1.66320534 3.19561208 2.15490697
159 2.30656599 3.24675007 2.73903229 2.12091127 3.49764476 2.14615865
160 1.72163025 3.10515211 1.48951850 1.52933720 3.14714523 2.03500993
161 1.61138632 1.54417352 3.04508855 2.13561587 1.70555920 1.33911881
162 2.00762753 3.32035324 1.66412532 1.83920119 3.33090945 2.34218998
163 2.75083857 4.08114869 2.43955047 2.25609572 4.30844701 2.74865477
164 2.25595088 3.41042582 2.01248772 2.18102472 3.38296901 2.58780577
165 1.76051083 2.09062938 2.92274071 2.07515044 2.27809917 1.51944821
166 1.78125733 2.88538067 1.96200477 1.80060971 2.89874098 2.03269239
167 1.85687839 2.59484537 2.66178131 1.92325644 2.79987196 1.68476831
168 2.37536701 3.41812587 2.24525005 2.35656633 3.37632603 2.68352152
169 1.80257054 2.84848829 2.28505601 1.69902905 3.03200942 1.74663873
170 1.75453449 3.03049444 1.75924464 1.60896402 3.09665951 1.97677137
171 2.07458860 2.83894793 2.76368873 2.06551847 3.05789845 1.89881755
172 2.07247876 3.39081028 1.73316657 1.86078953 3.42535605 2.36142151
173 2.20347648 3.10128397 2.69933323 2.08321646 3.32476426 2.06128835
174 2.25859235 3.21803584 2.30628566 2.30727415 3.17337899 2.54210283
175 2.18801662 2.33843985 3.32765752 2.47038208 2.55157469 1.89582066
176 2.26471225 3.44744233 2.00815214 2.14959304 3.44172870 2.56692348
177 2.30422114 2.11303201 3.60794308 2.70541347 2.31131037 1.97943299
178 2.04271034 3.40519266 1.67252271 1.78137774 3.46040040 2.31256303
179 2.48814385 2.25479388 3.76452604 2.88174129 2.43871808 2.17257741
180 2.37966134 3.34088940 2.38505790 2.39881725 3.30472587 2.64564759
181 2.03737385 2.96467088 2.49682528 1.98646979 3.11673023 2.00058858
182 2.45847147 3.50535996 2.33233941 2.40029117 3.49014261 2.71958969
183 2.34673335 2.78162720 3.20361441 2.48275294 2.97181673 2.13982630
184 2.60650818 3.71726429 2.32328811 2.48816498 3.70515990 2.88340964
185 1.99309093 2.76185441 2.61737509 2.06918772 2.88406332 1.95500322
186 2.81941603 3.84330914 2.56045771 2.74588921 3.80379236 3.10504675
187 2.38867932 2.43724927 3.49095002 2.71028025 2.58317512 2.15795006
188 2.38975037 3.58766564 2.14675378 2.19437782 3.63499433 2.60451685
189 2.45736489 3.09226578 3.08394487 2.47988392 3.27144650 2.31275159
190 2.54424774 3.41843877 2.62294825 2.57536189 3.39129385 2.76041724
191 2.42763185 3.35357998 2.73525405 2.29550837 3.52197110 2.37371378
192 2.35510932 3.41877684 2.32403441 2.26072968 3.45269260 2.54427698
193 3.04669887 3.84730254 3.32106798 2.90010874 4.03310505 2.94543736
194 2.96201893 3.67554112 3.08386680 3.03518044 3.62336836 3.15487476
195 3.05456080 3.36309340 3.78223783 3.17946338 3.50704516 2.88465824
196 3.01727699 3.81270677 3.07027523 3.01604450 3.80119186 3.17780086
197 3.09286073 3.48285706 3.70471163 3.19795494 3.59039482 2.98483129
198 3.20988150 4.05891931 3.16590796 3.14844172 4.06647563 3.35908147
199 3.69298031 4.41289982 3.85607471 3.56981672 4.54740150 3.63904920
200 3.73919269 4.55186820 3.60087387 3.66693309 4.53883921 3.90226780
            73         74         75         76         77         78
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74  0.27107070                                                       
75  0.18524835 0.38701997                                            
76  2.44639385 2.43994913 2.37787375                                 
77  1.09555735 1.09075610 1.02879885 1.36070506                      
78  1.44033874 1.47276920 1.36070506 1.02879885 0.40694851           
79  2.65563776 2.65761339 2.58439697 0.22829950 1.57539107 1.22679792
80  0.84661834 0.96809121 0.74159288 1.71082098 0.51326818 0.68489850
81  0.27443504 0.32681146 0.21093143 2.22223719 0.86252878 1.22251220
82  1.59922987 1.58273528 1.53491632 0.85991695 0.50705905 0.30655855
83  0.60850431 0.78211863 0.61803395 2.97792857 1.64204040 1.95176577
84  1.03204925 1.11515713 0.93785469 1.48318576 0.35579562 0.45659900
85  2.81315551 2.79631374 2.74773224 0.37631614 1.72505756 1.40409561
86  0.88014074 0.95452047 0.78840912 1.60509515 0.34583475 0.57790956
87  0.56622864 0.45293197 0.52582394 2.08492617 0.75033765 1.14719794
88  2.74318991 2.73360672 2.66922111 0.31071120 1.65227543 1.32171498
89  1.93352672 1.89237149 1.86535882 0.63652171 0.84661834 0.65086294
90  0.78660186 0.86902479 0.66317015 1.75242611 0.47412118 0.73597744
91  0.70667195 0.66850581 0.73980717 3.01292558 1.65927937 2.03162224
92  3.04193568 3.08136411 2.95039916 0.78590734 1.99702029 1.60937170
93  0.93963805 0.97795654 0.82357393 1.60313232 0.34971695 0.61779210
94  1.52194286 1.60584440 1.40559039 1.16212990 0.65858384 0.38491472
95  2.05820565 2.11107756 1.95591055 0.67276666 1.04867083 0.65890235
96  2.60769564 2.60970757 2.52337868 0.28050576 1.52107890 1.17817834
97  1.00848184 1.06419130 0.88890041 1.54455844 0.35590726 0.55208377
98  2.39317068 2.40411130 2.30507721 0.28513909 1.31380635 0.96138436
99  0.99339872 1.09876248 0.85358669 1.66352881 0.54644552 0.67305080
100 2.89394762 2.90661524 2.80565620 0.54130423 1.81603017 1.45685043
101 2.70563119 2.74988586 2.60545175 0.62635993 1.67005162 1.28346988
102 0.91122683 0.96166925 0.77893893 1.69048210 0.46071734 0.71265481
103 0.78090573 0.68800593 0.79793240 2.95717687 1.62083867 2.00253213
104 2.48734592 2.47677300 2.40198938 0.30704285 1.39599166 1.08198767
105 0.94990214 0.91040362 0.85247410 1.67622887 0.43389771 0.77707777
106 2.84198904 2.88051032 2.74414647 0.66093313 1.79612222 1.41307438
107 0.65648678 0.69531297 0.61808256 2.88806878 1.54625696 1.89412737
108 0.66556105 0.76120504 0.49702766 2.05697870 0.77845986 1.06200747
109 0.79180293 0.90906312 0.74599844 3.05595299 1.72578859 2.04271335
110 0.65648678 0.72487813 0.60830044 2.89325644 1.55399609 1.89254331
111 0.62177146 0.63015617 0.58257886 2.81391091 1.47268498 1.82875735
112 2.98280158 2.97751811 2.89662344 0.60706660 1.89293945 1.55929446
113 1.68462531 1.74882830 1.56283289 1.04826471 0.75994841 0.46845033
114 2.98533947 3.00810794 2.88894278 0.70145965 1.91904724 1.55272518
115 3.06066082 3.07605561 2.96505203 0.74657222 1.98715974 1.62965075
116 2.99036689 2.99912977 2.89627848 0.67119888 1.91133493 1.56249721
117 0.65289497 0.79102194 0.53046456 2.71524858 1.40917227 1.70993063
118 1.04700136 0.97966843 0.95069127 1.70993063 0.55801811 0.87860924
119 0.94235151 1.04281841 0.77263207 1.90509206 0.76120504 0.95003407
120 1.01359950 0.96587294 0.90002492 1.79173448 0.63015617 0.93750855
121 2.46439120 2.44943762 2.36941979 0.50607206 1.38523885 1.09865105
122 1.73803443 1.81195746 1.60575849 1.12998265 0.86575121 0.60121355
123 1.64154230 1.60598680 1.53545833 1.16387293 0.70126441 0.69001629
124 2.32992786 2.14948628 2.29765748 1.80143337 1.63586207 1.76181983
125 2.86276113 2.94767068 2.73835434 1.16381336 1.92748990 1.54709097
126 2.46280222 2.35606441 2.39551502 1.13688052 1.49642979 1.43085610
127 1.55378246 1.66782390 1.39527927 1.56247494 0.96192646 0.84763875
128 2.42121292 2.22935486 2.39248549 1.98599429 1.78670469 1.93171122
129 1.67624524 1.91860703 1.53700797 2.96183463 2.01708658 2.07891351
130 2.03306541 1.91337081 1.96331472 1.34841088 1.18145958 1.23799499
131 1.97602703 2.19497741 1.82271463 2.39072813 1.82828396 1.71782104
132 1.97812856 1.85489233 1.90905520 1.39510915 1.15292045 1.23177006
133 2.70495577 2.77581995 2.57822911 1.03664509 1.74954479 1.38443243
134 2.39526398 2.31276865 2.31326677 1.01546680 1.39999382 1.29539764
135 3.44522295 3.58702949 3.31107924 2.07564190 2.67979136 2.31212349
136 2.82357035 2.68835623 2.76700897 1.51754658 1.91630393 1.88221340
137 2.17348329 2.38311997 2.01883547 2.34441581 1.92393994 1.76807778
138 2.37663111 2.28429344 2.29628790 1.11765387 1.41039694 1.33735953
139 3.42497731 3.55284654 3.29124587 1.93239279 2.61091343 2.23723804
140 2.19799892 2.10281109 2.11398082 1.21688649 1.27814965 1.25368373
141 1.96349647 2.20284764 1.81797613 3.02731094 2.19824204 2.21202224
142 2.79767137 2.64134518 2.74741699 1.76199612 1.97602703 2.00097711
143 2.51974361 2.57129034 2.38745424 1.00798441 1.56079628 1.23917192
144 2.67639746 2.53748048 2.61473738 1.58718188 1.81692154 1.81946579
145 3.06389622 3.19964385 2.92027259 1.84857505 2.31030782 1.96554349
146 3.12401980 2.97073435 3.07256186 1.88681424 2.26959739 2.25948972
147 1.43113935 1.54743735 1.25235287 1.93211545 1.11640037 1.14488855
148 2.45189292 2.35805130 2.36557647 1.24545975 1.51467440 1.45208308
149 2.38620954 2.51680666 2.23050639 1.64272049 1.70181239 1.42589821
150 2.66863153 2.51680666 2.60972072 1.76250272 1.87296376 1.91434756
151 2.03791817 2.21323309 1.86990010 2.09020184 1.67300134 1.52387611
152 2.38272029 2.22082545 2.32500632 1.85325902 1.69010474 1.79984196
153 1.92602503 2.09568137 1.75534403 2.05642854 1.57262416 1.44659809
154 2.17026554 2.05345839 2.08713243 1.51615795 1.37090077 1.42518404
155 1.90672976 2.09807120 1.73609724 2.29354907 1.70540397 1.61915411
156 3.01937606 2.88969677 2.95430797 1.63618133 2.10685530 2.05471347
157 2.70231375 2.89546117 2.54724284 2.38062714 2.28425517 2.04784564
158 2.64761831 2.54451044 2.56631123 1.33444138 1.71034399 1.64227657
159 2.83827964 3.02275157 2.68533602 2.31846444 2.34732398 2.08135504
160 2.57147711 2.48638606 2.48164736 1.20761108 1.60868627 1.51151857
161 1.26295038 1.40087126 1.08077499 2.46162458 1.41843774 1.57205798
162 2.80668581 2.69019802 2.73161143 1.48770980 1.88879798 1.83387170
163 3.59317387 3.72935891 3.44986346 2.21548435 2.82419939 2.46768888
164 2.93362334 2.78493899 2.87187216 1.86165232 2.11199921 2.12332762
165 1.75542952 1.90732174 1.57146449 2.34959254 1.61690927 1.62214423
166 2.39610738 2.29542229 2.29776499 1.60214545 1.59184876 1.60258330
167 2.19094916 2.34148804 2.01460764 2.12834407 1.77864400 1.63724759
168 2.96440987 2.80988914 2.89892054 2.06308335 2.20626945 2.24679551
169 2.37952873 2.48947913 2.21120724 1.78446069 1.73420095 1.52379337
170 2.50922642 2.46490959 2.38714040 1.37280452 1.61079796 1.49800642
171 2.44496752 2.60904825 2.27204047 2.25917462 2.02634634 1.84813963
172 2.87157518 2.78811351 2.77112760 1.50347922 1.94562912 1.84656086
173 2.68648830 2.84771282 2.51843772 2.23479096 2.18322191 1.95602223
174 2.77652318 2.62294001 2.70670495 2.06312826 2.06750970 2.13630882
175 2.08918326 2.27902464 1.91321311 2.76782463 2.07995121 2.06172314
176 2.95946104 2.83815214 2.87515166 1.81475200 2.11231172 2.08653369
177 1.96144422 2.15279862 1.79344758 3.03386193 2.16961460 2.22917174
178 2.87643666 2.81557904 2.76572880 1.42066583 1.92874523 1.78973483
179 2.12660683 2.30883719 1.95905939 3.19139504 2.34311196 2.40591024
180 2.89897920 2.75985542 2.81592317 2.13621803 2.18409388 2.23119844
181 2.51923790 2.60325536 2.34480518 2.00654777 1.91563146 1.76362217
182 3.04514428 2.92738819 2.94908753 2.09771450 2.27584370 2.27458142
183 2.46533583 2.62014488 2.28212817 2.67155501 2.23091488 2.15034781
184 3.24740303 3.13054886 3.15269590 2.14151824 2.44036340 2.41368599
185 2.34105019 2.40081991 2.16607010 2.10379322 1.81972380 1.74987789
186 3.39820573 3.25784669 3.31576604 2.40628285 2.64418681 2.65488973
187 2.21182941 2.34318607 2.03066658 2.92738819 2.20872329 2.25175743
188 3.09184569 3.03876641 2.96451820 1.87526757 2.24068232 2.13072784
189 2.73085543 2.86406383 2.54765859 2.58583073 2.34648416 2.21963031
190 2.99453974 2.87836069 2.89083022 2.33111659 2.33049535 2.36969557
191 2.92403838 3.02808952 2.74722358 2.29120386 2.33457686 2.14528907
192 2.94781022 2.88845678 2.81819899 2.00060840 2.17497281 2.11419833
193 3.46558016 3.59784421 3.28500975 2.91038616 2.96997189 2.77426844
194 3.29835686 3.17346584 3.19520080 2.79946600 2.73178169 2.79988367
195 3.09875097 3.22002204 2.91437819 3.27718384 2.89619911 2.84626538
196 3.41404496 3.33157014 3.28663147 2.76891415 2.80013097 2.80780346
197 3.19176790 3.27135104 3.01008707 3.22157844 2.90724448 2.87102474
198 3.65075541 3.58840383 3.51339392 2.88082537 3.00702899 2.97599229
199 4.05352234 4.14190047 3.87085172 3.48057182 3.56223188 3.41526559
200 4.16148133 4.08382261 4.02985956 3.36594386 3.53399443 3.51224875
            79         80         81         82         83         84
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79                                                                   
80  1.90112038                                                       
81  2.43426767 0.67040806                                            
82  1.08007172 0.93462187 1.36894555                                 
83  3.17850259 1.28914861 0.81389701 2.14564549                      
84  1.67539314 0.22829950 0.83280771 0.71374371 1.50781010           
85  0.24080754 2.08690540 2.58758634 1.21944175 3.35078628 1.85913141
86  1.80469546 0.17063984 0.67274854 0.79620121 1.37386612 0.16277940
87  2.30536977 0.76251423 0.32714635 1.22783658 1.08829326 0.84974409
88  0.17795363 2.00059630 2.51292738 1.15107393 3.26871419 1.77378856
89  0.85980014 1.28923075 1.68986063 0.37772830 2.47898081 1.07006705
90  1.95271325 0.22871792 0.55838513 0.93947716 1.24166149 0.33344795
91  3.22912763 1.46276720 0.82481703 2.15603234 0.57903585 1.64257326
92  0.58805365 2.22768536 2.82504430 1.54273782 3.51292732 2.01680584
93  1.80793348 0.36164952 0.68795770 0.78653779 1.41356925 0.33192563
94  1.32256019 0.68795770 1.30945606 0.64038287 1.94668852 0.51055753
95  0.78564960 1.23823513 1.83755084 0.70007459 2.51623729 1.03083797
96  0.23939727 1.84528726 2.37370811 1.03446838 3.11596144 1.62127011
97  1.74399144 0.33192563 0.76723539 0.75050682 1.46835055 0.26609633
98  0.37440613 1.62127011 2.16007427 0.84247561 2.89364492 1.39863856
99  1.85038648 0.27596399 0.77948597 0.91483914 1.38656037 0.31229562
100 0.36145535 2.11054212 2.66322202 1.33619639 3.38931833 1.89019093
101 0.52366465 1.88641888 2.48332298 1.24086734 3.16452295 1.67846392
102 1.89237149 0.38309338 0.65897882 0.88676063 1.35153972 0.40359798
103 3.17611159 1.47870157 0.83738836 2.10395966 0.76068325 1.64017557
104 0.39037710 1.74847751 2.24535318 0.91144573 3.00022047 1.52450217
105 1.89237149 0.62184646 0.67693894 0.84520096 1.44588566 0.59568223
106 0.51306174 2.02744786 2.61836969 1.35175600 3.30728772 1.81706218
107 3.09822497 1.30170356 0.73076672 2.04271335 0.49397349 1.49039803
108 2.25748666 0.51916295 0.44836490 1.24531510 1.01043751 0.67186215
109 3.25828385 1.40318835 0.91295216 2.22386902 0.35852797 1.61222713
110 3.10112769 1.28547422 0.73892938 2.05150376 0.44274520 1.48030224
111 3.02611958 1.25670270 0.66850581 1.96642461 0.56512569 1.43645778
112 0.45322498 2.22386902 2.74426496 1.40318835 3.48972339 2.00082167
113 1.20331983 0.87467219 1.45480121 0.63118204 2.11100425 0.69205602
114 0.53003979 2.18659330 2.75363872 1.45480121 3.46262515 1.97151482
115 0.57228926 2.27029312 2.82552249 1.51616807 3.54306382 2.05357407
116 0.51322287 2.20988959 2.75263117 1.43628418 3.47910783 1.99130590
117 2.91485826 1.08689740 0.67517887 1.89585977 0.51322287 1.28761158
118 1.92696246 0.78024494 0.77418232 0.90525506 1.52370337 0.74761723
119 2.09385310 0.51670525 0.72487813 1.15195502 1.25016352 0.61204831
120 2.00459114 0.76649571 0.74167465 0.99445554 1.45255560 0.76184637
121 0.59243097 1.73760198 2.21239921 0.93090002 2.96343039 1.52017888
122 1.27042665 0.93331323 1.50879207 0.76314544 2.13456384 0.77263207
123 1.36425414 1.06073455 1.37138028 0.60013307 2.12024834 0.89697902
124 1.97963315 2.10692241 2.09425263 1.50822494 2.84479855 1.97226851
125 1.07906427 2.02208617 2.64972795 1.59307137 3.24167733 1.84918284
126 1.27918737 1.96684787 2.20207142 1.16103800 2.99268680 1.77685174
127 1.70358464 0.82274487 1.34434915 1.07092915 1.85060951 0.76585154
128 2.16164290 2.24640962 2.19161203 1.68486321 2.92020892 2.12222341
129 3.09537547 1.54029394 1.68486321 2.36265074 1.44794398 1.70823186
130 1.53794535 1.63464682 1.76994803 1.00934217 2.54211130 1.47919438
131 2.47860656 1.43961095 1.89120770 2.00178636 2.00109732 1.50367822
132 1.58875479 1.60139046 1.71554712 1.01187762 2.48399309 1.45297813
133 0.98794698 1.87549473 2.48007128 1.41317595 3.09566421 1.69694727
134 1.15715425 1.84152839 2.12927434 1.05103743 2.90876531 1.64800735
135 1.97028000 2.62414037 3.27294087 2.43570579 3.71311736 2.50369170
136 1.62826767 2.39714463 2.56787937 1.60357560 3.35200770 2.21529592
137 2.41245802 1.57747070 2.07185216 2.04030151 2.22885497 1.61143856
138 1.26480360 1.85619165 2.10998810 1.09255013 2.88732492 1.67000014
139 1.81854316 2.59377160 3.24048046 2.33805741 3.71863741 2.45952653
140 1.38478775 1.71286625 1.92912407 1.02924667 2.69604176 1.54130037
141 3.14261199 1.73786830 1.95253421 2.49764819 1.75931987 1.88154997
142 1.89081320 2.45371658 2.54705306 1.72891955 3.31238674 2.29002442
143 1.02258170 1.72267521 2.27880291 1.24558904 2.91509743 1.54467287
144 1.71863337 2.28457913 2.41826601 1.55617279 3.18629687 2.11631247
145 1.78512550 2.25128851 2.88017464 2.09896269 3.32685661 2.13598043
146 1.98282942 2.75010327 2.87225238 1.98105415 3.64200536 2.57673604
147 2.08654793 0.90882282 1.23262143 1.34932117 1.62921991 0.93985170
148 1.38121190 1.94511109 2.18244521 1.22175548 2.94578581 1.76661028
149 1.67472121 1.60868627 2.19250904 1.59687736 2.63763786 1.51615795
150 1.90275106 2.33303837 2.41387840 1.65950593 3.16484954 2.17854223
151 2.17298109 1.39882352 1.89022116 1.76875376 2.15651776 1.40509654
152 2.02246366 2.12616067 2.13267636 1.57262416 2.85750214 1.99731699
153 2.15187002 1.29957492 1.77261143 1.69010474 2.05116178 1.31119691
154 1.68872651 1.78566041 1.90321741 1.22323157 2.64231753 1.64272049
155 2.39379720 1.36718511 1.78449858 1.87907979 1.95501919 1.41978007
156 1.72333954 2.57447215 2.75909535 1.78566041 3.53405405 2.39199618
157 2.39579345 2.02329676 2.57561814 2.28317230 2.80116785 2.00569251
158 1.44907104 2.15138405 2.37993366 1.39865632 3.14700264 1.96987775
159 2.31418956 2.12340080 2.70090648 2.29994486 2.96902520 2.08462440
160 1.32189487 2.03127908 2.30145337 1.28406620 3.06370221 1.84609081
161 2.63062641 1.10932542 1.13799371 1.77939562 1.25701518 1.24094696
162 1.59109926 2.34023200 2.54152512 1.58012129 3.30928139 2.16053489
163 2.10981911 2.77883623 3.41027203 2.57987156 3.84805770 2.65961313
164 1.97624526 2.57246585 2.67700020 1.86367239 3.42830144 2.41046035
165 2.47844923 1.33495403 1.60668367 1.84178942 1.79207436 1.40033715
166 1.74712266 1.97286625 2.12528530 1.41894877 2.83750590 1.82938531
167 2.20680725 1.56885883 2.01954571 1.84482792 2.31271842 1.55889830
168 2.18394184 2.64738568 2.70913733 2.00296134 3.43239576 2.50017786
169 1.83900748 1.66796802 2.16849927 1.66577460 2.60718167 1.58886300
170 1.47485156 1.92898699 2.23551274 1.36348797 2.92953870 1.76760487
171 2.31095977 1.80412951 2.28584067 2.06019210 2.54759033 1.79003377
172 1.58114878 2.33916066 2.59851328 1.64040812 3.33269054 2.16336222
173 2.25609572 1.99506395 2.52178960 2.15308647 2.81861197 1.95566351
174 2.20091733 2.48870595 2.52178960 1.91103589 3.22550483 2.35502342
175 2.87515166 1.72714478 1.99230267 2.30769572 2.00112207 1.81696051
176 1.91321311 2.53554005 2.69233263 1.85602728 3.42463558 2.37338194
177 3.16329703 1.78439210 1.90376980 2.47486740 1.76198113 1.91699357
178 1.48024828 2.29113759 2.60266399 1.60927570 3.32429835 2.11258528
179 3.31841561 1.97307195 2.06840382 2.64303972 1.90421815 2.10251484
180 2.26013749 2.58153893 2.63933492 2.02187503 3.32461403 2.44909568
181 2.06993293 1.88898498 2.29599188 1.86514083 2.72287524 1.81972229
182 2.19748997 2.65792621 2.77853789 2.07507415 3.46334499 2.51595841
183 2.75142824 1.98639890 2.31732784 2.35239704 2.46580123 2.01683191
184 2.22135282 2.83362932 2.97945586 2.20331738 3.67683401 2.68154597
185 2.20211611 1.81023741 2.11266323 1.83452894 2.53096450 1.76099097
186 2.49464189 3.05314989 3.13759453 2.43078565 3.82803873 2.90856001
187 3.05003663 1.95350793 2.08363314 2.44033428 2.12171289 2.03224622
188 1.92723168 2.54478333 2.81877060 1.99201194 3.47707948 2.39298430
189 2.64157664 2.17847583 2.55459905 2.38580228 2.79438676 2.16837486
190 2.44533335 2.66820811 2.73387030 2.20242107 3.36282091 2.55221486
191 2.31555047 2.27485075 2.71425457 2.25789785 3.08985551 2.20902943
192 2.08062940 2.46064459 2.67756302 1.98971008 3.30665585 2.32856567
193 2.90891450 2.84456794 3.28187143 2.91321394 3.55011689 2.80279473
194 2.91205200 3.04412650 3.04884789 2.64378197 3.62007628 2.94731725
195 3.34810867 2.71085996 2.94346765 3.00175074 3.04986338 2.73776223
196 2.85406695 3.06135799 3.15762170 2.68782951 3.70508262 2.96169219
197 3.29529188 2.80904731 3.00766829 2.97643027 3.20134664 2.81137882
198 2.94206239 3.24521832 3.39279411 2.87065694 3.92754871 3.14148002
199 3.48354001 3.51158575 3.84998948 3.49626220 4.13007005 3.46476474
200 3.41740292 3.78909580 3.90613822 3.38970323 4.43254047 3.68499938
            85         86         87         88         89         90
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85                                                                   
86  1.97923198                                                       
87  2.43694597 0.69288988                                            
88  0.15546577 1.89705385 2.36522736                                 
89  0.95013965 1.14958840 1.50580312 0.88141741                      
90  2.12474002 0.20902812 0.58779800 2.03486720 1.26721817           
91  3.37086238 1.48579559 0.94094097 3.29388452 2.44194565 1.33541005
92  0.68282856 2.16470896 2.73036596 0.61782769 1.36188174 2.29926890
93  1.97080431 0.25628607 0.62098549 1.87918394 1.09164541 0.19948310
94  1.52826145 0.65890235 1.28528930 1.41804662 0.88888643 0.75647461
95  1.00482872 1.17817834 1.76292590 0.88257907 0.71565395 1.30007550
96  0.36850800 1.74871424 2.23425006 0.21689078 0.78373594 1.87725443
97  1.91479634 0.24250904 0.72282548 1.81987925 1.06080271 0.23112856
98  0.55691567 1.52845501 2.03144989 0.42267443 0.63786115 1.65552436
99  2.03576687 0.30826071 0.81129309 1.93414671 1.22611261 0.23987217
100 0.41488446 2.02541272 2.53425017 0.31253410 1.09496018 2.15378219
101 0.70510036 1.82570701 2.39109116 0.57903585 1.08840753 1.94848497
102 2.05718512 0.32233329 0.60884129 1.96102782 1.17991182 0.18524835
103 3.30796777 1.48196595 0.88073701 3.23075259 2.36759324 1.32576864
104 0.47633148 1.64152338 2.08796887 0.34385434 0.62342965 1.75968466
105 2.02781764 0.49785363 0.47615988 1.94258858 1.09555735 0.42222795
106 0.65588168 1.96282431 2.51878780 0.54294927 1.17266041 2.08735825
107 3.25091174 1.34231781 0.87649798 3.16403312 2.33107201 1.17139164
108 2.42480359 0.54946217 0.52273348 2.32837938 1.54273782 0.34385434
109 3.42517312 1.47675241 1.12056531 3.33346701 2.52859211 1.30772371
110 3.25828385 1.33559806 0.90677092 3.16971536 2.34518190 1.16368528
111 3.17432489 1.28547422 0.78653779 3.08889348 2.24878978 1.11502648
112 0.38911992 2.12679796 2.59187150 0.31592448 1.11502648 2.24878978
113 1.40121626 0.82548524 1.39138897 1.27921253 0.78742931 0.90229551
114 0.58899053 2.11064904 2.63222129 0.48848704 1.22440286 2.23092543
115 0.58565543 2.18943768 2.69415206 0.49824727 1.26447430 2.30753724
116 0.51902048 2.12350528 2.61349708 0.41998515 1.17219791 2.24050588
117 3.08371559 1.15842956 0.87072495 2.98719682 2.19414830 0.97498864
118 2.04918801 0.65875451 0.52798173 1.96282431 1.10706356 0.57409477
119 2.26961189 0.55190983 0.75124059 2.16119842 1.42542527 0.36883627
120 2.13421255 0.66853098 0.52400314 2.04174667 1.20118279 0.54668842
121 0.65648678 1.62939830 2.04174667 0.52400314 0.62651664 1.72578859
122 1.46949101 0.90080035 1.45322580 1.33951175 0.89400547 0.95360457
123 1.47569744 0.93278350 1.16696363 1.37209554 0.60488993 0.95069127
124 1.92875126 1.94368498 1.77586893 1.90610555 1.32083921 1.95758498
125 1.25190691 2.00185461 2.59881308 1.12419987 1.50662843 2.09237514
126 1.21795101 1.81472788 1.93343319 1.17723524 0.82960580 1.87079088
127 1.90396786 0.85352621 1.34735297 1.77311928 1.26385257 0.82313147
128 2.10578957 2.08504397 1.86818273 2.08419170 1.50547613 2.08756874
129 3.31543695 1.69588114 1.91799082 3.19421829 2.65488486 1.58021205
130 1.54461761 1.48072822 1.48274866 1.48185069 0.81509892 1.49802824
131 2.70892396 1.57384479 2.05246038 2.58073122 2.23862983 1.53102272
132 1.60162675 1.44747596 1.42458005 1.53785460 0.84291672 1.45815650
133 1.15971945 1.84298279 2.40876660 1.01666166 1.30879393 1.92431957
134 1.12963046 1.69939791 1.87920827 1.06073455 0.71532997 1.75253548
135 2.14086355 2.65741845 3.29563070 2.03483335 2.42215409 2.73115181
136 1.51406365 2.24022039 2.27706478 1.50175029 1.27669553 2.28722876
137 2.64257967 1.69887214 2.21169498 2.51127221 2.24743183 1.67078192
138 1.23583755 1.71126563 1.84918284 1.17022936 0.77465617 1.75492496
139 1.97810894 2.61403495 3.24277449 1.87128518 2.29632460 2.69061294
140 1.38625237 1.56832340 1.66214918 1.31087516 0.76952379 1.59307137
141 3.36686204 1.89081320 2.16852267 3.23981270 2.76877826 1.78629270
142 1.78964388 2.29429187 2.24000656 1.77413030 1.43961095 2.32204927
143 1.17732964 1.67495775 2.17832198 1.02235393 1.11982040 1.73321072
144 1.63441917 2.12939703 2.12024230 1.60354343 1.25831964 2.15658812
145 1.97116467 2.28283393 2.89226387 1.84355374 2.09605391 2.33661426
146 1.84858994 2.59174343 2.56838797 1.84650841 1.66154290 2.62756027
147 2.27245981 0.95750050 1.24769974 2.14137733 1.54645152 0.83292841
148 1.34919117 1.80400753 1.91695318 1.27814965 0.91527549 1.83286302
149 1.88096780 1.64413527 2.20062059 1.73501608 1.65687627 1.65997887
150 1.82595105 2.17775271 2.10590735 1.79282554 1.38905310 2.18973878
151 2.39053631 1.49139006 1.97434318 2.25048184 1.94104848 1.44641073
152 1.98405661 1.97366115 1.81681798 1.93735983 1.37245587 1.96091644
153 2.36619379 1.38949329 1.85061146 2.22634752 1.86859404 1.33343633
154 1.69037544 1.64227657 1.61436858 1.61632957 1.02261213 1.63322568
155 2.61152697 1.47977245 1.90066292 2.47448618 2.08545117 1.40555714
156 1.59844889 2.42233285 2.46944251 1.58142739 1.44641073 2.46242507
157 2.61717076 2.11936698 2.67802470 2.48296415 2.41785064 2.11720783
158 1.38253268 2.00772359 2.10761830 1.32685368 1.07131082 2.04090626
159 2.53055991 2.20818236 2.78772431 2.39791781 2.40829387 2.22000414
160 1.27827019 1.89435438 2.04441403 1.20545726 0.95669864 1.92948772
161 2.81239630 1.18972395 1.22475219 2.68804895 2.01416893 1.00260715
162 1.49923610 2.19293273 2.25901607 1.45890239 1.24927066 2.22535394
163 2.26542078 2.80845892 3.41890545 2.15175485 2.54089189 2.86574283
164 1.87421909 2.41875614 2.37145419 1.84809993 1.56397321 2.43504330
165 2.67283695 1.41894877 1.67337629 2.53286733 2.02539140 1.28709159
166 1.74126609 1.84178942 1.84929701 1.65552897 1.18940213 1.82273447
167 2.40776434 1.63786929 2.06169759 2.25964518 1.96565731 1.57422952
168 2.09469805 2.49759028 2.39841840 2.05877276 1.72586514 2.49359768
169 2.02022672 1.69054497 2.14377514 1.86675391 1.69489538 1.66280517
170 1.50090347 1.82316749 2.01323554 1.38314940 1.11943116 1.82014112
171 2.51631452 1.88139806 2.34400574 2.36861117 2.17167868 1.83429607
172 1.52171314 2.21125854 2.33964678 1.44533018 1.31947927 2.22724800
173 2.45850841 2.06398831 2.57093468 2.31208703 2.23351179 2.04132958
174 2.13744680 2.34301125 2.21092505 2.08854573 1.66589249 2.32307564
175 3.08282121 1.84141179 2.11562128 2.94118617 2.50552013 1.71994128
176 1.83084895 2.39488852 2.40243536 1.77824666 1.54931234 2.39872168
177 3.36700743 1.90507917 2.05229814 3.23017471 2.70058041 1.75320687
178 1.44089912 2.17463411 2.36480519 1.34726408 1.29508112 2.19292149
179 3.51819096 2.08818832 2.20542215 3.37864188 2.85514158 1.93040268
180 2.20053538 2.44420365 2.33755398 2.14050621 1.76933049 2.41495905
181 2.22024992 1.89587856 2.23461687 2.06536408 1.85112526 1.83435704
182 2.13578635 2.52816104 2.49119080 2.06711352 1.79974631 2.50291882
183 2.94188076 2.06592816 2.37163097 2.79069305 2.46860210 1.96022525
184 2.13905154 2.70217323 2.69271864 2.07869276 1.90346528 2.68786979
185 2.33906553 1.80556695 2.02556684 2.18884484 1.83009208 1.71037804
186 2.39789659 2.91483946 2.83565339 2.35167341 2.13816046 2.89604854
187 3.22739168 2.02792936 2.13192466 3.08143777 2.58334747 1.86765626
188 1.90650776 2.44497245 2.58695457 1.80121735 1.72070080 2.42621146
189 2.81598056 2.23445636 2.56761183 2.66135434 2.44117030 2.14749351
190 2.41024219 2.54938331 2.45165427 2.32840290 1.97312371 2.49414966
191 2.46579134 2.29744610 2.67663516 2.31104372 2.23347362 2.24514665
192 2.07763522 2.36341721 2.44127338 1.96819345 1.75426530 2.32145718
193 3.06342527 2.89215825 3.28257723 2.91181524 2.90604311 2.83399602
194 2.87414023 2.93176500 2.76768697 2.79309658 2.43067741 2.85651990
195 3.50708422 2.76934886 2.95411268 3.35221479 3.05640321 2.63971303
196 2.83633323 2.96878155 2.90942280 2.73557619 2.47362380 2.89109694
197 3.42458898 2.83669171 2.96036068 3.27197283 2.97635747 2.70500046
198 2.92716614 3.16266153 3.16172513 2.82054300 2.64904939 3.08854663
199 3.58990044 3.53185949 3.79313421 3.44136106 3.42240235 3.44719554
200 3.37864670 3.70131930 3.66302474 3.28347733 3.14997705 3.62627741
            91         92         93         94         95         96
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91                                                                   
92  3.62017692                                                       
93  1.45097092 2.17017454                                            
94  2.08725268 1.57585108 0.67040806                                 
95  2.62611816 1.00368893 1.17703183 0.57790956                      
96  3.15220171 0.60612536 1.72201235 1.23606789 0.69133129           
97  1.53538846 2.08933284 0.10546572 0.56972791 1.09112244 1.65784759
98  2.94169491 0.73349614 1.50382668 1.00798463 0.47338212 0.22829950
99  1.51957538 2.14930988 0.27373152 0.57916240 1.14602540 1.76160091
100 3.44486642 0.34967170 2.00479892 1.47404126 0.90160220 0.31135367
101 3.26871419 0.37571828 1.81788679 1.21997456 0.64992246 0.43860247
102 1.39159785 2.23860846 0.11145747 0.71893854 1.24129898 1.79798016
103 0.20534006 3.57817379 1.41625385 2.06955464 2.59170614 3.09109337
104 3.00882486 0.79683438 1.59378190 1.16088148 0.66612053 0.19948310
105 1.36549069 2.29680073 0.29052110 0.89710178 1.33444957 1.79798016
106 3.40396087 0.24630979 1.95325065 1.36448359 0.79113074 0.44930906
107 0.28492491 3.45716374 1.29419888 1.90454858 2.45625306 3.00982148
108 1.07196176 2.58888039 0.45938240 1.03512012 1.58663079 2.16316118
109 0.48901244 3.58342795 1.45496171 2.01104746 2.57995435 3.17111056
110 0.34230407 3.45021661 1.29419888 1.89032285 2.44769093 3.01280936
111 0.28777158 3.39486631 1.22783658 1.85254601 2.39662442 2.93729067
112 3.51128343 0.53079876 2.08816027 1.60217321 1.04645164 0.38361769
113 2.21402442 1.44486064 0.78047665 0.22291493 0.45572286 1.08517003
114 3.53017339 0.28081075 2.08484230 1.52878182 0.95564764 0.45309643
115 3.59686382 0.35449354 2.15638007 1.61634494 1.04626364 0.49469502
116 3.52052462 0.42282014 2.08509410 1.56403115 0.99914400 0.41274262
117 0.62947853 3.23043545 1.11502648 1.66153721 2.22768536 2.81999705
118 1.38787545 2.33728295 0.43740488 0.99633796 1.39665974 1.82007163
119 1.33781719 2.38318658 0.41368899 0.83941467 1.38656037 1.98202107
120 1.32634031 2.39256475 0.43301644 1.00840469 1.43834663 1.89019093
121 2.95108542 0.91939215 1.55064691 1.14934704 0.70218683 0.37569538
122 2.24553239 1.46429420 0.83962360 0.30253965 0.51138941 1.13640350
123 2.04358199 1.74891325 0.75290521 0.77671266 0.91065493 1.21791982
124 2.52948463 2.48070599 1.78263177 2.00572839 1.99223910 1.88449892
125 3.40097742 0.72073642 1.98689058 1.34441470 0.90193786 0.97126904
126 2.81370248 1.72769570 1.67381932 1.61647317 1.40963465 1.15468996
127 2.00287731 1.86163130 0.77294181 0.50893606 0.93218711 1.56805639
128 2.57407057 2.65741835 1.91741814 2.17062839 2.17156623 2.06398848
129 1.87803875 3.18951336 1.72072198 1.81288938 2.31352736 2.99565668
130 2.32826363 1.99803397 1.30444984 1.42579311 1.41171313 1.40467902
131 2.37525737 2.46052648 1.60619228 1.36660497 1.72090188 2.37888483
132 2.26240003 2.04993968 1.26657806 1.42039145 1.43511502 1.45661924
133 3.22209252 0.75470246 1.80474919 1.18986929 0.74553937 0.83650067
134 2.76488692 1.56865590 1.55421396 1.43699026 1.21450204 1.00060163
135 3.97999900 1.49935906 2.67692697 2.03269554 1.74237361 1.90776021
136 3.11638302 2.05348067 2.09185629 2.07848575 1.86124027 1.52202387
137 2.58669359 2.34135404 1.72401764 1.40000773 1.67926370 2.30900705
138 2.72242672 1.68051654 1.55584943 1.48526345 1.29849158 1.11098198
139 3.95818493 1.33130907 2.62199564 1.97325644 1.63883153 1.74857054
140 2.51800456 1.80230381 1.39408668 1.39564007 1.29609731 1.22639563
141 2.17718564 3.17950201 1.90904396 1.90897554 2.36263156 3.03636901
142 3.02953987 2.33032275 2.13102611 2.20600554 2.05586164 1.78183514
143 2.99263666 0.96587294 1.59450648 1.05311942 0.67756662 0.81794709
144 2.93191517 2.14394257 1.96173856 2.00291086 1.84600877 1.59250342
145 3.56622732 1.40781135 2.27658338 1.65760921 1.42115136 1.68029460
146 3.36369759 2.38428696 2.43389612 2.45540769 2.24436164 1.88084586
147 1.74954479 2.26260945 0.81998115 0.87801754 1.33598272 1.93769521
148 2.76634110 1.76271378 1.63343236 1.57493928 1.39803730 1.21355565
149 2.84262433 1.54161778 1.60228330 1.06772178 1.04403408 1.52701273
150 2.87827304 2.33146403 1.99872710 2.09835925 1.98625368 1.77413030
151 2.42727103 2.14243108 1.46060352 1.14414870 1.42372847 2.03879348
152 2.54287846 2.46898279 1.77922355 1.98237978 1.97329541 1.88843559
153 2.30480509 2.15613726 1.34640912 1.07308137 1.39047851 2.01373464
154 2.40766732 2.10004246 1.44060406 1.56000931 1.54521154 1.52901156
155 2.25037027 2.40217124 1.45184100 1.25878697 1.62371506 2.26364737
156 3.29718898 2.09605391 2.26472891 2.22176487 1.97746368 1.60272324
157 3.13383543 2.18464107 2.13185230 1.67232103 1.76595170 2.28826457
158 2.95239980 1.82049251 1.84152839 1.77413030 1.56000931 1.29146478
159 3.28941364 2.05780527 2.22016827 1.71319137 1.73521370 2.20964931
160 2.89987087 1.67237513 1.73027126 1.61715433 1.38970156 1.14694396
161 1.38478775 2.83441490 1.07014557 1.36847622 1.88377885 2.49086120
162 3.09033889 1.96091644 2.02653496 1.97891945 1.75790389 1.44655633
163 4.09328466 1.62794173 2.80220326 2.17629523 1.88634045 2.01989312
164 3.14368079 2.37119181 2.24131784 2.29492887 2.13185597 1.84693908
165 1.97521982 2.56223479 1.31140710 1.30858734 1.71764651 2.32035097
166 2.61294341 2.09137763 1.63024088 1.68077106 1.61896533 1.56116858
167 2.52151889 2.16099926 1.55742678 1.26501924 1.48936562 2.04350584
168 3.11991387 2.56565815 2.30349939 2.40151571 2.27977696 2.04151036
169 2.74952182 1.75807411 1.58761674 1.17991421 1.21497897 1.65286642
170 2.80608160 1.69314522 1.63175226 1.47581553 1.31075835 1.25148058
171 2.79276340 2.18918462 1.82433764 1.46627621 1.62662221 2.15628298
172 3.15212034 1.83915345 2.02986957 1.90570570 1.66487516 1.38998044
173 3.06933976 2.05864075 2.01880888 1.57746285 1.63533994 2.10712761
174 2.90467268 2.58791609 2.13715954 2.27895322 2.21081747 2.04793944
175 2.27515083 2.88426070 1.77818759 1.72268763 2.10891678 2.72674347
176 3.17179764 2.23466645 2.20223286 2.19592357 2.01498996 1.74771402
177 2.03246807 3.22991866 1.83915345 1.93239321 2.38620954 3.01887140
178 3.18240133 1.67627605 1.99908204 1.80657771 1.53551708 1.27122111
179 2.14747606 3.37395671 2.00890753 2.10769316 2.54759033 3.16572138
180 3.01555118 2.59947847 2.22834084 2.33574393 2.25383831 2.08904692
181 2.79488303 2.01611927 1.74298545 1.45829565 1.50419623 1.85753527
182 3.18997887 2.47676001 2.31287219 2.34213985 2.21081747 2.01147314
183 2.66168283 2.69004778 1.96144422 1.79303600 2.04716562 2.57420515
184 3.41065839 2.47740397 2.49482048 2.48362025 2.30488218 2.04078984
185 2.53755700 2.24418377 1.61429291 1.48711046 1.62279715 1.98477752
186 3.51635089 2.78568259 2.70560631 2.75489977 2.60030681 2.32937934
187 2.23666444 3.10356688 1.88640881 1.95579825 2.32444257 2.86787668
188 3.31814534 2.04029263 2.24232968 2.08577067 1.87950062 1.70373115
189 2.95089254 2.52610213 2.11353432 1.86514083 2.00815494 2.44915736
190 3.06655906 2.71478424 2.31554735 2.40810914 2.35267165 2.24752016
191 3.20409008 2.14575249 2.16760371 1.81609920 1.80060971 2.11044178
192 3.12121794 2.23306455 2.14291966 2.06627082 1.94256048 1.85518410
193 3.71717988 2.64824346 2.78313388 2.42046757 2.41052312 2.71850492
194 3.28371470 3.16637355 2.68881219 2.82716926 2.80302712 2.71243161
195 3.15196641 3.26207795 2.61854922 2.51664506 2.71761078 3.14214213
196 3.44072669 3.00673735 2.72659683 2.76181293 2.70512098 2.63285332
197 3.21115389 3.23985906 2.64990272 2.58042730 2.73396063 3.07218167
198 3.70004239 3.02404208 2.92638156 2.89413917 2.80180586 2.71446590
199 4.18497712 3.25840635 3.36865266 3.10621612 3.07547698 3.26439811
200 4.17075973 3.49323720 3.46247288 3.44673643 3.33707824 3.19693378
            97         98         99        100        101        102
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97                                                                   
98  1.43644644                                                       
99  0.20991374 1.53538846                                            
100 1.93477601 0.50404342 2.02268347                                 
101 1.73540014 0.45744900 1.79049996 0.37887328                      
102 0.16672397 1.57865583 0.24608766 2.07673457 1.88089878           
103 1.50718940 2.88561831 1.51157082 3.38701665 3.22603364 1.35714904
104 1.53680402 0.22002872 1.65385481 0.48982020 0.58312918 1.66866669
105 0.38439969 1.59378190 0.54817116 2.09399289 1.94979638 0.30979508
106 1.87285579 0.53503352 1.93322526 0.28293753 0.14831858 2.01785874
107 1.36987644 2.79423041 1.32746979 3.29411214 3.09814393 1.22003599
108 0.51541899 1.94240833 0.46290510 2.43792006 2.22795445 0.36819230
109 1.51559722 2.94977216 1.43428736 3.44486642 3.22257296 1.37439359
110 1.36549069 2.79530354 1.31155932 3.29411214 3.09038984 1.21757525
111 1.30802928 2.72380608 1.27937335 3.22441053 3.03691933 1.15644605
112 2.02590597 0.60416967 2.12875903 0.22002872 0.58040812 2.16047896
113 0.68977136 0.85980014 0.72492561 1.32171498 1.07719858 0.82454391
114 2.01058762 0.61250986 2.08492617 0.17795363 0.35395370 2.15035618
115 2.08509410 0.67626916 2.16550540 0.21258488 0.46329639 2.22213603
116 2.01680584 0.60350780 2.10452945 0.17267952 0.46530387 2.15204085
117 1.17139164 2.59833372 1.08524294 3.09075381 2.86680548 1.02712137
118 0.52218634 1.62421174 0.67948266 2.11731647 1.99078144 0.44101647
119 0.42073739 1.75964232 0.31592448 2.24299200 2.01494613 0.30696709
120 0.51682837 1.68981654 0.64038287 2.18183277 2.03863748 0.40352329
121 1.49745765 0.35357634 1.61434158 0.61382102 0.67501175 1.61634494
122 0.74807211 0.91710336 0.75541724 1.35427351 1.09123729 0.86735395
123 0.74160555 1.03897425 0.89702221 1.50470055 1.40905974 0.79755273
124 1.82991351 1.83743503 2.02690988 2.14197339 2.26536996 1.83199937
125 1.89279045 0.94248144 1.89044674 0.87371210 0.55562124 2.02445654
126 1.67526323 1.14897769 1.85349460 1.38317671 1.53759877 1.73618127
127 0.68799610 1.35082707 0.58869265 1.77478127 1.49039803 0.74520961
128 1.97016304 2.01943675 2.16454565 2.31688397 2.44360975 1.96088966
129 1.69021147 2.77560095 1.48531004 3.17884094 2.84757050 1.63792922
130 1.32897495 1.31633192 1.51343090 1.67901203 1.73320229 1.35303400
131 1.52996561 2.17854927 1.33533787 2.50603216 2.14588385 1.55524154
132 1.29578332 1.36036685 1.48091312 1.73455916 1.77844203 1.31266226
133 1.71538087 0.78303013 1.72694710 0.80057904 0.48881512 1.84138799
134 1.54415897 0.97573284 1.70809517 1.23340554 1.35002349 1.61203084
135 2.57413127 1.87955898 2.50588044 1.76406588 1.47138695 2.69406777
136 2.10384912 1.55912648 2.28732838 1.70431942 1.91636670 2.15049090
137 1.64025397 2.12102464 1.45867191 2.40952928 2.04179122 1.68056907
138 1.55298402 1.07999089 1.72097776 1.34553332 1.45810601 1.61049069
139 2.52087625 1.73534770 2.46787988 1.59090187 1.31599208 2.64317441
140 1.39975695 1.15667739 1.56865590 1.48031125 1.54524996 1.44116085
141 1.86651837 2.82401223 1.65896025 3.19421829 2.84826237 1.82912187
142 2.15692616 1.79638583 2.34445147 1.98122848 2.17139264 2.18235452
143 1.51479402 0.72538640 1.54338756 0.88068817 0.64322849 1.62483654
144 1.98077926 1.59754275 2.16211349 1.79708456 1.96782466 2.01147302
145 2.17629982 1.61394854 2.10515850 1.59754275 1.26799393 2.28504882
146 2.45314168 1.93303723 2.63765210 2.03816383 2.27089387 2.48729704
147 0.77814784 1.72419628 0.65198752 2.15459989 1.88854310 0.73974902
148 1.63254143 1.18777733 1.79404443 1.43048830 1.54087841 1.67955925
149 1.50764340 1.37711904 1.42239723 1.58637166 1.23795797 1.59307137
150 2.02693663 1.76638402 2.20871239 1.98599429 2.14282036 2.04191510
151 1.37887368 1.84787505 1.21831617 2.15997164 1.81238573 1.41304168
152 1.82166103 1.83657980 2.00178636 2.13303006 2.23508285 1.81187701
153 1.26846043 1.81668303 1.10757910 2.15218862 1.81450046 1.29417530
154 1.46489706 1.45033832 1.63245923 1.78116180 1.83334250 1.47202631
155 1.38230662 2.06229763 1.19907458 2.40580364 2.06401781 1.38822535
156 2.27262292 1.65847378 2.44775475 1.75196341 1.97689806 2.31781168
157 2.03844420 2.14070887 1.88674863 2.31408903 1.94290247 2.10276683
158 1.84168713 1.30056474 2.00569142 1.48072822 1.63558423 1.88964065
159 2.12340750 2.07876754 1.98599429 2.20871239 1.84133568 2.19925657
160 1.72175252 1.14414870 1.87628341 1.33983875 1.46893886 1.77717693
161 1.07440843 2.27389434 0.93334753 2.72125205 2.46043278 0.96097849
162 2.03154394 1.47541600 2.20011055 1.61811324 1.80241100 2.07504353
163 2.70227820 2.00097711 2.63489049 1.86766058 1.59648410 2.81216425
164 2.26369486 1.86922385 2.44157543 2.02561613 2.21498379 2.28481140
165 1.27021622 2.11677564 1.11327102 2.49809793 2.20003744 1.22383408
166 1.64370664 1.50278089 1.79052496 1.77781352 1.83478522 1.65109569
167 1.48366225 1.86617861 1.34770106 2.15580972 1.82929335 1.50391532
168 2.33225506 2.04965327 2.50427362 2.22377950 2.39169848 2.33655173
169 1.50887181 1.50504202 1.43363395 1.73714248 1.43736061 1.55993658
170 1.61050435 1.19929975 1.71848252 1.41838589 1.43070259 1.65059320
171 1.74395995 1.99393357 1.60283184 2.23008496 1.88751743 1.77710360
172 2.02051018 1.41390754 2.15936710 1.52369273 1.66362340 2.06378305
173 1.93126518 1.96753641 1.80373754 2.13839342 1.79253527 1.98430816
174 2.17106158 2.02907129 2.33812880 2.25046395 2.38169910 2.16223755
175 1.73151163 2.52831286 1.54916557 2.87192010 2.54273280 1.69205469
176 2.21323309 1.76807187 2.37073009 1.90319899 2.06584116 2.23502863
177 1.81443103 2.81039636 1.63169742 3.19223439 2.87600810 1.74013943
178 1.97792332 1.29531863 2.09999072 1.38120068 1.49586367 2.03017610
179 1.98736888 2.96138288 1.81112402 3.33407735 3.02124084 1.90763422
180 2.25595088 2.07507663 2.40946356 2.27118054 2.39406140 2.24561427
181 1.68356956 1.72709719 1.62749984 1.94759505 1.70343581 1.70224412
182 2.32775595 2.01397657 2.46856561 2.16092305 2.28637969 2.32856522
183 1.90629091 2.40421591 1.76017671 2.67998954 2.36714860 1.88623205
184 2.50488475 2.06860869 2.64719788 2.16344405 2.31856977 2.51553484
185 1.57649473 1.84140285 1.53553222 2.12207571 1.91074168 1.56012110
186 2.72669363 2.35872071 2.87921525 2.46185920 2.63406873 2.72672630
187 1.86579739 2.68075317 1.72908818 3.02998169 2.75010786 1.78794513
188 2.22444266 1.71108169 2.32012719 1.78569933 1.85099520 2.25048873
189 2.05291462 2.30604241 1.93532372 2.52045513 2.22732442 2.05082622
190 2.33791122 2.22090816 2.46329219 2.41091451 2.49119867 2.31426232
191 2.10004310 2.00615348 2.02556684 2.13899231 1.88222347 2.12770006
192 2.13522911 1.83024975 2.22761039 1.97355514 2.00688387 2.13989867
193 2.71243161 2.62711435 2.60889738 2.70307982 2.43227768 2.73527203
194 2.71850492 2.68567772 2.83420747 2.86800188 2.94490534 2.67642911
195 2.58064514 3.00033819 2.46271587 3.22724042 2.96067407 2.53625532
196 2.73718109 2.60916866 2.82225575 2.74750959 2.78924230 2.70593073
197 2.62228806 2.94970312 2.54257498 3.16052253 2.94472968 2.57283371
198 2.92588436 2.70303954 2.99535313 2.79281967 2.82591372 2.90385974
199 3.31798215 3.20288733 3.24787488 3.24839372 3.05981942 3.31432905
200 3.46688544 3.20530256 3.54319135 3.25867956 3.32422670 3.44109266
           103        104        105        106        107        108
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100                                                                  
101                                                                  
102                                                                  
103                                                                  
104 2.93915347                                                       
105 1.29379317 1.64695743                                            
106 3.35816241 0.61769436 2.07646006                                 
107 0.35782698 2.87027312 1.23954601 3.23650292                      
108 1.05875093 2.03486720 0.52870129 2.36775149 0.87289795           
109 0.62487302 3.04259253 1.45082631 3.36502950 0.30655855 1.00892937
110 0.43361650 2.87653571 1.25636877 3.23000975 0.07744877 0.86252878
111 0.30891385 2.79457024 1.15644605 3.17377334 0.10546572 0.82102020
112 3.44183969 0.50404342 2.14934475 0.48773730 3.36815493 2.52462615
113 2.17923239 0.99859138 0.95906472 1.21935982 2.02859353 1.15644605
114 3.47369379 0.61512183 2.18357303 0.22425555 3.36837011 2.50583595
115 3.53538022 0.64382223 2.24362687 0.33638333 3.43789444 2.57942146
116 3.45569585 0.54922364 2.16316118 0.35988665 3.36545284 2.51148480
117 0.69205046 2.69159945 1.12734979 3.00907404 0.35411884 0.65908712
118 1.29361940 1.65771198 0.16291958 2.11286386 1.26818933 0.62237031
119 1.31607640 1.85879549 0.55692731 2.15638007 1.11791412 0.28777158
120 1.23421178 1.73033788 0.20703817 2.16414483 1.18684365 0.53538599
121 2.87215345 0.20703817 1.58637888 0.71738916 2.80568276 1.97713480
122 2.21076129 1.05432593 1.01991267 1.23421178 2.04717386 1.17860228
123 1.95152281 1.04353720 0.70152040 1.51820356 1.90064732 1.12808149
124 2.37157508 1.69722118 1.55579080 2.30909566 2.51174984 2.05958504
125 3.37102740 1.07359807 2.15644823 0.60556027 3.19498446 2.33007541
126 2.68705364 0.97297951 1.55386428 1.56276337 2.72800073 2.05501705
127 1.98318092 1.48266327 0.98143904 1.63439776 1.77232897 0.94568178
128 2.40765086 1.87648245 1.67731290 2.48591081 2.56782439 2.16741893
129 1.97495017 2.93281547 1.91481991 2.99309011 1.62010631 1.43453004
130 2.19344217 1.20632005 1.13086529 1.79763723 2.24672674 1.63274169
131 2.43233355 2.35595447 1.85754836 2.28358504 2.11271982 1.54816297
132 2.12581286 1.25830271 1.08223726 1.84685254 2.18309923 1.58334442
133 3.18153717 0.90077782 1.95514403 0.56826962 3.01926169 2.15481689
134 2.64622743 0.81053790 1.46382092 1.38512733 2.65640685 1.94052177
135 3.98354716 2.02702702 2.89580452 1.49447352 3.74506132 2.93085520
136 2.97264594 1.36182485 1.93929219 1.91741814 3.05386223 2.44809285
137 2.63462184 2.30018182 1.97585641 2.17332841 2.32336809 1.71414433
138 2.59751527 0.91965036 1.44562168 1.49552263 2.61961798 1.92834434
139 3.95177853 1.86989343 2.82738172 1.32846231 3.72762703 2.89769243
140 2.38953394 1.02821427 1.26375616 1.60087722 2.41371950 1.74331223
141 2.26500021 2.98643146 2.11503415 2.98990409 1.91324123 1.66603072
142 2.87337124 1.61085876 1.94395167 2.18299741 2.98422932 2.44983074
143 2.93600925 0.80126746 1.71114370 0.73568645 2.79195602 1.93991536
144 2.78164682 1.41569169 1.79060326 1.98516007 2.86741481 2.29044406
145 3.56071804 1.76181983 2.48619751 1.32581302 3.32628114 2.51545526
146 3.20721567 1.72971648 2.25985628 2.26130465 3.31613754 2.76565163
147 1.72321215 1.82971850 0.96494590 2.02880747 1.49614422 0.78649404
148 2.63464114 1.02567136 1.51428790 1.57537993 2.65933114 1.98498168
149 2.82928073 1.52712950 1.80490272 1.35536318 2.59798619 1.79994550
150 2.71900747 1.59250342 1.80490272 2.16615001 2.82368339 2.29765748
151 2.44298769 2.00437857 1.68417650 1.94645745 2.16105861 1.48573185
152 2.37697646 1.69417195 1.55535891 2.28136243 2.49548905 2.03088134
153 2.31580013 1.96684787 1.56290552 1.95137589 2.03866190 1.36101064
154 2.26149470 1.33055417 1.26135780 1.89358258 2.31465948 1.72849920
155 2.27897013 2.21629334 1.67060664 2.20207142 1.97729500 1.38812660
156 3.14964313 1.45249434 2.11766400 1.96676388 3.22516664 2.61434403
157 3.16668885 2.31602283 2.37598064 2.05032148 2.86993532 2.20087483
158 2.81570104 1.11641165 1.71665878 1.65216741 2.85367344 2.19398334
159 3.31609523 2.25207761 2.46178495 1.93854811 3.02891893 2.32651936
160 2.77141516 0.96900025 1.62926353 1.49241366 2.78586786 2.09073848
161 1.37941535 2.37297419 1.15384786 2.60195771 1.10497897 0.75700111
162 2.94665438 1.28091058 1.88733011 1.80768144 3.00330903 2.37212271
163 4.08697981 2.12682127 3.00598576 1.61143856 3.85055801 3.04437710
164 2.98302591 1.67833888 2.05830998 2.22175292 3.08547582 2.54817859
165 1.97000755 2.23155212 1.45656936 2.33679667 1.69626000 1.17619852
166 2.46486984 1.37082134 1.47454138 1.88492668 2.50021752 1.90346162
167 2.51371849 1.99596825 1.74055889 1.95467963 2.25128851 1.58698510
168 2.95001596 1.86692714 2.10422535 2.40525545 3.06338034 2.57436037
169 2.71411548 1.61063736 1.74161802 1.54805581 2.49809793 1.74262268
170 2.68472912 1.08925451 1.56860836 1.47899164 2.64812571 1.93616039
171 2.79553758 2.13441113 2.02332248 2.00428959 2.52035806 1.86345494
172 3.01406403 1.23545256 1.92544950 1.67037841 3.02857929 2.35805589
173 3.07104896 2.11071765 2.22377950 1.89595348 2.80116785 2.10685530
174 2.73201307 1.86317091 1.92757395 2.40998273 2.84472707 2.38085976
175 2.30349939 2.66261153 1.94904739 2.67692561 1.99082334 1.59986008
176 3.01477326 1.58209779 2.04440273 2.07321678 3.08076036 2.50143322
177 2.07321678 2.93716987 1.97884700 3.01477326 1.75242039 1.55855791
178 3.05441160 1.13092248 1.92710399 1.50253966 3.04007198 2.33135155
179 2.18121805 3.08134394 2.13326317 3.15734531 1.87062085 1.72288834
180 2.84286448 1.90923277 2.03249601 2.41920557 2.93748625 2.46127211
181 2.73518057 1.78581959 1.83779759 1.79935207 2.54391474 1.85761105
182 3.02435812 1.84428017 2.14626316 2.30196826 3.08923522 2.56036011
183 2.65365534 2.51553484 2.10846426 2.48492290 2.37963248 1.88278015
184 3.24652558 1.88623205 2.33755398 2.31943889 3.31012053 2.76115592
185 2.45940297 1.87656110 1.65707274 2.01194166 2.29414437 1.67876833
186 3.34150315 2.17066390 2.52098000 2.63360124 3.43989748 2.95481663
187 2.21538518 2.76834549 1.96686521 2.87602864 1.96084797 1.67900214
188 3.18135444 1.57442076 2.16351741 1.86271268 3.15898566 2.50666094
189 2.92341736 2.39901270 2.24625285 2.32893345 2.67495320 2.10869950
190 2.89402302 2.07337968 2.13635973 2.52241769 2.96118410 2.50213029
191 3.15611627 2.07373132 2.28536906 1.96067219 2.94283605 2.27212505
192 2.97733682 1.70740131 2.04237145 2.03717802 2.96393327 2.36495824
193 3.68714328 2.70816212 2.92188570 2.49838617 3.44239914 2.83715311
194 3.10095290 2.54005401 2.49550318 2.97522946 3.18788515 2.82358319
195 3.11434203 3.06877461 2.70117530 3.05851925 2.87981750 2.51208056
196 3.27476014 2.48100432 2.58345571 2.81671598 3.30087943 2.86232023
197 3.13992017 2.98007681 2.68240773 3.03041159 2.95623676 2.57963357
198 3.54299535 2.58137247 2.81150315 2.84487329 3.54139258 3.06750249
199 4.11736224 3.22358941 3.43519250 3.10450693 3.92400954 3.40501837
200 4.00419726 3.06786268 3.33126523 3.33016648 4.02650993 3.59762090
           109        110        111        112        113        114
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108                                                                  
109                                                                  
110 0.24080754                                                       
111 0.40937534 0.17063984                                            
112 3.53353460 3.37260421 3.29391485                                 
113 2.14829796 2.01821790 1.97162819 1.43784823                      
114 3.50989510 3.36569789 3.30141048 0.31212596 1.36894555           
115 3.58539420 3.43702195 3.36901560 0.25477048 1.45097092 0.11212778
116 3.51904754 3.36634389 3.29479492 0.17260281 1.39550754 0.15950821
117 0.36594551 0.29901552 0.38439969 3.17941460 1.79049996 3.15220171
118 1.49656578 1.29162196 1.17949243 2.15766606 1.02709154 2.20615349
119 1.22647210 1.10169965 1.07196176 2.33502490 0.93841429 2.29657161
120 1.40624173 1.20689036 1.10169965 2.22744968 1.04326853 2.26259530
121 2.98182033 2.81315551 2.72896718 0.59763985 0.96283604 0.70070360
122 2.15613660 2.03394592 1.99375110 1.47211749 0.13800326 1.38457577
123 2.09937145 1.91479634 1.81909650 1.52845501 0.66380066 1.58498418
124 2.79590618 2.56140906 2.40776772 2.03837946 1.90836370 2.26335330
125 3.27757185 3.17615482 3.14710798 1.04415658 1.20775567 0.75336557
126 2.96989316 2.75861210 2.63295028 1.26580637 1.46296957 1.49373304
127 1.84165405 1.74847751 1.73392942 1.89366146 0.52213827 1.79005885
128 2.85751706 2.62100066 2.46341965 2.20761443 2.07457101 2.43546984
129 1.42949108 1.54816297 1.67273900 3.32641311 1.94219489 3.17923626
130 2.49811499 2.28117013 2.14987506 1.61372498 1.30540104 1.78387085
131 2.02145567 2.05515268 2.12741628 2.67342295 1.45573796 2.47824995
132 2.43684651 2.21853068 2.08575008 1.67450644 1.30736245 1.83903744
133 3.11680373 3.00432462 2.96695320 0.94959985 1.02704622 0.70228510
134 2.88250069 2.68113040 2.56572143 1.13523342 1.26689834 1.32965017
135 3.75734934 3.70965747 3.71955084 1.93663977 1.95722920 1.62583352
136 3.31304762 3.09192637 2.95466300 1.54626802 1.92500065 1.80973629
137 2.24504911 2.26850395 2.33272430 2.58078880 1.46249504 2.36668932
138 2.85240259 2.64695256 2.52726734 1.24594742 1.32022844 1.44107143
139 3.75670898 3.69611541 3.69655738 1.75459031 1.87897542 1.44513500
140 2.64902878 2.44213083 2.32109247 1.40470352 1.24125124 1.57181469
141 1.73038302 1.84297756 1.96196187 3.34803030 2.01949129 3.17746273
142 3.25565795 3.02812654 2.88276608 1.83185119 2.06404843 2.08663537
143 2.90826595 2.78227130 2.73434579 0.97673146 0.85276858 0.82330513
144 3.12886357 2.90688899 2.76817146 1.65653300 1.85199359 1.89620971
145 3.34675971 3.29275092 3.29893607 1.76461630 1.56865590 1.47070986
146 3.58558557 3.35926884 3.21504167 1.86331601 2.30079985 2.13553025
147 1.55160793 1.46985356 1.46596641 2.25385586 0.90080035 2.16905994
148 2.89254878 2.68737789 2.56724087 1.32288779 1.40179998 1.51219387
149 2.62899945 2.56662771 2.56916851 1.73631543 0.98282866 1.51688541
150 3.09239260 2.86690053 2.72330631 1.85004770 1.95477587 2.08335485
151 2.13138929 2.11618249 2.15487939 2.30887793 1.16167102 2.12063696
152 2.76996163 2.54192836 2.39456022 2.02720474 1.86074110 2.23142633
153 2.01773928 1.99554285 2.03020385 2.29403962 1.09289104 2.12150449
154 2.56348202 2.34938352 2.21942152 1.70351962 1.42043580 1.86648454
155 1.91816375 1.92659057 1.98242840 2.55133777 1.30879393 2.37729152
156 3.48050307 3.26215149 3.12716511 1.57833105 2.05348067 1.83978981
157 2.81002887 2.81932790 2.87129521 2.48975579 1.67631769 2.23185477
158 3.09244603 2.88399084 2.76000790 1.34536648 1.59861187 1.56198045
159 2.98254586 2.98101172 3.02512959 2.38569445 1.69909140 2.11514299
160 3.01261673 2.81158660 2.69541143 1.21967278 1.43289961 1.41329664
161 1.09774018 1.06630303 1.10434692 2.81570104 1.43528693 2.74286992
162 3.25040070 3.03707223 2.90754461 1.46448577 1.80611640 1.70045803
163 3.86516307 3.81613302 3.82441129 2.01746473 2.07891351 1.71456439
164 3.35176728 3.12795249 2.98573731 1.86775075 2.13786187 2.11411112
165 1.67194470 1.65509420 1.69363217 2.60808887 1.32707661 2.48273154
166 2.73585137 2.53121389 2.40930914 1.68640750 1.51420674 1.83887676
167 2.24152338 2.21231754 2.23905928 2.28283393 1.22857947 2.10387746
168 3.33158709 3.10808968 2.96433256 2.07173413 2.24545067 2.30359405
169 2.54294552 2.47154413 2.46619041 1.84640565 1.06054386 1.67010088
170 2.84190624 2.66393433 2.56850828 1.35000838 1.26990263 1.43746397
171 2.49045596 2.47714867 2.51371849 2.36976103 1.43125586 2.15867667
172 3.25116567 3.05421817 2.94006465 1.38253268 1.70656392 1.56304051
173 2.77771856 2.75909535 2.79107765 2.28455783 1.52411158 2.04727682
174 3.11177871 2.88970578 2.74666774 2.11693460 2.12985756 2.32830332
175 1.88879798 1.93583014 2.01319308 3.00126771 1.76084325 2.83704534
176 3.32848425 3.11657214 2.98618308 1.74976291 2.01646863 1.96326151
177 1.61063736 1.69323200 1.79166008 3.31384190 1.99450649 3.17344498
178 3.24566751 3.05973919 2.95625874 1.25355463 1.59632807 1.39865632
179 1.72652975 1.81363763 1.91168480 3.45014670 2.15749748 3.30971716
180 3.19343558 2.97905291 2.84293585 2.13542418 2.17262081 2.33114536
181 2.60423742 2.52379296 2.50865739 2.01543096 1.31670785 1.87961669
182 3.33018012 3.12494989 2.99834589 2.01925846 2.16016422 2.20091733
183 2.33062483 2.33638783 2.38300786 2.79151463 1.75981111 2.61777890
184 3.55064895 3.34527010 3.21882849 2.00543467 2.29433429 2.19851945
185 2.37457619 2.28103382 2.25476553 2.16713429 1.35477084 2.08077443
186 3.69480077 3.48149589 3.34561178 2.29597858 2.57681782 2.50923838
187 1.90762742 1.92222968 1.97205754 3.11779358 1.94481843 2.99801448
188 3.35112181 3.17697314 3.08104952 1.67399847 1.87369052 1.76788794
189 2.65876255 2.63883093 2.66612203 2.61776107 1.78556205 2.43851918
190 3.19567634 2.99742397 2.87442360 2.28943828 2.23564125 2.44269754
191 2.97378277 2.91621808 2.91639852 2.21665209 1.68173012 2.03745153
192 3.15827901 2.98410232 2.88679330 1.87693195 1.86616050 1.96576327
193 3.42619311 3.40649102 3.43146228 2.79313468 2.31131334 2.57883160
194 3.41925644 3.22715677 3.10496706 2.74353658 2.66101979 2.89261191
195 2.83954318 2.84524244 2.88334452 3.30045113 2.44434586 3.14855524
196 3.49772430 3.32802560 3.22726591 2.63798765 2.57780051 2.73696472
197 2.96680286 2.93485455 2.94400816 3.19868107 2.47333180 3.08585588
198 3.71971204 3.56250182 3.47277194 2.68690368 2.70044434 2.75936346
199 3.93915956 3.90024399 3.90543722 3.27836115 2.96197157 3.12518377
200 4.21159388 4.05175577 3.95689046 3.13358548 3.25173815 3.22459934
           115        116        117        118        119        120
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113                                                                  
114                                                                  
115                                                                  
116 0.10546572                                                       
117 3.22723070 3.16147261                                            
118 2.25971035 2.17570695 1.17827596                                 
119 2.37151685 2.30802431 0.86241293 0.64046021                      
120 2.31839658 2.23698899 1.07971802 0.13008267 0.54684732           
121 0.71893854 0.62270735 2.62694603 1.58102882 1.79032372 1.64695743
122 1.46685161 1.41625385 1.79505866 1.08038674 0.93785469 1.08228260
123 1.62895954 1.54245325 1.75258899 0.66317015 0.98147486 0.72094980
124 2.24853481 2.14333076 2.53575472 1.43917767 2.04909341 1.53603386
125 0.84006298 0.88292112 2.92056271 2.20230825 2.07959923 2.21914984
126 1.47087078 1.36652496 2.64904720 1.47733150 1.94844578 1.56936180
127 1.87311397 1.82795562 1.48257935 1.04901510 0.66869131 1.00005013
128 2.41766656 2.31275310 2.61113279 1.55265598 2.16751983 1.64348870
129 3.27410118 3.24539262 1.29218788 2.00491512 1.37358762 1.90036895
130 1.78752927 1.68506418 2.18876567 1.02770019 1.55718882 1.11669817
131 2.57738662 2.56724484 1.76000657 1.95489902 1.35598724 1.87732363
132 1.84536550 1.74336020 2.13063009 0.97393473 1.51549312 1.06261308
133 0.78489444 0.79963291 2.75546220 1.98999950 1.90315717 2.00809815
134 1.31544039 1.21256048 2.54841107 1.39548387 1.80604315 1.47654207
135 1.69882144 1.77046488 3.42545570 2.96233396 2.67253044 2.95284273
136 1.76413999 1.66452303 3.00891687 1.84493984 2.35991298 1.93733733
137 2.46533309 2.46341965 1.97135677 2.06778923 1.49891628 1.99640195
138 1.42634297 1.32367961 2.52333864 1.36665025 1.80328179 1.44792365
139 1.51259202 1.58642494 3.41641471 2.88619836 2.63662099 2.88243667
140 1.56914502 1.46803939 2.32300096 1.17272769 1.62606922 1.24959801
141 3.27297400 3.25294977 1.57950692 2.20129796 1.56289980 2.09731858
142 2.04598383 1.94518818 2.96963786 1.83289774 2.38573666 1.92266310
143 0.88535171 0.86050163 2.54296372 1.72532515 1.68578904 1.74102119
144 1.86029689 1.75909114 2.82903324 1.68288834 2.20694834 1.76845810
145 1.55026097 1.59957039 3.00830759 2.54423732 2.24730003 2.52676640
146 2.07887054 1.98403991 3.29534202 2.15270322 2.68862432 2.24157184
147 2.24430825 2.19375021 1.19803316 1.00356707 0.51435761 0.90927158
148 1.49228094 1.39232810 2.56411423 1.42379434 1.85366535 1.49624353
149 1.60331695 1.60427984 2.28389516 1.85767783 1.52241844 1.82326953
150 2.04991856 1.94868403 2.80489412 1.68497451 2.22912804 1.76645667
151 2.21111313 2.19769350 1.81895103 1.75349107 1.23170613 1.68102335
152 2.21456674 2.11193247 2.49669015 1.42077499 1.98746249 1.49552263
153 2.21019365 2.19033035 1.69949444 1.62909843 1.10444169 1.55332411
154 1.86293780 1.76315607 2.25410010 1.13949696 1.63539591 1.20611333
155 2.46787988 2.44872766 1.62791366 1.74304460 1.16214963 1.65599429
156 1.78350152 1.68932685 3.17170479 2.01865390 2.51004811 2.10284122
157 2.32541876 2.34646059 2.52082177 2.45510161 1.95578680 2.39669689
158 1.52727329 1.42854627 2.76817146 1.62368477 2.06697419 1.69899976
159 2.20668945 2.23573957 2.68330371 2.53823267 2.07405390 2.48797214
160 1.38570551 1.28777018 2.67869565 1.54561375 1.94551264 1.61529510
161 2.81737982 2.76355794 0.79448678 1.18279042 0.65790275 1.05784240
162 1.65565639 1.55872919 2.93387287 1.78822951 2.25575434 1.86613377
163 1.77452736 1.84600877 3.52957835 3.05877546 2.77438547 3.04365349
164 2.06732281 1.97022340 3.06067743 1.94036586 2.46636430 2.01930618
165 2.55994970 2.52357825 1.37087621 1.48929966 0.95298473 1.38230662
166 1.82577251 1.73150930 2.41895152 1.35270674 1.77716171 1.39999382
167 2.18329619 2.16791886 1.92160210 1.78080080 1.31593731 1.70417621
168 2.25940464 2.16341640 3.05063544 1.97348941 2.49771428 2.04199501
169 1.73877397 1.72508930 2.19577292 1.76160710 1.45492234 1.71286625
170 1.42949774 1.34948893 2.49525342 1.48547958 1.74060282 1.51467412
171 2.24030287 2.23931549 2.18224789 2.07118919 1.59673351 1.99887516
172 1.51897313 1.43316219 2.91803847 1.82907177 2.19690359 1.88310091
173 2.12777153 2.14055627 2.46385211 2.27336281 1.83465187 2.21288464
174 2.29460325 2.19725100 2.83513907 1.78905901 2.30941418 1.84966852
175 2.92027259 2.89837471 1.65425481 1.99651667 1.41210045 1.88758168
176 1.91577599 1.82493613 3.01999559 1.92615172 2.38159560 1.98753869
177 3.25567483 3.22467199 1.43897053 2.02117134 1.43738043 1.90066292
178 1.35766875 1.27913182 2.90209966 1.84313989 2.14588626 1.88843618
179 3.38890023 3.35849439 1.57468825 2.16462900 1.60283184 2.04151036
180 2.29407894 2.20176114 2.90978343 1.89262765 2.36736902 1.94062950
181 1.92829519 1.90543421 2.26498599 1.82086838 1.57814762 1.76294362
182 2.15736984 2.07218243 3.03017712 2.01460764 2.43462464 2.05577440
183 2.68876302 2.67423454 2.05799565 2.12789624 1.64221569 2.02986120
184 2.14430670 2.06312826 3.24645068 2.21125854 2.62870472 2.25702795
185 2.12325143 2.08268289 2.04453230 1.61355942 1.42157500 1.54446629
186 2.45238782 2.36821005 3.41018113 2.38561752 2.84906586 2.43590203
187 3.06334519 3.02823174 1.68379255 1.96056350 1.50440409 1.84141179
188 1.72945376 1.66723513 3.01557772 2.06401780 2.30737233 2.08268289
189 2.49906304 2.49131498 2.36375223 2.25088631 1.84523544 2.16636435
190 2.40968448 2.32621482 2.91108542 1.99324920 2.38265039 2.01465133
191 2.08384579 2.08314750 2.64631081 2.27810541 1.98986925 2.21904153
192 1.93881629 1.87100917 2.83404466 1.92983163 2.17771485 1.93779575
193 2.62532091 2.64378974 3.12876082 2.92442359 2.56218368 2.85463207
194 2.85701387 2.77682114 3.16194481 2.34426610 2.71817964 2.35347984
195 3.19852280 3.18376886 2.60580503 2.67923897 2.29067075 2.57660587
196 2.70319020 2.63783483 3.21657039 2.44732025 2.70691014 2.43943422
197 3.11925960 3.09582552 2.71879543 2.63004349 2.35966617 2.53680759
198 2.72253485 2.66905810 3.42928205 2.68560681 2.88742846 2.67206149
199 3.14148002 3.14904387 3.65744616 3.39362118 3.14490013 3.32331230
200 3.17644060 3.12537422 3.93636422 3.19821979 3.42964456 3.18853239
           121        122        123        124        125        126
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120                                                                  
121                                                                  
122 1.00198869                                                       
123 0.93694825 0.71565395                                            
124 1.60646790 1.97770715 1.27990826                                 
125 1.09006158 1.16084205 1.65639204 2.66040450                      
126 0.86968717 1.52219560 0.97872285 0.78952394 1.94499586           
127 1.41295167 0.43451239 0.91934629 2.18871433 1.45097092 1.83974531
128 1.78048513 2.14007388 1.43482430 0.18685940 2.83101595 0.94995476
129 2.88227996 1.88264021 2.27340823 3.41364613 2.67000584 3.24828886
130 1.08840753 1.36388306 0.67799362 0.62834319 2.08029215 0.50848648
131 2.32069902 1.37090829 1.96402542 3.22752880 1.88496981 2.87183268
132 1.14127086 1.36576048 0.66655925 0.62425191 2.11813155 0.57916240
133 0.88461014 0.97790621 1.42473234 2.42685348 0.25256040 1.72133890
134 0.67501175 1.31470360 0.82557641 0.96997883 1.72598819 0.24450622
135 2.05029250 1.88403131 2.50706816 3.60056823 0.96069031 2.89947380
136 1.26816917 1.98048358 1.41170234 0.74105376 2.32756676 0.46367483
137 2.26576985 1.36737566 2.00139742 3.27602411 1.73171518 2.86828416
138 0.78337860 1.36737566 0.82980729 0.87187601 1.82519335 0.20534006
139 1.89000519 1.80849946 2.39817918 3.45323819 0.80407517 2.73729012
140 0.88481893 1.28558222 0.67696045 0.81214744 1.87985937 0.37772830
141 2.93349843 1.94416498 2.39698578 3.57819366 2.61230874 3.35773045
142 1.50791766 2.11886284 1.48900993 0.55614317 2.56780318 0.65211747
143 0.71164314 0.79365599 1.13791576 2.14278398 0.60145900 1.46670753
144 1.29870373 1.90117766 1.28847106 0.58833259 2.34773676 0.45526789
145 1.75175453 1.47875166 2.10212786 3.23358692 0.72450555 2.56734063
146 1.63428193 2.35150198 1.76397037 0.87569966 2.67080470 0.84674965
147 1.73343255 0.82548524 1.07077198 2.24590747 1.82960423 2.01813328
148 0.87117334 1.43630208 0.89702221 0.88162597 1.87690650 0.29941998
149 1.46970298 0.86212683 1.49845313 2.71754077 0.88676063 2.16220294
150 1.46970298 2.00158548 1.35553553 0.49702766 2.50854437 0.62635993
151 1.94118182 1.04728149 1.63839320 2.90019029 1.53577249 2.49583937
152 1.56490561 1.90671355 1.21332774 0.36182245 2.57385535 0.77601921
153 1.89733948 0.97965541 1.53779232 2.79372684 1.57297065 2.41474220
154 1.18123862 1.45562949 0.78979832 0.67819543 2.13504152 0.58769539
155 2.15049090 1.20592794 1.73602577 2.98002126 1.81604922 2.64284508
156 1.34478421 2.09665931 1.55710917 0.92810300 2.36077357 0.62506820
157 2.28562861 1.56888080 2.24402999 3.50492510 1.50760975 2.98978723
158 0.97330479 1.63363886 1.10892788 0.88653771 1.98604459 0.31527768
159 2.22772040 1.59319100 2.27465110 3.52024414 1.37423952 2.96655704
160 0.80926171 1.46165171 0.98351151 1.00914999 1.80196263 0.34913276
161 2.27594740 1.38081114 1.50005448 2.51568650 2.39837619 2.44246101
162 1.14997243 1.84297756 1.30471748 0.86798941 2.16210040 0.43806725
163 2.12426675 1.99276878 2.58477371 3.65369765 1.05884670 2.94740124
164 1.55532738 2.17888753 1.56870316 0.73669862 2.57791714 0.74786101
165 2.12844228 1.22537831 1.55535891 2.70682644 2.01880439 2.46507317
166 1.19420515 1.52550287 0.94152868 0.89505153 2.08934128 0.67843985
167 1.90258375 1.09778850 1.61394854 2.83274346 1.53055134 2.42142958
168 1.72877432 2.27764225 1.65014341 0.79210041 2.72318477 0.93673103
169 1.50203015 0.92399990 1.41165396 2.58032382 1.13622795 2.07268017
170 0.88399394 1.24804426 0.91386418 1.37711904 1.60235880 0.84733842
171 2.05393361 1.30136064 1.87251772 3.09810175 1.51124858 2.64127111
172 1.06128257 1.71152035 1.28102021 1.21394335 1.92877296 0.68633889
173 2.04158187 1.39641231 2.00167434 3.21784568 1.35143009 2.69789987
174 1.71417693 2.15759266 1.51168271 0.71923506 2.69013768 0.94045898
175 2.57195323 1.65436314 2.07314162 3.24234806 2.27232181 2.97858083
176 1.42654314 2.03479016 1.48709543 0.98787838 2.36493481 0.77218370
177 2.84339856 1.90431122 2.22630578 3.32188115 2.65355584 3.15752518
178 0.94483409 1.58761369 1.25333047 1.40963345 1.71784669 0.80476420
179 2.97874095 2.06243873 2.36393386 3.43159755 2.78314080 3.27665128
180 1.74397161 2.18517986 1.58071727 0.95837177 2.66171688 1.04989208
181 1.63734120 1.18564599 1.48200533 2.52527871 1.44038607 2.06831052
182 1.66805173 2.15922560 1.62485477 1.19377666 2.51873056 1.08782539
183 2.40081130 1.63043031 2.04360961 3.18304952 2.03504034 2.83794632
184 1.71730961 2.29416967 1.78573253 1.32102151 2.55754240 1.15691420
185 1.70945372 1.23775346 1.36056278 2.31948625 1.74054401 1.97408011
186 2.01279027 2.58544422 2.02434864 1.33182006 2.89901541 1.35058765
187 2.63576171 1.83618578 2.05483969 3.06089466 2.52099524 2.88381161
188 1.37725291 1.83409415 1.54023605 1.70228606 1.94988753 1.24926929
189 2.27244559 1.64866845 2.04979925 3.14768957 1.85875788 2.73671124
190 1.88545878 2.22167793 1.68847544 1.33261727 2.67346010 1.34265695
191 1.93980916 1.54728210 1.92281931 2.95599864 1.50090347 2.44898527
192 1.50341440 1.82327811 1.47823940 1.62870131 2.09596350 1.29604581
193 2.58977117 2.17510531 2.60893109 3.64986961 1.96319467 3.13693139
194 2.35041912 2.63965907 2.11187242 1.67677982 3.09802928 1.79593338
195 2.91910805 2.31318890 2.58202050 3.54027840 2.61329505 3.24282382
196 2.27886874 2.52961762 2.13539112 2.01702707 2.84797377 1.92666696
197 2.80752626 2.34801614 2.48747981 3.29334670 2.65101261 3.02505205
198 2.37909876 2.63896411 2.32845251 2.32256466 2.82803066 2.13649988
199 3.06539560 2.83079972 3.07088791 3.86592917 2.66531383 3.42527422
200 2.87096789 3.19434544 2.85530267 2.68591152 3.33634947 2.56250996
           127        128        129        130        131        132
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126                                                                  
127                                                                  
128 2.33336735                                                       
129 1.47501916 3.52576816                                            
130 1.58979321 0.78761033 2.89866635                                 
131 1.04676168 3.36778704 0.86252878 2.63576610                      
132 1.57522065 0.77778912 2.86219386 0.07158705 2.61918746           
133 1.28971073 2.59507960 2.59208138 1.84073775 1.84906553 1.87794636
134 1.63794393 1.13150683 3.06882706 0.52588348 2.66040450 0.59449476
135 2.01652867 3.76858893 2.80258101 3.00235496 1.94054168 3.03376818
136 2.28529109 0.83628175 3.67546343 0.82117496 3.32040199 0.87846327
137 1.08930820 3.42060314 1.08758929 2.66914529 0.24066397 2.65856443
138 1.67071197 1.02935678 3.08319422 0.44304198 2.70206009 0.51274493
139 1.97537672 3.62042716 2.86602074 2.86335159 2.00806256 2.89804173
140 1.54723949 0.96666488 2.92315013 0.26956472 2.58898229 0.32945117
141 1.54183540 3.69470103 0.31253410 3.03663380 0.74810275 3.00525053
142 2.38492426 0.59763985 3.72051969 0.83279445 3.42888832 0.87187601
143 1.10760494 2.30443520 2.49443933 1.54456924 1.82410352 1.57902278
144 2.17052731 0.67837649 3.52614710 0.66080947 3.21134424 0.70942957
145 1.58299327 3.39644490 2.44496328 2.62108502 1.59563153 2.64734843
146 2.64000434 0.89226804 4.00847942 1.13598092 3.67626674 1.18240072
147 0.42638429 2.36647386 1.26866543 1.68686545 1.07261523 1.65775319
148 1.71846846 1.02052996 3.12088477 0.48803209 2.74608124 0.55208377
149 0.85997747 2.87171935 1.85887635 2.08933993 1.09111655 2.10034847
150 2.24106136 0.54130423 3.55427048 0.70030833 3.28265715 0.73249854
151 0.74625377 3.03983328 1.19872467 2.28991910 0.49899870 2.27982612
152 2.08933993 0.38682741 3.31842005 0.57409477 3.12376038 0.56961399
153 0.64308722 2.93055507 1.15998102 2.18900532 0.54644552 2.17609111
154 1.64922397 0.79553624 2.94393336 0.26931579 2.68658487 0.27866773
155 0.83329129 3.11143188 0.92004264 2.38875775 0.38014568 2.37045220
156 2.39910931 0.99553576 3.80028452 0.99249084 3.42318753 1.05019346
157 1.41033081 3.65614894 1.64357740 2.87886181 0.82430271 2.88153074
158 1.92609096 1.00840469 3.33354382 0.64226846 2.94814555 0.70684423
159 1.48984722 3.67502273 1.85038648 2.89218185 1.01640525 2.90014452
160 1.76139072 1.14424548 3.18516665 0.63640465 2.77386784 0.70152040
161 0.97920935 2.60829085 1.00132663 2.03776964 1.23352811 1.99327379
162 2.13359924 0.96374495 3.53253776 0.77707777 3.15671815 0.83738836
163 2.10865185 3.81464796 2.89801236 3.05661790 2.04614868 3.08913847
164 2.43464578 0.75237061 3.77437328 0.93911443 3.46956901 0.97918665
165 0.81037156 2.81710616 1.01815120 2.15001629 0.87385701 2.12242829
166 1.71305606 0.98282866 3.02280770 0.55192798 2.72697210 0.57467210
167 0.81773739 2.96340848 1.38876577 2.22359696 0.79732757 2.21551585
168 2.49742188 0.75978632 3.79097454 1.02670031 3.52441284 1.05379565
169 0.84745884 2.71793063 1.86170999 1.96128261 1.21534175 1.96780411
170 1.47202631 1.49487523 2.85689904 0.87836869 2.42835976 0.91550681
171 1.06912162 3.23330565 1.49235381 2.48112467 0.80386985 2.47802451
172 1.98077926 1.30724585 3.38204323 0.93998589 2.95859484 0.99558640
173 1.24877930 3.35969483 1.75601016 2.59370755 0.99633923 2.59864241
174 2.34400137 0.68307717 3.59455191 0.90828398 3.36478605 0.92228158
175 1.24893447 3.35261995 0.82222217 2.68099991 0.75567936 2.65506940
176 2.27715130 1.02609784 3.62821499 0.96351985 3.28496245 1.00771548
177 1.47371311 3.41711051 0.66937162 2.80487137 1.04547338 2.76901425
178 1.86128375 1.51615645 3.27279991 1.04547338 2.80487137 1.10040120
179 1.63549838 3.51999523 0.84564335 2.92259155 1.21534501 2.88642139
180 2.35919925 0.93124838 3.60725840 1.04170239 3.35831883 1.05878081
181 1.08532449 2.64156982 2.03017610 1.93850151 1.51185018 1.94246293
182 2.34530071 1.19557126 3.62642803 1.16012154 3.32024101 1.18848776
183 1.30488586 3.29219717 1.39529281 2.60446454 1.05635367 2.58966503
184 2.50470167 1.32300501 3.81575766 1.31350805 3.47506036 1.35006399
185 1.08673583 2.41749954 1.99313232 1.76807187 1.63420082 1.76081079
186 2.78692587 1.28645698 4.06660288 1.47995933 3.77230363 1.50910556
187 1.45127427 3.14141270 1.29853958 2.55283876 1.37592672 2.52153125
188 2.02256221 1.77082147 3.33191080 1.37499403 2.89390885 1.41358671
189 1.41094783 3.25775521 1.78851924 2.56419860 1.32848564 2.55919732
190 2.34189395 1.31010106 3.52236711 1.28641685 3.28116803 1.29633786
191 1.45445937 3.07289985 2.21433779 2.37092090 1.62616242 2.38062770
192 1.95908479 1.68110308 3.20388864 1.31258748 2.83477534 1.33772459
193 2.04029263 3.76278455 2.45660908 3.06868936 1.88761038 3.07786065
194 2.71807383 1.61295479 3.79663344 1.71494112 3.61322498 1.71643461
195 2.02580416 3.61808187 2.06300426 3.01921707 1.88521056 3.00475485
196 2.59069560 1.99813642 3.65601129 1.88431821 3.40094536 1.89381310
197 2.11638396 3.35333062 2.41307340 2.81935831 2.22417387 2.80751850
198 2.69926850 2.31827478 3.75137819 2.13801120 3.44584949 2.15353501
199 2.71440889 3.94125961 3.18181360 3.37211603 2.75482717 3.38197985
200 3.26123460 2.65385719 4.28931671 2.59586254 4.00090955 2.61258920
           133        134        135        136        137        138
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132                                                                  
133                                                                  
134 1.49579801                                                       
135 1.17928468 2.67464031                                            
136 2.11097475 0.67477884 3.27806254                                 
137 1.71600136 2.64760200 1.71983390 3.31538686                      
138 1.59167155 0.11212778 2.76983868 0.61929589 2.69631589           
139 1.02666685 2.51469398 0.20991374 3.10440860 1.79384691 2.61138851
140 1.63818792 0.29881993 2.80822257 0.75487150 2.59851262 0.22152099
141 2.55379915 3.16378085 2.64981514 3.78868849 0.93694825 3.18477442
142 2.34183437 0.86253524 3.51517968 0.29901552 3.44015044 0.77822213
143 0.35114255 1.22898769 1.47580852 1.86365207 1.71988710 1.31456545
144 2.11816409 0.64203630 3.29152954 0.24630979 3.21687790 0.55404321
145 0.87294689 2.33254388 0.47412118 2.96087011 1.38228147 2.41955249
146 2.45645842 1.04693725 3.61159291 0.38701997 3.67174351 0.98435062
147 1.65927937 1.83146484 2.34137940 2.43476314 1.16890304 1.84066315
148 1.63910826 0.23422516 2.81080814 0.60268862 2.73729012 0.15714169
149 0.82657530 1.92322528 1.21410907 2.58776351 0.94133741 1.98925658
150 2.27375551 0.79978520 3.44603162 0.41274262 3.29837899 0.70008384
151 1.46491261 2.27220453 1.72137995 2.93258513 0.43740488 2.31495281
152 2.33010688 0.90196759 3.49526138 0.74075034 3.16276611 0.79041517
153 1.48193195 2.19514555 1.82358875 2.85014876 0.53820926 2.23305010
154 1.88772805 0.58376910 3.04237043 0.81687263 2.71297269 0.48396913
155 1.73735634 2.42906040 1.98836610 3.07741084 0.45147391 2.46199679
156 2.14683689 0.78742931 3.29672163 0.24132741 3.40594230 0.74043914
157 1.55665808 2.75401670 1.24148042 3.42264921 0.58423959 2.81747592
158 1.75598605 0.36164952 2.92232138 0.43740488 2.93258513 0.30696709
159 1.44925082 2.72878012 1.03183140 3.39332641 0.77633490 2.79831230
160 1.56880915 0.25161353 2.73546336 0.61544316 2.75188019 0.23820021
161 2.23548047 2.28416843 2.83609323 2.82849982 1.40207457 2.27363307
162 1.93739864 0.55449930 3.09688878 0.29945918 3.14114751 0.49826348
163 1.25022149 2.71800270 0.31289045 3.30693804 1.81706218 2.80943049
164 2.34988079 0.91826741 3.51078299 0.38828341 3.47127209 0.83530332
165 1.88252485 2.26531456 2.34142995 2.86934110 0.96673805 2.27633868
166 1.84007226 0.63015617 2.97801985 0.84456181 2.73327190 0.54473755
167 1.43495047 2.19194376 1.75007097 2.83639028 0.72035645 2.22929834
168 2.48838032 1.08091694 3.64110464 0.63281950 3.53239400 0.98787974
169 1.00981848 1.83233876 1.52376049 2.47288617 1.10088057 1.88128361
170 1.35588361 0.65365310 2.46305982 1.12582604 2.39264705 0.65885012
171 1.46305752 2.40537861 1.55883959 3.05603359 0.64815567 2.45164999
172 1.70090495 0.62950796 2.82135412 0.73666754 2.92063332 0.61001580
173 1.34536648 2.45646333 1.27810004 3.10783990 0.79095071 2.51355248
174 2.44761812 1.05621788 3.59810453 0.74781648 3.38327621 0.95261148
175 2.18364995 2.77050148 2.38114176 3.38707251 0.84150498 2.78828400
176 2.13402893 0.84476783 3.26762399 0.58076475 3.26947600 0.77465617
177 2.54818658 2.96811217 2.80645634 3.55349028 1.19439522 2.97238053
178 1.49284454 0.67756662 2.59220886 0.94234344 2.75165085 0.69157470
179 2.67642924 3.08693712 2.91478835 3.66111628 1.34401874 3.08800739
180 2.41959293 1.12366620 3.54504699 0.87768789 3.36534432 1.02924667
181 1.28451115 1.83612651 1.84640565 2.42190821 1.42243749 1.86651811
182 2.28297668 1.11738210 3.37811641 0.94186105 3.30632810 1.04326903
183 1.94455301 2.61451315 2.12609306 3.22153753 1.01117991 2.63724016
184 2.33124611 1.19742245 3.41345969 0.95184715 3.44931921 1.13557932
185 1.55118909 1.76204767 2.23012353 2.30616306 1.60051051 1.76877273
186 2.67146333 1.44069879 3.76627700 1.05191929 3.75911795 1.36535688
187 2.38305816 2.69122056 2.75717426 3.23754770 1.44303544 2.68651204
188 1.73169444 1.13081813 2.72329010 1.31964337 2.83343556 1.12070846
189 1.77154967 2.50565872 1.94437472 3.09870764 1.22504648 2.53425265
190 2.43178481 1.34726408 3.49483656 1.25270327 3.27964517 1.26593572
191 1.41054446 2.21229195 1.67181466 2.78720172 1.48358392 2.25257687
192 1.86579185 1.18499308 2.86092430 1.37554670 2.79409988 1.15267166
193 1.94383858 2.89985112 1.78856498 3.46391221 1.71492922 2.94282773
194 2.85919862 1.81321657 3.88209696 1.65770643 3.61730633 1.72908818
195 2.51120430 3.03118366 2.66825253 3.55477556 1.83570164 3.03766358
196 2.62469852 1.87560513 3.54499087 1.87301029 3.37507420 1.81722852
197 2.51614015 2.82917943 2.84045815 3.28365501 2.17679200 2.82395211
198 2.62250446 2.06051332 3.45679524 2.10048196 3.39728540 2.01828749
199 2.59993277 3.21591157 2.63230565 3.65126024 2.61859758 3.23633593
200 3.13898906 2.51906963 3.94633373 2.44545720 3.95014577 2.47145775
           139        140        141        142        143        144
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138                                                                  
139                                                                  
140 2.66013204                                                       
141 2.72745555 3.03536040                                            
142 3.34635888 0.84195360 3.84911328                                 
143 1.33060882 1.33883417 2.47957859 2.07262142                      
144 3.12455944 0.62395984 3.64520960 0.23544517 1.84243402           
145 0.45114775 2.43392645 2.30802431 3.17736374 1.10600232 2.94748817
146 3.43197519 1.09608093 4.12408827 0.33434566 2.20761830 0.48311770
147 2.31011658 1.68005206 1.36454904 2.48794132 1.44059885 2.28336958
148 2.64979119 0.25527877 3.21686653 0.73969328 1.34794551 0.50485474
149 1.17991182 1.94351837 1.77690569 2.75552502 0.82228411 2.52230339
150 3.28230893 0.71706479 3.68218235 0.21689078 1.98475009 0.19948310
151 1.74599645 2.21074615 1.11059808 3.04872080 1.39718788 2.82379533
152 3.34611846 0.69934340 3.46468527 0.54922364 2.02012761 0.50833909
153 1.83741466 2.11970611 1.10296277 2.95673052 1.38475784 2.73411078
154 2.89920237 0.30546609 3.06959900 0.79430097 1.56898761 0.60970224
155 2.02359774 2.33748329 0.84081274 3.17129364 1.64911312 2.95266489
156 3.11609394 0.88575004 3.89952612 0.40639571 1.90037101 0.37405138
157 1.34352682 2.75736568 1.44461830 3.58240038 1.64370246 3.35034253
158 2.75269541 0.45309643 3.42639870 0.60905703 1.48043505 0.38439969
159 1.13917447 2.75457644 1.65771198 3.56734827 1.57198792 3.33424298
160 2.56809431 0.39091066 3.26848674 0.79584962 1.28815285 0.56587507
161 2.82651703 2.08546348 1.17385640 2.83189066 2.01700400 2.64947841
162 2.92232138 0.63417573 3.62827722 0.46826711 1.67059601 0.28837854
163 0.32942506 2.84860697 2.72988297 3.53991436 1.51272097 3.31443483
164 3.33760122 0.90240823 3.88962972 0.23939727 2.07236037 0.30878801
165 2.34182366 2.12169034 1.02829303 2.92180977 1.70049817 2.71251795
166 2.82704105 0.44048272 3.12296164 0.84428706 1.51075593 0.64447948
167 1.75204805 2.12478585 1.29068505 2.94603562 1.32258669 2.71827856
168 3.47097087 1.01119780 3.90817302 0.43188787 2.19301236 0.49604413
169 1.46949101 1.81294128 1.78732657 2.61206862 0.86995054 2.37820946
170 2.30724419 0.64231930 2.90796608 1.24834515 1.02502496 1.01939249
171 1.58697108 2.36498089 1.33632266 3.18339847 1.41652888 2.95213049
172 2.64495825 0.71385761 3.44478663 0.88125136 1.41858633 0.68799610
173 1.31378301 2.45244541 1.58310769 3.25903875 1.36125144 3.02463178
174 3.43644996 0.92192289 3.71739781 0.54059251 2.13500450 0.54303670
175 2.42454658 2.64295225 0.68489163 3.44850219 2.06246651 3.23578688
176 3.09285913 0.84033363 3.71747596 0.58220620 1.84454636 0.48035799
177 2.84891069 2.80485718 0.63250962 3.58227852 2.39962842 3.38332066
178 2.41498196 0.79095071 3.31654826 1.11214229 1.21450204 0.90704262
179 2.95750488 2.91885660 0.78207530 3.68299522 2.52140776 3.48512581
180 3.38120348 1.00457771 3.71274638 0.72752711 2.10214081 0.69177956
181 1.77568289 1.78512550 1.96078837 2.53173140 1.07254692 2.30295981
182 3.20850233 1.05208794 3.70719418 0.88039525 1.97341965 0.80048882
183 2.14671407 2.51539259 1.23971632 3.30071572 1.81638578 3.07893994
184 3.23587465 1.18463621 3.88782862 0.92220453 2.04004140 0.86558558
185 2.15580972 1.65031598 1.96987775 2.37125540 1.27844601 2.15336441
186 3.58837126 1.40405373 4.15491518 0.93780256 2.37896557 0.96814566
187 2.76196579 2.52226485 1.25196392 3.25573218 2.18041415 3.05584613
188 2.55273483 1.15406992 3.35285640 1.41392192 1.44280358 1.23667132
189 1.94241289 2.43717951 1.63228874 3.19580450 1.64806722 2.96981598
190 3.33695928 1.21560046 3.60469098 1.14650381 2.10271258 1.06993792
191 1.62037604 2.19652967 2.08166644 2.91632196 1.29407921 2.68692090
192 2.70282026 1.13081813 3.23754770 1.41430536 1.54916557 1.24202932
193 1.79312961 2.89268795 2.24912849 3.59622417 1.91003047 3.36875673
194 3.72741508 1.67103059 3.87738959 1.51120486 2.52930896 1.48088268
195 2.67191907 2.91685307 1.90509884 3.60271271 2.34951941 3.39395011
196 3.39393770 1.77225194 3.69154828 1.80984026 2.31050527 1.71713750
197 2.80534112 2.70839957 2.30254165 3.31243958 2.30673603 3.11611268
198 3.30577092 1.99296144 3.75671339 2.07649015 2.33228632 1.96913196
199 2.59144615 3.18942577 3.00478151 3.74265529 2.49034737 3.54027257
200 3.79010363 2.46233863 4.29321386 2.39641377 2.86133842 2.33206583
           145        146        147        148        149        150
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144                                                                  
145                                                                  
146 3.29857143                                                       
147 1.89069461 2.76221142                                            
148 2.45264927 0.93555975 1.86475608                                 
149 0.75266763 2.93616507 1.14009174 2.01911054                      
150 3.08868635 0.50933127 2.31919412 0.63705605 2.63325819           
151 1.30358875 3.27899491 0.81909396 2.34385749 0.67274854 2.89937103
152 3.10925304 0.86197726 2.11457081 0.73924115 2.58075172 0.36621844
153 1.39550754 3.19442831 0.68362042 2.26101231 0.72004782 2.80364099
154 2.64760200 1.08408213 1.70682307 0.43810653 2.11063137 0.61311710
155 1.58297199 3.41909339 0.77872044 2.48979693 0.95919760 3.01293286
156 2.98545582 0.32023010 2.54435834 0.68335372 2.64248297 0.50260337
157 0.95961250 3.77315010 1.56796749 2.84970498 0.84109230 3.45315504
158 2.58103256 0.75053055 2.07535775 0.21434013 2.18738929 0.54583378
159 0.77330440 3.74246576 1.68608272 2.83075955 0.81321209 3.44647028
160 2.38945538 0.94111921 1.92737554 0.15312747 1.99559457 0.71789507
161 2.39247094 3.12856923 0.57903300 2.28877412 1.65385481 2.64915657
162 2.76535106 0.55212361 2.27340823 0.41639723 2.38945538 0.45060690
163 0.53024773 3.62363400 2.40294937 2.83350667 1.26470683 3.46418193
164 3.16960796 0.30546609 2.52514609 0.75476241 2.76017059 0.26956472
165 1.89463293 3.18315974 0.51306174 2.28214987 1.18614892 2.74321482
166 2.58160613 1.07077198 1.76397037 0.41984592 2.07457101 0.65493152
167 1.30170356 3.16431028 0.82813082 2.23666254 0.65326502 2.78723683
168 3.28268081 0.50153288 2.54764775 0.88535749 2.84414339 0.36795365
169 1.04997928 2.79658282 1.00219034 1.88136259 0.41881685 2.46774051
170 2.07279402 1.40016768 1.59689669 0.57132392 1.63055473 1.10955418
171 1.13996508 3.38584437 1.12526441 2.46025873 0.65067234 3.03198065
172 2.47848937 0.93314406 2.11558560 0.47797170 2.12467016 0.79957097
173 0.87809439 3.43849519 1.37718350 2.52373313 0.59485909 3.12013098
174 3.21906053 0.71444571 2.36338662 0.84428706 2.73602821 0.37936317
175 1.97808341 3.70246632 1.02502496 2.79378168 1.38810391 3.27052972
176 2.91808343 0.61428973 2.36320835 0.64174931 2.52373313 0.50094971
177 2.40202093 3.85626783 1.16154576 2.97653088 1.78052569 3.39586789
178 2.25122897 1.16455914 2.01703735 0.58396165 1.92578308 1.02829303
179 2.51023121 3.95304158 1.31033890 3.08309812 1.90396391 3.49151374
180 3.16338522 0.83408202 2.36853280 0.89505153 2.69542911 0.57557744
181 1.38478775 2.70752037 1.10631412 1.83118037 0.84817054 2.36939146
182 3.00709961 0.91830961 2.37501957 0.89206925 2.58574621 0.75352848
183 1.70668511 3.51892737 1.14938918 2.61987711 1.17952754 3.12296849
184 3.06314228 0.87514187 2.55815566 0.98960720 2.69074855 0.84496406
185 1.76259281 2.57143386 0.98296655 1.71863337 1.15055264 2.18878865
186 3.41528699 0.84977367 2.81814670 1.23101261 3.02595511 0.89149166
187 2.31533974 3.50578574 1.11149008 2.65787209 1.68009818 3.05759601
188 2.36300245 1.44780064 2.10248226 0.98537388 2.03087318 1.29504230
189 1.52622335 3.38279738 1.33131585 2.50343239 1.09298354 3.02462804
190 3.09697986 1.23444888 2.30616306 1.11507304 2.62265837 0.98183566
191 1.25558502 3.06204543 1.49593269 2.21378519 0.95263454 2.76362419
192 2.47046214 1.49586367 1.98113824 1.00867889 2.05890253 1.26008957
193 1.49354710 3.72625598 2.05120366 2.90103345 1.44042614 3.44442633
194 3.47903006 1.56370199 2.63199593 1.58005569 2.99954524 1.36355430
195 2.27699353 3.79065942 1.81254097 2.97959527 1.86472280 3.41099626
196 3.15030555 1.84860020 2.51379073 1.66251636 2.72660682 1.65641321
197 2.43193620 3.47865927 1.90332206 2.74221112 2.00349706 3.11839599
198 3.08156258 2.08705812 2.63777459 1.86562041 2.72310192 1.93502380
199 2.35026174 3.82877219 2.64885310 3.14981134 2.25624069 3.58335614
200 3.59250960 2.35224382 3.19242968 2.31529685 3.27231647 2.28070266
           151        152        153        154        155        156
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151                                                                  
152 2.76430245                                                       
153 0.13645845 2.65747368                                            
154 2.31260647 0.47017437 2.21069356                                 
155 0.28895478 2.84636497 0.26479350 2.41113707                      
156 3.01425563 0.85991695 2.93607404 0.93462187 3.16877475           
157 0.75391072 3.37206239 0.89020123 2.90521101 0.92188698 3.48212617
158 2.53889838 0.75170403 2.45947610 0.57790956 2.69173136 0.47704433
159 0.89386415 3.38798223 1.02655648 2.91841080 1.09703249 3.44439293
160 2.35982030 0.86747115 2.28402209 0.58436063 2.52054931 0.65575477
161 1.16335210 2.38637887 1.03769565 2.04515154 0.97872285 2.94687909
162 2.74555162 0.74256960 2.66577071 0.70002149 2.89714685 0.27555989
163 1.78348428 3.52044339 1.88504444 3.06959900 2.05238023 3.30485252
164 3.06799067 0.61523750 2.97831714 0.83518573 3.19624298 0.34501467
165 0.66603889 2.54076733 0.55633230 2.13493186 0.51682837 2.95530467
166 2.31661874 0.60875484 2.22153912 0.30500790 2.43128604 0.88320431
167 0.33376135 2.65950123 0.33656285 2.20849443 0.49486020 2.89574263
168 3.11908302 0.59223682 3.02456466 0.87306416 3.23358692 0.57554317
169 0.72006087 2.39655407 0.72033309 1.93349551 0.95862275 2.50936213
170 1.97752768 1.14270123 1.90475631 0.74520961 2.14080495 1.12216383
171 0.43305298 2.92534960 0.52239247 2.46774051 0.61808256 3.10564922
172 2.51297800 0.99545835 2.44245110 0.79460016 2.68094554 0.64533811
173 0.66483771 3.04745373 0.77159461 2.58264978 0.88965918 3.14505752
174 2.96709557 0.43305298 2.86691696 0.72236423 3.06579047 0.73892938
175 0.76423587 3.07346118 0.73920400 2.66481321 0.53532786 3.46546758
176 2.85491299 0.75237061 2.77156385 0.78924079 2.99565255 0.45230590
177 1.14193657 3.16009999 1.08944656 2.78832818 0.87552899 3.64437830
178 2.34771072 1.19342672 2.28615152 0.91571325 2.53123663 0.86301407
179 1.28514026 3.25388015 1.23822785 2.88972968 1.03446632 3.74285845
180 2.94030560 0.64355130 2.84415155 0.81621340 3.04562168 0.80971934
181 1.02235393 2.29052146 0.99516979 1.85246345 1.19150142 2.43061980
182 2.87800163 0.88341496 2.79167199 0.92615350 3.00404795 0.81543053
183 0.79496477 2.97022055 0.79864672 2.54710801 0.76581499 3.26213981
184 3.02384909 1.04514060 2.94396939 1.10040388 3.16450080 0.77578781
185 1.17710550 2.06404176 1.10758872 1.65478924 1.27163239 2.32221232
186 3.33206501 1.08436605 3.24572381 1.27615744 3.45818651 0.88395595
187 1.20847759 2.83939776 1.14162743 2.47661724 1.05543023 3.29218419
188 2.41253197 1.40952828 2.35240339 1.17272884 2.58296864 1.19720007
189 0.96255484 2.91305416 0.98266553 2.48438451 1.04498898 3.11195560
190 2.84449860 0.98266553 2.75131082 1.02370779 2.94373797 1.15978765
191 1.17264613 2.71474635 1.19665356 2.28042165 1.35851667 2.77295607
192 2.36240583 1.30325409 2.29007803 1.07887984 2.50427362 1.27826517
193 1.55232788 3.39964323 1.61611079 2.97286929 1.69593654 3.43496815
194 3.18050189 1.33955455 3.08539262 1.45368171 3.25975657 1.54979778
195 1.62500029 3.26480086 1.62087837 2.89321846 1.59910321 3.54940340
196 2.94100155 1.66150299 2.86221300 1.61763705 3.04087385 1.74214524
197 1.88198674 2.98712178 1.85499973 2.65444243 1.89112780 3.25273126
198 2.97189243 1.97102871 2.90700075 1.87893960 3.08829491 1.95075601
199 2.38069715 3.55600517 2.40625973 3.20549525 2.49102128 3.56841987
200 3.52765744 2.34493509 3.46444763 2.33400738 3.64126016 2.26853194
           157        158        159        160        161        162
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157                                                                  
158 3.02359200                                                       
159 0.21476114 2.99549550                                            
160 2.83282950 0.19362193 2.80282138                                 
161 1.89340447 2.49769299 2.05312426 2.37300256                      
162 3.22685502 0.20991374 3.19573619 0.39564141 2.68159244           
163 1.30286009 2.93673069 1.09091639 2.75085162 2.89329232 3.10510896
164 3.59025963 0.59630223 3.57093786 0.78613135 2.87285917 0.41982747
165 1.36906643 2.48511017 1.52321774 2.33098293 0.59844930 2.68035640
166 2.87886181 0.51866850 2.88153074 0.51138941 2.12164873 0.63187808
167 0.87306416 2.42390465 0.98086928 2.24567316 1.18864576 2.62467746
168 3.66401996 0.75648934 3.65351498 0.92988915 2.86015409 0.60742567
169 1.06595437 2.04995392 1.07314157 1.86413941 1.49620550 2.24645564
170 2.45151275 0.68943684 2.42946413 0.53654069 2.05433085 0.85949362
171 0.61602018 2.63924363 0.71961650 2.45527405 1.45962190 2.83915433
172 2.95706097 0.38911992 2.91780703 0.37936317 2.55144461 0.44031061
173 0.49397349 2.68997349 0.50929748 2.50074665 1.75496273 2.88706382
174 3.54126382 0.77189764 3.54343387 0.91828990 2.64854429 0.68216722
175 1.23043084 2.99349906 1.42172637 2.83263135 0.96187854 3.19003459
176 3.35119736 0.49085137 3.32586958 0.63118204 2.73534688 0.36883627
177 1.64282515 3.18033902 1.84138799 3.03435522 0.85892334 3.37065947
178 2.75526430 0.55906194 2.70741969 0.46376468 2.48209765 0.65714184
179 1.74927151 3.28303419 1.94487385 3.13943833 0.99577203 3.46927247
180 3.49640114 0.81867060 3.49420188 0.94215729 2.66089163 0.73627060
181 1.40157325 1.98683938 1.41793156 1.81527252 1.52747897 2.16750102
182 3.38908275 0.79986556 3.37316810 0.89288331 2.70590278 0.72752711
183 1.13528267 2.80064243 1.26953661 2.63369576 1.27891159 2.98971599
184 3.50116201 0.85728107 3.47250225 0.96040516 2.91059066 0.74886752
185 1.69901992 1.88154997 1.74808008 1.72999547 1.32548116 2.05450455
186 3.83542752 1.08656819 3.81331732 1.22598520 3.13185681 0.93749150
187 1.74389393 2.84454728 1.90000220 2.70539582 0.95055995 3.02069337
188 2.81310437 0.96814566 2.77181249 0.90820574 2.52040195 1.02183473
189 1.17128146 2.66571419 1.24137647 2.49575219 1.57286477 2.84694590
190 3.39000887 1.07887984 3.39227567 1.14299677 2.57561814 1.04503132
191 1.29534980 2.35036843 1.27742270 2.17645430 1.87916956 2.52221729
192 2.82279637 1.02370779 2.80366912 0.97493849 2.34953700 1.08398396
193 1.38969784 3.02817438 1.36175971 2.85615562 2.34092358 3.19262952
194 3.73195553 1.53531603 3.74224032 1.60923271 2.83528532 1.47879538
195 1.84580787 3.13090224 1.93922958 2.98501255 1.84208072 3.29071767
196 3.42068159 1.63913035 3.41843362 1.65506300 2.75680806 1.62643635
197 2.18199446 2.87087618 2.24793417 2.74401722 1.97377330 3.00838169
198 3.38515807 1.83967888 3.36922489 1.83355521 2.90429007 1.83570164
199 2.36804258 3.23498217 2.34520934 3.09884693 2.87432301 3.35534854
200 3.92178570 2.25468833 3.90016510 2.27949288 3.43450913 2.20944542
           163        164        165        166        167        168
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163                                                                  
164 3.51435480                                                       
165 2.36840659 2.93339705                                            
166 2.97525899 0.79823232 2.14590985                                 
167 1.75630714 2.94067698 0.61920560 2.17305373                      
168 3.63142736 0.25047486 2.93632089 0.80461368 2.97493318           
169 1.50300432 2.59084268 1.00585304 1.86032960 0.50933127 2.64227566
170 2.44189312 1.18614133 1.92850340 0.55111977 1.81290924 1.24183018
171 1.55182294 3.17247328 0.87846327 2.41912621 0.30891385 3.21492188
172 2.79557145 0.76431144 2.46711222 0.57773665 2.35416978 0.85404828
173 1.25328196 3.24205134 1.18073398 2.51823660 0.57956606 3.29879115
174 3.58936376 0.42638429 2.74634349 0.66270395 2.82130314 0.24711975
175 2.39745879 3.45374084 0.53569963 2.66258315 0.76925181 3.45528287
176 3.24497336 0.38682741 2.73155809 0.61561751 2.69739094 0.41639723
177 2.83119519 3.59588297 0.72282548 2.80924987 1.16413596 3.57855259
178 2.55759342 1.00835690 2.34451179 0.69435764 2.18159208 1.09727053
179 2.92057185 3.68583516 0.85077383 2.89545760 1.26730269 3.65705669
180 3.51498522 0.55157673 2.71810706 0.65977685 2.76948989 0.35919311
181 1.76768206 2.47699860 1.06245255 1.72817529 0.72073642 2.49183156
182 3.32804890 0.67060193 2.69585437 0.68716055 2.68701255 0.54954039
183 2.07480324 3.27038709 0.71304287 2.48111614 0.57291372 3.26682106
184 3.35589092 0.69060023 2.87564930 0.86575121 2.82999458 0.60350642
185 2.16415035 2.31406939 0.97604073 1.53482781 0.88963941 2.29687694
186 3.71243785 0.70625427 3.14537448 1.09289104 3.14228285 0.54507484
187 2.72010297 3.22959880 0.67756662 2.43555125 1.04312776 3.18520526
188 2.63567346 1.25028274 2.34450762 0.87895586 2.18760935 1.24397535
189 1.84334293 3.14255463 1.00311719 2.37536843 0.66148418 3.14171198
190 3.43219399 0.96213673 2.58730564 0.78716894 2.63422605 0.78423247
191 1.52988185 2.84528927 1.33981265 2.13190874 0.87201936 2.86319359
192 2.77668205 1.25319516 2.21422705 0.77823983 2.12882544 1.19907458
193 1.58188184 3.51274275 1.76164862 2.81322426 1.29915893 3.52236845
194 3.79806652 1.31966684 2.86534071 1.24132731 2.94926119 1.09949281
195 2.53063060 3.52247013 1.40423133 2.75969308 1.35198836 3.46973634
196 3.42468787 1.60648243 2.67229467 1.34346694 2.67336927 1.44227336
197 2.68198803 3.20556414 1.60341152 2.48283739 1.56891320 3.12873082
198 3.30772554 1.86599959 2.74813480 1.58754761 2.68414480 1.72795598
199 2.38023417 3.60364563 2.38246767 2.97890901 2.07097382 3.55901481
200 3.78014984 2.16820048 3.29268671 2.04944798 3.23423042 2.00811486
           169        170        171        172        173        174
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169                                                                  
170 1.42318249                                                       
171 0.61311710 2.01913996                                            
172 1.94499586 0.54583378 2.54996773                                 
173 0.65831455 2.07227168 0.30901697 2.58141400                      
174 2.51708504 1.15893934 3.07259852 0.87255899 3.17539959           
175 1.26779001 2.40837639 0.85988790 2.95256801 1.15189862 3.26683954
176 2.32507421 0.90289823 2.91636270 0.45099599 2.97447501 0.48982020
177 1.64248175 2.63073720 1.29145364 3.16420059 1.58722919 3.37235898
178 1.74980181 0.42842977 2.36012743 0.24608766 2.37414865 1.09992160
179 1.73683166 2.71819488 1.37974802 3.24914728 1.66947560 3.44769316
180 2.45135395 1.09155901 3.01186022 0.80043861 3.10718688 0.25161353
181 0.43310072 1.30926475 0.85582246 1.82559113 0.93588597 2.35553977
182 2.33387841 0.96862730 2.90932886 0.63906675 2.98136210 0.53003979
183 0.95069127 2.15287578 0.60488993 2.68966346 0.85168311 3.09497539
184 2.45080486 1.07645842 3.03819350 0.65875451 3.09029890 0.67119888
185 0.74350673 1.21967351 1.10796427 1.73731797 1.26412347 2.13288013
186 2.78229528 1.40098408 3.36188018 0.97726147 3.42688499 0.65629585
187 1.39929498 2.24618371 1.21244253 2.76565163 1.49614422 2.97969444
188 1.76999928 0.63530340 2.35760615 0.59800083 2.37837912 1.21485133
189 0.80571605 1.98980178 0.63263013 2.50634366 0.75676937 2.98903778
190 2.32716208 1.08576884 2.86825916 0.92143468 2.96752914 0.66677001
191 0.64466658 1.67060664 0.83997031 2.14719614 0.80313786 2.74428363
192 1.76021414 0.65198752 2.32416882 0.71209762 2.38183317 1.11641165
193 1.25196392 2.34974293 1.12629644 2.79994053 1.01590566 3.40691773
194 2.67258564 1.52973926 3.18180375 1.36978326 3.29229005 1.00097056
195 1.54278169 2.45850841 1.35766116 2.94086497 1.50090347 3.29549526
196 2.37457800 1.41726898 2.87035128 1.36152153 2.95351530 1.35542998
197 1.61909665 2.21538518 1.63413461 2.64546422 1.76233869 2.96010910
198 2.36631282 1.54477253 2.84829495 1.51273530 2.90329813 1.66515218
199 1.95640310 2.58083271 1.99737893 2.92885237 1.94987699 3.45220748
200 2.91739919 2.06018980 3.38887220 1.93404338 3.43508262 1.98242458
           175        176        177        178        179        180
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175                                                                  
176 3.23598650                                                       
177 0.43644898 3.40251992                                            
178 2.81169300 0.69245967 3.04919849                                 
179 0.53744829 3.48136901 0.20703817 3.13371383                      
180 3.22618636 0.43399471 3.34400000 1.01268730 3.40784285           
181 1.34604074 2.17745248 1.67654181 1.63792922 1.72899238 2.25572010
182 3.18724845 0.37137327 3.33782757 0.82396296 3.39601481 0.30546609
183 0.57918027 3.00270868 0.93963805 2.52344016 0.95069202 3.01520417
184 3.36021689 0.39507607 3.52790172 0.84071907 3.58610717 0.47615988
185 1.34506811 2.02683529 1.58751407 1.59042969 1.62782898 2.03398086
186 3.63823913 0.59737179 3.77840386 1.18203030 3.83310012 0.50376910
187 0.66853098 2.99352537 0.66966187 2.64906430 0.60897551 2.91117780
188 2.78083436 0.86680333 3.01156694 0.50160761 3.06437386 1.03425435
189 0.98501131 2.84354443 1.34655222 2.32066066 1.34865223 2.88456282
190 3.06788228 0.71564911 3.18660546 1.06073455 3.22727501 0.43310072
191 1.46168637 2.52190108 1.83683642 1.93659038 1.86262417 2.62329801
192 2.66058706 0.88319961 2.85713756 0.67400469 2.90122316 0.92325421
193 1.67138300 3.17420351 2.04509981 2.58271798 2.02438485 3.26856385
194 3.32172965 1.12760081 3.40843920 1.50063257 3.42503160 0.79213019
195 1.27515706 3.21144575 1.45120661 2.78327298 1.34191261 3.16329264
196 3.08181982 1.29846396 3.21522198 1.40083926 3.21625885 1.11275447
197 1.63761047 2.87939083 1.79241634 2.50488475 1.69617116 2.80276390
198 3.11818287 1.52633236 3.28292314 1.50295027 3.27307625 1.41726898
199 2.35964217 3.23033854 2.63786592 2.74026633 2.56249281 3.25981604
200 3.64812681 1.86923400 3.79899425 1.95463019 3.77568988 1.73437678
           181        182        183        184        185        186
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181                                                                  
182 2.12152943                                                       
183 0.92191584 2.92664734                                            
184 2.24323592 0.23145255 3.07770874                                 
185 0.40158821 1.93221827 0.99665651 2.08324123                      
186 2.56761098 0.45579189 3.37587570 0.35782698 2.38005668           
187 1.26499281 2.87540071 0.68006879 3.05912717 1.09967211 3.30890919
188 1.54329134 0.76879939 2.42605972 0.78613135 1.46048581 1.13465519
189 0.68672170 2.75803887 0.41274262 2.88679248 0.86544190 3.20009102
190 2.06630726 0.36834931 2.81009667 0.54849548 1.82329883 0.65086294
191 0.46880115 2.45448778 0.93282962 2.54952451 0.81129309 2.88389986
192 1.49439830 0.69682451 2.32668267 0.78975346 1.33712949 1.10424722
193 1.14754309 3.08215188 1.12504188 3.16314072 1.43289961 3.49405287
194 2.36564128 0.77011802 3.05216454 0.86877041 2.09406470 0.81614437
195 1.28965574 3.04431279 0.84157041 3.18368237 1.27163239 3.45818651
196 2.02482494 0.94151531 2.73202806 1.00377870 1.79529858 1.11949260
197 1.25343747 2.67016605 1.18112493 2.80123332 1.14900731 3.05766630
198 1.99812520 1.19794421 2.71311187 1.21513059 1.81902660 1.36768021
199 1.65572588 3.04194707 1.79521912 3.09821365 1.78035600 3.38712527
200 2.54379760 1.53407571 3.23277691 1.49916223 2.36992085 1.54504683
           187        188        189        190        191        192
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188 2.52338739                                                       
189 0.97229267 2.18455398                                            
190 2.69186419 0.87587538 2.65747368                                 
191 1.43428736 1.79636671 0.55235439 2.40517706                      
192 2.35006412 0.29881993 2.11422801 0.68255934 1.78706628           
193 1.68897379 2.39485780 0.77097928 3.01364936 0.69820616 2.39374530
194 2.87267744 1.23064727 2.89875380 0.46845033 2.67600562 1.02725227
195 0.93295052 2.53538768 0.77777206 2.85981130 1.16554492 2.40506003
196 2.62860329 0.97768738 2.52345154 0.69141154 2.26423094 0.78423247
197 1.15978765 2.18777917 1.01503381 2.46050391 1.19349412 2.03806655
198 2.67120113 1.02078063 2.46050391 1.01503381 2.16512139 0.89684940
199 2.10072626 2.38948715 1.44650004 2.91365108 1.31671938 2.36139028
200 3.17026339 1.49553082 2.97119720 1.36610737 2.67511453 1.41073660
           193        194        195        196        197        198
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194 3.23399297                                                       
195 1.08233390 2.98684765                                            
196 2.76602657 0.57714210 2.58646142                                 
197 1.25808374 2.53927580 0.53723775 2.11306869                      
198 2.60427964 0.92889900 2.49996510 0.36850800 2.00977170           
199 0.99501964 3.00178650 1.25618368 2.45865665 1.09152972 2.20863776
200 3.05225003 1.12202305 2.93795609 0.75567936 2.42171144 0.56335491
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Calculate Distance Matrix

• Keep Categorical

# Notice use of `gower` cluster package/daisy function
library(cluster)
mall_dist = mall_customers |> mutate(Gender = as_factor(Gender)) |> 
  column_to_rownames(var = "CustomerID")  |> 
  daisy(metric = "gower")

Create Clusters

library(ggdendro)
mall_clusters = mall_dist |> 
  hclust(
  method = "average"
) 

mall_clusters |> 
  ggdendrogram( rotate = TRUE,labels=FALSE,leaf_labels = FALSE)

Tree objects

List of 7
 $ merge      : int [1:199, 1:2] -130 -66 -61 -4 -49 -115 -12 -113 -101 -158 ...
 $ height     : num [1:199] 0.00481 0.00481 0.0087 0.00941 0.00962 ...
 $ order      : int [1:200] 148 158 160 126 134 140 154 166 176 182 ...
 $ labels     : chr [1:200] "1" "2" "3" "4" ...
 $ method     : chr "average"
 $ call       : language hclust(d = mall_dist, method = "average")
 $ dist.method: NULL
 - attr(*, "class")= chr "hclust"

Cut to Assign Clusters

• cutree function assigns clusters at a given depth
• cutree(tree,k= num_groups)
• cutree(tree,h=depth_groups)

# A tibble: 200 × 2
   names     x
   <chr> <int>
 1 1         1
 2 2         1
 3 3         2
 4 4         3
 5 5         2
 6 6         3
 7 7         2
 8 8         3
 9 9         4
10 10        3
# ℹ 190 more rows

Visualizing Clusters

• Join clusters with original data frame

mall_customers = mall_customers |> left_join(
  mall_clusters |> cutree(k=4) |> tidy() |> mutate(names = as.numeric(names)),
  by = c("CustomerID" = "names") )|> 
  rename(clusters = x)

mall_customers |> ggplot(aes(x = `Annual Income (k$)`,y=`Spending Score (1-100)`,color = as_factor(clusters),fill = as_factor(clusters) )) +
  geom_point()  +
  scale_color_okabe_ito() +
  scale_fill_okabe_ito()

Visualizing Clusters

• Join clusters with original data frame

Visualizing Clusters

• Seems like Gender is main differentiator

Try Something Else

• Dropped Gender and Age

Try a Different Linkage

• Use the Ward Linkage Instead

mall_clusters = mall_dist |> 
  hclust(
  method = "ward"
) 

mall_customers = mall_customers |> left_join(
  mall_clusters |> cutree(k=5) |> tidy() |> mutate(names = as.numeric(names)),
  by = c("CustomerID" = "names") )|> 
  rename(clusters = x)

mall_customers |> ggplot(aes(x = `Annual Income (k$)`,y=`Spending Score (1-100)`,color = as_factor(clusters),fill = as_factor(clusters) )) +
  geom_point()  +
  scale_color_okabe_ito() +
  scale_fill_okabe_ito()  +
  theme_minimal(base_size = 16) +
  labs(title = "Cluster Differences")

Try a Different Linkage

• Use the Ward Linkage Instead

mall_clusters = mall_dist |> 
  hclust(
  method = "ward"
) 

mall_customers = mall_customers |> left_join(
  mall_clusters |> cutree(k=5) |> tidy() |> mutate(names = as.numeric(names)),
  by = c("CustomerID" = "names") )|> 
  rename(clusters = x)

mall_customers |> ggplot(aes(x = `Annual Income (k$)`,y=`Spending Score (1-100)`,color = as_factor(clusters),fill = as_factor(clusters) )) +
  geom_point()  +
  scale_color_okabe_ito() +
  scale_fill_okabe_ito()  +
  theme_minimal(base_size = 16) +
  labs(title = "Cluster Differences")

Try a Different Linkage

• Use the Ward Linkage Instead

Interpreting Clusters

• Similar procedure as to k-means
  • Summarize/average over the clusters
  • Plot distributions over the clusters
• Take advantage of Hierarchical Structure using Heatmaps

Clustered Heatmaps

Clustered Heatmaps

• tidyheatmaps package
  • pheatmap frontend
  • Others have similar names
• Not ggplot2 compatible

Clustered Heatmaps

• Need long-format data

US_state_stats

# A tibble: 50 × 15
   state       homeownership multiunit income med_income poverty fed_spend smoke
   <chr>               <dbl>     <dbl>  <dbl>      <dbl>   <dbl>     <dbl> <dbl>
 1 Alabama              71.1      15.5  22984      42081    17.1     11.7   24.8
 2 Alaska               64.7      24.6  30726      66521     9.5     16.8   25  
 3 Arizona              67.4      20.7  25680      50448    15.3      9.85  20.4
 4 Arkansas             67.7      15.2  21274      39267    18        9.61  23.5
 5 California           57.4      30.7  29188      60883    13.7      8.89  15.2
 6 Colorado             67.6      25.6  30151      56456    12.2      9.15  19.9
 7 Connecticut          69.2      34.6  36775      67740     9.2     14.8   16.5
 8 Delaware             73.6      17.7  29007      57599    11        8.89  20.7
 9 Florida              69.7      30    26551      47661    13.8      9.62  21.6
10 Georgia              67.2      20.5  25134      49347    15.7      8.88  22.2
# ℹ 40 more rows
# ℹ 7 more variables: soc_sec <dbl>, nuclear <dbl>, coal <dbl>,
#   tr_deaths <dbl>, tr_deaths_no_alc <dbl>, unempl <dbl>, popdens2010 <dbl>

Clustered Heatmaps

• Need long-format data

US_long = US_state_stats |> pivot_longer(
  names_to = "variable",
  cols=homeownership:popdens2010,
  values_to = "value")
US_long

# A tibble: 700 × 3
   state   variable        value
   <chr>   <chr>           <dbl>
 1 Alabama homeownership    71.1
 2 Alabama multiunit        15.5
 3 Alabama income        22984  
 4 Alabama med_income    42081  
 5 Alabama poverty          17.1
 6 Alabama fed_spend        11.7
 7 Alabama smoke            24.8
 8 Alabama soc_sec          18.5
 9 Alabama nuclear          16.3
10 Alabama coal             56.6
# ℹ 690 more rows

Clustered Heatmaps

• tidy_heatmap computes clusters for you, but takes a ton of arguments

library(tidyheatmaps)

US_long |> 
  tidy_heatmap(
                rows = state,
                columns = variable, 
                values = value,
                cluster_rows = TRUE, 
                cluster_cols = TRUE,
                scale = "column",
                fontsize_row = 6,
                fontsize_col=12,
                clustering_method = "ward",
                main = "Hierarchical Clustering of US States",
                fontsize = 12)

Clustered Heatmaps

• scale = column/row is very important

library(tidyheatmaps)

US_long |> 
  tidy_heatmap(
                rows = state,
                columns = variable, 
                values = value,
                cluster_rows = TRUE, 
                cluster_cols = TRUE,
                scale = "column",
                fontsize_row = 6,
                fontsize_col=12,
                clustering_method = "ward",
                main = "Hierarchical Clustering of US States",
                fontsize = 12)

Clustered Heatmaps

• scale = column/row is very important

Clustered Heatmaps

• scale = column/row is very important

Annotations

• Say we want to annotate the clusters with a categorical variable
• Add US-Regions to data frame

US_state_aug = US_state_stats |> 
  left_join(US_regions) |> 
  mutate(state = state_abr) |> 
  select(-state_abr) |> 
  pivot_longer(
    names_to = "variable",
    cols=homeownership:popdens2010,
    values_to = "value") 

Annotations

• Say we want to annotate the clusters with a categorical variable
• Add US-Regions to data frame

# A tibble: 700 × 5
   state region division           variable        value
   <chr> <chr>  <chr>              <chr>           <dbl>
 1 AL    South  East South Central homeownership    71.1
 2 AL    South  East South Central multiunit        15.5
 3 AL    South  East South Central income        22984  
 4 AL    South  East South Central med_income    42081  
 5 AL    South  East South Central poverty          17.1
 6 AL    South  East South Central fed_spend        11.7
 7 AL    South  East South Central smoke            24.8
 8 AL    South  East South Central soc_sec          18.5
 9 AL    South  East South Central nuclear          16.3
10 AL    South  East South Central coal             56.6
# ℹ 690 more rows

Annotations

US_state_aug |>
  tidy_heatmap(
                rows = state,
                columns = variable, 
                values = value,
                cluster_rows = TRUE, 
                cluster_cols = TRUE,
                scale = "column",
                fontsize_row = 6,
                fontsize_col=12,
                clustering_method = "ward",
                main = "Hierarchical Clustering of US States",
                fontsize = 12,
                annotation_row = region,
                annotation_colors =  list(  # specify colors for annotations
      region = c("Northeast" = "#56B4E9", "South" = "#E69F00", "West" = "#009E73", "Midwest" ="#F0E442")
    ))

Annotations

Multiple Annotations

Downsides of Hierarchical Clustering

• Computationally very challenging
  • Naive methods scale like \(O(n^3)\)
  • \(O(n^2)\) for memory
  • Need to become a pro….
• Bad with many features/high dimensions
• Bad if data is nonlinearly shaped

Thanks!