+1(978)310-4246 credencewriters@gmail.com
  

Counterfeiting banknotes has been a problem since the introduction of color photocopiers and computer image scanners. The banking industry has suffered from counterfeits due to inflation and reduction in the value of real money. Assume that you are a data mining expert who works in the banking industry.

The dataset called banknotes.csv Download banknotes.csv contains 5 variables (or columns) and the description-bank.docx Download description-bank.docxcontains a description of the dataset. The end goal is to build an appropriate model (or tool) to successfully predict forgery. Using SAS Studio, perform the following tasks:

Explore the dataset by providing summary statistics and graphical summaries of all the variables.

Explain some of the key aspects of data in part 1.

Examine if the dataset has any anomalies. Describe the method(s) you used as well as the results.

Examine if there are any association among the variables. Describe the approaches as well as the results.

Using one of the clustering techniques, analyze all the variables. Explain the results.

Using one of the classification techniques from the course, build the model that predicts forgery. Explain why you think the model you’ve chosen is most appropriate for this dataset.

Evaluate the model. How well does the model fit? Can you improve the model? Explain.

ATTACHED:

1. Dataset

2. Documentation for dataset

3. What I currently have completed

V1
3.6216
4.5459
3.866
3.4566
0.32924
4.3684
3.5912
2.0922
3.2032
1.5356
1.2247
3.9899
1.8993
-1.5768
3.404
4.6765
2.6719
0.80355
1.4479
5.2423
5.7867
0.3292
3.9362
0.93584
4.4338
0.7057
1.1432
-0.38214
6.5633
4.8906
-0.24811
1.4884
4.2969
-0.96511
-1.6162
2.4391
2.6881
3.6289
4.5679
3.4805
4.1711
-0.2062
-0.00689
0.96441
2.8561
-0.7869
V2
8.6661
8.1674
-2.6383
9.5228
-4.4552
9.6718
3.0129
-6.81
5.7588
9.1772
8.7779
-2.7066
7.6625
10.843
8.7261
-3.3895
3.0646
2.8473
-4.8794
11.0272
7.8902
-4.4552
10.1622
8.8855
9.887
-5.4981
-3.7413
8.3909
9.8187
-3.3584
-0.17797
3.6274
7.617
9.4111
0.80908
6.4417
6.0195
0.81322
3.1929
9.7008
8.722
9.2207
9.2931
5.8395
6.9176
9.5663
V3
V4
Class
-2.8073 -0.44699
-2.4586
-1.4621
1.9242 0.10645
-4.0112
-3.5944
4.5718
-0.9888
-3.9606
-3.1625
0.72888 0.56421
8.4636 -0.60216
-0.75345 -0.61251
-2.2718 -0.73535
-2.2135 -0.80647
2.3946 0.86291
0.15394
-3.1108
2.5462
-2.9362
-2.9915 -0.57242
3.4896
1.4771
0.37158 0.58619
4.3439
0.6017
8.3428
-2.1086
-4.353
-4.1013
-2.6196 -0.48708
4.5718
-0.9888
-3.8235
-4.0172
-1.6831
-1.6599
-4.6795
-3.7483
8.3368
-2.8715
5.5777 -0.63578
2.1624
-3.7405
-4.4113
-3.2258
3.4202
1.0905
4.9068 0.15429
3.308 0.48921
-2.3874 -0.96164
1.7305
-4.8629
8.1628 0.60817
-0.80743 -0.69139
-0.46641 -0.69268
1.6277 0.77627
-2.1055 0.29653
-3.7541
-3.4379
-3.0224 -0.59699
-3.7044
-6.8103
-0.41243
-1.9638
2.3235 0.066365
-0.79372 0.48403
-3.7867
-7.5034
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2.0843
-0.7869
3.9102
1.6349
4.3239
5.262
3.1452
2.549
4.9264
4.8265
2.5635
5.807
3.1377
-0.78289
2.888
0.49665
4.2586
1.7939
5.4021
2.5367
4.6054
2.4235
1.0009
0.12326
3.9529
4.1373
4.7181
4.1654
4.4069
2.3066
3.7935
0.049175
0.24835
1.1317
2.8033
4.4682
5.0185
1.8664
3.245
4.0296
-1.1313
0.87603
4.1197
3.8027
1.4806
4.0632
4.3064
6.6258
9.5663
6.065
3.286
-4.8835
3.9834
5.825
6.1499
5.496
0.80287
6.7769
5.0097
-4.1096
11.3603
0.44696
5.527
11.2962
-1.1174
3.1039
2.599
-4.0765
9.5332
7.7846
8.9848
-2.3548
0.49248
10.0153
-3.4495
10.9072
3.5364
7.9853
6.1437
7.6439
3.9647
9.0862
2.2907
8.5978
7.7763
6.63
2.6756
1.9037
6.8141
-2.7956
0.81529
7.6377
3.584
8.2068
0.48382
-2.2134
-3.7867
-7.5034
-2.4534 -0.68234
2.8753 0.087054
3.4356
-0.5776
-1.5572
1.0103
-0.51439
-1.4944
-1.1605
-1.2371
-2.4774 -0.50648
1.6371
1.1875
-0.61979 0.38576
-2.2384 0.43878
4.5701 0.98963
-0.37644
-7.0495
4.5907 -0.24398
1.7785 -0.47156
-4.0943
-4.3457
1.5454 -0.26079
-1.1536
1.5651
2.0938 0.20085
2.7587 0.31981
-3.0789
-2.7746
-0.28219
-2.6608
-0.9351
-2.4332
2.3792 0.48274
1.093
1.8276
-3.9486
-3.8582
3.643
1.0879
-4.5775
-4.4271
0.57551 0.41938
-2.5477
-1.872
1.7828 -0.72113
0.9885 -0.87371
3.3979 0.84351
-3.3668
-1.0224
0.95766 0.83058
-2.9375
-1.281
-0.23849
-2.9634
-0.63435 0.86937
0.80685 0.71679
7.5339
1.022
0.84198 -0.17156
2.0707 0.67412
2.1041
1.0245
-2.7876
-1.0341
0.72545 0.39481
-2.7824
-1.4336
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2.4486
3.2718
-0.64472
2.9543
2.1616
3.82
-2.7419
3.3669
4.5597
5.1129
3.3397
4.2027
3.5438
2.3136
-1.8584
3.106
2.9163
3.9922
1.518
3.2351
4.2188
1.7819
2.5331
3.8969
2.108
2.8969
0.9297
3.4642
4.0713
-1.4572
-1.5075
-0.91718
2.994
-2.343
3.7818
4.6689
3.4663
3.2697
5.1302
2.0139
0.4339
-1.0401
4.1605
5.438
5.032
5.2418
-0.2062
-6.3175
7.9632
1.7837
2.1161
-4.6062
8.347
1.076 0.64577
-6.8804
8.1517
10.9279
-4.0112
11.4038
2.5394
-5.1856
3.6935
-2.4211
2.6413
-0.49871 0.62863
-4.6145
3.9823
0.22761 0.96108
1.2395
1.997
10.6651
-3.5288
7.886
-1.6643
9.5414
-4.2536
10.8306
-3.3437
-4.4676
3.7304
5.6946 0.094818
9.647
-3.2074
6.8162
-1.2804
6.9176
-1.2744
2.9135
-0.822
7.4163
-1.8245
6.7955
-0.1708
0.70768
2.29
-3.7971
4.6429
10.6878
-3.4071
10.4023
-4.1722
9.1214
1.7425
1.9224
7.1466
9.9884
1.1804
7.2011
-1.2153
12.9516
3.3285
-2.8846
2.2558
1.3098 0.055404
1.1112
1.7425
-4.3414
3.6884
8.6703
-2.8913
6.1416 0.37929
5.5395
2.033
9.3987 0.85998
11.2196
-3.6136
9.4669
-4.9417
8.2026
-2.6256
10.5388
-4.1174
9.2207
-3.7044
0.20602
0.61334
-2.7099
0.89394
-0.08105
-5.0284
-5.5793
-1.1427
1.6168
1.1189
-0.23751
0.97282
2.1547
-4.7672
-1.8384
-4.003
-4.122
-0.1095
-0.02674
-2.5948
0.76076
-1.5759
-0.12243
0.14007
0.4905
1.8663
-0.2957
-4.109
-4.7582
-5.1241
0.89136
-5.2263
0.3211
-5.9426
-0.15734
1.909
1.3388
-0.29829
-1.5086
0.56938
-0.40432
-5.3336
-4.0819
-3.9202
-1.0341
-4.2797
-6.8103
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2.0911
1.7317
4.1736
3.9232
3.8481
0.5195
3.8584
1.7496
3.6277
2.7391
4.5447
-1.7599
5.0691
3.4591
1.9358
2.486
2.4226
3.9479
2.2634
1.3566
5.0452
3.5499
0.17346
2.4008
4.8851
4.1927
1.1166
1.0235
-1.803
0.11739
0.5706
4.0552
-1.6952
-1.1193
1.8799
3.583
0.19081
3.6582
-0.13144
2.3925
1.6426
-0.11783
-0.69572
2.9421
-1.7559
-1.2537
3.2585
0.94358
4.5512
1.234
-0.34765
4.1905 -0.99138
3.3336
-1.4244 0.60429
-3.2467
3.4579 0.83705
10.1539
-3.8561
-4.2228
-3.2633
3.0895
-0.9849
0.78425
1.1033
1.7008
-0.1759
5.1827
1.2922
0.9829 0.68861 0.63403
7.4018 0.071684
-2.5302
8.2274
-2.4166
-1.5875
11.9211
2.6756
-3.3241
0.21313 0.20278
1.2095
11.112
-4.2039
-5.0931
8.1654 -0.02343
-2.2586
-0.99533
5.3404 -0.15475
-4.5752
5.947 0.21507
-3.7723
2.883 0.019813
-4.4862
3.6558 -0.61251
4.2358
2.1341
0.3211
3.8964
-1.4304 0.86291
8.6165
-3.2794
-1.2009
7.8695 0.26876
-3.7883
9.3593
-3.3565
-3.3526
1.5995 -0.00029
1.6401
-3.2674
2.5839 0.21766
8.6496 -0.96252
-1.8112
6.901
-2.0062
-2.7125
11.8818
2.0458
-5.2728
6.2761
-1.5495
-2.4746
-0.0248
1.2421
-0.5621
-2.4583
2.2806
1.0323
1.0657
8.8294 0.94955
10.7271
2.0938
-5.6504
2.4707
2.4931 0.37671
-3.7971
3.4391 -0.12501
9.1297
-3.725
-5.8224
5.6864
-1.7157 -0.23751
-1.7775
8.3316 0.35214
9.798
-3.0361
-2.8224
3.0149 0.22849
-0.147
-1.5789
8.03 -0.02803
8.6165
1.8419
-4.3289
7.4101 -0.97709 -0.88406
11.9459
3.0946
-4.8978
10.8803
1.931
-4.3237
-4.4614
3.8024 -0.15087
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1.8314
4.5645
2.7365
0.9297
3.9663
1.4578
4.8272
-2.341
-1.8584
4.1454
1.9157
4.0215
5.8862
-2.0897
4.0026
-0.78689
4.1757
0.83292
4.8077
5.3063
2.5605
2.1059
2.1721
4.2899
3.5156
2.614
0.68087
4.1962
6.0919
1.3234
1.3264
-0.16735
-1.3
-2.2261
2.4196
1.0987
4.6464
-0.36038
1.3562
0.5706
-2.6479
3.1219
5.4944
-1.3389
-2.3361
2.2596
0.46901
6.3672 -0.03628 0.049554
-3.6275
2.8684 0.27714
-5.0325
6.6608 -0.57889
-3.7971
4.6429
-0.2957
10.1684
-4.1131
-4.6056
-0.08485
4.1785 0.59136
3.0687 0.68604 0.80731
12.3784 0.70403
-7.5836
7.886
-1.6643
-1.8384
7.257
-1.9153 -0.86078
6.0816 0.23705
-2.0116
-2.1914
2.4648
1.1409
5.8747
-2.8167 -0.30087
10.8265
2.3603
-3.4198
-3.5943
3.5573 0.26809
9.5663
-3.7867
-7.5034
10.2615
-3.8552
-4.3056
7.5404 0.65005 -0.92544
2.2327 -0.26334
1.5534
5.2684
-2.8904 -0.52716
9.2683
-3.5913
-1.356
7.6046 -0.47755
-1.8461
-0.73874
5.4672 -0.72371
9.1814
-4.6067
-4.3263
10.1891
-4.2759
-4.978
8.0081
-3.7258
-1.3069
2.3259
4.9085 0.54998
0.74493 0.83256
0.753
2.9673
-1.3267
1.4551
3.2964
0.2362 -0.11984
1.0326
5.6566 -0.41337
7.6274
1.2061
-3.6241
10.2678
-2.953
-5.8638
12.5398
2.9438
-3.5258
6.4665 -0.75688
0.228
0.6394
5.989 -0.58277
10.5326
-4.5852
-4.206
4.1158
3.1143 -0.37199
3.2136
4.3465 0.78662
-0.0248
1.2421
-0.5621
10.1374
-1.331
-5.4707
-3.137
1.9259 -0.37458
1.5478 0.041694
1.9284
1.552
7.0806
1.031
11.9604
3.0835
-5.4435
-0.03312
4.7355
-0.2776
-0.63321
7.3848 0.36507
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2.7296
2.0466
-1.3274
3.8905
3.9994
2.3952
3.2704
-1.3931
1.6406
2.7744
2.4287
4.2134
1.6472
2.0597
0.3798
1.0135
4.5691
0.57461
0.5734
5.2868
4.0102
4.1425
3.0934
2.2034
3.744
3.0329
3.7731
3.1557
1.8114
4.988
2.483
1.594
-0.0161
3.8496
0.9297
4.9342
3.8417
5.3915
4.4072
2.6946
5.2756
3.4312
4.052
1.3638
0.89566
1.9265
0.20977
2.8701
2.03
9.498
-2.1521
0.90427
9.5083
6.9321
1.5664
3.5488
6.8576
9.3821
-2.806
0.48213
-0.99326
0.7098
8.4551
-4.4552
10.1105
9.1938
3.257
10.6568
-3.6792
-2.9177
5.9947
0.79459
2.2948
7.2073
2.8908
7.6067
7.2052
6.6155
4.7055
9.7484
9.7939
-3.7971
2.4107
10.0215
9.9946
-0.07037
6.7976
0.13863
6.2637
-0.16555
-4.7759
7.7763
7.7557
-0.46146
0.51124
0.5099
2.1761 -0.08363
2.4408
-5.2689
2.6302
1.1047
1.1693
1.6892
-3.1783
-3.0086
-1.0456 0.23447
7.5382 0.78403
1.3964 -0.36424
-1.0671 0.075416
-3.2477
-1.4543
2.0116 0.67412
4.7449
1.225
5.2119 -0.29312
0.7572
-0.4444
-1.672
-2.0815
3.1769 0.004296
-1.6917
-4.3922
-0.9094
-1.872
-1.3721
1.1668
-4.1388
-5.0646
3.8281
1.6297
2.2232 0.22283
0.53009 0.84998
0.95851
1.0077
2.1135 0.35084
-1.6814 -0.94742
0.59693 0.79825
-0.9788
-2.4668
-3.2846
-1.1608
-0.79287 -0.90863
1.3758 0.081882
0.15394
-1.6134
-4.1508
-4.4582
4.6429
-0.2957
-0.17594
1.6245
-4.2699
-4.9159
-3.8081
-3.3642
2.0416
1.1319
-0.40301 0.44912
0.12138
1.1435
-1.9513 -0.36165
0.45383 0.51248
8.4182
-1.8836
-2.7473
-1.9353
-0.16823
-3.0771
7.7267 0.90946
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4.068
2.877
0.3223
-1.3
1.7747
1.3419
0.89606
0.44125
3.2422
2.5678
-2.2153
4.1349
1.934
2.5068
2.1464
0.051979
1.2706
1.143
2.2928
0.3292
2.9719
1.6849
-1.9177
2.3729
1.0284
0.27451
1.6032
4.616
4.2478
4.0215
5.0297
1.5902
2.1274
1.1811
0.3292
5.7353
2.6718
1.5799
2.9499
0.5195
3.7352
-1.7344
3.884
3.5257
4.4549
-0.16108
4.2164
-2.9363
2.1992 0.50084
-4.0599
3.6259 -0.32544
-0.89808
8.0883 0.69222
10.2678
-2.953
-5.8638
-6.4334
8.15 -0.89828
-4.4221
8.09
-1.7349
10.5471
-1.4175
-4.0327
2.9487
4.3225
0.7155
6.2265 0.12224
-1.4466
3.5136 0.61406 -0.40691
11.9625 0.078538
-7.7853
6.1189
-2.4294 -0.19613
-9E-06
4.816 -0.33967
1.1588
3.9249 0.12585
6.0795
-0.5778
-2.2302
7.0521
-2.0541
-3.1508
8.035 -0.19651
-2.1888
0.83391
5.4552 -0.56984
9.0386
-3.2417
-1.2991
-4.4552
4.5718
-0.9888
6.8369
-0.2702 0.71291
8.7489
-1.2641
-1.3858
11.6894
2.5454
-3.2763
10.4726
-3.0087
-3.2013
9.767
-1.3687
-1.7853
9.2186
-3.2863
-4.8448
-4.7863
8.5193
-2.1203
10.1788
-4.2185
-4.4245
7.6956
-2.7696
-1.0767
-2.7004
2.4957 0.36636
-4.9704
3.5025 -0.23751
2.2948
3.2403 0.18404
5.1939
-1.7971
-1.1763
8.3847
-2.0567 -0.90345
-4.4552
4.5718
-0.9888
5.2808
-2.2598 0.075416
5.6574 0.72974
-1.4892
-4.7076
7.9186
-1.5487
2.2493
1.3458 -0.03708
-3.2633
3.0895
-0.9849
9.5911
-3.9032
-3.3487
2.0175
7.7618 0.93532
10.0277
-3.9298
-4.0819
1.2829
1.9276
1.7991
2.4976
1.0313 0.96894
-6.4624
8.3573
-1.5216
9.4607
-4.9288
-5.2366
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3.5152
6.8224 -0.67377
1.6988
2.9094
2.9044
1.0607
2.4542
2.5188
2.0421
1.2436
4.2171
3.5594
1.3078
1.291
3.0009
5.8126
-2.2306
3.9294
1.4112
1.8076
3.4667
-4.0724
4.2882
3.966
3.9213 0.70574
1.0191
2.33
4.9334
0.96414
5.616
2.2138
1.8205
6.7562 0.009991
4.9923
7.8653
-2.3515
-1.1804 11.5093 0.15565
4.0329 0.23175 0.89082
0.66018 10.3878
-1.4029
3.5982
7.1307
-1.3035
-1.8584
7.886
-1.6643
4.0972 0.46972
1.6671
3.3299 0.91254
1.5806
3.1088
3.1122 0.80857
-4.2859
8.5234
3.1392
-1.2528 10.2036
2.1787
0.5195
-3.2633
3.0895
0.3292
-4.4552
4.5718
0.88872
5.3449
2.045
3.5458
9.3718
-4.0351
-0.21661
8.0329
1.8848
2.7206
9.0821
-3.3111
3.2051
8.6889
-2.9033
2.6917 10.8161
-3.3
-2.3242 11.5176
1.8231
2.7161
-4.2006
4.1914
3.3848
3.2674 0.90967
1.7452
4.8028
2.0878
2.805 0.57732
1.3424
5.7823
5.5788
-2.4089
3.8999
1.734
1.6011
3.5189
6.332
-1.7791
3.2294
7.7391 -0.37816
3.4985
3.1639 0.22677
2.1948
1.3781
1.1582
2.2526
9.9636
-3.1749
4.1529
-3.9358
2.8633
0.74307
11.17
-1.3824
1.9105
8.871
-2.3386
-1.5055 0.070346
6.8681
-0.46898
0.11033
-0.17027
0.90429
1.6556
-0.66553
0.89782
1.5418
0.33662
0.82929
-0.12501
0.39481
-0.71984
-6.8194
1.1823
-3.9151
0.21248
-1.8384
0.91593
0.39352
0.4336
-0.91639
-5.6038
-0.9849
-0.9888
-0.19355
-3.9564
-3.8853
-0.96811
-0.7819
-4.2888
-5.375
0.16981
0.25128
0.62627
1.2133
-0.05648
0.96765
-0.02027
-2.5405
-0.1651
0.85774
-2.9944
-0.01769
-4.0728
-0.75604
-0.50648
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.58836 10.7727
-1.3884
3.2303
7.8384
-3.5348
-1.9922 11.6542
2.6542
2.8523
9.0096
-3.761
4.2772
2.4955 0.48554
1.5099 0.039307
6.2332
5.4188 10.1457
-4.084
0.86202
2.6963
4.2908
3.8117 10.1457
-4.0463
0.54777 10.3754
-1.5435
2.3718
7.4908 0.015989
-2.4953 11.1472
1.9353
4.6361
-2.6611
2.8358
-2.2527 11.5321
2.5899
3.7982
10.423
-4.1602
-0.36279
8.2895
-1.9213
2.1265
6.8783 0.44784
0.86736
5.5643
1.6765
3.7831 10.0526
-3.8869
-2.2623 12.1177 0.28846
1.2616
4.4303
-1.3335
2.6799
3.1349 0.34073
-0.39816
5.9781
1.3912
4.3937 0.35798
2.0416
2.9695
5.6222 0.27561
1.3049 -0.15521
6.4911
2.2123
-5.8395
7.7687
1.9647
6.9383 0.57722
3.0864
-2.5845
2.2309
0.3798
0.7098
0.7572
0.58982
7.4266
1.2353
0.14783
7.946
1.0742
-0.06203
6.1975
1.099
4.223
1.1319 0.72202
0.64295
7.1018
0.3493
1.941 0.46351
4.6472
4.0047 0.45937
1.3621
3.7767
9.7794
-3.9075
3.4769 -0.15314
2.53
1.9818
9.2621
-3.521
3.8023
-3.8696
4.044
4.3483 11.1079
-4.0857
1.1518
1.3864
5.2727
-1.2576
1.5892
7.0078
1.9572
-5.1153
8.6127
-2.484 12.1611
2.8204
-1.1497
1.2954
7.701
-4.3276
-1.2151
-5.2107
-3.3371
0.36119
-0.30346
-3.6991
0.54739
-4.5629
-4.1633
-1.7414
-3.4638
1.1991
-3.2737
-4.9728
-3.3332
-2.2224
-0.16769
-3.7366
-7.7581
-1.7517
0.58489
-1.1621
1.2004
-1.1556
-0.75346
-0.85302
0.66377
0.30947
-0.4444
-2.9595
-3.3409
-1.131
0.96118
-0.41337
1.0879
1.6181
-3.5323
2.4495
-1.872
0.95343
-4.2539
-0.43536
0.42455
-1.4297
-3.7418
0.62627
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4.8368
-0.12196
1.9429
1.742
-1.5222
-1.3
3.4246
2.5503
1.5691
1.3087
5.1776
2.229
5.6272
1.2138
0.3798
0.5415
4.0524
4.7285
3.4359
0.86816
3.359
3.6702
1.3349
3.1887
2.4527
3.9121
3.9364
3.9414
3.6922
5.681
0.77124
3.5761
1.602
2.6682
2.0007
0.64215
4.3848
0.77445
0.96574
3.0948
4.9362
-1.9458
5.7403
-2.6989
1.1472
2.9742
4.5707
10.0132
-4.3239
-4.3276
8.8068 0.94566
-4.2267
6.3961 0.092248 0.58102
-4.809
8.2142
-2.0659
10.8409
2.7827
-4.0974
10.2678
-2.953
-5.8638
-0.14693 0.80342 0.29136
-4.9518
6.3729 -0.41596
6.3465
-0.1828
-2.4099
4.9228
2.0013 0.22024
8.2316
-3.2511
-1.5694
9.6325
-3.1123
-2.7164
10.0857
-4.2931
-3.8142
8.7986
-2.1672 -0.74182
0.7098
0.7572
-0.4444
6.0319
1.6825 -0.46122
5.6802
-1.9693 0.026279
2.1065 -0.28305
1.5625
0.66216
2.1041
1.8922
10.2429
-1.4912
-4.0082
9.8022
-3.8209
-3.7133
2.9942 0.85141 0.30688
6.1189 0.46497 0.49826
-3.4143
2.7742
-0.2026
2.9653 0.20021 -0.05648
2.9735 0.92852 0.60558
10.5885
-3.725
-4.3133
-3.2902
3.1674
1.0866
-3.9585
4.3439
1.3517
7.795
-2.6848 -0.92544
9.0862
-1.2281
-1.4996
9.7753
-3.9795
-3.4638
6.1251 0.52924 0.47886
10.216
-3.4414
-4.0069
1.8644
2.6491 0.47369
3.1287
4.2933 0.64696
-3.0729
3.0423
1.2741
9.0552
-2.4089
-1.3884
8.393
-1.361
-1.4659
8.7324
-2.9007 -0.96682
7.6046
-2.3429 -0.85302
11.2217
1.9079
-3.4405
-0.44284 0.38015
1.3763
12.1984 0.67661
-8.5482
3.5985
1.9387 -0.43406
8.96
-2.9024
-1.0379
7.2094
-3.2794
-1.4944
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.1848
0.87256
0.39559
3.8384
2.8209
2.5817
3.8213
0.3798
3.4893
-1.7781
2.0962
0.94732
2.8261
0.007125
0.96788
4.7432
3.6575
3.8832
3.4776
1.1315
2.8237
1.9321
3.0632
-1.8411
2.8084
2.5698
-0.12624
3.3756
-0.04801
0.5706
0.88444
3.8644
1.2999
2.0051
4.9294
2.8297
2.565
2.093
4.6014
5.0617
-0.2951
3.577
3.9433
2.6648
5.9374
2.0153
5.8782
6.5079
2.0133 -0.87242
9.2931
-0.7843
-2.1978
6.8866
1.0588 -0.67587
6.1851
-2.0439
-0.0332
7.3108 -0.81857
-1.8784
9.7546
-3.1749
-2.9957
0.23175
2.0133
2.0564
0.7098
0.7572
-0.4444
6.69
-1.2042 -0.38751
0.8546
7.1303 0.027572
2.4769
1.9379 -0.04096
-0.57113
7.1903 -0.67587
9.4007
-3.3034
-1.0509
8.3661 0.50781
-3.8155
7.1907
1.2798
-2.4565
2.1086
0.1368
1.6543
7.2797
-2.2692
-1.144
6.4023
-2.432 -0.98363
8.811
-3.1886 -0.92285
7.9212
1.093
-2.8444
2.8597 0.19678 0.57196
6.0423 0.26019
-2.053
-3.3315
5.1305
0.8267
10.8306
2.769
-3.0901
11.3045
-3.3394
-4.4194
-4.4076
5.9856 0.078002
10.3216
-3.7121
-6.1185
-4.0951
4.367
1.0698
-1.6037
8.4756 0.75558
-0.0248
1.2421
-0.5621
6.5906 0.55837 -0.44182
3.7061 0.70403 0.35214
2.5762
2.0107 -0.18967
-6.8638
8.132
-0.2401
0.27727 0.20792 0.33662
6.3485 -0.73546 -0.58665
8.633
-2.9941
-1.3082
8.3061 0.022844
-3.2724
5.6264
-2.1235 0.19309
-0.35799 0.44698 0.99868
9.0489 -0.52725
-2.0789
2.4004
1.8908 0.73231
2.5017
1.5215
0.903
10.754
-3.3994
-4.1685
6.1664
-2.5905 -0.36553
1.8479
3.1375 0.42843
5.9409
-2.8544 -0.60863
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
-2.3983
1.762
4.2406
3.4669
3.1896
0.81356
0.52855
2.1319
0.33111
1.2746
2.2091
2.5328
3.6244
-1.3885
5.7227
3.3583
2.5227
0.045304
4.8278
1.9476
2.7659
-0.10648
0.72252
4.2475
3.9772
3.6667
2.8232
-1.4217
4.2458
4.1038
1.4507
3.4647
1.8533
3.5288
3.9719
3.534
3.6894
3.0672
2.6463
2.2893
1.5673
4.0405
4.3846
2.0165
4.0446
-0.33729
-2.4604
12.606
4.3682
-2.4852
6.87
5.7526
9.1566
0.96427
-2.0403
4.5731
8.8172
7.4556
7.528
1.4609
12.5026
5.8312
10.3567
2.2369
6.7334
7.7598
-4.7738
0.66216
-0.76771
-0.05381
1.4816
0.33521
4.302
10.8513
11.6542
1.1981
-4.8069
8.7903
-3.9172
6.1458
0.71596
1.0367
9.3614
9.887
-4.4117
-4.8152
3.733
7.9274
0.51524
-4.8794
-0.25246
11.1741
-0.64976
12.7302
2.9464
-5.7888
2.1384 0.75429
1.608
0.7155
-1.0568 -0.73147
-0.18537 -0.30087
-2.1492
-4.1814
4.0243
-1.0483
2.5574 -0.06165
2.057 -0.18967
-1.5323
-1.7957
-1.3284
-3.3021
-0.41929
-2.6478
1.3501
1.9284
0.69118
-7.5487
-2.4097 -0.24527
-3.7301
-3.6991
2.7236 0.79438
1.0708
-0.9332
-2.4491
-1.2216
8.527
-1.8668
4.1494 -0.28406
7.7575 0.64179
5.6703
-1.3509
-0.48355 0.95343
2.2566
2.1625
0.55923 0.33791
-3.1466
-3.9784
-0.0577
-7.1025
0.66633 0.94696
3.3491 -0.49225
-2.2324 -0.65259
3.9746 0.36119
1.0176
-2.0401
1.9507
1.9375
0.75973
1.0013
-3.6316
-1.2461
-4.0788
-4.3664
3.8238 -0.81682
6.3549 0.003003
0.6312 -0.39786
-0.05684
-2.1694
1.0279
1.106
3.3662 -0.02932
5.1707
1.0763
-4.3582
-4.7401
7.6659 0.72326
0.91738
-7.6418
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4.1195
2.0193
1.5701
2.6415
5.0214
4.3435
1.8238
3.9382
2.2517
5.504
2.8521
1.1676
2.6104
0.32444
3.8962
2.1752
1.1588
4.7072
-1.9667
4.0552
2.3678
0.33565
4.3398
1.5456
1.4276
-0.27802
0.93611
4.6352
1.5268
0.95626
-2.7914
5.2032
3.1836
0.65497
5.6084
1.105
3.9292
1.1558
2.5581
2.7831
3.7635
-2.6479
1.0652
-1.4275
5.7456
5.086
3.4092
10.9258
0.82356
7.9129
7.586
8.0764
3.3295
-6.7748
0.9291
-5.1422
10.3671
9.171
9.1566
8.0081
10.067
-4.7904
-0.8091
8.9331
8.2957
11.8052
0.40143
-6.839
6.8369
-5.3036
8.5482
8.3847
8.1881
8.6413
-3.0087
-5.5871
2.4728
1.7734
3.5116
7.2321
5.1815
10.3009
7.4432
-2.9156
6.4003
2.6218
10.9796
2.7811
10.1374
8.3682
11.8797
10.1808
3.2798
5.4049
-3.8929
4.6369
0.29018
-0.28562
-3.0515
0.83598
8.3873
0.78543
4.2916
-4.413
-3.6461
-2.0867
-0.23592
-1.1982
3.3954
5.1022
-2.0807
-2.5605
-0.40472
1.4563
8.4207
0.69718
3.8803
0.4187
-2.0995
-3.1338
-1.6351
2.6773
8.6564
4.4578
6.7756
-1.2538
-1.0713
1.0673
-4.8003
0.41099
2.2129
1.5506
1.8513
-3.557
0.66119
-1.331
-1.4004
0.41613
-4.7857
-1.2701
-2.5228
-4.1802
1.4202
-2.1953
-1.6677
-1.7155
0.64955
-0.54139
0.6767
-1.2487
-4.0211
-1.2047
-0.80647
-1.7608
-4.1284
-0.53751
-0.67975
-1.1272
-1.4905
-7.8719
0.65343
-0.44829
-0.55691
-0.70432
-2.1784
-1.9677
-2.5276
-1.3043
1.212
-1.722
0.21636
-0.39915
1.0129
-2.5909
-0.42113
-4.3534
-3.0332
0.30817
0.6961
0.40257
-4.4039
0.34179
-5.4707
-1.6509
-6.9978
-4.3366
1.1189
-0.89958
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
-0.2361
3.8197
-1.1391
4.9249
2.5089
-0.2062
3.946
-0.278
1.8592
0.56953
3.4626
3.3951
5.0429
3.7758
4.6562
4.0948
1.8384
2.0153
3.5251
3.757
2.5989
1.8994
3.6941
4.4295
6.8248
1.8967
2.1526
3.3004
2.7213
3.8846
4.1665
0.94225
5.1321
0.38251
3.0333
2.9233
1.162
3.7791
0.77765
-0.38388
0.21084
2.9571
4.6439
3.3577
3.5127
2.6562
-1.3612
9.3221
8.9951
1.8127
0.68906
6.841
9.2207
6.8514
8.1881
3.2074
7.6294
-4.449
1.1484
-0.52974
7.1783
7.6398
-2.9674
6.063
0.43661
0.7201
-5.4236
3.5178
0.97462
-3.9482
-2.3507
5.2187
-2.5163
-6.1665
7.0811
7.05
-3.0336
-0.4449
5.8561
-0.03105
6.8121
-2.5928
6.0464
10.2926
2.5762
5.9781
-1.0471
9.4359
-4.5938
-3.3729
-4.3062
2.9073
10.7044
10.694
2.1307
-4.383
6.9144
0.77344
-0.02942
-3.7044
-1.5443
-3.1338
-0.15966
1.5754
3.5427
2.1401
0.50439
-1.5195
-2.4243
2.3689
0.54723
4.5864
1.6928
3.8255
0.7623
4.2265
4.2625
1.7048
-2.5425
2.8093
8.0831
-1.3258
-0.58808
2.5334
0.23448
1.8762
0.32616
1.8128
2.3183
-0.11168
-1.2821
1.3098
1.1941
8.0514
-0.09454
5.9068
2.5976
6.0241
1.0579
-3.3085
1.7022
-4.3793
-4.0327
0.70127
1.2095
0.44912
-6.8103
-0.5582
-2.5276
-0.26208
-3.2233
0.15429
2.0862
1.106
0.40128
-1.2384
0.75429
0.51248
-0.3151
0.64438
-1.2526
0.81119
0.81377
1.1577
0.90946
0.5461
-0.79742
-0.34355
0.22283
0.41809
0.20214
0.27843
-0.32544
1.1151
-0.61251
0.303
-0.58665
-4.0392
0.5655
-0.3526
0.49567
-1.859
0.57196
0.55257
0.18274
0.40774
-4.0767
-2.9026
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
-0.278
1.04
2.1881
4.2756
-0.11996
2.9736
3.7798
5.3586
1.8373
1.2262
-0.04801
0.5706
4.3634
3.482
0.51947
2.3164
-1.8348
1.3754
-0.16682
0.29961
0.25035
2.4673
0.77805
3.4465
2.2429
3.7321
4.3365
-2.0759
4.0715
0.76163
-0.53966
2.6213
3.0242
5.8519
0.5706
3.9771
1.5478
0.74054
0.49571
1.645
3.6077
3.2403
3.9166
3.9262
5.591
3.7522
1.3114
8.1881
-3.1338
-2.5276
-6.9321
8.2888
-1.2991
2.7356
1.3278
-0.1832
-2.6528
2.1375 0.94437
6.8741 0.91995
-0.6694
8.7944
-3.6359
-1.3754
-3.3109
2.6491 0.066365
3.7557
-1.7345
1.0789
6.1292 0.84027 0.55257
0.89599
5.7568 -0.11596
-0.56078
7.7215
0.453
-0.02484
1.2421 -0.56208
0.46351
1.4281
2.0202
-4.1634
3.5008 -0.07846
-3.2633
3.0895 -0.98492
-2.628
3.1529 -0.08622
11.0334
3.1863
-4.8888
8.8793
-1.9136 -0.53751
5.8974 0.49839 -0.70044
7.1328 -0.31475
-1.1828
9.3262
-3.6873
-6.2543
1.3926
1.7125 0.41421
6.6424
-1.1425
-1.0573
2.9508
1.0271
0.5461
-4.1427
5.2333 -0.40173
-3.884
3.3577 -0.00605
-3.584
3.6884 0.74912
10.8223
2.6439
-4.837
7.6398
-2.0824
-1.1698
5.8209
1.1959 -0.64613
7.3273 0.46583
-1.4543
5.7919 0.065686
-1.5759
-3.3378
2.5865 -0.54785
5.3905
-2.4037 -0.06165
-0.0248
1.2421
-0.5621
11.1513
-3.9272
-4.3444
9.1814
-1.6326
-1.7375
0.36625
2.1992 0.48403
10.2243
-1.097
-4.0159
7.8612 -0.87598
-3.5569
6.8576
-1.1622 0.28231
-3.7082
5.2804 0.41291
10.2491
-4.0926
-4.4659
6.0299
-2.0156 -0.06553
10.4643
-4.3839
-4.3379
-3.6978
3.9943
1.3051
4.5462
2.2935 0.22541
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3.7022
6.9942
4.364
-3.1039
3.5829
1.4423
4.65
-4.8297
5.1731
3.9606
3.2692
3.4184
2.4012
1.6223
1.7257
-4.4697
4.7965
6.9859
4.0962 10.1891
2.5559
3.3605
3.4916
8.5709
0.5195
-3.2633
2.9856
7.2673
4.0932
5.4132
1.7748 -0.76978
5.2012 0.32694
-0.45062
-1.3678
4.8451
8.1116
0.74841
7.2756
5.1213
8.5565
3.6181
-3.7454
0.040498
8.5234
-2.6479 10.1374
0.37984 0.70975
-0.95923 0.091039
2.8672 10.0008
1.0182
9.109
-2.7143 11.4535
3.8244
-3.1081
2.7961
2.121
3.5358
6.7086
-0.7056
8.7241
4.1542
7.2756
0.92703
9.4318
1.8216
-6.4748
-2.4473 12.6247
3.5862
-3.0957
0.66191
9.6594
4.7926
1.7071
4.9852
8.3516
0.75736
3.0294
4.6499
7.6336
-0.02358
7.1742
0.85574 0.008268
0.88298 0.66009
4.0422
-4.391
-1.8511
2.3757
1.0219
3.4553
-1.983
0.20706
3.0312
8.2219
-1.9967
-3.9323
2.0321
-3.0326
3.0895
-0.409
-1.8219
5.5854
0.17965
7.0858
-2.9512
1.1504
-3.3917
2.8273
1.4461
-1.331
0.75716
6.2204
-3.2049
-0.62064
2.1092
2.4537
1.8385
-0.81857
2.2215
-2.4766
-0.66263
8.0514
0.73573
2.8093
-0.28819
-0.0517
-2.5425
2.9164
-1.9427
0.78457
6.6042
6.0096
4.7466
-0.12889
0.78532
1.4008
-0.25174
0.40774
-0.06682
0.71679
-1.8073
-0.35001
-4.1827
0.26809
-0.59182
-0.9849
-2.2431
0.23576
1.3039
1.1797
-0.40303
-1.4724
-0.5388
-1.5474
-0.71208
-3.9306
-5.4707
-0.44441
-1.4828
-3.1095
-1.7129
-3.9629
0.52024
0.38317
0.47886
-4.5965
-1.2099
-1.6728
-0.41855
-7.6612
0.24481
-1.6638
1.4926
-1.2823
-0.06812
-0.37458
-0.75734
-0.53104
-0.43277
1.137
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2.2546
0.38478
3.1541
2.3969
4.7114
4.0127
2.6606
3.931
0.01727
3.2414
2.2504
-1.3971
0.39012
-1.6677
-3.8483
-3.5681
-2.2804
-1.7582
-0.89409
0.3434
-0.9854
-2.4115
-1.5252
-0.61442
-0.36506
-5.9034
-1.8215
-0.77461
-1.8187
-3.5801
-1.8219
-0.3481
0.47368
-3.4083
-1.6662
-2.0962
-2.6685
-0.47465
1.0552
1.1644
-4.4779
-2.7338
-2.286
-1.6244
0.50813
1.6408
0.81583
8.0992
6.5989
-5.1711
0.23589
2.0755
10.1477
3.1681
1.8541
8.693
0.40971
3.5757
3.3191
-0.14279
-7.1535
-12.8047
-8.213
-0.30626
2.7397
3.1991
0.12415
-6.661
-9.1359
-6.2534
-0.09106
2.8928
6.5679
2.7521
-1.8768
-9.0366
-12.9309
-6.8824
-0.38696
3.3605
4.8587
-0.30005
-7.1059
-10.4519
-4.3496
1.1857
3.8095
7.3708
0.45523
-5.4484
-6.3444
0.47799
4.2503
4.84
-0.24877
-3.2698
-0.3336 -0.56466
6.5991 0.57455
4.8477
1.437
-0.2702
1.2379
-3.9366
-4.0728
1.9619 0.18662
-0.02343
1.2314
1.3989
-3.9668
1.4015
1.1952
0.35273
0.2836
-1.3927
-1.9948
-0.03199 0.35084
7.8929 0.96765
15.6824
-1.281
10.083 0.96765
1.3347
1.3763
-2.5323
-2.234
-1.8219
-2.9452
-0.28733 0.14654
5.8245
0.5461
9.3444 -0.65259
5.3524 0.59912
-0.31818 0.50214
-3.6461
-3.0603
0.67661
-6.6797
-0.72261
-2.353
2.4023
1.1319
9.0162 -0.12243
13.1779
-2.5677
5.4681 0.057313
-0.47841 0.62627
-4.5064
-4.0431
-0.76888
-4.8668
1.4238 0.024986
6.6188 -0.33708
9.1139
-1.7323
1.9901
0.7517
-2.6411 0.11033
-4.9408
-4.0909
-0.31218
-6.7754
2.4391 0.21766
5.8039 0.88231
4.6575 0.16981
-1.9804 0.57714
-4.9023
-2.6621
-5.2613
-6.0823
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-5.4901
9.1048 -0.38758
-5.9763
-3.2238
2.7935 0.32274 -0.86078
-2.0631
-1.5147
1.219 0.44524
-0.91318
-2.0113 -0.19565 0.066365
0.6005
1.9327
-3.2888 -0.32415
0.91315
3.3377
-4.0557
-1.6741
-0.28015
3.0729
-3.3857
-2.9155
-3.6085
3.3253 -0.51954
-3.5737
-6.2003
8.6806 0.009134
-3.703
-4.2932
3.3419 0.77258 -0.99785
-3.0265 -0.06209 0.68604 -0.05519
-1.7015 -0.01036 -0.99337 -0.53104
-0.64326
2.4748
-2.9452
-1.0276
-0.86339
1.9348
-2.3729
-1.0897
-2.0659
1.0512 -0.46298
-1.0974
-2.1333
1.5685 -0.08426
-1.7453
-1.2568
-1.4733
2.8718 0.44653
-3.1128
-6.841 10.7402
-1.0172
-4.8554
-5.9037 10.9818 -0.82199
-2.588
3.8654
-0.3336
-1.2797
0.24394
1.4733
-1.4192 -0.58535
-1.5322
-5.0966
6.6779 0.17498
-4.0025 -13.4979 17.6772
-3.3202
-4.0173
-8.3123 12.4547
-1.4375
-3.0731 -0.53181
2.3877 0.77627
-1.979
3.2301
-1.3575
-2.5819
-0.4294 -0.14693 0.044265 -0.15605
-2.234
-7.0314
7.4936 0.61334
-4.211 -12.4736 14.9704
-1.3884
-3.8073
-8.0971 10.1772 0.65084
-2.5912 -0.10554
1.2798
1.0414
-2.2482
3.0915
-2.3969
-2.6711
-1.4427
3.2922
-1.9702
-3.4392
-0.39416
-0.0207 -0.06627 -0.44699
-1.522
-6.6383
5.7491 -0.10691
-2.8267
-9.0407
9.0694 -0.98233
-1.7263
-6.0237
5.2419 0.29524
-0.94255 0.039307 -0.24192 0.31593
-0.89569
3.0025
-3.6067
-3.4457
-6.2815
6.6651 0.52581
-7.0107
-2.3211
3.166
-1.0002
-2.7151
-1.3414
-2.0776
2.8093 0.60688
-2.258
-9.3263
9.3727 -0.85949
-3.8858 -12.8461 12.7957
-3.1353
-1.8969
-6.7893
5.2761 -0.32544
-0.52645 -0.24832 -0.45613 0.41938
0.009661
3.5612
-4.407
-4.4103
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-3.8826
-2.1405
-2.4824
-2.9098
-0.60975
0.83625
0.60731
-4.8861
-3.1366
-2.5754
-1.8782
0.24261
1.296
0.25943
-5.873
-3.4605
-2.3797
-1.2424
0.20216
0.59823
-0.77995
-4.1409
-6.5084
-4.4996
-3.3125
-1.9423
-0.75793
-0.95403
-2.2173
-2.799
-1.8629
-3.5916
-5.1216
-3.2854
-0.56877
-2.3518
-4.4861
-4.3876
-3.3604
-1.0112
0.030219
-1.6514
-3.2692
-2.5701
-1.3066
-1.6637
-0.55008
4.898
-0.16762
-7.3046
-10.0712
-4.002
1.1071
3.9544
7.0542
0.42212
-5.6574
-6.5865
0.57318
4.2855
5.0097
9.1752
2.6901
-1.4402
-1.7175
1.9182
3.5012
3.2322
3.4619
8.7696
3.4288
0.10139
0.3766
2.5349
1.9824
1.4671
1.9679
-0.84841
-6.2285
-5.3118
4.0372
1.4174
-4.8359
-13.2889
-7.7267
-0.32696
2.9984
-1.0512
-8.4985
-12.7406
-6.8452
0.25244
3.2881
2.8659
-0.92311
-5.0801
1.321 -0.20906
6.839 -0.59053
8.4156
-1.9948
1.8471
0.6017
-2.4706 -0.06295
-4.772
-4.4853
-0.17252
-6.959
2.6225 -0.06424
6.103 0.65214
4.8486 -0.02157
-1.9402 0.44007
-4.8457
-2.9013
-5.0394
-6.3862
-0.27448
-6.0422
0.16165
-1.0224
1.1273 0.16076
-0.52553 -0.21036
-3.2828 -0.61768
-3.9795
-1.7841
-3.282
-3.1004
-0.47841
-3.8879
0.23191
-3.937
0.56265
-1.1672
0.55323
-0.2957
-1.2898 -0.82458
-3.0464
-1.2629
-2.3163
-1.1957
-0.72689
-1.1724
-0.42357
-2.1125
2.5377 0.097399
10.2389
-1.1543
10.3846
-1.0612
-0.45356
-1.8228
-1.4252
-1.1246
6.6479 -0.06036
17.3087
-3.2194
11.9655
-1.4543
2.1324
0.6017
-1.1664
-1.6185
1.4024 0.77369
9.1122
1.2379
15.5573 -0.14182
8.9999
2.1353
0.7623
1.7758
-2.2701
-2.2224
-1.6488
-2.4319
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0.21431
-0.77288
-1.8391
-0.63298
0.004055
-0.28696
-5.2406
-1.4446
-0.65767
-1.5449
-2.8957
-0.81479
0.50225
0.74521
-2.9146
-1.3907
-1.786
-1.7322
0.55298
2.031
1.2279
-4.2249
-2.5346
-1.749
-0.539
1.5631
2.3917
0.89512
-5.4808
-2.8833
-1.4174
0.4283
1.5904
1.7425
-0.23356
-3.6227
-6.1536
-3.9172
-2.2214
-0.49241
0.26517
-0.10234
-1.6176
-1.8448
-1.2786
-2.902
-4.3773
-0.69529
-7.4473
-9.0883
-5.1277
0.62905
3.1784
6.6258
2.1438
-2.8018
-10.1498
-12.0205
-5.7381
0.65388
3.6357
4.0537
-1.3781
-8.1157
-9.2828
-3.4619
1.852
4.0309
6.2699
-0.77392
-6.332
-5.167
0.89599
4.5565
4.7738
8.1819
1.7713
-2.2535
-0.94981
2.2121
3.6833
3.2405
3.9958
7.9295
2.6652
-0.23798
0.89392
2.4066
1.8189
1.0926
1.254
-2.4087
-7.6563
-5.5167
0.87711 0.29653
6.492 0.36119
9.2416 -0.10432
4.5624
1.4797
-0.64121 0.75817
-3.5767
-3.1896
-0.19908
-6.8607
-0.47241
-1.6677
3.7115 0.99739
9.6152
-1.2332
11.9149
-2.7552
4.3919
0.3211
-1.1793 0.39998
-4.4044
-4.1414
-0.45699
-4.0327
2.3055 -0.02157
7.0858
-1.2112
7.719
-1.7168
1.7048
1.1008
-3.0121 0.003003
-4.6435
-3.9125
0.15822
-5.5457
3.3602 0.00171
6.0987 0.14266
3.4399 0.052141
-1.9702 0.65472
-4.9888
-2.8987
-4.8431
-5.5909
0.27818
-5.0323
0.68946
-0.4638
1.518 0.61981
-1.0731
0.3211
-3.1183 -0.11725
-4.0129
-1.7207
-3.0669
-2.7784
-0.35845
-3.9047
0.61663
-3.2646
0.78886
-0.7819
0.56008 0.05602
-1.6283 -0.56854
-2.8416 -0.59958
-2.2169 -0.56725
-0.35502 -0.59958
0.27218
-1.0728
4.5735 0.47627
11.8318 -0.84268
10.939
-0.4082
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-2.0529
0.18868
-1.7279
-3.3793
-3.1273
-2.121
-1.7697
-0.00129
-1.682
-3.4917
-3.1158
-2.0891
-1.6936
-1.2846
-0.09219
-1.0292
-2.2083
-1.0744
-0.51003
-0.36372
-6.3979
-2.2501
-1.1859
-1.8076
-3.3863
-1.4106
-0.21394
0.48797
-3.8167
-1.9555
-2.1786
-2.3299
0.00312
1.3518
1.2309
-5.0301
-3.0799
-2.2987
-1.239
0.75896
1.6799
0.63655
-6.0598
-3.518
-2.0336
-0.69745
0.75108
3.8385 -0.79544
-1.2138
0.70148 -0.51182 0.005589
-6.841
8.9494 0.68058
-13.7731 17.9274
-2.0323
-7.1121 11.3897 -0.08363
-0.05588
1.949
1.353
3.4329
-1.2144
-2.3789
0.13863 -0.19651 0.008175
-6.8121
7.1398
1.3323
-12.1736 14.3689 -0.61639
-8.6289 10.4403 0.97153
-0.48422
1.704
1.7435
2.7852
-2.1835
-1.9276
3.2715
-1.7671
-3.2608
0.39315 -0.32846 -0.13794
-6.3879
5.5255 0.79955
-9.1069
8.9991 -0.28406
-6.3113
5.355 0.80472
-0.23591 0.020273 0.76334
3.0439
-3.4816
-2.7836
6.4479
1.0836
-6.6176
3.3129 -0.88369
-2.8974
-1.2519
2.2635 0.77239
-8.8131
8.7086 -0.21682
-12.9889 13.0545
-2.7202
-7.108
5.6454 0.31335
-0.68287 0.096532
1.1965
3.5674
-4.3882
-3.8116
5.1401 -0.65063
-5.4306
0.20692
1.2473
-0.3707
-6.4479
6.0344 -0.20777
-9.9532
8.4756
-1.8733
-4.0061
1.7956 0.91722
1.0595
-2.3437 0.39998
3.8923
-4.8277
-4.0069
7.5032 -0.13396
-7.5034
0.60836
2.7039 -0.23751
-5.227
5.63 0.91722
-6.541
4.8151
-0.0332
0.29176
-1.6506 0.83834
4.2068
-4.5398
-2.3931
5.2022
-5.2159
-6.1211
9.2952 -0.43642
-6.3694
2.8763
0.1548
-1.2086
-1.4092
1.1582 0.36507
-1.7672 -0.34474 -0.12372
1.9161
-3.1098 -0.20518
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0.84546
-0.55648
-3.6817
-6.7526
-4.577
-2.9883
-1.4781
-0.46651
-0.8734
-2.1234
-2.3142
-1.4233
-3.0866
-4.7331
-2.8829
-0.03613
-1.7104
-3.8203
-3.7181
-2.899
-0.98193
-0.17296
-1.9409
-3.5713
-2.9915
-1.8483
-2.2677
-0.50816
0.14329
-0.90784
-2.0042
-0.93587
-0.40804
-0.8172
-4.8392
-1.2792
-0.66008
-1.7713
-3.0061
-1.1022
0.11806
0.11686
-2.7264
-1.2369
-1.8439
-1.8554
0.16358
3.4826
3.2136
3.2239
8.8172
3.4515
0.31245
0.14277
2.3383
1.6533
1.1815
2.0838
-0.98912
-6.6362
-6.1789
3.8964
1.525
-4.778
-13.0551
-8.5089
-0.60424
2.7956
-1.1816
-8.6848
-12.4922
-6.6258
0.31038
3.2964
2.868
-1.0885
-7.9026
-9.3676
-5.1008
0.54214
3.3812
6.6755
2.1376
-3.226
-10.7665
-12.2377
-5.8395
0.39108
3.735
3.9213
-1.6906
-8.6475
-9.6035
-3.3584
-3.6307
-1.3961
-3.3085
-2.7965
-0.69347
-3.4004
-0.06198
-3.725
0.66719 -0.94742
0.45041 0.068951
-1.1622 -0.48579
-2.9812
-1.0431
-2.1964 -0.78061
-0.55552 -0.81165
-0.46813
-1.6767
2.3586 0.39481
10.5405 -0.89182
11.388
-1.0741
-0.1888
-1.1672
-1.4089 -0.76121
6.2109
0.3974
16.9583
-2.3052
12.363 -0.95518
2.6045
1.3776
-1.2341
-1.5668
1.3818
0.7336
9.155 0.94049
14.8881 -0.47027
8.6521
1.8198
0.77344
1.4189
-2.2563
-2.4642
-1.8108
-2.2612
1.0039 0.48791
6.7807 0.34179
9.3333 -0.10303
4.5367
1.3866
-0.52725
0.6586
-3.6684
-3.456
-0.24278
-6.5775
-0.47584
-1.3974
3.8058
1.1836
10.2184
-1.0043
11.9552
-2.1603
4.5641 0.68705
-0.98223 0.42843
-4.4379
-4.3741
-0.49212
-3.6371
2.518 0.51636
7.6796 -0.66682
7.7764 -0.97716
1.3749
1.3569
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1.5077
0.67886
-3.9934
-2.3898
-1.7976
-0.70867
1.0194
1.7875
0.27331
-5.1661
-2.7028
-1.4904
-0.0149
0.88992
1.0637
-0.8471
-3.9594
-5.8818
-3.7747
-2.4198
-0.83535
-0.30432
-0.60254
-2.1059
-2.0441
-1.5621
-3.2305
-4.8426
-2.3147
-0.11716
-2.0066
-3.6961
-3.6012
-2.6286
-0.82601
0.31803
-1.4454
-3.1423
-2.5373
-1.366
-1.7064
-0.41965
0.37637
-0.55355
-1.6001
-0.37013
0.12126
1.9596
-3.0584 -0.12243
4.1199
-4.569
-4.1414
5.8333 0.54723
-4.9379
-0.78427
3.0141 0.76205
-6.7686
6.6753 0.89912
-5.5602
4.0483
0.903
1.1029
-2.3 0.59395
4.78
-5.1362
-3.2362
4.8773
-4.9194
-5.8198
8.0433 0.044265
-4.4983
1.6327 0.83598 -0.09139
-2.2183
1.6054 0.89394
-1.0243 -0.94024 0.64955
2.2638
-3.1046 -0.11855
3.6957
-4.1594
-1.9379
3.1329
-3.0112
-2.9388
4.0289 -0.35845
-3.8957
7.6584
0.5558
-2.9155
2.5162 0.83341 -0.30993
-0.24418 0.70146 0.41809
0.80494
-1.6411 -0.19225
2.6528
-2.7756 -0.65647
1.7237
-2.1501 -0.77027
1.1815 -0.53324 -0.82716
1.2271 0.18564
-1.091
-2.2121
4.2591 0.27972
-7.2135 11.6433 -0.94613
-4.9932 10.4052 -0.53104
3.6668
-0.6969
-1.2474
0.60422 -0.38587 -0.05907
-6.719
9.0162 0.099985
-13.6779 17.5795
-2.6181
-6.5389 10.5234 -0.48967
0.18002
1.7956 0.97282
2.9611
-1.2864
-1.4647
-0.99326
1.0947 0.88619
-8.4385
8.8483 0.96894
-13.0365 15.6773 -0.66165
-6.959
8.8054
1.5289
0.18416 0.90539
1.5806
3.3088
-2.2829
-2.1978
2.9094
-1.7859
-2.2069
-0.82358 0.78543 0.74524
-7.9233
6.7156 0.74394
-9.5828
9.4044 0.081882
-5.554
4.7749
1.547
0.22347 -0.47327 0.97024
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-0.27068
-5.119
-1.3946
-0.69879
-1.48
-2.6649
-0.62684
0.518
0.64376
-2.9821
-1.4628
-1.7101
-1.5572
0.74428
2.0177
1.164
-4.3667
-2.5919
-1.8046
-0.71868
1.4378
2.1943
0.7376
-5.637
-3.0193
-1.6706
-0.1269
1.2198
1.4501
-0.40857
-3.8952
-6.3679
-4.1429
-2.6864
-1.0555
-0.29858
-0.49948
-1.9881
-1.9389
-1.4375
-3.1875
-4.6765
-2.0285
0.26637
-1.7589
-3.5985
-3.3582
3.2674
-3.5562
-3.0888
6.6486 -0.04999
-6.5206
2.3134 -0.44499
-1.4905
-3.3771
4.1211
1.5043
-10.5244
9.9176
-0.5026
-12.813 12.6689
-1.9082
-6.301
4.7843
1.106
0.25865 -0.84085 0.96118
3.764
-4.4738
-4.0483
4.1986
-0.5898
-3.9642
-1.5706
2.4357 0.49826
-8.7903
7.9735 -0.45475
-9.8808
8.1088
-1.0806
-3.7723
1.6131
1.5754
1.7982
-2.9581
0.2099
3.913
-4.5544
-3.8672
6.0692 0.57208
-5.4668
-1.0553
3.8949 0.77757
-6.8141
6.7019
1.1681
-5.7154
3.8298
1.0233
0.66837
-2.0267
1.0271
4.5503
-4.976
-2.7254
4.8525
-4.7986
-5.6659
8.1261 0.13081
-5.0142
1.7775 0.73745 -0.45346
-2.09
1.584 0.71162
-1.1505 -0.95138 0.57843
2.0982
-3.1954 0.12843
3.6067
-4.0557
-1.5966
3.0977
-2.9607
-2.6892
3.8157 -0.31304
-3.8194
8.0102
0.4247
-3.2207
2.7749 0.68261 -0.71984
-0.09727 0.61663 0.061192
0.79459
-1.6968 -0.46768
2.4769
-2.9512 -0.66165
1.7734
-2.2469 -0.68104
0.99945 -0.28562 -0.70044
1.5706 0.045979
-1.122
-1.8624
4.026 0.55127
-7.5756 11.8678 -0.57889
-5.6636
10.969 -0.33449
3.8468 -0.63435
-1.175
0.73252 -0.67891 0.03533
-6.4624
8.4773 0.31981
-13.6593 17.6052
-2.4927
-7.2404 11.4419 -0.57113
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-2.3629
-2.1802
-0.40951
-2.2918
-4.0214
-3.3884
-2.0046
-1.7063
-1.6386
-0.41645
-1.5877
-2.5961
-1.5228
-0.53072
-0.49081
-6.5773
-2.4621
-1.3995
-2.3221
-3.73
-1.6988
-0.26654
0.33325
-4.2091
-2.3142
-2.4835
-2.7611
-0.36025
1.0117
0.96708
-5.2049
-3.3203
-2.565
-1.5951
0.7049
1.7331
0.6818
-6.3364
-3.8053
-2.1979
-0.87874
0.74067
0.98296
-0.3489
-3.8552
-6.9599
-4.7462
-0.10554
1.9336
1.1358
3.3791
-1.2256
-2.6621
-0.15521 0.060545 -0.08881
-7.257
7.9597
0.9211
-12.8006 15.6199 -0.95647
-8.215 10.3315 0.98187
-0.49457
1.333
1.6543
2.7956
-2.378
-2.3491
3.3584
-1.7302
-3.5646
0.32487 -0.33617 -0.36036
-6.6072
5.8022 0.31593
-9.349
9.7942 -0.28018
-6.4789
5.7568 0.87325
-0.09727 -0.21793
1.0426
2.8452
-3.6436
-3.1004
6.8017 0.85483
-7.5344
2.7645 -0.62578
-2.8573
-1.9162
2.5154 0.59912
-9.3304
9.233 -0.79871
-12.9723 12.9817
-2.684
-7.1163
5.7902 0.16723
-0.64562 -0.42014 0.89136
3.3108
-4.5081
-4.012
4.7283 -0.49126
-5.2159
-0.68494
1.9833 -0.44829
-7.4494
6.8964 -0.64484
-10.5099
9.0239
-1.9547
-4.449
2.1067 0.94308
0.9022
-2.3506 0.42714
3.8426
-4.9314
-4.1323
7.259 0.070827
-7.3004
-0.02691
2.9618 -0.44958
-5.7899
6.0122 0.046968
-6.572
4.7689 -0.94354
0.17174
-1.7859 0.36119
3.9544
-4.7412
-2.5017
4.8504
-5.2133
-6.1043
9.2848 0.014275
-6.7844
2.4273
0.6809
-1.0871
-2.1252
1.7151 0.45171
-2.2121
-0.0517 0.099985
1.7299
-3.1963
-0.1457
3.4226
-3.9692
-1.7116
3.1929
-3.4054
-3.1832
3.5219 -0.38415
-3.8608
8.9931
0.2182
-4.572
3.1205
1.075
-1.2966
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-3.2051 -0.14279
-1.7549 -0.08071
-0.59587
2.4811
-0.89542
2.0279
-2.0754
1.2767
-3.2778
1.8023
-2.2183
-1.254
-3.5895
-6.572
-5.0477
-5.8023
-3.5741
3.944
-0.7351
1.7361
-2.2617
-4.7428
-4.244 -13.0634
-4.0218
-8.304
-3.0201 -0.67253
-2.4941
3.5447
-0.83121 0.039307
-2.5665
-6.8824
-4.4018 -12.9371
-3.7573
-8.2916
-2.4725 -0.40145
-1.9725
2.8825
-2.0149
3.6874
-0.82053 0.65181
-1.7886
-6.3486
-2.9138
-9.4711
-1.8343
-6.5907
-0.8734 -0.03312
-0.70346
2.957
-6.7387
6.9879
-2.7723
3.2777
-1.6641
-1.3678
-2.4349
-9.2497
-3.793 -12.7095
-1.9551
-6.9756
-0.69078 -0.50077
0.025013
3.3998
-4.3967
4.9601
-2.456 -0.24418
-2.62
-6.8555
-2.9662 -10.3257
-0.71494
-4.4448
0.6005 0.99945
0.61652
3.8944
-5.4414
7.2363
-3.5798 0.45937
-2.7769
-5.6967
0.97565 0.045675
-0.75774
-0.3707
-2.8673 -0.89828
-2.3652
-1.2746
-0.64206
-1.2642
0.1805
-2.3931
2.9986 0.36378
10.5251 -0.16381
11.244
-0.3901
-0.07912
-2.1203
-1.4938
-1.1582
6.3489 0.11162
17.1116
-2.8017
12.555
-1.5099
2.7056 0.85774
-1.3721
-2.8483
0.05369 -0.23105
7.5416 0.70774
15.6559
-1.6806
10.3032 0.38059
1.4855
1.1189
-2.3086
-2.3724
-1.9385
-3.8918
-0.48869 -0.52716
5.6154 0.42584
9.7668 -0.60216
5.6429 0.54998
-0.20165 0.55774
-3.5947
-3.1457
0.67833
-7.5887
-0.9351
-3.1457
1.997 0.52283
8.9922 -0.50001
12.7957
-2.825
5.5383 -0.12889
-0.35417 0.47498
-4.4327
-4.2655
-0.64892
-5.4719
1.4041 -0.45863
6.2169 -0.62285
8.784
-2.1138
2.2241 0.49826
-2.2126 0.097399
-4.7275
-4.3948
0.10938
-7.5642
2.3457 -0.45734
5.9179 0.37671
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-1.8356
-6.7562
0.30081 0.17381
1.3403
4.1323
0.26877
4.987
-6.5235
9.6014
-4.0679
2.4955
-2.564
-1.7051
-1.3414
-1.9162
0.23874
2.0879
0.6212
3.6771
-0.77848
3.4019
-4.1244
3.7909
-7.0421
9.2
-4.9462
3.5716
-3.5359 0.30417
-2.0662 0.16967
-0.88728
2.808
-1.0941
2.3072
-2.4458
1.6285
-3.551
1.8955
-2.2811 -0.85669
-3.6053
-5.974
-5.0676
-5.1877
-3.9204
4.0723
-1.1306
1.8458
-2.4561
-4.5566
-4.4775 -13.0303
-4.1958
-8.1819
-3.38
-0.7077
-2.4365
3.6026
-0.77688 0.13036
-2.7083
-6.8266
-4.5531 -12.5854
-3.8894
-7.8322
-2.5084 -0.22763
-2.1652
3.0211
-1.8974
3.5074
-0.62043
0.5587
-1.8387
-6.301
-3
-9.1566
-1.9116
-6.1603
-1.005 0.084831
-0.87834
3.257
-6.651
6.7934
-2.5463
3.1101
-1.4377
-1.432
-2.4554
-9.0407
5.0585 -0.55044
-1.7542 0.48921
-4.7018
-2.5987
-5.1508
-6.3913
-0.25392
-6.9642
0.79571
-1.1039
1.5026 0.32757
-0.15538 -0.11984
-3.3522 -0.66553
-4.0771
-2.0711
-3.4859
-3.5569
-0.6532
-4.1802
0.25933
-4.6832
0.82742
-1.4957
0.6569
-0.2957
-1.0054 -0.82975
-3.1432
-1.2035
-2.5237
-1.4453
-0.88541
-1.4802
0.1865
-2.4409
2.7185 0.044382
10.0916 -0.82846
10.4266 -0.86725
-0.23678
-2.1151
-1.3575
-1.3806
6.4534 -0.05648
17.0834
-3.0345
12.1291
-1.6017
2.5325 0.71808
-1.4166
-2.8948
-0.03114 -0.35389
7.5339 0.59007
15.4417
-1.4983
9.8208 0.47498
1.488
1.2069
-2.4132
-2.4241
-1.7842
-3.8491
-0.38587 -0.66423
5.6506 0.19567
9.5766 -0.73018
5.606 0.48533
-0.2462 0.45688
-3.6778
-3.2944
0.68604
-7.5887
-0.83228
-3.0358
2.1144 0.42067
8.862 -0.86983
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-3.9411
-2.1241
-0.74324
-0.0715
-4.2333
-2.3675
-2.5526
-3.0986
-0.89809
0.56232
0.53936
-5.3012
-3.3553
-2.7908
-1.9983
0.15423
1.208
0.2952
-6.4247
-3.9933
-2.659
-1.4094
0.11032
0.52374
-0.76794
-3.9698
-7.0364
-4.9447
-3.5933
-2.1674
-0.9607
-1.0802
-2.3277
-3.7244
-2.5724
-3.9297
-5.2943
-3.8953
-1.2244
-2.6406
-4.6338
-4.2887
-3.3458
-1.1188
0.55939
-1.5078
-3.506
-12.8792 13.0597
-6.8969
5.5992
-0.32902 -0.42785
3.7412
-4.5415
4.9166 -0.49212
-0.43663
1.692
-7.3625
6.9255
-10.4602
8.9717
-4.4862
2.2009
1.0015
-2.2726
3.8944
-4.8166
7.3915 0.029699
0.35591
2.6473
-5.7133
5.953
-6.6072
4.8254
0.11794
-1.6823
4.0744
-4.7635
4.8856
-5.149
9.5311 0.022844
2.6218 0.62863
-1.6058
1.3647
-2.1252 -0.10397
1.9741
-3.3668
3.644
-4.0746
3.4598
-3.4405
3.6812 -0.60008
9.2931 0.16594
3.3005
1.063
0.22968
0.7126
0.12415
-1.0465
2.6963
-3.1226
2.1996
-2.5862
1.4381 -0.82114
1.9037 -0.03542
-0.95602
2.7073
-6.0816 10.0958
-5.1463 10.3332
4.0392
-0.3019
1.7485
-1.4801
-4.4159
5.983
-12.7509 16.7166
-7.8633 11.8387
-0.50491
2.6328
3.3357
-1.3455
-0.3104 0.18307
-7.3191
7.8981
-12.5667 15.1606
-3.3125
-0.47156
0.23317
-4.2526
-5.3207
-0.43018
-0.66811
-2.3427
0.50731
-0.00605
-4.3418
-7.3987
-0.37846
0.45946
-0.41984
0.59524
-2.6129
-6.2323
-6.8517
-1.1595
0.16464
-0.19225
-0.65259
-1.9909
-3.4276
-4.0133
-4.5396
-1.444
-0.3332
-0.86208
-1.3121
-1.2759
-1.2862
-2.5095
-0.16639
-1.0147
-1.1181
-2.1836
-1.4181
-0.13924
-3.2168
-1.8978
0.53705
-1.9573
0.44653
1.2289
-0.75216
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-2.9498
-1.6029
-1.2667
-0.49281
0.66365
-0.72068
-1.9966
-0.97325
-0.02531
0.062525
-5.525
-1.2943
-0.24037
-1.3968
-2.9672
-1.1005
0.22432
0.90407
-2.8619
-1.0833
-1.5681
-2.0545
0.2346
1.581
1.5514
-4.1479
-2.2625
-1.7479
-0.95923
1.3451
2.2279
1.2572
-5.3857
-2.9786
-1.5851
-0.21888
1.3183
1.4896
0.11592
-3.3924
-6.1632
-4.0786
-2.5899
-1.0116
0.066129
-0.24745
-1.5732
-8.273
-0.38903
2.8183
3.0605
-0.04553
-6.7583
-9.5001
-6.4168
-0.17383
2.9301
6.3258
2.6735
-1.7837
-9.6698
-13.2869
-7.2508
-0.52147
3.3708
4.5193
-0.31247
-7.2446
-10.8679
-4.5152
0.86909
3.8013
7.1225
-0.09934
-5.823
-6.7128
0.23589
4.0951
4.8731
9.1214
2.3445
-2.1562
-2.2038
1.9017
3.4288
3.2219
3.3564
8.7096
2.9239
-0.3911
-0.19038
2.4914
1.9368
1.0636
10.2646
1.1629
1.62
1.9103
-2.426
-1.8862
-1.8356
-2.834
-0.18794 0.23447
5.8408 0.62369
9.682 -0.12889
5.6026
1.0323
-0.11339
1.2198
-3.5467
-2.6737
0.89768
-6.6241
-0.84085
-2.0323
2.135
1.2418
9.4652 -0.34872
13.4727
-2.6271
6.0139 0.36895
-0.40386
1.2017
-4.4987
-3.6965
-0.58123
-4.2629
1.2815 0.41291
6.5537
-0.1276
9.4926
-1.4116
2.1195
1.4448
-2.3138 0.82412
-4.9143
-3.7483
-0.0834
-6.4172
2.8127 0.48662
5.8699
1.212
4.9857 0.32886
-1.8785
1.3258
-4.8037
-2.1112
-5.2861
-5.8741
-0.41929
-5.9181
0.52667 -0.40173
1.7082
0.9017
-0.0954 0.56421
-3.3111 0.065071
-4.0309
-1.4259
-3.4302
-2.8457
-0.72004
-3.5233
-0.21621
-3.6345
0.87026 -0.65389
0.93452 0.42972
-0.90597 0.003003
-2.9401 -0.62156
-2.4697 -0.80518
-0.71232
-0.8388
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
-2.1668
-1.1667
-2.8391
-4.5046
-2.41
0.40614
-1.3887
-3.7503
-3.5637
-2.5419
1.5933 0.045122
-1.4237
2.9241
-6.63 10.4849
-5.8126 10.8867
3.7433 -0.40215
1.3492
-1.4501
-4.8773
6.4774
-13.4586 17.5932
-8.3827
12.393
-0.65804
2.6842
-1.678
0.66119
-0.42113
-0.52846
-1.2953
-0.55949
0.34179
-2.7771
-1.2823
1.1952
2
2
2
2
2
2
2
2
2
2
Dua, D. and Graff, C. (2019). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA:
University of California, School of Information and Computer Science.
Data Set Information:
Data were extracted from images that were taken from genuine and forged banknote-like specimens. For
digitization, an industrial camera usually used for print inspection was used. The final images have 400x
400 pixels. Due to the object lens and distance to the investigated object gray-scale pictures with a
resolution of about 660 dpi were gained. Wavelet Transform tool were used to extract features from
images.
Attribute Information:
1. variance of Wavelet Transformed image (continuous)
2. skewness of Wavelet Transformed image (continuous)
3. kurtosis of Wavelet Transformed image (continuous)
4. entropy of image (continuous)
5. class (integer): 1- genuine, 2-forged
1
Portfolio Project Option 2: Counterfeiting Banknotes
Rachael Herman
Colorado State University Global
MIS450: Data Mining
Professor Mamdouh Babi
August 7, 2022
2
Portfolio Project Option 2: Counterfeiting Banknotes
The portfolio project uses the banknotes.csv file to build an appropriate model that will
successfully predict forgery. This dataset was uploaded into SAS in the milestone for this
project. Summary statistics and a graphical summary of histograms are provided, along with a
discussion of key aspects from that data. ____ is used for anomaly detection, and associations are
identified using ____. The clustering technique used in this project to analyze the variables is
____, and results are explained in detail. A classification model to predict forgeries is provided,
along with reasoning for its use. Finally, the model is evaluated and impressions on model fit
reviewed with any opportunities to improve on the model.
Figure 1
Dataset Upload to SAS
Summary Statistics and Histograms of Banknotes Dataset
There are two classes identified in the dataset, with 1 meaning the observation is genuine
and 2 that it is forged. Basic statistics are performed on each of these two variables to look more
closely at legitimate and counterfeit items. The data shows there are 762 genuine entries and 610
3
forgery entries. The Wavelet Transform tool extracts features from the images, which are
demonstrated in integers for four variables, including:
1. V1 = variance of Wavelet Transformed image, which measures the spread between these
numbers in the dataset (Sturdivant et al., 2016).
2. V2 = skewness of Wavelet Transformed image detects the symmetry of the curve in
terms of the image data features.
3. V3 = kurtosis of Wavelet Transformed image describes the degree of the tails and at the
peak of the curve in a frequency distribution (Sturdivant et al., 2016)
4. V4 = entropy of image measures the degree of randomness in the image features (Thum,
1984).
Summary statistics and histograms demonstrate a left skewness in genuine entries (class
= 1) for variance, skewness, and entropy. Kurtosis has a right skew that looks to be multi-modal.
Forgeries (class = 2) show a rightward skewness in variance and kurtosis, with a left skewness in
entropy. This suggests there is higher variance, skewness, and entropy in the images. When
classes are not separated, variance is multimodal but relatively normally distributed. Skewness is
left-skewed and multimodal, kurtosis is right-skewed and bimodal, and entropy is left-skewed.
Items with larger values of entropy and kurtosis tend to be a class = 2, forgery. Higher variance
and skewness values tend to be class =1, genuine.
Figure 2
Summary Statistics of Continuous Variables Separated by Class
4
Figure 3
Summary Statistics of Continuous Variables not Separated by Class
Figure 4
Figure 5
Histogram With Classes in V1 = Variance
Histogram Without Classes in V1
Figure 6
Figure 7
Histogram With Classes in V2 = Skewness
Histogram Without Classes in V2
5
Figure 8
Figure 9
Histogram With Classes in V3 = Kurtosis
Histogram Without Classes in V3
Figure 10
Figure 11
Histogram With Classes in V4 = Entropy
Histogram Without Classes in V4
Anomaly Detection
An important task in data analysis is to look for any outliers or anomalies in the dataset.
To do this, one must identify objects that do not conform to the normal patterns of behavior in
the dataset (Tan et al., 2018).
Clustering Technique for Variable Analysis
Variable Associations
Classification Model
6
A decision tree will be used for this dataset to predict forgery. A decision tree
classification model uses a series of questions about the attributes of an observation or instance
to determine its class, which are organized into a hierarchical structure (Tan et al., 2018).
Advancement of digitization with scan and print techniques has led to serious counterfeiting
issues, making it difficult to identify forgery with the naked eye (Upadhyaya et al., 2018).
Therefore, a decision tree model can perform variable scrutiny on the banknote dataset given the
variance, skewness, kurtosis, and entropy of those images, making it a good model for this task.
Model Evaluation
Summary statistics and histograms help with visualizing the data. After review of the
documentation and analysis of these summaries, I was able to determine a good classification
model. A decision tree will help predict forgery by asking specific questions about variance,
skewness, kurtosis, and entropy of the banknote images. This data will prove beneficial in the
final portfolio project, which will design a complete model for forgery prediction.
7
References
Sturdivant, R., Pardoe, I., Berrier, I., & Watts, K. (2016). Statistics for Data Analytics. zyBook
[online].
Tan, P.N., Steinback, M., Karpatne, A., & Kumar, V. (2018). Introduction to data mining (2nd
ed.). Pearson.
Thum, C. (1984). Measurement of entropy of an image with application to image focusing.
Optica Acta: International Journal of Optics, 31(2), 203-211. DOI: 10.1080/713821475
Upadhyaya, A., Shokeen, V., & Srivastava, G. (2018). Decision tree model for classification of
fake and genuine banknotes using SPSS. World Review of Entrepreneurship,
Management, and Sust. Development, 14(6), 683-693. DOI:
10.1504/WREMSD.2018.097696

Purchase answer to see full
attachment

  
error: Content is protected !!