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Learning Pandas

AMCDawes

Dec 2015

Some parts of our CCDimage code would be much improved by the use of pandas. In particular, some statistics and other anaylsis would be very straightforward. This is a place for my notes as I learn pandas.



In [38]:

    
# standard imports:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib

# use inline plots:
%matplotlib inline

# use ggplot style:
matplotlib.style.use('ggplot')

Our data is currently represented as a stack of 2D arrays (so a 3D "array"). In that implementation the third index is essentially a shot number and the first two are pixel row and pixel column. We'd like to make a dataframe of this data and then work with it in pandas instead of in an array. Another data type we have is the $K_p$ values (essentially the FFT output). In this case, it is a 1D array for each shot of data. The pandas version would be a dataframe with each element being a 1D array of $K_p$ values.

To test this, let's create a random dummy set that is 20 shots of 400 $K_p$ values:



In [10]:

    
# create an example dataframe:
df = pd.DataFrame(np.random.randn(20,400), index=np.arange(20), columns=1.23*np.arange(400))



In [11]:

    
df









    Out[11]:






  
    
      
      0.0
      1.23
      2.46
      3.69
      4.92
      6.15
      7.38
      8.61
      9.84
      11.07
      ...
      479.7
      480.93
      482.16
      483.39
      484.62
      485.85
      487.08
      488.31
      489.54
      490.77
    
  
  
    
      0
      0.184962
      -0.593215
      0.189440
      -0.041520
      -0.468275
      1.248782
      -1.325620
      0.712231
      -0.162094
      1.817380
      ...
      -1.343064
      -1.470482
      0.735458
      0.679417
      -0.240810
      -0.455247
      -0.493477
      0.546133
      -0.093801
      -0.870588
    
    
      1
      0.330364
      1.285958
      0.221395
      -0.679064
      -0.605855
      -1.138653
      0.432561
      -0.072273
      -0.031589
      -0.955335
      ...
      0.403545
      -0.294596
      -0.046364
      1.550566
      1.322492
      0.158821
      0.156565
      -0.445687
      -2.098845
      -1.161122
    
    
      2
      -0.248033
      -0.075215
      1.170656
      0.055841
      -0.277661
      0.005537
      0.479036
      0.754289
      -0.441990
      -1.282790
      ...
      -0.323793
      -3.010945
      0.336506
      -0.325221
      0.376113
      0.062601
      -0.838108
      -1.102468
      0.338594
      0.423082
    
    
      3
      1.721958
      -0.023670
      -1.054532
      1.613846
      0.368450
      1.702158
      -0.076590
      -1.169031
      0.483357
      0.935780
      ...
      -0.178595
      1.032906
      -2.016839
      2.064577
      1.685427
      -0.653712
      -1.918819
      0.239802
      0.550428
      -1.531779
    
    
      4
      1.571422
      -0.108286
      0.329186
      -0.399168
      -0.406936
      0.530031
      -1.320046
      -1.747431
      -1.522011
      1.004620
      ...
      -1.139332
      0.549895
      1.571382
      0.940728
      -0.602542
      0.138620
      -0.593473
      0.266806
      -0.832163
      -1.852263
    
    
      5
      -0.086009
      0.595296
      0.425701
      1.522184
      1.367878
      1.281471
      -0.541161
      1.061773
      -0.184506
      -0.372571
      ...
      0.419337
      -0.072765
      2.219141
      -0.960565
      -1.141693
      0.024791
      -1.159445
      1.722109
      -0.048243
      1.181456
    
    
      6
      0.663104
      1.017888
      -0.049473
      -0.651722
      0.167377
      0.377671
      -0.467855
      0.071341
      0.123341
      -0.587914
      ...
      -1.230849
      -1.044841
      0.162082
      -0.314299
      -0.799146
      -0.199157
      0.314127
      0.213541
      1.427636
      0.283838
    
    
      7
      -0.419924
      -0.354931
      0.916886
      -0.751909
      1.013355
      -1.736379
      0.522979
      0.470240
      -0.634015
      -0.360114
      ...
      1.375368
      -0.968433
      0.362897
      -1.411900
      0.530603
      1.166181
      0.625223
      -0.266564
      -0.570224
      -0.822201
    
    
      8
      0.168113
      0.887247
      -1.040347
      0.194861
      0.442004
      0.275889
      -0.243377
      1.089206
      0.664697
      0.223828
      ...
      -0.928463
      0.471350
      0.490348
      0.217929
      -0.883274
      -0.421726
      1.486858
      0.689218
      0.754216
      0.110106
    
    
      9
      1.186498
      -0.960690
      -0.348566
      0.990295
      0.675831
      0.761218
      -0.542745
      0.261024
      0.001028
      1.173646
      ...
      -0.059401
      0.616330
      -1.674507
      -1.064985
      0.535332
      -1.322795
      -1.539502
      0.532675
      0.173978
      1.202523
    
    
      10
      -1.352537
      -0.425472
      0.879962
      -0.239729
      -0.233018
      0.734855
      1.006921
      0.607420
      -1.669254
      -0.693078
      ...
      -0.659705
      0.788002
      0.248544
      -1.297290
      0.316705
      -0.207468
      -0.405590
      0.842259
      0.514191
      0.423534
    
    
      11
      1.599110
      -0.100259
      0.878009
      -0.890536
      1.438008
      1.520079
      -1.695664
      -1.685915
      -0.833511
      0.277582
      ...
      1.975432
      0.831157
      -0.004321
      -0.091759
      -0.384815
      -1.432872
      1.437886
      2.025241
      -1.649293
      -1.123986
    
    
      12
      0.663158
      -0.613900
      0.652613
      1.288169
      0.154322
      1.274050
      0.246589
      0.623908
      -0.535676
      0.181517
      ...
      -1.122317
      -2.191370
      -0.585120
      -1.325936
      -0.674683
      -1.193839
      0.398804
      0.260643
      -0.042832
      -0.139533
    
    
      13
      -0.645737
      -0.510152
      -1.005171
      -1.624530
      0.898106
      0.066679
      0.874028
      -1.401223
      -0.057903
      0.582753
      ...
      -1.380020
      -2.512605
      1.118588
      0.634844
      0.301920
      0.236669
      -0.509022
      0.171967
      -0.814506
      -0.306371
    
    
      14
      1.321814
      -0.774301
      -1.902708
      1.957949
      2.112021
      0.815829
      -2.043558
      -0.020623
      0.595277
      -0.107277
      ...
      -0.427886
      -0.090893
      0.283438
      0.656301
      0.766152
      -1.237433
      1.099856
      -0.036330
      -1.391981
      0.906868
    
    
      15
      -0.803413
      0.036083
      -0.761519
      -1.115538
      0.178751
      -0.937486
      0.237419
      0.474481
      -1.090644
      0.645634
      ...
      -1.528687
      0.021469
      0.147363
      0.549197
      0.077641
      -1.080116
      1.058282
      0.961617
      0.005075
      0.570475
    
    
      16
      0.761742
      0.049620
      0.740389
      -1.541954
      -0.477572
      -0.396389
      0.217273
      -0.255407
      0.067497
      0.006614
      ...
      0.082712
      0.449123
      -0.875030
      -0.495502
      -2.268136
      0.375531
      -1.265048
      0.530770
      -1.081555
      -1.910912
    
    
      17
      1.494090
      0.608071
      -0.028324
      0.413887
      0.340919
      -0.401112
      -0.439394
      -0.441322
      -0.155351
      1.351053
      ...
      -1.021816
      -0.639324
      0.622632
      0.691260
      -0.438366
      0.321922
      -0.595063
      1.005989
      -0.511210
      -0.248449
    
    
      18
      1.839444
      0.250622
      0.030625
      0.658200
      -0.525802
      1.183947
      0.920444
      0.297210
      0.194203
      0.366299
      ...
      1.459953
      0.212683
      0.216094
      -0.430931
      -0.885898
      -0.151657
      -0.829574
      0.051659
      0.822611
      -0.310205
    
    
      19
      -1.863444
      1.019783
      0.423566
      -1.553650
      0.802445
      0.083260
      -0.491350
      2.118290
      0.345122
      2.467606
      ...
      0.481893
      1.324027
      -0.285335
      -1.192188
      1.645913
      -0.321261
      2.514560
      -0.868827
      -0.813402
      -0.029505
    
  

20 rows × 400 columns

So we see a few nice features:

we can label the columns with useful things, this could be the actual mode index $p$ for the columns
we can also label rows, this could be shot number, or even a alphanumeric code for shot/run (can it be alphanumeric?)

To show this, we'll create a list of the row labels using a list comprehension. Note, this could also be done with a generator, but that is a more advanced pythonism



In [12]:

    
# nested string list comprehension:
rows = ["r{}s{}".format(i,j) for i in np.arange(4) for j in np.arange(5)]



In [13]:

    
# could also be a generator:
row_gen = ("r{}s{}".format(i,j) for i in np.arange(4) for j in np.arange(5))



In [14]:

    
for i in row_gen:
    print(i)









    



r0s0
r0s1
r0s2
r0s3
r0s4
r1s0
r1s1
r1s2
r1s3
r1s4
r2s0
r2s1
r2s2
r2s3
r2s4
r3s0
r3s1
r3s2
r3s3
r3s4



In [15]:

    
df2 = pd.DataFrame(np.random.randn(20,400), index=rows, columns=1.23*np.arange(400))



In [16]:

    
df2









    Out[16]:






  
    
      
      0.0
      1.23
      2.46
      3.69
      4.92
      6.15
      7.38
      8.61
      9.84
      11.07
      ...
      479.7
      480.93
      482.16
      483.39
      484.62
      485.85
      487.08
      488.31
      489.54
      490.77
    
  
  
    
      r0s0
      -0.075841
      -0.904605
      -1.094072
      0.605669
      -1.935258
      0.650063
      0.660024
      -2.170779
      1.076856
      -0.521928
      ...
      1.028115
      -0.131176
      1.219894
      0.364914
      1.028008
      -0.210408
      0.584433
      0.022389
      0.198800
      2.394047
    
    
      r0s1
      0.464307
      0.507541
      -0.215419
      -0.744910
      1.049569
      -0.146941
      0.288519
      0.591788
      -1.127253
      -0.838182
      ...
      0.611890
      -0.847824
      -0.776338
      -0.056745
      0.168138
      -0.413380
      -0.136623
      1.508007
      0.763493
      -1.961929
    
    
      r0s2
      0.549017
      -0.010613
      0.350341
      0.600244
      0.564113
      -0.135829
      -0.530846
      -0.960254
      0.759039
      -0.449446
      ...
      0.624111
      -0.088894
      -1.126249
      0.604857
      -1.559714
      1.838663
      -1.085178
      -1.633170
      -0.223984
      -0.287379
    
    
      r0s3
      0.854825
      1.083141
      -1.502872
      0.215501
      1.037609
      0.905728
      -0.099644
      -0.872863
      0.409028
      -0.392250
      ...
      -1.517258
      0.598385
      -0.585482
      0.333990
      -0.100666
      -0.024075
      -0.180373
      -1.391312
      2.034463
      1.557063
    
    
      r0s4
      -0.540168
      -2.024637
      1.521336
      0.458756
      0.031326
      -0.362836
      0.002126
      -0.623581
      0.187056
      -1.338258
      ...
      0.124124
      1.468026
      0.705380
      -1.086340
      -1.358901
      -0.294727
      -0.324702
      -0.815423
      0.256468
      1.090099
    
    
      r1s0
      0.826986
      -0.842467
      1.049514
      1.150837
      -0.785820
      0.429018
      1.115340
      1.307672
      0.376442
      0.854339
      ...
      -0.429645
      -0.675573
      -0.810689
      0.187499
      0.262096
      0.496407
      -0.978998
      -0.594335
      -0.133461
      2.547492
    
    
      r1s1
      -2.407435
      0.084073
      0.926649
      -1.474173
      1.498178
      0.161716
      1.031246
      -0.094132
      -0.994738
      -1.276429
      ...
      0.244866
      0.988604
      -0.210704
      -0.633346
      -1.639042
      2.043875
      0.916145
      1.058196
      -0.923993
      0.696969
    
    
      r1s2
      -0.553663
      0.260108
      0.565609
      0.348731
      -0.222907
      1.454296
      -0.804949
      -1.058964
      0.146190
      1.406294
      ...
      0.778546
      -0.583378
      -1.960605
      -2.030100
      0.323722
      -1.504652
      -0.222541
      0.062490
      0.261073
      0.655042
    
    
      r1s3
      -1.923620
      1.897037
      1.345015
      -1.532653
      0.272023
      0.384065
      1.002208
      0.272557
      -0.646553
      -0.312436
      ...
      -0.196265
      1.047866
      0.542254
      0.372460
      0.896880
      0.828275
      -1.182366
      -0.272894
      -0.625088
      0.087952
    
    
      r1s4
      -1.186381
      0.669413
      0.760152
      -0.552006
      0.521368
      -0.949405
      -0.020145
      -0.090695
      -1.702185
      -0.757083
      ...
      1.690140
      0.634193
      -1.026187
      1.614171
      -0.463188
      0.336056
      -1.407198
      -1.658494
      -2.787294
      -0.790165
    
    
      r2s0
      0.990522
      -0.961763
      0.439112
      0.885652
      1.450123
      -0.499534
      0.938854
      1.408904
      -0.740930
      -0.140112
      ...
      -0.063761
      -0.626640
      0.041427
      -0.345510
      0.431423
      -0.716702
      1.691901
      -0.428716
      -0.836942
      -0.288951
    
    
      r2s1
      -0.519180
      -1.298858
      0.250681
      -1.190024
      0.106520
      -0.095677
      0.615137
      0.495602
      -0.212434
      -0.349042
      ...
      -1.641367
      -0.665836
      0.256332
      0.451142
      1.305498
      -0.108231
      0.204788
      0.869855
      -0.266288
      1.509643
    
    
      r2s2
      0.734422
      0.476790
      -0.458226
      -0.700024
      -1.238566
      0.599671
      -0.427914
      0.844219
      -0.270551
      0.492769
      ...
      -1.239655
      1.126015
      -0.550496
      -0.761821
      -0.531756
      -0.332588
      -0.523914
      -0.290804
      0.246082
      -0.102039
    
    
      r2s3
      -0.853220
      -2.093568
      -0.643340
      0.200368
      -0.716152
      -1.126140
      -0.698815
      -0.416204
      -0.544038
      0.368496
      ...
      -1.466966
      1.246151
      0.064958
      -1.270758
      1.034440
      -0.975365
      -0.009970
      -0.033534
      -1.204973
      1.992776
    
    
      r2s4
      -1.734340
      1.018595
      1.145354
      -0.112782
      0.590931
      1.525264
      -1.583458
      0.948296
      1.711134
      0.053377
      ...
      0.133120
      0.159131
      1.151579
      -0.270983
      -0.793256
      -0.395818
      -0.000882
      -0.871829
      -0.321323
      0.475428
    
    
      r3s0
      -0.783272
      0.549246
      0.912964
      -0.846065
      -0.347537
      0.244262
      -1.921135
      0.290666
      1.023833
      0.347094
      ...
      -0.121621
      -0.236661
      0.837270
      -1.076396
      -0.592567
      -2.097988
      -0.013013
      0.231985
      -1.345679
      2.884452
    
    
      r3s1
      0.290483
      0.363594
      2.177999
      -0.156987
      -0.939555
      0.443229
      1.458815
      2.574376
      -1.076518
      -0.363016
      ...
      1.702962
      1.722178
      0.999881
      0.184068
      -0.614013
      -0.598080
      -0.728771
      -0.300455
      1.025306
      -0.240906
    
    
      r3s2
      -1.332260
      -0.925884
      -0.835553
      -0.015138
      1.851840
      0.090223
      0.281905
      -0.100410
      0.095656
      -1.359204
      ...
      0.326450
      -0.434180
      0.019184
      1.248174
      -0.215904
      0.850511
      0.770674
      0.306296
      1.293982
      -1.435372
    
    
      r3s3
      0.200371
      -0.846563
      1.856579
      -0.600437
      0.725963
      0.383318
      0.835080
      -0.656290
      -0.978341
      0.180849
      ...
      -0.889134
      -0.567104
      0.826408
      -0.337061
      -0.099261
      -0.017822
      -0.381713
      0.862280
      -0.116477
      -1.101553
    
    
      r3s4
      -0.753709
      -0.070955
      -0.344824
      -0.385953
      -0.344296
      -2.013347
      0.147098
      -0.802810
      -1.089017
      -0.130341
      ...
      0.140231
      -0.945284
      1.047795
      1.883125
      -0.141678
      -0.783196
      1.150965
      -0.080518
      -1.244698
      1.317814
    
  

20 rows × 400 columns

Now we can start to use these data structures in the CCDimage code. It is important to note, that the values can be complex too!



In [17]:

    
# complex example:
df3 = pd.DataFrame(np.random.randn(20,400) + 0.1*np.random.randn(20,400)*1j, index=rows, columns=1.23*np.arange(400))



In [18]:

    
df3









    Out[18]:






  
    
      
      0.0
      1.23
      2.46
      3.69
      4.92
      6.15
      7.38
      8.61
      9.84
      11.07
      ...
      479.7
      480.93
      482.16
      483.39
      484.62
      485.85
      487.08
      488.31
      489.54
      490.77
    
  
  
    
      r0s0
      (-1.23576271913-0.185847883574j)
      (0.0529216538903+0.129158233718j)
      (0.724415189064-0.104322240946j)
      (-1.65301916201+0.0720106546298j)
      (-0.141481016733+0.0361646764067j)
      (-0.222757669741+0.0400796456564j)
      (-0.21361548993-0.0837229942064j)
      (0.943233544682-0.140260846666j)
      (0.567894567351+0.0306696240982j)
      (-0.902016328789+0.114131753957j)
      ...
      (-1.85902244304+0.0287101151056j)
      (0.921572078908-0.0710246678393j)
      (1.10489339086-0.0788672179216j)
      (-0.612657340247+0.0228959362189j)
      (-1.1688038002-0.156471551294j)
      (-0.512148594723-0.0535613010007j)
      (-0.756125963407-0.044222458599j)
      (-0.0407041390489+0.0460788111033j)
      (0.534728902924-0.0871808137524j)
      (0.132200155724+0.112614834113j)
    
    
      r0s1
      (-0.981939512432-0.0248213642288j)
      (0.201676834287+0.0332533538591j)
      (0.0949735642599-0.0258463075781j)
      (0.689998693135-0.0221663676157j)
      (0.830687375073-0.122014801224j)
      (-0.0578329368654+0.000577935992641j)
      (-0.422836392466-0.00451085096533j)
      (1.89934636394+0.145107214683j)
      (-1.30492029544-0.0293904757063j)
      (0.41542992756+0.0502382949271j)
      ...
      (-0.907980881357-0.00268087934794j)
      (-1.52999786965+0.100707843497j)
      (-0.209042624375-0.0286618206328j)
      (1.7737107014-0.0612318574594j)
      (1.56208020143-0.047036681766j)
      (-0.113889705226-0.0855435839874j)
      (2.01444713869+0.138536183898j)
      (-0.00361846728525+0.0192697989978j)
      (-2.2019193176+0.0904283692218j)
      (1.89656761249+0.0496429097914j)
    
    
      r0s2
      (1.82821071571-0.128909197042j)
      (0.282695903252+0.242320343889j)
      (0.872022068555-0.038784238982j)
      (-0.260669350793+0.0452001076767j)
      (-1.03357135086+0.0921465638993j)
      (0.993268356513-0.0285577214136j)
      (0.664639869899+0.0123485504631j)
      (-0.308572119062+0.0510162819116j)
      (-1.3338067307+0.0699766785877j)
      (0.43264868511+0.249764435176j)
      ...
      (1.35273043652+0.16129558619j)
      (0.682096489939+0.0635030727058j)
      (0.939696576024+0.0486226908048j)
      (0.116823836128-0.0815454113263j)
      (0.159117521664-0.0160049236552j)
      (0.880833567556-0.0983183596752j)
      (-1.34766497156-0.0644888627501j)
      (0.203560604553-0.0904372028935j)
      (-0.902965768874+0.101847259066j)
      (-1.68656584589-0.34389148341j)
    
    
      r0s3
      (-1.65411525983+0.0603759040104j)
      (0.730948292173+0.0543433215511j)
      (0.800166204462-0.157672412276j)
      (0.774865308574+0.077598975352j)
      (0.412742895736-0.00391215940931j)
      (-1.55615539458-0.0218819585597j)
      (1.13983471196-0.0848267311961j)
      (0.98468757961-0.0669251013132j)
      (1.18987141395-0.022651511229j)
      (-0.142564399548-0.00580960750606j)
      ...
      (-0.521348681699+0.0828146100835j)
      (0.858624116016-0.234377466052j)
      (1.31582349083-0.0740040124741j)
      (0.661047036604-0.105962870648j)
      (-0.296258381424-0.106262729265j)
      (0.585448302958+0.00873285003745j)
      (0.0773041569774-0.0801649117916j)
      (-0.298031886124-0.179873551867j)
      (-0.424452912506+0.00641296571024j)
      (1.14277935313-0.0433534432288j)
    
    
      r0s4
      (0.532960469669+0.060992160528j)
      (-0.466207894849-0.141470109493j)
      (-0.535656789752-0.0190094466983j)
      (-1.50120745986-0.0304633480535j)
      (-1.09560350726+0.142564263722j)
      (-0.827240055295-0.119204632388j)
      (0.470986902616-0.00493941945321j)
      (-0.559715502024-0.0607958298194j)
      (0.674368139181-0.0539698630908j)
      (1.81803386204-0.103103778697j)
      ...
      (-1.00228309014-0.020852228131j)
      (-0.73659892209-0.00914835489865j)
      (2.46517819721-0.0175754150102j)
      (0.35829962055-0.053494484444j)
      (-1.68000068509+0.0381826143409j)
      (-1.18632981202+0.0312460319758j)
      (-1.57648660658+0.116982019007j)
      (0.0592202718681+0.10224268974j)
      (-0.705469232509+0.188978635528j)
      (0.940453997001+0.200955905689j)
    
    
      r1s0
      (-0.0831914112863+0.163198685809j)
      (-0.932399221793-0.0270127921806j)
      (0.427573887868-0.00445047155494j)
      (-0.000164779002153-0.0770934811935j)
      (-0.60524235923+0.00705692043108j)
      (0.502600036119+0.0137702987694j)
      (0.409688265918-0.0165393442579j)
      (1.22242718331+0.0143142027866j)
      (1.94188539922-0.00801615876049j)
      (0.617609373478+0.0584193356061j)
      ...
      (0.490887761887+0.0561030719528j)
      (-1.42813701998+0.133173571147j)
      (0.57084612047+0.105991452859j)
      (1.08312328436-0.0472424968793j)
      (-0.774689873352-0.0762190053713j)
      (-0.560759666671+0.0903862374683j)
      (0.118198608503+0.0267582492836j)
      (0.788042868258-0.0725105868995j)
      (-0.227261419287+0.00541815982323j)
      (-1.25674127573-0.0267763055207j)
    
    
      r1s1
      (-0.319712138997-0.152039426621j)
      (0.962655283964-0.243310222492j)
      (0.320005444684-0.0870593939857j)
      (1.27041390617-0.0120088668168j)
      (-2.51556821593+0.0685790831661j)
      (-0.201284566126+0.0260898243789j)
      (2.43213174024-0.087934813983j)
      (-0.0996718667154+0.0786513923389j)
      (-0.456466319497-0.142287806773j)
      (-0.23715405766+0.0540842593935j)
      ...
      (1.09841370877-0.1940510802j)
      (-0.33820358124-0.0492889902562j)
      (-0.051926884372+0.0973298562776j)
      (1.77457072607-0.0959492043426j)
      (-2.38103188069+0.069932995824j)
      (-0.970222044917+0.00067614039896j)
      (-1.12675579635+0.0335868951329j)
      (1.53142098606+0.152792493145j)
      (0.213834644546-0.16115113382j)
      (-0.0968034623865-0.171325028243j)
    
    
      r1s2
      (0.831727824633-0.00318901160347j)
      (0.670548044311-0.125513485758j)
      (-2.06714582736-0.00875867430169j)
      (-0.654725965821+0.0119019903557j)
      (-0.653645883852+0.0241122954628j)
      (1.20828629401+0.282712860759j)
      (-0.63336936082-0.137097406702j)
      (-0.427047335452+0.0667830651225j)
      (-0.0543230476242+0.0381590010805j)
      (-0.103057538537-0.0317915405261j)
      ...
      (-1.76133869177+0.022786358294j)
      (-1.26405242912-0.00412356178994j)
      (1.20109198572-0.0125398053077j)
      (-2.42626474326-0.103746205012j)
      (0.260087881332+0.190255710124j)
      (0.840563908149+0.0665444871917j)
      (0.853656651832-0.108262152423j)
      (-0.097265347589-0.0666623011706j)
      (-0.764838279961+0.132936391357j)
      (-0.655976301017+0.0658942429166j)
    
    
      r1s3
      (-1.37525605478+0.0678864165322j)
      (1.39843366771+0.149282493709j)
      (-1.07043186243-0.138601350921j)
      (0.226995259392-0.170678108606j)
      (-0.592956598071-0.011135640728j)
      (-1.13633140889-0.0977114880465j)
      (0.71793208664-0.0472079625352j)
      (0.484789162651+0.0190007791447j)
      (0.670024169896-0.182424052248j)
      (-1.64848135044-0.0356758571558j)
      ...
      (-0.523358560066+0.17072233912j)
      (-0.0573552953067+0.0234892239801j)
      (0.562182689716+0.154433036795j)
      (-1.09795087178+0.160299537214j)
      (-1.26272257316+0.0405699118969j)
      (1.0112775784-0.151859713973j)
      (1.34656374214+0.0209350360603j)
      (-0.352742637211+0.0387787941876j)
      (-2.10893766757+0.0289713708344j)
      (0.564553178309+0.0892860029922j)
    
    
      r1s4
      (-1.35864957725-0.0447250801488j)
      (0.779966888467+0.0136621556124j)
      (0.928722579336+0.0239251376435j)
      (0.704362820544-0.100896397765j)
      (1.11845252976-0.0201786108752j)
      (1.41187663+0.0561016914286j)
      (0.256765284857-0.0425308436599j)
      (-1.12964774924-0.0493718921286j)
      (-0.289643117248-0.0901042557157j)
      (1.82986058501-0.053617359593j)
      ...
      (0.775279336714-0.0020430818306j)
      (0.79349394592+0.0458080908247j)
      (-0.636097338349-0.0223110597175j)
      (-0.0942871617806-0.0385916912193j)
      (-0.54854356993-0.123682849729j)
      (-0.287895794729-0.139519267459j)
      (-1.65203801979+0.0580922015492j)
      (-0.850825581176+0.0911781358634j)
      (1.77223438561+0.112060054574j)
      (-0.142146663816-0.0392379373917j)
    
    
      r2s0
      (0.277619243623-0.0427957406739j)
      (0.454509711444+0.0363555439813j)
      (-1.40515793167-0.0131875788012j)
      (-0.815207408487-0.013487555092j)
      (-0.879677699096-0.0322959498321j)
      (-0.0412191284588+0.166378236118j)
      (2.17966690677+0.155304972191j)
      (0.190455011781+0.040304323902j)
      (0.609729657567-0.155021391074j)
      (1.70810811617-0.0639315943095j)
      ...
      (1.02422026105-0.0838735917413j)
      (0.739515224746-0.262301328956j)
      (-0.00569714348009-0.0630193480716j)
      (0.478751031276-0.0463151243236j)
      (1.47355875614+0.0810156047213j)
      (-2.1078851683-0.126895542499j)
      (-0.900674407479-6.03316465891e-05j)
      (-0.87699862263-0.0971644616491j)
      (1.03894530595-0.0753399206228j)
      (-1.02333376986-0.0265737025497j)
    
    
      r2s1
      (0.524313763169+0.0189397616475j)
      (-0.388311328443+0.071677014751j)
      (-0.644299314804+0.19351122174j)
      (-0.541380022681-0.178178835193j)
      (1.02854161477+0.104390852437j)
      (-0.707628295546+0.116185494295j)
      (0.685896371347+0.242698503057j)
      (0.119642948333+0.178675744246j)
      (-2.010728999-0.0271840451421j)
      (1.02711500043+0.0220540172164j)
      ...
      (-0.606532092063+0.177257146212j)
      (0.979674588224+0.157539648066j)
      (0.929940730983-0.0275762229916j)
      (0.141661562777-0.176059043843j)
      (-0.0226442496019-0.00766434004073j)
      (0.804932713132-0.0197916726564j)
      (-0.774998828128-0.109170097404j)
      (-1.21500939419-0.0226419409204j)
      (0.432351070057-0.112096207893j)
      (-0.623104127852+0.162751485932j)
    
    
      r2s2
      (0.19191303557-0.00443282551489j)
      (1.09113477106-0.0290818741361j)
      (-0.318858525415+0.0539055964992j)
      (1.46363984723-0.178994583996j)
      (-0.477411909318-0.0973601218972j)
      (0.961024377412+0.0610789859716j)
      (-1.6549532995+0.110539365688j)
      (0.265897462138+0.0369672524016j)
      (1.67912122761+0.122387494111j)
      (-0.934075683675-0.00994285460239j)
      ...
      (0.952272211831+0.0191264579956j)
      (1.48656439513+0.020229068593j)
      (1.08380360247+0.0721547133717j)
      (-0.545582249859-0.0144008488916j)
      (0.35824142991-0.181217990671j)
      (0.608126477974+0.0126074757375j)
      (0.504841780735+0.0357286720151j)
      (-0.318060048709-0.129518631333j)
      (-1.92077387202-0.00295015613251j)
      (1.23116071305-0.077373931922j)
    
    
      r2s3
      (0.193914147223-0.0685759408907j)
      (-0.0107207597223+0.0360968517764j)
      (0.0518486323549+0.0958714907186j)
      (-0.697514531795-0.222074097922j)
      (0.842644278679-0.0817592408113j)
      (-0.314372692329-0.0397710203659j)
      (1.01161575823+0.0342086303863j)
      (1.94968533822-0.0880207989501j)
      (-1.16107622524+0.0445044977446j)
      (-0.578112928577-0.255515206264j)
      ...
      (0.950842321374+0.0256744399117j)
      (-1.59482251819-0.0310176505923j)
      (2.40615779281+0.016482678391j)
      (1.44914992112-0.0825611459205j)
      (-1.67706630796-0.0991907682338j)
      (-0.406479825809-0.0474725552964j)
      (-0.103273724421+0.0318583452567j)
      (-0.82176688448+0.105537370183j)
      (1.04343824798+0.216775914389j)
      (-0.269981013517+0.0757249971957j)
    
    
      r2s4
      (1.26312298098+0.0353078386081j)
      (0.0533283352593+0.10201972423j)
      (1.60921928791-0.236581622652j)
      (0.522521249696+0.0108511353459j)
      (-0.967412770576+0.0812200386155j)
      (-0.193614131481-0.0774930960243j)
      (0.9006873442+0.131892223023j)
      (-0.357434703123+0.0680903962007j)
      (0.508501337968-0.166044855544j)
      (-0.962241021062-0.0554235959826j)
      ...
      (0.309937655799+0.229761610388j)
      (0.578970754697+0.138883337038j)
      (0.0562531454811+0.0570736542305j)
      (0.678386157803-0.0169637315075j)
      (0.299387418537-0.0813273573021j)
      (-0.924431274846+0.102748278726j)
      (-0.895829098463+0.0463847585675j)
      (0.393481278578-0.0160656428025j)
      (0.346289438182-0.0346145319213j)
      (-0.242447949706-0.0450311580246j)
    
    
      r3s0
      (0.373796254925+0.154708294713j)
      (-1.31989898631+0.0443768735327j)
      (0.90529876174+0.0212612189138j)
      (0.61297741336-0.15236636986j)
      (-0.395771039549-0.14107214228j)
      (-0.818347497072+0.114746699381j)
      (-0.843940397708+0.0106815881074j)
      (-0.00297870741756-0.0341999546688j)
      (-1.06812694201+0.0144676965427j)
      (-1.25812808785-0.0954030642623j)
      ...
      (-0.0469815160827+0.0232703058459j)
      (0.24470416322+0.164586916579j)
      (1.95366721279-0.169896505798j)
      (1.16027384463-0.0734668213404j)
      (-0.202029190031-0.160334075452j)
      (1.24668565404+0.126363573094j)
      (0.999094720001+0.0595224992118j)
      (1.33229853348-0.00655201071896j)
      (1.62795450112+0.0756362616671j)
      (-2.53887641653+0.0571107676056j)
    
    
      r3s1
      (-1.97452985187-0.00917296924165j)
      (-0.044038492442-0.0533890772792j)
      (0.0986571181164+0.0710607280918j)
      (-1.1207128996+0.0586751903985j)
      (-1.5802345318-0.0334258835107j)
      (0.12135481213-0.0837061277687j)
      (-0.822756383009+0.0918955806026j)
      (0.262795552307-0.163477735507j)
      (0.468747437275+0.107957622074j)
      (-1.28757025168+0.062082210564j)
      ...
      (0.324517453127-0.0994012120212j)
      (-0.726165686889-0.0214926813727j)
      (0.670027504726-0.067414825192j)
      (0.672493610096+0.0259248657871j)
      (1.15051072605-0.0835546880332j)
      (-1.38438661204+0.0219637888629j)
      (-0.00436738953142+0.0626452726052j)
      (-0.250798820508+0.0744165104815j)
      (1.2172410505-0.0602919040257j)
      (1.20402719323+0.0942937778706j)
    
    
      r3s2
      (-0.733355394908+0.056188510842j)
      (-0.296812258943-0.026928650419j)
      (2.09901585316+0.0526436018032j)
      (0.182775108299+0.115145887806j)
      (-1.1379775679-0.0759761080345j)
      (-1.14674798938-0.0278691624333j)
      (0.239838433415+0.0632058032046j)
      (-0.677137889436-0.0456090271711j)
      (0.489696281226-0.0696107586012j)
      (-0.205295893752+0.0645651443053j)
      ...
      (0.927739415542+0.0779916955444j)
      (0.214939857223+0.116549139614j)
      (-0.379743555744+0.0572046696832j)
      (-0.373751223244-0.212776530072j)
      (0.308789167635-0.182568076047j)
      (0.948144120608-0.124195507151j)
      (-1.15062672337-0.0303554524768j)
      (1.71342836304-0.0034973810374j)
      (0.425120909614-0.0466252376535j)
      (0.815838070076+0.00567032218644j)
    
    
      r3s3
      (-0.204728653523-0.0770652212807j)
      (-0.239887247958-0.0825695492337j)
      (-0.214408098315-0.0638810016771j)
      (0.792915996552-0.190837703973j)
      (1.12443529821+0.0606369062219j)
      (-0.232448865638-0.0762480375094j)
      (0.260266836464+0.13866206314j)
      (1.54180710593-0.0523163676016j)
      (0.970536907823-0.144805603398j)
      (-0.237802580149-0.00572604234727j)
      ...
      (0.402640963686-0.02172174908j)
      (1.25094400433+0.013017533622j)
      (-1.50153426709-0.145616537321j)
      (0.418055057174+0.103958323504j)
      (-0.296678124153-0.109653945176j)
      (1.4713497838-0.0613489063866j)
      (-0.537638774566+0.130145597662j)
      (-0.475989304026-0.114262040163j)
      (0.726076244451-0.0957531986279j)
      (-0.132013018173-0.0619341538463j)
    
    
      r3s4
      (1.05103685387-0.189742584952j)
      (-0.0509470053352+0.142728853561j)
      (-1.79861171511+0.16745376313j)
      (-0.945647204637+0.1164464946j)
      (-0.760497351997+0.0301875360999j)
      (1.22773767134+0.06532550402j)
      (0.881494668841-0.0154188411389j)
      (0.223888650066+0.104219802766j)
      (-1.83339245782-0.231777846886j)
      (0.426401310564+0.0241752261768j)
      ...
      (-1.31086262875+0.0397126601754j)
      (0.468717155464+0.0327314502877j)
      (-0.748550410265-0.0308808654089j)
      (-1.49144037642+0.00352974857982j)
      (-3.18461600504-0.0270045225108j)
      (0.312807130525+0.191219919879j)
      (-1.97125711411-0.0765881341189j)
      (-1.49054702473-0.202426634312j)
      (-0.827802382667-0.00395477668367j)
      (0.955755828135-0.0491122893626j)
    
  

20 rows × 400 columns

slicing a dataframe:

We make frequent use of array slicing in python to access portions of our data array or to stack and analyze different parts of the data. Now we'll tinker on the dataframe to find out the equivalent methods.

First, the [] operation slices by rows (can use their names):



In [19]:

    
df3["r3s1":"r3s4"]









    Out[19]:






  
    
      
      0.0
      1.23
      2.46
      3.69
      4.92
      6.15
      7.38
      8.61
      9.84
      11.07
      ...
      479.7
      480.93
      482.16
      483.39
      484.62
      485.85
      487.08
      488.31
      489.54
      490.77
    
  
  
    
      r3s1
      (-1.97452985187-0.00917296924165j)
      (-0.044038492442-0.0533890772792j)
      (0.0986571181164+0.0710607280918j)
      (-1.1207128996+0.0586751903985j)
      (-1.5802345318-0.0334258835107j)
      (0.12135481213-0.0837061277687j)
      (-0.822756383009+0.0918955806026j)
      (0.262795552307-0.163477735507j)
      (0.468747437275+0.107957622074j)
      (-1.28757025168+0.062082210564j)
      ...
      (0.324517453127-0.0994012120212j)
      (-0.726165686889-0.0214926813727j)
      (0.670027504726-0.067414825192j)
      (0.672493610096+0.0259248657871j)
      (1.15051072605-0.0835546880332j)
      (-1.38438661204+0.0219637888629j)
      (-0.00436738953142+0.0626452726052j)
      (-0.250798820508+0.0744165104815j)
      (1.2172410505-0.0602919040257j)
      (1.20402719323+0.0942937778706j)
    
    
      r3s2
      (-0.733355394908+0.056188510842j)
      (-0.296812258943-0.026928650419j)
      (2.09901585316+0.0526436018032j)
      (0.182775108299+0.115145887806j)
      (-1.1379775679-0.0759761080345j)
      (-1.14674798938-0.0278691624333j)
      (0.239838433415+0.0632058032046j)
      (-0.677137889436-0.0456090271711j)
      (0.489696281226-0.0696107586012j)
      (-0.205295893752+0.0645651443053j)
      ...
      (0.927739415542+0.0779916955444j)
      (0.214939857223+0.116549139614j)
      (-0.379743555744+0.0572046696832j)
      (-0.373751223244-0.212776530072j)
      (0.308789167635-0.182568076047j)
      (0.948144120608-0.124195507151j)
      (-1.15062672337-0.0303554524768j)
      (1.71342836304-0.0034973810374j)
      (0.425120909614-0.0466252376535j)
      (0.815838070076+0.00567032218644j)
    
    
      r3s3
      (-0.204728653523-0.0770652212807j)
      (-0.239887247958-0.0825695492337j)
      (-0.214408098315-0.0638810016771j)
      (0.792915996552-0.190837703973j)
      (1.12443529821+0.0606369062219j)
      (-0.232448865638-0.0762480375094j)
      (0.260266836464+0.13866206314j)
      (1.54180710593-0.0523163676016j)
      (0.970536907823-0.144805603398j)
      (-0.237802580149-0.00572604234727j)
      ...
      (0.402640963686-0.02172174908j)
      (1.25094400433+0.013017533622j)
      (-1.50153426709-0.145616537321j)
      (0.418055057174+0.103958323504j)
      (-0.296678124153-0.109653945176j)
      (1.4713497838-0.0613489063866j)
      (-0.537638774566+0.130145597662j)
      (-0.475989304026-0.114262040163j)
      (0.726076244451-0.0957531986279j)
      (-0.132013018173-0.0619341538463j)
    
    
      r3s4
      (1.05103685387-0.189742584952j)
      (-0.0509470053352+0.142728853561j)
      (-1.79861171511+0.16745376313j)
      (-0.945647204637+0.1164464946j)
      (-0.760497351997+0.0301875360999j)
      (1.22773767134+0.06532550402j)
      (0.881494668841-0.0154188411389j)
      (0.223888650066+0.104219802766j)
      (-1.83339245782-0.231777846886j)
      (0.426401310564+0.0241752261768j)
      ...
      (-1.31086262875+0.0397126601754j)
      (0.468717155464+0.0327314502877j)
      (-0.748550410265-0.0308808654089j)
      (-1.49144037642+0.00352974857982j)
      (-3.18461600504-0.0270045225108j)
      (0.312807130525+0.191219919879j)
      (-1.97125711411-0.0765881341189j)
      (-1.49054702473-0.202426634312j)
      (-0.827802382667-0.00395477668367j)
      (0.955755828135-0.0491122893626j)
    
  

4 rows × 400 columns

Select a few columns:



In [76]:

    
df4 = df3[df3.columns[4:10]]

Plotting

It's easy to plot using the built-in method .plot() from pandas. There are also ways to access the data and plot using matplotlib



In [75]:

    
onerow = df3.loc["r3s2"].apply(np.real) # take the real part to avoid issues plotting
onerow.plot()









    Out[75]:





<matplotlib.axes._subplots.AxesSubplot at 0x117955cf8>



In [77]:

    
# can also use the regular old plot calls from matplotlib
plt.plot(np.imag(df3.loc["r3s2"]))
plt.plot(np.real(df3.loc["r3s2"]))









    Out[77]:





[<matplotlib.lines.Line2D at 0x117e74208>]



In [41]:

    
plt.hexbin(np.real(df3.loc["r3s2"]),np.imag(df3.loc["r3s2"]))









    Out[41]:





<matplotlib.collections.PolyCollection at 0x10b911160>

More stats:

We can do a number of cool things with the data frame. For example, plotting different modes against each other using the scatter_matrix function.



In [58]:

    
from pandas.tools.plotting import scatter_matrix

Apply

How to change values in the columns:



In [69]:

    
# take the real part or abs of the columns (save as a different dataframes)
df4real = df4.apply(np.real)
df4abs = df4.apply(np.abs)



In [72]:

    
# the diagonal will be the kernel density estimate (kde)
scatter_matrix(df4abs, figsize=(8, 8), diagonal='kde')









    Out[72]:





array([[<matplotlib.axes._subplots.AxesSubplot object at 0x1161151d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x11614ab38>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1161957b8>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1161c8c18>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1163a3b70>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1163e5c18>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x116434748>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x11644aa90>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1164b5f98>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x11662de10>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116672f98>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1166c2438>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x1166fa908>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x11674c1d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1167103c8>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1167d10b8>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x11691a320>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1169595f8>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x1169ab048>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1169e19b0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116a28908>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116a68a20>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116ab7470>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116aca940>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x116c3cdd8>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116c8a908>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116cca710>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116d15c50>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116d52470>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116d9f198>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x116d68828>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116e21ef0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116e6df60>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116eb3080>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x116efba90>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1161af6a0>]], dtype=object)



In [1]:

    
# Format the notebook using style by Lorena Barba (http://lorenabarba.com/)
# run this cell first to use the nice format.
from IPython.core.display import HTML
def css_styling():
    styles = open("./styles/custom.css", "r").read()
    return HTML(styles)
css_styling()









    Out[1]:



In [ ]:

	0.0	1.23	2.46	3.69	4.92	6.15	7.38	8.61	9.84	11.07	...	479.7	480.93	482.16	483.39	484.62	485.85	487.08	488.31	489.54	490.77
0	0.184962	-0.593215	0.189440	-0.041520	-0.468275	1.248782	-1.325620	0.712231	-0.162094	1.817380	...	-1.343064	-1.470482	0.735458	0.679417	-0.240810	-0.455247	-0.493477	0.546133	-0.093801	-0.870588
1	0.330364	1.285958	0.221395	-0.679064	-0.605855	-1.138653	0.432561	-0.072273	-0.031589	-0.955335	...	0.403545	-0.294596	-0.046364	1.550566	1.322492	0.158821	0.156565	-0.445687	-2.098845	-1.161122
2	-0.248033	-0.075215	1.170656	0.055841	-0.277661	0.005537	0.479036	0.754289	-0.441990	-1.282790	...	-0.323793	-3.010945	0.336506	-0.325221	0.376113	0.062601	-0.838108	-1.102468	0.338594	0.423082
3	1.721958	-0.023670	-1.054532	1.613846	0.368450	1.702158	-0.076590	-1.169031	0.483357	0.935780	...	-0.178595	1.032906	-2.016839	2.064577	1.685427	-0.653712	-1.918819	0.239802	0.550428	-1.531779
4	1.571422	-0.108286	0.329186	-0.399168	-0.406936	0.530031	-1.320046	-1.747431	-1.522011	1.004620	...	-1.139332	0.549895	1.571382	0.940728	-0.602542	0.138620	-0.593473	0.266806	-0.832163	-1.852263
5	-0.086009	0.595296	0.425701	1.522184	1.367878	1.281471	-0.541161	1.061773	-0.184506	-0.372571	...	0.419337	-0.072765	2.219141	-0.960565	-1.141693	0.024791	-1.159445	1.722109	-0.048243	1.181456
6	0.663104	1.017888	-0.049473	-0.651722	0.167377	0.377671	-0.467855	0.071341	0.123341	-0.587914	...	-1.230849	-1.044841	0.162082	-0.314299	-0.799146	-0.199157	0.314127	0.213541	1.427636	0.283838
7	-0.419924	-0.354931	0.916886	-0.751909	1.013355	-1.736379	0.522979	0.470240	-0.634015	-0.360114	...	1.375368	-0.968433	0.362897	-1.411900	0.530603	1.166181	0.625223	-0.266564	-0.570224	-0.822201
8	0.168113	0.887247	-1.040347	0.194861	0.442004	0.275889	-0.243377	1.089206	0.664697	0.223828	...	-0.928463	0.471350	0.490348	0.217929	-0.883274	-0.421726	1.486858	0.689218	0.754216	0.110106
9	1.186498	-0.960690	-0.348566	0.990295	0.675831	0.761218	-0.542745	0.261024	0.001028	1.173646	...	-0.059401	0.616330	-1.674507	-1.064985	0.535332	-1.322795	-1.539502	0.532675	0.173978	1.202523
10	-1.352537	-0.425472	0.879962	-0.239729	-0.233018	0.734855	1.006921	0.607420	-1.669254	-0.693078	...	-0.659705	0.788002	0.248544	-1.297290	0.316705	-0.207468	-0.405590	0.842259	0.514191	0.423534
11	1.599110	-0.100259	0.878009	-0.890536	1.438008	1.520079	-1.695664	-1.685915	-0.833511	0.277582	...	1.975432	0.831157	-0.004321	-0.091759	-0.384815	-1.432872	1.437886	2.025241	-1.649293	-1.123986
12	0.663158	-0.613900	0.652613	1.288169	0.154322	1.274050	0.246589	0.623908	-0.535676	0.181517	...	-1.122317	-2.191370	-0.585120	-1.325936	-0.674683	-1.193839	0.398804	0.260643	-0.042832	-0.139533
13	-0.645737	-0.510152	-1.005171	-1.624530	0.898106	0.066679	0.874028	-1.401223	-0.057903	0.582753	...	-1.380020	-2.512605	1.118588	0.634844	0.301920	0.236669	-0.509022	0.171967	-0.814506	-0.306371
14	1.321814	-0.774301	-1.902708	1.957949	2.112021	0.815829	-2.043558	-0.020623	0.595277	-0.107277	...	-0.427886	-0.090893	0.283438	0.656301	0.766152	-1.237433	1.099856	-0.036330	-1.391981	0.906868
15	-0.803413	0.036083	-0.761519	-1.115538	0.178751	-0.937486	0.237419	0.474481	-1.090644	0.645634	...	-1.528687	0.021469	0.147363	0.549197	0.077641	-1.080116	1.058282	0.961617	0.005075	0.570475
16	0.761742	0.049620	0.740389	-1.541954	-0.477572	-0.396389	0.217273	-0.255407	0.067497	0.006614	...	0.082712	0.449123	-0.875030	-0.495502	-2.268136	0.375531	-1.265048	0.530770	-1.081555	-1.910912
17	1.494090	0.608071	-0.028324	0.413887	0.340919	-0.401112	-0.439394	-0.441322	-0.155351	1.351053	...	-1.021816	-0.639324	0.622632	0.691260	-0.438366	0.321922	-0.595063	1.005989	-0.511210	-0.248449
18	1.839444	0.250622	0.030625	0.658200	-0.525802	1.183947	0.920444	0.297210	0.194203	0.366299	...	1.459953	0.212683	0.216094	-0.430931	-0.885898	-0.151657	-0.829574	0.051659	0.822611	-0.310205
19	-1.863444	1.019783	0.423566	-1.553650	0.802445	0.083260	-0.491350	2.118290	0.345122	2.467606	...	0.481893	1.324027	-0.285335	-1.192188	1.645913	-0.321261	2.514560	-0.868827	-0.813402	-0.029505

	0.0	1.23	2.46	3.69	4.92	6.15	7.38	8.61	9.84	11.07	...	479.7	480.93	482.16	483.39	484.62	485.85	487.08	488.31	489.54	490.77
r0s0	-0.075841	-0.904605	-1.094072	0.605669	-1.935258	0.650063	0.660024	-2.170779	1.076856	-0.521928	...	1.028115	-0.131176	1.219894	0.364914	1.028008	-0.210408	0.584433	0.022389	0.198800	2.394047
r0s1	0.464307	0.507541	-0.215419	-0.744910	1.049569	-0.146941	0.288519	0.591788	-1.127253	-0.838182	...	0.611890	-0.847824	-0.776338	-0.056745	0.168138	-0.413380	-0.136623	1.508007	0.763493	-1.961929
r0s2	0.549017	-0.010613	0.350341	0.600244	0.564113	-0.135829	-0.530846	-0.960254	0.759039	-0.449446	...	0.624111	-0.088894	-1.126249	0.604857	-1.559714	1.838663	-1.085178	-1.633170	-0.223984	-0.287379
r0s3	0.854825	1.083141	-1.502872	0.215501	1.037609	0.905728	-0.099644	-0.872863	0.409028	-0.392250	...	-1.517258	0.598385	-0.585482	0.333990	-0.100666	-0.024075	-0.180373	-1.391312	2.034463	1.557063
r0s4	-0.540168	-2.024637	1.521336	0.458756	0.031326	-0.362836	0.002126	-0.623581	0.187056	-1.338258	...	0.124124	1.468026	0.705380	-1.086340	-1.358901	-0.294727	-0.324702	-0.815423	0.256468	1.090099
r1s0	0.826986	-0.842467	1.049514	1.150837	-0.785820	0.429018	1.115340	1.307672	0.376442	0.854339	...	-0.429645	-0.675573	-0.810689	0.187499	0.262096	0.496407	-0.978998	-0.594335	-0.133461	2.547492
r1s1	-2.407435	0.084073	0.926649	-1.474173	1.498178	0.161716	1.031246	-0.094132	-0.994738	-1.276429	...	0.244866	0.988604	-0.210704	-0.633346	-1.639042	2.043875	0.916145	1.058196	-0.923993	0.696969
r1s2	-0.553663	0.260108	0.565609	0.348731	-0.222907	1.454296	-0.804949	-1.058964	0.146190	1.406294	...	0.778546	-0.583378	-1.960605	-2.030100	0.323722	-1.504652	-0.222541	0.062490	0.261073	0.655042
r1s3	-1.923620	1.897037	1.345015	-1.532653	0.272023	0.384065	1.002208	0.272557	-0.646553	-0.312436	...	-0.196265	1.047866	0.542254	0.372460	0.896880	0.828275	-1.182366	-0.272894	-0.625088	0.087952
r1s4	-1.186381	0.669413	0.760152	-0.552006	0.521368	-0.949405	-0.020145	-0.090695	-1.702185	-0.757083	...	1.690140	0.634193	-1.026187	1.614171	-0.463188	0.336056	-1.407198	-1.658494	-2.787294	-0.790165
r2s0	0.990522	-0.961763	0.439112	0.885652	1.450123	-0.499534	0.938854	1.408904	-0.740930	-0.140112	...	-0.063761	-0.626640	0.041427	-0.345510	0.431423	-0.716702	1.691901	-0.428716	-0.836942	-0.288951
r2s1	-0.519180	-1.298858	0.250681	-1.190024	0.106520	-0.095677	0.615137	0.495602	-0.212434	-0.349042	...	-1.641367	-0.665836	0.256332	0.451142	1.305498	-0.108231	0.204788	0.869855	-0.266288	1.509643
r2s2	0.734422	0.476790	-0.458226	-0.700024	-1.238566	0.599671	-0.427914	0.844219	-0.270551	0.492769	...	-1.239655	1.126015	-0.550496	-0.761821	-0.531756	-0.332588	-0.523914	-0.290804	0.246082	-0.102039
r2s3	-0.853220	-2.093568	-0.643340	0.200368	-0.716152	-1.126140	-0.698815	-0.416204	-0.544038	0.368496	...	-1.466966	1.246151	0.064958	-1.270758	1.034440	-0.975365	-0.009970	-0.033534	-1.204973	1.992776
r2s4	-1.734340	1.018595	1.145354	-0.112782	0.590931	1.525264	-1.583458	0.948296	1.711134	0.053377	...	0.133120	0.159131	1.151579	-0.270983	-0.793256	-0.395818	-0.000882	-0.871829	-0.321323	0.475428
r3s0	-0.783272	0.549246	0.912964	-0.846065	-0.347537	0.244262	-1.921135	0.290666	1.023833	0.347094	...	-0.121621	-0.236661	0.837270	-1.076396	-0.592567	-2.097988	-0.013013	0.231985	-1.345679	2.884452
r3s1	0.290483	0.363594	2.177999	-0.156987	-0.939555	0.443229	1.458815	2.574376	-1.076518	-0.363016	...	1.702962	1.722178	0.999881	0.184068	-0.614013	-0.598080	-0.728771	-0.300455	1.025306	-0.240906
r3s2	-1.332260	-0.925884	-0.835553	-0.015138	1.851840	0.090223	0.281905	-0.100410	0.095656	-1.359204	...	0.326450	-0.434180	0.019184	1.248174	-0.215904	0.850511	0.770674	0.306296	1.293982	-1.435372
r3s3	0.200371	-0.846563	1.856579	-0.600437	0.725963	0.383318	0.835080	-0.656290	-0.978341	0.180849	...	-0.889134	-0.567104	0.826408	-0.337061	-0.099261	-0.017822	-0.381713	0.862280	-0.116477	-1.101553
r3s4	-0.753709	-0.070955	-0.344824	-0.385953	-0.344296	-2.013347	0.147098	-0.802810	-1.089017	-0.130341	...	0.140231	-0.945284	1.047795	1.883125	-0.141678	-0.783196	1.150965	-0.080518	-1.244698	1.317814

	0.0	1.23	2.46	3.69	4.92	6.15	7.38	8.61	9.84	11.07	...	479.7	480.93	482.16	483.39	484.62	485.85	487.08	488.31	489.54	490.77
r0s0	(-1.23576271913-0.185847883574j)	(0.0529216538903+0.129158233718j)	(0.724415189064-0.104322240946j)	(-1.65301916201+0.0720106546298j)	(-0.141481016733+0.0361646764067j)	(-0.222757669741+0.0400796456564j)	(-0.21361548993-0.0837229942064j)	(0.943233544682-0.140260846666j)	(0.567894567351+0.0306696240982j)	(-0.902016328789+0.114131753957j)	...	(-1.85902244304+0.0287101151056j)	(0.921572078908-0.0710246678393j)	(1.10489339086-0.0788672179216j)	(-0.612657340247+0.0228959362189j)	(-1.1688038002-0.156471551294j)	(-0.512148594723-0.0535613010007j)	(-0.756125963407-0.044222458599j)	(-0.0407041390489+0.0460788111033j)	(0.534728902924-0.0871808137524j)	(0.132200155724+0.112614834113j)
r0s1	(-0.981939512432-0.0248213642288j)	(0.201676834287+0.0332533538591j)	(0.0949735642599-0.0258463075781j)	(0.689998693135-0.0221663676157j)	(0.830687375073-0.122014801224j)	(-0.0578329368654+0.000577935992641j)	(-0.422836392466-0.00451085096533j)	(1.89934636394+0.145107214683j)	(-1.30492029544-0.0293904757063j)	(0.41542992756+0.0502382949271j)	...	(-0.907980881357-0.00268087934794j)	(-1.52999786965+0.100707843497j)	(-0.209042624375-0.0286618206328j)	(1.7737107014-0.0612318574594j)	(1.56208020143-0.047036681766j)	(-0.113889705226-0.0855435839874j)	(2.01444713869+0.138536183898j)	(-0.00361846728525+0.0192697989978j)	(-2.2019193176+0.0904283692218j)	(1.89656761249+0.0496429097914j)
r0s2	(1.82821071571-0.128909197042j)	(0.282695903252+0.242320343889j)	(0.872022068555-0.038784238982j)	(-0.260669350793+0.0452001076767j)	(-1.03357135086+0.0921465638993j)	(0.993268356513-0.0285577214136j)	(0.664639869899+0.0123485504631j)	(-0.308572119062+0.0510162819116j)	(-1.3338067307+0.0699766785877j)	(0.43264868511+0.249764435176j)	...	(1.35273043652+0.16129558619j)	(0.682096489939+0.0635030727058j)	(0.939696576024+0.0486226908048j)	(0.116823836128-0.0815454113263j)	(0.159117521664-0.0160049236552j)	(0.880833567556-0.0983183596752j)	(-1.34766497156-0.0644888627501j)	(0.203560604553-0.0904372028935j)	(-0.902965768874+0.101847259066j)	(-1.68656584589-0.34389148341j)
r0s3	(-1.65411525983+0.0603759040104j)	(0.730948292173+0.0543433215511j)	(0.800166204462-0.157672412276j)	(0.774865308574+0.077598975352j)	(0.412742895736-0.00391215940931j)	(-1.55615539458-0.0218819585597j)	(1.13983471196-0.0848267311961j)	(0.98468757961-0.0669251013132j)	(1.18987141395-0.022651511229j)	(-0.142564399548-0.00580960750606j)	...	(-0.521348681699+0.0828146100835j)	(0.858624116016-0.234377466052j)	(1.31582349083-0.0740040124741j)	(0.661047036604-0.105962870648j)	(-0.296258381424-0.106262729265j)	(0.585448302958+0.00873285003745j)	(0.0773041569774-0.0801649117916j)	(-0.298031886124-0.179873551867j)	(-0.424452912506+0.00641296571024j)	(1.14277935313-0.0433534432288j)
r0s4	(0.532960469669+0.060992160528j)	(-0.466207894849-0.141470109493j)	(-0.535656789752-0.0190094466983j)	(-1.50120745986-0.0304633480535j)	(-1.09560350726+0.142564263722j)	(-0.827240055295-0.119204632388j)	(0.470986902616-0.00493941945321j)	(-0.559715502024-0.0607958298194j)	(0.674368139181-0.0539698630908j)	(1.81803386204-0.103103778697j)	...	(-1.00228309014-0.020852228131j)	(-0.73659892209-0.00914835489865j)	(2.46517819721-0.0175754150102j)	(0.35829962055-0.053494484444j)	(-1.68000068509+0.0381826143409j)	(-1.18632981202+0.0312460319758j)	(-1.57648660658+0.116982019007j)	(0.0592202718681+0.10224268974j)	(-0.705469232509+0.188978635528j)	(0.940453997001+0.200955905689j)
r1s0	(-0.0831914112863+0.163198685809j)	(-0.932399221793-0.0270127921806j)	(0.427573887868-0.00445047155494j)	(-0.000164779002153-0.0770934811935j)	(-0.60524235923+0.00705692043108j)	(0.502600036119+0.0137702987694j)	(0.409688265918-0.0165393442579j)	(1.22242718331+0.0143142027866j)	(1.94188539922-0.00801615876049j)	(0.617609373478+0.0584193356061j)	...	(0.490887761887+0.0561030719528j)	(-1.42813701998+0.133173571147j)	(0.57084612047+0.105991452859j)	(1.08312328436-0.0472424968793j)	(-0.774689873352-0.0762190053713j)	(-0.560759666671+0.0903862374683j)	(0.118198608503+0.0267582492836j)	(0.788042868258-0.0725105868995j)	(-0.227261419287+0.00541815982323j)	(-1.25674127573-0.0267763055207j)
r1s1	(-0.319712138997-0.152039426621j)	(0.962655283964-0.243310222492j)	(0.320005444684-0.0870593939857j)	(1.27041390617-0.0120088668168j)	(-2.51556821593+0.0685790831661j)	(-0.201284566126+0.0260898243789j)	(2.43213174024-0.087934813983j)	(-0.0996718667154+0.0786513923389j)	(-0.456466319497-0.142287806773j)	(-0.23715405766+0.0540842593935j)	...	(1.09841370877-0.1940510802j)	(-0.33820358124-0.0492889902562j)	(-0.051926884372+0.0973298562776j)	(1.77457072607-0.0959492043426j)	(-2.38103188069+0.069932995824j)	(-0.970222044917+0.00067614039896j)	(-1.12675579635+0.0335868951329j)	(1.53142098606+0.152792493145j)	(0.213834644546-0.16115113382j)	(-0.0968034623865-0.171325028243j)
r1s2	(0.831727824633-0.00318901160347j)	(0.670548044311-0.125513485758j)	(-2.06714582736-0.00875867430169j)	(-0.654725965821+0.0119019903557j)	(-0.653645883852+0.0241122954628j)	(1.20828629401+0.282712860759j)	(-0.63336936082-0.137097406702j)	(-0.427047335452+0.0667830651225j)	(-0.0543230476242+0.0381590010805j)	(-0.103057538537-0.0317915405261j)	...	(-1.76133869177+0.022786358294j)	(-1.26405242912-0.00412356178994j)	(1.20109198572-0.0125398053077j)	(-2.42626474326-0.103746205012j)	(0.260087881332+0.190255710124j)	(0.840563908149+0.0665444871917j)	(0.853656651832-0.108262152423j)	(-0.097265347589-0.0666623011706j)	(-0.764838279961+0.132936391357j)	(-0.655976301017+0.0658942429166j)
r1s3	(-1.37525605478+0.0678864165322j)	(1.39843366771+0.149282493709j)	(-1.07043186243-0.138601350921j)	(0.226995259392-0.170678108606j)	(-0.592956598071-0.011135640728j)	(-1.13633140889-0.0977114880465j)	(0.71793208664-0.0472079625352j)	(0.484789162651+0.0190007791447j)	(0.670024169896-0.182424052248j)	(-1.64848135044-0.0356758571558j)	...	(-0.523358560066+0.17072233912j)	(-0.0573552953067+0.0234892239801j)	(0.562182689716+0.154433036795j)	(-1.09795087178+0.160299537214j)	(-1.26272257316+0.0405699118969j)	(1.0112775784-0.151859713973j)	(1.34656374214+0.0209350360603j)	(-0.352742637211+0.0387787941876j)	(-2.10893766757+0.0289713708344j)	(0.564553178309+0.0892860029922j)
r1s4	(-1.35864957725-0.0447250801488j)	(0.779966888467+0.0136621556124j)	(0.928722579336+0.0239251376435j)	(0.704362820544-0.100896397765j)	(1.11845252976-0.0201786108752j)	(1.41187663+0.0561016914286j)	(0.256765284857-0.0425308436599j)	(-1.12964774924-0.0493718921286j)	(-0.289643117248-0.0901042557157j)	(1.82986058501-0.053617359593j)	...	(0.775279336714-0.0020430818306j)	(0.79349394592+0.0458080908247j)	(-0.636097338349-0.0223110597175j)	(-0.0942871617806-0.0385916912193j)	(-0.54854356993-0.123682849729j)	(-0.287895794729-0.139519267459j)	(-1.65203801979+0.0580922015492j)	(-0.850825581176+0.0911781358634j)	(1.77223438561+0.112060054574j)	(-0.142146663816-0.0392379373917j)
r2s0	(0.277619243623-0.0427957406739j)	(0.454509711444+0.0363555439813j)	(-1.40515793167-0.0131875788012j)	(-0.815207408487-0.013487555092j)	(-0.879677699096-0.0322959498321j)	(-0.0412191284588+0.166378236118j)	(2.17966690677+0.155304972191j)	(0.190455011781+0.040304323902j)	(0.609729657567-0.155021391074j)	(1.70810811617-0.0639315943095j)	...	(1.02422026105-0.0838735917413j)	(0.739515224746-0.262301328956j)	(-0.00569714348009-0.0630193480716j)	(0.478751031276-0.0463151243236j)	(1.47355875614+0.0810156047213j)	(-2.1078851683-0.126895542499j)	(-0.900674407479-6.03316465891e-05j)	(-0.87699862263-0.0971644616491j)	(1.03894530595-0.0753399206228j)	(-1.02333376986-0.0265737025497j)
r2s1	(0.524313763169+0.0189397616475j)	(-0.388311328443+0.071677014751j)	(-0.644299314804+0.19351122174j)	(-0.541380022681-0.178178835193j)	(1.02854161477+0.104390852437j)	(-0.707628295546+0.116185494295j)	(0.685896371347+0.242698503057j)	(0.119642948333+0.178675744246j)	(-2.010728999-0.0271840451421j)	(1.02711500043+0.0220540172164j)	...	(-0.606532092063+0.177257146212j)	(0.979674588224+0.157539648066j)	(0.929940730983-0.0275762229916j)	(0.141661562777-0.176059043843j)	(-0.0226442496019-0.00766434004073j)	(0.804932713132-0.0197916726564j)	(-0.774998828128-0.109170097404j)	(-1.21500939419-0.0226419409204j)	(0.432351070057-0.112096207893j)	(-0.623104127852+0.162751485932j)
r2s2	(0.19191303557-0.00443282551489j)	(1.09113477106-0.0290818741361j)	(-0.318858525415+0.0539055964992j)	(1.46363984723-0.178994583996j)	(-0.477411909318-0.0973601218972j)	(0.961024377412+0.0610789859716j)	(-1.6549532995+0.110539365688j)	(0.265897462138+0.0369672524016j)	(1.67912122761+0.122387494111j)	(-0.934075683675-0.00994285460239j)	...	(0.952272211831+0.0191264579956j)	(1.48656439513+0.020229068593j)	(1.08380360247+0.0721547133717j)	(-0.545582249859-0.0144008488916j)	(0.35824142991-0.181217990671j)	(0.608126477974+0.0126074757375j)	(0.504841780735+0.0357286720151j)	(-0.318060048709-0.129518631333j)	(-1.92077387202-0.00295015613251j)	(1.23116071305-0.077373931922j)
r2s3	(0.193914147223-0.0685759408907j)	(-0.0107207597223+0.0360968517764j)	(0.0518486323549+0.0958714907186j)	(-0.697514531795-0.222074097922j)	(0.842644278679-0.0817592408113j)	(-0.314372692329-0.0397710203659j)	(1.01161575823+0.0342086303863j)	(1.94968533822-0.0880207989501j)	(-1.16107622524+0.0445044977446j)	(-0.578112928577-0.255515206264j)	...	(0.950842321374+0.0256744399117j)	(-1.59482251819-0.0310176505923j)	(2.40615779281+0.016482678391j)	(1.44914992112-0.0825611459205j)	(-1.67706630796-0.0991907682338j)	(-0.406479825809-0.0474725552964j)	(-0.103273724421+0.0318583452567j)	(-0.82176688448+0.105537370183j)	(1.04343824798+0.216775914389j)	(-0.269981013517+0.0757249971957j)
r2s4	(1.26312298098+0.0353078386081j)	(0.0533283352593+0.10201972423j)	(1.60921928791-0.236581622652j)	(0.522521249696+0.0108511353459j)	(-0.967412770576+0.0812200386155j)	(-0.193614131481-0.0774930960243j)	(0.9006873442+0.131892223023j)	(-0.357434703123+0.0680903962007j)	(0.508501337968-0.166044855544j)	(-0.962241021062-0.0554235959826j)	...	(0.309937655799+0.229761610388j)	(0.578970754697+0.138883337038j)	(0.0562531454811+0.0570736542305j)	(0.678386157803-0.0169637315075j)	(0.299387418537-0.0813273573021j)	(-0.924431274846+0.102748278726j)	(-0.895829098463+0.0463847585675j)	(0.393481278578-0.0160656428025j)	(0.346289438182-0.0346145319213j)	(-0.242447949706-0.0450311580246j)
r3s0	(0.373796254925+0.154708294713j)	(-1.31989898631+0.0443768735327j)	(0.90529876174+0.0212612189138j)	(0.61297741336-0.15236636986j)	(-0.395771039549-0.14107214228j)	(-0.818347497072+0.114746699381j)	(-0.843940397708+0.0106815881074j)	(-0.00297870741756-0.0341999546688j)	(-1.06812694201+0.0144676965427j)	(-1.25812808785-0.0954030642623j)	...	(-0.0469815160827+0.0232703058459j)	(0.24470416322+0.164586916579j)	(1.95366721279-0.169896505798j)	(1.16027384463-0.0734668213404j)	(-0.202029190031-0.160334075452j)	(1.24668565404+0.126363573094j)	(0.999094720001+0.0595224992118j)	(1.33229853348-0.00655201071896j)	(1.62795450112+0.0756362616671j)	(-2.53887641653+0.0571107676056j)
r3s1	(-1.97452985187-0.00917296924165j)	(-0.044038492442-0.0533890772792j)	(0.0986571181164+0.0710607280918j)	(-1.1207128996+0.0586751903985j)	(-1.5802345318-0.0334258835107j)	(0.12135481213-0.0837061277687j)	(-0.822756383009+0.0918955806026j)	(0.262795552307-0.163477735507j)	(0.468747437275+0.107957622074j)	(-1.28757025168+0.062082210564j)	...	(0.324517453127-0.0994012120212j)	(-0.726165686889-0.0214926813727j)	(0.670027504726-0.067414825192j)	(0.672493610096+0.0259248657871j)	(1.15051072605-0.0835546880332j)	(-1.38438661204+0.0219637888629j)	(-0.00436738953142+0.0626452726052j)	(-0.250798820508+0.0744165104815j)	(1.2172410505-0.0602919040257j)	(1.20402719323+0.0942937778706j)
r3s2	(-0.733355394908+0.056188510842j)	(-0.296812258943-0.026928650419j)	(2.09901585316+0.0526436018032j)	(0.182775108299+0.115145887806j)	(-1.1379775679-0.0759761080345j)	(-1.14674798938-0.0278691624333j)	(0.239838433415+0.0632058032046j)	(-0.677137889436-0.0456090271711j)	(0.489696281226-0.0696107586012j)	(-0.205295893752+0.0645651443053j)	...	(0.927739415542+0.0779916955444j)	(0.214939857223+0.116549139614j)	(-0.379743555744+0.0572046696832j)	(-0.373751223244-0.212776530072j)	(0.308789167635-0.182568076047j)	(0.948144120608-0.124195507151j)	(-1.15062672337-0.0303554524768j)	(1.71342836304-0.0034973810374j)	(0.425120909614-0.0466252376535j)	(0.815838070076+0.00567032218644j)
r3s3	(-0.204728653523-0.0770652212807j)	(-0.239887247958-0.0825695492337j)	(-0.214408098315-0.0638810016771j)	(0.792915996552-0.190837703973j)	(1.12443529821+0.0606369062219j)	(-0.232448865638-0.0762480375094j)	(0.260266836464+0.13866206314j)	(1.54180710593-0.0523163676016j)	(0.970536907823-0.144805603398j)	(-0.237802580149-0.00572604234727j)	...	(0.402640963686-0.02172174908j)	(1.25094400433+0.013017533622j)	(-1.50153426709-0.145616537321j)	(0.418055057174+0.103958323504j)	(-0.296678124153-0.109653945176j)	(1.4713497838-0.0613489063866j)	(-0.537638774566+0.130145597662j)	(-0.475989304026-0.114262040163j)	(0.726076244451-0.0957531986279j)	(-0.132013018173-0.0619341538463j)
r3s4	(1.05103685387-0.189742584952j)	(-0.0509470053352+0.142728853561j)	(-1.79861171511+0.16745376313j)	(-0.945647204637+0.1164464946j)	(-0.760497351997+0.0301875360999j)	(1.22773767134+0.06532550402j)	(0.881494668841-0.0154188411389j)	(0.223888650066+0.104219802766j)	(-1.83339245782-0.231777846886j)	(0.426401310564+0.0241752261768j)	...	(-1.31086262875+0.0397126601754j)	(0.468717155464+0.0327314502877j)	(-0.748550410265-0.0308808654089j)	(-1.49144037642+0.00352974857982j)	(-3.18461600504-0.0270045225108j)	(0.312807130525+0.191219919879j)	(-1.97125711411-0.0765881341189j)	(-1.49054702473-0.202426634312j)	(-0.827802382667-0.00395477668367j)	(0.955755828135-0.0491122893626j)