In [1]:
%matplotlib inline
import numpy as np
import pandas as pd
import pymc3 as pm
import seaborn as sns
In [2]:
k = 1000
n = 100

fake_data = np.random.random((n, k+1))
In [3]:
import theano.tensor as tt

with pm.Model() as model:
    
    y = fake_data[:, 0]
    X = fake_data[:, 1:]
    
    β = pm.Normal('β', 0, sd=10000, shape=k)
    σ = pm.Uniform('σ', 0, 1000)
    
    μ = tt.dot(X, β)
    
    likelihood = pm.Normal('likelihood', μ, sd=σ, observed=y)
Applied interval-transform to σ and added transformed σ_interval_ to model.
/Users/fonnescj/Repositories/pymc3/pymc3/distributions/continuous.py:59: UserWarning: The variable specified for sd has non-positive support for Normal, likely making it unsuitable for this parameter.
  warnings.warn(msg)
In [8]:
with model:
    tr = pm.sample(10000, step=pm.Metropolis())
100%|██████████| 10000/10000 [00:03<00:00, 2657.98it/s]
In [9]:
pm.summary(tr[-1000:])
β:

  Mean             SD               MC Error         95% HPD interval
  -------------------------------------------------------------------
  
  12.268           2.141            0.212            [9.025, 16.523]
  24.667           2.834            0.282            [17.306, 28.067]
  6.037            4.004            0.399            [-3.158, 11.874]
  -1.192           3.096            0.308            [-6.529, 3.364]
  30.398           2.613            0.259            [24.873, 33.920]
  30.075           3.499            0.349            [24.092, 36.511]
  1.986            1.479            0.144            [-1.033, 4.765]
  -26.996          1.373            0.133            [-29.969, -24.369]
  -10.862          2.907            0.289            [-16.051, -6.632]
  -4.642           2.486            0.246            [-9.126, -0.350]
  -6.264           4.842            0.483            [-12.645, 1.655]
  9.286            2.584            0.257            [4.527, 13.524]
  5.703            4.250            0.424            [0.162, 14.546]
  -4.108           2.716            0.270            [-8.533, 0.804]
  26.159           2.000            0.197            [22.771, 30.111]
  18.125           2.749            0.273            [13.844, 23.375]
  -29.331          5.529            0.552            [-37.002, -19.142]
  -24.338          5.135            0.512            [-33.090, -16.517]
  -12.870          2.080            0.205            [-16.375, -8.275]
  8.509            2.766            0.275            [3.749, 13.498]
  18.064           7.757            0.775            [6.629, 31.169]
  -9.898           2.774            0.276            [-15.504, -5.955]
  -15.673          2.713            0.269            [-20.814, -11.082]
  16.425           2.458            0.244            [12.477, 20.711]
  16.618           3.078            0.306            [11.701, 21.557]
  3.005            1.431            0.139            [0.694, 5.371]
  0.491            3.094            0.307            [-5.851, 5.229]
  -0.069           2.803            0.279            [-5.128, 4.183]
  -1.339           1.904            0.187            [-4.794, 2.513]
  -9.269           1.380            0.134            [-11.393, -6.626]
  9.354            2.133            0.211            [4.824, 12.270]
  0.091            4.207            0.419            [-5.264, 8.156]
  1.959            3.543            0.353            [-3.175, 7.941]
  -20.171          2.810            0.279            [-26.694, -16.133]
  4.748            4.937            0.493            [-1.145, 14.478]
  -24.234          1.641            0.161            [-26.973, -21.165]
  -11.031          3.251            0.324            [-16.014, -5.413]
  18.219           3.600            0.358            [12.205, 22.940]
  -1.395           3.476            0.346            [-8.614, 3.713]
  22.405           3.232            0.322            [17.302, 28.787]
  16.052           3.652            0.364            [10.940, 23.124]
  -10.264          2.863            0.285            [-14.093, -4.685]
  18.800           2.889            0.287            [13.029, 23.293]
  31.490           2.567            0.255            [25.875, 35.193]
  18.857           1.723            0.169            [15.050, 22.296]
  15.603           2.390            0.237            [11.840, 20.354]
  15.259           3.529            0.352            [10.141, 21.910]
  -24.006          1.678            0.164            [-27.170, -20.669]
  35.167           2.484            0.246            [29.867, 38.787]
  17.874           1.953            0.192            [13.141, 20.868]
  21.394           2.885            0.287            [17.040, 26.665]
  -36.914          2.360            0.233            [-40.466, -31.239]
  7.753            4.103            0.409            [0.818, 14.456]
  18.376           2.398            0.238            [14.914, 23.367]
  -11.205          1.990            0.196            [-14.712, -6.917]
  7.924            2.924            0.291            [2.859, 13.776]
  17.394           2.994            0.298            [12.112, 22.069]
  -0.663           2.819            0.280            [-4.506, 5.348]
  -25.882          4.662            0.465            [-32.754, -19.086]
  -5.673           1.852            0.183            [-8.934, -2.462]
  -14.789          3.101            0.308            [-20.527, -8.874]
  -24.672          1.433            0.140            [-27.530, -22.190]
  -11.748          1.767            0.173            [-15.132, -8.659]
  7.213            3.224            0.321            [3.554, 14.023]
  16.704           2.099            0.208            [12.878, 20.059]
  8.117            2.470            0.245            [4.101, 11.903]
  41.023           1.422            0.138            [38.404, 43.796]
  -5.275           2.789            0.277            [-10.286, -0.293]
  13.066           3.321            0.330            [7.302, 18.881]
  25.755           3.245            0.323            [21.180, 32.000]
  5.870            3.444            0.343            [-1.478, 11.369]
  -54.658          2.514            0.249            [-58.651, -49.739]
  23.774           1.236            0.119            [21.126, 25.555]
  -19.798          6.691            0.668            [-28.170, -5.682]
  0.516            2.072            0.205            [-2.701, 3.424]
  10.775           5.024            0.501            [2.999, 17.411]
  47.767           3.705            0.369            [42.121, 53.609]
  -4.812           2.851            0.283            [-9.054, 0.130]
  -6.138           2.227            0.220            [-9.851, -2.143]
  53.924           1.560            0.152            [51.587, 57.404]
  32.364           2.181            0.216            [28.845, 36.181]
  -20.960          6.664            0.666            [-31.251, -12.496]
  -38.865          2.374            0.235            [-43.237, -35.110]
  35.468           3.837            0.382            [29.104, 41.589]
  10.264           2.330            0.231            [5.669, 13.771]
  10.072           2.465            0.244            [5.594, 13.877]
  1.330            2.875            0.286            [-4.234, 5.882]
  24.432           2.296            0.227            [18.557, 27.733]
  8.477            1.886            0.186            [4.385, 10.983]
  8.794            2.775            0.276            [4.774, 14.168]
  19.470           4.609            0.460            [11.374, 25.128]
  -0.247           1.975            0.195            [-4.321, 2.695]
  4.140            2.619            0.260            [0.311, 8.317]
  -22.795          1.722            0.169            [-26.031, -20.099]
  11.138           2.502            0.248            [6.591, 15.234]
  -43.291          3.654            0.364            [-50.259, -37.771]
  8.257            3.087            0.307            [3.026, 13.057]
  -19.631          1.209            0.117            [-21.545, -16.886]
  -11.366          3.010            0.299            [-16.624, -4.186]
  27.470           2.810            0.279            [23.741, 32.414]
  -23.516          3.578            0.356            [-29.203, -18.085]
  22.660           2.580            0.257            [17.216, 26.148]
  11.698           2.377            0.235            [7.571, 15.266]
  -13.044          2.544            0.253            [-17.354, -8.469]
  3.247            2.347            0.232            [-0.766, 7.084]
  -28.666          3.406            0.339            [-33.037, -21.899]
  8.707            4.391            0.438            [2.382, 15.684]
  -12.531          1.853            0.182            [-15.413, -8.634]
  4.719            2.423            0.240            [0.305, 9.888]
  10.334           3.905            0.389            [3.413, 17.311]
  12.162           3.049            0.303            [5.793, 17.745]
  -2.075           2.236            0.221            [-5.409, 3.866]
  19.475           1.585            0.155            [16.226, 22.948]
  -6.775           2.524            0.250            [-11.326, -3.351]
  -14.188          2.076            0.205            [-17.515, -10.278]
  9.180            1.387            0.135            [6.573, 11.954]
  7.892            4.198            0.418            [2.890, 17.595]
  3.174            1.726            0.169            [-0.178, 5.847]
  14.228           2.788            0.277            [9.996, 20.133]
  16.227           1.986            0.196            [12.004, 19.640]
  19.112           1.482            0.145            [16.698, 22.379]
  -11.924          2.079            0.205            [-15.474, -7.760]
  0.856            2.036            0.201            [-1.974, 5.280]
  8.829            2.140            0.211            [5.080, 12.664]
  -24.791          3.069            0.305            [-30.988, -21.032]
  22.514           4.004            0.399            [15.554, 28.753]
  -4.670           1.742            0.171            [-7.428, -0.754]
  12.246           2.970            0.295            [7.619, 18.046]
  -32.278          1.527            0.149            [-35.305, -29.253]
  0.932            2.543            0.252            [-2.781, 4.878]
  11.722           3.185            0.317            [7.041, 18.347]
  20.508           6.527            0.652            [10.002, 29.993]
  -16.833          4.142            0.413            [-22.526, -8.875]
  -8.044           1.802            0.177            [-11.765, -5.506]
  -7.235           2.651            0.263            [-11.691, -2.492]
  -40.365          3.323            0.331            [-46.029, -35.977]
  18.347           3.182            0.316            [13.373, 23.372]
  25.064           3.820            0.381            [18.727, 30.760]
  -16.571          2.693            0.267            [-21.631, -13.197]
  17.749           2.636            0.262            [13.684, 22.307]
  2.648            3.738            0.373            [-1.580, 10.534]
  34.578           2.031            0.200            [31.437, 38.403]
  15.491           2.210            0.218            [12.071, 20.156]
  6.399            4.494            0.448            [-0.094, 13.807]
  16.413           3.920            0.391            [8.866, 22.979]
  -19.186          3.917            0.390            [-25.443, -11.828]
  3.701            3.728            0.371            [-5.068, 8.380]
  -4.817           3.264            0.325            [-9.207, 1.964]
  -27.939          2.330            0.231            [-32.622, -24.180]
  34.953           2.152            0.213            [30.337, 39.642]
  -24.014          5.775            0.577            [-31.218, -12.626]
  15.266           2.041            0.202            [11.751, 19.804]
  -5.526           2.624            0.260            [-11.284, -1.812]
  -2.723           2.455            0.243            [-6.654, 2.441]
  -31.187          2.627            0.261            [-35.876, -26.406]
  14.073           4.572            0.456            [7.945, 21.066]
  33.065           1.623            0.160            [30.910, 36.740]
  -12.048          2.412            0.239            [-18.089, -8.851]
  11.601           3.013            0.300            [6.337, 16.921]
  32.512           2.942            0.293            [26.317, 36.738]
  -5.545           2.718            0.270            [-9.547, -1.013]
  -16.592          1.959            0.193            [-19.824, -12.194]
  8.669            1.921            0.190            [5.407, 11.547]
  7.098            4.073            0.406            [0.723, 13.364]
  22.019           1.719            0.169            [19.587, 26.696]
  -12.815          4.413            0.440            [-18.689, -3.565]
  -13.782          2.463            0.244            [-17.031, -8.533]
  33.587           1.997            0.197            [29.838, 36.307]
  17.041           1.429            0.140            [14.709, 19.890]
  -9.178           4.352            0.434            [-17.286, -2.241]
  -27.934          2.522            0.250            [-32.509, -22.912]
  -0.389           1.431            0.140            [-2.972, 2.243]
  34.139           1.873            0.184            [31.103, 38.131]
  15.874           4.062            0.405            [8.959, 22.297]
  2.849            4.704            0.469            [-6.715, 9.742]
  -42.990          1.796            0.177            [-46.292, -40.224]
  8.587            3.445            0.343            [0.418, 13.371]
  -9.135           2.164            0.214            [-13.493, -6.340]
  41.805           3.259            0.324            [35.761, 47.211]
  10.349           2.305            0.228            [6.694, 14.174]
  -27.766          2.041            0.201            [-31.299, -23.766]
  -17.283          2.364            0.234            [-20.803, -12.617]
  45.151           2.693            0.267            [40.150, 49.720]
  -24.109          5.968            0.596            [-32.851, -13.742]
  -45.579          2.592            0.257            [-49.849, -41.716]
  -37.273          3.034            0.302            [-42.771, -30.213]
  10.044           5.172            0.516            [2.648, 17.546]
  -29.518          5.007            0.499            [-38.906, -22.999]
  -30.862          2.551            0.253            [-35.132, -26.690]
  -25.862          3.660            0.364            [-31.029, -20.287]
  0.918            4.633            0.462            [-6.878, 7.699]
  -12.336          3.170            0.315            [-16.730, -5.167]
  18.427           2.774            0.275            [14.435, 23.477]
  9.761            2.085            0.207            [5.774, 13.334]
  17.826           2.578            0.256            [13.663, 21.830]
  -7.807           3.580            0.356            [-15.097, -3.527]
  7.287            4.600            0.459            [0.333, 13.875]
  14.965           2.705            0.268            [9.370, 20.729]
  9.279            2.251            0.222            [4.173, 12.899]
  -23.526          2.224            0.220            [-27.739, -19.485]
  -3.583           3.493            0.348            [-10.645, 0.905]
  13.007           3.370            0.335            [7.108, 18.615]
  26.001           2.394            0.238            [21.883, 30.202]
  0.173            2.273            0.225            [-4.011, 3.417]
  -16.479          3.013            0.299            [-22.388, -11.684]
  29.839           2.295            0.227            [24.794, 33.827]
  -2.116           2.995            0.297            [-9.652, 3.241]
  30.551           4.318            0.431            [24.478, 38.420]
  9.617            4.516            0.450            [4.743, 19.322]
  -1.671           1.501            0.147            [-4.489, 0.954]
  41.595           2.397            0.238            [36.958, 45.602]
  -37.227          1.990            0.196            [-40.893, -34.070]
  9.214            2.600            0.258            [4.352, 12.889]
  14.544           4.528            0.452            [7.947, 21.068]
  35.101           2.844            0.283            [30.614, 40.262]
  -36.053          2.118            0.209            [-40.035, -32.793]
  11.597           1.320            0.129            [9.166, 14.042]
  -33.481          3.460            0.345            [-40.361, -28.617]
  29.036           4.255            0.424            [17.990, 34.967]
  32.089           2.863            0.285            [28.854, 38.032]
  1.298            3.868            0.385            [-3.796, 8.497]
  7.965            3.042            0.303            [3.316, 14.264]
  9.310            2.524            0.251            [4.869, 13.552]
  -5.917           3.461            0.344            [-11.794, 0.995]
  -25.643          2.076            0.205            [-29.375, -21.048]
  -4.647           2.435            0.241            [-8.675, -0.316]
  -3.798           1.874            0.185            [-6.885, -0.868]
  21.080           6.293            0.628            [8.491, 30.255]
  18.686           1.602            0.157            [15.696, 21.162]
  22.008           3.079            0.306            [16.749, 27.370]
  -19.833          4.270            0.426            [-27.137, -13.114]
  -5.539           1.947            0.192            [-8.278, -0.834]
  -7.475           2.077            0.206            [-11.273, -3.749]
  -7.795           4.579            0.457            [-14.653, -0.878]
  -2.082           2.297            0.228            [-6.000, 2.651]
  -1.516           3.322            0.331            [-5.298, 5.219]
  -24.084          3.616            0.360            [-30.848, -18.737]
  -19.184          4.771            0.476            [-27.617, -11.897]
  17.690           1.959            0.193            [13.854, 20.749]
  -31.107          1.299            0.127            [-33.546, -29.101]
  -4.473           4.004            0.399            [-11.023, 2.311]
  -36.993          3.531            0.352            [-43.890, -31.106]
  19.642           3.561            0.354            [11.787, 24.748]
  26.750           3.080            0.306            [22.103, 32.103]
  -20.832          3.551            0.354            [-26.253, -15.113]
  18.277           3.788            0.377            [12.878, 25.302]
  0.917            3.146            0.313            [-4.415, 5.984]
  -25.131          3.384            0.337            [-29.658, -18.310]
  -13.006          3.187            0.317            [-16.963, -4.659]
  -23.151          2.006            0.198            [-27.148, -19.031]
  27.807           5.233            0.522            [19.072, 35.047]
  -3.266           2.487            0.247            [-6.729, 1.431]
  29.656           4.347            0.433            [21.671, 37.291]
  39.177           1.356            0.132            [36.666, 41.571]
  3.903            3.010            0.299            [-0.702, 9.369]
  20.385           2.551            0.253            [16.120, 24.997]
  -0.367           3.360            0.335            [-4.721, 5.736]
  -6.224           5.434            0.542            [-14.605, 3.328]
  -24.483          1.948            0.192            [-27.775, -19.891]
  13.024           3.229            0.321            [8.746, 20.684]
  30.053           2.847            0.283            [25.208, 33.781]
  30.389           2.544            0.252            [25.372, 35.169]
  22.224           3.785            0.377            [16.796, 27.664]
  -35.325          4.213            0.420            [-41.526, -27.952]
  -15.243          8.904            0.890            [-28.754, -2.732]
  -5.839           8.184            0.818            [-18.344, 7.487]
  -9.956           2.848            0.283            [-13.984, -4.530]
  0.593            4.260            0.425            [-5.825, 7.802]
  -22.254          2.935            0.291            [-26.840, -17.135]
  -40.294          2.220            0.220            [-44.010, -36.824]
  29.068           2.204            0.218            [25.532, 33.034]
  3.017            2.799            0.278            [-2.261, 6.698]
  -15.416          2.859            0.284            [-20.615, -10.368]
  13.033           1.949            0.192            [10.150, 16.606]
  23.583           2.859            0.284            [20.431, 30.457]
  8.032            2.378            0.236            [4.053, 11.909]
  -35.077          5.918            0.591            [-44.532, -27.299]
  0.805            2.874            0.286            [-5.005, 6.841]
  3.841            2.763            0.274            [0.125, 9.347]
  -20.495          1.976            0.195            [-23.871, -16.665]
  37.181           2.624            0.260            [32.140, 40.724]
  15.940           2.668            0.265            [11.719, 22.427]
  17.027           1.777            0.175            [13.920, 20.173]
  5.559            3.675            0.366            [-0.895, 13.306]
  -24.375          5.441            0.543            [-32.249, -16.099]
  -3.432           1.364            0.132            [-5.800, -1.202]
  -10.245          2.659            0.264            [-14.709, -6.420]
  29.477           4.039            0.402            [22.983, 35.866]
  24.557           3.652            0.363            [18.435, 30.225]
  -0.946           2.923            0.291            [-5.372, 4.096]
  -0.784           2.739            0.272            [-4.026, 6.314]
  -2.080           1.605            0.157            [-4.977, 0.492]
  24.354           2.686            0.267            [20.263, 29.041]
  9.946            1.940            0.191            [6.644, 14.190]
  -13.960          2.159            0.213            [-17.742, -10.410]
  -46.616          3.730            0.371            [-52.753, -40.944]
  -34.956          3.098            0.308            [-40.627, -30.822]
  5.671            3.250            0.324            [-2.731, 9.350]
  5.857            2.830            0.281            [0.847, 10.299]
  -12.882          1.377            0.135            [-15.441, -10.302]
  12.141           1.599            0.157            [9.198, 15.726]
  11.086           1.716            0.168            [8.197, 15.159]
  35.693           2.156            0.213            [31.275, 38.877]
  -4.995           3.067            0.305            [-9.308, 0.169]
  -7.923           3.109            0.309            [-12.995, -3.098]
  2.206            2.452            0.243            [-2.828, 6.561]
  -15.922          2.617            0.260            [-20.852, -11.818]
  16.139           2.754            0.273            [10.759, 20.448]
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  -15.397          1.894            0.187            [-18.340, -10.901]
  -1.597           3.994            0.398            [-7.585, 5.721]
  11.271           3.952            0.394            [1.960, 15.651]
  -17.058          1.478            0.144            [-19.019, -13.799]
  -20.496          2.500            0.248            [-25.105, -16.560]
  18.626           1.372            0.133            [16.484, 21.795]
  12.504           2.079            0.205            [8.092, 15.714]
  40.946           1.411            0.138            [38.429, 44.050]
  6.196            2.266            0.225            [2.483, 10.664]
  -20.563          2.042            0.201            [-23.226, -15.515]
  -46.748          2.309            0.228            [-51.059, -42.805]
  -16.938          2.610            0.259            [-21.830, -13.666]
  8.444            2.907            0.289            [4.445, 14.465]
  -12.921          3.551            0.353            [-18.516, -6.255]
  -2.276           1.859            0.183            [-5.141, 1.838]
  13.192           1.302            0.127            [10.976, 15.725]
  -4.319           1.296            0.126            [-6.646, -1.751]
  -28.426          2.507            0.249            [-32.451, -24.410]
  -11.810          1.636            0.161            [-14.561, -8.962]
  -18.079          1.999            0.197            [-21.231, -14.734]
  -19.801          2.884            0.287            [-24.329, -15.401]
  -2.431           1.923            0.190            [-6.249, 1.466]
  -11.969          4.035            0.402            [-17.666, -5.351]
  5.994            1.540            0.151            [2.934, 8.497]
  -3.789           3.564            0.355            [-11.402, 0.967]
  1.119            3.853            0.384            [-4.586, 8.122]
  21.616           2.107            0.208            [17.748, 24.801]
  0.402            1.250            0.121            [-1.835, 2.461]
  1.784            3.583            0.357            [-3.418, 8.157]
  -7.894           2.605            0.259            [-12.528, -2.740]
  18.991           2.986            0.297            [14.579, 24.740]
  -35.419          2.905            0.289            [-39.750, -29.430]
  -1.037           3.081            0.306            [-7.072, 3.159]
  -10.099          4.500            0.449            [-17.250, -4.153]
  -49.865          2.612            0.259            [-55.940, -46.191]
  -7.759           3.125            0.311            [-12.575, -1.801]
  -2.342           2.925            0.291            [-7.176, 2.181]
  -26.566          3.877            0.387            [-31.540, -19.745]
  -7.106           1.689            0.166            [-10.546, -4.429]
  36.495           2.615            0.260            [31.779, 40.757]
  -16.000          2.147            0.213            [-21.258, -12.908]
  12.751           2.032            0.201            [8.717, 15.460]
  29.873           3.309            0.330            [23.403, 34.074]
  -13.470          4.385            0.437            [-21.030, -5.831]
  -32.493          2.248            0.222            [-36.275, -27.557]
  47.192           4.169            0.415            [41.408, 54.770]
  6.023            4.463            0.445            [-2.470, 11.684]
  22.710           1.391            0.135            [19.354, 24.823]
  -7.832           1.775            0.175            [-10.923, -4.785]
  45.958           1.895            0.187            [42.751, 48.961]
  -9.586           2.138            0.211            [-13.036, -5.905]
  -40.152          3.618            0.360            [-45.607, -34.854]
  -14.695          1.707            0.168            [-18.154, -12.322]
  -1.191           2.978            0.296            [-7.286, 2.064]

  Posterior quantiles:
  2.5            25             50             75             97.5
  |--------------|==============|==============|--------------|
  
  9.301          10.516         11.945         13.843         17.148
  17.320         23.573         25.417         26.527         28.267
  -3.494         4.009          5.888          9.469          11.874
  -6.925         -3.821         -0.080         1.290          3.281
  24.950         28.720         30.770         32.493         34.287
  22.784         26.990         31.497         32.568         35.909
  -0.708         1.074          1.953          2.767          5.365
  -29.938        -27.751        -27.166        -26.381        -24.031
  -16.213        -12.215        -10.346        -8.623         -6.715
  -9.244         -6.408         -4.784         -2.635         -0.405
  -12.593        -10.612        -7.831         -1.662         1.905
  4.363          7.390          8.519          11.726         13.524
  -0.415         2.219          3.782          9.423          14.361
  -8.521         -6.179         -4.677         -1.764         0.824
  22.829         24.323         26.377         27.199         30.389
  12.699         16.157         17.918         20.411         23.035
  -36.685        -35.112        -28.663        -25.566        -18.728
  -33.593        -28.416        -24.045        -19.350        -16.875
  -16.575        -14.475        -12.862        -11.582        -8.321
  3.188          6.930          8.361          10.512         13.352
  7.068          9.863          17.504         24.349         32.009
  -16.578        -11.484        -9.506         -7.589         -6.300
  -21.352        -17.712        -15.660        -13.630        -11.272
  12.299         14.271         16.200         18.438         20.635
  11.686         13.697         17.152         19.133         21.551
  0.592          1.891          3.078          4.175          5.355
  -5.351         -2.103         0.795          3.051          5.992
  -4.935         -1.761         -0.331         2.539          4.903
  -5.198         -2.367         -1.384         -0.061         2.420
  -11.935        -10.289        -9.354         -8.149         -6.960
  4.887          7.844          9.726          11.092         12.545
  -4.524         -3.421         -2.051         4.179          9.168
  -3.172         -0.938         1.625          4.780          8.093
  -27.337        -21.284        -19.525        -18.312        -16.463
  -0.894         1.091          2.775          8.354          14.886
  -26.988        -25.501        -24.231        -23.221        -21.165
  -15.964        -13.626        -11.957        -8.573         -5.330
  12.243         14.297         19.274         21.392         22.988
  -8.392         -2.969         -0.964         0.929          3.971
  17.978         19.783         22.052         23.950         30.566
  10.940         13.282         15.068         19.274         23.124
  -14.414        -12.523        -10.857        -8.148         -4.877
  12.525         16.462         19.312         21.084         23.030
  24.730         30.633         32.362         33.302         34.590
  15.050         17.957         18.952         19.745         22.515
  11.187         13.529         15.749         17.379         19.973
  9.616          12.414         14.463         18.849         21.628
  -26.785        -25.099        -24.365        -22.927        -20.172
  29.297         33.548         35.656         37.222         38.753
  13.500         16.792         17.974         19.217         21.483
  16.792         18.870         21.990         23.733         26.565
  -40.699        -38.573        -37.414        -36.007        -31.243
  0.167          4.733          8.501          11.187         14.146
  14.386         16.446         18.101         19.989         23.020
  -14.430        -12.534        -11.413        -10.105        -6.149
  2.686          6.092          8.125          10.038         13.712
  12.186         15.193         17.778         19.840         22.218
  -4.418         -2.733         -1.601         1.091          5.760
  -32.754        -30.365        -24.877        -21.564        -19.086
  -8.899         -7.013         -5.743         -4.178         -2.126
  -21.656        -16.614        -14.969        -12.213        -9.458
  -27.522        -25.399        -24.478        -23.740        -21.745
  -15.004        -13.104        -11.833        -10.377        -7.923
  3.221          4.587          5.959          9.398          13.953
  12.757         14.827         16.795         18.463         19.997
  3.702          6.069          8.460          10.217         11.774
  38.404         39.918         41.015         41.964         43.796
  -9.935         -7.348         -5.502         -3.948         0.759
  7.423          10.575         12.395         15.238         19.473
  21.059         22.934         24.945         28.235         32.000
  -1.412         3.715          5.723          8.995          12.157
  -58.539        -56.438        -55.308        -53.169        -48.844
  21.430         22.945         23.844         24.680         26.325
  -29.113        -25.707        -20.569        -16.109        -5.941
  -4.150         -0.851         1.065          2.252          3.388
  2.814          5.210          11.549         15.590         17.407
  42.121         44.613         47.448         51.022         53.709
  -9.639         -7.220         -4.506         -2.291         -0.226
  -9.851         -7.970         -6.595         -4.324         -1.897
  51.586         52.840         53.642         54.694         57.404
  28.845         30.756         32.275         33.925         36.226
  -31.245        -27.295        -20.272        -14.446        -11.963
  -42.746        -40.254        -38.900        -37.883        -32.184
  28.583         31.907         36.358         38.085         41.536
  5.678          8.943          10.170         12.218         14.031
  5.929          7.953          10.507         11.975         14.581
  -4.649         -0.670         1.569          3.650          5.841
  18.828         23.169         24.850         25.976         28.385
  4.398          7.362          9.003          9.847          11.114
  3.524          6.697          8.720          10.254         14.084
  11.627         14.110         21.631         22.946         25.508
  -4.313         -1.610         -0.227         1.489          2.847
  0.284          1.707          4.494          6.530          8.292
  -26.073        -24.327        -22.359        -21.336        -20.111
  6.767          9.445          10.766         13.165         15.439
  -50.131        -45.206        -42.663        -40.499        -37.602
  1.249          5.489          8.956          10.955         12.582
  -21.725        -20.464        -19.786        -19.058        -16.886
  -16.026        -13.257        -11.811        -10.185        -2.661
  22.595         24.973         27.158         30.015         32.067
  -29.064        -27.354        -22.634        -20.813        -17.772
  17.245         21.664         23.401         24.493         26.240
  7.588          9.759          12.151         13.769         15.435
  -17.698        -14.755        -13.563        -10.549        -8.628
  -0.763         1.249          3.244          5.177          7.849
  -33.037        -31.505        -29.514        -25.928        -21.899
  2.532          4.585          7.992          13.612         16.143
  -15.574        -13.847        -12.684        -11.630        -8.639
  0.739          3.045          4.504          6.058          10.957
  4.115          7.766          10.103         12.086         19.286
  4.275          11.181         12.425         14.314         16.555
  -6.742         -3.811         -1.961         -0.778         3.242
  16.471         18.569         19.329         20.214         23.284
  -11.619        -8.561         -6.004         -4.818         -3.377
  -18.108        -15.979        -14.213        -12.704        -10.313
  6.864          8.163          8.906          10.173         12.370
  2.890          4.520          7.512          9.007          17.667
  -1.311         2.122          3.407          4.565          5.612
  10.047         11.837         13.870         15.757         20.280
  12.212         14.987         16.380         17.595         19.971
  16.205         18.092         18.942         20.278         22.117
  -15.474        -13.373        -12.401        -10.483        -7.525
  -1.947         -0.713         0.314          1.931          5.437
  4.943          7.083          8.830          10.189         12.664
  -30.811        -28.195        -23.592        -22.590        -20.629
  14.818         20.564         22.059         26.538         28.662
  -7.333         -5.974         -4.984         -3.709         -0.560
  7.619          9.676          12.120         14.498         18.046
  -35.802        -33.492        -31.958        -31.277        -29.383
  -2.759         -1.540         1.155          3.181          4.949
  7.041          9.146          11.277         14.011         18.591
  9.415          14.032         22.263         26.549         29.515
  -22.526        -19.932        -18.267        -13.252        -8.454
  -11.660        -8.981         -7.949         -6.797         -5.089
  -12.296        -9.216         -7.052         -5.194         -2.560
  -45.899        -43.275        -40.623        -36.998        -35.775
  13.373         15.174         18.983         20.799         23.372
  18.920         21.509         26.083         27.889         31.326
  -21.631        -19.240        -15.646        -14.416        -13.197
  13.422         15.305         17.907         20.037         22.238
  -2.529         -0.363         1.137          5.953          10.158
  31.209         32.705         34.683         36.314         38.276
  12.221         13.708         15.356         16.504         20.482
  -0.471         2.907          5.460          11.004         13.592
  7.644          13.394         17.264         19.074         22.593
  -25.432        -22.831        -19.153        -16.398        -11.333
  -5.068         1.888          4.642          6.553          8.380
  -9.957         -7.552         -5.367         -2.303         1.811
  -32.554        -29.175        -27.567        -26.467        -24.047
  29.935         33.867         35.049         35.822         39.456
  -30.929        -29.335        -24.284        -19.985        -11.584
  11.727         14.051         15.116         16.173         19.804
  -10.996        -7.278         -4.862         -3.326         -1.266
  -6.813         -4.732         -2.828         -1.007         2.438
  -35.599        -33.153        -31.449        -29.205        -25.765
  7.713          10.160         13.101         18.938         21.057
  30.683         31.727         32.761         34.382         36.696
  -18.420        -13.321        -11.422        -10.365        -9.013
  5.763          9.653          11.724         13.607         16.599
  26.317         30.420         33.055         35.079         36.811
  -9.889         -7.856         -5.483         -3.215         -1.023
  -19.063        -17.606        -16.808        -16.055        -9.570
  4.711          7.119          8.920          10.356         11.340
  -0.035         3.458          6.367          11.094         13.079
  18.420         20.881         22.048         23.169         26.184
  -18.519        -16.131        -14.935        -10.266        -3.123
  -17.452        -15.490        -14.576        -12.498        -8.799
  29.606         31.935         34.324         35.302         36.307
  14.346         15.935         17.078         18.137         19.887
  -17.114        -12.414        -8.630         -6.371         -1.567
  -31.718        -29.562        -27.967        -26.777        -20.178
  -2.888         -1.460         -0.526         0.590          2.552
  30.579         32.807         34.072         35.403         38.111
  9.009          12.329         16.166         19.772         22.375
  -6.339         -1.357         4.223          6.637          10.553
  -45.937        -44.542        -43.061        -41.451        -39.823
  1.005          7.564          9.319          10.425         15.381
  -13.545        -10.226        -8.592         -7.418         -6.351
  35.599         39.313         42.205         44.318         47.128
  6.694          8.374          10.079         12.519         14.174
  -32.071        -29.240        -27.849        -26.293        -24.230
  -20.759        -19.249        -17.546        -15.690        -11.333
  38.849         43.095         45.495         47.240         49.176
  -32.225        -30.174        -23.544        -19.431        -12.062
  -49.846        -48.073        -45.296        -43.259        -41.604
  -42.433        -39.030        -37.751        -36.316        -29.424
  2.648          4.289          12.343         14.489         17.546
  -38.837        -33.489        -27.967        -25.530        -22.613
  -35.132        -32.588        -31.428        -28.346        -26.690
  -30.965        -28.893        -27.247        -21.993        -20.053
  -6.997         -2.948         1.241          5.434          7.692
  -16.418        -14.602        -13.480        -10.703        -4.515
  14.207         16.290         17.581         21.210         23.423
  5.915          8.160          9.831          11.248         13.512
  13.479         15.307         18.400         19.983         21.752
  -15.097        -10.848        -6.190         -4.996         -3.527
  0.464          2.434          9.106          11.193         14.136
  10.288         12.768         15.330         16.303         22.239
  3.576          8.200          9.739          10.658         12.711
  -27.749        -24.982        -23.386        -21.994        -19.485
  -11.184        -5.589         -3.019         -0.544         0.795
  6.330          10.278         12.765         16.044         18.489
  22.359         24.048         25.759         28.007         30.895
  -3.764         -1.801         0.125          2.191          4.595
  -22.432        -18.243        -16.546        -13.895        -11.684
  24.358         28.399         30.134         31.536         33.710
  -10.689        -3.080         -2.024         -0.368         2.383
  24.649         27.128         28.989         33.990         38.949
  4.552          6.126          7.540          13.541         19.277
  -4.671         -2.789         -1.627         -0.470         0.833
  36.761         39.886         41.024         43.681         45.594
  -40.907        -38.867        -37.515        -35.333        -34.070
  4.011          7.398          9.772          11.562         12.876
  8.059          10.209         14.165         19.800         21.238
  30.221         32.681         35.006         37.429         39.968
  -40.157        -37.639        -35.661        -34.267        -32.862
  8.693          10.682         11.644         12.662         13.987
  -40.178        -35.463        -32.732        -30.718        -28.298
  17.921         27.209         29.961         31.712         34.967
  28.746         29.819         30.777         34.057         37.970
  -3.725         -2.311         0.485          4.250          8.755
  2.539          5.518          8.066          9.895          14.032
  4.869          7.247          9.467          11.156         13.977
  -11.318        -8.743         -5.769         -3.663         1.904
  -29.758        -26.878        -25.593        -24.413        -21.067
  -9.384         -6.777         -4.064         -2.762         -0.619
  -6.863         -5.349         -4.074         -2.115         -0.382
  8.474          17.427         23.194         25.915         30.255
  15.802         17.309         18.710         20.012         21.585
  16.422         19.520         22.819         23.916         27.303
  -26.822        -23.922        -19.150        -16.888        -10.664
  -8.122         -7.028         -6.037         -4.267         -0.426
  -10.983        -8.769         -7.618         -5.961         -2.918
  -14.891        -13.039        -6.528         -4.036         -0.987
  -6.682         -3.577         -2.220         -0.760         2.432
  -5.561         -4.090         -2.799         1.213          5.092
  -30.325        -27.293        -23.349        -21.148        -18.083
  -27.838        -24.436        -18.012        -15.359        -11.969
  13.880         16.081         18.085         19.241         20.811
  -33.847        -32.020        -30.880        -30.089        -29.101
  -11.127        -7.746         -4.727         -1.231         2.311
  -43.850        -39.442        -36.370        -34.752        -30.720
  11.959         17.349         19.954         22.320         25.763
  21.810         24.136         26.284         29.615         31.986
  -26.247        -24.366        -20.131        -17.773        -14.743
  12.644         15.021         17.236         21.374         25.277
  -4.806         -1.831         1.339          3.599          5.777
  -29.610        -27.847        -25.871        -23.194        -18.077
  -16.995        -15.355        -13.392        -11.886        -4.659
  -27.148        -24.505        -23.207        -22.177        -19.031
  18.804         22.498         29.125         32.400         35.037
  -6.828         -5.539         -3.757         -0.882         1.385
  19.212         28.460         29.935         32.697         36.420
  36.694         38.207         39.175         40.194         41.737
  -1.100         1.142          3.900          6.615          9.319
  16.549         18.419         20.459         21.881         26.467
  -4.537         -3.261         -1.342         3.003          6.571
  -14.336        -10.600        -6.931         -2.847         3.706
  -27.775        -25.837        -24.681        -23.553        -19.891
  8.329          10.976         11.917         14.768         20.458
  25.282         27.184         30.838         32.531         33.920
  25.430         29.007         30.385         31.736         35.286
  16.796         18.176         23.198         25.558         27.664
  -41.413        -39.028        -36.181        -32.188        -27.529
  -28.754        -25.109        -11.638        -7.693         -2.174
  -18.670        -12.381        -8.162         2.707          7.472
  -14.186        -12.534        -10.442        -7.341         -4.611
  -6.031         -2.953         0.252          4.200          7.675
  -27.076        -24.669        -22.499        -19.570        -17.135
  -44.010        -42.121        -40.156        -38.471        -36.824
  25.532         27.163         29.060         30.675         33.148
  -2.456         1.115          3.413          5.468          6.660
  -20.555        -17.953        -14.922        -13.285        -10.294
  9.928          11.457         12.757         14.814         16.573
  20.431         21.779         22.506         24.396         30.510
  3.630          5.998          8.029          10.004         11.816
  -44.660        -40.933        -34.118        -28.939        -27.299
  -4.678         -1.009         0.057          3.019          7.530
  0.101          1.476          3.148          6.257          9.347
  -23.497        -22.042        -20.897        -19.534        -15.933
  32.164         34.804         38.152         39.224         40.935
  11.719         14.155         15.517         16.984         22.492
  13.385         15.769         16.914         18.463         20.115
  -0.378         3.282          5.348          7.534          15.622
  -32.249        -29.088        -25.605        -18.754        -16.049
  -5.699         -4.626         -3.501         -2.281         -0.653
  -14.709        -12.586        -9.530         -7.886         -6.420
  22.587         25.602         30.758         32.473         35.679
  18.942         21.058         24.688         27.725         31.757
  -5.203         -3.176         -1.575         2.139          4.433
  -3.808         -2.436         -1.692         -0.293         6.825
  -4.974         -3.360         -2.149         -0.764         0.638
  20.323         21.793         24.287         26.624         29.393
  6.712          8.600          9.735          10.788         14.513
  -17.721        -15.824        -14.145        -11.910        -10.374
  -54.160        -49.875        -45.798        -43.457        -41.400
  -40.946        -37.290        -34.359        -32.270        -31.000
  -2.744         4.244          6.656          8.056          9.350
  0.879          2.863          6.406          8.000          10.989
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  9.132          11.091         12.173         13.004         15.726
  8.197          9.799          11.008         12.054         15.159
  30.920         34.411         36.253         37.345         38.672
  -9.266         -7.567         -5.888         -2.254         0.429
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  -1.838         0.153          2.174          3.811          8.447
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  10.759         13.756         16.489         18.153         20.448
  -9.251         -4.238         0.373          2.009          3.554
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  -4.034         -1.211         -0.350         2.061          3.977
  -5.947         -2.827         -1.034         0.887          3.807
  0.993          3.043          5.259          7.162          11.374
  19.674         22.700         24.586         25.881         27.566
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  -33.750        -31.367        -30.156        -28.988        -27.264
  13.017         15.545         17.423         21.176         23.860
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  -4.510         -3.240         -2.489         -0.427         3.676
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  15.645         17.449         18.470         19.554         21.678
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  -1.395         -0.285         1.019          1.988          3.582
  -3.242         0.445          4.815          6.560          12.224
  -5.081         -2.110         0.672          2.526          5.324
  -2.152         -0.470         0.946          3.821          7.288
  10.393         13.312         14.416         17.876         20.827
  26.650         28.696         30.298         33.065         37.033
  -17.657        -12.960        -10.982        -8.191         -5.011
  -26.994        -24.468        -23.660        -22.380        -20.816
  -54.942        -48.783        -43.630        -41.464        -38.681
  -9.626         -7.404         -5.987         -4.919         -3.757
  -20.442        -16.600        -9.231         -4.333         -1.735
  8.811          12.052         14.577         17.299         20.016
  -4.874         -2.517         -0.464         1.838          4.301
  1.124          2.907          4.375          5.865          8.223
  -30.345        -24.517        -17.706        -10.362        -8.134
  -9.979         -8.036         -4.666         -1.714         1.311
  0.865          2.490          4.076          5.145          7.198
  -8.134         -5.432         -3.606         1.358          5.502
  6.609          8.058          9.481          11.449         16.396
  3.130          6.356          8.325          11.116         14.935
  35.520         37.392         39.637         42.282         44.550
  -10.174        -8.786         -7.151         -5.485         -2.593
  -18.639        -11.528        -9.996         -8.578         -6.045
  -1.061         1.373          3.834          4.866          7.565
  -0.134         1.084          2.441          5.047          7.191
  -21.356        -18.472        -17.133        -15.289        -13.706
  1.835          3.042          4.200          5.967          7.828
  -5.130         -2.379         1.439          2.982          4.755
  16.576         18.656         21.564         25.848         32.122
  2.715          5.460          6.589          8.344          11.334
  5.468          7.626          8.568          9.464          10.988
  13.276         14.850         16.033         18.767         21.136
  -22.125        -18.470        -16.405        -14.296        -10.966
  -27.493        -23.073        -21.684        -20.687        -19.078
  26.536         28.634         29.843         33.479         35.951
  21.402         26.210         28.428         30.852         33.108
  -5.018         -0.063         1.387          2.417          3.763
  -7.862         -2.763         1.328          5.841          9.661
  -15.841        -13.836        -12.127        -7.305         -5.305
  32.621         34.920         37.198         38.918         40.271
  -29.633        -28.145        -26.029        -18.596        -15.047
  28.020         29.890         32.217         33.788         38.618
  2.726          6.960          8.461          10.642         12.706
  1.320          3.057          6.179          8.219          10.082
  -48.392        -44.522        -39.544        -36.931        -35.087
  -13.287        -6.376         -4.070         -2.193         0.375
  -37.920        -30.949        -24.723        -22.786        -20.756
  15.906         18.369         19.528         22.385         28.121
  53.889         55.649         56.980         59.159         61.174
  13.720         15.971         22.781         26.817         29.484
  -30.120        -26.042        -23.476        -22.400        -20.682
  -19.848        -17.726        -15.016        -12.677        -9.345
  27.689         37.214         42.369         44.526         46.220
  -8.323         -4.932         -3.387         -2.328         0.031
  -10.400        -7.352         -6.310         -5.102         -3.127
  -53.165        -48.470        -46.166        -44.873        -42.835
  1.550          3.955          4.963          6.071          7.433
  -19.023        -16.377        -14.090        -12.793        -10.479
  -39.289        -32.276        -29.488        -26.314        -24.405
  19.386         21.486         23.816         25.402         27.331
  -41.167        -39.301        -37.993        -37.033        -34.768
  -61.338        -57.157        -46.069        -44.708        -41.667
  -30.572        -28.046        -26.449        -24.708        -20.215
  -27.453        -25.244        -23.779        -22.018        -20.306
  -15.039        -12.228        -9.015         -5.105         -2.279
  6.983          9.120          10.800         17.415         19.673
  -29.819        -28.257        -27.047        -24.819        -20.638
  -5.032         0.148          3.122          4.409          7.023
  -14.905        -12.966        -10.141        -6.609         -3.060
  3.817          5.930          8.270          10.568         15.731
  -59.291        -55.800        -53.071        -51.932        -50.881
  -13.871        -12.439        -11.341        -9.566         -7.865
  -32.039        -30.155        -28.916        -27.563        -26.591
  2.041          4.184          7.607          12.399         15.821
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  -40.538        -38.735        -37.726        -35.275        -33.644
  -55.333        -52.313        -49.726        -48.661        -46.403
  -24.613        -23.323        -21.828        -20.325        -18.619
  31.915         34.685         37.143         38.223         39.264
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  8.687          10.194         13.642         17.618         19.936
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  0.764          2.602          4.738          6.969          10.477
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  16.759         18.273         20.052         21.534         23.935
  21.152         23.848         25.640         27.884         30.562
  14.164         15.221         16.157         17.814         19.644
  29.721         31.075         32.366         34.287         36.107
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  -2.465         -0.320         3.639          6.719          8.201
  17.465         18.680         19.892         24.369         26.460
  1.996          5.294          8.833          11.690         14.002
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  -38.387        -34.765        -32.037        -29.325        -27.724
  -15.675        -12.677        -11.180        -9.851         -4.705
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  -7.466         -5.211         -1.253         7.778          9.897
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  10.843         14.206         16.672         18.114         21.170
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  16.628         20.198         23.894         25.831         27.802
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  -21.869        -18.048        -15.976        -14.578        -13.053
  -4.802         1.189          4.694          6.214          7.576
  20.879         28.209         29.356         30.215         33.133
  -8.086         -5.350         -3.801         -2.568         3.676
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  -3.264         -1.701         0.202          1.607          6.578
  10.822         12.006         13.106         14.272         16.180
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  10.314         11.677         12.915         14.364         16.309
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  -5.594         -2.498         -0.448         0.620          3.313
  7.683          14.195         16.153         17.246         18.869
  12.217         15.174         16.117         17.323         19.359
  9.549          11.792         13.062         14.471         15.878
  16.166         17.914         23.226         25.256         26.951
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  9.171          13.760         15.475         17.068         18.326
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  26.300         29.008         30.536         32.246         34.213
  3.569          6.380          8.359          10.368         15.635
  2.351          9.175          12.506         14.169         15.222
  32.930         34.439         36.601         40.371         41.737
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  22.091         24.499         26.765         28.521         30.429
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  16.797         21.250         23.165         24.850         26.944
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  16.381         18.482         21.074         22.712         24.397
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  15.343         18.089         20.498         21.998         25.882
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  3.682          5.984          7.424          9.178          12.277
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  -19.419        -16.368        -15.039        -13.794        -12.068
  -3.835         -1.563         0.075          1.198          2.829
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  23.527         25.794         28.508         33.179         35.826
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  25.637         27.645         29.642         31.111         33.570
  2.862          4.263          5.443          9.484          11.346
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  0.579          6.375          9.105          10.640         12.887
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  7.264          10.931         12.854         16.533         23.075
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  3.898          5.995          7.472          8.761          10.449
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  1.566          8.012          9.355          10.537         12.680
  7.844          9.547          10.611         11.560         15.467
  6.241          8.241          9.059          9.963          12.197
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  9.573          12.983         18.798         20.380         22.062
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  -8.980         -6.648         -3.122         -1.509         5.707
  26.112         29.238         31.772         35.987         40.246
  7.170          10.778         14.767         17.675         19.598
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  8.667          12.035         13.535         15.254         17.351
  4.543          7.792          8.557          9.493          11.441
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  -0.663         0.790          4.667          6.236          11.184
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  2.471          4.171          6.502          7.426          9.044
  34.519         37.028         39.086         41.689         43.587
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  -11.601        -7.599         -4.007         -3.265         -1.665
  12.067         15.738         22.550         25.467         28.743
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  -9.215         -6.557         -3.075         1.171          4.682
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  6.770          9.636          10.994         13.142         14.896
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  10.550         11.843         13.444         17.341         21.162
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  -6.825         -4.946         -2.146         0.017          2.507
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  31.145         35.798         42.129         49.197         56.698
  10.058         13.259         14.593         15.659         17.511
  12.324         16.487         17.454         18.652         20.576
  -0.069         1.608          3.030          7.767          9.593
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  -5.142         -3.972         -2.296         -1.058         1.084
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  10.680         13.099         15.613         19.339         22.012
  -6.049         0.092          2.013          3.811          5.798
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  22.943         25.028         26.034         27.896         29.845
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  -9.215         -5.709         -2.912         -1.097         0.956
  9.366          11.200         13.115         17.838         21.018
  24.390         27.558         29.802         32.163         33.790
  8.713          11.777         13.649         15.418         17.215
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  -10.177        -7.820         -5.253         -2.850         -0.761
  31.904         34.530         35.868         37.219         38.635
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  25.785         27.098         28.014         28.704         30.307
  7.141          9.207          11.066         13.219         15.873
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  -7.334         -5.183         -3.316         -1.871         1.112
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  -2.919         -0.381         3.809          11.249         18.126
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  -19.528        -16.382        -13.401        -8.875         -6.684
  3.283          5.706          8.695          10.810         13.877
  10.363         13.344         15.902         17.676         19.859
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  -33.994        -32.303        -31.271        -30.518        -28.923
  -18.528        -16.639        -15.297        -13.060        -10.701
  11.059         12.897         14.665         16.527         18.553
  -49.747        -46.870        -42.667        -39.300        -36.472
  24.630         26.268         29.702         32.840         35.766
  13.444         16.375         18.114         19.265         21.638
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  -6.406         1.644          4.608          6.050          9.790
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  10.169         12.279         13.458         14.522         16.442
  0.648          2.751          3.796          5.791          8.549
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  -0.041         1.636          3.525          5.129          7.063
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  -33.474        -29.908        -27.098        -24.389        -21.819
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  9.212          12.208         14.052         16.171         25.006
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  -19.349        -17.058        -15.870        -14.347        -11.935
  -5.500         -4.226         -3.240         -2.128         -0.471
  16.508         18.983         20.333         24.323         26.068
  -21.464        -18.319        -12.764        -9.973         -5.552
  -12.511        -8.890         -7.215         -5.945         -4.329
  -39.288        -35.552        -33.839        -32.677        -31.442
  21.466         23.324         24.404         25.971         28.759
  -12.457        -9.007         -6.826         -5.575         -3.285
  -18.627        -15.864        -14.750        -13.163        -11.437
  -3.246         -0.017         1.769          3.918          5.595
  14.283         20.368         24.256         28.749         30.248
  -42.165        -35.493        -34.124        -31.252        -29.084
  23.795         27.860         28.812         29.887         31.868
  -4.349         -1.583         0.582          1.834          3.790
  6.832          9.494          11.592         18.196         20.563
  7.031          9.117          9.998          11.886         14.077
  -30.724        -28.785        -25.555        -24.539        -22.132
  17.282         19.115         19.888         21.145         23.154
  -19.113        -17.190        -14.970        -12.575        -10.117
  -21.084        -15.918        -13.144        -11.024        -9.097
  -8.041         -6.366         -4.566         -3.300         -1.700
  0.075          3.958          6.853          9.796          12.438
  -17.528        -15.996        -14.509        -12.993        -8.428
  7.034          9.583          10.341         11.174         12.294
  15.141         18.584         20.745         21.899         23.682
  6.686          8.092          9.774          12.064         14.492
  15.020         17.515         19.233         20.964         23.898
  12.487         15.665         16.973         18.499         19.616
  -12.043        -7.314         -4.330         1.697          4.380
  15.199         18.855         19.509         20.182         21.963
  0.984          2.823          4.730          7.739          10.660
  -10.634        -9.184         -7.359         -6.044         -3.076
  -0.815         1.243          2.857          3.941          4.955
  11.208         13.338         15.469         17.981         19.981
  -39.393        -37.833        -36.676        -34.808        -32.110
  -7.791         -5.656         -4.538         -3.437         -1.225
  -4.464         -1.315         1.017          2.826          4.788
  11.658         14.753         16.937         19.784         22.960
  -50.277        -48.426        -44.306        -36.838        -32.205
  -2.261         0.430          1.576          3.021          4.891
  -61.555        -55.982        -52.873        -49.546        -47.422
  -1.099         0.987          3.336          4.158          5.492
  -30.514        -28.027        -19.463        -17.493        -15.238
  -4.960         -2.205         -0.657         0.093          1.963
  -22.313        -21.100        -19.300        -17.775        -14.070
  13.180         14.587         15.432         16.235         17.610
  43.706         45.547         48.664         57.703         60.348
  -35.958        -34.598        -32.559        -30.757        -28.220
  0.585          2.544          3.809          6.333          8.152
  -21.174        -17.067        -13.233        -11.462        -10.062
  4.744          6.491          8.320          9.596          12.014
  21.010         25.389         27.193         28.675         32.046
  -4.445         -2.347         -1.165         0.297          5.287
  -3.211         -2.020         -0.866         1.559          5.461
  -22.358        -19.792        -18.284        -15.567        -13.306
  -19.611        -13.355        -10.097        -7.566         -4.197
  -22.919        -20.463        -17.149        -15.246        -13.693
  3.820          8.595          13.486         14.644         16.169
  0.008          2.368          4.198          5.811          7.859
  3.770          5.380          6.499          8.382          11.119
  30.663         32.731         35.728         41.839         44.791
  -15.709        -13.852        -11.495        -9.231         -2.190
  -25.747        -22.955        -18.128        -16.370        -9.595
  -27.912        -25.602        -23.404        -22.123        -18.654
  6.189          7.502          8.851          10.111         11.378
  4.820          7.069          11.106         14.283         17.445
  59.022         65.410         69.542         71.902         74.754
  16.210         17.193         17.930         18.938         20.218
  32.172         33.769         34.661         36.142         43.128
  -16.663        -14.685        -9.562         -5.963         -1.935
  -15.128        -12.460        -10.444        -8.528         -5.183
  0.866          3.260          4.557          6.380          9.792
  38.172         44.340         45.880         48.536         51.821
  -39.877        -34.127        -30.842        -29.897        -27.381
  -9.618         -5.518         -3.341         -2.237         -0.710
  -41.733        -38.696        -37.553        -36.463        -34.835
  24.080         27.922         30.107         32.547         35.231
  5.725          9.279          13.766         15.246         18.046
  -28.192        -24.749        -21.581        -14.422        -11.674
  -4.054         -1.445         0.739          1.749          4.216
  -27.628        -25.467        -23.407        -21.807        -17.522
  37.025         38.542         40.307         43.177         45.592
  -24.192        -21.994        -20.673        -19.387        -14.141
  5.666          10.711         12.621         14.449         17.414
  -27.813        -25.833        -23.976        -20.968        -18.300
  9.596          11.855         12.894         13.598         15.384
  -32.927        -30.319        -28.893        -27.648        -26.305
  -13.730        -11.730        -10.359        -8.893         -4.805
  10.136         13.863         15.943         17.939         19.368
  8.436          11.823         13.352         14.781         16.364
  34.973         37.938         39.071         40.275         41.542
  -39.205        -36.198        -34.488        -32.650        -30.236
  13.310         15.311         16.085         18.430         19.982
  -15.149        -12.794        -10.977        -8.669         -7.242
  43.073         46.907         48.131         49.684         52.512
  -2.052         0.069          1.428          3.817          9.270
  17.848         19.597         20.969         22.791         24.807
  -2.884         0.013          1.865          3.878          6.260
  24.363         25.440         26.258         28.187         30.749
  -13.446        -8.388         -6.394         -4.576         -3.100
  4.653          5.696          6.415          7.594          9.480
  -26.524        -23.529        -22.121        -20.148        -15.431
  -56.325        -49.999        -44.570        -33.852        -30.707
  -12.715        -9.445         -5.255         0.596          4.584
  -29.590        -27.550        -26.302        -24.103        -20.216
  -9.157         -5.238         -3.879         -2.420         -0.455
  -26.085        -21.231        -19.536        -16.928        -12.397
  30.603         31.937         33.113         33.917         35.375
  -45.561        -42.634        -35.116        -32.941        -29.739
  10.812         13.519         14.542         15.386         16.962
  -41.843        -39.934        -39.128        -37.719        -36.289
  -10.169        -7.169         -5.880         -4.529         -1.916
  -0.157         1.859          3.920          6.363          9.144
  -21.261        -20.083        -18.744        -16.951        -14.872
  10.096         15.667         18.742         20.228         22.238
  -2.772         0.011          3.044          4.803          7.299
  3.215          5.674          7.590          8.787          10.776
  6.514          8.380          10.110         11.674         15.766
  -7.923         -6.081         0.841          2.252          4.102
  -50.711        -47.548        -44.313        -41.070        -37.920
  -38.494        -36.308        -34.746        -33.573        -32.193
  28.252         30.023         33.966         38.062         43.458
  -51.285        -47.509        -42.130        -39.439        -33.811
  17.903         22.645         23.885         26.905         28.381
  23.296         25.224         26.484         27.672         29.217
  34.851         37.356         38.884         39.826         42.665
  -51.357        -49.405        -48.349        -45.261        -41.972
  -26.709        -24.988        -24.023        -21.412        -18.679
  41.367         43.136         44.053         45.330         47.899
  19.552         23.493         25.771         27.738         30.451
  -18.219        -16.110        -11.804        -8.110         -1.455
  0.362          3.133          4.426          5.680          8.683
  -32.885        -30.883        -29.599        -24.158        -17.681
  -11.801        -10.211        -8.305         -6.643         -3.336
  -35.408        -33.378        -30.699        -29.421        -28.183
  6.758          7.806          8.627          9.735          11.484
  19.954         22.135         23.085         24.728         26.168
  -1.028         3.583          6.121          10.019         12.124
  28.787         33.024         38.330         42.200         48.205
  3.765          7.884          11.644         14.046         20.337
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  -29.629        -27.329        -24.626        -22.549        -20.960
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  -14.660        -12.477        -9.255         -1.098         0.271
  -2.310         -1.182         0.635          1.703          3.030
  -31.221        -29.222        -25.921        -18.976        -12.875
  -10.703        -8.863         -6.973         -4.789         -2.255
  -41.021        -38.270        -37.031        -35.401        -33.312
  -19.917        -17.745        -16.130        -14.844        -12.651
  34.757         36.674         37.662         38.487         39.817
  31.651         33.329         34.386         35.326         37.598
  0.135          2.521          3.798          5.056          8.747
  -13.966        -12.341        -10.978        -10.164        -7.032
  -33.394        -28.097        -26.433        -24.528        -22.687
  7.073          9.037          10.675         12.300         15.499
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  15.714         18.374         19.094         19.902         22.187
  -1.343         0.558          3.263          5.555          7.502
  -0.629         1.125          4.354          8.292          9.368
  -44.827        -42.702        -41.501        -38.730        -34.789
  -26.907        -25.432        -24.291        -23.201        -20.927
  -3.533         -2.352         -1.490         -0.508         1.714
  24.584         26.562         27.698         29.152         31.628
  -9.928         -7.287         -6.190         -5.114         -2.517
  -54.268        -52.646        -50.936        -49.282        -45.765
  -56.583        -54.771        -53.227        -49.187        -46.788
  6.148          8.792          10.928         13.086         14.608
  -23.900        -20.002        -15.759        -9.946         -6.704
  -15.403        -12.337        -11.317        -10.219        -8.306
  2.854          5.120          6.376          7.666          10.352
  -8.276         -6.529         -4.026         -2.920         -1.614
  22.494         24.299         25.294         26.465         30.364
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  -7.942         -5.941         -4.939         -3.868         -2.499
  -0.672         0.743          2.662          5.160          7.328
  -17.688        -16.086        -14.771        -12.704        -10.837
  -10.275        -7.062         -4.673         -1.762         0.413
  1.228          4.219          6.012          8.959          11.914
  -44.263        -41.549        -39.601        -37.819        -33.312
  5.393          7.914          9.682          13.998         16.720
  -23.777        -19.829        -18.553        -17.264        -14.781
  10.901         13.485         19.032         20.559         24.226
  -29.647        -26.548        -25.263        -23.370        -20.909
  -20.770        -19.167        -18.394        -17.568        -15.884
  -9.956         -8.492         -7.018         -5.177         0.086
  16.148         19.451         21.888         23.599         25.006
  23.075         25.352         28.384         32.020         34.135
  -14.660        -12.671        -11.769        -10.668        -9.059
  22.794         25.600         26.928         27.837         29.046
  29.780         30.733         31.616         32.919         34.259
  0.253          4.505          6.630          8.564          11.663
  27.933         30.107         32.225         34.564         36.445
  -46.228        -44.719        -43.359        -41.159        -39.165
  1.926          6.000          8.031          12.664         15.221
  -3.425         -0.693         1.174          3.759          5.982
  22.814         26.496         27.901         29.458         33.778
  56.081         58.629         60.141         61.788         63.290
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  18.158         20.394         22.017         27.089         29.052
  -18.977        -16.986        -15.668        -14.604        -10.427
  -7.128         -5.492         -3.972         -2.442         6.120
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  -0.710         5.320          7.022          7.977          9.344
  29.567         31.966         33.018         33.897         35.368
  27.463         31.365         32.758         33.794         35.719
  -2.643         -0.093         2.412          4.186          5.926
  9.318          13.614         14.815         15.688         18.189
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  -21.317        -17.976        -16.876        -14.397        -12.493
  -22.417        -19.385        -15.631        -14.067        -9.959
  -1.369         1.090          4.551          6.222          8.970
  21.646         24.347         26.483         27.993         29.395
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  -3.592         -0.913         0.915          4.096          7.545
  38.919         44.994         46.484         47.032         48.273
  7.167          8.820          10.336         11.796         14.620
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  -7.216         -5.044         -3.074         -0.726         2.307
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  -0.356         0.915          1.621          2.682          4.125
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  -8.549         -3.954         1.825          6.066          10.961
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  -7.249         -4.467         -1.363         1.648          3.242
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  -30.864        -29.066        -26.674        -24.384        -20.837
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  -7.000         -5.015         -3.258         -0.723         1.028
  -5.488         -2.175         1.160          2.746          5.426
  -8.434         -7.181         -5.837         -4.425         -1.789
  14.563         17.363         19.267         22.401         25.787
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  -1.762         3.714          5.135          7.078          9.083
  -28.366        -26.904        -25.045        -23.070        -19.681
  -1.305         1.058          2.339          3.806          7.474
  -2.928         -1.434         -0.499         0.354          2.366
  25.926         27.904         29.655         30.956         33.696
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  7.548          10.894         12.679         14.954         17.017
  -0.417         2.361          3.959          6.593          9.341
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  -6.405         -4.399         -2.728         -0.064         3.338
  7.224          10.504         12.141         13.259         15.313
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  28.157         29.597         32.235         33.620         37.156
  -3.014         -0.737         1.027          7.374          11.989
  8.631          10.826         12.715         14.052         16.732
  3.482          7.481          8.881          9.994          12.761
  -6.073         -3.711         -1.364         -0.308         1.059
  -25.737        -19.423        -17.725        -16.665        -15.459
  -6.890         -5.718         -5.130         -3.787         -2.627
  15.645         20.115         21.408         23.594         27.294
  -41.736        -39.057        -36.049        -33.046        -30.455
  -32.377        -26.155        -21.297        -17.904        -14.998
  13.053         16.397         23.514         26.852         31.338
  17.134         21.192         25.166         28.762         29.965
  -37.784        -31.021        -28.591        -26.586        -22.574
  -27.216        -21.119        -18.904        -15.911        -10.589
  -19.392        -16.192        -9.580         -8.633         -6.944
  12.548         13.845         14.896         15.990         18.117
  9.173          11.013         14.508         16.442         19.422
  7.310          8.267          9.511          10.284         11.278
  12.809         15.678         19.657         23.682         25.740
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  -5.453         -2.999         -0.005         1.519          4.047
  4.066          10.172         12.210         14.025         16.309
  19.616         23.352         27.415         28.438         30.130
  -3.712         -2.211         -0.268         1.166          2.934
  0.454          2.849          3.840          4.906          6.873
  -18.838        -16.508        -15.225        -13.324        -9.701
  33.640         40.362         42.449         44.895         48.750
  -5.732         -4.664         -3.228         -1.408         2.375
  41.639         42.831         44.264         45.994         48.157
  19.352         24.229         25.419         26.657         27.931
  -10.327        -6.251         -4.635         -1.448         0.633
  -12.720        -3.864         -1.848         0.501          2.215
  25.555         27.809         30.101         32.406         33.902
  -12.088        -8.628         -7.174         -4.231         -1.111
  -2.751         -0.635         0.840          1.827          3.245
  14.490         17.203         19.181         21.011         23.577
  18.758         24.048         26.296         31.418         34.104
  -3.113         -1.069         1.352          4.337          6.378
  23.843         26.675         27.608         28.467         30.460
  -7.134         -0.916         0.374          1.731          3.586
  -5.044         -3.457         -2.574         -1.540         0.233
  26.080         27.612         28.880         30.051         33.403
  36.628         40.557         42.657         44.036         47.177
  2.083          6.811          8.249          10.004         12.467
  10.628         15.642         16.736         17.441         22.326
  -9.747         -6.820         -2.883         1.760          5.242
  -51.961        -47.130        -45.564        -43.424        -41.795
  -6.409         -4.175         0.446          5.102          10.852
  4.599          7.895          16.790         19.144         21.058
  10.778         13.609         17.453         19.904         22.373
  -10.810        -8.727         -7.361         -6.242         -4.829
  7.527          11.177         13.289         19.229         25.481
  24.464         25.969         26.714         28.839         30.913
  3.130          5.096          7.097          10.872         12.350
  -25.051        -22.394        -19.718        -17.540        -15.762
  -1.530         2.861          4.495          6.446          8.344
  -8.634         -6.524         -4.604         -3.629         -2.207
  -22.380        -19.276        -17.797        -15.740        -14.483
  -20.573        -16.826        -15.636        -14.530        -12.985
  -1.363         1.984          5.769          7.051          8.113
  18.795         20.270         20.950         21.904         23.780
  -5.951         -4.199         -3.219         -2.330         -0.922
  -2.682         -0.706         3.351          5.011          6.314
  -14.759        -12.329        -10.700        -8.650         -4.343
  -23.140        -20.416        -17.377        -15.997        -10.064
  -1.263         1.313          5.481          7.275          9.328
  37.173         40.917         42.697         43.462         44.840
  22.119         23.473         25.014         27.744         29.720
  32.936         36.009         38.606         40.034         43.068
  4.567          7.861          9.810          10.905         13.563
  -7.135         -3.781         -2.410         -0.716         0.987
  -5.805         -2.979         -0.897         0.084          2.469
  -50.106        -48.381        -44.209        -41.856        -37.200
  -31.528        -29.165        -27.692        -24.921        -22.550
  -1.576         0.709          2.895          4.473          7.892
  25.225         26.330         27.213         27.975         29.953
  -24.932        -23.665        -20.290        -18.149        -13.186
  24.461         33.236         34.777         37.274         38.777
  -22.224        -17.953        -16.579        -14.321        -13.093
  -8.220         -6.194         -4.962         -3.022         -0.880
  -10.195        -8.294         -5.105         -3.823         -1.773
  24.395         26.848         31.145         33.137         36.446
  6.875          11.392         12.778         14.216         16.276
  -4.560         -0.018         2.706          5.040          7.426
  12.583         15.238         17.891         19.444         21.426
  -11.888        -9.320         -7.705         -6.412         -3.436
  18.434         20.184         22.070         24.015         26.080
  -3.978         -0.857         0.545          3.909          6.825
  -0.502         3.291          8.808          15.003         19.862
  -0.808         0.813          5.385          8.258          9.796
  -14.252        -11.767        -9.751         -8.203         -6.472
  1.446          3.806          6.800          9.930          11.706
  7.267          10.655         11.992         14.285         21.563
  2.008          5.275          7.253          9.054          12.334
  13.888         16.302         22.269         25.605         28.849
  3.789          6.276          7.880          9.946          12.229
  -26.145        -22.293        -20.522        -19.124        -17.830
  40.976         43.266         43.880         45.033         46.844
  6.380          8.851          10.595         12.156         13.828
  -12.111        -10.168        -8.710         -6.761         -1.233
  45.255         49.252         56.412         59.636         62.931
  -6.957         -5.617         -4.400         -3.122         -0.830
  1.751          3.893          4.980          6.410          8.209
  -13.353        -10.775        -9.650         -8.288         -4.773
  11.014         17.388         19.482         22.249         24.410
  12.584         17.810         21.179         24.677         26.788
  5.452          9.765          11.801         12.668         13.754
  -18.313        -16.606        -15.676        -14.634        -10.748
  -7.585         -4.632         -2.441         1.572          5.741
  1.960          10.456         12.547         14.057         15.651
  -19.353        -18.293        -17.193        -16.020        -13.948
  -25.230        -22.515        -20.577        -18.398        -16.598
  16.535         17.763         18.386         19.534         22.397
  7.999          11.334         12.919         14.023         15.714
  37.919         40.199         40.865         41.848         43.899
  2.612          4.287          5.958          7.919          11.107
  -23.583        -21.761        -21.091        -19.888        -15.755
  -51.059        -48.288        -46.289        -45.303        -42.773
  -22.212        -18.719        -16.370        -14.540        -13.726
  4.441          5.844          8.239          10.764         14.465
  -18.032        -15.645        -13.627        -10.809        -5.368
  -5.141         -3.635         -2.712         -1.009         1.877
  10.540         12.339         13.254         14.034         15.540
  -6.612         -5.322         -4.388         -3.399         -1.670
  -32.198        -30.479        -29.197        -26.247        -24.011
  -15.305        -13.074        -11.634        -10.516        -9.197
  -21.231        -19.855        -18.038        -16.448        -14.718
  -24.850        -22.416        -19.565        -17.070        -15.474
  -5.822         -3.663         -2.370         -1.390         2.118
  -18.345        -15.909        -12.379        -8.440         -5.488
  2.934          4.885          5.873          7.232          8.913
  -13.856        -5.390         -2.586         -1.433         0.590
  -4.560         -2.443         1.767          4.103          8.234
  17.762         20.242         21.732         23.296         25.624
  -2.258         -0.486         0.511          1.392          2.264
  -3.773         -0.984         1.223          5.409          7.950
  -13.624        -9.858         -7.404         -6.220         -3.240
  14.579         16.206         18.889         20.993         24.740
  -41.227        -37.081        -36.267        -33.797        -29.695
  -7.036         -2.977         -0.532         1.940          3.424
  -17.244        -15.138        -8.287         -6.047         -3.674
  -57.143        -51.024        -49.239        -48.070        -46.440
  -13.861        -10.084        -7.833         -5.648         -2.068
  -7.176         -5.102         -2.103         -0.001         2.326
  -31.646        -29.849        -27.661        -22.878        -19.770
  -10.417        -8.385         -6.829         -5.862         -4.092
  31.779         34.722         35.971         38.692         40.838
  -21.244        -16.756        -15.578        -14.490        -12.532
  8.969          11.252         13.292         14.242         15.958
  23.403         27.349         30.393         33.075         34.074
  -21.155        -16.776        -13.210        -9.625         -5.831
  -36.032        -34.008        -32.754        -31.528        -26.718
  41.287         44.189         45.673         51.309         54.770
  -2.667         2.462          7.652          9.659          11.617
  19.507         22.040         22.904         23.611         25.172
  -10.606        -9.364         -7.976         -6.518         -3.681
  42.861         44.518         45.675         47.798         49.385
  -13.036        -11.540        -9.461         -7.836         -5.827
  -45.605        -43.635        -38.909        -36.852        -34.453
  -18.332        -15.809        -14.388        -13.333        -12.332
  -7.254         -3.561         0.175          0.991          2.272


σ:

  Mean             SD               MC Error         95% HPD interval
  -------------------------------------------------------------------
  
  32.511           2.396            0.165            [27.857, 37.342]

  Posterior quantiles:
  2.5            25             50             75             97.5
  |--------------|==============|==============|--------------|
  
  28.232         30.947         32.530         34.037         37.730