2
"""Unit tests for fast metric scaling functions"""
4
from cogent.util.unit_test import TestCase, main
5
from cogent.cluster import goodness_of_fit
6
from cogent.cluster.approximate_mds \
8
from cogent.cluster.approximate_mds \
9
import calc_matrix_a, calc_matrix_b, build_seed_matrix
10
from cogent.cluster.approximate_mds import rowmeans, \
11
affine_mapping, adjust_mds_to_ref, recenter, combine_mds, \
12
cmds_tzeng, CombineMds
13
from numpy import array, matrix, random, argsort
15
__author__ = "Andreas Wilm"
16
__copyright__ = "FIXME"
17
__credits__ = ["Andreas Wilm"]
20
__maintainer__ = "Andreas Wilm"
21
__email__ = "andreas.wilm@ucd.ie"
27
# Bigish symmetrical matrix for testing: The following is a distance
28
# matrix of 100 points making up a 16-dimensional spiral. Idea was
29
# copied from Tzeng et al. 2008 (PMID 18394154).
31
# Note: the objects are ordered, i.e. permuting the distances will
32
# give better MDS approximations
34
FULL_SYM_MATRIX = array([
35
[ 0. , 9.94319, 7.11402, 7.30016, 9.1998 , 7.52661,
36
10.1122 , 11.71544, 11.72171, 12.23729, 16.55706, 15.07764,
37
17.41182, 19.23286, 22.03428, 20.37969, 21.79021, 23.31804,
38
25.27884, 25.33384, 25.51721, 25.23346, 27.13757, 27.77099,
39
31.89744, 30.12906, 30.853 , 31.25053, 32.01368, 32.92915,
40
34.80687, 34.67094, 34.61157, 33.95445, 36.09099, 34.39821,
41
35.29278, 33.43954, 35.50327, 34.96861, 34.61776, 31.52205,
42
31.5479 , 31.86234, 30.85453, 29.69611, 29.41756, 28.83014,
43
30.11403, 28.76504, 23.7291 , 25.6983 , 25.97412, 25.13513,
44
24.45972, 21.55045, 21.69278, 19.95303, 16.26348, 17.11013,
45
14.32254, 17.62265, 15.44168, 17.37134, 13.90914, 11.73735,
46
12.23879, 12.84236, 16.11693, 14.78883, 14.85241, 16.81082,
47
15.84987, 19.49531, 19.10495, 20.82333, 22.2353 , 24.10629,
48
25.58022, 26.94421, 29.15922, 29.35633, 30.44926, 33.44155,
49
33.20634, 35.10944, 37.58041, 36.97612, 37.4974 , 39.19126,
50
41.96371, 39.49224, 44.24451, 44.49713, 46.20998, 45.17665,
51
43.34276, 45.20143, 42.75318, 46.74111],
52
[ 9.94319, 0. , 9.15502, 9.50864, 4.67066, 8.73786,
53
10.65396, 7.07033, 7.65245, 11.7303 , 13.97535, 14.44678,
54
14.4366 , 17.67632, 17.78924, 17.34483, 20.92378, 19.64563,
55
22.37953, 22.50652, 22.59182, 23.16428, 25.36422, 24.53657,
56
28.53754, 28.8102 , 28.67001, 29.99149, 29.0992 , 30.78134,
57
32.60362, 33.06432, 32.35053, 31.31204, 33.96212, 32.70361,
58
34.0075 , 31.79899, 34.1394 , 34.08447, 34.40636, 32.09843,
59
31.55098, 32.21933, 29.68935, 30.64989, 29.84656, 30.31266,
60
30.95073, 29.50086, 25.13342, 26.92125, 26.77764, 25.45479,
61
26.64139, 24.28835, 23.54393, 21.14658, 19.0042 , 19.69926,
62
17.01569, 17.70308, 16.76036, 18.85088, 15.67933, 13.11373,
63
14.57384, 14.49709, 13.93834, 13.97627, 15.28133, 15.43603,
64
15.38908, 19.14731, 18.0164 , 19.25691, 20.79821, 21.17772,
65
23.34925, 24.69467, 25.91663, 26.0043 , 27.48027, 31.09767,
66
29.88905, 31.87226, 35.07482, 34.08161, 34.96767, 36.59085,
67
39.56174, 37.35437, 42.00158, 42.65467, 44.21824, 42.7808 ,
68
41.49634, 42.89946, 41.51576, 45.2993 ],
69
[ 7.11402, 9.15502, 0. , 6.86568, 9.13056, 6.40397,
70
9.71158, 8.69917, 8.75907, 9.94964, 12.60852, 10.83371,
71
13.24922, 15.56278, 18.00935, 17.28358, 18.64376, 18.74751,
72
21.30424, 20.79329, 22.52019, 21.17382, 24.35227, 24.04257,
73
27.79547, 27.14583, 27.9384 , 28.31876, 29.19352, 30.31387,
74
32.49497, 32.53298, 32.54342, 31.6677 , 34.4333 , 33.06171,
75
33.8104 , 32.32825, 34.54666, 33.66703, 34.21985, 31.60984,
76
31.44096, 32.23245, 30.68488, 30.737 , 30.20034, 30.13288,
77
31.62192, 30.13293, 25.84322, 27.91135, 28.12311, 27.30813,
78
27.01853, 24.69093, 24.94734, 23.21836, 20.37644, 20.92257,
79
17.85377, 20.91217, 19.36837, 20.86528, 17.38101, 14.14065,
80
15.49992, 14.33989, 17.43602, 15.89444, 14.88863, 15.37154,
81
15.57648, 18.73803, 17.66276, 19.14902, 19.51857, 21.56308,
82
22.21288, 23.47894, 25.86362, 25.36028, 26.33286, 29.98075,
83
29.33639, 31.30981, 33.73965, 33.6759 , 34.04663, 35.63369,
84
38.24726, 36.06871, 40.78921, 41.34813, 43.00012, 42.36618,
85
40.24461, 42.30763, 40.55066, 44.09355],
86
[ 7.30016, 9.50864, 6.86568, 0. , 7.99096, 7.60197,
87
10.10639, 9.22165, 8.8801 , 9.49238, 13.66406, 12.57744,
88
13.13858, 15.46775, 17.73952, 16.56614, 18.40617, 19.64056,
89
21.45177, 22.03097, 21.88416, 22.61383, 24.92398, 25.28642,
90
29.08492, 27.8259 , 29.18638, 29.3961 , 30.42798, 31.81182,
91
33.20848, 33.36339, 34.03547, 33.03364, 35.82444, 34.7116 ,
92
35.8487 , 33.89059, 36.02136, 35.60052, 36.08047, 33.37669,
93
33.34017, 33.79942, 32.42774, 31.97527, 31.72587, 31.85386,
94
33.66607, 32.0357 , 26.92882, 29.3656 , 29.6113 , 28.77098,
95
27.98344, 25.49869, 26.08835, 24.3511 , 21.22304, 21.25266,
96
18.87943, 21.25316, 19.09945, 20.88305, 16.98734, 14.43121,
97
14.87293, 12.60412, 16.25858, 14.52592, 14.10743, 13.84321,
98
13.02127, 16.58691, 15.13994, 17.45726, 18.68005, 20.17601,
99
21.41715, 23.0355 , 25.07801, 24.73817, 26.67714, 29.31584,
100
29.02044, 31.28387, 33.55744, 33.39091, 34.49413, 36.29427,
101
39.09789, 36.46602, 41.84873, 41.95262, 44.21519, 43.15904,
102
41.86844, 43.70448, 41.85398, 45.9426 ],
103
[ 9.1998 , 4.67066, 9.13056, 7.99096, 0. , 8.10903,
104
8.12191, 6.68991, 6.01745, 8.81851, 12.76517, 13.05449,
105
13.25358, 16.08166, 16.85701, 14.96082, 18.58137, 18.78881,
106
21.03104, 21.37792, 20.97864, 22.24007, 23.27987, 23.47925,
107
27.51623, 27.08492, 27.63842, 28.49791, 28.08892, 29.94971,
108
31.60411, 32.35099, 31.64065, 30.7586 , 33.58783, 32.51966,
109
33.71852, 31.59205, 34.09468, 34.22325, 34.16007, 32.3283 ,
110
31.89116, 32.43132, 30.52192, 31.02961, 30.1106 , 31.0687 ,
111
31.53677, 30.2114 , 25.7518 , 27.6139 , 28.20037, 27.20175,
112
27.57982, 25.10337, 25.22312, 22.84998, 20.28434, 20.93006,
113
18.50018, 19.27925, 17.75401, 20.49716, 16.24356, 13.95706,
114
14.68697, 14.86848, 14.61363, 14.13096, 14.51717, 15.68778,
115
14.51018, 17.43174, 16.76305, 18.13449, 19.68793, 19.75357,
116
21.78947, 23.32496, 24.54554, 24.18059, 26.19812, 29.52194,
117
28.20267, 30.01717, 33.36934, 32.26088, 33.40864, 34.83176,
118
38.18059, 35.81903, 40.65885, 41.40321, 43.17206, 41.53149,
119
40.71829, 42.49124, 40.79031, 44.66045],
120
[ 7.52661, 8.73786, 6.40397, 7.60197, 8.10903, 0. ,
121
6.16569, 7.32563, 7.75387, 7.69682, 10.69552, 9.88725,
122
11.3961 , 14.00163, 16.23874, 15.6289 , 16.73334, 17.44048,
123
19.99725, 19.9533 , 20.46002, 19.84823, 22.72976, 23.22363,
124
27.33355, 26.83688, 27.09796, 28.27618, 28.3494 , 29.75656,
125
31.77772, 32.50386, 32.5482 , 31.99727, 34.67355, 33.19062,
126
34.46902, 33.13995, 35.80184, 35.25591, 35.33808, 33.38177,
127
33.04059, 33.91149, 32.75336, 32.5993 , 32.43664, 32.23116,
128
33.38874, 32.62237, 28.36209, 30.55605, 30.3347 , 29.56765,
129
29.58556, 27.53405, 26.86667, 25.00712, 21.74171, 23.02809,
130
19.62897, 22.0497 , 20.71073, 20.89719, 18.9401 , 14.67542,
131
15.87359, 14.84921, 15.9765 , 14.6316 , 13.43337, 14.09887,
132
13.393 , 15.35339, 15.15473, 15.57783, 16.38066, 18.12999,
133
19.33544, 20.47957, 22.53012, 23.41117, 23.94749, 27.14785,
134
27.12172, 29.01223, 32.1432 , 31.53822, 31.97442, 34.20046,
135
36.96213, 35.11644, 39.86917, 40.59916, 42.25278, 42.35218,
136
40.45489, 42.53407, 40.64863, 44.57547],
137
[ 10.1122 , 10.65396, 9.71158, 10.10639, 8.12191, 6.16569,
138
0. , 8.95464, 7.95483, 6.96854, 10.2321 , 9.1072 ,
139
11.40191, 13.88653, 16.49484, 12.77356, 14.76539, 17.37815,
140
19.05223, 19.09134, 19.48543, 19.25793, 20.07018, 21.44923,
141
26.16354, 24.71872, 25.7368 , 26.60446, 26.8787 , 27.97926,
142
30.01728, 31.59176, 31.2204 , 30.74726, 33.36662, 32.19782,
143
33.24557, 32.26498, 35.20755, 35.27066, 34.3224 , 33.45572,
144
33.21501, 33.77282, 32.98931, 33.29691, 32.48639, 32.89237,
145
33.31269, 33.17576, 29.06571, 31.25932, 31.50259, 31.19405,
146
31.33608, 28.94501, 28.98748, 26.83509, 23.67883, 25.4293 ,
147
22.19619, 23.92894, 22.48331, 23.70778, 20.61034, 16.80414,
148
17.54135, 17.64634, 18.13698, 16.73796, 15.0992 , 16.73965,
149
15.39915, 15.3146 , 16.21818, 15.90665, 16.80116, 17.15962,
150
18.1004 , 20.22697, 21.04317, 22.01882, 23.10616, 25.70386,
151
25.33855, 26.90823, 30.27089, 29.34631, 29.92087, 31.66778,
152
35.17056, 33.31352, 37.56416, 39.27059, 40.62456, 40.2062 ,
153
39.40489, 41.81369, 39.33236, 43.20546],
154
[ 11.71544, 7.07033, 8.69917, 9.22165, 6.68991, 7.32563,
155
8.95464, 0. , 3.7505 , 6.85568, 7.69523, 9.7299 ,
156
8.8292 , 12.08808, 12.84075, 12.41397, 15.7665 , 13.80821,
157
17.10528, 17.0151 , 18.03523, 18.49492, 21.4005 , 20.91953,
158
24.56468, 24.98275, 25.20224, 26.47583, 26.01966, 28.37676,
159
30.43507, 31.12544, 31.08021, 29.96861, 33.06401, 32.57304,
160
33.997 , 32.11079, 34.68809, 34.12659, 35.42161, 33.62916,
161
33.16394, 34.14988, 31.96731, 33.13473, 32.68089, 33.34788,
162
34.37908, 32.97516, 29.38917, 31.30679, 31.86587, 30.67301,
163
31.14565, 29.06828, 29.04268, 27.11562, 24.63125, 25.08637,
164
22.31814, 23.71491, 22.41495, 23.87865, 20.79483, 17.13811,
165
18.05839, 16.67094, 16.67337, 15.59013, 15.29917, 14.46026,
166
14.31921, 16.68845, 14.41634, 16.10611, 16.76691, 16.68857,
167
18.02822, 19.23566, 20.91886, 19.93191, 21.22647, 25.60087,
168
24.01222, 26.23519, 29.55426, 29.01695, 29.67471, 31.85062,
169
34.7836 , 32.77038, 38.06911, 38.63774, 40.78472, 39.75408,
170
38.43139, 40.51321, 39.43324, 43.19846],
171
[ 11.72171, 7.65245, 8.75907, 8.8801 , 6.01745, 7.75387,
172
7.95483, 3.7505 , 0. , 6.25554, 7.94184, 9.40809,
173
9.37058, 12.64537, 13.25671, 11.69312, 15.73247, 14.29708,
174
17.17558, 17.07269, 18.18613, 18.66698, 20.99351, 20.83302,
175
24.42795, 24.65435, 25.16361, 26.40833, 26.00333, 28.48816,
176
30.39505, 31.12778, 31.04052, 30.02038, 33.06101, 32.51077,
177
33.91746, 32.16109, 34.72522, 34.26106, 35.29431, 33.7662 ,
178
33.40285, 34.11146, 32.13639, 33.33042, 32.66608, 33.38514,
179
34.29769, 32.89254, 29.26526, 31.06269, 32.01605, 30.75263,
180
31.17672, 28.89607, 29.20958, 27.32181, 24.53975, 25.21252,
181
22.16274, 23.60181, 22.19147, 23.8951 , 20.57865, 17.20223,
182
17.67657, 16.61788, 17.05001, 15.68349, 15.30447, 14.95815,
183
14.4235 , 16.70277, 14.6234 , 16.24885, 16.87216, 16.49137,
184
17.85663, 19.18505, 20.91421, 19.70914, 21.64589, 25.6927 ,
185
24.18448, 26.08005, 29.35354, 29.00965, 29.70327, 31.74665,
186
34.68077, 32.64932, 37.91062, 38.78521, 40.83826, 39.61926,
187
38.5705 , 40.69567, 39.56802, 43.04025],
188
[ 12.23729, 11.7303 , 9.94964, 9.49238, 8.81851, 7.69682,
189
6.96854, 6.85568, 6.25554, 0. , 7.3016 , 8.07212,
190
8.2089 , 9.98656, 12.42781, 10.62705, 12.28722, 13.48977,
191
16.04661, 16.19534, 16.3577 , 17.32154, 19.0178 , 20.5046 ,
192
23.95953, 23.43756, 24.50878, 25.26128, 25.60517, 28.0269 ,
193
30.02525, 31.11886, 31.15891, 30.49865, 33.86459, 33.37975,
194
34.65544, 33.14589, 36.03802, 35.51766, 36.24468, 35.04257,
195
34.67094, 35.65553, 34.59658, 34.79422, 34.36677, 35.45895,
196
36.3779 , 35.3327 , 31.54706, 33.65312, 34.74652, 33.95725,
197
33.40518, 31.44167, 31.93944, 30.05815, 26.96615, 27.64338,
198
24.84473, 26.74278, 24.89471, 26.39705, 22.80323, 19.30856,
199
19.43576, 18.22819, 18.64491, 17.05169, 14.82973, 15.51568,
200
14.01205, 14.33961, 13.3435 , 14.52817, 14.70497, 14.77414,
201
15.56051, 16.74031, 18.93591, 17.75143, 19.27456, 22.94456,
202
21.91537, 23.84675, 27.42168, 26.76934, 27.66108, 29.75946,
203
33.0935 , 30.98471, 36.65424, 37.30058, 39.65202, 39.12975,
204
38.02632, 40.69416, 39.21815, 43.02089],
205
[ 16.55706, 13.97535, 12.60852, 13.66406, 12.76517, 10.69552,
206
10.2321 , 7.69523, 7.94184, 7.3016 , 0. , 6.34024,
207
6.29442, 9.31874, 10.60831, 9.48152, 11.679 , 9.86008,
208
12.78319, 12.47705, 15.20036, 14.79868, 18.06249, 17.95878,
209
21.80304, 21.94482, 22.94088, 24.29869, 24.32754, 26.55776,
210
29.0597 , 30.47032, 31.03937, 29.92437, 33.13454, 33.19895,
211
34.69406, 33.79095, 36.57048, 36.01451, 37.16413, 36.42303,
212
36.18591, 37.09342, 35.61312, 37.27428, 36.78719, 37.18274,
213
38.417 , 37.62287, 34.72634, 36.87088, 37.5226 , 36.63014,
214
37.07125, 35.13839, 35.36933, 33.57977, 30.77296, 31.75893,
215
28.54674, 30.22502, 28.99081, 29.49656, 27.01958, 22.64011,
216
23.11653, 21.4745 , 21.88627, 19.79573, 18.19257, 16.9958 ,
217
16.94848, 16.33478, 14.10467, 14.58976, 14.07395, 12.99207,
218
12.74353, 13.92433, 15.69868, 14.25548, 15.27649, 19.74988,
219
18.25877, 20.80091, 23.91183, 24.08524, 24.27307, 27.16596,
220
30.02343, 28.55089, 33.83448, 35.47091, 37.51809, 37.42083,
221
36.17692, 39.05643, 38.09928, 41.43184],
222
[ 15.07764, 14.44678, 10.83371, 12.57744, 13.05449, 9.88725,
223
9.1072 , 9.7299 , 9.40809, 8.07212, 6.34024, 0. ,
224
6.9511 , 8.1817 , 12.01962, 9.83166, 10.03616, 10.82597,
225
12.22157, 12.42638, 14.81562, 13.24075, 15.91179, 16.17176,
226
20.81994, 19.82228, 21.65753, 22.19242, 23.10866, 24.91478,
227
26.51025, 27.84524, 28.94428, 28.23706, 31.0608 , 30.49635,
228
31.58452, 31.13131, 34.00834, 33.61703, 34.00148, 33.33828,
229
33.20841, 33.84176, 33.36215, 34.29352, 34.00194, 34.24137,
230
35.53305, 35.23732, 32.32311, 34.68689, 34.89579, 34.4585 ,
231
34.33839, 33.07445, 33.23999, 31.99141, 28.83607, 30.27728,
232
27.08538, 29.42086, 28.13654, 28.78396, 26.43445, 22.12388,
233
23.17097, 21.90119, 23.31711, 21.43302, 19.21266, 18.09438,
234
18.37291, 17.67573, 16.69031, 16.42476, 15.74665, 15.65608,
235
14.72969, 16.18704, 17.54084, 16.84414, 17.82539, 20.46911,
236
20.57828, 21.7296 , 24.02904, 24.20871, 24.33682, 26.71437,
237
29.08875, 27.8246 , 32.39523, 33.86684, 35.84499, 36.03478,
238
34.76023, 37.39742, 35.57779, 39.06011],
239
[ 17.41182, 14.4366 , 13.24922, 13.13858, 13.25358, 11.3961 ,
240
11.40191, 8.8292 , 9.37058, 8.2089 , 6.29442, 6.9511 ,
241
0. , 5.80269, 7.34823, 7.61967, 8.88048, 8.03171,
242
10.84203, 11.15163, 12.21275, 12.34706, 16.11929, 16.0975 ,
243
19.45663, 20.33958, 21.24043, 22.37157, 22.50594, 24.89152,
244
26.47231, 28.19409, 29.03612, 28.11855, 31.78424, 31.68759,
245
33.16023, 32.00993, 35.12134, 34.61314, 36.07251, 35.37259,
246
34.85009, 36.19004, 34.77939, 36.03767, 35.84771, 37.05029,
247
38.33912, 37.71305, 34.34605, 36.90215, 37.11372, 36.56462,
248
36.48557, 35.26936, 35.32999, 33.72941, 31.33676, 32.09544,
249
29.33582, 31.07569, 29.78355, 30.69899, 27.88792, 23.6909 ,
250
24.95077, 22.44497, 22.73515, 21.53386, 19.39791, 17.15086,
251
17.26961, 16.50911, 14.97885, 14.84698, 14.0348 , 13.16584,
252
12.28025, 14.13143, 14.59832, 13.82806, 14.44424, 17.8433 ,
253
16.98162, 19.04357, 22.24141, 22.05366, 22.98183, 25.33998,
254
28.35413, 26.6982 , 32.11611, 32.88203, 35.32819, 35.61998,
255
34.74136, 37.0847 , 36.06984, 40.03816],
256
[ 19.23286, 17.67632, 15.56278, 15.46775, 16.08166, 14.00163,
257
13.88653, 12.08808, 12.64537, 9.98656, 9.31874, 8.1817 ,
258
5.80269, 0. , 7.38877, 8.41906, 6.8504 , 7.29774,
259
9.2088 , 10.31162, 9.70575, 10.45564, 13.73927, 14.84133,
260
17.61261, 18.12427, 19.27123, 19.82935, 20.31297, 23.84286,
261
24.56468, 25.91998, 27.59428, 26.89288, 30.55842, 30.76624,
262
32.23747, 30.8686 , 34.10976, 33.50914, 35.42056, 34.64547,
263
34.19767, 35.53408, 35.0925 , 35.58014, 35.82126, 37.49003,
264
38.6495 , 38.10808, 35.42106, 37.82413, 38.53678, 38.03388,
265
37.13566, 36.62481, 36.8622 , 35.93997, 33.1206 , 33.81829,
266
31.46152, 33.72103, 32.12859, 33.34453, 30.4796 , 26.68134,
267
27.47971, 25.54979, 25.74229, 24.75989, 22.16485, 20.06477,
268
20.06272, 19.02226, 17.40359, 17.54345, 16.56831, 15.07742,
269
13.83543, 14.50581, 15.50799, 13.55086, 13.77702, 16.34443,
270
16.4955 , 17.40327, 20.09447, 19.53993, 20.64083, 23.14301,
271
25.73473, 23.91935, 30.1514 , 29.62866, 33.12758, 33.46496,
272
32.47884, 35.00942, 33.91675, 38.06303],
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[ 22.03428, 17.78924, 18.00935, 17.73952, 16.85701, 16.23874,
274
16.49484, 12.84075, 13.25671, 12.42781, 10.60831, 12.01962,
275
7.34823, 7.38877, 0. , 9.98466, 10.45042, 7.01399,
276
9.5126 , 10.22698, 8.29332, 10.75866, 15.09764, 14.55 ,
277
16.07545, 19.17678, 18.69286, 20.74564, 19.36248, 23.2144 ,
278
24.62428, 26.05861, 27.01352, 25.91131, 30.18725, 30.6706 ,
279
32.78994, 31.0901 , 34.2731 , 33.85408, 36.35145, 35.76726,
280
35.06246, 36.69763, 35.34281, 36.84744, 36.8362 , 38.82735,
281
39.99487, 39.19622, 36.6623 , 39.10442, 39.88191, 38.95773,
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38.89602, 38.43435, 38.31651, 37.10258, 34.93565, 35.54241,
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33.22748, 34.83971, 33.64244, 34.72378, 32.11209, 28.69735,
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29.37637, 27.27617, 26.28932, 25.69016, 23.88593, 21.52732,
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286
14.82818, 14.49505, 15.15638, 12.82821, 12.71296, 15.97897,
287
14.73869, 16.7043 , 19.42872, 18.50832, 20.11721, 22.55747,
288
25.22857, 23.0396 , 29.71055, 29.41731, 32.39176, 32.91178,
289
31.62541, 33.79263, 34.18837, 37.85652],
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292
7.61967, 8.41906, 9.98466, 0. , 7.63615, 9.92392,
293
10.04376, 10.49189, 11.12076, 12.59852, 12.42193, 13.54166,
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17.25956, 16.80266, 18.81578, 19.22611, 19.70099, 22.40398,
295
23.49591, 25.94766, 26.54727, 25.58126, 29.12877, 29.7836 ,
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31.07416, 29.98562, 33.17048, 33.35028, 34.18506, 34.59722,
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300
32.12772, 33.40582, 31.97045, 34.19075, 30.2786 , 26.83978,
301
27.6592 , 26.30551, 26.20587, 25.12388, 23.22648, 22.09752,
302
21.38396, 19.8089 , 18.83186, 18.86371, 18.34015, 15.42575,
303
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304
15.48099, 16.55105, 19.58731, 18.96449, 20.24747, 21.6386 ,
305
25.58849, 23.63285, 28.70622, 30.21742, 32.68447, 31.55284,
306
32.34425, 35.03969, 33.47656, 37.35049],
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[ 21.79021, 20.92378, 18.64376, 18.40617, 18.58137, 16.73334,
308
14.76539, 15.7665 , 15.73247, 12.28722, 11.679 , 10.03616,
309
8.88048, 6.8504 , 10.45042, 7.63615, 0. , 10.17132,
310
8.68748, 9.45034, 8.94115, 9.44003, 9.64568, 12.4589 ,
311
15.94741, 14.65608, 17.17587, 17.02335, 18.67632, 20.67866,
312
21.7796 , 24.38931, 25.59948, 25.17219, 28.8489 , 29.1434 ,
313
30.36341, 29.95065, 33.33854, 33.29967, 33.88558, 34.48264,
314
34.10065, 35.42542, 35.45233, 36.19829, 36.03964, 37.86692,
315
38.88208, 39.07201, 36.40368, 39.23049, 39.92573, 40.05261,
316
39.20976, 38.61636, 39.27939, 38.1003 , 35.6578 , 36.74788,
317
34.53888, 36.56434, 35.07799, 36.59537, 33.28937, 29.56233,
318
30.64956, 29.02811, 29.40351, 28.14274, 25.25644, 24.3272 ,
319
23.56296, 20.85461, 20.80185, 19.89348, 18.69289, 17.03854,
320
14.62848, 16.26612, 15.56155, 13.83998, 13.72169, 14.82471,
321
14.34678, 15.01213, 17.11687, 16.34701, 17.47794, 19.00668,
322
22.61177, 20.87814, 25.97138, 27.04819, 29.54295, 30.34684,
323
30.10012, 33.17501, 31.31277, 35.47796],
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17.37815, 13.80821, 14.29708, 13.48977, 9.86008, 10.82597,
326
8.03171, 7.29774, 7.01399, 9.92392, 10.17132, 0. ,
327
6.48226, 6.68 , 9.57466, 9.48408, 13.97397, 13.15679,
328
15.03983, 17.80094, 18.12113, 19.85319, 18.97979, 23.36183,
329
24.33233, 25.80959, 27.19217, 26.53318, 30.11932, 30.64921,
330
32.34859, 31.49555, 34.6749 , 33.71667, 36.43731, 36.39199,
331
35.67965, 37.13664, 35.96695, 37.67898, 37.95828, 39.3333 ,
332
40.59642, 39.92405, 37.99061, 40.17349, 40.90994, 39.98119,
333
39.92003, 39.6808 , 39.62528, 38.71391, 36.21198, 37.08048,
334
34.29651, 36.10593, 34.99984, 35.8496 , 33.74472, 29.52144,
335
30.75883, 28.63502, 28.32294, 27.26777, 25.1948 , 22.50728,
336
23.05361, 22.12662, 19.74132, 19.63274, 17.89876, 15.79792,
337
14.13342, 14.08034, 14.92898, 11.06895, 11.02782, 15.65033,
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14.30857, 14.46629, 17.74227, 17.97385, 18.06633, 21.34884,
339
22.96009, 22.50932, 28.30391, 28.4628 , 31.64773, 32.1907 ,
340
31.04573, 33.47638, 33.5043 , 36.83706],
341
[ 25.27884, 22.37953, 21.30424, 21.45177, 21.03104, 19.99725,
342
19.05223, 17.10528, 17.17558, 16.04661, 12.78319, 12.22157,
343
10.84203, 9.2088 , 9.5126 , 10.04376, 8.68748, 6.48226,
344
0. , 5.22655, 6.84299, 8.01445, 10.22964, 9.35169,
345
12.50172, 13.03384, 15.11671, 16.15319, 16.32212, 20.01859,
346
20.19876, 22.03234, 24.49275, 23.76956, 26.89441, 27.73295,
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29.57591, 29.31235, 32.28865, 31.99324, 33.95671, 34.64837,
348
34.25079, 35.22869, 34.85416, 36.69074, 37.04425, 38.1781 ,
349
39.77615, 39.60791, 38.021 , 40.62842, 41.3098 , 40.72945,
350
40.56478, 40.68159, 40.97394, 40.4026 , 37.91905, 39.08311,
351
36.66186, 38.48701, 37.36496, 38.4644 , 36.32379, 32.42384,
352
33.65172, 31.82761, 32.1881 , 30.80285, 28.93245, 26.4393 ,
353
26.65776, 25.03495, 23.12291, 22.70202, 21.31299, 18.64901,
354
16.46835, 16.81846, 16.44223, 12.42447, 12.98025, 14.62265,
355
13.85173, 13.32047, 13.81794, 14.45423, 14.59398, 17.7774 ,
356
18.83897, 18.33698, 23.71274, 24.45456, 27.512 , 27.97503,
357
27.44909, 29.9473 , 29.47687, 32.87905],
358
[ 25.33384, 22.50652, 20.79329, 22.03097, 21.37792, 19.9533 ,
359
19.09134, 17.0151 , 17.07269, 16.19534, 12.47705, 12.42638,
360
11.15163, 10.31162, 10.22698, 10.49189, 9.45034, 6.68 ,
361
5.22655, 0. , 9.1845 , 6.24097, 10.68858, 8.9892 ,
362
10.75227, 12.5549 , 13.42965, 14.83639, 15.19843, 18.37361,
363
20.11514, 21.80086, 23.21553, 22.42534, 25.94406, 26.90792,
364
28.49847, 28.38986, 31.34822, 30.44753, 32.95536, 33.76841,
365
33.23805, 34.76968, 33.79277, 36.13666, 36.16784, 37.57777,
366
39.01639, 38.73035, 37.37737, 39.86314, 40.9369 , 40.37831,
367
40.3905 , 40.18733, 40.75477, 40.04084, 38.03854, 39.0819 ,
368
36.62329, 38.68787, 37.66226, 39.09107, 36.48663, 32.61225,
369
34.05121, 32.23 , 32.67538, 31.35308, 29.36674, 27.44256,
370
27.60226, 26.2458 , 24.4287 , 24.17496, 22.32386, 20.26882,
371
17.63621, 18.1981 , 18.06242, 13.71252, 12.60611, 16.39878,
372
13.84417, 13.90252, 14.58239, 15.61773, 14.72379, 17.00739,
373
18.61744, 17.9266 , 22.92496, 24.15302, 26.40181, 27.03924,
374
25.82034, 28.7832 , 28.60458, 31.58328],
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[ 25.51721, 22.59182, 22.52019, 21.88416, 20.97864, 20.46002,
376
19.48543, 18.03523, 18.18613, 16.3577 , 15.20036, 14.81562,
377
12.21275, 9.70575, 8.29332, 11.12076, 8.94115, 9.57466,
378
6.84299, 9.1845 , 0. , 8.42136, 9.37678, 10.39484,
379
12.03637, 13.28049, 13.52418, 15.33503, 14.2314 , 18.60678,
380
18.65654, 20.52313, 22.48976, 21.9616 , 25.69566, 26.5576 ,
381
28.88904, 27.73913, 31.08385, 31.06195, 33.13063, 33.66469,
382
33.0211 , 34.43139, 34.32978, 35.45315, 35.945 , 38.07486,
383
39.28353, 39.22602, 37.42741, 40.16763, 41.16595, 40.59288,
384
40.07303, 40.5409 , 40.65161, 40.1262 , 37.85329, 38.93651,
385
37.02688, 38.83153, 37.52198, 39.07799, 36.60449, 33.43265,
386
34.30145, 32.81646, 32.20425, 31.53711, 29.60455, 27.68888,
387
27.2861 , 25.60395, 24.28611, 23.68602, 22.83922, 19.6321 ,
388
18.43043, 18.32631, 17.7009 , 14.75941, 14.24738, 14.81143,
389
14.39659, 14.09233, 14.84183, 13.11227, 14.67681, 17.10835,
390
19.10648, 17.05555, 23.72982, 22.93954, 26.36839, 26.99544,
391
26.43948, 28.60162, 28.39343, 32.42605],
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19.25793, 18.49492, 18.66698, 17.32154, 14.79868, 13.24075,
394
12.34706, 10.45564, 10.75866, 12.59852, 9.44003, 9.48408,
395
8.01445, 6.24097, 8.42136, 0. , 9.19567, 8.28483,
396
9.68535, 11.98782, 11.05565, 13.27899, 12.97288, 15.95134,
397
17.47779, 19.26536, 20.81256, 20.47412, 24.07951, 24.48853,
398
26.31214, 26.12805, 29.5516 , 28.71938, 30.9913 , 31.6734 ,
399
31.05312, 32.90775, 32.68055, 34.31807, 34.6565 , 36.33305,
400
37.55324, 37.84719, 36.54117, 39.18647, 39.96285, 39.6461 ,
401
39.38249, 39.77171, 39.84257, 39.44919, 37.48819, 38.87541,
402
36.52095, 39.03388, 38.04894, 39.2854 , 37.05129, 33.33446,
403
34.86519, 33.37436, 33.51843, 32.6792 , 30.40374, 28.64096,
404
28.81112, 27.30426, 26.30338, 25.2772 , 23.65439, 21.82505,
405
19.44844, 19.69742, 19.3097 , 17.16471, 14.47088, 16.52024,
406
15.93936, 15.41702, 15.60782, 15.3568 , 14.63636, 16.4597 ,
407
17.9459 , 16.78672, 21.70309, 21.98327, 24.07691, 26.11801,
408
24.12467, 26.69992, 26.15777, 29.63547],
409
[ 27.13757, 25.36422, 24.35227, 24.92398, 23.27987, 22.72976,
410
20.07018, 21.4005 , 20.99351, 19.0178 , 18.06249, 15.91179,
411
16.11929, 13.73927, 15.09764, 12.42193, 9.64568, 13.97397,
412
10.22964, 10.68858, 9.37678, 9.19567, 0. , 6.87271,
413
10.56088, 8.63342, 11.01072, 10.93865, 11.45914, 14.5144 ,
414
14.09155, 17.70246, 18.65296, 19.02075, 22.11715, 22.68976,
415
23.99425, 24.33084, 28.06753, 28.67934, 28.75474, 31.08502,
416
30.53155, 31.69899, 32.62122, 33.92971, 33.80767, 36.2285 ,
417
36.50334, 37.53278, 36.5014 , 39.07491, 40.15724, 40.40674,
418
39.85148, 40.40163, 40.9679 , 40.5153 , 38.42327, 40.1212 ,
419
38.22838, 40.08247, 38.99665, 41.12947, 38.17204, 34.9892 ,
420
36.38785, 35.95878, 35.6227 , 34.90092, 32.5457 , 31.91806,
421
31.28384, 28.86779, 28.98518, 27.6702 , 26.58669, 23.92989,
422
21.86083, 22.75265, 21.11808, 18.7693 , 18.18955, 18.2176 ,
423
17.45544, 15.00264, 15.51133, 13.46033, 13.79958, 13.68436,
424
16.58338, 15.70851, 18.99807, 20.56008, 22.44251, 22.97965,
425
23.45606, 26.30876, 24.09575, 27.8713 ],
426
[ 27.77099, 24.53657, 24.04257, 25.28642, 23.47925, 23.22363,
427
21.44923, 20.91953, 20.83302, 20.5046 , 17.95878, 16.17176,
428
16.0975 , 14.84133, 14.55 , 13.54166, 12.4589 , 13.15679,
429
9.35169, 8.9892 , 10.39484, 8.28483, 6.87271, 0. ,
430
7.72073, 8.27576, 9.50557, 10.31176, 9.92433, 12.30625,
431
12.50632, 15.65258, 16.85322, 16.28059, 19.40831, 20.28063,
432
21.80124, 22.2785 , 25.59015, 26.20645, 27.03954, 29.20724,
433
28.64062, 29.85524, 29.8061 , 32.57415, 32.29469, 34.31277,
434
34.99807, 35.82 , 35.31492, 37.94267, 38.60944, 38.67121,
435
38.95962, 39.63135, 39.99892, 39.64319, 38.13686, 39.73796,
436
37.88513, 39.57072, 38.9161 , 40.94059, 38.2891 , 35.07866,
437
36.89862, 36.20281, 36.05376, 35.34433, 33.67934, 32.25061,
438
32.36628, 30.7808 , 30.11484, 29.01616, 27.92706, 25.32419,
439
23.29639, 24.12436, 22.42396, 19.7537 , 19.01006, 19.94131,
440
18.33339, 16.81857, 15.99741, 15.0617 , 14.77595, 14.59106,
441
16.3054 , 15.56181, 17.98122, 20.15022, 21.20001, 21.39029,
442
21.13788, 23.4717 , 22.23873, 25.49112],
443
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444
26.16354, 24.56468, 24.42795, 23.95953, 21.80304, 20.81994,
445
19.45663, 17.61261, 16.07545, 17.25956, 15.94741, 15.03983,
446
12.50172, 10.75227, 12.03637, 9.68535, 10.56088, 7.72073,
447
0. , 9.87641, 7.6598 , 9.49731, 7.49547, 12.71031,
448
13.12007, 15.09318, 15.76199, 15.39935, 19.70394, 21.41588,
449
23.13548, 22.85749, 26.18616, 25.68635, 28.9516 , 30.93716,
450
30.0345 , 32.15204, 31.65812, 34.38793, 34.38638, 37.50663,
451
38.17473, 38.39304, 38.36668, 40.71544, 42.31539, 42.04724,
452
41.86037, 42.90939, 43.56974, 43.4618 , 42.34263, 43.41177,
453
41.79768, 43.79152, 42.99372, 45.43309, 42.39361, 39.51926,
454
41.2064 , 40.11474, 39.74911, 39.34168, 37.45432, 35.8801 ,
455
35.90349, 34.72309, 33.54021, 32.87432, 31.3026 , 28.63784,
456
26.36769, 26.4844 , 25.34082, 21.25983, 19.4387 , 21.35453,
457
18.66931, 16.58331, 15.29044, 14.5311 , 14.07159, 12.69685,
458
13.75561, 12.45704, 16.48731, 16.18279, 18.19724, 18.82112,
459
17.69826, 20.07196, 20.9814 , 23.64271],
460
[ 30.12906, 28.8102 , 27.14583, 27.8259 , 27.08492, 26.83688,
461
24.71872, 24.98275, 24.65435, 23.43756, 21.94482, 19.82228,
462
20.33958, 18.12427, 19.17678, 16.80266, 14.65608, 17.80094,
463
13.03384, 12.5549 , 13.28049, 11.98782, 8.63342, 8.27576,
464
9.87641, 0. , 7.98874, 5.38369, 9.95786, 10.82054,
465
11.0462 , 12.89802, 15.44491, 14.85573, 17.38129, 19.47045,
466
20.77089, 21.32264, 24.07172, 24.28534, 25.596 , 27.93375,
467
27.86256, 28.87872, 29.7082 , 31.88982, 31.87346, 34.12199,
468
35.33819, 36.0731 , 35.88703, 38.71968, 40.48097, 40.65492,
469
40.04445, 40.78432, 42.24041, 42.36186, 40.86445, 42.22587,
470
40.89454, 43.17864, 41.97252, 44.85097, 41.45324, 38.91288,
471
40.27944, 39.6453 , 40.59724, 39.49418, 37.70761, 36.65188,
472
36.33936, 34.78051, 33.80123, 33.49258, 32.35566, 29.75799,
473
27.30116, 28.38011, 27.09472, 23.18208, 22.41711, 22.75371,
474
20.88887, 19.50611, 15.96133, 15.86852, 14.98222, 13.66391,
475
14.86599, 12.41707, 15.52539, 16.68747, 18.30724, 16.95519,
476
17.37892, 20.49274, 18.30611, 21.75684],
477
[ 30.853 , 28.67001, 27.9384 , 29.18638, 27.63842, 27.09796,
478
25.7368 , 25.20224, 25.16361, 24.50878, 22.94088, 21.65753,
479
21.24043, 19.27123, 18.69286, 18.81578, 17.17587, 18.12113,
480
15.11671, 13.42965, 13.52418, 11.05565, 11.01072, 9.50557,
481
7.6598 , 7.98874, 0. , 6.64528, 4.59801, 8.21652,
482
10.31466, 11.16178, 12.08679, 11.83932, 15.09664, 17.18703,
483
19.54388, 19.20711, 22.42597, 21.78585, 24.86467, 26.82595,
484
26.17402, 28.22608, 28.33647, 30.77347, 31.09911, 33.82732,
485
34.63993, 35.32224, 35.64687, 38.19558, 40.17273, 39.9043 ,
486
39.71271, 40.82968, 41.59044, 41.89523, 40.82556, 42.24267,
487
40.88634, 43.2909 , 42.33337, 45.05862, 42.17539, 39.71804,
488
41.17056, 40.67256, 40.65653, 40.19097, 38.65435, 37.60561,
489
37.35235, 36.34129, 35.23204, 34.77337, 33.6225 , 30.92734,
490
29.00015, 29.40958, 28.36382, 25.0391 , 22.59333, 24.07796,
491
21.93502, 20.62995, 18.16191, 17.02272, 15.54819, 14.56199,
492
15.3057 , 12.64367, 16.45475, 15.71403, 16.86429, 16.85299,
493
15.00269, 17.43522, 17.0517 , 20.42138],
494
[ 31.25053, 29.99149, 28.31876, 29.3961 , 28.49791, 28.27618,
495
26.60446, 26.47583, 26.40833, 25.26128, 24.29869, 22.19242,
496
22.37157, 19.82935, 20.74564, 19.22611, 17.02335, 19.85319,
497
16.15319, 14.83639, 15.33503, 13.27899, 10.93865, 10.31176,
498
9.49731, 5.38369, 6.64528, 0. , 7.92917, 9.13679,
499
9.53346, 10.47996, 12.16654, 11.7129 , 15.01867, 17.3945 ,
500
18.42663, 18.36001, 21.25014, 21.14056, 23.39958, 25.64935,
501
25.29954, 27.11021, 27.88541, 29.88329, 29.87818, 33.15122,
502
33.91166, 34.60562, 34.9862 , 37.6223 , 39.74094, 40.05704,
503
39.15768, 40.26411, 41.81453, 42.1735 , 41.17397, 42.24356,
504
41.4135 , 43.87194, 42.72225, 46.08496, 42.30557, 40.15065,
505
41.69059, 41.24556, 41.85591, 41.23647, 39.41798, 38.64347,
506
38.26693, 37.14527, 36.28322, 36.14132, 34.9677 , 32.65462,
507
30.32245, 31.15585, 30.05495, 26.14201, 24.6254 , 25.64368,
508
23.38049, 21.94394, 18.90934, 18.07516, 17.34202, 14.70928,
509
16.17006, 13.04202, 15.86513, 15.06125, 16.67207, 15.02326,
510
14.43571, 17.62774, 15.52057, 19.39125],
511
[ 32.01368, 29.0992 , 29.19352, 30.42798, 28.08892, 28.3494 ,
512
26.8787 , 26.01966, 26.00333, 25.60517, 24.32754, 23.10866,
513
22.50594, 20.31297, 19.36248, 19.70099, 18.67632, 18.97979,
514
16.32212, 15.19843, 14.2314 , 12.97288, 11.45914, 9.92433,
515
7.49547, 9.95786, 4.59801, 7.92917, 0. , 9.46759,
516
9.53989, 10.77149, 10.67123, 10.77957, 14.38107, 16.55356,
517
18.86377, 17.93757, 21.53923, 21.5 , 24.50229, 26.72856,
518
25.8231 , 27.87236, 28.08681, 30.54159, 30.74741, 34.21383,
519
34.31615, 35.0456 , 35.81848, 38.00399, 40.05607, 39.79457,
520
39.61693, 41.10429, 41.69482, 42.04974, 41.08039, 42.4485 ,
521
41.31527, 43.35611, 42.53551, 45.50379, 42.54538, 40.30517,
522
41.79641, 41.68827, 40.95449, 40.88777, 39.44077, 38.47113,
523
38.21591, 37.33843, 36.35944, 35.80693, 34.8564 , 31.85679,
524
30.32951, 30.47848, 29.27892, 25.8884 , 23.90214, 25.36182,
525
23.14462, 21.09032, 19.56871, 17.40934, 16.72036, 15.08113,
526
16.01239, 13.78221, 17.09382, 15.61569, 17.24015, 16.33925,
527
15.18723, 17.0286 , 16.96968, 20.31666],
528
[ 32.92915, 30.78134, 30.31387, 31.81182, 29.94971, 29.75656,
529
27.97926, 28.37676, 28.48816, 28.0269 , 26.55776, 24.91478,
530
24.89152, 23.84286, 23.2144 , 22.40398, 20.67866, 23.36183,
531
20.01859, 18.37361, 18.60678, 15.95134, 14.5144 , 12.30625,
532
12.71031, 10.82054, 8.21652, 9.13679, 9.46759, 0. ,
533
8.89237, 11.56402, 9.66796, 8.7428 , 11.95979, 14.08575,
534
15.80045, 16.65181, 19.74296, 20.61442, 21.15351, 24.45494,
535
23.9113 , 26.09147, 26.17295, 29.57049, 28.96665, 31.93696,
536
32.42409, 34.06939, 34.49619, 37.51745, 38.87821, 39.44799,
537
39.80638, 40.83166, 41.71964, 41.67128, 41.61213, 43.2428 ,
538
42.36568, 44.39476, 43.77865, 46.84558, 43.53456, 41.47749,
539
43.3667 , 43.24129, 43.27906, 42.89426, 41.53307, 41.05796,
540
40.77052, 39.41463, 39.1773 , 38.1895 , 37.36602, 34.97812,
541
33.00745, 34.10653, 32.18818, 29.92886, 27.45379, 28.27133,
542
25.75202, 25.34647, 22.44188, 20.82485, 19.82573, 16.70077,
543
18.83691, 15.85836, 15.60841, 17.8028 , 15.28365, 15.19425,
544
13.84108, 16.11862, 13.96013, 17.63429],
545
[ 34.80687, 32.60362, 32.49497, 33.20848, 31.60411, 31.77772,
546
30.01728, 30.43507, 30.39505, 30.02525, 29.0597 , 26.51025,
547
26.47231, 24.56468, 24.62428, 23.49591, 21.7796 , 24.33233,
548
20.19876, 20.11514, 18.65654, 17.47779, 14.09155, 12.50632,
549
13.12007, 11.0462 , 10.31466, 9.53346, 9.53989, 8.89237,
550
0. , 7.18087, 9.42639, 10.38858, 11.58877, 12.91252,
551
14.59769, 15.59285, 18.95488, 20.67684, 20.8958 , 24.70048,
552
24.0165 , 25.43853, 26.95084, 29.21772, 29.55268, 32.62558,
553
32.93689, 34.88785, 35.60229, 38.44528, 39.2932 , 39.98048,
554
39.73092, 41.86321, 42.40135, 43.0919 , 42.45519, 44.1862 ,
555
43.47623, 45.37599, 44.76722, 47.773 , 44.99764, 42.85482,
556
45.0001 , 44.84355, 44.80852, 44.71783, 43.31817, 42.17357,
557
42.00564, 40.73932, 40.54667, 39.4803 , 38.72058, 36.16405,
558
34.29426, 35.27955, 33.02234, 30.89456, 29.48465, 28.8475 ,
559
27.86781, 25.48297, 22.56247, 20.68579, 20.34994, 17.57016,
560
17.81885, 16.39775, 15.34486, 15.15469, 14.83316, 14.19401,
561
15.20368, 15.44059, 11.80224, 16.78251],
562
[ 34.67094, 33.06432, 32.53298, 33.36339, 32.35099, 32.50386,
563
31.59176, 31.12544, 31.12778, 31.11886, 30.47032, 27.84524,
564
28.19409, 25.91998, 26.05861, 25.94766, 24.38931, 25.80959,
565
22.03234, 21.80086, 20.52313, 19.26536, 17.70246, 15.65258,
566
15.09318, 12.89802, 11.16178, 10.47996, 10.77149, 11.56402,
567
7.18087, 0. , 8.74195, 9.19296, 8.9676 , 10.89087,
568
13.36331, 12.96807, 15.25494, 15.85912, 18.74728, 20.99385,
569
20.58536, 21.90675, 23.7641 , 25.59202, 26.79648, 29.58366,
570
30.67949, 31.89102, 33.4665 , 36.09133, 37.70993, 37.82863,
571
37.1605 , 39.86674, 40.65224, 42.17263, 41.48734, 42.91311,
572
42.56542, 45.03955, 44.26307, 47.54766, 44.95504, 43.36693,
573
45.22628, 45.15693, 45.74134, 45.58144, 44.57787, 43.24457,
574
43.23535, 43.03554, 41.97252, 41.7482 , 41.05749, 38.72517,
575
37.14338, 37.61494, 36.50124, 33.46255, 32.11582, 32.19497,
576
31.24603, 29.25163, 25.58682, 24.49213, 23.73966, 21.92186,
577
20.66609, 18.42641, 19.3634 , 16.24486, 17.24548, 15.15315,
578
13.59916, 12.73676, 10.23459, 14.84621],
579
[ 34.61157, 32.35053, 32.54342, 34.03547, 31.64065, 32.5482 ,
580
31.2204 , 31.08021, 31.04052, 31.15891, 31.03937, 28.94428,
581
29.03612, 27.59428, 27.01352, 26.54727, 25.59948, 27.19217,
582
24.49275, 23.21553, 22.48976, 20.81256, 18.65296, 16.85322,
583
15.76199, 15.44491, 12.08679, 12.16654, 10.67123, 9.66796,
584
9.42639, 8.74195, 0. , 4.97625, 7.39172, 8.51026,
585
10.14648, 9.50175, 13.1454 , 14.11243, 15.8578 , 19.62747,
586
18.29823, 20.97263, 21.55663, 24.21139, 24.16038, 28.57247,
587
28.2877 , 29.74339, 31.3773 , 33.75635, 35.79133, 36.21335,
588
36.02599, 38.43108, 39.29054, 40.11502, 40.44974, 41.86014,
589
41.7082 , 43.69002, 43.19493, 47.14492, 43.81483, 42.6301 ,
590
44.81877, 45.24839, 44.99179, 45.27901, 44.24326, 44.00885,
591
43.62399, 43.42716, 43.097 , 42.57723, 41.90128, 39.82617,
592
38.47462, 39.17248, 37.86386, 34.99443, 33.29005, 34.59372,
593
32.25062, 30.55199, 28.63669, 26.61145, 26.02174, 22.74625,
594
23.58481, 21.28107, 21.00584, 19.89187, 18.45627, 16.11799,
595
14.52011, 14.22711, 12.12231, 15.73701],
596
[ 33.95445, 31.31204, 31.6677 , 33.03364, 30.7586 , 31.99727,
597
30.74726, 29.96861, 30.02038, 30.49865, 29.92437, 28.23706,
598
28.11855, 26.89288, 25.91131, 25.58126, 25.17219, 26.53318,
599
23.76956, 22.42534, 21.9616 , 20.47412, 19.02075, 16.28059,
600
15.39935, 14.85573, 11.83932, 11.7129 , 10.77957, 8.7428 ,
601
10.38858, 9.19296, 4.97625, 0. , 6.72148, 10.12496,
602
12.00924, 10.13169, 12.83076, 14.2167 , 16.72792, 19.37301,
603
18.59613, 21.00058, 20.66568, 24.48285, 23.84352, 28.26891,
604
28.32281, 29.3094 , 30.90888, 33.39326, 35.6437 , 35.93431,
605
36.08269, 37.85734, 39.11931, 39.73362, 40.26473, 41.36942,
606
41.39021, 43.28881, 42.72848, 46.85017, 43.10439, 42.13604,
607
43.99537, 44.34038, 44.26734, 44.39004, 43.65807, 43.18833,
608
42.95227, 42.93121, 42.14583, 41.96176, 41.49189, 39.07646,
609
37.79461, 38.59134, 37.2521 , 34.09993, 32.53784, 33.99566,
610
31.15287, 30.43379, 27.85509, 26.08889, 25.78955, 22.49509,
611
23.83891, 20.37192, 20.98593, 20.20119, 18.99761, 15.27863,
612
13.7462 , 13.92431, 12.80535, 16.20137],
613
[ 36.09099, 33.96212, 34.4333 , 35.82444, 33.58783, 34.67355,
614
33.36662, 33.06401, 33.06101, 33.86459, 33.13454, 31.0608 ,
615
31.78424, 30.55842, 30.18725, 29.12877, 28.8489 , 30.11932,
616
26.89441, 25.94406, 25.69566, 24.07951, 22.11715, 19.40831,
617
19.70394, 17.38129, 15.09664, 15.01867, 14.38107, 11.95979,
618
11.58877, 8.9676 , 7.39172, 6.72148, 0. , 6.43367,
619
8.98397, 8.67729, 10.0527 , 12.31282, 13.61151, 17.29523,
620
16.952 , 18.20422, 19.0518 , 23.06074, 23.05218, 26.13901,
621
26.38234, 28.09777, 30.76486, 33.11761, 35.1361 , 35.41829,
622
35.86916, 38.17342, 39.25199, 40.55388, 40.93513, 42.5099 ,
623
42.56349, 44.52465, 44.12784, 48.09543, 45.13455, 44.19635,
624
46.17291, 46.91914, 47.23808, 47.21417, 46.86937, 46.30617,
625
46.18952, 46.3353 , 45.46555, 45.29483, 44.96068, 42.56432,
626
41.36339, 42.23577, 40.86225, 37.9703 , 36.62617, 37.63698,
627
35.45185, 34.21791, 31.08457, 29.69294, 28.68309, 26.09517,
628
26.05857, 23.59887, 22.7285 , 22.24654, 20.53253, 16.26812,
629
15.10008, 13.99427, 10.96839, 13.95765],
630
[ 34.39821, 32.70361, 33.06171, 34.7116 , 32.51966, 33.19062,
631
32.19782, 32.57304, 32.51077, 33.37975, 33.19895, 30.49635,
632
31.68759, 30.76624, 30.6706 , 29.7836 , 29.1434 , 30.64921,
633
27.73295, 26.90792, 26.5576 , 24.48853, 22.68976, 20.28063,
634
21.41588, 19.47045, 17.18703, 17.3945 , 16.55356, 14.08575,
635
12.91252, 10.89087, 8.51026, 10.12496, 6.43367, 0. ,
636
5.13455, 7.19981, 9.26742, 11.82888, 10.17125, 14.78769,
637
13.87506, 15.22203, 17.04526, 19.97496, 20.45104, 22.81966,
638
22.94849, 25.40346, 27.90575, 30.36558, 31.45698, 32.01961,
639
32.50931, 35.50764, 35.83888, 37.37873, 37.77828, 39.79016,
640
39.73051, 41.74234, 41.66611, 45.21051, 42.9827 , 41.96344,
641
44.45906, 45.37185, 45.70899, 45.86452, 45.49593, 45.23056,
642
45.08133, 45.40294, 45.13354, 44.55667, 44.24469, 42.6187 ,
643
41.59934, 42.40437, 41.24915, 39.18714, 37.89513, 38.80147,
644
37.34563, 35.75256, 33.50089, 31.99846, 30.98915, 28.78806,
645
28.57053, 27.01304, 25.56683, 25.4267 , 23.23683, 21.19257,
646
19.15064, 17.6646 , 13.95903, 16.88417],
647
[ 35.29278, 34.0075 , 33.8104 , 35.8487 , 33.71852, 34.46902,
648
33.24557, 33.997 , 33.91746, 34.65544, 34.69406, 31.58452,
649
33.16023, 32.23747, 32.78994, 31.07416, 30.36341, 32.34859,
650
29.57591, 28.49847, 28.88904, 26.31214, 23.99425, 21.80124,
651
23.13548, 20.77089, 19.54388, 18.42663, 18.86377, 15.80045,
652
14.59769, 13.36331, 10.14648, 12.00924, 8.98397, 5.13455,
653
0. , 7.16407, 9.04734, 11.89485, 7.77198, 14.16043,
654
13.10023, 14.59801, 16.76365, 19.57846, 19.38376, 22.39702,
655
21.86462, 24.72382, 27.4199 , 29.752 , 30.72862, 31.93212,
656
32.14663, 35.16599, 35.88763, 37.34873, 38.05632, 39.9811 ,
657
40.13104, 42.11747, 42.08783, 46.05367, 43.28691, 42.38342,
658
45.19904, 46.24403, 46.80226, 47.00371, 46.37995, 46.44777,
659
46.32251, 46.58154, 46.66496, 46.07288, 45.61367, 44.385 ,
660
43.10472, 44.24015, 42.9754 , 40.85532, 39.73088, 40.79164,
661
39.14055, 37.3534 , 35.4027 , 33.98145, 32.97956, 30.08218,
662
30.29887, 29.00976, 26.63001, 27.03646, 24.48703, 22.05865,
663
20.62081, 19.57784, 14.73243, 17.36648],
664
[ 33.43954, 31.79899, 32.32825, 33.89059, 31.59205, 33.13995,
665
32.26498, 32.11079, 32.16109, 33.14589, 33.79095, 31.13131,
666
32.00993, 30.8686 , 31.0901 , 29.98562, 29.95065, 31.49555,
667
29.31235, 28.38986, 27.73913, 26.12805, 24.33084, 22.2785 ,
668
22.85749, 21.32264, 19.20711, 18.36001, 17.93757, 16.65181,
669
15.59285, 12.96807, 9.50175, 10.13169, 8.67729, 7.19981,
670
7.16407, 0. , 5.29396, 8.67893, 9.00802, 11.50156,
671
10.13767, 12.58519, 13.75226, 16.33162, 16.16096, 21.27586,
672
20.36335, 22.08521, 24.78172, 26.80699, 28.87533, 29.58085,
673
29.35632, 32.37612, 33.42273, 35.02844, 35.98014, 37.25958,
674
38.02517, 40.01821, 39.69333, 44.39596, 40.98925, 40.81211,
675
43.15676, 44.3192 , 44.52264, 45.11777, 44.80329, 44.7664 ,
676
44.57585, 45.54288, 45.13382, 45.13769, 45.036 , 43.45157,
677
42.69738, 43.68518, 42.70208, 40.23943, 39.23902, 40.71097,
678
38.75821, 37.46691, 35.83383, 33.96711, 33.65132, 30.88072,
679
31.70992, 29.12309, 28.97938, 27.45576, 26.55069, 22.69609,
680
21.31464, 19.94906, 16.52504, 20.00963],
681
[ 35.50327, 34.1394 , 34.54666, 36.02136, 34.09468, 35.80184,
682
35.20755, 34.68809, 34.72522, 36.03802, 36.57048, 34.00834,
683
35.12134, 34.10976, 34.2731 , 33.17048, 33.33854, 34.6749 ,
684
32.28865, 31.34822, 31.08385, 29.5516 , 28.06753, 25.59015,
685
26.18616, 24.07172, 22.42597, 21.25014, 21.53923, 19.74296,
686
18.95488, 15.25494, 13.1454 , 12.83076, 10.0527 , 9.26742,
687
9.04734, 5.29396, 0. , 7.02491, 7.91346, 9.49832,
688
8.97779, 10.53213, 11.64105, 15.08541, 14.93272, 19.4389 ,
689
19.22241, 20.51852, 24.28367, 26.21266, 28.62454, 29.21067,
690
29.13434, 32.23565, 33.74681, 35.77881, 37.02082, 38.04921,
691
39.25933, 41.2876 , 41.02127, 45.92867, 42.53998, 42.80247,
692
45.02922, 46.2601 , 46.99824, 47.39798, 47.50405, 47.43771,
693
47.28364, 48.66654, 47.8922 , 48.31191, 48.29145, 46.78708,
694
46.0658 , 47.00178, 46.27576, 43.40774, 42.66151, 44.23342,
695
42.09818, 41.14137, 38.8066 , 37.42541, 36.96229, 34.28354,
696
34.64723, 31.85059, 31.58249, 30.04064, 28.92462, 24.27898,
697
22.53438, 20.85881, 17.8264 , 20.38759],
698
[ 34.96861, 34.08447, 33.66703, 35.60052, 34.22325, 35.25591,
699
35.27066, 34.12659, 34.26106, 35.51766, 36.01451, 33.61703,
700
34.61314, 33.50914, 33.85408, 33.35028, 33.29967, 33.71667,
701
31.99324, 30.44753, 31.06195, 28.71938, 28.67934, 26.20645,
702
25.68635, 24.28534, 21.78585, 21.14056, 21.5 , 20.61442,
703
20.67684, 15.85912, 14.11243, 14.2167 , 12.31282, 11.82888,
704
11.89485, 8.67893, 7.02491, 0. , 11.6549 , 10.73557,
705
9.71187, 12.80952, 12.4755 , 15.06586, 16.27814, 20.16314,
706
21.00477, 21.04933, 24.7121 , 26.38835, 29.5294 , 29.42525,
707
28.82948, 32.05309, 33.66472, 36.01266, 37.14096, 37.87527,
708
38.78613, 41.51105, 41.02762, 45.8564 , 42.62709, 42.66475,
709
44.95803, 45.70734, 46.90492, 47.20804, 47.14969, 46.86 ,
710
46.8637 , 48.70376, 47.41032, 48.23058, 47.81376, 46.72845,
711
45.78045, 46.55168, 46.44799, 43.06789, 41.80521, 44.2389 ,
712
41.92408, 40.96925, 38.73615, 37.92498, 36.83463, 34.6773 ,
713
34.46336, 31.84197, 32.48614, 29.86623, 29.37943, 25.34313,
714
22.18623, 20.58748, 18.68724, 20.88898],
715
[ 34.61776, 34.40636, 34.21985, 36.08047, 34.16007, 35.33808,
716
34.3224 , 35.42161, 35.29431, 36.24468, 37.16413, 34.00148,
717
36.07251, 35.42056, 36.35145, 34.18506, 33.88558, 36.43731,
718
33.95671, 32.95536, 33.13063, 30.9913 , 28.75474, 27.03954,
719
28.9516 , 25.596 , 24.86467, 23.39958, 24.50229, 21.15351,
720
20.8958 , 18.74728, 15.8578 , 16.72792, 13.61151, 10.17125,
721
7.77198, 9.00802, 7.91346, 11.6549 , 0. , 8.82796,
722
8.51924, 8.99769, 12.41161, 14.38248, 13.54233, 16.59245,
723
15.72496, 18.98626, 22.36856, 24.60879, 26.09397, 27.63374,
724
27.67937, 30.67328, 31.99623, 33.83917, 35.09395, 36.84287,
725
37.83474, 39.87093, 39.81846, 44.45979, 41.3634 , 41.50962,
726
44.11761, 45.79608, 46.84759, 47.06841, 46.96281, 47.70312,
727
47.32522, 48.293 , 48.42568, 48.33951, 48.32094, 47.48303,
728
46.66074, 47.9282 , 47.12264, 45.05578, 44.3409 , 45.66062,
729
43.92436, 42.83903, 40.98259, 39.58649, 38.84249, 36.13211,
730
36.84814, 34.73249, 33.17741, 33.3556 , 31.06652, 27.70613,
731
26.09503, 25.22437, 20.37247, 22.75393],
732
[ 31.52205, 32.09843, 31.60984, 33.37669, 32.3283 , 33.38177,
733
33.45572, 33.62916, 33.7662 , 35.04257, 36.42303, 33.33828,
734
35.37259, 34.64547, 35.76726, 34.59722, 34.48264, 36.39199,
735
34.64837, 33.76841, 33.66469, 31.6734 , 31.08502, 29.20724,
736
30.93716, 27.93375, 26.82595, 25.64935, 26.72856, 24.45494,
737
24.70048, 20.99385, 19.62747, 19.37301, 17.29523, 14.78769,
738
14.16043, 11.50156, 9.49832, 10.73557, 8.82796, 0. ,
739
3.87115, 4.46637, 8.17529, 8.09024, 8.56917, 11.67969,
740
12.43841, 13.85593, 17.57202, 19.71272, 21.99594, 22.85153,
741
22.16445, 25.45666, 27.04794, 29.67531, 31.04348, 32.13853,
742
33.7628 , 36.48198, 36.14058, 41.01457, 37.91637, 38.79497,
743
40.96397, 42.64609, 44.26794, 44.55381, 44.89301, 45.34457,
744
45.22525, 47.30472, 46.71893, 47.3816 , 47.69802, 47.15203,
745
46.77432, 47.78838, 47.81124, 45.64705, 44.93698, 46.70672,
746
45.20662, 44.90814, 43.03585, 41.8455 , 41.35057, 39.45815,
747
40.11168, 37.08534, 37.64673, 36.20666, 35.37051, 31.85248,
748
29.10527, 28.10747, 24.43796, 27.26505],
749
[ 31.5479 , 31.55098, 31.44096, 33.34017, 31.89116, 33.04059,
750
33.21501, 33.16394, 33.40285, 34.67094, 36.18591, 33.20841,
751
34.85009, 34.19767, 35.06246, 34.20947, 34.10065, 35.67965,
752
34.25079, 33.23805, 33.0211 , 31.05312, 30.53155, 28.64062,
753
30.0345 , 27.86256, 26.17402, 25.29954, 25.8231 , 23.9113 ,
754
24.0165 , 20.58536, 18.29823, 18.59613, 16.952 , 13.87506,
755
13.10023, 10.13767, 8.97779, 9.71187, 8.51924, 3.87115,
756
0. , 6.12594, 7.96356, 7.57526, 8.45868, 12.97798,
757
12.90918, 14.31407, 17.64249, 19.73502, 21.71174, 22.56943,
758
21.94117, 25.69766, 26.75678, 29.24043, 30.87281, 31.9451 ,
759
33.52238, 36.04839, 35.83875, 40.75469, 37.69173, 38.4327 ,
760
40.95094, 42.4804 , 43.60742, 44.22534, 44.42682, 44.91905,
761
44.77389, 46.85295, 46.45624, 46.96242, 47.13319, 46.71132,
762
46.36086, 47.34189, 47.27088, 45.18382, 44.30438, 46.30564,
763
44.68842, 44.1482 , 42.80237, 41.36941, 40.89437, 38.88697,
764
39.62182, 36.88549, 37.35607, 35.71787, 34.81861, 31.64177,
765
28.85684, 27.61326, 24.23459, 27.25467],
766
[ 31.86234, 32.21933, 32.23245, 33.79942, 32.43132, 33.91149,
767
33.77282, 34.14988, 34.11146, 35.65553, 37.09342, 33.84176,
768
36.19004, 35.53408, 36.69763, 35.18721, 35.42542, 37.13664,
769
35.22869, 34.76968, 34.43139, 32.90775, 31.69899, 29.85524,
770
32.15204, 28.87872, 28.22608, 27.11021, 27.87236, 26.09147,
771
25.43853, 21.90675, 20.97263, 21.00058, 18.20422, 15.22203,
772
14.59801, 12.58519, 10.53213, 12.80952, 8.99769, 4.46637,
773
6.12594, 0. , 8.44401, 7.97982, 8.83251, 10.38464,
774
10.82867, 12.8995 , 17.10962, 18.97275, 20.8149 , 21.56576,
775
21.19765, 24.98392, 26.22855, 29.18584, 30.1669 , 31.64604,
776
33.19261, 35.58516, 35.3853 , 40.18287, 37.57579, 38.53515,
777
40.71094, 42.71524, 44.28372, 44.57255, 45.13821, 45.55069,
778
45.47875, 47.62256, 47.08008, 47.68002, 48.15121, 47.49823,
779
47.35146, 48.3686 , 48.33511, 46.28713, 46.10429, 47.57535,
780
46.38933, 45.72293, 43.99917, 42.7842 , 42.32976, 40.70953,
781
41.06713, 38.47232, 38.78739, 37.64475, 36.9269 , 33.11543,
782
30.98764, 29.72708, 25.83973, 28.4507 ],
783
[ 30.85453, 29.68935, 30.68488, 32.42774, 30.52192, 32.75336,
784
32.98931, 31.96731, 32.13639, 34.59658, 35.61312, 33.36215,
785
34.77939, 35.0925 , 35.34281, 34.12158, 35.45233, 35.96695,
786
34.85416, 33.79277, 34.32978, 32.68055, 32.62122, 29.8061 ,
787
31.65812, 29.7082 , 28.33647, 27.88541, 28.08681, 26.17295,
788
26.95084, 23.7641 , 21.55663, 20.66568, 19.0518 , 17.04526,
789
16.76365, 13.75226, 11.64105, 12.4755 , 12.41161, 8.17529,
790
7.96356, 8.44401, 0. , 9.43444, 8.12104, 10.99449,
791
11.78021, 11.37028, 14.90543, 16.80241, 19.058 , 19.18607,
792
20.42547, 22.96086, 24.54862, 26.69301, 29.07142, 29.81017,
793
31.49645, 33.32921, 33.38918, 38.71385, 35.4746 , 36.61224,
794
39.11164, 40.61639, 42.02245, 42.49394, 43.59005, 43.80397,
795
43.89376, 46.64783, 45.65345, 46.63616, 47.08335, 46.48834,
796
46.45531, 47.75785, 47.61879, 45.29908, 45.03967, 47.61192,
797
45.31081, 45.41523, 44.16385, 43.17606, 42.72795, 41.05225,
798
42.00461, 39.14698, 39.86511, 39.12616, 38.19473, 33.86518,
799
31.76617, 30.50207, 27.94986, 30.43803],
800
[ 29.69611, 30.64989, 30.737 , 31.97527, 31.02961, 32.5993 ,
801
33.29691, 33.13473, 33.33042, 34.79422, 37.27428, 34.29352,
802
36.03767, 35.58014, 36.84744, 35.88742, 36.19829, 37.67898,
803
36.69074, 36.13666, 35.45315, 34.31807, 33.92971, 32.57415,
804
34.38793, 31.88982, 30.77347, 29.88329, 30.54159, 29.57049,
805
29.21772, 25.59202, 24.21139, 24.48285, 23.06074, 19.97496,
806
19.57846, 16.33162, 15.08541, 15.06586, 14.38248, 8.09024,
807
7.57526, 7.97982, 9.43444, 0. , 6.60121, 9.85696,
808
10.89332, 10.39258, 12.86851, 14.75476, 17.21257, 17.61602,
809
15.71376, 20.40996, 21.66767, 25.03361, 26.60748, 27.25091,
810
29.58843, 32.22904, 31.80973, 37.16025, 34.28055, 35.884 ,
811
38.25288, 39.99024, 41.63577, 42.34816, 43.03802, 43.69836,
812
43.42436, 46.41609, 45.84523, 46.92581, 47.45754, 47.51112,
813
47.68894, 48.68155, 49.1594 , 47.14392, 46.92675, 49.05016,
814
47.7489 , 47.3948 , 46.55753, 45.24034, 45.04445, 43.71142,
815
44.46337, 41.62923, 43.11111, 40.95347, 40.97874, 37.50522,
816
35.00647, 33.76313, 30.48797, 33.78487],
817
[ 29.41756, 29.84656, 30.20034, 31.72587, 30.1106 , 32.43664,
818
32.48639, 32.68089, 32.66608, 34.36677, 36.78719, 34.00194,
819
35.84771, 35.82126, 36.8362 , 35.13336, 36.03964, 37.95828,
820
37.04425, 36.16784, 35.945 , 34.6565 , 33.80767, 32.29469,
821
34.38638, 31.87346, 31.09911, 29.87818, 30.74741, 28.96665,
822
29.55268, 26.79648, 24.16038, 23.84352, 23.05218, 20.45104,
823
19.38376, 16.16096, 14.93272, 16.27814, 13.54233, 8.56917,
824
8.45868, 8.83251, 8.12104, 6.60121, 0. , 10.17757,
825
8.53509, 8.32038, 10.85168, 12.70132, 15.99258, 17.25635,
826
16.51621, 19.26168, 21.60589, 23.78436, 26.22532, 26.73652,
827
29.27758, 31.33041, 31.04823, 37.12763, 32.98749, 35.06947,
828
37.28719, 39.461 , 40.85783, 41.59448, 42.32162, 43.57751,
829
43.1737 , 45.94993, 45.7186 , 46.70514, 47.35142, 47.22145,
830
47.41203, 48.74309, 48.88315, 46.89426, 46.8966 , 49.20629,
831
47.28112, 47.34997, 46.70348, 45.24956, 45.31637, 43.29447,
832
44.9994 , 41.76229, 42.8692 , 41.88106, 41.23793, 37.14262,
833
35.24283, 34.57233, 31.19456, 34.11927],
834
[ 28.83014, 30.31266, 30.13288, 31.85386, 31.0687 , 32.23116,
835
32.89237, 33.34788, 33.38514, 35.45895, 37.18274, 34.24137,
836
37.05029, 37.49003, 38.82735, 37.20982, 37.86692, 39.3333 ,
837
38.1781 , 37.57777, 38.07486, 36.33305, 36.2285 , 34.31277,
838
37.50663, 34.12199, 33.82732, 33.15122, 34.21383, 31.93696,
839
32.62558, 29.58366, 28.57247, 28.26891, 26.13901, 22.81966,
840
22.39702, 21.27586, 19.4389 , 20.16314, 16.59245, 11.67969,
841
12.97798, 10.38464, 10.99449, 9.85696, 10.17757, 0. ,
842
7.83858, 8.41089, 11.19326, 13.48331, 14.05563, 14.64482,
843
15.51254, 18.33828, 19.49451, 22.64066, 24.21162, 25.72832,
844
27.49107, 29.94017, 30.09775, 34.51412, 32.6424 , 34.1041 ,
845
36.48373, 38.65803, 41.22222, 41.17685, 42.52243, 43.43884,
846
43.36506, 46.36946, 45.84661, 46.8006 , 47.56391, 47.96634,
847
48.21386, 49.40067, 49.99774, 48.4731 , 48.58388, 50.70632,
848
49.48718, 49.72993, 48.60454, 47.90274, 47.29044, 46.48555,
849
47.1459 , 44.6641 , 45.39504, 45.2002 , 44.23507, 41.08682,
850
38.38866, 37.70556, 34.12645, 36.59337],
851
[ 30.11403, 30.95073, 31.62192, 33.66607, 31.53677, 33.38874,
852
33.31269, 34.37908, 34.29769, 36.3779 , 38.417 , 35.53305,
853
38.33912, 38.6495 , 39.99487, 37.74652, 38.88208, 40.59642,
854
39.77615, 39.01639, 39.28353, 37.55324, 36.50334, 34.99807,
855
38.17473, 35.33819, 34.63993, 33.91166, 34.31615, 32.42409,
856
32.93689, 30.67949, 28.2877 , 28.32281, 26.38234, 22.94849,
857
21.86462, 20.36335, 19.22241, 21.00477, 15.72496, 12.43841,
858
12.90918, 10.82867, 11.78021, 10.89332, 8.53509, 7.83858,
859
0. , 6.82238, 11.4934 , 11.88195, 13.2132 , 14.82213,
860
16.05954, 18.55392, 19.55994, 22.19041, 24.20944, 25.95339,
861
27.98701, 29.72961, 30.14266, 35.2683 , 32.68231, 34.49442,
862
36.84283, 39.96906, 41.25252, 41.86267, 43.03579, 44.67317,
863
44.36291, 47.1119 , 47.23168, 47.84897, 48.73064, 48.82056,
864
49.2878 , 50.56509, 50.75426, 49.53957, 49.65108, 51.8766 ,
865
50.44647, 50.26925, 49.99599, 48.57102, 48.20799, 46.79335,
866
48.1779 , 45.75658, 46.03133, 46.10588, 44.94675, 41.40908,
867
39.40758, 38.86882, 34.90814, 37.3594 ],
868
[ 28.76504, 29.50086, 30.13293, 32.0357 , 30.2114 , 32.62237,
869
33.17576, 32.97516, 32.89254, 35.3327 , 37.62287, 35.23732,
870
37.71305, 38.10808, 39.19622, 37.47408, 39.07201, 39.92405,
871
39.60791, 38.73035, 39.22602, 37.84719, 37.53278, 35.82 ,
872
38.39304, 36.0731 , 35.32224, 34.60562, 35.0456 , 34.06939,
873
34.88785, 31.89102, 29.74339, 29.3094 , 28.09777, 25.40346,
874
24.72382, 22.08521, 20.51852, 21.04933, 18.98626, 13.85593,
875
14.31407, 12.8995 , 11.37028, 10.39258, 8.32038, 8.41089,
876
6.82238, 0. , 8.71731, 7.76443, 12.45335, 12.2652 ,
877
12.90017, 15.09061, 17.41787, 20.38048, 22.61928, 23.14501,
878
25.76323, 27.71115, 27.8258 , 33.66319, 30.48156, 32.98226,
879
34.95939, 37.85604, 39.53608, 40.08616, 41.63043, 43.15796,
880
42.86376, 46.50258, 45.86231, 47.29211, 48.17182, 48.3848 ,
881
49.04825, 50.09211, 50.93521, 48.90653, 49.34591, 52.28837,
882
50.39015, 50.58997, 50.40001, 49.3039 , 49.05992, 47.89894,
883
49.234 , 46.43048, 47.85874, 47.20917, 46.79585, 42.67964,
884
40.30443, 39.8812 , 36.95114, 39.24277],
885
[ 23.7291 , 25.13342, 25.84322, 26.92882, 25.7518 , 28.36209,
886
29.06571, 29.38917, 29.26526, 31.54706, 34.72634, 32.32311,
887
34.34605, 35.42106, 36.6623 , 34.70021, 36.40368, 37.99061,
888
38.021 , 37.37737, 37.42741, 36.54117, 36.5014 , 35.31492,
889
38.36668, 35.88703, 35.64687, 34.9862 , 35.81848, 34.49619,
890
35.60229, 33.4665 , 31.3773 , 30.90888, 30.76486, 27.90575,
891
27.4199 , 24.78172, 24.28367, 24.7121 , 22.36856, 17.57202,
892
17.64249, 17.10962, 14.90543, 12.86851, 10.85168, 11.19326,
893
11.4934 , 8.71731, 0. , 5.57175, 8.63071, 9.25549,
894
9.12862, 9.36863, 12.44362, 14.25313, 17.25268, 17.45389,
895
20.41051, 22.31093, 22.02977, 28.4554 , 24.40348, 27.41917,
896
29.65847, 32.03859, 34.25637, 34.87194, 36.40332, 38.15373,
897
37.65245, 41.47684, 41.28355, 42.71965, 43.82151, 44.61234,
898
45.47536, 47.05548, 47.78609, 46.48006, 47.17699, 49.92586,
899
48.24647, 49.03127, 49.42958, 48.33632, 48.54484, 47.60107,
900
49.68564, 46.61442, 48.6812 , 48.31756, 48.12534, 44.56241,
901
42.7187 , 42.53511, 39.36061, 42.55081],
902
[ 25.6983 , 26.92125, 27.91135, 29.3656 , 27.6139 , 30.55605,
903
31.25932, 31.30679, 31.06269, 33.65312, 36.87088, 34.68689,
904
36.90215, 37.82413, 39.10442, 37.06721, 39.23049, 40.17349,
905
40.62842, 39.86314, 40.16763, 39.18647, 39.07491, 37.94267,
906
40.71544, 38.71968, 38.19558, 37.6223 , 38.00399, 37.51745,
907
38.44528, 36.09133, 33.75635, 33.39326, 33.11761, 30.36558,
908
29.752 , 26.80699, 26.21266, 26.38835, 24.60879, 19.71272,
909
19.73502, 18.97275, 16.80241, 14.75476, 12.70132, 13.48331,
910
11.88195, 7.76443, 5.57175, 0. , 9.15475, 8.56349,
911
8.47478, 8.49044, 11.99477, 14.44966, 17.32829, 17.19026,
912
20.41925, 22.11879, 22.02562, 28.80888, 24.85666, 28.34247,
913
30.26402, 33.37055, 35.15239, 36.01863, 37.78748, 39.81268,
914
39.32254, 43.59766, 43.22273, 44.89829, 46.04871, 46.77149,
915
47.87025, 49.21038, 50.23529, 48.6807 , 49.53981, 52.72328,
916
50.9 , 51.39158, 52.21003, 51.04052, 51.18106, 50.27656,
917
52.28684, 49.36971, 51.53462, 50.93333, 50.99637, 47.03863,
918
45.1501 , 44.98107, 42.0262 , 44.83658],
919
[ 25.97412, 26.77764, 28.12311, 29.6113 , 28.20037, 30.3347 ,
920
31.50259, 31.86587, 32.01605, 34.74652, 37.5226 , 34.89579,
921
37.11372, 38.53678, 39.88191, 38.15456, 39.92573, 40.90994,
922
41.3098 , 40.9369 , 41.16595, 39.96285, 40.15724, 38.60944,
923
42.31539, 40.48097, 40.17273, 39.74094, 40.05607, 38.87821,
924
39.2932 , 37.70993, 35.79133, 35.6437 , 35.1361 , 31.45698,
925
30.72862, 28.87533, 28.62454, 29.5294 , 26.09397, 21.99594,
926
21.71174, 20.8149 , 19.058 , 17.21257, 15.99258, 14.05563,
927
13.2132 , 12.45335, 8.63071, 9.15475, 0. , 5.69041,
928
8.86444, 10.50088, 9.15299, 11.56439, 15.31776, 16.37099,
929
19.20324, 20.11261, 21.17791, 26.23138, 24.1575 , 26.74297,
930
29.9642 , 32.63265, 34.33692, 35.4078 , 37.27436, 38.82324,
931
38.79999, 42.81333, 43.14353, 44.0194 , 45.29074, 46.65033,
932
47.77203, 49.32322, 49.88537, 49.61055, 50.40164, 52.96687,
933
51.90866, 52.35132, 53.40064, 52.18807, 52.39054, 51.76294,
934
53.60591, 51.35824, 52.66349, 52.69263, 52.29538, 49.4784 ,
935
47.59661, 47.05231, 43.63606, 46.86818],
936
[ 25.13513, 25.45479, 27.30813, 28.77098, 27.20175, 29.56765,
937
31.19405, 30.67301, 30.75263, 33.95725, 36.63014, 34.4585 ,
938
36.56462, 38.03388, 38.95773, 37.88232, 40.05261, 39.98119,
939
40.72945, 40.37831, 40.59288, 39.6461 , 40.40674, 38.67121,
940
42.04724, 40.65492, 39.9043 , 40.05704, 39.79457, 39.44799,
941
39.98048, 37.82863, 36.21335, 35.93431, 35.41829, 32.01961,
942
31.93212, 29.58085, 29.21067, 29.42525, 27.63374, 22.85153,
943
22.56943, 21.56576, 19.18607, 17.61602, 17.25635, 14.64482,
944
14.82213, 12.2652 , 9.25549, 8.56349, 5.69041, 0. ,
945
7.69056, 9.58872, 7.27847, 11.07301, 13.97117, 14.85007,
946
17.3385 , 18.54959, 19.51911, 24.47804, 23.22298, 25.99818,
947
28.67918, 31.37243, 33.06567, 34.08613, 36.44189, 37.65905,
948
37.7809 , 42.43773, 42.01543, 43.33093, 44.64622, 45.80397,
949
47.25139, 48.43046, 49.49756, 48.83554, 49.72558, 52.67093,
950
51.57562, 52.08085, 53.1481 , 52.11595, 52.16829, 52.09858,
951
53.53316, 51.2622 , 53.32599, 52.90649, 52.95174, 49.96028,
952
47.72114, 47.06461, 44.40938, 47.37281],
953
[ 24.45972, 26.64139, 27.01853, 27.98344, 27.57982, 29.58556,
954
31.33608, 31.14565, 31.17672, 33.40518, 37.07125, 34.33839,
955
36.48557, 37.13566, 38.89602, 37.77484, 39.20976, 39.92003,
956
40.56478, 40.3905 , 40.07303, 39.38249, 39.85148, 38.95962,
957
41.86037, 40.04445, 39.71271, 39.15768, 39.61693, 39.80638,
958
39.73092, 37.1605 , 36.02599, 36.08269, 35.86916, 32.50931,
959
32.14663, 29.35632, 29.13434, 28.82948, 27.67937, 22.16445,
960
21.94117, 21.19765, 20.42547, 15.71376, 16.51621, 15.51254,
961
16.05954, 12.90017, 9.12862, 8.47478, 8.86444, 7.69056,
962
0. , 8.27573, 8.48397, 13.22617, 14.5959 , 14.29243,
963
17.74386, 20.29587, 20.04847, 25.72337, 23.44249, 26.57937,
964
28.95484, 31.3744 , 33.67799, 34.68713, 36.28302, 37.6514 ,
965
37.46012, 42.17949, 41.8008 , 43.46606, 44.62028, 46.06782,
966
47.29764, 48.35452, 49.81537, 48.72589, 49.68722, 52.42257,
967
51.63792, 51.8305 , 52.84663, 51.78041, 52.05071, 51.83186,
968
53.22438, 50.71905, 53.35513, 51.86422, 52.68216, 49.67751,
969
47.40003, 46.87143, 43.90372, 47.26843],
970
[ 21.55045, 24.28835, 24.69093, 25.49869, 25.10337, 27.53405,
971
28.94501, 29.06828, 28.89607, 31.44167, 35.13839, 33.07445,
972
35.26936, 36.62481, 38.43435, 36.36806, 38.61636, 39.6808 ,
973
40.68159, 40.18733, 40.5409 , 39.77171, 40.40163, 39.63135,
974
42.90939, 40.78432, 40.82968, 40.26411, 41.10429, 40.83166,
975
41.86321, 39.86674, 38.43108, 37.85734, 38.17342, 35.50764,
976
35.16599, 32.37612, 32.23565, 32.05309, 30.67328, 25.45666,
977
25.69766, 24.98392, 22.96086, 20.40996, 19.26168, 18.33828,
978
18.55392, 15.09061, 9.36863, 8.49044, 10.50088, 9.58872,
979
8.27573, 0. , 7.81203, 9.63841, 11.81341, 10.38626,
980
14.34691, 16.65127, 16.01583, 22.86644, 18.67511, 22.78851,
981
24.49932, 27.34599, 30.249 , 30.89222, 32.98648, 35.07533,
982
34.59757, 39.54874, 39.14111, 41.24033, 42.66911, 44.16304,
983
45.54425, 47.06384, 48.51593, 47.55693, 48.77945, 51.948 ,
984
50.60804, 51.67431, 52.94916, 52.10773, 52.46879, 52.27757,
985
54.53359, 51.56906, 54.55259, 53.99784, 54.65517, 51.26881,
986
49.40055, 49.64106, 46.62981, 49.95592],
987
[ 21.69278, 23.54393, 24.94734, 26.08835, 25.22312, 26.86667,
988
28.98748, 29.04268, 29.20958, 31.93944, 35.36933, 33.23999,
989
35.32999, 36.8622 , 38.31651, 37.32521, 39.27939, 39.62528,
990
40.97394, 40.75477, 40.65161, 39.84257, 40.9679 , 39.99892,
991
43.56974, 42.24041, 41.59044, 41.81453, 41.69482, 41.71964,
992
42.40135, 40.65224, 39.29054, 39.11931, 39.25199, 35.83888,
993
35.88763, 33.42273, 33.74681, 33.66472, 31.99623, 27.04794,
994
26.75678, 26.22855, 24.54862, 21.66767, 21.60589, 19.49451,
995
19.55994, 17.41787, 12.44362, 11.99477, 9.15299, 7.27847,
996
8.48397, 7.81203, 0. , 6.39087, 8.34311, 9.09498,
997
12.01051, 14.03886, 14.66736, 19.35195, 18.37439, 21.53225,
998
24.01021, 26.91727, 28.70851, 29.95311, 32.23778, 33.96847,
999
33.87564, 38.86784, 38.83989, 40.22175, 41.76582, 43.56084,
1000
45.32808, 46.48406, 47.93843, 47.98325, 48.86364, 51.79319,
1001
51.20293, 51.97604, 53.74581, 52.60551, 52.8835 , 53.24671,
1002
55.09278, 52.73899, 55.52021, 54.91969, 55.45876, 53.12569,
1003
50.8073 , 50.61611, 47.78862, 51.26349],
1004
[ 19.95303, 21.14658, 23.21836, 24.3511 , 22.84998, 25.00712,
1005
26.83509, 27.11562, 27.32181, 30.05815, 33.57977, 31.99141,
1006
33.72941, 35.93997, 37.10258, 35.80232, 38.1003 , 38.71391,
1007
40.4026 , 40.04084, 40.1262 , 39.44919, 40.5153 , 39.64319,
1008
43.4618 , 42.36186, 41.89523, 42.1735 , 42.04974, 41.67128,
1009
43.0919 , 42.17263, 40.11502, 39.73362, 40.55388, 37.37873,
1010
37.34873, 35.02844, 35.77881, 36.01266, 33.83917, 29.67531,
1011
29.24043, 29.18584, 26.69301, 25.03361, 23.78436, 22.64066,
1012
22.19041, 20.38048, 14.25313, 14.44966, 11.56439, 11.07301,
1013
13.22617, 9.63841, 6.39087, 0. , 7.5008 , 7.8237 ,
1014
10.40305, 10.70596, 11.78864, 17.10573, 14.52165, 18.11827,
1015
20.90729, 23.93647, 25.20954, 26.57818, 28.98693, 31.46102,
1016
31.12039, 35.92599, 36.4427 , 37.60689, 39.32328, 41.32062,
1017
43.23691, 44.71995, 45.92899, 46.36053, 47.3359 , 50.52313,
1018
49.48781, 50.80266, 53.15541, 51.87092, 52.39965, 52.58596,
1019
55.23165, 52.76786, 55.52018, 55.73155, 55.94518, 53.73325,
1020
51.74464, 51.99425, 49.21381, 52.79329],
1021
[ 16.26348, 19.0042 , 20.37644, 21.22304, 20.28434, 21.74171,
1022
23.67883, 24.63125, 24.53975, 26.96615, 30.77296, 28.83607,
1023
31.33676, 33.1206 , 34.93565, 33.52616, 35.6578 , 36.21198,
1024
37.91905, 38.03854, 37.85329, 37.48819, 38.42327, 38.13686,
1025
42.34263, 40.86445, 40.82556, 41.17397, 41.08039, 41.61213,
1026
42.45519, 41.48734, 40.44974, 40.26473, 40.93513, 37.77828,
1027
38.05632, 35.98014, 37.02082, 37.14096, 35.09395, 31.04348,
1028
30.87281, 30.1669 , 29.07142, 26.60748, 26.22532, 24.21162,
1029
24.20944, 22.61928, 17.25268, 17.32829, 15.31776, 13.97117,
1030
14.5959 , 11.81341, 8.34311, 7.5008 , 0. , 5.83413,
1031
5.46876, 8.07889, 8.10377, 12.28344, 11.70756, 14.58617,
1032
16.50391, 20.31629, 22.0821 , 22.97453, 25.272 , 27.72545,
1033
27.36277, 32.25835, 32.61786, 33.89607, 35.73057, 37.77336,
1034
39.95231, 41.07814, 42.85021, 43.44198, 44.85383, 47.6269 ,
1035
47.47827, 48.41191, 50.90451, 49.78713, 50.24847, 51.22179,
1036
53.41837, 51.29034, 54.5929 , 54.6199 , 55.51699, 53.60744,
1037
51.63282, 52.1621 , 49.27814, 52.86302],
1038
[ 17.11013, 19.69926, 20.92257, 21.25266, 20.93006, 23.02809,
1039
25.4293 , 25.08637, 25.21252, 27.64338, 31.75893, 30.27728,
1040
32.09544, 33.81829, 35.54241, 34.40962, 36.74788, 37.08048,
1041
39.08311, 39.0819 , 38.93651, 38.87541, 40.1212 , 39.73796,
1042
43.41177, 42.22587, 42.24267, 42.24356, 42.4485 , 43.2428 ,
1043
44.1862 , 42.91311, 41.86014, 41.36942, 42.5099 , 39.79016,
1044
39.9811 , 37.25958, 38.04921, 37.87527, 36.84287, 32.13853,
1045
31.9451 , 31.64604, 29.81017, 27.25091, 26.73652, 25.72832,
1046
25.95339, 23.14501, 17.45389, 17.19026, 16.37099, 14.85007,
1047
14.29243, 10.38626, 9.09498, 7.8237 , 5.83413, 0. ,
1048
6.41631, 8.54307, 7.54798, 13.83722, 10.47169, 14.98237,
1049
16.51711, 19.64403, 21.76762, 22.8833 , 25.40245, 27.78937,
1050
27.30865, 32.95778, 32.79115, 34.89289, 36.70972, 38.8788 ,
1051
41.05635, 42.15574, 44.18684, 44.13238, 45.71765, 48.95971,
1052
48.28665, 49.59359, 52.1083 , 51.08147, 51.81738, 52.5753 ,
1053
55.01953, 52.46332, 56.32081, 55.78484, 57.09844, 54.71573,
1054
52.72249, 53.32 , 50.79307, 54.50537],
1055
[ 14.32254, 17.01569, 17.85377, 18.87943, 18.50018, 19.62897,
1056
22.19619, 22.31814, 22.16274, 24.84473, 28.54674, 27.08538,
1057
29.33582, 31.46152, 33.22748, 32.12772, 34.53888, 34.29651,
1058
36.66186, 36.62329, 37.02688, 36.52095, 38.22838, 37.88513,
1059
41.79768, 40.89454, 40.88634, 41.4135 , 41.31527, 42.36568,
1060
43.47623, 42.56542, 41.7082 , 41.39021, 42.56349, 39.73051,
1061
40.13104, 38.02517, 39.25933, 38.78613, 37.83474, 33.7628 ,
1062
33.52238, 33.19261, 31.49645, 29.58843, 29.27758, 27.49107,
1063
27.98701, 25.76323, 20.41051, 20.41925, 19.20324, 17.3385 ,
1064
17.74386, 14.34691, 12.01051, 10.40305, 5.46876, 6.41631,
1065
0. , 6.56254, 5.82652, 9.42892, 8.76253, 11.01716,
1066
12.97536, 16.14407, 18.65999, 19.26615, 21.70973, 23.98596,
1067
23.83313, 29.46502, 29.31874, 31.04096, 32.71498, 35.20378,
1068
37.43086, 38.47346, 40.74117, 41.15986, 42.72724, 46.03943,
1069
45.7643 , 46.92375, 49.81399, 49.07544, 49.48923, 50.83285,
1070
53.02921, 51.02381, 54.85708, 54.85699, 56.10978, 54.39723,
1071
52.29678, 53.08869, 50.68305, 54.16762],
1072
[ 17.62265, 17.70308, 20.91217, 21.25316, 19.27925, 22.0497 ,
1073
23.92894, 23.71491, 23.60181, 26.74278, 30.22502, 29.42086,
1074
31.07569, 33.72103, 34.83971, 33.40582, 36.56434, 36.10593,
1075
38.48701, 38.68787, 38.83153, 39.03388, 40.08247, 39.57072,
1076
43.79152, 43.17864, 43.2909 , 43.87194, 43.35611, 44.39476,
1077
45.37599, 45.03955, 43.69002, 43.28881, 44.52465, 41.74234,
1078
42.11747, 40.01821, 41.2876 , 41.51105, 39.87093, 36.48198,
1079
36.04839, 35.58516, 33.32921, 32.22904, 31.33041, 29.94017,
1080
29.72961, 27.71115, 22.31093, 22.11879, 20.11261, 18.54959,
1081
20.29587, 16.65127, 14.03886, 10.70596, 8.07889, 8.54307,
1082
6.56254, 0. , 4.33833, 8.76183, 7.88595, 10.96004,
1083
13.3731 , 17.00054, 17.6708 , 18.90909, 22.24521, 24.80605,
1084
24.44948, 29.94102, 30.21988, 31.68858, 33.75574, 35.95484,
1085
38.6216 , 39.86389, 41.58399, 42.28369, 44.38077, 47.67845,
1086
47.02336, 48.24653, 51.67294, 50.62617, 51.37421, 52.55434,
1087
55.1481 , 53.295 , 56.77537, 57.33105, 58.35886, 56.29047,
1088
54.80877, 55.50578, 53.14199, 56.6705 ],
1089
[ 15.44168, 16.76036, 19.36837, 19.09945, 17.75401, 20.71073,
1090
22.48331, 22.41495, 22.19147, 24.89471, 28.99081, 28.13654,
1091
29.78355, 32.12859, 33.64244, 31.97045, 35.07799, 34.99984,
1092
37.36496, 37.66226, 37.52198, 38.04894, 38.99665, 38.9161 ,
1093
42.99372, 41.97252, 42.33337, 42.72225, 42.53551, 43.77865,
1094
44.76722, 44.26307, 43.19493, 42.72848, 44.12784, 41.66611,
1095
42.08783, 39.69333, 41.02127, 41.02762, 39.81846, 36.14058,
1096
35.83875, 35.3853 , 33.38918, 31.80973, 31.04823, 30.09775,
1097
30.14266, 27.8258 , 22.02977, 22.02562, 21.17791, 19.51911,
1098
20.04847, 16.01583, 14.66736, 11.78864, 8.10377, 7.54798,
1099
5.82652, 4.33833, 0. , 9.49269, 5.60066, 10.13634,
1100
11.30708, 15.06618, 16.60802, 17.5898 , 20.66387, 23.36406,
1101
22.74647, 28.44725, 28.42199, 30.43171, 32.53739, 34.61086,
1102
37.28059, 38.61696, 40.54339, 40.91422, 43.13823, 46.37182,
1103
45.76609, 47.10957, 50.41253, 49.41508, 50.26066, 51.50842,
1104
54.21112, 52.03406, 56.08765, 56.26153, 57.72116, 55.39809,
1105
54.07596, 54.94413, 52.52346, 56.22352],
1106
[ 17.37134, 18.85088, 20.86528, 20.88305, 20.49716, 20.89719,
1107
23.70778, 23.87865, 23.8951 , 26.39705, 29.49656, 28.78396,
1108
30.69899, 33.34453, 34.72378, 34.19075, 36.59537, 35.8496 ,
1109
38.4644 , 39.09107, 39.07799, 39.2854 , 41.12947, 40.94059,
1110
45.43309, 44.85097, 45.05862, 46.08496, 45.50379, 46.84558,
1111
47.773 , 47.54766, 47.14492, 46.85017, 48.09543, 45.21051,
1112
46.05367, 44.39596, 45.92867, 45.8564 , 44.45979, 41.01457,
1113
40.75469, 40.18287, 38.71385, 37.16025, 37.12763, 34.51412,
1114
35.2683 , 33.66319, 28.4554 , 28.80888, 26.23138, 24.47804,
1115
25.72337, 22.86644, 19.35195, 17.10573, 12.28344, 13.83722,
1116
9.42892, 8.76183, 9.49269, 0. , 10.77901, 10.05965,
1117
11.4491 , 14.23453, 15.65154, 15.89031, 19.35493, 21.37071,
1118
21.35245, 26.88469, 27.14093, 28.27884, 30.5466 , 33.50676,
1119
36.4934 , 37.19752, 39.64894, 41.31134, 43.32302, 46.1664 ,
1120
46.66713, 48.02232, 51.58657, 50.8496 , 51.44928, 53.70231,
1121
55.7896 , 54.36972, 58.30467, 58.85498, 60.2241 , 59.29777,
1122
57.3284 , 58.22332, 56.01087, 59.61459],
1123
[ 13.90914, 15.67933, 17.38101, 16.98734, 16.24356, 18.9401 ,
1124
20.61034, 20.79483, 20.57865, 22.80323, 27.01958, 26.43445,
1125
27.88792, 30.4796 , 32.11209, 30.2786 , 33.28937, 33.74472,
1126
36.32379, 36.48663, 36.60449, 37.05129, 38.17204, 38.2891 ,
1127
42.39361, 41.45324, 42.17539, 42.30557, 42.54538, 43.53456,
1128
44.99764, 44.95504, 43.81483, 43.10439, 45.13455, 42.9827 ,
1129
43.28691, 40.98925, 42.53998, 42.62709, 41.3634 , 37.91637,
1130
37.69173, 37.57579, 35.4746 , 34.28055, 32.98749, 32.6424 ,
1131
32.68231, 30.48156, 24.40348, 24.85666, 24.1575 , 23.22298,
1132
23.44249, 18.67511, 18.37439, 14.52165, 11.70756, 10.47169,
1133
8.76253, 7.88595, 5.60066, 10.77901, 0. , 7.37848,
1134
7.94763, 11.60285, 13.60009, 14.22662, 16.93863, 20.48684,
1135
19.57347, 25.10732, 25.49894, 27.55298, 29.7128 , 32.13686,
1136
34.70808, 36.23865, 38.20019, 38.77183, 41.07158, 44.37704,
1137
43.59581, 45.48707, 49.01208, 48.08088, 49.19229, 50.28702,
1138
53.56762, 51.16563, 55.41252, 55.96844, 57.4112 , 55.34975,
1139
54.10888, 55.4712 , 53.09032, 56.86156],
1140
[ 11.73735, 13.11373, 14.14065, 14.43121, 13.95706, 14.67542,
1141
16.80414, 17.13811, 17.20223, 19.30856, 22.64011, 22.12388,
1142
23.6909 , 26.68134, 28.69735, 26.83978, 29.56233, 29.52144,
1143
32.42384, 32.61225, 33.43265, 33.33446, 34.9892 , 35.07866,
1144
39.51926, 38.91288, 39.71804, 40.15065, 40.30517, 41.47749,
1145
42.85482, 43.36693, 42.6301 , 42.13604, 44.19635, 41.96344,
1146
42.38342, 40.81211, 42.80247, 42.66475, 41.50962, 38.79497,
1147
38.4327 , 38.53515, 36.61224, 35.884 , 35.06947, 34.1041 ,
1148
34.49442, 32.98226, 27.41917, 28.34247, 26.74297, 25.99818,
1149
26.57937, 22.78851, 21.53225, 18.11827, 14.58617, 14.98237,
1150
11.01716, 10.96004, 10.13634, 10.05965, 7.37848, 0. ,
1151
6.85229, 8.33375, 10.64638, 10.34292, 12.47002, 15.48307,
1152
15.00604, 20.17726, 20.87708, 22.2614 , 24.11224, 27.27657,
1153
29.58244, 31.1899 , 33.13339, 34.40247, 36.49848, 39.87239,
1154
39.52611, 41.18787, 45.18565, 44.54115, 45.31625, 47.01201,
1155
50.01015, 48.42501, 52.3525 , 53.37068, 54.80933, 53.68554,
1156
52.36036, 53.92575, 51.51095, 55.33784],
1157
[ 12.23879, 14.57384, 15.49992, 14.87293, 14.68697, 15.87359,
1158
17.54135, 18.05839, 17.67657, 19.43576, 23.11653, 23.17097,
1159
24.95077, 27.47971, 29.37637, 27.6592 , 30.64956, 30.75883,
1160
33.65172, 34.05121, 34.30145, 34.86519, 36.38785, 36.89862,
1161
41.2064 , 40.27944, 41.17056, 41.69059, 41.79641, 43.3667 ,
1162
45.0001 , 45.22628, 44.81877, 43.99537, 46.17291, 44.45906,
1163
45.19904, 43.15676, 45.02922, 44.95803, 44.11761, 40.96397,
1164
40.95094, 40.71094, 39.11164, 38.25288, 37.28719, 36.48373,
1165
36.84283, 34.95939, 29.65847, 30.26402, 29.9642 , 28.67918,
1166
28.95484, 24.49932, 24.01021, 20.90729, 16.50391, 16.51711,
1167
12.97536, 13.3731 , 11.30708, 11.4491 , 7.94763, 6.85229,
1168
0. , 7.42181, 9.81149, 8.48963, 11.54921, 15.39613,
1169
14.38347, 19.86861, 19.77106, 22.06307, 24.50788, 26.82158,
1170
29.77616, 30.96037, 33.5255 , 34.52259, 36.99302, 40.18245,
1171
39.99496, 42.1269 , 45.88592, 45.21708, 46.21675, 48.21974,
1172
51.36139, 49.18705, 54.05609, 54.84453, 56.72943, 55.20246,
1173
53.91346, 55.78262, 53.64081, 57.31579],
1174
[ 12.84236, 14.49709, 14.33989, 12.60412, 14.86848, 14.84921,
1175
17.64634, 16.67094, 16.61788, 18.22819, 21.4745 , 21.90119,
1176
22.44497, 25.54979, 27.27617, 26.30551, 29.02811, 28.63502,
1177
31.82761, 32.23 , 32.81646, 33.37436, 35.95878, 36.20281,
1178
40.11474, 39.6453 , 40.67256, 41.24556, 41.68827, 43.24129,
1179
44.84355, 45.15693, 45.24839, 44.34038, 46.91914, 45.37185,
1180
46.24403, 44.3192 , 46.2601 , 45.70734, 45.79608, 42.64609,
1181
42.4804 , 42.71524, 40.61639, 39.99024, 39.461 , 38.65803,
1182
39.96906, 37.85604, 32.03859, 33.37055, 32.63265, 31.37243,
1183
31.3744 , 27.34599, 26.91727, 23.93647, 20.31629, 19.64403,
1184
16.14407, 17.00054, 15.06618, 14.23453, 11.60285, 8.33375,
1185
7.42181, 0. , 9.27097, 6.7636 , 9.28897, 10.82079,
1186
10.31003, 16.92184, 15.97901, 18.91758, 20.92638, 24.2509 ,
1187
26.79505, 28.28992, 30.96807, 32.00602, 34.44939, 37.75691,
1188
37.62064, 40.16677, 43.88795, 43.79662, 44.82826, 47.13516,
1189
50.10628, 48.05767, 53.25517, 53.82784, 55.9775 , 54.96514,
1190
53.63403, 55.43629, 53.67147, 57.5573 ],
1191
[ 16.11693, 13.93834, 17.43602, 16.25858, 14.61363, 15.9765 ,
1192
18.13698, 16.67337, 17.05001, 18.64491, 21.88627, 23.31711,
1193
22.73515, 25.74229, 26.28932, 26.20587, 29.40351, 28.32294,
1194
32.1881 , 32.67538, 32.20425, 33.51843, 35.6227 , 36.05376,
1195
39.74911, 40.59724, 40.65653, 41.85591, 40.95449, 43.27906,
1196
44.80852, 45.74134, 44.99179, 44.26734, 47.23808, 45.70899,
1197
46.80226, 44.52264, 46.99824, 46.90492, 46.84759, 44.26794,
1198
43.60742, 44.28372, 42.02245, 41.63577, 40.85783, 41.22222,
1199
41.25252, 39.53608, 34.25637, 35.15239, 34.33692, 33.06567,
1200
33.67799, 30.249 , 28.70851, 25.20954, 22.0821 , 21.76762,
1201
18.65999, 17.6708 , 16.60802, 15.65154, 13.60009, 10.64638,
1202
9.81149, 9.27097, 0. , 5.4579 , 8.31392, 11.37399,
1203
10.06637, 15.80099, 16.19604, 17.81404, 20.35224, 22.68455,
1204
26.33321, 27.22424, 29.39485, 31.26857, 33.44303, 36.96176,
1205
36.64784, 38.92403, 43.95773, 42.77504, 44.24492, 46.45457,
1206
49.95585, 48.08682, 53.30444, 53.83046, 55.9695 , 55.1559 ,
1207
54.03066, 55.76022, 54.37677, 58.38252],
1208
[ 14.78883, 13.97627, 15.89444, 14.52592, 14.13096, 14.6316 ,
1209
16.73796, 15.59013, 15.68349, 17.05169, 19.79573, 21.43302,
1210
21.53386, 24.75989, 25.69016, 25.12388, 28.14274, 27.26777,
1211
30.80285, 31.35308, 31.53711, 32.6792 , 34.90092, 35.34433,
1212
39.34168, 39.49418, 40.19097, 41.23647, 40.88777, 42.89426,
1213
44.71783, 45.58144, 45.27901, 44.39004, 47.21417, 45.86452,
1214
47.00371, 45.11777, 47.39798, 47.20804, 47.06841, 44.55381,
1215
44.22534, 44.57255, 42.49394, 42.34816, 41.59448, 41.17685,
1216
41.86267, 40.08616, 34.87194, 36.01863, 35.4078 , 34.08613,
1217
34.68713, 30.89222, 29.95311, 26.57818, 22.97453, 22.8833 ,
1218
19.26615, 18.90909, 17.5898 , 15.89031, 14.22662, 10.34292,
1219
8.48963, 6.7636 , 5.4579 , 0. , 6.20725, 9.55298,
1220
8.01646, 13.88004, 13.47562, 15.73658, 18.32946, 21.00988,
1221
24.41039, 25.357 , 28.05329, 29.56878, 32.10165, 35.5989 ,
1222
35.30488, 37.94608, 42.47888, 41.88941, 43.10642, 45.66534,
1223
48.94918, 47.14171, 52.39688, 53.39353, 55.47101, 54.71155,
1224
53.48973, 55.54874, 54.10548, 57.89195],
1225
[ 14.85241, 15.28133, 14.88863, 14.10743, 14.51717, 13.43337,
1226
15.0992 , 15.29917, 15.30447, 14.82973, 18.19257, 19.21266,
1227
19.39791, 22.16485, 23.88593, 23.22648, 25.25644, 25.1948 ,
1228
28.93245, 29.36674, 29.60455, 30.40374, 32.5457 , 33.67934,
1229
37.45432, 37.70761, 38.65435, 39.41798, 39.44077, 41.53307,
1230
43.31817, 44.57787, 44.24326, 43.65807, 46.86937, 45.49593,
1231
46.37995, 44.80329, 47.50405, 47.14969, 46.96281, 44.89301,
1232
44.42682, 45.13821, 43.59005, 43.03802, 42.32162, 42.52243,
1233
43.03579, 41.63043, 36.40332, 37.78748, 37.27436, 36.44189,
1234
36.28302, 32.98648, 32.23778, 28.98693, 25.272 , 25.40245,
1235
21.70973, 22.24521, 20.66387, 19.35493, 16.93863, 12.47002,
1236
11.54921, 9.28897, 8.31392, 6.20725, 0. , 8.05145,
1237
5.69215, 9.9497 , 11.36293, 12.71091, 14.59198, 18.34641,
1238
21.18762, 22.23008, 25.12185, 26.96778, 29.22174, 32.55304,
1239
32.67088, 35.01998, 40.03592, 39.3736 , 40.65807, 43.06865,
1240
46.5909 , 44.99134, 50.2539 , 51.23541, 53.43403, 53.31284,
1241
52.11044, 54.48838, 52.87226, 56.74007],
1242
[ 16.81082, 15.43603, 15.37154, 13.84321, 15.68778, 14.09887,
1243
16.73965, 14.46026, 14.95815, 15.51568, 16.9958 , 18.09438,
1244
17.15086, 20.06477, 21.52732, 22.09752, 24.3272 , 22.50728,
1245
26.4393 , 27.44256, 27.68888, 28.64096, 31.91806, 32.25061,
1246
35.8801 , 36.65188, 37.60561, 38.64347, 38.47113, 41.05796,
1247
42.17357, 43.24457, 44.00885, 43.18833, 46.30617, 45.23056,
1248
46.44777, 44.7664 , 47.43771, 46.86 , 47.70312, 45.34457,
1249
44.91905, 45.55069, 43.80397, 43.69836, 43.57751, 43.43884,
1250
44.67317, 43.15796, 38.15373, 39.81268, 38.82324, 37.65905,
1251
37.6514 , 35.07533, 33.96847, 31.46102, 27.72545, 27.78937,
1252
23.98596, 24.80605, 23.36406, 21.37071, 20.48684, 15.48307,
1253
15.39613, 10.82079, 11.37399, 9.55298, 8.05145, 0. ,
1254
5.15882, 10.42401, 8.2677 , 10.41686, 12.23247, 15.69246,
1255
18.50621, 19.6109 , 22.38789, 24.44886, 26.89026, 29.8127 ,
1256
30.67153, 32.99654, 37.56207, 37.45707, 38.73435, 41.86474,
1257
44.60558, 43.27327, 48.91205, 49.33654, 52.18163, 52.20071,
1258
51.11608, 53.03856, 51.85091, 55.85643],
1259
[ 15.84987, 15.38908, 15.57648, 13.02127, 14.51018, 13.393 ,
1260
15.39915, 14.31921, 14.4235 , 14.01205, 16.94848, 18.37291,
1261
17.26961, 20.06272, 21.55272, 21.38396, 23.56296, 23.05361,
1262
26.65776, 27.60226, 27.2861 , 28.81112, 31.28384, 32.36628,
1263
35.90349, 36.33936, 37.35235, 38.26693, 38.21591, 40.77052,
1264
42.00564, 43.23535, 43.62399, 42.95227, 46.18952, 45.08133,
1265
46.32251, 44.57585, 47.28364, 46.8637 , 47.32522, 45.22525,
1266
44.77389, 45.47875, 43.89376, 43.42436, 43.1737 , 43.36506,
1267
44.36291, 42.86376, 37.65245, 39.32254, 38.79999, 37.7809 ,
1268
37.46012, 34.59757, 33.87564, 31.12039, 27.36277, 27.30865,
1269
23.83313, 24.44948, 22.74647, 21.35245, 19.57347, 15.00604,
1270
14.38347, 10.31003, 10.06637, 8.01646, 5.69215, 5.15882,
1271
0. , 7.97303, 7.41391, 9.92165, 12.10268, 15.51953,
1272
18.54691, 19.63637, 22.4477 , 24.28556, 26.89341, 29.828 ,
1273
30.30008, 32.67363, 37.5192 , 37.10411, 38.59252, 41.46073,
1274
44.64997, 43.08337, 48.79588, 49.29285, 52.03523, 51.96351,
1275
51.03286, 53.18936, 51.82288, 55.93366],
1276
[ 19.49531, 19.14731, 18.73803, 16.58691, 17.43174, 15.35339,
1277
15.3146 , 16.68845, 16.70277, 14.33961, 16.33478, 17.67573,
1278
16.50911, 19.02226, 20.82185, 19.8089 , 20.85461, 22.12662,
1279
25.03495, 26.2458 , 25.60395, 27.30426, 28.86779, 30.7808 ,
1280
34.72309, 34.78051, 36.34129, 37.14527, 37.33843, 39.41463,
1281
40.73932, 43.03554, 43.42716, 42.93121, 46.3353 , 45.40294,
1282
46.58154, 45.54288, 48.66654, 48.70376, 48.293 , 47.30472,
1283
46.85295, 47.62256, 46.64783, 46.41609, 45.94993, 46.36946,
1284
47.1119 , 46.50258, 41.47684, 43.59766, 42.81333, 42.43773,
1285
42.17949, 39.54874, 38.86784, 35.92599, 32.25835, 32.95778,
1286
29.46502, 29.94102, 28.44725, 26.88469, 25.10732, 20.17726,
1287
19.86861, 16.92184, 15.80099, 13.88004, 9.9497 , 10.42401,
1288
7.97303, 0. , 7.5317 , 5.31432, 7.67385, 11.29427,
1289
13.88518, 15.65731, 17.41581, 21.03678, 23.50462, 25.23083,
1290
26.39159, 28.81917, 34.13332, 33.45212, 35.14618, 38.06477,
1291
41.77849, 40.61566, 45.83126, 47.30105, 49.72211, 50.48444,
1292
50.07272, 52.69689, 50.98398, 55.16405],
1293
[ 19.10495, 18.0164 , 17.66276, 15.13994, 16.76305, 15.15473,
1294
16.21818, 14.41634, 14.6234 , 13.3435 , 14.10467, 16.69031,
1295
14.97885, 17.40359, 18.79088, 18.83186, 20.80185, 19.74132,
1296
23.12291, 24.4287 , 24.28611, 26.30338, 28.98518, 30.11484,
1297
33.54021, 33.80123, 35.23204, 36.28322, 36.35944, 39.1773 ,
1298
40.54667, 41.97252, 43.097 , 42.14583, 45.46555, 45.13354,
1299
46.66496, 45.13382, 47.8922 , 47.41032, 48.42568, 46.71893,
1300
46.45624, 47.08008, 45.65345, 45.84523, 45.7186 , 45.84661,
1301
47.23168, 45.86231, 41.28355, 43.22273, 43.14353, 42.01543,
1302
41.8008 , 39.14111, 38.83989, 36.4427 , 32.61786, 32.79115,
1303
29.31874, 30.21988, 28.42199, 27.14093, 25.49894, 20.87708,
1304
19.77106, 15.97901, 16.19604, 13.47562, 11.36293, 8.2677 ,
1305
7.41391, 7.5317 , 0. , 6.63347, 8.51215, 10.2156 ,
1306
13.17845, 14.2086 , 17.41713, 18.82641, 21.82783, 24.56628,
1307
25.20903, 28.13747, 32.64308, 32.72029, 34.13216, 37.76093,
1308
40.74152, 39.28459, 45.54548, 46.22894, 49.39464, 49.45139,
1309
48.79067, 51.31535, 50.31884, 54.28067],
1310
[ 20.82333, 19.25691, 19.14902, 17.45726, 18.13449, 15.57783,
1311
15.90665, 16.10611, 16.24885, 14.52817, 14.58976, 16.42476,
1312
14.84698, 17.54345, 18.59526, 18.86371, 19.89348, 19.63274,
1313
22.70202, 24.17496, 23.68602, 25.2772 , 27.6702 , 29.01616,
1314
32.87432, 33.49258, 34.77337, 36.14132, 35.80693, 38.1895 ,
1315
39.4803 , 41.7482 , 42.57723, 41.96176, 45.29483, 44.55667,
1316
46.07288, 45.13769, 48.31191, 48.23058, 48.33951, 47.3816 ,
1317
46.96242, 47.68002, 46.63616, 46.92581, 46.70514, 46.8006 ,
1318
47.84897, 47.29211, 42.71965, 44.89829, 44.0194 , 43.33093,
1319
43.46606, 41.24033, 40.22175, 37.60689, 33.89607, 34.89289,
1320
31.04096, 31.68858, 30.43171, 28.27884, 27.55298, 22.2614 ,
1321
22.06307, 18.91758, 17.81404, 15.73658, 12.71091, 10.41686,
1322
9.92165, 5.31432, 6.63347, 0. , 4.70483, 7.62293,
1323
10.77344, 12.04317, 14.09367, 18.36526, 20.64699, 22.23753,
1324
23.95215, 26.43932, 31.57022, 31.17569, 32.66191, 36.26804,
1325
39.40728, 38.57361, 43.9427 , 45.43841, 47.97621, 49.1094 ,
1326
48.50627, 50.97824, 49.73738, 53.71283],
1327
[ 22.2353 , 20.79821, 19.51857, 18.68005, 19.68793, 16.38066,
1328
16.80116, 16.76691, 16.87216, 14.70497, 14.07395, 15.74665,
1329
14.0348 , 16.56831, 17.84671, 18.34015, 18.69289, 17.89876,
1330
21.31299, 22.32386, 22.83922, 23.65439, 26.58669, 27.92706,
1331
31.3026 , 32.35566, 33.6225 , 34.9677 , 34.8564 , 37.36602,
1332
38.72058, 41.05749, 41.90128, 41.49189, 44.96068, 44.24469,
1333
45.61367, 45.036 , 48.29145, 47.81376, 48.32094, 47.69802,
1334
47.13319, 48.15121, 47.08335, 47.45754, 47.35142, 47.56391,
1335
48.73064, 48.17182, 43.82151, 46.04871, 45.29074, 44.64622,
1336
44.62028, 42.66911, 41.76582, 39.32328, 35.73057, 36.70972,
1337
32.71498, 33.75574, 32.53739, 30.5466 , 29.7128 , 24.11224,
1338
24.50788, 20.92638, 20.35224, 18.32946, 14.59198, 12.23247,
1339
12.10268, 7.67385, 8.51215, 4.70483, 0. , 7.52323,
1340
8.61132, 9.93048, 12.5578 , 16.40777, 18.25766, 20.46284,
1341
22.14114, 24.25493, 29.68935, 29.77053, 30.84631, 34.5401 ,
1342
37.42484, 37.09933, 42.31915, 43.87867, 46.39273, 48.0183 ,
1343
47.23087, 49.8669 , 48.80525, 52.57763],
1344
[ 24.10629, 21.17772, 21.56308, 20.17601, 19.75357, 18.12999,
1345
17.15962, 16.68857, 16.49137, 14.77414, 12.99207, 15.65608,
1346
13.16584, 15.07742, 15.16618, 15.42575, 17.03854, 15.79792,
1347
18.64901, 20.26882, 19.6321 , 21.82505, 23.92989, 25.32419,
1348
28.63784, 29.75799, 30.92734, 32.65462, 31.85679, 34.97812,
1349
36.16405, 38.72517, 39.82617, 39.07646, 42.56432, 42.6187 ,
1350
44.385 , 43.45157, 46.78708, 46.72845, 47.48303, 47.15203,
1351
46.71132, 47.49823, 46.48834, 47.51112, 47.22145, 47.96634,
1352
48.82056, 48.3848 , 44.61234, 46.77149, 46.65033, 45.80397,
1353
46.06782, 44.16304, 43.56084, 41.32062, 37.77336, 38.8788 ,
1354
35.20378, 35.95484, 34.61086, 33.50676, 32.13686, 27.27657,
1355
26.82158, 24.2509 , 22.68455, 21.00988, 18.34641, 15.69246,
1356
15.51953, 11.29427, 10.2156 , 7.62293, 7.52323, 0. ,
1357
5.61253, 7.21393, 8.09939, 12.2139 , 14.96738, 16.37581,
1358
17.99627, 20.35805, 25.70473, 25.34467, 26.89611, 30.90733,
1359
34.04257, 33.31594, 39.15504, 40.74492, 43.65432, 44.59624,
1360
44.58934, 47.23448, 46.50554, 50.1937 ],
1361
[ 25.58022, 23.34925, 22.21288, 21.41715, 21.78947, 19.33544,
1362
18.1004 , 18.02822, 17.85663, 15.56051, 12.74353, 14.72969,
1363
12.28025, 13.83543, 14.82818, 14.24007, 14.62848, 14.13342,
1364
16.46835, 17.63621, 18.43043, 19.44844, 21.86083, 23.29639,
1365
26.36769, 27.30116, 29.00015, 30.32245, 30.32951, 33.00745,
1366
34.29426, 37.14338, 38.47462, 37.79461, 41.36339, 41.59934,
1367
43.10472, 42.69738, 46.0658 , 45.78045, 46.66074, 46.77432,
1368
46.36086, 47.35146, 46.45531, 47.68894, 47.41203, 48.21386,
1369
49.2878 , 49.04825, 45.47536, 47.87025, 47.77203, 47.25139,
1370
47.29764, 45.54425, 45.32808, 43.23691, 39.95231, 41.05635,
1371
37.43086, 38.6216 , 37.28059, 36.4934 , 34.70808, 29.58244,
1372
29.77616, 26.79505, 26.33321, 24.41039, 21.18762, 18.50621,
1373
18.54691, 13.88518, 13.17845, 10.77344, 8.61132, 5.61253,
1374
0. , 6.28487, 5.75247, 9.62946, 11.75449, 13.17307,
1375
14.78111, 17.10354, 22.23733, 22.66218, 23.80291, 27.72151,
1376
30.83746, 30.51189, 35.9164 , 37.93316, 40.70448, 42.1526 ,
1377
42.22162, 45.16766, 44.28871, 47.87966],
1378
[ 26.94421, 24.69467, 23.47894, 23.0355 , 23.32496, 20.47957,
1379
20.22697, 19.23566, 19.18505, 16.74031, 13.92433, 16.18704,
1380
14.13143, 14.50581, 14.49505, 16.84456, 16.26612, 14.08034,
1381
16.81846, 18.1981 , 18.32631, 19.69742, 22.75265, 24.12436,
1382
26.4844 , 28.38011, 29.40958, 31.15585, 30.47848, 34.10653,
1383
35.27955, 37.61494, 39.17248, 38.59134, 42.23577, 42.40437,
1384
44.24015, 43.68518, 47.00178, 46.55168, 47.9282 , 47.78838,
1385
47.34189, 48.3686 , 47.75785, 48.68155, 48.74309, 49.40067,
1386
50.56509, 50.09211, 47.05548, 49.21038, 49.32322, 48.43046,
1387
48.35452, 47.06384, 46.48406, 44.71995, 41.07814, 42.15574,
1388
38.47346, 39.86389, 38.61696, 37.19752, 36.23865, 31.1899 ,
1389
30.96037, 28.28992, 27.22424, 25.357 , 22.23008, 19.6109 ,
1390
19.63637, 15.65731, 14.2086 , 12.04317, 9.93048, 7.21393,
1391
6.28487, 0. , 7.47856, 9.53171, 11.18018, 13.01788,
1392
15.47366, 17.28446, 22.4102 , 22.68226, 23.79207, 28.38873,
1393
30.63132, 30.55106, 36.61026, 37.86975, 41.02305, 43.05683,
1394
42.18162, 45.17244, 45.04898, 48.29225],
1395
[ 29.15922, 25.91663, 25.86362, 25.07801, 24.54554, 22.53012,
1396
21.04317, 20.91886, 20.91421, 18.93591, 15.69868, 17.54084,
1397
14.59832, 15.50799, 15.15638, 15.52977, 15.56155, 14.92898,
1398
16.44223, 18.06242, 17.7009 , 19.3097 , 21.11808, 22.42396,
1399
25.34082, 27.09472, 28.36382, 30.05495, 29.27892, 32.18818,
1400
33.02234, 36.50124, 37.86386, 37.2521 , 40.86225, 41.24915,
1401
42.9754 , 42.70208, 46.27576, 46.44799, 47.12264, 47.81124,
1402
47.27088, 48.33511, 47.61879, 49.1594 , 48.88315, 49.99774,
1403
50.75426, 50.93521, 47.78609, 50.23529, 49.88537, 49.49756,
1404
49.81537, 48.51593, 47.93843, 45.92899, 42.85021, 44.18684,
1405
40.74117, 41.58399, 40.54339, 39.64894, 38.20019, 33.13339,
1406
33.5255 , 30.96807, 29.39485, 28.05329, 25.12185, 22.38789,
1407
22.4477 , 17.41581, 17.41713, 14.09367, 12.5578 , 8.09939,
1408
5.75247, 7.47856, 0. , 9.46928, 10.77391, 10.07175,
1409
12.78621, 14.47174, 20.14208, 19.79391, 21.44302, 25.49215,
1410
28.64581, 28.7825 , 33.76637, 36.05478, 38.72334, 40.7433 ,
1411
41.16185, 43.95332, 43.33299, 46.9185 ],
1412
[ 29.35633, 26.0043 , 25.36028, 24.73817, 24.18059, 23.41117,
1413
22.01882, 19.93191, 19.70914, 17.75143, 14.25548, 16.84414,
1414
13.82806, 13.55086, 12.82821, 13.17945, 13.83998, 11.06895,
1415
12.42447, 13.71252, 14.75941, 17.16471, 18.7693 , 19.7537 ,
1416
21.25983, 23.18208, 25.0391 , 26.14201, 25.8884 , 29.92886,
1417
30.89456, 33.46255, 34.99443, 34.09993, 37.9703 , 39.18714,
1418
40.85532, 40.23943, 43.40774, 43.06789, 45.05578, 45.64705,
1419
45.18382, 46.28713, 45.29908, 47.14392, 46.89426, 48.4731 ,
1420
49.53957, 48.90653, 46.48006, 48.6807 , 49.61055, 48.83554,
1421
48.72589, 47.55693, 47.98325, 46.36053, 43.44198, 44.13238,
1422
41.15986, 42.28369, 40.91422, 41.31134, 38.77183, 34.40247,
1423
34.52259, 32.00602, 31.26857, 29.56878, 26.96778, 24.44886,
1424
24.28556, 21.03678, 18.82641, 18.36526, 16.40777, 12.2139 ,
1425
9.62946, 9.53171, 9.46928, 0. , 7.70034, 11.03984,
1426
9.3173 , 11.00972, 16.06011, 16.8982 , 18.3223 , 22.22843,
1427
24.9604 , 24.69864, 30.94594, 32.41159, 35.92687, 36.56528,
1428
36.93542, 40.15198, 40.34494, 43.38612],
1429
[ 30.44926, 27.48027, 26.33286, 26.67714, 26.19812, 23.94749,
1430
23.10616, 21.22647, 21.64589, 19.27456, 15.27649, 17.82539,
1431
14.44424, 13.77702, 12.71296, 15.12571, 13.72169, 11.02782,
1432
12.98025, 12.60611, 14.24738, 14.47088, 18.18955, 19.01006,
1433
19.4387 , 22.41711, 22.59333, 24.6254 , 23.90214, 27.45379,
1434
29.48465, 32.11582, 33.29005, 32.53784, 36.62617, 37.89513,
1435
39.73088, 39.23902, 42.66151, 41.80521, 44.3409 , 44.93698,
1436
44.30438, 46.10429, 45.03967, 46.92675, 46.8966 , 48.58388,
1437
49.65108, 49.34591, 47.17699, 49.53981, 50.40164, 49.72558,
1438
49.68722, 48.77945, 48.86364, 47.3359 , 44.85383, 45.71765,
1439
42.72724, 44.38077, 43.13823, 43.32302, 41.07158, 36.49848,
1440
36.99302, 34.44939, 33.44303, 32.10165, 29.22174, 26.89026,
1441
26.89341, 23.50462, 21.82783, 20.64699, 18.25766, 14.96738,
1442
11.75449, 11.18018, 10.77391, 7.70034, 0. , 9.07328,
1443
6.77896, 9.73201, 14.62719, 15.04701, 15.37031, 19.6617 ,
1444
22.50593, 22.25054, 28.56357, 29.72752, 32.81706, 34.96093,
1445
34.29057, 37.67062, 38.17835, 41.31302],
1446
[ 33.44155, 31.09767, 29.98075, 29.31584, 29.52194, 27.14785,
1447
25.70386, 25.60087, 25.6927 , 22.94456, 19.74988, 20.46911,
1448
17.8433 , 16.34443, 15.97897, 17.63489, 14.82471, 15.65033,
1449
14.62265, 16.39878, 14.81143, 16.52024, 18.2176 , 19.94131,
1450
21.35453, 22.75371, 24.07796, 25.64368, 25.36182, 28.27133,
1451
28.8475 , 32.19497, 34.59372, 33.99566, 37.63698, 38.80147,
1452
40.79164, 40.71097, 44.23342, 44.2389 , 45.66062, 46.70672,
1453
46.30564, 47.57535, 47.61192, 49.05016, 49.20629, 50.70632,
1454
51.8766 , 52.28837, 49.92586, 52.72328, 52.96687, 52.67093,
1455
52.42257, 51.948 , 51.79319, 50.52313, 47.6269 , 48.95971,
1456
46.03943, 47.67845, 46.37182, 46.1664 , 44.37704, 39.87239,
1457
40.18245, 37.75691, 36.96176, 35.5989 , 32.55304, 29.8127 ,
1458
29.828 , 25.23083, 24.56628, 22.23753, 20.46284, 16.37581,
1459
13.17307, 13.01788, 10.07175, 11.03984, 9.07328, 0. ,
1460
8.87214, 9.85187, 12.31734, 12.2625 , 14.04632, 18.81453,
1461
21.19061, 21.12454, 27.04242, 28.49102, 31.8115 , 34.8203 ,
1462
35.12966, 38.15204, 38.01118, 41.47549],
1463
[ 33.20634, 29.88905, 29.33639, 29.02044, 28.20267, 27.12172,
1464
25.33855, 24.01222, 24.18448, 21.91537, 18.25877, 20.57828,
1465
16.98162, 16.4955 , 14.73869, 15.48099, 14.34678, 14.30857,
1466
13.85173, 13.84417, 14.39659, 15.93936, 17.45544, 18.33339,
1467
18.66931, 20.88887, 21.93502, 23.38049, 23.14462, 25.75202,
1468
27.86781, 31.24603, 32.25062, 31.15287, 35.45185, 37.34563,
1469
39.14055, 38.75821, 42.09818, 41.92408, 43.92436, 45.20662,
1470
44.68842, 46.38933, 45.31081, 47.7489 , 47.28112, 49.48718,
1471
50.44647, 50.39015, 48.24647, 50.9 , 51.90866, 51.57562,
1472
51.63792, 50.60804, 51.20293, 49.48781, 47.47827, 48.28665,
1473
45.7643 , 47.02336, 45.76609, 46.66713, 43.59581, 39.52611,
1474
39.99496, 37.62064, 36.64784, 35.30488, 32.67088, 30.67153,
1475
30.30008, 26.39159, 25.20903, 23.95215, 22.14114, 17.99627,
1476
14.78111, 15.47366, 12.78621, 9.3173 , 6.77896, 8.87214,
1477
0. , 8.06218, 11.429 , 11.46571, 13.13148, 16.10375,
1478
20.41288, 19.36076, 25.3713 , 27.60118, 30.25563, 31.87386,
1479
32.4665 , 36.03614, 36.48471, 39.63076],
1480
[ 35.10944, 31.87226, 31.30981, 31.28387, 30.01717, 29.01223,
1481
26.90823, 26.23519, 26.08005, 23.84675, 20.80091, 21.7296 ,
1482
19.04357, 17.40327, 16.7043 , 16.55105, 15.01213, 14.46629,
1483
13.32047, 13.90252, 14.09233, 15.41702, 15.00264, 16.81857,
1484
16.58331, 19.50611, 20.62995, 21.94394, 21.09032, 25.34647,
1485
25.48297, 29.25163, 30.55199, 30.43379, 34.21791, 35.75256,
1486
37.3534 , 37.46691, 41.14137, 40.96925, 42.83903, 44.90814,
1487
44.1482 , 45.72293, 45.41523, 47.3948 , 47.34997, 49.72993,
1488
50.26925, 50.58997, 49.03127, 51.39158, 52.35132, 52.08085,
1489
51.8305 , 51.67431, 51.97604, 50.80266, 48.41191, 49.59359,
1490
46.92375, 48.24653, 47.10957, 48.02232, 45.48707, 41.18787,
1491
42.1269 , 40.16677, 38.92403, 37.94608, 35.01998, 32.99654,
1492
32.67363, 28.81917, 28.13747, 26.43932, 24.25493, 20.35805,
1493
17.10354, 17.28446, 14.47174, 11.00972, 9.73201, 9.85187,
1494
8.06218, 0. , 9.67155, 9.04695, 10.17736, 13.59906,
1495
16.54233, 17.9564 , 22.847 , 24.60167, 27.9245 , 29.98479,
1496
31.1793 , 34.37541, 34.48999, 37.48156],
1497
[ 37.58041, 35.07482, 33.73965, 33.55744, 33.36934, 32.1432 ,
1498
30.27089, 29.55426, 29.35354, 27.42168, 23.91183, 24.02904,
1499
22.24141, 20.09447, 19.42872, 19.58731, 17.11687, 17.74227,
1500
13.81794, 14.58239, 14.84183, 15.60782, 15.51133, 15.99741,
1501
15.29044, 15.96133, 18.16191, 18.90934, 19.56871, 22.44188,
1502
22.56247, 25.58682, 28.63669, 27.85509, 31.08457, 33.50089,
1503
35.4027 , 35.83383, 38.8066 , 38.73615, 40.98259, 43.03585,
1504
42.80237, 43.99917, 44.16385, 46.55753, 46.70348, 48.60454,
1505
49.99599, 50.40001, 49.42958, 52.21003, 53.40064, 53.1481 ,
1506
52.84663, 52.94916, 53.74581, 53.15541, 50.90451, 52.1083 ,
1507
49.81399, 51.67294, 50.41253, 51.58657, 49.01208, 45.18565,
1508
45.88592, 43.88795, 43.95773, 42.47888, 40.03592, 37.56207,
1509
37.5192 , 34.13332, 32.64308, 31.57022, 29.68935, 25.70473,
1510
22.23733, 22.4102 , 20.14208, 16.06011, 14.62719, 12.31734,
1511
11.429 , 9.67155, 0. , 6.56064, 6.38088, 10.37223,
1512
11.02495, 11.31594, 17.26136, 19.1381 , 22.65982, 24.77406,
1513
25.9365 , 29.3083 , 29.80644, 32.34705],
1514
[ 36.97612, 34.08161, 33.6759 , 33.39091, 32.26088, 31.53822,
1515
29.34631, 29.01695, 29.00965, 26.76934, 24.08524, 24.20871,
1516
22.05366, 19.53993, 18.50832, 18.96449, 16.34701, 17.97385,
1517
14.45423, 15.61773, 13.11227, 15.3568 , 13.46033, 15.0617 ,
1518
14.5311 , 15.86852, 17.02272, 18.07516, 17.40934, 20.82485,
1519
20.68579, 24.49213, 26.61145, 26.08889, 29.69294, 31.99846,
1520
33.98145, 33.96711, 37.42541, 37.92498, 39.58649, 41.8455 ,
1521
41.36941, 42.7842 , 43.17606, 45.24034, 45.24956, 47.90274,
1522
48.57102, 49.3039 , 48.33632, 51.04052, 52.18807, 52.11595,
1523
51.78041, 52.10773, 52.60551, 51.87092, 49.78713, 51.08147,
1524
49.07544, 50.62617, 49.41508, 50.8496 , 48.08088, 44.54115,
1525
45.21708, 43.79662, 42.77504, 41.88941, 39.3736 , 37.45707,
1526
37.10411, 33.45212, 32.72029, 31.17569, 29.77053, 25.34467,
1527
22.66218, 22.68226, 19.79391, 16.8982 , 15.04701, 12.2625 ,
1528
11.46571, 9.04695, 6.56064, 0. , 5.98419, 8.35946,
1529
11.68013, 10.99161, 17.01812, 18.26248, 21.8055 , 23.90279,
1530
25.4595 , 28.64282, 28.83705, 32.02712],
1531
[ 37.4974 , 34.96767, 34.04663, 34.49413, 33.40864, 31.97442,
1532
29.92087, 29.67471, 29.70327, 27.66108, 24.27307, 24.33682,
1533
22.98183, 20.64083, 20.11721, 20.24747, 17.47794, 18.06633,
1534
14.59398, 14.72379, 14.67681, 14.63636, 13.79958, 14.77595,
1535
14.07159, 14.98222, 15.54819, 17.34202, 16.72036, 19.82573,
1536
20.34994, 23.73966, 26.02174, 25.78955, 28.68309, 30.98915,
1537
32.97956, 33.65132, 36.96229, 36.83463, 38.84249, 41.35057,
1538
40.89437, 42.32976, 42.72795, 45.04445, 45.31637, 47.29044,
1539
48.20799, 49.05992, 48.54484, 51.18106, 52.39054, 52.16829,
1540
52.05071, 52.46879, 52.8835 , 52.39965, 50.24847, 51.81738,
1541
49.48923, 51.37421, 50.26066, 51.44928, 49.19229, 45.31625,
1542
46.21675, 44.82826, 44.24492, 43.10642, 40.65807, 38.73435,
1543
38.59252, 35.14618, 34.13216, 32.66191, 30.84631, 26.89611,
1544
23.80291, 23.79207, 21.44302, 18.3223 , 15.37031, 14.04632,
1545
13.13148, 10.17736, 6.38088, 5.98419, 0. , 7.87813,
1546
8.5264 , 10.22297, 15.17486, 17.26896, 20.15363, 23.01967,
1547
23.76411, 27.20938, 27.40981, 30.03519],
1548
[ 39.19126, 36.59085, 35.63369, 36.29427, 34.83176, 34.20046,
1549
31.66778, 31.85062, 31.74665, 29.75946, 27.16596, 26.71437,
1550
25.33998, 23.14301, 22.55747, 21.6386 , 19.00668, 21.34884,
1551
17.7774 , 17.00739, 17.10835, 16.4597 , 13.68436, 14.59106,
1552
12.69685, 13.66391, 14.56199, 14.70928, 15.08113, 16.70077,
1553
17.57016, 21.92186, 22.74625, 22.49509, 26.09517, 28.78806,
1554
30.08218, 30.88072, 34.28354, 34.6773 , 36.13211, 39.45815,
1555
38.88697, 40.70953, 41.05225, 43.71142, 43.29447, 46.48555,
1556
46.79335, 47.89894, 47.60107, 50.27656, 51.76294, 52.09858,
1557
51.83186, 52.27757, 53.24671, 52.58596, 51.22179, 52.5753 ,
1558
50.83285, 52.55434, 51.50842, 53.70231, 50.28702, 47.01201,
1559
48.21974, 47.13516, 46.45457, 45.66534, 43.06865, 41.86474,
1560
41.46073, 38.06477, 37.76093, 36.26804, 34.5401 , 30.90733,
1561
27.72151, 28.38873, 25.49215, 22.22843, 19.6617 , 18.81453,
1562
16.10375, 13.59906, 10.37223, 8.35946, 7.87813, 0. ,
1563
8.67141, 8.22265, 10.68938, 14.39115, 15.81638, 18.19258,
1564
20.24196, 24.13398, 23.94398, 26.50431],
1565
[ 41.96371, 39.56174, 38.24726, 39.09789, 38.18059, 36.96213,
1566
35.17056, 34.7836 , 34.68077, 33.0935 , 30.02343, 29.08875,
1567
28.35413, 25.73473, 25.22857, 25.58849, 22.61177, 22.96009,
1568
18.83897, 18.61744, 19.10648, 17.9459 , 16.58338, 16.3054 ,
1569
13.75561, 14.86599, 15.3057 , 16.17006, 16.01239, 18.83691,
1570
17.81885, 20.66609, 23.58481, 23.83891, 26.05857, 28.57053,
1571
30.29887, 31.70992, 34.64723, 34.46336, 36.84814, 40.11168,
1572
39.62182, 41.06713, 42.00461, 44.46337, 44.9994 , 47.1459 ,
1573
48.1779 , 49.234 , 49.68564, 52.28684, 53.60591, 53.53316,
1574
53.22438, 54.53359, 55.09278, 55.23165, 53.41837, 55.01953,
1575
53.02921, 55.1481 , 54.21112, 55.7896 , 53.56762, 50.01015,
1576
51.36139, 50.10628, 49.95585, 48.94918, 46.5909 , 44.60558,
1577
44.64997, 41.77849, 40.74152, 39.40728, 37.42484, 34.04257,
1578
30.83746, 30.63132, 28.64581, 24.9604 , 22.50593, 21.19061,
1579
20.41288, 16.54233, 11.02495, 11.68013, 8.5264 , 8.67141,
1580
0. , 8.20946, 9.70989, 11.26803, 13.99325, 18.01633,
1581
18.62262, 21.68822, 22.49918, 24.09327],
1582
[ 39.49224, 37.35437, 36.06871, 36.46602, 35.81903, 35.11644,
1583
33.31352, 32.77038, 32.64932, 30.98471, 28.55089, 27.8246 ,
1584
26.6982 , 23.91935, 23.0396 , 23.63285, 20.87814, 22.50932,
1585
18.33698, 17.9266 , 17.05555, 16.78672, 15.70851, 15.56181,
1586
12.45704, 12.41707, 12.64367, 13.04202, 13.78221, 15.85836,
1587
16.39775, 18.42641, 21.28107, 20.37192, 23.59887, 27.01304,
1588
29.00976, 29.12309, 31.85059, 31.84197, 34.73249, 37.08534,
1589
36.88549, 38.47232, 39.14698, 41.62923, 41.76229, 44.6641 ,
1590
45.75658, 46.43048, 46.61442, 49.36971, 51.35824, 51.2622 ,
1591
50.71905, 51.56906, 52.73899, 52.76786, 51.29034, 52.46332,
1592
51.02381, 53.295 , 52.03406, 54.36972, 51.16563, 48.42501,
1593
49.18705, 48.05767, 48.08682, 47.14171, 44.99134, 43.27327,
1594
43.08337, 40.61566, 39.28459, 38.57361, 37.09933, 33.31594,
1595
30.51189, 30.55106, 28.7825 , 24.69864, 22.25054, 21.12454,
1596
19.36076, 17.9564 , 11.31594, 10.99161, 10.22297, 8.22265,
1597
8.20946, 0. , 10.97595, 10.25467, 13.79501, 15.37994,
1598
15.98122, 19.6484 , 20.7999 , 23.08624],
1599
[ 44.24451, 42.00158, 40.78921, 41.84873, 40.65885, 39.86917,
1600
37.56416, 38.06911, 37.91062, 36.65424, 33.83448, 32.39523,
1601
32.11611, 30.1514 , 29.71055, 28.70622, 25.97138, 28.30391,
1602
23.71274, 22.92496, 23.72982, 21.70309, 18.99807, 17.98122,
1603
16.48731, 15.52539, 16.45475, 15.86513, 17.09382, 15.60841,
1604
15.34486, 19.3634 , 21.00584, 20.98593, 22.7285 , 25.56683,
1605
26.63001, 28.97938, 31.58249, 32.48614, 33.17741, 37.64673,
1606
37.35607, 38.78739, 39.86511, 43.11111, 42.8692 , 45.39504,
1607
46.03133, 47.85874, 48.6812 , 51.53462, 52.66349, 53.32599,
1608
53.35513, 54.55259, 55.52021, 55.52018, 54.5929 , 56.32081,
1609
54.85708, 56.77537, 56.08765, 58.30467, 55.41252, 52.3525 ,
1610
54.05609, 53.25517, 53.30444, 52.39688, 50.2539 , 48.91205,
1611
48.79588, 45.83126, 45.54548, 43.9427 , 42.31915, 39.15504,
1612
35.9164 , 36.61026, 33.76637, 30.94594, 28.56357, 27.04242,
1613
25.3713 , 22.847 , 17.26136, 17.01812, 15.17486, 10.68938,
1614
9.70989, 10.97595, 0. , 11.45306, 8.11042, 12.83722,
1615
15.11178, 18.41451, 17.69405, 18.89004],
1616
[ 44.49713, 42.65467, 41.34813, 41.95262, 41.40321, 40.59916,
1617
39.27059, 38.63774, 38.78521, 37.30058, 35.47091, 33.86684,
1618
32.88203, 29.62866, 29.41731, 30.21742, 27.04819, 28.4628 ,
1619
24.45456, 24.15302, 22.93954, 21.98327, 20.56008, 20.15022,
1620
16.18279, 16.68747, 15.71403, 15.06125, 15.61569, 17.8028 ,
1621
15.15469, 16.24486, 19.89187, 20.20119, 22.24654, 25.4267 ,
1622
27.03646, 27.45576, 30.04064, 29.86623, 33.3556 , 36.20666,
1623
35.71787, 37.64475, 39.12616, 40.95347, 41.88106, 45.2002 ,
1624
46.10588, 47.20917, 48.31756, 50.93333, 52.69263, 52.90649,
1625
51.86422, 53.99784, 54.91969, 55.73155, 54.6199 , 55.78484,
1626
54.85699, 57.33105, 56.26153, 58.85498, 55.96844, 53.37068,
1627
54.84453, 53.82784, 53.83046, 53.39353, 51.23541, 49.33654,
1628
49.29285, 47.30105, 46.22894, 45.43841, 43.87867, 40.74492,
1629
37.93316, 37.86975, 36.05478, 32.41159, 29.72752, 28.49102,
1630
27.60118, 24.60167, 19.1381 , 18.26248, 17.26896, 14.39115,
1631
11.26803, 10.25467, 11.45306, 0. , 9.27356, 12.57009,
1632
12.95849, 14.74353, 15.81852, 18.51871],
1633
[ 46.20998, 44.21824, 43.00012, 44.21519, 43.17206, 42.25278,
1634
40.62456, 40.78472, 40.83826, 39.65202, 37.51809, 35.84499,
1635
35.32819, 33.12758, 32.39176, 32.68447, 29.54295, 31.64773,
1636
27.512 , 26.40181, 26.36839, 24.07691, 22.44251, 21.20001,
1637
18.19724, 18.30724, 16.86429, 16.67207, 17.24015, 15.28365,
1638
14.83316, 17.24548, 18.45627, 18.99761, 20.53253, 23.23683,
1639
24.48703, 26.55069, 28.92462, 29.37943, 31.06652, 35.37051,
1640
34.81861, 36.9269 , 38.19473, 40.97874, 41.23793, 44.23507,
1641
44.94675, 46.79585, 48.12534, 50.99637, 52.29538, 52.95174,
1642
52.68216, 54.65517, 55.45876, 55.94518, 55.51699, 57.09844,
1643
56.10978, 58.35886, 57.72116, 60.2241 , 57.4112 , 54.80933,
1644
56.72943, 55.9775 , 55.9695 , 55.47101, 53.43403, 52.18163,
1645
52.03523, 49.72211, 49.39464, 47.97621, 46.39273, 43.65432,
1646
40.70448, 41.02305, 38.72334, 35.92687, 32.81706, 31.8115 ,
1647
30.25563, 27.9245 , 22.65982, 21.8055 , 20.15363, 15.81638,
1648
13.99325, 13.79501, 8.11042, 9.27356, 0. , 11.3311 ,
1649
10.74328, 12.86819, 13.30844, 14.52224],
1650
[ 45.17665, 42.7808 , 42.36618, 43.15904, 41.53149, 42.35218,
1651
40.2062 , 39.75408, 39.61926, 39.12975, 37.42083, 36.03478,
1652
35.61998, 33.46496, 32.91178, 31.55284, 30.34684, 32.1907 ,
1653
27.97503, 27.03924, 26.99544, 26.11801, 22.97965, 21.39029,
1654
18.82112, 16.95519, 16.85299, 15.02326, 16.33925, 15.19425,
1655
14.19401, 15.15315, 16.11799, 15.27863, 16.26812, 21.19257,
1656
22.05865, 22.69609, 24.27898, 25.34313, 27.70613, 31.85248,
1657
31.64177, 33.11543, 33.86518, 37.50522, 37.14262, 41.08682,
1658
41.40908, 42.67964, 44.56241, 47.03863, 49.4784 , 49.96028,
1659
49.67751, 51.26881, 53.12569, 53.73325, 53.60744, 54.71573,
1660
54.39723, 56.29047, 55.39809, 59.29777, 55.34975, 53.68554,
1661
55.20246, 54.96514, 55.1559 , 54.71155, 53.31284, 52.20071,
1662
51.96351, 50.48444, 49.45139, 49.1094 , 48.0183 , 44.59624,
1663
42.1526 , 43.05683, 40.7433 , 36.56528, 34.96093, 34.8203 ,
1664
31.87386, 29.98479, 24.77406, 23.90279, 23.01967, 18.19258,
1665
18.01633, 15.37994, 12.83722, 12.57009, 11.3311 , 0. ,
1666
9.90814, 11.78426, 11.47244, 12.76638],
1667
[ 43.34276, 41.49634, 40.24461, 41.86844, 40.71829, 40.45489,
1668
39.40489, 38.43139, 38.5705 , 38.02632, 36.17692, 34.76023,
1669
34.74136, 32.47884, 31.62541, 32.34425, 30.10012, 31.04573,
1670
27.44909, 25.82034, 26.43948, 24.12467, 23.45606, 21.13788,
1671
17.69826, 17.37892, 15.00269, 14.43571, 15.18723, 13.84108,
1672
15.20368, 13.59916, 14.52011, 13.7462 , 15.10008, 19.15064,
1673
20.62081, 21.31464, 22.53438, 22.18623, 26.09503, 29.10527,
1674
28.85684, 30.98764, 31.76617, 35.00647, 35.24283, 38.38866,
1675
39.40758, 40.30443, 42.7187 , 45.1501 , 47.59661, 47.72114,
1676
47.40003, 49.40055, 50.8073 , 51.74464, 51.63282, 52.72249,
1677
52.29678, 54.80877, 54.07596, 57.3284 , 54.10888, 52.36036,
1678
53.91346, 53.63403, 54.03066, 53.48973, 52.11044, 51.11608,
1679
51.03286, 50.07272, 48.79067, 48.50627, 47.23087, 44.58934,
1680
42.22162, 42.18162, 41.16185, 36.93542, 34.29057, 35.12966,
1681
32.4665 , 31.1793 , 25.9365 , 25.4595 , 23.76411, 20.24196,
1682
18.62262, 15.98122, 15.11178, 12.95849, 10.74328, 9.90814,
1683
0. , 6.63421, 10.22093, 9.98474],
1684
[ 45.20143, 42.89946, 42.30763, 43.70448, 42.49124, 42.53407,
1685
41.81369, 40.51321, 40.69567, 40.69416, 39.05643, 37.39742,
1686
37.0847 , 35.00942, 33.79263, 35.03969, 33.17501, 33.47638,
1687
29.9473 , 28.7832 , 28.60162, 26.69992, 26.30876, 23.4717 ,
1688
20.07196, 20.49274, 17.43522, 17.62774, 17.0286 , 16.11862,
1689
15.44059, 12.73676, 14.22711, 13.92431, 13.99427, 17.6646 ,
1690
19.57784, 19.94906, 20.85881, 20.58748, 25.22437, 28.10747,
1691
27.61326, 29.72708, 30.50207, 33.76313, 34.57233, 37.70556,
1692
38.86882, 39.8812 , 42.53511, 44.98107, 47.05231, 47.06461,
1693
46.87143, 49.64106, 50.61611, 51.99425, 52.1621 , 53.32 ,
1694
53.08869, 55.50578, 54.94413, 58.22332, 55.4712 , 53.92575,
1695
55.78262, 55.43629, 55.76022, 55.54874, 54.48838, 53.03856,
1696
53.18936, 52.69689, 51.31535, 50.97824, 49.8669 , 47.23448,
1697
45.16766, 45.17244, 43.95332, 40.15198, 37.67062, 38.15204,
1698
36.03614, 34.37541, 29.3083 , 28.64282, 27.20938, 24.13398,
1699
21.68822, 19.6484 , 18.41451, 14.74353, 12.86819, 11.78426,
1700
6.63421, 0. , 8.83043, 8.80103],
1701
[ 42.75318, 41.51576, 40.55066, 41.85398, 40.79031, 40.64863,
1702
39.33236, 39.43324, 39.56802, 39.21815, 38.09928, 35.57779,
1703
36.06984, 33.91675, 34.18837, 33.47656, 31.31277, 33.5043 ,
1704
29.47687, 28.60458, 28.39343, 26.15777, 24.09575, 22.23873,
1705
20.9814 , 18.30611, 17.0517 , 15.52057, 16.96968, 13.96013,
1706
11.80224, 10.23459, 12.12231, 12.80535, 10.96839, 13.95903,
1707
14.73243, 16.52504, 17.8264 , 18.68724, 20.37247, 24.43796,
1708
24.23459, 25.83973, 27.94986, 30.48797, 31.19456, 34.12645,
1709
34.90814, 36.95114, 39.36061, 42.0262 , 43.63606, 44.40938,
1710
43.90372, 46.62981, 47.78862, 49.21381, 49.27814, 50.79307,
1711
50.68305, 53.14199, 52.52346, 56.01087, 53.09032, 51.51095,
1712
53.64081, 53.67147, 54.37677, 54.10548, 52.87226, 51.85091,
1713
51.82288, 50.98398, 50.31884, 49.73738, 48.80525, 46.50554,
1714
44.28871, 45.04898, 43.33299, 40.34494, 38.17835, 38.01118,
1715
36.48471, 34.48999, 29.80644, 28.83705, 27.40981, 23.94398,
1716
22.49918, 20.7999 , 17.69405, 15.81852, 13.30844, 11.47244,
1717
10.22093, 8.83043, 0. , 7.46263],
1718
[ 46.74111, 45.2993 , 44.09355, 45.9426 , 44.66045, 44.57547,
1719
43.20546, 43.19846, 43.04025, 43.02089, 41.43184, 39.06011,
1720
40.03816, 38.06303, 37.85652, 37.35049, 35.47796, 36.83706,
1721
32.87905, 31.58328, 32.42605, 29.63547, 27.8713 , 25.49112,
1722
23.64271, 21.75684, 20.42138, 19.39125, 20.31666, 17.63429,
1723
16.78251, 14.84621, 15.73701, 16.20137, 13.95765, 16.88417,
1724
17.36648, 20.00963, 20.38759, 20.88898, 22.75393, 27.26505,
1725
27.25467, 28.4507 , 30.43803, 33.78487, 34.11927, 36.59337,
1726
37.3594 , 39.24277, 42.55081, 44.83658, 46.86818, 47.37281,
1727
47.26843, 49.95592, 51.26349, 52.79329, 52.86302, 54.50537,
1728
54.16762, 56.6705 , 56.22352, 59.61459, 56.86156, 55.33784,
1729
57.31579, 57.5573 , 58.38252, 57.89195, 56.74007, 55.85643,
1730
55.93366, 55.16405, 54.28067, 53.71283, 52.57763, 50.1937 ,
1731
47.87966, 48.29225, 46.9185 , 43.38612, 41.31302, 41.47549,
1732
39.63076, 37.48156, 32.34705, 32.02712, 30.03519, 26.50431,
1733
24.09327, 23.08624, 18.89004, 18.51871, 14.52224, 12.76638,
1734
9.98474, 8.80103, 7.46263, 0. ]])
1738
class FastMetricScmdsScalingTests(TestCase):
1739
"""test the functions to do metric scaling"""
1743
"""creates inputs"""
1745
self.dist_func = lambda x, y: (FULL_SYM_MATRIX[x, y])
1746
self.num_objects = FULL_SYM_MATRIX.shape[0]
1749
def test_scmds_cmds_tzeng(self):
1750
"""cmds_tzeng() should return eigenvectors and eigenvalues,
1751
sorted by the eigenvalues
1755
(eigvec, eigval) = cmds_tzeng(FULL_SYM_MATRIX, dim)
1756
self.assertTrue(len(eigval) == dim)
1757
self.assertTrue(eigvec.shape == (FULL_SYM_MATRIX.shape[0], dim))
1758
self.assertTrue(sorted(eigval, reverse=True) == eigval.tolist())
1760
self.assertFloatEqual(eigval[0], 27336.883436)
1761
self.assertFloatEqual(eigval[-1], 536.736247)
1762
self.assertFloatEqual(eigvec[0, 0], -14.978621)
1763
self.assertFloatEqual(eigvec[-1, -1], 0.673001)
1766
dim = FULL_SYM_MATRIX.shape[0]
1767
(eigvec, eigval) = cmds_tzeng(FULL_SYM_MATRIX, dim)
1768
self.assertTrue(len(eigval) == dim)
1769
self.assertTrue(eigvec.shape == (FULL_SYM_MATRIX.shape[0], dim))
1770
self.assertTrue(sorted(eigval, reverse=True) == eigval.tolist())
1772
self.assertFloatEqual(eigval[0], 27336.883436043929)
1773
self.assertFloatEqual(eigval[-1], 0.000000)
1774
self.assertFloatEqual(eigvec[0, 0], -14.978621)
1775
self.assertFloatEqual(eigvec[-1, -1], 0.000000)
1778
def test_scmds_rowmeans(self):
1779
"""rowmeans() should return a vector of row-means for a 2d matrix.
1782
rm = rowmeans(FULL_SYM_MATRIX[:10])
1783
self.assertTrue(rm.shape[0] == 10)
1784
self.assertFloatEqual(float(rm[0]), 25.983320)
1785
self.assertFloatEqual(float(rm[-1]), 23.967050)
1789
def test_scmds_recenter(self):
1790
"""recenter() should recenter an mds solution
1793
mds_coords = matrix([
1794
[-3.78333558, -2.90925004, 2.75333034],
1795
[ 5.18887751, -1.2130882 , -0.86476508],
1796
[-3.10404298, -0.6620052 , -3.91668873],
1797
[-2.53758526, 3.99102424, 0.86289149],
1798
[ 4.23608631, 0.7933192 , 1.16523198]])
1800
centered_coords = recenter(mds_coords)
1801
self.assertTrue(centered_coords.shape == mds_coords.shape)
1802
center_of_gravity = sum([centered_coords[:, x].sum() \
1803
for x in range(centered_coords.shape[1])])
1804
self.assertFloatEqual(center_of_gravity, 0.0)
1807
def test_scmds_affine_mapping(self):
1808
"""affine_mapping() should return a touple of two matrices of
1813
[-24.03457111, 10.10355666, -23.17039728, 28.48438894,
1815
[ 0.62716392, 20.84502664, 6.42317521, -7.66901011,
1817
[ -2.60793417, 2.83532649, 2.91024821, 1.37414959,
1820
[-29.81089477, -2.01312927, -30.5925487 , 23.05985801,
1822
[ -4.68879117, 23.62633294, 1.07934315, 0.57461989,
1824
[ -0.51503505, 1.18377044, 0.83671471, 1.81751358,
1827
dim = matrix_x.shape[0]
1829
(tu, tb) = affine_mapping(matrix_x, matrix_y)
1830
self.assertTrue(tu.shape[0] == dim and tb.shape[0] == dim)
1831
self.assertTrue(tu.shape[0] == tu.shape[1])
1832
self.assertFloatEqual(tu[0, 0], 0.966653)
1833
self.assertFloatEqual(tu[-1, -1], 0.994816)
1834
self.assertFloatEqual(tb[0, 0], -6.480975)
1835
self.assertFloatEqual(tb[-1, -1], 0.686521)
1839
def test_scmds_adjust_mds_to_ref(self):
1840
"""adjust_mds_to_ref() should return an adjusted mds solutions"""
1845
fake_mds_coords_ref = FULL_SYM_MATRIX[:size, :dim]
1846
fake_mds_coords_add = FULL_SYM_MATRIX[overlap:size+overlap, :dim]
1848
mds_adj = adjust_mds_to_ref(fake_mds_coords_ref,
1849
fake_mds_coords_add, overlap)
1850
self.assertTrue(mds_adj.shape == fake_mds_coords_add.shape)
1851
self.assertFloatEqual(mds_adj[0, 0], 7.526609)
1852
self.assertFloatEqual(mds_adj[-1, -1], 18.009350)
1856
def test_scmds_combine_mds(self):
1857
"""combine_mds() should merge two mds solutions
1862
mds_coords_1 = matrix([
1863
[-3.78333558, -2.90925004, 2.75333034],
1864
[ 5.18887751, -1.2130882 , -0.86476508],
1865
[-3.10404298, -0.6620052 , -3.91668873],
1866
[-2.53758526, 3.99102424, 0.86289149],
1867
[ 4.23608631, 0.7933192 , 1.16523198]])
1868
mds_coords_2 = matrix([
1869
[-3.78333558, -2.90925004, 2.75333034],
1870
[ 5.18887751, -1.2130882 , -0.86476508],
1871
[-3.10404298, -0.6620052 , -3.91668873],
1872
[-2.53758526, 3.99102424, 0.86289149],
1873
[ 4.23608631, 0.7933192 , 1.16523198]])
1875
comb_mds = combine_mds(mds_coords_1,
1876
mds_coords_2, overlap)
1877
self.assertTrue(comb_mds.shape == (
1878
mds_coords_1.shape[0]*2-overlap, dim))
1879
self.assertFloatEqual(comb_mds[0, 0], -3.783335)
1880
#self.assertFloatEqual(comb_mds[-1, -1], 0.349951)
1883
def test_scmds_class_combinemds(self):
1884
"""class CombineMds() should be able to join MDS solutions
1888
# tile1 = FULL_SYM_MATRIX[0:5, 0:5]
1889
# tile2 = FULL_SYM_MATRIX[2:7, 2:7]
1890
# mds_coords_1 = cmds_tzeng(tile1, 3)
1891
# mds_coords_2 = cmds_tzeng(tile2, 3)
1893
mds_coords_1 = matrix([
1894
[-3.78333558, -2.90925004, 2.75333034],
1895
[ 5.18887751, -1.2130882 , -0.86476508],
1896
[-3.10404298, -0.6620052 , -3.91668873],
1897
[-2.53758526, 3.99102424, 0.86289149],
1898
[ 4.23608631, 0.7933192 , 1.16523198]])
1899
mds_coords_2 = matrix([
1900
[-3.78333558, -2.90925004, 2.75333034],
1901
[ 5.18887751, -1.2130882 , -0.86476508],
1902
[-3.10404298, -0.6620052 , -3.91668873],
1903
[-2.53758526, 3.99102424, 0.86289149],
1904
[ 4.23608631, 0.7933192 , 1.16523198]])
1906
comb_mds = CombineMds()
1907
comb_mds.add(mds_coords_1, overlap)
1908
comb_mds.add(mds_coords_2, overlap)
1909
final_mds = comb_mds.getFinalMDS()
1911
self.assertTrue(final_mds.shape == (mds_coords_1.shape[0]*2-overlap,
1912
mds_coords_1.shape[1]))
1913
#self.assertFloatEqual(final_mds[0, 0], 0.0393279)
1914
#self.assertFloatEqual(final_mds[-1, -1], -5.322599)
1919
class FastMetricNystromScalingTests(TestCase):
1920
"""test the functions to do metric scaling"""
1924
"""creates inputs"""
1926
self.big_seed_matrix = FULL_SYM_MATRIX[:49]
1927
self.small_seed_matrix = FULL_SYM_MATRIX[:25]
1930
def test_calc_matrix_a(self):
1931
"""calc_matrix_a should calculate a k x k matrix of
1932
(predefined) association matrix K of certain (predefined)
1935
nseeds = self.small_seed_matrix.shape[0]
1936
matrix_e = self.small_seed_matrix[:, 0:nseeds]
1937
matrix_a = calc_matrix_a(matrix_e)
1938
self.assertFloatEqual(matrix_a[0, 0], 250.032270)
1939
self.assertFloatEqual(matrix_a[-1][-1], 316.875461)
1942
def test_nystrom_build_seed_matrix(self):
1943
"""build_seed_matrix() should return a seedmatrix and an order
1947
dist_func = lambda x, y: (FULL_SYM_MATRIX[x, y])
1948
(seedmat, order) = build_seed_matrix(
1949
FULL_SYM_MATRIX.shape[0], seedmat_dim, dist_func)
1950
self.assertTrue(len(order) == FULL_SYM_MATRIX.shape[0])
1951
self.assertTrue(sorted(order) == range(FULL_SYM_MATRIX.shape[0]))
1952
self.assertTrue(seedmat.shape == (
1953
seedmat_dim, FULL_SYM_MATRIX.shape[0]))
1955
# build_seed_matrix randomises order
1956
ind = argsort(order)
1957
i = random.randint(0, seedmat.shape[0])
1958
j = random.randint(0, seedmat.shape[1])
1959
self.assertFloatEqual(seedmat[i, j], FULL_SYM_MATRIX[ind[i], ind[j]])
1962
def test_nystrom(self):
1963
"""nystrom() should return an MDS approximation"""
1966
mds_coords = nystrom(self.big_seed_matrix, dim)
1967
self.assertTrue(len(mds_coords.shape) == 2)
1968
self.assertTrue(mds_coords.shape[0] == self.big_seed_matrix.shape[1])
1969
self.assertTrue(mds_coords.shape[1] == dim)
1970
self.assertFloatEqual(mds_coords[0, 0], -10.709626)
1971
self.assertFloatEqual(mds_coords[-1, -1], -1.778160)
1974
def test_nystrom_seed_number(self):
1975
"""nystrom() should give better MDS approximations the more
1979
mds_coords = nystrom(self.big_seed_matrix, dim)
1980
stress = goodness_of_fit.Stress(FULL_SYM_MATRIX, mds_coords)
1981
kruskal_stress_big_mat = stress.calcKruskalStress()
1983
print("INFO: Kruskal stress for Nystrom MDS (big_seed_matrix, dim=%d) = %f" % \
1984
(dim, kruskal_stress_big_mat))
1985
self.assertTrue(kruskal_stress_big_mat < 0.04)
1988
mds_coords = nystrom(self.small_seed_matrix, dim)
1989
stress = goodness_of_fit.Stress(FULL_SYM_MATRIX, mds_coords)
1990
kruskal_stress_small_mat = stress.calcKruskalStress()
1992
print("INFO: Kruskal stress for Nystrom MDS (small_seed_matrix, dim=%d) = %f" % \
1993
(dim, kruskal_stress_small_mat))
1994
self.assertTrue(kruskal_stress_small_mat < 0.06)
1996
self.assertTrue(kruskal_stress_small_mat > kruskal_stress_big_mat)
1998
def test_calc_matrix_b(self):
1999
"""calc_matrix_b should calculate a k x n-k matrix of
2000
association matrix K
2003
nseeds = self.small_seed_matrix.shape[0]
2004
matrix_e = self.small_seed_matrix[:, 0:nseeds]
2005
matrix_f = self.small_seed_matrix[:, nseeds:]
2006
matrix_b = calc_matrix_b(matrix_e, matrix_f)
2008
self.assertTrue(matrix_b.shape == matrix_f.shape)
2009
self.assertFloatEqual(matrix_b[0, 0], -272.711227)
2010
self.assertFloatEqual(matrix_b[-1, -1], -64.898372)
2013
#run if called from the command line
2014
if __name__ == '__main__':
added
removed
tests/test_cluster/test_approximate_mds.py
