# mue(0.05) = 0.729 or 0.729
# mue(0.1) = 0.754 or 0.754
# mue(0.15) = 0.779 or 0.779
# mue(0.2) = 0.804 or 0.804
# mue(0.25) = 0.829 or 0.829
# mue(0.3) = 0.854 or 0.854
# mue(0.35) = 0.879 or 0.879
# mue(0.4) = 0.904 or 0.904
# mue(0.45) = 0.929 or 0.929
# mue(0.5) = 0.954 or 0.954
# mue(0.55) = 0.979 or 0.979
# mue(0.6) = 1.004 or 1.004
# mue(0.65) = 1.029 or 1.029
# mue(0.7) = 1.054 or 1.054
# mue(0.75) = 1.079 or 1.079
# mue(0.8) = 1.104 or 1.104
# mue(0.85) = 1.129 or 1.129
# mue(0.9) = 1.154 or 1.154
# The design matrix is given by :
#0	2.74348	-1.37174	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	
#1	-1.32626	2.65252	-1.32626	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	
#2	0	-1.2837	2.56739	-1.2837	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	
#3	0	0	-1.24378	2.48756	-1.24378	0	0	0	0	0	0	0	0	0	0	0	0	0	0	
#4	0	0	0	-1.20627	2.41255	-1.20627	0	0	0	0	0	0	0	0	0	0	0	0	0	
#5	0	0	0	0	-1.17096	2.34192	-1.17096	0	0	0	0	0	0	0	0	0	0	0	0	
#6	0	0	0	0	0	-1.13766	2.27531	-1.13766	0	0	0	0	0	0	0	0	0	0	0	
#7	0	0	0	0	0	0	-1.10619	2.21239	-1.10619	0	0	0	0	0	0	0	0	0	0	
#8	0	0	0	0	0	0	0	-1.07643	2.15285	-1.07643	0	0	0	0	0	0	0	0	0	
#9	0	0	0	0	0	0	0	0	-1.04822	2.09644	-1.04822	0	0	0	0	0	0	0	0	
#10	0	0	0	0	0	0	0	0	0	-1.02145	2.0429	-1.02145	0	0	0	0	0	0	0	
#11	0	0	0	0	0	0	0	0	0	0	-0.996016	1.99203	-0.996016	0	0	0	0	0	0	
#12	0	0	0	0	0	0	0	0	0	0	0	-0.971817	1.94363	-0.971817	0	0	0	0	0	
#13	0	0	0	0	0	0	0	0	0	0	0	0	-0.948767	1.89753	-0.948767	0	0	0	0	
#14	0	0	0	0	0	0	0	0	0	0	0	0	0	-0.926784	1.85357	-0.926784	0	0	0	
#15	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-0.905797	1.81159	-0.905797	0	0	
#16	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-0.88574	1.77148	-0.88574	0	
#17	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-0.866551	1.7331	-0.866551	
#18	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-0.848176	1.69635	


# Plot of possible eigenvalue vs. the determinant of the secular equation 
0.01	28.3729	28.3729
0.02	7.91268	7.91268
0.03	-4.42398	4.42398
0.04	-10.8641	10.8641
0.05	-13.1721	13.1721
0.06	-12.7261	12.7261
0.07	-10.5842	10.5842
0.08	-7.54162	7.54162
0.09	-4.1794	4.1794
0.1	-0.905959	0.905959
0.11	2.00752	2.00752
0.12	4.39734	4.39734
0.13	6.18241	6.18241
0.14	7.34347	7.34347
0.15	7.90612	7.90612
0.16	7.92687	7.92687
0.17	7.48196	7.48196
0.18	6.6585	6.6585
0.19	5.54756	5.54756
0.2	4.23892	4.23892
0.21	2.81721	2.81721
0.22	1.35919	1.35919
0.23	-0.0679753	0.0679753
0.24	-1.40775	1.40775
0.25	-2.61457	2.61457
0.26	-3.6538	3.6538
0.27	-4.5012	4.5012
0.28	-5.14224	5.14224
0.29	-5.57115	5.57115
0.3	-5.7899	5.7899
0.31	-5.80706	5.80706
0.32	-5.63669	5.63669
0.33	-5.29721	5.29721
0.34	-4.81031	4.81031
0.35	-4.19999	4.19999
0.36	-3.49159	3.49159
0.37	-2.71094	2.71094
0.38	-1.88368	1.88368
0.39	-1.03457	1.03457
0.4	-0.186966	0.186966
0.41	0.637613	0.637613
0.42	1.41983	1.41983
0.43	2.14277	2.14277
0.44	2.79213	2.79213
0.45	3.35631	3.35631
0.46	3.82641	3.82641
0.47	4.19623	4.19623
0.48	4.46216	4.46216
0.49	4.62305	4.62305
0.5	4.68003	4.68003
0.51	4.63633	4.63633
0.52	4.49705	4.49705
0.53	4.2689	4.2689
0.54	3.96	3.96
0.55	3.57959	3.57959
0.56	3.13777	3.13777
0.57	2.64528	2.64528
0.58	2.11326	2.11326
0.59	1.55302	1.55302
0.6	0.975809	0.975809
0.61	0.392646	0.392646
0.62	-0.185866	0.185866
0.63	-0.749693	0.749693
0.64	-1.28951	1.28951
0.65	-1.79682	1.79682
0.66	-2.26402	2.26402
0.67	-2.68452	2.68452
0.68	-3.05275	3.05275
0.69	-3.36422	3.36422
0.7	-3.61554	3.61554
0.71	-3.80437	3.80437
0.72	-3.92948	3.92948
0.73	-3.99062	3.99062
0.74	-3.98858	3.98858
0.75	-3.92503	3.92503
0.76	-3.80252	3.80252
0.77	-3.62439	3.62439
0.78	-3.39466	3.39466
0.79	-3.11798	3.11798
0.8	-2.79949	2.79949
0.81	-2.44479	2.44479
0.82	-2.05977	2.05977
0.83	-1.6506	1.6506
0.84	-1.22355	1.22355
0.85	-0.784964	0.784964
0.86	-0.341139	0.341139
0.87	0.10174	0.10174
0.88	0.537685	0.537685
0.89	0.960972	0.960972
0.9	1.36621	1.36621
0.91	1.74839	1.74839
0.92	2.10295	2.10295
0.93	2.42579	2.42579
0.94	2.71334	2.71334
0.95	2.96256	2.96256
0.96	3.17098	3.17098
0.97	3.33671	3.33671
0.98	3.45841	3.45841
0.99	3.53533	3.53533
1	3.5673	3.5673
1.01	3.55467	3.55467
1.02	3.49835	3.49835
1.03	3.39973	3.39973
1.04	3.26069	3.26069
1.05	3.08353	3.08353
1.06	2.87097	2.87097
1.07	2.62606	2.62606
1.08	2.35218	2.35218
1.09	2.05296	2.05296
1.1	1.73227	1.73227
1.11	1.39411	1.39411
1.12	1.04263	1.04263
1.13	0.682037	0.682037
1.14	0.316562	0.316562
1.15	-0.0495926	0.0495926
1.16	-0.412293	0.412293
1.17	-0.767519	0.767519
1.18	-1.11141	1.11141
1.19	-1.44029	1.44029
1.2	-1.75071	1.75071
1.21	-2.0395	2.0395
1.22	-2.30375	2.30375
1.23	-2.54088	2.54088
1.24	-2.74864	2.74864
1.25	-2.92511	2.92511
1.26	-3.06876	3.06876
1.27	-3.17841	3.17841
1.28	-3.25326	3.25326
1.29	-3.29288	3.29288
1.3	-3.29724	3.29724
1.31	-3.26664	3.26664
1.32	-3.20176	3.20176
1.33	-3.10361	3.10361
1.34	-2.97353	2.97353
1.35	-2.81318	2.81318
1.36	-2.6245	2.6245
1.37	-2.40967	2.40967
1.38	-2.17114	2.17114
1.39	-1.91154	1.91154
1.4	-1.6337	1.6337
1.41	-1.34059	1.34059
1.42	-1.0353	1.0353
1.43	-0.720982	0.720982
1.44	-0.400877	0.400877
1.45	-0.0782257	0.0782257
1.46	0.243737	0.243737
1.47	0.561817	0.561817
1.48	0.872893	0.872893
1.49	1.17394	1.17394
1.5	1.46207	1.46207
1.51	1.73454	1.73454
1.52	1.98878	1.98878
1.53	2.22244	2.22244
1.54	2.43336	2.43336
1.55	2.61966	2.61966
1.56	2.77966	2.77966
1.57	2.91198	2.91198
1.58	3.01551	3.01551
1.59	3.08942	3.08942
1.6	3.13316	3.13316
1.61	3.14648	3.14648
1.62	3.12941	3.12941
1.63	3.08227	3.08227
1.64	3.00567	3.00567
1.65	2.90048	2.90048
1.66	2.76782	2.76782
1.67	2.60909	2.60909
1.68	2.4259	2.4259
1.69	2.22008	2.22008
1.7	1.99368	1.99368
1.71	1.74889	1.74889
1.72	1.4881	1.4881
1.73	1.21381	1.21381
1.74	0.928641	0.928641
1.75	0.635288	0.635288
1.76	0.336524	0.336524
1.77	0.0351505	0.0351505
1.78	-0.266017	0.266017
1.79	-0.564178	0.564178
1.8	-0.856572	0.856572
1.81	-1.1405	1.1405
1.82	-1.41335	1.41335
1.83	-1.67263	1.67263
1.84	-1.91596	1.91596
1.85	-2.14114	2.14114
1.86	-2.34611	2.34611
1.87	-2.52904	2.52904
1.88	-2.68826	2.68826
1.89	-2.82235	2.82235
1.9	-2.93011	2.93011
1.91	-3.0106	3.0106
1.92	-3.06309	3.06309
1.93	-3.08715	3.08715
1.94	-3.08257	3.08257
1.95	-3.04942	3.04942
1.96	-2.98803	2.98803
1.97	-2.89898	2.89898
1.98	-2.78309	2.78309
1.99	-2.64145	2.64145
2	-2.47534	2.47534
2.01	-2.28631	2.28631
2.02	-2.07607	2.07607
2.03	-1.84656	1.84656
2.04	-1.59986	1.59986
2.05	-1.33825	1.33825
2.06	-1.0641	1.0641
2.07	-0.779928	0.779928
2.08	-0.488332	0.488332
2.09	-0.191982	0.191982
2.1	0.106405	0.106405
2.11	0.404088	0.404088
2.12	0.698329	0.698329
2.13	0.986414	0.986414
2.14	1.26568	1.26568
2.15	1.53354	1.53354
2.16	1.78749	1.78749
2.17	2.02518	2.02518
2.18	2.24435	2.24435
2.19	2.44295	2.44295
2.2	2.61907	2.61907
2.21	2.77104	2.77104
2.22	2.89737	2.89737
2.23	2.9968	2.9968
2.24	3.06834	3.06834
2.25	3.11122	3.11122
2.26	3.12494	3.12494
2.27	3.10927	3.10927
2.28	3.06424	3.06424
2.29	2.99015	2.99015
2.3	2.88759	2.88759
2.31	2.75739	2.75739
2.32	2.60065	2.60065
2.33	2.41873	2.41873
2.34	2.21321	2.21321
2.35	1.98593	1.98593
2.36	1.73892	1.73892
2.37	1.47441	1.47441
2.38	1.19483	1.19483
2.39	0.902752	0.902752
2.4	0.60088	0.60088
2.41	0.292043	0.292043
2.42	-0.0208452	0.0208452
2.43	-0.334809	0.334809
2.44	-0.646837	0.646837
2.45	-0.95391	0.95391
2.46	-1.25303	1.25303
2.47	-1.54123	1.54123
2.48	-1.81566	1.81566
2.49	-2.07352	2.07352
2.5	-2.31219	2.31219
2.51	-2.52916	2.52916
2.52	-2.72215	2.72215
2.53	-2.88906	2.88906
2.54	-3.02801	3.02801
2.55	-3.1374	3.1374
2.56	-3.21587	3.21587
2.57	-3.26236	3.26236
2.58	-3.27612	3.27612
2.59	-3.2567	3.2567
2.6	-3.20397	3.20397
2.61	-3.11813	3.11813
2.62	-2.99971	2.99971
2.63	-2.84959	2.84959
2.64	-2.66895	2.66895
2.65	-2.45932	2.45932
2.66	-2.22253	2.22253
2.67	-1.96071	1.96071
2.68	-1.67629	1.67629
2.69	-1.37195	1.37195
2.7	-1.05064	1.05064
2.71	-0.71552	0.71552
2.72	-0.369938	0.369938
2.73	-0.0174213	0.0174213
2.74	0.338375	0.338375
2.75	0.693693	0.693693
2.76	1.04471	1.04471
2.77	1.38759	1.38759
2.78	1.71849	1.71849
2.79	2.03363	2.03363
2.8	2.32932	2.32932
2.81	2.60201	2.60201
2.82	2.84831	2.84831
2.83	3.06506	3.06506
2.84	3.24935	3.24935
2.85	3.39854	3.39854
2.86	3.51034	3.51034
2.87	3.58282	3.58282
2.88	3.61443	3.61443
2.89	3.60404	3.60404
2.9	3.55097	3.55097
2.91	3.45501	3.45501
2.92	3.31642	3.31642
2.93	3.13597	3.13597
2.94	2.91491	2.91491
2.95	2.65501	2.65501
2.96	2.35856	2.35856
2.97	2.0283	2.0283
2.98	1.66749	1.66749
2.99	1.27983	1.27983
3	0.869467	0.869467
3.01	0.440936	0.440936
3.02	-0.000848565	0.000848565
3.03	-0.450652	0.450652
3.04	-0.902965	0.902965
3.05	-1.35206	1.35206
3.06	-1.79203	1.79203
3.07	-2.2169	2.2169
3.08	-2.62063	2.62063
3.09	-2.99724	2.99724
3.1	-3.34087	3.34087
3.11	-3.64582	3.64582
3.12	-3.90668	3.90668
3.13	-4.11841	4.11841
3.14	-4.27637	4.27637
3.15	-4.37643	4.37643
3.16	-4.41508	4.41508
3.17	-4.38944	4.38944
3.18	-4.29739	4.29739
3.19	-4.1376	4.1376
3.2	-3.90961	3.90961
3.21	-3.6139	3.6139
3.22	-3.25189	3.25189
3.23	-2.82603	2.82603
3.24	-2.33981	2.33981
3.25	-1.79777	1.79777
3.26	-1.20552	1.20552
3.27	-0.569714	0.569714
3.28	0.101934	0.101934
3.29	0.800726	0.800726
3.3	1.51701	1.51701
3.31	2.24023	2.24023
3.32	2.95906	2.95906
3.33	3.66144	3.66144
3.34	4.33474	4.33474
3.35	4.96587	4.96587
3.36	5.54145	5.54145
3.37	6.04794	6.04794
3.38	6.47187	6.47187
3.39	6.80002	6.80002
3.4	7.01963	7.01963
3.41	7.11861	7.11861
3.42	7.08581	7.08581
3.43	6.91126	6.91126
3.44	6.58642	6.58642
3.45	6.10441	6.10441
3.46	5.46035	5.46035
3.47	4.65155	4.65155
3.48	3.67779	3.67779
3.49	2.54158	2.54158
3.5	1.24842	1.24842
3.51	-0.19302	0.19302
3.52	-1.77067	1.77067
3.53	-3.46888	3.46888
3.54	-5.26826	5.26826
3.55	-7.14559	7.14559
3.56	-9.07372	9.07372
3.57	-11.0216	11.0216
3.58	-12.9541	12.9541
3.59	-14.8324	14.8324
3.6	-16.6139	16.6139
3.61	-18.2526	18.2526
3.62	-19.6991	19.6991
3.63	-20.9013	20.9013
3.64	-21.8046	21.8046
3.65	-22.3527	22.3527
3.66	-22.488	22.488
3.67	-22.1524	22.1524
3.68	-21.288	21.288
3.69	-19.8386	19.8386
3.7	-17.75	17.75
3.71	-14.9716	14.9716
3.72	-11.4576	11.4576
3.73	-7.16845	7.16845
3.74	-2.07199	2.07199
3.75	3.85457	3.85457
3.76	10.6232	10.6232
3.77	18.2331	18.2331
3.78	26.6693	26.6693
3.79	35.9001	35.9001
3.8	45.8758	45.8758
3.81	56.5262	56.5262
3.82	67.7589	67.7589
3.83	79.4573	79.4573
3.84	91.4784	91.4784
3.85	103.651	103.651
3.86	115.775	115.775
3.87	127.617	127.617
3.88	138.912	138.912
3.89	149.36	149.36
3.9	158.627	158.627
3.91	166.341	166.341
3.92	172.096	172.096
3.93	175.447	175.447
3.94	175.917	175.917
3.95	172.993	172.993
3.96	166.129	166.129
3.97	154.751	154.751
3.98	138.257	138.257
3.99	116.025	116.025
4	87.4133	87.4133
4.01	51.7729	51.7729
4.02	8.4506	8.4506
4.03	-43.2003	43.2003
4.04	-103.81	103.81
4.05	-173.981	173.981
4.06	-254.274	254.274
4.07	-345.191	345.191
4.08	-447.164	447.164
4.09	-560.53	560.53
4.1	-685.513	685.513
4.11	-822.201	822.201
4.12	-970.519	970.519
4.13	-1130.2	1130.2
4.14	-1300.77	1300.77
4.15	-1481.49	1481.49
4.16	-1671.34	1671.34
4.17	-1868.97	1868.97
4.18	-2072.67	2072.67
4.19	-2280.33	2280.33
4.2	-2489.37	2489.37
4.21	-2696.74	2696.74
4.22	-2898.81	2898.81
4.23	-3091.36	3091.36
4.24	-3269.53	3269.53
4.25	-3427.72	3427.72
4.26	-3559.59	3559.59
4.27	-3657.95	3657.95
4.28	-3714.74	3714.74
4.29	-3720.96	3720.96
4.3	-3666.58	3666.58
4.31	-3540.54	3540.54
4.32	-3330.65	3330.65
4.33	-3023.55	3023.55
4.34	-2604.66	2604.66
4.35	-2058.15	2058.15
4.36	-1366.89	1366.89
4.37	-512.409	512.409
4.38	525.094	525.094
4.39	1766.78	1766.78
4.4	3235.16	3235.16
4.41	4954.06	4954.06
4.42	6948.61	6948.61
4.43	9245.14	9245.14
4.44	11871.1	11871.1
4.45	14855.1	14855.1
4.46	18226.3	18226.3
4.47	22014.9	22014.9
4.48	26251.3	26251.3
4.49	30966.3	30966.3
4.5	36190.3	36190.3
4.51	41953.5	41953.5
4.52	48284.8	48284.8
4.53	55211.9	55211.9
4.54	62760.1	62760.1
4.55	70952.3	70952.3
4.56	79807.4	79807.4
4.57	89340.2	89340.2
4.58	99559.8	99559.8
4.59	110469	110469
4.6	122062	122062
4.61	134324	134324
4.62	147230	147230
4.63	160742	160742
4.64	174805	174805
4.65	189349	189349
4.66	204285	204285
4.67	219501	219501
4.68	234859	234859
4.69	250193	250193
4.7	265305	265305
4.71	279959	279959
4.72	293880	293880
4.73	306747	306747
4.74	318186	318186
4.75	327768	327768
4.76	335000	335000
4.77	339317	339317
4.78	340080	340080
4.79	336559	336559
4.8	327931	327931
4.81	313267	313267
4.82	291523	291523
4.83	261527	261527
4.84	221966	221966
4.85	171374	171374
4.86	108118	108118
4.87	30377.3	30377.3
4.88	-63867.2	63867.2
4.89	-176856	176856
4.9	-311071	311071
4.91	-469254	469254
4.92	-654432	654432
4.93	-869944	869944
4.94	-1.11947e+006	1.11947e+006
4.95	-1.40704e+006	1.40704e+006
4.96	-1.7371e+006	1.7371e+006
4.97	-2.11452e+006	2.11452e+006
4.98	-2.54464e+006	2.54464e+006
4.99	-3.0333e+006	3.0333e+006
5	-3.5869e+006	3.5869e+006
# The eigenvalues without the common factor were found to be 
# e0 = 0.025733709335327
# e1 = 0.10294966697693
# e2 = 0.22951259613037
# The eigenfrequencies are given by 
# w0 = 101.45680723407
# w1 = 202.92823064022
# w2 = 302.9934627218
# The Eigenvalues given by QR decomposition algorithm are : 
# 0.025733694051901
# 0.10294961606234
# 0.22951241170916
# 0.40223444390314
# 0.61676755020534
# 0.86769370002648
# 1.1486425284325
# 1.4524238860231
# 1.7711650006948
# 2.0964360587002
# 2.4193359027321
# 2.7304909419341
# 3.0199810029908
# 3.278511237298
# 3.5087158110022
# 3.7436601018555
# 4.0217563474895
# 4.3751716888437
# 4.8734321096519

# The eigenvectors are give by the matrix 
#0	0.046299970256347	0.091731359415455	0.13538286617399	0.17632041385255	0.21360991156062	0.24634241938904	0.27366116463097	0.29478971702322	0.30906049975316	0.31594269619135	0.31506851709119	0.30625672658012	0.28953229469829	0.26514105599734	0.23355831330471	0.19549043729817	0.15186867831337	0.10383462689339	0.052717031480791	
#1	-0.09086453557762	-0.17490966321677	-0.2453776013199	-0.29616680767286	-0.32244184567699	-0.32119800964699	-0.29171477476272	-0.23583347862836	-0.15800399715819	-0.065062982854177	0.03426812293573	0.13014542431831	0.21257071054919	0.27247728562486	0.30281765143493	0.29952023437766	0.26218043290257	0.19436736915818	0.1034627122953	
#2	0.13353716339487	0.24473161663697	0.31357468643797	0.32635368514395	0.2789112978865	0.17840163239006	0.042924604770724	-0.10121209313413	-0.22434938488222	-0.2996515669962	-0.30934358797188	-0.24952837807674	-0.13221422889996	0.016324726203488	0.16091463075229	0.26565500982416	0.30308327022199	0.26197674129611	0.15148375395284	
#3	-0.17329339770404	-0.29577216135752	-0.32854773287336	-0.25837595019402	-0.10464629137272	0.083977919643731	0.24375502537612	0.31734911074452	0.27554873236546	0.13078246142548	-0.064169180468644	-0.2338517998883	-0.3090949176294	-0.25640388301769	-0.095009113547533	0.10762065297447	0.26245965771062	0.29810977741439	0.19538373341457	
#4	-0.2092420611206	-0.32440396514543	-0.28870416267009	-0.11429300342148	0.11679389727073	0.288164043353	0.30775257209629	0.16049652867366	-0.076245616678057	-0.26930077319444	-0.30390036655425	-0.1550002289042	0.089881416654206	0.27771947876021	0.28501960672877	0.10264141337114	-0.14962648594078	-0.29770488988101	-0.23389191200031	
#5	-0.24060317776183	-0.3290131264535	-0.20216918188968	0.061327663611512	0.28204075272085	0.29987682985659	0.095501051405227	-0.18171364275768	-0.31639304506174	-0.19603198532073	0.086600390028108	0.29566814739951	0.24716031841867	-0.022026285835052	-0.2710687688842	-0.26632542051884	-0.0064599381001157	0.25973386885002	0.26585134009605	
#6	-0.26671629720065	-0.31009492823007	-0.084907639557607	0.21625437070113	0.3177036113739	0.11662763997378	-0.19885313247031	-0.31356049099593	-0.10267515018608	0.2177737046084	0.29958505109499	0.044506705753225	-0.26189842379724	-0.25875188328137	0.05765759922574	0.30260710150076	0.16382012942261	-0.18741163935286	-0.29022300603464	
#7	0.28705072959268	0.27016726312415	-0.042583832526369	-0.30715395304704	-0.21304541214178	0.13758246020204	0.3175571765689	0.092112807548658	-0.25427486654224	-0.25756900802632	0.096027658586707	0.31308039031558	0.073588783156096	-0.27588451148825	-0.20301868413269	0.1880109950715	0.27756956155088	-0.088026710497809	-0.30608166268343	
#8	0.30120992109313	0.21350383148175	-0.15932774556102	-0.31232885160008	-0.020568469387477	0.30139250974251	0.1674747403952	-0.22717675439924	-0.25808801440118	0.13566191527044	0.30018507195552	-0.055803841381328	-0.31255959271621	0.00033351092555693	0.31260401373318	0.027461038571988	-0.31137832215239	-0.02757148888926	0.31258938355678	
#9	-0.30892325458402	-0.14571851631322	0.24782534418015	0.23663976417805	-0.17341032399838	-0.28208272120069	0.11427348517224	0.30005025031582	-0.082821676963031	-0.3043910090665	0.082821676963031	0.30005025031582	-0.11427348517224	-0.28208272120069	0.17341032399838	0.23663976417805	-0.24782534418016	-0.14571851631322	0.30892325458402	
#10	0.3100129905057	0.073257349051675	-0.29713282996592	-0.10752785684171	0.29123450398169	0.10588836287094	-0.29823508659063	-0.06813291675469	0.31098136922413	-0.0088545806350053	-0.3082537470826	0.1224552874316	0.25571880668969	-0.24762878509122	-0.11952791719367	0.32059620848351	-0.095575094719511	-0.2506896945706	0.29409968118993	
#11	0.30431473000689	0.0028825005674838	-0.30448419270591	0.035802960204117	0.2974913476546	-0.1142148344268	-0.25959038101351	0.21807734510994	0.15745084445418	-0.30256957535827	0.025569969348126	0.28535713432743	-0.23713743147257	-0.093352841992956	0.31909538778337	-0.20857512660622	-0.10750384771803	0.32497215201911	-0.26653472740298	
#12	-0.29161167099738	0.058779042162198	0.27532601593108	-0.15584941440028	-0.2086123789955	0.26089915087849	0.057535131388032	-0.29855953643949	0.16043208772433	0.16932148655155	-0.30961479445702	0.12684407529191	0.17870398052644	-0.32476953675183	0.20551786020295	0.066113080916032	-0.29371661262172	0.34789768238001	-0.22293165072334	
#13	0.27311723107824	-0.10652519510082	-0.22283760818805	0.22996837310114	0.076595422460415	-0.28495514043456	0.15132554672507	0.15151455161313	-0.29735135620916	0.15943674557028	0.11755458281089	-0.30163811625431	0.27204883423259	-0.0720449150495	-0.16718379731831	0.32909228131308	-0.36577338765735	0.29324889397575	-0.15720726692645	
#14	-0.26053051913533	0.14533794694689	0.16670445052617	-0.26758058958721	0.052981223602568	0.2194352055886	-0.27163596456509	0.075061967139122	0.18367241458434	-0.30641518740559	0.22916532799775	-0.022444570074868	-0.19498784378307	0.33646636392624	-0.37639478129572	0.33573871709791	-0.2526527510404	0.15979926768261	-0.074785224133042	
#15	-0.26716561565708	0.19479798825375	0.10690146992793	-0.29275300451323	0.18875058617199	0.084467822813123	-0.28986581125104	0.28965537938811	-0.11109507351393	-0.12547238797928	0.30826887557085	-0.38780861930497	0.37374483568788	-0.30445137421805	0.21866205147243	-0.14149003615738	0.083136302115224	-0.043620610241285	0.018071529260641	
#16	0.28298277078652	-0.26370043156015	-0.010737315021902	0.27586525323007	-0.32954029643475	0.16375336964172	0.094623000390595	-0.30901139235475	0.41081696479886	-0.40425380663936	0.33169846038004	-0.23834544292827	0.15401222094737	-0.090992331551435	0.049713348237063	-0.025310808734167	0.012045506172752	-0.0052915575565779	0.0019300626048219	
#17	0.3033819369786	-0.36087286293123	0.16534840996813	0.12801951852102	-0.35963570086036	0.45711399928399	-0.43409550348984	0.34412902564755	-0.23873015278664	0.14873761071668	-0.08461259041408	0.044457731742486	-0.021760196207961	0.0099874034717366	-0.0043212184285561	0.0017698119309441	-0.00068768479410405	0.00025168485927972	-7.9689286675774e-005	
#18	-0.33174659713138	0.51511355988982	-0.53084598910362	0.43850009310481	-0.31030217347991	0.1945396813828	-0.11027530784843	0.057301202724026	-0.027567469937869	0.012373328861737	-0.005212623920538	0.0020713213424887	-0.00077955511013575	0.00027885150046299	-9.5089793352995e-005	3.099224358357e-005	-9.6723283933423e-006	2.8812646109276e-006	-7.6920356668058e-007	
# The plot of the matrix is given by 
0	0.046299970256347	-0.09086453557762	0.13353716339487	-0.17329339770404	-0.2092420611206	-0.24060317776183	-0.26671629720065	0.28705072959268	0.30120992109313	-0.30892325458402	0.3100129905057	0.30431473000689	-0.29161167099738	0.27311723107824	-0.26053051913533	-0.26716561565708	0.28298277078652	0.3033819369786	-0.33174659713138	
1	0.091731359415455	-0.17490966321677	0.24473161663697	-0.29577216135752	-0.32440396514543	-0.3290131264535	-0.31009492823007	0.27016726312415	0.21350383148175	-0.14571851631322	0.073257349051675	0.0028825005674838	0.058779042162198	-0.10652519510082	0.14533794694689	0.19479798825375	-0.26370043156015	-0.36087286293123	0.51511355988982	
2	0.13538286617399	-0.2453776013199	0.31357468643797	-0.32854773287336	-0.28870416267009	-0.20216918188968	-0.084907639557607	-0.042583832526369	-0.15932774556102	0.24782534418015	-0.29713282996592	-0.30448419270591	0.27532601593108	-0.22283760818805	0.16670445052617	0.10690146992793	-0.010737315021902	0.16534840996813	-0.53084598910362	
3	0.17632041385255	-0.29616680767286	0.32635368514395	-0.25837595019402	-0.11429300342148	0.061327663611512	0.21625437070113	-0.30715395304704	-0.31232885160008	0.23663976417805	-0.10752785684171	0.035802960204117	-0.15584941440028	0.22996837310114	-0.26758058958721	-0.29275300451323	0.27586525323007	0.12801951852102	0.43850009310481	
4	0.21360991156062	-0.32244184567699	0.2789112978865	-0.10464629137272	0.11679389727073	0.28204075272085	0.3177036113739	-0.21304541214178	-0.020568469387477	-0.17341032399838	0.29123450398169	0.2974913476546	-0.2086123789955	0.076595422460415	0.052981223602568	0.18875058617199	-0.32954029643475	-0.35963570086036	-0.31030217347991	
5	0.24634241938904	-0.32119800964699	0.17840163239006	0.083977919643731	0.288164043353	0.29987682985659	0.11662763997378	0.13758246020204	0.30139250974251	-0.28208272120069	0.10588836287094	-0.1142148344268	0.26089915087849	-0.28495514043456	0.2194352055886	0.084467822813123	0.16375336964172	0.45711399928399	0.1945396813828	
6	0.27366116463097	-0.29171477476272	0.042924604770724	0.24375502537612	0.30775257209629	0.095501051405227	-0.19885313247031	0.3175571765689	0.1674747403952	0.11427348517224	-0.29823508659063	-0.25959038101351	0.057535131388032	0.15132554672507	-0.27163596456509	-0.28986581125104	0.094623000390595	-0.43409550348984	-0.11027530784843	
7	0.29478971702322	-0.23583347862836	-0.10121209313413	0.31734911074452	0.16049652867366	-0.18171364275768	-0.31356049099593	0.092112807548658	-0.22717675439924	0.30005025031582	-0.06813291675469	0.21807734510994	-0.29855953643949	0.15151455161313	0.075061967139122	0.28965537938811	-0.30901139235475	0.34412902564755	0.057301202724026	
8	0.30906049975316	-0.15800399715819	-0.22434938488222	0.27554873236546	-0.076245616678057	-0.31639304506174	-0.10267515018608	-0.25427486654224	-0.25808801440118	-0.082821676963031	0.31098136922413	0.15745084445418	0.16043208772433	-0.29735135620916	0.18367241458434	-0.11109507351393	0.41081696479886	-0.23873015278664	-0.027567469937869	
9	0.31594269619135	-0.065062982854177	-0.2996515669962	0.13078246142548	-0.26930077319444	-0.19603198532073	0.2177737046084	-0.25756900802632	0.13566191527044	-0.3043910090665	-0.0088545806350053	-0.30256957535827	0.16932148655155	0.15943674557028	-0.30641518740559	-0.12547238797928	-0.40425380663936	0.14873761071668	0.012373328861737	
10	0.31506851709119	0.03426812293573	-0.30934358797188	-0.064169180468644	-0.30390036655425	0.086600390028108	0.29958505109499	0.096027658586707	0.30018507195552	0.082821676963031	-0.3082537470826	0.025569969348126	-0.30961479445702	0.11755458281089	0.22916532799775	0.30826887557085	0.33169846038004	-0.08461259041408	-0.005212623920538	
11	0.30625672658012	0.13014542431831	-0.24952837807674	-0.2338517998883	-0.1550002289042	0.29566814739951	0.044506705753225	0.31308039031558	-0.055803841381328	0.30005025031582	0.1224552874316	0.28535713432743	0.12684407529191	-0.30163811625431	-0.022444570074868	-0.38780861930497	-0.23834544292827	0.044457731742486	0.0020713213424887	
12	0.28953229469829	0.21257071054919	-0.13221422889996	-0.3090949176294	0.089881416654206	0.24716031841867	-0.26189842379724	0.073588783156096	-0.31255959271621	-0.11427348517224	0.25571880668969	-0.23713743147257	0.17870398052644	0.27204883423259	-0.19498784378307	0.37374483568788	0.15401222094737	-0.021760196207961	-0.00077955511013575	
13	0.26514105599734	0.27247728562486	0.016324726203488	-0.25640388301769	0.27771947876021	-0.022026285835052	-0.25875188328137	-0.27588451148825	0.00033351092555693	-0.28208272120069	-0.24762878509122	-0.093352841992956	-0.32476953675183	-0.0720449150495	0.33646636392624	-0.30445137421805	-0.090992331551435	0.0099874034717366	0.00027885150046299	
14	0.23355831330471	0.30281765143493	0.16091463075229	-0.095009113547533	0.28501960672877	-0.2710687688842	0.05765759922574	-0.20301868413269	0.31260401373318	0.17341032399838	-0.11952791719367	0.31909538778337	0.20551786020295	-0.16718379731831	-0.37639478129572	0.21866205147243	0.049713348237063	-0.0043212184285561	-9.5089793352995e-005	
15	0.19549043729817	0.29952023437766	0.26565500982416	0.10762065297447	0.10264141337114	-0.26632542051884	0.30260710150076	0.1880109950715	0.027461038571988	0.23663976417805	0.32059620848351	-0.20857512660622	0.066113080916032	0.32909228131308	0.33573871709791	-0.14149003615738	-0.025310808734167	0.0017698119309441	3.099224358357e-005	
16	0.15186867831337	0.26218043290257	0.30308327022199	0.26245965771062	-0.14962648594078	-0.0064599381001157	0.16382012942261	0.27756956155088	-0.31137832215239	-0.24782534418016	-0.095575094719511	-0.10750384771803	-0.29371661262172	-0.36577338765735	-0.2526527510404	0.083136302115224	0.012045506172752	-0.00068768479410405	-9.6723283933423e-006	
17	0.10383462689339	0.19436736915818	0.26197674129611	0.29810977741439	-0.29770488988101	0.25973386885002	-0.18741163935286	-0.088026710497809	-0.02757148888926	-0.14571851631322	-0.2506896945706	0.32497215201911	0.34789768238001	0.29324889397575	0.15979926768261	-0.043620610241285	-0.0052915575565779	0.00025168485927972	2.8812646109276e-006	
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