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Fourier Analysis of SRS (ProShares UltraShort Real Estat)


SRS (ProShares UltraShort Real Estat) appears to have interesting cyclic behaviour every 44 weeks (198.8648*sine), 41 weeks (197.2108*sine), and 17 weeks (149.4157*cosine).

SRS (ProShares UltraShort Real Estat) has an average price of 1,249.47 (topmost row, frequency = 0).



Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest.

Right click on the graph above to see the menu of operations (download, full screen, etc.)

Fourier Analysis

Using data from 2/1/2007 to 3/20/2017 for SRS (ProShares UltraShort Real Estat), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,249.474   0 
11,520.898 1,446.939 (1*2π)/530530 weeks
2217.6082 1,565.176 (2*2π)/530265 weeks
3-478.5939 859.8256 (3*2π)/530177 weeks
4-371.6143 188.1412 (4*2π)/530133 weeks
53.19964 56.76552 (5*2π)/530106 weeks
6125.831 248.1341 (6*2π)/53088 weeks
7-47.68854 342.8215 (7*2π)/53076 weeks
8-196.3923 182.1235 (8*2π)/53066 weeks
9-118.8338 -10.81328 (9*2π)/53059 weeks
1056.85134 -38.68238 (10*2π)/53053 weeks
11144.7895 90.64524 (11*2π)/53048 weeks
1277.34996 198.8648 (12*2π)/53044 weeks
13-34.03352 197.2108 (13*2π)/53041 weeks
14-93.24116 120.1411 (14*2π)/53038 weeks
15-76.30421 40.17662 (15*2π)/53035 weeks
16-26.212 6.52541 (16*2π)/53033 weeks
1723.0658 9.01587 (17*2π)/53031 weeks
1841.30487 42.54588 (18*2π)/53029 weeks
1928.20068 62.97137 (19*2π)/53028 weeks
206.88447 55.41191 (20*2π)/53027 weeks
2110.948 24.53628 (21*2π)/53025 weeks
2258.41722 11.44121 (22*2π)/53024 weeks
23109.0862 66.41817 (23*2π)/53023 weeks
2476.09675 164.4698 (24*2π)/53022 weeks
25-48.78045 187.53 (25*2π)/53021 weeks
26-140.2831 76.81607 (26*2π)/53020 weeks
27-86.2475 -60.33988 (27*2π)/53020 weeks
2865.11939 -76.06369 (28*2π)/53019 weeks
29140.3837 60.81561 (29*2π)/53018 weeks
3038.01914 187.1576 (30*2π)/53018 weeks
31-123.9712 140.7022 (31*2π)/53017 weeks
32-149.4157 -28.51883 (32*2π)/53017 weeks
33-11.16348 -119.8064 (33*2π)/53016 weeks
34116.527 -40.59165 (34*2π)/53016 weeks
3599.54916 87.62082 (35*2π)/53015 weeks
36-7.15756 118.3264 (36*2π)/53015 weeks
37-64.96254 44.95878 (37*2π)/53014 weeks
38-26.46362 -26.86577 (38*2π)/53014 weeks
3945.94759 -19.54597 (39*2π)/53014 weeks
4066.6026 45.2673 (40*2π)/53013 weeks
4118.53705 82.60453 (41*2π)/53013 weeks
42-27.72042 61.03304 (42*2π)/53013 weeks
43-27.19455 15.83982 (43*2π)/53012 weeks
448.6066 3.37574 (44*2π)/53012 weeks
4528.91456 27.76304 (45*2π)/53012 weeks
4616.63976 54.07722 (46*2π)/53012 weeks
47-13.9105 58.21244 (47*2π)/53011 weeks
48-35.16408 37.41239 (48*2π)/53011 weeks
49-34.20246 6.18622 (49*2π)/53011 weeks
50-12.72042 -10.69903 (50*2π)/53011 weeks
5111.36782 -8.53292 (51*2π)/53010 weeks
5223.85463 8.04302 (52*2π)/53010 weeks
5319.25639 24.8587 (53*2π)/53010 weeks
543.69495 28.67047 (54*2π)/53010 weeks
55-6.3594 13.2015 (55*2π)/53010 weeks
5611.1353 -1.63516 (56*2π)/5309 weeks
5735.7268 15.07406 (57*2π)/5309 weeks
5827.94352 51.28449 (58*2π)/5309 weeks
59-16.83956 63.52425 (59*2π)/5309 weeks
60-52.8155 21.8789 (60*2π)/5309 weeks
61-30.94641 -28.26987 (61*2π)/5309 weeks
6218.77617 -34.9547 (62*2π)/5309 weeks
6344.02227 1.52208 (63*2π)/5308 weeks
6424.61137 28.72753 (64*2π)/5308 weeks
656.42477 18.36065 (65*2π)/5308 weeks
6616.7541 5.33945 (66*2π)/5308 weeks
6736.68599 21.28604 (67*2π)/5308 weeks
6821.83663 54.3945 (68*2π)/5308 weeks
69-20.31589 53.5664 (69*2π)/5308 weeks
70-40.13322 15.73235 (70*2π)/5308 weeks
71-18.01194 -20.25802 (71*2π)/5307 weeks
7220.27665 -14.99709 (72*2π)/5307 weeks
7329.32693 14.45945 (73*2π)/5307 weeks
748.16285 34.33764 (74*2π)/5307 weeks
75-21.88894 19.55236 (75*2π)/5307 weeks
76-15.53566 -18.10003 (76*2π)/5307 weeks
7723.44162 -28.47119 (77*2π)/5307 weeks
7854.53655 2.88394 (78*2π)/5307 weeks
7939.9068 48.23658 (79*2π)/5307 weeks
80-7.32731 56.95763 (80*2π)/5307 weeks
81-39.37723 19.66752 (81*2π)/5307 weeks
82-19.53641 -28.21059 (82*2π)/5306 weeks
8330.35486 -30.0777 (83*2π)/5306 weeks
8454.57208 9.15881 (84*2π)/5306 weeks
8534.53642 46.80194 (85*2π)/5306 weeks
86-3.21588 49.13982 (86*2π)/5306 weeks
87-22.07796 22.05933 (87*2π)/5306 weeks
88-7.83629 -2.5777 (88*2π)/5306 weeks
8915.79266 2.10967 (89*2π)/5306 weeks
9018.1066 24.94973 (90*2π)/5306 weeks
91-3.70122 36.80676 (91*2π)/5306 weeks
92-28.99302 23.14248 (92*2π)/5306 weeks
93-31.94908 -10.01929 (93*2π)/5306 weeks
94-4.66307 -32.63243 (94*2π)/5306 weeks
9528.57247 -21.46378 (95*2π)/5306 weeks
9635.2657 10.09054 (96*2π)/5306 weeks
9712.45297 29.09318 (97*2π)/5305 weeks
98-14.70678 17.46765 (98*2π)/5305 weeks
99-15.65423 -14.69096 (99*2π)/5305 weeks
10014.64978 -31.37736 (100*2π)/5305 weeks
10145.49438 -12.96742 (101*2π)/5305 weeks
10246.11418 24.05416 (102*2π)/5305 weeks
10314.41327 42.08947 (103*2π)/5305 weeks
104-15.30342 23.0791 (104*2π)/5305 weeks
105-10.79608 -12.01812 (105*2π)/5305 weeks
10624.66256 -22.04611 (106*2π)/5305 weeks
10749.66763 7.29231 (107*2π)/5305 weeks
10834.87766 43.32822 (108*2π)/5305 weeks
109-2.63743 47.71493 (109*2π)/5305 weeks
110-24.53878 19.49718 (110*2π)/5305 weeks
111-10.54148 -10.93064 (111*2π)/5305 weeks
11219.74841 -10.8693 (112*2π)/5305 weeks
11330.59469 16.35027 (113*2π)/5305 weeks
1149.61398 36.55777 (114*2π)/5305 weeks
115-18.77178 25.71464 (115*2π)/5305 weeks
116-22.47029 -6.42633 (116*2π)/5305 weeks
1176.61928 -25.93658 (117*2π)/5305 weeks
11837.15538 -8.06507 (118*2π)/5304 weeks
11935.05872 27.66361 (119*2π)/5304 weeks
1202.32565 41.18063 (120*2π)/5304 weeks
121-23.36963 20.04812 (121*2π)/5304 weeks
122-17.67789 -10.17969 (122*2π)/5304 weeks
1238.59369 -19.0559 (123*2π)/5304 weeks
12425.62227 -1.70532 (124*2π)/5304 weeks
12516.64045 17.79666 (125*2π)/5304 weeks
126-3.94097 15.18575 (126*2π)/5304 weeks
127-8.45634 -7.84532 (127*2π)/5304 weeks
12815.211 -23.50071 (128*2π)/5304 weeks
12942.79018 -8.09175 (129*2π)/5304 weeks
13045.43377 25.46292 (130*2π)/5304 weeks
13118.59959 49.18515 (131*2π)/5304 weeks
132-16.82927 40.38636 (132*2π)/5304 weeks
133-29.21688 8.17676 (133*2π)/5304 weeks
134-12.46359 -18.31762 (134*2π)/5304 weeks
13516.99606 -19.76512 (135*2π)/5304 weeks
13631.67086 3.54143 (136*2π)/5304 weeks
13718.56202 26.34341 (137*2π)/5304 weeks
138-8.54773 22.44259 (138*2π)/5304 weeks
139-13.52964 -6.27393 (139*2π)/5304 weeks
14013.97791 -20.75058 (140*2π)/5304 weeks
14139.40585 .03675 (141*2π)/5304 weeks
14230.43627 34.82612 (142*2π)/5304 weeks
143-6.86174 41.71354 (143*2π)/5304 weeks
144-30.30973 11.40674 (144*2π)/5304 weeks
145-14.77957 -23.66192 (145*2π)/5304 weeks
14622.8298 -25.93163 (146*2π)/5304 weeks
14740.68268 4.58323 (147*2π)/5304 weeks
14823.38614 32.17268 (148*2π)/5304 weeks
149-5.96659 29.47721 (149*2π)/5304 weeks
150-15.92168 4.00122 (150*2π)/5304 weeks
1512.50239 -14.09197 (151*2π)/5304 weeks
15225.62566 -4.13368 (152*2π)/5303 weeks
15324.60567 21.21324 (153*2π)/5303 weeks
1541.76992 30.27381 (154*2π)/5303 weeks
155-17.1954 16.03036 (155*2π)/5303 weeks
156-16.23648 -7.92856 (156*2π)/5303 weeks
1574.90464 -21.14982 (157*2π)/5303 weeks
15827.89008 -9.51091 (158*2π)/5303 weeks
15929.26459 16.05429 (159*2π)/5303 weeks
1608.94168 30.57362 (160*2π)/5303 weeks
161-14.94742 20.63267 (161*2π)/5303 weeks
162-18.24933 -5.22564 (162*2π)/5303 weeks
1631.85474 -20.68418 (163*2π)/5303 weeks
16424.32849 -11.01622 (164*2π)/5303 weeks
16525.37322 12.52366 (165*2π)/5303 weeks
1664.92136 23.06015 (166*2π)/5303 weeks
167-13.26719 8.26439 (167*2π)/5303 weeks
168-7.5624 -16.91826 (168*2π)/5303 weeks
16920.30806 -23.77608 (169*2π)/5303 weeks
17041.06817 -1.04596 (170*2π)/5303 weeks
17131.38224 30.126 (171*2π)/5303 weeks
172-1.83906 36.72178 (172*2π)/5303 weeks
173-22.54597 10.20517 (173*2π)/5303 weeks
174-8.41824 -18.61369 (174*2π)/5303 weeks
17522.82205 -18.65983 (175*2π)/5303 weeks
17635.3149 8.93075 (176*2π)/5303 weeks
17716.79731 30.44017 (177*2π)/5303 weeks
178-7.96475 23.22861 (178*2π)/5303 weeks
179-9.91391 1.80788 (179*2π)/5303 weeks
1805.74237 -4.21234 (180*2π)/5303 weeks
18111.66697 7.62164 (181*2π)/5303 weeks
182.61099 14.36305 (182*2π)/5303 weeks
183-9.67156 3.98387 (183*2π)/5303 weeks
184-4.46702 -9.87932 (184*2π)/5303 weeks
1858.95908 -12.51113 (185*2π)/5303 weeks
18617.3374 -5.83214 (186*2π)/5303 weeks
18718.8609 1.92284 (187*2π)/5303 weeks
18816.80282 8.26096 (188*2π)/5303 weeks
18912.61275 10.34119 (189*2π)/5303 weeks
19010.48214 12.83069 (190*2π)/5303 weeks
1915.15297 15.25518 (191*2π)/5303 weeks
192-2.73873 12.52551 (192*2π)/5303 weeks
193-5.38985 3.2987 (193*2π)/5303 weeks
1942.19603 -1.35857 (194*2π)/5303 weeks
1954.58894 4.62803 (195*2π)/5303 weeks
196-2.45738 6.39557 (196*2π)/5303 weeks
197-9.08826 -3.34055 (197*2π)/5303 weeks
198-.6786 -17.10254 (198*2π)/5303 weeks
19916.36179 -15.15879 (199*2π)/5303 weeks
20021.47016 -1.11438 (200*2π)/5303 weeks
20112.79396 6.19494 (201*2π)/5303 weeks
2028.0359 -.32844 (202*2π)/5303 weeks
20316.83984 -3.34141 (203*2π)/5303 weeks
20422.67134 8.51387 (204*2π)/5303 weeks
20512.00659 20.83037 (205*2π)/5303 weeks
206-6.42433 16.70783 (206*2π)/5303 weeks
207-10.04596 -3.64477 (207*2π)/5303 weeks
2086.59755 -14.38737 (208*2π)/5303 weeks
20921.22614 -3.52835 (209*2π)/5303 weeks
21015.62155 11.31983 (210*2π)/5303 weeks
2112.98439 8.10511 (211*2π)/5303 weeks
2126.18371 -3.17178 (212*2π)/5303 weeks
21319.7948 -.66175 (213*2π)/5302 weeks
21421.91687 16.75831 (214*2π)/5302 weeks
2154.08672 29.10289 (215*2π)/5302 weeks
216-17.96824 17.11422 (216*2π)/5302 weeks
217-17.55367 -8.23172 (217*2π)/5302 weeks
2183.98274 -19.11093 (218*2π)/5302 weeks
21921.99696 -4.86898 (219*2π)/5302 weeks
22014.51014 15.42468 (220*2π)/5302 weeks
221-5.31071 14.9788 (221*2π)/5302 weeks
222-12.24037 -3.47517 (222*2π)/5302 weeks
2232.90085 -17.05069 (223*2π)/5302 weeks
22420.69666 -7.48753 (224*2π)/5302 weeks
22518.80249 12.58571 (225*2π)/5302 weeks
226-1.39841 19.04309 (226*2π)/5302 weeks
227-15.84264 2.59582 (227*2π)/5302 weeks
228-7.52508 -17.17807 (228*2π)/5302 weeks
22911.07771 -19.64157 (229*2π)/5302 weeks
23023.07681 -7.74001 (230*2π)/5302 weeks
23119.71007 7.58602 (231*2π)/5302 weeks
2327.667 11.76532 (232*2π)/5302 weeks
233-1.10676 4.89287 (233*2π)/5302 weeks
2341.34314 -4.41673 (234*2π)/5302 weeks
2358.76147 -5.6373 (235*2π)/5302 weeks
23613.63739 -.25891 (236*2π)/5302 weeks
23710.39058 7.54543 (237*2π)/5302 weeks
238.48494 8.41734 (238*2π)/5302 weeks
239-6.10719 -.9128 (239*2π)/5302 weeks
240-1.0168 -14.06706 (240*2π)/5302 weeks
24115.26999 -15.80426 (241*2π)/5302 weeks
24225.09649 -2.04791 (242*2π)/5302 weeks
24318.72151 14.42963 (243*2π)/5302 weeks
244-.87426 18.16569 (244*2π)/5302 weeks
245-15.00564 .58999 (245*2π)/5302 weeks
246-5.04168 -21.89101 (246*2π)/5302 weeks
24722.20736 -23.56193 (247*2π)/5302 weeks
24835.97852 2.31272 (248*2π)/5302 weeks
24918.13855 25.87336 (249*2π)/5302 weeks
250-10.64032 20.92794 (250*2π)/5302 weeks
251-19.54434 -7.78467 (251*2π)/5302 weeks
2522.99056 -27.35777 (252*2π)/5302 weeks
25328.48534 -15.12872 (253*2π)/5302 weeks
25426.3889 10.54181 (254*2π)/5302 weeks
2554.96383 17.36249 (255*2π)/5302 weeks
256-8.03029 1.34305 (256*2π)/5302 weeks
2571.60258 -15.60774 (257*2π)/5302 weeks
25821.57993 -13.1119 (258*2π)/5302 weeks
25926.98409 7.0914 (259*2π)/5302 weeks
2609.92811 20.27285 (260*2π)/5302 weeks
261-8.21843 11.20335 (261*2π)/5302 weeks
262-10.37737 -7.84929 (262*2π)/5302 weeks
2633.73946 -19.78499 (263*2π)/5302 weeks
26421.24071 -16.44679 (264*2π)/5302 weeks
26529.61038   (265*2π)/5302 weeks
26621.24071 16.44679 (266*2π)/5302 weeks
2673.73946 19.78499 (267*2π)/5302 weeks
268-10.37737 7.84929 (268*2π)/5302 weeks
269-8.21843 -11.20335 (269*2π)/5302 weeks
2709.92811 -20.27285 (270*2π)/5302 weeks
27126.98409 -7.0914 (271*2π)/5302 weeks
27221.57993 13.1119 (272*2π)/5302 weeks
2731.60258 15.60774 (273*2π)/5302 weeks
274-8.03029 -1.34305 (274*2π)/5302 weeks
2754.96383 -17.36249 (275*2π)/5302 weeks
27626.3889 -10.54181 (276*2π)/5302 weeks
27728.48534 15.12872 (277*2π)/5302 weeks
2782.99056 27.35777 (278*2π)/5302 weeks
279-19.54434 7.78467 (279*2π)/5302 weeks
280-10.64032 -20.92794 (280*2π)/5302 weeks
28118.13855 -25.87336 (281*2π)/5302 weeks
28235.97852 -2.31272 (282*2π)/5302 weeks
28322.20736 23.56193 (283*2π)/5302 weeks
284-5.04168 21.89101 (284*2π)/5302 weeks
285-15.00564 -.58999 (285*2π)/5302 weeks
286-.87426 -18.16569 (286*2π)/5302 weeks
28718.72151 -14.42963 (287*2π)/5302 weeks
28825.09649 2.04791 (288*2π)/5302 weeks
28915.26999 15.80426 (289*2π)/5302 weeks
290-1.0168 14.06706 (290*2π)/5302 weeks
291-6.10719 .9128 (291*2π)/5302 weeks
292.48494 -8.41734 (292*2π)/5302 weeks
29310.39058 -7.54543 (293*2π)/5302 weeks
29413.63739 .25891 (294*2π)/5302 weeks
2958.76147 5.6373 (295*2π)/5302 weeks
2961.34314 4.41673 (296*2π)/5302 weeks
297-1.10676 -4.89287 (297*2π)/5302 weeks
2987.667 -11.76532 (298*2π)/5302 weeks
29919.71007 -7.58602 (299*2π)/5302 weeks
30023.07681 7.74001 (300*2π)/5302 weeks
30111.07771 19.64157 (301*2π)/5302 weeks
302-7.52508 17.17807 (302*2π)/5302 weeks
303-15.84264 -2.59582 (303*2π)/5302 weeks
304-1.39841 -19.04309 (304*2π)/5302 weeks
30518.80249 -12.58571 (305*2π)/5302 weeks
30620.69666 7.48753 (306*2π)/5302 weeks
3072.90085 17.05069 (307*2π)/5302 weeks
308-12.24037 3.47517 (308*2π)/5302 weeks
309-5.31071 -14.9788 (309*2π)/5302 weeks
31014.51014 -15.42468 (310*2π)/5302 weeks
31121.99696 4.86898 (311*2π)/5302 weeks
3123.98274 19.11093 (312*2π)/5302 weeks
313-17.55367 8.23172 (313*2π)/5302 weeks
314-17.96824 -17.11422 (314*2π)/5302 weeks
3154.08672 -29.10289 (315*2π)/5302 weeks
31621.91687 -16.75831 (316*2π)/5302 weeks
31719.7948 .66175 (317*2π)/5302 weeks
3186.18371 3.17178 (318*2π)/5302 weeks
3192.98439 -8.10511 (319*2π)/5302 weeks
32015.62155 -11.31983 (320*2π)/5302 weeks
32121.22614 3.52835 (321*2π)/5302 weeks
3226.59755 14.38737 (322*2π)/5302 weeks
323-10.04596 3.64477 (323*2π)/5302 weeks
324-6.42433 -16.70783 (324*2π)/5302 weeks
32512.00659 -20.83037 (325*2π)/5302 weeks
32622.67134 -8.51387 (326*2π)/5302 weeks
32716.83984 3.34141 (327*2π)/5302 weeks
3288.0359 .32844 (328*2π)/5302 weeks
32912.79396 -6.19494 (329*2π)/5302 weeks
33021.47016 1.11438 (330*2π)/5302 weeks
33116.36179 15.15879 (331*2π)/5302 weeks
332-.6786 17.10254 (332*2π)/5302 weeks
333-9.08826 3.34055 (333*2π)/5302 weeks
334-2.45738 -6.39557 (334*2π)/5302 weeks
3354.58894 -4.62803 (335*2π)/5302 weeks
3362.19603 1.35857 (336*2π)/5302 weeks
337-5.38985 -3.2987 (337*2π)/5302 weeks
338-2.73873 -12.52551 (338*2π)/5302 weeks
3395.15297 -15.25518 (339*2π)/5302 weeks
34010.48214 -12.83069 (340*2π)/5302 weeks
34112.61275 -10.34119 (341*2π)/5302 weeks
34216.80282 -8.26096 (342*2π)/5302 weeks
34318.8609 -1.92284 (343*2π)/5302 weeks
34417.3374 5.83214 (344*2π)/5302 weeks
3458.95908 12.51113 (345*2π)/5302 weeks
346-4.46702 9.87932 (346*2π)/5302 weeks
347-9.67156 -3.98387 (347*2π)/5302 weeks
348.61099 -14.36305 (348*2π)/5302 weeks
34911.66697 -7.62164 (349*2π)/5302 weeks
3505.74237 4.21234 (350*2π)/5302 weeks
351-9.91391 -1.80788 (351*2π)/5302 weeks
352-7.96475 -23.22861 (352*2π)/5302 weeks
35316.79731 -30.44017 (353*2π)/5302 weeks
35435.3149 -8.93075 (354*2π)/5301 weeks
35522.82205 18.65983 (355*2π)/5301 weeks
356-8.41824 18.61369 (356*2π)/5301 weeks
357-22.54597 -10.20517 (357*2π)/5301 weeks
358-1.83906 -36.72178 (358*2π)/5301 weeks
35931.38224 -30.126 (359*2π)/5301 weeks
36041.06817 1.04596 (360*2π)/5301 weeks
36120.30806 23.77608 (361*2π)/5301 weeks
362-7.5624 16.91826 (362*2π)/5301 weeks
363-13.26719 -8.26439 (363*2π)/5301 weeks
3644.92136 -23.06015 (364*2π)/5301 weeks
36525.37322 -12.52366 (365*2π)/5301 weeks
36624.32849 11.01622 (366*2π)/5301 weeks
3671.85474 20.68418 (367*2π)/5301 weeks
368-18.24933 5.22564 (368*2π)/5301 weeks
369-14.94742 -20.63267 (369*2π)/5301 weeks
3708.94168 -30.57362 (370*2π)/5301 weeks
37129.26459 -16.05429 (371*2π)/5301 weeks
37227.89008 9.51091 (372*2π)/5301 weeks
3734.90464 21.14982 (373*2π)/5301 weeks
374-16.23648 7.92856 (374*2π)/5301 weeks
375-17.1954 -16.03036 (375*2π)/5301 weeks
3761.76992 -30.27381 (376*2π)/5301 weeks
37724.60567 -21.21324 (377*2π)/5301 weeks
37825.62566 4.13368 (378*2π)/5301 weeks
3792.50239 14.09197 (379*2π)/5301 weeks
380-15.92168 -4.00122 (380*2π)/5301 weeks
381-5.96659 -29.47721 (381*2π)/5301 weeks
38223.38614 -32.17268 (382*2π)/5301 weeks
38340.68268 -4.58323 (383*2π)/5301 weeks
38422.8298 25.93163 (384*2π)/5301 weeks
385-14.77957 23.66192 (385*2π)/5301 weeks
386-30.30973 -11.40674 (386*2π)/5301 weeks
387-6.86174 -41.71354 (387*2π)/5301 weeks
38830.43627 -34.82612 (388*2π)/5301 weeks
38939.40585 -.03675 (389*2π)/5301 weeks
39013.97791 20.75058 (390*2π)/5301 weeks
391-13.52964 6.27393 (391*2π)/5301 weeks
392-8.54773 -22.44259 (392*2π)/5301 weeks
39318.56202 -26.34341 (393*2π)/5301 weeks
39431.67086 -3.54143 (394*2π)/5301 weeks
39516.99606 19.76512 (395*2π)/5301 weeks
396-12.46359 18.31762 (396*2π)/5301 weeks
397-29.21688 -8.17676 (397*2π)/5301 weeks
398-16.82927 -40.38636 (398*2π)/5301 weeks
39918.59959 -49.18515 (399*2π)/5301 weeks
40045.43377 -25.46292 (400*2π)/5301 weeks
40142.79018 8.09175 (401*2π)/5301 weeks
40215.211 23.50071 (402*2π)/5301 weeks
403-8.45634 7.84532 (403*2π)/5301 weeks
404-3.94097 -15.18575 (404*2π)/5301 weeks
40516.64045 -17.79666 (405*2π)/5301 weeks
40625.62227 1.70532 (406*2π)/5301 weeks
4078.59369 19.0559 (407*2π)/5301 weeks
408-17.67789 10.17969 (408*2π)/5301 weeks
409-23.36963 -20.04812 (409*2π)/5301 weeks
4102.32565 -41.18063 (410*2π)/5301 weeks
41135.05872 -27.66361 (411*2π)/5301 weeks
41237.15538 8.06507 (412*2π)/5301 weeks
4136.61928 25.93658 (413*2π)/5301 weeks
414-22.47029 6.42633 (414*2π)/5301 weeks
415-18.77178 -25.71464 (415*2π)/5301 weeks
4169.61398 -36.55777 (416*2π)/5301 weeks
41730.59469 -16.35027 (417*2π)/5301 weeks
41819.74841 10.8693 (418*2π)/5301 weeks
419-10.54148 10.93064 (419*2π)/5301 weeks
420-24.53878 -19.49718 (420*2π)/5301 weeks
421-2.63743 -47.71493 (421*2π)/5301 weeks
42234.87766 -43.32822 (422*2π)/5301 weeks
42349.66763 -7.29231 (423*2π)/5301 weeks
42424.66256 22.04611 (424*2π)/5301 weeks
425-10.79608 12.01812 (425*2π)/5301 weeks
426-15.30342 -23.0791 (426*2π)/5301 weeks
42714.41327 -42.08947 (427*2π)/5301 weeks
42846.11418 -24.05416 (428*2π)/5301 weeks
42945.49438 12.96742 (429*2π)/5301 weeks
43014.64978 31.37736 (430*2π)/5301 weeks
431-15.65423 14.69096 (431*2π)/5301 weeks
432-14.70678 -17.46765 (432*2π)/5301 weeks
43312.45297 -29.09318 (433*2π)/5301 weeks
43435.2657 -10.09054 (434*2π)/5301 weeks
43528.57247 21.46378 (435*2π)/5301 weeks
436-4.66307 32.63243 (436*2π)/5301 weeks
437-31.94908 10.01929 (437*2π)/5301 weeks
438-28.99302 -23.14248 (438*2π)/5301 weeks
439-3.70122 -36.80676 (439*2π)/5301 weeks
44018.1066 -24.94973 (440*2π)/5301 weeks
44115.79266 -2.10967 (441*2π)/5301 weeks
442-7.83629 2.5777 (442*2π)/5301 weeks
443-22.07796 -22.05933 (443*2π)/5301 weeks
444-3.21588 -49.13982 (444*2π)/5301 weeks
44534.53642 -46.80194 (445*2π)/5301 weeks
44654.57208 -9.15881 (446*2π)/5301 weeks
44730.35486 30.0777 (447*2π)/5301 weeks
448-19.53641 28.21059 (448*2π)/5301 weeks
449-39.37723 -19.66752 (449*2π)/5301 weeks
450-7.32731 -56.95763 (450*2π)/5301 weeks
45139.9068 -48.23658 (451*2π)/5301 weeks
45254.53655 -2.88394 (452*2π)/5301 weeks
45323.44162 28.47119 (453*2π)/5301 weeks
454-15.53566 18.10003 (454*2π)/5301 weeks
455-21.88894 -19.55236 (455*2π)/5301 weeks
4568.16285 -34.33764 (456*2π)/5301 weeks
45729.32693 -14.45945 (457*2π)/5301 weeks
45820.27665 14.99709 (458*2π)/5301 weeks
459-18.01194 20.25802 (459*2π)/5301 weeks
460-40.13322 -15.73235 (460*2π)/5301 weeks
461-20.31589 -53.5664 (461*2π)/5301 weeks
46221.83663 -54.3945 (462*2π)/5301 weeks
46336.68599 -21.28604 (463*2π)/5301 weeks
46416.7541 -5.33945 (464*2π)/5301 weeks
4656.42477 -18.36065 (465*2π)/5301 weeks
46624.61137 -28.72753 (466*2π)/5301 weeks
46744.02227 -1.52208 (467*2π)/5301 weeks
46818.77617 34.9547 (468*2π)/5301 weeks
469-30.94641 28.26987 (469*2π)/5301 weeks
470-52.8155 -21.8789 (470*2π)/5301 weeks
471-16.83956 -63.52425 (471*2π)/5301 weeks
47227.94352 -51.28449 (472*2π)/5301 weeks
47335.7268 -15.07406 (473*2π)/5301 weeks
47411.1353 1.63516 (474*2π)/5301 weeks
475-6.3594 -13.2015 (475*2π)/5301 weeks
4763.69495 -28.67047 (476*2π)/5301 weeks
47719.25639 -24.8587 (477*2π)/5301 weeks
47823.85463 -8.04302 (478*2π)/5301 weeks
47911.36782 8.53292 (479*2π)/5301 weeks
480-12.72042 10.69903 (480*2π)/5301 weeks
481-34.20246 -6.18622 (481*2π)/5301 weeks
482-35.16408 -37.41239 (482*2π)/5301 weeks
483-13.9105 -58.21244 (483*2π)/5301 weeks
48416.63976 -54.07722 (484*2π)/5301 weeks
48528.91456 -27.76304 (485*2π)/5301 weeks
4868.6066 -3.37574 (486*2π)/5301 weeks
487-27.19455 -15.83982 (487*2π)/5301 weeks
488-27.72042 -61.03304 (488*2π)/5301 weeks
48918.53705 -82.60453 (489*2π)/5301 weeks
49066.6026 -45.2673 (490*2π)/5301 weeks
49145.94759 19.54597 (491*2π)/5301 weeks
492-26.46362 26.86577 (492*2π)/5301 weeks
493-64.96254 -44.95878 (493*2π)/5301 weeks
494-7.15756 -118.3264 (494*2π)/5301 weeks
49599.54916 -87.62082 (495*2π)/5301 weeks
496116.527 40.59165 (496*2π)/5301 weeks
497-11.16348 119.8064 (497*2π)/5301 weeks
498-149.4157 28.51883 (498*2π)/5301 weeks
499-123.9712 -140.7022 (499*2π)/5301 weeks
50038.01914 -187.1576 (500*2π)/5301 weeks
501140.3837 -60.81561 (501*2π)/5301 weeks
50265.11939 76.06369 (502*2π)/5301 weeks
503-86.2475 60.33988 (503*2π)/5301 weeks
504-140.2831 -76.81607 (504*2π)/5301 weeks
505-48.78045 -187.53 (505*2π)/5301 weeks
50676.09675 -164.4698 (506*2π)/5301 weeks
507109.0862 -66.41817 (507*2π)/5301 weeks
50858.41722 -11.44121 (508*2π)/5301 weeks
50910.948 -24.53628 (509*2π)/5301 weeks
5106.88447 -55.41191 (510*2π)/5301 weeks
51128.20068 -62.97137 (511*2π)/5301 weeks
51241.30487 -42.54588 (512*2π)/5301 weeks
51323.0658 -9.01587 (513*2π)/5301 weeks
514-26.212 -6.52541 (514*2π)/5301 weeks
515-76.30421 -40.17662 (515*2π)/5301 weeks
516-93.24116 -120.1411 (516*2π)/5301 weeks
517-34.03352 -197.2108 (517*2π)/5301 weeks
51877.34996 -198.8648 (518*2π)/5301 weeks
519144.7895 -90.64524 (519*2π)/5301 weeks
52056.85134 38.68238 (520*2π)/5301 weeks
521-118.8338 10.81328 (521*2π)/5301 weeks
522-196.3923 -182.1235 (522*2π)/5301 weeks
523-47.68854 -342.8215 (523*2π)/5301 weeks
524125.831 -248.1341 (524*2π)/5301 weeks
5253.19964 -56.76552 (525*2π)/5301 weeks
526-371.6143 -188.1412 (526*2π)/5301 weeks
527-478.5939 -859.8256 (527*2π)/5301 weeks
528217.6082 -1,565.176 (528*2π)/5301 weeks

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