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Fourier Analysis of SRS (ProShares UltraShort Real Estate ETF)


SRS (ProShares UltraShort Real Estate ETF) appears to have interesting cyclic behaviour every 42 weeks (205.2474*sine), 18 weeks (185.4349*sine), and 22 weeks (177.2795*sine).

SRS (ProShares UltraShort Real Estate ETF) has an average price of 1,213.58 (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 7/10/2017 for SRS (ProShares UltraShort Real Estate ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,213.578   0 
11,513.677 1,383.455 (1*2π)/546546 weeks
2275.6005 1,542.098 (2*2π)/546273 weeks
3-439.6267 905.1943 (3*2π)/546182 weeks
4-400.4697 234.9441 (4*2π)/546137 weeks
5-40.49639 45.13238 (5*2π)/546109 weeks
6127.6097 202.7822 (6*2π)/54691 weeks
7-2.77114 335.0602 (7*2π)/54678 weeks
8-176.1114 227.731 (8*2π)/54668 weeks
9-152.9915 26.75196 (9*2π)/54661 weeks
105.26022 -47.79191 (10*2π)/54655 weeks
11132.751 40.55475 (11*2π)/54650 weeks
12108.7076 167.1204 (12*2π)/54646 weeks
135.42004 205.2474 (13*2π)/54642 weeks
14-75.09055 152.7569 (14*2π)/54639 weeks
15-87.83231 68.81653 (15*2π)/54636 weeks
16-47.83882 15.62089 (16*2π)/54634 weeks
17-1.12512 2.01871 (17*2π)/54632 weeks
1836.56541 23.52105 (18*2π)/54630 weeks
1936.68248 52.26257 (19*2π)/54629 weeks
2017.8919 61.90978 (20*2π)/54627 weeks
213.54177 43.46801 (21*2π)/54626 weeks
2222.57236 14.32507 (22*2π)/54625 weeks
2376.40202 19.99988 (23*2π)/54624 weeks
24107.9981 92.23765 (24*2π)/54623 weeks
2546.38548 177.2795 (25*2π)/54622 weeks
26-77.91629 167.3141 (26*2π)/54621 weeks
27-137.5296 43.70757 (27*2π)/54620 weeks
28-60.73033 -73.14127 (28*2π)/54620 weeks
2983.52697 -60.82698 (29*2π)/54619 weeks
30133.3673 78.63889 (30*2π)/54618 weeks
3121.81768 185.4349 (31*2π)/54618 weeks
32-127.2047 128.0612 (32*2π)/54617 weeks
33-142.5855 -32.87542 (33*2π)/54617 weeks
34-10.24575 -116.252 (34*2π)/54616 weeks
35111.5125 -42.73692 (35*2π)/54616 weeks
36100.8556 79.80234 (36*2π)/54615 weeks
371.60408 117.3708 (37*2π)/54615 weeks
38-61.65771 53.61254 (38*2π)/54614 weeks
39-35.47742 -19.94716 (39*2π)/54614 weeks
4034.30557 -25.62299 (40*2π)/54614 weeks
4167.12421 30.31018 (41*2π)/54613 weeks
4230.83816 77.89687 (42*2π)/54613 weeks
43-18.05249 69.21715 (43*2π)/54613 weeks
44-31.68682 26.82361 (44*2π)/54612 weeks
45-2.91583 1.85556 (45*2π)/54612 weeks
4624.85679 16.32161 (46*2π)/54612 weeks
4723.33047 44.42991 (47*2π)/54612 weeks
48-.93656 58.87853 (48*2π)/54611 weeks
49-26.96674 46.93052 (49*2π)/54611 weeks
50-37.27403 20.03519 (50*2π)/54611 weeks
51-23.42064 -4.70206 (51*2π)/54611 weeks
52-.63949 -12.03737 (52*2π)/54611 weeks
5318.269 -2.31855 (53*2π)/54610 weeks
5422.82699 15.34294 (54*2π)/54610 weeks
5513.05978 27.83898 (55*2π)/54610 weeks
56-1.84696 25.07874 (56*2π)/54610 weeks
57-3.19996 6.0692 (57*2π)/54610 weeks
5819.22361 -.55757 (58*2π)/5469 weeks
5936.68597 23.94743 (59*2π)/5469 weeks
6019.18591 56.56273 (60*2π)/5469 weeks
61-26.83702 57.35796 (61*2π)/5469 weeks
62-51.47761 10.61805 (62*2π)/5469 weeks
63-23.18307 -31.69153 (63*2π)/5469 weeks
6423.67826 -31.16022 (64*2π)/5469 weeks
6542.46783 5.28929 (65*2π)/5468 weeks
6622.04423 28.18744 (66*2π)/5468 weeks
676.17453 17.17984 (67*2π)/5468 weeks
6816.43137 5.15045 (68*2π)/5468 weeks
6935.42457 19.95048 (69*2π)/5468 weeks
7022.9473 51.61057 (70*2π)/5468 weeks
71-16.65397 53.77515 (71*2π)/5468 weeks
72-38.78819 19.97019 (72*2π)/5468 weeks
73-22.60751 -16.5833 (73*2π)/5467 weeks
7414.901 -18.3315 (74*2π)/5467 weeks
7529.21576 8.20492 (75*2π)/5467 weeks
7614.41478 31.15997 (76*2π)/5467 weeks
77-15.47691 26.68848 (77*2π)/5467 weeks
78-21.4882 -8.10344 (78*2π)/5467 weeks
799.7468 -28.8903 (79*2π)/5467 weeks
8046.10244 -11.71783 (80*2π)/5467 weeks
8149.80345 32.40857 (81*2π)/5467 weeks
8212.19305 57.83564 (82*2π)/5467 weeks
83-29.4157 39.04802 (83*2π)/5467 weeks
84-34.81684 -8.66708 (84*2π)/5467 weeks
856.14216 -35.133 (85*2π)/5466 weeks
8645.88646 -13.74116 (86*2π)/5466 weeks
8748.76841 28.44482 (87*2π)/5466 weeks
8817.90588 51.16032 (88*2π)/5466 weeks
89-13.78368 39.51098 (89*2π)/5466 weeks
90-19.64225 10.39277 (90*2π)/5466 weeks
91.86375 -4.35089 (91*2π)/5466 weeks
9218.96539 8.19025 (92*2π)/5466 weeks
9313.41086 29.53561 (93*2π)/5466 weeks
94-10.07458 34.93985 (94*2π)/5466 weeks
95-31.3926 16.26306 (95*2π)/5466 weeks
96-27.97629 -15.50368 (96*2π)/5466 weeks
971.22394 -32.29977 (97*2π)/5466 weeks
9830.41974 -17.40413 (98*2π)/5466 weeks
9933.0643 12.65187 (99*2π)/5466 weeks
10010.06113 28.44508 (100*2π)/5465 weeks
101-14.97812 15.88523 (101*2π)/5465 weeks
102-14.99736 -14.57823 (102*2π)/5465 weeks
10313.56586 -30.45889 (103*2π)/5465 weeks
10443.23652 -14.06405 (104*2π)/5465 weeks
10546.10506 20.7393 (105*2π)/5465 weeks
10617.8511 40.71023 (106*2π)/5465 weeks
107-12.4489 26.6293 (107*2π)/5465 weeks
108-13.9329 -6.61611 (108*2π)/5465 weeks
10916.69671 -22.7327 (109*2π)/5465 weeks
11045.94296 -1.522 (110*2π)/5465 weeks
11140.99899 34.88631 (111*2π)/5465 weeks
1127.49916 48.89141 (112*2π)/5465 weeks
113-20.70627 29.52162 (113*2π)/5465 weeks
114-18.56882 -2.83727 (114*2π)/5465 weeks
1158.67559 -14.38033 (115*2π)/5465 weeks
11629.67286 4.13207 (116*2π)/5465 weeks
11721.03008 30.05463 (117*2π)/5465 weeks
118-6.82053 33.63448 (118*2π)/5465 weeks
119-24.25802 9.56311 (119*2π)/5465 weeks
120-11.32931 -19.45576 (120*2π)/5465 weeks
12122.13509 -21.3546 (121*2π)/5465 weeks
12240.02185 7.08231 (122*2π)/5464 weeks
12323.32008 36.55707 (123*2π)/5464 weeks
124-9.34491 35.57091 (124*2π)/5464 weeks
125-24.31889 8.6147 (125*2π)/5464 weeks
126-10.27961 -15.67437 (126*2π)/5464 weeks
12715.02202 -15.74305 (127*2π)/5464 weeks
12825.01228 4.0565 (128*2π)/5464 weeks
12911.79872 18.89643 (129*2π)/5464 weeks
130-6.65902 11.407 (130*2π)/5464 weeks
131-6.27794 -11.46775 (131*2π)/5464 weeks
13218.83757 -22.54571 (132*2π)/5464 weeks
13343.2045 -4.84938 (133*2π)/5464 weeks
13443.08552 27.04834 (134*2π)/5464 weeks
13516.44726 48.10194 (135*2π)/5464 weeks
136-16.72942 38.84929 (136*2π)/5464 weeks
137-28.41048 8.42192 (137*2π)/5464 weeks
138-13.2439 -17.06182 (138*2π)/5464 weeks
13914.51369 -20.06864 (139*2π)/5464 weeks
14030.51345 .73558 (140*2π)/5464 weeks
14121.08401 23.70376 (141*2π)/5464 weeks
142-4.57927 24.70927 (142*2π)/5464 weeks
143-15.00281 -.41849 (143*2π)/5464 weeks
1446.55609 -20.04963 (144*2π)/5464 weeks
14534.40706 -7.70645 (145*2π)/5464 weeks
14636.01293 25.42357 (146*2π)/5464 weeks
1475.04431 42.84732 (147*2π)/5464 weeks
148-25.51956 23.53954 (148*2π)/5464 weeks
149-24.13732 -12.67448 (149*2π)/5464 weeks
1507.81093 -29.29817 (150*2π)/5464 weeks
15136.42743 -10.07814 (151*2π)/5464 weeks
15233.85677 21.68591 (152*2π)/5464 weeks
1537.13446 33.70886 (153*2π)/5464 weeks
154-14.24524 17.80865 (154*2π)/5464 weeks
155-9.88236 -6.96153 (155*2π)/5464 weeks
15613.29135 -12.95151 (156*2π)/5464 weeks
15728.08025 5.85791 (157*2π)/5463 weeks
15816.73532 26.83662 (158*2π)/5463 weeks
159-6.02806 26.85283 (159*2π)/5463 weeks
160-18.8269 8.48875 (160*2π)/5463 weeks
161-11.51517 -13.15494 (161*2π)/5463 weeks
16211.36058 -19.99296 (162*2π)/5463 weeks
16329.73244 -3.98848 (163*2π)/5463 weeks
16425.8144 19.67911 (164*2π)/5463 weeks
1654.40899 29.84821 (165*2π)/5463 weeks
166-16.50705 17.01139 (166*2π)/5463 weeks
167-16.50743 -7.54796 (167*2π)/5463 weeks
1683.74247 -20.22418 (168*2π)/5463 weeks
16924.27124 -9.704 (169*2π)/5463 weeks
17024.40978 12.52791 (170*2π)/5463 weeks
1715.04417 22.41614 (171*2π)/5463 weeks
172-12.50387 8.94766 (172*2π)/5463 weeks
173-8.62771 -14.99004 (173*2π)/5463 weeks
17416.78816 -23.81237 (174*2π)/5463 weeks
17538.66684 -4.94584 (175*2π)/5463 weeks
17634.0655 25.28761 (176*2π)/5463 weeks
1774.46689 37.235 (177*2π)/5463 weeks
178-20.30779 17.09363 (178*2π)/5463 weeks
179-14.19178 -12.99817 (179*2π)/5463 weeks
18014.15796 -21.62046 (180*2π)/5463 weeks
18134.07728 -.54312 (181*2π)/5463 weeks
18224.63018 25.24861 (182*2π)/5463 weeks
183-.53683 28.27639 (183*2π)/5463 weeks
184-11.98877 9.44944 (184*2π)/5463 weeks
185-1.19597 -4.51857 (185*2π)/5463 weeks
18611.1677 1.40589 (186*2π)/5463 weeks
1877.09058 12.63062 (187*2π)/5463 weeks
188-5.86783 10.6934 (188*2π)/5463 weeks
189-8.81236 -3.08371 (189*2π)/5463 weeks
1901.22459 -12.48022 (190*2π)/5463 weeks
19112.74349 -10.14045 (191*2π)/5463 weeks
19217.89038 -2.61367 (192*2π)/5463 weeks
19317.96617 4.10446 (193*2π)/5463 weeks
19414.73969 9.34651 (194*2π)/5463 weeks
19511.79659 10.47113 (195*2π)/5463 weeks
1969.16717 13.26477 (196*2π)/5463 weeks
1973.30967 14.93057 (197*2π)/5463 weeks
198-3.79542 10.79858 (198*2π)/5463 weeks
199-4.49322 1.61967 (199*2π)/5463 weeks
2003.18305 -.86761 (200*2π)/5463 weeks
2013.99119 5.06145 (201*2π)/5463 weeks
202-3.10891 5.92854 (202*2π)/5463 weeks
203-8.83343 -3.98954 (203*2π)/5463 weeks
204-.29915 -16.76089 (204*2π)/5463 weeks
20515.78397 -14.7854 (205*2π)/5463 weeks
20620.94772 -1.5672 (206*2π)/5463 weeks
20713.09404 6.02923 (207*2π)/5463 weeks
2087.59087 .4882 (208*2π)/5463 weeks
20914.94312 -3.6958 (209*2π)/5463 weeks
21022.0923 5.97341 (210*2π)/5463 weeks
21114.58589 18.94404 (211*2π)/5463 weeks
212-2.68605 18.8764 (212*2π)/5463 weeks
213-11.16088 1.30977 (213*2π)/5463 weeks
2141.02042 -13.22216 (214*2π)/5463 weeks
21518.06743 -8.18375 (215*2π)/5463 weeks
21619.03613 7.5621 (216*2π)/5463 weeks
2176.27508 11.1278 (217*2π)/5463 weeks
2182.70155 .46073 (218*2π)/5463 weeks
21913.71867 -4.02389 (219*2π)/5462 weeks
22022.77777 8.09371 (220*2π)/5462 weeks
22114.38529 24.60053 (221*2π)/5462 weeks
222-8.10513 25.69664 (222*2π)/5462 weeks
223-20.61172 5.08689 (223*2π)/5462 weeks
224-9.25342 -15.54059 (224*2π)/5462 weeks
22512.9772 -15.5565 (225*2π)/5462 weeks
22621.71225 3.94777 (226*2π)/5462 weeks
2277.34937 17.4922 (227*2π)/5462 weeks
228-9.58454 9.94544 (228*2π)/5462 weeks
229-9.53762 -8.82635 (229*2π)/5462 weeks
2308.33078 -16.24745 (230*2π)/5462 weeks
23121.7493 -2.84507 (231*2π)/5462 weeks
23215.2459 15.22772 (232*2π)/5462 weeks
233-4.92154 17.05685 (233*2π)/5462 weeks
234-15.61397 -.67461 (234*2π)/5462 weeks
235-5.29326 -17.89106 (235*2π)/5462 weeks
23612.12459 -18.54212 (236*2π)/5462 weeks
23722.65721 -6.63449 (237*2π)/5462 weeks
23818.86808 7.62008 (238*2π)/5462 weeks
2397.48702 11.42303 (239*2π)/5462 weeks
240-.94744 5.0852 (240*2π)/5462 weeks
241.88871 -3.92281 (241*2π)/5462 weeks
2427.90403 -5.65142 (242*2π)/5462 weeks
24312.97414 -1.18692 (243*2π)/5462 weeks
24411.10919 6.43791 (244*2π)/5462 weeks
2452.32346 8.85139 (245*2π)/5462 weeks
246-5.25409 1.55812 (246*2π)/5462 weeks
247-3.55208 -10.9739 (247*2π)/5462 weeks
24810.46689 -16.66845 (248*2π)/5462 weeks
24922.99615 -6.90291 (249*2π)/5462 weeks
25021.93696 9.39819 (250*2π)/5462 weeks
2516.55169 18.72951 (251*2π)/5462 weeks
252-11.48484 9.16977 (252*2π)/5462 weeks
253-11.8272 -13.33705 (253*2π)/5462 weeks
2549.30992 -25.94268 (254*2π)/5462 weeks
25532.29655 -11.69114 (255*2π)/5462 weeks
25629.54839 16.16711 (256*2π)/5462 weeks
2573.90083 26.63535 (257*2π)/5462 weeks
258-18.1161 9.54603 (258*2π)/5462 weeks
259-12.79235 -18.51194 (259*2π)/5462 weeks
26013.99119 -25.49234 (260*2π)/5462 weeks
26130.57245 -5.31597 (261*2π)/5462 weeks
26219.76629 15.16013 (262*2π)/5462 weeks
263-.81779 13.99003 (263*2π)/5462 weeks
264-7.26041 -4.02913 (264*2π)/5462 weeks
2656.02199 -16.75744 (265*2π)/5462 weeks
26623.81855 -9.47035 (266*2π)/5462 weeks
26724.61777 10.45381 (267*2π)/5462 weeks
2686.50364 19.63221 (268*2π)/5462 weeks
269-9.11305 8.90871 (269*2π)/5462 weeks
270-9.34474 -9.16994 (270*2π)/5462 weeks
2714.66218 -19.42436 (271*2π)/5462 weeks
27221.05888 -15.64347 (272*2π)/5462 weeks
27328.75056   (273*2π)/5462 weeks
27421.05888 15.64347 (274*2π)/5462 weeks
2754.66218 19.42436 (275*2π)/5462 weeks
276-9.34474 9.16994 (276*2π)/5462 weeks
277-9.11305 -8.90871 (277*2π)/5462 weeks
2786.50364 -19.63221 (278*2π)/5462 weeks
27924.61777 -10.45381 (279*2π)/5462 weeks
28023.81855 9.47035 (280*2π)/5462 weeks
2816.02199 16.75744 (281*2π)/5462 weeks
282-7.26041 4.02913 (282*2π)/5462 weeks
283-.81779 -13.99003 (283*2π)/5462 weeks
28419.76629 -15.16013 (284*2π)/5462 weeks
28530.57245 5.31597 (285*2π)/5462 weeks
28613.99119 25.49234 (286*2π)/5462 weeks
287-12.79235 18.51194 (287*2π)/5462 weeks
288-18.1161 -9.54603 (288*2π)/5462 weeks
2893.90083 -26.63535 (289*2π)/5462 weeks
29029.54839 -16.16711 (290*2π)/5462 weeks
29132.29655 11.69114 (291*2π)/5462 weeks
2929.30992 25.94268 (292*2π)/5462 weeks
293-11.8272 13.33705 (293*2π)/5462 weeks
294-11.48484 -9.16977 (294*2π)/5462 weeks
2956.55169 -18.72951 (295*2π)/5462 weeks
29621.93696 -9.39819 (296*2π)/5462 weeks
29722.99615 6.90291 (297*2π)/5462 weeks
29810.46689 16.66845 (298*2π)/5462 weeks
299-3.55208 10.9739 (299*2π)/5462 weeks
300-5.25409 -1.55812 (300*2π)/5462 weeks
3012.32346 -8.85139 (301*2π)/5462 weeks
30211.10919 -6.43791 (302*2π)/5462 weeks
30312.97414 1.18692 (303*2π)/5462 weeks
3047.90403 5.65142 (304*2π)/5462 weeks
305.88871 3.92281 (305*2π)/5462 weeks
306-.94744 -5.0852 (306*2π)/5462 weeks
3077.48702 -11.42303 (307*2π)/5462 weeks
30818.86808 -7.62008 (308*2π)/5462 weeks
30922.65721 6.63449 (309*2π)/5462 weeks
31012.12459 18.54212 (310*2π)/5462 weeks
311-5.29326 17.89106 (311*2π)/5462 weeks
312-15.61397 .67461 (312*2π)/5462 weeks
313-4.92154 -17.05685 (313*2π)/5462 weeks
31415.2459 -15.22772 (314*2π)/5462 weeks
31521.7493 2.84507 (315*2π)/5462 weeks
3168.33078 16.24745 (316*2π)/5462 weeks
317-9.53762 8.82635 (317*2π)/5462 weeks
318-9.58454 -9.94544 (318*2π)/5462 weeks
3197.34937 -17.4922 (319*2π)/5462 weeks
32021.71225 -3.94777 (320*2π)/5462 weeks
32112.9772 15.5565 (321*2π)/5462 weeks
322-9.25342 15.54059 (322*2π)/5462 weeks
323-20.61172 -5.08689 (323*2π)/5462 weeks
324-8.10513 -25.69664 (324*2π)/5462 weeks
32514.38529 -24.60053 (325*2π)/5462 weeks
32622.77777 -8.09371 (326*2π)/5462 weeks
32713.71867 4.02389 (327*2π)/5462 weeks
3282.70155 -.46073 (328*2π)/5462 weeks
3296.27508 -11.1278 (329*2π)/5462 weeks
33019.03613 -7.5621 (330*2π)/5462 weeks
33118.06743 8.18375 (331*2π)/5462 weeks
3321.02042 13.22216 (332*2π)/5462 weeks
333-11.16088 -1.30977 (333*2π)/5462 weeks
334-2.68605 -18.8764 (334*2π)/5462 weeks
33514.58589 -18.94404 (335*2π)/5462 weeks
33622.0923 -5.97341 (336*2π)/5462 weeks
33714.94312 3.6958 (337*2π)/5462 weeks
3387.59087 -.4882 (338*2π)/5462 weeks
33913.09404 -6.02923 (339*2π)/5462 weeks
34020.94772 1.5672 (340*2π)/5462 weeks
34115.78397 14.7854 (341*2π)/5462 weeks
342-.29915 16.76089 (342*2π)/5462 weeks
343-8.83343 3.98954 (343*2π)/5462 weeks
344-3.10891 -5.92854 (344*2π)/5462 weeks
3453.99119 -5.06145 (345*2π)/5462 weeks
3463.18305 .86761 (346*2π)/5462 weeks
347-4.49322 -1.61967 (347*2π)/5462 weeks
348-3.79542 -10.79858 (348*2π)/5462 weeks
3493.30967 -14.93057 (349*2π)/5462 weeks
3509.16717 -13.26477 (350*2π)/5462 weeks
35111.79659 -10.47113 (351*2π)/5462 weeks
35214.73969 -9.34651 (352*2π)/5462 weeks
35317.96617 -4.10446 (353*2π)/5462 weeks
35417.89038 2.61367 (354*2π)/5462 weeks
35512.74349 10.14045 (355*2π)/5462 weeks
3561.22459 12.48022 (356*2π)/5462 weeks
357-8.81236 3.08371 (357*2π)/5462 weeks
358-5.86783 -10.6934 (358*2π)/5462 weeks
3597.09058 -12.63062 (359*2π)/5462 weeks
36011.1677 -1.40589 (360*2π)/5462 weeks
361-1.19597 4.51857 (361*2π)/5462 weeks
362-11.98877 -9.44944 (362*2π)/5462 weeks
363-.53683 -28.27639 (363*2π)/5462 weeks
36424.63018 -25.24861 (364*2π)/5462 weeks
36534.07728 .54312 (365*2π)/5461 weeks
36614.15796 21.62046 (366*2π)/5461 weeks
367-14.19178 12.99817 (367*2π)/5461 weeks
368-20.30779 -17.09363 (368*2π)/5461 weeks
3694.46689 -37.235 (369*2π)/5461 weeks
37034.0655 -25.28761 (370*2π)/5461 weeks
37138.66684 4.94584 (371*2π)/5461 weeks
37216.78816 23.81237 (372*2π)/5461 weeks
373-8.62771 14.99004 (373*2π)/5461 weeks
374-12.50387 -8.94766 (374*2π)/5461 weeks
3755.04417 -22.41614 (375*2π)/5461 weeks
37624.40978 -12.52791 (376*2π)/5461 weeks
37724.27124 9.704 (377*2π)/5461 weeks
3783.74247 20.22418 (378*2π)/5461 weeks
379-16.50743 7.54796 (379*2π)/5461 weeks
380-16.50705 -17.01139 (380*2π)/5461 weeks
3814.40899 -29.84821 (381*2π)/5461 weeks
38225.8144 -19.67911 (382*2π)/5461 weeks
38329.73244 3.98848 (383*2π)/5461 weeks
38411.36058 19.99296 (384*2π)/5461 weeks
385-11.51517 13.15494 (385*2π)/5461 weeks
386-18.8269 -8.48875 (386*2π)/5461 weeks
387-6.02806 -26.85283 (387*2π)/5461 weeks
38816.73532 -26.83662 (388*2π)/5461 weeks
38928.08025 -5.85791 (389*2π)/5461 weeks
39013.29135 12.95151 (390*2π)/5461 weeks
391-9.88236 6.96153 (391*2π)/5461 weeks
392-14.24524 -17.80865 (392*2π)/5461 weeks
3937.13446 -33.70886 (393*2π)/5461 weeks
39433.85677 -21.68591 (394*2π)/5461 weeks
39536.42743 10.07814 (395*2π)/5461 weeks
3967.81093 29.29817 (396*2π)/5461 weeks
397-24.13732 12.67448 (397*2π)/5461 weeks
398-25.51956 -23.53954 (398*2π)/5461 weeks
3995.04431 -42.84732 (399*2π)/5461 weeks
40036.01293 -25.42357 (400*2π)/5461 weeks
40134.40706 7.70645 (401*2π)/5461 weeks
4026.55609 20.04963 (402*2π)/5461 weeks
403-15.00281 .41849 (403*2π)/5461 weeks
404-4.57927 -24.70927 (404*2π)/5461 weeks
40521.08401 -23.70376 (405*2π)/5461 weeks
40630.51345 -.73558 (406*2π)/5461 weeks
40714.51369 20.06864 (407*2π)/5461 weeks
408-13.2439 17.06182 (408*2π)/5461 weeks
409-28.41048 -8.42192 (409*2π)/5461 weeks
410-16.72942 -38.84929 (410*2π)/5461 weeks
41116.44726 -48.10194 (411*2π)/5461 weeks
41243.08552 -27.04834 (412*2π)/5461 weeks
41343.2045 4.84938 (413*2π)/5461 weeks
41418.83757 22.54571 (414*2π)/5461 weeks
415-6.27794 11.46775 (415*2π)/5461 weeks
416-6.65902 -11.407 (416*2π)/5461 weeks
41711.79872 -18.89643 (417*2π)/5461 weeks
41825.01228 -4.0565 (418*2π)/5461 weeks
41915.02202 15.74305 (419*2π)/5461 weeks
420-10.27961 15.67437 (420*2π)/5461 weeks
421-24.31889 -8.6147 (421*2π)/5461 weeks
422-9.34491 -35.57091 (422*2π)/5461 weeks
42323.32008 -36.55707 (423*2π)/5461 weeks
42440.02185 -7.08231 (424*2π)/5461 weeks
42522.13509 21.3546 (425*2π)/5461 weeks
426-11.32931 19.45576 (426*2π)/5461 weeks
427-24.25802 -9.56311 (427*2π)/5461 weeks
428-6.82053 -33.63448 (428*2π)/5461 weeks
42921.03008 -30.05463 (429*2π)/5461 weeks
43029.67286 -4.13207 (430*2π)/5461 weeks
4318.67559 14.38033 (431*2π)/5461 weeks
432-18.56882 2.83727 (432*2π)/5461 weeks
433-20.70627 -29.52162 (433*2π)/5461 weeks
4347.49916 -48.89141 (434*2π)/5461 weeks
43540.99899 -34.88631 (435*2π)/5461 weeks
43645.94296 1.522 (436*2π)/5461 weeks
43716.69671 22.7327 (437*2π)/5461 weeks
438-13.9329 6.61611 (438*2π)/5461 weeks
439-12.4489 -26.6293 (439*2π)/5461 weeks
44017.8511 -40.71023 (440*2π)/5461 weeks
44146.10506 -20.7393 (441*2π)/5461 weeks
44243.23652 14.06405 (442*2π)/5461 weeks
44313.56586 30.45889 (443*2π)/5461 weeks
444-14.99736 14.57823 (444*2π)/5461 weeks
445-14.97812 -15.88523 (445*2π)/5461 weeks
44610.06113 -28.44508 (446*2π)/5461 weeks
44733.0643 -12.65187 (447*2π)/5461 weeks
44830.41974 17.40413 (448*2π)/5461 weeks
4491.22394 32.29977 (449*2π)/5461 weeks
450-27.97629 15.50368 (450*2π)/5461 weeks
451-31.3926 -16.26306 (451*2π)/5461 weeks
452-10.07458 -34.93985 (452*2π)/5461 weeks
45313.41086 -29.53561 (453*2π)/5461 weeks
45418.96539 -8.19025 (454*2π)/5461 weeks
455.86375 4.35089 (455*2π)/5461 weeks
456-19.64225 -10.39277 (456*2π)/5461 weeks
457-13.78368 -39.51098 (457*2π)/5461 weeks
45817.90588 -51.16032 (458*2π)/5461 weeks
45948.76841 -28.44482 (459*2π)/5461 weeks
46045.88646 13.74116 (460*2π)/5461 weeks
4616.14216 35.133 (461*2π)/5461 weeks
462-34.81684 8.66708 (462*2π)/5461 weeks
463-29.4157 -39.04802 (463*2π)/5461 weeks
46412.19305 -57.83564 (464*2π)/5461 weeks
46549.80345 -32.40857 (465*2π)/5461 weeks
46646.10244 11.71783 (466*2π)/5461 weeks
4679.7468 28.8903 (467*2π)/5461 weeks
468-21.4882 8.10344 (468*2π)/5461 weeks
469-15.47691 -26.68848 (469*2π)/5461 weeks
47014.41478 -31.15997 (470*2π)/5461 weeks
47129.21576 -8.20492 (471*2π)/5461 weeks
47214.901 18.3315 (472*2π)/5461 weeks
473-22.60751 16.5833 (473*2π)/5461 weeks
474-38.78819 -19.97019 (474*2π)/5461 weeks
475-16.65397 -53.77515 (475*2π)/5461 weeks
47622.9473 -51.61057 (476*2π)/5461 weeks
47735.42457 -19.95048 (477*2π)/5461 weeks
47816.43137 -5.15045 (478*2π)/5461 weeks
4796.17453 -17.17984 (479*2π)/5461 weeks
48022.04423 -28.18744 (480*2π)/5461 weeks
48142.46783 -5.28929 (481*2π)/5461 weeks
48223.67826 31.16022 (482*2π)/5461 weeks
483-23.18307 31.69153 (483*2π)/5461 weeks
484-51.47761 -10.61805 (484*2π)/5461 weeks
485-26.83702 -57.35796 (485*2π)/5461 weeks
48619.18591 -56.56273 (486*2π)/5461 weeks
48736.68597 -23.94743 (487*2π)/5461 weeks
48819.22361 .55757 (488*2π)/5461 weeks
489-3.19996 -6.0692 (489*2π)/5461 weeks
490-1.84696 -25.07874 (490*2π)/5461 weeks
49113.05978 -27.83898 (491*2π)/5461 weeks
49222.82699 -15.34294 (492*2π)/5461 weeks
49318.269 2.31855 (493*2π)/5461 weeks
494-.63949 12.03737 (494*2π)/5461 weeks
495-23.42064 4.70206 (495*2π)/5461 weeks
496-37.27403 -20.03519 (496*2π)/5461 weeks
497-26.96674 -46.93052 (497*2π)/5461 weeks
498-.93656 -58.87853 (498*2π)/5461 weeks
49923.33047 -44.42991 (499*2π)/5461 weeks
50024.85679 -16.32161 (500*2π)/5461 weeks
501-2.91583 -1.85556 (501*2π)/5461 weeks
502-31.68682 -26.82361 (502*2π)/5461 weeks
503-18.05249 -69.21715 (503*2π)/5461 weeks
50430.83816 -77.89687 (504*2π)/5461 weeks
50567.12421 -30.31018 (505*2π)/5461 weeks
50634.30557 25.62299 (506*2π)/5461 weeks
507-35.47742 19.94716 (507*2π)/5461 weeks
508-61.65771 -53.61254 (508*2π)/5461 weeks
5091.60408 -117.3708 (509*2π)/5461 weeks
510100.8556 -79.80234 (510*2π)/5461 weeks
511111.5125 42.73692 (511*2π)/5461 weeks
512-10.24575 116.252 (512*2π)/5461 weeks
513-142.5855 32.87542 (513*2π)/5461 weeks
514-127.2047 -128.0612 (514*2π)/5461 weeks
51521.81768 -185.4349 (515*2π)/5461 weeks
516133.3673 -78.63889 (516*2π)/5461 weeks
51783.52697 60.82698 (517*2π)/5461 weeks
518-60.73033 73.14127 (518*2π)/5461 weeks
519-137.5296 -43.70757 (519*2π)/5461 weeks
520-77.91629 -167.3141 (520*2π)/5461 weeks
52146.38548 -177.2795 (521*2π)/5461 weeks
522107.9981 -92.23765 (522*2π)/5461 weeks
52376.40202 -19.99988 (523*2π)/5461 weeks
52422.57236 -14.32507 (524*2π)/5461 weeks
5253.54177 -43.46801 (525*2π)/5461 weeks
52617.8919 -61.90978 (526*2π)/5461 weeks
52736.68248 -52.26257 (527*2π)/5461 weeks
52836.56541 -23.52105 (528*2π)/5461 weeks
529-1.12512 -2.01871 (529*2π)/5461 weeks
530-47.83882 -15.62089 (530*2π)/5461 weeks
531-87.83231 -68.81653 (531*2π)/5461 weeks
532-75.09055 -152.7569 (532*2π)/5461 weeks
5335.42004 -205.2474 (533*2π)/5461 weeks
534108.7076 -167.1204 (534*2π)/5461 weeks
535132.751 -40.55475 (535*2π)/5461 weeks
5365.26022 47.79191 (536*2π)/5461 weeks
537-152.9915 -26.75196 (537*2π)/5461 weeks
538-176.1114 -227.731 (538*2π)/5461 weeks
539-2.77114 -335.0602 (539*2π)/5461 weeks
540127.6097 -202.7822 (540*2π)/5461 weeks
541-40.49639 -45.13238 (541*2π)/5461 weeks
542-400.4697 -234.9441 (542*2π)/5461 weeks
543-439.6267 -905.1943 (543*2π)/5461 weeks
544275.6005 -1,542.098 (544*2π)/5461 weeks



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