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Fourier Analysis of SDS (ProShares UltraShort S&P 500 ETF)


SDS (ProShares UltraShort S&P 500 ETF) appears to have interesting cyclic behaviour every 41 weeks (9.2932*sine), 52 weeks (8.0184*cosine), and 52 weeks (7.7034*sine).

SDS (ProShares UltraShort S&P 500 ETF) has an average price of 135.89 (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 7/13/2006 to 7/17/2017 for SDS (ProShares UltraShort S&P 500 ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0135.8879   0 
110.34125 52.76424 (1*2π)/576576 weeks
2-33.34063 47.11418 (2*2π)/576288 weeks
33.25951 -18.797 (3*2π)/576192 weeks
42.50513 4.44808 (4*2π)/576144 weeks
521.80744 22.3735 (5*2π)/576115 weeks
6-11.99736 13.07457 (6*2π)/57696 weeks
7-2.88368 9.21452 (7*2π)/57682 weeks
86.56923 -9.21262 (8*2π)/57672 weeks
94.72629 17.54196 (9*2π)/57664 weeks
10.90169 4.57188 (10*2π)/57658 weeks
11-8.01845 7.70337 (11*2π)/57652 weeks
123.9519 -.38589 (12*2π)/57648 weeks
13.80831 .82665 (13*2π)/57644 weeks
145.4484 9.29317 (14*2π)/57641 weeks
15-1.17172 1.31563 (15*2π)/57638 weeks
16-.30196 7.12401 (16*2π)/57636 weeks
172.98244 .01827 (17*2π)/57634 weeks
18-3.65261 3.6408 (18*2π)/57632 weeks
194.69284 .99971 (19*2π)/57630 weeks
20-1.3235 2.17477 (20*2π)/57629 weeks
213.78107 5.22541 (21*2π)/57627 weeks
22-1.09708 2.85834 (22*2π)/57626 weeks
23-.40004 5.56186 (23*2π)/57625 weeks
24.97322 -1.97779 (24*2π)/57624 weeks
25-.581 4.89933 (25*2π)/57623 weeks
26.5113 2.79929 (26*2π)/57622 weeks
27-5.0337 .92357 (27*2π)/57621 weeks
284.33465 .05796 (28*2π)/57621 weeks
292.00073 .99362 (29*2π)/57620 weeks
302.52499 6.46447 (30*2π)/57619 weeks
31-2.8714 .79611 (31*2π)/57619 weeks
32-1.87413 -.68739 (32*2π)/57618 weeks
334.13007 -2.14698 (33*2π)/57617 weeks
342.38469 5.70403 (34*2π)/57617 weeks
35-.20999 5.91945 (35*2π)/57616 weeks
36-4.50357 -.32836 (36*2π)/57616 weeks
372.09516 -.05633 (37*2π)/57616 weeks
381.72457 -.06319 (38*2π)/57615 weeks
39.30496 4.15656 (39*2π)/57615 weeks
40.0903 .60935 (40*2π)/57614 weeks
41-.87932 1.66987 (41*2π)/57614 weeks
421.40859 .05351 (42*2π)/57614 weeks
43.32522 2.08164 (43*2π)/57613 weeks
44.74027 1.75421 (44*2π)/57613 weeks
45-.36886 .00119 (45*2π)/57613 weeks
46.58272 2.42799 (46*2π)/57613 weeks
47.03198 -.04163 (47*2π)/57612 weeks
48-.10052 1.27893 (48*2π)/57612 weeks
491.87974 -1.17015 (49*2π)/57612 weeks
50-.10674 2.16241 (50*2π)/57612 weeks
512.01602 2.22451 (51*2π)/57611 weeks
52-.98449 1.03393 (52*2π)/57611 weeks
53.55479 1.35692 (53*2π)/57611 weeks
54.53872 -.12649 (54*2π)/57611 weeks
55.02237 2.51599 (55*2π)/57610 weeks
56-.38933 .766 (56*2π)/57610 weeks
57-1.36042 .58189 (57*2π)/57610 weeks
581.83803 -.8304 (58*2π)/57610 weeks
591.29434 2.04489 (59*2π)/57610 weeks
60.7509 2.20977 (60*2π)/57610 weeks
61-1.46423 -.09877 (61*2π)/5769 weeks
62.8215 .72672 (62*2π)/5769 weeks
631.37386 -.17921 (63*2π)/5769 weeks
64-.16272 2.42841 (64*2π)/5769 weeks
65.41852 -.56338 (65*2π)/5769 weeks
66.09724 .67393 (66*2π)/5769 weeks
672.38261 1.35392 (67*2π)/5769 weeks
68-.6859 1.17487 (68*2π)/5768 weeks
69-.38409 1.32563 (69*2π)/5768 weeks
70.80879 -.03686 (70*2π)/5768 weeks
71.47673 1.19068 (71*2π)/5768 weeks
72.5933 .84504 (72*2π)/5768 weeks
73-.48857 .34427 (73*2π)/5768 weeks
742.05697 .29517 (74*2π)/5768 weeks
75.44203 2.19006 (75*2π)/5768 weeks
76-.17376 1.80194 (76*2π)/5768 weeks
77-1.65314 -.6999 (77*2π)/5767 weeks
781.22907 .26076 (78*2π)/5767 weeks
791.15445 .60773 (79*2π)/5767 weeks
80.25876 1.5023 (80*2π)/5767 weeks
81-.37177 .9903 (81*2π)/5767 weeks
82-.92341 -.62677 (82*2π)/5767 weeks
832.41449 -.01157 (83*2π)/5767 weeks
84.68554 1.43853 (84*2π)/5767 weeks
85.00597 2.19525 (85*2π)/5767 weeks
86-1.14476 -.43651 (86*2π)/5767 weeks
87.53008 .34704 (87*2π)/5767 weeks
881.62937 -.15322 (88*2π)/5767 weeks
89.45496 2.52806 (89*2π)/5766 weeks
90-.67338 1.10384 (90*2π)/5766 weeks
91-1.16634 -.39069 (91*2π)/5766 weeks
921.69017 -.31872 (92*2π)/5766 weeks
93.9045 .28203 (93*2π)/5766 weeks
94.26134 1.80939 (94*2π)/5766 weeks
95-.42795 -.10405 (95*2π)/5766 weeks
96.14843 .58263 (96*2π)/5766 weeks
971.06427 .40109 (97*2π)/5766 weeks
98-.65161 1.0913 (98*2π)/5766 weeks
99.85209 .02063 (99*2π)/5766 weeks
100.08997 .6448 (100*2π)/5766 weeks
101.40935 1.07152 (101*2π)/5766 weeks
102-.22246 -.73325 (102*2π)/5766 weeks
103.91331 .31526 (103*2π)/5766 weeks
1041.54798 .28599 (104*2π)/5766 weeks
105-.43472 1.58299 (105*2π)/5765 weeks
106-.11712 .45201 (106*2π)/5765 weeks
107-.08328 -.42437 (107*2π)/5765 weeks
1082.05744 .62831 (108*2π)/5765 weeks
109.31729 1.28618 (109*2π)/5765 weeks
110-.63304 1.93032 (110*2π)/5765 weeks
111-.66296 -1.1938 (111*2π)/5765 weeks
112.18413 -.36696 (112*2π)/5765 weeks
1132.01088 .1663 (113*2π)/5765 weeks
114.05688 1.74693 (114*2π)/5765 weeks
115-.05872 .79542 (115*2π)/5765 weeks
116-.30228 -1.15193 (116*2π)/5765 weeks
1171.56386 .25125 (117*2π)/5765 weeks
1181.09078 .62663 (118*2π)/5765 weeks
119-.00964 2.03415 (119*2π)/5765 weeks
120-.54559 -.0299 (120*2π)/5765 weeks
121-.11495 -.27204 (121*2π)/5765 weeks
1221.92261 .12831 (122*2π)/5765 weeks
123.38629 .68832 (123*2π)/5765 weeks
124.27322 1.34142 (124*2π)/5765 weeks
125-.52636 -.5595 (125*2π)/5765 weeks
126.38181 .41519 (126*2π)/5765 weeks
1271.37559 .3648 (127*2π)/5765 weeks
128-.14668 1.49026 (128*2π)/5765 weeks
129-.28073 .41194 (129*2π)/5764 weeks
130-.09149 -.49741 (130*2π)/5764 weeks
1311.15225 .0241 (131*2π)/5764 weeks
132.13638 .33281 (132*2π)/5764 weeks
133.30739 .90451 (133*2π)/5764 weeks
134.24098 .1364 (134*2π)/5764 weeks
135-.06423 .49424 (135*2π)/5764 weeks
136.78653 -.42478 (136*2π)/5764 weeks
137.38101 .69517 (137*2π)/5764 weeks
138.75003 .3958 (138*2π)/5764 weeks
139.09433 -.31668 (139*2π)/5764 weeks
140.91157 .67506 (140*2π)/5764 weeks
141.16503 .31123 (141*2π)/5764 weeks
142.24571 1.31891 (142*2π)/5764 weeks
143.20873 -.12468 (143*2π)/5764 weeks
144.10145 .2625 (144*2π)/5764 weeks
145.55661 .05424 (145*2π)/5764 weeks
146.07036 -.0876 (146*2π)/5764 weeks
147.9129 .68222 (147*2π)/5764 weeks
148.31617 .63278 (148*2π)/5764 weeks
149-.18842 .81545 (149*2π)/5764 weeks
150.69306 -.46768 (150*2π)/5764 weeks
151.77961 .98571 (151*2π)/5764 weeks
152.40213 .2315 (152*2π)/5764 weeks
153-.37324 .14356 (153*2π)/5764 weeks
154.8903 .12247 (154*2π)/5764 weeks
155.41396 .49683 (155*2π)/5764 weeks
156.37956 .88326 (156*2π)/5764 weeks
157-.21347 -.15797 (157*2π)/5764 weeks
158.33569 -.0156 (158*2π)/5764 weeks
1591.07675 .25164 (159*2π)/5764 weeks
160-.17584 .72202 (160*2π)/5764 weeks
161.43002 .21706 (161*2π)/5764 weeks
162.07547 .07137 (162*2π)/5764 weeks
163.67773 .62472 (163*2π)/5764 weeks
164.18959 .12724 (164*2π)/5764 weeks
165.49698 .58494 (165*2π)/5763 weeks
166.03223 -.1945 (166*2π)/5763 weeks
167.60045 .2807 (167*2π)/5763 weeks
168.70157 .25838 (168*2π)/5763 weeks
169-.08838 .32535 (169*2π)/5763 weeks
170.76542 .38468 (170*2π)/5763 weeks
171.14569 .11468 (171*2π)/5763 weeks
172.29977 .23379 (172*2π)/5763 weeks
173.49409 -.14466 (173*2π)/5763 weeks
174.70271 .49169 (174*2π)/5763 weeks
175.56475 .51449 (175*2π)/5763 weeks
176-.29405 .71063 (176*2π)/5763 weeks
177.39467 -.05721 (177*2π)/5763 weeks
178.22788 .08922 (178*2π)/5763 weeks
179.60235 .62899 (179*2π)/5763 weeks
180-.09083 .24574 (180*2π)/5763 weeks
181.39724 .21129 (181*2π)/5763 weeks
182.49938 -.36308 (182*2π)/5763 weeks
183.58037 .60033 (183*2π)/5763 weeks
184.63122 .45637 (184*2π)/5763 weeks
185-.38226 .7385 (185*2π)/5763 weeks
186.21865 .18546 (186*2π)/5763 weeks
187.05274 -.51596 (187*2π)/5763 weeks
1881.03409 .42835 (188*2π)/5763 weeks
189.41604 .32143 (189*2π)/5763 weeks
190-.14368 .8649 (190*2π)/5763 weeks
191.14602 -.51762 (191*2π)/5763 weeks
192.23029 .17146 (192*2π)/5763 weeks
1931.1459 .2981 (193*2π)/5763 weeks
194-.13217 .49779 (194*2π)/5763 weeks
195.42662 .38137 (195*2π)/5763 weeks
196-.0213 -.39222 (196*2π)/5763 weeks
197.62685 .61492 (197*2π)/5763 weeks
198.33339 .37453 (198*2π)/5763 weeks
199-.3498 .41227 (199*2π)/5763 weeks
200.34173 -.42081 (200*2π)/5763 weeks
201.18935 -.24754 (201*2π)/5763 weeks
202.99707 .39239 (202*2π)/5763 weeks
203.37516 .16279 (203*2π)/5763 weeks
204.32898 1.19479 (204*2π)/5763 weeks
205-.28438 -.55913 (205*2π)/5763 weeks
206.08408 .21393 (206*2π)/5763 weeks
207.76154 -.23105 (207*2π)/5763 weeks
208.00572 .28246 (208*2π)/5763 weeks
209.54046 .21926 (209*2π)/5763 weeks
210.34822 .02351 (210*2π)/5763 weeks
211.46349 .27981 (211*2π)/5763 weeks
212.78769 .11775 (212*2π)/5763 weeks
213.11529 .86695 (213*2π)/5763 weeks
214.28316 .19402 (214*2π)/5763 weeks
215-.51811 .0991 (215*2π)/5763 weeks
216.52057 -.67849 (216*2π)/5763 weeks
217.74636 .27426 (217*2π)/5763 weeks
218.65995 .95843 (218*2π)/5763 weeks
219-.65279 .12821 (219*2π)/5763 weeks
220.1718 -.252 (220*2π)/5763 weeks
221.83305 -.21949 (221*2π)/5763 weeks
222.44286 .95849 (222*2π)/5763 weeks
223.09152 .33805 (223*2π)/5763 weeks
224-.78476 -.49748 (224*2π)/5763 weeks
2251.08481 -.43918 (225*2π)/5763 weeks
226.82027 .31786 (226*2π)/5763 weeks
227.35403 1.02321 (227*2π)/5763 weeks
228-.24995 -.27248 (228*2π)/5763 weeks
229.35102 .06476 (229*2π)/5763 weeks
230.48676 .01975 (230*2π)/5763 weeks
231-.0066 .2582 (231*2π)/5762 weeks
232.75807 -.08118 (232*2π)/5762 weeks
233.19591 .03252 (233*2π)/5762 weeks
234.85583 .57514 (234*2π)/5762 weeks
235-.23306 .4388 (235*2π)/5762 weeks
236-.15158 .11728 (236*2π)/5762 weeks
237.26244 -.48768 (237*2π)/5762 weeks
238.53249 .52035 (238*2π)/5762 weeks
239.19481 .44186 (239*2π)/5762 weeks
240-.42361 -.03026 (240*2π)/5762 weeks
241.50202 -.40906 (241*2π)/5762 weeks
242.32585 -.55304 (242*2π)/5762 weeks
243.69104 .60525 (243*2π)/5762 weeks
244-.05813 .04151 (244*2π)/5762 weeks
245-.14229 .05866 (245*2π)/5762 weeks
246.78504 -.78258 (246*2π)/5762 weeks
247.71328 .36385 (247*2π)/5762 weeks
248.62246 .76849 (248*2π)/5762 weeks
249-.53944 .12029 (249*2π)/5762 weeks
250-.00555 -.07623 (250*2π)/5762 weeks
251.78129 -.4785 (251*2π)/5762 weeks
252.55627 .55783 (252*2π)/5762 weeks
253.37991 .22521 (253*2π)/5762 weeks
254-.30124 .11067 (254*2π)/5762 weeks
255.5678 -.21908 (255*2π)/5762 weeks
256.17452 .06129 (256*2π)/5762 weeks
257.68462 .3014 (257*2π)/5762 weeks
258-.07752 .10472 (258*2π)/5762 weeks
259-.06002 -.13233 (259*2π)/5762 weeks
260.12297 -.45138 (260*2π)/5762 weeks
261.70854 .02219 (261*2π)/5762 weeks
262.85679 .17532 (262*2π)/5762 weeks
263-.24688 .54177 (263*2π)/5762 weeks
264-.03816 -.04867 (264*2π)/5762 weeks
265-.04691 -.5702 (265*2π)/5762 weeks
266.94672 -.49358 (266*2π)/5762 weeks
267.79523 .16367 (267*2π)/5762 weeks
268.30395 1.23974 (268*2π)/5762 weeks
269-.67569 -.21309 (269*2π)/5762 weeks
270.04641 -.6357 (270*2π)/5762 weeks
2711.13069 -.36807 (271*2π)/5762 weeks
272.6114 .50167 (272*2π)/5762 weeks
273.02693 .72447 (273*2π)/5762 weeks
274-.59241 -.62503 (274*2π)/5762 weeks
275.76292 -.7971 (275*2π)/5762 weeks
276.77872 -.11285 (276*2π)/5762 weeks
277.21697 .7457 (277*2π)/5762 weeks
278-.02286 -.22004 (278*2π)/5762 weeks
279.09793 -.38992 (279*2π)/5762 weeks
2801.24026 -.65124 (280*2π)/5762 weeks
281.72597 .46813 (281*2π)/5762 weeks
282.02035 .82066 (282*2π)/5762 weeks
283-.34419 -.51385 (283*2π)/5762 weeks
284.61259 .06577 (284*2π)/5762 weeks
2851.01837 -.25665 (285*2π)/5762 weeks
286.37133 .556 (286*2π)/5762 weeks
287.46467 .38478 (287*2π)/5762 weeks
288-.73829   (288*2π)/5762 weeks
289.46467 -.38478 (289*2π)/5762 weeks
290.37133 -.556 (290*2π)/5762 weeks
2911.01837 .25665 (291*2π)/5762 weeks
292.61259 -.06577 (292*2π)/5762 weeks
293-.34419 .51385 (293*2π)/5762 weeks
294.02035 -.82066 (294*2π)/5762 weeks
295.72597 -.46813 (295*2π)/5762 weeks
2961.24026 .65124 (296*2π)/5762 weeks
297.09793 .38992 (297*2π)/5762 weeks
298-.02286 .22004 (298*2π)/5762 weeks
299.21697 -.7457 (299*2π)/5762 weeks
300.77872 .11285 (300*2π)/5762 weeks
301.76292 .7971 (301*2π)/5762 weeks
302-.59241 .62503 (302*2π)/5762 weeks
303.02693 -.72447 (303*2π)/5762 weeks
304.6114 -.50167 (304*2π)/5762 weeks
3051.13069 .36807 (305*2π)/5762 weeks
306.04641 .6357 (306*2π)/5762 weeks
307-.67569 .21309 (307*2π)/5762 weeks
308.30395 -1.23974 (308*2π)/5762 weeks
309.79523 -.16367 (309*2π)/5762 weeks
310.94672 .49358 (310*2π)/5762 weeks
311-.04691 .5702 (311*2π)/5762 weeks
312-.03816 .04867 (312*2π)/5762 weeks
313-.24688 -.54177 (313*2π)/5762 weeks
314.85679 -.17532 (314*2π)/5762 weeks
315.70854 -.02219 (315*2π)/5762 weeks
316.12297 .45138 (316*2π)/5762 weeks
317-.06002 .13233 (317*2π)/5762 weeks
318-.07752 -.10472 (318*2π)/5762 weeks
319.68462 -.3014 (319*2π)/5762 weeks
320.17452 -.06129 (320*2π)/5762 weeks
321.5678 .21908 (321*2π)/5762 weeks
322-.30124 -.11067 (322*2π)/5762 weeks
323.37991 -.22521 (323*2π)/5762 weeks
324.55627 -.55783 (324*2π)/5762 weeks
325.78129 .4785 (325*2π)/5762 weeks
326-.00555 .07623 (326*2π)/5762 weeks
327-.53944 -.12029 (327*2π)/5762 weeks
328.62246 -.76849 (328*2π)/5762 weeks
329.71328 -.36385 (329*2π)/5762 weeks
330.78504 .78258 (330*2π)/5762 weeks
331-.14229 -.05866 (331*2π)/5762 weeks
332-.05813 -.04151 (332*2π)/5762 weeks
333.69104 -.60525 (333*2π)/5762 weeks
334.32585 .55304 (334*2π)/5762 weeks
335.50202 .40906 (335*2π)/5762 weeks
336-.42361 .03026 (336*2π)/5762 weeks
337.19481 -.44186 (337*2π)/5762 weeks
338.53249 -.52035 (338*2π)/5762 weeks
339.26244 .48768 (339*2π)/5762 weeks
340-.15158 -.11728 (340*2π)/5762 weeks
341-.23306 -.4388 (341*2π)/5762 weeks
342.85583 -.57514 (342*2π)/5762 weeks
343.19591 -.03252 (343*2π)/5762 weeks
344.75807 .08118 (344*2π)/5762 weeks
345-.0066 -.2582 (345*2π)/5762 weeks
346.48676 -.01975 (346*2π)/5762 weeks
347.35102 -.06476 (347*2π)/5762 weeks
348-.24995 .27248 (348*2π)/5762 weeks
349.35403 -1.02321 (349*2π)/5762 weeks
350.82027 -.31786 (350*2π)/5762 weeks
3511.08481 .43918 (351*2π)/5762 weeks
352-.78476 .49748 (352*2π)/5762 weeks
353.09152 -.33805 (353*2π)/5762 weeks
354.44286 -.95849 (354*2π)/5762 weeks
355.83305 .21949 (355*2π)/5762 weeks
356.1718 .252 (356*2π)/5762 weeks
357-.65279 -.12821 (357*2π)/5762 weeks
358.65995 -.95843 (358*2π)/5762 weeks
359.74636 -.27426 (359*2π)/5762 weeks
360.52057 .67849 (360*2π)/5762 weeks
361-.51811 -.0991 (361*2π)/5762 weeks
362.28316 -.19402 (362*2π)/5762 weeks
363.11529 -.86695 (363*2π)/5762 weeks
364.78769 -.11775 (364*2π)/5762 weeks
365.46349 -.27981 (365*2π)/5762 weeks
366.34822 -.02351 (366*2π)/5762 weeks
367.54046 -.21926 (367*2π)/5762 weeks
368.00572 -.28246 (368*2π)/5762 weeks
369.76154 .23105 (369*2π)/5762 weeks
370.08408 -.21393 (370*2π)/5762 weeks
371-.28438 .55913 (371*2π)/5762 weeks
372.32898 -1.19479 (372*2π)/5762 weeks
373.37516 -.16279 (373*2π)/5762 weeks
374.99707 -.39239 (374*2π)/5762 weeks
375.18935 .24754 (375*2π)/5762 weeks
376.34173 .42081 (376*2π)/5762 weeks
377-.3498 -.41227 (377*2π)/5762 weeks
378.33339 -.37453 (378*2π)/5762 weeks
379.62685 -.61492 (379*2π)/5762 weeks
380-.0213 .39222 (380*2π)/5762 weeks
381.42662 -.38137 (381*2π)/5762 weeks
382-.13217 -.49779 (382*2π)/5762 weeks
3831.1459 -.2981 (383*2π)/5762 weeks
384.23029 -.17146 (384*2π)/5762 weeks
385.14602 .51762 (385*2π)/5761 weeks
386-.14368 -.8649 (386*2π)/5761 weeks
387.41604 -.32143 (387*2π)/5761 weeks
3881.03409 -.42835 (388*2π)/5761 weeks
389.05274 .51596 (389*2π)/5761 weeks
390.21865 -.18546 (390*2π)/5761 weeks
391-.38226 -.7385 (391*2π)/5761 weeks
392.63122 -.45637 (392*2π)/5761 weeks
393.58037 -.60033 (393*2π)/5761 weeks
394.49938 .36308 (394*2π)/5761 weeks
395.39724 -.21129 (395*2π)/5761 weeks
396-.09083 -.24574 (396*2π)/5761 weeks
397.60235 -.62899 (397*2π)/5761 weeks
398.22788 -.08922 (398*2π)/5761 weeks
399.39467 .05721 (399*2π)/5761 weeks
400-.29405 -.71063 (400*2π)/5761 weeks
401.56475 -.51449 (401*2π)/5761 weeks
402.70271 -.49169 (402*2π)/5761 weeks
403.49409 .14466 (403*2π)/5761 weeks
404.29977 -.23379 (404*2π)/5761 weeks
405.14569 -.11468 (405*2π)/5761 weeks
406.76542 -.38468 (406*2π)/5761 weeks
407-.08838 -.32535 (407*2π)/5761 weeks
408.70157 -.25838 (408*2π)/5761 weeks
409.60045 -.2807 (409*2π)/5761 weeks
410.03223 .1945 (410*2π)/5761 weeks
411.49698 -.58494 (411*2π)/5761 weeks
412.18959 -.12724 (412*2π)/5761 weeks
413.67773 -.62472 (413*2π)/5761 weeks
414.07547 -.07137 (414*2π)/5761 weeks
415.43002 -.21706 (415*2π)/5761 weeks
416-.17584 -.72202 (416*2π)/5761 weeks
4171.07675 -.25164 (417*2π)/5761 weeks
418.33569 .0156 (418*2π)/5761 weeks
419-.21347 .15797 (419*2π)/5761 weeks
420.37956 -.88326 (420*2π)/5761 weeks
421.41396 -.49683 (421*2π)/5761 weeks
422.8903 -.12247 (422*2π)/5761 weeks
423-.37324 -.14356 (423*2π)/5761 weeks
424.40213 -.2315 (424*2π)/5761 weeks
425.77961 -.98571 (425*2π)/5761 weeks
426.69306 .46768 (426*2π)/5761 weeks
427-.18842 -.81545 (427*2π)/5761 weeks
428.31617 -.63278 (428*2π)/5761 weeks
429.9129 -.68222 (429*2π)/5761 weeks
430.07036 .0876 (430*2π)/5761 weeks
431.55661 -.05424 (431*2π)/5761 weeks
432.10145 -.2625 (432*2π)/5761 weeks
433.20873 .12468 (433*2π)/5761 weeks
434.24571 -1.31891 (434*2π)/5761 weeks
435.16503 -.31123 (435*2π)/5761 weeks
436.91157 -.67506 (436*2π)/5761 weeks
437.09433 .31668 (437*2π)/5761 weeks
438.75003 -.3958 (438*2π)/5761 weeks
439.38101 -.69517 (439*2π)/5761 weeks
440.78653 .42478 (440*2π)/5761 weeks
441-.06423 -.49424 (441*2π)/5761 weeks
442.24098 -.1364 (442*2π)/5761 weeks
443.30739 -.90451 (443*2π)/5761 weeks
444.13638 -.33281 (444*2π)/5761 weeks
4451.15225 -.0241 (445*2π)/5761 weeks
446-.09149 .49741 (446*2π)/5761 weeks
447-.28073 -.41194 (447*2π)/5761 weeks
448-.14668 -1.49026 (448*2π)/5761 weeks
4491.37559 -.3648 (449*2π)/5761 weeks
450.38181 -.41519 (450*2π)/5761 weeks
451-.52636 .5595 (451*2π)/5761 weeks
452.27322 -1.34142 (452*2π)/5761 weeks
453.38629 -.68832 (453*2π)/5761 weeks
4541.92261 -.12831 (454*2π)/5761 weeks
455-.11495 .27204 (455*2π)/5761 weeks
456-.54559 .0299 (456*2π)/5761 weeks
457-.00964 -2.03415 (457*2π)/5761 weeks
4581.09078 -.62663 (458*2π)/5761 weeks
4591.56386 -.25125 (459*2π)/5761 weeks
460-.30228 1.15193 (460*2π)/5761 weeks
461-.05872 -.79542 (461*2π)/5761 weeks
462.05688 -1.74693 (462*2π)/5761 weeks
4632.01088 -.1663 (463*2π)/5761 weeks
464.18413 .36696 (464*2π)/5761 weeks
465-.66296 1.1938 (465*2π)/5761 weeks
466-.63304 -1.93032 (466*2π)/5761 weeks
467.31729 -1.28618 (467*2π)/5761 weeks
4682.05744 -.62831 (468*2π)/5761 weeks
469-.08328 .42437 (469*2π)/5761 weeks
470-.11712 -.45201 (470*2π)/5761 weeks
471-.43472 -1.58299 (471*2π)/5761 weeks
4721.54798 -.28599 (472*2π)/5761 weeks
473.91331 -.31526 (473*2π)/5761 weeks
474-.22246 .73325 (474*2π)/5761 weeks
475.40935 -1.07152 (475*2π)/5761 weeks
476.08997 -.6448 (476*2π)/5761 weeks
477.85209 -.02063 (477*2π)/5761 weeks
478-.65161 -1.0913 (478*2π)/5761 weeks
4791.06427 -.40109 (479*2π)/5761 weeks
480.14843 -.58263 (480*2π)/5761 weeks
481-.42795 .10405 (481*2π)/5761 weeks
482.26134 -1.80939 (482*2π)/5761 weeks
483.9045 -.28203 (483*2π)/5761 weeks
4841.69017 .31872 (484*2π)/5761 weeks
485-1.16634 .39069 (485*2π)/5761 weeks
486-.67338 -1.10384 (486*2π)/5761 weeks
487.45496 -2.52806 (487*2π)/5761 weeks
4881.62937 .15322 (488*2π)/5761 weeks
489.53008 -.34704 (489*2π)/5761 weeks
490-1.14476 .43651 (490*2π)/5761 weeks
491.00597 -2.19525 (491*2π)/5761 weeks
492.68554 -1.43853 (492*2π)/5761 weeks
4932.41449 .01157 (493*2π)/5761 weeks
494-.92341 .62677 (494*2π)/5761 weeks
495-.37177 -.9903 (495*2π)/5761 weeks
496.25876 -1.5023 (496*2π)/5761 weeks
4971.15445 -.60773 (497*2π)/5761 weeks
4981.22907 -.26076 (498*2π)/5761 weeks
499-1.65314 .6999 (499*2π)/5761 weeks
500-.17376 -1.80194 (500*2π)/5761 weeks
501.44203 -2.19006 (501*2π)/5761 weeks
5022.05697 -.29517 (502*2π)/5761 weeks
503-.48857 -.34427 (503*2π)/5761 weeks
504.5933 -.84504 (504*2π)/5761 weeks
505.47673 -1.19068 (505*2π)/5761 weeks
506.80879 .03686 (506*2π)/5761 weeks
507-.38409 -1.32563 (507*2π)/5761 weeks
508-.6859 -1.17487 (508*2π)/5761 weeks
5092.38261 -1.35392 (509*2π)/5761 weeks
510.09724 -.67393 (510*2π)/5761 weeks
511.41852 .56338 (511*2π)/5761 weeks
512-.16272 -2.42841 (512*2π)/5761 weeks
5131.37386 .17921 (513*2π)/5761 weeks
514.8215 -.72672 (514*2π)/5761 weeks
515-1.46423 .09877 (515*2π)/5761 weeks
516.7509 -2.20977 (516*2π)/5761 weeks
5171.29434 -2.04489 (517*2π)/5761 weeks
5181.83803 .8304 (518*2π)/5761 weeks
519-1.36042 -.58189 (519*2π)/5761 weeks
520-.38933 -.766 (520*2π)/5761 weeks
521.02237 -2.51599 (521*2π)/5761 weeks
522.53872 .12649 (522*2π)/5761 weeks
523.55479 -1.35692 (523*2π)/5761 weeks
524-.98449 -1.03393 (524*2π)/5761 weeks
5252.01602 -2.22451 (525*2π)/5761 weeks
526-.10674 -2.16241 (526*2π)/5761 weeks
5271.87974 1.17015 (527*2π)/5761 weeks
528-.10052 -1.27893 (528*2π)/5761 weeks
529.03198 .04163 (529*2π)/5761 weeks
530.58272 -2.42799 (530*2π)/5761 weeks
531-.36886 -.00119 (531*2π)/5761 weeks
532.74027 -1.75421 (532*2π)/5761 weeks
533.32522 -2.08164 (533*2π)/5761 weeks
5341.40859 -.05351 (534*2π)/5761 weeks
535-.87932 -1.66987 (535*2π)/5761 weeks
536.0903 -.60935 (536*2π)/5761 weeks
537.30496 -4.15656 (537*2π)/5761 weeks
5381.72457 .06319 (538*2π)/5761 weeks
5392.09516 .05633 (539*2π)/5761 weeks
540-4.50357 .32836 (540*2π)/5761 weeks
541-.20999 -5.91945 (541*2π)/5761 weeks
5422.38469 -5.70403 (542*2π)/5761 weeks
5434.13007 2.14698 (543*2π)/5761 weeks
544-1.87413 .68739 (544*2π)/5761 weeks
545-2.8714 -.79611 (545*2π)/5761 weeks
5462.52499 -6.46447 (546*2π)/5761 weeks
5472.00073 -.99362 (547*2π)/5761 weeks
5484.33465 -.05796 (548*2π)/5761 weeks
549-5.0337 -.92357 (549*2π)/5761 weeks
550.5113 -2.79929 (550*2π)/5761 weeks
551-.581 -4.89933 (551*2π)/5761 weeks
552.97322 1.97779 (552*2π)/5761 weeks
553-.40004 -5.56186 (553*2π)/5761 weeks
554-1.09708 -2.85834 (554*2π)/5761 weeks
5553.78107 -5.22541 (555*2π)/5761 weeks
556-1.3235 -2.17477 (556*2π)/5761 weeks
5574.69284 -.99971 (557*2π)/5761 weeks
558-3.65261 -3.6408 (558*2π)/5761 weeks
5592.98244 -.01827 (559*2π)/5761 weeks
560-.30196 -7.12401 (560*2π)/5761 weeks
561-1.17172 -1.31563 (561*2π)/5761 weeks
5625.4484 -9.29317 (562*2π)/5761 weeks
563.80831 -.82665 (563*2π)/5761 weeks
5643.9519 .38589 (564*2π)/5761 weeks
565-8.01845 -7.70337 (565*2π)/5761 weeks
566.90169 -4.57188 (566*2π)/5761 weeks
5674.72629 -17.54196 (567*2π)/5761 weeks
5686.56923 9.21262 (568*2π)/5761 weeks
569-2.88368 -9.21452 (569*2π)/5761 weeks
570-11.99736 -13.07457 (570*2π)/5761 weeks
57121.80744 -22.3735 (571*2π)/5761 weeks
5722.50513 -4.44808 (572*2π)/5761 weeks
5733.25951 18.797 (573*2π)/5761 weeks
574-33.34063 -47.11418 (574*2π)/5761 weeks



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