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Fourier Analysis of DXD (ProShares UltraShort Dow30)


DXD (ProShares UltraShort Dow30) appears to have interesting cyclic behaviour every 17 weeks (5.5887*sine), 55 weeks (5.2739*sine), and 42 weeks (5.2352*sine).

DXD (ProShares UltraShort Dow30) has an average price of 89.34 (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 1/9/2017 for DXD (ProShares UltraShort Dow30), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
089.34011   0 
112.95589 82.49835 (1*2π)/549549 weeks
2-17.71937 23.75168 (2*2π)/549275 weeks
3.3208 -1.65496 (3*2π)/549183 weeks
415.07916 9.13456 (4*2π)/549137 weeks
55.87694 19.81635 (5*2π)/549110 weeks
6-5.92364 12.76284 (6*2π)/54992 weeks
7-1.34763 1.89875 (7*2π)/54978 weeks
87.70949 6.20946 (8*2π)/54969 weeks
9-.11137 11.1864 (9*2π)/54961 weeks
10-1.40046 5.27389 (10*2π)/54955 weeks
11-1.16505 3.12943 (11*2π)/54950 weeks
122.57884 2.59274 (12*2π)/54946 weeks
131.94598 5.23521 (13*2π)/54942 weeks
14.8831 4.05757 (14*2π)/54939 weeks
15.8705 3.96511 (15*2π)/54937 weeks
161.75701 4.02795 (16*2π)/54934 weeks
17-1.00055 4.20891 (17*2π)/54932 weeks
18.73445 2.12867 (18*2π)/54931 weeks
191.31196 2.66547 (19*2π)/54929 weeks
201.86944 3.83276 (20*2π)/54927 weeks
21.47275 4.95285 (21*2π)/54926 weeks
22-1.23551 3.25475 (22*2π)/54925 weeks
23.65698 1.41464 (23*2π)/54924 weeks
24.88741 3.0597 (24*2π)/54923 weeks
25-1.29407 3.43289 (25*2π)/54922 weeks
26-1.19241 -.27497 (26*2π)/54921 weeks
272.03357 .67336 (27*2π)/54920 weeks
282.44369 3.07025 (28*2π)/54920 weeks
29-.25884 4.65621 (29*2π)/54919 weeks
30-2.18233 1.3551 (30*2π)/54918 weeks
311.11805 -.96098 (31*2π)/54918 weeks
324.15332 1.87651 (32*2π)/54917 weeks
33.97957 5.58865 (33*2π)/54917 weeks
34-2.8828 2.29855 (34*2π)/54916 weeks
35-.21711 -.40845 (35*2π)/54916 weeks
361.67962 1.07396 (36*2π)/54915 weeks
37.61283 2.59086 (37*2π)/54915 weeks
38-.12523 1.73729 (38*2π)/54914 weeks
39-.0205 1.33949 (39*2π)/54914 weeks
40.26188 .84715 (40*2π)/54914 weeks
41.90692 1.66107 (41*2π)/54913 weeks
42-.10111 1.24366 (42*2π)/54913 weeks
43.86869 1.24823 (43*2π)/54913 weeks
44-.07686 1.42073 (44*2π)/54912 weeks
45.21045 1.00585 (45*2π)/54912 weeks
46.44707 .50274 (46*2π)/54912 weeks
471.54908 .87937 (47*2π)/54912 weeks
481.03089 1.65144 (48*2π)/54911 weeks
49.26581 2.05087 (49*2π)/54911 weeks
50-.24662 1.38322 (50*2π)/54911 weeks
51.36357 .69756 (51*2π)/54911 weeks
52.71509 1.56783 (52*2π)/54911 weeks
53-.06164 1.52184 (53*2π)/54910 weeks
54-.60877 .60923 (54*2π)/54910 weeks
55.67509 -.47842 (55*2π)/54910 weeks
562.1156 1.1203 (56*2π)/54910 weeks
57.3004 2.31217 (57*2π)/54910 weeks
58-.67013 .96692 (58*2π)/5499 weeks
59.25978 .11184 (59*2π)/5499 weeks
601.34178 .76265 (60*2π)/5499 weeks
61.25944 1.81799 (61*2π)/5499 weeks
62-.28045 .37673 (62*2π)/5499 weeks
63.80018 .2553 (63*2π)/5499 weeks
641.31976 1.20921 (64*2π)/5499 weeks
65.26258 1.68475 (65*2π)/5498 weeks
66-.18362 .50554 (66*2π)/5498 weeks
67.42468 .85704 (67*2π)/5498 weeks
68.6854 .74472 (68*2π)/5498 weeks
69-.02787 1.01021 (69*2π)/5498 weeks
70.77214 .13044 (70*2π)/5498 weeks
711.30636 1.38402 (71*2π)/5498 weeks
72-.15188 1.83946 (72*2π)/5498 weeks
73-.77683 .63017 (73*2π)/5498 weeks
74.54613 -.35652 (74*2π)/5497 weeks
751.20225 .90753 (75*2π)/5497 weeks
76.29045 1.03298 (76*2π)/5497 weeks
77-.01724 1.23324 (77*2π)/5497 weeks
78-.23396 -.239 (78*2π)/5497 weeks
791.52919 .20931 (79*2π)/5497 weeks
80.97092 1.52521 (80*2π)/5497 weeks
81-.13041 1.53384 (81*2π)/5497 weeks
82-.47666 .2167 (82*2π)/5497 weeks
83.5901 .0125 (83*2π)/5497 weeks
841.32062 .6037 (84*2π)/5497 weeks
85.48129 1.8578 (85*2π)/5496 weeks
86-.68727 .82088 (86*2π)/5496 weeks
87-.09043 -.16967 (87*2π)/5496 weeks
88.98652 .26889 (88*2π)/5496 weeks
89.76511 1.06979 (89*2π)/5496 weeks
90-.05931 .91924 (90*2π)/5496 weeks
91.21899 .11307 (91*2π)/5496 weeks
92.77819 .53106 (92*2π)/5496 weeks
93.28755 1.02063 (93*2π)/5496 weeks
94-.0493 .19247 (94*2π)/5496 weeks
95.76083 .41572 (95*2π)/5496 weeks
96.25582 .73677 (96*2π)/5496 weeks
97-.00327 .17538 (97*2π)/5496 weeks
98.73461 -.06727 (98*2π)/5496 weeks
991.10588 .68722 (99*2π)/5496 weeks
100.29232 1.16246 (100*2π)/5495 weeks
101-.27833 .51438 (101*2π)/5495 weeks
102.55972 -.17871 (102*2π)/5495 weeks
1031.33887 .62637 (103*2π)/5495 weeks
104.44265 1.57353 (104*2π)/5495 weeks
105-.72272 .82582 (105*2π)/5495 weeks
106-.02941 -.44126 (106*2π)/5495 weeks
107.94853 -.24037 (107*2π)/5495 weeks
1081.19818 .82527 (108*2π)/5495 weeks
109.05544 1.18758 (109*2π)/5495 weeks
110-.30274 .23957 (110*2π)/5495 weeks
111.65681 -.25955 (111*2π)/5495 weeks
1121.17508 .50731 (112*2π)/5495 weeks
113.72276 1.14632 (113*2π)/5495 weeks
114-.28124 1.02928 (114*2π)/5495 weeks
115-.10108 -.15349 (115*2π)/5495 weeks
116.86385 -.1149 (116*2π)/5495 weeks
117.94281 .68629 (117*2π)/5495 weeks
118.30214 1.09564 (118*2π)/5495 weeks
119-.22062 .42102 (119*2π)/5495 weeks
120.34186 .02898 (120*2π)/5495 weeks
121.97356 .50182 (121*2π)/5495 weeks
122.33255 1.13294 (122*2π)/5495 weeks
123-.43318 .48422 (123*2π)/5494 weeks
124.27721 -.20033 (124*2π)/5494 weeks
125.74764 .16987 (125*2π)/5494 weeks
126.48595 .53703 (126*2π)/5494 weeks
127.35594 .43177 (127*2π)/5494 weeks
128.21253 .45593 (128*2π)/5494 weeks
129.25052 .09779 (129*2π)/5494 weeks
130.70715 .19246 (130*2π)/5494 weeks
131.42158 .61906 (131*2π)/5494 weeks
132.21984 .23607 (132*2π)/5494 weeks
133.71818 .21195 (133*2π)/5494 weeks
134.69544 .60783 (134*2π)/5494 weeks
135.50836 .66373 (135*2π)/5494 weeks
136.04437 .5486 (136*2π)/5494 weeks
137.21808 .11281 (137*2π)/5494 weeks
138.30878 .23822 (138*2π)/5494 weeks
139.52698 .08158 (139*2π)/5494 weeks
140.7418 .43857 (140*2π)/5494 weeks
141.54942 .83541 (141*2π)/5494 weeks
142-.18203 .45963 (142*2π)/5494 weeks
143.54324 -.12374 (143*2π)/5494 weeks
144.74488 .60509 (144*2π)/5494 weeks
145.24343 .49708 (145*2π)/5494 weeks
146.27415 .19371 (146*2π)/5494 weeks
147.55486 .24186 (147*2π)/5494 weeks
148.40894 .57023 (148*2π)/5494 weeks
149.23792 .48054 (149*2π)/5494 weeks
150.09204 .13794 (150*2π)/5494 weeks
151.64924 .05371 (151*2π)/5494 weeks
152.44401 .54526 (152*2π)/5494 weeks
153.28957 .2724 (153*2π)/5494 weeks
154.43171 .19406 (154*2π)/5494 weeks
155.53962 .41122 (155*2π)/5494 weeks
156.29567 .34263 (156*2π)/5494 weeks
157.39953 .26735 (157*2π)/5493 weeks
158.15331 .31975 (158*2π)/5493 weeks
159.56529 .00793 (159*2π)/5493 weeks
160.46985 .44888 (160*2π)/5493 weeks
161.31803 .24922 (161*2π)/5493 weeks
162.44586 .27672 (162*2π)/5493 weeks
163.40096 .34171 (163*2π)/5493 weeks
164.30885 .07865 (164*2π)/5493 weeks
165.56198 .23234 (165*2π)/5493 weeks
166.70407 .29989 (166*2π)/5493 weeks
167.39247 .65387 (167*2π)/5493 weeks
168.16166 .38463 (168*2π)/5493 weeks
169.30108 .17879 (169*2π)/5493 weeks
170.4826 .28468 (170*2π)/5493 weeks
171.33501 .34604 (171*2π)/5493 weeks
172.24086 .21062 (172*2π)/5493 weeks
173.43003 .23188 (173*2π)/5493 weeks
174.51321 .24919 (174*2π)/5493 weeks
175.50522 .46742 (175*2π)/5493 weeks
176.3022 .544 (176*2π)/5493 weeks
177.04935 .38854 (177*2π)/5493 weeks
178.11737 -.0553 (178*2π)/5493 weeks
179.58669 .04707 (179*2π)/5493 weeks
180.57416 .44637 (180*2π)/5493 weeks
181.11327 .53165 (181*2π)/5493 weeks
182.0977 -.03093 (182*2π)/5493 weeks
183.46777 .04094 (183*2π)/5493 weeks
184.65555 .31514 (184*2π)/5493 weeks
185.26989 .46477 (185*2π)/5493 weeks
186.27564 .24714 (186*2π)/5493 weeks
187.27227 .13523 (187*2π)/5493 weeks
188.42502 .30779 (188*2π)/5493 weeks
189.06994 .3231 (189*2π)/5493 weeks
190.18724 .04943 (190*2π)/5493 weeks
191.35233 -.05863 (191*2π)/5493 weeks
192.6125 .08869 (192*2π)/5493 weeks
193.48243 .19175 (193*2π)/5493 weeks
194.59132 .50687 (194*2π)/5493 weeks
195-.1415 .37366 (195*2π)/5493 weeks
196.3189 -.03999 (196*2π)/5493 weeks
197.34137 .06109 (197*2π)/5493 weeks
198.46232 .12286 (198*2π)/5493 weeks
199.36248 .14358 (199*2π)/5493 weeks
200.59435 .17447 (200*2π)/5493 weeks
201.30004 .1776 (201*2π)/5493 weeks
202.72561 .23762 (202*2π)/5493 weeks
203.29786 .49355 (203*2π)/5493 weeks
204.22772 .40183 (204*2π)/5493 weeks
205-.11822 .05286 (205*2π)/5493 weeks
206.44978 -.38447 (206*2π)/5493 weeks
207.87923 .3045 (207*2π)/5493 weeks
208.28744 .73629 (208*2π)/5493 weeks
209-.25933 .16969 (209*2π)/5493 weeks
210.35247 -.39518 (210*2π)/5493 weeks
211.75055 .17215 (211*2π)/5493 weeks
212.41416 .61812 (212*2π)/5493 weeks
213-.3164 .36425 (213*2π)/5493 weeks
214.20097 -.60752 (214*2π)/5493 weeks
215.9407 -.07522 (215*2π)/5493 weeks
216.61952 .56878 (216*2π)/5493 weeks
217.03378 .3733 (217*2π)/5493 weeks
218.19218 -.00213 (218*2π)/5493 weeks
219.31799 .1219 (219*2π)/5493 weeks
220.30314 -.01989 (220*2π)/5492 weeks
221.55838 .02166 (221*2π)/5492 weeks
222.47964 .19951 (222*2π)/5492 weeks
223.55203 .37248 (223*2π)/5492 weeks
224.04576 .53221 (224*2π)/5492 weeks
225.01497 -.07068 (225*2π)/5492 weeks
226.35552 -.1012 (226*2π)/5492 weeks
227.56489 .33309 (227*2π)/5492 weeks
228-.11135 .40462 (228*2π)/5492 weeks
229.02506 -.13387 (229*2π)/5492 weeks
230.30256 -.24867 (230*2π)/5492 weeks
231.71391 -.03107 (231*2π)/5492 weeks
232.37132 .37557 (232*2π)/5492 weeks
233-.00144 .1032 (233*2π)/5492 weeks
234.24219 -.36614 (234*2π)/5492 weeks
235.84848 -.11897 (235*2π)/5492 weeks
236.60912 .578 (236*2π)/5492 weeks
237-.04462 .36404 (237*2π)/5492 weeks
238-.01755 -.16155 (238*2π)/5492 weeks
239.66293 -.27883 (239*2π)/5492 weeks
240.50961 .27868 (240*2π)/5492 weeks
241.29364 .26924 (241*2π)/5492 weeks
242.05021 .00416 (242*2π)/5492 weeks
243.44558 -.0336 (243*2π)/5492 weeks
244.31159 .11997 (244*2π)/5492 weeks
245.35723 .14372 (245*2π)/5492 weeks
246.08964 .13223 (246*2π)/5492 weeks
247.17232 -.30029 (247*2π)/5492 weeks
248.38371 -.22903 (248*2π)/5492 weeks
249.71958 .01384 (249*2π)/5492 weeks
250.42572 .43608 (250*2π)/5492 weeks
251-.01423 .18071 (251*2π)/5492 weeks
252-.01416 -.27392 (252*2π)/5492 weeks
253.42376 -.45251 (253*2π)/5492 weeks
254.91222 -.09667 (254*2π)/5492 weeks
255.68203 .51203 (255*2π)/5492 weeks
256-.23079 .41246 (256*2π)/5492 weeks
257.03503 -.52807 (257*2π)/5492 weeks
258.67937 -.29704 (258*2π)/5492 weeks
259.78037 .14363 (259*2π)/5492 weeks
260.18637 .52597 (260*2π)/5492 weeks
261-.25282 -.18956 (261*2π)/5492 weeks
262.48487 -.64251 (262*2π)/5492 weeks
263.73702 .06904 (263*2π)/5492 weeks
264.32182 .2709 (264*2π)/5492 weeks
265.07934 -.09019 (265*2π)/5492 weeks
266.39102 -.38819 (266*2π)/5492 weeks
267.93429 -.30849 (267*2π)/5492 weeks
268.78904 .54465 (268*2π)/5492 weeks
269-.07365 .20419 (269*2π)/5492 weeks
270.24734 -.31815 (270*2π)/5492 weeks
271.60964 -.11373 (271*2π)/5492 weeks
272.59575 .23685 (272*2π)/5492 weeks
273.38788 .28551 (273*2π)/5492 weeks
274.04323 .32688 (274*2π)/5492 weeks
275.04323 -.32688 (275*2π)/5492 weeks
276.38788 -.28551 (276*2π)/5492 weeks
277.59575 -.23685 (277*2π)/5492 weeks
278.60964 .11373 (278*2π)/5492 weeks
279.24734 .31815 (279*2π)/5492 weeks
280-.07365 -.20419 (280*2π)/5492 weeks
281.78904 -.54465 (281*2π)/5492 weeks
282.93429 .30849 (282*2π)/5492 weeks
283.39102 .38819 (283*2π)/5492 weeks
284.07934 .09019 (284*2π)/5492 weeks
285.32182 -.2709 (285*2π)/5492 weeks
286.73702 -.06904 (286*2π)/5492 weeks
287.48487 .64251 (287*2π)/5492 weeks
288-.25282 .18956 (288*2π)/5492 weeks
289.18637 -.52597 (289*2π)/5492 weeks
290.78037 -.14363 (290*2π)/5492 weeks
291.67937 .29704 (291*2π)/5492 weeks
292.03503 .52807 (292*2π)/5492 weeks
293-.23079 -.41246 (293*2π)/5492 weeks
294.68203 -.51203 (294*2π)/5492 weeks
295.91222 .09667 (295*2π)/5492 weeks
296.42376 .45251 (296*2π)/5492 weeks
297-.01416 .27392 (297*2π)/5492 weeks
298-.01423 -.18071 (298*2π)/5492 weeks
299.42572 -.43608 (299*2π)/5492 weeks
300.71958 -.01384 (300*2π)/5492 weeks
301.38371 .22903 (301*2π)/5492 weeks
302.17232 .30029 (302*2π)/5492 weeks
303.08964 -.13223 (303*2π)/5492 weeks
304.35723 -.14372 (304*2π)/5492 weeks
305.31159 -.11997 (305*2π)/5492 weeks
306.44558 .0336 (306*2π)/5492 weeks
307.05021 -.00416 (307*2π)/5492 weeks
308.29364 -.26924 (308*2π)/5492 weeks
309.50961 -.27868 (309*2π)/5492 weeks
310.66293 .27883 (310*2π)/5492 weeks
311-.01755 .16155 (311*2π)/5492 weeks
312-.04462 -.36404 (312*2π)/5492 weeks
313.60912 -.578 (313*2π)/5492 weeks
314.84848 .11897 (314*2π)/5492 weeks
315.24219 .36614 (315*2π)/5492 weeks
316-.00144 -.1032 (316*2π)/5492 weeks
317.37132 -.37557 (317*2π)/5492 weeks
318.71391 .03107 (318*2π)/5492 weeks
319.30256 .24867 (319*2π)/5492 weeks
320.02506 .13387 (320*2π)/5492 weeks
321-.11135 -.40462 (321*2π)/5492 weeks
322.56489 -.33309 (322*2π)/5492 weeks
323.35552 .1012 (323*2π)/5492 weeks
324.01497 .07068 (324*2π)/5492 weeks
325.04576 -.53221 (325*2π)/5492 weeks
326.55203 -.37248 (326*2π)/5492 weeks
327.47964 -.19951 (327*2π)/5492 weeks
328.55838 -.02166 (328*2π)/5492 weeks
329.30314 .01989 (329*2π)/5492 weeks
330.31799 -.1219 (330*2π)/5492 weeks
331.19218 .00213 (331*2π)/5492 weeks
332.03378 -.3733 (332*2π)/5492 weeks
333.61952 -.56878 (333*2π)/5492 weeks
334.9407 .07522 (334*2π)/5492 weeks
335.20097 .60752 (335*2π)/5492 weeks
336-.3164 -.36425 (336*2π)/5492 weeks
337.41416 -.61812 (337*2π)/5492 weeks
338.75055 -.17215 (338*2π)/5492 weeks
339.35247 .39518 (339*2π)/5492 weeks
340-.25933 -.16969 (340*2π)/5492 weeks
341.28744 -.73629 (341*2π)/5492 weeks
342.87923 -.3045 (342*2π)/5492 weeks
343.44978 .38447 (343*2π)/5492 weeks
344-.11822 -.05286 (344*2π)/5492 weeks
345.22772 -.40183 (345*2π)/5492 weeks
346.29786 -.49355 (346*2π)/5492 weeks
347.72561 -.23762 (347*2π)/5492 weeks
348.30004 -.1776 (348*2π)/5492 weeks
349.59435 -.17447 (349*2π)/5492 weeks
350.36248 -.14358 (350*2π)/5492 weeks
351.46232 -.12286 (351*2π)/5492 weeks
352.34137 -.06109 (352*2π)/5492 weeks
353.3189 .03999 (353*2π)/5492 weeks
354-.1415 -.37366 (354*2π)/5492 weeks
355.59132 -.50687 (355*2π)/5492 weeks
356.48243 -.19175 (356*2π)/5492 weeks
357.6125 -.08869 (357*2π)/5492 weeks
358.35233 .05863 (358*2π)/5492 weeks
359.18724 -.04943 (359*2π)/5492 weeks
360.06994 -.3231 (360*2π)/5492 weeks
361.42502 -.30779 (361*2π)/5492 weeks
362.27227 -.13523 (362*2π)/5492 weeks
363.27564 -.24714 (363*2π)/5492 weeks
364.26989 -.46477 (364*2π)/5492 weeks
365.65555 -.31514 (365*2π)/5492 weeks
366.46777 -.04094 (366*2π)/5492 weeks
367.0977 .03093 (367*2π)/5491 weeks
368.11327 -.53165 (368*2π)/5491 weeks
369.57416 -.44637 (369*2π)/5491 weeks
370.58669 -.04707 (370*2π)/5491 weeks
371.11737 .0553 (371*2π)/5491 weeks
372.04935 -.38854 (372*2π)/5491 weeks
373.3022 -.544 (373*2π)/5491 weeks
374.50522 -.46742 (374*2π)/5491 weeks
375.51321 -.24919 (375*2π)/5491 weeks
376.43003 -.23188 (376*2π)/5491 weeks
377.24086 -.21062 (377*2π)/5491 weeks
378.33501 -.34604 (378*2π)/5491 weeks
379.4826 -.28468 (379*2π)/5491 weeks
380.30108 -.17879 (380*2π)/5491 weeks
381.16166 -.38463 (381*2π)/5491 weeks
382.39247 -.65387 (382*2π)/5491 weeks
383.70407 -.29989 (383*2π)/5491 weeks
384.56198 -.23234 (384*2π)/5491 weeks
385.30885 -.07865 (385*2π)/5491 weeks
386.40096 -.34171 (386*2π)/5491 weeks
387.44586 -.27672 (387*2π)/5491 weeks
388.31803 -.24922 (388*2π)/5491 weeks
389.46985 -.44888 (389*2π)/5491 weeks
390.56529 -.00793 (390*2π)/5491 weeks
391.15331 -.31975 (391*2π)/5491 weeks
392.39953 -.26735 (392*2π)/5491 weeks
393.29567 -.34263 (393*2π)/5491 weeks
394.53962 -.41122 (394*2π)/5491 weeks
395.43171 -.19406 (395*2π)/5491 weeks
396.28957 -.2724 (396*2π)/5491 weeks
397.44401 -.54526 (397*2π)/5491 weeks
398.64924 -.05371 (398*2π)/5491 weeks
399.09204 -.13794 (399*2π)/5491 weeks
400.23792 -.48054 (400*2π)/5491 weeks
401.40894 -.57023 (401*2π)/5491 weeks
402.55486 -.24186 (402*2π)/5491 weeks
403.27415 -.19371 (403*2π)/5491 weeks
404.24343 -.49708 (404*2π)/5491 weeks
405.74488 -.60509 (405*2π)/5491 weeks
406.54324 .12374 (406*2π)/5491 weeks
407-.18203 -.45963 (407*2π)/5491 weeks
408.54942 -.83541 (408*2π)/5491 weeks
409.7418 -.43857 (409*2π)/5491 weeks
410.52698 -.08158 (410*2π)/5491 weeks
411.30878 -.23822 (411*2π)/5491 weeks
412.21808 -.11281 (412*2π)/5491 weeks
413.04437 -.5486 (413*2π)/5491 weeks
414.50836 -.66373 (414*2π)/5491 weeks
415.69544 -.60783 (415*2π)/5491 weeks
416.71818 -.21195 (416*2π)/5491 weeks
417.21984 -.23607 (417*2π)/5491 weeks
418.42158 -.61906 (418*2π)/5491 weeks
419.70715 -.19246 (419*2π)/5491 weeks
420.25052 -.09779 (420*2π)/5491 weeks
421.21253 -.45593 (421*2π)/5491 weeks
422.35594 -.43177 (422*2π)/5491 weeks
423.48595 -.53703 (423*2π)/5491 weeks
424.74764 -.16987 (424*2π)/5491 weeks
425.27721 .20033 (425*2π)/5491 weeks
426-.43318 -.48422 (426*2π)/5491 weeks
427.33255 -1.13294 (427*2π)/5491 weeks
428.97356 -.50182 (428*2π)/5491 weeks
429.34186 -.02898 (429*2π)/5491 weeks
430-.22062 -.42102 (430*2π)/5491 weeks
431.30214 -1.09564 (431*2π)/5491 weeks
432.94281 -.68629 (432*2π)/5491 weeks
433.86385 .1149 (433*2π)/5491 weeks
434-.10108 .15349 (434*2π)/5491 weeks
435-.28124 -1.02928 (435*2π)/5491 weeks
436.72276 -1.14632 (436*2π)/5491 weeks
4371.17508 -.50731 (437*2π)/5491 weeks
438.65681 .25955 (438*2π)/5491 weeks
439-.30274 -.23957 (439*2π)/5491 weeks
440.05544 -1.18758 (440*2π)/5491 weeks
4411.19818 -.82527 (441*2π)/5491 weeks
442.94853 .24037 (442*2π)/5491 weeks
443-.02941 .44126 (443*2π)/5491 weeks
444-.72272 -.82582 (444*2π)/5491 weeks
445.44265 -1.57353 (445*2π)/5491 weeks
4461.33887 -.62637 (446*2π)/5491 weeks
447.55972 .17871 (447*2π)/5491 weeks
448-.27833 -.51438 (448*2π)/5491 weeks
449.29232 -1.16246 (449*2π)/5491 weeks
4501.10588 -.68722 (450*2π)/5491 weeks
451.73461 .06727 (451*2π)/5491 weeks
452-.00327 -.17538 (452*2π)/5491 weeks
453.25582 -.73677 (453*2π)/5491 weeks
454.76083 -.41572 (454*2π)/5491 weeks
455-.0493 -.19247 (455*2π)/5491 weeks
456.28755 -1.02063 (456*2π)/5491 weeks
457.77819 -.53106 (457*2π)/5491 weeks
458.21899 -.11307 (458*2π)/5491 weeks
459-.05931 -.91924 (459*2π)/5491 weeks
460.76511 -1.06979 (460*2π)/5491 weeks
461.98652 -.26889 (461*2π)/5491 weeks
462-.09043 .16967 (462*2π)/5491 weeks
463-.68727 -.82088 (463*2π)/5491 weeks
464.48129 -1.8578 (464*2π)/5491 weeks
4651.32062 -.6037 (465*2π)/5491 weeks
466.5901 -.0125 (466*2π)/5491 weeks
467-.47666 -.2167 (467*2π)/5491 weeks
468-.13041 -1.53384 (468*2π)/5491 weeks
469.97092 -1.52521 (469*2π)/5491 weeks
4701.52919 -.20931 (470*2π)/5491 weeks
471-.23396 .239 (471*2π)/5491 weeks
472-.01724 -1.23324 (472*2π)/5491 weeks
473.29045 -1.03298 (473*2π)/5491 weeks
4741.20225 -.90753 (474*2π)/5491 weeks
475.54613 .35652 (475*2π)/5491 weeks
476-.77683 -.63017 (476*2π)/5491 weeks
477-.15188 -1.83946 (477*2π)/5491 weeks
4781.30636 -1.38402 (478*2π)/5491 weeks
479.77214 -.13044 (479*2π)/5491 weeks
480-.02787 -1.01021 (480*2π)/5491 weeks
481.6854 -.74472 (481*2π)/5491 weeks
482.42468 -.85704 (482*2π)/5491 weeks
483-.18362 -.50554 (483*2π)/5491 weeks
484.26258 -1.68475 (484*2π)/5491 weeks
4851.31976 -1.20921 (485*2π)/5491 weeks
486.80018 -.2553 (486*2π)/5491 weeks
487-.28045 -.37673 (487*2π)/5491 weeks
488.25944 -1.81799 (488*2π)/5491 weeks
4891.34178 -.76265 (489*2π)/5491 weeks
490.25978 -.11184 (490*2π)/5491 weeks
491-.67013 -.96692 (491*2π)/5491 weeks
492.3004 -2.31217 (492*2π)/5491 weeks
4932.1156 -1.1203 (493*2π)/5491 weeks
494.67509 .47842 (494*2π)/5491 weeks
495-.60877 -.60923 (495*2π)/5491 weeks
496-.06164 -1.52184 (496*2π)/5491 weeks
497.71509 -1.56783 (497*2π)/5491 weeks
498.36357 -.69756 (498*2π)/5491 weeks
499-.24662 -1.38322 (499*2π)/5491 weeks
500.26581 -2.05087 (500*2π)/5491 weeks
5011.03089 -1.65144 (501*2π)/5491 weeks
5021.54908 -.87937 (502*2π)/5491 weeks
503.44707 -.50274 (503*2π)/5491 weeks
504.21045 -1.00585 (504*2π)/5491 weeks
505-.07686 -1.42073 (505*2π)/5491 weeks
506.86869 -1.24823 (506*2π)/5491 weeks
507-.10111 -1.24366 (507*2π)/5491 weeks
508.90692 -1.66107 (508*2π)/5491 weeks
509.26188 -.84715 (509*2π)/5491 weeks
510-.0205 -1.33949 (510*2π)/5491 weeks
511-.12523 -1.73729 (511*2π)/5491 weeks
512.61283 -2.59086 (512*2π)/5491 weeks
5131.67962 -1.07396 (513*2π)/5491 weeks
514-.21711 .40845 (514*2π)/5491 weeks
515-2.8828 -2.29855 (515*2π)/5491 weeks
516.97957 -5.58865 (516*2π)/5491 weeks
5174.15332 -1.87651 (517*2π)/5491 weeks
5181.11805 .96098 (518*2π)/5491 weeks
519-2.18233 -1.3551 (519*2π)/5491 weeks
520-.25884 -4.65621 (520*2π)/5491 weeks
5212.44369 -3.07025 (521*2π)/5491 weeks
5222.03357 -.67336 (522*2π)/5491 weeks
523-1.19241 .27497 (523*2π)/5491 weeks
524-1.29407 -3.43289 (524*2π)/5491 weeks
525.88741 -3.0597 (525*2π)/5491 weeks
526.65698 -1.41464 (526*2π)/5491 weeks
527-1.23551 -3.25475 (527*2π)/5491 weeks
528.47275 -4.95285 (528*2π)/5491 weeks
5291.86944 -3.83276 (529*2π)/5491 weeks
5301.31196 -2.66547 (530*2π)/5491 weeks
531.73445 -2.12867 (531*2π)/5491 weeks
532-1.00055 -4.20891 (532*2π)/5491 weeks
5331.75701 -4.02795 (533*2π)/5491 weeks
534.8705 -3.96511 (534*2π)/5491 weeks
535.8831 -4.05757 (535*2π)/5491 weeks
5361.94598 -5.23521 (536*2π)/5491 weeks
5372.57884 -2.59274 (537*2π)/5491 weeks
538-1.16505 -3.12943 (538*2π)/5491 weeks
539-1.40046 -5.27389 (539*2π)/5491 weeks
540-.11137 -11.1864 (540*2π)/5491 weeks
5417.70949 -6.20946 (541*2π)/5491 weeks
542-1.34763 -1.89875 (542*2π)/5491 weeks
543-5.92364 -12.76284 (543*2π)/5491 weeks
5445.87694 -19.81635 (544*2π)/5491 weeks
54515.07916 -9.13456 (545*2π)/5491 weeks
546.3208 1.65496 (546*2π)/5491 weeks
547-17.71937 -23.75168 (547*2π)/5491 weeks

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