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# Fourier Analysis of UYG (ProShares Ultra Financials)

UYG (ProShares Ultra Financials) appears to have interesting cyclic behaviour every 59 weeks (7.3393*sine), 53 weeks (6.3329*sine), and 49 weeks (3.0022*cosine).

UYG (ProShares Ultra Financials) has an average price of 76.42 (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.

## Fourier Analysis

Using data from 2/1/2007 to 4/23/2018 for UYG (ProShares Ultra Financials), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
076.42094   0
165.54566 -9.75698 (1*2π)/587587 weeks
240.86359 20.06278 (2*2π)/587294 weeks
330.58693 23.85475 (3*2π)/587196 weeks
410.49425 22.79591 (4*2π)/587147 weeks
5.83165 15.41772 (5*2π)/587117 weeks
6-1.12436 12.37685 (6*2π)/58798 weeks
72.05981 9.15155 (7*2π)/58784 weeks
84.40318 8.09561 (8*2π)/58773 weeks
91.85392 9.82682 (9*2π)/58765 weeks
10-1.27133 7.3393 (10*2π)/58759 weeks
11-1.44223 6.33294 (11*2π)/58753 weeks
12-3.00221 3.98297 (12*2π)/58749 weeks
13-.80495 2.22002 (13*2π)/58745 weeks
14-.14246 3.12833 (14*2π)/58742 weeks
15-.1788 3.90474 (15*2π)/58739 weeks
16.27352 4.40781 (16*2π)/58737 weeks
17.1581 3.88285 (17*2π)/58735 weeks
18.57714 3.7951 (18*2π)/58733 weeks
19-.37334 2.85653 (19*2π)/58731 weeks
20-.11983 2.57905 (20*2π)/58729 weeks
21-.81002 3.08905 (21*2π)/58728 weeks
22-1.20281 3.80894 (22*2π)/58727 weeks
23-1.25497 3.13594 (23*2π)/58726 weeks
24-1.05877 1.18951 (24*2π)/58724 weeks
25-1.09444 .96099 (25*2π)/58723 weeks
26.23229 1.00521 (26*2π)/58723 weeks
271.18472 .81861 (27*2π)/58722 weeks
282.47426 .64433 (28*2π)/58721 weeks
291.38654 1.61216 (29*2π)/58720 weeks
30.59251 1.93738 (30*2π)/58720 weeks
31.1972 2.33164 (31*2π)/58719 weeks
32.66073 1.6065 (32*2π)/58718 weeks
331.55988 .16694 (33*2π)/58718 weeks
341.85107 .26976 (34*2π)/58717 weeks
352.50373 1.9267 (35*2π)/58717 weeks
362.33928 3.66474 (36*2π)/58716 weeks
371.09577 3.70634 (37*2π)/58716 weeks
38.34187 3.25819 (38*2π)/58715 weeks
39-.11243 2.61419 (39*2π)/58715 weeks
40.21866 1.9316 (40*2π)/58715 weeks
41.3844 1.00565 (41*2π)/58714 weeks
42.55874 .91285 (42*2π)/58714 weeks
43.84028 1.23727 (43*2π)/58714 weeks
44.17892 1.44453 (44*2π)/58713 weeks
45.41559 1.31701 (45*2π)/58713 weeks
46.62397 1.59111 (46*2π)/58713 weeks
47.47626 .86403 (47*2π)/58712 weeks
48.53194 1.03487 (48*2π)/58712 weeks
49.85949 1.02181 (49*2π)/58712 weeks
50.92818 .67723 (50*2π)/58712 weeks
51.30955 1.20994 (51*2π)/58712 weeks
521.03495 1.36951 (52*2π)/58711 weeks
531.12871 1.35782 (53*2π)/58711 weeks
541.05416 1.86664 (54*2π)/58711 weeks
55.77643 1.99046 (55*2π)/58711 weeks
56.69198 2.4403 (56*2π)/58710 weeks
57.65743 2.17404 (57*2π)/58710 weeks
58.25082 1.7461 (58*2π)/58710 weeks
59-.12518 1.44026 (59*2π)/58710 weeks
60-.461 .95296 (60*2π)/58710 weeks
61.07584 1.02133 (61*2π)/58710 weeks
62.38437 .73658 (62*2π)/5879 weeks
63.53129 .85272 (63*2π)/5879 weeks
64.71359 .9364 (64*2π)/5879 weeks
65.66966 .93139 (65*2π)/5879 weeks
66.90169 .96734 (66*2π)/5879 weeks
67.69025 1.49053 (67*2π)/5879 weeks
68.78086 1.45909 (68*2π)/5879 weeks
69.24502 1.6044 (69*2π)/5879 weeks
70.04965 1.71241 (70*2π)/5878 weeks
71-.05205 1.19282 (71*2π)/5878 weeks
72-.64748 1.0792 (72*2π)/5878 weeks
73-.25764 .67682 (73*2π)/5878 weeks
74.00334 .32083 (74*2π)/5878 weeks
75.48356 .11332 (75*2π)/5878 weeks
76.92888 .41811 (76*2π)/5878 weeks
771.18151 .86486 (77*2π)/5878 weeks
781.08935 .7678 (78*2π)/5878 weeks
79.60823 .86453 (79*2π)/5877 weeks
80.71218 .68017 (80*2π)/5877 weeks
811.05622 .83673 (81*2π)/5877 weeks
82.73525 .94918 (82*2π)/5877 weeks
831.00614 1.06239 (83*2π)/5877 weeks
84.74257 1.50342 (84*2π)/5877 weeks
85.06245 1.32526 (85*2π)/5877 weeks
86-.04307 1.13569 (86*2π)/5877 weeks
87.06523 .56135 (87*2π)/5877 weeks
88.36108 .35216 (88*2π)/5877 weeks
89.37061 .47629 (89*2π)/5877 weeks
90.57443 .68366 (90*2π)/5877 weeks
91.14298 .96896 (91*2π)/5876 weeks
92-.29116 .82098 (92*2π)/5876 weeks
93-.44318 .7202 (93*2π)/5876 weeks
94-.14576 .16512 (94*2π)/5876 weeks
95-.01621 -.20475 (95*2π)/5876 weeks
96.15482 -.17531 (96*2π)/5876 weeks
97.37149 .13378 (97*2π)/5876 weeks
98.54118 .34982 (98*2π)/5876 weeks
99.62807 .50302 (99*2π)/5876 weeks
100.70551 .63306 (100*2π)/5876 weeks
101.60009 .71613 (101*2π)/5876 weeks
102.52287 .50695 (102*2π)/5876 weeks
103.42286 .90092 (103*2π)/5876 weeks
104.44012 1.05021 (104*2π)/5876 weeks
105.35616 1.11056 (105*2π)/5876 weeks
106.25488 1.07587 (106*2π)/5876 weeks
107.18807 .80736 (107*2π)/5875 weeks
108.05001 .91135 (108*2π)/5875 weeks
109.2596 1.12121 (109*2π)/5875 weeks
110.23467 1.08077 (110*2π)/5875 weeks
111-.01032 1.14716 (111*2π)/5875 weeks
112-.09921 .97842 (112*2π)/5875 weeks
113-.48403 .63476 (113*2π)/5875 weeks
114-.26599 .58669 (114*2π)/5875 weeks
115-.01033 .28278 (115*2π)/5875 weeks
116.26056 .10612 (116*2π)/5875 weeks
117.07049 .26258 (117*2π)/5875 weeks
118-.03276 .38912 (118*2π)/5875 weeks
119.0434 .26773 (119*2π)/5875 weeks
120.18623 .1483 (120*2π)/5875 weeks
121.2627 .16038 (121*2π)/5875 weeks
122.55048 .07295 (122*2π)/5875 weeks
123.54989 .46304 (123*2π)/5875 weeks
124.52924 .62668 (124*2π)/5875 weeks
125.50016 .44347 (125*2π)/5875 weeks
126.26348 .46858 (126*2π)/5875 weeks
127.11365 .4504 (127*2π)/5875 weeks
128.39237 .65778 (128*2π)/5875 weeks
129.53799 .67335 (129*2π)/5875 weeks
130.10971 .62135 (130*2π)/5875 weeks
131-.07916 .61423 (131*2π)/5874 weeks
132-.1421 .23749 (132*2π)/5874 weeks
133.15431 .20567 (133*2π)/5874 weeks
134.49375 .10487 (134*2π)/5874 weeks
135.55158 .18519 (135*2π)/5874 weeks
136.49198 .32684 (136*2π)/5874 weeks
137.43813 .52015 (137*2π)/5874 weeks
138.31767 .6468 (138*2π)/5874 weeks
139.03576 .55206 (139*2π)/5874 weeks
140.00685 .3532 (140*2π)/5874 weeks
141-.16829 .24606 (141*2π)/5874 weeks
142-.37349 .12131 (142*2π)/5874 weeks
143-.14358 .12983 (143*2π)/5874 weeks
144.18944 -.04352 (144*2π)/5874 weeks
145.32925 -.31644 (145*2π)/5874 weeks
146.56131 -.1237 (146*2π)/5874 weeks
147.69361 .11154 (147*2π)/5874 weeks
148.85163 .24023 (148*2π)/5874 weeks
149.83885 .36266 (149*2π)/5874 weeks
150.56178 .48771 (150*2π)/5874 weeks
151.38537 .7682 (151*2π)/5874 weeks
152.12849 .57889 (152*2π)/5874 weeks
153.27029 .50464 (153*2π)/5874 weeks
154.3991 .35737 (154*2π)/5874 weeks
155.20693 .1234 (155*2π)/5874 weeks
156.21887 .11081 (156*2π)/5874 weeks
157.38661 .2132 (157*2π)/5874 weeks
158.52838 .2141 (158*2π)/5874 weeks
159.40282 .38124 (159*2π)/5874 weeks
160.4288 .48869 (160*2π)/5874 weeks
161.49077 .48411 (161*2π)/5874 weeks
162.4617 .28541 (162*2π)/5874 weeks
163.49412 .23023 (163*2π)/5874 weeks
164.45462 .23225 (164*2π)/5874 weeks
165.37947 .24262 (165*2π)/5874 weeks
166.27721 .20924 (166*2π)/5874 weeks
167.43331 .20844 (167*2π)/5874 weeks
168.57227 .06414 (168*2π)/5873 weeks
169.4828 -.00461 (169*2π)/5873 weeks
170.68562 .07906 (170*2π)/5873 weeks
171.49171 .29281 (171*2π)/5873 weeks
172.3187 .36314 (172*2π)/5873 weeks
173.24362 .33801 (173*2π)/5873 weeks
174.03783 .30368 (174*2π)/5873 weeks
175.06496 .23274 (175*2π)/5873 weeks
176.23731 -.02908 (176*2π)/5873 weeks
177.34574 -.12495 (177*2π)/5873 weeks
178.61638 -.24684 (178*2π)/5873 weeks
179.59213 -.08523 (179*2π)/5873 weeks
180.54932 .09852 (180*2π)/5873 weeks
181.50941 .22079 (181*2π)/5873 weeks
182.42043 .08592 (182*2π)/5873 weeks
183.41676 .21673 (183*2π)/5873 weeks
184.48286 .30283 (184*2π)/5873 weeks
185.23898 .39636 (185*2π)/5873 weeks
186.13081 .36592 (186*2π)/5873 weeks
187-.03756 .23241 (187*2π)/5873 weeks
188.07218 .08198 (188*2π)/5873 weeks
189.14448 .02694 (189*2π)/5873 weeks
190.25747 .00018 (190*2π)/5873 weeks
191.35819 .13485 (191*2π)/5873 weeks
192.27414 .28486 (192*2π)/5873 weeks
193.19489 .37132 (193*2π)/5873 weeks
194.01685 .37025 (194*2π)/5873 weeks
195-.0623 .09799 (195*2π)/5873 weeks
196-.05105 .03005 (196*2π)/5873 weeks
197.15925 -.06763 (197*2π)/5873 weeks
198.33626 -.06908 (198*2π)/5873 weeks
199.43679 -.05735 (199*2π)/5873 weeks
200.41987 .06404 (200*2π)/5873 weeks
201.49136 .14941 (201*2π)/5873 weeks
202.59252 .16961 (202*2π)/5873 weeks
203.46578 .41767 (203*2π)/5873 weeks
204.37701 .5186 (204*2π)/5873 weeks
205.27219 .57506 (205*2π)/5873 weeks
206.1117 .42371 (206*2π)/5873 weeks
207-.01194 .41156 (207*2π)/5873 weeks
208-.078 .22629 (208*2π)/5873 weeks
209.21433 -.07402 (209*2π)/5873 weeks
210.25106 -.06287 (210*2π)/5873 weeks
211.40935 -.0769 (211*2π)/5873 weeks
212.45298 -.06516 (212*2π)/5873 weeks
213.65574 -.00005 (213*2π)/5873 weeks
214.93745 .06831 (214*2π)/5873 weeks
215.8901 .22355 (215*2π)/5873 weeks
216.9663 .22373 (216*2π)/5873 weeks
217.76974 .44754 (217*2π)/5873 weeks
218.58874 .45907 (218*2π)/5873 weeks
219.49401 .62069 (219*2π)/5873 weeks
220.32057 .61203 (220*2π)/5873 weeks
221.10629 .34259 (221*2π)/5873 weeks
222.1105 .25195 (222*2π)/5873 weeks
223.1483 .13507 (223*2π)/5873 weeks
224.1352 .07163 (224*2π)/5873 weeks
225.13448 -.01795 (225*2π)/5873 weeks
226.32618 -.1608 (226*2π)/5873 weeks
227.49939 -.24911 (227*2π)/5873 weeks
228.54786 -.23588 (228*2π)/5873 weeks
229.76789 .07297 (229*2π)/5873 weeks
230.75995 .16767 (230*2π)/5873 weeks
231.53206 .22572 (231*2π)/5873 weeks
232.33071 .18715 (232*2π)/5873 weeks
233.31987 .14215 (233*2π)/5873 weeks
234.27301 .09771 (234*2π)/5873 weeks
235.16295 .00668 (235*2π)/5872 weeks
236.24107 -.10267 (236*2π)/5872 weeks
237.51139 -.06503 (237*2π)/5872 weeks
238.58067 -.11118 (238*2π)/5872 weeks
239.66483 -.04427 (239*2π)/5872 weeks
240.65821 .13488 (240*2π)/5872 weeks
241.45169 .08237 (241*2π)/5872 weeks
242.39973 .14346 (242*2π)/5872 weeks
243.39839 .04465 (243*2π)/5872 weeks
244.53389 -.04215 (244*2π)/5872 weeks
245.45833 -.06901 (245*2π)/5872 weeks
246.41878 .04568 (246*2π)/5872 weeks
247.49358 .17893 (247*2π)/5872 weeks
248.61834 .16013 (248*2π)/5872 weeks
249.58363 .18196 (249*2π)/5872 weeks
250.56275 .19958 (250*2π)/5872 weeks
251.59334 .21873 (251*2π)/5872 weeks
252.49651 .21529 (252*2π)/5872 weeks
253.29738 .25069 (253*2π)/5872 weeks
254.29943 .07907 (254*2π)/5872 weeks
255.11584 .16508 (255*2π)/5872 weeks
256.33392 .0393 (256*2π)/5872 weeks
257.34347 -.00953 (257*2π)/5872 weeks
258.47958 -.0284 (258*2π)/5872 weeks
259.44716 .00432 (259*2π)/5872 weeks
260.52577 -.07037 (260*2π)/5872 weeks
261.51939 .01073 (261*2π)/5872 weeks
262.49239 .08938 (262*2π)/5872 weeks
263.51763 .25875 (263*2π)/5872 weeks
264.56174 .41922 (264*2π)/5872 weeks
265.40565 .2807 (265*2π)/5872 weeks
266.16836 .29934 (266*2π)/5872 weeks
267.19501 .12857 (267*2π)/5872 weeks
268.33423 -.17948 (268*2π)/5872 weeks
269.44601 -.07352 (269*2π)/5872 weeks
270.67365 .08012 (270*2π)/5872 weeks
271.62663 .04942 (271*2π)/5872 weeks
272.42502 .28638 (272*2π)/5872 weeks
273.35693 .37362 (273*2π)/5872 weeks
274.08377 .16044 (274*2π)/5872 weeks
275.16411 -.09815 (275*2π)/5872 weeks
276.31976 -.18793 (276*2π)/5872 weeks
277.37777 -.21659 (277*2π)/5872 weeks
278.54949 .03176 (278*2π)/5872 weeks
279.52367 .27433 (279*2π)/5872 weeks
280.43952 .4192 (280*2π)/5872 weeks
281.43986 .20401 (281*2π)/5872 weeks
282.25428 .217 (282*2π)/5872 weeks
283.13764 .28294 (283*2π)/5872 weeks
284.12894 .30996 (284*2π)/5872 weeks
285.1859 .13231 (285*2π)/5872 weeks
286.03679 .07145 (286*2π)/5872 weeks
287.05179 -.01361 (287*2π)/5872 weeks
288.35262 .10169 (288*2π)/5872 weeks
289.49914 .18236 (289*2π)/5872 weeks
290.40395 .15327 (290*2π)/5872 weeks
291.06271 .28338 (291*2π)/5872 weeks
292-.06504 .2376 (292*2π)/5872 weeks
293-.20807 .1506 (293*2π)/5872 weeks
294-.20807 -.1506 (294*2π)/5872 weeks
295-.06504 -.2376 (295*2π)/5872 weeks
296.06271 -.28338 (296*2π)/5872 weeks
297.40395 -.15327 (297*2π)/5872 weeks
298.49914 -.18236 (298*2π)/5872 weeks
299.35262 -.10169 (299*2π)/5872 weeks
300.05179 .01361 (300*2π)/5872 weeks
301.03679 -.07145 (301*2π)/5872 weeks
302.1859 -.13231 (302*2π)/5872 weeks
303.12894 -.30996 (303*2π)/5872 weeks
304.13764 -.28294 (304*2π)/5872 weeks
305.25428 -.217 (305*2π)/5872 weeks
306.43986 -.20401 (306*2π)/5872 weeks
307.43952 -.4192 (307*2π)/5872 weeks
308.52367 -.27433 (308*2π)/5872 weeks
309.54949 -.03176 (309*2π)/5872 weeks
310.37777 .21659 (310*2π)/5872 weeks
311.31976 .18793 (311*2π)/5872 weeks
312.16411 .09815 (312*2π)/5872 weeks
313.08377 -.16044 (313*2π)/5872 weeks
314.35693 -.37362 (314*2π)/5872 weeks
315.42502 -.28638 (315*2π)/5872 weeks
316.62663 -.04942 (316*2π)/5872 weeks
317.67365 -.08012 (317*2π)/5872 weeks
318.44601 .07352 (318*2π)/5872 weeks
319.33423 .17948 (319*2π)/5872 weeks
320.19501 -.12857 (320*2π)/5872 weeks
321.16836 -.29934 (321*2π)/5872 weeks
322.40565 -.2807 (322*2π)/5872 weeks
323.56174 -.41922 (323*2π)/5872 weeks
324.51763 -.25875 (324*2π)/5872 weeks
325.49239 -.08938 (325*2π)/5872 weeks
326.51939 -.01073 (326*2π)/5872 weeks
327.52577 .07037 (327*2π)/5872 weeks
328.44716 -.00432 (328*2π)/5872 weeks
329.47958 .0284 (329*2π)/5872 weeks
330.34347 .00953 (330*2π)/5872 weeks
331.33392 -.0393 (331*2π)/5872 weeks
332.11584 -.16508 (332*2π)/5872 weeks
333.29943 -.07907 (333*2π)/5872 weeks
334.29738 -.25069 (334*2π)/5872 weeks
335.49651 -.21529 (335*2π)/5872 weeks
336.59334 -.21873 (336*2π)/5872 weeks
337.56275 -.19958 (337*2π)/5872 weeks
338.58363 -.18196 (338*2π)/5872 weeks
339.61834 -.16013 (339*2π)/5872 weeks
340.49358 -.17893 (340*2π)/5872 weeks
341.41878 -.04568 (341*2π)/5872 weeks
342.45833 .06901 (342*2π)/5872 weeks
343.53389 .04215 (343*2π)/5872 weeks
344.39839 -.04465 (344*2π)/5872 weeks
345.39973 -.14346 (345*2π)/5872 weeks
346.45169 -.08237 (346*2π)/5872 weeks
347.65821 -.13488 (347*2π)/5872 weeks
348.66483 .04427 (348*2π)/5872 weeks
349.58067 .11118 (349*2π)/5872 weeks
350.51139 .06503 (350*2π)/5872 weeks
351.24107 .10267 (351*2π)/5872 weeks
352.16295 -.00668 (352*2π)/5872 weeks
353.27301 -.09771 (353*2π)/5872 weeks
354.31987 -.14215 (354*2π)/5872 weeks
355.33071 -.18715 (355*2π)/5872 weeks
356.53206 -.22572 (356*2π)/5872 weeks
357.75995 -.16767 (357*2π)/5872 weeks
358.76789 -.07297 (358*2π)/5872 weeks
359.54786 .23588 (359*2π)/5872 weeks
360.49939 .24911 (360*2π)/5872 weeks
361.32618 .1608 (361*2π)/5872 weeks
362.13448 .01795 (362*2π)/5872 weeks
363.1352 -.07163 (363*2π)/5872 weeks
364.1483 -.13507 (364*2π)/5872 weeks
365.1105 -.25195 (365*2π)/5872 weeks
366.10629 -.34259 (366*2π)/5872 weeks
367.32057 -.61203 (367*2π)/5872 weeks
368.49401 -.62069 (368*2π)/5872 weeks
369.58874 -.45907 (369*2π)/5872 weeks
370.76974 -.44754 (370*2π)/5872 weeks
371.9663 -.22373 (371*2π)/5872 weeks
372.8901 -.22355 (372*2π)/5872 weeks
373.93745 -.06831 (373*2π)/5872 weeks
374.65574 .00005 (374*2π)/5872 weeks
375.45298 .06516 (375*2π)/5872 weeks
376.40935 .0769 (376*2π)/5872 weeks
377.25106 .06287 (377*2π)/5872 weeks
378.21433 .07402 (378*2π)/5872 weeks
379-.078 -.22629 (379*2π)/5872 weeks
380-.01194 -.41156 (380*2π)/5872 weeks
381.1117 -.42371 (381*2π)/5872 weeks
382.27219 -.57506 (382*2π)/5872 weeks
383.37701 -.5186 (383*2π)/5872 weeks
384.46578 -.41767 (384*2π)/5872 weeks
385.59252 -.16961 (385*2π)/5872 weeks
386.49136 -.14941 (386*2π)/5872 weeks
387.41987 -.06404 (387*2π)/5872 weeks
388.43679 .05735 (388*2π)/5872 weeks
389.33626 .06908 (389*2π)/5872 weeks
390.15925 .06763 (390*2π)/5872 weeks
391-.05105 -.03005 (391*2π)/5872 weeks
392-.0623 -.09799 (392*2π)/5871 weeks
393.01685 -.37025 (393*2π)/5871 weeks
394.19489 -.37132 (394*2π)/5871 weeks
395.27414 -.28486 (395*2π)/5871 weeks
396.35819 -.13485 (396*2π)/5871 weeks
397.25747 -.00018 (397*2π)/5871 weeks
398.14448 -.02694 (398*2π)/5871 weeks
399.07218 -.08198 (399*2π)/5871 weeks
400-.03756 -.23241 (400*2π)/5871 weeks
401.13081 -.36592 (401*2π)/5871 weeks
402.23898 -.39636 (402*2π)/5871 weeks
403.48286 -.30283 (403*2π)/5871 weeks
404.41676 -.21673 (404*2π)/5871 weeks
405.42043 -.08592 (405*2π)/5871 weeks
406.50941 -.22079 (406*2π)/5871 weeks
407.54932 -.09852 (407*2π)/5871 weeks
408.59213 .08523 (408*2π)/5871 weeks
409.61638 .24684 (409*2π)/5871 weeks
410.34574 .12495 (410*2π)/5871 weeks
411.23731 .02908 (411*2π)/5871 weeks
412.06496 -.23274 (412*2π)/5871 weeks
413.03783 -.30368 (413*2π)/5871 weeks
414.24362 -.33801 (414*2π)/5871 weeks
415.3187 -.36314 (415*2π)/5871 weeks
416.49171 -.29281 (416*2π)/5871 weeks
417.68562 -.07906 (417*2π)/5871 weeks
418.4828 .00461 (418*2π)/5871 weeks
419.57227 -.06414 (419*2π)/5871 weeks
420.43331 -.20844 (420*2π)/5871 weeks
421.27721 -.20924 (421*2π)/5871 weeks
422.37947 -.24262 (422*2π)/5871 weeks
423.45462 -.23225 (423*2π)/5871 weeks
424.49412 -.23023 (424*2π)/5871 weeks
425.4617 -.28541 (425*2π)/5871 weeks
426.49077 -.48411 (426*2π)/5871 weeks
427.4288 -.48869 (427*2π)/5871 weeks
428.40282 -.38124 (428*2π)/5871 weeks
429.52838 -.2141 (429*2π)/5871 weeks
430.38661 -.2132 (430*2π)/5871 weeks
431.21887 -.11081 (431*2π)/5871 weeks
432.20693 -.1234 (432*2π)/5871 weeks
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