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# Fourier Analysis of EUM (ProShares Short MSCI Emerging Markets)

EUM (ProShares Short MSCI Emerging Markets) appears to have interesting cyclic behaviour every 46 weeks (2.6281*sine), 50 weeks (2.2192*sine), and 55 weeks (1.5857*sine).

EUM (ProShares Short MSCI Emerging Markets) has an average price of 35.87 (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 11/1/2007 to 4/23/2018 for EUM (ProShares Short MSCI Emerging Markets), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
035.86647   0
110.57785 11.87092 (1*2π)/548548 weeks
23.17838 11.86032 (2*2π)/548274 weeks
3-1.71187 10.81371 (3*2π)/548183 weeks
4-2.87972 6.84549 (4*2π)/548137 weeks
5-2.47364 3.02671 (5*2π)/548110 weeks
6-2.67048 .85692 (6*2π)/54891 weeks
7-.37839 -.37308 (7*2π)/54878 weeks
81.5387 .60705 (8*2π)/54869 weeks
91.98332 1.7083 (9*2π)/54861 weeks
101.15797 1.58569 (10*2π)/54855 weeks
11.87048 2.21923 (11*2π)/54850 weeks
12-.0348 2.62809 (12*2π)/54846 weeks
13.20626 1.86431 (13*2π)/54842 weeks
14-.80931 2.07984 (14*2π)/54839 weeks
15-.40529 1.24169 (15*2π)/54837 weeks
16-.17786 .93857 (16*2π)/54834 weeks
17-.78357 1.05983 (17*2π)/54832 weeks
18-.45581 .37134 (18*2π)/54830 weeks
19-.21113 .56426 (19*2π)/54829 weeks
20-.07338 .12276 (20*2π)/54827 weeks
21-.00724 .33324 (21*2π)/54826 weeks
22.49651 .37996 (22*2π)/54825 weeks
23.92375 .57257 (23*2π)/54824 weeks
24.47574 .81477 (24*2π)/54823 weeks
25-.034 .94793 (25*2π)/54822 weeks
26-.55023 1.15022 (26*2π)/54821 weeks
27-.28062 .43941 (27*2π)/54820 weeks
28-.21497 .14012 (28*2π)/54820 weeks
29-.07466 -.30677 (29*2π)/54819 weeks
30.3396 -.08327 (30*2π)/54818 weeks
31.63586 .10513 (31*2π)/54818 weeks
32.98394 .46144 (32*2π)/54817 weeks
33.7475 .93822 (33*2π)/54817 weeks
34-.03162 1.05995 (34*2π)/54816 weeks
35-.12356 .85015 (35*2π)/54816 weeks
36-.29885 .72852 (36*2π)/54815 weeks
37-.19519 .34858 (37*2π)/54815 weeks
38-.10159 .34278 (38*2π)/54814 weeks
39-.18093 .18623 (39*2π)/54814 weeks
40.02598 -.06496 (40*2π)/54814 weeks
41.38025 .16964 (41*2π)/54813 weeks
42.09242 .47151 (42*2π)/54813 weeks
43.22497 .32412 (43*2π)/54813 weeks
44.25148 .33226 (44*2π)/54812 weeks
45.1272 .3251 (45*2π)/54812 weeks
46.12707 .53194 (46*2π)/54812 weeks
47.10402 .47781 (47*2π)/54812 weeks
48.07661 .18788 (48*2π)/54811 weeks
49-.05927 .3956 (49*2π)/54811 weeks
50.18462 .21413 (50*2π)/54811 weeks
51.18349 .31821 (51*2π)/54811 weeks
52.11391 .18842 (52*2π)/54811 weeks
53.13864 .22175 (53*2π)/54810 weeks
54.25942 .21 (54*2π)/54810 weeks
55.23105 .30757 (55*2π)/54810 weeks
56.38522 .46769 (56*2π)/54810 weeks
57.10133 .48393 (57*2π)/54810 weeks
58.01649 .52711 (58*2π)/5489 weeks
59-.07289 .37288 (59*2π)/5489 weeks
60-.13131 .29803 (60*2π)/5489 weeks
61-.05217 .04642 (61*2π)/5489 weeks
62.14999 .16245 (62*2π)/5489 weeks
63.12944 .21582 (63*2π)/5489 weeks
64.19938 .23482 (64*2π)/5489 weeks
65.12432 .31114 (65*2π)/5488 weeks
66-.0497 .23113 (66*2π)/5488 weeks
67.08269 .29224 (67*2π)/5488 weeks
68-.00602 .29796 (68*2π)/5488 weeks
69.13762 .21607 (69*2π)/5488 weeks
70.09882 .47336 (70*2π)/5488 weeks
71-.08006 .43439 (71*2π)/5488 weeks
72-.21815 .25882 (72*2π)/5488 weeks
73-.25987 .12007 (73*2π)/5488 weeks
74-.09085 -.145 (74*2π)/5487 weeks
75.10167 -.08612 (75*2π)/5487 weeks
76.16434 .07569 (76*2π)/5487 weeks
77.24136 -.06231 (77*2π)/5487 weeks
78.47632 .2297 (78*2π)/5487 weeks
79.21157 .47167 (79*2π)/5487 weeks
80.09125 .39169 (80*2π)/5487 weeks
81-.02484 .48456 (81*2π)/5487 weeks
82-.27647 .15736 (82*2π)/5487 weeks
83-.07815 .07345 (83*2π)/5487 weeks
84-.05035 .03299 (84*2π)/5487 weeks
85.11769 -.14532 (85*2π)/5486 weeks
86.33068 .01755 (86*2π)/5486 weeks
87.39801 .07148 (87*2π)/5486 weeks
88.33418 .27053 (88*2π)/5486 weeks
89.23438 .47921 (89*2π)/5486 weeks
90.02633 .47684 (90*2π)/5486 weeks
91-.05756 .32518 (91*2π)/5486 weeks
92-.15065 .14352 (92*2π)/5486 weeks
93-.09556 .06018 (93*2π)/5486 weeks
94.04814 .09584 (94*2π)/5486 weeks
95-.0493 .10297 (95*2π)/5486 weeks
96.09997 .07163 (96*2π)/5486 weeks
97.10342 -.00507 (97*2π)/5486 weeks
98.12381 .06633 (98*2π)/5486 weeks
99.15627 .18233 (99*2π)/5486 weeks
100.20005 .2703 (100*2π)/5485 weeks
101.20133 .22098 (101*2π)/5485 weeks
102.07461 .17899 (102*2π)/5485 weeks
103-.08304 .23665 (103*2π)/5485 weeks
104-.10306 .21017 (104*2π)/5485 weeks
105-.06278 .12301 (105*2π)/5485 weeks
106-.03341 -.039 (106*2π)/5485 weeks
107-.02222 -.06115 (107*2π)/5485 weeks
108.11996 -.08541 (108*2π)/5485 weeks
109.27528 -.01423 (109*2π)/5485 weeks
110.34205 .05082 (110*2π)/5485 weeks
111.22745 .23135 (111*2π)/5485 weeks
112.10603 .3325 (112*2π)/5485 weeks
113.09009 .32965 (113*2π)/5485 weeks
114-.07057 .33418 (114*2π)/5485 weeks
115-.15761 .08845 (115*2π)/5485 weeks
116-.13756 .02259 (116*2π)/5485 weeks
117-.00343 -.01971 (117*2π)/5485 weeks
118.09004 -.07993 (118*2π)/5485 weeks
119.20489 -.06036 (119*2π)/5485 weeks
120.22591 .06116 (120*2π)/5485 weeks
121.25386 .20199 (121*2π)/5485 weeks
122.17562 .3416 (122*2π)/5484 weeks
123.01164 .35665 (123*2π)/5484 weeks
124-.06933 .15851 (124*2π)/5484 weeks
125-.13 .14019 (125*2π)/5484 weeks
126-.07832 .00483 (126*2π)/5484 weeks
127.10306 .0102 (127*2π)/5484 weeks
128.09061 .05798 (128*2π)/5484 weeks
129.08575 .05079 (129*2π)/5484 weeks
130.11977 .053 (130*2π)/5484 weeks
131.07945 .12705 (131*2π)/5484 weeks
132.0211 .16419 (132*2π)/5484 weeks
133.01499 .06431 (133*2π)/5484 weeks
134-.01455 -.02824 (134*2π)/5484 weeks
135.03087 .03463 (135*2π)/5484 weeks
136.11899 -.01358 (136*2π)/5484 weeks
137.20655 .04416 (137*2π)/5484 weeks
138.05783 .14831 (138*2π)/5484 weeks
139-.00854 .08622 (139*2π)/5484 weeks
140.03555 .02142 (140*2π)/5484 weeks
141.05906 -.01819 (141*2π)/5484 weeks
142.17427 -.05378 (142*2π)/5484 weeks
143.15403 .08665 (143*2π)/5484 weeks
144.0639 .11107 (144*2π)/5484 weeks
145.10455 .08218 (145*2π)/5484 weeks
146.05938 .07085 (146*2π)/5484 weeks
147.02271 -.02071 (147*2π)/5484 weeks
148.12281 .03879 (148*2π)/5484 weeks
149.09814 .02109 (149*2π)/5484 weeks
150.16355 .03656 (150*2π)/5484 weeks
151.09091 .09456 (151*2π)/5484 weeks
152.0565 .06772 (152*2π)/5484 weeks
153.11083 .08774 (153*2π)/5484 weeks
154.083 .10891 (154*2π)/5484 weeks
155.09323 .07578 (155*2π)/5484 weeks
156.03106 .0534 (156*2π)/5484 weeks
157.01041 .04016 (157*2π)/5483 weeks
158.12706 -.05036 (158*2π)/5483 weeks
159.11802 .07166 (159*2π)/5483 weeks
160.07064 .03852 (160*2π)/5483 weeks
161.14026 .03378 (161*2π)/5483 weeks
162.20532 .08804 (162*2π)/5483 weeks
163.18852 .14885 (163*2π)/5483 weeks
164.06186 .16853 (164*2π)/5483 weeks
165.00559 .14211 (165*2π)/5483 weeks
166-.03484 .07702 (166*2π)/5483 weeks
167-.00901 .00129 (167*2π)/5483 weeks
168.07301 -.00351 (168*2π)/5483 weeks
169.07533 -.02519 (169*2π)/5483 weeks
170.1545 -.00303 (170*2π)/5483 weeks
171.18353 .00586 (171*2π)/5483 weeks
172.17722 .13366 (172*2π)/5483 weeks
173.16668 .15412 (173*2π)/5483 weeks
174.12874 .18107 (174*2π)/5483 weeks
175.0302 .1364 (175*2π)/5483 weeks
176-.0092 .12694 (176*2π)/5483 weeks
177-.05152 .05759 (177*2π)/5483 weeks
178.00348 -.05431 (178*2π)/5483 weeks
179.07287 -.09202 (179*2π)/5483 weeks
180.13018 -.11513 (180*2π)/5483 weeks
181.18434 -.07444 (181*2π)/5483 weeks
182.22308 .0176 (182*2π)/5483 weeks
183.2251 .02422 (183*2π)/5483 weeks
184.1642 .11642 (184*2π)/5483 weeks
185.1255 .12568 (185*2π)/5483 weeks
186.08266 .13416 (186*2π)/5483 weeks
187.01329 .05955 (187*2π)/5483 weeks
188.02944 -.03433 (188*2π)/5483 weeks
189.0765 -.00395 (189*2π)/5483 weeks
190.14931 -.05562 (190*2π)/5483 weeks
191.20103 -.05063 (191*2π)/5483 weeks
192.21337 .03759 (192*2π)/5483 weeks
193.28719 .07211 (193*2π)/5483 weeks
194.25226 .19139 (194*2π)/5483 weeks
195.02478 .22541 (195*2π)/5483 weeks
196.0091 .19566 (196*2π)/5483 weeks
197-.03382 .13241 (197*2π)/5483 weeks
198-.02486 .02068 (198*2π)/5483 weeks
199.03023 -.00856 (199*2π)/5483 weeks
200.00494 -.00809 (200*2π)/5483 weeks
201.14198 -.08452 (201*2π)/5483 weeks
202.20508 .03557 (202*2π)/5483 weeks
203.15026 .02537 (203*2π)/5483 weeks
204.22759 .08866 (204*2π)/5483 weeks
205.16172 .2219 (205*2π)/5483 weeks
206.05833 .24425 (206*2π)/5483 weeks
207-.05462 .1861 (207*2π)/5483 weeks
208-.13042 .08134 (208*2π)/5483 weeks
209-.05588 -.03589 (209*2π)/5483 weeks
210.00479 -.04261 (210*2π)/5483 weeks
211.08743 -.0707 (211*2π)/5483 weeks
212.12203 -.04635 (212*2π)/5483 weeks
213.20477 .10568 (213*2π)/5483 weeks
214.12047 .06456 (214*2π)/5483 weeks
215.07025 .15462 (215*2π)/5483 weeks
216-.00382 .11145 (216*2π)/5483 weeks
217.06732 .03654 (217*2π)/5483 weeks
218.04803 .05515 (218*2π)/5483 weeks
219.01305 .11526 (219*2π)/5483 weeks
220-.01892 .07173 (220*2π)/5482 weeks
221-.02826 -.02063 (221*2π)/5482 weeks
222.01726 -.0503 (222*2π)/5482 weeks
223.00867 -.04757 (223*2π)/5482 weeks
224.08432 -.10439 (224*2π)/5482 weeks
225.16573 -.04355 (225*2π)/5482 weeks
226.20257 .02044 (226*2π)/5482 weeks
227.17467 .08796 (227*2π)/5482 weeks
228.05608 .18451 (228*2π)/5482 weeks
229.01996 .14168 (229*2π)/5482 weeks
230-.01279 .06371 (230*2π)/5482 weeks
231-.06047 -.01898 (231*2π)/5482 weeks
232-.05053 -.06483 (232*2π)/5482 weeks
233.02542 -.11301 (233*2π)/5482 weeks
234.05991 -.13885 (234*2π)/5482 weeks
235.1665 -.11115 (235*2π)/5482 weeks
236.21185 -.01859 (236*2π)/5482 weeks
237.24103 .04564 (237*2π)/5482 weeks
238.21946 .11532 (238*2π)/5482 weeks
239.06104 .15228 (239*2π)/5482 weeks
240.01693 .11136 (240*2π)/5482 weeks
241-.0269 .13008 (241*2π)/5482 weeks
242-.045 -.0362 (242*2π)/5482 weeks
243.02461 -.07549 (243*2π)/5482 weeks
244.04923 -.0707 (244*2π)/5482 weeks
245.13876 -.13456 (245*2π)/5482 weeks
246.23975 -.10935 (246*2π)/5482 weeks
247.21974 .03075 (247*2π)/5482 weeks
248.24903 .12579 (248*2π)/5482 weeks
249.16386 .20229 (249*2π)/5482 weeks
250.0706 .20577 (250*2π)/5482 weeks
251-.0112 .14242 (251*2π)/5482 weeks
252-.10358 .11047 (252*2π)/5482 weeks
253-.08524 .02959 (253*2π)/5482 weeks
254-.04155 -.03437 (254*2π)/5482 weeks
255-.04716 -.16041 (255*2π)/5482 weeks
256.08399 -.21364 (256*2π)/5482 weeks
257.18827 -.09361 (257*2π)/5482 weeks
258.19055 -.02003 (258*2π)/5482 weeks
259.2524 .04581 (259*2π)/5482 weeks
260.19111 .142 (260*2π)/5482 weeks
261.03738 .16103 (261*2π)/5482 weeks
262-.10084 .10307 (262*2π)/5482 weeks
263-.03869 .0246 (263*2π)/5482 weeks
264-.00391 -.06943 (264*2π)/5482 weeks
265.06061 -.12771 (265*2π)/5482 weeks
266.02466 -.14236 (266*2π)/5482 weeks
267.21051 -.1132 (267*2π)/5482 weeks
268.28974 .01677 (268*2π)/5482 weeks
269.19846 .09968 (269*2π)/5482 weeks
270.11915 .11263 (270*2π)/5482 weeks
271.06776 .16891 (271*2π)/5482 weeks
272.05464 .09607 (272*2π)/5482 weeks
273-.04201 .10169 (273*2π)/5482 weeks
274-.10446   (274*2π)/5482 weeks
275-.04201 -.10169 (275*2π)/5482 weeks
276.05464 -.09607 (276*2π)/5482 weeks
277.06776 -.16891 (277*2π)/5482 weeks
278.11915 -.11263 (278*2π)/5482 weeks
279.19846 -.09968 (279*2π)/5482 weeks
280.28974 -.01677 (280*2π)/5482 weeks
281.21051 .1132 (281*2π)/5482 weeks
282.02466 .14236 (282*2π)/5482 weeks
283.06061 .12771 (283*2π)/5482 weeks
284-.00391 .06943 (284*2π)/5482 weeks
285-.03869 -.0246 (285*2π)/5482 weeks
286-.10084 -.10307 (286*2π)/5482 weeks
287.03738 -.16103 (287*2π)/5482 weeks
288.19111 -.142 (288*2π)/5482 weeks
289.2524 -.04581 (289*2π)/5482 weeks
290.19055 .02003 (290*2π)/5482 weeks
291.18827 .09361 (291*2π)/5482 weeks
292.08399 .21364 (292*2π)/5482 weeks
293-.04716 .16041 (293*2π)/5482 weeks
294-.04155 .03437 (294*2π)/5482 weeks
295-.08524 -.02959 (295*2π)/5482 weeks
296-.10358 -.11047 (296*2π)/5482 weeks
297-.0112 -.14242 (297*2π)/5482 weeks
298.0706 -.20577 (298*2π)/5482 weeks
299.16386 -.20229 (299*2π)/5482 weeks
300.24903 -.12579 (300*2π)/5482 weeks
301.21974 -.03075 (301*2π)/5482 weeks
302.23975 .10935 (302*2π)/5482 weeks
303.13876 .13456 (303*2π)/5482 weeks
304.04923 .0707 (304*2π)/5482 weeks
305.02461 .07549 (305*2π)/5482 weeks
306-.045 .0362 (306*2π)/5482 weeks
307-.0269 -.13008 (307*2π)/5482 weeks
308.01693 -.11136 (308*2π)/5482 weeks
309.06104 -.15228 (309*2π)/5482 weeks
310.21946 -.11532 (310*2π)/5482 weeks
311.24103 -.04564 (311*2π)/5482 weeks
312.21185 .01859 (312*2π)/5482 weeks
313.1665 .11115 (313*2π)/5482 weeks
314.05991 .13885 (314*2π)/5482 weeks
315.02542 .11301 (315*2π)/5482 weeks
316-.05053 .06483 (316*2π)/5482 weeks
317-.06047 .01898 (317*2π)/5482 weeks
318-.01279 -.06371 (318*2π)/5482 weeks
319.01996 -.14168 (319*2π)/5482 weeks
320.05608 -.18451 (320*2π)/5482 weeks
321.17467 -.08796 (321*2π)/5482 weeks
322.20257 -.02044 (322*2π)/5482 weeks
323.16573 .04355 (323*2π)/5482 weeks
324.08432 .10439 (324*2π)/5482 weeks
325.00867 .04757 (325*2π)/5482 weeks
326.01726 .0503 (326*2π)/5482 weeks
327-.02826 .02063 (327*2π)/5482 weeks
328-.01892 -.07173 (328*2π)/5482 weeks
329.01305 -.11526 (329*2π)/5482 weeks
330.04803 -.05515 (330*2π)/5482 weeks
331.06732 -.03654 (331*2π)/5482 weeks
332-.00382 -.11145 (332*2π)/5482 weeks
333.07025 -.15462 (333*2π)/5482 weeks
334.12047 -.06456 (334*2π)/5482 weeks
335.20477 -.10568 (335*2π)/5482 weeks
336.12203 .04635 (336*2π)/5482 weeks
337.08743 .0707 (337*2π)/5482 weeks
338.00479 .04261 (338*2π)/5482 weeks
339-.05588 .03589 (339*2π)/5482 weeks
340-.13042 -.08134 (340*2π)/5482 weeks
341-.05462 -.1861 (341*2π)/5482 weeks
342.05833 -.24425 (342*2π)/5482 weeks
343.16172 -.2219 (343*2π)/5482 weeks
344.22759 -.08866 (344*2π)/5482 weeks
345.15026 -.02537 (345*2π)/5482 weeks
346.20508 -.03557 (346*2π)/5482 weeks
347.14198 .08452 (347*2π)/5482 weeks
348.00494 .00809 (348*2π)/5482 weeks
349.03023 .00856 (349*2π)/5482 weeks
350-.02486 -.02068 (350*2π)/5482 weeks
351-.03382 -.13241 (351*2π)/5482 weeks
352.0091 -.19566 (352*2π)/5482 weeks
353.02478 -.22541 (353*2π)/5482 weeks
354.25226 -.19139 (354*2π)/5482 weeks
355.28719 -.07211 (355*2π)/5482 weeks
356.21337 -.03759 (356*2π)/5482 weeks
357.20103 .05063 (357*2π)/5482 weeks
358.14931 .05562 (358*2π)/5482 weeks
359.0765 .00395 (359*2π)/5482 weeks
360.02944 .03433 (360*2π)/5482 weeks
361.01329 -.05955 (361*2π)/5482 weeks
362.08266 -.13416 (362*2π)/5482 weeks
363.1255 -.12568 (363*2π)/5482 weeks
364.1642 -.11642 (364*2π)/5482 weeks
365.2251 -.02422 (365*2π)/5482 weeks
366.22308 -.0176 (366*2π)/5481 weeks
367.18434 .07444 (367*2π)/5481 weeks
368.13018 .11513 (368*2π)/5481 weeks
369.07287 .09202 (369*2π)/5481 weeks
370.00348 .05431 (370*2π)/5481 weeks
371-.05152 -.05759 (371*2π)/5481 weeks
372-.0092 -.12694 (372*2π)/5481 weeks
373.0302 -.1364 (373*2π)/5481 weeks
374.12874 -.18107 (374*2π)/5481 weeks
375.16668 -.15412 (375*2π)/5481 weeks
376.17722 -.13366 (376*2π)/5481 weeks
377.18353 -.00586 (377*2π)/5481 weeks
378.1545 .00303 (378*2π)/5481 weeks
379.07533 .02519 (379*2π)/5481 weeks
380.07301 .00351 (380*2π)/5481 weeks
381-.00901 -.00129 (381*2π)/5481 weeks
382-.03484 -.07702 (382*2π)/5481 weeks
383.00559 -.14211 (383*2π)/5481 weeks
384.06186 -.16853 (384*2π)/5481 weeks
385.18852 -.14885 (385*2π)/5481 weeks
386.20532 -.08804 (386*2π)/5481 weeks
387.14026 -.03378 (387*2π)/5481 weeks
388.07064 -.03852 (388*2π)/5481 weeks
389.11802 -.07166 (389*2π)/5481 weeks
390.12706 .05036 (390*2π)/5481 weeks
391.01041 -.04016 (391*2π)/5481 weeks
392.03106 -.0534 (392*2π)/5481 weeks
393.09323 -.07578 (393*2π)/5481 weeks
394.083 -.10891 (394*2π)/5481 weeks
395.11083 -.08774 (395*2π)/5481 weeks
396.0565 -.06772 (396*2π)/5481 weeks
397.09091 -.09456 (397*2π)/5481 weeks
398.16355 -.03656 (398*2π)/5481 weeks
399.09814 -.02109 (399*2π)/5481 weeks
400.12281 -.03879 (400*2π)/5481 weeks
401.02271 .02071 (401*2π)/5481 weeks
402.05938 -.07085 (402*2π)/5481 weeks
403.10455 -.08218 (403*2π)/5481 weeks
404.0639 -.11107 (404*2π)/5481 weeks
405.15403 -.08665 (405*2π)/5481 weeks
406.17427 .05378 (406*2π)/5481 weeks
407.05906 .01819 (407*2π)/5481 weeks
408.03555 -.02142 (408*2π)/5481 weeks
409-.00854 -.08622 (409*2π)/5481 weeks
410.05783 -.14831 (410*2π)/5481 weeks
411.20655 -.04416 (411*2π)/5481 weeks
412.11899 .01358 (412*2π)/5481 weeks
413.03087 -.03463 (413*2π)/5481 weeks
414-.01455 .02824 (414*2π)/5481 weeks
415.01499 -.06431 (415*2π)/5481 weeks
416.0211 -.16419 (416*2π)/5481 weeks
417.07945 -.12705 (417*2π)/5481 weeks
418.11977 -.053 (418*2π)/5481 weeks
419.08575 -.05079 (419*2π)/5481 weeks
420.09061 -.05798 (420*2π)/5481 weeks
421.10306 -.0102 (421*2π)/5481 weeks
422-.07832 -.00483 (422*2π)/5481 weeks
423-.13 -.14019 (423*2π)/5481 weeks
424-.06933 -.15851 (424*2π)/5481 weeks
425.01164 -.35665 (425*2π)/5481 weeks
426.17562 -.3416 (426*2π)/5481 weeks
427.25386 -.20199 (427*2π)/5481 weeks
428.22591 -.06116 (428*2π)/5481 weeks
429.20489 .06036 (429*2π)/5481 weeks
430.09004 .07993 (430*2π)/5481 weeks
431-.00343 .01971 (431*2π)/5481 weeks
432-.13756 -.02259 (432*2π)/5481 weeks
433-.15761 -.08845 (433*2π)/5481 weeks
434-.07057 -.33418 (434*2π)/5481 weeks
435.09009 -.32965 (435*2π)/5481 weeks
436.10603 -.3325 (436*2π)/5481 weeks
437.22745 -.23135 (437*2π)/5481 weeks
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