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Fourier Analysis of EWV (ProShares UltraShort MSCI Japan ETF)


EWV (ProShares UltraShort MSCI Japan ETF) appears to have interesting cyclic behaviour every 46 weeks (10.4599*sine), 51 weeks (10.0865*sine), and 28 weeks (6.2949*cosine).

EWV (ProShares UltraShort MSCI Japan ETF) has an average price of 131.84 (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 11/8/2007 to 7/17/2017 for EWV (ProShares UltraShort MSCI Japan ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0131.8381   0 
123.88839 90.04242 (1*2π)/507507 weeks
27.59912 47.91284 (2*2π)/507254 weeks
3-16.70133 36.48626 (3*2π)/507169 weeks
4-9.74392 14.85129 (4*2π)/507127 weeks
5-14.1966 9.03323 (5*2π)/507101 weeks
6-.95558 .51859 (6*2π)/50785 weeks
76.26926 -.86095 (7*2π)/50772 weeks
89.7359 9.22349 (8*2π)/50763 weeks
91.21858 8.39829 (9*2π)/50756 weeks
103.26139 10.08648 (10*2π)/50751 weeks
11-1.17638 10.4599 (11*2π)/50746 weeks
12-2.10723 5.98604 (12*2π)/50742 weeks
13-1.7006 3.28462 (13*2π)/50739 weeks
143.21451 5.83701 (14*2π)/50736 weeks
151.62782 9.41176 (15*2π)/50734 weeks
16-5.32976 6.33059 (16*2π)/50732 weeks
17-3.99512 4.88454 (17*2π)/50730 weeks
18-6.2949 1.08354 (18*2π)/50728 weeks
19-1.34659 -1.64599 (19*2π)/50727 weeks
20.16165 -.41007 (20*2π)/50725 weeks
212.94373 -1.7878 (21*2π)/50724 weeks
223.78294 2.05768 (22*2π)/50723 weeks
232.75505 4.96536 (23*2π)/50722 weeks
24-1.00492 6.59408 (24*2π)/50721 weeks
25-2.69968 2.92421 (25*2π)/50720 weeks
26-2.70712 2.96633 (26*2π)/50720 weeks
27-2.59573 -2.61737 (27*2π)/50719 weeks
281.822 -3.03655 (28*2π)/50718 weeks
293.29665 -1.22535 (29*2π)/50717 weeks
305.25526 2.45736 (30*2π)/50717 weeks
313.08851 5.41071 (31*2π)/50716 weeks
32-.62522 4.52434 (32*2π)/50716 weeks
33-.64066 2.64247 (33*2π)/50715 weeks
34-1.08609 1.87958 (34*2π)/50715 weeks
35-.20641 1.78141 (35*2π)/50714 weeks
36-1.00081 .67892 (36*2π)/50714 weeks
37.12545 .31954 (37*2π)/50714 weeks
381.56725 .30036 (38*2π)/50713 weeks
39.25134 2.39873 (39*2π)/50713 weeks
40-.07616 .24517 (40*2π)/50713 weeks
41.47655 1.31777 (41*2π)/50712 weeks
42.90375 .24537 (42*2π)/50712 weeks
431.84052 .60026 (43*2π)/50712 weeks
44.38765 2.21984 (44*2π)/50712 weeks
451.21408 1.47128 (45*2π)/50711 weeks
46.58847 2.22082 (46*2π)/50711 weeks
47-.5369 2.12709 (47*2π)/50711 weeks
48-1.48817 -.04107 (48*2π)/50711 weeks
49.08551 .03742 (49*2π)/50710 weeks
50.05339 -1.01281 (50*2π)/50710 weeks
512.47454 -.48407 (51*2π)/50710 weeks
522.96933 1.93979 (52*2π)/50710 weeks
531.33142 1.99791 (53*2π)/50710 weeks
54.75473 2.76677 (54*2π)/5079 weeks
55-.60829 1.80454 (55*2π)/5079 weeks
56-.78792 1.29849 (56*2π)/5079 weeks
57.04051 -.26688 (57*2π)/5079 weeks
58.38202 .93017 (58*2π)/5079 weeks
59.74529 .05135 (59*2π)/5079 weeks
601.06585 .80889 (60*2π)/5078 weeks
61.31791 1.02552 (61*2π)/5078 weeks
62.9253 .38048 (62*2π)/5078 weeks
63.97678 .72262 (63*2π)/5078 weeks
641.47414 .76057 (64*2π)/5078 weeks
651.52507 1.79002 (65*2π)/5078 weeks
661.1548 2.53091 (66*2π)/5078 weeks
67-.09347 2.43175 (67*2π)/5078 weeks
68-1.0139 1.73395 (68*2π)/5077 weeks
69-1.74008 .98341 (69*2π)/5077 weeks
70-.89576 -.43325 (70*2π)/5077 weeks
71-.80798 -1.39147 (71*2π)/5077 weeks
721.83342 -1.53394 (72*2π)/5077 weeks
732.87309 .36294 (73*2π)/5077 weeks
742.07479 .88566 (74*2π)/5077 weeks
751.81967 2.46423 (75*2π)/5077 weeks
76.01791 2.25814 (76*2π)/5077 weeks
77-.43008 2.2163 (77*2π)/5077 weeks
78-1.53852 1.08538 (78*2π)/5077 weeks
79-1.15581 -.23238 (79*2π)/5076 weeks
80.2802 -.85165 (80*2π)/5076 weeks
811.32788 -.79295 (81*2π)/5076 weeks
821.82789 .09814 (82*2π)/5076 weeks
831.32101 1.2655 (83*2π)/5076 weeks
84.74605 .92978 (84*2π)/5076 weeks
85.79532 1.13274 (85*2π)/5076 weeks
86.57861 1.21333 (86*2π)/5076 weeks
871.26545 1.45649 (87*2π)/5076 weeks
88-.03417 1.81931 (88*2π)/5076 weeks
89-.64249 1.12043 (89*2π)/5076 weeks
90-.64893 -.0352 (90*2π)/5076 weeks
91.17293 -.14242 (91*2π)/5076 weeks
92.2837 -.06731 (92*2π)/5076 weeks
93.68275 -.11925 (93*2π)/5075 weeks
941.74673 .51383 (94*2π)/5075 weeks
951.76627 1.28124 (95*2π)/5075 weeks
96.84562 1.75781 (96*2π)/5075 weeks
97.1463 1.98059 (97*2π)/5075 weeks
98-.81328 1.11056 (98*2π)/5075 weeks
99-.43959 .89393 (99*2π)/5075 weeks
100-1.11987 .39716 (100*2π)/5075 weeks
101.17077 -.54382 (101*2π)/5075 weeks
102.40113 -.71147 (102*2π)/5075 weeks
103.93403 -.44847 (103*2π)/5075 weeks
1041.21237 -.00933 (104*2π)/5075 weeks
1051.76635 .78405 (105*2π)/5075 weeks
106.57152 1.54206 (106*2π)/5075 weeks
107.40016 1.29505 (107*2π)/5075 weeks
108-.09714 .63324 (108*2π)/5075 weeks
109.05664 .80766 (109*2π)/5075 weeks
110-.18623 .13223 (110*2π)/5075 weeks
111.04023 .17645 (111*2π)/5075 weeks
112.46875 -.14566 (112*2π)/5075 weeks
113.8911 -.32557 (113*2π)/5074 weeks
1141.38627 .47222 (114*2π)/5074 weeks
1151.17122 .6151 (115*2π)/5074 weeks
116.83489 .77039 (116*2π)/5074 weeks
117.65398 1.25391 (117*2π)/5074 weeks
118.73805 1.00431 (118*2π)/5074 weeks
119.66236 1.57334 (119*2π)/5074 weeks
120-.49661 1.0542 (120*2π)/5074 weeks
121-.02229 .76631 (121*2π)/5074 weeks
122.02142 .51309 (122*2π)/5074 weeks
123-.35614 .4367 (123*2π)/5074 weeks
124-.02596 .29942 (124*2π)/5074 weeks
125.16867 .42113 (125*2π)/5074 weeks
126.16333 -.02898 (126*2π)/5074 weeks
127.86474 -.2033 (127*2π)/5074 weeks
128.98815 .62712 (128*2π)/5074 weeks
129.44087 1.08668 (129*2π)/5074 weeks
130.22435 1.21874 (130*2π)/5074 weeks
131-.45903 .88967 (131*2π)/5074 weeks
132-.26979 .53585 (132*2π)/5074 weeks
133.0227 .54691 (133*2π)/5074 weeks
134-.35537 -.13212 (134*2π)/5074 weeks
135-.10482 -.19327 (135*2π)/5074 weeks
136.18728 -.51879 (136*2π)/5074 weeks
137.8197 -.40294 (137*2π)/5074 weeks
138.87817 .18168 (138*2π)/5074 weeks
1391.13027 .39106 (139*2π)/5074 weeks
140.72238 1.25121 (140*2π)/5074 weeks
141-.17146 .86662 (141*2π)/5074 weeks
142-.3518 .32802 (142*2π)/5074 weeks
143-.05154 -.19456 (143*2π)/5074 weeks
144.45581 .11939 (144*2π)/5074 weeks
145.51586 .35951 (145*2π)/5073 weeks
146.02832 .18876 (146*2π)/5073 weeks
147.73284 -.03858 (147*2π)/5073 weeks
148.59398 .22685 (148*2π)/5073 weeks
149.51759 .38529 (149*2π)/5073 weeks
150.23291 .33793 (150*2π)/5073 weeks
151.80043 -.06512 (151*2π)/5073 weeks
152.32392 .75967 (152*2π)/5073 weeks
153.43438 .34608 (153*2π)/5073 weeks
154.19079 .74478 (154*2π)/5073 weeks
155-.23903 .37681 (155*2π)/5073 weeks
156.00302 .05441 (156*2π)/5073 weeks
157.15524 -.45697 (157*2π)/5073 weeks
158.69015 -.32403 (158*2π)/5073 weeks
159.95055 .05592 (159*2π)/5073 weeks
160.87246 .2004 (160*2π)/5073 weeks
161.83159 .52276 (161*2π)/5073 weeks
162.68604 .67177 (162*2π)/5073 weeks
163.31905 1.06241 (163*2π)/5073 weeks
164-.16566 .95351 (164*2π)/5073 weeks
165-.28098 .22047 (165*2π)/5073 weeks
166-.03604 .13462 (166*2π)/5073 weeks
167-.12118 -.07967 (167*2π)/5073 weeks
168.12392 -.21242 (168*2π)/5073 weeks
169.2226 -.33193 (169*2π)/5073 weeks
170.90954 -.10399 (170*2π)/5073 weeks
171.8711 .20168 (171*2π)/5073 weeks
172.62857 .4941 (172*2π)/5073 weeks
173.35732 .80338 (173*2π)/5073 weeks
174-.34373 .6171 (174*2π)/5073 weeks
175-.11348 -.0781 (175*2π)/5073 weeks
176-.31639 -.06005 (176*2π)/5073 weeks
177-.00445 -.59809 (177*2π)/5073 weeks
178.29898 -.4827 (178*2π)/5073 weeks
179.80372 -.64566 (179*2π)/5073 weeks
1801.55253 -.31495 (180*2π)/5073 weeks
181.88152 .62123 (181*2π)/5073 weeks
182.71066 .48466 (182*2π)/5073 weeks
183.27194 .79202 (183*2π)/5073 weeks
184-.18438 .3233 (184*2π)/5073 weeks
185.23076 .28842 (185*2π)/5073 weeks
186-.44258 .08652 (186*2π)/5073 weeks
187.16467 -1.03835 (187*2π)/5073 weeks
188.50743 -.36966 (188*2π)/5073 weeks
1891.10982 -.71747 (189*2π)/5073 weeks
1901.44957 -.13393 (190*2π)/5073 weeks
1911.47071 .69913 (191*2π)/5073 weeks
192.71389 .9814 (192*2π)/5073 weeks
193.18859 1.06146 (193*2π)/5073 weeks
194-.12721 .47477 (194*2π)/5073 weeks
195-.34236 .16381 (195*2π)/5073 weeks
196-.25403 -.21156 (196*2π)/5073 weeks
197.22182 -.90463 (197*2π)/5073 weeks
198.8734 -.51127 (198*2π)/5073 weeks
1991.22796 -.12346 (199*2π)/5073 weeks
2001.29532 .5456 (200*2π)/5073 weeks
201.78162 .66929 (201*2π)/5073 weeks
202.37607 .53421 (202*2π)/5073 weeks
203.45511 .5934 (203*2π)/5072 weeks
204.3042 .44964 (204*2π)/5072 weeks
205.11516 .28225 (205*2π)/5072 weeks
206.2455 .27352 (206*2π)/5072 weeks
207.10201 .16273 (207*2π)/5072 weeks
208.07792 -.03598 (208*2π)/5072 weeks
209.34073 -.09067 (209*2π)/5072 weeks
210.38597 -.06422 (210*2π)/5072 weeks
211.75822 .03321 (211*2π)/5072 weeks
212.65031 .08233 (212*2π)/5072 weeks
213.64742 .07722 (213*2π)/5072 weeks
214.81767 .66876 (214*2π)/5072 weeks
215.31549 .6099 (215*2π)/5072 weeks
216.00662 .75119 (216*2π)/5072 weeks
217-.20218 .42802 (217*2π)/5072 weeks
218-.27499 .1602 (218*2π)/5072 weeks
219-.15813 -.09265 (219*2π)/5072 weeks
220-.30068 -.55583 (220*2π)/5072 weeks
221.92158 -.72429 (221*2π)/5072 weeks
222.64812 -.32914 (222*2π)/5072 weeks
2231.02697 -.1149 (223*2π)/5072 weeks
224.77908 .69318 (224*2π)/5072 weeks
225.45122 .61111 (225*2π)/5072 weeks
226.10971 .62619 (226*2π)/5072 weeks
227-.43567 .07363 (227*2π)/5072 weeks
228-.30402 -.57852 (228*2π)/5072 weeks
229.27998 -.58121 (229*2π)/5072 weeks
230.46267 -.63037 (230*2π)/5072 weeks
231.9348 -.51807 (231*2π)/5072 weeks
232.84929 -.05742 (232*2π)/5072 weeks
2331.06779 -.03928 (233*2π)/5072 weeks
234.99916 .16707 (234*2π)/5072 weeks
235.99249 .50113 (235*2π)/5072 weeks
2361.13682 .9015 (236*2π)/5072 weeks
237-.24361 1.12211 (237*2π)/5072 weeks
238-.33383 .2337 (238*2π)/5072 weeks
239-.13496 .16466 (239*2π)/5072 weeks
240-.11507 -.42414 (240*2π)/5072 weeks
241.37757 -.75998 (241*2π)/5072 weeks
2421.11384 -.39255 (242*2π)/5072 weeks
243.91235 .21402 (243*2π)/5072 weeks
244.63035 .4714 (244*2π)/5072 weeks
245.60514 .76167 (245*2π)/5072 weeks
246.31895 .77586 (246*2π)/5072 weeks
247-.50106 .80558 (247*2π)/5072 weeks
248-.69038 -.19347 (248*2π)/5072 weeks
249-.33823 -.34815 (249*2π)/5072 weeks
250.00934 -.62003 (250*2π)/5072 weeks
251.71106 -.72212 (251*2π)/5072 weeks
252.60628 -.47433 (252*2π)/5072 weeks
253.93386 -.40383 (253*2π)/5072 weeks
254.93386 .40383 (254*2π)/5072 weeks
255.60628 .47433 (255*2π)/5072 weeks
256.71106 .72212 (256*2π)/5072 weeks
257.00934 .62003 (257*2π)/5072 weeks
258-.33823 .34815 (258*2π)/5072 weeks
259-.69038 .19347 (259*2π)/5072 weeks
260-.50106 -.80558 (260*2π)/5072 weeks
261.31895 -.77586 (261*2π)/5072 weeks
262.60514 -.76167 (262*2π)/5072 weeks
263.63035 -.4714 (263*2π)/5072 weeks
264.91235 -.21402 (264*2π)/5072 weeks
2651.11384 .39255 (265*2π)/5072 weeks
266.37757 .75998 (266*2π)/5072 weeks
267-.11507 .42414 (267*2π)/5072 weeks
268-.13496 -.16466 (268*2π)/5072 weeks
269-.33383 -.2337 (269*2π)/5072 weeks
270-.24361 -1.12211 (270*2π)/5072 weeks
2711.13682 -.9015 (271*2π)/5072 weeks
272.99249 -.50113 (272*2π)/5072 weeks
273.99916 -.16707 (273*2π)/5072 weeks
2741.06779 .03928 (274*2π)/5072 weeks
275.84929 .05742 (275*2π)/5072 weeks
276.9348 .51807 (276*2π)/5072 weeks
277.46267 .63037 (277*2π)/5072 weeks
278.27998 .58121 (278*2π)/5072 weeks
279-.30402 .57852 (279*2π)/5072 weeks
280-.43567 -.07363 (280*2π)/5072 weeks
281.10971 -.62619 (281*2π)/5072 weeks
282.45122 -.61111 (282*2π)/5072 weeks
283.77908 -.69318 (283*2π)/5072 weeks
2841.02697 .1149 (284*2π)/5072 weeks
285.64812 .32914 (285*2π)/5072 weeks
286.92158 .72429 (286*2π)/5072 weeks
287-.30068 .55583 (287*2π)/5072 weeks
288-.15813 .09265 (288*2π)/5072 weeks
289-.27499 -.1602 (289*2π)/5072 weeks
290-.20218 -.42802 (290*2π)/5072 weeks
291.00662 -.75119 (291*2π)/5072 weeks
292.31549 -.6099 (292*2π)/5072 weeks
293.81767 -.66876 (293*2π)/5072 weeks
294.64742 -.07722 (294*2π)/5072 weeks
295.65031 -.08233 (295*2π)/5072 weeks
296.75822 -.03321 (296*2π)/5072 weeks
297.38597 .06422 (297*2π)/5072 weeks
298.34073 .09067 (298*2π)/5072 weeks
299.07792 .03598 (299*2π)/5072 weeks
300.10201 -.16273 (300*2π)/5072 weeks
301.2455 -.27352 (301*2π)/5072 weeks
302.11516 -.28225 (302*2π)/5072 weeks
303.3042 -.44964 (303*2π)/5072 weeks
304.45511 -.5934 (304*2π)/5072 weeks
305.37607 -.53421 (305*2π)/5072 weeks
306.78162 -.66929 (306*2π)/5072 weeks
3071.29532 -.5456 (307*2π)/5072 weeks
3081.22796 .12346 (308*2π)/5072 weeks
309.8734 .51127 (309*2π)/5072 weeks
310.22182 .90463 (310*2π)/5072 weeks
311-.25403 .21156 (311*2π)/5072 weeks
312-.34236 -.16381 (312*2π)/5072 weeks
313-.12721 -.47477 (313*2π)/5072 weeks
314.18859 -1.06146 (314*2π)/5072 weeks
315.71389 -.9814 (315*2π)/5072 weeks
3161.47071 -.69913 (316*2π)/5072 weeks
3171.44957 .13393 (317*2π)/5072 weeks
3181.10982 .71747 (318*2π)/5072 weeks
319.50743 .36966 (319*2π)/5072 weeks
320.16467 1.03835 (320*2π)/5072 weeks
321-.44258 -.08652 (321*2π)/5072 weeks
322.23076 -.28842 (322*2π)/5072 weeks
323-.18438 -.3233 (323*2π)/5072 weeks
324.27194 -.79202 (324*2π)/5072 weeks
325.71066 -.48466 (325*2π)/5072 weeks
326.88152 -.62123 (326*2π)/5072 weeks
3271.55253 .31495 (327*2π)/5072 weeks
328.80372 .64566 (328*2π)/5072 weeks
329.29898 .4827 (329*2π)/5072 weeks
330-.00445 .59809 (330*2π)/5072 weeks
331-.31639 .06005 (331*2π)/5072 weeks
332-.11348 .0781 (332*2π)/5072 weeks
333-.34373 -.6171 (333*2π)/5072 weeks
334.35732 -.80338 (334*2π)/5072 weeks
335.62857 -.4941 (335*2π)/5072 weeks
336.8711 -.20168 (336*2π)/5072 weeks
337.90954 .10399 (337*2π)/5072 weeks
338.2226 .33193 (338*2π)/5072 weeks
339.12392 .21242 (339*2π)/5071 weeks
340-.12118 .07967 (340*2π)/5071 weeks
341-.03604 -.13462 (341*2π)/5071 weeks
342-.28098 -.22047 (342*2π)/5071 weeks
343-.16566 -.95351 (343*2π)/5071 weeks
344.31905 -1.06241 (344*2π)/5071 weeks
345.68604 -.67177 (345*2π)/5071 weeks
346.83159 -.52276 (346*2π)/5071 weeks
347.87246 -.2004 (347*2π)/5071 weeks
348.95055 -.05592 (348*2π)/5071 weeks
349.69015 .32403 (349*2π)/5071 weeks
350.15524 .45697 (350*2π)/5071 weeks
351.00302 -.05441 (351*2π)/5071 weeks
352-.23903 -.37681 (352*2π)/5071 weeks
353.19079 -.74478 (353*2π)/5071 weeks
354.43438 -.34608 (354*2π)/5071 weeks
355.32392 -.75967 (355*2π)/5071 weeks
356.80043 .06512 (356*2π)/5071 weeks
357.23291 -.33793 (357*2π)/5071 weeks
358.51759 -.38529 (358*2π)/5071 weeks
359.59398 -.22685 (359*2π)/5071 weeks
360.73284 .03858 (360*2π)/5071 weeks
361.02832 -.18876 (361*2π)/5071 weeks
362.51586 -.35951 (362*2π)/5071 weeks
363.45581 -.11939 (363*2π)/5071 weeks
364-.05154 .19456 (364*2π)/5071 weeks
365-.3518 -.32802 (365*2π)/5071 weeks
366-.17146 -.86662 (366*2π)/5071 weeks
367.72238 -1.25121 (367*2π)/5071 weeks
3681.13027 -.39106 (368*2π)/5071 weeks
369.87817 -.18168 (369*2π)/5071 weeks
370.8197 .40294 (370*2π)/5071 weeks
371.18728 .51879 (371*2π)/5071 weeks
372-.10482 .19327 (372*2π)/5071 weeks
373-.35537 .13212 (373*2π)/5071 weeks
374.0227 -.54691 (374*2π)/5071 weeks
375-.26979 -.53585 (375*2π)/5071 weeks
376-.45903 -.88967 (376*2π)/5071 weeks
377.22435 -1.21874 (377*2π)/5071 weeks
378.44087 -1.08668 (378*2π)/5071 weeks
379.98815 -.62712 (379*2π)/5071 weeks
380.86474 .2033 (380*2π)/5071 weeks
381.16333 .02898 (381*2π)/5071 weeks
382.16867 -.42113 (382*2π)/5071 weeks
383-.02596 -.29942 (383*2π)/5071 weeks
384-.35614 -.4367 (384*2π)/5071 weeks
385.02142 -.51309 (385*2π)/5071 weeks
386-.02229 -.76631 (386*2π)/5071 weeks
387-.49661 -1.0542 (387*2π)/5071 weeks
388.66236 -1.57334 (388*2π)/5071 weeks
389.73805 -1.00431 (389*2π)/5071 weeks
390.65398 -1.25391 (390*2π)/5071 weeks
391.83489 -.77039 (391*2π)/5071 weeks
3921.17122 -.6151 (392*2π)/5071 weeks
3931.38627 -.47222 (393*2π)/5071 weeks
394.8911 .32557 (394*2π)/5071 weeks
395.46875 .14566 (395*2π)/5071 weeks
396.04023 -.17645 (396*2π)/5071 weeks
397-.18623 -.13223 (397*2π)/5071 weeks
398.05664 -.80766 (398*2π)/5071 weeks
399-.09714 -.63324 (399*2π)/5071 weeks
400.40016 -1.29505 (400*2π)/5071 weeks
401.57152 -1.54206 (401*2π)/5071 weeks
4021.76635 -.78405 (402*2π)/5071 weeks
4031.21237 .00933 (403*2π)/5071 weeks
404.93403 .44847 (404*2π)/5071 weeks
405.40113 .71147 (405*2π)/5071 weeks
406.17077 .54382 (406*2π)/5071 weeks
407-1.11987 -.39716 (407*2π)/5071 weeks
408-.43959 -.89393 (408*2π)/5071 weeks
409-.81328 -1.11056 (409*2π)/5071 weeks
410.1463 -1.98059 (410*2π)/5071 weeks
411.84562 -1.75781 (411*2π)/5071 weeks
4121.76627 -1.28124 (412*2π)/5071 weeks
4131.74673 -.51383 (413*2π)/5071 weeks
414.68275 .11925 (414*2π)/5071 weeks
415.2837 .06731 (415*2π)/5071 weeks
416.17293 .14242 (416*2π)/5071 weeks
417-.64893 .0352 (417*2π)/5071 weeks
418-.64249 -1.12043 (418*2π)/5071 weeks
419-.03417 -1.81931 (419*2π)/5071 weeks
4201.26545 -1.45649 (420*2π)/5071 weeks
421.57861 -1.21333 (421*2π)/5071 weeks
422.79532 -1.13274 (422*2π)/5071 weeks
423.74605 -.92978 (423*2π)/5071 weeks
4241.32101 -1.2655 (424*2π)/5071 weeks
4251.82789 -.09814 (425*2π)/5071 weeks
4261.32788 .79295 (426*2π)/5071 weeks
427.2802 .85165 (427*2π)/5071 weeks
428-1.15581 .23238 (428*2π)/5071 weeks
429-1.53852 -1.08538 (429*2π)/5071 weeks
430-.43008 -2.2163 (430*2π)/5071 weeks
431.01791 -2.25814 (431*2π)/5071 weeks
4321.81967 -2.46423 (432*2π)/5071 weeks
4332.07479 -.88566 (433*2π)/5071 weeks
4342.87309 -.36294 (434*2π)/5071 weeks
4351.83342 1.53394 (435*2π)/5071 weeks
436-.80798 1.39147 (436*2π)/5071 weeks
437-.89576 .43325 (437*2π)/5071 weeks
438-1.74008 -.98341 (438*2π)/5071 weeks
439-1.0139 -1.73395 (439*2π)/5071 weeks
440-.09347 -2.43175 (440*2π)/5071 weeks
4411.1548 -2.53091 (441*2π)/5071 weeks
4421.52507 -1.79002 (442*2π)/5071 weeks
4431.47414 -.76057 (443*2π)/5071 weeks
444.97678 -.72262 (444*2π)/5071 weeks
445.9253 -.38048 (445*2π)/5071 weeks
446.31791 -1.02552 (446*2π)/5071 weeks
4471.06585 -.80889 (447*2π)/5071 weeks
448.74529 -.05135 (448*2π)/5071 weeks
449.38202 -.93017 (449*2π)/5071 weeks
450.04051 .26688 (450*2π)/5071 weeks
451-.78792 -1.29849 (451*2π)/5071 weeks
452-.60829 -1.80454 (452*2π)/5071 weeks
453.75473 -2.76677 (453*2π)/5071 weeks
4541.33142 -1.99791 (454*2π)/5071 weeks
4552.96933 -1.93979 (455*2π)/5071 weeks
4562.47454 .48407 (456*2π)/5071 weeks
457.05339 1.01281 (457*2π)/5071 weeks
458.08551 -.03742 (458*2π)/5071 weeks
459-1.48817 .04107 (459*2π)/5071 weeks
460-.5369 -2.12709 (460*2π)/5071 weeks
461.58847 -2.22082 (461*2π)/5071 weeks
4621.21408 -1.47128 (462*2π)/5071 weeks
463.38765 -2.21984 (463*2π)/5071 weeks
4641.84052 -.60026 (464*2π)/5071 weeks
465.90375 -.24537 (465*2π)/5071 weeks
466.47655 -1.31777 (466*2π)/5071 weeks
467-.07616 -.24517 (467*2π)/5071 weeks
468.25134 -2.39873 (468*2π)/5071 weeks
4691.56725 -.30036 (469*2π)/5071 weeks
470.12545 -.31954 (470*2π)/5071 weeks
471-1.00081 -.67892 (471*2π)/5071 weeks
472-.20641 -1.78141 (472*2π)/5071 weeks
473-1.08609 -1.87958 (473*2π)/5071 weeks
474-.64066 -2.64247 (474*2π)/5071 weeks
475-.62522 -4.52434 (475*2π)/5071 weeks
4763.08851 -5.41071 (476*2π)/5071 weeks
4775.25526 -2.45736 (477*2π)/5071 weeks
4783.29665 1.22535 (478*2π)/5071 weeks
4791.822 3.03655 (479*2π)/5071 weeks
480-2.59573 2.61737 (480*2π)/5071 weeks
481-2.70712 -2.96633 (481*2π)/5071 weeks
482-2.69968 -2.92421 (482*2π)/5071 weeks
483-1.00492 -6.59408 (483*2π)/5071 weeks
4842.75505 -4.96536 (484*2π)/5071 weeks
4853.78294 -2.05768 (485*2π)/5071 weeks
4862.94373 1.7878 (486*2π)/5071 weeks
487.16165 .41007 (487*2π)/5071 weeks
488-1.34659 1.64599 (488*2π)/5071 weeks
489-6.2949 -1.08354 (489*2π)/5071 weeks
490-3.99512 -4.88454 (490*2π)/5071 weeks
491-5.32976 -6.33059 (491*2π)/5071 weeks
4921.62782 -9.41176 (492*2π)/5071 weeks
4933.21451 -5.83701 (493*2π)/5071 weeks
494-1.7006 -3.28462 (494*2π)/5071 weeks
495-2.10723 -5.98604 (495*2π)/5071 weeks
496-1.17638 -10.4599 (496*2π)/5071 weeks
4973.26139 -10.08648 (497*2π)/5071 weeks
4981.21858 -8.39829 (498*2π)/5071 weeks
4999.7359 -9.22349 (499*2π)/5071 weeks
5006.26926 .86095 (500*2π)/5071 weeks
501-.95558 -.51859 (501*2π)/5071 weeks
502-14.1966 -9.03323 (502*2π)/5071 weeks
503-9.74392 -14.85129 (503*2π)/5071 weeks
504-16.70133 -36.48626 (504*2π)/5071 weeks
5057.59912 -47.91284 (505*2π)/5071 weeks



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