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Fourier Analysis of EFU (ProShares UltraShort MSCI EAFE ETF)


EFU (ProShares UltraShort MSCI EAFE ETF) appears to have interesting cyclic behaviour every 51 weeks (14.082*sine), 46 weeks (12.7898*sine), and 18 weeks (6.9563*cosine).

EFU (ProShares UltraShort MSCI EAFE ETF) has an average price of 121.29 (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 10/25/2007 to 7/10/2017 for EFU (ProShares UltraShort MSCI EAFE ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0121.287   0 
161.3735 98.43314 (1*2π)/508508 weeks
210.49288 72.24786 (2*2π)/508254 weeks
3-24.37805 51.96211 (3*2π)/508169 weeks
4-26.91393 21.19584 (4*2π)/508127 weeks
5-22.31781 3.01466 (5*2π)/508102 weeks
6-5.8982 -10.98753 (6*2π)/50885 weeks
714.1329 -5.09308 (7*2π)/50873 weeks
815.31388 9.83653 (8*2π)/50864 weeks
94.45875 14.66117 (9*2π)/50856 weeks
101.77537 14.08196 (10*2π)/50851 weeks
11-3.08623 12.78981 (11*2π)/50846 weeks
12-2.65478 7.57435 (12*2π)/50842 weeks
13-3.97686 7.28869 (13*2π)/50839 weeks
14-1.79787 4.44231 (14*2π)/50836 weeks
15-.85146 6.8831 (15*2π)/50834 weeks
16-5.81067 4.66549 (16*2π)/50832 weeks
17-3.91071 1.12088 (17*2π)/50830 weeks
18-2.97466 -.70879 (18*2π)/50828 weeks
19.67374 -.87289 (19*2π)/50827 weeks
202.10295 -.7827 (20*2π)/50825 weeks
215.35804 1.33623 (21*2π)/50824 weeks
223.26919 5.7787 (22*2π)/50823 weeks
23-.46505 7.63896 (23*2π)/50822 weeks
24-5.98211 5.39114 (24*2π)/50821 weeks
25-4.54248 -.80704 (25*2π)/50820 weeks
26-2.01444 -2.5098 (26*2π)/50820 weeks
272.66701 -4.80584 (27*2π)/50819 weeks
286.30339 -1.59561 (28*2π)/50818 weeks
296.95633 2.228 (29*2π)/50818 weeks
305.43739 6.9606 (30*2π)/50817 weeks
31-.00017 9.02599 (31*2π)/50816 weeks
32-3.92145 4.6543 (32*2π)/50816 weeks
33-3.01102 1.24399 (33*2π)/50815 weeks
34-1.16778 -.35189 (34*2π)/50815 weeks
35.27574 .57065 (35*2π)/50815 weeks
36.26226 .06658 (36*2π)/50814 weeks
371.81429 -.08659 (37*2π)/50814 weeks
382.70082 2.64039 (38*2π)/50813 weeks
39-.1672 2.42099 (39*2π)/50813 weeks
40.65995 1.20648 (40*2π)/50813 weeks
41.71409 1.9495 (41*2π)/50812 weeks
421.10228 1.67014 (42*2π)/50812 weeks
43.80032 2.34158 (43*2π)/50812 weeks
44-.40173 1.59592 (44*2π)/50812 weeks
45.47885 2.15374 (45*2π)/50811 weeks
46.03908 1.70997 (46*2π)/50811 weeks
47-.4492 1.24261 (47*2π)/50811 weeks
48-.03412 -.01262 (48*2π)/50811 weeks
49.83198 .23323 (49*2π)/50810 weeks
501.98082 .75785 (50*2π)/50810 weeks
512.07253 2.48039 (51*2π)/50810 weeks
52.6375 3.89828 (52*2π)/50810 weeks
53-.9246 3.09586 (53*2π)/50810 weeks
54-1.95944 1.51927 (54*2π)/5089 weeks
55-1.31053 .50062 (55*2π)/5089 weeks
56-.82411 -.57456 (56*2π)/5089 weeks
571.32019 -.44133 (57*2π)/5089 weeks
581.07864 1.06503 (58*2π)/5089 weeks
591.02699 1.1776 (59*2π)/5089 weeks
60.50868 1.67205 (60*2π)/5088 weeks
61-.1435 1.05745 (61*2π)/5088 weeks
62.75517 1.30555 (62*2π)/5088 weeks
63.34602 1.33106 (63*2π)/5088 weeks
64.67089 2.01642 (64*2π)/5088 weeks
65-.82014 2.61989 (65*2π)/5088 weeks
66-2.30801 1.48688 (66*2π)/5088 weeks
67-2.12786 -.73354 (67*2π)/5088 weeks
68-.58199 -2.17929 (68*2π)/5087 weeks
691.68414 -1.92763 (69*2π)/5087 weeks
702.70432 -.02073 (70*2π)/5087 weeks
712.66191 .23408 (71*2π)/5087 weeks
723.25414 2.94894 (72*2π)/5087 weeks
73.34663 4.33873 (73*2π)/5087 weeks
74-1.48863 2.74388 (74*2π)/5087 weeks
75-2.56663 1.34091 (75*2π)/5087 weeks
76-1.76917 -1.33732 (76*2π)/5087 weeks
77-.07746 -1.31203 (77*2π)/5087 weeks
781.01355 -1.86748 (78*2π)/5087 weeks
793.02542 -.39301 (79*2π)/5086 weeks
802.78776 1.68495 (80*2π)/5086 weeks
811.70296 3.18796 (81*2π)/5086 weeks
82-.09073 2.99758 (82*2π)/5086 weeks
83-1.4447 1.99457 (83*2π)/5086 weeks
84-1.45913 .29877 (84*2π)/5086 weeks
85-.53997 -.2759 (85*2π)/5086 weeks
86.25012 -.02918 (86*2π)/5086 weeks
87.35789 .81257 (87*2π)/5086 weeks
88-.31773 .28155 (88*2π)/5086 weeks
89.21357 -.0175 (89*2π)/5086 weeks
90.84915 -.18059 (90*2π)/5086 weeks
911.38656 .25582 (91*2π)/5086 weeks
921.25486 .90729 (92*2π)/5086 weeks
93.79968 1.56957 (93*2π)/5085 weeks
94-.1917 2.0398 (94*2π)/5085 weeks
95-1.09053 1.68629 (95*2π)/5085 weeks
96-1.31665 .33105 (96*2π)/5085 weeks
97-.94286 -.56163 (97*2π)/5085 weeks
98.2438 -1.29814 (98*2π)/5085 weeks
99.99186 -1.09171 (99*2π)/5085 weeks
1002.17879 -.35761 (100*2π)/5085 weeks
1012.25829 1.5232 (101*2π)/5085 weeks
1021.24221 2.34119 (102*2π)/5085 weeks
103.03157 2.3635 (103*2π)/5085 weeks
104-.8901 1.62212 (104*2π)/5085 weeks
105-1.49472 1.0342 (105*2π)/5085 weeks
106-1.50966 -.68039 (106*2π)/5085 weeks
107-.17555 -1.04959 (107*2π)/5085 weeks
108.92691 -.78724 (108*2π)/5085 weeks
1091.27086 -.33445 (109*2π)/5085 weeks
1101.55921 .59015 (110*2π)/5085 weeks
111.91228 1.21133 (111*2π)/5085 weeks
112.30374 1.61873 (112*2π)/5085 weeks
113-.49785 1.43559 (113*2π)/5084 weeks
114-1.11424 .45766 (114*2π)/5084 weeks
115-.29882 -.18722 (115*2π)/5084 weeks
116.03001 -.38087 (116*2π)/5084 weeks
117.21743 -.34638 (117*2π)/5084 weeks
118.28732 -.04496 (118*2π)/5084 weeks
119.41253 -.26774 (119*2π)/5084 weeks
120.9648 -.03043 (120*2π)/5084 weeks
121.42616 .56906 (121*2π)/5084 weeks
122.20421 .21051 (122*2π)/5084 weeks
123.53361 -.22792 (123*2π)/5084 weeks
124.81745 -.18854 (124*2π)/5084 weeks
125.74511 .25612 (125*2π)/5084 weeks
126.95011 .52596 (126*2π)/5084 weeks
127.62173 1.08965 (127*2π)/5084 weeks
128-.14043 .45282 (128*2π)/5084 weeks
129.20309 -.07459 (129*2π)/5084 weeks
130.35582 -.25509 (130*2π)/5084 weeks
1311.11309 .13857 (131*2π)/5084 weeks
132.51276 .90092 (132*2π)/5084 weeks
133.13001 .24057 (133*2π)/5084 weeks
134.85428 .16927 (134*2π)/5084 weeks
135.79386 .40517 (135*2π)/5084 weeks
136.80769 .60309 (136*2π)/5084 weeks
137.35985 1.02337 (137*2π)/5084 weeks
138.26164 .68436 (138*2π)/5084 weeks
139-.15231 .92499 (139*2π)/5084 weeks
140-.49108 -.07114 (140*2π)/5084 weeks
141.37489 -.45643 (141*2π)/5084 weeks
142.72145 -.04258 (142*2π)/5084 weeks
143.65849 .26896 (143*2π)/5084 weeks
144.41385 .30217 (144*2π)/5084 weeks
145.66495 .23765 (145*2π)/5084 weeks
146.98276 .77828 (146*2π)/5083 weeks
147-.04932 1.03102 (147*2π)/5083 weeks
148.0217 .2332 (148*2π)/5083 weeks
149.31555 .3572 (149*2π)/5083 weeks
150.17835 .51424 (150*2π)/5083 weeks
151-.20267 .48408 (151*2π)/5083 weeks
152-.02259 -.34926 (152*2π)/5083 weeks
153.27102 -.18307 (153*2π)/5083 weeks
154.66448 -.54498 (154*2π)/5083 weeks
1551.19772 .03045 (155*2π)/5083 weeks
1561.00747 .57795 (156*2π)/5083 weeks
157.76038 1.00943 (157*2π)/5083 weeks
158.08562 1.11177 (158*2π)/5083 weeks
159-.63 .72523 (159*2π)/5083 weeks
160-.45601 .16009 (160*2π)/5083 weeks
161-.43814 -.57436 (161*2π)/5083 weeks
162.38315 -1.02541 (162*2π)/5083 weeks
163.95385 -.87256 (163*2π)/5083 weeks
1641.53162 -.35671 (164*2π)/5083 weeks
1651.78074 .58163 (165*2π)/5083 weeks
1661.07064 1.15462 (166*2π)/5083 weeks
167.54418 1.32531 (167*2π)/5083 weeks
168-.16158 1.08748 (168*2π)/5083 weeks
169-.28821 .43559 (169*2π)/5083 weeks
170-.30407 .14453 (170*2π)/5083 weeks
171.14784 -.21618 (171*2π)/5083 weeks
172.49897 -.14247 (172*2π)/5083 weeks
173.92783 -.13699 (173*2π)/5083 weeks
1741.09705 .64496 (174*2π)/5083 weeks
175.37338 .99135 (175*2π)/5083 weeks
176.33017 .87638 (176*2π)/5083 weeks
177-.23311 1.00841 (177*2π)/5083 weeks
178-.46498 .31326 (178*2π)/5083 weeks
179-.51195 .4214 (179*2π)/5083 weeks
180-.89935 -.30291 (180*2π)/5083 weeks
181.22518 -.90517 (181*2π)/5083 weeks
182.52792 -.52539 (182*2π)/5083 weeks
183.99957 -.35574 (183*2π)/5083 weeks
184.90397 .37294 (184*2π)/5083 weeks
185.40879 .283 (185*2π)/5083 weeks
186.75414 .69362 (186*2π)/5083 weeks
187-.33927 .96837 (187*2π)/5083 weeks
188-.36207 .14033 (188*2π)/5083 weeks
189-.73042 .11578 (189*2π)/5083 weeks
190-.71142 -1.04527 (190*2π)/5083 weeks
191.39095 -1.6682 (191*2π)/5083 weeks
1921.47828 -1.24681 (192*2π)/5083 weeks
1932.14368 -.25673 (193*2π)/5083 weeks
1941.80211 1.01492 (194*2π)/5083 weeks
195.81137 1.4815 (195*2π)/5083 weeks
196-.10327 1.37766 (196*2π)/5083 weeks
197-1.01812 .82671 (197*2π)/5083 weeks
198-.83876 -.67078 (198*2π)/5083 weeks
199-.05317 -1.02638 (199*2π)/5083 weeks
200.73601 -1.09467 (200*2π)/5083 weeks
2011.29074 -.28575 (201*2π)/5083 weeks
202.90985 .24346 (202*2π)/5083 weeks
203.68186 .00429 (203*2π)/5083 weeks
204.89728 .05328 (204*2π)/5082 weeks
205.91673 .45153 (205*2π)/5082 weeks
206.659 .50855 (206*2π)/5082 weeks
207.70112 .63261 (207*2π)/5082 weeks
208.15325 .97663 (208*2π)/5082 weeks
209-.33853 .41285 (209*2π)/5082 weeks
210-.47737 -.02562 (210*2π)/5082 weeks
211-.20768 -.9394 (211*2π)/5082 weeks
212.79153 -.69774 (212*2π)/5082 weeks
2131.08439 -.29881 (213*2π)/5082 weeks
2141.28967 .10195 (214*2π)/5082 weeks
2151.1672 .63404 (215*2π)/5082 weeks
216.71363 .94623 (216*2π)/5082 weeks
217.2454 .95636 (217*2π)/5082 weeks
218-.224 .78401 (218*2π)/5082 weeks
219-.38503 .22634 (219*2π)/5082 weeks
220-.41153 .01992 (220*2π)/5082 weeks
221-.41786 -.69924 (221*2π)/5082 weeks
222.35918 -.53549 (222*2π)/5082 weeks
223.44255 -.58671 (223*2π)/5082 weeks
2241.14868 -.31061 (224*2π)/5082 weeks
225.8987 .23411 (225*2π)/5082 weeks
226.79819 .42126 (226*2π)/5082 weeks
227.44982 1.02789 (227*2π)/5082 weeks
228-.41933 .75829 (228*2π)/5082 weeks
229-.54702 .04583 (229*2π)/5082 weeks
230-.70545 -.45302 (230*2π)/5082 weeks
231-.18068 -1.15921 (231*2π)/5082 weeks
232.57187 -1.25148 (232*2π)/5082 weeks
2331.13802 -1.03636 (233*2π)/5082 weeks
2341.68114 -.50218 (234*2π)/5082 weeks
2351.77806 .27154 (235*2π)/5082 weeks
2361.56088 .72981 (236*2π)/5082 weeks
237.89663 1.64771 (237*2π)/5082 weeks
238-.40728 1.19298 (238*2π)/5082 weeks
239-.51312 .38302 (239*2π)/5082 weeks
240-.84459 .00453 (240*2π)/5082 weeks
241-.46491 -.96467 (241*2π)/5082 weeks
242.62966 -1.28025 (242*2π)/5082 weeks
2431.66365 -.64821 (243*2π)/5082 weeks
2441.64146 .12295 (244*2π)/5082 weeks
2451.39798 .70997 (245*2π)/5082 weeks
246.86801 1.14235 (246*2π)/5082 weeks
247.14925 1.68675 (247*2π)/5082 weeks
248-1.19701 .9853 (248*2π)/5082 weeks
249-1.04655 -.45023 (249*2π)/5082 weeks
250-.40629 -.84284 (250*2π)/5082 weeks
251.09401 -1.16396 (251*2π)/5082 weeks
252.71443 -.86273 (252*2π)/5082 weeks
2531.18014 -.79779 (253*2π)/5082 weeks
2541.71835   (254*2π)/5082 weeks
2551.18014 .79779 (255*2π)/5082 weeks
256.71443 .86273 (256*2π)/5082 weeks
257.09401 1.16396 (257*2π)/5082 weeks
258-.40629 .84284 (258*2π)/5082 weeks
259-1.04655 .45023 (259*2π)/5082 weeks
260-1.19701 -.9853 (260*2π)/5082 weeks
261.14925 -1.68675 (261*2π)/5082 weeks
262.86801 -1.14235 (262*2π)/5082 weeks
2631.39798 -.70997 (263*2π)/5082 weeks
2641.64146 -.12295 (264*2π)/5082 weeks
2651.66365 .64821 (265*2π)/5082 weeks
266.62966 1.28025 (266*2π)/5082 weeks
267-.46491 .96467 (267*2π)/5082 weeks
268-.84459 -.00453 (268*2π)/5082 weeks
269-.51312 -.38302 (269*2π)/5082 weeks
270-.40728 -1.19298 (270*2π)/5082 weeks
271.89663 -1.64771 (271*2π)/5082 weeks
2721.56088 -.72981 (272*2π)/5082 weeks
2731.77806 -.27154 (273*2π)/5082 weeks
2741.68114 .50218 (274*2π)/5082 weeks
2751.13802 1.03636 (275*2π)/5082 weeks
276.57187 1.25148 (276*2π)/5082 weeks
277-.18068 1.15921 (277*2π)/5082 weeks
278-.70545 .45302 (278*2π)/5082 weeks
279-.54702 -.04583 (279*2π)/5082 weeks
280-.41933 -.75829 (280*2π)/5082 weeks
281.44982 -1.02789 (281*2π)/5082 weeks
282.79819 -.42126 (282*2π)/5082 weeks
283.8987 -.23411 (283*2π)/5082 weeks
2841.14868 .31061 (284*2π)/5082 weeks
285.44255 .58671 (285*2π)/5082 weeks
286.35918 .53549 (286*2π)/5082 weeks
287-.41786 .69924 (287*2π)/5082 weeks
288-.41153 -.01992 (288*2π)/5082 weeks
289-.38503 -.22634 (289*2π)/5082 weeks
290-.224 -.78401 (290*2π)/5082 weeks
291.2454 -.95636 (291*2π)/5082 weeks
292.71363 -.94623 (292*2π)/5082 weeks
2931.1672 -.63404 (293*2π)/5082 weeks
2941.28967 -.10195 (294*2π)/5082 weeks
2951.08439 .29881 (295*2π)/5082 weeks
296.79153 .69774 (296*2π)/5082 weeks
297-.20768 .9394 (297*2π)/5082 weeks
298-.47737 .02562 (298*2π)/5082 weeks
299-.33853 -.41285 (299*2π)/5082 weeks
300.15325 -.97663 (300*2π)/5082 weeks
301.70112 -.63261 (301*2π)/5082 weeks
302.659 -.50855 (302*2π)/5082 weeks
303.91673 -.45153 (303*2π)/5082 weeks
304.89728 -.05328 (304*2π)/5082 weeks
305.68186 -.00429 (305*2π)/5082 weeks
306.90985 -.24346 (306*2π)/5082 weeks
3071.29074 .28575 (307*2π)/5082 weeks
308.73601 1.09467 (308*2π)/5082 weeks
309-.05317 1.02638 (309*2π)/5082 weeks
310-.83876 .67078 (310*2π)/5082 weeks
311-1.01812 -.82671 (311*2π)/5082 weeks
312-.10327 -1.37766 (312*2π)/5082 weeks
313.81137 -1.4815 (313*2π)/5082 weeks
3141.80211 -1.01492 (314*2π)/5082 weeks
3152.14368 .25673 (315*2π)/5082 weeks
3161.47828 1.24681 (316*2π)/5082 weeks
317.39095 1.6682 (317*2π)/5082 weeks
318-.71142 1.04527 (318*2π)/5082 weeks
319-.73042 -.11578 (319*2π)/5082 weeks
320-.36207 -.14033 (320*2π)/5082 weeks
321-.33927 -.96837 (321*2π)/5082 weeks
322.75414 -.69362 (322*2π)/5082 weeks
323.40879 -.283 (323*2π)/5082 weeks
324.90397 -.37294 (324*2π)/5082 weeks
325.99957 .35574 (325*2π)/5082 weeks
326.52792 .52539 (326*2π)/5082 weeks
327.22518 .90517 (327*2π)/5082 weeks
328-.89935 .30291 (328*2π)/5082 weeks
329-.51195 -.4214 (329*2π)/5082 weeks
330-.46498 -.31326 (330*2π)/5082 weeks
331-.23311 -1.00841 (331*2π)/5082 weeks
332.33017 -.87638 (332*2π)/5082 weeks
333.37338 -.99135 (333*2π)/5082 weeks
3341.09705 -.64496 (334*2π)/5082 weeks
335.92783 .13699 (335*2π)/5082 weeks
336.49897 .14247 (336*2π)/5082 weeks
337.14784 .21618 (337*2π)/5082 weeks
338-.30407 -.14453 (338*2π)/5082 weeks
339-.28821 -.43559 (339*2π)/5081 weeks
340-.16158 -1.08748 (340*2π)/5081 weeks
341.54418 -1.32531 (341*2π)/5081 weeks
3421.07064 -1.15462 (342*2π)/5081 weeks
3431.78074 -.58163 (343*2π)/5081 weeks
3441.53162 .35671 (344*2π)/5081 weeks
345.95385 .87256 (345*2π)/5081 weeks
346.38315 1.02541 (346*2π)/5081 weeks
347-.43814 .57436 (347*2π)/5081 weeks
348-.45601 -.16009 (348*2π)/5081 weeks
349-.63 -.72523 (349*2π)/5081 weeks
350.08562 -1.11177 (350*2π)/5081 weeks
351.76038 -1.00943 (351*2π)/5081 weeks
3521.00747 -.57795 (352*2π)/5081 weeks
3531.19772 -.03045 (353*2π)/5081 weeks
354.66448 .54498 (354*2π)/5081 weeks
355.27102 .18307 (355*2π)/5081 weeks
356-.02259 .34926 (356*2π)/5081 weeks
357-.20267 -.48408 (357*2π)/5081 weeks
358.17835 -.51424 (358*2π)/5081 weeks
359.31555 -.3572 (359*2π)/5081 weeks
360.0217 -.2332 (360*2π)/5081 weeks
361-.04932 -1.03102 (361*2π)/5081 weeks
362.98276 -.77828 (362*2π)/5081 weeks
363.66495 -.23765 (363*2π)/5081 weeks
364.41385 -.30217 (364*2π)/5081 weeks
365.65849 -.26896 (365*2π)/5081 weeks
366.72145 .04258 (366*2π)/5081 weeks
367.37489 .45643 (367*2π)/5081 weeks
368-.49108 .07114 (368*2π)/5081 weeks
369-.15231 -.92499 (369*2π)/5081 weeks
370.26164 -.68436 (370*2π)/5081 weeks
371.35985 -1.02337 (371*2π)/5081 weeks
372.80769 -.60309 (372*2π)/5081 weeks
373.79386 -.40517 (373*2π)/5081 weeks
374.85428 -.16927 (374*2π)/5081 weeks
375.13001 -.24057 (375*2π)/5081 weeks
376.51276 -.90092 (376*2π)/5081 weeks
3771.11309 -.13857 (377*2π)/5081 weeks
378.35582 .25509 (378*2π)/5081 weeks
379.20309 .07459 (379*2π)/5081 weeks
380-.14043 -.45282 (380*2π)/5081 weeks
381.62173 -1.08965 (381*2π)/5081 weeks
382.95011 -.52596 (382*2π)/5081 weeks
383.74511 -.25612 (383*2π)/5081 weeks
384.81745 .18854 (384*2π)/5081 weeks
385.53361 .22792 (385*2π)/5081 weeks
386.20421 -.21051 (386*2π)/5081 weeks
387.42616 -.56906 (387*2π)/5081 weeks
388.9648 .03043 (388*2π)/5081 weeks
389.41253 .26774 (389*2π)/5081 weeks
390.28732 .04496 (390*2π)/5081 weeks
391.21743 .34638 (391*2π)/5081 weeks
392.03001 .38087 (392*2π)/5081 weeks
393-.29882 .18722 (393*2π)/5081 weeks
394-1.11424 -.45766 (394*2π)/5081 weeks
395-.49785 -1.43559 (395*2π)/5081 weeks
396.30374 -1.61873 (396*2π)/5081 weeks
397.91228 -1.21133 (397*2π)/5081 weeks
3981.55921 -.59015 (398*2π)/5081 weeks
3991.27086 .33445 (399*2π)/5081 weeks
400.92691 .78724 (400*2π)/5081 weeks
401-.17555 1.04959 (401*2π)/5081 weeks
402-1.50966 .68039 (402*2π)/5081 weeks
403-1.49472 -1.0342 (403*2π)/5081 weeks
404-.8901 -1.62212 (404*2π)/5081 weeks
405.03157 -2.3635 (405*2π)/5081 weeks
4061.24221 -2.34119 (406*2π)/5081 weeks
4072.25829 -1.5232 (407*2π)/5081 weeks
4082.17879 .35761 (408*2π)/5081 weeks
409.99186 1.09171 (409*2π)/5081 weeks
410.2438 1.29814 (410*2π)/5081 weeks
411-.94286 .56163 (411*2π)/5081 weeks
412-1.31665 -.33105 (412*2π)/5081 weeks
413-1.09053 -1.68629 (413*2π)/5081 weeks
414-.1917 -2.0398 (414*2π)/5081 weeks
415.79968 -1.56957 (415*2π)/5081 weeks
4161.25486 -.90729 (416*2π)/5081 weeks
4171.38656 -.25582 (417*2π)/5081 weeks
418.84915 .18059 (418*2π)/5081 weeks
419.21357 .0175 (419*2π)/5081 weeks
420-.31773 -.28155 (420*2π)/5081 weeks
421.35789 -.81257 (421*2π)/5081 weeks
422.25012 .02918 (422*2π)/5081 weeks
423-.53997 .2759 (423*2π)/5081 weeks
424-1.45913 -.29877 (424*2π)/5081 weeks
425-1.4447 -1.99457 (425*2π)/5081 weeks
426-.09073 -2.99758 (426*2π)/5081 weeks
4271.70296 -3.18796 (427*2π)/5081 weeks
4282.78776 -1.68495 (428*2π)/5081 weeks
4293.02542 .39301 (429*2π)/5081 weeks
4301.01355 1.86748 (430*2π)/5081 weeks
431-.07746 1.31203 (431*2π)/5081 weeks
432-1.76917 1.33732 (432*2π)/5081 weeks
433-2.56663 -1.34091 (433*2π)/5081 weeks
434-1.48863 -2.74388 (434*2π)/5081 weeks
435.34663 -4.33873 (435*2π)/5081 weeks
4363.25414 -2.94894 (436*2π)/5081 weeks
4372.66191 -.23408 (437*2π)/5081 weeks
4382.70432 .02073 (438*2π)/5081 weeks
4391.68414 1.92763 (439*2π)/5081 weeks
440-.58199 2.17929 (440*2π)/5081 weeks
441-2.12786 .73354 (441*2π)/5081 weeks
442-2.30801 -1.48688 (442*2π)/5081 weeks
443-.82014 -2.61989 (443*2π)/5081 weeks
444.67089 -2.01642 (444*2π)/5081 weeks
445.34602 -1.33106 (445*2π)/5081 weeks
446.75517 -1.30555 (446*2π)/5081 weeks
447-.1435 -1.05745 (447*2π)/5081 weeks
448.50868 -1.67205 (448*2π)/5081 weeks
4491.02699 -1.1776 (449*2π)/5081 weeks
4501.07864 -1.06503 (450*2π)/5081 weeks
4511.32019 .44133 (451*2π)/5081 weeks
452-.82411 .57456 (452*2π)/5081 weeks
453-1.31053 -.50062 (453*2π)/5081 weeks
454-1.95944 -1.51927 (454*2π)/5081 weeks
455-.9246 -3.09586 (455*2π)/5081 weeks
456.6375 -3.89828 (456*2π)/5081 weeks
4572.07253 -2.48039 (457*2π)/5081 weeks
4581.98082 -.75785 (458*2π)/5081 weeks
459.83198 -.23323 (459*2π)/5081 weeks
460-.03412 .01262 (460*2π)/5081 weeks
461-.4492 -1.24261 (461*2π)/5081 weeks
462.03908 -1.70997 (462*2π)/5081 weeks
463.47885 -2.15374 (463*2π)/5081 weeks
464-.40173 -1.59592 (464*2π)/5081 weeks
465.80032 -2.34158 (465*2π)/5081 weeks
4661.10228 -1.67014 (466*2π)/5081 weeks
467.71409 -1.9495 (467*2π)/5081 weeks
468.65995 -1.20648 (468*2π)/5081 weeks
469-.1672 -2.42099 (469*2π)/5081 weeks
4702.70082 -2.64039 (470*2π)/5081 weeks
4711.81429 .08659 (471*2π)/5081 weeks
472.26226 -.06658 (472*2π)/5081 weeks
473.27574 -.57065 (473*2π)/5081 weeks
474-1.16778 .35189 (474*2π)/5081 weeks
475-3.01102 -1.24399 (475*2π)/5081 weeks
476-3.92145 -4.6543 (476*2π)/5081 weeks
477-.00017 -9.02599 (477*2π)/5081 weeks
4785.43739 -6.9606 (478*2π)/5081 weeks
4796.95633 -2.228 (479*2π)/5081 weeks
4806.30339 1.59561 (480*2π)/5081 weeks
4812.66701 4.80584 (481*2π)/5081 weeks
482-2.01444 2.5098 (482*2π)/5081 weeks
483-4.54248 .80704 (483*2π)/5081 weeks
484-5.98211 -5.39114 (484*2π)/5081 weeks
485-.46505 -7.63896 (485*2π)/5081 weeks
4863.26919 -5.7787 (486*2π)/5081 weeks
4875.35804 -1.33623 (487*2π)/5081 weeks
4882.10295 .7827 (488*2π)/5081 weeks
489.67374 .87289 (489*2π)/5081 weeks
490-2.97466 .70879 (490*2π)/5081 weeks
491-3.91071 -1.12088 (491*2π)/5081 weeks
492-5.81067 -4.66549 (492*2π)/5081 weeks
493-.85146 -6.8831 (493*2π)/5081 weeks
494-1.79787 -4.44231 (494*2π)/5081 weeks
495-3.97686 -7.28869 (495*2π)/5081 weeks
496-2.65478 -7.57435 (496*2π)/5081 weeks
497-3.08623 -12.78981 (497*2π)/5081 weeks
4981.77537 -14.08196 (498*2π)/5081 weeks
4994.45875 -14.66117 (499*2π)/5081 weeks
50015.31388 -9.83653 (500*2π)/5081 weeks
50114.1329 5.09308 (501*2π)/5081 weeks
502-5.8982 10.98753 (502*2π)/5081 weeks
503-22.31781 -3.01466 (503*2π)/5081 weeks
504-26.91393 -21.19584 (504*2π)/5081 weeks
505-24.37805 -51.96211 (505*2π)/5081 weeks
50610.49288 -72.24786 (506*2π)/5081 weeks



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