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Fourier Analysis of EEV (ProShares UltraShort MSCI Emerging Markets ETF)


EEV (ProShares UltraShort MSCI Emerging Markets ETF) appears to have interesting cyclic behaviour every 39 weeks (19.8004*sine), 42 weeks (18.9995*sine), and 46 weeks (17.8432*sine).

EEV (ProShares UltraShort MSCI Emerging Markets ETF) has an average price of 82.88 (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 11/1/2007 to 7/17/2017 for EEV (ProShares UltraShort MSCI Emerging Markets ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
082.8849   0 
192.30987 61.2442 (1*2π)/508508 weeks
248.34747 77.68309 (2*2π)/508254 weeks
38.49559 73.084 (3*2π)/508169 weeks
4-15.19858 53.01041 (4*2π)/508127 weeks
5-21.93719 29.92839 (5*2π)/508102 weeks
6-17.57043 8.54256 (6*2π)/50885 weeks
7-3.95738 -1.06472 (7*2π)/50873 weeks
86.67239 .48281 (8*2π)/50864 weeks
910.71281 5.87789 (9*2π)/50856 weeks
1012.74345 12.02521 (10*2π)/50851 weeks
119.4708 17.84321 (11*2π)/50846 weeks
125.36545 18.99947 (12*2π)/50842 weeks
13-1.35829 19.80043 (13*2π)/50839 weeks
14-5.08639 16.16718 (14*2π)/50836 weeks
15-7.35075 12.46856 (15*2π)/50834 weeks
16-9.89802 7.44023 (16*2π)/50832 weeks
17-7.69011 2.01829 (17*2π)/50830 weeks
18-4.78392 -1.04785 (18*2π)/50828 weeks
19.25232 -2.41401 (19*2π)/50827 weeks
204.42709 -1.48523 (20*2π)/50825 weeks
217.05241 2.1721 (21*2π)/50824 weeks
225.9753 7.19398 (22*2π)/50823 weeks
232.21876 9.95534 (23*2π)/50822 weeks
24-2.38268 9.71094 (24*2π)/50821 weeks
25-4.66683 5.25205 (25*2π)/50820 weeks
26-4.48767 .95471 (26*2π)/50820 weeks
27-1.52159 -2.87499 (27*2π)/50819 weeks
282.88486 -3.09547 (28*2π)/50818 weeks
296.65751 -.88201 (29*2π)/50818 weeks
308.40206 3.80499 (30*2π)/50817 weeks
316.33128 8.16415 (31*2π)/50816 weeks
322.53093 9.07636 (32*2π)/50816 weeks
33-.7099 8.51314 (33*2π)/50815 weeks
34-3.00861 6.02105 (34*2π)/50815 weeks
35-3.38718 3.61233 (35*2π)/50815 weeks
36-3.04463 1.22106 (36*2π)/50814 weeks
37-1.08498 -.83414 (37*2π)/50814 weeks
381.64145 -.58498 (38*2π)/50813 weeks
392.43447 .66025 (39*2π)/50813 weeks
403.45111 1.60297 (40*2π)/50813 weeks
413.56514 3.00564 (41*2π)/50812 weeks
422.95042 3.95823 (42*2π)/50812 weeks
431.47327 4.75819 (43*2π)/50812 weeks
44-.0322 4.41585 (44*2π)/50812 weeks
45-.38161 3.57003 (45*2π)/50811 weeks
46-.76883 1.88771 (46*2π)/50811 weeks
47.02594 1.09942 (47*2π)/50811 weeks
48.79208 .46495 (48*2π)/50811 weeks
492.219 .56584 (49*2π)/50810 weeks
503.51546 1.47181 (50*2π)/50810 weeks
513.79024 3.14035 (51*2π)/50810 weeks
523.31886 5.0152 (52*2π)/50810 weeks
531.27112 5.76053 (53*2π)/50810 weeks
54-.73525 5.4513 (54*2π)/5089 weeks
55-1.94128 3.96135 (55*2π)/5089 weeks
56-2.28108 2.04314 (56*2π)/5089 weeks
57-.91676 .50702 (57*2π)/5089 weeks
58.34518 .39331 (58*2π)/5089 weeks
591.42792 .6933 (59*2π)/5089 weeks
601.99522 1.73911 (60*2π)/5088 weeks
611.67955 2.59451 (61*2π)/5088 weeks
621.62183 3.2741 (62*2π)/5088 weeks
63.68142 3.84605 (63*2π)/5088 weeks
64.03792 3.83246 (64*2π)/5088 weeks
65-1.24544 4.06444 (65*2π)/5088 weeks
66-2.67984 2.95747 (66*2π)/5088 weeks
67-3.12612 .91874 (67*2π)/5088 weeks
68-2.4435 -1.13699 (68*2π)/5087 weeks
69-.19636 -2.32834 (69*2π)/5087 weeks
702.01037 -1.87832 (70*2π)/5087 weeks
713.22799 -.6738 (71*2π)/5087 weeks
724.34802 1.32764 (72*2π)/5087 weeks
733.19587 3.88694 (73*2π)/5087 weeks
741.04083 4.55205 (74*2π)/5087 weeks
75-1.00261 4.262 (75*2π)/5087 weeks
76-2.70313 2.09217 (76*2π)/5087 weeks
77-2.17564 .00168 (77*2π)/5087 weeks
78-.97454 -1.51707 (78*2π)/5087 weeks
791.362 -2.20458 (79*2π)/5086 weeks
803.3402 -.94387 (80*2π)/5086 weeks
814.37988 1.04213 (81*2π)/5086 weeks
823.91486 3.18205 (82*2π)/5086 weeks
832.06227 4.62077 (83*2π)/5086 weeks
84-.03717 4.50398 (84*2π)/5086 weeks
85-1.56374 3.47337 (85*2π)/5086 weeks
86-1.99042 1.92475 (86*2π)/5086 weeks
87-1.49846 .67858 (87*2π)/5086 weeks
88-1.00701 -.12215 (88*2π)/5086 weeks
89.22785 -.65314 (89*2π)/5086 weeks
901.31803 -.59496 (90*2π)/5086 weeks
912.10871 .19605 (91*2π)/5086 weeks
922.30552 1.38184 (92*2π)/5086 weeks
931.79821 2.54478 (93*2π)/5085 weeks
94.9074 3.25758 (94*2π)/5085 weeks
95-.22757 3.2504 (95*2π)/5085 weeks
96-1.38164 2.36048 (96*2π)/5085 weeks
97-1.89134 .99875 (97*2π)/5085 weeks
98-1.65404 -.40605 (98*2π)/5085 weeks
99-.57923 -1.28785 (99*2π)/5085 weeks
1001.01363 -1.59375 (100*2π)/5085 weeks
1012.51985 -.8339 (101*2π)/5085 weeks
1023.24983 .57452 (102*2π)/5085 weeks
1032.74525 2.23745 (103*2π)/5085 weeks
1041.42492 3.20413 (104*2π)/5085 weeks
105.04525 3.3844 (105*2π)/5085 weeks
106-1.43833 2.56343 (106*2π)/5085 weeks
107-1.6927 .94166 (107*2π)/5085 weeks
108-1.13609 -.41583 (108*2π)/5085 weeks
109-.04693 -1.03959 (109*2π)/5085 weeks
1101.24889 -.87724 (110*2π)/5085 weeks
1112.11475 .11753 (111*2π)/5085 weeks
1122.27435 1.32451 (112*2π)/5085 weeks
1131.54235 2.40805 (113*2π)/5084 weeks
114.24467 2.61664 (114*2π)/5084 weeks
115-.61997 1.8049 (115*2π)/5084 weeks
116-1.00608 .98809 (116*2π)/5084 weeks
117-.59649 .10131 (117*2π)/5084 weeks
118.12874 .06281 (118*2π)/5084 weeks
119.45487 .21041 (119*2π)/5084 weeks
120.64242 .45695 (120*2π)/5084 weeks
121.60024 .79871 (121*2π)/5084 weeks
122.24417 .88275 (122*2π)/5084 weeks
123-.15556 .51466 (123*2π)/5084 weeks
124-.14257 .05324 (124*2π)/5084 weeks
125.34079 -.12852 (125*2π)/5084 weeks
126.8205 -.22892 (126*2π)/5084 weeks
1271.2577 .18346 (127*2π)/5084 weeks
128.90108 .6876 (128*2π)/5084 weeks
129.59017 .62638 (129*2π)/5084 weeks
130.54734 .53056 (130*2π)/5084 weeks
131.5594 .36833 (131*2π)/5084 weeks
132.81632 .48862 (132*2π)/5084 weeks
133.54438 .61351 (133*2π)/5084 weeks
134.37353 .2742 (134*2π)/5084 weeks
135.43338 .10542 (135*2π)/5084 weeks
136.6115 -.17013 (136*2π)/5084 weeks
1371.27795 -.14117 (137*2π)/5084 weeks
1381.50853 .21529 (138*2π)/5084 weeks
1391.69786 .72325 (139*2π)/5084 weeks
1401.26789 1.30787 (140*2π)/5084 weeks
141.69458 1.38333 (141*2π)/5084 weeks
142.27588 1.32222 (142*2π)/5084 weeks
143-.19146 .95233 (143*2π)/5084 weeks
144-.26104 .39222 (144*2π)/5084 weeks
145-.04328 -.2539 (145*2π)/5084 weeks
146.50978 -.74527 (146*2π)/5083 weeks
1471.42649 -.44227 (147*2π)/5083 weeks
1481.69186 .07257 (148*2π)/5083 weeks
1491.91122 .60473 (149*2π)/5083 weeks
1501.76251 1.32313 (150*2π)/5083 weeks
1511.08761 1.88573 (151*2π)/5083 weeks
152.02356 1.89162 (152*2π)/5083 weeks
153-.72373 1.22651 (153*2π)/5083 weeks
154-.92848 .2174 (154*2π)/5083 weeks
155-.45252 -.69966 (155*2π)/5083 weeks
156.4106 -1.03307 (156*2π)/5083 weeks
1571.2773 -.99997 (157*2π)/5083 weeks
1581.97026 -.36533 (158*2π)/5083 weeks
1592.2874 .55658 (159*2π)/5083 weeks
1601.8202 1.38851 (160*2π)/5083 weeks
1611.01137 1.87956 (161*2π)/5083 weeks
162-.03532 1.80416 (162*2π)/5083 weeks
163-.74358 1.17905 (163*2π)/5083 weeks
164-1.04379 .16182 (164*2π)/5083 weeks
165-.59069 -.92817 (165*2π)/5083 weeks
166.35092 -1.47055 (166*2π)/5083 weeks
1671.41096 -1.44498 (167*2π)/5083 weeks
1682.2294 -.78812 (168*2π)/5083 weeks
1692.44846 .20198 (169*2π)/5083 weeks
1702.24524 1.06388 (170*2π)/5083 weeks
1711.464 1.52763 (171*2π)/5083 weeks
172.69062 1.48679 (172*2π)/5083 weeks
173.02694 .99656 (173*2π)/5083 weeks
174-.03307 .14697 (174*2π)/5083 weeks
175.52129 -.36767 (175*2π)/5083 weeks
1761.21931 -.62374 (176*2π)/5083 weeks
1771.94625 -.31097 (177*2π)/5083 weeks
1782.33486 .47324 (178*2π)/5083 weeks
1792.40538 1.33415 (179*2π)/5083 weeks
1801.76733 2.24556 (180*2π)/5083 weeks
181.53615 2.27892 (181*2π)/5083 weeks
182-.26065 1.8566 (182*2π)/5083 weeks
183-.71761 1.05132 (183*2π)/5083 weeks
184-.49756 .18384 (184*2π)/5083 weeks
185.03382 -.27407 (185*2π)/5083 weeks
186.74432 -.65499 (186*2π)/5083 weeks
1871.60538 -.16756 (187*2π)/5083 weeks
1881.74792 .51284 (188*2π)/5083 weeks
1891.84207 1.24978 (189*2π)/5083 weeks
1901.22119 2.09198 (190*2π)/5083 weeks
191.18846 2.25064 (191*2π)/5083 weeks
192-.76145 1.69832 (192*2π)/5083 weeks
193-1.1786 .65265 (193*2π)/5083 weeks
194-.72876 -.25977 (194*2π)/5083 weeks
195-.05252 -.6894 (195*2π)/5083 weeks
196.78313 -.63099 (196*2π)/5083 weeks
1971.45011 -.15235 (197*2π)/5083 weeks
1981.30297 .66124 (198*2π)/5083 weeks
1991.05464 1.19651 (199*2π)/5083 weeks
200.40735 1.32288 (200*2π)/5083 weeks
201.07438 1.03024 (201*2π)/5083 weeks
202-.2219 .90765 (202*2π)/5083 weeks
203-.53049 .69897 (203*2π)/5083 weeks
204-.69168 .15466 (204*2π)/5082 weeks
205-.47358 -.51452 (205*2π)/5082 weeks
206.093 -.84944 (206*2π)/5082 weeks
207.62917 -.94266 (207*2π)/5082 weeks
2081.37405 -.66133 (208*2π)/5082 weeks
2091.71314 .11016 (209*2π)/5082 weeks
2101.51575 .99162 (210*2π)/5082 weeks
211.78283 1.62299 (211*2π)/5082 weeks
212-.24462 1.41296 (212*2π)/5082 weeks
213-.9542 .72297 (213*2π)/5082 weeks
214-1.19926 -.24329 (214*2π)/5082 weeks
215-.76366 -1.18652 (215*2π)/5082 weeks
216.21029 -1.76807 (216*2π)/5082 weeks
2171.28195 -1.76336 (217*2π)/5082 weeks
2182.28163 -1.03246 (218*2π)/5082 weeks
2192.57669 .15433 (219*2π)/5082 weeks
2202.22548 1.29841 (220*2π)/5082 weeks
2211.22884 2.08897 (221*2π)/5082 weeks
222-.05451 1.87333 (222*2π)/5082 weeks
223-.85993 1.12875 (223*2π)/5082 weeks
224-1.30685 -.08372 (224*2π)/5082 weeks
225-.66878 -1.1934 (225*2π)/5082 weeks
226.35155 -1.68999 (226*2π)/5082 weeks
2271.57215 -1.73135 (227*2π)/5082 weeks
2282.68553 -.90233 (228*2π)/5082 weeks
2292.94868 .5625 (229*2π)/5082 weeks
2302.51063 1.95537 (230*2π)/5082 weeks
2311.21194 2.84109 (231*2π)/5082 weeks
232-.33284 2.80545 (232*2π)/5082 weeks
233-1.53831 1.93096 (233*2π)/5082 weeks
234-2.19238 .47013 (234*2π)/5082 weeks
235-1.89069 -1.00997 (235*2π)/5082 weeks
236-.94637 -2.04503 (236*2π)/5082 weeks
237.65007 -2.468 (237*2π)/5082 weeks
2382.18067 -1.66638 (238*2π)/5082 weeks
2392.74508 -.26985 (239*2π)/5082 weeks
2402.55359 1.12502 (240*2π)/5082 weeks
2411.38875 2.22815 (241*2π)/5082 weeks
242-.31678 2.2709 (242*2π)/5082 weeks
243-1.67445 1.1853 (243*2π)/5082 weeks
244-1.88351 -.29434 (244*2π)/5082 weeks
245-1.2061 -1.66968 (245*2π)/5082 weeks
246.13751 -2.36008 (246*2π)/5082 weeks
2471.64967 -2.46088 (247*2π)/5082 weeks
2482.95974 -1.27396 (248*2π)/5082 weeks
2493.12079 .48123 (249*2π)/5082 weeks
2502.33454 1.78508 (250*2π)/5082 weeks
2511.12132 2.48093 (251*2π)/5082 weeks
252-.29911 2.25888 (252*2π)/5082 weeks
253-1.51866 1.5092 (253*2π)/5082 weeks
254-2.08143   (254*2π)/5082 weeks
255-1.51866 -1.5092 (255*2π)/5082 weeks
256-.29911 -2.25888 (256*2π)/5082 weeks
2571.12132 -2.48093 (257*2π)/5082 weeks
2582.33454 -1.78508 (258*2π)/5082 weeks
2593.12079 -.48123 (259*2π)/5082 weeks
2602.95974 1.27396 (260*2π)/5082 weeks
2611.64967 2.46088 (261*2π)/5082 weeks
262.13751 2.36008 (262*2π)/5082 weeks
263-1.2061 1.66968 (263*2π)/5082 weeks
264-1.88351 .29434 (264*2π)/5082 weeks
265-1.67445 -1.1853 (265*2π)/5082 weeks
266-.31678 -2.2709 (266*2π)/5082 weeks
2671.38875 -2.22815 (267*2π)/5082 weeks
2682.55359 -1.12502 (268*2π)/5082 weeks
2692.74508 .26985 (269*2π)/5082 weeks
2702.18067 1.66638 (270*2π)/5082 weeks
271.65007 2.468 (271*2π)/5082 weeks
272-.94637 2.04503 (272*2π)/5082 weeks
273-1.89069 1.00997 (273*2π)/5082 weeks
274-2.19238 -.47013 (274*2π)/5082 weeks
275-1.53831 -1.93096 (275*2π)/5082 weeks
276-.33284 -2.80545 (276*2π)/5082 weeks
2771.21194 -2.84109 (277*2π)/5082 weeks
2782.51063 -1.95537 (278*2π)/5082 weeks
2792.94868 -.5625 (279*2π)/5082 weeks
2802.68553 .90233 (280*2π)/5082 weeks
2811.57215 1.73135 (281*2π)/5082 weeks
282.35155 1.68999 (282*2π)/5082 weeks
283-.66878 1.1934 (283*2π)/5082 weeks
284-1.30685 .08372 (284*2π)/5082 weeks
285-.85993 -1.12875 (285*2π)/5082 weeks
286-.05451 -1.87333 (286*2π)/5082 weeks
2871.22884 -2.08897 (287*2π)/5082 weeks
2882.22548 -1.29841 (288*2π)/5082 weeks
2892.57669 -.15433 (289*2π)/5082 weeks
2902.28163 1.03246 (290*2π)/5082 weeks
2911.28195 1.76336 (291*2π)/5082 weeks
292.21029 1.76807 (292*2π)/5082 weeks
293-.76366 1.18652 (293*2π)/5082 weeks
294-1.19926 .24329 (294*2π)/5082 weeks
295-.9542 -.72297 (295*2π)/5082 weeks
296-.24462 -1.41296 (296*2π)/5082 weeks
297.78283 -1.62299 (297*2π)/5082 weeks
2981.51575 -.99162 (298*2π)/5082 weeks
2991.71314 -.11016 (299*2π)/5082 weeks
3001.37405 .66133 (300*2π)/5082 weeks
301.62917 .94266 (301*2π)/5082 weeks
302.093 .84944 (302*2π)/5082 weeks
303-.47358 .51452 (303*2π)/5082 weeks
304-.69168 -.15466 (304*2π)/5082 weeks
305-.53049 -.69897 (305*2π)/5082 weeks
306-.2219 -.90765 (306*2π)/5082 weeks
307.07438 -1.03024 (307*2π)/5082 weeks
308.40735 -1.32288 (308*2π)/5082 weeks
3091.05464 -1.19651 (309*2π)/5082 weeks
3101.30297 -.66124 (310*2π)/5082 weeks
3111.45011 .15235 (311*2π)/5082 weeks
312.78313 .63099 (312*2π)/5082 weeks
313-.05252 .6894 (313*2π)/5082 weeks
314-.72876 .25977 (314*2π)/5082 weeks
315-1.1786 -.65265 (315*2π)/5082 weeks
316-.76145 -1.69832 (316*2π)/5082 weeks
317.18846 -2.25064 (317*2π)/5082 weeks
3181.22119 -2.09198 (318*2π)/5082 weeks
3191.84207 -1.24978 (319*2π)/5082 weeks
3201.74792 -.51284 (320*2π)/5082 weeks
3211.60538 .16756 (321*2π)/5082 weeks
322.74432 .65499 (322*2π)/5082 weeks
323.03382 .27407 (323*2π)/5082 weeks
324-.49756 -.18384 (324*2π)/5082 weeks
325-.71761 -1.05132 (325*2π)/5082 weeks
326-.26065 -1.8566 (326*2π)/5082 weeks
327.53615 -2.27892 (327*2π)/5082 weeks
3281.76733 -2.24556 (328*2π)/5082 weeks
3292.40538 -1.33415 (329*2π)/5082 weeks
3302.33486 -.47324 (330*2π)/5082 weeks
3311.94625 .31097 (331*2π)/5082 weeks
3321.21931 .62374 (332*2π)/5082 weeks
333.52129 .36767 (333*2π)/5082 weeks
334-.03307 -.14697 (334*2π)/5082 weeks
335.02694 -.99656 (335*2π)/5082 weeks
336.69062 -1.48679 (336*2π)/5082 weeks
3371.464 -1.52763 (337*2π)/5082 weeks
3382.24524 -1.06388 (338*2π)/5082 weeks
3392.44846 -.20198 (339*2π)/5081 weeks
3402.2294 .78812 (340*2π)/5081 weeks
3411.41096 1.44498 (341*2π)/5081 weeks
342.35092 1.47055 (342*2π)/5081 weeks
343-.59069 .92817 (343*2π)/5081 weeks
344-1.04379 -.16182 (344*2π)/5081 weeks
345-.74358 -1.17905 (345*2π)/5081 weeks
346-.03532 -1.80416 (346*2π)/5081 weeks
3471.01137 -1.87956 (347*2π)/5081 weeks
3481.8202 -1.38851 (348*2π)/5081 weeks
3492.2874 -.55658 (349*2π)/5081 weeks
3501.97026 .36533 (350*2π)/5081 weeks
3511.2773 .99997 (351*2π)/5081 weeks
352.4106 1.03307 (352*2π)/5081 weeks
353-.45252 .69966 (353*2π)/5081 weeks
354-.92848 -.2174 (354*2π)/5081 weeks
355-.72373 -1.22651 (355*2π)/5081 weeks
356.02356 -1.89162 (356*2π)/5081 weeks
3571.08761 -1.88573 (357*2π)/5081 weeks
3581.76251 -1.32313 (358*2π)/5081 weeks
3591.91122 -.60473 (359*2π)/5081 weeks
3601.69186 -.07257 (360*2π)/5081 weeks
3611.42649 .44227 (361*2π)/5081 weeks
362.50978 .74527 (362*2π)/5081 weeks
363-.04328 .2539 (363*2π)/5081 weeks
364-.26104 -.39222 (364*2π)/5081 weeks
365-.19146 -.95233 (365*2π)/5081 weeks
366.27588 -1.32222 (366*2π)/5081 weeks
367.69458 -1.38333 (367*2π)/5081 weeks
3681.26789 -1.30787 (368*2π)/5081 weeks
3691.69786 -.72325 (369*2π)/5081 weeks
3701.50853 -.21529 (370*2π)/5081 weeks
3711.27795 .14117 (371*2π)/5081 weeks
372.6115 .17013 (372*2π)/5081 weeks
373.43338 -.10542 (373*2π)/5081 weeks
374.37353 -.2742 (374*2π)/5081 weeks
375.54438 -.61351 (375*2π)/5081 weeks
376.81632 -.48862 (376*2π)/5081 weeks
377.5594 -.36833 (377*2π)/5081 weeks
378.54734 -.53056 (378*2π)/5081 weeks
379.59017 -.62638 (379*2π)/5081 weeks
380.90108 -.6876 (380*2π)/5081 weeks
3811.2577 -.18346 (381*2π)/5081 weeks
382.8205 .22892 (382*2π)/5081 weeks
383.34079 .12852 (383*2π)/5081 weeks
384-.14257 -.05324 (384*2π)/5081 weeks
385-.15556 -.51466 (385*2π)/5081 weeks
386.24417 -.88275 (386*2π)/5081 weeks
387.60024 -.79871 (387*2π)/5081 weeks
388.64242 -.45695 (388*2π)/5081 weeks
389.45487 -.21041 (389*2π)/5081 weeks
390.12874 -.06281 (390*2π)/5081 weeks
391-.59649 -.10131 (391*2π)/5081 weeks
392-1.00608 -.98809 (392*2π)/5081 weeks
393-.61997 -1.8049 (393*2π)/5081 weeks
394.24467 -2.61664 (394*2π)/5081 weeks
3951.54235 -2.40805 (395*2π)/5081 weeks
3962.27435 -1.32451 (396*2π)/5081 weeks
3972.11475 -.11753 (397*2π)/5081 weeks
3981.24889 .87724 (398*2π)/5081 weeks
399-.04693 1.03959 (399*2π)/5081 weeks
400-1.13609 .41583 (400*2π)/5081 weeks
401-1.6927 -.94166 (401*2π)/5081 weeks
402-1.43833 -2.56343 (402*2π)/5081 weeks
403.04525 -3.3844 (403*2π)/5081 weeks
4041.42492 -3.20413 (404*2π)/5081 weeks
4052.74525 -2.23745 (405*2π)/5081 weeks
4063.24983 -.57452 (406*2π)/5081 weeks
4072.51985 .8339 (407*2π)/5081 weeks
4081.01363 1.59375 (408*2π)/5081 weeks
409-.57923 1.28785 (409*2π)/5081 weeks
410-1.65404 .40605 (410*2π)/5081 weeks
411-1.89134 -.99875 (411*2π)/5081 weeks
412-1.38164 -2.36048 (412*2π)/5081 weeks
413-.22757 -3.2504 (413*2π)/5081 weeks
414.9074 -3.25758 (414*2π)/5081 weeks
4151.79821 -2.54478 (415*2π)/5081 weeks
4162.30552 -1.38184 (416*2π)/5081 weeks
4172.10871 -.19605 (417*2π)/5081 weeks
4181.31803 .59496 (418*2π)/5081 weeks
419.22785 .65314 (419*2π)/5081 weeks
420-1.00701 .12215 (420*2π)/5081 weeks
421-1.49846 -.67858 (421*2π)/5081 weeks
422-1.99042 -1.92475 (422*2π)/5081 weeks
423-1.56374 -3.47337 (423*2π)/5081 weeks
424-.03717 -4.50398 (424*2π)/5081 weeks
4252.06227 -4.62077 (425*2π)/5081 weeks
4263.91486 -3.18205 (426*2π)/5081 weeks
4274.37988 -1.04213 (427*2π)/5081 weeks
4283.3402 .94387 (428*2π)/5081 weeks
4291.362 2.20458 (429*2π)/5081 weeks
430-.97454 1.51707 (430*2π)/5081 weeks
431-2.17564 -.00168 (431*2π)/5081 weeks
432-2.70313 -2.09217 (432*2π)/5081 weeks
433-1.00261 -4.262 (433*2π)/5081 weeks
4341.04083 -4.55205 (434*2π)/5081 weeks
4353.19587 -3.88694 (435*2π)/5081 weeks
4364.34802 -1.32764 (436*2π)/5081 weeks
4373.22799 .6738 (437*2π)/5081 weeks
4382.01037 1.87832 (438*2π)/5081 weeks
439-.19636 2.32834 (439*2π)/5081 weeks
440-2.4435 1.13699 (440*2π)/5081 weeks
441-3.12612 -.91874 (441*2π)/5081 weeks
442-2.67984 -2.95747 (442*2π)/5081 weeks
443-1.24544 -4.06444 (443*2π)/5081 weeks
444.03792 -3.83246 (444*2π)/5081 weeks
445.68142 -3.84605 (445*2π)/5081 weeks
4461.62183 -3.2741 (446*2π)/5081 weeks
4471.67955 -2.59451 (447*2π)/5081 weeks
4481.99522 -1.73911 (448*2π)/5081 weeks
4491.42792 -.6933 (449*2π)/5081 weeks
450.34518 -.39331 (450*2π)/5081 weeks
451-.91676 -.50702 (451*2π)/5081 weeks
452-2.28108 -2.04314 (452*2π)/5081 weeks
453-1.94128 -3.96135 (453*2π)/5081 weeks
454-.73525 -5.4513 (454*2π)/5081 weeks
4551.27112 -5.76053 (455*2π)/5081 weeks
4563.31886 -5.0152 (456*2π)/5081 weeks
4573.79024 -3.14035 (457*2π)/5081 weeks
4583.51546 -1.47181 (458*2π)/5081 weeks
4592.219 -.56584 (459*2π)/5081 weeks
460.79208 -.46495 (460*2π)/5081 weeks
461.02594 -1.09942 (461*2π)/5081 weeks
462-.76883 -1.88771 (462*2π)/5081 weeks
463-.38161 -3.57003 (463*2π)/5081 weeks
464-.0322 -4.41585 (464*2π)/5081 weeks
4651.47327 -4.75819 (465*2π)/5081 weeks
4662.95042 -3.95823 (466*2π)/5081 weeks
4673.56514 -3.00564 (467*2π)/5081 weeks
4683.45111 -1.60297 (468*2π)/5081 weeks
4692.43447 -.66025 (469*2π)/5081 weeks
4701.64145 .58498 (470*2π)/5081 weeks
471-1.08498 .83414 (471*2π)/5081 weeks
472-3.04463 -1.22106 (472*2π)/5081 weeks
473-3.38718 -3.61233 (473*2π)/5081 weeks
474-3.00861 -6.02105 (474*2π)/5081 weeks
475-.7099 -8.51314 (475*2π)/5081 weeks
4762.53093 -9.07636 (476*2π)/5081 weeks
4776.33128 -8.16415 (477*2π)/5081 weeks
4788.40206 -3.80499 (478*2π)/5081 weeks
4796.65751 .88201 (479*2π)/5081 weeks
4802.88486 3.09547 (480*2π)/5081 weeks
481-1.52159 2.87499 (481*2π)/5081 weeks
482-4.48767 -.95471 (482*2π)/5081 weeks
483-4.66683 -5.25205 (483*2π)/5081 weeks
484-2.38268 -9.71094 (484*2π)/5081 weeks
4852.21876 -9.95534 (485*2π)/5081 weeks
4865.9753 -7.19398 (486*2π)/5081 weeks
4877.05241 -2.1721 (487*2π)/5081 weeks
4884.42709 1.48523 (488*2π)/5081 weeks
489.25232 2.41401 (489*2π)/5081 weeks
490-4.78392 1.04785 (490*2π)/5081 weeks
491-7.69011 -2.01829 (491*2π)/5081 weeks
492-9.89802 -7.44023 (492*2π)/5081 weeks
493-7.35075 -12.46856 (493*2π)/5081 weeks
494-5.08639 -16.16718 (494*2π)/5081 weeks
495-1.35829 -19.80043 (495*2π)/5081 weeks
4965.36545 -18.99947 (496*2π)/5081 weeks
4979.4708 -17.84321 (497*2π)/5081 weeks
49812.74345 -12.02521 (498*2π)/5081 weeks
49910.71281 -5.87789 (499*2π)/5081 weeks
5006.67239 -.48281 (500*2π)/5081 weeks
501-3.95738 1.06472 (501*2π)/5081 weeks
502-17.57043 -8.54256 (502*2π)/5081 weeks
503-21.93719 -29.92839 (503*2π)/5081 weeks
504-15.19858 -53.01041 (504*2π)/5081 weeks
5058.49559 -73.084 (505*2π)/5081 weeks
50648.34747 -77.68309 (506*2π)/5081 weeks



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