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Fourier Analysis of EEV (PROSHARES ULTRASHORT MSCI EMERGING MARKETS PROSHARES ULTRASHORT MSCI EMERGING MARKETS)


EEV (PROSHARES ULTRASHORT MSCI EMERGING MARKETS PROSHARES ULTRASHORT MSCI EMERGING MARKETS) appears to have interesting cyclic behaviour every 41 weeks (18.9856*sine), 45 weeks (17.3041*sine), and 49 weeks (14.0266*sine).

EEV (PROSHARES ULTRASHORT MSCI EMERGING MARKETS PROSHARES ULTRASHORT MSCI EMERGING MARKETS) has an average price of 78.21 (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 1/16/2018 for EEV (PROSHARES ULTRASHORT MSCI EMERGING MARKETS PROSHARES ULTRASHORT MSCI EMERGING MARKETS), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
078.20782   0 
187.10004 56.5338 (1*2π)/534534 weeks
247.34013 72.83321 (2*2π)/534267 weeks
311.39666 71.30047 (3*2π)/534178 weeks
4-11.35003 53.94716 (4*2π)/534134 weeks
5-19.85607 31.66249 (5*2π)/534107 weeks
6-19.5762 11.75834 (6*2π)/53489 weeks
7-8.50656 -.23374 (7*2π)/53476 weeks
83.15608 -.82202 (8*2π)/53467 weeks
99.87344 4.02355 (9*2π)/53459 weeks
1012.53004 8.15094 (10*2π)/53453 weeks
1111.58403 14.02657 (11*2π)/53449 weeks
126.52368 17.30407 (12*2π)/53445 weeks
133.04149 18.98559 (13*2π)/53441 weeks
14-3.24468 17.13756 (14*2π)/53438 weeks
15-6.05452 14.02361 (15*2π)/53436 weeks
16-7.6826 10.85417 (16*2π)/53433 weeks
17-9.21571 5.50464 (17*2π)/53431 weeks
18-6.6958 1.12955 (18*2π)/53430 weeks
19-3.97607 -1.49168 (19*2π)/53428 weeks
20.65694 -2.3467 (20*2π)/53427 weeks
214.34357 -1.42147 (21*2π)/53425 weeks
226.62011 1.93909 (22*2π)/53424 weeks
235.93766 6.73538 (23*2π)/53423 weeks
242.83605 9.54851 (24*2π)/53422 weeks
25-1.13796 9.58638 (25*2π)/53421 weeks
26-4.50002 5.67668 (26*2π)/53421 weeks
27-4.99685 1.8636 (27*2π)/53420 weeks
28-3.27502 -1.80362 (28*2π)/53419 weeks
291.09555 -3.20234 (29*2π)/53418 weeks
305.02408 -2.22703 (30*2π)/53418 weeks
317.87549 .85539 (31*2π)/53417 weeks
327.60752 5.37655 (32*2π)/53417 weeks
334.32562 8.46154 (33*2π)/53416 weeks
341.26278 8.75075 (34*2π)/53416 weeks
35-1.62494 7.72416 (35*2π)/53415 weeks
36-3.11419 5.1412 (36*2π)/53415 weeks
37-3.34229 2.95961 (37*2π)/53414 weeks
38-2.83554 .67517 (38*2π)/53414 weeks
39-.82237 -1.08373 (39*2π)/53414 weeks
401.64064 -.683 (40*2π)/53413 weeks
412.35952 .46444 (41*2π)/53413 weeks
423.35701 1.34808 (42*2π)/53413 weeks
433.51848 2.66078 (43*2π)/53412 weeks
442.88998 3.63361 (44*2π)/53412 weeks
451.68015 4.64545 (45*2π)/53412 weeks
46.31788 4.54955 (46*2π)/53412 weeks
47-.29378 3.44308 (47*2π)/53411 weeks
48-1.1579 2.37254 (48*2π)/53411 weeks
49-.4392 1.25442 (49*2π)/53411 weeks
50.25046 .6933 (50*2π)/53411 weeks
511.49228 .20137 (51*2π)/53410 weeks
522.7253 .59464 (52*2π)/53410 weeks
533.67302 1.91378 (53*2π)/53410 weeks
543.65333 3.3902 (54*2π)/53410 weeks
552.57829 5.21207 (55*2π)/53410 weeks
56.80482 5.53307 (56*2π)/53410 weeks
57-1.04906 4.92175 (57*2π)/5349 weeks
58-2.01469 3.51748 (58*2π)/5349 weeks
59-2.19004 1.67714 (59*2π)/5349 weeks
60-.85539 .41107 (60*2π)/5349 weeks
61.26499 .28349 (61*2π)/5349 weeks
621.27383 .5174 (62*2π)/5349 weeks
631.8742 1.45034 (63*2π)/5348 weeks
641.70048 2.31706 (64*2π)/5348 weeks
651.72044 2.8466 (65*2π)/5348 weeks
66.99313 3.55965 (66*2π)/5348 weeks
67.26591 3.56604 (67*2π)/5348 weeks
68-.59094 3.9353 (68*2π)/5348 weeks
69-2.08007 3.31302 (69*2π)/5348 weeks
70-3.01846 1.69894 (70*2π)/5348 weeks
71-2.83 -.15407 (71*2π)/5348 weeks
72-1.45525 -1.95177 (72*2π)/5347 weeks
73.6852 -2.25801 (73*2π)/5347 weeks
742.4086 -1.34168 (74*2π)/5347 weeks
753.52844 -.27205 (75*2π)/5347 weeks
764.11666 2.02503 (76*2π)/5347 weeks
772.54667 3.96782 (77*2π)/5347 weeks
78.65934 4.33084 (78*2π)/5347 weeks
79-1.26582 3.93476 (79*2π)/5347 weeks
80-2.57222 1.75861 (80*2π)/5347 weeks
81-2.06753 -.05108 (81*2π)/5347 weeks
82-.99108 -1.43163 (82*2π)/5347 weeks
831.10402 -2.12365 (83*2π)/5346 weeks
842.98827 -1.08269 (84*2π)/5346 weeks
854.06782 .55985 (85*2π)/5346 weeks
863.83405 2.52083 (86*2π)/5346 weeks
872.4137 4.1221 (87*2π)/5346 weeks
88.48874 4.41881 (88*2π)/5346 weeks
89-.96571 3.75671 (89*2π)/5346 weeks
90-1.71366 2.35591 (90*2π)/5346 weeks
91-1.63878 1.01245 (91*2π)/5346 weeks
92-1.16749 .28142 (92*2π)/5346 weeks
93-.5168 -.56433 (93*2π)/5346 weeks
94.48358 -.60879 (94*2π)/5346 weeks
951.56422 -.25991 (95*2π)/5346 weeks
962.21186 .50346 (96*2π)/5346 weeks
972.21763 1.48264 (97*2π)/5346 weeks
981.55009 2.37222 (98*2π)/5345 weeks
99.59925 3.0001 (99*2π)/5345 weeks
100-.40489 3.0222 (100*2π)/5345 weeks
101-1.33205 2.17082 (101*2π)/5345 weeks
102-1.75546 .92329 (102*2π)/5345 weeks
103-1.5788 -.33455 (103*2π)/5345 weeks
104-.63853 -1.13627 (104*2π)/5345 weeks
105.75318 -1.52611 (105*2π)/5345 weeks
1062.1409 -1.01839 (106*2π)/5345 weeks
1072.87437 .15697 (107*2π)/5345 weeks
1082.72424 1.77888 (108*2π)/5345 weeks
1091.78541 2.8824 (109*2π)/5345 weeks
110.61207 3.14537 (110*2π)/5345 weeks
111-.7744 2.81499 (111*2π)/5345 weeks
112-1.64274 1.43708 (112*2π)/5345 weeks
113-1.49707 .21959 (113*2π)/5345 weeks
114-.60962 -.6574 (114*2π)/5345 weeks
115.50966 -.99356 (115*2π)/5345 weeks
1161.58786 -.58664 (116*2π)/5345 weeks
1172.06479 .38896 (117*2π)/5345 weeks
1181.97742 1.51939 (118*2π)/5345 weeks
1191.14101 2.3726 (119*2π)/5344 weeks
120-.01753 2.3819 (120*2π)/5344 weeks
121-.624 1.59105 (121*2π)/5344 weeks
122-.93393 .81218 (122*2π)/5344 weeks
123-.52331 .045 (123*2π)/5344 weeks
124.15509 .03879 (124*2π)/5344 weeks
125.45737 .19327 (125*2π)/5344 weeks
126.63091 .41958 (126*2π)/5344 weeks
127.61941 .71595 (127*2π)/5344 weeks
128.27567 .85012 (128*2π)/5344 weeks
129-.16484 .67444 (129*2π)/5344 weeks
130-.185 .25413 (130*2π)/5344 weeks
131.19817 -.1922 (131*2π)/5344 weeks
132.48918 -.31826 (132*2π)/5344 weeks
133.97753 -.12557 (133*2π)/5344 weeks
1341.11896 .51383 (134*2π)/5344 weeks
135.75563 .65846 (135*2π)/5344 weeks
136.58574 .52235 (136*2π)/5344 weeks
137.51085 .45934 (137*2π)/5344 weeks
138.57306 .31868 (138*2π)/5344 weeks
139.68724 .57321 (139*2π)/5344 weeks
140.40365 .59259 (140*2π)/5344 weeks
141.3333 .23242 (141*2π)/5344 weeks
142.3706 .04833 (142*2π)/5344 weeks
143.5506 -.21981 (143*2π)/5344 weeks
1441.18481 -.18782 (144*2π)/5344 weeks
1451.41284 .13858 (145*2π)/5344 weeks
1461.61173 .57777 (146*2π)/5344 weeks
1471.2987 1.19017 (147*2π)/5344 weeks
148.76989 1.357 (148*2π)/5344 weeks
149.40305 1.3069 (149*2π)/5344 weeks
150-.05679 1.07335 (150*2π)/5344 weeks
151-.2578 .52044 (151*2π)/5344 weeks
152-.25848 -.04363 (152*2π)/5344 weeks
153.11559 -.50691 (153*2π)/5343 weeks
154.96361 -.74586 (154*2π)/5343 weeks
1551.46051 -.233 (155*2π)/5343 weeks
1561.66051 .17419 (156*2π)/5343 weeks
1571.77989 .78554 (157*2π)/5343 weeks
1581.51799 1.47149 (158*2π)/5343 weeks
159.82295 1.8989 (159*2π)/5343 weeks
160-.13641 1.70831 (160*2π)/5343 weeks
161-.7613 1.03645 (161*2π)/5343 weeks
162-.88108 .10395 (162*2π)/5343 weeks
163-.41523 -.70766 (163*2π)/5343 weeks
164.3594 -.99666 (164*2π)/5343 weeks
1651.14356 -.98822 (165*2π)/5343 weeks
1661.80884 -.44319 (166*2π)/5343 weeks
1672.15714 .33141 (167*2π)/5343 weeks
1681.79925 1.16398 (168*2π)/5343 weeks
1691.14605 1.70948 (169*2π)/5343 weeks
170.248 1.83488 (170*2π)/5343 weeks
171-.48078 1.34783 (171*2π)/5343 weeks
172-.94934 .53394 (172*2π)/5343 weeks
173-.88088 -.4975 (173*2π)/5343 weeks
174-.17876 -1.21377 (174*2π)/5343 weeks
175.73943 -1.43639 (175*2π)/5343 weeks
1761.68049 -1.13286 (176*2π)/5343 weeks
1772.26654 -.39593 (177*2π)/5343 weeks
1782.25844 .41999 (178*2π)/5343 weeks
1791.90353 1.21211 (179*2π)/5343 weeks
1801.19816 1.48452 (180*2π)/5343 weeks
181.52236 1.36746 (181*2π)/5343 weeks
182-.0388 .83593 (182*2π)/5343 weeks
183-.03132 .07074 (183*2π)/5343 weeks
184.47558 -.35478 (184*2π)/5343 weeks
1851.10767 -.59709 (185*2π)/5343 weeks
1861.76002 -.33794 (186*2π)/5343 weeks
1872.16331 .34777 (187*2π)/5343 weeks
1882.27192 1.06172 (188*2π)/5343 weeks
1891.81523 1.91309 (189*2π)/5343 weeks
190.68902 2.2317 (190*2π)/5343 weeks
191-.0395 1.928 (191*2π)/5343 weeks
192-.55666 1.29852 (192*2π)/5343 weeks
193-.59556 .43388 (193*2π)/5343 weeks
194-.19475 -.14211 (194*2π)/5343 weeks
195.24099 -.46225 (195*2π)/5343 weeks
1961.13252 -.48725 (196*2π)/5343 weeks
1971.62253 .16882 (197*2π)/5343 weeks
1981.70888 .65734 (198*2π)/5343 weeks
1991.6339 1.43142 (199*2π)/5343 weeks
200.8793 2.045 (200*2π)/5343 weeks
201-.05804 2.05411 (201*2π)/5343 weeks
202-.823 1.45 (202*2π)/5343 weeks
203-1.0894 .45982 (203*2π)/5343 weeks
204-.63401 -.30357 (204*2π)/5343 weeks
205-.02146 -.66725 (205*2π)/5343 weeks
206.73196 -.60692 (206*2π)/5343 weeks
2071.32651 -.20748 (207*2π)/5343 weeks
2081.26081 .59574 (208*2π)/5343 weeks
2091.08224 1.03565 (209*2π)/5343 weeks
210.49443 1.24668 (210*2π)/5343 weeks
211.06037 1.00798 (211*2π)/5343 weeks
212-.12914 .92714 (212*2π)/5343 weeks
213-.33797 .74245 (213*2π)/5343 weeks
214-.60966 .32348 (214*2π)/5342 weeks
215-.6256 -.23227 (215*2π)/5342 weeks
216-.21571 -.68838 (216*2π)/5342 weeks
217.29805 -.80874 (217*2π)/5342 weeks
218.87509 -.84179 (218*2π)/5342 weeks
2191.47313 -.37674 (219*2π)/5342 weeks
2201.6278 .34804 (220*2π)/5342 weeks
2211.2802 1.09575 (221*2π)/5342 weeks
222.4861 1.58797 (222*2π)/5342 weeks
223-.35672 1.28765 (223*2π)/5342 weeks
224-.93923 .59747 (224*2π)/5342 weeks
225-1.12968 -.29736 (225*2π)/5342 weeks
226-.72287 -1.13168 (226*2π)/5342 weeks
227.15143 -1.66547 (227*2π)/5342 weeks
2281.10331 -1.68036 (228*2π)/5342 weeks
2292.05086 -1.09292 (229*2π)/5342 weeks
2302.44348 -.03483 (230*2π)/5342 weeks
2312.26158 .9995 (231*2π)/5342 weeks
2321.50496 1.79479 (232*2π)/5342 weeks
233.24797 1.91143 (233*2π)/5342 weeks
234-.63623 1.36136 (234*2π)/5342 weeks
235-1.20126 .53671 (235*2π)/5342 weeks
236-1.00587 -.71428 (236*2π)/5342 weeks
237-.20943 -1.45111 (237*2π)/5342 weeks
238.74074 -1.69779 (238*2π)/5342 weeks
2391.92189 -1.4051 (239*2π)/5342 weeks
2402.79474 -.39904 (240*2π)/5342 weeks
2412.77485 .85731 (241*2π)/5342 weeks
2422.14348 2.09413 (242*2π)/5342 weeks
243.86441 2.74188 (243*2π)/5342 weeks
244-.52583 2.58722 (244*2π)/5342 weeks
245-1.55364 1.74183 (245*2π)/5342 weeks
246-2.09405 .38141 (246*2π)/5342 weeks
247-1.81455 -.95647 (247*2π)/5342 weeks
248-.96504 -1.88935 (248*2π)/5342 weeks
249.45494 -2.35685 (249*2π)/5342 weeks
2501.93093 -1.78815 (250*2π)/5342 weeks
2512.59631 -.55489 (251*2π)/5342 weeks
2522.53866 .70437 (252*2π)/5342 weeks
2531.70658 1.9039 (253*2π)/5342 weeks
254.23151 2.3587 (254*2π)/5342 weeks
255-1.16075 1.77043 (255*2π)/5342 weeks
256-1.75134 .34776 (256*2π)/5342 weeks
257-1.59518 -1.04913 (257*2π)/5342 weeks
258-.68501 -2.07298 (258*2π)/5342 weeks
259.53944 -2.35594 (259*2π)/5342 weeks
2602.10661 -2.03269 (260*2π)/5342 weeks
2613.04554 -.73088 (261*2π)/5342 weeks
2622.86938 .79312 (262*2π)/5342 weeks
2632.0115 1.86145 (263*2π)/5342 weeks
264.8304 2.4263 (264*2π)/5342 weeks
265-.40421 2.13306 (265*2π)/5342 weeks
266-1.5137 1.38729 (266*2π)/5342 weeks
267-2.00843   (267*2π)/5342 weeks
268-1.5137 -1.38729 (268*2π)/5342 weeks
269-.40421 -2.13306 (269*2π)/5342 weeks
270.8304 -2.4263 (270*2π)/5342 weeks
2712.0115 -1.86145 (271*2π)/5342 weeks
2722.86938 -.79312 (272*2π)/5342 weeks
2733.04554 .73088 (273*2π)/5342 weeks
2742.10661 2.03269 (274*2π)/5342 weeks
275.53944 2.35594 (275*2π)/5342 weeks
276-.68501 2.07298 (276*2π)/5342 weeks
277-1.59518 1.04913 (277*2π)/5342 weeks
278-1.75134 -.34776 (278*2π)/5342 weeks
279-1.16075 -1.77043 (279*2π)/5342 weeks
280.23151 -2.3587 (280*2π)/5342 weeks
2811.70658 -1.9039 (281*2π)/5342 weeks
2822.53866 -.70437 (282*2π)/5342 weeks
2832.59631 .55489 (283*2π)/5342 weeks
2841.93093 1.78815 (284*2π)/5342 weeks
285.45494 2.35685 (285*2π)/5342 weeks
286-.96504 1.88935 (286*2π)/5342 weeks
287-1.81455 .95647 (287*2π)/5342 weeks
288-2.09405 -.38141 (288*2π)/5342 weeks
289-1.55364 -1.74183 (289*2π)/5342 weeks
290-.52583 -2.58722 (290*2π)/5342 weeks
291.86441 -2.74188 (291*2π)/5342 weeks
2922.14348 -2.09413 (292*2π)/5342 weeks
2932.77485 -.85731 (293*2π)/5342 weeks
2942.79474 .39904 (294*2π)/5342 weeks
2951.92189 1.4051 (295*2π)/5342 weeks
296.74074 1.69779 (296*2π)/5342 weeks
297-.20943 1.45111 (297*2π)/5342 weeks
298-1.00587 .71428 (298*2π)/5342 weeks
299-1.20126 -.53671 (299*2π)/5342 weeks
300-.63623 -1.36136 (300*2π)/5342 weeks
301.24797 -1.91143 (301*2π)/5342 weeks
3021.50496 -1.79479 (302*2π)/5342 weeks
3032.26158 -.9995 (303*2π)/5342 weeks
3042.44348 .03483 (304*2π)/5342 weeks
3052.05086 1.09292 (305*2π)/5342 weeks
3061.10331 1.68036 (306*2π)/5342 weeks
307.15143 1.66547 (307*2π)/5342 weeks
308-.72287 1.13168 (308*2π)/5342 weeks
309-1.12968 .29736 (309*2π)/5342 weeks
310-.93923 -.59747 (310*2π)/5342 weeks
311-.35672 -1.28765 (311*2π)/5342 weeks
312.4861 -1.58797 (312*2π)/5342 weeks
3131.2802 -1.09575 (313*2π)/5342 weeks
3141.6278 -.34804 (314*2π)/5342 weeks
3151.47313 .37674 (315*2π)/5342 weeks
316.87509 .84179 (316*2π)/5342 weeks
317.29805 .80874 (317*2π)/5342 weeks
318-.21571 .68838 (318*2π)/5342 weeks
319-.6256 .23227 (319*2π)/5342 weeks
320-.60966 -.32348 (320*2π)/5342 weeks
321-.33797 -.74245 (321*2π)/5342 weeks
322-.12914 -.92714 (322*2π)/5342 weeks
323.06037 -1.00798 (323*2π)/5342 weeks
324.49443 -1.24668 (324*2π)/5342 weeks
3251.08224 -1.03565 (325*2π)/5342 weeks
3261.26081 -.59574 (326*2π)/5342 weeks
3271.32651 .20748 (327*2π)/5342 weeks
328.73196 .60692 (328*2π)/5342 weeks
329-.02146 .66725 (329*2π)/5342 weeks
330-.63401 .30357 (330*2π)/5342 weeks
331-1.0894 -.45982 (331*2π)/5342 weeks
332-.823 -1.45 (332*2π)/5342 weeks
333-.05804 -2.05411 (333*2π)/5342 weeks
334.8793 -2.045 (334*2π)/5342 weeks
3351.6339 -1.43142 (335*2π)/5342 weeks
3361.70888 -.65734 (336*2π)/5342 weeks
3371.62253 -.16882 (337*2π)/5342 weeks
3381.13252 .48725 (338*2π)/5342 weeks
339.24099 .46225 (339*2π)/5342 weeks
340-.19475 .14211 (340*2π)/5342 weeks
341-.59556 -.43388 (341*2π)/5342 weeks
342-.55666 -1.29852 (342*2π)/5342 weeks
343-.0395 -1.928 (343*2π)/5342 weeks
344.68902 -2.2317 (344*2π)/5342 weeks
3451.81523 -1.91309 (345*2π)/5342 weeks
3462.27192 -1.06172 (346*2π)/5342 weeks
3472.16331 -.34777 (347*2π)/5342 weeks
3481.76002 .33794 (348*2π)/5342 weeks
3491.10767 .59709 (349*2π)/5342 weeks
350.47558 .35478 (350*2π)/5342 weeks
351-.03132 -.07074 (351*2π)/5342 weeks
352-.0388 -.83593 (352*2π)/5342 weeks
353.52236 -1.36746 (353*2π)/5342 weeks
3541.19816 -1.48452 (354*2π)/5342 weeks
3551.90353 -1.21211 (355*2π)/5342 weeks
3562.25844 -.41999 (356*2π)/5342 weeks
3572.26654 .39593 (357*2π)/5341 weeks
3581.68049 1.13286 (358*2π)/5341 weeks
359.73943 1.43639 (359*2π)/5341 weeks
360-.17876 1.21377 (360*2π)/5341 weeks
361-.88088 .4975 (361*2π)/5341 weeks
362-.94934 -.53394 (362*2π)/5341 weeks
363-.48078 -1.34783 (363*2π)/5341 weeks
364.248 -1.83488 (364*2π)/5341 weeks
3651.14605 -1.70948 (365*2π)/5341 weeks
3661.79925 -1.16398 (366*2π)/5341 weeks
3672.15714 -.33141 (367*2π)/5341 weeks
3681.80884 .44319 (368*2π)/5341 weeks
3691.14356 .98822 (369*2π)/5341 weeks
370.3594 .99666 (370*2π)/5341 weeks
371-.41523 .70766 (371*2π)/5341 weeks
372-.88108 -.10395 (372*2π)/5341 weeks
373-.7613 -1.03645 (373*2π)/5341 weeks
374-.13641 -1.70831 (374*2π)/5341 weeks
375.82295 -1.8989 (375*2π)/5341 weeks
3761.51799 -1.47149 (376*2π)/5341 weeks
3771.77989 -.78554 (377*2π)/5341 weeks
3781.66051 -.17419 (378*2π)/5341 weeks
3791.46051 .233 (379*2π)/5341 weeks
380.96361 .74586 (380*2π)/5341 weeks
381.11559 .50691 (381*2π)/5341 weeks
382-.25848 .04363 (382*2π)/5341 weeks
383-.2578 -.52044 (383*2π)/5341 weeks
384-.05679 -1.07335 (384*2π)/5341 weeks
385.40305 -1.3069 (385*2π)/5341 weeks
386.76989 -1.357 (386*2π)/5341 weeks
3871.2987 -1.19017 (387*2π)/5341 weeks
3881.61173 -.57777 (388*2π)/5341 weeks
3891.41284 -.13858 (389*2π)/5341 weeks
3901.18481 .18782 (390*2π)/5341 weeks
391.5506 .21981 (391*2π)/5341 weeks
392.3706 -.04833 (392*2π)/5341 weeks
393.3333 -.23242 (393*2π)/5341 weeks
394.40365 -.59259 (394*2π)/5341 weeks
395.68724 -.57321 (395*2π)/5341 weeks
396.57306 -.31868 (396*2π)/5341 weeks
397.51085 -.45934 (397*2π)/5341 weeks
398.58574 -.52235 (398*2π)/5341 weeks
399.75563 -.65846 (399*2π)/5341 weeks
4001.11896 -.51383 (400*2π)/5341 weeks
401.97753 .12557 (401*2π)/5341 weeks
402.48918 .31826 (402*2π)/5341 weeks
403.19817 .1922 (403*2π)/5341 weeks
404-.185 -.25413 (404*2π)/5341 weeks
405-.16484 -.67444 (405*2π)/5341 weeks
406.27567 -.85012 (406*2π)/5341 weeks
407.61941 -.71595 (407*2π)/5341 weeks
408.63091 -.41958 (408*2π)/5341 weeks
409.45737 -.19327 (409*2π)/5341 weeks
410.15509 -.03879 (410*2π)/5341 weeks
411-.52331 -.045 (411*2π)/5341 weeks
412-.93393 -.81218 (412*2π)/5341 weeks
413-.624 -1.59105 (413*2π)/5341 weeks
414-.01753 -2.3819 (414*2π)/5341 weeks
4151.14101 -2.3726 (415*2π)/5341 weeks
4161.97742 -1.51939 (416*2π)/5341 weeks
4172.06479 -.38896 (417*2π)/5341 weeks
4181.58786 .58664 (418*2π)/5341 weeks
419.50966 .99356 (419*2π)/5341 weeks
420-.60962 .6574 (420*2π)/5341 weeks
421-1.49707 -.21959 (421*2π)/5341 weeks
422-1.64274 -1.43708 (422*2π)/5341 weeks
423-.7744 -2.81499 (423*2π)/5341 weeks
424.61207 -3.14537 (424*2π)/5341 weeks
4251.78541 -2.8824 (425*2π)/5341 weeks
4262.72424 -1.77888 (426*2π)/5341 weeks
4272.87437 -.15697 (427*2π)/5341 weeks
4282.1409 1.01839 (428*2π)/5341 weeks
429.75318 1.52611 (429*2π)/5341 weeks
430-.63853 1.13627 (430*2π)/5341 weeks
431-1.5788 .33455 (431*2π)/5341 weeks
432-1.75546 -.92329 (432*2π)/5341 weeks
433-1.33205 -2.17082 (433*2π)/5341 weeks
434-.40489 -3.0222 (434*2π)/5341 weeks
435.59925 -3.0001 (435*2π)/5341 weeks
4361.55009 -2.37222 (436*2π)/5341 weeks
4372.21763 -1.48264 (437*2π)/5341 weeks
4382.21186 -.50346 (438*2π)/5341 weeks
4391.56422 .25991 (439*2π)/5341 weeks
440.48358 .60879 (440*2π)/5341 weeks
441-.5168 .56433 (441*2π)/5341 weeks
442-1.16749 -.28142 (442*2π)/5341 weeks
443-1.63878 -1.01245 (443*2π)/5341 weeks
444-1.71366 -2.35591 (444*2π)/5341 weeks
445-.96571 -3.75671 (445*2π)/5341 weeks
446.48874 -4.41881 (446*2π)/5341 weeks
4472.4137 -4.1221 (447*2π)/5341 weeks
4483.83405 -2.52083 (448*2π)/5341 weeks
4494.06782 -.55985 (449*2π)/5341 weeks
4502.98827 1.08269 (450*2π)/5341 weeks
4511.10402 2.12365 (451*2π)/5341 weeks
452-.99108 1.43163 (452*2π)/5341 weeks
453-2.06753 .05108 (453*2π)/5341 weeks
454-2.57222 -1.75861 (454*2π)/5341 weeks
455-1.26582 -3.93476 (455*2π)/5341 weeks
456.65934 -4.33084 (456*2π)/5341 weeks
4572.54667 -3.96782 (457*2π)/5341 weeks
4584.11666 -2.02503 (458*2π)/5341 weeks
4593.52844 .27205 (459*2π)/5341 weeks
4602.4086 1.34168 (460*2π)/5341 weeks
461.6852 2.25801 (461*2π)/5341 weeks
462-1.45525 1.95177 (462*2π)/5341 weeks
463-2.83 .15407 (463*2π)/5341 weeks
464-3.01846 -1.69894 (464*2π)/5341 weeks
465-2.08007 -3.31302 (465*2π)/5341 weeks
466-.59094 -3.9353 (466*2π)/5341 weeks
467.26591 -3.56604 (467*2π)/5341 weeks
468.99313 -3.55965 (468*2π)/5341 weeks
4691.72044 -2.8466 (469*2π)/5341 weeks
4701.70048 -2.31706 (470*2π)/5341 weeks
4711.8742 -1.45034 (471*2π)/5341 weeks
4721.27383 -.5174 (472*2π)/5341 weeks
473.26499 -.28349 (473*2π)/5341 weeks
474-.85539 -.41107 (474*2π)/5341 weeks
475-2.19004 -1.67714 (475*2π)/5341 weeks
476-2.01469 -3.51748 (476*2π)/5341 weeks
477-1.04906 -4.92175 (477*2π)/5341 weeks
478.80482 -5.53307 (478*2π)/5341 weeks
4792.57829 -5.21207 (479*2π)/5341 weeks
4803.65333 -3.3902 (480*2π)/5341 weeks
4813.67302 -1.91378 (481*2π)/5341 weeks
4822.7253 -.59464 (482*2π)/5341 weeks
4831.49228 -.20137 (483*2π)/5341 weeks
484.25046 -.6933 (484*2π)/5341 weeks
485-.4392 -1.25442 (485*2π)/5341 weeks
486-1.1579 -2.37254 (486*2π)/5341 weeks
487-.29378 -3.44308 (487*2π)/5341 weeks
488.31788 -4.54955 (488*2π)/5341 weeks
4891.68015 -4.64545 (489*2π)/5341 weeks
4902.88998 -3.63361 (490*2π)/5341 weeks
4913.51848 -2.66078 (491*2π)/5341 weeks
4923.35701 -1.34808 (492*2π)/5341 weeks
4932.35952 -.46444 (493*2π)/5341 weeks
4941.64064 .683 (494*2π)/5341 weeks
495-.82237 1.08373 (495*2π)/5341 weeks
496-2.83554 -.67517 (496*2π)/5341 weeks
497-3.34229 -2.95961 (497*2π)/5341 weeks
498-3.11419 -5.1412 (498*2π)/5341 weeks
499-1.62494 -7.72416 (499*2π)/5341 weeks
5001.26278 -8.75075 (500*2π)/5341 weeks
5014.32562 -8.46154 (501*2π)/5341 weeks
5027.60752 -5.37655 (502*2π)/5341 weeks
5037.87549 -.85539 (503*2π)/5341 weeks
5045.02408 2.22703 (504*2π)/5341 weeks
5051.09555 3.20234 (505*2π)/5341 weeks
506-3.27502 1.80362 (506*2π)/5341 weeks
507-4.99685 -1.8636 (507*2π)/5341 weeks
508-4.50002 -5.67668 (508*2π)/5341 weeks
509-1.13796 -9.58638 (509*2π)/5341 weeks
5102.83605 -9.54851 (510*2π)/5341 weeks
5115.93766 -6.73538 (511*2π)/5341 weeks
5126.62011 -1.93909 (512*2π)/5341 weeks
5134.34357 1.42147 (513*2π)/5341 weeks
514.65694 2.3467 (514*2π)/5341 weeks
515-3.97607 1.49168 (515*2π)/5341 weeks
516-6.6958 -1.12955 (516*2π)/5341 weeks
517-9.21571 -5.50464 (517*2π)/5341 weeks
518-7.6826 -10.85417 (518*2π)/5341 weeks
519-6.05452 -14.02361 (519*2π)/5341 weeks
520-3.24468 -17.13756 (520*2π)/5341 weeks
5213.04149 -18.98559 (521*2π)/5341 weeks
5226.52368 -17.30407 (522*2π)/5341 weeks
52311.58403 -14.02657 (523*2π)/5341 weeks
52412.53004 -8.15094 (524*2π)/5341 weeks
5259.87344 -4.02355 (525*2π)/5341 weeks
5263.15608 .82202 (526*2π)/5341 weeks
527-8.50656 .23374 (527*2π)/5341 weeks
528-19.5762 -11.75834 (528*2π)/5341 weeks
529-19.85607 -31.66249 (529*2π)/5341 weeks
530-11.35003 -53.94716 (530*2π)/5341 weeks
53111.39666 -71.30047 (531*2π)/5341 weeks
53247.34013 -72.83321 (532*2π)/5341 weeks



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