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Fourier Analysis of EEV (ProShares UltraShort MSCI Emerging Markets)


EEV (ProShares UltraShort MSCI Emerging Markets) appears to have interesting cyclic behaviour every 39 weeks (18.2328*sine), 42 weeks (17.7115*sine), and 46 weeks (16.8509*sine).

EEV (ProShares UltraShort MSCI Emerging Markets) has an average price of 76.41 (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 4/23/2018 for EEV (ProShares UltraShort MSCI Emerging Markets), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
076.40602   0 
185.46869 54.62313 (1*2π)/548548 weeks
247.70014 71.11025 (2*2π)/548274 weeks
313.70388 70.92702 (3*2π)/548183 weeks
4-8.88632 54.68787 (4*2π)/548137 weeks
5-18.88953 33.04671 (5*2π)/548110 weeks
6-20.24785 14.3783 (6*2π)/54891 weeks
7-10.5724 1.33685 (7*2π)/54878 weeks
81.46674 -1.05226 (8*2π)/54869 weeks
99.10399 2.42301 (9*2π)/54861 weeks
1011.3994 6.35826 (10*2π)/54855 weeks
1111.66438 12.18929 (11*2π)/54850 weeks
127.8675 16.85094 (12*2π)/54846 weeks
134.5478 17.71153 (13*2π)/54842 weeks
14-1.40275 18.23281 (14*2π)/54839 weeks
15-4.63017 14.86591 (15*2π)/54837 weeks
16-6.69748 11.47286 (16*2π)/54834 weeks
17-8.99692 7.97395 (17*2π)/54832 weeks
18-7.89361 2.69343 (18*2π)/54830 weeks
19-5.1864 -.10202 (19*2π)/54829 weeks
20-1.70252 -2.50114 (20*2π)/54827 weeks
211.99353 -1.90602 (21*2π)/54826 weeks
225.56224 .28412 (22*2π)/54825 weeks
237.18389 3.95601 (23*2π)/54824 weeks
245.0899 7.49388 (24*2π)/54823 weeks
251.2036 9.20099 (25*2π)/54822 weeks
26-3.02033 8.61892 (26*2π)/54821 weeks
27-4.5808 4.65418 (27*2π)/54820 weeks
28-4.39157 .8001 (28*2π)/54820 weeks
29-2.08928 -2.67046 (29*2π)/54819 weeks
301.9039 -3.15897 (30*2π)/54818 weeks
315.50758 -1.67753 (31*2π)/54818 weeks
327.94856 1.72272 (32*2π)/54817 weeks
337.19794 5.85939 (33*2π)/54817 weeks
343.75823 8.26965 (34*2π)/54816 weeks
35.89129 8.46672 (35*2π)/54816 weeks
36-1.80915 7.36212 (36*2π)/54815 weeks
37-3.06188 4.89012 (37*2π)/54815 weeks
38-3.25294 2.82266 (38*2π)/54814 weeks
39-2.758 .64603 (39*2π)/54814 weeks
40-.86333 -1.03825 (40*2π)/54814 weeks
411.5124 -.71945 (41*2π)/54813 weeks
422.27849 .44062 (42*2π)/54813 weeks
433.23687 1.16334 (43*2π)/54813 weeks
443.44271 2.3944 (44*2π)/54812 weeks
452.84955 3.43902 (45*2π)/54812 weeks
461.95715 4.5155 (46*2π)/54812 weeks
47.67663 4.49726 (47*2π)/54812 weeks
48-.2943 3.4427 (48*2π)/54811 weeks
49-1.03026 2.84023 (49*2π)/54811 weeks
50-.55715 1.41958 (50*2π)/54811 weeks
51.11655 .8022 (51*2π)/54811 weeks
52.97191 .15519 (52*2π)/54811 weeks
532.19241 .37543 (53*2π)/54810 weeks
543.34359 1.27398 (54*2π)/54810 weeks
553.59161 2.75952 (55*2π)/54810 weeks
563.29754 4.39169 (56*2π)/54810 weeks
571.50774 5.2886 (57*2π)/54810 weeks
58-.19989 5.28371 (58*2π)/5489 weeks
59-1.55408 4.13331 (59*2π)/5489 weeks
60-2.17843 2.64064 (60*2π)/5489 weeks
61-1.67199 .83916 (61*2π)/5489 weeks
62-.33694 .3081 (62*2π)/5489 weeks
63.64751 .31468 (63*2π)/5489 weeks
641.6056 .77216 (64*2π)/5489 weeks
651.88965 1.68353 (65*2π)/5488 weeks
661.56956 2.26177 (66*2π)/5488 weeks
671.49903 3.02004 (67*2π)/5488 weeks
68.67539 3.51299 (68*2π)/5488 weeks
69.1278 3.53838 (69*2π)/5488 weeks
70-.92533 3.839 (70*2π)/5488 weeks
71-2.2595 3.03158 (71*2π)/5488 weeks
72-2.96538 1.35589 (72*2π)/5488 weeks
73-2.6768 -.40309 (73*2π)/5488 weeks
74-1.18089 -2.01277 (74*2π)/5487 weeks
75.83125 -2.18034 (75*2π)/5487 weeks
762.39613 -1.24088 (76*2π)/5487 weeks
773.4744 -.21178 (77*2π)/5487 weeks
784.00324 1.99596 (78*2π)/5487 weeks
792.51523 3.85344 (79*2π)/5487 weeks
80.71734 4.22437 (80*2π)/5487 weeks
81-1.08767 3.90534 (81*2π)/5487 weeks
82-2.50724 1.9487 (82*2π)/5487 weeks
83-2.09406 .14696 (83*2π)/5487 weeks
84-1.14628 -1.20154 (84*2π)/5487 weeks
85.69245 -2.08356 (85*2π)/5486 weeks
862.67497 -1.33635 (86*2π)/5486 weeks
873.79735 .05442 (87*2π)/5486 weeks
883.8286 2.00832 (88*2π)/5486 weeks
892.84128 3.75069 (89*2π)/5486 weeks
901.06966 4.37679 (90*2π)/5486 weeks
91-.4629 3.88338 (91*2π)/5486 weeks
92-1.57367 2.71432 (92*2π)/5486 weeks
93-1.79338 1.44134 (93*2π)/5486 weeks
94-1.31777 .5403 (94*2π)/5486 weeks
95-.91834 -.16099 (95*2π)/5486 weeks
96.15572 -.60238 (96*2π)/5486 weeks
971.04908 -.61576 (97*2π)/5486 weeks
981.76648 .03658 (98*2π)/5486 weeks
992.12932 1.05046 (99*2π)/5486 weeks
1001.99996 2.05622 (100*2π)/5485 weeks
1011.37642 2.62199 (101*2π)/5485 weeks
102.28082 2.80635 (102*2π)/5485 weeks
103-.91154 2.62391 (103*2π)/5485 weeks
104-1.60796 1.78565 (104*2π)/5485 weeks
105-1.69798 .60237 (105*2π)/5485 weeks
106-1.23535 -.64868 (106*2π)/5485 weeks
107-.33905 -1.32882 (107*2π)/5485 weeks
1081.04062 -1.43648 (108*2π)/5485 weeks
1092.30534 -.72918 (109*2π)/5485 weeks
1102.92646 .43356 (110*2π)/5485 weeks
1112.54891 1.89211 (111*2π)/5485 weeks
1121.53042 2.8613 (112*2π)/5485 weeks
113.43266 3.08591 (113*2π)/5485 weeks
114-.87362 2.67895 (114*2π)/5485 weeks
115-1.59927 1.31156 (115*2π)/5485 weeks
116-1.44732 .16347 (116*2π)/5485 weeks
117-.59073 -.64575 (117*2π)/5485 weeks
118.47451 -.96998 (118*2π)/5485 weeks
1191.50055 -.60353 (119*2π)/5485 weeks
1201.98494 .32637 (120*2π)/5485 weeks
1211.96841 1.40012 (121*2π)/5485 weeks
1221.25472 2.26259 (122*2π)/5484 weeks
123.16002 2.36758 (123*2π)/5484 weeks
124-.57951 1.6407 (124*2π)/5484 weeks
125-.9174 .99364 (125*2π)/5484 weeks
126-.64388 .19723 (126*2π)/5484 weeks
127.07757 -.00839 (127*2π)/5484 weeks
128.39729 .12265 (128*2π)/5484 weeks
129.58562 .30816 (129*2π)/5484 weeks
130.62168 .57075 (130*2π)/5484 weeks
131.36472 .83161 (131*2π)/5484 weeks
132.01073 .82087 (132*2π)/5484 weeks
133-.15604 .363 (133*2π)/5484 weeks
134-.07641 -.11868 (134*2π)/5484 weeks
135.29452 -.184 (135*2π)/5484 weeks
136.77577 -.23627 (136*2π)/5484 weeks
1371.16803 .12753 (137*2π)/5484 weeks
138.87507 .60536 (138*2π)/5484 weeks
139.5947 .60764 (139*2π)/5484 weeks
140.55473 .51554 (140*2π)/5484 weeks
141.51025 .40115 (141*2π)/5484 weeks
142.68706 .32175 (142*2π)/5484 weeks
143.56286 .57848 (143*2π)/5484 weeks
144.27381 .48391 (144*2π)/5484 weeks
145.35594 .20724 (145*2π)/5484 weeks
146.4146 -.0196 (146*2π)/5484 weeks
147.66046 -.31548 (147*2π)/5484 weeks
1481.2105 -.09722 (148*2π)/5484 weeks
1491.41479 .19633 (149*2π)/5484 weeks
1501.57581 .67328 (150*2π)/5484 weeks
1511.19039 1.19015 (151*2π)/5484 weeks
152.68354 1.30191 (152*2π)/5484 weeks
153.33536 1.26703 (153*2π)/5484 weeks
154-.09499 1.0224 (154*2π)/5484 weeks
155-.25857 .49309 (155*2π)/5484 weeks
156-.25488 -.0508 (156*2π)/5484 weeks
157.09973 -.48667 (157*2π)/5483 weeks
158.89658 -.73589 (158*2π)/5483 weeks
1591.39917 -.24933 (159*2π)/5483 weeks
1601.59109 .14474 (160*2π)/5483 weeks
1611.74434 .70264 (161*2π)/5483 weeks
1621.55653 1.34463 (162*2π)/5483 weeks
163.93795 1.78745 (163*2π)/5483 weeks
164-.00042 1.74723 (164*2π)/5483 weeks
165-.66172 1.19 (165*2π)/5483 weeks
166-.90004 .33804 (166*2π)/5483 weeks
167-.58676 -.49317 (167*2π)/5483 weeks
168.14372 -.92173 (168*2π)/5483 weeks
169.84723 -.99797 (169*2π)/5483 weeks
1701.59905 -.64142 (170*2π)/5483 weeks
1711.9978 -.00702 (171*2π)/5483 weeks
1721.93017 .92336 (172*2π)/5483 weeks
1731.46229 1.52213 (173*2π)/5483 weeks
174.70598 1.80354 (174*2π)/5483 weeks
175-.17554 1.54598 (175*2π)/5483 weeks
176-.76151 .97175 (176*2π)/5483 weeks
177-.9681 .08267 (177*2π)/5483 weeks
178-.55135 -.84874 (178*2π)/5483 weeks
179.24016 -1.34297 (179*2π)/5483 weeks
1801.13072 -1.38776 (180*2π)/5483 weeks
1811.89496 -.89799 (181*2π)/5483 weeks
1822.26262 -.07266 (182*2π)/5483 weeks
1832.18014 .63709 (183*2π)/5483 weeks
1841.63536 1.29022 (184*2π)/5483 weeks
185.96793 1.44647 (185*2π)/5483 weeks
186.35364 1.25824 (186*2π)/5483 weeks
187-.07541 .63858 (187*2π)/5483 weeks
188.0498 -.08162 (188*2π)/5483 weeks
189.524 -.40159 (189*2π)/5483 weeks
1901.18719 -.56318 (190*2π)/5483 weeks
1911.7937 -.2804 (191*2π)/5483 weeks
1922.11387 .3926 (192*2π)/5483 weeks
1932.20586 1.09578 (193*2π)/5483 weeks
1941.7386 1.89091 (194*2π)/5483 weeks
195.65215 2.1592 (195*2π)/5483 weeks
196-.03646 1.8756 (196*2π)/5483 weeks
197-.53178 1.28243 (197*2π)/5483 weeks
198-.60007 .45689 (198*2π)/5483 weeks
199-.23927 -.11199 (199*2π)/5483 weeks
200.17373 -.40388 (200*2π)/5483 weeks
201.99222 -.53514 (201*2π)/5483 weeks
2021.55412 .03979 (202*2π)/5483 weeks
2031.61848 .53636 (203*2π)/5483 weeks
2041.6473 1.21973 (204*2π)/5483 weeks
2051.0666 1.91608 (205*2π)/5483 weeks
206.1926 2.04558 (206*2π)/5483 weeks
207-.64322 1.61095 (207*2π)/5483 weeks
208-1.08659 .77912 (208*2π)/5483 weeks
209-.81336 -.09855 (209*2π)/5483 weeks
210-.25947 -.53824 (210*2π)/5483 weeks
211.44408 -.68775 (211*2π)/5483 weeks
2121.02289 -.41553 (212*2π)/5483 weeks
2131.39411 .32692 (213*2π)/5483 weeks
2141.15379 .74136 (214*2π)/5483 weeks
215.74672 1.19161 (215*2π)/5483 weeks
216.21524 1.17013 (216*2π)/5483 weeks
217.03651 .9304 (217*2π)/5483 weeks
218-.22593 .79046 (218*2π)/5483 weeks
219-.49366 .6164 (219*2π)/5483 weeks
220-.62173 .15662 (220*2π)/5482 weeks
221-.48089 -.42321 (221*2π)/5482 weeks
222-.02657 -.76013 (222*2π)/5482 weeks
223.41535 -.82786 (223*2π)/5482 weeks
2241.03034 -.75006 (224*2π)/5482 weeks
2251.50311 -.18734 (225*2π)/5482 weeks
2261.56655 .52492 (226*2π)/5482 weeks
2271.14097 1.17363 (227*2π)/5482 weeks
228.27098 1.53639 (228*2π)/5482 weeks
229-.46516 1.20563 (229*2π)/5482 weeks
230-.94512 .50277 (230*2π)/5482 weeks
231-1.07212 -.38627 (231*2π)/5482 weeks
232-.65975 -1.16067 (232*2π)/5482 weeks
233.19181 -1.63164 (233*2π)/5482 weeks
2341.09614 -1.63376 (234*2π)/5482 weeks
2351.99414 -1.06702 (235*2π)/5482 weeks
2362.381 -.06257 (236*2π)/5482 weeks
2372.23189 .91676 (237*2π)/5482 weeks
2381.53967 1.69031 (238*2π)/5482 weeks
239.34677 1.90393 (239*2π)/5482 weeks
240-.5331 1.43126 (240*2π)/5482 weeks
241-1.0821 .6977 (241*2π)/5482 weeks
242-1.08311 -.51591 (242*2π)/5482 weeks
243-.39469 -1.30672 (243*2π)/5482 weeks
244.50283 -1.61292 (244*2π)/5482 weeks
2451.60429 -1.54247 (245*2π)/5482 weeks
2462.52578 -.77801 (246*2π)/5482 weeks
2472.72196 .49848 (247*2π)/5482 weeks
2482.39851 1.69942 (248*2π)/5482 weeks
2491.35391 2.54686 (249*2π)/5482 weeks
250.02418 2.65963 (250*2π)/5482 weeks
251-1.16351 2.04887 (251*2π)/5482 weeks
252-1.9597 1.01603 (252*2π)/5482 weeks
253-1.97611 -.30761 (253*2π)/5482 weeks
254-1.33138 -1.42664 (254*2π)/5482 weeks
255-.30755 -2.21719 (255*2π)/5482 weeks
2561.13338 -2.22009 (256*2π)/5482 weeks
2572.22743 -1.24904 (257*2π)/5482 weeks
2582.54495 -.00334 (258*2π)/5482 weeks
2592.29671 1.21412 (259*2π)/5482 weeks
2601.23749 2.11369 (260*2π)/5482 weeks
261-.25874 2.15651 (261*2π)/5482 weeks
262-1.4952 1.31676 (262*2π)/5482 weeks
263-1.7609 .01173 (263*2π)/5482 weeks
264-1.35688 -1.29168 (264*2π)/5482 weeks
265-.34366 -2.15402 (265*2π)/5482 weeks
266.79042 -2.36278 (266*2π)/5482 weeks
2672.25189 -1.78904 (267*2π)/5482 weeks
2683.01687 -.44733 (268*2π)/5482 weeks
2692.7316 .93577 (269*2π)/5482 weeks
2701.85972 1.87945 (270*2π)/5482 weeks
271.69408 2.37429 (271*2π)/5482 weeks
272-.44508 2.06298 (272*2π)/5482 weeks
273-1.49423 1.32305 (273*2π)/5482 weeks
274-1.95559   (274*2π)/5482 weeks
275-1.49423 -1.32305 (275*2π)/5482 weeks
276-.44508 -2.06298 (276*2π)/5482 weeks
277.69408 -2.37429 (277*2π)/5482 weeks
2781.85972 -1.87945 (278*2π)/5482 weeks
2792.7316 -.93577 (279*2π)/5482 weeks
2803.01687 .44733 (280*2π)/5482 weeks
2812.25189 1.78904 (281*2π)/5482 weeks
282.79042 2.36278 (282*2π)/5482 weeks
283-.34366 2.15402 (283*2π)/5482 weeks
284-1.35688 1.29168 (284*2π)/5482 weeks
285-1.7609 -.01173 (285*2π)/5482 weeks
286-1.4952 -1.31676 (286*2π)/5482 weeks
287-.25874 -2.15651 (287*2π)/5482 weeks
2881.23749 -2.11369 (288*2π)/5482 weeks
2892.29671 -1.21412 (289*2π)/5482 weeks
2902.54495 .00334 (290*2π)/5482 weeks
2912.22743 1.24904 (291*2π)/5482 weeks
2921.13338 2.22009 (292*2π)/5482 weeks
293-.30755 2.21719 (293*2π)/5482 weeks
294-1.33138 1.42664 (294*2π)/5482 weeks
295-1.97611 .30761 (295*2π)/5482 weeks
296-1.9597 -1.01603 (296*2π)/5482 weeks
297-1.16351 -2.04887 (297*2π)/5482 weeks
298.02418 -2.65963 (298*2π)/5482 weeks
2991.35391 -2.54686 (299*2π)/5482 weeks
3002.39851 -1.69942 (300*2π)/5482 weeks
3012.72196 -.49848 (301*2π)/5482 weeks
3022.52578 .77801 (302*2π)/5482 weeks
3031.60429 1.54247 (303*2π)/5482 weeks
304.50283 1.61292 (304*2π)/5482 weeks
305-.39469 1.30672 (305*2π)/5482 weeks
306-1.08311 .51591 (306*2π)/5482 weeks
307-1.0821 -.6977 (307*2π)/5482 weeks
308-.5331 -1.43126 (308*2π)/5482 weeks
309.34677 -1.90393 (309*2π)/5482 weeks
3101.53967 -1.69031 (310*2π)/5482 weeks
3112.23189 -.91676 (311*2π)/5482 weeks
3122.381 .06257 (312*2π)/5482 weeks
3131.99414 1.06702 (313*2π)/5482 weeks
3141.09614 1.63376 (314*2π)/5482 weeks
315.19181 1.63164 (315*2π)/5482 weeks
316-.65975 1.16067 (316*2π)/5482 weeks
317-1.07212 .38627 (317*2π)/5482 weeks
318-.94512 -.50277 (318*2π)/5482 weeks
319-.46516 -1.20563 (319*2π)/5482 weeks
320.27098 -1.53639 (320*2π)/5482 weeks
3211.14097 -1.17363 (321*2π)/5482 weeks
3221.56655 -.52492 (322*2π)/5482 weeks
3231.50311 .18734 (323*2π)/5482 weeks
3241.03034 .75006 (324*2π)/5482 weeks
325.41535 .82786 (325*2π)/5482 weeks
326-.02657 .76013 (326*2π)/5482 weeks
327-.48089 .42321 (327*2π)/5482 weeks
328-.62173 -.15662 (328*2π)/5482 weeks
329-.49366 -.6164 (329*2π)/5482 weeks
330-.22593 -.79046 (330*2π)/5482 weeks
331.03651 -.9304 (331*2π)/5482 weeks
332.21524 -1.17013 (332*2π)/5482 weeks
333.74672 -1.19161 (333*2π)/5482 weeks
3341.15379 -.74136 (334*2π)/5482 weeks
3351.39411 -.32692 (335*2π)/5482 weeks
3361.02289 .41553 (336*2π)/5482 weeks
337.44408 .68775 (337*2π)/5482 weeks
338-.25947 .53824 (338*2π)/5482 weeks
339-.81336 .09855 (339*2π)/5482 weeks
340-1.08659 -.77912 (340*2π)/5482 weeks
341-.64322 -1.61095 (341*2π)/5482 weeks
342.1926 -2.04558 (342*2π)/5482 weeks
3431.0666 -1.91608 (343*2π)/5482 weeks
3441.6473 -1.21973 (344*2π)/5482 weeks
3451.61848 -.53636 (345*2π)/5482 weeks
3461.55412 -.03979 (346*2π)/5482 weeks
347.99222 .53514 (347*2π)/5482 weeks
348.17373 .40388 (348*2π)/5482 weeks
349-.23927 .11199 (349*2π)/5482 weeks
350-.60007 -.45689 (350*2π)/5482 weeks
351-.53178 -1.28243 (351*2π)/5482 weeks
352-.03646 -1.8756 (352*2π)/5482 weeks
353.65215 -2.1592 (353*2π)/5482 weeks
3541.7386 -1.89091 (354*2π)/5482 weeks
3552.20586 -1.09578 (355*2π)/5482 weeks
3562.11387 -.3926 (356*2π)/5482 weeks
3571.7937 .2804 (357*2π)/5482 weeks
3581.18719 .56318 (358*2π)/5482 weeks
359.524 .40159 (359*2π)/5482 weeks
360.0498 .08162 (360*2π)/5482 weeks
361-.07541 -.63858 (361*2π)/5482 weeks
362.35364 -1.25824 (362*2π)/5482 weeks
363.96793 -1.44647 (363*2π)/5482 weeks
3641.63536 -1.29022 (364*2π)/5482 weeks
3652.18014 -.63709 (365*2π)/5482 weeks
3662.26262 .07266 (366*2π)/5481 weeks
3671.89496 .89799 (367*2π)/5481 weeks
3681.13072 1.38776 (368*2π)/5481 weeks
369.24016 1.34297 (369*2π)/5481 weeks
370-.55135 .84874 (370*2π)/5481 weeks
371-.9681 -.08267 (371*2π)/5481 weeks
372-.76151 -.97175 (372*2π)/5481 weeks
373-.17554 -1.54598 (373*2π)/5481 weeks
374.70598 -1.80354 (374*2π)/5481 weeks
3751.46229 -1.52213 (375*2π)/5481 weeks
3761.93017 -.92336 (376*2π)/5481 weeks
3771.9978 .00702 (377*2π)/5481 weeks
3781.59905 .64142 (378*2π)/5481 weeks
379.84723 .99797 (379*2π)/5481 weeks
380.14372 .92173 (380*2π)/5481 weeks
381-.58676 .49317 (381*2π)/5481 weeks
382-.90004 -.33804 (382*2π)/5481 weeks
383-.66172 -1.19 (383*2π)/5481 weeks
384-.00042 -1.74723 (384*2π)/5481 weeks
385.93795 -1.78745 (385*2π)/5481 weeks
3861.55653 -1.34463 (386*2π)/5481 weeks
3871.74434 -.70264 (387*2π)/5481 weeks
3881.59109 -.14474 (388*2π)/5481 weeks
3891.39917 .24933 (389*2π)/5481 weeks
390.89658 .73589 (390*2π)/5481 weeks
391.09973 .48667 (391*2π)/5481 weeks
392-.25488 .0508 (392*2π)/5481 weeks
393-.25857 -.49309 (393*2π)/5481 weeks
394-.09499 -1.0224 (394*2π)/5481 weeks
395.33536 -1.26703 (395*2π)/5481 weeks
396.68354 -1.30191 (396*2π)/5481 weeks
3971.19039 -1.19015 (397*2π)/5481 weeks
3981.57581 -.67328 (398*2π)/5481 weeks
3991.41479 -.19633 (399*2π)/5481 weeks
4001.2105 .09722 (400*2π)/5481 weeks
401.66046 .31548 (401*2π)/5481 weeks
402.4146 .0196 (402*2π)/5481 weeks
403.35594 -.20724 (403*2π)/5481 weeks
404.27381 -.48391 (404*2π)/5481 weeks
405.56286 -.57848 (405*2π)/5481 weeks
406.68706 -.32175 (406*2π)/5481 weeks
407.51025 -.40115 (407*2π)/5481 weeks
408.55473 -.51554 (408*2π)/5481 weeks
409.5947 -.60764 (409*2π)/5481 weeks
410.87507 -.60536 (410*2π)/5481 weeks
4111.16803 -.12753 (411*2π)/5481 weeks
412.77577 .23627 (412*2π)/5481 weeks
413.29452 .184 (413*2π)/5481 weeks
414-.07641 .11868 (414*2π)/5481 weeks
415-.15604 -.363 (415*2π)/5481 weeks
416.01073 -.82087 (416*2π)/5481 weeks
417.36472 -.83161 (417*2π)/5481 weeks
418.62168 -.57075 (418*2π)/5481 weeks
419.58562 -.30816 (419*2π)/5481 weeks
420.39729 -.12265 (420*2π)/5481 weeks
421.07757 .00839 (421*2π)/5481 weeks
422-.64388 -.19723 (422*2π)/5481 weeks
423-.9174 -.99364 (423*2π)/5481 weeks
424-.57951 -1.6407 (424*2π)/5481 weeks
425.16002 -2.36758 (425*2π)/5481 weeks
4261.25472 -2.26259 (426*2π)/5481 weeks
4271.96841 -1.40012 (427*2π)/5481 weeks
4281.98494 -.32637 (428*2π)/5481 weeks
4291.50055 .60353 (429*2π)/5481 weeks
430.47451 .96998 (430*2π)/5481 weeks
431-.59073 .64575 (431*2π)/5481 weeks
432-1.44732 -.16347 (432*2π)/5481 weeks
433-1.59927 -1.31156 (433*2π)/5481 weeks
434-.87362 -2.67895 (434*2π)/5481 weeks
435.43266 -3.08591 (435*2π)/5481 weeks
4361.53042 -2.8613 (436*2π)/5481 weeks
4372.54891 -1.89211 (437*2π)/5481 weeks
4382.92646 -.43356 (438*2π)/5481 weeks
4392.30534 .72918 (439*2π)/5481 weeks
4401.04062 1.43648 (440*2π)/5481 weeks
441-.33905 1.32882 (441*2π)/5481 weeks
442-1.23535 .64868 (442*2π)/5481 weeks
443-1.69798 -.60237 (443*2π)/5481 weeks
444-1.60796 -1.78565 (444*2π)/5481 weeks
445-.91154 -2.62391 (445*2π)/5481 weeks
446.28082 -2.80635 (446*2π)/5481 weeks
4471.37642 -2.62199 (447*2π)/5481 weeks
4481.99996 -2.05622 (448*2π)/5481 weeks
4492.12932 -1.05046 (449*2π)/5481 weeks
4501.76648 -.03658 (450*2π)/5481 weeks
4511.04908 .61576 (451*2π)/5481 weeks
452.15572 .60238 (452*2π)/5481 weeks
453-.91834 .16099 (453*2π)/5481 weeks
454-1.31777 -.5403 (454*2π)/5481 weeks
455-1.79338 -1.44134 (455*2π)/5481 weeks
456-1.57367 -2.71432 (456*2π)/5481 weeks
457-.4629 -3.88338 (457*2π)/5481 weeks
4581.06966 -4.37679 (458*2π)/5481 weeks
4592.84128 -3.75069 (459*2π)/5481 weeks
4603.8286 -2.00832 (460*2π)/5481 weeks
4613.79735 -.05442 (461*2π)/5481 weeks
4622.67497 1.33635 (462*2π)/5481 weeks
463.69245 2.08356 (463*2π)/5481 weeks
464-1.14628 1.20154 (464*2π)/5481 weeks
465-2.09406 -.14696 (465*2π)/5481 weeks
466-2.50724 -1.9487 (466*2π)/5481 weeks
467-1.08767 -3.90534 (467*2π)/5481 weeks
468.71734 -4.22437 (468*2π)/5481 weeks
4692.51523 -3.85344 (469*2π)/5481 weeks
4704.00324 -1.99596 (470*2π)/5481 weeks
4713.4744 .21178 (471*2π)/5481 weeks
4722.39613 1.24088 (472*2π)/5481 weeks
473.83125 2.18034 (473*2π)/5481 weeks
474-1.18089 2.01277 (474*2π)/5481 weeks
475-2.6768 .40309 (475*2π)/5481 weeks
476-2.96538 -1.35589 (476*2π)/5481 weeks
477-2.2595 -3.03158 (477*2π)/5481 weeks
478-.92533 -3.839 (478*2π)/5481 weeks
479.1278 -3.53838 (479*2π)/5481 weeks
480.67539 -3.51299 (480*2π)/5481 weeks
4811.49903 -3.02004 (481*2π)/5481 weeks
4821.56956 -2.26177 (482*2π)/5481 weeks
4831.88965 -1.68353 (483*2π)/5481 weeks
4841.6056 -.77216 (484*2π)/5481 weeks
485.64751 -.31468 (485*2π)/5481 weeks
486-.33694 -.3081 (486*2π)/5481 weeks
487-1.67199 -.83916 (487*2π)/5481 weeks
488-2.17843 -2.64064 (488*2π)/5481 weeks
489-1.55408 -4.13331 (489*2π)/5481 weeks
490-.19989 -5.28371 (490*2π)/5481 weeks
4911.50774 -5.2886 (491*2π)/5481 weeks
4923.29754 -4.39169 (492*2π)/5481 weeks
4933.59161 -2.75952 (493*2π)/5481 weeks
4943.34359 -1.27398 (494*2π)/5481 weeks
4952.19241 -.37543 (495*2π)/5481 weeks
496.97191 -.15519 (496*2π)/5481 weeks
497.11655 -.8022 (497*2π)/5481 weeks
498-.55715 -1.41958 (498*2π)/5481 weeks
499-1.03026 -2.84023 (499*2π)/5481 weeks
500-.2943 -3.4427 (500*2π)/5481 weeks
501.67663 -4.49726 (501*2π)/5481 weeks
5021.95715 -4.5155 (502*2π)/5481 weeks
5032.84955 -3.43902 (503*2π)/5481 weeks
5043.44271 -2.3944 (504*2π)/5481 weeks
5053.23687 -1.16334 (505*2π)/5481 weeks
5062.27849 -.44062 (506*2π)/5481 weeks
5071.5124 .71945 (507*2π)/5481 weeks
508-.86333 1.03825 (508*2π)/5481 weeks
509-2.758 -.64603 (509*2π)/5481 weeks
510-3.25294 -2.82266 (510*2π)/5481 weeks
511-3.06188 -4.89012 (511*2π)/5481 weeks
512-1.80915 -7.36212 (512*2π)/5481 weeks
513.89129 -8.46672 (513*2π)/5481 weeks
5143.75823 -8.26965 (514*2π)/5481 weeks
5157.19794 -5.85939 (515*2π)/5481 weeks
5167.94856 -1.72272 (516*2π)/5481 weeks
5175.50758 1.67753 (517*2π)/5481 weeks
5181.9039 3.15897 (518*2π)/5481 weeks
519-2.08928 2.67046 (519*2π)/5481 weeks
520-4.39157 -.8001 (520*2π)/5481 weeks
521-4.5808 -4.65418 (521*2π)/5481 weeks
522-3.02033 -8.61892 (522*2π)/5481 weeks
5231.2036 -9.20099 (523*2π)/5481 weeks
5245.0899 -7.49388 (524*2π)/5481 weeks
5257.18389 -3.95601 (525*2π)/5481 weeks
5265.56224 -.28412 (526*2π)/5481 weeks
5271.99353 1.90602 (527*2π)/5481 weeks
528-1.70252 2.50114 (528*2π)/5481 weeks
529-5.1864 .10202 (529*2π)/5481 weeks
530-7.89361 -2.69343 (530*2π)/5481 weeks
531-8.99692 -7.97395 (531*2π)/5481 weeks
532-6.69748 -11.47286 (532*2π)/5481 weeks
533-4.63017 -14.86591 (533*2π)/5481 weeks
534-1.40275 -18.23281 (534*2π)/5481 weeks
5354.5478 -17.71153 (535*2π)/5481 weeks
5367.8675 -16.85094 (536*2π)/5481 weeks
53711.66438 -12.18929 (537*2π)/5481 weeks
53811.3994 -6.35826 (538*2π)/5481 weeks
5399.10399 -2.42301 (539*2π)/5481 weeks
5401.46674 1.05226 (540*2π)/5481 weeks
541-10.5724 -1.33685 (541*2π)/5481 weeks
542-20.24785 -14.3783 (542*2π)/5481 weeks
543-18.88953 -33.04671 (543*2π)/5481 weeks
544-8.88632 -54.68787 (544*2π)/5481 weeks
54513.70388 -70.92702 (545*2π)/5481 weeks
54647.70014 -71.11025 (546*2π)/5481 weeks



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