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Fourier Analysis of MZZ (ProShares UltraShort MidCap400)


MZZ (ProShares UltraShort MidCap400) appears to have interesting cyclic behaviour every 56 weeks (46.2333*sine), 40 weeks (30.0175*sine), and 51 weeks (23.8738*cosine).

MZZ (ProShares UltraShort MidCap400) has an average price of 297.79 (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 7/13/2006 to 3/20/2017 for MZZ (ProShares UltraShort MidCap400), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0297.791   0 
1120.3365 333.8416 (1*2π)/559559 weeks
2-75.33955 141.1732 (2*2π)/559280 weeks
3-24.02388 -5.87997 (3*2π)/559186 weeks
464.02817 23.42342 (4*2π)/559140 weeks
538.82795 81.93512 (5*2π)/559112 weeks
6-21.79468 66.89172 (6*2π)/55993 weeks
7-17.26402 7.10634 (7*2π)/55980 weeks
836.91187 9.43924 (8*2π)/55970 weeks
924.8645 54.4347 (9*2π)/55962 weeks
10-8.78122 46.23329 (10*2π)/55956 weeks
11-23.87377 20.9705 (11*2π)/55951 weeks
121.97319 -5.29219 (12*2π)/55947 weeks
1321.64582 16.22626 (13*2π)/55943 weeks
1410.06396 30.01753 (14*2π)/55940 weeks
15-4.43573 26.62051 (15*2π)/55937 weeks
16-6.06537 14.50093 (16*2π)/55935 weeks
17-2.85546 9.14921 (17*2π)/55933 weeks
188.50425 4.78391 (18*2π)/55931 weeks
1910.74442 16.61694 (19*2π)/55929 weeks
204.41136 18.08768 (20*2π)/55928 weeks
21.59853 16.58711 (21*2π)/55927 weeks
22-1.79424 12.89938 (22*2π)/55925 weeks
232.0219 8.04156 (23*2π)/55924 weeks
244.60309 15.16668 (24*2π)/55923 weeks
25-3.35378 16.79494 (25*2π)/55922 weeks
26-9.48931 5.1765 (26*2π)/55922 weeks
276.11069 -3.59034 (27*2π)/55921 weeks
2814.38246 9.60304 (28*2π)/55920 weeks
294.93172 22.38294 (29*2π)/55919 weeks
30-13.00352 13.32362 (30*2π)/55919 weeks
31-5.14729 -6.37421 (31*2π)/55918 weeks
3214.9292 -.24839 (32*2π)/55917 weeks
3312.47554 21.52367 (33*2π)/55917 weeks
34-11.5943 21.22372 (34*2π)/55916 weeks
35-12.17112 -2.49858 (35*2π)/55916 weeks
365.92531 -4.6214 (36*2π)/55916 weeks
3710.97332 7.76765 (37*2π)/55915 weeks
38.51218 13.8771 (38*2π)/55915 weeks
39-4.41643 6.02629 (39*2π)/55914 weeks
40-.02272 .94628 (40*2π)/55914 weeks
415.76969 2.58556 (41*2π)/55914 weeks
424.0666 9.85271 (42*2π)/55913 weeks
43-1.12465 6.4251 (43*2π)/55913 weeks
441.70031 4.38548 (44*2π)/55913 weeks
451.93963 5.33004 (45*2π)/55912 weeks
46.22551 5.15955 (46*2π)/55912 weeks
471.57149 1.81104 (47*2π)/55912 weeks
486.04101 3.94637 (48*2π)/55912 weeks
494.50137 7.01555 (49*2π)/55911 weeks
501.06948 7.90147 (50*2π)/55911 weeks
51.5398 5.58443 (51*2π)/55911 weeks
522.14274 4.58684 (52*2π)/55911 weeks
531.85467 7.52559 (53*2π)/55911 weeks
54-1.9309 6.43158 (54*2π)/55910 weeks
55-2.66709 2.06965 (55*2π)/55910 weeks
562.55694 -1.67419 (56*2π)/55910 weeks
578.02928 4.764 (57*2π)/55910 weeks
58.55708 9.1101 (58*2π)/55910 weeks
59-2.84588 3.40767 (59*2π)/5599 weeks
601.58743 .63734 (60*2π)/5599 weeks
614.11234 3.1739 (61*2π)/5599 weeks
62.64902 5.69815 (62*2π)/5599 weeks
63.41969 .27608 (63*2π)/5599 weeks
645.54484 2.06139 (64*2π)/5599 weeks
655.33929 6.61543 (65*2π)/5599 weeks
66-.47388 7.55019 (66*2π)/5598 weeks
67-1.3981 1.97544 (67*2π)/5598 weeks
682.96067 2.43632 (68*2π)/5598 weeks
692.75124 3.6461 (69*2π)/5598 weeks
70.7295 4.51699 (70*2π)/5598 weeks
711.98242 .31193 (71*2π)/5598 weeks
727.15074 4.69078 (72*2π)/5598 weeks
731.6004 10.21518 (73*2π)/5598 weeks
74-4.69614 5.86353 (74*2π)/5598 weeks
75-2.36512 -2.32623 (75*2π)/5597 weeks
765.69614 .2089 (76*2π)/5597 weeks
773.62365 5.19004 (77*2π)/5597 weeks
781.26278 6.40726 (78*2π)/5597 weeks
79-3.50107 2.39384 (79*2π)/5597 weeks
802.81299 -2.57598 (80*2π)/5597 weeks
816.80397 3.88118 (81*2π)/5597 weeks
822.48508 8.30048 (82*2π)/5597 weeks
83-3.71557 5.008 (83*2π)/5597 weeks
84-.82793 -1.16423 (84*2π)/5597 weeks
854.20346 -.38096 (85*2π)/5597 weeks
866.05233 5.73073 (86*2π)/5597 weeks
87-1.68735 8.23934 (87*2π)/5596 weeks
88-4.40542 .8299 (88*2π)/5596 weeks
891.29421 -2.94364 (89*2π)/5596 weeks
905.39886 1.42062 (90*2π)/5596 weeks
912.40449 5.14706 (91*2π)/5596 weeks
92-.46297 3.18749 (92*2π)/5596 weeks
93.81554 .82014 (93*2π)/5596 weeks
942.87615 1.94348 (94*2π)/5596 weeks
951.3499 3.2432 (95*2π)/5596 weeks
961.58447 1.69058 (96*2π)/5596 weeks
971.68318 3.24959 (97*2π)/5596 weeks
98-.25968 2.02697 (98*2π)/5596 weeks
99.94807 -.83871 (99*2π)/5596 weeks
1005.02961 -.12604 (100*2π)/5596 weeks
1015.17201 4.65144 (101*2π)/5596 weeks
102.22076 5.69603 (102*2π)/5595 weeks
103-1.56931 1.28982 (103*2π)/5595 weeks
1042.88327 -1.12821 (104*2π)/5595 weeks
1055.83732 3.73692 (105*2π)/5595 weeks
1061.00237 6.9647 (106*2π)/5595 weeks
107-3.71607 3.13723 (107*2π)/5595 weeks
108-.33943 -2.85995 (108*2π)/5595 weeks
1095.33117 -1.16938 (109*2π)/5595 weeks
1105.38087 5.08116 (110*2π)/5595 weeks
111-1.43119 5.80262 (111*2π)/5595 weeks
112-2.40366 -.74129 (112*2π)/5595 weeks
1134.12559 -2.66424 (113*2π)/5595 weeks
1146.70521 3.22619 (114*2π)/5595 weeks
1152.42082 6.57418 (115*2π)/5595 weeks
116-2.39466 4.16766 (116*2π)/5595 weeks
117-.67159 -1.57237 (117*2π)/5595 weeks
1184.27437 -.38645 (118*2π)/5595 weeks
1194.10234 3.6807 (119*2π)/5595 weeks
1201.10193 4.75882 (120*2π)/5595 weeks
121-.91963 2.35321 (121*2π)/5595 weeks
1221.16694 .02345 (122*2π)/5595 weeks
1233.92308 1.72169 (123*2π)/5595 weeks
1241.71413 4.91848 (124*2π)/5595 weeks
125-2.01812 2.62118 (125*2π)/5594 weeks
126.41792 -1.44444 (126*2π)/5594 weeks
1273.57141 .30944 (127*2π)/5594 weeks
1282.94325 3.22271 (128*2π)/5594 weeks
129.68028 3.30922 (129*2π)/5594 weeks
130-.128 2.10901 (130*2π)/5594 weeks
131.13968 .19847 (131*2π)/5594 weeks
1322.27236 -.0466 (132*2π)/5594 weeks
1332.64494 1.9843 (133*2π)/5594 weeks
134.97512 1.65125 (134*2π)/5594 weeks
1352.17575 -.0866 (135*2π)/5594 weeks
1363.65122 1.84982 (136*2π)/5594 weeks
1372.07065 3.39072 (137*2π)/5594 weeks
138.06569 3.25397 (138*2π)/5594 weeks
139-.3074 .59619 (139*2π)/5594 weeks
1401.7658 .19819 (140*2π)/5594 weeks
1412.13557 .35226 (141*2π)/5594 weeks
1423.38502 1.39252 (142*2π)/5594 weeks
1432.37092 2.68588 (143*2π)/5594 weeks
144.46749 2.87949 (144*2π)/5594 weeks
145.40348 -.28625 (145*2π)/5594 weeks
1463.86342 .9157 (146*2π)/5594 weeks
1471.77405 3.98658 (147*2π)/5594 weeks
148-.33937 1.88899 (148*2π)/5594 weeks
1491.02023 -.33896 (149*2π)/5594 weeks
1503.85772 .98958 (150*2π)/5594 weeks
1512.03979 3.73448 (151*2π)/5594 weeks
152-.4357 2.60061 (152*2π)/5594 weeks
153-.01182 -.49276 (153*2π)/5594 weeks
1543.40794 .34562 (154*2π)/5594 weeks
1552.19947 2.63428 (155*2π)/5594 weeks
1561.06126 2.27665 (156*2π)/5594 weeks
157.73782 1.3411 (157*2π)/5594 weeks
1581.26156 .86794 (158*2π)/5594 weeks
1591.84346 .86473 (159*2π)/5594 weeks
1602.13964 1.79571 (160*2π)/5593 weeks
161.2731 1.83394 (161*2π)/5593 weeks
1621.31748 -.05161 (162*2π)/5593 weeks
1632.08146 .81597 (163*2π)/5593 weeks
1642.44593 1.00998 (164*2π)/5593 weeks
1652.44594 2.1726 (165*2π)/5593 weeks
166.78453 2.50814 (166*2π)/5593 weeks
167.1903 .17468 (167*2π)/5593 weeks
1682.68265 -.14964 (168*2π)/5593 weeks
1693.75084 2.13911 (169*2π)/5593 weeks
1701.17272 4.13652 (170*2π)/5593 weeks
171-1.19607 1.65951 (171*2π)/5593 weeks
172.54698 -.82364 (172*2π)/5593 weeks
1733.01507 .36777 (173*2π)/5593 weeks
1742.24198 2.45653 (174*2π)/5593 weeks
175.07679 2.14288 (175*2π)/5593 weeks
176.29029 -.09115 (176*2π)/5593 weeks
1772.64988 -.46067 (177*2π)/5593 weeks
1783.76372 1.99505 (178*2π)/5593 weeks
1791.35234 3.78968 (179*2π)/5593 weeks
180-1.06022 2.01828 (180*2π)/5593 weeks
181-.23475 -.91494 (181*2π)/5593 weeks
1823.09086 -.75381 (182*2π)/5593 weeks
1833.25622 2.47339 (183*2π)/5593 weeks
184.3793 3.11792 (184*2π)/5593 weeks
185-.70817 .40997 (185*2π)/5593 weeks
1861.77103 -.74745 (186*2π)/5593 weeks
1873.0909 .91409 (187*2π)/5593 weeks
1881.48608 2.54283 (188*2π)/5593 weeks
189.51413 1.17659 (189*2π)/5593 weeks
1901.05595 .43628 (190*2π)/5593 weeks
1912.36439 1.17101 (191*2π)/5593 weeks
1921.03172 2.65743 (192*2π)/5593 weeks
193-.71699 1.0568 (193*2π)/5593 weeks
194.25105 -.75824 (194*2π)/5593 weeks
1952.26388 -.88095 (195*2π)/5593 weeks
1963.0281 .80329 (196*2π)/5593 weeks
1972.88156 1.95136 (197*2π)/5593 weeks
198.49788 3.44286 (198*2π)/5593 weeks
199-.87695 .10658 (199*2π)/5593 weeks
2001.18597 -.618 (200*2π)/5593 weeks
2012.45833 .09467 (201*2π)/5593 weeks
2021.88834 1.38107 (202*2π)/5593 weeks
2031.37875 .73146 (203*2π)/5593 weeks
2041.60748 1.19421 (204*2π)/5593 weeks
2051.83344 .25324 (205*2π)/5593 weeks
2062.53114 2.12397 (206*2π)/5593 weeks
2071.07577 2.29327 (207*2π)/5593 weeks
208-.29293 2.21188 (208*2π)/5593 weeks
209-.55531 -.73387 (209*2π)/5593 weeks
2102.73665 -.97238 (210*2π)/5593 weeks
2112.9295 2.38251 (211*2π)/5593 weeks
212-.42661 2.87668 (212*2π)/5593 weeks
213-.97716 -.87663 (213*2π)/5593 weeks
2142.80685 -1.11095 (214*2π)/5593 weeks
2152.76767 2.1943 (215*2π)/5593 weeks
216-.02961 2.68898 (216*2π)/5593 weeks
217-1.66067 -.25068 (217*2π)/5593 weeks
2181.99064 -2.37739 (218*2π)/5593 weeks
2193.9817 .91853 (219*2π)/5593 weeks
2201.14687 3.18604 (220*2π)/5593 weeks
221-1.09672 .44625 (221*2π)/5593 weeks
2221.65932 -1.30801 (222*2π)/5593 weeks
2232.55808 1.27423 (223*2π)/5593 weeks
224.49873 1.44758 (224*2π)/5592 weeks
225.66053 -.10411 (225*2π)/5592 weeks
2261.83017 -.4437 (226*2π)/5592 weeks
2273.16179 1.36866 (227*2π)/5592 weeks
228.58684 3.11045 (228*2π)/5592 weeks
229-.95117 .63994 (229*2π)/5592 weeks
230.52641 -.82862 (230*2π)/5592 weeks
2312.38018 .63695 (231*2π)/5592 weeks
232.04961 2.04973 (232*2π)/5592 weeks
233-.77827 -.17636 (233*2π)/5592 weeks
234.59243 -1.66082 (234*2π)/5592 weeks
2352.85444 -.90458 (235*2π)/5592 weeks
2362.05466 1.62922 (236*2π)/5592 weeks
237-.17833 1.06955 (237*2π)/5592 weeks
238-.04827 -1.33855 (238*2π)/5592 weeks
2393.02221 -1.57656 (239*2π)/5592 weeks
2403.40642 1.82443 (240*2π)/5592 weeks
241.36597 2.49076 (241*2π)/5592 weeks
242-.8599 .56981 (242*2π)/5592 weeks
243.33162 -2.02751 (243*2π)/5592 weeks
2442.78174 -.17591 (244*2π)/5592 weeks
2451.85472 .93846 (245*2π)/5592 weeks
246.46134 1.28849 (246*2π)/5592 weeks
247.4161 -.47553 (247*2π)/5592 weeks
2481.19818 -.30655 (248*2π)/5592 weeks
2491.89078 -.2962 (249*2π)/5592 weeks
2501.81451 1.38532 (250*2π)/5592 weeks
251-.33758 1.07008 (251*2π)/5592 weeks
252-.27907 -.91939 (252*2π)/5592 weeks
2531.83892 -2.17188 (253*2π)/5592 weeks
2543.55863 .29885 (254*2π)/5592 weeks
2551.29034 2.41113 (255*2π)/5592 weeks
256-.89647 .85876 (256*2π)/5592 weeks
257-.63699 -1.8413 (257*2π)/5592 weeks
2582.56101 -2.77978 (258*2π)/5592 weeks
2594.29959 .85608 (259*2π)/5592 weeks
2601.21873 3.50889 (260*2π)/5592 weeks
261-2.87302 .46385 (261*2π)/5592 weeks
262.27144 -3.87342 (262*2π)/5592 weeks
2633.98918 -1.65057 (263*2π)/5592 weeks
2643.32482 1.99902 (264*2π)/5592 weeks
265-.98038 2.05346 (265*2π)/5592 weeks
266-1.47351 -2.56409 (266*2π)/5592 weeks
2673.39295 -3.60696 (267*2π)/5592 weeks
2684.13856 .85497 (268*2π)/5592 weeks
269.92064 1.87643 (269*2π)/5592 weeks
270-.78322 -.80482 (270*2π)/5592 weeks
2711.67422 -3.06416 (271*2π)/5592 weeks
2724.96529 -1.35057 (272*2π)/5592 weeks
2733.6946 2.82987 (273*2π)/5592 weeks
274-.59751 1.53566 (274*2π)/5592 weeks
275.68436 -1.73912 (275*2π)/5592 weeks
2762.78201 -1.05003 (276*2π)/5592 weeks
2773.09876 .70105 (277*2π)/5592 weeks
2782.02614 1.74774 (278*2π)/5592 weeks
279-.26281 1.53003 (279*2π)/5592 weeks
280-.26281 -1.53003 (280*2π)/5592 weeks
2812.02614 -1.74774 (281*2π)/5592 weeks
2823.09876 -.70105 (282*2π)/5592 weeks
2832.78201 1.05003 (283*2π)/5592 weeks
284.68436 1.73912 (284*2π)/5592 weeks
285-.59751 -1.53566 (285*2π)/5592 weeks
2863.6946 -2.82987 (286*2π)/5592 weeks
2874.96529 1.35057 (287*2π)/5592 weeks
2881.67422 3.06416 (288*2π)/5592 weeks
289-.78322 .80482 (289*2π)/5592 weeks
290.92064 -1.87643 (290*2π)/5592 weeks
2914.13856 -.85497 (291*2π)/5592 weeks
2923.39295 3.60696 (292*2π)/5592 weeks
293-1.47351 2.56409 (293*2π)/5592 weeks
294-.98038 -2.05346 (294*2π)/5592 weeks
2953.32482 -1.99902 (295*2π)/5592 weeks
2963.98918 1.65057 (296*2π)/5592 weeks
297.27144 3.87342 (297*2π)/5592 weeks
298-2.87302 -.46385 (298*2π)/5592 weeks
2991.21873 -3.50889 (299*2π)/5592 weeks
3004.29959 -.85608 (300*2π)/5592 weeks
3012.56101 2.77978 (301*2π)/5592 weeks
302-.63699 1.8413 (302*2π)/5592 weeks
303-.89647 -.85876 (303*2π)/5592 weeks
3041.29034 -2.41113 (304*2π)/5592 weeks
3053.55863 -.29885 (305*2π)/5592 weeks
3061.83892 2.17188 (306*2π)/5592 weeks
307-.27907 .91939 (307*2π)/5592 weeks
308-.33758 -1.07008 (308*2π)/5592 weeks
3091.81451 -1.38532 (309*2π)/5592 weeks
3101.89078 .2962 (310*2π)/5592 weeks
3111.19818 .30655 (311*2π)/5592 weeks
312.4161 .47553 (312*2π)/5592 weeks
313.46134 -1.28849 (313*2π)/5592 weeks
3141.85472 -.93846 (314*2π)/5592 weeks
3152.78174 .17591 (315*2π)/5592 weeks
316.33162 2.02751 (316*2π)/5592 weeks
317-.8599 -.56981 (317*2π)/5592 weeks
318.36597 -2.49076 (318*2π)/5592 weeks
3193.40642 -1.82443 (319*2π)/5592 weeks
3203.02221 1.57656 (320*2π)/5592 weeks
321-.04827 1.33855 (321*2π)/5592 weeks
322-.17833 -1.06955 (322*2π)/5592 weeks
3232.05466 -1.62922 (323*2π)/5592 weeks
3242.85444 .90458 (324*2π)/5592 weeks
325.59243 1.66082 (325*2π)/5592 weeks
326-.77827 .17636 (326*2π)/5592 weeks
327.04961 -2.04973 (327*2π)/5592 weeks
3282.38018 -.63695 (328*2π)/5592 weeks
329.52641 .82862 (329*2π)/5592 weeks
330-.95117 -.63994 (330*2π)/5592 weeks
331.58684 -3.11045 (331*2π)/5592 weeks
3323.16179 -1.36866 (332*2π)/5592 weeks
3331.83017 .4437 (333*2π)/5592 weeks
334.66053 .10411 (334*2π)/5592 weeks
335.49873 -1.44758 (335*2π)/5592 weeks
3362.55808 -1.27423 (336*2π)/5592 weeks
3371.65932 1.30801 (337*2π)/5592 weeks
338-1.09672 -.44625 (338*2π)/5592 weeks
3391.14687 -3.18604 (339*2π)/5592 weeks
3403.9817 -.91853 (340*2π)/5592 weeks
3411.99064 2.37739 (341*2π)/5592 weeks
342-1.66067 .25068 (342*2π)/5592 weeks
343-.02961 -2.68898 (343*2π)/5592 weeks
3442.76767 -2.1943 (344*2π)/5592 weeks
3452.80685 1.11095 (345*2π)/5592 weeks
346-.97716 .87663 (346*2π)/5592 weeks
347-.42661 -2.87668 (347*2π)/5592 weeks
3482.9295 -2.38251 (348*2π)/5592 weeks
3492.73665 .97238 (349*2π)/5592 weeks
350-.55531 .73387 (350*2π)/5592 weeks
351-.29293 -2.21188 (351*2π)/5592 weeks
3521.07577 -2.29327 (352*2π)/5592 weeks
3532.53114 -2.12397 (353*2π)/5592 weeks
3541.83344 -.25324 (354*2π)/5592 weeks
3551.60748 -1.19421 (355*2π)/5592 weeks
3561.37875 -.73146 (356*2π)/5592 weeks
3571.88834 -1.38107 (357*2π)/5592 weeks
3582.45833 -.09467 (358*2π)/5592 weeks
3591.18597 .618 (359*2π)/5592 weeks
360-.87695 -.10658 (360*2π)/5592 weeks
361.49788 -3.44286 (361*2π)/5592 weeks
3622.88156 -1.95136 (362*2π)/5592 weeks
3633.0281 -.80329 (363*2π)/5592 weeks
3642.26388 .88095 (364*2π)/5592 weeks
365.25105 .75824 (365*2π)/5592 weeks
366-.71699 -1.0568 (366*2π)/5592 weeks
3671.03172 -2.65743 (367*2π)/5592 weeks
3682.36439 -1.17101 (368*2π)/5592 weeks
3691.05595 -.43628 (369*2π)/5592 weeks
370.51413 -1.17659 (370*2π)/5592 weeks
3711.48608 -2.54283 (371*2π)/5592 weeks
3723.0909 -.91409 (372*2π)/5592 weeks
3731.77103 .74745 (373*2π)/5591 weeks
374-.70817 -.40997 (374*2π)/5591 weeks
375.3793 -3.11792 (375*2π)/5591 weeks
3763.25622 -2.47339 (376*2π)/5591 weeks
3773.09086 .75381 (377*2π)/5591 weeks
378-.23475 .91494 (378*2π)/5591 weeks
379-1.06022 -2.01828 (379*2π)/5591 weeks
3801.35234 -3.78968 (380*2π)/5591 weeks
3813.76372 -1.99505 (381*2π)/5591 weeks
3822.64988 .46067 (382*2π)/5591 weeks
383.29029 .09115 (383*2π)/5591 weeks
384.07679 -2.14288 (384*2π)/5591 weeks
3852.24198 -2.45653 (385*2π)/5591 weeks
3863.01507 -.36777 (386*2π)/5591 weeks
387.54698 .82364 (387*2π)/5591 weeks
388-1.19607 -1.65951 (388*2π)/5591 weeks
3891.17272 -4.13652 (389*2π)/5591 weeks
3903.75084 -2.13911 (390*2π)/5591 weeks
3912.68265 .14964 (391*2π)/5591 weeks
392.1903 -.17468 (392*2π)/5591 weeks
393.78453 -2.50814 (393*2π)/5591 weeks
3942.44594 -2.1726 (394*2π)/5591 weeks
3952.44593 -1.00998 (395*2π)/5591 weeks
3962.08146 -.81597 (396*2π)/5591 weeks
3971.31748 .05161 (397*2π)/5591 weeks
398.2731 -1.83394 (398*2π)/5591 weeks
3992.13964 -1.79571 (399*2π)/5591 weeks
4001.84346 -.86473 (400*2π)/5591 weeks
4011.26156 -.86794 (401*2π)/5591 weeks
402.73782 -1.3411 (402*2π)/5591 weeks
4031.06126 -2.27665 (403*2π)/5591 weeks
4042.19947 -2.63428 (404*2π)/5591 weeks
4053.40794 -.34562 (405*2π)/5591 weeks
406-.01182 .49276 (406*2π)/5591 weeks
407-.4357 -2.60061 (407*2π)/5591 weeks
4082.03979 -3.73448 (408*2π)/5591 weeks
4093.85772 -.98958 (409*2π)/5591 weeks
4101.02023 .33896 (410*2π)/5591 weeks
411-.33937 -1.88899 (411*2π)/5591 weeks
4121.77405 -3.98658 (412*2π)/5591 weeks
4133.86342 -.9157 (413*2π)/5591 weeks
414.40348 .28625 (414*2π)/5591 weeks
415.46749 -2.87949 (415*2π)/5591 weeks
4162.37092 -2.68588 (416*2π)/5591 weeks
4173.38502 -1.39252 (417*2π)/5591 weeks
4182.13557 -.35226 (418*2π)/5591 weeks
4191.7658 -.19819 (419*2π)/5591 weeks
420-.3074 -.59619 (420*2π)/5591 weeks
421.06569 -3.25397 (421*2π)/5591 weeks
4222.07065 -3.39072 (422*2π)/5591 weeks
4233.65122 -1.84982 (423*2π)/5591 weeks
4242.17575 .0866 (424*2π)/5591 weeks
425.97512 -1.65125 (425*2π)/5591 weeks
4262.64494 -1.9843 (426*2π)/5591 weeks
4272.27236 .0466 (427*2π)/5591 weeks
428.13968 -.19847 (428*2π)/5591 weeks
429-.128 -2.10901 (429*2π)/5591 weeks
430.68028 -3.30922 (430*2π)/5591 weeks
4312.94325 -3.22271 (431*2π)/5591 weeks
4323.57141 -.30944 (432*2π)/5591 weeks
433.41792 1.44444 (433*2π)/5591 weeks
434-2.01812 -2.62118 (434*2π)/5591 weeks
4351.71413 -4.91848 (435*2π)/5591 weeks
4363.92308 -1.72169 (436*2π)/5591 weeks
4371.16694 -.02345 (437*2π)/5591 weeks
438-.91963 -2.35321 (438*2π)/5591 weeks
4391.10193 -4.75882 (439*2π)/5591 weeks
4404.10234 -3.6807 (440*2π)/5591 weeks
4414.27437 .38645 (441*2π)/5591 weeks
442-.67159 1.57237 (442*2π)/5591 weeks
443-2.39466 -4.16766 (443*2π)/5591 weeks
4442.42082 -6.57418 (444*2π)/5591 weeks
4456.70521 -3.22619 (445*2π)/5591 weeks
4464.12559 2.66424 (446*2π)/5591 weeks
447-2.40366 .74129 (447*2π)/5591 weeks
448-1.43119 -5.80262 (448*2π)/5591 weeks
4495.38087 -5.08116 (449*2π)/5591 weeks
4505.33117 1.16938 (450*2π)/5591 weeks
451-.33943 2.85995 (451*2π)/5591 weeks
452-3.71607 -3.13723 (452*2π)/5591 weeks
4531.00237 -6.9647 (453*2π)/5591 weeks
4545.83732 -3.73692 (454*2π)/5591 weeks
4552.88327 1.12821 (455*2π)/5591 weeks
456-1.56931 -1.28982 (456*2π)/5591 weeks
457.22076 -5.69603 (457*2π)/5591 weeks
4585.17201 -4.65144 (458*2π)/5591 weeks
4595.02961 .12604 (459*2π)/5591 weeks
460.94807 .83871 (460*2π)/5591 weeks
461-.25968 -2.02697 (461*2π)/5591 weeks
4621.68318 -3.24959 (462*2π)/5591 weeks
4631.58447 -1.69058 (463*2π)/5591 weeks
4641.3499 -3.2432 (464*2π)/5591 weeks
4652.87615 -1.94348 (465*2π)/5591 weeks
466.81554 -.82014 (466*2π)/5591 weeks
467-.46297 -3.18749 (467*2π)/5591 weeks
4682.40449 -5.14706 (468*2π)/5591 weeks
4695.39886 -1.42062 (469*2π)/5591 weeks
4701.29421 2.94364 (470*2π)/5591 weeks
471-4.40542 -.8299 (471*2π)/5591 weeks
472-1.68735 -8.23934 (472*2π)/5591 weeks
4736.05233 -5.73073 (473*2π)/5591 weeks
4744.20346 .38096 (474*2π)/5591 weeks
475-.82793 1.16423 (475*2π)/5591 weeks
476-3.71557 -5.008 (476*2π)/5591 weeks
4772.48508 -8.30048 (477*2π)/5591 weeks
4786.80397 -3.88118 (478*2π)/5591 weeks
4792.81299 2.57598 (479*2π)/5591 weeks
480-3.50107 -2.39384 (480*2π)/5591 weeks
4811.26278 -6.40726 (481*2π)/5591 weeks
4823.62365 -5.19004 (482*2π)/5591 weeks
4835.69614 -.2089 (483*2π)/5591 weeks
484-2.36512 2.32623 (484*2π)/5591 weeks
485-4.69614 -5.86353 (485*2π)/5591 weeks
4861.6004 -10.21518 (486*2π)/5591 weeks
4877.15074 -4.69078 (487*2π)/5591 weeks
4881.98242 -.31193 (488*2π)/5591 weeks
489.7295 -4.51699 (489*2π)/5591 weeks
4902.75124 -3.6461 (490*2π)/5591 weeks
4912.96067 -2.43632 (491*2π)/5591 weeks
492-1.3981 -1.97544 (492*2π)/5591 weeks
493-.47388 -7.55019 (493*2π)/5591 weeks
4945.33929 -6.61543 (494*2π)/5591 weeks
4955.54484 -2.06139 (495*2π)/5591 weeks
496.41969 -.27608 (496*2π)/5591 weeks
497.64902 -5.69815 (497*2π)/5591 weeks
4984.11234 -3.1739 (498*2π)/5591 weeks
4991.58743 -.63734 (499*2π)/5591 weeks
500-2.84588 -3.40767 (500*2π)/5591 weeks
501.55708 -9.1101 (501*2π)/5591 weeks
5028.02928 -4.764 (502*2π)/5591 weeks
5032.55694 1.67419 (503*2π)/5591 weeks
504-2.66709 -2.06965 (504*2π)/5591 weeks
505-1.9309 -6.43158 (505*2π)/5591 weeks
5061.85467 -7.52559 (506*2π)/5591 weeks
5072.14274 -4.58684 (507*2π)/5591 weeks
508.5398 -5.58443 (508*2π)/5591 weeks
5091.06948 -7.90147 (509*2π)/5591 weeks
5104.50137 -7.01555 (510*2π)/5591 weeks
5116.04101 -3.94637 (511*2π)/5591 weeks
5121.57149 -1.81104 (512*2π)/5591 weeks
513.22551 -5.15955 (513*2π)/5591 weeks
5141.93963 -5.33004 (514*2π)/5591 weeks
5151.70031 -4.38548 (515*2π)/5591 weeks
516-1.12465 -6.4251 (516*2π)/5591 weeks
5174.0666 -9.85271 (517*2π)/5591 weeks
5185.76969 -2.58556 (518*2π)/5591 weeks
519-.02272 -.94628 (519*2π)/5591 weeks
520-4.41643 -6.02629 (520*2π)/5591 weeks
521.51218 -13.8771 (521*2π)/5591 weeks
52210.97332 -7.76765 (522*2π)/5591 weeks
5235.92531 4.6214 (523*2π)/5591 weeks
524-12.17112 2.49858 (524*2π)/5591 weeks
525-11.5943 -21.22372 (525*2π)/5591 weeks
52612.47554 -21.52367 (526*2π)/5591 weeks
52714.9292 .24839 (527*2π)/5591 weeks
528-5.14729 6.37421 (528*2π)/5591 weeks
529-13.00352 -13.32362 (529*2π)/5591 weeks
5304.93172 -22.38294 (530*2π)/5591 weeks
53114.38246 -9.60304 (531*2π)/5591 weeks
5326.11069 3.59034 (532*2π)/5591 weeks
533-9.48931 -5.1765 (533*2π)/5591 weeks
534-3.35378 -16.79494 (534*2π)/5591 weeks
5354.60309 -15.16668 (535*2π)/5591 weeks
5362.0219 -8.04156 (536*2π)/5591 weeks
537-1.79424 -12.89938 (537*2π)/5591 weeks
538.59853 -16.58711 (538*2π)/5591 weeks
5394.41136 -18.08768 (539*2π)/5591 weeks
54010.74442 -16.61694 (540*2π)/5591 weeks
5418.50425 -4.78391 (541*2π)/5591 weeks
542-2.85546 -9.14921 (542*2π)/5591 weeks
543-6.06537 -14.50093 (543*2π)/5591 weeks
544-4.43573 -26.62051 (544*2π)/5591 weeks
54510.06396 -30.01753 (545*2π)/5591 weeks
54621.64582 -16.22626 (546*2π)/5591 weeks
5471.97319 5.29219 (547*2π)/5591 weeks
548-23.87377 -20.9705 (548*2π)/5591 weeks
549-8.78122 -46.23329 (549*2π)/5591 weeks
55024.8645 -54.4347 (550*2π)/5591 weeks
55136.91187 -9.43924 (551*2π)/5591 weeks
552-17.26402 -7.10634 (552*2π)/5591 weeks
553-21.79468 -66.89172 (553*2π)/5591 weeks
55438.82795 -81.93512 (554*2π)/5591 weeks
55564.02817 -23.42342 (555*2π)/5591 weeks
556-24.02388 5.87997 (556*2π)/5591 weeks
557-75.33955 -141.1732 (557*2π)/5591 weeks

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