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Fourier Analysis of SPXU (ProShares UltraPro Short S&P 500 ETF)


SPXU (ProShares UltraPro Short S&P 500 ETF) appears to have interesting cyclic behaviour every 43 weeks (39.2737*sine), 39 weeks (34.5214*sine), and 31 weeks (17.9828*cosine).

SPXU (ProShares UltraPro Short S&P 500 ETF) has an average price of 226.64 (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 6/25/2009 to 9/5/2017 for SPXU (ProShares UltraPro Short S&P 500 ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0226.641   0 
1178.4062 211.8717 (1*2π)/429429 weeks
264.30996 139.9961 (2*2π)/429215 weeks
341.21192 106.7454 (3*2π)/429143 weeks
425.14206 84.51268 (4*2π)/429107 weeks
515.78936 62.65174 (5*2π)/42986 weeks
619.54936 39.6938 (6*2π)/42972 weeks
737.3223 40.40672 (7*2π)/42961 weeks
832.04836 57.64887 (8*2π)/42954 weeks
912.97563 53.34103 (9*2π)/42948 weeks
109.16811 39.27369 (10*2π)/42943 weeks
1113.10195 34.52139 (11*2π)/42939 weeks
1210.11732 34.10197 (12*2π)/42936 weeks
138.02631 24.33932 (13*2π)/42933 weeks
1417.98281 23.45172 (14*2π)/42931 weeks
1517.27723 29.19224 (15*2π)/42929 weeks
1615.29461 29.52254 (16*2π)/42927 weeks
1712.07007 30.43567 (17*2π)/42925 weeks
186.75762 27.65406 (18*2π)/42924 weeks
198.84064 25.33777 (19*2π)/42923 weeks
204.84961 25.58818 (20*2π)/42921 weeks
212.84844 16.70471 (21*2π)/42920 weeks
229.0597 14.44789 (22*2π)/42920 weeks
2310.2469 17.31497 (23*2π)/42919 weeks
249.50258 17.37577 (24*2π)/42918 weeks
2511.67508 15.0991 (25*2π)/42917 weeks
2614.30647 16.89903 (26*2π)/42917 weeks
2712.60065 21.35516 (27*2π)/42916 weeks
288.86618 21.06182 (28*2π)/42915 weeks
298.70716 20.37236 (29*2π)/42915 weeks
306.39999 20.78511 (30*2π)/42914 weeks
313.45714 19.94659 (31*2π)/42914 weeks
32.84094 14.55977 (32*2π)/42913 weeks
335.66316 10.87424 (33*2π)/42913 weeks
348.73164 14.00826 (34*2π)/42913 weeks
355.65101 15.05137 (35*2π)/42912 weeks
365.78518 12.50638 (36*2π)/42912 weeks
378.72869 12.6579 (37*2π)/42912 weeks
386.79163 14.26977 (38*2π)/42911 weeks
396.71145 13.83785 (39*2π)/42911 weeks
406.09816 13.22051 (40*2π)/42911 weeks
417.33571 12.2352 (41*2π)/42910 weeks
427.62305 13.84749 (42*2π)/42910 weeks
436.24967 15.08006 (43*2π)/42910 weeks
443.45838 14.63988 (44*2π)/42910 weeks
453.52216 11.95402 (45*2π)/42910 weeks
464.71231 10.61094 (46*2π)/4299 weeks
476.35624 11.76173 (47*2π)/4299 weeks
484.62554 13.09449 (48*2π)/4299 weeks
493.28486 10.77559 (49*2π)/4299 weeks
505.26623 10.36683 (50*2π)/4299 weeks
515.38272 11.41968 (51*2π)/4298 weeks
522.57369 11.86401 (52*2π)/4298 weeks
533.76488 7.43858 (53*2π)/4298 weeks
547.53886 9.29864 (54*2π)/4298 weeks
556.17288 11.87067 (55*2π)/4298 weeks
564.7076 11.66479 (56*2π)/4298 weeks
575.06277 10.66946 (57*2π)/4298 weeks
585.15945 13.02133 (58*2π)/4297 weeks
591.43233 14.34641 (59*2π)/4297 weeks
60-2.45404 9.54443 (60*2π)/4297 weeks
611.08641 4.98754 (61*2π)/4297 weeks
624.78426 6.40538 (62*2π)/4297 weeks
634.15392 7.90712 (63*2π)/4297 weeks
644.55549 6.89527 (64*2π)/4297 weeks
656.56823 8.57122 (65*2π)/4297 weeks
664.53788 10.91025 (66*2π)/4297 weeks
672.46494 9.33848 (67*2π)/4296 weeks
683.27081 8.13941 (68*2π)/4296 weeks
693.47931 7.77802 (69*2π)/4296 weeks
703.98459 8.08091 (70*2π)/4296 weeks
714.10905 8.62597 (71*2π)/4296 weeks
724.24336 8.98692 (72*2π)/4296 weeks
733.60854 10.41883 (73*2π)/4296 weeks
74.97947 9.98471 (74*2π)/4296 weeks
75.89992 7.61663 (75*2π)/4296 weeks
761.43894 7.38603 (76*2π)/4296 weeks
771.35071 6.94981 (77*2π)/4296 weeks
781.4651 6.46214 (78*2π)/4296 weeks
792.35222 6.12498 (79*2π)/4295 weeks
802.50661 6.27355 (80*2π)/4295 weeks
812.09222 6.51775 (81*2π)/4295 weeks
822.35892 6.02547 (82*2π)/4295 weeks
831.81574 6.83247 (83*2π)/4295 weeks
841.26339 5.46475 (84*2π)/4295 weeks
852.06939 4.60134 (85*2π)/4295 weeks
862.40448 4.62718 (86*2π)/4295 weeks
873.37664 4.75305 (87*2π)/4295 weeks
883.76323 5.81947 (88*2π)/4295 weeks
892.33574 6.34471 (89*2π)/4295 weeks
901.76952 5.03854 (90*2π)/4295 weeks
912.18254 4.30473 (91*2π)/4295 weeks
923.3504 4.44874 (92*2π)/4295 weeks
933.28055 5.03726 (93*2π)/4295 weeks
943.47172 4.36161 (94*2π)/4295 weeks
953.8518 4.88595 (95*2π)/4295 weeks
964.33864 5.31723 (96*2π)/4294 weeks
973.8532 6.45964 (97*2π)/4294 weeks
983.77104 6.49475 (98*2π)/4294 weeks
993.18753 7.27424 (99*2π)/4294 weeks
1001.62772 7.63974 (100*2π)/4294 weeks
101.53865 6.93732 (101*2π)/4294 weeks
102-.19933 5.7613 (102*2π)/4294 weeks
103-.07688 4.66577 (103*2π)/4294 weeks
104.91458 3.49822 (104*2π)/4294 weeks
1052.03435 3.9103 (105*2π)/4294 weeks
1061.35347 5.55466 (106*2π)/4294 weeks
107-.21536 4.98667 (107*2π)/4294 weeks
108-.18718 3.14066 (108*2π)/4294 weeks
109.68246 3.10176 (109*2π)/4294 weeks
110-.50159 3.24588 (110*2π)/4294 weeks
111-.45922 .9723 (111*2π)/4294 weeks
1121.82571 .28098 (112*2π)/4294 weeks
1133.36011 1.42546 (113*2π)/4294 weeks
1142.7596 2.24267 (114*2π)/4294 weeks
1152.59846 2.15057 (115*2π)/4294 weeks
1163.17882 2.68881 (116*2π)/4294 weeks
1171.94395 3.34124 (117*2π)/4294 weeks
118.94692 1.67215 (118*2π)/4294 weeks
1192.63945 .47618 (119*2π)/4294 weeks
1203.47119 1.47971 (120*2π)/4294 weeks
1213.36902 1.53187 (121*2π)/4294 weeks
1224.19437 1.47476 (122*2π)/4294 weeks
1235.31052 2.37387 (123*2π)/4293 weeks
1244.42565 4.68118 (124*2π)/4293 weeks
1252.20672 4.22347 (125*2π)/4293 weeks
1262.03717 3.02181 (126*2π)/4293 weeks
1272.32703 2.78772 (127*2π)/4293 weeks
1282.20836 2.08291 (128*2π)/4293 weeks
1293.33147 2.49898 (129*2π)/4293 weeks
1302.51044 3.23532 (130*2π)/4293 weeks
1312.14964 2.76264 (131*2π)/4293 weeks
1322.0914 2.58036 (132*2π)/4293 weeks
1331.99535 2.2534 (133*2π)/4293 weeks
1342.23451 2.26806 (134*2π)/4293 weeks
1351.79765 1.81266 (135*2π)/4293 weeks
1362.33122 1.61072 (136*2π)/4293 weeks
1372.35613 1.94021 (137*2π)/4293 weeks
1382.14784 1.79676 (138*2π)/4293 weeks
1392.1374 1.24427 (139*2π)/4293 weeks
1402.64768 1.35587 (140*2π)/4293 weeks
1412.37978 1.64211 (141*2π)/4293 weeks
1422.30304 1.07907 (142*2π)/4293 weeks
1432.99709 1.28625 (143*2π)/4293 weeks
1442.36513 1.39646 (144*2π)/4293 weeks
1452.86479 .76044 (145*2π)/4293 weeks
1463.48413 1.81992 (146*2π)/4293 weeks
1472.48541 2.28143 (147*2π)/4293 weeks
1481.74074 1.49835 (148*2π)/4293 weeks
1492.25673 1.19632 (149*2π)/4293 weeks
1501.93644 1.72239 (150*2π)/4293 weeks
151.53372 .67094 (151*2π)/4293 weeks
1521.57371 -1.58612 (152*2π)/4293 weeks
1534.02618 -.70998 (153*2π)/4293 weeks
1543.42545 .59973 (154*2π)/4293 weeks
1552.96756 .02188 (155*2π)/4293 weeks
1564.00748 -.42275 (156*2π)/4293 weeks
1574.41716 1.67296 (157*2π)/4293 weeks
1581.77402 1.72896 (158*2π)/4293 weeks
1591.91381 -.93439 (159*2π)/4293 weeks
1604.0455 -.92556 (160*2π)/4293 weeks
1614.54165 .1127 (161*2π)/4293 weeks
1623.93904 .6735 (162*2π)/4293 weeks
1634.06901 .45501 (163*2π)/4293 weeks
1644.38152 1.09767 (164*2π)/4293 weeks
1653.29442 1.88893 (165*2π)/4293 weeks
1662.12992 1.07269 (166*2π)/4293 weeks
1672.78554 -.48545 (167*2π)/4293 weeks
1683.45538 -.0219 (168*2π)/4293 weeks
1693.27473 -.03607 (169*2π)/4293 weeks
1703.66313 -.60061 (170*2π)/4293 weeks
1714.48997 -.61646 (171*2π)/4293 weeks
1725.12263 .13923 (172*2π)/4292 weeks
1735.1854 1.38652 (173*2π)/4292 weeks
1743.77812 2.05307 (174*2π)/4292 weeks
1752.81024 1.01981 (175*2π)/4292 weeks
1763.55897 .3366 (176*2π)/4292 weeks
1773.29038 1.19796 (177*2π)/4292 weeks
1782.36684 .29891 (178*2π)/4292 weeks
1793.38912 -.80535 (179*2π)/4292 weeks
1804.33172 -.38149 (180*2π)/4292 weeks
1813.94595 .29218 (181*2π)/4292 weeks
1823.84144 -.00627 (182*2π)/4292 weeks
1834.28943 -.06609 (183*2π)/4292 weeks
1844.44375 .37567 (184*2π)/4292 weeks
1853.9828 .81829 (185*2π)/4292 weeks
1863.37785 -.02284 (186*2π)/4292 weeks
1874.95891 -.17835 (187*2π)/4292 weeks
1884.31979 1.1599 (188*2π)/4292 weeks
1893.53395 .09728 (189*2π)/4292 weeks
1904.78882 -.08105 (190*2π)/4292 weeks
1914.95681 1.09216 (191*2π)/4292 weeks
1923.92934 1.37108 (192*2π)/4292 weeks
1933.31822 .56456 (193*2π)/4292 weeks
1944.50522 .34191 (194*2π)/4292 weeks
1954.54487 1.16955 (195*2π)/4292 weeks
1963.80531 1.68313 (196*2π)/4292 weeks
1973.25259 1.48498 (197*2π)/4292 weeks
1982.73952 .95762 (198*2π)/4292 weeks
1992.76601 .90052 (199*2π)/4292 weeks
2002.12385 -.13213 (200*2π)/4292 weeks
2013.425 -1.27839 (201*2π)/4292 weeks
2024.81088 -.24589 (202*2π)/4292 weeks
2034.19427 .99811 (203*2π)/4292 weeks
2043.34025 1.06774 (204*2π)/4292 weeks
2052.36925 .82656 (205*2π)/4292 weeks
2062.50503 -.46151 (206*2π)/4292 weeks
2072.97708 -.89381 (207*2π)/4292 weeks
2083.34373 -1.60586 (208*2π)/4292 weeks
2094.97766 -1.4406 (209*2π)/4292 weeks
2105.70449 .08892 (210*2π)/4292 weeks
2114.84304 1.13585 (211*2π)/4292 weeks
2123.77637 1.00049 (212*2π)/4292 weeks
2133.51168 1.2537 (213*2π)/4292 weeks
2142.28957 .9012 (214*2π)/4292 weeks
2152.28957 -.9012 (215*2π)/4292 weeks
2163.51168 -1.2537 (216*2π)/4292 weeks
2173.77637 -1.00049 (217*2π)/4292 weeks
2184.84304 -1.13585 (218*2π)/4292 weeks
2195.70449 -.08892 (219*2π)/4292 weeks
2204.97766 1.4406 (220*2π)/4292 weeks
2213.34373 1.60586 (221*2π)/4292 weeks
2222.97708 .89381 (222*2π)/4292 weeks
2232.50503 .46151 (223*2π)/4292 weeks
2242.36925 -.82656 (224*2π)/4292 weeks
2253.34025 -1.06774 (225*2π)/4292 weeks
2264.19427 -.99811 (226*2π)/4292 weeks
2274.81088 .24589 (227*2π)/4292 weeks
2283.425 1.27839 (228*2π)/4292 weeks
2292.12385 .13213 (229*2π)/4292 weeks
2302.76601 -.90052 (230*2π)/4292 weeks
2312.73952 -.95762 (231*2π)/4292 weeks
2323.25259 -1.48498 (232*2π)/4292 weeks
2333.80531 -1.68313 (233*2π)/4292 weeks
2344.54487 -1.16955 (234*2π)/4292 weeks
2354.50522 -.34191 (235*2π)/4292 weeks
2363.31822 -.56456 (236*2π)/4292 weeks
2373.92934 -1.37108 (237*2π)/4292 weeks
2384.95681 -1.09216 (238*2π)/4292 weeks
2394.78882 .08105 (239*2π)/4292 weeks
2403.53395 -.09728 (240*2π)/4292 weeks
2414.31979 -1.1599 (241*2π)/4292 weeks
2424.95891 .17835 (242*2π)/4292 weeks
2433.37785 .02284 (243*2π)/4292 weeks
2443.9828 -.81829 (244*2π)/4292 weeks
2454.44375 -.37567 (245*2π)/4292 weeks
2464.28943 .06609 (246*2π)/4292 weeks
2473.84144 .00627 (247*2π)/4292 weeks
2483.94595 -.29218 (248*2π)/4292 weeks
2494.33172 .38149 (249*2π)/4292 weeks
2503.38912 .80535 (250*2π)/4292 weeks
2512.36684 -.29891 (251*2π)/4292 weeks
2523.29038 -1.19796 (252*2π)/4292 weeks
2533.55897 -.3366 (253*2π)/4292 weeks
2542.81024 -1.01981 (254*2π)/4292 weeks
2553.77812 -2.05307 (255*2π)/4292 weeks
2565.1854 -1.38652 (256*2π)/4292 weeks
2575.12263 -.13923 (257*2π)/4292 weeks
2584.48997 .61646 (258*2π)/4292 weeks
2593.66313 .60061 (259*2π)/4292 weeks
2603.27473 .03607 (260*2π)/4292 weeks
2613.45538 .0219 (261*2π)/4292 weeks
2622.78554 .48545 (262*2π)/4292 weeks
2632.12992 -1.07269 (263*2π)/4292 weeks
2643.29442 -1.88893 (264*2π)/4292 weeks
2654.38152 -1.09767 (265*2π)/4292 weeks
2664.06901 -.45501 (266*2π)/4292 weeks
2673.93904 -.6735 (267*2π)/4292 weeks
2684.54165 -.1127 (268*2π)/4292 weeks
2694.0455 .92556 (269*2π)/4292 weeks
2701.91381 .93439 (270*2π)/4292 weeks
2711.77402 -1.72896 (271*2π)/4292 weeks
2724.41716 -1.67296 (272*2π)/4292 weeks
2734.00748 .42275 (273*2π)/4292 weeks
2742.96756 -.02188 (274*2π)/4292 weeks
2753.42545 -.59973 (275*2π)/4292 weeks
2764.02618 .70998 (276*2π)/4292 weeks
2771.57371 1.58612 (277*2π)/4292 weeks
278.53372 -.67094 (278*2π)/4292 weeks
2791.93644 -1.72239 (279*2π)/4292 weeks
2802.25673 -1.19632 (280*2π)/4292 weeks
2811.74074 -1.49835 (281*2π)/4292 weeks
2822.48541 -2.28143 (282*2π)/4292 weeks
2833.48413 -1.81992 (283*2π)/4292 weeks
2842.86479 -.76044 (284*2π)/4292 weeks
2852.36513 -1.39646 (285*2π)/4292 weeks
2862.99709 -1.28625 (286*2π)/4292 weeks
2872.30304 -1.07907 (287*2π)/4291 weeks
2882.37978 -1.64211 (288*2π)/4291 weeks
2892.64768 -1.35587 (289*2π)/4291 weeks
2902.1374 -1.24427 (290*2π)/4291 weeks
2912.14784 -1.79676 (291*2π)/4291 weeks
2922.35613 -1.94021 (292*2π)/4291 weeks
2932.33122 -1.61072 (293*2π)/4291 weeks
2941.79765 -1.81266 (294*2π)/4291 weeks
2952.23451 -2.26806 (295*2π)/4291 weeks
2961.99535 -2.2534 (296*2π)/4291 weeks
2972.0914 -2.58036 (297*2π)/4291 weeks
2982.14964 -2.76264 (298*2π)/4291 weeks
2992.51044 -3.23532 (299*2π)/4291 weeks
3003.33147 -2.49898 (300*2π)/4291 weeks
3012.20836 -2.08291 (301*2π)/4291 weeks
3022.32703 -2.78772 (302*2π)/4291 weeks
3032.03717 -3.02181 (303*2π)/4291 weeks
3042.20672 -4.22347 (304*2π)/4291 weeks
3054.42565 -4.68118 (305*2π)/4291 weeks
3065.31052 -2.37387 (306*2π)/4291 weeks
3074.19437 -1.47476 (307*2π)/4291 weeks
3083.36902 -1.53187 (308*2π)/4291 weeks
3093.47119 -1.47971 (309*2π)/4291 weeks
3102.63945 -.47618 (310*2π)/4291 weeks
311.94692 -1.67215 (311*2π)/4291 weeks
3121.94395 -3.34124 (312*2π)/4291 weeks
3133.17882 -2.68881 (313*2π)/4291 weeks
3142.59846 -2.15057 (314*2π)/4291 weeks
3152.7596 -2.24267 (315*2π)/4291 weeks
3163.36011 -1.42546 (316*2π)/4291 weeks
3171.82571 -.28098 (317*2π)/4291 weeks
318-.45922 -.9723 (318*2π)/4291 weeks
319-.50159 -3.24588 (319*2π)/4291 weeks
320.68246 -3.10176 (320*2π)/4291 weeks
321-.18718 -3.14066 (321*2π)/4291 weeks
322-.21536 -4.98667 (322*2π)/4291 weeks
3231.35347 -5.55466 (323*2π)/4291 weeks
3242.03435 -3.9103 (324*2π)/4291 weeks
325.91458 -3.49822 (325*2π)/4291 weeks
326-.07688 -4.66577 (326*2π)/4291 weeks
327-.19933 -5.7613 (327*2π)/4291 weeks
328.53865 -6.93732 (328*2π)/4291 weeks
3291.62772 -7.63974 (329*2π)/4291 weeks
3303.18753 -7.27424 (330*2π)/4291 weeks
3313.77104 -6.49475 (331*2π)/4291 weeks
3323.8532 -6.45964 (332*2π)/4291 weeks
3334.33864 -5.31723 (333*2π)/4291 weeks
3343.8518 -4.88595 (334*2π)/4291 weeks
3353.47172 -4.36161 (335*2π)/4291 weeks
3363.28055 -5.03726 (336*2π)/4291 weeks
3373.3504 -4.44874 (337*2π)/4291 weeks
3382.18254 -4.30473 (338*2π)/4291 weeks
3391.76952 -5.03854 (339*2π)/4291 weeks
3402.33574 -6.34471 (340*2π)/4291 weeks
3413.76323 -5.81947 (341*2π)/4291 weeks
3423.37664 -4.75305 (342*2π)/4291 weeks
3432.40448 -4.62718 (343*2π)/4291 weeks
3442.06939 -4.60134 (344*2π)/4291 weeks
3451.26339 -5.46475 (345*2π)/4291 weeks
3461.81574 -6.83247 (346*2π)/4291 weeks
3472.35892 -6.02547 (347*2π)/4291 weeks
3482.09222 -6.51775 (348*2π)/4291 weeks
3492.50661 -6.27355 (349*2π)/4291 weeks
3502.35222 -6.12498 (350*2π)/4291 weeks
3511.4651 -6.46214 (351*2π)/4291 weeks
3521.35071 -6.94981 (352*2π)/4291 weeks
3531.43894 -7.38603 (353*2π)/4291 weeks
354.89992 -7.61663 (354*2π)/4291 weeks
355.97947 -9.98471 (355*2π)/4291 weeks
3563.60854 -10.41883 (356*2π)/4291 weeks
3574.24336 -8.98692 (357*2π)/4291 weeks
3584.10905 -8.62597 (358*2π)/4291 weeks
3593.98459 -8.08091 (359*2π)/4291 weeks
3603.47931 -7.77802 (360*2π)/4291 weeks
3613.27081 -8.13941 (361*2π)/4291 weeks
3622.46494 -9.33848 (362*2π)/4291 weeks
3634.53788 -10.91025 (363*2π)/4291 weeks
3646.56823 -8.57122 (364*2π)/4291 weeks
3654.55549 -6.89527 (365*2π)/4291 weeks
3664.15392 -7.90712 (366*2π)/4291 weeks
3674.78426 -6.40538 (367*2π)/4291 weeks
3681.08641 -4.98754 (368*2π)/4291 weeks
369-2.45404 -9.54443 (369*2π)/4291 weeks
3701.43233 -14.34641 (370*2π)/4291 weeks
3715.15945 -13.02133 (371*2π)/4291 weeks
3725.06277 -10.66946 (372*2π)/4291 weeks
3734.7076 -11.66479 (373*2π)/4291 weeks
3746.17288 -11.87067 (374*2π)/4291 weeks
3757.53886 -9.29864 (375*2π)/4291 weeks
3763.76488 -7.43858 (376*2π)/4291 weeks
3772.57369 -11.86401 (377*2π)/4291 weeks
3785.38272 -11.41968 (378*2π)/4291 weeks
3795.26623 -10.36683 (379*2π)/4291 weeks
3803.28486 -10.77559 (380*2π)/4291 weeks
3814.62554 -13.09449 (381*2π)/4291 weeks
3826.35624 -11.76173 (382*2π)/4291 weeks
3834.71231 -10.61094 (383*2π)/4291 weeks
3843.52216 -11.95402 (384*2π)/4291 weeks
3853.45838 -14.63988 (385*2π)/4291 weeks
3866.24967 -15.08006 (386*2π)/4291 weeks
3877.62305 -13.84749 (387*2π)/4291 weeks
3887.33571 -12.2352 (388*2π)/4291 weeks
3896.09816 -13.22051 (389*2π)/4291 weeks
3906.71145 -13.83785 (390*2π)/4291 weeks
3916.79163 -14.26977 (391*2π)/4291 weeks
3928.72869 -12.6579 (392*2π)/4291 weeks
3935.78518 -12.50638 (393*2π)/4291 weeks
3945.65101 -15.05137 (394*2π)/4291 weeks
3958.73164 -14.00826 (395*2π)/4291 weeks
3965.66316 -10.87424 (396*2π)/4291 weeks
397.84094 -14.55977 (397*2π)/4291 weeks
3983.45714 -19.94659 (398*2π)/4291 weeks
3996.39999 -20.78511 (399*2π)/4291 weeks
4008.70716 -20.37236 (400*2π)/4291 weeks
4018.86618 -21.06182 (401*2π)/4291 weeks
40212.60065 -21.35516 (402*2π)/4291 weeks
40314.30647 -16.89903 (403*2π)/4291 weeks
40411.67508 -15.0991 (404*2π)/4291 weeks
4059.50258 -17.37577 (405*2π)/4291 weeks
40610.2469 -17.31497 (406*2π)/4291 weeks
4079.0597 -14.44789 (407*2π)/4291 weeks
4082.84844 -16.70471 (408*2π)/4291 weeks
4094.84961 -25.58818 (409*2π)/4291 weeks
4108.84064 -25.33777 (410*2π)/4291 weeks
4116.75762 -27.65406 (411*2π)/4291 weeks
41212.07007 -30.43567 (412*2π)/4291 weeks
41315.29461 -29.52254 (413*2π)/4291 weeks
41417.27723 -29.19224 (414*2π)/4291 weeks
41517.98281 -23.45172 (415*2π)/4291 weeks
4168.02631 -24.33932 (416*2π)/4291 weeks
41710.11732 -34.10197 (417*2π)/4291 weeks
41813.10195 -34.52139 (418*2π)/4291 weeks
4199.16811 -39.27369 (419*2π)/4291 weeks
42012.97563 -53.34103 (420*2π)/4291 weeks
42132.04836 -57.64887 (421*2π)/4291 weeks
42237.3223 -40.40672 (422*2π)/4291 weeks
42319.54936 -39.6938 (423*2π)/4291 weeks
42415.78936 -62.65174 (424*2π)/4291 weeks
42525.14206 -84.51268 (425*2π)/4291 weeks
42641.21192 -106.7454 (426*2π)/4291 weeks
42764.30996 -139.9961 (427*2π)/4291 weeks



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