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Fourier Analysis of UCO (ProShares Ultra Bloomberg Crude Oil ETF)


UCO (ProShares Ultra Bloomberg Crude Oil ETF) appears to have interesting cyclic behaviour every 42 weeks (26.8876*cosine), 24 weeks (17.884*cosine), and 24 weeks (14.7965*sine).

UCO (ProShares Ultra Bloomberg Crude Oil ETF) has an average price of 275.71 (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 11/25/2008 to 10/16/2017 for UCO (ProShares Ultra Bloomberg Crude Oil ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0275.7069   0 
1-51.51755 194.2502 (1*2π)/465465 weeks
212.68759 109.6194 (2*2π)/465233 weeks
315.32848 7.92574 (3*2π)/465155 weeks
4-17.38951 48.85712 (4*2π)/465116 weeks
55.66227 30.56372 (5*2π)/46593 weeks
6-7.53085 6.36742 (6*2π)/46578 weeks
7-4.3059 1.61195 (7*2π)/46566 weeks
837.40603 19.03633 (8*2π)/46558 weeks
9-.01434 16.6521 (9*2π)/46552 weeks
10-10.85219 10.70596 (10*2π)/46547 weeks
1126.88756 1.07067 (11*2π)/46542 weeks
127.52677 16.18857 (12*2π)/46539 weeks
137.03385 6.0442 (13*2π)/46536 weeks
1416.26912 12.01805 (14*2π)/46533 weeks
1512.99396 14.87075 (15*2π)/46531 weeks
16.1208 9.86327 (16*2π)/46529 weeks
178.89797 13.8733 (17*2π)/46527 weeks
188.4329 3.77194 (18*2π)/46526 weeks
1917.88402 14.79648 (19*2π)/46524 weeks
20-.19046 15.50211 (20*2π)/46523 weeks
2110.00071 12.92283 (21*2π)/46522 weeks
221.3451 16.88025 (22*2π)/46521 weeks
23-1.06564 9.38892 (23*2π)/46520 weeks
243.08647 10.22355 (24*2π)/46519 weeks
25-5.62279 4.45912 (25*2π)/46519 weeks
2610.1571 1.34882 (26*2π)/46518 weeks
279.80387 11.50871 (27*2π)/46517 weeks
28-1.22409 10.44397 (28*2π)/46517 weeks
29.50203 7.04293 (29*2π)/46516 weeks
306.58583 4.83325 (30*2π)/46516 weeks
311.62336 8.81027 (31*2π)/46515 weeks
322.60263 5.83238 (32*2π)/46515 weeks
335.67093 4.53637 (33*2π)/46514 weeks
346.25457 10.52735 (34*2π)/46514 weeks
35-.38007 9.6447 (35*2π)/46513 weeks
36-1.18731 5.18982 (36*2π)/46513 weeks
373.30696 3.18821 (37*2π)/46513 weeks
384.91004 4.82356 (38*2π)/46512 weeks
394.14604 11.14483 (39*2π)/46512 weeks
40-.32756 6.91217 (40*2π)/46512 weeks
41-1.17025 6.67807 (41*2π)/46511 weeks
42-1.35121 6.26255 (42*2π)/46511 weeks
43-2.40691 3.95939 (43*2π)/46511 weeks
44-1.68029 -.29545 (44*2π)/46511 weeks
45-1.21639 1.41712 (45*2π)/46510 weeks
462.38082 -2.22012 (46*2π)/46510 weeks
473.00838 -2.05521 (47*2π)/46510 weeks
485.53741 .98988 (48*2π)/46510 weeks
496.52694 .60405 (49*2π)/4659 weeks
505.87994 3.88448 (50*2π)/4659 weeks
516.85751 1.84406 (51*2π)/4659 weeks
526.00719 7.66047 (52*2π)/4659 weeks
531.64491 5.65692 (53*2π)/4659 weeks
542.8745 2.56008 (54*2π)/4659 weeks
552.15116 3.80332 (55*2π)/4658 weeks
562.9634 1.2323 (56*2π)/4658 weeks
575.50959 2.5194 (57*2π)/4658 weeks
586.24783 6.98594 (58*2π)/4658 weeks
59-1.16588 4.62346 (59*2π)/4658 weeks
604.25034 4.4886 (60*2π)/4658 weeks
61.65002 2.44163 (61*2π)/4658 weeks
621.19611 1.18517 (62*2π)/4658 weeks
636.06025 -.91179 (63*2π)/4657 weeks
647.96695 4.90438 (64*2π)/4657 weeks
652.69659 6.92226 (65*2π)/4657 weeks
661.68466 4.95195 (66*2π)/4657 weeks
672.77638 2.23785 (67*2π)/4657 weeks
682.84822 4.59917 (68*2π)/4657 weeks
69.9055 3.62815 (69*2π)/4657 weeks
703.47713 .12328 (70*2π)/4657 weeks
715.76421 4.51383 (71*2π)/4657 weeks
721.06141 7.04813 (72*2π)/4656 weeks
73-.19335 1.5977 (73*2π)/4656 weeks
743.14349 2.04332 (74*2π)/4656 weeks
752.16373 5.25636 (75*2π)/4656 weeks
76.19385 2.23817 (76*2π)/4656 weeks
77.66285 .69273 (77*2π)/4656 weeks
784.13706 .2285 (78*2π)/4656 weeks
793.58905 2.51797 (79*2π)/4656 weeks
804.16437 .99517 (80*2π)/4656 weeks
814.70538 4.35382 (81*2π)/4656 weeks
823.70572 3.8528 (82*2π)/4656 weeks
832.6082 5.91333 (83*2π)/4656 weeks
84-.16256 2.92913 (84*2π)/4656 weeks
85.69701 2.32983 (85*2π)/4655 weeks
862.24641 .35943 (86*2π)/4655 weeks
872.54319 3.46702 (87*2π)/4655 weeks
882.61555 1.76946 (88*2π)/4655 weeks
891.75129 1.82752 (89*2π)/4655 weeks
902.30758 2.32087 (90*2π)/4655 weeks
913.12276 1.55912 (91*2π)/4655 weeks
922.30856 3.32686 (92*2π)/4655 weeks
931.86787 2.64627 (93*2π)/4655 weeks
94.94494 1.16542 (94*2π)/4655 weeks
952.26163 1.97701 (95*2π)/4655 weeks
963.6179 .05744 (96*2π)/4655 weeks
972.46752 3.49909 (97*2π)/4655 weeks
982.62916 1.44555 (98*2π)/4655 weeks
993.14807 1.91746 (99*2π)/4655 weeks
1002.88295 1.67419 (100*2π)/4655 weeks
1012.98338 3.53031 (101*2π)/4655 weeks
1022.7469 1.62134 (102*2π)/4655 weeks
1031.89675 4.08865 (103*2π)/4655 weeks
1041.80637 2.22792 (104*2π)/4654 weeks
105.94803 .47002 (105*2π)/4654 weeks
1063.8047 1.88333 (106*2π)/4654 weeks
1073.63503 2.72372 (107*2π)/4654 weeks
1081.96692 3.62948 (108*2π)/4654 weeks
109.76688 1.95048 (109*2π)/4654 weeks
1103.74453 1.0275 (110*2π)/4654 weeks
1112.34514 4.40893 (111*2π)/4654 weeks
1122.00979 3.42873 (112*2π)/4654 weeks
113.29606 2.79575 (113*2π)/4654 weeks
1141.07955 1.65733 (114*2π)/4654 weeks
1152.11002 2.66667 (115*2π)/4654 weeks
116-.51613 4.41124 (116*2π)/4654 weeks
117-1.43164 -.58499 (117*2π)/4654 weeks
1182.09169 .02336 (118*2π)/4654 weeks
1192.13834 .86651 (119*2π)/4654 weeks
1201.63884 .90403 (120*2π)/4654 weeks
1212.94776 1.83924 (121*2π)/4654 weeks
1222.07505 2.65527 (122*2π)/4654 weeks
123.21274 1.44207 (123*2π)/4654 weeks
1241.72842 1.73619 (124*2π)/4654 weeks
1251.46865 1.98782 (125*2π)/4654 weeks
126.58605 1.736 (126*2π)/4654 weeks
1271.04116 2.64977 (127*2π)/4654 weeks
128-1.33433 1.42023 (128*2π)/4654 weeks
129-.50043 -1.02948 (129*2π)/4654 weeks
1301.3527 .19112 (130*2π)/4654 weeks
1311.02778 -.05646 (131*2π)/4654 weeks
1321.07268 -.29679 (132*2π)/4654 weeks
1332.50865 -.25138 (133*2π)/4653 weeks
1341.62343 2.08387 (134*2π)/4653 weeks
135-.11577 .37103 (135*2π)/4653 weeks
136.44548 -.95291 (136*2π)/4653 weeks
1372.4065 -1.3573 (137*2π)/4653 weeks
1382.60554 .9589 (138*2π)/4653 weeks
139.91755 1.02211 (139*2π)/4653 weeks
140.59294 -.60488 (140*2π)/4653 weeks
1411.9577 -.63391 (141*2π)/4653 weeks
1421.96536 -.11112 (142*2π)/4653 weeks
1431.55749 -1.14768 (143*2π)/4653 weeks
1443.12084 .64536 (144*2π)/4653 weeks
1452.01911 -.3869 (145*2π)/4653 weeks
1461.60652 .69746 (146*2π)/4653 weeks
1471.99182 .05881 (147*2π)/4653 weeks
1481.48905 .74132 (148*2π)/4653 weeks
1491.34738 -.17954 (149*2π)/4653 weeks
150.50888 -1.01551 (150*2π)/4653 weeks
1513.20364 -1.11153 (151*2π)/4653 weeks
1521.61732 .93831 (152*2π)/4653 weeks
153.68649 -.86436 (153*2π)/4653 weeks
1542.13685 -1.50388 (154*2π)/4653 weeks
1552.113 -.1705 (155*2π)/4653 weeks
1561.71206 -.29445 (156*2π)/4653 weeks
157.40765 -1.15265 (157*2π)/4653 weeks
1582.37423 -2.6916 (158*2π)/4653 weeks
1594.14154 -1.82505 (159*2π)/4653 weeks
1602.33177 1.06623 (160*2π)/4653 weeks
1611.65462 -1.00773 (161*2π)/4653 weeks
1622.2312 -2.38944 (162*2π)/4653 weeks
1632.57117 -.85989 (163*2π)/4653 weeks
1642.20234 -2.1257 (164*2π)/4653 weeks
1653.57852 -2.99831 (165*2π)/4653 weeks
1664.73848 -1.15224 (166*2π)/4653 weeks
1674.47242 -.79525 (167*2π)/4653 weeks
1683.40773 -1.14993 (168*2π)/4653 weeks
1695.35462 .04745 (169*2π)/4653 weeks
1703.67289 .10603 (170*2π)/4653 weeks
1713.61607 .63064 (171*2π)/4653 weeks
1722.62264 .9306 (172*2π)/4653 weeks
1732.11849 -1.16063 (173*2π)/4653 weeks
1743.93111 -.76066 (174*2π)/4653 weeks
1753.0773 -.24441 (175*2π)/4653 weeks
1762.77154 -1.27253 (176*2π)/4653 weeks
1774.77289 -1.70888 (177*2π)/4653 weeks
1784.56376 -.13413 (178*2π)/4653 weeks
1794.5614 .52321 (179*2π)/4653 weeks
1803.77197 -.9306 (180*2π)/4653 weeks
1815.55941 .42588 (181*2π)/4653 weeks
1823.97303 1.49205 (182*2π)/4653 weeks
1834.21886 .23922 (183*2π)/4653 weeks
1844.40428 1.1835 (184*2π)/4653 weeks
1853.95421 2.0876 (185*2π)/4653 weeks
1862.82584 2.03723 (186*2π)/4653 weeks
1871.26938 .93906 (187*2π)/4652 weeks
1883.20704 -.66517 (188*2π)/4652 weeks
1894.26889 .45924 (189*2π)/4652 weeks
1902.58333 1.63044 (190*2π)/4652 weeks
1912.74372 -.0228 (191*2π)/4652 weeks
1923.40952 .21463 (192*2π)/4652 weeks
1932.91499 1.03825 (193*2π)/4652 weeks
1942.86145 .73006 (194*2π)/4652 weeks
1952.68846 .07757 (195*2π)/4652 weeks
1963.18846 .38495 (196*2π)/4652 weeks
1973.03306 .55293 (197*2π)/4652 weeks
1983.09728 -.08633 (198*2π)/4652 weeks
1992.97623 .51795 (199*2π)/4652 weeks
2003.97568 .13271 (200*2π)/4652 weeks
2013.404 1.053 (201*2π)/4652 weeks
2023.16211 1.64886 (202*2π)/4652 weeks
2032.1637 .44454 (203*2π)/4652 weeks
2043.79694 1.01389 (204*2π)/4652 weeks
2051.2393 1.54657 (205*2π)/4652 weeks
2062.46515 .02796 (206*2π)/4652 weeks
2072.72678 .09499 (207*2π)/4652 weeks
2082.20801 .52332 (208*2π)/4652 weeks
2093.33861 -.24106 (209*2π)/4652 weeks
2102.8452 1.04959 (210*2π)/4652 weeks
2113.08778 .26728 (211*2π)/4652 weeks
2122.34616 1.90952 (212*2π)/4652 weeks
2131.54785 .2059 (213*2π)/4652 weeks
2142.45102 -.00234 (214*2π)/4652 weeks
2152.33123 .80577 (215*2π)/4652 weeks
2161.77468 -.23584 (216*2π)/4652 weeks
2172.19042 -.73238 (217*2π)/4652 weeks
2183.08474 .21254 (218*2π)/4652 weeks
2192.22987 -.69619 (219*2π)/4652 weeks
2203.31591 -1.1529 (220*2π)/4652 weeks
2213.98667 .8573 (221*2π)/4652 weeks
2223.01439 1.06347 (222*2π)/4652 weeks
2231.76192 .5571 (223*2π)/4652 weeks
2241.13237 -.27784 (224*2π)/4652 weeks
2253.22058 -1.27789 (225*2π)/4652 weeks
2263.71754 -.5588 (226*2π)/4652 weeks
2273.02364 1.44086 (227*2π)/4652 weeks
2282.40303 .28436 (228*2π)/4652 weeks
2291.70183 -.13116 (229*2π)/4652 weeks
2302.61676 -.69847 (230*2π)/4652 weeks
2312.69232 -.50638 (231*2π)/4652 weeks
2323.87064 -1.57839 (232*2π)/4652 weeks
2333.87064 1.57839 (233*2π)/4652 weeks
2342.69232 .50638 (234*2π)/4652 weeks
2352.61676 .69847 (235*2π)/4652 weeks
2361.70183 .13116 (236*2π)/4652 weeks
2372.40303 -.28436 (237*2π)/4652 weeks
2383.02364 -1.44086 (238*2π)/4652 weeks
2393.71754 .5588 (239*2π)/4652 weeks
2403.22058 1.27789 (240*2π)/4652 weeks
2411.13237 .27784 (241*2π)/4652 weeks
2421.76192 -.5571 (242*2π)/4652 weeks
2433.01439 -1.06347 (243*2π)/4652 weeks
2443.98667 -.8573 (244*2π)/4652 weeks
2453.31591 1.1529 (245*2π)/4652 weeks
2462.22987 .69619 (246*2π)/4652 weeks
2473.08474 -.21254 (247*2π)/4652 weeks
2482.19042 .73238 (248*2π)/4652 weeks
2491.77468 .23584 (249*2π)/4652 weeks
2502.33123 -.80577 (250*2π)/4652 weeks
2512.45102 .00234 (251*2π)/4652 weeks
2521.54785 -.2059 (252*2π)/4652 weeks
2532.34616 -1.90952 (253*2π)/4652 weeks
2543.08778 -.26728 (254*2π)/4652 weeks
2552.8452 -1.04959 (255*2π)/4652 weeks
2563.33861 .24106 (256*2π)/4652 weeks
2572.20801 -.52332 (257*2π)/4652 weeks
2582.72678 -.09499 (258*2π)/4652 weeks
2592.46515 -.02796 (259*2π)/4652 weeks
2601.2393 -1.54657 (260*2π)/4652 weeks
2613.79694 -1.01389 (261*2π)/4652 weeks
2622.1637 -.44454 (262*2π)/4652 weeks
2633.16211 -1.64886 (263*2π)/4652 weeks
2643.404 -1.053 (264*2π)/4652 weeks
2653.97568 -.13271 (265*2π)/4652 weeks
2662.97623 -.51795 (266*2π)/4652 weeks
2673.09728 .08633 (267*2π)/4652 weeks
2683.03306 -.55293 (268*2π)/4652 weeks
2693.18846 -.38495 (269*2π)/4652 weeks
2702.68846 -.07757 (270*2π)/4652 weeks
2712.86145 -.73006 (271*2π)/4652 weeks
2722.91499 -1.03825 (272*2π)/4652 weeks
2733.40952 -.21463 (273*2π)/4652 weeks
2742.74372 .0228 (274*2π)/4652 weeks
2752.58333 -1.63044 (275*2π)/4652 weeks
2764.26889 -.45924 (276*2π)/4652 weeks
2773.20704 .66517 (277*2π)/4652 weeks
2781.26938 -.93906 (278*2π)/4652 weeks
2792.82584 -2.03723 (279*2π)/4652 weeks
2803.95421 -2.0876 (280*2π)/4652 weeks
2814.40428 -1.1835 (281*2π)/4652 weeks
2824.21886 -.23922 (282*2π)/4652 weeks
2833.97303 -1.49205 (283*2π)/4652 weeks
2845.55941 -.42588 (284*2π)/4652 weeks
2853.77197 .9306 (285*2π)/4652 weeks
2864.5614 -.52321 (286*2π)/4652 weeks
2874.56376 .13413 (287*2π)/4652 weeks
2884.77289 1.70888 (288*2π)/4652 weeks
2892.77154 1.27253 (289*2π)/4652 weeks
2903.0773 .24441 (290*2π)/4652 weeks
2913.93111 .76066 (291*2π)/4652 weeks
2922.11849 1.16063 (292*2π)/4652 weeks
2932.62264 -.9306 (293*2π)/4652 weeks
2943.61607 -.63064 (294*2π)/4652 weeks
2953.67289 -.10603 (295*2π)/4652 weeks
2965.35462 -.04745 (296*2π)/4652 weeks
2973.40773 1.14993 (297*2π)/4652 weeks
2984.47242 .79525 (298*2π)/4652 weeks
2994.73848 1.15224 (299*2π)/4652 weeks
3003.57852 2.99831 (300*2π)/4652 weeks
3012.20234 2.1257 (301*2π)/4652 weeks
3022.57117 .85989 (302*2π)/4652 weeks
3032.2312 2.38944 (303*2π)/4652 weeks
3041.65462 1.00773 (304*2π)/4652 weeks
3052.33177 -1.06623 (305*2π)/4652 weeks
3064.14154 1.82505 (306*2π)/4652 weeks
3072.37423 2.6916 (307*2π)/4652 weeks
308.40765 1.15265 (308*2π)/4652 weeks
3091.71206 .29445 (309*2π)/4652 weeks
3102.113 .1705 (310*2π)/4652 weeks
3112.13685 1.50388 (311*2π)/4651 weeks
312.68649 .86436 (312*2π)/4651 weeks
3131.61732 -.93831 (313*2π)/4651 weeks
3143.20364 1.11153 (314*2π)/4651 weeks
315.50888 1.01551 (315*2π)/4651 weeks
3161.34738 .17954 (316*2π)/4651 weeks
3171.48905 -.74132 (317*2π)/4651 weeks
3181.99182 -.05881 (318*2π)/4651 weeks
3191.60652 -.69746 (319*2π)/4651 weeks
3202.01911 .3869 (320*2π)/4651 weeks
3213.12084 -.64536 (321*2π)/4651 weeks
3221.55749 1.14768 (322*2π)/4651 weeks
3231.96536 .11112 (323*2π)/4651 weeks
3241.9577 .63391 (324*2π)/4651 weeks
325.59294 .60488 (325*2π)/4651 weeks
326.91755 -1.02211 (326*2π)/4651 weeks
3272.60554 -.9589 (327*2π)/4651 weeks
3282.4065 1.3573 (328*2π)/4651 weeks
329.44548 .95291 (329*2π)/4651 weeks
330-.11577 -.37103 (330*2π)/4651 weeks
3311.62343 -2.08387 (331*2π)/4651 weeks
3322.50865 .25138 (332*2π)/4651 weeks
3331.07268 .29679 (333*2π)/4651 weeks
3341.02778 .05646 (334*2π)/4651 weeks
3351.3527 -.19112 (335*2π)/4651 weeks
336-.50043 1.02948 (336*2π)/4651 weeks
337-1.33433 -1.42023 (337*2π)/4651 weeks
3381.04116 -2.64977 (338*2π)/4651 weeks
339.58605 -1.736 (339*2π)/4651 weeks
3401.46865 -1.98782 (340*2π)/4651 weeks
3411.72842 -1.73619 (341*2π)/4651 weeks
342.21274 -1.44207 (342*2π)/4651 weeks
3432.07505 -2.65527 (343*2π)/4651 weeks
3442.94776 -1.83924 (344*2π)/4651 weeks
3451.63884 -.90403 (345*2π)/4651 weeks
3462.13834 -.86651 (346*2π)/4651 weeks
3472.09169 -.02336 (347*2π)/4651 weeks
348-1.43164 .58499 (348*2π)/4651 weeks
349-.51613 -4.41124 (349*2π)/4651 weeks
3502.11002 -2.66667 (350*2π)/4651 weeks
3511.07955 -1.65733 (351*2π)/4651 weeks
352.29606 -2.79575 (352*2π)/4651 weeks
3532.00979 -3.42873 (353*2π)/4651 weeks
3542.34514 -4.40893 (354*2π)/4651 weeks
3553.74453 -1.0275 (355*2π)/4651 weeks
356.76688 -1.95048 (356*2π)/4651 weeks
3571.96692 -3.62948 (357*2π)/4651 weeks
3583.63503 -2.72372 (358*2π)/4651 weeks
3593.8047 -1.88333 (359*2π)/4651 weeks
360.94803 -.47002 (360*2π)/4651 weeks
3611.80637 -2.22792 (361*2π)/4651 weeks
3621.89675 -4.08865 (362*2π)/4651 weeks
3632.7469 -1.62134 (363*2π)/4651 weeks
3642.98338 -3.53031 (364*2π)/4651 weeks
3652.88295 -1.67419 (365*2π)/4651 weeks
3663.14807 -1.91746 (366*2π)/4651 weeks
3672.62916 -1.44555 (367*2π)/4651 weeks
3682.46752 -3.49909 (368*2π)/4651 weeks
3693.6179 -.05744 (369*2π)/4651 weeks
3702.26163 -1.97701 (370*2π)/4651 weeks
371.94494 -1.16542 (371*2π)/4651 weeks
3721.86787 -2.64627 (372*2π)/4651 weeks
3732.30856 -3.32686 (373*2π)/4651 weeks
3743.12276 -1.55912 (374*2π)/4651 weeks
3752.30758 -2.32087 (375*2π)/4651 weeks
3761.75129 -1.82752 (376*2π)/4651 weeks
3772.61555 -1.76946 (377*2π)/4651 weeks
3782.54319 -3.46702 (378*2π)/4651 weeks
3792.24641 -.35943 (379*2π)/4651 weeks
380.69701 -2.32983 (380*2π)/4651 weeks
381-.16256 -2.92913 (381*2π)/4651 weeks
3822.6082 -5.91333 (382*2π)/4651 weeks
3833.70572 -3.8528 (383*2π)/4651 weeks
3844.70538 -4.35382 (384*2π)/4651 weeks
3854.16437 -.99517 (385*2π)/4651 weeks
3863.58905 -2.51797 (386*2π)/4651 weeks
3874.13706 -.2285 (387*2π)/4651 weeks
388.66285 -.69273 (388*2π)/4651 weeks
389.19385 -2.23817 (389*2π)/4651 weeks
3902.16373 -5.25636 (390*2π)/4651 weeks
3913.14349 -2.04332 (391*2π)/4651 weeks
392-.19335 -1.5977 (392*2π)/4651 weeks
3931.06141 -7.04813 (393*2π)/4651 weeks
3945.76421 -4.51383 (394*2π)/4651 weeks
3953.47713 -.12328 (395*2π)/4651 weeks
396.9055 -3.62815 (396*2π)/4651 weeks
3972.84822 -4.59917 (397*2π)/4651 weeks
3982.77638 -2.23785 (398*2π)/4651 weeks
3991.68466 -4.95195 (399*2π)/4651 weeks
4002.69659 -6.92226 (400*2π)/4651 weeks
4017.96695 -4.90438 (401*2π)/4651 weeks
4026.06025 .91179 (402*2π)/4651 weeks
4031.19611 -1.18517 (403*2π)/4651 weeks
404.65002 -2.44163 (404*2π)/4651 weeks
4054.25034 -4.4886 (405*2π)/4651 weeks
406-1.16588 -4.62346 (406*2π)/4651 weeks
4076.24783 -6.98594 (407*2π)/4651 weeks
4085.50959 -2.5194 (408*2π)/4651 weeks
4092.9634 -1.2323 (409*2π)/4651 weeks
4102.15116 -3.80332 (410*2π)/4651 weeks
4112.8745 -2.56008 (411*2π)/4651 weeks
4121.64491 -5.65692 (412*2π)/4651 weeks
4136.00719 -7.66047 (413*2π)/4651 weeks
4146.85751 -1.84406 (414*2π)/4651 weeks
4155.87994 -3.88448 (415*2π)/4651 weeks
4166.52694 -.60405 (416*2π)/4651 weeks
4175.53741 -.98988 (417*2π)/4651 weeks
4183.00838 2.05521 (418*2π)/4651 weeks
4192.38082 2.22012 (419*2π)/4651 weeks
420-1.21639 -1.41712 (420*2π)/4651 weeks
421-1.68029 .29545 (421*2π)/4651 weeks
422-2.40691 -3.95939 (422*2π)/4651 weeks
423-1.35121 -6.26255 (423*2π)/4651 weeks
424-1.17025 -6.67807 (424*2π)/4651 weeks
425-.32756 -6.91217 (425*2π)/4651 weeks
4264.14604 -11.14483 (426*2π)/4651 weeks
4274.91004 -4.82356 (427*2π)/4651 weeks
4283.30696 -3.18821 (428*2π)/4651 weeks
429-1.18731 -5.18982 (429*2π)/4651 weeks
430-.38007 -9.6447 (430*2π)/4651 weeks
4316.25457 -10.52735 (431*2π)/4651 weeks
4325.67093 -4.53637 (432*2π)/4651 weeks
4332.60263 -5.83238 (433*2π)/4651 weeks
4341.62336 -8.81027 (434*2π)/4651 weeks
4356.58583 -4.83325 (435*2π)/4651 weeks
436.50203 -7.04293 (436*2π)/4651 weeks
437-1.22409 -10.44397 (437*2π)/4651 weeks
4389.80387 -11.50871 (438*2π)/4651 weeks
43910.1571 -1.34882 (439*2π)/4651 weeks
440-5.62279 -4.45912 (440*2π)/4651 weeks
4413.08647 -10.22355 (441*2π)/4651 weeks
442-1.06564 -9.38892 (442*2π)/4651 weeks
4431.3451 -16.88025 (443*2π)/4651 weeks
44410.00071 -12.92283 (444*2π)/4651 weeks
445-.19046 -15.50211 (445*2π)/4651 weeks
44617.88402 -14.79648 (446*2π)/4651 weeks
4478.4329 -3.77194 (447*2π)/4651 weeks
4488.89797 -13.8733 (448*2π)/4651 weeks
449.1208 -9.86327 (449*2π)/4651 weeks
45012.99396 -14.87075 (450*2π)/4651 weeks
45116.26912 -12.01805 (451*2π)/4651 weeks
4527.03385 -6.0442 (452*2π)/4651 weeks
4537.52677 -16.18857 (453*2π)/4651 weeks
45426.88756 -1.07067 (454*2π)/4651 weeks
455-10.85219 -10.70596 (455*2π)/4651 weeks
456-.01434 -16.6521 (456*2π)/4651 weeks
45737.40603 -19.03633 (457*2π)/4651 weeks
458-4.3059 -1.61195 (458*2π)/4651 weeks
459-7.53085 -6.36742 (459*2π)/4651 weeks
4605.66227 -30.56372 (460*2π)/4651 weeks
461-17.38951 -48.85712 (461*2π)/4651 weeks
46215.32848 -7.92574 (462*2π)/4651 weeks
46312.68759 -109.6194 (463*2π)/4651 weeks



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