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Fourier Analysis of UCO (ProShares Ultra DJ-UBS Crude Oil ETF)


UCO (ProShares Ultra DJ-UBS Crude Oil ETF) appears to have interesting cyclic behaviour every 24 weeks (21.7031*sine), 48 weeks (18.8104*sine), and 40 weeks (18.6544*sine).

UCO (ProShares Ultra DJ-UBS Crude Oil ETF) has an average price of 268.82 (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 1/16/2018 for UCO (ProShares Ultra DJ-UBS Crude Oil ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0268.8192   0 
1-45.70652 202.4296 (1*2π)/478478 weeks
220.75535 104.1436 (2*2π)/478239 weeks
33.78179 5.42311 (3*2π)/478159 weeks
4-10.54544 55.87416 (4*2π)/478120 weeks
57.50315 24.98187 (5*2π)/47896 weeks
6-11.89544 10.71946 (6*2π)/47880 weeks
7-2.39425 8.18642 (7*2π)/47868 weeks
835.57736 1.42495 (8*2π)/47860 weeks
9-.61589 24.42701 (9*2π)/47853 weeks
10-2.57433 18.8104 (10*2π)/47848 weeks
1115.40429 -11.473 (11*2π)/47843 weeks
1212.85016 18.65438 (12*2π)/47840 weeks
135.39967 9.19373 (13*2π)/47837 weeks
1414.97597 5.89298 (14*2π)/47834 weeks
1511.39993 12.96594 (15*2π)/47832 weeks
164.63967 18.5907 (16*2π)/47830 weeks
1710.11882 6.30783 (17*2π)/47828 weeks
182.92965 8.60696 (18*2π)/47827 weeks
1914.50484 5.873 (19*2π)/47825 weeks
2010.04277 21.70306 (20*2π)/47824 weeks
213.82919 8.07782 (21*2π)/47823 weeks
227.20677 16.4353 (22*2π)/47822 weeks
23-1.09186 13.85561 (23*2π)/47821 weeks
24.66116 7.64594 (24*2π)/47820 weeks
25.74696 11.67914 (25*2π)/47819 weeks
26-2.34822 -1.05456 (26*2π)/47818 weeks
2710.73864 4.70339 (27*2π)/47818 weeks
287.68841 13.46961 (28*2π)/47817 weeks
29-.62576 7.78304 (29*2π)/47816 weeks
30.17236 5.55424 (30*2π)/47816 weeks
316.83782 6.19748 (31*2π)/47815 weeks
321.1862 7.67952 (32*2π)/47815 weeks
332.48806 5.49588 (33*2π)/47814 weeks
345.86833 4.61611 (34*2π)/47814 weeks
355.80456 10.46882 (35*2π)/47814 weeks
36-.41547 9.23279 (36*2π)/47813 weeks
37-1.15183 5.03295 (37*2π)/47813 weeks
383.10409 2.9621 (38*2π)/47813 weeks
394.60346 4.57861 (39*2π)/47812 weeks
404.85773 10.32524 (40*2π)/47812 weeks
41-.67485 7.00949 (41*2π)/47812 weeks
42-.88962 6.8701 (42*2π)/47811 weeks
43-.81435 5.96766 (43*2π)/47811 weeks
44-2.30493 3.95803 (44*2π)/47811 weeks
45-2.89168 .57937 (45*2π)/47811 weeks
46-.03764 1.66113 (46*2π)/47810 weeks
47.49321 -2.59716 (47*2π)/47810 weeks
482.28464 -.95 (48*2π)/47810 weeks
496.0429 -.31097 (49*2π)/47810 weeks
505.27561 .20441 (50*2π)/47810 weeks
516.93197 2.74189 (51*2π)/4789 weeks
524.73292 2.16827 (52*2π)/4789 weeks
538.06379 5.08214 (53*2π)/4789 weeks
542.75958 6.87824 (54*2π)/4789 weeks
551.22593 3.60215 (55*2π)/4789 weeks
563.46663 3.7165 (56*2π)/4789 weeks
571.94846 2.51455 (57*2π)/4788 weeks
584.57034 1.23257 (58*2π)/4788 weeks
596.30087 3.06339 (59*2π)/4788 weeks
603.35003 8.18114 (60*2π)/4788 weeks
61.58122 1.33583 (61*2π)/4788 weeks
622.06102 5.38209 (62*2π)/4788 weeks
631.31616 1.88373 (63*2π)/4788 weeks
641.44553 -.06967 (64*2π)/4787 weeks
657.07213 .10705 (65*2π)/4787 weeks
667.08126 5.84681 (66*2π)/4787 weeks
672.04474 6.00206 (67*2π)/4787 weeks
681.25402 4.51968 (68*2π)/4787 weeks
693.1336 2.33139 (69*2π)/4787 weeks
702.52059 4.44531 (70*2π)/4787 weeks
71.72861 3.28932 (71*2π)/4787 weeks
723.62598 .13075 (72*2π)/4787 weeks
735.56119 4.41197 (73*2π)/4787 weeks
741.08291 6.84599 (74*2π)/4786 weeks
75-.3854 1.67616 (75*2π)/4786 weeks
762.93244 1.85631 (76*2π)/4786 weeks
772.60117 4.93679 (77*2π)/4786 weeks
78.01314 2.4004 (78*2π)/4786 weeks
79.55276 1.01935 (79*2π)/4786 weeks
803.47446 -.33317 (80*2π)/4786 weeks
813.85197 2.24404 (81*2π)/4786 weeks
823.24276 1.08989 (82*2π)/4786 weeks
835.31303 3.42562 (83*2π)/4786 weeks
843.31437 3.63346 (84*2π)/4786 weeks
853.37358 4.9683 (85*2π)/4786 weeks
86-.39227 4.36937 (86*2π)/4786 weeks
87.8475 2.38911 (87*2π)/4785 weeks
88.83054 .90181 (88*2π)/4785 weeks
893.69562 2.11626 (89*2π)/4785 weeks
901.35846 1.92752 (90*2π)/4785 weeks
912.06527 2.6249 (91*2π)/4785 weeks
922.52449 1.73931 (92*2π)/4785 weeks
932.01379 1.66121 (93*2π)/4785 weeks
943.36655 2.55367 (94*2π)/4785 weeks
951.71525 2.71119 (95*2π)/4785 weeks
961.2838 2.61385 (96*2π)/4785 weeks
971.96911 .63214 (97*2π)/4785 weeks
981.43175 1.35319 (98*2π)/4785 weeks
994.51605 1.2979 (99*2π)/4785 weeks
1001.55089 2.56927 (100*2π)/4785 weeks
1012.69701 1.57565 (101*2π)/4785 weeks
1022.98703 2.10806 (102*2π)/4785 weeks
1033.20303 1.61451 (103*2π)/4785 weeks
1042.3122 3.38638 (104*2π)/4785 weeks
1053.12751 1.74254 (105*2π)/4785 weeks
1061.36829 3.74143 (106*2π)/4785 weeks
1071.7383 2.28844 (107*2π)/4784 weeks
1081.12694 .23044 (108*2π)/4784 weeks
1093.63622 1.89736 (109*2π)/4784 weeks
1103.5192 2.65455 (110*2π)/4784 weeks
1111.92749 3.5264 (111*2π)/4784 weeks
112.71561 2.01533 (112*2π)/4784 weeks
1133.36158 .79094 (113*2π)/4784 weeks
1142.69415 4.29925 (114*2π)/4784 weeks
1151.91114 3.09661 (115*2π)/4784 weeks
116.29313 3.04979 (116*2π)/4784 weeks
117.7915 1.7301 (117*2π)/4784 weeks
1181.9815 2.23514 (118*2π)/4784 weeks
119.67664 4.30354 (119*2π)/4784 weeks
120-2.27472 .67518 (120*2π)/4784 weeks
1211.58892 -.69947 (121*2π)/4784 weeks
1221.91944 .6768 (122*2π)/4784 weeks
1231.7107 1.26739 (123*2π)/4784 weeks
1242.7283 .86252 (124*2π)/4784 weeks
1252.1306 2.2432 (125*2π)/4784 weeks
126.57081 2.75656 (126*2π)/4784 weeks
1271.51643 .95629 (127*2π)/4784 weeks
1281.35762 1.75647 (128*2π)/4784 weeks
129.94846 2.20534 (129*2π)/4784 weeks
1301.09943 1.5041 (130*2π)/4784 weeks
131-.33648 2.75714 (131*2π)/4784 weeks
132-1.26513 .43076 (132*2π)/4784 weeks
133.81026 -1.15921 (133*2π)/4784 weeks
134.88382 .23042 (134*2π)/4784 weeks
1351.04275 -.03418 (135*2π)/4784 weeks
1361.27015 -.5507 (136*2π)/4784 weeks
1372.71259 .33338 (137*2π)/4783 weeks
138.73975 1.93916 (138*2π)/4783 weeks
139-.03694 .01597 (139*2π)/4783 weeks
140.64394 -1.17523 (140*2π)/4783 weeks
1412.67263 -1.05954 (141*2π)/4783 weeks
1422.25673 1.05798 (142*2π)/4783 weeks
143.70931 .86081 (143*2π)/4783 weeks
144.64164 -.71949 (144*2π)/4783 weeks
1451.88612 -.57138 (145*2π)/4783 weeks
1461.86966 -.09213 (146*2π)/4783 weeks
1471.49364 -1.12482 (147*2π)/4783 weeks
1483.06953 .55396 (148*2π)/4783 weeks
1491.81542 -.35498 (149*2π)/4783 weeks
1501.67695 .76415 (150*2π)/4783 weeks
1511.86914 -.00498 (151*2π)/4783 weeks
1521.63401 .68876 (152*2π)/4783 weeks
1531.1429 -.22121 (153*2π)/4783 weeks
154.45827 -.45888 (154*2π)/4783 weeks
1552.60996 -1.64475 (155*2π)/4783 weeks
1562.21702 .90829 (156*2π)/4783 weeks
157.53054 -.30275 (157*2π)/4783 weeks
1581.56401 -1.49418 (158*2π)/4783 weeks
1592.46915 -.40232 (159*2π)/4783 weeks
1601.73484 -.38366 (160*2π)/4783 weeks
161.87891 -.34295 (161*2π)/4783 weeks
1621.26877 -2.62851 (162*2π)/4783 weeks
1633.10979 -2.30652 (163*2π)/4783 weeks
1644.13418 .24682 (164*2π)/4783 weeks
1651.13861 -.40876 (165*2π)/4783 weeks
1661.33561 -1.3685 (166*2π)/4783 weeks
1673.14312 -1.64627 (167*2π)/4783 weeks
1681.9418 -1.30372 (168*2π)/4783 weeks
1692.45834 -2.44776 (169*2π)/4783 weeks
1704.40491 -2.55828 (170*2π)/4783 weeks
1714.18612 -.92886 (171*2π)/4783 weeks
1724.11899 -.32249 (172*2π)/4783 weeks
1733.9744 -1.61892 (173*2π)/4783 weeks
1744.61427 .68994 (174*2π)/4783 weeks
1753.79171 .04425 (175*2π)/4783 weeks
1763.38752 .59098 (176*2π)/4783 weeks
1772.15003 .70287 (177*2π)/4783 weeks
1782.35746 -1.38726 (178*2π)/4783 weeks
1793.77831 -.5291 (179*2π)/4783 weeks
1802.90758 -.30517 (180*2π)/4783 weeks
1812.72712 -1.37624 (181*2π)/4783 weeks
1824.71365 -1.57529 (182*2π)/4783 weeks
1834.4016 -.14128 (183*2π)/4783 weeks
1844.42452 .49928 (184*2π)/4783 weeks
1853.57597 -.85485 (185*2π)/4783 weeks
1865.40718 .27381 (186*2π)/4783 weeks
1874.01812 1.49898 (187*2π)/4783 weeks
1883.89208 .20834 (188*2π)/4783 weeks
1894.30393 1.10216 (189*2π)/4783 weeks
1904.04699 1.88999 (190*2π)/4783 weeks
1912.90234 1.99486 (191*2π)/4783 weeks
1921.50843 1.49523 (192*2π)/4782 weeks
1932.51977 -.80733 (193*2π)/4782 weeks
1943.86802 -.00545 (194*2π)/4782 weeks
1953.24262 1.73998 (195*2π)/4782 weeks
1962.16607 .25564 (196*2π)/4782 weeks
1973.07492 .18049 (197*2π)/4782 weeks
1983.36677 .9528 (198*2π)/4782 weeks
1992.77194 .58897 (199*2π)/4782 weeks
2002.43104 .47217 (200*2π)/4782 weeks
2013.05322 .11468 (201*2π)/4782 weeks
2023.00949 .42314 (202*2π)/4782 weeks
2032.64452 .36213 (203*2π)/4782 weeks
2043.39345 .30948 (204*2π)/4782 weeks
2052.94162 -.04422 (205*2π)/4782 weeks
2063.88055 .82942 (206*2π)/4782 weeks
2073.36263 .99375 (207*2π)/4782 weeks
2082.44268 1.58626 (208*2π)/4782 weeks
2092.62214 .06577 (209*2π)/4782 weeks
2103.4056 1.77887 (210*2π)/4782 weeks
2111.0947 .58145 (211*2π)/4782 weeks
2122.4324 .18712 (212*2π)/4782 weeks
2132.78821 .21947 (213*2π)/4782 weeks
2142.03063 .21022 (214*2π)/4782 weeks
2153.41033 .00036 (215*2π)/4782 weeks
2162.58211 .94756 (216*2π)/4782 weeks
2173.13981 .34586 (217*2π)/4782 weeks
2182.06748 1.81704 (218*2π)/4782 weeks
2191.53152 .15124 (219*2π)/4782 weeks
2202.38282 .00274 (220*2π)/4782 weeks
2212.2765 .77524 (221*2π)/4782 weeks
2221.69038 -.21196 (222*2π)/4782 weeks
2232.06879 -.66844 (223*2π)/4782 weeks
2243.10022 .02069 (224*2π)/4782 weeks
2252.02576 -.56149 (225*2π)/4782 weeks
2262.93381 -1.09512 (226*2π)/4782 weeks
2274.13198 .46912 (227*2π)/4782 weeks
2282.95617 .88723 (228*2π)/4782 weeks
2291.72964 .88201 (229*2π)/4782 weeks
2301.35515 .26498 (230*2π)/4782 weeks
2312.48335 -1.59443 (231*2π)/4782 weeks
2323.28475 -.59511 (232*2π)/4782 weeks
2333.84231 .93678 (233*2π)/4782 weeks
2342.04621 .42914 (234*2π)/4782 weeks
2351.90419 .40799 (235*2π)/4782 weeks
2362.15988 -.75745 (236*2π)/4782 weeks
2372.6633 -.54361 (237*2π)/4782 weeks
2382.53979 -1.07348 (238*2π)/4782 weeks
2394.92521   (239*2π)/4782 weeks
2402.53979 1.07348 (240*2π)/4782 weeks
2412.6633 .54361 (241*2π)/4782 weeks
2422.15988 .75745 (242*2π)/4782 weeks
2431.90419 -.40799 (243*2π)/4782 weeks
2442.04621 -.42914 (244*2π)/4782 weeks
2453.84231 -.93678 (245*2π)/4782 weeks
2463.28475 .59511 (246*2π)/4782 weeks
2472.48335 1.59443 (247*2π)/4782 weeks
2481.35515 -.26498 (248*2π)/4782 weeks
2491.72964 -.88201 (249*2π)/4782 weeks
2502.95617 -.88723 (250*2π)/4782 weeks
2514.13198 -.46912 (251*2π)/4782 weeks
2522.93381 1.09512 (252*2π)/4782 weeks
2532.02576 .56149 (253*2π)/4782 weeks
2543.10022 -.02069 (254*2π)/4782 weeks
2552.06879 .66844 (255*2π)/4782 weeks
2561.69038 .21196 (256*2π)/4782 weeks
2572.2765 -.77524 (257*2π)/4782 weeks
2582.38282 -.00274 (258*2π)/4782 weeks
2591.53152 -.15124 (259*2π)/4782 weeks
2602.06748 -1.81704 (260*2π)/4782 weeks
2613.13981 -.34586 (261*2π)/4782 weeks
2622.58211 -.94756 (262*2π)/4782 weeks
2633.41033 -.00036 (263*2π)/4782 weeks
2642.03063 -.21022 (264*2π)/4782 weeks
2652.78821 -.21947 (265*2π)/4782 weeks
2662.4324 -.18712 (266*2π)/4782 weeks
2671.0947 -.58145 (267*2π)/4782 weeks
2683.4056 -1.77887 (268*2π)/4782 weeks
2692.62214 -.06577 (269*2π)/4782 weeks
2702.44268 -1.58626 (270*2π)/4782 weeks
2713.36263 -.99375 (271*2π)/4782 weeks
2723.88055 -.82942 (272*2π)/4782 weeks
2732.94162 .04422 (273*2π)/4782 weeks
2743.39345 -.30948 (274*2π)/4782 weeks
2752.64452 -.36213 (275*2π)/4782 weeks
2763.00949 -.42314 (276*2π)/4782 weeks
2773.05322 -.11468 (277*2π)/4782 weeks
2782.43104 -.47217 (278*2π)/4782 weeks
2792.77194 -.58897 (279*2π)/4782 weeks
2803.36677 -.9528 (280*2π)/4782 weeks
2813.07492 -.18049 (281*2π)/4782 weeks
2822.16607 -.25564 (282*2π)/4782 weeks
2833.24262 -1.73998 (283*2π)/4782 weeks
2843.86802 .00545 (284*2π)/4782 weeks
2852.51977 .80733 (285*2π)/4782 weeks
2861.50843 -1.49523 (286*2π)/4782 weeks
2872.90234 -1.99486 (287*2π)/4782 weeks
2884.04699 -1.88999 (288*2π)/4782 weeks
2894.30393 -1.10216 (289*2π)/4782 weeks
2903.89208 -.20834 (290*2π)/4782 weeks
2914.01812 -1.49898 (291*2π)/4782 weeks
2925.40718 -.27381 (292*2π)/4782 weeks
2933.57597 .85485 (293*2π)/4782 weeks
2944.42452 -.49928 (294*2π)/4782 weeks
2954.4016 .14128 (295*2π)/4782 weeks
2964.71365 1.57529 (296*2π)/4782 weeks
2972.72712 1.37624 (297*2π)/4782 weeks
2982.90758 .30517 (298*2π)/4782 weeks
2993.77831 .5291 (299*2π)/4782 weeks
3002.35746 1.38726 (300*2π)/4782 weeks
3012.15003 -.70287 (301*2π)/4782 weeks
3023.38752 -.59098 (302*2π)/4782 weeks
3033.79171 -.04425 (303*2π)/4782 weeks
3044.61427 -.68994 (304*2π)/4782 weeks
3053.9744 1.61892 (305*2π)/4782 weeks
3064.11899 .32249 (306*2π)/4782 weeks
3074.18612 .92886 (307*2π)/4782 weeks
3084.40491 2.55828 (308*2π)/4782 weeks
3092.45834 2.44776 (309*2π)/4782 weeks
3101.9418 1.30372 (310*2π)/4782 weeks
3113.14312 1.64627 (311*2π)/4782 weeks
3121.33561 1.3685 (312*2π)/4782 weeks
3131.13861 .40876 (313*2π)/4782 weeks
3144.13418 -.24682 (314*2π)/4782 weeks
3153.10979 2.30652 (315*2π)/4782 weeks
3161.26877 2.62851 (316*2π)/4782 weeks
317.87891 .34295 (317*2π)/4782 weeks
3181.73484 .38366 (318*2π)/4782 weeks
3192.46915 .40232 (319*2π)/4781 weeks
3201.56401 1.49418 (320*2π)/4781 weeks
321.53054 .30275 (321*2π)/4781 weeks
3222.21702 -.90829 (322*2π)/4781 weeks
3232.60996 1.64475 (323*2π)/4781 weeks
324.45827 .45888 (324*2π)/4781 weeks
3251.1429 .22121 (325*2π)/4781 weeks
3261.63401 -.68876 (326*2π)/4781 weeks
3271.86914 .00498 (327*2π)/4781 weeks
3281.67695 -.76415 (328*2π)/4781 weeks
3291.81542 .35498 (329*2π)/4781 weeks
3303.06953 -.55396 (330*2π)/4781 weeks
3311.49364 1.12482 (331*2π)/4781 weeks
3321.86966 .09213 (332*2π)/4781 weeks
3331.88612 .57138 (333*2π)/4781 weeks
334.64164 .71949 (334*2π)/4781 weeks
335.70931 -.86081 (335*2π)/4781 weeks
3362.25673 -1.05798 (336*2π)/4781 weeks
3372.67263 1.05954 (337*2π)/4781 weeks
338.64394 1.17523 (338*2π)/4781 weeks
339-.03694 -.01597 (339*2π)/4781 weeks
340.73975 -1.93916 (340*2π)/4781 weeks
3412.71259 -.33338 (341*2π)/4781 weeks
3421.27015 .5507 (342*2π)/4781 weeks
3431.04275 .03418 (343*2π)/4781 weeks
344.88382 -.23042 (344*2π)/4781 weeks
345.81026 1.15921 (345*2π)/4781 weeks
346-1.26513 -.43076 (346*2π)/4781 weeks
347-.33648 -2.75714 (347*2π)/4781 weeks
3481.09943 -1.5041 (348*2π)/4781 weeks
349.94846 -2.20534 (349*2π)/4781 weeks
3501.35762 -1.75647 (350*2π)/4781 weeks
3511.51643 -.95629 (351*2π)/4781 weeks
352.57081 -2.75656 (352*2π)/4781 weeks
3532.1306 -2.2432 (353*2π)/4781 weeks
3542.7283 -.86252 (354*2π)/4781 weeks
3551.7107 -1.26739 (355*2π)/4781 weeks
3561.91944 -.6768 (356*2π)/4781 weeks
3571.58892 .69947 (357*2π)/4781 weeks
358-2.27472 -.67518 (358*2π)/4781 weeks
359.67664 -4.30354 (359*2π)/4781 weeks
3601.9815 -2.23514 (360*2π)/4781 weeks
361.7915 -1.7301 (361*2π)/4781 weeks
362.29313 -3.04979 (362*2π)/4781 weeks
3631.91114 -3.09661 (363*2π)/4781 weeks
3642.69415 -4.29925 (364*2π)/4781 weeks
3653.36158 -.79094 (365*2π)/4781 weeks
366.71561 -2.01533 (366*2π)/4781 weeks
3671.92749 -3.5264 (367*2π)/4781 weeks
3683.5192 -2.65455 (368*2π)/4781 weeks
3693.63622 -1.89736 (369*2π)/4781 weeks
3701.12694 -.23044 (370*2π)/4781 weeks
3711.7383 -2.28844 (371*2π)/4781 weeks
3721.36829 -3.74143 (372*2π)/4781 weeks
3733.12751 -1.74254 (373*2π)/4781 weeks
3742.3122 -3.38638 (374*2π)/4781 weeks
3753.20303 -1.61451 (375*2π)/4781 weeks
3762.98703 -2.10806 (376*2π)/4781 weeks
3772.69701 -1.57565 (377*2π)/4781 weeks
3781.55089 -2.56927 (378*2π)/4781 weeks
3794.51605 -1.2979 (379*2π)/4781 weeks
3801.43175 -1.35319 (380*2π)/4781 weeks
3811.96911 -.63214 (381*2π)/4781 weeks
3821.2838 -2.61385 (382*2π)/4781 weeks
3831.71525 -2.71119 (383*2π)/4781 weeks
3843.36655 -2.55367 (384*2π)/4781 weeks
3852.01379 -1.66121 (385*2π)/4781 weeks
3862.52449 -1.73931 (386*2π)/4781 weeks
3872.06527 -2.6249 (387*2π)/4781 weeks
3881.35846 -1.92752 (388*2π)/4781 weeks
3893.69562 -2.11626 (389*2π)/4781 weeks
390.83054 -.90181 (390*2π)/4781 weeks
391.8475 -2.38911 (391*2π)/4781 weeks
392-.39227 -4.36937 (392*2π)/4781 weeks
3933.37358 -4.9683 (393*2π)/4781 weeks
3943.31437 -3.63346 (394*2π)/4781 weeks
3955.31303 -3.42562 (395*2π)/4781 weeks
3963.24276 -1.08989 (396*2π)/4781 weeks
3973.85197 -2.24404 (397*2π)/4781 weeks
3983.47446 .33317 (398*2π)/4781 weeks
399.55276 -1.01935 (399*2π)/4781 weeks
400.01314 -2.4004 (400*2π)/4781 weeks
4012.60117 -4.93679 (401*2π)/4781 weeks
4022.93244 -1.85631 (402*2π)/4781 weeks
403-.3854 -1.67616 (403*2π)/4781 weeks
4041.08291 -6.84599 (404*2π)/4781 weeks
4055.56119 -4.41197 (405*2π)/4781 weeks
4063.62598 -.13075 (406*2π)/4781 weeks
407.72861 -3.28932 (407*2π)/4781 weeks
4082.52059 -4.44531 (408*2π)/4781 weeks
4093.1336 -2.33139 (409*2π)/4781 weeks
4101.25402 -4.51968 (410*2π)/4781 weeks
4112.04474 -6.00206 (411*2π)/4781 weeks
4127.08126 -5.84681 (412*2π)/4781 weeks
4137.07213 -.10705 (413*2π)/4781 weeks
4141.44553 .06967 (414*2π)/4781 weeks
4151.31616 -1.88373 (415*2π)/4781 weeks
4162.06102 -5.38209 (416*2π)/4781 weeks
417.58122 -1.33583 (417*2π)/4781 weeks
4183.35003 -8.18114 (418*2π)/4781 weeks
4196.30087 -3.06339 (419*2π)/4781 weeks
4204.57034 -1.23257 (420*2π)/4781 weeks
4211.94846 -2.51455 (421*2π)/4781 weeks
4223.46663 -3.7165 (422*2π)/4781 weeks
4231.22593 -3.60215 (423*2π)/4781 weeks
4242.75958 -6.87824 (424*2π)/4781 weeks
4258.06379 -5.08214 (425*2π)/4781 weeks
4264.73292 -2.16827 (426*2π)/4781 weeks
4276.93197 -2.74189 (427*2π)/4781 weeks
4285.27561 -.20441 (428*2π)/4781 weeks
4296.0429 .31097 (429*2π)/4781 weeks
4302.28464 .95 (430*2π)/4781 weeks
431.49321 2.59716 (431*2π)/4781 weeks
432-.03764 -1.66113 (432*2π)/4781 weeks
433-2.89168 -.57937 (433*2π)/4781 weeks
434-2.30493 -3.95803 (434*2π)/4781 weeks
435-.81435 -5.96766 (435*2π)/4781 weeks
436-.88962 -6.8701 (436*2π)/4781 weeks
437-.67485 -7.00949 (437*2π)/4781 weeks
4384.85773 -10.32524 (438*2π)/4781 weeks
4394.60346 -4.57861 (439*2π)/4781 weeks
4403.10409 -2.9621 (440*2π)/4781 weeks
441-1.15183 -5.03295 (441*2π)/4781 weeks
442-.41547 -9.23279 (442*2π)/4781 weeks
4435.80456 -10.46882 (443*2π)/4781 weeks
4445.86833 -4.61611 (444*2π)/4781 weeks
4452.48806 -5.49588 (445*2π)/4781 weeks
4461.1862 -7.67952 (446*2π)/4781 weeks
4476.83782 -6.19748 (447*2π)/4781 weeks
448.17236 -5.55424 (448*2π)/4781 weeks
449-.62576 -7.78304 (449*2π)/4781 weeks
4507.68841 -13.46961 (450*2π)/4781 weeks
45110.73864 -4.70339 (451*2π)/4781 weeks
452-2.34822 1.05456 (452*2π)/4781 weeks
453.74696 -11.67914 (453*2π)/4781 weeks
454.66116 -7.64594 (454*2π)/4781 weeks
455-1.09186 -13.85561 (455*2π)/4781 weeks
4567.20677 -16.4353 (456*2π)/4781 weeks
4573.82919 -8.07782 (457*2π)/4781 weeks
45810.04277 -21.70306 (458*2π)/4781 weeks
45914.50484 -5.873 (459*2π)/4781 weeks
4602.92965 -8.60696 (460*2π)/4781 weeks
46110.11882 -6.30783 (461*2π)/4781 weeks
4624.63967 -18.5907 (462*2π)/4781 weeks
46311.39993 -12.96594 (463*2π)/4781 weeks
46414.97597 -5.89298 (464*2π)/4781 weeks
4655.39967 -9.19373 (465*2π)/4781 weeks
46612.85016 -18.65438 (466*2π)/4781 weeks
46715.40429 11.473 (467*2π)/4781 weeks
468-2.57433 -18.8104 (468*2π)/4781 weeks
469-.61589 -24.42701 (469*2π)/4781 weeks
47035.57736 -1.42495 (470*2π)/4781 weeks
471-2.39425 -8.18642 (471*2π)/4781 weeks
472-11.89544 -10.71946 (472*2π)/4781 weeks
4737.50315 -24.98187 (473*2π)/4781 weeks
474-10.54544 -55.87416 (474*2π)/4781 weeks
4753.78179 -5.42311 (475*2π)/4781 weeks
47620.75535 -104.1436 (476*2π)/4781 weeks



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