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Fourier Analysis of UCO (ProShares Ultra Bloomberg Crude Oil)


UCO (ProShares Ultra Bloomberg Crude Oil) appears to have interesting cyclic behaviour every 41 weeks (21.1121*cosine), 25 weeks (17.0294*cosine), and 25 weeks (12.6905*sine).

UCO (ProShares Ultra Bloomberg Crude Oil) has an average price of 262.4 (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 4/16/2018 for UCO (ProShares Ultra Bloomberg Crude Oil), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0262.3995   0 
1-39.01608 209.5278 (1*2π)/491491 weeks
227.03553 97.39878 (2*2π)/491246 weeks
3-7.19019 6.32124 (3*2π)/491164 weeks
4-1.42975 59.47002 (4*2π)/491123 weeks
56.02138 19.43445 (5*2π)/49198 weeks
6-13.4463 16.56529 (6*2π)/49182 weeks
71.23733 9.53843 (7*2π)/49170 weeks
824.18223 -10.31153 (8*2π)/49161 weeks
97.14946 31.72371 (9*2π)/49155 weeks
104.10302 16.93229 (10*2π)/49149 weeks
11-1.6338 -10.36846 (11*2π)/49145 weeks
1221.11206 15.32978 (12*2π)/49141 weeks
135.46252 11.84483 (13*2π)/49138 weeks
149.5106 3.90925 (14*2π)/49135 weeks
1513.492 13.04526 (15*2π)/49133 weeks
1611.71793 15.85242 (16*2π)/49131 weeks
171.18026 6.9985 (17*2π)/49129 weeks
187.59465 13.19167 (18*2π)/49127 weeks
197.84459 3.46429 (19*2π)/49126 weeks
2017.02938 12.69047 (20*2π)/49125 weeks
21.59129 17.01522 (21*2π)/49123 weeks
228.98537 10.03399 (22*2π)/49122 weeks
233.20033 16.60511 (23*2π)/49121 weeks
24-1.63161 10.66019 (24*2π)/49120 weeks
252.41567 7.73424 (25*2π)/49120 weeks
26-3.09613 10.30155 (26*2π)/49119 weeks
273.21262 -2.74924 (27*2π)/49118 weeks
2810.18374 6.87062 (28*2π)/49118 weeks
294.45423 14.2516 (29*2π)/49117 weeks
30.60102 6.66725 (30*2π)/49116 weeks
31.70649 3.99395 (31*2π)/49116 weeks
326.40957 7.43028 (32*2π)/49115 weeks
331.13788 6.69668 (33*2π)/49115 weeks
342.42491 5.12335 (34*2π)/49114 weeks
356.02217 4.74564 (35*2π)/49114 weeks
365.38338 10.39236 (36*2π)/49114 weeks
37-.4274 8.85967 (37*2π)/49113 weeks
38-1.1048 4.88668 (38*2π)/49113 weeks
392.91697 2.75496 (39*2π)/49113 weeks
404.34864 4.36135 (40*2π)/49112 weeks
415.35446 9.41509 (41*2π)/49112 weeks
42-.9056 7.29465 (42*2π)/49112 weeks
43-.51366 6.87873 (43*2π)/49111 weeks
44-.60522 5.51835 (44*2π)/49111 weeks
45-2.40649 4.14657 (45*2π)/49111 weeks
46-3.30425 1.81685 (46*2π)/49111 weeks
47.49527 .828 (47*2π)/49110 weeks
48-1.22068 -1.55972 (48*2π)/49110 weeks
492.65591 -.74239 (49*2π)/49110 weeks
504.87255 -1.93936 (50*2π)/49110 weeks
514.60938 .67947 (51*2π)/49110 weeks
526.64002 1.22634 (52*2π)/4919 weeks
534.78146 3.45764 (53*2π)/4919 weeks
547.14087 2.1994 (54*2π)/4919 weeks
555.03749 7.36058 (55*2π)/4919 weeks
561.43981 5.23318 (56*2π)/4919 weeks
572.5937 2.40026 (57*2π)/4919 weeks
582.12086 3.75253 (58*2π)/4918 weeks
592.3923 1.43787 (59*2π)/4918 weeks
605.05236 2.18748 (60*2π)/4918 weeks
616.60218 5.10097 (61*2π)/4918 weeks
62.14152 7.02533 (62*2π)/4918 weeks
633.51441 1.64008 (63*2π)/4918 weeks
64.44835 4.17548 (64*2π)/4918 weeks
651.50708 1.8878 (65*2π)/4918 weeks
662.49687 -1.02207 (66*2π)/4917 weeks
677.585 1.35472 (67*2π)/4917 weeks
686.01612 6.53893 (68*2π)/4917 weeks
691.85995 5.259 (69*2π)/4917 weeks
70.98131 3.97413 (70*2π)/4917 weeks
713.38716 2.57915 (71*2π)/4917 weeks
722.28654 4.308 (72*2π)/4917 weeks
73.63324 2.98588 (73*2π)/4917 weeks
743.79473 .19474 (74*2π)/4917 weeks
755.4157 4.34441 (75*2π)/4917 weeks
761.14409 6.68072 (76*2π)/4916 weeks
77-.505 1.78531 (77*2π)/4916 weeks
782.78108 1.7069 (78*2π)/4916 weeks
792.96608 4.5468 (79*2π)/4916 weeks
80-.09211 2.64376 (80*2π)/4916 weeks
81.5446 1.24392 (81*2π)/4916 weeks
822.70126 -.61479 (82*2π)/4916 weeks
834.01027 1.85388 (83*2π)/4916 weeks
842.76256 1.52318 (84*2π)/4916 weeks
855.30335 2.25913 (85*2π)/4916 weeks
863.2197 3.87597 (86*2π)/4916 weeks
873.53164 4.20601 (87*2π)/4916 weeks
88.76526 5.54463 (88*2π)/4916 weeks
89.48733 2.26481 (89*2π)/4916 weeks
90.51592 1.79517 (90*2π)/4915 weeks
912.84062 .53634 (91*2π)/4915 weeks
921.86962 3.16999 (92*2π)/4915 weeks
932.56245 1.81782 (93*2π)/4915 weeks
941.66755 1.66577 (94*2π)/4915 weeks
952.20504 2.17887 (95*2π)/4915 weeks
962.76108 1.36368 (96*2π)/4915 weeks
972.48333 3.15384 (97*2π)/4915 weeks
981.76791 2.41143 (98*2π)/4915 weeks
99.71821 1.82801 (99*2π)/4915 weeks
1002.56727 1.30653 (100*2π)/4915 weeks
1011.81839 .20941 (101*2π)/4915 weeks
1024.08763 2.73404 (102*2π)/4915 weeks
1031.61926 1.63473 (103*2π)/4915 weeks
1042.67856 1.58551 (104*2π)/4915 weeks
1052.69965 2.15038 (105*2π)/4915 weeks
1063.49483 1.86468 (106*2π)/4915 weeks
1071.83914 2.99989 (107*2π)/4915 weeks
1083.39133 2.06665 (108*2π)/4915 weeks
1091.04689 3.3094 (109*2π)/4915 weeks
1101.64156 2.33416 (110*2π)/4914 weeks
1111.36483 .05374 (111*2π)/4914 weeks
1123.52065 1.8944 (112*2π)/4914 weeks
1133.45433 2.58199 (113*2π)/4914 weeks
1141.93348 3.41757 (114*2π)/4914 weeks
115.72193 2.05345 (115*2π)/4914 weeks
1163.03495 .60488 (116*2π)/4914 weeks
1173.0553 4.05579 (117*2π)/4914 weeks
1181.74813 2.85531 (118*2π)/4914 weeks
119.45448 3.2614 (119*2π)/4914 weeks
120.63232 1.80507 (120*2π)/4914 weeks
1211.82215 1.85023 (121*2π)/4914 weeks
1221.46481 3.71481 (122*2π)/4914 weeks
123-2.3144 2.09426 (123*2π)/4914 weeks
124.60154 -1.1779 (124*2π)/4914 weeks
1251.8882 .51603 (125*2π)/4914 weeks
1261.97212 1.08837 (126*2π)/4914 weeks
1271.89833 .50067 (127*2π)/4914 weeks
1282.45482 2.03826 (128*2π)/4914 weeks
1291.67501 2.709 (129*2π)/4914 weeks
130.36822 1.003 (130*2π)/4914 weeks
1311.53606 1.65099 (131*2π)/4914 weeks
1321.33598 1.84863 (132*2π)/4914 weeks
133.48976 1.66431 (133*2π)/4914 weeks
1341.09716 2.27911 (134*2π)/4914 weeks
135-1.23899 1.71543 (135*2π)/4914 weeks
136-.98169 -.53056 (136*2π)/4914 weeks
1371.38662 -.32808 (137*2π)/4914 weeks
138.78784 -.00481 (138*2π)/4914 weeks
139.9434 -.07074 (139*2π)/4914 weeks
1401.63126 -.61715 (140*2π)/4914 weeks
1412.56442 1.03446 (141*2π)/4913 weeks
142.1196 1.47722 (142*2π)/4913 weeks
143.03074 -.22304 (143*2π)/4913 weeks
144.88562 -1.3171 (144*2π)/4913 weeks
1452.8213 -.66891 (145*2π)/4913 weeks
1461.95031 1.1072 (146*2π)/4913 weeks
147.54606 .70654 (147*2π)/4913 weeks
148.70673 -.79056 (148*2π)/4913 weeks
1491.81963 -.50142 (149*2π)/4913 weeks
1501.78816 -.05684 (150*2π)/4913 weeks
1511.44699 -1.08392 (151*2π)/4913 weeks
1523.02992 .48472 (152*2π)/4913 weeks
1531.65576 -.28418 (153*2π)/4913 weeks
1541.78369 .80038 (154*2π)/4913 weeks
1551.7593 -.04065 (155*2π)/4913 weeks
1561.74438 .59377 (156*2π)/4913 weeks
157.95928 -.12252 (157*2π)/4913 weeks
158.65604 -.07379 (158*2π)/4913 weeks
1591.9152 -1.8506 (159*2π)/4913 weeks
1602.75646 .5432 (160*2π)/4913 weeks
161.66511 .21795 (161*2π)/4913 weeks
1621.13341 -1.33159 (162*2π)/4913 weeks
1632.48193 -.96491 (163*2π)/4913 weeks
1641.71731 -.30803 (164*2π)/4913 weeks
1651.37724 -.22715 (165*2π)/4913 weeks
166.41157 -1.74371 (166*2π)/4913 weeks
1672.46619 -2.46196 (167*2π)/4913 weeks
1684.08075 -1.46948 (168*2π)/4913 weeks
1691.95465 .91798 (169*2π)/4913 weeks
1701.52473 -.97604 (170*2π)/4913 weeks
1711.90997 -2.25009 (171*2π)/4913 weeks
1722.59235 -.85057 (172*2π)/4913 weeks
1731.92882 -1.85429 (173*2π)/4913 weeks
1742.87168 -2.7499 (174*2π)/4913 weeks
1754.62364 -1.63837 (175*2π)/4913 weeks
1764.01552 -.97784 (176*2π)/4913 weeks
1773.39633 -.30312 (177*2π)/4913 weeks
1784.68798 -1.30419 (178*2π)/4913 weeks
1793.78357 .74633 (179*2π)/4913 weeks
1803.77521 .26722 (180*2π)/4913 weeks
1813.21262 .64767 (181*2π)/4913 weeks
1821.79488 .37963 (182*2π)/4913 weeks
1832.61684 -1.45261 (183*2π)/4913 weeks
1843.5764 -.32887 (184*2π)/4913 weeks
1852.75749 -.33524 (185*2π)/4913 weeks
1862.70486 -1.43646 (186*2π)/4913 weeks
1874.64653 -1.41397 (187*2π)/4913 weeks
1884.25725 -.11597 (188*2π)/4913 weeks
1894.30397 .51024 (189*2π)/4913 weeks
1903.41202 -.74685 (190*2π)/4913 weeks
1915.26554 .16513 (191*2π)/4913 weeks
1924.07735 1.50336 (192*2π)/4913 weeks
1933.6147 .27503 (193*2π)/4913 weeks
1944.25636 1.03251 (194*2π)/4913 weeks
1954.09539 1.68587 (195*2π)/4913 weeks
1962.9901 1.99756 (196*2π)/4913 weeks
1971.87038 1.78628 (197*2π)/4912 weeks
1981.79666 -.57325 (198*2π)/4912 weeks
1993.51809 -.20063 (199*2π)/4912 weeks
2003.81334 1.36147 (200*2π)/4912 weeks
2011.98955 .88259 (201*2π)/4912 weeks
2022.90856 .08323 (202*2π)/4912 weeks
2033.42321 .4224 (203*2π)/4912 weeks
2042.6186 .80029 (204*2π)/4912 weeks
2052.61605 .70116 (205*2π)/4912 weeks
2062.62286 .0268 (206*2π)/4912 weeks
2073.00449 .36907 (207*2π)/4912 weeks
2082.87159 .51299 (208*2π)/4912 weeks
2092.83429 -.07614 (209*2π)/4912 weeks
2102.93159 .56103 (210*2π)/4912 weeks
2113.51787 -.10162 (211*2π)/4912 weeks
2123.36175 1.05661 (212*2π)/4912 weeks
2133.27689 1.27841 (213*2π)/4912 weeks
2141.95874 1.06782 (214*2π)/4912 weeks
2153.15164 .18205 (215*2π)/4912 weeks
2162.51715 2.16446 (216*2π)/4912 weeks
2171.48703 -.02244 (217*2π)/4912 weeks
2182.32706 .20038 (218*2π)/4912 weeks
2192.73521 .41941 (219*2π)/4912 weeks
2202.0483 -.09875 (220*2π)/4912 weeks
2213.38905 .25656 (221*2π)/4912 weeks
2222.39435 .80898 (222*2π)/4912 weeks
2233.17214 .4655 (223*2π)/4912 weeks
2241.83636 1.70296 (224*2π)/4912 weeks
2251.526 .10934 (225*2π)/4912 weeks
2262.32846 .01122 (226*2π)/4912 weeks
2272.23452 .74952 (227*2π)/4912 weeks
2281.62213 -.18421 (228*2π)/4912 weeks
2291.97586 -.60741 (229*2π)/4912 weeks
2303.06012 -.17008 (230*2π)/4912 weeks
2311.87837 -.38055 (231*2π)/4912 weeks
2322.66027 -.9838 (232*2π)/4912 weeks
2334.11543 .02847 (233*2π)/4912 weeks
2342.88756 .87579 (234*2π)/4912 weeks
2351.958 1.17589 (235*2π)/4912 weeks
2361.63315 .40984 (236*2π)/4912 weeks
2371.63675 -1.40125 (237*2π)/4912 weeks
2383.19708 -.65027 (238*2π)/4912 weeks
2393.93213 .0436 (239*2π)/4912 weeks
2402.13701 1.05388 (240*2π)/4912 weeks
2412.24549 .40783 (241*2π)/4912 weeks
2421.67333 -.40859 (242*2π)/4912 weeks
2432.51549 -.61609 (243*2π)/4912 weeks
2442.49856 -.50161 (244*2π)/4912 weeks
2453.74539 -1.47017 (245*2π)/4912 weeks
2463.74539 1.47017 (246*2π)/4912 weeks
2472.49856 .50161 (247*2π)/4912 weeks
2482.51549 .61609 (248*2π)/4912 weeks
2491.67333 .40859 (249*2π)/4912 weeks
2502.24549 -.40783 (250*2π)/4912 weeks
2512.13701 -1.05388 (251*2π)/4912 weeks
2523.93213 -.0436 (252*2π)/4912 weeks
2533.19708 .65027 (253*2π)/4912 weeks
2541.63675 1.40125 (254*2π)/4912 weeks
2551.63315 -.40984 (255*2π)/4912 weeks
2561.958 -1.17589 (256*2π)/4912 weeks
2572.88756 -.87579 (257*2π)/4912 weeks
2584.11543 -.02847 (258*2π)/4912 weeks
2592.66027 .9838 (259*2π)/4912 weeks
2601.87837 .38055 (260*2π)/4912 weeks
2613.06012 .17008 (261*2π)/4912 weeks
2621.97586 .60741 (262*2π)/4912 weeks
2631.62213 .18421 (263*2π)/4912 weeks
2642.23452 -.74952 (264*2π)/4912 weeks
2652.32846 -.01122 (265*2π)/4912 weeks
2661.526 -.10934 (266*2π)/4912 weeks
2671.83636 -1.70296 (267*2π)/4912 weeks
2683.17214 -.4655 (268*2π)/4912 weeks
2692.39435 -.80898 (269*2π)/4912 weeks
2703.38905 -.25656 (270*2π)/4912 weeks
2712.0483 .09875 (271*2π)/4912 weeks
2722.73521 -.41941 (272*2π)/4912 weeks
2732.32706 -.20038 (273*2π)/4912 weeks
2741.48703 .02244 (274*2π)/4912 weeks
2752.51715 -2.16446 (275*2π)/4912 weeks
2763.15164 -.18205 (276*2π)/4912 weeks
2771.95874 -1.06782 (277*2π)/4912 weeks
2783.27689 -1.27841 (278*2π)/4912 weeks
2793.36175 -1.05661 (279*2π)/4912 weeks
2803.51787 .10162 (280*2π)/4912 weeks
2812.93159 -.56103 (281*2π)/4912 weeks
2822.83429 .07614 (282*2π)/4912 weeks
2832.87159 -.51299 (283*2π)/4912 weeks
2843.00449 -.36907 (284*2π)/4912 weeks
2852.62286 -.0268 (285*2π)/4912 weeks
2862.61605 -.70116 (286*2π)/4912 weeks
2872.6186 -.80029 (287*2π)/4912 weeks
2883.42321 -.4224 (288*2π)/4912 weeks
2892.90856 -.08323 (289*2π)/4912 weeks
2901.98955 -.88259 (290*2π)/4912 weeks
2913.81334 -1.36147 (291*2π)/4912 weeks
2923.51809 .20063 (292*2π)/4912 weeks
2931.79666 .57325 (293*2π)/4912 weeks
2941.87038 -1.78628 (294*2π)/4912 weeks
2952.9901 -1.99756 (295*2π)/4912 weeks
2964.09539 -1.68587 (296*2π)/4912 weeks
2974.25636 -1.03251 (297*2π)/4912 weeks
2983.6147 -.27503 (298*2π)/4912 weeks
2994.07735 -1.50336 (299*2π)/4912 weeks
3005.26554 -.16513 (300*2π)/4912 weeks
3013.41202 .74685 (301*2π)/4912 weeks
3024.30397 -.51024 (302*2π)/4912 weeks
3034.25725 .11597 (303*2π)/4912 weeks
3044.64653 1.41397 (304*2π)/4912 weeks
3052.70486 1.43646 (305*2π)/4912 weeks
3062.75749 .33524 (306*2π)/4912 weeks
3073.5764 .32887 (307*2π)/4912 weeks
3082.61684 1.45261 (308*2π)/4912 weeks
3091.79488 -.37963 (309*2π)/4912 weeks
3103.21262 -.64767 (310*2π)/4912 weeks
3113.77521 -.26722 (311*2π)/4912 weeks
3123.78357 -.74633 (312*2π)/4912 weeks
3134.68798 1.30419 (313*2π)/4912 weeks
3143.39633 .30312 (314*2π)/4912 weeks
3154.01552 .97784 (315*2π)/4912 weeks
3164.62364 1.63837 (316*2π)/4912 weeks
3172.87168 2.7499 (317*2π)/4912 weeks
3181.92882 1.85429 (318*2π)/4912 weeks
3192.59235 .85057 (319*2π)/4912 weeks
3201.90997 2.25009 (320*2π)/4912 weeks
3211.52473 .97604 (321*2π)/4912 weeks
3221.95465 -.91798 (322*2π)/4912 weeks
3234.08075 1.46948 (323*2π)/4912 weeks
3242.46619 2.46196 (324*2π)/4912 weeks
325.41157 1.74371 (325*2π)/4912 weeks
3261.37724 .22715 (326*2π)/4912 weeks
3271.71731 .30803 (327*2π)/4912 weeks
3282.48193 .96491 (328*2π)/4911 weeks
3291.13341 1.33159 (329*2π)/4911 weeks
330.66511 -.21795 (330*2π)/4911 weeks
3312.75646 -.5432 (331*2π)/4911 weeks
3321.9152 1.8506 (332*2π)/4911 weeks
333.65604 .07379 (333*2π)/4911 weeks
334.95928 .12252 (334*2π)/4911 weeks
3351.74438 -.59377 (335*2π)/4911 weeks
3361.7593 .04065 (336*2π)/4911 weeks
3371.78369 -.80038 (337*2π)/4911 weeks
3381.65576 .28418 (338*2π)/4911 weeks
3393.02992 -.48472 (339*2π)/4911 weeks
3401.44699 1.08392 (340*2π)/4911 weeks
3411.78816 .05684 (341*2π)/4911 weeks
3421.81963 .50142 (342*2π)/4911 weeks
343.70673 .79056 (343*2π)/4911 weeks
344.54606 -.70654 (344*2π)/4911 weeks
3451.95031 -1.1072 (345*2π)/4911 weeks
3462.8213 .66891 (346*2π)/4911 weeks
347.88562 1.3171 (347*2π)/4911 weeks
348.03074 .22304 (348*2π)/4911 weeks
349.1196 -1.47722 (349*2π)/4911 weeks
3502.56442 -1.03446 (350*2π)/4911 weeks
3511.63126 .61715 (351*2π)/4911 weeks
352.9434 .07074 (352*2π)/4911 weeks
353.78784 .00481 (353*2π)/4911 weeks
3541.38662 .32808 (354*2π)/4911 weeks
355-.98169 .53056 (355*2π)/4911 weeks
356-1.23899 -1.71543 (356*2π)/4911 weeks
3571.09716 -2.27911 (357*2π)/4911 weeks
358.48976 -1.66431 (358*2π)/4911 weeks
3591.33598 -1.84863 (359*2π)/4911 weeks
3601.53606 -1.65099 (360*2π)/4911 weeks
361.36822 -1.003 (361*2π)/4911 weeks
3621.67501 -2.709 (362*2π)/4911 weeks
3632.45482 -2.03826 (363*2π)/4911 weeks
3641.89833 -.50067 (364*2π)/4911 weeks
3651.97212 -1.08837 (365*2π)/4911 weeks
3661.8882 -.51603 (366*2π)/4911 weeks
367.60154 1.1779 (367*2π)/4911 weeks
368-2.3144 -2.09426 (368*2π)/4911 weeks
3691.46481 -3.71481 (369*2π)/4911 weeks
3701.82215 -1.85023 (370*2π)/4911 weeks
371.63232 -1.80507 (371*2π)/4911 weeks
372.45448 -3.2614 (372*2π)/4911 weeks
3731.74813 -2.85531 (373*2π)/4911 weeks
3743.0553 -4.05579 (374*2π)/4911 weeks
3753.03495 -.60488 (375*2π)/4911 weeks
376.72193 -2.05345 (376*2π)/4911 weeks
3771.93348 -3.41757 (377*2π)/4911 weeks
3783.45433 -2.58199 (378*2π)/4911 weeks
3793.52065 -1.8944 (379*2π)/4911 weeks
3801.36483 -.05374 (380*2π)/4911 weeks
3811.64156 -2.33416 (381*2π)/4911 weeks
3821.04689 -3.3094 (382*2π)/4911 weeks
3833.39133 -2.06665 (383*2π)/4911 weeks
3841.83914 -2.99989 (384*2π)/4911 weeks
3853.49483 -1.86468 (385*2π)/4911 weeks
3862.69965 -2.15038 (386*2π)/4911 weeks
3872.67856 -1.58551 (387*2π)/4911 weeks
3881.61926 -1.63473 (388*2π)/4911 weeks
3894.08763 -2.73404 (389*2π)/4911 weeks
3901.81839 -.20941 (390*2π)/4911 weeks
3912.56727 -1.30653 (391*2π)/4911 weeks
392.71821 -1.82801 (392*2π)/4911 weeks
3931.76791 -2.41143 (393*2π)/4911 weeks
3942.48333 -3.15384 (394*2π)/4911 weeks
3952.76108 -1.36368 (395*2π)/4911 weeks
3962.20504 -2.17887 (396*2π)/4911 weeks
3971.66755 -1.66577 (397*2π)/4911 weeks
3982.56245 -1.81782 (398*2π)/4911 weeks
3991.86962 -3.16999 (399*2π)/4911 weeks
4002.84062 -.53634 (400*2π)/4911 weeks
401.51592 -1.79517 (401*2π)/4911 weeks
402.48733 -2.26481 (402*2π)/4911 weeks
403.76526 -5.54463 (403*2π)/4911 weeks
4043.53164 -4.20601 (404*2π)/4911 weeks
4053.2197 -3.87597 (405*2π)/4911 weeks
4065.30335 -2.25913 (406*2π)/4911 weeks
4072.76256 -1.52318 (407*2π)/4911 weeks
4084.01027 -1.85388 (408*2π)/4911 weeks
4092.70126 .61479 (409*2π)/4911 weeks
410.5446 -1.24392 (410*2π)/4911 weeks
411-.09211 -2.64376 (411*2π)/4911 weeks
4122.96608 -4.5468 (412*2π)/4911 weeks
4132.78108 -1.7069 (413*2π)/4911 weeks
414-.505 -1.78531 (414*2π)/4911 weeks
4151.14409 -6.68072 (415*2π)/4911 weeks
4165.4157 -4.34441 (416*2π)/4911 weeks
4173.79473 -.19474 (417*2π)/4911 weeks
418.63324 -2.98588 (418*2π)/4911 weeks
4192.28654 -4.308 (419*2π)/4911 weeks
4203.38716 -2.57915 (420*2π)/4911 weeks
421.98131 -3.97413 (421*2π)/4911 weeks
4221.85995 -5.259 (422*2π)/4911 weeks
4236.01612 -6.53893 (423*2π)/4911 weeks
4247.585 -1.35472 (424*2π)/4911 weeks
4252.49687 1.02207 (425*2π)/4911 weeks
4261.50708 -1.8878 (426*2π)/4911 weeks
427.44835 -4.17548 (427*2π)/4911 weeks
4283.51441 -1.64008 (428*2π)/4911 weeks
429.14152 -7.02533 (429*2π)/4911 weeks
4306.60218 -5.10097 (430*2π)/4911 weeks
4315.05236 -2.18748 (431*2π)/4911 weeks
4322.3923 -1.43787 (432*2π)/4911 weeks
4332.12086 -3.75253 (433*2π)/4911 weeks
4342.5937 -2.40026 (434*2π)/4911 weeks
4351.43981 -5.23318 (435*2π)/4911 weeks
4365.03749 -7.36058 (436*2π)/4911 weeks
4377.14087 -2.1994 (437*2π)/4911 weeks
4384.78146 -3.45764 (438*2π)/4911 weeks
4396.64002 -1.22634 (439*2π)/4911 weeks
4404.60938 -.67947 (440*2π)/4911 weeks
4414.87255 1.93936 (441*2π)/4911 weeks
4422.65591 .74239 (442*2π)/4911 weeks
443-1.22068 1.55972 (443*2π)/4911 weeks
444.49527 -.828 (444*2π)/4911 weeks
445-3.30425 -1.81685 (445*2π)/4911 weeks
446-2.40649 -4.14657 (446*2π)/4911 weeks
447-.60522 -5.51835 (447*2π)/4911 weeks
448-.51366 -6.87873 (448*2π)/4911 weeks
449-.9056 -7.29465 (449*2π)/4911 weeks
4505.35446 -9.41509 (450*2π)/4911 weeks
4514.34864 -4.36135 (451*2π)/4911 weeks
4522.91697 -2.75496 (452*2π)/4911 weeks
453-1.1048 -4.88668 (453*2π)/4911 weeks
454-.4274 -8.85967 (454*2π)/4911 weeks
4555.38338 -10.39236 (455*2π)/4911 weeks
4566.02217 -4.74564 (456*2π)/4911 weeks
4572.42491 -5.12335 (457*2π)/4911 weeks
4581.13788 -6.69668 (458*2π)/4911 weeks
4596.40957 -7.43028 (459*2π)/4911 weeks
460.70649 -3.99395 (460*2π)/4911 weeks
461.60102 -6.66725 (461*2π)/4911 weeks
4624.45423 -14.2516 (462*2π)/4911 weeks
46310.18374 -6.87062 (463*2π)/4911 weeks
4643.21262 2.74924 (464*2π)/4911 weeks
465-3.09613 -10.30155 (465*2π)/4911 weeks
4662.41567 -7.73424 (466*2π)/4911 weeks
467-1.63161 -10.66019 (467*2π)/4911 weeks
4683.20033 -16.60511 (468*2π)/4911 weeks
4698.98537 -10.03399 (469*2π)/4911 weeks
470.59129 -17.01522 (470*2π)/4911 weeks
47117.02938 -12.69047 (471*2π)/4911 weeks
4727.84459 -3.46429 (472*2π)/4911 weeks
4737.59465 -13.19167 (473*2π)/4911 weeks
4741.18026 -6.9985 (474*2π)/4911 weeks
47511.71793 -15.85242 (475*2π)/4911 weeks
47613.492 -13.04526 (476*2π)/4911 weeks
4779.5106 -3.90925 (477*2π)/4911 weeks
4785.46252 -11.84483 (478*2π)/4911 weeks
47921.11206 -15.32978 (479*2π)/4911 weeks
480-1.6338 10.36846 (480*2π)/4911 weeks
4814.10302 -16.93229 (481*2π)/4911 weeks
4827.14946 -31.72371 (482*2π)/4911 weeks
48324.18223 10.31153 (483*2π)/4911 weeks
4841.23733 -9.53843 (484*2π)/4911 weeks
485-13.4463 -16.56529 (485*2π)/4911 weeks
4866.02138 -19.43445 (486*2π)/4911 weeks
487-1.42975 -59.47002 (487*2π)/4911 weeks
488-7.19019 -6.32124 (488*2π)/4911 weeks
48927.03553 -97.39878 (489*2π)/4911 weeks



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