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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 41 weeks (24.399*cosine), 24 weeks (23.3126*sine), and 30 weeks (20.3451*sine).

UCO (ProShares Ultra Bloomberg Crude Oil ETF) has an average price of 283.16 (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 7/17/2017 for UCO (ProShares Ultra Bloomberg Crude Oil ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0283.1572   0 
1-56.10009 185.0447 (1*2π)/452452 weeks
23.11206 113.286 (2*2π)/452226 weeks
326.38612 14.2967 (3*2π)/452151 weeks
4-20.35534 39.67899 (4*2π)/452113 weeks
5.85783 34.4224 (5*2π)/45290 weeks
6-1.69368 5.27462 (6*2π)/45275 weeks
7.62598 -7.91261 (7*2π)/45265 weeks
827.34908 33.841 (8*2π)/45257 weeks
94.61148 15.70971 (9*2π)/45250 weeks
10-8.07377 -5.21679 (10*2π)/45245 weeks
1124.399 15.72893 (11*2π)/45241 weeks
125.92526 12.94794 (12*2π)/45238 weeks
1312.22271 4.58656 (13*2π)/45235 weeks
1412.75607 14.68774 (14*2π)/45232 weeks
158.11197 20.34508 (15*2π)/45230 weeks
169.30437 5.87989 (16*2π)/45228 weeks
173.0511 9.71517 (17*2π)/45227 weeks
1815.70005 6.79553 (18*2π)/45225 weeks
198.11385 23.31264 (19*2π)/45224 weeks
206.59656 8.63509 (20*2π)/45223 weeks
215.39099 18.26116 (21*2π)/45222 weeks
22-1.80244 12.55644 (22*2π)/45221 weeks
232.53288 8.49121 (23*2π)/45220 weeks
24-4.22799 10.50018 (24*2π)/45219 weeks
256.57706 -2.10347 (25*2π)/45218 weeks
2610.71757 9.44994 (26*2π)/45217 weeks
27.09614 13.80585 (27*2π)/45217 weeks
281.22076 7.76915 (28*2π)/45216 weeks
295.47868 3.66058 (29*2π)/45216 weeks
302.49799 9.83753 (30*2π)/45215 weeks
312.67153 6.06362 (31*2π)/45215 weeks
325.39151 4.47469 (32*2π)/45214 weeks
336.70113 10.51925 (33*2π)/45214 weeks
34-.3401 10.06 (34*2π)/45213 weeks
35-1.22535 5.32609 (35*2π)/45213 weeks
363.51828 3.40996 (36*2π)/45213 weeks
375.27651 5.09463 (37*2π)/45212 weeks
383.24214 11.78127 (38*2π)/45212 weeks
39.04802 7.04477 (39*2π)/45212 weeks
40-1.22733 6.40281 (40*2π)/45211 weeks
41-2.03271 6.19573 (41*2π)/45211 weeks
42-2.88213 3.82557 (42*2π)/45211 weeks
43-.15802 -.14406 (43*2π)/45211 weeks
44-1.81095 -.1562 (44*2π)/45210 weeks
453.09628 -.97829 (45*2π)/45210 weeks
465.17889 -2.08403 (46*2π)/45210 weeks
475.06952 .75134 (47*2π)/45210 weeks
487.43454 1.98314 (48*2π)/4529 weeks
494.8113 3.1202 (49*2π)/4529 weeks
508.63882 4.51197 (50*2π)/4529 weeks
513.18565 7.56666 (51*2π)/4529 weeks
521.27253 3.94121 (52*2π)/4529 weeks
533.54822 4.14731 (53*2π)/4529 weeks
542.10947 2.48832 (54*2π)/4528 weeks
555.2456 1.82485 (55*2π)/4528 weeks
567.16769 4.44616 (56*2π)/4528 weeks
57.83608 8.15629 (57*2π)/4528 weeks
583.8314 1.83011 (58*2π)/4528 weeks
59.29011 4.03152 (59*2π)/4528 weeks
601.47563 1.9661 (60*2π)/4528 weeks
614.45352 -1.45829 (61*2π)/4527 weeks
628.4934 3.65959 (62*2π)/4527 weeks
633.79228 7.6345 (63*2π)/4527 weeks
642.01852 5.15737 (64*2π)/4527 weeks
652.24725 2.28353 (65*2π)/4527 weeks
663.17141 4.65053 (66*2π)/4527 weeks
671.06879 3.90543 (67*2π)/4527 weeks
683.25965 .09032 (68*2π)/4527 weeks
695.94264 4.56446 (69*2π)/4527 weeks
701.00039 7.20578 (70*2π)/4526 weeks
71.00028 1.47587 (71*2π)/4526 weeks
723.35196 2.2027 (72*2π)/4526 weeks
731.61896 5.38599 (73*2π)/4526 weeks
74.35872 2.0849 (74*2π)/4526 weeks
75.91969 .20436 (75*2π)/4526 weeks
764.53769 .88456 (76*2π)/4526 weeks
773.24443 2.46589 (77*2π)/4526 weeks
785.22202 1.45513 (78*2π)/4526 weeks
793.87905 4.52566 (79*2π)/4526 weeks
803.90303 4.43113 (80*2π)/4526 weeks
81.92837 6.08452 (81*2π)/4526 weeks
82.70826 2.48034 (82*2π)/4526 weeks
83.624 1.60134 (83*2π)/4525 weeks
843.85178 1.47567 (84*2π)/4525 weeks
851.38225 2.46075 (85*2π)/4525 weeks
862.36017 2.81005 (86*2π)/4525 weeks
872.71509 1.87971 (87*2π)/4525 weeks
882.23608 1.69601 (88*2π)/4525 weeks
893.44771 3.0407 (89*2π)/4525 weeks
901.87133 2.71749 (90*2π)/4525 weeks
91.95789 2.42729 (91*2π)/4525 weeks
922.78967 1.28235 (92*2π)/4525 weeks
932.08813 .19559 (93*2π)/4525 weeks
944.03446 3.40602 (94*2π)/4525 weeks
952.18582 1.47451 (95*2π)/4525 weeks
963.08847 1.78757 (96*2π)/4525 weeks
972.71645 2.00697 (97*2π)/4525 weeks
983.6281 3.34687 (98*2π)/4525 weeks
992.29531 1.77784 (99*2π)/4525 weeks
1002.53257 4.26393 (100*2π)/4525 weeks
1011.7659 2.18387 (101*2π)/4524 weeks
102.78 .77324 (102*2π)/4524 weeks
1033.95931 1.8504 (103*2π)/4524 weeks
1043.73736 2.79415 (104*2π)/4524 weeks
1051.9875 3.73491 (105*2π)/4524 weeks
106.81692 1.86931 (106*2π)/4524 weeks
1074.10984 1.34153 (107*2π)/4524 weeks
1081.99691 4.38764 (108*2π)/4524 weeks
1091.92453 3.8091 (109*2π)/4524 weeks
110.38211 2.58502 (110*2π)/4524 weeks
1111.44135 1.6923 (111*2π)/4524 weeks
1122.12834 3.24004 (112*2π)/4524 weeks
113-1.81204 3.72649 (113*2π)/4524 weeks
114-.07783 -1.2168 (114*2π)/4524 weeks
1152.11511 .57212 (115*2π)/4524 weeks
1162.17269 1.26472 (116*2π)/4524 weeks
1172.31589 .60506 (117*2π)/4524 weeks
1182.44991 2.38384 (118*2π)/4524 weeks
1191.11984 3.15028 (119*2π)/4524 weeks
1201.41135 .91633 (120*2π)/4524 weeks
1211.4593 1.8879 (121*2π)/4524 weeks
122.99749 2.35165 (122*2π)/4524 weeks
1231.27783 1.70928 (123*2π)/4524 weeks
124-.73887 2.70135 (124*2π)/4524 weeks
125-1.23667 .02382 (125*2π)/4524 weeks
1261.4728 -.66001 (126*2π)/4524 weeks
127.90375 .04668 (127*2π)/4524 weeks
1281.07822 -.06924 (128*2π)/4524 weeks
1292.064 -.60021 (129*2π)/4524 weeks
1302.48176 1.72143 (130*2π)/4523 weeks
131-.13404 .8922 (131*2π)/4523 weeks
132.28266 -.6954 (132*2π)/4523 weeks
1332.03774 -1.54966 (133*2π)/4523 weeks
1342.95 .74688 (134*2π)/4523 weeks
1351.14107 1.15593 (135*2π)/4523 weeks
136.53506 -.47085 (136*2π)/4523 weeks
1371.99873 -.71293 (137*2π)/4523 weeks
1382.04123 -.13598 (138*2π)/4523 weeks
1391.60247 -1.17304 (139*2π)/4523 weeks
1403.14381 .73989 (140*2π)/4523 weeks
1412.22241 -.38801 (141*2π)/4523 weeks
1421.54526 .59044 (142*2π)/4523 weeks
1432.08266 .13729 (143*2π)/4523 weeks
1441.28637 .70307 (144*2π)/4523 weeks
1451.41223 -.0249 (145*2π)/4523 weeks
146.86161 -1.59488 (146*2π)/4523 weeks
1473.4517 -.32602 (147*2π)/4523 weeks
1481.072 .66859 (148*2π)/4523 weeks
1491.05508 -1.29738 (149*2π)/4523 weeks
1502.67323 -1.12733 (150*2π)/4523 weeks
1511.87803 -.31868 (151*2π)/4523 weeks
1521.37309 -.21112 (152*2π)/4523 weeks
153.81843 -2.41813 (153*2π)/4523 weeks
1543.08592 -2.48758 (154*2π)/4523 weeks
1554.5613 -.08583 (155*2π)/4523 weeks
1561.21052 -.34514 (156*2π)/4523 weeks
1571.42144 -1.50941 (157*2π)/4523 weeks
1583.34929 -1.50518 (158*2π)/4523 weeks
1592.04027 -1.60907 (159*2π)/4523 weeks
1602.85289 -2.79317 (160*2π)/4523 weeks
1615.04596 -2.0558 (161*2π)/4523 weeks
1624.40521 -1.06036 (162*2π)/4523 weeks
1633.63109 -.42128 (163*2π)/4523 weeks
1645.46741 -.99528 (164*2π)/4523 weeks
1653.76988 .4892 (165*2π)/4523 weeks
1663.95191 .59868 (166*2π)/4523 weeks
1673.12011 .96606 (167*2π)/4523 weeks
1681.94243 -.81634 (168*2π)/4523 weeks
1693.9896 -1.05072 (169*2π)/4523 weeks
1703.26067 -.19662 (170*2π)/4523 weeks
1712.82633 -1.16866 (171*2π)/4523 weeks
1724.80479 -1.85249 (172*2π)/4523 weeks
1734.72478 -.13463 (173*2π)/4523 weeks
1744.69196 .54321 (174*2π)/4523 weeks
1753.97589 -1.01073 (175*2π)/4523 weeks
1765.69144 .58445 (176*2π)/4523 weeks
1773.91909 1.43921 (177*2π)/4523 weeks
1784.53347 .34411 (178*2π)/4523 weeks
1794.53296 1.27624 (179*2π)/4523 weeks
1803.80422 2.2194 (180*2π)/4523 weeks
1812.67056 2.09033 (181*2π)/4522 weeks
1821.34877 .15072 (182*2π)/4522 weeks
1833.65135 -.39004 (183*2π)/4522 weeks
1844.3251 1.20373 (184*2π)/4522 weeks
1852.18269 1.04009 (185*2π)/4522 weeks
1863.18743 .11457 (186*2π)/4522 weeks
1873.75082 .65808 (187*2π)/4522 weeks
1882.86519 .68401 (188*2π)/4522 weeks
1892.63547 .62297 (189*2π)/4522 weeks
1903.20342 .08346 (190*2π)/4522 weeks
1913.19942 .44843 (191*2π)/4522 weeks
1922.80287 .33675 (192*2π)/4522 weeks
1933.56715 .4601 (193*2π)/4522 weeks
1943.37051 -.17109 (194*2π)/4522 weeks
1953.87209 1.1114 (195*2π)/4522 weeks
1963.61098 1.29076 (196*2π)/4522 weeks
1972.14629 1.16897 (197*2π)/4522 weeks
1983.59074 .32003 (198*2π)/4522 weeks
1992.1159 2.29741 (199*2π)/4522 weeks
2002.20122 -.15709 (200*2π)/4522 weeks
2012.62754 .09818 (201*2π)/4522 weeks
2022.53722 .70752 (202*2π)/4522 weeks
2033.14701 -.4274 (203*2π)/4522 weeks
2043.14957 1.07431 (204*2π)/4522 weeks
2053.00556 .22961 (205*2π)/4522 weeks
2062.64767 1.95517 (206*2π)/4522 weeks
2071.55411 .26105 (207*2π)/4522 weeks
2082.51226 -.01882 (208*2π)/4522 weeks
2092.37821 .82586 (209*2π)/4522 weeks
2101.85506 -.27158 (210*2π)/4522 weeks
2112.32667 -.81359 (211*2π)/4522 weeks
2122.99044 .35881 (212*2π)/4522 weeks
2132.44313 -.79689 (213*2π)/4522 weeks
2143.77515 -1.11299 (214*2π)/4522 weeks
2153.7198 1.07511 (215*2π)/4522 weeks
2162.86907 1.30946 (216*2π)/4522 weeks
2171.91465 .41774 (217*2π)/4522 weeks
2181.36813 -1.11198 (218*2π)/4522 weeks
2193.518 -.81772 (219*2π)/4522 weeks
2204.29098 -.00577 (220*2π)/4522 weeks
2212.25567 1.00216 (221*2π)/4522 weeks
2222.33623 .49872 (222*2π)/4522 weeks
2232.09741 -.71762 (223*2π)/4522 weeks
2242.8334 -.59725 (224*2π)/4522 weeks
2252.6724 -1.02774 (225*2π)/4522 weeks
2265.24237   (226*2π)/4522 weeks
2272.6724 1.02774 (227*2π)/4522 weeks
2282.8334 .59725 (228*2π)/4522 weeks
2292.09741 .71762 (229*2π)/4522 weeks
2302.33623 -.49872 (230*2π)/4522 weeks
2312.25567 -1.00216 (231*2π)/4522 weeks
2324.29098 .00577 (232*2π)/4522 weeks
2333.518 .81772 (233*2π)/4522 weeks
2341.36813 1.11198 (234*2π)/4522 weeks
2351.91465 -.41774 (235*2π)/4522 weeks
2362.86907 -1.30946 (236*2π)/4522 weeks
2373.7198 -1.07511 (237*2π)/4522 weeks
2383.77515 1.11299 (238*2π)/4522 weeks
2392.44313 .79689 (239*2π)/4522 weeks
2402.99044 -.35881 (240*2π)/4522 weeks
2412.32667 .81359 (241*2π)/4522 weeks
2421.85506 .27158 (242*2π)/4522 weeks
2432.37821 -.82586 (243*2π)/4522 weeks
2442.51226 .01882 (244*2π)/4522 weeks
2451.55411 -.26105 (245*2π)/4522 weeks
2462.64767 -1.95517 (246*2π)/4522 weeks
2473.00556 -.22961 (247*2π)/4522 weeks
2483.14957 -1.07431 (248*2π)/4522 weeks
2493.14701 .4274 (249*2π)/4522 weeks
2502.53722 -.70752 (250*2π)/4522 weeks
2512.62754 -.09818 (251*2π)/4522 weeks
2522.20122 .15709 (252*2π)/4522 weeks
2532.1159 -2.29741 (253*2π)/4522 weeks
2543.59074 -.32003 (254*2π)/4522 weeks
2552.14629 -1.16897 (255*2π)/4522 weeks
2563.61098 -1.29076 (256*2π)/4522 weeks
2573.87209 -1.1114 (257*2π)/4522 weeks
2583.37051 .17109 (258*2π)/4522 weeks
2593.56715 -.4601 (259*2π)/4522 weeks
2602.80287 -.33675 (260*2π)/4522 weeks
2613.19942 -.44843 (261*2π)/4522 weeks
2623.20342 -.08346 (262*2π)/4522 weeks
2632.63547 -.62297 (263*2π)/4522 weeks
2642.86519 -.68401 (264*2π)/4522 weeks
2653.75082 -.65808 (265*2π)/4522 weeks
2663.18743 -.11457 (266*2π)/4522 weeks
2672.18269 -1.04009 (267*2π)/4522 weeks
2684.3251 -1.20373 (268*2π)/4522 weeks
2693.65135 .39004 (269*2π)/4522 weeks
2701.34877 -.15072 (270*2π)/4522 weeks
2712.67056 -2.09033 (271*2π)/4522 weeks
2723.80422 -2.2194 (272*2π)/4522 weeks
2734.53296 -1.27624 (273*2π)/4522 weeks
2744.53347 -.34411 (274*2π)/4522 weeks
2753.91909 -1.43921 (275*2π)/4522 weeks
2765.69144 -.58445 (276*2π)/4522 weeks
2773.97589 1.01073 (277*2π)/4522 weeks
2784.69196 -.54321 (278*2π)/4522 weeks
2794.72478 .13463 (279*2π)/4522 weeks
2804.80479 1.85249 (280*2π)/4522 weeks
2812.82633 1.16866 (281*2π)/4522 weeks
2823.26067 .19662 (282*2π)/4522 weeks
2833.9896 1.05072 (283*2π)/4522 weeks
2841.94243 .81634 (284*2π)/4522 weeks
2853.12011 -.96606 (285*2π)/4522 weeks
2863.95191 -.59868 (286*2π)/4522 weeks
2873.76988 -.4892 (287*2π)/4522 weeks
2885.46741 .99528 (288*2π)/4522 weeks
2893.63109 .42128 (289*2π)/4522 weeks
2904.40521 1.06036 (290*2π)/4522 weeks
2915.04596 2.0558 (291*2π)/4522 weeks
2922.85289 2.79317 (292*2π)/4522 weeks
2932.04027 1.60907 (293*2π)/4522 weeks
2943.34929 1.50518 (294*2π)/4522 weeks
2951.42144 1.50941 (295*2π)/4522 weeks
2961.21052 .34514 (296*2π)/4522 weeks
2974.5613 .08583 (297*2π)/4522 weeks
2983.08592 2.48758 (298*2π)/4522 weeks
299.81843 2.41813 (299*2π)/4522 weeks
3001.37309 .21112 (300*2π)/4522 weeks
3011.87803 .31868 (301*2π)/4522 weeks
3022.67323 1.12733 (302*2π)/4521 weeks
3031.05508 1.29738 (303*2π)/4521 weeks
3041.072 -.66859 (304*2π)/4521 weeks
3053.4517 .32602 (305*2π)/4521 weeks
306.86161 1.59488 (306*2π)/4521 weeks
3071.41223 .0249 (307*2π)/4521 weeks
3081.28637 -.70307 (308*2π)/4521 weeks
3092.08266 -.13729 (309*2π)/4521 weeks
3101.54526 -.59044 (310*2π)/4521 weeks
3112.22241 .38801 (311*2π)/4521 weeks
3123.14381 -.73989 (312*2π)/4521 weeks
3131.60247 1.17304 (313*2π)/4521 weeks
3142.04123 .13598 (314*2π)/4521 weeks
3151.99873 .71293 (315*2π)/4521 weeks
316.53506 .47085 (316*2π)/4521 weeks
3171.14107 -1.15593 (317*2π)/4521 weeks
3182.95 -.74688 (318*2π)/4521 weeks
3192.03774 1.54966 (319*2π)/4521 weeks
320.28266 .6954 (320*2π)/4521 weeks
321-.13404 -.8922 (321*2π)/4521 weeks
3222.48176 -1.72143 (322*2π)/4521 weeks
3232.064 .60021 (323*2π)/4521 weeks
3241.07822 .06924 (324*2π)/4521 weeks
325.90375 -.04668 (325*2π)/4521 weeks
3261.4728 .66001 (326*2π)/4521 weeks
327-1.23667 -.02382 (327*2π)/4521 weeks
328-.73887 -2.70135 (328*2π)/4521 weeks
3291.27783 -1.70928 (329*2π)/4521 weeks
330.99749 -2.35165 (330*2π)/4521 weeks
3311.4593 -1.8879 (331*2π)/4521 weeks
3321.41135 -.91633 (332*2π)/4521 weeks
3331.11984 -3.15028 (333*2π)/4521 weeks
3342.44991 -2.38384 (334*2π)/4521 weeks
3352.31589 -.60506 (335*2π)/4521 weeks
3362.17269 -1.26472 (336*2π)/4521 weeks
3372.11511 -.57212 (337*2π)/4521 weeks
338-.07783 1.2168 (338*2π)/4521 weeks
339-1.81204 -3.72649 (339*2π)/4521 weeks
3402.12834 -3.24004 (340*2π)/4521 weeks
3411.44135 -1.6923 (341*2π)/4521 weeks
342.38211 -2.58502 (342*2π)/4521 weeks
3431.92453 -3.8091 (343*2π)/4521 weeks
3441.99691 -4.38764 (344*2π)/4521 weeks
3454.10984 -1.34153 (345*2π)/4521 weeks
346.81692 -1.86931 (346*2π)/4521 weeks
3471.9875 -3.73491 (347*2π)/4521 weeks
3483.73736 -2.79415 (348*2π)/4521 weeks
3493.95931 -1.8504 (349*2π)/4521 weeks
350.78 -.77324 (350*2π)/4521 weeks
3511.7659 -2.18387 (351*2π)/4521 weeks
3522.53257 -4.26393 (352*2π)/4521 weeks
3532.29531 -1.77784 (353*2π)/4521 weeks
3543.6281 -3.34687 (354*2π)/4521 weeks
3552.71645 -2.00697 (355*2π)/4521 weeks
3563.08847 -1.78757 (356*2π)/4521 weeks
3572.18582 -1.47451 (357*2π)/4521 weeks
3584.03446 -3.40602 (358*2π)/4521 weeks
3592.08813 -.19559 (359*2π)/4521 weeks
3602.78967 -1.28235 (360*2π)/4521 weeks
361.95789 -2.42729 (361*2π)/4521 weeks
3621.87133 -2.71749 (362*2π)/4521 weeks
3633.44771 -3.0407 (363*2π)/4521 weeks
3642.23608 -1.69601 (364*2π)/4521 weeks
3652.71509 -1.87971 (365*2π)/4521 weeks
3662.36017 -2.81005 (366*2π)/4521 weeks
3671.38225 -2.46075 (367*2π)/4521 weeks
3683.85178 -1.47567 (368*2π)/4521 weeks
369.624 -1.60134 (369*2π)/4521 weeks
370.70826 -2.48034 (370*2π)/4521 weeks
371.92837 -6.08452 (371*2π)/4521 weeks
3723.90303 -4.43113 (372*2π)/4521 weeks
3733.87905 -4.52566 (373*2π)/4521 weeks
3745.22202 -1.45513 (374*2π)/4521 weeks
3753.24443 -2.46589 (375*2π)/4521 weeks
3764.53769 -.88456 (376*2π)/4521 weeks
377.91969 -.20436 (377*2π)/4521 weeks
378.35872 -2.0849 (378*2π)/4521 weeks
3791.61896 -5.38599 (379*2π)/4521 weeks
3803.35196 -2.2027 (380*2π)/4521 weeks
381.00028 -1.47587 (381*2π)/4521 weeks
3821.00039 -7.20578 (382*2π)/4521 weeks
3835.94264 -4.56446 (383*2π)/4521 weeks
3843.25965 -.09032 (384*2π)/4521 weeks
3851.06879 -3.90543 (385*2π)/4521 weeks
3863.17141 -4.65053 (386*2π)/4521 weeks
3872.24725 -2.28353 (387*2π)/4521 weeks
3882.01852 -5.15737 (388*2π)/4521 weeks
3893.79228 -7.6345 (389*2π)/4521 weeks
3908.4934 -3.65959 (390*2π)/4521 weeks
3914.45352 1.45829 (391*2π)/4521 weeks
3921.47563 -1.9661 (392*2π)/4521 weeks
393.29011 -4.03152 (393*2π)/4521 weeks
3943.8314 -1.83011 (394*2π)/4521 weeks
395.83608 -8.15629 (395*2π)/4521 weeks
3967.16769 -4.44616 (396*2π)/4521 weeks
3975.2456 -1.82485 (397*2π)/4521 weeks
3982.10947 -2.48832 (398*2π)/4521 weeks
3993.54822 -4.14731 (399*2π)/4521 weeks
4001.27253 -3.94121 (400*2π)/4521 weeks
4013.18565 -7.56666 (401*2π)/4521 weeks
4028.63882 -4.51197 (402*2π)/4521 weeks
4034.8113 -3.1202 (403*2π)/4521 weeks
4047.43454 -1.98314 (404*2π)/4521 weeks
4055.06952 -.75134 (405*2π)/4521 weeks
4065.17889 2.08403 (406*2π)/4521 weeks
4073.09628 .97829 (407*2π)/4521 weeks
408-1.81095 .1562 (408*2π)/4521 weeks
409-.15802 .14406 (409*2π)/4521 weeks
410-2.88213 -3.82557 (410*2π)/4521 weeks
411-2.03271 -6.19573 (411*2π)/4521 weeks
412-1.22733 -6.40281 (412*2π)/4521 weeks
413.04802 -7.04477 (413*2π)/4521 weeks
4143.24214 -11.78127 (414*2π)/4521 weeks
4155.27651 -5.09463 (415*2π)/4521 weeks
4163.51828 -3.40996 (416*2π)/4521 weeks
417-1.22535 -5.32609 (417*2π)/4521 weeks
418-.3401 -10.06 (418*2π)/4521 weeks
4196.70113 -10.51925 (419*2π)/4521 weeks
4205.39151 -4.47469 (420*2π)/4521 weeks
4212.67153 -6.06362 (421*2π)/4521 weeks
4222.49799 -9.83753 (422*2π)/4521 weeks
4235.47868 -3.66058 (423*2π)/4521 weeks
4241.22076 -7.76915 (424*2π)/4521 weeks
425.09614 -13.80585 (425*2π)/4521 weeks
42610.71757 -9.44994 (426*2π)/4521 weeks
4276.57706 2.10347 (427*2π)/4521 weeks
428-4.22799 -10.50018 (428*2π)/4521 weeks
4292.53288 -8.49121 (429*2π)/4521 weeks
430-1.80244 -12.55644 (430*2π)/4521 weeks
4315.39099 -18.26116 (431*2π)/4521 weeks
4326.59656 -8.63509 (432*2π)/4521 weeks
4338.11385 -23.31264 (433*2π)/4521 weeks
43415.70005 -6.79553 (434*2π)/4521 weeks
4353.0511 -9.71517 (435*2π)/4521 weeks
4369.30437 -5.87989 (436*2π)/4521 weeks
4378.11197 -20.34508 (437*2π)/4521 weeks
43812.75607 -14.68774 (438*2π)/4521 weeks
43912.22271 -4.58656 (439*2π)/4521 weeks
4405.92526 -12.94794 (440*2π)/4521 weeks
44124.399 -15.72893 (441*2π)/4521 weeks
442-8.07377 5.21679 (442*2π)/4521 weeks
4434.61148 -15.70971 (443*2π)/4521 weeks
44427.34908 -33.841 (444*2π)/4521 weeks
445.62598 7.91261 (445*2π)/4521 weeks
446-1.69368 -5.27462 (446*2π)/4521 weeks
447.85783 -34.4224 (447*2π)/4521 weeks
448-20.35534 -39.67899 (448*2π)/4521 weeks
44926.38612 -14.2967 (449*2π)/4521 weeks
4503.11206 -113.286 (450*2π)/4521 weeks



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