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Fourier Analysis of UCO (ProShares Ultra Bloomberg Crude)


UCO (ProShares Ultra Bloomberg Crude) appears to have interesting cyclic behaviour every 43 weeks (28.0084*cosine), 24 weeks (23.4768*sine), and 30 weeks (20.6462*sine).

UCO (ProShares Ultra Bloomberg Crude) has an average price of 300 (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 1/9/2017 for UCO (ProShares Ultra Bloomberg Crude), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0300.0026   0 
1-61.77049 163.0177 (1*2π)/425425 weeks
2-21.06218 112.3696 (2*2π)/425213 weeks
339.93622 38.86417 (3*2π)/425142 weeks
4-12.96641 22.47303 (4*2π)/425106 weeks
5-13.37878 30.48773 (5*2π)/42585 weeks
61.9058 11.2989 (6*2π)/42571 weeks
733.18419 -7.17775 (7*2π)/42561 weeks
8-1.16069 27.68968 (8*2π)/42553 weeks
9-7.91886 18.47101 (9*2π)/42547 weeks
1028.00838 -2.33994 (10*2π)/42543 weeks
117.70023 17.06703 (11*2π)/42539 weeks
129.03857 5.28893 (12*2π)/42535 weeks
1315.37713 15.24594 (13*2π)/42533 weeks
1411.16369 20.64617 (14*2π)/42530 weeks
158.77499 5.60283 (15*2π)/42528 weeks
163.22988 9.8197 (16*2π)/42527 weeks
1717.61679 8.14007 (17*2π)/42525 weeks
184.5082 23.47681 (18*2π)/42524 weeks
199.98981 10.99463 (19*2π)/42522 weeks
202.61437 18.94451 (20*2π)/42521 weeks
21-1.28237 10.38903 (21*2π)/42520 weeks
223.09192 11.72596 (22*2π)/42519 weeks
23-4.79407 1.19972 (23*2π)/42518 weeks
2412.04834 5.27876 (24*2π)/42518 weeks
256.96731 16.1329 (25*2π)/42517 weeks
26.83893 7.74595 (26*2π)/42516 weeks
272.37243 3.46647 (27*2π)/42516 weeks
284.70037 10.73877 (28*2π)/42515 weeks
292.58017 6.32766 (29*2π)/42515 weeks
305.0773 4.48872 (30*2π)/42514 weeks
317.23062 10.84209 (31*2π)/42514 weeks
32-.51048 10.39055 (32*2π)/42513 weeks
33-1.15076 4.95658 (33*2π)/42513 weeks
344.17714 4.05701 (34*2π)/42513 weeks
356.59465 6.20064 (35*2π)/42512 weeks
36.19268 11.61421 (36*2π)/42512 weeks
37.17604 8.00743 (37*2π)/42511 weeks
38-.68874 6.32861 (38*2π)/42511 weeks
39-2.71065 4.73895 (39*2π)/42511 weeks
40-3.31678 .75652 (40*2π)/42511 weeks
41-.62038 1.91953 (41*2π)/42510 weeks
422.31914 -2.63399 (42*2π)/42510 weeks
433.55895 -2.40883 (43*2π)/42510 weeks
445.63067 1.09258 (44*2π)/42510 weeks
457.71259 1.42108 (45*2π)/4259 weeks
465.19782 3.58206 (46*2π)/4259 weeks
479.17011 4.59556 (47*2π)/4259 weeks
483.13893 7.79544 (48*2π)/4259 weeks
491.55142 3.56029 (49*2π)/4259 weeks
503.20319 4.54615 (50*2π)/4259 weeks
512.63164 1.80596 (51*2π)/4258 weeks
525.96031 2.56218 (52*2π)/4258 weeks
536.96073 7.49471 (53*2π)/4258 weeks
54-1.10462 3.98703 (54*2π)/4258 weeks
553.5734 5.93804 (55*2π)/4258 weeks
561.54234 2.19259 (56*2π)/4258 weeks
572.13368 -.53728 (57*2π)/4257 weeks
588.82001 1.67852 (58*2π)/4257 weeks
595.93923 8.11502 (59*2π)/4257 weeks
602.28102 5.55654 (60*2π)/4257 weeks
611.80743 2.70461 (61*2π)/4257 weeks
623.55261 4.89733 (62*2π)/4257 weeks
631.14451 4.18371 (63*2π)/4257 weeks
643.97821 .19522 (64*2π)/4257 weeks
656.11744 5.55439 (65*2π)/4257 weeks
66-.1631 6.84985 (66*2π)/4256 weeks
671.45449 1.14206 (67*2π)/4256 weeks
684.15028 3.33435 (68*2π)/4256 weeks
69-.05573 4.34911 (69*2π)/4256 weeks
70.60607 1.72582 (70*2π)/4256 weeks
713.20894 -.59715 (71*2π)/4256 weeks
724.32595 2.54953 (72*2π)/4256 weeks
733.94785 1.12118 (73*2π)/4256 weeks
745.21029 4.66981 (74*2π)/4256 weeks
754.0253 4.25724 (75*2π)/4256 weeks
761.98045 6.61298 (76*2π)/4256 weeks
77.4527 2.62464 (77*2π)/4256 weeks
78.59925 1.77593 (78*2π)/4255 weeks
794.09958 1.60947 (79*2π)/4255 weeks
801.51549 2.23197 (80*2π)/4255 weeks
812.101 2.85167 (81*2π)/4255 weeks
822.88602 2.32843 (82*2π)/4255 weeks
832.94069 1.52721 (83*2π)/4255 weeks
842.76991 3.65007 (84*2π)/4255 weeks
852.04368 2.87354 (85*2π)/4255 weeks
861.27485 .98078 (86*2π)/4255 weeks
871.91253 1.97915 (87*2π)/4255 weeks
885.06753 1.30878 (88*2π)/4255 weeks
891.71285 2.49466 (89*2π)/4255 weeks
903.10167 1.84351 (90*2π)/4255 weeks
912.96863 2.4309 (91*2π)/4255 weeks
924.15003 3.04621 (92*2π)/4255 weeks
932.15076 2.07589 (93*2π)/4255 weeks
942.82649 4.49236 (94*2π)/4255 weeks
951.91118 2.34385 (95*2π)/4254 weeks
961.15645 .36081 (96*2π)/4254 weeks
973.94127 2.3049 (97*2π)/4254 weeks
983.80052 3.51538 (98*2π)/4254 weeks
991.57193 3.70573 (99*2π)/4254 weeks
1001.62063 .91029 (100*2π)/4254 weeks
1014.66777 3.62729 (101*2π)/4254 weeks
1021.76432 3.39753 (102*2π)/4254 weeks
103.53367 3.84422 (103*2π)/4254 weeks
104.87066 1.99229 (104*2π)/4254 weeks
1052.28004 2.69029 (105*2π)/4254 weeks
106-.42834 4.86398 (106*2π)/4254 weeks
107-1.22034 -.89489 (107*2π)/4254 weeks
1082.29508 .3854 (108*2π)/4254 weeks
1092.34776 1.23877 (109*2π)/4254 weeks
1102.42706 .62192 (110*2π)/4254 weeks
1112.53495 2.52452 (111*2π)/4254 weeks
112.76672 3.1761 (112*2π)/4254 weeks
1131.87885 1.24228 (113*2π)/4254 weeks
1141.5888 1.98858 (114*2π)/4254 weeks
115.67243 2.17854 (115*2π)/4254 weeks
1161.31974 2.70879 (116*2π)/4254 weeks
117-1.45424 1.52408 (117*2π)/4254 weeks
118-.15731 -1.30845 (118*2π)/4254 weeks
1191.19402 .34892 (119*2π)/4254 weeks
1201.19616 -.0098 (120*2π)/4254 weeks
1211.57759 -.64264 (121*2π)/4254 weeks
1223.0574 1.05392 (122*2π)/4253 weeks
123.01198 1.46925 (123*2π)/4253 weeks
124.20407 -.56489 (124*2π)/4253 weeks
1251.98951 -1.67598 (125*2π)/4253 weeks
1263.11205 .79535 (126*2π)/4253 weeks
1271.07595 1.15583 (127*2π)/4253 weeks
128.70298 -.75287 (128*2π)/4253 weeks
1292.15276 -.56729 (129*2π)/4253 weeks
1301.91671 .01032 (130*2π)/4253 weeks
1312.76627 -1.48238 (131*2π)/4253 weeks
1321.95719 .89347 (132*2π)/4253 weeks
1332.81344 .55502 (133*2π)/4253 weeks
1341.87293 -.07504 (134*2π)/4253 weeks
1352.07218 .65465 (135*2π)/4253 weeks
1361.26535 -.22753 (136*2π)/4253 weeks
137.51231 -.75487 (137*2π)/4253 weeks
1383.4831 -1.24018 (138*2π)/4253 weeks
1391.54 .97012 (139*2π)/4253 weeks
140.95684 -1.22729 (140*2π)/4253 weeks
1412.78223 -1.26983 (141*2π)/4253 weeks
1421.97151 -.33754 (142*2π)/4253 weeks
1431.29246 -.23781 (143*2π)/4253 weeks
1441.29133 -2.88501 (144*2π)/4253 weeks
1453.65199 -2.53665 (145*2π)/4253 weeks
1463.86348 1.00405 (146*2π)/4253 weeks
1471.65869 -1.06768 (147*2π)/4253 weeks
1482.18643 -2.55802 (148*2π)/4253 weeks
1492.74083 -.94052 (149*2π)/4253 weeks
1502.48405 -2.44682 (150*2π)/4253 weeks
1514.50499 -3.15932 (151*2π)/4253 weeks
1524.73865 -1.03582 (152*2π)/4253 weeks
1534.46759 -.28758 (153*2π)/4253 weeks
1545.18105 -1.69769 (154*2π)/4253 weeks
1554.23296 .76373 (155*2π)/4253 weeks
1564.27795 .54416 (156*2π)/4253 weeks
1573.35044 .99425 (157*2π)/4253 weeks
1582.09829 -.98864 (158*2π)/4253 weeks
1594.29219 -.92424 (159*2π)/4253 weeks
1603.32382 -.32011 (160*2π)/4253 weeks
1613.17171 -1.69809 (161*2π)/4253 weeks
1625.59505 -1.29486 (162*2π)/4253 weeks
1634.95916 -.29157 (163*2π)/4253 weeks
1643.91727 .50599 (164*2π)/4253 weeks
1655.70536 -.8039 (165*2π)/4253 weeks
1665.19344 1.60087 (166*2π)/4253 weeks
1674.06991 .34739 (167*2π)/4253 weeks
1684.86959 1.21353 (168*2π)/4253 weeks
1694.45501 2.19786 (169*2π)/4253 weeks
1703.07816 2.21756 (170*2π)/4253 weeks
1711.33561 .67421 (171*2π)/4252 weeks
1723.78777 -.51057 (172*2π)/4252 weeks
1734.59681 1.24038 (173*2π)/4252 weeks
1742.28155 .95008 (174*2π)/4252 weeks
1753.42333 .16171 (175*2π)/4252 weeks
1763.86297 .99105 (176*2π)/4252 weeks
1773.16463 .65722 (177*2π)/4252 weeks
1782.76729 .30259 (178*2π)/4252 weeks
1793.51784 .3398 (179*2π)/4252 weeks
1803.34668 .5834 (180*2π)/4252 weeks
1813.443 -.0961 (181*2π)/4252 weeks
1823.16368 .39746 (182*2π)/4252 weeks
1834.46777 .60231 (183*2π)/4252 weeks
1843.76057 1.09636 (184*2π)/4252 weeks
1852.61291 1.70245 (185*2π)/4252 weeks
1863.39964 .0905 (186*2π)/4252 weeks
1872.75577 2.50504 (187*2π)/4252 weeks
1882.19611 -.19048 (188*2π)/4252 weeks
1892.78901 .08095 (189*2π)/4252 weeks
1902.57933 .68168 (190*2π)/4252 weeks
1913.6243 -.32581 (191*2π)/4252 weeks
1923.0136 1.0895 (192*2π)/4252 weeks
1933.6625 .47129 (193*2π)/4252 weeks
1941.85375 1.73398 (194*2π)/4252 weeks
1952.09595 -.09844 (195*2π)/4252 weeks
1962.90639 .26342 (196*2π)/4252 weeks
1971.71889 .39333 (197*2π)/4252 weeks
1982.18815 -.47315 (198*2π)/4252 weeks
1993.51772 -.37526 (199*2π)/4252 weeks
2002.21125 -.49448 (200*2π)/4252 weeks
2013.41175 -1.22005 (201*2π)/4252 weeks
2024.3011 .98021 (202*2π)/4252 weeks
2033.16978 1.29984 (203*2π)/4252 weeks
2041.9844 .46694 (204*2π)/4252 weeks
2051.46502 -1.24313 (205*2π)/4252 weeks
2063.69152 -.7606 (206*2π)/4252 weeks
2074.55971 .48522 (207*2π)/4252 weeks
2082.27234 .5905 (208*2π)/4252 weeks
2092.06073 .40158 (209*2π)/4252 weeks
2102.65454 -.84514 (210*2π)/4252 weeks
2112.98254 -.54714 (211*2π)/4252 weeks
2124.02354 -1.75541 (212*2π)/4252 weeks
2134.02354 1.75541 (213*2π)/4252 weeks
2142.98254 .54714 (214*2π)/4252 weeks
2152.65454 .84514 (215*2π)/4252 weeks
2162.06073 -.40158 (216*2π)/4252 weeks
2172.27234 -.5905 (217*2π)/4252 weeks
2184.55971 -.48522 (218*2π)/4252 weeks
2193.69152 .7606 (219*2π)/4252 weeks
2201.46502 1.24313 (220*2π)/4252 weeks
2211.9844 -.46694 (221*2π)/4252 weeks
2223.16978 -1.29984 (222*2π)/4252 weeks
2234.3011 -.98021 (223*2π)/4252 weeks
2243.41175 1.22005 (224*2π)/4252 weeks
2252.21125 .49448 (225*2π)/4252 weeks
2263.51772 .37526 (226*2π)/4252 weeks
2272.18815 .47315 (227*2π)/4252 weeks
2281.71889 -.39333 (228*2π)/4252 weeks
2292.90639 -.26342 (229*2π)/4252 weeks
2302.09595 .09844 (230*2π)/4252 weeks
2311.85375 -1.73398 (231*2π)/4252 weeks
2323.6625 -.47129 (232*2π)/4252 weeks
2333.0136 -1.0895 (233*2π)/4252 weeks
2343.6243 .32581 (234*2π)/4252 weeks
2352.57933 -.68168 (235*2π)/4252 weeks
2362.78901 -.08095 (236*2π)/4252 weeks
2372.19611 .19048 (237*2π)/4252 weeks
2382.75577 -2.50504 (238*2π)/4252 weeks
2393.39964 -.0905 (239*2π)/4252 weeks
2402.61291 -1.70245 (240*2π)/4252 weeks
2413.76057 -1.09636 (241*2π)/4252 weeks
2424.46777 -.60231 (242*2π)/4252 weeks
2433.16368 -.39746 (243*2π)/4252 weeks
2443.443 .0961 (244*2π)/4252 weeks
2453.34668 -.5834 (245*2π)/4252 weeks
2463.51784 -.3398 (246*2π)/4252 weeks
2472.76729 -.30259 (247*2π)/4252 weeks
2483.16463 -.65722 (248*2π)/4252 weeks
2493.86297 -.99105 (249*2π)/4252 weeks
2503.42333 -.16171 (250*2π)/4252 weeks
2512.28155 -.95008 (251*2π)/4252 weeks
2524.59681 -1.24038 (252*2π)/4252 weeks
2533.78777 .51057 (253*2π)/4252 weeks
2541.33561 -.67421 (254*2π)/4252 weeks
2553.07816 -2.21756 (255*2π)/4252 weeks
2564.45501 -2.19786 (256*2π)/4252 weeks
2574.86959 -1.21353 (257*2π)/4252 weeks
2584.06991 -.34739 (258*2π)/4252 weeks
2595.19344 -1.60087 (259*2π)/4252 weeks
2605.70536 .8039 (260*2π)/4252 weeks
2613.91727 -.50599 (261*2π)/4252 weeks
2624.95916 .29157 (262*2π)/4252 weeks
2635.59505 1.29486 (263*2π)/4252 weeks
2643.17171 1.69809 (264*2π)/4252 weeks
2653.32382 .32011 (265*2π)/4252 weeks
2664.29219 .92424 (266*2π)/4252 weeks
2672.09829 .98864 (267*2π)/4252 weeks
2683.35044 -.99425 (268*2π)/4252 weeks
2694.27795 -.54416 (269*2π)/4252 weeks
2704.23296 -.76373 (270*2π)/4252 weeks
2715.18105 1.69769 (271*2π)/4252 weeks
2724.46759 .28758 (272*2π)/4252 weeks
2734.73865 1.03582 (273*2π)/4252 weeks
2744.50499 3.15932 (274*2π)/4252 weeks
2752.48405 2.44682 (275*2π)/4252 weeks
2762.74083 .94052 (276*2π)/4252 weeks
2772.18643 2.55802 (277*2π)/4252 weeks
2781.65869 1.06768 (278*2π)/4252 weeks
2793.86348 -1.00405 (279*2π)/4252 weeks
2803.65199 2.53665 (280*2π)/4252 weeks
2811.29133 2.88501 (281*2π)/4252 weeks
2821.29246 .23781 (282*2π)/4252 weeks
2831.97151 .33754 (283*2π)/4252 weeks
2842.78223 1.26983 (284*2π)/4251 weeks
285.95684 1.22729 (285*2π)/4251 weeks
2861.54 -.97012 (286*2π)/4251 weeks
2873.4831 1.24018 (287*2π)/4251 weeks
288.51231 .75487 (288*2π)/4251 weeks
2891.26535 .22753 (289*2π)/4251 weeks
2902.07218 -.65465 (290*2π)/4251 weeks
2911.87293 .07504 (291*2π)/4251 weeks
2922.81344 -.55502 (292*2π)/4251 weeks
2931.95719 -.89347 (293*2π)/4251 weeks
2942.76627 1.48238 (294*2π)/4251 weeks
2951.91671 -.01032 (295*2π)/4251 weeks
2962.15276 .56729 (296*2π)/4251 weeks
297.70298 .75287 (297*2π)/4251 weeks
2981.07595 -1.15583 (298*2π)/4251 weeks
2993.11205 -.79535 (299*2π)/4251 weeks
3001.98951 1.67598 (300*2π)/4251 weeks
301.20407 .56489 (301*2π)/4251 weeks
302.01198 -1.46925 (302*2π)/4251 weeks
3033.0574 -1.05392 (303*2π)/4251 weeks
3041.57759 .64264 (304*2π)/4251 weeks
3051.19616 .0098 (305*2π)/4251 weeks
3061.19402 -.34892 (306*2π)/4251 weeks
307-.15731 1.30845 (307*2π)/4251 weeks
308-1.45424 -1.52408 (308*2π)/4251 weeks
3091.31974 -2.70879 (309*2π)/4251 weeks
310.67243 -2.17854 (310*2π)/4251 weeks
3111.5888 -1.98858 (311*2π)/4251 weeks
3121.87885 -1.24228 (312*2π)/4251 weeks
313.76672 -3.1761 (313*2π)/4251 weeks
3142.53495 -2.52452 (314*2π)/4251 weeks
3152.42706 -.62192 (315*2π)/4251 weeks
3162.34776 -1.23877 (316*2π)/4251 weeks
3172.29508 -.3854 (317*2π)/4251 weeks
318-1.22034 .89489 (318*2π)/4251 weeks
319-.42834 -4.86398 (319*2π)/4251 weeks
3202.28004 -2.69029 (320*2π)/4251 weeks
321.87066 -1.99229 (321*2π)/4251 weeks
322.53367 -3.84422 (322*2π)/4251 weeks
3231.76432 -3.39753 (323*2π)/4251 weeks
3244.66777 -3.62729 (324*2π)/4251 weeks
3251.62063 -.91029 (325*2π)/4251 weeks
3261.57193 -3.70573 (326*2π)/4251 weeks
3273.80052 -3.51538 (327*2π)/4251 weeks
3283.94127 -2.3049 (328*2π)/4251 weeks
3291.15645 -.36081 (329*2π)/4251 weeks
3301.91118 -2.34385 (330*2π)/4251 weeks
3312.82649 -4.49236 (331*2π)/4251 weeks
3322.15076 -2.07589 (332*2π)/4251 weeks
3334.15003 -3.04621 (333*2π)/4251 weeks
3342.96863 -2.4309 (334*2π)/4251 weeks
3353.10167 -1.84351 (335*2π)/4251 weeks
3361.71285 -2.49466 (336*2π)/4251 weeks
3375.06753 -1.30878 (337*2π)/4251 weeks
3381.91253 -1.97915 (338*2π)/4251 weeks
3391.27485 -.98078 (339*2π)/4251 weeks
3402.04368 -2.87354 (340*2π)/4251 weeks
3412.76991 -3.65007 (341*2π)/4251 weeks
3422.94069 -1.52721 (342*2π)/4251 weeks
3432.88602 -2.32843 (343*2π)/4251 weeks
3442.101 -2.85167 (344*2π)/4251 weeks
3451.51549 -2.23197 (345*2π)/4251 weeks
3464.09958 -1.60947 (346*2π)/4251 weeks
347.59925 -1.77593 (347*2π)/4251 weeks
348.4527 -2.62464 (348*2π)/4251 weeks
3491.98045 -6.61298 (349*2π)/4251 weeks
3504.0253 -4.25724 (350*2π)/4251 weeks
3515.21029 -4.66981 (351*2π)/4251 weeks
3523.94785 -1.12118 (352*2π)/4251 weeks
3534.32595 -2.54953 (353*2π)/4251 weeks
3543.20894 .59715 (354*2π)/4251 weeks
355.60607 -1.72582 (355*2π)/4251 weeks
356-.05573 -4.34911 (356*2π)/4251 weeks
3574.15028 -3.33435 (357*2π)/4251 weeks
3581.45449 -1.14206 (358*2π)/4251 weeks
359-.1631 -6.84985 (359*2π)/4251 weeks
3606.11744 -5.55439 (360*2π)/4251 weeks
3613.97821 -.19522 (361*2π)/4251 weeks
3621.14451 -4.18371 (362*2π)/4251 weeks
3633.55261 -4.89733 (363*2π)/4251 weeks
3641.80743 -2.70461 (364*2π)/4251 weeks
3652.28102 -5.55654 (365*2π)/4251 weeks
3665.93923 -8.11502 (366*2π)/4251 weeks
3678.82001 -1.67852 (367*2π)/4251 weeks
3682.13368 .53728 (368*2π)/4251 weeks
3691.54234 -2.19259 (369*2π)/4251 weeks
3703.5734 -5.93804 (370*2π)/4251 weeks
371-1.10462 -3.98703 (371*2π)/4251 weeks
3726.96073 -7.49471 (372*2π)/4251 weeks
3735.96031 -2.56218 (373*2π)/4251 weeks
3742.63164 -1.80596 (374*2π)/4251 weeks
3753.20319 -4.54615 (375*2π)/4251 weeks
3761.55142 -3.56029 (376*2π)/4251 weeks
3773.13893 -7.79544 (377*2π)/4251 weeks
3789.17011 -4.59556 (378*2π)/4251 weeks
3795.19782 -3.58206 (379*2π)/4251 weeks
3807.71259 -1.42108 (380*2π)/4251 weeks
3815.63067 -1.09258 (381*2π)/4251 weeks
3823.55895 2.40883 (382*2π)/4251 weeks
3832.31914 2.63399 (383*2π)/4251 weeks
384-.62038 -1.91953 (384*2π)/4251 weeks
385-3.31678 -.75652 (385*2π)/4251 weeks
386-2.71065 -4.73895 (386*2π)/4251 weeks
387-.68874 -6.32861 (387*2π)/4251 weeks
388.17604 -8.00743 (388*2π)/4251 weeks
389.19268 -11.61421 (389*2π)/4251 weeks
3906.59465 -6.20064 (390*2π)/4251 weeks
3914.17714 -4.05701 (391*2π)/4251 weeks
392-1.15076 -4.95658 (392*2π)/4251 weeks
393-.51048 -10.39055 (393*2π)/4251 weeks
3947.23062 -10.84209 (394*2π)/4251 weeks
3955.0773 -4.48872 (395*2π)/4251 weeks
3962.58017 -6.32766 (396*2π)/4251 weeks
3974.70037 -10.73877 (397*2π)/4251 weeks
3982.37243 -3.46647 (398*2π)/4251 weeks
399.83893 -7.74595 (399*2π)/4251 weeks
4006.96731 -16.1329 (400*2π)/4251 weeks
40112.04834 -5.27876 (401*2π)/4251 weeks
402-4.79407 -1.19972 (402*2π)/4251 weeks
4033.09192 -11.72596 (403*2π)/4251 weeks
404-1.28237 -10.38903 (404*2π)/4251 weeks
4052.61437 -18.94451 (405*2π)/4251 weeks
4069.98981 -10.99463 (406*2π)/4251 weeks
4074.5082 -23.47681 (407*2π)/4251 weeks
40817.61679 -8.14007 (408*2π)/4251 weeks
4093.22988 -9.8197 (409*2π)/4251 weeks
4108.77499 -5.60283 (410*2π)/4251 weeks
41111.16369 -20.64617 (411*2π)/4251 weeks
41215.37713 -15.24594 (412*2π)/4251 weeks
4139.03857 -5.28893 (413*2π)/4251 weeks
4147.70023 -17.06703 (414*2π)/4251 weeks
41528.00838 2.33994 (415*2π)/4251 weeks
416-7.91886 -18.47101 (416*2π)/4251 weeks
417-1.16069 -27.68968 (417*2π)/4251 weeks
41833.18419 7.17775 (418*2π)/4251 weeks
4191.9058 -11.2989 (419*2π)/4251 weeks
420-13.37878 -30.48773 (420*2π)/4251 weeks
421-12.96641 -22.47303 (421*2π)/4251 weeks
42239.93622 -38.86417 (422*2π)/4251 weeks
423-21.06218 -112.3696 (423*2π)/4251 weeks

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