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Fourier Analysis of SKF (ProShares UltraShort Financials)


SKF (ProShares UltraShort Financials) appears to have interesting cyclic behaviour every 46 weeks (74.6721*sine), 18 weeks (58.6217*sine), and 17 weeks (51.5364*cosine).

SKF (ProShares UltraShort Financials) has an average price of 453.84 (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 2/1/2007 to 6/18/2018 for SKF (ProShares UltraShort Financials), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0453.844   0 
1400.3723 516.299 (1*2π)/595595 weeks
220.99244 465.9141 (2*2π)/595298 weeks
3-199.8882 269.7682 (3*2π)/595198 weeks
4-178.9326 13.55038 (4*2π)/595149 weeks
5-19.08336 -65.85799 (5*2π)/595119 weeks
678.61375 -1.6007 (6*2π)/59599 weeks
760.82984 89.7345 (7*2π)/59585 weeks
8-26.42795 102.3887 (8*2π)/59574 weeks
9-58.08352 21.73615 (9*2π)/59566 weeks
10-3.54204 -18.4837 (10*2π)/59560 weeks
1137.06831 -1.3043 (11*2π)/59554 weeks
1251.00256 43.0845 (12*2π)/59550 weeks
133.67205 74.67207 (13*2π)/59546 weeks
14-34.62764 36.53414 (14*2π)/59543 weeks
15-16.79695 -1.38111 (15*2π)/59540 weeks
1615.449 -3.47882 (16*2π)/59537 weeks
1730.88468 26.01464 (17*2π)/59535 weeks
184.95503 47.94375 (18*2π)/59533 weeks
19-20.03054 33.21508 (19*2π)/59531 weeks
20-24.6237 5.48029 (20*2π)/59530 weeks
21-.87196 -15.6244 (21*2π)/59528 weeks
2226.94094 -3.08344 (22*2π)/59527 weeks
2328.76612 24.84077 (23*2π)/59526 weeks
247.15221 36.97895 (24*2π)/59525 weeks
25-7.85337 21.23827 (25*2π)/59524 weeks
26.92231 8.71756 (26*2π)/59523 weeks
2716.09919 17.33313 (27*2π)/59522 weeks
284.80755 39.12997 (28*2π)/59521 weeks
29-22.77112 29.94016 (29*2π)/59521 weeks
30-29.58113 1.85664 (30*2π)/59520 weeks
31-7.33772 -23.89999 (31*2π)/59519 weeks
3232.63617 -13.77534 (32*2π)/59519 weeks
3342.13499 29.58806 (33*2π)/59518 weeks
346.93663 58.62165 (34*2π)/59518 weeks
35-39.51111 44.74487 (35*2π)/59517 weeks
36-51.53639 -4.72816 (36*2π)/59517 weeks
37-14.09953 -37.58614 (37*2π)/59516 weeks
3825.82796 -23.73131 (38*2π)/59516 weeks
3934.51508 10.60676 (39*2π)/59515 weeks
4012.13535 32.56924 (40*2π)/59515 weeks
41-12.1649 23.32792 (41*2π)/59515 weeks
42-14.46632 2.4467 (42*2π)/59514 weeks
43-.0687 -6.73857 (43*2π)/59514 weeks
4414.10098 .24396 (44*2π)/59514 weeks
4512.1681 18.50735 (45*2π)/59513 weeks
46-6.25007 19.60327 (46*2π)/59513 weeks
47-10.57474 5.17439 (47*2π)/59513 weeks
48-3.5732 -4.39924 (48*2π)/59512 weeks
4910.61161 -3.0455 (49*2π)/59512 weeks
5014.09859 11.02215 (50*2π)/59512 weeks
514.2938 18.85517 (51*2π)/59512 weeks
52-6.168 18.03347 (52*2π)/59511 weeks
53-12.20341 6.6272 (53*2π)/59511 weeks
54-6.48135 -1.76006 (54*2π)/59511 weeks
551.34113 -2.03347 (55*2π)/59511 weeks
563.81017 3.12596 (56*2π)/59511 weeks
571.14633 4.5743 (57*2π)/59510 weeks
58.12637 1.44097 (58*2π)/59510 weeks
593.88821 .19316 (59*2π)/59510 weeks
607.5648 3.94029 (60*2π)/59510 weeks
614.47932 10.25399 (61*2π)/59510 weeks
62-2.52063 6.95508 (62*2π)/59510 weeks
63-.72085 -.55004 (63*2π)/5959 weeks
648.32112 -.36129 (64*2π)/5959 weeks
6511.96214 9.33259 (65*2π)/5959 weeks
663.96111 20.1017 (66*2π)/5959 weeks
67-13.5805 16.61592 (67*2π)/5959 weeks
68-17.49381 -1.82708 (68*2π)/5959 weeks
69-6.36308 -14.57291 (69*2π)/5959 weeks
7011.93102 -13.59333 (70*2π)/5959 weeks
7119.80573 3.01677 (71*2π)/5958 weeks
728.64517 14.61058 (72*2π)/5958 weeks
73-.9226 10.56244 (73*2π)/5958 weeks
74-2.50417 2.10579 (74*2π)/5958 weeks
756.96716 -1.44165 (75*2π)/5958 weeks
7612.43707 9.51881 (76*2π)/5958 weeks
772.55606 18.64573 (77*2π)/5958 weeks
78-10.67866 14.26289 (78*2π)/5958 weeks
79-15.29983 .095 (79*2π)/5958 weeks
80-3.1899 -12.63963 (80*2π)/5957 weeks
8112.35526 -6.44626 (81*2π)/5957 weeks
8214.0921 7.2219 (82*2π)/5957 weeks
835.46473 18.02809 (83*2π)/5957 weeks
84-13.36355 15.11608 (84*2π)/5957 weeks
85-17.06643 -6.54174 (85*2π)/5957 weeks
86.5327 -17.77727 (86*2π)/5957 weeks
8718.19079 -10.40188 (87*2π)/5957 weeks
8822.23682 10.13044 (88*2π)/5957 weeks
895.71781 22.78127 (89*2π)/5957 weeks
90-10.97337 16.13852 (90*2π)/5957 weeks
91-16.78631 -.25443 (91*2π)/5957 weeks
92-4.53691 -15.29681 (92*2π)/5956 weeks
9312.85988 -10.8753 (93*2π)/5956 weeks
9417.15575 2.68206 (94*2π)/5956 weeks
9510.47969 13.01513 (95*2π)/5956 weeks
96.50607 12.69564 (96*2π)/5956 weeks
97-2.9677 6.34871 (97*2π)/5956 weeks
98-.64909 2.85205 (98*2π)/5956 weeks
991.11937 4.04978 (99*2π)/5956 weeks
100-.68801 5.27683 (100*2π)/5956 weeks
101-3.27319 2.51766 (101*2π)/5956 weeks
102-.1685 -2.00626 (102*2π)/5956 weeks
1034.63953 .58205 (103*2π)/5956 weeks
1043.22066 4.28428 (104*2π)/5956 weeks
105-.2934 5.49852 (105*2π)/5956 weeks
106-3.55058 1.48429 (106*2π)/5956 weeks
107-.1463 -3.59809 (107*2π)/5956 weeks
1085.9629 -2.44775 (108*2π)/5956 weeks
1097.84483 3.48833 (109*2π)/5955 weeks
1102.52257 9.02779 (110*2π)/5955 weeks
111-5.33968 5.66573 (111*2π)/5955 weeks
112-6.07014 -4.05917 (112*2π)/5955 weeks
1132.52268 -10.00598 (113*2π)/5955 weeks
11413.70518 -5.93558 (114*2π)/5955 weeks
11515.41037 7.0866 (115*2π)/5955 weeks
1166.37424 15.09641 (116*2π)/5955 weeks
117-6.33321 12.28943 (117*2π)/5955 weeks
118-10.27148 -1.5489 (118*2π)/5955 weeks
119.45571 -10.7452 (119*2π)/5955 weeks
12013.86326 -5.9194 (120*2π)/5955 weeks
12116.40706 8.23097 (121*2π)/5955 weeks
1225.81773 17.69372 (122*2π)/5955 weeks
123-7.85694 15.01551 (123*2π)/5955 weeks
124-14.17134 1.26991 (124*2π)/5955 weeks
125-4.88924 -11.09791 (125*2π)/5955 weeks
1269.3483 -9.18885 (126*2π)/5955 weeks
12714.02876 2.57983 (127*2π)/5955 weeks
1287.75348 12.51126 (128*2π)/5955 weeks
129-4.39109 12.84286 (129*2π)/5955 weeks
130-10.66177 1.68561 (130*2π)/5955 weeks
131-4.59982 -9.35777 (131*2π)/5955 weeks
1327.63566 -9.60652 (132*2π)/5955 weeks
13314.65202 -.22544 (133*2π)/5954 weeks
13410.43999 10.42568 (134*2π)/5954 weeks
135.87013 12.06781 (135*2π)/5954 weeks
136-5.52787 6.25535 (136*2π)/5954 weeks
137-4.05815 -.87278 (137*2π)/5954 weeks
138.91556 -2.69376 (138*2π)/5954 weeks
1394.21951 -1.07594 (139*2π)/5954 weeks
1405.03036 1.78111 (140*2π)/5954 weeks
1413.22877 4.05027 (141*2π)/5954 weeks
142.07456 3.08102 (142*2π)/5954 weeks
143.41347 -.72466 (143*2π)/5954 weeks
1444.70876 -1.85857 (144*2π)/5954 weeks
1458.05075 .89357 (145*2π)/5954 weeks
1468.55386 5.94697 (146*2π)/5954 weeks
1474.39567 11.46525 (147*2π)/5954 weeks
148-3.76876 10.69389 (148*2π)/5954 weeks
149-7.69285 3.98276 (149*2π)/5954 weeks
150-6.08684 -2.79901 (150*2π)/5954 weeks
151.24075 -6.42168 (151*2π)/5954 weeks
1526.67495 -3.0816 (152*2π)/5954 weeks
1537.39376 2.51186 (153*2π)/5954 weeks
1543.53488 7.11501 (154*2π)/5954 weeks
155-3.56904 4.68616 (155*2π)/5954 weeks
156-2.96965 -3.27428 (156*2π)/5954 weeks
1575.21184 -5.0447 (157*2π)/5954 weeks
15810.20363 1.16891 (158*2π)/5954 weeks
1597.32111 9.18281 (159*2π)/5954 weeks
160-2.01689 10.8645 (160*2π)/5954 weeks
161-7.47628 3.38135 (161*2π)/5954 weeks
162-4.86002 -4.40733 (162*2π)/5954 weeks
1633.10277 -6.9037 (163*2π)/5954 weeks
1649.02387 -.72707 (164*2π)/5954 weeks
1655.93124 5.87979 (165*2π)/5954 weeks
166.24412 5.91035 (166*2π)/5954 weeks
167-2.04592 1.43844 (167*2π)/5954 weeks
1681.14879 -2.03576 (168*2π)/5954 weeks
1695.04187 -.29442 (169*2π)/5954 weeks
1705.37337 3.82014 (170*2π)/5954 weeks
1712.34789 6.47551 (171*2π)/5953 weeks
172-2.8356 5.2596 (172*2π)/5953 weeks
173-3.43223 -.31541 (173*2π)/5953 weeks
174-.31591 -2.34797 (174*2π)/5953 weeks
1751.79163 -2.38736 (175*2π)/5953 weeks
1763.77883 -2.07089 (176*2π)/5953 weeks
1775.78146 -.68913 (177*2π)/5953 weeks
1787.00851 2.79202 (178*2π)/5953 weeks
1794.97415 6.31193 (179*2π)/5953 weeks
180.16957 8.04426 (180*2π)/5953 weeks
181-4.95692 4.0094 (181*2π)/5953 weeks
182-4.2827 -2.51607 (182*2π)/5953 weeks
1831.66835 -5.6944 (183*2π)/5953 weeks
1847.73733 -1.78193 (184*2π)/5953 weeks
1856.73668 5.25197 (185*2π)/5953 weeks
186-.0573 7.81024 (186*2π)/5953 weeks
187-5.49077 2.39675 (187*2π)/5953 weeks
188-3.83826 -4.8386 (188*2π)/5953 weeks
1893.95376 -8.1918 (189*2π)/5953 weeks
19011.44282 -2.46223 (190*2π)/5953 weeks
19110.88522 6.70702 (191*2π)/5953 weeks
1923.04448 12.32278 (192*2π)/5953 weeks
193-7.0419 8.74774 (193*2π)/5953 weeks
194-9.10231 -1.95247 (194*2π)/5953 weeks
195-1.88997 -9.01702 (195*2π)/5953 weeks
1967.84046 -7.79043 (196*2π)/5953 weeks
19712.24727 1.40772 (197*2π)/5953 weeks
1986.41522 8.88666 (198*2π)/5953 weeks
199-1.40037 8.01828 (199*2π)/5953 weeks
200-4.44333 1.19414 (200*2π)/5953 weeks
201.49241 -3.72263 (201*2π)/5953 weeks
2025.90085 -1.12413 (202*2π)/5953 weeks
2036.1176 4.70513 (203*2π)/5953 weeks
204.39712 7.9716 (204*2π)/5953 weeks
205-5.75289 3.5052 (205*2π)/5953 weeks
206-4.05992 -3.5383 (206*2π)/5953 weeks
2071.46283 -5.72897 (207*2π)/5953 weeks
2086.44472 -3.14333 (208*2π)/5953 weeks
2096.27475 2.08731 (209*2π)/5953 weeks
2103.5253 3.01673 (210*2π)/5953 weeks
2112.41164 3.16026 (211*2π)/5953 weeks
212.55787 1.78671 (212*2π)/5953 weeks
2132.40293 .385 (213*2π)/5953 weeks
2143.21398 1.89549 (214*2π)/5953 weeks
2152.80862 2.98799 (215*2π)/5953 weeks
2161.41026 3.98054 (216*2π)/5953 weeks
217-.55451 2.8452 (217*2π)/5953 weeks
218.06365 2.46919 (218*2π)/5953 weeks
219-2.52836 2.73556 (219*2π)/5953 weeks
220-3.37049 -1.12757 (220*2π)/5953 weeks
221-1.56402 -3.8094 (221*2π)/5953 weeks
2222.39884 -6.04868 (222*2π)/5953 weeks
2237.90656 -2.812 (223*2π)/5953 weeks
2247.04702 4.16997 (224*2π)/5953 weeks
225.75345 5.76157 (225*2π)/5953 weeks
226-3.28718 .9126 (226*2π)/5953 weeks
227.08914 -5.37873 (227*2π)/5953 weeks
2288.2452 -4.26029 (228*2π)/5953 weeks
22910.5798 4.31968 (229*2π)/5953 weeks
2304.39562 10.9718 (230*2π)/5953 weeks
231-5.28518 9.74896 (231*2π)/5953 weeks
232-9.77568 -.3885 (232*2π)/5953 weeks
233-2.70625 -8.4512 (233*2π)/5953 weeks
2346.75159 -6.21415 (234*2π)/5953 weeks
2358.61709 2.43161 (235*2π)/5953 weeks
2361.59317 6.76069 (236*2π)/5953 weeks
237-4.13009 1.55272 (237*2π)/5953 weeks
238-.70296 -5.4305 (238*2π)/5953 weeks
2397.27487 -4.48309 (239*2π)/5952 weeks
2409.89212 3.40322 (240*2π)/5952 weeks
2414.38597 10.55621 (241*2π)/5952 weeks
242-6.14326 9.21737 (242*2π)/5952 weeks
243-9.87823 -1.67803 (243*2π)/5952 weeks
244-2.28476 -9.38578 (244*2π)/5952 weeks
2457.13565 -7.69533 (245*2π)/5952 weeks
24611.10746 1.44983 (246*2π)/5952 weeks
2474.54506 8.76885 (247*2π)/5952 weeks
248-3.39218 6.27863 (248*2π)/5952 weeks
249-5.48982 -.77606 (249*2π)/5952 weeks
250-.35577 -5.89476 (250*2π)/5952 weeks
2515.97583 -2.96128 (251*2π)/5952 weeks
2525.78992 2.8422 (252*2π)/5952 weeks
2531.09236 5.41847 (253*2π)/5952 weeks
254-3.75152 2.46132 (254*2π)/5952 weeks
255-3.14293 -3.68056 (255*2π)/5952 weeks
2562.78278 -5.6802 (256*2π)/5952 weeks
2576.29909 -1.28145 (257*2π)/5952 weeks
2584.88835 2.27407 (258*2π)/5952 weeks
2591.33562 3.90609 (259*2π)/5952 weeks
260-.83131 .47077 (260*2π)/5952 weeks
2611.29253 -.96524 (261*2π)/5952 weeks
2622.824 -.35427 (262*2π)/5952 weeks
2632.86867 2.25933 (263*2π)/5952 weeks
264-.64557 2.37859 (264*2π)/5952 weeks
265-1.18027 -.7548 (265*2π)/5952 weeks
266.76574 -1.80902 (266*2π)/5952 weeks
2672.15655 -1.06312 (267*2π)/5952 weeks
2681.9907 .44145 (268*2π)/5952 weeks
269-.58854 -.37792 (269*2π)/5952 weeks
270.74779 -3.95108 (270*2π)/5952 weeks
2715.57805 -3.92808 (271*2π)/5952 weeks
2728.28361 .83738 (272*2π)/5952 weeks
2735.69691 7.17945 (273*2π)/5952 weeks
274-2.62384 8.63903 (274*2π)/5952 weeks
275-9.60807 1.24275 (275*2π)/5952 weeks
276-6.38173 -9.64521 (276*2π)/5952 weeks
2775.88256 -13.60612 (277*2π)/5952 weeks
27816.36525 -3.41378 (278*2π)/5952 weeks
27912.0085 10.493 (279*2π)/5952 weeks
280-1.13878 14.12658 (280*2π)/5952 weeks
281-11.9734 5.77734 (281*2π)/5952 weeks
282-10.39538 -8.67673 (282*2π)/5952 weeks
2832.72076 -14.21005 (283*2π)/5952 weeks
28413.30377 -5.77812 (284*2π)/5952 weeks
28510.22497 6.2609 (285*2π)/5952 weeks
286-.06838 8.62132 (286*2π)/5952 weeks
287-6.20811 1.04055 (287*2π)/5952 weeks
288-2.07546 -7.13382 (288*2π)/5952 weeks
2896.1181 -7.18282 (289*2π)/5952 weeks
29010.74691 .15862 (290*2π)/5952 weeks
2915.66026 8.05177 (291*2π)/5952 weeks
292-3.47753 6.07304 (292*2π)/5952 weeks
293-5.37896 -1.71195 (293*2π)/5952 weeks
294-.82337 -6.39908 (294*2π)/5952 weeks
2955.01606 -5.36663 (295*2π)/5952 weeks
2965.92443 -1.50253 (296*2π)/5952 weeks
2975.21041 -.43582 (297*2π)/5952 weeks
2985.21041 .43582 (298*2π)/5952 weeks
2995.92443 1.50253 (299*2π)/5952 weeks
3005.01606 5.36663 (300*2π)/5952 weeks
301-.82337 6.39908 (301*2π)/5952 weeks
302-5.37896 1.71195 (302*2π)/5952 weeks
303-3.47753 -6.07304 (303*2π)/5952 weeks
3045.66026 -8.05177 (304*2π)/5952 weeks
30510.74691 -.15862 (305*2π)/5952 weeks
3066.1181 7.18282 (306*2π)/5952 weeks
307-2.07546 7.13382 (307*2π)/5952 weeks
308-6.20811 -1.04055 (308*2π)/5952 weeks
309-.06838 -8.62132 (309*2π)/5952 weeks
31010.22497 -6.2609 (310*2π)/5952 weeks
31113.30377 5.77812 (311*2π)/5952 weeks
3122.72076 14.21005 (312*2π)/5952 weeks
313-10.39538 8.67673 (313*2π)/5952 weeks
314-11.9734 -5.77734 (314*2π)/5952 weeks
315-1.13878 -14.12658 (315*2π)/5952 weeks
31612.0085 -10.493 (316*2π)/5952 weeks
31716.36525 3.41378 (317*2π)/5952 weeks
3185.88256 13.60612 (318*2π)/5952 weeks
319-6.38173 9.64521 (319*2π)/5952 weeks
320-9.60807 -1.24275 (320*2π)/5952 weeks
321-2.62384 -8.63903 (321*2π)/5952 weeks
3225.69691 -7.17945 (322*2π)/5952 weeks
3238.28361 -.83738 (323*2π)/5952 weeks
3245.57805 3.92808 (324*2π)/5952 weeks
325.74779 3.95108 (325*2π)/5952 weeks
326-.58854 .37792 (326*2π)/5952 weeks
3271.9907 -.44145 (327*2π)/5952 weeks
3282.15655 1.06312 (328*2π)/5952 weeks
329.76574 1.80902 (329*2π)/5952 weeks
330-1.18027 .7548 (330*2π)/5952 weeks
331-.64557 -2.37859 (331*2π)/5952 weeks
3322.86867 -2.25933 (332*2π)/5952 weeks
3332.824 .35427 (333*2π)/5952 weeks
3341.29253 .96524 (334*2π)/5952 weeks
335-.83131 -.47077 (335*2π)/5952 weeks
3361.33562 -3.90609 (336*2π)/5952 weeks
3374.88835 -2.27407 (337*2π)/5952 weeks
3386.29909 1.28145 (338*2π)/5952 weeks
3392.78278 5.6802 (339*2π)/5952 weeks
340-3.14293 3.68056 (340*2π)/5952 weeks
341-3.75152 -2.46132 (341*2π)/5952 weeks
3421.09236 -5.41847 (342*2π)/5952 weeks
3435.78992 -2.8422 (343*2π)/5952 weeks
3445.97583 2.96128 (344*2π)/5952 weeks
345-.35577 5.89476 (345*2π)/5952 weeks
346-5.48982 .77606 (346*2π)/5952 weeks
347-3.39218 -6.27863 (347*2π)/5952 weeks
3484.54506 -8.76885 (348*2π)/5952 weeks
34911.10746 -1.44983 (349*2π)/5952 weeks
3507.13565 7.69533 (350*2π)/5952 weeks
351-2.28476 9.38578 (351*2π)/5952 weeks
352-9.87823 1.67803 (352*2π)/5952 weeks
353-6.14326 -9.21737 (353*2π)/5952 weeks
3544.38597 -10.55621 (354*2π)/5952 weeks
3559.89212 -3.40322 (355*2π)/5952 weeks
3567.27487 4.48309 (356*2π)/5952 weeks
357-.70296 5.4305 (357*2π)/5952 weeks
358-4.13009 -1.55272 (358*2π)/5952 weeks
3591.59317 -6.76069 (359*2π)/5952 weeks
3608.61709 -2.43161 (360*2π)/5952 weeks
3616.75159 6.21415 (361*2π)/5952 weeks
362-2.70625 8.4512 (362*2π)/5952 weeks
363-9.77568 .3885 (363*2π)/5952 weeks
364-5.28518 -9.74896 (364*2π)/5952 weeks
3654.39562 -10.9718 (365*2π)/5952 weeks
36610.5798 -4.31968 (366*2π)/5952 weeks
3678.2452 4.26029 (367*2π)/5952 weeks
368.08914 5.37873 (368*2π)/5952 weeks
369-3.28718 -.9126 (369*2π)/5952 weeks
370.75345 -5.76157 (370*2π)/5952 weeks
3717.04702 -4.16997 (371*2π)/5952 weeks
3727.90656 2.812 (372*2π)/5952 weeks
3732.39884 6.04868 (373*2π)/5952 weeks
374-1.56402 3.8094 (374*2π)/5952 weeks
375-3.37049 1.12757 (375*2π)/5952 weeks
376-2.52836 -2.73556 (376*2π)/5952 weeks
377.06365 -2.46919 (377*2π)/5952 weeks
378-.55451 -2.8452 (378*2π)/5952 weeks
3791.41026 -3.98054 (379*2π)/5952 weeks
3802.80862 -2.98799 (380*2π)/5952 weeks
3813.21398 -1.89549 (381*2π)/5952 weeks
3822.40293 -.385 (382*2π)/5952 weeks
383.55787 -1.78671 (383*2π)/5952 weeks
3842.41164 -3.16026 (384*2π)/5952 weeks
3853.5253 -3.01673 (385*2π)/5952 weeks
3866.27475 -2.08731 (386*2π)/5952 weeks
3876.44472 3.14333 (387*2π)/5952 weeks
3881.46283 5.72897 (388*2π)/5952 weeks
389-4.05992 3.5383 (389*2π)/5952 weeks
390-5.75289 -3.5052 (390*2π)/5952 weeks
391.39712 -7.9716 (391*2π)/5952 weeks
3926.1176 -4.70513 (392*2π)/5952 weeks
3935.90085 1.12413 (393*2π)/5952 weeks
394.49241 3.72263 (394*2π)/5952 weeks
395-4.44333 -1.19414 (395*2π)/5952 weeks
396-1.40037 -8.01828 (396*2π)/5952 weeks
3976.41522 -8.88666 (397*2π)/5951 weeks
39812.24727 -1.40772 (398*2π)/5951 weeks
3997.84046 7.79043 (399*2π)/5951 weeks
400-1.88997 9.01702 (400*2π)/5951 weeks
401-9.10231 1.95247 (401*2π)/5951 weeks
402-7.0419 -8.74774 (402*2π)/5951 weeks
4033.04448 -12.32278 (403*2π)/5951 weeks
40410.88522 -6.70702 (404*2π)/5951 weeks
40511.44282 2.46223 (405*2π)/5951 weeks
4063.95376 8.1918 (406*2π)/5951 weeks
407-3.83826 4.8386 (407*2π)/5951 weeks
408-5.49077 -2.39675 (408*2π)/5951 weeks
409-.0573 -7.81024 (409*2π)/5951 weeks
4106.73668 -5.25197 (410*2π)/5951 weeks
4117.73733 1.78193 (411*2π)/5951 weeks
4121.66835 5.6944 (412*2π)/5951 weeks
413-4.2827 2.51607 (413*2π)/5951 weeks
414-4.95692 -4.0094 (414*2π)/5951 weeks
415.16957 -8.04426 (415*2π)/5951 weeks
4164.97415 -6.31193 (416*2π)/5951 weeks
4177.00851 -2.79202 (417*2π)/5951 weeks
4185.78146 .68913 (418*2π)/5951 weeks
4193.77883 2.07089 (419*2π)/5951 weeks
4201.79163 2.38736 (420*2π)/5951 weeks
421-.31591 2.34797 (421*2π)/5951 weeks
422-3.43223 .31541 (422*2π)/5951 weeks
423-2.8356 -5.2596 (423*2π)/5951 weeks
4242.34789 -6.47551 (424*2π)/5951 weeks
4255.37337 -3.82014 (425*2π)/5951 weeks
4265.04187 .29442 (426*2π)/5951 weeks
4271.14879 2.03576 (427*2π)/5951 weeks
428-2.04592 -1.43844 (428*2π)/5951 weeks
429.24412 -5.91035 (429*2π)/5951 weeks
4305.93124 -5.87979 (430*2π)/5951 weeks
4319.02387 .72707 (431*2π)/5951 weeks
4323.10277 6.9037 (432*2π)/5951 weeks
433-4.86002 4.40733 (433*2π)/5951 weeks
434-7.47628 -3.38135 (434*2π)/5951 weeks
435-2.01689 -10.8645 (435*2π)/5951 weeks
4367.32111 -9.18281 (436*2π)/5951 weeks
43710.20363 -1.16891 (437*2π)/5951 weeks
4385.21184 5.0447 (438*2π)/5951 weeks
439-2.96965 3.27428 (439*2π)/5951 weeks
440-3.56904 -4.68616 (440*2π)/5951 weeks
4413.53488 -7.11501 (441*2π)/5951 weeks
4427.39376 -2.51186 (442*2π)/5951 weeks
4436.67495 3.0816 (443*2π)/5951 weeks
444.24075 6.42168 (444*2π)/5951 weeks
445-6.08684 2.79901 (445*2π)/5951 weeks
446-7.69285 -3.98276 (446*2π)/5951 weeks
447-3.76876 -10.69389 (447*2π)/5951 weeks
4484.39567 -11.46525 (448*2π)/5951 weeks
4498.55386 -5.94697 (449*2π)/5951 weeks
4508.05075 -.89357 (450*2π)/5951 weeks
4514.70876 1.85857 (451*2π)/5951 weeks
452.41347 .72466 (452*2π)/5951 weeks
453.07456 -3.08102 (453*2π)/5951 weeks
4543.22877 -4.05027 (454*2π)/5951 weeks
4555.03036 -1.78111 (455*2π)/5951 weeks
4564.21951 1.07594 (456*2π)/5951 weeks
457.91556 2.69376 (457*2π)/5951 weeks
458-4.05815 .87278 (458*2π)/5951 weeks
459-5.52787 -6.25535 (459*2π)/5951 weeks
460.87013 -12.06781 (460*2π)/5951 weeks
46110.43999 -10.42568 (461*2π)/5951 weeks
46214.65202 .22544 (462*2π)/5951 weeks
4637.63566 9.60652 (463*2π)/5951 weeks
464-4.59982 9.35777 (464*2π)/5951 weeks
465-10.66177 -1.68561 (465*2π)/5951 weeks
466-4.39109 -12.84286 (466*2π)/5951 weeks
4677.75348 -12.51126 (467*2π)/5951 weeks
46814.02876 -2.57983 (468*2π)/5951 weeks
4699.3483 9.18885 (469*2π)/5951 weeks
470-4.88924 11.09791 (470*2π)/5951 weeks
471-14.17134 -1.26991 (471*2π)/5951 weeks
472-7.85694 -15.01551 (472*2π)/5951 weeks
4735.81773 -17.69372 (473*2π)/5951 weeks
47416.40706 -8.23097 (474*2π)/5951 weeks
47513.86326 5.9194 (475*2π)/5951 weeks
476.45571 10.7452 (476*2π)/5951 weeks
477-10.27148 1.5489 (477*2π)/5951 weeks
478-6.33321 -12.28943 (478*2π)/5951 weeks
4796.37424 -15.09641 (479*2π)/5951 weeks
48015.41037 -7.0866 (480*2π)/5951 weeks
48113.70518 5.93558 (481*2π)/5951 weeks
4822.52268 10.00598 (482*2π)/5951 weeks
483-6.07014 4.05917 (483*2π)/5951 weeks
484-5.33968 -5.66573 (484*2π)/5951 weeks
4852.52257 -9.02779 (485*2π)/5951 weeks
4867.84483 -3.48833 (486*2π)/5951 weeks
4875.9629 2.44775 (487*2π)/5951 weeks
488-.1463 3.59809 (488*2π)/5951 weeks
489-3.55058 -1.48429 (489*2π)/5951 weeks
490-.2934 -5.49852 (490*2π)/5951 weeks
4913.22066 -4.28428 (491*2π)/5951 weeks
4924.63953 -.58205 (492*2π)/5951 weeks
493-.1685 2.00626 (493*2π)/5951 weeks
494-3.27319 -2.51766 (494*2π)/5951 weeks
495-.68801 -5.27683 (495*2π)/5951 weeks
4961.11937 -4.04978 (496*2π)/5951 weeks
497-.64909 -2.85205 (497*2π)/5951 weeks
498-2.9677 -6.34871 (498*2π)/5951 weeks
499.50607 -12.69564 (499*2π)/5951 weeks
50010.47969 -13.01513 (500*2π)/5951 weeks
50117.15575 -2.68206 (501*2π)/5951 weeks
50212.85988 10.8753 (502*2π)/5951 weeks
503-4.53691 15.29681 (503*2π)/5951 weeks
504-16.78631 .25443 (504*2π)/5951 weeks
505-10.97337 -16.13852 (505*2π)/5951 weeks
5065.71781 -22.78127 (506*2π)/5951 weeks
50722.23682 -10.13044 (507*2π)/5951 weeks
50818.19079 10.40188 (508*2π)/5951 weeks
509.5327 17.77727 (509*2π)/5951 weeks
510-17.06643 6.54174 (510*2π)/5951 weeks
511-13.36355 -15.11608 (511*2π)/5951 weeks
5125.46473 -18.02809 (512*2π)/5951 weeks
51314.0921 -7.2219 (513*2π)/5951 weeks
51412.35526 6.44626 (514*2π)/5951 weeks
515-3.1899 12.63963 (515*2π)/5951 weeks
516-15.29983 -.095 (516*2π)/5951 weeks
517-10.67866 -14.26289 (517*2π)/5951 weeks
5182.55606 -18.64573 (518*2π)/5951 weeks
51912.43707 -9.51881 (519*2π)/5951 weeks
5206.96716 1.44165 (520*2π)/5951 weeks
521-2.50417 -2.10579 (521*2π)/5951 weeks
522-.9226 -10.56244 (522*2π)/5951 weeks
5238.64517 -14.61058 (523*2π)/5951 weeks
52419.80573 -3.01677 (524*2π)/5951 weeks
52511.93102 13.59333 (525*2π)/5951 weeks
526-6.36308 14.57291 (526*2π)/5951 weeks
527-17.49381 1.82708 (527*2π)/5951 weeks
528-13.5805 -16.61592 (528*2π)/5951 weeks
5293.96111 -20.1017 (529*2π)/5951 weeks
53011.96214 -9.33259 (530*2π)/5951 weeks
5318.32112 .36129 (531*2π)/5951 weeks
532-.72085 .55004 (532*2π)/5951 weeks
533-2.52063 -6.95508 (533*2π)/5951 weeks
5344.47932 -10.25399 (534*2π)/5951 weeks
5357.5648 -3.94029 (535*2π)/5951 weeks
5363.88821 -.19316 (536*2π)/5951 weeks
537.12637 -1.44097 (537*2π)/5951 weeks
5381.14633 -4.5743 (538*2π)/5951 weeks
5393.81017 -3.12596 (539*2π)/5951 weeks
5401.34113 2.03347 (540*2π)/5951 weeks
541-6.48135 1.76006 (541*2π)/5951 weeks
542-12.20341 -6.6272 (542*2π)/5951 weeks
543-6.168 -18.03347 (543*2π)/5951 weeks
5444.2938 -18.85517 (544*2π)/5951 weeks
54514.09859 -11.02215 (545*2π)/5951 weeks
54610.61161 3.0455 (546*2π)/5951 weeks
547-3.5732 4.39924 (547*2π)/5951 weeks
548-10.57474 -5.17439 (548*2π)/5951 weeks
549-6.25007 -19.60327 (549*2π)/5951 weeks
55012.1681 -18.50735 (550*2π)/5951 weeks
55114.10098 -.24396 (551*2π)/5951 weeks
552-.0687 6.73857 (552*2π)/5951 weeks
553-14.46632 -2.4467 (553*2π)/5951 weeks
554-12.1649 -23.32792 (554*2π)/5951 weeks
55512.13535 -32.56924 (555*2π)/5951 weeks
55634.51508 -10.60676 (556*2π)/5951 weeks
55725.82796 23.73131 (557*2π)/5951 weeks
558-14.09953 37.58614 (558*2π)/5951 weeks
559-51.53639 4.72816 (559*2π)/5951 weeks
560-39.51111 -44.74487 (560*2π)/5951 weeks
5616.93663 -58.62165 (561*2π)/5951 weeks
56242.13499 -29.58806 (562*2π)/5951 weeks
56332.63617 13.77534 (563*2π)/5951 weeks
564-7.33772 23.89999 (564*2π)/5951 weeks
565-29.58113 -1.85664 (565*2π)/5951 weeks
566-22.77112 -29.94016 (566*2π)/5951 weeks
5674.80755 -39.12997 (567*2π)/5951 weeks
56816.09919 -17.33313 (568*2π)/5951 weeks
569.92231 -8.71756 (569*2π)/5951 weeks
570-7.85337 -21.23827 (570*2π)/5951 weeks
5717.15221 -36.97895 (571*2π)/5951 weeks
57228.76612 -24.84077 (572*2π)/5951 weeks
57326.94094 3.08344 (573*2π)/5951 weeks
574-.87196 15.6244 (574*2π)/5951 weeks
575-24.6237 -5.48029 (575*2π)/5951 weeks
576-20.03054 -33.21508 (576*2π)/5951 weeks
5774.95503 -47.94375 (577*2π)/5951 weeks
57830.88468 -26.01464 (578*2π)/5951 weeks
57915.449 3.47882 (579*2π)/5951 weeks
580-16.79695 1.38111 (580*2π)/5951 weeks
581-34.62764 -36.53414 (581*2π)/5951 weeks
5823.67205 -74.67207 (582*2π)/5951 weeks
58351.00256 -43.0845 (583*2π)/5951 weeks
58437.06831 1.3043 (584*2π)/5951 weeks
585-3.54204 18.4837 (585*2π)/5951 weeks
586-58.08352 -21.73615 (586*2π)/5951 weeks
587-26.42795 -102.3887 (587*2π)/5951 weeks
58860.82984 -89.7345 (588*2π)/5951 weeks
58978.61375 1.6007 (589*2π)/5951 weeks
590-19.08336 65.85799 (590*2π)/5951 weeks
591-178.9326 -13.55038 (591*2π)/5951 weeks
592-199.8882 -269.7682 (592*2π)/5951 weeks
59320.99244 -465.9141 (593*2π)/5951 weeks



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