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Fourier Analysis of FXP (ProShares UltraShort FTSE China 50)


FXP (ProShares UltraShort FTSE China 50) appears to have interesting cyclic behaviour every 39 weeks (70.7046*sine), 36 weeks (64.2224*sine), and 42 weeks (60.8947*sine).

FXP (ProShares UltraShort FTSE China 50) has an average price of 270.41 (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 11/8/2007 to 4/16/2018 for FXP (ProShares UltraShort FTSE China 50), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0270.4114   0 
1327.7799 192.9951 (1*2π)/546546 weeks
2228.99 244.3947 (2*2π)/546273 weeks
3112.8395 265.6041 (3*2π)/546182 weeks
418.41297 234.8722 (4*2π)/546137 weeks
5-34.41943 175.6357 (5*2π)/546109 weeks
6-62.1941 108.6228 (6*2π)/54691 weeks
7-50.69043 53.66132 (7*2π)/54678 weeks
8-18.21305 27.45858 (8*2π)/54668 weeks
99.056 23.86494 (9*2π)/54661 weeks
1022.14037 28.55057 (10*2π)/54655 weeks
1133.34144 40.74288 (11*2π)/54650 weeks
1225.21966 56.11226 (12*2π)/54646 weeks
1322.51116 60.8947 (13*2π)/54642 weeks
144.13374 70.7046 (14*2π)/54639 weeks
15-9.28673 64.22239 (15*2π)/54636 weeks
16-20.58559 55.51817 (16*2π)/54634 weeks
17-33.66854 43.97771 (17*2π)/54632 weeks
18-35.68687 23.18542 (18*2π)/54630 weeks
19-28.53659 8.84933 (19*2π)/54629 weeks
20-18.48828 -3.8666 (20*2π)/54627 weeks
21-3.22548 -9.04163 (21*2π)/54626 weeks
2211.98825 -4.26753 (22*2π)/54625 weeks
2321.91395 7.55587 (23*2π)/54624 weeks
2419.98579 20.22321 (24*2π)/54623 weeks
259.27263 28.20521 (25*2π)/54622 weeks
26-3.4892 29.31659 (26*2π)/54621 weeks
27-11.07959 19.66918 (27*2π)/54620 weeks
28-14.07936 7.74445 (28*2π)/54620 weeks
29-8.69578 -5.77122 (29*2π)/54619 weeks
303.73561 -11.12118 (30*2π)/54618 weeks
3116.24385 -11.67207 (31*2π)/54618 weeks
3230.26398 -3.28604 (32*2π)/54617 weeks
3336.10859 11.72972 (33*2π)/54617 weeks
3429.35757 26.05022 (34*2π)/54616 weeks
3520.36347 34.15674 (35*2π)/54616 weeks
367.02619 36.58207 (36*2π)/54615 weeks
37-1.4401 31.7544 (37*2π)/54615 weeks
38-8.532 25.62134 (38*2π)/54614 weeks
39-11.52728 17.28088 (39*2π)/54614 weeks
40-9.27736 7.19118 (40*2π)/54614 weeks
41-2.08168 5.06112 (41*2π)/54613 weeks
42.70682 4.51161 (42*2π)/54613 weeks
435.46019 5.4269 (43*2π)/54613 weeks
446.35514 8.60278 (44*2π)/54612 weeks
455.50433 10.00177 (45*2π)/54612 weeks
463.78141 13.17056 (46*2π)/54612 weeks
47.42848 11.61802 (47*2π)/54612 weeks
48-.55487 8.47346 (48*2π)/54611 weeks
49-2.11288 5.76816 (49*2π)/54611 weeks
50.84317 1.04127 (50*2π)/54611 weeks
514.78602 .48664 (51*2π)/54611 weeks
528.06104 -.3879 (52*2π)/54611 weeks
5312.66421 .96351 (53*2π)/54610 weeks
5416.30348 5.56761 (54*2π)/54610 weeks
5515.87093 11.19456 (55*2π)/54610 weeks
5614.44803 16.18647 (56*2π)/54610 weeks
578.10225 18.76949 (57*2π)/54610 weeks
583.13036 18.40124 (58*2π)/5469 weeks
59-1.17043 15.01441 (59*2π)/5469 weeks
60-2.89597 10.8824 (60*2π)/5469 weeks
61-1.36897 5.00582 (61*2π)/5469 weeks
622.64666 3.53177 (62*2π)/5469 weeks
635.73051 3.81235 (63*2π)/5469 weeks
649.06559 5.14625 (64*2π)/5469 weeks
659.73217 9.00989 (65*2π)/5468 weeks
668.31165 10.50821 (66*2π)/5468 weeks
677.98493 13.19803 (67*2π)/5468 weeks
684.49003 14.6036 (68*2π)/5468 weeks
693.38709 13.8956 (69*2π)/5468 weeks
70.90862 15.58134 (70*2π)/5468 weeks
71-2.67487 14.44477 (71*2π)/5468 weeks
72-6.20202 11.5239 (72*2π)/5468 weeks
73-8.50244 7.03029 (73*2π)/5467 weeks
74-6.66371 .94308 (74*2π)/5467 weeks
75-2.31861 -2.56301 (75*2π)/5467 weeks
761.79528 -2.49957 (76*2π)/5467 weeks
775.73854 -2.76089 (77*2π)/5467 weeks
789.85016 1.09548 (78*2π)/5467 weeks
799.42614 5.8665 (79*2π)/5467 weeks
807.55264 7.8868 (80*2π)/5467 weeks
814.54492 10.65201 (81*2π)/5467 weeks
82-.30405 8.10952 (82*2π)/5467 weeks
83-.54764 4.89764 (83*2π)/5467 weeks
84-.59235 2.41391 (84*2π)/5467 weeks
852.0445 -1.59511 (85*2π)/5466 weeks
866.49537 -1.54267 (86*2π)/5466 weeks
879.98678 -.4626 (87*2π)/5466 weeks
8812.21473 3.38858 (88*2π)/5466 weeks
8911.84749 7.95948 (89*2π)/5466 weeks
908.62917 10.89819 (90*2π)/5466 weeks
915.7001 11.32253 (91*2π)/5466 weeks
922.61629 9.26569 (92*2π)/5466 weeks
932.07263 6.92552 (93*2π)/5466 weeks
943.26281 6.05389 (94*2π)/5466 weeks
953.09119 5.08797 (95*2π)/5466 weeks
964.96138 4.55797 (96*2π)/5466 weeks
976.0036 4.90383 (97*2π)/5466 weeks
986.82561 5.86032 (98*2π)/5466 weeks
997.2482 7.75803 (99*2π)/5466 weeks
1006.87094 9.62628 (100*2π)/5465 weeks
1015.57843 11.08692 (101*2π)/5465 weeks
1023.72425 11.6731 (102*2π)/5465 weeks
103.82728 12.02098 (103*2π)/5465 weeks
104-1.75362 10.75491 (104*2π)/5465 weeks
105-3.34977 8.88866 (105*2π)/5465 weeks
106-4.13313 5.98517 (106*2π)/5465 weeks
107-4.11145 2.83886 (107*2π)/5465 weeks
108-1.98712 -.03491 (108*2π)/5465 weeks
1091.27285 -.81753 (109*2π)/5465 weeks
1104.34996 -.40472 (110*2π)/5465 weeks
1116.25014 1.80551 (111*2π)/5465 weeks
1125.97445 4.42313 (112*2π)/5465 weeks
1135.4755 6.19175 (113*2π)/5465 weeks
1143.54076 7.97914 (114*2π)/5465 weeks
115.69714 7.01216 (115*2π)/5465 weeks
116-.90317 5.10548 (116*2π)/5465 weeks
117-.75318 2.85372 (117*2π)/5465 weeks
118.42734 .69883 (118*2π)/5465 weeks
1193.13791 -.62626 (119*2π)/5465 weeks
1205.53672 -.15821 (120*2π)/5465 weeks
1217.53183 1.97483 (121*2π)/5465 weeks
1228.33337 4.98058 (122*2π)/5464 weeks
1236.75106 7.75879 (123*2π)/5464 weeks
1244.40707 8.53269 (124*2π)/5464 weeks
1251.87993 8.3572 (125*2π)/5464 weeks
126.43862 6.38804 (126*2π)/5464 weeks
1271.11002 5.00243 (127*2π)/5464 weeks
1281.81376 4.56801 (128*2π)/5464 weeks
1292.26951 4.89776 (129*2π)/5464 weeks
1302.29634 5.4269 (130*2π)/5464 weeks
1311.61638 6.07082 (131*2π)/5464 weeks
132.42227 6.4657 (132*2π)/5464 weeks
133-1.08316 5.63943 (133*2π)/5464 weeks
134-1.99623 3.78427 (134*2π)/5464 weeks
135-2.27068 1.92222 (135*2π)/5464 weeks
136-.93396 -.42988 (136*2π)/5464 weeks
1372.35857 -.87627 (137*2π)/5464 weeks
1383.56359 .52036 (138*2π)/5464 weeks
1393.91978 1.65651 (139*2π)/5464 weeks
1404.08997 2.65294 (140*2π)/5464 weeks
1413.27303 3.59897 (141*2π)/5464 weeks
1423.04771 3.34177 (142*2π)/5464 weeks
1432.6088 3.87631 (143*2π)/5464 weeks
1441.33797 3.6664 (144*2π)/5464 weeks
1451.26658 2.79241 (145*2π)/5464 weeks
1461.13256 2.21507 (146*2π)/5464 weeks
1471.66392 .19915 (147*2π)/5464 weeks
1483.61539 .41877 (148*2π)/5464 weeks
1494.67851 1.09545 (149*2π)/5464 weeks
1506.21273 2.38913 (150*2π)/5464 weeks
1516.02867 4.7764 (151*2π)/5464 weeks
1524.45725 6.24907 (152*2π)/5464 weeks
1533.17687 7.18031 (153*2π)/5464 weeks
154.6587 7.48679 (154*2π)/5464 weeks
155-1.06069 6.59921 (155*2π)/5464 weeks
156-2.74421 4.99655 (156*2π)/5464 weeks
157-4.16927 2.68348 (157*2π)/5463 weeks
158-3.11456 -.93176 (158*2π)/5463 weeks
159-1.03135 -2.08117 (159*2π)/5463 weeks
160.93945 -3.26546 (160*2π)/5463 weeks
1613.78465 -3.23863 (161*2π)/5463 weeks
1626.45502 -1.42165 (162*2π)/5463 weeks
1637.60915 1.59778 (163*2π)/5463 weeks
1646.70802 4.61186 (164*2π)/5463 weeks
1654.38832 6.71268 (165*2π)/5463 weeks
1661.28756 6.94774 (166*2π)/5463 weeks
167-1.43335 5.62951 (167*2π)/5463 weeks
168-2.78654 3.35855 (168*2π)/5463 weeks
169-2.68823 .42309 (169*2π)/5463 weeks
170-1.50864 -1.58383 (170*2π)/5463 weeks
171.73927 -3.28854 (171*2π)/5463 weeks
1723.33815 -2.89189 (172*2π)/5463 weeks
1735.44681 -1.68011 (173*2π)/5463 weeks
1746.89063 .68355 (174*2π)/5463 weeks
1756.72311 3.18244 (175*2π)/5463 weeks
1765.273 5.77596 (176*2π)/5463 weeks
1772.556 7.16072 (177*2π)/5463 weeks
178-.5893 6.76398 (178*2π)/5463 weeks
179-3.10252 4.92062 (179*2π)/5463 weeks
180-4.05478 2.12975 (180*2π)/5463 weeks
181-3.83985 -1.00775 (181*2π)/5463 weeks
182-2.20926 -3.07219 (182*2π)/5463 weeks
183.76176 -4.34925 (183*2π)/5463 weeks
1843.0795 -3.41016 (184*2π)/5463 weeks
1854.33 -1.87948 (185*2π)/5463 weeks
1864.73184 .31569 (186*2π)/5463 weeks
1873.30448 1.81708 (187*2π)/5463 weeks
1881.69235 2.03947 (188*2π)/5463 weeks
189-.04401 1.26099 (189*2π)/5463 weeks
190-.77653 -.3105 (190*2π)/5463 weeks
191-.4226 -2.55354 (191*2π)/5463 weeks
192.69252 -3.90693 (192*2π)/5463 weeks
1933.05133 -4.85165 (193*2π)/5463 weeks
1945.71032 -4.07018 (194*2π)/5463 weeks
1956.54117 -2.34366 (195*2π)/5463 weeks
1967.09861 -.52687 (196*2π)/5463 weeks
1976.45565 1.78206 (197*2π)/5463 weeks
1984.7554 2.57819 (198*2π)/5463 weeks
1993.28024 2.91182 (199*2π)/5463 weeks
200.79284 2.46381 (200*2π)/5463 weeks
201-.37449 .03798 (201*2π)/5463 weeks
202.25921 -1.99932 (202*2π)/5463 weeks
2031.18946 -4.25552 (203*2π)/5463 weeks
2044.23268 -5.31362 (204*2π)/5463 weeks
2056.85879 -4.43073 (205*2π)/5463 weeks
2068.829 -1.99713 (206*2π)/5463 weeks
2078.68874 .74534 (207*2π)/5463 weeks
2087.02698 2.80077 (208*2π)/5463 weeks
2095.25134 3.27208 (209*2π)/5463 weeks
2103.09713 2.9571 (210*2π)/5463 weeks
2112.17007 1.36726 (211*2π)/5463 weeks
2122.01748 -.84055 (212*2π)/5463 weeks
2133.6008 -1.56047 (213*2π)/5463 weeks
2145.37616 -2.34918 (214*2π)/5463 weeks
2157.10088 -.92431 (215*2π)/5463 weeks
2167.08573 .68676 (216*2π)/5463 weeks
2177.15187 1.7252 (217*2π)/5463 weeks
2186.53535 2.7211 (218*2π)/5463 weeks
2195.975 3.49299 (219*2π)/5462 weeks
2204.6863 4.57819 (220*2π)/5462 weeks
2213.20857 4.26169 (221*2π)/5462 weeks
2222.01828 3.66941 (222*2π)/5462 weeks
223.86758 2.68974 (223*2π)/5462 weeks
224.54196 .71619 (224*2π)/5462 weeks
2251.33254 -.72185 (225*2π)/5462 weeks
2262.91964 -1.79049 (226*2π)/5462 weeks
2275.07942 -2.12096 (227*2π)/5462 weeks
2286.78643 -.25622 (228*2π)/5462 weeks
2297.28688 2.06912 (229*2π)/5462 weeks
2306.54188 4.23412 (230*2π)/5462 weeks
2314.46709 5.87148 (231*2π)/5462 weeks
2321.65428 6.0104 (232*2π)/5462 weeks
233-.51601 4.88704 (233*2π)/5462 weeks
234-2.54847 2.53237 (234*2π)/5462 weeks
235-2.52628 -.86523 (235*2π)/5462 weeks
236-.91899 -3.45834 (236*2π)/5462 weeks
2372.16682 -4.91836 (237*2π)/5462 weeks
2385.8126 -4.17771 (238*2π)/5462 weeks
2397.68783 -1.37799 (239*2π)/5462 weeks
2407.95003 1.44248 (240*2π)/5462 weeks
2416.50285 4.76887 (241*2π)/5462 weeks
2423.16552 6.05998 (242*2π)/5462 weeks
243-.08845 5.2821 (243*2π)/5462 weeks
244-2.7252 3.35208 (244*2π)/5462 weeks
245-4.10724 -.21714 (245*2π)/5462 weeks
246-2.63879 -4.28242 (246*2π)/5462 weeks
247-.06499 -6.58942 (247*2π)/5462 weeks
2483.67944 -7.61103 (248*2π)/5462 weeks
2497.51157 -6.08479 (249*2π)/5462 weeks
2509.34424 -3.10165 (250*2π)/5462 weeks
25110.11929 -.17377 (251*2π)/5462 weeks
2528.90043 2.90061 (252*2π)/5462 weeks
2536.87994 4.72728 (253*2π)/5462 weeks
2544.21945 5.9233 (254*2π)/5462 weeks
255.75028 5.2748 (255*2π)/5462 weeks
256-1.08654 2.03435 (256*2π)/5462 weeks
257-.84671 -.8668 (257*2π)/5462 weeks
258.4371 -3.24128 (258*2π)/5462 weeks
2593.42058 -4.69081 (259*2π)/5462 weeks
2607.111 -3.70529 (260*2π)/5462 weeks
2619.20244 -.66989 (261*2π)/5462 weeks
2628.81443 2.85013 (262*2π)/5462 weeks
2636.6134 5.9533 (263*2π)/5462 weeks
2642.99883 6.88301 (264*2π)/5462 weeks
265.29774 6.38928 (265*2π)/5462 weeks
266-3.35639 4.15846 (266*2π)/5462 weeks
267-4.58116 -.17807 (267*2π)/5462 weeks
268-3.11145 -3.82584 (268*2π)/5462 weeks
269-.12652 -6.22633 (269*2π)/5462 weeks
2703.37472 -7.08157 (270*2π)/5462 weeks
2716.48769 -5.76069 (271*2π)/5462 weeks
2729.07844 -3.76478 (272*2π)/5462 weeks
27310.51324   (273*2π)/5462 weeks
2749.07844 3.76478 (274*2π)/5462 weeks
2756.48769 5.76069 (275*2π)/5462 weeks
2763.37472 7.08157 (276*2π)/5462 weeks
277-.12652 6.22633 (277*2π)/5462 weeks
278-3.11145 3.82584 (278*2π)/5462 weeks
279-4.58116 .17807 (279*2π)/5462 weeks
280-3.35639 -4.15846 (280*2π)/5462 weeks
281.29774 -6.38928 (281*2π)/5462 weeks
2822.99883 -6.88301 (282*2π)/5462 weeks
2836.6134 -5.9533 (283*2π)/5462 weeks
2848.81443 -2.85013 (284*2π)/5462 weeks
2859.20244 .66989 (285*2π)/5462 weeks
2867.111 3.70529 (286*2π)/5462 weeks
2873.42058 4.69081 (287*2π)/5462 weeks
288.4371 3.24128 (288*2π)/5462 weeks
289-.84671 .8668 (289*2π)/5462 weeks
290-1.08654 -2.03435 (290*2π)/5462 weeks
291.75028 -5.2748 (291*2π)/5462 weeks
2924.21945 -5.9233 (292*2π)/5462 weeks
2936.87994 -4.72728 (293*2π)/5462 weeks
2948.90043 -2.90061 (294*2π)/5462 weeks
29510.11929 .17377 (295*2π)/5462 weeks
2969.34424 3.10165 (296*2π)/5462 weeks
2977.51157 6.08479 (297*2π)/5462 weeks
2983.67944 7.61103 (298*2π)/5462 weeks
299-.06499 6.58942 (299*2π)/5462 weeks
300-2.63879 4.28242 (300*2π)/5462 weeks
301-4.10724 .21714 (301*2π)/5462 weeks
302-2.7252 -3.35208 (302*2π)/5462 weeks
303-.08845 -5.2821 (303*2π)/5462 weeks
3043.16552 -6.05998 (304*2π)/5462 weeks
3056.50285 -4.76887 (305*2π)/5462 weeks
3067.95003 -1.44248 (306*2π)/5462 weeks
3077.68783 1.37799 (307*2π)/5462 weeks
3085.8126 4.17771 (308*2π)/5462 weeks
3092.16682 4.91836 (309*2π)/5462 weeks
310-.91899 3.45834 (310*2π)/5462 weeks
311-2.52628 .86523 (311*2π)/5462 weeks
312-2.54847 -2.53237 (312*2π)/5462 weeks
313-.51601 -4.88704 (313*2π)/5462 weeks
3141.65428 -6.0104 (314*2π)/5462 weeks
3154.46709 -5.87148 (315*2π)/5462 weeks
3166.54188 -4.23412 (316*2π)/5462 weeks
3177.28688 -2.06912 (317*2π)/5462 weeks
3186.78643 .25622 (318*2π)/5462 weeks
3195.07942 2.12096 (319*2π)/5462 weeks
3202.91964 1.79049 (320*2π)/5462 weeks
3211.33254 .72185 (321*2π)/5462 weeks
322.54196 -.71619 (322*2π)/5462 weeks
323.86758 -2.68974 (323*2π)/5462 weeks
3242.01828 -3.66941 (324*2π)/5462 weeks
3253.20857 -4.26169 (325*2π)/5462 weeks
3264.6863 -4.57819 (326*2π)/5462 weeks
3275.975 -3.49299 (327*2π)/5462 weeks
3286.53535 -2.7211 (328*2π)/5462 weeks
3297.15187 -1.7252 (329*2π)/5462 weeks
3307.08573 -.68676 (330*2π)/5462 weeks
3317.10088 .92431 (331*2π)/5462 weeks
3325.37616 2.34918 (332*2π)/5462 weeks
3333.6008 1.56047 (333*2π)/5462 weeks
3342.01748 .84055 (334*2π)/5462 weeks
3352.17007 -1.36726 (335*2π)/5462 weeks
3363.09713 -2.9571 (336*2π)/5462 weeks
3375.25134 -3.27208 (337*2π)/5462 weeks
3387.02698 -2.80077 (338*2π)/5462 weeks
3398.68874 -.74534 (339*2π)/5462 weeks
3408.829 1.99713 (340*2π)/5462 weeks
3416.85879 4.43073 (341*2π)/5462 weeks
3424.23268 5.31362 (342*2π)/5462 weeks
3431.18946 4.25552 (343*2π)/5462 weeks
344.25921 1.99932 (344*2π)/5462 weeks
345-.37449 -.03798 (345*2π)/5462 weeks
346.79284 -2.46381 (346*2π)/5462 weeks
3473.28024 -2.91182 (347*2π)/5462 weeks
3484.7554 -2.57819 (348*2π)/5462 weeks
3496.45565 -1.78206 (349*2π)/5462 weeks
3507.09861 .52687 (350*2π)/5462 weeks
3516.54117 2.34366 (351*2π)/5462 weeks
3525.71032 4.07018 (352*2π)/5462 weeks
3533.05133 4.85165 (353*2π)/5462 weeks
354.69252 3.90693 (354*2π)/5462 weeks
355-.4226 2.55354 (355*2π)/5462 weeks
356-.77653 .3105 (356*2π)/5462 weeks
357-.04401 -1.26099 (357*2π)/5462 weeks
3581.69235 -2.03947 (358*2π)/5462 weeks
3593.30448 -1.81708 (359*2π)/5462 weeks
3604.73184 -.31569 (360*2π)/5462 weeks
3614.33 1.87948 (361*2π)/5462 weeks
3623.0795 3.41016 (362*2π)/5462 weeks
363.76176 4.34925 (363*2π)/5462 weeks
364-2.20926 3.07219 (364*2π)/5462 weeks
365-3.83985 1.00775 (365*2π)/5461 weeks
366-4.05478 -2.12975 (366*2π)/5461 weeks
367-3.10252 -4.92062 (367*2π)/5461 weeks
368-.5893 -6.76398 (368*2π)/5461 weeks
3692.556 -7.16072 (369*2π)/5461 weeks
3705.273 -5.77596 (370*2π)/5461 weeks
3716.72311 -3.18244 (371*2π)/5461 weeks
3726.89063 -.68355 (372*2π)/5461 weeks
3735.44681 1.68011 (373*2π)/5461 weeks
3743.33815 2.89189 (374*2π)/5461 weeks
375.73927 3.28854 (375*2π)/5461 weeks
376-1.50864 1.58383 (376*2π)/5461 weeks
377-2.68823 -.42309 (377*2π)/5461 weeks
378-2.78654 -3.35855 (378*2π)/5461 weeks
379-1.43335 -5.62951 (379*2π)/5461 weeks
3801.28756 -6.94774 (380*2π)/5461 weeks
3814.38832 -6.71268 (381*2π)/5461 weeks
3826.70802 -4.61186 (382*2π)/5461 weeks
3837.60915 -1.59778 (383*2π)/5461 weeks
3846.45502 1.42165 (384*2π)/5461 weeks
3853.78465 3.23863 (385*2π)/5461 weeks
386.93945 3.26546 (386*2π)/5461 weeks
387-1.03135 2.08117 (387*2π)/5461 weeks
388-3.11456 .93176 (388*2π)/5461 weeks
389-4.16927 -2.68348 (389*2π)/5461 weeks
390-2.74421 -4.99655 (390*2π)/5461 weeks
391-1.06069 -6.59921 (391*2π)/5461 weeks
392.6587 -7.48679 (392*2π)/5461 weeks
3933.17687 -7.18031 (393*2π)/5461 weeks
3944.45725 -6.24907 (394*2π)/5461 weeks
3956.02867 -4.7764 (395*2π)/5461 weeks
3966.21273 -2.38913 (396*2π)/5461 weeks
3974.67851 -1.09545 (397*2π)/5461 weeks
3983.61539 -.41877 (398*2π)/5461 weeks
3991.66392 -.19915 (399*2π)/5461 weeks
4001.13256 -2.21507 (400*2π)/5461 weeks
4011.26658 -2.79241 (401*2π)/5461 weeks
4021.33797 -3.6664 (402*2π)/5461 weeks
4032.6088 -3.87631 (403*2π)/5461 weeks
4043.04771 -3.34177 (404*2π)/5461 weeks
4053.27303 -3.59897 (405*2π)/5461 weeks
4064.08997 -2.65294 (406*2π)/5461 weeks
4073.91978 -1.65651 (407*2π)/5461 weeks
4083.56359 -.52036 (408*2π)/5461 weeks
4092.35857 .87627 (409*2π)/5461 weeks
410-.93396 .42988 (410*2π)/5461 weeks
411-2.27068 -1.92222 (411*2π)/5461 weeks
412-1.99623 -3.78427 (412*2π)/5461 weeks
413-1.08316 -5.63943 (413*2π)/5461 weeks
414.42227 -6.4657 (414*2π)/5461 weeks
4151.61638 -6.07082 (415*2π)/5461 weeks
4162.29634 -5.4269 (416*2π)/5461 weeks
4172.26951 -4.89776 (417*2π)/5461 weeks
4181.81376 -4.56801 (418*2π)/5461 weeks
4191.11002 -5.00243 (419*2π)/5461 weeks
420.43862 -6.38804 (420*2π)/5461 weeks
4211.87993 -8.3572 (421*2π)/5461 weeks
4224.40707 -8.53269 (422*2π)/5461 weeks
4236.75106 -7.75879 (423*2π)/5461 weeks
4248.33337 -4.98058 (424*2π)/5461 weeks
4257.53183 -1.97483 (425*2π)/5461 weeks
4265.53672 .15821 (426*2π)/5461 weeks
4273.13791 .62626 (427*2π)/5461 weeks
428.42734 -.69883 (428*2π)/5461 weeks
429-.75318 -2.85372 (429*2π)/5461 weeks
430-.90317 -5.10548 (430*2π)/5461 weeks
431.69714 -7.01216 (431*2π)/5461 weeks
4323.54076 -7.97914 (432*2π)/5461 weeks
4335.4755 -6.19175 (433*2π)/5461 weeks
4345.97445 -4.42313 (434*2π)/5461 weeks
4356.25014 -1.80551 (435*2π)/5461 weeks
4364.34996 .40472 (436*2π)/5461 weeks
4371.27285 .81753 (437*2π)/5461 weeks
438-1.98712 .03491 (438*2π)/5461 weeks
439-4.11145 -2.83886 (439*2π)/5461 weeks
440-4.13313 -5.98517 (440*2π)/5461 weeks
441-3.34977 -8.88866 (441*2π)/5461 weeks
442-1.75362 -10.75491 (442*2π)/5461 weeks
443.82728 -12.02098 (443*2π)/5461 weeks
4443.72425 -11.6731 (444*2π)/5461 weeks
4455.57843 -11.08692 (445*2π)/5461 weeks
4466.87094 -9.62628 (446*2π)/5461 weeks
4477.2482 -7.75803 (447*2π)/5461 weeks
4486.82561 -5.86032 (448*2π)/5461 weeks
4496.0036 -4.90383 (449*2π)/5461 weeks
4504.96138 -4.55797 (450*2π)/5461 weeks
4513.09119 -5.08797 (451*2π)/5461 weeks
4523.26281 -6.05389 (452*2π)/5461 weeks
4532.07263 -6.92552 (453*2π)/5461 weeks
4542.61629 -9.26569 (454*2π)/5461 weeks
4555.7001 -11.32253 (455*2π)/5461 weeks
4568.62917 -10.89819 (456*2π)/5461 weeks
45711.84749 -7.95948 (457*2π)/5461 weeks
45812.21473 -3.38858 (458*2π)/5461 weeks
4599.98678 .4626 (459*2π)/5461 weeks
4606.49537 1.54267 (460*2π)/5461 weeks
4612.0445 1.59511 (461*2π)/5461 weeks
462-.59235 -2.41391 (462*2π)/5461 weeks
463-.54764 -4.89764 (463*2π)/5461 weeks
464-.30405 -8.10952 (464*2π)/5461 weeks
4654.54492 -10.65201 (465*2π)/5461 weeks
4667.55264 -7.8868 (466*2π)/5461 weeks
4679.42614 -5.8665 (467*2π)/5461 weeks
4689.85016 -1.09548 (468*2π)/5461 weeks
4695.73854 2.76089 (469*2π)/5461 weeks
4701.79528 2.49957 (470*2π)/5461 weeks
471-2.31861 2.56301 (471*2π)/5461 weeks
472-6.66371 -.94308 (472*2π)/5461 weeks
473-8.50244 -7.03029 (473*2π)/5461 weeks
474-6.20202 -11.5239 (474*2π)/5461 weeks
475-2.67487 -14.44477 (475*2π)/5461 weeks
476.90862 -15.58134 (476*2π)/5461 weeks
4773.38709 -13.8956 (477*2π)/5461 weeks
4784.49003 -14.6036 (478*2π)/5461 weeks
4797.98493 -13.19803 (479*2π)/5461 weeks
4808.31165 -10.50821 (480*2π)/5461 weeks
4819.73217 -9.00989 (481*2π)/5461 weeks
4829.06559 -5.14625 (482*2π)/5461 weeks
4835.73051 -3.81235 (483*2π)/5461 weeks
4842.64666 -3.53177 (484*2π)/5461 weeks
485-1.36897 -5.00582 (485*2π)/5461 weeks
486-2.89597 -10.8824 (486*2π)/5461 weeks
487-1.17043 -15.01441 (487*2π)/5461 weeks
4883.13036 -18.40124 (488*2π)/5461 weeks
4898.10225 -18.76949 (489*2π)/5461 weeks
49014.44803 -16.18647 (490*2π)/5461 weeks
49115.87093 -11.19456 (491*2π)/5461 weeks
49216.30348 -5.56761 (492*2π)/5461 weeks
49312.66421 -.96351 (493*2π)/5461 weeks
4948.06104 .3879 (494*2π)/5461 weeks
4954.78602 -.48664 (495*2π)/5461 weeks
496.84317 -1.04127 (496*2π)/5461 weeks
497-2.11288 -5.76816 (497*2π)/5461 weeks
498-.55487 -8.47346 (498*2π)/5461 weeks
499.42848 -11.61802 (499*2π)/5461 weeks
5003.78141 -13.17056 (500*2π)/5461 weeks
5015.50433 -10.00177 (501*2π)/5461 weeks
5026.35514 -8.60278 (502*2π)/5461 weeks
5035.46019 -5.4269 (503*2π)/5461 weeks
504.70682 -4.51161 (504*2π)/5461 weeks
505-2.08168 -5.06112 (505*2π)/5461 weeks
506-9.27736 -7.19118 (506*2π)/5461 weeks
507-11.52728 -17.28088 (507*2π)/5461 weeks
508-8.532 -25.62134 (508*2π)/5461 weeks
509-1.4401 -31.7544 (509*2π)/5461 weeks
5107.02619 -36.58207 (510*2π)/5461 weeks
51120.36347 -34.15674 (511*2π)/5461 weeks
51229.35757 -26.05022 (512*2π)/5461 weeks
51336.10859 -11.72972 (513*2π)/5461 weeks
51430.26398 3.28604 (514*2π)/5461 weeks
51516.24385 11.67207 (515*2π)/5461 weeks
5163.73561 11.12118 (516*2π)/5461 weeks
517-8.69578 5.77122 (517*2π)/5461 weeks
518-14.07936 -7.74445 (518*2π)/5461 weeks
519-11.07959 -19.66918 (519*2π)/5461 weeks
520-3.4892 -29.31659 (520*2π)/5461 weeks
5219.27263 -28.20521 (521*2π)/5461 weeks
52219.98579 -20.22321 (522*2π)/5461 weeks
52321.91395 -7.55587 (523*2π)/5461 weeks
52411.98825 4.26753 (524*2π)/5461 weeks
525-3.22548 9.04163 (525*2π)/5461 weeks
526-18.48828 3.8666 (526*2π)/5461 weeks
527-28.53659 -8.84933 (527*2π)/5461 weeks
528-35.68687 -23.18542 (528*2π)/5461 weeks
529-33.66854 -43.97771 (529*2π)/5461 weeks
530-20.58559 -55.51817 (530*2π)/5461 weeks
531-9.28673 -64.22239 (531*2π)/5461 weeks
5324.13374 -70.7046 (532*2π)/5461 weeks
53322.51116 -60.8947 (533*2π)/5461 weeks
53425.21966 -56.11226 (534*2π)/5461 weeks
53533.34144 -40.74288 (535*2π)/5461 weeks
53622.14037 -28.55057 (536*2π)/5461 weeks
5379.056 -23.86494 (537*2π)/5461 weeks
538-18.21305 -27.45858 (538*2π)/5461 weeks
539-50.69043 -53.66132 (539*2π)/5461 weeks
540-62.1941 -108.6228 (540*2π)/5461 weeks
541-34.41943 -175.6357 (541*2π)/5461 weeks
54218.41297 -234.8722 (542*2π)/5461 weeks
543112.8395 -265.6041 (543*2π)/5461 weeks
544228.99 -244.3947 (544*2π)/5461 weeks



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