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Fourier Analysis of FXP (ProShares Ultrashort FTSE China)


FXP (ProShares Ultrashort FTSE China) appears to have interesting cyclic behaviour every 41 weeks (74.5011*sine), 38 weeks (73.9129*sine), and 45 weeks (62.0462*sine).

FXP (ProShares Ultrashort FTSE China) has an average price of 299.18 (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 3/20/2017 for FXP (ProShares Ultrashort FTSE China), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0299.1815   0 
1352.0267 219.4979 (1*2π)/490490 weeks
2229.1591 283.1567 (2*2π)/490245 weeks
388.20022 285.9691 (3*2π)/490163 weeks
4-13.97422 227.8203 (4*2π)/490123 weeks
5-64.38567 155.3959 (5*2π)/49098 weeks
6-63.35107 77.41843 (6*2π)/49082 weeks
7-26.40102 32.68596 (7*2π)/49070 weeks
88.06834 24.89603 (8*2π)/49061 weeks
925.09231 31.35089 (9*2π)/49054 weeks
1037.88248 48.19169 (10*2π)/49049 weeks
1125.7179 62.04618 (11*2π)/49045 weeks
1220.85983 74.50114 (12*2π)/49041 weeks
13-4.15222 73.9129 (13*2π)/49038 weeks
14-19.58895 65.73921 (14*2π)/49035 weeks
15-33.71518 54.71941 (15*2π)/49033 weeks
16-40.67844 29.37332 (16*2π)/49031 weeks
17-32.38161 10.26094 (17*2π)/49029 weeks
18-19.7531 -5.2916 (18*2π)/49027 weeks
19-.32038 -10.6835 (19*2π)/49026 weeks
2016.77034 -2.79495 (20*2π)/49025 weeks
2123.64145 14.83057 (21*2π)/49023 weeks
2216.83029 29.68148 (22*2π)/49022 weeks
232.97902 33.85692 (23*2π)/49021 weeks
24-10.83496 24.16814 (24*2π)/49020 weeks
25-15.88403 10.55268 (25*2π)/49020 weeks
26-10.20589 -6.15784 (26*2π)/49019 weeks
275.1797 -12.73204 (27*2π)/49018 weeks
2821.32505 -12.61424 (28*2π)/49018 weeks
2936.23265 .95071 (29*2π)/49017 weeks
3038.32835 21.73521 (30*2π)/49016 weeks
3127.91242 34.16117 (31*2π)/49016 weeks
3213.33102 41.20938 (32*2π)/49015 weeks
33.17205 36.21374 (33*2π)/49015 weeks
34-8.80599 29.49977 (34*2π)/49014 weeks
35-12.80926 19.18258 (35*2π)/49014 weeks
36-9.24348 7.03093 (36*2π)/49014 weeks
37-1.43925 5.71315 (37*2π)/49013 weeks
382.47139 4.48703 (38*2π)/49013 weeks
396.80356 7.93273 (39*2π)/49013 weeks
406.30218 11.03466 (40*2π)/49012 weeks
415.99967 13.68579 (41*2π)/49012 weeks
421.03815 13.10392 (42*2π)/49012 weeks
43-.74427 9.36977 (43*2π)/49011 weeks
44-2.38042 6.00142 (44*2π)/49011 weeks
451.70756 .59035 (45*2π)/49011 weeks
466.00184 .24516 (46*2π)/49011 weeks
4710.95496 -.23002 (47*2π)/49010 weeks
4816.55921 3.10953 (48*2π)/49010 weeks
4918.44484 10.31986 (49*2π)/49010 weeks
5016.85357 15.93505 (50*2π)/49010 weeks
519.89223 20.96704 (51*2π)/49010 weeks
523.67194 20.5262 (52*2π)/4909 weeks
53-1.59565 16.27429 (53*2π)/4909 weeks
54-3.61037 10.86468 (54*2π)/4909 weeks
55-.01941 4.50288 (55*2π)/4909 weeks
564.5446 3.66574 (56*2π)/4909 weeks
578.15123 4.40032 (57*2π)/4909 weeks
5811.08466 8.58811 (58*2π)/4908 weeks
599.37503 11.77305 (59*2π)/4908 weeks
609.21047 14.34219 (60*2π)/4908 weeks
615.03521 16.39524 (61*2π)/4908 weeks
623.61205 15.6029 (62*2π)/4908 weeks
63-.12206 17.18264 (63*2π)/4908 weeks
64-4.44231 15.40932 (64*2π)/4908 weeks
65-7.93017 10.94032 (65*2π)/4908 weeks
66-8.95061 3.5343 (66*2π)/4907 weeks
67-4.48125 -1.93499 (67*2π)/4907 weeks
681.40277 -2.83485 (68*2π)/4907 weeks
695.79112 -3.11151 (69*2π)/4907 weeks
7010.99101 1.31853 (70*2π)/4907 weeks
7110.14905 7.02858 (71*2π)/4907 weeks
728.0436 9.44652 (72*2π)/4907 weeks
732.67049 11.77348 (73*2π)/4907 weeks
74-.60966 6.91454 (74*2π)/4907 weeks
75-.45282 3.78425 (75*2π)/4907 weeks
76.72258 -.92937 (76*2π)/4906 weeks
776.51023 -2.15797 (77*2π)/4906 weeks
7810.73207 -.81537 (78*2π)/4906 weeks
7913.66124 3.90237 (79*2π)/4906 weeks
8012.82015 9.46038 (80*2π)/4906 weeks
818.45703 12.17297 (81*2π)/4906 weeks
824.41707 12.34346 (82*2π)/4906 weeks
832.39632 9.16505 (83*2π)/4906 weeks
843.25028 6.62212 (84*2π)/4906 weeks
853.36461 6.17111 (85*2π)/4906 weeks
865.27538 4.84068 (86*2π)/4906 weeks
876.61647 5.3773 (87*2π)/4906 weeks
887.70259 6.57063 (88*2π)/4906 weeks
897.97979 8.8366 (89*2π)/4906 weeks
907.04164 11.10275 (90*2π)/4905 weeks
914.93176 12.73642 (91*2π)/4905 weeks
922.50981 13.71558 (92*2π)/4905 weeks
93-.90222 12.75196 (93*2π)/4905 weeks
94-3.12166 10.38941 (94*2π)/4905 weeks
95-4.54744 7.01119 (95*2π)/4905 weeks
96-4.59397 3.2872 (96*2π)/4905 weeks
97-1.91733 -.19797 (97*2π)/4905 weeks
981.90221 -.86005 (98*2π)/4905 weeks
995.56679 .41843 (99*2π)/4905 weeks
1007.17018 3.61309 (100*2π)/4905 weeks
1016.43986 5.78611 (101*2π)/4905 weeks
1024.95717 8.11958 (102*2π)/4905 weeks
1031.18986 8.10337 (103*2π)/4905 weeks
104-.8283 5.96139 (104*2π)/4905 weeks
105-.74615 3.13337 (105*2π)/4905 weeks
106.74933 .57853 (106*2π)/4905 weeks
1074.21525 -.39153 (107*2π)/4905 weeks
1087.29109 .62024 (108*2π)/4905 weeks
1099.06007 3.53343 (109*2π)/4904 weeks
1108.44032 7.45165 (110*2π)/4904 weeks
1115.45526 9.25016 (111*2π)/4904 weeks
1122.56547 9.42899 (112*2π)/4904 weeks
113.52119 7.18224 (113*2π)/4904 weeks
1141.32196 5.4056 (114*2π)/4904 weeks
1152.24515 5.0297 (115*2π)/4904 weeks
1162.66912 5.59799 (116*2π)/4904 weeks
1172.47656 6.46714 (117*2π)/4904 weeks
1181.35221 7.0719 (118*2π)/4904 weeks
119-.73426 6.76019 (119*2π)/4904 weeks
120-2.35775 4.88342 (120*2π)/4904 weeks
121-2.68453 2.61066 (121*2π)/4904 weeks
122-1.2853 -.45072 (122*2π)/4904 weeks
1232.72105 -1.00166 (123*2π)/4904 weeks
1244.14713 .70522 (124*2π)/4904 weeks
1254.52627 2.03438 (125*2π)/4904 weeks
1264.48199 3.49219 (126*2π)/4904 weeks
1273.27674 3.76653 (127*2π)/4904 weeks
1283.14834 4.23801 (128*2π)/4904 weeks
1291.78517 4.50258 (129*2π)/4904 weeks
1301.3411 3.22489 (130*2π)/4904 weeks
1311.16508 2.46811 (131*2π)/4904 weeks
1322.01946 .06936 (132*2π)/4904 weeks
1334.27511 .51703 (133*2π)/4904 weeks
1345.65959 1.29321 (134*2π)/4904 weeks
1357.05256 3.84846 (135*2π)/4904 weeks
1365.8627 6.51487 (136*2π)/4904 weeks
1374.13012 7.58423 (137*2π)/4904 weeks
1381.397 8.56996 (138*2π)/4904 weeks
139-.97165 7.47028 (139*2π)/4904 weeks
140-3.10493 5.58179 (140*2π)/4904 weeks
141-4.7835 2.51722 (141*2π)/4903 weeks
142-2.80662 -1.5186 (142*2π)/4903 weeks
143-.55761 -2.76919 (143*2π)/4903 weeks
1442.51586 -3.82604 (144*2π)/4903 weeks
1456.11612 -2.74784 (145*2π)/4903 weeks
1468.26166 .57954 (146*2π)/4903 weeks
1477.73828 4.53017 (147*2π)/4903 weeks
1485.10637 7.31984 (148*2π)/4903 weeks
1491.30362 7.68917 (149*2π)/4903 weeks
150-1.89771 5.83493 (150*2π)/4903 weeks
151-3.36408 2.85463 (151*2π)/4903 weeks
152-2.51228 -.40627 (152*2π)/4903 weeks
153-.71241 -2.7548 (153*2π)/4903 weeks
1542.82629 -3.42868 (154*2π)/4903 weeks
1555.50507 -2.31511 (155*2π)/4903 weeks
1567.5213 .22234 (156*2π)/4903 weeks
1577.43764 3.36656 (157*2π)/4903 weeks
1585.65398 6.48175 (158*2π)/4903 weeks
1592.18545 7.931 (159*2π)/4903 weeks
160-1.50435 6.94154 (160*2π)/4903 weeks
161-4.07406 4.02227 (161*2π)/4903 weeks
162-4.6918 .6061 (162*2π)/4903 weeks
163-2.9974 -2.59468 (163*2π)/4903 weeks
164-.08023 -4.77654 (164*2π)/4903 weeks
1653.0893 -3.89014 (165*2π)/4903 weeks
1664.69342 -2.04861 (166*2π)/4903 weeks
1675.04297 .60007 (167*2π)/4903 weeks
1683.15216 2.11049 (168*2π)/4903 weeks
1691.18563 2.09756 (169*2π)/4903 weeks
170-.47569 .45101 (170*2π)/4903 weeks
171-.97567 -1.88853 (171*2π)/4903 weeks
172.47042 -3.82275 (172*2π)/4903 weeks
1732.87808 -5.39149 (173*2π)/4903 weeks
1746.11344 -4.74819 (174*2π)/4903 weeks
1757.25295 -2.4843 (175*2π)/4903 weeks
1767.82667 -.21946 (176*2π)/4903 weeks
1776.50338 2.40363 (177*2π)/4903 weeks
1784.52535 3.02998 (178*2π)/4903 weeks
1792.41476 3.36952 (179*2π)/4903 weeks
180-.13033 1.14546 (180*2π)/4903 weeks
181.09127 -1.88042 (181*2π)/4903 weeks
182.95782 -4.27909 (182*2π)/4903 weeks
1834.5042 -5.94641 (183*2π)/4903 weeks
1847.78448 -4.81819 (184*2π)/4903 weeks
1859.92395 -1.61644 (185*2π)/4903 weeks
1869.33993 1.674 (186*2π)/4903 weeks
1876.86024 3.43575 (187*2π)/4903 weeks
1884.60713 3.77624 (188*2π)/4903 weeks
1892.5443 2.06143 (189*2π)/4903 weeks
1901.88464 -.17991 (190*2π)/4903 weeks
1913.90045 -1.78722 (191*2π)/4903 weeks
1925.86871 -2.70385 (192*2π)/4903 weeks
1938.03622 -.90065 (193*2π)/4903 weeks
1947.90678 .95566 (194*2π)/4903 weeks
1957.79393 2.43879 (195*2π)/4903 weeks
1966.97438 3.46532 (196*2π)/4903 weeks
1976.13008 4.63255 (197*2π)/4902 weeks
1983.94492 4.86579 (198*2π)/4902 weeks
1992.45467 4.25254 (199*2π)/4902 weeks
2001.11103 3.17227 (200*2π)/4902 weeks
201.59517 .81283 (201*2π)/4902 weeks
2021.60668 -.96179 (202*2π)/4902 weeks
2033.63005 -2.04614 (203*2π)/4902 weeks
2046.63008 -1.74832 (204*2π)/4902 weeks
2058.05073 .72664 (205*2π)/4902 weeks
2067.73546 3.5779 (206*2π)/4902 weeks
2075.81633 6.04064 (207*2π)/4902 weeks
2082.4873 6.81168 (208*2π)/4902 weeks
209-.33913 5.53376 (209*2π)/4902 weeks
210-2.84803 2.77558 (210*2π)/4902 weeks
211-2.63107 -1.35207 (211*2π)/4902 weeks
212-.33869 -4.43704 (212*2π)/4902 weeks
2133.74848 -5.55689 (213*2π)/4902 weeks
2147.66382 -3.25113 (214*2π)/4902 weeks
2158.73007 .32875 (215*2π)/4902 weeks
2168.09056 4.24961 (216*2π)/4902 weeks
2174.22765 6.60237 (217*2π)/4902 weeks
218.12896 5.96797 (218*2π)/4902 weeks
219-3.09828 3.57916 (219*2π)/4902 weeks
220-4.60227 -.97582 (220*2π)/4902 weeks
221-2.20868 -5.41151 (221*2π)/4902 weeks
2221.3952 -7.91977 (222*2π)/4902 weeks
2236.37071 -7.95007 (223*2π)/4902 weeks
2249.85613 -4.7469 (224*2π)/4902 weeks
22511.02039 -1.29381 (225*2π)/4902 weeks
22610.15644 2.74207 (226*2π)/4902 weeks
2277.74964 5.09535 (227*2π)/4902 weeks
2284.47973 6.5171 (228*2π)/4902 weeks
229.20226 5.32351 (229*2π)/4902 weeks
230-1.25065 1.35051 (230*2π)/4902 weeks
231-.39153 -1.90015 (231*2π)/4902 weeks
2322.11973 -4.63255 (232*2π)/4902 weeks
2336.48822 -4.93254 (233*2π)/4902 weeks
2349.71646 -1.75838 (234*2π)/4902 weeks
2359.82538 2.70913 (235*2π)/4902 weeks
2367.37894 6.53184 (236*2π)/4902 weeks
2372.95993 7.52022 (237*2π)/4902 weeks
238-.51084 6.9486 (238*2π)/4902 weeks
239-4.42075 3.24102 (239*2π)/4902 weeks
240-4.4231 -2.14587 (240*2π)/4902 weeks
241-1.74525 -6.01422 (241*2π)/4902 weeks
2422.26159 -7.66811 (242*2π)/4902 weeks
2436.57512 -6.68036 (243*2π)/4902 weeks
2449.72907 -4.48661 (244*2π)/4902 weeks
24511.61238   (245*2π)/4902 weeks
2469.72907 4.48661 (246*2π)/4902 weeks
2476.57512 6.68036 (247*2π)/4902 weeks
2482.26159 7.66811 (248*2π)/4902 weeks
249-1.74525 6.01422 (249*2π)/4902 weeks
250-4.4231 2.14587 (250*2π)/4902 weeks
251-4.42075 -3.24102 (251*2π)/4902 weeks
252-.51084 -6.9486 (252*2π)/4902 weeks
2532.95993 -7.52022 (253*2π)/4902 weeks
2547.37894 -6.53184 (254*2π)/4902 weeks
2559.82538 -2.70913 (255*2π)/4902 weeks
2569.71646 1.75838 (256*2π)/4902 weeks
2576.48822 4.93254 (257*2π)/4902 weeks
2582.11973 4.63255 (258*2π)/4902 weeks
259-.39153 1.90015 (259*2π)/4902 weeks
260-1.25065 -1.35051 (260*2π)/4902 weeks
261.20226 -5.32351 (261*2π)/4902 weeks
2624.47973 -6.5171 (262*2π)/4902 weeks
2637.74964 -5.09535 (263*2π)/4902 weeks
26410.15644 -2.74207 (264*2π)/4902 weeks
26511.02039 1.29381 (265*2π)/4902 weeks
2669.85613 4.7469 (266*2π)/4902 weeks
2676.37071 7.95007 (267*2π)/4902 weeks
2681.3952 7.91977 (268*2π)/4902 weeks
269-2.20868 5.41151 (269*2π)/4902 weeks
270-4.60227 .97582 (270*2π)/4902 weeks
271-3.09828 -3.57916 (271*2π)/4902 weeks
272.12896 -5.96797 (272*2π)/4902 weeks
2734.22765 -6.60237 (273*2π)/4902 weeks
2748.09056 -4.24961 (274*2π)/4902 weeks
2758.73007 -.32875 (275*2π)/4902 weeks
2767.66382 3.25113 (276*2π)/4902 weeks
2773.74848 5.55689 (277*2π)/4902 weeks
278-.33869 4.43704 (278*2π)/4902 weeks
279-2.63107 1.35207 (279*2π)/4902 weeks
280-2.84803 -2.77558 (280*2π)/4902 weeks
281-.33913 -5.53376 (281*2π)/4902 weeks
2822.4873 -6.81168 (282*2π)/4902 weeks
2835.81633 -6.04064 (283*2π)/4902 weeks
2847.73546 -3.5779 (284*2π)/4902 weeks
2858.05073 -.72664 (285*2π)/4902 weeks
2866.63008 1.74832 (286*2π)/4902 weeks
2873.63005 2.04614 (287*2π)/4902 weeks
2881.60668 .96179 (288*2π)/4902 weeks
289.59517 -.81283 (289*2π)/4902 weeks
2901.11103 -3.17227 (290*2π)/4902 weeks
2912.45467 -4.25254 (291*2π)/4902 weeks
2923.94492 -4.86579 (292*2π)/4902 weeks
2936.13008 -4.63255 (293*2π)/4902 weeks
2946.97438 -3.46532 (294*2π)/4902 weeks
2957.79393 -2.43879 (295*2π)/4902 weeks
2967.90678 -.95566 (296*2π)/4902 weeks
2978.03622 .90065 (297*2π)/4902 weeks
2985.86871 2.70385 (298*2π)/4902 weeks
2993.90045 1.78722 (299*2π)/4902 weeks
3001.88464 .17991 (300*2π)/4902 weeks
3012.5443 -2.06143 (301*2π)/4902 weeks
3024.60713 -3.77624 (302*2π)/4902 weeks
3036.86024 -3.43575 (303*2π)/4902 weeks
3049.33993 -1.674 (304*2π)/4902 weeks
3059.92395 1.61644 (305*2π)/4902 weeks
3067.78448 4.81819 (306*2π)/4902 weeks
3074.5042 5.94641 (307*2π)/4902 weeks
308.95782 4.27909 (308*2π)/4902 weeks
309.09127 1.88042 (309*2π)/4902 weeks
310-.13033 -1.14546 (310*2π)/4902 weeks
3112.41476 -3.36952 (311*2π)/4902 weeks
3124.52535 -3.02998 (312*2π)/4902 weeks
3136.50338 -2.40363 (313*2π)/4902 weeks
3147.82667 .21946 (314*2π)/4902 weeks
3157.25295 2.4843 (315*2π)/4902 weeks
3166.11344 4.74819 (316*2π)/4902 weeks
3172.87808 5.39149 (317*2π)/4902 weeks
318.47042 3.82275 (318*2π)/4902 weeks
319-.97567 1.88853 (319*2π)/4902 weeks
320-.47569 -.45101 (320*2π)/4902 weeks
3211.18563 -2.09756 (321*2π)/4902 weeks
3223.15216 -2.11049 (322*2π)/4902 weeks
3235.04297 -.60007 (323*2π)/4902 weeks
3244.69342 2.04861 (324*2π)/4902 weeks
3253.0893 3.89014 (325*2π)/4902 weeks
326-.08023 4.77654 (326*2π)/4902 weeks
327-2.9974 2.59468 (327*2π)/4901 weeks
328-4.6918 -.6061 (328*2π)/4901 weeks
329-4.07406 -4.02227 (329*2π)/4901 weeks
330-1.50435 -6.94154 (330*2π)/4901 weeks
3312.18545 -7.931 (331*2π)/4901 weeks
3325.65398 -6.48175 (332*2π)/4901 weeks
3337.43764 -3.36656 (333*2π)/4901 weeks
3347.5213 -.22234 (334*2π)/4901 weeks
3355.50507 2.31511 (335*2π)/4901 weeks
3362.82629 3.42868 (336*2π)/4901 weeks
337-.71241 2.7548 (337*2π)/4901 weeks
338-2.51228 .40627 (338*2π)/4901 weeks
339-3.36408 -2.85463 (339*2π)/4901 weeks
340-1.89771 -5.83493 (340*2π)/4901 weeks
3411.30362 -7.68917 (341*2π)/4901 weeks
3425.10637 -7.31984 (342*2π)/4901 weeks
3437.73828 -4.53017 (343*2π)/4901 weeks
3448.26166 -.57954 (344*2π)/4901 weeks
3456.11612 2.74784 (345*2π)/4901 weeks
3462.51586 3.82604 (346*2π)/4901 weeks
347-.55761 2.76919 (347*2π)/4901 weeks
348-2.80662 1.5186 (348*2π)/4901 weeks
349-4.7835 -2.51722 (349*2π)/4901 weeks
350-3.10493 -5.58179 (350*2π)/4901 weeks
351-.97165 -7.47028 (351*2π)/4901 weeks
3521.397 -8.56996 (352*2π)/4901 weeks
3534.13012 -7.58423 (353*2π)/4901 weeks
3545.8627 -6.51487 (354*2π)/4901 weeks
3557.05256 -3.84846 (355*2π)/4901 weeks
3565.65959 -1.29321 (356*2π)/4901 weeks
3574.27511 -.51703 (357*2π)/4901 weeks
3582.01946 -.06936 (358*2π)/4901 weeks
3591.16508 -2.46811 (359*2π)/4901 weeks
3601.3411 -3.22489 (360*2π)/4901 weeks
3611.78517 -4.50258 (361*2π)/4901 weeks
3623.14834 -4.23801 (362*2π)/4901 weeks
3633.27674 -3.76653 (363*2π)/4901 weeks
3644.48199 -3.49219 (364*2π)/4901 weeks
3654.52627 -2.03438 (365*2π)/4901 weeks
3664.14713 -.70522 (366*2π)/4901 weeks
3672.72105 1.00166 (367*2π)/4901 weeks
368-1.2853 .45072 (368*2π)/4901 weeks
369-2.68453 -2.61066 (369*2π)/4901 weeks
370-2.35775 -4.88342 (370*2π)/4901 weeks
371-.73426 -6.76019 (371*2π)/4901 weeks
3721.35221 -7.0719 (372*2π)/4901 weeks
3732.47656 -6.46714 (373*2π)/4901 weeks
3742.66912 -5.59799 (374*2π)/4901 weeks
3752.24515 -5.0297 (375*2π)/4901 weeks
3761.32196 -5.4056 (376*2π)/4901 weeks
377.52119 -7.18224 (377*2π)/4901 weeks
3782.56547 -9.42899 (378*2π)/4901 weeks
3795.45526 -9.25016 (379*2π)/4901 weeks
3808.44032 -7.45165 (380*2π)/4901 weeks
3819.06007 -3.53343 (381*2π)/4901 weeks
3827.29109 -.62024 (382*2π)/4901 weeks
3834.21525 .39153 (383*2π)/4901 weeks
384.74933 -.57853 (384*2π)/4901 weeks
385-.74615 -3.13337 (385*2π)/4901 weeks
386-.8283 -5.96139 (386*2π)/4901 weeks
3871.18986 -8.10337 (387*2π)/4901 weeks
3884.95717 -8.11958 (388*2π)/4901 weeks
3896.43986 -5.78611 (389*2π)/4901 weeks
3907.17018 -3.61309 (390*2π)/4901 weeks
3915.56679 -.41843 (391*2π)/4901 weeks
3921.90221 .86005 (392*2π)/4901 weeks
393-1.91733 .19797 (393*2π)/4901 weeks
394-4.59397 -3.2872 (394*2π)/4901 weeks
395-4.54744 -7.01119 (395*2π)/4901 weeks
396-3.12166 -10.38941 (396*2π)/4901 weeks
397-.90222 -12.75196 (397*2π)/4901 weeks
3982.50981 -13.71558 (398*2π)/4901 weeks
3994.93176 -12.73642 (399*2π)/4901 weeks
4007.04164 -11.10275 (400*2π)/4901 weeks
4017.97979 -8.8366 (401*2π)/4901 weeks
4027.70259 -6.57063 (402*2π)/4901 weeks
4036.61647 -5.3773 (403*2π)/4901 weeks
4045.27538 -4.84068 (404*2π)/4901 weeks
4053.36461 -6.17111 (405*2π)/4901 weeks
4063.25028 -6.62212 (406*2π)/4901 weeks
4072.39632 -9.16505 (407*2π)/4901 weeks
4084.41707 -12.34346 (408*2π)/4901 weeks
4098.45703 -12.17297 (409*2π)/4901 weeks
41012.82015 -9.46038 (410*2π)/4901 weeks
41113.66124 -3.90237 (411*2π)/4901 weeks
41210.73207 .81537 (412*2π)/4901 weeks
4136.51023 2.15797 (413*2π)/4901 weeks
414.72258 .92937 (414*2π)/4901 weeks
415-.45282 -3.78425 (415*2π)/4901 weeks
416-.60966 -6.91454 (416*2π)/4901 weeks
4172.67049 -11.77348 (417*2π)/4901 weeks
4188.0436 -9.44652 (418*2π)/4901 weeks
41910.14905 -7.02858 (419*2π)/4901 weeks
42010.99101 -1.31853 (420*2π)/4901 weeks
4215.79112 3.11151 (421*2π)/4901 weeks
4221.40277 2.83485 (422*2π)/4901 weeks
423-4.48125 1.93499 (423*2π)/4901 weeks
424-8.95061 -3.5343 (424*2π)/4901 weeks
425-7.93017 -10.94032 (425*2π)/4901 weeks
426-4.44231 -15.40932 (426*2π)/4901 weeks
427-.12206 -17.18264 (427*2π)/4901 weeks
4283.61205 -15.6029 (428*2π)/4901 weeks
4295.03521 -16.39524 (429*2π)/4901 weeks
4309.21047 -14.34219 (430*2π)/4901 weeks
4319.37503 -11.77305 (431*2π)/4901 weeks
43211.08466 -8.58811 (432*2π)/4901 weeks
4338.15123 -4.40032 (433*2π)/4901 weeks
4344.5446 -3.66574 (434*2π)/4901 weeks
435-.01941 -4.50288 (435*2π)/4901 weeks
436-3.61037 -10.86468 (436*2π)/4901 weeks
437-1.59565 -16.27429 (437*2π)/4901 weeks
4383.67194 -20.5262 (438*2π)/4901 weeks
4399.89223 -20.96704 (439*2π)/4901 weeks
44016.85357 -15.93505 (440*2π)/4901 weeks
44118.44484 -10.31986 (441*2π)/4901 weeks
44216.55921 -3.10953 (442*2π)/4901 weeks
44310.95496 .23002 (443*2π)/4901 weeks
4446.00184 -.24516 (444*2π)/4901 weeks
4451.70756 -.59035 (445*2π)/4901 weeks
446-2.38042 -6.00142 (446*2π)/4901 weeks
447-.74427 -9.36977 (447*2π)/4901 weeks
4481.03815 -13.10392 (448*2π)/4901 weeks
4495.99967 -13.68579 (449*2π)/4901 weeks
4506.30218 -11.03466 (450*2π)/4901 weeks
4516.80356 -7.93273 (451*2π)/4901 weeks
4522.47139 -4.48703 (452*2π)/4901 weeks
453-1.43925 -5.71315 (453*2π)/4901 weeks
454-9.24348 -7.03093 (454*2π)/4901 weeks
455-12.80926 -19.18258 (455*2π)/4901 weeks
456-8.80599 -29.49977 (456*2π)/4901 weeks
457.17205 -36.21374 (457*2π)/4901 weeks
45813.33102 -41.20938 (458*2π)/4901 weeks
45927.91242 -34.16117 (459*2π)/4901 weeks
46038.32835 -21.73521 (460*2π)/4901 weeks
46136.23265 -.95071 (461*2π)/4901 weeks
46221.32505 12.61424 (462*2π)/4901 weeks
4635.1797 12.73204 (463*2π)/4901 weeks
464-10.20589 6.15784 (464*2π)/4901 weeks
465-15.88403 -10.55268 (465*2π)/4901 weeks
466-10.83496 -24.16814 (466*2π)/4901 weeks
4672.97902 -33.85692 (467*2π)/4901 weeks
46816.83029 -29.68148 (468*2π)/4901 weeks
46923.64145 -14.83057 (469*2π)/4901 weeks
47016.77034 2.79495 (470*2π)/4901 weeks
471-.32038 10.6835 (471*2π)/4901 weeks
472-19.7531 5.2916 (472*2π)/4901 weeks
473-32.38161 -10.26094 (473*2π)/4901 weeks
474-40.67844 -29.37332 (474*2π)/4901 weeks
475-33.71518 -54.71941 (475*2π)/4901 weeks
476-19.58895 -65.73921 (476*2π)/4901 weeks
477-4.15222 -73.9129 (477*2π)/4901 weeks
47820.85983 -74.50114 (478*2π)/4901 weeks
47925.7179 -62.04618 (479*2π)/4901 weeks
48037.88248 -48.19169 (480*2π)/4901 weeks
48125.09231 -31.35089 (481*2π)/4901 weeks
4828.06834 -24.89603 (482*2π)/4901 weeks
483-26.40102 -32.68596 (483*2π)/4901 weeks
484-63.35107 -77.41843 (484*2π)/4901 weeks
485-64.38567 -155.3959 (485*2π)/4901 weeks
486-13.97422 -227.8203 (486*2π)/4901 weeks
48788.20022 -285.9691 (487*2π)/4901 weeks
488229.1591 -283.1567 (488*2π)/4901 weeks

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