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Fourier Analysis of JJC (iPath Bloomberg Copper Subindex)


JJC (iPath Bloomberg Copper Subindex) appears to have interesting cyclic behaviour every 45 weeks (1.0504*cosine), 41 weeks (.825*sine), and 49 weeks (.7973*cosine).

JJC (iPath Bloomberg Copper Subindex) has an average price of 39.45 (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 10/26/2007 to 3/20/2017 for JJC (iPath Bloomberg Copper Subindex), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
039.44648   0 
1-7.56617 5.8844 (1*2π)/492492 weeks
21.93035 -.27618 (2*2π)/492246 weeks
35.18687 3.38882 (3*2π)/492164 weeks
42.2309 3.87221 (4*2π)/492123 weeks
51.24059 2.38134 (5*2π)/49298 weeks
6-.53092 4.18445 (6*2π)/49282 weeks
7-2.8868 1.00567 (7*2π)/49270 weeks
8-1.25823 -.56664 (8*2π)/49262 weeks
9-.38242 .18696 (9*2π)/49255 weeks
10-.79732 -.58028 (10*2π)/49249 weeks
111.05043 -.66817 (11*2π)/49245 weeks
12.40264 -.82496 (12*2π)/49241 weeks
13.48505 .82269 (13*2π)/49238 weeks
14-.34411 .40238 (14*2π)/49235 weeks
15.44017 .11729 (15*2π)/49233 weeks
16-.5525 .57128 (16*2π)/49231 weeks
17-.37733 -.21448 (17*2π)/49229 weeks
18-.37246 .38059 (18*2π)/49227 weeks
19-.0259 -.60541 (19*2π)/49226 weeks
20.71006 .1741 (20*2π)/49225 weeks
21.10099 -.18508 (21*2π)/49223 weeks
22-.06216 -.25135 (22*2π)/49222 weeks
23.4486 .54448 (23*2π)/49221 weeks
24.03455 .59588 (24*2π)/49221 weeks
25.36384 .07382 (25*2π)/49220 weeks
26.22799 .36462 (26*2π)/49219 weeks
27.38125 .31474 (27*2π)/49218 weeks
28-.10136 .41572 (28*2π)/49218 weeks
29-.06427 .02909 (29*2π)/49217 weeks
30.32191 -.3707 (30*2π)/49216 weeks
31.29062 .38973 (31*2π)/49216 weeks
32.30165 .16276 (32*2π)/49215 weeks
33-.02488 .31694 (33*2π)/49215 weeks
34-.14758 .01769 (34*2π)/49214 weeks
35.10423 .26026 (35*2π)/49214 weeks
36-.13616 .32007 (36*2π)/49214 weeks
37-.09258 -.07614 (37*2π)/49213 weeks
38.11972 .0883 (38*2π)/49213 weeks
39.02727 .07145 (39*2π)/49213 weeks
40.03069 -.04432 (40*2π)/49212 weeks
41.00104 .06561 (41*2π)/49212 weeks
42.31683 .12379 (42*2π)/49212 weeks
43-.15579 .28773 (43*2π)/49211 weeks
44.22899 .22215 (44*2π)/49211 weeks
45-.16372 .24615 (45*2π)/49211 weeks
46.15507 .04253 (46*2π)/49211 weeks
47-.12876 .22112 (47*2π)/49210 weeks
48-.16937 .24081 (48*2π)/49210 weeks
49-.15967 .18483 (49*2π)/49210 weeks
50-.07004 -.14736 (50*2π)/49210 weeks
51.2882 -.09238 (51*2π)/49210 weeks
52.44132 .18293 (52*2π)/4929 weeks
53.16135 .05006 (53*2π)/4929 weeks
54.38821 .35785 (54*2π)/4929 weeks
55.10152 .03842 (55*2π)/4929 weeks
56.16591 .02378 (56*2π)/4929 weeks
57.03503 .20506 (57*2π)/4929 weeks
58.06861 .22477 (58*2π)/4928 weeks
59.11645 .1124 (59*2π)/4928 weeks
60.10557 -.04134 (60*2π)/4928 weeks
61.14727 .13961 (61*2π)/4928 weeks
62-.09863 .0414 (62*2π)/4928 weeks
63.13619 .07209 (63*2π)/4928 weeks
64.05036 .17507 (64*2π)/4928 weeks
65-.08141 .1783 (65*2π)/4928 weeks
66.08227 .18245 (66*2π)/4927 weeks
67-.29851 .02691 (67*2π)/4927 weeks
68.08422 -.18896 (68*2π)/4927 weeks
69.01166 .36888 (69*2π)/4927 weeks
70-.08067 -.01043 (70*2π)/4927 weeks
71.21832 .08431 (71*2π)/4927 weeks
72-.07716 .18293 (72*2π)/4927 weeks
73.22771 .0162 (73*2π)/4927 weeks
74-.16634 .20269 (74*2π)/4927 weeks
75.00737 -.08643 (75*2π)/4927 weeks
76.10402 .00274 (76*2π)/4926 weeks
77-.05197 -.0314 (77*2π)/4926 weeks
78.03163 .16905 (78*2π)/4926 weeks
79-.0252 .00871 (79*2π)/4926 weeks
80.23545 -.14112 (80*2π)/4926 weeks
81.23419 .03597 (81*2π)/4926 weeks
82.12364 .11804 (82*2π)/4926 weeks
83.08414 .04759 (83*2π)/4926 weeks
84.07095 .00747 (84*2π)/4926 weeks
85.1823 .10267 (85*2π)/4926 weeks
86.02158 .15135 (86*2π)/4926 weeks
87-.02318 .12898 (87*2π)/4926 weeks
88-.00176 .15262 (88*2π)/4926 weeks
89.15712 .09574 (89*2π)/4926 weeks
90.02467 .10386 (90*2π)/4925 weeks
91.03514 .06874 (91*2π)/4925 weeks
92.12886 -.08142 (92*2π)/4925 weeks
93.03876 .08915 (93*2π)/4925 weeks
94.06954 -.02186 (94*2π)/4925 weeks
95.01158 -.00216 (95*2π)/4925 weeks
96.0622 .11002 (96*2π)/4925 weeks
97-.00298 .00853 (97*2π)/4925 weeks
98.06329 .01364 (98*2π)/4925 weeks
99.0567 -.03678 (99*2π)/4925 weeks
100.1505 -.03232 (100*2π)/4925 weeks
101-.02141 .04055 (101*2π)/4925 weeks
102.21456 -.03189 (102*2π)/4925 weeks
103.17706 .14375 (103*2π)/4925 weeks
104.02079 .09844 (104*2π)/4925 weeks
105.03082 .00534 (105*2π)/4925 weeks
106.03244 .20141 (106*2π)/4925 weeks
107-.07856 .06407 (107*2π)/4925 weeks
108-.0763 -.01937 (108*2π)/4925 weeks
109.09828 .07661 (109*2π)/4925 weeks
110.12112 .02236 (110*2π)/4924 weeks
111-.01023 .14239 (111*2π)/4924 weeks
112.05537 -.03105 (112*2π)/4924 weeks
113.06344 .12545 (113*2π)/4924 weeks
114.05777 .04425 (114*2π)/4924 weeks
115.03298 .04071 (115*2π)/4924 weeks
116.00345 .02254 (116*2π)/4924 weeks
117.00462 -.03681 (117*2π)/4924 weeks
118-.05134 .16568 (118*2π)/4924 weeks
119.0082 .09125 (119*2π)/4924 weeks
120-.09008 .08364 (120*2π)/4924 weeks
121.04605 -.09142 (121*2π)/4924 weeks
122.06036 .03311 (122*2π)/4924 weeks
123.11996 -.13976 (123*2π)/4924 weeks
124.20003 .01076 (124*2π)/4924 weeks
125.03154 .01774 (125*2π)/4924 weeks
126.11109 .04551 (126*2π)/4924 weeks
127.09826 .10656 (127*2π)/4924 weeks
128.04816 .05806 (128*2π)/4924 weeks
129.04197 .01629 (129*2π)/4924 weeks
130.05316 .04602 (130*2π)/4924 weeks
131.07672 .04509 (131*2π)/4924 weeks
132.00372 .04817 (132*2π)/4924 weeks
133.07439 .02078 (133*2π)/4924 weeks
134.04879 .12983 (134*2π)/4924 weeks
135.14585 .01845 (135*2π)/4924 weeks
136.12687 .10132 (136*2π)/4924 weeks
137-.0584 .09364 (137*2π)/4924 weeks
138.07362 .03374 (138*2π)/4924 weeks
139.04025 .10748 (139*2π)/4924 weeks
140.06333 .06119 (140*2π)/4924 weeks
141-.02376 .09553 (141*2π)/4923 weeks
142-.0859 -.07865 (142*2π)/4923 weeks
143.06587 .03554 (143*2π)/4923 weeks
144-.08255 .07795 (144*2π)/4923 weeks
145.03086 -.13017 (145*2π)/4923 weeks
146.05823 -.05695 (146*2π)/4923 weeks
147.10141 .0468 (147*2π)/4923 weeks
148.1058 .03386 (148*2π)/4923 weeks
149.03635 .0594 (149*2π)/4923 weeks
150.06265 -.0089 (150*2π)/4923 weeks
151.04223 .07055 (151*2π)/4923 weeks
152.05678 -.02065 (152*2π)/4923 weeks
153.06407 .03714 (153*2π)/4923 weeks
154.00058 -.05175 (154*2π)/4923 weeks
155.11583 .02247 (155*2π)/4923 weeks
156.02215 .1119 (156*2π)/4923 weeks
157-.034 .0089 (157*2π)/4923 weeks
158.06198 .01583 (158*2π)/4923 weeks
159.01187 .0665 (159*2π)/4923 weeks
160.03724 -.04145 (160*2π)/4923 weeks
161.00896 .0548 (161*2π)/4923 weeks
162-.0316 -.00913 (162*2π)/4923 weeks
163.06472 -.03658 (163*2π)/4923 weeks
164.02352 -.01714 (164*2π)/4923 weeks
165.02585 .00102 (165*2π)/4923 weeks
166.02239 -.02654 (166*2π)/4923 weeks
167.13844 -.05244 (167*2π)/4923 weeks
168.0368 .03799 (168*2π)/4923 weeks
169.09389 -.06863 (169*2π)/4923 weeks
170.0348 .10037 (170*2π)/4923 weeks
171.00127 -.05191 (171*2π)/4923 weeks
172.19184 -.04215 (172*2π)/4923 weeks
173.04523 -.02001 (173*2π)/4923 weeks
174.17174 -.03758 (174*2π)/4923 weeks
175.11639 .1376 (175*2π)/4923 weeks
176.06927 .10898 (176*2π)/4923 weeks
177.01176 .05172 (177*2π)/4923 weeks
178.03807 -.03727 (178*2π)/4923 weeks
179.05298 .05912 (179*2π)/4923 weeks
180.00341 .0183 (180*2π)/4923 weeks
181.09509 .00558 (181*2π)/4923 weeks
182-.0288 .10557 (182*2π)/4923 weeks
183.12027 -.0441 (183*2π)/4923 weeks
184.08896 .08597 (184*2π)/4923 weeks
185.01783 .04212 (185*2π)/4923 weeks
186.05852 .08833 (186*2π)/4923 weeks
187-.02805 .09797 (187*2π)/4923 weeks
188.02126 .00959 (188*2π)/4923 weeks
189.03357 .03495 (189*2π)/4923 weeks
190-.02694 -.00377 (190*2π)/4923 weeks
191.11466 -.00465 (191*2π)/4923 weeks
192.00478 .0466 (192*2π)/4923 weeks
193.07825 .02785 (193*2π)/4923 weeks
194.00769 .05651 (194*2π)/4923 weeks
195.04228 -.01918 (195*2π)/4923 weeks
196.04319 .02254 (196*2π)/4923 weeks
197.10587 .02186 (197*2π)/4922 weeks
198.01211 .07226 (198*2π)/4922 weeks
199.05264 -.02665 (199*2π)/4922 weeks
200.07974 .06344 (200*2π)/4922 weeks
201.00147 -.04259 (201*2π)/4922 weeks
202.15599 .03925 (202*2π)/4922 weeks
203.06968 .0586 (203*2π)/4922 weeks
204.08226 .00394 (204*2π)/4922 weeks
205.05814 .08476 (205*2π)/4922 weeks
206.00141 .14639 (206*2π)/4922 weeks
207-.02741 .01404 (207*2π)/4922 weeks
208.02193 .07162 (208*2π)/4922 weeks
209-.03208 .09693 (209*2π)/4922 weeks
210-.05158 .05719 (210*2π)/4922 weeks
211.02906 .04928 (211*2π)/4922 weeks
212.00947 .03506 (212*2π)/4922 weeks
213.06678 -.00633 (213*2π)/4922 weeks
214.05866 .05241 (214*2π)/4922 weeks
215-.00262 -.01625 (215*2π)/4922 weeks
216.1387 .04173 (216*2π)/4922 weeks
217-.00455 .07057 (217*2π)/4922 weeks
218.03678 -.06496 (218*2π)/4922 weeks
219.06524 .03741 (219*2π)/4922 weeks
220.05271 .00021 (220*2π)/4922 weeks
221.0661 -.07932 (221*2π)/4922 weeks
222.10497 -.03346 (222*2π)/4922 weeks
223.07792 -.02445 (223*2π)/4922 weeks
224.10628 .10954 (224*2π)/4922 weeks
225.03345 .02253 (225*2π)/4922 weeks
226.09429 -.00722 (226*2π)/4922 weeks
227.0445 -.00415 (227*2π)/4922 weeks
228.09139 .00096 (228*2π)/4922 weeks
229-.07111 -.04761 (229*2π)/4922 weeks
230.0901 -.11429 (230*2π)/4922 weeks
231.12752 .02989 (231*2π)/4922 weeks
232.0425 -.06171 (232*2π)/4922 weeks
233.06055 -.00229 (233*2π)/4922 weeks
234-.00618 .06241 (234*2π)/4922 weeks
235.01307 .08622 (235*2π)/4922 weeks
236.04086 .01969 (236*2π)/4922 weeks
237.01837 .04494 (237*2π)/4922 weeks
238.00324 .08512 (238*2π)/4922 weeks
239-.13982 -.06443 (239*2π)/4922 weeks
240.11269 -.11295 (240*2π)/4922 weeks
241.08096 .01381 (241*2π)/4922 weeks
242.0183 .01977 (242*2π)/4922 weeks
243.07089 -.01556 (243*2π)/4922 weeks
244.07493 .04513 (244*2π)/4922 weeks
245.01902 .03927 (245*2π)/4922 weeks
246.0237   (246*2π)/4922 weeks
247.01902 -.03927 (247*2π)/4922 weeks
248.07493 -.04513 (248*2π)/4922 weeks
249.07089 .01556 (249*2π)/4922 weeks
250.0183 -.01977 (250*2π)/4922 weeks
251.08096 -.01381 (251*2π)/4922 weeks
252.11269 .11295 (252*2π)/4922 weeks
253-.13982 .06443 (253*2π)/4922 weeks
254.00324 -.08512 (254*2π)/4922 weeks
255.01837 -.04494 (255*2π)/4922 weeks
256.04086 -.01969 (256*2π)/4922 weeks
257.01307 -.08622 (257*2π)/4922 weeks
258-.00618 -.06241 (258*2π)/4922 weeks
259.06055 .00229 (259*2π)/4922 weeks
260.0425 .06171 (260*2π)/4922 weeks
261.12752 -.02989 (261*2π)/4922 weeks
262.0901 .11429 (262*2π)/4922 weeks
263-.07111 .04761 (263*2π)/4922 weeks
264.09139 -.00096 (264*2π)/4922 weeks
265.0445 .00415 (265*2π)/4922 weeks
266.09429 .00722 (266*2π)/4922 weeks
267.03345 -.02253 (267*2π)/4922 weeks
268.10628 -.10954 (268*2π)/4922 weeks
269.07792 .02445 (269*2π)/4922 weeks
270.10497 .03346 (270*2π)/4922 weeks
271.0661 .07932 (271*2π)/4922 weeks
272.05271 -.00021 (272*2π)/4922 weeks
273.06524 -.03741 (273*2π)/4922 weeks
274.03678 .06496 (274*2π)/4922 weeks
275-.00455 -.07057 (275*2π)/4922 weeks
276.1387 -.04173 (276*2π)/4922 weeks
277-.00262 .01625 (277*2π)/4922 weeks
278.05866 -.05241 (278*2π)/4922 weeks
279.06678 .00633 (279*2π)/4922 weeks
280.00947 -.03506 (280*2π)/4922 weeks
281.02906 -.04928 (281*2π)/4922 weeks
282-.05158 -.05719 (282*2π)/4922 weeks
283-.03208 -.09693 (283*2π)/4922 weeks
284.02193 -.07162 (284*2π)/4922 weeks
285-.02741 -.01404 (285*2π)/4922 weeks
286.00141 -.14639 (286*2π)/4922 weeks
287.05814 -.08476 (287*2π)/4922 weeks
288.08226 -.00394 (288*2π)/4922 weeks
289.06968 -.0586 (289*2π)/4922 weeks
290.15599 -.03925 (290*2π)/4922 weeks
291.00147 .04259 (291*2π)/4922 weeks
292.07974 -.06344 (292*2π)/4922 weeks
293.05264 .02665 (293*2π)/4922 weeks
294.01211 -.07226 (294*2π)/4922 weeks
295.10587 -.02186 (295*2π)/4922 weeks
296.04319 -.02254 (296*2π)/4922 weeks
297.04228 .01918 (297*2π)/4922 weeks
298.00769 -.05651 (298*2π)/4922 weeks
299.07825 -.02785 (299*2π)/4922 weeks
300.00478 -.0466 (300*2π)/4922 weeks
301.11466 .00465 (301*2π)/4922 weeks
302-.02694 .00377 (302*2π)/4922 weeks
303.03357 -.03495 (303*2π)/4922 weeks
304.02126 -.00959 (304*2π)/4922 weeks
305-.02805 -.09797 (305*2π)/4922 weeks
306.05852 -.08833 (306*2π)/4922 weeks
307.01783 -.04212 (307*2π)/4922 weeks
308.08896 -.08597 (308*2π)/4922 weeks
309.12027 .0441 (309*2π)/4922 weeks
310-.0288 -.10557 (310*2π)/4922 weeks
311.09509 -.00558 (311*2π)/4922 weeks
312.00341 -.0183 (312*2π)/4922 weeks
313.05298 -.05912 (313*2π)/4922 weeks
314.03807 .03727 (314*2π)/4922 weeks
315.01176 -.05172 (315*2π)/4922 weeks
316.06927 -.10898 (316*2π)/4922 weeks
317.11639 -.1376 (317*2π)/4922 weeks
318.17174 .03758 (318*2π)/4922 weeks
319.04523 .02001 (319*2π)/4922 weeks
320.19184 .04215 (320*2π)/4922 weeks
321.00127 .05191 (321*2π)/4922 weeks
322.0348 -.10037 (322*2π)/4922 weeks
323.09389 .06863 (323*2π)/4922 weeks
324.0368 -.03799 (324*2π)/4922 weeks
325.13844 .05244 (325*2π)/4922 weeks
326.02239 .02654 (326*2π)/4922 weeks
327.02585 -.00102 (327*2π)/4922 weeks
328.02352 .01714 (328*2π)/4922 weeks
329.06472 .03658 (329*2π)/4921 weeks
330-.0316 .00913 (330*2π)/4921 weeks
331.00896 -.0548 (331*2π)/4921 weeks
332.03724 .04145 (332*2π)/4921 weeks
333.01187 -.0665 (333*2π)/4921 weeks
334.06198 -.01583 (334*2π)/4921 weeks
335-.034 -.0089 (335*2π)/4921 weeks
336.02215 -.1119 (336*2π)/4921 weeks
337.11583 -.02247 (337*2π)/4921 weeks
338.00058 .05175 (338*2π)/4921 weeks
339.06407 -.03714 (339*2π)/4921 weeks
340.05678 .02065 (340*2π)/4921 weeks
341.04223 -.07055 (341*2π)/4921 weeks
342.06265 .0089 (342*2π)/4921 weeks
343.03635 -.0594 (343*2π)/4921 weeks
344.1058 -.03386 (344*2π)/4921 weeks
345.10141 -.0468 (345*2π)/4921 weeks
346.05823 .05695 (346*2π)/4921 weeks
347.03086 .13017 (347*2π)/4921 weeks
348-.08255 -.07795 (348*2π)/4921 weeks
349.06587 -.03554 (349*2π)/4921 weeks
350-.0859 .07865 (350*2π)/4921 weeks
351-.02376 -.09553 (351*2π)/4921 weeks
352.06333 -.06119 (352*2π)/4921 weeks
353.04025 -.10748 (353*2π)/4921 weeks
354.07362 -.03374 (354*2π)/4921 weeks
355-.0584 -.09364 (355*2π)/4921 weeks
356.12687 -.10132 (356*2π)/4921 weeks
357.14585 -.01845 (357*2π)/4921 weeks
358.04879 -.12983 (358*2π)/4921 weeks
359.07439 -.02078 (359*2π)/4921 weeks
360.00372 -.04817 (360*2π)/4921 weeks
361.07672 -.04509 (361*2π)/4921 weeks
362.05316 -.04602 (362*2π)/4921 weeks
363.04197 -.01629 (363*2π)/4921 weeks
364.04816 -.05806 (364*2π)/4921 weeks
365.09826 -.10656 (365*2π)/4921 weeks
366.11109 -.04551 (366*2π)/4921 weeks
367.03154 -.01774 (367*2π)/4921 weeks
368.20003 -.01076 (368*2π)/4921 weeks
369.11996 .13976 (369*2π)/4921 weeks
370.06036 -.03311 (370*2π)/4921 weeks
371.04605 .09142 (371*2π)/4921 weeks
372-.09008 -.08364 (372*2π)/4921 weeks
373.0082 -.09125 (373*2π)/4921 weeks
374-.05134 -.16568 (374*2π)/4921 weeks
375.00462 .03681 (375*2π)/4921 weeks
376.00345 -.02254 (376*2π)/4921 weeks
377.03298 -.04071 (377*2π)/4921 weeks
378.05777 -.04425 (378*2π)/4921 weeks
379.06344 -.12545 (379*2π)/4921 weeks
380.05537 .03105 (380*2π)/4921 weeks
381-.01023 -.14239 (381*2π)/4921 weeks
382.12112 -.02236 (382*2π)/4921 weeks
383.09828 -.07661 (383*2π)/4921 weeks
384-.0763 .01937 (384*2π)/4921 weeks
385-.07856 -.06407 (385*2π)/4921 weeks
386.03244 -.20141 (386*2π)/4921 weeks
387.03082 -.00534 (387*2π)/4921 weeks
388.02079 -.09844 (388*2π)/4921 weeks
389.17706 -.14375 (389*2π)/4921 weeks
390.21456 .03189 (390*2π)/4921 weeks
391-.02141 -.04055 (391*2π)/4921 weeks
392.1505 .03232 (392*2π)/4921 weeks
393.0567 .03678 (393*2π)/4921 weeks
394.06329 -.01364 (394*2π)/4921 weeks
395-.00298 -.00853 (395*2π)/4921 weeks
396.0622 -.11002 (396*2π)/4921 weeks
397.01158 .00216 (397*2π)/4921 weeks
398.06954 .02186 (398*2π)/4921 weeks
399.03876 -.08915 (399*2π)/4921 weeks
400.12886 .08142 (400*2π)/4921 weeks
401.03514 -.06874 (401*2π)/4921 weeks
402.02467 -.10386 (402*2π)/4921 weeks
403.15712 -.09574 (403*2π)/4921 weeks
404-.00176 -.15262 (404*2π)/4921 weeks
405-.02318 -.12898 (405*2π)/4921 weeks
406.02158 -.15135 (406*2π)/4921 weeks
407.1823 -.10267 (407*2π)/4921 weeks
408.07095 -.00747 (408*2π)/4921 weeks
409.08414 -.04759 (409*2π)/4921 weeks
410.12364 -.11804 (410*2π)/4921 weeks
411.23419 -.03597 (411*2π)/4921 weeks
412.23545 .14112 (412*2π)/4921 weeks
413-.0252 -.00871 (413*2π)/4921 weeks
414.03163 -.16905 (414*2π)/4921 weeks
415-.05197 .0314 (415*2π)/4921 weeks
416.10402 -.00274 (416*2π)/4921 weeks
417.00737 .08643 (417*2π)/4921 weeks
418-.16634 -.20269 (418*2π)/4921 weeks
419.22771 -.0162 (419*2π)/4921 weeks
420-.07716 -.18293 (420*2π)/4921 weeks
421.21832 -.08431 (421*2π)/4921 weeks
422-.08067 .01043 (422*2π)/4921 weeks
423.01166 -.36888 (423*2π)/4921 weeks
424.08422 .18896 (424*2π)/4921 weeks
425-.29851 -.02691 (425*2π)/4921 weeks
426.08227 -.18245 (426*2π)/4921 weeks
427-.08141 -.1783 (427*2π)/4921 weeks
428.05036 -.17507 (428*2π)/4921 weeks
429.13619 -.07209 (429*2π)/4921 weeks
430-.09863 -.0414 (430*2π)/4921 weeks
431.14727 -.13961 (431*2π)/4921 weeks
432.10557 .04134 (432*2π)/4921 weeks
433.11645 -.1124 (433*2π)/4921 weeks
434.06861 -.22477 (434*2π)/4921 weeks
435.03503 -.20506 (435*2π)/4921 weeks
436.16591 -.02378 (436*2π)/4921 weeks
437.10152 -.03842 (437*2π)/4921 weeks
438.38821 -.35785 (438*2π)/4921 weeks
439.16135 -.05006 (439*2π)/4921 weeks
440.44132 -.18293 (440*2π)/4921 weeks
441.2882 .09238 (441*2π)/4921 weeks
442-.07004 .14736 (442*2π)/4921 weeks
443-.15967 -.18483 (443*2π)/4921 weeks
444-.16937 -.24081 (444*2π)/4921 weeks
445-.12876 -.22112 (445*2π)/4921 weeks
446.15507 -.04253 (446*2π)/4921 weeks
447-.16372 -.24615 (447*2π)/4921 weeks
448.22899 -.22215 (448*2π)/4921 weeks
449-.15579 -.28773 (449*2π)/4921 weeks
450.31683 -.12379 (450*2π)/4921 weeks
451.00104 -.06561 (451*2π)/4921 weeks
452.03069 .04432 (452*2π)/4921 weeks
453.02727 -.07145 (453*2π)/4921 weeks
454.11972 -.0883 (454*2π)/4921 weeks
455-.09258 .07614 (455*2π)/4921 weeks
456-.13616 -.32007 (456*2π)/4921 weeks
457.10423 -.26026 (457*2π)/4921 weeks
458-.14758 -.01769 (458*2π)/4921 weeks
459-.02488 -.31694 (459*2π)/4921 weeks
460.30165 -.16276 (460*2π)/4921 weeks
461.29062 -.38973 (461*2π)/4921 weeks
462.32191 .3707 (462*2π)/4921 weeks
463-.06427 -.02909 (463*2π)/4921 weeks
464-.10136 -.41572 (464*2π)/4921 weeks
465.38125 -.31474 (465*2π)/4921 weeks
466.22799 -.36462 (466*2π)/4921 weeks
467.36384 -.07382 (467*2π)/4921 weeks
468.03455 -.59588 (468*2π)/4921 weeks
469.4486 -.54448 (469*2π)/4921 weeks
470-.06216 .25135 (470*2π)/4921 weeks
471.10099 .18508 (471*2π)/4921 weeks
472.71006 -.1741 (472*2π)/4921 weeks
473-.0259 .60541 (473*2π)/4921 weeks
474-.37246 -.38059 (474*2π)/4921 weeks
475-.37733 .21448 (475*2π)/4921 weeks
476-.5525 -.57128 (476*2π)/4921 weeks
477.44017 -.11729 (477*2π)/4921 weeks
478-.34411 -.40238 (478*2π)/4921 weeks
479.48505 -.82269 (479*2π)/4921 weeks
480.40264 .82496 (480*2π)/4921 weeks
4811.05043 .66817 (481*2π)/4921 weeks
482-.79732 .58028 (482*2π)/4921 weeks
483-.38242 -.18696 (483*2π)/4921 weeks
484-1.25823 .56664 (484*2π)/4921 weeks
485-2.8868 -1.00567 (485*2π)/4921 weeks
486-.53092 -4.18445 (486*2π)/4921 weeks
4871.24059 -2.38134 (487*2π)/4921 weeks
4882.2309 -3.87221 (488*2π)/4921 weeks
4895.18687 -3.38882 (489*2π)/4921 weeks
4901.93035 .27618 (490*2π)/4921 weeks

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