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Fourier Analysis of ACWX (iShares MSCI ACWI ex US Index F)


ACWX (iShares MSCI ACWI ex US Index F) appears to have interesting cyclic behaviour every 45 weeks (.702*sine), 32 weeks (.5979*sine), and 45 weeks (.5282*cosine).

ACWX (iShares MSCI ACWI ex US Index F) has an average price of 37.11 (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 4/1/2008 to 11/28/2016 for ACWX (iShares MSCI ACWI ex US Index F), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
037.1113   0 
1-.8568 -5.38998 (1*2π)/453453 weeks
2-1.5116 -2.07364 (2*2π)/453227 weeks
32.50058 -1.17054 (3*2π)/453151 weeks
41.59972 -.16002 (4*2π)/453113 weeks
52.00465 -.59801 (5*2π)/45391 weeks
62.29464 .95622 (6*2π)/45376 weeks
7.7035 .9832 (7*2π)/45365 weeks
8-.36957 .06407 (8*2π)/45357 weeks
9-.00171 .66691 (9*2π)/45350 weeks
10-.52819 .70202 (10*2π)/45345 weeks
11.39523 .35626 (11*2π)/45341 weeks
12-.4844 .02875 (12*2π)/45338 weeks
13-.24434 -.08384 (13*2π)/45335 weeks
14.03249 .59792 (14*2π)/45332 weeks
15-.32608 .00924 (15*2π)/45330 weeks
16.02701 .15821 (16*2π)/45328 weeks
17.09573 -.19964 (17*2π)/45327 weeks
18-.04883 .02144 (18*2π)/45325 weeks
19-.35439 -.18514 (19*2π)/45324 weeks
20-.20592 -.04916 (20*2π)/45323 weeks
21-.10962 -.09792 (21*2π)/45322 weeks
22.34927 .3159 (22*2π)/45321 weeks
23-.02173 .22688 (23*2π)/45320 weeks
24.33544 .33711 (24*2π)/45319 weeks
25.12572 .31298 (25*2π)/45318 weeks
26.15866 .23054 (26*2π)/45317 weeks
27-.06072 .32281 (27*2π)/45317 weeks
28-.49147 .10209 (28*2π)/45316 weeks
29-.16581 -.05782 (29*2π)/45316 weeks
30-.16157 -.00813 (30*2π)/45315 weeks
31.07678 .02054 (31*2π)/45315 weeks
32-.15359 .07987 (32*2π)/45314 weeks
33-.21346 -.103 (33*2π)/45314 weeks
34.20105 -.1888 (34*2π)/45313 weeks
35-.0808 .11308 (35*2π)/45313 weeks
36-.11982 -.03748 (36*2π)/45313 weeks
37.01979 .08816 (37*2π)/45312 weeks
38.06638 .03041 (38*2π)/45312 weeks
39.20799 -.10637 (39*2π)/45312 weeks
40-.18137 -.02081 (40*2π)/45311 weeks
41-.11923 .16588 (41*2π)/45311 weeks
42-.06586 -.00225 (42*2π)/45311 weeks
43.03146 .12673 (43*2π)/45311 weeks
44.04798 -.02174 (44*2π)/45310 weeks
45.01767 .09423 (45*2π)/45310 weeks
46.02717 .17326 (46*2π)/45310 weeks
47-.01869 -.07462 (47*2π)/45310 weeks
48-.10673 -.04149 (48*2π)/4539 weeks
49-.02345 .02544 (49*2π)/4539 weeks
50-.08366 -.07434 (50*2π)/4539 weeks
51.11112 -.07167 (51*2π)/4539 weeks
52-.02405 .01514 (52*2π)/4539 weeks
53.07698 -.00685 (53*2π)/4539 weeks
54.12449 -.00539 (54*2π)/4538 weeks
55-.04963 -.09754 (55*2π)/4538 weeks
56.05666 .04832 (56*2π)/4538 weeks
57-.04973 -.05899 (57*2π)/4538 weeks
58.11885 -.03467 (58*2π)/4538 weeks
59.16112 -.00435 (59*2π)/4538 weeks
60.08205 .04183 (60*2π)/4538 weeks
61.01652 .18053 (61*2π)/4537 weeks
62-.06901 .11633 (62*2π)/4537 weeks
63.04236 -.10869 (63*2π)/4537 weeks
64-.05026 .22054 (64*2π)/4537 weeks
65-.15969 .05975 (65*2π)/4537 weeks
66.01331 -.02982 (66*2π)/4537 weeks
67-.12937 .00131 (67*2π)/4537 weeks
68.10576 -.117 (68*2π)/4537 weeks
69-.00519 .02032 (69*2π)/4537 weeks
70.01466 -.1273 (70*2π)/4536 weeks
71.10697 -.02468 (71*2π)/4536 weeks
72.13667 -.08941 (72*2π)/4536 weeks
73.05016 -.03315 (73*2π)/4536 weeks
74.04739 .07081 (74*2π)/4536 weeks
75-.05656 .06874 (75*2π)/4536 weeks
76-.07472 .0685 (76*2π)/4536 weeks
77-.05411 .04926 (77*2π)/4536 weeks
78.06573 -.02598 (78*2π)/4536 weeks
79-.04295 .07648 (79*2π)/4536 weeks
80-.00003 .13068 (80*2π)/4536 weeks
81-.00456 .087 (81*2π)/4536 weeks
82.01246 .05456 (82*2π)/4536 weeks
83.04743 .00418 (83*2π)/4535 weeks
84.03407 -.06146 (84*2π)/4535 weeks
85-.04063 -.10744 (85*2π)/4535 weeks
86-.00486 -.05 (86*2π)/4535 weeks
87-.03136 -.09892 (87*2π)/4535 weeks
88-.04719 .01256 (88*2π)/4535 weeks
89.02949 -.02795 (89*2π)/4535 weeks
90.11481 .05284 (90*2π)/4535 weeks
91.10486 .0487 (91*2π)/4535 weeks
92.05905 .02633 (92*2π)/4535 weeks
93.00819 -.00906 (93*2π)/4535 weeks
94.06091 .09998 (94*2π)/4535 weeks
95-.0979 .00512 (95*2π)/4535 weeks
96-.09097 .04745 (96*2π)/4535 weeks
97-.00913 .06332 (97*2π)/4535 weeks
98-.07363 .02297 (98*2π)/4535 weeks
99-.01619 .01072 (99*2π)/4535 weeks
100-.02392 -.0587 (100*2π)/4535 weeks
101-.02865 -.08402 (101*2π)/4534 weeks
102.12268 -.03863 (102*2π)/4534 weeks
103.00174 -.06887 (103*2π)/4534 weeks
104-.01975 -.03362 (104*2π)/4534 weeks
105-.03558 .04607 (105*2π)/4534 weeks
106-.0173 -.02827 (106*2π)/4534 weeks
107.08042 -.03329 (107*2π)/4534 weeks
108-.04476 .04778 (108*2π)/4534 weeks
109-.05904 .03706 (109*2π)/4534 weeks
110.02637 .0278 (110*2π)/4534 weeks
111.07187 -.02649 (111*2π)/4534 weeks
112-.00057 -.08118 (112*2π)/4534 weeks
113.0518 -.05626 (113*2π)/4534 weeks
114-.00487 .08728 (114*2π)/4534 weeks
115-.0583 .04243 (115*2π)/4534 weeks
116-.02116 .08334 (116*2π)/4534 weeks
117-.06942 -.00988 (117*2π)/4534 weeks
118.04087 -.01448 (118*2π)/4534 weeks
119.04243 .06688 (119*2π)/4534 weeks
120.00687 -.00958 (120*2π)/4534 weeks
121.00183 -.00376 (121*2π)/4534 weeks
122-.07897 -.00919 (122*2π)/4534 weeks
123.01057 .00086 (123*2π)/4534 weeks
124-.06317 -.00151 (124*2π)/4534 weeks
125.02048 -.04512 (125*2π)/4534 weeks
126.04215 .02483 (126*2π)/4534 weeks
127.01925 .01455 (127*2π)/4534 weeks
128.01581 .03855 (128*2π)/4534 weeks
129.02535 -.03336 (129*2π)/4534 weeks
130.03914 -.07289 (130*2π)/4533 weeks
131.05541 .07695 (131*2π)/4533 weeks
132-.02884 .01513 (132*2π)/4533 weeks
133.00701 -.03206 (133*2π)/4533 weeks
134.02743 .01143 (134*2π)/4533 weeks
135.06648 .06011 (135*2π)/4533 weeks
136-.00683 -.01877 (136*2π)/4533 weeks
137.0237 .05809 (137*2π)/4533 weeks
138-.0295 .00564 (138*2π)/4533 weeks
139.00334 -.03553 (139*2π)/4533 weeks
140-.04897 -.02106 (140*2π)/4533 weeks
141-.00086 -.01157 (141*2π)/4533 weeks
142.04634 -.08196 (142*2π)/4533 weeks
143-.0303 -.06301 (143*2π)/4533 weeks
144.02533 -.07368 (144*2π)/4533 weeks
145.00232 -.02335 (145*2π)/4533 weeks
146.02522 -.01221 (146*2π)/4533 weeks
147.0688 .00354 (147*2π)/4533 weeks
148.01038 .02054 (148*2π)/4533 weeks
149.02827 .0228 (149*2π)/4533 weeks
150.0328 .02939 (150*2π)/4533 weeks
151.01606 -.01848 (151*2π)/4533 weeks
152-.01671 .01433 (152*2π)/4533 weeks
153-.00539 .02471 (153*2π)/4533 weeks
154-.03401 .05653 (154*2π)/4533 weeks
155-.02099 -.01474 (155*2π)/4533 weeks
156.0601 -.01032 (156*2π)/4533 weeks
157-.01571 -.02072 (157*2π)/4533 weeks
158.00382 -.04072 (158*2π)/4533 weeks
159-.02986 .0479 (159*2π)/4533 weeks
160.01181 -.02865 (160*2π)/4533 weeks
161.13548 .0339 (161*2π)/4533 weeks
162.02755 .00677 (162*2π)/4533 weeks
163.04078 .03328 (163*2π)/4533 weeks
164-.01082 .03119 (164*2π)/4533 weeks
165-.01052 -.05327 (165*2π)/4533 weeks
166.03408 .05955 (166*2π)/4533 weeks
167-.06519 -.00353 (167*2π)/4533 weeks
168.0548 .00603 (168*2π)/4533 weeks
169-.04901 .03422 (169*2π)/4533 weeks
170-.0566 -.00769 (170*2π)/4533 weeks
171-.01618 -.04449 (171*2π)/4533 weeks
172.00017 -.05705 (172*2π)/4533 weeks
173.04907 -.04192 (173*2π)/4533 weeks
174.02679 -.02335 (174*2π)/4533 weeks
175.02575 -.00634 (175*2π)/4533 weeks
176.11438 .04166 (176*2π)/4533 weeks
177.00927 .00701 (177*2π)/4533 weeks
178.00963 .04229 (178*2π)/4533 weeks
179-.05599 .03727 (179*2π)/4533 weeks
180-.03624 .00345 (180*2π)/4533 weeks
181.04292 -.01443 (181*2π)/4533 weeks
182.02967 .02586 (182*2π)/4532 weeks
183-.02822 .00716 (183*2π)/4532 weeks
184-.00734 -.01628 (184*2π)/4532 weeks
185.01153 .03903 (185*2π)/4532 weeks
186-.04855 .00191 (186*2π)/4532 weeks
187-.01792 .00356 (187*2π)/4532 weeks
188-.08283 -.00085 (188*2π)/4532 weeks
189.01635 -.00725 (189*2π)/4532 weeks
190.03364 .00403 (190*2π)/4532 weeks
191.02056 -.0032 (191*2π)/4532 weeks
192.01798 -.01074 (192*2π)/4532 weeks
193.00989 .00095 (193*2π)/4532 weeks
194.01119 -.01248 (194*2π)/4532 weeks
195.02577 .01408 (195*2π)/4532 weeks
196.02434 .00802 (196*2π)/4532 weeks
197.09087 .02821 (197*2π)/4532 weeks
198.00267 -.01811 (198*2π)/4532 weeks
199.05375 -.00613 (199*2π)/4532 weeks
200-.03176 .01259 (200*2π)/4532 weeks
201-.00061 .00397 (201*2π)/4532 weeks
202.01235 .05255 (202*2π)/4532 weeks
203-.01805 .00856 (203*2π)/4532 weeks
204.02038 -.05882 (204*2π)/4532 weeks
205-.03662 -.03189 (205*2π)/4532 weeks
206-.00162 -.03316 (206*2π)/4532 weeks
207.0192 -.02983 (207*2π)/4532 weeks
208-.00398 -.0447 (208*2π)/4532 weeks
209.00955 -.0103 (209*2π)/4532 weeks
210-.00933 .00477 (210*2π)/4532 weeks
211.06378 -.06536 (211*2π)/4532 weeks
212.06786 .03848 (212*2π)/4532 weeks
213.00022 .03495 (213*2π)/4532 weeks
214.09211 .01387 (214*2π)/4532 weeks
215.06088 .05434 (215*2π)/4532 weeks
216.03133 .03387 (216*2π)/4532 weeks
217.00432 -.04963 (217*2π)/4532 weeks
218.01921 -.02396 (218*2π)/4532 weeks
219-.01033 -.02575 (219*2π)/4532 weeks
220-.06034 .03915 (220*2π)/4532 weeks
221-.02573 -.05419 (221*2π)/4532 weeks
222.05774 -.0249 (222*2π)/4532 weeks
223.03901 -.00368 (223*2π)/4532 weeks
224.05879 -.04326 (224*2π)/4532 weeks
225-.01285 -.0215 (225*2π)/4532 weeks
226.02841 -.04041 (226*2π)/4532 weeks
227.02841 .04041 (227*2π)/4532 weeks
228-.01285 .0215 (228*2π)/4532 weeks
229.05879 .04326 (229*2π)/4532 weeks
230.03901 .00368 (230*2π)/4532 weeks
231.05774 .0249 (231*2π)/4532 weeks
232-.02573 .05419 (232*2π)/4532 weeks
233-.06034 -.03915 (233*2π)/4532 weeks
234-.01033 .02575 (234*2π)/4532 weeks
235.01921 .02396 (235*2π)/4532 weeks
236.00432 .04963 (236*2π)/4532 weeks
237.03133 -.03387 (237*2π)/4532 weeks
238.06088 -.05434 (238*2π)/4532 weeks
239.09211 -.01387 (239*2π)/4532 weeks
240.00022 -.03495 (240*2π)/4532 weeks
241.06786 -.03848 (241*2π)/4532 weeks
242.06378 .06536 (242*2π)/4532 weeks
243-.00933 -.00477 (243*2π)/4532 weeks
244.00955 .0103 (244*2π)/4532 weeks
245-.00398 .0447 (245*2π)/4532 weeks
246.0192 .02983 (246*2π)/4532 weeks
247-.00162 .03316 (247*2π)/4532 weeks
248-.03662 .03189 (248*2π)/4532 weeks
249.02038 .05882 (249*2π)/4532 weeks
250-.01805 -.00856 (250*2π)/4532 weeks
251.01235 -.05255 (251*2π)/4532 weeks
252-.00061 -.00397 (252*2π)/4532 weeks
253-.03176 -.01259 (253*2π)/4532 weeks
254.05375 .00613 (254*2π)/4532 weeks
255.00267 .01811 (255*2π)/4532 weeks
256.09087 -.02821 (256*2π)/4532 weeks
257.02434 -.00802 (257*2π)/4532 weeks
258.02577 -.01408 (258*2π)/4532 weeks
259.01119 .01248 (259*2π)/4532 weeks
260.00989 -.00095 (260*2π)/4532 weeks
261.01798 .01074 (261*2π)/4532 weeks
262.02056 .0032 (262*2π)/4532 weeks
263.03364 -.00403 (263*2π)/4532 weeks
264.01635 .00725 (264*2π)/4532 weeks
265-.08283 .00085 (265*2π)/4532 weeks
266-.01792 -.00356 (266*2π)/4532 weeks
267-.04855 -.00191 (267*2π)/4532 weeks
268.01153 -.03903 (268*2π)/4532 weeks
269-.00734 .01628 (269*2π)/4532 weeks
270-.02822 -.00716 (270*2π)/4532 weeks
271.02967 -.02586 (271*2π)/4532 weeks
272.04292 .01443 (272*2π)/4532 weeks
273-.03624 -.00345 (273*2π)/4532 weeks
274-.05599 -.03727 (274*2π)/4532 weeks
275.00963 -.04229 (275*2π)/4532 weeks
276.00927 -.00701 (276*2π)/4532 weeks
277.11438 -.04166 (277*2π)/4532 weeks
278.02575 .00634 (278*2π)/4532 weeks
279.02679 .02335 (279*2π)/4532 weeks
280.04907 .04192 (280*2π)/4532 weeks
281.00017 .05705 (281*2π)/4532 weeks
282-.01618 .04449 (282*2π)/4532 weeks
283-.0566 .00769 (283*2π)/4532 weeks
284-.04901 -.03422 (284*2π)/4532 weeks
285.0548 -.00603 (285*2π)/4532 weeks
286-.06519 .00353 (286*2π)/4532 weeks
287.03408 -.05955 (287*2π)/4532 weeks
288-.01052 .05327 (288*2π)/4532 weeks
289-.01082 -.03119 (289*2π)/4532 weeks
290.04078 -.03328 (290*2π)/4532 weeks
291.02755 -.00677 (291*2π)/4532 weeks
292.13548 -.0339 (292*2π)/4532 weeks
293.01181 .02865 (293*2π)/4532 weeks
294-.02986 -.0479 (294*2π)/4532 weeks
295.00382 .04072 (295*2π)/4532 weeks
296-.01571 .02072 (296*2π)/4532 weeks
297.0601 .01032 (297*2π)/4532 weeks
298-.02099 .01474 (298*2π)/4532 weeks
299-.03401 -.05653 (299*2π)/4532 weeks
300-.00539 -.02471 (300*2π)/4532 weeks
301-.01671 -.01433 (301*2π)/4532 weeks
302.01606 .01848 (302*2π)/4532 weeks
303.0328 -.02939 (303*2π)/4531 weeks
304.02827 -.0228 (304*2π)/4531 weeks
305.01038 -.02054 (305*2π)/4531 weeks
306.0688 -.00354 (306*2π)/4531 weeks
307.02522 .01221 (307*2π)/4531 weeks
308.00232 .02335 (308*2π)/4531 weeks
309.02533 .07368 (309*2π)/4531 weeks
310-.0303 .06301 (310*2π)/4531 weeks
311.04634 .08196 (311*2π)/4531 weeks
312-.00086 .01157 (312*2π)/4531 weeks
313-.04897 .02106 (313*2π)/4531 weeks
314.00334 .03553 (314*2π)/4531 weeks
315-.0295 -.00564 (315*2π)/4531 weeks
316.0237 -.05809 (316*2π)/4531 weeks
317-.00683 .01877 (317*2π)/4531 weeks
318.06648 -.06011 (318*2π)/4531 weeks
319.02743 -.01143 (319*2π)/4531 weeks
320.00701 .03206 (320*2π)/4531 weeks
321-.02884 -.01513 (321*2π)/4531 weeks
322.05541 -.07695 (322*2π)/4531 weeks
323.03914 .07289 (323*2π)/4531 weeks
324.02535 .03336 (324*2π)/4531 weeks
325.01581 -.03855 (325*2π)/4531 weeks
326.01925 -.01455 (326*2π)/4531 weeks
327.04215 -.02483 (327*2π)/4531 weeks
328.02048 .04512 (328*2π)/4531 weeks
329-.06317 .00151 (329*2π)/4531 weeks
330.01057 -.00086 (330*2π)/4531 weeks
331-.07897 .00919 (331*2π)/4531 weeks
332.00183 .00376 (332*2π)/4531 weeks
333.00687 .00958 (333*2π)/4531 weeks
334.04243 -.06688 (334*2π)/4531 weeks
335.04087 .01448 (335*2π)/4531 weeks
336-.06942 .00988 (336*2π)/4531 weeks
337-.02116 -.08334 (337*2π)/4531 weeks
338-.0583 -.04243 (338*2π)/4531 weeks
339-.00487 -.08728 (339*2π)/4531 weeks
340.0518 .05626 (340*2π)/4531 weeks
341-.00057 .08118 (341*2π)/4531 weeks
342.07187 .02649 (342*2π)/4531 weeks
343.02637 -.0278 (343*2π)/4531 weeks
344-.05904 -.03706 (344*2π)/4531 weeks
345-.04476 -.04778 (345*2π)/4531 weeks
346.08042 .03329 (346*2π)/4531 weeks
347-.0173 .02827 (347*2π)/4531 weeks
348-.03558 -.04607 (348*2π)/4531 weeks
349-.01975 .03362 (349*2π)/4531 weeks
350.00174 .06887 (350*2π)/4531 weeks
351.12268 .03863 (351*2π)/4531 weeks
352-.02865 .08402 (352*2π)/4531 weeks
353-.02392 .0587 (353*2π)/4531 weeks
354-.01619 -.01072 (354*2π)/4531 weeks
355-.07363 -.02297 (355*2π)/4531 weeks
356-.00913 -.06332 (356*2π)/4531 weeks
357-.09097 -.04745 (357*2π)/4531 weeks
358-.0979 -.00512 (358*2π)/4531 weeks
359.06091 -.09998 (359*2π)/4531 weeks
360.00819 .00906 (360*2π)/4531 weeks
361.05905 -.02633 (361*2π)/4531 weeks
362.10486 -.0487 (362*2π)/4531 weeks
363.11481 -.05284 (363*2π)/4531 weeks
364.02949 .02795 (364*2π)/4531 weeks
365-.04719 -.01256 (365*2π)/4531 weeks
366-.03136 .09892 (366*2π)/4531 weeks
367-.00486 .05 (367*2π)/4531 weeks
368-.04063 .10744 (368*2π)/4531 weeks
369.03407 .06146 (369*2π)/4531 weeks
370.04743 -.00418 (370*2π)/4531 weeks
371.01246 -.05456 (371*2π)/4531 weeks
372-.00456 -.087 (372*2π)/4531 weeks
373-.00003 -.13068 (373*2π)/4531 weeks
374-.04295 -.07648 (374*2π)/4531 weeks
375.06573 .02598 (375*2π)/4531 weeks
376-.05411 -.04926 (376*2π)/4531 weeks
377-.07472 -.0685 (377*2π)/4531 weeks
378-.05656 -.06874 (378*2π)/4531 weeks
379.04739 -.07081 (379*2π)/4531 weeks
380.05016 .03315 (380*2π)/4531 weeks
381.13667 .08941 (381*2π)/4531 weeks
382.10697 .02468 (382*2π)/4531 weeks
383.01466 .1273 (383*2π)/4531 weeks
384-.00519 -.02032 (384*2π)/4531 weeks
385.10576 .117 (385*2π)/4531 weeks
386-.12937 -.00131 (386*2π)/4531 weeks
387.01331 .02982 (387*2π)/4531 weeks
388-.15969 -.05975 (388*2π)/4531 weeks
389-.05026 -.22054 (389*2π)/4531 weeks
390.04236 .10869 (390*2π)/4531 weeks
391-.06901 -.11633 (391*2π)/4531 weeks
392.01652 -.18053 (392*2π)/4531 weeks
393.08205 -.04183 (393*2π)/4531 weeks
394.16112 .00435 (394*2π)/4531 weeks
395.11885 .03467 (395*2π)/4531 weeks
396-.04973 .05899 (396*2π)/4531 weeks
397.05666 -.04832 (397*2π)/4531 weeks
398-.04963 .09754 (398*2π)/4531 weeks
399.12449 .00539 (399*2π)/4531 weeks
400.07698 .00685 (400*2π)/4531 weeks
401-.02405 -.01514 (401*2π)/4531 weeks
402.11112 .07167 (402*2π)/4531 weeks
403-.08366 .07434 (403*2π)/4531 weeks
404-.02345 -.02544 (404*2π)/4531 weeks
405-.10673 .04149 (405*2π)/4531 weeks
406-.01869 .07462 (406*2π)/4531 weeks
407.02717 -.17326 (407*2π)/4531 weeks
408.01767 -.09423 (408*2π)/4531 weeks
409.04798 .02174 (409*2π)/4531 weeks
410.03146 -.12673 (410*2π)/4531 weeks
411-.06586 .00225 (411*2π)/4531 weeks
412-.11923 -.16588 (412*2π)/4531 weeks
413-.18137 .02081 (413*2π)/4531 weeks
414.20799 .10637 (414*2π)/4531 weeks
415.06638 -.03041 (415*2π)/4531 weeks
416.01979 -.08816 (416*2π)/4531 weeks
417-.11982 .03748 (417*2π)/4531 weeks
418-.0808 -.11308 (418*2π)/4531 weeks
419.20105 .1888 (419*2π)/4531 weeks
420-.21346 .103 (420*2π)/4531 weeks
421-.15359 -.07987 (421*2π)/4531 weeks
422.07678 -.02054 (422*2π)/4531 weeks
423-.16157 .00813 (423*2π)/4531 weeks
424-.16581 .05782 (424*2π)/4531 weeks
425-.49147 -.10209 (425*2π)/4531 weeks
426-.06072 -.32281 (426*2π)/4531 weeks
427.15866 -.23054 (427*2π)/4531 weeks
428.12572 -.31298 (428*2π)/4531 weeks
429.33544 -.33711 (429*2π)/4531 weeks
430-.02173 -.22688 (430*2π)/4531 weeks
431.34927 -.3159 (431*2π)/4531 weeks
432-.10962 .09792 (432*2π)/4531 weeks
433-.20592 .04916 (433*2π)/4531 weeks
434-.35439 .18514 (434*2π)/4531 weeks
435-.04883 -.02144 (435*2π)/4531 weeks
436.09573 .19964 (436*2π)/4531 weeks
437.02701 -.15821 (437*2π)/4531 weeks
438-.32608 -.00924 (438*2π)/4531 weeks
439.03249 -.59792 (439*2π)/4531 weeks
440-.24434 .08384 (440*2π)/4531 weeks
441-.4844 -.02875 (441*2π)/4531 weeks
442.39523 -.35626 (442*2π)/4531 weeks
443-.52819 -.70202 (443*2π)/4531 weeks
444-.00171 -.66691 (444*2π)/4531 weeks
445-.36957 -.06407 (445*2π)/4531 weeks
446.7035 -.9832 (446*2π)/4531 weeks
4472.29464 -.95622 (447*2π)/4531 weeks
4482.00465 .59801 (448*2π)/4531 weeks
4491.59972 .16002 (449*2π)/4531 weeks
4502.50058 1.17054 (450*2π)/4531 weeks
451-1.5116 2.07364 (451*2π)/4531 weeks

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