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# Fourier Analysis of YCL (ProShares Ultra Yen)

YCL (ProShares Ultra Yen) appears to have interesting cyclic behaviour every 50 weeks (4.0358*cosine), 46 weeks (2.8349*sine), and 65 weeks (2.4584*sine).

YCL (ProShares Ultra Yen) has an average price of 83.57 (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 11/25/2008 to 4/12/2021 for YCL (ProShares Ultra Yen), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
083.57121   0
18.09526 37.17327 (1*2π)/646646 weeks
2-14.72434 8.96806 (2*2π)/646323 weeks
31.75641 -1.79996 (3*2π)/646215 weeks
42.1945 2.40729 (4*2π)/646162 weeks
5.73432 5.98261 (5*2π)/646129 weeks
6-.99414 -.92358 (6*2π)/646108 weeks
71.50972 4.50907 (7*2π)/64692 weeks
8-.4082 1.04275 (8*2π)/64681 weeks
9.03969 -.32341 (9*2π)/64672 weeks
10.62802 2.45842 (10*2π)/64665 weeks
11-.80097 .58398 (11*2π)/64659 weeks
12-.01619 -.37926 (12*2π)/64654 weeks
134.03579 1.45265 (13*2π)/64650 weeks
14-.31806 2.83492 (14*2π)/64646 weeks
15-.31656 1.50766 (15*2π)/64643 weeks
161.204 1.82781 (16*2π)/64640 weeks
17-.40703 .83279 (17*2π)/64638 weeks
18-.30669 1.41144 (18*2π)/64636 weeks
19.16187 .96923 (19*2π)/64634 weeks
20.23127 1.27234 (20*2π)/64632 weeks
21.31012 1.28035 (21*2π)/64631 weeks
22.3088 1.16599 (22*2π)/64629 weeks
23-.20337 1.01788 (23*2π)/64628 weeks
24.35283 1.40476 (24*2π)/64627 weeks
25-.10883 .42833 (25*2π)/64626 weeks
26-.44857 1.38794 (26*2π)/64625 weeks
27.27784 .76609 (27*2π)/64624 weeks
28.65123 .83707 (28*2π)/64623 weeks
29-.20837 1.29313 (29*2π)/64622 weeks
30-.42759 .77998 (30*2π)/64622 weeks
31.16287 .67609 (31*2π)/64621 weeks
32.17974 1.13363 (32*2π)/64620 weeks
33-.14343 1.2938 (33*2π)/64620 weeks
34-.56772 .43793 (34*2π)/64619 weeks
35-.12854 .61448 (35*2π)/64618 weeks
36-.07381 .81213 (36*2π)/64618 weeks
37-.52283 .37682 (37*2π)/64617 weeks
38.07143 .28375 (38*2π)/64617 weeks
39.12968 .19558 (39*2π)/64617 weeks
40.38618 .58187 (40*2π)/64616 weeks
41-.30857 .9128 (41*2π)/64616 weeks
42-.28697 .10588 (42*2π)/64615 weeks
43-.03875 .54058 (43*2π)/64615 weeks
44.09966 .62532 (44*2π)/64615 weeks
45-.2135 -.06818 (45*2π)/64614 weeks
46.15551 .37445 (46*2π)/64614 weeks
47.12412 .67625 (47*2π)/64614 weeks
48-.11242 .25357 (48*2π)/64613 weeks
49-.20248 .27009 (49*2π)/64613 weeks
50.29839 .03976 (50*2π)/64613 weeks
51.20375 .58327 (51*2π)/64613 weeks
52.24798 .4272 (52*2π)/64612 weeks
53-.19342 .52116 (53*2π)/64612 weeks
54-.00131 .03008 (54*2π)/64612 weeks
55.19081 .54245 (55*2π)/64612 weeks
56-.29044 .16543 (56*2π)/64612 weeks
57-.17793 -.01279 (57*2π)/64611 weeks
58.28378 .05908 (58*2π)/64611 weeks
59.36172 .14436 (59*2π)/64611 weeks
60.38959 .27585 (60*2π)/64611 weeks
61.24323 .64433 (61*2π)/64611 weeks
62.00077 .23111 (62*2π)/64610 weeks
63-.04485 .27917 (63*2π)/64610 weeks
64.17914 .52549 (64*2π)/64610 weeks
65.37998 .28144 (65*2π)/64610 weeks
66.02128 .53738 (66*2π)/64610 weeks
67-.04751 .3183 (67*2π)/64610 weeks
68-.19964 .21536 (68*2π)/64610 weeks
69-.19134 .234 (69*2π)/6469 weeks
70.04779 -.01215 (70*2π)/6469 weeks
71.21327 .15592 (71*2π)/6469 weeks
72-.07072 .39503 (72*2π)/6469 weeks
73-.02523 -.08572 (73*2π)/6469 weeks
74.30347 .34291 (74*2π)/6469 weeks
75.15405 .01814 (75*2π)/6469 weeks
76.18885 .1381 (76*2π)/6469 weeks
77.50955 .34206 (77*2π)/6468 weeks
78.14199 .28184 (78*2π)/6468 weeks
79.10847 .54634 (79*2π)/6468 weeks
80.06204 .26313 (80*2π)/6468 weeks
81.0318 .05182 (81*2π)/6468 weeks
82.25028 .36611 (82*2π)/6468 weeks
83-.13056 .30075 (83*2π)/6468 weeks
84.25657 .10151 (84*2π)/6468 weeks
85.14944 .36489 (85*2π)/6468 weeks
86.08553 .36836 (86*2π)/6468 weeks
87.15647 .45258 (87*2π)/6467 weeks
88.06939 .33157 (88*2π)/6467 weeks
89-.13465 .44146 (89*2π)/6467 weeks
90-.00109 .0992 (90*2π)/6467 weeks
91-.19273 .08423 (91*2π)/6467 weeks
92.11154 .19047 (92*2π)/6467 weeks
93-.01119 .34827 (93*2π)/6467 weeks
94-.28991 .1842 (94*2π)/6467 weeks
95-.00144 .19831 (95*2π)/6467 weeks
96-.06856 .02283 (96*2π)/6467 weeks
97.03408 .0362 (97*2π)/6467 weeks
98.25424 .2276 (98*2π)/6467 weeks
99-.08739 .29088 (99*2π)/6467 weeks
100-.09309 .13218 (100*2π)/6466 weeks
101.1689 .07614 (101*2π)/6466 weeks
102-.05361 .19657 (102*2π)/6466 weeks
103.31086 .15734 (103*2π)/6466 weeks
104-.05947 .18747 (104*2π)/6466 weeks
105-.15923 .24593 (105*2π)/6466 weeks
106.14326 .05397 (106*2π)/6466 weeks
107.00503 .0852 (107*2π)/6466 weeks
108.1643 .25289 (108*2π)/6466 weeks
109.12825 .20281 (109*2π)/6466 weeks
110-.1671 .34496 (110*2π)/6466 weeks
111-.08524 -.06304 (111*2π)/6466 weeks
112.04644 .07871 (112*2π)/6466 weeks
113.06482 .20823 (113*2π)/6466 weeks
114-.05066 .07568 (114*2π)/6466 weeks
115-.04518 -.00002 (115*2π)/6466 weeks
116-.05386 .10126 (116*2π)/6466 weeks
117.22226 .04975 (117*2π)/6466 weeks
118.12223 .21927 (118*2π)/6465 weeks
119.13725 .1977 (119*2π)/6465 weeks
120.18766 .17456 (120*2π)/6465 weeks
121-.2162 .19424 (121*2π)/6465 weeks
122-.01422 -.02753 (122*2π)/6465 weeks
123.11908 .03569 (123*2π)/6465 weeks
124.02625 .14309 (124*2π)/6465 weeks
125.12463 -.02849 (125*2π)/6465 weeks
126.0211 .1154 (126*2π)/6465 weeks
127.0352 .2768 (127*2π)/6465 weeks
128.18489 .0473 (128*2π)/6465 weeks
129.08341 .43094 (129*2π)/6465 weeks
130-.06515 .13552 (130*2π)/6465 weeks
131.11958 -.00831 (131*2π)/6465 weeks
132.13201 .18164 (132*2π)/6465 weeks
133.0413 .21957 (133*2π)/6465 weeks
134.1318 .02943 (134*2π)/6465 weeks
135.02706 .08279 (135*2π)/6465 weeks
136-.06356 .21005 (136*2π)/6465 weeks
137.03477 .19194 (137*2π)/6465 weeks
138-.16154 .19071 (138*2π)/6465 weeks
139-.10764 .02959 (139*2π)/6465 weeks
140.00105 .04267 (140*2π)/6465 weeks
141.06657 .20618 (141*2π)/6465 weeks
142-.04727 .12076 (142*2π)/6465 weeks
143.02183 -.03633 (143*2π)/6465 weeks
144-.07891 .01679 (144*2π)/6464 weeks
145.0374 .01514 (145*2π)/6464 weeks
146-.05229 -.0426 (146*2π)/6464 weeks
147-.0418 -.11053 (147*2π)/6464 weeks
148.02824 .02379 (148*2π)/6464 weeks
149.12421 -.06429 (149*2π)/6464 weeks
150.12298 .10283 (150*2π)/6464 weeks
151.08579 -.04515 (151*2π)/6464 weeks
152.03131 .02779 (152*2π)/6464 weeks
153.2246 -.18571 (153*2π)/6464 weeks
154.19398 -.14454 (154*2π)/6464 weeks
155.30995 .16581 (155*2π)/6464 weeks
156.04068 .07909 (156*2π)/6464 weeks
157-.09989 .03908 (157*2π)/6464 weeks
158.18928 -.04354 (158*2π)/6464 weeks
159.10298 -.02988 (159*2π)/6464 weeks
160.19604 .13721 (160*2π)/6464 weeks
161.2515 .12861 (161*2π)/6464 weeks
162.08352 .18477 (162*2π)/6464 weeks
163.17401 .10064 (163*2π)/6464 weeks
164-.03606 .20217 (164*2π)/6464 weeks
165.07782 .00961 (165*2π)/6464 weeks
166.13062 -.08654 (166*2π)/6464 weeks
167.03474 .28547 (167*2π)/6464 weeks
168.06287 .03272 (168*2π)/6464 weeks
169-.12956 .08745 (169*2π)/6464 weeks
170-.04313 -.02174 (170*2π)/6464 weeks
171.1054 -.0769 (171*2π)/6464 weeks
172.18394 .18267 (172*2π)/6464 weeks
173.06717 .11465 (173*2π)/6464 weeks
174.07878 -.07219 (174*2π)/6464 weeks
175.09258 .10669 (175*2π)/6464 weeks
176.12786 .02997 (176*2π)/6464 weeks
177.04321 .03276 (177*2π)/6464 weeks
178.10904 .07339 (178*2π)/6464 weeks
179.02415 .10241 (179*2π)/6464 weeks
180-.02717 .12365 (180*2π)/6464 weeks
181-.07242 .03174 (181*2π)/6464 weeks
182.17945 .00338 (182*2π)/6464 weeks
183.06257 .1184 (183*2π)/6464 weeks
184.05753 .06383 (184*2π)/6464 weeks
185.02285 .11103 (185*2π)/6463 weeks
186.02557 -.05083 (186*2π)/6463 weeks
187.19096 -.06231 (187*2π)/6463 weeks
188.1818 .10332 (188*2π)/6463 weeks
189.17028 .19481 (189*2π)/6463 weeks
190.04676 .0252 (190*2π)/6463 weeks
191.04875 .04281 (191*2π)/6463 weeks
192.04731 .22434 (192*2π)/6463 weeks
193-.11463 .00998 (193*2π)/6463 weeks
194-.06085 .06149 (194*2π)/6463 weeks
195.04289 .00116 (195*2π)/6463 weeks
196-.01405 -.14586 (196*2π)/6463 weeks
197.14247 -.01348 (197*2π)/6463 weeks
198.15288 -.00721 (198*2π)/6463 weeks
199.05334 .04535 (199*2π)/6463 weeks
200.10772 .02883 (200*2π)/6463 weeks
201.09837 .04928 (201*2π)/6463 weeks
202.05697 .1171 (202*2π)/6463 weeks
203.01789 -.04561 (203*2π)/6463 weeks
204.12716 .05328 (204*2π)/6463 weeks
205.09649 .12354 (205*2π)/6463 weeks
206-.01577 .02957 (206*2π)/6463 weeks
207.13244 .04071 (207*2π)/6463 weeks
208.14403 -.03628 (208*2π)/6463 weeks
209.18166 .0869 (209*2π)/6463 weeks
210.23455 .08696 (210*2π)/6463 weeks
211-.13893 .03875 (211*2π)/6463 weeks
212-.0582 -.10726 (212*2π)/6463 weeks
213.15 -.05479 (213*2π)/6463 weeks
214-.04123 .08355 (214*2π)/6463 weeks
215.15525 .01724 (215*2π)/6463 weeks
216.09308 -.05295 (216*2π)/6463 weeks
217.13064 .05179 (217*2π)/6463 weeks
218.19374 .06488 (218*2π)/6463 weeks
219.10716 .02137 (219*2π)/6463 weeks
220.10068 -.0459 (220*2π)/6463 weeks
221.17819 .01699 (221*2π)/6463 weeks
222.06552 .13319 (222*2π)/6463 weeks
223.09648 -.04997 (223*2π)/6463 weeks
224.11794 -.02402 (224*2π)/6463 weeks
225.14663 .00663 (225*2π)/6463 weeks
226.15166 .114 (226*2π)/6463 weeks
227.16928 .1628 (227*2π)/6463 weeks
228.07852 .15887 (228*2π)/6463 weeks
229.11017 .19388 (229*2π)/6463 weeks
230-.01003 .16177 (230*2π)/6463 weeks
231.01813 .07944 (231*2π)/6463 weeks
232.0345 -.04784 (232*2π)/6463 weeks
233-.00798 .06701 (233*2π)/6463 weeks
234.09865 -.04708 (234*2π)/6463 weeks
235.0329 -.03 (235*2π)/6463 weeks
236.01354 .02205 (236*2π)/6463 weeks
237.1698 -.1132 (237*2π)/6463 weeks
238.20217 .11261 (238*2π)/6463 weeks
239.15347 .14163 (239*2π)/6463 weeks
240.06836 .04755 (240*2π)/6463 weeks
241.06539 .10559 (241*2π)/6463 weeks
242.22018 .01245 (242*2π)/6463 weeks
243.10199 .16187 (243*2π)/6463 weeks
244.0849 .20084 (244*2π)/6463 weeks
245.11711 .01326 (245*2π)/6463 weeks
246-.01949 .09235 (246*2π)/6463 weeks
247.10681 .00109 (247*2π)/6463 weeks
248.07698 .07036 (248*2π)/6463 weeks
249.04286 .06983 (249*2π)/6463 weeks
250.18678 .00541 (250*2π)/6463 weeks
251.14153 .11776 (251*2π)/6463 weeks
252.05558 .13926 (252*2π)/6463 weeks
253-.0893 .1844 (253*2π)/6463 weeks
254-.0201 .07475 (254*2π)/6463 weeks
255-.0489 -.07445 (255*2π)/6463 weeks
256-.04311 -.0198 (256*2π)/6463 weeks
257.0808 -.03287 (257*2π)/6463 weeks
258.05928 .00912 (258*2π)/6463 weeks
259.11172 .05712 (259*2π)/6462 weeks
260.13174 .00159 (260*2π)/6462 weeks
261.05738 .16107 (261*2π)/6462 weeks
262.01677 .09907 (262*2π)/6462 weeks
263-.09788 -.04698 (263*2π)/6462 weeks
264.03633 -.06906 (264*2π)/6462 weeks
265.23038 .03375 (265*2π)/6462 weeks
266.0154 .12501 (266*2π)/6462 weeks
267-.04127 .0088 (267*2π)/6462 weeks
268.10627 -.07068 (268*2π)/6462 weeks
269.09688 .15476 (269*2π)/6462 weeks
270-.01294 -.05353 (270*2π)/6462 weeks
271.06183 -.06989 (271*2π)/6462 weeks
272.11452 .01669 (272*2π)/6462 weeks
273.11299 .02723 (273*2π)/6462 weeks
274.02096 .04114 (274*2π)/6462 weeks
275.06404 -.07066 (275*2π)/6462 weeks
276.09402 -.03975 (276*2π)/6462 weeks
277.05396 .06104 (277*2π)/6462 weeks
278.12589 -.05608 (278*2π)/6462 weeks
279.14932 .06236 (279*2π)/6462 weeks
280.0046 .05738 (280*2π)/6462 weeks
281.05288 .03924 (281*2π)/6462 weeks
282.04905 -.00742 (282*2π)/6462 weeks
283.09856 -.0493 (283*2π)/6462 weeks
284.03487 .09179 (284*2π)/6462 weeks
285.12138 .05398 (285*2π)/6462 weeks
286.12768 .05834 (286*2π)/6462 weeks
287.05927 .0706 (287*2π)/6462 weeks
288.04977 .06693 (288*2π)/6462 weeks
289.07299 .10987 (289*2π)/6462 weeks
290-.00974 .06845 (290*2π)/6462 weeks
291-.07834 -.00443 (291*2π)/6462 weeks
292-.00797 -.03628 (292*2π)/6462 weeks
293.05216 -.05772 (293*2π)/6462 weeks
294-.02484 -.08134 (294*2π)/6462 weeks
295.10699 -.01416 (295*2π)/6462 weeks
296.0366 -.09328 (296*2π)/6462 weeks
297.23182 -.15645 (297*2π)/6462 weeks
298.18644 .11648 (298*2π)/6462 weeks
299-.01069 -.00857 (299*2π)/6462 weeks
300.10963 -.02235 (300*2π)/6462 weeks
301.11983 .05152 (301*2π)/6462 weeks
302.08263 .04493 (302*2π)/6462 weeks
303.13679 .04981 (303*2π)/6462 weeks
304.0498 .03175 (304*2π)/6462 weeks
305-.08759 -.01988 (305*2π)/6462 weeks
306-.01352 -.08041 (306*2π)/6462 weeks
307.04669 -.05463 (307*2π)/6462 weeks
308.05347 .00518 (308*2π)/6462 weeks
309.0333 .00944 (309*2π)/6462 weeks
310.06802 -.08749 (310*2π)/6462 weeks
311.21045 .01004 (311*2π)/6462 weeks
312.08634 .14702 (312*2π)/6462 weeks
313.09305 -.07149 (313*2π)/6462 weeks
314.09869 .01611 (314*2π)/6462 weeks
315.05454 .01519 (315*2π)/6462 weeks
316.0493 -.01624 (316*2π)/6462 weeks
317.06466 -.03097 (317*2π)/6462 weeks
318.04325 -.06691 (318*2π)/6462 weeks
319.11987 .01435 (319*2π)/6462 weeks
320.20525 -.08595 (320*2π)/6462 weeks
321.10131 .07315 (321*2π)/6462 weeks
322.0971 .07428 (322*2π)/6462 weeks
323.04582   (323*2π)/6462 weeks
324.0971 -.07428 (324*2π)/6462 weeks
325.10131 -.07315 (325*2π)/6462 weeks
326.20525 .08595 (326*2π)/6462 weeks
327.11987 -.01435 (327*2π)/6462 weeks
328.04325 .06691 (328*2π)/6462 weeks
329.06466 .03097 (329*2π)/6462 weeks
330.0493 .01624 (330*2π)/6462 weeks
331.05454 -.01519 (331*2π)/6462 weeks
332.09869 -.01611 (332*2π)/6462 weeks
333.09305 .07149 (333*2π)/6462 weeks
334.08634 -.14702 (334*2π)/6462 weeks
335.21045 -.01004 (335*2π)/6462 weeks
336.06802 .08749 (336*2π)/6462 weeks
337.0333 -.00944 (337*2π)/6462 weeks
338.05347 -.00518 (338*2π)/6462 weeks
339.04669 .05463 (339*2π)/6462 weeks
340-.01352 .08041 (340*2π)/6462 weeks
341-.08759 .01988 (341*2π)/6462 weeks
342.0498 -.03175 (342*2π)/6462 weeks
343.13679 -.04981 (343*2π)/6462 weeks
344.08263 -.04493 (344*2π)/6462 weeks
345.11983 -.05152 (345*2π)/6462 weeks
346.10963 .02235 (346*2π)/6462 weeks
347-.01069 .00857 (347*2π)/6462 weeks
348.18644 -.11648 (348*2π)/6462 weeks
349.23182 .15645 (349*2π)/6462 weeks
350.0366 .09328 (350*2π)/6462 weeks
351.10699 .01416 (351*2π)/6462 weeks
352-.02484 .08134 (352*2π)/6462 weeks
353.05216 .05772 (353*2π)/6462 weeks
354-.00797 .03628 (354*2π)/6462 weeks
355-.07834 .00443 (355*2π)/6462 weeks
356-.00974 -.06845 (356*2π)/6462 weeks
357.07299 -.10987 (357*2π)/6462 weeks
358.04977 -.06693 (358*2π)/6462 weeks
359.05927 -.0706 (359*2π)/6462 weeks
360.12768 -.05834 (360*2π)/6462 weeks
361.12138 -.05398 (361*2π)/6462 weeks
362.03487 -.09179 (362*2π)/6462 weeks
363.09856 .0493 (363*2π)/6462 weeks
364.04905 .00742 (364*2π)/6462 weeks
365.05288 -.03924 (365*2π)/6462 weeks
366.0046 -.05738 (366*2π)/6462 weeks
367.14932 -.06236 (367*2π)/6462 weeks
368.12589 .05608 (368*2π)/6462 weeks
369.05396 -.06104 (369*2π)/6462 weeks
370.09402 .03975 (370*2π)/6462 weeks
371.06404 .07066 (371*2π)/6462 weeks
372.02096 -.04114 (372*2π)/6462 weeks
373.11299 -.02723 (373*2π)/6462 weeks
374.11452 -.01669 (374*2π)/6462 weeks
375.06183 .06989 (375*2π)/6462 weeks
376-.01294 .05353 (376*2π)/6462 weeks
377.09688 -.15476 (377*2π)/6462 weeks
378.10627 .07068 (378*2π)/6462 weeks
379-.04127 -.0088 (379*2π)/6462 weeks
380.0154 -.12501 (380*2π)/6462 weeks
381.23038 -.03375 (381*2π)/6462 weeks
382.03633 .06906 (382*2π)/6462 weeks
383-.09788 .04698 (383*2π)/6462 weeks
384.01677 -.09907 (384*2π)/6462 weeks
385.05738 -.16107 (385*2π)/6462 weeks
386.13174 -.00159 (386*2π)/6462 weeks
387.11172 -.05712 (387*2π)/6462 weeks
388.05928 -.00912 (388*2π)/6462 weeks
389.0808 .03287 (389*2π)/6462 weeks
390-.04311 .0198 (390*2π)/6462 weeks
391-.0489 .07445 (391*2π)/6462 weeks
392-.0201 -.07475 (392*2π)/6462 weeks
393-.0893 -.1844 (393*2π)/6462 weeks
394.05558 -.13926 (394*2π)/6462 weeks
395.14153 -.11776 (395*2π)/6462 weeks
396.18678 -.00541 (396*2π)/6462 weeks
397.04286 -.06983 (397*2π)/6462 weeks
398.07698 -.07036 (398*2π)/6462 weeks
399.10681 -.00109 (399*2π)/6462 weeks
400-.01949 -.09235 (400*2π)/6462 weeks
401.11711 -.01326 (401*2π)/6462 weeks
402.0849 -.20084 (402*2π)/6462 weeks
403.10199 -.16187 (403*2π)/6462 weeks
404.22018 -.01245 (404*2π)/6462 weeks
405.06539 -.10559 (405*2π)/6462 weeks
406.06836 -.04755 (406*2π)/6462 weeks
407.15347 -.14163 (407*2π)/6462 weeks
408.20217 -.11261 (408*2π)/6462 weeks
409.1698 .1132 (409*2π)/6462 weeks
410.01354 -.02205 (410*2π)/6462 weeks
411.0329 .03 (411*2π)/6462 weeks
412.09865 .04708 (412*2π)/6462 weeks
413-.00798 -.06701 (413*2π)/6462 weeks
414.0345 .04784 (414*2π)/6462 weeks
415.01813 -.07944 (415*2π)/6462 weeks
416-.01003 -.16177 (416*2π)/6462 weeks
417.11017 -.19388 (417*2π)/6462 weeks
418.07852 -.15887 (418*2π)/6462 weeks
419.16928 -.1628 (419*2π)/6462 weeks
420.15166 -.114 (420*2π)/6462 weeks
421.14663 -.00663 (421*2π)/6462 weeks
422.11794 .02402 (422*2π)/6462 weeks
423.09648 .04997 (423*2π)/6462 weeks
424.06552 -.13319 (424*2π)/6462 weeks
425.17819 -.01699 (425*2π)/6462 weeks
426.10068 .0459 (426*2π)/6462 weeks
427.10716 -.02137 (427*2π)/6462 weeks
428.19374 -.06488 (428*2π)/6462 weeks
429.13064 -.05179 (429*2π)/6462 weeks
430.09308 .05295 (430*2π)/6462 weeks
431.15525 -.01724 (431*2π)/6461 weeks
432-.04123 -.08355 (432*2π)/6461 weeks
433.15 .05479 (433*2π)/6461 weeks
434-.0582 .10726 (434*2π)/6461 weeks
435-.13893 -.03875 (435*2π)/6461 weeks
436.23455 -.08696 (436*2π)/6461 weeks
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