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Fourier Analysis of AGQ (ProShares Ultra Silver)


AGQ (ProShares Ultra Silver) appears to have interesting cyclic behaviour every 26 weeks (11.6636*sine), 19 weeks (9.843*cosine), and 16 weeks (6.235*cosine).

AGQ (ProShares Ultra Silver) has an average price of 126.4 (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 12/4/2008 to 3/20/2017 for AGQ (ProShares Ultra Silver), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0126.3996   0 
1-56.75795 111.1767 (1*2π)/434434 weeks
2-34.02913 -36.88315 (2*2π)/434217 weeks
326.72334 -15.0897 (3*2π)/434145 weeks
416.4731 25.6839 (4*2π)/434109 weeks
5-34.04502 12.14485 (5*2π)/43487 weeks
61.86692 -24.34313 (6*2π)/43472 weeks
78.2427 6.41849 (7*2π)/43462 weeks
8-.05168 8.11151 (8*2π)/43454 weeks
9-7.09647 1.99093 (9*2π)/43448 weeks
106.95585 -3.91534 (10*2π)/43443 weeks
11-2.14643 9.15197 (11*2π)/43439 weeks
12-.36349 -1.83328 (12*2π)/43436 weeks
131.10518 2.47061 (13*2π)/43433 weeks
14-3.92438 -.15965 (14*2π)/43431 weeks
152.77646 -1.19948 (15*2π)/43429 weeks
16-4.75151 4.36044 (16*2π)/43427 weeks
17-.27296 -11.66361 (17*2π)/43426 weeks
189.6708 5.68186 (18*2π)/43424 weeks
19-4.33385 7.04511 (19*2π)/43423 weeks
20-8.34416 -4.75489 (20*2π)/43422 weeks
216.35169 -4.39945 (21*2π)/43421 weeks
223.4182 8.95051 (22*2π)/43420 weeks
23-9.84296 1.07668 (23*2π)/43419 weeks
241.59839 -8.20371 (24*2π)/43418 weeks
255.7325 3.38234 (25*2π)/43417 weeks
26-5.34776 5.61991 (26*2π)/43417 weeks
27-5.47499 -5.80377 (27*2π)/43416 weeks
286.23496 -3.67465 (28*2π)/43416 weeks
29-1.84686 5.7938 (29*2π)/43415 weeks
30-4.80076 -4.70732 (30*2π)/43414 weeks
315.1336 -3.15112 (31*2π)/43414 weeks
32-.37788 3.62508 (32*2π)/43414 weeks
33-.47566 -1.69848 (33*2π)/43413 weeks
341.32582 1.11009 (34*2π)/43413 weeks
35.32256 .06886 (35*2π)/43412 weeks
36.30349 -.27755 (36*2π)/43412 weeks
371.93254 1.06596 (37*2π)/43412 weeks
38-1.93995 .38694 (38*2π)/43411 weeks
392.23284 -1.00649 (39*2π)/43411 weeks
40-.59254 3.73406 (40*2π)/43411 weeks
41-3.89747 -2.06215 (41*2π)/43411 weeks
424.3132 -.96994 (42*2π)/43410 weeks
43-1.90044 4.71747 (43*2π)/43410 weeks
44-2.73589 -1.76174 (44*2π)/43410 weeks
451.77418 -2.36329 (45*2π)/43410 weeks
464.05959 3.53982 (46*2π)/4349 weeks
47-5.72309 .67335 (47*2π)/4349 weeks
481.3776 -4.4257 (48*2π)/4349 weeks
492.94746 1.699 (49*2π)/4349 weeks
50-2.01045 2.18775 (50*2π)/4349 weeks
51-2.1172 -2.20865 (51*2π)/4349 weeks
523.51752 -2.08413 (52*2π)/4348 weeks
53.55875 3.59767 (53*2π)/4348 weeks
54-.42791 .34187 (54*2π)/4348 weeks
55-1.39194 .2578 (55*2π)/4348 weeks
561.01288 -.79445 (56*2π)/4348 weeks
57.42002 2.41142 (57*2π)/4348 weeks
58-2.10069 .48187 (58*2π)/4347 weeks
59-.92477 -3.3065 (59*2π)/4347 weeks
604.00341 .55347 (60*2π)/4347 weeks
61-1.3719 4.68217 (61*2π)/4347 weeks
62-3.52344 -1.92903 (62*2π)/4347 weeks
632.94236 -2.69188 (63*2π)/4347 weeks
641.28229 4.61246 (64*2π)/4347 weeks
65-5.18825 -.82209 (65*2π)/4347 weeks
662.67257 -4.75608 (66*2π)/4347 weeks
673.02389 4.10873 (67*2π)/4346 weeks
68-4.19216 .65634 (68*2π)/4346 weeks
69.62219 -3.08035 (69*2π)/4346 weeks
702.27568 2.09035 (70*2π)/4346 weeks
71-2.50693 2.26013 (71*2π)/4346 weeks
72-1.98795 -1.92082 (72*2π)/4346 weeks
731.31623 -1.97976 (73*2π)/4346 weeks
74.40839 1.70771 (74*2π)/4346 weeks
75-1.36173 -.52279 (75*2π)/4346 weeks
76.87136 -1.82371 (76*2π)/4346 weeks
772.30389 .97815 (77*2π)/4346 weeks
78-1.44646 2.60535 (78*2π)/4346 weeks
79-1.32277 -1.70362 (79*2π)/4345 weeks
801.79138 -.57452 (80*2π)/4345 weeks
81.74348 1.30681 (81*2π)/4345 weeks
82-1.50606 -.12757 (82*2π)/4345 weeks
83.44668 -1.24961 (83*2π)/4345 weeks
84.81999 -.22455 (84*2π)/4345 weeks
85-.41523 .86598 (85*2π)/4345 weeks
86-.81849 -1.55094 (86*2π)/4345 weeks
872.09527 -.42571 (87*2π)/4345 weeks
881.08098 1.76207 (88*2π)/4345 weeks
89-2.16938 .39041 (89*2π)/4345 weeks
90.74585 -1.35675 (90*2π)/4345 weeks
911.00819 1.24813 (91*2π)/4345 weeks
92-1.32184 .90794 (92*2π)/4345 weeks
93-.76369 -.96972 (93*2π)/4345 weeks
94.59725 -.10735 (94*2π)/4345 weeks
95-.106 .3893 (95*2π)/4345 weeks
96-.62324 -.01628 (96*2π)/4345 weeks
97.11963 -.91317 (97*2π)/4344 weeks
98.95461 1.01781 (98*2π)/4344 weeks
99-.68046 .26227 (99*2π)/4344 weeks
100-.34912 -.42254 (100*2π)/4344 weeks
101.56943 .05909 (101*2π)/4344 weeks
102.25128 1.10431 (102*2π)/4344 weeks
103-1.67513 -.5269 (103*2π)/4344 weeks
104.63837 -2.00834 (104*2π)/4344 weeks
1052.11458 .67974 (105*2π)/4344 weeks
106-1.75691 2.03823 (106*2π)/4344 weeks
107-1.27564 -2.96252 (107*2π)/4344 weeks
1083.08949 -.17556 (108*2π)/4344 weeks
109-.659 3.07555 (109*2π)/4344 weeks
110-2.47368 -1.38057 (110*2π)/4344 weeks
1111.99656 -1.53419 (111*2π)/4344 weeks
112.55386 2.19931 (112*2π)/4344 weeks
113-1.492 -.51971 (113*2π)/4344 weeks
114.55934 -.89897 (114*2π)/4344 weeks
115.7479 .60828 (115*2π)/4344 weeks
116-1.03459 .24485 (116*2π)/4344 weeks
117.08989 -1.14606 (117*2π)/4344 weeks
118.79518 -.24599 (118*2π)/4344 weeks
119.40908 .68528 (119*2π)/4344 weeks
120-.35344 -.08433 (120*2π)/4344 weeks
121.15153 -.34304 (121*2π)/4344 weeks
122.56896 .56256 (122*2π)/4344 weeks
123-.3023 1.09464 (123*2π)/4344 weeks
124-1.27836 -.66479 (124*2π)/4344 weeks
1251.29871 -.92715 (125*2π)/4343 weeks
1261.03405 1.55198 (126*2π)/4343 weeks
127-1.98037 .60531 (127*2π)/4343 weeks
128-.11523 -1.57132 (128*2π)/4343 weeks
1291.51262 .19739 (129*2π)/4343 weeks
130-.66399 1.61592 (130*2π)/4343 weeks
131-1.20997 -.96418 (131*2π)/4343 weeks
1321.21806 -.71085 (132*2π)/4343 weeks
133-.01221 1.50019 (133*2π)/4343 weeks
134-.99285 -.9467 (134*2π)/4343 weeks
135.96793 -.65741 (135*2π)/4343 weeks
136.65004 1.19255 (136*2π)/4343 weeks
137-1.11741 .22591 (137*2π)/4343 weeks
138.00968 -.74333 (138*2π)/4343 weeks
139.38044 .3633 (139*2π)/4343 weeks
140-.57184 .7181 (140*2π)/4343 weeks
141-.38755 -.495 (141*2π)/4343 weeks
142-.38232 .15095 (142*2π)/4343 weeks
143.04034 -.27099 (143*2π)/4343 weeks
144.05161 .35528 (144*2π)/4343 weeks
145.13737 -.06297 (145*2π)/4343 weeks
146-.25994 -.08519 (146*2π)/4343 weeks
147.32124 .33942 (147*2π)/4343 weeks
148-.79335 -.12055 (148*2π)/4343 weeks
149.32634 -1.03685 (149*2π)/4343 weeks
150.53452 .40357 (150*2π)/4343 weeks
151-.71043 .32751 (151*2π)/4343 weeks
152-.04698 -.84074 (152*2π)/4343 weeks
153.7056 .18391 (153*2π)/4343 weeks
154-.69624 .84983 (154*2π)/4343 weeks
155-.79599 -.6048 (155*2π)/4343 weeks
156.39809 -.66561 (156*2π)/4343 weeks
157.47103 .04759 (157*2π)/4343 weeks
158-.03933 .46492 (158*2π)/4343 weeks
159-.06084 .03383 (159*2π)/4343 weeks
160.16861 -.36804 (160*2π)/4343 weeks
161.56791 .73041 (161*2π)/4343 weeks
162-.89128 .32522 (162*2π)/4343 weeks
163.43559 -.62091 (163*2π)/4343 weeks
164.27342 .89841 (164*2π)/4343 weeks
165-1.06594 -.14397 (165*2π)/4343 weeks
166-.10103 -1.2586 (166*2π)/4343 weeks
1671.24522 .08329 (167*2π)/4343 weeks
168-.56981 1.3727 (168*2π)/4343 weeks
169-.83988 -1.27532 (169*2π)/4343 weeks
1701.38026 -.13903 (170*2π)/4343 weeks
171-.39857 1.15084 (171*2π)/4343 weeks
172-1.06413 -.38556 (172*2π)/4343 weeks
173.45893 -1.37868 (173*2π)/4343 weeks
1741.15942 .66354 (174*2π)/4342 weeks
175-.30576 .80251 (175*2π)/4342 weeks
176-.63185 .02432 (176*2π)/4342 weeks
177.24542 -.70515 (177*2π)/4342 weeks
178.62222 .48684 (178*2π)/4342 weeks
179-.8814 .40733 (179*2π)/4342 weeks
180.20838 -.85881 (180*2π)/4342 weeks
181.67666 .27635 (181*2π)/4342 weeks
182-.20134 1.23662 (182*2π)/4342 weeks
183-1.34608 -.41214 (183*2π)/4342 weeks
184.70026 -.59953 (184*2π)/4342 weeks
185.05684 .55645 (185*2π)/4342 weeks
186-.80295 .55426 (186*2π)/4342 weeks
187-.85302 -1.53259 (187*2π)/4342 weeks
1881.67264 -.52841 (188*2π)/4342 weeks
189-.15036 1.30868 (189*2π)/4342 weeks
190-1.41179 -.87393 (190*2π)/4342 weeks
1911.28622 -1.37878 (191*2π)/4342 weeks
1921.00593 1.08637 (192*2π)/4342 weeks
193-1.18981 .43988 (193*2π)/4342 weeks
194-.22638 -.98941 (194*2π)/4342 weeks
195.8383 .18358 (195*2π)/4342 weeks
196-.52534 .01967 (196*2π)/4342 weeks
197.30387 -.66257 (197*2π)/4342 weeks
198.67218 .12518 (198*2π)/4342 weeks
199.22538 .8225 (199*2π)/4342 weeks
200-.52976 -.63024 (200*2π)/4342 weeks
2011.27438 .15743 (201*2π)/4342 weeks
202-.42381 1.03839 (202*2π)/4342 weeks
203-.66578 -.44656 (203*2π)/4342 weeks
204.27886 -.36934 (204*2π)/4342 weeks
205.22474 .25949 (205*2π)/4342 weeks
206-.33333 .30287 (206*2π)/4342 weeks
207-.40938 -.19569 (207*2π)/4342 weeks
208.2996 -.62432 (208*2π)/4342 weeks
2091.14127 -.00211 (209*2π)/4342 weeks
210.04725 1.75604 (210*2π)/4342 weeks
211-1.92965 -.62328 (211*2π)/4342 weeks
2121.2771 -1.09274 (212*2π)/4342 weeks
213.18821 1.18296 (213*2π)/4342 weeks
214-1.25194 -.34749 (214*2π)/4342 weeks
215.837 -1.0598 (215*2π)/4342 weeks
216.68032 1.19494 (216*2π)/4342 weeks
217-1.26654   (217*2π)/4342 weeks
218.68032 -1.19494 (218*2π)/4342 weeks
219.837 1.0598 (219*2π)/4342 weeks
220-1.25194 .34749 (220*2π)/4342 weeks
221.18821 -1.18296 (221*2π)/4342 weeks
2221.2771 1.09274 (222*2π)/4342 weeks
223-1.92965 .62328 (223*2π)/4342 weeks
224.04725 -1.75604 (224*2π)/4342 weeks
2251.14127 .00211 (225*2π)/4342 weeks
226.2996 .62432 (226*2π)/4342 weeks
227-.40938 .19569 (227*2π)/4342 weeks
228-.33333 -.30287 (228*2π)/4342 weeks
229.22474 -.25949 (229*2π)/4342 weeks
230.27886 .36934 (230*2π)/4342 weeks
231-.66578 .44656 (231*2π)/4342 weeks
232-.42381 -1.03839 (232*2π)/4342 weeks
2331.27438 -.15743 (233*2π)/4342 weeks
234-.52976 .63024 (234*2π)/4342 weeks
235.22538 -.8225 (235*2π)/4342 weeks
236.67218 -.12518 (236*2π)/4342 weeks
237.30387 .66257 (237*2π)/4342 weeks
238-.52534 -.01967 (238*2π)/4342 weeks
239.8383 -.18358 (239*2π)/4342 weeks
240-.22638 .98941 (240*2π)/4342 weeks
241-1.18981 -.43988 (241*2π)/4342 weeks
2421.00593 -1.08637 (242*2π)/4342 weeks
2431.28622 1.37878 (243*2π)/4342 weeks
244-1.41179 .87393 (244*2π)/4342 weeks
245-.15036 -1.30868 (245*2π)/4342 weeks
2461.67264 .52841 (246*2π)/4342 weeks
247-.85302 1.53259 (247*2π)/4342 weeks
248-.80295 -.55426 (248*2π)/4342 weeks
249.05684 -.55645 (249*2π)/4342 weeks
250.70026 .59953 (250*2π)/4342 weeks
251-1.34608 .41214 (251*2π)/4342 weeks
252-.20134 -1.23662 (252*2π)/4342 weeks
253.67666 -.27635 (253*2π)/4342 weeks
254.20838 .85881 (254*2π)/4342 weeks
255-.8814 -.40733 (255*2π)/4342 weeks
256.62222 -.48684 (256*2π)/4342 weeks
257.24542 .70515 (257*2π)/4342 weeks
258-.63185 -.02432 (258*2π)/4342 weeks
259-.30576 -.80251 (259*2π)/4342 weeks
2601.15942 -.66354 (260*2π)/4342 weeks
261.45893 1.37868 (261*2π)/4342 weeks
262-1.06413 .38556 (262*2π)/4342 weeks
263-.39857 -1.15084 (263*2π)/4342 weeks
2641.38026 .13903 (264*2π)/4342 weeks
265-.83988 1.27532 (265*2π)/4342 weeks
266-.56981 -1.3727 (266*2π)/4342 weeks
2671.24522 -.08329 (267*2π)/4342 weeks
268-.10103 1.2586 (268*2π)/4342 weeks
269-1.06594 .14397 (269*2π)/4342 weeks
270.27342 -.89841 (270*2π)/4342 weeks
271.43559 .62091 (271*2π)/4342 weeks
272-.89128 -.32522 (272*2π)/4342 weeks
273.56791 -.73041 (273*2π)/4342 weeks
274.16861 .36804 (274*2π)/4342 weeks
275-.06084 -.03383 (275*2π)/4342 weeks
276-.03933 -.46492 (276*2π)/4342 weeks
277.47103 -.04759 (277*2π)/4342 weeks
278.39809 .66561 (278*2π)/4342 weeks
279-.79599 .6048 (279*2π)/4342 weeks
280-.69624 -.84983 (280*2π)/4342 weeks
281.7056 -.18391 (281*2π)/4342 weeks
282-.04698 .84074 (282*2π)/4342 weeks
283-.71043 -.32751 (283*2π)/4342 weeks
284.53452 -.40357 (284*2π)/4342 weeks
285.32634 1.03685 (285*2π)/4342 weeks
286-.79335 .12055 (286*2π)/4342 weeks
287.32124 -.33942 (287*2π)/4342 weeks
288-.25994 .08519 (288*2π)/4342 weeks
289.13737 .06297 (289*2π)/4342 weeks
290.05161 -.35528 (290*2π)/4341 weeks
291.04034 .27099 (291*2π)/4341 weeks
292-.38232 -.15095 (292*2π)/4341 weeks
293-.38755 .495 (293*2π)/4341 weeks
294-.57184 -.7181 (294*2π)/4341 weeks
295.38044 -.3633 (295*2π)/4341 weeks
296.00968 .74333 (296*2π)/4341 weeks
297-1.11741 -.22591 (297*2π)/4341 weeks
298.65004 -1.19255 (298*2π)/4341 weeks
299.96793 .65741 (299*2π)/4341 weeks
300-.99285 .9467 (300*2π)/4341 weeks
301-.01221 -1.50019 (301*2π)/4341 weeks
3021.21806 .71085 (302*2π)/4341 weeks
303-1.20997 .96418 (303*2π)/4341 weeks
304-.66399 -1.61592 (304*2π)/4341 weeks
3051.51262 -.19739 (305*2π)/4341 weeks
306-.11523 1.57132 (306*2π)/4341 weeks
307-1.98037 -.60531 (307*2π)/4341 weeks
3081.03405 -1.55198 (308*2π)/4341 weeks
3091.29871 .92715 (309*2π)/4341 weeks
310-1.27836 .66479 (310*2π)/4341 weeks
311-.3023 -1.09464 (311*2π)/4341 weeks
312.56896 -.56256 (312*2π)/4341 weeks
313.15153 .34304 (313*2π)/4341 weeks
314-.35344 .08433 (314*2π)/4341 weeks
315.40908 -.68528 (315*2π)/4341 weeks
316.79518 .24599 (316*2π)/4341 weeks
317.08989 1.14606 (317*2π)/4341 weeks
318-1.03459 -.24485 (318*2π)/4341 weeks
319.7479 -.60828 (319*2π)/4341 weeks
320.55934 .89897 (320*2π)/4341 weeks
321-1.492 .51971 (321*2π)/4341 weeks
322.55386 -2.19931 (322*2π)/4341 weeks
3231.99656 1.53419 (323*2π)/4341 weeks
324-2.47368 1.38057 (324*2π)/4341 weeks
325-.659 -3.07555 (325*2π)/4341 weeks
3263.08949 .17556 (326*2π)/4341 weeks
327-1.27564 2.96252 (327*2π)/4341 weeks
328-1.75691 -2.03823 (328*2π)/4341 weeks
3292.11458 -.67974 (329*2π)/4341 weeks
330.63837 2.00834 (330*2π)/4341 weeks
331-1.67513 .5269 (331*2π)/4341 weeks
332.25128 -1.10431 (332*2π)/4341 weeks
333.56943 -.05909 (333*2π)/4341 weeks
334-.34912 .42254 (334*2π)/4341 weeks
335-.68046 -.26227 (335*2π)/4341 weeks
336.95461 -1.01781 (336*2π)/4341 weeks
337.11963 .91317 (337*2π)/4341 weeks
338-.62324 .01628 (338*2π)/4341 weeks
339-.106 -.3893 (339*2π)/4341 weeks
340.59725 .10735 (340*2π)/4341 weeks
341-.76369 .96972 (341*2π)/4341 weeks
342-1.32184 -.90794 (342*2π)/4341 weeks
3431.00819 -1.24813 (343*2π)/4341 weeks
344.74585 1.35675 (344*2π)/4341 weeks
345-2.16938 -.39041 (345*2π)/4341 weeks
3461.08098 -1.76207 (346*2π)/4341 weeks
3472.09527 .42571 (347*2π)/4341 weeks
348-.81849 1.55094 (348*2π)/4341 weeks
349-.41523 -.86598 (349*2π)/4341 weeks
350.81999 .22455 (350*2π)/4341 weeks
351.44668 1.24961 (351*2π)/4341 weeks
352-1.50606 .12757 (352*2π)/4341 weeks
353.74348 -1.30681 (353*2π)/4341 weeks
3541.79138 .57452 (354*2π)/4341 weeks
355-1.32277 1.70362 (355*2π)/4341 weeks
356-1.44646 -2.60535 (356*2π)/4341 weeks
3572.30389 -.97815 (357*2π)/4341 weeks
358.87136 1.82371 (358*2π)/4341 weeks
359-1.36173 .52279 (359*2π)/4341 weeks
360.40839 -1.70771 (360*2π)/4341 weeks
3611.31623 1.97976 (361*2π)/4341 weeks
362-1.98795 1.92082 (362*2π)/4341 weeks
363-2.50693 -2.26013 (363*2π)/4341 weeks
3642.27568 -2.09035 (364*2π)/4341 weeks
365.62219 3.08035 (365*2π)/4341 weeks
366-4.19216 -.65634 (366*2π)/4341 weeks
3673.02389 -4.10873 (367*2π)/4341 weeks
3682.67257 4.75608 (368*2π)/4341 weeks
369-5.18825 .82209 (369*2π)/4341 weeks
3701.28229 -4.61246 (370*2π)/4341 weeks
3712.94236 2.69188 (371*2π)/4341 weeks
372-3.52344 1.92903 (372*2π)/4341 weeks
373-1.3719 -4.68217 (373*2π)/4341 weeks
3744.00341 -.55347 (374*2π)/4341 weeks
375-.92477 3.3065 (375*2π)/4341 weeks
376-2.10069 -.48187 (376*2π)/4341 weeks
377.42002 -2.41142 (377*2π)/4341 weeks
3781.01288 .79445 (378*2π)/4341 weeks
379-1.39194 -.2578 (379*2π)/4341 weeks
380-.42791 -.34187 (380*2π)/4341 weeks
381.55875 -3.59767 (381*2π)/4341 weeks
3823.51752 2.08413 (382*2π)/4341 weeks
383-2.1172 2.20865 (383*2π)/4341 weeks
384-2.01045 -2.18775 (384*2π)/4341 weeks
3852.94746 -1.699 (385*2π)/4341 weeks
3861.3776 4.4257 (386*2π)/4341 weeks
387-5.72309 -.67335 (387*2π)/4341 weeks
3884.05959 -3.53982 (388*2π)/4341 weeks
3891.77418 2.36329 (389*2π)/4341 weeks
390-2.73589 1.76174 (390*2π)/4341 weeks
391-1.90044 -4.71747 (391*2π)/4341 weeks
3924.3132 .96994 (392*2π)/4341 weeks
393-3.89747 2.06215 (393*2π)/4341 weeks
394-.59254 -3.73406 (394*2π)/4341 weeks
3952.23284 1.00649 (395*2π)/4341 weeks
396-1.93995 -.38694 (396*2π)/4341 weeks
3971.93254 -1.06596 (397*2π)/4341 weeks
398.30349 .27755 (398*2π)/4341 weeks
399.32256 -.06886 (399*2π)/4341 weeks
4001.32582 -1.11009 (400*2π)/4341 weeks
401-.47566 1.69848 (401*2π)/4341 weeks
402-.37788 -3.62508 (402*2π)/4341 weeks
4035.1336 3.15112 (403*2π)/4341 weeks
404-4.80076 4.70732 (404*2π)/4341 weeks
405-1.84686 -5.7938 (405*2π)/4341 weeks
4066.23496 3.67465 (406*2π)/4341 weeks
407-5.47499 5.80377 (407*2π)/4341 weeks
408-5.34776 -5.61991 (408*2π)/4341 weeks
4095.7325 -3.38234 (409*2π)/4341 weeks
4101.59839 8.20371 (410*2π)/4341 weeks
411-9.84296 -1.07668 (411*2π)/4341 weeks
4123.4182 -8.95051 (412*2π)/4341 weeks
4136.35169 4.39945 (413*2π)/4341 weeks
414-8.34416 4.75489 (414*2π)/4341 weeks
415-4.33385 -7.04511 (415*2π)/4341 weeks
4169.6708 -5.68186 (416*2π)/4341 weeks
417-.27296 11.66361 (417*2π)/4341 weeks
418-4.75151 -4.36044 (418*2π)/4341 weeks
4192.77646 1.19948 (419*2π)/4341 weeks
420-3.92438 .15965 (420*2π)/4341 weeks
4211.10518 -2.47061 (421*2π)/4341 weeks
422-.36349 1.83328 (422*2π)/4341 weeks
423-2.14643 -9.15197 (423*2π)/4341 weeks
4246.95585 3.91534 (424*2π)/4341 weeks
425-7.09647 -1.99093 (425*2π)/4341 weeks
426-.05168 -8.11151 (426*2π)/4341 weeks
4278.2427 -6.41849 (427*2π)/4341 weeks
4281.86692 24.34313 (428*2π)/4341 weeks
429-34.04502 -12.14485 (429*2π)/4341 weeks
43016.4731 -25.6839 (430*2π)/4341 weeks
43126.72334 15.0897 (431*2π)/4341 weeks
432-34.02913 36.88315 (432*2π)/4341 weeks

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