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Fourier Analysis of AGQ (ProShares Ultra Silver ETF)


AGQ (ProShares Ultra Silver ETF) appears to have interesting cyclic behaviour every 25 weeks (10.3897*sine), 19 weeks (9.0606*cosine), and 16 weeks (7.2313*cosine).

AGQ (ProShares Ultra Silver ETF) has an average price of 122.2 (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 8/14/2017 for AGQ (ProShares Ultra Silver ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0122.2049   0 
1-45.69204 114.0626 (1*2π)/455455 weeks
2-41.69223 -32.08881 (2*2π)/455228 weeks
321.09374 -20.8656 (3*2π)/455152 weeks
419.73321 19.07533 (4*2π)/455114 weeks
5-25.03514 25.8572 (5*2π)/45591 weeks
6-12.62064 -22.6793 (6*2π)/45576 weeks
714.81272 .9688 (7*2π)/45565 weeks
83.51398 6.38815 (8*2π)/45557 weeks
9-4.02301 4.7949 (9*2π)/45551 weeks
10-2.74783 -6.91214 (10*2π)/45546 weeks
116.40209 5.40223 (11*2π)/45541 weeks
12-6.74332 1.74487 (12*2π)/45538 weeks
13.39435 .48109 (13*2π)/45535 weeks
14-1.40807 4.04358 (14*2π)/45533 weeks
15-2.77188 -1.59309 (15*2π)/45530 weeks
162.90012 2.02784 (16*2π)/45528 weeks
17-6.99749 2.31362 (17*2π)/45527 weeks
184.24295 -10.38972 (18*2π)/45525 weeks
197.6885 7.39835 (19*2π)/45524 weeks
20-4.53957 6.40725 (20*2π)/45523 weeks
21-7.55795 -4.90789 (21*2π)/45522 weeks
226.03493 -4.26421 (22*2π)/45521 weeks
234.2443 8.06037 (23*2π)/45520 weeks
24-9.06063 2.86212 (24*2π)/45519 weeks
25-.92443 -8.20591 (25*2π)/45518 weeks
266.28269 1.15931 (26*2π)/45518 weeks
27-2.3451 6.89285 (27*2π)/45517 weeks
28-7.23132 -2.45224 (28*2π)/45516 weeks
292.57959 -6.53824 (29*2π)/45516 weeks
303.72504 5.11107 (30*2π)/45515 weeks
31-5.86368 .4725 (31*2π)/45515 weeks
321.25017 -6.08056 (32*2π)/45514 weeks
334.77014 2.01508 (33*2π)/45514 weeks
34-1.97596 .60041 (34*2π)/45513 weeks
351.32654 -1.46577 (35*2π)/45513 weeks
36.09823 .92364 (36*2π)/45513 weeks
37.30183 .24174 (37*2π)/45512 weeks
38.61011 -.34958 (38*2π)/45512 weeks
391.45884 1.95771 (39*2π)/45512 weeks
40-1.57449 -.37112 (40*2π)/45511 weeks
412.62427 -.3611 (41*2π)/45511 weeks
42-.85117 3.52717 (42*2π)/45511 weeks
43-3.54273 -2.07044 (43*2π)/45511 weeks
444.15272 -1.18103 (44*2π)/45510 weeks
45-.90134 4.77918 (45*2π)/45510 weeks
46-2.80545 -1.30117 (46*2π)/45510 weeks
471.23921 -2.76223 (47*2π)/45510 weeks
484.39927 .96462 (48*2π)/4559 weeks
49-4.42694 3.58691 (49*2π)/4559 weeks
50-1.39441 -4.59402 (50*2π)/4559 weeks
513.56873 -.30242 (51*2π)/4559 weeks
52-.00341 2.9826 (52*2π)/4559 weeks
53-2.62329 -.29609 (53*2π)/4559 weeks
54.47614 -3.48409 (54*2π)/4558 weeks
553.85424 1.28836 (55*2π)/4558 weeks
56-1.38697 1.71602 (56*2π)/4558 weeks
57-.29335 .74374 (57*2π)/4558 weeks
58-1.10968 -.78899 (58*2π)/4558 weeks
591.36974 -.09235 (59*2π)/4558 weeks
60-.74048 2.33336 (60*2π)/4558 weeks
61-2.22652 .12232 (61*2π)/4557 weeks
62-.02642 -3.38366 (62*2π)/4557 weeks
633.66487 1.1952 (63*2π)/4557 weeks
64-1.73213 4.42459 (64*2π)/4557 weeks
65-3.37526 -1.75986 (65*2π)/4557 weeks
662.5446 -2.74415 (66*2π)/4557 weeks
671.9978 4.05954 (67*2π)/4557 weeks
68-4.96102 .57908 (68*2π)/4557 weeks
69.75294 -5.09347 (69*2π)/4557 weeks
704.40938 2.33184 (70*2π)/4557 weeks
71-3.27691 2.98498 (71*2π)/4556 weeks
72-1.24961 -2.81586 (72*2π)/4556 weeks
733.05156 -.01747 (73*2π)/4556 weeks
74-.43135 2.99429 (74*2π)/4556 weeks
75-2.96195 -.43047 (75*2π)/4556 weeks
76-.3927 -2.37589 (76*2π)/4556 weeks
772.11587 -.21469 (77*2π)/4556 weeks
78-.99885 .92674 (78*2π)/4556 weeks
79-.94351 -1.38007 (79*2π)/4556 weeks
801.58711 -1.33839 (80*2π)/4556 weeks
811.66129 1.73306 (81*2π)/4556 weeks
82-2.36622 1.61819 (82*2π)/4556 weeks
83-.80179 -1.81853 (83*2π)/4555 weeks
841.61506 -.07723 (84*2π)/4555 weeks
85.51656 1.4287 (85*2π)/4555 weeks
86-1.43286 -.17438 (86*2π)/4555 weeks
87.371 -1.19514 (87*2π)/4555 weeks
88.69741 -.24337 (88*2π)/4555 weeks
89-.20509 .92602 (89*2π)/4555 weeks
90-1.13505 -1.00345 (90*2π)/4555 weeks
911.76013 -.99706 (91*2π)/4555 weeks
921.34044 1.28244 (92*2π)/4555 weeks
93-1.554 1.737 (93*2π)/4555 weeks
94-.40136 -1.45639 (94*2π)/4555 weeks
951.46104 .39233 (95*2π)/4555 weeks
96-.39191 1.6411 (96*2π)/4555 weeks
97-1.25111 -.13615 (97*2π)/4555 weeks
98.30459 -.83466 (98*2π)/4555 weeks
99.38294 .32895 (99*2π)/4555 weeks
100-.20993 .31322 (100*2π)/4555 weeks
101-.49593 -.38568 (101*2π)/4555 weeks
102.74263 -.81417 (102*2π)/4554 weeks
103.25042 1.22179 (103*2π)/4554 weeks
104-.562 .07696 (104*2π)/4554 weeks
105-.1793 -.50378 (105*2π)/4554 weeks
106.52252 .15734 (106*2π)/4554 weeks
107.13808 1.15471 (107*2π)/4554 weeks
108-1.55318 -.55348 (108*2π)/4554 weeks
109.52916 -1.95868 (109*2π)/4554 weeks
1102.05265 .35878 (110*2π)/4554 weeks
111-1.12595 2.25103 (111*2π)/4554 weeks
112-2.06377 -2.18701 (112*2π)/4554 weeks
1132.71219 -1.26445 (113*2π)/4554 weeks
114.87587 2.90326 (114*2π)/4554 weeks
115-2.74722 .17354 (115*2π)/4554 weeks
116.5488 -2.50576 (116*2π)/4554 weeks
1171.95068 1.0602 (117*2π)/4554 weeks
118-1.56013 1.05542 (118*2π)/4554 weeks
119-.36828 -1.13024 (119*2π)/4554 weeks
120.84946 -.21172 (120*2π)/4554 weeks
121-.02744 1.0058 (121*2π)/4554 weeks
122-.91973 -.47304 (122*2π)/4554 weeks
123.58058 -.79321 (123*2π)/4554 weeks
124.85111 .00148 (124*2π)/4554 weeks
125.1226 .69179 (125*2π)/4554 weeks
126-.15686 -.21098 (126*2π)/4554 weeks
127.30512 -.38577 (127*2π)/4554 weeks
128.47219 .55685 (128*2π)/4554 weeks
129-.38009 1.0199 (129*2π)/4554 weeks
130-1.23073 -.65393 (130*2π)/4554 weeks
1311.14106 -1.00856 (131*2π)/4553 weeks
1321.13457 1.2577 (132*2π)/4553 weeks
133-1.74011 1.06782 (133*2π)/4553 weeks
134-.6342 -1.44668 (134*2π)/4553 weeks
1351.33832 -.3897 (135*2π)/4553 weeks
136.17963 1.62626 (136*2π)/4553 weeks
137-1.5912 -.11725 (137*2π)/4553 weeks
138.36578 -1.29418 (138*2π)/4553 weeks
1391.02369 .88274 (139*2π)/4553 weeks
140-1.41846 .47565 (140*2π)/4553 weeks
141.14061 -1.05577 (141*2π)/4553 weeks
1421.17319 .23322 (142*2π)/4553 weeks
143-.29398 1.35665 (143*2π)/4553 weeks
144-.78359 -.27744 (144*2π)/4553 weeks
145.49549 -.4144 (145*2π)/4553 weeks
146.2956 .49768 (146*2π)/4553 weeks
147-.74735 .44514 (147*2π)/4553 weeks
148-.10988 -.44105 (148*2π)/4553 weeks
149-.44369 .0218 (149*2π)/4553 weeks
150.05971 -.23043 (150*2π)/4553 weeks
151.01396 .36376 (151*2π)/4553 weeks
152.13312 -.05488 (152*2π)/4553 weeks
153-.25021 -.02291 (153*2π)/4553 weeks
154.35797 .17351 (154*2π)/4553 weeks
155-.75254 .09777 (155*2π)/4553 weeks
156-.12409 -.9883 (156*2π)/4553 weeks
157.68196 .2145 (157*2π)/4553 weeks
158-.33423 .68282 (158*2π)/4553 weeks
159-.49692 -.53248 (159*2π)/4553 weeks
160.69278 -.21642 (160*2π)/4553 weeks
161.26929 .94824 (161*2π)/4553 weeks
162-.90553 .00306 (162*2π)/4553 weeks
163-.12148 -.90173 (163*2π)/4553 weeks
164.58822 -.30659 (164*2π)/4553 weeks
165.45288 .1758 (165*2π)/4553 weeks
166-.21138 .1504 (166*2π)/4553 weeks
167-.12544 -.02721 (167*2π)/4553 weeks
168.41934 -.31144 (168*2π)/4553 weeks
169.24357 .88095 (169*2π)/4553 weeks
170-.89434 .02447 (170*2π)/4553 weeks
171.55965 -.43006 (171*2π)/4553 weeks
172.16756 .92193 (172*2π)/4553 weeks
173-.99288 -.15753 (173*2π)/4553 weeks
174-.14358 -1.1847 (174*2π)/4553 weeks
1751.20083 -.07036 (175*2π)/4553 weeks
176-.17078 1.37579 (176*2π)/4553 weeks
177-1.18146 -.86522 (177*2π)/4553 weeks
1781.16757 -.68992 (178*2π)/4553 weeks
179.21639 1.20195 (179*2π)/4553 weeks
180-1.03995 .10038 (180*2π)/4553 weeks
181-.3175 -1.22219 (181*2π)/4553 weeks
1821.41487 -.25482 (182*2π)/4553 weeks
183.23182 .95714 (183*2π)/4552 weeks
184-.5374 .3425 (184*2π)/4552 weeks
185-.50829 -.46455 (185*2π)/4552 weeks
186.63547 -.25667 (186*2π)/4552 weeks
187.16452 .83801 (187*2π)/4552 weeks
188-.878 -.24441 (188*2π)/4552 weeks
189.59292 -.52452 (189*2π)/4552 weeks
190.61897 .45445 (190*2π)/4552 weeks
191-.569 1.13954 (191*2π)/4552 weeks
192-1.11376 -.68653 (192*2π)/4552 weeks
193.73573 -.37177 (193*2π)/4552 weeks
194.03015 .54206 (194*2π)/4552 weeks
195-.74876 .5356 (195*2π)/4552 weeks
196-.90115 -1.38114 (196*2π)/4552 weeks
1971.51988 -.79848 (197*2π)/4552 weeks
198.2085 1.25007 (198*2π)/4552 weeks
199-1.48212 -.30177 (199*2π)/4552 weeks
200.60322 -1.69005 (200*2π)/4552 weeks
2011.3835 .58341 (201*2π)/4552 weeks
202-.66951 1.15706 (202*2π)/4552 weeks
203-.68448 -.66199 (203*2π)/4552 weeks
204.7525 -.60901 (204*2π)/4552 weeks
205-.03231 .57011 (205*2π)/4552 weeks
206-.22245 -.53342 (206*2π)/4552 weeks
207.66829 -.34598 (207*2π)/4552 weeks
208.57048 .28846 (208*2π)/4552 weeks
209-.43719 .7074 (209*2π)/4552 weeks
210.12804 -.85545 (210*2π)/4552 weeks
2111.01976 .80467 (211*2π)/4552 weeks
212-.64555 .78812 (212*2π)/4552 weeks
213-.37979 -.50971 (213*2π)/4552 weeks
214.37282 -.26402 (214*2π)/4552 weeks
215.22876 .27494 (215*2π)/4552 weeks
216-.29342 .27856 (216*2π)/4552 weeks
217-.34677 -.17111 (217*2π)/4552 weeks
218.28184 -.61431 (218*2π)/4552 weeks
2191.04833 -.1636 (219*2π)/4552 weeks
220.48007 1.50776 (220*2π)/4552 weeks
221-1.90838 .16147 (221*2π)/4552 weeks
222.56773 -1.64309 (222*2π)/4552 weeks
223.85565 .89778 (223*2π)/4552 weeks
224-1.0513 .47632 (224*2π)/4552 weeks
225-.06098 -1.29041 (225*2π)/4552 weeks
2261.308 .22958 (226*2π)/4552 weeks
227-.67103 1.04107 (227*2π)/4552 weeks
228-.67103 -1.04107 (228*2π)/4552 weeks
2291.308 -.22958 (229*2π)/4552 weeks
230-.06098 1.29041 (230*2π)/4552 weeks
231-1.0513 -.47632 (231*2π)/4552 weeks
232.85565 -.89778 (232*2π)/4552 weeks
233.56773 1.64309 (233*2π)/4552 weeks
234-1.90838 -.16147 (234*2π)/4552 weeks
235.48007 -1.50776 (235*2π)/4552 weeks
2361.04833 .1636 (236*2π)/4552 weeks
237.28184 .61431 (237*2π)/4552 weeks
238-.34677 .17111 (238*2π)/4552 weeks
239-.29342 -.27856 (239*2π)/4552 weeks
240.22876 -.27494 (240*2π)/4552 weeks
241.37282 .26402 (241*2π)/4552 weeks
242-.37979 .50971 (242*2π)/4552 weeks
243-.64555 -.78812 (243*2π)/4552 weeks
2441.01976 -.80467 (244*2π)/4552 weeks
245.12804 .85545 (245*2π)/4552 weeks
246-.43719 -.7074 (246*2π)/4552 weeks
247.57048 -.28846 (247*2π)/4552 weeks
248.66829 .34598 (248*2π)/4552 weeks
249-.22245 .53342 (249*2π)/4552 weeks
250-.03231 -.57011 (250*2π)/4552 weeks
251.7525 .60901 (251*2π)/4552 weeks
252-.68448 .66199 (252*2π)/4552 weeks
253-.66951 -1.15706 (253*2π)/4552 weeks
2541.3835 -.58341 (254*2π)/4552 weeks
255.60322 1.69005 (255*2π)/4552 weeks
256-1.48212 .30177 (256*2π)/4552 weeks
257.2085 -1.25007 (257*2π)/4552 weeks
2581.51988 .79848 (258*2π)/4552 weeks
259-.90115 1.38114 (259*2π)/4552 weeks
260-.74876 -.5356 (260*2π)/4552 weeks
261.03015 -.54206 (261*2π)/4552 weeks
262.73573 .37177 (262*2π)/4552 weeks
263-1.11376 .68653 (263*2π)/4552 weeks
264-.569 -1.13954 (264*2π)/4552 weeks
265.61897 -.45445 (265*2π)/4552 weeks
266.59292 .52452 (266*2π)/4552 weeks
267-.878 .24441 (267*2π)/4552 weeks
268.16452 -.83801 (268*2π)/4552 weeks
269.63547 .25667 (269*2π)/4552 weeks
270-.50829 .46455 (270*2π)/4552 weeks
271-.5374 -.3425 (271*2π)/4552 weeks
272.23182 -.95714 (272*2π)/4552 weeks
2731.41487 .25482 (273*2π)/4552 weeks
274-.3175 1.22219 (274*2π)/4552 weeks
275-1.03995 -.10038 (275*2π)/4552 weeks
276.21639 -1.20195 (276*2π)/4552 weeks
2771.16757 .68992 (277*2π)/4552 weeks
278-1.18146 .86522 (278*2π)/4552 weeks
279-.17078 -1.37579 (279*2π)/4552 weeks
2801.20083 .07036 (280*2π)/4552 weeks
281-.14358 1.1847 (281*2π)/4552 weeks
282-.99288 .15753 (282*2π)/4552 weeks
283.16756 -.92193 (283*2π)/4552 weeks
284.55965 .43006 (284*2π)/4552 weeks
285-.89434 -.02447 (285*2π)/4552 weeks
286.24357 -.88095 (286*2π)/4552 weeks
287.41934 .31144 (287*2π)/4552 weeks
288-.12544 .02721 (288*2π)/4552 weeks
289-.21138 -.1504 (289*2π)/4552 weeks
290.45288 -.1758 (290*2π)/4552 weeks
291.58822 .30659 (291*2π)/4552 weeks
292-.12148 .90173 (292*2π)/4552 weeks
293-.90553 -.00306 (293*2π)/4552 weeks
294.26929 -.94824 (294*2π)/4552 weeks
295.69278 .21642 (295*2π)/4552 weeks
296-.49692 .53248 (296*2π)/4552 weeks
297-.33423 -.68282 (297*2π)/4552 weeks
298.68196 -.2145 (298*2π)/4552 weeks
299-.12409 .9883 (299*2π)/4552 weeks
300-.75254 -.09777 (300*2π)/4552 weeks
301.35797 -.17351 (301*2π)/4552 weeks
302-.25021 .02291 (302*2π)/4552 weeks
303.13312 .05488 (303*2π)/4552 weeks
304.01396 -.36376 (304*2π)/4551 weeks
305.05971 .23043 (305*2π)/4551 weeks
306-.44369 -.0218 (306*2π)/4551 weeks
307-.10988 .44105 (307*2π)/4551 weeks
308-.74735 -.44514 (308*2π)/4551 weeks
309.2956 -.49768 (309*2π)/4551 weeks
310.49549 .4144 (310*2π)/4551 weeks
311-.78359 .27744 (311*2π)/4551 weeks
312-.29398 -1.35665 (312*2π)/4551 weeks
3131.17319 -.23322 (313*2π)/4551 weeks
314.14061 1.05577 (314*2π)/4551 weeks
315-1.41846 -.47565 (315*2π)/4551 weeks
3161.02369 -.88274 (316*2π)/4551 weeks
317.36578 1.29418 (317*2π)/4551 weeks
318-1.5912 .11725 (318*2π)/4551 weeks
319.17963 -1.62626 (319*2π)/4551 weeks
3201.33832 .3897 (320*2π)/4551 weeks
321-.6342 1.44668 (321*2π)/4551 weeks
322-1.74011 -1.06782 (322*2π)/4551 weeks
3231.13457 -1.2577 (323*2π)/4551 weeks
3241.14106 1.00856 (324*2π)/4551 weeks
325-1.23073 .65393 (325*2π)/4551 weeks
326-.38009 -1.0199 (326*2π)/4551 weeks
327.47219 -.55685 (327*2π)/4551 weeks
328.30512 .38577 (328*2π)/4551 weeks
329-.15686 .21098 (329*2π)/4551 weeks
330.1226 -.69179 (330*2π)/4551 weeks
331.85111 -.00148 (331*2π)/4551 weeks
332.58058 .79321 (332*2π)/4551 weeks
333-.91973 .47304 (333*2π)/4551 weeks
334-.02744 -1.0058 (334*2π)/4551 weeks
335.84946 .21172 (335*2π)/4551 weeks
336-.36828 1.13024 (336*2π)/4551 weeks
337-1.56013 -1.05542 (337*2π)/4551 weeks
3381.95068 -1.0602 (338*2π)/4551 weeks
339.5488 2.50576 (339*2π)/4551 weeks
340-2.74722 -.17354 (340*2π)/4551 weeks
341.87587 -2.90326 (341*2π)/4551 weeks
3422.71219 1.26445 (342*2π)/4551 weeks
343-2.06377 2.18701 (343*2π)/4551 weeks
344-1.12595 -2.25103 (344*2π)/4551 weeks
3452.05265 -.35878 (345*2π)/4551 weeks
346.52916 1.95868 (346*2π)/4551 weeks
347-1.55318 .55348 (347*2π)/4551 weeks
348.13808 -1.15471 (348*2π)/4551 weeks
349.52252 -.15734 (349*2π)/4551 weeks
350-.1793 .50378 (350*2π)/4551 weeks
351-.562 -.07696 (351*2π)/4551 weeks
352.25042 -1.22179 (352*2π)/4551 weeks
353.74263 .81417 (353*2π)/4551 weeks
354-.49593 .38568 (354*2π)/4551 weeks
355-.20993 -.31322 (355*2π)/4551 weeks
356.38294 -.32895 (356*2π)/4551 weeks
357.30459 .83466 (357*2π)/4551 weeks
358-1.25111 .13615 (358*2π)/4551 weeks
359-.39191 -1.6411 (359*2π)/4551 weeks
3601.46104 -.39233 (360*2π)/4551 weeks
361-.40136 1.45639 (361*2π)/4551 weeks
362-1.554 -1.737 (362*2π)/4551 weeks
3631.34044 -1.28244 (363*2π)/4551 weeks
3641.76013 .99706 (364*2π)/4551 weeks
365-1.13505 1.00345 (365*2π)/4551 weeks
366-.20509 -.92602 (366*2π)/4551 weeks
367.69741 .24337 (367*2π)/4551 weeks
368.371 1.19514 (368*2π)/4551 weeks
369-1.43286 .17438 (369*2π)/4551 weeks
370.51656 -1.4287 (370*2π)/4551 weeks
3711.61506 .07723 (371*2π)/4551 weeks
372-.80179 1.81853 (372*2π)/4551 weeks
373-2.36622 -1.61819 (373*2π)/4551 weeks
3741.66129 -1.73306 (374*2π)/4551 weeks
3751.58711 1.33839 (375*2π)/4551 weeks
376-.94351 1.38007 (376*2π)/4551 weeks
377-.99885 -.92674 (377*2π)/4551 weeks
3782.11587 .21469 (378*2π)/4551 weeks
379-.3927 2.37589 (379*2π)/4551 weeks
380-2.96195 .43047 (380*2π)/4551 weeks
381-.43135 -2.99429 (381*2π)/4551 weeks
3823.05156 .01747 (382*2π)/4551 weeks
383-1.24961 2.81586 (383*2π)/4551 weeks
384-3.27691 -2.98498 (384*2π)/4551 weeks
3854.40938 -2.33184 (385*2π)/4551 weeks
386.75294 5.09347 (386*2π)/4551 weeks
387-4.96102 -.57908 (387*2π)/4551 weeks
3881.9978 -4.05954 (388*2π)/4551 weeks
3892.5446 2.74415 (389*2π)/4551 weeks
390-3.37526 1.75986 (390*2π)/4551 weeks
391-1.73213 -4.42459 (391*2π)/4551 weeks
3923.66487 -1.1952 (392*2π)/4551 weeks
393-.02642 3.38366 (393*2π)/4551 weeks
394-2.22652 -.12232 (394*2π)/4551 weeks
395-.74048 -2.33336 (395*2π)/4551 weeks
3961.36974 .09235 (396*2π)/4551 weeks
397-1.10968 .78899 (397*2π)/4551 weeks
398-.29335 -.74374 (398*2π)/4551 weeks
399-1.38697 -1.71602 (399*2π)/4551 weeks
4003.85424 -1.28836 (400*2π)/4551 weeks
401.47614 3.48409 (401*2π)/4551 weeks
402-2.62329 .29609 (402*2π)/4551 weeks
403-.00341 -2.9826 (403*2π)/4551 weeks
4043.56873 .30242 (404*2π)/4551 weeks
405-1.39441 4.59402 (405*2π)/4551 weeks
406-4.42694 -3.58691 (406*2π)/4551 weeks
4074.39927 -.96462 (407*2π)/4551 weeks
4081.23921 2.76223 (408*2π)/4551 weeks
409-2.80545 1.30117 (409*2π)/4551 weeks
410-.90134 -4.77918 (410*2π)/4551 weeks
4114.15272 1.18103 (411*2π)/4551 weeks
412-3.54273 2.07044 (412*2π)/4551 weeks
413-.85117 -3.52717 (413*2π)/4551 weeks
4142.62427 .3611 (414*2π)/4551 weeks
415-1.57449 .37112 (415*2π)/4551 weeks
4161.45884 -1.95771 (416*2π)/4551 weeks
417.61011 .34958 (417*2π)/4551 weeks
418.30183 -.24174 (418*2π)/4551 weeks
419.09823 -.92364 (419*2π)/4551 weeks
4201.32654 1.46577 (420*2π)/4551 weeks
421-1.97596 -.60041 (421*2π)/4551 weeks
4224.77014 -2.01508 (422*2π)/4551 weeks
4231.25017 6.08056 (423*2π)/4551 weeks
424-5.86368 -.4725 (424*2π)/4551 weeks
4253.72504 -5.11107 (425*2π)/4551 weeks
4262.57959 6.53824 (426*2π)/4551 weeks
427-7.23132 2.45224 (427*2π)/4551 weeks
428-2.3451 -6.89285 (428*2π)/4551 weeks
4296.28269 -1.15931 (429*2π)/4551 weeks
430-.92443 8.20591 (430*2π)/4551 weeks
431-9.06063 -2.86212 (431*2π)/4551 weeks
4324.2443 -8.06037 (432*2π)/4551 weeks
4336.03493 4.26421 (433*2π)/4551 weeks
434-7.55795 4.90789 (434*2π)/4551 weeks
435-4.53957 -6.40725 (435*2π)/4551 weeks
4367.6885 -7.39835 (436*2π)/4551 weeks
4374.24295 10.38972 (437*2π)/4551 weeks
438-6.99749 -2.31362 (438*2π)/4551 weeks
4392.90012 -2.02784 (439*2π)/4551 weeks
440-2.77188 1.59309 (440*2π)/4551 weeks
441-1.40807 -4.04358 (441*2π)/4551 weeks
442.39435 -.48109 (442*2π)/4551 weeks
443-6.74332 -1.74487 (443*2π)/4551 weeks
4446.40209 -5.40223 (444*2π)/4551 weeks
445-2.74783 6.91214 (445*2π)/4551 weeks
446-4.02301 -4.7949 (446*2π)/4551 weeks
4473.51398 -6.38815 (447*2π)/4551 weeks
44814.81272 -.9688 (448*2π)/4551 weeks
449-12.62064 22.6793 (449*2π)/4551 weeks
450-25.03514 -25.8572 (450*2π)/4551 weeks
45119.73321 -19.07533 (451*2π)/4551 weeks
45221.09374 20.8656 (452*2π)/4551 weeks
453-41.69223 32.08881 (453*2π)/4551 weeks



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