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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 (10.6887*cosine), 19 weeks (9.3004*sine), and 23 weeks (8.9792*sine).

AGQ (ProShares Ultra Silver ETF) has an average price of 119.97 (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 11/6/2017 for AGQ (ProShares Ultra Silver ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0119.9693   0 
1-39.74085 115.0206 (1*2π)/467467 weeks
2-45.57077 -28.83585 (2*2π)/467234 weeks
317.67282 -23.18128 (3*2π)/467156 weeks
421.01116 15.97125 (4*2π)/467117 weeks
5-17.65809 30.379 (5*2π)/46793 weeks
6-19.18495 -18.65748 (6*2π)/46778 weeks
716.08211 -5.33239 (7*2π)/46767 weeks
84.02327 5.41439 (8*2π)/46758 weeks
9-3.01233 5.76594 (9*2π)/46752 weeks
10-6.45599 -3.13333 (10*2π)/46747 weeks
117.7531 .66974 (11*2π)/46742 weeks
12-4.56596 7.05498 (12*2π)/46739 weeks
13.29779 -1.12354 (13*2π)/46736 weeks
141.13187 2.3827 (14*2π)/46733 weeks
15-3.6484 .19803 (15*2π)/46731 weeks
161.72908 -2.24439 (16*2π)/46729 weeks
17-2.02002 4.60669 (17*2π)/46727 weeks
18-6.29979 -7.8129 (18*2π)/46726 weeks
1910.68868 -1.47291 (19*2π)/46725 weeks
20-.06758 8.9792 (20*2π)/46723 weeks
21-7.68649 3.08679 (21*2π)/46722 weeks
22-1.02846 -8.13109 (22*2π)/46721 weeks
237.29926 .49495 (23*2π)/46720 weeks
24-2.03825 9.30036 (24*2π)/46719 weeks
25-8.6343 -2.51477 (25*2π)/46719 weeks
263.63764 -6.24585 (26*2π)/46718 weeks
274.76786 4.14474 (27*2π)/46717 weeks
28-5.17525 5.16199 (28*2π)/46717 weeks
29-5.54066 -4.8719 (29*2π)/46716 weeks
304.80523 -4.68209 (30*2π)/46716 weeks
31.85321 5.88452 (31*2π)/46715 weeks
32-5.76288 -1.44391 (32*2π)/46715 weeks
332.58584 -5.2428 (33*2π)/46714 weeks
343.71868 3.0119 (34*2π)/46714 weeks
35-1.81682 .07864 (35*2π)/46713 weeks
361.56581 -1.15543 (36*2π)/46713 weeks
37.01829 .83089 (37*2π)/46713 weeks
38.29512 .27554 (38*2π)/46712 weeks
39.61506 -.30497 (39*2π)/46712 weeks
401.54631 1.82988 (40*2π)/46712 weeks
41-1.59205 -.10745 (41*2π)/46711 weeks
422.33352 -.74827 (42*2π)/46711 weeks
43-.17296 3.513 (43*2π)/46711 weeks
44-3.77644 -.95184 (44*2π)/46711 weeks
453.43241 -2.46008 (45*2π)/46710 weeks
46.92488 4.57857 (46*2π)/46710 weeks
47-3.34273 -.57118 (47*2π)/46710 weeks
48.0119 -3.11854 (48*2π)/46710 weeks
493.32866 -.89734 (49*2π)/46710 weeks
50-1.54489 5.51162 (50*2π)/4679 weeks
51-3.88254 -3.07216 (51*2π)/4679 weeks
523.0477 -2.27498 (52*2π)/4679 weeks
531.72822 2.56867 (53*2π)/4679 weeks
54-2.3459 1.36749 (54*2π)/4679 weeks
55-1.5924 -2.40485 (55*2π)/4678 weeks
563.46435 -1.60041 (56*2π)/4678 weeks
57.77117 3.44931 (57*2π)/4678 weeks
58-.52557 .36408 (58*2π)/4678 weeks
59-.98794 .69937 (59*2π)/4678 weeks
60.41691 -1.09748 (60*2π)/4678 weeks
611.47632 1.31497 (61*2π)/4678 weeks
62-1.66422 1.2358 (62*2π)/4678 weeks
63-2.27326 -1.20721 (63*2π)/4677 weeks
642.34717 -2.81938 (64*2π)/4677 weeks
652.69264 2.8104 (65*2π)/4677 weeks
66-3.64335 2.64005 (66*2π)/4677 weeks
67-2.22933 -2.96109 (67*2π)/4677 weeks
683.4329 -1.21189 (68*2π)/4677 weeks
69-.02451 4.63801 (69*2π)/4677 weeks
70-4.79426 -1.1675 (70*2π)/4677 weeks
712.27822 -4.42106 (71*2π)/4677 weeks
723.41264 3.38065 (72*2π)/4676 weeks
73-3.71498 2.01707 (73*2π)/4676 weeks
74-.73474 -2.81158 (74*2π)/4676 weeks
752.91158 .47177 (75*2π)/4676 weeks
76-.65137 2.94984 (76*2π)/4676 weeks
77-2.86869 -.45869 (77*2π)/4676 weeks
78-.40733 -2.26997 (78*2π)/4676 weeks
792.0476 -.30022 (79*2π)/4676 weeks
80-.87811 1.09006 (80*2π)/4676 weeks
81-1.06209 -1.11527 (81*2π)/4676 weeks
821.29976 -1.4152 (82*2π)/4676 weeks
831.89999 1.39754 (83*2π)/4676 weeks
84-1.67398 2.29517 (84*2π)/4676 weeks
85-1.24498 -1.50704 (85*2π)/4675 weeks
861.63245 -.77295 (86*2π)/4675 weeks
87.88315 .96758 (87*2π)/4675 weeks
88-1.42841 .55769 (88*2π)/4675 weeks
89-.3246 -1.25378 (89*2π)/4675 weeks
90.58436 -.23717 (90*2π)/4675 weeks
91.55547 .84329 (91*2π)/4675 weeks
92-1.08724 .07566 (92*2π)/4675 weeks
93.7716 -1.74759 (93*2π)/4675 weeks
941.82854 .59034 (94*2π)/4675 weeks
95.28449 2.13986 (95*2π)/4675 weeks
96-1.70937 -.57221 (96*2π)/4675 weeks
971.09889 -.98583 (97*2π)/4675 weeks
98.82727 1.25732 (98*2π)/4675 weeks
99-1.21669 .81664 (99*2π)/4675 weeks
100-.82104 -.83493 (100*2π)/4675 weeks
101.57017 -.28393 (101*2π)/4675 weeks
102.04215 .40268 (102*2π)/4675 weeks
103-.4254 .21872 (103*2π)/4675 weeks
104-.2815 -.62792 (104*2π)/4674 weeks
1051.21965 -.23386 (105*2π)/4674 weeks
106-.37511 .96061 (106*2π)/4674 weeks
107-.49448 -.06091 (107*2π)/4674 weeks
108.06822 -.5511 (108*2π)/4674 weeks
109.41119 .25431 (109*2π)/4674 weeks
110-.34488 1.29746 (110*2π)/4674 weeks
111-1.36044 -.8414 (111*2π)/4674 weeks
112.9036 -1.76997 (112*2π)/4674 weeks
1131.98869 .66403 (113*2π)/4674 weeks
114-1.3856 2.02568 (114*2π)/4674 weeks
115-1.82529 -2.33311 (115*2π)/4674 weeks
1162.67136 -1.15632 (116*2π)/4674 weeks
117.87555 2.80792 (117*2π)/4674 weeks
118-2.68503 .31324 (118*2π)/4674 weeks
119.24666 -2.50925 (119*2π)/4674 weeks
1202.03003 .72935 (120*2π)/4674 weeks
121-1.31502 1.40608 (121*2π)/4674 weeks
122-.6459 -1.03671 (122*2π)/4674 weeks
123.76255 -.40575 (123*2π)/4674 weeks
124.33401 .89567 (124*2π)/4674 weeks
125-1.0029 -.0813 (125*2π)/4674 weeks
126.2448 -.99693 (126*2π)/4674 weeks
127.72939 -.19426 (127*2π)/4674 weeks
128.40677 .64032 (128*2π)/4674 weeks
129-.41878 .08698 (129*2π)/4674 weeks
130.02126 -.17451 (130*2π)/4674 weeks
131.70541 .33242 (131*2π)/4674 weeks
132.17212 .90263 (132*2π)/4674 weeks
133-1.18748 .37741 (133*2π)/4674 weeks
134.0261 -1.41042 (134*2π)/4673 weeks
1351.50625 .28003 (135*2π)/4673 weeks
136-.15696 1.97861 (136*2π)/4673 weeks
137-1.63321 -.48577 (137*2π)/4673 weeks
138.56202 -1.30226 (138*2π)/4673 weeks
1391.36821 .62822 (139*2π)/4673 weeks
140-.85737 1.33681 (140*2π)/4673 weeks
141-1.01678 -.98382 (141*2π)/4673 weeks
1421.11193 -.7672 (142*2π)/4673 weeks
143.31977 1.30998 (143*2π)/4673 weeks
144-1.25848 -.50986 (144*2π)/4673 weeks
145.56058 -.90611 (145*2π)/4673 weeks
1461.00851 .62278 (146*2π)/4673 weeks
147-.76762 1.03265 (147*2π)/4673 weeks
148-.60514 -.45594 (148*2π)/4673 weeks
149.57275 -.16529 (149*2π)/4673 weeks
150.21789 .57551 (150*2π)/4673 weeks
151-.7876 .26602 (151*2π)/4673 weeks
152-.00182 -.37415 (152*2π)/4673 weeks
153-.45513 -.06634 (153*2π)/4673 weeks
154.05696 -.22236 (154*2π)/4673 weeks
155-.01779 .35827 (155*2π)/4673 weeks
156.11964 -.05476 (156*2π)/4673 weeks
157-.25058 .00621 (157*2π)/4673 weeks
158.34372 .09288 (158*2π)/4673 weeks
159-.70926 .21772 (159*2π)/4673 weeks
160-.31303 -.87102 (160*2π)/4673 weeks
161.76222 .07456 (161*2π)/4673 weeks
162-.06566 .73044 (162*2π)/4673 weeks
163-.59935 -.31352 (163*2π)/4673 weeks
164.58626 -.48095 (164*2π)/4673 weeks
165.58646 .62002 (165*2π)/4673 weeks
166-.86943 .35723 (166*2π)/4673 weeks
167-.51053 -.7687 (167*2π)/4673 weeks
168.46415 -.53079 (168*2π)/4673 weeks
169.45022 .05998 (169*2π)/4673 weeks
170.00164 .44178 (170*2π)/4673 weeks
171-.01843 .02323 (171*2π)/4673 weeks
172.05991 -.30998 (172*2π)/4673 weeks
173.73932 .33105 (173*2π)/4673 weeks
174-.51453 .68263 (174*2π)/4673 weeks
175-.29269 -.75618 (175*2π)/4673 weeks
176.64516 .24533 (176*2π)/4673 weeks
177-.73223 .77004 (177*2π)/4673 weeks
178-.75352 -.57874 (178*2π)/4673 weeks
179.65004 -1.02995 (179*2π)/4673 weeks
1801.04973 .61965 (180*2π)/4673 weeks
181-1.03684 .93994 (181*2π)/4673 weeks
182-.37401 -1.34538 (182*2π)/4673 weeks
1831.30568 .04556 (183*2π)/4673 weeks
184-.34343 1.06468 (184*2π)/4673 weeks
185-.98959 -.25937 (185*2π)/4673 weeks
186.12299 -1.31066 (186*2π)/4673 weeks
1871.33962 .19398 (187*2π)/4672 weeks
188.02922 .88413 (188*2π)/4672 weeks
189-.52967 .23064 (189*2π)/4672 weeks
190-.38035 -.57819 (190*2π)/4672 weeks
191.65422 -.15573 (191*2π)/4672 weeks
192.05763 .8366 (192*2π)/4672 weeks
193-.82659 -.31583 (193*2π)/4672 weeks
194.59377 -.49559 (194*2π)/4672 weeks
195.60982 .43174 (195*2π)/4672 weeks
196-.47653 1.12891 (196*2π)/4672 weeks
197-1.15278 -.5498 (197*2π)/4672 weeks
198.68248 -.53565 (198*2π)/4672 weeks
199.13437 .5105 (199*2π)/4672 weeks
200-.53656 .53481 (200*2π)/4672 weeks
201-1.15876 -1.04047 (201*2π)/4672 weeks
2021.15328 -1.26738 (202*2π)/4672 weeks
203.69891 1.0895 (203*2π)/4672 weeks
204-1.33188 .36266 (204*2π)/4672 weeks
205-.16477 -1.68264 (205*2π)/4672 weeks
2061.61305 -.07262 (206*2π)/4672 weeks
207.149 1.34143 (207*2π)/4672 weeks
208-.98197 -.24387 (208*2π)/4672 weeks
209.2041 -.95882 (209*2π)/4672 weeks
210.62206 .39316 (210*2π)/4672 weeks
211-.45921 -.12927 (211*2π)/4672 weeks
212.32667 -.63439 (212*2π)/4672 weeks
213.66481 .05986 (213*2π)/4672 weeks
214.38847 .63396 (214*2π)/4672 weeks
215-.70639 -.26067 (215*2π)/4672 weeks
216.9741 -.49896 (216*2π)/4672 weeks
217.16185 1.11295 (217*2π)/4672 weeks
218-.90975 .15712 (218*2π)/4672 weeks
219-.05488 -.50016 (219*2π)/4672 weeks
220.39013 -.01349 (220*2π)/4672 weeks
221.08318 .33614 (221*2π)/4672 weeks
222-.38047 .08281 (222*2π)/4672 weeks
223-.36498 -.35713 (223*2π)/4672 weeks
224.38908 -.50974 (224*2π)/4672 weeks
2251.12236 .18307 (225*2π)/4672 weeks
226-.01975 1.66426 (226*2π)/4672 weeks
227-1.8149 -.42365 (227*2π)/4672 weeks
228.95759 -1.31682 (228*2π)/4672 weeks
229.5953 1.00484 (229*2π)/4672 weeks
230-1.10862 .28258 (230*2π)/4672 weeks
231.08537 -1.25663 (231*2π)/4672 weeks
2321.25128 .3148 (232*2π)/4672 weeks
233-.68423 .99538 (233*2π)/4672 weeks
234-.68423 -.99538 (234*2π)/4672 weeks
2351.25128 -.3148 (235*2π)/4672 weeks
236.08537 1.25663 (236*2π)/4672 weeks
237-1.10862 -.28258 (237*2π)/4672 weeks
238.5953 -1.00484 (238*2π)/4672 weeks
239.95759 1.31682 (239*2π)/4672 weeks
240-1.8149 .42365 (240*2π)/4672 weeks
241-.01975 -1.66426 (241*2π)/4672 weeks
2421.12236 -.18307 (242*2π)/4672 weeks
243.38908 .50974 (243*2π)/4672 weeks
244-.36498 .35713 (244*2π)/4672 weeks
245-.38047 -.08281 (245*2π)/4672 weeks
246.08318 -.33614 (246*2π)/4672 weeks
247.39013 .01349 (247*2π)/4672 weeks
248-.05488 .50016 (248*2π)/4672 weeks
249-.90975 -.15712 (249*2π)/4672 weeks
250.16185 -1.11295 (250*2π)/4672 weeks
251.9741 .49896 (251*2π)/4672 weeks
252-.70639 .26067 (252*2π)/4672 weeks
253.38847 -.63396 (253*2π)/4672 weeks
254.66481 -.05986 (254*2π)/4672 weeks
255.32667 .63439 (255*2π)/4672 weeks
256-.45921 .12927 (256*2π)/4672 weeks
257.62206 -.39316 (257*2π)/4672 weeks
258.2041 .95882 (258*2π)/4672 weeks
259-.98197 .24387 (259*2π)/4672 weeks
260.149 -1.34143 (260*2π)/4672 weeks
2611.61305 .07262 (261*2π)/4672 weeks
262-.16477 1.68264 (262*2π)/4672 weeks
263-1.33188 -.36266 (263*2π)/4672 weeks
264.69891 -1.0895 (264*2π)/4672 weeks
2651.15328 1.26738 (265*2π)/4672 weeks
266-1.15876 1.04047 (266*2π)/4672 weeks
267-.53656 -.53481 (267*2π)/4672 weeks
268.13437 -.5105 (268*2π)/4672 weeks
269.68248 .53565 (269*2π)/4672 weeks
270-1.15278 .5498 (270*2π)/4672 weeks
271-.47653 -1.12891 (271*2π)/4672 weeks
272.60982 -.43174 (272*2π)/4672 weeks
273.59377 .49559 (273*2π)/4672 weeks
274-.82659 .31583 (274*2π)/4672 weeks
275.05763 -.8366 (275*2π)/4672 weeks
276.65422 .15573 (276*2π)/4672 weeks
277-.38035 .57819 (277*2π)/4672 weeks
278-.52967 -.23064 (278*2π)/4672 weeks
279.02922 -.88413 (279*2π)/4672 weeks
2801.33962 -.19398 (280*2π)/4672 weeks
281.12299 1.31066 (281*2π)/4672 weeks
282-.98959 .25937 (282*2π)/4672 weeks
283-.34343 -1.06468 (283*2π)/4672 weeks
2841.30568 -.04556 (284*2π)/4672 weeks
285-.37401 1.34538 (285*2π)/4672 weeks
286-1.03684 -.93994 (286*2π)/4672 weeks
2871.04973 -.61965 (287*2π)/4672 weeks
288.65004 1.02995 (288*2π)/4672 weeks
289-.75352 .57874 (289*2π)/4672 weeks
290-.73223 -.77004 (290*2π)/4672 weeks
291.64516 -.24533 (291*2π)/4672 weeks
292-.29269 .75618 (292*2π)/4672 weeks
293-.51453 -.68263 (293*2π)/4672 weeks
294.73932 -.33105 (294*2π)/4672 weeks
295.05991 .30998 (295*2π)/4672 weeks
296-.01843 -.02323 (296*2π)/4672 weeks
297.00164 -.44178 (297*2π)/4672 weeks
298.45022 -.05998 (298*2π)/4672 weeks
299.46415 .53079 (299*2π)/4672 weeks
300-.51053 .7687 (300*2π)/4672 weeks
301-.86943 -.35723 (301*2π)/4672 weeks
302.58646 -.62002 (302*2π)/4672 weeks
303.58626 .48095 (303*2π)/4672 weeks
304-.59935 .31352 (304*2π)/4672 weeks
305-.06566 -.73044 (305*2π)/4672 weeks
306.76222 -.07456 (306*2π)/4672 weeks
307-.31303 .87102 (307*2π)/4672 weeks
308-.70926 -.21772 (308*2π)/4672 weeks
309.34372 -.09288 (309*2π)/4672 weeks
310-.25058 -.00621 (310*2π)/4672 weeks
311.11964 .05476 (311*2π)/4672 weeks
312-.01779 -.35827 (312*2π)/4671 weeks
313.05696 .22236 (313*2π)/4671 weeks
314-.45513 .06634 (314*2π)/4671 weeks
315-.00182 .37415 (315*2π)/4671 weeks
316-.7876 -.26602 (316*2π)/4671 weeks
317.21789 -.57551 (317*2π)/4671 weeks
318.57275 .16529 (318*2π)/4671 weeks
319-.60514 .45594 (319*2π)/4671 weeks
320-.76762 -1.03265 (320*2π)/4671 weeks
3211.00851 -.62278 (321*2π)/4671 weeks
322.56058 .90611 (322*2π)/4671 weeks
323-1.25848 .50986 (323*2π)/4671 weeks
324.31977 -1.30998 (324*2π)/4671 weeks
3251.11193 .7672 (325*2π)/4671 weeks
326-1.01678 .98382 (326*2π)/4671 weeks
327-.85737 -1.33681 (327*2π)/4671 weeks
3281.36821 -.62822 (328*2π)/4671 weeks
329.56202 1.30226 (329*2π)/4671 weeks
330-1.63321 .48577 (330*2π)/4671 weeks
331-.15696 -1.97861 (331*2π)/4671 weeks
3321.50625 -.28003 (332*2π)/4671 weeks
333.0261 1.41042 (333*2π)/4671 weeks
334-1.18748 -.37741 (334*2π)/4671 weeks
335.17212 -.90263 (335*2π)/4671 weeks
336.70541 -.33242 (336*2π)/4671 weeks
337.02126 .17451 (337*2π)/4671 weeks
338-.41878 -.08698 (338*2π)/4671 weeks
339.40677 -.64032 (339*2π)/4671 weeks
340.72939 .19426 (340*2π)/4671 weeks
341.2448 .99693 (341*2π)/4671 weeks
342-1.0029 .0813 (342*2π)/4671 weeks
343.33401 -.89567 (343*2π)/4671 weeks
344.76255 .40575 (344*2π)/4671 weeks
345-.6459 1.03671 (345*2π)/4671 weeks
346-1.31502 -1.40608 (346*2π)/4671 weeks
3472.03003 -.72935 (347*2π)/4671 weeks
348.24666 2.50925 (348*2π)/4671 weeks
349-2.68503 -.31324 (349*2π)/4671 weeks
350.87555 -2.80792 (350*2π)/4671 weeks
3512.67136 1.15632 (351*2π)/4671 weeks
352-1.82529 2.33311 (352*2π)/4671 weeks
353-1.3856 -2.02568 (353*2π)/4671 weeks
3541.98869 -.66403 (354*2π)/4671 weeks
355.9036 1.76997 (355*2π)/4671 weeks
356-1.36044 .8414 (356*2π)/4671 weeks
357-.34488 -1.29746 (357*2π)/4671 weeks
358.41119 -.25431 (358*2π)/4671 weeks
359.06822 .5511 (359*2π)/4671 weeks
360-.49448 .06091 (360*2π)/4671 weeks
361-.37511 -.96061 (361*2π)/4671 weeks
3621.21965 .23386 (362*2π)/4671 weeks
363-.2815 .62792 (363*2π)/4671 weeks
364-.4254 -.21872 (364*2π)/4671 weeks
365.04215 -.40268 (365*2π)/4671 weeks
366.57017 .28393 (366*2π)/4671 weeks
367-.82104 .83493 (367*2π)/4671 weeks
368-1.21669 -.81664 (368*2π)/4671 weeks
369.82727 -1.25732 (369*2π)/4671 weeks
3701.09889 .98583 (370*2π)/4671 weeks
371-1.70937 .57221 (371*2π)/4671 weeks
372.28449 -2.13986 (372*2π)/4671 weeks
3731.82854 -.59034 (373*2π)/4671 weeks
374.7716 1.74759 (374*2π)/4671 weeks
375-1.08724 -.07566 (375*2π)/4671 weeks
376.55547 -.84329 (376*2π)/4671 weeks
377.58436 .23717 (377*2π)/4671 weeks
378-.3246 1.25378 (378*2π)/4671 weeks
379-1.42841 -.55769 (379*2π)/4671 weeks
380.88315 -.96758 (380*2π)/4671 weeks
3811.63245 .77295 (381*2π)/4671 weeks
382-1.24498 1.50704 (382*2π)/4671 weeks
383-1.67398 -2.29517 (383*2π)/4671 weeks
3841.89999 -1.39754 (384*2π)/4671 weeks
3851.29976 1.4152 (385*2π)/4671 weeks
386-1.06209 1.11527 (386*2π)/4671 weeks
387-.87811 -1.09006 (387*2π)/4671 weeks
3882.0476 .30022 (388*2π)/4671 weeks
389-.40733 2.26997 (389*2π)/4671 weeks
390-2.86869 .45869 (390*2π)/4671 weeks
391-.65137 -2.94984 (391*2π)/4671 weeks
3922.91158 -.47177 (392*2π)/4671 weeks
393-.73474 2.81158 (393*2π)/4671 weeks
394-3.71498 -2.01707 (394*2π)/4671 weeks
3953.41264 -3.38065 (395*2π)/4671 weeks
3962.27822 4.42106 (396*2π)/4671 weeks
397-4.79426 1.1675 (397*2π)/4671 weeks
398-.02451 -4.63801 (398*2π)/4671 weeks
3993.4329 1.21189 (399*2π)/4671 weeks
400-2.22933 2.96109 (400*2π)/4671 weeks
401-3.64335 -2.64005 (401*2π)/4671 weeks
4022.69264 -2.8104 (402*2π)/4671 weeks
4032.34717 2.81938 (403*2π)/4671 weeks
404-2.27326 1.20721 (404*2π)/4671 weeks
405-1.66422 -1.2358 (405*2π)/4671 weeks
4061.47632 -1.31497 (406*2π)/4671 weeks
407.41691 1.09748 (407*2π)/4671 weeks
408-.98794 -.69937 (408*2π)/4671 weeks
409-.52557 -.36408 (409*2π)/4671 weeks
410.77117 -3.44931 (410*2π)/4671 weeks
4113.46435 1.60041 (411*2π)/4671 weeks
412-1.5924 2.40485 (412*2π)/4671 weeks
413-2.3459 -1.36749 (413*2π)/4671 weeks
4141.72822 -2.56867 (414*2π)/4671 weeks
4153.0477 2.27498 (415*2π)/4671 weeks
416-3.88254 3.07216 (416*2π)/4671 weeks
417-1.54489 -5.51162 (417*2π)/4671 weeks
4183.32866 .89734 (418*2π)/4671 weeks
419.0119 3.11854 (419*2π)/4671 weeks
420-3.34273 .57118 (420*2π)/4671 weeks
421.92488 -4.57857 (421*2π)/4671 weeks
4223.43241 2.46008 (422*2π)/4671 weeks
423-3.77644 .95184 (423*2π)/4671 weeks
424-.17296 -3.513 (424*2π)/4671 weeks
4252.33352 .74827 (425*2π)/4671 weeks
426-1.59205 .10745 (426*2π)/4671 weeks
4271.54631 -1.82988 (427*2π)/4671 weeks
428.61506 .30497 (428*2π)/4671 weeks
429.29512 -.27554 (429*2π)/4671 weeks
430.01829 -.83089 (430*2π)/4671 weeks
4311.56581 1.15543 (431*2π)/4671 weeks
432-1.81682 -.07864 (432*2π)/4671 weeks
4333.71868 -3.0119 (433*2π)/4671 weeks
4342.58584 5.2428 (434*2π)/4671 weeks
435-5.76288 1.44391 (435*2π)/4671 weeks
436.85321 -5.88452 (436*2π)/4671 weeks
4374.80523 4.68209 (437*2π)/4671 weeks
438-5.54066 4.8719 (438*2π)/4671 weeks
439-5.17525 -5.16199 (439*2π)/4671 weeks
4404.76786 -4.14474 (440*2π)/4671 weeks
4413.63764 6.24585 (441*2π)/4671 weeks
442-8.6343 2.51477 (442*2π)/4671 weeks
443-2.03825 -9.30036 (443*2π)/4671 weeks
4447.29926 -.49495 (444*2π)/4671 weeks
445-1.02846 8.13109 (445*2π)/4671 weeks
446-7.68649 -3.08679 (446*2π)/4671 weeks
447-.06758 -8.9792 (447*2π)/4671 weeks
44810.68868 1.47291 (448*2π)/4671 weeks
449-6.29979 7.8129 (449*2π)/4671 weeks
450-2.02002 -4.60669 (450*2π)/4671 weeks
4511.72908 2.24439 (451*2π)/4671 weeks
452-3.6484 -.19803 (452*2π)/4671 weeks
4531.13187 -2.3827 (453*2π)/4671 weeks
454.29779 1.12354 (454*2π)/4671 weeks
455-4.56596 -7.05498 (455*2π)/4671 weeks
4567.7531 -.66974 (456*2π)/4671 weeks
457-6.45599 3.13333 (457*2π)/4671 weeks
458-3.01233 -5.76594 (458*2π)/4671 weeks
4594.02327 -5.41439 (459*2π)/4671 weeks
46016.08211 5.33239 (460*2π)/4671 weeks
461-19.18495 18.65748 (461*2π)/4671 weeks
462-17.65809 -30.379 (462*2π)/4671 weeks
46321.01116 -15.97125 (463*2π)/4671 weeks
46417.67282 23.18128 (464*2π)/4671 weeks
465-45.57077 28.83585 (465*2π)/4671 weeks



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