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Fourier Analysis of AGQ (ProShares Ultra Silver ETF)


AGQ (ProShares Ultra Silver ETF) appears to have interesting cyclic behaviour every 24 weeks (10.6828*cosine), 26 weeks (10.0679*sine), and 22 weeks (8.6078*cosine).

AGQ (ProShares Ultra Silver ETF) has an average price of 120.71 (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 10/9/2017 for AGQ (ProShares Ultra Silver ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0120.7117   0 
1-41.67434 114.7513 (1*2π)/463463 weeks
2-44.30299 -29.95635 (2*2π)/463232 weeks
318.83319 -22.48075 (3*2π)/463154 weeks
420.62458 16.97188 (4*2π)/463116 weeks
5-20.17949 29.16921 (5*2π)/46393 weeks
6-17.14469 -20.17489 (6*2π)/46377 weeks
716.0162 -3.09702 (7*2π)/46366 weeks
83.9383 5.63223 (8*2π)/46358 weeks
9-3.33966 5.40148 (9*2π)/46351 weeks
10-5.61794 -4.60591 (10*2π)/46346 weeks
117.63362 2.33481 (11*2π)/46342 weeks
12-5.84575 5.57755 (12*2π)/46339 weeks
13.5948 -.39298 (13*2π)/46336 weeks
14.67603 3.22182 (14*2π)/46333 weeks
15-3.3778 -.43671 (15*2π)/46331 weeks
162.74677 -1.12212 (16*2π)/46329 weeks
17-3.53671 4.38898 (17*2π)/46327 weeks
18-3.3325 -10.06793 (18*2π)/46326 weeks
1910.68277 1.75571 (19*2π)/46324 weeks
20-1.95095 8.17969 (20*2π)/46323 weeks
21-8.60776 .80767 (21*2π)/46322 weeks
221.92833 -7.6721 (22*2π)/46321 weeks
237.25208 2.93079 (23*2π)/46320 weeks
24-5.19772 8.07297 (24*2π)/46319 weeks
25-7.03208 -5.3961 (25*2π)/46319 weeks
265.52286 -4.02329 (26*2π)/46318 weeks
272.98413 5.88037 (27*2π)/46317 weeks
28-6.80594 2.96609 (28*2π)/46317 weeks
29-3.22034 -6.56902 (29*2π)/46316 weeks
306.45032 -1.73048 (30*2π)/46315 weeks
31-2.44113 5.13814 (31*2π)/46315 weeks
32-4.55821 -4.35139 (32*2π)/46314 weeks
334.45471 -3.51543 (33*2π)/46314 weeks
34.87565 3.79751 (34*2π)/46314 weeks
35-1.15542 -1.12825 (35*2π)/46313 weeks
361.91943 .11889 (36*2π)/46313 weeks
37-.05265 .13156 (37*2π)/46313 weeks
38.07573 .04932 (38*2π)/46312 weeks
391.10626 -.31591 (39*2π)/46312 weeks
40-.18868 2.43276 (40*2π)/46312 weeks
41-.72641 -1.32161 (41*2π)/46311 weeks
422.70798 1.40064 (42*2π)/46311 weeks
43-2.29726 2.89018 (43*2π)/46311 weeks
44-1.99101 -3.61077 (44*2π)/46311 weeks
454.1804 .85097 (45*2π)/46310 weeks
46-2.75899 3.85139 (46*2π)/46310 weeks
47-2.35174 -1.70483 (47*2π)/46310 weeks
481.7394 -2.12789 (48*2π)/46310 weeks
494.21516 2.63491 (49*2π)/4639 weeks
50-5.02384 2.1945 (50*2π)/4639 weeks
51-.28779 -4.52206 (51*2π)/4639 weeks
523.44351 .33071 (52*2π)/4639 weeks
53-.39824 2.91543 (53*2π)/4639 weeks
54-2.51785 -.50569 (54*2π)/4639 weeks
55.79791 -3.37908 (55*2π)/4638 weeks
563.72054 1.52645 (56*2π)/4638 weeks
57-1.35941 1.64965 (57*2π)/4638 weeks
58-.27415 .76956 (58*2π)/4638 weeks
59-1.12066 -.67719 (59*2π)/4638 weeks
601.31698 -.12939 (60*2π)/4638 weeks
61-.47445 2.40976 (61*2π)/4638 weeks
62-2.08475 .33393 (62*2π)/4637 weeks
63-.53676 -3.12248 (63*2π)/4637 weeks
643.78322 .58375 (64*2π)/4637 weeks
65-.62812 4.5999 (65*2π)/4637 weeks
66-3.64866 -.98852 (66*2π)/4637 weeks
671.60387 -3.32324 (67*2π)/4637 weeks
683.09522 2.95483 (68*2π)/4637 weeks
69-4.32993 2.20211 (69*2π)/4637 weeks
70-1.20103 -4.88137 (70*2π)/4637 weeks
714.99715 .27614 (71*2π)/4637 weeks
72-1.55046 4.2815 (72*2π)/4636 weeks
73-2.53474 -2.10148 (73*2π)/4636 weeks
742.48807 -1.67099 (74*2π)/4636 weeks
75.86709 2.74196 (75*2π)/4636 weeks
76-2.96531 1.02261 (76*2π)/4636 weeks
77-1.35585 -2.07533 (77*2π)/4636 weeks
781.57387 -1.53612 (78*2π)/4636 weeks
79.16006 1.61532 (79*2π)/4636 weeks
80-1.25867 -.44002 (80*2π)/4636 weeks
81.65277 -1.73875 (81*2π)/4636 weeks
822.32355 .44503 (82*2π)/4636 weeks
83-.25821 2.68407 (83*2π)/4636 weeks
84-1.99142 -1.04522 (84*2π)/4636 weeks
851.0663 -1.69254 (85*2π)/4635 weeks
86.9877 .60223 (86*2π)/4635 weeks
87-1.07303 1.22616 (87*2π)/4635 weeks
88-.83769 -1.05299 (88*2π)/4635 weeks
89.69279 -.4049 (89*2π)/4635 weeks
90.87037 .43638 (90*2π)/4635 weeks
91-.86566 .42789 (91*2π)/4635 weeks
92.03952 -1.85767 (92*2π)/4635 weeks
931.96268 .09434 (93*2π)/4635 weeks
94.78223 1.84061 (94*2π)/4635 weeks
95-2.02181 .10076 (95*2π)/4635 weeks
96.64875 -1.31922 (96*2π)/4635 weeks
971.05183 1.01785 (97*2π)/4635 weeks
98-1.08361 1.13908 (98*2π)/4635 weeks
99-1.04999 -.63316 (99*2π)/4635 weeks
100.52328 -.46396 (100*2π)/4635 weeks
101.13117 .40819 (101*2π)/4635 weeks
102-.36161 .26745 (102*2π)/4635 weeks
103-.37304 -.56016 (103*2π)/4634 weeks
1041.09586 -.48058 (104*2π)/4634 weeks
105-.22083 1.08251 (105*2π)/4634 weeks
106-.52479 -.02323 (106*2π)/4634 weeks
107-.02986 -.55315 (107*2π)/4634 weeks
108.43301 .23024 (108*2π)/4634 weeks
109-.18099 1.27331 (109*2π)/4634 weeks
110-1.43391 -.75893 (110*2π)/4634 weeks
111.77977 -1.84601 (111*2π)/4634 weeks
1122.00691 .55897 (112*2π)/4634 weeks
113-1.31277 2.09918 (113*2π)/4634 weeks
114-1.9123 -2.29136 (114*2π)/4634 weeks
1152.67803 -1.19418 (115*2π)/4634 weeks
116.86914 2.83631 (116*2π)/4634 weeks
117-2.71258 .26544 (117*2π)/4634 weeks
118.33907 -2.51507 (118*2π)/4634 weeks
1192.00407 .83472 (119*2π)/4634 weeks
120-1.41186 1.2946 (120*2π)/4634 weeks
121-.56214 -1.07702 (121*2π)/4634 weeks
122.78896 -.3463 (122*2π)/4634 weeks
123.21923 .94506 (123*2π)/4634 weeks
124-.99622 -.21566 (124*2π)/4634 weeks
125.36749 -.95036 (125*2π)/4634 weeks
126.76568 -.14935 (126*2π)/4634 weeks
127.31171 .66514 (127*2π)/4634 weeks
128-.37031 -.05156 (128*2π)/4634 weeks
129.05392 -.26059 (129*2π)/4634 weeks
130.61974 .44564 (130*2π)/4634 weeks
131.01353 .98252 (131*2π)/4634 weeks
132-1.30264 .07596 (132*2π)/4634 weeks
133.41563 -1.38108 (133*2π)/4633 weeks
1341.42774 .61796 (134*2π)/4633 weeks
135-.7713 1.90948 (135*2π)/4633 weeks
136-1.38752 -.87938 (136*2π)/4633 weeks
137.90121 -1.0447 (137*2π)/4633 weeks
1381.13077 1.09754 (138*2π)/4633 weeks
139-1.26601 .99137 (139*2π)/4633 weeks
140-.58661 -1.21781 (140*2π)/4633 weeks
1411.34865 -.21768 (141*2π)/4633 weeks
142-.29471 1.38905 (142*2π)/4633 weeks
143-.77981 -.95774 (143*2π)/4633 weeks
144.92762 -.65327 (144*2π)/4633 weeks
145.78151 .99661 (145*2π)/4633 weeks
146-1.01332 .51226 (146*2π)/4633 weeks
147-.29175 -.65702 (147*2π)/4633 weeks
148.53727 .16356 (148*2π)/4633 weeks
149-.01814 .74835 (149*2π)/4633 weeks
150-.72813 -.12366 (150*2π)/4633 weeks
151.16393 -.03626 (151*2π)/4633 weeks
152-.24822 -.37342 (152*2π)/4633 weeks
153.22559 -.2094 (153*2π)/4633 weeks
154-.30158 .08543 (154*2π)/4633 weeks
155.05269 .15241 (155*2π)/4633 weeks
156-.14333 -.22025 (156*2π)/4633 weeks
157.11358 .51494 (157*2π)/4633 weeks
158-.72477 -.23681 (158*2π)/4633 weeks
159.3913 -.94754 (159*2π)/4633 weeks
160.5108 .35418 (160*2π)/4633 weeks
161-.60614 .42012 (161*2π)/4633 weeks
162-.28061 -.723 (162*2π)/4633 weeks
163.66881 -.03205 (163*2π)/4633 weeks
164-.0909 1.00325 (164*2π)/4633 weeks
165-.87841 -.17188 (165*2π)/4633 weeks
166.03732 -.86349 (166*2π)/4633 weeks
167.57517 -.21456 (167*2π)/4633 weeks
168.42413 .22818 (168*2π)/4633 weeks
169-.20238 .07497 (169*2π)/4633 weeks
170-.14102 -.06566 (170*2π)/4633 weeks
171.44774 -.29165 (171*2π)/4633 weeks
172.1845 .87052 (172*2π)/4633 weeks
173-.88805 -.00248 (173*2π)/4633 weeks
174.53575 -.43771 (174*2π)/4633 weeks
175.19791 .87953 (175*2π)/4633 weeks
176-1.00231 -.10417 (176*2π)/4633 weeks
177-.2552 -1.13189 (177*2π)/4633 weeks
1781.15723 -.20939 (178*2π)/4633 weeks
179.07364 1.33708 (179*2π)/4633 weeks
180-1.33585 -.56861 (180*2π)/4633 weeks
181.9515 -.94491 (181*2π)/4633 weeks
182.53267 1.10578 (182*2π)/4633 weeks
183-.98275 .33683 (183*2π)/4633 weeks
184-.58822 -1.02134 (184*2π)/4633 weeks
1851.24587 -.70399 (185*2π)/4633 weeks
186.52927 .93061 (186*2π)/4632 weeks
187-.46776 .52137 (187*2π)/4632 weeks
188-.59545 -.18012 (188*2π)/4632 weeks
189.4469 -.53094 (189*2π)/4632 weeks
190.52351 .57735 (190*2π)/4632 weeks
191-.83363 .31438 (191*2π)/4632 weeks
192.17154 -.82281 (192*2π)/4632 weeks
193.67448 .18669 (193*2π)/4632 weeks
194.11985 1.08021 (194*2π)/4632 weeks
195-1.30444 .09068 (195*2π)/4632 weeks
196.24049 -1.04702 (196*2π)/4632 weeks
197.38726 .38777 (197*2π)/4632 weeks
198-.32167 .48842 (198*2π)/4632 weeks
199-1.38618 -.38746 (199*2π)/4632 weeks
200.47167 -1.65406 (200*2π)/4632 weeks
2011.23751 .71108 (201*2π)/4632 weeks
202-.95248 .89587 (202*2π)/4632 weeks
203-.78311 -1.44132 (203*2π)/4632 weeks
2041.57092 -.71086 (204*2π)/4632 weeks
205.6484 1.2041 (205*2π)/4632 weeks
206-1.11758 .1632 (206*2π)/4632 weeks
207-.1494 -.95945 (207*2π)/4632 weeks
208.81472 .10287 (208*2π)/4632 weeks
209-.45991 .13004 (209*2π)/4632 weeks
210.13048 -.66215 (210*2π)/4632 weeks
211.69129 -.05385 (211*2π)/4632 weeks
212.48941 .49114 (212*2π)/4632 weeks
213-.77526 .08461 (213*2π)/4632 weeks
214.71516 -.71024 (214*2π)/4632 weeks
215.42845 1.11489 (215*2π)/4632 weeks
216-.88903 .39534 (216*2π)/4632 weeks
217-.15167 -.5099 (217*2π)/4632 weeks
218.39753 -.08624 (218*2π)/4632 weeks
219.12747 .3238 (219*2π)/4632 weeks
220-.37453 .15261 (220*2π)/4632 weeks
221-.37779 -.28052 (221*2π)/4632 weeks
222.3572 -.53494 (222*2π)/4632 weeks
2231.10944 .06618 (223*2π)/4632 weeks
224.15197 1.63311 (224*2π)/4632 weeks
225-1.87115 -.23605 (225*2π)/4632 weeks
226.83937 -1.43462 (226*2π)/4632 weeks
227.67608 .97704 (227*2π)/4632 weeks
228-1.09832 .34736 (228*2π)/4632 weeks
229.0337 -1.26937 (229*2π)/4632 weeks
2301.26574 .28771 (230*2π)/4632 weeks
231-.6849 1.01038 (231*2π)/4632 weeks
232-.6849 -1.01038 (232*2π)/4632 weeks
2331.26574 -.28771 (233*2π)/4632 weeks
234.0337 1.26937 (234*2π)/4632 weeks
235-1.09832 -.34736 (235*2π)/4632 weeks
236.67608 -.97704 (236*2π)/4632 weeks
237.83937 1.43462 (237*2π)/4632 weeks
238-1.87115 .23605 (238*2π)/4632 weeks
239.15197 -1.63311 (239*2π)/4632 weeks
2401.10944 -.06618 (240*2π)/4632 weeks
241.3572 .53494 (241*2π)/4632 weeks
242-.37779 .28052 (242*2π)/4632 weeks
243-.37453 -.15261 (243*2π)/4632 weeks
244.12747 -.3238 (244*2π)/4632 weeks
245.39753 .08624 (245*2π)/4632 weeks
246-.15167 .5099 (246*2π)/4632 weeks
247-.88903 -.39534 (247*2π)/4632 weeks
248.42845 -1.11489 (248*2π)/4632 weeks
249.71516 .71024 (249*2π)/4632 weeks
250-.77526 -.08461 (250*2π)/4632 weeks
251.48941 -.49114 (251*2π)/4632 weeks
252.69129 .05385 (252*2π)/4632 weeks
253.13048 .66215 (253*2π)/4632 weeks
254-.45991 -.13004 (254*2π)/4632 weeks
255.81472 -.10287 (255*2π)/4632 weeks
256-.1494 .95945 (256*2π)/4632 weeks
257-1.11758 -.1632 (257*2π)/4632 weeks
258.6484 -1.2041 (258*2π)/4632 weeks
2591.57092 .71086 (259*2π)/4632 weeks
260-.78311 1.44132 (260*2π)/4632 weeks
261-.95248 -.89587 (261*2π)/4632 weeks
2621.23751 -.71108 (262*2π)/4632 weeks
263.47167 1.65406 (263*2π)/4632 weeks
264-1.38618 .38746 (264*2π)/4632 weeks
265-.32167 -.48842 (265*2π)/4632 weeks
266.38726 -.38777 (266*2π)/4632 weeks
267.24049 1.04702 (267*2π)/4632 weeks
268-1.30444 -.09068 (268*2π)/4632 weeks
269.11985 -1.08021 (269*2π)/4632 weeks
270.67448 -.18669 (270*2π)/4632 weeks
271.17154 .82281 (271*2π)/4632 weeks
272-.83363 -.31438 (272*2π)/4632 weeks
273.52351 -.57735 (273*2π)/4632 weeks
274.4469 .53094 (274*2π)/4632 weeks
275-.59545 .18012 (275*2π)/4632 weeks
276-.46776 -.52137 (276*2π)/4632 weeks
277.52927 -.93061 (277*2π)/4632 weeks
2781.24587 .70399 (278*2π)/4632 weeks
279-.58822 1.02134 (279*2π)/4632 weeks
280-.98275 -.33683 (280*2π)/4632 weeks
281.53267 -1.10578 (281*2π)/4632 weeks
282.9515 .94491 (282*2π)/4632 weeks
283-1.33585 .56861 (283*2π)/4632 weeks
284.07364 -1.33708 (284*2π)/4632 weeks
2851.15723 .20939 (285*2π)/4632 weeks
286-.2552 1.13189 (286*2π)/4632 weeks
287-1.00231 .10417 (287*2π)/4632 weeks
288.19791 -.87953 (288*2π)/4632 weeks
289.53575 .43771 (289*2π)/4632 weeks
290-.88805 .00248 (290*2π)/4632 weeks
291.1845 -.87052 (291*2π)/4632 weeks
292.44774 .29165 (292*2π)/4632 weeks
293-.14102 .06566 (293*2π)/4632 weeks
294-.20238 -.07497 (294*2π)/4632 weeks
295.42413 -.22818 (295*2π)/4632 weeks
296.57517 .21456 (296*2π)/4632 weeks
297.03732 .86349 (297*2π)/4632 weeks
298-.87841 .17188 (298*2π)/4632 weeks
299-.0909 -1.00325 (299*2π)/4632 weeks
300.66881 .03205 (300*2π)/4632 weeks
301-.28061 .723 (301*2π)/4632 weeks
302-.60614 -.42012 (302*2π)/4632 weeks
303.5108 -.35418 (303*2π)/4632 weeks
304.3913 .94754 (304*2π)/4632 weeks
305-.72477 .23681 (305*2π)/4632 weeks
306.11358 -.51494 (306*2π)/4632 weeks
307-.14333 .22025 (307*2π)/4632 weeks
308.05269 -.15241 (308*2π)/4632 weeks
309-.30158 -.08543 (309*2π)/4631 weeks
310.22559 .2094 (310*2π)/4631 weeks
311-.24822 .37342 (311*2π)/4631 weeks
312.16393 .03626 (312*2π)/4631 weeks
313-.72813 .12366 (313*2π)/4631 weeks
314-.01814 -.74835 (314*2π)/4631 weeks
315.53727 -.16356 (315*2π)/4631 weeks
316-.29175 .65702 (316*2π)/4631 weeks
317-1.01332 -.51226 (317*2π)/4631 weeks
318.78151 -.99661 (318*2π)/4631 weeks
319.92762 .65327 (319*2π)/4631 weeks
320-.77981 .95774 (320*2π)/4631 weeks
321-.29471 -1.38905 (321*2π)/4631 weeks
3221.34865 .21768 (322*2π)/4631 weeks
323-.58661 1.21781 (323*2π)/4631 weeks
324-1.26601 -.99137 (324*2π)/4631 weeks
3251.13077 -1.09754 (325*2π)/4631 weeks
326.90121 1.0447 (326*2π)/4631 weeks
327-1.38752 .87938 (327*2π)/4631 weeks
328-.7713 -1.90948 (328*2π)/4631 weeks
3291.42774 -.61796 (329*2π)/4631 weeks
330.41563 1.38108 (330*2π)/4631 weeks
331-1.30264 -.07596 (331*2π)/4631 weeks
332.01353 -.98252 (332*2π)/4631 weeks
333.61974 -.44564 (333*2π)/4631 weeks
334.05392 .26059 (334*2π)/4631 weeks
335-.37031 .05156 (335*2π)/4631 weeks
336.31171 -.66514 (336*2π)/4631 weeks
337.76568 .14935 (337*2π)/4631 weeks
338.36749 .95036 (338*2π)/4631 weeks
339-.99622 .21566 (339*2π)/4631 weeks
340.21923 -.94506 (340*2π)/4631 weeks
341.78896 .3463 (341*2π)/4631 weeks
342-.56214 1.07702 (342*2π)/4631 weeks
343-1.41186 -1.2946 (343*2π)/4631 weeks
3442.00407 -.83472 (344*2π)/4631 weeks
345.33907 2.51507 (345*2π)/4631 weeks
346-2.71258 -.26544 (346*2π)/4631 weeks
347.86914 -2.83631 (347*2π)/4631 weeks
3482.67803 1.19418 (348*2π)/4631 weeks
349-1.9123 2.29136 (349*2π)/4631 weeks
350-1.31277 -2.09918 (350*2π)/4631 weeks
3512.00691 -.55897 (351*2π)/4631 weeks
352.77977 1.84601 (352*2π)/4631 weeks
353-1.43391 .75893 (353*2π)/4631 weeks
354-.18099 -1.27331 (354*2π)/4631 weeks
355.43301 -.23024 (355*2π)/4631 weeks
356-.02986 .55315 (356*2π)/4631 weeks
357-.52479 .02323 (357*2π)/4631 weeks
358-.22083 -1.08251 (358*2π)/4631 weeks
3591.09586 .48058 (359*2π)/4631 weeks
360-.37304 .56016 (360*2π)/4631 weeks
361-.36161 -.26745 (361*2π)/4631 weeks
362.13117 -.40819 (362*2π)/4631 weeks
363.52328 .46396 (363*2π)/4631 weeks
364-1.04999 .63316 (364*2π)/4631 weeks
365-1.08361 -1.13908 (365*2π)/4631 weeks
3661.05183 -1.01785 (366*2π)/4631 weeks
367.64875 1.31922 (367*2π)/4631 weeks
368-2.02181 -.10076 (368*2π)/4631 weeks
369.78223 -1.84061 (369*2π)/4631 weeks
3701.96268 -.09434 (370*2π)/4631 weeks
371.03952 1.85767 (371*2π)/4631 weeks
372-.86566 -.42789 (372*2π)/4631 weeks
373.87037 -.43638 (373*2π)/4631 weeks
374.69279 .4049 (374*2π)/4631 weeks
375-.83769 1.05299 (375*2π)/4631 weeks
376-1.07303 -1.22616 (376*2π)/4631 weeks
377.9877 -.60223 (377*2π)/4631 weeks
3781.0663 1.69254 (378*2π)/4631 weeks
379-1.99142 1.04522 (379*2π)/4631 weeks
380-.25821 -2.68407 (380*2π)/4631 weeks
3812.32355 -.44503 (381*2π)/4631 weeks
382.65277 1.73875 (382*2π)/4631 weeks
383-1.25867 .44002 (383*2π)/4631 weeks
384.16006 -1.61532 (384*2π)/4631 weeks
3851.57387 1.53612 (385*2π)/4631 weeks
386-1.35585 2.07533 (386*2π)/4631 weeks
387-2.96531 -1.02261 (387*2π)/4631 weeks
388.86709 -2.74196 (388*2π)/4631 weeks
3892.48807 1.67099 (389*2π)/4631 weeks
390-2.53474 2.10148 (390*2π)/4631 weeks
391-1.55046 -4.2815 (391*2π)/4631 weeks
3924.99715 -.27614 (392*2π)/4631 weeks
393-1.20103 4.88137 (393*2π)/4631 weeks
394-4.32993 -2.20211 (394*2π)/4631 weeks
3953.09522 -2.95483 (395*2π)/4631 weeks
3961.60387 3.32324 (396*2π)/4631 weeks
397-3.64866 .98852 (397*2π)/4631 weeks
398-.62812 -4.5999 (398*2π)/4631 weeks
3993.78322 -.58375 (399*2π)/4631 weeks
400-.53676 3.12248 (400*2π)/4631 weeks
401-2.08475 -.33393 (401*2π)/4631 weeks
402-.47445 -2.40976 (402*2π)/4631 weeks
4031.31698 .12939 (403*2π)/4631 weeks
404-1.12066 .67719 (404*2π)/4631 weeks
405-.27415 -.76956 (405*2π)/4631 weeks
406-1.35941 -1.64965 (406*2π)/4631 weeks
4073.72054 -1.52645 (407*2π)/4631 weeks
408.79791 3.37908 (408*2π)/4631 weeks
409-2.51785 .50569 (409*2π)/4631 weeks
410-.39824 -2.91543 (410*2π)/4631 weeks
4113.44351 -.33071 (411*2π)/4631 weeks
412-.28779 4.52206 (412*2π)/4631 weeks
413-5.02384 -2.1945 (413*2π)/4631 weeks
4144.21516 -2.63491 (414*2π)/4631 weeks
4151.7394 2.12789 (415*2π)/4631 weeks
416-2.35174 1.70483 (416*2π)/4631 weeks
417-2.75899 -3.85139 (417*2π)/4631 weeks
4184.1804 -.85097 (418*2π)/4631 weeks
419-1.99101 3.61077 (419*2π)/4631 weeks
420-2.29726 -2.89018 (420*2π)/4631 weeks
4212.70798 -1.40064 (421*2π)/4631 weeks
422-.72641 1.32161 (422*2π)/4631 weeks
423-.18868 -2.43276 (423*2π)/4631 weeks
4241.10626 .31591 (424*2π)/4631 weeks
425.07573 -.04932 (425*2π)/4631 weeks
426-.05265 -.13156 (426*2π)/4631 weeks
4271.91943 -.11889 (427*2π)/4631 weeks
428-1.15542 1.12825 (428*2π)/4631 weeks
429.87565 -3.79751 (429*2π)/4631 weeks
4304.45471 3.51543 (430*2π)/4631 weeks
431-4.55821 4.35139 (431*2π)/4631 weeks
432-2.44113 -5.13814 (432*2π)/4631 weeks
4336.45032 1.73048 (433*2π)/4631 weeks
434-3.22034 6.56902 (434*2π)/4631 weeks
435-6.80594 -2.96609 (435*2π)/4631 weeks
4362.98413 -5.88037 (436*2π)/4631 weeks
4375.52286 4.02329 (437*2π)/4631 weeks
438-7.03208 5.3961 (438*2π)/4631 weeks
439-5.19772 -8.07297 (439*2π)/4631 weeks
4407.25208 -2.93079 (440*2π)/4631 weeks
4411.92833 7.6721 (441*2π)/4631 weeks
442-8.60776 -.80767 (442*2π)/4631 weeks
443-1.95095 -8.17969 (443*2π)/4631 weeks
44410.68277 -1.75571 (444*2π)/4631 weeks
445-3.3325 10.06793 (445*2π)/4631 weeks
446-3.53671 -4.38898 (446*2π)/4631 weeks
4472.74677 1.12212 (447*2π)/4631 weeks
448-3.3778 .43671 (448*2π)/4631 weeks
449.67603 -3.22182 (449*2π)/4631 weeks
450.5948 .39298 (450*2π)/4631 weeks
451-5.84575 -5.57755 (451*2π)/4631 weeks
4527.63362 -2.33481 (452*2π)/4631 weeks
453-5.61794 4.60591 (453*2π)/4631 weeks
454-3.33966 -5.40148 (454*2π)/4631 weeks
4553.9383 -5.63223 (455*2π)/4631 weeks
45616.0162 3.09702 (456*2π)/4631 weeks
457-17.14469 20.17489 (457*2π)/4631 weeks
458-20.17949 -29.16921 (458*2π)/4631 weeks
45920.62458 -16.97188 (459*2π)/4631 weeks
46018.83319 22.48075 (460*2π)/4631 weeks
461-44.30299 29.95635 (461*2π)/4631 weeks



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