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Fourier Analysis of AGQ (ProShares Ultra Silver ETF)


AGQ (ProShares Ultra Silver ETF) appears to have interesting cyclic behaviour every 20 weeks (9.7265*sine), 24 weeks (9.3378*sine), and 19 weeks (9.2756*cosine).

AGQ (ProShares Ultra Silver ETF) has an average price of 123.19 (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 7/10/2017 for AGQ (ProShares Ultra Silver ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0123.186   0 
1-48.22085 113.522 (1*2π)/450450 weeks
2-39.93023 -33.34497 (2*2π)/450225 weeks
322.5333 -19.70523 (3*2π)/450150 weeks
419.15724 20.47886 (4*2π)/450113 weeks
5-27.73681 23.1895 (5*2π)/45090 weeks
6-9.4232 -23.82175 (6*2π)/45075 weeks
713.54514 3.0336 (7*2π)/45064 weeks
83.04543 6.96203 (8*2π)/45056 weeks
9-4.5103 4.43651 (9*2π)/45050 weeks
10-.265 -7.54405 (10*2π)/45045 weeks
115.10074 7.02572 (11*2π)/45041 weeks
12-5.86111 -.54072 (12*2π)/45038 weeks
13.3907 .5645 (13*2π)/45035 weeks
14-2.8029 3.5354 (14*2π)/45032 weeks
15-1.98831 -2.41638 (15*2π)/45030 weeks
161.75703 3.65595 (16*2π)/45028 weeks
17-8.55283 -.7579 (17*2π)/45026 weeks
188.29464 -7.78941 (18*2π)/45025 weeks
194.35768 9.33781 (19*2π)/45024 weeks
20-6.12263 5.26283 (20*2π)/45023 weeks
21-4.4552 -7.66244 (21*2π)/45021 weeks
227.30078 -1.49635 (22*2π)/45020 weeks
23.20414 9.7265 (23*2π)/45020 weeks
24-9.27557 -1.24539 (24*2π)/45019 weeks
253.18893 -6.98953 (25*2π)/45018 weeks
265.11512 4.11566 (26*2π)/45017 weeks
27-5.48883 5.16399 (27*2π)/45017 weeks
28-5.20537 -5.55928 (28*2π)/45016 weeks
295.80892 -3.8794 (29*2π)/45016 weeks
30-.87285 5.91413 (30*2π)/45015 weeks
31-5.34016 -3.42274 (31*2π)/45015 weeks
324.20589 -4.17698 (32*2π)/45014 weeks
331.43335 3.94617 (33*2π)/45014 weeks
34-1.18923 -1.09933 (34*2π)/45013 weeks
352.01856 .1781 (35*2π)/45013 weeks
36.04769 .08737 (36*2π)/45013 weeks
37.14109 -.02164 (37*2π)/45012 weeks
381.42278 -.2172 (38*2π)/45012 weeks
39-.81818 2.24043 (39*2π)/45012 weeks
40-.01556 -1.66089 (40*2π)/45011 weeks
412.28791 2.50543 (41*2π)/45011 weeks
42-3.30168 1.97704 (42*2π)/45011 weeks
43.3344 -4.2981 (43*2π)/45010 weeks
443.43635 3.02706 (44*2π)/45010 weeks
45-4.05886 1.46112 (45*2π)/45010 weeks
46-1.43155 -2.8014 (46*2π)/45010 weeks
472.53453 -1.47287 (47*2π)/45010 weeks
48.82944 5.86518 (48*2π)/4509 weeks
49-4.85566 -1.94402 (49*2π)/4509 weeks
502.76865 -2.96241 (50*2π)/4509 weeks
512.12979 2.51424 (51*2π)/4509 weeks
52-2.35075 1.61427 (52*2π)/4509 weeks
53-1.63842 -2.46041 (53*2π)/4508 weeks
543.72068 -1.38083 (54*2π)/4508 weeks
55.24423 3.52841 (55*2π)/4508 weeks
56-.35854 .46605 (56*2π)/4508 weeks
57-1.27084 .45598 (57*2π)/4508 weeks
58.89528 -.76646 (58*2π)/4508 weeks
59.8973 2.23119 (59*2π)/4508 weeks
60-1.87415 .82126 (60*2π)/4508 weeks
61-1.66639 -2.44997 (61*2π)/4507 weeks
623.84982 -.8201 (62*2π)/4507 weeks
63.80895 4.51355 (63*2π)/4507 weeks
64-4.06775 -.17142 (64*2π)/4507 weeks
65.77166 -3.73245 (65*2π)/4507 weeks
663.55058 2.35265 (66*2π)/4507 weeks
67-4.18832 2.76061 (67*2π)/4507 weeks
68-1.59389 -4.92796 (68*2π)/4507 weeks
695.11198 .22005 (69*2π)/4507 weeks
70-1.80826 4.32047 (70*2π)/4506 weeks
71-2.38405 -2.33932 (71*2π)/4506 weeks
722.79181 -1.27292 (72*2π)/4506 weeks
73.40309 2.95302 (73*2π)/4506 weeks
74-3.15562 .38107 (74*2π)/4506 weeks
75-.93362 -2.31006 (75*2π)/4506 weeks
762.00376 -.89851 (76*2π)/4506 weeks
77-.69127 1.32181 (77*2π)/4506 weeks
78-1.17759 -1.06058 (78*2π)/4506 weeks
791.30717 -1.52123 (79*2π)/4506 weeks
801.91944 1.47791 (80*2π)/4506 weeks
81-2.01865 2.12474 (81*2π)/4506 weeks
82-1.05281 -1.71911 (82*2π)/4505 weeks
831.69901 -.32513 (83*2π)/4505 weeks
84.67302 1.32701 (84*2π)/4505 weeks
85-1.48618 -.03004 (85*2π)/4505 weeks
86.27357 -1.25237 (86*2π)/4505 weeks
87.6751 -.24894 (87*2π)/4505 weeks
88-.16081 .96118 (88*2π)/4505 weeks
89-1.16167 -.96669 (89*2π)/4505 weeks
901.78042 -.99531 (90*2π)/4505 weeks
911.34288 1.325 (91*2π)/4505 weeks
92-1.6465 1.68763 (92*2π)/4505 weeks
93-.29952 -1.47275 (93*2π)/4505 weeks
941.4387 .5237 (94*2π)/4505 weeks
95-.55088 1.62888 (95*2π)/4505 weeks
96-1.24082 -.23055 (96*2π)/4505 weeks
97.4049 -.72095 (97*2π)/4505 weeks
98.30521 .40557 (98*2π)/4505 weeks
99-.26831 .33338 (99*2π)/4505 weeks
100-.44329 -.46092 (100*2π)/4505 weeks
101.99674 -.62754 (101*2π)/4504 weeks
102-.09963 1.19904 (102*2π)/4504 weeks
103-.53765 .02105 (103*2π)/4504 weeks
104-.01907 -.5369 (104*2π)/4504 weeks
105.43559 .2843 (105*2π)/4504 weeks
106-.37722 1.38049 (106*2π)/4504 weeks
107-1.36982 -.91566 (107*2π)/4504 weeks
1081.15864 -1.65346 (108*2π)/4504 weeks
1091.9644 1.16144 (109*2π)/4504 weeks
110-1.99328 1.68293 (110*2π)/4504 weeks
111-.87211 -2.96753 (111*2π)/4504 weeks
1123.0159 -.05578 (112*2π)/4504 weeks
113-.50498 3.01158 (113*2π)/4504 weeks
114-2.48721 -1.06633 (114*2π)/4504 weeks
1151.69379 -1.80064 (115*2π)/4504 weeks
1161.1037 1.9487 (116*2π)/4504 weeks
117-1.64219 -.00433 (117*2π)/4504 weeks
118.24311 -1.04442 (118*2π)/4504 weeks
119.86998 .24299 (119*2π)/4504 weeks
120-.70129 .76993 (120*2π)/4504 weeks
121-.50794 -.9498 (121*2π)/4504 weeks
122.71334 -.4025 (122*2π)/4504 weeks
123.76053 .43781 (123*2π)/4504 weeks
124-.312 .52006 (124*2π)/4504 weeks
125.05515 -.11665 (125*2π)/4504 weeks
126.77761 -.00558 (126*2π)/4504 weeks
127.33708 .77605 (127*2π)/4504 weeks
128-1.03891 .67483 (128*2π)/4504 weeks
129-.32259 -1.41794 (129*2π)/4503 weeks
1301.57886 .07654 (130*2π)/4503 weeks
131.01682 2.03146 (131*2π)/4503 weeks
132-1.71807 -.47025 (132*2π)/4503 weeks
133.62994 -1.31892 (133*2π)/4503 weeks
1341.35337 .81387 (134*2π)/4503 weeks
135-1.11421 1.22409 (135*2π)/4503 weeks
136-.76639 -1.19185 (136*2π)/4503 weeks
1371.35795 -.34348 (137*2π)/4503 weeks
138-.26954 1.43354 (138*2π)/4503 weeks
139-.77285 -1.00233 (139*2π)/4503 weeks
1401.00292 -.60249 (140*2π)/4503 weeks
141.68995 1.13064 (141*2π)/4503 weeks
142-1.05315 .32038 (142*2π)/4503 weeks
143-.10361 -.71458 (143*2π)/4503 weeks
144.46206 .29581 (144*2π)/4503 weeks
145-.28723 .79579 (145*2π)/4503 weeks
146-.58459 -.34392 (146*2π)/4503 weeks
147-.03926 .21665 (147*2π)/4503 weeks
148-.01261 -.34564 (148*2π)/4503 weeks
149.34492 .07616 (149*2π)/4503 weeks
150-.12184 -.20142 (150*2π)/4503 weeks
151-.17025 .1482 (151*2π)/4503 weeks
152.21484 -.20289 (152*2π)/4503 weeks
153-.53731 .47892 (153*2π)/4503 weeks
154-.53497 -.72582 (154*2π)/4503 weeks
155.86818 -.16476 (155*2π)/4503 weeks
156.1002 .71202 (156*2π)/4503 weeks
157-.64978 -.27433 (157*2π)/4503 weeks
158.58276 -.56216 (158*2π)/4503 weeks
159.60387 .6316 (159*2π)/4503 weeks
160-.91303 .28314 (160*2π)/4503 weeks
161-.4223 -.8751 (161*2π)/4503 weeks
162.53693 -.48761 (162*2π)/4503 weeks
163.45798 .07891 (163*2π)/4503 weeks
164-.16498 .30755 (164*2π)/4503 weeks
165-.07564 .01459 (165*2π)/4503 weeks
166.27769 -.36654 (166*2π)/4503 weeks
167.48182 .76841 (167*2π)/4503 weeks
168-.85326 .25613 (168*2π)/4503 weeks
169.4305 -.62201 (169*2π)/4503 weeks
170.35757 .80153 (170*2π)/4503 weeks
171-1.03904 -.02528 (171*2π)/4503 weeks
172-.30195 -1.1479 (172*2π)/4503 weeks
1731.20445 -.2275 (173*2π)/4503 weeks
174.01883 1.37575 (174*2π)/4503 weeks
175-1.28347 -.74456 (175*2π)/4503 weeks
1761.12736 -.80925 (176*2π)/4503 weeks
177.30383 1.19508 (177*2π)/4503 weeks
178-1.04046 .1234 (178*2π)/4503 weeks
179-.33282 -1.23778 (179*2π)/4503 weeks
1801.43865 -.26967 (180*2π)/4503 weeks
181.22791 .95383 (181*2π)/4502 weeks
182-.53744 .31756 (182*2π)/4502 weeks
183-.47772 -.51984 (183*2π)/4502 weeks
184.66842 -.22231 (184*2π)/4502 weeks
185.08273 .85661 (185*2π)/4502 weeks
186-.83284 -.38515 (186*2π)/4502 weeks
187.66527 -.44404 (187*2π)/4502 weeks
188.61317 .525 (188*2π)/4502 weeks
189-.76512 1.04976 (189*2π)/4502 weeks
190-.93893 -.90955 (190*2π)/4502 weeks
191.75021 -.157 (191*2π)/4502 weeks
192-.06996 .53233 (192*2π)/4502 weeks
193-.98303 .43037 (193*2π)/4502 weeks
194-.54784 -1.61775 (194*2π)/4502 weeks
1951.66109 -.29001 (195*2π)/4502 weeks
196-.1997 1.24503 (196*2π)/4502 weeks
197-1.34522 -.84105 (197*2π)/4502 weeks
1981.16523 -1.43057 (198*2π)/4502 weeks
1991.11786 .92155 (199*2π)/4502 weeks
200-1.04236 .69103 (200*2π)/4502 weeks
201-.41285 -.88027 (201*2π)/4502 weeks
202.90642 -.19331 (202*2π)/4502 weeks
203-.36565 .31802 (203*2π)/4502 weeks
204.04287 -.66921 (204*2π)/4502 weeks
205.73701 -.11849 (205*2π)/4502 weeks
206.54205 .461 (206*2π)/4502 weeks
207-.77208 .13015 (207*2π)/4502 weeks
208.77515 -.72364 (208*2π)/4502 weeks
209.38497 1.15553 (209*2π)/4502 weeks
210-.91964 .28548 (210*2π)/4502 weeks
211-.0615 -.5206 (211*2π)/4502 weeks
212.42114 -.00753 (212*2π)/4502 weeks
213.08163 .35625 (213*2π)/4502 weeks
214-.37547 .03214 (214*2π)/4502 weeks
215-.31635 -.48659 (215*2π)/4502 weeks
216.49183 -.50765 (216*2π)/4502 weeks
2171.16176 .52992 (217*2π)/4502 weeks
218-.73331 1.69149 (218*2π)/4502 weeks
219-1.3925 -1.28668 (219*2π)/4502 weeks
2201.46957 -.45512 (220*2π)/4502 weeks
221-.11301 1.14097 (221*2π)/4502 weeks
222-1.09525 -.58886 (222*2π)/4502 weeks
223.96221 -.90131 (223*2π)/4502 weeks
224.59432 1.19869 (224*2π)/4502 weeks
225-1.19476   (225*2π)/4502 weeks
226.59432 -1.19869 (226*2π)/4502 weeks
227.96221 .90131 (227*2π)/4502 weeks
228-1.09525 .58886 (228*2π)/4502 weeks
229-.11301 -1.14097 (229*2π)/4502 weeks
2301.46957 .45512 (230*2π)/4502 weeks
231-1.3925 1.28668 (231*2π)/4502 weeks
232-.73331 -1.69149 (232*2π)/4502 weeks
2331.16176 -.52992 (233*2π)/4502 weeks
234.49183 .50765 (234*2π)/4502 weeks
235-.31635 .48659 (235*2π)/4502 weeks
236-.37547 -.03214 (236*2π)/4502 weeks
237.08163 -.35625 (237*2π)/4502 weeks
238.42114 .00753 (238*2π)/4502 weeks
239-.0615 .5206 (239*2π)/4502 weeks
240-.91964 -.28548 (240*2π)/4502 weeks
241.38497 -1.15553 (241*2π)/4502 weeks
242.77515 .72364 (242*2π)/4502 weeks
243-.77208 -.13015 (243*2π)/4502 weeks
244.54205 -.461 (244*2π)/4502 weeks
245.73701 .11849 (245*2π)/4502 weeks
246.04287 .66921 (246*2π)/4502 weeks
247-.36565 -.31802 (247*2π)/4502 weeks
248.90642 .19331 (248*2π)/4502 weeks
249-.41285 .88027 (249*2π)/4502 weeks
250-1.04236 -.69103 (250*2π)/4502 weeks
2511.11786 -.92155 (251*2π)/4502 weeks
2521.16523 1.43057 (252*2π)/4502 weeks
253-1.34522 .84105 (253*2π)/4502 weeks
254-.1997 -1.24503 (254*2π)/4502 weeks
2551.66109 .29001 (255*2π)/4502 weeks
256-.54784 1.61775 (256*2π)/4502 weeks
257-.98303 -.43037 (257*2π)/4502 weeks
258-.06996 -.53233 (258*2π)/4502 weeks
259.75021 .157 (259*2π)/4502 weeks
260-.93893 .90955 (260*2π)/4502 weeks
261-.76512 -1.04976 (261*2π)/4502 weeks
262.61317 -.525 (262*2π)/4502 weeks
263.66527 .44404 (263*2π)/4502 weeks
264-.83284 .38515 (264*2π)/4502 weeks
265.08273 -.85661 (265*2π)/4502 weeks
266.66842 .22231 (266*2π)/4502 weeks
267-.47772 .51984 (267*2π)/4502 weeks
268-.53744 -.31756 (268*2π)/4502 weeks
269.22791 -.95383 (269*2π)/4502 weeks
2701.43865 .26967 (270*2π)/4502 weeks
271-.33282 1.23778 (271*2π)/4502 weeks
272-1.04046 -.1234 (272*2π)/4502 weeks
273.30383 -1.19508 (273*2π)/4502 weeks
2741.12736 .80925 (274*2π)/4502 weeks
275-1.28347 .74456 (275*2π)/4502 weeks
276.01883 -1.37575 (276*2π)/4502 weeks
2771.20445 .2275 (277*2π)/4502 weeks
278-.30195 1.1479 (278*2π)/4502 weeks
279-1.03904 .02528 (279*2π)/4502 weeks
280.35757 -.80153 (280*2π)/4502 weeks
281.4305 .62201 (281*2π)/4502 weeks
282-.85326 -.25613 (282*2π)/4502 weeks
283.48182 -.76841 (283*2π)/4502 weeks
284.27769 .36654 (284*2π)/4502 weeks
285-.07564 -.01459 (285*2π)/4502 weeks
286-.16498 -.30755 (286*2π)/4502 weeks
287.45798 -.07891 (287*2π)/4502 weeks
288.53693 .48761 (288*2π)/4502 weeks
289-.4223 .8751 (289*2π)/4502 weeks
290-.91303 -.28314 (290*2π)/4502 weeks
291.60387 -.6316 (291*2π)/4502 weeks
292.58276 .56216 (292*2π)/4502 weeks
293-.64978 .27433 (293*2π)/4502 weeks
294.1002 -.71202 (294*2π)/4502 weeks
295.86818 .16476 (295*2π)/4502 weeks
296-.53497 .72582 (296*2π)/4502 weeks
297-.53731 -.47892 (297*2π)/4502 weeks
298.21484 .20289 (298*2π)/4502 weeks
299-.17025 -.1482 (299*2π)/4502 weeks
300-.12184 .20142 (300*2π)/4502 weeks
301.34492 -.07616 (301*2π)/4501 weeks
302-.01261 .34564 (302*2π)/4501 weeks
303-.03926 -.21665 (303*2π)/4501 weeks
304-.58459 .34392 (304*2π)/4501 weeks
305-.28723 -.79579 (305*2π)/4501 weeks
306.46206 -.29581 (306*2π)/4501 weeks
307-.10361 .71458 (307*2π)/4501 weeks
308-1.05315 -.32038 (308*2π)/4501 weeks
309.68995 -1.13064 (309*2π)/4501 weeks
3101.00292 .60249 (310*2π)/4501 weeks
311-.77285 1.00233 (311*2π)/4501 weeks
312-.26954 -1.43354 (312*2π)/4501 weeks
3131.35795 .34348 (313*2π)/4501 weeks
314-.76639 1.19185 (314*2π)/4501 weeks
315-1.11421 -1.22409 (315*2π)/4501 weeks
3161.35337 -.81387 (316*2π)/4501 weeks
317.62994 1.31892 (317*2π)/4501 weeks
318-1.71807 .47025 (318*2π)/4501 weeks
319.01682 -2.03146 (319*2π)/4501 weeks
3201.57886 -.07654 (320*2π)/4501 weeks
321-.32259 1.41794 (321*2π)/4501 weeks
322-1.03891 -.67483 (322*2π)/4501 weeks
323.33708 -.77605 (323*2π)/4501 weeks
324.77761 .00558 (324*2π)/4501 weeks
325.05515 .11665 (325*2π)/4501 weeks
326-.312 -.52006 (326*2π)/4501 weeks
327.76053 -.43781 (327*2π)/4501 weeks
328.71334 .4025 (328*2π)/4501 weeks
329-.50794 .9498 (329*2π)/4501 weeks
330-.70129 -.76993 (330*2π)/4501 weeks
331.86998 -.24299 (331*2π)/4501 weeks
332.24311 1.04442 (332*2π)/4501 weeks
333-1.64219 .00433 (333*2π)/4501 weeks
3341.1037 -1.9487 (334*2π)/4501 weeks
3351.69379 1.80064 (335*2π)/4501 weeks
336-2.48721 1.06633 (336*2π)/4501 weeks
337-.50498 -3.01158 (337*2π)/4501 weeks
3383.0159 .05578 (338*2π)/4501 weeks
339-.87211 2.96753 (339*2π)/4501 weeks
340-1.99328 -1.68293 (340*2π)/4501 weeks
3411.9644 -1.16144 (341*2π)/4501 weeks
3421.15864 1.65346 (342*2π)/4501 weeks
343-1.36982 .91566 (343*2π)/4501 weeks
344-.37722 -1.38049 (344*2π)/4501 weeks
345.43559 -.2843 (345*2π)/4501 weeks
346-.01907 .5369 (346*2π)/4501 weeks
347-.53765 -.02105 (347*2π)/4501 weeks
348-.09963 -1.19904 (348*2π)/4501 weeks
349.99674 .62754 (349*2π)/4501 weeks
350-.44329 .46092 (350*2π)/4501 weeks
351-.26831 -.33338 (351*2π)/4501 weeks
352.30521 -.40557 (352*2π)/4501 weeks
353.4049 .72095 (353*2π)/4501 weeks
354-1.24082 .23055 (354*2π)/4501 weeks
355-.55088 -1.62888 (355*2π)/4501 weeks
3561.4387 -.5237 (356*2π)/4501 weeks
357-.29952 1.47275 (357*2π)/4501 weeks
358-1.6465 -1.68763 (358*2π)/4501 weeks
3591.34288 -1.325 (359*2π)/4501 weeks
3601.78042 .99531 (360*2π)/4501 weeks
361-1.16167 .96669 (361*2π)/4501 weeks
362-.16081 -.96118 (362*2π)/4501 weeks
363.6751 .24894 (363*2π)/4501 weeks
364.27357 1.25237 (364*2π)/4501 weeks
365-1.48618 .03004 (365*2π)/4501 weeks
366.67302 -1.32701 (366*2π)/4501 weeks
3671.69901 .32513 (367*2π)/4501 weeks
368-1.05281 1.71911 (368*2π)/4501 weeks
369-2.01865 -2.12474 (369*2π)/4501 weeks
3701.91944 -1.47791 (370*2π)/4501 weeks
3711.30717 1.52123 (371*2π)/4501 weeks
372-1.17759 1.06058 (372*2π)/4501 weeks
373-.69127 -1.32181 (373*2π)/4501 weeks
3742.00376 .89851 (374*2π)/4501 weeks
375-.93362 2.31006 (375*2π)/4501 weeks
376-3.15562 -.38107 (376*2π)/4501 weeks
377.40309 -2.95302 (377*2π)/4501 weeks
3782.79181 1.27292 (378*2π)/4501 weeks
379-2.38405 2.33932 (379*2π)/4501 weeks
380-1.80826 -4.32047 (380*2π)/4501 weeks
3815.11198 -.22005 (381*2π)/4501 weeks
382-1.59389 4.92796 (382*2π)/4501 weeks
383-4.18832 -2.76061 (383*2π)/4501 weeks
3843.55058 -2.35265 (384*2π)/4501 weeks
385.77166 3.73245 (385*2π)/4501 weeks
386-4.06775 .17142 (386*2π)/4501 weeks
387.80895 -4.51355 (387*2π)/4501 weeks
3883.84982 .8201 (388*2π)/4501 weeks
389-1.66639 2.44997 (389*2π)/4501 weeks
390-1.87415 -.82126 (390*2π)/4501 weeks
391.8973 -2.23119 (391*2π)/4501 weeks
392.89528 .76646 (392*2π)/4501 weeks
393-1.27084 -.45598 (393*2π)/4501 weeks
394-.35854 -.46605 (394*2π)/4501 weeks
395.24423 -3.52841 (395*2π)/4501 weeks
3963.72068 1.38083 (396*2π)/4501 weeks
397-1.63842 2.46041 (397*2π)/4501 weeks
398-2.35075 -1.61427 (398*2π)/4501 weeks
3992.12979 -2.51424 (399*2π)/4501 weeks
4002.76865 2.96241 (400*2π)/4501 weeks
401-4.85566 1.94402 (401*2π)/4501 weeks
402.82944 -5.86518 (402*2π)/4501 weeks
4032.53453 1.47287 (403*2π)/4501 weeks
404-1.43155 2.8014 (404*2π)/4501 weeks
405-4.05886 -1.46112 (405*2π)/4501 weeks
4063.43635 -3.02706 (406*2π)/4501 weeks
407.3344 4.2981 (407*2π)/4501 weeks
408-3.30168 -1.97704 (408*2π)/4501 weeks
4092.28791 -2.50543 (409*2π)/4501 weeks
410-.01556 1.66089 (410*2π)/4501 weeks
411-.81818 -2.24043 (411*2π)/4501 weeks
4121.42278 .2172 (412*2π)/4501 weeks
413.14109 .02164 (413*2π)/4501 weeks
414.04769 -.08737 (414*2π)/4501 weeks
4152.01856 -.1781 (415*2π)/4501 weeks
416-1.18923 1.09933 (416*2π)/4501 weeks
4171.43335 -3.94617 (417*2π)/4501 weeks
4184.20589 4.17698 (418*2π)/4501 weeks
419-5.34016 3.42274 (419*2π)/4501 weeks
420-.87285 -5.91413 (420*2π)/4501 weeks
4215.80892 3.8794 (421*2π)/4501 weeks
422-5.20537 5.55928 (422*2π)/4501 weeks
423-5.48883 -5.16399 (423*2π)/4501 weeks
4245.11512 -4.11566 (424*2π)/4501 weeks
4253.18893 6.98953 (425*2π)/4501 weeks
426-9.27557 1.24539 (426*2π)/4501 weeks
427.20414 -9.7265 (427*2π)/4501 weeks
4287.30078 1.49635 (428*2π)/4501 weeks
429-4.4552 7.66244 (429*2π)/4501 weeks
430-6.12263 -5.26283 (430*2π)/4501 weeks
4314.35768 -9.33781 (431*2π)/4501 weeks
4328.29464 7.78941 (432*2π)/4501 weeks
433-8.55283 .7579 (433*2π)/4501 weeks
4341.75703 -3.65595 (434*2π)/4501 weeks
435-1.98831 2.41638 (435*2π)/4501 weeks
436-2.8029 -3.5354 (436*2π)/4501 weeks
437.3907 -.5645 (437*2π)/4501 weeks
438-5.86111 .54072 (438*2π)/4501 weeks
4395.10074 -7.02572 (439*2π)/4501 weeks
440-.265 7.54405 (440*2π)/4501 weeks
441-4.5103 -4.43651 (441*2π)/4501 weeks
4423.04543 -6.96203 (442*2π)/4501 weeks
44313.54514 -3.0336 (443*2π)/4501 weeks
444-9.4232 23.82175 (444*2π)/4501 weeks
445-27.73681 -23.1895 (445*2π)/4501 weeks
44619.15724 -20.47886 (446*2π)/4501 weeks
44722.5333 19.70523 (447*2π)/4501 weeks
448-39.93023 33.34497 (448*2π)/4501 weeks



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