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Fourier Analysis of AGQ (ProShares Ultra Silver)


AGQ (ProShares Ultra Silver) appears to have interesting cyclic behaviour every 24 weeks (8.1863*sine), 25 weeks (7.9598*cosine), and 26 weeks (7.8307*cosine).

AGQ (ProShares Ultra Silver) has an average price of 114.35 (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 6/18/2018 for AGQ (ProShares Ultra Silver), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0114.3481   0 
1-25.58541 115.7089 (1*2π)/499499 weeks
2-54.16034 -18.77854 (2*2π)/499250 weeks
38.69138 -26.64452 (3*2π)/499166 weeks
423.48327 8.3506 (4*2π)/499125 weeks
5.86151 31.10176 (5*2π)/499100 weeks
6-29.03834 -2.18966 (6*2π)/49983 weeks
75.55345 -19.44102 (7*2π)/49971 weeks
87.99376 5.62762 (8*2π)/49962 weeks
91.83415 6.99266 (9*2π)/49955 weeks
10-4.13378 4.09733 (10*2π)/49950 weeks
11-1.8629 -6.38348 (11*2π)/49945 weeks
126.37137 4.24411 (12*2π)/49942 weeks
13-5.86534 4.2397 (13*2π)/49938 weeks
14.55216 -.36007 (14*2π)/49936 weeks
15.97386 2.53273 (15*2π)/49933 weeks
16-3.45838 .37477 (16*2π)/49931 weeks
17.84343 -2.45571 (17*2π)/49929 weeks
18-.49354 4.29878 (18*2π)/49928 weeks
19-7.83073 -3.17602 (19*2π)/49926 weeks
207.95981 -6.33455 (20*2π)/49925 weeks
214.90079 8.18626 (21*2π)/49924 weeks
22-4.44709 5.65452 (22*2π)/49923 weeks
23-7.06763 -4.03087 (23*2π)/49922 weeks
244.74367 -4.99655 (24*2π)/49921 weeks
255.91384 5.13534 (25*2π)/49920 weeks
26-6.19104 6.29856 (26*2π)/49919 weeks
27-5.96559 -5.55082 (27*2π)/49918 weeks
285.02009 -3.95096 (28*2π)/49918 weeks
293.512 4.87635 (29*2π)/49917 weeks
30-5.41945 4.21932 (30*2π)/49917 weeks
31-5.12892 -4.66256 (31*2π)/49916 weeks
324.02668 -4.80483 (32*2π)/49916 weeks
332.23783 5.239 (33*2π)/49915 weeks
34-5.3792 .47651 (34*2π)/49915 weeks
35.29543 -5.66409 (35*2π)/49914 weeks
364.96955 .28628 (36*2π)/49914 weeks
37-1.40252 2.21026 (37*2π)/49913 weeks
38-.19179 -1.48315 (38*2π)/49913 weeks
391.45728 .83389 (39*2π)/49913 weeks
40.12019 .08824 (40*2π)/49912 weeks
41.1223 .07437 (41*2π)/49912 weeks
421.0306 -.24417 (42*2π)/49912 weeks
43.4374 2.32551 (43*2π)/49912 weeks
44-1.10401 -.70861 (44*2π)/49911 weeks
452.55028 -.12141 (45*2π)/49911 weeks
46-.38063 3.26362 (46*2π)/49911 weeks
47-3.50949 -.82325 (47*2π)/49911 weeks
482.7746 -2.87871 (48*2π)/49910 weeks
491.95924 3.73277 (49*2π)/49910 weeks
50-3.65246 .55969 (50*2π)/49910 weeks
51-1.38226 -2.55831 (51*2π)/49910 weeks
521.96335 -1.49755 (52*2π)/49910 weeks
532.85824 4.12008 (53*2π)/4999 weeks
54-4.92573 1.06773 (54*2π)/4999 weeks
55-.04072 -4.11929 (55*2π)/4999 weeks
563.22183 .15537 (56*2π)/4999 weeks
57.13596 2.82244 (57*2π)/4999 weeks
58-2.38763 .24801 (58*2π)/4999 weeks
59-.60935 -2.82268 (59*2π)/4998 weeks
603.63926 -.60738 (60*2π)/4998 weeks
61.22091 3.14423 (61*2π)/4998 weeks
62-.38482 .34293 (62*2π)/4998 weeks
63-.79874 .68367 (63*2π)/4998 weeks
64.13006 -1.14998 (64*2π)/4998 weeks
651.49233 .60334 (65*2π)/4998 weeks
66-1.23274 1.70128 (66*2π)/4998 weeks
67-2.12443 -.15374 (67*2π)/4997 weeks
68-.0161 -3.09862 (68*2π)/4997 weeks
693.44709 .63095 (69*2π)/4997 weeks
70-.23635 4.23863 (70*2π)/4997 weeks
71-3.6501 -.32994 (71*2π)/4997 weeks
72.19096 -3.45653 (72*2π)/4997 weeks
733.50296 .90933 (73*2π)/4997 weeks
74-2.11303 3.95561 (74*2π)/4997 weeks
75-3.91668 -2.50873 (75*2π)/4997 weeks
763.02537 -3.49735 (76*2π)/4997 weeks
772.79962 3.5242 (77*2π)/4996 weeks
78-3.45615 1.93598 (78*2π)/4996 weeks
79-.96671 -2.54308 (79*2π)/4996 weeks
802.79083 -.27766 (80*2π)/4996 weeks
81.22206 2.72416 (81*2π)/4996 weeks
82-2.797 .58592 (82*2π)/4996 weeks
83-1.21911 -1.94386 (83*2π)/4996 weeks
841.31061 -1.58436 (84*2π)/4996 weeks
85.66636 1.44616 (85*2π)/4996 weeks
86-1.18794 -.03648 (86*2π)/4996 weeks
87-.11614 -1.66103 (87*2π)/4996 weeks
881.88009 -.68505 (88*2π)/4996 weeks
891.12966 1.93815 (89*2π)/4996 weeks
90-2.3432 1.21803 (90*2π)/4996 weeks
91-.80455 -1.56295 (91*2π)/4995 weeks
921.55398 -.34548 (92*2π)/4995 weeks
93.81508 .99782 (93*2π)/4995 weeks
94-1.29078 .61421 (94*2π)/4995 weeks
95-.4687 -1.11316 (95*2π)/4995 weeks
96.64321 -.30109 (96*2π)/4995 weeks
97.83262 .40187 (97*2π)/4995 weeks
98-.70958 .47086 (98*2π)/4995 weeks
99-.43451 -1.5939 (99*2π)/4995 weeks
1001.76342 -.46705 (100*2π)/4995 weeks
1011.08337 1.27872 (101*2π)/4995 weeks
102-1.47937 1.57261 (102*2π)/4995 weeks
103-.64023 -1.24994 (103*2π)/4995 weeks
1041.35794 -.0434 (104*2π)/4995 weeks
105.26442 1.50333 (105*2π)/4995 weeks
106-1.20456 .43559 (106*2π)/4995 weeks
107-.52358 -.87726 (107*2π)/4995 weeks
108.54745 -.15507 (108*2π)/4995 weeks
109.04598 .39615 (109*2π)/4995 weeks
110-.35016 .24163 (110*2π)/4995 weeks
111-.328 -.50731 (111*2π)/4994 weeks
112.91007 -.5909 (112*2π)/4994 weeks
113.13494 1.09848 (113*2π)/4994 weeks
114-.53959 .08832 (114*2π)/4994 weeks
115-.28964 -.39875 (115*2π)/4994 weeks
116.50043 -.09496 (116*2π)/4994 weeks
117.39261 .52744 (117*2π)/4994 weeks
118-1.44938 .59213 (118*2π)/4994 weeks
119-.86376 -1.3624 (119*2π)/4994 weeks
1201.43163 -1.02287 (120*2π)/4994 weeks
1211.55513 1.45672 (121*2π)/4994 weeks
122-1.86558 1.44658 (122*2π)/4994 weeks
123-1.21054 -2.51256 (123*2π)/4994 weeks
1242.56112 -.85666 (124*2π)/4994 weeks
125.87629 2.63156 (125*2π)/4994 weeks
126-2.48873 .67844 (126*2π)/4994 weeks
127-.42397 -2.31138 (127*2π)/4994 weeks
1282.0544 .00468 (128*2π)/4994 weeks
129-.35011 1.95604 (129*2π)/4994 weeks
130-1.17219 -.52023 (130*2π)/4994 weeks
131.43145 -.78775 (131*2π)/4994 weeks
132.79669 .30025 (132*2π)/4994 weeks
133-.51367 .79038 (133*2π)/4994 weeks
134-.64507 -.66744 (134*2π)/4994 weeks
135.61421 -.59549 (135*2π)/4994 weeks
136.79483 .02736 (136*2π)/4994 weeks
137.20595 .64786 (137*2π)/4994 weeks
138-.2869 -.07433 (138*2π)/4994 weeks
139.06172 -.20539 (139*2π)/4994 weeks
140.66942 .34616 (140*2π)/4994 weeks
141.22302 .82722 (141*2π)/4994 weeks
142-.97889 .53541 (142*2π)/4994 weeks
143-.36931 -1.24226 (143*2π)/4993 weeks
1441.41795 -.26052 (144*2π)/4993 weeks
145.69673 1.53528 (145*2π)/4993 weeks
146-1.69718 .56268 (146*2π)/4993 weeks
147-.47578 -1.34392 (147*2π)/4993 weeks
1481.18931 -.43899 (148*2π)/4993 weeks
149.52383 1.40923 (149*2π)/4993 weeks
150-1.39077 .5217 (150*2π)/4993 weeks
151-.3219 -1.17169 (151*2π)/4993 weeks
1521.27326 -.0989 (152*2π)/4993 weeks
153-.15424 1.31224 (153*2π)/4993 weeks
154-.93677 -.72262 (154*2π)/4993 weeks
155.63475 -.79126 (155*2π)/4993 weeks
156.97215 .58763 (156*2π)/4993 weeks
157-.57674 1.07921 (157*2π)/4993 weeks
158-.64053 -.3112 (158*2π)/4993 weeks
159.45986 -.40137 (159*2π)/4993 weeks
160.33001 .39884 (160*2π)/4993 weeks
161-.47877 .61229 (161*2π)/4993 weeks
162-.40902 -.37934 (162*2π)/4993 weeks
163-.00534 .17845 (163*2π)/4993 weeks
164-.0643 -.36728 (164*2π)/4993 weeks
165.27175 -.15725 (165*2π)/4993 weeks
166-.28688 .03443 (166*2π)/4993 weeks
167.05958 .10915 (167*2π)/4993 weeks
168-.21408 -.14877 (168*2π)/4993 weeks
169.26299 .28219 (169*2π)/4993 weeks
170-.7153 .08332 (170*2π)/4993 weeks
171-.2637 -.8342 (171*2π)/4993 weeks
172.71835 .04858 (172*2π)/4993 weeks
173.06579 .68452 (173*2π)/4993 weeks
174-.615 -.12032 (174*2π)/4993 weeks
175.31061 -.65622 (175*2π)/4993 weeks
176.63714 .24731 (176*2π)/4993 weeks
177-.49251 .82149 (177*2π)/4993 weeks
178-.75999 -.3018 (178*2π)/4993 weeks
179.1398 -.74779 (179*2π)/4993 weeks
180.55279 -.17043 (180*2π)/4993 weeks
181.422 .19439 (181*2π)/4993 weeks
182-.1788 .18976 (182*2π)/4993 weeks
183-.065 .03219 (183*2π)/4993 weeks
184.20947 -.30938 (184*2π)/4993 weeks
185.63598 .51289 (185*2π)/4993 weeks
186-.5356 .57766 (186*2π)/4993 weeks
187-.24005 -.71401 (187*2π)/4993 weeks
188.63144 .15617 (188*2π)/4993 weeks
189-.46953 .83852 (189*2π)/4993 weeks
190-.773 -.39997 (190*2π)/4993 weeks
191.17302 -1.12372 (191*2π)/4993 weeks
1921.1022 .04217 (192*2π)/4993 weeks
193-.10982 1.24747 (193*2π)/4993 weeks
194-1.23051 -.53796 (194*2π)/4993 weeks
195.77175 -.9828 (195*2π)/4993 weeks
196.76868 .88683 (196*2π)/4993 weeks
197-.77536 .61034 (197*2π)/4993 weeks
198-.79137 -.60417 (198*2π)/4993 weeks
199.59647 -1.14111 (199*2π)/4993 weeks
2001.11022 .50364 (200*2π)/4992 weeks
201-.06291 .79965 (201*2π)/4992 weeks
202-.47932 .19988 (202*2π)/4992 weeks
203-.35423 -.5189 (203*2π)/4992 weeks
204.60849 -.22192 (204*2π)/4992 weeks
205.28225 .71953 (205*2π)/4992 weeks
206-.80226 .06121 (206*2π)/4992 weeks
207.28298 -.7297 (207*2π)/4992 weeks
208.64999 .16146 (208*2π)/4992 weeks
209.23927 .93241 (209*2π)/4992 weeks
210-1.13949 .35818 (210*2π)/4992 weeks
211-.25276 -1.0805 (211*2π)/4992 weeks
212.59169 .10734 (212*2π)/4992 weeks
213-.1162 .46711 (213*2π)/4992 weeks
214-.86393 .39886 (214*2π)/4992 weeks
215-.7302 -1.3315 (215*2π)/4992 weeks
2161.3377 -.86404 (216*2π)/4992 weeks
217.48488 1.06968 (217*2π)/4992 weeks
218-1.26362 .28008 (218*2π)/4992 weeks
219-.26377 -1.56149 (219*2π)/4992 weeks
2201.5197 -.34336 (220*2π)/4992 weeks
221.49728 1.15619 (221*2π)/4992 weeks
222-1.04044 .17724 (222*2π)/4992 weeks
223-.26268 -.85539 (223*2π)/4992 weeks
224.79765 -.16218 (224*2π)/4992 weeks
225-.2535 .40152 (225*2π)/4992 weeks
226-.14816 -.52105 (226*2π)/4992 weeks
227.60529 -.32262 (227*2π)/4992 weeks
228.54233 .22859 (228*2π)/4992 weeks
229-.04765 .75964 (229*2π)/4992 weeks
230-.3552 -.61486 (230*2π)/4992 weeks
2311.11927 -.10565 (231*2π)/4992 weeks
232-.02665 1.00247 (232*2π)/4992 weeks
233-.83861 .0451 (233*2π)/4992 weeks
234-.0543 -.47614 (234*2π)/4992 weeks
235.36877 -.06026 (235*2π)/4992 weeks
236.12687 .28892 (236*2π)/4992 weeks
237-.32367 .19743 (237*2π)/4992 weeks
238-.33197 -.16066 (238*2π)/4992 weeks
239.19035 -.58409 (239*2π)/4992 weeks
240.79793 -.31583 (240*2π)/4992 weeks
241.80362 1.0188 (241*2π)/4992 weeks
242-1.30992 1.14952 (242*2π)/4992 weeks
243-.89045 -1.43085 (243*2π)/4992 weeks
2441.32802 -.27813 (244*2π)/4992 weeks
245.01083 1.0564 (245*2π)/4992 weeks
246-1.07489 -.18122 (246*2π)/4992 weeks
247.42637 -1.09485 (247*2π)/4992 weeks
2481.12516 .50444 (248*2π)/4992 weeks
249-.67203 .88857 (249*2π)/4992 weeks
250-.67203 -.88857 (250*2π)/4992 weeks
2511.12516 -.50444 (251*2π)/4992 weeks
252.42637 1.09485 (252*2π)/4992 weeks
253-1.07489 .18122 (253*2π)/4992 weeks
254.01083 -1.0564 (254*2π)/4992 weeks
2551.32802 .27813 (255*2π)/4992 weeks
256-.89045 1.43085 (256*2π)/4992 weeks
257-1.30992 -1.14952 (257*2π)/4992 weeks
258.80362 -1.0188 (258*2π)/4992 weeks
259.79793 .31583 (259*2π)/4992 weeks
260.19035 .58409 (260*2π)/4992 weeks
261-.33197 .16066 (261*2π)/4992 weeks
262-.32367 -.19743 (262*2π)/4992 weeks
263.12687 -.28892 (263*2π)/4992 weeks
264.36877 .06026 (264*2π)/4992 weeks
265-.0543 .47614 (265*2π)/4992 weeks
266-.83861 -.0451 (266*2π)/4992 weeks
267-.02665 -1.00247 (267*2π)/4992 weeks
2681.11927 .10565 (268*2π)/4992 weeks
269-.3552 .61486 (269*2π)/4992 weeks
270-.04765 -.75964 (270*2π)/4992 weeks
271.54233 -.22859 (271*2π)/4992 weeks
272.60529 .32262 (272*2π)/4992 weeks
273-.14816 .52105 (273*2π)/4992 weeks
274-.2535 -.40152 (274*2π)/4992 weeks
275.79765 .16218 (275*2π)/4992 weeks
276-.26268 .85539 (276*2π)/4992 weeks
277-1.04044 -.17724 (277*2π)/4992 weeks
278.49728 -1.15619 (278*2π)/4992 weeks
2791.5197 .34336 (279*2π)/4992 weeks
280-.26377 1.56149 (280*2π)/4992 weeks
281-1.26362 -.28008 (281*2π)/4992 weeks
282.48488 -1.06968 (282*2π)/4992 weeks
2831.3377 .86404 (283*2π)/4992 weeks
284-.7302 1.3315 (284*2π)/4992 weeks
285-.86393 -.39886 (285*2π)/4992 weeks
286-.1162 -.46711 (286*2π)/4992 weeks
287.59169 -.10734 (287*2π)/4992 weeks
288-.25276 1.0805 (288*2π)/4992 weeks
289-1.13949 -.35818 (289*2π)/4992 weeks
290.23927 -.93241 (290*2π)/4992 weeks
291.64999 -.16146 (291*2π)/4992 weeks
292.28298 .7297 (292*2π)/4992 weeks
293-.80226 -.06121 (293*2π)/4992 weeks
294.28225 -.71953 (294*2π)/4992 weeks
295.60849 .22192 (295*2π)/4992 weeks
296-.35423 .5189 (296*2π)/4992 weeks
297-.47932 -.19988 (297*2π)/4992 weeks
298-.06291 -.79965 (298*2π)/4992 weeks
2991.11022 -.50364 (299*2π)/4992 weeks
300.59647 1.14111 (300*2π)/4992 weeks
301-.79137 .60417 (301*2π)/4992 weeks
302-.77536 -.61034 (302*2π)/4992 weeks
303.76868 -.88683 (303*2π)/4992 weeks
304.77175 .9828 (304*2π)/4992 weeks
305-1.23051 .53796 (305*2π)/4992 weeks
306-.10982 -1.24747 (306*2π)/4992 weeks
3071.1022 -.04217 (307*2π)/4992 weeks
308.17302 1.12372 (308*2π)/4992 weeks
309-.773 .39997 (309*2π)/4992 weeks
310-.46953 -.83852 (310*2π)/4992 weeks
311.63144 -.15617 (311*2π)/4992 weeks
312-.24005 .71401 (312*2π)/4992 weeks
313-.5356 -.57766 (313*2π)/4992 weeks
314.63598 -.51289 (314*2π)/4992 weeks
315.20947 .30938 (315*2π)/4992 weeks
316-.065 -.03219 (316*2π)/4992 weeks
317-.1788 -.18976 (317*2π)/4992 weeks
318.422 -.19439 (318*2π)/4992 weeks
319.55279 .17043 (319*2π)/4992 weeks
320.1398 .74779 (320*2π)/4992 weeks
321-.75999 .3018 (321*2π)/4992 weeks
322-.49251 -.82149 (322*2π)/4992 weeks
323.63714 -.24731 (323*2π)/4992 weeks
324.31061 .65622 (324*2π)/4992 weeks
325-.615 .12032 (325*2π)/4992 weeks
326.06579 -.68452 (326*2π)/4992 weeks
327.71835 -.04858 (327*2π)/4992 weeks
328-.2637 .8342 (328*2π)/4992 weeks
329-.7153 -.08332 (329*2π)/4992 weeks
330.26299 -.28219 (330*2π)/4992 weeks
331-.21408 .14877 (331*2π)/4992 weeks
332.05958 -.10915 (332*2π)/4992 weeks
333-.28688 -.03443 (333*2π)/4991 weeks
334.27175 .15725 (334*2π)/4991 weeks
335-.0643 .36728 (335*2π)/4991 weeks
336-.00534 -.17845 (336*2π)/4991 weeks
337-.40902 .37934 (337*2π)/4991 weeks
338-.47877 -.61229 (338*2π)/4991 weeks
339.33001 -.39884 (339*2π)/4991 weeks
340.45986 .40137 (340*2π)/4991 weeks
341-.64053 .3112 (341*2π)/4991 weeks
342-.57674 -1.07921 (342*2π)/4991 weeks
343.97215 -.58763 (343*2π)/4991 weeks
344.63475 .79126 (344*2π)/4991 weeks
345-.93677 .72262 (345*2π)/4991 weeks
346-.15424 -1.31224 (346*2π)/4991 weeks
3471.27326 .0989 (347*2π)/4991 weeks
348-.3219 1.17169 (348*2π)/4991 weeks
349-1.39077 -.5217 (349*2π)/4991 weeks
350.52383 -1.40923 (350*2π)/4991 weeks
3511.18931 .43899 (351*2π)/4991 weeks
352-.47578 1.34392 (352*2π)/4991 weeks
353-1.69718 -.56268 (353*2π)/4991 weeks
354.69673 -1.53528 (354*2π)/4991 weeks
3551.41795 .26052 (355*2π)/4991 weeks
356-.36931 1.24226 (356*2π)/4991 weeks
357-.97889 -.53541 (357*2π)/4991 weeks
358.22302 -.82722 (358*2π)/4991 weeks
359.66942 -.34616 (359*2π)/4991 weeks
360.06172 .20539 (360*2π)/4991 weeks
361-.2869 .07433 (361*2π)/4991 weeks
362.20595 -.64786 (362*2π)/4991 weeks
363.79483 -.02736 (363*2π)/4991 weeks
364.61421 .59549 (364*2π)/4991 weeks
365-.64507 .66744 (365*2π)/4991 weeks
366-.51367 -.79038 (366*2π)/4991 weeks
367.79669 -.30025 (367*2π)/4991 weeks
368.43145 .78775 (368*2π)/4991 weeks
369-1.17219 .52023 (369*2π)/4991 weeks
370-.35011 -1.95604 (370*2π)/4991 weeks
3712.0544 -.00468 (371*2π)/4991 weeks
372-.42397 2.31138 (372*2π)/4991 weeks
373-2.48873 -.67844 (373*2π)/4991 weeks
374.87629 -2.63156 (374*2π)/4991 weeks
3752.56112 .85666 (375*2π)/4991 weeks
376-1.21054 2.51256 (376*2π)/4991 weeks
377-1.86558 -1.44658 (377*2π)/4991 weeks
3781.55513 -1.45672 (378*2π)/4991 weeks
3791.43163 1.02287 (379*2π)/4991 weeks
380-.86376 1.3624 (380*2π)/4991 weeks
381-1.44938 -.59213 (381*2π)/4991 weeks
382.39261 -.52744 (382*2π)/4991 weeks
383.50043 .09496 (383*2π)/4991 weeks
384-.28964 .39875 (384*2π)/4991 weeks
385-.53959 -.08832 (385*2π)/4991 weeks
386.13494 -1.09848 (386*2π)/4991 weeks
387.91007 .5909 (387*2π)/4991 weeks
388-.328 .50731 (388*2π)/4991 weeks
389-.35016 -.24163 (389*2π)/4991 weeks
390.04598 -.39615 (390*2π)/4991 weeks
391.54745 .15507 (391*2π)/4991 weeks
392-.52358 .87726 (392*2π)/4991 weeks
393-1.20456 -.43559 (393*2π)/4991 weeks
394.26442 -1.50333 (394*2π)/4991 weeks
3951.35794 .0434 (395*2π)/4991 weeks
396-.64023 1.24994 (396*2π)/4991 weeks
397-1.47937 -1.57261 (397*2π)/4991 weeks
3981.08337 -1.27872 (398*2π)/4991 weeks
3991.76342 .46705 (399*2π)/4991 weeks
400-.43451 1.5939 (400*2π)/4991 weeks
401-.70958 -.47086 (401*2π)/4991 weeks
402.83262 -.40187 (402*2π)/4991 weeks
403.64321 .30109 (403*2π)/4991 weeks
404-.4687 1.11316 (404*2π)/4991 weeks
405-1.29078 -.61421 (405*2π)/4991 weeks
406.81508 -.99782 (406*2π)/4991 weeks
4071.55398 .34548 (407*2π)/4991 weeks
408-.80455 1.56295 (408*2π)/4991 weeks
409-2.3432 -1.21803 (409*2π)/4991 weeks
4101.12966 -1.93815 (410*2π)/4991 weeks
4111.88009 .68505 (411*2π)/4991 weeks
412-.11614 1.66103 (412*2π)/4991 weeks
413-1.18794 .03648 (413*2π)/4991 weeks
414.66636 -1.44616 (414*2π)/4991 weeks
4151.31061 1.58436 (415*2π)/4991 weeks
416-1.21911 1.94386 (416*2π)/4991 weeks
417-2.797 -.58592 (417*2π)/4991 weeks
418.22206 -2.72416 (418*2π)/4991 weeks
4192.79083 .27766 (419*2π)/4991 weeks
420-.96671 2.54308 (420*2π)/4991 weeks
421-3.45615 -1.93598 (421*2π)/4991 weeks
4222.79962 -3.5242 (422*2π)/4991 weeks
4233.02537 3.49735 (423*2π)/4991 weeks
424-3.91668 2.50873 (424*2π)/4991 weeks
425-2.11303 -3.95561 (425*2π)/4991 weeks
4263.50296 -.90933 (426*2π)/4991 weeks
427.19096 3.45653 (427*2π)/4991 weeks
428-3.6501 .32994 (428*2π)/4991 weeks
429-.23635 -4.23863 (429*2π)/4991 weeks
4303.44709 -.63095 (430*2π)/4991 weeks
431-.0161 3.09862 (431*2π)/4991 weeks
432-2.12443 .15374 (432*2π)/4991 weeks
433-1.23274 -1.70128 (433*2π)/4991 weeks
4341.49233 -.60334 (434*2π)/4991 weeks
435.13006 1.14998 (435*2π)/4991 weeks
436-.79874 -.68367 (436*2π)/4991 weeks
437-.38482 -.34293 (437*2π)/4991 weeks
438.22091 -3.14423 (438*2π)/4991 weeks
4393.63926 .60738 (439*2π)/4991 weeks
440-.60935 2.82268 (440*2π)/4991 weeks
441-2.38763 -.24801 (441*2π)/4991 weeks
442.13596 -2.82244 (442*2π)/4991 weeks
4433.22183 -.15537 (443*2π)/4991 weeks
444-.04072 4.11929 (444*2π)/4991 weeks
445-4.92573 -1.06773 (445*2π)/4991 weeks
4462.85824 -4.12008 (446*2π)/4991 weeks
4471.96335 1.49755 (447*2π)/4991 weeks
448-1.38226 2.55831 (448*2π)/4991 weeks
449-3.65246 -.55969 (449*2π)/4991 weeks
4501.95924 -3.73277 (450*2π)/4991 weeks
4512.7746 2.87871 (451*2π)/4991 weeks
452-3.50949 .82325 (452*2π)/4991 weeks
453-.38063 -3.26362 (453*2π)/4991 weeks
4542.55028 .12141 (454*2π)/4991 weeks
455-1.10401 .70861 (455*2π)/4991 weeks
456.4374 -2.32551 (456*2π)/4991 weeks
4571.0306 .24417 (457*2π)/4991 weeks
458.1223 -.07437 (458*2π)/4991 weeks
459.12019 -.08824 (459*2π)/4991 weeks
4601.45728 -.83389 (460*2π)/4991 weeks
461-.19179 1.48315 (461*2π)/4991 weeks
462-1.40252 -2.21026 (462*2π)/4991 weeks
4634.96955 -.28628 (463*2π)/4991 weeks
464.29543 5.66409 (464*2π)/4991 weeks
465-5.3792 -.47651 (465*2π)/4991 weeks
4662.23783 -5.239 (466*2π)/4991 weeks
4674.02668 4.80483 (467*2π)/4991 weeks
468-5.12892 4.66256 (468*2π)/4991 weeks
469-5.41945 -4.21932 (469*2π)/4991 weeks
4703.512 -4.87635 (470*2π)/4991 weeks
4715.02009 3.95096 (471*2π)/4991 weeks
472-5.96559 5.55082 (472*2π)/4991 weeks
473-6.19104 -6.29856 (473*2π)/4991 weeks
4745.91384 -5.13534 (474*2π)/4991 weeks
4754.74367 4.99655 (475*2π)/4991 weeks
476-7.06763 4.03087 (476*2π)/4991 weeks
477-4.44709 -5.65452 (477*2π)/4991 weeks
4784.90079 -8.18626 (478*2π)/4991 weeks
4797.95981 6.33455 (479*2π)/4991 weeks
480-7.83073 3.17602 (480*2π)/4991 weeks
481-.49354 -4.29878 (481*2π)/4991 weeks
482.84343 2.45571 (482*2π)/4991 weeks
483-3.45838 -.37477 (483*2π)/4991 weeks
484.97386 -2.53273 (484*2π)/4991 weeks
485.55216 .36007 (485*2π)/4991 weeks
486-5.86534 -4.2397 (486*2π)/4991 weeks
4876.37137 -4.24411 (487*2π)/4991 weeks
488-1.8629 6.38348 (488*2π)/4991 weeks
489-4.13378 -4.09733 (489*2π)/4991 weeks
4901.83415 -6.99266 (490*2π)/4991 weeks
4917.99376 -5.62762 (491*2π)/4991 weeks
4925.55345 19.44102 (492*2π)/4991 weeks
493-29.03834 2.18966 (493*2π)/4991 weeks
494.86151 -31.10176 (494*2π)/4991 weeks
49523.48327 -8.3506 (495*2π)/4991 weeks
4968.69138 26.64452 (496*2π)/4991 weeks
497-54.16034 18.77854 (497*2π)/4991 weeks



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