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Fourier Analysis of GLL (ProShares UltraShort Gold)


GLL (ProShares UltraShort Gold) appears to have interesting cyclic behaviour every 49 weeks (6.4388*sine), 33 weeks (6.4364*sine), and 54 weeks (6.3111*sine).

GLL (ProShares UltraShort Gold) has an average price of 137.13 (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 12/28/2006 to 4/16/2018 for GLL (ProShares UltraShort Gold), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0137.1263   0 
149.35411 75.45577 (1*2π)/591591 weeks
2-33.08895 52.13538 (2*2π)/591296 weeks
3-11.69453 4.84838 (3*2π)/591197 weeks
45.58482 3.63951 (4*2π)/591148 weeks
511.70223 8.82427 (5*2π)/591118 weeks
6-.1017 16.15462 (6*2π)/59199 weeks
7-7.68907 15.906 (7*2π)/59184 weeks
8-6.21426 3.7135 (8*2π)/59174 weeks
9.82968 2.49682 (9*2π)/59166 weeks
105.75097 -.0752 (10*2π)/59159 weeks
112.11764 6.31112 (11*2π)/59154 weeks
12-1.96976 6.43878 (12*2π)/59149 weeks
13-1.69796 6.26406 (13*2π)/59145 weeks
14-2.13505 3.52191 (14*2π)/59142 weeks
15-1.84117 1.44644 (15*2π)/59139 weeks
163.05631 .64671 (16*2π)/59137 weeks
172.8897 3.18936 (17*2π)/59135 weeks
181.47562 6.43642 (18*2π)/59133 weeks
19-2.53853 5.38562 (19*2π)/59131 weeks
20-4.63444 -.06689 (20*2π)/59130 weeks
21.24676 -2.11501 (21*2π)/59128 weeks
222.38296 1.3493 (22*2π)/59127 weeks
233.08399 6.00262 (23*2π)/59126 weeks
24-.06373 2.96107 (24*2π)/59125 weeks
25.20437 3.64153 (25*2π)/59124 weeks
26-1.50169 1.3876 (26*2π)/59123 weeks
27-1.67943 -1.50514 (27*2π)/59122 weeks
283.26428 1.29494 (28*2π)/59121 weeks
293.52674 3.1748 (29*2π)/59120 weeks
30.0824 3.78916 (30*2π)/59120 weeks
31-3.13675 3.02201 (31*2π)/59119 weeks
32-2.71 .09293 (32*2π)/59118 weeks
331.29813 -.99309 (33*2π)/59118 weeks
343.1824 .29804 (34*2π)/59117 weeks
351.7704 3.0913 (35*2π)/59117 weeks
36-1.76879 3.90963 (36*2π)/59116 weeks
37-2.99276 1.24792 (37*2π)/59116 weeks
38-.91863 -1.55135 (38*2π)/59116 weeks
391.06969 -.39053 (39*2π)/59115 weeks
403.44338 1.0642 (40*2π)/59115 weeks
411.30987 4.22752 (41*2π)/59114 weeks
42-1.81112 2.9741 (42*2π)/59114 weeks
43-1.61383 .08096 (43*2π)/59114 weeks
44.1561 -1.34913 (44*2π)/59113 weeks
452.38502 .38285 (45*2π)/59113 weeks
46.37717 2.88389 (46*2π)/59113 weeks
47-.05748 2.0908 (47*2π)/59113 weeks
48-1.15931 1.38766 (48*2π)/59112 weeks
49-.98358 .56787 (49*2π)/59112 weeks
50.91728 .10391 (50*2π)/59112 weeks
51-.04579 .53665 (51*2π)/59112 weeks
52.88649 .61078 (52*2π)/59111 weeks
53-.11855 2.04399 (53*2π)/59111 weeks
54-.26984 1.27294 (54*2π)/59111 weeks
55-.53213 .51728 (55*2π)/59111 weeks
56-.44908 .13519 (56*2π)/59111 weeks
571.17754 .45428 (57*2π)/59110 weeks
58.87256 1.15041 (58*2π)/59110 weeks
59.96878 1.96714 (59*2π)/59110 weeks
60-.56385 1.47028 (60*2π)/59110 weeks
61-.56733 .30384 (61*2π)/59110 weeks
62-.23514 -1.16034 (62*2π)/59110 weeks
63.62226 -.17001 (63*2π)/5919 weeks
641.96315 1.61962 (64*2π)/5919 weeks
65.17178 2.41254 (65*2π)/5919 weeks
66-.82815 .79196 (66*2π)/5919 weeks
67-.91957 -.33419 (67*2π)/5919 weeks
68.14737 -.66865 (68*2π)/5919 weeks
691.55953 .32861 (69*2π)/5919 weeks
701.41085 1.73781 (70*2π)/5918 weeks
71-.49268 1.40709 (71*2π)/5918 weeks
72-.36009 .77208 (72*2π)/5918 weeks
73-.35008 -.09861 (73*2π)/5918 weeks
74-.17537 .21036 (74*2π)/5918 weeks
75.73162 -.2933 (75*2π)/5918 weeks
76.95191 .30958 (76*2π)/5918 weeks
77.01971 1.65865 (77*2π)/5918 weeks
78-.66518 1.35771 (78*2π)/5918 weeks
79-.4547 -.43323 (79*2π)/5917 weeks
80.42567 -.64886 (80*2π)/5917 weeks
811.07751 .80015 (81*2π)/5917 weeks
821.21937 1.15555 (82*2π)/5917 weeks
83.60259 1.18889 (83*2π)/5917 weeks
84-.6733 1.11956 (84*2π)/5917 weeks
85-.96198 -.37178 (85*2π)/5917 weeks
86.43635 -.59681 (86*2π)/5917 weeks
871.19127 .18877 (87*2π)/5917 weeks
881.21423 1.1843 (88*2π)/5917 weeks
89-.2746 1.97829 (89*2π)/5917 weeks
90-1.04793 .22344 (90*2π)/5917 weeks
91-.05635 -.31466 (91*2π)/5916 weeks
92.80295 -.62405 (92*2π)/5916 weeks
931.05334 .55622 (93*2π)/5916 weeks
941.0873 1.43218 (94*2π)/5916 weeks
95.38006 1.31901 (95*2π)/5916 weeks
96-.75245 .97663 (96*2π)/5916 weeks
97-.86037 -.83715 (97*2π)/5916 weeks
98.77315 -.85607 (98*2π)/5916 weeks
992.02734 .55151 (99*2π)/5916 weeks
100.25073 1.86011 (100*2π)/5916 weeks
101-.70135 1.28699 (101*2π)/5916 weeks
102-.69503 -.51379 (102*2π)/5916 weeks
103.46053 -.74066 (103*2π)/5916 weeks
104.82479 -.21338 (104*2π)/5916 weeks
105.89678 .81349 (105*2π)/5916 weeks
106.63714 .92929 (106*2π)/5916 weeks
107-.68873 1.20529 (107*2π)/5916 weeks
108-.76389 -.05383 (108*2π)/5915 weeks
109-.00475 -.57473 (109*2π)/5915 weeks
1101.4166 .06633 (110*2π)/5915 weeks
1111.19011 .83243 (111*2π)/5915 weeks
112-.01707 1.66936 (112*2π)/5915 weeks
113-.70812 .46708 (113*2π)/5915 weeks
114-1.02219 -.20711 (114*2π)/5915 weeks
115.51906 -.7747 (115*2π)/5915 weeks
1161.43655 .22193 (116*2π)/5915 weeks
1171.11349 1.32607 (117*2π)/5915 weeks
118-.42796 .70346 (118*2π)/5915 weeks
119-.4998 .48929 (119*2π)/5915 weeks
120.35738 -.40293 (120*2π)/5915 weeks
121.04739 -.58701 (121*2π)/5915 weeks
122.7592 -.19434 (122*2π)/5915 weeks
123.70849 .53661 (123*2π)/5915 weeks
124.4135 1.1821 (124*2π)/5915 weeks
125-.36795 .6998 (125*2π)/5915 weeks
126-.5343 -.22367 (126*2π)/5915 weeks
127.40657 -.7325 (127*2π)/5915 weeks
1281.25012 -.15376 (128*2π)/5915 weeks
1291.08902 1.18055 (129*2π)/5915 weeks
130-.11034 1.24432 (130*2π)/5915 weeks
131-.8982 .16082 (131*2π)/5915 weeks
132-.52534 -.76385 (132*2π)/5914 weeks
1331.03193 -.78316 (133*2π)/5914 weeks
1341.60055 .15297 (134*2π)/5914 weeks
135.54711 1.38249 (135*2π)/5914 weeks
136-.14193 1.17448 (136*2π)/5914 weeks
137-.55598 .12508 (137*2π)/5914 weeks
138-.31563 -.97897 (138*2π)/5914 weeks
1391.25235 -.26004 (139*2π)/5914 weeks
1401.60167 .95563 (140*2π)/5914 weeks
141.34723 1.52233 (141*2π)/5914 weeks
142-.68129 .39853 (142*2π)/5914 weeks
143-.39817 -.73384 (143*2π)/5914 weeks
144.43686 -.32193 (144*2π)/5914 weeks
1451.11119 -.07102 (145*2π)/5914 weeks
146.8936 1.17439 (146*2π)/5914 weeks
147.0163 .72167 (147*2π)/5914 weeks
148-.17243 .31988 (148*2π)/5914 weeks
149-.24144 .16275 (149*2π)/5914 weeks
150.41305 -.40208 (150*2π)/5914 weeks
1511.02706 .22861 (151*2π)/5914 weeks
152.66375 .6587 (152*2π)/5914 weeks
153.35689 .71399 (153*2π)/5914 weeks
154-.30382 .48669 (154*2π)/5914 weeks
155-.06878 .04705 (155*2π)/5914 weeks
156.38099 -.4276 (156*2π)/5914 weeks
157.92132 .00066 (157*2π)/5914 weeks
158.48455 .76627 (158*2π)/5914 weeks
159-.08232 .64683 (159*2π)/5914 weeks
160.21166 -.03733 (160*2π)/5914 weeks
161.09746 -.1013 (161*2π)/5914 weeks
162.4571 .11926 (162*2π)/5914 weeks
163.64799 .08879 (163*2π)/5914 weeks
164.46551 .37732 (164*2π)/5914 weeks
165.19984 .50541 (165*2π)/5914 weeks
166.03324 .68026 (166*2π)/5914 weeks
167-.13858 -.06744 (167*2π)/5914 weeks
168.09965 -.34174 (168*2π)/5914 weeks
169.96016 .05463 (169*2π)/5913 weeks
170.58917 .29413 (170*2π)/5913 weeks
171.27979 .85551 (171*2π)/5913 weeks
172.01514 .46327 (172*2π)/5913 weeks
173-.26944 -.40072 (173*2π)/5913 weeks
174.48014 -.40373 (174*2π)/5913 weeks
175.78103 -.05263 (175*2π)/5913 weeks
176.64073 .47608 (176*2π)/5913 weeks
177.37574 .80796 (177*2π)/5913 weeks
178-.34475 .56452 (178*2π)/5913 weeks
179-.3686 -.18828 (179*2π)/5913 weeks
180.5276 -.51848 (180*2π)/5913 weeks
181.95904 -.0079 (181*2π)/5913 weeks
182.67647 .79604 (182*2π)/5913 weeks
183.17311 .5212 (183*2π)/5913 weeks
184-.16129 .45084 (184*2π)/5913 weeks
185-.13172 -.20247 (185*2π)/5913 weeks
186.27127 -.74156 (186*2π)/5913 weeks
187.98411 .0291 (187*2π)/5913 weeks
188.83796 .70514 (188*2π)/5913 weeks
189.03499 .89981 (189*2π)/5913 weeks
190-.49043 .18854 (190*2π)/5913 weeks
191-.19539 -.6208 (191*2π)/5913 weeks
1921.01622 -.60766 (192*2π)/5913 weeks
1931.0574 .14181 (193*2π)/5913 weeks
194.51339 1.06059 (194*2π)/5913 weeks
195-.40346 .73758 (195*2π)/5913 weeks
196-.33407 -.01234 (196*2π)/5913 weeks
197.45578 -.54831 (197*2π)/5913 weeks
198.8253 -.27436 (198*2π)/5913 weeks
1991.15179 .52487 (199*2π)/5913 weeks
200.42916 1.03728 (200*2π)/5913 weeks
201-.37862 .70559 (201*2π)/5913 weeks
202-.329 -.32853 (202*2π)/5913 weeks
203.52426 -.61995 (203*2π)/5913 weeks
2041.0276 -.09572 (204*2π)/5913 weeks
205.7411 .64596 (205*2π)/5913 weeks
206.20937 .91333 (206*2π)/5913 weeks
207-.34808 .29657 (207*2π)/5913 weeks
208-.21803 -.09317 (208*2π)/5913 weeks
209.30079 -.36348 (209*2π)/5913 weeks
210.91251 -.22382 (210*2π)/5913 weeks
211.82595 .69368 (211*2π)/5913 weeks
212.07572 .68185 (212*2π)/5913 weeks
213-.28928 .17922 (213*2π)/5913 weeks
214-.15528 -.46516 (214*2π)/5913 weeks
215.37037 -.44151 (215*2π)/5913 weeks
216.96691 .02462 (216*2π)/5913 weeks
217.83586 .64451 (217*2π)/5913 weeks
218.08267 .80019 (218*2π)/5913 weeks
219-.07601 .26122 (219*2π)/5913 weeks
220-.05745 -.22137 (220*2π)/5913 weeks
221.39014 -.6447 (221*2π)/5913 weeks
222.81373 .06667 (222*2π)/5913 weeks
223.67197 .67268 (223*2π)/5913 weeks
224-.01821 1.04419 (224*2π)/5913 weeks
225-.37568 .03164 (225*2π)/5913 weeks
226.03698 -.70801 (226*2π)/5913 weeks
227.46344 -.13591 (227*2π)/5913 weeks
228.56058 .22849 (228*2π)/5913 weeks
229.42258 .61783 (229*2π)/5913 weeks
230-.10893 .34086 (230*2π)/5913 weeks
231-.30436 -.04578 (231*2π)/5913 weeks
232-.11083 -.38849 (232*2π)/5913 weeks
233.70666 -.28827 (233*2π)/5913 weeks
234.79758 .34411 (234*2π)/5913 weeks
235.29192 .54062 (235*2π)/5913 weeks
236-.09414 .10822 (236*2π)/5913 weeks
237-.03953 .08534 (237*2π)/5912 weeks
238.04079 -.16033 (238*2π)/5912 weeks
239.45383 -.36606 (239*2π)/5912 weeks
240.91856 -.00242 (240*2π)/5912 weeks
241.52017 .5701 (241*2π)/5912 weeks
242-.08542 .71881 (242*2π)/5912 weeks
243-.19709 .14202 (243*2π)/5912 weeks
244-.06551 -.55509 (244*2π)/5912 weeks
245.60002 -.35265 (245*2π)/5912 weeks
246.88547 .05046 (246*2π)/5912 weeks
247.772 .9015 (247*2π)/5912 weeks
248-.28476 .93238 (248*2π)/5912 weeks
249-.66502 -.17994 (249*2π)/5912 weeks
250.23532 -.89231 (250*2π)/5912 weeks
251.90046 -.43259 (251*2π)/5912 weeks
252.95736 .76327 (252*2π)/5912 weeks
253.00819 .91285 (253*2π)/5912 weeks
254-.48592 .41574 (254*2π)/5912 weeks
255-.26019 -.54173 (255*2π)/5912 weeks
256.48688 -.39785 (256*2π)/5912 weeks
257.75105 -.04587 (257*2π)/5912 weeks
258.64203 .59802 (258*2π)/5912 weeks
259-.0749 .71035 (259*2π)/5912 weeks
260-.30386 -.06281 (260*2π)/5912 weeks
261-.04111 -.4062 (261*2π)/5912 weeks
262.37925 -.37995 (262*2π)/5912 weeks
263.91348 .15694 (263*2π)/5912 weeks
264.73926 .41363 (264*2π)/5912 weeks
265-.11568 .60611 (265*2π)/5912 weeks
266-.24137 .07332 (266*2π)/5912 weeks
267.13446 -.42126 (267*2π)/5912 weeks
268.51727 -.30678 (268*2π)/5912 weeks
269.53597 .00963 (269*2π)/5912 weeks
270.47749 .40571 (270*2π)/5912 weeks
271.25817 .41403 (271*2π)/5912 weeks
272-.29789 .23841 (272*2π)/5912 weeks
273-.04586 -.26072 (273*2π)/5912 weeks
274.11636 -.63485 (274*2π)/5912 weeks
275.91313 -.26122 (275*2π)/5912 weeks
276.73124 .6457 (276*2π)/5912 weeks
277-.02869 .70717 (277*2π)/5912 weeks
278-.45639 .18344 (278*2π)/5912 weeks
279-.13888 -.51718 (279*2π)/5912 weeks
280.55168 -.69998 (280*2π)/5912 weeks
2811.07197 .16907 (281*2π)/5912 weeks
282.55764 .70595 (282*2π)/5912 weeks
283-.24741 .5219 (283*2π)/5912 weeks
284-.48789 -.12974 (284*2π)/5912 weeks
285.02059 -.64298 (285*2π)/5912 weeks
286.50321 -.51006 (286*2π)/5912 weeks
2871.17955 .09557 (287*2π)/5912 weeks
288.3286 .90382 (288*2π)/5912 weeks
289-.15801 .35438 (289*2π)/5912 weeks
290-.41863 -.34754 (290*2π)/5912 weeks
291.13565 -.61139 (291*2π)/5912 weeks
292.87466 -.21314 (292*2π)/5912 weeks
293.78927 .24487 (293*2π)/5912 weeks
294.36564 .64387 (294*2π)/5912 weeks
295-.34455 .331 (295*2π)/5912 weeks
296-.34455 -.331 (296*2π)/5912 weeks
297.36564 -.64387 (297*2π)/5912 weeks
298.78927 -.24487 (298*2π)/5912 weeks
299.87466 .21314 (299*2π)/5912 weeks
300.13565 .61139 (300*2π)/5912 weeks
301-.41863 .34754 (301*2π)/5912 weeks
302-.15801 -.35438 (302*2π)/5912 weeks
303.3286 -.90382 (303*2π)/5912 weeks
3041.17955 -.09557 (304*2π)/5912 weeks
305.50321 .51006 (305*2π)/5912 weeks
306.02059 .64298 (306*2π)/5912 weeks
307-.48789 .12974 (307*2π)/5912 weeks
308-.24741 -.5219 (308*2π)/5912 weeks
309.55764 -.70595 (309*2π)/5912 weeks
3101.07197 -.16907 (310*2π)/5912 weeks
311.55168 .69998 (311*2π)/5912 weeks
312-.13888 .51718 (312*2π)/5912 weeks
313-.45639 -.18344 (313*2π)/5912 weeks
314-.02869 -.70717 (314*2π)/5912 weeks
315.73124 -.6457 (315*2π)/5912 weeks
316.91313 .26122 (316*2π)/5912 weeks
317.11636 .63485 (317*2π)/5912 weeks
318-.04586 .26072 (318*2π)/5912 weeks
319-.29789 -.23841 (319*2π)/5912 weeks
320.25817 -.41403 (320*2π)/5912 weeks
321.47749 -.40571 (321*2π)/5912 weeks
322.53597 -.00963 (322*2π)/5912 weeks
323.51727 .30678 (323*2π)/5912 weeks
324.13446 .42126 (324*2π)/5912 weeks
325-.24137 -.07332 (325*2π)/5912 weeks
326-.11568 -.60611 (326*2π)/5912 weeks
327.73926 -.41363 (327*2π)/5912 weeks
328.91348 -.15694 (328*2π)/5912 weeks
329.37925 .37995 (329*2π)/5912 weeks
330-.04111 .4062 (330*2π)/5912 weeks
331-.30386 .06281 (331*2π)/5912 weeks
332-.0749 -.71035 (332*2π)/5912 weeks
333.64203 -.59802 (333*2π)/5912 weeks
334.75105 .04587 (334*2π)/5912 weeks
335.48688 .39785 (335*2π)/5912 weeks
336-.26019 .54173 (336*2π)/5912 weeks
337-.48592 -.41574 (337*2π)/5912 weeks
338.00819 -.91285 (338*2π)/5912 weeks
339.95736 -.76327 (339*2π)/5912 weeks
340.90046 .43259 (340*2π)/5912 weeks
341.23532 .89231 (341*2π)/5912 weeks
342-.66502 .17994 (342*2π)/5912 weeks
343-.28476 -.93238 (343*2π)/5912 weeks
344.772 -.9015 (344*2π)/5912 weeks
345.88547 -.05046 (345*2π)/5912 weeks
346.60002 .35265 (346*2π)/5912 weeks
347-.06551 .55509 (347*2π)/5912 weeks
348-.19709 -.14202 (348*2π)/5912 weeks
349-.08542 -.71881 (349*2π)/5912 weeks
350.52017 -.5701 (350*2π)/5912 weeks
351.91856 .00242 (351*2π)/5912 weeks
352.45383 .36606 (352*2π)/5912 weeks
353.04079 .16033 (353*2π)/5912 weeks
354-.03953 -.08534 (354*2π)/5912 weeks
355-.09414 -.10822 (355*2π)/5912 weeks
356.29192 -.54062 (356*2π)/5912 weeks
357.79758 -.34411 (357*2π)/5912 weeks
358.70666 .28827 (358*2π)/5912 weeks
359-.11083 .38849 (359*2π)/5912 weeks
360-.30436 .04578 (360*2π)/5912 weeks
361-.10893 -.34086 (361*2π)/5912 weeks
362.42258 -.61783 (362*2π)/5912 weeks
363.56058 -.22849 (363*2π)/5912 weeks
364.46344 .13591 (364*2π)/5912 weeks
365.03698 .70801 (365*2π)/5912 weeks
366-.37568 -.03164 (366*2π)/5912 weeks
367-.01821 -1.04419 (367*2π)/5912 weeks
368.67197 -.67268 (368*2π)/5912 weeks
369.81373 -.06667 (369*2π)/5912 weeks
370.39014 .6447 (370*2π)/5912 weeks
371-.05745 .22137 (371*2π)/5912 weeks
372-.07601 -.26122 (372*2π)/5912 weeks
373.08267 -.80019 (373*2π)/5912 weeks
374.83586 -.64451 (374*2π)/5912 weeks
375.96691 -.02462 (375*2π)/5912 weeks
376.37037 .44151 (376*2π)/5912 weeks
377-.15528 .46516 (377*2π)/5912 weeks
378-.28928 -.17922 (378*2π)/5912 weeks
379.07572 -.68185 (379*2π)/5912 weeks
380.82595 -.69368 (380*2π)/5912 weeks
381.91251 .22382 (381*2π)/5912 weeks
382.30079 .36348 (382*2π)/5912 weeks
383-.21803 .09317 (383*2π)/5912 weeks
384-.34808 -.29657 (384*2π)/5912 weeks
385.20937 -.91333 (385*2π)/5912 weeks
386.7411 -.64596 (386*2π)/5912 weeks
3871.0276 .09572 (387*2π)/5912 weeks
388.52426 .61995 (388*2π)/5912 weeks
389-.329 .32853 (389*2π)/5912 weeks
390-.37862 -.70559 (390*2π)/5912 weeks
391.42916 -1.03728 (391*2π)/5912 weeks
3921.15179 -.52487 (392*2π)/5912 weeks
393.8253 .27436 (393*2π)/5912 weeks
394.45578 .54831 (394*2π)/5912 weeks
395-.33407 .01234 (395*2π)/5911 weeks
396-.40346 -.73758 (396*2π)/5911 weeks
397.51339 -1.06059 (397*2π)/5911 weeks
3981.0574 -.14181 (398*2π)/5911 weeks
3991.01622 .60766 (399*2π)/5911 weeks
400-.19539 .6208 (400*2π)/5911 weeks
401-.49043 -.18854 (401*2π)/5911 weeks
402.03499 -.89981 (402*2π)/5911 weeks
403.83796 -.70514 (403*2π)/5911 weeks
404.98411 -.0291 (404*2π)/5911 weeks
405.27127 .74156 (405*2π)/5911 weeks
406-.13172 .20247 (406*2π)/5911 weeks
407-.16129 -.45084 (407*2π)/5911 weeks
408.17311 -.5212 (408*2π)/5911 weeks
409.67647 -.79604 (409*2π)/5911 weeks
410.95904 .0079 (410*2π)/5911 weeks
411.5276 .51848 (411*2π)/5911 weeks
412-.3686 .18828 (412*2π)/5911 weeks
413-.34475 -.56452 (413*2π)/5911 weeks
414.37574 -.80796 (414*2π)/5911 weeks
415.64073 -.47608 (415*2π)/5911 weeks
416.78103 .05263 (416*2π)/5911 weeks
417.48014 .40373 (417*2π)/5911 weeks
418-.26944 .40072 (418*2π)/5911 weeks
419.01514 -.46327 (419*2π)/5911 weeks
420.27979 -.85551 (420*2π)/5911 weeks
421.58917 -.29413 (421*2π)/5911 weeks
422.96016 -.05463 (422*2π)/5911 weeks
423.09965 .34174 (423*2π)/5911 weeks
424-.13858 .06744 (424*2π)/5911 weeks
425.03324 -.68026 (425*2π)/5911 weeks
426.19984 -.50541 (426*2π)/5911 weeks
427.46551 -.37732 (427*2π)/5911 weeks
428.64799 -.08879 (428*2π)/5911 weeks
429.4571 -.11926 (429*2π)/5911 weeks
430.09746 .1013 (430*2π)/5911 weeks
431.21166 .03733 (431*2π)/5911 weeks
432-.08232 -.64683 (432*2π)/5911 weeks
433.48455 -.76627 (433*2π)/5911 weeks
434.92132 -.00066 (434*2π)/5911 weeks
435.38099 .4276 (435*2π)/5911 weeks
436-.06878 -.04705 (436*2π)/5911 weeks
437-.30382 -.48669 (437*2π)/5911 weeks
438.35689 -.71399 (438*2π)/5911 weeks
439.66375 -.6587 (439*2π)/5911 weeks
4401.02706 -.22861 (440*2π)/5911 weeks
441.41305 .40208 (441*2π)/5911 weeks
442-.24144 -.16275 (442*2π)/5911 weeks
443-.17243 -.31988 (443*2π)/5911 weeks
444.0163 -.72167 (444*2π)/5911 weeks
445.8936 -1.17439 (445*2π)/5911 weeks
4461.11119 .07102 (446*2π)/5911 weeks
447.43686 .32193 (447*2π)/5911 weeks
448-.39817 .73384 (448*2π)/5911 weeks
449-.68129 -.39853 (449*2π)/5911 weeks
450.34723 -1.52233 (450*2π)/5911 weeks
4511.60167 -.95563 (451*2π)/5911 weeks
4521.25235 .26004 (452*2π)/5911 weeks
453-.31563 .97897 (453*2π)/5911 weeks
454-.55598 -.12508 (454*2π)/5911 weeks
455-.14193 -1.17448 (455*2π)/5911 weeks
456.54711 -1.38249 (456*2π)/5911 weeks
4571.60055 -.15297 (457*2π)/5911 weeks
4581.03193 .78316 (458*2π)/5911 weeks
459-.52534 .76385 (459*2π)/5911 weeks
460-.8982 -.16082 (460*2π)/5911 weeks
461-.11034 -1.24432 (461*2π)/5911 weeks
4621.08902 -1.18055 (462*2π)/5911 weeks
4631.25012 .15376 (463*2π)/5911 weeks
464.40657 .7325 (464*2π)/5911 weeks
465-.5343 .22367 (465*2π)/5911 weeks
466-.36795 -.6998 (466*2π)/5911 weeks
467.4135 -1.1821 (467*2π)/5911 weeks
468.70849 -.53661 (468*2π)/5911 weeks
469.7592 .19434 (469*2π)/5911 weeks
470.04739 .58701 (470*2π)/5911 weeks
471.35738 .40293 (471*2π)/5911 weeks
472-.4998 -.48929 (472*2π)/5911 weeks
473-.42796 -.70346 (473*2π)/5911 weeks
4741.11349 -1.32607 (474*2π)/5911 weeks
4751.43655 -.22193 (475*2π)/5911 weeks
476.51906 .7747 (476*2π)/5911 weeks
477-1.02219 .20711 (477*2π)/5911 weeks
478-.70812 -.46708 (478*2π)/5911 weeks
479-.01707 -1.66936 (479*2π)/5911 weeks
4801.19011 -.83243 (480*2π)/5911 weeks
4811.4166 -.06633 (481*2π)/5911 weeks
482-.00475 .57473 (482*2π)/5911 weeks
483-.76389 .05383 (483*2π)/5911 weeks
484-.68873 -1.20529 (484*2π)/5911 weeks
485.63714 -.92929 (485*2π)/5911 weeks
486.89678 -.81349 (486*2π)/5911 weeks
487.82479 .21338 (487*2π)/5911 weeks
488.46053 .74066 (488*2π)/5911 weeks
489-.69503 .51379 (489*2π)/5911 weeks
490-.70135 -1.28699 (490*2π)/5911 weeks
491.25073 -1.86011 (491*2π)/5911 weeks
4922.02734 -.55151 (492*2π)/5911 weeks
493.77315 .85607 (493*2π)/5911 weeks
494-.86037 .83715 (494*2π)/5911 weeks
495-.75245 -.97663 (495*2π)/5911 weeks
496.38006 -1.31901 (496*2π)/5911 weeks
4971.0873 -1.43218 (497*2π)/5911 weeks
4981.05334 -.55622 (498*2π)/5911 weeks
499.80295 .62405 (499*2π)/5911 weeks
500-.05635 .31466 (500*2π)/5911 weeks
501-1.04793 -.22344 (501*2π)/5911 weeks
502-.2746 -1.97829 (502*2π)/5911 weeks
5031.21423 -1.1843 (503*2π)/5911 weeks
5041.19127 -.18877 (504*2π)/5911 weeks
505.43635 .59681 (505*2π)/5911 weeks
506-.96198 .37178 (506*2π)/5911 weeks
507-.6733 -1.11956 (507*2π)/5911 weeks
508.60259 -1.18889 (508*2π)/5911 weeks
5091.21937 -1.15555 (509*2π)/5911 weeks
5101.07751 -.80015 (510*2π)/5911 weeks
511.42567 .64886 (511*2π)/5911 weeks
512-.4547 .43323 (512*2π)/5911 weeks
513-.66518 -1.35771 (513*2π)/5911 weeks
514.01971 -1.65865 (514*2π)/5911 weeks
515.95191 -.30958 (515*2π)/5911 weeks
516.73162 .2933 (516*2π)/5911 weeks
517-.17537 -.21036 (517*2π)/5911 weeks
518-.35008 .09861 (518*2π)/5911 weeks
519-.36009 -.77208 (519*2π)/5911 weeks
520-.49268 -1.40709 (520*2π)/5911 weeks
5211.41085 -1.73781 (521*2π)/5911 weeks
5221.55953 -.32861 (522*2π)/5911 weeks
523.14737 .66865 (523*2π)/5911 weeks
524-.91957 .33419 (524*2π)/5911 weeks
525-.82815 -.79196 (525*2π)/5911 weeks
526.17178 -2.41254 (526*2π)/5911 weeks
5271.96315 -1.61962 (527*2π)/5911 weeks
528.62226 .17001 (528*2π)/5911 weeks
529-.23514 1.16034 (529*2π)/5911 weeks
530-.56733 -.30384 (530*2π)/5911 weeks
531-.56385 -1.47028 (531*2π)/5911 weeks
532.96878 -1.96714 (532*2π)/5911 weeks
533.87256 -1.15041 (533*2π)/5911 weeks
5341.17754 -.45428 (534*2π)/5911 weeks
535-.44908 -.13519 (535*2π)/5911 weeks
536-.53213 -.51728 (536*2π)/5911 weeks
537-.26984 -1.27294 (537*2π)/5911 weeks
538-.11855 -2.04399 (538*2π)/5911 weeks
539.88649 -.61078 (539*2π)/5911 weeks
540-.04579 -.53665 (540*2π)/5911 weeks
541.91728 -.10391 (541*2π)/5911 weeks
542-.98358 -.56787 (542*2π)/5911 weeks
543-1.15931 -1.38766 (543*2π)/5911 weeks
544-.05748 -2.0908 (544*2π)/5911 weeks
545.37717 -2.88389 (545*2π)/5911 weeks
5462.38502 -.38285 (546*2π)/5911 weeks
547.1561 1.34913 (547*2π)/5911 weeks
548-1.61383 -.08096 (548*2π)/5911 weeks
549-1.81112 -2.9741 (549*2π)/5911 weeks
5501.30987 -4.22752 (550*2π)/5911 weeks
5513.44338 -1.0642 (551*2π)/5911 weeks
5521.06969 .39053 (552*2π)/5911 weeks
553-.91863 1.55135 (553*2π)/5911 weeks
554-2.99276 -1.24792 (554*2π)/5911 weeks
555-1.76879 -3.90963 (555*2π)/5911 weeks
5561.7704 -3.0913 (556*2π)/5911 weeks
5573.1824 -.29804 (557*2π)/5911 weeks
5581.29813 .99309 (558*2π)/5911 weeks
559-2.71 -.09293 (559*2π)/5911 weeks
560-3.13675 -3.02201 (560*2π)/5911 weeks
561.0824 -3.78916 (561*2π)/5911 weeks
5623.52674 -3.1748 (562*2π)/5911 weeks
5633.26428 -1.29494 (563*2π)/5911 weeks
564-1.67943 1.50514 (564*2π)/5911 weeks
565-1.50169 -1.3876 (565*2π)/5911 weeks
566.20437 -3.64153 (566*2π)/5911 weeks
567-.06373 -2.96107 (567*2π)/5911 weeks
5683.08399 -6.00262 (568*2π)/5911 weeks
5692.38296 -1.3493 (569*2π)/5911 weeks
570.24676 2.11501 (570*2π)/5911 weeks
571-4.63444 .06689 (571*2π)/5911 weeks
572-2.53853 -5.38562 (572*2π)/5911 weeks
5731.47562 -6.43642 (573*2π)/5911 weeks
5742.8897 -3.18936 (574*2π)/5911 weeks
5753.05631 -.64671 (575*2π)/5911 weeks
576-1.84117 -1.44644 (576*2π)/5911 weeks
577-2.13505 -3.52191 (577*2π)/5911 weeks
578-1.69796 -6.26406 (578*2π)/5911 weeks
579-1.96976 -6.43878 (579*2π)/5911 weeks
5802.11764 -6.31112 (580*2π)/5911 weeks
5815.75097 .0752 (581*2π)/5911 weeks
582.82968 -2.49682 (582*2π)/5911 weeks
583-6.21426 -3.7135 (583*2π)/5911 weeks
584-7.68907 -15.906 (584*2π)/5911 weeks
585-.1017 -16.15462 (585*2π)/5911 weeks
58611.70223 -8.82427 (586*2π)/5911 weeks
5875.58482 -3.63951 (587*2π)/5911 weeks
588-11.69453 -4.84838 (588*2π)/5911 weeks
589-33.08895 -52.13538 (589*2π)/5911 weeks



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