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Fourier Analysis of EFU (ProShares UltraShort MSCI EAFE)


EFU (ProShares UltraShort MSCI EAFE) appears to have interesting cyclic behaviour every 49 weeks (13.9841*sine), 45 weeks (10.3801*sine), and 18 weeks (7.0434*cosine).

EFU (ProShares UltraShort MSCI EAFE) has an average price of 124.31 (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 10/25/2007 to 3/20/2017 for EFU (ProShares UltraShort MSCI EAFE), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0124.3104   0 
160.46204 100.9056 (1*2π)/492492 weeks
29.58539 73.78933 (2*2π)/492246 weeks
3-26.5157 49.12374 (3*2π)/492164 weeks
4-26.93519 18.67396 (4*2π)/492123 weeks
5-21.41677 -.72585 (5*2π)/49298 weeks
6-1.97587 -12.44814 (6*2π)/49282 weeks
716.30939 -1.1097 (7*2π)/49270 weeks
813.99349 13.67656 (8*2π)/49262 weeks
94.047 13.66571 (9*2π)/49255 weeks
10.5246 13.98414 (10*2π)/49249 weeks
11-4.54176 10.38009 (11*2π)/49245 weeks
12-2.36649 8.05252 (12*2π)/49241 weeks
13-3.98832 5.11198 (13*2π)/49238 weeks
14-1.03717 4.90908 (14*2π)/49235 weeks
15-4.04991 7.65838 (15*2π)/49233 weeks
16-5.29356 2.12996 (16*2π)/49231 weeks
17-3.5288 .52192 (17*2π)/49229 weeks
18-.57471 -1.84221 (18*2π)/49227 weeks
191.11098 -.82086 (19*2π)/49226 weeks
204.12043 -.10482 (20*2π)/49225 weeks
214.38607 5.3952 (21*2π)/49223 weeks
221.05829 7.78017 (22*2π)/49222 weeks
23-4.49133 7.03753 (23*2π)/49221 weeks
24-5.3346 -.24036 (24*2π)/49221 weeks
25-2.2727 -2.50434 (25*2π)/49220 weeks
261.58965 -5.3662 (26*2π)/49219 weeks
276.06637 -2.24267 (27*2π)/49218 weeks
287.04341 1.93127 (28*2π)/49218 weeks
295.7954 6.91489 (29*2π)/49217 weeks
30.13563 9.29089 (30*2π)/49216 weeks
31-4.09807 4.71627 (31*2π)/49216 weeks
32-3.08367 1.1563 (32*2π)/49215 weeks
33-1.03641 -.44125 (33*2π)/49215 weeks
34.19277 .61735 (34*2π)/49214 weeks
35.40341 -.06819 (35*2π)/49214 weeks
362.23817 .05629 (36*2π)/49214 weeks
372.14796 3.25952 (37*2π)/49213 weeks
38-.2041 1.88624 (38*2π)/49213 weeks
39.95656 1.33837 (39*2π)/49213 weeks
40.50033 1.72266 (40*2π)/49212 weeks
411.04687 2.03831 (41*2π)/49212 weeks
42.31746 2.66254 (42*2π)/49212 weeks
43.34695 1.19104 (43*2π)/49211 weeks
44-.17215 1.95804 (44*2π)/49211 weeks
45-.38912 1.75393 (45*2π)/49211 weeks
46-.67836 .82976 (46*2π)/49211 weeks
47.70453 .3019 (47*2π)/49210 weeks
481.60804 .37925 (48*2π)/49210 weeks
492.45571 1.84827 (49*2π)/49210 weeks
501.61729 3.51042 (50*2π)/49210 weeks
51-.65715 3.35721 (51*2π)/49210 weeks
52-1.99201 2.26189 (52*2π)/4929 weeks
53-1.4797 .66768 (53*2π)/4929 weeks
54-1.10804 -.25035 (54*2π)/4929 weeks
55.95463 -.84338 (55*2π)/4929 weeks
561.29013 .99358 (56*2π)/4929 weeks
571.02762 1.09508 (57*2π)/4929 weeks
58.60387 1.69038 (58*2π)/4928 weeks
59-.16775 1.19003 (59*2π)/4928 weeks
60.79974 1.2609 (60*2π)/4928 weeks
61.35234 1.34671 (61*2π)/4928 weeks
62.68116 2.07137 (62*2π)/4928 weeks
63-.93952 2.64435 (63*2π)/4928 weeks
64-2.4826 1.32236 (64*2π)/4928 weeks
65-2.08354 -.9827 (65*2π)/4928 weeks
66-.25427 -2.38291 (66*2π)/4927 weeks
672.07809 -1.79256 (67*2π)/4927 weeks
682.57564 .26039 (68*2π)/4927 weeks
693.23771 .51222 (69*2π)/4927 weeks
702.65402 3.73989 (70*2π)/4927 weeks
71-.68181 4.09106 (71*2π)/4927 weeks
72-1.88593 2.49786 (72*2π)/4927 weeks
73-2.86947 .36284 (73*2π)/4927 weeks
74-.78738 -1.54968 (74*2π)/4927 weeks
75.1954 -1.45904 (75*2π)/4927 weeks
762.34936 -1.59478 (76*2π)/4926 weeks
773.28352 .75726 (77*2π)/4926 weeks
782.49738 2.43135 (78*2π)/4926 weeks
79.41013 3.25298 (79*2π)/4926 weeks
80-1.12888 2.67454 (80*2π)/4926 weeks
81-1.80239 .99821 (81*2π)/4926 weeks
82-.837 -.07388 (82*2π)/4926 weeks
83.1563 -.11126 (83*2π)/4926 weeks
84.62437 .56323 (84*2π)/4926 weeks
85-.2863 .50647 (85*2π)/4926 weeks
86.20285 -.07725 (86*2π)/4926 weeks
87.72767 -.31635 (87*2π)/4926 weeks
881.31491 .09862 (88*2π)/4926 weeks
891.24979 .87409 (89*2π)/4926 weeks
90.84555 1.60249 (90*2π)/4925 weeks
91-.13688 2.12279 (91*2π)/4925 weeks
92-1.10809 1.72952 (92*2π)/4925 weeks
93-1.35466 .29806 (93*2π)/4925 weeks
94-.95154 -.65047 (94*2π)/4925 weeks
95.38407 -1.30811 (95*2π)/4925 weeks
961.19736 -1.1563 (96*2π)/4925 weeks
972.40866 -.20181 (97*2π)/4925 weeks
982.0563 1.73691 (98*2π)/4925 weeks
99.90414 2.50222 (99*2π)/4925 weeks
100-.34153 2.38848 (100*2π)/4925 weeks
101-1.01399 1.54969 (101*2π)/4925 weeks
102-1.77185 .64913 (102*2π)/4925 weeks
103-.93934 -1.09178 (103*2π)/4925 weeks
104.19781 -1.19201 (104*2π)/4925 weeks
1051.02562 -.49767 (105*2π)/4925 weeks
1061.55838 .04421 (106*2π)/4925 weeks
1071.35307 1.12225 (107*2π)/4925 weeks
108.80743 1.46274 (108*2π)/4925 weeks
109-.10411 1.54569 (109*2π)/4925 weeks
110-.98988 .979 (110*2π)/4924 weeks
111-.67579 -.29853 (111*2π)/4924 weeks
112-.27463 -.35548 (112*2π)/4924 weeks
113.08048 -.26109 (113*2π)/4924 weeks
114.39613 -.05385 (114*2π)/4924 weeks
115.34878 -.23209 (115*2π)/4924 weeks
116.87736 -.20807 (116*2π)/4924 weeks
117.62736 .60741 (117*2π)/4924 weeks
118.24434 .23868 (118*2π)/4924 weeks
119.44414 -.27106 (119*2π)/4924 weeks
120.7538 -.2073 (120*2π)/4924 weeks
121.77719 .2899 (121*2π)/4924 weeks
122.98728 .52721 (122*2π)/4924 weeks
123.63979 1.12214 (123*2π)/4924 weeks
124-.14285 .44158 (124*2π)/4924 weeks
125.25073 -.07435 (125*2π)/4924 weeks
126.4563 -.32218 (126*2π)/4924 weeks
1271.17877 .25447 (127*2π)/4924 weeks
128.35272 .83503 (128*2π)/4924 weeks
129.19067 .0645 (129*2π)/4924 weeks
130.84214 .32393 (130*2π)/4924 weeks
131.8177 .49701 (131*2π)/4924 weeks
132.85063 .78228 (132*2π)/4924 weeks
133.1762 .88341 (133*2π)/4924 weeks
134.25263 .81007 (134*2π)/4924 weeks
135-.5452 .67833 (135*2π)/4924 weeks
136-.2036 -.38405 (136*2π)/4924 weeks
137.63217 -.21727 (137*2π)/4924 weeks
138.77207 .19916 (138*2π)/4924 weeks
139.62108 .41658 (139*2π)/4924 weeks
140.62102 .18282 (140*2π)/4924 weeks
141.97842 .36057 (141*2π)/4923 weeks
142.42091 1.21369 (142*2π)/4923 weeks
143-.16383 .38151 (143*2π)/4923 weeks
144.29791 .26724 (144*2π)/4923 weeks
145.25467 .48289 (145*2π)/4923 weeks
146-.04331 .52336 (146*2π)/4923 weeks
147-.24713 -.29075 (147*2π)/4923 weeks
148.28299 -.20863 (148*2π)/4923 weeks
149.51387 -.56659 (149*2π)/4923 weeks
1501.19589 -.06526 (150*2π)/4923 weeks
1511.04784 .56759 (151*2π)/4923 weeks
152.80586 1.00907 (152*2π)/4923 weeks
153.09297 1.14466 (153*2π)/4923 weeks
154-.66513 .7307 (154*2π)/4923 weeks
155-.4982 .15197 (155*2π)/4923 weeks
156-.42748 -.644 (156*2π)/4923 weeks
157.48656 -1.02398 (157*2π)/4923 weeks
1581.10526 -.87102 (158*2π)/4923 weeks
1591.66231 -.27531 (159*2π)/4923 weeks
1601.72501 .81585 (160*2π)/4923 weeks
161.97952 1.20934 (161*2π)/4923 weeks
162.35392 1.3671 (162*2π)/4923 weeks
163-.30796 .91508 (163*2π)/4923 weeks
164-.2229 .36341 (164*2π)/4923 weeks
165-.20543 -.12532 (165*2π)/4923 weeks
166.29894 -.25339 (166*2π)/4923 weeks
167.56264 -.1797 (167*2π)/4923 weeks
1681.16202 .21643 (168*2π)/4923 weeks
169.83167 1.02933 (169*2π)/4923 weeks
170.29923 .80322 (170*2π)/4923 weeks
171.07033 1.07228 (171*2π)/4923 weeks
172-.59194 .6482 (172*2π)/4923 weeks
173-.30937 .42486 (173*2π)/4923 weeks
174-.82509 .05813 (174*2π)/4923 weeks
175-.1773 -1.08377 (175*2π)/4923 weeks
176.48373 -.6123 (176*2π)/4923 weeks
177.84726 -.52189 (177*2π)/4923 weeks
1781.00028 .25786 (178*2π)/4923 weeks
179.4096 .39726 (179*2π)/4923 weeks
180.80305 .55825 (180*2π)/4923 weeks
181-.21563 1.07901 (181*2π)/4923 weeks
182-.42039 .1425 (182*2π)/4923 weeks
183-.72564 .14469 (183*2π)/4923 weeks
184-.75899 -1.07114 (184*2π)/4923 weeks
185.41373 -1.73025 (185*2π)/4923 weeks
1861.55747 -1.26012 (186*2π)/4923 weeks
1872.22042 -.15906 (187*2π)/4923 weeks
1881.73884 1.14928 (188*2π)/4923 weeks
189.68687 1.54144 (189*2π)/4923 weeks
190-.26375 1.35305 (190*2π)/4923 weeks
191-1.24389 .53398 (191*2π)/4923 weeks
192-.6244 -.83065 (192*2π)/4923 weeks
193.14639 -1.10416 (193*2π)/4923 weeks
1941.08105 -.97769 (194*2π)/4923 weeks
1951.25249 -.04859 (195*2π)/4923 weeks
196.73152 .20736 (196*2π)/4923 weeks
197.80651 -.02164 (197*2π)/4922 weeks
1981.02549 .18157 (198*2π)/4922 weeks
199.77616 .51373 (199*2π)/4922 weeks
200.66399 .49047 (200*2π)/4922 weeks
201.51342 .90871 (201*2π)/4922 weeks
202-.30521 .71758 (202*2π)/4922 weeks
203-.43436 .20032 (203*2π)/4922 weeks
204-.50362 -.55625 (204*2π)/4922 weeks
205.66519 -.93009 (205*2π)/4922 weeks
2061.07313 -.46495 (206*2π)/4922 weeks
2071.28251 -.08109 (207*2π)/4922 weeks
2081.24941 .50001 (208*2π)/4922 weeks
209.81789 .9226 (209*2π)/4922 weeks
210.30797 .9847 (210*2π)/4922 weeks
211-.1799 .84601 (211*2π)/4922 weeks
212-.44037 .27184 (212*2π)/4922 weeks
213-.42963 .04152 (213*2π)/4922 weeks
214-.47577 -.68012 (214*2π)/4922 weeks
215.3659 -.55886 (215*2π)/4922 weeks
216.46067 -.61903 (216*2π)/4922 weeks
2171.19305 -.26677 (217*2π)/4922 weeks
218.90977 .24882 (218*2π)/4922 weeks
219.83074 .46052 (219*2π)/4922 weeks
220.28302 1.07554 (220*2π)/4922 weeks
221-.56341 .63251 (221*2π)/4922 weeks
222-.56933 -.00895 (222*2π)/4922 weeks
223-.67723 -.71375 (223*2π)/4922 weeks
224.03594 -1.29222 (224*2π)/4922 weeks
225.79177 -1.24593 (225*2π)/4922 weeks
2261.39279 -.97784 (226*2π)/4922 weeks
2271.79894 -.26706 (227*2π)/4922 weeks
2281.62796 .52005 (228*2π)/4922 weeks
2291.49687 1.19658 (229*2π)/4922 weeks
230.13482 1.71723 (230*2π)/4922 weeks
231-.59702 .74633 (231*2π)/4922 weeks
232-.57403 .34429 (232*2π)/4922 weeks
233-.70353 -.66668 (233*2π)/4922 weeks
234.21771 -1.41075 (234*2π)/4922 weeks
2351.38113 -1.16977 (235*2π)/4922 weeks
2361.61482 -.1159 (236*2π)/4922 weeks
2371.44541 .5806 (237*2π)/4922 weeks
238.98753 1.15718 (238*2π)/4922 weeks
239.44558 1.64572 (239*2π)/4922 weeks
240-1.05846 1.29146 (240*2π)/4922 weeks
241-1.24064 -.29962 (241*2π)/4922 weeks
242-.50791 -.83406 (242*2π)/4922 weeks
243-.00649 -1.16185 (243*2π)/4922 weeks
244.71607 -.90364 (244*2π)/4922 weeks
2451.17929 -.83432 (245*2π)/4922 weeks
2461.75771   (246*2π)/4922 weeks
2471.17929 .83432 (247*2π)/4922 weeks
248.71607 .90364 (248*2π)/4922 weeks
249-.00649 1.16185 (249*2π)/4922 weeks
250-.50791 .83406 (250*2π)/4922 weeks
251-1.24064 .29962 (251*2π)/4922 weeks
252-1.05846 -1.29146 (252*2π)/4922 weeks
253.44558 -1.64572 (253*2π)/4922 weeks
254.98753 -1.15718 (254*2π)/4922 weeks
2551.44541 -.5806 (255*2π)/4922 weeks
2561.61482 .1159 (256*2π)/4922 weeks
2571.38113 1.16977 (257*2π)/4922 weeks
258.21771 1.41075 (258*2π)/4922 weeks
259-.70353 .66668 (259*2π)/4922 weeks
260-.57403 -.34429 (260*2π)/4922 weeks
261-.59702 -.74633 (261*2π)/4922 weeks
262.13482 -1.71723 (262*2π)/4922 weeks
2631.49687 -1.19658 (263*2π)/4922 weeks
2641.62796 -.52005 (264*2π)/4922 weeks
2651.79894 .26706 (265*2π)/4922 weeks
2661.39279 .97784 (266*2π)/4922 weeks
267.79177 1.24593 (267*2π)/4922 weeks
268.03594 1.29222 (268*2π)/4922 weeks
269-.67723 .71375 (269*2π)/4922 weeks
270-.56933 .00895 (270*2π)/4922 weeks
271-.56341 -.63251 (271*2π)/4922 weeks
272.28302 -1.07554 (272*2π)/4922 weeks
273.83074 -.46052 (273*2π)/4922 weeks
274.90977 -.24882 (274*2π)/4922 weeks
2751.19305 .26677 (275*2π)/4922 weeks
276.46067 .61903 (276*2π)/4922 weeks
277.3659 .55886 (277*2π)/4922 weeks
278-.47577 .68012 (278*2π)/4922 weeks
279-.42963 -.04152 (279*2π)/4922 weeks
280-.44037 -.27184 (280*2π)/4922 weeks
281-.1799 -.84601 (281*2π)/4922 weeks
282.30797 -.9847 (282*2π)/4922 weeks
283.81789 -.9226 (283*2π)/4922 weeks
2841.24941 -.50001 (284*2π)/4922 weeks
2851.28251 .08109 (285*2π)/4922 weeks
2861.07313 .46495 (286*2π)/4922 weeks
287.66519 .93009 (287*2π)/4922 weeks
288-.50362 .55625 (288*2π)/4922 weeks
289-.43436 -.20032 (289*2π)/4922 weeks
290-.30521 -.71758 (290*2π)/4922 weeks
291.51342 -.90871 (291*2π)/4922 weeks
292.66399 -.49047 (292*2π)/4922 weeks
293.77616 -.51373 (293*2π)/4922 weeks
2941.02549 -.18157 (294*2π)/4922 weeks
295.80651 .02164 (295*2π)/4922 weeks
296.73152 -.20736 (296*2π)/4922 weeks
2971.25249 .04859 (297*2π)/4922 weeks
2981.08105 .97769 (298*2π)/4922 weeks
299.14639 1.10416 (299*2π)/4922 weeks
300-.6244 .83065 (300*2π)/4922 weeks
301-1.24389 -.53398 (301*2π)/4922 weeks
302-.26375 -1.35305 (302*2π)/4922 weeks
303.68687 -1.54144 (303*2π)/4922 weeks
3041.73884 -1.14928 (304*2π)/4922 weeks
3052.22042 .15906 (305*2π)/4922 weeks
3061.55747 1.26012 (306*2π)/4922 weeks
307.41373 1.73025 (307*2π)/4922 weeks
308-.75899 1.07114 (308*2π)/4922 weeks
309-.72564 -.14469 (309*2π)/4922 weeks
310-.42039 -.1425 (310*2π)/4922 weeks
311-.21563 -1.07901 (311*2π)/4922 weeks
312.80305 -.55825 (312*2π)/4922 weeks
313.4096 -.39726 (313*2π)/4922 weeks
3141.00028 -.25786 (314*2π)/4922 weeks
315.84726 .52189 (315*2π)/4922 weeks
316.48373 .6123 (316*2π)/4922 weeks
317-.1773 1.08377 (317*2π)/4922 weeks
318-.82509 -.05813 (318*2π)/4922 weeks
319-.30937 -.42486 (319*2π)/4922 weeks
320-.59194 -.6482 (320*2π)/4922 weeks
321.07033 -1.07228 (321*2π)/4922 weeks
322.29923 -.80322 (322*2π)/4922 weeks
323.83167 -1.02933 (323*2π)/4922 weeks
3241.16202 -.21643 (324*2π)/4922 weeks
325.56264 .1797 (325*2π)/4922 weeks
326.29894 .25339 (326*2π)/4922 weeks
327-.20543 .12532 (327*2π)/4922 weeks
328-.2229 -.36341 (328*2π)/4922 weeks
329-.30796 -.91508 (329*2π)/4921 weeks
330.35392 -1.3671 (330*2π)/4921 weeks
331.97952 -1.20934 (331*2π)/4921 weeks
3321.72501 -.81585 (332*2π)/4921 weeks
3331.66231 .27531 (333*2π)/4921 weeks
3341.10526 .87102 (334*2π)/4921 weeks
335.48656 1.02398 (335*2π)/4921 weeks
336-.42748 .644 (336*2π)/4921 weeks
337-.4982 -.15197 (337*2π)/4921 weeks
338-.66513 -.7307 (338*2π)/4921 weeks
339.09297 -1.14466 (339*2π)/4921 weeks
340.80586 -1.00907 (340*2π)/4921 weeks
3411.04784 -.56759 (341*2π)/4921 weeks
3421.19589 .06526 (342*2π)/4921 weeks
343.51387 .56659 (343*2π)/4921 weeks
344.28299 .20863 (344*2π)/4921 weeks
345-.24713 .29075 (345*2π)/4921 weeks
346-.04331 -.52336 (346*2π)/4921 weeks
347.25467 -.48289 (347*2π)/4921 weeks
348.29791 -.26724 (348*2π)/4921 weeks
349-.16383 -.38151 (349*2π)/4921 weeks
350.42091 -1.21369 (350*2π)/4921 weeks
351.97842 -.36057 (351*2π)/4921 weeks
352.62102 -.18282 (352*2π)/4921 weeks
353.62108 -.41658 (353*2π)/4921 weeks
354.77207 -.19916 (354*2π)/4921 weeks
355.63217 .21727 (355*2π)/4921 weeks
356-.2036 .38405 (356*2π)/4921 weeks
357-.5452 -.67833 (357*2π)/4921 weeks
358.25263 -.81007 (358*2π)/4921 weeks
359.1762 -.88341 (359*2π)/4921 weeks
360.85063 -.78228 (360*2π)/4921 weeks
361.8177 -.49701 (361*2π)/4921 weeks
362.84214 -.32393 (362*2π)/4921 weeks
363.19067 -.0645 (363*2π)/4921 weeks
364.35272 -.83503 (364*2π)/4921 weeks
3651.17877 -.25447 (365*2π)/4921 weeks
366.4563 .32218 (366*2π)/4921 weeks
367.25073 .07435 (367*2π)/4921 weeks
368-.14285 -.44158 (368*2π)/4921 weeks
369.63979 -1.12214 (369*2π)/4921 weeks
370.98728 -.52721 (370*2π)/4921 weeks
371.77719 -.2899 (371*2π)/4921 weeks
372.7538 .2073 (372*2π)/4921 weeks
373.44414 .27106 (373*2π)/4921 weeks
374.24434 -.23868 (374*2π)/4921 weeks
375.62736 -.60741 (375*2π)/4921 weeks
376.87736 .20807 (376*2π)/4921 weeks
377.34878 .23209 (377*2π)/4921 weeks
378.39613 .05385 (378*2π)/4921 weeks
379.08048 .26109 (379*2π)/4921 weeks
380-.27463 .35548 (380*2π)/4921 weeks
381-.67579 .29853 (381*2π)/4921 weeks
382-.98988 -.979 (382*2π)/4921 weeks
383-.10411 -1.54569 (383*2π)/4921 weeks
384.80743 -1.46274 (384*2π)/4921 weeks
3851.35307 -1.12225 (385*2π)/4921 weeks
3861.55838 -.04421 (386*2π)/4921 weeks
3871.02562 .49767 (387*2π)/4921 weeks
388.19781 1.19201 (388*2π)/4921 weeks
389-.93934 1.09178 (389*2π)/4921 weeks
390-1.77185 -.64913 (390*2π)/4921 weeks
391-1.01399 -1.54969 (391*2π)/4921 weeks
392-.34153 -2.38848 (392*2π)/4921 weeks
393.90414 -2.50222 (393*2π)/4921 weeks
3942.0563 -1.73691 (394*2π)/4921 weeks
3952.40866 .20181 (395*2π)/4921 weeks
3961.19736 1.1563 (396*2π)/4921 weeks
397.38407 1.30811 (397*2π)/4921 weeks
398-.95154 .65047 (398*2π)/4921 weeks
399-1.35466 -.29806 (399*2π)/4921 weeks
400-1.10809 -1.72952 (400*2π)/4921 weeks
401-.13688 -2.12279 (401*2π)/4921 weeks
402.84555 -1.60249 (402*2π)/4921 weeks
4031.24979 -.87409 (403*2π)/4921 weeks
4041.31491 -.09862 (404*2π)/4921 weeks
405.72767 .31635 (405*2π)/4921 weeks
406.20285 .07725 (406*2π)/4921 weeks
407-.2863 -.50647 (407*2π)/4921 weeks
408.62437 -.56323 (408*2π)/4921 weeks
409.1563 .11126 (409*2π)/4921 weeks
410-.837 .07388 (410*2π)/4921 weeks
411-1.80239 -.99821 (411*2π)/4921 weeks
412-1.12888 -2.67454 (412*2π)/4921 weeks
413.41013 -3.25298 (413*2π)/4921 weeks
4142.49738 -2.43135 (414*2π)/4921 weeks
4153.28352 -.75726 (415*2π)/4921 weeks
4162.34936 1.59478 (416*2π)/4921 weeks
417.1954 1.45904 (417*2π)/4921 weeks
418-.78738 1.54968 (418*2π)/4921 weeks
419-2.86947 -.36284 (419*2π)/4921 weeks
420-1.88593 -2.49786 (420*2π)/4921 weeks
421-.68181 -4.09106 (421*2π)/4921 weeks
4222.65402 -3.73989 (422*2π)/4921 weeks
4233.23771 -.51222 (423*2π)/4921 weeks
4242.57564 -.26039 (424*2π)/4921 weeks
4252.07809 1.79256 (425*2π)/4921 weeks
426-.25427 2.38291 (426*2π)/4921 weeks
427-2.08354 .9827 (427*2π)/4921 weeks
428-2.4826 -1.32236 (428*2π)/4921 weeks
429-.93952 -2.64435 (429*2π)/4921 weeks
430.68116 -2.07137 (430*2π)/4921 weeks
431.35234 -1.34671 (431*2π)/4921 weeks
432.79974 -1.2609 (432*2π)/4921 weeks
433-.16775 -1.19003 (433*2π)/4921 weeks
434.60387 -1.69038 (434*2π)/4921 weeks
4351.02762 -1.09508 (435*2π)/4921 weeks
4361.29013 -.99358 (436*2π)/4921 weeks
437.95463 .84338 (437*2π)/4921 weeks
438-1.10804 .25035 (438*2π)/4921 weeks
439-1.4797 -.66768 (439*2π)/4921 weeks
440-1.99201 -2.26189 (440*2π)/4921 weeks
441-.65715 -3.35721 (441*2π)/4921 weeks
4421.61729 -3.51042 (442*2π)/4921 weeks
4432.45571 -1.84827 (443*2π)/4921 weeks
4441.60804 -.37925 (444*2π)/4921 weeks
445.70453 -.3019 (445*2π)/4921 weeks
446-.67836 -.82976 (446*2π)/4921 weeks
447-.38912 -1.75393 (447*2π)/4921 weeks
448-.17215 -1.95804 (448*2π)/4921 weeks
449.34695 -1.19104 (449*2π)/4921 weeks
450.31746 -2.66254 (450*2π)/4921 weeks
4511.04687 -2.03831 (451*2π)/4921 weeks
452.50033 -1.72266 (452*2π)/4921 weeks
453.95656 -1.33837 (453*2π)/4921 weeks
454-.2041 -1.88624 (454*2π)/4921 weeks
4552.14796 -3.25952 (455*2π)/4921 weeks
4562.23817 -.05629 (456*2π)/4921 weeks
457.40341 .06819 (457*2π)/4921 weeks
458.19277 -.61735 (458*2π)/4921 weeks
459-1.03641 .44125 (459*2π)/4921 weeks
460-3.08367 -1.1563 (460*2π)/4921 weeks
461-4.09807 -4.71627 (461*2π)/4921 weeks
462.13563 -9.29089 (462*2π)/4921 weeks
4635.7954 -6.91489 (463*2π)/4921 weeks
4647.04341 -1.93127 (464*2π)/4921 weeks
4656.06637 2.24267 (465*2π)/4921 weeks
4661.58965 5.3662 (466*2π)/4921 weeks
467-2.2727 2.50434 (467*2π)/4921 weeks
468-5.3346 .24036 (468*2π)/4921 weeks
469-4.49133 -7.03753 (469*2π)/4921 weeks
4701.05829 -7.78017 (470*2π)/4921 weeks
4714.38607 -5.3952 (471*2π)/4921 weeks
4724.12043 .10482 (472*2π)/4921 weeks
4731.11098 .82086 (473*2π)/4921 weeks
474-.57471 1.84221 (474*2π)/4921 weeks
475-3.5288 -.52192 (475*2π)/4921 weeks
476-5.29356 -2.12996 (476*2π)/4921 weeks
477-4.04991 -7.65838 (477*2π)/4921 weeks
478-1.03717 -4.90908 (478*2π)/4921 weeks
479-3.98832 -5.11198 (479*2π)/4921 weeks
480-2.36649 -8.05252 (480*2π)/4921 weeks
481-4.54176 -10.38009 (481*2π)/4921 weeks
482.5246 -13.98414 (482*2π)/4921 weeks
4834.047 -13.66571 (483*2π)/4921 weeks
48413.99349 -13.67656 (484*2π)/4921 weeks
48516.30939 1.1097 (485*2π)/4921 weeks
486-1.97587 12.44814 (486*2π)/4921 weeks
487-21.41677 .72585 (487*2π)/4921 weeks
488-26.93519 -18.67396 (488*2π)/4921 weeks
489-26.5157 -49.12374 (489*2π)/4921 weeks
4909.58539 -73.78933 (490*2π)/4921 weeks

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