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Fourier Analysis of EWV (ProShares UltraShort MSCI Japan)


EWV (ProShares UltraShort MSCI Japan) appears to have interesting cyclic behaviour every 48 weeks (12.4101*sine), 44 weeks (9.9198*sine), and 32 weeks (7.122*cosine).

EWV (ProShares UltraShort MSCI Japan) has an average price of 142.27 (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 11/8/2007 to 1/9/2017 for EWV (ProShares UltraShort MSCI Japan), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0142.2735   0 
130.14974 93.64309 (1*2π)/480480 weeks
213.69549 56.99215 (2*2π)/480240 weeks
3-16.22155 38.9147 (3*2π)/480160 weeks
4-9.26642 21.68542 (4*2π)/480120 weeks
5-15.37195 6.04228 (5*2π)/48096 weeks
6-3.26582 1.69437 (6*2π)/48080 weeks
78.27753 2.3463 (7*2π)/48069 weeks
85.33343 12.27824 (8*2π)/48060 weeks
95.76515 7.97713 (9*2π)/48053 weeks
103.30461 12.41013 (10*2π)/48048 weeks
11-1.36391 9.91978 (11*2π)/48044 weeks
12-1.79463 7.93757 (12*2π)/48040 weeks
132.55504 6.50023 (13*2π)/48037 weeks
14.76537 9.84953 (14*2π)/48034 weeks
15-7.12199 8.33673 (15*2π)/48032 weeks
16-4.8493 4.6164 (16*2π)/48030 weeks
17-6.62438 .80086 (17*2π)/48028 weeks
18-.65186 -1.98134 (18*2π)/48027 weeks
191.00977 .0016 (19*2π)/48025 weeks
204.42175 -.36803 (20*2π)/48024 weeks
214.16254 3.62121 (21*2π)/48023 weeks
221.96528 6.35593 (22*2π)/48022 weeks
23-3.19805 5.93575 (23*2π)/48021 weeks
24-2.81291 2.01644 (24*2π)/48020 weeks
25-4.8993 .74144 (25*2π)/48019 weeks
26-.18014 -3.44603 (26*2π)/48018 weeks
273.86157 -1.25211 (27*2π)/48018 weeks
286.32575 .84113 (28*2π)/48017 weeks
294.69483 5.28609 (29*2π)/48017 weeks
30.04324 6.28482 (30*2π)/48016 weeks
31-1.20948 3.44587 (31*2π)/48015 weeks
32-1.43751 2.54987 (32*2π)/48015 weeks
33-.29504 1.70813 (33*2π)/48015 weeks
34-1.05621 .91155 (34*2π)/48014 weeks
35.33998 .5015 (35*2π)/48014 weeks
361.90455 .70663 (36*2π)/48013 weeks
37.07289 2.84231 (37*2π)/48013 weeks
38.18791 .51925 (38*2π)/48013 weeks
39-.0061 1.38725 (39*2π)/48012 weeks
401.08217 .5167 (40*2π)/48012 weeks
412.41365 1.49859 (41*2π)/48012 weeks
42.50317 1.42402 (42*2π)/48011 weeks
431.29414 2.30338 (43*2π)/48011 weeks
44.15594 2.84667 (44*2π)/48011 weeks
45-1.64379 2.0999 (45*2π)/48011 weeks
46-.16455 -.0138 (46*2π)/48010 weeks
47-.34639 -.20354 (47*2π)/48010 weeks
482.15287 -1.19697 (48*2π)/48010 weeks
493.61921 1.04643 (49*2π)/48010 weeks
501.7645 2.19382 (50*2π)/48010 weeks
511.46945 3.05154 (51*2π)/4809 weeks
52-.30626 2.47451 (52*2π)/4809 weeks
53-.71207 1.92959 (53*2π)/4809 weeks
54-.0115 .16103 (54*2π)/4809 weeks
55-.01763 1.1311 (55*2π)/4809 weeks
56.76822 .0903 (56*2π)/4809 weeks
571.12203 .75604 (57*2π)/4808 weeks
58.57054 .50793 (58*2π)/4808 weeks
591.63778 .61363 (59*2π)/4808 weeks
601.66582 .96236 (60*2π)/4808 weeks
612.17483 1.71301 (61*2π)/4808 weeks
621.44984 2.60671 (62*2π)/4808 weeks
63-.01676 3.23855 (63*2π)/4808 weeks
64-1.23037 2.55556 (64*2π)/4808 weeks
65-1.70318 1.50667 (65*2π)/4807 weeks
66-1.39507 -.58069 (66*2π)/4807 weeks
67-.80622 -1.10769 (67*2π)/4807 weeks
681.9682 -1.97124 (68*2π)/4807 weeks
693.44449 .20687 (69*2π)/4807 weeks
702.39457 1.28033 (70*2π)/4807 weeks
712.01807 3.00319 (71*2π)/4807 weeks
72-.06565 2.64045 (72*2π)/4807 weeks
73-.75313 2.45727 (73*2π)/4807 weeks
74-1.72214 .8114 (74*2π)/4806 weeks
75-1.055 -.70135 (75*2π)/4806 weeks
76.54762 -.8778 (76*2π)/4806 weeks
771.88628 -.32707 (77*2π)/4806 weeks
782.29857 .87487 (78*2π)/4806 weeks
791.18712 1.51844 (79*2π)/4806 weeks
801.1645 1.23604 (80*2π)/4806 weeks
81.94896 1.3654 (81*2π)/4806 weeks
821.04653 .99621 (82*2π)/4806 weeks
83.323 2.19817 (83*2π)/4806 weeks
84-.58308 1.52911 (84*2π)/4806 weeks
85-.88056 .41265 (85*2π)/4806 weeks
86.10578 -.02294 (86*2π)/4806 weeks
87.31325 .08964 (87*2π)/4806 weeks
88.77123 -.04946 (88*2π)/4805 weeks
891.94118 .57715 (89*2π)/4805 weeks
901.97672 1.52701 (90*2π)/4805 weeks
911.00793 2.02422 (91*2π)/4805 weeks
92.0763 2.3187 (92*2π)/4805 weeks
93-.65882 1.13488 (93*2π)/4805 weeks
94-.67984 1.11608 (94*2π)/4805 weeks
95-1.28868 -.27097 (95*2π)/4805 weeks
96-.08659 -.29607 (96*2π)/4805 weeks
97.74418 -.57384 (97*2π)/4805 weeks
981.42045 -.23775 (98*2π)/4805 weeks
991.98993 .19353 (99*2π)/4805 weeks
1001.56792 1.78845 (100*2π)/4805 weeks
101.76738 1.43357 (101*2π)/4805 weeks
102-.09843 1.24389 (102*2π)/4805 weeks
103.13413 1.08001 (103*2π)/4805 weeks
104-.4225 .42095 (104*2π)/4805 weeks
105-.02963 .21152 (105*2π)/4805 weeks
106.48633 -.2937 (106*2π)/4805 weeks
1071.12391 -.48237 (107*2π)/4804 weeks
1081.71851 .52476 (108*2π)/4804 weeks
1091.6147 .86219 (109*2π)/4804 weeks
1101.28869 1.04775 (110*2π)/4804 weeks
111.66539 1.47696 (111*2π)/4804 weeks
112.75857 1.46254 (112*2π)/4804 weeks
113.05818 2.09091 (113*2π)/4804 weeks
114-.37166 .79355 (114*2π)/4804 weeks
115-.23416 .73171 (115*2π)/4804 weeks
116-.02717 .80764 (116*2π)/4804 weeks
117.14176 .29257 (117*2π)/4804 weeks
118.3818 .31636 (118*2π)/4804 weeks
119.09479 .18886 (119*2π)/4804 weeks
120.60121 -.14567 (120*2π)/4804 weeks
1211.04519 .69385 (121*2π)/4804 weeks
122.55978 1.2571 (122*2π)/4804 weeks
123.32142 1.29118 (123*2π)/4804 weeks
124-.41672 .99305 (124*2π)/4804 weeks
125-.23256 .61815 (125*2π)/4804 weeks
126-.01865 .75366 (126*2π)/4804 weeks
127-.25101 -.05084 (127*2π)/4804 weeks
128-.11052 -.18693 (128*2π)/4804 weeks
129.35538 -.57664 (129*2π)/4804 weeks
1301.07243 -.28007 (130*2π)/4804 weeks
1311.03796 .08455 (131*2π)/4804 weeks
1321.37878 .77902 (132*2π)/4804 weeks
133.33758 1.3705 (133*2π)/4804 weeks
134-.13748 .8157 (134*2π)/4804 weeks
135-.15222 .21062 (135*2π)/4804 weeks
136.48245 .05676 (136*2π)/4804 weeks
137.48564 .23726 (137*2π)/4804 weeks
138.04641 .28886 (138*2π)/4803 weeks
139.66257 -.33849 (139*2π)/4803 weeks
140.72859 .11576 (140*2π)/4803 weeks
141.75177 .37148 (141*2π)/4803 weeks
142.45228 .45184 (142*2π)/4803 weeks
1431.02946 .15084 (143*2π)/4803 weeks
144.27726 .9206 (144*2π)/4803 weeks
145.43017 .55449 (145*2π)/4803 weeks
146-.05411 .75757 (146*2π)/4803 weeks
147-.33249 .09456 (147*2π)/4803 weeks
148-.08532 -.14767 (148*2π)/4803 weeks
149.57992 -.56903 (149*2π)/4803 weeks
1501.08447 -.21745 (150*2π)/4803 weeks
1511.08114 .33052 (151*2π)/4803 weeks
1521.09863 .62777 (152*2π)/4803 weeks
153.81608 .88934 (153*2π)/4803 weeks
154.60516 1.19853 (154*2π)/4803 weeks
155-.0163 1.07319 (155*2π)/4803 weeks
156-.43951 .32098 (156*2π)/4803 weeks
157-.0464 .07768 (157*2π)/4803 weeks
158-.08427 -.06255 (158*2π)/4803 weeks
159.21441 -.20567 (159*2π)/4803 weeks
160.31997 -.2959 (160*2π)/4803 weeks
1611.00281 .01509 (161*2π)/4803 weeks
162.94177 .35207 (162*2π)/4803 weeks
163.66166 .59074 (163*2π)/4803 weeks
164.2386 .88911 (164*2π)/4803 weeks
165-.45372 .3728 (165*2π)/4803 weeks
166.02547 .04448 (166*2π)/4803 weeks
167-.22994 -.36124 (167*2π)/4803 weeks
168.35791 -.63585 (168*2π)/4803 weeks
169.53025 -.78727 (169*2π)/4803 weeks
1701.17303 -.69046 (170*2π)/4803 weeks
1711.42647 .61425 (171*2π)/4803 weeks
172.83045 .52329 (172*2π)/4803 weeks
173.6294 .90104 (173*2π)/4803 weeks
174-.03251 .6002 (174*2π)/4803 weeks
175.33304 .26982 (175*2π)/4803 weeks
176-.38737 .23117 (176*2π)/4803 weeks
177.09443 -1.09052 (177*2π)/4803 weeks
178.55403 -.4524 (178*2π)/4803 weeks
1791.32013 -.79147 (179*2π)/4803 weeks
1801.73787 -.12555 (180*2π)/4803 weeks
1811.63958 .91084 (181*2π)/4803 weeks
182.88044 1.12447 (182*2π)/4803 weeks
183.08218 1.1462 (183*2π)/4803 weeks
184-.10255 .66024 (184*2π)/4803 weeks
185-.30791 .06976 (185*2π)/4803 weeks
186-.28369 -.56319 (186*2π)/4803 weeks
187.80334 -.88343 (187*2π)/4803 weeks
1881.29729 -.55887 (188*2π)/4803 weeks
1891.64331 .06439 (189*2π)/4803 weeks
1901.13184 .678 (190*2π)/4803 weeks
191.68953 .81128 (191*2π)/4803 weeks
192.69828 .76613 (192*2π)/4803 weeks
193.33644 .67804 (193*2π)/4802 weeks
194.03574 .48019 (194*2π)/4802 weeks
195.1549 .31635 (195*2π)/4802 weeks
196.05014 .09054 (196*2π)/4802 weeks
197.14272 -.20168 (197*2π)/4802 weeks
198.52004 -.20218 (198*2π)/4802 weeks
199.62025 -.15442 (199*2π)/4802 weeks
200.90826 .24834 (200*2π)/4802 weeks
201.83668 .34126 (201*2π)/4802 weeks
202.96719 .32822 (202*2π)/4802 weeks
203.51933 .9356 (203*2π)/4802 weeks
204.3126 .77084 (204*2π)/4802 weeks
205-.15006 .51996 (205*2π)/4802 weeks
206-.21092 .19229 (206*2π)/4802 weeks
207-.14699 -.14787 (207*2π)/4802 weeks
208-.23256 -.34187 (208*2π)/4802 weeks
209.71186 -1.05923 (209*2π)/4802 weeks
210.68191 -.23692 (210*2π)/4802 weeks
2111.05264 -.15286 (211*2π)/4802 weeks
212.93544 .70417 (212*2π)/4802 weeks
213.52873 .61732 (213*2π)/4802 weeks
214.15755 .66013 (214*2π)/4802 weeks
215-.36796 .0285 (215*2π)/4802 weeks
216-.12815 -.68932 (216*2π)/4802 weeks
217.36565 -.60355 (217*2π)/4802 weeks
218.63123 -.73796 (218*2π)/4802 weeks
2191.15098 -.44577 (219*2π)/4802 weeks
220.98348 -.28876 (220*2π)/4802 weeks
2211.24494 .04954 (221*2π)/4802 weeks
2221.33977 .30242 (222*2π)/4802 weeks
2231.22964 .62265 (223*2π)/4802 weeks
224.46296 1.69864 (224*2π)/4802 weeks
225-.4049 .66423 (225*2π)/4802 weeks
226-.14522 .22596 (226*2π)/4802 weeks
227-.3585 -.34453 (227*2π)/4802 weeks
228.18565 -.85236 (228*2π)/4802 weeks
2291.15523 -.64119 (229*2π)/4802 weeks
2301.13863 .14531 (230*2π)/4802 weeks
231.89268 .52924 (231*2π)/4802 weeks
232.78697 .96897 (232*2π)/4802 weeks
233.37732 1.09354 (233*2π)/4802 weeks
234-.7179 .90757 (234*2π)/4802 weeks
235-.70231 -.27397 (235*2π)/4802 weeks
236-.48454 -.62755 (236*2π)/4802 weeks
237-.0115 -1.00089 (237*2π)/4802 weeks
238.8136 -.61219 (238*2π)/4802 weeks
2391.03335 -.56631 (239*2π)/4802 weeks
2401.60026   (240*2π)/4802 weeks
2411.03335 .56631 (241*2π)/4802 weeks
242.8136 .61219 (242*2π)/4802 weeks
243-.0115 1.00089 (243*2π)/4802 weeks
244-.48454 .62755 (244*2π)/4802 weeks
245-.70231 .27397 (245*2π)/4802 weeks
246-.7179 -.90757 (246*2π)/4802 weeks
247.37732 -1.09354 (247*2π)/4802 weeks
248.78697 -.96897 (248*2π)/4802 weeks
249.89268 -.52924 (249*2π)/4802 weeks
2501.13863 -.14531 (250*2π)/4802 weeks
2511.15523 .64119 (251*2π)/4802 weeks
252.18565 .85236 (252*2π)/4802 weeks
253-.3585 .34453 (253*2π)/4802 weeks
254-.14522 -.22596 (254*2π)/4802 weeks
255-.4049 -.66423 (255*2π)/4802 weeks
256.46296 -1.69864 (256*2π)/4802 weeks
2571.22964 -.62265 (257*2π)/4802 weeks
2581.33977 -.30242 (258*2π)/4802 weeks
2591.24494 -.04954 (259*2π)/4802 weeks
260.98348 .28876 (260*2π)/4802 weeks
2611.15098 .44577 (261*2π)/4802 weeks
262.63123 .73796 (262*2π)/4802 weeks
263.36565 .60355 (263*2π)/4802 weeks
264-.12815 .68932 (264*2π)/4802 weeks
265-.36796 -.0285 (265*2π)/4802 weeks
266.15755 -.66013 (266*2π)/4802 weeks
267.52873 -.61732 (267*2π)/4802 weeks
268.93544 -.70417 (268*2π)/4802 weeks
2691.05264 .15286 (269*2π)/4802 weeks
270.68191 .23692 (270*2π)/4802 weeks
271.71186 1.05923 (271*2π)/4802 weeks
272-.23256 .34187 (272*2π)/4802 weeks
273-.14699 .14787 (273*2π)/4802 weeks
274-.21092 -.19229 (274*2π)/4802 weeks
275-.15006 -.51996 (275*2π)/4802 weeks
276.3126 -.77084 (276*2π)/4802 weeks
277.51933 -.9356 (277*2π)/4802 weeks
278.96719 -.32822 (278*2π)/4802 weeks
279.83668 -.34126 (279*2π)/4802 weeks
280.90826 -.24834 (280*2π)/4802 weeks
281.62025 .15442 (281*2π)/4802 weeks
282.52004 .20218 (282*2π)/4802 weeks
283.14272 .20168 (283*2π)/4802 weeks
284.05014 -.09054 (284*2π)/4802 weeks
285.1549 -.31635 (285*2π)/4802 weeks
286.03574 -.48019 (286*2π)/4802 weeks
287.33644 -.67804 (287*2π)/4802 weeks
288.69828 -.76613 (288*2π)/4802 weeks
289.68953 -.81128 (289*2π)/4802 weeks
2901.13184 -.678 (290*2π)/4802 weeks
2911.64331 -.06439 (291*2π)/4802 weeks
2921.29729 .55887 (292*2π)/4802 weeks
293.80334 .88343 (293*2π)/4802 weeks
294-.28369 .56319 (294*2π)/4802 weeks
295-.30791 -.06976 (295*2π)/4802 weeks
296-.10255 -.66024 (296*2π)/4802 weeks
297.08218 -1.1462 (297*2π)/4802 weeks
298.88044 -1.12447 (298*2π)/4802 weeks
2991.63958 -.91084 (299*2π)/4802 weeks
3001.73787 .12555 (300*2π)/4802 weeks
3011.32013 .79147 (301*2π)/4802 weeks
302.55403 .4524 (302*2π)/4802 weeks
303.09443 1.09052 (303*2π)/4802 weeks
304-.38737 -.23117 (304*2π)/4802 weeks
305.33304 -.26982 (305*2π)/4802 weeks
306-.03251 -.6002 (306*2π)/4802 weeks
307.6294 -.90104 (307*2π)/4802 weeks
308.83045 -.52329 (308*2π)/4802 weeks
3091.42647 -.61425 (309*2π)/4802 weeks
3101.17303 .69046 (310*2π)/4802 weeks
311.53025 .78727 (311*2π)/4802 weeks
312.35791 .63585 (312*2π)/4802 weeks
313-.22994 .36124 (313*2π)/4802 weeks
314.02547 -.04448 (314*2π)/4802 weeks
315-.45372 -.3728 (315*2π)/4802 weeks
316.2386 -.88911 (316*2π)/4802 weeks
317.66166 -.59074 (317*2π)/4802 weeks
318.94177 -.35207 (318*2π)/4802 weeks
3191.00281 -.01509 (319*2π)/4802 weeks
320.31997 .2959 (320*2π)/4802 weeks
321.21441 .20567 (321*2π)/4801 weeks
322-.08427 .06255 (322*2π)/4801 weeks
323-.0464 -.07768 (323*2π)/4801 weeks
324-.43951 -.32098 (324*2π)/4801 weeks
325-.0163 -1.07319 (325*2π)/4801 weeks
326.60516 -1.19853 (326*2π)/4801 weeks
327.81608 -.88934 (327*2π)/4801 weeks
3281.09863 -.62777 (328*2π)/4801 weeks
3291.08114 -.33052 (329*2π)/4801 weeks
3301.08447 .21745 (330*2π)/4801 weeks
331.57992 .56903 (331*2π)/4801 weeks
332-.08532 .14767 (332*2π)/4801 weeks
333-.33249 -.09456 (333*2π)/4801 weeks
334-.05411 -.75757 (334*2π)/4801 weeks
335.43017 -.55449 (335*2π)/4801 weeks
336.27726 -.9206 (336*2π)/4801 weeks
3371.02946 -.15084 (337*2π)/4801 weeks
338.45228 -.45184 (338*2π)/4801 weeks
339.75177 -.37148 (339*2π)/4801 weeks
340.72859 -.11576 (340*2π)/4801 weeks
341.66257 .33849 (341*2π)/4801 weeks
342.04641 -.28886 (342*2π)/4801 weeks
343.48564 -.23726 (343*2π)/4801 weeks
344.48245 -.05676 (344*2π)/4801 weeks
345-.15222 -.21062 (345*2π)/4801 weeks
346-.13748 -.8157 (346*2π)/4801 weeks
347.33758 -1.3705 (347*2π)/4801 weeks
3481.37878 -.77902 (348*2π)/4801 weeks
3491.03796 -.08455 (349*2π)/4801 weeks
3501.07243 .28007 (350*2π)/4801 weeks
351.35538 .57664 (351*2π)/4801 weeks
352-.11052 .18693 (352*2π)/4801 weeks
353-.25101 .05084 (353*2π)/4801 weeks
354-.01865 -.75366 (354*2π)/4801 weeks
355-.23256 -.61815 (355*2π)/4801 weeks
356-.41672 -.99305 (356*2π)/4801 weeks
357.32142 -1.29118 (357*2π)/4801 weeks
358.55978 -1.2571 (358*2π)/4801 weeks
3591.04519 -.69385 (359*2π)/4801 weeks
360.60121 .14567 (360*2π)/4801 weeks
361.09479 -.18886 (361*2π)/4801 weeks
362.3818 -.31636 (362*2π)/4801 weeks
363.14176 -.29257 (363*2π)/4801 weeks
364-.02717 -.80764 (364*2π)/4801 weeks
365-.23416 -.73171 (365*2π)/4801 weeks
366-.37166 -.79355 (366*2π)/4801 weeks
367.05818 -2.09091 (367*2π)/4801 weeks
368.75857 -1.46254 (368*2π)/4801 weeks
369.66539 -1.47696 (369*2π)/4801 weeks
3701.28869 -1.04775 (370*2π)/4801 weeks
3711.6147 -.86219 (371*2π)/4801 weeks
3721.71851 -.52476 (372*2π)/4801 weeks
3731.12391 .48237 (373*2π)/4801 weeks
374.48633 .2937 (374*2π)/4801 weeks
375-.02963 -.21152 (375*2π)/4801 weeks
376-.4225 -.42095 (376*2π)/4801 weeks
377.13413 -1.08001 (377*2π)/4801 weeks
378-.09843 -1.24389 (378*2π)/4801 weeks
379.76738 -1.43357 (379*2π)/4801 weeks
3801.56792 -1.78845 (380*2π)/4801 weeks
3811.98993 -.19353 (381*2π)/4801 weeks
3821.42045 .23775 (382*2π)/4801 weeks
383.74418 .57384 (383*2π)/4801 weeks
384-.08659 .29607 (384*2π)/4801 weeks
385-1.28868 .27097 (385*2π)/4801 weeks
386-.67984 -1.11608 (386*2π)/4801 weeks
387-.65882 -1.13488 (387*2π)/4801 weeks
388.0763 -2.3187 (388*2π)/4801 weeks
3891.00793 -2.02422 (389*2π)/4801 weeks
3901.97672 -1.52701 (390*2π)/4801 weeks
3911.94118 -.57715 (391*2π)/4801 weeks
392.77123 .04946 (392*2π)/4801 weeks
393.31325 -.08964 (393*2π)/4801 weeks
394.10578 .02294 (394*2π)/4801 weeks
395-.88056 -.41265 (395*2π)/4801 weeks
396-.58308 -1.52911 (396*2π)/4801 weeks
397.323 -2.19817 (397*2π)/4801 weeks
3981.04653 -.99621 (398*2π)/4801 weeks
399.94896 -1.3654 (399*2π)/4801 weeks
4001.1645 -1.23604 (400*2π)/4801 weeks
4011.18712 -1.51844 (401*2π)/4801 weeks
4022.29857 -.87487 (402*2π)/4801 weeks
4031.88628 .32707 (403*2π)/4801 weeks
404.54762 .8778 (404*2π)/4801 weeks
405-1.055 .70135 (405*2π)/4801 weeks
406-1.72214 -.8114 (406*2π)/4801 weeks
407-.75313 -2.45727 (407*2π)/4801 weeks
408-.06565 -2.64045 (408*2π)/4801 weeks
4092.01807 -3.00319 (409*2π)/4801 weeks
4102.39457 -1.28033 (410*2π)/4801 weeks
4113.44449 -.20687 (411*2π)/4801 weeks
4121.9682 1.97124 (412*2π)/4801 weeks
413-.80622 1.10769 (413*2π)/4801 weeks
414-1.39507 .58069 (414*2π)/4801 weeks
415-1.70318 -1.50667 (415*2π)/4801 weeks
416-1.23037 -2.55556 (416*2π)/4801 weeks
417-.01676 -3.23855 (417*2π)/4801 weeks
4181.44984 -2.60671 (418*2π)/4801 weeks
4192.17483 -1.71301 (419*2π)/4801 weeks
4201.66582 -.96236 (420*2π)/4801 weeks
4211.63778 -.61363 (421*2π)/4801 weeks
422.57054 -.50793 (422*2π)/4801 weeks
4231.12203 -.75604 (423*2π)/4801 weeks
424.76822 -.0903 (424*2π)/4801 weeks
425-.01763 -1.1311 (425*2π)/4801 weeks
426-.0115 -.16103 (426*2π)/4801 weeks
427-.71207 -1.92959 (427*2π)/4801 weeks
428-.30626 -2.47451 (428*2π)/4801 weeks
4291.46945 -3.05154 (429*2π)/4801 weeks
4301.7645 -2.19382 (430*2π)/4801 weeks
4313.61921 -1.04643 (431*2π)/4801 weeks
4322.15287 1.19697 (432*2π)/4801 weeks
433-.34639 .20354 (433*2π)/4801 weeks
434-.16455 .0138 (434*2π)/4801 weeks
435-1.64379 -2.0999 (435*2π)/4801 weeks
436.15594 -2.84667 (436*2π)/4801 weeks
4371.29414 -2.30338 (437*2π)/4801 weeks
438.50317 -1.42402 (438*2π)/4801 weeks
4392.41365 -1.49859 (439*2π)/4801 weeks
4401.08217 -.5167 (440*2π)/4801 weeks
441-.0061 -1.38725 (441*2π)/4801 weeks
442.18791 -.51925 (442*2π)/4801 weeks
443.07289 -2.84231 (443*2π)/4801 weeks
4441.90455 -.70663 (444*2π)/4801 weeks
445.33998 -.5015 (445*2π)/4801 weeks
446-1.05621 -.91155 (446*2π)/4801 weeks
447-.29504 -1.70813 (447*2π)/4801 weeks
448-1.43751 -2.54987 (448*2π)/4801 weeks
449-1.20948 -3.44587 (449*2π)/4801 weeks
450.04324 -6.28482 (450*2π)/4801 weeks
4514.69483 -5.28609 (451*2π)/4801 weeks
4526.32575 -.84113 (452*2π)/4801 weeks
4533.86157 1.25211 (453*2π)/4801 weeks
454-.18014 3.44603 (454*2π)/4801 weeks
455-4.8993 -.74144 (455*2π)/4801 weeks
456-2.81291 -2.01644 (456*2π)/4801 weeks
457-3.19805 -5.93575 (457*2π)/4801 weeks
4581.96528 -6.35593 (458*2π)/4801 weeks
4594.16254 -3.62121 (459*2π)/4801 weeks
4604.42175 .36803 (460*2π)/4801 weeks
4611.00977 -.0016 (461*2π)/4801 weeks
462-.65186 1.98134 (462*2π)/4801 weeks
463-6.62438 -.80086 (463*2π)/4801 weeks
464-4.8493 -4.6164 (464*2π)/4801 weeks
465-7.12199 -8.33673 (465*2π)/4801 weeks
466.76537 -9.84953 (466*2π)/4801 weeks
4672.55504 -6.50023 (467*2π)/4801 weeks
468-1.79463 -7.93757 (468*2π)/4801 weeks
469-1.36391 -9.91978 (469*2π)/4801 weeks
4703.30461 -12.41013 (470*2π)/4801 weeks
4715.76515 -7.97713 (471*2π)/4801 weeks
4725.33343 -12.27824 (472*2π)/4801 weeks
4738.27753 -2.3463 (473*2π)/4801 weeks
474-3.26582 -1.69437 (474*2π)/4801 weeks
475-15.37195 -6.04228 (475*2π)/4801 weeks
476-9.26642 -21.68542 (476*2π)/4801 weeks
477-16.22155 -38.9147 (477*2π)/4801 weeks
47813.69549 -56.99215 (478*2π)/4801 weeks

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