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Fourier Analysis of EWV (ProShares UltraShort MSCI Japan)


EWV (ProShares UltraShort MSCI Japan) appears to have interesting cyclic behaviour every 49 weeks (11.7893*sine), 33 weeks (11.0594*sine), and 44 weeks (10.8104*sine).

EWV (ProShares UltraShort MSCI Japan) has an average price of 140.35 (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 11/8/2007 to 3/13/2017 for EWV (ProShares UltraShort MSCI Japan), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0140.3478   0 
130.97009 93.6531 (1*2π)/489489 weeks
213.86751 55.87756 (2*2π)/489245 weeks
3-15.56114 40.55193 (3*2π)/489163 weeks
4-9.26023 21.41124 (4*2π)/489122 weeks
5-16.31269 8.58266 (5*2π)/48998 weeks
6-3.42131 2.48912 (6*2π)/48982 weeks
77.20931 1.186 (7*2π)/48970 weeks
87.21347 11.65591 (8*2π)/48961 weeks
94.65215 7.09378 (9*2π)/48954 weeks
104.03934 11.78933 (10*2π)/48949 weeks
11-1.08922 10.81037 (11*2π)/48944 weeks
12-1.22253 8.39845 (12*2π)/48941 weeks
131.24334 4.99393 (13*2π)/48938 weeks
14.77358 9.00079 (14*2π)/48935 weeks
15-5.3179 11.05937 (15*2π)/48933 weeks
16-4.87134 4.54304 (16*2π)/48931 weeks
17-6.26965 2.97686 (17*2π)/48929 weeks
18-2.50916 -2.48606 (18*2π)/48927 weeks
19.92035 -.61051 (19*2π)/48926 weeks
201.9214 -1.25916 (20*2π)/48924 weeks
214.17639 2.93594 (21*2π)/48923 weeks
223.02104 5.79157 (22*2π)/48922 weeks
23-.65624 7.50501 (23*2π)/48921 weeks
24-3.41905 3.30323 (24*2π)/48920 weeks
25-2.6118 2.64697 (25*2π)/48920 weeks
26-2.67825 -2.99442 (26*2π)/48919 weeks
272.47022 -3.25078 (27*2π)/48918 weeks
284.18485 -.95137 (28*2π)/48917 weeks
295.76177 3.4648 (29*2π)/48917 weeks
302.81962 6.59234 (30*2π)/48916 weeks
31-1.07725 4.9364 (31*2π)/48916 weeks
32-.95101 3.09415 (32*2π)/48915 weeks
33-1.18804 1.6852 (33*2π)/48915 weeks
34-.59282 1.99395 (34*2π)/48914 weeks
35-.43083 .39601 (35*2π)/48914 weeks
36.53437 .41102 (36*2π)/48914 weeks
372.13527 1.81192 (37*2π)/48913 weeks
38-.58202 2.08337 (38*2π)/48913 weeks
39.8293 .78193 (39*2π)/48913 weeks
40-.06595 .72938 (40*2π)/48912 weeks
411.1681 .53361 (41*2π)/48912 weeks
422.06319 2.26752 (42*2π)/48912 weeks
43.96717 1.1592 (43*2π)/48911 weeks
441.13543 2.37196 (44*2π)/48911 weeks
45-.06921 2.71723 (45*2π)/48911 weeks
46-1.84557 1.5063 (46*2π)/48911 weeks
47-.04649 .13429 (47*2π)/48910 weeks
48-.32588 -.4419 (48*2π)/48910 weeks
492.32986 -.96115 (49*2π)/48910 weeks
503.5387 1.34796 (50*2π)/48910 weeks
511.74813 2.12485 (51*2π)/48910 weeks
521.37914 3.04893 (52*2π)/4899 weeks
53-.29918 2.39725 (53*2π)/4899 weeks
54-.70199 1.89398 (54*2π)/4899 weeks
55-.03665 .16467 (55*2π)/4899 weeks
56.03444 1.14625 (56*2π)/4899 weeks
57.69183 .05976 (57*2π)/4899 weeks
581.09929 .69866 (58*2π)/4898 weeks
59.53177 .61963 (59*2π)/4898 weeks
601.56811 .5023 (60*2π)/4898 weeks
611.58271 .93597 (61*2π)/4898 weeks
622.08811 1.48873 (62*2π)/4898 weeks
631.46584 2.51717 (63*2π)/4898 weeks
64.32495 3.32839 (64*2π)/4898 weeks
65-.90168 2.7581 (65*2π)/4898 weeks
66-1.44225 1.62895 (66*2π)/4897 weeks
67-1.77754 -.21641 (67*2π)/4897 weeks
68-.7405 -.71926 (68*2π)/4897 weeks
691.05285 -2.31754 (69*2π)/4897 weeks
703.07516 -.61965 (70*2π)/4897 weeks
712.33538 1.40126 (71*2π)/4897 weeks
722.48447 2.41165 (72*2π)/4897 weeks
73.37137 3.18206 (73*2π)/4897 weeks
74-.1794 2.5087 (74*2π)/4897 weeks
75-1.52133 1.65441 (75*2π)/4897 weeks
76-1.23712 -.03467 (76*2π)/4896 weeks
77.23344 -1.07692 (77*2π)/4896 weeks
781.37988 -.9645 (78*2π)/4896 weeks
792.0681 .10212 (79*2π)/4896 weeks
801.65408 1.47101 (80*2π)/4896 weeks
81.93056 1.18235 (81*2π)/4896 weeks
82.92159 1.36777 (82*2π)/4896 weeks
83.63193 1.38676 (83*2π)/4896 weeks
841.30592 1.8458 (84*2π)/4896 weeks
85-.07142 1.97079 (85*2π)/4896 weeks
86-.63904 1.19506 (86*2π)/4896 weeks
87-.31131 -.04536 (87*2π)/4896 weeks
88.41282 -.0001 (88*2π)/4896 weeks
89.57651 -.16684 (89*2π)/4895 weeks
901.12063 -.3731 (90*2π)/4895 weeks
911.71147 .77603 (91*2π)/4895 weeks
921.54223 1.90241 (92*2π)/4895 weeks
93.79497 2.12399 (93*2π)/4895 weeks
94-.34984 2.19202 (94*2π)/4895 weeks
95-.43561 1.04961 (95*2π)/4895 weeks
96-.81259 1.02407 (96*2π)/4895 weeks
97-.8173 -.69008 (97*2π)/4895 weeks
98-.12729 -.4894 (98*2π)/4895 weeks
99.76384 -.53132 (99*2π)/4895 weeks
1001.39146 -.1244 (100*2π)/4895 weeks
1012.04983 .39535 (101*2π)/4895 weeks
1021.29947 1.83176 (102*2π)/4895 weeks
103.74971 1.47839 (103*2π)/4895 weeks
104-.09064 1.12492 (104*2π)/4895 weeks
105.09376 1.08441 (105*2π)/4895 weeks
106-.38708 .36156 (106*2π)/4895 weeks
107-.039 .19866 (107*2π)/4895 weeks
108.48701 -.2796 (108*2π)/4895 weeks
1091.10111 -.46944 (109*2π)/4894 weeks
1101.70645 .49394 (110*2π)/4894 weeks
1111.5847 .80627 (111*2π)/4894 weeks
1121.22826 1.01944 (112*2π)/4894 weeks
113.70319 1.5254 (113*2π)/4894 weeks
114.76813 1.4223 (114*2π)/4894 weeks
115.2907 2.04852 (115*2π)/4894 weeks
116-.47524 .88135 (116*2π)/4894 weeks
117-.18281 .80813 (117*2π)/4894 weeks
118.10863 .72349 (118*2π)/4894 weeks
119.0232 .22581 (119*2π)/4894 weeks
120.2537 .23264 (120*2π)/4894 weeks
121.03915 .36665 (121*2π)/4894 weeks
122.37193 -.01873 (122*2π)/4894 weeks
1231.13939 .52941 (123*2π)/4894 weeks
124.87109 1.18287 (124*2π)/4894 weeks
125.47324 1.12068 (125*2π)/4894 weeks
126-.16527 1.19549 (126*2π)/4894 weeks
127-.15303 .5487 (127*2π)/4894 weeks
128.04847 .34374 (128*2π)/4894 weeks
129-.59013 .17082 (129*2π)/4894 weeks
130-.18509 -.06409 (130*2π)/4894 weeks
131.02037 -.45619 (131*2π)/4894 weeks
132.72689 -.51104 (132*2π)/4894 weeks
133.99476 .09885 (133*2π)/4894 weeks
1341.2847 .29671 (134*2π)/4894 weeks
135.96887 1.29274 (135*2π)/4894 weeks
136-.00483 .9975 (136*2π)/4894 weeks
137-.25522 .47431 (137*2π)/4894 weeks
138.01515 -.07674 (138*2π)/4894 weeks
139.36468 .23523 (139*2π)/4894 weeks
140.3562 .43803 (140*2π)/4893 weeks
141-.02139 -.07015 (141*2π)/4893 weeks
142.80424 .05006 (142*2π)/4893 weeks
143.79033 .22913 (143*2π)/4893 weeks
144.69577 .47121 (144*2π)/4893 weeks
145.39377 .27448 (145*2π)/4893 weeks
1461.14675 .6585 (146*2π)/4893 weeks
147.20154 .65112 (147*2π)/4893 weeks
148.43447 .69155 (148*2π)/4893 weeks
149-.15581 .62775 (149*2π)/4893 weeks
150-.18055 -.07064 (150*2π)/4893 weeks
151-.0682 -.32571 (151*2π)/4893 weeks
152.69846 -.5024 (152*2π)/4893 weeks
1531.13116 -.11744 (153*2π)/4893 weeks
1541.03016 .33142 (154*2π)/4893 weeks
1551.02958 .67579 (155*2π)/4893 weeks
156.75598 .88466 (156*2π)/4893 weeks
157.49179 1.22768 (157*2π)/4893 weeks
158-.07474 1.06467 (158*2π)/4893 weeks
159-.38914 .27476 (159*2π)/4893 weeks
160-.02718 .08765 (160*2π)/4893 weeks
161-.06982 -.07232 (161*2π)/4893 weeks
162.2186 -.19727 (162*2π)/4893 weeks
163.31787 -.28454 (163*2π)/4893 weeks
164.99253 .00391 (164*2π)/4893 weeks
165.92947 .32598 (165*2π)/4893 weeks
166.65359 .57251 (166*2π)/4893 weeks
167.28736 .871 (167*2π)/4893 weeks
168-.42084 .47082 (168*2π)/4893 weeks
169.02435 -.00863 (169*2π)/4893 weeks
170-.26465 -.26172 (170*2π)/4893 weeks
171.25635 -.65511 (171*2π)/4893 weeks
172.39736 -.68076 (172*2π)/4893 weeks
1731.00348 -.643 (173*2π)/4893 weeks
1741.65539 .38276 (174*2π)/4893 weeks
175.84816 .55231 (175*2π)/4893 weeks
176.81257 .77971 (176*2π)/4893 weeks
177.12482 .72283 (177*2π)/4893 weeks
178.2076 .10285 (178*2π)/4893 weeks
179-.15265 .4143 (179*2π)/4893 weeks
180-.40921 -.75747 (180*2π)/4893 weeks
181.7649 -.52868 (181*2π)/4893 weeks
182.87459 -.93717 (182*2π)/4893 weeks
1831.55786 -.34938 (183*2π)/4893 weeks
1841.80548 .46992 (184*2π)/4893 weeks
1851.04989 1.10545 (185*2π)/4893 weeks
186.50098 1.24993 (186*2π)/4893 weeks
187-.07718 .6993 (187*2π)/4893 weeks
188-.36568 .37072 (188*2π)/4893 weeks
189-.32448 -.14264 (189*2π)/4893 weeks
190.16924 -.98709 (190*2π)/4893 weeks
191.93722 -.65546 (191*2π)/4893 weeks
1921.41095 -.23484 (192*2π)/4893 weeks
1931.49019 .58303 (193*2π)/4893 weeks
1941.03293 .77992 (194*2π)/4893 weeks
195.63205 .64101 (195*2π)/4893 weeks
196.47892 .84328 (196*2π)/4892 weeks
197.26997 .70986 (197*2π)/4892 weeks
198.10504 .34523 (198*2π)/4892 weeks
199.11116 .30791 (199*2π)/4892 weeks
200.10555 .03893 (200*2π)/4892 weeks
201.31131 -.269 (201*2π)/4892 weeks
202.59119 -.17067 (202*2π)/4892 weeks
203.75013 -.20853 (203*2π)/4892 weeks
204.7759 .25204 (204*2π)/4892 weeks
205.73772 .37082 (205*2π)/4892 weeks
2061.00813 .49931 (206*2π)/4892 weeks
207.37352 .866 (207*2π)/4892 weeks
208.22393 .82087 (208*2π)/4892 weeks
209-.14955 .4749 (209*2π)/4892 weeks
210-.19789 .16924 (210*2π)/4892 weeks
211-.09942 -.14821 (211*2π)/4892 weeks
212-.23064 -.40634 (212*2π)/4892 weeks
213.84407 -.95732 (213*2π)/4892 weeks
214.6798 -.26658 (214*2π)/4892 weeks
2151.05733 -.13952 (215*2π)/4892 weeks
216.8961 .69744 (216*2π)/4892 weeks
217.52371 .60683 (217*2π)/4892 weeks
218.1692 .64262 (218*2π)/4892 weeks
219-.36278 .04308 (219*2π)/4892 weeks
220-.1701 -.65172 (220*2π)/4892 weeks
221.35007 -.59302 (221*2π)/4892 weeks
222.57576 -.71335 (222*2π)/4892 weeks
2231.09733 -.50545 (223*2π)/4892 weeks
224.92981 -.23724 (224*2π)/4892 weeks
2251.24079 .00653 (225*2π)/4892 weeks
2261.28649 .22217 (226*2π)/4892 weeks
2271.15443 .59424 (227*2π)/4892 weeks
228.87276 1.60285 (228*2π)/4892 weeks
229-.38224 .84879 (229*2π)/4892 weeks
230-.19639 .20085 (230*2π)/4892 weeks
231-.44478 -.08741 (231*2π)/4892 weeks
232-.01623 -.66665 (232*2π)/4892 weeks
233.87968 -.77085 (233*2π)/4892 weeks
2341.22862 .08665 (234*2π)/4892 weeks
2351.07742 .50568 (235*2π)/4892 weeks
2361.00424 .69845 (236*2π)/4892 weeks
237.4696 .91524 (237*2π)/4892 weeks
238-.29299 1.1838 (238*2π)/4892 weeks
239-.93085 .14504 (239*2π)/4892 weeks
240-.46835 -.32034 (240*2π)/4892 weeks
241-.09542 -.7935 (241*2π)/4892 weeks
242.69743 -1.0615 (242*2π)/4892 weeks
243.78675 -.67286 (243*2π)/4892 weeks
2441.23297 -.4959 (244*2π)/4892 weeks
2451.23297 .4959 (245*2π)/4892 weeks
246.78675 .67286 (246*2π)/4892 weeks
247.69743 1.0615 (247*2π)/4892 weeks
248-.09542 .7935 (248*2π)/4892 weeks
249-.46835 .32034 (249*2π)/4892 weeks
250-.93085 -.14504 (250*2π)/4892 weeks
251-.29299 -1.1838 (251*2π)/4892 weeks
252.4696 -.91524 (252*2π)/4892 weeks
2531.00424 -.69845 (253*2π)/4892 weeks
2541.07742 -.50568 (254*2π)/4892 weeks
2551.22862 -.08665 (255*2π)/4892 weeks
256.87968 .77085 (256*2π)/4892 weeks
257-.01623 .66665 (257*2π)/4892 weeks
258-.44478 .08741 (258*2π)/4892 weeks
259-.19639 -.20085 (259*2π)/4892 weeks
260-.38224 -.84879 (260*2π)/4892 weeks
261.87276 -1.60285 (261*2π)/4892 weeks
2621.15443 -.59424 (262*2π)/4892 weeks
2631.28649 -.22217 (263*2π)/4892 weeks
2641.24079 -.00653 (264*2π)/4892 weeks
265.92981 .23724 (265*2π)/4892 weeks
2661.09733 .50545 (266*2π)/4892 weeks
267.57576 .71335 (267*2π)/4892 weeks
268.35007 .59302 (268*2π)/4892 weeks
269-.1701 .65172 (269*2π)/4892 weeks
270-.36278 -.04308 (270*2π)/4892 weeks
271.1692 -.64262 (271*2π)/4892 weeks
272.52371 -.60683 (272*2π)/4892 weeks
273.8961 -.69744 (273*2π)/4892 weeks
2741.05733 .13952 (274*2π)/4892 weeks
275.6798 .26658 (275*2π)/4892 weeks
276.84407 .95732 (276*2π)/4892 weeks
277-.23064 .40634 (277*2π)/4892 weeks
278-.09942 .14821 (278*2π)/4892 weeks
279-.19789 -.16924 (279*2π)/4892 weeks
280-.14955 -.4749 (280*2π)/4892 weeks
281.22393 -.82087 (281*2π)/4892 weeks
282.37352 -.866 (282*2π)/4892 weeks
2831.00813 -.49931 (283*2π)/4892 weeks
284.73772 -.37082 (284*2π)/4892 weeks
285.7759 -.25204 (285*2π)/4892 weeks
286.75013 .20853 (286*2π)/4892 weeks
287.59119 .17067 (287*2π)/4892 weeks
288.31131 .269 (288*2π)/4892 weeks
289.10555 -.03893 (289*2π)/4892 weeks
290.11116 -.30791 (290*2π)/4892 weeks
291.10504 -.34523 (291*2π)/4892 weeks
292.26997 -.70986 (292*2π)/4892 weeks
293.47892 -.84328 (293*2π)/4892 weeks
294.63205 -.64101 (294*2π)/4892 weeks
2951.03293 -.77992 (295*2π)/4892 weeks
2961.49019 -.58303 (296*2π)/4892 weeks
2971.41095 .23484 (297*2π)/4892 weeks
298.93722 .65546 (298*2π)/4892 weeks
299.16924 .98709 (299*2π)/4892 weeks
300-.32448 .14264 (300*2π)/4892 weeks
301-.36568 -.37072 (301*2π)/4892 weeks
302-.07718 -.6993 (302*2π)/4892 weeks
303.50098 -1.24993 (303*2π)/4892 weeks
3041.04989 -1.10545 (304*2π)/4892 weeks
3051.80548 -.46992 (305*2π)/4892 weeks
3061.55786 .34938 (306*2π)/4892 weeks
307.87459 .93717 (307*2π)/4892 weeks
308.7649 .52868 (308*2π)/4892 weeks
309-.40921 .75747 (309*2π)/4892 weeks
310-.15265 -.4143 (310*2π)/4892 weeks
311.2076 -.10285 (311*2π)/4892 weeks
312.12482 -.72283 (312*2π)/4892 weeks
313.81257 -.77971 (313*2π)/4892 weeks
314.84816 -.55231 (314*2π)/4892 weeks
3151.65539 -.38276 (315*2π)/4892 weeks
3161.00348 .643 (316*2π)/4892 weeks
317.39736 .68076 (317*2π)/4892 weeks
318.25635 .65511 (318*2π)/4892 weeks
319-.26465 .26172 (319*2π)/4892 weeks
320.02435 .00863 (320*2π)/4892 weeks
321-.42084 -.47082 (321*2π)/4892 weeks
322.28736 -.871 (322*2π)/4892 weeks
323.65359 -.57251 (323*2π)/4892 weeks
324.92947 -.32598 (324*2π)/4892 weeks
325.99253 -.00391 (325*2π)/4892 weeks
326.31787 .28454 (326*2π)/4892 weeks
327.2186 .19727 (327*2π)/4891 weeks
328-.06982 .07232 (328*2π)/4891 weeks
329-.02718 -.08765 (329*2π)/4891 weeks
330-.38914 -.27476 (330*2π)/4891 weeks
331-.07474 -1.06467 (331*2π)/4891 weeks
332.49179 -1.22768 (332*2π)/4891 weeks
333.75598 -.88466 (333*2π)/4891 weeks
3341.02958 -.67579 (334*2π)/4891 weeks
3351.03016 -.33142 (335*2π)/4891 weeks
3361.13116 .11744 (336*2π)/4891 weeks
337.69846 .5024 (337*2π)/4891 weeks
338-.0682 .32571 (338*2π)/4891 weeks
339-.18055 .07064 (339*2π)/4891 weeks
340-.15581 -.62775 (340*2π)/4891 weeks
341.43447 -.69155 (341*2π)/4891 weeks
342.20154 -.65112 (342*2π)/4891 weeks
3431.14675 -.6585 (343*2π)/4891 weeks
344.39377 -.27448 (344*2π)/4891 weeks
345.69577 -.47121 (345*2π)/4891 weeks
346.79033 -.22913 (346*2π)/4891 weeks
347.80424 -.05006 (347*2π)/4891 weeks
348-.02139 .07015 (348*2π)/4891 weeks
349.3562 -.43803 (349*2π)/4891 weeks
350.36468 -.23523 (350*2π)/4891 weeks
351.01515 .07674 (351*2π)/4891 weeks
352-.25522 -.47431 (352*2π)/4891 weeks
353-.00483 -.9975 (353*2π)/4891 weeks
354.96887 -1.29274 (354*2π)/4891 weeks
3551.2847 -.29671 (355*2π)/4891 weeks
356.99476 -.09885 (356*2π)/4891 weeks
357.72689 .51104 (357*2π)/4891 weeks
358.02037 .45619 (358*2π)/4891 weeks
359-.18509 .06409 (359*2π)/4891 weeks
360-.59013 -.17082 (360*2π)/4891 weeks
361.04847 -.34374 (361*2π)/4891 weeks
362-.15303 -.5487 (362*2π)/4891 weeks
363-.16527 -1.19549 (363*2π)/4891 weeks
364.47324 -1.12068 (364*2π)/4891 weeks
365.87109 -1.18287 (365*2π)/4891 weeks
3661.13939 -.52941 (366*2π)/4891 weeks
367.37193 .01873 (367*2π)/4891 weeks
368.03915 -.36665 (368*2π)/4891 weeks
369.2537 -.23264 (369*2π)/4891 weeks
370.0232 -.22581 (370*2π)/4891 weeks
371.10863 -.72349 (371*2π)/4891 weeks
372-.18281 -.80813 (372*2π)/4891 weeks
373-.47524 -.88135 (373*2π)/4891 weeks
374.2907 -2.04852 (374*2π)/4891 weeks
375.76813 -1.4223 (375*2π)/4891 weeks
376.70319 -1.5254 (376*2π)/4891 weeks
3771.22826 -1.01944 (377*2π)/4891 weeks
3781.5847 -.80627 (378*2π)/4891 weeks
3791.70645 -.49394 (379*2π)/4891 weeks
3801.10111 .46944 (380*2π)/4891 weeks
381.48701 .2796 (381*2π)/4891 weeks
382-.039 -.19866 (382*2π)/4891 weeks
383-.38708 -.36156 (383*2π)/4891 weeks
384.09376 -1.08441 (384*2π)/4891 weeks
385-.09064 -1.12492 (385*2π)/4891 weeks
386.74971 -1.47839 (386*2π)/4891 weeks
3871.29947 -1.83176 (387*2π)/4891 weeks
3882.04983 -.39535 (388*2π)/4891 weeks
3891.39146 .1244 (389*2π)/4891 weeks
390.76384 .53132 (390*2π)/4891 weeks
391-.12729 .4894 (391*2π)/4891 weeks
392-.8173 .69008 (392*2π)/4891 weeks
393-.81259 -1.02407 (393*2π)/4891 weeks
394-.43561 -1.04961 (394*2π)/4891 weeks
395-.34984 -2.19202 (395*2π)/4891 weeks
396.79497 -2.12399 (396*2π)/4891 weeks
3971.54223 -1.90241 (397*2π)/4891 weeks
3981.71147 -.77603 (398*2π)/4891 weeks
3991.12063 .3731 (399*2π)/4891 weeks
400.57651 .16684 (400*2π)/4891 weeks
401.41282 .0001 (401*2π)/4891 weeks
402-.31131 .04536 (402*2π)/4891 weeks
403-.63904 -1.19506 (403*2π)/4891 weeks
404-.07142 -1.97079 (404*2π)/4891 weeks
4051.30592 -1.8458 (405*2π)/4891 weeks
406.63193 -1.38676 (406*2π)/4891 weeks
407.92159 -1.36777 (407*2π)/4891 weeks
408.93056 -1.18235 (408*2π)/4891 weeks
4091.65408 -1.47101 (409*2π)/4891 weeks
4102.0681 -.10212 (410*2π)/4891 weeks
4111.37988 .9645 (411*2π)/4891 weeks
412.23344 1.07692 (412*2π)/4891 weeks
413-1.23712 .03467 (413*2π)/4891 weeks
414-1.52133 -1.65441 (414*2π)/4891 weeks
415-.1794 -2.5087 (415*2π)/4891 weeks
416.37137 -3.18206 (416*2π)/4891 weeks
4172.48447 -2.41165 (417*2π)/4891 weeks
4182.33538 -1.40126 (418*2π)/4891 weeks
4193.07516 .61965 (419*2π)/4891 weeks
4201.05285 2.31754 (420*2π)/4891 weeks
421-.7405 .71926 (421*2π)/4891 weeks
422-1.77754 .21641 (422*2π)/4891 weeks
423-1.44225 -1.62895 (423*2π)/4891 weeks
424-.90168 -2.7581 (424*2π)/4891 weeks
425.32495 -3.32839 (425*2π)/4891 weeks
4261.46584 -2.51717 (426*2π)/4891 weeks
4272.08811 -1.48873 (427*2π)/4891 weeks
4281.58271 -.93597 (428*2π)/4891 weeks
4291.56811 -.5023 (429*2π)/4891 weeks
430.53177 -.61963 (430*2π)/4891 weeks
4311.09929 -.69866 (431*2π)/4891 weeks
432.69183 -.05976 (432*2π)/4891 weeks
433.03444 -1.14625 (433*2π)/4891 weeks
434-.03665 -.16467 (434*2π)/4891 weeks
435-.70199 -1.89398 (435*2π)/4891 weeks
436-.29918 -2.39725 (436*2π)/4891 weeks
4371.37914 -3.04893 (437*2π)/4891 weeks
4381.74813 -2.12485 (438*2π)/4891 weeks
4393.5387 -1.34796 (439*2π)/4891 weeks
4402.32986 .96115 (440*2π)/4891 weeks
441-.32588 .4419 (441*2π)/4891 weeks
442-.04649 -.13429 (442*2π)/4891 weeks
443-1.84557 -1.5063 (443*2π)/4891 weeks
444-.06921 -2.71723 (444*2π)/4891 weeks
4451.13543 -2.37196 (445*2π)/4891 weeks
446.96717 -1.1592 (446*2π)/4891 weeks
4472.06319 -2.26752 (447*2π)/4891 weeks
4481.1681 -.53361 (448*2π)/4891 weeks
449-.06595 -.72938 (449*2π)/4891 weeks
450.8293 -.78193 (450*2π)/4891 weeks
451-.58202 -2.08337 (451*2π)/4891 weeks
4522.13527 -1.81192 (452*2π)/4891 weeks
453.53437 -.41102 (453*2π)/4891 weeks
454-.43083 -.39601 (454*2π)/4891 weeks
455-.59282 -1.99395 (455*2π)/4891 weeks
456-1.18804 -1.6852 (456*2π)/4891 weeks
457-.95101 -3.09415 (457*2π)/4891 weeks
458-1.07725 -4.9364 (458*2π)/4891 weeks
4592.81962 -6.59234 (459*2π)/4891 weeks
4605.76177 -3.4648 (460*2π)/4891 weeks
4614.18485 .95137 (461*2π)/4891 weeks
4622.47022 3.25078 (462*2π)/4891 weeks
463-2.67825 2.99442 (463*2π)/4891 weeks
464-2.6118 -2.64697 (464*2π)/4891 weeks
465-3.41905 -3.30323 (465*2π)/4891 weeks
466-.65624 -7.50501 (466*2π)/4891 weeks
4673.02104 -5.79157 (467*2π)/4891 weeks
4684.17639 -2.93594 (468*2π)/4891 weeks
4691.9214 1.25916 (469*2π)/4891 weeks
470.92035 .61051 (470*2π)/4891 weeks
471-2.50916 2.48606 (471*2π)/4891 weeks
472-6.26965 -2.97686 (472*2π)/4891 weeks
473-4.87134 -4.54304 (473*2π)/4891 weeks
474-5.3179 -11.05937 (474*2π)/4891 weeks
475.77358 -9.00079 (475*2π)/4891 weeks
4761.24334 -4.99393 (476*2π)/4891 weeks
477-1.22253 -8.39845 (477*2π)/4891 weeks
478-1.08922 -10.81037 (478*2π)/4891 weeks
4794.03934 -11.78933 (479*2π)/4891 weeks
4804.65215 -7.09378 (480*2π)/4891 weeks
4817.21347 -11.65591 (481*2π)/4891 weeks
4827.20931 -1.186 (482*2π)/4891 weeks
483-3.42131 -2.48912 (483*2π)/4891 weeks
484-16.31269 -8.58266 (484*2π)/4891 weeks
485-9.26023 -21.41124 (485*2π)/4891 weeks
486-15.56114 -40.55193 (486*2π)/4891 weeks
48713.86751 -55.87756 (487*2π)/4891 weeks

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