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Fourier Analysis of EWV (PROSHARES ULTRASHORT MSCI JAPAN PROSHARES ULTRASHORT MSCI JAPAN)


EWV (PROSHARES ULTRASHORT MSCI JAPAN PROSHARES ULTRASHORT MSCI JAPAN) appears to have interesting cyclic behaviour every 47 weeks (11.9971*sine), 33 weeks (10.1875*sine), and 52 weeks (9.1461*sine).

EWV (PROSHARES ULTRASHORT MSCI JAPAN PROSHARES ULTRASHORT MSCI JAPAN) has an average price of 134.1 (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 10/16/2017 for EWV (PROSHARES ULTRASHORT MSCI JAPAN PROSHARES ULTRASHORT MSCI JAPAN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0134.1034   0 
133.76511 93.51106 (1*2π)/520520 weeks
213.66511 53.11292 (2*2π)/520260 weeks
3-11.88685 45.6336 (3*2π)/520173 weeks
4-10.28649 21.70633 (4*2π)/520130 weeks
5-14.93279 16.5276 (5*2π)/520104 weeks
6-4.44901 2.27577 (6*2π)/52087 weeks
71.7853 -.91591 (7*2π)/52074 weeks
89.12335 6.16794 (8*2π)/52065 weeks
92.03587 9.76019 (9*2π)/52058 weeks
105.63665 9.14609 (10*2π)/52052 weeks
112.30501 11.99712 (11*2π)/52047 weeks
12-1.20448 9.14051 (12*2π)/52043 weeks
13-1.63591 7.61739 (13*2π)/52040 weeks
142.11628 5.73713 (14*2π)/52037 weeks
15.71813 8.79402 (15*2π)/52035 weeks
16-5.41193 10.18752 (16*2π)/52033 weeks
17-4.59662 4.38624 (17*2π)/52031 weeks
18-5.69958 3.22414 (18*2π)/52029 weeks
19-3.25778 -2.1545 (19*2π)/52027 weeks
20.58802 -.84677 (20*2π)/52026 weeks
21.87505 -.45447 (21*2π)/52025 weeks
224.58604 1.74652 (22*2π)/52024 weeks
233.83327 4.29806 (23*2π)/52023 weeks
241.47707 6.29575 (24*2π)/52022 weeks
25-3.16353 5.14268 (25*2π)/52021 weeks
26-2.63686 1.93846 (26*2π)/52020 weeks
27-4.36098 1.36738 (27*2π)/52019 weeks
28-.7871 -3.03179 (28*2π)/52019 weeks
293.3713 -1.94451 (29*2π)/52018 weeks
304.77037 -.53049 (30*2π)/52017 weeks
315.07472 3.86047 (31*2π)/52017 weeks
322.17525 6.42852 (32*2π)/52016 weeks
33-1.0607 4.66432 (33*2π)/52016 weeks
34-.88794 3.01991 (34*2π)/52015 weeks
35-1.20956 1.82469 (35*2π)/52015 weeks
36-.33955 1.90974 (36*2π)/52014 weeks
37-.7303 .64659 (37*2π)/52014 weeks
38.38918 .53776 (38*2π)/52014 weeks
391.79717 .71974 (39*2π)/52013 weeks
40.33947 2.77883 (40*2π)/52013 weeks
41-.1747 .66404 (41*2π)/52013 weeks
42.44913 1.54973 (42*2π)/52012 weeks
43.69655 .31544 (43*2π)/52012 weeks
441.64294 .51367 (44*2π)/52012 weeks
45.91309 2.4525 (45*2π)/52012 weeks
461.3744 1.39409 (46*2π)/52011 weeks
47.94598 2.41238 (47*2π)/52011 weeks
48-.21713 2.56951 (48*2π)/52011 weeks
49-1.78158 1.18403 (49*2π)/52011 weeks
50-.05709 .21728 (50*2π)/52010 weeks
51-.33028 -.25493 (51*2π)/52010 weeks
521.98834 -1.0241 (52*2π)/52010 weeks
533.31831 .77395 (53*2π)/52010 weeks
541.71352 2.24645 (54*2π)/52010 weeks
551.65673 2.63384 (55*2π)/5209 weeks
56.02988 2.86824 (56*2π)/5209 weeks
57-.22479 2.0232 (57*2π)/5209 weeks
58-.83927 .81595 (58*2π)/5209 weeks
59.65015 .78072 (59*2π)/5209 weeks
60-.1649 .46356 (60*2π)/5209 weeks
61.94353 .38407 (61*2π)/5209 weeks
621.00127 .90831 (62*2π)/5208 weeks
63.68177 .3412 (63*2π)/5208 weeks
641.55825 .67877 (64*2π)/5208 weeks
651.5684 .93605 (65*2π)/5208 weeks
662.01247 1.52848 (66*2π)/5208 weeks
671.39188 2.41913 (67*2π)/5208 weeks
68.43068 3.1977 (68*2π)/5208 weeks
69-.66714 2.70382 (69*2π)/5208 weeks
70-1.28076 1.63077 (70*2π)/5207 weeks
71-1.8897 .33849 (71*2π)/5207 weeks
72-.67961 -.59266 (72*2π)/5207 weeks
73-.17326 -1.87535 (73*2π)/5207 weeks
742.37108 -1.21907 (74*2π)/5207 weeks
753.06055 .92099 (75*2π)/5207 weeks
762.38798 1.30932 (76*2π)/5207 weeks
771.74146 2.89838 (77*2π)/5207 weeks
78-.05276 2.46274 (78*2π)/5207 weeks
79-.58194 2.34358 (79*2π)/5207 weeks
80-1.59953 1.11596 (80*2π)/5207 weeks
81-1.13443 -.214 (81*2π)/5206 weeks
82.35068 -.89255 (82*2π)/5206 weeks
831.38458 -.82111 (83*2π)/5206 weeks
841.93478 .13159 (84*2π)/5206 weeks
851.63279 1.4075 (85*2π)/5206 weeks
86.87208 1.25386 (86*2π)/5206 weeks
87.97515 1.35677 (87*2π)/5206 weeks
88.80255 1.42298 (88*2π)/5206 weeks
891.22352 1.15549 (89*2π)/5206 weeks
90.24381 2.04066 (90*2π)/5206 weeks
91-.50372 1.46264 (91*2π)/5206 weeks
92-.80919 .56888 (92*2π)/5206 weeks
93.07293 .05067 (93*2π)/5206 weeks
94.41406 .22507 (94*2π)/5206 weeks
95.8057 .00792 (95*2π)/5205 weeks
961.64216 -.16558 (96*2π)/5205 weeks
971.71285 .78425 (97*2π)/5205 weeks
981.26828 1.84847 (98*2π)/5205 weeks
99.68611 2.05034 (99*2π)/5205 weeks
100-.37235 2.05619 (100*2π)/5205 weeks
101-.41059 1.01408 (101*2π)/5205 weeks
102-.70067 1.02027 (102*2π)/5205 weeks
103-1.05729 -.38922 (103*2π)/5205 weeks
104-.06289 -.2374 (104*2π)/5205 weeks
105.69009 -.53553 (105*2π)/5205 weeks
1061.29346 -.32794 (106*2π)/5205 weeks
1071.65526 -.0105 (107*2π)/5205 weeks
1081.90403 1.2688 (108*2π)/5205 weeks
109.67312 1.43122 (109*2π)/5205 weeks
110.33682 1.58566 (110*2π)/5205 weeks
111.12424 .85203 (111*2π)/5205 weeks
112-.13681 .99827 (112*2π)/5205 weeks
113-.1486 .15123 (113*2π)/5205 weeks
114-.06991 .03399 (114*2π)/5205 weeks
115.50552 -.24299 (115*2π)/5205 weeks
1161.14019 -.41469 (116*2π)/5204 weeks
1171.60554 .49503 (117*2π)/5204 weeks
1181.49446 .73797 (118*2π)/5204 weeks
1191.11465 .98458 (119*2π)/5204 weeks
120.81342 1.5492 (120*2π)/5204 weeks
121.76181 1.29913 (121*2π)/5204 weeks
122.6254 1.74164 (122*2π)/5204 weeks
123-.58187 1.28909 (123*2π)/5204 weeks
124-.07788 .77271 (124*2π)/5204 weeks
125-.04538 .49453 (125*2π)/5204 weeks
126-.24023 .6041 (126*2π)/5204 weeks
127.1569 .38247 (127*2π)/5204 weeks
128.39702 .43812 (128*2π)/5204 weeks
129.1577 .1756 (129*2π)/5204 weeks
130.58592 -.10024 (130*2π)/5204 weeks
1311.02035 .64394 (131*2π)/5204 weeks
132.71199 1.19491 (132*2π)/5204 weeks
133.45915 1.11212 (133*2π)/5204 weeks
134-.13438 1.13727 (134*2π)/5204 weeks
135-.13355 .51804 (135*2π)/5204 weeks
136-.0256 .28989 (136*2π)/5204 weeks
137-.55554 .42738 (137*2π)/5204 weeks
138-.14367 .01723 (138*2π)/5204 weeks
139-.05271 -.25598 (139*2π)/5204 weeks
140.49528 -.49696 (140*2π)/5204 weeks
1411.05047 -.11167 (141*2π)/5204 weeks
1421.01503 .09358 (142*2π)/5204 weeks
1431.2987 .7294 (143*2π)/5204 weeks
144.42712 1.30542 (144*2π)/5204 weeks
145-.04857 .81576 (145*2π)/5204 weeks
146-.15761 .29577 (146*2π)/5204 weeks
147.2509 -.10778 (147*2π)/5204 weeks
148.34466 .19435 (148*2π)/5204 weeks
149.277 .42849 (149*2π)/5203 weeks
150.01617 -.11556 (150*2π)/5203 weeks
151.77391 .05874 (151*2π)/5203 weeks
152.76285 .20711 (152*2π)/5203 weeks
153.70528 .42665 (153*2π)/5203 weeks
154.40958 .37987 (154*2π)/5203 weeks
1551.05422 .25842 (155*2π)/5203 weeks
156.28593 .87365 (156*2π)/5203 weeks
157.40622 .51012 (157*2π)/5203 weeks
158.07087 .77566 (158*2π)/5203 weeks
159-.29329 .3075 (159*2π)/5203 weeks
160.02895 -.0517 (160*2π)/5203 weeks
161.25641 -.54669 (161*2π)/5203 weeks
162.85614 -.37749 (162*2π)/5203 weeks
1631.15216 .0553 (163*2π)/5203 weeks
1641.01505 .31305 (164*2π)/5203 weeks
165.94311 .66997 (165*2π)/5203 weeks
166.70285 .82907 (166*2π)/5203 weeks
167.43423 1.16405 (167*2π)/5203 weeks
168-.04684 1.00075 (168*2π)/5203 weeks
169-.38908 .30049 (169*2π)/5203 weeks
170-.04857 .07312 (170*2π)/5203 weeks
171-.07752 .018 (171*2π)/5203 weeks
172.17063 -.16835 (172*2π)/5203 weeks
173.31272 -.16553 (173*2π)/5203 weeks
174.81311 -.34149 (174*2π)/5203 weeks
175.79819 .16455 (175*2π)/5203 weeks
176.70528 .53225 (176*2π)/5203 weeks
177.55379 .69692 (177*2π)/5203 weeks
178.00876 .82076 (178*2π)/5203 weeks
179-.37268 .12554 (179*2π)/5203 weeks
180-.01088 .11446 (180*2π)/5203 weeks
181-.16738 -.3575 (181*2π)/5203 weeks
182.3487 -.56868 (182*2π)/5203 weeks
183.44739 -.67643 (183*2π)/5203 weeks
184.97994 -.59704 (184*2π)/5203 weeks
1851.60467 .32968 (185*2π)/5203 weeks
186.8422 .544 (186*2π)/5203 weeks
187.84598 .64661 (187*2π)/5203 weeks
188.24441 .7435 (188*2π)/5203 weeks
189.0135 .16189 (189*2π)/5203 weeks
190.13968 .44978 (190*2π)/5203 weeks
191-.49646 -.12008 (191*2π)/5203 weeks
192.49743 -.95195 (192*2π)/5203 weeks
193.47428 -.52346 (193*2π)/5203 weeks
1941.29688 -.67305 (194*2π)/5203 weeks
1951.62888 -.11967 (195*2π)/5203 weeks
1961.59455 .76639 (196*2π)/5203 weeks
197.8872 1.02339 (197*2π)/5203 weeks
198.30577 1.16168 (198*2π)/5203 weeks
199-.03916 .61952 (199*2π)/5203 weeks
200-.33809 .28727 (200*2π)/5203 weeks
201-.29803 -.14529 (201*2π)/5203 weeks
202.11713 -.90994 (202*2π)/5203 weeks
203.87167 -.62627 (203*2π)/5203 weeks
2041.32633 -.30417 (204*2π)/5203 weeks
2051.54903 .3248 (205*2π)/5203 weeks
2061.04873 .64047 (206*2π)/5203 weeks
207.6296 .72363 (207*2π)/5203 weeks
208.6631 .71328 (208*2π)/5203 weeks
209.32276 .639 (209*2π)/5202 weeks
210.05753 .53406 (210*2π)/5202 weeks
211.15298 .29784 (211*2π)/5202 weeks
212.0405 .19947 (212*2π)/5202 weeks
213.09595 -.01527 (213*2π)/5202 weeks
214.40852 -.22777 (214*2π)/5202 weeks
215.6001 -.12209 (215*2π)/5202 weeks
216.80947 -.17453 (216*2π)/5202 weeks
217.73302 .22519 (217*2π)/5202 weeks
218.7071 .35168 (218*2π)/5202 weeks
219.95698 .4237 (219*2π)/5202 weeks
220.43665 .85093 (220*2π)/5202 weeks
221.30314 .70979 (221*2π)/5202 weeks
222-.12498 .50079 (222*2π)/5202 weeks
223-.1981 .2086 (223*2π)/5202 weeks
224-.2034 -.07464 (224*2π)/5202 weeks
225-.14571 -.16561 (225*2π)/5202 weeks
226.01498 -.89555 (226*2π)/5202 weeks
227.94104 -.23005 (227*2π)/5202 weeks
228.83034 -.28994 (228*2π)/5202 weeks
2291.1625 .06698 (229*2π)/5202 weeks
230.59498 .6177 (230*2π)/5202 weeks
231.39309 .6185 (231*2π)/5202 weeks
232.04933 .65192 (232*2π)/5202 weeks
233-.2977 .00426 (233*2π)/5202 weeks
234-.09172 -.62863 (234*2π)/5202 weeks
235.34842 -.55089 (235*2π)/5202 weeks
236.52982 -.65275 (236*2π)/5202 weeks
237.99901 -.53328 (237*2π)/5202 weeks
238.91076 -.15044 (238*2π)/5202 weeks
2391.20233 -.10098 (239*2π)/5202 weeks
2401.18343 .13599 (240*2π)/5202 weeks
2411.198 .53109 (241*2π)/5202 weeks
2421.2994 .9314 (242*2π)/5202 weeks
243-.0626 1.34153 (243*2π)/5202 weeks
244-.34069 .43828 (244*2π)/5202 weeks
245-.14451 .22938 (245*2π)/5202 weeks
246-.27181 -.37784 (246*2π)/5202 weeks
247.18149 -.79838 (247*2π)/5202 weeks
2481.00932 -.64952 (248*2π)/5202 weeks
2491.08922 .11723 (249*2π)/5202 weeks
250.95729 .50547 (250*2π)/5202 weeks
251.94188 .6931 (251*2π)/5202 weeks
252.4487 .86681 (252*2π)/5202 weeks
253-.1735 1.15222 (253*2π)/5202 weeks
254-.87543 .32674 (254*2π)/5202 weeks
255-.42034 -.28237 (255*2π)/5202 weeks
256-.21695 -.73997 (256*2π)/5202 weeks
257.23435 -1.07876 (257*2π)/5202 weeks
258.71228 -.53819 (258*2π)/5202 weeks
259.99845 -.50288 (259*2π)/5202 weeks
2601.50903   (260*2π)/5202 weeks
261.99845 .50288 (261*2π)/5202 weeks
262.71228 .53819 (262*2π)/5202 weeks
263.23435 1.07876 (263*2π)/5202 weeks
264-.21695 .73997 (264*2π)/5202 weeks
265-.42034 .28237 (265*2π)/5202 weeks
266-.87543 -.32674 (266*2π)/5202 weeks
267-.1735 -1.15222 (267*2π)/5202 weeks
268.4487 -.86681 (268*2π)/5202 weeks
269.94188 -.6931 (269*2π)/5202 weeks
270.95729 -.50547 (270*2π)/5202 weeks
2711.08922 -.11723 (271*2π)/5202 weeks
2721.00932 .64952 (272*2π)/5202 weeks
273.18149 .79838 (273*2π)/5202 weeks
274-.27181 .37784 (274*2π)/5202 weeks
275-.14451 -.22938 (275*2π)/5202 weeks
276-.34069 -.43828 (276*2π)/5202 weeks
277-.0626 -1.34153 (277*2π)/5202 weeks
2781.2994 -.9314 (278*2π)/5202 weeks
2791.198 -.53109 (279*2π)/5202 weeks
2801.18343 -.13599 (280*2π)/5202 weeks
2811.20233 .10098 (281*2π)/5202 weeks
282.91076 .15044 (282*2π)/5202 weeks
283.99901 .53328 (283*2π)/5202 weeks
284.52982 .65275 (284*2π)/5202 weeks
285.34842 .55089 (285*2π)/5202 weeks
286-.09172 .62863 (286*2π)/5202 weeks
287-.2977 -.00426 (287*2π)/5202 weeks
288.04933 -.65192 (288*2π)/5202 weeks
289.39309 -.6185 (289*2π)/5202 weeks
290.59498 -.6177 (290*2π)/5202 weeks
2911.1625 -.06698 (291*2π)/5202 weeks
292.83034 .28994 (292*2π)/5202 weeks
293.94104 .23005 (293*2π)/5202 weeks
294.01498 .89555 (294*2π)/5202 weeks
295-.14571 .16561 (295*2π)/5202 weeks
296-.2034 .07464 (296*2π)/5202 weeks
297-.1981 -.2086 (297*2π)/5202 weeks
298-.12498 -.50079 (298*2π)/5202 weeks
299.30314 -.70979 (299*2π)/5202 weeks
300.43665 -.85093 (300*2π)/5202 weeks
301.95698 -.4237 (301*2π)/5202 weeks
302.7071 -.35168 (302*2π)/5202 weeks
303.73302 -.22519 (303*2π)/5202 weeks
304.80947 .17453 (304*2π)/5202 weeks
305.6001 .12209 (305*2π)/5202 weeks
306.40852 .22777 (306*2π)/5202 weeks
307.09595 .01527 (307*2π)/5202 weeks
308.0405 -.19947 (308*2π)/5202 weeks
309.15298 -.29784 (309*2π)/5202 weeks
310.05753 -.53406 (310*2π)/5202 weeks
311.32276 -.639 (311*2π)/5202 weeks
312.6631 -.71328 (312*2π)/5202 weeks
313.6296 -.72363 (313*2π)/5202 weeks
3141.04873 -.64047 (314*2π)/5202 weeks
3151.54903 -.3248 (315*2π)/5202 weeks
3161.32633 .30417 (316*2π)/5202 weeks
317.87167 .62627 (317*2π)/5202 weeks
318.11713 .90994 (318*2π)/5202 weeks
319-.29803 .14529 (319*2π)/5202 weeks
320-.33809 -.28727 (320*2π)/5202 weeks
321-.03916 -.61952 (321*2π)/5202 weeks
322.30577 -1.16168 (322*2π)/5202 weeks
323.8872 -1.02339 (323*2π)/5202 weeks
3241.59455 -.76639 (324*2π)/5202 weeks
3251.62888 .11967 (325*2π)/5202 weeks
3261.29688 .67305 (326*2π)/5202 weeks
327.47428 .52346 (327*2π)/5202 weeks
328.49743 .95195 (328*2π)/5202 weeks
329-.49646 .12008 (329*2π)/5202 weeks
330.13968 -.44978 (330*2π)/5202 weeks
331.0135 -.16189 (331*2π)/5202 weeks
332.24441 -.7435 (332*2π)/5202 weeks
333.84598 -.64661 (333*2π)/5202 weeks
334.8422 -.544 (334*2π)/5202 weeks
3351.60467 -.32968 (335*2π)/5202 weeks
336.97994 .59704 (336*2π)/5202 weeks
337.44739 .67643 (337*2π)/5202 weeks
338.3487 .56868 (338*2π)/5202 weeks
339-.16738 .3575 (339*2π)/5202 weeks
340-.01088 -.11446 (340*2π)/5202 weeks
341-.37268 -.12554 (341*2π)/5202 weeks
342.00876 -.82076 (342*2π)/5202 weeks
343.55379 -.69692 (343*2π)/5202 weeks
344.70528 -.53225 (344*2π)/5202 weeks
345.79819 -.16455 (345*2π)/5202 weeks
346.81311 .34149 (346*2π)/5202 weeks
347.31272 .16553 (347*2π)/5201 weeks
348.17063 .16835 (348*2π)/5201 weeks
349-.07752 -.018 (349*2π)/5201 weeks
350-.04857 -.07312 (350*2π)/5201 weeks
351-.38908 -.30049 (351*2π)/5201 weeks
352-.04684 -1.00075 (352*2π)/5201 weeks
353.43423 -1.16405 (353*2π)/5201 weeks
354.70285 -.82907 (354*2π)/5201 weeks
355.94311 -.66997 (355*2π)/5201 weeks
3561.01505 -.31305 (356*2π)/5201 weeks
3571.15216 -.0553 (357*2π)/5201 weeks
358.85614 .37749 (358*2π)/5201 weeks
359.25641 .54669 (359*2π)/5201 weeks
360.02895 .0517 (360*2π)/5201 weeks
361-.29329 -.3075 (361*2π)/5201 weeks
362.07087 -.77566 (362*2π)/5201 weeks
363.40622 -.51012 (363*2π)/5201 weeks
364.28593 -.87365 (364*2π)/5201 weeks
3651.05422 -.25842 (365*2π)/5201 weeks
366.40958 -.37987 (366*2π)/5201 weeks
367.70528 -.42665 (367*2π)/5201 weeks
368.76285 -.20711 (368*2π)/5201 weeks
369.77391 -.05874 (369*2π)/5201 weeks
370.01617 .11556 (370*2π)/5201 weeks
371.277 -.42849 (371*2π)/5201 weeks
372.34466 -.19435 (372*2π)/5201 weeks
373.2509 .10778 (373*2π)/5201 weeks
374-.15761 -.29577 (374*2π)/5201 weeks
375-.04857 -.81576 (375*2π)/5201 weeks
376.42712 -1.30542 (376*2π)/5201 weeks
3771.2987 -.7294 (377*2π)/5201 weeks
3781.01503 -.09358 (378*2π)/5201 weeks
3791.05047 .11167 (379*2π)/5201 weeks
380.49528 .49696 (380*2π)/5201 weeks
381-.05271 .25598 (381*2π)/5201 weeks
382-.14367 -.01723 (382*2π)/5201 weeks
383-.55554 -.42738 (383*2π)/5201 weeks
384-.0256 -.28989 (384*2π)/5201 weeks
385-.13355 -.51804 (385*2π)/5201 weeks
386-.13438 -1.13727 (386*2π)/5201 weeks
387.45915 -1.11212 (387*2π)/5201 weeks
388.71199 -1.19491 (388*2π)/5201 weeks
3891.02035 -.64394 (389*2π)/5201 weeks
390.58592 .10024 (390*2π)/5201 weeks
391.1577 -.1756 (391*2π)/5201 weeks
392.39702 -.43812 (392*2π)/5201 weeks
393.1569 -.38247 (393*2π)/5201 weeks
394-.24023 -.6041 (394*2π)/5201 weeks
395-.04538 -.49453 (395*2π)/5201 weeks
396-.07788 -.77271 (396*2π)/5201 weeks
397-.58187 -1.28909 (397*2π)/5201 weeks
398.6254 -1.74164 (398*2π)/5201 weeks
399.76181 -1.29913 (399*2π)/5201 weeks
400.81342 -1.5492 (400*2π)/5201 weeks
4011.11465 -.98458 (401*2π)/5201 weeks
4021.49446 -.73797 (402*2π)/5201 weeks
4031.60554 -.49503 (403*2π)/5201 weeks
4041.14019 .41469 (404*2π)/5201 weeks
405.50552 .24299 (405*2π)/5201 weeks
406-.06991 -.03399 (406*2π)/5201 weeks
407-.1486 -.15123 (407*2π)/5201 weeks
408-.13681 -.99827 (408*2π)/5201 weeks
409.12424 -.85203 (409*2π)/5201 weeks
410.33682 -1.58566 (410*2π)/5201 weeks
411.67312 -1.43122 (411*2π)/5201 weeks
4121.90403 -1.2688 (412*2π)/5201 weeks
4131.65526 .0105 (413*2π)/5201 weeks
4141.29346 .32794 (414*2π)/5201 weeks
415.69009 .53553 (415*2π)/5201 weeks
416-.06289 .2374 (416*2π)/5201 weeks
417-1.05729 .38922 (417*2π)/5201 weeks
418-.70067 -1.02027 (418*2π)/5201 weeks
419-.41059 -1.01408 (419*2π)/5201 weeks
420-.37235 -2.05619 (420*2π)/5201 weeks
421.68611 -2.05034 (421*2π)/5201 weeks
4221.26828 -1.84847 (422*2π)/5201 weeks
4231.71285 -.78425 (423*2π)/5201 weeks
4241.64216 .16558 (424*2π)/5201 weeks
425.8057 -.00792 (425*2π)/5201 weeks
426.41406 -.22507 (426*2π)/5201 weeks
427.07293 -.05067 (427*2π)/5201 weeks
428-.80919 -.56888 (428*2π)/5201 weeks
429-.50372 -1.46264 (429*2π)/5201 weeks
430.24381 -2.04066 (430*2π)/5201 weeks
4311.22352 -1.15549 (431*2π)/5201 weeks
432.80255 -1.42298 (432*2π)/5201 weeks
433.97515 -1.35677 (433*2π)/5201 weeks
434.87208 -1.25386 (434*2π)/5201 weeks
4351.63279 -1.4075 (435*2π)/5201 weeks
4361.93478 -.13159 (436*2π)/5201 weeks
4371.38458 .82111 (437*2π)/5201 weeks
438.35068 .89255 (438*2π)/5201 weeks
439-1.13443 .214 (439*2π)/5201 weeks
440-1.59953 -1.11596 (440*2π)/5201 weeks
441-.58194 -2.34358 (441*2π)/5201 weeks
442-.05276 -2.46274 (442*2π)/5201 weeks
4431.74146 -2.89838 (443*2π)/5201 weeks
4442.38798 -1.30932 (444*2π)/5201 weeks
4453.06055 -.92099 (445*2π)/5201 weeks
4462.37108 1.21907 (446*2π)/5201 weeks
447-.17326 1.87535 (447*2π)/5201 weeks
448-.67961 .59266 (448*2π)/5201 weeks
449-1.8897 -.33849 (449*2π)/5201 weeks
450-1.28076 -1.63077 (450*2π)/5201 weeks
451-.66714 -2.70382 (451*2π)/5201 weeks
452.43068 -3.1977 (452*2π)/5201 weeks
4531.39188 -2.41913 (453*2π)/5201 weeks
4542.01247 -1.52848 (454*2π)/5201 weeks
4551.5684 -.93605 (455*2π)/5201 weeks
4561.55825 -.67877 (456*2π)/5201 weeks
457.68177 -.3412 (457*2π)/5201 weeks
4581.00127 -.90831 (458*2π)/5201 weeks
459.94353 -.38407 (459*2π)/5201 weeks
460-.1649 -.46356 (460*2π)/5201 weeks
461.65015 -.78072 (461*2π)/5201 weeks
462-.83927 -.81595 (462*2π)/5201 weeks
463-.22479 -2.0232 (463*2π)/5201 weeks
464.02988 -2.86824 (464*2π)/5201 weeks
4651.65673 -2.63384 (465*2π)/5201 weeks
4661.71352 -2.24645 (466*2π)/5201 weeks
4673.31831 -.77395 (467*2π)/5201 weeks
4681.98834 1.0241 (468*2π)/5201 weeks
469-.33028 .25493 (469*2π)/5201 weeks
470-.05709 -.21728 (470*2π)/5201 weeks
471-1.78158 -1.18403 (471*2π)/5201 weeks
472-.21713 -2.56951 (472*2π)/5201 weeks
473.94598 -2.41238 (473*2π)/5201 weeks
4741.3744 -1.39409 (474*2π)/5201 weeks
475.91309 -2.4525 (475*2π)/5201 weeks
4761.64294 -.51367 (476*2π)/5201 weeks
477.69655 -.31544 (477*2π)/5201 weeks
478.44913 -1.54973 (478*2π)/5201 weeks
479-.1747 -.66404 (479*2π)/5201 weeks
480.33947 -2.77883 (480*2π)/5201 weeks
4811.79717 -.71974 (481*2π)/5201 weeks
482.38918 -.53776 (482*2π)/5201 weeks
483-.7303 -.64659 (483*2π)/5201 weeks
484-.33955 -1.90974 (484*2π)/5201 weeks
485-1.20956 -1.82469 (485*2π)/5201 weeks
486-.88794 -3.01991 (486*2π)/5201 weeks
487-1.0607 -4.66432 (487*2π)/5201 weeks
4882.17525 -6.42852 (488*2π)/5201 weeks
4895.07472 -3.86047 (489*2π)/5201 weeks
4904.77037 .53049 (490*2π)/5201 weeks
4913.3713 1.94451 (491*2π)/5201 weeks
492-.7871 3.03179 (492*2π)/5201 weeks
493-4.36098 -1.36738 (493*2π)/5201 weeks
494-2.63686 -1.93846 (494*2π)/5201 weeks
495-3.16353 -5.14268 (495*2π)/5201 weeks
4961.47707 -6.29575 (496*2π)/5201 weeks
4973.83327 -4.29806 (497*2π)/5201 weeks
4984.58604 -1.74652 (498*2π)/5201 weeks
499.87505 .45447 (499*2π)/5201 weeks
500.58802 .84677 (500*2π)/5201 weeks
501-3.25778 2.1545 (501*2π)/5201 weeks
502-5.69958 -3.22414 (502*2π)/5201 weeks
503-4.59662 -4.38624 (503*2π)/5201 weeks
504-5.41193 -10.18752 (504*2π)/5201 weeks
505.71813 -8.79402 (505*2π)/5201 weeks
5062.11628 -5.73713 (506*2π)/5201 weeks
507-1.63591 -7.61739 (507*2π)/5201 weeks
508-1.20448 -9.14051 (508*2π)/5201 weeks
5092.30501 -11.99712 (509*2π)/5201 weeks
5105.63665 -9.14609 (510*2π)/5201 weeks
5112.03587 -9.76019 (511*2π)/5201 weeks
5129.12335 -6.16794 (512*2π)/5201 weeks
5131.7853 .91591 (513*2π)/5201 weeks
514-4.44901 -2.27577 (514*2π)/5201 weeks
515-14.93279 -16.5276 (515*2π)/5201 weeks
516-10.28649 -21.70633 (516*2π)/5201 weeks
517-11.88685 -45.6336 (517*2π)/5201 weeks
51813.66511 -53.11292 (518*2π)/5201 weeks



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