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Fourier Analysis of EWV (ProShares UltraShort MSCI Japan)


EWV (ProShares UltraShort MSCI Japan) appears to have interesting cyclic behaviour every 46 weeks (11.17*sine), 50 weeks (10.6769*sine), and 55 weeks (6.7738*sine).

EWV (ProShares UltraShort MSCI Japan) has an average price of 128.95 (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 4/16/2018 for EWV (ProShares UltraShort MSCI Japan), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0128.9478   0 
135.41248 93.13785 (1*2π)/546546 weeks
212.58428 51.8425 (2*2π)/546273 weeks
3-7.96853 48.49054 (3*2π)/546182 weeks
4-11.53093 23.12067 (4*2π)/546137 weeks
5-11.34411 19.62836 (5*2π)/546109 weeks
6-8.34615 2.38113 (6*2π)/54691 weeks
7-2.08316 1.06512 (7*2π)/54678 weeks
87.45336 3.04807 (8*2π)/54668 weeks
95.83667 11.2705 (9*2π)/54661 weeks
103.9853 6.77382 (10*2π)/54655 weeks
114.25674 10.67692 (11*2π)/54650 weeks
12.08138 11.16995 (12*2π)/54646 weeks
13-.73185 8.11447 (13*2π)/54642 weeks
14-1.48898 5.83583 (14*2π)/54639 weeks
152.3055 7.32623 (15*2π)/54636 weeks
16.66672 9.30667 (16*2π)/54634 weeks
17-6.04274 8.1532 (17*2π)/54632 weeks
18-4.12439 4.27354 (18*2π)/54630 weeks
19-5.52634 2.73491 (19*2π)/54629 weeks
20-2.71057 -2.07002 (20*2π)/54627 weeks
21.62384 -.77817 (21*2π)/54626 weeks
22.81482 -.28292 (22*2π)/54625 weeks
234.43457 1.175 (23*2π)/54624 weeks
243.70994 3.63126 (24*2π)/54623 weeks
251.74671 5.70978 (25*2π)/54622 weeks
26-2.30232 6.09707 (26*2π)/54621 weeks
27-2.94553 2.5581 (27*2π)/54620 weeks
28-2.63282 2.53291 (28*2π)/54620 weeks
29-2.50746 -2.48382 (29*2π)/54619 weeks
301.6045 -3.02307 (30*2π)/54618 weeks
313.415 -.69503 (31*2π)/54618 weeks
325.72706 1.59586 (32*2π)/54617 weeks
334.14256 4.76165 (33*2π)/54617 weeks
34.44974 5.82823 (34*2π)/54616 weeks
35-1.19277 3.57051 (35*2π)/54616 weeks
36-1.00111 2.77581 (36*2π)/54615 weeks
37-.87602 1.43663 (37*2π)/54615 weeks
38-.58594 1.87081 (38*2π)/54614 weeks
39-.50232 .49201 (39*2π)/54614 weeks
40.38638 .52383 (40*2π)/54614 weeks
411.76867 .81919 (41*2π)/54613 weeks
42.29833 2.6716 (42*2π)/54613 weeks
43-.28626 .72904 (43*2π)/54613 weeks
44.56247 1.4763 (44*2π)/54612 weeks
45.38637 .35318 (45*2π)/54612 weeks
461.21192 .5231 (46*2π)/54612 weeks
471.57724 2.35071 (47*2π)/54612 weeks
48.84614 1.17875 (48*2π)/54611 weeks
491.11359 2.21536 (49*2π)/54611 weeks
50.25237 2.66041 (50*2π)/54611 weeks
51-1.00535 2.32419 (51*2π)/54611 weeks
52-.64963 -.03931 (52*2π)/54611 weeks
53-.08068 .29501 (53*2π)/54610 weeks
54.30109 -1.12407 (54*2π)/54610 weeks
552.43468 -.38814 (55*2π)/54610 weeks
563.0095 1.76281 (56*2π)/54610 weeks
571.61114 1.95266 (57*2π)/54610 weeks
581.34477 2.75342 (58*2π)/5469 weeks
59-.16736 2.47032 (59*2π)/5469 weeks
60-.29972 1.93217 (60*2π)/5469 weeks
61-.68694 .60887 (61*2π)/5469 weeks
62.63218 .82116 (62*2π)/5469 weeks
63-.13858 .44085 (63*2π)/5469 weeks
64.89953 .32843 (64*2π)/5469 weeks
65.99985 .79776 (65*2π)/5468 weeks
66.54397 .45105 (66*2π)/5468 weeks
671.43172 .48561 (67*2π)/5468 weeks
681.41111 .87865 (68*2π)/5468 weeks
691.78971 1.20262 (69*2π)/5468 weeks
701.57897 2.24147 (70*2π)/5468 weeks
711.08063 2.81038 (71*2π)/5468 weeks
72-.2725 2.66927 (72*2π)/5468 weeks
73-1.22709 2.02302 (73*2π)/5467 weeks
74-1.56408 1.31271 (74*2π)/5467 weeks
75-1.33439 -.39547 (75*2π)/5467 weeks
76-.67641 -.64798 (76*2π)/5467 weeks
77.82669 -2.03327 (77*2π)/5467 weeks
782.57871 -.73827 (78*2π)/5467 weeks
792.50933 1.29825 (79*2π)/5467 weeks
802.40001 1.54389 (80*2π)/5467 weeks
811.4094 2.92628 (81*2π)/5467 weeks
82-.04363 2.26444 (82*2π)/5467 weeks
83-.61436 2.2308 (83*2π)/5467 weeks
84-1.52446 1.09333 (84*2π)/5467 weeks
85-1.09021 -.10634 (85*2π)/5466 weeks
86.24001 -.87575 (86*2π)/5466 weeks
871.09867 -.83305 (87*2π)/5466 weeks
881.75705 .06357 (88*2π)/5466 weeks
891.86498 1.21371 (89*2π)/5466 weeks
901.0117 1.37549 (90*2π)/5466 weeks
911.09142 1.14983 (91*2π)/5466 weeks
92.88771 1.2076 (92*2π)/5466 weeks
93.63981 .98204 (93*2π)/5466 weeks
94.93162 1.95447 (94*2π)/5466 weeks
95-.10612 1.76809 (95*2π)/5466 weeks
96-.53847 1.11417 (96*2π)/5466 weeks
97-.42914 .04957 (97*2π)/5466 weeks
98.22775 -.00264 (98*2π)/5466 weeks
99.31847 .09822 (99*2π)/5466 weeks
100.74012 .0484 (100*2π)/5465 weeks
1011.78181 .17317 (101*2π)/5465 weeks
1021.75139 .85126 (102*2π)/5465 weeks
1031.14369 1.75483 (103*2π)/5465 weeks
104.63418 1.95896 (104*2π)/5465 weeks
105-.34192 1.95368 (105*2π)/5465 weeks
106-.40691 .96072 (106*2π)/5465 weeks
107-.6064 .99495 (107*2π)/5465 weeks
108-1.16058 -.07464 (108*2π)/5465 weeks
109.065 -.24096 (109*2π)/5465 weeks
110.50959 -.66721 (110*2π)/5465 weeks
1111.00678 -.50934 (111*2π)/5465 weeks
1121.31488 -.092 (112*2π)/5465 weeks
1131.90838 .64296 (113*2π)/5465 weeks
1141.00669 1.65329 (114*2π)/5465 weeks
115.68218 1.34319 (115*2π)/5465 weeks
116-.07176 1.15516 (116*2π)/5465 weeks
117.18405 .93849 (117*2π)/5465 weeks
118-.35416 .70387 (118*2π)/5465 weeks
119.06603 .18055 (119*2π)/5465 weeks
120.06134 -.18922 (120*2π)/5465 weeks
121.52912 -.26125 (121*2π)/5465 weeks
1221.2717 -.30342 (122*2π)/5464 weeks
1231.45071 .57314 (123*2π)/5464 weeks
1241.43865 .78633 (124*2π)/5464 weeks
1251.08043 .93458 (125*2π)/5464 weeks
126.77109 1.48435 (126*2π)/5464 weeks
127.72529 1.23413 (127*2π)/5464 weeks
128.64873 1.58964 (128*2π)/5464 weeks
129-.49675 1.45851 (129*2π)/5464 weeks
130-.11122 .71049 (130*2π)/5464 weeks
131-.1546 .57511 (131*2π)/5464 weeks
132-.02502 .74413 (132*2π)/5464 weeks
133.13188 .25529 (133*2π)/5464 weeks
134.26572 .23028 (134*2π)/5464 weeks
135.08081 .41858 (135*2π)/5464 weeks
136.29946 .08874 (136*2π)/5464 weeks
1371.02587 .16071 (137*2π)/5464 weeks
138.93784 .7617 (138*2π)/5464 weeks
139.39641 1.04665 (139*2π)/5464 weeks
140.25455 1.18535 (140*2π)/5464 weeks
141-.31045 .9501 (141*2π)/5464 weeks
142-.09847 .5777 (142*2π)/5464 weeks
143.12546 .39425 (143*2π)/5464 weeks
144-.50661 .21892 (144*2π)/5464 weeks
145-.13092 .00317 (145*2π)/5464 weeks
146-.03193 -.26398 (146*2π)/5464 weeks
147.48161 -.47426 (147*2π)/5464 weeks
1481.00311 -.14549 (148*2π)/5464 weeks
149.93648 .08063 (149*2π)/5464 weeks
1501.25091 .55756 (150*2π)/5464 weeks
151.61929 1.25652 (151*2π)/5464 weeks
152-.00367 .84752 (152*2π)/5464 weeks
153-.20556 .42558 (153*2π)/5464 weeks
154-.01774 -.00516 (154*2π)/5464 weeks
155.40813 .22231 (155*2π)/5464 weeks
156.45472 .30167 (156*2π)/5464 weeks
157.05975 .25641 (157*2π)/5463 weeks
158.49424 -.33868 (158*2π)/5463 weeks
159.63511 .12138 (159*2π)/5463 weeks
160.70237 .2861 (160*2π)/5463 weeks
161.58173 .46416 (161*2π)/5463 weeks
162.38645 .20259 (162*2π)/5463 weeks
1631.05087 .58105 (163*2π)/5463 weeks
164.19815 .68591 (164*2π)/5463 weeks
165.41136 .52712 (165*2π)/5463 weeks
166.01007 .70722 (166*2π)/5463 weeks
167-.28945 .25282 (167*2π)/5463 weeks
168.02027 -.05494 (168*2π)/5463 weeks
169.19252 -.51654 (169*2π)/5463 weeks
170.75703 -.39245 (170*2π)/5463 weeks
1711.05396 -.02993 (171*2π)/5463 weeks
172.91773 .30063 (172*2π)/5463 weeks
173.93335 .60364 (173*2π)/5463 weeks
174.72152 .8058 (174*2π)/5463 weeks
175.61712 .99599 (175*2π)/5463 weeks
176.06324 .98089 (176*2π)/5463 weeks
177-.44549 .69375 (177*2π)/5463 weeks
178-.18875 .16573 (178*2π)/5463 weeks
179-.00124 .15659 (179*2π)/5463 weeks
180.01897 -.0902 (180*2π)/5463 weeks
181.23945 -.14312 (181*2π)/5463 weeks
182.3084 -.21764 (182*2π)/5463 weeks
183.91972 -.05484 (183*2π)/5463 weeks
184.82514 .22085 (184*2π)/5463 weeks
185.63065 .53115 (185*2π)/5463 weeks
186.49124 .73044 (186*2π)/5463 weeks
187-.04216 .78366 (187*2π)/5463 weeks
188-.31874 .10563 (188*2π)/5463 weeks
189.00933 .13223 (189*2π)/5463 weeks
190-.15235 -.29671 (190*2π)/5463 weeks
191.30836 -.54673 (191*2π)/5463 weeks
192.38139 -.55661 (192*2π)/5463 weeks
193.89559 -.54222 (193*2π)/5463 weeks
1941.62637 -.05905 (194*2π)/5463 weeks
195.91238 .567 (195*2π)/5463 weeks
196.80254 .47263 (196*2π)/5463 weeks
197.43732 .80159 (197*2π)/5463 weeks
198-.02649 .49494 (198*2π)/5463 weeks
199.31744 .21749 (199*2π)/5463 weeks
200-.19313 .33614 (200*2π)/5463 weeks
201-.31994 -.67963 (201*2π)/5463 weeks
202.73483 -.53403 (202*2π)/5463 weeks
203.60458 -.74728 (203*2π)/5463 weeks
2041.36056 -.44067 (204*2π)/5463 weeks
2051.64145 .06746 (205*2π)/5463 weeks
2061.41094 .88308 (206*2π)/5463 weeks
207.83012 .98949 (207*2π)/5463 weeks
208.23638 1.08069 (208*2π)/5463 weeks
209-.0109 .58276 (209*2π)/5463 weeks
210-.30203 .2708 (210*2π)/5463 weeks
211-.26119 -.11547 (211*2π)/5463 weeks
212.03055 -.81443 (212*2π)/5463 weeks
213.82676 -.63303 (213*2π)/5463 weeks
2141.23577 -.40726 (214*2π)/5463 weeks
2151.47986 .06568 (215*2π)/5463 weeks
2161.05505 .60473 (216*2π)/5463 weeks
217.76287 .76765 (217*2π)/5463 weeks
218.63894 .56945 (218*2π)/5463 weeks
219.38367 .7331 (219*2π)/5462 weeks
220.25181 .6432 (220*2π)/5462 weeks
221.10287 .32563 (221*2π)/5462 weeks
222.15036 .2826 (222*2π)/5462 weeks
223.07873 .06855 (223*2π)/5462 weeks
224.12813 -.14512 (224*2π)/5462 weeks
225.45293 -.18396 (225*2π)/5462 weeks
226.57694 -.08279 (226*2π)/5462 weeks
227.88496 -.07306 (227*2π)/5462 weeks
228.70943 .18693 (228*2π)/5462 weeks
229.65858 .32055 (229*2π)/5462 weeks
230.92751 .44011 (230*2π)/5462 weeks
231.42824 .81044 (231*2π)/5462 weeks
232.31041 .6592 (232*2π)/5462 weeks
233-.1065 .51345 (233*2π)/5462 weeks
234-.18776 .24731 (234*2π)/5462 weeks
235-.2054 .01714 (235*2π)/5462 weeks
236-.06736 -.10864 (236*2π)/5462 weeks
237-.1541 -.57546 (237*2π)/5462 weeks
238.95134 -.64813 (238*2π)/5462 weeks
239.6523 -.26131 (239*2π)/5462 weeks
240.96053 -.14409 (240*2π)/5462 weeks
241.99265 .53749 (241*2π)/5462 weeks
242.53058 .46081 (242*2π)/5462 weeks
243.24871 .50327 (243*2π)/5462 weeks
244-.27846 .44021 (244*2π)/5462 weeks
245-.3062 -.12209 (245*2π)/5462 weeks
246.13929 -.62379 (246*2π)/5462 weeks
247.37319 -.52712 (247*2π)/5462 weeks
248.59364 -.64871 (248*2π)/5462 weeks
2491.00963 -.4494 (249*2π)/5462 weeks
250.85662 -.17584 (250*2π)/5462 weeks
2511.1525 -.07804 (251*2π)/5462 weeks
2521.13213 .12464 (252*2π)/5462 weeks
2531.1608 .48403 (253*2π)/5462 weeks
2541.23484 .7634 (254*2π)/5462 weeks
255.11932 1.39986 (255*2π)/5462 weeks
256-.34018 .54044 (256*2π)/5462 weeks
257-.12193 .18699 (257*2π)/5462 weeks
258-.38049 -.14006 (258*2π)/5462 weeks
259-.01565 -.57021 (259*2π)/5462 weeks
260.70726 -.72591 (260*2π)/5462 weeks
2611.2318 -.10956 (261*2π)/5462 weeks
2621.09214 .22485 (262*2π)/5462 weeks
263.8276 .40806 (263*2π)/5462 weeks
264.65484 .85411 (264*2π)/5462 weeks
265.37321 .92754 (265*2π)/5462 weeks
266-.48676 .90979 (266*2π)/5462 weeks
267-.79368 -.02917 (267*2π)/5462 weeks
268-.4279 -.30477 (268*2π)/5462 weeks
269-.1161 -.72431 (269*2π)/5462 weeks
270.38948 -1.05269 (270*2π)/5462 weeks
271.646 -.53083 (271*2π)/5462 weeks
272.94709 -.47211 (272*2π)/5462 weeks
2731.42664   (273*2π)/5462 weeks
274.94709 .47211 (274*2π)/5462 weeks
275.646 .53083 (275*2π)/5462 weeks
276.38948 1.05269 (276*2π)/5462 weeks
277-.1161 .72431 (277*2π)/5462 weeks
278-.4279 .30477 (278*2π)/5462 weeks
279-.79368 .02917 (279*2π)/5462 weeks
280-.48676 -.90979 (280*2π)/5462 weeks
281.37321 -.92754 (281*2π)/5462 weeks
282.65484 -.85411 (282*2π)/5462 weeks
283.8276 -.40806 (283*2π)/5462 weeks
2841.09214 -.22485 (284*2π)/5462 weeks
2851.2318 .10956 (285*2π)/5462 weeks
286.70726 .72591 (286*2π)/5462 weeks
287-.01565 .57021 (287*2π)/5462 weeks
288-.38049 .14006 (288*2π)/5462 weeks
289-.12193 -.18699 (289*2π)/5462 weeks
290-.34018 -.54044 (290*2π)/5462 weeks
291.11932 -1.39986 (291*2π)/5462 weeks
2921.23484 -.7634 (292*2π)/5462 weeks
2931.1608 -.48403 (293*2π)/5462 weeks
2941.13213 -.12464 (294*2π)/5462 weeks
2951.1525 .07804 (295*2π)/5462 weeks
296.85662 .17584 (296*2π)/5462 weeks
2971.00963 .4494 (297*2π)/5462 weeks
298.59364 .64871 (298*2π)/5462 weeks
299.37319 .52712 (299*2π)/5462 weeks
300.13929 .62379 (300*2π)/5462 weeks
301-.3062 .12209 (301*2π)/5462 weeks
302-.27846 -.44021 (302*2π)/5462 weeks
303.24871 -.50327 (303*2π)/5462 weeks
304.53058 -.46081 (304*2π)/5462 weeks
305.99265 -.53749 (305*2π)/5462 weeks
306.96053 .14409 (306*2π)/5462 weeks
307.6523 .26131 (307*2π)/5462 weeks
308.95134 .64813 (308*2π)/5462 weeks
309-.1541 .57546 (309*2π)/5462 weeks
310-.06736 .10864 (310*2π)/5462 weeks
311-.2054 -.01714 (311*2π)/5462 weeks
312-.18776 -.24731 (312*2π)/5462 weeks
313-.1065 -.51345 (313*2π)/5462 weeks
314.31041 -.6592 (314*2π)/5462 weeks
315.42824 -.81044 (315*2π)/5462 weeks
316.92751 -.44011 (316*2π)/5462 weeks
317.65858 -.32055 (317*2π)/5462 weeks
318.70943 -.18693 (318*2π)/5462 weeks
319.88496 .07306 (319*2π)/5462 weeks
320.57694 .08279 (320*2π)/5462 weeks
321.45293 .18396 (321*2π)/5462 weeks
322.12813 .14512 (322*2π)/5462 weeks
323.07873 -.06855 (323*2π)/5462 weeks
324.15036 -.2826 (324*2π)/5462 weeks
325.10287 -.32563 (325*2π)/5462 weeks
326.25181 -.6432 (326*2π)/5462 weeks
327.38367 -.7331 (327*2π)/5462 weeks
328.63894 -.56945 (328*2π)/5462 weeks
329.76287 -.76765 (329*2π)/5462 weeks
3301.05505 -.60473 (330*2π)/5462 weeks
3311.47986 -.06568 (331*2π)/5462 weeks
3321.23577 .40726 (332*2π)/5462 weeks
333.82676 .63303 (333*2π)/5462 weeks
334.03055 .81443 (334*2π)/5462 weeks
335-.26119 .11547 (335*2π)/5462 weeks
336-.30203 -.2708 (336*2π)/5462 weeks
337-.0109 -.58276 (337*2π)/5462 weeks
338.23638 -1.08069 (338*2π)/5462 weeks
339.83012 -.98949 (339*2π)/5462 weeks
3401.41094 -.88308 (340*2π)/5462 weeks
3411.64145 -.06746 (341*2π)/5462 weeks
3421.36056 .44067 (342*2π)/5462 weeks
343.60458 .74728 (343*2π)/5462 weeks
344.73483 .53403 (344*2π)/5462 weeks
345-.31994 .67963 (345*2π)/5462 weeks
346-.19313 -.33614 (346*2π)/5462 weeks
347.31744 -.21749 (347*2π)/5462 weeks
348-.02649 -.49494 (348*2π)/5462 weeks
349.43732 -.80159 (349*2π)/5462 weeks
350.80254 -.47263 (350*2π)/5462 weeks
351.91238 -.567 (351*2π)/5462 weeks
3521.62637 .05905 (352*2π)/5462 weeks
353.89559 .54222 (353*2π)/5462 weeks
354.38139 .55661 (354*2π)/5462 weeks
355.30836 .54673 (355*2π)/5462 weeks
356-.15235 .29671 (356*2π)/5462 weeks
357.00933 -.13223 (357*2π)/5462 weeks
358-.31874 -.10563 (358*2π)/5462 weeks
359-.04216 -.78366 (359*2π)/5462 weeks
360.49124 -.73044 (360*2π)/5462 weeks
361.63065 -.53115 (361*2π)/5462 weeks
362.82514 -.22085 (362*2π)/5462 weeks
363.91972 .05484 (363*2π)/5462 weeks
364.3084 .21764 (364*2π)/5462 weeks
365.23945 .14312 (365*2π)/5461 weeks
366.01897 .0902 (366*2π)/5461 weeks
367-.00124 -.15659 (367*2π)/5461 weeks
368-.18875 -.16573 (368*2π)/5461 weeks
369-.44549 -.69375 (369*2π)/5461 weeks
370.06324 -.98089 (370*2π)/5461 weeks
371.61712 -.99599 (371*2π)/5461 weeks
372.72152 -.8058 (372*2π)/5461 weeks
373.93335 -.60364 (373*2π)/5461 weeks
374.91773 -.30063 (374*2π)/5461 weeks
3751.05396 .02993 (375*2π)/5461 weeks
376.75703 .39245 (376*2π)/5461 weeks
377.19252 .51654 (377*2π)/5461 weeks
378.02027 .05494 (378*2π)/5461 weeks
379-.28945 -.25282 (379*2π)/5461 weeks
380.01007 -.70722 (380*2π)/5461 weeks
381.41136 -.52712 (381*2π)/5461 weeks
382.19815 -.68591 (382*2π)/5461 weeks
3831.05087 -.58105 (383*2π)/5461 weeks
384.38645 -.20259 (384*2π)/5461 weeks
385.58173 -.46416 (385*2π)/5461 weeks
386.70237 -.2861 (386*2π)/5461 weeks
387.63511 -.12138 (387*2π)/5461 weeks
388.49424 .33868 (388*2π)/5461 weeks
389.05975 -.25641 (389*2π)/5461 weeks
390.45472 -.30167 (390*2π)/5461 weeks
391.40813 -.22231 (391*2π)/5461 weeks
392-.01774 .00516 (392*2π)/5461 weeks
393-.20556 -.42558 (393*2π)/5461 weeks
394-.00367 -.84752 (394*2π)/5461 weeks
395.61929 -1.25652 (395*2π)/5461 weeks
3961.25091 -.55756 (396*2π)/5461 weeks
397.93648 -.08063 (397*2π)/5461 weeks
3981.00311 .14549 (398*2π)/5461 weeks
399.48161 .47426 (399*2π)/5461 weeks
400-.03193 .26398 (400*2π)/5461 weeks
401-.13092 -.00317 (401*2π)/5461 weeks
402-.50661 -.21892 (402*2π)/5461 weeks
403.12546 -.39425 (403*2π)/5461 weeks
404-.09847 -.5777 (404*2π)/5461 weeks
405-.31045 -.9501 (405*2π)/5461 weeks
406.25455 -1.18535 (406*2π)/5461 weeks
407.39641 -1.04665 (407*2π)/5461 weeks
408.93784 -.7617 (408*2π)/5461 weeks
4091.02587 -.16071 (409*2π)/5461 weeks
410.29946 -.08874 (410*2π)/5461 weeks
411.08081 -.41858 (411*2π)/5461 weeks
412.26572 -.23028 (412*2π)/5461 weeks
413.13188 -.25529 (413*2π)/5461 weeks
414-.02502 -.74413 (414*2π)/5461 weeks
415-.1546 -.57511 (415*2π)/5461 weeks
416-.11122 -.71049 (416*2π)/5461 weeks
417-.49675 -1.45851 (417*2π)/5461 weeks
418.64873 -1.58964 (418*2π)/5461 weeks
419.72529 -1.23413 (419*2π)/5461 weeks
420.77109 -1.48435 (420*2π)/5461 weeks
4211.08043 -.93458 (421*2π)/5461 weeks
4221.43865 -.78633 (422*2π)/5461 weeks
4231.45071 -.57314 (423*2π)/5461 weeks
4241.2717 .30342 (424*2π)/5461 weeks
425.52912 .26125 (425*2π)/5461 weeks
426.06134 .18922 (426*2π)/5461 weeks
427.06603 -.18055 (427*2π)/5461 weeks
428-.35416 -.70387 (428*2π)/5461 weeks
429.18405 -.93849 (429*2π)/5461 weeks
430-.07176 -1.15516 (430*2π)/5461 weeks
431.68218 -1.34319 (431*2π)/5461 weeks
4321.00669 -1.65329 (432*2π)/5461 weeks
4331.90838 -.64296 (433*2π)/5461 weeks
4341.31488 .092 (434*2π)/5461 weeks
4351.00678 .50934 (435*2π)/5461 weeks
436.50959 .66721 (436*2π)/5461 weeks
437.065 .24096 (437*2π)/5461 weeks
438-1.16058 .07464 (438*2π)/5461 weeks
439-.6064 -.99495 (439*2π)/5461 weeks
440-.40691 -.96072 (440*2π)/5461 weeks
441-.34192 -1.95368 (441*2π)/5461 weeks
442.63418 -1.95896 (442*2π)/5461 weeks
4431.14369 -1.75483 (443*2π)/5461 weeks
4441.75139 -.85126 (444*2π)/5461 weeks
4451.78181 -.17317 (445*2π)/5461 weeks
446.74012 -.0484 (446*2π)/5461 weeks
447.31847 -.09822 (447*2π)/5461 weeks
448.22775 .00264 (448*2π)/5461 weeks
449-.42914 -.04957 (449*2π)/5461 weeks
450-.53847 -1.11417 (450*2π)/5461 weeks
451-.10612 -1.76809 (451*2π)/5461 weeks
452.93162 -1.95447 (452*2π)/5461 weeks
453.63981 -.98204 (453*2π)/5461 weeks
454.88771 -1.2076 (454*2π)/5461 weeks
4551.09142 -1.14983 (455*2π)/5461 weeks
4561.0117 -1.37549 (456*2π)/5461 weeks
4571.86498 -1.21371 (457*2π)/5461 weeks
4581.75705 -.06357 (458*2π)/5461 weeks
4591.09867 .83305 (459*2π)/5461 weeks
460.24001 .87575 (460*2π)/5461 weeks
461-1.09021 .10634 (461*2π)/5461 weeks
462-1.52446 -1.09333 (462*2π)/5461 weeks
463-.61436 -2.2308 (463*2π)/5461 weeks
464-.04363 -2.26444 (464*2π)/5461 weeks
4651.4094 -2.92628 (465*2π)/5461 weeks
4662.40001 -1.54389 (466*2π)/5461 weeks
4672.50933 -1.29825 (467*2π)/5461 weeks
4682.57871 .73827 (468*2π)/5461 weeks
469.82669 2.03327 (469*2π)/5461 weeks
470-.67641 .64798 (470*2π)/5461 weeks
471-1.33439 .39547 (471*2π)/5461 weeks
472-1.56408 -1.31271 (472*2π)/5461 weeks
473-1.22709 -2.02302 (473*2π)/5461 weeks
474-.2725 -2.66927 (474*2π)/5461 weeks
4751.08063 -2.81038 (475*2π)/5461 weeks
4761.57897 -2.24147 (476*2π)/5461 weeks
4771.78971 -1.20262 (477*2π)/5461 weeks
4781.41111 -.87865 (478*2π)/5461 weeks
4791.43172 -.48561 (479*2π)/5461 weeks
480.54397 -.45105 (480*2π)/5461 weeks
481.99985 -.79776 (481*2π)/5461 weeks
482.89953 -.32843 (482*2π)/5461 weeks
483-.13858 -.44085 (483*2π)/5461 weeks
484.63218 -.82116 (484*2π)/5461 weeks
485-.68694 -.60887 (485*2π)/5461 weeks
486-.29972 -1.93217 (486*2π)/5461 weeks
487-.16736 -2.47032 (487*2π)/5461 weeks
4881.34477 -2.75342 (488*2π)/5461 weeks
4891.61114 -1.95266 (489*2π)/5461 weeks
4903.0095 -1.76281 (490*2π)/5461 weeks
4912.43468 .38814 (491*2π)/5461 weeks
492.30109 1.12407 (492*2π)/5461 weeks
493-.08068 -.29501 (493*2π)/5461 weeks
494-.64963 .03931 (494*2π)/5461 weeks
495-1.00535 -2.32419 (495*2π)/5461 weeks
496.25237 -2.66041 (496*2π)/5461 weeks
4971.11359 -2.21536 (497*2π)/5461 weeks
498.84614 -1.17875 (498*2π)/5461 weeks
4991.57724 -2.35071 (499*2π)/5461 weeks
5001.21192 -.5231 (500*2π)/5461 weeks
501.38637 -.35318 (501*2π)/5461 weeks
502.56247 -1.4763 (502*2π)/5461 weeks
503-.28626 -.72904 (503*2π)/5461 weeks
504.29833 -2.6716 (504*2π)/5461 weeks
5051.76867 -.81919 (505*2π)/5461 weeks
506.38638 -.52383 (506*2π)/5461 weeks
507-.50232 -.49201 (507*2π)/5461 weeks
508-.58594 -1.87081 (508*2π)/5461 weeks
509-.87602 -1.43663 (509*2π)/5461 weeks
510-1.00111 -2.77581 (510*2π)/5461 weeks
511-1.19277 -3.57051 (511*2π)/5461 weeks
512.44974 -5.82823 (512*2π)/5461 weeks
5134.14256 -4.76165 (513*2π)/5461 weeks
5145.72706 -1.59586 (514*2π)/5461 weeks
5153.415 .69503 (515*2π)/5461 weeks
5161.6045 3.02307 (516*2π)/5461 weeks
517-2.50746 2.48382 (517*2π)/5461 weeks
518-2.63282 -2.53291 (518*2π)/5461 weeks
519-2.94553 -2.5581 (519*2π)/5461 weeks
520-2.30232 -6.09707 (520*2π)/5461 weeks
5211.74671 -5.70978 (521*2π)/5461 weeks
5223.70994 -3.63126 (522*2π)/5461 weeks
5234.43457 -1.175 (523*2π)/5461 weeks
524.81482 .28292 (524*2π)/5461 weeks
525.62384 .77817 (525*2π)/5461 weeks
526-2.71057 2.07002 (526*2π)/5461 weeks
527-5.52634 -2.73491 (527*2π)/5461 weeks
528-4.12439 -4.27354 (528*2π)/5461 weeks
529-6.04274 -8.1532 (529*2π)/5461 weeks
530.66672 -9.30667 (530*2π)/5461 weeks
5312.3055 -7.32623 (531*2π)/5461 weeks
532-1.48898 -5.83583 (532*2π)/5461 weeks
533-.73185 -8.11447 (533*2π)/5461 weeks
534.08138 -11.16995 (534*2π)/5461 weeks
5354.25674 -10.67692 (535*2π)/5461 weeks
5363.9853 -6.77382 (536*2π)/5461 weeks
5375.83667 -11.2705 (537*2π)/5461 weeks
5387.45336 -3.04807 (538*2π)/5461 weeks
539-2.08316 -1.06512 (539*2π)/5461 weeks
540-8.34615 -2.38113 (540*2π)/5461 weeks
541-11.34411 -19.62836 (541*2π)/5461 weeks
542-11.53093 -23.12067 (542*2π)/5461 weeks
543-7.96853 -48.49054 (543*2π)/5461 weeks
54412.58428 -51.8425 (544*2π)/5461 weeks



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