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Fourier Analysis of EFU (ProShares UltraShort MSCI EAFE ETF)


EFU (ProShares UltraShort MSCI EAFE ETF) appears to have interesting cyclic behaviour every 52 weeks (13.0648*sine), 47 weeks (10.2198*sine), and 17 weeks (6.1509*cosine).

EFU (ProShares UltraShort MSCI EAFE ETF) has an average price of 112.53 (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 9/5/2017 for EFU (ProShares UltraShort MSCI EAFE ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0112.5333   0 
148.72939 91.48254 (1*2π)/516516 weeks
21.97522 61.80862 (2*2π)/516258 weeks
3-26.65774 42.18602 (3*2π)/516172 weeks
4-25.46727 12.91255 (4*2π)/516129 weeks
5-18.18636 -1.3371 (5*2π)/516103 weeks
6-2.91271 -12.20791 (6*2π)/51686 weeks
715.45506 -5.8992 (7*2π)/51674 weeks
815.58739 10.15505 (8*2π)/51665 weeks
93.13867 16.53058 (9*2π)/51657 weeks
10-.86736 13.06477 (10*2π)/51652 weeks
11-4.77376 10.21983 (11*2π)/51647 weeks
12-4.28866 3.35934 (12*2π)/51643 weeks
13-2.22436 3.67879 (13*2π)/51640 weeks
14.20392 1.48815 (14*2π)/51637 weeks
152.45117 4.87757 (15*2π)/51634 weeks
16-3.13685 6.97476 (16*2π)/51632 weeks
17-3.91413 3.06474 (17*2π)/51630 weeks
18-4.21491 1.36036 (18*2π)/51629 weeks
19-1.73626 -1.48841 (19*2π)/51627 weeks
20-.3075 -2.00544 (20*2π)/51626 weeks
213.41956 -1.98699 (21*2π)/51625 weeks
224.8233 3.18522 (22*2π)/51623 weeks
232.73253 6.16683 (23*2π)/51622 weeks
24-2.01038 6.97218 (24*2π)/51622 weeks
25-4.84114 1.23133 (25*2π)/51621 weeks
26-2.84421 -1.2299 (26*2π)/51620 weeks
27-1.50164 -4.10014 (27*2π)/51619 weeks
283.28108 -3.16284 (28*2π)/51618 weeks
295.3587 -.14052 (29*2π)/51618 weeks
306.15092 3.28907 (30*2π)/51617 weeks
313.17004 6.94039 (31*2π)/51617 weeks
32-2.35762 6.0985 (32*2π)/51616 weeks
33-3.0526 2.28402 (33*2π)/51616 weeks
34-1.90548 .54869 (34*2π)/51615 weeks
35-.14275 .13343 (35*2π)/51615 weeks
36-.45875 .65559 (36*2π)/51614 weeks
37.18633 -.43974 (37*2π)/51614 weeks
382.2296 -.05167 (38*2π)/51614 weeks
391.26603 2.64695 (39*2π)/51613 weeks
40.11642 1.0139 (40*2π)/51613 weeks
411.26564 1.1282 (41*2π)/51613 weeks
42.61186 1.59884 (42*2π)/51612 weeks
43.85174 2.01401 (43*2π)/51612 weeks
44.01486 2.44046 (44*2π)/51612 weeks
45-.31005 .75658 (45*2π)/51611 weeks
46-.30273 1.44828 (46*2π)/51611 weeks
47-.14796 1.11296 (47*2π)/51611 weeks
48-.26364 .58882 (48*2π)/51611 weeks
49.76883 -.18899 (49*2π)/51611 weeks
501.27185 .19903 (50*2π)/51610 weeks
512.05413 1.09867 (51*2π)/51610 weeks
521.52291 2.59406 (52*2π)/51610 weeks
53-.35387 3.41734 (53*2π)/51610 weeks
54-1.46219 2.3148 (54*2π)/51610 weeks
55-1.8378 .44577 (55*2π)/5169 weeks
56-.90849 -.23974 (56*2π)/5169 weeks
57-.10966 -1.02802 (57*2π)/5169 weeks
581.85809 -.14822 (58*2π)/5169 weeks
591.10156 1.38761 (59*2π)/5169 weeks
60.70631 1.52132 (60*2π)/5169 weeks
61-.14933 1.6702 (61*2π)/5168 weeks
62-.77988 .58201 (62*2π)/5168 weeks
63.32136 .54866 (63*2π)/5168 weeks
64.36443 .43172 (64*2π)/5168 weeks
651.10588 1.28604 (65*2π)/5168 weeks
66-.11029 2.31696 (66*2π)/5168 weeks
67-1.65769 1.72809 (67*2π)/5168 weeks
68-1.93422 -.13694 (68*2π)/5168 weeks
69-.97238 -1.56585 (69*2π)/5167 weeks
70.88306 -1.72823 (70*2π)/5167 weeks
711.98473 -.38342 (71*2π)/5167 weeks
721.86185 -.33603 (72*2π)/5167 weeks
733.2067 1.74411 (73*2π)/5167 weeks
74.99712 3.61024 (74*2π)/5167 weeks
75-.99115 2.51365 (75*2π)/5167 weeks
76-1.97668 1.65178 (76*2π)/5167 weeks
77-2.06516 -.70564 (77*2π)/5167 weeks
78-.37655 -1.02791 (78*2π)/5167 weeks
79.14352 -1.50411 (79*2π)/5167 weeks
802.24667 -1.00651 (80*2π)/5166 weeks
812.56805 .90393 (81*2π)/5166 weeks
821.97133 2.19638 (82*2π)/5166 weeks
83.21878 2.54569 (83*2π)/5166 weeks
84-1.03459 2.07632 (84*2π)/5166 weeks
85-1.51022 .70391 (85*2π)/5166 weeks
86-.66351 -.07842 (86*2π)/5166 weeks
87.15455 -.07909 (87*2π)/5166 weeks
88.54777 .43907 (88*2π)/5166 weeks
89-.33306 .56433 (89*2π)/5166 weeks
90-.03245 -.20477 (90*2π)/5166 weeks
91.32872 -.425 (91*2π)/5166 weeks
92.9304 -.10351 (92*2π)/5166 weeks
931.14984 .71365 (93*2π)/5166 weeks
941.03412 1.34039 (94*2π)/5165 weeks
95.52051 1.80277 (95*2π)/5165 weeks
96-.47561 1.51774 (96*2π)/5165 weeks
97-1.38542 .61877 (97*2π)/5165 weeks
98-1.08145 -.31753 (98*2π)/5165 weeks
99-.52481 -1.09994 (99*2π)/5165 weeks
100.67172 -.93365 (100*2π)/5165 weeks
1011.49468 -.8084 (101*2π)/5165 weeks
1022.2848 .33696 (102*2π)/5165 weeks
1031.39936 1.69065 (103*2π)/5165 weeks
104.28851 2.10152 (104*2π)/5165 weeks
105-.67516 1.79258 (105*2π)/5165 weeks
106-.96455 1.02922 (106*2π)/5165 weeks
107-1.46749 .28129 (107*2π)/5165 weeks
108-.62303 -1.10868 (108*2π)/5165 weeks
109.33875 -.97455 (109*2π)/5165 weeks
1101.00926 -.25175 (110*2π)/5165 weeks
1111.21928 .12946 (111*2π)/5165 weeks
1121.07776 .93923 (112*2π)/5165 weeks
113.45988 1.06088 (113*2π)/5165 weeks
114-.15834 1.16317 (114*2π)/5165 weeks
115-.71453 .83662 (115*2π)/5164 weeks
116-.85429 -.18355 (116*2π)/5164 weeks
117.02665 -.24419 (117*2π)/5164 weeks
118.38341 -.17178 (118*2π)/5164 weeks
119.40558 -.04722 (119*2π)/5164 weeks
120.12015 .19686 (120*2π)/5164 weeks
121.14433 -.1433 (121*2π)/5164 weeks
122.6283 .01305 (122*2π)/5164 weeks
123.09477 .30516 (123*2π)/5164 weeks
124.08732 -.08248 (124*2π)/5164 weeks
125.61523 -.39306 (125*2π)/5164 weeks
126.94983 -.21744 (126*2π)/5164 weeks
127.77061 .32962 (127*2π)/5164 weeks
128.82509 .66675 (128*2π)/5164 weeks
129.36487 1.15625 (129*2π)/5164 weeks
130-.44993 .40038 (130*2π)/5164 weeks
131-.08237 -.27291 (131*2π)/5164 weeks
132.18834 -.49139 (132*2π)/5164 weeks
1331.09382 -.14626 (133*2π)/5164 weeks
134.69591 .79443 (134*2π)/5164 weeks
135.19307 .34598 (135*2π)/5164 weeks
136.75547 .19494 (136*2π)/5164 weeks
137.55336 .46547 (137*2π)/5164 weeks
138.46272 .52652 (138*2π)/5164 weeks
139.19645 .83026 (139*2π)/5164 weeks
140.05594 .34528 (140*2π)/5164 weeks
141.03012 .59086 (141*2π)/5164 weeks
142-.42519 -.06795 (142*2π)/5164 weeks
143.34274 -.5089 (143*2π)/5164 weeks
144.75248 .03778 (144*2π)/5164 weeks
145.59453 .46522 (145*2π)/5164 weeks
146.23084 .55242 (146*2π)/5164 weeks
147.27798 .19072 (147*2π)/5164 weeks
148.66916 .23565 (148*2π)/5163 weeks
149.15141 .81915 (149*2π)/5163 weeks
150-.10536 .01162 (150*2π)/5163 weeks
151.46942 .03876 (151*2π)/5163 weeks
152.48025 .43104 (152*2π)/5163 weeks
153.13791 .64461 (153*2π)/5163 weeks
154-.41554 .09149 (154*2π)/5163 weeks
155.02749 -.07211 (155*2π)/5163 weeks
156-.03614 -.41368 (156*2π)/5163 weeks
157.7434 -.42298 (157*2π)/5163 weeks
158.95251 .13666 (158*2π)/5163 weeks
159.92605 .47808 (159*2π)/5163 weeks
160.53875 .94943 (160*2π)/5163 weeks
161-.05129 .99322 (161*2π)/5163 weeks
162-.47013 .30893 (162*2π)/5163 weeks
163-.67657 .03753 (163*2π)/5163 weeks
164-.38816 -.71483 (164*2π)/5163 weeks
165.3625 -.80258 (165*2π)/5163 weeks
1661.00283 -.74334 (166*2π)/5163 weeks
1671.5083 -.2326 (167*2π)/5163 weeks
1681.40076 .76348 (168*2π)/5163 weeks
169.83808 1.03979 (169*2π)/5163 weeks
170.25174 1.22005 (170*2π)/5163 weeks
171-.34857 .81364 (171*2π)/5163 weeks
172-.30054 .33114 (172*2π)/5163 weeks
173-.34588 -.135 (173*2π)/5163 weeks
174.11804 -.32443 (174*2π)/5163 weeks
175.40713 -.2636 (175*2π)/5163 weeks
1761.00405 -.07803 (176*2π)/5163 weeks
177.94582 .72535 (177*2π)/5163 weeks
178.25827 .77871 (178*2π)/5163 weeks
179.23077 .88592 (179*2π)/5163 weeks
180-.4143 .84908 (180*2π)/5163 weeks
181-.37611 .19932 (181*2π)/5163 weeks
182-.60917 .26833 (182*2π)/5163 weeks
183-.83052 -.58495 (183*2π)/5163 weeks
184.342 -.78983 (184*2π)/5163 weeks
185.53708 -.44724 (185*2π)/5163 weeks
186.97683 -.16812 (186*2π)/5163 weeks
187.7172 .48445 (187*2π)/5163 weeks
188.26244 .24022 (188*2π)/5163 weeks
189.55686 .67341 (189*2π)/5163 weeks
190-.47581 .77297 (190*2π)/5163 weeks
191-.32764 .01755 (191*2π)/5163 weeks
192-.64399 .05547 (192*2π)/5163 weeks
193-.59264 -.95351 (193*2π)/5163 weeks
194.39729 -1.44703 (194*2π)/5163 weeks
1951.31414 -1.00612 (195*2π)/5163 weeks
1961.82847 -.12686 (196*2π)/5163 weeks
1971.46502 .97459 (197*2π)/5163 weeks
198.53101 1.3009 (198*2π)/5163 weeks
199-.23099 1.10916 (199*2π)/5163 weeks
200-.90879 .63011 (200*2π)/5163 weeks
201-.79545 -.74311 (201*2π)/5163 weeks
202.06929 -.97287 (202*2π)/5163 weeks
203.72559 -.89413 (203*2π)/5163 weeks
2041.24897 -.1139 (204*2π)/5163 weeks
205.75896 .48618 (205*2π)/5163 weeks
206.24772 .19322 (206*2π)/5163 weeks
207.42209 -.04621 (207*2π)/5162 weeks
208.65568 .09647 (208*2π)/5162 weeks
209.56315 .16413 (209*2π)/5162 weeks
210.74543 .23092 (210*2π)/5162 weeks
211.55299 .80149 (211*2π)/5162 weeks
212-.14985 .63601 (212*2π)/5162 weeks
213-.36965 .34105 (213*2π)/5162 weeks
214-.56669 -.35587 (214*2π)/5162 weeks
215.38955 -.73597 (215*2π)/5162 weeks
216.70412 -.45968 (216*2π)/5162 weeks
217.92529 -.25904 (217*2π)/5162 weeks
2181.04472 .18964 (218*2π)/5162 weeks
219.82367 .63504 (219*2π)/5162 weeks
220.43734 .82505 (220*2π)/5162 weeks
221.02798 .84872 (221*2π)/5162 weeks
222-.41418 .52128 (222*2π)/5162 weeks
223-.38071 .22979 (223*2π)/5162 weeks
224-.59067 -.1299 (224*2π)/5162 weeks
225.1107 -.77231 (225*2π)/5162 weeks
226.29528 -.51219 (226*2π)/5162 weeks
227.7057 -.68871 (227*2π)/5162 weeks
2281.01229 .07395 (228*2π)/5162 weeks
229.77148 .3153 (229*2π)/5162 weeks
230.73319 .60558 (230*2π)/5162 weeks
231-.06781 .94489 (231*2π)/5162 weeks
232-.6763 .34981 (232*2π)/5162 weeks
233-.58412 -.10991 (233*2π)/5162 weeks
234-.55324 -.79086 (234*2π)/5162 weeks
235.13977 -1.16615 (235*2π)/5162 weeks
236.76024 -1.01268 (236*2π)/5162 weeks
2371.18403 -.72659 (237*2π)/5162 weeks
2381.43569 -.12412 (238*2π)/5162 weeks
2391.24585 .50479 (239*2π)/5162 weeks
2401.14296 .84676 (240*2π)/5162 weeks
241.2221 1.43464 (241*2π)/5162 weeks
242-.57789 .62732 (242*2π)/5162 weeks
243-.35215 .09667 (243*2π)/5162 weeks
244-.6417 -.33278 (244*2π)/5162 weeks
245-.14878 -.99217 (245*2π)/5162 weeks
246.75966 -.96703 (246*2π)/5162 weeks
2471.40789 -.13604 (247*2π)/5162 weeks
2481.20447 .39477 (248*2π)/5162 weeks
249.91994 .70775 (249*2π)/5162 weeks
250.52194 .85135 (250*2π)/5162 weeks
251-.08447 1.28063 (251*2π)/5162 weeks
252-1.07463 .51874 (252*2π)/5162 weeks
253-.64917 -.59365 (253*2π)/5162 weeks
254-.0794 -.67154 (254*2π)/5162 weeks
255.23728 -.79321 (255*2π)/5162 weeks
256.53723 -.44531 (256*2π)/5162 weeks
257.77099 -.52296 (257*2π)/5162 weeks
2581.19978   (258*2π)/5162 weeks
259.77099 .52296 (259*2π)/5162 weeks
260.53723 .44531 (260*2π)/5162 weeks
261.23728 .79321 (261*2π)/5162 weeks
262-.0794 .67154 (262*2π)/5162 weeks
263-.64917 .59365 (263*2π)/5162 weeks
264-1.07463 -.51874 (264*2π)/5162 weeks
265-.08447 -1.28063 (265*2π)/5162 weeks
266.52194 -.85135 (266*2π)/5162 weeks
267.91994 -.70775 (267*2π)/5162 weeks
2681.20447 -.39477 (268*2π)/5162 weeks
2691.40789 .13604 (269*2π)/5162 weeks
270.75966 .96703 (270*2π)/5162 weeks
271-.14878 .99217 (271*2π)/5162 weeks
272-.6417 .33278 (272*2π)/5162 weeks
273-.35215 -.09667 (273*2π)/5162 weeks
274-.57789 -.62732 (274*2π)/5162 weeks
275.2221 -1.43464 (275*2π)/5162 weeks
2761.14296 -.84676 (276*2π)/5162 weeks
2771.24585 -.50479 (277*2π)/5162 weeks
2781.43569 .12412 (278*2π)/5162 weeks
2791.18403 .72659 (279*2π)/5162 weeks
280.76024 1.01268 (280*2π)/5162 weeks
281.13977 1.16615 (281*2π)/5162 weeks
282-.55324 .79086 (282*2π)/5162 weeks
283-.58412 .10991 (283*2π)/5162 weeks
284-.6763 -.34981 (284*2π)/5162 weeks
285-.06781 -.94489 (285*2π)/5162 weeks
286.73319 -.60558 (286*2π)/5162 weeks
287.77148 -.3153 (287*2π)/5162 weeks
2881.01229 -.07395 (288*2π)/5162 weeks
289.7057 .68871 (289*2π)/5162 weeks
290.29528 .51219 (290*2π)/5162 weeks
291.1107 .77231 (291*2π)/5162 weeks
292-.59067 .1299 (292*2π)/5162 weeks
293-.38071 -.22979 (293*2π)/5162 weeks
294-.41418 -.52128 (294*2π)/5162 weeks
295.02798 -.84872 (295*2π)/5162 weeks
296.43734 -.82505 (296*2π)/5162 weeks
297.82367 -.63504 (297*2π)/5162 weeks
2981.04472 -.18964 (298*2π)/5162 weeks
299.92529 .25904 (299*2π)/5162 weeks
300.70412 .45968 (300*2π)/5162 weeks
301.38955 .73597 (301*2π)/5162 weeks
302-.56669 .35587 (302*2π)/5162 weeks
303-.36965 -.34105 (303*2π)/5162 weeks
304-.14985 -.63601 (304*2π)/5162 weeks
305.55299 -.80149 (305*2π)/5162 weeks
306.74543 -.23092 (306*2π)/5162 weeks
307.56315 -.16413 (307*2π)/5162 weeks
308.65568 -.09647 (308*2π)/5162 weeks
309.42209 .04621 (309*2π)/5162 weeks
310.24772 -.19322 (310*2π)/5162 weeks
311.75896 -.48618 (311*2π)/5162 weeks
3121.24897 .1139 (312*2π)/5162 weeks
313.72559 .89413 (313*2π)/5162 weeks
314.06929 .97287 (314*2π)/5162 weeks
315-.79545 .74311 (315*2π)/5162 weeks
316-.90879 -.63011 (316*2π)/5162 weeks
317-.23099 -1.10916 (317*2π)/5162 weeks
318.53101 -1.3009 (318*2π)/5162 weeks
3191.46502 -.97459 (319*2π)/5162 weeks
3201.82847 .12686 (320*2π)/5162 weeks
3211.31414 1.00612 (321*2π)/5162 weeks
322.39729 1.44703 (322*2π)/5162 weeks
323-.59264 .95351 (323*2π)/5162 weeks
324-.64399 -.05547 (324*2π)/5162 weeks
325-.32764 -.01755 (325*2π)/5162 weeks
326-.47581 -.77297 (326*2π)/5162 weeks
327.55686 -.67341 (327*2π)/5162 weeks
328.26244 -.24022 (328*2π)/5162 weeks
329.7172 -.48445 (329*2π)/5162 weeks
330.97683 .16812 (330*2π)/5162 weeks
331.53708 .44724 (331*2π)/5162 weeks
332.342 .78983 (332*2π)/5162 weeks
333-.83052 .58495 (333*2π)/5162 weeks
334-.60917 -.26833 (334*2π)/5162 weeks
335-.37611 -.19932 (335*2π)/5162 weeks
336-.4143 -.84908 (336*2π)/5162 weeks
337.23077 -.88592 (337*2π)/5162 weeks
338.25827 -.77871 (338*2π)/5162 weeks
339.94582 -.72535 (339*2π)/5162 weeks
3401.00405 .07803 (340*2π)/5162 weeks
341.40713 .2636 (341*2π)/5162 weeks
342.11804 .32443 (342*2π)/5162 weeks
343-.34588 .135 (343*2π)/5162 weeks
344-.30054 -.33114 (344*2π)/5162 weeks
345-.34857 -.81364 (345*2π)/5161 weeks
346.25174 -1.22005 (346*2π)/5161 weeks
347.83808 -1.03979 (347*2π)/5161 weeks
3481.40076 -.76348 (348*2π)/5161 weeks
3491.5083 .2326 (349*2π)/5161 weeks
3501.00283 .74334 (350*2π)/5161 weeks
351.3625 .80258 (351*2π)/5161 weeks
352-.38816 .71483 (352*2π)/5161 weeks
353-.67657 -.03753 (353*2π)/5161 weeks
354-.47013 -.30893 (354*2π)/5161 weeks
355-.05129 -.99322 (355*2π)/5161 weeks
356.53875 -.94943 (356*2π)/5161 weeks
357.92605 -.47808 (357*2π)/5161 weeks
358.95251 -.13666 (358*2π)/5161 weeks
359.7434 .42298 (359*2π)/5161 weeks
360-.03614 .41368 (360*2π)/5161 weeks
361.02749 .07211 (361*2π)/5161 weeks
362-.41554 -.09149 (362*2π)/5161 weeks
363.13791 -.64461 (363*2π)/5161 weeks
364.48025 -.43104 (364*2π)/5161 weeks
365.46942 -.03876 (365*2π)/5161 weeks
366-.10536 -.01162 (366*2π)/5161 weeks
367.15141 -.81915 (367*2π)/5161 weeks
368.66916 -.23565 (368*2π)/5161 weeks
369.27798 -.19072 (369*2π)/5161 weeks
370.23084 -.55242 (370*2π)/5161 weeks
371.59453 -.46522 (371*2π)/5161 weeks
372.75248 -.03778 (372*2π)/5161 weeks
373.34274 .5089 (373*2π)/5161 weeks
374-.42519 .06795 (374*2π)/5161 weeks
375.03012 -.59086 (375*2π)/5161 weeks
376.05594 -.34528 (376*2π)/5161 weeks
377.19645 -.83026 (377*2π)/5161 weeks
378.46272 -.52652 (378*2π)/5161 weeks
379.55336 -.46547 (379*2π)/5161 weeks
380.75547 -.19494 (380*2π)/5161 weeks
381.19307 -.34598 (381*2π)/5161 weeks
382.69591 -.79443 (382*2π)/5161 weeks
3831.09382 .14626 (383*2π)/5161 weeks
384.18834 .49139 (384*2π)/5161 weeks
385-.08237 .27291 (385*2π)/5161 weeks
386-.44993 -.40038 (386*2π)/5161 weeks
387.36487 -1.15625 (387*2π)/5161 weeks
388.82509 -.66675 (388*2π)/5161 weeks
389.77061 -.32962 (389*2π)/5161 weeks
390.94983 .21744 (390*2π)/5161 weeks
391.61523 .39306 (391*2π)/5161 weeks
392.08732 .08248 (392*2π)/5161 weeks
393.09477 -.30516 (393*2π)/5161 weeks
394.6283 -.01305 (394*2π)/5161 weeks
395.14433 .1433 (395*2π)/5161 weeks
396.12015 -.19686 (396*2π)/5161 weeks
397.40558 .04722 (397*2π)/5161 weeks
398.38341 .17178 (398*2π)/5161 weeks
399.02665 .24419 (399*2π)/5161 weeks
400-.85429 .18355 (400*2π)/5161 weeks
401-.71453 -.83662 (401*2π)/5161 weeks
402-.15834 -1.16317 (402*2π)/5161 weeks
403.45988 -1.06088 (403*2π)/5161 weeks
4041.07776 -.93923 (404*2π)/5161 weeks
4051.21928 -.12946 (405*2π)/5161 weeks
4061.00926 .25175 (406*2π)/5161 weeks
407.33875 .97455 (407*2π)/5161 weeks
408-.62303 1.10868 (408*2π)/5161 weeks
409-1.46749 -.28129 (409*2π)/5161 weeks
410-.96455 -1.02922 (410*2π)/5161 weeks
411-.67516 -1.79258 (411*2π)/5161 weeks
412.28851 -2.10152 (412*2π)/5161 weeks
4131.39936 -1.69065 (413*2π)/5161 weeks
4142.2848 -.33696 (414*2π)/5161 weeks
4151.49468 .8084 (415*2π)/5161 weeks
416.67172 .93365 (416*2π)/5161 weeks
417-.52481 1.09994 (417*2π)/5161 weeks
418-1.08145 .31753 (418*2π)/5161 weeks
419-1.38542 -.61877 (419*2π)/5161 weeks
420-.47561 -1.51774 (420*2π)/5161 weeks
421.52051 -1.80277 (421*2π)/5161 weeks
4221.03412 -1.34039 (422*2π)/5161 weeks
4231.14984 -.71365 (423*2π)/5161 weeks
424.9304 .10351 (424*2π)/5161 weeks
425.32872 .425 (425*2π)/5161 weeks
426-.03245 .20477 (426*2π)/5161 weeks
427-.33306 -.56433 (427*2π)/5161 weeks
428.54777 -.43907 (428*2π)/5161 weeks
429.15455 .07909 (429*2π)/5161 weeks
430-.66351 .07842 (430*2π)/5161 weeks
431-1.51022 -.70391 (431*2π)/5161 weeks
432-1.03459 -2.07632 (432*2π)/5161 weeks
433.21878 -2.54569 (433*2π)/5161 weeks
4341.97133 -2.19638 (434*2π)/5161 weeks
4352.56805 -.90393 (435*2π)/5161 weeks
4362.24667 1.00651 (436*2π)/5161 weeks
437.14352 1.50411 (437*2π)/5161 weeks
438-.37655 1.02791 (438*2π)/5161 weeks
439-2.06516 .70564 (439*2π)/5161 weeks
440-1.97668 -1.65178 (440*2π)/5161 weeks
441-.99115 -2.51365 (441*2π)/5161 weeks
442.99712 -3.61024 (442*2π)/5161 weeks
4433.2067 -1.74411 (443*2π)/5161 weeks
4441.86185 .33603 (444*2π)/5161 weeks
4451.98473 .38342 (445*2π)/5161 weeks
446.88306 1.72823 (446*2π)/5161 weeks
447-.97238 1.56585 (447*2π)/5161 weeks
448-1.93422 .13694 (448*2π)/5161 weeks
449-1.65769 -1.72809 (449*2π)/5161 weeks
450-.11029 -2.31696 (450*2π)/5161 weeks
4511.10588 -1.28604 (451*2π)/5161 weeks
452.36443 -.43172 (452*2π)/5161 weeks
453.32136 -.54866 (453*2π)/5161 weeks
454-.77988 -.58201 (454*2π)/5161 weeks
455-.14933 -1.6702 (455*2π)/5161 weeks
456.70631 -1.52132 (456*2π)/5161 weeks
4571.10156 -1.38761 (457*2π)/5161 weeks
4581.85809 .14822 (458*2π)/5161 weeks
459-.10966 1.02802 (459*2π)/5161 weeks
460-.90849 .23974 (460*2π)/5161 weeks
461-1.8378 -.44577 (461*2π)/5161 weeks
462-1.46219 -2.3148 (462*2π)/5161 weeks
463-.35387 -3.41734 (463*2π)/5161 weeks
4641.52291 -2.59406 (464*2π)/5161 weeks
4652.05413 -1.09867 (465*2π)/5161 weeks
4661.27185 -.19903 (466*2π)/5161 weeks
467.76883 .18899 (467*2π)/5161 weeks
468-.26364 -.58882 (468*2π)/5161 weeks
469-.14796 -1.11296 (469*2π)/5161 weeks
470-.30273 -1.44828 (470*2π)/5161 weeks
471-.31005 -.75658 (471*2π)/5161 weeks
472.01486 -2.44046 (472*2π)/5161 weeks
473.85174 -2.01401 (473*2π)/5161 weeks
474.61186 -1.59884 (474*2π)/5161 weeks
4751.26564 -1.1282 (475*2π)/5161 weeks
476.11642 -1.0139 (476*2π)/5161 weeks
4771.26603 -2.64695 (477*2π)/5161 weeks
4782.2296 .05167 (478*2π)/5161 weeks
479.18633 .43974 (479*2π)/5161 weeks
480-.45875 -.65559 (480*2π)/5161 weeks
481-.14275 -.13343 (481*2π)/5161 weeks
482-1.90548 -.54869 (482*2π)/5161 weeks
483-3.0526 -2.28402 (483*2π)/5161 weeks
484-2.35762 -6.0985 (484*2π)/5161 weeks
4853.17004 -6.94039 (485*2π)/5161 weeks
4866.15092 -3.28907 (486*2π)/5161 weeks
4875.3587 .14052 (487*2π)/5161 weeks
4883.28108 3.16284 (488*2π)/5161 weeks
489-1.50164 4.10014 (489*2π)/5161 weeks
490-2.84421 1.2299 (490*2π)/5161 weeks
491-4.84114 -1.23133 (491*2π)/5161 weeks
492-2.01038 -6.97218 (492*2π)/5161 weeks
4932.73253 -6.16683 (493*2π)/5161 weeks
4944.8233 -3.18522 (494*2π)/5161 weeks
4953.41956 1.98699 (495*2π)/5161 weeks
496-.3075 2.00544 (496*2π)/5161 weeks
497-1.73626 1.48841 (497*2π)/5161 weeks
498-4.21491 -1.36036 (498*2π)/5161 weeks
499-3.91413 -3.06474 (499*2π)/5161 weeks
500-3.13685 -6.97476 (500*2π)/5161 weeks
5012.45117 -4.87757 (501*2π)/5161 weeks
502.20392 -1.48815 (502*2π)/5161 weeks
503-2.22436 -3.67879 (503*2π)/5161 weeks
504-4.28866 -3.35934 (504*2π)/5161 weeks
505-4.77376 -10.21983 (505*2π)/5161 weeks
506-.86736 -13.06477 (506*2π)/5161 weeks
5073.13867 -16.53058 (507*2π)/5161 weeks
50815.58739 -10.15505 (508*2π)/5161 weeks
50915.45506 5.8992 (509*2π)/5161 weeks
510-2.91271 12.20791 (510*2π)/5161 weeks
511-18.18636 1.3371 (511*2π)/5161 weeks
512-25.46727 -12.91255 (512*2π)/5161 weeks
513-26.65774 -42.18602 (513*2π)/5161 weeks
5141.97522 -61.80862 (514*2π)/5161 weeks



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