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Fourier Analysis of UKPIX (Ultra Short Japan ProFunds Inve)


UKPIX (Ultra Short Japan ProFunds Inve) appears to have interesting cyclic behaviour every 44 weeks (8.8829*sine), 48 weeks (7.6918*cosine), and 41 weeks (4.9632*cosine).

UKPIX (Ultra Short Japan ProFunds Inve) has an average price of 100.06 (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 3/28/2006 to 3/13/2017 for UKPIX (Ultra Short Japan ProFunds Inve), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0100.0593   0 
1-14.76397 85.37657 (1*2π)/573573 weeks
2-9.56497 24.53528 (2*2π)/573287 weeks
3-6.85956 -9.50139 (3*2π)/573191 weeks
417.81109 10.11255 (4*2π)/573143 weeks
58.44795 16.35232 (5*2π)/573115 weeks
6-9.13036 13.37299 (6*2π)/57396 weeks
7.27541 2.70594 (7*2π)/57382 weeks
87.13873 7.86604 (8*2π)/57372 weeks
9-4.53494 12.64849 (9*2π)/57364 weeks
10-3.20217 4.13377 (10*2π)/57357 weeks
11-3.38896 -1.02944 (11*2π)/57352 weeks
127.69181 4.14435 (12*2π)/57348 weeks
13-.55761 8.88292 (13*2π)/57344 weeks
14-4.96315 5.10564 (14*2π)/57341 weeks
15-.52154 .17046 (15*2π)/57338 weeks
16-.49329 2.74479 (16*2π)/57336 weeks
171.0927 .37006 (17*2π)/57334 weeks
182.12454 6.19319 (18*2π)/57332 weeks
19-2.21725 4.10142 (19*2π)/57330 weeks
20-3.87233 2.54738 (20*2π)/57329 weeks
21-.26676 -1.84574 (21*2π)/57327 weeks
222.39648 1.4576 (22*2π)/57326 weeks
231.30115 3.84235 (23*2π)/57325 weeks
24-3.16428 2.89596 (24*2π)/57324 weeks
25-1.01181 .27909 (25*2π)/57323 weeks
261.15768 .25988 (26*2π)/57322 weeks
27-.53787 4.63553 (27*2π)/57321 weeks
28-3.05659 -.38567 (28*2π)/57320 weeks
29-.68322 -1.23142 (29*2π)/57320 weeks
304.22981 -.89542 (30*2π)/57319 weeks
31.11974 4.98181 (31*2π)/57318 weeks
32-3.12226 .67801 (32*2π)/57318 weeks
33-.52134 -3.48207 (33*2π)/57317 weeks
344.92578 .89324 (34*2π)/57317 weeks
35.17282 5.29733 (35*2π)/57316 weeks
36-2.92447 .85918 (36*2π)/57316 weeks
37-.83773 -1.47764 (37*2π)/57315 weeks
382.36514 -.58992 (38*2π)/57315 weeks
391.49799 1.93728 (39*2π)/57315 weeks
40-.32299 2.5957 (40*2π)/57314 weeks
41-1.22639 .0657 (41*2π)/57314 weeks
421.07549 -.3717 (42*2π)/57314 weeks
431.01156 2.05852 (43*2π)/57313 weeks
44-.91659 .60263 (44*2π)/57313 weeks
45.25799 .6037 (45*2π)/57313 weeks
46.47042 -.26938 (46*2π)/57312 weeks
47.86818 .17673 (47*2π)/57312 weeks
481.60891 .74034 (48*2π)/57312 weeks
49.39247 2.6746 (49*2π)/57312 weeks
50-.23795 .15215 (50*2π)/57311 weeks
51.10997 .90848 (51*2π)/57311 weeks
52.41068 .287 (52*2π)/57311 weeks
531.00977 1.20585 (53*2π)/57311 weeks
54-1.00227 1.26062 (54*2π)/57311 weeks
55.58263 -.36391 (55*2π)/57310 weeks
561.41915 .32272 (56*2π)/57310 weeks
571.37925 2.93025 (57*2π)/57310 weeks
58-2.43437 2.22103 (58*2π)/57310 weeks
59-.86685 -2.04815 (59*2π)/57310 weeks
602.03635 -.5121 (60*2π)/57310 weeks
611.30393 2.26712 (61*2π)/5739 weeks
62-.82553 1.15623 (62*2π)/5739 weeks
63-.89572 .00819 (63*2π)/5739 weeks
641.18098 -.1698 (64*2π)/5739 weeks
65-.07357 .39345 (65*2π)/5739 weeks
66.44909 .49714 (66*2π)/5739 weeks
67.55606 -.03224 (67*2π)/5739 weeks
681.01957 .44603 (68*2π)/5738 weeks
691.11413 .85274 (69*2π)/5738 weeks
70.54774 1.94382 (70*2π)/5738 weeks
71-.77287 .6192 (71*2π)/5738 weeks
72.11237 -.10454 (72*2π)/5738 weeks
731.45746 -.08411 (73*2π)/5738 weeks
741.44909 1.68513 (74*2π)/5738 weeks
75-.68656 2.77413 (75*2π)/5738 weeks
76-1.88972 -.0265 (76*2π)/5738 weeks
77.62959 -1.15268 (77*2π)/5737 weeks
781.82194 1.00818 (78*2π)/5737 weeks
79-.49264 1.91578 (79*2π)/5737 weeks
80-1.20264 .81347 (80*2π)/5737 weeks
81-.4027 -1.65215 (81*2π)/5737 weeks
822.51198 .36429 (82*2π)/5737 weeks
83-.09002 2.11928 (83*2π)/5737 weeks
84-1.05644 1.21444 (84*2π)/5737 weeks
85-.75841 -1.05498 (85*2π)/5737 weeks
861.3822 -.11802 (86*2π)/5737 weeks
87.87392 1.55207 (87*2π)/5737 weeks
88-1.22287 1.18995 (88*2π)/5737 weeks
89-.72991 -1.12306 (89*2π)/5736 weeks
901.86855 -.5596 (90*2π)/5736 weeks
911.17184 1.74973 (91*2π)/5736 weeks
92-1.18768 1.22582 (92*2π)/5736 weeks
93-.78017 -.85076 (93*2π)/5736 weeks
941.03531 -.55711 (94*2π)/5736 weeks
95.93285 .68095 (95*2π)/5736 weeks
96-.15861 1.10404 (96*2π)/5736 weeks
97-.28522 -.18544 (97*2π)/5736 weeks
98.13473 .44395 (98*2π)/5736 weeks
99.53918 -.39391 (99*2π)/5736 weeks
100.88268 .66009 (100*2π)/5736 weeks
101.02016 .94042 (101*2π)/5736 weeks
102-.38788 -.26551 (102*2π)/5736 weeks
103.67971 -.23006 (103*2π)/5736 weeks
104.85826 .43667 (104*2π)/5736 weeks
105.22725 .70188 (105*2π)/5735 weeks
106-.25777 .17593 (106*2π)/5735 weeks
107.38463 -.30376 (107*2π)/5735 weeks
1081.30513 .40952 (108*2π)/5735 weeks
109.30179 1.38956 (109*2π)/5735 weeks
110-.82656 .53698 (110*2π)/5735 weeks
111.1271 -.74338 (111*2π)/5735 weeks
112.96767 -.4902 (112*2π)/5735 weeks
1131.57569 1.02861 (113*2π)/5735 weeks
114-.24219 .83463 (114*2π)/5735 weeks
115-.28595 .19754 (115*2π)/5735 weeks
116.85246 -.40419 (116*2π)/5735 weeks
1171.15742 .78396 (117*2π)/5735 weeks
118.40118 1.5101 (118*2π)/5735 weeks
119-.7492 .35823 (119*2π)/5735 weeks
120.4519 -.12559 (120*2π)/5735 weeks
1211.08004 .45729 (121*2π)/5735 weeks
122.19514 1.34436 (122*2π)/5735 weeks
123-.72745 .82632 (123*2π)/5735 weeks
124-.11066 -.53702 (124*2π)/5735 weeks
125.6863 .28436 (125*2π)/5735 weeks
126.52034 1.1883 (126*2π)/5735 weeks
127-.87961 .72399 (127*2π)/5735 weeks
128-.37633 -.74789 (128*2π)/5734 weeks
1291.20387 -.12828 (129*2π)/5734 weeks
130.61377 1.37922 (130*2π)/5734 weeks
131-.74217 .82476 (131*2π)/5734 weeks
132-.68164 -.38861 (132*2π)/5734 weeks
133.32391 -.11551 (133*2π)/5734 weeks
134.38066 .02397 (134*2π)/5734 weeks
135.34917 .7839 (135*2π)/5734 weeks
136-.19761 .01187 (136*2π)/5734 weeks
137.19473 .41158 (137*2π)/5734 weeks
138-.22098 .17478 (138*2π)/5734 weeks
139.00371 -.24885 (139*2π)/5734 weeks
140.31613 -.2885 (140*2π)/5734 weeks
141.65233 .05464 (141*2π)/5734 weeks
142.02155 .557 (142*2π)/5734 weeks
143.0647 -.29092 (143*2π)/5734 weeks
144.60344 .4361 (144*2π)/5734 weeks
145-.2985 .46072 (145*2π)/5734 weeks
146.11931 -.25008 (146*2π)/5734 weeks
147.39337 -.24501 (147*2π)/5734 weeks
148.59384 .56379 (148*2π)/5734 weeks
149-.15155 .07224 (149*2π)/5734 weeks
150.40224 -.23353 (150*2π)/5734 weeks
151.16821 -.00055 (151*2π)/5734 weeks
152.5346 -.18978 (152*2π)/5734 weeks
153.53853 .29757 (153*2π)/5734 weeks
154.26883 .33182 (154*2π)/5734 weeks
155.08908 -.06171 (155*2π)/5734 weeks
156.56322 .03272 (156*2π)/5734 weeks
157.61863 .27975 (157*2π)/5734 weeks
158.04524 .63534 (158*2π)/5734 weeks
159.09105 -.16494 (159*2π)/5734 weeks
160.44369 .14097 (160*2π)/5734 weeks
161.41291 .18631 (161*2π)/5734 weeks
162.11321 .1769 (162*2π)/5734 weeks
163.45158 .14783 (163*2π)/5734 weeks
164.19671 .42973 (164*2π)/5733 weeks
165.18006 -.29134 (165*2π)/5733 weeks
166.65675 .53481 (166*2π)/5733 weeks
167.07698 .15787 (167*2π)/5733 weeks
168.53151 .22951 (168*2π)/5733 weeks
169.2331 .4741 (169*2π)/5733 weeks
170-.09583 .10617 (170*2π)/5733 weeks
171.7155 .28905 (171*2π)/5733 weeks
172-.19122 .33477 (172*2π)/5733 weeks
173.04751 -.06074 (173*2π)/5733 weeks
174.50812 -.35486 (174*2π)/5733 weeks
175.63429 .53053 (175*2π)/5733 weeks
176.06114 .27563 (176*2π)/5733 weeks
177-.04118 -.0132 (177*2π)/5733 weeks
178.47198 -.02618 (178*2π)/5733 weeks
179.42769 .2748 (179*2π)/5733 weeks
180-.01372 .38876 (180*2π)/5733 weeks
181-.04645 -.07024 (181*2π)/5733 weeks
182.37264 -.49155 (182*2π)/5733 weeks
1831.06327 .13511 (183*2π)/5733 weeks
184.59307 .79297 (184*2π)/5733 weeks
185-.13244 .5572 (185*2π)/5733 weeks
186-.02347 -.14406 (186*2π)/5733 weeks
187.57318 -.21121 (187*2π)/5733 weeks
188.60028 .52112 (188*2π)/5733 weeks
189.08294 .40981 (189*2π)/5733 weeks
190.06098 .03589 (190*2π)/5733 weeks
191.335 -.00461 (191*2π)/5733 weeks
192.64047 .42237 (192*2π)/5733 weeks
193.13673 .63371 (193*2π)/5733 weeks
194-.17837 .30163 (194*2π)/5733 weeks
195.00392 -.10918 (195*2π)/5733 weeks
196.44498 .11474 (196*2π)/5733 weeks
197-.05443 .46424 (197*2π)/5733 weeks
198.08279 -.02018 (198*2π)/5733 weeks
199.02616 -.18059 (199*2π)/5733 weeks
200.62401 -.01339 (200*2π)/5733 weeks
201.50591 .42609 (201*2π)/5733 weeks
202-.26902 .80377 (202*2π)/5733 weeks
203-.68193 -.45815 (203*2π)/5733 weeks
204.91968 -.55328 (204*2π)/5733 weeks
205.63165 .36643 (205*2π)/5733 weeks
206.25514 .61949 (206*2π)/5733 weeks
207-.23031 -.02425 (207*2π)/5733 weeks
208.3334 .04486 (208*2π)/5733 weeks
209.1969 -.02451 (209*2π)/5733 weeks
210.21656 .53849 (210*2π)/5733 weeks
211-.65341 -.19264 (211*2π)/5733 weeks
212.37794 -.65662 (212*2π)/5733 weeks
2131.1078 -.29609 (213*2π)/5733 weeks
214.59105 1.05917 (214*2π)/5733 weeks
215-.63222 .50281 (215*2π)/5733 weeks
216-.17971 -.81115 (216*2π)/5733 weeks
2171.10507 -.31173 (217*2π)/5733 weeks
218.64904 .91538 (218*2π)/5733 weeks
219-.32709 .45568 (219*2π)/5733 weeks
220-.25845 -.44035 (220*2π)/5733 weeks
221.75521 -.35954 (221*2π)/5733 weeks
222.86229 .70029 (222*2π)/5733 weeks
223-.6269 .62881 (223*2π)/5733 weeks
224-.36324 -.66497 (224*2π)/5733 weeks
225.92236 -.50167 (225*2π)/5733 weeks
226.71911 .73382 (226*2π)/5733 weeks
227-.12802 .51751 (227*2π)/5733 weeks
228-.23806 -.0249 (228*2π)/5733 weeks
229-.01254 -.46333 (229*2π)/5733 weeks
230.89413 -.28625 (230*2π)/5732 weeks
231.62516 .64905 (231*2π)/5732 weeks
232-.04939 .45929 (232*2π)/5732 weeks
233-.18514 .05044 (233*2π)/5732 weeks
234.03895 -.32332 (234*2π)/5732 weeks
235.69109 -.05797 (235*2π)/5732 weeks
236.07904 .39021 (236*2π)/5732 weeks
237-.16914 .07991 (237*2π)/5732 weeks
238.07072 -.69803 (238*2π)/5732 weeks
239.77558 -.09024 (239*2π)/5732 weeks
240.68819 .47705 (240*2π)/5732 weeks
241-.25242 .70654 (241*2π)/5732 weeks
242-.34515 -.5158 (242*2π)/5732 weeks
243.65239 -.43646 (243*2π)/5732 weeks
244.82728 .47387 (244*2π)/5732 weeks
245-.17771 .73475 (245*2π)/5732 weeks
246-.63532 -.34621 (246*2π)/5732 weeks
247.55097 -.7951 (247*2π)/5732 weeks
248.89644 -.0095 (248*2π)/5732 weeks
249.36072 .90648 (249*2π)/5732 weeks
250-.60934 -.18696 (250*2π)/5732 weeks
251.24758 -.67864 (251*2π)/5732 weeks
252.98958 -.31893 (252*2π)/5732 weeks
253.49598 .85825 (253*2π)/5732 weeks
254-.13274 .13289 (254*2π)/5732 weeks
255.03074 -.1893 (255*2π)/5732 weeks
256.78576 -.15105 (256*2π)/5732 weeks
257.37611 .72443 (257*2π)/5732 weeks
258-.51128 .33971 (258*2π)/5732 weeks
259-.34028 -.47887 (259*2π)/5732 weeks
260.48954 -.79689 (260*2π)/5732 weeks
2611.14222 .35498 (261*2π)/5732 weeks
262-.0854 .77221 (262*2π)/5732 weeks
263-.83477 -.11837 (263*2π)/5732 weeks
264.19152 -.90896 (264*2π)/5732 weeks
265.97215 -.5306 (265*2π)/5732 weeks
266.86752 .64885 (266*2π)/5732 weeks
267-.55982 .91977 (267*2π)/5732 weeks
268-.59263 -1.043 (268*2π)/5732 weeks
269.93095 -.75246 (269*2π)/5732 weeks
2701.016 .26967 (270*2π)/5732 weeks
271-.21561 .81376 (271*2π)/5732 weeks
272-.62447 -.68648 (272*2π)/5732 weeks
2731.0257 -.99411 (273*2π)/5732 weeks
2741.11916 .61293 (274*2π)/5732 weeks
275-.27881 .59358 (275*2π)/5732 weeks
276-.17453 -.41 (276*2π)/5732 weeks
277.68056 -.82435 (277*2π)/5732 weeks
2781.22248 .26301 (278*2π)/5732 weeks
279.23592 1.2633 (279*2π)/5732 weeks
280-1.1143 -.22377 (280*2π)/5732 weeks
281.42724 -1.12315 (281*2π)/5732 weeks
2821.32458 -.11522 (282*2π)/5732 weeks
283.4386 .9425 (283*2π)/5732 weeks
284-.54142 -.0422 (284*2π)/5732 weeks
285-.06025 -.83683 (285*2π)/5732 weeks
2861.23613 -.88749 (286*2π)/5732 weeks
2871.23613 .88749 (287*2π)/5732 weeks
288-.06025 .83683 (288*2π)/5732 weeks
289-.54142 .0422 (289*2π)/5732 weeks
290.4386 -.9425 (290*2π)/5732 weeks
2911.32458 .11522 (291*2π)/5732 weeks
292.42724 1.12315 (292*2π)/5732 weeks
293-1.1143 .22377 (293*2π)/5732 weeks
294.23592 -1.2633 (294*2π)/5732 weeks
2951.22248 -.26301 (295*2π)/5732 weeks
296.68056 .82435 (296*2π)/5732 weeks
297-.17453 .41 (297*2π)/5732 weeks
298-.27881 -.59358 (298*2π)/5732 weeks
2991.11916 -.61293 (299*2π)/5732 weeks
3001.0257 .99411 (300*2π)/5732 weeks
301-.62447 .68648 (301*2π)/5732 weeks
302-.21561 -.81376 (302*2π)/5732 weeks
3031.016 -.26967 (303*2π)/5732 weeks
304.93095 .75246 (304*2π)/5732 weeks
305-.59263 1.043 (305*2π)/5732 weeks
306-.55982 -.91977 (306*2π)/5732 weeks
307.86752 -.64885 (307*2π)/5732 weeks
308.97215 .5306 (308*2π)/5732 weeks
309.19152 .90896 (309*2π)/5732 weeks
310-.83477 .11837 (310*2π)/5732 weeks
311-.0854 -.77221 (311*2π)/5732 weeks
3121.14222 -.35498 (312*2π)/5732 weeks
313.48954 .79689 (313*2π)/5732 weeks
314-.34028 .47887 (314*2π)/5732 weeks
315-.51128 -.33971 (315*2π)/5732 weeks
316.37611 -.72443 (316*2π)/5732 weeks
317.78576 .15105 (317*2π)/5732 weeks
318.03074 .1893 (318*2π)/5732 weeks
319-.13274 -.13289 (319*2π)/5732 weeks
320.49598 -.85825 (320*2π)/5732 weeks
321.98958 .31893 (321*2π)/5732 weeks
322.24758 .67864 (322*2π)/5732 weeks
323-.60934 .18696 (323*2π)/5732 weeks
324.36072 -.90648 (324*2π)/5732 weeks
325.89644 .0095 (325*2π)/5732 weeks
326.55097 .7951 (326*2π)/5732 weeks
327-.63532 .34621 (327*2π)/5732 weeks
328-.17771 -.73475 (328*2π)/5732 weeks
329.82728 -.47387 (329*2π)/5732 weeks
330.65239 .43646 (330*2π)/5732 weeks
331-.34515 .5158 (331*2π)/5732 weeks
332-.25242 -.70654 (332*2π)/5732 weeks
333.68819 -.47705 (333*2π)/5732 weeks
334.77558 .09024 (334*2π)/5732 weeks
335.07072 .69803 (335*2π)/5732 weeks
336-.16914 -.07991 (336*2π)/5732 weeks
337.07904 -.39021 (337*2π)/5732 weeks
338.69109 .05797 (338*2π)/5732 weeks
339.03895 .32332 (339*2π)/5732 weeks
340-.18514 -.05044 (340*2π)/5732 weeks
341-.04939 -.45929 (341*2π)/5732 weeks
342.62516 -.64905 (342*2π)/5732 weeks
343.89413 .28625 (343*2π)/5732 weeks
344-.01254 .46333 (344*2π)/5732 weeks
345-.23806 .0249 (345*2π)/5732 weeks
346-.12802 -.51751 (346*2π)/5732 weeks
347.71911 -.73382 (347*2π)/5732 weeks
348.92236 .50167 (348*2π)/5732 weeks
349-.36324 .66497 (349*2π)/5732 weeks
350-.6269 -.62881 (350*2π)/5732 weeks
351.86229 -.70029 (351*2π)/5732 weeks
352.75521 .35954 (352*2π)/5732 weeks
353-.25845 .44035 (353*2π)/5732 weeks
354-.32709 -.45568 (354*2π)/5732 weeks
355.64904 -.91538 (355*2π)/5732 weeks
3561.10507 .31173 (356*2π)/5732 weeks
357-.17971 .81115 (357*2π)/5732 weeks
358-.63222 -.50281 (358*2π)/5732 weeks
359.59105 -1.05917 (359*2π)/5732 weeks
3601.1078 .29609 (360*2π)/5732 weeks
361.37794 .65662 (361*2π)/5732 weeks
362-.65341 .19264 (362*2π)/5732 weeks
363.21656 -.53849 (363*2π)/5732 weeks
364.1969 .02451 (364*2π)/5732 weeks
365.3334 -.04486 (365*2π)/5732 weeks
366-.23031 .02425 (366*2π)/5732 weeks
367.25514 -.61949 (367*2π)/5732 weeks
368.63165 -.36643 (368*2π)/5732 weeks
369.91968 .55328 (369*2π)/5732 weeks
370-.68193 .45815 (370*2π)/5732 weeks
371-.26902 -.80377 (371*2π)/5732 weeks
372.50591 -.42609 (372*2π)/5732 weeks
373.62401 .01339 (373*2π)/5732 weeks
374.02616 .18059 (374*2π)/5732 weeks
375.08279 .02018 (375*2π)/5732 weeks
376-.05443 -.46424 (376*2π)/5732 weeks
377.44498 -.11474 (377*2π)/5732 weeks
378.00392 .10918 (378*2π)/5732 weeks
379-.17837 -.30163 (379*2π)/5732 weeks
380.13673 -.63371 (380*2π)/5732 weeks
381.64047 -.42237 (381*2π)/5732 weeks
382.335 .00461 (382*2π)/5732 weeks
383.06098 -.03589 (383*2π)/5731 weeks
384.08294 -.40981 (384*2π)/5731 weeks
385.60028 -.52112 (385*2π)/5731 weeks
386.57318 .21121 (386*2π)/5731 weeks
387-.02347 .14406 (387*2π)/5731 weeks
388-.13244 -.5572 (388*2π)/5731 weeks
389.59307 -.79297 (389*2π)/5731 weeks
3901.06327 -.13511 (390*2π)/5731 weeks
391.37264 .49155 (391*2π)/5731 weeks
392-.04645 .07024 (392*2π)/5731 weeks
393-.01372 -.38876 (393*2π)/5731 weeks
394.42769 -.2748 (394*2π)/5731 weeks
395.47198 .02618 (395*2π)/5731 weeks
396-.04118 .0132 (396*2π)/5731 weeks
397.06114 -.27563 (397*2π)/5731 weeks
398.63429 -.53053 (398*2π)/5731 weeks
399.50812 .35486 (399*2π)/5731 weeks
400.04751 .06074 (400*2π)/5731 weeks
401-.19122 -.33477 (401*2π)/5731 weeks
402.7155 -.28905 (402*2π)/5731 weeks
403-.09583 -.10617 (403*2π)/5731 weeks
404.2331 -.4741 (404*2π)/5731 weeks
405.53151 -.22951 (405*2π)/5731 weeks
406.07698 -.15787 (406*2π)/5731 weeks
407.65675 -.53481 (407*2π)/5731 weeks
408.18006 .29134 (408*2π)/5731 weeks
409.19671 -.42973 (409*2π)/5731 weeks
410.45158 -.14783 (410*2π)/5731 weeks
411.11321 -.1769 (411*2π)/5731 weeks
412.41291 -.18631 (412*2π)/5731 weeks
413.44369 -.14097 (413*2π)/5731 weeks
414.09105 .16494 (414*2π)/5731 weeks
415.04524 -.63534 (415*2π)/5731 weeks
416.61863 -.27975 (416*2π)/5731 weeks
417.56322 -.03272 (417*2π)/5731 weeks
418.08908 .06171 (418*2π)/5731 weeks
419.26883 -.33182 (419*2π)/5731 weeks
420.53853 -.29757 (420*2π)/5731 weeks
421.5346 .18978 (421*2π)/5731 weeks
422.16821 .00055 (422*2π)/5731 weeks
423.40224 .23353 (423*2π)/5731 weeks
424-.15155 -.07224 (424*2π)/5731 weeks
425.59384 -.56379 (425*2π)/5731 weeks
426.39337 .24501 (426*2π)/5731 weeks
427.11931 .25008 (427*2π)/5731 weeks
428-.2985 -.46072 (428*2π)/5731 weeks
429.60344 -.4361 (429*2π)/5731 weeks
430.0647 .29092 (430*2π)/5731 weeks
431.02155 -.557 (431*2π)/5731 weeks
432.65233 -.05464 (432*2π)/5731 weeks
433.31613 .2885 (433*2π)/5731 weeks
434.00371 .24885 (434*2π)/5731 weeks
435-.22098 -.17478 (435*2π)/5731 weeks
436.19473 -.41158 (436*2π)/5731 weeks
437-.19761 -.01187 (437*2π)/5731 weeks
438.34917 -.7839 (438*2π)/5731 weeks
439.38066 -.02397 (439*2π)/5731 weeks
440.32391 .11551 (440*2π)/5731 weeks
441-.68164 .38861 (441*2π)/5731 weeks
442-.74217 -.82476 (442*2π)/5731 weeks
443.61377 -1.37922 (443*2π)/5731 weeks
4441.20387 .12828 (444*2π)/5731 weeks
445-.37633 .74789 (445*2π)/5731 weeks
446-.87961 -.72399 (446*2π)/5731 weeks
447.52034 -1.1883 (447*2π)/5731 weeks
448.6863 -.28436 (448*2π)/5731 weeks
449-.11066 .53702 (449*2π)/5731 weeks
450-.72745 -.82632 (450*2π)/5731 weeks
451.19514 -1.34436 (451*2π)/5731 weeks
4521.08004 -.45729 (452*2π)/5731 weeks
453.4519 .12559 (453*2π)/5731 weeks
454-.7492 -.35823 (454*2π)/5731 weeks
455.40118 -1.5101 (455*2π)/5731 weeks
4561.15742 -.78396 (456*2π)/5731 weeks
457.85246 .40419 (457*2π)/5731 weeks
458-.28595 -.19754 (458*2π)/5731 weeks
459-.24219 -.83463 (459*2π)/5731 weeks
4601.57569 -1.02861 (460*2π)/5731 weeks
461.96767 .4902 (461*2π)/5731 weeks
462.1271 .74338 (462*2π)/5731 weeks
463-.82656 -.53698 (463*2π)/5731 weeks
464.30179 -1.38956 (464*2π)/5731 weeks
4651.30513 -.40952 (465*2π)/5731 weeks
466.38463 .30376 (466*2π)/5731 weeks
467-.25777 -.17593 (467*2π)/5731 weeks
468.22725 -.70188 (468*2π)/5731 weeks
469.85826 -.43667 (469*2π)/5731 weeks
470.67971 .23006 (470*2π)/5731 weeks
471-.38788 .26551 (471*2π)/5731 weeks
472.02016 -.94042 (472*2π)/5731 weeks
473.88268 -.66009 (473*2π)/5731 weeks
474.53918 .39391 (474*2π)/5731 weeks
475.13473 -.44395 (475*2π)/5731 weeks
476-.28522 .18544 (476*2π)/5731 weeks
477-.15861 -1.10404 (477*2π)/5731 weeks
478.93285 -.68095 (478*2π)/5731 weeks
4791.03531 .55711 (479*2π)/5731 weeks
480-.78017 .85076 (480*2π)/5731 weeks
481-1.18768 -1.22582 (481*2π)/5731 weeks
4821.17184 -1.74973 (482*2π)/5731 weeks
4831.86855 .5596 (483*2π)/5731 weeks
484-.72991 1.12306 (484*2π)/5731 weeks
485-1.22287 -1.18995 (485*2π)/5731 weeks
486.87392 -1.55207 (486*2π)/5731 weeks
4871.3822 .11802 (487*2π)/5731 weeks
488-.75841 1.05498 (488*2π)/5731 weeks
489-1.05644 -1.21444 (489*2π)/5731 weeks
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4912.51198 -.36429 (491*2π)/5731 weeks
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493-1.20264 -.81347 (493*2π)/5731 weeks
494-.49264 -1.91578 (494*2π)/5731 weeks
4951.82194 -1.00818 (495*2π)/5731 weeks
496.62959 1.15268 (496*2π)/5731 weeks
497-1.88972 .0265 (497*2π)/5731 weeks
498-.68656 -2.77413 (498*2π)/5731 weeks
4991.44909 -1.68513 (499*2π)/5731 weeks
5001.45746 .08411 (500*2π)/5731 weeks
501.11237 .10454 (501*2π)/5731 weeks
502-.77287 -.6192 (502*2π)/5731 weeks
503.54774 -1.94382 (503*2π)/5731 weeks
5041.11413 -.85274 (504*2π)/5731 weeks
5051.01957 -.44603 (505*2π)/5731 weeks
506.55606 .03224 (506*2π)/5731 weeks
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511-.82553 -1.15623 (511*2π)/5731 weeks
5121.30393 -2.26712 (512*2π)/5731 weeks
5132.03635 .5121 (513*2π)/5731 weeks
514-.86685 2.04815 (514*2π)/5731 weeks
515-2.43437 -2.22103 (515*2π)/5731 weeks
5161.37925 -2.93025 (516*2π)/5731 weeks
5171.41915 -.32272 (517*2π)/5731 weeks
518.58263 .36391 (518*2π)/5731 weeks
519-1.00227 -1.26062 (519*2π)/5731 weeks
5201.00977 -1.20585 (520*2π)/5731 weeks
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522.10997 -.90848 (522*2π)/5731 weeks
523-.23795 -.15215 (523*2π)/5731 weeks
524.39247 -2.6746 (524*2π)/5731 weeks
5251.60891 -.74034 (525*2π)/5731 weeks
526.86818 -.17673 (526*2π)/5731 weeks
527.47042 .26938 (527*2π)/5731 weeks
528.25799 -.6037 (528*2π)/5731 weeks
529-.91659 -.60263 (529*2π)/5731 weeks
5301.01156 -2.05852 (530*2π)/5731 weeks
5311.07549 .3717 (531*2π)/5731 weeks
532-1.22639 -.0657 (532*2π)/5731 weeks
533-.32299 -2.5957 (533*2π)/5731 weeks
5341.49799 -1.93728 (534*2π)/5731 weeks
5352.36514 .58992 (535*2π)/5731 weeks
536-.83773 1.47764 (536*2π)/5731 weeks
537-2.92447 -.85918 (537*2π)/5731 weeks
538.17282 -5.29733 (538*2π)/5731 weeks
5394.92578 -.89324 (539*2π)/5731 weeks
540-.52134 3.48207 (540*2π)/5731 weeks
541-3.12226 -.67801 (541*2π)/5731 weeks
542.11974 -4.98181 (542*2π)/5731 weeks
5434.22981 .89542 (543*2π)/5731 weeks
544-.68322 1.23142 (544*2π)/5731 weeks
545-3.05659 .38567 (545*2π)/5731 weeks
546-.53787 -4.63553 (546*2π)/5731 weeks
5471.15768 -.25988 (547*2π)/5731 weeks
548-1.01181 -.27909 (548*2π)/5731 weeks
549-3.16428 -2.89596 (549*2π)/5731 weeks
5501.30115 -3.84235 (550*2π)/5731 weeks
5512.39648 -1.4576 (551*2π)/5731 weeks
552-.26676 1.84574 (552*2π)/5731 weeks
553-3.87233 -2.54738 (553*2π)/5731 weeks
554-2.21725 -4.10142 (554*2π)/5731 weeks
5552.12454 -6.19319 (555*2π)/5731 weeks
5561.0927 -.37006 (556*2π)/5731 weeks
557-.49329 -2.74479 (557*2π)/5731 weeks
558-.52154 -.17046 (558*2π)/5731 weeks
559-4.96315 -5.10564 (559*2π)/5731 weeks
560-.55761 -8.88292 (560*2π)/5731 weeks
5617.69181 -4.14435 (561*2π)/5731 weeks
562-3.38896 1.02944 (562*2π)/5731 weeks
563-3.20217 -4.13377 (563*2π)/5731 weeks
564-4.53494 -12.64849 (564*2π)/5731 weeks
5657.13873 -7.86604 (565*2π)/5731 weeks
566.27541 -2.70594 (566*2π)/5731 weeks
567-9.13036 -13.37299 (567*2π)/5731 weeks
5688.44795 -16.35232 (568*2π)/5731 weeks
56917.81109 -10.11255 (569*2π)/5731 weeks
570-6.85956 9.50139 (570*2π)/5731 weeks
571-9.56497 -24.53528 (571*2π)/5731 weeks

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