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Fourier Analysis of EEV (ProShares UltraShort MSCI Emerging Markets ETF)


EEV (ProShares UltraShort MSCI Emerging Markets ETF) appears to have interesting cyclic behaviour every 40 weeks (19.7653*sine), 43 weeks (17.8034*sine), and 47 weeks (16.1154*sine).

EEV (ProShares UltraShort MSCI Emerging Markets ETF) has an average price of 79.95 (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 11/1/2007 to 10/16/2017 for EEV (ProShares UltraShort MSCI Emerging Markets ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
079.94556   0 
188.63165 58.47694 (1*2π)/521521 weeks
246.98071 74.57962 (2*2π)/521261 weeks
39.28635 71.48253 (3*2π)/521174 weeks
4-13.66532 52.85969 (4*2π)/521130 weeks
5-20.91564 30.20413 (5*2π)/521104 weeks
6-18.57689 9.46017 (6*2π)/52187 weeks
7-6.13428 -1.34677 (7*2π)/52174 weeks
84.97747 -.59599 (8*2π)/52165 weeks
910.2712 5.06022 (9*2π)/52158 weeks
1012.92313 10.18697 (10*2π)/52152 weeks
1110.9017 16.11539 (11*2π)/52147 weeks
125.82287 17.80343 (12*2π)/52143 weeks
13.8502 19.76527 (13*2π)/52140 weeks
14-4.19663 16.23148 (14*2π)/52137 weeks
15-6.91581 12.7207 (15*2π)/52135 weeks
16-9.16583 9.3743 (16*2π)/52133 weeks
17-8.64705 3.34377 (17*2π)/52131 weeks
18-5.64334 .02996 (18*2π)/52129 weeks
19-1.89999 -2.64193 (19*2π)/52127 weeks
202.18543 -2.02742 (20*2π)/52126 weeks
215.93659 .59291 (21*2π)/52125 weeks
227.40212 5.0068 (22*2π)/52124 weeks
234.89491 8.55859 (23*2π)/52123 weeks
24.52802 9.59326 (24*2π)/52122 weeks
25-4.32274 7.53874 (25*2π)/52121 weeks
26-5.27147 3.57533 (26*2π)/52120 weeks
27-4.1122 -.45983 (27*2π)/52119 weeks
28-.02249 -3.31279 (28*2π)/52119 weeks
294.11236 -2.93646 (29*2π)/52118 weeks
307.40275 -.23782 (30*2π)/52117 weeks
318.06307 4.59407 (31*2π)/52117 weeks
325.31386 8.4533 (32*2π)/52116 weeks
331.90767 8.95997 (33*2π)/52116 weeks
34-1.20128 8.14634 (34*2π)/52115 weeks
35-3.12142 5.54033 (35*2π)/52115 weeks
36-3.43534 3.22749 (36*2π)/52114 weeks
37-3.00657 .85656 (37*2π)/52114 weeks
38-.99057 -1.07024 (38*2π)/52114 weeks
391.63625 -.74468 (39*2π)/52113 weeks
402.42377 .4633 (40*2π)/52113 weeks
413.45296 1.40504 (41*2π)/52113 weeks
423.59748 2.79772 (42*2π)/52112 weeks
432.95737 3.78563 (43*2π)/52112 weeks
441.5731 4.72659 (44*2π)/52112 weeks
45.10126 4.537 (45*2π)/52112 weeks
46-.35756 3.51364 (46*2π)/52111 weeks
47-1.08856 2.06649 (47*2π)/52111 weeks
48-.31274 1.10144 (48*2π)/52111 weeks
49.3941 .50426 (49*2π)/52111 weeks
501.82861 .28669 (50*2π)/52110 weeks
513.1478 .88243 (51*2π)/52110 weeks
523.81484 2.46346 (52*2π)/52110 weeks
533.68756 4.07817 (53*2π)/52110 weeks
541.92185 5.52977 (54*2π)/52110 weeks
55.08779 5.64238 (55*2π)/5219 weeks
56-1.54617 4.48732 (56*2π)/5219 weeks
57-2.28164 2.86838 (57*2π)/5219 weeks
58-1.753 .8827 (58*2π)/5219 weeks
59-.29476 .32538 (59*2π)/5219 weeks
60.78511 .36438 (60*2π)/5219 weeks
611.79998 .99967 (61*2π)/5219 weeks
621.99129 2.00827 (62*2π)/5218 weeks
631.74088 2.46838 (63*2π)/5218 weeks
641.36885 3.3882 (64*2π)/5218 weeks
65.42542 3.63148 (65*2π)/5218 weeks
66-.17722 3.88175 (66*2π)/5218 weeks
67-1.7277 3.72069 (67*2π)/5218 weeks
68-2.96168 2.35325 (68*2π)/5218 weeks
69-3.03976 .37504 (69*2π)/5218 weeks
70-2.03808 -1.62418 (70*2π)/5217 weeks
71.22192 -2.33629 (71*2π)/5217 weeks
722.22657 -1.6387 (72*2π)/5217 weeks
733.36798 -.53966 (73*2π)/5217 weeks
744.26562 1.64554 (74*2π)/5217 weeks
752.87402 3.91851 (75*2π)/5217 weeks
76.85839 4.42929 (76*2π)/5217 weeks
77-1.13113 4.10451 (77*2π)/5217 weeks
78-2.64865 1.93098 (78*2π)/5217 weeks
79-2.14947 -.01144 (79*2π)/5217 weeks
80-1.02989 -1.46957 (80*2π)/5217 weeks
811.17247 -2.1788 (81*2π)/5216 weeks
823.10545 -1.05166 (82*2π)/5216 weeks
834.18635 .73927 (83*2π)/5216 weeks
843.86408 2.77568 (84*2π)/5216 weeks
852.24592 4.31198 (85*2π)/5216 weeks
86.23117 4.42716 (86*2π)/5216 weeks
87-1.26192 3.63156 (87*2π)/5216 weeks
88-1.84259 2.16998 (88*2π)/5216 weeks
89-1.55881 .84946 (89*2π)/5216 weeks
90-1.10866 .12299 (90*2π)/5216 weeks
91-.15513 -.67219 (91*2π)/5216 weeks
92.7917 -.68388 (92*2π)/5216 weeks
931.7459 -.04465 (93*2π)/5216 weeks
942.27382 .98484 (94*2π)/5216 weeks
952.17014 2.06302 (95*2π)/5215 weeks
961.45978 2.72928 (96*2π)/5215 weeks
97.27616 2.95499 (97*2π)/5215 weeks
98-1.03137 2.66919 (98*2π)/5215 weeks
99-1.78718 1.69129 (99*2π)/5215 weeks
100-1.81168 .42769 (100*2π)/5215 weeks
101-1.0604 -.83856 (101*2π)/5215 weeks
102.06146 -1.56171 (102*2π)/5215 weeks
1031.55466 -1.40318 (103*2π)/5215 weeks
1042.66364 -.29631 (104*2π)/5215 weeks
1053.07778 1.28911 (105*2π)/5215 weeks
1062.33676 2.59092 (106*2π)/5215 weeks
1071.01202 3.09727 (107*2π)/5215 weeks
108-.40102 3.067 (108*2π)/5215 weeks
109-1.63526 1.94574 (109*2π)/5215 weeks
110-1.60051 .57549 (110*2π)/5215 weeks
111-.82983 -.56078 (111*2π)/5215 weeks
112.25209 -1.04281 (112*2π)/5215 weeks
1131.41709 -.74329 (113*2π)/5215 weeks
1142.05941 .26136 (114*2π)/5215 weeks
1152.09141 1.42599 (115*2π)/5215 weeks
1161.30516 2.37872 (116*2π)/5214 weeks
117.08649 2.46747 (117*2π)/5214 weeks
118-.62998 1.65372 (118*2π)/5214 weeks
119-.96452 .86036 (119*2π)/5214 weeks
120-.54331 .04573 (120*2π)/5214 weeks
121.16159 .03778 (121*2π)/5214 weeks
122.4719 .20285 (122*2π)/5214 weeks
123.64344 .44906 (123*2π)/5214 weeks
124.60842 .77148 (124*2π)/5214 weeks
125.24646 .87442 (125*2π)/5214 weeks
126-.19953 .59621 (126*2π)/5214 weeks
127-.20921 .16216 (127*2π)/5214 weeks
128.2683 -.16872 (128*2π)/5214 weeks
129.64804 -.32514 (129*2π)/5214 weeks
1301.12207 -.03768 (130*2π)/5214 weeks
1311.0045 .61906 (131*2π)/5214 weeks
132.67039 .66937 (132*2π)/5214 weeks
133.59473 .54303 (133*2π)/5214 weeks
134.53411 .43013 (134*2π)/5214 weeks
135.72018 .34143 (135*2π)/5214 weeks
136.57982 .61207 (136*2π)/5214 weeks
137.26527 .46581 (137*2π)/5214 weeks
138.36825 .21064 (138*2π)/5214 weeks
139.47153 -.0477 (139*2π)/5214 weeks
140.89168 -.3615 (140*2π)/5214 weeks
1411.3349 .00153 (141*2π)/5214 weeks
1421.56433 .35145 (142*2π)/5214 weeks
1431.56725 1.0193 (143*2π)/5214 weeks
1441.03927 1.36429 (144*2π)/5214 weeks
145.5713 1.31316 (145*2π)/5214 weeks
146.09263 1.1958 (146*2π)/5214 weeks
147-.28563 .70087 (147*2π)/5214 weeks
148-.33245 .18051 (148*2π)/5214 weeks
149.00583 -.37861 (149*2π)/5213 weeks
150.71685 -.80936 (150*2π)/5213 weeks
1511.42996 -.34316 (151*2π)/5213 weeks
1521.65657 .10655 (152*2π)/5213 weeks
1531.84877 .68673 (153*2π)/5213 weeks
1541.65201 1.39387 (154*2π)/5213 weeks
155.96427 1.88892 (155*2π)/5213 weeks
156-.0605 1.79628 (156*2π)/5213 weeks
157-.75091 1.13225 (157*2π)/5213 weeks
158-.91834 .16278 (158*2π)/5213 weeks
159-.45311 -.7029 (159*2π)/5213 weeks
160.36115 -1.0194 (160*2π)/5213 weeks
1611.18617 -1.00673 (161*2π)/5213 weeks
1621.87038 -.42417 (162*2π)/5213 weeks
1632.21499 .41819 (163*2π)/5213 weeks
1641.80976 1.25111 (164*2π)/5213 weeks
1651.08442 1.77885 (165*2π)/5213 weeks
166.10829 1.82546 (166*2π)/5213 weeks
167-.60599 1.28203 (167*2π)/5213 weeks
168-1.00247 .36852 (168*2π)/5213 weeks
169-.76141 -.71783 (169*2π)/5213 weeks
170.05157 -1.36183 (170*2π)/5213 weeks
1711.02863 -1.47976 (171*2π)/5213 weeks
1721.92296 -.99341 (172*2π)/5213 weeks
1732.36841 -.10191 (173*2π)/5213 weeks
1742.28062 .69052 (174*2π)/5213 weeks
1751.66215 1.38166 (175*2π)/5213 weeks
176.92145 1.51571 (176*2π)/5213 weeks
177.24794 1.25891 (177*2π)/5213 weeks
178-.10124 .51061 (178*2π)/5213 weeks
179.20668 -.23237 (179*2π)/5213 weeks
180.70995 -.54311 (180*2π)/5213 weeks
1811.48003 -.49332 (181*2π)/5213 weeks
1822.11296 .00308 (182*2π)/5213 weeks
1832.27134 .71467 (183*2π)/5213 weeks
1842.09301 1.65463 (184*2π)/5213 weeks
1851.18429 2.37347 (185*2π)/5213 weeks
186.26163 2.0982 (186*2π)/5213 weeks
187-.41629 1.5482 (187*2π)/5213 weeks
188-.6878 .68688 (188*2π)/5213 weeks
189-.3561 -.01483 (189*2π)/5213 weeks
190.12246 -.3551 (190*2π)/5213 weeks
191.95596 -.59548 (191*2π)/5213 weeks
1921.6247 .0049 (192*2π)/5213 weeks
1931.70564 .56757 (193*2π)/5213 weeks
1941.7226 1.32913 (194*2π)/5213 weeks
1951.02648 2.05644 (195*2π)/5213 weeks
196.05008 2.13176 (196*2π)/5213 weeks
197-.79756 1.54831 (197*2π)/5213 weeks
198-1.13159 .53388 (198*2π)/5213 weeks
199-.67443 -.29369 (199*2π)/5213 weeks
200-.03241 -.68191 (200*2π)/5213 weeks
201.75631 -.6176 (201*2π)/5213 weeks
2021.38057 -.17974 (202*2π)/5213 weeks
2031.26758 .62925 (203*2π)/5213 weeks
2041.05819 1.11267 (204*2π)/5213 weeks
205.43974 1.27709 (205*2π)/5213 weeks
206.05394 .99535 (206*2π)/5213 weeks
207-.18842 .90509 (207*2π)/5213 weeks
208-.42785 .72512 (208*2π)/5213 weeks
209-.63879 .23657 (209*2π)/5212 weeks
210-.55669 -.38928 (210*2π)/5212 weeks
211-.06948 -.78872 (211*2π)/5212 weeks
212.4286 -.87028 (212*2π)/5212 weeks
2131.10765 -.77783 (213*2π)/5212 weeks
2141.59653 -.13429 (214*2π)/5212 weeks
2151.61353 .67172 (215*2π)/5212 weeks
2161.08637 1.34284 (216*2π)/5212 weeks
217.03837 1.52898 (217*2π)/5212 weeks
218-.7345 1.08852 (218*2π)/5212 weeks
219-1.11487 .27761 (219*2π)/5212 weeks
220-.97448 -.73691 (220*2π)/5212 weeks
221-.32311 -1.52318 (221*2π)/5212 weeks
222.67981 -1.7429 (222*2π)/5212 weeks
2231.75086 -1.4688 (223*2π)/5212 weeks
2242.45734 -.52055 (224*2π)/5212 weeks
2252.45555 .57748 (225*2π)/5212 weeks
2261.8449 1.56149 (226*2π)/5212 weeks
227.64692 2.07167 (227*2π)/5212 weeks
228-.40911 1.63707 (228*2π)/5212 weeks
229-1.05331 .85344 (229*2π)/5212 weeks
230-1.18354 -.45827 (230*2π)/5212 weeks
231-.4433 -1.36078 (231*2π)/5212 weeks
232.54796 -1.70395 (232*2π)/5212 weeks
2331.77095 -1.57775 (233*2π)/5212 weeks
2342.76051 -.65564 (234*2π)/5212 weeks
2352.84868 .71259 (235*2π)/5212 weeks
2362.30632 2.03362 (236*2π)/5212 weeks
2371.01153 2.79067 (237*2π)/5212 weeks
238-.45283 2.68461 (238*2π)/5212 weeks
239-1.56117 1.81725 (239*2π)/5212 weeks
240-2.14961 .40484 (240*2π)/5212 weeks
241-1.85178 -1.00061 (241*2π)/5212 weeks
242-.95123 -1.97774 (242*2π)/5212 weeks
243.55738 -2.41734 (243*2π)/5212 weeks
2442.06537 -1.72762 (244*2π)/5212 weeks
2452.68138 -.40676 (245*2π)/5212 weeks
2462.55838 .91555 (246*2π)/5212 weeks
2471.55105 2.07596 (247*2π)/5212 weeks
248-.06793 2.34101 (248*2π)/5212 weeks
249-1.47535 1.53051 (249*2π)/5212 weeks
250-1.84435 .06608 (250*2π)/5212 weeks
251-1.42303 -1.36968 (251*2π)/5212 weeks
252-.27751 -2.28908 (252*2π)/5212 weeks
2531.0066 -2.51099 (253*2π)/5212 weeks
2542.53401 -1.70633 (254*2π)/5212 weeks
2553.17057 -.10631 (255*2π)/5212 weeks
2562.6859 1.31919 (256*2π)/5212 weeks
2571.63453 2.17377 (257*2π)/5212 weeks
258.19148 2.41386 (258*2π)/5212 weeks
259-.97073 1.96506 (259*2π)/5212 weeks
260-1.89929 .79405 (260*2π)/5212 weeks
261-1.89929 -.79405 (261*2π)/5212 weeks
262-.97073 -1.96506 (262*2π)/5212 weeks
263.19148 -2.41386 (263*2π)/5212 weeks
2641.63453 -2.17377 (264*2π)/5212 weeks
2652.6859 -1.31919 (265*2π)/5212 weeks
2663.17057 .10631 (266*2π)/5212 weeks
2672.53401 1.70633 (267*2π)/5212 weeks
2681.0066 2.51099 (268*2π)/5212 weeks
269-.27751 2.28908 (269*2π)/5212 weeks
270-1.42303 1.36968 (270*2π)/5212 weeks
271-1.84435 -.06608 (271*2π)/5212 weeks
272-1.47535 -1.53051 (272*2π)/5212 weeks
273-.06793 -2.34101 (273*2π)/5212 weeks
2741.55105 -2.07596 (274*2π)/5212 weeks
2752.55838 -.91555 (275*2π)/5212 weeks
2762.68138 .40676 (276*2π)/5212 weeks
2772.06537 1.72762 (277*2π)/5212 weeks
278.55738 2.41734 (278*2π)/5212 weeks
279-.95123 1.97774 (279*2π)/5212 weeks
280-1.85178 1.00061 (280*2π)/5212 weeks
281-2.14961 -.40484 (281*2π)/5212 weeks
282-1.56117 -1.81725 (282*2π)/5212 weeks
283-.45283 -2.68461 (283*2π)/5212 weeks
2841.01153 -2.79067 (284*2π)/5212 weeks
2852.30632 -2.03362 (285*2π)/5212 weeks
2862.84868 -.71259 (286*2π)/5212 weeks
2872.76051 .65564 (287*2π)/5212 weeks
2881.77095 1.57775 (288*2π)/5212 weeks
289.54796 1.70395 (289*2π)/5212 weeks
290-.4433 1.36078 (290*2π)/5212 weeks
291-1.18354 .45827 (291*2π)/5212 weeks
292-1.05331 -.85344 (292*2π)/5212 weeks
293-.40911 -1.63707 (293*2π)/5212 weeks
294.64692 -2.07167 (294*2π)/5212 weeks
2951.8449 -1.56149 (295*2π)/5212 weeks
2962.45555 -.57748 (296*2π)/5212 weeks
2972.45734 .52055 (297*2π)/5212 weeks
2981.75086 1.4688 (298*2π)/5212 weeks
299.67981 1.7429 (299*2π)/5212 weeks
300-.32311 1.52318 (300*2π)/5212 weeks
301-.97448 .73691 (301*2π)/5212 weeks
302-1.11487 -.27761 (302*2π)/5212 weeks
303-.7345 -1.08852 (303*2π)/5212 weeks
304.03837 -1.52898 (304*2π)/5212 weeks
3051.08637 -1.34284 (305*2π)/5212 weeks
3061.61353 -.67172 (306*2π)/5212 weeks
3071.59653 .13429 (307*2π)/5212 weeks
3081.10765 .77783 (308*2π)/5212 weeks
309.4286 .87028 (309*2π)/5212 weeks
310-.06948 .78872 (310*2π)/5212 weeks
311-.55669 .38928 (311*2π)/5212 weeks
312-.63879 -.23657 (312*2π)/5212 weeks
313-.42785 -.72512 (313*2π)/5212 weeks
314-.18842 -.90509 (314*2π)/5212 weeks
315.05394 -.99535 (315*2π)/5212 weeks
316.43974 -1.27709 (316*2π)/5212 weeks
3171.05819 -1.11267 (317*2π)/5212 weeks
3181.26758 -.62925 (318*2π)/5212 weeks
3191.38057 .17974 (319*2π)/5212 weeks
320.75631 .6176 (320*2π)/5212 weeks
321-.03241 .68191 (321*2π)/5212 weeks
322-.67443 .29369 (322*2π)/5212 weeks
323-1.13159 -.53388 (323*2π)/5212 weeks
324-.79756 -1.54831 (324*2π)/5212 weeks
325.05008 -2.13176 (325*2π)/5212 weeks
3261.02648 -2.05644 (326*2π)/5212 weeks
3271.7226 -1.32913 (327*2π)/5212 weeks
3281.70564 -.56757 (328*2π)/5212 weeks
3291.6247 -.0049 (329*2π)/5212 weeks
330.95596 .59548 (330*2π)/5212 weeks
331.12246 .3551 (331*2π)/5212 weeks
332-.3561 .01483 (332*2π)/5212 weeks
333-.6878 -.68688 (333*2π)/5212 weeks
334-.41629 -1.5482 (334*2π)/5212 weeks
335.26163 -2.0982 (335*2π)/5212 weeks
3361.18429 -2.37347 (336*2π)/5212 weeks
3372.09301 -1.65463 (337*2π)/5212 weeks
3382.27134 -.71467 (338*2π)/5212 weeks
3392.11296 -.00308 (339*2π)/5212 weeks
3401.48003 .49332 (340*2π)/5212 weeks
341.70995 .54311 (341*2π)/5212 weeks
342.20668 .23237 (342*2π)/5212 weeks
343-.10124 -.51061 (343*2π)/5212 weeks
344.24794 -1.25891 (344*2π)/5212 weeks
345.92145 -1.51571 (345*2π)/5212 weeks
3461.66215 -1.38166 (346*2π)/5212 weeks
3472.28062 -.69052 (347*2π)/5212 weeks
3482.36841 .10191 (348*2π)/5211 weeks
3491.92296 .99341 (349*2π)/5211 weeks
3501.02863 1.47976 (350*2π)/5211 weeks
351.05157 1.36183 (351*2π)/5211 weeks
352-.76141 .71783 (352*2π)/5211 weeks
353-1.00247 -.36852 (353*2π)/5211 weeks
354-.60599 -1.28203 (354*2π)/5211 weeks
355.10829 -1.82546 (355*2π)/5211 weeks
3561.08442 -1.77885 (356*2π)/5211 weeks
3571.80976 -1.25111 (357*2π)/5211 weeks
3582.21499 -.41819 (358*2π)/5211 weeks
3591.87038 .42417 (359*2π)/5211 weeks
3601.18617 1.00673 (360*2π)/5211 weeks
361.36115 1.0194 (361*2π)/5211 weeks
362-.45311 .7029 (362*2π)/5211 weeks
363-.91834 -.16278 (363*2π)/5211 weeks
364-.75091 -1.13225 (364*2π)/5211 weeks
365-.0605 -1.79628 (365*2π)/5211 weeks
366.96427 -1.88892 (366*2π)/5211 weeks
3671.65201 -1.39387 (367*2π)/5211 weeks
3681.84877 -.68673 (368*2π)/5211 weeks
3691.65657 -.10655 (369*2π)/5211 weeks
3701.42996 .34316 (370*2π)/5211 weeks
371.71685 .80936 (371*2π)/5211 weeks
372.00583 .37861 (372*2π)/5211 weeks
373-.33245 -.18051 (373*2π)/5211 weeks
374-.28563 -.70087 (374*2π)/5211 weeks
375.09263 -1.1958 (375*2π)/5211 weeks
376.5713 -1.31316 (376*2π)/5211 weeks
3771.03927 -1.36429 (377*2π)/5211 weeks
3781.56725 -1.0193 (378*2π)/5211 weeks
3791.56433 -.35145 (379*2π)/5211 weeks
3801.3349 -.00153 (380*2π)/5211 weeks
381.89168 .3615 (381*2π)/5211 weeks
382.47153 .0477 (382*2π)/5211 weeks
383.36825 -.21064 (383*2π)/5211 weeks
384.26527 -.46581 (384*2π)/5211 weeks
385.57982 -.61207 (385*2π)/5211 weeks
386.72018 -.34143 (386*2π)/5211 weeks
387.53411 -.43013 (387*2π)/5211 weeks
388.59473 -.54303 (388*2π)/5211 weeks
389.67039 -.66937 (389*2π)/5211 weeks
3901.0045 -.61906 (390*2π)/5211 weeks
3911.12207 .03768 (391*2π)/5211 weeks
392.64804 .32514 (392*2π)/5211 weeks
393.2683 .16872 (393*2π)/5211 weeks
394-.20921 -.16216 (394*2π)/5211 weeks
395-.19953 -.59621 (395*2π)/5211 weeks
396.24646 -.87442 (396*2π)/5211 weeks
397.60842 -.77148 (397*2π)/5211 weeks
398.64344 -.44906 (398*2π)/5211 weeks
399.4719 -.20285 (399*2π)/5211 weeks
400.16159 -.03778 (400*2π)/5211 weeks
401-.54331 -.04573 (401*2π)/5211 weeks
402-.96452 -.86036 (402*2π)/5211 weeks
403-.62998 -1.65372 (403*2π)/5211 weeks
404.08649 -2.46747 (404*2π)/5211 weeks
4051.30516 -2.37872 (405*2π)/5211 weeks
4062.09141 -1.42599 (406*2π)/5211 weeks
4072.05941 -.26136 (407*2π)/5211 weeks
4081.41709 .74329 (408*2π)/5211 weeks
409.25209 1.04281 (409*2π)/5211 weeks
410-.82983 .56078 (410*2π)/5211 weeks
411-1.60051 -.57549 (411*2π)/5211 weeks
412-1.63526 -1.94574 (412*2π)/5211 weeks
413-.40102 -3.067 (413*2π)/5211 weeks
4141.01202 -3.09727 (414*2π)/5211 weeks
4152.33676 -2.59092 (415*2π)/5211 weeks
4163.07778 -1.28911 (416*2π)/5211 weeks
4172.66364 .29631 (417*2π)/5211 weeks
4181.55466 1.40318 (418*2π)/5211 weeks
419.06146 1.56171 (419*2π)/5211 weeks
420-1.0604 .83856 (420*2π)/5211 weeks
421-1.81168 -.42769 (421*2π)/5211 weeks
422-1.78718 -1.69129 (422*2π)/5211 weeks
423-1.03137 -2.66919 (423*2π)/5211 weeks
424.27616 -2.95499 (424*2π)/5211 weeks
4251.45978 -2.72928 (425*2π)/5211 weeks
4262.17014 -2.06302 (426*2π)/5211 weeks
4272.27382 -.98484 (427*2π)/5211 weeks
4281.7459 .04465 (428*2π)/5211 weeks
429.7917 .68388 (429*2π)/5211 weeks
430-.15513 .67219 (430*2π)/5211 weeks
431-1.10866 -.12299 (431*2π)/5211 weeks
432-1.55881 -.84946 (432*2π)/5211 weeks
433-1.84259 -2.16998 (433*2π)/5211 weeks
434-1.26192 -3.63156 (434*2π)/5211 weeks
435.23117 -4.42716 (435*2π)/5211 weeks
4362.24592 -4.31198 (436*2π)/5211 weeks
4373.86408 -2.77568 (437*2π)/5211 weeks
4384.18635 -.73927 (438*2π)/5211 weeks
4393.10545 1.05166 (439*2π)/5211 weeks
4401.17247 2.1788 (440*2π)/5211 weeks
441-1.02989 1.46957 (441*2π)/5211 weeks
442-2.14947 .01144 (442*2π)/5211 weeks
443-2.64865 -1.93098 (443*2π)/5211 weeks
444-1.13113 -4.10451 (444*2π)/5211 weeks
445.85839 -4.42929 (445*2π)/5211 weeks
4462.87402 -3.91851 (446*2π)/5211 weeks
4474.26562 -1.64554 (447*2π)/5211 weeks
4483.36798 .53966 (448*2π)/5211 weeks
4492.22657 1.6387 (449*2π)/5211 weeks
450.22192 2.33629 (450*2π)/5211 weeks
451-2.03808 1.62418 (451*2π)/5211 weeks
452-3.03976 -.37504 (452*2π)/5211 weeks
453-2.96168 -2.35325 (453*2π)/5211 weeks
454-1.7277 -3.72069 (454*2π)/5211 weeks
455-.17722 -3.88175 (455*2π)/5211 weeks
456.42542 -3.63148 (456*2π)/5211 weeks
4571.36885 -3.3882 (457*2π)/5211 weeks
4581.74088 -2.46838 (458*2π)/5211 weeks
4591.99129 -2.00827 (459*2π)/5211 weeks
4601.79998 -.99967 (460*2π)/5211 weeks
461.78511 -.36438 (461*2π)/5211 weeks
462-.29476 -.32538 (462*2π)/5211 weeks
463-1.753 -.8827 (463*2π)/5211 weeks
464-2.28164 -2.86838 (464*2π)/5211 weeks
465-1.54617 -4.48732 (465*2π)/5211 weeks
466.08779 -5.64238 (466*2π)/5211 weeks
4671.92185 -5.52977 (467*2π)/5211 weeks
4683.68756 -4.07817 (468*2π)/5211 weeks
4693.81484 -2.46346 (469*2π)/5211 weeks
4703.1478 -.88243 (470*2π)/5211 weeks
4711.82861 -.28669 (471*2π)/5211 weeks
472.3941 -.50426 (472*2π)/5211 weeks
473-.31274 -1.10144 (473*2π)/5211 weeks
474-1.08856 -2.06649 (474*2π)/5211 weeks
475-.35756 -3.51364 (475*2π)/5211 weeks
476.10126 -4.537 (476*2π)/5211 weeks
4771.5731 -4.72659 (477*2π)/5211 weeks
4782.95737 -3.78563 (478*2π)/5211 weeks
4793.59748 -2.79772 (479*2π)/5211 weeks
4803.45296 -1.40504 (480*2π)/5211 weeks
4812.42377 -.4633 (481*2π)/5211 weeks
4821.63625 .74468 (482*2π)/5211 weeks
483-.99057 1.07024 (483*2π)/5211 weeks
484-3.00657 -.85656 (484*2π)/5211 weeks
485-3.43534 -3.22749 (485*2π)/5211 weeks
486-3.12142 -5.54033 (486*2π)/5211 weeks
487-1.20128 -8.14634 (487*2π)/5211 weeks
4881.90767 -8.95997 (488*2π)/5211 weeks
4895.31386 -8.4533 (489*2π)/5211 weeks
4908.06307 -4.59407 (490*2π)/5211 weeks
4917.40275 .23782 (491*2π)/5211 weeks
4924.11236 2.93646 (492*2π)/5211 weeks
493-.02249 3.31279 (493*2π)/5211 weeks
494-4.1122 .45983 (494*2π)/5211 weeks
495-5.27147 -3.57533 (495*2π)/5211 weeks
496-4.32274 -7.53874 (496*2π)/5211 weeks
497.52802 -9.59326 (497*2π)/5211 weeks
4984.89491 -8.55859 (498*2π)/5211 weeks
4997.40212 -5.0068 (499*2π)/5211 weeks
5005.93659 -.59291 (500*2π)/5211 weeks
5012.18543 2.02742 (501*2π)/5211 weeks
502-1.89999 2.64193 (502*2π)/5211 weeks
503-5.64334 -.02996 (503*2π)/5211 weeks
504-8.64705 -3.34377 (504*2π)/5211 weeks
505-9.16583 -9.3743 (505*2π)/5211 weeks
506-6.91581 -12.7207 (506*2π)/5211 weeks
507-4.19663 -16.23148 (507*2π)/5211 weeks
508.8502 -19.76527 (508*2π)/5211 weeks
5095.82287 -17.80343 (509*2π)/5211 weeks
51010.9017 -16.11539 (510*2π)/5211 weeks
51112.92313 -10.18697 (511*2π)/5211 weeks
51210.2712 -5.06022 (512*2π)/5211 weeks
5134.97747 .59599 (513*2π)/5211 weeks
514-6.13428 1.34677 (514*2π)/5211 weeks
515-18.57689 -9.46017 (515*2π)/5211 weeks
516-20.91564 -30.20413 (516*2π)/5211 weeks
517-13.66532 -52.85969 (517*2π)/5211 weeks
5189.28635 -71.48253 (518*2π)/5211 weeks
51946.98071 -74.57962 (519*2π)/5211 weeks



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