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# Fourier Analysis of EFU (ProShares UltraShort MSCI EAFE)

EFU (ProShares UltraShort MSCI EAFE) appears to have interesting cyclic behaviour every 51 weeks (12.9513*sine), 56 weeks (12.8533*sine), and 17 weeks (6.537*cosine).

EFU (ProShares UltraShort MSCI EAFE) has an average price of 112.76 (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.

## Fourier Analysis

Using data from 10/25/2007 to 6/18/2018 for EFU (ProShares UltraShort MSCI EAFE), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0112.759   0
162.96522 91.70343 (1*2π)/557557 weeks
212.28355 69.93137 (2*2π)/557279 weeks
3-15.36472 58.61602 (3*2π)/557186 weeks
4-24.98 28.47249 (4*2π)/557139 weeks
5-21.43409 10.86077 (5*2π)/557111 weeks
6-14.26339 -5.11265 (6*2π)/55793 weeks
72.26238 -10.70007 (7*2π)/55780 weeks
814.75312 .41929 (8*2π)/55770 weeks
912.96248 11.7261 (9*2π)/55762 weeks
103.81896 12.85327 (10*2π)/55756 weeks
111.60516 12.95128 (11*2π)/55751 weeks
12-2.36208 12.06446 (12*2π)/55746 weeks
13-2.71854 7.16118 (13*2π)/55743 weeks
14-2.844 7.41632 (14*2π)/55740 weeks
15-2.51127 4.05226 (15*2π)/55737 weeks
16-.6066 4.72544 (16*2π)/55735 weeks
17-3.62936 6.80242 (17*2π)/55733 weeks
18-4.84657 2.29763 (18*2π)/55731 weeks
19-3.13521 .79078 (19*2π)/55729 weeks
20-1.95503 -1.30327 (20*2π)/55728 weeks
21.70865 -.51968 (21*2π)/55727 weeks
222.07941 -.59972 (22*2π)/55725 weeks
234.80559 1.17857 (23*2π)/55724 weeks
243.20219 5.23182 (24*2π)/55723 weeks
25.50455 7.07774 (25*2π)/55722 weeks
26-3.7257 6.43038 (26*2π)/55721 weeks
27-5.19729 .42371 (27*2π)/55721 weeks
28-2.66197 -2.00356 (28*2π)/55720 weeks
29-1.10519 -3.83937 (29*2π)/55719 weeks
303.88067 -3.19385 (30*2π)/55719 weeks
316.20765 -.14257 (31*2π)/55718 weeks
326.53698 2.83947 (32*2π)/55717 weeks
334.64979 6.75011 (33*2π)/55717 weeks
34-.01698 8.30474 (34*2π)/55716 weeks
35-3.49524 4.63563 (35*2π)/55716 weeks
36-2.97673 1.50196 (36*2π)/55715 weeks
37-1.63432 -.035 (37*2π)/55715 weeks
38.22439 .14392 (38*2π)/55715 weeks
39.03776 .4616 (39*2π)/55714 weeks
40.84413 -.11302 (40*2π)/55714 weeks
412.47828 .51425 (41*2π)/55714 weeks
421.62285 3.08026 (42*2π)/55713 weeks
43-.13457 1.74672 (43*2π)/55713 weeks
44.7561 1.13912 (44*2π)/55713 weeks
45.61337 1.76742 (45*2π)/55712 weeks
46.97715 1.48036 (46*2π)/55712 weeks
47.75857 2.04949 (47*2π)/55712 weeks
48-.38523 1.97137 (48*2π)/55712 weeks
49.66883 1.52237 (49*2π)/55711 weeks
50-.14408 1.61563 (50*2π)/55711 weeks
51-.37283 1.58078 (51*2π)/55711 weeks
52-.55541 .90564 (52*2π)/55711 weeks
53.55688 .16546 (53*2π)/55711 weeks
541.08624 .20142 (54*2π)/55710 weeks
551.99775 .89113 (55*2π)/55710 weeks
561.86087 2.36302 (56*2π)/55710 weeks
57.63598 3.5861 (57*2π)/55710 weeks
58-.73285 2.90048 (58*2π)/55710 weeks
59-1.79798 1.82229 (59*2π)/5579 weeks
60-1.28988 .66636 (60*2π)/5579 weeks
61-1.01371 -.00593 (61*2π)/5579 weeks
62.34221 -.87509 (62*2π)/5579 weeks
631.45434 .47018 (63*2π)/5579 weeks
64.85838 .92607 (64*2π)/5579 weeks
65.94 1.2532 (65*2π)/5579 weeks
66.36683 1.50565 (66*2π)/5578 weeks
67-.05695 .81358 (67*2π)/5578 weeks
68.67295 1.21355 (68*2π)/5578 weeks
69.28404 1.25878 (69*2π)/5578 weeks
70.64722 1.67536 (70*2π)/5578 weeks
71-.3455 2.46903 (71*2π)/5578 weeks
72-1.69221 1.8711 (72*2π)/5578 weeks
73-2.28642 .09888 (73*2π)/5578 weeks
74-1.42041 -1.37957 (74*2π)/5578 weeks
75.3524 -2.1098 (75*2π)/5577 weeks
762.07141 -1.35305 (76*2π)/5577 weeks
772.28351 .28813 (77*2π)/5577 weeks
782.69068 .34896 (78*2π)/5577 weeks
792.88495 2.85479 (79*2π)/5577 weeks
80.44691 3.9943 (80*2π)/5577 weeks
81-1.28658 2.65838 (81*2π)/5577 weeks
82-2.15067 1.64299 (82*2π)/5577 weeks
83-2.27123 -.56915 (83*2π)/5577 weeks
84-.38859 -1.25221 (84*2π)/5577 weeks
85.25444 -1.29997 (85*2π)/5577 weeks
862.03062 -1.43322 (86*2π)/5576 weeks
872.9441 .3592 (87*2π)/5576 weeks
882.38329 1.81039 (88*2π)/5576 weeks
891.17281 3.02748 (89*2π)/5576 weeks
90-.17138 2.718 (90*2π)/5576 weeks
91-1.31072 1.81377 (91*2π)/5576 weeks
92-1.44023 .39518 (92*2π)/5576 weeks
93-.66091 -.1397 (93*2π)/5576 weeks
94.13796 -.06081 (94*2π)/5576 weeks
95.57137 .42196 (95*2π)/5576 weeks
96-.16566 .63201 (96*2π)/5576 weeks
97-.03481 -.06285 (97*2π)/5576 weeks
98.22428 -.1507 (98*2π)/5576 weeks
99.85093 .00699 (99*2π)/5576 weeks
1001.31519 .49763 (100*2π)/5576 weeks
1011.18942 .92282 (101*2π)/5576 weeks
102.72619 1.44995 (102*2π)/5575 weeks
103-.09472 1.93006 (103*2π)/5575 weeks
104-.75398 1.66782 (104*2π)/5575 weeks
105-1.22126 .51185 (105*2π)/5575 weeks
106-.97461 -.28168 (106*2π)/5575 weeks
107-.41495 -1.08171 (107*2π)/5575 weeks
108.61759 -.90079 (108*2π)/5575 weeks
1091.46536 -.86368 (109*2π)/5575 weeks
1102.29661 .09296 (110*2π)/5575 weeks
1111.77549 1.58848 (111*2π)/5575 weeks
112.92282 2.22499 (112*2π)/5575 weeks
113-.0286 2.17212 (113*2π)/5575 weeks
114-.79643 1.50562 (114*2π)/5575 weeks
115-1.27696 1.05448 (115*2π)/5575 weeks
116-1.57931 -.25405 (116*2π)/5575 weeks
117-.3659 -.95534 (117*2π)/5575 weeks
118.48583 -1.0068 (118*2π)/5575 weeks
119.93165 -.39593 (119*2π)/5575 weeks
1201.394 .05654 (120*2π)/5575 weeks
1211.31102 .91336 (121*2π)/5575 weeks
122.8058 1.17007 (122*2π)/5575 weeks
123.1364 1.45289 (123*2π)/5575 weeks
124-.53219 1.27342 (124*2π)/5574 weeks
125-1.01371 .41815 (125*2π)/5574 weeks
126-.30487 -.20621 (126*2π)/5574 weeks
127-.10668 -.36853 (127*2π)/5574 weeks
128.08297 -.24564 (128*2π)/5574 weeks
129.37574 -.05051 (129*2π)/5574 weeks
130.29055 -.15579 (130*2π)/5574 weeks
131.61866 -.25322 (131*2π)/5574 weeks
132.89 .34144 (132*2π)/5574 weeks
133.26161 .40052 (133*2π)/5574 weeks
134.15391 .1335 (134*2π)/5574 weeks
135.56679 -.14382 (135*2π)/5574 weeks
136.79602 -.15788 (136*2π)/5574 weeks
137.70517 .24982 (137*2π)/5574 weeks
138.91612 .4123 (138*2π)/5574 weeks
139.78045 .82537 (139*2π)/5574 weeks
140-.09622 .66304 (140*2π)/5574 weeks
141-.02091 .06402 (141*2π)/5574 weeks
142.29528 .01409 (142*2π)/5574 weeks
143.74691 -.27274 (143*2π)/5574 weeks
1441.06301 .41156 (144*2π)/5574 weeks
145.26396 .67921 (145*2π)/5574 weeks
146.15195 .08661 (146*2π)/5574 weeks
147.77351 .19999 (147*2π)/5574 weeks
148.7148 .36411 (148*2π)/5574 weeks
149.71074 .52424 (149*2π)/5574 weeks
150.48087 .95145 (150*2π)/5574 weeks
151.17723 .62898 (151*2π)/5574 weeks
152.13314 .81292 (152*2π)/5574 weeks
153-.54315 .44308 (153*2π)/5574 weeks
154-.14635 -.3405 (154*2π)/5574 weeks
155.55485 -.22241 (155*2π)/5574 weeks
156.72114 .09185 (156*2π)/5574 weeks
157.62469 .2852 (157*2π)/5574 weeks
158.40142 .23953 (158*2π)/5574 weeks
159.62376 .23131 (159*2π)/5574 weeks
160.9342 .65043 (160*2π)/5573 weeks
161.13631 1.05331 (161*2π)/5573 weeks
162-.08237 .29698 (162*2π)/5573 weeks
163.27651 .23538 (163*2π)/5573 weeks
164.26243 .40061 (164*2π)/5573 weeks
165.06326 .44359 (165*2π)/5573 weeks
166-.37052 .11154 (166*2π)/5573 weeks
167.18949 -.2837 (167*2π)/5573 weeks
168.24305 -.20684 (168*2π)/5573 weeks
169.74692 -.46197 (169*2π)/5573 weeks
1701.12065 .05863 (170*2π)/5573 weeks
171.94097 .51607 (171*2π)/5573 weeks
172.76267 .85965 (172*2π)/5573 weeks
173.20767 1.03339 (173*2π)/5573 weeks
174-.34852 .87099 (174*2π)/5573 weeks
175-.46248 .11266 (175*2π)/5573 weeks
176-.5926 -.19753 (176*2π)/5573 weeks
177-.21881 -.79893 (177*2π)/5573 weeks
178.54306 -.81843 (178*2π)/5573 weeks
1791.05847 -.71568 (179*2π)/5573 weeks
1801.45931 -.2314 (180*2π)/5573 weeks
1811.58124 .62662 (181*2π)/5573 weeks
182.9688 1.07719 (182*2π)/5573 weeks
183.54516 1.22601 (183*2π)/5573 weeks
184-.05486 1.11129 (184*2π)/5573 weeks
185-.31975 .56584 (185*2π)/5573 weeks
186-.21396 .32003 (186*2π)/5573 weeks
187-.06696 -.15144 (187*2π)/5573 weeks
188.30387 -.20127 (188*2π)/5573 weeks
189.5013 -.12631 (189*2π)/5573 weeks
1901.01083 .07555 (190*2π)/5573 weeks
191.95546 .74991 (191*2π)/5573 weeks
192.31606 .87356 (192*2π)/5573 weeks
193.32566 .82403 (193*2π)/5573 weeks
194-.13994 .95036 (194*2π)/5573 weeks
195-.46551 .3851 (195*2π)/5573 weeks
196-.30122 .41505 (196*2π)/5573 weeks
197-.70634 .04626 (197*2π)/5573 weeks
198-.29865 -.94391 (198*2π)/5573 weeks
199.39603 -.60779 (199*2π)/5573 weeks
200.56325 -.49658 (200*2π)/5573 weeks
201.99093 -.08512 (201*2π)/5573 weeks
202.71742 .4242 (202*2π)/5573 weeks
203.43025 .19038 (203*2π)/5573 weeks
204.67557 .67797 (204*2π)/5573 weeks
205-.26297 .91186 (205*2π)/5573 weeks
206-.37 .14364 (206*2π)/5573 weeks
207-.50618 .20099 (207*2π)/5573 weeks
208-.81298 -.65716 (208*2π)/5573 weeks
209-.12742 -1.42233 (209*2π)/5573 weeks
210.9216 -1.39055 (210*2π)/5573 weeks
2111.65733 -.82329 (211*2π)/5573 weeks
2121.96206 .20248 (212*2π)/5573 weeks
2131.40499 1.12872 (213*2π)/5573 weeks
214.5948 1.37816 (214*2π)/5573 weeks
215-.15104 1.24245 (215*2π)/5573 weeks
216-.91848 .77124 (216*2π)/5573 weeks
217-.8453 -.52474 (217*2π)/5573 weeks
218-.15922 -.87803 (218*2π)/5573 weeks
219.44687 -.99348 (219*2π)/5573 weeks
2201.16432 -.55316 (220*2π)/5573 weeks
2211.05349 .0876 (221*2π)/5573 weeks
222.6325 .16641 (222*2π)/5573 weeks
223.72256 -.01269 (223*2π)/5572 weeks
224.89398 .1129 (224*2π)/5572 weeks
225.77228 .45071 (225*2π)/5572 weeks
226.5952 .46017 (226*2π)/5572 weeks
227.64743 .59436 (227*2π)/5572 weeks
228.19967 .89477 (228*2π)/5572 weeks
229-.2969 .45106 (229*2π)/5572 weeks
230-.39329 .10724 (230*2π)/5572 weeks
231-.41037 -.52863 (231*2π)/5572 weeks
232.5502 -.86202 (232*2π)/5572 weeks
233.89842 -.49028 (233*2π)/5572 weeks
2341.04393 -.1799 (234*2π)/5572 weeks
2351.14547 .26156 (235*2π)/5572 weeks
236.9685 .69598 (236*2π)/5572 weeks
237.58287 .8926 (237*2π)/5572 weeks
238.20685 .87296 (238*2π)/5572 weeks
239-.18468 .72122 (239*2π)/5572 weeks
240-.37088 .24797 (240*2π)/5572 weeks
241-.34964 .08716 (241*2π)/5572 weeks
242-.4898 -.31746 (242*2π)/5572 weeks
243.28429 -.6539 (243*2π)/5572 weeks
244.37099 -.45562 (244*2π)/5572 weeks
245.69578 -.62513 (245*2π)/5572 weeks
2461.03236 .0065 (246*2π)/5572 weeks
247.79468 .2428 (247*2π)/5572 weeks
248.74428 .42031 (248*2π)/5572 weeks
249.31281 .94419 (249*2π)/5572 weeks
250-.38477 .68079 (250*2π)/5572 weeks
251-.50283 .06 (251*2π)/5572 weeks
252-.62266 -.2815 (252*2π)/5572 weeks
253-.31822 -.9529 (253*2π)/5572 weeks
254.31964 -1.17214 (254*2π)/5572 weeks
255.85238 -1.04902 (255*2π)/5572 weeks
2561.32867 -.81166 (256*2π)/5572 weeks
2571.60163 -.2336 (257*2π)/5572 weeks
2581.48915 .4243 (258*2π)/5572 weeks
2591.40911 .83869 (259*2π)/5572 weeks
260.63856 1.55629 (260*2π)/5572 weeks
261-.39504 1.05334 (261*2π)/5572 weeks
262-.48235 .36941 (262*2π)/5572 weeks
263-.70562 .14334 (263*2π)/5572 weeks
264-.51567 -.71989 (264*2π)/5572 weeks
265.3036 -1.24608 (265*2π)/5572 weeks
2661.18624 -1.07241 (266*2π)/5572 weeks
2671.43671 -.16573 (267*2π)/5572 weeks
2681.38048 .42516 (268*2π)/5572 weeks
2691.1624 .89864 (269*2π)/5572 weeks
270.74283 1.13785 (270*2π)/5572 weeks
271-.08408 1.56363 (271*2π)/5572 weeks
272-1.14522 .81102 (272*2π)/5572 weeks
273-.9722 -.39331 (273*2π)/5572 weeks
274-.42303 -.74501 (274*2π)/5572 weeks
275-.0492 -.99109 (275*2π)/5572 weeks
276.62829 -.88386 (276*2π)/5572 weeks
277.87123 -.80319 (277*2π)/5572 weeks
2781.43619 -.454 (278*2π)/5572 weeks
2791.43619 .454 (279*2π)/5572 weeks
280.87123 .80319 (280*2π)/5572 weeks
281.62829 .88386 (281*2π)/5572 weeks
282-.0492 .99109 (282*2π)/5572 weeks
283-.42303 .74501 (283*2π)/5572 weeks
284-.9722 .39331 (284*2π)/5572 weeks
285-1.14522 -.81102 (285*2π)/5572 weeks
286-.08408 -1.56363 (286*2π)/5572 weeks
287.74283 -1.13785 (287*2π)/5572 weeks
2881.1624 -.89864 (288*2π)/5572 weeks
2891.38048 -.42516 (289*2π)/5572 weeks
2901.43671 .16573 (290*2π)/5572 weeks
2911.18624 1.07241 (291*2π)/5572 weeks
292.3036 1.24608 (292*2π)/5572 weeks
293-.51567 .71989 (293*2π)/5572 weeks
294-.70562 -.14334 (294*2π)/5572 weeks
295-.48235 -.36941 (295*2π)/5572 weeks
296-.39504 -1.05334 (296*2π)/5572 weeks
297.63856 -1.55629 (297*2π)/5572 weeks
2981.40911 -.83869 (298*2π)/5572 weeks
2991.48915 -.4243 (299*2π)/5572 weeks
3001.60163 .2336 (300*2π)/5572 weeks
3011.32867 .81166 (301*2π)/5572 weeks
302.85238 1.04902 (302*2π)/5572 weeks
303.31964 1.17214 (303*2π)/5572 weeks
304-.31822 .9529 (304*2π)/5572 weeks
305-.62266 .2815 (305*2π)/5572 weeks
306-.50283 -.06 (306*2π)/5572 weeks
307-.38477 -.68079 (307*2π)/5572 weeks
308.31281 -.94419 (308*2π)/5572 weeks
309.74428 -.42031 (309*2π)/5572 weeks
310.79468 -.2428 (310*2π)/5572 weeks
3111.03236 -.0065 (311*2π)/5572 weeks
312.69578 .62513 (312*2π)/5572 weeks
313.37099 .45562 (313*2π)/5572 weeks
314.28429 .6539 (314*2π)/5572 weeks
315-.4898 .31746 (315*2π)/5572 weeks
316-.34964 -.08716 (316*2π)/5572 weeks
317-.37088 -.24797 (317*2π)/5572 weeks
318-.18468 -.72122 (318*2π)/5572 weeks
319.20685 -.87296 (319*2π)/5572 weeks
320.58287 -.8926 (320*2π)/5572 weeks
321.9685 -.69598 (321*2π)/5572 weeks
3221.14547 -.26156 (322*2π)/5572 weeks
3231.04393 .1799 (323*2π)/5572 weeks
324.89842 .49028 (324*2π)/5572 weeks
325.5502 .86202 (325*2π)/5572 weeks
326-.41037 .52863 (326*2π)/5572 weeks
327-.39329 -.10724 (327*2π)/5572 weeks
328-.2969 -.45106 (328*2π)/5572 weeks
329.19967 -.89477 (329*2π)/5572 weeks
330.64743 -.59436 (330*2π)/5572 weeks
331.5952 -.46017 (331*2π)/5572 weeks
332.77228 -.45071 (332*2π)/5572 weeks
333.89398 -.1129 (333*2π)/5572 weeks
334.72256 .01269 (334*2π)/5572 weeks
335.6325 -.16641 (335*2π)/5572 weeks
3361.05349 -.0876 (336*2π)/5572 weeks
3371.16432 .55316 (337*2π)/5572 weeks
338.44687 .99348 (338*2π)/5572 weeks
339-.15922 .87803 (339*2π)/5572 weeks
340-.8453 .52474 (340*2π)/5572 weeks
341-.91848 -.77124 (341*2π)/5572 weeks
342-.15104 -1.24245 (342*2π)/5572 weeks
343.5948 -1.37816 (343*2π)/5572 weeks
3441.40499 -1.12872 (344*2π)/5572 weeks
3451.96206 -.20248 (345*2π)/5572 weeks
3461.65733 .82329 (346*2π)/5572 weeks
347.9216 1.39055 (347*2π)/5572 weeks
348-.12742 1.42233 (348*2π)/5572 weeks
349-.81298 .65716 (349*2π)/5572 weeks
350-.50618 -.20099 (350*2π)/5572 weeks
351-.37 -.14364 (351*2π)/5572 weeks
352-.26297 -.91186 (352*2π)/5572 weeks
353.67557 -.67797 (353*2π)/5572 weeks
354.43025 -.19038 (354*2π)/5572 weeks
355.71742 -.4242 (355*2π)/5572 weeks
356.99093 .08512 (356*2π)/5572 weeks
357.56325 .49658 (357*2π)/5572 weeks
358.39603 .60779 (358*2π)/5572 weeks
359-.29865 .94391 (359*2π)/5572 weeks
360-.70634 -.04626 (360*2π)/5572 weeks
361-.30122 -.41505 (361*2π)/5572 weeks
362-.46551 -.3851 (362*2π)/5572 weeks
363-.13994 -.95036 (363*2π)/5572 weeks
364.32566 -.82403 (364*2π)/5572 weeks
365.31606 -.87356 (365*2π)/5572 weeks
366.95546 -.74991 (366*2π)/5572 weeks
3671.01083 -.07555 (367*2π)/5572 weeks
368.5013 .12631 (368*2π)/5572 weeks
369.30387 .20127 (369*2π)/5572 weeks
370-.06696 .15144 (370*2π)/5572 weeks
371-.21396 -.32003 (371*2π)/5572 weeks
372-.31975 -.56584 (372*2π)/5571 weeks
373-.05486 -1.11129 (373*2π)/5571 weeks
374.54516 -1.22601 (374*2π)/5571 weeks
375.9688 -1.07719 (375*2π)/5571 weeks
3761.58124 -.62662 (376*2π)/5571 weeks
3771.45931 .2314 (377*2π)/5571 weeks
3781.05847 .71568 (378*2π)/5571 weeks
379.54306 .81843 (379*2π)/5571 weeks
380-.21881 .79893 (380*2π)/5571 weeks
381-.5926 .19753 (381*2π)/5571 weeks
382-.46248 -.11266 (382*2π)/5571 weeks
383-.34852 -.87099 (383*2π)/5571 weeks
384.20767 -1.03339 (384*2π)/5571 weeks
385.76267 -.85965 (385*2π)/5571 weeks
386.94097 -.51607 (386*2π)/5571 weeks
3871.12065 -.05863 (387*2π)/5571 weeks
388.74692 .46197 (388*2π)/5571 weeks
389.24305 .20684 (389*2π)/5571 weeks
390.18949 .2837 (390*2π)/5571 weeks
391-.37052 -.11154 (391*2π)/5571 weeks
392.06326 -.44359 (392*2π)/5571 weeks
393.26243 -.40061 (393*2π)/5571 weeks
394.27651 -.23538 (394*2π)/5571 weeks
395-.08237 -.29698 (395*2π)/5571 weeks
396.13631 -1.05331 (396*2π)/5571 weeks
397.9342 -.65043 (397*2π)/5571 weeks
398.62376 -.23131 (398*2π)/5571 weeks
399.40142 -.23953 (399*2π)/5571 weeks
400.62469 -.2852 (400*2π)/5571 weeks
401.72114 -.09185 (401*2π)/5571 weeks
402.55485 .22241 (402*2π)/5571 weeks
403-.14635 .3405 (403*2π)/5571 weeks
404-.54315 -.44308 (404*2π)/5571 weeks
405.13314 -.81292 (405*2π)/5571 weeks
406.17723 -.62898 (406*2π)/5571 weeks
407.48087 -.95145 (407*2π)/5571 weeks
408.71074 -.52424 (408*2π)/5571 weeks
409.7148 -.36411 (409*2π)/5571 weeks
410.77351 -.19999 (410*2π)/5571 weeks
411.15195 -.08661 (411*2π)/5571 weeks
412.26396 -.67921 (412*2π)/5571 weeks
4131.06301 -.41156 (413*2π)/5571 weeks
414.74691 .27274 (414*2π)/5571 weeks
415.29528 -.01409 (415*2π)/5571 weeks
416-.02091 -.06402 (416*2π)/5571 weeks
417-.09622 -.66304 (417*2π)/5571 weeks
418.78045 -.82537 (418*2π)/5571 weeks
419.91612 -.4123 (419*2π)/5571 weeks
420.70517 -.24982 (420*2π)/5571 weeks
421.79602 .15788 (421*2π)/5571 weeks
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