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Fourier Analysis of SIJ (ProShares UltraShort Industrials ETF)


SIJ (ProShares UltraShort Industrials ETF) appears to have interesting cyclic behaviour every 46 weeks (38.6397*sine), 50 weeks (26.4007*cosine), and 50 weeks (20.5275*sine).

SIJ (ProShares UltraShort Industrials ETF) has an average price of 259.74 (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 2/1/2007 to 7/17/2017 for SIJ (ProShares UltraShort Industrials ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0259.7435   0 
1107.9248 292.1898 (1*2π)/547547 weeks
2-68.65153 149.9661 (2*2π)/547274 weeks
3-76.72148 12.88635 (3*2π)/547182 weeks
412.24768 -27.82379 (4*2π)/547137 weeks
556.22245 15.40981 (5*2π)/547109 weeks
635.99088 62.74347 (6*2π)/54791 weeks
7-15.9887 63.04782 (7*2π)/54778 weeks
8-36.55693 9.70264 (8*2π)/54768 weeks
94.32299 -13.04271 (9*2π)/54761 weeks
1020.39134 6.20881 (10*2π)/54755 weeks
1126.40073 20.52746 (11*2π)/54750 weeks
125.65216 38.63974 (12*2π)/54746 weeks
13-10.84303 20.44702 (13*2π)/54742 weeks
14-4.77721 9.82663 (14*2π)/54739 weeks
151.92217 7.12206 (15*2π)/54736 weeks
163.81049 12.74519 (16*2π)/54734 weeks
17-2.00351 8.38314 (17*2π)/54732 weeks
184.71663 7.28997 (18*2π)/54730 weeks
193.58516 9.02881 (19*2π)/54729 weeks
206.6446 10.79184 (20*2π)/54727 weeks
213.2145 16.25569 (21*2π)/54726 weeks
22-5.06635 12.91946 (22*2π)/54725 weeks
23-3.32795 1.13672 (23*2π)/54724 weeks
247.81793 2.0264 (24*2π)/54723 weeks
2512.67194 15.20501 (25*2π)/54722 weeks
26-4.1129 24.4261 (26*2π)/54721 weeks
27-15.04906 9.93324 (27*2π)/54720 weeks
28-11.19087 -4.87088 (28*2π)/54720 weeks
296.46975 -11.8648 (29*2π)/54719 weeks
3020.13663 4.67883 (30*2π)/54718 weeks
318.71421 23.23861 (31*2π)/54718 weeks
32-12.14907 21.3659 (32*2π)/54717 weeks
33-18.95543 -.36132 (33*2π)/54717 weeks
34.41584 -13.19986 (34*2π)/54716 weeks
3513.75611 -.57915 (35*2π)/54716 weeks
369.12976 11.84341 (36*2π)/54715 weeks
37-2.05897 13.17679 (37*2π)/54715 weeks
38-5.79571 4.31554 (38*2π)/54714 weeks
39-.75838 .36629 (39*2π)/54714 weeks
402.88017 .78306 (40*2π)/54714 weeks
415.94534 5.81454 (41*2π)/54713 weeks
42-.38593 8.14102 (42*2π)/54713 weeks
43-1.18779 2.67886 (43*2π)/54713 weeks
441.69929 3.24602 (44*2π)/54712 weeks
453.10557 4.69996 (45*2π)/54712 weeks
46.84043 8.06484 (46*2π)/54712 weeks
47-4.01254 5.50411 (47*2π)/54712 weeks
48-3.67323 1.7466 (48*2π)/54711 weeks
49.30386 -1.14116 (49*2π)/54711 weeks
503.51347 1.22828 (50*2π)/54711 weeks
512.60461 5.3585 (51*2π)/54711 weeks
52-1.66092 4.59843 (52*2π)/54711 weeks
53-2.10674 .81506 (53*2π)/54710 weeks
541.05581 -1.86512 (54*2π)/54710 weeks
556.65763 -.19788 (55*2π)/54710 weeks
566.25067 8.05871 (56*2π)/54710 weeks
57-1.74497 7.55299 (57*2π)/54710 weeks
58-3.04759 1.84557 (58*2π)/5479 weeks
59.70779 -.46665 (59*2π)/5479 weeks
604.5669 1.40924 (60*2π)/5479 weeks
612.94627 7.07106 (61*2π)/5479 weeks
62-3.19528 5.26399 (62*2π)/5479 weeks
63-2.97149 .16473 (63*2π)/5479 weeks
641.73318 -2.66148 (64*2π)/5479 weeks
655.76538 1.68812 (65*2π)/5478 weeks
662.068 6.1727 (66*2π)/5478 weeks
67-.23451 3.29468 (67*2π)/5478 weeks
68-.58687 1.36006 (68*2π)/5478 weeks
693.94398 .35954 (69*2π)/5478 weeks
703.71594 6.79704 (70*2π)/5478 weeks
71-3.08404 6.70027 (71*2π)/5478 weeks
72-4.65414 .34541 (72*2π)/5478 weeks
73-.56661 -3.79319 (73*2π)/5477 weeks
745.49507 -.96979 (74*2π)/5477 weeks
753.91853 4.11864 (75*2π)/5477 weeks
761.84736 3.89122 (76*2π)/5477 weeks
77-1.21816 5.20885 (77*2π)/5477 weeks
78-3.3869 -.57271 (78*2π)/5477 weeks
792.77815 -2.82086 (79*2π)/5477 weeks
805.37517 1.08794 (80*2π)/5477 weeks
814.36175 5.57124 (81*2π)/5477 weeks
82-.89687 6.07081 (82*2π)/5477 weeks
83-2.80796 3.07072 (83*2π)/5477 weeks
84-2.97447 -1.58765 (84*2π)/5477 weeks
853.31246 -3.52683 (85*2π)/5476 weeks
866.11807 2.04689 (86*2π)/5476 weeks
872.66903 5.63559 (87*2π)/5476 weeks
88-1.40419 4.01736 (88*2π)/5476 weeks
89-1.24421 .17703 (89*2π)/5476 weeks
902.11785 -.40806 (90*2π)/5476 weeks
913.31973 2.72242 (91*2π)/5476 weeks
92.42763 4.67412 (92*2π)/5476 weeks
93-2.82335 1.67832 (93*2π)/5476 weeks
94.8473 -2.05945 (94*2π)/5476 weeks
953.6129 1.48049 (95*2π)/5476 weeks
961.28859 3.67548 (96*2π)/5476 weeks
97-1.51537 2.03171 (97*2π)/5476 weeks
98-.81548 -1.34389 (98*2π)/5476 weeks
992.97007 -2.22775 (99*2π)/5476 weeks
1005.08002 1.3924 (100*2π)/5475 weeks
1012.79428 5.28366 (101*2π)/5475 weeks
102-2.20684 4.18524 (102*2π)/5475 weeks
103-2.46906 -1.33197 (103*2π)/5475 weeks
1042.14108 -3.46856 (104*2π)/5475 weeks
1056.49982 -.31832 (105*2π)/5475 weeks
1065.00664 4.9885 (106*2π)/5475 weeks
107.18726 6.49059 (107*2π)/5475 weeks
108-3.70546 2.5026 (108*2π)/5475 weeks
109-1.13915 -2.75013 (109*2π)/5475 weeks
1104.15549 -2.369 (110*2π)/5475 weeks
1115.51363 2.4975 (111*2π)/5475 weeks
1122.25444 5.13209 (112*2π)/5475 weeks
113-.99099 4.44773 (113*2π)/5475 weeks
114-2.94534 .77214 (114*2π)/5475 weeks
115.51148 -2.10357 (115*2π)/5475 weeks
1163.39497 -.33649 (116*2π)/5475 weeks
1173.17183 1.53739 (117*2π)/5475 weeks
1181.97307 3.07016 (118*2π)/5475 weeks
119-.06546 2.59621 (119*2π)/5475 weeks
120-.80409 .70449 (120*2π)/5475 weeks
1211.28885 -1.44915 (121*2π)/5475 weeks
1224.24132 .15488 (122*2π)/5474 weeks
1233.41272 3.80906 (123*2π)/5474 weeks
124.23764 3.63801 (124*2π)/5474 weeks
125-.75026 1.51926 (125*2π)/5474 weeks
126.49093 .44918 (126*2π)/5474 weeks
1271.0588 1.02502 (127*2π)/5474 weeks
1281.06477 .62568 (128*2π)/5474 weeks
1291.76291 1.03629 (129*2π)/5474 weeks
1301.22199 1.83591 (130*2π)/5474 weeks
131.44104 .87221 (131*2π)/5474 weeks
1321.44373 -.2516 (132*2π)/5474 weeks
1332.7368 .82298 (133*2π)/5474 weeks
1342.38593 2.16292 (134*2π)/5474 weeks
1351.80915 3.21822 (135*2π)/5474 weeks
136-.26464 2.76657 (136*2π)/5474 weeks
137-.02858 1.0411 (137*2π)/5474 weeks
138-.01737 1.15319 (138*2π)/5474 weeks
139.01692 -.05886 (139*2π)/5474 weeks
1401.33367 -.3388 (140*2π)/5474 weeks
1413.20262 .44114 (141*2π)/5474 weeks
1422.26199 3.73664 (142*2π)/5474 weeks
143-1.41148 2.52356 (143*2π)/5474 weeks
144-.50841 -1.067 (144*2π)/5474 weeks
1452.36705 -.9163 (145*2π)/5474 weeks
1463.48111 1.51333 (146*2π)/5474 weeks
1471.25699 3.77957 (147*2π)/5474 weeks
148-1.18784 2.04026 (148*2π)/5474 weeks
149-1.03483 -.26599 (149*2π)/5474 weeks
1501.5964 -1.64261 (150*2π)/5474 weeks
1513.05663 .93638 (151*2π)/5474 weeks
1521.70649 1.92657 (152*2π)/5474 weeks
153.77651 1.81279 (153*2π)/5474 weeks
154.41434 1.0588 (154*2π)/5474 weeks
155.75966 .67185 (155*2π)/5474 weeks
156.95166 .19932 (156*2π)/5474 weeks
1572.42342 .33563 (157*2π)/5473 weeks
1581.80525 2.36861 (158*2π)/5473 weeks
159.62323 1.54394 (159*2π)/5473 weeks
160.72752 1.45251 (160*2π)/5473 weeks
161-.02096 1.11254 (161*2π)/5473 weeks
162.32944 .00615 (162*2π)/5473 weeks
1631.71165 -.4658 (163*2π)/5473 weeks
1642.52395 1.36833 (164*2π)/5473 weeks
1651.70647 2.62989 (165*2π)/5473 weeks
166-.67243 2.6942 (166*2π)/5473 weeks
167-1.42933 .30492 (167*2π)/5473 weeks
168.16219 -1.29101 (168*2π)/5473 weeks
1692.24648 -.56595 (169*2π)/5473 weeks
1702.31744 1.20171 (170*2π)/5473 weeks
1711.12423 2.14523 (171*2π)/5473 weeks
172-.14335 1.34633 (172*2π)/5473 weeks
173-.40747 .06955 (173*2π)/5473 weeks
174.39304 -1.27199 (174*2π)/5473 weeks
1752.66693 -1.19295 (175*2π)/5473 weeks
1763.7571 1.08292 (176*2π)/5473 weeks
1772.38253 3.44721 (177*2π)/5473 weeks
178-.86753 3.09128 (178*2π)/5473 weeks
179-1.70313 .09094 (179*2π)/5473 weeks
180.56441 -1.79722 (180*2π)/5473 weeks
1813.14925 -.49049 (181*2π)/5473 weeks
1822.60556 2.05045 (182*2π)/5473 weeks
183.77306 2.78708 (183*2π)/5473 weeks
184-.94778 1.03719 (184*2π)/5473 weeks
185.27023 -.39879 (185*2π)/5473 weeks
1861.22847 -.55825 (186*2π)/5473 weeks
1872.35803 .95058 (187*2π)/5473 weeks
188.75351 2.17973 (188*2π)/5473 weeks
189-.38117 .89842 (189*2π)/5473 weeks
190-.17978 -.23786 (190*2π)/5473 weeks
191.91626 -.87781 (191*2π)/5473 weeks
1921.39487 .04167 (192*2π)/5473 weeks
1931.69918 -.69639 (193*2π)/5473 weeks
1943.21916 1.25958 (194*2π)/5473 weeks
195.85472 1.86707 (195*2π)/5473 weeks
196.83714 1.22565 (196*2π)/5473 weeks
197.35579 .98587 (197*2π)/5473 weeks
198.86505 .57042 (198*2π)/5473 weeks
199.1973 .92768 (199*2π)/5473 weeks
200.91713 -.42971 (200*2π)/5473 weeks
2011.31338 1.13867 (201*2π)/5473 weeks
202.57816 .44905 (202*2π)/5473 weeks
203.72131 1.00979 (203*2π)/5473 weeks
204-.49576 -.3973 (204*2π)/5473 weeks
2051.60194 -1.40137 (205*2π)/5473 weeks
2062.92854 .61254 (206*2π)/5473 weeks
2071.49072 2.20242 (207*2π)/5473 weeks
208-.73765 1.44142 (208*2π)/5473 weeks
209-.32999 -1.17387 (209*2π)/5473 weeks
2102.14525 -.88972 (210*2π)/5473 weeks
2112.63173 .59114 (211*2π)/5473 weeks
2121.96351 2.46694 (212*2π)/5473 weeks
213-1.19575 2.06198 (213*2π)/5473 weeks
214-1.00365 -1.09971 (214*2π)/5473 weeks
2151.673 -1.74245 (215*2π)/5473 weeks
2163.107 .41646 (216*2π)/5473 weeks
2171.27611 2.15204 (217*2π)/5473 weeks
218-.24904 .55695 (218*2π)/5473 weeks
2191.1203 -.5857 (219*2π)/5472 weeks
2202.05891 .46082 (220*2π)/5472 weeks
2211.83393 1.36111 (221*2π)/5472 weeks
222.58744 2.51768 (222*2π)/5472 weeks
223-1.6978 1.05028 (223*2π)/5472 weeks
224-.4846 -1.59328 (224*2π)/5472 weeks
2251.70091 -1.49576 (225*2π)/5472 weeks
2263.12739 .66656 (226*2π)/5472 weeks
227.67885 2.64383 (227*2π)/5472 weeks
228-.77824 .94514 (228*2π)/5472 weeks
229-.88306 -.61778 (229*2π)/5472 weeks
230.74548 -2.00828 (230*2π)/5472 weeks
2312.73953 -.68399 (231*2π)/5472 weeks
2322.27549 1.45763 (232*2π)/5472 weeks
233.33369 2.24908 (233*2π)/5472 weeks
234-1.64713 .41619 (234*2π)/5472 weeks
235-.37236 -2.00289 (235*2π)/5472 weeks
2361.91014 -1.85523 (236*2π)/5472 weeks
2372.96915 -.50795 (237*2π)/5472 weeks
2382.33345 1.94428 (238*2π)/5472 weeks
239.13172 1.14397 (239*2π)/5472 weeks
240.21256 .38437 (240*2π)/5472 weeks
241.50577 -.61156 (241*2π)/5472 weeks
2421.21014 .0516 (242*2π)/5472 weeks
243.86085 -.16211 (243*2π)/5472 weeks
2441.59961 .01922 (244*2π)/5472 weeks
2451.00374 .89067 (245*2π)/5472 weeks
246.24498 .12357 (246*2π)/5472 weeks
247.04559 -.23231 (247*2π)/5472 weeks
248.97586 -1.46916 (248*2π)/5472 weeks
2492.65991 -.78856 (249*2π)/5472 weeks
2502.37827 1.04767 (250*2π)/5472 weeks
2511.28428 1.81772 (251*2π)/5472 weeks
252-.43965 1.71653 (252*2π)/5472 weeks
253-1.75563 -.30191 (253*2π)/5472 weeks
254-.53619 -2.72739 (254*2π)/5472 weeks
2553.18774 -3.08409 (255*2π)/5472 weeks
2564.5322 .91871 (256*2π)/5472 weeks
2571.65155 2.88005 (257*2π)/5472 weeks
258-.72485 2.15403 (258*2π)/5472 weeks
259-1.96483 -.9864 (259*2π)/5472 weeks
2601.01769 -3.20518 (260*2π)/5472 weeks
2614.08894 -1.02312 (261*2π)/5472 weeks
2622.33952 2.40098 (262*2π)/5472 weeks
263-.40502 1.7967 (263*2π)/5472 weeks
264-1.14904 -.35934 (264*2π)/5472 weeks
265.26595 -2.11119 (265*2π)/5472 weeks
2662.60189 -2.25847 (266*2π)/5472 weeks
2674.03762 .58851 (267*2π)/5472 weeks
2681.00384 2.89344 (268*2π)/5472 weeks
269-1.17138 .54988 (269*2π)/5472 weeks
270.22037 -1.34155 (270*2π)/5472 weeks
2711.63805 -1.2316 (271*2π)/5472 weeks
2721.63026 -.41556 (272*2π)/5472 weeks
2732.01407 -.51789 (273*2π)/5472 weeks
2742.01407 .51789 (274*2π)/5472 weeks
2751.63026 .41556 (275*2π)/5472 weeks
2761.63805 1.2316 (276*2π)/5472 weeks
277.22037 1.34155 (277*2π)/5472 weeks
278-1.17138 -.54988 (278*2π)/5472 weeks
2791.00384 -2.89344 (279*2π)/5472 weeks
2804.03762 -.58851 (280*2π)/5472 weeks
2812.60189 2.25847 (281*2π)/5472 weeks
282.26595 2.11119 (282*2π)/5472 weeks
283-1.14904 .35934 (283*2π)/5472 weeks
284-.40502 -1.7967 (284*2π)/5472 weeks
2852.33952 -2.40098 (285*2π)/5472 weeks
2864.08894 1.02312 (286*2π)/5472 weeks
2871.01769 3.20518 (287*2π)/5472 weeks
288-1.96483 .9864 (288*2π)/5472 weeks
289-.72485 -2.15403 (289*2π)/5472 weeks
2901.65155 -2.88005 (290*2π)/5472 weeks
2914.5322 -.91871 (291*2π)/5472 weeks
2923.18774 3.08409 (292*2π)/5472 weeks
293-.53619 2.72739 (293*2π)/5472 weeks
294-1.75563 .30191 (294*2π)/5472 weeks
295-.43965 -1.71653 (295*2π)/5472 weeks
2961.28428 -1.81772 (296*2π)/5472 weeks
2972.37827 -1.04767 (297*2π)/5472 weeks
2982.65991 .78856 (298*2π)/5472 weeks
299.97586 1.46916 (299*2π)/5472 weeks
300.04559 .23231 (300*2π)/5472 weeks
301.24498 -.12357 (301*2π)/5472 weeks
3021.00374 -.89067 (302*2π)/5472 weeks
3031.59961 -.01922 (303*2π)/5472 weeks
304.86085 .16211 (304*2π)/5472 weeks
3051.21014 -.0516 (305*2π)/5472 weeks
306.50577 .61156 (306*2π)/5472 weeks
307.21256 -.38437 (307*2π)/5472 weeks
308.13172 -1.14397 (308*2π)/5472 weeks
3092.33345 -1.94428 (309*2π)/5472 weeks
3102.96915 .50795 (310*2π)/5472 weeks
3111.91014 1.85523 (311*2π)/5472 weeks
312-.37236 2.00289 (312*2π)/5472 weeks
313-1.64713 -.41619 (313*2π)/5472 weeks
314.33369 -2.24908 (314*2π)/5472 weeks
3152.27549 -1.45763 (315*2π)/5472 weeks
3162.73953 .68399 (316*2π)/5472 weeks
317.74548 2.00828 (317*2π)/5472 weeks
318-.88306 .61778 (318*2π)/5472 weeks
319-.77824 -.94514 (319*2π)/5472 weeks
320.67885 -2.64383 (320*2π)/5472 weeks
3213.12739 -.66656 (321*2π)/5472 weeks
3221.70091 1.49576 (322*2π)/5472 weeks
323-.4846 1.59328 (323*2π)/5472 weeks
324-1.6978 -1.05028 (324*2π)/5472 weeks
325.58744 -2.51768 (325*2π)/5472 weeks
3261.83393 -1.36111 (326*2π)/5472 weeks
3272.05891 -.46082 (327*2π)/5472 weeks
3281.1203 .5857 (328*2π)/5472 weeks
329-.24904 -.55695 (329*2π)/5472 weeks
3301.27611 -2.15204 (330*2π)/5472 weeks
3313.107 -.41646 (331*2π)/5472 weeks
3321.673 1.74245 (332*2π)/5472 weeks
333-1.00365 1.09971 (333*2π)/5472 weeks
334-1.19575 -2.06198 (334*2π)/5472 weeks
3351.96351 -2.46694 (335*2π)/5472 weeks
3362.63173 -.59114 (336*2π)/5472 weeks
3372.14525 .88972 (337*2π)/5472 weeks
338-.32999 1.17387 (338*2π)/5472 weeks
339-.73765 -1.44142 (339*2π)/5472 weeks
3401.49072 -2.20242 (340*2π)/5472 weeks
3412.92854 -.61254 (341*2π)/5472 weeks
3421.60194 1.40137 (342*2π)/5472 weeks
343-.49576 .3973 (343*2π)/5472 weeks
344.72131 -1.00979 (344*2π)/5472 weeks
345.57816 -.44905 (345*2π)/5472 weeks
3461.31338 -1.13867 (346*2π)/5472 weeks
347.91713 .42971 (347*2π)/5472 weeks
348.1973 -.92768 (348*2π)/5472 weeks
349.86505 -.57042 (349*2π)/5472 weeks
350.35579 -.98587 (350*2π)/5472 weeks
351.83714 -1.22565 (351*2π)/5472 weeks
352.85472 -1.86707 (352*2π)/5472 weeks
3533.21916 -1.25958 (353*2π)/5472 weeks
3541.69918 .69639 (354*2π)/5472 weeks
3551.39487 -.04167 (355*2π)/5472 weeks
356.91626 .87781 (356*2π)/5472 weeks
357-.17978 .23786 (357*2π)/5472 weeks
358-.38117 -.89842 (358*2π)/5472 weeks
359.75351 -2.17973 (359*2π)/5472 weeks
3602.35803 -.95058 (360*2π)/5472 weeks
3611.22847 .55825 (361*2π)/5472 weeks
362.27023 .39879 (362*2π)/5472 weeks
363-.94778 -1.03719 (363*2π)/5472 weeks
364.77306 -2.78708 (364*2π)/5472 weeks
3652.60556 -2.05045 (365*2π)/5471 weeks
3663.14925 .49049 (366*2π)/5471 weeks
367.56441 1.79722 (367*2π)/5471 weeks
368-1.70313 -.09094 (368*2π)/5471 weeks
369-.86753 -3.09128 (369*2π)/5471 weeks
3702.38253 -3.44721 (370*2π)/5471 weeks
3713.7571 -1.08292 (371*2π)/5471 weeks
3722.66693 1.19295 (372*2π)/5471 weeks
373.39304 1.27199 (373*2π)/5471 weeks
374-.40747 -.06955 (374*2π)/5471 weeks
375-.14335 -1.34633 (375*2π)/5471 weeks
3761.12423 -2.14523 (376*2π)/5471 weeks
3772.31744 -1.20171 (377*2π)/5471 weeks
3782.24648 .56595 (378*2π)/5471 weeks
379.16219 1.29101 (379*2π)/5471 weeks
380-1.42933 -.30492 (380*2π)/5471 weeks
381-.67243 -2.6942 (381*2π)/5471 weeks
3821.70647 -2.62989 (382*2π)/5471 weeks
3832.52395 -1.36833 (383*2π)/5471 weeks
3841.71165 .4658 (384*2π)/5471 weeks
385.32944 -.00615 (385*2π)/5471 weeks
386-.02096 -1.11254 (386*2π)/5471 weeks
387.72752 -1.45251 (387*2π)/5471 weeks
388.62323 -1.54394 (388*2π)/5471 weeks
3891.80525 -2.36861 (389*2π)/5471 weeks
3902.42342 -.33563 (390*2π)/5471 weeks
391.95166 -.19932 (391*2π)/5471 weeks
392.75966 -.67185 (392*2π)/5471 weeks
393.41434 -1.0588 (393*2π)/5471 weeks
394.77651 -1.81279 (394*2π)/5471 weeks
3951.70649 -1.92657 (395*2π)/5471 weeks
3963.05663 -.93638 (396*2π)/5471 weeks
3971.5964 1.64261 (397*2π)/5471 weeks
398-1.03483 .26599 (398*2π)/5471 weeks
399-1.18784 -2.04026 (399*2π)/5471 weeks
4001.25699 -3.77957 (400*2π)/5471 weeks
4013.48111 -1.51333 (401*2π)/5471 weeks
4022.36705 .9163 (402*2π)/5471 weeks
403-.50841 1.067 (403*2π)/5471 weeks
404-1.41148 -2.52356 (404*2π)/5471 weeks
4052.26199 -3.73664 (405*2π)/5471 weeks
4063.20262 -.44114 (406*2π)/5471 weeks
4071.33367 .3388 (407*2π)/5471 weeks
408.01692 .05886 (408*2π)/5471 weeks
409-.01737 -1.15319 (409*2π)/5471 weeks
410-.02858 -1.0411 (410*2π)/5471 weeks
411-.26464 -2.76657 (411*2π)/5471 weeks
4121.80915 -3.21822 (412*2π)/5471 weeks
4132.38593 -2.16292 (413*2π)/5471 weeks
4142.7368 -.82298 (414*2π)/5471 weeks
4151.44373 .2516 (415*2π)/5471 weeks
416.44104 -.87221 (416*2π)/5471 weeks
4171.22199 -1.83591 (417*2π)/5471 weeks
4181.76291 -1.03629 (418*2π)/5471 weeks
4191.06477 -.62568 (419*2π)/5471 weeks
4201.0588 -1.02502 (420*2π)/5471 weeks
421.49093 -.44918 (421*2π)/5471 weeks
422-.75026 -1.51926 (422*2π)/5471 weeks
423.23764 -3.63801 (423*2π)/5471 weeks
4243.41272 -3.80906 (424*2π)/5471 weeks
4254.24132 -.15488 (425*2π)/5471 weeks
4261.28885 1.44915 (426*2π)/5471 weeks
427-.80409 -.70449 (427*2π)/5471 weeks
428-.06546 -2.59621 (428*2π)/5471 weeks
4291.97307 -3.07016 (429*2π)/5471 weeks
4303.17183 -1.53739 (430*2π)/5471 weeks
4313.39497 .33649 (431*2π)/5471 weeks
432.51148 2.10357 (432*2π)/5471 weeks
433-2.94534 -.77214 (433*2π)/5471 weeks
434-.99099 -4.44773 (434*2π)/5471 weeks
4352.25444 -5.13209 (435*2π)/5471 weeks
4365.51363 -2.4975 (436*2π)/5471 weeks
4374.15549 2.369 (437*2π)/5471 weeks
438-1.13915 2.75013 (438*2π)/5471 weeks
439-3.70546 -2.5026 (439*2π)/5471 weeks
440.18726 -6.49059 (440*2π)/5471 weeks
4415.00664 -4.9885 (441*2π)/5471 weeks
4426.49982 .31832 (442*2π)/5471 weeks
4432.14108 3.46856 (443*2π)/5471 weeks
444-2.46906 1.33197 (444*2π)/5471 weeks
445-2.20684 -4.18524 (445*2π)/5471 weeks
4462.79428 -5.28366 (446*2π)/5471 weeks
4475.08002 -1.3924 (447*2π)/5471 weeks
4482.97007 2.22775 (448*2π)/5471 weeks
449-.81548 1.34389 (449*2π)/5471 weeks
450-1.51537 -2.03171 (450*2π)/5471 weeks
4511.28859 -3.67548 (451*2π)/5471 weeks
4523.6129 -1.48049 (452*2π)/5471 weeks
453.8473 2.05945 (453*2π)/5471 weeks
454-2.82335 -1.67832 (454*2π)/5471 weeks
455.42763 -4.67412 (455*2π)/5471 weeks
4563.31973 -2.72242 (456*2π)/5471 weeks
4572.11785 .40806 (457*2π)/5471 weeks
458-1.24421 -.17703 (458*2π)/5471 weeks
459-1.40419 -4.01736 (459*2π)/5471 weeks
4602.66903 -5.63559 (460*2π)/5471 weeks
4616.11807 -2.04689 (461*2π)/5471 weeks
4623.31246 3.52683 (462*2π)/5471 weeks
463-2.97447 1.58765 (463*2π)/5471 weeks
464-2.80796 -3.07072 (464*2π)/5471 weeks
465-.89687 -6.07081 (465*2π)/5471 weeks
4664.36175 -5.57124 (466*2π)/5471 weeks
4675.37517 -1.08794 (467*2π)/5471 weeks
4682.77815 2.82086 (468*2π)/5471 weeks
469-3.3869 .57271 (469*2π)/5471 weeks
470-1.21816 -5.20885 (470*2π)/5471 weeks
4711.84736 -3.89122 (471*2π)/5471 weeks
4723.91853 -4.11864 (472*2π)/5471 weeks
4735.49507 .96979 (473*2π)/5471 weeks
474-.56661 3.79319 (474*2π)/5471 weeks
475-4.65414 -.34541 (475*2π)/5471 weeks
476-3.08404 -6.70027 (476*2π)/5471 weeks
4773.71594 -6.79704 (477*2π)/5471 weeks
4783.94398 -.35954 (478*2π)/5471 weeks
479-.58687 -1.36006 (479*2π)/5471 weeks
480-.23451 -3.29468 (480*2π)/5471 weeks
4812.068 -6.1727 (481*2π)/5471 weeks
4825.76538 -1.68812 (482*2π)/5471 weeks
4831.73318 2.66148 (483*2π)/5471 weeks
484-2.97149 -.16473 (484*2π)/5471 weeks
485-3.19528 -5.26399 (485*2π)/5471 weeks
4862.94627 -7.07106 (486*2π)/5471 weeks
4874.5669 -1.40924 (487*2π)/5471 weeks
488.70779 .46665 (488*2π)/5471 weeks
489-3.04759 -1.84557 (489*2π)/5471 weeks
490-1.74497 -7.55299 (490*2π)/5471 weeks
4916.25067 -8.05871 (491*2π)/5471 weeks
4926.65763 .19788 (492*2π)/5471 weeks
4931.05581 1.86512 (493*2π)/5471 weeks
494-2.10674 -.81506 (494*2π)/5471 weeks
495-1.66092 -4.59843 (495*2π)/5471 weeks
4962.60461 -5.3585 (496*2π)/5471 weeks
4973.51347 -1.22828 (497*2π)/5471 weeks
498.30386 1.14116 (498*2π)/5471 weeks
499-3.67323 -1.7466 (499*2π)/5471 weeks
500-4.01254 -5.50411 (500*2π)/5471 weeks
501.84043 -8.06484 (501*2π)/5471 weeks
5023.10557 -4.69996 (502*2π)/5471 weeks
5031.69929 -3.24602 (503*2π)/5471 weeks
504-1.18779 -2.67886 (504*2π)/5471 weeks
505-.38593 -8.14102 (505*2π)/5471 weeks
5065.94534 -5.81454 (506*2π)/5471 weeks
5072.88017 -.78306 (507*2π)/5471 weeks
508-.75838 -.36629 (508*2π)/5471 weeks
509-5.79571 -4.31554 (509*2π)/5471 weeks
510-2.05897 -13.17679 (510*2π)/5471 weeks
5119.12976 -11.84341 (511*2π)/5471 weeks
51213.75611 .57915 (512*2π)/5471 weeks
513.41584 13.19986 (513*2π)/5471 weeks
514-18.95543 .36132 (514*2π)/5471 weeks
515-12.14907 -21.3659 (515*2π)/5471 weeks
5168.71421 -23.23861 (516*2π)/5471 weeks
51720.13663 -4.67883 (517*2π)/5471 weeks
5186.46975 11.8648 (518*2π)/5471 weeks
519-11.19087 4.87088 (519*2π)/5471 weeks
520-15.04906 -9.93324 (520*2π)/5471 weeks
521-4.1129 -24.4261 (521*2π)/5471 weeks
52212.67194 -15.20501 (522*2π)/5471 weeks
5237.81793 -2.0264 (523*2π)/5471 weeks
524-3.32795 -1.13672 (524*2π)/5471 weeks
525-5.06635 -12.91946 (525*2π)/5471 weeks
5263.2145 -16.25569 (526*2π)/5471 weeks
5276.6446 -10.79184 (527*2π)/5471 weeks
5283.58516 -9.02881 (528*2π)/5471 weeks
5294.71663 -7.28997 (529*2π)/5471 weeks
530-2.00351 -8.38314 (530*2π)/5471 weeks
5313.81049 -12.74519 (531*2π)/5471 weeks
5321.92217 -7.12206 (532*2π)/5471 weeks
533-4.77721 -9.82663 (533*2π)/5471 weeks
534-10.84303 -20.44702 (534*2π)/5471 weeks
5355.65216 -38.63974 (535*2π)/5471 weeks
53626.40073 -20.52746 (536*2π)/5471 weeks
53720.39134 -6.20881 (537*2π)/5471 weeks
5384.32299 13.04271 (538*2π)/5471 weeks
539-36.55693 -9.70264 (539*2π)/5471 weeks
540-15.9887 -63.04782 (540*2π)/5471 weeks
54135.99088 -62.74347 (541*2π)/5471 weeks
54256.22245 -15.40981 (542*2π)/5471 weeks
54312.24768 27.82379 (543*2π)/5471 weeks
544-76.72148 -12.88635 (544*2π)/5471 weeks
545-68.65153 -149.9661 (545*2π)/5471 weeks



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