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Fourier Analysis of SSG (ProShares UltraShort Semiconductors ETF)


SSG (ProShares UltraShort Semiconductors ETF) appears to have interesting cyclic behaviour every 46 weeks (74.8661*sine), 50 weeks (63.3171*cosine), and 55 weeks (41.0915*cosine).

SSG (ProShares UltraShort Semiconductors ETF) has an average price of 359.97 (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 SSG (ProShares UltraShort Semiconductors ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0359.9681   0 
1137.253 404.2247 (1*2π)/547547 weeks
2-104.4508 233.8659 (2*2π)/547274 weeks
3-130.1916 7.00257 (3*2π)/547182 weeks
4-2.71969 -58.97752 (4*2π)/547137 weeks
593.57966 -2.67029 (5*2π)/547109 weeks
666.18066 92.71312 (6*2π)/54791 weeks
7-22.04225 98.11638 (7*2π)/54778 weeks
8-70.17612 16.43098 (8*2π)/54768 weeks
9-1.03206 -38.77035 (9*2π)/54761 weeks
1041.09148 -13.00423 (10*2π)/54755 weeks
1163.31706 30.34149 (11*2π)/54750 weeks
1219.33572 74.86606 (12*2π)/54746 weeks
13-30.92513 48.92043 (13*2π)/54742 weeks
14-25.21633 9.22769 (14*2π)/54739 weeks
15-4.8807 .14558 (15*2π)/54736 weeks
169.34469 5.94661 (16*2π)/54734 weeks
177.71715 11.72821 (17*2π)/54732 weeks
185.86975 19.19476 (18*2π)/54730 weeks
19-5.07153 12.87473 (19*2π)/54729 weeks
204.06614 5.26991 (20*2π)/54727 weeks
219.57615 12.0605 (21*2π)/54726 weeks
226.4533 18.53571 (22*2π)/54725 weeks
231.66622 15.5772 (23*2π)/54724 weeks
24-5.79832 17.21012 (24*2π)/54723 weeks
25-3.63762 5.69777 (25*2π)/54722 weeks
26.94243 13.07881 (26*2π)/54721 weeks
27-1.34149 8.97563 (27*2π)/54720 weeks
28-6.59235 8.32458 (28*2π)/54720 weeks
29-1.54118 -4.03937 (29*2π)/54719 weeks
3012.84273 -.65903 (30*2π)/54718 weeks
3114.16071 15.63032 (31*2π)/54718 weeks
32.33525 25.26484 (32*2π)/54717 weeks
33-17.7904 14.46895 (33*2π)/54717 weeks
34-9.55584 -7.38715 (34*2π)/54716 weeks
356.80311 -4.0678 (35*2π)/54716 weeks
369.59139 4.54248 (36*2π)/54715 weeks
377.31735 11.96154 (37*2π)/54715 weeks
38-.76811 13.97552 (38*2π)/54714 weeks
39-8.10463 8.87736 (39*2π)/54714 weeks
40-5.42776 -3.10553 (40*2π)/54714 weeks
417.51841 .15269 (41*2π)/54713 weeks
425.41415 7.4081 (42*2π)/54713 weeks
433.05144 6.9064 (43*2π)/54713 weeks
44.01018 7.74645 (44*2π)/54712 weeks
451.75154 5.88963 (45*2π)/54712 weeks
46.69083 9.94343 (46*2π)/54712 weeks
47-5.89054 6.14994 (47*2π)/54712 weeks
48-3.39385 3.38365 (48*2π)/54711 weeks
49-1.89055 .23335 (49*2π)/54711 weeks
501.88327 .74215 (50*2π)/54711 weeks
51.90277 3.66791 (51*2π)/54711 weeks
52-1.08633 1.50283 (52*2π)/54711 weeks
531.54333 .21802 (53*2π)/54710 weeks
541.76781 .58245 (54*2π)/54710 weeks
555.92026 -.13471 (55*2π)/54710 weeks
566.55146 8.56953 (56*2π)/54710 weeks
57-1.40813 6.20022 (57*2π)/54710 weeks
58-1.63574 2.18945 (58*2π)/5479 weeks
592.68009 -1.03223 (59*2π)/5479 weeks
606.47649 4.10005 (60*2π)/5479 weeks
611.72097 9.01664 (61*2π)/5479 weeks
62-5.72036 4.26934 (62*2π)/5479 weeks
63-2.86777 -3.75725 (63*2π)/5479 weeks
646.68588 -6.05029 (64*2π)/5479 weeks
6511.99501 3.82593 (65*2π)/5478 weeks
664.95586 11.08905 (66*2π)/5478 weeks
67-.81573 8.50238 (67*2π)/5478 weeks
68-4.38247 3.12791 (68*2π)/5478 weeks
692.96815 -3.19279 (69*2π)/5478 weeks
708.88978 4.47149 (70*2π)/5478 weeks
712.5482 12.12034 (71*2π)/5478 weeks
72-7.23696 7.5593 (72*2π)/5478 weeks
73-6.08962 -2.91298 (73*2π)/5477 weeks
742.98217 -4.19633 (74*2π)/5477 weeks
756.31071 .67301 (75*2π)/5477 weeks
766.69055 3.91544 (76*2π)/5477 weeks
771.65932 9.20081 (77*2π)/5477 weeks
78-4.49775 3.4904 (78*2π)/5477 weeks
79-.07229 -2.18068 (79*2π)/5477 weeks
805.32735 -1.35869 (80*2π)/5477 weeks
818.25445 5.52832 (81*2π)/5477 weeks
821.39559 9.26235 (82*2π)/5477 weeks
83-3.25874 8.24448 (83*2π)/5477 weeks
84-8.26481 .32546 (84*2π)/5477 weeks
85-.48364 -6.34312 (85*2π)/5476 weeks
868.15178 -4.3038 (86*2π)/5476 weeks
8710.37812 6.27879 (87*2π)/5476 weeks
881.20825 10.78672 (88*2π)/5476 weeks
89-5.9704 5.27486 (89*2π)/5476 weeks
90-3.26 -2.8176 (90*2π)/5476 weeks
913.97074 -2.90012 (91*2π)/5476 weeks
926.75466 3.58973 (92*2π)/5476 weeks
93.98978 7.03971 (93*2π)/5476 weeks
94-1.14643 3.49724 (94*2π)/5476 weeks
95-1.81547 2.2673 (95*2π)/5476 weeks
96-.80326 .34691 (96*2π)/5476 weeks
97-1.13224 -1.09456 (97*2π)/5476 weeks
982.91843 -3.86419 (98*2π)/5476 weeks
997.25495 -.11156 (99*2π)/5476 weeks
1005.1775 5.48004 (100*2π)/5475 weeks
101.60787 6.49434 (101*2π)/5475 weeks
102-2.69891 3.03783 (102*2π)/5475 weeks
103-1.44777 -2.28945 (103*2π)/5475 weeks
1043.77316 -3.80288 (104*2π)/5475 weeks
1059.14609 1.71509 (105*2π)/5475 weeks
1064.38333 7.80766 (106*2π)/5475 weeks
107-1.83383 7.7478 (107*2π)/5475 weeks
108-5.45437 2.31146 (108*2π)/5475 weeks
109-2.02873 -5.13638 (109*2π)/5475 weeks
1107.13984 -5.13534 (110*2π)/5475 weeks
1119.20283 3.60091 (111*2π)/5475 weeks
1124.38482 8.92729 (112*2π)/5475 weeks
113-2.86955 8.40776 (113*2π)/5475 weeks
114-7.01149 .60143 (114*2π)/5475 weeks
115.07079 -6.12044 (115*2π)/5475 weeks
1167.34393 -1.62495 (116*2π)/5475 weeks
1175.67961 5.06866 (117*2π)/5475 weeks
118-.34824 5.87166 (118*2π)/5475 weeks
119-2.64417 1.40683 (119*2π)/5475 weeks
120-.80895 -1.77604 (120*2π)/5475 weeks
1214.04859 -3.43762 (121*2π)/5475 weeks
1227.44648 1.87707 (122*2π)/5474 weeks
1233.65152 7.55774 (123*2π)/5474 weeks
124-2.74004 4.08058 (124*2π)/5474 weeks
125-1.86518 -1.08671 (125*2π)/5474 weeks
1262.87893 -2.17706 (126*2π)/5474 weeks
1274.74931 1.9139 (127*2π)/5474 weeks
1282.97395 4.00488 (128*2π)/5474 weeks
129-.16597 3.54501 (129*2π)/5474 weeks
130-1.06327 .83874 (130*2π)/5474 weeks
131.7947 -2.408 (131*2π)/5474 weeks
1325.87827 -1.86237 (132*2π)/5474 weeks
1336.69229 4.08628 (133*2π)/5474 weeks
1341.96979 6.542 (134*2π)/5474 weeks
135-1.29847 4.83523 (135*2π)/5474 weeks
136-2.11846 .00514 (136*2π)/5474 weeks
1373.24495 -1.93431 (137*2π)/5474 weeks
1384.49723 3.64346 (138*2π)/5474 weeks
139.15152 5.05732 (139*2π)/5474 weeks
140-2.86968 1.87087 (140*2π)/5474 weeks
141.01786 -3.09637 (141*2π)/5474 weeks
1425.40012 .18447 (142*2π)/5474 weeks
1433.44415 3.70856 (143*2π)/5474 weeks
1441.03229 3.912 (144*2π)/5474 weeks
145-1.14833 2.02003 (145*2π)/5474 weeks
146.34637 -.18881 (146*2π)/5474 weeks
1471.76403 .39432 (147*2π)/5474 weeks
1483.03461 1.09584 (148*2π)/5474 weeks
1491.379 3.58268 (149*2π)/5474 weeks
150-.26279 1.36942 (150*2π)/5474 weeks
151.19035 1.18157 (151*2π)/5474 weeks
152.23718 -1.48967 (152*2π)/5474 weeks
1533.87138 -.40289 (153*2π)/5474 weeks
1543.44142 1.97244 (154*2π)/5474 weeks
1551.95597 3.09016 (155*2π)/5474 weeks
156.50669 2.22197 (156*2π)/5474 weeks
1571.50251 .60756 (157*2π)/5473 weeks
1581.82303 2.16233 (158*2π)/5473 weeks
1591.2789 .99974 (159*2π)/5473 weeks
1602.20172 2.48488 (160*2π)/5473 weeks
161-.02638 3.18392 (161*2π)/5473 weeks
162-1.17713 1.03075 (162*2π)/5473 weeks
1631.02811 -1.41671 (163*2π)/5473 weeks
1643.02264 .67642 (164*2π)/5473 weeks
1652.94109 2.37312 (165*2π)/5473 weeks
166.21236 4.03708 (166*2π)/5473 weeks
167-2.44619 1.1061 (167*2π)/5473 weeks
168-.27014 -1.975 (168*2π)/5473 weeks
1692.61105 -1.42364 (169*2π)/5473 weeks
1703.45063 .49098 (170*2π)/5473 weeks
1713.36812 2.35979 (171*2π)/5473 weeks
1721.12355 3.96082 (172*2π)/5473 weeks
173-2.18086 1.77959 (173*2π)/5473 weeks
174-.73932 -2.69959 (174*2π)/5473 weeks
1754.05244 -2.19879 (175*2π)/5473 weeks
1765.49535 1.70383 (176*2π)/5473 weeks
1773.52501 5.02798 (177*2π)/5473 weeks
178-1.02779 4.99582 (178*2π)/5473 weeks
179-3.37422 1.22369 (179*2π)/5473 weeks
180-1.16262 -2.63683 (180*2π)/5473 weeks
1813.07754 -2.73651 (181*2π)/5473 weeks
1824.5923 .72204 (182*2π)/5473 weeks
1833.22677 3.49436 (183*2π)/5473 weeks
184.36767 3.13357 (184*2π)/5473 weeks
185-.39043 2.1207 (185*2π)/5473 weeks
186-.65254 -.47773 (186*2π)/5473 weeks
1871.91504 -.14687 (187*2π)/5473 weeks
1881.83698 .92653 (188*2π)/5473 weeks
1891.83193 1.97412 (189*2π)/5473 weeks
190-.49536 2.43782 (190*2π)/5473 weeks
191-1.18739 -.43094 (191*2π)/5473 weeks
192.14615 -1.88428 (192*2π)/5473 weeks
1933.76686 -2.68265 (193*2π)/5473 weeks
1946.20665 2.72185 (194*2π)/5473 weeks
195.93012 5.54361 (195*2π)/5473 weeks
196-2.32423 2.94167 (196*2π)/5473 weeks
197-2.67239 -1.12028 (197*2π)/5473 weeks
1981.51131 -2.63173 (198*2π)/5473 weeks
1992.91326 .39081 (199*2π)/5473 weeks
2002.89465 1.06785 (200*2π)/5473 weeks
201.36351 4.05001 (201*2π)/5473 weeks
202-2.5104 .23752 (202*2π)/5473 weeks
203-.95766 -1.79236 (203*2π)/5473 weeks
2041.62897 -3.92812 (204*2π)/5473 weeks
2055.66731 -1.32931 (205*2π)/5473 weeks
2064.63043 3.8737 (206*2π)/5473 weeks
207-.35343 4.40142 (207*2π)/5473 weeks
208-3.35784 .42574 (208*2π)/5473 weeks
209.44277 -4.10796 (209*2π)/5473 weeks
2104.88365 -1.37777 (210*2π)/5473 weeks
2114.5135 2.48329 (211*2π)/5473 weeks
2121.15272 4.78302 (212*2π)/5473 weeks
213-3.74949 1.67353 (213*2π)/5473 weeks
214-1.54156 -3.56076 (214*2π)/5473 weeks
2153.8115 -4.05742 (215*2π)/5473 weeks
2166.7127 1.19669 (216*2π)/5473 weeks
2172.34 5.37581 (217*2π)/5473 weeks
218-2.74466 2.10367 (218*2π)/5473 weeks
219-.4518 -2.36206 (219*2π)/5472 weeks
2203.58515 -1.3369 (220*2π)/5472 weeks
2214.47545 2.10353 (221*2π)/5472 weeks
222.99219 5.21154 (222*2π)/5472 weeks
223-3.84409 2.57557 (223*2π)/5472 weeks
224-2.68674 -3.19541 (224*2π)/5472 weeks
2251.60361 -3.88536 (225*2π)/5472 weeks
2265.48444 -1.31589 (226*2π)/5472 weeks
2273.82575 3.58206 (227*2π)/5472 weeks
228-.42052 3.75257 (228*2π)/5472 weeks
229-2.81368 .48741 (229*2π)/5472 weeks
230-1.02406 -3.8074 (230*2π)/5472 weeks
2314.35403 -3.21205 (231*2π)/5472 weeks
2325.3428 2.3065 (232*2π)/5472 weeks
233.78238 5.21408 (233*2π)/5472 weeks
234-3.92263 1.5969 (234*2π)/5472 weeks
235-2.27893 -3.43724 (235*2π)/5472 weeks
2362.24428 -4.29197 (236*2π)/5472 weeks
2375.55128 -1.84549 (237*2π)/5472 weeks
2384.48377 3.96061 (238*2π)/5472 weeks
239-.94057 3.05845 (239*2π)/5472 weeks
240-1.51531 .13417 (240*2π)/5472 weeks
241.03591 -2.50338 (241*2π)/5472 weeks
2422.38129 -1.45547 (242*2π)/5472 weeks
2432.63091 -.07064 (243*2π)/5472 weeks
2442.40065 .82976 (244*2π)/5472 weeks
245.85126 1.65694 (245*2π)/5472 weeks
246-.37652 -.16482 (246*2π)/5472 weeks
247.12678 -1.10772 (247*2π)/5472 weeks
2481.65206 -2.10581 (248*2π)/5472 weeks
2494.0661 -1.56945 (249*2π)/5472 weeks
2504.44164 2.5245 (250*2π)/5472 weeks
251.48516 4.01982 (251*2π)/5472 weeks
252-2.59793 1.64603 (252*2π)/5472 weeks
253-3.12103 -2.61052 (253*2π)/5472 weeks
2541.16289 -5.23038 (254*2π)/5472 weeks
2555.77639 -3.29094 (255*2π)/5472 weeks
2565.82559 2.49426 (256*2π)/5472 weeks
257.58085 4.24854 (257*2π)/5472 weeks
258-1.85892 .5598 (258*2π)/5472 weeks
259-.42215 -2.54139 (259*2π)/5472 weeks
2602.59108 -2.80943 (260*2π)/5472 weeks
2614.72632 -.56211 (261*2π)/5472 weeks
2622.3051 2.73243 (262*2π)/5472 weeks
263-.15516 1.48548 (263*2π)/5472 weeks
264-.96725 -.71234 (264*2π)/5472 weeks
2651.22719 -2.38321 (265*2π)/5472 weeks
2662.79039 -2.40362 (266*2π)/5472 weeks
2674.60524 .19809 (267*2π)/5472 weeks
2681.40681 3.20998 (268*2π)/5472 weeks
269-1.51484 -.121 (269*2π)/5472 weeks
2701.03845 -2.4328 (270*2π)/5472 weeks
2713.11082 -2.02868 (271*2π)/5472 weeks
2723.00491 -.10518 (272*2π)/5472 weeks
2732.82176 -.55568 (273*2π)/5472 weeks
2742.82176 .55568 (274*2π)/5472 weeks
2753.00491 .10518 (275*2π)/5472 weeks
2763.11082 2.02868 (276*2π)/5472 weeks
2771.03845 2.4328 (277*2π)/5472 weeks
278-1.51484 .121 (278*2π)/5472 weeks
2791.40681 -3.20998 (279*2π)/5472 weeks
2804.60524 -.19809 (280*2π)/5472 weeks
2812.79039 2.40362 (281*2π)/5472 weeks
2821.22719 2.38321 (282*2π)/5472 weeks
283-.96725 .71234 (283*2π)/5472 weeks
284-.15516 -1.48548 (284*2π)/5472 weeks
2852.3051 -2.73243 (285*2π)/5472 weeks
2864.72632 .56211 (286*2π)/5472 weeks
2872.59108 2.80943 (287*2π)/5472 weeks
288-.42215 2.54139 (288*2π)/5472 weeks
289-1.85892 -.5598 (289*2π)/5472 weeks
290.58085 -4.24854 (290*2π)/5472 weeks
2915.82559 -2.49426 (291*2π)/5472 weeks
2925.77639 3.29094 (292*2π)/5472 weeks
2931.16289 5.23038 (293*2π)/5472 weeks
294-3.12103 2.61052 (294*2π)/5472 weeks
295-2.59793 -1.64603 (295*2π)/5472 weeks
296.48516 -4.01982 (296*2π)/5472 weeks
2974.44164 -2.5245 (297*2π)/5472 weeks
2984.0661 1.56945 (298*2π)/5472 weeks
2991.65206 2.10581 (299*2π)/5472 weeks
300.12678 1.10772 (300*2π)/5472 weeks
301-.37652 .16482 (301*2π)/5472 weeks
302.85126 -1.65694 (302*2π)/5472 weeks
3032.40065 -.82976 (303*2π)/5472 weeks
3042.63091 .07064 (304*2π)/5472 weeks
3052.38129 1.45547 (305*2π)/5472 weeks
306.03591 2.50338 (306*2π)/5472 weeks
307-1.51531 -.13417 (307*2π)/5472 weeks
308-.94057 -3.05845 (308*2π)/5472 weeks
3094.48377 -3.96061 (309*2π)/5472 weeks
3105.55128 1.84549 (310*2π)/5472 weeks
3112.24428 4.29197 (311*2π)/5472 weeks
312-2.27893 3.43724 (312*2π)/5472 weeks
313-3.92263 -1.5969 (313*2π)/5472 weeks
314.78238 -5.21408 (314*2π)/5472 weeks
3155.3428 -2.3065 (315*2π)/5472 weeks
3164.35403 3.21205 (316*2π)/5472 weeks
317-1.02406 3.8074 (317*2π)/5472 weeks
318-2.81368 -.48741 (318*2π)/5472 weeks
319-.42052 -3.75257 (319*2π)/5472 weeks
3203.82575 -3.58206 (320*2π)/5472 weeks
3215.48444 1.31589 (321*2π)/5472 weeks
3221.60361 3.88536 (322*2π)/5472 weeks
323-2.68674 3.19541 (323*2π)/5472 weeks
324-3.84409 -2.57557 (324*2π)/5472 weeks
325.99219 -5.21154 (325*2π)/5472 weeks
3264.47545 -2.10353 (326*2π)/5472 weeks
3273.58515 1.3369 (327*2π)/5472 weeks
328-.4518 2.36206 (328*2π)/5472 weeks
329-2.74466 -2.10367 (329*2π)/5472 weeks
3302.34 -5.37581 (330*2π)/5472 weeks
3316.7127 -1.19669 (331*2π)/5472 weeks
3323.8115 4.05742 (332*2π)/5472 weeks
333-1.54156 3.56076 (333*2π)/5472 weeks
334-3.74949 -1.67353 (334*2π)/5472 weeks
3351.15272 -4.78302 (335*2π)/5472 weeks
3364.5135 -2.48329 (336*2π)/5472 weeks
3374.88365 1.37777 (337*2π)/5472 weeks
338.44277 4.10796 (338*2π)/5472 weeks
339-3.35784 -.42574 (339*2π)/5472 weeks
340-.35343 -4.40142 (340*2π)/5472 weeks
3414.63043 -3.8737 (341*2π)/5472 weeks
3425.66731 1.32931 (342*2π)/5472 weeks
3431.62897 3.92812 (343*2π)/5472 weeks
344-.95766 1.79236 (344*2π)/5472 weeks
345-2.5104 -.23752 (345*2π)/5472 weeks
346.36351 -4.05001 (346*2π)/5472 weeks
3472.89465 -1.06785 (347*2π)/5472 weeks
3482.91326 -.39081 (348*2π)/5472 weeks
3491.51131 2.63173 (349*2π)/5472 weeks
350-2.67239 1.12028 (350*2π)/5472 weeks
351-2.32423 -2.94167 (351*2π)/5472 weeks
352.93012 -5.54361 (352*2π)/5472 weeks
3536.20665 -2.72185 (353*2π)/5472 weeks
3543.76686 2.68265 (354*2π)/5472 weeks
355.14615 1.88428 (355*2π)/5472 weeks
356-1.18739 .43094 (356*2π)/5472 weeks
357-.49536 -2.43782 (357*2π)/5472 weeks
3581.83193 -1.97412 (358*2π)/5472 weeks
3591.83698 -.92653 (359*2π)/5472 weeks
3601.91504 .14687 (360*2π)/5472 weeks
361-.65254 .47773 (361*2π)/5472 weeks
362-.39043 -2.1207 (362*2π)/5472 weeks
363.36767 -3.13357 (363*2π)/5472 weeks
3643.22677 -3.49436 (364*2π)/5472 weeks
3654.5923 -.72204 (365*2π)/5471 weeks
3663.07754 2.73651 (366*2π)/5471 weeks
367-1.16262 2.63683 (367*2π)/5471 weeks
368-3.37422 -1.22369 (368*2π)/5471 weeks
369-1.02779 -4.99582 (369*2π)/5471 weeks
3703.52501 -5.02798 (370*2π)/5471 weeks
3715.49535 -1.70383 (371*2π)/5471 weeks
3724.05244 2.19879 (372*2π)/5471 weeks
373-.73932 2.69959 (373*2π)/5471 weeks
374-2.18086 -1.77959 (374*2π)/5471 weeks
3751.12355 -3.96082 (375*2π)/5471 weeks
3763.36812 -2.35979 (376*2π)/5471 weeks
3773.45063 -.49098 (377*2π)/5471 weeks
3782.61105 1.42364 (378*2π)/5471 weeks
379-.27014 1.975 (379*2π)/5471 weeks
380-2.44619 -1.1061 (380*2π)/5471 weeks
381.21236 -4.03708 (381*2π)/5471 weeks
3822.94109 -2.37312 (382*2π)/5471 weeks
3833.02264 -.67642 (383*2π)/5471 weeks
3841.02811 1.41671 (384*2π)/5471 weeks
385-1.17713 -1.03075 (385*2π)/5471 weeks
386-.02638 -3.18392 (386*2π)/5471 weeks
3872.20172 -2.48488 (387*2π)/5471 weeks
3881.2789 -.99974 (388*2π)/5471 weeks
3891.82303 -2.16233 (389*2π)/5471 weeks
3901.50251 -.60756 (390*2π)/5471 weeks
391.50669 -2.22197 (391*2π)/5471 weeks
3921.95597 -3.09016 (392*2π)/5471 weeks
3933.44142 -1.97244 (393*2π)/5471 weeks
3943.87138 .40289 (394*2π)/5471 weeks
395.23718 1.48967 (395*2π)/5471 weeks
396.19035 -1.18157 (396*2π)/5471 weeks
397-.26279 -1.36942 (397*2π)/5471 weeks
3981.379 -3.58268 (398*2π)/5471 weeks
3993.03461 -1.09584 (399*2π)/5471 weeks
4001.76403 -.39432 (400*2π)/5471 weeks
401.34637 .18881 (401*2π)/5471 weeks
402-1.14833 -2.02003 (402*2π)/5471 weeks
4031.03229 -3.912 (403*2π)/5471 weeks
4043.44415 -3.70856 (404*2π)/5471 weeks
4055.40012 -.18447 (405*2π)/5471 weeks
406.01786 3.09637 (406*2π)/5471 weeks
407-2.86968 -1.87087 (407*2π)/5471 weeks
408.15152 -5.05732 (408*2π)/5471 weeks
4094.49723 -3.64346 (409*2π)/5471 weeks
4103.24495 1.93431 (410*2π)/5471 weeks
411-2.11846 -.00514 (411*2π)/5471 weeks
412-1.29847 -4.83523 (412*2π)/5471 weeks
4131.96979 -6.542 (413*2π)/5471 weeks
4146.69229 -4.08628 (414*2π)/5471 weeks
4155.87827 1.86237 (415*2π)/5471 weeks
416.7947 2.408 (416*2π)/5471 weeks
417-1.06327 -.83874 (417*2π)/5471 weeks
418-.16597 -3.54501 (418*2π)/5471 weeks
4192.97395 -4.00488 (419*2π)/5471 weeks
4204.74931 -1.9139 (420*2π)/5471 weeks
4212.87893 2.17706 (421*2π)/5471 weeks
422-1.86518 1.08671 (422*2π)/5471 weeks
423-2.74004 -4.08058 (423*2π)/5471 weeks
4243.65152 -7.55774 (424*2π)/5471 weeks
4257.44648 -1.87707 (425*2π)/5471 weeks
4264.04859 3.43762 (426*2π)/5471 weeks
427-.80895 1.77604 (427*2π)/5471 weeks
428-2.64417 -1.40683 (428*2π)/5471 weeks
429-.34824 -5.87166 (429*2π)/5471 weeks
4305.67961 -5.06866 (430*2π)/5471 weeks
4317.34393 1.62495 (431*2π)/5471 weeks
432.07079 6.12044 (432*2π)/5471 weeks
433-7.01149 -.60143 (433*2π)/5471 weeks
434-2.86955 -8.40776 (434*2π)/5471 weeks
4354.38482 -8.92729 (435*2π)/5471 weeks
4369.20283 -3.60091 (436*2π)/5471 weeks
4377.13984 5.13534 (437*2π)/5471 weeks
438-2.02873 5.13638 (438*2π)/5471 weeks
439-5.45437 -2.31146 (439*2π)/5471 weeks
440-1.83383 -7.7478 (440*2π)/5471 weeks
4414.38333 -7.80766 (441*2π)/5471 weeks
4429.14609 -1.71509 (442*2π)/5471 weeks
4433.77316 3.80288 (443*2π)/5471 weeks
444-1.44777 2.28945 (444*2π)/5471 weeks
445-2.69891 -3.03783 (445*2π)/5471 weeks
446.60787 -6.49434 (446*2π)/5471 weeks
4475.1775 -5.48004 (447*2π)/5471 weeks
4487.25495 .11156 (448*2π)/5471 weeks
4492.91843 3.86419 (449*2π)/5471 weeks
450-1.13224 1.09456 (450*2π)/5471 weeks
451-.80326 -.34691 (451*2π)/5471 weeks
452-1.81547 -2.2673 (452*2π)/5471 weeks
453-1.14643 -3.49724 (453*2π)/5471 weeks
454.98978 -7.03971 (454*2π)/5471 weeks
4556.75466 -3.58973 (455*2π)/5471 weeks
4563.97074 2.90012 (456*2π)/5471 weeks
457-3.26 2.8176 (457*2π)/5471 weeks
458-5.9704 -5.27486 (458*2π)/5471 weeks
4591.20825 -10.78672 (459*2π)/5471 weeks
46010.37812 -6.27879 (460*2π)/5471 weeks
4618.15178 4.3038 (461*2π)/5471 weeks
462-.48364 6.34312 (462*2π)/5471 weeks
463-8.26481 -.32546 (463*2π)/5471 weeks
464-3.25874 -8.24448 (464*2π)/5471 weeks
4651.39559 -9.26235 (465*2π)/5471 weeks
4668.25445 -5.52832 (466*2π)/5471 weeks
4675.32735 1.35869 (467*2π)/5471 weeks
468-.07229 2.18068 (468*2π)/5471 weeks
469-4.49775 -3.4904 (469*2π)/5471 weeks
4701.65932 -9.20081 (470*2π)/5471 weeks
4716.69055 -3.91544 (471*2π)/5471 weeks
4726.31071 -.67301 (472*2π)/5471 weeks
4732.98217 4.19633 (473*2π)/5471 weeks
474-6.08962 2.91298 (474*2π)/5471 weeks
475-7.23696 -7.5593 (475*2π)/5471 weeks
4762.5482 -12.12034 (476*2π)/5471 weeks
4778.88978 -4.47149 (477*2π)/5471 weeks
4782.96815 3.19279 (478*2π)/5471 weeks
479-4.38247 -3.12791 (479*2π)/5471 weeks
480-.81573 -8.50238 (480*2π)/5471 weeks
4814.95586 -11.08905 (481*2π)/5471 weeks
48211.99501 -3.82593 (482*2π)/5471 weeks
4836.68588 6.05029 (483*2π)/5471 weeks
484-2.86777 3.75725 (484*2π)/5471 weeks
485-5.72036 -4.26934 (485*2π)/5471 weeks
4861.72097 -9.01664 (486*2π)/5471 weeks
4876.47649 -4.10005 (487*2π)/5471 weeks
4882.68009 1.03223 (488*2π)/5471 weeks
489-1.63574 -2.18945 (489*2π)/5471 weeks
490-1.40813 -6.20022 (490*2π)/5471 weeks
4916.55146 -8.56953 (491*2π)/5471 weeks
4925.92026 .13471 (492*2π)/5471 weeks
4931.76781 -.58245 (493*2π)/5471 weeks
4941.54333 -.21802 (494*2π)/5471 weeks
495-1.08633 -1.50283 (495*2π)/5471 weeks
496.90277 -3.66791 (496*2π)/5471 weeks
4971.88327 -.74215 (497*2π)/5471 weeks
498-1.89055 -.23335 (498*2π)/5471 weeks
499-3.39385 -3.38365 (499*2π)/5471 weeks
500-5.89054 -6.14994 (500*2π)/5471 weeks
501.69083 -9.94343 (501*2π)/5471 weeks
5021.75154 -5.88963 (502*2π)/5471 weeks
503.01018 -7.74645 (503*2π)/5471 weeks
5043.05144 -6.9064 (504*2π)/5471 weeks
5055.41415 -7.4081 (505*2π)/5471 weeks
5067.51841 -.15269 (506*2π)/5471 weeks
507-5.42776 3.10553 (507*2π)/5471 weeks
508-8.10463 -8.87736 (508*2π)/5471 weeks
509-.76811 -13.97552 (509*2π)/5471 weeks
5107.31735 -11.96154 (510*2π)/5471 weeks
5119.59139 -4.54248 (511*2π)/5471 weeks
5126.80311 4.0678 (512*2π)/5471 weeks
513-9.55584 7.38715 (513*2π)/5471 weeks
514-17.7904 -14.46895 (514*2π)/5471 weeks
515.33525 -25.26484 (515*2π)/5471 weeks
51614.16071 -15.63032 (516*2π)/5471 weeks
51712.84273 .65903 (517*2π)/5471 weeks
518-1.54118 4.03937 (518*2π)/5471 weeks
519-6.59235 -8.32458 (519*2π)/5471 weeks
520-1.34149 -8.97563 (520*2π)/5471 weeks
521.94243 -13.07881 (521*2π)/5471 weeks
522-3.63762 -5.69777 (522*2π)/5471 weeks
523-5.79832 -17.21012 (523*2π)/5471 weeks
5241.66622 -15.5772 (524*2π)/5471 weeks
5256.4533 -18.53571 (525*2π)/5471 weeks
5269.57615 -12.0605 (526*2π)/5471 weeks
5274.06614 -5.26991 (527*2π)/5471 weeks
528-5.07153 -12.87473 (528*2π)/5471 weeks
5295.86975 -19.19476 (529*2π)/5471 weeks
5307.71715 -11.72821 (530*2π)/5471 weeks
5319.34469 -5.94661 (531*2π)/5471 weeks
532-4.8807 -.14558 (532*2π)/5471 weeks
533-25.21633 -9.22769 (533*2π)/5471 weeks
534-30.92513 -48.92043 (534*2π)/5471 weeks
53519.33572 -74.86606 (535*2π)/5471 weeks
53663.31706 -30.34149 (536*2π)/5471 weeks
53741.09148 13.00423 (537*2π)/5471 weeks
538-1.03206 38.77035 (538*2π)/5471 weeks
539-70.17612 -16.43098 (539*2π)/5471 weeks
540-22.04225 -98.11638 (540*2π)/5471 weeks
54166.18066 -92.71312 (541*2π)/5471 weeks
54293.57966 2.67029 (542*2π)/5471 weeks
543-2.71969 58.97752 (543*2π)/5471 weeks
544-130.1916 -7.00257 (544*2π)/5471 weeks
545-104.4508 -233.8659 (545*2π)/5471 weeks



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