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Fourier Analysis of TWM (ProShares UltraShort Russell 2000 ETF)


TWM (ProShares UltraShort Russell 2000 ETF) appears to have interesting cyclic behaviour every 46 weeks (49.8865*sine), 50 weeks (30.9479*cosine), and 50 weeks (30.0751*sine).

TWM (ProShares UltraShort Russell 2000 ETF) has an average price of 311.84 (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 1/25/2007 to 7/17/2017 for TWM (ProShares UltraShort Russell 2000 ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0311.8388   0 
1192.5752 356.882 (1*2π)/548548 weeks
2-48.01145 227.7072 (2*2π)/548274 weeks
3-91.45735 69.14026 (3*2π)/548183 weeks
4-16.07937 -1.34097 (4*2π)/548137 weeks
535.86237 19.12749 (5*2π)/548110 weeks
630.28363 61.99501 (6*2π)/54891 weeks
7-13.98013 65.30824 (7*2π)/54878 weeks
8-34.35524 14.02813 (8*2π)/54869 weeks
95.68452 -9.20289 (9*2π)/54861 weeks
1024.60689 9.23168 (10*2π)/54855 weeks
1130.94786 30.07509 (11*2π)/54850 weeks
124.39258 49.88652 (12*2π)/54846 weeks
13-17.87653 27.76206 (13*2π)/54842 weeks
14-10.04976 9.83607 (14*2π)/54839 weeks
15.6668 6.26129 (15*2π)/54837 weeks
163.90274 11.09979 (16*2π)/54834 weeks
172.94832 6.31636 (17*2π)/54832 weeks
1811.33266 11.69393 (18*2π)/54830 weeks
195.21697 16.0297 (19*2π)/54829 weeks
205.63108 15.367 (20*2π)/54827 weeks
212.00966 17.42121 (21*2π)/54826 weeks
22-2.33541 13.37255 (22*2π)/54825 weeks
232.48363 5.78799 (23*2π)/54824 weeks
248.66712 11.73801 (24*2π)/54823 weeks
255.96141 21.61988 (25*2π)/54822 weeks
26-9.95407 22.93878 (26*2π)/54821 weeks
27-15.30056 6.14579 (27*2π)/54820 weeks
28-6.21458 -7.12979 (28*2π)/54820 weeks
2913.91129 -6.49795 (29*2π)/54819 weeks
3019.96834 14.60887 (30*2π)/54818 weeks
311.05595 28.19904 (31*2π)/54818 weeks
32-18.65362 17.91183 (32*2π)/54817 weeks
33-17.79836 -6.69922 (33*2π)/54817 weeks
346.31289 -13.66864 (34*2π)/54816 weeks
3516.70343 2.84807 (35*2π)/54816 weeks
3610.33328 14.98124 (36*2π)/54815 weeks
37-2.45967 15.41566 (37*2π)/54815 weeks
38-5.52593 5.79542 (38*2π)/54814 weeks
39-.8975 .90626 (39*2π)/54814 weeks
404.8331 1.09183 (40*2π)/54814 weeks
418.27009 8.38093 (41*2π)/54813 weeks
42.1773 12.04643 (42*2π)/54813 weeks
43-1.80017 5.0842 (43*2π)/54813 weeks
441.09525 4.50798 (44*2π)/54812 weeks
453.06384 6.68573 (45*2π)/54812 weeks
46-1.11624 9.48634 (46*2π)/54812 weeks
47-4.63445 4.74623 (47*2π)/54812 weeks
48-2.3926 1.62203 (48*2π)/54811 weeks
492.04089 .47681 (49*2π)/54811 weeks
502.89187 3.68376 (50*2π)/54811 weeks
511.07373 5.82053 (51*2π)/54811 weeks
52-1.44908 3.40576 (52*2π)/54811 weeks
53.03717 .96554 (53*2π)/54810 weeks
542.79409 -.22148 (54*2π)/54810 weeks
557.27934 3.28998 (55*2π)/54810 weeks
563.40754 10.07659 (56*2π)/54810 weeks
57-3.35922 5.8706 (57*2π)/54810 weeks
58-1.51363 .28413 (58*2π)/5489 weeks
593.25982 .8404 (59*2π)/5489 weeks
604.18042 4.54827 (60*2π)/5489 weeks
61-1.11322 7.15011 (61*2π)/5489 weeks
62-4.2331 .04194 (62*2π)/5489 weeks
631.98873 -3.57981 (63*2π)/5489 weeks
647.99611 -1.02274 (64*2π)/5489 weeks
657.89242 6.38696 (65*2π)/5488 weeks
661.34127 8.37729 (66*2π)/5488 weeks
67.22481 4.16227 (67*2π)/5488 weeks
681.18976 2.70476 (68*2π)/5488 weeks
694.36732 4.60883 (69*2π)/5488 weeks
70-.06091 9.43172 (70*2π)/5488 weeks
71-6.58008 3.97084 (71*2π)/5488 weeks
72-3.59232 -3.7777 (72*2π)/5488 weeks
733.99101 -5.40285 (73*2π)/5488 weeks
749.25878 2.09922 (74*2π)/5487 weeks
753.52973 7.30347 (75*2π)/5487 weeks
76.62754 5.83039 (76*2π)/5487 weeks
77-4.08791 3.65861 (77*2π)/5487 weeks
78-1.0037 -4.49712 (78*2π)/5487 weeks
797.58592 -2.19818 (79*2π)/5487 weeks
808.2524 4.36974 (80*2π)/5487 weeks
813.30069 9.2742 (81*2π)/5487 weeks
82-3.33174 5.92966 (82*2π)/5487 weeks
83-3.0563 .16153 (83*2π)/5487 weeks
84.98177 -4.14251 (84*2π)/5487 weeks
858.87257 -1.46592 (85*2π)/5486 weeks
868.6157 6.8063 (86*2π)/5486 weeks
872.08024 9.80506 (87*2π)/5486 weeks
88-2.94181 5.65427 (88*2π)/5486 weeks
89-1.79442 1.03896 (89*2π)/5486 weeks
901.32091 .7305 (90*2π)/5486 weeks
912.19971 2.64735 (91*2π)/5486 weeks
92.3201 3.67148 (92*2π)/5486 weeks
93-.72911 1.27038 (93*2π)/5486 weeks
942.10188 .73317 (94*2π)/5486 weeks
951.21772 2.89039 (95*2π)/5486 weeks
96-.48564 1.06397 (96*2π)/5486 weeks
971.01172 -1.6875 (97*2π)/5486 weeks
984.97875 -1.3779 (98*2π)/5486 weeks
996.58415 2.72138 (99*2π)/5486 weeks
1003.23057 6.41618 (100*2π)/5485 weeks
101-1.51764 4.94125 (101*2π)/5485 weeks
102-2.04857 -.86212 (102*2π)/5485 weeks
1033.95779 -3.3705 (103*2π)/5485 weeks
1048.07151 1.16708 (104*2π)/5485 weeks
1056.58666 7.03055 (105*2π)/5485 weeks
106.214 8.28428 (106*2π)/5485 weeks
107-3.74679 4.48798 (107*2π)/5485 weeks
108-2.35469 -1.98278 (108*2π)/5485 weeks
1094.84076 -2.64687 (109*2π)/5485 weeks
1107.51661 3.43891 (110*2π)/5485 weeks
1112.99877 8.03295 (111*2π)/5485 weeks
112-2.09663 6.26863 (112*2π)/5485 weeks
113-3.85112 2.54486 (113*2π)/5485 weeks
114-1.98944 -2.51154 (114*2π)/5485 weeks
1153.96207 -2.11544 (115*2π)/5485 weeks
1164.94613 2.37198 (116*2π)/5485 weeks
1172.40429 4.04409 (117*2π)/5485 weeks
118.02579 3.69106 (118*2π)/5485 weeks
119-1.16867 1.09718 (119*2π)/5485 weeks
120.74097 -1.1223 (120*2π)/5485 weeks
1214.64011 -.2516 (121*2π)/5485 weeks
1224.95563 4.00295 (122*2π)/5484 weeks
123.80119 5.74584 (123*2π)/5484 weeks
124-1.42035 2.66863 (124*2π)/5484 weeks
125-.5409 .31403 (125*2π)/5484 weeks
1261.27806 .03084 (126*2π)/5484 weeks
1272.12502 .75165 (127*2π)/5484 weeks
1282.7898 1.38913 (128*2π)/5484 weeks
1292.36279 2.58081 (129*2π)/5484 weeks
1301.15047 2.57996 (130*2π)/5484 weeks
1311.27257 1.18098 (131*2π)/5484 weeks
1322.94819 1.63299 (132*2π)/5484 weeks
1332.03744 3.93968 (133*2π)/5484 weeks
134-.2787 3.74958 (134*2π)/5484 weeks
135-1.37419 2.59004 (135*2π)/5484 weeks
136-1.1832 .01162 (136*2π)/5484 weeks
1371.0537 -.41312 (137*2π)/5484 weeks
138.89504 .12336 (138*2π)/5484 weeks
1392.30699 -.3967 (139*2π)/5484 weeks
1402.84966 1.33715 (140*2π)/5484 weeks
1412.62904 2.77336 (141*2π)/5484 weeks
142-.39621 3.37224 (142*2π)/5484 weeks
143-.84391 -.79019 (143*2π)/5484 weeks
1443.39002 -1.47315 (144*2π)/5484 weeks
1454.47767 2.14535 (145*2π)/5484 weeks
1461.74745 4.52986 (146*2π)/5484 weeks
147-1.72445 2.80116 (147*2π)/5484 weeks
148-.5937 -.76367 (148*2π)/5484 weeks
1492.13674 -1.21915 (149*2π)/5484 weeks
1504.29217 1.24871 (150*2π)/5484 weeks
1511.68056 4.07811 (151*2π)/5484 weeks
152-.56665 2.23953 (152*2π)/5484 weeks
153-.37459 .84592 (153*2π)/5484 weeks
154.56861 .13121 (154*2π)/5484 weeks
1551.26497 .14776 (155*2π)/5484 weeks
1562.10313 .30559 (156*2π)/5484 weeks
1572.47754 1.85056 (157*2π)/5483 weeks
158-.05756 2.1617 (158*2π)/5483 weeks
159.26505 -.04558 (159*2π)/5483 weeks
1601.18879 .15405 (160*2π)/5483 weeks
1611.52634 -.08676 (161*2π)/5483 weeks
1622.51822 .22481 (162*2π)/5483 weeks
1632.89058 1.93903 (163*2π)/5483 weeks
164.37173 3.00669 (164*2π)/5483 weeks
165-1.22319 1.0479 (165*2π)/5483 weeks
166-.69236 -1.78387 (166*2π)/5483 weeks
1672.79549 -2.60122 (167*2π)/5483 weeks
1684.93953 .21493 (168*2π)/5483 weeks
1693.45547 3.28695 (169*2π)/5483 weeks
170.42268 3.06064 (170*2π)/5483 weeks
171-.70563 1.03747 (171*2π)/5483 weeks
172.52651 -1.29279 (172*2π)/5483 weeks
1733.30175 -1.24327 (173*2π)/5483 weeks
1744.46502 1.50604 (174*2π)/5483 weeks
1752.46149 3.99881 (175*2π)/5483 weeks
176-.70598 3.57452 (176*2π)/5483 weeks
177-1.9933 .7484 (177*2π)/5483 weeks
178-.44044 -2.26459 (178*2π)/5483 weeks
1793.23757 -2.05631 (179*2π)/5483 weeks
1804.52786 1.05018 (180*2π)/5483 weeks
1812.16225 3.67229 (181*2π)/5483 weeks
182-.97469 2.33023 (182*2π)/5483 weeks
183-.90153 -.3926 (183*2π)/5483 weeks
1841.47243 -1.80693 (184*2π)/5483 weeks
1853.04608 .12605 (185*2π)/5483 weeks
1862.29895 1.24333 (186*2π)/5483 weeks
187.81789 1.70652 (187*2π)/5483 weeks
188-.07317 -.2716 (188*2π)/5483 weeks
1892.00867 -1.57146 (189*2π)/5483 weeks
1903.47459 -.2232 (190*2π)/5483 weeks
1913.62364 1.481 (191*2π)/5483 weeks
1922.18755 2.60002 (192*2π)/5483 weeks
1931.66341 2.61522 (193*2π)/5483 weeks
194-.66947 3.21639 (194*2π)/5483 weeks
195-1.81813 -.18704 (195*2π)/5483 weeks
196.01378 -1.12078 (196*2π)/5483 weeks
1971.20047 -1.44024 (197*2π)/5483 weeks
1981.98461 -.51451 (198*2π)/5483 weeks
1991.7426 -.38518 (199*2π)/5483 weeks
2002.39549 .22776 (200*2π)/5483 weeks
201.80745 .10169 (201*2π)/5483 weeks
2022.35059 -1.21654 (202*2π)/5483 weeks
2032.89503 -.34342 (203*2π)/5483 weeks
2044.10393 .23022 (204*2π)/5483 weeks
2053.34899 3.03858 (205*2π)/5483 weeks
206.18553 3.07656 (206*2π)/5483 weeks
207-.78242 .26518 (207*2π)/5483 weeks
2081.35137 -1.54413 (208*2π)/5483 weeks
2093.46138 .40399 (209*2π)/5483 weeks
2101.72961 2.41815 (210*2π)/5483 weeks
211-.11922 1.5071 (211*2π)/5483 weeks
212-.81996 -.55571 (212*2π)/5483 weeks
2131.23959 -2.94571 (213*2π)/5483 weeks
2144.71366 -1.26823 (214*2π)/5483 weeks
2154.26973 2.45299 (215*2π)/5483 weeks
216.67245 3.32525 (216*2π)/5483 weeks
217-.93747 .12702 (217*2π)/5483 weeks
2181.75566 -1.59029 (218*2π)/5483 weeks
2193.03371 .65845 (219*2π)/5483 weeks
2201.36933 1.62188 (220*2π)/5482 weeks
221.47557 .86441 (221*2π)/5482 weeks
222-.33171 -.38646 (222*2π)/5482 weeks
2231.3898 -2.54401 (223*2π)/5482 weeks
2244.11633 -.80277 (224*2π)/5482 weeks
2253.19887 1.42819 (225*2π)/5482 weeks
2261.16779 1.96362 (226*2π)/5482 weeks
227.05611 -.40659 (227*2π)/5482 weeks
2282.35607 -1.39769 (228*2π)/5482 weeks
2293.62508 -.24749 (229*2π)/5482 weeks
2303.452 1.61489 (230*2π)/5482 weeks
2311.04454 2.64112 (231*2π)/5482 weeks
232-.57894 .36447 (232*2π)/5482 weeks
233.75929 -1.88199 (233*2π)/5482 weeks
2343.79474 -2.07088 (234*2π)/5482 weeks
2355.29117 1.35754 (235*2π)/5482 weeks
2362.73428 3.57306 (236*2π)/5482 weeks
237.54643 2.88509 (237*2π)/5482 weeks
238-1.22784 1.13578 (238*2π)/5482 weeks
239.88318 -1.366 (239*2π)/5482 weeks
2402.1513 -.23028 (240*2π)/5482 weeks
2412.62724 .49604 (241*2π)/5482 weeks
2421.48733 1.47967 (242*2π)/5482 weeks
2431.19886 .5289 (243*2π)/5482 weeks
244.93861 .7868 (244*2π)/5482 weeks
245.5379 -.6459 (245*2π)/5482 weeks
2462.28367 -1.26976 (246*2π)/5482 weeks
2473.45898 -.10244 (247*2π)/5482 weeks
2483.66766 2.30958 (248*2π)/5482 weeks
249.59397 3.39933 (249*2π)/5482 weeks
250-1.47051 .84365 (250*2π)/5482 weeks
251-.36002 -1.62972 (251*2π)/5482 weeks
2522.09264 -2.61099 (252*2π)/5482 weeks
2534.93516 -1.05802 (253*2π)/5482 weeks
2544.71108 2.88858 (254*2π)/5482 weeks
2551.38377 5.05376 (255*2π)/5482 weeks
256-3.06523 2.52288 (256*2π)/5482 weeks
257-1.92659 -2.35597 (257*2π)/5482 weeks
2581.86705 -3.21356 (258*2π)/5482 weeks
2594.89175 -1.17376 (259*2π)/5482 weeks
2604.06096 3.0895 (260*2π)/5482 weeks
261-.31304 3.70056 (261*2π)/5482 weeks
262-2.18814 -.52176 (262*2π)/5482 weeks
2631.19245 -2.7327 (263*2π)/5482 weeks
2643.80704 -1.04219 (264*2π)/5482 weeks
2654.07564 1.86153 (265*2π)/5482 weeks
2661.83948 3.94606 (266*2π)/5482 weeks
267-2.19147 3.03248 (267*2π)/5482 weeks
268-2.82656 -1.7788 (268*2π)/5482 weeks
2691.49485 -3.43176 (269*2π)/5482 weeks
2703.65342 -.59519 (270*2π)/5482 weeks
2712.84678 1.38655 (271*2π)/5482 weeks
2721.30811 1.84423 (272*2π)/5482 weeks
273.06159 1.88618 (273*2π)/5482 weeks
274-1.57371   (274*2π)/5482 weeks
275.06159 -1.88618 (275*2π)/5482 weeks
2761.30811 -1.84423 (276*2π)/5482 weeks
2772.84678 -1.38655 (277*2π)/5482 weeks
2783.65342 .59519 (278*2π)/5482 weeks
2791.49485 3.43176 (279*2π)/5482 weeks
280-2.82656 1.7788 (280*2π)/5482 weeks
281-2.19147 -3.03248 (281*2π)/5482 weeks
2821.83948 -3.94606 (282*2π)/5482 weeks
2834.07564 -1.86153 (283*2π)/5482 weeks
2843.80704 1.04219 (284*2π)/5482 weeks
2851.19245 2.7327 (285*2π)/5482 weeks
286-2.18814 .52176 (286*2π)/5482 weeks
287-.31304 -3.70056 (287*2π)/5482 weeks
2884.06096 -3.0895 (288*2π)/5482 weeks
2894.89175 1.17376 (289*2π)/5482 weeks
2901.86705 3.21356 (290*2π)/5482 weeks
291-1.92659 2.35597 (291*2π)/5482 weeks
292-3.06523 -2.52288 (292*2π)/5482 weeks
2931.38377 -5.05376 (293*2π)/5482 weeks
2944.71108 -2.88858 (294*2π)/5482 weeks
2954.93516 1.05802 (295*2π)/5482 weeks
2962.09264 2.61099 (296*2π)/5482 weeks
297-.36002 1.62972 (297*2π)/5482 weeks
298-1.47051 -.84365 (298*2π)/5482 weeks
299.59397 -3.39933 (299*2π)/5482 weeks
3003.66766 -2.30958 (300*2π)/5482 weeks
3013.45898 .10244 (301*2π)/5482 weeks
3022.28367 1.26976 (302*2π)/5482 weeks
303.5379 .6459 (303*2π)/5482 weeks
304.93861 -.7868 (304*2π)/5482 weeks
3051.19886 -.5289 (305*2π)/5482 weeks
3061.48733 -1.47967 (306*2π)/5482 weeks
3072.62724 -.49604 (307*2π)/5482 weeks
3082.1513 .23028 (308*2π)/5482 weeks
309.88318 1.366 (309*2π)/5482 weeks
310-1.22784 -1.13578 (310*2π)/5482 weeks
311.54643 -2.88509 (311*2π)/5482 weeks
3122.73428 -3.57306 (312*2π)/5482 weeks
3135.29117 -1.35754 (313*2π)/5482 weeks
3143.79474 2.07088 (314*2π)/5482 weeks
315.75929 1.88199 (315*2π)/5482 weeks
316-.57894 -.36447 (316*2π)/5482 weeks
3171.04454 -2.64112 (317*2π)/5482 weeks
3183.452 -1.61489 (318*2π)/5482 weeks
3193.62508 .24749 (319*2π)/5482 weeks
3202.35607 1.39769 (320*2π)/5482 weeks
321.05611 .40659 (321*2π)/5482 weeks
3221.16779 -1.96362 (322*2π)/5482 weeks
3233.19887 -1.42819 (323*2π)/5482 weeks
3244.11633 .80277 (324*2π)/5482 weeks
3251.3898 2.54401 (325*2π)/5482 weeks
326-.33171 .38646 (326*2π)/5482 weeks
327.47557 -.86441 (327*2π)/5482 weeks
3281.36933 -1.62188 (328*2π)/5482 weeks
3293.03371 -.65845 (329*2π)/5482 weeks
3301.75566 1.59029 (330*2π)/5482 weeks
331-.93747 -.12702 (331*2π)/5482 weeks
332.67245 -3.32525 (332*2π)/5482 weeks
3334.26973 -2.45299 (333*2π)/5482 weeks
3344.71366 1.26823 (334*2π)/5482 weeks
3351.23959 2.94571 (335*2π)/5482 weeks
336-.81996 .55571 (336*2π)/5482 weeks
337-.11922 -1.5071 (337*2π)/5482 weeks
3381.72961 -2.41815 (338*2π)/5482 weeks
3393.46138 -.40399 (339*2π)/5482 weeks
3401.35137 1.54413 (340*2π)/5482 weeks
341-.78242 -.26518 (341*2π)/5482 weeks
342.18553 -3.07656 (342*2π)/5482 weeks
3433.34899 -3.03858 (343*2π)/5482 weeks
3444.10393 -.23022 (344*2π)/5482 weeks
3452.89503 .34342 (345*2π)/5482 weeks
3462.35059 1.21654 (346*2π)/5482 weeks
347.80745 -.10169 (347*2π)/5482 weeks
3482.39549 -.22776 (348*2π)/5482 weeks
3491.7426 .38518 (349*2π)/5482 weeks
3501.98461 .51451 (350*2π)/5482 weeks
3511.20047 1.44024 (351*2π)/5482 weeks
352.01378 1.12078 (352*2π)/5482 weeks
353-1.81813 .18704 (353*2π)/5482 weeks
354-.66947 -3.21639 (354*2π)/5482 weeks
3551.66341 -2.61522 (355*2π)/5482 weeks
3562.18755 -2.60002 (356*2π)/5482 weeks
3573.62364 -1.481 (357*2π)/5482 weeks
3583.47459 .2232 (358*2π)/5482 weeks
3592.00867 1.57146 (359*2π)/5482 weeks
360-.07317 .2716 (360*2π)/5482 weeks
361.81789 -1.70652 (361*2π)/5482 weeks
3622.29895 -1.24333 (362*2π)/5482 weeks
3633.04608 -.12605 (363*2π)/5482 weeks
3641.47243 1.80693 (364*2π)/5482 weeks
365-.90153 .3926 (365*2π)/5482 weeks
366-.97469 -2.33023 (366*2π)/5481 weeks
3672.16225 -3.67229 (367*2π)/5481 weeks
3684.52786 -1.05018 (368*2π)/5481 weeks
3693.23757 2.05631 (369*2π)/5481 weeks
370-.44044 2.26459 (370*2π)/5481 weeks
371-1.9933 -.7484 (371*2π)/5481 weeks
372-.70598 -3.57452 (372*2π)/5481 weeks
3732.46149 -3.99881 (373*2π)/5481 weeks
3744.46502 -1.50604 (374*2π)/5481 weeks
3753.30175 1.24327 (375*2π)/5481 weeks
376.52651 1.29279 (376*2π)/5481 weeks
377-.70563 -1.03747 (377*2π)/5481 weeks
378.42268 -3.06064 (378*2π)/5481 weeks
3793.45547 -3.28695 (379*2π)/5481 weeks
3804.93953 -.21493 (380*2π)/5481 weeks
3812.79549 2.60122 (381*2π)/5481 weeks
382-.69236 1.78387 (382*2π)/5481 weeks
383-1.22319 -1.0479 (383*2π)/5481 weeks
384.37173 -3.00669 (384*2π)/5481 weeks
3852.89058 -1.93903 (385*2π)/5481 weeks
3862.51822 -.22481 (386*2π)/5481 weeks
3871.52634 .08676 (387*2π)/5481 weeks
3881.18879 -.15405 (388*2π)/5481 weeks
389.26505 .04558 (389*2π)/5481 weeks
390-.05756 -2.1617 (390*2π)/5481 weeks
3912.47754 -1.85056 (391*2π)/5481 weeks
3922.10313 -.30559 (392*2π)/5481 weeks
3931.26497 -.14776 (393*2π)/5481 weeks
394.56861 -.13121 (394*2π)/5481 weeks
395-.37459 -.84592 (395*2π)/5481 weeks
396-.56665 -2.23953 (396*2π)/5481 weeks
3971.68056 -4.07811 (397*2π)/5481 weeks
3984.29217 -1.24871 (398*2π)/5481 weeks
3992.13674 1.21915 (399*2π)/5481 weeks
400-.5937 .76367 (400*2π)/5481 weeks
401-1.72445 -2.80116 (401*2π)/5481 weeks
4021.74745 -4.52986 (402*2π)/5481 weeks
4034.47767 -2.14535 (403*2π)/5481 weeks
4043.39002 1.47315 (404*2π)/5481 weeks
405-.84391 .79019 (405*2π)/5481 weeks
406-.39621 -3.37224 (406*2π)/5481 weeks
4072.62904 -2.77336 (407*2π)/5481 weeks
4082.84966 -1.33715 (408*2π)/5481 weeks
4092.30699 .3967 (409*2π)/5481 weeks
410.89504 -.12336 (410*2π)/5481 weeks
4111.0537 .41312 (411*2π)/5481 weeks
412-1.1832 -.01162 (412*2π)/5481 weeks
413-1.37419 -2.59004 (413*2π)/5481 weeks
414-.2787 -3.74958 (414*2π)/5481 weeks
4152.03744 -3.93968 (415*2π)/5481 weeks
4162.94819 -1.63299 (416*2π)/5481 weeks
4171.27257 -1.18098 (417*2π)/5481 weeks
4181.15047 -2.57996 (418*2π)/5481 weeks
4192.36279 -2.58081 (419*2π)/5481 weeks
4202.7898 -1.38913 (420*2π)/5481 weeks
4212.12502 -.75165 (421*2π)/5481 weeks
4221.27806 -.03084 (422*2π)/5481 weeks
423-.5409 -.31403 (423*2π)/5481 weeks
424-1.42035 -2.66863 (424*2π)/5481 weeks
425.80119 -5.74584 (425*2π)/5481 weeks
4264.95563 -4.00295 (426*2π)/5481 weeks
4274.64011 .2516 (427*2π)/5481 weeks
428.74097 1.1223 (428*2π)/5481 weeks
429-1.16867 -1.09718 (429*2π)/5481 weeks
430.02579 -3.69106 (430*2π)/5481 weeks
4312.40429 -4.04409 (431*2π)/5481 weeks
4324.94613 -2.37198 (432*2π)/5481 weeks
4333.96207 2.11544 (433*2π)/5481 weeks
434-1.98944 2.51154 (434*2π)/5481 weeks
435-3.85112 -2.54486 (435*2π)/5481 weeks
436-2.09663 -6.26863 (436*2π)/5481 weeks
4372.99877 -8.03295 (437*2π)/5481 weeks
4387.51661 -3.43891 (438*2π)/5481 weeks
4394.84076 2.64687 (439*2π)/5481 weeks
440-2.35469 1.98278 (440*2π)/5481 weeks
441-3.74679 -4.48798 (441*2π)/5481 weeks
442.214 -8.28428 (442*2π)/5481 weeks
4436.58666 -7.03055 (443*2π)/5481 weeks
4448.07151 -1.16708 (444*2π)/5481 weeks
4453.95779 3.3705 (445*2π)/5481 weeks
446-2.04857 .86212 (446*2π)/5481 weeks
447-1.51764 -4.94125 (447*2π)/5481 weeks
4483.23057 -6.41618 (448*2π)/5481 weeks
4496.58415 -2.72138 (449*2π)/5481 weeks
4504.97875 1.3779 (450*2π)/5481 weeks
4511.01172 1.6875 (451*2π)/5481 weeks
452-.48564 -1.06397 (452*2π)/5481 weeks
4531.21772 -2.89039 (453*2π)/5481 weeks
4542.10188 -.73317 (454*2π)/5481 weeks
455-.72911 -1.27038 (455*2π)/5481 weeks
456.3201 -3.67148 (456*2π)/5481 weeks
4572.19971 -2.64735 (457*2π)/5481 weeks
4581.32091 -.7305 (458*2π)/5481 weeks
459-1.79442 -1.03896 (459*2π)/5481 weeks
460-2.94181 -5.65427 (460*2π)/5481 weeks
4612.08024 -9.80506 (461*2π)/5481 weeks
4628.6157 -6.8063 (462*2π)/5481 weeks
4638.87257 1.46592 (463*2π)/5481 weeks
464.98177 4.14251 (464*2π)/5481 weeks
465-3.0563 -.16153 (465*2π)/5481 weeks
466-3.33174 -5.92966 (466*2π)/5481 weeks
4673.30069 -9.2742 (467*2π)/5481 weeks
4688.2524 -4.36974 (468*2π)/5481 weeks
4697.58592 2.19818 (469*2π)/5481 weeks
470-1.0037 4.49712 (470*2π)/5481 weeks
471-4.08791 -3.65861 (471*2π)/5481 weeks
472.62754 -5.83039 (472*2π)/5481 weeks
4733.52973 -7.30347 (473*2π)/5481 weeks
4749.25878 -2.09922 (474*2π)/5481 weeks
4753.99101 5.40285 (475*2π)/5481 weeks
476-3.59232 3.7777 (476*2π)/5481 weeks
477-6.58008 -3.97084 (477*2π)/5481 weeks
478-.06091 -9.43172 (478*2π)/5481 weeks
4794.36732 -4.60883 (479*2π)/5481 weeks
4801.18976 -2.70476 (480*2π)/5481 weeks
481.22481 -4.16227 (481*2π)/5481 weeks
4821.34127 -8.37729 (482*2π)/5481 weeks
4837.89242 -6.38696 (483*2π)/5481 weeks
4847.99611 1.02274 (484*2π)/5481 weeks
4851.98873 3.57981 (485*2π)/5481 weeks
486-4.2331 -.04194 (486*2π)/5481 weeks
487-1.11322 -7.15011 (487*2π)/5481 weeks
4884.18042 -4.54827 (488*2π)/5481 weeks
4893.25982 -.8404 (489*2π)/5481 weeks
490-1.51363 -.28413 (490*2π)/5481 weeks
491-3.35922 -5.8706 (491*2π)/5481 weeks
4923.40754 -10.07659 (492*2π)/5481 weeks
4937.27934 -3.28998 (493*2π)/5481 weeks
4942.79409 .22148 (494*2π)/5481 weeks
495.03717 -.96554 (495*2π)/5481 weeks
496-1.44908 -3.40576 (496*2π)/5481 weeks
4971.07373 -5.82053 (497*2π)/5481 weeks
4982.89187 -3.68376 (498*2π)/5481 weeks
4992.04089 -.47681 (499*2π)/5481 weeks
500-2.3926 -1.62203 (500*2π)/5481 weeks
501-4.63445 -4.74623 (501*2π)/5481 weeks
502-1.11624 -9.48634 (502*2π)/5481 weeks
5033.06384 -6.68573 (503*2π)/5481 weeks
5041.09525 -4.50798 (504*2π)/5481 weeks
505-1.80017 -5.0842 (505*2π)/5481 weeks
506.1773 -12.04643 (506*2π)/5481 weeks
5078.27009 -8.38093 (507*2π)/5481 weeks
5084.8331 -1.09183 (508*2π)/5481 weeks
509-.8975 -.90626 (509*2π)/5481 weeks
510-5.52593 -5.79542 (510*2π)/5481 weeks
511-2.45967 -15.41566 (511*2π)/5481 weeks
51210.33328 -14.98124 (512*2π)/5481 weeks
51316.70343 -2.84807 (513*2π)/5481 weeks
5146.31289 13.66864 (514*2π)/5481 weeks
515-17.79836 6.69922 (515*2π)/5481 weeks
516-18.65362 -17.91183 (516*2π)/5481 weeks
5171.05595 -28.19904 (517*2π)/5481 weeks
51819.96834 -14.60887 (518*2π)/5481 weeks
51913.91129 6.49795 (519*2π)/5481 weeks
520-6.21458 7.12979 (520*2π)/5481 weeks
521-15.30056 -6.14579 (521*2π)/5481 weeks
522-9.95407 -22.93878 (522*2π)/5481 weeks
5235.96141 -21.61988 (523*2π)/5481 weeks
5248.66712 -11.73801 (524*2π)/5481 weeks
5252.48363 -5.78799 (525*2π)/5481 weeks
526-2.33541 -13.37255 (526*2π)/5481 weeks
5272.00966 -17.42121 (527*2π)/5481 weeks
5285.63108 -15.367 (528*2π)/5481 weeks
5295.21697 -16.0297 (529*2π)/5481 weeks
53011.33266 -11.69393 (530*2π)/5481 weeks
5312.94832 -6.31636 (531*2π)/5481 weeks
5323.90274 -11.09979 (532*2π)/5481 weeks
533.6668 -6.26129 (533*2π)/5481 weeks
534-10.04976 -9.83607 (534*2π)/5481 weeks
535-17.87653 -27.76206 (535*2π)/5481 weeks
5364.39258 -49.88652 (536*2π)/5481 weeks
53730.94786 -30.07509 (537*2π)/5481 weeks
53824.60689 -9.23168 (538*2π)/5481 weeks
5395.68452 9.20289 (539*2π)/5481 weeks
540-34.35524 -14.02813 (540*2π)/5481 weeks
541-13.98013 -65.30824 (541*2π)/5481 weeks
54230.28363 -61.99501 (542*2π)/5481 weeks
54335.86237 -19.12749 (543*2π)/5481 weeks
544-16.07937 1.34097 (544*2π)/5481 weeks
545-91.45735 -69.14026 (545*2π)/5481 weeks
546-48.01145 -227.7072 (546*2π)/5481 weeks



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