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Fourier Analysis of DUG (ProShares UltraShort Oil & Gas ETF)


DUG (ProShares UltraShort Oil & Gas ETF) appears to have interesting cyclic behaviour every 39 weeks (34.442*sine), 42 weeks (33.4207*sine), and 46 weeks (31.5897*sine).

DUG (ProShares UltraShort Oil & Gas ETF) has an average price of 226.78 (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 7/10/2017 for DUG (ProShares UltraShort Oil & Gas ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0226.7806   0 
1164.039 200.8372 (1*2π)/546546 weeks
233.31232 135.4266 (2*2π)/546273 weeks
34.63633 76.64481 (3*2π)/546182 weeks
414.26098 55.15937 (4*2π)/546137 weeks
527.91083 40.46369 (5*2π)/546109 weeks
637.57741 52.90224 (6*2π)/54691 weeks
711.93485 61.41707 (7*2π)/54678 weeks
8-2.96062 37.28109 (8*2π)/54668 weeks
97.74278 25.20482 (9*2π)/54661 weeks
105.44729 25.0197 (10*2π)/54655 weeks
1115.58959 19.13638 (11*2π)/54650 weeks
1221.61357 31.58965 (12*2π)/54646 weeks
1311.74712 33.42072 (13*2π)/54642 weeks
144.47343 34.44196 (14*2π)/54639 weeks
15-3.5759 27.54232 (15*2π)/54636 weeks
16-3.51679 18.12698 (16*2π)/54634 weeks
17-.11194 7.45385 (17*2π)/54632 weeks
1811.66187 10.48672 (18*2π)/54630 weeks
1913.19149 17.01583 (19*2π)/54629 weeks
2012.98367 25.07922 (20*2π)/54627 weeks
215.66783 27.58048 (21*2π)/54626 weeks
22-2.60007 23.22052 (22*2π)/54625 weeks
23-3.21326 11.63053 (23*2π)/54624 weeks
244.5327 10.74967 (24*2π)/54623 weeks
258.22608 17.72113 (25*2π)/54622 weeks
26.35493 23.0565 (26*2π)/54621 weeks
27-3.72803 16.71097 (27*2π)/54620 weeks
28-4.25272 9.47551 (28*2π)/54620 weeks
292.89276 5.1683 (29*2π)/54619 weeks
306.67131 10.85166 (30*2π)/54618 weeks
314.14643 15.33337 (31*2π)/54618 weeks
32-1.4183 17.32864 (32*2π)/54617 weeks
33-5.85281 10.05369 (33*2π)/54617 weeks
34-.25966 5.22303 (34*2π)/54616 weeks
351.91175 6.30411 (35*2π)/54616 weeks
363.73992 7.03347 (36*2π)/54615 weeks
373.70664 8.91023 (37*2π)/54615 weeks
382.99747 10.13528 (38*2π)/54614 weeks
391.07357 10.54172 (39*2π)/54614 weeks
40.6067 7.40015 (40*2π)/54614 weeks
413.37569 7.323 (41*2π)/54613 weeks
423.11831 7.45424 (42*2π)/54613 weeks
435.88204 9.25115 (43*2π)/54613 weeks
444.04333 14.0119 (44*2π)/54612 weeks
45-.93403 14.50491 (45*2π)/54612 weeks
46-5.6992 10.55896 (46*2π)/54612 weeks
47-5.25089 4.4149 (47*2π)/54612 weeks
48-1.2623 2.93138 (48*2π)/54611 weeks
492.37335 3.48556 (49*2π)/54611 weeks
503.01888 5.90696 (50*2π)/54611 weeks
51.91972 8.21645 (51*2π)/54611 weeks
52-2.3312 6.59315 (52*2π)/54611 weeks
53-2.32591 2.48005 (53*2π)/54610 weeks
542.31015 -.61339 (54*2π)/54610 weeks
557.75096 2.83576 (55*2π)/54610 weeks
567.65451 10.35777 (56*2π)/54610 weeks
57.41353 13.07686 (57*2π)/54610 weeks
58-5.13986 7.96893 (58*2π)/5469 weeks
59-4.32946 2.00721 (59*2π)/5469 weeks
601.07157 -1.15241 (60*2π)/5469 weeks
614.73225 2.81651 (61*2π)/5469 weeks
623.82402 4.98229 (62*2π)/5469 weeks
633.19146 6.39649 (63*2π)/5469 weeks
641.69899 5.85421 (64*2π)/5469 weeks
65.8934 5.31729 (65*2π)/5468 weeks
66.28179 5.10913 (66*2π)/5468 weeks
671.69931 4.78463 (67*2π)/5468 weeks
68-.16391 5.04992 (68*2π)/5468 weeks
691.30174 3.98344 (69*2π)/5468 weeks
70-.33094 6.42906 (70*2π)/5468 weeks
71-3.40104 4.27811 (71*2π)/5468 weeks
72-2.06318 -.43926 (72*2π)/5468 weeks
732.63831 -2.35077 (73*2π)/5467 weeks
746.2524 2.10865 (74*2π)/5467 weeks
753.90096 5.06282 (75*2π)/5467 weeks
762.97965 5.14821 (76*2π)/5467 weeks
77-1.02741 5.60016 (77*2π)/5467 weeks
78-1.50511 .6097 (78*2π)/5467 weeks
793.19006 .09598 (79*2π)/5467 weeks
804.76138 1.88265 (80*2π)/5467 weeks
814.40798 4.77385 (81*2π)/5467 weeks
82.9805 5.03689 (82*2π)/5467 weeks
83.48308 3.69086 (83*2π)/5467 weeks
84-.04465 .9937 (84*2π)/5467 weeks
854.20987 -.70713 (85*2π)/5466 weeks
866.58218 3.58384 (86*2π)/5466 weeks
874.33507 7.37797 (87*2π)/5466 weeks
88.21407 6.98066 (88*2π)/5466 weeks
89-1.94476 3.22359 (89*2π)/5466 weeks
90.38417 .16946 (90*2π)/5466 weeks
913.15096 .70222 (91*2π)/5466 weeks
923.93884 2.76897 (92*2π)/5466 weeks
932.2829 3.73958 (93*2π)/5466 weeks
942.47623 3.46653 (94*2π)/5466 weeks
951.33234 5.36382 (95*2π)/5466 weeks
96-.84391 3.56817 (96*2π)/5466 weeks
97-.45662 -.03054 (97*2π)/5466 weeks
982.99879 -1.23771 (98*2π)/5466 weeks
995.29752 1.04956 (99*2π)/5466 weeks
1004.53633 4.10054 (100*2π)/5465 weeks
1011.6653 5.51554 (101*2π)/5465 weeks
102-1.16768 3.28496 (102*2π)/5465 weeks
103.63294 -.42811 (103*2π)/5465 weeks
1044.17996 -.75389 (104*2π)/5465 weeks
1056.27795 1.97804 (105*2π)/5465 weeks
1064.69798 4.90442 (106*2π)/5465 weeks
1071.66062 5.90264 (107*2π)/5465 weeks
108-.79757 3.56567 (108*2π)/5465 weeks
109.91193 .64215 (109*2π)/5465 weeks
1103.93263 .83333 (110*2π)/5465 weeks
1114.70006 3.19748 (111*2π)/5465 weeks
1123.69869 5.13556 (112*2π)/5465 weeks
113.74683 6.49312 (113*2π)/5465 weeks
114-2.30854 3.59728 (114*2π)/5465 weeks
115-1.2793 .4931 (115*2π)/5465 weeks
1161.50947 -1.09776 (116*2π)/5465 weeks
1174.48147 .21293 (117*2π)/5465 weeks
1184.42594 3.53727 (118*2π)/5465 weeks
1191.63387 4.34983 (119*2π)/5465 weeks
120-.25418 2.96573 (120*2π)/5465 weeks
121.15345 .15845 (121*2π)/5465 weeks
1222.92089 -.60813 (122*2π)/5464 weeks
1234.50955 1.48255 (123*2π)/5464 weeks
1244.2579 3.1961 (124*2π)/5464 weeks
1252.85096 3.61981 (125*2π)/5464 weeks
1261.62983 3.62828 (126*2π)/5464 weeks
127.31211 2.60998 (127*2π)/5464 weeks
1281.1578 .29512 (128*2π)/5464 weeks
1294.04247 .47701 (129*2π)/5464 weeks
1304.4506 3.36165 (130*2π)/5464 weeks
1312.91685 4.07156 (131*2π)/5464 weeks
1322.31546 3.59612 (132*2π)/5464 weeks
1331.14153 3.84775 (133*2π)/5464 weeks
134-.15941 2.26234 (134*2π)/5464 weeks
1351.35812 1.59061 (135*2π)/5464 weeks
1362.22582 1.76654 (136*2π)/5464 weeks
1373.42225 2.93723 (137*2π)/5464 weeks
1381.3585 4.8027 (138*2π)/5464 weeks
139-1.16496 3.07978 (139*2π)/5464 weeks
140-1.22289 .28995 (140*2π)/5464 weeks
1411.60359 -1.20095 (141*2π)/5464 weeks
1423.31418 1.13903 (142*2π)/5464 weeks
1432.66863 2.14191 (143*2π)/5464 weeks
1442.60328 2.62611 (144*2π)/5464 weeks
1451.21121 2.79124 (145*2π)/5464 weeks
146.33402 2.0033 (146*2π)/5464 weeks
147.23326 .87082 (147*2π)/5464 weeks
1481.48869 .03283 (148*2π)/5464 weeks
1492.5221 .13471 (149*2π)/5464 weeks
1504.09745 1.1637 (150*2π)/5464 weeks
1512.72133 3.43079 (151*2π)/5464 weeks
152.63778 1.97279 (152*2π)/5464 weeks
1531.4808 .55764 (153*2π)/5464 weeks
1542.55928 1.02901 (154*2π)/5464 weeks
1552.40822 1.98561 (155*2π)/5464 weeks
1562.03295 1.76747 (156*2π)/5464 weeks
1572.45969 2.14745 (157*2π)/5463 weeks
1581.09343 2.21904 (158*2π)/5463 weeks
1591.45555 .90391 (159*2π)/5463 weeks
1602.26038 1.4306 (160*2π)/5463 weeks
1611.97036 1.91976 (161*2π)/5463 weeks
1621.55677 1.87384 (162*2π)/5463 weeks
1631.82879 1.64618 (163*2π)/5463 weeks
1641.35813 1.54996 (164*2π)/5463 weeks
1651.74757 1.38468 (165*2π)/5463 weeks
1661.27515 1.32798 (166*2π)/5463 weeks
1671.5452 1.10526 (167*2π)/5463 weeks
1681.54734 1.16921 (168*2π)/5463 weeks
1691.80495 1.23204 (169*2π)/5463 weeks
1701.21137 1.24409 (170*2π)/5463 weeks
171.89086 .81111 (171*2π)/5463 weeks
1721.57993 .23191 (172*2π)/5463 weeks
1732.45435 .30142 (173*2π)/5463 weeks
1742.89802 .92119 (174*2π)/5463 weeks
1752.72635 1.32506 (175*2π)/5463 weeks
1762.62504 1.74759 (176*2π)/5463 weeks
1771.72948 2.57852 (177*2π)/5463 weeks
178.61315 1.50411 (178*2π)/5463 weeks
1791.14697 .82338 (179*2π)/5463 weeks
1801.64612 .50256 (180*2π)/5463 weeks
1812.10484 1.10772 (181*2π)/5463 weeks
1821.51656 1.08179 (182*2π)/5463 weeks
1831.25619 .87283 (183*2π)/5463 weeks
1841.55887 .35381 (184*2π)/5463 weeks
1851.95487 .55405 (185*2π)/5463 weeks
1862.59681 .12807 (186*2π)/5463 weeks
1873.2419 1.51291 (187*2π)/5463 weeks
1881.60022 2.2107 (188*2π)/5463 weeks
189.74664 1.49332 (189*2π)/5463 weeks
190.66054 .18879 (190*2π)/5463 weeks
1912.03687 -.8982 (191*2π)/5463 weeks
1923.42023 -.4228 (192*2π)/5463 weeks
1934.49869 .96863 (193*2π)/5463 weeks
1943.47651 3.72745 (194*2π)/5463 weeks
195.63915 3.18974 (195*2π)/5463 weeks
196.02569 1.38862 (196*2π)/5463 weeks
197.92777 -.02294 (197*2π)/5463 weeks
1982.48255 .18566 (198*2π)/5463 weeks
1992.40522 1.36855 (199*2π)/5463 weeks
2002.31198 2.21526 (200*2π)/5463 weeks
201.23487 2.381 (201*2π)/5463 weeks
202.1366 .15002 (202*2π)/5463 weeks
203.92428 -.63883 (203*2π)/5463 weeks
2042.70914 -1.16142 (204*2π)/5463 weeks
2054.19666 .51021 (205*2π)/5463 weeks
2063.12161 3.04627 (206*2π)/5463 weeks
207.3381 3.17837 (207*2π)/5463 weeks
208-.87437 .47118 (208*2π)/5463 weeks
2091.30753 -1.804 (209*2π)/5463 weeks
2103.61342 -.52628 (210*2π)/5463 weeks
2113.82442 1.5527 (211*2π)/5463 weeks
2122.2094 3.48392 (212*2π)/5463 weeks
213-.18667 2.09154 (213*2π)/5463 weeks
214-.02083 .0483 (214*2π)/5463 weeks
2151.68336 -.83758 (215*2π)/5463 weeks
2162.82597 .6981 (216*2π)/5463 weeks
2171.97114 1.50386 (217*2π)/5463 weeks
2181.58338 1.17253 (218*2π)/5463 weeks
2191.58108 1.40113 (219*2π)/5462 weeks
220.60641 1.49031 (220*2π)/5462 weeks
221.73356 .47508 (221*2π)/5462 weeks
2221.08378 .70285 (222*2π)/5462 weeks
2231.02589 .40748 (223*2π)/5462 weeks
2241.54222 .75258 (224*2π)/5462 weeks
2251.00986 .70054 (225*2π)/5462 weeks
226.2768 .47921 (226*2π)/5462 weeks
227-.11275 -.79558 (227*2π)/5462 weeks
2281.34768 -1.22725 (228*2π)/5462 weeks
2292.35557 -.47891 (229*2π)/5462 weeks
2302.65177 .17917 (230*2π)/5462 weeks
2311.81911 1.06462 (231*2π)/5462 weeks
232.68733 .98405 (232*2π)/5462 weeks
233-.1021 -.04804 (233*2π)/5462 weeks
234.34542 -1.63425 (234*2π)/5462 weeks
2351.9062 -2.07064 (235*2π)/5462 weeks
2363.09919 -1.20937 (236*2π)/5462 weeks
2373.56262 .12634 (237*2π)/5462 weeks
2381.8281 1.06944 (238*2π)/5462 weeks
2391.47661 .20353 (239*2π)/5462 weeks
2401.13328 -.29497 (240*2π)/5462 weeks
2412.49814 -1.05621 (241*2π)/5462 weeks
2422.89824 -.0181 (242*2π)/5462 weeks
2432.51973 .81498 (243*2π)/5462 weeks
2441.34075 1.56458 (244*2π)/5462 weeks
245.06783 .40265 (245*2π)/5462 weeks
246.42395 -1.4266 (246*2π)/5462 weeks
2471.62201 -2.37763 (247*2π)/5462 weeks
2483.59174 -1.66562 (248*2π)/5462 weeks
2493.9364 .34911 (249*2π)/5462 weeks
2502.63582 1.24683 (250*2π)/5462 weeks
2511.28526 1.04862 (251*2π)/5462 weeks
252.57062 -.04431 (252*2π)/5462 weeks
2531.30401 -1.61677 (253*2π)/5462 weeks
2542.84075 -2.16588 (254*2π)/5462 weeks
2554.58585 -.15863 (255*2π)/5462 weeks
2562.98221 2.08896 (256*2π)/5462 weeks
2571.1289 1.46143 (257*2π)/5462 weeks
258-.00627 -.10227 (258*2π)/5462 weeks
259.70506 -2.14163 (259*2π)/5462 weeks
2603.2618 -2.05435 (260*2π)/5462 weeks
2614.24423 .29463 (261*2π)/5462 weeks
2622.52785 1.31644 (262*2π)/5462 weeks
263.68053 .74076 (263*2π)/5462 weeks
264.13153 -1.17268 (264*2π)/5462 weeks
2651.41942 -2.91625 (265*2π)/5462 weeks
2664.48705 -2.93474 (266*2π)/5462 weeks
2675.45771 .23854 (267*2π)/5462 weeks
2683.46607 1.85252 (268*2π)/5462 weeks
2691.72886 1.16514 (269*2π)/5462 weeks
270.92863 -.12931 (270*2π)/5462 weeks
2711.6671 -1.40781 (271*2π)/5462 weeks
2723.33637 -1.78516 (272*2π)/5462 weeks
2735.12327   (273*2π)/5462 weeks
2743.33637 1.78516 (274*2π)/5462 weeks
2751.6671 1.40781 (275*2π)/5462 weeks
276.92863 .12931 (276*2π)/5462 weeks
2771.72886 -1.16514 (277*2π)/5462 weeks
2783.46607 -1.85252 (278*2π)/5462 weeks
2795.45771 -.23854 (279*2π)/5462 weeks
2804.48705 2.93474 (280*2π)/5462 weeks
2811.41942 2.91625 (281*2π)/5462 weeks
282.13153 1.17268 (282*2π)/5462 weeks
283.68053 -.74076 (283*2π)/5462 weeks
2842.52785 -1.31644 (284*2π)/5462 weeks
2854.24423 -.29463 (285*2π)/5462 weeks
2863.2618 2.05435 (286*2π)/5462 weeks
287.70506 2.14163 (287*2π)/5462 weeks
288-.00627 .10227 (288*2π)/5462 weeks
2891.1289 -1.46143 (289*2π)/5462 weeks
2902.98221 -2.08896 (290*2π)/5462 weeks
2914.58585 .15863 (291*2π)/5462 weeks
2922.84075 2.16588 (292*2π)/5462 weeks
2931.30401 1.61677 (293*2π)/5462 weeks
294.57062 .04431 (294*2π)/5462 weeks
2951.28526 -1.04862 (295*2π)/5462 weeks
2962.63582 -1.24683 (296*2π)/5462 weeks
2973.9364 -.34911 (297*2π)/5462 weeks
2983.59174 1.66562 (298*2π)/5462 weeks
2991.62201 2.37763 (299*2π)/5462 weeks
300.42395 1.4266 (300*2π)/5462 weeks
301.06783 -.40265 (301*2π)/5462 weeks
3021.34075 -1.56458 (302*2π)/5462 weeks
3032.51973 -.81498 (303*2π)/5462 weeks
3042.89824 .0181 (304*2π)/5462 weeks
3052.49814 1.05621 (305*2π)/5462 weeks
3061.13328 .29497 (306*2π)/5462 weeks
3071.47661 -.20353 (307*2π)/5462 weeks
3081.8281 -1.06944 (308*2π)/5462 weeks
3093.56262 -.12634 (309*2π)/5462 weeks
3103.09919 1.20937 (310*2π)/5462 weeks
3111.9062 2.07064 (311*2π)/5462 weeks
312.34542 1.63425 (312*2π)/5462 weeks
313-.1021 .04804 (313*2π)/5462 weeks
314.68733 -.98405 (314*2π)/5462 weeks
3151.81911 -1.06462 (315*2π)/5462 weeks
3162.65177 -.17917 (316*2π)/5462 weeks
3172.35557 .47891 (317*2π)/5462 weeks
3181.34768 1.22725 (318*2π)/5462 weeks
319-.11275 .79558 (319*2π)/5462 weeks
320.2768 -.47921 (320*2π)/5462 weeks
3211.00986 -.70054 (321*2π)/5462 weeks
3221.54222 -.75258 (322*2π)/5462 weeks
3231.02589 -.40748 (323*2π)/5462 weeks
3241.08378 -.70285 (324*2π)/5462 weeks
325.73356 -.47508 (325*2π)/5462 weeks
326.60641 -1.49031 (326*2π)/5462 weeks
3271.58108 -1.40113 (327*2π)/5462 weeks
3281.58338 -1.17253 (328*2π)/5462 weeks
3291.97114 -1.50386 (329*2π)/5462 weeks
3302.82597 -.6981 (330*2π)/5462 weeks
3311.68336 .83758 (331*2π)/5462 weeks
332-.02083 -.0483 (332*2π)/5462 weeks
333-.18667 -2.09154 (333*2π)/5462 weeks
3342.2094 -3.48392 (334*2π)/5462 weeks
3353.82442 -1.5527 (335*2π)/5462 weeks
3363.61342 .52628 (336*2π)/5462 weeks
3371.30753 1.804 (337*2π)/5462 weeks
338-.87437 -.47118 (338*2π)/5462 weeks
339.3381 -3.17837 (339*2π)/5462 weeks
3403.12161 -3.04627 (340*2π)/5462 weeks
3414.19666 -.51021 (341*2π)/5462 weeks
3422.70914 1.16142 (342*2π)/5462 weeks
343.92428 .63883 (343*2π)/5462 weeks
344.1366 -.15002 (344*2π)/5462 weeks
345.23487 -2.381 (345*2π)/5462 weeks
3462.31198 -2.21526 (346*2π)/5462 weeks
3472.40522 -1.36855 (347*2π)/5462 weeks
3482.48255 -.18566 (348*2π)/5462 weeks
349.92777 .02294 (349*2π)/5462 weeks
350.02569 -1.38862 (350*2π)/5462 weeks
351.63915 -3.18974 (351*2π)/5462 weeks
3523.47651 -3.72745 (352*2π)/5462 weeks
3534.49869 -.96863 (353*2π)/5462 weeks
3543.42023 .4228 (354*2π)/5462 weeks
3552.03687 .8982 (355*2π)/5462 weeks
356.66054 -.18879 (356*2π)/5462 weeks
357.74664 -1.49332 (357*2π)/5462 weeks
3581.60022 -2.2107 (358*2π)/5462 weeks
3593.2419 -1.51291 (359*2π)/5462 weeks
3602.59681 -.12807 (360*2π)/5462 weeks
3611.95487 -.55405 (361*2π)/5462 weeks
3621.55887 -.35381 (362*2π)/5462 weeks
3631.25619 -.87283 (363*2π)/5462 weeks
3641.51656 -1.08179 (364*2π)/5462 weeks
3652.10484 -1.10772 (365*2π)/5461 weeks
3661.64612 -.50256 (366*2π)/5461 weeks
3671.14697 -.82338 (367*2π)/5461 weeks
368.61315 -1.50411 (368*2π)/5461 weeks
3691.72948 -2.57852 (369*2π)/5461 weeks
3702.62504 -1.74759 (370*2π)/5461 weeks
3712.72635 -1.32506 (371*2π)/5461 weeks
3722.89802 -.92119 (372*2π)/5461 weeks
3732.45435 -.30142 (373*2π)/5461 weeks
3741.57993 -.23191 (374*2π)/5461 weeks
375.89086 -.81111 (375*2π)/5461 weeks
3761.21137 -1.24409 (376*2π)/5461 weeks
3771.80495 -1.23204 (377*2π)/5461 weeks
3781.54734 -1.16921 (378*2π)/5461 weeks
3791.5452 -1.10526 (379*2π)/5461 weeks
3801.27515 -1.32798 (380*2π)/5461 weeks
3811.74757 -1.38468 (381*2π)/5461 weeks
3821.35813 -1.54996 (382*2π)/5461 weeks
3831.82879 -1.64618 (383*2π)/5461 weeks
3841.55677 -1.87384 (384*2π)/5461 weeks
3851.97036 -1.91976 (385*2π)/5461 weeks
3862.26038 -1.4306 (386*2π)/5461 weeks
3871.45555 -.90391 (387*2π)/5461 weeks
3881.09343 -2.21904 (388*2π)/5461 weeks
3892.45969 -2.14745 (389*2π)/5461 weeks
3902.03295 -1.76747 (390*2π)/5461 weeks
3912.40822 -1.98561 (391*2π)/5461 weeks
3922.55928 -1.02901 (392*2π)/5461 weeks
3931.4808 -.55764 (393*2π)/5461 weeks
394.63778 -1.97279 (394*2π)/5461 weeks
3952.72133 -3.43079 (395*2π)/5461 weeks
3964.09745 -1.1637 (396*2π)/5461 weeks
3972.5221 -.13471 (397*2π)/5461 weeks
3981.48869 -.03283 (398*2π)/5461 weeks
399.23326 -.87082 (399*2π)/5461 weeks
400.33402 -2.0033 (400*2π)/5461 weeks
4011.21121 -2.79124 (401*2π)/5461 weeks
4022.60328 -2.62611 (402*2π)/5461 weeks
4032.66863 -2.14191 (403*2π)/5461 weeks
4043.31418 -1.13903 (404*2π)/5461 weeks
4051.60359 1.20095 (405*2π)/5461 weeks
406-1.22289 -.28995 (406*2π)/5461 weeks
407-1.16496 -3.07978 (407*2π)/5461 weeks
4081.3585 -4.8027 (408*2π)/5461 weeks
4093.42225 -2.93723 (409*2π)/5461 weeks
4102.22582 -1.76654 (410*2π)/5461 weeks
4111.35812 -1.59061 (411*2π)/5461 weeks
412-.15941 -2.26234 (412*2π)/5461 weeks
4131.14153 -3.84775 (413*2π)/5461 weeks
4142.31546 -3.59612 (414*2π)/5461 weeks
4152.91685 -4.07156 (415*2π)/5461 weeks
4164.4506 -3.36165 (416*2π)/5461 weeks
4174.04247 -.47701 (417*2π)/5461 weeks
4181.1578 -.29512 (418*2π)/5461 weeks
419.31211 -2.60998 (419*2π)/5461 weeks
4201.62983 -3.62828 (420*2π)/5461 weeks
4212.85096 -3.61981 (421*2π)/5461 weeks
4224.2579 -3.1961 (422*2π)/5461 weeks
4234.50955 -1.48255 (423*2π)/5461 weeks
4242.92089 .60813 (424*2π)/5461 weeks
425.15345 -.15845 (425*2π)/5461 weeks
426-.25418 -2.96573 (426*2π)/5461 weeks
4271.63387 -4.34983 (427*2π)/5461 weeks
4284.42594 -3.53727 (428*2π)/5461 weeks
4294.48147 -.21293 (429*2π)/5461 weeks
4301.50947 1.09776 (430*2π)/5461 weeks
431-1.2793 -.4931 (431*2π)/5461 weeks
432-2.30854 -3.59728 (432*2π)/5461 weeks
433.74683 -6.49312 (433*2π)/5461 weeks
4343.69869 -5.13556 (434*2π)/5461 weeks
4354.70006 -3.19748 (435*2π)/5461 weeks
4363.93263 -.83333 (436*2π)/5461 weeks
437.91193 -.64215 (437*2π)/5461 weeks
438-.79757 -3.56567 (438*2π)/5461 weeks
4391.66062 -5.90264 (439*2π)/5461 weeks
4404.69798 -4.90442 (440*2π)/5461 weeks
4416.27795 -1.97804 (441*2π)/5461 weeks
4424.17996 .75389 (442*2π)/5461 weeks
443.63294 .42811 (443*2π)/5461 weeks
444-1.16768 -3.28496 (444*2π)/5461 weeks
4451.6653 -5.51554 (445*2π)/5461 weeks
4464.53633 -4.10054 (446*2π)/5461 weeks
4475.29752 -1.04956 (447*2π)/5461 weeks
4482.99879 1.23771 (448*2π)/5461 weeks
449-.45662 .03054 (449*2π)/5461 weeks
450-.84391 -3.56817 (450*2π)/5461 weeks
4511.33234 -5.36382 (451*2π)/5461 weeks
4522.47623 -3.46653 (452*2π)/5461 weeks
4532.2829 -3.73958 (453*2π)/5461 weeks
4543.93884 -2.76897 (454*2π)/5461 weeks
4553.15096 -.70222 (455*2π)/5461 weeks
456.38417 -.16946 (456*2π)/5461 weeks
457-1.94476 -3.22359 (457*2π)/5461 weeks
458.21407 -6.98066 (458*2π)/5461 weeks
4594.33507 -7.37797 (459*2π)/5461 weeks
4606.58218 -3.58384 (460*2π)/5461 weeks
4614.20987 .70713 (461*2π)/5461 weeks
462-.04465 -.9937 (462*2π)/5461 weeks
463.48308 -3.69086 (463*2π)/5461 weeks
464.9805 -5.03689 (464*2π)/5461 weeks
4654.40798 -4.77385 (465*2π)/5461 weeks
4664.76138 -1.88265 (466*2π)/5461 weeks
4673.19006 -.09598 (467*2π)/5461 weeks
468-1.50511 -.6097 (468*2π)/5461 weeks
469-1.02741 -5.60016 (469*2π)/5461 weeks
4702.97965 -5.14821 (470*2π)/5461 weeks
4713.90096 -5.06282 (471*2π)/5461 weeks
4726.2524 -2.10865 (472*2π)/5461 weeks
4732.63831 2.35077 (473*2π)/5461 weeks
474-2.06318 .43926 (474*2π)/5461 weeks
475-3.40104 -4.27811 (475*2π)/5461 weeks
476-.33094 -6.42906 (476*2π)/5461 weeks
4771.30174 -3.98344 (477*2π)/5461 weeks
478-.16391 -5.04992 (478*2π)/5461 weeks
4791.69931 -4.78463 (479*2π)/5461 weeks
480.28179 -5.10913 (480*2π)/5461 weeks
481.8934 -5.31729 (481*2π)/5461 weeks
4821.69899 -5.85421 (482*2π)/5461 weeks
4833.19146 -6.39649 (483*2π)/5461 weeks
4843.82402 -4.98229 (484*2π)/5461 weeks
4854.73225 -2.81651 (485*2π)/5461 weeks
4861.07157 1.15241 (486*2π)/5461 weeks
487-4.32946 -2.00721 (487*2π)/5461 weeks
488-5.13986 -7.96893 (488*2π)/5461 weeks
489.41353 -13.07686 (489*2π)/5461 weeks
4907.65451 -10.35777 (490*2π)/5461 weeks
4917.75096 -2.83576 (491*2π)/5461 weeks
4922.31015 .61339 (492*2π)/5461 weeks
493-2.32591 -2.48005 (493*2π)/5461 weeks
494-2.3312 -6.59315 (494*2π)/5461 weeks
495.91972 -8.21645 (495*2π)/5461 weeks
4963.01888 -5.90696 (496*2π)/5461 weeks
4972.37335 -3.48556 (497*2π)/5461 weeks
498-1.2623 -2.93138 (498*2π)/5461 weeks
499-5.25089 -4.4149 (499*2π)/5461 weeks
500-5.6992 -10.55896 (500*2π)/5461 weeks
501-.93403 -14.50491 (501*2π)/5461 weeks
5024.04333 -14.0119 (502*2π)/5461 weeks
5035.88204 -9.25115 (503*2π)/5461 weeks
5043.11831 -7.45424 (504*2π)/5461 weeks
5053.37569 -7.323 (505*2π)/5461 weeks
506.6067 -7.40015 (506*2π)/5461 weeks
5071.07357 -10.54172 (507*2π)/5461 weeks
5082.99747 -10.13528 (508*2π)/5461 weeks
5093.70664 -8.91023 (509*2π)/5461 weeks
5103.73992 -7.03347 (510*2π)/5461 weeks
5111.91175 -6.30411 (511*2π)/5461 weeks
512-.25966 -5.22303 (512*2π)/5461 weeks
513-5.85281 -10.05369 (513*2π)/5461 weeks
514-1.4183 -17.32864 (514*2π)/5461 weeks
5154.14643 -15.33337 (515*2π)/5461 weeks
5166.67131 -10.85166 (516*2π)/5461 weeks
5172.89276 -5.1683 (517*2π)/5461 weeks
518-4.25272 -9.47551 (518*2π)/5461 weeks
519-3.72803 -16.71097 (519*2π)/5461 weeks
520.35493 -23.0565 (520*2π)/5461 weeks
5218.22608 -17.72113 (521*2π)/5461 weeks
5224.5327 -10.74967 (522*2π)/5461 weeks
523-3.21326 -11.63053 (523*2π)/5461 weeks
524-2.60007 -23.22052 (524*2π)/5461 weeks
5255.66783 -27.58048 (525*2π)/5461 weeks
52612.98367 -25.07922 (526*2π)/5461 weeks
52713.19149 -17.01583 (527*2π)/5461 weeks
52811.66187 -10.48672 (528*2π)/5461 weeks
529-.11194 -7.45385 (529*2π)/5461 weeks
530-3.51679 -18.12698 (530*2π)/5461 weeks
531-3.5759 -27.54232 (531*2π)/5461 weeks
5324.47343 -34.44196 (532*2π)/5461 weeks
53311.74712 -33.42072 (533*2π)/5461 weeks
53421.61357 -31.58965 (534*2π)/5461 weeks
53515.58959 -19.13638 (535*2π)/5461 weeks
5365.44729 -25.0197 (536*2π)/5461 weeks
5377.74278 -25.20482 (537*2π)/5461 weeks
538-2.96062 -37.28109 (538*2π)/5461 weeks
53911.93485 -61.41707 (539*2π)/5461 weeks
54037.57741 -52.90224 (540*2π)/5461 weeks
54127.91083 -40.46369 (541*2π)/5461 weeks
54214.26098 -55.15937 (542*2π)/5461 weeks
5434.63633 -76.64481 (543*2π)/5461 weeks
54433.31232 -135.4266 (544*2π)/5461 weeks



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