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Fourier Analysis of DUG (PROSHARES ULTRASHORT OIL & GAS PROSHARES ULTRASHORT OIL & GAS)


DUG (PROSHARES ULTRASHORT OIL & GAS PROSHARES ULTRASHORT OIL & GAS) appears to have interesting cyclic behaviour every 40 weeks (32.7937*sine), 43 weeks (32.4184*sine), and 56 weeks (25.5846*sine).

DUG (PROSHARES ULTRASHORT OIL & GAS PROSHARES ULTRASHORT OIL & GAS) has an average price of 216.76 (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.

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 11/6/2017 for DUG (PROSHARES ULTRASHORT OIL & GAS PROSHARES ULTRASHORT OIL & GAS), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0216.7576   0 
1157.5147 191.0816 (1*2π)/563563 weeks
229.50169 130.2863 (2*2π)/563282 weeks
32.25963 74.70493 (3*2π)/563188 weeks
415.68718 51.49943 (4*2π)/563141 weeks
526.55468 35.80338 (5*2π)/563113 weeks
637.22762 44.12465 (6*2π)/56394 weeks
716.26383 58.77156 (7*2π)/56380 weeks
8-5.36952 40.45021 (8*2π)/56370 weeks
92.14214 23.21729 (9*2π)/56363 weeks
106.39577 25.58459 (10*2π)/56356 weeks
1111.37465 16.60662 (11*2π)/56351 weeks
1221.62113 22.90951 (12*2π)/56347 weeks
1312.23618 32.41838 (13*2π)/56343 weeks
146.87798 32.79367 (14*2π)/56340 weeks
15-1.90376 29.58478 (15*2π)/56338 weeks
16-5.29705 20.26059 (16*2π)/56335 weeks
17-3.83316 13.49979 (17*2π)/56333 weeks
187.5923 6.72068 (18*2π)/56331 weeks
1913.59967 13.26379 (19*2π)/56330 weeks
2013.75337 17.51981 (20*2π)/56328 weeks
218.36697 24.46015 (21*2π)/56327 weeks
22.98004 25.24629 (22*2π)/56326 weeks
23-4.86572 19.06199 (23*2π)/56324 weeks
24.16617 9.24645 (24*2π)/56323 weeks
256.73726 10.49074 (25*2π)/56323 weeks
267.36023 18.39674 (26*2π)/56322 weeks
27-2.22886 21.00916 (27*2π)/56321 weeks
28-4.84562 15.28002 (28*2π)/56320 weeks
29-4.01705 7.88381 (29*2π)/56319 weeks
303.7867 4.67976 (30*2π)/56319 weeks
316.83002 10.35213 (31*2π)/56318 weeks
324.15986 14.72822 (32*2π)/56318 weeks
33-1.43401 16.76014 (33*2π)/56317 weeks
34-5.96117 9.83708 (34*2π)/56317 weeks
35-.88282 4.59921 (35*2π)/56316 weeks
361.56985 5.57582 (36*2π)/56316 weeks
373.48793 6.2222 (37*2π)/56315 weeks
383.86448 8.41846 (38*2π)/56315 weeks
393.28515 9.78851 (39*2π)/56314 weeks
401.60531 10.37594 (40*2π)/56314 weeks
41-.06932 7.61876 (41*2π)/56314 weeks
422.46833 6.0638 (42*2π)/56313 weeks
432.75962 7.14312 (43*2π)/56313 weeks
445.27848 7.21503 (44*2π)/56313 weeks
455.61888 11.6367 (45*2π)/56313 weeks
46.87439 13.82077 (46*2π)/56312 weeks
47-4.33551 12.3499 (47*2π)/56312 weeks
48-6.17191 6.80621 (48*2π)/56312 weeks
49-2.46255 2.55443 (49*2π)/56311 weeks
50.61552 1.98667 (50*2π)/56311 weeks
512.95927 4.49737 (51*2π)/56311 weeks
522.82763 7.0895 (52*2π)/56311 weeks
53-.38634 7.90613 (53*2π)/56311 weeks
54-2.75919 4.81723 (54*2π)/56310 weeks
55-1.49361 .59811 (55*2π)/56310 weeks
564.19501 -.74522 (56*2π)/56310 weeks
578.32042 3.93262 (57*2π)/56310 weeks
585.90904 11.12553 (58*2π)/56310 weeks
59-1.3294 12.08506 (59*2π)/56310 weeks
60-5.26434 6.40178 (60*2π)/5639 weeks
61-3.81367 .93533 (61*2π)/5639 weeks
621.83522 -1.27366 (62*2π)/5639 weeks
634.55234 2.7716 (63*2π)/5639 weeks
643.67959 4.7054 (64*2π)/5639 weeks
652.94356 6.19437 (65*2π)/5639 weeks
661.43372 5.59556 (66*2π)/5639 weeks
67.53814 4.96409 (67*2π)/5638 weeks
68.06539 4.70053 (68*2π)/5638 weeks
691.51524 4.03961 (69*2π)/5638 weeks
70.06808 4.87314 (70*2π)/5638 weeks
711.07024 3.61492 (71*2π)/5638 weeks
72.46275 6.29362 (72*2π)/5638 weeks
73-2.75951 4.97128 (73*2π)/5638 weeks
74-2.86768 .20496 (74*2π)/5638 weeks
75.79735 -2.47387 (75*2π)/5638 weeks
765.75825 .14421 (76*2π)/5637 weeks
774.62606 4.33559 (77*2π)/5637 weeks
782.65834 4.64124 (78*2π)/5637 weeks
79.72608 6.44859 (79*2π)/5637 weeks
80-2.22003 2.76109 (80*2π)/5637 weeks
811.18572 -.97884 (81*2π)/5637 weeks
823.69312 .74133 (82*2π)/5637 weeks
834.80126 3.12254 (83*2π)/5637 weeks
842.91306 5.63474 (84*2π)/5637 weeks
85.76185 3.99769 (85*2π)/5637 weeks
86-.22619 2.92812 (86*2π)/5637 weeks
87.73277 -.39079 (87*2π)/5636 weeks
885.42487 .14107 (88*2π)/5636 weeks
895.9976 4.35799 (89*2π)/5636 weeks
902.82111 7.241 (90*2π)/5636 weeks
91-.7009 6.20883 (91*2π)/5636 weeks
92-1.71367 2.33164 (92*2π)/5636 weeks
93.89185 .13152 (93*2π)/5636 weeks
943.20539 .90743 (94*2π)/5636 weeks
953.68975 2.78836 (95*2π)/5636 weeks
962.16034 3.27186 (96*2π)/5636 weeks
972.51144 3.24362 (97*2π)/5636 weeks
981.14447 5.15871 (98*2π)/5636 weeks
99-.91228 3.45535 (99*2π)/5636 weeks
100-.65638 -.02457 (100*2π)/5636 weeks
1012.51789 -1.39491 (101*2π)/5636 weeks
1024.8671 .6148 (102*2π)/5636 weeks
1034.50983 3.67749 (103*2π)/5635 weeks
1042.12763 5.42116 (104*2π)/5635 weeks
105-.79776 3.89936 (105*2π)/5635 weeks
106-.13141 -.09078 (106*2π)/5635 weeks
1072.96221 -1.17128 (107*2π)/5635 weeks
1085.46273 .83718 (108*2π)/5635 weeks
1094.97173 4.23367 (109*2π)/5635 weeks
1102.78363 5.86895 (110*2π)/5635 weeks
111-.05015 4.67942 (111*2π)/5635 weeks
112-.06303 1.21825 (112*2π)/5635 weeks
1132.43694 .09134 (113*2π)/5635 weeks
1144.2799 1.93571 (114*2π)/5635 weeks
1154.05448 4.03316 (115*2π)/5635 weeks
1162.65593 5.81243 (116*2π)/5635 weeks
117-.92326 5.45212 (117*2π)/5635 weeks
118-1.85987 1.79692 (118*2π)/5635 weeks
119-.43163 -.56869 (119*2π)/5635 weeks
1202.45711 -1.03102 (120*2π)/5635 weeks
1214.65406 1.22571 (121*2π)/5635 weeks
1223.45361 4.00538 (122*2π)/5635 weeks
1231.05077 3.86499 (123*2π)/5635 weeks
124-.4735 2.11888 (124*2π)/5635 weeks
125.58208 -.31683 (125*2π)/5635 weeks
1263.19753 -.43285 (126*2π)/5634 weeks
1274.12185 1.61684 (127*2π)/5634 weeks
1283.77079 3.206 (128*2π)/5634 weeks
1292.63922 3.41738 (129*2π)/5634 weeks
1301.49335 3.38284 (130*2π)/5634 weeks
131.2248 2.3773 (131*2π)/5634 weeks
1321.05055 .23051 (132*2π)/5634 weeks
1333.73738 .35986 (133*2π)/5634 weeks
1344.26199 3.01857 (134*2π)/5634 weeks
1352.84315 3.72486 (135*2π)/5634 weeks
1362.13451 3.25225 (136*2π)/5634 weeks
1371.18407 3.69982 (137*2π)/5634 weeks
138-.22699 2.69388 (138*2π)/5634 weeks
1391.1737 1.46189 (139*2π)/5634 weeks
1402.00161 1.45684 (140*2π)/5634 weeks
1413.05837 1.92907 (141*2π)/5634 weeks
1422.06213 4.23331 (142*2π)/5634 weeks
143-.75526 3.73286 (143*2π)/5634 weeks
144-1.47543 1.36951 (144*2π)/5634 weeks
145.29479 -.93743 (145*2π)/5634 weeks
1463.16693 -.00004 (146*2π)/5634 weeks
1472.79816 1.61971 (147*2π)/5634 weeks
1482.32388 1.90515 (148*2π)/5634 weeks
1491.67131 2.87905 (149*2π)/5634 weeks
150.72446 2.48541 (150*2π)/5634 weeks
151.29788 1.46763 (151*2π)/5634 weeks
152.56689 .15803 (152*2π)/5634 weeks
1531.70461 -.06776 (153*2π)/5634 weeks
1542.69717 .07278 (154*2π)/5634 weeks
1553.78518 2.01687 (155*2π)/5634 weeks
1561.64244 3.38145 (156*2π)/5634 weeks
157.6276 1.4604 (157*2π)/5634 weeks
1581.73664 .49112 (158*2π)/5634 weeks
1592.51256 1.08956 (159*2π)/5634 weeks
1602.11574 1.84766 (160*2π)/5634 weeks
1611.93248 1.59578 (161*2π)/5633 weeks
1622.27943 2.1933 (162*2π)/5633 weeks
163.94736 2.02566 (163*2π)/5633 weeks
1641.40222 .82862 (164*2π)/5633 weeks
1652.10357 1.33761 (165*2π)/5633 weeks
1661.84741 1.76775 (166*2π)/5633 weeks
1671.50203 1.73303 (167*2π)/5633 weeks
1681.75556 1.46409 (168*2π)/5633 weeks
1691.29797 1.51511 (169*2π)/5633 weeks
1701.57364 1.23533 (170*2π)/5633 weeks
1711.13431 1.37288 (171*2π)/5633 weeks
1721.33917 1.01838 (172*2π)/5633 weeks
1731.45507 1.09106 (173*2π)/5633 weeks
1741.655 1.01704 (174*2π)/5633 weeks
1751.2797 1.41338 (175*2π)/5633 weeks
1761.04349 1.13839 (176*2π)/5633 weeks
1771.32286 .27026 (177*2π)/5633 weeks
1781.98006 .02773 (178*2π)/5633 weeks
1792.51222 .44516 (179*2π)/5633 weeks
1802.48436 1.09715 (180*2π)/5633 weeks
1812.46953 1.49463 (181*2π)/5633 weeks
1822.34234 2.20728 (182*2π)/5633 weeks
183.91074 2.24425 (183*2π)/5633 weeks
184.79081 .9438 (184*2π)/5633 weeks
1851.16949 .5891 (185*2π)/5633 weeks
1861.84694 .50615 (186*2π)/5633 weeks
1871.78935 1.23489 (187*2π)/5633 weeks
1881.51653 1.01169 (188*2π)/5633 weeks
1891.24335 .63605 (189*2π)/5633 weeks
1901.61685 .26618 (190*2π)/5633 weeks
1911.69175 .40982 (191*2π)/5633 weeks
1922.65632 .19152 (192*2π)/5633 weeks
1932.94701 1.68447 (193*2π)/5633 weeks
1941.3916 1.94335 (194*2π)/5633 weeks
195.63621 1.29291 (195*2π)/5633 weeks
196.61227 .10336 (196*2π)/5633 weeks
1971.95019 -.82552 (197*2π)/5633 weeks
1983.19196 -.41105 (198*2π)/5633 weeks
1994.21528 .83801 (199*2π)/5633 weeks
2003.40646 3.4371 (200*2π)/5633 weeks
201.70568 3.12908 (201*2π)/5633 weeks
202.0194 1.4758 (202*2π)/5633 weeks
203.69227 .07103 (203*2π)/5633 weeks
2042.14534 -.00905 (204*2π)/5633 weeks
2052.39873 1.2054 (205*2π)/5633 weeks
2062.37332 1.72704 (206*2π)/5633 weeks
207.81985 2.49393 (207*2π)/5633 weeks
208-.19812 .50583 (208*2π)/5633 weeks
209.6298 -.36075 (209*2π)/5633 weeks
2101.75299 -1.18988 (210*2π)/5633 weeks
2113.54661 -.26893 (211*2π)/5633 weeks
2123.77418 2.1272 (212*2π)/5633 weeks
2131.54864 3.2923 (213*2π)/5633 weeks
214-.73055 1.70453 (214*2π)/5633 weeks
215-.25675 -1.04471 (215*2π)/5633 weeks
2162.58157 -1.37302 (216*2π)/5633 weeks
2173.76912 .43291 (217*2π)/5633 weeks
2183.36597 2.26404 (218*2π)/5633 weeks
219.82124 3.1395 (219*2π)/5633 weeks
220-.38462 1.1784 (220*2π)/5633 weeks
221.38507 -.47005 (221*2π)/5633 weeks
2222.24498 -.62047 (222*2π)/5633 weeks
2232.52519 1.01718 (223*2π)/5633 weeks
2241.61787 1.40021 (224*2π)/5633 weeks
2251.47477 1.08061 (225*2π)/5633 weeks
2261.41052 1.36601 (226*2π)/5632 weeks
227.44038 1.17424 (227*2π)/5632 weeks
228.77908 .35207 (228*2π)/5632 weeks
229.98957 .65547 (229*2π)/5632 weeks
230.96785 .37187 (230*2π)/5632 weeks
2311.43432 .74941 (231*2π)/5632 weeks
232.93956 .65021 (232*2π)/5632 weeks
233.24978 .46409 (233*2π)/5632 weeks
234-.18257 -.6266 (234*2π)/5632 weeks
2351.21257 -1.16183 (235*2π)/5632 weeks
2362.2508 -.59857 (236*2π)/5632 weeks
2372.43382 -.05936 (237*2π)/5632 weeks
2381.83504 .93216 (238*2π)/5632 weeks
239.82807 1.02168 (239*2π)/5632 weeks
240-.01032 .25525 (240*2π)/5632 weeks
241.00841 -1.17751 (241*2π)/5632 weeks
2421.34006 -1.95839 (242*2π)/5632 weeks
2432.675 -1.48441 (243*2π)/5632 weeks
2443.21518 -.47198 (244*2π)/5632 weeks
2452.47784 1.16301 (245*2π)/5632 weeks
2461.31051 .37965 (246*2π)/5632 weeks
2471.24935 .0321 (247*2π)/5632 weeks
2481.39594 -1.09145 (248*2π)/5632 weeks
2492.6618 -.42374 (249*2π)/5632 weeks
2502.66811 .45583 (250*2π)/5632 weeks
2512.17696 1.12549 (251*2π)/5632 weeks
252.54818 1.13392 (252*2π)/5632 weeks
253-.20681 -.28547 (253*2π)/5632 weeks
254.68302 -1.59412 (254*2π)/5632 weeks
2552.18876 -2.32063 (255*2π)/5632 weeks
2563.68152 -1.13042 (256*2π)/5632 weeks
2573.39778 .74041 (257*2π)/5632 weeks
2582.15744 1.26661 (258*2π)/5632 weeks
259.95177 .83366 (259*2π)/5632 weeks
260.40396 -.28747 (260*2π)/5632 weeks
2611.3568 -1.59911 (261*2π)/5632 weeks
2622.92143 -2.03292 (262*2π)/5632 weeks
2634.35927 .05586 (263*2π)/5632 weeks
2642.70596 2.07083 (264*2π)/5632 weeks
265.99104 1.41791 (265*2π)/5632 weeks
266-.09243 -.05581 (266*2π)/5632 weeks
267.5044 -1.96915 (267*2π)/5632 weeks
2682.9713 -2.10539 (268*2π)/5632 weeks
2694.18582 -.06788 (269*2π)/5632 weeks
2702.56603 1.22977 (270*2π)/5632 weeks
271.7696 1.02856 (271*2π)/5632 weeks
272-.04503 -.6253 (272*2π)/5632 weeks
273.85719 -2.44262 (273*2π)/5632 weeks
2743.37902 -3.24967 (274*2π)/5632 weeks
2755.35255 -.72859 (275*2π)/5632 weeks
2763.93661 1.58005 (276*2π)/5632 weeks
2771.88676 1.58312 (277*2π)/5632 weeks
278.9641 .62843 (278*2π)/5632 weeks
2791.18483 -.93444 (279*2π)/5632 weeks
2802.38487 -1.83083 (280*2π)/5632 weeks
2814.202 -1.38118 (281*2π)/5632 weeks
2824.202 1.38118 (282*2π)/5632 weeks
2832.38487 1.83083 (283*2π)/5632 weeks
2841.18483 .93444 (284*2π)/5632 weeks
285.9641 -.62843 (285*2π)/5632 weeks
2861.88676 -1.58312 (286*2π)/5632 weeks
2873.93661 -1.58005 (287*2π)/5632 weeks
2885.35255 .72859 (288*2π)/5632 weeks
2893.37902 3.24967 (289*2π)/5632 weeks
290.85719 2.44262 (290*2π)/5632 weeks
291-.04503 .6253 (291*2π)/5632 weeks
292.7696 -1.02856 (292*2π)/5632 weeks
2932.56603 -1.22977 (293*2π)/5632 weeks
2944.18582 .06788 (294*2π)/5632 weeks
2952.9713 2.10539 (295*2π)/5632 weeks
296.5044 1.96915 (296*2π)/5632 weeks
297-.09243 .05581 (297*2π)/5632 weeks
298.99104 -1.41791 (298*2π)/5632 weeks
2992.70596 -2.07083 (299*2π)/5632 weeks
3004.35927 -.05586 (300*2π)/5632 weeks
3012.92143 2.03292 (301*2π)/5632 weeks
3021.3568 1.59911 (302*2π)/5632 weeks
303.40396 .28747 (303*2π)/5632 weeks
304.95177 -.83366 (304*2π)/5632 weeks
3052.15744 -1.26661 (305*2π)/5632 weeks
3063.39778 -.74041 (306*2π)/5632 weeks
3073.68152 1.13042 (307*2π)/5632 weeks
3082.18876 2.32063 (308*2π)/5632 weeks
309.68302 1.59412 (309*2π)/5632 weeks
310-.20681 .28547 (310*2π)/5632 weeks
311.54818 -1.13392 (311*2π)/5632 weeks
3122.17696 -1.12549 (312*2π)/5632 weeks
3132.66811 -.45583 (313*2π)/5632 weeks
3142.6618 .42374 (314*2π)/5632 weeks
3151.39594 1.09145 (315*2π)/5632 weeks
3161.24935 -.0321 (316*2π)/5632 weeks
3171.31051 -.37965 (317*2π)/5632 weeks
3182.47784 -1.16301 (318*2π)/5632 weeks
3193.21518 .47198 (319*2π)/5632 weeks
3202.675 1.48441 (320*2π)/5632 weeks
3211.34006 1.95839 (321*2π)/5632 weeks
322.00841 1.17751 (322*2π)/5632 weeks
323-.01032 -.25525 (323*2π)/5632 weeks
324.82807 -1.02168 (324*2π)/5632 weeks
3251.83504 -.93216 (325*2π)/5632 weeks
3262.43382 .05936 (326*2π)/5632 weeks
3272.2508 .59857 (327*2π)/5632 weeks
3281.21257 1.16183 (328*2π)/5632 weeks
329-.18257 .6266 (329*2π)/5632 weeks
330.24978 -.46409 (330*2π)/5632 weeks
331.93956 -.65021 (331*2π)/5632 weeks
3321.43432 -.74941 (332*2π)/5632 weeks
333.96785 -.37187 (333*2π)/5632 weeks
334.98957 -.65547 (334*2π)/5632 weeks
335.77908 -.35207 (335*2π)/5632 weeks
336.44038 -1.17424 (336*2π)/5632 weeks
3371.41052 -1.36601 (337*2π)/5632 weeks
3381.47477 -1.08061 (338*2π)/5632 weeks
3391.61787 -1.40021 (339*2π)/5632 weeks
3402.52519 -1.01718 (340*2π)/5632 weeks
3412.24498 .62047 (341*2π)/5632 weeks
342.38507 .47005 (342*2π)/5632 weeks
343-.38462 -1.1784 (343*2π)/5632 weeks
344.82124 -3.1395 (344*2π)/5632 weeks
3453.36597 -2.26404 (345*2π)/5632 weeks
3463.76912 -.43291 (346*2π)/5632 weeks
3472.58157 1.37302 (347*2π)/5632 weeks
348-.25675 1.04471 (348*2π)/5632 weeks
349-.73055 -1.70453 (349*2π)/5632 weeks
3501.54864 -3.2923 (350*2π)/5632 weeks
3513.77418 -2.1272 (351*2π)/5632 weeks
3523.54661 .26893 (352*2π)/5632 weeks
3531.75299 1.18988 (353*2π)/5632 weeks
354.6298 .36075 (354*2π)/5632 weeks
355-.19812 -.50583 (355*2π)/5632 weeks
356.81985 -2.49393 (356*2π)/5632 weeks
3572.37332 -1.72704 (357*2π)/5632 weeks
3582.39873 -1.2054 (358*2π)/5632 weeks
3592.14534 .00905 (359*2π)/5632 weeks
360.69227 -.07103 (360*2π)/5632 weeks
361.0194 -1.4758 (361*2π)/5632 weeks
362.70568 -3.12908 (362*2π)/5632 weeks
3633.40646 -3.4371 (363*2π)/5632 weeks
3644.21528 -.83801 (364*2π)/5632 weeks
3653.19196 .41105 (365*2π)/5632 weeks
3661.95019 .82552 (366*2π)/5632 weeks
367.61227 -.10336 (367*2π)/5632 weeks
368.63621 -1.29291 (368*2π)/5632 weeks
3691.3916 -1.94335 (369*2π)/5632 weeks
3702.94701 -1.68447 (370*2π)/5632 weeks
3712.65632 -.19152 (371*2π)/5632 weeks
3721.69175 -.40982 (372*2π)/5632 weeks
3731.61685 -.26618 (373*2π)/5632 weeks
3741.24335 -.63605 (374*2π)/5632 weeks
3751.51653 -1.01169 (375*2π)/5632 weeks
3761.78935 -1.23489 (376*2π)/5631 weeks
3771.84694 -.50615 (377*2π)/5631 weeks
3781.16949 -.5891 (378*2π)/5631 weeks
379.79081 -.9438 (379*2π)/5631 weeks
380.91074 -2.24425 (380*2π)/5631 weeks
3812.34234 -2.20728 (381*2π)/5631 weeks
3822.46953 -1.49463 (382*2π)/5631 weeks
3832.48436 -1.09715 (383*2π)/5631 weeks
3842.51222 -.44516 (384*2π)/5631 weeks
3851.98006 -.02773 (385*2π)/5631 weeks
3861.32286 -.27026 (386*2π)/5631 weeks
3871.04349 -1.13839 (387*2π)/5631 weeks
3881.2797 -1.41338 (388*2π)/5631 weeks
3891.655 -1.01704 (389*2π)/5631 weeks
3901.45507 -1.09106 (390*2π)/5631 weeks
3911.33917 -1.01838 (391*2π)/5631 weeks
3921.13431 -1.37288 (392*2π)/5631 weeks
3931.57364 -1.23533 (393*2π)/5631 weeks
3941.29797 -1.51511 (394*2π)/5631 weeks
3951.75556 -1.46409 (395*2π)/5631 weeks
3961.50203 -1.73303 (396*2π)/5631 weeks
3971.84741 -1.76775 (397*2π)/5631 weeks
3982.10357 -1.33761 (398*2π)/5631 weeks
3991.40222 -.82862 (399*2π)/5631 weeks
400.94736 -2.02566 (400*2π)/5631 weeks
4012.27943 -2.1933 (401*2π)/5631 weeks
4021.93248 -1.59578 (402*2π)/5631 weeks
4032.11574 -1.84766 (403*2π)/5631 weeks
4042.51256 -1.08956 (404*2π)/5631 weeks
4051.73664 -.49112 (405*2π)/5631 weeks
406.6276 -1.4604 (406*2π)/5631 weeks
4071.64244 -3.38145 (407*2π)/5631 weeks
4083.78518 -2.01687 (408*2π)/5631 weeks
4092.69717 -.07278 (409*2π)/5631 weeks
4101.70461 .06776 (410*2π)/5631 weeks
411.56689 -.15803 (411*2π)/5631 weeks
412.29788 -1.46763 (412*2π)/5631 weeks
413.72446 -2.48541 (413*2π)/5631 weeks
4141.67131 -2.87905 (414*2π)/5631 weeks
4152.32388 -1.90515 (415*2π)/5631 weeks
4162.79816 -1.61971 (416*2π)/5631 weeks
4173.16693 .00004 (417*2π)/5631 weeks
418.29479 .93743 (418*2π)/5631 weeks
419-1.47543 -1.36951 (419*2π)/5631 weeks
420-.75526 -3.73286 (420*2π)/5631 weeks
4212.06213 -4.23331 (421*2π)/5631 weeks
4223.05837 -1.92907 (422*2π)/5631 weeks
4232.00161 -1.45684 (423*2π)/5631 weeks
4241.1737 -1.46189 (424*2π)/5631 weeks
425-.22699 -2.69388 (425*2π)/5631 weeks
4261.18407 -3.69982 (426*2π)/5631 weeks
4272.13451 -3.25225 (427*2π)/5631 weeks
4282.84315 -3.72486 (428*2π)/5631 weeks
4294.26199 -3.01857 (429*2π)/5631 weeks
4303.73738 -.35986 (430*2π)/5631 weeks
4311.05055 -.23051 (431*2π)/5631 weeks
432.2248 -2.3773 (432*2π)/5631 weeks
4331.49335 -3.38284 (433*2π)/5631 weeks
4342.63922 -3.41738 (434*2π)/5631 weeks
4353.77079 -3.206 (435*2π)/5631 weeks
4364.12185 -1.61684 (436*2π)/5631 weeks
4373.19753 .43285 (437*2π)/5631 weeks
438.58208 .31683 (438*2π)/5631 weeks
439-.4735 -2.11888 (439*2π)/5631 weeks
4401.05077 -3.86499 (440*2π)/5631 weeks
4413.45361 -4.00538 (441*2π)/5631 weeks
4424.65406 -1.22571 (442*2π)/5631 weeks
4432.45711 1.03102 (443*2π)/5631 weeks
444-.43163 .56869 (444*2π)/5631 weeks
445-1.85987 -1.79692 (445*2π)/5631 weeks
446-.92326 -5.45212 (446*2π)/5631 weeks
4472.65593 -5.81243 (447*2π)/5631 weeks
4484.05448 -4.03316 (448*2π)/5631 weeks
4494.2799 -1.93571 (449*2π)/5631 weeks
4502.43694 -.09134 (450*2π)/5631 weeks
451-.06303 -1.21825 (451*2π)/5631 weeks
452-.05015 -4.67942 (452*2π)/5631 weeks
4532.78363 -5.86895 (453*2π)/5631 weeks
4544.97173 -4.23367 (454*2π)/5631 weeks
4555.46273 -.83718 (455*2π)/5631 weeks
4562.96221 1.17128 (456*2π)/5631 weeks
457-.13141 .09078 (457*2π)/5631 weeks
458-.79776 -3.89936 (458*2π)/5631 weeks
4592.12763 -5.42116 (459*2π)/5631 weeks
4604.50983 -3.67749 (460*2π)/5631 weeks
4614.8671 -.6148 (461*2π)/5631 weeks
4622.51789 1.39491 (462*2π)/5631 weeks
463-.65638 .02457 (463*2π)/5631 weeks
464-.91228 -3.45535 (464*2π)/5631 weeks
4651.14447 -5.15871 (465*2π)/5631 weeks
4662.51144 -3.24362 (466*2π)/5631 weeks
4672.16034 -3.27186 (467*2π)/5631 weeks
4683.68975 -2.78836 (468*2π)/5631 weeks
4693.20539 -.90743 (469*2π)/5631 weeks
470.89185 -.13152 (470*2π)/5631 weeks
471-1.71367 -2.33164 (471*2π)/5631 weeks
472-.7009 -6.20883 (472*2π)/5631 weeks
4732.82111 -7.241 (473*2π)/5631 weeks
4745.9976 -4.35799 (474*2π)/5631 weeks
4755.42487 -.14107 (475*2π)/5631 weeks
476.73277 .39079 (476*2π)/5631 weeks
477-.22619 -2.92812 (477*2π)/5631 weeks
478.76185 -3.99769 (478*2π)/5631 weeks
4792.91306 -5.63474 (479*2π)/5631 weeks
4804.80126 -3.12254 (480*2π)/5631 weeks
4813.69312 -.74133 (481*2π)/5631 weeks
4821.18572 .97884 (482*2π)/5631 weeks
483-2.22003 -2.76109 (483*2π)/5631 weeks
484.72608 -6.44859 (484*2π)/5631 weeks
4852.65834 -4.64124 (485*2π)/5631 weeks
4864.62606 -4.33559 (486*2π)/5631 weeks
4875.75825 -.14421 (487*2π)/5631 weeks
488.79735 2.47387 (488*2π)/5631 weeks
489-2.86768 -.20496 (489*2π)/5631 weeks
490-2.75951 -4.97128 (490*2π)/5631 weeks
491.46275 -6.29362 (491*2π)/5631 weeks
4921.07024 -3.61492 (492*2π)/5631 weeks
493.06808 -4.87314 (493*2π)/5631 weeks
4941.51524 -4.03961 (494*2π)/5631 weeks
495.06539 -4.70053 (495*2π)/5631 weeks
496.53814 -4.96409 (496*2π)/5631 weeks
4971.43372 -5.59556 (497*2π)/5631 weeks
4982.94356 -6.19437 (498*2π)/5631 weeks
4993.67959 -4.7054 (499*2π)/5631 weeks
5004.55234 -2.7716 (500*2π)/5631 weeks
5011.83522 1.27366 (501*2π)/5631 weeks
502-3.81367 -.93533 (502*2π)/5631 weeks
503-5.26434 -6.40178 (503*2π)/5631 weeks
504-1.3294 -12.08506 (504*2π)/5631 weeks
5055.90904 -11.12553 (505*2π)/5631 weeks
5068.32042 -3.93262 (506*2π)/5631 weeks
5074.19501 .74522 (507*2π)/5631 weeks
508-1.49361 -.59811 (508*2π)/5631 weeks
509-2.75919 -4.81723 (509*2π)/5631 weeks
510-.38634 -7.90613 (510*2π)/5631 weeks
5112.82763 -7.0895 (511*2π)/5631 weeks
5122.95927 -4.49737 (512*2π)/5631 weeks
513.61552 -1.98667 (513*2π)/5631 weeks
514-2.46255 -2.55443 (514*2π)/5631 weeks
515-6.17191 -6.80621 (515*2π)/5631 weeks
516-4.33551 -12.3499 (516*2π)/5631 weeks
517.87439 -13.82077 (517*2π)/5631 weeks
5185.61888 -11.6367 (518*2π)/5631 weeks
5195.27848 -7.21503 (519*2π)/5631 weeks
5202.75962 -7.14312 (520*2π)/5631 weeks
5212.46833 -6.0638 (521*2π)/5631 weeks
522-.06932 -7.61876 (522*2π)/5631 weeks
5231.60531 -10.37594 (523*2π)/5631 weeks
5243.28515 -9.78851 (524*2π)/5631 weeks
5253.86448 -8.41846 (525*2π)/5631 weeks
5263.48793 -6.2222 (526*2π)/5631 weeks
5271.56985 -5.57582 (527*2π)/5631 weeks
528-.88282 -4.59921 (528*2π)/5631 weeks
529-5.96117 -9.83708 (529*2π)/5631 weeks
530-1.43401 -16.76014 (530*2π)/5631 weeks
5314.15986 -14.72822 (531*2π)/5631 weeks
5326.83002 -10.35213 (532*2π)/5631 weeks
5333.7867 -4.67976 (533*2π)/5631 weeks
534-4.01705 -7.88381 (534*2π)/5631 weeks
535-4.84562 -15.28002 (535*2π)/5631 weeks
536-2.22886 -21.00916 (536*2π)/5631 weeks
5377.36023 -18.39674 (537*2π)/5631 weeks
5386.73726 -10.49074 (538*2π)/5631 weeks
539.16617 -9.24645 (539*2π)/5631 weeks
540-4.86572 -19.06199 (540*2π)/5631 weeks
541.98004 -25.24629 (541*2π)/5631 weeks
5428.36697 -24.46015 (542*2π)/5631 weeks
54313.75337 -17.51981 (543*2π)/5631 weeks
54413.59967 -13.26379 (544*2π)/5631 weeks
5457.5923 -6.72068 (545*2π)/5631 weeks
546-3.83316 -13.49979 (546*2π)/5631 weeks
547-5.29705 -20.26059 (547*2π)/5631 weeks
548-1.90376 -29.58478 (548*2π)/5631 weeks
5496.87798 -32.79367 (549*2π)/5631 weeks
55012.23618 -32.41838 (550*2π)/5631 weeks
55121.62113 -22.90951 (551*2π)/5631 weeks
55211.37465 -16.60662 (552*2π)/5631 weeks
5536.39577 -25.58459 (553*2π)/5631 weeks
5542.14214 -23.21729 (554*2π)/5631 weeks
555-5.36952 -40.45021 (555*2π)/5631 weeks
55616.26383 -58.77156 (556*2π)/5631 weeks
55737.22762 -44.12465 (557*2π)/5631 weeks
55826.55468 -35.80338 (558*2π)/5631 weeks
55915.68718 -51.49943 (559*2π)/5631 weeks
5602.25963 -74.70493 (560*2π)/5631 weeks
56129.50169 -130.2863 (561*2π)/5631 weeks



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