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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 47 weeks (47.9017*sine), 43 weeks (35.2919*sine), and 51 weeks (30.5757*cosine).

TWM (ProShares UltraShort Russell 2000 ETF) has an average price of 307.15 (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 10/9/2017 for TWM (ProShares UltraShort Russell 2000 ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0307.1541   0 
1199.1366 351.5663 (1*2π)/560560 weeks
2-41.29818 232.0902 (2*2π)/560280 weeks
3-92.32467 79.05676 (3*2π)/560187 weeks
4-22.7644 .99828 (4*2π)/560140 weeks
532.24218 14.75301 (5*2π)/560112 weeks
634.73114 56.22513 (6*2π)/56093 weeks
7-6.01447 66.403 (7*2π)/56080 weeks
8-36.31706 23.95971 (8*2π)/56070 weeks
9-3.05175 -9.18815 (9*2π)/56062 weeks
1022.30433 6.03409 (10*2π)/56056 weeks
1130.57572 22.68847 (11*2π)/56051 weeks
1214.40825 47.90169 (12*2π)/56047 weeks
13-15.16016 35.29192 (13*2π)/56043 weeks
14-13.28536 13.17886 (14*2π)/56040 weeks
15-3.22375 6.18148 (15*2π)/56037 weeks
163.72353 9.2176 (16*2π)/56035 weeks
171.21202 9.31644 (17*2π)/56033 weeks
1810.04767 7.65173 (18*2π)/56031 weeks
198.38606 16.57792 (19*2π)/56029 weeks
205.24407 14.47193 (20*2π)/56028 weeks
214.1401 16.63124 (21*2π)/56027 weeks
22-.79614 15.34479 (22*2π)/56025 weeks
23-2.07748 8.54093 (23*2π)/56024 weeks
247.16861 8.09861 (24*2π)/56023 weeks
259.11561 15.86031 (25*2π)/56022 weeks
26.0676 24.21353 (26*2π)/56022 weeks
27-15.19808 15.54116 (27*2π)/56021 weeks
28-13.26499 .01216 (28*2π)/56020 weeks
29.3681 -9.52135 (29*2π)/56019 weeks
3018.65335 .59502 (30*2π)/56019 weeks
3115.80924 22.0376 (31*2π)/56018 weeks
32-5.66017 26.76227 (32*2π)/56018 weeks
33-21.12195 10.66595 (33*2π)/56017 weeks
34-12.30427 -11.89157 (34*2π)/56016 weeks
3511.05293 -10.23343 (35*2π)/56016 weeks
3615.83389 6.3723 (36*2π)/56016 weeks
377.75772 16.27556 (37*2π)/56015 weeks
38-4.14505 13.61765 (38*2π)/56015 weeks
39-4.99997 4.5264 (39*2π)/56014 weeks
40-.09402 .64258 (40*2π)/56014 weeks
415.51638 1.46959 (41*2π)/56014 weeks
427.6937 9.28219 (42*2π)/56013 weeks
43-.53603 11.66026 (43*2π)/56013 weeks
44-1.56205 4.91202 (44*2π)/56013 weeks
451.12141 4.47204 (45*2π)/56012 weeks
463.0285 6.67049 (46*2π)/56012 weeks
47-1.01386 9.41267 (47*2π)/56012 weeks
48-4.58146 4.97829 (48*2π)/56012 weeks
49-2.47839 1.834 (49*2π)/56011 weeks
501.61445 .28888 (50*2π)/56011 weeks
512.87751 3.43697 (51*2π)/56011 weeks
521.55406 5.66372 (52*2π)/56011 weeks
53-1.30539 3.94802 (53*2π)/56011 weeks
54-.23995 1.31199 (54*2π)/56010 weeks
552.06145 -.01135 (55*2π)/56010 weeks
566.68245 1.87649 (56*2π)/56010 weeks
575.29104 8.83238 (57*2π)/56010 weeks
58-2.62013 7.41767 (58*2π)/56010 weeks
59-2.61559 1.50349 (59*2π)/5609 weeks
602.11407 .13313 (60*2π)/5609 weeks
614.04159 3.21735 (61*2π)/5609 weeks
621.31783 7.17858 (62*2π)/5609 weeks
63-4.34058 3.13315 (63*2π)/5609 weeks
64-.33843 -3.15883 (64*2π)/5609 weeks
655.59815 -2.65769 (65*2π)/5609 weeks
668.96555 3.52128 (66*2π)/5608 weeks
674.54019 8.55794 (67*2π)/5608 weeks
68-.24566 5.45099 (68*2π)/5608 weeks
69.69824 3.52322 (69*2π)/5608 weeks
702.91165 2.6324 (70*2π)/5608 weeks
713.41153 7.4417 (71*2π)/5608 weeks
72-4.09345 8.05153 (72*2π)/5608 weeks
73-6.35143 .13591 (73*2π)/5608 weeks
74-.63796 -4.98333 (74*2π)/5608 weeks
757.30714 -3.40291 (75*2π)/5607 weeks
767.86982 5.29985 (76*2π)/5607 weeks
771.76933 6.5555 (77*2π)/5607 weeks
78-.41676 5.90292 (78*2π)/5607 weeks
79-4.5399 .85916 (79*2π)/5607 weeks
801.80411 -5.14746 (80*2π)/5607 weeks
818.28377 -.2069 (81*2π)/5607 weeks
827.61749 5.81624 (82*2π)/5607 weeks
831.46917 9.2066 (83*2π)/5607 weeks
84-3.69241 4.48094 (84*2π)/5607 weeks
85-2.60771 -.67765 (85*2π)/5607 weeks
862.19144 -4.42514 (86*2π)/5607 weeks
879.29261 -.3073 (87*2π)/5606 weeks
887.87363 7.44176 (88*2π)/5606 weeks
891.37971 9.61175 (89*2π)/5606 weeks
90-2.9474 5.21136 (90*2π)/5606 weeks
91-1.56965 .91602 (91*2π)/5606 weeks
921.36894 .77278 (92*2π)/5606 weeks
932.16006 2.64079 (93*2π)/5606 weeks
94.3561 3.65028 (94*2π)/5606 weeks
95-.73971 1.39401 (95*2π)/5606 weeks
961.96253 .60944 (96*2π)/5606 weeks
971.43896 2.80374 (97*2π)/5606 weeks
98-.4141 1.30292 (98*2π)/5606 weeks
99.63041 -1.40758 (99*2π)/5606 weeks
1004.34894 -1.67491 (100*2π)/5606 weeks
1016.49374 1.94479 (101*2π)/5606 weeks
1024.14524 6.04961 (102*2π)/5605 weeks
103-.55346 5.59708 (103*2π)/5605 weeks
104-2.50699 .4986 (104*2π)/5605 weeks
1052.14875 -3.5048 (105*2π)/5605 weeks
1067.36536 -.369 (106*2π)/5605 weeks
1077.52221 5.33232 (107*2π)/5605 weeks
1082.19026 8.72917 (108*2π)/5605 weeks
109-2.52095 6.08473 (109*2π)/5605 weeks
110-3.69825 .17185 (110*2π)/5605 weeks
1112.02586 -3.59983 (111*2π)/5605 weeks
1127.11755 .66445 (112*2π)/5605 weeks
1135.42502 6.80449 (113*2π)/5605 weeks
114-.20753 7.59693 (114*2π)/5605 weeks
115-3.13609 4.31125 (115*2π)/5605 weeks
116-3.69617 -.10202 (116*2π)/5605 weeks
1171.03091 -3.40245 (117*2π)/5605 weeks
1184.98237 -.00183 (118*2π)/5605 weeks
1193.70623 3.63528 (119*2π)/5605 weeks
1201.45088 4.23483 (120*2π)/5605 weeks
121-.67779 2.99822 (121*2π)/5605 weeks
122-.53196 .04969 (122*2π)/5605 weeks
1232.09998 -1.55802 (123*2π)/5605 weeks
1245.22276 1.03989 (124*2π)/5605 weeks
1253.90695 5.07156 (125*2π)/5604 weeks
126-.39771 5.05083 (126*2π)/5604 weeks
127-1.30003 1.98273 (127*2π)/5604 weeks
128.0215 .02629 (128*2π)/5604 weeks
1291.58927 .07483 (129*2π)/5604 weeks
1302.1982 .74293 (130*2π)/5604 weeks
1312.81843 1.62799 (131*2π)/5604 weeks
1322.14097 2.687 (132*2π)/5604 weeks
133.95023 2.42934 (133*2π)/5604 weeks
1341.42656 1.10517 (134*2π)/5604 weeks
1353.05357 1.85343 (135*2π)/5604 weeks
1361.87647 3.93988 (136*2π)/5604 weeks
137-.32125 3.60451 (137*2π)/5604 weeks
138-1.4227 2.50425 (138*2π)/5604 weeks
139-1.16136 -.01421 (139*2π)/5604 weeks
1401.01066 -.43693 (140*2π)/5604 weeks
141.90633 .10433 (141*2π)/5604 weeks
1422.23094 -.41892 (142*2π)/5604 weeks
1432.87587 1.30067 (143*2π)/5604 weeks
1442.68979 2.58502 (144*2π)/5604 weeks
145.02466 3.49327 (145*2π)/5604 weeks
146-1.14638 -.36557 (146*2π)/5604 weeks
1472.71423 -1.84094 (147*2π)/5604 weeks
1484.50003 1.5212 (148*2π)/5604 weeks
1492.40922 4.34472 (149*2π)/5604 weeks
150-1.16783 3.5881 (150*2π)/5604 weeks
151-1.22098 -.24771 (151*2π)/5604 weeks
1521.3814 -1.30937 (152*2π)/5604 weeks
1533.92774 .19368 (153*2π)/5604 weeks
1542.8724 3.77615 (154*2π)/5604 weeks
155-.26551 3.04729 (155*2π)/5604 weeks
156-.40603 1.28893 (156*2π)/5604 weeks
157.24142 .16188 (157*2π)/5604 weeks
1581.05498 .00779 (158*2π)/5604 weeks
1591.66018 .05551 (159*2π)/5604 weeks
1602.46403 .97343 (160*2π)/5604 weeks
1611.15482 2.70853 (161*2π)/5603 weeks
162-.42181 .77078 (162*2π)/5603 weeks
163.95459 -.06143 (163*2π)/5603 weeks
1641.2358 .06954 (164*2π)/5603 weeks
1651.96347 -.05377 (165*2π)/5603 weeks
1662.85318 .85487 (166*2π)/5603 weeks
1672.12115 2.88214 (167*2π)/5603 weeks
168-.51574 2.30494 (168*2π)/5603 weeks
169-1.31404 .02484 (169*2π)/5603 weeks
170.42225 -2.5652 (170*2π)/5603 weeks
1713.85059 -1.90249 (171*2π)/5603 weeks
1724.7993 1.33179 (172*2π)/5603 weeks
1732.43452 3.5753 (173*2π)/5603 weeks
174-.06157 2.48815 (174*2π)/5603 weeks
175-.7113 .33422 (175*2π)/5603 weeks
1761.09439 -1.48637 (176*2π)/5603 weeks
1773.76432 -.73836 (177*2π)/5603 weeks
1784.29563 2.1058 (178*2π)/5603 weeks
1791.91499 4.07548 (179*2π)/5603 weeks
180-1.05617 3.17112 (180*2π)/5603 weeks
181-1.94233 .3444 (181*2π)/5603 weeks
182-.07093 -2.40028 (182*2π)/5603 weeks
1833.41373 -1.8069 (183*2π)/5603 weeks
1844.42827 1.25194 (184*2π)/5603 weeks
1852.00114 3.63141 (185*2π)/5603 weeks
186-.96358 2.23911 (186*2π)/5603 weeks
187-.86682 -.36796 (187*2π)/5603 weeks
1881.38204 -1.77529 (188*2π)/5603 weeks
1893.01452 .02237 (189*2π)/5603 weeks
1902.30204 1.1633 (190*2π)/5603 weeks
191.99604 1.71787 (191*2π)/5603 weeks
192-.10944 -.003 (192*2π)/5603 weeks
1931.63534 -1.57717 (193*2π)/5603 weeks
1943.31386 -.43666 (194*2π)/5603 weeks
1953.64194 1.15054 (195*2π)/5603 weeks
1962.50731 2.54215 (196*2π)/5603 weeks
1971.68686 2.37752 (197*2π)/5603 weeks
198.15855 3.35073 (198*2π)/5603 weeks
199-2.0976 .80668 (199*2π)/5603 weeks
200-.29231 -1.03361 (200*2π)/5603 weeks
201.73136 -1.39374 (201*2π)/5603 weeks
2021.93628 -.85686 (202*2π)/5603 weeks
2031.76652 -.28135 (203*2π)/5603 weeks
2042.27231 -.32764 (204*2π)/5603 weeks
2051.4366 .71107 (205*2π)/5603 weeks
2061.35565 -1.17772 (206*2π)/5603 weeks
2072.81172 -.5383 (207*2π)/5603 weeks
2083.29261 -.32464 (208*2π)/5603 weeks
2094.24767 1.75883 (209*2π)/5603 weeks
2101.81344 3.50401 (210*2π)/5603 weeks
211-.69934 1.79278 (211*2π)/5603 weeks
212-.12582 -.85451 (212*2π)/5603 weeks
2132.6144 -1.12705 (213*2π)/5603 weeks
2143.07458 1.52768 (214*2π)/5603 weeks
215.78958 2.16868 (215*2π)/5603 weeks
216-.533 .90822 (216*2π)/5603 weeks
217-.52116 -1.46703 (217*2π)/5603 weeks
2182.53868 -2.90233 (218*2π)/5603 weeks
2194.96102 -.10824 (219*2π)/5603 weeks
2203.3549 3.08275 (220*2π)/5603 weeks
221-.16912 2.69983 (221*2π)/5603 weeks
222-.53893 -.62285 (222*2π)/5603 weeks
2232.34742 -1.21988 (223*2π)/5603 weeks
2242.74714 1.0651 (224*2π)/5603 weeks
2251.08444 1.4691 (225*2π)/5602 weeks
226.39911 .75299 (226*2π)/5602 weeks
227-.28313 -.70449 (227*2π)/5602 weeks
2281.77744 -2.52532 (228*2π)/5602 weeks
2294.07413 -.48651 (229*2π)/5602 weeks
2303.03581 1.46648 (230*2π)/5602 weeks
2311.04114 1.85741 (231*2π)/5602 weeks
232.12152 -.48018 (232*2π)/5602 weeks
2332.3527 -1.3448 (233*2π)/5602 weeks
2343.55111 -.24669 (234*2π)/5602 weeks
2353.40631 1.52449 (235*2π)/5602 weeks
2361.19112 2.63575 (236*2π)/5602 weeks
237-.53816 .58411 (237*2π)/5602 weeks
238.56796 -1.67693 (238*2π)/5602 weeks
2393.35137 -2.17675 (239*2π)/5602 weeks
2405.30665 .79054 (240*2π)/5602 weeks
2413.20366 3.41931 (241*2π)/5602 weeks
242.83709 3.01407 (242*2π)/5602 weeks
243-.86773 1.79956 (243*2π)/5602 weeks
244.16827 -1.2636 (244*2π)/5602 weeks
2452.07953 -.47267 (245*2π)/5602 weeks
2462.44149 .11515 (246*2π)/5602 weeks
2471.97787 1.40916 (247*2π)/5602 weeks
248.99883 .67362 (248*2π)/5602 weeks
2491.2076 .736 (249*2π)/5602 weeks
250.3321 .04557 (250*2π)/5602 weeks
2511.48207 -1.25108 (251*2π)/5602 weeks
2523.0871 -.55243 (252*2π)/5602 weeks
2533.91715 1.02456 (253*2π)/5602 weeks
2542.11833 3.38161 (254*2π)/5602 weeks
255-.90686 2.32654 (255*2π)/5602 weeks
256-1.09062 -.61977 (256*2π)/5602 weeks
257.66449 -2.30956 (257*2π)/5602 weeks
2583.44068 -2.22767 (258*2π)/5602 weeks
2595.43667 .755 (259*2π)/5602 weeks
2603.59477 3.96958 (260*2π)/5602 weeks
261-.67189 4.73524 (261*2π)/5602 weeks
262-3.33542 .36848 (262*2π)/5602 weeks
263-.53888 -3.11947 (263*2π)/5602 weeks
2642.88327 -2.83389 (264*2π)/5602 weeks
2655.18311 .26516 (265*2π)/5602 weeks
2662.87815 3.81965 (266*2π)/5602 weeks
267-1.32493 2.90093 (267*2π)/5602 weeks
268-1.51446 -1.55857 (268*2π)/5602 weeks
2691.98693 -2.55111 (269*2π)/5602 weeks
2704.02066 -.53143 (270*2π)/5602 weeks
2713.74668 2.3316 (271*2π)/5602 weeks
2721.23358 4.10577 (272*2π)/5602 weeks
273-2.58915 2.45369 (273*2π)/5602 weeks
274-2.39023 -2.30396 (274*2π)/5602 weeks
2751.87325 -3.25164 (275*2π)/5602 weeks
2763.57514 -.39662 (276*2π)/5602 weeks
2772.75269 1.4546 (277*2π)/5602 weeks
2781.27581 1.85443 (278*2π)/5602 weeks
279.00847 1.89143 (279*2π)/5602 weeks
280-1.57818   (280*2π)/5602 weeks
281.00847 -1.89143 (281*2π)/5602 weeks
2821.27581 -1.85443 (282*2π)/5602 weeks
2832.75269 -1.4546 (283*2π)/5602 weeks
2843.57514 .39662 (284*2π)/5602 weeks
2851.87325 3.25164 (285*2π)/5602 weeks
286-2.39023 2.30396 (286*2π)/5602 weeks
287-2.58915 -2.45369 (287*2π)/5602 weeks
2881.23358 -4.10577 (288*2π)/5602 weeks
2893.74668 -2.3316 (289*2π)/5602 weeks
2904.02066 .53143 (290*2π)/5602 weeks
2911.98693 2.55111 (291*2π)/5602 weeks
292-1.51446 1.55857 (292*2π)/5602 weeks
293-1.32493 -2.90093 (293*2π)/5602 weeks
2942.87815 -3.81965 (294*2π)/5602 weeks
2955.18311 -.26516 (295*2π)/5602 weeks
2962.88327 2.83389 (296*2π)/5602 weeks
297-.53888 3.11947 (297*2π)/5602 weeks
298-3.33542 -.36848 (298*2π)/5602 weeks
299-.67189 -4.73524 (299*2π)/5602 weeks
3003.59477 -3.96958 (300*2π)/5602 weeks
3015.43667 -.755 (301*2π)/5602 weeks
3023.44068 2.22767 (302*2π)/5602 weeks
303.66449 2.30956 (303*2π)/5602 weeks
304-1.09062 .61977 (304*2π)/5602 weeks
305-.90686 -2.32654 (305*2π)/5602 weeks
3062.11833 -3.38161 (306*2π)/5602 weeks
3073.91715 -1.02456 (307*2π)/5602 weeks
3083.0871 .55243 (308*2π)/5602 weeks
3091.48207 1.25108 (309*2π)/5602 weeks
310.3321 -.04557 (310*2π)/5602 weeks
3111.2076 -.736 (311*2π)/5602 weeks
312.99883 -.67362 (312*2π)/5602 weeks
3131.97787 -1.40916 (313*2π)/5602 weeks
3142.44149 -.11515 (314*2π)/5602 weeks
3152.07953 .47267 (315*2π)/5602 weeks
316.16827 1.2636 (316*2π)/5602 weeks
317-.86773 -1.79956 (317*2π)/5602 weeks
318.83709 -3.01407 (318*2π)/5602 weeks
3193.20366 -3.41931 (319*2π)/5602 weeks
3205.30665 -.79054 (320*2π)/5602 weeks
3213.35137 2.17675 (321*2π)/5602 weeks
322.56796 1.67693 (322*2π)/5602 weeks
323-.53816 -.58411 (323*2π)/5602 weeks
3241.19112 -2.63575 (324*2π)/5602 weeks
3253.40631 -1.52449 (325*2π)/5602 weeks
3263.55111 .24669 (326*2π)/5602 weeks
3272.3527 1.3448 (327*2π)/5602 weeks
328.12152 .48018 (328*2π)/5602 weeks
3291.04114 -1.85741 (329*2π)/5602 weeks
3303.03581 -1.46648 (330*2π)/5602 weeks
3314.07413 .48651 (331*2π)/5602 weeks
3321.77744 2.52532 (332*2π)/5602 weeks
333-.28313 .70449 (333*2π)/5602 weeks
334.39911 -.75299 (334*2π)/5602 weeks
3351.08444 -1.4691 (335*2π)/5602 weeks
3362.74714 -1.0651 (336*2π)/5602 weeks
3372.34742 1.21988 (337*2π)/5602 weeks
338-.53893 .62285 (338*2π)/5602 weeks
339-.16912 -2.69983 (339*2π)/5602 weeks
3403.3549 -3.08275 (340*2π)/5602 weeks
3414.96102 .10824 (341*2π)/5602 weeks
3422.53868 2.90233 (342*2π)/5602 weeks
343-.52116 1.46703 (343*2π)/5602 weeks
344-.533 -.90822 (344*2π)/5602 weeks
345.78958 -2.16868 (345*2π)/5602 weeks
3463.07458 -1.52768 (346*2π)/5602 weeks
3472.6144 1.12705 (347*2π)/5602 weeks
348-.12582 .85451 (348*2π)/5602 weeks
349-.69934 -1.79278 (349*2π)/5602 weeks
3501.81344 -3.50401 (350*2π)/5602 weeks
3514.24767 -1.75883 (351*2π)/5602 weeks
3523.29261 .32464 (352*2π)/5602 weeks
3532.81172 .5383 (353*2π)/5602 weeks
3541.35565 1.17772 (354*2π)/5602 weeks
3551.4366 -.71107 (355*2π)/5602 weeks
3562.27231 .32764 (356*2π)/5602 weeks
3571.76652 .28135 (357*2π)/5602 weeks
3581.93628 .85686 (358*2π)/5602 weeks
359.73136 1.39374 (359*2π)/5602 weeks
360-.29231 1.03361 (360*2π)/5602 weeks
361-2.0976 -.80668 (361*2π)/5602 weeks
362.15855 -3.35073 (362*2π)/5602 weeks
3631.68686 -2.37752 (363*2π)/5602 weeks
3642.50731 -2.54215 (364*2π)/5602 weeks
3653.64194 -1.15054 (365*2π)/5602 weeks
3663.31386 .43666 (366*2π)/5602 weeks
3671.63534 1.57717 (367*2π)/5602 weeks
368-.10944 .003 (368*2π)/5602 weeks
369.99604 -1.71787 (369*2π)/5602 weeks
3702.30204 -1.1633 (370*2π)/5602 weeks
3713.01452 -.02237 (371*2π)/5602 weeks
3721.38204 1.77529 (372*2π)/5602 weeks
373-.86682 .36796 (373*2π)/5602 weeks
374-.96358 -2.23911 (374*2π)/5601 weeks
3752.00114 -3.63141 (375*2π)/5601 weeks
3764.42827 -1.25194 (376*2π)/5601 weeks
3773.41373 1.8069 (377*2π)/5601 weeks
378-.07093 2.40028 (378*2π)/5601 weeks
379-1.94233 -.3444 (379*2π)/5601 weeks
380-1.05617 -3.17112 (380*2π)/5601 weeks
3811.91499 -4.07548 (381*2π)/5601 weeks
3824.29563 -2.1058 (382*2π)/5601 weeks
3833.76432 .73836 (383*2π)/5601 weeks
3841.09439 1.48637 (384*2π)/5601 weeks
385-.7113 -.33422 (385*2π)/5601 weeks
386-.06157 -2.48815 (386*2π)/5601 weeks
3872.43452 -3.5753 (387*2π)/5601 weeks
3884.7993 -1.33179 (388*2π)/5601 weeks
3893.85059 1.90249 (389*2π)/5601 weeks
390.42225 2.5652 (390*2π)/5601 weeks
391-1.31404 -.02484 (391*2π)/5601 weeks
392-.51574 -2.30494 (392*2π)/5601 weeks
3932.12115 -2.88214 (393*2π)/5601 weeks
3942.85318 -.85487 (394*2π)/5601 weeks
3951.96347 .05377 (395*2π)/5601 weeks
3961.2358 -.06954 (396*2π)/5601 weeks
397.95459 .06143 (397*2π)/5601 weeks
398-.42181 -.77078 (398*2π)/5601 weeks
3991.15482 -2.70853 (399*2π)/5601 weeks
4002.46403 -.97343 (400*2π)/5601 weeks
4011.66018 -.05551 (401*2π)/5601 weeks
4021.05498 -.00779 (402*2π)/5601 weeks
403.24142 -.16188 (403*2π)/5601 weeks
404-.40603 -1.28893 (404*2π)/5601 weeks
405-.26551 -3.04729 (405*2π)/5601 weeks
4062.8724 -3.77615 (406*2π)/5601 weeks
4073.92774 -.19368 (407*2π)/5601 weeks
4081.3814 1.30937 (408*2π)/5601 weeks
409-1.22098 .24771 (409*2π)/5601 weeks
410-1.16783 -3.5881 (410*2π)/5601 weeks
4112.40922 -4.34472 (411*2π)/5601 weeks
4124.50003 -1.5212 (412*2π)/5601 weeks
4132.71423 1.84094 (413*2π)/5601 weeks
414-1.14638 .36557 (414*2π)/5601 weeks
415.02466 -3.49327 (415*2π)/5601 weeks
4162.68979 -2.58502 (416*2π)/5601 weeks
4172.87587 -1.30067 (417*2π)/5601 weeks
4182.23094 .41892 (418*2π)/5601 weeks
419.90633 -.10433 (419*2π)/5601 weeks
4201.01066 .43693 (420*2π)/5601 weeks
421-1.16136 .01421 (421*2π)/5601 weeks
422-1.4227 -2.50425 (422*2π)/5601 weeks
423-.32125 -3.60451 (423*2π)/5601 weeks
4241.87647 -3.93988 (424*2π)/5601 weeks
4253.05357 -1.85343 (425*2π)/5601 weeks
4261.42656 -1.10517 (426*2π)/5601 weeks
427.95023 -2.42934 (427*2π)/5601 weeks
4282.14097 -2.687 (428*2π)/5601 weeks
4292.81843 -1.62799 (429*2π)/5601 weeks
4302.1982 -.74293 (430*2π)/5601 weeks
4311.58927 -.07483 (431*2π)/5601 weeks
432.0215 -.02629 (432*2π)/5601 weeks
433-1.30003 -1.98273 (433*2π)/5601 weeks
434-.39771 -5.05083 (434*2π)/5601 weeks
4353.90695 -5.07156 (435*2π)/5601 weeks
4365.22276 -1.03989 (436*2π)/5601 weeks
4372.09998 1.55802 (437*2π)/5601 weeks
438-.53196 -.04969 (438*2π)/5601 weeks
439-.67779 -2.99822 (439*2π)/5601 weeks
4401.45088 -4.23483 (440*2π)/5601 weeks
4413.70623 -3.63528 (441*2π)/5601 weeks
4424.98237 .00183 (442*2π)/5601 weeks
4431.03091 3.40245 (443*2π)/5601 weeks
444-3.69617 .10202 (444*2π)/5601 weeks
445-3.13609 -4.31125 (445*2π)/5601 weeks
446-.20753 -7.59693 (446*2π)/5601 weeks
4475.42502 -6.80449 (447*2π)/5601 weeks
4487.11755 -.66445 (448*2π)/5601 weeks
4492.02586 3.59983 (449*2π)/5601 weeks
450-3.69825 -.17185 (450*2π)/5601 weeks
451-2.52095 -6.08473 (451*2π)/5601 weeks
4522.19026 -8.72917 (452*2π)/5601 weeks
4537.52221 -5.33232 (453*2π)/5601 weeks
4547.36536 .369 (454*2π)/5601 weeks
4552.14875 3.5048 (455*2π)/5601 weeks
456-2.50699 -.4986 (456*2π)/5601 weeks
457-.55346 -5.59708 (457*2π)/5601 weeks
4584.14524 -6.04961 (458*2π)/5601 weeks
4596.49374 -1.94479 (459*2π)/5601 weeks
4604.34894 1.67491 (460*2π)/5601 weeks
461.63041 1.40758 (461*2π)/5601 weeks
462-.4141 -1.30292 (462*2π)/5601 weeks
4631.43896 -2.80374 (463*2π)/5601 weeks
4641.96253 -.60944 (464*2π)/5601 weeks
465-.73971 -1.39401 (465*2π)/5601 weeks
466.3561 -3.65028 (466*2π)/5601 weeks
4672.16006 -2.64079 (467*2π)/5601 weeks
4681.36894 -.77278 (468*2π)/5601 weeks
469-1.56965 -.91602 (469*2π)/5601 weeks
470-2.9474 -5.21136 (470*2π)/5601 weeks
4711.37971 -9.61175 (471*2π)/5601 weeks
4727.87363 -7.44176 (472*2π)/5601 weeks
4739.29261 .3073 (473*2π)/5601 weeks
4742.19144 4.42514 (474*2π)/5601 weeks
475-2.60771 .67765 (475*2π)/5601 weeks
476-3.69241 -4.48094 (476*2π)/5601 weeks
4771.46917 -9.2066 (477*2π)/5601 weeks
4787.61749 -5.81624 (478*2π)/5601 weeks
4798.28377 .2069 (479*2π)/5601 weeks
4801.80411 5.14746 (480*2π)/5601 weeks
481-4.5399 -.85916 (481*2π)/5601 weeks
482-.41676 -5.90292 (482*2π)/5601 weeks
4831.76933 -6.5555 (483*2π)/5601 weeks
4847.86982 -5.29985 (484*2π)/5601 weeks
4857.30714 3.40291 (485*2π)/5601 weeks
486-.63796 4.98333 (486*2π)/5601 weeks
487-6.35143 -.13591 (487*2π)/5601 weeks
488-4.09345 -8.05153 (488*2π)/5601 weeks
4893.41153 -7.4417 (489*2π)/5601 weeks
4902.91165 -2.6324 (490*2π)/5601 weeks
491.69824 -3.52322 (491*2π)/5601 weeks
492-.24566 -5.45099 (492*2π)/5601 weeks
4934.54019 -8.55794 (493*2π)/5601 weeks
4948.96555 -3.52128 (494*2π)/5601 weeks
4955.59815 2.65769 (495*2π)/5601 weeks
496-.33843 3.15883 (496*2π)/5601 weeks
497-4.34058 -3.13315 (497*2π)/5601 weeks
4981.31783 -7.17858 (498*2π)/5601 weeks
4994.04159 -3.21735 (499*2π)/5601 weeks
5002.11407 -.13313 (500*2π)/5601 weeks
501-2.61559 -1.50349 (501*2π)/5601 weeks
502-2.62013 -7.41767 (502*2π)/5601 weeks
5035.29104 -8.83238 (503*2π)/5601 weeks
5046.68245 -1.87649 (504*2π)/5601 weeks
5052.06145 .01135 (505*2π)/5601 weeks
506-.23995 -1.31199 (506*2π)/5601 weeks
507-1.30539 -3.94802 (507*2π)/5601 weeks
5081.55406 -5.66372 (508*2π)/5601 weeks
5092.87751 -3.43697 (509*2π)/5601 weeks
5101.61445 -.28888 (510*2π)/5601 weeks
511-2.47839 -1.834 (511*2π)/5601 weeks
512-4.58146 -4.97829 (512*2π)/5601 weeks
513-1.01386 -9.41267 (513*2π)/5601 weeks
5143.0285 -6.67049 (514*2π)/5601 weeks
5151.12141 -4.47204 (515*2π)/5601 weeks
516-1.56205 -4.91202 (516*2π)/5601 weeks
517-.53603 -11.66026 (517*2π)/5601 weeks
5187.6937 -9.28219 (518*2π)/5601 weeks
5195.51638 -1.46959 (519*2π)/5601 weeks
520-.09402 -.64258 (520*2π)/5601 weeks
521-4.99997 -4.5264 (521*2π)/5601 weeks
522-4.14505 -13.61765 (522*2π)/5601 weeks
5237.75772 -16.27556 (523*2π)/5601 weeks
52415.83389 -6.3723 (524*2π)/5601 weeks
52511.05293 10.23343 (525*2π)/5601 weeks
526-12.30427 11.89157 (526*2π)/5601 weeks
527-21.12195 -10.66595 (527*2π)/5601 weeks
528-5.66017 -26.76227 (528*2π)/5601 weeks
52915.80924 -22.0376 (529*2π)/5601 weeks
53018.65335 -.59502 (530*2π)/5601 weeks
531.3681 9.52135 (531*2π)/5601 weeks
532-13.26499 -.01216 (532*2π)/5601 weeks
533-15.19808 -15.54116 (533*2π)/5601 weeks
534.0676 -24.21353 (534*2π)/5601 weeks
5359.11561 -15.86031 (535*2π)/5601 weeks
5367.16861 -8.09861 (536*2π)/5601 weeks
537-2.07748 -8.54093 (537*2π)/5601 weeks
538-.79614 -15.34479 (538*2π)/5601 weeks
5394.1401 -16.63124 (539*2π)/5601 weeks
5405.24407 -14.47193 (540*2π)/5601 weeks
5418.38606 -16.57792 (541*2π)/5601 weeks
54210.04767 -7.65173 (542*2π)/5601 weeks
5431.21202 -9.31644 (543*2π)/5601 weeks
5443.72353 -9.2176 (544*2π)/5601 weeks
545-3.22375 -6.18148 (545*2π)/5601 weeks
546-13.28536 -13.17886 (546*2π)/5601 weeks
547-15.16016 -35.29192 (547*2π)/5601 weeks
54814.40825 -47.90169 (548*2π)/5601 weeks
54930.57572 -22.68847 (549*2π)/5601 weeks
55022.30433 -6.03409 (550*2π)/5601 weeks
551-3.05175 9.18815 (551*2π)/5601 weeks
552-36.31706 -23.95971 (552*2π)/5601 weeks
553-6.01447 -66.403 (553*2π)/5601 weeks
55434.73114 -56.22513 (554*2π)/5601 weeks
55532.24218 -14.75301 (555*2π)/5601 weeks
556-22.7644 -.99828 (556*2π)/5601 weeks
557-92.32467 -79.05676 (557*2π)/5601 weeks
558-41.29818 -232.0902 (558*2π)/5601 weeks



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