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Fourier Analysis of REW (ProShares UltraShort Technology)


REW (ProShares UltraShort Technology) appears to have interesting cyclic behaviour every 45 weeks (50.1959*sine), 42 weeks (41.694*sine), and 49 weeks (33.0485*cosine).

REW (ProShares UltraShort Technology) has an average price of 296.5 (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 2/2/2007 to 4/23/2018 for REW (ProShares UltraShort Technology), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0296.5011   0 
1166.1185 315.8358 (1*2π)/587587 weeks
2-25.07084 213.8705 (2*2π)/587294 weeks
3-82.72844 81.67494 (3*2π)/587196 weeks
4-34.03169 -1.94318 (4*2π)/587147 weeks
540.10131 -11.32001 (5*2π)/587117 weeks
659.29104 41.74985 (6*2π)/58798 weeks
727.68048 75.56667 (7*2π)/58784 weeks
8-25.47194 63.92403 (8*2π)/58773 weeks
9-27.26144 9.69041 (9*2π)/58765 weeks
106.81599 -1.82462 (10*2π)/58759 weeks
1123.56253 7.79883 (11*2π)/58753 weeks
1233.04845 28.0071 (12*2π)/58749 weeks
1313.65657 50.19591 (13*2π)/58745 weeks
14-13.20143 41.69397 (14*2π)/58742 weeks
15-19.67469 20.85188 (15*2π)/58739 weeks
16-12.10489 5.80599 (16*2π)/58737 weeks
17.32053 1.71392 (17*2π)/58735 weeks
186.91743 2.8599 (18*2π)/58733 weeks
1914.03098 11.79499 (19*2π)/58731 weeks
207.75993 18.2885 (20*2π)/58729 weeks
213.88299 17.24312 (21*2π)/58728 weeks
221.52391 14.94098 (22*2π)/58727 weeks
232.20783 14.72502 (23*2π)/58726 weeks
24-1.04853 12.99715 (24*2π)/58724 weeks
255.25795 10.77347 (25*2π)/58723 weeks
262.47723 15.42776 (26*2π)/58723 weeks
27-.50693 16.84018 (27*2π)/58722 weeks
28-9.21699 15.68216 (28*2π)/58721 weeks
29-7.68666 4.24402 (29*2π)/58720 weeks
30-2.94372 .84026 (30*2π)/58720 weeks
315.55241 -2.3167 (31*2π)/58719 weeks
3212.42978 6.73186 (32*2π)/58718 weeks
338.33737 17.55767 (33*2π)/58718 weeks
34-2.20676 19.90442 (34*2π)/58717 weeks
35-11.95423 11.97432 (35*2π)/58717 weeks
36-9.77022 -3.03591 (36*2π)/58716 weeks
374.34604 -4.45812 (37*2π)/58716 weeks
389.42903 4.03729 (38*2π)/58715 weeks
396.69583 11.25317 (39*2π)/58715 weeks
40.10208 11.24008 (40*2π)/58715 weeks
41-1.75198 8.11168 (41*2π)/58714 weeks
42-2.58342 5.02935 (42*2π)/58714 weeks
43.82806 1.16059 (43*2π)/58714 weeks
446.23064 5.95501 (44*2π)/58713 weeks
451.38757 9.61106 (45*2π)/58713 weeks
46-1.44741 5.98782 (46*2π)/58713 weeks
47.95385 5.56147 (47*2π)/58712 weeks
48.98589 5.03693 (48*2π)/58712 weeks
492.12233 7.89688 (49*2π)/58712 weeks
50-3.15867 8.72512 (50*2π)/58712 weeks
51-3.39042 4.08931 (51*2π)/58712 weeks
52-3.05264 1.06013 (52*2π)/58711 weeks
53.47737 -.01365 (53*2π)/58711 weeks
543.86657 1.74979 (54*2π)/58711 weeks
552.84911 5.20329 (55*2π)/58711 weeks
56.74667 4.20574 (56*2π)/58710 weeks
57.00933 3.58319 (57*2π)/58710 weeks
58.35469 1.36203 (58*2π)/58710 weeks
594.54499 1.16345 (59*2π)/58710 weeks
604.67935 7.15097 (60*2π)/58710 weeks
61-.27572 6.36552 (61*2π)/58710 weeks
62-1.03453 3.86979 (62*2π)/5879 weeks
63.39526 1.66106 (63*2π)/5879 weeks
642.52835 2.47943 (64*2π)/5879 weeks
652.20095 5.12987 (65*2π)/5879 weeks
66-1.14911 4.81993 (66*2π)/5879 weeks
67-1.06874 1.04183 (67*2π)/5879 weeks
681.60276 -.91492 (68*2π)/5879 weeks
695.8499 1.06634 (69*2π)/5879 weeks
705.57025 5.63602 (70*2π)/5878 weeks
71.85168 7.44689 (71*2π)/5878 weeks
72-.56831 4.79751 (72*2π)/5878 weeks
73-1.15307 2.62836 (73*2π)/5878 weeks
742.69553 .56122 (74*2π)/5878 weeks
754.1638 5.58042 (75*2π)/5878 weeks
76-.30115 7.48629 (76*2π)/5878 weeks
77-4.4939 3.97259 (77*2π)/5878 weeks
78-2.88941 -1.47222 (78*2π)/5878 weeks
793.43015 -2.33453 (79*2π)/5877 weeks
805.07082 2.61422 (80*2π)/5877 weeks
812.00481 4.0347 (81*2π)/5877 weeks
821.81092 4.62121 (82*2π)/5877 weeks
83-1.96978 4.08028 (83*2π)/5877 weeks
84-1.38258 -1.25804 (84*2π)/5877 weeks
853.65272 -1.42223 (85*2π)/5877 weeks
865.91693 1.61015 (86*2π)/5877 weeks
874.98593 6.01219 (87*2π)/5877 weeks
88.43338 6.51644 (88*2π)/5877 weeks
89-1.61827 4.89791 (89*2π)/5877 weeks
90-3.19225 1.31455 (90*2π)/5877 weeks
91.58501 -2.50398 (91*2π)/5876 weeks
925.16241 -.37963 (92*2π)/5876 weeks
935.19609 3.99418 (93*2π)/5876 weeks
941.70215 6.12454 (94*2π)/5876 weeks
95-1.40698 4.5582 (95*2π)/5876 weeks
96-1.44188 .97214 (96*2π)/5876 weeks
971.08229 -.7371 (97*2π)/5876 weeks
983.5045 .88838 (98*2π)/5876 weeks
992.7564 3.68891 (99*2π)/5876 weeks
100.24058 3.1789 (100*2π)/5876 weeks
1011.16192 1.55796 (101*2π)/5876 weeks
1021.23666 2.80774 (102*2π)/5876 weeks
103.09483 2.29814 (103*2π)/5876 weeks
104-.76395 1.02355 (104*2π)/5876 weeks
105.56513 -1.51735 (105*2π)/5876 weeks
1063.93662 -1.13561 (106*2π)/5876 weeks
1075.41208 2.088 (107*2π)/5875 weeks
1083.50602 4.94638 (108*2π)/5875 weeks
109-.24849 4.76653 (109*2π)/5875 weeks
110-2.23842 1.252 (110*2π)/5875 weeks
111.3124 -2.05306 (111*2π)/5875 weeks
1124.45563 -2.43833 (112*2π)/5875 weeks
1137.36084 2.56121 (113*2π)/5875 weeks
1144.23306 6.11013 (114*2π)/5875 weeks
115-.20624 6.60113 (115*2π)/5875 weeks
116-3.24477 2.92683 (116*2π)/5875 weeks
117-1.48057 -1.68039 (117*2π)/5875 weeks
1183.43929 -2.73276 (118*2π)/5875 weeks
1196.12241 1.43255 (119*2π)/5875 weeks
1204.22267 4.9591 (120*2π)/5875 weeks
1211.1593 5.98846 (121*2π)/5875 weeks
122-2.5443 3.96416 (122*2π)/5875 weeks
123-1.97907 -.71758 (123*2π)/5875 weeks
1241.69678 -1.88667 (124*2π)/5875 weeks
1254.03912 .34263 (125*2π)/5875 weeks
1263.75469 2.8051 (126*2π)/5875 weeks
1271.56128 3.91593 (127*2π)/5875 weeks
128.04808 2.08598 (128*2π)/5875 weeks
129-.15505 .84473 (129*2π)/5875 weeks
1301.82687 -.93173 (130*2π)/5875 weeks
1314.37918 .59675 (131*2π)/5874 weeks
1323.89274 3.94308 (132*2π)/5874 weeks
133.96761 3.71206 (133*2π)/5874 weeks
134.10964 2.5128 (134*2π)/5874 weeks
135.60521 1.44418 (135*2π)/5874 weeks
1361.38554 1.63139 (136*2π)/5874 weeks
137.86864 1.08037 (137*2π)/5874 weeks
1381.7929 1.14648 (138*2π)/5874 weeks
1391.64746 1.99932 (139*2π)/5874 weeks
140.26322 1.62239 (140*2π)/5874 weeks
141.8543 -.08475 (141*2π)/5874 weeks
1423.02339 -.17095 (142*2π)/5874 weeks
1433.60091 1.73525 (143*2π)/5874 weeks
1442.63396 2.51721 (144*2π)/5874 weeks
1451.70166 3.56407 (145*2π)/5874 weeks
146.28604 2.09455 (146*2π)/5874 weeks
1471.61281 .96311 (147*2π)/5874 weeks
1481.74476 2.42263 (148*2π)/5874 weeks
149.6319 2.24906 (149*2π)/5874 weeks
150.50398 1.86218 (150*2π)/5874 weeks
151.69152 .30991 (151*2π)/5874 weeks
1522.58745 1.0025 (152*2π)/5874 weeks
1531.29982 2.34947 (153*2π)/5874 weeks
154.34339 1.53738 (154*2π)/5874 weeks
155.8652 .73901 (155*2π)/5874 weeks
1561.73108 .5911 (156*2π)/5874 weeks
1572.26019 1.306 (157*2π)/5874 weeks
1581.29154 2.07177 (158*2π)/5874 weeks
1591.17547 1.69513 (159*2π)/5874 weeks
160.2748 1.10958 (160*2π)/5874 weeks
1611.71102 -.38841 (161*2π)/5874 weeks
1622.90232 1.56305 (162*2π)/5874 weeks
1631.689 1.77607 (163*2π)/5874 weeks
1641.63465 2.01258 (164*2π)/5874 weeks
1651.00829 1.7304 (165*2π)/5874 weeks
1661.17479 1.43625 (166*2π)/5874 weeks
1671.11366 1.16075 (167*2π)/5874 weeks
1681.48478 .6029 (168*2π)/5873 weeks
1692.52108 1.90121 (169*2π)/5873 weeks
170.73209 2.49935 (170*2π)/5873 weeks
171.68763 1.31571 (171*2π)/5873 weeks
172.90718 1.31914 (172*2π)/5873 weeks
173.69627 .96923 (173*2π)/5873 weeks
1741.14592 .60419 (174*2π)/5873 weeks
1752.42645 .67692 (175*2π)/5873 weeks
1762.00187 2.37688 (176*2π)/5873 weeks
1771.09128 2.3975 (177*2π)/5873 weeks
178-.20206 2.21316 (178*2π)/5873 weeks
179-.76223 .74742 (179*2π)/5873 weeks
180.5758 -.8334 (180*2π)/5873 weeks
1812.32749 .10144 (181*2π)/5873 weeks
1822.00317 1.33167 (182*2π)/5873 weeks
1831.60888 1.66847 (183*2π)/5873 weeks
184.69076 1.83655 (184*2π)/5873 weeks
185-.0681 1.26963 (185*2π)/5873 weeks
186-.12843 -.29704 (186*2π)/5873 weeks
1871.61049 -1.31967 (187*2π)/5873 weeks
1883.58961 -.1806 (188*2π)/5873 weeks
1893.25741 2.14338 (189*2π)/5873 weeks
1902.1765 3.14307 (190*2π)/5873 weeks
191-.23749 2.97527 (191*2π)/5873 weeks
192-1.11284 .63062 (192*2π)/5873 weeks
193.55152 -1.18637 (193*2π)/5873 weeks
1942.53693 -.54914 (194*2π)/5873 weeks
1953.14133 1.45243 (195*2π)/5873 weeks
1962.02796 2.75073 (196*2π)/5873 weeks
197-.12826 2.5847 (197*2π)/5873 weeks
198-.42895 .85419 (198*2π)/5873 weeks
199-.06823 .17404 (199*2π)/5873 weeks
2001.35565 -.61685 (200*2π)/5873 weeks
2011.94427 .81806 (201*2π)/5873 weeks
2021.02085 1.16116 (202*2π)/5873 weeks
203.85942 1.0684 (203*2π)/5873 weeks
204.21158 .51764 (204*2π)/5873 weeks
205.59519 -.26294 (205*2π)/5873 weeks
206.88861 -.52892 (206*2π)/5873 weeks
2072.53817 -1.521 (207*2π)/5873 weeks
2084.51275 1.09129 (208*2π)/5873 weeks
2091.97999 3.5099 (209*2π)/5873 weeks
210.08451 2.79689 (210*2π)/5873 weeks
211-1.21945 1.42225 (211*2π)/5873 weeks
212-.46552 -.90732 (212*2π)/5873 weeks
2131.40268 -1.13396 (213*2π)/5873 weeks
2142.15023 -.2324 (214*2π)/5873 weeks
2152.84562 1.37027 (215*2π)/5873 weeks
216.16194 2.50983 (216*2π)/5873 weeks
217-.63974 .05499 (217*2π)/5873 weeks
218.18994 -.74956 (218*2π)/5873 weeks
2191.35599 -2.05343 (219*2π)/5873 weeks
2203.85401 -1.03529 (220*2π)/5873 weeks
2214.01821 2.16988 (221*2π)/5873 weeks
2221.32315 3.25197 (222*2π)/5873 weeks
223-.96726 1.94792 (223*2π)/5873 weeks
224-.6847 -.9671 (224*2π)/5873 weeks
2251.87908 -1.30153 (225*2π)/5873 weeks
2262.90216 -.14756 (226*2π)/5873 weeks
2272.84802 1.67255 (227*2π)/5873 weeks
228.956 3.04473 (228*2π)/5873 weeks
229-1.13405 .92124 (229*2π)/5873 weeks
230-.22434 -1.09006 (230*2π)/5873 weeks
2311.65307 -1.5525 (231*2π)/5873 weeks
2323.07908 -.00846 (232*2π)/5873 weeks
2332.22036 1.32459 (233*2π)/5873 weeks
2341.1723 .95626 (234*2π)/5873 weeks
2351.7347 .64592 (235*2π)/5872 weeks
2361.73485 1.43631 (236*2π)/5872 weeks
2371.05793 1.37218 (237*2π)/5872 weeks
238.72339 1.70962 (238*2π)/5872 weeks
239-.86075 1.32369 (239*2π)/5872 weeks
240-.49119 -1.16637 (240*2π)/5872 weeks
2411.52627 -1.11786 (241*2π)/5872 weeks
2422.49469 -.19654 (242*2π)/5872 weeks
2431.98825 1.77411 (243*2π)/5872 weeks
244-.193 1.51192 (244*2π)/5872 weeks
245-.46119 .05612 (245*2π)/5872 weeks
246.01592 -1.03352 (246*2π)/5872 weeks
2471.40375 -2.18976 (247*2π)/5872 weeks
2483.57057 -.71912 (248*2π)/5872 weeks
2492.82593 1.88639 (249*2π)/5872 weeks
250.65223 2.58022 (250*2π)/5872 weeks
251-1.49857 .67156 (251*2π)/5872 weeks
252-.36837 -1.95835 (252*2π)/5872 weeks
2531.92439 -2.06708 (253*2π)/5872 weeks
2543.11905 -.90079 (254*2π)/5872 weeks
2553.62432 1.16885 (255*2π)/5872 weeks
256.98492 2.25876 (256*2π)/5872 weeks
257.12751 .81886 (257*2π)/5872 weeks
258.01491 -.09611 (258*2π)/5872 weeks
2591.03323 -.88675 (259*2π)/5872 weeks
2601.49161 -.24359 (260*2π)/5872 weeks
2611.37823 -.33952 (261*2π)/5872 weeks
2622.10481 .02247 (262*2π)/5872 weeks
2631.30666 .96273 (263*2π)/5872 weeks
264.51068 -.03658 (264*2π)/5872 weeks
265.6411 -.3202 (265*2π)/5872 weeks
2661.26428 -1.25706 (266*2π)/5872 weeks
2672.73621 -1.16768 (267*2π)/5872 weeks
2683.39763 .85732 (268*2π)/5872 weeks
2691.9616 2.22612 (269*2π)/5872 weeks
270.11882 2.17321 (270*2π)/5872 weeks
271-1.58183 .76591 (271*2π)/5872 weeks
272-1.138 -2.06119 (272*2π)/5872 weeks
2731.17792 -3.35672 (273*2π)/5872 weeks
2744.16297 -2.04942 (274*2π)/5872 weeks
2753.88973 1.31028 (275*2π)/5872 weeks
2761.37452 2.07204 (276*2π)/5872 weeks
277.00908 1.03508 (277*2π)/5872 weeks
278-.4264 -.84286 (278*2π)/5872 weeks
2791.31036 -2.12356 (279*2π)/5872 weeks
2803.25093 -1.34629 (280*2π)/5872 weeks
2812.92203 1.00166 (281*2π)/5872 weeks
2821.34842 1.45463 (282*2π)/5872 weeks
283.15584 .56301 (283*2π)/5872 weeks
284.21751 -1.07132 (284*2π)/5872 weeks
2851.00436 -1.9178 (285*2π)/5872 weeks
2863.30597 -1.88997 (286*2π)/5872 weeks
2874.5198 .84484 (287*2π)/5872 weeks
2881.63336 2.5624 (288*2π)/5872 weeks
289-.23034 .83985 (289*2π)/5872 weeks
290-.14933 -.40691 (290*2π)/5872 weeks
291.97079 -1.71369 (291*2π)/5872 weeks
2922.03014 -1.94934 (292*2π)/5872 weeks
2933.93507 -1.34558 (293*2π)/5872 weeks
2943.93507 1.34558 (294*2π)/5872 weeks
2952.03014 1.94934 (295*2π)/5872 weeks
296.97079 1.71369 (296*2π)/5872 weeks
297-.14933 .40691 (297*2π)/5872 weeks
298-.23034 -.83985 (298*2π)/5872 weeks
2991.63336 -2.5624 (299*2π)/5872 weeks
3004.5198 -.84484 (300*2π)/5872 weeks
3013.30597 1.88997 (301*2π)/5872 weeks
3021.00436 1.9178 (302*2π)/5872 weeks
303.21751 1.07132 (303*2π)/5872 weeks
304.15584 -.56301 (304*2π)/5872 weeks
3051.34842 -1.45463 (305*2π)/5872 weeks
3062.92203 -1.00166 (306*2π)/5872 weeks
3073.25093 1.34629 (307*2π)/5872 weeks
3081.31036 2.12356 (308*2π)/5872 weeks
309-.4264 .84286 (309*2π)/5872 weeks
310.00908 -1.03508 (310*2π)/5872 weeks
3111.37452 -2.07204 (311*2π)/5872 weeks
3123.88973 -1.31028 (312*2π)/5872 weeks
3134.16297 2.04942 (313*2π)/5872 weeks
3141.17792 3.35672 (314*2π)/5872 weeks
315-1.138 2.06119 (315*2π)/5872 weeks
316-1.58183 -.76591 (316*2π)/5872 weeks
317.11882 -2.17321 (317*2π)/5872 weeks
3181.9616 -2.22612 (318*2π)/5872 weeks
3193.39763 -.85732 (319*2π)/5872 weeks
3202.73621 1.16768 (320*2π)/5872 weeks
3211.26428 1.25706 (321*2π)/5872 weeks
322.6411 .3202 (322*2π)/5872 weeks
323.51068 .03658 (323*2π)/5872 weeks
3241.30666 -.96273 (324*2π)/5872 weeks
3252.10481 -.02247 (325*2π)/5872 weeks
3261.37823 .33952 (326*2π)/5872 weeks
3271.49161 .24359 (327*2π)/5872 weeks
3281.03323 .88675 (328*2π)/5872 weeks
329.01491 .09611 (329*2π)/5872 weeks
330.12751 -.81886 (330*2π)/5872 weeks
331.98492 -2.25876 (331*2π)/5872 weeks
3323.62432 -1.16885 (332*2π)/5872 weeks
3333.11905 .90079 (333*2π)/5872 weeks
3341.92439 2.06708 (334*2π)/5872 weeks
335-.36837 1.95835 (335*2π)/5872 weeks
336-1.49857 -.67156 (336*2π)/5872 weeks
337.65223 -2.58022 (337*2π)/5872 weeks
3382.82593 -1.88639 (338*2π)/5872 weeks
3393.57057 .71912 (339*2π)/5872 weeks
3401.40375 2.18976 (340*2π)/5872 weeks
341.01592 1.03352 (341*2π)/5872 weeks
342-.46119 -.05612 (342*2π)/5872 weeks
343-.193 -1.51192 (343*2π)/5872 weeks
3441.98825 -1.77411 (344*2π)/5872 weeks
3452.49469 .19654 (345*2π)/5872 weeks
3461.52627 1.11786 (346*2π)/5872 weeks
347-.49119 1.16637 (347*2π)/5872 weeks
348-.86075 -1.32369 (348*2π)/5872 weeks
349.72339 -1.70962 (349*2π)/5872 weeks
3501.05793 -1.37218 (350*2π)/5872 weeks
3511.73485 -1.43631 (351*2π)/5872 weeks
3521.7347 -.64592 (352*2π)/5872 weeks
3531.1723 -.95626 (353*2π)/5872 weeks
3542.22036 -1.32459 (354*2π)/5872 weeks
3553.07908 .00846 (355*2π)/5872 weeks
3561.65307 1.5525 (356*2π)/5872 weeks
357-.22434 1.09006 (357*2π)/5872 weeks
358-1.13405 -.92124 (358*2π)/5872 weeks
359.956 -3.04473 (359*2π)/5872 weeks
3602.84802 -1.67255 (360*2π)/5872 weeks
3612.90216 .14756 (361*2π)/5872 weeks
3621.87908 1.30153 (362*2π)/5872 weeks
363-.6847 .9671 (363*2π)/5872 weeks
364-.96726 -1.94792 (364*2π)/5872 weeks
3651.32315 -3.25197 (365*2π)/5872 weeks
3664.01821 -2.16988 (366*2π)/5872 weeks
3673.85401 1.03529 (367*2π)/5872 weeks
3681.35599 2.05343 (368*2π)/5872 weeks
369.18994 .74956 (369*2π)/5872 weeks
370-.63974 -.05499 (370*2π)/5872 weeks
371.16194 -2.50983 (371*2π)/5872 weeks
3722.84562 -1.37027 (372*2π)/5872 weeks
3732.15023 .2324 (373*2π)/5872 weeks
3741.40268 1.13396 (374*2π)/5872 weeks
375-.46552 .90732 (375*2π)/5872 weeks
376-1.21945 -1.42225 (376*2π)/5872 weeks
377.08451 -2.79689 (377*2π)/5872 weeks
3781.97999 -3.5099 (378*2π)/5872 weeks
3794.51275 -1.09129 (379*2π)/5872 weeks
3802.53817 1.521 (380*2π)/5872 weeks
381.88861 .52892 (381*2π)/5872 weeks
382.59519 .26294 (382*2π)/5872 weeks
383.21158 -.51764 (383*2π)/5872 weeks
384.85942 -1.0684 (384*2π)/5872 weeks
3851.02085 -1.16116 (385*2π)/5872 weeks
3861.94427 -.81806 (386*2π)/5872 weeks
3871.35565 .61685 (387*2π)/5872 weeks
388-.06823 -.17404 (388*2π)/5872 weeks
389-.42895 -.85419 (389*2π)/5872 weeks
390-.12826 -2.5847 (390*2π)/5872 weeks
3912.02796 -2.75073 (391*2π)/5872 weeks
3923.14133 -1.45243 (392*2π)/5871 weeks
3932.53693 .54914 (393*2π)/5871 weeks
394.55152 1.18637 (394*2π)/5871 weeks
395-1.11284 -.63062 (395*2π)/5871 weeks
396-.23749 -2.97527 (396*2π)/5871 weeks
3972.1765 -3.14307 (397*2π)/5871 weeks
3983.25741 -2.14338 (398*2π)/5871 weeks
3993.58961 .1806 (399*2π)/5871 weeks
4001.61049 1.31967 (400*2π)/5871 weeks
401-.12843 .29704 (401*2π)/5871 weeks
402-.0681 -1.26963 (402*2π)/5871 weeks
403.69076 -1.83655 (403*2π)/5871 weeks
4041.60888 -1.66847 (404*2π)/5871 weeks
4052.00317 -1.33167 (405*2π)/5871 weeks
4062.32749 -.10144 (406*2π)/5871 weeks
407.5758 .8334 (407*2π)/5871 weeks
408-.76223 -.74742 (408*2π)/5871 weeks
409-.20206 -2.21316 (409*2π)/5871 weeks
4101.09128 -2.3975 (410*2π)/5871 weeks
4112.00187 -2.37688 (411*2π)/5871 weeks
4122.42645 -.67692 (412*2π)/5871 weeks
4131.14592 -.60419 (413*2π)/5871 weeks
414.69627 -.96923 (414*2π)/5871 weeks
415.90718 -1.31914 (415*2π)/5871 weeks
416.68763 -1.31571 (416*2π)/5871 weeks
417.73209 -2.49935 (417*2π)/5871 weeks
4182.52108 -1.90121 (418*2π)/5871 weeks
4191.48478 -.6029 (419*2π)/5871 weeks
4201.11366 -1.16075 (420*2π)/5871 weeks
4211.17479 -1.43625 (421*2π)/5871 weeks
4221.00829 -1.7304 (422*2π)/5871 weeks
4231.63465 -2.01258 (423*2π)/5871 weeks
4241.689 -1.77607 (424*2π)/5871 weeks
4252.90232 -1.56305 (425*2π)/5871 weeks
4261.71102 .38841 (426*2π)/5871 weeks
427.2748 -1.10958 (427*2π)/5871 weeks
4281.17547 -1.69513 (428*2π)/5871 weeks
4291.29154 -2.07177 (429*2π)/5871 weeks
4302.26019 -1.306 (430*2π)/5871 weeks
4311.73108 -.5911 (431*2π)/5871 weeks
432.8652 -.73901 (432*2π)/5871 weeks
433.34339 -1.53738 (433*2π)/5871 weeks
4341.29982 -2.34947 (434*2π)/5871 weeks
4352.58745 -1.0025 (435*2π)/5871 weeks
436.69152 -.30991 (436*2π)/5871 weeks
437.50398 -1.86218 (437*2π)/5871 weeks
438.6319 -2.24906 (438*2π)/5871 weeks
4391.74476 -2.42263 (439*2π)/5871 weeks
4401.61281 -.96311 (440*2π)/5871 weeks
441.28604 -2.09455 (441*2π)/5871 weeks
4421.70166 -3.56407 (442*2π)/5871 weeks
4432.63396 -2.51721 (443*2π)/5871 weeks
4443.60091 -1.73525 (444*2π)/5871 weeks
4453.02339 .17095 (445*2π)/5871 weeks
446.8543 .08475 (446*2π)/5871 weeks
447.26322 -1.62239 (447*2π)/5871 weeks
4481.64746 -1.99932 (448*2π)/5871 weeks
4491.7929 -1.14648 (449*2π)/5871 weeks
450.86864 -1.08037 (450*2π)/5871 weeks
4511.38554 -1.63139 (451*2π)/5871 weeks
452.60521 -1.44418 (452*2π)/5871 weeks
453.10964 -2.5128 (453*2π)/5871 weeks
454.96761 -3.71206 (454*2π)/5871 weeks
4553.89274 -3.94308 (455*2π)/5871 weeks
4564.37918 -.59675 (456*2π)/5871 weeks
4571.82687 .93173 (457*2π)/5871 weeks
458-.15505 -.84473 (458*2π)/5871 weeks
459.04808 -2.08598 (459*2π)/5871 weeks
4601.56128 -3.91593 (460*2π)/5871 weeks
4613.75469 -2.8051 (461*2π)/5871 weeks
4624.03912 -.34263 (462*2π)/5871 weeks
4631.69678 1.88667 (463*2π)/5871 weeks
464-1.97907 .71758 (464*2π)/5871 weeks
465-2.5443 -3.96416 (465*2π)/5871 weeks
4661.1593 -5.98846 (466*2π)/5871 weeks
4674.22267 -4.9591 (467*2π)/5871 weeks
4686.12241 -1.43255 (468*2π)/5871 weeks
4693.43929 2.73276 (469*2π)/5871 weeks
470-1.48057 1.68039 (470*2π)/5871 weeks
471-3.24477 -2.92683 (471*2π)/5871 weeks
472-.20624 -6.60113 (472*2π)/5871 weeks
4734.23306 -6.11013 (473*2π)/5871 weeks
4747.36084 -2.56121 (474*2π)/5871 weeks
4754.45563 2.43833 (475*2π)/5871 weeks
476.3124 2.05306 (476*2π)/5871 weeks
477-2.23842 -1.252 (477*2π)/5871 weeks
478-.24849 -4.76653 (478*2π)/5871 weeks
4793.50602 -4.94638 (479*2π)/5871 weeks
4805.41208 -2.088 (480*2π)/5871 weeks
4813.93662 1.13561 (481*2π)/5871 weeks
482.56513 1.51735 (482*2π)/5871 weeks
483-.76395 -1.02355 (483*2π)/5871 weeks
484.09483 -2.29814 (484*2π)/5871 weeks
4851.23666 -2.80774 (485*2π)/5871 weeks
4861.16192 -1.55796 (486*2π)/5871 weeks
487.24058 -3.1789 (487*2π)/5871 weeks
4882.7564 -3.68891 (488*2π)/5871 weeks
4893.5045 -.88838 (489*2π)/5871 weeks
4901.08229 .7371 (490*2π)/5871 weeks
491-1.44188 -.97214 (491*2π)/5871 weeks
492-1.40698 -4.5582 (492*2π)/5871 weeks
4931.70215 -6.12454 (493*2π)/5871 weeks
4945.19609 -3.99418 (494*2π)/5871 weeks
4955.16241 .37963 (495*2π)/5871 weeks
496.58501 2.50398 (496*2π)/5871 weeks
497-3.19225 -1.31455 (497*2π)/5871 weeks
498-1.61827 -4.89791 (498*2π)/5871 weeks
499.43338 -6.51644 (499*2π)/5871 weeks
5004.98593 -6.01219 (500*2π)/5871 weeks
5015.91693 -1.61015 (501*2π)/5871 weeks
5023.65272 1.42223 (502*2π)/5871 weeks
503-1.38258 1.25804 (503*2π)/5871 weeks
504-1.96978 -4.08028 (504*2π)/5871 weeks
5051.81092 -4.62121 (505*2π)/5871 weeks
5062.00481 -4.0347 (506*2π)/5871 weeks
5075.07082 -2.61422 (507*2π)/5871 weeks
5083.43015 2.33453 (508*2π)/5871 weeks
509-2.88941 1.47222 (509*2π)/5871 weeks
510-4.4939 -3.97259 (510*2π)/5871 weeks
511-.30115 -7.48629 (511*2π)/5871 weeks
5124.1638 -5.58042 (512*2π)/5871 weeks
5132.69553 -.56122 (513*2π)/5871 weeks
514-1.15307 -2.62836 (514*2π)/5871 weeks
515-.56831 -4.79751 (515*2π)/5871 weeks
516.85168 -7.44689 (516*2π)/5871 weeks
5175.57025 -5.63602 (517*2π)/5871 weeks
5185.8499 -1.06634 (518*2π)/5871 weeks
5191.60276 .91492 (519*2π)/5871 weeks
520-1.06874 -1.04183 (520*2π)/5871 weeks
521-1.14911 -4.81993 (521*2π)/5871 weeks
5222.20095 -5.12987 (522*2π)/5871 weeks
5232.52835 -2.47943 (523*2π)/5871 weeks
524.39526 -1.66106 (524*2π)/5871 weeks
525-1.03453 -3.86979 (525*2π)/5871 weeks
526-.27572 -6.36552 (526*2π)/5871 weeks
5274.67935 -7.15097 (527*2π)/5871 weeks
5284.54499 -1.16345 (528*2π)/5871 weeks
529.35469 -1.36203 (529*2π)/5871 weeks
530.00933 -3.58319 (530*2π)/5871 weeks
531.74667 -4.20574 (531*2π)/5871 weeks
5322.84911 -5.20329 (532*2π)/5871 weeks
5333.86657 -1.74979 (533*2π)/5871 weeks
534.47737 .01365 (534*2π)/5871 weeks
535-3.05264 -1.06013 (535*2π)/5871 weeks
536-3.39042 -4.08931 (536*2π)/5871 weeks
537-3.15867 -8.72512 (537*2π)/5871 weeks
5382.12233 -7.89688 (538*2π)/5871 weeks
539.98589 -5.03693 (539*2π)/5871 weeks
540.95385 -5.56147 (540*2π)/5871 weeks
541-1.44741 -5.98782 (541*2π)/5871 weeks
5421.38757 -9.61106 (542*2π)/5871 weeks
5436.23064 -5.95501 (543*2π)/5871 weeks
544.82806 -1.16059 (544*2π)/5871 weeks
545-2.58342 -5.02935 (545*2π)/5871 weeks
546-1.75198 -8.11168 (546*2π)/5871 weeks
547.10208 -11.24008 (547*2π)/5871 weeks
5486.69583 -11.25317 (548*2π)/5871 weeks
5499.42903 -4.03729 (549*2π)/5871 weeks
5504.34604 4.45812 (550*2π)/5871 weeks
551-9.77022 3.03591 (551*2π)/5871 weeks
552-11.95423 -11.97432 (552*2π)/5871 weeks
553-2.20676 -19.90442 (553*2π)/5871 weeks
5548.33737 -17.55767 (554*2π)/5871 weeks
55512.42978 -6.73186 (555*2π)/5871 weeks
5565.55241 2.3167 (556*2π)/5871 weeks
557-2.94372 -.84026 (557*2π)/5871 weeks
558-7.68666 -4.24402 (558*2π)/5871 weeks
559-9.21699 -15.68216 (559*2π)/5871 weeks
560-.50693 -16.84018 (560*2π)/5871 weeks
5612.47723 -15.42776 (561*2π)/5871 weeks
5625.25795 -10.77347 (562*2π)/5871 weeks
563-1.04853 -12.99715 (563*2π)/5871 weeks
5642.20783 -14.72502 (564*2π)/5871 weeks
5651.52391 -14.94098 (565*2π)/5871 weeks
5663.88299 -17.24312 (566*2π)/5871 weeks
5677.75993 -18.2885 (567*2π)/5871 weeks
56814.03098 -11.79499 (568*2π)/5871 weeks
5696.91743 -2.8599 (569*2π)/5871 weeks
570.32053 -1.71392 (570*2π)/5871 weeks
571-12.10489 -5.80599 (571*2π)/5871 weeks
572-19.67469 -20.85188 (572*2π)/5871 weeks
573-13.20143 -41.69397 (573*2π)/5871 weeks
57413.65657 -50.19591 (574*2π)/5871 weeks
57533.04845 -28.0071 (575*2π)/5871 weeks
57623.56253 -7.79883 (576*2π)/5871 weeks
5776.81599 1.82462 (577*2π)/5871 weeks
578-27.26144 -9.69041 (578*2π)/5871 weeks
579-25.47194 -63.92403 (579*2π)/5871 weeks
58027.68048 -75.56667 (580*2π)/5871 weeks
58159.29104 -41.74985 (581*2π)/5871 weeks
58240.10131 11.32001 (582*2π)/5871 weeks
583-34.03169 1.94318 (583*2π)/5871 weeks
584-82.72844 -81.67494 (584*2π)/5871 weeks
585-25.07084 -213.8705 (585*2π)/5871 weeks



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