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Fourier Analysis of REW (ProShares UltraShort Technology ETF)


REW (ProShares UltraShort Technology ETF) appears to have interesting cyclic behaviour every 46 weeks (52.4117*sine), 42 weeks (45.5988*sine), and 50 weeks (35.0066*cosine).

REW (ProShares UltraShort Technology ETF) has an average price of 316.95 (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 7/17/2017 for REW (ProShares UltraShort Technology ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0316.9456   0 
1155.0041 331.66 (1*2π)/547547 weeks
2-43.28952 209.2197 (2*2π)/547274 weeks
3-82.22617 57.41151 (3*2π)/547182 weeks
4-16.04264 -16.49916 (4*2π)/547137 weeks
559.94092 7.6535 (5*2π)/547109 weeks
652.68803 64.57646 (6*2π)/54791 weeks
7.58637 84.05717 (7*2π)/54778 weeks
8-38.50982 32.05786 (8*2π)/54768 weeks
9-3.67498 -3.62527 (9*2π)/54761 weeks
1021.13725 5.07343 (10*2π)/54755 weeks
1135.00656 24.01507 (11*2π)/54750 weeks
1218.58748 52.41167 (12*2π)/54746 weeks
13-13.27849 45.59876 (13*2π)/54742 weeks
14-21.16608 21.69381 (14*2π)/54739 weeks
15-11.96632 5.11628 (15*2π)/54736 weeks
161.84686 2.44657 (16*2π)/54734 weeks
1710.3004 3.7195 (17*2π)/54732 weeks
1813.72213 16.21899 (18*2π)/54730 weeks
196.01872 19.10992 (19*2π)/54729 weeks
202.58385 17.81996 (20*2π)/54727 weeks
212.4451 15.08308 (21*2π)/54726 weeks
22.3948 15.72705 (22*2π)/54725 weeks
232.7446 9.55989 (23*2π)/54724 weeks
243.43199 16.40695 (24*2π)/54723 weeks
25.11111 17.80145 (25*2π)/54722 weeks
26-8.72464 17.81449 (26*2π)/54721 weeks
27-8.44467 4.59004 (27*2π)/54720 weeks
28-3.00089 .63865 (28*2π)/54720 weeks
297.58106 -1.91652 (29*2π)/54719 weeks
3013.61369 9.40131 (30*2π)/54718 weeks
315.95328 20.13696 (31*2π)/54718 weeks
32-6.89653 19.76495 (32*2π)/54717 weeks
33-14.51332 6.62275 (33*2π)/54717 weeks
34-2.55999 -6.55261 (34*2π)/54716 weeks
359.25455 .11203 (35*2π)/54716 weeks
369.2397 9.41554 (36*2π)/54715 weeks
371.6941 12.85931 (37*2π)/54715 weeks
38-1.73366 9.20996 (38*2π)/54714 weeks
39-2.82897 6.02159 (39*2π)/54714 weeks
40.33168 1.37888 (40*2π)/54714 weeks
416.68174 6.33566 (41*2π)/54713 weeks
421.09402 10.20913 (42*2π)/54713 weeks
43-1.17333 5.74465 (43*2π)/54713 weeks
44.86591 6.16834 (44*2π)/54712 weeks
451.95076 5.53651 (45*2π)/54712 weeks
46.80742 9.72921 (46*2π)/54712 weeks
47-4.76548 6.43254 (47*2π)/54712 weeks
48-3.90517 3.40106 (48*2π)/54711 weeks
49-.79855 .00271 (49*2π)/54711 weeks
503.13441 .4778 (50*2π)/54711 weeks
513.81484 4.75324 (51*2π)/54711 weeks
52.70707 4.77872 (52*2π)/54711 weeks
53.07432 4.05673 (53*2π)/54710 weeks
54.23979 1.60335 (54*2π)/54710 weeks
554.95488 1.30591 (55*2π)/54710 weeks
564.35244 8.05274 (56*2π)/54710 weeks
57-.62134 6.30776 (57*2π)/54710 weeks
58-1.09206 3.50914 (58*2π)/5479 weeks
591.35074 1.78963 (59*2π)/5479 weeks
603.1886 3.62623 (60*2π)/5479 weeks
61.79852 5.95877 (61*2π)/5479 weeks
62-2.02384 2.76268 (62*2π)/5479 weeks
63.22387 -.25578 (63*2π)/5479 weeks
645.09248 -.25207 (64*2π)/5479 weeks
656.42013 4.95563 (65*2π)/5478 weeks
661.93603 8.34637 (66*2π)/5478 weeks
67-.54267 5.2733 (67*2π)/5478 weeks
68-1.23341 2.88529 (68*2π)/5478 weeks
693.16531 .68511 (69*2π)/5478 weeks
704.04271 6.51472 (70*2π)/5478 weeks
71-1.35808 7.78779 (71*2π)/5478 weeks
72-4.95372 2.46238 (72*2π)/5478 weeks
73-1.22352 -3.03743 (73*2π)/5477 weeks
745.27651 -.35807 (74*2π)/5477 weeks
753.86358 4.57891 (75*2π)/5477 weeks
762.25878 4.00412 (76*2π)/5477 weeks
77-.47109 5.43235 (77*2π)/5477 weeks
78-2.63357 .16665 (78*2π)/5477 weeks
792.95695 -2.10995 (79*2π)/5477 weeks
806.10825 1.08709 (80*2π)/5477 weeks
815.63292 6.07113 (81*2π)/5477 weeks
82.46855 6.9497 (82*2π)/5477 weeks
83-1.9294 5.05029 (83*2π)/5477 weeks
84-3.32143 .53871 (84*2π)/5477 weeks
851.87041 -2.71189 (85*2π)/5476 weeks
866.07053 1.01423 (86*2π)/5476 weeks
874.58439 5.58241 (87*2π)/5476 weeks
88.2014 6.03827 (88*2π)/5476 weeks
89-2.27475 2.72149 (89*2π)/5476 weeks
90-.36926 -.32628 (90*2π)/5476 weeks
913.09837 .11486 (91*2π)/5476 weeks
923.61505 3.34049 (92*2π)/5476 weeks
93.62745 3.85399 (93*2π)/5476 weeks
94.97616 1.63066 (94*2π)/5476 weeks
951.38953 2.94966 (95*2π)/5476 weeks
96.06214 2.43287 (96*2π)/5476 weeks
97-.87349 .83459 (97*2π)/5476 weeks
981.18796 -1.89036 (98*2π)/5476 weeks
994.86977 -.65308 (99*2π)/5476 weeks
1005.3895 3.36431 (100*2π)/5475 weeks
1012.14226 5.82197 (101*2π)/5475 weeks
102-1.68372 3.83559 (102*2π)/5475 weeks
103-1.36116 -1.05588 (103*2π)/5475 weeks
1042.73681 -2.83295 (104*2π)/5475 weeks
1057.80167 .4992 (105*2π)/5475 weeks
1065.41158 6.0162 (106*2π)/5475 weeks
107.67518 7.3864 (107*2π)/5475 weeks
108-3.32703 3.69327 (108*2π)/5475 weeks
109-1.70939 -1.7152 (109*2π)/5475 weeks
1103.93272 -2.82919 (110*2π)/5475 weeks
1116.5312 2.10005 (111*2π)/5475 weeks
1123.92019 5.63287 (112*2π)/5475 weeks
113.11493 6.33164 (113*2π)/5475 weeks
114-3.30897 2.50734 (114*2π)/5475 weeks
115-.54451 -1.7743 (115*2π)/5475 weeks
1163.52356 -1.17061 (116*2π)/5475 weeks
1174.43727 1.82291 (117*2π)/5475 weeks
1182.68511 3.99026 (118*2π)/5475 weeks
119-.00598 2.91247 (119*2π)/5475 weeks
120-.09496 1.42001 (120*2π)/5475 weeks
1211.45561 -.92563 (121*2π)/5475 weeks
1224.55598 .39944 (122*2π)/5474 weeks
1234.18194 4.20576 (123*2π)/5474 weeks
124.95551 3.86984 (124*2π)/5474 weeks
125.08822 2.40904 (125*2π)/5474 weeks
126.77862 1.38166 (126*2π)/5474 weeks
1271.17301 1.94834 (127*2π)/5474 weeks
1281.33148 .96442 (128*2π)/5474 weeks
1292.0296 1.63527 (129*2π)/5474 weeks
1301.06063 2.34706 (130*2π)/5474 weeks
131.38272 .50984 (131*2π)/5474 weeks
1322.34606 -.59345 (132*2π)/5474 weeks
1333.88198 1.30255 (133*2π)/5474 weeks
1342.89968 2.71938 (134*2π)/5474 weeks
1352.15457 3.75366 (135*2π)/5474 weeks
136.29205 2.36013 (136*2π)/5474 weeks
1371.75603 1.05239 (137*2π)/5474 weeks
1381.74666 2.65339 (138*2π)/5474 weeks
139.59852 2.20703 (139*2π)/5474 weeks
140.21889 1.78017 (140*2π)/5474 weeks
1411.37484 .18147 (141*2π)/5474 weeks
1422.58365 2.16853 (142*2π)/5474 weeks
143.86162 2.3297 (143*2π)/5474 weeks
144.66474 1.00029 (144*2π)/5474 weeks
1451.43702 .51351 (145*2π)/5474 weeks
1462.26945 1.06405 (146*2π)/5474 weeks
1471.78394 2.30751 (147*2π)/5474 weeks
1481.28925 1.73611 (148*2π)/5474 weeks
149.35242 1.37738 (149*2π)/5474 weeks
1501.73898 -.42626 (150*2π)/5474 weeks
1513.05363 1.76423 (151*2π)/5474 weeks
1521.81896 1.84333 (152*2π)/5474 weeks
1531.59161 2.19746 (153*2π)/5474 weeks
1541.06507 1.66878 (154*2π)/5474 weeks
1551.16623 1.52883 (155*2π)/5474 weeks
1561.21444 1.14237 (156*2π)/5474 weeks
1572.48127 .91153 (157*2π)/5473 weeks
1581.77836 2.90489 (158*2π)/5473 weeks
159.50698 1.6782 (159*2π)/5473 weeks
160.98887 1.38348 (160*2π)/5473 weeks
161.75581 1.21142 (161*2π)/5473 weeks
1621.18945 .68503 (162*2π)/5473 weeks
1632.48051 .5749 (163*2π)/5473 weeks
1642.1586 2.53154 (164*2π)/5473 weeks
1651.13034 2.59094 (165*2π)/5473 weeks
166-.36018 2.16981 (166*2π)/5473 weeks
167-.74885 .3236 (167*2π)/5473 weeks
1681.32189 -.91385 (168*2π)/5473 weeks
1692.54986 .72165 (169*2π)/5473 weeks
1701.88421 1.54145 (170*2π)/5473 weeks
1711.29118 2.05575 (171*2π)/5473 weeks
172.30725 1.66451 (172*2π)/5473 weeks
173-.34704 .29339 (173*2π)/5473 weeks
1741.0498 -1.35049 (174*2π)/5473 weeks
1753.48945 -.65614 (175*2π)/5473 weeks
1763.6807 2.08218 (176*2π)/5473 weeks
1772.40265 3.2733 (177*2π)/5473 weeks
178-.32351 3.15854 (178*2π)/5473 weeks
179-1.16221 .43965 (179*2π)/5473 weeks
1801.01919 -1.30855 (180*2π)/5473 weeks
1813.07954 -.22704 (181*2π)/5473 weeks
1823.01668 2.09443 (182*2π)/5473 weeks
1831.34073 3.29725 (183*2π)/5473 weeks
184-.60548 1.85117 (184*2π)/5473 weeks
185-.11825 .50826 (185*2π)/5473 weeks
186.53346 -.66696 (186*2π)/5473 weeks
1872.16435 .3791 (187*2π)/5473 weeks
1881.29286 1.34894 (188*2π)/5473 weeks
189.98563 1.08959 (189*2π)/5473 weeks
190.22636 .67957 (190*2π)/5473 weeks
191.60234 -.25899 (191*2π)/5473 weeks
192.94679 -.60121 (192*2π)/5473 weeks
1933.09365 -1.52495 (193*2π)/5473 weeks
1944.70695 1.98291 (194*2π)/5473 weeks
1951.40436 3.59883 (195*2π)/5473 weeks
196-.41903 2.62128 (196*2π)/5473 weeks
197-1.47708 .36045 (197*2π)/5473 weeks
198.44864 -1.31056 (198*2π)/5473 weeks
1992.11599 -.55039 (199*2π)/5473 weeks
2002.98529 .46103 (200*2π)/5473 weeks
2011.27328 2.91544 (201*2π)/5473 weeks
202-.88306 .57382 (202*2π)/5473 weeks
203.14974 -.71526 (203*2π)/5473 weeks
2041.2198 -2.13162 (204*2π)/5473 weeks
2054.11378 -1.13666 (205*2π)/5473 weeks
2064.15561 2.51647 (206*2π)/5473 weeks
2071.04845 3.43107 (207*2π)/5473 weeks
208-1.32125 1.44444 (208*2π)/5473 weeks
209.02508 -1.59732 (209*2π)/5473 weeks
2102.47914 -.91665 (210*2π)/5473 weeks
2113.37538 .66655 (211*2π)/5473 weeks
2122.40984 2.64895 (212*2π)/5473 weeks
213-.84542 2.31151 (213*2π)/5473 weeks
214-.78152 -.5525 (214*2π)/5473 weeks
2151.18346 -1.68465 (215*2π)/5473 weeks
2163.22515 -.50019 (216*2π)/5473 weeks
2172.54762 1.32591 (217*2π)/5473 weeks
2181.2703 1.09121 (218*2π)/5473 weeks
2191.86619 .6938 (219*2π)/5472 weeks
2201.77287 1.60019 (220*2π)/5472 weeks
2211.13625 1.46225 (221*2π)/5472 weeks
222.50362 1.91939 (222*2π)/5472 weeks
223-1.30155 .60347 (223*2π)/5472 weeks
224.43669 -1.6123 (224*2π)/5472 weeks
2252.06471 -.82114 (225*2π)/5472 weeks
2262.80772 .94731 (226*2π)/5472 weeks
227.62791 2.17994 (227*2π)/5472 weeks
228-.50224 .44864 (228*2π)/5472 weeks
229-.16724 -.90343 (229*2π)/5472 weeks
230.97932 -2.22909 (230*2π)/5472 weeks
2313.67286 -1.06538 (231*2π)/5472 weeks
2323.10332 1.96725 (232*2π)/5472 weeks
233.58036 2.75195 (233*2π)/5472 weeks
234-1.67035 .33061 (234*2π)/5472 weeks
235.07293 -2.34104 (235*2π)/5472 weeks
2362.49341 -1.94221 (236*2π)/5472 weeks
2373.63657 -.47753 (237*2π)/5472 weeks
2382.98616 2.38573 (238*2π)/5472 weeks
239.29334 1.61015 (239*2π)/5472 weeks
240.07402 .4039 (240*2π)/5472 weeks
241.54176 -.87958 (241*2π)/5472 weeks
2421.62858 -.45271 (242*2π)/5472 weeks
2431.42871 -.27454 (243*2π)/5472 weeks
2442.17583 -.18677 (244*2π)/5472 weeks
2451.52533 1.00724 (245*2π)/5472 weeks
246.53126 -.03097 (246*2π)/5472 weeks
247.65385 -.40816 (247*2π)/5472 weeks
2481.51855 -1.39815 (248*2π)/5472 weeks
2493.30448 -.951 (249*2π)/5472 weeks
2503.32652 1.49604 (250*2π)/5472 weeks
2511.39125 2.5224 (251*2π)/5472 weeks
252-.69042 1.91339 (252*2π)/5472 weeks
253-1.95825 -.79391 (253*2π)/5472 weeks
254.03855 -3.18844 (254*2π)/5472 weeks
2553.45663 -3.16203 (255*2π)/5472 weeks
2564.7064 .56893 (256*2π)/5472 weeks
2571.99815 2.33175 (257*2π)/5472 weeks
258.15963 1.26622 (258*2π)/5472 weeks
259-.51 -.76808 (259*2π)/5472 weeks
2601.42109 -2.28093 (260*2π)/5472 weeks
2613.62389 -1.23848 (261*2π)/5472 weeks
2622.84424 1.2359 (262*2π)/5472 weeks
2631.02465 1.43488 (263*2π)/5472 weeks
264-.08609 .13628 (264*2π)/5472 weeks
265.64334 -1.41537 (265*2π)/5472 weeks
2662.11323 -2.53788 (266*2π)/5472 weeks
2674.56244 -.93159 (267*2π)/5472 weeks
2683.12302 2.68132 (268*2π)/5472 weeks
269.02348 1.75255 (269*2π)/5472 weeks
270-.07055 -.09814 (270*2π)/5472 weeks
271.72145 -1.80041 (271*2π)/5472 weeks
2721.99568 -2.05952 (272*2π)/5472 weeks
2734.1228 -1.52463 (273*2π)/5472 weeks
2744.1228 1.52463 (274*2π)/5472 weeks
2751.99568 2.05952 (275*2π)/5472 weeks
276.72145 1.80041 (276*2π)/5472 weeks
277-.07055 .09814 (277*2π)/5472 weeks
278.02348 -1.75255 (278*2π)/5472 weeks
2793.12302 -2.68132 (279*2π)/5472 weeks
2804.56244 .93159 (280*2π)/5472 weeks
2812.11323 2.53788 (281*2π)/5472 weeks
282.64334 1.41537 (282*2π)/5472 weeks
283-.08609 -.13628 (283*2π)/5472 weeks
2841.02465 -1.43488 (284*2π)/5472 weeks
2852.84424 -1.2359 (285*2π)/5472 weeks
2863.62389 1.23848 (286*2π)/5472 weeks
2871.42109 2.28093 (287*2π)/5472 weeks
288-.51 .76808 (288*2π)/5472 weeks
289.15963 -1.26622 (289*2π)/5472 weeks
2901.99815 -2.33175 (290*2π)/5472 weeks
2914.7064 -.56893 (291*2π)/5472 weeks
2923.45663 3.16203 (292*2π)/5472 weeks
293.03855 3.18844 (293*2π)/5472 weeks
294-1.95825 .79391 (294*2π)/5472 weeks
295-.69042 -1.91339 (295*2π)/5472 weeks
2961.39125 -2.5224 (296*2π)/5472 weeks
2973.32652 -1.49604 (297*2π)/5472 weeks
2983.30448 .951 (298*2π)/5472 weeks
2991.51855 1.39815 (299*2π)/5472 weeks
300.65385 .40816 (300*2π)/5472 weeks
301.53126 .03097 (301*2π)/5472 weeks
3021.52533 -1.00724 (302*2π)/5472 weeks
3032.17583 .18677 (303*2π)/5472 weeks
3041.42871 .27454 (304*2π)/5472 weeks
3051.62858 .45271 (305*2π)/5472 weeks
306.54176 .87958 (306*2π)/5472 weeks
307.07402 -.4039 (307*2π)/5472 weeks
308.29334 -1.61015 (308*2π)/5472 weeks
3092.98616 -2.38573 (309*2π)/5472 weeks
3103.63657 .47753 (310*2π)/5472 weeks
3112.49341 1.94221 (311*2π)/5472 weeks
312.07293 2.34104 (312*2π)/5472 weeks
313-1.67035 -.33061 (313*2π)/5472 weeks
314.58036 -2.75195 (314*2π)/5472 weeks
3153.10332 -1.96725 (315*2π)/5472 weeks
3163.67286 1.06538 (316*2π)/5472 weeks
317.97932 2.22909 (317*2π)/5472 weeks
318-.16724 .90343 (318*2π)/5472 weeks
319-.50224 -.44864 (319*2π)/5472 weeks
320.62791 -2.17994 (320*2π)/5472 weeks
3212.80772 -.94731 (321*2π)/5472 weeks
3222.06471 .82114 (322*2π)/5472 weeks
323.43669 1.6123 (323*2π)/5472 weeks
324-1.30155 -.60347 (324*2π)/5472 weeks
325.50362 -1.91939 (325*2π)/5472 weeks
3261.13625 -1.46225 (326*2π)/5472 weeks
3271.77287 -1.60019 (327*2π)/5472 weeks
3281.86619 -.6938 (328*2π)/5472 weeks
3291.2703 -1.09121 (329*2π)/5472 weeks
3302.54762 -1.32591 (330*2π)/5472 weeks
3313.22515 .50019 (331*2π)/5472 weeks
3321.18346 1.68465 (332*2π)/5472 weeks
333-.78152 .5525 (333*2π)/5472 weeks
334-.84542 -2.31151 (334*2π)/5472 weeks
3352.40984 -2.64895 (335*2π)/5472 weeks
3363.37538 -.66655 (336*2π)/5472 weeks
3372.47914 .91665 (337*2π)/5472 weeks
338.02508 1.59732 (338*2π)/5472 weeks
339-1.32125 -1.44444 (339*2π)/5472 weeks
3401.04845 -3.43107 (340*2π)/5472 weeks
3414.15561 -2.51647 (341*2π)/5472 weeks
3424.11378 1.13666 (342*2π)/5472 weeks
3431.2198 2.13162 (343*2π)/5472 weeks
344.14974 .71526 (344*2π)/5472 weeks
345-.88306 -.57382 (345*2π)/5472 weeks
3461.27328 -2.91544 (346*2π)/5472 weeks
3472.98529 -.46103 (347*2π)/5472 weeks
3482.11599 .55039 (348*2π)/5472 weeks
349.44864 1.31056 (349*2π)/5472 weeks
350-1.47708 -.36045 (350*2π)/5472 weeks
351-.41903 -2.62128 (351*2π)/5472 weeks
3521.40436 -3.59883 (352*2π)/5472 weeks
3534.70695 -1.98291 (353*2π)/5472 weeks
3543.09365 1.52495 (354*2π)/5472 weeks
355.94679 .60121 (355*2π)/5472 weeks
356.60234 .25899 (356*2π)/5472 weeks
357.22636 -.67957 (357*2π)/5472 weeks
358.98563 -1.08959 (358*2π)/5472 weeks
3591.29286 -1.34894 (359*2π)/5472 weeks
3602.16435 -.3791 (360*2π)/5472 weeks
361.53346 .66696 (361*2π)/5472 weeks
362-.11825 -.50826 (362*2π)/5472 weeks
363-.60548 -1.85117 (363*2π)/5472 weeks
3641.34073 -3.29725 (364*2π)/5472 weeks
3653.01668 -2.09443 (365*2π)/5471 weeks
3663.07954 .22704 (366*2π)/5471 weeks
3671.01919 1.30855 (367*2π)/5471 weeks
368-1.16221 -.43965 (368*2π)/5471 weeks
369-.32351 -3.15854 (369*2π)/5471 weeks
3702.40265 -3.2733 (370*2π)/5471 weeks
3713.6807 -2.08218 (371*2π)/5471 weeks
3723.48945 .65614 (372*2π)/5471 weeks
3731.0498 1.35049 (373*2π)/5471 weeks
374-.34704 -.29339 (374*2π)/5471 weeks
375.30725 -1.66451 (375*2π)/5471 weeks
3761.29118 -2.05575 (376*2π)/5471 weeks
3771.88421 -1.54145 (377*2π)/5471 weeks
3782.54986 -.72165 (378*2π)/5471 weeks
3791.32189 .91385 (379*2π)/5471 weeks
380-.74885 -.3236 (380*2π)/5471 weeks
381-.36018 -2.16981 (381*2π)/5471 weeks
3821.13034 -2.59094 (382*2π)/5471 weeks
3832.1586 -2.53154 (383*2π)/5471 weeks
3842.48051 -.5749 (384*2π)/5471 weeks
3851.18945 -.68503 (385*2π)/5471 weeks
386.75581 -1.21142 (386*2π)/5471 weeks
387.98887 -1.38348 (387*2π)/5471 weeks
388.50698 -1.6782 (388*2π)/5471 weeks
3891.77836 -2.90489 (389*2π)/5471 weeks
3902.48127 -.91153 (390*2π)/5471 weeks
3911.21444 -1.14237 (391*2π)/5471 weeks
3921.16623 -1.52883 (392*2π)/5471 weeks
3931.06507 -1.66878 (393*2π)/5471 weeks
3941.59161 -2.19746 (394*2π)/5471 weeks
3951.81896 -1.84333 (395*2π)/5471 weeks
3963.05363 -1.76423 (396*2π)/5471 weeks
3971.73898 .42626 (397*2π)/5471 weeks
398.35242 -1.37738 (398*2π)/5471 weeks
3991.28925 -1.73611 (399*2π)/5471 weeks
4001.78394 -2.30751 (400*2π)/5471 weeks
4012.26945 -1.06405 (401*2π)/5471 weeks
4021.43702 -.51351 (402*2π)/5471 weeks
403.66474 -1.00029 (403*2π)/5471 weeks
404.86162 -2.3297 (404*2π)/5471 weeks
4052.58365 -2.16853 (405*2π)/5471 weeks
4061.37484 -.18147 (406*2π)/5471 weeks
407.21889 -1.78017 (407*2π)/5471 weeks
408.59852 -2.20703 (408*2π)/5471 weeks
4091.74666 -2.65339 (409*2π)/5471 weeks
4101.75603 -1.05239 (410*2π)/5471 weeks
411.29205 -2.36013 (411*2π)/5471 weeks
4122.15457 -3.75366 (412*2π)/5471 weeks
4132.89968 -2.71938 (413*2π)/5471 weeks
4143.88198 -1.30255 (414*2π)/5471 weeks
4152.34606 .59345 (415*2π)/5471 weeks
416.38272 -.50984 (416*2π)/5471 weeks
4171.06063 -2.34706 (417*2π)/5471 weeks
4182.0296 -1.63527 (418*2π)/5471 weeks
4191.33148 -.96442 (419*2π)/5471 weeks
4201.17301 -1.94834 (420*2π)/5471 weeks
421.77862 -1.38166 (421*2π)/5471 weeks
422.08822 -2.40904 (422*2π)/5471 weeks
423.95551 -3.86984 (423*2π)/5471 weeks
4244.18194 -4.20576 (424*2π)/5471 weeks
4254.55598 -.39944 (425*2π)/5471 weeks
4261.45561 .92563 (426*2π)/5471 weeks
427-.09496 -1.42001 (427*2π)/5471 weeks
428-.00598 -2.91247 (428*2π)/5471 weeks
4292.68511 -3.99026 (429*2π)/5471 weeks
4304.43727 -1.82291 (430*2π)/5471 weeks
4313.52356 1.17061 (431*2π)/5471 weeks
432-.54451 1.7743 (432*2π)/5471 weeks
433-3.30897 -2.50734 (433*2π)/5471 weeks
434.11493 -6.33164 (434*2π)/5471 weeks
4353.92019 -5.63287 (435*2π)/5471 weeks
4366.5312 -2.10005 (436*2π)/5471 weeks
4373.93272 2.82919 (437*2π)/5471 weeks
438-1.70939 1.7152 (438*2π)/5471 weeks
439-3.32703 -3.69327 (439*2π)/5471 weeks
440.67518 -7.3864 (440*2π)/5471 weeks
4415.41158 -6.0162 (441*2π)/5471 weeks
4427.80167 -.4992 (442*2π)/5471 weeks
4432.73681 2.83295 (443*2π)/5471 weeks
444-1.36116 1.05588 (444*2π)/5471 weeks
445-1.68372 -3.83559 (445*2π)/5471 weeks
4462.14226 -5.82197 (446*2π)/5471 weeks
4475.3895 -3.36431 (447*2π)/5471 weeks
4484.86977 .65308 (448*2π)/5471 weeks
4491.18796 1.89036 (449*2π)/5471 weeks
450-.87349 -.83459 (450*2π)/5471 weeks
451.06214 -2.43287 (451*2π)/5471 weeks
4521.38953 -2.94966 (452*2π)/5471 weeks
453.97616 -1.63066 (453*2π)/5471 weeks
454.62745 -3.85399 (454*2π)/5471 weeks
4553.61505 -3.34049 (455*2π)/5471 weeks
4563.09837 -.11486 (456*2π)/5471 weeks
457-.36926 .32628 (457*2π)/5471 weeks
458-2.27475 -2.72149 (458*2π)/5471 weeks
459.2014 -6.03827 (459*2π)/5471 weeks
4604.58439 -5.58241 (460*2π)/5471 weeks
4616.07053 -1.01423 (461*2π)/5471 weeks
4621.87041 2.71189 (462*2π)/5471 weeks
463-3.32143 -.53871 (463*2π)/5471 weeks
464-1.9294 -5.05029 (464*2π)/5471 weeks
465.46855 -6.9497 (465*2π)/5471 weeks
4665.63292 -6.07113 (466*2π)/5471 weeks
4676.10825 -1.08709 (467*2π)/5471 weeks
4682.95695 2.10995 (468*2π)/5471 weeks
469-2.63357 -.16665 (469*2π)/5471 weeks
470-.47109 -5.43235 (470*2π)/5471 weeks
4712.25878 -4.00412 (471*2π)/5471 weeks
4723.86358 -4.57891 (472*2π)/5471 weeks
4735.27651 .35807 (473*2π)/5471 weeks
474-1.22352 3.03743 (474*2π)/5471 weeks
475-4.95372 -2.46238 (475*2π)/5471 weeks
476-1.35808 -7.78779 (476*2π)/5471 weeks
4774.04271 -6.51472 (477*2π)/5471 weeks
4783.16531 -.68511 (478*2π)/5471 weeks
479-1.23341 -2.88529 (479*2π)/5471 weeks
480-.54267 -5.2733 (480*2π)/5471 weeks
4811.93603 -8.34637 (481*2π)/5471 weeks
4826.42013 -4.95563 (482*2π)/5471 weeks
4835.09248 .25207 (483*2π)/5471 weeks
484.22387 .25578 (484*2π)/5471 weeks
485-2.02384 -2.76268 (485*2π)/5471 weeks
486.79852 -5.95877 (486*2π)/5471 weeks
4873.1886 -3.62623 (487*2π)/5471 weeks
4881.35074 -1.78963 (488*2π)/5471 weeks
489-1.09206 -3.50914 (489*2π)/5471 weeks
490-.62134 -6.30776 (490*2π)/5471 weeks
4914.35244 -8.05274 (491*2π)/5471 weeks
4924.95488 -1.30591 (492*2π)/5471 weeks
493.23979 -1.60335 (493*2π)/5471 weeks
494.07432 -4.05673 (494*2π)/5471 weeks
495.70707 -4.77872 (495*2π)/5471 weeks
4963.81484 -4.75324 (496*2π)/5471 weeks
4973.13441 -.4778 (497*2π)/5471 weeks
498-.79855 -.00271 (498*2π)/5471 weeks
499-3.90517 -3.40106 (499*2π)/5471 weeks
500-4.76548 -6.43254 (500*2π)/5471 weeks
501.80742 -9.72921 (501*2π)/5471 weeks
5021.95076 -5.53651 (502*2π)/5471 weeks
503.86591 -6.16834 (503*2π)/5471 weeks
504-1.17333 -5.74465 (504*2π)/5471 weeks
5051.09402 -10.20913 (505*2π)/5471 weeks
5066.68174 -6.33566 (506*2π)/5471 weeks
507.33168 -1.37888 (507*2π)/5471 weeks
508-2.82897 -6.02159 (508*2π)/5471 weeks
509-1.73366 -9.20996 (509*2π)/5471 weeks
5101.6941 -12.85931 (510*2π)/5471 weeks
5119.2397 -9.41554 (511*2π)/5471 weeks
5129.25455 -.11203 (512*2π)/5471 weeks
513-2.55999 6.55261 (513*2π)/5471 weeks
514-14.51332 -6.62275 (514*2π)/5471 weeks
515-6.89653 -19.76495 (515*2π)/5471 weeks
5165.95328 -20.13696 (516*2π)/5471 weeks
51713.61369 -9.40131 (517*2π)/5471 weeks
5187.58106 1.91652 (518*2π)/5471 weeks
519-3.00089 -.63865 (519*2π)/5471 weeks
520-8.44467 -4.59004 (520*2π)/5471 weeks
521-8.72464 -17.81449 (521*2π)/5471 weeks
522.11111 -17.80145 (522*2π)/5471 weeks
5233.43199 -16.40695 (523*2π)/5471 weeks
5242.7446 -9.55989 (524*2π)/5471 weeks
525.3948 -15.72705 (525*2π)/5471 weeks
5262.4451 -15.08308 (526*2π)/5471 weeks
5272.58385 -17.81996 (527*2π)/5471 weeks
5286.01872 -19.10992 (528*2π)/5471 weeks
52913.72213 -16.21899 (529*2π)/5471 weeks
53010.3004 -3.7195 (530*2π)/5471 weeks
5311.84686 -2.44657 (531*2π)/5471 weeks
532-11.96632 -5.11628 (532*2π)/5471 weeks
533-21.16608 -21.69381 (533*2π)/5471 weeks
534-13.27849 -45.59876 (534*2π)/5471 weeks
53518.58748 -52.41167 (535*2π)/5471 weeks
53635.00656 -24.01507 (536*2π)/5471 weeks
53721.13725 -5.07343 (537*2π)/5471 weeks
538-3.67498 3.62527 (538*2π)/5471 weeks
539-38.50982 -32.05786 (539*2π)/5471 weeks
540.58637 -84.05717 (540*2π)/5471 weeks
54152.68803 -64.57646 (541*2π)/5471 weeks
54259.94092 -7.6535 (542*2π)/5471 weeks
543-16.04264 16.49916 (543*2π)/5471 weeks
544-82.22617 -57.41151 (544*2π)/5471 weeks
545-43.28952 -209.2197 (545*2π)/5471 weeks



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