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Fourier Analysis of FXP (ProShares UltraShort FTSE China 50 ETF)


FXP (ProShares UltraShort FTSE China 50 ETF) appears to have interesting cyclic behaviour every 39 weeks (76.0196*sine), 36 weeks (68.7312*sine), and 42 weeks (64.1604*sine).

FXP (ProShares UltraShort FTSE China 50 ETF) has an average price of 289.94 (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 11/8/2007 to 7/17/2017 for FXP (ProShares UltraShort FTSE China 50 ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0289.9382   0 
1344.4696 210.5881 (1*2π)/507507 weeks
2230.1604 270.2118 (2*2π)/507254 weeks
396.59128 279.5048 (3*2π)/507169 weeks
4-4.71311 231.1484 (4*2π)/507127 weeks
5-55.19495 164.8347 (5*2π)/507101 weeks
6-63.4578 87.74091 (6*2π)/50785 weeks
7-34.43932 36.333 (7*2π)/50772 weeks
8-.75353 22.58067 (8*2π)/50763 weeks
918.86796 28.85222 (9*2π)/50756 weeks
1033.7244 39.19626 (10*2π)/50751 weeks
1129.41972 59.5683 (11*2π)/50746 weeks
1224.51364 64.16041 (12*2π)/50742 weeks
134.45765 76.01957 (13*2π)/50739 weeks
14-11.22515 68.7312 (14*2π)/50736 weeks
15-23.78835 58.77783 (15*2π)/50734 weeks
16-38.27678 42.03763 (16*2π)/50732 weeks
17-36.40388 18.91467 (17*2π)/50730 weeks
18-28.02558 3.94759 (18*2π)/50728 weeks
19-12.44295 -7.80687 (19*2π)/50727 weeks
206.56754 -8.81132 (20*2π)/50725 weeks
2120.49664 .9782 (21*2π)/50724 weeks
2222.07752 17.57231 (22*2π)/50723 weeks
2312.56525 29.952 (23*2π)/50722 weeks
24-1.01023 32.56692 (24*2π)/50721 weeks
25-11.44767 21.89236 (25*2π)/50720 weeks
26-15.22697 8.39123 (26*2π)/50720 weeks
27-8.44027 -7.02883 (27*2π)/50719 weeks
285.85632 -12.33423 (28*2π)/50718 weeks
2921.0618 -11.97789 (29*2π)/50717 weeks
3034.89578 .86576 (30*2π)/50717 weeks
3137.35682 20.23401 (31*2π)/50716 weeks
3227.73786 32.22602 (32*2π)/50716 weeks
3314.76017 39.53021 (33*2π)/50715 weeks
341.33628 35.71675 (34*2π)/50715 weeks
35-7.1463 30.16338 (35*2π)/50714 weeks
36-11.82215 20.74493 (36*2π)/50714 weeks
37-11.11334 9.26985 (37*2π)/50714 weeks
38-2.57414 5.4391 (38*2π)/50713 weeks
39.73075 4.88223 (39*2π)/50713 weeks
406.04883 6.1691 (40*2π)/50713 weeks
416.74765 9.68606 (41*2π)/50712 weeks
426.26256 11.04284 (42*2π)/50712 weeks
432.42002 13.61692 (43*2π)/50712 weeks
44-.67768 11.05657 (44*2π)/50712 weeks
45-1.04 8.4681 (45*2π)/50711 weeks
46-1.13508 2.78193 (46*2π)/50711 weeks
473.95214 .31858 (47*2π)/50711 weeks
487.20056 -.2525 (48*2π)/50711 weeks
4912.42235 .48952 (49*2π)/50710 weeks
5017.11682 5.06286 (50*2π)/50710 weeks
5117.14194 11.71773 (51*2π)/50710 weeks
5215.43605 17.40095 (52*2π)/50710 weeks
538.2197 20.12012 (53*2π)/50710 weeks
542.40833 19.36833 (54*2π)/5079 weeks
55-1.83644 14.91576 (55*2π)/5079 weeks
56-3.55491 9.65202 (56*2π)/5079 weeks
57.44141 4.28637 (57*2π)/5079 weeks
584.55393 3.65897 (58*2π)/5079 weeks
597.87706 4.33366 (59*2π)/5079 weeks
6010.60455 8.2517 (60*2π)/5078 weeks
619.04951 11.32909 (61*2π)/5078 weeks
629.03109 13.49063 (62*2π)/5078 weeks
635.40074 15.89778 (63*2π)/5078 weeks
643.62026 14.8954 (64*2π)/5078 weeks
65.92701 16.74718 (65*2π)/5078 weeks
66-3.22124 15.40458 (66*2π)/5078 weeks
67-7.03161 11.72332 (67*2π)/5078 weeks
68-9.26736 5.76136 (68*2π)/5077 weeks
69-6.0043 -.41189 (69*2π)/5077 weeks
70-.29926 -3.00862 (70*2π)/5077 weeks
713.4838 -2.94586 (71*2π)/5077 weeks
729.17155 -1.26974 (72*2π)/5077 weeks
7310.85911 4.59013 (73*2π)/5077 weeks
748.49626 7.9549 (74*2π)/5077 weeks
756.15502 10.95927 (75*2π)/5077 weeks
76.0202 9.5062 (76*2π)/5077 weeks
77-.6135 5.43631 (77*2π)/5077 weeks
78-.66515 2.51665 (78*2π)/5077 weeks
792.57564 -1.96379 (79*2π)/5076 weeks
807.44226 -1.52418 (80*2π)/5076 weeks
8111.72081 .34766 (81*2π)/5076 weeks
8213.57278 5.05599 (82*2π)/5076 weeks
8311.83689 10.0182 (83*2π)/5076 weeks
847.69263 11.70811 (84*2π)/5076 weeks
853.67409 11.49605 (85*2π)/5076 weeks
862.25015 8.61214 (86*2π)/5076 weeks
873.28014 6.48309 (87*2π)/5076 weeks
883.20916 5.94866 (88*2π)/5076 weeks
895.06631 4.73456 (89*2π)/5076 weeks
906.29398 5.17314 (90*2π)/5076 weeks
917.3212 6.24968 (91*2π)/5076 weeks
927.74548 8.37367 (92*2π)/5076 weeks
937.08869 10.54432 (93*2π)/5075 weeks
945.34469 12.23866 (94*2π)/5075 weeks
953.28761 13.10026 (95*2π)/5075 weeks
96-.05735 12.6403 (96*2π)/5075 weeks
97-2.53792 10.54166 (97*2π)/5075 weeks
98-4.38109 7.78187 (98*2π)/5075 weeks
99-4.72869 4.56719 (99*2π)/5075 weeks
100-3.06252 .82336 (100*2π)/5075 weeks
101.65589 -.90929 (101*2π)/5075 weeks
1024.08628 -.74804 (102*2π)/5075 weeks
1036.54031 1.69744 (103*2π)/5075 weeks
1046.4048 4.72738 (104*2π)/5075 weeks
1055.78237 6.77034 (105*2π)/5075 weeks
1063.21917 8.67115 (106*2π)/5075 weeks
107.41042 7.19578 (107*2π)/5075 weeks
108-.96581 4.54571 (108*2π)/5075 weeks
109-.53544 2.03135 (109*2π)/5075 weeks
1101.41473 -.21233 (110*2π)/5075 weeks
1114.64959 -.23963 (111*2π)/5075 weeks
1127.58699 1.28928 (112*2π)/5075 weeks
1139.01005 4.23168 (113*2π)/5074 weeks
1147.8387 7.77313 (114*2π)/5074 weeks
1155.02576 9.05513 (115*2π)/5074 weeks
1162.19829 9.04634 (116*2π)/5074 weeks
117.47431 6.80569 (117*2π)/5074 weeks
1181.25983 5.26749 (118*2π)/5074 weeks
1192.10942 4.89381 (119*2π)/5074 weeks
1202.51696 5.37463 (120*2π)/5074 weeks
1212.40985 6.13087 (121*2π)/5074 weeks
1221.43621 6.70596 (122*2π)/5074 weeks
123-.4413 6.64496 (123*2π)/5074 weeks
124-2.05644 5.16661 (124*2π)/5074 weeks
125-2.39512 3.10799 (125*2π)/5074 weeks
126-1.65169 .24145 (126*2π)/5074 weeks
1271.72321 -1.37694 (127*2π)/5074 weeks
1283.62659 .2959 (128*2π)/5074 weeks
1294.18546 1.64591 (129*2π)/5074 weeks
1304.41703 2.79512 (130*2π)/5074 weeks
1313.45275 3.8271 (131*2π)/5074 weeks
1323.32906 3.70639 (132*2π)/5074 weeks
1332.63194 4.32486 (133*2π)/5074 weeks
1341.333 3.51969 (134*2π)/5074 weeks
1351.27452 2.74073 (135*2π)/5074 weeks
136.79612 1.60782 (136*2π)/5074 weeks
1373.09458 .21478 (137*2π)/5074 weeks
1384.60828 .92683 (138*2π)/5074 weeks
1396.16625 1.76841 (139*2π)/5074 weeks
1406.62184 4.5321 (140*2π)/5074 weeks
1415.04952 6.5743 (141*2π)/5074 weeks
1423.59492 7.60036 (142*2π)/5074 weeks
143.75866 8.05856 (143*2π)/5074 weeks
144-1.26526 7.06826 (144*2π)/5074 weeks
145-3.12246 5.17403 (145*2π)/5073 weeks
146-4.62086 2.02376 (146*2π)/5073 weeks
147-2.49946 -1.49107 (147*2π)/5073 weeks
148-.50714 -2.67199 (148*2π)/5073 weeks
1492.38088 -3.68344 (149*2π)/5073 weeks
1505.76139 -2.7656 (150*2π)/5073 weeks
1517.89195 .2481 (151*2π)/5073 weeks
1527.6553 3.98732 (152*2π)/5073 weeks
1535.43765 6.77308 (153*2π)/5073 weeks
1541.88665 7.54575 (154*2π)/5073 weeks
155-1.30286 6.27391 (155*2π)/5073 weeks
156-2.94095 3.66567 (156*2π)/5073 weeks
157-2.76723 .34697 (157*2π)/5073 weeks
158-1.36307 -1.92712 (158*2π)/5073 weeks
1591.60042 -3.53475 (159*2π)/5073 weeks
1604.32073 -2.84766 (160*2π)/5073 weeks
1616.56308 -1.08452 (161*2π)/5073 weeks
1627.33533 2.00621 (162*2π)/5073 weeks
1636.6779 4.97863 (163*2π)/5073 weeks
1644.0313 7.21378 (164*2π)/5073 weeks
165.39476 7.54644 (165*2π)/5073 weeks
166-2.71271 5.85754 (166*2π)/5073 weeks
167-4.2198 2.67791 (167*2π)/5073 weeks
168-4.23197 -.82933 (168*2π)/5073 weeks
169-2.37683 -3.27391 (169*2π)/5073 weeks
1701.042 -4.59523 (170*2π)/5073 weeks
1713.5573 -3.39926 (171*2π)/5073 weeks
1724.85529 -1.60158 (172*2π)/5073 weeks
1734.6663 .99275 (173*2π)/5073 weeks
1742.80823 2.09346 (174*2π)/5073 weeks
175.93239 1.98941 (175*2π)/5073 weeks
176-.47986 .33398 (176*2π)/5073 weeks
177-.90159 -1.94905 (177*2π)/5073 weeks
178.43953 -3.70482 (178*2π)/5073 weeks
1792.71515 -5.2194 (179*2π)/5073 weeks
1805.75546 -4.73379 (180*2π)/5073 weeks
1816.92546 -2.59139 (181*2π)/5073 weeks
1827.58303 -.52638 (182*2π)/5073 weeks
1836.70555 2.07928 (183*2π)/5073 weeks
1844.7861 2.86291 (184*2π)/5073 weeks
1853.00588 3.24557 (185*2π)/5073 weeks
186.22399 1.84397 (186*2π)/5073 weeks
187-.27098 -1.1408 (187*2π)/5073 weeks
188.43226 -3.17745 (188*2π)/5073 weeks
1892.94053 -5.613 (189*2π)/5073 weeks
1906.37031 -5.22839 (190*2π)/5073 weeks
1919.11465 -3.13624 (191*2π)/5073 weeks
1929.48913 .22142 (192*2π)/5073 weeks
1937.90739 2.87482 (193*2π)/5073 weeks
1945.73952 3.52478 (194*2π)/5073 weeks
1953.26686 3.20156 (195*2π)/5073 weeks
1962.20683 1.35418 (196*2π)/5073 weeks
1972.42567 -1.2917 (197*2π)/5073 weeks
1983.98891 -1.94518 (198*2π)/5073 weeks
1996.55539 -2.22213 (199*2π)/5073 weeks
2007.88486 -.18853 (200*2π)/5073 weeks
2017.68127 1.10001 (201*2π)/5073 weeks
2027.36728 2.56771 (202*2π)/5073 weeks
2036.66956 3.48252 (203*2π)/5072 weeks
2045.71565 4.73098 (204*2π)/5072 weeks
2053.71342 4.69618 (205*2π)/5072 weeks
2062.28929 4.10038 (206*2π)/5072 weeks
207.97365 3.03429 (207*2π)/5072 weeks
208.53796 .76195 (208*2π)/5072 weeks
2091.4791 -.9278 (209*2π)/5072 weeks
2103.39308 -2.01571 (210*2π)/5072 weeks
2116.19952 -1.95432 (211*2π)/5072 weeks
2127.70709 .3263 (212*2π)/5072 weeks
2137.65485 3.06953 (213*2π)/5072 weeks
2146.16208 5.53047 (214*2π)/5072 weeks
2153.19414 6.68581 (215*2π)/5072 weeks
216.26387 5.7486 (216*2π)/5072 weeks
217-2.29577 3.76631 (217*2π)/5072 weeks
218-3.03344 -.10804 (218*2π)/5072 weeks
219-1.39581 -3.29567 (219*2π)/5072 weeks
2202.01639 -5.26078 (220*2π)/5072 weeks
2216.2291 -4.52249 (221*2π)/5072 weeks
2228.33291 -1.25568 (222*2π)/5072 weeks
2238.55341 2.06244 (223*2π)/5072 weeks
2246.22565 5.68178 (224*2π)/5072 weeks
2252.26445 6.52926 (225*2π)/5072 weeks
226-1.12587 5.08881 (226*2π)/5072 weeks
227-3.83166 1.94621 (227*2π)/5072 weeks
228-4.11931 -2.8951 (228*2π)/5072 weeks
229-1.33044 -6.13741 (229*2π)/5072 weeks
2302.56944 -8.04593 (230*2π)/5072 weeks
2317.26535 -7.15865 (231*2π)/5072 weeks
2329.89284 -3.83466 (232*2π)/5072 weeks
23310.86675 -.51714 (233*2π)/5072 weeks
2349.58477 3.09569 (234*2π)/5072 weeks
2357.24149 5.17605 (235*2π)/5072 weeks
2363.98401 6.39329 (236*2π)/5072 weeks
237-.04981 5.02518 (237*2π)/5072 weeks
238-1.28885 1.27209 (238*2π)/5072 weeks
239-.47031 -1.81734 (239*2π)/5072 weeks
2401.82741 -4.46111 (240*2π)/5072 weeks
2415.88601 -4.97768 (241*2π)/5072 weeks
2429.15895 -2.20432 (242*2π)/5072 weeks
2439.7113 2.0714 (243*2π)/5072 weeks
2447.9111 5.8368 (244*2π)/5072 weeks
2453.8541 7.46258 (245*2π)/5072 weeks
246.60402 6.87503 (246*2π)/5072 weeks
247-3.59781 4.48402 (247*2π)/5072 weeks
248-4.85017 -.5538 (248*2π)/5072 weeks
249-2.973 -4.64561 (249*2π)/5072 weeks
250.63365 -6.97275 (250*2π)/5072 weeks
2514.91928 -7.30439 (251*2π)/5072 weeks
2528.04881 -5.57088 (252*2π)/5072 weeks
25310.76985 -2.41559 (253*2π)/5072 weeks
25410.76985 2.41559 (254*2π)/5072 weeks
2558.04881 5.57088 (255*2π)/5072 weeks
2564.91928 7.30439 (256*2π)/5072 weeks
257.63365 6.97275 (257*2π)/5072 weeks
258-2.973 4.64561 (258*2π)/5072 weeks
259-4.85017 .5538 (259*2π)/5072 weeks
260-3.59781 -4.48402 (260*2π)/5072 weeks
261.60402 -6.87503 (261*2π)/5072 weeks
2623.8541 -7.46258 (262*2π)/5072 weeks
2637.9111 -5.8368 (263*2π)/5072 weeks
2649.7113 -2.0714 (264*2π)/5072 weeks
2659.15895 2.20432 (265*2π)/5072 weeks
2665.88601 4.97768 (266*2π)/5072 weeks
2671.82741 4.46111 (267*2π)/5072 weeks
268-.47031 1.81734 (268*2π)/5072 weeks
269-1.28885 -1.27209 (269*2π)/5072 weeks
270-.04981 -5.02518 (270*2π)/5072 weeks
2713.98401 -6.39329 (271*2π)/5072 weeks
2727.24149 -5.17605 (272*2π)/5072 weeks
2739.58477 -3.09569 (273*2π)/5072 weeks
27410.86675 .51714 (274*2π)/5072 weeks
2759.89284 3.83466 (275*2π)/5072 weeks
2767.26535 7.15865 (276*2π)/5072 weeks
2772.56944 8.04593 (277*2π)/5072 weeks
278-1.33044 6.13741 (278*2π)/5072 weeks
279-4.11931 2.8951 (279*2π)/5072 weeks
280-3.83166 -1.94621 (280*2π)/5072 weeks
281-1.12587 -5.08881 (281*2π)/5072 weeks
2822.26445 -6.52926 (282*2π)/5072 weeks
2836.22565 -5.68178 (283*2π)/5072 weeks
2848.55341 -2.06244 (284*2π)/5072 weeks
2858.33291 1.25568 (285*2π)/5072 weeks
2866.2291 4.52249 (286*2π)/5072 weeks
2872.01639 5.26078 (287*2π)/5072 weeks
288-1.39581 3.29567 (288*2π)/5072 weeks
289-3.03344 .10804 (289*2π)/5072 weeks
290-2.29577 -3.76631 (290*2π)/5072 weeks
291.26387 -5.7486 (291*2π)/5072 weeks
2923.19414 -6.68581 (292*2π)/5072 weeks
2936.16208 -5.53047 (293*2π)/5072 weeks
2947.65485 -3.06953 (294*2π)/5072 weeks
2957.70709 -.3263 (295*2π)/5072 weeks
2966.19952 1.95432 (296*2π)/5072 weeks
2973.39308 2.01571 (297*2π)/5072 weeks
2981.4791 .9278 (298*2π)/5072 weeks
299.53796 -.76195 (299*2π)/5072 weeks
300.97365 -3.03429 (300*2π)/5072 weeks
3012.28929 -4.10038 (301*2π)/5072 weeks
3023.71342 -4.69618 (302*2π)/5072 weeks
3035.71565 -4.73098 (303*2π)/5072 weeks
3046.66956 -3.48252 (304*2π)/5072 weeks
3057.36728 -2.56771 (305*2π)/5072 weeks
3067.68127 -1.10001 (306*2π)/5072 weeks
3077.88486 .18853 (307*2π)/5072 weeks
3086.55539 2.22213 (308*2π)/5072 weeks
3093.98891 1.94518 (309*2π)/5072 weeks
3102.42567 1.2917 (310*2π)/5072 weeks
3112.20683 -1.35418 (311*2π)/5072 weeks
3123.26686 -3.20156 (312*2π)/5072 weeks
3135.73952 -3.52478 (313*2π)/5072 weeks
3147.90739 -2.87482 (314*2π)/5072 weeks
3159.48913 -.22142 (315*2π)/5072 weeks
3169.11465 3.13624 (316*2π)/5072 weeks
3176.37031 5.22839 (317*2π)/5072 weeks
3182.94053 5.613 (318*2π)/5072 weeks
319.43226 3.17745 (319*2π)/5072 weeks
320-.27098 1.1408 (320*2π)/5072 weeks
321.22399 -1.84397 (321*2π)/5072 weeks
3223.00588 -3.24557 (322*2π)/5072 weeks
3234.7861 -2.86291 (323*2π)/5072 weeks
3246.70555 -2.07928 (324*2π)/5072 weeks
3257.58303 .52638 (325*2π)/5072 weeks
3266.92546 2.59139 (326*2π)/5072 weeks
3275.75546 4.73379 (327*2π)/5072 weeks
3282.71515 5.2194 (328*2π)/5072 weeks
329.43953 3.70482 (329*2π)/5072 weeks
330-.90159 1.94905 (330*2π)/5072 weeks
331-.47986 -.33398 (331*2π)/5072 weeks
332.93239 -1.98941 (332*2π)/5072 weeks
3332.80823 -2.09346 (333*2π)/5072 weeks
3344.6663 -.99275 (334*2π)/5072 weeks
3354.85529 1.60158 (335*2π)/5072 weeks
3363.5573 3.39926 (336*2π)/5072 weeks
3371.042 4.59523 (337*2π)/5072 weeks
338-2.37683 3.27391 (338*2π)/5072 weeks
339-4.23197 .82933 (339*2π)/5071 weeks
340-4.2198 -2.67791 (340*2π)/5071 weeks
341-2.71271 -5.85754 (341*2π)/5071 weeks
342.39476 -7.54644 (342*2π)/5071 weeks
3434.0313 -7.21378 (343*2π)/5071 weeks
3446.6779 -4.97863 (344*2π)/5071 weeks
3457.33533 -2.00621 (345*2π)/5071 weeks
3466.56308 1.08452 (346*2π)/5071 weeks
3474.32073 2.84766 (347*2π)/5071 weeks
3481.60042 3.53475 (348*2π)/5071 weeks
349-1.36307 1.92712 (349*2π)/5071 weeks
350-2.76723 -.34697 (350*2π)/5071 weeks
351-2.94095 -3.66567 (351*2π)/5071 weeks
352-1.30286 -6.27391 (352*2π)/5071 weeks
3531.88665 -7.54575 (353*2π)/5071 weeks
3545.43765 -6.77308 (354*2π)/5071 weeks
3557.6553 -3.98732 (355*2π)/5071 weeks
3567.89195 -.2481 (356*2π)/5071 weeks
3575.76139 2.7656 (357*2π)/5071 weeks
3582.38088 3.68344 (358*2π)/5071 weeks
359-.50714 2.67199 (359*2π)/5071 weeks
360-2.49946 1.49107 (360*2π)/5071 weeks
361-4.62086 -2.02376 (361*2π)/5071 weeks
362-3.12246 -5.17403 (362*2π)/5071 weeks
363-1.26526 -7.06826 (363*2π)/5071 weeks
364.75866 -8.05856 (364*2π)/5071 weeks
3653.59492 -7.60036 (365*2π)/5071 weeks
3665.04952 -6.5743 (366*2π)/5071 weeks
3676.62184 -4.5321 (367*2π)/5071 weeks
3686.16625 -1.76841 (368*2π)/5071 weeks
3694.60828 -.92683 (369*2π)/5071 weeks
3703.09458 -.21478 (370*2π)/5071 weeks
371.79612 -1.60782 (371*2π)/5071 weeks
3721.27452 -2.74073 (372*2π)/5071 weeks
3731.333 -3.51969 (373*2π)/5071 weeks
3742.63194 -4.32486 (374*2π)/5071 weeks
3753.32906 -3.70639 (375*2π)/5071 weeks
3763.45275 -3.8271 (376*2π)/5071 weeks
3774.41703 -2.79512 (377*2π)/5071 weeks
3784.18546 -1.64591 (378*2π)/5071 weeks
3793.62659 -.2959 (379*2π)/5071 weeks
3801.72321 1.37694 (380*2π)/5071 weeks
381-1.65169 -.24145 (381*2π)/5071 weeks
382-2.39512 -3.10799 (382*2π)/5071 weeks
383-2.05644 -5.16661 (383*2π)/5071 weeks
384-.4413 -6.64496 (384*2π)/5071 weeks
3851.43621 -6.70596 (385*2π)/5071 weeks
3862.40985 -6.13087 (386*2π)/5071 weeks
3872.51696 -5.37463 (387*2π)/5071 weeks
3882.10942 -4.89381 (388*2π)/5071 weeks
3891.25983 -5.26749 (389*2π)/5071 weeks
390.47431 -6.80569 (390*2π)/5071 weeks
3912.19829 -9.04634 (391*2π)/5071 weeks
3925.02576 -9.05513 (392*2π)/5071 weeks
3937.8387 -7.77313 (393*2π)/5071 weeks
3949.01005 -4.23168 (394*2π)/5071 weeks
3957.58699 -1.28928 (395*2π)/5071 weeks
3964.64959 .23963 (396*2π)/5071 weeks
3971.41473 .21233 (397*2π)/5071 weeks
398-.53544 -2.03135 (398*2π)/5071 weeks
399-.96581 -4.54571 (399*2π)/5071 weeks
400.41042 -7.19578 (400*2π)/5071 weeks
4013.21917 -8.67115 (401*2π)/5071 weeks
4025.78237 -6.77034 (402*2π)/5071 weeks
4036.4048 -4.72738 (403*2π)/5071 weeks
4046.54031 -1.69744 (404*2π)/5071 weeks
4054.08628 .74804 (405*2π)/5071 weeks
406.65589 .90929 (406*2π)/5071 weeks
407-3.06252 -.82336 (407*2π)/5071 weeks
408-4.72869 -4.56719 (408*2π)/5071 weeks
409-4.38109 -7.78187 (409*2π)/5071 weeks
410-2.53792 -10.54166 (410*2π)/5071 weeks
411-.05735 -12.6403 (411*2π)/5071 weeks
4123.28761 -13.10026 (412*2π)/5071 weeks
4135.34469 -12.23866 (413*2π)/5071 weeks
4147.08869 -10.54432 (414*2π)/5071 weeks
4157.74548 -8.37367 (415*2π)/5071 weeks
4167.3212 -6.24968 (416*2π)/5071 weeks
4176.29398 -5.17314 (417*2π)/5071 weeks
4185.06631 -4.73456 (418*2π)/5071 weeks
4193.20916 -5.94866 (419*2π)/5071 weeks
4203.28014 -6.48309 (420*2π)/5071 weeks
4212.25015 -8.61214 (421*2π)/5071 weeks
4223.67409 -11.49605 (422*2π)/5071 weeks
4237.69263 -11.70811 (423*2π)/5071 weeks
42411.83689 -10.0182 (424*2π)/5071 weeks
42513.57278 -5.05599 (425*2π)/5071 weeks
42611.72081 -.34766 (426*2π)/5071 weeks
4277.44226 1.52418 (427*2π)/5071 weeks
4282.57564 1.96379 (428*2π)/5071 weeks
429-.66515 -2.51665 (429*2π)/5071 weeks
430-.6135 -5.43631 (430*2π)/5071 weeks
431.0202 -9.5062 (431*2π)/5071 weeks
4326.15502 -10.95927 (432*2π)/5071 weeks
4338.49626 -7.9549 (433*2π)/5071 weeks
43410.85911 -4.59013 (434*2π)/5071 weeks
4359.17155 1.26974 (435*2π)/5071 weeks
4363.4838 2.94586 (436*2π)/5071 weeks
437-.29926 3.00862 (437*2π)/5071 weeks
438-6.0043 .41189 (438*2π)/5071 weeks
439-9.26736 -5.76136 (439*2π)/5071 weeks
440-7.03161 -11.72332 (440*2π)/5071 weeks
441-3.22124 -15.40458 (441*2π)/5071 weeks
442.92701 -16.74718 (442*2π)/5071 weeks
4433.62026 -14.8954 (443*2π)/5071 weeks
4445.40074 -15.89778 (444*2π)/5071 weeks
4459.03109 -13.49063 (445*2π)/5071 weeks
4469.04951 -11.32909 (446*2π)/5071 weeks
44710.60455 -8.2517 (447*2π)/5071 weeks
4487.87706 -4.33366 (448*2π)/5071 weeks
4494.55393 -3.65897 (449*2π)/5071 weeks
450.44141 -4.28637 (450*2π)/5071 weeks
451-3.55491 -9.65202 (451*2π)/5071 weeks
452-1.83644 -14.91576 (452*2π)/5071 weeks
4532.40833 -19.36833 (453*2π)/5071 weeks
4548.2197 -20.12012 (454*2π)/5071 weeks
45515.43605 -17.40095 (455*2π)/5071 weeks
45617.14194 -11.71773 (456*2π)/5071 weeks
45717.11682 -5.06286 (457*2π)/5071 weeks
45812.42235 -.48952 (458*2π)/5071 weeks
4597.20056 .2525 (459*2π)/5071 weeks
4603.95214 -.31858 (460*2π)/5071 weeks
461-1.13508 -2.78193 (461*2π)/5071 weeks
462-1.04 -8.4681 (462*2π)/5071 weeks
463-.67768 -11.05657 (463*2π)/5071 weeks
4642.42002 -13.61692 (464*2π)/5071 weeks
4656.26256 -11.04284 (465*2π)/5071 weeks
4666.74765 -9.68606 (466*2π)/5071 weeks
4676.04883 -6.1691 (467*2π)/5071 weeks
468.73075 -4.88223 (468*2π)/5071 weeks
469-2.57414 -5.4391 (469*2π)/5071 weeks
470-11.11334 -9.26985 (470*2π)/5071 weeks
471-11.82215 -20.74493 (471*2π)/5071 weeks
472-7.1463 -30.16338 (472*2π)/5071 weeks
4731.33628 -35.71675 (473*2π)/5071 weeks
47414.76017 -39.53021 (474*2π)/5071 weeks
47527.73786 -32.22602 (475*2π)/5071 weeks
47637.35682 -20.23401 (476*2π)/5071 weeks
47734.89578 -.86576 (477*2π)/5071 weeks
47821.0618 11.97789 (478*2π)/5071 weeks
4795.85632 12.33423 (479*2π)/5071 weeks
480-8.44027 7.02883 (480*2π)/5071 weeks
481-15.22697 -8.39123 (481*2π)/5071 weeks
482-11.44767 -21.89236 (482*2π)/5071 weeks
483-1.01023 -32.56692 (483*2π)/5071 weeks
48412.56525 -29.952 (484*2π)/5071 weeks
48522.07752 -17.57231 (485*2π)/5071 weeks
48620.49664 -.9782 (486*2π)/5071 weeks
4876.56754 8.81132 (487*2π)/5071 weeks
488-12.44295 7.80687 (488*2π)/5071 weeks
489-28.02558 -3.94759 (489*2π)/5071 weeks
490-36.40388 -18.91467 (490*2π)/5071 weeks
491-38.27678 -42.03763 (491*2π)/5071 weeks
492-23.78835 -58.77783 (492*2π)/5071 weeks
493-11.22515 -68.7312 (493*2π)/5071 weeks
4944.45765 -76.01957 (494*2π)/5071 weeks
49524.51364 -64.16041 (495*2π)/5071 weeks
49629.41972 -59.5683 (496*2π)/5071 weeks
49733.7244 -39.19626 (497*2π)/5071 weeks
49818.86796 -28.85222 (498*2π)/5071 weeks
499-.75353 -22.58067 (499*2π)/5071 weeks
500-34.43932 -36.333 (500*2π)/5071 weeks
501-63.4578 -87.74091 (501*2π)/5071 weeks
502-55.19495 -164.8347 (502*2π)/5071 weeks
503-4.71311 -231.1484 (503*2π)/5071 weeks
50496.59128 -279.5048 (504*2π)/5071 weeks
505230.1604 -270.2118 (505*2π)/5071 weeks



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