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Fourier Analysis of FXP (PROSHARES ULTRASHORT FTSE CHINA 50 PROSHARES ULTRASHORT FTSE CHINA 50)


FXP (PROSHARES ULTRASHORT FTSE CHINA 50 PROSHARES ULTRASHORT FTSE CHINA 50) appears to have interesting cyclic behaviour every 40 weeks (73.9081*sine), 37 weeks (68.4098*sine), and 43 weeks (59.3062*sine).

FXP (PROSHARES ULTRASHORT FTSE CHINA 50 PROSHARES ULTRASHORT FTSE CHINA 50) has an average price of 283.14 (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 10/16/2017 for FXP (PROSHARES ULTRASHORT FTSE CHINA 50 PROSHARES ULTRASHORT FTSE CHINA 50), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0283.1367   0 
1338.7149 204.2751 (1*2π)/520520 weeks
2230.1509 260.9524 (2*2π)/520260 weeks
3102.3314 274.6966 (3*2π)/520173 weeks
42.80838 233.0994 (4*2π)/520130 weeks
5-47.75414 169.83 (5*2π)/520104 weeks
6-63.21336 94.70892 (6*2π)/52087 weeks
7-40.89473 40.67012 (7*2π)/52074 weeks
8-7.73206 23.28184 (8*2π)/52065 weeks
915.26374 27.88871 (9*2π)/52058 weeks
1029.78675 34.80379 (10*2π)/52052 weeks
1133.12132 54.70074 (11*2π)/52047 weeks
1223.67295 59.3062 (12*2π)/52043 weeks
1313.35626 73.90807 (13*2π)/52040 weeks
14-6.11704 68.40982 (14*2π)/52037 weeks
15-19.73393 60.33729 (15*2π)/52035 weeks
16-32.92586 50.17318 (16*2π)/52033 weeks
17-38.12225 27.42482 (17*2π)/52031 weeks
18-30.67981 10.46992 (18*2π)/52029 weeks
19-20.25291 -3.60515 (19*2π)/52027 weeks
20-3.44961 -9.55899 (20*2π)/52026 weeks
2113.05747 -4.15492 (21*2π)/52025 weeks
2223.01679 9.70757 (22*2π)/52024 weeks
2320.10144 23.48333 (23*2π)/52023 weeks
247.97479 30.08874 (24*2π)/52022 weeks
25-7.06213 28.03319 (25*2π)/52021 weeks
26-13.59338 17.45113 (26*2π)/52020 weeks
27-14.29286 3.34353 (27*2π)/52019 weeks
28-3.70836 -9.39901 (28*2π)/52019 weeks
299.61709 -12.40932 (29*2π)/52018 weeks
3025.16995 -9.84764 (30*2π)/52017 weeks
3135.76627 4.38116 (31*2π)/52017 weeks
3234.52936 23.17185 (32*2π)/52016 weeks
3325.24196 33.24553 (33*2π)/52016 weeks
3411.8972 38.97815 (34*2π)/52015 weeks
35.3044 34.30463 (35*2π)/52015 weeks
36-7.77787 28.58992 (36*2π)/52014 weeks
37-11.77567 19.50423 (37*2π)/52014 weeks
38-10.49319 8.45351 (38*2π)/52014 weeks
39-2.36948 5.26682 (39*2π)/52013 weeks
40.77499 4.72034 (40*2π)/52013 weeks
415.91717 5.89361 (41*2π)/52013 weeks
426.69933 9.31637 (42*2π)/52012 weeks
436.04547 10.64712 (43*2π)/52012 weeks
442.87062 13.61529 (44*2π)/52012 weeks
45-.34571 11.44143 (45*2π)/52012 weeks
46-.71676 8.57962 (46*2π)/52011 weeks
47-1.80278 3.79819 (47*2π)/52011 weeks
482.8212 .37174 (48*2π)/52011 weeks
496.07695 .0937 (49*2π)/52011 weeks
5010.82035 .00828 (50*2π)/52010 weeks
5115.77795 3.26121 (51*2π)/52010 weeks
5217.36237 9.6953 (52*2π)/52010 weeks
5316.0008 14.58918 (53*2π)/52010 weeks
5410.25948 19.776 (54*2π)/52010 weeks
554.69496 19.6629 (55*2π)/5209 weeks
56-.60215 16.72107 (56*2π)/5209 weeks
57-2.74831 12.14941 (57*2π)/5209 weeks
58-1.94496 5.69611 (58*2π)/5209 weeks
592.58076 3.74979 (59*2π)/5209 weeks
605.99502 4.01792 (60*2π)/5209 weeks
619.65166 5.63103 (61*2π)/5209 weeks
6210.08857 9.85169 (62*2π)/5208 weeks
638.85999 11.21641 (63*2π)/5208 weeks
647.8663 14.4683 (64*2π)/5208 weeks
654.04367 14.94125 (65*2π)/5208 weeks
663.32495 15.07226 (66*2π)/5208 weeks
67-.64759 16.0514 (67*2π)/5208 weeks
68-4.50697 14.42241 (68*2π)/5208 weeks
69-7.54305 10.37157 (69*2π)/5208 weeks
70-8.6317 3.73371 (70*2π)/5207 weeks
71-4.87009 -1.3614 (71*2π)/5207 weeks
72.59588 -2.79243 (72*2π)/5207 weeks
734.16271 -3.00036 (73*2π)/5207 weeks
749.55107 -.46516 (74*2π)/5207 weeks
7510.40663 5.10217 (75*2π)/5207 weeks
768.15068 7.89857 (76*2π)/5207 weeks
775.62726 10.88876 (77*2π)/5207 weeks
78-.09298 9.00764 (78*2π)/5207 weeks
79-.56151 5.26027 (79*2π)/5207 weeks
80-.61733 2.50668 (80*2π)/5207 weeks
812.39344 -1.80321 (81*2π)/5206 weeks
827.10943 -1.49407 (82*2π)/5206 weeks
8311.12194 .0464 (83*2π)/5206 weeks
8413.10514 4.42743 (84*2π)/5206 weeks
8511.86327 9.28706 (85*2π)/5206 weeks
867.90389 11.45167 (86*2π)/5206 weeks
874.34442 11.70745 (87*2π)/5206 weeks
882.42227 8.8894 (88*2π)/5206 weeks
892.86632 6.41202 (89*2π)/5206 weeks
903.26877 6.1898 (90*2π)/5206 weeks
914.3172 4.5328 (91*2π)/5206 weeks
925.69362 5.01701 (92*2π)/5206 weeks
936.87365 5.94049 (93*2π)/5206 weeks
947.83422 7.58841 (94*2π)/5206 weeks
957.58137 9.47528 (95*2π)/5205 weeks
966.21502 11.17202 (96*2π)/5205 weeks
974.05381 12.04186 (97*2π)/5205 weeks
981.10465 12.71608 (98*2π)/5205 weeks
99-1.75143 11.41068 (99*2π)/5205 weeks
100-3.53659 9.32383 (100*2π)/5205 weeks
101-4.37604 6.15373 (101*2π)/5205 weeks
102-4.18782 2.61717 (102*2π)/5205 weeks
103-1.59573 -.37765 (103*2π)/5205 weeks
1041.82911 -.8766 (104*2π)/5205 weeks
1055.20686 .19106 (105*2π)/5205 weeks
1066.88922 2.94107 (106*2π)/5205 weeks
1076.20463 5.12135 (107*2π)/5205 weeks
1085.20224 7.22434 (108*2π)/5205 weeks
1092.00415 8.31712 (109*2π)/5205 weeks
110-.13151 6.64914 (110*2π)/5205 weeks
111-.85684 3.88738 (111*2π)/5205 weeks
112-.21599 1.44247 (112*2π)/5205 weeks
1131.99082 -.5757 (113*2π)/5205 weeks
1144.89507 -.27587 (114*2π)/5205 weeks
1157.59361 1.54634 (115*2π)/5205 weeks
1168.83984 4.50764 (116*2π)/5204 weeks
1177.49833 7.79427 (117*2π)/5204 weeks
1184.83757 8.886 (118*2π)/5204 weeks
1192.1031 8.83079 (119*2π)/5204 weeks
120.46605 6.69026 (120*2π)/5204 weeks
1211.19382 5.20236 (121*2π)/5204 weeks
1221.97959 4.79172 (122*2π)/5204 weeks
1232.40113 5.20325 (123*2π)/5204 weeks
1242.35962 5.85537 (124*2π)/5204 weeks
1251.49004 6.43183 (125*2π)/5204 weeks
126-.1616 6.59554 (126*2π)/5204 weeks
127-1.72204 5.40666 (127*2π)/5204 weeks
128-2.1419 3.37696 (128*2π)/5204 weeks
129-1.91946 .77851 (129*2π)/5204 weeks
130.64596 -1.38223 (130*2π)/5204 weeks
1313.26567 .00944 (131*2π)/5204 weeks
1324.0379 1.36271 (132*2π)/5204 weeks
1334.27555 2.37024 (133*2π)/5204 weeks
1343.84212 3.64067 (134*2π)/5204 weeks
1353.09388 3.42445 (135*2π)/5204 weeks
1362.85135 3.98432 (136*2π)/5204 weeks
1371.56498 4.0612 (137*2π)/5204 weeks
1381.34159 2.98719 (138*2π)/5204 weeks
1391.21069 2.35503 (139*2π)/5204 weeks
1401.72925 .21106 (140*2π)/5204 weeks
1413.85079 .47053 (141*2π)/5204 weeks
1425.00929 1.19216 (142*2π)/5204 weeks
1436.60745 2.93192 (143*2π)/5204 weeks
1446.08855 5.4923 (144*2π)/5204 weeks
1454.35144 6.73157 (145*2π)/5204 weeks
1462.67025 7.88459 (146*2π)/5204 weeks
147-.03665 7.43851 (147*2π)/5204 weeks
148-2.00405 6.41363 (148*2π)/5204 weeks
149-3.53961 4.44585 (149*2π)/5203 weeks
150-4.36954 .76686 (150*2π)/5203 weeks
151-1.84832 -1.75566 (151*2π)/5203 weeks
152-.01124 -2.93731 (152*2π)/5203 weeks
1532.95256 -3.55814 (153*2π)/5203 weeks
1546.13489 -2.28998 (154*2π)/5203 weeks
1557.88549 .7594 (155*2π)/5203 weeks
1567.34709 4.26552 (156*2π)/5203 weeks
1575.0591 6.80407 (157*2π)/5203 weeks
1581.64036 7.35798 (158*2π)/5203 weeks
159-1.38699 6.04604 (159*2π)/5203 weeks
160-2.91408 3.53524 (160*2π)/5203 weeks
161-2.75089 .3352 (161*2π)/5203 weeks
162-1.406 -1.84976 (162*2π)/5203 weeks
1631.32822 -3.51682 (163*2π)/5203 weeks
1644.00993 -2.9139 (164*2π)/5203 weeks
1656.21222 -1.33933 (165*2π)/5203 weeks
1667.25837 1.57266 (166*2π)/5203 weeks
1676.82258 4.34581 (167*2π)/5203 weeks
1684.54098 6.76117 (168*2π)/5203 weeks
1691.16001 7.54122 (169*2π)/5203 weeks
170-1.99473 6.2742 (170*2π)/5203 weeks
171-4.02092 3.40387 (171*2π)/5203 weeks
172-4.50475 .28157 (172*2π)/5203 weeks
173-2.8971 -2.52933 (173*2π)/5203 weeks
174-.30267 -4.57614 (174*2π)/5203 weeks
1752.67853 -3.91416 (175*2π)/5203 weeks
1764.30949 -2.29551 (176*2π)/5203 weeks
1775.0445 -.0603 (177*2π)/5203 weeks
1783.62949 1.80844 (178*2π)/5203 weeks
1791.84071 2.12661 (179*2π)/5203 weeks
180-.06516 1.30466 (180*2π)/5203 weeks
181-.87602 -.44675 (181*2π)/5203 weeks
182-.32138 -2.86428 (182*2π)/5203 weeks
183.95086 -4.41659 (183*2π)/5203 weeks
1843.64876 -5.11747 (184*2π)/5203 weeks
1856.32441 -3.62835 (185*2π)/5203 weeks
1867.14769 -1.93271 (186*2π)/5203 weeks
1877.49097 .24118 (187*2π)/5203 weeks
1885.9244 2.36693 (188*2π)/5203 weeks
1894.24373 2.91163 (189*2π)/5203 weeks
1902.26938 3.2669 (190*2π)/5203 weeks
191-.04538 1.2672 (191*2π)/5203 weeks
192-.02465 -1.50311 (192*2π)/5203 weeks
193.58995 -3.55001 (193*2π)/5203 weeks
1943.39774 -5.56927 (194*2π)/5203 weeks
1956.52096 -4.95832 (195*2π)/5203 weeks
1969.02906 -2.74445 (196*2π)/5203 weeks
1979.20078 .38919 (197*2π)/5203 weeks
1987.59775 2.83265 (198*2π)/5203 weeks
1995.58763 3.41704 (199*2π)/5203 weeks
2003.23757 3.11004 (200*2π)/5203 weeks
2012.2267 1.37194 (201*2π)/5203 weeks
2022.29216 -1.11428 (202*2π)/5203 weeks
2033.84942 -1.75345 (203*2π)/5203 weeks
2046.14995 -2.26402 (204*2π)/5203 weeks
2057.63301 -.43594 (205*2π)/5203 weeks
2067.41241 .94429 (206*2π)/5203 weeks
2077.2938 2.29944 (207*2π)/5203 weeks
2086.62024 3.19655 (208*2π)/5203 weeks
2095.94028 4.23736 (209*2π)/5202 weeks
2103.96996 4.66339 (210*2π)/5202 weeks
2112.60371 4.21238 (211*2π)/5202 weeks
2121.40198 3.38265 (212*2π)/5202 weeks
213.46296 1.53087 (213*2π)/5202 weeks
2141.1601 -.32522 (214*2π)/5202 weeks
2152.59008 -1.76139 (215*2π)/5202 weeks
2164.68685 -2.29988 (216*2π)/5202 weeks
2176.97371 -.52372 (217*2π)/5202 weeks
2187.70177 1.93302 (218*2π)/5202 weeks
2196.94223 4.32918 (219*2π)/5202 weeks
2204.68637 6.1657 (220*2π)/5202 weeks
2211.59075 6.26561 (221*2π)/5202 weeks
222-.79168 4.99895 (222*2π)/5202 weeks
223-2.84168 2.15131 (223*2π)/5202 weeks
224-2.36775 -1.49813 (224*2π)/5202 weeks
225-.26757 -4.2387 (225*2π)/5202 weeks
2263.37071 -5.26952 (226*2π)/5202 weeks
2277.03811 -3.41069 (227*2π)/5202 weeks
2288.27192 -.19405 (228*2π)/5202 weeks
2298.12201 3.13831 (229*2π)/5202 weeks
2305.11102 5.98377 (230*2π)/5202 weeks
2311.31587 6.19113 (231*2π)/5202 weeks
232-1.71215 4.56922 (232*2π)/5202 weeks
233-3.95973 1.18483 (233*2π)/5202 weeks
234-3.60738 -3.533 (234*2π)/5202 weeks
235-.88679 -6.34229 (235*2π)/5202 weeks
2362.98846 -7.92381 (236*2π)/5202 weeks
2377.39913 -6.77418 (237*2π)/5202 weeks
2389.72433 -3.55109 (238*2π)/5202 weeks
23910.61719 -.37465 (239*2π)/5202 weeks
2409.3457 3.0441 (240*2π)/5202 weeks
2417.11082 5.02846 (241*2π)/5202 weeks
2424.06451 6.23927 (242*2π)/5202 weeks
243.21657 5.1499 (243*2π)/5202 weeks
244-1.22296 1.54859 (244*2π)/5202 weeks
245-.59396 -1.49298 (245*2π)/5202 weeks
2461.28864 -4.09576 (246*2π)/5202 weeks
2474.96249 -5.01002 (247*2π)/5202 weeks
2488.47 -2.78687 (248*2π)/5202 weeks
2499.70158 1.20029 (249*2π)/5202 weeks
2508.52254 4.83352 (250*2π)/5202 weeks
2514.97327 7.13008 (251*2π)/5202 weeks
2521.45547 6.7172 (252*2π)/5202 weeks
253-2.41991 5.65929 (253*2π)/5202 weeks
254-4.78305 1.32641 (254*2π)/5202 weeks
255-3.71422 -3.14222 (255*2π)/5202 weeks
256-.79675 -6.24139 (256*2π)/5202 weeks
2572.9133 -7.43435 (257*2π)/5202 weeks
2586.57321 -6.19025 (258*2π)/5202 weeks
2599.42654 -4.09965 (259*2π)/5202 weeks
26011.05657   (260*2π)/5202 weeks
2619.42654 4.09965 (261*2π)/5202 weeks
2626.57321 6.19025 (262*2π)/5202 weeks
2632.9133 7.43435 (263*2π)/5202 weeks
264-.79675 6.24139 (264*2π)/5202 weeks
265-3.71422 3.14222 (265*2π)/5202 weeks
266-4.78305 -1.32641 (266*2π)/5202 weeks
267-2.41991 -5.65929 (267*2π)/5202 weeks
2681.45547 -6.7172 (268*2π)/5202 weeks
2694.97327 -7.13008 (269*2π)/5202 weeks
2708.52254 -4.83352 (270*2π)/5202 weeks
2719.70158 -1.20029 (271*2π)/5202 weeks
2728.47 2.78687 (272*2π)/5202 weeks
2734.96249 5.01002 (273*2π)/5202 weeks
2741.28864 4.09576 (274*2π)/5202 weeks
275-.59396 1.49298 (275*2π)/5202 weeks
276-1.22296 -1.54859 (276*2π)/5202 weeks
277.21657 -5.1499 (277*2π)/5202 weeks
2784.06451 -6.23927 (278*2π)/5202 weeks
2797.11082 -5.02846 (279*2π)/5202 weeks
2809.3457 -3.0441 (280*2π)/5202 weeks
28110.61719 .37465 (281*2π)/5202 weeks
2829.72433 3.55109 (282*2π)/5202 weeks
2837.39913 6.77418 (283*2π)/5202 weeks
2842.98846 7.92381 (284*2π)/5202 weeks
285-.88679 6.34229 (285*2π)/5202 weeks
286-3.60738 3.533 (286*2π)/5202 weeks
287-3.95973 -1.18483 (287*2π)/5202 weeks
288-1.71215 -4.56922 (288*2π)/5202 weeks
2891.31587 -6.19113 (289*2π)/5202 weeks
2905.11102 -5.98377 (290*2π)/5202 weeks
2918.12201 -3.13831 (291*2π)/5202 weeks
2928.27192 .19405 (292*2π)/5202 weeks
2937.03811 3.41069 (293*2π)/5202 weeks
2943.37071 5.26952 (294*2π)/5202 weeks
295-.26757 4.2387 (295*2π)/5202 weeks
296-2.36775 1.49813 (296*2π)/5202 weeks
297-2.84168 -2.15131 (297*2π)/5202 weeks
298-.79168 -4.99895 (298*2π)/5202 weeks
2991.59075 -6.26561 (299*2π)/5202 weeks
3004.68637 -6.1657 (300*2π)/5202 weeks
3016.94223 -4.32918 (301*2π)/5202 weeks
3027.70177 -1.93302 (302*2π)/5202 weeks
3036.97371 .52372 (303*2π)/5202 weeks
3044.68685 2.29988 (304*2π)/5202 weeks
3052.59008 1.76139 (305*2π)/5202 weeks
3061.1601 .32522 (306*2π)/5202 weeks
307.46296 -1.53087 (307*2π)/5202 weeks
3081.40198 -3.38265 (308*2π)/5202 weeks
3092.60371 -4.21238 (309*2π)/5202 weeks
3103.96996 -4.66339 (310*2π)/5202 weeks
3115.94028 -4.23736 (311*2π)/5202 weeks
3126.62024 -3.19655 (312*2π)/5202 weeks
3137.2938 -2.29944 (313*2π)/5202 weeks
3147.41241 -.94429 (314*2π)/5202 weeks
3157.63301 .43594 (315*2π)/5202 weeks
3166.14995 2.26402 (316*2π)/5202 weeks
3173.84942 1.75345 (317*2π)/5202 weeks
3182.29216 1.11428 (318*2π)/5202 weeks
3192.2267 -1.37194 (319*2π)/5202 weeks
3203.23757 -3.11004 (320*2π)/5202 weeks
3215.58763 -3.41704 (321*2π)/5202 weeks
3227.59775 -2.83265 (322*2π)/5202 weeks
3239.20078 -.38919 (323*2π)/5202 weeks
3249.02906 2.74445 (324*2π)/5202 weeks
3256.52096 4.95832 (325*2π)/5202 weeks
3263.39774 5.56927 (326*2π)/5202 weeks
327.58995 3.55001 (327*2π)/5202 weeks
328-.02465 1.50311 (328*2π)/5202 weeks
329-.04538 -1.2672 (329*2π)/5202 weeks
3302.26938 -3.2669 (330*2π)/5202 weeks
3314.24373 -2.91163 (331*2π)/5202 weeks
3325.9244 -2.36693 (332*2π)/5202 weeks
3337.49097 -.24118 (333*2π)/5202 weeks
3347.14769 1.93271 (334*2π)/5202 weeks
3356.32441 3.62835 (335*2π)/5202 weeks
3363.64876 5.11747 (336*2π)/5202 weeks
337.95086 4.41659 (337*2π)/5202 weeks
338-.32138 2.86428 (338*2π)/5202 weeks
339-.87602 .44675 (339*2π)/5202 weeks
340-.06516 -1.30466 (340*2π)/5202 weeks
3411.84071 -2.12661 (341*2π)/5202 weeks
3423.62949 -1.80844 (342*2π)/5202 weeks
3435.0445 .0603 (343*2π)/5202 weeks
3444.30949 2.29551 (344*2π)/5202 weeks
3452.67853 3.91416 (345*2π)/5202 weeks
346-.30267 4.57614 (346*2π)/5202 weeks
347-2.8971 2.52933 (347*2π)/5201 weeks
348-4.50475 -.28157 (348*2π)/5201 weeks
349-4.02092 -3.40387 (349*2π)/5201 weeks
350-1.99473 -6.2742 (350*2π)/5201 weeks
3511.16001 -7.54122 (351*2π)/5201 weeks
3524.54098 -6.76117 (352*2π)/5201 weeks
3536.82258 -4.34581 (353*2π)/5201 weeks
3547.25837 -1.57266 (354*2π)/5201 weeks
3556.21222 1.33933 (355*2π)/5201 weeks
3564.00993 2.9139 (356*2π)/5201 weeks
3571.32822 3.51682 (357*2π)/5201 weeks
358-1.406 1.84976 (358*2π)/5201 weeks
359-2.75089 -.3352 (359*2π)/5201 weeks
360-2.91408 -3.53524 (360*2π)/5201 weeks
361-1.38699 -6.04604 (361*2π)/5201 weeks
3621.64036 -7.35798 (362*2π)/5201 weeks
3635.0591 -6.80407 (363*2π)/5201 weeks
3647.34709 -4.26552 (364*2π)/5201 weeks
3657.88549 -.7594 (365*2π)/5201 weeks
3666.13489 2.28998 (366*2π)/5201 weeks
3672.95256 3.55814 (367*2π)/5201 weeks
368-.01124 2.93731 (368*2π)/5201 weeks
369-1.84832 1.75566 (369*2π)/5201 weeks
370-4.36954 -.76686 (370*2π)/5201 weeks
371-3.53961 -4.44585 (371*2π)/5201 weeks
372-2.00405 -6.41363 (372*2π)/5201 weeks
373-.03665 -7.43851 (373*2π)/5201 weeks
3742.67025 -7.88459 (374*2π)/5201 weeks
3754.35144 -6.73157 (375*2π)/5201 weeks
3766.08855 -5.4923 (376*2π)/5201 weeks
3776.60745 -2.93192 (377*2π)/5201 weeks
3785.00929 -1.19216 (378*2π)/5201 weeks
3793.85079 -.47053 (379*2π)/5201 weeks
3801.72925 -.21106 (380*2π)/5201 weeks
3811.21069 -2.35503 (381*2π)/5201 weeks
3821.34159 -2.98719 (382*2π)/5201 weeks
3831.56498 -4.0612 (383*2π)/5201 weeks
3842.85135 -3.98432 (384*2π)/5201 weeks
3853.09388 -3.42445 (385*2π)/5201 weeks
3863.84212 -3.64067 (386*2π)/5201 weeks
3874.27555 -2.37024 (387*2π)/5201 weeks
3884.0379 -1.36271 (388*2π)/5201 weeks
3893.26567 -.00944 (389*2π)/5201 weeks
390.64596 1.38223 (390*2π)/5201 weeks
391-1.91946 -.77851 (391*2π)/5201 weeks
392-2.1419 -3.37696 (392*2π)/5201 weeks
393-1.72204 -5.40666 (393*2π)/5201 weeks
394-.1616 -6.59554 (394*2π)/5201 weeks
3951.49004 -6.43183 (395*2π)/5201 weeks
3962.35962 -5.85537 (396*2π)/5201 weeks
3972.40113 -5.20325 (397*2π)/5201 weeks
3981.97959 -4.79172 (398*2π)/5201 weeks
3991.19382 -5.20236 (399*2π)/5201 weeks
400.46605 -6.69026 (400*2π)/5201 weeks
4012.1031 -8.83079 (401*2π)/5201 weeks
4024.83757 -8.886 (402*2π)/5201 weeks
4037.49833 -7.79427 (403*2π)/5201 weeks
4048.83984 -4.50764 (404*2π)/5201 weeks
4057.59361 -1.54634 (405*2π)/5201 weeks
4064.89507 .27587 (406*2π)/5201 weeks
4071.99082 .5757 (407*2π)/5201 weeks
408-.21599 -1.44247 (408*2π)/5201 weeks
409-.85684 -3.88738 (409*2π)/5201 weeks
410-.13151 -6.64914 (410*2π)/5201 weeks
4112.00415 -8.31712 (411*2π)/5201 weeks
4125.20224 -7.22434 (412*2π)/5201 weeks
4136.20463 -5.12135 (413*2π)/5201 weeks
4146.88922 -2.94107 (414*2π)/5201 weeks
4155.20686 -.19106 (415*2π)/5201 weeks
4161.82911 .8766 (416*2π)/5201 weeks
417-1.59573 .37765 (417*2π)/5201 weeks
418-4.18782 -2.61717 (418*2π)/5201 weeks
419-4.37604 -6.15373 (419*2π)/5201 weeks
420-3.53659 -9.32383 (420*2π)/5201 weeks
421-1.75143 -11.41068 (421*2π)/5201 weeks
4221.10465 -12.71608 (422*2π)/5201 weeks
4234.05381 -12.04186 (423*2π)/5201 weeks
4246.21502 -11.17202 (424*2π)/5201 weeks
4257.58137 -9.47528 (425*2π)/5201 weeks
4267.83422 -7.58841 (426*2π)/5201 weeks
4276.87365 -5.94049 (427*2π)/5201 weeks
4285.69362 -5.01701 (428*2π)/5201 weeks
4294.3172 -4.5328 (429*2π)/5201 weeks
4303.26877 -6.1898 (430*2π)/5201 weeks
4312.86632 -6.41202 (431*2π)/5201 weeks
4322.42227 -8.8894 (432*2π)/5201 weeks
4334.34442 -11.70745 (433*2π)/5201 weeks
4347.90389 -11.45167 (434*2π)/5201 weeks
43511.86327 -9.28706 (435*2π)/5201 weeks
43613.10514 -4.42743 (436*2π)/5201 weeks
43711.12194 -.0464 (437*2π)/5201 weeks
4387.10943 1.49407 (438*2π)/5201 weeks
4392.39344 1.80321 (439*2π)/5201 weeks
440-.61733 -2.50668 (440*2π)/5201 weeks
441-.56151 -5.26027 (441*2π)/5201 weeks
442-.09298 -9.00764 (442*2π)/5201 weeks
4435.62726 -10.88876 (443*2π)/5201 weeks
4448.15068 -7.89857 (444*2π)/5201 weeks
44510.40663 -5.10217 (445*2π)/5201 weeks
4469.55107 .46516 (446*2π)/5201 weeks
4474.16271 3.00036 (447*2π)/5201 weeks
448.59588 2.79243 (448*2π)/5201 weeks
449-4.87009 1.3614 (449*2π)/5201 weeks
450-8.6317 -3.73371 (450*2π)/5201 weeks
451-7.54305 -10.37157 (451*2π)/5201 weeks
452-4.50697 -14.42241 (452*2π)/5201 weeks
453-.64759 -16.0514 (453*2π)/5201 weeks
4543.32495 -15.07226 (454*2π)/5201 weeks
4554.04367 -14.94125 (455*2π)/5201 weeks
4567.8663 -14.4683 (456*2π)/5201 weeks
4578.85999 -11.21641 (457*2π)/5201 weeks
45810.08857 -9.85169 (458*2π)/5201 weeks
4599.65166 -5.63103 (459*2π)/5201 weeks
4605.99502 -4.01792 (460*2π)/5201 weeks
4612.58076 -3.74979 (461*2π)/5201 weeks
462-1.94496 -5.69611 (462*2π)/5201 weeks
463-2.74831 -12.14941 (463*2π)/5201 weeks
464-.60215 -16.72107 (464*2π)/5201 weeks
4654.69496 -19.6629 (465*2π)/5201 weeks
46610.25948 -19.776 (466*2π)/5201 weeks
46716.0008 -14.58918 (467*2π)/5201 weeks
46817.36237 -9.6953 (468*2π)/5201 weeks
46915.77795 -3.26121 (469*2π)/5201 weeks
47010.82035 -.00828 (470*2π)/5201 weeks
4716.07695 -.0937 (471*2π)/5201 weeks
4722.8212 -.37174 (472*2π)/5201 weeks
473-1.80278 -3.79819 (473*2π)/5201 weeks
474-.71676 -8.57962 (474*2π)/5201 weeks
475-.34571 -11.44143 (475*2π)/5201 weeks
4762.87062 -13.61529 (476*2π)/5201 weeks
4776.04547 -10.64712 (477*2π)/5201 weeks
4786.69933 -9.31637 (478*2π)/5201 weeks
4795.91717 -5.89361 (479*2π)/5201 weeks
480.77499 -4.72034 (480*2π)/5201 weeks
481-2.36948 -5.26682 (481*2π)/5201 weeks
482-10.49319 -8.45351 (482*2π)/5201 weeks
483-11.77567 -19.50423 (483*2π)/5201 weeks
484-7.77787 -28.58992 (484*2π)/5201 weeks
485.3044 -34.30463 (485*2π)/5201 weeks
48611.8972 -38.97815 (486*2π)/5201 weeks
48725.24196 -33.24553 (487*2π)/5201 weeks
48834.52936 -23.17185 (488*2π)/5201 weeks
48935.76627 -4.38116 (489*2π)/5201 weeks
49025.16995 9.84764 (490*2π)/5201 weeks
4919.61709 12.40932 (491*2π)/5201 weeks
492-3.70836 9.39901 (492*2π)/5201 weeks
493-14.29286 -3.34353 (493*2π)/5201 weeks
494-13.59338 -17.45113 (494*2π)/5201 weeks
495-7.06213 -28.03319 (495*2π)/5201 weeks
4967.97479 -30.08874 (496*2π)/5201 weeks
49720.10144 -23.48333 (497*2π)/5201 weeks
49823.01679 -9.70757 (498*2π)/5201 weeks
49913.05747 4.15492 (499*2π)/5201 weeks
500-3.44961 9.55899 (500*2π)/5201 weeks
501-20.25291 3.60515 (501*2π)/5201 weeks
502-30.67981 -10.46992 (502*2π)/5201 weeks
503-38.12225 -27.42482 (503*2π)/5201 weeks
504-32.92586 -50.17318 (504*2π)/5201 weeks
505-19.73393 -60.33729 (505*2π)/5201 weeks
506-6.11704 -68.40982 (506*2π)/5201 weeks
50713.35626 -73.90807 (507*2π)/5201 weeks
50823.67295 -59.3062 (508*2π)/5201 weeks
50933.12132 -54.70074 (509*2π)/5201 weeks
51029.78675 -34.80379 (510*2π)/5201 weeks
51115.26374 -27.88871 (511*2π)/5201 weeks
512-7.73206 -23.28184 (512*2π)/5201 weeks
513-40.89473 -40.67012 (513*2π)/5201 weeks
514-63.21336 -94.70892 (514*2π)/5201 weeks
515-47.75414 -169.83 (515*2π)/5201 weeks
5162.80838 -233.0994 (516*2π)/5201 weeks
517102.3314 -274.6966 (517*2π)/5201 weeks
518230.1509 -260.9524 (518*2π)/5201 weeks



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