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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 38 weeks (69.3638*sine), 41 weeks (67.7873*sine), and 44 weeks (57.3257*sine).

FXP (PROSHARES ULTRASHORT FTSE CHINA 50 PROSHARES ULTRASHORT FTSE CHINA 50) has an average price of 276.65 (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 1/16/2018 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
0276.6458   0 
1333.1691 198.4413 (1*2π)/533533 weeks
2229.7298 252.389 (2*2π)/533267 weeks
3107.7012 270.1274 (3*2π)/533178 weeks
410.55241 234.4182 (4*2π)/533133 weeks
5-40.7592 173.2914 (5*2π)/533107 weeks
6-62.95491 101.5614 (6*2π)/53389 weeks
7-46.63217 46.63012 (7*2π)/53376 weeks
8-13.58692 25.27351 (8*2π)/53367 weeks
912.40188 26.26943 (9*2π)/53359 weeks
1026.04186 31.30246 (10*2π)/53353 weeks
1134.69194 47.60892 (11*2π)/53348 weeks
1223.3861 57.32572 (12*2π)/53344 weeks
1320.01766 67.78729 (13*2π)/53341 weeks
14-2.07407 69.36382 (14*2π)/53338 weeks
15-15.04303 63.20858 (15*2π)/53336 weeks
16-25.64737 54.41523 (16*2π)/53333 weeks
17-37.06195 36.05193 (17*2π)/53331 weeks
18-33.38864 16.06093 (18*2π)/53330 weeks
19-25.80912 2.77628 (19*2π)/53328 weeks
20-11.33593 -7.37559 (20*2π)/53327 weeks
215.85533 -8.3676 (21*2π)/53325 weeks
2218.5055 .08366 (22*2π)/53324 weeks
2321.16142 15.52123 (23*2π)/53323 weeks
2414.36549 27.88632 (24*2π)/53322 weeks
252.9969 31.14645 (25*2π)/53321 weeks
26-9.42779 23.2055 (26*2π)/53321 weeks
27-14.47042 12.37214 (27*2π)/53320 weeks
28-12.26655 -1.66022 (28*2π)/53319 weeks
29.25084 -10.46552 (29*2π)/53318 weeks
3012.9425 -12.11761 (30*2π)/53318 weeks
3128.3008 -6.71233 (31*2π)/53317 weeks
3236.25494 7.95571 (32*2π)/53317 weeks
3331.72306 24.93516 (33*2π)/53316 weeks
3422.74037 33.85572 (34*2π)/53316 weeks
359.28046 37.95321 (35*2π)/53315 weeks
36-.59332 33.00188 (36*2π)/53315 weeks
37-8.21453 27.08567 (37*2π)/53314 weeks
38-11.66291 18.38088 (38*2π)/53314 weeks
39-9.87787 7.80153 (39*2π)/53314 weeks
40-2.22081 5.18048 (40*2π)/53313 weeks
41.737 4.62912 (41*2π)/53313 weeks
425.68076 5.66459 (42*2π)/53313 weeks
436.52454 8.95619 (43*2π)/53312 weeks
445.74996 10.29389 (44*2π)/53312 weeks
453.31195 13.45023 (45*2π)/53312 weeks
46.03681 11.60028 (46*2π)/53312 weeks
47-.56253 8.52099 (47*2π)/53311 weeks
48-2.12047 4.82557 (48*2π)/53311 weeks
491.76826 .63732 (49*2π)/53311 weeks
505.34525 .40882 (50*2π)/53311 weeks
519.38934 -.25732 (51*2π)/53310 weeks
5214.23392 1.91437 (52*2π)/53310 weeks
5317.05421 7.54992 (53*2π)/53310 weeks
5415.80707 12.66993 (54*2π)/53310 weeks
5512.68345 18.57715 (55*2π)/53310 weeks
566.59436 19.23394 (56*2π)/53310 weeks
571.18125 17.87607 (57*2π)/5339 weeks
58-1.97163 13.53174 (58*2π)/5339 weeks
59-3.32641 8.38979 (59*2π)/5339 weeks
60.72459 4.07193 (60*2π)/5339 weeks
614.3733 3.56087 (61*2π)/5339 weeks
627.34407 4.13856 (62*2π)/5339 weeks
6310.04429 7.5659 (63*2π)/5338 weeks
648.85088 10.71873 (64*2π)/5338 weeks
658.83223 12.19737 (65*2π)/5338 weeks
666.21314 15.04171 (66*2π)/5338 weeks
673.60286 14.16656 (67*2π)/5338 weeks
682.43225 15.55496 (68*2π)/5338 weeks
69-1.699 15.16587 (69*2π)/5338 weeks
70-5.55344 13.01279 (70*2π)/5338 weeks
71-8.10307 8.8617 (71*2π)/5338 weeks
72-7.63466 2.1476 (72*2π)/5337 weeks
73-3.58073 -2.10705 (73*2π)/5337 weeks
741.29586 -2.592 (74*2π)/5337 weeks
754.96586 -2.94078 (75*2π)/5337 weeks
769.79377 .35177 (76*2π)/5337 weeks
779.943 5.5462 (77*2π)/5337 weeks
787.85536 7.89196 (78*2π)/5337 weeks
795.09525 10.79866 (79*2π)/5337 weeks
80-.19523 8.54848 (80*2π)/5337 weeks
81-.53618 5.07962 (81*2π)/5337 weeks
82-.58668 2.4646 (82*2π)/5337 weeks
832.22846 -1.69222 (83*2π)/5336 weeks
846.81202 -1.51391 (84*2π)/5336 weeks
8510.56287 -.23442 (85*2π)/5336 weeks
8612.67004 3.86889 (86*2π)/5336 weeks
8711.88371 8.6042 (87*2π)/5336 weeks
888.24852 11.21151 (88*2π)/5336 weeks
895.09623 11.63719 (89*2π)/5336 weeks
902.56412 9.0647 (90*2π)/5336 weeks
912.42004 6.56759 (91*2π)/5336 weeks
923.33276 6.18647 (92*2π)/5336 weeks
933.57213 4.68787 (93*2π)/5336 weeks
945.33385 4.86341 (94*2π)/5336 weeks
956.56725 5.40864 (95*2π)/5336 weeks
967.51718 6.48495 (96*2π)/5336 weeks
977.41085 8.34821 (97*2π)/5335 weeks
986.4045 10.28808 (98*2π)/5335 weeks
994.56577 11.73542 (99*2π)/5335 weeks
1002.64442 12.63415 (100*2π)/5335 weeks
101-.30328 11.98043 (101*2π)/5335 weeks
102-2.46741 9.9858 (102*2π)/5335 weeks
103-4.16508 7.47508 (103*2π)/5335 weeks
104-4.48488 4.60695 (104*2π)/5335 weeks
105-3.19258 1.13791 (105*2π)/5335 weeks
106.0505 -.85727 (106*2π)/5335 weeks
1073.05057 -.91326 (107*2π)/5335 weeks
1085.72918 1.01971 (108*2π)/5335 weeks
1096.48653 4.0053 (109*2π)/5335 weeks
1105.95755 5.70396 (110*2π)/5335 weeks
1114.51787 7.68676 (111*2π)/5335 weeks
1121.19267 7.6547 (112*2π)/5335 weeks
113-.61096 5.95051 (113*2π)/5335 weeks
114-.76791 3.38615 (114*2π)/5335 weeks
115.14746 1.04349 (115*2π)/5335 weeks
1162.62045 -.6843 (116*2π)/5335 weeks
1175.20888 -.24711 (117*2π)/5335 weeks
1187.56687 1.78628 (118*2π)/5335 weeks
1198.60371 4.7716 (119*2π)/5334 weeks
1207.12637 7.7947 (120*2π)/5334 weeks
1214.62532 8.70934 (121*2π)/5334 weeks
1221.99609 8.5914 (122*2π)/5334 weeks
123.46091 6.53801 (123*2π)/5334 weeks
1241.15906 5.10217 (124*2π)/5334 weeks
1251.90243 4.67704 (125*2π)/5334 weeks
1262.34232 5.04644 (126*2π)/5334 weeks
1272.34078 5.63096 (127*2π)/5334 weeks
1281.55988 6.24117 (128*2π)/5334 weeks
129.13871 6.56052 (129*2π)/5334 weeks
130-1.38124 5.57283 (130*2π)/5334 weeks
131-2.02674 3.57331 (131*2π)/5334 weeks
132-2.16606 1.33846 (132*2π)/5334 weeks
133-.30708 -.99174 (133*2π)/5334 weeks
1342.90366 -.39295 (134*2π)/5334 weeks
1353.86665 .93757 (135*2π)/5334 weeks
1364.10816 1.96838 (136*2π)/5334 weeks
1374.08516 3.14272 (137*2π)/5334 weeks
1382.99778 3.51494 (138*2π)/5334 weeks
1393.04564 3.69982 (139*2π)/5334 weeks
1402.2401 4.16148 (140*2π)/5334 weeks
1411.28955 3.15968 (141*2π)/5334 weeks
1421.24705 2.49658 (142*2π)/5334 weeks
143.81142 1.41863 (143*2π)/5334 weeks
1442.96621 .17513 (144*2π)/5334 weeks
1454.38127 .83216 (145*2π)/5334 weeks
1465.673 1.50797 (146*2π)/5334 weeks
1476.41388 3.95681 (147*2π)/5334 weeks
1485.23614 6.09416 (148*2π)/5334 weeks
1493.81753 6.93522 (149*2π)/5334 weeks
1501.63114 7.88141 (150*2π)/5334 weeks
151-.51094 6.97172 (151*2π)/5334 weeks
152-2.45515 5.66897 (152*2π)/5334 weeks
153-3.91418 3.64673 (153*2π)/5333 weeks
154-3.81159 -.22415 (154*2π)/5333 weeks
155-1.38734 -1.90101 (155*2π)/5333 weeks
156.46036 -3.12195 (156*2π)/5333 weeks
1573.39541 -3.39588 (157*2π)/5333 weeks
1586.34515 -1.83365 (158*2π)/5333 weeks
1597.7839 1.203 (159*2π)/5333 weeks
1607.03758 4.45718 (160*2π)/5333 weeks
1614.72746 6.76889 (161*2π)/5333 weeks
1621.4683 7.15114 (162*2π)/5333 weeks
163-1.39985 5.83447 (163*2π)/5333 weeks
164-2.83506 3.44674 (164*2π)/5333 weeks
165-2.70526 .38192 (165*2π)/5333 weeks
166-1.44654 -1.71217 (166*2π)/5333 weeks
1671.03561 -3.4141 (167*2π)/5333 weeks
1683.66924 -2.91496 (168*2π)/5333 weeks
1695.82398 -1.53279 (169*2π)/5333 weeks
1707.1033 1.11659 (170*2π)/5333 weeks
1716.82044 3.7169 (171*2π)/5333 weeks
1724.9485 6.25797 (172*2π)/5333 weeks
1731.89749 7.38984 (173*2π)/5333 weeks
174-1.27831 6.55379 (174*2π)/5333 weeks
175-3.65757 4.20191 (175*2π)/5333 weeks
176-4.35151 1.3402 (176*2π)/5333 weeks
177-3.36758 -1.82511 (177*2π)/5333 weeks
178-1.48976 -3.92281 (178*2π)/5333 weeks
1791.78398 -4.166 (179*2π)/5333 weeks
1803.79094 -2.86375 (180*2π)/5333 weeks
1814.86099 -1.1334 (181*2π)/5333 weeks
1824.32439 1.20099 (182*2π)/5333 weeks
1832.59757 2.06061 (183*2π)/5333 weeks
184.86619 1.93783 (184*2π)/5333 weeks
185-.4414 .41307 (185*2π)/5333 weeks
186-.9327 -1.61602 (186*2π)/5333 weeks
187.2623 -3.34944 (187*2π)/5333 weeks
1882.04034 -4.91753 (188*2π)/5333 weeks
1894.73181 -4.90243 (189*2π)/5333 weeks
1906.36245 -2.85902 (190*2π)/5333 weeks
1917.15409 -1.18 (191*2π)/5333 weeks
1927.10901 1.11066 (192*2π)/5333 weeks
1935.27231 2.48281 (193*2π)/5333 weeks
1943.72243 2.89325 (194*2π)/5333 weeks
1951.43912 2.98486 (195*2π)/5333 weeks
196-.2707 .66412 (196*2π)/5333 weeks
197.15903 -1.76929 (197*2π)/5333 weeks
198.85483 -3.92966 (198*2π)/5333 weeks
1993.8443 -5.4652 (199*2π)/5333 weeks
2006.69658 -4.6893 (200*2π)/5333 weeks
2018.94248 -2.34951 (201*2π)/5333 weeks
2028.9389 .58253 (202*2π)/5333 weeks
2037.30078 2.82803 (203*2π)/5333 weeks
2045.41374 3.3503 (204*2π)/5333 weeks
2053.16517 3.03907 (205*2π)/5333 weeks
2062.19843 1.37814 (206*2π)/5333 weeks
2072.14504 -.96839 (207*2π)/5333 weeks
2083.71953 -1.6357 (208*2π)/5333 weeks
2095.75993 -2.31687 (209*2π)/5333 weeks
2107.37933 -.68962 (210*2π)/5333 weeks
2117.22908 .81791 (211*2π)/5333 weeks
2127.24492 2.02384 (212*2π)/5333 weeks
2136.58795 2.95516 (213*2π)/5333 weeks
2146.00262 3.82488 (214*2π)/5332 weeks
2154.2938 4.68149 (215*2π)/5332 weeks
2162.92748 4.28906 (216*2π)/5332 weeks
2171.75953 3.571 (217*2π)/5332 weeks
218.60453 2.19842 (218*2π)/5332 weeks
219.84258 .15358 (219*2π)/5332 weeks
2201.81613 -1.30263 (220*2π)/5332 weeks
2213.62083 -2.00643 (221*2π)/5332 weeks
2226.30547 -1.42203 (222*2π)/5332 weeks
2237.4509 .64764 (223*2π)/5332 weeks
2247.22327 3.08568 (224*2π)/5332 weeks
2255.79293 5.28649 (225*2π)/5332 weeks
2263.11472 6.32684 (226*2π)/5332 weeks
227.42124 5.52939 (227*2π)/5332 weeks
228-1.88887 3.92772 (228*2π)/5332 weeks
229-2.93833 .54896 (229*2π)/5332 weeks
230-1.69634 -2.50894 (230*2π)/5332 weeks
231.99389 -4.73996 (231*2π)/5332 weeks
2324.71021 -4.93455 (232*2π)/5332 weeks
2337.47426 -2.36878 (233*2π)/5332 weeks
2348.1041 .65448 (234*2π)/5332 weeks
2357.40433 4.08523 (235*2π)/5332 weeks
2364.09707 6.09223 (236*2π)/5332 weeks
237.53364 5.75797 (237*2π)/5332 weeks
238-2.26269 4.00656 (238*2π)/5332 weeks
239-4.0557 .49197 (239*2π)/5332 weeks
240-3.10041 -3.968 (240*2π)/5332 weeks
241-.47046 -6.48321 (241*2π)/5332 weeks
2423.34832 -7.77149 (242*2π)/5332 weeks
2437.46995 -6.41332 (243*2π)/5332 weeks
2449.53444 -3.30811 (244*2π)/5332 weeks
24510.36603 -.26237 (245*2π)/5332 weeks
2469.12031 2.97814 (246*2π)/5332 weeks
2476.99636 4.8812 (247*2π)/5332 weeks
2484.15048 6.0889 (248*2π)/5332 weeks
249.49312 5.24185 (249*2π)/5332 weeks
250-1.14928 1.81278 (250*2π)/5332 weeks
251-.71991 -1.16675 (251*2π)/5332 weeks
252.81894 -3.66814 (252*2π)/5332 weeks
2534.13189 -4.87887 (253*2π)/5332 weeks
2547.79867 -3.2619 (254*2π)/5332 weeks
2559.56071 .26326 (255*2π)/5332 weeks
2568.79735 3.78124 (256*2π)/5332 weeks
2575.87623 6.58469 (257*2π)/5332 weeks
2582.14284 6.78793 (258*2π)/5332 weeks
259-.97612 6.33795 (259*2π)/5332 weeks
260-4.16199 2.92618 (260*2π)/5332 weeks
261-4.23218 -1.73532 (261*2π)/5332 weeks
262-2.15741 -5.17652 (262*2π)/5332 weeks
2631.20698 -6.87417 (263*2π)/5332 weeks
2645.15601 -6.76879 (264*2π)/5332 weeks
2657.91051 -5.16842 (265*2π)/5332 weeks
26610.32902 -2.20201 (266*2π)/5332 weeks
26710.32902 2.20201 (267*2π)/5332 weeks
2687.91051 5.16842 (268*2π)/5332 weeks
2695.15601 6.76879 (269*2π)/5332 weeks
2701.20698 6.87417 (270*2π)/5332 weeks
271-2.15741 5.17652 (271*2π)/5332 weeks
272-4.23218 1.73532 (272*2π)/5332 weeks
273-4.16199 -2.92618 (273*2π)/5332 weeks
274-.97612 -6.33795 (274*2π)/5332 weeks
2752.14284 -6.78793 (275*2π)/5332 weeks
2765.87623 -6.58469 (276*2π)/5332 weeks
2778.79735 -3.78124 (277*2π)/5332 weeks
2789.56071 -.26326 (278*2π)/5332 weeks
2797.79867 3.2619 (279*2π)/5332 weeks
2804.13189 4.87887 (280*2π)/5332 weeks
281.81894 3.66814 (281*2π)/5332 weeks
282-.71991 1.16675 (282*2π)/5332 weeks
283-1.14928 -1.81278 (283*2π)/5332 weeks
284.49312 -5.24185 (284*2π)/5332 weeks
2854.15048 -6.0889 (285*2π)/5332 weeks
2866.99636 -4.8812 (286*2π)/5332 weeks
2879.12031 -2.97814 (287*2π)/5332 weeks
28810.36603 .26237 (288*2π)/5332 weeks
2899.53444 3.30811 (289*2π)/5332 weeks
2907.46995 6.41332 (290*2π)/5332 weeks
2913.34832 7.77149 (291*2π)/5332 weeks
292-.47046 6.48321 (292*2π)/5332 weeks
293-3.10041 3.968 (293*2π)/5332 weeks
294-4.0557 -.49197 (294*2π)/5332 weeks
295-2.26269 -4.00656 (295*2π)/5332 weeks
296.53364 -5.75797 (296*2π)/5332 weeks
2974.09707 -6.09223 (297*2π)/5332 weeks
2987.40433 -4.08523 (298*2π)/5332 weeks
2998.1041 -.65448 (299*2π)/5332 weeks
3007.47426 2.36878 (300*2π)/5332 weeks
3014.71021 4.93455 (301*2π)/5332 weeks
302.99389 4.73996 (302*2π)/5332 weeks
303-1.69634 2.50894 (303*2π)/5332 weeks
304-2.93833 -.54896 (304*2π)/5332 weeks
305-1.88887 -3.92772 (305*2π)/5332 weeks
306.42124 -5.52939 (306*2π)/5332 weeks
3073.11472 -6.32684 (307*2π)/5332 weeks
3085.79293 -5.28649 (308*2π)/5332 weeks
3097.22327 -3.08568 (309*2π)/5332 weeks
3107.4509 -.64764 (310*2π)/5332 weeks
3116.30547 1.42203 (311*2π)/5332 weeks
3123.62083 2.00643 (312*2π)/5332 weeks
3131.81613 1.30263 (313*2π)/5332 weeks
314.84258 -.15358 (314*2π)/5332 weeks
315.60453 -2.19842 (315*2π)/5332 weeks
3161.75953 -3.571 (316*2π)/5332 weeks
3172.92748 -4.28906 (317*2π)/5332 weeks
3184.2938 -4.68149 (318*2π)/5332 weeks
3196.00262 -3.82488 (319*2π)/5332 weeks
3206.58795 -2.95516 (320*2π)/5332 weeks
3217.24492 -2.02384 (321*2π)/5332 weeks
3227.22908 -.81791 (322*2π)/5332 weeks
3237.37933 .68962 (323*2π)/5332 weeks
3245.75993 2.31687 (324*2π)/5332 weeks
3253.71953 1.6357 (325*2π)/5332 weeks
3262.14504 .96839 (326*2π)/5332 weeks
3272.19843 -1.37814 (327*2π)/5332 weeks
3283.16517 -3.03907 (328*2π)/5332 weeks
3295.41374 -3.3503 (329*2π)/5332 weeks
3307.30078 -2.82803 (330*2π)/5332 weeks
3318.9389 -.58253 (331*2π)/5332 weeks
3328.94248 2.34951 (332*2π)/5332 weeks
3336.69658 4.6893 (333*2π)/5332 weeks
3343.8443 5.4652 (334*2π)/5332 weeks
335.85483 3.92966 (335*2π)/5332 weeks
336.15903 1.76929 (336*2π)/5332 weeks
337-.2707 -.66412 (337*2π)/5332 weeks
3381.43912 -2.98486 (338*2π)/5332 weeks
3393.72243 -2.89325 (339*2π)/5332 weeks
3405.27231 -2.48281 (340*2π)/5332 weeks
3417.10901 -1.11066 (341*2π)/5332 weeks
3427.15409 1.18 (342*2π)/5332 weeks
3436.36245 2.85902 (343*2π)/5332 weeks
3444.73181 4.90243 (344*2π)/5332 weeks
3452.04034 4.91753 (345*2π)/5332 weeks
346.2623 3.34944 (346*2π)/5332 weeks
347-.9327 1.61602 (347*2π)/5332 weeks
348-.4414 -.41307 (348*2π)/5332 weeks
349.86619 -1.93783 (349*2π)/5332 weeks
3502.59757 -2.06061 (350*2π)/5332 weeks
3514.32439 -1.20099 (351*2π)/5332 weeks
3524.86099 1.1334 (352*2π)/5332 weeks
3533.79094 2.86375 (353*2π)/5332 weeks
3541.78398 4.166 (354*2π)/5332 weeks
355-1.48976 3.92281 (355*2π)/5332 weeks
356-3.36758 1.82511 (356*2π)/5331 weeks
357-4.35151 -1.3402 (357*2π)/5331 weeks
358-3.65757 -4.20191 (358*2π)/5331 weeks
359-1.27831 -6.55379 (359*2π)/5331 weeks
3601.89749 -7.38984 (360*2π)/5331 weeks
3614.9485 -6.25797 (361*2π)/5331 weeks
3626.82044 -3.7169 (362*2π)/5331 weeks
3637.1033 -1.11659 (363*2π)/5331 weeks
3645.82398 1.53279 (364*2π)/5331 weeks
3653.66924 2.91496 (365*2π)/5331 weeks
3661.03561 3.4141 (366*2π)/5331 weeks
367-1.44654 1.71217 (367*2π)/5331 weeks
368-2.70526 -.38192 (368*2π)/5331 weeks
369-2.83506 -3.44674 (369*2π)/5331 weeks
370-1.39985 -5.83447 (370*2π)/5331 weeks
3711.4683 -7.15114 (371*2π)/5331 weeks
3724.72746 -6.76889 (372*2π)/5331 weeks
3737.03758 -4.45718 (373*2π)/5331 weeks
3747.7839 -1.203 (374*2π)/5331 weeks
3756.34515 1.83365 (375*2π)/5331 weeks
3763.39541 3.39588 (376*2π)/5331 weeks
377.46036 3.12195 (377*2π)/5331 weeks
378-1.38734 1.90101 (378*2π)/5331 weeks
379-3.81159 .22415 (379*2π)/5331 weeks
380-3.91418 -3.64673 (380*2π)/5331 weeks
381-2.45515 -5.66897 (381*2π)/5331 weeks
382-.51094 -6.97172 (382*2π)/5331 weeks
3831.63114 -7.88141 (383*2π)/5331 weeks
3843.81753 -6.93522 (384*2π)/5331 weeks
3855.23614 -6.09416 (385*2π)/5331 weeks
3866.41388 -3.95681 (386*2π)/5331 weeks
3875.673 -1.50797 (387*2π)/5331 weeks
3884.38127 -.83216 (388*2π)/5331 weeks
3892.96621 -.17513 (389*2π)/5331 weeks
390.81142 -1.41863 (390*2π)/5331 weeks
3911.24705 -2.49658 (391*2π)/5331 weeks
3921.28955 -3.15968 (392*2π)/5331 weeks
3932.2401 -4.16148 (393*2π)/5331 weeks
3943.04564 -3.69982 (394*2π)/5331 weeks
3952.99778 -3.51494 (395*2π)/5331 weeks
3964.08516 -3.14272 (396*2π)/5331 weeks
3974.10816 -1.96838 (397*2π)/5331 weeks
3983.86665 -.93757 (398*2π)/5331 weeks
3992.90366 .39295 (399*2π)/5331 weeks
400-.30708 .99174 (400*2π)/5331 weeks
401-2.16606 -1.33846 (401*2π)/5331 weeks
402-2.02674 -3.57331 (402*2π)/5331 weeks
403-1.38124 -5.57283 (403*2π)/5331 weeks
404.13871 -6.56052 (404*2π)/5331 weeks
4051.55988 -6.24117 (405*2π)/5331 weeks
4062.34078 -5.63096 (406*2π)/5331 weeks
4072.34232 -5.04644 (407*2π)/5331 weeks
4081.90243 -4.67704 (408*2π)/5331 weeks
4091.15906 -5.10217 (409*2π)/5331 weeks
410.46091 -6.53801 (410*2π)/5331 weeks
4111.99609 -8.5914 (411*2π)/5331 weeks
4124.62532 -8.70934 (412*2π)/5331 weeks
4137.12637 -7.7947 (413*2π)/5331 weeks
4148.60371 -4.7716 (414*2π)/5331 weeks
4157.56687 -1.78628 (415*2π)/5331 weeks
4165.20888 .24711 (416*2π)/5331 weeks
4172.62045 .6843 (417*2π)/5331 weeks
418.14746 -1.04349 (418*2π)/5331 weeks
419-.76791 -3.38615 (419*2π)/5331 weeks
420-.61096 -5.95051 (420*2π)/5331 weeks
4211.19267 -7.6547 (421*2π)/5331 weeks
4224.51787 -7.68676 (422*2π)/5331 weeks
4235.95755 -5.70396 (423*2π)/5331 weeks
4246.48653 -4.0053 (424*2π)/5331 weeks
4255.72918 -1.01971 (425*2π)/5331 weeks
4263.05057 .91326 (426*2π)/5331 weeks
427.0505 .85727 (427*2π)/5331 weeks
428-3.19258 -1.13791 (428*2π)/5331 weeks
429-4.48488 -4.60695 (429*2π)/5331 weeks
430-4.16508 -7.47508 (430*2π)/5331 weeks
431-2.46741 -9.9858 (431*2π)/5331 weeks
432-.30328 -11.98043 (432*2π)/5331 weeks
4332.64442 -12.63415 (433*2π)/5331 weeks
4344.56577 -11.73542 (434*2π)/5331 weeks
4356.4045 -10.28808 (435*2π)/5331 weeks
4367.41085 -8.34821 (436*2π)/5331 weeks
4377.51718 -6.48495 (437*2π)/5331 weeks
4386.56725 -5.40864 (438*2π)/5331 weeks
4395.33385 -4.86341 (439*2π)/5331 weeks
4403.57213 -4.68787 (440*2π)/5331 weeks
4413.33276 -6.18647 (441*2π)/5331 weeks
4422.42004 -6.56759 (442*2π)/5331 weeks
4432.56412 -9.0647 (443*2π)/5331 weeks
4445.09623 -11.63719 (444*2π)/5331 weeks
4458.24852 -11.21151 (445*2π)/5331 weeks
44611.88371 -8.6042 (446*2π)/5331 weeks
44712.67004 -3.86889 (447*2π)/5331 weeks
44810.56287 .23442 (448*2π)/5331 weeks
4496.81202 1.51391 (449*2π)/5331 weeks
4502.22846 1.69222 (450*2π)/5331 weeks
451-.58668 -2.4646 (451*2π)/5331 weeks
452-.53618 -5.07962 (452*2π)/5331 weeks
453-.19523 -8.54848 (453*2π)/5331 weeks
4545.09525 -10.79866 (454*2π)/5331 weeks
4557.85536 -7.89196 (455*2π)/5331 weeks
4569.943 -5.5462 (456*2π)/5331 weeks
4579.79377 -.35177 (457*2π)/5331 weeks
4584.96586 2.94078 (458*2π)/5331 weeks
4591.29586 2.592 (459*2π)/5331 weeks
460-3.58073 2.10705 (460*2π)/5331 weeks
461-7.63466 -2.1476 (461*2π)/5331 weeks
462-8.10307 -8.8617 (462*2π)/5331 weeks
463-5.55344 -13.01279 (463*2π)/5331 weeks
464-1.699 -15.16587 (464*2π)/5331 weeks
4652.43225 -15.55496 (465*2π)/5331 weeks
4663.60286 -14.16656 (466*2π)/5331 weeks
4676.21314 -15.04171 (467*2π)/5331 weeks
4688.83223 -12.19737 (468*2π)/5331 weeks
4698.85088 -10.71873 (469*2π)/5331 weeks
47010.04429 -7.5659 (470*2π)/5331 weeks
4717.34407 -4.13856 (471*2π)/5331 weeks
4724.3733 -3.56087 (472*2π)/5331 weeks
473.72459 -4.07193 (473*2π)/5331 weeks
474-3.32641 -8.38979 (474*2π)/5331 weeks
475-1.97163 -13.53174 (475*2π)/5331 weeks
4761.18125 -17.87607 (476*2π)/5331 weeks
4776.59436 -19.23394 (477*2π)/5331 weeks
47812.68345 -18.57715 (478*2π)/5331 weeks
47915.80707 -12.66993 (479*2π)/5331 weeks
48017.05421 -7.54992 (480*2π)/5331 weeks
48114.23392 -1.91437 (481*2π)/5331 weeks
4829.38934 .25732 (482*2π)/5331 weeks
4835.34525 -.40882 (483*2π)/5331 weeks
4841.76826 -.63732 (484*2π)/5331 weeks
485-2.12047 -4.82557 (485*2π)/5331 weeks
486-.56253 -8.52099 (486*2π)/5331 weeks
487.03681 -11.60028 (487*2π)/5331 weeks
4883.31195 -13.45023 (488*2π)/5331 weeks
4895.74996 -10.29389 (489*2π)/5331 weeks
4906.52454 -8.95619 (490*2π)/5331 weeks
4915.68076 -5.66459 (491*2π)/5331 weeks
492.737 -4.62912 (492*2π)/5331 weeks
493-2.22081 -5.18048 (493*2π)/5331 weeks
494-9.87787 -7.80153 (494*2π)/5331 weeks
495-11.66291 -18.38088 (495*2π)/5331 weeks
496-8.21453 -27.08567 (496*2π)/5331 weeks
497-.59332 -33.00188 (497*2π)/5331 weeks
4989.28046 -37.95321 (498*2π)/5331 weeks
49922.74037 -33.85572 (499*2π)/5331 weeks
50031.72306 -24.93516 (500*2π)/5331 weeks
50136.25494 -7.95571 (501*2π)/5331 weeks
50228.3008 6.71233 (502*2π)/5331 weeks
50312.9425 12.11761 (503*2π)/5331 weeks
504.25084 10.46552 (504*2π)/5331 weeks
505-12.26655 1.66022 (505*2π)/5331 weeks
506-14.47042 -12.37214 (506*2π)/5331 weeks
507-9.42779 -23.2055 (507*2π)/5331 weeks
5082.9969 -31.14645 (508*2π)/5331 weeks
50914.36549 -27.88632 (509*2π)/5331 weeks
51021.16142 -15.52123 (510*2π)/5331 weeks
51118.5055 -.08366 (511*2π)/5331 weeks
5125.85533 8.3676 (512*2π)/5331 weeks
513-11.33593 7.37559 (513*2π)/5331 weeks
514-25.80912 -2.77628 (514*2π)/5331 weeks
515-33.38864 -16.06093 (515*2π)/5331 weeks
516-37.06195 -36.05193 (516*2π)/5331 weeks
517-25.64737 -54.41523 (517*2π)/5331 weeks
518-15.04303 -63.20858 (518*2π)/5331 weeks
519-2.07407 -69.36382 (519*2π)/5331 weeks
52020.01766 -67.78729 (520*2π)/5331 weeks
52123.3861 -57.32572 (521*2π)/5331 weeks
52234.69194 -47.60892 (522*2π)/5331 weeks
52326.04186 -31.30246 (523*2π)/5331 weeks
52412.40188 -26.26943 (524*2π)/5331 weeks
525-13.58692 -25.27351 (525*2π)/5331 weeks
526-46.63217 -46.63012 (526*2π)/5331 weeks
527-62.95491 -101.5614 (527*2π)/5331 weeks
528-40.7592 -173.2914 (528*2π)/5331 weeks
52910.55241 -234.4182 (529*2π)/5331 weeks
530107.7012 -270.1274 (530*2π)/5331 weeks
531229.7298 -252.389 (531*2π)/5331 weeks



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