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Fourier Analysis of FXP (ProShares Ultrashort FTSE China)


FXP (ProShares Ultrashort FTSE China) appears to have interesting cyclic behaviour every 40 weeks (79.9173*sine), 37 weeks (73.6492*sine), and 44 weeks (63.5486*sine).

FXP (ProShares Ultrashort FTSE China) has an average price of 304.82 (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 1/9/2017 for FXP (ProShares Ultrashort FTSE China), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0304.8216   0 
1356.4989 225.0768 (1*2π)/480480 weeks
2227.9719 291.1382 (2*2π)/480240 weeks
382.70977 289.8019 (3*2π)/480160 weeks
4-19.05701 225.6802 (4*2π)/480120 weeks
5-68.76303 148.4079 (5*2π)/48096 weeks
6-62.34109 70.39124 (6*2π)/48080 weeks
7-22.0141 30.78583 (7*2π)/48069 weeks
812.03552 27.27201 (8*2π)/48060 weeks
928.94216 33.98546 (9*2π)/48053 weeks
1038.10258 54.99058 (10*2π)/48048 weeks
1125.77107 63.54858 (11*2π)/48044 weeks
1214.60672 79.91725 (12*2π)/48040 weeks
13-7.62649 73.64915 (13*2π)/48037 weeks
14-22.90361 63.54156 (14*2π)/48034 weeks
15-39.14682 48.30272 (15*2π)/48032 weeks
16-39.40217 21.84384 (16*2π)/48030 weeks
17-30.01476 4.73931 (17*2π)/48028 weeks
18-12.85624 -8.44499 (18*2π)/48027 weeks
198.30034 -8.76487 (19*2π)/48025 weeks
2023.30227 3.32489 (20*2π)/48024 weeks
2123.04445 21.10256 (21*2π)/48023 weeks
2210.26864 32.01363 (22*2π)/48022 weeks
23-6.59354 31.45247 (23*2π)/48021 weeks
24-14.79432 18.85078 (24*2π)/48020 weeks
25-15.26893 2.13146 (25*2π)/48019 weeks
26-1.6227 -11.20535 (26*2π)/48018 weeks
2714.01687 -13.623 (27*2π)/48018 weeks
2832.63543 -6.22143 (28*2π)/48017 weeks
2940.99084 12.94035 (29*2π)/48017 weeks
3032.26867 30.72193 (30*2π)/48016 weeks
3119.66227 40.46223 (31*2π)/48015 weeks
323.08341 39.01964 (32*2π)/48015 weeks
33-6.41763 33.03017 (33*2π)/48015 weeks
34-12.34319 22.69127 (34*2π)/48014 weeks
35-12.02483 10.04343 (35*2π)/48014 weeks
36-2.59185 5.64994 (36*2π)/48013 weeks
371.16528 4.91365 (37*2π)/48013 weeks
386.72407 7.17687 (38*2π)/48013 weeks
396.84996 10.89081 (39*2π)/48012 weeks
406.66066 12.95573 (40*2π)/48012 weeks
411.44896 13.62465 (41*2π)/48012 weeks
42-.94939 9.92336 (42*2π)/48011 weeks
43-2.38098 6.87811 (43*2π)/48011 weeks
441.21295 .79768 (44*2π)/48011 weeks
455.92732 .28726 (45*2π)/48011 weeks
4610.92412 -.32178 (46*2π)/48010 weeks
4716.78394 3.02403 (47*2π)/48010 weeks
4818.81204 10.51245 (48*2π)/48010 weeks
4917.15282 16.41075 (49*2π)/48010 weeks
509.78758 21.36717 (50*2π)/48010 weeks
513.31161 20.797 (51*2π)/4809 weeks
52-1.85568 16.10962 (52*2π)/4809 weeks
53-3.79201 10.24652 (53*2π)/4809 weeks
54.67133 4.35112 (54*2π)/4809 weeks
555.25096 3.82921 (55*2π)/4809 weeks
569.1521 4.80081 (56*2π)/4809 weeks
5711.26564 9.64983 (57*2π)/4808 weeks
589.4575 12.06929 (58*2π)/4808 weeks
598.71194 15.51506 (59*2π)/4808 weeks
604.22862 16.25263 (60*2π)/4808 weeks
613.26789 16.51974 (61*2π)/4808 weeks
62-1.55003 16.96024 (62*2π)/4808 weeks
63-6.13056 14.4514 (63*2π)/4808 weeks
64-9.23841 9.21774 (64*2π)/4808 weeks
65-7.76455 1.24155 (65*2π)/4807 weeks
66-2.08225 -3.10071 (66*2π)/4807 weeks
672.7755 -2.90693 (67*2π)/4807 weeks
688.67451 -2.15241 (68*2π)/4807 weeks
6911.49329 4.16332 (69*2π)/4807 weeks
708.98172 8.27688 (70*2π)/4807 weeks
716.42371 11.47611 (71*2π)/4807 weeks
72-.21945 9.6161 (72*2π)/4807 weeks
73-.6717 5.24939 (73*2π)/4807 weeks
74-.68529 1.70083 (74*2π)/4806 weeks
754.07546 -2.46259 (75*2π)/4806 weeks
768.80741 -1.38645 (76*2π)/4806 weeks
7713.26051 2.11743 (77*2π)/4806 weeks
7814.04113 7.77104 (78*2π)/4806 weeks
7910.41803 12.20542 (79*2π)/4806 weeks
806.37102 12.84487 (80*2π)/4806 weeks
812.7645 10.1175 (81*2π)/4806 weeks
822.69015 7.07713 (82*2π)/4806 weeks
833.55499 6.67213 (83*2π)/4806 weeks
844.66971 4.81712 (84*2π)/4806 weeks
856.28669 5.37188 (85*2π)/4806 weeks
867.53834 6.51591 (86*2π)/4806 weeks
878.22503 8.73688 (87*2π)/4806 weeks
887.52228 11.08173 (88*2π)/4805 weeks
895.51942 12.91226 (89*2π)/4805 weeks
903.12078 13.86265 (90*2π)/4805 weeks
91-.5339 13.13491 (91*2π)/4805 weeks
92-3.00116 10.72349 (92*2π)/4805 weeks
93-4.64016 7.32279 (93*2π)/4805 weeks
94-4.7527 3.51216 (94*2π)/4805 weeks
95-2.04577 -.1745 (95*2π)/4805 weeks
961.93766 -.90725 (96*2π)/4805 weeks
975.72438 .4564 (97*2π)/4805 weeks
987.28545 3.82631 (98*2π)/4805 weeks
996.54187 6.04328 (99*2π)/4805 weeks
1004.82256 8.46866 (100*2π)/4805 weeks
101.99152 8.01551 (101*2π)/4805 weeks
102-.97607 5.59192 (102*2π)/4805 weeks
103-.70654 2.73102 (103*2π)/4805 weeks
1041.1329 .14874 (104*2π)/4805 weeks
1054.75073 -.25185 (105*2π)/4805 weeks
1067.94511 1.2936 (106*2π)/4805 weeks
1079.46993 4.57901 (107*2π)/4804 weeks
1087.991 8.42265 (108*2π)/4804 weeks
1094.93323 9.58636 (109*2π)/4804 weeks
1101.78202 9.13293 (110*2π)/4804 weeks
111.60633 6.40113 (111*2π)/4804 weeks
1121.59223 5.25987 (112*2π)/4804 weeks
1132.5285 5.28623 (113*2π)/4804 weeks
1142.71116 5.96461 (114*2π)/4804 weeks
1152.05746 6.92569 (115*2π)/4804 weeks
116.53654 7.44648 (116*2π)/4804 weeks
117-1.50936 6.35962 (117*2π)/4804 weeks
118-2.41063 3.90932 (118*2π)/4804 weeks
119-2.34879 .9893 (119*2π)/4804 weeks
120.62465 -1.63006 (120*2π)/4804 weeks
1213.62892 -.01972 (121*2π)/4804 weeks
1224.45712 1.5656 (122*2π)/4804 weeks
1234.73133 2.85773 (123*2π)/4804 weeks
1243.70725 4.10826 (124*2π)/4804 weeks
1253.48047 4.01248 (125*2π)/4804 weeks
1262.57921 4.66205 (126*2π)/4804 weeks
1271.34464 3.53359 (127*2π)/4804 weeks
1281.29474 2.6834 (128*2π)/4804 weeks
1291.07482 .75346 (129*2π)/4804 weeks
1303.84088 .33491 (130*2π)/4804 weeks
1315.30108 1.17921 (131*2π)/4804 weeks
1327.17263 3.12152 (132*2π)/4804 weeks
1336.47927 6.13929 (133*2π)/4804 weeks
1344.51496 7.46583 (134*2π)/4804 weeks
1352.09771 8.75641 (135*2π)/4804 weeks
136-.64581 7.74457 (136*2π)/4804 weeks
137-2.96944 6.01667 (137*2π)/4804 weeks
138-4.76834 3.14977 (138*2π)/4803 weeks
139-3.23121 -1.33883 (139*2π)/4803 weeks
140-.75672 -2.69979 (140*2π)/4803 weeks
1412.32663 -3.91118 (141*2π)/4803 weeks
1426.08302 -2.91791 (142*2π)/4803 weeks
1438.39328 .50241 (143*2π)/4803 weeks
1447.88509 4.62153 (144*2π)/4803 weeks
1455.12321 7.50945 (145*2π)/4803 weeks
1461.17685 7.81414 (146*2π)/4803 weeks
147-2.06711 5.7576 (147*2π)/4803 weeks
148-3.49227 2.56504 (148*2π)/4803 weeks
149-2.4312 -.68555 (149*2π)/4803 weeks
150-.37866 -3.11877 (150*2π)/4803 weeks
1513.26551 -3.37871 (151*2π)/4803 weeks
1525.98705 -2.03235 (152*2π)/4803 weeks
1537.79019 .93518 (153*2π)/4803 weeks
1547.45841 4.14258 (154*2π)/4803 weeks
1555.06496 7.1148 (155*2π)/4803 weeks
1561.19366 8.07515 (156*2π)/4803 weeks
157-2.41089 6.51563 (157*2π)/4803 weeks
158-4.39704 3.07925 (158*2π)/4803 weeks
159-4.52872 -.72333 (159*2π)/4803 weeks
160-2.45693 -3.47006 (160*2π)/4803 weeks
1611.33225 -4.76687 (161*2π)/4803 weeks
1623.96058 -3.30559 (162*2π)/4803 weeks
1635.2515 -1.21167 (163*2π)/4803 weeks
1644.43194 1.50171 (164*2π)/4803 weeks
1652.31799 2.21262 (165*2π)/4803 weeks
166.15125 1.57978 (166*2π)/4803 weeks
167-.85269 -.46631 (167*2π)/4803 weeks
168-.24828 -3.22851 (168*2π)/4803 weeks
1691.36984 -5.00921 (169*2π)/4803 weeks
1704.57852 -5.50503 (170*2π)/4803 weeks
1717.05814 -3.24397 (171*2π)/4803 weeks
1727.90693 -1.19619 (172*2π)/4803 weeks
1737.62415 1.61568 (173*2π)/4803 weeks
1745.35527 2.90051 (174*2π)/4803 weeks
1753.4621 3.28488 (175*2π)/4803 weeks
176.38148 2.16472 (176*2π)/4803 weeks
177-.31357 -1.14456 (177*2π)/4803 weeks
178.52876 -3.42776 (178*2π)/4803 weeks
1793.458 -5.98244 (179*2π)/4803 weeks
1807.15376 -5.30271 (180*2π)/4803 weeks
1819.93186 -2.54752 (181*2π)/4803 weeks
1829.79401 1.04851 (182*2π)/4803 weeks
1837.46392 3.41464 (183*2π)/4803 weeks
1845.16592 3.86476 (184*2π)/4803 weeks
1852.70667 2.43099 (185*2π)/4803 weeks
1861.91217 .25361 (186*2π)/4803 weeks
1873.83901 -1.82409 (187*2π)/4803 weeks
1885.68669 -2.77646 (188*2π)/4803 weeks
1898.11804 -1.0686 (189*2π)/4803 weeks
1908.06511 .94583 (190*2π)/4803 weeks
1917.96417 2.46387 (191*2π)/4803 weeks
1927.10809 3.54325 (192*2π)/4803 weeks
1936.21023 4.76987 (193*2π)/4802 weeks
1943.95497 4.94803 (194*2π)/4802 weeks
1952.41435 4.28292 (195*2π)/4802 weeks
1961.00438 3.08809 (196*2π)/4802 weeks
197.68401 .58219 (197*2π)/4802 weeks
1981.80298 -1.22371 (198*2π)/4802 weeks
1993.97318 -2.18558 (199*2π)/4802 weeks
2007.13042 -1.31287 (200*2π)/4802 weeks
2018.33521 1.35942 (201*2π)/4802 weeks
2027.68184 4.24065 (202*2π)/4802 weeks
2035.25096 6.54217 (203*2π)/4802 weeks
2041.66522 6.73339 (204*2π)/4802 weeks
205-1.11892 5.20587 (205*2π)/4802 weeks
206-3.20277 1.61482 (206*2π)/4802 weeks
207-2.10389 -2.37953 (207*2π)/4802 weeks
208.99351 -5.19202 (208*2π)/4802 weeks
2095.55909 -5.30165 (209*2π)/4802 weeks
2108.54036 -1.94319 (210*2π)/4802 weeks
2118.96146 1.71082 (211*2π)/4802 weeks
2126.78073 5.81087 (212*2π)/4802 weeks
2132.40331 6.85064 (213*2π)/4802 weeks
214-1.32929 5.23054 (214*2π)/4802 weeks
215-4.15517 1.59691 (215*2π)/4802 weeks
216-3.86917 -3.82021 (216*2π)/4802 weeks
217-.64158 -7.05037 (217*2π)/4802 weeks
2184.04978 -8.57259 (218*2π)/4802 weeks
2198.84837 -6.50253 (219*2π)/4802 weeks
22010.75336 -2.74255 (220*2π)/4802 weeks
22111.13402 1.39484 (221*2π)/4802 weeks
2228.91864 4.48493 (222*2π)/4802 weeks
2236.01108 6.32158 (223*2π)/4802 weeks
2241.7074 6.28604 (224*2π)/4802 weeks
225-1.17233 2.4859 (225*2π)/4802 weeks
226-.82332 -1.16328 (226*2π)/4802 weeks
2271.12112 -4.17662 (227*2π)/4802 weeks
2285.33417 -5.34377 (228*2π)/4802 weeks
2299.2966 -2.68521 (229*2π)/4802 weeks
23010.22232 1.97684 (230*2π)/4802 weeks
2318.2803 6.11469 (231*2π)/4802 weeks
2323.76646 7.8006 (232*2π)/4802 weeks
233.18083 7.17499 (233*2π)/4802 weeks
234-4.2159 3.92253 (234*2π)/4802 weeks
235-4.72962 -1.71477 (235*2π)/4802 weeks
236-2.13612 -5.88317 (236*2π)/4802 weeks
2372.00836 -7.7568 (237*2π)/4802 weeks
2386.56951 -6.90017 (238*2π)/4802 weeks
2399.8551 -4.64985 (239*2π)/4802 weeks
24011.84185   (240*2π)/4802 weeks
2419.8551 4.64985 (241*2π)/4802 weeks
2426.56951 6.90017 (242*2π)/4802 weeks
2432.00836 7.7568 (243*2π)/4802 weeks
244-2.13612 5.88317 (244*2π)/4802 weeks
245-4.72962 1.71477 (245*2π)/4802 weeks
246-4.2159 -3.92253 (246*2π)/4802 weeks
247.18083 -7.17499 (247*2π)/4802 weeks
2483.76646 -7.8006 (248*2π)/4802 weeks
2498.2803 -6.11469 (249*2π)/4802 weeks
25010.22232 -1.97684 (250*2π)/4802 weeks
2519.2966 2.68521 (251*2π)/4802 weeks
2525.33417 5.34377 (252*2π)/4802 weeks
2531.12112 4.17662 (253*2π)/4802 weeks
254-.82332 1.16328 (254*2π)/4802 weeks
255-1.17233 -2.4859 (255*2π)/4802 weeks
2561.7074 -6.28604 (256*2π)/4802 weeks
2576.01108 -6.32158 (257*2π)/4802 weeks
2588.91864 -4.48493 (258*2π)/4802 weeks
25911.13402 -1.39484 (259*2π)/4802 weeks
26010.75336 2.74255 (260*2π)/4802 weeks
2618.84837 6.50253 (261*2π)/4802 weeks
2624.04978 8.57259 (262*2π)/4802 weeks
263-.64158 7.05037 (263*2π)/4802 weeks
264-3.86917 3.82021 (264*2π)/4802 weeks
265-4.15517 -1.59691 (265*2π)/4802 weeks
266-1.32929 -5.23054 (266*2π)/4802 weeks
2672.40331 -6.85064 (267*2π)/4802 weeks
2686.78073 -5.81087 (268*2π)/4802 weeks
2698.96146 -1.71082 (269*2π)/4802 weeks
2708.54036 1.94319 (270*2π)/4802 weeks
2715.55909 5.30165 (271*2π)/4802 weeks
272.99351 5.19202 (272*2π)/4802 weeks
273-2.10389 2.37953 (273*2π)/4802 weeks
274-3.20277 -1.61482 (274*2π)/4802 weeks
275-1.11892 -5.20587 (275*2π)/4802 weeks
2761.66522 -6.73339 (276*2π)/4802 weeks
2775.25096 -6.54217 (277*2π)/4802 weeks
2787.68184 -4.24065 (278*2π)/4802 weeks
2798.33521 -1.35942 (279*2π)/4802 weeks
2807.13042 1.31287 (280*2π)/4802 weeks
2813.97318 2.18558 (281*2π)/4802 weeks
2821.80298 1.22371 (282*2π)/4802 weeks
283.68401 -.58219 (283*2π)/4802 weeks
2841.00438 -3.08809 (284*2π)/4802 weeks
2852.41435 -4.28292 (285*2π)/4802 weeks
2863.95497 -4.94803 (286*2π)/4802 weeks
2876.21023 -4.76987 (287*2π)/4802 weeks
2887.10809 -3.54325 (288*2π)/4802 weeks
2897.96417 -2.46387 (289*2π)/4802 weeks
2908.06511 -.94583 (290*2π)/4802 weeks
2918.11804 1.0686 (291*2π)/4802 weeks
2925.68669 2.77646 (292*2π)/4802 weeks
2933.83901 1.82409 (293*2π)/4802 weeks
2941.91217 -.25361 (294*2π)/4802 weeks
2952.70667 -2.43099 (295*2π)/4802 weeks
2965.16592 -3.86476 (296*2π)/4802 weeks
2977.46392 -3.41464 (297*2π)/4802 weeks
2989.79401 -1.04851 (298*2π)/4802 weeks
2999.93186 2.54752 (299*2π)/4802 weeks
3007.15376 5.30271 (300*2π)/4802 weeks
3013.458 5.98244 (301*2π)/4802 weeks
302.52876 3.42776 (302*2π)/4802 weeks
303-.31357 1.14456 (303*2π)/4802 weeks
304.38148 -2.16472 (304*2π)/4802 weeks
3053.4621 -3.28488 (305*2π)/4802 weeks
3065.35527 -2.90051 (306*2π)/4802 weeks
3077.62415 -1.61568 (307*2π)/4802 weeks
3087.90693 1.19619 (308*2π)/4802 weeks
3097.05814 3.24397 (309*2π)/4802 weeks
3104.57852 5.50503 (310*2π)/4802 weeks
3111.36984 5.00921 (311*2π)/4802 weeks
312-.24828 3.22851 (312*2π)/4802 weeks
313-.85269 .46631 (313*2π)/4802 weeks
314.15125 -1.57978 (314*2π)/4802 weeks
3152.31799 -2.21262 (315*2π)/4802 weeks
3164.43194 -1.50171 (316*2π)/4802 weeks
3175.2515 1.21167 (317*2π)/4802 weeks
3183.96058 3.30559 (318*2π)/4802 weeks
3191.33225 4.76687 (319*2π)/4802 weeks
320-2.45693 3.47006 (320*2π)/4802 weeks
321-4.52872 .72333 (321*2π)/4801 weeks
322-4.39704 -3.07925 (322*2π)/4801 weeks
323-2.41089 -6.51563 (323*2π)/4801 weeks
3241.19366 -8.07515 (324*2π)/4801 weeks
3255.06496 -7.1148 (325*2π)/4801 weeks
3267.45841 -4.14258 (326*2π)/4801 weeks
3277.79019 -.93518 (327*2π)/4801 weeks
3285.98705 2.03235 (328*2π)/4801 weeks
3293.26551 3.37871 (329*2π)/4801 weeks
330-.37866 3.11877 (330*2π)/4801 weeks
331-2.4312 .68555 (331*2π)/4801 weeks
332-3.49227 -2.56504 (332*2π)/4801 weeks
333-2.06711 -5.7576 (333*2π)/4801 weeks
3341.17685 -7.81414 (334*2π)/4801 weeks
3355.12321 -7.50945 (335*2π)/4801 weeks
3367.88509 -4.62153 (336*2π)/4801 weeks
3378.39328 -.50241 (337*2π)/4801 weeks
3386.08302 2.91791 (338*2π)/4801 weeks
3392.32663 3.91118 (339*2π)/4801 weeks
340-.75672 2.69979 (340*2π)/4801 weeks
341-3.23121 1.33883 (341*2π)/4801 weeks
342-4.76834 -3.14977 (342*2π)/4801 weeks
343-2.96944 -6.01667 (343*2π)/4801 weeks
344-.64581 -7.74457 (344*2π)/4801 weeks
3452.09771 -8.75641 (345*2π)/4801 weeks
3464.51496 -7.46583 (346*2π)/4801 weeks
3476.47927 -6.13929 (347*2π)/4801 weeks
3487.17263 -3.12152 (348*2π)/4801 weeks
3495.30108 -1.17921 (349*2π)/4801 weeks
3503.84088 -.33491 (350*2π)/4801 weeks
3511.07482 -.75346 (351*2π)/4801 weeks
3521.29474 -2.6834 (352*2π)/4801 weeks
3531.34464 -3.53359 (353*2π)/4801 weeks
3542.57921 -4.66205 (354*2π)/4801 weeks
3553.48047 -4.01248 (355*2π)/4801 weeks
3563.70725 -4.10826 (356*2π)/4801 weeks
3574.73133 -2.85773 (357*2π)/4801 weeks
3584.45712 -1.5656 (358*2π)/4801 weeks
3593.62892 .01972 (359*2π)/4801 weeks
360.62465 1.63006 (360*2π)/4801 weeks
361-2.34879 -.9893 (361*2π)/4801 weeks
362-2.41063 -3.90932 (362*2π)/4801 weeks
363-1.50936 -6.35962 (363*2π)/4801 weeks
364.53654 -7.44648 (364*2π)/4801 weeks
3652.05746 -6.92569 (365*2π)/4801 weeks
3662.71116 -5.96461 (366*2π)/4801 weeks
3672.5285 -5.28623 (367*2π)/4801 weeks
3681.59223 -5.25987 (368*2π)/4801 weeks
369.60633 -6.40113 (369*2π)/4801 weeks
3701.78202 -9.13293 (370*2π)/4801 weeks
3714.93323 -9.58636 (371*2π)/4801 weeks
3727.991 -8.42265 (372*2π)/4801 weeks
3739.46993 -4.57901 (373*2π)/4801 weeks
3747.94511 -1.2936 (374*2π)/4801 weeks
3754.75073 .25185 (375*2π)/4801 weeks
3761.1329 -.14874 (376*2π)/4801 weeks
377-.70654 -2.73102 (377*2π)/4801 weeks
378-.97607 -5.59192 (378*2π)/4801 weeks
379.99152 -8.01551 (379*2π)/4801 weeks
3804.82256 -8.46866 (380*2π)/4801 weeks
3816.54187 -6.04328 (381*2π)/4801 weeks
3827.28545 -3.82631 (382*2π)/4801 weeks
3835.72438 -.4564 (383*2π)/4801 weeks
3841.93766 .90725 (384*2π)/4801 weeks
385-2.04577 .1745 (385*2π)/4801 weeks
386-4.7527 -3.51216 (386*2π)/4801 weeks
387-4.64016 -7.32279 (387*2π)/4801 weeks
388-3.00116 -10.72349 (388*2π)/4801 weeks
389-.5339 -13.13491 (389*2π)/4801 weeks
3903.12078 -13.86265 (390*2π)/4801 weeks
3915.51942 -12.91226 (391*2π)/4801 weeks
3927.52228 -11.08173 (392*2π)/4801 weeks
3938.22503 -8.73688 (393*2π)/4801 weeks
3947.53834 -6.51591 (394*2π)/4801 weeks
3956.28669 -5.37188 (395*2π)/4801 weeks
3964.66971 -4.81712 (396*2π)/4801 weeks
3973.55499 -6.67213 (397*2π)/4801 weeks
3982.69015 -7.07713 (398*2π)/4801 weeks
3992.7645 -10.1175 (399*2π)/4801 weeks
4006.37102 -12.84487 (400*2π)/4801 weeks
40110.41803 -12.20542 (401*2π)/4801 weeks
40214.04113 -7.77104 (402*2π)/4801 weeks
40313.26051 -2.11743 (403*2π)/4801 weeks
4048.80741 1.38645 (404*2π)/4801 weeks
4054.07546 2.46259 (405*2π)/4801 weeks
406-.68529 -1.70083 (406*2π)/4801 weeks
407-.6717 -5.24939 (407*2π)/4801 weeks
408-.21945 -9.6161 (408*2π)/4801 weeks
4096.42371 -11.47611 (409*2π)/4801 weeks
4108.98172 -8.27688 (410*2π)/4801 weeks
41111.49329 -4.16332 (411*2π)/4801 weeks
4128.67451 2.15241 (412*2π)/4801 weeks
4132.7755 2.90693 (413*2π)/4801 weeks
414-2.08225 3.10071 (414*2π)/4801 weeks
415-7.76455 -1.24155 (415*2π)/4801 weeks
416-9.23841 -9.21774 (416*2π)/4801 weeks
417-6.13056 -14.4514 (417*2π)/4801 weeks
418-1.55003 -16.96024 (418*2π)/4801 weeks
4193.26789 -16.51974 (419*2π)/4801 weeks
4204.22862 -16.25263 (420*2π)/4801 weeks
4218.71194 -15.51506 (421*2π)/4801 weeks
4229.4575 -12.06929 (422*2π)/4801 weeks
42311.26564 -9.64983 (423*2π)/4801 weeks
4249.1521 -4.80081 (424*2π)/4801 weeks
4255.25096 -3.82921 (425*2π)/4801 weeks
426.67133 -4.35112 (426*2π)/4801 weeks
427-3.79201 -10.24652 (427*2π)/4801 weeks
428-1.85568 -16.10962 (428*2π)/4801 weeks
4293.31161 -20.797 (429*2π)/4801 weeks
4309.78758 -21.36717 (430*2π)/4801 weeks
43117.15282 -16.41075 (431*2π)/4801 weeks
43218.81204 -10.51245 (432*2π)/4801 weeks
43316.78394 -3.02403 (433*2π)/4801 weeks
43410.92412 .32178 (434*2π)/4801 weeks
4355.92732 -.28726 (435*2π)/4801 weeks
4361.21295 -.79768 (436*2π)/4801 weeks
437-2.38098 -6.87811 (437*2π)/4801 weeks
438-.94939 -9.92336 (438*2π)/4801 weeks
4391.44896 -13.62465 (439*2π)/4801 weeks
4406.66066 -12.95573 (440*2π)/4801 weeks
4416.84996 -10.89081 (441*2π)/4801 weeks
4426.72407 -7.17687 (442*2π)/4801 weeks
4431.16528 -4.91365 (443*2π)/4801 weeks
444-2.59185 -5.64994 (444*2π)/4801 weeks
445-12.02483 -10.04343 (445*2π)/4801 weeks
446-12.34319 -22.69127 (446*2π)/4801 weeks
447-6.41763 -33.03017 (447*2π)/4801 weeks
4483.08341 -39.01964 (448*2π)/4801 weeks
44919.66227 -40.46223 (449*2π)/4801 weeks
45032.26867 -30.72193 (450*2π)/4801 weeks
45140.99084 -12.94035 (451*2π)/4801 weeks
45232.63543 6.22143 (452*2π)/4801 weeks
45314.01687 13.623 (453*2π)/4801 weeks
454-1.6227 11.20535 (454*2π)/4801 weeks
455-15.26893 -2.13146 (455*2π)/4801 weeks
456-14.79432 -18.85078 (456*2π)/4801 weeks
457-6.59354 -31.45247 (457*2π)/4801 weeks
45810.26864 -32.01363 (458*2π)/4801 weeks
45923.04445 -21.10256 (459*2π)/4801 weeks
46023.30227 -3.32489 (460*2π)/4801 weeks
4618.30034 8.76487 (461*2π)/4801 weeks
462-12.85624 8.44499 (462*2π)/4801 weeks
463-30.01476 -4.73931 (463*2π)/4801 weeks
464-39.40217 -21.84384 (464*2π)/4801 weeks
465-39.14682 -48.30272 (465*2π)/4801 weeks
466-22.90361 -63.54156 (466*2π)/4801 weeks
467-7.62649 -73.64915 (467*2π)/4801 weeks
46814.60672 -79.91725 (468*2π)/4801 weeks
46925.77107 -63.54858 (469*2π)/4801 weeks
47038.10258 -54.99058 (470*2π)/4801 weeks
47128.94216 -33.98546 (471*2π)/4801 weeks
47212.03552 -27.27201 (472*2π)/4801 weeks
473-22.0141 -30.78583 (473*2π)/4801 weeks
474-62.34109 -70.39124 (474*2π)/4801 weeks
475-68.76303 -148.4079 (475*2π)/4801 weeks
476-19.05701 -225.6802 (476*2π)/4801 weeks
47782.70977 -289.8019 (477*2π)/4801 weeks
478227.9719 -291.1382 (478*2π)/4801 weeks

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