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Fourier Analysis of SKF (ProShares UltraShort Financials)


SKF (ProShares UltraShort Financials) appears to have interesting cyclic behaviour every 47 weeks (79.836*sine), 17 weeks (68.3935*sine), and 17 weeks (58.9078*cosine).

SKF (ProShares UltraShort Financials) has an average price of 515.8 (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 2/1/2007 to 1/9/2017 for SKF (ProShares UltraShort Financials), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0515.7979   0 
1378.8835 597.8535 (1*2π)/520520 weeks
2-62.70691 483.9766 (2*2π)/520260 weeks
3-256.1836 165.4408 (3*2π)/520173 weeks
4-100.6687 -67.69042 (4*2π)/520130 weeks
569.65601 -32.01783 (5*2π)/520104 weeks
678.80399 91.68752 (6*2π)/52087 weeks
7-31.2699 115.9478 (7*2π)/52074 weeks
8-60.51137 10.67708 (8*2π)/52065 weeks
913.03942 -18.79783 (9*2π)/52058 weeks
1055.43871 16.06643 (10*2π)/52052 weeks
1133.2026 79.83596 (11*2π)/52047 weeks
12-35.27591 57.30271 (12*2π)/52043 weeks
13-23.8867 1.37693 (13*2π)/52040 weeks
1418.32898 -3.84564 (14*2π)/52037 weeks
1533.33205 36.07569 (15*2π)/52035 weeks
16-6.01293 52.19436 (16*2π)/52033 weeks
17-29.02861 24.79022 (17*2π)/52031 weeks
18-15.91029 -11.75489 (18*2π)/52029 weeks
1924.73504 -10.00892 (19*2π)/52027 weeks
2034.63919 25.06036 (20*2π)/52026 weeks
217.37415 42.1106 (21*2π)/52025 weeks
22-8.33224 20.61185 (22*2π)/52024 weeks
237.43269 9.26579 (23*2π)/52023 weeks
2417.86259 32.12608 (24*2π)/52022 weeks
25-16.2139 42.9028 (25*2π)/52021 weeks
26-34.85029 11.17179 (26*2π)/52020 weeks
27-12.80974 -25.32785 (27*2π)/52019 weeks
2838.61346 -14.38659 (28*2π)/52019 weeks
2943.59866 43.06136 (29*2π)/52018 weeks
30-10.02919 68.39345 (30*2π)/52017 weeks
31-58.90775 26.67985 (31*2π)/52017 weeks
32-36.63044 -35.29275 (32*2π)/52016 weeks
3321.15615 -34.79491 (33*2π)/52016 weeks
3440.19159 8.26684 (34*2π)/52015 weeks
3512.1095 37.45183 (35*2π)/52015 weeks
36-16.65262 22.21886 (36*2π)/52014 weeks
37-11.96868 -2.99589 (37*2π)/52014 weeks
388.54881 -6.05484 (38*2π)/52014 weeks
3918.48213 13.54749 (39*2π)/52013 weeks
40-2.69371 24.73625 (40*2π)/52013 weeks
41-12.48591 7.05352 (41*2π)/52013 weeks
42-3.31353 -5.54366 (42*2π)/52012 weeks
4314.57932 -.77538 (43*2π)/52012 weeks
4413.21782 17.39067 (44*2π)/52012 weeks
45-.5792 21.7571 (45*2π)/52012 weeks
46-13.72337 13.05153 (46*2π)/52011 weeks
47-9.48067 -.724 (47*2π)/52011 weeks
48.85628 -2.69381 (48*2π)/52011 weeks
494.10825 3.82923 (49*2π)/52011 weeks
50.55651 4.96334 (50*2π)/52010 weeks
511.4952 .66024 (51*2π)/52010 weeks
527.11708 1.56807 (52*2π)/52010 weeks
537.82338 9.43051 (53*2π)/52010 weeks
54-2.01693 9.47091 (54*2π)/52010 weeks
55-1.40176 -.2621 (55*2π)/5209 weeks
5610.2261 .09635 (56*2π)/5209 weeks
5713.02968 13.59158 (57*2π)/5209 weeks
58-2.72651 24.4458 (58*2π)/5209 weeks
59-21.06321 8.49554 (59*2π)/5209 weeks
60-13.05899 -12.78926 (60*2π)/5209 weeks
619.55271 -17.69771 (61*2π)/5209 weeks
6222.76739 2.11885 (62*2π)/5208 weeks
638.4764 16.723 (63*2π)/5208 weeks
64-2.41238 10.27209 (64*2π)/5208 weeks
65-.01439 -.91345 (65*2π)/5208 weeks
6613.33603 3.42349 (66*2π)/5208 weeks
677.9602 19.29831 (67*2π)/5208 weeks
68-9.80751 18.35899 (68*2π)/5208 weeks
69-17.58039 .97462 (69*2π)/5208 weeks
70-1.59571 -14.79436 (70*2π)/5207 weeks
7116.05568 -3.55365 (71*2π)/5207 weeks
7213.73642 13.37369 (72*2π)/5207 weeks
73-4.93552 22.36303 (73*2π)/5207 weeks
74-21.71574 .87846 (74*2π)/5207 weeks
75-3.65519 -19.92167 (75*2π)/5207 weeks
7620.18491 -12.61228 (76*2π)/5207 weeks
7724.28527 14.04262 (77*2π)/5207 weeks
78.71574 25.7537 (78*2π)/5207 weeks
79-17.09991 12.04174 (79*2π)/5207 weeks
80-14.40089 -11.6447 (80*2π)/5207 weeks
819.53901 -16.29178 (81*2π)/5206 weeks
8219.75188 .47172 (82*2π)/5206 weeks
8312.31322 14.6983 (83*2π)/5206 weeks
84-.47523 13.87391 (84*2π)/5206 weeks
85-3.10029 5.77675 (85*2π)/5206 weeks
86.63388 3.40927 (86*2π)/5206 weeks
87.66402 5.66937 (87*2π)/5206 weeks
88-3.10242 4.34287 (88*2π)/5206 weeks
89-1.29918 -1.95164 (89*2π)/5206 weeks
905.26282 .51974 (90*2π)/5206 weeks
913.36528 5.15281 (91*2π)/5206 weeks
92-1.77589 5.61149 (92*2π)/5206 weeks
93-3.47485 -1.35283 (93*2π)/5206 weeks
943.86192 -4.4574 (94*2π)/5206 weeks
958.96953 1.70657 (95*2π)/5205 weeks
964.417 9.84717 (96*2π)/5205 weeks
97-6.05332 6.50031 (97*2π)/5205 weeks
98-6.12091 -6.09593 (98*2π)/5205 weeks
996.51846 -11.55155 (99*2π)/5205 weeks
10018.68418 -.81109 (100*2π)/5205 weeks
10112.68294 14.24547 (101*2π)/5205 weeks
102-3.39495 16.44982 (102*2π)/5205 weeks
103-12.35227 .68734 (103*2π)/5205 weeks
104.53693 -12.31985 (104*2π)/5205 weeks
10517.27053 -4.78234 (105*2π)/5205 weeks
10616.38827 13.76857 (106*2π)/5205 weeks
107-.38582 20.57519 (107*2π)/5205 weeks
108-15.13962 9.11865 (108*2π)/5205 weeks
109-9.92112 -10.25094 (109*2π)/5205 weeks
1108.86138 -11.8299 (110*2π)/5205 weeks
11116.03673 3.09493 (111*2π)/5205 weeks
1126.87103 15.21602 (112*2π)/5205 weeks
113-8.81454 11.76507 (113*2π)/5205 weeks
114-10.89247 -4.427 (114*2π)/5205 weeks
1153.22536 -12.61794 (115*2π)/5205 weeks
11615.76588 -3.90741 (116*2π)/5204 weeks
11713.22397 10.87321 (117*2π)/5204 weeks
118.76648 13.79957 (118*2π)/5204 weeks
119-6.70598 5.60758 (119*2π)/5204 weeks
120-2.91986 -2.47521 (120*2π)/5204 weeks
1213.01215 -2.68421 (121*2π)/5204 weeks
1225.75299 .65259 (122*2π)/5204 weeks
1234.54901 4.23014 (123*2π)/5204 weeks
124.40038 3.99159 (124*2π)/5204 weeks
125.47217 -.93003 (125*2π)/5204 weeks
1266.06228 -1.80598 (126*2π)/5204 weeks
1279.84634 2.70184 (127*2π)/5204 weeks
1288.71686 9.87993 (128*2π)/5204 weeks
129-.69202 13.72177 (129*2π)/5204 weeks
130-8.3901 6.73681 (130*2π)/5204 weeks
131-7.49154 -2.38508 (131*2π)/5204 weeks
132.52798 -7.39328 (132*2π)/5204 weeks
1338.13315 -2.35844 (133*2π)/5204 weeks
1347.76584 4.82244 (134*2π)/5204 weeks
135.02776 8.40655 (135*2π)/5204 weeks
136-4.93566 -.23145 (136*2π)/5204 weeks
1373.6968 -6.36278 (137*2π)/5204 weeks
13811.38046 .41067 (138*2π)/5204 weeks
1397.93819 10.7783 (139*2π)/5204 weeks
140-4.24011 11.26161 (140*2π)/5204 weeks
141-8.29505 .56064 (141*2π)/5204 weeks
142-1.50693 -7.48262 (142*2π)/5204 weeks
1438.97089 -4.31851 (143*2π)/5204 weeks
1448.18586 5.59652 (144*2π)/5204 weeks
145.68629 6.92848 (145*2π)/5204 weeks
146-2.28193 1.20429 (146*2π)/5204 weeks
1472.52596 -2.42786 (147*2π)/5204 weeks
1486.58706 1.18441 (148*2π)/5204 weeks
1494.74212 6.1459 (149*2π)/5203 weeks
150-1.23431 7.45967 (150*2π)/5203 weeks
151-4.60881 .86218 (151*2π)/5203 weeks
152-.63895 -2.70156 (152*2π)/5203 weeks
1532.24499 -2.76363 (153*2π)/5203 weeks
1544.91889 -2.09806 (154*2π)/5203 weeks
1557.50211 .31151 (155*2π)/5203 weeks
1567.1055 5.43359 (156*2π)/5203 weeks
1572.48101 8.96264 (157*2π)/5203 weeks
158-4.99212 6.03643 (158*2π)/5203 weeks
159-5.172 -2.44317 (159*2π)/5203 weeks
1602.59566 -6.45223 (160*2π)/5203 weeks
1619.4036 -.09326 (161*2π)/5203 weeks
1625.33436 8.07554 (162*2π)/5203 weeks
163-4.28898 6.69499 (163*2π)/5203 weeks
164-5.92087 -2.86591 (164*2π)/5203 weeks
1652.34795 -9.38301 (165*2π)/5203 weeks
16612.88169 -3.40051 (166*2π)/5203 weeks
16711.99325 8.53875 (167*2π)/5203 weeks
168.63778 14.31856 (168*2π)/5203 weeks
169-10.51945 5.7102 (169*2π)/5203 weeks
170-6.98393 -7.55672 (170*2π)/5203 weeks
1715.36587 -10.60823 (171*2π)/5203 weeks
17214.02242 -.76496 (172*2π)/5203 weeks
1737.79256 10.01346 (173*2π)/5203 weeks
174-2.35928 8.66943 (174*2π)/5203 weeks
175-4.50674 -.64773 (175*2π)/5203 weeks
1763.42695 -3.96307 (176*2π)/5203 weeks
1777.79016 2.10095 (177*2π)/5203 weeks
1783.13196 8.67277 (178*2π)/5203 weeks
179-5.87283 5.59898 (179*2π)/5203 weeks
180-4.93655 -3.83164 (180*2π)/5203 weeks
1812.27067 -6.53257 (181*2π)/5203 weeks
1828.05335 -2.08798 (182*2π)/5203 weeks
1835.65661 3.33439 (183*2π)/5203 weeks
1843.34514 3.40059 (184*2π)/5203 weeks
185.95362 3.12345 (185*2π)/5203 weeks
1862.18883 .38927 (186*2π)/5203 weeks
1873.59221 2.11106 (187*2π)/5203 weeks
1883.05966 3.55945 (188*2π)/5203 weeks
189.91964 4.62908 (189*2π)/5203 weeks
190-.3501 2.57253 (190*2π)/5203 weeks
191-1.05018 3.73216 (191*2π)/5203 weeks
192-4.23606 .0714 (192*2π)/5203 weeks
193-2.2566 -3.95573 (193*2π)/5203 weeks
1942.57862 -6.99488 (194*2π)/5203 weeks
1959.5086 -2.31363 (195*2π)/5203 weeks
1966.33636 6.13839 (196*2π)/5203 weeks
197-1.79103 5.08307 (197*2π)/5203 weeks
198-2.91326 -3.42426 (198*2π)/5203 weeks
1996.66598 -6.53853 (199*2π)/5203 weeks
20012.38292 3.24029 (200*2π)/5203 weeks
2015.17975 12.4391 (201*2π)/5203 weeks
202-7.32519 10.13617 (202*2π)/5203 weeks
203-9.94955 -3.92508 (203*2π)/5203 weeks
2041.82404 -10.04445 (204*2π)/5203 weeks
20510.25915 -1.74886 (205*2π)/5203 weeks
2064.55417 7.37851 (206*2π)/5203 weeks
207-4.32628 2.98119 (207*2π)/5203 weeks
208-.73739 -6.21149 (208*2π)/5203 weeks
2099.36493 -4.02782 (209*2π)/5202 weeks
21010.3625 6.70398 (210*2π)/5202 weeks
211-.3044 13.03534 (211*2π)/5202 weeks
212-11.43021 3.79655 (212*2π)/5202 weeks
213-5.77189 -9.5485 (213*2π)/5202 weeks
2146.93041 -9.63528 (214*2π)/5202 weeks
21512.71904 1.84544 (215*2π)/5202 weeks
2163.40814 10.3542 (216*2π)/5202 weeks
217-5.58736 5.12712 (217*2π)/5202 weeks
218-4.63097 -4.35153 (218*2π)/5202 weeks
2194.6075 -5.98424 (219*2π)/5202 weeks
2207.45115 1.5727 (220*2π)/5202 weeks
2212.12372 6.1929 (221*2π)/5202 weeks
222-4.40645 2.78284 (222*2π)/5202 weeks
223-2.89203 -5.06273 (223*2π)/5202 weeks
2245.08606 -5.5171 (224*2π)/5202 weeks
2256.72124 .65826 (225*2π)/5202 weeks
2263.74866 4.16438 (226*2π)/5202 weeks
227-.96472 1.75705 (227*2π)/5202 weeks
2281.22563 -1.03964 (228*2π)/5202 weeks
2293.16787 -.31305 (229*2π)/5202 weeks
2302.60966 3.01775 (230*2π)/5202 weeks
231-1.50847 1.49015 (231*2π)/5202 weeks
232-.22237 -1.93265 (232*2π)/5202 weeks
2332.11839 -1.78682 (233*2π)/5202 weeks
2342.59082 .06035 (234*2π)/5202 weeks
235-.55373 .02053 (235*2π)/5202 weeks
236.90337 -4.67871 (236*2π)/5202 weeks
2377.23557 -3.89852 (237*2π)/5202 weeks
2389.43119 3.22955 (238*2π)/5202 weeks
2392.50406 10.15749 (239*2π)/5202 weeks
240-8.80608 5.98783 (240*2π)/5202 weeks
241-9.32393 -8.35167 (241*2π)/5202 weeks
2425.04591 -15.83594 (242*2π)/5202 weeks
24318.86564 -3.16302 (243*2π)/5202 weeks
24411.26076 13.82205 (244*2π)/5202 weeks
245-6.17756 14.30434 (245*2π)/5202 weeks
246-15.09095 -1.56245 (246*2π)/5202 weeks
247-3.22891 -15.8582 (247*2π)/5202 weeks
24813.41622 -9.94412 (248*2π)/5202 weeks
24912.48854 6.25431 (249*2π)/5202 weeks
250-.71701 9.51586 (250*2π)/5202 weeks
251-7.04022 -1.12431 (251*2π)/5202 weeks
252.98467 -9.18097 (252*2π)/5202 weeks
25310.67956 -4.97374 (253*2π)/5202 weeks
2549.79759 6.66696 (254*2π)/5202 weeks
255-2.25158 8.39276 (255*2π)/5202 weeks
256-6.32586 -1.3611 (256*2π)/5202 weeks
257-.4268 -7.50535 (257*2π)/5202 weeks
2586.5078 -5.05249 (258*2π)/5202 weeks
2596.245 -.94462 (259*2π)/5202 weeks
2605.92412   (260*2π)/5202 weeks
2616.245 .94462 (261*2π)/5202 weeks
2626.5078 5.05249 (262*2π)/5202 weeks
263-.4268 7.50535 (263*2π)/5202 weeks
264-6.32586 1.3611 (264*2π)/5202 weeks
265-2.25158 -8.39276 (265*2π)/5202 weeks
2669.79759 -6.66696 (266*2π)/5202 weeks
26710.67956 4.97374 (267*2π)/5202 weeks
268.98467 9.18097 (268*2π)/5202 weeks
269-7.04022 1.12431 (269*2π)/5202 weeks
270-.71701 -9.51586 (270*2π)/5202 weeks
27112.48854 -6.25431 (271*2π)/5202 weeks
27213.41622 9.94412 (272*2π)/5202 weeks
273-3.22891 15.8582 (273*2π)/5202 weeks
274-15.09095 1.56245 (274*2π)/5202 weeks
275-6.17756 -14.30434 (275*2π)/5202 weeks
27611.26076 -13.82205 (276*2π)/5202 weeks
27718.86564 3.16302 (277*2π)/5202 weeks
2785.04591 15.83594 (278*2π)/5202 weeks
279-9.32393 8.35167 (279*2π)/5202 weeks
280-8.80608 -5.98783 (280*2π)/5202 weeks
2812.50406 -10.15749 (281*2π)/5202 weeks
2829.43119 -3.22955 (282*2π)/5202 weeks
2837.23557 3.89852 (283*2π)/5202 weeks
284.90337 4.67871 (284*2π)/5202 weeks
285-.55373 -.02053 (285*2π)/5202 weeks
2862.59082 -.06035 (286*2π)/5202 weeks
2872.11839 1.78682 (287*2π)/5202 weeks
288-.22237 1.93265 (288*2π)/5202 weeks
289-1.50847 -1.49015 (289*2π)/5202 weeks
2902.60966 -3.01775 (290*2π)/5202 weeks
2913.16787 .31305 (291*2π)/5202 weeks
2921.22563 1.03964 (292*2π)/5202 weeks
293-.96472 -1.75705 (293*2π)/5202 weeks
2943.74866 -4.16438 (294*2π)/5202 weeks
2956.72124 -.65826 (295*2π)/5202 weeks
2965.08606 5.5171 (296*2π)/5202 weeks
297-2.89203 5.06273 (297*2π)/5202 weeks
298-4.40645 -2.78284 (298*2π)/5202 weeks
2992.12372 -6.1929 (299*2π)/5202 weeks
3007.45115 -1.5727 (300*2π)/5202 weeks
3014.6075 5.98424 (301*2π)/5202 weeks
302-4.63097 4.35153 (302*2π)/5202 weeks
303-5.58736 -5.12712 (303*2π)/5202 weeks
3043.40814 -10.3542 (304*2π)/5202 weeks
30512.71904 -1.84544 (305*2π)/5202 weeks
3066.93041 9.63528 (306*2π)/5202 weeks
307-5.77189 9.5485 (307*2π)/5202 weeks
308-11.43021 -3.79655 (308*2π)/5202 weeks
309-.3044 -13.03534 (309*2π)/5202 weeks
31010.3625 -6.70398 (310*2π)/5202 weeks
3119.36493 4.02782 (311*2π)/5202 weeks
312-.73739 6.21149 (312*2π)/5202 weeks
313-4.32628 -2.98119 (313*2π)/5202 weeks
3144.55417 -7.37851 (314*2π)/5202 weeks
31510.25915 1.74886 (315*2π)/5202 weeks
3161.82404 10.04445 (316*2π)/5202 weeks
317-9.94955 3.92508 (317*2π)/5202 weeks
318-7.32519 -10.13617 (318*2π)/5202 weeks
3195.17975 -12.4391 (319*2π)/5202 weeks
32012.38292 -3.24029 (320*2π)/5202 weeks
3216.66598 6.53853 (321*2π)/5202 weeks
322-2.91326 3.42426 (322*2π)/5202 weeks
323-1.79103 -5.08307 (323*2π)/5202 weeks
3246.33636 -6.13839 (324*2π)/5202 weeks
3259.5086 2.31363 (325*2π)/5202 weeks
3262.57862 6.99488 (326*2π)/5202 weeks
327-2.2566 3.95573 (327*2π)/5202 weeks
328-4.23606 -.0714 (328*2π)/5202 weeks
329-1.05018 -3.73216 (329*2π)/5202 weeks
330-.3501 -2.57253 (330*2π)/5202 weeks
331.91964 -4.62908 (331*2π)/5202 weeks
3323.05966 -3.55945 (332*2π)/5202 weeks
3333.59221 -2.11106 (333*2π)/5202 weeks
3342.18883 -.38927 (334*2π)/5202 weeks
335.95362 -3.12345 (335*2π)/5202 weeks
3363.34514 -3.40059 (336*2π)/5202 weeks
3375.65661 -3.33439 (337*2π)/5202 weeks
3388.05335 2.08798 (338*2π)/5202 weeks
3392.27067 6.53257 (339*2π)/5202 weeks
340-4.93655 3.83164 (340*2π)/5202 weeks
341-5.87283 -5.59898 (341*2π)/5202 weeks
3423.13196 -8.67277 (342*2π)/5202 weeks
3437.79016 -2.10095 (343*2π)/5202 weeks
3443.42695 3.96307 (344*2π)/5202 weeks
345-4.50674 .64773 (345*2π)/5202 weeks
346-2.35928 -8.66943 (346*2π)/5202 weeks
3477.79256 -10.01346 (347*2π)/5201 weeks
34814.02242 .76496 (348*2π)/5201 weeks
3495.36587 10.60823 (349*2π)/5201 weeks
350-6.98393 7.55672 (350*2π)/5201 weeks
351-10.51945 -5.7102 (351*2π)/5201 weeks
352.63778 -14.31856 (352*2π)/5201 weeks
35311.99325 -8.53875 (353*2π)/5201 weeks
35412.88169 3.40051 (354*2π)/5201 weeks
3552.34795 9.38301 (355*2π)/5201 weeks
356-5.92087 2.86591 (356*2π)/5201 weeks
357-4.28898 -6.69499 (357*2π)/5201 weeks
3585.33436 -8.07554 (358*2π)/5201 weeks
3599.4036 .09326 (359*2π)/5201 weeks
3602.59566 6.45223 (360*2π)/5201 weeks
361-5.172 2.44317 (361*2π)/5201 weeks
362-4.99212 -6.03643 (362*2π)/5201 weeks
3632.48101 -8.96264 (363*2π)/5201 weeks
3647.1055 -5.43359 (364*2π)/5201 weeks
3657.50211 -.31151 (365*2π)/5201 weeks
3664.91889 2.09806 (366*2π)/5201 weeks
3672.24499 2.76363 (367*2π)/5201 weeks
368-.63895 2.70156 (368*2π)/5201 weeks
369-4.60881 -.86218 (369*2π)/5201 weeks
370-1.23431 -7.45967 (370*2π)/5201 weeks
3714.74212 -6.1459 (371*2π)/5201 weeks
3726.58706 -1.18441 (372*2π)/5201 weeks
3732.52596 2.42786 (373*2π)/5201 weeks
374-2.28193 -1.20429 (374*2π)/5201 weeks
375.68629 -6.92848 (375*2π)/5201 weeks
3768.18586 -5.59652 (376*2π)/5201 weeks
3778.97089 4.31851 (377*2π)/5201 weeks
378-1.50693 7.48262 (378*2π)/5201 weeks
379-8.29505 -.56064 (379*2π)/5201 weeks
380-4.24011 -11.26161 (380*2π)/5201 weeks
3817.93819 -10.7783 (381*2π)/5201 weeks
38211.38046 -.41067 (382*2π)/5201 weeks
3833.6968 6.36278 (383*2π)/5201 weeks
384-4.93566 .23145 (384*2π)/5201 weeks
385.02776 -8.40655 (385*2π)/5201 weeks
3867.76584 -4.82244 (386*2π)/5201 weeks
3878.13315 2.35844 (387*2π)/5201 weeks
388.52798 7.39328 (388*2π)/5201 weeks
389-7.49154 2.38508 (389*2π)/5201 weeks
390-8.3901 -6.73681 (390*2π)/5201 weeks
391-.69202 -13.72177 (391*2π)/5201 weeks
3928.71686 -9.87993 (392*2π)/5201 weeks
3939.84634 -2.70184 (393*2π)/5201 weeks
3946.06228 1.80598 (394*2π)/5201 weeks
395.47217 .93003 (395*2π)/5201 weeks
396.40038 -3.99159 (396*2π)/5201 weeks
3974.54901 -4.23014 (397*2π)/5201 weeks
3985.75299 -.65259 (398*2π)/5201 weeks
3993.01215 2.68421 (399*2π)/5201 weeks
400-2.91986 2.47521 (400*2π)/5201 weeks
401-6.70598 -5.60758 (401*2π)/5201 weeks
402.76648 -13.79957 (402*2π)/5201 weeks
40313.22397 -10.87321 (403*2π)/5201 weeks
40415.76588 3.90741 (404*2π)/5201 weeks
4053.22536 12.61794 (405*2π)/5201 weeks
406-10.89247 4.427 (406*2π)/5201 weeks
407-8.81454 -11.76507 (407*2π)/5201 weeks
4086.87103 -15.21602 (408*2π)/5201 weeks
40916.03673 -3.09493 (409*2π)/5201 weeks
4108.86138 11.8299 (410*2π)/5201 weeks
411-9.92112 10.25094 (411*2π)/5201 weeks
412-15.13962 -9.11865 (412*2π)/5201 weeks
413-.38582 -20.57519 (413*2π)/5201 weeks
41416.38827 -13.76857 (414*2π)/5201 weeks
41517.27053 4.78234 (415*2π)/5201 weeks
416.53693 12.31985 (416*2π)/5201 weeks
417-12.35227 -.68734 (417*2π)/5201 weeks
418-3.39495 -16.44982 (418*2π)/5201 weeks
41912.68294 -14.24547 (419*2π)/5201 weeks
42018.68418 .81109 (420*2π)/5201 weeks
4216.51846 11.55155 (421*2π)/5201 weeks
422-6.12091 6.09593 (422*2π)/5201 weeks
423-6.05332 -6.50031 (423*2π)/5201 weeks
4244.417 -9.84717 (424*2π)/5201 weeks
4258.96953 -1.70657 (425*2π)/5201 weeks
4263.86192 4.4574 (426*2π)/5201 weeks
427-3.47485 1.35283 (427*2π)/5201 weeks
428-1.77589 -5.61149 (428*2π)/5201 weeks
4293.36528 -5.15281 (429*2π)/5201 weeks
4305.26282 -.51974 (430*2π)/5201 weeks
431-1.29918 1.95164 (431*2π)/5201 weeks
432-3.10242 -4.34287 (432*2π)/5201 weeks
433.66402 -5.66937 (433*2π)/5201 weeks
434.63388 -3.40927 (434*2π)/5201 weeks
435-3.10029 -5.77675 (435*2π)/5201 weeks
436-.47523 -13.87391 (436*2π)/5201 weeks
43712.31322 -14.6983 (437*2π)/5201 weeks
43819.75188 -.47172 (438*2π)/5201 weeks
4399.53901 16.29178 (439*2π)/5201 weeks
440-14.40089 11.6447 (440*2π)/5201 weeks
441-17.09991 -12.04174 (441*2π)/5201 weeks
442.71574 -25.7537 (442*2π)/5201 weeks
44324.28527 -14.04262 (443*2π)/5201 weeks
44420.18491 12.61228 (444*2π)/5201 weeks
445-3.65519 19.92167 (445*2π)/5201 weeks
446-21.71574 -.87846 (446*2π)/5201 weeks
447-4.93552 -22.36303 (447*2π)/5201 weeks
44813.73642 -13.37369 (448*2π)/5201 weeks
44916.05568 3.55365 (449*2π)/5201 weeks
450-1.59571 14.79436 (450*2π)/5201 weeks
451-17.58039 -.97462 (451*2π)/5201 weeks
452-9.80751 -18.35899 (452*2π)/5201 weeks
4537.9602 -19.29831 (453*2π)/5201 weeks
45413.33603 -3.42349 (454*2π)/5201 weeks
455-.01439 .91345 (455*2π)/5201 weeks
456-2.41238 -10.27209 (456*2π)/5201 weeks
4578.4764 -16.723 (457*2π)/5201 weeks
45822.76739 -2.11885 (458*2π)/5201 weeks
4599.55271 17.69771 (459*2π)/5201 weeks
460-13.05899 12.78926 (460*2π)/5201 weeks
461-21.06321 -8.49554 (461*2π)/5201 weeks
462-2.72651 -24.4458 (462*2π)/5201 weeks
46313.02968 -13.59158 (463*2π)/5201 weeks
46410.2261 -.09635 (464*2π)/5201 weeks
465-1.40176 .2621 (465*2π)/5201 weeks
466-2.01693 -9.47091 (466*2π)/5201 weeks
4677.82338 -9.43051 (467*2π)/5201 weeks
4687.11708 -1.56807 (468*2π)/5201 weeks
4691.4952 -.66024 (469*2π)/5201 weeks
470.55651 -4.96334 (470*2π)/5201 weeks
4714.10825 -3.82923 (471*2π)/5201 weeks
472.85628 2.69381 (472*2π)/5201 weeks
473-9.48067 .724 (473*2π)/5201 weeks
474-13.72337 -13.05153 (474*2π)/5201 weeks
475-.5792 -21.7571 (475*2π)/5201 weeks
47613.21782 -17.39067 (476*2π)/5201 weeks
47714.57932 .77538 (477*2π)/5201 weeks
478-3.31353 5.54366 (478*2π)/5201 weeks
479-12.48591 -7.05352 (479*2π)/5201 weeks
480-2.69371 -24.73625 (480*2π)/5201 weeks
48118.48213 -13.54749 (481*2π)/5201 weeks
4828.54881 6.05484 (482*2π)/5201 weeks
483-11.96868 2.99589 (483*2π)/5201 weeks
484-16.65262 -22.21886 (484*2π)/5201 weeks
48512.1095 -37.45183 (485*2π)/5201 weeks
48640.19159 -8.26684 (486*2π)/5201 weeks
48721.15615 34.79491 (487*2π)/5201 weeks
488-36.63044 35.29275 (488*2π)/5201 weeks
489-58.90775 -26.67985 (489*2π)/5201 weeks
490-10.02919 -68.39345 (490*2π)/5201 weeks
49143.59866 -43.06136 (491*2π)/5201 weeks
49238.61346 14.38659 (492*2π)/5201 weeks
493-12.80974 25.32785 (493*2π)/5201 weeks
494-34.85029 -11.17179 (494*2π)/5201 weeks
495-16.2139 -42.9028 (495*2π)/5201 weeks
49617.86259 -32.12608 (496*2π)/5201 weeks
4977.43269 -9.26579 (497*2π)/5201 weeks
498-8.33224 -20.61185 (498*2π)/5201 weeks
4997.37415 -42.1106 (499*2π)/5201 weeks
50034.63919 -25.06036 (500*2π)/5201 weeks
50124.73504 10.00892 (501*2π)/5201 weeks
502-15.91029 11.75489 (502*2π)/5201 weeks
503-29.02861 -24.79022 (503*2π)/5201 weeks
504-6.01293 -52.19436 (504*2π)/5201 weeks
50533.33205 -36.07569 (505*2π)/5201 weeks
50618.32898 3.84564 (506*2π)/5201 weeks
507-23.8867 -1.37693 (507*2π)/5201 weeks
508-35.27591 -57.30271 (508*2π)/5201 weeks
50933.2026 -79.83596 (509*2π)/5201 weeks
51055.43871 -16.06643 (510*2π)/5201 weeks
51113.03942 18.79783 (511*2π)/5201 weeks
512-60.51137 -10.67708 (512*2π)/5201 weeks
513-31.2699 -115.9478 (513*2π)/5201 weeks
51478.80399 -91.68752 (514*2π)/5201 weeks
51569.65601 32.01783 (515*2π)/5201 weeks
516-100.6687 67.69042 (516*2π)/5201 weeks
517-256.1836 -165.4408 (517*2π)/5201 weeks
518-62.70691 -483.9766 (518*2π)/5201 weeks

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