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Fourier Analysis of SDS (ProShares UltraShort S&P500)


SDS (ProShares UltraShort S&P500) appears to have interesting cyclic behaviour every 62 weeks (52.2043*sine), 57 weeks (33.6228*sine), and 45 weeks (18.521*cosine).

SDS (ProShares UltraShort S&P500) has an average price of 377.48 (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 7/13/2006 to 6/18/2018 for SDS (ProShares UltraShort S&P500), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0377.4755   0 
1103.7549 395.8591 (1*2π)/624624 weeks
2-86.62464 154.9403 (2*2π)/624312 weeks
3-55.26525 12.87634 (3*2π)/624208 weeks
447.35353 -3.28614 (4*2π)/624156 weeks
564.28897 61.23633 (5*2π)/624125 weeks
610.48297 85.7606 (6*2π)/624104 weeks
7-31.8441 47.11121 (7*2π)/62489 weeks
8-10.61436 -1.55892 (8*2π)/62478 weeks
938.24218 14.43681 (9*2π)/62469 weeks
1015.05748 52.20425 (10*2π)/62462 weeks
11-9.18765 33.62278 (11*2π)/62457 weeks
12-11.3814 22.17445 (12*2π)/62452 weeks
13-3.22746 2.41053 (13*2π)/62448 weeks
1418.52095 10.36023 (14*2π)/62445 weeks
1511.2625 25.34306 (15*2π)/62442 weeks
162.14235 22.55641 (16*2π)/62439 weeks
17-1.56045 16.98952 (17*2π)/62437 weeks
182.67038 13.04 (18*2π)/62435 weeks
19-1.587 16.34385 (19*2π)/62433 weeks
202.54954 6.33921 (20*2π)/62431 weeks
217.46565 11.68827 (21*2π)/62430 weeks
227.20969 12.64077 (22*2π)/62428 weeks
235.79182 16.69084 (23*2π)/62427 weeks
24.48943 18.85429 (24*2π)/62426 weeks
25-5.13718 12.63219 (25*2π)/62425 weeks
262.20883 5.13433 (26*2π)/62424 weeks
274.41545 13.07075 (27*2π)/62423 weeks
28-1.70564 16.69026 (28*2π)/62422 weeks
29-10.13589 7.08111 (29*2π)/62422 weeks
303.24252 -4.60098 (30*2π)/62421 weeks
3111.5863 5.07162 (31*2π)/62420 weeks
329.72648 15.1758 (32*2π)/62420 weeks
33-3.66552 20.03627 (33*2π)/62419 weeks
34-11.28401 5.10198 (34*2π)/62418 weeks
352.32559 -6.76596 (35*2π)/62418 weeks
3616.27643 1.78601 (36*2π)/62417 weeks
3712.41638 20.93323 (37*2π)/62417 weeks
38-8.40228 21.83552 (38*2π)/62416 weeks
39-11.41045 1.66728 (39*2π)/62416 weeks
402.61327 -3.00112 (40*2π)/62416 weeks
418.63935 4.63231 (41*2π)/62415 weeks
423.85153 11.72556 (42*2π)/62415 weeks
43-1.14075 8.46817 (43*2π)/62415 weeks
44-.95434 5.17145 (44*2π)/62414 weeks
45.69919 3.67048 (45*2π)/62414 weeks
464.56906 3.7158 (46*2π)/62414 weeks
472.15961 9.60779 (47*2π)/62413 weeks
48-1.22794 4.76937 (48*2π)/62413 weeks
492.80512 4.91452 (49*2π)/62413 weeks
50.13092 5.90885 (50*2π)/62412 weeks
51.54565 4.61087 (51*2π)/62412 weeks
52.12286 2.27648 (52*2π)/62412 weeks
534.52538 .84847 (53*2π)/62412 weeks
545.39256 6.47493 (54*2π)/62412 weeks
554.00142 7.70373 (55*2π)/62411 weeks
56.21383 7.6547 (56*2π)/62411 weeks
57-.75185 4.85359 (57*2π)/62411 weeks
581.94532 3.04186 (58*2π)/62411 weeks
593.42035 6.31622 (59*2π)/62411 weeks
60.26835 6.90446 (60*2π)/62410 weeks
61-2.75942 4.65328 (61*2π)/62410 weeks
62-1.4691 -.80694 (62*2π)/62410 weeks
635.93234 -.80104 (63*2π)/62410 weeks
646.95068 7.99314 (64*2π)/62410 weeks
65-.4789 8.42681 (65*2π)/62410 weeks
66-2.56552 3.079 (66*2π)/6249 weeks
671.09884 .30098 (67*2π)/6249 weeks
684.86557 2.07726 (68*2π)/6249 weeks
692.88222 6.8644 (69*2π)/6249 weeks
70-1.42474 3.47079 (70*2π)/6249 weeks
712.64527 .6908 (71*2π)/6249 weeks
724.8593 2.84463 (72*2π)/6249 weeks
734.06951 7.03882 (73*2π)/6249 weeks
74-.7517 6.48341 (74*2π)/6248 weeks
75-.82288 1.16864 (75*2π)/6248 weeks
762.84842 3.10384 (76*2π)/6248 weeks
772.48478 3.14706 (77*2π)/6248 weeks
781.3349 5.43182 (78*2π)/6248 weeks
79-.43167 1.06536 (79*2π)/6248 weeks
805.48306 1.37151 (80*2π)/6248 weeks
814.98919 7.46143 (81*2π)/6248 weeks
82-1.24639 8.24119 (82*2π)/6248 weeks
83-4.51573 3.20218 (83*2π)/6248 weeks
84.63785 -2.47224 (84*2π)/6247 weeks
855.52634 2.09403 (85*2π)/6247 weeks
862.34706 5.10109 (86*2π)/6247 weeks
871.89185 5.51471 (87*2π)/6247 weeks
88-3.5379 4.05822 (88*2π)/6247 weeks
89.33782 -3.31855 (89*2π)/6247 weeks
907.1944 1.24624 (90*2π)/6247 weeks
914.75864 6.70536 (91*2π)/6247 weeks
92-.61014 7.5726 (92*2π)/6247 weeks
93-3.3148 1.89245 (93*2π)/6247 weeks
941.47037 -.83008 (94*2π)/6247 weeks
954.52575 .66556 (95*2π)/6247 weeks
965.78907 5.86272 (96*2π)/6247 weeks
97-1.33301 8.16159 (97*2π)/6246 weeks
98-4.14187 1.53107 (98*2π)/6246 weeks
99.06572 -2.39998 (99*2π)/6246 weeks
1005.13697 .16892 (100*2π)/6246 weeks
1014.42801 4.51154 (101*2π)/6246 weeks
102.31238 5.04687 (102*2π)/6246 weeks
103-1.01617 1.67054 (103*2π)/6246 weeks
1041.81824 .61368 (104*2π)/6246 weeks
1052.92962 2.89436 (105*2π)/6246 weeks
106.30108 3.93237 (106*2π)/6246 weeks
107.37948 .48182 (107*2π)/6246 weeks
1083.04801 2.30046 (108*2π)/6246 weeks
109.55599 3.28961 (109*2π)/6246 weeks
110-.58942 1.42705 (110*2π)/6246 weeks
1111.49221 -.93693 (111*2π)/6246 weeks
1124.87026 .90066 (112*2π)/6246 weeks
1134.00102 4.7933 (113*2π)/6246 weeks
114-.02517 4.73221 (114*2π)/6245 weeks
115-1.70511 1.2824 (115*2π)/6245 weeks
1162.01738 -1.31831 (116*2π)/6245 weeks
1175.86903 1.84621 (117*2π)/6245 weeks
1183.22985 6.52089 (118*2π)/6245 weeks
119-2.0527 5.97112 (119*2π)/6245 weeks
120-3.79459 -.16318 (120*2π)/6245 weeks
1211.11344 -2.72251 (121*2π)/6245 weeks
1225.49104 -.65447 (122*2π)/6245 weeks
1235.0293 4.68931 (123*2π)/6245 weeks
124-.69426 5.28673 (124*2π)/6245 weeks
125-2.26666 .4756 (125*2π)/6245 weeks
1262.35302 -2.42174 (126*2π)/6245 weeks
1275.77472 .96602 (127*2π)/6245 weeks
1284.16857 4.74344 (128*2π)/6245 weeks
129.26776 5.91051 (129*2π)/6245 weeks
130-2.83621 1.63054 (130*2π)/6245 weeks
1311.00934 -1.94893 (131*2π)/6245 weeks
1324.69449 .17591 (132*2π)/6245 weeks
1333.76083 3.48433 (133*2π)/6245 weeks
1341.00769 4.69604 (134*2π)/6245 weeks
135-1.27432 2.11044 (135*2π)/6245 weeks
1361.15954 -.41498 (136*2π)/6245 weeks
1373.74781 .47754 (137*2π)/6245 weeks
1383.33919 4.15584 (138*2π)/6245 weeks
139-.37588 4.62473 (139*2π)/6244 weeks
140-2.11683 .7673 (140*2π)/6244 weeks
1411.48907 -1.18356 (141*2π)/6244 weeks
1423.37103 .51977 (142*2π)/6244 weeks
1432.22472 2.61133 (143*2π)/6244 weeks
1441.06428 2.13116 (144*2π)/6244 weeks
1451.24572 1.94896 (145*2π)/6244 weeks
146.33901 1.15098 (146*2π)/6244 weeks
1471.44218 -.23123 (147*2π)/6244 weeks
1483.23724 .9989 (148*2π)/6244 weeks
1491.73863 2.39631 (149*2π)/6244 weeks
150.95297 1.05202 (150*2π)/6244 weeks
1512.97342 .71272 (151*2π)/6244 weeks
1522.84891 2.27897 (152*2π)/6244 weeks
1531.77675 2.42318 (153*2π)/6244 weeks
154.76435 3.08149 (154*2π)/6244 weeks
155.02177 .98736 (155*2π)/6244 weeks
1561.77822 .53001 (156*2π)/6244 weeks
1571.05533 1.11021 (157*2π)/6244 weeks
1582.00705 .1958 (158*2π)/6244 weeks
1592.94701 1.51515 (159*2π)/6244 weeks
1602.8432 2.60088 (160*2π)/6244 weeks
161.08124 3.02991 (161*2π)/6244 weeks
162.31416 -.65145 (162*2π)/6244 weeks
1633.46711 .70645 (163*2π)/6244 weeks
1641.82925 3.35649 (164*2π)/6244 weeks
165.35118 1.87193 (165*2π)/6244 weeks
166.81893 .22806 (166*2π)/6244 weeks
1672.63386 .44927 (167*2π)/6244 weeks
1682.54932 2.73947 (168*2π)/6244 weeks
169.70283 2.49524 (169*2π)/6244 weeks
170-.2536 1.24225 (170*2π)/6244 weeks
1711.15695 -1.0089 (171*2π)/6244 weeks
1723.82013 1.28504 (172*2π)/6244 weeks
1731.30873 2.87203 (173*2π)/6244 weeks
174.73857 1.43525 (174*2π)/6244 weeks
1751.15657 .64017 (175*2π)/6244 weeks
1762.09686 .99693 (176*2π)/6244 weeks
1771.44528 1.63237 (177*2π)/6244 weeks
1781.3135 1.25916 (178*2π)/6244 weeks
1791.37146 1.73402 (179*2π)/6243 weeks
180.47758 .20735 (180*2π)/6243 weeks
1812.99993 .37662 (181*2π)/6243 weeks
1821.85216 2.06535 (182*2π)/6243 weeks
1831.23176 1.14582 (183*2π)/6243 weeks
1841.74942 1.11904 (184*2π)/6243 weeks
1851.58614 1.37521 (185*2π)/6243 weeks
186.72289 .95351 (186*2π)/6243 weeks
1872.06726 .21059 (187*2π)/6243 weeks
1882.47468 .8121 (188*2π)/6243 weeks
1893.09588 2.13391 (189*2π)/6243 weeks
1901.05864 2.98029 (190*2π)/6243 weeks
191-.00645 1.32565 (191*2π)/6243 weeks
1921.05131 .0814 (192*2π)/6243 weeks
1932.30708 .86659 (193*2π)/6243 weeks
1941.55615 1.90128 (194*2π)/6243 weeks
195.52219 1.58535 (195*2π)/6243 weeks
196.88494 -.00297 (196*2π)/6243 weeks
1971.93077 .09451 (197*2π)/6243 weeks
1982.80356 .92296 (198*2π)/6243 weeks
1992.32209 2.52051 (199*2π)/6243 weeks
200.73483 2.63734 (200*2π)/6243 weeks
201-.34293 1.38656 (201*2π)/6243 weeks
202-.03177 -.43344 (202*2π)/6243 weeks
2032.47454 -.65358 (203*2π)/6243 weeks
2043.08112 1.55832 (204*2π)/6243 weeks
2051.59828 2.76607 (205*2π)/6243 weeks
206-.42446 1.77818 (206*2π)/6243 weeks
207.42699 -.6207 (207*2π)/6243 weeks
2082.24327 -.11431 (208*2π)/6243 weeks
2093.02871 1.28607 (209*2π)/6243 weeks
2101.30399 2.46942 (210*2π)/6243 weeks
211.4709 1.10897 (211*2π)/6243 weeks
212.72085 .5102 (212*2π)/6243 weeks
2132.22306 .21523 (213*2π)/6243 weeks
2142.21105 2.22033 (214*2π)/6243 weeks
215-.14495 1.96326 (215*2π)/6243 weeks
216-.11553 .22101 (216*2π)/6243 weeks
217.95041 -.95765 (217*2π)/6243 weeks
2182.86201 -.4599 (218*2π)/6243 weeks
2192.58254 1.16656 (219*2π)/6243 weeks
2202.66624 1.6549 (220*2π)/6243 weeks
221.73927 3.25343 (221*2π)/6243 weeks
222-1.0057 .00146 (222*2π)/6243 weeks
2231.32072 -.49236 (223*2π)/6243 weeks
2241.78282 -.03703 (224*2π)/6243 weeks
2252.06461 .77026 (225*2π)/6243 weeks
2261.25057 .77971 (226*2π)/6243 weeks
2271.94042 .00419 (227*2π)/6243 weeks
2281.55965 1.1097 (228*2π)/6243 weeks
2292.24724 -.10074 (229*2π)/6243 weeks
2302.66687 2.44611 (230*2π)/6243 weeks
231.5769 1.92928 (231*2π)/6243 weeks
232.42839 1.79256 (232*2π)/6243 weeks
233-.89682 -.09803 (233*2π)/6243 weeks
2341.55677 -2.02709 (234*2π)/6243 weeks
2354.05265 .62604 (235*2π)/6243 weeks
2362.16842 3.13276 (236*2π)/6243 weeks
237-.92693 2.24843 (237*2π)/6243 weeks
238-.54825 -1.26125 (238*2π)/6243 weeks
2392.93592 -1.07829 (239*2π)/6243 weeks
2402.95268 1.56651 (240*2π)/6243 weeks
241.95526 2.72356 (241*2π)/6243 weeks
242-1.57181 1.26404 (242*2π)/6243 weeks
243.15958 -2.81782 (243*2π)/6243 weeks
2443.87007 -1.21614 (244*2π)/6243 weeks
2453.65908 2.19493 (245*2π)/6243 weeks
246.58897 2.95226 (246*2π)/6243 weeks
247-.51817 .1585 (247*2π)/6243 weeks
2481.57832 -.64746 (248*2π)/6243 weeks
2491.84368 .88203 (249*2π)/6243 weeks
250.97074 .53696 (250*2π)/6242 weeks
2511.60507 -.1084 (251*2π)/6242 weeks
2521.91957 .50922 (252*2π)/6242 weeks
2532.44325 .79181 (253*2π)/6242 weeks
2541.7436 2.6856 (254*2π)/6242 weeks
255-.86529 1.49838 (255*2π)/6242 weeks
256.2122 -.70424 (256*2π)/6242 weeks
2571.70112 -.7514 (257*2π)/6242 weeks
2582.56639 1.40208 (258*2π)/6242 weeks
259-.18715 2.07603 (259*2π)/6242 weeks
260-.4797 -.38677 (260*2π)/6242 weeks
261.67002 -1.34239 (261*2π)/6242 weeks
2622.19317 -1.25713 (262*2π)/6242 weeks
2632.81371 .95304 (263*2π)/6242 weeks
264.91261 1.61449 (264*2π)/6242 weeks
265-.19333 -.01094 (265*2π)/6242 weeks
2661.04877 -1.80446 (266*2π)/6242 weeks
2673.67744 -.93813 (267*2π)/6242 weeks
2683.4237 2.11348 (268*2π)/6242 weeks
269.45904 2.52251 (269*2π)/6242 weeks
270-.62792 .52757 (270*2π)/6242 weeks
271.10576 -1.72584 (271*2π)/6242 weeks
2723.28974 -.67908 (272*2π)/6242 weeks
2732.27526 1.22815 (273*2π)/6242 weeks
2741.31834 1.62744 (274*2π)/6242 weeks
275-.30535 .40265 (275*2π)/6242 weeks
2761.30232 -.76832 (276*2π)/6242 weeks
2771.69625 .1252 (277*2π)/6242 weeks
2781.81071 .34159 (278*2π)/6242 weeks
2791.13181 1.39025 (279*2π)/6242 weeks
280-.30102 .49777 (280*2π)/6242 weeks
281.6903 -1.09897 (281*2π)/6242 weeks
2821.43541 -1.34939 (282*2π)/6242 weeks
2833.1178 -.36452 (283*2π)/6242 weeks
2842.46111 1.82108 (284*2π)/6242 weeks
285.07522 1.59225 (285*2π)/6242 weeks
286-.62652 -.19947 (286*2π)/6242 weeks
287.49752 -1.83476 (287*2π)/6242 weeks
2882.62351 -2.16656 (288*2π)/6242 weeks
2894.1862 .52758 (289*2π)/6242 weeks
2902.46814 3.0995 (290*2π)/6242 weeks
291-1.75916 2.22768 (291*2π)/6242 weeks
292-1.18353 -2.52581 (292*2π)/6242 weeks
2932.66997 -2.39617 (293*2π)/6242 weeks
2943.67988 -.01646 (294*2π)/6242 weeks
2952.37604 2.64068 (295*2π)/6242 weeks
296-1.31889 1.73601 (296*2π)/6242 weeks
297-1.07164 -2.24985 (297*2π)/6242 weeks
2982.97032 -3.06398 (298*2π)/6242 weeks
2993.6685 .53025 (299*2π)/6242 weeks
3001.5293 1.73764 (300*2π)/6242 weeks
301-.22334 .297 (301*2π)/6242 weeks
302.69497 -1.91515 (302*2π)/6242 weeks
3032.73513 -2.24183 (303*2π)/6242 weeks
3044.83639 .45463 (304*2π)/6242 weeks
3051.90541 3.35558 (305*2π)/6242 weeks
306-.89323 .46 (306*2π)/6242 weeks
307.88497 -1.7958 (307*2π)/6242 weeks
3082.5397 -1.04042 (308*2π)/6242 weeks
3093.18384 .66347 (309*2π)/6242 weeks
3102.16148 1.47531 (310*2π)/6242 weeks
311.78072 2.01399 (311*2π)/6242 weeks
312-1.24537   (312*2π)/6242 weeks
313.78072 -2.01399 (313*2π)/6242 weeks
3142.16148 -1.47531 (314*2π)/6242 weeks
3153.18384 -.66347 (315*2π)/6242 weeks
3162.5397 1.04042 (316*2π)/6242 weeks
317.88497 1.7958 (317*2π)/6242 weeks
318-.89323 -.46 (318*2π)/6242 weeks
3191.90541 -3.35558 (319*2π)/6242 weeks
3204.83639 -.45463 (320*2π)/6242 weeks
3212.73513 2.24183 (321*2π)/6242 weeks
322.69497 1.91515 (322*2π)/6242 weeks
323-.22334 -.297 (323*2π)/6242 weeks
3241.5293 -1.73764 (324*2π)/6242 weeks
3253.6685 -.53025 (325*2π)/6242 weeks
3262.97032 3.06398 (326*2π)/6242 weeks
327-1.07164 2.24985 (327*2π)/6242 weeks
328-1.31889 -1.73601 (328*2π)/6242 weeks
3292.37604 -2.64068 (329*2π)/6242 weeks
3303.67988 .01646 (330*2π)/6242 weeks
3312.66997 2.39617 (331*2π)/6242 weeks
332-1.18353 2.52581 (332*2π)/6242 weeks
333-1.75916 -2.22768 (333*2π)/6242 weeks
3342.46814 -3.0995 (334*2π)/6242 weeks
3354.1862 -.52758 (335*2π)/6242 weeks
3362.62351 2.16656 (336*2π)/6242 weeks
337.49752 1.83476 (337*2π)/6242 weeks
338-.62652 .19947 (338*2π)/6242 weeks
339.07522 -1.59225 (339*2π)/6242 weeks
3402.46111 -1.82108 (340*2π)/6242 weeks
3413.1178 .36452 (341*2π)/6242 weeks
3421.43541 1.34939 (342*2π)/6242 weeks
343.6903 1.09897 (343*2π)/6242 weeks
344-.30102 -.49777 (344*2π)/6242 weeks
3451.13181 -1.39025 (345*2π)/6242 weeks
3461.81071 -.34159 (346*2π)/6242 weeks
3471.69625 -.1252 (347*2π)/6242 weeks
3481.30232 .76832 (348*2π)/6242 weeks
349-.30535 -.40265 (349*2π)/6242 weeks
3501.31834 -1.62744 (350*2π)/6242 weeks
3512.27526 -1.22815 (351*2π)/6242 weeks
3523.28974 .67908 (352*2π)/6242 weeks
353.10576 1.72584 (353*2π)/6242 weeks
354-.62792 -.52757 (354*2π)/6242 weeks
355.45904 -2.52251 (355*2π)/6242 weeks
3563.4237 -2.11348 (356*2π)/6242 weeks
3573.67744 .93813 (357*2π)/6242 weeks
3581.04877 1.80446 (358*2π)/6242 weeks
359-.19333 .01094 (359*2π)/6242 weeks
360.91261 -1.61449 (360*2π)/6242 weeks
3612.81371 -.95304 (361*2π)/6242 weeks
3622.19317 1.25713 (362*2π)/6242 weeks
363.67002 1.34239 (363*2π)/6242 weeks
364-.4797 .38677 (364*2π)/6242 weeks
365-.18715 -2.07603 (365*2π)/6242 weeks
3662.56639 -1.40208 (366*2π)/6242 weeks
3671.70112 .7514 (367*2π)/6242 weeks
368.2122 .70424 (368*2π)/6242 weeks
369-.86529 -1.49838 (369*2π)/6242 weeks
3701.7436 -2.6856 (370*2π)/6242 weeks
3712.44325 -.79181 (371*2π)/6242 weeks
3721.91957 -.50922 (372*2π)/6242 weeks
3731.60507 .1084 (373*2π)/6242 weeks
374.97074 -.53696 (374*2π)/6242 weeks
3751.84368 -.88203 (375*2π)/6242 weeks
3761.57832 .64746 (376*2π)/6242 weeks
377-.51817 -.1585 (377*2π)/6242 weeks
378.58897 -2.95226 (378*2π)/6242 weeks
3793.65908 -2.19493 (379*2π)/6242 weeks
3803.87007 1.21614 (380*2π)/6242 weeks
381.15958 2.81782 (381*2π)/6242 weeks
382-1.57181 -1.26404 (382*2π)/6242 weeks
383.95526 -2.72356 (383*2π)/6242 weeks
3842.95268 -1.56651 (384*2π)/6242 weeks
3852.93592 1.07829 (385*2π)/6242 weeks
386-.54825 1.26125 (386*2π)/6242 weeks
387-.92693 -2.24843 (387*2π)/6242 weeks
3882.16842 -3.13276 (388*2π)/6242 weeks
3894.05265 -.62604 (389*2π)/6242 weeks
3901.55677 2.02709 (390*2π)/6242 weeks
391-.89682 .09803 (391*2π)/6242 weeks
392.42839 -1.79256 (392*2π)/6242 weeks
393.5769 -1.92928 (393*2π)/6242 weeks
3942.66687 -2.44611 (394*2π)/6242 weeks
3952.24724 .10074 (395*2π)/6242 weeks
3961.55965 -1.1097 (396*2π)/6242 weeks
3971.94042 -.00419 (397*2π)/6242 weeks
3981.25057 -.77971 (398*2π)/6242 weeks
3992.06461 -.77026 (399*2π)/6242 weeks
4001.78282 .03703 (400*2π)/6242 weeks
4011.32072 .49236 (401*2π)/6242 weeks
402-1.0057 -.00146 (402*2π)/6242 weeks
403.73927 -3.25343 (403*2π)/6242 weeks
4042.66624 -1.6549 (404*2π)/6242 weeks
4052.58254 -1.16656 (405*2π)/6242 weeks
4062.86201 .4599 (406*2π)/6242 weeks
407.95041 .95765 (407*2π)/6242 weeks
408-.11553 -.22101 (408*2π)/6242 weeks
409-.14495 -1.96326 (409*2π)/6242 weeks
4102.21105 -2.22033 (410*2π)/6242 weeks
4112.22306 -.21523 (411*2π)/6242 weeks
412.72085 -.5102 (412*2π)/6242 weeks
413.4709 -1.10897 (413*2π)/6242 weeks
4141.30399 -2.46942 (414*2π)/6242 weeks
4153.02871 -1.28607 (415*2π)/6242 weeks
4162.24327 .11431 (416*2π)/6242 weeks
417.42699 .6207 (417*2π)/6241 weeks
418-.42446 -1.77818 (418*2π)/6241 weeks
4191.59828 -2.76607 (419*2π)/6241 weeks
4203.08112 -1.55832 (420*2π)/6241 weeks
4212.47454 .65358 (421*2π)/6241 weeks
422-.03177 .43344 (422*2π)/6241 weeks
423-.34293 -1.38656 (423*2π)/6241 weeks
424.73483 -2.63734 (424*2π)/6241 weeks
4252.32209 -2.52051 (425*2π)/6241 weeks
4262.80356 -.92296 (426*2π)/6241 weeks
4271.93077 -.09451 (427*2π)/6241 weeks
428.88494 .00297 (428*2π)/6241 weeks
429.52219 -1.58535 (429*2π)/6241 weeks
4301.55615 -1.90128 (430*2π)/6241 weeks
4312.30708 -.86659 (431*2π)/6241 weeks
4321.05131 -.0814 (432*2π)/6241 weeks
433-.00645 -1.32565 (433*2π)/6241 weeks
4341.05864 -2.98029 (434*2π)/6241 weeks
4353.09588 -2.13391 (435*2π)/6241 weeks
4362.47468 -.8121 (436*2π)/6241 weeks
4372.06726 -.21059 (437*2π)/6241 weeks
438.72289 -.95351 (438*2π)/6241 weeks
4391.58614 -1.37521 (439*2π)/6241 weeks
4401.74942 -1.11904 (440*2π)/6241 weeks
4411.23176 -1.14582 (441*2π)/6241 weeks
4421.85216 -2.06535 (442*2π)/6241 weeks
4432.99993 -.37662 (443*2π)/6241 weeks
444.47758 -.20735 (444*2π)/6241 weeks
4451.37146 -1.73402 (445*2π)/6241 weeks
4461.3135 -1.25916 (446*2π)/6241 weeks
4471.44528 -1.63237 (447*2π)/6241 weeks
4482.09686 -.99693 (448*2π)/6241 weeks
4491.15657 -.64017 (449*2π)/6241 weeks
450.73857 -1.43525 (450*2π)/6241 weeks
4511.30873 -2.87203 (451*2π)/6241 weeks
4523.82013 -1.28504 (452*2π)/6241 weeks
4531.15695 1.0089 (453*2π)/6241 weeks
454-.2536 -1.24225 (454*2π)/6241 weeks
455.70283 -2.49524 (455*2π)/6241 weeks
4562.54932 -2.73947 (456*2π)/6241 weeks
4572.63386 -.44927 (457*2π)/6241 weeks
458.81893 -.22806 (458*2π)/6241 weeks
459.35118 -1.87193 (459*2π)/6241 weeks
4601.82925 -3.35649 (460*2π)/6241 weeks
4613.46711 -.70645 (461*2π)/6241 weeks
462.31416 .65145 (462*2π)/6241 weeks
463.08124 -3.02991 (463*2π)/6241 weeks
4642.8432 -2.60088 (464*2π)/6241 weeks
4652.94701 -1.51515 (465*2π)/6241 weeks
4662.00705 -.1958 (466*2π)/6241 weeks
4671.05533 -1.11021 (467*2π)/6241 weeks
4681.77822 -.53001 (468*2π)/6241 weeks
469.02177 -.98736 (469*2π)/6241 weeks
470.76435 -3.08149 (470*2π)/6241 weeks
4711.77675 -2.42318 (471*2π)/6241 weeks
4722.84891 -2.27897 (472*2π)/6241 weeks
4732.97342 -.71272 (473*2π)/6241 weeks
474.95297 -1.05202 (474*2π)/6241 weeks
4751.73863 -2.39631 (475*2π)/6241 weeks
4763.23724 -.9989 (476*2π)/6241 weeks
4771.44218 .23123 (477*2π)/6241 weeks
478.33901 -1.15098 (478*2π)/6241 weeks
4791.24572 -1.94896 (479*2π)/6241 weeks
4801.06428 -2.13116 (480*2π)/6241 weeks
4812.22472 -2.61133 (481*2π)/6241 weeks
4823.37103 -.51977 (482*2π)/6241 weeks
4831.48907 1.18356 (483*2π)/6241 weeks
484-2.11683 -.7673 (484*2π)/6241 weeks
485-.37588 -4.62473 (485*2π)/6241 weeks
4863.33919 -4.15584 (486*2π)/6241 weeks
4873.74781 -.47754 (487*2π)/6241 weeks
4881.15954 .41498 (488*2π)/6241 weeks
489-1.27432 -2.11044 (489*2π)/6241 weeks
4901.00769 -4.69604 (490*2π)/6241 weeks
4913.76083 -3.48433 (491*2π)/6241 weeks
4924.69449 -.17591 (492*2π)/6241 weeks
4931.00934 1.94893 (493*2π)/6241 weeks
494-2.83621 -1.63054 (494*2π)/6241 weeks
495.26776 -5.91051 (495*2π)/6241 weeks
4964.16857 -4.74344 (496*2π)/6241 weeks
4975.77472 -.96602 (497*2π)/6241 weeks
4982.35302 2.42174 (498*2π)/6241 weeks
499-2.26666 -.4756 (499*2π)/6241 weeks
500-.69426 -5.28673 (500*2π)/6241 weeks
5015.0293 -4.68931 (501*2π)/6241 weeks
5025.49104 .65447 (502*2π)/6241 weeks
5031.11344 2.72251 (503*2π)/6241 weeks
504-3.79459 .16318 (504*2π)/6241 weeks
505-2.0527 -5.97112 (505*2π)/6241 weeks
5063.22985 -6.52089 (506*2π)/6241 weeks
5075.86903 -1.84621 (507*2π)/6241 weeks
5082.01738 1.31831 (508*2π)/6241 weeks
509-1.70511 -1.2824 (509*2π)/6241 weeks
510-.02517 -4.73221 (510*2π)/6241 weeks
5114.00102 -4.7933 (511*2π)/6241 weeks
5124.87026 -.90066 (512*2π)/6241 weeks
5131.49221 .93693 (513*2π)/6241 weeks
514-.58942 -1.42705 (514*2π)/6241 weeks
515.55599 -3.28961 (515*2π)/6241 weeks
5163.04801 -2.30046 (516*2π)/6241 weeks
517.37948 -.48182 (517*2π)/6241 weeks
518.30108 -3.93237 (518*2π)/6241 weeks
5192.92962 -2.89436 (519*2π)/6241 weeks
5201.81824 -.61368 (520*2π)/6241 weeks
521-1.01617 -1.67054 (521*2π)/6241 weeks
522.31238 -5.04687 (522*2π)/6241 weeks
5234.42801 -4.51154 (523*2π)/6241 weeks
5245.13697 -.16892 (524*2π)/6241 weeks
525.06572 2.39998 (525*2π)/6241 weeks
526-4.14187 -1.53107 (526*2π)/6241 weeks
527-1.33301 -8.16159 (527*2π)/6241 weeks
5285.78907 -5.86272 (528*2π)/6241 weeks
5294.52575 -.66556 (529*2π)/6241 weeks
5301.47037 .83008 (530*2π)/6241 weeks
531-3.3148 -1.89245 (531*2π)/6241 weeks
532-.61014 -7.5726 (532*2π)/6241 weeks
5334.75864 -6.70536 (533*2π)/6241 weeks
5347.1944 -1.24624 (534*2π)/6241 weeks
535.33782 3.31855 (535*2π)/6241 weeks
536-3.5379 -4.05822 (536*2π)/6241 weeks
5371.89185 -5.51471 (537*2π)/6241 weeks
5382.34706 -5.10109 (538*2π)/6241 weeks
5395.52634 -2.09403 (539*2π)/6241 weeks
540.63785 2.47224 (540*2π)/6241 weeks
541-4.51573 -3.20218 (541*2π)/6241 weeks
542-1.24639 -8.24119 (542*2π)/6241 weeks
5434.98919 -7.46143 (543*2π)/6241 weeks
5445.48306 -1.37151 (544*2π)/6241 weeks
545-.43167 -1.06536 (545*2π)/6241 weeks
5461.3349 -5.43182 (546*2π)/6241 weeks
5472.48478 -3.14706 (547*2π)/6241 weeks
5482.84842 -3.10384 (548*2π)/6241 weeks
549-.82288 -1.16864 (549*2π)/6241 weeks
550-.7517 -6.48341 (550*2π)/6241 weeks
5514.06951 -7.03882 (551*2π)/6241 weeks
5524.8593 -2.84463 (552*2π)/6241 weeks
5532.64527 -.6908 (553*2π)/6241 weeks
554-1.42474 -3.47079 (554*2π)/6241 weeks
5552.88222 -6.8644 (555*2π)/6241 weeks
5564.86557 -2.07726 (556*2π)/6241 weeks
5571.09884 -.30098 (557*2π)/6241 weeks
558-2.56552 -3.079 (558*2π)/6241 weeks
559-.4789 -8.42681 (559*2π)/6241 weeks
5606.95068 -7.99314 (560*2π)/6241 weeks
5615.93234 .80104 (561*2π)/6241 weeks
562-1.4691 .80694 (562*2π)/6241 weeks
563-2.75942 -4.65328 (563*2π)/6241 weeks
564.26835 -6.90446 (564*2π)/6241 weeks
5653.42035 -6.31622 (565*2π)/6241 weeks
5661.94532 -3.04186 (566*2π)/6241 weeks
567-.75185 -4.85359 (567*2π)/6241 weeks
568.21383 -7.6547 (568*2π)/6241 weeks
5694.00142 -7.70373 (569*2π)/6241 weeks
5705.39256 -6.47493 (570*2π)/6241 weeks
5714.52538 -.84847 (571*2π)/6241 weeks
572.12286 -2.27648 (572*2π)/6241 weeks
573.54565 -4.61087 (573*2π)/6241 weeks
574.13092 -5.90885 (574*2π)/6241 weeks
5752.80512 -4.91452 (575*2π)/6241 weeks
576-1.22794 -4.76937 (576*2π)/6241 weeks
5772.15961 -9.60779 (577*2π)/6241 weeks
5784.56906 -3.7158 (578*2π)/6241 weeks
579.69919 -3.67048 (579*2π)/6241 weeks
580-.95434 -5.17145 (580*2π)/6241 weeks
581-1.14075 -8.46817 (581*2π)/6241 weeks
5823.85153 -11.72556 (582*2π)/6241 weeks
5838.63935 -4.63231 (583*2π)/6241 weeks
5842.61327 3.00112 (584*2π)/6241 weeks
585-11.41045 -1.66728 (585*2π)/6241 weeks
586-8.40228 -21.83552 (586*2π)/6241 weeks
58712.41638 -20.93323 (587*2π)/6241 weeks
58816.27643 -1.78601 (588*2π)/6241 weeks
5892.32559 6.76596 (589*2π)/6241 weeks
590-11.28401 -5.10198 (590*2π)/6241 weeks
591-3.66552 -20.03627 (591*2π)/6241 weeks
5929.72648 -15.1758 (592*2π)/6241 weeks
59311.5863 -5.07162 (593*2π)/6241 weeks
5943.24252 4.60098 (594*2π)/6241 weeks
595-10.13589 -7.08111 (595*2π)/6241 weeks
596-1.70564 -16.69026 (596*2π)/6241 weeks
5974.41545 -13.07075 (597*2π)/6241 weeks
5982.20883 -5.13433 (598*2π)/6241 weeks
599-5.13718 -12.63219 (599*2π)/6241 weeks
600.48943 -18.85429 (600*2π)/6241 weeks
6015.79182 -16.69084 (601*2π)/6241 weeks
6027.20969 -12.64077 (602*2π)/6241 weeks
6037.46565 -11.68827 (603*2π)/6241 weeks
6042.54954 -6.33921 (604*2π)/6241 weeks
605-1.587 -16.34385 (605*2π)/6241 weeks
6062.67038 -13.04 (606*2π)/6241 weeks
607-1.56045 -16.98952 (607*2π)/6241 weeks
6082.14235 -22.55641 (608*2π)/6241 weeks
60911.2625 -25.34306 (609*2π)/6241 weeks
61018.52095 -10.36023 (610*2π)/6241 weeks
611-3.22746 -2.41053 (611*2π)/6241 weeks
612-11.3814 -22.17445 (612*2π)/6241 weeks
613-9.18765 -33.62278 (613*2π)/6241 weeks
61415.05748 -52.20425 (614*2π)/6241 weeks
61538.24218 -14.43681 (615*2π)/6241 weeks
616-10.61436 1.55892 (616*2π)/6241 weeks
617-31.8441 -47.11121 (617*2π)/6241 weeks
61810.48297 -85.7606 (618*2π)/6241 weeks
61964.28897 -61.23633 (619*2π)/6241 weeks
62047.35353 3.28614 (620*2π)/6241 weeks
621-55.26525 -12.87634 (621*2π)/6241 weeks
622-86.62464 -154.9403 (622*2π)/6241 weeks



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