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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 (52.8242*sine), 56 weeks (31.4432*sine), and 44 weeks (19.2688*cosine).

SDS (ProShares UltraShort S&P500) has an average price of 381.89 (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 4/23/2018 for SDS (ProShares UltraShort S&P500), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0381.8874   0 
199.22068 398.0181 (1*2π)/616616 weeks
2-88.06164 151.5846 (2*2π)/616308 weeks
3-52.48754 8.64872 (3*2π)/616205 weeks
451.10186 -.61095 (4*2π)/616154 weeks
562.77045 65.9049 (5*2π)/616123 weeks
66.07967 85.9207 (6*2π)/616103 weeks
7-32.9902 42.1253 (7*2π)/61688 weeks
8-5.43882 -4.30349 (8*2π)/61677 weeks
940.07985 21.13953 (9*2π)/61668 weeks
109.51266 52.82424 (10*2π)/61662 weeks
11-9.17759 31.44315 (11*2π)/61656 weeks
12-12.42703 19.62149 (12*2π)/61651 weeks
13.91652 .96466 (13*2π)/61647 weeks
1419.26876 14.76411 (14*2π)/61644 weeks
158.75218 26.27294 (15*2π)/61641 weeks
161.36574 22.28158 (16*2π)/61639 weeks
17-1.09493 15.68972 (17*2π)/61636 weeks
183.93293 14.36559 (18*2π)/61634 weeks
19-3.27221 13.6053 (19*2π)/61632 weeks
205.42719 7.15311 (20*2π)/61631 weeks
216.92454 12.71238 (21*2π)/61629 weeks
227.95851 14.16158 (22*2π)/61628 weeks
235.17905 17.65789 (23*2π)/61627 weeks
24-1.84058 17.92761 (24*2π)/61626 weeks
25-4.82853 9.14299 (25*2π)/61625 weeks
265.68187 7.78631 (26*2π)/61624 weeks
273.39981 14.40139 (27*2π)/61623 weeks
28-5.91044 15.11079 (28*2π)/61622 weeks
29-8.60853 .02381 (29*2π)/61621 weeks
308.84591 -.93771 (30*2π)/61621 weeks
3112.39575 9.39644 (31*2π)/61620 weeks
326.43238 19.07692 (32*2π)/61619 weeks
33-9.5783 14.65444 (33*2π)/61619 weeks
34-8.07635 -2.79748 (34*2π)/61618 weeks
359.73387 -4.44131 (35*2π)/61618 weeks
3618.56239 11.26157 (36*2π)/61617 weeks
373.2518 24.99103 (37*2π)/61617 weeks
38-14.30389 11.64479 (38*2π)/61616 weeks
39-4.53864 -3.58585 (39*2π)/61616 weeks
406.93058 .49049 (40*2π)/61615 weeks
417.53073 9.5618 (41*2π)/61615 weeks
42-.0976 10.5638 (42*2π)/61615 weeks
43-1.48101 6.59254 (43*2π)/61614 weeks
44-.01386 4.27524 (44*2π)/61614 weeks
452.446 2.97 (45*2π)/61614 weeks
465.06249 8.06857 (46*2π)/61613 weeks
47-1.42692 7.27527 (47*2π)/61613 weeks
481.73803 3.56115 (48*2π)/61613 weeks
491.20598 6.66729 (49*2π)/61613 weeks
50.4271 4.56458 (50*2π)/61612 weeks
51-.29878 3.51653 (51*2π)/61612 weeks
522.57366 .73768 (52*2π)/61612 weeks
536.70299 5.14901 (53*2π)/61612 weeks
544.34698 6.90664 (54*2π)/61611 weeks
551.12652 8.42141 (55*2π)/61611 weeks
56-.69193 5.75435 (56*2π)/61611 weeks
571.05236 2.9814 (57*2π)/61611 weeks
583.78929 5.1734 (58*2π)/61611 weeks
59.71959 7.05027 (59*2π)/61610 weeks
60-2.37228 5.68225 (60*2π)/61610 weeks
61-2.47056 .38091 (61*2π)/61610 weeks
624.57733 -1.60506 (62*2π)/61610 weeks
638.13814 6.46982 (63*2π)/61610 weeks
64.43458 9.05318 (64*2π)/61610 weeks
65-2.82578 4.01624 (65*2π)/6169 weeks
66.49609 .37419 (66*2π)/6169 weeks
674.51489 1.54943 (67*2π)/6169 weeks
683.59862 6.66354 (68*2π)/6169 weeks
69-1.41608 4.17625 (69*2π)/6169 weeks
702.26467 .5483 (70*2π)/6169 weeks
714.76076 2.66129 (71*2π)/6169 weeks
724.39343 6.88308 (72*2π)/6169 weeks
73-.58284 6.72679 (73*2π)/6168 weeks
74-1.06026 1.348 (74*2π)/6168 weeks
752.9172 3.05641 (75*2π)/6168 weeks
762.48865 3.16496 (76*2π)/6168 weeks
771.34786 5.48697 (77*2π)/6168 weeks
78-.38712 .9919 (78*2π)/6168 weeks
795.65269 1.51366 (79*2π)/6168 weeks
804.86131 7.72466 (80*2π)/6168 weeks
81-1.5418 8.13854 (81*2π)/6168 weeks
82-4.61872 2.70886 (82*2π)/6168 weeks
831.29155 -2.48285 (83*2π)/6167 weeks
845.53561 2.67888 (84*2π)/6167 weeks
852.10183 4.98758 (85*2π)/6167 weeks
861.5425 5.94329 (86*2π)/6167 weeks
87-3.96587 2.98809 (87*2π)/6167 weeks
881.74251 -3.54056 (88*2π)/6167 weeks
897.29512 2.43926 (89*2π)/6167 weeks
904.04248 7.25259 (90*2π)/6167 weeks
91-1.7119 7.03134 (91*2π)/6167 weeks
92-2.82011 .65138 (92*2π)/6167 weeks
932.15555 -.54303 (93*2π)/6167 weeks
945.21054 1.39651 (94*2π)/6167 weeks
954.73486 7.52112 (95*2π)/6166 weeks
96-3.03508 7.08049 (96*2π)/6166 weeks
97-3.4231 .09596 (97*2π)/6166 weeks
981.78083 -2.52279 (98*2π)/6166 weeks
995.39243 1.6526 (99*2π)/6166 weeks
1003.31799 5.54917 (100*2π)/6166 weeks
101-.50264 4.42553 (101*2π)/6166 weeks
102-.0902 .7781 (102*2π)/6166 weeks
1032.67847 1.1338 (103*2π)/6166 weeks
1042.42181 3.73358 (104*2π)/6166 weeks
105-.62474 2.83523 (105*2π)/6166 weeks
1061.91274 .41151 (106*2π)/6166 weeks
1072.31246 3.51857 (107*2π)/6166 weeks
108.05555 2.77647 (108*2π)/6166 weeks
109-.14397 .14043 (109*2π)/6166 weeks
1103.26719 -.86324 (110*2π)/6166 weeks
1115.14369 2.6866 (111*2π)/6166 weeks
1122.06068 5.62703 (112*2π)/6166 weeks
113-1.09529 3.62229 (113*2π)/6165 weeks
114-.2634 -.78537 (114*2π)/6165 weeks
1154.41272 -.66891 (115*2π)/6165 weeks
1165.36272 4.72733 (116*2π)/6165 weeks
117.47191 6.96165 (117*2π)/6165 weeks
118-4.14402 3.18377 (118*2π)/6165 weeks
119-1.12736 -2.54364 (119*2π)/6165 weeks
1203.67773 -2.3335 (120*2π)/6165 weeks
1216.07237 2.4786 (121*2π)/6165 weeks
1221.72853 6.30613 (122*2π)/6165 weeks
123-2.27882 2.6068 (123*2π)/6165 weeks
124.06892 -2.30607 (124*2π)/6165 weeks
1255.05777 -.7617 (125*2π)/6165 weeks
1265.16726 3.79404 (126*2π)/6165 weeks
1271.97922 5.98066 (127*2π)/6165 weeks
128-2.52 3.64729 (128*2π)/6165 weeks
129-.66902 -1.63955 (129*2π)/6165 weeks
1303.85188 -.98108 (130*2π)/6165 weeks
1314.34673 2.94714 (131*2π)/6165 weeks
1322.10425 4.76714 (132*2π)/6165 weeks
133-.95043 3.14838 (133*2π)/6165 weeks
134.30737 -.36932 (134*2π)/6165 weeks
1353.05558 -.04815 (135*2π)/6165 weeks
1363.9808 3.49145 (136*2π)/6165 weeks
137.49275 4.98217 (137*2π)/6164 weeks
138-2.25286 1.78518 (138*2π)/6164 weeks
139.76863 -1.4047 (139*2π)/6164 weeks
1403.12385 .08933 (140*2π)/6164 weeks
1412.59768 2.58438 (141*2π)/6164 weeks
1421.18899 2.31671 (142*2π)/6164 weeks
1431.32969 1.85981 (143*2π)/6164 weeks
144.35639 1.36758 (144*2π)/6164 weeks
1451.20125 -.16429 (145*2π)/6164 weeks
1463.20472 .74004 (146*2π)/6164 weeks
1471.93706 2.46684 (147*2π)/6164 weeks
148.94505 1.21299 (148*2π)/6164 weeks
1492.90461 .57136 (149*2π)/6164 weeks
1502.90739 2.22798 (150*2π)/6164 weeks
1511.78075 2.46641 (151*2π)/6164 weeks
152.8322 3.13488 (152*2π)/6164 weeks
153-.00131 1.02176 (153*2π)/6164 weeks
1541.79232 .53446 (154*2π)/6164 weeks
1551.05495 1.10221 (155*2π)/6164 weeks
1562.06987 .19638 (156*2π)/6164 weeks
1572.94917 1.582 (157*2π)/6164 weeks
1582.8239 2.76441 (158*2π)/6164 weeks
159-.09561 2.91367 (159*2π)/6164 weeks
160.66884 -.81314 (160*2π)/6164 weeks
1613.60607 .99306 (161*2π)/6164 weeks
1621.4882 3.32648 (162*2π)/6164 weeks
163.2995 1.7302 (163*2π)/6164 weeks
1641.07683 .11182 (164*2π)/6164 weeks
1652.89559 .67339 (165*2π)/6164 weeks
1662.19528 2.94301 (166*2π)/6164 weeks
167.54475 2.38456 (167*2π)/6164 weeks
168-.29061 .82109 (168*2π)/6164 weeks
1691.93864 -1.11766 (169*2π)/6164 weeks
1703.60796 2.05555 (170*2π)/6164 weeks
171.86753 2.51878 (171*2π)/6164 weeks
172.74717 1.26571 (172*2π)/6164 weeks
1731.41771 .57453 (173*2π)/6164 weeks
1742.13002 1.33257 (174*2π)/6164 weeks
1751.34462 1.48391 (175*2π)/6164 weeks
1761.41875 1.16567 (176*2π)/6164 weeks
177.80194 1.72043 (177*2π)/6163 weeks
1781.12646 -.3981 (178*2π)/6163 weeks
1793.01152 1.33869 (179*2π)/6163 weeks
1801.35145 1.88784 (180*2π)/6163 weeks
1811.42744 1.01188 (181*2π)/6163 weeks
1821.7079 1.31469 (182*2π)/6163 weeks
1831.37956 1.56081 (183*2π)/6163 weeks
1841.02362 .25657 (184*2π)/6163 weeks
1852.34166 .59646 (185*2π)/6163 weeks
1862.85599 1.03879 (186*2π)/6163 weeks
1872.38112 2.9992 (187*2π)/6163 weeks
188.26215 2.48437 (188*2π)/6163 weeks
189.28339 .64047 (189*2π)/6163 weeks
1901.83689 .2528 (190*2π)/6163 weeks
1912.1971 1.6465 (191*2π)/6163 weeks
1921.10709 1.9029 (192*2π)/6163 weeks
193.26177 .75006 (193*2π)/6163 weeks
1941.58138 .08857 (194*2π)/6163 weeks
1952.5603 .4477 (195*2π)/6163 weeks
1962.94698 1.87189 (196*2π)/6163 weeks
1971.46496 2.7987 (197*2π)/6163 weeks
198-.0156 2.11956 (198*2π)/6163 weeks
199-.31502 .4456 (199*2π)/6163 weeks
2001.55003 -1.08154 (200*2π)/6163 weeks
2013.33461 .64659 (201*2π)/6163 weeks
2022.36277 2.46025 (202*2π)/6163 weeks
203.23428 2.47796 (203*2π)/6163 weeks
204-.2958 -.0371 (204*2π)/6163 weeks
2051.93699 -.51222 (205*2π)/6163 weeks
2062.94417 .55308 (206*2π)/6163 weeks
2072.02682 2.45724 (207*2π)/6163 weeks
208.41909 1.52376 (208*2π)/6163 weeks
209.74698 .72086 (209*2π)/6163 weeks
2101.74855 -.10007 (210*2π)/6163 weeks
2112.57454 1.66077 (211*2π)/6163 weeks
212.31192 2.41186 (212*2π)/6163 weeks
213-.23478 .46432 (213*2π)/6163 weeks
214.56722 -.84006 (214*2π)/6163 weeks
2152.51057 -.85002 (215*2π)/6163 weeks
2162.78791 1.03109 (216*2π)/6163 weeks
2172.60183 1.38058 (217*2π)/6163 weeks
2181.34281 3.20929 (218*2π)/6163 weeks
219-1.31592 .6131 (219*2π)/6163 weeks
2201.13965 -.63775 (220*2π)/6163 weeks
2211.70978 -.07266 (221*2π)/6163 weeks
2222.12329 .65393 (222*2π)/6163 weeks
2231.30327 .85689 (223*2π)/6163 weeks
2241.7778 -.03778 (224*2π)/6163 weeks
2251.68639 1.16524 (225*2π)/6163 weeks
2262.08677 -.11149 (226*2π)/6163 weeks
2272.82382 2.36732 (227*2π)/6163 weeks
228.58884 2.01362 (228*2π)/6163 weeks
229.46298 1.80306 (229*2π)/6163 weeks
230-.92813 -.0605 (230*2π)/6163 weeks
2311.56734 -2.05653 (231*2π)/6163 weeks
2324.09194 .67891 (232*2π)/6163 weeks
2332.10706 3.19678 (233*2π)/6163 weeks
234-1.03488 2.15047 (234*2π)/6163 weeks
235-.40835 -1.41325 (235*2π)/6163 weeks
2363.10085 -.89939 (236*2π)/6163 weeks
2372.89215 1.72824 (237*2π)/6163 weeks
238.72736 2.7321 (238*2π)/6163 weeks
239-1.7919 .85861 (239*2π)/6163 weeks
240.75396 -2.98117 (240*2π)/6163 weeks
2414.12186 -.81998 (241*2π)/6163 weeks
2423.32148 2.55572 (242*2π)/6163 weeks
243.09849 2.70958 (243*2π)/6163 weeks
244-.26269 -.24558 (244*2π)/6163 weeks
2451.89497 -.43046 (245*2π)/6163 weeks
2461.59525 .98585 (246*2π)/6163 weeks
247.96278 .34536 (247*2π)/6162 weeks
2481.84519 -.00363 (248*2π)/6162 weeks
2491.92526 .49867 (249*2π)/6162 weeks
2502.59938 1.17307 (250*2π)/6162 weeks
251.93789 2.89601 (251*2π)/6162 weeks
252-.98014 .67016 (252*2π)/6162 weeks
253.67592 -.75106 (253*2π)/6162 weeks
2542.31648 -.44117 (254*2π)/6162 weeks
2551.94894 2.12291 (255*2π)/6162 weeks
256-.8589 1.23139 (256*2π)/6162 weeks
257-.16561 -.74845 (257*2π)/6162 weeks
2581.20802 -1.38962 (258*2π)/6162 weeks
2592.92237 -.71798 (259*2π)/6162 weeks
2602.16756 1.48872 (260*2π)/6162 weeks
261.18564 1.1725 (261*2π)/6162 weeks
262-.02789 -.84764 (262*2π)/6162 weeks
2632.19542 -1.94154 (263*2π)/6162 weeks
2644.09438 .39411 (264*2π)/6162 weeks
2652.13754 2.90676 (265*2π)/6162 weeks
266-.35913 1.71 (266*2π)/6162 weeks
267-.59355 -.37135 (267*2π)/6162 weeks
2681.94635 -2.13724 (268*2π)/6162 weeks
2693.0223 .71503 (269*2π)/6162 weeks
2701.80287 1.39728 (270*2π)/6162 weeks
271.2684 1.53724 (271*2π)/6162 weeks
272.36537 -.71647 (272*2π)/6162 weeks
2731.78018 -.18111 (273*2π)/6162 weeks
2741.66691 .23176 (274*2π)/6162 weeks
2751.80471 1.05596 (275*2π)/6162 weeks
276.22026 1.11518 (276*2π)/6162 weeks
277-.05135 -.85654 (277*2π)/6162 weeks
2781.07577 -1.05829 (278*2π)/6162 weeks
2792.68767 -1.09283 (279*2π)/6162 weeks
2803.07808 1.09764 (280*2π)/6162 weeks
281.768 2.09114 (281*2π)/6162 weeks
282-.56218 .48084 (282*2π)/6162 weeks
283-.0416 -1.47871 (283*2π)/6162 weeks
2841.81822 -2.23987 (284*2π)/6162 weeks
2854.24939 -.47868 (285*2π)/6162 weeks
2863.28054 2.46187 (286*2π)/6162 weeks
287-.71343 3.18542 (287*2π)/6162 weeks
288-2.08785 -1.52279 (288*2π)/6162 weeks
2891.98612 -2.89909 (289*2π)/6162 weeks
2903.67767 -.55494 (290*2π)/6162 weeks
2913.09228 2.15356 (291*2π)/6162 weeks
292-.67962 2.37781 (292*2π)/6162 weeks
293-1.54991 -1.6354 (293*2π)/6162 weeks
2942.1613 -3.46705 (294*2π)/6162 weeks
2953.97052 .08544 (295*2π)/6162 weeks
2961.95966 1.74597 (296*2π)/6162 weeks
297-.08706 .60763 (297*2π)/6162 weeks
298.41543 -1.79292 (298*2π)/6162 weeks
2992.45473 -2.28298 (299*2π)/6162 weeks
3004.89415 .00554 (300*2π)/6162 weeks
3012.37043 3.33179 (301*2π)/6162 weeks
302-.93388 .74641 (302*2π)/6162 weeks
303.69259 -1.77875 (303*2π)/6162 weeks
3042.50867 -1.08596 (304*2π)/6162 weeks
3053.25432 .59262 (305*2π)/6162 weeks
3062.19991 1.47429 (306*2π)/6162 weeks
307.80697 2.03644 (307*2π)/6162 weeks
308-1.27524   (308*2π)/6162 weeks
309.80697 -2.03644 (309*2π)/6162 weeks
3102.19991 -1.47429 (310*2π)/6162 weeks
3113.25432 -.59262 (311*2π)/6162 weeks
3122.50867 1.08596 (312*2π)/6162 weeks
313.69259 1.77875 (313*2π)/6162 weeks
314-.93388 -.74641 (314*2π)/6162 weeks
3152.37043 -3.33179 (315*2π)/6162 weeks
3164.89415 -.00554 (316*2π)/6162 weeks
3172.45473 2.28298 (317*2π)/6162 weeks
318.41543 1.79292 (318*2π)/6162 weeks
319-.08706 -.60763 (319*2π)/6162 weeks
3201.95966 -1.74597 (320*2π)/6162 weeks
3213.97052 -.08544 (321*2π)/6162 weeks
3222.1613 3.46705 (322*2π)/6162 weeks
323-1.54991 1.6354 (323*2π)/6162 weeks
324-.67962 -2.37781 (324*2π)/6162 weeks
3253.09228 -2.15356 (325*2π)/6162 weeks
3263.67767 .55494 (326*2π)/6162 weeks
3271.98612 2.89909 (327*2π)/6162 weeks
328-2.08785 1.52279 (328*2π)/6162 weeks
329-.71343 -3.18542 (329*2π)/6162 weeks
3303.28054 -2.46187 (330*2π)/6162 weeks
3314.24939 .47868 (331*2π)/6162 weeks
3321.81822 2.23987 (332*2π)/6162 weeks
333-.0416 1.47871 (333*2π)/6162 weeks
334-.56218 -.48084 (334*2π)/6162 weeks
335.768 -2.09114 (335*2π)/6162 weeks
3363.07808 -1.09764 (336*2π)/6162 weeks
3372.68767 1.09283 (337*2π)/6162 weeks
3381.07577 1.05829 (338*2π)/6162 weeks
339-.05135 .85654 (339*2π)/6162 weeks
340.22026 -1.11518 (340*2π)/6162 weeks
3411.80471 -1.05596 (341*2π)/6162 weeks
3421.66691 -.23176 (342*2π)/6162 weeks
3431.78018 .18111 (343*2π)/6162 weeks
344.36537 .71647 (344*2π)/6162 weeks
345.2684 -1.53724 (345*2π)/6162 weeks
3461.80287 -1.39728 (346*2π)/6162 weeks
3473.0223 -.71503 (347*2π)/6162 weeks
3481.94635 2.13724 (348*2π)/6162 weeks
349-.59355 .37135 (349*2π)/6162 weeks
350-.35913 -1.71 (350*2π)/6162 weeks
3512.13754 -2.90676 (351*2π)/6162 weeks
3524.09438 -.39411 (352*2π)/6162 weeks
3532.19542 1.94154 (353*2π)/6162 weeks
354-.02789 .84764 (354*2π)/6162 weeks
355.18564 -1.1725 (355*2π)/6162 weeks
3562.16756 -1.48872 (356*2π)/6162 weeks
3572.92237 .71798 (357*2π)/6162 weeks
3581.20802 1.38962 (358*2π)/6162 weeks
359-.16561 .74845 (359*2π)/6162 weeks
360-.8589 -1.23139 (360*2π)/6162 weeks
3611.94894 -2.12291 (361*2π)/6162 weeks
3622.31648 .44117 (362*2π)/6162 weeks
363.67592 .75106 (363*2π)/6162 weeks
364-.98014 -.67016 (364*2π)/6162 weeks
365.93789 -2.89601 (365*2π)/6162 weeks
3662.59938 -1.17307 (366*2π)/6162 weeks
3671.92526 -.49867 (367*2π)/6162 weeks
3681.84519 .00363 (368*2π)/6162 weeks
369.96278 -.34536 (369*2π)/6162 weeks
3701.59525 -.98585 (370*2π)/6162 weeks
3711.89497 .43046 (371*2π)/6162 weeks
372-.26269 .24558 (372*2π)/6162 weeks
373.09849 -2.70958 (373*2π)/6162 weeks
3743.32148 -2.55572 (374*2π)/6162 weeks
3754.12186 .81998 (375*2π)/6162 weeks
376.75396 2.98117 (376*2π)/6162 weeks
377-1.7919 -.85861 (377*2π)/6162 weeks
378.72736 -2.7321 (378*2π)/6162 weeks
3792.89215 -1.72824 (379*2π)/6162 weeks
3803.10085 .89939 (380*2π)/6162 weeks
381-.40835 1.41325 (381*2π)/6162 weeks
382-1.03488 -2.15047 (382*2π)/6162 weeks
3832.10706 -3.19678 (383*2π)/6162 weeks
3844.09194 -.67891 (384*2π)/6162 weeks
3851.56734 2.05653 (385*2π)/6162 weeks
386-.92813 .0605 (386*2π)/6162 weeks
387.46298 -1.80306 (387*2π)/6162 weeks
388.58884 -2.01362 (388*2π)/6162 weeks
3892.82382 -2.36732 (389*2π)/6162 weeks
3902.08677 .11149 (390*2π)/6162 weeks
3911.68639 -1.16524 (391*2π)/6162 weeks
3921.7778 .03778 (392*2π)/6162 weeks
3931.30327 -.85689 (393*2π)/6162 weeks
3942.12329 -.65393 (394*2π)/6162 weeks
3951.70978 .07266 (395*2π)/6162 weeks
3961.13965 .63775 (396*2π)/6162 weeks
397-1.31592 -.6131 (397*2π)/6162 weeks
3981.34281 -3.20929 (398*2π)/6162 weeks
3992.60183 -1.38058 (399*2π)/6162 weeks
4002.78791 -1.03109 (400*2π)/6162 weeks
4012.51057 .85002 (401*2π)/6162 weeks
402.56722 .84006 (402*2π)/6162 weeks
403-.23478 -.46432 (403*2π)/6162 weeks
404.31192 -2.41186 (404*2π)/6162 weeks
4052.57454 -1.66077 (405*2π)/6162 weeks
4061.74855 .10007 (406*2π)/6162 weeks
407.74698 -.72086 (407*2π)/6162 weeks
408.41909 -1.52376 (408*2π)/6162 weeks
4092.02682 -2.45724 (409*2π)/6162 weeks
4102.94417 -.55308 (410*2π)/6162 weeks
4111.93699 .51222 (411*2π)/6161 weeks
412-.2958 .0371 (412*2π)/6161 weeks
413.23428 -2.47796 (413*2π)/6161 weeks
4142.36277 -2.46025 (414*2π)/6161 weeks
4153.33461 -.64659 (415*2π)/6161 weeks
4161.55003 1.08154 (416*2π)/6161 weeks
417-.31502 -.4456 (417*2π)/6161 weeks
418-.0156 -2.11956 (418*2π)/6161 weeks
4191.46496 -2.7987 (419*2π)/6161 weeks
4202.94698 -1.87189 (420*2π)/6161 weeks
4212.5603 -.4477 (421*2π)/6161 weeks
4221.58138 -.08857 (422*2π)/6161 weeks
423.26177 -.75006 (423*2π)/6161 weeks
4241.10709 -1.9029 (424*2π)/6161 weeks
4252.1971 -1.6465 (425*2π)/6161 weeks
4261.83689 -.2528 (426*2π)/6161 weeks
427.28339 -.64047 (427*2π)/6161 weeks
428.26215 -2.48437 (428*2π)/6161 weeks
4292.38112 -2.9992 (429*2π)/6161 weeks
4302.85599 -1.03879 (430*2π)/6161 weeks
4312.34166 -.59646 (431*2π)/6161 weeks
4321.02362 -.25657 (432*2π)/6161 weeks
4331.37956 -1.56081 (433*2π)/6161 weeks
4341.7079 -1.31469 (434*2π)/6161 weeks
4351.42744 -1.01188 (435*2π)/6161 weeks
4361.35145 -1.88784 (436*2π)/6161 weeks
4373.01152 -1.33869 (437*2π)/6161 weeks
4381.12646 .3981 (438*2π)/6161 weeks
439.80194 -1.72043 (439*2π)/6161 weeks
4401.41875 -1.16567 (440*2π)/6161 weeks
4411.34462 -1.48391 (441*2π)/6161 weeks
4422.13002 -1.33257 (442*2π)/6161 weeks
4431.41771 -.57453 (443*2π)/6161 weeks
444.74717 -1.26571 (444*2π)/6161 weeks
445.86753 -2.51878 (445*2π)/6161 weeks
4463.60796 -2.05555 (446*2π)/6161 weeks
4471.93864 1.11766 (447*2π)/6161 weeks
448-.29061 -.82109 (448*2π)/6161 weeks
449.54475 -2.38456 (449*2π)/6161 weeks
4502.19528 -2.94301 (450*2π)/6161 weeks
4512.89559 -.67339 (451*2π)/6161 weeks
4521.07683 -.11182 (452*2π)/6161 weeks
453.2995 -1.7302 (453*2π)/6161 weeks
4541.4882 -3.32648 (454*2π)/6161 weeks
4553.60607 -.99306 (455*2π)/6161 weeks
456.66884 .81314 (456*2π)/6161 weeks
457-.09561 -2.91367 (457*2π)/6161 weeks
4582.8239 -2.76441 (458*2π)/6161 weeks
4592.94917 -1.582 (459*2π)/6161 weeks
4602.06987 -.19638 (460*2π)/6161 weeks
4611.05495 -1.10221 (461*2π)/6161 weeks
4621.79232 -.53446 (462*2π)/6161 weeks
463-.00131 -1.02176 (463*2π)/6161 weeks
464.8322 -3.13488 (464*2π)/6161 weeks
4651.78075 -2.46641 (465*2π)/6161 weeks
4662.90739 -2.22798 (466*2π)/6161 weeks
4672.90461 -.57136 (467*2π)/6161 weeks
468.94505 -1.21299 (468*2π)/6161 weeks
4691.93706 -2.46684 (469*2π)/6161 weeks
4703.20472 -.74004 (470*2π)/6161 weeks
4711.20125 .16429 (471*2π)/6161 weeks
472.35639 -1.36758 (472*2π)/6161 weeks
4731.32969 -1.85981 (473*2π)/6161 weeks
4741.18899 -2.31671 (474*2π)/6161 weeks
4752.59768 -2.58438 (475*2π)/6161 weeks
4763.12385 -.08933 (476*2π)/6161 weeks
477.76863 1.4047 (477*2π)/6161 weeks
478-2.25286 -1.78518 (478*2π)/6161 weeks
479.49275 -4.98217 (479*2π)/6161 weeks
4803.9808 -3.49145 (480*2π)/6161 weeks
4813.05558 .04815 (481*2π)/6161 weeks
482.30737 .36932 (482*2π)/6161 weeks
483-.95043 -3.14838 (483*2π)/6161 weeks
4842.10425 -4.76714 (484*2π)/6161 weeks
4854.34673 -2.94714 (485*2π)/6161 weeks
4863.85188 .98108 (486*2π)/6161 weeks
487-.66902 1.63955 (487*2π)/6161 weeks
488-2.52 -3.64729 (488*2π)/6161 weeks
4891.97922 -5.98066 (489*2π)/6161 weeks
4905.16726 -3.79404 (490*2π)/6161 weeks
4915.05777 .7617 (491*2π)/6161 weeks
492.06892 2.30607 (492*2π)/6161 weeks
493-2.27882 -2.6068 (493*2π)/6161 weeks
4941.72853 -6.30613 (494*2π)/6161 weeks
4956.07237 -2.4786 (495*2π)/6161 weeks
4963.67773 2.3335 (496*2π)/6161 weeks
497-1.12736 2.54364 (497*2π)/6161 weeks
498-4.14402 -3.18377 (498*2π)/6161 weeks
499.47191 -6.96165 (499*2π)/6161 weeks
5005.36272 -4.72733 (500*2π)/6161 weeks
5014.41272 .66891 (501*2π)/6161 weeks
502-.2634 .78537 (502*2π)/6161 weeks
503-1.09529 -3.62229 (503*2π)/6161 weeks
5042.06068 -5.62703 (504*2π)/6161 weeks
5055.14369 -2.6866 (505*2π)/6161 weeks
5063.26719 .86324 (506*2π)/6161 weeks
507-.14397 -.14043 (507*2π)/6161 weeks
508.05555 -2.77647 (508*2π)/6161 weeks
5092.31246 -3.51857 (509*2π)/6161 weeks
5101.91274 -.41151 (510*2π)/6161 weeks
511-.62474 -2.83523 (511*2π)/6161 weeks
5122.42181 -3.73358 (512*2π)/6161 weeks
5132.67847 -1.1338 (513*2π)/6161 weeks
514-.0902 -.7781 (514*2π)/6161 weeks
515-.50264 -4.42553 (515*2π)/6161 weeks
5163.31799 -5.54917 (516*2π)/6161 weeks
5175.39243 -1.6526 (517*2π)/6161 weeks
5181.78083 2.52279 (518*2π)/6161 weeks
519-3.4231 -.09596 (519*2π)/6161 weeks
520-3.03508 -7.08049 (520*2π)/6161 weeks
5214.73486 -7.52112 (521*2π)/6161 weeks
5225.21054 -1.39651 (522*2π)/6161 weeks
5232.15555 .54303 (523*2π)/6161 weeks
524-2.82011 -.65138 (524*2π)/6161 weeks
525-1.7119 -7.03134 (525*2π)/6161 weeks
5264.04248 -7.25259 (526*2π)/6161 weeks
5277.29512 -2.43926 (527*2π)/6161 weeks
5281.74251 3.54056 (528*2π)/6161 weeks
529-3.96587 -2.98809 (529*2π)/6161 weeks
5301.5425 -5.94329 (530*2π)/6161 weeks
5312.10183 -4.98758 (531*2π)/6161 weeks
5325.53561 -2.67888 (532*2π)/6161 weeks
5331.29155 2.48285 (533*2π)/6161 weeks
534-4.61872 -2.70886 (534*2π)/6161 weeks
535-1.5418 -8.13854 (535*2π)/6161 weeks
5364.86131 -7.72466 (536*2π)/6161 weeks
5375.65269 -1.51366 (537*2π)/6161 weeks
538-.38712 -.9919 (538*2π)/6161 weeks
5391.34786 -5.48697 (539*2π)/6161 weeks
5402.48865 -3.16496 (540*2π)/6161 weeks
5412.9172 -3.05641 (541*2π)/6161 weeks
542-1.06026 -1.348 (542*2π)/6161 weeks
543-.58284 -6.72679 (543*2π)/6161 weeks
5444.39343 -6.88308 (544*2π)/6161 weeks
5454.76076 -2.66129 (545*2π)/6161 weeks
5462.26467 -.5483 (546*2π)/6161 weeks
547-1.41608 -4.17625 (547*2π)/6161 weeks
5483.59862 -6.66354 (548*2π)/6161 weeks
5494.51489 -1.54943 (549*2π)/6161 weeks
550.49609 -.37419 (550*2π)/6161 weeks
551-2.82578 -4.01624 (551*2π)/6161 weeks
552.43458 -9.05318 (552*2π)/6161 weeks
5538.13814 -6.46982 (553*2π)/6161 weeks
5544.57733 1.60506 (554*2π)/6161 weeks
555-2.47056 -.38091 (555*2π)/6161 weeks
556-2.37228 -5.68225 (556*2π)/6161 weeks
557.71959 -7.05027 (557*2π)/6161 weeks
5583.78929 -5.1734 (558*2π)/6161 weeks
5591.05236 -2.9814 (559*2π)/6161 weeks
560-.69193 -5.75435 (560*2π)/6161 weeks
5611.12652 -8.42141 (561*2π)/6161 weeks
5624.34698 -6.90664 (562*2π)/6161 weeks
5636.70299 -5.14901 (563*2π)/6161 weeks
5642.57366 -.73768 (564*2π)/6161 weeks
565-.29878 -3.51653 (565*2π)/6161 weeks
566.4271 -4.56458 (566*2π)/6161 weeks
5671.20598 -6.66729 (567*2π)/6161 weeks
5681.73803 -3.56115 (568*2π)/6161 weeks
569-1.42692 -7.27527 (569*2π)/6161 weeks
5705.06249 -8.06857 (570*2π)/6161 weeks
5712.446 -2.97 (571*2π)/6161 weeks
572-.01386 -4.27524 (572*2π)/6161 weeks
573-1.48101 -6.59254 (573*2π)/6161 weeks
574-.0976 -10.5638 (574*2π)/6161 weeks
5757.53073 -9.5618 (575*2π)/6161 weeks
5766.93058 -.49049 (576*2π)/6161 weeks
577-4.53864 3.58585 (577*2π)/6161 weeks
578-14.30389 -11.64479 (578*2π)/6161 weeks
5793.2518 -24.99103 (579*2π)/6161 weeks
58018.56239 -11.26157 (580*2π)/6161 weeks
5819.73387 4.44131 (581*2π)/6161 weeks
582-8.07635 2.79748 (582*2π)/6161 weeks
583-9.5783 -14.65444 (583*2π)/6161 weeks
5846.43238 -19.07692 (584*2π)/6161 weeks
58512.39575 -9.39644 (585*2π)/6161 weeks
5868.84591 .93771 (586*2π)/6161 weeks
587-8.60853 -.02381 (587*2π)/6161 weeks
588-5.91044 -15.11079 (588*2π)/6161 weeks
5893.39981 -14.40139 (589*2π)/6161 weeks
5905.68187 -7.78631 (590*2π)/6161 weeks
591-4.82853 -9.14299 (591*2π)/6161 weeks
592-1.84058 -17.92761 (592*2π)/6161 weeks
5935.17905 -17.65789 (593*2π)/6161 weeks
5947.95851 -14.16158 (594*2π)/6161 weeks
5956.92454 -12.71238 (595*2π)/6161 weeks
5965.42719 -7.15311 (596*2π)/6161 weeks
597-3.27221 -13.6053 (597*2π)/6161 weeks
5983.93293 -14.36559 (598*2π)/6161 weeks
599-1.09493 -15.68972 (599*2π)/6161 weeks
6001.36574 -22.28158 (600*2π)/6161 weeks
6018.75218 -26.27294 (601*2π)/6161 weeks
60219.26876 -14.76411 (602*2π)/6161 weeks
603.91652 -.96466 (603*2π)/6161 weeks
604-12.42703 -19.62149 (604*2π)/6161 weeks
605-9.17759 -31.44315 (605*2π)/6161 weeks
6069.51266 -52.82424 (606*2π)/6161 weeks
60740.07985 -21.13953 (607*2π)/6161 weeks
608-5.43882 4.30349 (608*2π)/6161 weeks
609-32.9902 -42.1253 (609*2π)/6161 weeks
6106.07967 -85.9207 (610*2π)/6161 weeks
61162.77045 -65.9049 (611*2π)/6161 weeks
61251.10186 .61095 (612*2π)/6161 weeks
613-52.48754 -8.64872 (613*2π)/6161 weeks
614-88.06164 -151.5846 (614*2π)/6161 weeks



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